LMFDB - Embedded newform 98.14.c.o.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,14,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not 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:	$105.086310373$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.4
Root			$-35.6648 + 61.7733i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.14.c.o.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 + 55.4256i) q^{2} +(746.854 - 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(7178.20 + 12433.0i) q^{5} +95597.3 q^{6} -262144. q^{8} +(-318420. - 551520. i) q^{9} +O(q^{10})$	\(q+(32.0000 + 55.4256i) q^{2} +(746.854 - 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(7178.20 + 12433.0i) q^{5} +95597.3 q^{6} -262144. q^{8} +(-318420. - 551520. i) q^{9} +(-459405. + 795712. i) q^{10} +(2.14272e6 - 3.71130e6i) q^{11} +(3.05911e6 + 5.29854e6i) q^{12} -5.50861e6 q^{13} +2.14443e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(-1.98554e7 + 3.43905e7i) q^{17} +(2.03789e7 - 3.52973e7i) q^{18} +(2.25114e7 + 3.89910e7i) q^{19} -5.88038e7 q^{20} +2.74268e8 q^{22} +(-3.77343e8 - 6.53577e8i) q^{23} +(-1.95783e8 + 3.39107e8i) q^{24} +(5.07299e8 - 8.78667e8i) q^{25} +(-1.76275e8 - 3.05318e8i) q^{26} +1.43020e9 q^{27} -2.46353e9 q^{29} +(6.86216e8 + 1.18856e9i) q^{30} +(3.06703e9 - 5.31225e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(-3.20060e9 - 5.54359e9i) q^{33} -2.54149e9 q^{34} +2.60850e9 q^{36} +(9.52417e9 + 1.64963e10i) q^{37} +(-1.44073e9 + 2.49542e9i) q^{38} +(-4.11413e9 + 7.12588e9i) q^{39} +(-1.88172e9 - 3.25924e9i) q^{40} +4.23093e10 q^{41} -7.42867e10 q^{43} +(8.77657e9 + 1.52015e10i) q^{44} +(4.57137e9 - 7.91784e9i) q^{45} +(2.41499e10 - 4.18289e10i) q^{46} +(4.03508e10 + 6.98897e10i) q^{47} -2.50603e10 q^{48} +6.49342e10 q^{50} +(2.96581e10 + 5.13694e10i) q^{51} +(1.12816e10 - 1.95404e10i) q^{52} +(1.10539e11 - 1.91459e11i) q^{53} +(4.57664e10 + 7.92697e10i) q^{54} +6.15234e10 q^{55} +6.72511e10 q^{57} +(-7.88329e10 - 1.36543e11i) q^{58} +(2.29890e11 - 3.98181e11i) q^{59} +(-4.39178e10 + 7.60679e10i) q^{60} +(3.23925e10 + 5.61055e10i) q^{61} +3.92580e11 q^{62} +6.87195e10 q^{64} +(-3.95419e10 - 6.84885e10i) q^{65} +(2.04838e11 - 3.54790e11i) q^{66} +(2.07214e11 - 3.58905e11i) q^{67} +(-8.13276e10 - 1.40864e11i) q^{68} -1.12728e12 q^{69} -6.38110e11 q^{71} +(8.34720e10 + 1.44578e11i) q^{72} +(2.92998e11 - 5.07488e11i) q^{73} +(-6.09547e11 + 1.05577e12i) q^{74} +(-7.57756e11 - 1.31247e12i) q^{75} -1.84414e11 q^{76} -5.26608e11 q^{78} +(-1.22943e12 - 2.12943e12i) q^{79} +(1.20430e11 - 2.08591e11i) q^{80} +(1.57581e12 - 2.72939e12i) q^{81} +(1.35390e12 + 2.34502e12i) q^{82} -3.32114e12 q^{83} -5.70103e11 q^{85} +(-2.37717e12 - 4.11739e12i) q^{86} +(-1.83990e12 + 3.18679e12i) q^{87} +(-5.61701e11 + 9.72894e11i) q^{88} +(-1.39203e12 - 2.41106e12i) q^{89} +5.85135e11 q^{90} +3.09119e12 q^{92} +(-4.58125e12 - 7.93495e12i) q^{93} +(-2.58245e12 + 4.47294e12i) q^{94} +(-3.23183e11 + 5.59770e11i) q^{95} +(-8.01928e11 - 1.38898e12i) q^{96} +7.80467e12 q^{97} -2.72914e12 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} - 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 - 2097152 * q^8 + 599840 * q^9	\( 8 q + 256 q^{2} - 182 q^{3} - 16384 q^{4} - 1792 q^{5} - 23296 q^{6} - 2097152 q^{8} + 599840 q^{9} + 114688 q^{10} - 8726914 q^{11} - 745472 q^{12} - 1438416 q^{13} - 136873212 q^{15} - 67108864 q^{16} + 7943068 q^{17} - 38389760 q^{18} + 215706806 q^{19} + 14680064 q^{20} - 1117044992 q^{22} - 61927978 q^{23} + 47710208 q^{24} - 1327844792 q^{25} - 46029312 q^{26} + 3268643812 q^{27} - 6325846064 q^{29} - 4379942784 q^{30} - 6113775570 q^{31} + 4294967296 q^{32} - 25235960652 q^{33} + 1016712704 q^{34} - 4913889280 q^{36} - 3945652880 q^{37} - 13805235584 q^{38} - 23545599116 q^{39} + 469762048 q^{40} - 86378579952 q^{41} - 109074124256 q^{43} - 35745439744 q^{44} + 104964468168 q^{45} + 3963390592 q^{46} + 3141202722 q^{47} + 6106906624 q^{48} - 169964133376 q^{50} - 241278267462 q^{51} + 2945875968 q^{52} + 149625680376 q^{53} + 104596601984 q^{54} - 174912009748 q^{55} - 128207489960 q^{57} - 202427074048 q^{58} + 866297313938 q^{59} + 280316338176 q^{60} + 477908594184 q^{61} - 782563272960 q^{62} + 549755813888 q^{64} - 1099748343120 q^{65} + 1615101481728 q^{66} + 1895501016278 q^{67} + 32534806528 q^{68} - 3503301895632 q^{69} + 638832672128 q^{71} - 157244456960 q^{72} + 2966596192756 q^{73} + 252521784320 q^{74} + 1331079867376 q^{75} - 1767070154752 q^{76} - 3013836686848 q^{78} - 6505959677634 q^{79} - 30064771072 q^{80} + 2449216493684 q^{81} - 2764114558464 q^{82} + 3379817135968 q^{83} - 16684556982464 q^{85} - 3490371976192 q^{86} + 5273311164492 q^{87} + 2287708143616 q^{88} - 9586601667468 q^{89} + 13435451925504 q^{90} + 507313995776 q^{92} - 14195747226896 q^{93} - 201036974208 q^{94} + 14384410136978 q^{95} + 195421011968 q^{96} + 44560735311568 q^{97} + 24706419985464 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 - 182 * q^3 - 16384 * q^4 - 1792 * q^5 - 23296 * q^6 - 2097152 * q^8 + 599840 * q^9 + 114688 * q^10 - 8726914 * q^11 - 745472 * q^12 - 1438416 * q^13 - 136873212 * q^15 - 67108864 * q^16 + 7943068 * q^17 - 38389760 * q^18 + 215706806 * q^19 + 14680064 * q^20 - 1117044992 * q^22 - 61927978 * q^23 + 47710208 * q^24 - 1327844792 * q^25 - 46029312 * q^26 + 3268643812 * q^27 - 6325846064 * q^29 - 4379942784 * q^30 - 6113775570 * q^31 + 4294967296 * q^32 - 25235960652 * q^33 + 1016712704 * q^34 - 4913889280 * q^36 - 3945652880 * q^37 - 13805235584 * q^38 - 23545599116 * q^39 + 469762048 * q^40 - 86378579952 * q^41 - 109074124256 * q^43 - 35745439744 * q^44 + 104964468168 * q^45 + 3963390592 * q^46 + 3141202722 * q^47 + 6106906624 * q^48 - 169964133376 * q^50 - 241278267462 * q^51 + 2945875968 * q^52 + 149625680376 * q^53 + 104596601984 * q^54 - 174912009748 * q^55 - 128207489960 * q^57 - 202427074048 * q^58 + 866297313938 * q^59 + 280316338176 * q^60 + 477908594184 * q^61 - 782563272960 * q^62 + 549755813888 * q^64 - 1099748343120 * q^65 + 1615101481728 * q^66 + 1895501016278 * q^67 + 32534806528 * q^68 - 3503301895632 * q^69 + 638832672128 * q^71 - 157244456960 * q^72 + 2966596192756 * q^73 + 252521784320 * q^74 + 1331079867376 * q^75 - 1767070154752 * q^76 - 3013836686848 * q^78 - 6505959677634 * q^79 - 30064771072 * q^80 + 2449216493684 * q^81 - 2764114558464 * q^82 + 3379817135968 * q^83 - 16684556982464 * q^85 - 3490371976192 * q^86 + 5273311164492 * q^87 + 2287708143616 * q^88 - 9586601667468 * q^89 + 13435451925504 * q^90 + 507313995776 * q^92 - 14195747226896 * q^93 - 201036974208 * q^94 + 14384410136978 * q^95 + 195421011968 * q^96 + 44560735311568 * q^97 + 24706419985464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

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
$3$	746.854	−	1293.59i	0.591490	−	1.02449i	−0.402542	−	0.915402i	$-0.631873\pi$
$3$	746.854	−	1293.59i	0.591490	−	1.02449i	0.994032	−	0.109090i	$-0.0347935\pi$
$4$	−2048.00	+	3547.24i	−0.250000	+	0.433013i
$5$	7178.20	+	12433.0i	0.205452	+	0.355853i	0.950277	−	0.311407i	$-0.100800\pi$
$5$	7178.20	+	12433.0i	0.205452	+	0.355853i	−0.744825	+	0.667260i	$0.767467\pi$
$6$	95597.3			0.836494
$7$		0			0
$7$		0			0
$8$	−262144.			−0.353553
$9$	−318420.	−	551520.i	−0.199721	−	0.345928i
$10$	−459405.	+	795712.i	−0.145276	+	0.251626i
$11$	2.14272e6	−	3.71130e6i	0.364681	−	0.631645i	−0.624044	−	0.781389i	$-0.714512\pi$
$11$	2.14272e6	−	3.71130e6i	0.364681	−	0.631645i	0.988725	+	0.149744i	$0.0478449\pi$
$12$	3.05911e6	+	5.29854e6i	0.295745	+	0.512246i
$13$	−5.50861e6			−0.316527			−0.158263	−	0.987397i	$-0.550589\pi$
$13$	−5.50861e6			−0.316527			−0.158263	+	0.987397i	$0.550589\pi$
$14$		0			0
$15$	2.14443e7			0.486091
$16$	−8.38861e6	−	1.45295e7i	−0.125000	−	0.216506i
$17$	−1.98554e7	+	3.43905e7i	−0.199508	+	0.345558i	−0.948369	−	0.317169i	$-0.897268\pi$
$17$	−1.98554e7	+	3.43905e7i	−0.199508	+	0.345558i	0.748861	+	0.662727i	$0.230601\pi$
$18$	2.03789e7	−	3.52973e7i	0.141224	−	0.244608i
$19$	2.25114e7	+	3.89910e7i	0.109775	+	0.190137i	0.915679	−	0.401910i	$-0.131654\pi$
$19$	2.25114e7	+	3.89910e7i	0.109775	+	0.190137i	−0.805904	+	0.592046i	$0.798320\pi$
$20$	−5.88038e7			−0.205452
$21$		0			0
$22$	2.74268e8			0.515736
$23$	−3.77343e8	−	6.53577e8i	−0.531502	−	0.920589i	−0.999324	−	0.0367661i	$-0.988294\pi$
$23$	−3.77343e8	−	6.53577e8i	−0.531502	−	0.920589i	0.467822	−	0.883823i	$-0.345039\pi$
$24$	−1.95783e8	+	3.39107e8i	−0.209123	+	0.362212i
$25$	5.07299e8	−	8.78667e8i	0.415579	−	0.719804i
$26$	−1.76275e8	−	3.05318e8i	−0.111909	−	0.193832i
$27$	1.43020e9			0.710447
$28$		0			0
$29$	−2.46353e9			−0.769078			−0.384539	−	0.923109i	$-0.625640\pi$
$29$	−2.46353e9			−0.769078			−0.384539	+	0.923109i	$0.625640\pi$
$30$	6.86216e8	+	1.18856e9i	0.171859	+	0.297669i
$31$	3.06703e9	−	5.31225e9i	0.620679	−	1.07505i	−0.368681	−	0.929556i	$-0.620190\pi$
$31$	3.06703e9	−	5.31225e9i	0.620679	−	1.07505i	0.989360	−	0.145491i	$-0.0464762\pi$
$32$	5.36871e8	−	9.29888e8i	0.0883883	−	0.153093i
$33$	−3.20060e9	−	5.54359e9i	−0.431410	−	0.747224i
$34$	−2.54149e9			−0.282147
$35$		0			0
$36$	2.60850e9			0.199721
$37$	9.52417e9	+	1.64963e10i	0.610261	+	1.05700i	0.991196	+	0.132401i	$0.0422688\pi$
$37$	9.52417e9	+	1.64963e10i	0.610261	+	1.05700i	−0.380935	+	0.924602i	$0.624398\pi$
$38$	−1.44073e9	+	2.49542e9i	−0.0776229	+	0.134447i
$39$	−4.11413e9	+	7.12588e9i	−0.187222	+	0.324279i
$40$	−1.88172e9	−	3.25924e9i	−0.0726382	−	0.125813i
$41$	4.23093e10			1.39104			0.695522	−	0.718505i	$-0.255173\pi$
$41$	4.23093e10			1.39104			0.695522	+	0.718505i	$0.255173\pi$
$42$		0			0
$43$	−7.42867e10			−1.79212			−0.896058	−	0.443937i	$-0.853581\pi$
$43$	−7.42867e10			−1.79212			−0.896058	+	0.443937i	$0.853581\pi$
$44$	8.77657e9	+	1.52015e10i	0.182340	+	0.315823i
$45$	4.57137e9	−	7.91784e9i	0.0820663	−	0.142143i
$46$	2.41499e10	−	4.18289e10i	0.375829	−	0.650955i
$47$	4.03508e10	+	6.98897e10i	0.546030	+	0.945751i	0.998541	+	0.0539926i	$0.0171947\pi$
$47$	4.03508e10	+	6.98897e10i	0.546030	+	0.945751i	−0.452512	+	0.891758i	$0.649472\pi$
$48$	−2.50603e10			−0.295745
$49$		0			0
$50$	6.49342e10			0.587717
$51$	2.96581e10	+	5.13694e10i	0.236014	+	0.408788i
$52$	1.12816e10	−	1.95404e10i	0.0791316	−	0.137060i
$53$	1.10539e11	−	1.91459e11i	0.685049	−	1.18654i	−0.288372	−	0.957518i	$-0.593114\pi$
$53$	1.10539e11	−	1.91459e11i	0.685049	−	1.18654i	0.973421	−	0.229021i	$-0.0735526\pi$
$54$	4.57664e10	+	7.92697e10i	0.251181	+	0.435058i
$55$	6.15234e10			0.299697
$56$		0			0
$57$	6.72511e10			0.259724
$58$	−7.88329e10	−	1.36543e11i	−0.271910	−	0.470962i
$59$	2.29890e11	−	3.98181e11i	0.709548	−	1.22897i	−0.255477	−	0.966815i	$-0.582233\pi$
$59$	2.29890e11	−	3.98181e11i	0.709548	−	1.22897i	0.965025	−	0.262158i	$-0.0844342\pi$
$60$	−4.39178e10	+	7.60679e10i	−0.121523	+	0.210484i
$61$	3.23925e10	+	5.61055e10i	0.0805009	+	0.139432i	0.903465	−	0.428661i	$-0.141015\pi$
$61$	3.23925e10	+	5.61055e10i	0.0805009	+	0.139432i	−0.822964	+	0.568093i	$0.807681\pi$
$62$	3.92580e11			0.877772
$63$		0			0
$64$	6.87195e10			0.125000
$65$	−3.95419e10	−	6.84885e10i	−0.0650310	−	0.112637i
$66$	2.04838e11	−	3.54790e11i	0.305053	−	0.528367i
$67$	2.07214e11	−	3.58905e11i	0.279855	−	0.484722i	−0.691494	−	0.722382i	$-0.743047\pi$
$67$	2.07214e11	−	3.58905e11i	0.279855	−	0.484722i	0.971348	+	0.237660i	$0.0763804\pi$
$68$	−8.13276e10	−	1.40864e11i	−0.0997540	−	0.172779i
$69$	−1.12728e12			−1.25751
$70$		0			0
$71$	−6.38110e11			−0.591175			−0.295588	−	0.955316i	$-0.595515\pi$
$71$	−6.38110e11			−0.591175			−0.295588	+	0.955316i	$0.595515\pi$
$72$	8.34720e10	+	1.44578e11i	0.0706122	+	0.122304i
$73$	2.92998e11	−	5.07488e11i	0.226603	−	0.392488i	−0.730196	−	0.683238i	$-0.760571\pi$
$73$	2.92998e11	−	5.07488e11i	0.226603	−	0.392488i	0.956799	+	0.290749i	$0.0939046\pi$
$74$	−6.09547e11	+	1.05577e12i	−0.431520	+	0.747414i
$75$	−7.57756e11	−	1.31247e12i	−0.491622	−	0.851514i
$76$	−1.84414e11			−0.109775
$77$		0			0
$78$	−5.26608e11			−0.264772
$79$	−1.22943e12	−	2.12943e12i	−0.569019	−	0.985571i	−0.996663	−	0.0816233i	$-0.973990\pi$
$79$	−1.22943e12	−	2.12943e12i	−0.569019	−	0.985571i	0.427644	−	0.903947i	$-0.359344\pi$
$80$	1.20430e11	−	2.08591e11i	0.0513630	−	0.0889633i
$81$	1.57581e12	−	2.72939e12i	0.619944	−	1.07377i
$82$	1.35390e12	+	2.34502e12i	0.491808	+	0.851837i
$83$	−3.32114e12			−1.11501			−0.557506	−	0.830173i	$-0.688242\pi$
$83$	−3.32114e12			−1.11501			−0.557506	+	0.830173i	$0.688242\pi$
$84$		0			0
$85$	−5.70103e11			−0.163957
$86$	−2.37717e12	−	4.11739e12i	−0.633609	−	1.09744i
$87$	−1.83990e12	+	3.18679e12i	−0.454902	+	0.787913i
$88$	−5.61701e11	+	9.72894e11i	−0.128934	+	0.223320i
$89$	−1.39203e12	−	2.41106e12i	−0.296902	−	0.514249i	0.678523	−	0.734579i	$-0.262620\pi$
$89$	−1.39203e12	−	2.41106e12i	−0.296902	−	0.514249i	−0.975426	+	0.220329i	$0.929287\pi$
$90$	5.85135e11			0.116059
$91$		0			0
$92$	3.09119e12			0.531502
$93$	−4.58125e12	−	7.93495e12i	−0.734251	−	1.27176i
$94$	−2.58245e12	+	4.47294e12i	−0.386101	+	0.668747i
$95$	−3.23183e11	+	5.59770e11i	−0.0451071	+	0.0781279i
$96$	−8.01928e11	−	1.38898e12i	−0.104562	−	0.181106i
$97$	7.80467e12			0.951345			0.475672	−	0.879622i	$-0.342205\pi$
$97$	7.80467e12			0.951345			0.475672	+	0.879622i	$0.342205\pi$
$98$		0			0
$99$	−2.72914e12			−0.291338
$100$	2.07789e12	+	3.59902e12i	0.207789	+	0.359902i
$101$	6.58305e12	−	1.14022e13i	0.617076	−	1.06881i	−0.372941	−	0.927855i	$-0.621651\pi$
$101$	6.58305e12	−	1.14022e13i	0.617076	−	1.06881i	0.990017	−	0.140951i	$-0.0450160\pi$
$102$	−1.89812e12	+	3.28764e12i	−0.166887	+	0.289057i
$103$	−8.84393e12	−	1.53181e13i	−0.729799	−	1.26405i	−0.956968	−	0.290194i	$-0.906280\pi$
$103$	−8.84393e12	−	1.53181e13i	−0.729799	−	1.26405i	0.227168	−	0.973855i	$-0.427053\pi$
$104$	1.44405e12			0.111909
$105$		0			0
$106$	1.41490e13			0.968806
$107$	7.23079e12	+	1.25241e13i	0.465791	+	0.806774i	0.999237	−	0.0390602i	$-0.0124364\pi$
$107$	7.23079e12	+	1.25241e13i	0.465791	+	0.806774i	−0.533446	+	0.845834i	$0.679103\pi$
$108$	−2.92905e12	+	5.07326e12i	−0.177612	+	0.307633i
$109$	7.96586e12	−	1.37973e13i	0.454947	−	0.787991i	−0.543738	−	0.839255i	$-0.682992\pi$
$109$	7.96586e12	−	1.37973e13i	0.454947	−	0.787991i	0.998685	+	0.0512639i	$0.0163250\pi$
$110$	1.96875e12	+	3.40997e12i	0.105959	+	0.183526i
$111$	2.84526e13			1.44385
$112$		0			0
$113$	4.86885e12			0.219997			0.109998	−	0.993932i	$-0.464915\pi$
$113$	4.86885e12			0.219997			0.109998	+	0.993932i	$0.464915\pi$
$114$	2.15203e12	+	3.72743e12i	0.0918264	+	0.159048i
$115$	5.41728e12	−	9.38301e12i	0.218396	−	0.378274i
$116$	5.04530e12	−	8.73872e12i	0.192269	−	0.333020i
$117$	1.75405e12	+	3.03811e12i	0.0632171	+	0.109495i
$118$	2.94259e13			1.00345
$119$		0			0
$120$	−5.62148e12			−0.171859
$121$	8.07887e12	+	1.39930e13i	0.234016	+	0.405328i
$122$	−2.07312e12	+	3.59075e12i	−0.0569227	+	0.0985930i
$123$	3.15989e13	−	5.47309e13i	0.822789	−	1.42511i
$124$	1.25626e13	+	2.17590e13i	0.310339	+	0.537524i
$125$	3.20908e13			0.752430
$126$		0			0
$127$	1.02773e12			0.0217347			0.0108674	−	0.999941i	$-0.496541\pi$
$127$	1.02773e12			0.0217347			0.0108674	+	0.999941i	$0.496541\pi$
$128$	2.19902e12	+	3.80882e12i	0.0441942	+	0.0765466i
$129$	−5.54813e13	+	9.60965e13i	−1.06002	+	1.83601i
$130$	2.53068e12	−	4.38327e12i	0.0459839	−	0.0796464i
$131$	−3.08691e13	−	5.34668e13i	−0.533654	−	0.924317i	−0.999227	−	0.0393070i	$-0.987485\pi$
$131$	−3.08691e13	−	5.34668e13i	−0.533654	−	0.924317i	0.465573	−	0.885010i	$-0.345848\pi$
$132$	2.62193e13			0.431410
$133$		0			0
$134$	2.65234e13			0.395774
$135$	1.02662e13	+	1.77817e13i	0.145963	+	0.252815i
$136$	5.20497e12	−	9.01527e12i	0.0705367	−	0.122173i
$137$	6.61761e13	−	1.14620e14i	0.855102	−	1.48108i	−0.0214489	−	0.999770i	$-0.506828\pi$
$137$	6.61761e13	−	1.14620e14i	0.855102	−	1.48108i	0.876551	−	0.481310i	$-0.159839\pi$
$138$	−3.60730e13	−	6.24802e13i	−0.444598	−	0.770067i
$139$	1.66284e14			1.95548			0.977742	−	0.209810i	$-0.0672845\pi$
$139$	1.66284e14			1.95548			0.977742	+	0.209810i	$0.0672845\pi$
$140$		0			0
$141$	1.20545e14			1.29188
$142$	−2.04195e13	−	3.53676e13i	−0.209012	−	0.362019i
$143$	−1.18034e13	+	2.04441e13i	−0.115431	+	0.199932i
$144$	−5.34221e12	+	9.25298e12i	−0.0499304	+	0.0864819i
$145$	−1.76837e13	−	3.06290e13i	−0.158009	−	0.273679i
$146$	3.75038e13			0.320465
$147$		0			0
$148$	−7.80220e13			−0.610261
$149$	−8.54482e13	−	1.48001e14i	−0.639723	−	1.10803i	−0.985493	−	0.169714i	$-0.945716\pi$
$149$	−8.54482e13	−	1.48001e14i	−0.639723	−	1.10803i	0.345770	−	0.938319i	$-0.387618\pi$
$150$	4.84964e13	−	8.39982e13i	0.347629	−	0.602111i
$151$	−1.34805e14	+	2.33490e14i	−0.925458	+	1.60294i	−0.134635	+	0.990895i	$0.542986\pi$
$151$	−1.34805e14	+	2.33490e14i	−0.925458	+	1.60294i	−0.790823	+	0.612045i	$0.790347\pi$
$152$	−5.90124e12	−	1.02212e13i	−0.0388115	−	0.0672234i
$153$	2.52894e13			0.159384
$154$		0			0
$155$	8.80630e13			0.510079
$156$	−1.68515e13	−	2.91876e13i	−0.0936112	−	0.162139i
$157$	−2.65409e13	+	4.59702e13i	−0.141439	+	0.244979i	−0.928039	−	0.372484i	$-0.878506\pi$
$157$	−2.65409e13	+	4.59702e13i	−0.141439	+	0.244979i	0.786600	+	0.617463i	$0.211839\pi$
$158$	7.86834e13	−	1.36284e14i	0.402358	−	0.696904i
$159$	−1.65113e14	−	2.85984e14i	−0.810400	−	1.40365i
$160$	1.54151e13			0.0726382
$161$		0			0
$162$	2.01704e14			0.876733
$163$	−1.25923e14	−	2.18105e14i	−0.525878	−	0.910847i	−0.999546	−	0.0301433i	$-0.990404\pi$
$163$	−1.25923e14	−	2.18105e14i	−0.525878	−	0.910847i	0.473668	−	0.880704i	$-0.342930\pi$
$164$	−8.66495e13	+	1.50081e14i	−0.347761	+	0.602340i
$165$	4.59490e13	−	7.95860e13i	0.177268	−	0.307037i
$166$	−1.06277e14	−	1.84076e14i	−0.394216	−	0.682803i
$167$	5.21452e12			0.0186019			0.00930095	−	0.999957i	$-0.497039\pi$
$167$	5.21452e12			0.0186019			0.00930095	+	0.999957i	$0.497039\pi$
$168$		0			0
$169$	−2.72530e14			−0.899811
$170$	−1.82433e13	−	3.15983e13i	−0.0579676	−	0.100403i
$171$	1.43362e13	−	2.48310e13i	0.0438490	−	0.0759487i
$172$	1.52139e14	−	2.63513e14i	0.448029	−	0.776009i
$173$	1.31565e14	+	2.27877e14i	0.373113	+	0.646251i	0.990043	−	0.140767i	$-0.0449569\pi$
$173$	1.31565e14	+	2.27877e14i	0.373113	+	0.646251i	−0.616929	+	0.787019i	$0.711624\pi$
$174$	−2.35507e14			−0.643329
$175$		0			0
$176$	−7.18977e13			−0.182340
$177$	−3.43388e14	−	5.94766e14i	−0.839381	−	1.45385i
$178$	8.90899e13	−	1.54308e14i	0.209941	−	0.363629i
$179$	1.81035e14	−	3.13562e14i	0.411357	−	0.712490i	−0.583682	−	0.811982i	$-0.698388\pi$
$179$	1.81035e14	−	3.13562e14i	0.411357	−	0.712490i	0.995038	+	0.0994921i	$0.0317218\pi$
$180$	1.87243e13	+	3.24315e13i	0.0410332	+	0.0710715i
$181$	6.76438e14			1.42994			0.714969	−	0.699156i	$-0.246441\pi$
$181$	6.76438e14			1.42994			0.714969	+	0.699156i	$0.246441\pi$
$182$		0			0
$183$	9.67699e13			0.190462
$184$	9.89182e13	+	1.71331e14i	0.187914	+	0.325477i
$185$	−1.36733e14	+	2.36828e14i	−0.250759	+	0.434327i
$186$	2.93200e14	−	5.07837e14i	0.519194	−	0.899270i
$187$	8.50890e13	+	1.47378e14i	0.145513	+	0.252037i
$188$	−3.30554e14			−0.546030
$189$		0			0
$190$	−4.13674e13			−0.0637911
$191$	3.80180e14	+	6.58492e14i	0.566595	+	0.981372i	0.996899	+	0.0786877i	$0.0250730\pi$
$191$	3.80180e14	+	6.58492e14i	0.566595	+	0.981372i	−0.430304	+	0.902684i	$0.641594\pi$
$192$	5.13234e13	−	8.88948e13i	0.0739363	−	0.128061i
$193$	3.21102e12	−	5.56164e12i	0.00447219	−	0.00774605i	−0.863781	−	0.503868i	$-0.831910\pi$
$193$	3.21102e12	−	5.56164e12i	0.00447219	−	0.00774605i	0.868253	+	0.496122i	$0.165243\pi$
$194$	2.49749e14	+	4.32578e14i	0.336351	+	0.582577i
$195$	−1.18128e14			−0.153861
$196$		0			0
$197$	4.19711e14			0.511588			0.255794	−	0.966731i	$-0.417663\pi$
$197$	4.19711e14			0.511588			0.255794	+	0.966731i	$0.417663\pi$
$198$	−8.73325e13	−	1.51264e14i	−0.103004	−	0.178407i
$199$	7.53847e14	−	1.30570e15i	0.860475	−	1.49039i	−0.0109964	−	0.999940i	$-0.503500\pi$
$199$	7.53847e14	−	1.30570e15i	0.860475	−	1.49039i	0.871471	−	0.490447i	$-0.163166\pi$
$200$	−1.32985e14	+	2.30337e14i	−0.146929	+	0.254489i
$201$	−3.09517e14	−	5.36099e14i	−0.331062	−	0.573417i
$202$	8.42631e14			0.872677
$203$		0			0
$204$	−2.42960e14			−0.236014
$205$	3.03705e14	+	5.26032e14i	0.285793	+	0.495008i
$206$	5.66012e14	−	9.80361e14i	0.516046	−	0.893818i
$207$	−2.40307e14	+	4.16225e14i	−0.212305	+	0.367723i
$208$	4.62096e13	+	8.00373e13i	0.0395658	+	0.0685300i
$209$	1.92943e14			0.160132
$210$		0			0
$211$	−9.49543e14			−0.740762			−0.370381	−	0.928880i	$-0.620773\pi$
$211$	−9.49543e14			−0.740762			−0.370381	+	0.928880i	$0.620773\pi$
$212$	4.52767e14	+	7.84215e14i	0.342525	+	0.593270i
$213$	−4.76575e14	+	8.25452e14i	−0.349674	+	0.605654i
$214$	−4.62771e14	+	8.01543e14i	−0.329364	+	0.570476i
$215$	−5.33245e14	−	9.23607e14i	−0.368194	−	0.637730i
$216$	−3.74918e14			−0.251181
$217$		0			0
$218$	1.01963e15			0.643392
$219$	−4.37654e14	−	7.58038e14i	−0.268067	−	0.464306i
$220$	−1.26000e14	+	2.18238e14i	−0.0749243	+	0.129773i
$221$	1.09376e14	−	1.89444e14i	0.0631496	−	0.109378i
$222$	9.10485e14	+	1.57701e15i	0.510479	+	0.884176i
$223$	−6.07949e14			−0.331044			−0.165522	−	0.986206i	$-0.552931\pi$
$223$	−6.07949e14			−0.331044			−0.165522	+	0.986206i	$0.552931\pi$
$224$		0			0
$225$	−6.46137e14			−0.332000
$226$	1.55803e14	+	2.69859e14i	0.0777806	+	0.134720i
$227$	−1.39309e15	+	2.41290e15i	−0.675788	+	1.17050i	0.300450	+	0.953798i	$0.402863\pi$
$227$	−1.39309e15	+	2.41290e15i	−0.675788	+	1.17050i	−0.976238	+	0.216702i	$0.930470\pi$
$228$	−1.37730e14	+	2.38556e14i	−0.0649311	+	0.112464i
$229$	5.67556e14	+	9.83036e14i	0.260063	+	0.450442i	0.966258	−	0.257575i	$-0.0829235\pi$
$229$	5.67556e14	+	9.83036e14i	0.260063	+	0.450442i	−0.706196	+	0.708017i	$0.749590\pi$
$230$	6.93412e14			0.308859
$231$		0			0
$232$	6.45799e14			0.271910
$233$	1.01995e15	+	1.76660e15i	0.417604	+	0.723312i	0.995698	−	0.0926588i	$-0.0295366\pi$
$233$	1.01995e15	+	1.76660e15i	0.417604	+	0.723312i	−0.578094	+	0.815970i	$0.696203\pi$
$234$	−1.12259e14	+	1.94439e14i	−0.0447013	+	0.0774249i
$235$	−5.79292e14	+	1.00336e15i	−0.224366	+	0.388613i
$236$	9.41629e14	+	1.63095e15i	0.354774	+	0.614487i
$237$	−3.67281e15			−1.34628
$238$		0			0
$239$	−3.57648e15			−1.24128			−0.620639	−	0.784096i	$-0.713127\pi$
$239$	−3.57648e15			−1.24128			−0.620639	+	0.784096i	$0.713127\pi$
$240$	−1.79888e14	−	3.11574e14i	−0.0607614	−	0.105242i
$241$	−9.08192e14	+	1.57304e15i	−0.298584	+	0.517163i	−0.975812	−	0.218610i	$-0.929848\pi$
$241$	−9.08192e14	+	1.57304e15i	−0.298584	+	0.517163i	0.677228	+	0.735773i	$0.263181\pi$
$242$	−5.17048e14	+	8.95553e14i	−0.165474	+	0.286610i
$243$	−1.21371e15	−	2.10220e15i	−0.378158	−	0.654989i
$244$	−2.65359e14			−0.0805009
$245$		0			0
$246$	4.04466e15			1.16360
$247$	−1.24007e14	−	2.14786e14i	−0.0347468	−	0.0601833i
$248$	−8.04003e14	+	1.39257e15i	−0.219443	+	0.380087i
$249$	−2.48041e15	+	4.29619e15i	−0.659519	+	1.14232i
$250$	1.02691e15	+	1.77866e15i	0.266024	+	0.460767i
$251$	−5.30330e15			−1.33865			−0.669325	−	0.742970i	$-0.733417\pi$
$251$	−5.30330e15			−1.33865			−0.669325	+	0.742970i	$0.733417\pi$
$252$		0			0
$253$	−3.23416e15			−0.775314
$254$	3.28873e13	+	5.69625e13i	0.00768439	+	0.0133098i
$255$	−4.25784e14	+	7.37479e14i	−0.0969791	+	0.167973i
$256$	−1.40737e14	+	2.43764e14i	−0.0312500	+	0.0541266i
$257$	−1.07805e15	−	1.86724e15i	−0.233385	−	0.404235i	0.725417	−	0.688310i	$-0.241647\pi$
$257$	−1.07805e15	−	1.86724e15i	−0.233385	−	0.404235i	−0.958802	+	0.284074i	$0.908314\pi$
$258$	−7.10161e15			−1.49909
$259$		0			0
$260$	3.23927e14			0.0650310
$261$	7.84437e14	+	1.35869e15i	0.153601	+	0.266045i
$262$	1.97562e15	−	3.42188e15i	0.377351	−	0.653591i
$263$	−2.88067e15	+	4.98946e15i	−0.536761	+	0.929697i	0.462315	+	0.886716i	$0.347019\pi$
$263$	−2.88067e15	+	4.98946e15i	−0.536761	+	0.929697i	−0.999076	+	0.0429812i	$0.986314\pi$
$264$	8.39017e14	+	1.45322e15i	0.152526	+	0.264184i
$265$	3.17388e15			0.562979
$266$		0			0
$267$	−4.15857e15			−0.702459
$268$	8.48748e14	+	1.47007e15i	0.139927	+	0.242361i
$269$	4.23859e15	−	7.34146e15i	0.682074	−	1.18139i	−0.292272	−	0.956335i	$-0.594411\pi$
$269$	4.23859e15	−	7.34146e15i	0.682074	−	1.18139i	0.974347	−	0.225052i	$-0.0722553\pi$
$270$	−6.57040e14	+	1.13803e15i	−0.103211	+	0.178767i
$271$	−4.24299e14	−	7.34908e14i	−0.0650687	−	0.112702i	0.831656	−	0.555292i	$-0.187393\pi$
$271$	−4.24299e14	−	7.34908e14i	−0.0650687	−	0.112702i	−0.896724	+	0.442589i	$0.854060\pi$
$272$	6.66236e14			0.0997540
$273$		0			0
$274$	8.47055e15			1.20930
$275$	−2.17400e15	−	3.76547e15i	−0.303107	−	0.524997i
$276$	2.30867e15	−	3.99873e15i	0.314378	−	0.544519i
$277$	−3.47520e15	+	6.01923e15i	−0.462234	+	0.800613i	−0.999072	−	0.0430726i	$-0.986285\pi$
$277$	−3.47520e15	+	6.01923e15i	−0.462234	+	0.800613i	0.536838	+	0.843685i	$0.319619\pi$
$278$	5.32109e15	+	9.21640e15i	0.691368	+	1.19748i
$279$	−3.90642e15			−0.495851
$280$		0			0
$281$	−1.13665e15			−0.137732			−0.0688661	−	0.997626i	$-0.521938\pi$
$281$	−1.13665e15			−0.137732			−0.0688661	+	0.997626i	$0.521938\pi$
$282$	3.85743e15	+	6.68126e15i	0.456750	+	0.791115i
$283$	−5.46610e15	+	9.46756e15i	−0.632508	+	1.09554i	0.354530	+	0.935045i	$0.384641\pi$
$283$	−5.46610e15	+	9.46756e15i	−0.632508	+	1.09554i	−0.987037	+	0.160491i	$0.948692\pi$
$284$	1.30685e15	−	2.26353e15i	0.147794	−	0.255986i
$285$	4.82741e14	+	8.36133e14i	0.0533609	+	0.0924237i
$286$	−1.51083e15			−0.163244
$287$		0			0
$288$	−6.83803e14			−0.0706122
$289$	4.16382e15	+	7.21194e15i	0.420393	+	0.728142i
$290$	1.13176e15	−	1.96026e15i	0.111729	−	0.193520i
$291$	5.82895e15	−	1.00960e16i	0.562711	−	0.974644i
$292$	1.20012e15	+	2.07867e15i	0.113302	+	0.196244i
$293$	1.63957e15			0.151388			0.0756940	−	0.997131i	$-0.475883\pi$
$293$	1.63957e15			0.151388			0.0756940	+	0.997131i	$0.475883\pi$
$294$		0			0
$295$	6.60078e15			0.583112
$296$	−2.49670e15	−	4.32442e15i	−0.215760	−	0.373707i
$297$	3.06451e15	−	5.30789e15i	0.259086	−	0.448751i
$298$	5.46868e15	−	9.47204e15i	0.452352	−	0.783497i
$299$	2.07863e15	+	3.60030e15i	0.168235	+	0.291391i
$300$	6.20754e15			0.491622
$301$		0			0
$302$	−1.72551e16			−1.30880
$303$	−9.83316e15	−	1.70315e16i	−0.729988	−	1.26438i
$304$	3.77679e14	−	6.54160e14i	0.0274438	−	0.0475341i
$305$	−4.65040e14	+	8.05472e14i	−0.0330781	+	0.0572930i
$306$	8.09262e14	+	1.40168e15i	0.0563508	+	0.0976024i
$307$	−5.69931e15			−0.388528			−0.194264	−	0.980949i	$-0.562232\pi$
$307$	−5.69931e15			−0.388528			−0.194264	+	0.980949i	$0.562232\pi$
$308$		0			0
$309$	−2.64205e16			−1.72668
$310$	2.81801e15	+	4.88094e15i	0.180340	+	0.312358i
$311$	−4.65552e15	+	8.06360e15i	−0.291760	+	0.505343i	−0.974226	−	0.225574i	$-0.927574\pi$
$311$	−4.65552e15	+	8.06360e15i	−0.291760	+	0.505343i	0.682466	+	0.730917i	$0.260907\pi$
$312$	1.07849e15	−	1.86801e15i	0.0661931	−	0.114650i
$313$	−2.82191e15	−	4.88770e15i	−0.169631	−	0.293810i	0.768659	−	0.639659i	$-0.220924\pi$
$313$	−2.82191e15	−	4.88770e15i	−0.169631	−	0.293810i	−0.938290	+	0.345849i	$0.887591\pi$
$314$	−3.39724e15			−0.200024
$315$		0			0
$316$	1.00715e16			0.569019
$317$	6.10586e15	+	1.05757e16i	0.337957	+	0.585359i	0.984048	−	0.177901i	$-0.0569308\pi$
$317$	6.10586e15	+	1.05757e16i	0.337957	+	0.585359i	−0.646091	+	0.763260i	$0.723597\pi$
$318$	1.05672e16	−	1.83030e16i	0.573039	−	0.992533i
$319$	−5.27864e15	+	9.14288e15i	−0.280468	+	0.485784i
$320$	4.93282e14	+	8.54389e14i	0.0256815	+	0.0444817i
$321$	2.16014e16			1.10204
$322$		0			0
$323$	−1.78789e15			−0.0876043
$324$	6.45454e15	+	1.11796e16i	0.309972	+	0.536887i
$325$	−2.79451e15	+	4.84023e15i	−0.131542	+	0.227837i
$326$	8.05906e15	−	1.39587e16i	0.371852	−	0.644066i
$327$	−1.18987e16	−	2.06091e16i	−0.538193	−	0.932178i
$328$	−1.10911e16			−0.491808
$329$		0			0
$330$	5.88147e15			0.250695
$331$	−6.64365e15	−	1.15071e16i	−0.277667	−	0.480934i	0.693137	−	0.720806i	$-0.256228\pi$
$331$	−6.64365e15	−	1.15071e16i	−0.277667	−	0.480934i	−0.970805	+	0.239872i	$0.922895\pi$
$332$	6.80170e15	−	1.17809e16i	0.278753	−	0.482815i
$333$	6.06538e15	−	1.05055e16i	0.243764	−	0.422212i
$334$	1.66865e14	+	2.89018e14i	0.00657676	+	0.0113913i
$335$	5.94968e15			0.229987
$336$		0			0
$337$	2.83215e16			1.05323			0.526614	−	0.850105i	$-0.323461\pi$
$337$	2.83215e16			1.05323			0.526614	+	0.850105i	$0.323461\pi$
$338$	−8.72097e15	−	1.51052e16i	−0.318131	−	0.551019i
$339$	3.63632e15	−	6.29829e15i	0.130126	−	0.225385i
$340$	1.16757e15	−	2.02229e15i	0.0409893	−	0.0709956i
$341$	−1.31436e16	−	2.27653e16i	−0.452699	−	0.784098i
$342$	1.83504e15			0.0620118
$343$		0			0
$344$	1.94738e16			0.633609
$345$	−8.09184e15	−	1.40155e16i	−0.258359	−	0.447490i
$346$	−8.42016e15	+	1.45841e16i	−0.263831	+	0.456969i
$347$	−2.42080e16	+	4.19294e16i	−0.744417	+	1.28937i	0.206049	+	0.978542i	$0.433939\pi$
$347$	−2.42080e16	+	4.19294e16i	−0.744417	+	1.28937i	−0.950467	+	0.310827i	$0.899394\pi$
$348$	−7.53621e15	−	1.30531e16i	−0.227451	−	0.393957i
$349$	3.92608e16			1.16304			0.581519	−	0.813533i	$-0.302459\pi$
$349$	3.92608e16			1.16304			0.581519	+	0.813533i	$0.302459\pi$
$350$		0			0
$351$	−7.87840e15			−0.224875
$352$	−2.30073e15	−	3.98497e15i	−0.0644670	−	0.111660i
$353$	−1.09539e16	+	1.89728e16i	−0.301325	+	0.521909i	−0.976436	−	0.215806i	$-0.930762\pi$
$353$	−1.09539e16	+	1.89728e16i	−0.301325	+	0.521909i	0.675112	+	0.737716i	$0.264095\pi$
$354$	2.19769e16	−	3.80650e16i	0.593532	−	1.02803i
$355$	−4.58048e15	−	7.93362e15i	−0.121458	−	0.210372i
$356$	1.14035e16			0.296902
$357$		0			0
$358$	2.31725e16			0.581746
$359$	−2.51750e16	−	4.36043e16i	−0.620662	−	1.07502i	−0.989363	−	0.145470i	$-0.953531\pi$
$359$	−2.51750e16	−	4.36043e16i	−0.620662	−	1.07502i	0.368701	−	0.929548i	$-0.379803\pi$
$360$	−1.19836e15	+	2.07562e15i	−0.0290148	+	0.0502552i
$361$	2.00130e16	−	3.46635e16i	0.475899	−	0.824281i
$362$	2.16460e16	+	3.74920e16i	0.505559	+	0.875655i
$363$	2.41350e16			0.553673
$364$		0			0
$365$	8.41279e15			0.186224
$366$	3.09664e15	+	5.36353e15i	0.0673385	+	0.116634i
$367$	−4.30705e16	+	7.46002e16i	−0.920132	+	1.59372i	−0.120923	+	0.992662i	$0.538585\pi$
$367$	−4.30705e16	+	7.46002e16i	−0.920132	+	1.59372i	−0.799209	+	0.601053i	$0.794748\pi$
$368$	−6.33076e15	+	1.09652e16i	−0.132876	+	0.230147i
$369$	−1.34722e16	−	2.33345e16i	−0.277821	−	0.481201i
$370$	−1.75018e16			−0.354626
$371$		0			0
$372$	3.75296e16			0.734251
$373$	−1.65426e16	−	2.86526e16i	−0.318051	−	0.550880i	0.662030	−	0.749477i	$-0.269695\pi$
$373$	−1.65426e16	−	2.86526e16i	−0.318051	−	0.550880i	−0.980081	+	0.198597i	$0.936362\pi$
$374$	−5.44569e15	+	9.43222e15i	−0.102893	+	0.178217i
$375$	2.39672e16	−	4.15124e16i	0.445055	−	0.770858i
$376$	−1.05777e16	−	1.83212e16i	−0.193051	−	0.334373i
$377$	1.35706e16			0.243434
$378$		0			0
$379$	2.13699e16			0.370380			0.185190	−	0.982703i	$-0.440710\pi$
$379$	2.13699e16			0.370380			0.185190	+	0.982703i	$0.440710\pi$
$380$	−1.32376e15	−	2.29282e15i	−0.0225536	−	0.0390639i
$381$	7.67564e14	−	1.32946e15i	0.0128559	−	0.0222670i
$382$	−2.43315e16	+	4.21435e16i	−0.400643	+	0.693935i
$383$	−1.11443e16	−	1.93025e16i	−0.180410	−	0.312479i	0.761610	−	0.648035i	$-0.224409\pi$
$383$	−1.11443e16	−	1.93025e16i	−0.180410	−	0.312479i	−0.942020	+	0.335556i	$0.891076\pi$
$384$	6.56940e15			0.104562
$385$		0			0
$386$	4.11010e14			0.00632463
$387$	2.36544e16	+	4.09706e16i	0.357924	+	0.619943i
$388$	−1.59840e16	+	2.76850e16i	−0.237836	+	0.411944i
$389$	1.09136e16	−	1.89028e16i	0.159696	−	0.276602i	−0.775063	−	0.631884i	$-0.782282\pi$
$389$	1.09136e16	−	1.89028e16i	0.159696	−	0.276602i	0.934759	+	0.355282i	$0.115615\pi$
$390$	−3.78010e15	−	6.54732e15i	−0.0543980	−	0.0942201i
$391$	2.99691e16			0.424156
$392$		0			0
$393$	−9.22188e16			−1.26261
$394$	1.34308e16	+	2.32628e16i	0.180874	+	0.313282i
$395$	1.76502e16	−	3.05710e16i	0.233812	−	0.404975i
$396$	5.58928e15	−	9.68092e15i	0.0728345	−	0.126153i
$397$	1.31629e16	+	2.27988e16i	0.168738	+	0.292263i	0.937977	−	0.346699i	$-0.112697\pi$
$397$	1.31629e16	+	2.27988e16i	0.168738	+	0.292263i	−0.769238	+	0.638962i	$0.779364\pi$
$398$	9.64924e16			1.21690
$399$		0			0
$400$	−1.70221e16			−0.207789
$401$	8.00434e16	+	1.38639e17i	0.961362	+	1.66513i	0.719086	+	0.694921i	$0.244561\pi$
$401$	8.00434e16	+	1.38639e17i	0.961362	+	1.66513i	0.242276	+	0.970207i	$0.422106\pi$
$402$	1.98091e16	−	3.43103e16i	0.234097	−	0.405467i
$403$	−1.68951e16	+	2.92631e16i	−0.196461	+	0.340281i
$404$	2.69642e16	+	4.67033e16i	0.308538	+	0.534403i
$405$	4.52460e16			0.509475
$406$		0			0
$407$	8.16304e16			0.890202
$408$	−7.77470e15	−	1.34662e16i	−0.0834436	−	0.144528i
$409$	9.81791e15	−	1.70051e16i	0.103709	−	0.179630i	−0.809501	−	0.587119i	$-0.800262\pi$
$409$	9.81791e15	−	1.70051e16i	0.103709	−	0.179630i	0.913210	+	0.407489i	$0.133596\pi$
$410$	−1.94371e16	+	3.36660e16i	−0.202086	+	0.350023i
$411$	−9.88478e16	−	1.71209e17i	−1.01157	−	1.75209i
$412$	7.24495e16			0.729799
$413$		0			0
$414$	−3.07593e16			−0.300244
$415$	−2.38398e16	−	4.12917e16i	−0.229081	−	0.396781i
$416$	−2.95741e15	+	5.12239e15i	−0.0279773	+	0.0484580i
$417$	1.24190e17	−	2.15103e17i	1.15665	−	2.00338i
$418$	6.17417e15	+	1.06940e16i	0.0566151	+	0.0980603i
$419$	−1.22382e17			−1.10491			−0.552454	−	0.833544i	$-0.686308\pi$
$419$	−1.22382e17			−1.10491			−0.552454	+	0.833544i	$0.686308\pi$
$420$		0			0
$421$	−2.43087e16			−0.212778			−0.106389	−	0.994325i	$-0.533929\pi$
$421$	−2.43087e16			−0.212778			−0.106389	+	0.994325i	$0.533929\pi$
$422$	−3.03854e16	−	5.26290e16i	−0.261899	−	0.453622i
$423$	2.56971e16	−	4.45086e16i	0.218108	−	0.377774i
$424$	−2.89771e16	+	5.01898e16i	−0.242201	+	0.419505i
$425$	2.01452e16	+	3.48925e16i	0.165823	+	0.287213i
$426$	−6.10016e16			−0.494514
$427$		0			0
$428$	−5.92347e16			−0.465791
$429$	1.76308e16	+	3.05375e16i	0.136553	+	0.236516i
$430$	3.41277e16	−	5.91108e16i	0.260352	−	0.450943i
$431$	−6.14438e16	+	1.06424e17i	−0.461717	+	0.799717i	−0.999047	−	0.0436554i	$-0.986100\pi$
$431$	−6.14438e16	+	1.06424e17i	−0.461717	+	0.799717i	0.537330	+	0.843372i	$0.319433\pi$
$432$	−1.19974e16	−	2.07801e16i	−0.0888059	−	0.153816i
$433$	1.41055e17			1.02853			0.514267	−	0.857630i	$-0.328064\pi$
$433$	1.41055e17			1.02853			0.514267	+	0.857630i	$0.328064\pi$
$434$		0			0
$435$	−5.28285e16			−0.373842
$436$	3.26282e16	+	5.65136e16i	0.227473	+	0.393995i
$437$	1.69891e16	−	2.94259e16i	0.116692	−	0.202116i
$438$	2.80098e16	−	4.85145e16i	0.189552	−	0.328314i
$439$	7.34941e16	+	1.27296e17i	0.490042	+	0.848777i	0.999934	−	0.0114609i	$-0.00364820\pi$
$439$	7.34941e16	+	1.27296e17i	0.490042	+	0.848777i	−0.509893	+	0.860238i	$0.670315\pi$
$440$	−1.61280e16			−0.105959
$441$		0			0
$442$	1.40001e16			0.0893070
$443$	−9.34433e16	−	1.61849e17i	−0.587386	−	1.01738i	−0.994573	−	0.104038i	$-0.966824\pi$
$443$	−9.34433e16	−	1.61849e17i	−0.587386	−	1.01738i	0.407187	−	0.913345i	$-0.366510\pi$
$444$	−5.82710e16	+	1.00928e17i	−0.360964	+	0.625207i
$445$	1.99845e16	−	3.46142e16i	0.121998	−	0.211307i
$446$	−1.94544e16	−	3.36959e16i	−0.117042	−	0.202722i
$447$	−2.55269e17			−1.51356
$448$		0			0
$449$	2.15477e17			1.24108			0.620540	−	0.784175i	$-0.286913\pi$
$449$	2.15477e17			1.24108			0.620540	+	0.784175i	$0.286913\pi$
$450$	−2.06764e16	−	3.58125e16i	−0.117380	−	0.203308i
$451$	9.06570e16	−	1.57022e17i	0.507287	−	0.878647i
$452$	−9.97141e15	+	1.72710e16i	−0.0549992	+	0.0952614i
$453$	2.01360e17	+	3.48765e17i	1.09480	+	1.89625i
$454$	−1.78315e17			−0.955709
$455$		0			0
$456$	−1.76295e16			−0.0918264
$457$	1.91954e16	+	3.32474e16i	0.0985694	+	0.170727i	0.911093	−	0.412201i	$-0.135240\pi$
$457$	1.91954e16	+	3.32474e16i	0.0985694	+	0.170727i	−0.812523	+	0.582929i	$0.801907\pi$
$458$	−3.63236e16	+	6.29143e16i	−0.183892	+	0.318510i
$459$	−2.83971e16	+	4.91853e16i	−0.141740	+	0.245501i
$460$	2.21892e16	+	3.84328e16i	0.109198	+	0.189137i
$461$	−3.15284e17			−1.52984			−0.764921	−	0.644124i	$-0.777222\pi$
$461$	−3.15284e17			−1.52984			−0.764921	+	0.644124i	$0.777222\pi$
$462$		0			0
$463$	−2.28642e17			−1.07865			−0.539323	−	0.842099i	$-0.681320\pi$
$463$	−2.28642e17			−1.07865			−0.539323	+	0.842099i	$0.681320\pi$
$464$	2.06656e16	+	3.57938e16i	0.0961347	+	0.166510i
$465$	6.57702e16	−	1.13917e17i	0.301707	−	0.522571i
$466$	−6.52767e16	+	1.13063e17i	−0.295291	+	0.511458i
$467$	1.06511e17	+	1.84482e17i	0.475153	+	0.822989i	0.999595	−	0.0284570i	$-0.00905938\pi$
$467$	1.06511e17	+	1.84482e17i	0.475153	+	0.822989i	−0.524442	+	0.851446i	$0.675726\pi$
$468$	−1.43692e16			−0.0632171
$469$		0			0
$470$	−7.41494e16			−0.317301
$471$	3.96444e16	+	6.86661e16i	0.167319	+	0.289805i
$472$	−6.02643e16	+	1.04381e17i	−0.250863	+	0.434508i
$473$	−1.59175e17	+	2.75700e17i	−0.653550	+	1.13198i
$474$	−1.17530e17	−	2.03568e17i	−0.475981	−	0.824424i
$475$	4.56801e16			0.182481
$476$		0			0
$477$	−1.40791e17			−0.547276
$478$	−1.14447e17	−	1.98228e17i	−0.438858	−	0.760124i
$479$	1.57833e16	−	2.73374e16i	0.0597058	−	0.103413i	−0.834628	−	0.550815i	$-0.814317\pi$
$479$	1.57833e16	−	2.73374e16i	0.0597058	−	0.103413i	0.894333	+	0.447401i	$0.147650\pi$
$480$	1.15128e16	−	1.99408e16i	0.0429648	−	0.0744172i
$481$	−5.24649e16	−	9.08719e16i	−0.193164	−	0.334570i
$482$	−1.16249e17			−0.422262
$483$		0			0
$484$	−6.61821e16			−0.234016
$485$	5.60234e16	+	9.70354e16i	0.195456	+	0.338539i
$486$	7.76773e16	−	1.34541e17i	0.267398	−	0.463147i
$487$	−2.71494e17	+	4.70241e17i	−0.922193	+	1.59729i	−0.126179	+	0.992008i	$0.540271\pi$
$487$	−2.71494e17	+	4.70241e17i	−0.922193	+	1.59729i	−0.796014	+	0.605278i	$0.793062\pi$
$488$	−8.49150e15	−	1.47077e16i	−0.0284614	−	0.0492965i
$489$	−3.76184e17			−1.24421
$490$		0			0
$491$	2.87085e17			0.924658			0.462329	−	0.886708i	$-0.347014\pi$
$491$	2.87085e17			0.924658			0.462329	+	0.886708i	$0.347014\pi$
$492$	1.29429e17	+	2.24178e17i	0.411395	+	0.712556i
$493$	4.89143e16	−	8.47220e16i	0.153437	−	0.265761i
$494$	7.93643e15	−	1.37463e16i	0.0245697	−	0.0425560i
$495$	−1.95903e16	−	3.39314e16i	−0.0598560	−	0.103674i
$496$	−1.02912e17			−0.310339
$497$		0			0
$498$	−3.17492e17			−0.932701
$499$	−2.64712e15	−	4.58495e15i	−0.00767575	−	0.0132948i	0.862162	−	0.506633i	$-0.169110\pi$
$499$	−2.64712e15	−	4.58495e15i	−0.00767575	−	0.0132948i	−0.869838	+	0.493338i	$0.835777\pi$
$500$	−6.57221e16	+	1.13834e17i	−0.188108	+	0.325812i
$501$	3.89449e15	−	6.74545e15i	0.0110028	−	0.0190575i
$502$	−1.69706e17	−	2.93939e17i	−0.473284	−	0.819753i
$503$	−9.65557e16			−0.265819			−0.132909	−	0.991128i	$-0.542432\pi$
$503$	−9.65557e16			−0.265819			−0.132909	+	0.991128i	$0.542432\pi$
$504$		0			0
$505$	1.89018e17			0.507118
$506$	−1.03493e17	−	1.79255e17i	−0.274115	−	0.474781i
$507$	−2.03540e17	+	3.52542e17i	−0.532229	+	0.921848i
$508$	−2.10479e15	+	3.64560e15i	−0.00543369	+	0.00941142i
$509$	2.70435e17	+	4.68407e17i	0.689283	+	1.19387i	0.972070	+	0.234691i	$0.0754077\pi$
$509$	2.70435e17	+	4.68407e17i	0.689283	+	1.19387i	−0.282787	+	0.959183i	$0.591259\pi$
$510$	−5.45003e16			−0.137149
$511$		0			0
$512$	−1.80144e16			−0.0441942
$513$	3.21958e16	+	5.57648e16i	0.0779896	+	0.135082i
$514$	6.89952e16	−	1.19503e17i	0.165028	−	0.285838i
$515$	1.26967e17	−	2.19913e17i	0.299877	−	0.519403i
$516$	−2.27252e17	−	3.93611e17i	−0.530010	−	0.918004i
$517$	3.45842e17			0.796506
$518$		0			0
$519$	3.93040e17			0.882772
$520$	1.03657e16	+	1.79539e16i	0.0229919	+	0.0398232i
$521$	6.51595e16	−	1.12860e17i	0.142736	−	0.247225i	−0.785790	−	0.618493i	$-0.787743\pi$
$521$	6.51595e16	−	1.12860e17i	0.142736	−	0.247225i	0.928526	+	0.371268i	$0.121077\pi$
$522$	−5.02040e16	+	8.69559e16i	−0.108613	+	0.188122i
$523$	4.34304e17	+	7.52237e17i	0.927969	+	1.60729i	0.786716	+	0.617315i	$0.211780\pi$
$523$	4.34304e17	+	7.52237e17i	0.927969	+	1.60729i	0.141253	+	0.989974i	$0.454887\pi$
$524$	2.52879e17			0.533654
$525$		0			0
$526$	−3.68725e17			−0.759094
$527$	1.21794e17	+	2.10954e17i	0.247661	+	0.428961i
$528$	−5.36971e16	+	9.30061e16i	−0.107853	+	0.186806i
$529$	−3.27570e16	+	5.67368e16i	−0.0649894	+	0.112565i
$530$	1.01564e17	+	1.75914e17i	0.199043	+	0.344753i
$531$	−2.92807e17			−0.566848
$532$		0			0
$533$	−2.33065e17			−0.440302
$534$	−1.33074e17	−	2.30491e17i	−0.248357	−	0.430166i
$535$	−1.03808e17	+	1.79801e17i	−0.191396	+	0.331507i
$536$	−5.43198e16	+	9.40847e16i	−0.0989435	+	0.171375i
$537$	−2.70414e17	−	4.68370e17i	−0.486627	−	0.842862i
$538$	5.42540e17			0.964599
$539$		0			0
$540$	−8.41011e16			−0.145963
$541$	2.99150e17	+	5.18143e17i	0.512988	+	0.888520i	0.999887	+	0.0150622i	$0.00479462\pi$
$541$	2.99150e17	+	5.18143e17i	0.512988	+	0.888520i	−0.486899	+	0.873458i	$0.661872\pi$
$542$	2.71552e16	−	4.70341e16i	0.0460105	−	0.0796925i
$543$	5.05200e17	−	8.75033e17i	0.845794	−	1.46496i
$544$	2.13196e16	+	3.69265e16i	0.0352684	+	0.0610866i
$545$	2.28722e17			0.373879
$546$		0			0
$547$	6.94479e17			1.10851			0.554257	−	0.832345i	$-0.313002\pi$
$547$	6.94479e17			1.10851			0.554257	+	0.832345i	$0.313002\pi$
$548$	2.71057e17	+	4.69485e17i	0.427551	+	0.740540i
$549$	2.06289e16	−	3.57303e16i	0.0321555	−	0.0556950i
$550$	1.39136e17	−	2.40990e17i	0.214329	−	0.371229i
$551$	−5.54576e16	−	9.60553e16i	−0.0844258	−	0.146230i
$552$	2.95510e17			0.444598
$553$		0			0
$554$	−4.44826e17			−0.653698
$555$	2.04239e17	+	3.53752e17i	0.296643	+	0.513800i
$556$	−3.40550e17	+	5.89849e17i	−0.488871	+	0.846750i
$557$	−4.32451e17	+	7.49027e17i	−0.613590	+	1.06277i	0.377040	+	0.926197i	$0.376942\pi$
$557$	−4.32451e17	+	7.49027e17i	−0.613590	+	1.06277i	−0.990630	+	0.136572i	$0.956391\pi$
$558$	−1.25005e17	−	2.16516e17i	−0.175310	−	0.303646i
$559$	4.09216e17			0.567252
$560$		0			0
$561$	2.54196e17			0.344279
$562$	−3.63728e16	−	6.29995e16i	−0.0486957	−	0.0843434i
$563$	6.04730e16	−	1.04742e17i	0.0800307	−	0.138617i	−0.823232	−	0.567705i	$-0.807831\pi$
$563$	6.04730e16	−	1.04742e17i	0.0800307	−	0.138617i	0.903263	+	0.429088i	$0.141165\pi$
$564$	−2.46875e17	+	4.27601e17i	−0.322971	+	0.559403i
$565$	3.49496e16	+	6.05344e16i	0.0451988	+	0.0782866i
$566$	−6.99661e17			−0.894501
$567$		0			0
$568$	1.67277e17			0.209012
$569$	3.13843e17	+	5.43592e17i	0.387688	+	0.671496i	0.992138	−	0.125147i	$-0.0399404\pi$
$569$	3.13843e17	+	5.43592e17i	0.387688	+	0.671496i	−0.604450	+	0.796643i	$0.706607\pi$
$570$	−3.08954e16	+	5.35125e16i	−0.0377318	+	0.0653535i
$571$	6.18567e17	−	1.07139e18i	0.746882	−	1.29364i	−0.202428	−	0.979297i	$-0.564883\pi$
$571$	6.18567e17	−	1.07139e18i	0.746882	−	1.29364i	0.949310	−	0.314340i	$-0.101783\pi$
$572$	−4.83467e16	−	8.37390e16i	−0.0577155	−	0.0999662i
$573$	1.13576e18			1.34054
$574$		0			0
$575$	−7.65702e17			−0.883525
$576$	−2.18817e16	−	3.79002e16i	−0.0249652	−	0.0432410i
$577$	4.22370e17	−	7.31566e17i	0.476486	−	0.825298i	−0.523151	−	0.852240i	$-0.675244\pi$
$577$	4.22370e17	−	7.31566e17i	0.476486	−	0.825298i	0.999637	+	0.0269418i	$0.00857688\pi$
$578$	−2.66484e17	+	4.61564e17i	−0.297263	+	0.514874i
$579$	−4.79632e15	−	8.30747e15i	−0.00529051	−	0.00916343i
$580$	1.44865e17			0.158009
$581$		0			0
$582$	7.46105e17			0.795794
$583$	−4.73707e17	−	8.20485e17i	−0.499648	−	0.865416i
$584$	−7.68077e16	+	1.33035e17i	−0.0801164	+	0.138766i
$585$	−2.51819e16	+	4.36163e16i	−0.0259762	+	0.0449920i
$586$	5.24663e16	+	9.08744e16i	0.0535237	+	0.0927058i
$587$	9.19950e17			0.928146			0.464073	−	0.885797i	$-0.346387\pi$
$587$	9.19950e17			0.928146			0.464073	+	0.885797i	$0.346387\pi$
$588$		0			0
$589$	2.76173e17			0.272541
$590$	2.11225e17	+	3.65852e17i	0.206161	+	0.357082i
$591$	3.13463e17	−	5.42934e17i	0.302599	−	0.524117i
$592$	1.59789e17	−	2.76763e17i	0.152565	−	0.264251i
$593$	−3.65725e16	−	6.33454e16i	−0.0345381	−	0.0598218i	0.848240	−	0.529613i	$-0.177663\pi$
$593$	−3.65725e16	−	6.33454e16i	−0.0345381	−	0.0598218i	−0.882778	+	0.469791i	$0.844329\pi$
$594$	3.92258e17			0.366403
$595$		0			0
$596$	6.99991e17			0.639723
$597$	−1.12603e18	−	1.95034e18i	−1.01792	−	1.76310i
$598$	−1.33033e17	+	2.30419e17i	−0.118960	+	0.206044i
$599$	1.99308e17	−	3.45212e17i	0.176299	−	0.305360i	−0.764311	−	0.644848i	$-0.776921\pi$
$599$	1.99308e17	−	3.45212e17i	0.176299	−	0.305360i	0.940610	+	0.339489i	$0.110254\pi$
$600$	1.98641e17	+	3.44057e17i	0.173815	+	0.301056i
$601$	−2.02331e18			−1.75137			−0.875686	−	0.482882i	$-0.839590\pi$
$601$	−2.02331e18			−1.75137			−0.875686	+	0.482882i	$0.839590\pi$
$602$		0			0
$603$	−2.63924e17			−0.223572
$604$	−5.52162e17	−	9.56373e17i	−0.462729	−	0.801470i
$605$	−1.15983e17	+	2.00889e17i	−0.0961582	+	0.166551i
$606$	6.29322e17	−	1.09002e18i	0.516180	−	0.894049i
$607$	−9.11136e17	−	1.57813e18i	−0.739361	−	1.28061i	−0.952783	−	0.303651i	$-0.901794\pi$
$607$	−9.11136e17	−	1.57813e18i	−0.739361	−	1.28061i	0.213422	−	0.976960i	$-0.431539\pi$
$608$	4.83430e16			0.0388115
$609$		0			0
$610$	−5.95251e16			−0.0467795
$611$	−2.22277e17	−	3.84995e17i	−0.172833	−	0.299355i
$612$	−5.17928e16	+	8.97077e16i	−0.0398460	+	0.0690153i
$613$	8.93380e17	−	1.54738e18i	0.680054	−	1.17789i	−0.294910	−	0.955525i	$-0.595290\pi$
$613$	8.93380e17	−	1.54738e18i	0.680054	−	1.17789i	0.974964	−	0.222363i	$-0.0713769\pi$
$614$	−1.82378e17	−	3.15888e17i	−0.137366	−	0.237924i
$615$	9.07292e17			0.676175
$616$		0			0
$617$	8.80000e17			0.642139			0.321070	−	0.947056i	$-0.395958\pi$
$617$	8.80000e17			0.642139			0.321070	+	0.947056i	$0.395958\pi$
$618$	−8.45456e17	−	1.46437e18i	−0.610472	−	1.05737i
$619$	−4.84990e16	+	8.40027e16i	−0.0346532	+	0.0600211i	−0.882832	−	0.469689i	$-0.844366\pi$
$619$	−4.84990e16	+	8.40027e16i	−0.0346532	+	0.0600211i	0.848179	+	0.529710i	$0.177699\pi$
$620$	−1.80353e17	+	3.12380e17i	−0.127520	+	0.220871i
$621$	−5.39675e17	−	9.34745e17i	−0.377604	−	0.654030i
$622$	−5.95906e17			−0.412611
$623$		0			0
$624$	1.38047e17			0.0936112
$625$	−3.88906e17	−	6.73606e17i	−0.260991	−	0.452049i
$626$	1.80602e17	−	3.12813e17i	0.119947	−	0.207755i
$627$	1.44100e17	−	2.49589e17i	0.0947164	−	0.164054i
$628$	−1.08712e17	−	1.88294e17i	−0.0707193	−	0.122489i
$629$	−7.56424e17			−0.487008
$630$		0			0
$631$	−8.85605e15			−0.00558533			−0.00279267	−	0.999996i	$-0.500889\pi$
$631$	−8.85605e15			−0.00558533			−0.00279267	+	0.999996i	$0.500889\pi$
$632$	3.22287e17	+	5.58218e17i	0.201179	+	0.348452i
$633$	−7.09170e17	+	1.22832e18i	−0.438153	+	0.758904i
$634$	−3.90775e17	+	6.76842e17i	−0.238972	+	0.413911i
$635$	7.37724e15	+	1.27778e16i	0.00446545	+	0.00773438i
$636$	1.35260e18			0.810400
$637$		0			0
$638$	−6.75666e17			−0.396641
$639$	2.03187e17	+	3.51931e17i	0.118070	+	0.204504i
$640$	−3.15700e16	+	5.46809e16i	−0.0181596	+	0.0314533i
$641$	−3.07694e17	+	5.32941e17i	−0.175203	+	0.303460i	−0.940232	−	0.340536i	$-0.889392\pi$
$641$	−3.07694e17	+	5.32941e17i	−0.175203	+	0.303460i	0.765029	+	0.643996i	$0.222725\pi$
$642$	6.91244e17	+	1.19727e18i	0.389631	+	0.674861i
$643$	9.48803e17			0.529425			0.264713	−	0.964327i	$-0.414723\pi$
$643$	9.48803e17			0.529425			0.264713	+	0.964327i	$0.414723\pi$
$644$		0			0
$645$	−1.59302e18			−0.871132
$646$	−5.72126e16	−	9.90951e16i	−0.0309728	−	0.0536464i
$647$	9.09981e16	−	1.57613e17i	0.0487702	−	0.0844725i	−0.840610	−	0.541641i	$-0.817803\pi$
$647$	9.09981e16	−	1.57613e17i	0.0487702	−	0.0844725i	0.889380	+	0.457169i	$0.151136\pi$
$648$	−4.13090e17	+	7.15494e17i	−0.219183	+	0.379637i
$649$	−9.85178e17	−	1.70638e18i	−0.517517	−	0.896365i
$650$	−3.57697e17			−0.186028
$651$		0			0
$652$	1.03156e18			0.525878
$653$	−1.38478e18	−	2.39851e18i	−0.698947	−	1.21061i	−0.968832	−	0.247720i	$-0.920319\pi$
$653$	−1.38478e18	−	2.39851e18i	−0.698947	−	1.21061i	0.269884	−	0.962893i	$-0.413015\pi$
$654$	7.61515e17	−	1.31898e18i	0.380560	−	0.659149i
$655$	4.43169e17	−	7.67590e17i	0.219281	−	0.379805i
$656$	−3.54916e17	−	6.14733e17i	−0.173881	−	0.301170i
$657$	−3.73186e17			−0.181030
$658$		0			0
$659$	−1.98995e18			−0.946427			−0.473213	−	0.880948i	$-0.656906\pi$
$659$	−1.98995e18			−0.946427			−0.473213	+	0.880948i	$0.656906\pi$
$660$	1.88207e17	+	3.25984e17i	0.0886340	+	0.153519i
$661$	−5.81844e17	+	1.00778e18i	−0.271330	+	0.469957i	−0.969203	−	0.246265i	$-0.920797\pi$
$661$	−5.81844e17	+	1.00778e18i	−0.271330	+	0.469957i	0.697873	+	0.716222i	$0.254130\pi$
$662$	4.25194e17	−	7.36457e17i	0.196340	−	0.340072i
$663$	−1.63375e17	−	2.82974e17i	−0.0747047	−	0.129392i
$664$	8.70617e17			0.394216
$665$		0			0
$666$	7.76368e17			0.344735
$667$	9.29594e17	+	1.61010e18i	0.408767	+	0.708005i
$668$	−1.06793e16	+	1.84972e16i	−0.00465047	+	0.00805486i
$669$	−4.54049e17	+	7.86436e17i	−0.195809	+	0.339151i
$670$	1.90390e17	+	3.29765e17i	0.0813126	+	0.140837i
$671$	2.77632e17			0.117428
$672$		0			0
$673$	1.44542e18			0.599650			0.299825	−	0.953994i	$-0.403072\pi$
$673$	1.44542e18			0.599650			0.299825	+	0.953994i	$0.403072\pi$
$674$	9.06289e17	+	1.56974e18i	0.372372	+	0.644967i
$675$	7.25538e17	−	1.25667e18i	0.295247	−	0.511383i
$676$	5.58142e17	−	9.66731e17i	0.224953	−	0.389630i
$677$	1.90818e18	+	3.30507e18i	0.761716	+	1.31933i	0.941965	+	0.335710i	$0.108976\pi$
$677$	1.90818e18	+	3.30507e18i	0.761716	+	1.31933i	−0.180249	+	0.983621i	$0.557690\pi$
$678$	4.65449e17			0.184026
$679$		0			0
$680$	1.49449e17			0.0579676
$681$	2.08087e18	+	3.60417e18i	0.799444	+	1.38468i
$682$	8.41188e17	−	1.45698e18i	0.320107	−	0.554441i
$683$	−1.14349e17	+	1.98058e17i	−0.0431019	+	0.0746547i	−0.886772	−	0.462208i	$-0.847057\pi$
$683$	−1.14349e17	+	1.98058e17i	−0.0431019	+	0.0746547i	0.843670	+	0.536863i	$0.180391\pi$
$684$	5.87211e16	+	1.01708e17i	0.0219245	+	0.0379743i
$685$	1.90010e18			0.702729
$686$		0			0
$687$	1.69553e18			0.615298
$688$	6.23162e17	+	1.07935e18i	0.224015	+	0.388005i
$689$	−6.08915e17	+	1.05467e18i	−0.216836	+	0.375571i
$690$	5.17878e17	−	8.96990e17i	0.182687	−	0.316423i
$691$	−1.65297e18	−	2.86303e18i	−0.577642	−	1.00051i	−0.995749	−	0.0921074i	$-0.970640\pi$
$691$	−1.65297e18	−	2.86303e18i	−0.577642	−	1.00051i	0.418107	−	0.908398i	$-0.362694\pi$
$692$	−1.07778e18			−0.373113
$693$		0			0
$694$	−3.09862e18			−1.05276
$695$	1.19362e18	+	2.06741e18i	0.401758	+	0.695866i
$696$	4.82317e17	−	8.35398e17i	0.160832	−	0.278569i
$697$	−8.40068e17	+	1.45504e18i	−0.277524	+	0.480686i
$698$	1.25634e18	+	2.17605e18i	0.411196	+	0.712212i
$699$	3.04701e18			0.988035
$700$		0			0
$701$	−1.97078e18			−0.627293			−0.313647	−	0.949540i	$-0.601551\pi$
$701$	−1.97078e18			−0.627293			−0.313647	+	0.949540i	$0.601551\pi$
$702$	−2.52109e17	−	4.36666e17i	−0.0795055	−	0.137708i
$703$	−4.28805e17	+	7.42713e17i	−0.133983	+	0.232066i
$704$	1.47246e17	−	2.55038e17i	0.0455851	−	0.0789557i
$705$	8.65293e17	+	1.49873e18i	0.265420	+	0.459721i
$706$	−1.40210e18			−0.426137
$707$		0			0
$708$	2.81304e18			0.839381
$709$	−1.90872e18	−	3.30601e18i	−0.564342	−	0.977470i	−0.997111	−	0.0759644i	$-0.975796\pi$
$709$	−1.90872e18	−	3.30601e18i	−0.564342	−	0.977470i	0.432768	−	0.901505i	$-0.357537\pi$
$710$	2.93151e17	−	5.07752e17i	0.0858839	−	0.148755i
$711$	−7.82950e17	+	1.35611e18i	−0.227291	+	0.393679i
$712$	3.64912e17	+	6.32046e17i	0.104971	+	0.181815i
$713$	−4.62929e18			−1.31957
$714$		0			0
$715$	−3.38908e17			−0.0948622
$716$	7.41520e17	+	1.28435e18i	0.205678	+	0.356245i
$717$	−2.67111e18	+	4.62649e18i	−0.734204	+	1.27168i
$718$	1.61120e18	−	2.79068e18i	0.438874	−	0.760152i
$719$	1.80548e18	+	3.12718e18i	0.487365	+	0.844141i	0.999894	−	0.0145287i	$-0.00462480\pi$
$719$	1.80548e18	+	3.12718e18i	0.487365	+	0.844141i	−0.512529	+	0.858670i	$0.671291\pi$
$720$	−1.53390e17			−0.0410332
$721$		0			0
$722$	2.56166e18			0.673022
$723$	1.35657e18	+	2.34966e18i	0.353219	+	0.611794i
$724$	−1.38534e18	+	2.39949e18i	−0.357484	+	0.619181i
$725$	−1.24974e18	+	2.16462e18i	−0.319613	+	0.553585i
$726$	7.72319e17	+	1.33769e18i	0.195753	+	0.339054i
$727$	3.60755e18			0.906230			0.453115	−	0.891452i	$-0.350313\pi$
$727$	3.60755e18			0.906230			0.453115	+	0.891452i	$0.350313\pi$
$728$		0			0
$729$	1.39886e18			0.345181
$730$	2.69209e17	+	4.66284e17i	0.0658403	+	0.114039i
$731$	1.47499e18	−	2.55476e18i	0.357541	−	0.619280i
$732$	−1.98185e17	+	3.43266e17i	−0.0476155	+	0.0824724i
$733$	−5.46187e17	−	9.46024e17i	−0.130067	−	0.225282i	0.793635	−	0.608394i	$-0.208186\pi$
$733$	−5.46187e17	−	9.46024e17i	−0.130067	−	0.225282i	−0.923702	+	0.383112i	$0.874852\pi$
$734$	−5.51302e18			−1.30126
$735$		0			0
$736$	−8.10337e17			−0.187914
$737$	−8.88001e17	−	1.53806e18i	−0.204115	−	0.353538i
$738$	8.62218e17	−	1.49341e18i	0.196449	−	0.340260i
$739$	−2.64348e18	+	4.57864e18i	−0.597018	+	1.03407i	0.396241	+	0.918147i	$0.370315\pi$
$739$	−2.64348e18	+	4.57864e18i	−0.597018	+	1.03407i	−0.993259	+	0.115919i	$0.963019\pi$
$740$	−5.60057e17	−	9.70047e17i	−0.125379	−	0.217163i
$741$	−3.70460e17			−0.0822096
$742$		0			0
$743$	−1.06272e18			−0.231736			−0.115868	−	0.993265i	$-0.536965\pi$
$743$	−1.06272e18			−0.231736			−0.115868	+	0.993265i	$0.536965\pi$
$744$	1.20095e18	+	2.08010e18i	0.259597	+	0.449635i
$745$	1.22673e18	−	2.12475e18i	0.262865	−	0.455295i
$746$	1.05873e18	−	1.83377e18i	0.224896	−	0.389531i
$747$	1.05752e18	+	1.83168e18i	0.222692	+	0.385714i
$748$	−6.97049e17			−0.145513
$749$		0			0
$750$	3.06780e18			0.629403
$751$	−4.48188e17	−	7.76285e17i	−0.0911593	−	0.157892i	0.816840	−	0.576864i	$-0.195724\pi$
$751$	−4.48188e17	−	7.76285e17i	−0.0911593	−	0.157892i	−0.907999	+	0.418972i	$0.862391\pi$
$752$	6.76974e17	−	1.17255e18i	0.136507	−	0.236438i
$753$	−3.96079e18	+	6.86029e18i	−0.791799	+	1.37144i
$754$	4.34259e17	+	7.52159e17i	0.0860668	+	0.149072i
$755$	−3.87063e18			−0.760549
$756$		0			0
$757$	−6.71607e18			−1.29716			−0.648578	−	0.761148i	$-0.724636\pi$
$757$	−6.71607e18			−1.29716			−0.648578	+	0.761148i	$0.724636\pi$
$758$	6.83837e17	+	1.18444e18i	0.130949	+	0.226811i
$759$	−2.41544e18	+	4.18367e18i	−0.458591	+	0.794303i
$760$	8.47205e16	−	1.46740e17i	0.0159478	−	0.0276224i
$761$	−3.56938e18	−	6.18234e18i	−0.666181	−	1.15386i	−0.978964	−	0.204034i	$-0.934595\pi$
$761$	−3.56938e18	−	6.18234e18i	−0.666181	−	1.15386i	0.312783	−	0.949825i	$-0.398739\pi$
$762$	9.82481e16			0.0181810
$763$		0			0
$764$	−3.11444e18			−0.566595
$765$	1.81533e17	+	3.14424e17i	0.0327458	+	0.0567173i
$766$	7.13234e17	−	1.23536e18i	0.127569	−	0.220956i
$767$	−1.26637e18	+	2.19342e18i	−0.224591	+	0.389003i
$768$	2.10221e17	+	3.64113e17i	0.0369681	+	0.0640307i
$769$	−9.57731e18			−1.67002			−0.835011	−	0.550233i	$-0.814539\pi$
$769$	−9.57731e18			−1.67002			−0.835011	+	0.550233i	$0.814539\pi$
$770$		0			0
$771$	−3.22059e18			−0.552181
$772$	1.31523e16	+	2.27805e16i	0.00223609	+	0.00387303i
$773$	1.07825e18	−	1.86758e18i	0.181783	−	0.314857i	−0.760705	−	0.649098i	$-0.775147\pi$
$773$	1.07825e18	−	1.86758e18i	0.181783	−	0.314857i	0.942488	+	0.334241i	$0.108480\pi$
$774$	−1.51388e18	+	2.62212e18i	−0.253090	+	0.438366i
$775$	−3.11180e18	−	5.38979e18i	−0.515882	−	0.893534i
$776$	−2.04595e18			−0.336351
$777$		0			0
$778$	1.39694e18			0.225844
$779$	9.52444e17	+	1.64968e18i	0.152702	+	0.264488i
$780$	2.41926e17	−	4.19029e17i	0.0384652	−	0.0666237i
$781$	−1.36729e18	+	2.36822e18i	−0.215590	+	0.373413i
$782$	9.59012e17	+	1.66106e18i	0.149962	+	0.259741i
$783$	−3.52333e18			−0.546389
$784$		0			0
$785$	−7.62063e17			−0.116235
$786$	−2.95100e18	−	5.11128e18i	−0.446398	−	0.773185i
$787$	−1.41242e18	+	2.44639e18i	−0.211899	+	0.367020i	−0.952309	−	0.305136i	$-0.901298\pi$
$787$	−1.41242e18	+	2.44639e18i	−0.211899	+	0.367020i	0.740410	+	0.672156i	$0.234631\pi$
$788$	−8.59569e17	+	1.48882e18i	−0.127897	+	0.221524i
$789$	4.30288e18	+	7.45280e18i	0.634977	+	1.09981i
$790$	2.25922e18			0.330661
$791$		0			0
$792$	7.15428e17			0.103004
$793$	−1.78438e17	−	3.09063e17i	−0.0254807	−	0.0441338i
$794$	−8.42427e17	+	1.45913e18i	−0.119316	+	0.206661i
$795$	2.37042e18	−	4.10569e18i	0.332996	−	0.576767i
$796$	3.08776e18	+	5.34815e18i	0.430237	+	0.745193i
$797$	−8.37611e18			−1.15761			−0.578806	−	0.815465i	$-0.696481\pi$
$797$	−8.37611e18			−1.15761			−0.578806	+	0.815465i	$0.696481\pi$
$798$		0			0
$799$	−3.20472e18			−0.435749
$800$	−5.44708e17	−	9.43461e17i	−0.0734647	−	0.127245i
$801$	−8.86501e17	+	1.53546e18i	−0.118595	+	0.205413i
$802$	−5.12278e18	+	8.87291e18i	−0.679786	+	1.17742i
$803$	−1.25562e18	−	2.17481e18i	−0.165276	−	0.286266i
$804$	2.53556e18			0.331062
$805$		0			0
$806$	−2.16257e18			−0.277838
$807$	−6.33122e18	−	1.09660e19i	−0.806881	−	1.39756i
$808$	−1.72571e18	+	2.98901e18i	−0.218169	+	0.377880i
$809$	1.08897e18	−	1.88615e18i	0.136569	−	0.236544i	−0.789627	−	0.613587i	$-0.789726\pi$
$809$	1.08897e18	−	1.88615e18i	0.136569	−	0.236544i	0.926196	+	0.377043i	$0.123059\pi$
$810$	1.44787e18	+	2.50779e18i	0.180127	+	0.311988i
$811$	1.05998e19			1.30817			0.654084	−	0.756422i	$-0.273054\pi$
$811$	1.05998e19			1.30817			0.654084	+	0.756422i	$0.273054\pi$
$812$		0			0
$813$	−1.26756e18			−0.153950
$814$	2.61217e18	+	4.52442e18i	0.314734	+	0.545135i
$815$	1.80780e18	−	3.13120e18i	0.216085	−	0.374271i
$816$	4.97581e17	−	8.61836e17i	0.0590035	−	0.102197i
$817$	−1.67230e18	−	2.89651e18i	−0.196730	−	0.340747i
$818$	1.25669e18			0.146667
$819$		0			0
$820$	−2.48795e18			−0.285793
$821$	−5.15388e16	−	8.92679e16i	−0.00587360	−	0.0101734i	0.863074	−	0.505078i	$-0.168536\pi$
$821$	−5.15388e16	−	8.92679e16i	−0.00587360	−	0.0101734i	−0.868947	+	0.494905i	$0.835203\pi$
$822$	6.32626e18	−	1.09574e19i	0.715287	−	1.23891i
$823$	5.26006e18	−	9.11070e18i	0.590054	−	1.02200i	−0.404170	−	0.914684i	$-0.632440\pi$
$823$	5.26006e18	−	9.11070e18i	0.590054	−	1.02200i	0.994224	−	0.107320i	$-0.0342271\pi$
$824$	2.31838e18	+	4.01556e18i	0.258023	+	0.446909i
$825$	−6.49463e18			−0.717140
$826$		0			0
$827$	1.20216e19			1.30670			0.653350	−	0.757056i	$-0.273363\pi$
$827$	1.20216e19			1.30670			0.653350	+	0.757056i	$0.273363\pi$
$828$	−9.84299e17	−	1.70486e18i	−0.106152	−	0.183861i
$829$	1.57256e18	−	2.72375e18i	0.168268	−	0.291449i	−0.769543	−	0.638595i	$-0.779516\pi$
$829$	1.57256e18	−	2.72375e18i	0.168268	−	0.291449i	0.937811	+	0.347146i	$0.112849\pi$
$830$	1.52575e18	−	2.64267e18i	0.161985	−	0.280566i
$831$	5.19094e18	+	8.99097e18i	0.546814	+	0.947109i
$832$	−3.78549e17			−0.0395658
$833$		0			0
$834$	1.58963e19			1.63575
$835$	3.74308e16	+	6.48321e16i	0.00382180	+	0.00661955i
$836$	−3.95147e17	+	6.84414e17i	−0.0400330	+	0.0693391i
$837$	4.38646e18	−	7.59757e18i	0.440960	−	0.763765i
$838$	−3.91622e18	−	6.78309e18i	−0.390644	−	0.676615i
$839$	−5.05894e18			−0.500734			−0.250367	−	0.968151i	$-0.580551\pi$
$839$	−5.05894e18			−0.500734			−0.250367	+	0.968151i	$0.580551\pi$
$840$		0			0
$841$	−4.19166e18			−0.408519
$842$	−7.77878e17	−	1.34732e18i	−0.0752286	−	0.130300i
$843$	−8.48911e17	+	1.47036e18i	−0.0814672	+	0.141105i
$844$	1.94466e18	−	3.36826e18i	0.185190	−	0.320759i
$845$	−1.95628e18	−	3.38837e18i	−0.184868	−	0.320201i
$846$	3.28922e18			0.308451
$847$		0			0
$848$	−3.70907e18			−0.342525
$849$	8.16476e18	+	1.41418e19i	0.748244	+	1.29600i
$850$	−1.28929e18	+	2.23312e18i	−0.117254	+	0.203090i
$851$	7.18775e18	−	1.24495e19i	0.648710	−	1.12360i
$852$	−1.95205e18	−	3.38105e18i	−0.174837	−	0.302827i
$853$	1.27122e19			1.12993			0.564967	−	0.825114i	$-0.308889\pi$
$853$	1.27122e19			1.12993			0.564967	+	0.825114i	$0.308889\pi$
$854$		0			0
$855$	4.11633e17			0.0360355
$856$	−1.89551e18	−	3.28312e18i	−0.164682	−	0.285238i
$857$	9.91400e18	−	1.71715e19i	0.854818	−	1.48059i	−0.0219964	−	0.999758i	$-0.507002\pi$
$857$	9.91400e18	−	1.71715e19i	0.854818	−	1.48059i	0.876814	−	0.480830i	$-0.159664\pi$
$858$	−1.12837e18	+	1.95440e18i	−0.0965573	+	0.167242i
$859$	−3.16105e18	−	5.47510e18i	−0.268458	−	0.464982i	0.700006	−	0.714137i	$-0.253181\pi$
$859$	−3.16105e18	−	5.47510e18i	−0.268458	−	0.464982i	−0.968464	+	0.249155i	$0.919847\pi$
$860$	4.36834e18			0.368194
$861$		0			0
$862$	−7.86480e18			−0.652966
$863$	3.01615e18	+	5.22413e18i	0.248532	+	0.430471i	0.963119	−	0.269076i	$-0.0867184\pi$
$863$	3.01615e18	+	5.22413e18i	0.248532	+	0.430471i	−0.714586	+	0.699547i	$0.753385\pi$
$864$	7.67832e17	−	1.32992e18i	0.0627953	−	0.108765i
$865$	−1.88880e18	+	3.27150e18i	−0.153314	+	0.265547i
$866$	4.51377e18	+	7.81808e18i	0.363641	+	0.629845i
$867$	1.24391e19			0.994634
$868$		0			0
$869$	−1.05373e19			−0.830041
$870$	−1.69051e18	−	2.92805e18i	−0.132173	−	0.228931i
$871$	−1.14146e18	+	1.97707e18i	−0.0885814	+	0.153427i
$872$	−2.08820e18	+	3.61687e18i	−0.160848	+	0.278597i
$873$	−2.48517e18	−	4.30443e18i	−0.190004	−	0.329097i
$874$	2.17460e18			0.165027
$875$		0			0
$876$	3.58526e18			0.268067
$877$	1.59022e18	+	2.75435e18i	0.118021	+	0.204419i	0.918984	−	0.394296i	$-0.129012\pi$
$877$	1.59022e18	+	2.75435e18i	0.118021	+	0.204419i	−0.800962	+	0.598715i	$0.795678\pi$
$878$	−4.70362e18	+	8.14691e18i	−0.346512	+	0.600176i
$879$	1.22452e18	−	2.12093e18i	0.0895445	−	0.155096i
$880$	−5.16096e17	−	8.93904e17i	−0.0374622	−	0.0648864i
$881$	2.33099e19			1.67956			0.839782	−	0.542924i	$-0.182683\pi$
$881$	2.33099e19			1.67956			0.839782	+	0.542924i	$0.182683\pi$
$882$		0			0
$883$	−1.95630e18			−0.138896			−0.0694482	−	0.997586i	$-0.522124\pi$
$883$	−1.95630e18			−0.138896			−0.0694482	+	0.997586i	$0.522124\pi$
$884$	4.48002e17	+	7.75962e17i	0.0315748	+	0.0546891i
$885$	4.92982e18	−	8.53870e18i	0.344905	−	0.597393i
$886$	5.98037e18	−	1.03583e19i	0.415345	−	0.719399i
$887$	−5.03283e18	−	8.71712e18i	−0.346983	−	0.600993i	0.638729	−	0.769432i	$-0.279461\pi$
$887$	−5.03283e18	−	8.71712e18i	−0.346983	−	0.600993i	−0.985712	+	0.168439i	$0.946127\pi$
$888$	−7.45869e18			−0.510479
$889$		0			0
$890$	2.55802e18			0.172532
$891$	−6.75305e18	−	1.16966e19i	−0.452163	−	0.783170i
$892$	1.24508e18	−	2.15654e18i	0.0827609	−	0.143346i
$893$	−1.81671e18	+	3.14663e18i	−0.119881	+	0.207640i
$894$	−8.16862e18	−	1.41485e19i	−0.535124	−	0.926862i
$895$	5.19803e18			0.338056
$896$		0			0
$897$	6.20974e18			0.398036
$898$	6.89527e18	+	1.19430e19i	0.438788	+	0.760003i
$899$	−7.55571e18	+	1.30869e19i	−0.477350	+	0.826795i
$900$	1.32329e18	−	2.29200e18i	0.0830000	−	0.143760i
$901$	4.38958e18	+	7.60298e18i	0.273345	+	0.473448i
$902$	1.16041e19			0.717412
$903$		0			0
$904$	−1.27634e18			−0.0777806
$905$	4.85560e18	+	8.41015e18i	0.293784	+	0.508848i
$906$	−1.28870e19	+	2.23210e19i	−0.774140	+	1.34085i
$907$	6.24089e18	−	1.08095e19i	0.372220	−	0.644703i	−0.617687	−	0.786424i	$-0.711930\pi$
$907$	6.24089e18	−	1.08095e19i	0.372220	−	0.644703i	0.989907	+	0.141721i	$0.0452635\pi$
$908$	−5.70609e18	−	9.88324e18i	−0.337894	−	0.585250i
$909$	−8.38471e18			−0.492973
$910$		0			0
$911$	2.22935e19			1.29214			0.646068	−	0.763280i	$-0.276412\pi$
$911$	2.22935e19			1.29214			0.646068	+	0.763280i	$0.276412\pi$
$912$	−5.64143e17	−	9.77124e17i	−0.0324655	−	0.0562320i
$913$	−7.11627e18	+	1.23257e19i	−0.406623	+	0.704292i
$914$	−1.22851e18	+	2.12784e18i	−0.0696991	+	0.120722i
$915$	6.94633e17	+	1.20314e18i	0.0391308	+	0.0677765i
$916$	−4.64942e18			−0.260063
$917$		0			0
$918$	−3.63483e18			−0.200451
$919$	−1.24631e19	−	2.15867e19i	−0.682455	−	1.18205i	−0.974229	−	0.225560i	$-0.927579\pi$
$919$	−1.24631e19	−	2.15867e19i	−0.682455	−	1.18205i	0.291774	−	0.956487i	$-0.405754\pi$
$920$	−1.42011e18	+	2.45970e18i	−0.0772148	+	0.133740i
$921$	−4.25655e18	+	7.37256e18i	−0.229811	+	0.398044i
$922$	−1.00891e19	−	1.74748e19i	−0.540881	−	0.936833i
$923$	3.51510e18			0.187123
$924$		0			0
$925$	1.93264e19			1.01445
$926$	−7.31653e18	−	1.26726e19i	−0.381359	−	0.660533i
$927$	−5.63218e18	+	9.75522e18i	−0.291513	+	0.504916i
$928$	−1.32260e18	+	2.29080e18i	−0.0679775	+	0.117741i
$929$	1.55121e19	+	2.68677e19i	0.791713	+	1.37129i	0.924906	+	0.380197i	$0.124144\pi$
$929$	1.55121e19	+	2.68677e19i	0.791713	+	1.37129i	−0.133193	+	0.991090i	$0.542523\pi$
$930$	8.41858e18			0.426678
$931$		0			0
$932$	−8.35542e18			−0.417604
$933$	6.95399e18	+	1.20447e19i	0.345146	+	0.597811i
$934$	−6.81668e18	+	1.18068e19i	−0.335984	+	0.581941i
$935$	−1.22157e18	+	2.11582e18i	−0.0597920	+	0.103563i
$936$	−4.59815e17	−	7.96422e17i	−0.0223506	−	0.0387124i
$937$	−4.17037e17			−0.0201311			−0.0100655	−	0.999949i	$-0.503204\pi$
$937$	−4.17037e17			−0.0201311			−0.0100655	+	0.999949i	$0.503204\pi$
$938$		0			0
$939$	−8.43023e18			−0.401340
$940$	−2.37278e18	−	4.10978e18i	−0.112183	−	0.194306i
$941$	−9.59391e17	+	1.66171e18i	−0.0450467	+	0.0780232i	−0.887670	−	0.460481i	$-0.847677\pi$
$941$	−9.59391e17	+	1.66171e18i	−0.0450467	+	0.0780232i	0.842623	+	0.538504i	$0.181010\pi$
$942$	−2.53724e18	+	4.39463e18i	−0.118312	+	0.204923i
$943$	−1.59651e19	−	2.76524e19i	−0.739343	−	1.28058i
$944$	−7.71382e18			−0.354774
$945$		0			0
$946$	−2.03745e19			−0.924259
$947$	−1.75162e19	−	3.03389e19i	−0.789158	−	1.36686i	−0.926483	−	0.376336i	$-0.877184\pi$
$947$	−1.75162e19	−	3.03389e19i	−0.789158	−	1.36686i	0.137325	−	0.990526i	$-0.456150\pi$
$948$	7.52192e18	−	1.30284e19i	0.336569	−	0.582955i
$949$	−1.61401e18	+	2.79555e18i	−0.0717260	+	0.124233i
$950$	1.46176e18	+	2.53185e18i	0.0645169	+	0.111747i
$951$	1.82407e19			0.799593
$952$		0			0
$953$	3.82110e19			1.65228			0.826142	−	0.563462i	$-0.190531\pi$
$953$	3.82110e19			1.65228			0.826142	+	0.563462i	$0.190531\pi$
$954$	−4.50532e18	−	7.80345e18i	−0.193491	−	0.335137i
$955$	−5.45802e18	+	9.45357e18i	−0.232816	+	0.403250i
$956$	7.32462e18	−	1.26866e19i	0.310320	−	0.537489i
$957$	7.88475e18	+	1.36568e19i	0.331788	+	0.574673i
$958$	2.02026e18			0.0844368
$959$		0			0
$960$	1.47364e18			0.0607614
$961$	−6.60457e18	−	1.14394e19i	−0.270484	−	0.468493i
$962$	3.35775e18	−	5.81580e18i	0.136587	−	0.236576i
$963$	4.60487e18	−	7.97586e18i	0.186057	−	0.322260i
$964$	−3.71996e18	−	6.44315e18i	−0.149292	−	0.258582i
$965$	9.21972e16			0.00367528
$966$		0			0
$967$	3.71357e19			1.46056			0.730281	−	0.683147i	$-0.239389\pi$
$967$	3.71357e19			1.46056			0.730281	+	0.683147i	$0.239389\pi$
$968$	−2.11783e18	−	3.66819e18i	−0.0827372	−	0.143305i
$969$	−1.33530e18	+	2.31280e18i	−0.0518171	+	0.0897498i
$970$	−3.58550e18	+	6.21027e18i	−0.138208	+	0.239383i
$971$	−5.96924e18	−	1.03390e19i	−0.228557	−	0.395872i	0.728824	−	0.684701i	$-0.240067\pi$
$971$	−5.96924e18	−	1.03390e19i	−0.228557	−	0.395872i	−0.957381	+	0.288829i	$0.906734\pi$
$972$	9.94270e18			0.378158
$973$		0			0
$974$	−3.47512e19			−1.30418
$975$	4.17418e18	+	7.22989e18i	0.155611	+	0.269527i
$976$	5.43456e17	−	9.41293e17i	0.0201252	−	0.0348579i
$977$	4.03279e18	−	6.98499e18i	0.148351	−	0.256952i	−0.782267	−	0.622943i	$-0.785937\pi$
$977$	4.03279e18	−	6.98499e18i	0.148351	−	0.256952i	0.930618	+	0.365992i	$0.119270\pi$
$978$	−1.20379e19	−	2.08502e19i	−0.439893	−	0.761918i
$979$	−1.19309e19			−0.433098
$980$		0			0
$981$	−1.01460e19			−0.363450
$982$	9.18673e18	+	1.59119e19i	0.326916	+	0.566235i
$983$	1.32814e19	−	2.30040e19i	0.469511	−	0.813216i	−0.529882	−	0.848072i	$-0.677764\pi$
$983$	1.32814e19	−	2.30040e19i	0.469511	−	0.813216i	0.999392	+	0.0348552i	$0.0110970\pi$
$984$	−8.28346e18	+	1.43474e19i	−0.290900	+	0.503853i
$985$	3.01277e18	+	5.21827e18i	0.105107	+	0.182050i
$986$	6.26103e18			0.216993
$987$		0			0
$988$	1.01586e18			0.0347468
$989$	2.80316e19	+	4.85521e19i	0.952514	+	1.64980i
$990$	1.25378e18	−	2.17161e18i	0.0423246	−	0.0733083i
$991$	−1.86864e19	+	3.23658e19i	−0.626682	+	1.08544i	0.361531	+	0.932360i	$0.382254\pi$
$991$	−1.86864e19	+	3.23658e19i	−0.626682	+	1.08544i	−0.988213	+	0.153085i	$0.951079\pi$
$992$	−3.29320e18	−	5.70399e18i	−0.109722	−	0.190043i
$993$	−1.98473e19			−0.656950
$994$		0			0
$995$	2.16450e19			0.707145
$996$	−1.01597e19	−	1.75972e19i	−0.329759	−	0.571160i
$997$	7.48500e17	−	1.29644e18i	0.0241364	−	0.0418055i	−0.853705	−	0.520757i	$-0.825650\pi$
$997$	7.48500e17	−	1.29644e18i	0.0241364	−	0.0418055i	0.877841	+	0.478952i	$0.158983\pi$
$998$	1.69416e17	−	2.93437e17i	0.00542757	−	0.00940083i
$999$	1.36214e19	+	2.35930e19i	0.433558	+	0.750945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.14.c.o.67.4		8
7.2	even	3	inner	98.14.c.o.79.4		8
7.3	odd	6		98.14.a.h.1.4		4
7.4	even	3		98.14.a.j.1.1		4
7.5	odd	6		14.14.c.b.9.1	✓	8
7.6	odd	2		14.14.c.b.11.1	yes	8
21.5	even	6		126.14.g.b.37.2		8
21.20	even	2		126.14.g.b.109.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.1	✓	8	7.5	odd	6
14.14.c.b.11.1	yes	8	7.6	odd	2
98.14.a.h.1.4		4	7.3	odd	6
98.14.a.j.1.1		4	7.4	even	3
98.14.c.o.67.4		8	1.1	even	1	trivial
98.14.c.o.79.4		8	7.2	even	3	inner
126.14.g.b.37.2		8	21.5	even	6
126.14.g.b.109.2		8	21.20	even	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(32.0000 + 55.4256i) q^{2} +(746.854 - 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(7178.20 + 12433.0i) q^{5} +95597.3 q^{6} -262144. q^{8} +(-318420. - 551520. i) q^{9} +O(q^{10})\)	\(q+(32.0000 + 55.4256i) q^{2} +(746.854 - 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(7178.20 + 12433.0i) q^{5} +95597.3 q^{6} -262144. q^{8} +(-318420. - 551520. i) q^{9} +(-459405. + 795712. i) q^{10} +(2.14272e6 - 3.71130e6i) q^{11} +(3.05911e6 + 5.29854e6i) q^{12} -5.50861e6 q^{13} +2.14443e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(-1.98554e7 + 3.43905e7i) q^{17} +(2.03789e7 - 3.52973e7i) q^{18} +(2.25114e7 + 3.89910e7i) q^{19} -5.88038e7 q^{20} +2.74268e8 q^{22} +(-3.77343e8 - 6.53577e8i) q^{23} +(-1.95783e8 + 3.39107e8i) q^{24} +(5.07299e8 - 8.78667e8i) q^{25} +(-1.76275e8 - 3.05318e8i) q^{26} +1.43020e9 q^{27} -2.46353e9 q^{29} +(6.86216e8 + 1.18856e9i) q^{30} +(3.06703e9 - 5.31225e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(-3.20060e9 - 5.54359e9i) q^{33} -2.54149e9 q^{34} +2.60850e9 q^{36} +(9.52417e9 + 1.64963e10i) q^{37} +(-1.44073e9 + 2.49542e9i) q^{38} +(-4.11413e9 + 7.12588e9i) q^{39} +(-1.88172e9 - 3.25924e9i) q^{40} +4.23093e10 q^{41} -7.42867e10 q^{43} +(8.77657e9 + 1.52015e10i) q^{44} +(4.57137e9 - 7.91784e9i) q^{45} +(2.41499e10 - 4.18289e10i) q^{46} +(4.03508e10 + 6.98897e10i) q^{47} -2.50603e10 q^{48} +6.49342e10 q^{50} +(2.96581e10 + 5.13694e10i) q^{51} +(1.12816e10 - 1.95404e10i) q^{52} +(1.10539e11 - 1.91459e11i) q^{53} +(4.57664e10 + 7.92697e10i) q^{54} +6.15234e10 q^{55} +6.72511e10 q^{57} +(-7.88329e10 - 1.36543e11i) q^{58} +(2.29890e11 - 3.98181e11i) q^{59} +(-4.39178e10 + 7.60679e10i) q^{60} +(3.23925e10 + 5.61055e10i) q^{61} +3.92580e11 q^{62} +6.87195e10 q^{64} +(-3.95419e10 - 6.84885e10i) q^{65} +(2.04838e11 - 3.54790e11i) q^{66} +(2.07214e11 - 3.58905e11i) q^{67} +(-8.13276e10 - 1.40864e11i) q^{68} -1.12728e12 q^{69} -6.38110e11 q^{71} +(8.34720e10 + 1.44578e11i) q^{72} +(2.92998e11 - 5.07488e11i) q^{73} +(-6.09547e11 + 1.05577e12i) q^{74} +(-7.57756e11 - 1.31247e12i) q^{75} -1.84414e11 q^{76} -5.26608e11 q^{78} +(-1.22943e12 - 2.12943e12i) q^{79} +(1.20430e11 - 2.08591e11i) q^{80} +(1.57581e12 - 2.72939e12i) q^{81} +(1.35390e12 + 2.34502e12i) q^{82} -3.32114e12 q^{83} -5.70103e11 q^{85} +(-2.37717e12 - 4.11739e12i) q^{86} +(-1.83990e12 + 3.18679e12i) q^{87} +(-5.61701e11 + 9.72894e11i) q^{88} +(-1.39203e12 - 2.41106e12i) q^{89} +5.85135e11 q^{90} +3.09119e12 q^{92} +(-4.58125e12 - 7.93495e12i) q^{93} +(-2.58245e12 + 4.47294e12i) q^{94} +(-3.23183e11 + 5.59770e11i) q^{95} +(-8.01928e11 - 1.38898e12i) q^{96} +7.80467e12 q^{97} -2.72914e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{2} - 182 q^{3} - 16384 q^{4} - 1792 q^{5} - 23296 q^{6} - 2097152 q^{8} + 599840 q^{9}+O(q^{10}) \) 8 * q + 256 * q^2 - 182 * q^3 - 16384 * q^4 - 1792 * q^5 - 23296 * q^6 - 2097152 * q^8 + 599840 * q^9	\( 8 q + 256 q^{2} - 182 q^{3} - 16384 q^{4} - 1792 q^{5} - 23296 q^{6} - 2097152 q^{8} + 599840 q^{9} + 114688 q^{10} - 8726914 q^{11} - 745472 q^{12} - 1438416 q^{13} - 136873212 q^{15} - 67108864 q^{16} + 7943068 q^{17} - 38389760 q^{18} + 215706806 q^{19} + 14680064 q^{20} - 1117044992 q^{22} - 61927978 q^{23} + 47710208 q^{24} - 1327844792 q^{25} - 46029312 q^{26} + 3268643812 q^{27} - 6325846064 q^{29} - 4379942784 q^{30} - 6113775570 q^{31} + 4294967296 q^{32} - 25235960652 q^{33} + 1016712704 q^{34} - 4913889280 q^{36} - 3945652880 q^{37} - 13805235584 q^{38} - 23545599116 q^{39} + 469762048 q^{40} - 86378579952 q^{41} - 109074124256 q^{43} - 35745439744 q^{44} + 104964468168 q^{45} + 3963390592 q^{46} + 3141202722 q^{47} + 6106906624 q^{48} - 169964133376 q^{50} - 241278267462 q^{51} + 2945875968 q^{52} + 149625680376 q^{53} + 104596601984 q^{54} - 174912009748 q^{55} - 128207489960 q^{57} - 202427074048 q^{58} + 866297313938 q^{59} + 280316338176 q^{60} + 477908594184 q^{61} - 782563272960 q^{62} + 549755813888 q^{64} - 1099748343120 q^{65} + 1615101481728 q^{66} + 1895501016278 q^{67} + 32534806528 q^{68} - 3503301895632 q^{69} + 638832672128 q^{71} - 157244456960 q^{72} + 2966596192756 q^{73} + 252521784320 q^{74} + 1331079867376 q^{75} - 1767070154752 q^{76} - 3013836686848 q^{78} - 6505959677634 q^{79} - 30064771072 q^{80} + 2449216493684 q^{81} - 2764114558464 q^{82} + 3379817135968 q^{83} - 16684556982464 q^{85} - 3490371976192 q^{86} + 5273311164492 q^{87} + 2287708143616 q^{88} - 9586601667468 q^{89} + 13435451925504 q^{90} + 507313995776 q^{92} - 14195747226896 q^{93} - 201036974208 q^{94} + 14384410136978 q^{95} + 195421011968 q^{96} + 44560735311568 q^{97} + 24706419985464 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 - 182 * q^3 - 16384 * q^4 - 1792 * q^5 - 23296 * q^6 - 2097152 * q^8 + 599840 * q^9 + 114688 * q^10 - 8726914 * q^11 - 745472 * q^12 - 1438416 * q^13 - 136873212 * q^15 - 67108864 * q^16 + 7943068 * q^17 - 38389760 * q^18 + 215706806 * q^19 + 14680064 * q^20 - 1117044992 * q^22 - 61927978 * q^23 + 47710208 * q^24 - 1327844792 * q^25 - 46029312 * q^26 + 3268643812 * q^27 - 6325846064 * q^29 - 4379942784 * q^30 - 6113775570 * q^31 + 4294967296 * q^32 - 25235960652 * q^33 + 1016712704 * q^34 - 4913889280 * q^36 - 3945652880 * q^37 - 13805235584 * q^38 - 23545599116 * q^39 + 469762048 * q^40 - 86378579952 * q^41 - 109074124256 * q^43 - 35745439744 * q^44 + 104964468168 * q^45 + 3963390592 * q^46 + 3141202722 * q^47 + 6106906624 * q^48 - 169964133376 * q^50 - 241278267462 * q^51 + 2945875968 * q^52 + 149625680376 * q^53 + 104596601984 * q^54 - 174912009748 * q^55 - 128207489960 * q^57 - 202427074048 * q^58 + 866297313938 * q^59 + 280316338176 * q^60 + 477908594184 * q^61 - 782563272960 * q^62 + 549755813888 * q^64 - 1099748343120 * q^65 + 1615101481728 * q^66 + 1895501016278 * q^67 + 32534806528 * q^68 - 3503301895632 * q^69 + 638832672128 * q^71 - 157244456960 * q^72 + 2966596192756 * q^73 + 252521784320 * q^74 + 1331079867376 * q^75 - 1767070154752 * q^76 - 3013836686848 * q^78 - 6505959677634 * q^79 - 30064771072 * q^80 + 2449216493684 * q^81 - 2764114558464 * q^82 + 3379817135968 * q^83 - 16684556982464 * q^85 - 3490371976192 * q^86 + 5273311164492 * q^87 + 2287708143616 * q^88 - 9586601667468 * q^89 + 13435451925504 * q^90 + 507313995776 * q^92 - 14195747226896 * q^93 - 201036974208 * q^94 + 14384410136978 * q^95 + 195421011968 * q^96 + 44560735311568 * q^97 + 24706419985464 * q^99

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