LMFDB - Embedded newform 180.9.c.a.91.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$73.3281498110$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15630052 x^{14} + 100431843210026 x^{12} + \cdots + 41\!\cdots\!25 $ x^16 + 15630052x^14 + 100431843210026x^12 + 340815019972466359600x^10 + 649371842679456980126645875x^8 + 673266389314517670870339888950000x^6 + 325232066696204458027621996847496406250x^4 + 40989992790937256917294995464570014826562500*x^2 + 414509653712510017117723543124903397237712890625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{58}\cdot 3^{4}\cdot 5^{16} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Root			$-1662.79i$ of defining polynomial
Character	$\chi$	$=$	180.91
Dual form			180.9.c.a.91.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.5676 + 11.0540i) q^{2} +(11.6196 - 255.736i) q^{4} -279.508 q^{5} -3325.58i q^{7} +(2692.49 + 3086.70i) q^{8} +(3233.25 - 3089.68i) q^{10} +6361.21i q^{11} -30777.4 q^{13} +(36760.8 + 38469.0i) q^{14} +(-65266.0 - 5943.09i) q^{16} -122375. q^{17} +7554.43i q^{19} +(-3247.77 + 71480.4i) q^{20} +(-70316.6 - 73584.1i) q^{22} -406311. i q^{23} +78125.0 q^{25} +(356021. - 340213. i) q^{26} +(-850471. - 38641.8i) q^{28} -828838. q^{29} +1.39549e6i q^{31} +(820666. - 652701. i) q^{32} +(1.41559e6 - 1.35273e6i) q^{34} +929527. i q^{35} -386059. q^{37} +(-83506.4 - 87386.8i) q^{38} +(-752574. - 862759. i) q^{40} +972335. q^{41} -4.61450e6i q^{43} +(1.62679e6 + 73914.5i) q^{44} +(4.49135e6 + 4.70005e6i) q^{46} +1.87219e6i q^{47} -5.29467e6 q^{49} +(-903720. + 863591. i) q^{50} +(-357620. + 7.87090e6i) q^{52} +8.01944e6 q^{53} -1.77801e6i q^{55} +(1.02651e7 - 8.95408e6i) q^{56} +(9.58768e6 - 9.16195e6i) q^{58} -6.18263e6i q^{59} +9.79320e6 q^{61} +(-1.54257e7 - 1.61425e7i) q^{62} +(-2.27822e6 + 1.66218e7i) q^{64} +8.60255e6 q^{65} +1.19411e6i q^{67} +(-1.42195e6 + 3.12958e7i) q^{68} +(-1.02750e7 - 1.07524e7i) q^{70} -3.62332e7i q^{71} +3.35548e7 q^{73} +(4.46578e6 - 4.26748e6i) q^{74} +(1.93194e6 + 87779.2i) q^{76} +2.11547e7 q^{77} -1.22874e6i q^{79} +(1.82424e7 + 1.66114e6i) q^{80} +(-1.12476e7 + 1.07482e7i) q^{82} +6.96923e7i q^{83} +3.42049e7 q^{85} +(5.10086e7 + 5.33788e7i) q^{86} +(-1.96352e7 + 1.71275e7i) q^{88} -5.58347e7 q^{89} +1.02353e8i q^{91} +(-1.03908e8 - 4.72116e6i) q^{92} +(-2.06951e7 - 2.16567e7i) q^{94} -2.11153e6i q^{95} -5.97582e7 q^{97} +(6.12467e7 - 5.85271e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) $ 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−11.5676	+	11.0540i	−0.722976	+	0.690873i
$2$	−11.5676	+	11.0540i	−0.722976	+	0.690873i
$3$		0			0
$3$		0			0
$4$	11.6196	−	255.736i	0.0453889	−	0.998969i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$		0			0
$7$		−	3325.58i		−	1.38508i	−0.721379	−	0.692540i	$-0.756492\pi$
$7$		−	3325.58i		−	1.38508i	0.721379	−	0.692540i	$-0.243508\pi$
$8$	2692.49	+	3086.70i	0.657346	+	0.753589i
$9$		0			0
$10$	3233.25	−	3089.68i	0.323325	−	0.308968i
$11$			6361.21i			0.434479i	0.976118	+	0.217240i	$0.0697053\pi$
$11$			6361.21i			0.434479i	−0.976118	+	0.217240i	$0.930295\pi$
$12$		0			0
$13$	−30777.4			−1.07760			−0.538801	−	0.842433i	$-0.681123\pi$
$13$	−30777.4			−1.07760			−0.538801	+	0.842433i	$0.681123\pi$
$14$	36760.8	+	38469.0i	0.956915	+	1.00138i
$15$		0			0
$16$	−65266.0	−	5943.09i	−0.995880	−	0.0906843i
$17$	−122375.			−1.46520			−0.732601	−	0.680658i	$-0.761694\pi$
$17$	−122375.			−1.46520			−0.732601	+	0.680658i	$0.761694\pi$
$18$		0			0
$19$			7554.43i			0.0579679i	0.999580	+	0.0289839i	$0.00922717\pi$
$19$			7554.43i			0.0579679i	−0.999580	+	0.0289839i	$0.990773\pi$
$20$	−3247.77	+	71480.4i	−0.0202985	+	0.446753i
$21$		0			0
$22$	−70316.6	−	73584.1i	−0.300170	−	0.314118i
$23$		−	406311.i		−	1.45194i	−0.687729	−	0.725968i	$-0.741392\pi$
$23$		−	406311.i		−	1.45194i	0.687729	−	0.725968i	$-0.258608\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	356021.	−	340213.i	0.779081	−	0.744487i
$27$		0			0
$28$	−850471.	−	38641.8i	−1.38365	−	0.0628673i
$29$	−828838.			−1.17187			−0.585933	−	0.810360i	$-0.699272\pi$
$29$	−828838.			−1.17187			−0.585933	+	0.810360i	$0.699272\pi$
$30$		0			0
$31$			1.39549e6i			1.51106i	0.655116	+	0.755528i	$0.272620\pi$
$31$			1.39549e6i			1.51106i	−0.655116	+	0.755528i	$0.727380\pi$
$32$	820666.	−	652701.i	0.782649	−	0.622464i
$33$		0			0
$34$	1.41559e6	−	1.35273e6i	1.05931	−	1.01227i
$35$			929527.i			0.619427i
$36$		0			0
$37$	−386059.			−0.205990			−0.102995	−	0.994682i	$-0.532843\pi$
$37$	−386059.			−0.205990			−0.102995	+	0.994682i	$0.532843\pi$
$38$	−83506.4	−	87386.8i	−0.0400484	−	0.0419094i
$39$		0			0
$40$	−752574.	−	862759.i	−0.293974	−	0.337015i
$41$	972335.			0.344097			0.172048	−	0.985089i	$-0.444961\pi$
$41$	972335.			0.344097			0.172048	+	0.985089i	$0.444961\pi$
$42$		0			0
$43$		−	4.61450e6i		−	1.34974i	−0.737935	−	0.674871i	$-0.764199\pi$
$43$		−	4.61450e6i		−	1.34974i	0.737935	−	0.674871i	$-0.235801\pi$
$44$	1.62679e6	+	73914.5i	0.434032	+	0.0197205i
$45$		0			0
$46$	4.49135e6	+	4.70005e6i	1.00310	+	1.04971i
$47$			1.87219e6i			0.383670i	0.981427	+	0.191835i	$0.0614438\pi$
$47$			1.87219e6i			0.383670i	−0.981427	+	0.191835i	$0.938556\pi$
$48$		0			0
$49$	−5.29467e6			−0.918447
$50$	−903720.	+	863591.i	−0.144595	+	0.138175i
$51$		0			0
$52$	−357620.	+	7.87090e6i	−0.0489112	+	1.07649i
$53$	8.01944e6			1.01634			0.508172	−	0.861256i	$-0.330322\pi$
$53$	8.01944e6			1.01634			0.508172	+	0.861256i	$0.330322\pi$
$54$		0			0
$55$		−	1.77801e6i		−	0.194305i
$56$	1.02651e7	−	8.95408e6i	1.04378	−	0.910477i
$57$		0			0
$58$	9.58768e6	−	9.16195e6i	0.847231	−	0.809610i
$59$		−	6.18263e6i		−	0.510229i	−0.966911	−	0.255115i	$-0.917887\pi$
$59$		−	6.18263e6i		−	0.510229i	0.966911	−	0.255115i	$-0.0821132\pi$
$60$		0			0
$61$	9.79320e6			0.707303			0.353651	−	0.935377i	$-0.384940\pi$
$61$	9.79320e6			0.707303			0.353651	+	0.935377i	$0.384940\pi$
$62$	−1.54257e7	−	1.61425e7i	−1.04395	−	1.09246i
$63$		0			0
$64$	−2.27822e6	+	1.66218e7i	−0.135793	+	0.990737i
$65$	8.60255e6			0.481919
$66$		0			0
$67$			1.19411e6i			0.0592579i	0.999561	+	0.0296290i	$0.00943257\pi$
$67$			1.19411e6i			0.0592579i	−0.999561	+	0.0296290i	$0.990567\pi$
$68$	−1.42195e6	+	3.12958e7i	−0.0665039	+	1.46369i
$69$		0			0
$70$	−1.02750e7	−	1.07524e7i	−0.427945	−	0.447831i
$71$		−	3.62332e7i		−	1.42585i	−0.701242	−	0.712923i	$-0.747371\pi$
$71$		−	3.62332e7i		−	1.42585i	0.701242	−	0.712923i	$-0.252629\pi$
$72$		0			0
$73$	3.35548e7			1.18158			0.590790	−	0.806826i	$-0.298816\pi$
$73$	3.35548e7			1.18158			0.590790	+	0.806826i	$0.298816\pi$
$74$	4.46578e6	−	4.26748e6i	0.148926	−	0.142313i
$75$		0			0
$76$	1.93194e6	+	87779.2i	0.0579081	+	0.00263110i
$77$	2.11547e7			0.601789
$78$		0			0
$79$		−	1.22874e6i		−	0.0315466i	−0.999876	−	0.0157733i	$-0.994979\pi$
$79$		−	1.22874e6i		−	0.0315466i	0.999876	−	0.0157733i	$-0.00502101\pi$
$80$	1.82424e7	+	1.66114e6i	0.445371	+	0.0405552i
$81$		0			0
$82$	−1.12476e7	+	1.07482e7i	−0.248774	+	0.237727i
$83$			6.96923e7i			1.46849i	0.678882	+	0.734247i	$0.262465\pi$
$83$			6.96923e7i			1.46849i	−0.678882	+	0.734247i	$0.737535\pi$
$84$		0			0
$85$	3.42049e7			0.655258
$86$	5.10086e7	+	5.33788e7i	0.932501	+	0.975832i
$87$		0			0
$88$	−1.96352e7	+	1.71275e7i	−0.327419	+	0.285603i
$89$	−5.58347e7			−0.889907			−0.444953	−	0.895554i	$-0.646780\pi$
$89$	−5.58347e7			−0.889907			−0.444953	+	0.895554i	$0.646780\pi$
$90$		0			0
$91$			1.02353e8i			1.49257i
$92$	−1.03908e8	−	4.72116e6i	−1.45044	−	0.0659018i
$93$		0			0
$94$	−2.06951e7	−	2.16567e7i	−0.265067	−	0.277384i
$95$		−	2.11153e6i		−	0.0259240i
$96$		0			0
$97$	−5.97582e7			−0.675010			−0.337505	−	0.941324i	$-0.609583\pi$
$97$	−5.97582e7			−0.675010			−0.337505	+	0.941324i	$0.609583\pi$
$98$	6.12467e7	−	5.85271e7i	0.664016	−	0.634531i
$99$		0			0
$100$	907778.	−	1.99794e7i	0.00907778	−	0.199794i
$101$	−9.62751e7			−0.925185			−0.462593	−	0.886571i	$-0.653081\pi$
$101$	−9.62751e7			−0.925185			−0.462593	+	0.886571i	$0.653081\pi$
$102$		0			0
$103$			1.96312e8i			1.74421i	0.489320	+	0.872104i	$0.337245\pi$
$103$			1.96312e8i			1.74421i	−0.489320	+	0.872104i	$0.662755\pi$
$104$	−8.28678e7	−	9.50006e7i	−0.708358	−	0.812070i
$105$		0			0
$106$	−9.27658e7	+	8.86466e7i	−0.734792	+	0.702164i
$107$			1.64435e8i			1.25447i	0.778832	+	0.627233i	$0.215813\pi$
$107$			1.64435e8i			1.25447i	−0.778832	+	0.627233i	$0.784187\pi$
$108$		0			0
$109$	−1.81680e8			−1.28707			−0.643534	−	0.765417i	$-0.722533\pi$
$109$	−1.81680e8			−1.28707			−0.643534	+	0.765417i	$0.722533\pi$
$110$	1.96541e7	+	2.05674e7i	0.134240	+	0.140478i
$111$		0			0
$112$	−1.97642e7	+	2.17047e8i	−0.125605	+	1.37937i
$113$	1.30629e8			0.801172			0.400586	−	0.916259i	$-0.368807\pi$
$113$	1.30629e8			0.801172			0.400586	+	0.916259i	$0.368807\pi$
$114$		0			0
$115$			1.13567e8i			0.649325i
$116$	−9.63074e6	+	2.11964e8i	−0.0531897	+	1.17066i
$117$		0			0
$118$	6.83426e7	+	7.15183e7i	0.352504	+	0.368883i
$119$			4.06968e8i			2.02942i
$120$		0			0
$121$	1.73894e8			0.811228
$122$	−1.13284e8	+	1.08254e8i	−0.511363	+	0.488656i
$123$		0			0
$124$	3.56878e8	+	1.62150e7i	1.50950	+	0.0685852i
$125$	−2.18366e7			−0.0894427
$126$		0			0
$127$		−	4.45982e8i		−	1.71436i	−0.515015	−	0.857181i	$-0.672214\pi$
$127$		−	4.45982e8i		−	1.71436i	0.515015	−	0.857181i	$-0.327786\pi$
$128$	−1.57383e8	−	2.17458e8i	−0.586299	−	0.810095i
$129$		0			0
$130$	−9.95110e7	+	9.50923e7i	−0.348416	+	0.332945i
$131$			1.31555e8i			0.446707i	0.974738	+	0.223353i	$0.0717004\pi$
$131$			1.31555e8i			0.446707i	−0.974738	+	0.223353i	$0.928300\pi$
$132$		0			0
$133$	2.51228e7			0.0802902
$134$	−1.31997e7	−	1.38130e7i	−0.0409397	−	0.0428421i
$135$		0			0
$136$	−3.29494e8	−	3.77735e8i	−0.963145	−	1.10416i
$137$	3.26396e8			0.926536			0.463268	−	0.886218i	$-0.346677\pi$
$137$	3.26396e8			0.926536			0.463268	+	0.886218i	$0.346677\pi$
$138$		0			0
$139$			6.48927e8i			1.73835i	0.494506	+	0.869174i	$0.335349\pi$
$139$			6.48927e8i			1.73835i	−0.494506	+	0.869174i	$0.664651\pi$
$140$	2.37714e8	+	1.08007e7i	0.618788	+	0.0281151i
$141$		0			0
$142$	4.00520e8	+	4.19131e8i	0.985079	+	1.03085i
$143$		−	1.95782e8i		−	0.468196i
$144$		0			0
$145$	2.31667e8			0.524074
$146$	−3.88149e8	+	3.70913e8i	−0.854253	+	0.816321i
$147$		0			0
$148$	−4.48584e6	+	9.87292e7i	−0.00934968	+	0.205778i
$149$	7.30660e8			1.48242			0.741208	−	0.671276i	$-0.234253\pi$
$149$	7.30660e8			1.48242			0.741208	+	0.671276i	$0.234253\pi$
$150$		0			0
$151$			7.74114e8i			1.48901i	0.667618	+	0.744504i	$0.267314\pi$
$151$			7.74114e8i			1.48901i	−0.667618	+	0.744504i	$0.732686\pi$
$152$	−2.33183e7	+	2.03402e7i	−0.0436840	+	0.0381049i
$153$		0			0
$154$	−2.44710e8	+	2.33843e8i	−0.435079	+	0.415760i
$155$		−	3.90052e8i		−	0.675765i
$156$		0			0
$157$	3.17523e8			0.522609			0.261304	−	0.965256i	$-0.415847\pi$
$157$	3.17523e8			0.522609			0.261304	+	0.965256i	$0.415847\pi$
$158$	1.35825e7	+	1.42136e7i	0.0217947	+	0.0228075i
$159$		0			0
$160$	−2.29383e8	+	1.82435e8i	−0.350011	+	0.278374i
$161$	−1.35122e9			−2.01105
$162$		0			0
$163$			2.02004e7i			0.0286161i	0.999898	+	0.0143081i	$0.00455455\pi$
$163$			2.02004e7i			0.0286161i	−0.999898	+	0.0143081i	$0.995445\pi$
$164$	1.12981e7	−	2.48661e8i	0.0156182	−	0.343742i
$165$		0			0
$166$	−7.70376e8	−	8.06174e8i	−1.01454	−	1.06169i
$167$		−	5.65743e7i		−	0.0727366i	−0.999338	−	0.0363683i	$-0.988421\pi$
$167$		−	5.65743e7i		−	0.0727366i	0.999338	−	0.0363683i	$-0.0115789\pi$
$168$		0			0
$169$	1.31518e8			0.161228
$170$	−3.95669e8	+	3.78100e8i	−0.473736	+	0.452700i
$171$		0			0
$172$	−1.18009e9	−	5.36185e7i	−1.34835	−	0.0612634i
$173$	1.09785e9			1.22563			0.612813	−	0.790228i	$-0.290038\pi$
$173$	1.09785e9			1.22563			0.612813	+	0.790228i	$0.290038\pi$
$174$		0			0
$175$		−	2.59811e8i		−	0.277016i
$176$	3.78052e7	−	4.15171e8i	0.0394004	−	0.432689i
$177$		0			0
$178$	6.45875e8	−	6.17196e8i	0.643381	−	0.614813i
$179$			6.44793e8i			0.628070i	0.949411	+	0.314035i	$0.101681\pi$
$179$			6.44793e8i			0.628070i	−0.949411	+	0.314035i	$0.898319\pi$
$180$		0			0
$181$	−6.79018e8			−0.632655			−0.316328	−	0.948650i	$-0.602450\pi$
$181$	−6.79018e8			−0.632655			−0.316328	+	0.948650i	$0.602450\pi$
$182$	−1.13140e9	−	1.18398e9i	−1.03117	−	1.07909i
$183$		0			0
$184$	1.25416e9	−	1.09399e9i	1.09416	−	0.954424i
$185$	1.07907e8			0.0921217
$186$		0			0
$187$		−	7.78454e8i		−	0.636600i
$188$	4.78786e8	+	2.17540e7i	0.383275	+	0.0174144i
$189$		0			0
$190$	2.33408e7	+	2.44253e7i	0.0179102	+	0.0187424i
$191$			1.53738e8i			0.115518i	0.998331	+	0.0577588i	$0.0183954\pi$
$191$			1.53738e8i			0.115518i	−0.998331	+	0.0577588i	$0.981605\pi$
$192$		0			0
$193$	9.67761e7			0.0697491			0.0348746	−	0.999392i	$-0.488897\pi$
$193$	9.67761e7			0.0697491			0.0348746	+	0.999392i	$0.488897\pi$
$194$	6.91259e8	−	6.60565e8i	0.488016	−	0.466346i
$195$		0			0
$196$	−6.15217e7	+	1.35404e9i	−0.0416873	+	0.917501i
$197$	2.84766e9			1.89070			0.945352	−	0.326051i	$-0.105718\pi$
$197$	2.84766e9			1.89070			0.945352	+	0.326051i	$0.105718\pi$
$198$		0			0
$199$		−	8.71254e8i		−	0.555562i	−0.960644	−	0.277781i	$-0.910401\pi$
$199$		−	8.71254e8i		−	0.555562i	0.960644	−	0.277781i	$-0.0895990\pi$
$200$	2.10351e8	+	2.41148e8i	0.131469	+	0.150718i
$201$		0			0
$202$	1.11367e9	−	1.06422e9i	0.668887	−	0.639185i
$203$			2.75637e9i			1.62313i
$204$		0			0
$205$	−2.71776e8			−0.153885
$206$	−2.17003e9	−	2.27087e9i	−1.20503	−	1.26102i
$207$		0			0
$208$	2.00872e9	+	1.82913e8i	1.07316	+	0.0977216i
$209$	−4.80553e7			−0.0251858
$210$		0			0
$211$			2.22378e9i			1.12192i	0.827843	+	0.560960i	$0.189568\pi$
$211$			2.22378e9i			1.12192i	−0.827843	+	0.560960i	$0.810432\pi$
$212$	9.31824e7	−	2.05086e9i	0.0461307	−	1.01530i
$213$		0			0
$214$	−1.81766e9	−	1.90212e9i	−0.866676	−	0.906949i
$215$			1.28979e9i			0.603623i
$216$		0			0
$217$	4.64082e9			2.09293
$218$	2.10161e9	−	2.00829e9i	0.930520	−	0.889201i
$219$		0			0
$220$	−4.54702e8	−	2.06597e7i	−0.194105	−	0.00881930i
$221$	3.76639e9			1.57891
$222$		0			0
$223$		−	1.76089e9i		−	0.712054i	−0.934476	−	0.356027i	$-0.884131\pi$
$223$		−	1.76089e9i		−	0.712054i	0.934476	−	0.356027i	$-0.115869\pi$
$224$	−2.17061e9	−	2.72919e9i	−0.862162	−	1.08403i
$225$		0			0
$226$	−1.51107e9	+	1.44397e9i	−0.579228	+	0.553508i
$227$		−	1.85447e9i		−	0.698418i	−0.937045	−	0.349209i	$-0.886450\pi$
$227$		−	1.85447e9i		−	0.698418i	0.937045	−	0.349209i	$-0.113550\pi$
$228$		0			0
$229$	−1.13087e9			−0.411218			−0.205609	−	0.978634i	$-0.565917\pi$
$229$	−1.13087e9			−0.411218			−0.205609	+	0.978634i	$0.565917\pi$
$230$	−1.25537e9	−	1.31370e9i	−0.448601	−	0.469447i
$231$		0			0
$232$	−2.23164e9	−	2.55837e9i	−0.770321	−	0.883105i
$233$	−2.24935e9			−0.763191			−0.381596	−	0.924329i	$-0.624625\pi$
$233$	−2.24935e9			−0.763191			−0.381596	+	0.924329i	$0.624625\pi$
$234$		0			0
$235$		−	5.23292e8i		−	0.171582i
$236$	−1.58112e9	−	7.18395e7i	−0.509703	−	0.0231587i
$237$		0			0
$238$	−4.49861e9	−	4.70765e9i	−1.40207	−	1.46722i
$239$		−	2.77234e9i		−	0.849679i	−0.905269	−	0.424840i	$-0.860331\pi$
$239$		−	2.77234e9i		−	0.849679i	0.905269	−	0.424840i	$-0.139669\pi$
$240$		0			0
$241$	−1.60515e8			−0.0475826			−0.0237913	−	0.999717i	$-0.507574\pi$
$241$	−1.60515e8			−0.0475826			−0.0237913	+	0.999717i	$0.507574\pi$
$242$	−2.01154e9	+	1.92222e9i	−0.586498	+	0.560455i
$243$		0			0
$244$	1.13793e8	−	2.50448e9i	0.0321037	−	0.706574i
$245$	1.47990e9			0.410742
$246$		0			0
$247$		−	2.32506e8i		−	0.0624663i
$248$	−4.30747e9	+	3.75735e9i	−1.13872	+	0.993287i
$249$		0			0
$250$	2.52597e8	−	2.41381e8i	0.0646649	−	0.0617936i
$251$			5.77680e9i			1.45543i	0.685877	+	0.727717i	$0.259419\pi$
$251$			5.77680e9i			1.45543i	−0.685877	+	0.727717i	$0.740581\pi$
$252$		0			0
$253$	2.58463e9			0.630836
$254$	4.92987e9	+	5.15895e9i	1.18441	+	1.23944i
$255$		0			0
$256$	4.22433e9	+	7.75762e8i	0.983553	+	0.180621i
$257$	−4.57743e9			−1.04928			−0.524638	−	0.851326i	$-0.675799\pi$
$257$	−4.57743e9			−1.04928			−0.524638	+	0.851326i	$0.675799\pi$
$258$		0			0
$259$			1.28387e9i			0.285313i
$260$	9.99578e7	−	2.19998e9i	0.0218738	−	0.481422i
$261$		0			0
$262$	−1.45421e9	−	1.52178e9i	−0.308618	−	0.322958i
$263$		−	4.85941e8i		−	0.101569i	−0.998710	−	0.0507844i	$-0.983828\pi$
$263$		−	4.85941e8i		−	0.101569i	0.998710	−	0.0507844i	$-0.0161721\pi$
$264$		0			0
$265$	−2.24150e9			−0.454523
$266$	−2.90612e8	+	2.77707e8i	−0.0580479	+	0.0554703i
$267$		0			0
$268$	3.05378e8	+	1.38751e7i	0.0591968	+	0.00268965i
$269$	1.48731e9			0.284049			0.142024	−	0.989863i	$-0.454639\pi$
$269$	1.48731e9			0.284049			0.142024	+	0.989863i	$0.454639\pi$
$270$		0			0
$271$		−	6.79398e9i		−	1.25964i	−0.776740	−	0.629821i	$-0.783128\pi$
$271$		−	6.79398e9i		−	1.25964i	0.776740	−	0.629821i	$-0.216872\pi$
$272$	7.98693e9	+	7.27286e8i	1.45917	+	0.132871i
$273$		0			0
$274$	−3.77562e9	+	3.60797e9i	−0.669863	+	0.640118i
$275$			4.96970e8i			0.0868959i
$276$		0			0
$277$	1.54730e9			0.262818			0.131409	−	0.991328i	$-0.458050\pi$
$277$	1.54730e9			0.262818			0.131409	+	0.991328i	$0.458050\pi$
$278$	−7.17322e9	−	7.50654e9i	−1.20098	−	1.25678i
$279$		0			0
$280$	−2.86917e9	+	2.50274e9i	−0.466793	+	0.407178i
$281$	9.33090e9			1.49657			0.748287	−	0.663375i	$-0.230877\pi$
$281$	9.33090e9			1.49657			0.748287	+	0.663375i	$0.230877\pi$
$282$		0			0
$283$			7.43824e9i			1.15964i	0.814743	+	0.579822i	$0.196878\pi$
$283$			7.43824e9i			1.15964i	−0.814743	+	0.579822i	$0.803122\pi$
$284$	−9.26613e9	−	4.21013e8i	−1.42438	−	0.0647176i
$285$		0			0
$286$	2.16416e9	+	2.26473e9i	0.323464	+	0.338495i
$287$		−	3.23358e9i		−	0.476602i
$288$		0			0
$289$	7.99992e9			1.14682
$290$	−2.67984e9	+	2.56084e9i	−0.378893	+	0.362069i
$291$		0			0
$292$	3.89892e8	−	8.58117e9i	0.0536306	−	1.18036i
$293$	1.59214e9			0.216028			0.108014	−	0.994149i	$-0.465551\pi$
$293$	1.59214e9			0.216028			0.108014	+	0.994149i	$0.465551\pi$
$294$		0			0
$295$			1.72810e9i			0.228181i
$296$	−1.03946e9	−	1.19165e9i	−0.135407	−	0.155232i
$297$		0			0
$298$	−8.45199e9	+	8.07669e9i	−1.07175	+	1.02416i
$299$			1.25052e10i			1.56461i
$300$		0			0
$301$	−1.53459e10			−1.86950
$302$	−8.55703e9	−	8.95465e9i	−1.02872	−	1.07652i
$303$		0			0
$304$	4.48966e7	−	4.93047e8i	0.00525678	−	0.0577290i
$305$	−2.73728e9			−0.316315
$306$		0			0
$307$		−	3.36362e9i		−	0.378663i	−0.981913	−	0.189332i	$-0.939368\pi$
$307$		−	3.36362e9i		−	0.378663i	0.981913	−	0.189332i	$-0.0606321\pi$
$308$	2.45808e8	−	5.41002e9i	0.0273145	−	0.601169i
$309$		0			0
$310$	4.31162e9	+	4.51197e9i	0.466868	+	0.488562i
$311$			1.23254e10i			1.31752i	0.752352	+	0.658761i	$0.228919\pi$
$311$			1.23254e10i			1.31752i	−0.752352	+	0.658761i	$0.771081\pi$
$312$		0			0
$313$	2.77987e9			0.289633			0.144816	−	0.989459i	$-0.453741\pi$
$313$	2.77987e9			0.289633			0.144816	+	0.989459i	$0.453741\pi$
$314$	−3.67299e9	+	3.50989e9i	−0.377834	+	0.361056i
$315$		0			0
$316$	−3.14234e8	−	1.42775e7i	−0.0315141	−	0.00143187i
$317$	5.40177e8			0.0534933			0.0267466	−	0.999642i	$-0.491485\pi$
$317$	5.40177e8			0.0534933			0.0267466	+	0.999642i	$0.491485\pi$
$318$		0			0
$319$		−	5.27241e9i		−	0.509151i
$320$	6.36783e8	−	4.64594e9i	0.0607284	−	0.443071i
$321$		0			0
$322$	1.56304e10	−	1.49363e10i	1.45394	−	1.38938i
$323$		−	9.24475e8i		−	0.0849347i
$324$		0			0
$325$	−2.40449e9			−0.215521
$326$	−2.23295e8	−	2.33671e8i	−0.0197701	−	0.0206888i
$327$		0			0
$328$	2.61800e9	+	3.00131e9i	0.226191	+	0.259307i
$329$	6.22610e9			0.531414
$330$		0			0
$331$			1.21115e10i			1.00899i	0.863414	+	0.504495i	$0.168321\pi$
$331$			1.21115e10i			1.00899i	−0.863414	+	0.504495i	$0.831679\pi$
$332$	1.78228e10	+	8.09794e8i	1.46698	+	0.0666534i
$333$		0			0
$334$	6.25370e8	+	6.54429e8i	0.0502518	+	0.0525868i
$335$		−	3.33765e8i		−	0.0265009i
$336$		0			0
$337$	−9.48812e9			−0.735632			−0.367816	−	0.929899i	$-0.619894\pi$
$337$	−9.48812e9			−0.735632			−0.367816	+	0.929899i	$0.619894\pi$
$338$	−1.52135e9	+	1.45380e9i	−0.116564	+	0.111388i
$339$		0			0
$340$	3.97446e8	−	8.74743e9i	0.0297415	−	0.654583i
$341$	−8.87702e9			−0.656523
$342$		0			0
$343$		−	1.56347e9i		−	0.112957i
$344$	1.42436e10	−	1.24245e10i	1.01715	−	0.887248i
$345$		0			0
$346$	−1.26995e10	+	1.21356e10i	−0.886099	+	0.846752i
$347$		−	9.01032e9i		−	0.621473i	−0.950496	−	0.310737i	$-0.899424\pi$
$347$		−	9.01032e9i		−	0.621473i	0.950496	−	0.310737i	$-0.100576\pi$
$348$		0			0
$349$	2.17409e10			1.46547			0.732733	−	0.680517i	$-0.238245\pi$
$349$	2.17409e10			1.46547			0.732733	+	0.680517i	$0.238245\pi$
$350$	2.87194e9	+	3.00539e9i	0.191383	+	0.200276i
$351$		0			0
$352$	4.15197e9	+	5.22043e9i	0.270448	+	0.340045i
$353$	5.60018e9			0.360664			0.180332	−	0.983606i	$-0.442283\pi$
$353$	5.60018e9			0.360664			0.180332	+	0.983606i	$0.442283\pi$
$354$		0			0
$355$			1.01275e10i			0.637658i
$356$	−6.48775e8	+	1.42790e10i	−0.0403919	+	0.888990i
$357$		0			0
$358$	−7.12752e9	−	7.45872e9i	−0.433917	−	0.454080i
$359$		−	1.31213e10i		−	0.789952i	−0.918692	−	0.394976i	$-0.870753\pi$
$359$		−	1.31213e10i		−	0.789952i	0.918692	−	0.394976i	$-0.129247\pi$
$360$		0			0
$361$	1.69265e10			0.996640
$362$	7.85462e9	−	7.50585e9i	0.457395	−	0.437085i
$363$		0			0
$364$	2.61753e10	+	1.18929e9i	1.49103	+	0.0677460i
$365$	−9.37884e9			−0.528418
$366$		0			0
$367$			9.89380e9i			0.545379i	0.962102	+	0.272690i	$0.0879132\pi$
$367$			9.89380e9i			0.545379i	−0.962102	+	0.272690i	$0.912087\pi$
$368$	−2.41474e9	+	2.65183e10i	−0.131668	+	1.44595i
$369$		0			0
$370$	−1.24822e9	+	1.19280e9i	−0.0666018	+	0.0636444i
$371$		−	2.66693e10i		−	1.40772i
$372$		0			0
$373$	1.01496e10			0.524339			0.262170	−	0.965022i	$-0.415562\pi$
$373$	1.01496e10			0.524339			0.262170	+	0.965022i	$0.415562\pi$
$374$	8.60501e9	+	9.00486e9i	0.439810	+	0.460247i
$375$		0			0
$376$	−5.77888e9	+	5.04084e9i	−0.289129	+	0.252204i
$377$	2.55095e10			1.26281
$378$		0			0
$379$			1.39748e10i			0.677312i	0.940910	+	0.338656i	$0.109972\pi$
$379$			1.39748e10i			0.677312i	−0.940910	+	0.338656i	$0.890028\pi$
$380$	−5.39994e8	−	2.45350e7i	−0.0258973	−	0.00117666i
$381$		0			0
$382$	−1.69942e9	−	1.77838e9i	−0.0798080	−	0.0835165i
$383$			2.31617e10i			1.07640i	0.842816	+	0.538201i	$0.180896\pi$
$383$			2.31617e10i			1.07640i	−0.842816	+	0.538201i	$0.819104\pi$
$384$		0			0
$385$	−5.91292e9			−0.269128
$386$	−1.11947e9	+	1.06976e9i	−0.0504269	+	0.0481878i
$387$		0			0
$388$	−6.94364e8	+	1.52823e10i	−0.0306380	+	0.674314i
$389$	1.13177e10			0.494267			0.247133	−	0.968981i	$-0.420511\pi$
$389$	1.13177e10			0.494267			0.247133	+	0.968981i	$0.420511\pi$
$390$		0			0
$391$			4.97224e10i			2.12738i
$392$	−1.42558e10	−	1.63430e10i	−0.603738	−	0.692132i
$393$		0			0
$394$	−3.29407e10	+	3.14780e10i	−1.36693	+	1.30624i
$395$			3.43444e8i			0.0141081i
$396$		0			0
$397$	1.01291e10			0.407765			0.203882	−	0.978995i	$-0.434644\pi$
$397$	1.01291e10			0.407765			0.203882	+	0.978995i	$0.434644\pi$
$398$	9.63082e9	+	1.00783e10i	0.383823	+	0.401658i
$399$		0			0
$400$	−5.09890e9	−	4.64304e8i	−0.199176	−	0.0181369i
$401$	−1.52259e10			−0.588850			−0.294425	−	0.955675i	$-0.595128\pi$
$401$	−1.52259e10			−0.588850			−0.294425	+	0.955675i	$0.595128\pi$
$402$		0			0
$403$		−	4.29496e10i		−	1.62832i
$404$	−1.11867e9	+	2.46210e10i	−0.0419931	+	0.924232i
$405$		0			0
$406$	−3.04688e10	−	3.18846e10i	−1.12137	−	1.17348i
$407$		−	2.45580e9i		−	0.0894985i
$408$		0			0
$409$	−5.16482e10			−1.84570			−0.922851	−	0.385156i	$-0.874148\pi$
$409$	−5.16482e10			−1.84570			−0.922851	+	0.385156i	$0.874148\pi$
$410$	3.14380e9	−	3.00420e9i	0.111255	−	0.106315i
$411$		0			0
$412$	5.02041e10	+	2.28106e9i	1.74241	+	0.0791678i
$413$	−2.05608e10			−0.706708
$414$		0			0
$415$		−	1.94796e10i		−	0.656731i
$416$	−2.52580e10	+	2.00884e10i	−0.843384	+	0.670769i
$417$		0			0
$418$	5.55886e8	−	5.31202e8i	0.0182088	−	0.0174002i
$419$			2.90780e10i			0.943427i	0.881752	+	0.471714i	$0.156364\pi$
$419$			2.90780e10i			0.943427i	−0.881752	+	0.471714i	$0.843636\pi$
$420$		0			0
$421$	−2.02634e9			−0.0645037			−0.0322519	−	0.999480i	$-0.510268\pi$
$421$	−2.02634e9			−0.0645037			−0.0322519	+	0.999480i	$0.510268\pi$
$422$	−2.45816e10	−	2.57239e10i	−0.775105	−	0.811122i
$423$		0			0
$424$	2.15923e10	+	2.47536e10i	0.668089	+	0.765905i
$425$	−9.56056e9			−0.293040
$426$		0			0
$427$		−	3.25681e10i		−	0.979671i
$428$	4.20519e10	+	1.91066e9i	1.25317	+	0.0569388i
$429$		0			0
$430$	−1.42573e10	−	1.49198e10i	−0.417027	−	0.436405i
$431$		−	2.31188e10i		−	0.669972i	−0.942223	−	0.334986i	$-0.891268\pi$
$431$		−	2.31188e10i		−	0.669972i	0.942223	−	0.334986i	$-0.108732\pi$
$432$		0			0
$433$	−5.16117e10			−1.46824			−0.734119	−	0.679021i	$-0.762405\pi$
$433$	−5.16117e10			−1.46824			−0.734119	+	0.679021i	$0.762405\pi$
$434$	−5.36832e10	+	5.12995e10i	−1.51314	+	1.44595i
$435$		0			0
$436$	−2.11105e9	+	4.64622e10i	−0.0584187	+	1.28574i
$437$	3.06945e9			0.0841656
$438$		0			0
$439$		−	4.07914e10i		−	1.09827i	−0.835733	−	0.549137i	$-0.814957\pi$
$439$		−	4.07914e10i		−	1.09827i	0.835733	−	0.549137i	$-0.185043\pi$
$440$	5.48819e9	−	4.78728e9i	0.146426	−	0.127726i
$441$		0			0
$442$	−4.35682e10	+	4.16336e10i	−1.14151	+	1.09082i
$443$		−	1.78192e9i		−	0.0462671i	−0.999732	−	0.0231336i	$-0.992636\pi$
$443$		−	1.78192e9i		−	0.0462671i	0.999732	−	0.0231336i	$-0.00736430\pi$
$444$		0			0
$445$	1.56063e10			0.397978
$446$	1.94648e10	+	2.03693e10i	0.491939	+	0.514798i
$447$		0			0
$448$	5.52771e10	+	7.57641e9i	1.37225	+	0.188084i
$449$	−5.74811e10			−1.41429			−0.707147	−	0.707067i	$-0.750018\pi$
$449$	−5.74811e10			−1.41429			−0.707147	+	0.707067i	$0.750018\pi$
$450$		0			0
$451$			6.18523e9i			0.149503i
$452$	1.51785e9	−	3.34066e10i	0.0363643	−	0.800347i
$453$		0			0
$454$	2.04992e10	+	2.14518e10i	0.482518	+	0.504940i
$455$		−	2.86084e10i		−	0.667496i
$456$		0			0
$457$	−4.50957e10			−1.03388			−0.516941	−	0.856021i	$-0.672929\pi$
$457$	−4.50957e10			−1.03388			−0.516941	+	0.856021i	$0.672929\pi$
$458$	1.30815e10	−	1.25006e10i	0.297301	−	0.284099i
$459$		0			0
$460$	2.90433e10	+	1.31960e9i	0.648656	+	0.0294722i
$461$	−7.73092e10			−1.71170			−0.855850	−	0.517225i	$-0.826965\pi$
$461$	−7.73092e10			−1.71170			−0.855850	+	0.517225i	$0.826965\pi$
$462$		0			0
$463$			8.52854e10i			1.85588i	0.372726	+	0.927941i	$0.378423\pi$
$463$			8.52854e10i			1.85588i	−0.372726	+	0.927941i	$0.621577\pi$
$464$	5.40949e10	+	4.92586e9i	1.16704	+	0.106270i
$465$		0			0
$466$	2.60196e10	−	2.48643e10i	0.551769	−	0.527268i
$467$		−	3.20726e10i		−	0.674320i	−0.941447	−	0.337160i	$-0.890534\pi$
$467$		−	3.20726e10i		−	0.674320i	0.941447	−	0.337160i	$-0.109466\pi$
$468$		0			0
$469$	3.97112e9			0.0820770
$470$	5.78446e9	+	6.05324e9i	0.118542	+	0.124050i
$471$		0			0
$472$	1.90839e10	−	1.66467e10i	0.384503	−	0.335397i
$473$	2.93538e10			0.586435
$474$		0			0
$475$			5.90190e8i			0.0115936i
$476$	1.04076e11	+	4.72879e9i	2.02733	+	0.0921133i
$477$		0			0
$478$	3.06454e10	+	3.20694e10i	0.587020	+	0.614298i
$479$			3.58893e10i			0.681746i	0.940109	+	0.340873i	$0.110723\pi$
$479$			3.58893e10i			0.681746i	−0.940109	+	0.340873i	$0.889277\pi$
$480$		0			0
$481$	1.18819e10			0.221976
$482$	1.85678e9	−	1.77433e9i	0.0344010	−	0.0328735i
$483$		0			0
$484$	2.02057e9	−	4.44710e10i	0.0368208	−	0.810392i
$485$	1.67029e10			0.301874
$486$		0			0
$487$		−	5.98567e10i		−	1.06414i	−0.846702	−	0.532068i	$-0.821415\pi$
$487$		−	5.98567e10i		−	1.06414i	0.846702	−	0.532068i	$-0.178585\pi$
$488$	2.63681e10	+	3.02287e10i	0.464943	+	0.533016i
$489$		0			0
$490$	−1.71190e10	+	1.63588e10i	−0.296957	+	0.283771i
$491$			3.00275e10i			0.516645i	0.966059	+	0.258323i	$0.0831698\pi$
$491$			3.00275e10i			0.516645i	−0.966059	+	0.258323i	$0.916830\pi$
$492$		0			0
$493$	1.01429e11			1.71702
$494$	2.57011e9	+	2.68954e9i	0.0431563	+	0.0451617i
$495$		0			0
$496$	8.29353e9	−	9.10782e10i	0.137029	−	1.50483i
$497$	−1.20496e11			−1.97491
$498$		0			0
$499$			2.32602e10i			0.375156i	0.982250	+	0.187578i	$0.0600637\pi$
$499$			2.32602e10i			0.375156i	−0.982250	+	0.187578i	$0.939936\pi$
$500$	−2.53732e8	+	5.58441e9i	−0.00405971	+	0.0893505i
$501$		0			0
$502$	−6.38566e10	−	6.68238e10i	−1.00552	−	1.05224i
$503$		−	2.16574e10i		−	0.338326i	−0.985588	−	0.169163i	$-0.945894\pi$
$503$		−	2.16574e10i		−	0.338326i	0.985588	−	0.169163i	$-0.0541064\pi$
$504$		0			0
$505$	2.69097e10			0.413755
$506$	−2.98980e10	+	2.85704e10i	−0.456079	+	0.435828i
$507$		0			0
$508$	−1.14054e11	−	5.18212e9i	−1.71260	−	0.0778131i
$509$	−1.21565e10			−0.181108			−0.0905541	−	0.995892i	$-0.528864\pi$
$509$	−1.21565e10			−0.181108			−0.0905541	+	0.995892i	$0.528864\pi$
$510$		0			0
$511$		−	1.11589e11i		−	1.63658i
$512$	−5.74407e10	+	3.77219e10i	−0.835871	+	0.548925i
$513$		0			0
$514$	5.29500e10	−	5.05988e10i	0.758601	−	0.724916i
$515$		−	5.48709e10i		−	0.780034i
$516$		0			0
$517$	−1.19094e10			−0.166697
$518$	−1.41918e10	−	1.48513e10i	−0.197115	−	0.206275i
$519$		0			0
$520$	2.31623e10	+	2.65535e10i	0.316787	+	0.363169i
$521$	5.20805e10			0.706845			0.353422	−	0.935464i	$-0.385018\pi$
$521$	5.20805e10			0.706845			0.353422	+	0.935464i	$0.385018\pi$
$522$		0			0
$523$		−	2.42007e10i		−	0.323461i	−0.986835	−	0.161731i	$-0.948292\pi$
$523$		−	2.42007e10i		−	0.323461i	0.986835	−	0.161731i	$-0.0517075\pi$
$524$	3.36434e10	+	1.52861e9i	0.446246	+	0.0202755i
$525$		0			0
$526$	5.37158e9	+	5.62118e9i	0.0701712	+	0.0734319i
$527$		−	1.70774e11i		−	2.21400i
$528$		0			0
$529$	−8.67778e10			−1.10812
$530$	2.59288e10	−	2.47775e10i	0.328609	−	0.314017i
$531$		0			0
$532$	2.91917e8	−	6.42482e9i	0.00364428	−	0.0802074i
$533$	−2.99260e10			−0.370800
$534$		0			0
$535$		−	4.59609e10i		−	0.561014i
$536$	−3.68587e9	+	3.21514e9i	−0.0446561	+	0.0389530i
$537$		0			0
$538$	−1.72047e10	+	1.64407e10i	−0.205361	+	0.196242i
$539$		−	3.36805e10i		−	0.399046i
$540$		0			0
$541$	−7.39316e10			−0.863060			−0.431530	−	0.902099i	$-0.642026\pi$
$541$	−7.39316e10			−0.863060			−0.431530	+	0.902099i	$0.642026\pi$
$542$	7.51005e10	+	7.85902e10i	0.870253	+	0.910692i
$543$		0			0
$544$	−1.00429e11	+	7.98743e10i	−1.14674	+	0.912035i
$545$	5.07812e10			0.575595
$546$		0			0
$547$		−	9.08736e10i		−	1.01505i	−0.861636	−	0.507526i	$-0.830560\pi$
$547$		−	9.08736e10i		−	1.01505i	0.861636	−	0.507526i	$-0.169440\pi$
$548$	3.79257e9	−	8.34712e10i	0.0420544	−	0.925581i
$549$		0			0
$550$	−5.49349e9	−	5.74875e9i	−0.0600340	−	0.0628236i
$551$		−	6.26140e9i		−	0.0679305i
$552$		0			0
$553$	−4.08628e9			−0.0436946
$554$	−1.78985e10	+	1.71038e10i	−0.190011	+	0.181574i
$555$		0			0
$556$	1.65954e11	+	7.54025e9i	1.73656	+	0.0789018i
$557$	7.25820e9			0.0754064			0.0377032	−	0.999289i	$-0.487996\pi$
$557$	7.25820e9			0.0754064			0.0377032	+	0.999289i	$0.487996\pi$
$558$		0			0
$559$			1.42022e11i			1.45449i
$560$	5.52426e9	−	6.06665e10i	0.0561723	−	0.616875i
$561$		0			0
$562$	−1.07936e11	+	1.03143e11i	−1.08199	+	1.03394i
$563$			4.02851e10i			0.400969i	0.979697	+	0.200485i	$0.0642517\pi$
$563$			4.02851e10i			0.400969i	−0.979697	+	0.200485i	$0.935748\pi$
$564$		0			0
$565$	−3.65119e10			−0.358295
$566$	−8.22221e10	−	8.60427e10i	−0.801166	−	0.838394i
$567$		0			0
$568$	1.11841e11	−	9.75574e10i	1.07450	−	0.937274i
$569$	−4.42204e10			−0.421866			−0.210933	−	0.977501i	$-0.567650\pi$
$569$	−4.42204e10			−0.421866			−0.210933	+	0.977501i	$0.567650\pi$
$570$		0			0
$571$		−	1.92416e11i		−	1.81008i	−0.425327	−	0.905040i	$-0.639841\pi$
$571$		−	1.92416e11i		−	1.81008i	0.425327	−	0.905040i	$-0.360159\pi$
$572$	−5.00684e10	−	2.27490e9i	−0.467714	−	0.0212509i
$573$		0			0
$574$	3.57438e10	+	3.74048e10i	0.329271	+	0.344572i
$575$		−	3.17431e10i		−	0.290387i
$576$		0			0
$577$	5.62180e10			0.507192			0.253596	−	0.967310i	$-0.418387\pi$
$577$	5.62180e10			0.507192			0.253596	+	0.967310i	$0.418387\pi$
$578$	−9.25400e10	+	8.84309e10i	−0.829122	+	0.792305i
$579$		0			0
$580$	2.69187e9	−	5.92457e10i	0.0237872	−	0.523534i
$581$	2.31767e11			2.03398
$582$		0			0
$583$			5.10133e10i			0.441580i
$584$	9.03458e10	+	1.03574e11i	0.776706	+	0.890425i
$585$		0			0
$586$	−1.84172e10	+	1.75994e10i	−0.156183	+	0.149248i
$587$		−	2.12589e11i		−	1.79056i	−0.445508	−	0.895278i	$-0.646977\pi$
$587$		−	2.12589e11i		−	1.79056i	0.445508	−	0.895278i	$-0.353023\pi$
$588$		0			0
$589$	−1.05422e10			−0.0875927
$590$	−1.91023e10	−	1.99900e10i	−0.157644	−	0.164970i
$591$		0			0
$592$	2.51965e10	+	2.29438e9i	0.205142	+	0.0186801i
$593$	3.64674e10			0.294908			0.147454	−	0.989069i	$-0.452892\pi$
$593$	3.64674e10			0.294908			0.147454	+	0.989069i	$0.452892\pi$
$594$		0			0
$595$		−	1.13751e11i		−	0.907585i
$596$	8.48995e9	−	1.86856e11i	0.0672853	−	1.48089i
$597$		0			0
$598$	−1.38232e11	−	1.44655e11i	−1.08095	−	1.13118i
$599$			1.54791e11i			1.20237i	0.799111	+	0.601184i	$0.205304\pi$
$599$			1.54791e11i			1.20237i	−0.799111	+	0.601184i	$0.794696\pi$
$600$		0			0
$601$	1.37850e11			1.05659			0.528297	−	0.849059i	$-0.322831\pi$
$601$	1.37850e11			1.05659			0.528297	+	0.849059i	$0.322831\pi$
$602$	1.77515e11	−	1.69633e11i	1.35161	−	1.29159i
$603$		0			0
$604$	1.97969e11	+	8.99487e9i	1.48747	+	0.0675845i
$605$	−4.86048e10			−0.362792
$606$		0			0
$607$			4.21916e10i			0.310793i	0.987852	+	0.155396i	$0.0496655\pi$
$607$			4.21916e10i			0.310793i	−0.987852	+	0.155396i	$0.950335\pi$
$608$	4.93078e9	+	6.19967e9i	0.0360829	+	0.0453685i
$609$		0			0
$610$	3.16638e10	−	3.02578e10i	0.228689	−	0.218534i
$611$		−	5.76211e10i		−	0.413444i
$612$		0			0
$613$	−1.76436e11			−1.24953			−0.624763	−	0.780815i	$-0.714804\pi$
$613$	−1.76436e11			−1.24953			−0.624763	+	0.780815i	$0.714804\pi$
$614$	3.71813e10	+	3.89091e10i	0.261608	+	0.273765i
$615$		0			0
$616$	5.69588e10	+	6.52982e10i	0.395583	+	0.453501i
$617$	−3.80722e10			−0.262705			−0.131352	−	0.991336i	$-0.541932\pi$
$617$	−3.80722e10			−0.262705			−0.131352	+	0.991336i	$0.541932\pi$
$618$		0			0
$619$		−	4.67363e10i		−	0.318340i	−0.987251	−	0.159170i	$-0.949118\pi$
$619$		−	4.67363e10i		−	0.318340i	0.987251	−	0.159170i	$-0.0508818\pi$
$620$	−9.97504e10	−	4.53223e9i	−0.675069	−	0.0306722i
$621$		0			0
$622$	−1.36244e11	−	1.42575e11i	−0.910240	−	0.952537i
$623$			1.85683e11i			1.23259i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	−3.21565e10	+	3.07286e10i	−0.209398	+	0.200099i
$627$		0			0
$628$	3.68948e9	−	8.12021e10i	0.0237206	−	0.522070i
$629$	4.72440e10			0.301817
$630$		0			0
$631$			1.82629e11i			1.15200i	0.817450	+	0.576000i	$0.195387\pi$
$631$			1.82629e11i			1.15200i	−0.817450	+	0.576000i	$0.804613\pi$
$632$	3.79276e9	−	3.30838e9i	0.0237732	−	0.0207370i
$633$		0			0
$634$	−6.24857e9	+	5.97110e9i	−0.0386744	+	0.0369571i
$635$			1.24656e11i			0.766686i
$636$		0			0
$637$	1.62956e11			0.989721
$638$	5.82811e10	+	6.09893e10i	0.351759	+	0.368104i
$639$		0			0
$640$	4.39900e10	+	6.07814e10i	0.262201	+	0.362285i
$641$	−1.05531e11			−0.625100			−0.312550	−	0.949901i	$-0.601183\pi$
$641$	−1.05531e11			−0.625100			−0.312550	+	0.949901i	$0.601183\pi$
$642$		0			0
$643$			1.09834e11i			0.642528i	0.946990	+	0.321264i	$0.104108\pi$
$643$			1.09834e11i			0.642528i	−0.946990	+	0.321264i	$0.895892\pi$
$644$	−1.57006e10	+	3.45556e11i	−0.0912793	+	2.00898i
$645$		0			0
$646$	1.02191e10	+	1.06940e10i	0.0586791	+	0.0614057i
$647$		−	4.48807e9i		−	0.0256119i	−0.999918	−	0.0128060i	$-0.995924\pi$
$647$		−	4.48807e9i		−	0.0256119i	0.999918	−	0.0128060i	$-0.00407638\pi$
$648$		0			0
$649$	3.93290e10			0.221684
$650$	2.78142e10	−	2.65791e10i	0.155816	−	0.148897i
$651$		0			0
$652$	5.16599e9	+	2.34720e8i	0.0285866	+	0.00129885i
$653$	−2.96586e11			−1.63117			−0.815583	−	0.578640i	$-0.803584\pi$
$653$	−2.96586e11			−1.63117			−0.815583	+	0.578640i	$0.803584\pi$
$654$		0			0
$655$		−	3.67708e10i		−	0.199773i
$656$	−6.34604e10	−	5.77867e9i	−0.342679	−	0.0312042i
$657$		0			0
$658$	−7.20212e10	+	6.88232e10i	−0.384199	+	0.367139i
$659$			8.22505e10i			0.436111i	0.975936	+	0.218056i	$0.0699714\pi$
$659$			8.22505e10i			0.436111i	−0.975936	+	0.218056i	$0.930029\pi$
$660$		0			0
$661$	−1.54172e11			−0.807608			−0.403804	−	0.914845i	$-0.632312\pi$
$661$	−1.54172e11			−0.807608			−0.403804	+	0.914845i	$0.632312\pi$
$662$	−1.33881e11	−	1.40102e11i	−0.697085	−	0.729476i
$663$		0			0
$664$	−2.15119e11	+	1.87646e11i	−1.10664	+	0.965309i
$665$	−7.02205e9			−0.0359068
$666$		0			0
$667$			3.36766e11i			1.70147i
$668$	−1.44681e10	−	6.57368e8i	−0.0726616	−	0.00330144i
$669$		0			0
$670$	3.68943e9	+	3.86086e9i	0.0183088	+	0.0191596i
$671$			6.22966e10i			0.307308i
$672$		0			0
$673$	2.82157e11			1.37541			0.687703	−	0.725992i	$-0.258619\pi$
$673$	2.82157e11			1.37541			0.687703	+	0.725992i	$0.258619\pi$
$674$	1.09755e11	−	1.04881e11i	0.531844	−	0.508228i
$675$		0			0
$676$	1.52818e9	−	3.36340e10i	0.00731794	−	0.161061i
$677$	2.70699e11			1.28864			0.644320	−	0.764756i	$-0.277140\pi$
$677$	2.70699e11			1.28864			0.644320	+	0.764756i	$0.277140\pi$
$678$		0			0
$679$			1.98730e11i			0.934943i
$680$	9.20963e10	+	1.05580e11i	0.430731	+	0.493795i
$681$		0			0
$682$	1.02686e11	−	9.81263e10i	0.474650	−	0.453574i
$683$			3.96155e10i			0.182046i	0.995849	+	0.0910232i	$0.0290137\pi$
$683$			3.96155e10i			0.182046i	−0.995849	+	0.0910232i	$0.970986\pi$
$684$		0			0
$685$	−9.12304e10			−0.414359
$686$	1.72825e10	+	1.80856e10i	0.0780389	+	0.0816651i
$687$		0			0
$688$	−2.74244e10	+	3.01170e11i	−0.122400	+	1.34418i
$689$	−2.46818e11			−1.09521
$690$		0			0
$691$			1.26869e11i			0.556472i	0.960513	+	0.278236i	$0.0897497\pi$
$691$			1.26869e11i			0.556472i	−0.960513	+	0.278236i	$0.910250\pi$
$692$	1.27565e10	−	2.80760e11i	0.0556299	−	1.22436i
$693$		0			0
$694$	9.95998e10	+	1.04228e11i	0.429359	+	0.449310i
$695$		−	1.81381e11i		−	0.777413i
$696$		0			0
$697$	−1.18990e11			−0.504171
$698$	−2.51490e11	+	2.40323e11i	−1.05950	+	1.01245i
$699$		0			0
$700$	−6.64430e10	−	3.01889e9i	−0.276731	−	0.0125735i
$701$	6.26836e10			0.259587			0.129793	−	0.991541i	$-0.458569\pi$
$701$	6.26836e10			0.259587			0.129793	+	0.991541i	$0.458569\pi$
$702$		0			0
$703$		−	2.91646e9i		−	0.0119408i
$704$	−1.05735e11	−	1.44923e10i	−0.430455	−	0.0589991i
$705$		0			0
$706$	−6.47808e10	+	6.19042e10i	−0.260752	+	0.249173i
$707$			3.20170e11i			1.28146i
$708$		0			0
$709$	−3.57762e11			−1.41582			−0.707912	−	0.706300i	$-0.750363\pi$
$709$	−3.57762e11			−1.41582			−0.707912	+	0.706300i	$0.750363\pi$
$710$	−1.11949e11	−	1.17151e11i	−0.440541	−	0.461011i
$711$		0			0
$712$	−1.50334e11	−	1.72345e11i	−0.584977	−	0.670624i
$713$	5.67004e11			2.19396
$714$		0			0
$715$			5.47226e10i			0.209384i
$716$	1.64897e11	+	7.49222e9i	0.627423	+	0.0285074i
$717$		0			0
$718$	1.45043e11	+	1.51783e11i	0.545756	+	0.571116i
$719$			1.70342e11i			0.637392i	0.947857	+	0.318696i	$0.103245\pi$
$719$			1.70342e11i			0.637392i	−0.947857	+	0.318696i	$0.896755\pi$
$720$		0			0
$721$	6.52852e11			2.41587
$722$	−1.95799e11	+	1.87105e11i	−0.720547	+	0.688552i
$723$		0			0
$724$	−7.88990e9	+	1.73650e11i	−0.0287155	+	0.632003i
$725$	−6.47530e10			−0.234373
$726$		0			0
$727$		−	6.56094e10i		−	0.234870i	−0.993081	−	0.117435i	$-0.962533\pi$
$727$		−	6.56094e10i		−	0.234870i	0.993081	−	0.117435i	$-0.0374672\pi$
$728$	−3.15932e11	+	2.75583e11i	−1.12478	+	0.981132i
$729$		0			0
$730$	1.08491e11	−	1.03673e11i	0.382034	−	0.365070i
$731$			5.64700e11i			1.97765i
$732$		0			0
$733$	2.60967e11			0.904003			0.452001	−	0.892017i	$-0.350710\pi$
$733$	2.60967e11			0.904003			0.452001	+	0.892017i	$0.350710\pi$
$734$	−1.09366e11	−	1.14448e11i	−0.376788	−	0.394296i
$735$		0			0
$736$	−2.65200e11	−	3.33446e11i	−0.903778	−	1.13636i
$737$	−7.59601e9			−0.0257463
$738$		0			0
$739$		−	4.19763e11i		−	1.40743i	−0.710483	−	0.703715i	$-0.751523\pi$
$739$		−	4.19763e11i		−	1.40743i	0.710483	−	0.703715i	$-0.248477\pi$
$740$	1.25383e9	−	2.75957e10i	0.00418130	−	0.0920267i
$741$		0			0
$742$	2.94801e11	+	3.08500e11i	0.972554	+	1.01775i
$743$			1.42604e11i			0.467925i	0.972246	+	0.233962i	$0.0751693\pi$
$743$			1.42604e11i			0.467925i	−0.972246	+	0.233962i	$0.924831\pi$
$744$		0			0
$745$	−2.04226e11			−0.662957
$746$	−1.17406e11	+	1.12193e11i	−0.379085	+	0.362252i
$747$		0			0
$748$	−1.99079e11	−	9.04530e9i	−0.635944	−	0.0288946i
$749$	5.46841e11			1.73754
$750$		0			0
$751$		−	3.26311e10i		−	0.102582i	−0.998684	−	0.0512911i	$-0.983666\pi$
$751$		−	3.26311e10i		−	0.102582i	0.998684	−	0.0512911i	$-0.0163336\pi$
$752$	1.11266e10	−	1.22190e11i	0.0347928	−	0.382089i
$753$		0			0
$754$	−2.95084e11	+	2.81981e11i	−0.912978	+	0.872438i
$755$		−	2.16371e11i		−	0.665905i
$756$		0			0
$757$	−4.36612e11			−1.32957			−0.664787	−	0.747033i	$-0.731478\pi$
$757$	−4.36612e11			−1.32957			−0.664787	+	0.747033i	$0.731478\pi$
$758$	−1.54477e11	−	1.61655e11i	−0.467937	−	0.489680i
$759$		0			0
$760$	6.51765e9	−	5.68526e9i	0.0195361	−	0.0170410i
$761$	1.98059e11			0.590548			0.295274	−	0.955413i	$-0.404589\pi$
$761$	1.98059e11			0.590548			0.295274	+	0.955413i	$0.404589\pi$
$762$		0			0
$763$			6.04192e11i			1.78269i
$764$	3.93164e10	+	1.78637e9i	0.115399	+	0.00524322i
$765$		0			0
$766$	−2.56028e11	−	2.67925e11i	−0.743657	−	0.778213i
$767$			1.90285e11i			0.549824i
$768$		0			0
$769$	−1.42097e10			−0.0406329			−0.0203165	−	0.999794i	$-0.506467\pi$
$769$	−1.42097e10			−0.0406329			−0.0203165	+	0.999794i	$0.506467\pi$
$770$	6.83984e10	−	6.53612e10i	0.194573	−	0.185933i
$771$		0			0
$772$	1.12450e9	−	2.47491e10i	0.00316584	−	0.0696772i
$773$	−6.62483e10			−0.185548			−0.0927741	−	0.995687i	$-0.529573\pi$
$773$	−6.62483e10			−0.185548			−0.0927741	+	0.995687i	$0.529573\pi$
$774$		0			0
$775$			1.09023e11i			0.302211i
$776$	−1.60898e11	−	1.84456e11i	−0.443715	−	0.508680i
$777$		0			0
$778$	−1.30919e11	+	1.25106e11i	−0.357343	+	0.341476i
$779$			7.34544e9i			0.0199466i
$780$		0			0
$781$	2.30487e11			0.619501
$782$	−5.49630e11	−	5.75170e11i	−1.46975	−	1.53804i
$783$		0			0
$784$	3.45562e11	+	3.14667e10i	0.914663	+	0.0832887i
$785$	−8.87504e10			−0.233718
$786$		0			0
$787$		−	7.13437e10i		−	0.185976i	−0.995667	−	0.0929880i	$-0.970358\pi$
$787$		−	7.13437e10i		−	0.185976i	0.995667	−	0.0929880i	$-0.0296418\pi$
$788$	3.30886e10	−	7.28250e11i	0.0858170	−	1.88876i
$789$		0			0
$790$	−3.79642e9	−	3.97283e9i	−0.00974689	−	0.0101998i
$791$		−	4.34417e11i		−	1.10969i
$792$		0			0
$793$	−3.01409e11			−0.762191
$794$	−1.17170e11	+	1.11967e11i	−0.294804	+	0.281714i
$795$		0			0
$796$	−2.22811e11	−	1.01236e10i	−0.554990	−	0.0252164i
$797$	−1.11980e11			−0.277527			−0.138764	−	0.990326i	$-0.544313\pi$
$797$	−1.11980e11			−0.277527			−0.138764	+	0.990326i	$0.544313\pi$
$798$		0			0
$799$		−	2.29109e11i		−	0.562154i
$800$	6.41146e10	−	5.09922e10i	0.156530	−	0.124493i
$801$		0			0
$802$	1.76127e11	−	1.68306e11i	0.425725	−	0.406821i
$803$			2.13449e11i			0.513372i
$804$		0			0
$805$	3.77677e11			0.899368
$806$	4.74764e11	+	4.96825e11i	1.12496	+	1.17724i
$807$		0			0
$808$	−2.59220e11	−	2.97172e11i	−0.608167	−	0.697209i
$809$	−5.57023e10			−0.130041			−0.0650203	−	0.997884i	$-0.520711\pi$
$809$	−5.57023e10			−0.130041			−0.0650203	+	0.997884i	$0.520711\pi$
$810$		0			0
$811$			7.06448e11i			1.63304i	0.577317	+	0.816520i	$0.304100\pi$
$811$			7.06448e11i			1.63304i	−0.577317	+	0.816520i	$0.695900\pi$
$812$	7.04902e11	+	3.20278e10i	1.62145	+	0.0736720i
$813$		0			0
$814$	2.71464e10	+	2.84078e10i	0.0618321	+	0.0647053i
$815$		−	5.64620e9i		−	0.0127975i
$816$		0			0
$817$	3.48599e10			0.0782417
$818$	5.97446e11	−	5.70917e11i	1.33440	−	1.27515i
$819$		0			0
$820$	−3.15792e9	+	6.95029e10i	−0.00698466	+	0.153726i
$821$	8.39733e10			0.184828			0.0924142	−	0.995721i	$-0.470542\pi$
$821$	8.39733e10			0.184828			0.0924142	+	0.995721i	$0.470542\pi$
$822$		0			0
$823$			1.90143e11i			0.414459i	0.978292	+	0.207229i	$0.0664446\pi$
$823$			1.90143e11i			0.414459i	−0.978292	+	0.207229i	$0.933555\pi$
$824$	−6.05957e11	+	5.28569e11i	−1.31442	+	1.14655i
$825$		0			0
$826$	2.37840e11	−	2.27279e11i	0.510933	−	0.488246i
$827$		−	3.98982e11i		−	0.852965i	−0.904496	−	0.426483i	$-0.859753\pi$
$827$		−	3.98982e11i		−	0.852965i	0.904496	−	0.426483i	$-0.140247\pi$
$828$		0			0
$829$	9.18641e11			1.94504			0.972518	−	0.232827i	$-0.0747977\pi$
$829$	9.18641e11			1.94504			0.972518	+	0.232827i	$0.0747977\pi$
$830$	2.15327e11	+	2.25332e11i	0.453718	+	0.474801i
$831$		0			0
$832$	7.01178e10	−	5.11576e11i	0.146331	−	1.06762i
$833$	6.47936e11			1.34571
$834$		0			0
$835$			1.58130e10i			0.0325288i
$836$	−5.58382e8	+	1.22895e10i	−0.00114316	+	0.0251599i
$837$		0			0
$838$	−3.21427e11	−	3.36363e11i	−0.651789	−	0.682075i
$839$			4.31925e11i			0.871688i	0.900022	+	0.435844i	$0.143550\pi$
$839$			4.31925e11i			0.871688i	−0.900022	+	0.435844i	$0.856450\pi$
$840$		0			0
$841$	1.86726e11			0.373268
$842$	2.34400e10	−	2.23991e10i	0.0466347	−	0.0445639i
$843$		0			0
$844$	5.68701e11	+	2.58394e10i	1.12076	+	0.0509228i
$845$	−3.67605e10			−0.0721031
$846$		0			0
$847$		−	5.78298e11i		−	1.12362i
$848$	−5.23396e11	−	4.76602e10i	−1.01216	−	0.0921664i
$849$		0			0
$850$	1.10593e11	−	1.05682e11i	0.211861	−	0.202454i
$851$			1.56860e11i			0.299085i
$852$		0			0
$853$	9.29871e11			1.75641			0.878206	−	0.478282i	$-0.158740\pi$
$853$	9.29871e11			1.75641			0.878206	+	0.478282i	$0.158740\pi$
$854$	3.60006e11	+	3.76735e11i	0.676828	+	0.708279i
$855$		0			0
$856$	−5.07561e11	+	4.42739e11i	−0.945351	+	0.824618i
$857$	−1.19713e11			−0.221931			−0.110965	−	0.993824i	$-0.535394\pi$
$857$	−1.19713e11			−0.221931			−0.110965	+	0.993824i	$0.535394\pi$
$858$		0			0
$859$		−	4.22514e11i		−	0.776012i	−0.921657	−	0.388006i	$-0.873164\pi$
$859$		−	4.22514e11i		−	0.776012i	0.921657	−	0.388006i	$-0.126836\pi$
$860$	3.29847e11	+	1.49868e10i	0.603001	+	0.0273978i
$861$		0			0
$862$	2.55555e11	+	2.67430e11i	0.462865	+	0.484374i
$863$		−	2.84698e11i		−	0.513264i	−0.966509	−	0.256632i	$-0.917387\pi$
$863$		−	2.84698e11i		−	0.513264i	0.966509	−	0.256632i	$-0.0826129\pi$
$864$		0			0
$865$	−3.06858e11			−0.548117
$866$	5.97024e11	−	5.70514e11i	1.06150	−	1.01437i
$867$		0			0
$868$	5.39243e10	−	1.18683e12i	0.0949961	−	2.09078i
$869$	7.81630e9			0.0137064
$870$		0			0
$871$		−	3.67517e10i		−	0.0638565i
$872$	−4.89172e11	−	5.60793e11i	−0.846049	−	0.969921i
$873$		0			0
$874$	−3.55062e10	+	3.39296e10i	−0.0608497	+	0.0581478i
$875$			7.26193e10i			0.123885i
$876$		0			0
$877$	1.94476e11			0.328752			0.164376	−	0.986398i	$-0.447439\pi$
$877$	1.94476e11			0.328752			0.164376	+	0.986398i	$0.447439\pi$
$878$	4.50907e11	+	4.71859e11i	0.758767	+	0.794025i
$879$		0			0
$880$	−1.05669e10	+	1.16044e11i	−0.0176204	+	0.193504i
$881$	−9.06691e11			−1.50507			−0.752533	−	0.658555i	$-0.771168\pi$
$881$	−9.06691e11			−1.50507			−0.752533	+	0.658555i	$0.771168\pi$
$882$		0			0
$883$		−	2.26542e11i		−	0.372654i	−0.982488	−	0.186327i	$-0.940342\pi$
$883$		−	2.26542e11i		−	0.372654i	0.982488	−	0.186327i	$-0.0596584\pi$
$884$	4.37638e10	−	9.63202e11i	0.0716648	−	1.57728i
$885$		0			0
$886$	1.96973e10	+	2.06125e10i	0.0319647	+	0.0334500i
$887$			1.70744e11i			0.275837i	0.990444	+	0.137918i	$0.0440412\pi$
$887$			1.70744e11i			0.275837i	−0.990444	+	0.137918i	$0.955959\pi$
$888$		0			0
$889$	−1.48315e12			−2.37453
$890$	−1.80528e11	+	1.72511e11i	−0.287729	+	0.274953i
$891$		0			0
$892$	−4.50323e11	−	2.04608e10i	−0.711320	−	0.0323193i
$893$	−1.41433e10			−0.0222405
$894$		0			0
$895$		−	1.80225e11i		−	0.280882i
$896$	−7.23174e11	+	5.23391e11i	−1.12205	+	0.812071i
$897$		0			0
$898$	6.64919e11	−	6.35394e11i	1.02250	−	0.977097i
$899$		−	1.15664e12i		−	1.77075i
$900$		0			0
$901$	−9.81380e11			−1.48915
$902$	−6.83713e10	−	7.15484e10i	−0.103288	−	0.108087i
$903$		0			0
$904$	3.51717e11	+	4.03213e11i	0.526647	+	0.603755i
$905$	1.89791e11			0.282932
$906$		0			0
$907$		−	5.20431e11i		−	0.769013i	−0.923122	−	0.384507i	$-0.874372\pi$
$907$		−	5.20431e11i		−	0.769013i	0.923122	−	0.384507i	$-0.125628\pi$
$908$	−4.74254e11	−	2.15481e10i	−0.697698	−	0.0317004i
$909$		0			0
$910$	3.16237e11	+	3.30932e11i	0.461155	+	0.482584i
$911$		−	5.42499e11i		−	0.787635i	−0.919189	−	0.393818i	$-0.871154\pi$
$911$		−	5.42499e11i		−	0.787635i	0.919189	−	0.393818i	$-0.128846\pi$
$912$		0			0
$913$	−4.43327e11			−0.638030
$914$	5.21650e11	−	4.98487e11i	0.747472	−	0.714281i
$915$		0			0
$916$	−1.31403e10	+	2.89205e11i	−0.0186647	+	0.410794i
$917$	4.37497e11			0.618725
$918$		0			0
$919$		−	6.49225e11i		−	0.910192i	−0.890442	−	0.455096i	$-0.849605\pi$
$919$		−	6.49225e11i		−	0.910192i	0.890442	−	0.455096i	$-0.150395\pi$
$920$	−3.50549e11	+	3.05779e11i	−0.489325	+	0.426831i
$921$		0			0
$922$	8.94283e11	−	8.54573e11i	1.23752	−	1.18257i
$923$			1.11516e12i			1.53650i
$924$		0			0
$925$	−3.01609e10			−0.0411981
$926$	−9.42742e11	−	9.86549e11i	−1.28218	−	1.34176i
$927$		0			0
$928$	−6.80200e11	+	5.40983e11i	−0.917159	+	0.729444i
$929$	−4.98636e11			−0.669455			−0.334727	−	0.942315i	$-0.608644\pi$
$929$	−4.98636e11			−0.669455			−0.334727	+	0.942315i	$0.608644\pi$
$930$		0			0
$931$		−	3.99982e10i		−	0.0532404i
$932$	−2.61365e10	+	5.75240e11i	−0.0346404	+	0.762405i
$933$		0			0
$934$	3.54529e11	+	3.71003e11i	0.465870	+	0.487518i
$935$			2.17585e11i			0.284696i
$936$		0			0
$937$	4.01408e11			0.520748			0.260374	−	0.965508i	$-0.416154\pi$
$937$	4.01408e11			0.520748			0.260374	+	0.965508i	$0.416154\pi$
$938$	−4.59364e10	+	4.38966e10i	−0.0593397	+	0.0567048i
$939$		0			0
$940$	−1.33825e11	−	6.08043e9i	−0.171406	−	0.00778794i
$941$	2.64682e10			0.0337572			0.0168786	−	0.999858i	$-0.494627\pi$
$941$	2.64682e10			0.0337572			0.0168786	+	0.999858i	$0.494627\pi$
$942$		0			0
$943$		−	3.95071e11i		−	0.499606i
$944$	−3.67439e10	+	4.03515e11i	−0.0462698	+	0.508127i
$945$		0			0
$946$	−3.39554e11	+	3.24476e11i	−0.423979	+	0.405152i
$947$		−	5.71352e11i		−	0.710401i	−0.934790	−	0.355201i	$-0.884413\pi$
$947$		−	5.71352e11i		−	0.710401i	0.934790	−	0.355201i	$-0.115587\pi$
$948$		0			0
$949$	−1.03273e12			−1.27327
$950$	−6.52394e9	−	6.82709e9i	−0.00800969	−	0.00838188i
$951$		0			0
$952$	−1.25619e12	+	1.09576e12i	−1.52935	+	1.33403i
$953$	1.09917e12			1.33258			0.666288	−	0.745694i	$-0.267882\pi$
$953$	1.09917e12			1.33258			0.666288	+	0.745694i	$0.267882\pi$
$954$		0			0
$955$		−	4.29711e10i		−	0.0516611i
$956$	−7.08988e11	−	3.22134e10i	−0.848803	−	0.0385660i
$957$		0			0
$958$	−3.96719e11	−	4.15153e11i	−0.471000	−	0.492886i
$959$		−	1.08545e12i		−	1.28333i
$960$		0			0
$961$	−1.09451e12			−1.28329
$962$	−1.37445e11	+	1.31342e11i	−0.160483	+	0.153357i
$963$		0			0
$964$	−1.86512e9	+	4.10495e10i	−0.00215972	+	0.0475335i
$965$	−2.70497e10			−0.0311928
$966$		0			0
$967$			8.78566e11i			1.00477i	0.864643	+	0.502387i	$0.167545\pi$
$967$			8.78566e11i			1.00477i	−0.864643	+	0.502387i	$0.832455\pi$
$968$	4.68207e11	+	5.36758e11i	0.533257	+	0.611332i
$969$		0			0
$970$	−1.93213e11	+	1.84633e11i	−0.218247	+	0.208556i
$971$			7.91945e11i			0.890878i	0.895312	+	0.445439i	$0.146952\pi$
$971$			7.91945e11i			0.890878i	−0.895312	+	0.445439i	$0.853048\pi$
$972$		0			0
$973$	2.15806e12			2.40775
$974$	6.61654e11	+	6.92399e11i	0.735182	+	0.769344i
$975$		0			0
$976$	−6.39163e11	−	5.82018e10i	−0.704389	−	0.0641413i
$977$	5.46919e11			0.600268			0.300134	−	0.953897i	$-0.402969\pi$
$977$	5.46919e11			0.600268			0.300134	+	0.953897i	$0.402969\pi$
$978$		0			0
$979$		−	3.55177e11i		−	0.386646i
$980$	1.71958e10	−	3.78465e11i	0.0186431	−	0.410319i
$981$		0			0
$982$	−3.31923e11	−	3.47346e11i	−0.356936	−	0.373522i
$983$		−	7.38083e11i		−	0.790481i	−0.918578	−	0.395240i	$-0.870661\pi$
$983$		−	7.38083e11i		−	0.790481i	0.918578	−	0.395240i	$-0.129339\pi$
$984$		0			0
$985$	−7.95946e11			−0.845549
$986$	−1.17329e12	+	1.12119e12i	−1.24136	+	1.18624i
$987$		0			0
$988$	−5.94601e10	−	2.70162e9i	−0.0624020	−	0.00283528i
$989$	−1.87492e12			−1.95974
$990$		0			0
$991$		−	3.73877e11i		−	0.387645i	−0.981037	−	0.193823i	$-0.937911\pi$
$991$		−	3.73877e11i		−	0.387645i	0.981037	−	0.193823i	$-0.0620886\pi$
$992$	9.10839e11	+	1.14523e12i	0.940578	+	1.18263i
$993$		0			0
$994$	1.39385e12	−	1.33196e12i	1.42781	−	1.36441i
$995$			2.43523e11i			0.248455i
$996$		0			0
$997$	1.14224e12			1.15605			0.578025	−	0.816019i	$-0.303823\pi$
$997$	1.14224e12			1.15605			0.578025	+	0.816019i	$0.303823\pi$
$998$	−2.57118e11	−	2.69066e11i	−0.259185	−	0.271229i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.a.91.4		16
3.2	odd	2		20.9.b.a.11.13	✓	16
4.3	odd	2	inner	180.9.c.a.91.3		16
12.11	even	2		20.9.b.a.11.14	yes	16
15.2	even	4		100.9.d.c.99.24		32
15.8	even	4		100.9.d.c.99.9		32
15.14	odd	2		100.9.b.d.51.4		16
24.5	odd	2		320.9.b.d.191.7		16
24.11	even	2		320.9.b.d.191.10		16
60.23	odd	4		100.9.d.c.99.23		32
60.47	odd	4		100.9.d.c.99.10		32
60.59	even	2		100.9.b.d.51.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.13	✓	16	3.2	odd	2
20.9.b.a.11.14	yes	16	12.11	even	2
100.9.b.d.51.3		16	60.59	even	2
100.9.b.d.51.4		16	15.14	odd	2
100.9.d.c.99.9		32	15.8	even	4
100.9.d.c.99.10		32	60.47	odd	4
100.9.d.c.99.23		32	60.23	odd	4
100.9.d.c.99.24		32	15.2	even	4
180.9.c.a.91.3		16	4.3	odd	2	inner
180.9.c.a.91.4		16	1.1	even	1	trivial
320.9.b.d.191.7		16	24.5	odd	2
320.9.b.d.191.10		16	24.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.5676 + 11.0540i) q^{2} +(11.6196 - 255.736i) q^{4} -279.508 q^{5} -3325.58i q^{7} +(2692.49 + 3086.70i) q^{8} +(3233.25 - 3089.68i) q^{10} +6361.21i q^{11} -30777.4 q^{13} +(36760.8 + 38469.0i) q^{14} +(-65266.0 - 5943.09i) q^{16} -122375. q^{17} +7554.43i q^{19} +(-3247.77 + 71480.4i) q^{20} +(-70316.6 - 73584.1i) q^{22} -406311. i q^{23} +78125.0 q^{25} +(356021. - 340213. i) q^{26} +(-850471. - 38641.8i) q^{28} -828838. q^{29} +1.39549e6i q^{31} +(820666. - 652701. i) q^{32} +(1.41559e6 - 1.35273e6i) q^{34} +929527. i q^{35} -386059. q^{37} +(-83506.4 - 87386.8i) q^{38} +(-752574. - 862759. i) q^{40} +972335. q^{41} -4.61450e6i q^{43} +(1.62679e6 + 73914.5i) q^{44} +(4.49135e6 + 4.70005e6i) q^{46} +1.87219e6i q^{47} -5.29467e6 q^{49} +(-903720. + 863591. i) q^{50} +(-357620. + 7.87090e6i) q^{52} +8.01944e6 q^{53} -1.77801e6i q^{55} +(1.02651e7 - 8.95408e6i) q^{56} +(9.58768e6 - 9.16195e6i) q^{58} -6.18263e6i q^{59} +9.79320e6 q^{61} +(-1.54257e7 - 1.61425e7i) q^{62} +(-2.27822e6 + 1.66218e7i) q^{64} +8.60255e6 q^{65} +1.19411e6i q^{67} +(-1.42195e6 + 3.12958e7i) q^{68} +(-1.02750e7 - 1.07524e7i) q^{70} -3.62332e7i q^{71} +3.35548e7 q^{73} +(4.46578e6 - 4.26748e6i) q^{74} +(1.93194e6 + 87779.2i) q^{76} +2.11547e7 q^{77} -1.22874e6i q^{79} +(1.82424e7 + 1.66114e6i) q^{80} +(-1.12476e7 + 1.07482e7i) q^{82} +6.96923e7i q^{83} +3.42049e7 q^{85} +(5.10086e7 + 5.33788e7i) q^{86} +(-1.96352e7 + 1.71275e7i) q^{88} -5.58347e7 q^{89} +1.02353e8i q^{91} +(-1.03908e8 - 4.72116e6i) q^{92} +(-2.06951e7 - 2.16567e7i) q^{94} -2.11153e6i q^{95} -5.97582e7 q^{97} +(6.12467e7 - 5.85271e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 52 q^{4} + 14184 q^{8} + 8750 q^{10} + 51392 q^{13} - 68472 q^{14} - 81424 q^{16} - 27552 q^{17} - 172500 q^{20} - 389120 q^{22} + 1250000 q^{25} - 1037124 q^{26} + 1288520 q^{28} - 2764896 q^{29}+ \cdots + 285387714 q^{98}+O(q^{100}) \) 16 * q - 6 * q^2 - 52 * q^4 + 14184 * q^8 + 8750 * q^10 + 51392 * q^13 - 68472 * q^14 - 81424 * q^16 - 27552 * q^17 - 172500 * q^20 - 389120 * q^22 + 1250000 * q^25 - 1037124 * q^26 + 1288520 * q^28 - 2764896 * q^29 + 4379904 * q^32 + 3793964 * q^34 + 9009472 * q^37 + 3087360 * q^38 + 385000 * q^40 + 8576448 * q^41 - 16921200 * q^44 - 7974152 * q^46 - 32803600 * q^49 - 468750 * q^50 + 6679352 * q^52 - 2452032 * q^53 - 34134768 * q^56 + 52156572 * q^58 + 8371712 * q^61 - 1290000 * q^62 - 47543872 * q^64 - 9060000 * q^65 - 16095192 * q^68 + 10500000 * q^70 + 61907232 * q^73 + 138210876 * q^74 + 2570400 * q^76 + 156997440 * q^77 - 37590000 * q^80 + 83921012 * q^82 - 106960000 * q^85 + 101724672 * q^86 + 44728480 * q^88 - 106647456 * q^89 + 13876200 * q^92 + 55264632 * q^94 + 171851232 * q^97 + 285387714 * q^98

Introduction

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