LMFDB - Embedded newform 14.14.c.b.9.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,14,Mod(9,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.0123300533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209077 x^{6} - 47718852 x^{5} + 40973427094 x^{4} - 4988457209802 x^{3} + \cdots + 75\!\cdots\!25 $ x^8 + 209077x^6 - 47718852x^5 + 40973427094x^4 - 4988457209802x^3 + 1142094021456771x^2 + 65369216338084710x + 7506311351102577225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.2
Root			$-248.013 - 429.572i$ of defining polynomial
Character	$\chi$	$=$	14.9
Dual form			14.14.c.b.11.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 - 55.4256i) q^{2} +(-244.702 - 423.837i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(34096.3 - 59056.5i) q^{5} -31321.9 q^{6} +(100530. + 294589. i) q^{7} -262144. q^{8} +(677403. - 1.17330e6i) q^{9} +O(q^{10})$	\(q+(32.0000 - 55.4256i) q^{2} +(-244.702 - 423.837i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(34096.3 - 59056.5i) q^{5} -31321.9 q^{6} +(100530. + 294589. i) q^{7} -262144. q^{8} +(677403. - 1.17330e6i) q^{9} +(-2.18216e6 - 3.77962e6i) q^{10} +(-1.01364e6 - 1.75568e6i) q^{11} +(-1.00230e6 + 1.73604e6i) q^{12} -1.22100e7 q^{13} +(1.95447e7 + 3.85491e6i) q^{14} -3.33738e7 q^{15} +(-8.38861e6 + 1.45295e7i) q^{16} +(-4.76426e7 - 8.25194e7i) q^{17} +(-4.33538e7 - 7.50910e7i) q^{18} +(-1.03590e8 + 1.79423e8i) q^{19} -2.79317e8 q^{20} +(1.00258e8 - 1.14695e8i) q^{21} -1.29746e8 q^{22} +(-1.66859e8 + 2.89008e8i) q^{23} +(6.41473e7 + 1.11106e8i) q^{24} +(-1.71476e9 - 2.97005e9i) q^{25} +(-3.90720e8 + 6.76747e8i) q^{26} -1.44332e9 q^{27} +(8.39093e8 - 9.59922e8i) q^{28} +4.91794e9 q^{29} +(-1.06796e9 + 1.84976e9i) q^{30} +(2.19527e9 + 3.80232e9i) q^{31} +(5.36871e8 + 9.29888e8i) q^{32} +(-4.96081e8 + 8.59238e8i) q^{33} -6.09825e9 q^{34} +(2.08251e10 + 4.10745e9i) q^{35} -5.54929e9 q^{36} +(4.86831e9 - 8.43216e9i) q^{37} +(6.62975e9 + 1.14831e10i) q^{38} +(2.98782e9 + 5.17505e9i) q^{39} +(-8.93813e9 + 1.54813e10i) q^{40} +2.57081e10 q^{41} +(-3.14879e9 - 9.22709e9i) q^{42} +2.25490e9 q^{43} +(-4.15188e9 + 7.19127e9i) q^{44} +(-4.61938e10 - 8.00101e10i) q^{45} +(1.06790e10 + 1.84965e10i) q^{46} +(6.30189e10 - 1.09152e11i) q^{47} +8.21085e9 q^{48} +(-7.66765e10 + 5.92301e10i) q^{49} -2.19489e11 q^{50} +(-2.33165e10 + 4.03854e10i) q^{51} +(2.50061e10 + 4.33118e10i) q^{52} +(8.56595e10 + 1.48367e11i) q^{53} +(-4.61862e10 + 7.99968e10i) q^{54} -1.38246e11 q^{55} +(-2.63533e10 - 7.72248e10i) q^{56} +1.01395e11 q^{57} +(1.57374e11 - 2.72580e11i) q^{58} +(-2.75382e11 - 4.76975e11i) q^{59} +(6.83495e10 + 1.18385e11i) q^{60} +(-2.20984e10 + 3.82756e10i) q^{61} +2.80995e11 q^{62} +(4.13740e11 + 8.16041e10i) q^{63} +6.87195e10 q^{64} +(-4.16316e11 + 7.21080e11i) q^{65} +(3.17492e10 + 5.49913e10i) q^{66} +(6.07062e10 + 1.05146e11i) q^{67} +(-1.95144e11 + 3.37999e11i) q^{68} +1.63323e11 q^{69} +(8.94061e11 - 1.02281e12i) q^{70} +1.25945e12 q^{71} +(-1.77577e11 + 3.07573e11i) q^{72} +(-7.26655e10 - 1.25860e11i) q^{73} +(-3.11572e11 - 5.39658e11i) q^{74} +(-8.39212e11 + 1.45356e12i) q^{75} +8.48608e11 q^{76} +(4.15303e11 - 4.75107e11i) q^{77} +3.82441e11 q^{78} +(-1.26635e12 + 2.19338e12i) q^{79} +(5.72041e11 + 9.90803e11i) q^{80} +(-7.26816e11 - 1.25888e12i) q^{81} +(8.22660e11 - 1.42489e12i) q^{82} -1.98753e11 q^{83} +(-6.12179e11 - 1.20743e11i) q^{84} -6.49774e12 q^{85} +(7.21568e10 - 1.24979e11i) q^{86} +(-1.20343e12 - 2.08440e12i) q^{87} +(2.65720e11 + 4.60241e11i) q^{88} +(2.74228e12 - 4.74977e12i) q^{89} -5.91281e12 q^{90} +(-1.22747e12 - 3.59693e12i) q^{91} +1.36691e12 q^{92} +(1.07438e12 - 1.86088e12i) q^{93} +(-4.03321e12 - 6.98572e12i) q^{94} +(7.06406e12 + 1.22353e13i) q^{95} +(2.62747e11 - 4.55091e11i) q^{96} +3.38474e12 q^{97} +(8.29217e11 + 6.14520e12i) q^{98} -2.74658e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9}+O(q^{10}) $ 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9	\( 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9} - 114688 q^{10} - 8726914 q^{11} + 745472 q^{12} + 1438416 q^{13} + 27004544 q^{14} - 136873212 q^{15} - 67108864 q^{16} - 7943068 q^{17} - 38389760 q^{18} - 215706806 q^{19} - 14680064 q^{20} - 414124312 q^{21} - 1117044992 q^{22} - 61927978 q^{23} - 47710208 q^{24} - 1327844792 q^{25} + 46029312 q^{26} - 3268643812 q^{27} + 2827460608 q^{28} - 6325846064 q^{29} - 4379942784 q^{30} + 6113775570 q^{31} + 4294967296 q^{32} + 25235960652 q^{33} - 1016712704 q^{34} + 41542225382 q^{35} - 4913889280 q^{36} - 3945652880 q^{37} + 13805235584 q^{38} - 23545599116 q^{39} - 469762048 q^{40} + 86378579952 q^{41} + 16061065216 q^{42} - 109074124256 q^{43} - 35745439744 q^{44} - 104964468168 q^{45} + 3963390592 q^{46} - 3141202722 q^{47} - 6106906624 q^{48} + 151080461672 q^{49} - 169964133376 q^{50} - 241278267462 q^{51} - 2945875968 q^{52} + 149625680376 q^{53} - 104596601984 q^{54} + 174912009748 q^{55} + 70346866688 q^{56} - 128207489960 q^{57} - 202427074048 q^{58} - 866297313938 q^{59} + 280316338176 q^{60} - 477908594184 q^{61} + 782563272960 q^{62} + 953051390564 q^{63} + 549755813888 q^{64} - 1099748343120 q^{65} - 1615101481728 q^{66} + 1895501016278 q^{67} - 32534806528 q^{68} + 3503301895632 q^{69} + 1443396653440 q^{70} + 638832672128 q^{71} - 157244456960 q^{72} - 2966596192756 q^{73} + 252521784320 q^{74} - 1331079867376 q^{75} + 1767070154752 q^{76} + 6943031627392 q^{77} - 3013836686848 q^{78} - 6505959677634 q^{79} + 30064771072 q^{80} + 2449216493684 q^{81} + 2764114558464 q^{82} - 3379817135968 q^{83} + 2724161355776 q^{84} - 16684556982464 q^{85} - 3490371976192 q^{86} - 5273311164492 q^{87} + 2287708143616 q^{88} + 9586601667468 q^{89} - 13435451925504 q^{90} + 16069253407200 q^{91} + 507313995776 q^{92} - 14195747226896 q^{93} + 201036974208 q^{94} + 14384410136978 q^{95} - 195421011968 q^{96} - 44560735311568 q^{97} - 2146516623104 q^{98} + 24706419985464 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9 - 114688 * q^10 - 8726914 * q^11 + 745472 * q^12 + 1438416 * q^13 + 27004544 * q^14 - 136873212 * q^15 - 67108864 * q^16 - 7943068 * q^17 - 38389760 * q^18 - 215706806 * q^19 - 14680064 * q^20 - 414124312 * q^21 - 1117044992 * q^22 - 61927978 * q^23 - 47710208 * q^24 - 1327844792 * q^25 + 46029312 * q^26 - 3268643812 * q^27 + 2827460608 * q^28 - 6325846064 * q^29 - 4379942784 * q^30 + 6113775570 * q^31 + 4294967296 * q^32 + 25235960652 * q^33 - 1016712704 * q^34 + 41542225382 * q^35 - 4913889280 * q^36 - 3945652880 * q^37 + 13805235584 * q^38 - 23545599116 * q^39 - 469762048 * q^40 + 86378579952 * q^41 + 16061065216 * q^42 - 109074124256 * q^43 - 35745439744 * q^44 - 104964468168 * q^45 + 3963390592 * q^46 - 3141202722 * q^47 - 6106906624 * q^48 + 151080461672 * q^49 - 169964133376 * q^50 - 241278267462 * q^51 - 2945875968 * q^52 + 149625680376 * q^53 - 104596601984 * q^54 + 174912009748 * q^55 + 70346866688 * q^56 - 128207489960 * q^57 - 202427074048 * q^58 - 866297313938 * q^59 + 280316338176 * q^60 - 477908594184 * q^61 + 782563272960 * q^62 + 953051390564 * q^63 + 549755813888 * q^64 - 1099748343120 * q^65 - 1615101481728 * q^66 + 1895501016278 * q^67 - 32534806528 * q^68 + 3503301895632 * q^69 + 1443396653440 * q^70 + 638832672128 * q^71 - 157244456960 * q^72 - 2966596192756 * q^73 + 252521784320 * q^74 - 1331079867376 * q^75 + 1767070154752 * q^76 + 6943031627392 * q^77 - 3013836686848 * q^78 - 6505959677634 * q^79 + 30064771072 * q^80 + 2449216493684 * q^81 + 2764114558464 * q^82 - 3379817135968 * q^83 + 2724161355776 * q^84 - 16684556982464 * q^85 - 3490371976192 * q^86 - 5273311164492 * q^87 + 2287708143616 * q^88 + 9586601667468 * q^89 - 13435451925504 * q^90 + 16069253407200 * q^91 + 507313995776 * q^92 - 14195747226896 * q^93 + 201036974208 * q^94 + 14384410136978 * q^95 - 195421011968 * q^96 - 44560735311568 * q^97 - 2146516623104 * q^98 + 24706419985464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	32.0000	−	55.4256i	0.353553	−	0.612372i
$2$	32.0000	−	55.4256i	0.353553	−	0.612372i
$3$	−244.702	−	423.837i	−0.193798	−	0.335669i	0.752708	−	0.658355i	$-0.228747\pi$
$3$	−244.702	−	423.837i	−0.193798	−	0.335669i	−0.946506	+	0.322686i	$0.895414\pi$
$4$	−2048.00	−	3547.24i	−0.250000	−	0.433013i
$5$	34096.3	−	59056.5i	0.975892	−	1.69030i	0.298934	−	0.954274i	$-0.403369\pi$
$5$	34096.3	−	59056.5i	0.975892	−	1.69030i	0.676958	−	0.736022i	$-0.263298\pi$
$6$	−31321.9			−0.274072
$7$	100530.	+	294589.i	0.322967	+	0.946410i
$7$	100530.	+	294589.i	0.322967	+	0.946410i
$8$	−262144.			−0.353553
$9$	677403.	−	1.17330e6i	0.424884	−	0.735921i
$10$	−2.18216e6	−	3.77962e6i	−0.690060	−	1.19522i
$11$	−1.01364e6	−	1.75568e6i	−0.172517	−	0.298809i	0.766782	−	0.641908i	$-0.221857\pi$
$11$	−1.01364e6	−	1.75568e6i	−0.172517	−	0.298809i	−0.939299	+	0.343099i	$0.888523\pi$
$12$	−1.00230e6	+	1.73604e6i	−0.0968992	+	0.167834i
$13$	−1.22100e7			−0.701591			−0.350796	−	0.936452i	$-0.614089\pi$
$13$	−1.22100e7			−0.701591			−0.350796	+	0.936452i	$0.614089\pi$
$14$	1.95447e7	+	3.85491e6i	0.693742	+	0.136830i
$15$	−3.33738e7			−0.756505
$16$	−8.38861e6	+	1.45295e7i	−0.125000	+	0.216506i
$17$	−4.76426e7	−	8.25194e7i	−0.478715	−	0.829159i	0.520987	−	0.853565i	$-0.325564\pi$
$17$	−4.76426e7	−	8.25194e7i	−0.478715	−	0.829159i	−0.999702	+	0.0244054i	$0.992231\pi$
$18$	−4.33538e7	−	7.50910e7i	−0.300439	−	0.520375i
$19$	−1.03590e8	+	1.79423e8i	−0.505148	+	0.874942i	0.494834	+	0.868988i	$0.335229\pi$
$19$	−1.03590e8	+	1.79423e8i	−0.505148	+	0.874942i	−0.999982	+	0.00595495i	$0.998104\pi$
$20$	−2.79317e8			−0.975892
$21$	1.00258e8	−	1.14695e8i	0.255090	−	0.291823i
$22$	−1.29746e8			−0.243976
$23$	−1.66859e8	+	2.89008e8i	−0.235027	+	0.407079i	−0.959281	−	0.282455i	$-0.908851\pi$
$23$	−1.66859e8	+	2.89008e8i	−0.235027	+	0.407079i	0.724253	+	0.689534i	$0.242185\pi$
$24$	6.41473e7	+	1.11106e8i	0.0685181	+	0.118677i
$25$	−1.71476e9	−	2.97005e9i	−1.40473	−	2.43307i
$26$	−3.90720e8	+	6.76747e8i	−0.248050	+	0.429635i
$27$	−1.44332e9			−0.716964
$28$	8.39093e8	−	9.59922e8i	0.329066	−	0.376451i
$29$	4.91794e9			1.53531			0.767655	−	0.640864i	$-0.221424\pi$
$29$	4.91794e9			1.53531			0.767655	+	0.640864i	$0.221424\pi$
$30$	−1.06796e9	+	1.84976e9i	−0.267465	+	0.463263i
$31$	2.19527e9	+	3.80232e9i	0.444260	+	0.769481i	0.998000	−	0.0632083i	$-0.0201332\pi$
$31$	2.19527e9	+	3.80232e9i	0.444260	+	0.769481i	−0.553740	+	0.832690i	$0.686800\pi$
$32$	5.36871e8	+	9.29888e8i	0.0883883	+	0.153093i
$33$	−4.96081e8	+	8.59238e8i	−0.0668671	+	0.115817i
$34$	−6.09825e9			−0.677006
$35$	2.08251e10	+	4.10745e9i	1.91489	+	0.377685i
$36$	−5.54929e9			−0.424884
$37$	4.86831e9	−	8.43216e9i	0.311937	−	0.540291i	−0.666845	−	0.745197i	$-0.732356\pi$
$37$	4.86831e9	−	8.43216e9i	0.311937	−	0.540291i	0.978782	+	0.204906i	$0.0656889\pi$
$38$	6.62975e9	+	1.14831e10i	0.357194	+	0.618678i
$39$	2.98782e9	+	5.17505e9i	0.135967	+	0.235502i
$40$	−8.93813e9	+	1.54813e10i	−0.345030	+	0.597610i
$41$	2.57081e10			0.845230			0.422615	−	0.906309i	$-0.361112\pi$
$41$	2.57081e10			0.845230			0.422615	+	0.906309i	$0.361112\pi$
$42$	−3.14879e9	−	9.22709e9i	−0.0885163	−	0.259385i
$43$	2.25490e9			0.0543980			0.0271990	−	0.999630i	$-0.491341\pi$
$43$	2.25490e9			0.0543980			0.0271990	+	0.999630i	$0.491341\pi$
$44$	−4.15188e9	+	7.19127e9i	−0.0862586	+	0.149404i
$45$	−4.61938e10	−	8.00101e10i	−0.829283	−	1.43636i
$46$	1.06790e10	+	1.84965e10i	0.166189	+	0.287848i
$47$	6.30189e10	−	1.09152e11i	0.852775	−	1.47705i	−0.0259191	−	0.999664i	$-0.508251\pi$
$47$	6.30189e10	−	1.09152e11i	0.852775	−	1.47705i	0.878694	−	0.477385i	$-0.158415\pi$
$48$	8.21085e9			0.0968992
$49$	−7.66765e10	+	5.92301e10i	−0.791384	+	0.611319i
$50$	−2.19489e11			−1.98659
$51$	−2.33165e10	+	4.03854e10i	−0.185548	+	0.321379i
$52$	2.50061e10	+	4.33118e10i	0.175398	+	0.303798i
$53$	8.56595e10	+	1.48367e11i	0.530863	+	0.919482i	0.999351	+	0.0360120i	$0.0114655\pi$
$53$	8.56595e10	+	1.48367e11i	0.530863	+	0.919482i	−0.468488	+	0.883470i	$0.655201\pi$
$54$	−4.61862e10	+	7.99968e10i	−0.253485	+	0.439049i
$55$	−1.38246e11			−0.673433
$56$	−2.63533e10	−	7.72248e10i	−0.114186	−	0.334607i
$57$	1.01395e11			0.391588
$58$	1.57374e11	−	2.72580e11i	0.542814	−	0.940181i
$59$	−2.75382e11	−	4.76975e11i	−0.849957	−	1.47217i	−0.881246	−	0.472658i	$-0.843295\pi$
$59$	−2.75382e11	−	4.76975e11i	−0.849957	−	1.47217i	0.0312897	−	0.999510i	$-0.490039\pi$
$60$	6.83495e10	+	1.18385e11i	0.189126	+	0.327576i
$61$	−2.20984e10	+	3.82756e10i	−0.0549184	+	0.0951214i	−0.892178	−	0.451685i	$-0.850823\pi$
$61$	−2.20984e10	+	3.82756e10i	−0.0549184	+	0.0951214i	0.837259	+	0.546806i	$0.184157\pi$
$62$	2.80995e11			0.628279
$63$	4.13740e11	+	8.16041e10i	0.833707	+	0.164437i
$64$	6.87195e10			0.125000
$65$	−4.16316e11	+	7.21080e11i	−0.684677	+	1.18590i
$66$	3.17492e10	+	5.49913e10i	0.0472822	+	0.0818951i
$67$	6.07062e10	+	1.05146e11i	0.0819874	+	0.142006i	0.904104	−	0.427314i	$-0.140540\pi$
$67$	6.07062e10	+	1.05146e11i	0.0819874	+	0.142006i	−0.822116	+	0.569320i	$0.807207\pi$
$68$	−1.95144e11	+	3.37999e11i	−0.239358	+	0.414580i
$69$	1.63323e11			0.182191
$70$	8.94061e11	−	1.02281e12i	0.908301	−	1.03910i
$71$	1.25945e12			1.16682			0.583408	−	0.812179i	$-0.301719\pi$
$71$	1.25945e12			1.16682			0.583408	+	0.812179i	$0.301719\pi$
$72$	−1.77577e11	+	3.07573e11i	−0.150219	+	0.260188i
$73$	−7.26655e10	−	1.25860e11i	−0.0561992	−	0.0973398i	0.836557	−	0.547880i	$-0.184565\pi$
$73$	−7.26655e10	−	1.25860e11i	−0.0561992	−	0.0973398i	−0.892756	+	0.450540i	$0.851232\pi$
$74$	−3.11572e11	−	5.39658e11i	−0.220573	−	0.382043i
$75$	−8.39212e11	+	1.45356e12i	−0.544470	+	0.943049i
$76$	8.48608e11			0.505148
$77$	4.15303e11	−	4.75107e11i	0.227078	−	0.259777i
$78$	3.82441e11			0.192287
$79$	−1.26635e12	+	2.19338e12i	−0.586108	+	1.01517i	0.408628	+	0.912701i	$0.366007\pi$
$79$	−1.26635e12	+	2.19338e12i	−0.586108	+	1.01517i	−0.994736	+	0.102468i	$0.967326\pi$
$80$	5.72041e11	+	9.90803e11i	0.243973	+	0.422574i
$81$	−7.26816e11	−	1.25888e12i	−0.285938	−	0.495259i
$82$	8.22660e11	−	1.42489e12i	0.298834	−	0.517596i
$83$	−1.98753e11			−0.0667276			−0.0333638	−	0.999443i	$-0.510622\pi$
$83$	−1.98753e11			−0.0667276			−0.0333638	+	0.999443i	$0.510622\pi$
$84$	−6.12179e11	−	1.20743e11i	−0.190135	−	0.0375014i
$85$	−6.49774e12			−1.86870
$86$	7.21568e10	−	1.24979e11i	0.0192326	−	0.0333118i
$87$	−1.20343e12	−	2.08440e12i	−0.297540	−	0.515355i
$88$	2.65720e11	+	4.60241e11i	0.0609940	+	0.105645i
$89$	2.74228e12	−	4.74977e12i	0.584894	−	1.01307i	−0.409995	−	0.912088i	$-0.634470\pi$
$89$	2.74228e12	−	4.74977e12i	0.584894	−	1.01307i	0.994889	−	0.100978i	$-0.0321971\pi$
$90$	−5.91281e12			−1.17278
$91$	−1.22747e12	−	3.59693e12i	−0.226591	−	0.663993i
$92$	1.36691e12			0.235027
$93$	1.07438e12	−	1.86088e12i	0.172194	−	0.298248i
$94$	−4.03321e12	−	6.98572e12i	−0.603003	−	1.04443i
$95$	7.06406e12	+	1.22353e13i	0.985941	+	1.70770i
$96$	2.62747e11	−	4.55091e11i	0.0342590	−	0.0593384i
$97$	3.38474e12			0.412581			0.206290	−	0.978491i	$-0.433861\pi$
$97$	3.38474e12			0.412581			0.206290	+	0.978491i	$0.433861\pi$
$98$	8.29217e11	+	6.14520e12i	0.0945581	+	0.700756i
$99$	−2.74658e12			−0.293199
$100$	−7.02366e12	+	1.21653e13i	−0.702366	+	1.21653i
$101$	4.71449e12	+	8.16574e12i	0.441922	+	0.765432i	0.997832	−	0.0658107i	$-0.0209634\pi$
$101$	4.71449e12	+	8.16574e12i	0.441922	+	0.765432i	−0.555910	+	0.831243i	$0.687630\pi$
$102$	1.49226e12	+	2.58466e12i	0.131203	+	0.227250i
$103$	9.52601e12	−	1.64995e13i	0.786084	−	1.36154i	−0.142265	−	0.989829i	$-0.545438\pi$
$103$	9.52601e12	−	1.64995e13i	0.786084	−	1.36154i	0.928349	−	0.371709i	$-0.121228\pi$
$104$	3.20078e12			0.248050
$105$	−3.35506e12	−	9.83155e12i	−0.244326	−	0.715964i
$106$	1.09644e13			0.750754
$107$	1.88106e12	−	3.25809e12i	0.121173	−	0.209879i	−0.799057	−	0.601255i	$-0.794668\pi$
$107$	1.88106e12	−	3.25809e12i	0.121173	−	0.209879i	0.920231	+	0.391376i	$0.128001\pi$
$108$	2.95591e12	+	5.11979e12i	0.179241	+	0.310455i
$109$	7.35138e12	+	1.27330e13i	0.419852	+	0.727206i	0.995924	−	0.0901934i	$-0.0287485\pi$
$109$	7.35138e12	+	1.27330e13i	0.419852	+	0.727206i	−0.576072	+	0.817399i	$0.695415\pi$
$110$	−4.42386e12	+	7.66236e12i	−0.238094	+	0.412392i
$111$	−4.76515e12			−0.241811
$112$	−5.12354e12	−	1.01054e12i	−0.245275	−	0.0483768i
$113$	1.91564e13			0.865572			0.432786	−	0.901497i	$-0.357531\pi$
$113$	1.91564e13			0.865572			0.432786	+	0.901497i	$0.357531\pi$
$114$	3.24463e12	−	5.61987e12i	0.138447	−	0.239797i
$115$	1.13785e13	+	1.97082e13i	0.458722	+	0.794530i
$116$	−1.00719e13	−	1.74451e13i	−0.383827	−	0.664809i
$117$	−8.27109e12	+	1.43260e13i	−0.298095	+	0.516316i
$118$	−3.52488e13			−1.20202
$119$	1.95198e13	−	2.23307e13i	0.630116	−	0.720852i
$120$	8.74873e12			0.267465
$121$	1.52064e13	−	2.63383e13i	0.440476	−	0.762926i
$122$	1.41430e12	+	2.44964e12i	0.0388332	+	0.0672610i
$123$	−6.29084e12	−	1.08960e13i	−0.163804	−	0.283717i
$124$	8.99184e12	−	1.55743e13i	0.222130	−	0.384741i
$125$	−1.50625e14			−3.53169
$126$	1.77626e13	−	2.03204e13i	0.395456	−	0.452402i
$127$	4.62943e13			0.979046			0.489523	−	0.871990i	$-0.337171\pi$
$127$	4.62943e13			0.979046			0.489523	+	0.871990i	$0.337171\pi$
$128$	2.19902e12	−	3.80882e12i	0.0441942	−	0.0765466i
$129$	−5.51780e11	−	9.55711e11i	−0.0105422	−	0.0182597i
$130$	2.66442e13	+	4.61491e13i	0.484140	+	0.838555i
$131$	−1.05855e13	+	1.83346e13i	−0.182999	+	0.316963i	−0.942900	−	0.333075i	$-0.891914\pi$
$131$	−1.05855e13	+	1.83346e13i	−0.182999	+	0.316963i	0.759902	+	0.650038i	$0.225247\pi$
$132$	4.06390e12			0.0668671
$133$	−6.32699e13	−	1.24791e13i	−0.991201	−	0.195500i
$134$	7.77040e12			0.115948
$135$	−4.92118e13	+	8.52373e13i	−0.699680	+	1.21188i
$136$	1.24892e13	+	2.16320e13i	0.169251	+	0.293152i
$137$	1.97958e13	+	3.42873e13i	0.255793	+	0.443046i	0.965111	−	0.261843i	$-0.0843301\pi$
$137$	1.97958e13	+	3.42873e13i	0.255793	+	0.443046i	−0.709318	+	0.704889i	$0.750997\pi$
$138$	5.22633e12	−	9.05227e12i	0.0644144	−	0.111569i
$139$	9.29027e11			0.0109253			0.00546264	−	0.999985i	$-0.498261\pi$
$139$	9.29027e11			0.0109253			0.00546264	+	0.999985i	$0.498261\pi$
$140$	−2.80797e13	−	8.22837e13i	−0.315181	−	0.923595i
$141$	−6.16835e13			−0.661065
$142$	4.03025e13	−	6.98059e13i	0.412532	−	0.714526i
$143$	1.23766e13	+	2.14369e13i	0.121037	+	0.209641i
$144$	1.13649e13	+	1.96846e13i	0.106221	+	0.183980i
$145$	1.67683e14	−	2.90436e14i	1.49830	−	2.59513i
$146$	−9.30119e12			−0.0794776
$147$	4.38668e13	+	1.80046e13i	0.358569	+	0.147170i
$148$	−3.98812e13			−0.311937
$149$	−8.78519e13	+	1.52164e14i	−0.657719	+	1.13920i	0.323486	+	0.946233i	$0.395145\pi$
$149$	−8.78519e13	+	1.52164e14i	−0.657719	+	1.13920i	−0.981205	+	0.192970i	$0.938188\pi$
$150$	5.37096e13	+	9.30277e13i	0.384998	+	0.666836i
$151$	1.22477e14	+	2.12136e14i	0.840823	+	1.45635i	0.889200	+	0.457519i	$0.151262\pi$
$151$	1.22477e14	+	2.12136e14i	0.840823	+	1.45635i	−0.0483769	+	0.998829i	$0.515405\pi$
$152$	2.71555e13	−	4.70346e13i	0.178597	−	0.309339i
$153$	−1.29093e14			−0.813595
$154$	−1.30434e13	−	3.82218e13i	−0.0787963	−	0.230902i
$155$	2.99402e14			1.73420
$156$	1.22381e13	−	2.11970e13i	0.0679836	−	0.117751i
$157$	−1.76805e13	−	3.06236e13i	−0.0942210	−	0.163196i	0.815062	−	0.579373i	$-0.196703\pi$
$157$	−1.76805e13	−	3.06236e13i	−0.0942210	−	0.163196i	−0.909283	+	0.416178i	$0.863369\pi$
$158$	8.10464e13	+	1.40376e14i	0.414441	+	0.717833i
$159$	4.19222e13	−	7.26113e13i	0.205761	−	0.356388i
$160$	7.32212e13			0.345030
$161$	−1.01913e14	−	2.01008e13i	−0.461170	−	0.0909590i
$162$	−9.30324e13			−0.404377
$163$	3.33119e13	−	5.76980e13i	0.139117	−	0.240958i	−0.788046	−	0.615617i	$-0.788907\pi$
$163$	3.33119e13	−	5.76980e13i	0.139117	−	0.240958i	0.927163	+	0.374659i	$0.122240\pi$
$164$	−5.26502e13	−	9.11928e13i	−0.211308	−	0.365995i
$165$	3.38291e13	+	5.85937e13i	0.130510	+	0.226050i
$166$	−6.36009e12	+	1.10160e13i	−0.0235918	+	0.0408622i
$167$	−3.09178e14			−1.10294			−0.551469	−	0.834195i	$-0.685933\pi$
$167$	−3.09178e14			−1.10294			−0.551469	+	0.834195i	$0.685933\pi$
$168$	−2.62820e13	+	3.00666e13i	−0.0901878	+	0.103175i
$169$	−1.53791e14			−0.507770
$170$	−2.07928e14	+	3.60141e14i	−0.660685	+	1.14434i
$171$	1.40344e14	+	2.43083e14i	0.429259	+	0.743499i
$172$	−4.61804e12	−	7.99868e12i	−0.0135995	−	0.0235550i
$173$	−5.20918e12	+	9.02256e12i	−0.0147730	+	0.0255876i	−0.873317	−	0.487152i	$-0.838036\pi$
$173$	−5.20918e12	+	9.02256e12i	−0.0147730	+	0.0255876i	0.858544	+	0.512739i	$0.171369\pi$
$174$	−1.54039e14			−0.420786
$175$	7.02560e14	−	8.03729e14i	1.84900	−	2.11525i
$176$	3.40122e13			0.0862586
$177$	−1.34773e14	+	2.33434e14i	−0.329440	+	0.570607i
$178$	−1.75506e14	−	3.03985e14i	−0.413582	−	0.716346i
$179$	−2.19409e14	−	3.80028e14i	−0.498552	−	0.863517i	0.501447	−	0.865188i	$-0.332801\pi$
$179$	−2.19409e14	−	3.80028e14i	−0.498552	−	0.863517i	−0.999999	+	0.00167147i	$0.999468\pi$
$180$	−1.89210e14	+	3.27721e14i	−0.414641	+	0.718180i
$181$	−1.08144e13			−0.0228607			−0.0114304	−	0.999935i	$-0.503638\pi$
$181$	−1.08144e13			−0.0228607			−0.0114304	+	0.999935i	$0.503638\pi$
$182$	−2.38641e14	−	4.70685e13i	−0.486723	−	0.0959990i
$183$	2.16302e13			0.0425724
$184$	4.37410e13	−	7.57617e13i	0.0830946	−	0.143924i
$185$	−3.31982e14	−	5.75010e14i	−0.608834	−	1.05453i
$186$	−6.87601e13	−	1.19096e14i	−0.121759	−	0.210893i
$187$	−9.65851e13	+	1.67290e14i	−0.165173	+	0.286088i
$188$	−5.16250e14			−0.852775
$189$	−1.45097e14	−	4.25186e14i	−0.231556	−	0.678542i
$190$	9.04199e14			1.39433
$191$	−2.98828e14	+	5.17585e14i	−0.445353	+	0.771374i	−0.998077	−	0.0619904i	$-0.980255\pi$
$191$	−2.98828e14	+	5.17585e14i	−0.445353	+	0.771374i	0.552724	+	0.833365i	$0.313589\pi$
$192$	−1.68158e13	−	2.91259e13i	−0.0242248	−	0.0419586i
$193$	2.27823e14	+	3.94600e14i	0.317303	+	0.549585i	0.979924	−	0.199370i	$-0.0638894\pi$
$193$	2.27823e14	+	3.94600e14i	0.317303	+	0.549585i	−0.662621	+	0.748955i	$0.730556\pi$
$194$	1.08312e14	−	1.87601e14i	0.145869	−	0.252653i
$195$	4.07494e14			0.530757
$196$	3.67137e14	+	1.50687e14i	0.462555	+	0.189850i
$197$	−8.49836e14			−1.03587			−0.517934	−	0.855421i	$-0.673299\pi$
$197$	−8.49836e14			−1.03587			−0.517934	+	0.855421i	$0.673299\pi$
$198$	−8.78905e13	+	1.52231e14i	−0.103662	+	0.179547i
$199$	7.26924e14	+	1.25907e15i	0.829743	+	1.43716i	0.898240	+	0.439506i	$0.144847\pi$
$199$	7.26924e14	+	1.25907e15i	0.829743	+	1.43716i	−0.0684964	+	0.997651i	$0.521820\pi$
$200$	4.49514e14	+	7.78582e14i	0.496648	+	0.860219i
$201$	2.97099e13	−	5.14591e13i	0.0317780	−	0.0550412i
$202$	6.03455e14			0.624972
$203$	4.94400e14	+	1.44877e15i	0.495854	+	1.45303i
$204$	1.91009e14			0.185548
$205$	8.76551e14	−	1.51823e15i	0.824854	−	1.42869i
$206$	−6.09665e14	−	1.05597e15i	−0.555846	−	0.962753i
$207$	2.26061e14	+	3.91549e14i	0.199719	+	0.345923i
$208$	1.02425e14	−	1.77405e14i	0.0876989	−	0.151899i
$209$	4.20012e14			0.348587
$210$	−6.52282e14	−	1.28653e14i	−0.524819	−	0.103513i
$211$	−1.00855e14			−0.0786797			−0.0393399	−	0.999226i	$-0.512526\pi$
$211$	−1.00855e14			−0.0786797			−0.0393399	+	0.999226i	$0.512526\pi$
$212$	3.50861e14	−	6.07710e14i	0.265431	−	0.459741i
$213$	−3.08191e14	−	5.33802e14i	−0.226127	−	0.391663i
$214$	−1.20388e14	−	2.08518e14i	−0.0856826	−	0.148407i
$215$	7.68837e13	−	1.33167e14i	0.0530866	−	0.0919486i
$216$	3.78357e14			0.253485
$217$	−8.99432e14	+	1.02895e15i	−0.584763	+	0.668969i
$218$	9.40977e14			0.593761
$219$	−3.55629e13	+	6.15967e13i	−0.0217826	+	0.0377286i
$220$	2.83127e14	+	4.90391e14i	0.168358	+	0.291605i
$221$	5.81716e14	+	1.00756e15i	0.335862	+	0.581731i
$222$	−1.52485e14	+	2.64111e14i	−0.0854933	+	0.148079i
$223$	−7.82121e14			−0.425885			−0.212942	−	0.977065i	$-0.568305\pi$
$223$	−7.82121e14			−0.425885			−0.212942	+	0.977065i	$0.568305\pi$
$224$	−2.19963e14	+	2.51638e14i	−0.116342	+	0.133096i
$225$	−4.64634e15			−2.38740
$226$	6.13003e14	−	1.06175e15i	0.306026	−	0.530052i
$227$	−1.40236e14	−	2.42895e14i	−0.0680284	−	0.117829i	0.830005	−	0.557756i	$-0.188338\pi$
$227$	−1.40236e14	−	2.42895e14i	−0.0680284	−	0.117829i	−0.898033	+	0.439927i	$0.855004\pi$
$228$	−2.07656e14	−	3.59672e14i	−0.0978969	−	0.169562i
$229$	1.53748e15	−	2.66299e15i	0.704496	−	1.22022i	−0.262378	−	0.964965i	$-0.584507\pi$
$229$	1.53748e15	−	2.66299e15i	0.704496	−	1.22022i	0.966873	−	0.255257i	$-0.0821600\pi$
$230$	1.45645e15			0.648731
$231$	−3.02993e14	−	5.97610e13i	−0.131206	−	0.0258785i
$232$	−1.28921e15			−0.542814
$233$	−1.55317e15	+	2.69017e15i	−0.635925	+	1.10145i	0.350394	+	0.936603i	$0.386048\pi$
$233$	−1.55317e15	+	2.69017e15i	−0.635925	+	1.10145i	−0.986318	+	0.164851i	$0.947286\pi$
$234$	5.29350e14	+	9.16861e14i	0.210785	+	0.365090i
$235$	−4.29742e15	−	7.44334e15i	−1.66443	−	2.88288i
$236$	−1.12796e15	+	1.95369e15i	−0.424978	+	0.736084i
$237$	1.23952e15			0.454347
$238$	−6.13057e14	−	1.79648e15i	−0.218651	−	0.640725i
$239$	5.08395e15			1.76447			0.882237	−	0.470805i	$-0.156037\pi$
$239$	5.08395e15			1.76447			0.882237	+	0.470805i	$0.156037\pi$
$240$	2.79959e14	−	4.84904e14i	0.0945632	−	0.163788i
$241$	1.06886e15	+	1.85132e15i	0.351407	+	0.608655i	0.986496	−	0.163784i	$-0.0523699\pi$
$241$	1.06886e15	+	1.85132e15i	0.351407	+	0.608655i	−0.635089	+	0.772439i	$0.719037\pi$
$242$	−9.73210e14	−	1.68565e15i	−0.311463	−	0.539470i
$243$	−1.50626e15	+	2.60893e15i	−0.469311	+	0.812870i
$244$	1.81030e14			0.0549184
$245$	8.83538e14	+	6.54777e15i	0.261003	+	1.93425i
$246$	−8.05227e14			−0.231654
$247$	1.26483e15	−	2.19075e15i	0.354408	−	0.613852i
$248$	−5.75477e14	−	9.96756e14i	−0.157070	−	0.272053i
$249$	4.86353e13	+	8.42388e13i	0.0129317	+	0.0223984i
$250$	−4.82000e15	+	8.34848e15i	−1.24864	+	2.16271i
$251$	−1.27798e15			−0.322585			−0.161293	−	0.986907i	$-0.551566\pi$
$251$	−1.27798e15			−0.322585			−0.161293	+	0.986907i	$0.551566\pi$
$252$	−5.57869e14	−	1.63476e15i	−0.137224	−	0.402115i
$253$	6.76540e14			0.162185
$254$	1.48142e15	−	2.56589e15i	0.346145	−	0.599541i
$255$	1.59001e15	+	2.75398e15i	0.362151	+	0.627264i
$256$	−1.40737e14	−	2.43764e14i	−0.0312500	−	0.0541266i
$257$	2.34815e15	−	4.06711e15i	0.508346	−	0.880482i	−0.491607	−	0.870817i	$-0.663590\pi$
$257$	2.34815e15	−	4.06711e15i	0.508346	−	0.880482i	0.999953	−	0.00966455i	$-0.00307637\pi$
$258$	−7.06278e13			−0.0149090
$259$	2.97343e15	+	5.86466e14i	0.612082	+	0.120724i
$260$	3.41046e15			0.684677
$261$	3.33142e15	−	5.77020e15i	0.652329	−	1.12987i
$262$	6.77472e14	+	1.17342e15i	0.129400	+	0.224127i
$263$	−4.72518e15	−	8.18424e15i	−0.880452	−	1.52499i	−0.850839	−	0.525426i	$-0.823906\pi$
$263$	−4.72518e15	−	8.18424e15i	−0.880452	−	1.52499i	−0.0296123	−	0.999561i	$-0.509427\pi$
$264$	1.30045e14	−	2.25244e14i	0.0236411	−	0.0409476i
$265$	1.16827e16			2.07226
$266$	−2.71630e15	+	3.10744e15i	−0.470161	+	0.537864i
$267$	−2.68417e15			−0.453406
$268$	2.48653e14	−	4.30679e14i	0.0409937	−	0.0710032i
$269$	−1.73652e15	−	3.00774e15i	−0.279441	−	0.484005i	0.691805	−	0.722084i	$-0.256816\pi$
$269$	−1.73652e15	−	3.00774e15i	−0.279441	−	0.484005i	−0.971246	+	0.238079i	$0.923482\pi$
$270$	3.14955e15	+	5.45519e15i	0.494748	+	0.856929i
$271$	−2.33839e15	+	4.05021e15i	−0.358605	+	0.621122i	−0.987728	−	0.156184i	$-0.950081\pi$
$271$	−2.33839e15	+	4.05021e15i	−0.358605	+	0.621122i	0.629123	+	0.777306i	$0.283414\pi$
$272$	1.59862e15			0.239358
$273$	−1.22415e15	+	1.40043e15i	−0.178969	+	0.204740i
$274$	2.53386e15			0.361746
$275$	−3.47631e15	+	6.02114e15i	−0.484681	+	0.839492i
$276$	−3.34485e14	−	5.79346e14i	−0.0455479	−	0.0788912i
$277$	3.58150e15	+	6.20334e15i	0.476372	+	0.825101i	0.999634	−	0.0270712i	$-0.00861810\pi$
$277$	3.58150e15	+	6.20334e15i	0.476372	+	0.825101i	−0.523261	+	0.852172i	$0.675285\pi$
$278$	2.97289e13	−	5.14919e13i	0.00386267	−	0.00669034i
$279$	5.94834e15			0.755037
$280$	−5.45917e15	−	1.07674e15i	−0.677017	−	0.133532i
$281$	−3.65564e15			−0.442968			−0.221484	−	0.975164i	$-0.571090\pi$
$281$	−3.65564e15			−0.442968			−0.221484	+	0.975164i	$0.571090\pi$
$282$	−1.97387e15	+	3.41884e15i	−0.233722	+	0.404818i
$283$	−2.03067e14	−	3.51722e14i	−0.0234978	−	0.0406993i	0.854037	−	0.520212i	$-0.174147\pi$
$283$	−2.03067e14	−	3.51722e14i	−0.0234978	−	0.0406993i	−0.877535	+	0.479512i	$0.840814\pi$
$284$	−2.57936e15	−	4.46758e15i	−0.291704	−	0.505246i
$285$	3.45718e15	−	5.98802e15i	0.382147	−	0.661899i
$286$	1.58420e15			0.171171
$287$	2.58444e15	+	7.57333e15i	0.272982	+	0.799935i
$288$	1.45471e15			0.150219
$289$	4.12656e14	−	7.14740e14i	0.0416631	−	0.0721626i
$290$	−1.07317e16	−	1.85879e16i	−1.05946	−	1.83503i
$291$	−8.28254e14	−	1.43458e15i	−0.0799575	−	0.138490i
$292$	−2.97638e14	+	5.15524e14i	−0.0280996	+	0.0486699i
$293$	−1.50550e15			−0.139008			−0.0695041	−	0.997582i	$-0.522142\pi$
$293$	−1.50550e15			−0.139008			−0.0695041	+	0.997582i	$0.522142\pi$
$294$	2.40165e15	−	1.85520e15i	0.216897	−	0.167545i
$295$	−3.75579e16			−3.31786
$296$	−1.27620e15	+	2.21044e15i	−0.110286	+	0.191022i
$297$	1.46301e15	+	2.53400e15i	0.123689	+	0.214235i
$298$	5.62252e15	+	9.73849e15i	0.465078	+	0.805538i
$299$	2.03735e15	−	3.52879e15i	0.164893	−	0.285603i
$300$	6.87483e15			0.544470
$301$	2.26685e14	+	6.64269e14i	0.0175688	+	0.0514828i
$302$	1.56771e16			1.18910
$303$	2.30729e15	−	3.99635e15i	0.171288	−	0.296679i
$304$	−1.73795e15	−	3.01022e15i	−0.126287	−	0.218736i
$305$	1.50695e15	+	2.61011e15i	0.107189	+	0.185657i
$306$	−4.13097e15	+	7.15506e15i	−0.287649	+	0.498223i
$307$	−1.99255e16			−1.35835			−0.679173	−	0.733978i	$-0.737661\pi$
$307$	−1.99255e16			−1.35835			−0.679173	+	0.733978i	$0.737661\pi$
$308$	−2.53586e15	−	5.00161e14i	−0.169256	−	0.0333833i
$309$	−9.32415e15			−0.609367
$310$	9.58088e15	−	1.65946e16i	0.613133	−	1.06198i
$311$	2.21010e13	+	3.82801e13i	0.00138506	+	0.00239900i	0.866717	−	0.498800i	$-0.166226\pi$
$311$	2.21010e13	+	3.82801e13i	0.00138506	+	0.00239900i	−0.865332	+	0.501199i	$0.832892\pi$
$312$	−7.83238e14	−	1.35661e15i	−0.0480717	−	0.0832626i
$313$	−2.12499e15	+	3.68058e15i	−0.127737	+	0.221248i	−0.922800	−	0.385280i	$-0.874105\pi$
$313$	−2.12499e15	+	3.68058e15i	−0.127737	+	0.221248i	0.795062	+	0.606528i	$0.207438\pi$
$314$	−2.26311e15			−0.133249
$315$	1.89262e16	−	2.16516e16i	1.09155	−	1.24874i
$316$	1.03739e16			0.586108
$317$	−5.50321e15	+	9.53184e15i	−0.304601	+	0.527584i	−0.977172	−	0.212448i	$-0.931856\pi$
$317$	−5.50321e15	+	9.53184e15i	−0.304601	+	0.527584i	0.672572	+	0.740032i	$0.265190\pi$
$318$	−2.68302e15	−	4.64713e15i	−0.145495	−	0.252004i
$319$	−4.98503e15	−	8.63432e15i	−0.264867	−	0.458764i
$320$	2.34308e15	−	4.05833e15i	0.121987	−	0.211287i
$321$	−1.84120e15			−0.0939329
$322$	−4.37531e15	+	5.00536e15i	−0.218749	+	0.250249i
$323$	1.97412e16			0.967289
$324$	−2.97704e15	+	5.15638e15i	−0.142969	+	0.247630i
$325$	2.09372e16	+	3.62644e16i	0.985548	+	1.70702i
$326$	−2.13196e15	−	3.69267e15i	−0.0983706	−	0.170383i
$327$	3.59780e15	−	6.23157e15i	0.162733	−	0.281862i
$328$	−6.73923e15			−0.298834
$329$	3.84902e16	+	7.59163e15i	1.67331	+	0.330036i
$330$	4.33012e15			0.184569
$331$	−2.11676e16	+	3.66633e16i	−0.884687	+	1.53232i	−0.0386146	+	0.999254i	$0.512294\pi$
$331$	−2.11676e16	+	3.66633e16i	−0.884687	+	1.53232i	−0.846072	+	0.533068i	$0.821039\pi$
$332$	4.07046e14	+	7.05024e14i	0.0166819	+	0.0288939i
$333$	−6.59561e15	−	1.14239e16i	−0.265074	−	0.459122i
$334$	−9.89369e15	+	1.71364e16i	−0.389948	+	0.675409i
$335$	8.27943e15			0.320043
$336$	8.25436e14	+	2.41883e15i	0.0312952	+	0.0917064i
$337$	2.81461e16			1.04670			0.523352	−	0.852117i	$-0.324681\pi$
$337$	2.81461e16			1.04670			0.523352	+	0.852117i	$0.324681\pi$
$338$	−4.92131e15	+	8.52395e15i	−0.179524	+	0.310944i
$339$	−4.68761e15	−	8.11917e15i	−0.167746	−	0.290545i
$340$	1.33074e16	+	2.30490e16i	0.467175	+	0.809170i
$341$	4.45044e15	−	7.70839e15i	0.153285	−	0.265497i
$342$	1.79641e16			0.607064
$343$	−2.51568e16	−	1.66337e16i	−0.834149	−	0.551539i
$344$	−5.91109e14			−0.0192326
$345$	5.56870e15	−	9.64528e15i	0.177799	−	0.307957i
$346$	3.33387e14	+	5.77444e14i	0.0104461	+	0.0180932i
$347$	1.37022e16	+	2.37330e16i	0.421357	+	0.729811i	0.996072	−	0.0885421i	$-0.0282208\pi$
$347$	1.37022e16	+	2.37330e16i	0.421357	+	0.729811i	−0.574716	+	0.818353i	$0.694887\pi$
$348$	−4.92925e15	+	8.53772e15i	−0.148770	+	0.257678i
$349$	−5.20113e16			−1.54075			−0.770375	−	0.637591i	$-0.779931\pi$
$349$	−5.20113e16			−1.54075			−0.770375	+	0.637591i	$0.779931\pi$
$350$	−2.20653e16	−	6.46592e16i	−0.641604	−	1.88013i
$351$	1.76229e16			0.503016
$352$	1.08839e15	−	1.88515e15i	0.0304970	−	0.0528224i
$353$	−1.02686e16	−	1.77857e16i	−0.282471	−	0.489254i	0.689522	−	0.724265i	$-0.257821\pi$
$353$	−1.02686e16	−	1.77857e16i	−0.282471	−	0.489254i	−0.971993	+	0.235011i	$0.924487\pi$
$354$	8.62547e15	+	1.49398e16i	0.232949	+	0.403480i
$355$	4.29426e16	−	7.43788e16i	1.13869	−	1.97226i
$356$	−2.24648e16			−0.584894
$357$	−1.42411e16	−	2.80885e15i	−0.364083	−	0.0718100i
$358$	−2.80844e16			−0.705059
$359$	−2.44701e15	+	4.23835e15i	−0.0603285	+	0.104492i	−0.894612	−	0.446843i	$-0.852548\pi$
$359$	−2.44701e15	+	4.23835e15i	−0.0603285	+	0.104492i	0.834284	+	0.551335i	$0.185881\pi$
$360$	1.21094e16	+	2.09742e16i	0.293196	+	0.507830i
$361$	−4.35230e14	−	7.53840e14i	−0.0103496	−	0.0179259i
$362$	−3.46059e14	+	5.99392e14i	−0.00808248	+	0.0139993i
$363$	−1.48842e16			−0.341454
$364$	−1.02453e16	+	1.17207e16i	−0.230870	+	0.264115i
$365$	−9.91050e15			−0.219377
$366$	6.92165e14	−	1.19887e15i	0.0150516	−	0.0260701i
$367$	−6.03722e13	−	1.04568e14i	−0.00128976	−	0.00223392i	0.865380	−	0.501117i	$-0.167077\pi$
$367$	−6.03722e13	−	1.04568e14i	−0.00128976	−	0.00223392i	−0.866670	+	0.498883i	$0.833744\pi$
$368$	−2.79942e15	−	4.84875e15i	−0.0587568	−	0.101770i
$369$	1.74148e16	−	3.01632e16i	0.359125	−	0.622023i
$370$	−4.24937e16			−0.861021
$371$	−3.50958e16	+	4.01497e16i	−0.698756	+	0.799376i
$372$	−8.80129e15			−0.172194
$373$	7.37286e15	−	1.27702e16i	0.141752	−	0.245521i	−0.786405	−	0.617712i	$-0.788060\pi$
$373$	7.37286e15	−	1.27702e16i	0.141752	−	0.245521i	0.928156	+	0.372190i	$0.121393\pi$
$374$	6.18145e15	+	1.07066e16i	0.116795	+	0.202295i
$375$	3.68583e16	+	6.38404e16i	0.684435	+	1.18548i
$376$	−1.65200e16	+	2.86135e16i	−0.301501	+	0.522216i
$377$	−6.00480e16			−1.07716
$378$	−2.82093e16	−	5.56387e15i	−0.497388	−	0.0981025i
$379$	2.32876e15			0.0403617			0.0201809	−	0.999796i	$-0.493576\pi$
$379$	2.32876e15			0.0403617			0.0201809	+	0.999796i	$0.493576\pi$
$380$	2.89344e16	−	5.01158e16i	0.492970	−	0.853850i
$381$	−1.13283e16	−	1.96212e16i	−0.189737	−	0.328635i
$382$	1.91250e16	+	3.31255e16i	0.314912	+	0.545444i
$383$	1.86847e16	−	3.23629e16i	0.302479	−	0.523909i	−0.674218	−	0.738532i	$-0.735519\pi$
$383$	1.86847e16	−	3.23629e16i	0.302479	−	0.523909i	0.976697	+	0.214624i	$0.0688525\pi$
$384$	−2.15242e15			−0.0342590
$385$	−1.38978e16	−	4.07257e16i	−0.217497	−	0.637344i
$386$	2.91613e16			0.448734
$387$	1.52748e15	−	2.64567e15i	0.0231128	−	0.0400326i
$388$	−6.93195e15	−	1.20065e16i	−0.103145	−	0.178653i
$389$	−2.40310e15	−	4.16229e15i	−0.0351641	−	0.0609060i	0.847908	−	0.530144i	$-0.177862\pi$
$389$	−2.40310e15	−	4.16229e15i	−0.0351641	−	0.0609060i	−0.883072	+	0.469238i	$0.844529\pi$
$390$	1.30398e16	−	2.25856e16i	0.187651	−	0.325021i
$391$	3.17983e16			0.450044
$392$	2.01003e16	−	1.55268e16i	0.279797	−	0.216134i
$393$	1.03612e16			0.141859
$394$	−2.71947e16	+	4.71027e16i	−0.366235	+	0.634337i
$395$	8.63556e16	+	1.49572e17i	1.14396	+	1.98139i
$396$	5.62499e15	+	9.74277e15i	0.0732999	+	0.126959i
$397$	−1.18316e16	+	2.04930e16i	−0.151672	+	0.262704i	−0.931842	−	0.362863i	$-0.881799\pi$
$397$	−1.18316e16	+	2.04930e16i	−0.151672	+	0.262704i	0.780170	+	0.625568i	$0.215133\pi$
$398$	9.30462e16			1.17343
$399$	1.01932e16	+	2.98698e16i	0.126470	+	0.370602i
$400$	5.75378e16			0.702366
$401$	−2.64431e16	+	4.58009e16i	−0.317596	+	0.550092i	−0.979986	−	0.199067i	$-0.936209\pi$
$401$	−2.64431e16	+	4.58009e16i	−0.317596	+	0.550092i	0.662390	+	0.749159i	$0.269542\pi$
$402$	−1.90143e15	−	3.29338e15i	−0.0224705	−	0.0389200i
$403$	−2.68043e16	−	4.64264e16i	−0.311689	−	0.539861i
$404$	1.93106e16	−	3.34469e16i	0.220961	−	0.382716i
$405$	−9.91269e16			−1.11618
$406$	9.61198e16	+	1.89582e16i	1.06511	+	0.210077i
$407$	−1.97389e16			−0.215258
$408$	6.11228e15	−	1.05868e16i	0.0656013	−	0.113625i
$409$	2.17697e16	+	3.77062e16i	0.229959	+	0.398301i	0.957796	−	0.287450i	$-0.0928074\pi$
$409$	2.17697e16	+	3.77062e16i	0.229959	+	0.398301i	−0.727837	+	0.685751i	$0.759474\pi$
$410$	−5.60993e16	−	9.71668e16i	−0.583260	−	1.01024i
$411$	9.68814e15	−	1.67804e16i	0.0991445	−	0.171723i
$412$	−7.80371e16			−0.786084
$413$	1.12827e17	−	1.29075e17i	1.11877	−	1.27987i
$414$	2.89358e16			0.282445
$415$	−6.77673e15	+	1.17376e16i	−0.0651190	+	0.112789i
$416$	−6.55520e15	−	1.13539e16i	−0.0620125	−	0.107409i
$417$	−2.27335e14	−	3.93756e14i	−0.00211730	−	0.00366727i
$418$	1.34404e16	−	2.32794e16i	0.123244	−	0.213465i
$419$	5.69881e16			0.514509			0.257255	−	0.966344i	$-0.417182\pi$
$419$	5.69881e16			0.514509			0.257255	+	0.966344i	$0.417182\pi$
$420$	−2.80037e16	+	3.20362e16i	−0.248940	+	0.284787i
$421$	6.97807e16			0.610803			0.305402	−	0.952224i	$-0.401209\pi$
$421$	6.97807e16			0.610803			0.305402	+	0.952224i	$0.401209\pi$
$422$	−3.22737e15	+	5.58997e15i	−0.0278175	+	0.0481813i
$423$	−8.53783e16	−	1.47880e17i	−0.724662	−	1.25515i
$424$	−2.24551e16	−	3.88934e16i	−0.187688	−	0.325086i
$425$	−1.63391e17	+	2.83002e17i	−1.34493	+	2.32949i
$426$	−3.94484e16			−0.319792
$427$	−1.34971e16	−	2.66211e15i	−0.107761	−	0.0212542i
$428$	−1.54096e16			−0.121173
$429$	6.05716e15	−	1.04913e16i	0.0469134	−	0.0812563i
$430$	−4.92056e15	−	8.52266e15i	−0.0375379	−	0.0650175i
$431$	1.26096e17	+	2.18405e17i	0.947545	+	1.64120i	0.750573	+	0.660787i	$0.229777\pi$
$431$	1.26096e17	+	2.18405e17i	0.947545	+	1.64120i	0.196972	+	0.980409i	$0.436889\pi$
$432$	1.21074e16	−	2.09707e16i	0.0896205	−	0.155227i
$433$	−1.42066e16			−0.103590			−0.0517952	−	0.998658i	$-0.516494\pi$
$433$	−1.42066e16			−0.103590			−0.0517952	+	0.998658i	$0.516494\pi$
$434$	2.82484e16	+	8.27780e16i	0.202913	+	0.594609i
$435$	−1.64130e17			−1.16147
$436$	3.01112e16	−	5.21542e16i	0.209926	−	0.363603i
$437$	−3.45697e16	−	5.98766e16i	−0.237447	−	0.411270i
$438$	2.27602e15	+	3.94219e15i	0.0154026	+	0.0266781i
$439$	2.71324e16	−	4.69947e16i	0.180912	−	0.313350i	−0.761279	−	0.648424i	$-0.775428\pi$
$439$	2.71324e16	−	4.69947e16i	0.180912	−	0.313350i	0.942192	+	0.335075i	$0.108762\pi$
$440$	3.62403e16			0.238094
$441$	1.75536e16	+	1.30087e17i	0.113636	+	0.842137i
$442$	7.44597e16			0.474981
$443$	1.22671e17	−	2.12472e17i	0.771110	−	1.33560i	−0.165845	−	0.986152i	$-0.553035\pi$
$443$	1.22671e17	−	2.12472e17i	0.771110	−	1.33560i	0.936955	−	0.349450i	$-0.113631\pi$
$444$	9.75902e15	+	1.69031e16i	0.0604529	+	0.104707i
$445$	−1.87003e17	−	3.23899e17i	−1.14159	−	1.97729i
$446$	−2.50279e16	+	4.33495e16i	−0.150573	+	0.260800i
$447$	8.59903e16			0.509859
$448$	6.90837e15	+	2.02440e16i	0.0403709	+	0.118301i
$449$	−3.17982e17			−1.83148			−0.915739	−	0.401773i	$-0.868394\pi$
$449$	−3.17982e17			−1.83148			−0.915739	+	0.401773i	$0.868394\pi$
$450$	−1.48683e17	+	2.57526e17i	−0.844072	+	1.46197i
$451$	−2.60588e16	−	4.51352e16i	−0.145817	−	0.252562i
$452$	−3.92322e16	−	6.79522e16i	−0.216393	−	0.374804i
$453$	5.99409e16	−	1.03821e17i	0.325900	−	0.564476i
$454$	−1.79502e16			−0.0962066
$455$	−2.54275e17	−	5.01519e16i	−1.34347	−	0.264980i
$456$	−2.65800e16			−0.138447
$457$	−2.38520e16	+	4.13129e16i	−0.122481	+	0.212144i	−0.920746	−	0.390163i	$-0.872419\pi$
$457$	−2.38520e16	+	4.13129e16i	−0.122481	+	0.212144i	0.798264	+	0.602307i	$0.205752\pi$
$458$	−9.83986e16	−	1.70431e17i	−0.498154	−	0.862827i
$459$	6.87634e16	+	1.19102e17i	0.343222	+	0.594478i
$460$	4.66064e16	−	8.07247e16i	0.229361	−	0.397265i
$461$	3.80845e17			1.84796			0.923979	−	0.382444i	$-0.124917\pi$
$461$	3.80845e17			1.84796			0.923979	+	0.382444i	$0.124917\pi$
$462$	−1.30081e16	+	1.48812e16i	−0.0622358	+	0.0711978i
$463$	3.17540e17			1.49803			0.749017	−	0.662550i	$-0.230526\pi$
$463$	3.17540e17			1.49803			0.749017	+	0.662550i	$0.230526\pi$
$464$	−4.12546e16	+	7.14551e16i	−0.191914	+	0.332404i
$465$	−7.32645e16	−	1.26898e17i	−0.336085	−	0.582117i
$466$	9.94029e16	+	1.72171e17i	0.449667	+	0.778846i
$467$	−1.35003e17	+	2.33833e17i	−0.602261	+	1.04315i	0.390217	+	0.920723i	$0.372400\pi$
$467$	−1.35003e17	+	2.33833e17i	−0.602261	+	1.04315i	−0.992478	+	0.122424i	$0.960933\pi$
$468$	6.77568e16			0.298095
$469$	−2.48721e16	+	2.84537e16i	−0.107917	+	0.123457i
$470$	−5.50069e17			−2.35386
$471$	−8.65294e15	+	1.49873e16i	−0.0365197	+	0.0632540i
$472$	7.21896e16	+	1.25036e17i	0.300505	+	0.520490i
$473$	−2.28566e15	−	3.95889e15i	−0.00938458	−	0.0162546i
$474$	3.96645e16	−	6.87009e16i	0.160636	−	0.278230i
$475$	7.10527e17			2.83839
$476$	−1.19189e17	−	2.35082e16i	−0.469667	−	0.0926350i
$477$	2.32104e17			0.902222
$478$	1.62687e17	−	2.81781e17i	0.623836	−	1.08052i
$479$	−2.00045e16	−	3.46489e16i	−0.0756742	−	0.131072i	0.825705	−	0.564102i	$-0.190778\pi$
$479$	−2.00045e16	−	3.46489e16i	−0.0756742	−	0.131072i	−0.901379	+	0.433031i	$0.857444\pi$
$480$	−1.79174e16	−	3.10339e16i	−0.0668663	−	0.115816i
$481$	−5.94421e16	+	1.02957e17i	−0.218852	+	0.379063i
$482$	1.36814e17			0.496965
$483$	1.64188e16	+	4.81131e16i	0.0588418	+	0.172428i
$484$	−1.24571e17			−0.440476
$485$	1.15407e17	−	1.99891e17i	0.402635	−	0.697384i
$486$	9.64009e16	+	1.66971e17i	0.331853	+	0.574786i
$487$	−5.31091e16	−	9.19877e16i	−0.180398	−	0.312458i	0.761618	−	0.648026i	$-0.224405\pi$
$487$	−5.31091e16	−	9.19877e16i	−0.180398	−	0.312458i	−0.942016	+	0.335568i	$0.891072\pi$
$488$	5.79298e15	−	1.00337e16i	0.0194166	−	0.0336305i
$489$	−3.26060e16			−0.107843
$490$	3.91187e17	+	1.60558e17i	1.27676	+	0.524031i
$491$	2.75703e16			0.0887998			0.0443999	−	0.999014i	$-0.485862\pi$
$491$	2.75703e16			0.0887998			0.0443999	+	0.999014i	$0.485862\pi$
$492$	−2.57673e16	+	4.46302e16i	−0.0819021	+	0.141859i
$493$	−2.34303e17	−	4.05825e17i	−0.734976	−	1.27302i
$494$	−8.09493e16	−	1.40208e17i	−0.250604	−	0.434059i
$495$	−9.36481e16	+	1.62203e17i	−0.286131	+	0.495594i
$496$	−7.36611e16			−0.222130
$497$	1.26613e17	+	3.71021e17i	0.376843	+	1.10429i
$498$	6.22532e15			0.0182882
$499$	−2.30486e17	+	3.99213e17i	−0.668329	+	1.15758i	0.310042	+	0.950723i	$0.399657\pi$
$499$	−2.30486e17	+	3.99213e17i	−0.668329	+	1.15758i	−0.978371	+	0.206857i	$0.933677\pi$
$500$	3.08480e17	+	5.34303e17i	0.882921	+	1.52926i
$501$	7.56566e16	+	1.31041e17i	0.213748	+	0.370222i
$502$	−4.08953e16	+	7.08328e16i	−0.114051	+	0.197542i
$503$	−5.56693e17			−1.53258			−0.766291	−	0.642494i	$-0.777900\pi$
$503$	−5.56693e17			−1.53258			−0.766291	+	0.642494i	$0.777900\pi$
$504$	−1.08459e17	−	2.13920e16i	−0.294760	−	0.0581371i
$505$	6.42986e17			1.72507
$506$	2.16493e16	−	3.74977e16i	0.0573410	−	0.0993175i
$507$	3.76330e16	+	6.51823e16i	0.0984050	+	0.170442i
$508$	−9.48107e16	−	1.64217e17i	−0.244762	−	0.423939i
$509$	−2.46492e17	+	4.26937e17i	−0.628257	+	1.08817i	0.359644	+	0.933090i	$0.382898\pi$
$509$	−2.46492e17	+	4.26937e17i	−0.628257	+	1.08817i	−0.987901	+	0.155084i	$0.950435\pi$
$510$	2.03522e17			0.512159
$511$	2.97720e16	−	3.40592e16i	0.0739729	−	0.0846250i
$512$	−1.80144e16			−0.0441942
$513$	1.49513e17	−	2.58964e17i	0.362173	−	0.627302i
$514$	−1.50281e17	−	2.60295e17i	−0.359455	−	0.622595i
$515$	−6.49603e17	−	1.12515e18i	−1.53427	−	2.65743i
$516$	−2.26009e15	+	3.91459e15i	−0.00527112	+	0.00912984i
$517$	−2.55514e17			−0.588473
$518$	1.27655e17	−	1.46037e17i	0.290332	−	0.332140i
$519$	5.09879e15			0.0114520
$520$	1.09135e17	−	1.89027e17i	0.242070	−	0.419278i
$521$	2.89798e17	+	5.01944e17i	0.634819	+	1.09954i	0.986553	+	0.163439i	$0.0522586\pi$
$521$	2.89798e17	+	5.01944e17i	0.634819	+	1.09954i	−0.351735	+	0.936100i	$0.614408\pi$
$522$	−2.13211e17	−	3.69293e17i	−0.461266	−	0.798937i
$523$	6.21615e16	−	1.07667e17i	0.132819	−	0.230049i	−0.791943	−	0.610595i	$-0.790930\pi$
$523$	6.21615e16	−	1.07667e17i	0.132819	−	0.230049i	0.924762	+	0.380546i	$0.124264\pi$
$524$	8.67164e16			0.182999
$525$	−5.12568e17	−	1.01097e17i	−1.06836	−	0.210718i
$526$	−6.04822e17			−1.24515
$527$	2.09177e17	−	3.62305e17i	0.425348	−	0.736725i
$528$	−8.32287e15	−	1.44156e16i	−0.0167168	−	0.0289543i
$529$	1.96335e17	+	3.40061e17i	0.389525	+	0.674676i
$530$	3.73846e17	−	6.47520e17i	0.732655	−	1.26900i
$531$	−7.46177e17			−1.44453
$532$	8.53106e16	+	2.49991e17i	0.163146	+	0.478077i
$533$	−3.13896e17			−0.593006
$534$	−8.58935e16	+	1.48772e17i	−0.160303	+	0.277653i
$535$	−1.28274e17	−	2.22177e17i	−0.236505	−	0.409638i
$536$	−1.59138e16	−	2.75635e16i	−0.0289869	−	0.0502068i
$537$	−1.07380e17	+	1.85988e17i	−0.193237	+	0.334696i
$538$	−2.22274e17			−0.395189
$539$	1.81712e17	+	7.45812e16i	0.319195	+	0.131009i
$540$	4.03143e17			0.699680
$541$	−4.09563e16	+	7.09384e16i	−0.0702325	+	0.121646i	−0.899003	−	0.437942i	$-0.855707\pi$
$541$	−4.09563e16	+	7.09384e16i	−0.0702325	+	0.121646i	0.828771	+	0.559588i	$0.189041\pi$
$542$	1.49657e17	+	2.59213e17i	0.253572	+	0.439200i
$543$	2.64630e15	+	4.58352e15i	0.00443037	+	0.00767362i
$544$	5.11558e16	−	8.86045e16i	0.0846257	−	0.146576i
$545$	1.00262e18			1.63892
$546$	3.84467e16	+	1.12663e17i	0.0621023	+	0.181982i
$547$	−3.99955e17			−0.638402			−0.319201	−	0.947687i	$-0.603414\pi$
$547$	−3.99955e17			−0.638402			−0.319201	+	0.947687i	$0.603414\pi$
$548$	8.10835e16	−	1.40441e17i	0.127897	−	0.221523i
$549$	2.99391e16	+	5.18561e16i	0.0466679	+	0.0808312i
$550$	2.22484e17	+	3.85353e17i	0.342721	+	0.593610i
$551$	−5.09448e17	+	8.82391e17i	−0.775559	+	1.34331i
$552$	−4.28141e16			−0.0644144
$553$	−7.73453e17	−	1.52552e17i	−1.15006	−	0.226832i
$554$	4.58432e17			0.673692
$555$	−1.62474e17	+	2.81413e17i	−0.235982	+	0.408733i
$556$	−1.90265e15	−	3.29548e15i	−0.00273132	−	0.00473078i
$557$	5.23201e17	+	9.06211e17i	0.742352	+	1.28579i	0.951422	+	0.307891i	$0.0996232\pi$
$557$	5.23201e17	+	9.06211e17i	0.742352	+	1.28579i	−0.209069	+	0.977901i	$0.567043\pi$
$558$	1.90347e17	−	3.29690e17i	0.266946	−	0.462364i
$559$	−2.75324e16			−0.0381651
$560$	−2.34373e17	+	2.68122e17i	−0.321133	+	0.367376i
$561$	9.45384e16			0.128041
$562$	−1.16981e17	+	2.02616e17i	−0.156613	+	0.271261i
$563$	−3.38309e17	−	5.85968e17i	−0.447722	−	0.775478i	0.550515	−	0.834825i	$-0.314431\pi$
$563$	−3.38309e17	−	5.85968e17i	−0.447722	−	0.775478i	−0.998237	+	0.0593473i	$0.981098\pi$
$564$	1.26328e17	+	2.18806e17i	0.165266	+	0.286250i
$565$	6.53160e17	−	1.13131e18i	0.844705	−	1.46307i
$566$	−2.59925e16			−0.0332309
$567$	2.97786e17	−	3.40667e17i	0.376370	−	0.430567i
$568$	−3.30158e17			−0.412532
$569$	5.76178e17	−	9.97969e17i	0.711749	−	1.23279i	−0.252451	−	0.967610i	$-0.581237\pi$
$569$	5.76178e17	−	9.97969e17i	0.711749	−	1.23279i	0.964200	−	0.265176i	$-0.0854300\pi$
$570$	−2.21260e17	−	3.83233e17i	−0.270219	−	0.468033i
$571$	6.95800e17	+	1.20516e18i	0.840137	+	1.45516i	0.889779	+	0.456392i	$0.150859\pi$
$571$	6.95800e17	+	1.20516e18i	0.840137	+	1.45516i	−0.0496423	+	0.998767i	$0.515808\pi$
$572$	5.06945e16	−	8.78054e16i	0.0605183	−	0.104821i
$573$	2.92496e17			0.345235
$574$	5.02458e17	+	9.91026e16i	0.586372	+	0.115653i
$575$	1.14449e18			1.32060
$576$	4.65508e16	−	8.06283e16i	0.0531106	−	0.0919902i
$577$	6.39661e17	+	1.10793e18i	0.721618	+	1.24988i	0.960351	+	0.278794i	$0.0899346\pi$
$577$	6.39661e17	+	1.10793e18i	0.721618	+	1.24988i	−0.238733	+	0.971085i	$0.576732\pi$
$578$	−2.64100e16	−	4.57434e16i	−0.0294603	−	0.0510267i
$579$	1.11497e17	−	1.93119e17i	0.122986	−	0.213017i
$580$	−1.37366e18			−1.49830
$581$	−1.99806e16	−	5.85504e16i	−0.0215508	−	0.0631517i
$582$	−1.06017e17			−0.113077
$583$	1.73656e17	−	3.00781e17i	0.183166	−	0.317253i
$584$	1.90488e16	+	3.29935e16i	0.0198694	+	0.0344148i
$585$	5.64027e17	+	9.76924e17i	0.581818	+	1.00774i
$586$	−4.81759e16	+	8.34431e16i	−0.0491468	+	0.0851248i
$587$	−5.72711e17			−0.577813			−0.288907	−	0.957357i	$-0.593292\pi$
$587$	−5.72711e17			−0.577813			−0.288907	+	0.957357i	$0.593292\pi$
$588$	−2.59726e16	−	1.92479e17i	−0.0259157	−	0.192058i
$589$	−9.09632e17			−0.897669
$590$	−1.20185e18	+	2.08167e18i	−1.17304	+	2.03177i
$591$	2.07957e17	+	3.60192e17i	0.200750	+	0.347708i
$592$	8.16767e16	+	1.41468e17i	0.0779842	+	0.135073i
$593$	5.24473e17	−	9.08413e17i	0.495299	−	0.857883i	−0.504686	−	0.863303i	$-0.668392\pi$
$593$	5.24473e17	−	9.08413e17i	0.495299	−	0.857883i	0.999985	+	0.00541985i	$0.00172520\pi$
$594$	1.87265e17			0.174922
$595$	−6.53218e17	−	1.91416e18i	−0.603528	−	1.76856i
$596$	7.19683e17			0.657719
$597$	3.55760e17	−	6.16194e17i	0.321606	−	0.557037i
$598$	−1.30390e17	−	2.25842e17i	−0.116597	−	0.201952i
$599$	−3.84295e17	−	6.65618e17i	−0.339931	−	0.588777i	0.644489	−	0.764614i	$-0.277070\pi$
$599$	−3.84295e17	−	6.65618e17i	−0.339931	−	0.588777i	−0.984419	+	0.175837i	$0.943737\pi$
$600$	2.19994e17	−	3.81042e17i	0.192499	−	0.333418i
$601$	−9.28666e16			−0.0803851			−0.0401926	−	0.999192i	$-0.512797\pi$
$601$	−9.28666e16			−0.0803851			−0.0401926	+	0.999192i	$0.512797\pi$
$602$	4.40715e16	+	8.69245e15i	0.0377381	+	0.00744329i
$603$	1.64490e17			0.139341
$604$	5.01666e17	−	8.68911e17i	0.420411	−	0.728174i
$605$	−1.03696e18	−	1.79607e18i	−0.859714	−	1.48907i
$606$	−1.47667e17	−	2.55766e17i	−0.121119	−	0.209784i
$607$	−7.85335e17	+	1.36024e18i	−0.637278	+	1.10380i	0.348750	+	0.937216i	$0.386606\pi$
$607$	−7.85335e17	+	1.36024e18i	−0.637278	+	1.10380i	−0.986028	+	0.166581i	$0.946727\pi$
$608$	−2.22458e17			−0.178597
$609$	4.93062e17	−	5.64063e17i	0.391642	−	0.448038i
$610$	1.92890e17			0.151588
$611$	−7.69461e17	+	1.33274e18i	−0.598299	+	1.03628i
$612$	2.64382e17	+	4.57924e17i	0.203399	+	0.352297i
$613$	−6.44651e17	−	1.11657e18i	−0.490718	−	0.849948i	0.509225	−	0.860633i	$-0.329932\pi$
$613$	−6.44651e17	−	1.11657e18i	−0.490718	−	0.849948i	−0.999943	+	0.0106854i	$0.996599\pi$
$614$	−6.37617e17	+	1.10438e18i	−0.480248	+	0.831813i
$615$	−8.57976e17			−0.639421
$616$	−1.08869e17	+	1.24546e17i	−0.0802842	+	0.0918452i
$617$	8.41398e17			0.613971			0.306985	−	0.951714i	$-0.400680\pi$
$617$	8.41398e17			0.613971			0.306985	+	0.951714i	$0.400680\pi$
$618$	−2.98373e17	+	5.16797e17i	−0.215444	+	0.373160i
$619$	5.89250e17	+	1.02061e18i	0.421028	+	0.729241i	0.996040	−	0.0889034i	$-0.0283362\pi$
$619$	5.89250e17	+	1.02061e18i	0.421028	+	0.729241i	−0.575013	+	0.818144i	$0.695003\pi$
$620$	−6.13176e17	−	1.06205e18i	−0.433550	−	0.750931i
$621$	2.40830e17	−	4.17130e17i	0.168506	−	0.291861i
$622$	2.82893e15			0.00195878
$623$	1.67491e18	+	3.30352e17i	1.14768	+	0.226362i
$624$	−1.00255e17			−0.0679836
$625$	−3.04254e18	+	5.26983e18i	−2.04181	+	3.53652i
$626$	1.35999e17	+	2.35557e17i	0.0903240	+	0.156446i
$627$	−1.02778e17	−	1.78017e17i	−0.0675556	−	0.117010i
$628$	−7.24195e16	+	1.25434e17i	−0.0471105	+	0.0815978i
$629$	−9.27755e17			−0.597316
$630$	−5.94415e17	−	1.74185e18i	−0.378770	−	1.10993i
$631$	−1.91515e17			−0.120785			−0.0603923	−	0.998175i	$-0.519235\pi$
$631$	−1.91515e17			−0.120785			−0.0603923	+	0.998175i	$0.519235\pi$
$632$	3.31966e17	−	5.74982e17i	0.207220	−	0.358916i
$633$	2.46795e16	+	4.27462e16i	0.0152480	+	0.0264103i
$634$	3.52205e17	+	6.10038e17i	0.215385	+	0.373058i
$635$	1.57846e18	−	2.73398e18i	0.955444	−	1.65488i
$636$	−3.43426e17			−0.205761
$637$	9.36220e17	−	7.23199e17i	0.555228	−	0.428896i
$638$	−6.38084e17			−0.374579
$639$	8.53156e17	−	1.47771e18i	0.495762	−	0.858685i
$640$	−1.49957e17	−	2.59733e17i	−0.0862575	−	0.149402i
$641$	7.31765e17	+	1.26745e18i	0.416672	+	0.721697i	0.995602	−	0.0936800i	$-0.0298631\pi$
$641$	7.31765e17	+	1.26745e18i	0.416672	+	0.721697i	−0.578930	+	0.815377i	$0.696530\pi$
$642$	−5.89183e16	+	1.02050e17i	−0.0332103	+	0.0575219i
$643$	−1.79993e18			−1.00435			−0.502173	−	0.864767i	$-0.667466\pi$
$643$	−1.79993e18			−1.00435			−0.502173	+	0.864767i	$0.667466\pi$
$644$	1.37415e17	+	4.02676e17i	0.0759060	+	0.222432i
$645$	−7.52545e16			−0.0411523
$646$	6.31717e17	−	1.09417e18i	0.341988	−	0.592341i
$647$	−1.13239e18	−	1.96136e18i	−0.606902	−	1.05119i	−0.991748	−	0.128204i	$-0.959079\pi$
$647$	−1.13239e18	−	1.96136e18i	−0.606902	−	1.05119i	0.384846	−	0.922981i	$-0.374255\pi$
$648$	1.90530e17	+	3.30008e17i	0.101094	+	0.175101i
$649$	−5.58277e17	+	9.66964e17i	−0.293264	+	0.507949i
$650$	2.67997e18			1.39377
$651$	6.56201e17	+	1.29426e17i	0.337878	+	0.0666415i
$652$	−2.72891e17			−0.139117
$653$	9.13054e17	−	1.58146e18i	0.460851	−	0.798218i	−0.538152	−	0.842848i	$-0.680877\pi$
$653$	9.13054e17	−	1.58146e18i	0.460851	−	0.798218i	0.999004	+	0.0446297i	$0.0142108\pi$
$654$	−2.30259e17	−	3.98821e17i	−0.115070	−	0.199307i
$655$	7.21852e17	+	1.25029e18i	0.357174	+	0.618644i
$656$	−2.15655e17	+	3.73526e17i	−0.105654	+	0.182998i
$657$	−1.96895e17			−0.0955126
$658$	1.65246e18	−	1.89041e18i	0.793711	−	0.908005i
$659$	1.72001e18			0.818044			0.409022	−	0.912525i	$-0.365870\pi$
$659$	1.72001e18			0.818044			0.409022	+	0.912525i	$0.365870\pi$
$660$	1.38564e17	−	2.40000e17i	0.0652551	−	0.113025i
$661$	−7.91910e16	−	1.37163e17i	−0.0369289	−	0.0639627i	0.846970	−	0.531640i	$-0.178424\pi$
$661$	−7.91910e16	−	1.37163e17i	−0.0369289	−	0.0639627i	−0.883899	+	0.467678i	$0.845091\pi$
$662$	1.35473e18	+	2.34645e18i	0.625568	+	1.08352i
$663$	2.84695e17	−	4.93106e17i	0.130179	−	0.225477i
$664$	5.21019e16			0.0235918
$665$	−2.89424e18	+	3.31101e18i	−1.29776	+	1.48464i
$666$	−8.44238e17			−0.374872
$667$	−8.20601e17	+	1.42132e18i	−0.360839	+	0.624992i
$668$	6.33196e17	+	1.09673e18i	0.275735	+	0.477587i
$669$	1.91387e17	+	3.31492e17i	0.0825358	+	0.142956i
$670$	2.64942e17	−	4.58892e17i	0.113152	−	0.195986i
$671$	8.95997e16			0.0378975
$672$	1.60479e17	+	3.16521e16i	0.0672230	+	0.0132587i
$673$	−2.70067e18			−1.12040			−0.560201	−	0.828356i	$-0.689276\pi$
$673$	−2.70067e18			−1.12040			−0.560201	+	0.828356i	$0.689276\pi$
$674$	9.00675e17	−	1.56002e18i	0.370066	−	0.640973i
$675$	2.47494e18	+	4.28673e18i	1.00714	+	1.74442i
$676$	3.14964e17	+	5.45533e17i	0.126942	+	0.219871i
$677$	1.21728e18	−	2.10839e18i	0.485919	−	0.841637i	−0.513950	−	0.857820i	$-0.671818\pi$
$677$	1.21728e18	−	2.10839e18i	0.485919	−	0.841637i	0.999869	+	0.0161835i	$0.00515159\pi$
$678$	−6.00014e17			−0.237229
$679$	3.40268e17	+	9.97108e17i	0.133250	+	0.390471i
$680$	1.70334e18			0.660685
$681$	−6.86319e16	+	1.18874e17i	−0.0263676	+	0.0456700i
$682$	−2.84828e17	−	4.93337e17i	−0.108389	−	0.187735i
$683$	−7.37572e16	−	1.27751e17i	−0.0278016	−	0.0481538i	0.851790	−	0.523884i	$-0.175517\pi$
$683$	−7.37572e16	−	1.27751e17i	−0.0278016	−	0.0481538i	−0.879591	+	0.475730i	$0.842184\pi$
$684$	5.74850e17	−	9.95669e17i	0.214630	−	0.371749i
$685$	2.69985e18			0.998506
$686$	−1.72695e18	+	8.62055e17i	−0.632663	+	0.315812i
$687$	−1.50490e18			−0.546120
$688$	−1.89155e16	+	3.27626e16i	−0.00679974	+	0.0117775i
$689$	−1.04590e18	−	1.81156e18i	−0.372449	−	0.645100i
$690$	−3.56397e17	−	6.17298e17i	−0.125723	−	0.217759i
$691$	1.28877e18	−	2.23222e18i	0.450369	−	0.780062i	−0.548040	−	0.836452i	$-0.684626\pi$
$691$	1.28877e18	−	2.23222e18i	0.450369	−	0.780062i	0.998409	+	0.0563901i	$0.0179591\pi$
$692$	4.26736e16			0.0147730
$693$	−2.76113e17	−	8.09112e17i	−0.0946938	−	0.277487i
$694$	1.75389e18			0.595888
$695$	3.16764e16	−	5.48651e16i	0.0106619	−	0.0184669i
$696$	3.15472e17	+	5.46414e17i	0.105196	+	0.182206i
$697$	−1.22480e18	−	2.12142e18i	−0.404625	−	0.700831i
$698$	−1.66436e18	+	2.88276e18i	−0.544737	+	0.943513i
$699$	1.52026e18			0.492965
$700$	−4.28986e18	−	8.46113e17i	−1.37818	−	0.271826i
$701$	−1.66664e18			−0.530486			−0.265243	−	0.964182i	$-0.585452\pi$
$701$	−1.66664e18			−0.530486			−0.265243	+	0.964182i	$0.585452\pi$
$702$	5.63933e17	−	9.76761e17i	0.177843	−	0.308033i
$703$	1.00861e18	+	1.74697e18i	0.315149	+	0.545854i
$704$	−6.96570e16	−	1.20649e17i	−0.0215646	−	0.0373511i
$705$	−2.10318e18	+	3.64281e18i	−0.645129	+	1.11740i
$706$	−1.31438e18			−0.399475
$707$	−1.93159e18	+	2.20974e18i	−0.581686	+	0.665449i
$708$	1.10406e18			0.329440
$709$	2.58063e18	−	4.46978e18i	0.763000	−	1.32156i	−0.178297	−	0.983977i	$-0.557059\pi$
$709$	2.58063e18	−	4.46978e18i	0.763000	−	1.32156i	0.941297	−	0.337578i	$-0.109608\pi$
$710$	−2.74833e18	−	4.76024e18i	−0.805173	−	1.39460i
$711$	1.71566e18	+	2.97161e18i	0.498056	+	0.862659i
$712$	−7.18873e17	+	1.24512e18i	−0.206791	+	0.358173i
$713$	−1.46520e18			−0.417653
$714$	−6.11397e17	+	6.99439e17i	−0.172697	+	0.197566i
$715$	1.68798e18			0.472475
$716$	−8.98700e17	+	1.55659e18i	−0.249276	+	0.431758i
$717$	−1.24406e18	−	2.15477e18i	−0.341952	−	0.592279i
$718$	1.56609e17	+	2.71254e17i	0.0426587	+	0.0738870i
$719$	−1.80992e18	+	3.13488e18i	−0.488565	+	0.846220i	−0.999913	−	0.0131535i	$-0.995813\pi$
$719$	−1.80992e18	+	3.13488e18i	−0.488565	+	0.846220i	0.511348	+	0.859374i	$0.329146\pi$
$720$	1.55001e18			0.414641
$721$	5.81823e18	+	1.14756e18i	1.54245	+	0.304226i
$722$	−5.57094e16			−0.0146365
$723$	5.23106e17	−	9.06047e17i	0.136204	−	0.235913i
$724$	2.21478e16	+	3.83611e16i	0.00571518	+	0.00989898i
$725$	−8.43309e18	−	1.46065e19i	−2.15670	−	3.73551i
$726$	−4.76294e17	+	8.24965e17i	−0.120722	+	0.209097i
$727$	−4.45477e18			−1.11906			−0.559528	−	0.828811i	$-0.689018\pi$
$727$	−4.45477e18			−1.11906			−0.559528	+	0.828811i	$0.689018\pi$
$728$	3.21774e17	+	9.42915e17i	0.0801120	+	0.234757i
$729$	−8.43212e17			−0.208069
$730$	−3.17136e17	+	5.49295e17i	−0.0775616	+	0.134341i
$731$	−1.07429e17	−	1.86073e17i	−0.0260411	−	0.0451046i
$732$	−4.42986e16	−	7.67274e16i	−0.0106431	−	0.0184344i
$733$	7.49497e17	−	1.29817e18i	0.178482	−	0.309139i	−0.762879	−	0.646541i	$-0.776215\pi$
$733$	7.49497e17	−	1.29817e18i	0.178482	−	0.309139i	0.941361	+	0.337402i	$0.109548\pi$
$734$	−7.72764e15			−0.00182399
$735$	2.55898e18	−	1.97673e18i	0.598687	−	0.462466i
$736$	−3.58326e17			−0.0830946
$737$	1.23069e17	−	2.13161e17i	0.0282885	−	0.0489971i
$738$	−1.11454e18	−	1.93045e18i	−0.253940	−	0.439837i
$739$	−9.95675e17	−	1.72456e18i	−0.224869	−	0.389484i	0.731411	−	0.681936i	$-0.238862\pi$
$739$	−9.95675e17	−	1.72456e18i	−0.224869	−	0.389484i	−0.956280	+	0.292453i	$0.905529\pi$
$740$	−1.35980e18	+	2.35524e18i	−0.304417	+	0.527266i
$741$	−1.23803e18			−0.274734
$742$	1.10225e18	+	3.23000e18i	0.242469	+	0.710521i
$743$	−3.75670e18			−0.819179			−0.409590	−	0.912270i	$-0.634328\pi$
$743$	−3.75670e18			−0.819179			−0.409590	+	0.912270i	$0.634328\pi$
$744$	−2.81641e17	+	4.87817e17i	−0.0608797	+	0.105447i
$745$	5.99085e18	+	1.03764e19i	1.28373	+	2.22348i
$746$	−4.71863e17	−	8.17291e17i	−0.100234	−	0.173610i
$747$	−1.34636e17	+	2.33196e17i	−0.0283515	+	0.0491063i
$748$	7.91225e17			0.165173
$749$	1.14890e18	+	2.26604e17i	0.237766	+	0.0468959i
$750$	4.71786e18			0.967937
$751$	4.62860e18	−	8.01697e18i	0.941435	−	1.63061i	0.178697	−	0.983904i	$-0.442812\pi$
$751$	4.62860e18	−	8.01697e18i	0.941435	−	1.63061i	0.762737	−	0.646708i	$-0.223855\pi$
$752$	1.05728e18	+	1.83126e18i	0.213194	+	0.369262i
$753$	3.12725e17	+	5.41655e17i	0.0625165	+	0.108282i
$754$	−1.92154e18	+	3.32820e18i	−0.380833	+	0.659623i
$755$	1.67040e19			3.28221
$756$	−1.21108e18	+	1.38547e18i	−0.235928	+	0.269902i
$757$	9.65926e17			0.186561			0.0932805	−	0.995640i	$-0.470265\pi$
$757$	9.65926e17			0.186561			0.0932805	+	0.995640i	$0.470265\pi$
$758$	7.45203e16	−	1.29073e17i	0.0142700	−	0.0247164i
$759$	−1.65551e17	−	2.86743e17i	−0.0314312	−	0.0544404i
$760$	−1.85180e18	−	3.20741e18i	−0.348583	−	0.603763i
$761$	−2.76601e18	+	4.79088e18i	−0.516243	+	0.894159i	0.483579	+	0.875301i	$0.339337\pi$
$761$	−2.76601e18	+	4.79088e18i	−0.516243	+	0.894159i	−0.999822	+	0.0188585i	$0.993997\pi$
$762$	−1.45002e18			−0.268329
$763$	−3.01196e18	+	3.44568e18i	−0.552636	+	0.632216i
$764$	2.44800e18			0.445353
$765$	−4.40159e18	+	7.62378e18i	−0.793981	+	1.37522i
$766$	−1.19582e18	−	2.07123e18i	−0.213885	−	0.370460i
$767$	3.36241e18	+	5.82386e18i	0.596322	+	1.03286i
$768$	−6.88776e16	+	1.19299e17i	−0.0121124	+	0.0209793i
$769$	5.13853e18			0.896021			0.448010	−	0.894028i	$-0.352133\pi$
$769$	5.13853e18			0.896021			0.448010	+	0.894028i	$0.352133\pi$
$770$	−2.70198e18	−	5.32926e17i	−0.467188	−	0.0921461i
$771$	−2.29839e18			−0.394067
$772$	9.33161e17	−	1.61628e18i	0.158652	−	0.274793i
$773$	4.12593e18	+	7.14631e18i	0.695592	+	1.20480i	0.969981	+	0.243182i	$0.0781913\pi$
$773$	4.12593e18	+	7.14631e18i	0.695592	+	1.20480i	−0.274388	+	0.961619i	$0.588475\pi$
$774$	−9.77585e16	−	1.69323e17i	−0.0163432	−	0.0283073i
$775$	7.52873e18	−	1.30402e19i	1.24813	−	2.16183i
$776$	−8.87289e17			−0.145869
$777$	−4.79040e17	−	1.40376e18i	−0.0780971	−	0.228853i
$778$	−3.07597e17			−0.0497295
$779$	−2.66310e18	+	4.61262e18i	−0.426967	+	0.739528i
$780$	−8.34547e17	−	1.44548e18i	−0.132689	−	0.229825i
$781$	−1.27663e18	−	2.21120e18i	−0.201296	−	0.348655i
$782$	1.01755e18	−	1.76244e18i	0.159115	−	0.275595i
$783$	−7.09815e18			−1.10076
$784$	−2.17374e17	−	1.61093e18i	−0.0334313	−	0.247755i
$785$	−2.41136e18			−0.367798
$786$	3.31558e17	−	5.74275e17i	0.0501549	−	0.0868708i
$787$	−4.89986e18	−	8.48681e18i	−0.735103	−	1.27324i	−0.954678	−	0.297640i	$-0.903800\pi$
$787$	−4.89986e18	−	8.48681e18i	−0.735103	−	1.27324i	0.219575	−	0.975596i	$-0.429533\pi$
$788$	1.74046e18	+	3.01457e18i	0.258967	+	0.448544i
$789$	−2.31252e18	+	4.00541e18i	−0.341260	+	0.591080i
$790$	1.10535e19			1.61780
$791$	1.92579e18	+	5.64325e18i	0.279551	+	0.819186i
$792$	7.19999e17			0.103662
$793$	2.69822e17	−	4.67346e17i	0.0385303	−	0.0667364i
$794$	7.57224e17	+	1.31155e18i	0.107249	+	0.185760i
$795$	−2.85878e18	−	4.95155e18i	−0.401601	−	0.695593i
$796$	2.97748e18	−	5.15714e18i	0.414872	−	0.718579i
$797$	4.47372e18			0.618287			0.309143	−	0.951015i	$-0.399958\pi$
$797$	4.47372e18			0.618287			0.309143	+	0.951015i	$0.399958\pi$
$798$	1.98173e18	+	3.90868e17i	0.271661	+	0.0535811i
$799$	−1.20095e19			−1.63295
$800$	1.84121e18	−	3.18907e18i	0.248324	−	0.430110i
$801$	−3.71526e18	−	6.43502e18i	−0.497024	−	0.860872i
$802$	1.69236e18	+	2.93125e18i	0.224574	+	0.388974i
$803$	−1.47314e17	+	2.55155e17i	−0.0193906	+	0.0335856i
$804$	−2.43384e17			−0.0317780
$805$	−4.66193e18	+	5.33325e18i	−0.603800	+	0.690747i
$806$	−3.43095e18			−0.440795
$807$	−8.49860e17	+	1.47200e18i	−0.108310	+	0.187599i
$808$	−1.23588e18	−	2.14060e18i	−0.156243	−	0.270621i
$809$	2.27729e17	+	3.94437e17i	0.0285596	+	0.0494667i	0.879952	−	0.475063i	$-0.157575\pi$
$809$	2.27729e17	+	3.94437e17i	0.0285596	+	0.0494667i	−0.851392	+	0.524529i	$0.824241\pi$
$810$	−3.17206e18	+	5.49417e18i	−0.394629	+	0.683517i
$811$	−2.22500e17			−0.0274596			−0.0137298	−	0.999906i	$-0.504370\pi$
$811$	−2.22500e17			−0.0274596			−0.0137298	+	0.999906i	$0.504370\pi$
$812$	4.12661e18	−	4.72084e18i	0.505218	−	0.577969i
$813$	2.28884e18			0.277988
$814$	−6.31645e17	+	1.09404e18i	−0.0761052	+	0.131818i
$815$	−2.27163e18	−	3.93457e18i	−0.271527	−	0.470298i
$816$	−3.91186e17	−	6.77554e17i	−0.0463871	−	0.0803449i
$817$	−2.33585e17	+	4.04581e17i	−0.0274790	+	0.0475951i
$818$	2.78652e18			0.325212
$819$	−5.05176e18	−	9.96386e17i	−0.584922	−	0.115367i
$820$	−7.18071e18			−0.824854
$821$	3.97412e18	−	6.88338e18i	0.452909	−	0.784461i	−0.545656	−	0.838009i	$-0.683720\pi$
$821$	3.97412e18	−	6.88338e18i	0.452909	−	0.784461i	0.998565	+	0.0535477i	$0.0170529\pi$
$822$	−6.20041e17	−	1.07394e18i	−0.0701058	−	0.121427i
$823$	6.95051e18	+	1.20386e19i	0.779682	+	1.35045i	0.932125	+	0.362137i	$0.117953\pi$
$823$	6.95051e18	+	1.20386e19i	0.779682	+	1.35045i	−0.152443	+	0.988312i	$0.548714\pi$
$824$	−2.49719e18	+	4.32525e18i	−0.277923	+	0.481376i
$825$	3.40264e18			0.375721
$826$	−3.54356e18	−	1.03839e19i	−0.388213	−	1.13760i
$827$	−9.22759e18			−1.00300			−0.501502	−	0.865157i	$-0.667219\pi$
$827$	−9.22759e18			−1.00300			−0.501502	+	0.865157i	$0.667219\pi$
$828$	9.25947e17	−	1.60379e18i	0.0998594	−	0.172961i
$829$	−7.78317e18	−	1.34808e19i	−0.832821	−	1.44249i	−0.895792	−	0.444473i	$-0.853391\pi$
$829$	−7.78317e18	−	1.34808e19i	−0.832821	−	1.44249i	0.0629708	−	0.998015i	$-0.479942\pi$
$830$	4.33711e17	+	7.51209e17i	0.0460461	+	0.0797541i
$831$	1.75280e18	−	3.03594e18i	0.184640	−	0.319806i
$832$	−8.39065e17			−0.0876989
$833$	8.54069e18	+	3.50542e18i	0.885729	+	0.363536i
$834$	−2.90989e16			−0.00299431
$835$	−1.05418e19	+	1.82590e19i	−1.07635	+	1.86429i
$836$	−8.60185e17	−	1.48988e18i	−0.0871468	−	0.150943i
$837$	−3.16848e18	−	5.48796e18i	−0.318519	−	0.551691i
$838$	1.82362e18	−	3.15860e18i	0.181907	−	0.315071i
$839$	−1.58146e19			−1.56532			−0.782662	−	0.622447i	$-0.786139\pi$
$839$	−1.58146e19			−1.56532			−0.782662	+	0.622447i	$0.786139\pi$
$840$	8.79510e17	+	2.57728e18i	0.0863824	+	0.253132i
$841$	1.39255e19			1.35718
$842$	2.23298e18	−	3.86764e18i	0.215952	−	0.374039i
$843$	8.94544e17	+	1.54940e18i	0.0858465	+	0.148690i
$844$	2.06552e17	+	3.57758e17i	0.0196699	+	0.0340693i
$845$	−5.24370e18	+	9.08235e18i	−0.495529	+	0.858281i
$846$	−1.09284e19			−1.02483
$847$	9.28767e18	+	1.83186e18i	0.864300	+	0.170471i
$848$	−2.87426e18			−0.265431
$849$	−9.93818e16	+	1.72134e17i	−0.00910766	+	0.0157749i
$850$	1.04570e19	+	1.81121e19i	0.951012	+	1.64720i
$851$	1.62464e18	+	2.81396e18i	0.146627	+	0.253966i
$852$	−1.26235e18	+	2.18645e18i	−0.113063	+	0.195832i
$853$	−5.27149e18			−0.468560			−0.234280	−	0.972169i	$-0.575273\pi$
$853$	−5.27149e18			−0.468560			−0.234280	+	0.972169i	$0.575273\pi$
$854$	−5.79458e17	+	6.62900e17i	−0.0511147	+	0.0584752i
$855$	1.91409e19			1.67564
$856$	−4.93108e17	+	8.54088e17i	−0.0428413	+	0.0742033i
$857$	1.56219e18	+	2.70580e18i	0.134697	+	0.233303i	0.925482	−	0.378792i	$-0.123660\pi$
$857$	1.56219e18	+	2.70580e18i	0.134697	+	0.233303i	−0.790784	+	0.612095i	$0.790327\pi$
$858$	−3.87658e17	−	6.71444e17i	−0.0331728	−	0.0574569i
$859$	1.98460e18	−	3.43743e18i	0.168546	−	0.291930i	−0.769363	−	0.638812i	$-0.779426\pi$
$859$	1.98460e18	−	3.43743e18i	0.168546	−	0.291930i	0.937909	+	0.346882i	$0.112760\pi$
$860$	−6.29832e17			−0.0530866
$861$	2.57744e18	−	2.94859e18i	0.215610	−	0.246657i
$862$	1.61403e19			1.34003
$863$	1.29141e18	−	2.23679e18i	0.106413	−	0.184313i	−0.807902	−	0.589317i	$-0.799397\pi$
$863$	1.29141e18	−	2.23679e18i	0.106413	−	0.184313i	0.914315	+	0.405005i	$0.132730\pi$
$864$	−7.74875e17	−	1.34212e18i	−0.0633713	−	0.109762i
$865$	3.55227e17	+	6.15272e17i	0.0288338	+	0.0499416i
$866$	−4.54612e17	+	7.87411e17i	−0.0366247	+	0.0634359i
$867$	−4.03911e17			−0.0322970
$868$	5.49197e18	+	1.08321e18i	0.435863	+	0.0859676i
$869$	5.13450e18			0.404455
$870$	−5.25216e18	+	9.09701e18i	−0.410642	+	0.711252i
$871$	−7.41223e17	−	1.28384e18i	−0.0575216	−	0.0996304i
$872$	−1.92712e18	−	3.33787e18i	−0.148440	−	0.257106i
$873$	2.29283e18	−	3.97130e18i	0.175299	−	0.303627i
$874$	−4.42493e18			−0.335801
$875$	−1.51423e19	−	4.43725e19i	−1.14062	−	3.34242i
$876$	2.91331e17			0.0217826
$877$	6.52945e18	−	1.13093e19i	0.484595	−	0.839344i	−0.515248	−	0.857041i	$-0.672300\pi$
$877$	6.52945e18	−	1.13093e19i	0.484595	−	0.839344i	0.999843	+	0.0176973i	$0.00563353\pi$
$878$	−1.73647e18	−	3.00766e18i	−0.127924	−	0.221572i
$879$	3.68399e17	+	6.38085e17i	0.0269396	+	0.0466607i
$880$	1.15969e18	−	2.00864e18i	0.0841791	−	0.145802i
$881$	1.15631e19			0.833164			0.416582	−	0.909098i	$-0.363228\pi$
$881$	1.15631e19			0.833164			0.416582	+	0.909098i	$0.363228\pi$
$882$	7.77186e18	+	3.18986e18i	0.555877	+	0.228153i
$883$	2.08991e19			1.48383			0.741914	−	0.670495i	$-0.233918\pi$
$883$	2.08991e19			1.48383			0.741914	+	0.670495i	$0.233918\pi$
$884$	2.38271e18	−	4.12698e18i	0.167931	−	0.290865i
$885$	9.19052e18	+	1.59184e19i	0.642997	+	1.11370i
$886$	−7.85092e18	−	1.35982e19i	−0.545257	−	0.944413i
$887$	−2.95066e18	+	5.11068e18i	−0.203430	+	0.352351i	−0.949631	−	0.313369i	$-0.898542\pi$
$887$	−2.95066e18	+	5.11068e18i	−0.203430	+	0.352351i	0.746201	+	0.665720i	$0.231876\pi$
$888$	1.24915e18			0.0854933
$889$	4.65396e18	+	1.36378e19i	0.316200	+	0.926579i
$890$	−2.39364e19			−1.61445
$891$	−1.47346e18	+	2.55211e18i	−0.0986584	+	0.170881i
$892$	1.60178e18	+	2.77437e18i	0.106471	+	0.184414i
$893$	1.30562e19	+	2.26141e19i	0.861556	+	1.49226i
$894$	2.75169e18	−	4.76606e18i	0.180263	−	0.312224i
$895$	−2.99242e19			−1.94613
$896$	1.34310e18	+	2.64908e17i	0.0867177	+	0.0171038i
$897$	−1.99417e18			−0.127824
$898$	−1.01754e19	+	1.76244e19i	−0.647525	+	1.12155i
$899$	1.07962e19	+	1.86996e19i	0.682077	+	1.18139i
$900$	9.51570e18	+	1.64817e19i	0.596849	+	1.03377i
$901$	8.16208e18	−	1.41371e19i	0.508265	−	0.880340i
$902$	−3.33553e18			−0.206216
$903$	2.26072e17	−	2.58626e17i	0.0138764	−	0.0158746i
$904$	−5.02172e18			−0.306026
$905$	−3.68729e17	+	6.38658e17i	−0.0223096	+	0.0386414i
$906$	−3.83621e18	−	6.64452e18i	−0.230446	−	0.399145i
$907$	−3.07728e18	−	5.33000e18i	−0.183535	−	0.317892i	0.759547	−	0.650453i	$-0.225421\pi$
$907$	−3.07728e18	−	5.33000e18i	−0.183535	−	0.317892i	−0.943082	+	0.332560i	$0.892087\pi$
$908$	−5.74405e17	+	9.94898e17i	−0.0340142	+	0.0589143i
$909$	1.27744e19			0.751064
$910$	−1.09165e19	+	1.24885e19i	−0.637256	+	0.729021i
$911$	−6.88604e18			−0.399117			−0.199558	−	0.979886i	$-0.563951\pi$
$911$	−6.88604e18			−0.399117			−0.199558	+	0.979886i	$0.563951\pi$
$912$	−8.50561e17	+	1.47321e18i	−0.0489484	+	0.0847812i
$913$	2.01464e17	+	3.48946e17i	0.0115117	+	0.0199388i
$914$	1.52653e18	+	2.64403e18i	0.0866075	+	0.150009i
$915$	7.37508e17	−	1.27740e18i	0.0415461	−	0.0719599i
$916$	−1.25950e19			−0.704496
$917$	−6.46534e18	−	1.27519e18i	−0.359080	−	0.0708232i
$918$	8.80172e18			0.485389
$919$	1.09053e19	−	1.88886e19i	0.597157	−	1.03431i	−0.396081	−	0.918215i	$-0.629630\pi$
$919$	1.09053e19	−	1.88886e19i	0.597157	−	1.03431i	0.993239	−	0.116091i	$-0.0370365\pi$
$920$	−2.98281e18	−	5.16638e18i	−0.162183	−	0.280909i
$921$	4.87582e18	+	8.44517e18i	0.263245	+	0.455954i
$922$	1.21870e19	−	2.11086e19i	0.653352	−	1.13164i
$923$	−1.53779e19			−0.818628
$924$	4.08544e17	+	1.19718e18i	0.0215959	+	0.0632837i
$925$	−3.33919e19			−1.75275
$926$	1.01613e19	−	1.75998e19i	0.529635	−	0.917355i
$927$	−1.29059e19	−	2.23537e19i	−0.667990	−	1.15699i
$928$	2.64030e18	+	4.57313e18i	0.135703	+	0.235045i
$929$	4.12509e18	−	7.14487e18i	0.210538	−	0.364663i	−0.741345	−	0.671124i	$-0.765812\pi$
$929$	4.12509e18	−	7.14487e18i	0.210538	−	0.364663i	0.951883	+	0.306461i	$0.0991450\pi$
$930$	−9.37786e18			−0.475296
$931$	−2.68433e18	−	1.98931e19i	−0.135102	−	1.00122i
$932$	1.27236e19			0.635925
$933$	1.08164e16	−	1.87345e16i	0.000536846	−	0.000929845i
$934$	8.64021e18	+	1.49653e19i	0.425863	+	0.737616i
$935$	6.58639e18	+	1.14080e19i	0.322383	+	0.558383i
$936$	2.16822e18	−	3.75546e18i	0.105393	−	0.182545i
$937$	−2.57007e19			−1.24061			−0.620307	−	0.784359i	$-0.712992\pi$
$937$	−2.57007e19			−1.24061			−0.620307	+	0.784359i	$0.712992\pi$
$938$	7.81158e17	+	2.28907e18i	0.0374473	+	0.109734i
$939$	2.07996e18			0.0990212
$940$	−1.76022e19	+	3.04879e19i	−0.832217	+	1.44144i
$941$	−7.80119e18	−	1.35121e19i	−0.366293	−	0.634438i	0.622690	−	0.782469i	$-0.286040\pi$
$941$	−7.80119e18	−	1.35121e19i	−0.366293	−	0.634438i	−0.988983	+	0.148031i	$0.952706\pi$
$942$	5.53788e17	+	9.59189e17i	0.0258234	+	0.0447274i
$943$	−4.28962e18	+	7.42984e18i	−0.198652	+	0.344075i
$944$	9.24027e18			0.424978
$945$	−3.00572e19	−	5.92835e18i	−1.37291	−	0.270786i
$946$	−2.92565e17			−0.0132718
$947$	−1.24939e19	+	2.16400e19i	−0.562889	+	0.974952i	0.434354	+	0.900742i	$0.356977\pi$
$947$	−1.24939e19	+	2.16400e19i	−0.562889	+	0.974952i	−0.997243	+	0.0742096i	$0.976357\pi$
$948$	−2.53853e18	−	4.39686e18i	−0.113587	−	0.196738i
$949$	8.87247e17	+	1.53676e18i	0.0394288	+	0.0682927i
$950$	2.27369e19	−	3.93814e19i	1.00352	−	1.73815i
$951$	5.38659e18			0.236124
$952$	−5.11700e18	+	5.85385e18i	−0.222780	+	0.254860i
$953$	8.45730e18			0.365702			0.182851	−	0.983141i	$-0.441467\pi$
$953$	8.45730e18			0.365702			0.182851	+	0.983141i	$0.441467\pi$
$954$	7.42733e18	−	1.28645e19i	0.318984	−	0.552496i
$955$	2.03778e19	+	3.52955e19i	0.869233	+	1.50556i
$956$	−1.04119e19	−	1.80340e19i	−0.441119	−	0.764040i
$957$	−2.43970e18	+	4.22568e18i	−0.102662	+	0.177815i
$958$	−2.56058e18			−0.107020
$959$	−8.11059e18	+	9.27852e18i	−0.336691	+	0.385175i
$960$	−2.29343e18			−0.0945632
$961$	2.57033e18	−	4.45195e18i	0.105266	−	0.182326i
$962$	3.80429e18	+	6.58923e18i	0.154752	+	0.268038i
$963$	−2.54847e18	−	4.41408e18i	−0.102969	−	0.178348i
$964$	4.37806e18	−	7.58302e18i	0.175704	−	0.304328i
$965$	3.10716e19			1.23861
$966$	3.19210e18	+	6.29596e17i	0.126394	+	0.0249293i
$967$	8.33453e18			0.327800			0.163900	−	0.986477i	$-0.447593\pi$
$967$	8.33453e18			0.327800			0.163900	+	0.986477i	$0.447593\pi$
$968$	−3.98627e18	+	6.90442e18i	−0.155732	+	0.269735i
$969$	−4.83071e18	−	8.36703e18i	−0.187459	−	0.324689i
$970$	−7.38605e18	−	1.27930e19i	−0.284706	−	0.493125i
$971$	−3.66422e18	+	6.34661e18i	−0.140299	+	0.243006i	−0.927609	−	0.373552i	$-0.878140\pi$
$971$	−3.66422e18	+	6.34661e18i	−0.140299	+	0.243006i	0.787310	+	0.616557i	$0.211473\pi$
$972$	1.23393e19			0.469311
$973$	9.33951e16	+	2.73681e17i	0.00352850	+	0.0103398i
$974$	−6.79797e18			−0.255121
$975$	1.02468e19	−	1.77480e19i	0.381995	−	0.661635i
$976$	−3.70750e17	−	6.42159e17i	−0.0137296	−	0.0237804i
$977$	−4.95634e18	−	8.58463e18i	−0.182325	−	0.315796i	0.760347	−	0.649517i	$-0.225029\pi$
$977$	−4.95634e18	−	8.58463e18i	−0.182325	−	0.315796i	−0.942672	+	0.333721i	$0.891696\pi$
$978$	−1.04339e18	+	1.80721e18i	−0.0381281	+	0.0660399i
$979$	−1.11188e19			−0.403617
$980$	2.14170e19	−	1.65439e19i	0.772306	−	0.596581i
$981$	1.99194e19			0.713555
$982$	8.82250e17	−	1.52810e18i	0.0313955	−	0.0543785i
$983$	1.36007e19	+	2.35572e19i	0.480800	+	0.832771i	0.999757	−	0.0220298i	$-0.00701287\pi$
$983$	1.36007e19	+	2.35572e19i	0.480800	+	0.832771i	−0.518957	+	0.854800i	$0.673680\pi$
$984$	1.64910e18	+	2.85633e18i	0.0579135	+	0.100309i
$985$	−2.89762e19	+	5.01883e19i	−1.01090	+	1.75092i
$986$	−2.99908e19			−1.03941
$987$	−6.20104e18	−	1.81713e19i	−0.213502	−	0.625639i
$988$	−1.03615e19			−0.354408
$989$	−3.76250e17	+	6.51684e17i	−0.0127850	+	0.0221443i
$990$	5.99348e18	+	1.03810e19i	0.202325	+	0.350438i
$991$	5.63784e18	+	9.76503e18i	0.189075	+	0.327488i	0.944942	−	0.327238i	$-0.106118\pi$
$991$	5.63784e18	+	9.76503e18i	0.189075	+	0.327488i	−0.755867	+	0.654725i	$0.772784\pi$
$992$	−2.35716e18	+	4.08271e18i	−0.0785348	+	0.136026i
$993$	2.07190e19			0.685803
$994$	2.46157e19	+	4.85508e18i	0.809469	+	0.159656i
$995$	9.91415e19			3.23896
$996$	1.99210e17	−	3.45042e17i	0.00646585	−	0.0111992i
$997$	−1.67826e19	−	2.90684e19i	−0.541180	−	0.937351i	−0.998837	−	0.0482224i	$-0.984644\pi$
$997$	−1.67826e19	−	2.90684e19i	−0.541180	−	0.937351i	0.457657	−	0.889129i	$-0.348689\pi$
$998$	1.47511e19	+	2.55496e19i	0.472580	+	0.818532i
$999$	−7.02652e18	+	1.21703e19i	−0.223648	+	0.387369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.c.b.9.2	✓	8
3.2	odd	2		126.14.g.b.37.1		8
7.2	even	3		98.14.a.h.1.3		4
7.3	odd	6		98.14.c.o.67.3		8
7.4	even	3	inner	14.14.c.b.11.2	yes	8
7.5	odd	6		98.14.a.j.1.2		4
7.6	odd	2		98.14.c.o.79.3		8
21.11	odd	6		126.14.g.b.109.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.2	✓	8	1.1	even	1	trivial
14.14.c.b.11.2	yes	8	7.4	even	3	inner
98.14.a.h.1.3		4	7.2	even	3
98.14.a.j.1.2		4	7.5	odd	6
98.14.c.o.67.3		8	7.3	odd	6
98.14.c.o.79.3		8	7.6	odd	2
126.14.g.b.37.1		8	3.2	odd	2
126.14.g.b.109.1		8	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(32.0000 - 55.4256i) q^{2} +(-244.702 - 423.837i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(34096.3 - 59056.5i) q^{5} -31321.9 q^{6} +(100530. + 294589. i) q^{7} -262144. q^{8} +(677403. - 1.17330e6i) q^{9} +O(q^{10})\)	\(q+(32.0000 - 55.4256i) q^{2} +(-244.702 - 423.837i) q^{3} +(-2048.00 - 3547.24i) q^{4} +(34096.3 - 59056.5i) q^{5} -31321.9 q^{6} +(100530. + 294589. i) q^{7} -262144. q^{8} +(677403. - 1.17330e6i) q^{9} +(-2.18216e6 - 3.77962e6i) q^{10} +(-1.01364e6 - 1.75568e6i) q^{11} +(-1.00230e6 + 1.73604e6i) q^{12} -1.22100e7 q^{13} +(1.95447e7 + 3.85491e6i) q^{14} -3.33738e7 q^{15} +(-8.38861e6 + 1.45295e7i) q^{16} +(-4.76426e7 - 8.25194e7i) q^{17} +(-4.33538e7 - 7.50910e7i) q^{18} +(-1.03590e8 + 1.79423e8i) q^{19} -2.79317e8 q^{20} +(1.00258e8 - 1.14695e8i) q^{21} -1.29746e8 q^{22} +(-1.66859e8 + 2.89008e8i) q^{23} +(6.41473e7 + 1.11106e8i) q^{24} +(-1.71476e9 - 2.97005e9i) q^{25} +(-3.90720e8 + 6.76747e8i) q^{26} -1.44332e9 q^{27} +(8.39093e8 - 9.59922e8i) q^{28} +4.91794e9 q^{29} +(-1.06796e9 + 1.84976e9i) q^{30} +(2.19527e9 + 3.80232e9i) q^{31} +(5.36871e8 + 9.29888e8i) q^{32} +(-4.96081e8 + 8.59238e8i) q^{33} -6.09825e9 q^{34} +(2.08251e10 + 4.10745e9i) q^{35} -5.54929e9 q^{36} +(4.86831e9 - 8.43216e9i) q^{37} +(6.62975e9 + 1.14831e10i) q^{38} +(2.98782e9 + 5.17505e9i) q^{39} +(-8.93813e9 + 1.54813e10i) q^{40} +2.57081e10 q^{41} +(-3.14879e9 - 9.22709e9i) q^{42} +2.25490e9 q^{43} +(-4.15188e9 + 7.19127e9i) q^{44} +(-4.61938e10 - 8.00101e10i) q^{45} +(1.06790e10 + 1.84965e10i) q^{46} +(6.30189e10 - 1.09152e11i) q^{47} +8.21085e9 q^{48} +(-7.66765e10 + 5.92301e10i) q^{49} -2.19489e11 q^{50} +(-2.33165e10 + 4.03854e10i) q^{51} +(2.50061e10 + 4.33118e10i) q^{52} +(8.56595e10 + 1.48367e11i) q^{53} +(-4.61862e10 + 7.99968e10i) q^{54} -1.38246e11 q^{55} +(-2.63533e10 - 7.72248e10i) q^{56} +1.01395e11 q^{57} +(1.57374e11 - 2.72580e11i) q^{58} +(-2.75382e11 - 4.76975e11i) q^{59} +(6.83495e10 + 1.18385e11i) q^{60} +(-2.20984e10 + 3.82756e10i) q^{61} +2.80995e11 q^{62} +(4.13740e11 + 8.16041e10i) q^{63} +6.87195e10 q^{64} +(-4.16316e11 + 7.21080e11i) q^{65} +(3.17492e10 + 5.49913e10i) q^{66} +(6.07062e10 + 1.05146e11i) q^{67} +(-1.95144e11 + 3.37999e11i) q^{68} +1.63323e11 q^{69} +(8.94061e11 - 1.02281e12i) q^{70} +1.25945e12 q^{71} +(-1.77577e11 + 3.07573e11i) q^{72} +(-7.26655e10 - 1.25860e11i) q^{73} +(-3.11572e11 - 5.39658e11i) q^{74} +(-8.39212e11 + 1.45356e12i) q^{75} +8.48608e11 q^{76} +(4.15303e11 - 4.75107e11i) q^{77} +3.82441e11 q^{78} +(-1.26635e12 + 2.19338e12i) q^{79} +(5.72041e11 + 9.90803e11i) q^{80} +(-7.26816e11 - 1.25888e12i) q^{81} +(8.22660e11 - 1.42489e12i) q^{82} -1.98753e11 q^{83} +(-6.12179e11 - 1.20743e11i) q^{84} -6.49774e12 q^{85} +(7.21568e10 - 1.24979e11i) q^{86} +(-1.20343e12 - 2.08440e12i) q^{87} +(2.65720e11 + 4.60241e11i) q^{88} +(2.74228e12 - 4.74977e12i) q^{89} -5.91281e12 q^{90} +(-1.22747e12 - 3.59693e12i) q^{91} +1.36691e12 q^{92} +(1.07438e12 - 1.86088e12i) q^{93} +(-4.03321e12 - 6.98572e12i) q^{94} +(7.06406e12 + 1.22353e13i) q^{95} +(2.62747e11 - 4.55091e11i) q^{96} +3.38474e12 q^{97} +(8.29217e11 + 6.14520e12i) q^{98} -2.74658e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9}+O(q^{10}) \) 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9	\( 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9} - 114688 q^{10} - 8726914 q^{11} + 745472 q^{12} + 1438416 q^{13} + 27004544 q^{14} - 136873212 q^{15} - 67108864 q^{16} - 7943068 q^{17} - 38389760 q^{18} - 215706806 q^{19} - 14680064 q^{20} - 414124312 q^{21} - 1117044992 q^{22} - 61927978 q^{23} - 47710208 q^{24} - 1327844792 q^{25} + 46029312 q^{26} - 3268643812 q^{27} + 2827460608 q^{28} - 6325846064 q^{29} - 4379942784 q^{30} + 6113775570 q^{31} + 4294967296 q^{32} + 25235960652 q^{33} - 1016712704 q^{34} + 41542225382 q^{35} - 4913889280 q^{36} - 3945652880 q^{37} + 13805235584 q^{38} - 23545599116 q^{39} - 469762048 q^{40} + 86378579952 q^{41} + 16061065216 q^{42} - 109074124256 q^{43} - 35745439744 q^{44} - 104964468168 q^{45} + 3963390592 q^{46} - 3141202722 q^{47} - 6106906624 q^{48} + 151080461672 q^{49} - 169964133376 q^{50} - 241278267462 q^{51} - 2945875968 q^{52} + 149625680376 q^{53} - 104596601984 q^{54} + 174912009748 q^{55} + 70346866688 q^{56} - 128207489960 q^{57} - 202427074048 q^{58} - 866297313938 q^{59} + 280316338176 q^{60} - 477908594184 q^{61} + 782563272960 q^{62} + 953051390564 q^{63} + 549755813888 q^{64} - 1099748343120 q^{65} - 1615101481728 q^{66} + 1895501016278 q^{67} - 32534806528 q^{68} + 3503301895632 q^{69} + 1443396653440 q^{70} + 638832672128 q^{71} - 157244456960 q^{72} - 2966596192756 q^{73} + 252521784320 q^{74} - 1331079867376 q^{75} + 1767070154752 q^{76} + 6943031627392 q^{77} - 3013836686848 q^{78} - 6505959677634 q^{79} + 30064771072 q^{80} + 2449216493684 q^{81} + 2764114558464 q^{82} - 3379817135968 q^{83} + 2724161355776 q^{84} - 16684556982464 q^{85} - 3490371976192 q^{86} - 5273311164492 q^{87} + 2287708143616 q^{88} + 9586601667468 q^{89} - 13435451925504 q^{90} + 16069253407200 q^{91} + 507313995776 q^{92} - 14195747226896 q^{93} + 201036974208 q^{94} + 14384410136978 q^{95} - 195421011968 q^{96} - 44560735311568 q^{97} - 2146516623104 q^{98} + 24706419985464 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9 - 114688 * q^10 - 8726914 * q^11 + 745472 * q^12 + 1438416 * q^13 + 27004544 * q^14 - 136873212 * q^15 - 67108864 * q^16 - 7943068 * q^17 - 38389760 * q^18 - 215706806 * q^19 - 14680064 * q^20 - 414124312 * q^21 - 1117044992 * q^22 - 61927978 * q^23 - 47710208 * q^24 - 1327844792 * q^25 + 46029312 * q^26 - 3268643812 * q^27 + 2827460608 * q^28 - 6325846064 * q^29 - 4379942784 * q^30 + 6113775570 * q^31 + 4294967296 * q^32 + 25235960652 * q^33 - 1016712704 * q^34 + 41542225382 * q^35 - 4913889280 * q^36 - 3945652880 * q^37 + 13805235584 * q^38 - 23545599116 * q^39 - 469762048 * q^40 + 86378579952 * q^41 + 16061065216 * q^42 - 109074124256 * q^43 - 35745439744 * q^44 - 104964468168 * q^45 + 3963390592 * q^46 - 3141202722 * q^47 - 6106906624 * q^48 + 151080461672 * q^49 - 169964133376 * q^50 - 241278267462 * q^51 - 2945875968 * q^52 + 149625680376 * q^53 - 104596601984 * q^54 + 174912009748 * q^55 + 70346866688 * q^56 - 128207489960 * q^57 - 202427074048 * q^58 - 866297313938 * q^59 + 280316338176 * q^60 - 477908594184 * q^61 + 782563272960 * q^62 + 953051390564 * q^63 + 549755813888 * q^64 - 1099748343120 * q^65 - 1615101481728 * q^66 + 1895501016278 * q^67 - 32534806528 * q^68 + 3503301895632 * q^69 + 1443396653440 * q^70 + 638832672128 * q^71 - 157244456960 * q^72 - 2966596192756 * q^73 + 252521784320 * q^74 - 1331079867376 * q^75 + 1767070154752 * q^76 + 6943031627392 * q^77 - 3013836686848 * q^78 - 6505959677634 * q^79 + 30064771072 * q^80 + 2449216493684 * q^81 + 2764114558464 * q^82 - 3379817135968 * q^83 + 2724161355776 * q^84 - 16684556982464 * q^85 - 3490371976192 * q^86 - 5273311164492 * q^87 + 2287708143616 * q^88 + 9586601667468 * q^89 - 13435451925504 * q^90 + 16069253407200 * q^91 + 507313995776 * q^92 - 14195747226896 * q^93 + 201036974208 * q^94 + 14384410136978 * q^95 - 195421011968 * q^96 - 44560735311568 * q^97 - 2146516623104 * q^98 + 24706419985464 * q^99

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