LMFDB - Embedded newform 14.14.c.b.11.4

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			11.4
Root			$114.279 - 197.937i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.14.c.b.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 + 55.4256i) q^{2} +(888.214 - 1538.43i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-13071.0 - 22639.6i) q^{5} +113691. q^{6} +(-218721. - 221472. i) q^{7} -262144. q^{8} +(-780686. - 1.35219e6i) q^{9} +O(q^{10})$	\(q+(32.0000 + 55.4256i) q^{2} +(888.214 - 1538.43i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-13071.0 - 22639.6i) q^{5} +113691. q^{6} +(-218721. - 221472. i) q^{7} -262144. q^{8} +(-780686. - 1.35219e6i) q^{9} +(836543. - 1.44893e6i) q^{10} +(-5.60522e6 + 9.70852e6i) q^{11} +(3.63812e6 + 6.30141e6i) q^{12} -1.74220e7 q^{13} +(5.27615e6 - 1.92099e7i) q^{14} -4.64393e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(8.48313e7 - 1.46932e8i) q^{17} +(4.99639e7 - 8.65400e7i) q^{18} +(-8.89700e7 - 1.54101e8i) q^{19} +1.07077e8 q^{20} +(-5.34991e8 + 1.39773e8i) q^{21} -7.17468e8 q^{22} +(2.23644e7 + 3.87364e7i) q^{23} +(-2.32840e8 + 4.03291e8i) q^{24} +(2.68651e8 - 4.65316e8i) q^{25} +(-5.57504e8 - 9.65626e8i) q^{26} +5.85356e7 q^{27} +(1.23356e9 - 3.22282e8i) q^{28} -3.14386e9 q^{29} +(-1.48606e9 - 2.57393e9i) q^{30} +(1.48731e9 - 2.57609e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(9.95727e9 + 1.72465e10i) q^{33} +1.08584e10 q^{34} +(-2.15514e9 + 7.84663e9i) q^{35} +6.39538e9 q^{36} +(-2.86014e9 - 4.95391e9i) q^{37} +(5.69408e9 - 9.86244e9i) q^{38} +(-1.54745e10 + 2.68026e10i) q^{39} +(3.42648e9 + 5.93484e9i) q^{40} +2.70618e10 q^{41} +(-2.48667e10 - 2.51795e10i) q^{42} +2.32764e10 q^{43} +(-2.29590e10 - 3.97661e10i) q^{44} +(-2.04087e10 + 3.53488e10i) q^{45} +(-1.43132e9 + 2.47913e9i) q^{46} +(-1.66537e10 - 2.88451e10i) q^{47} -2.98035e10 q^{48} +(-1.21086e9 + 9.68814e10i) q^{49} +3.43873e10 q^{50} +(-1.50697e11 - 2.61014e11i) q^{51} +(3.56803e10 - 6.18001e10i) q^{52} +(-1.01723e11 + 1.76189e11i) q^{53} +(1.87314e9 + 3.24437e9i) q^{54} +2.93063e11 q^{55} +(5.73365e10 + 5.80576e10i) q^{56} -3.16098e11 q^{57} +(-1.00603e11 - 1.74250e11i) q^{58} +(1.44370e11 - 2.50056e11i) q^{59} +(9.51077e10 - 1.64731e11i) q^{60} +(-1.05582e11 - 1.82874e11i) q^{61} +1.90375e11 q^{62} +(-1.28719e11 + 4.68653e11i) q^{63} +6.87195e10 q^{64} +(2.27723e11 + 3.94427e11i) q^{65} +(-6.37265e11 + 1.10378e12i) q^{66} +(2.96224e11 - 5.13074e11i) q^{67} +(3.47469e11 + 6.01834e11i) q^{68} +7.94576e10 q^{69} +(-5.03869e11 + 1.31642e11i) q^{70} +1.43181e12 q^{71} +(2.04652e11 + 3.54468e11i) q^{72} +(-3.23132e11 + 5.59681e11i) q^{73} +(1.83049e11 - 3.17050e11i) q^{74} +(-4.77238e11 - 8.26601e11i) q^{75} +7.28843e11 q^{76} +(3.37615e12 - 8.82062e11i) q^{77} -1.98073e12 q^{78} +(-9.00359e11 - 1.55947e12i) q^{79} +(-2.19295e11 + 3.79829e11i) q^{80} +(1.29666e12 - 2.24588e12i) q^{81} +(8.65979e11 + 1.49992e12i) q^{82} -4.71815e12 q^{83} +(5.99852e11 - 2.18400e12i) q^{84} -4.43531e12 q^{85} +(7.44845e11 + 1.29011e12i) q^{86} +(-2.79242e12 + 4.83661e12i) q^{87} +(1.46937e12 - 2.54503e12i) q^{88} +(-1.31611e12 - 2.27956e12i) q^{89} -2.61231e12 q^{90} +(3.81057e12 + 3.85849e12i) q^{91} -1.83210e11 q^{92} +(-2.64209e12 - 4.57624e12i) q^{93} +(1.06584e12 - 1.84609e12i) q^{94} +(-2.32585e12 + 4.02849e12i) q^{95} +(-9.53712e11 - 1.65188e12i) q^{96} -7.42070e12 q^{97} +(-5.40846e12 + 3.03309e12i) q^{98} +1.75037e13 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 $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	888.214	−	1538.43i	0.703444	−	1.21840i	−0.263807	−	0.964576i	$-0.584978\pi$
$3$	888.214	−	1538.43i	0.703444	−	1.21840i	0.967250	−	0.253825i	$-0.0816886\pi$
$4$	−2048.00	+	3547.24i	−0.250000	+	0.433013i
$5$	−13071.0	−	22639.6i	−0.374113	−	0.647983i	0.616081	−	0.787683i	$-0.288720\pi$
$5$	−13071.0	−	22639.6i	−0.374113	−	0.647983i	−0.990194	+	0.139700i	$0.955386\pi$
$6$	113691.			0.994820
$7$	−218721.	−	221472.i	−0.702674	−	0.711512i
$7$	−218721.	−	221472.i	−0.702674	−	0.711512i
$8$	−262144.			−0.353553
$9$	−780686.	−	1.35219e6i	−0.489666	−	0.848126i
$10$	836543.	−	1.44893e6i	0.264538	−	0.458193i
$11$	−5.60522e6	+	9.70852e6i	−0.953982	+	1.65235i	−0.217301	+	0.976105i	$0.569725\pi$
$11$	−5.60522e6	+	9.70852e6i	−0.953982	+	1.65235i	−0.736681	+	0.676241i	$0.763608\pi$
$12$	3.63812e6	+	6.30141e6i	0.351722	+	0.609200i
$13$	−1.74220e7			−1.00107			−0.500537	−	0.865715i	$-0.666864\pi$
$13$	−1.74220e7			−1.00107			−0.500537	+	0.865715i	$0.666864\pi$
$14$	5.27615e6	−	1.92099e7i	0.187277	−	0.681856i
$15$	−4.64393e7			−1.05267
$16$	−8.38861e6	−	1.45295e7i	−0.125000	−	0.216506i
$17$	8.48313e7	−	1.46932e8i	0.852390	−	1.47638i	−0.0266563	−	0.999645i	$-0.508486\pi$
$17$	8.48313e7	−	1.46932e8i	0.852390	−	1.47638i	0.879046	−	0.476737i	$-0.158181\pi$
$18$	4.99639e7	−	8.65400e7i	0.346246	−	0.599716i
$19$	−8.89700e7	−	1.54101e8i	−0.433856	−	0.751460i	0.563346	−	0.826221i	$-0.309514\pi$
$19$	−8.89700e7	−	1.54101e8i	−0.433856	−	0.751460i	−0.997201	+	0.0747610i	$0.976181\pi$
$20$	1.07077e8			0.374113
$21$	−5.34991e8	+	1.39773e8i	−1.36120	+	0.355630i
$22$	−7.17468e8			−1.34913
$23$	2.23644e7	+	3.87364e7i	0.0315012	+	0.0545617i	0.881346	−	0.472471i	$-0.156638\pi$
$23$	2.23644e7	+	3.87364e7i	0.0315012	+	0.0545617i	−0.849845	+	0.527033i	$0.823305\pi$
$24$	−2.32840e8	+	4.03291e8i	−0.248705	+	0.430770i
$25$	2.68651e8	−	4.65316e8i	0.220079	−	0.381187i
$26$	−5.57504e8	−	9.65626e8i	−0.353933	−	0.613031i
$27$	5.85356e7			0.0290774
$28$	1.23356e9	−	3.22282e8i	0.483762	−	0.126389i
$29$	−3.14386e9			−0.981468			−0.490734	−	0.871310i	$-0.663271\pi$
$29$	−3.14386e9			−0.981468			−0.490734	+	0.871310i	$0.663271\pi$
$30$	−1.48606e9	−	2.57393e9i	−0.372175	−	0.644626i
$31$	1.48731e9	−	2.57609e9i	0.300988	−	0.521327i	−0.675372	−	0.737477i	$-0.736017\pi$
$31$	1.48731e9	−	2.57609e9i	0.300988	−	0.521327i	0.976360	+	0.216151i	$0.0693502\pi$
$32$	5.36871e8	−	9.29888e8i	0.0883883	−	0.153093i
$33$	9.95727e9	+	1.72465e10i	1.34215	+	2.32466i
$34$	1.08584e10			1.20546
$35$	−2.15514e9	+	7.84663e9i	−0.198168	+	0.721507i
$36$	6.39538e9			0.489666
$37$	−2.86014e9	−	4.95391e9i	−0.183264	−	0.317422i	0.759726	−	0.650243i	$-0.225333\pi$
$37$	−2.86014e9	−	4.95391e9i	−0.183264	−	0.317422i	−0.942990	+	0.332821i	$0.892000\pi$
$38$	5.69408e9	−	9.86244e9i	0.306782	−	0.531363i
$39$	−1.54745e10	+	2.68026e10i	−0.704200	+	1.21971i
$40$	3.42648e9	+	5.93484e9i	0.132269	+	0.229097i
$41$	2.70618e10			0.889738			0.444869	−	0.895596i	$-0.353250\pi$
$41$	2.70618e10			0.889738			0.444869	+	0.895596i	$0.353250\pi$
$42$	−2.48667e10	−	2.51795e10i	−0.699034	−	0.707826i
$43$	2.32764e10			0.561527			0.280764	−	0.959777i	$-0.409412\pi$
$43$	2.32764e10			0.561527			0.280764	+	0.959777i	$0.409412\pi$
$44$	−2.29590e10	−	3.97661e10i	−0.476991	−	0.826173i
$45$	−2.04087e10	+	3.53488e10i	−0.366381	+	0.634591i
$46$	−1.43132e9	+	2.47913e9i	−0.0222747	+	0.0385809i
$47$	−1.66537e10	−	2.88451e10i	−0.225359	−	0.390334i	0.731068	−	0.682305i	$-0.239022\pi$
$47$	−1.66537e10	−	2.88451e10i	−0.225359	−	0.390334i	−0.956427	+	0.291971i	$0.905689\pi$
$48$	−2.98035e10			−0.351722
$49$	−1.21086e9	+	9.68814e10i	−0.0124974	+	0.999922i
$50$	3.43873e10			0.311238
$51$	−1.50697e11	−	2.61014e11i	−1.19922	−	2.07710i
$52$	3.56803e10	−	6.18001e10i	0.250269	−	0.433478i
$53$	−1.01723e11	+	1.76189e11i	−0.630411	+	1.09190i	0.357056	+	0.934083i	$0.383780\pi$
$53$	−1.01723e11	+	1.76189e11i	−0.630411	+	1.09190i	−0.987468	+	0.157822i	$0.949553\pi$
$54$	1.87314e9	+	3.24437e9i	0.0102804	+	0.0178062i
$55$	2.93063e11			1.42759
$56$	5.73365e10	+	5.80576e10i	0.248433	+	0.251557i
$57$	−3.16098e11			−1.22077
$58$	−1.00603e11	−	1.74250e11i	−0.347001	−	0.601024i
$59$	1.44370e11	−	2.50056e11i	0.445593	−	0.771790i	−0.552500	−	0.833513i	$-0.686326\pi$
$59$	1.44370e11	−	2.50056e11i	0.445593	−	0.771790i	0.998093	+	0.0617228i	$0.0196595\pi$
$60$	9.51077e10	−	1.64731e11i	0.263168	−	0.455820i
$61$	−1.05582e11	−	1.82874e11i	−0.262390	−	0.454472i	0.704487	−	0.709717i	$-0.251177\pi$
$61$	−1.05582e11	−	1.82874e11i	−0.262390	−	0.454472i	−0.966876	+	0.255245i	$0.917844\pi$
$62$	1.90375e11			0.425661
$63$	−1.28719e11	+	4.68653e11i	−0.259376	+	0.944360i
$64$	6.87195e10			0.125000
$65$	2.27723e11	+	3.94427e11i	0.374515	+	0.648680i
$66$	−6.37265e11	+	1.10378e12i	−0.949040	+	1.64379i
$67$	2.96224e11	−	5.13074e11i	0.400068	−	0.692937i	−0.593666	−	0.804712i	$-0.702320\pi$
$67$	2.96224e11	−	5.13074e11i	0.400068	−	0.692937i	0.993734	+	0.111774i	$0.0356533\pi$
$68$	3.47469e11	+	6.01834e11i	0.426195	+	0.738191i
$69$	7.94576e10			0.0886373
$70$	−5.03869e11	+	1.31642e11i	−0.511894	+	0.133739i
$71$	1.43181e12			1.32649			0.663247	−	0.748401i	$-0.269178\pi$
$71$	1.43181e12			1.32649			0.663247	+	0.748401i	$0.269178\pi$
$72$	2.04652e11	+	3.54468e11i	0.173123	+	0.299858i
$73$	−3.23132e11	+	5.59681e11i	−0.249909	+	0.432854i	−0.963500	−	0.267708i	$-0.913734\pi$
$73$	−3.23132e11	+	5.59681e11i	−0.249909	+	0.432854i	0.713592	+	0.700562i	$0.247067\pi$
$74$	1.83049e11	−	3.17050e11i	0.129587	−	0.224451i
$75$	−4.77238e11	−	8.26601e11i	−0.309626	−	0.536287i
$76$	7.28843e11			0.433856
$77$	3.37615e12	−	8.82062e11i	1.84600	−	0.482292i
$78$	−1.98073e12			−0.995889
$79$	−9.00359e11	−	1.55947e12i	−0.416716	−	0.721773i	0.578891	−	0.815405i	$-0.303486\pi$
$79$	−9.00359e11	−	1.55947e12i	−0.416716	−	0.721773i	−0.995607	+	0.0936322i	$0.970152\pi$
$80$	−2.19295e11	+	3.79829e11i	−0.0935283	+	0.161996i
$81$	1.29666e12	−	2.24588e12i	0.510120	−	0.883554i
$82$	8.65979e11	+	1.49992e12i	0.314570	+	0.544851i
$83$	−4.71815e12			−1.58403			−0.792017	−	0.610499i	$-0.790969\pi$
$83$	−4.71815e12			−1.58403			−0.792017	+	0.610499i	$0.790969\pi$
$84$	5.99852e11	−	2.18400e12i	0.186307	−	0.678323i
$85$	−4.43531e12			−1.27556
$86$	7.44845e11	+	1.29011e12i	0.198530	+	0.343864i
$87$	−2.79242e12	+	4.83661e12i	−0.690407	+	1.19582i
$88$	1.46937e12	−	2.54503e12i	0.337284	−	0.584192i
$89$	−1.31611e12	−	2.27956e12i	−0.280709	−	0.486202i	0.690851	−	0.722998i	$-0.257236\pi$
$89$	−1.31611e12	−	2.27956e12i	−0.280709	−	0.486202i	−0.971560	+	0.236795i	$0.923903\pi$
$90$	−2.61231e12			−0.518141
$91$	3.81057e12	+	3.85849e12i	0.703430	+	0.712276i
$92$	−1.83210e11			−0.0315012
$93$	−2.64209e12	−	4.57624e12i	−0.423456	−	0.733448i
$94$	1.06584e12	−	1.84609e12i	0.159353	−	0.276008i
$95$	−2.32585e12	+	4.02849e12i	−0.324622	+	0.562263i
$96$	−9.53712e11	−	1.65188e12i	−0.124352	−	0.215385i
$97$	−7.42070e12			−0.904542			−0.452271	−	0.891881i	$-0.649386\pi$
$97$	−7.42070e12			−0.904542			−0.452271	+	0.891881i	$0.649386\pi$
$98$	−5.40846e12	+	3.03309e12i	−0.616743	+	0.345873i
$99$	1.75037e13			1.86853
$100$	1.10039e12	+	1.90594e12i	0.110039	+	0.190594i
$101$	7.57462e12	−	1.31196e13i	0.710022	−	1.22979i	−0.254827	−	0.966987i	$-0.582018\pi$
$101$	7.57462e12	−	1.31196e13i	0.710022	−	1.22979i	0.964848	−	0.262807i	$-0.0846483\pi$
$102$	9.64459e12	−	1.67049e13i	0.847974	−	1.46873i
$103$	2.23826e12	+	3.87678e12i	0.184701	+	0.319911i	0.943476	−	0.331442i	$-0.107535\pi$
$103$	2.23826e12	+	3.87678e12i	0.184701	+	0.319911i	−0.758775	+	0.651353i	$0.774202\pi$
$104$	4.56708e12			0.353933
$105$	1.01573e13	+	1.02850e13i	0.739685	+	0.748987i
$106$	−1.30205e13			−0.891536
$107$	1.22649e13	+	2.12434e13i	0.790075	+	1.36845i	0.925920	+	0.377720i	$0.123292\pi$
$107$	1.22649e13	+	2.12434e13i	0.790075	+	1.36845i	−0.135845	+	0.990730i	$0.543375\pi$
$108$	−1.19881e11	+	2.07640e11i	−0.00726935	+	0.0125909i
$109$	−1.31592e13	+	2.27923e13i	−0.751547	+	1.30172i	0.195526	+	0.980698i	$0.437359\pi$
$109$	−1.31592e13	+	2.27923e13i	−0.751547	+	1.30172i	−0.947073	+	0.321019i	$0.895975\pi$
$110$	9.37801e12	+	1.62432e13i	0.504729	+	0.874216i
$111$	−1.01617e13			−0.515663
$112$	−1.38311e12	+	5.03576e12i	−0.0662125	+	0.241072i
$113$	5.80988e12			0.262517			0.131258	−	0.991348i	$-0.458098\pi$
$113$	5.80988e12			0.262517			0.131258	+	0.991348i	$0.458098\pi$
$114$	−1.01151e13	−	1.75199e13i	−0.431608	−	0.747567i
$115$	5.84650e11	−	1.01264e12i	0.0235700	−	0.0408245i
$116$	6.43862e12	−	1.11520e13i	0.245367	−	0.424988i
$117$	1.36011e13	+	2.35578e13i	0.490192	+	0.849038i
$118$	1.84793e13			0.630164
$119$	−5.10958e13	+	1.33494e13i	−1.64942	+	0.430931i
$120$	1.21738e13			0.372175
$121$	−4.55756e13	−	7.89393e13i	−1.32016	−	2.28659i
$122$	6.75726e12	−	1.17039e13i	0.185538	−	0.321360i
$123$	2.40367e13	−	4.16328e13i	0.625881	−	1.08406i
$124$	6.09200e12	+	1.05517e13i	0.150494	+	0.260663i
$125$	−4.59577e13			−1.07756
$126$	−3.00944e13	+	7.86254e12i	−0.670003	+	0.175047i
$127$	7.00151e13			1.48070			0.740350	−	0.672221i	$-0.234660\pi$
$127$	7.00151e13			1.48070			0.740350	+	0.672221i	$0.234660\pi$
$128$	2.19902e12	+	3.80882e12i	0.0441942	+	0.0765466i
$129$	2.06744e13	−	3.58091e13i	0.395003	−	0.684165i
$130$	−1.45743e13	+	2.52434e13i	−0.264822	+	0.458686i
$131$	5.84582e12	+	1.01253e13i	0.101061	+	0.175042i	0.912122	−	0.409919i	$-0.134443\pi$
$131$	5.84582e12	+	1.01253e13i	0.101061	+	0.175042i	−0.811061	+	0.584961i	$0.801110\pi$
$132$	−8.15699e13			−1.34215
$133$	−1.46693e13	+	5.34095e13i	−0.229813	+	0.836725i
$134$	3.79166e13			0.565781
$135$	−7.65118e11	−	1.32522e12i	−0.0108782	−	0.0188417i
$136$	−2.22380e13	+	3.85174e13i	−0.301365	+	0.521980i
$137$	4.59295e13	−	7.95522e13i	0.593482	−	1.02794i	−0.400277	−	0.916394i	$-0.631086\pi$
$137$	4.59295e13	−	7.95522e13i	0.593482	−	1.02794i	0.993759	−	0.111547i	$-0.0355806\pi$
$138$	2.54264e12	+	4.40399e12i	0.0313380	+	0.0542790i
$139$	−7.33962e13			−0.863132			−0.431566	−	0.902081i	$-0.642039\pi$
$139$	−7.33962e13			−0.863132			−0.431566	+	0.902081i	$0.642039\pi$
$140$	−2.34201e13	−	2.37147e13i	−0.262880	−	0.266186i
$141$	−5.91683e13			−0.634110
$142$	4.58178e13	+	7.93588e13i	0.468986	+	0.812308i
$143$	9.76542e13	−	1.69142e14i	0.955007	−	1.65412i
$144$	−1.30977e13	+	2.26859e13i	−0.122417	+	0.212032i
$145$	4.10933e13	+	7.11757e13i	0.367180	+	0.635975i
$146$	−4.13609e13			−0.353424
$147$	1.47970e14	+	8.79143e13i	1.20951	+	0.718616i
$148$	2.34303e13			0.183264
$149$	−4.61464e12	−	7.99279e12i	−0.0345483	−	0.0598394i	0.848234	−	0.529621i	$-0.177666\pi$
$149$	−4.61464e12	−	7.99279e12i	−0.0345483	−	0.0598394i	−0.882783	+	0.469782i	$0.844333\pi$
$150$	3.05432e13	−	5.29025e13i	0.218938	−	0.379212i
$151$	2.95582e13	−	5.11963e13i	0.202922	−	0.351470i	−0.746547	−	0.665333i	$-0.768290\pi$
$151$	2.95582e13	−	5.11963e13i	0.202922	−	0.351470i	0.949469	+	0.313862i	$0.101623\pi$
$152$	2.33230e13	+	4.03966e13i	0.153391	+	0.265681i
$153$	−2.64906e14			−1.66954
$154$	1.56926e14	+	1.58899e14i	0.948002	+	0.959925i
$155$	−7.77622e13			−0.450414
$156$	−6.33834e13	−	1.09783e14i	−0.352100	−	0.609855i
$157$	−1.05245e14	+	1.82289e14i	−0.560857	+	0.971433i	0.436565	+	0.899673i	$0.356195\pi$
$157$	−1.05245e14	+	1.82289e14i	−0.560857	+	0.971433i	−0.997422	+	0.0717600i	$0.977138\pi$
$158$	5.76230e13	−	9.98060e13i	0.294662	−	0.510370i
$159$	1.80703e14	+	3.12986e14i	0.886918	+	1.53619i
$160$	−2.80697e13			−0.132269
$161$	3.68744e12	−	1.34256e13i	0.0166862	−	0.0607526i
$162$	1.65972e14			0.721419
$163$	1.90304e14	+	3.29617e14i	0.794748	+	1.37654i	0.922999	+	0.384802i	$0.125730\pi$
$163$	1.90304e14	+	3.29617e14i	0.794748	+	1.37654i	−0.128251	+	0.991742i	$0.540936\pi$
$164$	−5.54226e13	+	9.59948e13i	−0.222435	+	0.385268i
$165$	2.60302e14	−	4.50857e14i	1.00423	−	1.73937i
$166$	−1.50981e14	−	2.61507e14i	−0.560041	−	0.970019i
$167$	4.07830e12			0.0145486			0.00727431	−	0.999974i	$-0.497684\pi$
$167$	4.07830e12			0.0145486			0.00727431	+	0.999974i	$0.497684\pi$
$168$	1.40245e14	−	3.66407e13i	0.481256	−	0.125734i
$169$	6.51455e11			0.00215090
$170$	−1.41930e14	−	2.45830e14i	−0.450979	−	0.781118i
$171$	−1.38915e14	+	2.40608e14i	−0.424889	+	0.735929i
$172$	−4.76700e13	+	8.25669e13i	−0.140382	+	0.243148i
$173$	−1.89881e14	−	3.28883e14i	−0.538494	−	0.932699i	−0.998985	−	0.0450349i	$-0.985660\pi$
$173$	−1.89881e14	−	3.28883e14i	−0.538494	−	0.932699i	0.460491	−	0.887664i	$-0.347673\pi$
$174$	−3.57430e14			−0.976383
$175$	−1.61814e14	+	4.22761e13i	−0.425863	+	0.111262i
$176$	1.88080e14			0.476991
$177$	−2.56463e14	−	4.44206e14i	−0.626899	−	1.08582i
$178$	8.42309e13	−	1.45892e14i	0.198491	−	0.343797i
$179$	1.77670e14	−	3.07733e14i	0.403710	−	0.699245i	−0.590461	−	0.807066i	$-0.701054\pi$
$179$	1.77670e14	−	3.07733e14i	0.403710	−	0.699245i	0.994170	+	0.107821i	$0.0343873\pi$
$180$	−8.35939e13	−	1.44789e14i	−0.183191	−	0.317295i
$181$	−4.78841e14			−1.01223			−0.506117	−	0.862465i	$-0.668919\pi$
$181$	−4.78841e14			−1.01223			−0.506117	+	0.862465i	$0.668919\pi$
$182$	−9.19211e13	+	3.34675e14i	−0.187478	+	0.682589i
$183$	−3.75118e14			−0.738305
$184$	−5.86270e12	−	1.01545e13i	−0.0111374	−	0.0192905i
$185$	−7.47697e13	+	1.29505e14i	−0.137123	+	0.237504i
$186$	1.69094e14	−	2.92879e14i	0.299429	−	0.518626i
$187$	9.50996e14	+	1.64717e15i	1.62633	+	2.81688i
$188$	1.36427e14			0.225359
$189$	−1.28030e13	−	1.29640e13i	−0.0204320	−	0.0206889i
$190$	−2.97709e14			−0.459085
$191$	−5.26670e14	−	9.12220e14i	−0.784914	−	1.35951i	−0.929050	−	0.369953i	$-0.879374\pi$
$191$	−5.26670e14	−	9.12220e14i	−0.784914	−	1.35951i	0.144136	−	0.989558i	$-0.453960\pi$
$192$	6.10376e13	−	1.05720e14i	0.0879305	−	0.152300i
$193$	−2.76447e14	+	4.78821e14i	−0.385026	+	0.666884i	−0.991773	−	0.128011i	$-0.959141\pi$
$193$	−2.76447e14	+	4.78821e14i	−0.385026	+	0.666884i	0.606747	+	0.794895i	$0.292474\pi$
$194$	−2.37462e14	−	4.11297e14i	−0.319804	−	0.553916i
$195$	8.09066e14			1.05380
$196$	−3.41182e14	−	2.02708e14i	−0.429855	−	0.255392i
$197$	2.54122e14			0.309750			0.154875	−	0.987934i	$-0.450502\pi$
$197$	2.54122e14			0.309750			0.154875	+	0.987934i	$0.450502\pi$
$198$	5.60117e14	+	9.70151e14i	0.660625	+	1.14424i
$199$	−2.34714e14	+	4.06536e14i	−0.267913	+	0.464039i	−0.968323	−	0.249702i	$-0.919667\pi$
$199$	−2.34714e14	+	4.06536e14i	−0.267913	+	0.464039i	0.700410	+	0.713741i	$0.253001\pi$
$200$	−7.04251e13	+	1.21980e14i	−0.0778095	+	0.134770i
$201$	−5.26220e14	−	9.11439e14i	−0.562850	−	0.974885i
$202$	9.69551e14			1.00412
$203$	6.87629e14	+	6.96277e14i	0.689652	+	0.698326i
$204$	1.23451e15			1.19922
$205$	−3.53725e14	−	6.12669e14i	−0.332863	−	0.576535i
$206$	−1.43249e14	+	2.48114e14i	−0.130603	+	0.226211i
$207$	3.49192e13	−	6.04818e13i	0.0308501	−	0.0534340i
$208$	1.46146e14	+	2.53133e14i	0.125134	+	0.216739i
$209$	1.99479e15			1.65556
$210$	−2.45021e14	+	8.92093e14i	−0.197141	+	0.717769i
$211$	2.12280e14			0.165605			0.0828026	−	0.996566i	$-0.473613\pi$
$211$	2.12280e14			0.165605			0.0828026	+	0.996566i	$0.473613\pi$
$212$	−4.16656e14	−	7.21669e14i	−0.315206	−	0.545952i
$213$	1.27175e15	−	2.20274e15i	0.933114	−	1.61620i
$214$	−7.84951e14	+	1.35958e15i	−0.558667	+	0.967640i
$215$	−3.04245e14	−	5.26968e14i	−0.210075	−	0.363860i
$216$	−1.53448e13			−0.0102804
$217$	−8.95838e14	+	2.34049e14i	−0.582426	+	0.152166i
$218$	−1.68437e15			−1.06285
$219$	5.74020e14	+	9.94232e14i	0.351593	+	0.608977i
$220$	−6.00193e14	+	1.03956e15i	−0.356897	+	0.618164i
$221$	−1.47793e15	+	2.55985e15i	−0.853306	+	1.47797i
$222$	−3.25174e14	−	5.63217e14i	−0.182314	−	0.315778i
$223$	−2.01582e15			−1.09766			−0.548832	−	0.835933i	$-0.684927\pi$
$223$	−2.01582e15			−1.09766			−0.548832	+	0.835933i	$0.684927\pi$
$224$	−3.23369e14	+	8.44844e13i	−0.171036	+	0.0446853i
$225$	−8.38927e14			−0.431060
$226$	1.85916e14	+	3.22016e14i	0.0928138	+	0.160758i
$227$	1.03207e15	−	1.78760e15i	0.500658	−	0.867165i	−0.499342	−	0.866405i	$-0.666425\pi$
$227$	1.03207e15	−	1.78760e15i	0.500658	−	0.867165i	1.00000		0.000759878i	$-0.000241877\pi$
$228$	6.47368e14	−	1.12127e15i	0.305193	−	0.528610i
$229$	6.95631e14	+	1.20487e15i	0.318749	+	0.552089i	0.980227	−	0.197875i	$-0.0634040\pi$
$229$	6.95631e14	+	1.20487e15i	0.318749	+	0.552089i	−0.661478	+	0.749964i	$0.730071\pi$
$230$	7.48352e13			0.0333331
$231$	1.64175e15	−	5.97743e15i	0.710934	−	2.58843i
$232$	8.24144e14			0.347001
$233$	5.49511e14	+	9.51781e14i	0.224990	+	0.389694i	0.956316	−	0.292334i	$-0.0944318\pi$
$233$	5.49511e14	+	9.51781e14i	0.224990	+	0.389694i	−0.731327	+	0.682027i	$0.761098\pi$
$234$	−8.70472e14	+	1.50770e15i	−0.346618	+	0.600361i
$235$	−4.35361e14	+	7.54068e14i	−0.168620	+	0.292058i
$236$	5.91339e14	+	1.02423e15i	0.222797	+	0.385895i
$237$	−3.19885e15			−1.17254
$238$	−2.37497e15	−	2.40483e15i	−0.847046	−	0.857699i
$239$	−2.56720e15			−0.890991			−0.445496	−	0.895284i	$-0.646972\pi$
$239$	−2.56720e15			−0.890991			−0.445496	+	0.895284i	$0.646972\pi$
$240$	3.89561e14	+	6.74740e14i	0.131584	+	0.227910i
$241$	9.42088e14	−	1.63174e15i	0.309728	−	0.536465i	−0.668575	−	0.743645i	$-0.733095\pi$
$241$	9.42088e14	−	1.63174e15i	0.309728	−	0.536465i	0.978303	+	0.207180i	$0.0664286\pi$
$242$	2.91684e15	−	5.05211e15i	0.933496	−	1.61686i
$243$	−2.25676e15	−	3.90882e15i	−0.703143	−	1.21788i
$244$	8.64929e14			0.262390
$245$	2.20918e15	−	1.23892e15i	0.652608	−	0.365986i
$246$	3.07670e15			0.885129
$247$	1.55004e15	+	2.68474e15i	0.434322	+	0.752268i
$248$	−3.89888e14	+	6.75306e14i	−0.106415	+	0.184317i
$249$	−4.19073e15	+	7.25856e15i	−1.11428	+	1.92999i
$250$	−1.47065e15	−	2.54723e15i	−0.380976	−	0.659870i
$251$	5.62418e15			1.41965			0.709823	−	0.704380i	$-0.248775\pi$
$251$	5.62418e15			1.41965			0.709823	+	0.704380i	$0.248775\pi$
$252$	−1.39881e15	−	1.41640e15i	−0.344076	−	0.348403i
$253$	−5.01430e14			−0.120206
$254$	2.24048e15	+	3.88063e15i	0.523507	+	0.906740i
$255$	−3.93951e15	+	6.82342e15i	−0.897285	+	1.55414i
$256$	−1.40737e14	+	2.43764e14i	−0.0312500	+	0.0541266i
$257$	1.18486e15	+	2.05224e15i	0.256509	+	0.444286i	0.965304	−	0.261128i	$-0.0840944\pi$
$257$	1.18486e15	+	2.05224e15i	0.256509	+	0.444286i	−0.708795	+	0.705414i	$0.750761\pi$
$258$	2.64632e15			0.558618
$259$	−4.71579e14	+	1.71697e15i	−0.0970748	+	0.353439i
$260$	−1.86551e15			−0.374515
$261$	2.45437e15	+	4.25109e15i	0.480591	+	0.832409i
$262$	−3.74133e14	+	6.48017e14i	−0.0714607	+	0.123774i
$263$	9.63982e14	−	1.66967e15i	0.179621	−	0.311112i	−0.762130	−	0.647424i	$-0.775846\pi$
$263$	9.63982e14	−	1.66967e15i	0.179621	−	0.311112i	0.941751	+	0.336312i	$0.109180\pi$
$264$	−2.61024e15	−	4.52106e15i	−0.474520	−	0.821893i
$265$	5.31845e15			0.943381
$266$	−3.42967e15	+	8.96046e14i	−0.593639	+	0.155096i
$267$	−4.67594e15			−0.789852
$268$	1.21333e15	+	2.10155e15i	0.200034	+	0.346469i
$269$	2.46115e15	−	4.26284e15i	0.396049	−	0.685976i	−0.597186	−	0.802103i	$-0.703715\pi$
$269$	2.46115e15	−	4.26284e15i	0.396049	−	0.685976i	0.993234	+	0.116127i	$0.0370479\pi$
$270$	4.89676e13	−	8.48143e13i	0.00769208	−	0.0133231i
$271$	−1.09879e15	−	1.90315e15i	−0.168505	−	0.291859i	0.769389	−	0.638780i	$-0.220561\pi$
$271$	−1.09879e15	−	1.90315e15i	−0.168505	−	0.291859i	−0.937894	+	0.346921i	$0.887227\pi$
$272$	−2.84647e15			−0.426195
$273$	9.32062e15	−	2.43513e15i	1.36266	−	0.356013i
$274$	5.87897e15			0.839311
$275$	3.01169e15	+	5.21640e15i	0.419902	+	0.727291i
$276$	−1.62729e14	+	2.81855e14i	−0.0221593	+	0.0383811i
$277$	−5.28042e14	+	9.14596e14i	−0.0702345	+	0.121650i	−0.899004	−	0.437940i	$-0.855708\pi$
$277$	−5.28042e14	+	9.14596e14i	−0.0702345	+	0.121650i	0.828770	+	0.559590i	$0.189041\pi$
$278$	−2.34868e15	−	4.06803e15i	−0.305163	−	0.528559i
$279$	−4.64447e15			−0.589534
$280$	5.64957e14	−	2.05695e15i	0.0700629	−	0.255091i
$281$	−2.64590e15			−0.320614			−0.160307	−	0.987067i	$-0.551248\pi$
$281$	−2.64590e15			−0.320614			−0.160307	+	0.987067i	$0.551248\pi$
$282$	−1.89339e15	−	3.27944e15i	−0.224192	−	0.388312i
$283$	3.50100e15	−	6.06390e15i	0.405116	−	0.701682i	−0.589219	−	0.807974i	$-0.700564\pi$
$283$	3.50100e15	−	6.06390e15i	0.405116	−	0.701682i	0.994335	+	0.106291i	$0.0338977\pi$
$284$	−2.93234e15	+	5.07896e15i	−0.331623	+	0.574389i
$285$	4.13171e15	+	7.15632e15i	0.456707	+	0.791040i
$286$	1.24997e16			1.35058
$287$	−5.91900e15	−	5.99344e15i	−0.625196	−	0.633059i
$288$	−1.67651e15			−0.173123
$289$	−9.44041e15	−	1.63513e16i	−0.953136	−	1.65088i
$290$	−2.62997e15	+	4.55524e15i	−0.259636	+	0.449702i
$291$	−6.59117e15	+	1.14162e16i	−0.636294	+	1.10209i
$292$	−1.32355e15	−	2.29245e15i	−0.124954	−	0.216427i
$293$	8.77788e15			0.810495			0.405247	−	0.914207i	$-0.367185\pi$
$293$	8.77788e15			0.810495			0.405247	+	0.914207i	$0.367185\pi$
$294$	−1.37664e14	+	1.10146e16i	−0.0124326	+	0.994742i
$295$	−7.54822e15			−0.666809
$296$	7.49769e14	+	1.29864e15i	0.0647935	+	0.112226i
$297$	−3.28105e14	+	5.68295e14i	−0.0277393	+	0.0480459i
$298$	2.95337e14	−	5.11538e14i	0.0244294	−	0.0423129i
$299$	−3.89634e14	−	6.74865e14i	−0.0315351	−	0.0546203i
$300$	3.90954e15			0.309626
$301$	−5.09105e15	−	5.15507e15i	−0.394571	−	0.399533i
$302$	3.78345e15			0.286974
$303$	−1.34558e16	−	2.33061e16i	−0.998921	−	1.73018i
$304$	−1.49267e15	+	2.58538e15i	−0.108464	+	0.187865i
$305$	−2.76013e15	+	4.78068e15i	−0.196327	+	0.340048i
$306$	−8.47700e15	−	1.46826e16i	−0.590273	−	1.02238i
$307$	−9.75008e15			−0.664674			−0.332337	−	0.943161i	$-0.607837\pi$
$307$	−9.75008e15			−0.664674			−0.332337	+	0.943161i	$0.607837\pi$
$308$	−3.78547e15	+	1.37825e16i	−0.252662	+	0.919915i
$309$	7.95222e15			0.519706
$310$	−2.48839e15	−	4.31002e15i	−0.159246	−	0.275821i
$311$	1.93994e15	−	3.36007e15i	0.121575	−	0.210574i	−0.798814	−	0.601578i	$-0.794539\pi$
$311$	1.93994e15	−	3.36007e15i	0.121575	−	0.210574i	0.920389	+	0.391004i	$0.127872\pi$
$312$	4.05654e15	−	7.02613e15i	0.248972	−	0.431233i
$313$	8.38718e15	+	1.45270e16i	0.504171	+	0.873250i	0.999988	+	0.00482294i	$0.00153520\pi$
$313$	8.38718e15	+	1.45270e16i	0.504171	+	0.873250i	−0.495817	+	0.868427i	$0.665131\pi$
$314$	−1.34713e16			−0.793171
$315$	1.22926e16	−	3.21160e15i	0.708965	−	0.185226i
$316$	7.37574e15			0.416716
$317$	−7.59188e15	−	1.31495e16i	−0.420208	−	0.727821i	0.575752	−	0.817625i	$-0.304710\pi$
$317$	−7.59188e15	−	1.31495e16i	−0.420208	−	0.727821i	−0.995960	+	0.0898033i	$0.971376\pi$
$318$	−1.15650e16	+	2.00311e16i	−0.627146	+	1.08625i
$319$	1.76220e16	−	3.05222e16i	0.936302	−	1.62172i
$320$	−8.98231e14	−	1.55578e15i	−0.0467642	−	0.0809979i
$321$	4.35753e16			2.22309
$322$	8.62119e14	−	2.25240e14i	0.0431027	−	0.0112611i
$323$	−3.01898e16			−1.47926
$324$	5.31111e15	+	9.19911e15i	0.255060	+	0.441777i
$325$	−4.68043e15	+	8.10675e15i	−0.220315	+	0.381597i
$326$	−1.21795e16	+	2.10955e16i	−0.561972	+	0.973363i
$327$	2.33763e16	+	4.04889e16i	1.05734	+	1.83137i
$328$	−7.09410e15			−0.314570
$329$	−2.74586e15	+	9.99738e15i	−0.119373	+	0.434623i
$330$	3.33187e16			1.42019
$331$	1.56486e16	+	2.71041e16i	0.654022	+	1.13280i	0.982138	+	0.188162i	$0.0602529\pi$
$331$	1.56486e16	+	2.71041e16i	0.654022	+	1.13280i	−0.328116	+	0.944637i	$0.606414\pi$
$332$	9.66278e15	−	1.67364e16i	0.396008	−	0.685907i
$333$	−4.46575e15	+	7.73490e15i	−0.179476	+	0.310862i
$334$	1.30506e14	+	2.26042e14i	0.00514372	+	0.00890918i
$335$	−1.54877e16			−0.598682
$336$	6.51867e15	+	6.60065e15i	0.247146	+	0.250254i
$337$	−1.55957e16			−0.579978			−0.289989	−	0.957030i	$-0.593652\pi$
$337$	−1.55957e16			−0.579978			−0.289989	+	0.957030i	$0.593652\pi$
$338$	2.08466e13	+	3.61073e13i	0.000760459	+	0.00131715i
$339$	5.16042e15	−	8.93810e15i	0.184666	−	0.319851i
$340$	9.08352e15	−	1.57331e16i	0.318890	−	0.552334i
$341$	1.66733e16	+	2.88791e16i	0.574274	+	0.994672i
$342$	−1.77812e16			−0.600884
$343$	2.17214e16	−	2.09219e16i	0.720238	−	0.693728i
$344$	−6.10177e15			−0.198530
$345$	−1.03859e15	−	1.79889e15i	−0.0331604	−	0.0574355i
$346$	1.21524e16	−	2.10485e16i	0.380773	−	0.659518i
$347$	3.14836e16	−	5.45312e16i	0.968150	−	1.67688i	0.267247	−	0.963628i	$-0.413886\pi$
$347$	3.14836e16	−	5.45312e16i	0.968150	−	1.67688i	0.700903	−	0.713257i	$-0.252781\pi$
$348$	−1.14377e16	−	1.98108e16i	−0.345204	−	0.597910i
$349$	−6.18328e16			−1.83170			−0.915848	−	0.401524i	$-0.868481\pi$
$349$	−6.18328e16			−1.83170			−0.915848	+	0.401524i	$0.868481\pi$
$350$	−7.52123e15	−	7.61582e15i	−0.218699	−	0.221449i
$351$	−1.01981e15			−0.0291087
$352$	6.01856e15	+	1.04244e16i	0.168642	+	0.292096i
$353$	−5.56148e15	+	9.63276e15i	−0.152987	+	0.264981i	−0.932324	−	0.361623i	$-0.882223\pi$
$353$	−5.56148e15	+	9.63276e15i	−0.152987	+	0.264981i	0.779337	+	0.626605i	$0.215556\pi$
$354$	1.64136e16	−	2.84292e16i	0.443285	−	0.767792i
$355$	−1.87151e16	−	3.24155e16i	−0.496259	−	0.859546i
$356$	1.07815e16			0.280709
$357$	−2.48468e16	+	9.04645e16i	−0.635224	+	2.31278i
$358$	2.27417e16			0.570932
$359$	3.10479e16	+	5.37765e16i	0.765453	+	1.32580i	0.940007	+	0.341155i	$0.110818\pi$
$359$	3.10479e16	+	5.37765e16i	0.765453	+	1.32580i	−0.174554	+	0.984648i	$0.555848\pi$
$360$	5.35001e15	−	9.26648e15i	0.129535	−	0.224362i
$361$	5.19515e15	−	8.99827e15i	0.123538	−	0.213975i
$362$	−1.53229e16	−	2.65401e16i	−0.357879	−	0.619864i
$363$	−1.61924e17			−3.71464
$364$	−2.14910e16	+	5.61481e15i	−0.484282	+	0.126525i
$365$	1.68946e16			0.373976
$366$	−1.20038e16	−	2.07912e16i	−0.261030	−	0.452118i
$367$	1.01257e16	−	1.75383e16i	0.216320	−	0.374678i	−0.737360	−	0.675500i	$-0.763928\pi$
$367$	1.01257e16	−	1.75383e16i	0.216320	−	0.374678i	0.953680	+	0.300822i	$0.0972612\pi$
$368$	3.75213e14	−	6.49888e14i	0.00787530	−	0.0136404i
$369$	−2.11268e16	−	3.65927e16i	−0.435675	−	0.754610i
$370$	−9.57053e15			−0.193921
$371$	6.12698e16	−	1.60075e16i	1.21988	−	0.318708i
$372$	2.16440e16			0.423456
$373$	−1.91899e16	−	3.32379e16i	−0.368949	−	0.639038i	0.620453	−	0.784244i	$-0.286949\pi$
$373$	−1.91899e16	−	3.32379e16i	−0.368949	−	0.639038i	−0.989401	+	0.145206i	$0.953616\pi$
$374$	−6.08637e16	+	1.05419e17i	−1.14999	+	1.99184i
$375$	−4.08202e16	+	7.07027e16i	−0.758005	+	1.31290i
$376$	4.36568e15	+	7.56157e15i	0.0796766	+	0.138004i
$377$	5.47723e16			0.982523
$378$	3.08843e14	−	1.12446e15i	0.00544554	−	0.0198266i
$379$	5.21687e16			0.904180			0.452090	−	0.891972i	$-0.350679\pi$
$379$	5.21687e16			0.904180			0.452090	+	0.891972i	$0.350679\pi$
$380$	−9.52669e15	−	1.65007e16i	−0.162311	−	0.281131i
$381$	6.21883e16	−	1.07713e17i	1.04159	−	1.80409i
$382$	3.37069e16	−	5.83821e16i	0.555018	−	0.961319i
$383$	4.92433e16	+	8.52919e16i	0.797178	+	1.38075i	0.921447	+	0.388504i	$0.127008\pi$
$383$	4.92433e16	+	8.52919e16i	0.797178	+	1.38075i	−0.124269	+	0.992249i	$0.539659\pi$
$384$	7.81281e15			0.124352
$385$	−6.40991e16	−	6.49053e16i	−1.00313	−	1.01575i
$386$	−3.53852e16			−0.544509
$387$	−1.81715e16	−	3.14740e16i	−0.274961	−	0.476246i
$388$	1.51976e16	−	2.63230e16i	0.226135	−	0.391678i
$389$	3.52381e16	−	6.10343e16i	0.515633	−	0.893102i	−0.484202	−	0.874956i	$-0.660890\pi$
$389$	3.52381e16	−	6.10343e16i	0.515633	−	0.893102i	0.999835	−	0.0181464i	$-0.00577650\pi$
$390$	2.58901e16	+	4.48430e16i	0.372575	+	0.645319i
$391$	7.58882e15			0.107405
$392$	3.17419e14	−	2.53969e16i	0.00441848	−	0.353526i
$393$	2.07694e16			0.284362
$394$	8.13190e15	+	1.40849e16i	0.109513	+	0.189683i
$395$	−2.35372e16	+	4.07675e16i	−0.311798	+	0.540049i
$396$	−3.58475e16	+	6.20897e16i	−0.467133	+	0.809097i
$397$	6.16634e16	+	1.06804e17i	0.790477	+	1.36915i	0.925672	+	0.378327i	$0.123501\pi$
$397$	6.16634e16	+	1.06804e17i	0.790477	+	1.36915i	−0.135195	+	0.990819i	$0.543166\pi$
$398$	−3.00434e16			−0.378886
$399$	6.91373e16	+	7.00068e16i	0.857806	+	0.868594i
$400$	−9.01442e15			−0.110039
$401$	−3.63043e16	−	6.28809e16i	−0.436033	−	0.755232i	0.561346	−	0.827581i	$-0.310284\pi$
$401$	−3.63043e16	−	6.28809e16i	−0.436033	−	0.755232i	−0.997379	+	0.0723493i	$0.976950\pi$
$402$	3.36781e16	−	5.83321e16i	0.397995	−	0.689348i
$403$	−2.59119e16	+	4.48807e16i	−0.301312	+	0.521887i
$404$	3.10256e16	+	5.37380e16i	0.355011	+	0.614897i
$405$	−6.77943e16			−0.763371
$406$	−1.65875e16	+	6.03932e16i	−0.183806	+	0.669219i
$407$	6.41269e16			0.699321
$408$	3.95042e16	+	6.84233e16i	0.423987	+	0.734367i
$409$	3.12800e16	−	5.41785e16i	0.330419	−	0.572302i	−0.652175	−	0.758068i	$-0.726143\pi$
$409$	3.12800e16	−	5.41785e16i	0.330419	−	0.572302i	0.982594	+	0.185766i	$0.0594766\pi$
$410$	2.26384e16	−	3.92108e16i	0.235370	−	0.407672i
$411$	−8.15904e16	−	1.41319e17i	−0.834963	−	1.44620i
$412$	−1.83358e16			−0.184701
$413$	−8.69572e16	+	2.27187e16i	−0.862244	+	0.225272i
$414$	4.46966e15			0.0436287
$415$	6.16709e16	+	1.06817e17i	0.592608	+	1.02643i
$416$	−9.35337e15	+	1.62005e16i	−0.0884834	+	0.153258i
$417$	−6.51915e16	+	1.12915e17i	−0.607165	+	1.05164i
$418$	6.38332e16	+	1.10562e17i	0.585330	+	1.01382i
$419$	1.88865e17			1.70514			0.852569	−	0.522615i	$-0.175044\pi$
$419$	1.88865e17			1.70514			0.852569	+	0.522615i	$0.175044\pi$
$420$	−5.72855e16	+	1.49666e16i	−0.509242	+	0.133046i
$421$	−1.13170e17			−0.990597			−0.495299	−	0.868723i	$-0.664941\pi$
$421$	−1.13170e17			−0.990597			−0.495299	+	0.868723i	$0.664941\pi$
$422$	6.79297e15	+	1.17658e16i	0.0585502	+	0.101412i
$423$	−2.60027e16	+	4.50379e16i	−0.220702	+	0.382266i
$424$	2.66660e16	−	4.61868e16i	0.222884	−	0.386047i
$425$	−4.55799e16	−	7.89468e16i	−0.375185	−	0.649840i
$426$	1.62784e17			1.31962
$427$	−1.74084e16	+	6.33819e16i	−0.138988	+	0.506039i
$428$	−1.00474e17			−0.790075
$429$	−1.73476e17	−	3.00469e17i	−1.34359	−	2.32716i
$430$	1.94717e16	−	3.37260e16i	0.148545	−	0.257288i
$431$	5.90084e16	−	1.02205e17i	0.443416	−	0.768019i	−0.554524	−	0.832167i	$-0.687100\pi$
$431$	5.90084e16	−	1.02205e17i	0.443416	−	0.768019i	0.997940	+	0.0641485i	$0.0204331\pi$
$432$	−4.91032e14	−	8.50493e14i	−0.00363468	−	0.00629545i
$433$	1.18291e17			0.862540			0.431270	−	0.902223i	$-0.358066\pi$
$433$	1.18291e17			0.862540			0.431270	+	0.902223i	$0.358066\pi$
$434$	−4.16391e16	−	4.21628e16i	−0.299101	−	0.302863i
$435$	1.45999e17			1.03316
$436$	−5.38999e16	−	9.33574e16i	−0.375773	−	0.650859i
$437$	3.97953e15	−	6.89275e15i	0.0273340	−	0.0473438i
$438$	−3.67373e16	+	6.36309e16i	−0.248614	+	0.430612i
$439$	−3.45621e16	−	5.98633e16i	−0.230452	−	0.399155i	0.727489	−	0.686119i	$-0.240687\pi$
$439$	−3.45621e16	−	5.98633e16i	−0.230452	−	0.399155i	−0.957941	+	0.286965i	$0.907354\pi$
$440$	−7.68247e16			−0.504729
$441$	1.31947e17	−	7.39967e16i	0.854180	−	0.479028i
$442$	−1.89175e17			−1.20676
$443$	−2.99317e15	−	5.18432e15i	−0.0188151	−	0.0325888i	0.856465	−	0.516206i	$-0.172656\pi$
$443$	−2.99317e15	−	5.18432e15i	−0.0188151	−	0.0325888i	−0.875280	+	0.483617i	$0.839323\pi$
$444$	2.08111e16	−	3.60459e16i	0.128916	−	0.223289i
$445$	−3.44056e16	+	5.95923e16i	−0.210034	+	0.363789i
$446$	−6.45061e16	−	1.11728e17i	−0.388083	−	0.672179i
$447$	−1.63951e16			−0.0972112
$448$	−1.50304e16	−	1.52195e16i	−0.0878343	−	0.0889389i
$449$	−1.34988e16			−0.0777491			−0.0388745	−	0.999244i	$-0.512377\pi$
$449$	−1.34988e16			−0.0777491			−0.0388745	+	0.999244i	$0.512377\pi$
$450$	−2.68457e16	−	4.64980e16i	−0.152403	−	0.263969i
$451$	−1.51688e17	+	2.62730e17i	−0.848794	+	1.47015i
$452$	−1.18986e16	+	2.06090e16i	−0.0656292	+	0.113673i
$453$	−5.25080e16	−	9.09466e16i	−0.285488	−	0.494479i
$454$	1.32105e17			0.708037
$455$	3.75469e16	−	1.36704e17i	0.198381	−	0.722283i
$456$	8.28631e16			0.431608
$457$	1.48650e17	+	2.57470e17i	0.763327	+	1.32212i	0.941127	+	0.338054i	$0.109769\pi$
$457$	1.48650e17	+	2.57470e17i	0.763327	+	1.32212i	−0.177800	+	0.984067i	$0.556898\pi$
$458$	−4.45204e16	+	7.71116e16i	−0.225389	+	0.390386i
$459$	4.96565e15	−	8.60076e15i	0.0247853	−	0.0429294i
$460$	2.39473e15	+	4.14779e15i	0.0117850	+	0.0204123i
$461$	−4.11410e16			−0.199627			−0.0998135	−	0.995006i	$-0.531825\pi$
$461$	−4.11410e16			−0.199627			−0.0998135	+	0.995006i	$0.531825\pi$
$462$	3.83839e17	−	1.00283e17i	1.83644	−	0.479793i
$463$	−3.23516e17			−1.52623			−0.763114	−	0.646264i	$-0.776331\pi$
$463$	−3.23516e17			−1.52623			−0.763114	+	0.646264i	$0.776331\pi$
$464$	2.63726e16	+	4.56787e16i	0.122683	+	0.212494i
$465$	−6.90694e16	+	1.19632e17i	−0.316841	+	0.548785i
$466$	−3.51687e16	+	6.09140e16i	−0.159092	+	0.275555i
$467$	−8.99909e16	−	1.55869e17i	−0.401457	−	0.695344i	0.592445	−	0.805611i	$-0.298163\pi$
$467$	−8.99909e16	−	1.55869e17i	−0.401457	−	0.695344i	−0.993902	+	0.110267i	$0.964829\pi$
$468$	−1.11420e17			−0.490192
$469$	−1.78422e17	+	4.66151e16i	−0.774150	+	0.202257i
$470$	−5.57262e16			−0.238464
$471$	1.86959e17	+	3.23823e17i	0.789063	+	1.36670i
$472$	−3.78457e16	+	6.55507e16i	−0.157541	+	0.272869i
$473$	−1.30469e17	+	2.25979e17i	−0.535687	+	0.927837i
$474$	−1.02363e17	−	1.77298e17i	−0.414557	−	0.718033i
$475$	−9.56074e16			−0.381929
$476$	5.72906e16	−	2.08589e17i	0.225755	−	0.821950i
$477$	3.17653e17			1.23476
$478$	−8.21504e16	−	1.42289e17i	−0.315013	−	0.545618i
$479$	−9.02899e15	+	1.56387e16i	−0.0341553	+	0.0591588i	−0.882598	−	0.470129i	$-0.844207\pi$
$479$	−9.02899e15	+	1.56387e16i	−0.0341553	+	0.0591588i	0.848442	+	0.529288i	$0.177541\pi$
$480$	−2.49319e16	+	4.31833e16i	−0.0930438	+	0.161157i
$481$	4.98295e16	+	8.63071e16i	0.183461	+	0.317763i
$482$	1.20587e17			0.438022
$483$	−1.73791e16	−	1.75977e16i	−0.0622832	−	0.0630665i
$484$	3.73355e17			1.32016
$485$	9.69958e16	+	1.68002e17i	0.338401	+	0.586128i
$486$	1.44432e17	−	2.50164e17i	0.497197	−	0.861171i
$487$	2.06142e17	−	3.57048e17i	0.700209	−	1.21280i	−0.268184	−	0.963368i	$-0.586423\pi$
$487$	2.06142e17	−	3.57048e17i	0.700209	−	1.21280i	0.968393	−	0.249430i	$-0.0802432\pi$
$488$	2.76777e16	+	4.79393e16i	0.0927688	+	0.160680i
$489$	6.76124e17			2.23624
$490$	1.39362e17	+	8.27999e16i	0.454851	+	0.270244i
$491$	3.06256e17			0.986405			0.493203	−	0.869915i	$-0.335826\pi$
$491$	3.06256e17			0.986405			0.493203	+	0.869915i	$0.335826\pi$
$492$	9.84543e16	+	1.70528e17i	0.312940	+	0.542029i
$493$	−2.66698e17	+	4.61934e17i	−0.836593	+	1.44902i
$494$	−9.92024e16	+	1.71824e17i	−0.307112	+	0.531934i
$495$	−2.28790e17	−	3.96276e17i	−0.699042	−	1.21078i
$496$	−4.99057e16			−0.150494
$497$	−3.13167e17	−	3.17105e17i	−0.932093	−	0.943816i
$498$	−5.36413e17			−1.57583
$499$	1.78606e17	+	3.09354e17i	0.517895	+	0.897021i	0.999784	+	0.0207882i	$0.00661756\pi$
$499$	1.78606e17	+	3.09354e17i	0.517895	+	0.897021i	−0.481889	+	0.876232i	$0.660049\pi$
$500$	9.41213e16	−	1.63023e17i	0.269391	−	0.466599i
$501$	3.62240e15	−	6.27418e15i	0.0102341	−	0.0177261i
$502$	1.79974e17	+	3.11724e17i	0.501921	+	0.869352i
$503$	1.26023e17			0.346944			0.173472	−	0.984839i	$-0.444501\pi$
$503$	1.26023e17			0.346944			0.173472	+	0.984839i	$0.444501\pi$
$504$	3.37430e16	−	1.22854e17i	0.0917033	−	0.333882i
$505$	−3.96031e17			−1.06251
$506$	−1.60458e16	−	2.77921e16i	−0.0424994	−	0.0736110i
$507$	5.78631e14	−	1.00222e15i	0.00151304	−	0.00262066i
$508$	−1.43391e17	+	2.48360e17i	−0.370175	+	0.641162i
$509$	−2.09517e16	−	3.62895e16i	−0.0534016	−	0.0924943i	0.838089	−	0.545534i	$-0.183673\pi$
$509$	−2.09517e16	−	3.62895e16i	−0.0534016	−	0.0924943i	−0.891490	+	0.453039i	$0.850340\pi$
$510$	−5.04257e17			−1.26895
$511$	1.94630e17	−	5.08495e16i	0.483585	−	0.126343i
$512$	−1.80144e16			−0.0441942
$513$	−5.20792e15	−	9.02038e15i	−0.0126154	−	0.0218505i
$514$	−7.58311e16	+	1.31343e17i	−0.181379	+	0.314158i
$515$	5.85125e16	−	1.01347e17i	0.138198	−	0.239366i
$516$	8.46824e16	+	1.46674e17i	0.197501	+	0.342082i
$517$	3.73391e17			0.859955
$518$	−1.10255e17	+	2.88054e16i	−0.250757	+	0.0655135i
$519$	−6.74618e17			−1.51520
$520$	−5.96962e16	−	1.03397e17i	−0.132411	−	0.229343i
$521$	3.14279e17	−	5.44347e17i	0.688446	−	1.19242i	−0.283894	−	0.958856i	$-0.591626\pi$
$521$	3.14279e17	−	5.44347e17i	0.688446	−	1.19242i	0.972340	−	0.233568i	$-0.0750402\pi$
$522$	−1.57079e17	+	2.72070e17i	−0.339829	+	0.588602i
$523$	5.09947e16	+	8.83254e16i	0.108959	+	0.188723i	0.915349	−	0.402662i	$-0.131915\pi$
$523$	5.09947e16	+	8.83254e16i	0.108959	+	0.188723i	−0.806390	+	0.591385i	$0.798582\pi$
$524$	−4.78890e16			−0.101061
$525$	−7.86869e16	+	2.86490e17i	−0.164009	+	0.597138i
$526$	1.23390e17			0.254022
$527$	−2.52340e17	−	4.37066e17i	−0.513118	−	0.888747i
$528$	1.67055e17	−	2.89348e17i	0.335536	−	0.581166i
$529$	2.51018e17	−	4.34776e17i	0.498015	−	0.862588i
$530$	1.70191e17	+	2.94779e17i	0.333536	+	0.577701i
$531$	−4.50830e17			−0.872767
$532$	−1.59414e17	−	1.61418e17i	−0.304859	−	0.308693i
$533$	−4.71472e17			−0.890694
$534$	−1.49630e17	−	2.59167e17i	−0.279255	−	0.483683i
$535$	3.20628e17	−	5.55343e17i	0.591155	−	1.02391i
$536$	−7.76532e16	+	1.34499e17i	−0.141445	+	0.244990i
$537$	−3.15618e17	−	5.46666e17i	−0.567974	−	0.983760i
$538$	3.15027e17			0.560097
$539$	−9.33789e17	−	5.54797e17i	−1.64029	−	0.974557i
$540$	6.26785e15			0.0108782
$541$	−1.79876e17	−	3.11555e17i	−0.308455	−	0.534259i	0.669570	−	0.742749i	$-0.266478\pi$
$541$	−1.79876e17	−	3.11555e17i	−0.308455	−	0.534259i	−0.978025	+	0.208490i	$0.933145\pi$
$542$	7.03224e16	−	1.21802e17i	0.119151	−	0.206376i
$543$	−4.25313e17	+	7.36664e17i	−0.712049	+	1.23331i
$544$	−9.10869e16	−	1.57767e17i	−0.150683	−	0.260990i
$545$	6.88013e17			1.12465
$546$	4.33229e17	+	4.38677e17i	0.699786	+	0.708586i
$547$	7.34678e17			1.17268			0.586340	−	0.810065i	$-0.300568\pi$
$547$	7.34678e17			1.17268			0.586340	+	0.810065i	$0.300568\pi$
$548$	1.88127e17	+	3.25846e17i	0.296741	+	0.513971i
$549$	−1.64853e17	+	2.85534e17i	−0.256967	+	0.445079i
$550$	−1.92748e17	+	3.33850e17i	−0.296915	+	0.514273i
$551$	2.79709e17	+	4.84471e17i	0.425815	+	0.737534i
$552$	−2.08293e16			−0.0313380
$553$	−1.48451e17	+	5.40494e17i	−0.220734	+	0.803669i
$554$	−6.75894e16			−0.0993265
$555$	1.32823e17	+	2.30056e17i	0.192916	+	0.334141i
$556$	1.50315e17	−	2.60354e17i	0.215783	−	0.373747i
$557$	−2.47501e17	+	4.28683e17i	−0.351170	+	0.608244i	−0.986455	−	0.164034i	$-0.947549\pi$
$557$	−2.47501e17	+	4.28683e17i	−0.351170	+	0.608244i	0.635285	+	0.772278i	$0.280883\pi$
$558$	−1.48623e17	−	2.57423e17i	−0.208432	−	0.361015i
$559$	−4.05522e17			−0.562131
$560$	1.32086e17	−	3.45092e16i	0.180982	−	0.0472838i
$561$	3.37875e18			4.57612
$562$	−8.46688e16	−	1.46651e17i	−0.113354	−	0.196335i
$563$	−2.63438e17	+	4.56288e17i	−0.348637	+	0.603857i	−0.986008	−	0.166700i	$-0.946689\pi$
$563$	−2.63438e17	+	4.56288e17i	−0.348637	+	0.603857i	0.637371	+	0.770557i	$0.280022\pi$
$564$	1.21177e17	−	2.09884e17i	0.158528	−	0.274578i
$565$	−7.59408e16	−	1.31533e17i	−0.0982111	−	0.170107i
$566$	4.48128e17			0.572921
$567$	−7.81006e17	+	2.04048e17i	−0.987108	+	0.257895i
$568$	−3.75340e17			−0.468986
$569$	4.42870e17	+	7.67074e17i	0.547075	+	0.947562i	0.998473	+	0.0552391i	$0.0175921\pi$
$569$	4.42870e17	+	7.67074e17i	0.547075	+	0.947562i	−0.451398	+	0.892323i	$0.649075\pi$
$570$	−2.64429e17	+	4.58005e17i	−0.322941	+	0.559350i
$571$	2.52094e17	−	4.36639e17i	0.304388	−	0.527215i	−0.672737	−	0.739882i	$-0.734881\pi$
$571$	2.52094e17	−	4.36639e17i	0.304388	−	0.527215i	0.977125	+	0.212666i	$0.0682147\pi$
$572$	3.99992e17	+	6.92806e17i	0.477504	+	0.827061i
$573$	−1.87118e18			−2.20857
$574$	1.42782e17	−	5.19855e17i	0.166628	−	0.606673i
$575$	2.40329e16			0.0277310
$576$	−5.36483e16	−	9.29216e16i	−0.0612083	−	0.106016i
$577$	1.73113e17	−	2.99840e17i	0.195293	−	0.338257i	−0.751704	−	0.659501i	$-0.770768\pi$
$577$	1.73113e17	−	2.99840e17i	0.195293	−	0.338257i	0.946996	+	0.321244i	$0.104101\pi$
$578$	6.04186e17	−	1.04648e18i	0.673969	−	1.16735i
$579$	4.91088e17	+	8.50590e17i	0.541688	+	0.938231i
$580$	−3.36636e17			−0.367180
$581$	1.03196e18	+	1.04494e18i	1.11306	+	1.12706i
$582$	−8.43670e17			−0.899856
$583$	−1.14035e18	−	1.97515e18i	−1.20280	−	2.08331i
$584$	8.47071e16	−	1.46717e17i	0.0883560	−	0.153037i
$585$	3.55560e17	−	6.15848e17i	0.366775	−	0.635273i
$586$	2.80892e17	+	4.86520e17i	0.286553	+	0.496325i
$587$	9.20829e17			0.929033			0.464517	−	0.885564i	$-0.346228\pi$
$587$	9.20829e17			0.929033			0.464517	+	0.885564i	$0.346228\pi$
$588$	−6.14895e17	+	3.44837e17i	−0.613548	+	0.344081i
$589$	−5.29303e17			−0.522342
$590$	−2.41543e17	−	4.18365e17i	−0.235753	−	0.408336i
$591$	2.25715e17	−	3.90949e17i	0.217892	−	0.377400i
$592$	−4.79852e16	+	8.31129e16i	−0.0458159	+	0.0793555i
$593$	−2.62681e17	−	4.54977e17i	−0.248069	−	0.429669i	0.714921	−	0.699205i	$-0.246463\pi$
$593$	−2.62681e17	−	4.54977e17i	−0.248069	−	0.429669i	−0.962990	+	0.269537i	$0.913129\pi$
$594$	−4.19974e16			−0.0392293
$595$	9.70098e17	+	9.82298e17i	0.896304	+	0.907576i
$596$	3.78031e16			0.0345483
$597$	4.16952e17	+	7.22182e17i	0.376923	+	0.652850i
$598$	2.49366e16	−	4.31914e16i	0.0222987	−	0.0386224i
$599$	−4.11615e17	+	7.12937e17i	−0.364096	+	0.630634i	−0.988631	−	0.150364i	$-0.951955\pi$
$599$	−4.11615e17	+	7.12937e17i	−0.364096	+	0.630634i	0.624534	+	0.780997i	$0.285289\pi$
$600$	1.25105e17	+	2.16688e17i	0.109469	+	0.189606i
$601$	−1.43103e18			−1.23869			−0.619347	−	0.785118i	$-0.712602\pi$
$601$	−1.43103e18			−1.23869			−0.619347	+	0.785118i	$0.712602\pi$
$602$	1.22810e17	−	4.47137e17i	0.105161	−	0.382880i
$603$	−9.25030e17			−0.783598
$604$	1.21070e17	+	2.09700e17i	0.101461	+	0.175735i
$605$	−1.19144e18	+	2.06363e18i	−0.987781	+	1.71089i
$606$	8.61168e17	−	1.49159e18i	0.706344	−	1.22342i
$607$	−3.30113e17	−	5.71773e17i	−0.267878	−	0.463978i	0.700436	−	0.713715i	$-0.252989\pi$
$607$	−3.30113e17	−	5.71773e17i	−0.267878	−	0.463978i	−0.968314	+	0.249738i	$0.919656\pi$
$608$	−1.91062e17			−0.153391
$609$	1.68194e18	−	4.39427e17i	1.33597	−	0.349040i
$610$	−3.53296e17			−0.277648
$611$	2.90142e17	+	5.02540e17i	0.225602	+	0.390753i
$612$	5.42528e17	−	9.39686e17i	0.417386	−	0.722934i
$613$	4.67096e17	−	8.09034e17i	0.355560	−	0.615848i	−0.631654	−	0.775251i	$-0.717624\pi$
$613$	4.67096e17	−	8.09034e17i	0.355560	−	0.615848i	0.987214	+	0.159403i	$0.0509568\pi$
$614$	−3.12003e17	−	5.40404e17i	−0.234998	−	0.407028i
$615$	−1.25673e18			−0.936601
$616$	−8.85037e17	+	2.31227e17i	−0.652660	+	0.170516i
$617$	−2.39791e18			−1.74977			−0.874883	−	0.484334i	$-0.839062\pi$
$617$	−2.39791e18			−1.74977			−0.874883	+	0.484334i	$0.839062\pi$
$618$	2.54471e17	+	4.40757e17i	0.183744	+	0.318254i
$619$	−5.77253e16	+	9.99832e16i	−0.0412456	+	0.0714394i	−0.885911	−	0.463855i	$-0.846466\pi$
$619$	−5.77253e16	+	9.99832e16i	−0.0412456	+	0.0714394i	0.844666	+	0.535294i	$0.179799\pi$
$620$	1.59257e17	−	2.75841e17i	0.112604	−	0.195035i
$621$	1.30912e15	+	2.26746e15i	0.000915974	+	0.00158651i
$622$	2.48312e17			0.171933
$623$	−2.16999e17	+	7.90071e17i	−0.148691	+	0.541369i
$624$	5.19237e17			0.352100
$625$	2.72769e17	+	4.72450e17i	0.183052	+	0.317056i
$626$	−5.36780e17	+	9.29730e17i	−0.356503	+	0.617481i
$627$	1.77180e18	−	3.06884e18i	1.16459	−	2.01714i
$628$	−4.31082e17	−	7.46656e17i	−0.280428	−	0.485716i
$629$	−9.70519e17			−0.624848
$630$	5.71368e17	+	5.78554e17i	0.364085	+	0.368663i
$631$	1.98112e18			1.24945			0.624726	−	0.780844i	$-0.285211\pi$
$631$	1.98112e18			1.24945			0.624726	+	0.780844i	$0.285211\pi$
$632$	2.36024e17	+	4.08805e17i	0.147331	+	0.255185i
$633$	1.88550e17	−	3.26579e17i	0.116494	−	0.201773i
$634$	4.85880e17	−	8.41569e17i	0.297132	−	0.514647i
$635$	−9.15165e17	−	1.58511e18i	−0.553950	−	0.959469i
$636$	−1.48032e18			−0.886918
$637$	2.10956e16	−	1.68787e18i	0.0125108	−	1.00100i
$638$	2.25562e18			1.32413
$639$	−1.11779e18	−	1.93607e18i	−0.649539	−	1.12503i
$640$	5.74868e16	−	9.95700e16i	0.0330673	−	0.0572742i
$641$	−4.73875e17	+	8.20775e17i	−0.269828	+	0.467355i	−0.968817	−	0.247777i	$-0.920300\pi$
$641$	−4.73875e17	+	8.20775e17i	−0.269828	+	0.467355i	0.698990	+	0.715132i	$0.253633\pi$
$642$	1.39441e18	+	2.41519e18i	0.785982	+	1.36136i
$643$	−2.02473e16			−0.0112978			−0.00564891	−	0.999984i	$-0.501798\pi$
$643$	−2.02473e16			−0.0112978			−0.00564891	+	0.999984i	$0.501798\pi$
$644$	4.00719e16	+	4.05758e16i	0.0221351	+	0.0224135i
$645$	−1.08094e18			−0.591103
$646$	−9.66073e17	−	1.67329e18i	−0.522996	−	0.905856i
$647$	4.30875e17	−	7.46297e17i	0.230926	−	0.399976i	−0.727155	−	0.686474i	$-0.759158\pi$
$647$	4.30875e17	−	7.46297e17i	0.230926	−	0.399976i	0.958081	+	0.286498i	$0.0924911\pi$
$648$	−3.39911e17	+	5.88743e17i	−0.180355	+	0.312384i
$649$	1.61845e18	+	2.80324e18i	0.850176	+	1.47255i
$650$	−5.99095e17			−0.311573
$651$	−4.35627e17	+	1.58607e18i	−0.224305	+	0.816669i
$652$	−1.55897e18			−0.794748
$653$	1.73045e16	+	2.99723e16i	0.00873422	+	0.0151281i	0.870359	−	0.492417i	$-0.163886\pi$
$653$	1.73045e16	+	2.99723e16i	0.00873422	+	0.0151281i	−0.861625	+	0.507545i	$0.830553\pi$
$654$	−1.49608e18	+	2.59129e18i	−0.747653	+	1.29497i
$655$	1.52821e17	−	2.64694e17i	0.0756163	−	0.130971i
$656$	−2.27011e17	−	3.93195e17i	−0.111217	−	0.192634i
$657$	1.00906e18			0.489487
$658$	−6.41979e17	+	1.67725e17i	−0.308356	+	0.0805620i
$659$	−4.84217e17			−0.230295			−0.115148	−	0.993348i	$-0.536734\pi$
$659$	−4.84217e17			−0.230295			−0.115148	+	0.993348i	$0.536734\pi$
$660$	1.06620e18	+	1.84671e18i	0.502114	+	0.869687i
$661$	1.47958e18	−	2.56271e18i	0.689970	−	1.19506i	−0.281878	−	0.959450i	$-0.590957\pi$
$661$	1.47958e18	−	2.56271e18i	0.689970	−	1.19506i	0.971847	−	0.235612i	$-0.0757095\pi$
$662$	−1.00151e18	+	1.73466e18i	−0.462463	+	0.801010i
$663$	2.62544e18	+	4.54739e18i	1.20051	+	2.07934i
$664$	1.23684e18			0.560041
$665$	1.40091e18	−	3.66006e17i	0.628160	−	0.164115i
$666$	−5.71616e17			−0.253817
$667$	−7.03106e16	−	1.21782e17i	−0.0309174	−	0.0535505i
$668$	−8.35236e15	+	1.44667e16i	−0.00363716	+	0.00629974i
$669$	−1.79048e18	+	3.10119e18i	−0.772144	+	1.33739i
$670$	−4.95607e17	−	8.58417e17i	−0.211666	−	0.366617i
$671$	2.36725e18			1.00126
$672$	−1.57248e17	+	5.72522e17i	−0.0658695	+	0.239824i
$673$	2.37383e18			0.984807			0.492404	−	0.870367i	$-0.336118\pi$
$673$	2.37383e18			0.984807			0.492404	+	0.870367i	$0.336118\pi$
$674$	−4.99063e17	−	8.64403e17i	−0.205053	−	0.355162i
$675$	1.57256e16	−	2.72376e16i	0.00639932	−	0.0110839i
$676$	−1.33418e15	+	2.31087e15i	−0.000537726	+	0.000931368i
$677$	−1.88783e18	−	3.26982e18i	−0.753594	−	1.30526i	−0.946070	−	0.323962i	$-0.894985\pi$
$677$	−1.88783e18	−	3.26982e18i	−0.753594	−	1.30526i	0.192476	−	0.981302i	$-0.438348\pi$
$678$	6.60533e17			0.261157
$679$	1.62307e18	+	1.64348e18i	0.635598	+	0.643592i
$680$	1.16269e18			0.450979
$681$	−1.83340e18	−	3.17554e18i	−0.704369	−	1.22000i
$682$	−1.06709e18	+	1.84826e18i	−0.406073	+	0.703339i
$683$	−1.00170e18	+	1.73500e18i	−0.377576	+	0.653981i	−0.990709	−	0.135999i	$-0.956576\pi$
$683$	−1.00170e18	+	1.73500e18i	−0.377576	+	0.653981i	0.613133	+	0.789980i	$0.289909\pi$
$684$	−5.68997e17	−	9.85532e17i	−0.212444	−	0.367965i
$685$	−2.40137e18			−0.888118
$686$	1.85469e18	+	5.34421e17i	0.679462	+	0.195784i
$687$	2.47148e18			0.896887
$688$	−1.95257e17	−	3.38194e17i	−0.0701909	−	0.121574i
$689$	1.77221e18	−	3.06956e18i	0.631089	−	1.09308i
$690$	6.64697e16	−	1.15129e17i	0.0234479	−	0.0406130i
$691$	−1.63537e16	−	2.83255e16i	−0.00571491	−	0.00989852i	0.863154	−	0.504941i	$-0.168486\pi$
$691$	−1.63537e16	−	2.83255e16i	−0.00571491	−	0.00989852i	−0.868869	+	0.495043i	$0.835152\pi$
$692$	1.55550e18			0.538494
$693$	−3.82843e18	−	3.87657e18i	−1.31297	−	1.32948i
$694$	4.02990e18			1.36917
$695$	9.59360e17	+	1.66166e18i	0.322909	+	0.559295i
$696$	7.32016e17	−	1.26789e18i	0.244096	−	0.422786i
$697$	2.29569e18	−	3.97625e18i	0.758403	−	1.31359i
$698$	−1.97865e18	−	3.42712e18i	−0.647603	−	1.12168i
$699$	1.95233e18			0.633071
$700$	1.81432e17	−	6.60575e17i	0.0582878	−	0.212219i
$701$	−5.10250e18			−1.62411			−0.812057	−	0.583579i	$-0.801652\pi$
$701$	−5.10250e18			−1.62411			−0.812057	+	0.583579i	$0.801652\pi$
$702$	−3.26339e16	−	5.65235e16i	−0.0102915	−	0.0178253i
$703$	−5.08934e17	+	8.81500e17i	−0.159020	+	0.275431i
$704$	−3.85188e17	+	6.67165e17i	−0.119248	+	0.206543i
$705$	7.73388e17	+	1.33955e18i	0.237229	+	0.410893i
$706$	−7.11869e17			−0.216356
$707$	−4.56236e18	+	1.19198e18i	−1.37393	+	0.358956i
$708$	2.10094e18			0.626899
$709$	1.12804e18	+	1.95383e18i	0.333522	+	0.577678i	0.983200	−	0.182532i	$-0.0584294\pi$
$709$	1.12804e18	+	1.95383e18i	0.333522	+	0.577678i	−0.649677	+	0.760210i	$0.725096\pi$
$710$	1.19777e18	−	2.07459e18i	0.350908	−	0.607791i
$711$	−1.40580e18	+	2.43491e18i	−0.408103	+	0.706855i
$712$	3.45010e17	+	5.97574e17i	0.0992456	+	0.171898i
$713$	1.33051e17			0.0379259
$714$	−5.80915e18	+	1.51772e18i	−1.64087	+	0.428698i
$715$	−5.10574e18			−1.42912
$716$	7.27736e17	+	1.26048e18i	0.201855	+	0.349623i
$717$	−2.28022e18	+	3.94946e18i	−0.626762	+	1.08558i
$718$	−1.98707e18	+	3.44170e18i	−0.541257	+	0.937484i
$719$	1.13496e18	+	1.96581e18i	0.306368	+	0.530645i	0.977565	−	0.210634i	$-0.0675528\pi$
$719$	1.13496e18	+	1.96581e18i	0.306368	+	0.530645i	−0.671197	+	0.741279i	$0.734219\pi$
$720$	6.84801e17			0.183191
$721$	3.69044e17	−	1.34365e18i	0.0978360	−	0.356210i
$722$	6.64980e17			0.174710
$723$	−1.67355e18	−	2.89868e18i	−0.435753	−	0.754746i
$724$	9.80666e17	−	1.69856e18i	0.253058	−	0.438310i
$725$	−8.44599e17	+	1.46289e18i	−0.216000	+	0.374123i
$726$	−5.18155e18	−	8.97471e18i	−1.31332	−	2.27474i
$727$	3.34385e18			0.839988			0.419994	−	0.907527i	$-0.362032\pi$
$727$	3.34385e18			0.839988			0.419994	+	0.907527i	$0.362032\pi$
$728$	−9.98918e17	−	1.01148e18i	−0.248700	−	0.251828i
$729$	−3.88334e18			−0.958246
$730$	5.40627e17	+	9.36393e17i	0.132221	+	0.229013i
$731$	1.97457e18	−	3.42005e18i	0.478640	−	0.829028i
$732$	7.68242e17	−	1.33063e18i	0.184576	−	0.319696i
$733$	−3.50530e17	−	6.07135e17i	−0.0834736	−	0.144580i	0.821266	−	0.570545i	$-0.193268\pi$
$733$	−3.50530e17	−	6.07135e17i	−0.0834736	−	0.144580i	−0.904740	+	0.425965i	$0.859935\pi$
$734$	1.29609e18			0.305923
$735$	5.62313e16	−	4.49911e18i	0.0131556	−	1.05259i
$736$	4.80273e16			0.0111374
$737$	3.32080e18	+	5.75179e18i	0.763314	+	1.32210i
$738$	1.35211e18	−	2.34193e18i	0.308068	−	0.533590i
$739$	−3.88505e18	+	6.72910e18i	−0.877420	+	1.51974i	−0.0232577	+	0.999730i	$0.507404\pi$
$739$	−3.88505e18	+	6.72910e18i	−0.877420	+	1.51974i	−0.854162	+	0.520006i	$0.825930\pi$
$740$	−3.06257e17	−	5.30452e17i	−0.0685614	−	0.118752i
$741$	5.50706e18			1.22208
$742$	2.84786e18	+	2.88368e18i	0.626460	+	0.634338i
$743$	2.35319e18			0.513132			0.256566	−	0.966527i	$-0.417409\pi$
$743$	2.35319e18			0.513132			0.256566	+	0.966527i	$0.417409\pi$
$744$	6.92608e17	+	1.19963e18i	0.149714	+	0.259313i
$745$	−1.20636e17	+	2.08947e17i	−0.0258500	+	0.0447735i
$746$	1.22816e18	−	2.12723e18i	0.260886	−	0.451868i
$747$	3.68340e18	+	6.37983e18i	0.775648	+	1.34346i
$748$	−7.79056e18			−1.62633
$749$	2.02223e18	−	7.36271e18i	0.418502	−	1.52372i
$750$	−5.22499e18			−1.07198
$751$	9.97951e17	+	1.72850e18i	0.202978	+	0.351569i	0.949487	−	0.313807i	$-0.101605\pi$
$751$	9.97951e17	+	1.72850e18i	0.202978	+	0.351569i	−0.746508	+	0.665376i	$0.768271\pi$
$752$	−2.79403e17	+	4.83941e17i	−0.0563398	+	0.0975835i
$753$	4.99547e18	−	8.65241e18i	0.998641	−	1.72970i
$754$	1.75271e18	+	3.03579e18i	0.347374	+	0.601670i
$755$	−1.54542e18			−0.303663
$756$	7.22070e16	−	1.88650e16i	0.0140666	−	0.00367507i
$757$	−5.58530e18			−1.07876			−0.539378	−	0.842064i	$-0.681340\pi$
$757$	−5.58530e18			−1.07876			−0.539378	+	0.842064i	$0.681340\pi$
$758$	1.66940e18	+	2.89148e18i	0.319676	+	0.553695i
$759$	−4.45377e17	+	7.71416e17i	−0.0845584	+	0.146459i
$760$	6.09708e17	−	1.05605e18i	0.114771	−	0.198790i
$761$	−1.92256e18	−	3.32997e18i	−0.358823	−	0.621499i	0.628942	−	0.777452i	$-0.283488\pi$
$761$	−1.92256e18	−	3.32997e18i	−0.358823	−	0.621499i	−0.987764	+	0.155953i	$0.950155\pi$
$762$	7.96011e18			1.47303
$763$	7.92606e18	−	2.07078e18i	1.45428	−	0.379949i
$764$	4.31448e18			0.784914
$765$	3.46259e18	+	5.99737e18i	0.624599	+	1.08184i
$766$	−3.15157e18	+	5.45868e18i	−0.563690	+	0.976340i
$767$	−2.51521e18	+	4.35648e18i	−0.446072	+	0.772620i
$768$	2.50010e17	+	4.33030e17i	0.0439652	+	0.0761500i
$769$	−1.59052e18			−0.277343			−0.138671	−	0.990338i	$-0.544283\pi$
$769$	−1.59052e18			−0.277343			−0.138671	+	0.990338i	$0.544283\pi$
$770$	1.54624e18	−	5.62970e18i	0.267355	−	0.973410i
$771$	4.20964e18			0.721758
$772$	−1.13233e18	−	1.96125e18i	−0.192513	−	0.333442i
$773$	−4.24436e18	+	7.35145e18i	−0.715559	+	1.23939i	0.247184	+	0.968969i	$0.420495\pi$
$773$	−4.24436e18	+	7.35145e18i	−0.715559	+	1.23939i	−0.962743	+	0.270417i	$0.912839\pi$
$774$	1.16298e18	−	2.01434e18i	0.194427	−	0.336757i
$775$	−7.99131e17	−	1.38414e18i	−0.132482	−	0.229466i
$776$	1.94529e18			0.319804
$777$	2.22258e18	+	2.25053e18i	0.362343	+	0.366900i
$778$	4.51048e18			0.729215
$779$	−2.40769e18	−	4.17025e18i	−0.386018	−	0.668603i
$780$	−1.65697e18	+	2.86995e18i	−0.263450	+	0.456310i
$781$	−8.02559e18	+	1.39007e19i	−1.26545	+	2.19183i
$782$	2.42842e17	+	4.20615e17i	0.0379735	+	0.0657720i
$783$	−1.84028e17			−0.0285385
$784$	1.41780e18	−	7.95107e17i	0.218052	−	0.122284i
$785$	5.50260e18			0.839296
$786$	6.64620e17	+	1.15115e18i	0.100537	+	0.174135i
$787$	3.38035e18	−	5.85494e18i	0.507138	−	0.878389i	−0.492828	−	0.870127i	$-0.664037\pi$
$787$	3.38035e18	−	5.85494e18i	0.507138	−	0.878389i	0.999966	−	0.00826189i	$-0.00262987\pi$
$788$	−5.20442e17	+	9.01432e17i	−0.0774376	+	0.134126i
$789$	−1.71244e18	−	2.96604e18i	−0.252706	−	0.437700i
$790$	−3.01276e18			−0.440948
$791$	−1.27075e18	−	1.28673e18i	−0.184464	−	0.186784i
$792$	−4.58848e18			−0.660625
$793$	1.83945e18	+	3.18603e18i	0.262672	+	0.454961i
$794$	−3.94646e18	+	6.83547e18i	−0.558952	+	0.968133i
$795$	4.72392e18	−	8.18208e18i	0.663616	−	1.14942i
$796$	−9.61387e17	−	1.66517e18i	−0.133956	−	0.232019i
$797$	−8.33383e17			−0.115177			−0.0575885	−	0.998340i	$-0.518341\pi$
$797$	−8.33383e17			−0.115177			−0.0575885	+	0.998340i	$0.518341\pi$
$798$	−1.66778e18	+	6.07220e18i	−0.228623	+	0.832391i
$799$	−5.65103e18			−0.768376
$800$	−2.88461e17	−	4.99630e17i	−0.0389048	−	0.0673850i
$801$	−2.05493e18	+	3.55925e18i	−0.274907	+	0.476153i
$802$	2.32348e18	−	4.02438e18i	0.308322	−	0.534030i
$803$	−3.62245e18	−	6.27427e18i	−0.476816	−	0.825870i
$804$	4.31079e18			0.562850
$805$	−3.52148e17	+	9.20032e16i	−0.0456092	+	0.0119160i
$806$	−3.31672e18			−0.426119
$807$	−4.37206e18	−	7.57262e18i	−0.557196	−	0.965091i
$808$	−1.98564e18	+	3.43923e18i	−0.251031	+	0.434798i
$809$	1.30255e18	−	2.25608e18i	0.163354	−	0.282937i	−0.772716	−	0.634752i	$-0.781102\pi$
$809$	1.30255e18	−	2.25608e18i	0.163354	−	0.282937i	0.936069	+	0.351815i	$0.114435\pi$
$810$	−2.16942e18	−	3.75754e18i	−0.269892	−	0.467467i
$811$	−8.39030e18			−1.03548			−0.517740	−	0.855538i	$-0.673227\pi$
$811$	−8.39030e18			−1.03548			−0.517740	+	0.855538i	$0.673227\pi$
$812$	−3.87813e18	+	1.01321e18i	−0.474797	+	0.124047i
$813$	−3.90383e18			−0.474135
$814$	2.05206e18	+	3.55427e18i	0.247247	+	0.428245i
$815$	4.97493e18	−	8.61683e18i	0.594651	−	1.02997i
$816$	−2.52827e18	+	4.37909e18i	−0.299804	+	0.519276i
$817$	−2.07090e18	−	3.58691e18i	−0.243622	−	0.421965i
$818$	4.00384e18			0.467283
$819$	2.24255e18	−	8.16487e18i	0.259655	−	0.945375i
$820$	2.89771e18			0.332863
$821$	−3.01483e18	−	5.22184e18i	−0.343583	−	0.595104i	0.641512	−	0.767113i	$-0.278307\pi$
$821$	−3.01483e18	−	5.22184e18i	−0.343583	−	0.595104i	−0.985095	+	0.172009i	$0.944974\pi$
$822$	5.22178e18	−	9.04439e18i	0.590408	−	1.02262i
$823$	−2.95985e16	+	5.12662e16i	−0.00332025	+	0.00575085i	−0.867681	−	0.497122i	$-0.834390\pi$
$823$	−2.95985e16	+	5.12662e16i	−0.00332025	+	0.00575085i	0.864361	+	0.502873i	$0.167724\pi$
$824$	−5.86747e17	−	1.01627e18i	−0.0653016	−	0.113106i
$825$	1.07001e19			1.18151
$826$	−4.04183e18	−	4.09266e18i	−0.442800	−	0.448369i
$827$	−5.98297e18			−0.650326			−0.325163	−	0.945658i	$-0.605419\pi$
$827$	−5.98297e18			−0.650326			−0.325163	+	0.945658i	$0.605419\pi$
$828$	1.43029e17	+	2.47734e17i	0.0154251	+	0.0267170i
$829$	5.18792e18	−	8.98574e18i	0.555122	−	0.961500i	−0.442772	−	0.896634i	$-0.646005\pi$
$829$	5.18792e18	−	8.98574e18i	0.555122	−	0.961500i	0.997894	−	0.0648656i	$-0.0206619\pi$
$830$	−3.94694e18	+	6.83630e18i	−0.419037	+	0.725794i
$831$	9.38029e17	+	1.62471e18i	0.0988120	+	0.171147i
$832$	−1.19723e18			−0.125134
$833$	1.41323e19	+	8.39649e18i	1.46561	+	0.870774i
$834$	−8.34451e18			−0.858661
$835$	−5.33074e16	−	9.23311e16i	−0.00544284	−	0.00942727i
$836$	−4.08532e18	+	7.07599e18i	−0.413891	+	0.716880i
$837$	8.70604e16	−	1.50793e17i	0.00875195	−	0.0151588i
$838$	6.04367e18	+	1.04679e19i	0.602857	+	1.04418i
$839$	1.62942e18			0.161280			0.0806400	−	0.996743i	$-0.474304\pi$
$839$	1.62942e18			0.161280			0.0806400	+	0.996743i	$0.474304\pi$
$840$	−2.66267e18	−	2.69615e18i	−0.261518	−	0.264807i
$841$	−3.76784e17			−0.0367213
$842$	−3.62144e18	−	6.27251e18i	−0.350229	−	0.606614i
$843$	−2.35012e18	+	4.07054e18i	−0.225534	+	0.390636i
$844$	−4.34750e17	+	7.53009e17i	−0.0414013	+	0.0717091i
$845$	−8.51515e15	−	1.47487e16i	−0.000804681	−	0.00139375i
$846$	−3.32834e18			−0.312119
$847$	−7.51449e18	+	2.73594e19i	−0.699290	+	2.54604i
$848$	3.41324e18			0.315206
$849$	−6.21927e18	−	1.07721e19i	−0.569953	−	0.987188i
$850$	2.91712e18	−	5.05259e18i	0.265296	−	0.459506i
$851$	1.27931e17	−	2.21583e17i	0.0115461	−	0.0199984i
$852$	5.20909e18	+	9.02241e18i	0.466557	+	0.808100i
$853$	1.81502e19			1.61329			0.806644	−	0.591038i	$-0.201282\pi$
$853$	1.81502e19			1.61329			0.806644	+	0.591038i	$0.201282\pi$
$854$	−4.07005e18	+	1.06335e18i	−0.359024	+	0.0937997i
$855$	7.26304e18			0.635826
$856$	−3.21516e18	−	5.56882e18i	−0.279334	−	0.483820i
$857$	−2.68334e18	+	4.64769e18i	−0.231367	+	0.400739i	−0.958211	−	0.286064i	$-0.907653\pi$
$857$	−2.68334e18	+	4.64769e18i	−0.231367	+	0.400739i	0.726844	+	0.686803i	$0.240986\pi$
$858$	1.11024e19	−	1.92300e19i	0.950060	−	1.64555i
$859$	−1.72767e17	−	2.99242e17i	−0.0146726	−	0.0254136i	0.858596	−	0.512653i	$-0.171337\pi$
$859$	−1.72767e17	−	2.99242e17i	−0.0146726	−	0.0254136i	−0.873268	+	0.487239i	$0.838004\pi$
$860$	2.49238e18			0.210075
$861$	−1.44778e19	+	3.78252e18i	−1.21111	+	0.316418i
$862$	7.55307e18			0.627085
$863$	−3.68850e18	−	6.38867e18i	−0.303934	−	0.526430i	0.673089	−	0.739561i	$-0.264967\pi$
$863$	−3.68850e18	−	6.38867e18i	−0.303934	−	0.526430i	−0.977023	+	0.213132i	$0.931634\pi$
$864$	3.14261e16	−	5.44316e16i	0.00257010	−	0.00445155i
$865$	−4.96385e18	+	8.59764e18i	−0.402916	+	0.697870i
$866$	3.78530e18	+	6.55634e18i	0.304954	+	0.528196i
$867$	−3.35404e19			−2.68191
$868$	1.00445e18	−	3.65708e18i	0.0797166	−	0.290240i
$869$	2.01868e19			1.59016
$870$	4.67195e18	+	8.09206e18i	0.365278	+	0.632680i
$871$	−5.16081e18	+	8.93879e18i	−0.400498	+	0.693682i
$872$	3.44960e18	−	5.97487e18i	0.265712	−	0.460226i
$873$	5.79324e18	+	1.00342e19i	0.442923	+	0.767166i
$874$	5.09380e17			0.0386561
$875$	1.00519e19	+	1.01783e19i	0.757176	+	0.766699i
$876$	−4.70237e18			−0.351593
$877$	−2.63293e18	−	4.56036e18i	−0.195408	−	0.338456i	0.751626	−	0.659589i	$-0.229270\pi$
$877$	−2.63293e18	−	4.56036e18i	−0.195408	−	0.338456i	−0.947034	+	0.321133i	$0.895936\pi$
$878$	2.21197e18	−	3.83125e18i	0.162954	−	0.282245i
$879$	7.79663e18	−	1.35042e19i	0.570137	−	0.987507i
$880$	−2.45839e18	−	4.25805e18i	−0.178449	−	0.309082i
$881$	2.11091e19			1.52099			0.760494	−	0.649344i	$-0.224957\pi$
$881$	2.11091e19			1.52099			0.760494	+	0.649344i	$0.224957\pi$
$882$	8.32362e18	+	4.94536e18i	0.595342	+	0.353714i
$883$	9.58202e18			0.680319			0.340159	−	0.940368i	$-0.389519\pi$
$883$	9.58202e18			0.680319			0.340159	+	0.940368i	$0.389519\pi$
$884$	−6.05361e18	−	1.04852e19i	−0.426653	−	0.738984i
$885$	−6.70444e18	+	1.16124e19i	−0.469063	+	0.812441i
$886$	1.91563e17	−	3.31797e17i	0.0133043	−	0.0230437i
$887$	−6.92733e18	−	1.19985e19i	−0.477598	−	0.827223i	0.522073	−	0.852901i	$-0.325159\pi$
$887$	−6.92733e18	−	1.19985e19i	−0.477598	−	0.827223i	−0.999670	+	0.0256778i	$0.991826\pi$
$888$	2.66382e18			0.182314
$889$	−1.53138e19	−	1.55064e19i	−1.04045	−	1.05354i
$890$	−4.40392e18			−0.297033
$891$	1.45361e19	+	2.51773e19i	0.973291	+	1.68579i
$892$	4.12839e18	−	7.15058e18i	0.274416	−	0.475302i
$893$	−2.96337e18	+	5.13270e18i	−0.195547	+	0.338697i
$894$	−5.24645e17	−	9.08711e17i	−0.0343693	−	0.0595295i
$895$	−9.28928e18			−0.604132
$896$	3.62574e17	−	1.32009e18i	0.0234096	−	0.0852320i
$897$	−1.38431e18			−0.0887326
$898$	−4.31963e17	−	7.48182e17i	−0.0274885	−	0.0476114i
$899$	−4.67588e18	+	8.09886e18i	−0.295410	+	0.511665i
$900$	1.71812e18	−	2.97587e18i	0.107765	−	0.186654i
$901$	1.72585e19	+	2.98926e19i	1.07471	+	1.86146i
$902$	−1.94160e19			−1.20038
$903$	−1.24527e19	+	3.25342e18i	−0.764349	+	0.199696i
$904$	−1.52303e18			−0.0928138
$905$	6.25892e18	+	1.08408e19i	0.378690	+	0.655910i
$906$	3.36051e18	−	5.82058e18i	0.201870	−	0.349650i
$907$	6.77394e18	−	1.17328e19i	0.404012	−	0.699769i	−0.590194	−	0.807262i	$-0.700949\pi$
$907$	6.77394e18	−	1.17328e19i	0.404012	−	0.699769i	0.994206	+	0.107492i	$0.0342821\pi$
$908$	4.22736e18	+	7.32200e18i	0.250329	+	0.433582i
$909$	−2.36536e19			−1.39069
$910$	8.77840e18	−	2.29347e18i	0.512444	−	0.133883i
$911$	3.29525e18			0.190994			0.0954969	−	0.995430i	$-0.469556\pi$
$911$	3.29525e18			0.190994			0.0954969	+	0.995430i	$0.469556\pi$
$912$	2.65162e18	+	4.59274e18i	0.152597	+	0.264305i
$913$	2.64463e19	−	4.58063e19i	1.51114	−	2.61737i
$914$	−9.51362e18	+	1.64781e19i	−0.539753	+	0.934880i
$915$	4.90316e18	+	8.49253e18i	0.276210	+	0.478410i
$916$	−5.69861e18			−0.318749
$917$	9.63857e17	−	3.50930e18i	0.0535318	−	0.194904i
$918$	6.35604e17			0.0350517
$919$	−8.57441e18	−	1.48513e19i	−0.469519	−	0.813231i	0.529874	−	0.848077i	$-0.322239\pi$
$919$	−8.57441e18	−	1.48513e19i	−0.469519	−	0.813231i	−0.999393	+	0.0348456i	$0.988906\pi$
$920$	−1.53263e17	+	2.65459e17i	−0.00833327	+	0.0144336i
$921$	−8.66016e18	+	1.49998e19i	−0.467561	+	0.809839i
$922$	−1.31651e18	−	2.28027e18i	−0.0705788	−	0.122246i
$923$	−2.49450e19			−1.32792
$924$	1.78411e19	+	1.80655e19i	0.943091	+	0.954952i
$925$	−3.07352e18			−0.161330
$926$	−1.03525e19	−	1.79311e19i	−0.539603	−	0.934620i
$927$	3.49476e18	−	6.05310e18i	0.180883	−	0.313299i
$928$	−1.68785e18	+	2.92344e18i	−0.0867503	+	0.150256i
$929$	−5.00038e18	−	8.66092e18i	−0.255212	−	0.442040i	0.709741	−	0.704463i	$-0.248812\pi$
$929$	−5.00038e18	−	8.66092e18i	−0.255212	−	0.442040i	−0.964953	+	0.262422i	$0.915479\pi$
$930$	−8.84089e18			−0.448081
$931$	1.50372e19	−	8.43295e18i	0.756824	−	0.424431i
$932$	−4.50159e18			−0.224990
$933$	−3.44616e18	−	5.96892e18i	−0.171043	−	0.296254i
$934$	5.75942e18	−	9.97561e18i	0.283873	−	0.491682i
$935$	2.48609e19	−	4.30603e19i	1.21686	−	2.10767i
$936$	−3.56545e18	−	6.17554e18i	−0.173309	−	0.300180i
$937$	−2.08207e19			−1.00505			−0.502525	−	0.864562i	$-0.667596\pi$
$937$	−2.08207e19			−1.00505			−0.502525	+	0.864562i	$0.667596\pi$
$938$	−8.29318e18	−	8.39748e18i	−0.397560	−	0.402560i
$939$	2.97984e19			1.41862
$940$	−1.78324e18	−	3.08866e18i	−0.0843099	−	0.146029i
$941$	−4.13796e18	+	7.16716e18i	−0.194291	+	0.336523i	−0.946668	−	0.322211i	$-0.895574\pi$
$941$	−4.13796e18	+	7.16716e18i	−0.194291	+	0.336523i	0.752377	+	0.658733i	$0.228907\pi$
$942$	−1.19654e19	+	2.07247e19i	−0.557951	+	0.966400i
$943$	6.05223e17	+	1.04828e18i	0.0280278	+	0.0485456i
$944$	−4.84425e18			−0.222797
$945$	−1.26152e17	+	4.59307e17i	−0.00576220	+	0.0209796i
$946$	−1.67001e19			−0.757575
$947$	1.08265e19	+	1.87520e19i	0.487767	+	0.844837i	0.999901	−	0.0140688i	$-0.00447837\pi$
$947$	1.08265e19	+	1.87520e19i	0.487767	+	0.844837i	−0.512134	+	0.858905i	$0.671145\pi$
$948$	6.55124e18	−	1.13471e19i	0.293136	−	0.507726i
$949$	5.62961e18	−	9.75076e18i	0.250177	−	0.433320i
$950$	−3.05944e18	−	5.29910e18i	−0.135032	−	0.233883i
$951$	−2.69729e19			−1.18237
$952$	1.33945e19	−	3.49947e18i	0.583156	−	0.152357i
$953$	−9.75657e18			−0.421884			−0.210942	−	0.977499i	$-0.567653\pi$
$953$	−9.75657e18			−0.421884			−0.210942	+	0.977499i	$0.567653\pi$
$954$	1.01649e19	+	1.76061e19i	0.436555	+	0.756136i
$955$	−1.37682e19	+	2.38472e19i	−0.587293	+	1.01722i
$956$	5.25763e18	−	9.10647e18i	0.222748	−	0.385810i
$957$	−3.13042e19	−	5.42205e19i	−1.31727	−	2.28158i
$958$	−1.15571e18			−0.0483029
$959$	−2.76644e19	+	7.22767e18i	−1.14842	+	0.300039i
$960$	−3.19128e18			−0.131584
$961$	7.78462e18	+	1.34834e19i	0.318812	+	0.552199i
$962$	−3.18909e18	+	5.52366e18i	−0.129726	+	0.224693i
$963$	1.91500e19	−	3.31688e19i	0.773746	−	1.34017i
$964$	3.85879e18	+	6.68362e18i	0.154864	+	0.268232i
$965$	1.44537e19			0.576173
$966$	4.19230e17	−	1.52637e18i	0.0165997	−	0.0604378i
$967$	−4.86140e19			−1.91201			−0.956003	−	0.293358i	$-0.905227\pi$
$967$	−4.86140e19			−1.91201			−0.956003	+	0.293358i	$0.905227\pi$
$968$	1.19474e19	+	2.06935e19i	0.466748	+	0.808431i
$969$	−2.68150e19	+	4.64449e19i	−1.04057	+	1.80233i
$970$	−6.20773e18	+	1.07521e19i	−0.239286	+	0.414455i
$971$	9.82587e18	+	1.70189e19i	0.376224	+	0.651639i	0.990509	−	0.137445i	$-0.0438891\pi$
$971$	9.82587e18	+	1.70189e19i	0.376224	+	0.651639i	−0.614286	+	0.789084i	$0.710556\pi$
$972$	1.84873e19			0.703143
$973$	1.60533e19	+	1.62552e19i	0.606501	+	0.614129i
$974$	2.63861e19			0.990245
$975$	8.31445e18	+	1.44011e19i	0.309959	+	0.536864i
$976$	−1.77138e18	+	3.06811e18i	−0.0655974	+	0.113618i
$977$	−4.37285e18	+	7.57400e18i	−0.160861	+	0.278619i	−0.935178	−	0.354179i	$-0.884760\pi$
$977$	−4.37285e18	+	7.57400e18i	−0.160861	+	0.278619i	0.774317	+	0.632798i	$0.218094\pi$
$978$	2.16360e19	+	3.74746e19i	0.790631	+	1.36941i
$979$	2.95083e19			1.07116
$980$	−1.29655e17	+	1.03738e19i	−0.00467543	+	0.374084i
$981$	4.10927e19			1.47203
$982$	9.80020e18	+	1.69744e19i	0.348747	+	0.604047i
$983$	5.27981e18	−	9.14490e18i	0.186647	−	0.323282i	−0.757483	−	0.652854i	$-0.773571\pi$
$983$	5.27981e18	−	9.14490e18i	0.186647	−	0.323282i	0.944130	+	0.329573i	$0.106905\pi$
$984$	−6.30108e18	+	1.09138e19i	−0.221282	+	0.383272i
$985$	−3.32162e18	−	5.75322e18i	−0.115882	−	0.200713i
$986$	−3.41373e19			−1.18312
$987$	1.29414e19	+	1.31041e19i	0.445573	+	0.451177i
$988$	−1.26979e19			−0.434322
$989$	5.20564e17	+	9.01642e17i	0.0176888	+	0.0306379i
$990$	1.46426e19	−	2.53617e19i	0.494297	−	0.856148i
$991$	2.40484e19	−	4.16530e19i	0.806505	−	1.39691i	−0.108765	−	0.994068i	$-0.534690\pi$
$991$	2.40484e19	−	4.16530e19i	0.806505	−	1.39691i	0.915270	−	0.402841i	$-0.131977\pi$
$992$	−1.59698e18	−	2.76605e18i	−0.0532077	−	0.0921584i
$993$	5.55970e19			1.84027
$994$	7.55443e18	−	2.75048e19i	0.248422	−	0.904477i
$995$	1.22718e19			0.400919
$996$	−1.71652e19	−	2.97310e19i	−0.557139	−	0.964994i
$997$	2.09456e19	−	3.62788e19i	0.675421	−	1.16986i	−0.300925	−	0.953648i	$-0.597295\pi$
$997$	2.09456e19	−	3.62788e19i	0.675421	−	1.16986i	0.976346	−	0.216215i	$-0.0693713\pi$
$998$	−1.14308e19	+	1.97987e19i	−0.366207	+	0.634289i
$999$	−1.67420e17	−	2.89980e17i	−0.00532884	−	0.00922982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.c.b.11.4	yes	8
3.2	odd	2		126.14.g.b.109.4		8
7.2	even	3	inner	14.14.c.b.9.4	✓	8
7.3	odd	6		98.14.a.j.1.4		4
7.4	even	3		98.14.a.h.1.1		4
7.5	odd	6		98.14.c.o.79.1		8
7.6	odd	2		98.14.c.o.67.1		8
21.2	odd	6		126.14.g.b.37.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.4	✓	8	7.2	even	3	inner
14.14.c.b.11.4	yes	8	1.1	even	1	trivial
98.14.a.h.1.1		4	7.4	even	3
98.14.a.j.1.4		4	7.3	odd	6
98.14.c.o.67.1		8	7.6	odd	2
98.14.c.o.79.1		8	7.5	odd	6
126.14.g.b.37.4		8	21.2	odd	6
126.14.g.b.109.4		8	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(32.0000 + 55.4256i) q^{2} +(888.214 - 1538.43i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-13071.0 - 22639.6i) q^{5} +113691. q^{6} +(-218721. - 221472. i) q^{7} -262144. q^{8} +(-780686. - 1.35219e6i) q^{9} +O(q^{10})\)	\(q+(32.0000 + 55.4256i) q^{2} +(888.214 - 1538.43i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-13071.0 - 22639.6i) q^{5} +113691. q^{6} +(-218721. - 221472. i) q^{7} -262144. q^{8} +(-780686. - 1.35219e6i) q^{9} +(836543. - 1.44893e6i) q^{10} +(-5.60522e6 + 9.70852e6i) q^{11} +(3.63812e6 + 6.30141e6i) q^{12} -1.74220e7 q^{13} +(5.27615e6 - 1.92099e7i) q^{14} -4.64393e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(8.48313e7 - 1.46932e8i) q^{17} +(4.99639e7 - 8.65400e7i) q^{18} +(-8.89700e7 - 1.54101e8i) q^{19} +1.07077e8 q^{20} +(-5.34991e8 + 1.39773e8i) q^{21} -7.17468e8 q^{22} +(2.23644e7 + 3.87364e7i) q^{23} +(-2.32840e8 + 4.03291e8i) q^{24} +(2.68651e8 - 4.65316e8i) q^{25} +(-5.57504e8 - 9.65626e8i) q^{26} +5.85356e7 q^{27} +(1.23356e9 - 3.22282e8i) q^{28} -3.14386e9 q^{29} +(-1.48606e9 - 2.57393e9i) q^{30} +(1.48731e9 - 2.57609e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(9.95727e9 + 1.72465e10i) q^{33} +1.08584e10 q^{34} +(-2.15514e9 + 7.84663e9i) q^{35} +6.39538e9 q^{36} +(-2.86014e9 - 4.95391e9i) q^{37} +(5.69408e9 - 9.86244e9i) q^{38} +(-1.54745e10 + 2.68026e10i) q^{39} +(3.42648e9 + 5.93484e9i) q^{40} +2.70618e10 q^{41} +(-2.48667e10 - 2.51795e10i) q^{42} +2.32764e10 q^{43} +(-2.29590e10 - 3.97661e10i) q^{44} +(-2.04087e10 + 3.53488e10i) q^{45} +(-1.43132e9 + 2.47913e9i) q^{46} +(-1.66537e10 - 2.88451e10i) q^{47} -2.98035e10 q^{48} +(-1.21086e9 + 9.68814e10i) q^{49} +3.43873e10 q^{50} +(-1.50697e11 - 2.61014e11i) q^{51} +(3.56803e10 - 6.18001e10i) q^{52} +(-1.01723e11 + 1.76189e11i) q^{53} +(1.87314e9 + 3.24437e9i) q^{54} +2.93063e11 q^{55} +(5.73365e10 + 5.80576e10i) q^{56} -3.16098e11 q^{57} +(-1.00603e11 - 1.74250e11i) q^{58} +(1.44370e11 - 2.50056e11i) q^{59} +(9.51077e10 - 1.64731e11i) q^{60} +(-1.05582e11 - 1.82874e11i) q^{61} +1.90375e11 q^{62} +(-1.28719e11 + 4.68653e11i) q^{63} +6.87195e10 q^{64} +(2.27723e11 + 3.94427e11i) q^{65} +(-6.37265e11 + 1.10378e12i) q^{66} +(2.96224e11 - 5.13074e11i) q^{67} +(3.47469e11 + 6.01834e11i) q^{68} +7.94576e10 q^{69} +(-5.03869e11 + 1.31642e11i) q^{70} +1.43181e12 q^{71} +(2.04652e11 + 3.54468e11i) q^{72} +(-3.23132e11 + 5.59681e11i) q^{73} +(1.83049e11 - 3.17050e11i) q^{74} +(-4.77238e11 - 8.26601e11i) q^{75} +7.28843e11 q^{76} +(3.37615e12 - 8.82062e11i) q^{77} -1.98073e12 q^{78} +(-9.00359e11 - 1.55947e12i) q^{79} +(-2.19295e11 + 3.79829e11i) q^{80} +(1.29666e12 - 2.24588e12i) q^{81} +(8.65979e11 + 1.49992e12i) q^{82} -4.71815e12 q^{83} +(5.99852e11 - 2.18400e12i) q^{84} -4.43531e12 q^{85} +(7.44845e11 + 1.29011e12i) q^{86} +(-2.79242e12 + 4.83661e12i) q^{87} +(1.46937e12 - 2.54503e12i) q^{88} +(-1.31611e12 - 2.27956e12i) q^{89} -2.61231e12 q^{90} +(3.81057e12 + 3.85849e12i) q^{91} -1.83210e11 q^{92} +(-2.64209e12 - 4.57624e12i) q^{93} +(1.06584e12 - 1.84609e12i) q^{94} +(-2.32585e12 + 4.02849e12i) q^{95} +(-9.53712e11 - 1.65188e12i) q^{96} -7.42070e12 q^{97} +(-5.40846e12 + 3.03309e12i) q^{98} +1.75037e13 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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