LMFDB - Embedded newform 490.2.l.d.117.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(117,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("490.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (of order $12$, degree $4$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.7
Character	$\chi$	$=$	490.117
Dual form			490.2.l.d.423.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(0.100966 - 0.376812i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.579738 - 2.15961i) q^{5} -0.390104i q^{6} +(0.707107 - 0.707107i) q^{8} +(2.46628 + 1.42391i) q^{9} +(0.00103668 - 2.23607i) q^{10} +(-0.360409 - 0.624247i) q^{11} +(-0.100966 - 0.376812i) q^{12} +(0.0516746 + 0.0516746i) q^{13} +(-0.755231 - 0.436500i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.84178 - 1.29735i) q^{17} +(2.75078 + 0.737070i) q^{18} +(2.80818 - 4.86391i) q^{19} +(-0.577736 - 2.16014i) q^{20} +(-0.509696 - 0.509696i) q^{22} +(2.10844 + 7.86881i) q^{23} +(-0.195052 - 0.337840i) q^{24} +(-4.32781 - 2.50401i) q^{25} +(0.0632882 + 0.0365395i) q^{26} +(1.61309 - 1.61309i) q^{27} -7.15442i q^{29} +(-0.842472 - 0.226158i) q^{30} +(-2.35254 + 1.35824i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.271613 + 0.0727785i) q^{33} -5.01258 q^{34} +2.84782 q^{36} +(5.87196 - 1.57339i) q^{37} +(1.45362 - 5.42498i) q^{38} +(0.0246890 - 0.0142542i) q^{39} +(-1.11714 - 1.93701i) q^{40} +8.93661i q^{41} +(-3.33812 + 3.33812i) q^{43} +(-0.624247 - 0.360409i) q^{44} +(4.50488 - 4.50071i) q^{45} +(4.07320 + 7.05498i) q^{46} +(2.81795 + 10.5167i) q^{47} +(-0.275845 - 0.275845i) q^{48} +(-4.82843 - 1.29857i) q^{50} +(-0.977714 + 1.69345i) q^{51} +(0.0705888 + 0.0189142i) q^{52} +(-4.79433 - 1.28464i) q^{53} +(1.14063 - 1.97563i) q^{54} +(-1.55707 + 0.416443i) q^{55} +(-1.54925 - 1.54925i) q^{57} +(-1.85170 - 6.91064i) q^{58} +(6.38944 + 11.0668i) q^{59} +(-0.872300 - 0.000404413i) q^{60} +(-1.21675 - 0.702489i) q^{61} +(-1.92084 + 1.92084i) q^{62} -1.00000i q^{64} +(0.141555 - 0.0816391i) q^{65} +(-0.243522 + 0.140597i) q^{66} +(-1.29911 + 4.84836i) q^{67} +(-4.84178 + 1.29735i) q^{68} +3.17794 q^{69} +7.76446 q^{71} +(2.75078 - 0.737070i) q^{72} +(-0.737063 + 2.75076i) q^{73} +(5.26466 - 3.03955i) q^{74} +(-1.38051 + 1.37795i) q^{75} -5.61636i q^{76} +(0.0201585 - 0.0201585i) q^{78} +(-14.3489 - 8.28432i) q^{79} +(-1.58041 - 1.58187i) q^{80} +(3.82676 + 6.62815i) q^{81} +(2.31297 + 8.63210i) q^{82} +(0.827536 + 0.827536i) q^{83} +(-5.60873 + 9.70421i) q^{85} +(-2.36041 + 4.08835i) q^{86} +(-2.69587 - 0.722356i) q^{87} +(-0.696257 - 0.186562i) q^{88} +(3.14690 - 5.45059i) q^{89} +(3.18651 - 5.51330i) q^{90} +(5.76037 + 5.76037i) q^{92} +(0.274273 + 1.02360i) q^{93} +(5.44386 + 9.42904i) q^{94} +(-8.87612 - 8.88435i) q^{95} +(-0.337840 - 0.195052i) q^{96} +(5.41317 - 5.41317i) q^{97} -2.05276i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{11} - 48 q^{15} + 16 q^{16} + 16 q^{18} + 32 q^{22} - 16 q^{23} - 32 q^{25} - 40 q^{30} - 96 q^{36} + 48 q^{37} + 32 q^{43} + 16 q^{46} - 64 q^{50} + 80 q^{51} - 32 q^{53} + 96 q^{57} - 16 q^{58}+ \cdots - 40 q^{95}+O(q^{100}) $ 32 * q + 16 * q^11 - 48 * q^15 + 16 * q^16 + 16 * q^18 + 32 * q^22 - 16 * q^23 - 32 * q^25 - 40 * q^30 - 96 * q^36 + 48 * q^37 + 32 * q^43 + 16 * q^46 - 64 * q^50 + 80 * q^51 - 32 * q^53 + 96 * q^57 - 16 * q^58 - 40 * q^60 - 32 * q^65 - 16 * q^67 + 32 * q^71 + 16 * q^72 + 112 * q^81 + 48 * q^85 - 48 * q^86 + 16 * q^88 + 32 * q^92 - 64 * q^93 - 40 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.100966	−	0.376812i	0.0582930	−	0.217552i	−0.930635	−	0.365949i	$-0.880745\pi$
$3$	0.100966	−	0.376812i	0.0582930	−	0.217552i	0.988928	+	0.148396i	$0.0474112\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.579738	−	2.15961i	0.259267	−	0.965806i
$5$	0.579738	−	2.15961i	0.259267	−	0.965806i
$6$		−	0.390104i		−	0.159259i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.46628	+	1.42391i	0.822094	+	0.474636i
$10$	0.00103668	−	2.23607i	0.000327827	−	0.707107i
$11$	−0.360409	−	0.624247i	−0.108668	−	0.188218i	0.806563	−	0.591148i	$-0.201325\pi$
$11$	−0.360409	−	0.624247i	−0.108668	−	0.188218i	−0.915231	+	0.402930i	$0.867992\pi$
$12$	−0.100966	−	0.376812i	−0.0291465	−	0.108776i
$13$	0.0516746	+	0.0516746i	0.0143320	+	0.0143320i	0.714236	−	0.699904i	$-0.246774\pi$
$13$	0.0516746	+	0.0516746i	0.0143320	+	0.0143320i	−0.699904	+	0.714236i	$0.746774\pi$
$14$		0			0
$15$	−0.755231	−	0.436500i	−0.195000	−	0.112704i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−4.84178	−	1.29735i	−1.17430	−	0.314654i	−0.381639	−	0.924312i	$-0.624640\pi$
$17$	−4.84178	−	1.29735i	−1.17430	−	0.314654i	−0.792665	+	0.609658i	$0.791307\pi$
$18$	2.75078	+	0.737070i	0.648365	+	0.173729i
$19$	2.80818	−	4.86391i	0.644240	−	1.11586i	−0.340236	−	0.940340i	$-0.610507\pi$
$19$	2.80818	−	4.86391i	0.644240	−	1.11586i	0.984476	−	0.175517i	$-0.0561596\pi$
$20$	−0.577736	−	2.16014i	−0.129186	−	0.483023i
$21$		0			0
$22$	−0.509696	−	0.509696i	−0.108668	−	0.108668i
$23$	2.10844	+	7.86881i	0.439640	+	1.64076i	0.729711	+	0.683755i	$0.239654\pi$
$23$	2.10844	+	7.86881i	0.439640	+	1.64076i	−0.290071	+	0.957005i	$0.593679\pi$
$24$	−0.195052	−	0.337840i	−0.0398148	−	0.0689613i
$25$	−4.32781	−	2.50401i	−0.865561	−	0.500803i
$26$	0.0632882	+	0.0365395i	0.0124118	+	0.00716598i
$27$	1.61309	−	1.61309i	0.310440	−	0.310440i
$28$		0			0
$29$		−	7.15442i		−	1.32854i	−0.747491	−	0.664272i	$-0.768742\pi$
$29$		−	7.15442i		−	1.32854i	0.747491	−	0.664272i	$-0.231258\pi$
$30$	−0.842472	−	0.226158i	−0.153814	−	0.0412907i
$31$	−2.35254	+	1.35824i	−0.422528	+	0.243947i	−0.696158	−	0.717888i	$-0.745109\pi$
$31$	−2.35254	+	1.35824i	−0.422528	+	0.243947i	0.273630	+	0.961835i	$0.411776\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−0.271613	+	0.0727785i	−0.0472817	+	0.0126691i
$34$	−5.01258			−0.859650
$35$		0			0
$36$	2.84782			0.474636
$37$	5.87196	−	1.57339i	0.965344	−	0.258663i	0.258483	−	0.966016i	$-0.416777\pi$
$37$	5.87196	−	1.57339i	0.965344	−	0.258663i	0.706861	+	0.707353i	$0.250111\pi$
$38$	1.45362	−	5.42498i	0.235808	−	0.880049i
$39$	0.0246890	−	0.0142542i	0.00395340	−	0.00228250i
$40$	−1.11714	−	1.93701i	−0.176635	−	0.306268i
$41$			8.93661i			1.39566i	0.716261	+	0.697832i	$0.245852\pi$
$41$			8.93661i			1.39566i	−0.716261	+	0.697832i	$0.754148\pi$
$42$		0			0
$43$	−3.33812	+	3.33812i	−0.509059	+	0.509059i	−0.914238	−	0.405179i	$-0.867209\pi$
$43$	−3.33812	+	3.33812i	−0.509059	+	0.509059i	0.405179	+	0.914238i	$0.367209\pi$
$44$	−0.624247	−	0.360409i	−0.0941088	−	0.0543338i
$45$	4.50488	−	4.50071i	0.671548	−	0.670926i
$46$	4.07320	+	7.05498i	0.600560	+	1.04020i
$47$	2.81795	+	10.5167i	0.411040	+	1.53402i	0.792637	+	0.609694i	$0.208708\pi$
$47$	2.81795	+	10.5167i	0.411040	+	1.53402i	−0.381597	+	0.924329i	$0.624626\pi$
$48$	−0.275845	−	0.275845i	−0.0398148	−	0.0398148i
$49$		0			0
$50$	−4.82843	−	1.29857i	−0.682843	−	0.183646i
$51$	−0.977714	+	1.69345i	−0.136907	+	0.237130i
$52$	0.0705888	+	0.0189142i	0.00978891	+	0.00262293i
$53$	−4.79433	−	1.28464i	−0.658552	−	0.176459i	−0.0859597	−	0.996299i	$-0.527396\pi$
$53$	−4.79433	−	1.28464i	−0.658552	−	0.176459i	−0.572593	+	0.819840i	$0.694062\pi$
$54$	1.14063	−	1.97563i	0.155220	−	0.268849i
$55$	−1.55707	+	0.416443i	−0.209956	+	0.0561531i
$56$		0			0
$57$	−1.54925	−	1.54925i	−0.205203	−	0.205203i
$58$	−1.85170	−	6.91064i	−0.243140	−	0.907412i
$59$	6.38944	+	11.0668i	0.831834	+	1.44078i	0.896582	+	0.442877i	$0.146042\pi$
$59$	6.38944	+	11.0668i	0.831834	+	1.44078i	−0.0647485	+	0.997902i	$0.520625\pi$
$60$	−0.872300		0.000404413i	−0.112613		5.22096e-5i
$61$	−1.21675	−	0.702489i	−0.155788	−	0.0899445i	0.420079	−	0.907487i	$-0.362002\pi$
$61$	−1.21675	−	0.702489i	−0.155788	−	0.0899445i	−0.575868	+	0.817543i	$0.695336\pi$
$62$	−1.92084	+	1.92084i	−0.243947	+	0.243947i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	0.141555	−	0.0816391i	0.0175577	−	0.0101261i
$66$	−0.243522	+	0.140597i	−0.0299754	+	0.0173063i
$67$	−1.29911	+	4.84836i	−0.158712	+	0.592321i	0.840047	+	0.542514i	$0.182527\pi$
$67$	−1.29911	+	4.84836i	−0.158712	+	0.592321i	−0.998759	+	0.0498075i	$0.984139\pi$
$68$	−4.84178	+	1.29735i	−0.587152	+	0.157327i
$69$	3.17794			0.382579
$70$		0			0
$71$	7.76446			0.921472			0.460736	−	0.887537i	$-0.347585\pi$
$71$	7.76446			0.921472			0.460736	+	0.887537i	$0.347585\pi$
$72$	2.75078	−	0.737070i	0.324183	−	0.0868645i
$73$	−0.737063	+	2.75076i	−0.0862667	+	0.321952i	−0.995551	−	0.0942238i	$-0.969963\pi$
$73$	−0.737063	+	2.75076i	−0.0862667	+	0.321952i	0.909284	+	0.416175i	$0.136630\pi$
$74$	5.26466	−	3.03955i	0.612004	−	0.353341i
$75$	−1.38051	+	1.37795i	−0.159407	+	0.159112i
$76$		−	5.61636i		−	0.644240i
$77$		0			0
$78$	0.0201585	−	0.0201585i	0.00228250	−	0.00228250i
$79$	−14.3489	−	8.28432i	−1.61437	−	0.932059i	−0.988340	−	0.152262i	$-0.951344\pi$
$79$	−14.3489	−	8.28432i	−1.61437	−	0.932059i	−0.626033	−	0.779797i	$-0.715322\pi$
$80$	−1.58041	−	1.58187i	−0.176695	−	0.176859i
$81$	3.82676	+	6.62815i	0.425196	+	0.736461i
$82$	2.31297	+	8.63210i	0.255424	+	0.953256i
$83$	0.827536	+	0.827536i	0.0908339	+	0.0908339i	0.751064	−	0.660230i	$-0.229541\pi$
$83$	0.827536	+	0.827536i	0.0908339	+	0.0908339i	−0.660230	+	0.751064i	$0.729541\pi$
$84$		0			0
$85$	−5.60873	+	9.70421i	−0.608352	+	1.05257i
$86$	−2.36041	+	4.08835i	−0.254529	+	0.440858i
$87$	−2.69587	−	0.722356i	−0.289028	−	0.0774447i
$88$	−0.696257	−	0.186562i	−0.0742213	−	0.0198875i
$89$	3.14690	−	5.45059i	0.333571	−	0.577762i	−0.649638	−	0.760243i	$-0.725080\pi$
$89$	3.14690	−	5.45059i	0.333571	−	0.577762i	0.983209	+	0.182482i	$0.0584130\pi$
$90$	3.18651	−	5.51330i	0.335888	−	0.581153i
$91$		0			0
$92$	5.76037	+	5.76037i	0.600560	+	0.600560i
$93$	0.274273	+	1.02360i	0.0284408	+	0.106142i
$94$	5.44386	+	9.42904i	0.561491	+	0.972531i
$95$	−8.87612	−	8.88435i	−0.910671	−	0.911516i
$96$	−0.337840	−	0.195052i	−0.0344807	−	0.0199074i
$97$	5.41317	−	5.41317i	0.549625	−	0.549625i	−0.376708	−	0.926332i	$-0.622944\pi$
$97$	5.41317	−	5.41317i	0.549625	−	0.549625i	0.926332	+	0.376708i	$0.122944\pi$
$98$		0			0
$99$		−	2.05276i		−	0.206310i
$100$	−5.00000	−	0.00463618i	−0.500000	−	0.000463618i
$101$	−13.5588	+	7.82817i	−1.34915	+	0.778932i	−0.988129	−	0.153625i	$-0.950905\pi$
$101$	−13.5588	+	7.82817i	−1.34915	+	0.778932i	−0.361021	+	0.932558i	$0.617572\pi$
$102$	−0.506102	+	1.88880i	−0.0501115	+	0.187019i
$103$	−12.6694	+	3.39475i	−1.24835	+	0.334495i	−0.821699	−	0.569922i	$-0.806974\pi$
$103$	−12.6694	+	3.39475i	−1.24835	+	0.334495i	−0.426652	+	0.904416i	$0.640307\pi$
$104$	0.0730789			0.00716598
$105$		0			0
$106$	−4.96346			−0.482094
$107$	−13.0975	+	3.50946i	−1.26618	+	0.339273i	−0.828567	−	0.559890i	$-0.810843\pi$
$107$	−13.0975	+	3.50946i	−1.26618	+	0.339273i	−0.437615	+	0.899162i	$0.644177\pi$
$108$	0.590433	−	2.20353i	0.0568145	−	0.212034i
$109$	4.66416	−	2.69285i	0.446745	−	0.257928i	−0.259709	−	0.965687i	$-0.583627\pi$
$109$	4.66416	−	2.69285i	0.446745	−	0.257928i	0.706455	+	0.707758i	$0.250293\pi$
$110$	−1.39623	+	0.805253i	−0.133126	+	0.0767778i
$111$		−	2.37148i		−	0.225091i
$112$		0			0
$113$	−6.70143	+	6.70143i	−0.630417	+	0.630417i	−0.948173	−	0.317755i	$-0.897071\pi$
$113$	−6.70143	+	6.70143i	−0.630417	+	0.630417i	0.317755	+	0.948173i	$0.397071\pi$
$114$	−1.89743	−	1.09548i	−0.177711	−	0.102601i
$115$	18.2159	+	0.00844521i	1.69864	+	0.000787519i
$116$	−3.57721	−	6.19591i	−0.332136	−	0.575276i
$117$	0.0538643	+	0.201024i	0.00497975	+	0.0185847i
$118$	9.03603	+	9.03603i	0.831834	+	0.831834i
$119$		0			0
$120$	−0.842681	+	0.225377i	−0.0769259	+	0.0205740i
$121$	5.24021	−	9.07631i	0.476383	−	0.825119i
$122$	−1.35710	−	0.363635i	−0.122866	−	0.0329220i
$123$	3.36742	+	0.902298i	0.303630	+	0.0813574i
$124$	−1.35824	+	2.35254i	−0.121973	+	0.211264i
$125$	−7.91668	+	7.89469i	−0.708090	+	0.706123i
$126$		0			0
$127$	13.9068	+	13.9068i	1.23403	+	1.23403i	0.962404	+	0.271621i	$0.0875598\pi$
$127$	13.9068	+	13.9068i	1.23403	+	1.23403i	0.271621	+	0.962404i	$0.412440\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.920806	+	1.59488i	0.0810724	+	0.140422i
$130$	0.115601	−	0.115494i	0.0101389	−	0.0101295i
$131$	9.62423	+	5.55655i	0.840873	+	0.485478i	0.857561	−	0.514383i	$-0.171979\pi$
$131$	9.62423	+	5.55655i	0.840873	+	0.485478i	−0.0166879	+	0.999861i	$0.505312\pi$
$132$	−0.198834	+	0.198834i	−0.0173063	+	0.0173063i
$133$		0			0
$134$			5.01939i			0.433609i
$135$	−2.54848	−	4.41882i	−0.219338	−	0.380312i
$136$	−4.34102	+	2.50629i	−0.372239	+	0.214912i
$137$	0.940187	−	3.50882i	0.0803256	−	0.299779i	−0.914062	−	0.405573i	$-0.867072\pi$
$137$	0.940187	−	3.50882i	0.0803256	−	0.299779i	0.994388	+	0.105794i	$0.0337385\pi$
$138$	3.06966	−	0.822512i	0.261306	−	0.0700169i
$139$	14.8910			1.26304			0.631518	−	0.775361i	$-0.282432\pi$
$139$	14.8910			1.26304			0.631518	+	0.775361i	$0.282432\pi$
$140$		0			0
$141$	4.24735			0.357691
$142$	7.49990	−	2.00959i	0.629377	−	0.168641i
$143$	0.0136337	−	0.0508817i	0.00114011	−	0.00425494i
$144$	2.46628	−	1.42391i	0.205524	−	0.118659i
$145$	−15.4507	−	4.14769i	−1.28311	−	0.344447i
$146$			2.84779i			0.235685i
$147$		0			0
$148$	4.29857	−	4.29857i	0.353341	−	0.353341i
$149$	−2.36707	−	1.36663i	−0.193918	−	0.111959i	0.399897	−	0.916560i	$-0.369046\pi$
$149$	−2.36707	−	1.36663i	−0.193918	−	0.111959i	−0.593816	+	0.804601i	$0.702379\pi$
$150$	−0.976827	+	1.68830i	−0.0797576	+	0.137849i
$151$	2.19096	+	3.79486i	0.178298	+	0.308821i	0.941298	−	0.337578i	$-0.109608\pi$
$151$	2.19096	+	3.79486i	0.178298	+	0.308821i	−0.763000	+	0.646399i	$0.776274\pi$
$152$	−1.45362	−	5.42498i	−0.117904	−	0.440024i
$153$	−10.0939	−	10.0939i	−0.816042	−	0.816042i
$154$		0			0
$155$	1.56940	+	5.86798i	0.126058	+	0.471327i
$156$	0.0142542	−	0.0246890i	0.00114125	−	0.00197670i
$157$	−7.56329	−	2.02658i	−0.603616	−	0.161739i	−0.0559476	−	0.998434i	$-0.517818\pi$
$157$	−7.56329	−	2.02658i	−0.603616	−	0.161739i	−0.547669	+	0.836695i	$0.684485\pi$
$158$	−16.0041	−	4.28828i	−1.27322	−	0.341157i
$159$	−0.968133	+	1.67686i	−0.0767780	+	0.132983i
$160$	−1.93597	−	1.11893i	−0.153052	−	0.0884593i
$161$		0			0
$162$	5.41186	+	5.41186i	0.425196	+	0.425196i
$163$	−1.48568	−	5.54462i	−0.116367	−	0.434288i	0.883018	−	0.469338i	$-0.155508\pi$
$163$	−1.48568	−	5.54462i	−0.116367	−	0.434288i	−0.999386	+	0.0350503i	$0.988841\pi$
$164$	4.46831	+	7.73933i	0.348916	+	0.604340i
$165$	−0.000291509		0.628770i	−2.26939e−5		0.0489497i
$166$	1.01352	+	0.585156i	0.0786645	+	0.0454169i
$167$	−0.780209	+	0.780209i	−0.0603743	+	0.0603743i	−0.736649	−	0.676275i	$-0.763593\pi$
$167$	−0.780209	+	0.780209i	−0.0603743	+	0.0603743i	0.676275	+	0.736649i	$0.263593\pi$
$168$		0			0
$169$		−	12.9947i		−	0.999589i
$170$	−2.90598	+	10.8252i	−0.222879	+	0.830255i
$171$	13.8515	−	7.99718i	1.05925	−	0.611560i
$172$	−1.22184	+	4.55996i	−0.0931643	+	0.347694i
$173$	1.70827	−	0.457730i	0.129877	−	0.0348006i	−0.193295	−	0.981141i	$-0.561917\pi$
$173$	1.70827	−	0.457730i	0.129877	−	0.0348006i	0.323172	+	0.946340i	$0.395251\pi$
$174$	−2.79097			−0.211583
$175$		0			0
$176$	−0.720819			−0.0543338
$177$	4.81523	−	1.29024i	0.361935	−	0.0969802i
$178$	1.62896	−	6.07935i	0.122095	−	0.455666i
$179$	12.5236	−	7.23051i	0.936059	−	0.540434i	0.0473364	−	0.998879i	$-0.484927\pi$
$179$	12.5236	−	7.23051i	0.936059	−	0.540434i	0.888723	+	0.458445i	$0.151593\pi$
$180$	1.65099	−	6.15017i	0.123057	−	0.458407i
$181$		−	12.7727i		−	0.949389i	−0.880151	−	0.474695i	$-0.842558\pi$
$181$		−	12.7727i		−	0.949389i	0.880151	−	0.474695i	$-0.157442\pi$
$182$		0			0
$183$	−0.387557	+	0.387557i	−0.0286490	+	0.0286490i
$184$	7.05498	+	4.07320i	0.520100	+	0.300280i
$185$	0.00630208	−	13.5933i	0.000463338	−	0.999398i
$186$	0.529854	+	0.917734i	0.0388508	+	0.0672916i
$187$	0.935154	+	3.49004i	0.0683852	+	0.255217i
$188$	7.69878	+	7.69878i	0.561491	+	0.561491i
$189$		0			0
$190$	−10.8731	−	6.28432i	−0.788819	−	0.455912i
$191$	−1.45589	+	2.52168i	−0.105345	+	0.182462i	−0.913879	−	0.405987i	$-0.866928\pi$
$191$	−1.45589	+	2.52168i	−0.105345	+	0.182462i	0.808534	+	0.588449i	$0.200261\pi$
$192$	−0.376812	−	0.100966i	−0.0271940	−	0.00728662i
$193$	10.6329	+	2.84909i	0.765376	+	0.205082i	0.620328	−	0.784343i	$-0.287000\pi$
$193$	10.6329	+	2.84909i	0.765376	+	0.205082i	0.145048	+	0.989425i	$0.453666\pi$
$194$	3.82769	−	6.62976i	0.274812	−	0.475989i
$195$	−0.0164703	−	0.0615822i	−0.00117946	−	0.00441000i
$196$		0			0
$197$	−13.9159	−	13.9159i	−0.991465	−	0.991465i	0.00849869	−	0.999964i	$-0.497295\pi$
$197$	−13.9159	−	13.9159i	−0.991465	−	0.991465i	−0.999964	+	0.00849869i	$0.997295\pi$
$198$	−0.531294	−	1.98281i	−0.0377574	−	0.140913i
$199$	−2.88897	−	5.00385i	−0.204794	−	0.354713i	0.745273	−	0.666759i	$-0.232319\pi$
$199$	−2.88897	−	5.00385i	−0.204794	−	0.354713i	−0.950067	+	0.312046i	$0.898986\pi$
$200$	−4.83083	+	1.28962i	−0.341591	+	0.0911897i
$201$	1.69575	+	0.979043i	0.119609	+	0.0690564i
$202$	−11.0707	+	11.0707i	−0.778932	+	0.778932i
$203$		0			0
$204$			1.95543i			0.136907i
$205$	19.2996	+	5.18090i	1.34794	+	0.361849i
$206$	−11.3591	+	6.55815i	−0.791423	+	0.456928i
$207$	−6.00446	+	22.4089i	−0.417339	+	1.55753i
$208$	0.0705888	−	0.0189142i	0.00489445	−	0.00131146i
$209$	−4.04837			−0.280032
$210$		0			0
$211$	−4.84449			−0.333509			−0.166754	−	0.985998i	$-0.553329\pi$
$211$	−4.84449			−0.333509			−0.166754	+	0.985998i	$0.553329\pi$
$212$	−4.79433	+	1.28464i	−0.329276	+	0.0882293i
$213$	0.783950	−	2.92574i	0.0537154	−	0.200468i
$214$	−11.7429	+	6.77976i	−0.802727	+	0.463455i
$215$	5.27380	+	9.14427i	0.359670	+	0.623634i
$216$		−	2.28126i		−	0.155220i
$217$		0			0
$218$	3.80827	−	3.80827i	0.257928	−	0.257928i
$219$	0.962098	+	0.555468i	0.0650126	+	0.0375350i
$220$	−1.14024	+	1.13919i	−0.0768751	+	0.0768039i
$221$	−0.183157	−	0.317237i	−0.0123205	−	0.0213397i
$222$	−0.613785	−	2.29068i	−0.0411945	−	0.153740i
$223$	−15.8173	−	15.8173i	−1.05921	−	1.05921i	−0.998133	−	0.0610748i	$-0.980547\pi$
$223$	−15.8173	−	15.8173i	−1.05921	−	1.05921i	−0.0610748	−	0.998133i	$-0.519453\pi$
$224$		0			0
$225$	−7.10811	−	12.3380i	−0.473874	−	0.822534i
$226$	−4.73862	+	8.20754i	−0.315209	+	0.545957i
$227$	−14.8759	−	3.98599i	−0.987350	−	0.264560i	−0.271213	−	0.962519i	$-0.587425\pi$
$227$	−14.8759	−	3.98599i	−0.987350	−	0.264560i	−0.716137	+	0.697960i	$0.754091\pi$
$228$	−2.11631	−	0.567063i	−0.140156	−	0.0375547i
$229$	4.89802	−	8.48363i	0.323670	−	0.560614i	−0.657572	−	0.753392i	$-0.728416\pi$
$229$	4.89802	−	8.48363i	0.323670	−	0.560614i	0.981242	+	0.192778i	$0.0617497\pi$
$230$	17.5974	−	4.70646i	1.16034	−	0.310335i
$231$		0			0
$232$	−5.05894	−	5.05894i	−0.332136	−	0.332136i
$233$	3.34071	+	12.4677i	0.218857	+	0.816787i	0.984773	+	0.173846i	$0.0556194\pi$
$233$	3.34071	+	12.4677i	0.218857	+	0.816787i	−0.765915	+	0.642941i	$0.777714\pi$
$234$	0.104058	+	0.180233i	0.00680247	+	0.0117822i
$235$	24.3457	+	0.0112871i	1.58814	+	0.000736288i
$236$	11.0668	+	6.38944i	0.720389	+	0.415917i
$237$	−4.57038	+	4.57038i	−0.296878	+	0.296878i
$238$		0			0
$239$		−	16.5971i		−	1.07358i	−0.843716	−	0.536790i	$-0.819637\pi$
$239$		−	16.5971i		−	1.07358i	0.843716	−	0.536790i	$-0.180363\pi$
$240$	−0.755636	+	0.435800i	−0.0487761	+	0.0281307i
$241$	−3.66606	+	2.11660i	−0.236151	+	0.136342i	−0.613407	−	0.789767i	$-0.710201\pi$
$241$	−3.66606	+	2.11660i	−0.236151	+	0.136342i	0.377255	+	0.926109i	$0.376868\pi$
$242$	2.71253	−	10.1233i	0.174368	−	0.650751i
$243$	9.49452	−	2.54405i	0.609074	−	0.163201i
$244$	−1.40498			−0.0899445
$245$		0			0
$246$	3.48621			0.222273
$247$	0.396452	−	0.106229i	0.0252256	−	0.00675919i
$248$	−0.703075	+	2.62391i	−0.0446453	+	0.166619i
$249$	0.395379	−	0.228272i	0.0250561	−	0.0144661i
$250$	−5.60363	+	9.67467i	−0.354405	+	0.611880i
$251$			20.6471i			1.30323i	0.758548	+	0.651617i	$0.225909\pi$
$251$			20.6471i			1.30323i	−0.758548	+	0.651617i	$0.774091\pi$
$252$		0			0
$253$	4.15218	−	4.15218i	0.261045	−	0.261045i
$254$	17.0322	+	9.83356i	1.06870	+	0.617013i
$255$	3.09037	+	3.09323i	0.193526	+	0.193706i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.57626	−	24.5429i	−0.410216	−	1.53095i	−0.794229	−	0.607618i	$-0.792125\pi$
$257$	−6.57626	−	24.5429i	−0.410216	−	1.53095i	0.384014	−	0.923327i	$-0.374541\pi$
$258$	1.30222	+	1.30222i	0.0810724	+	0.0810724i
$259$		0			0
$260$	0.0817703	−	0.141479i	0.00507118	−	0.00877414i
$261$	10.1873	−	17.6448i	0.630575	−	1.09219i
$262$	10.7344	+	2.87628i	0.663176	+	0.177697i
$263$	−16.2316	−	4.34924i	−1.00088	−	0.268186i	−0.279067	−	0.960272i	$-0.590025\pi$
$263$	−16.2316	−	4.34924i	−1.00088	−	0.268186i	−0.721815	+	0.692086i	$0.756692\pi$
$264$	−0.140597	+	0.243522i	−0.00865316	+	0.0149877i
$265$	−5.55377	+	9.60912i	−0.341165	+	0.590284i
$266$		0			0
$267$	−1.73612	−	1.73612i	−0.106249	−	0.106249i
$268$	1.29911	+	4.84836i	0.0793560	+	0.296161i
$269$	−7.93152	−	13.7378i	−0.483594	−	0.837609i	0.516229	−	0.856451i	$-0.327335\pi$
$269$	−7.93152	−	13.7378i	−0.483594	−	0.837609i	−0.999822	+	0.0188421i	$0.994002\pi$
$270$	−3.60531	−	3.60866i	−0.219412	−	0.219616i
$271$	−1.53420	−	0.885773i	−0.0931963	−	0.0538069i	0.452678	−	0.891674i	$-0.350469\pi$
$271$	−1.53420	−	0.885773i	−0.0931963	−	0.0538069i	−0.545874	+	0.837867i	$0.683802\pi$
$272$	−3.54443	+	3.54443i	−0.214912	+	0.214912i
$273$		0			0
$274$		−	3.63260i		−	0.219453i
$275$	−0.00334184	+	3.60409i	−0.000201521	+	0.217335i
$276$	2.75218	−	1.58897i	0.165662	−	0.0956448i
$277$	0.546707	−	2.04034i	0.0328484	−	0.122592i	−0.947555	−	0.319593i	$-0.896454\pi$
$277$	0.546707	−	2.04034i	0.0328484	−	0.122592i	0.980403	+	0.197001i	$0.0631203\pi$
$278$	14.3836	−	3.85407i	0.862670	−	0.231152i
$279$	−7.73603			−0.463144
$280$		0			0
$281$	7.99529			0.476959			0.238480	−	0.971147i	$-0.423351\pi$
$281$	7.99529			0.476959			0.238480	+	0.971147i	$0.423351\pi$
$282$	4.10262	−	1.09929i	0.244308	−	0.0654620i
$283$	4.00251	−	14.9376i	0.237924	−	0.887945i	−0.738885	−	0.673832i	$-0.764647\pi$
$283$	4.00251	−	14.9376i	0.237924	−	0.887945i	0.976809	−	0.214113i	$-0.0686862\pi$
$284$	6.72422	−	3.88223i	0.399009	−	0.230368i
$285$	−4.24392	+	2.44761i	−0.251388	+	0.144984i
$286$		−	0.0526767i		−	0.00311484i
$287$		0			0
$288$	2.01371	−	2.01371i	0.118659	−	0.118659i
$289$	7.03725	+	4.06296i	0.413956	+	0.238998i
$290$	−15.9978	−	0.00741685i	−0.939422	−	0.000435533i
$291$	−1.49320	−	2.58630i	−0.0875329	−	0.151611i
$292$	0.737063	+	2.75076i	0.0431333	+	0.160976i
$293$	−8.90037	−	8.90037i	−0.519965	−	0.519965i	0.397596	−	0.917561i	$-0.369845\pi$
$293$	−8.90037	−	8.90037i	−0.519965	−	0.519965i	−0.917561	+	0.397596i	$0.869845\pi$
$294$		0			0
$295$	27.6042	−	7.38281i	1.60718	−	0.429844i
$296$	3.03955	−	5.26466i	0.176670	−	0.306002i
$297$	−1.58834	−	0.425595i	−0.0921650	−	0.0246955i
$298$	−2.64013	−	0.707420i	−0.152939	−	0.0409798i
$299$	−0.297665	+	0.515570i	−0.0172144	+	0.0298162i
$300$	−0.506579	+	1.88359i	−0.0292473	+	0.108749i
$301$		0			0
$302$	3.09849	+	3.09849i	0.178298	+	0.178298i
$303$	1.58077	+	5.89950i	0.0908126	+	0.338917i
$304$	−2.80818	−	4.86391i	−0.161060	−	0.278964i
$305$	−2.22250	+	2.22044i	−0.127260	+	0.127142i
$306$	−12.3624	−	7.13745i	−0.706713	−	0.408021i
$307$	6.16270	−	6.16270i	0.351724	−	0.351724i	−0.509027	−	0.860751i	$-0.669995\pi$
$307$	6.16270	−	6.16270i	0.351724	−	0.351724i	0.860751	+	0.509027i	$0.169995\pi$
$308$		0			0
$309$			5.11673i			0.291080i
$310$	3.03467	+	5.26184i	0.172358	+	0.298852i
$311$	17.2457	−	9.95683i	0.977916	−	0.564600i	0.0762760	−	0.997087i	$-0.475697\pi$
$311$	17.2457	−	9.95683i	0.977916	−	0.564600i	0.901640	+	0.432486i	$0.142364\pi$
$312$	0.00737852	−	0.0275370i	0.000417726	−	0.00155898i
$313$	17.3413	−	4.64659i	0.980188	−	0.262641i	0.267064	−	0.963679i	$-0.413946\pi$
$313$	17.3413	−	4.64659i	0.980188	−	0.262641i	0.713124	+	0.701038i	$0.247280\pi$
$314$	−7.83010			−0.441878
$315$		0			0
$316$	−16.5686			−0.932059
$317$	−6.79678	+	1.82119i	−0.381745	+	0.102288i	−0.444588	−	0.895735i	$-0.646650\pi$
$317$	−6.79678	+	1.82119i	−0.381745	+	0.102288i	0.0628430	+	0.998023i	$0.479983\pi$
$318$	−0.501143	+	1.87029i	−0.0281027	+	0.104881i
$319$	−4.46613	+	2.57852i	−0.250055	+	0.144369i
$320$	−2.15961	−	0.579738i	−0.120726	−	0.0324084i
$321$			5.28963i			0.295238i
$322$		0			0
$323$	−19.9068	+	19.9068i	−1.10764	+	1.10764i
$324$	6.62815	+	3.82676i	0.368230	+	0.212598i
$325$	−0.0942438	−	0.353032i	−0.00522770	−	0.0195827i
$326$	−2.87011	−	4.97117i	−0.158960	−	0.275328i
$327$	−0.543775	−	2.02940i	−0.0300708	−	0.112226i
$328$	6.31914	+	6.31914i	0.348916	+	0.348916i
$329$		0			0
$330$	0.162456	+	0.607420i	0.00894291	+	0.0334374i
$331$	−3.10139	+	5.37176i	−0.170468	+	0.295259i	−0.938583	−	0.345052i	$-0.887861\pi$
$331$	−3.10139	+	5.37176i	−0.170468	+	0.295259i	0.768116	+	0.640311i	$0.221194\pi$
$332$	1.13044	+	0.302899i	0.0620407	+	0.0166238i
$333$	16.7223	+	4.48072i	0.916375	+	0.245542i
$334$	−0.551691	+	0.955556i	−0.0301872	+	0.0522857i
$335$	9.71741	+	5.61636i	0.530919	+	0.306854i
$336$		0			0
$337$	0.0548476	+	0.0548476i	0.00298774	+	0.00298774i	0.708599	−	0.705611i	$-0.249328\pi$
$337$	0.0548476	+	0.0548476i	0.00298774	+	0.00298774i	−0.705611	+	0.708599i	$0.749328\pi$
$338$	−3.36327	−	12.5519i	−0.182938	−	0.682732i
$339$	1.84856	+	3.20180i	0.100400	+	0.173898i
$340$	−0.00519644	+	11.2085i	−0.000281816	+	0.607864i
$341$	1.69575	+	0.979043i	0.0918301	+	0.0530182i
$342$	11.3097	−	11.3097i	0.611560	−	0.611560i
$343$		0			0
$344$			4.72082i			0.254529i
$345$	1.84237	−	6.86311i	0.0991901	−	0.369497i
$346$	1.53159	−	0.884266i	0.0823390	−	0.0475384i
$347$	1.84916	−	6.90115i	0.0992680	−	0.370473i	−0.898364	−	0.439252i	$-0.855244\pi$
$347$	1.84916	−	6.90115i	0.0992680	−	0.370473i	0.997632	+	0.0687787i	$0.0219102\pi$
$348$	−2.69587	+	0.722356i	−0.144514	+	0.0387224i
$349$	12.2000			0.653054			0.326527	−	0.945188i	$-0.394122\pi$
$349$	12.2000			0.653054			0.326527	+	0.945188i	$0.394122\pi$
$350$		0			0
$351$	0.166712			0.00889843
$352$	−0.696257	+	0.186562i	−0.0371106	+	0.00994377i
$353$	−5.65400	+	21.1010i	−0.300932	+	1.12309i	0.635459	+	0.772135i	$0.280811\pi$
$353$	−5.65400	+	21.1010i	−0.300932	+	1.12309i	−0.936391	+	0.350959i	$0.885856\pi$
$354$	4.31722	−	2.49255i	0.229458	−	0.132477i
$355$	4.50136	−	16.7682i	0.238907	−	0.889963i
$356$		−	6.29380i		−	0.333571i
$357$		0			0
$358$	10.2255	−	10.2255i	0.540434	−	0.540434i
$359$	−2.26832	−	1.30961i	−0.119717	−	0.0691188i	0.438946	−	0.898514i	$-0.355352\pi$
$359$	−2.26832	−	1.30961i	−0.119717	−	0.0691188i	−0.558663	+	0.829395i	$0.688685\pi$
$360$	0.00295228	−	6.36792i	0.000155599	−	0.335619i
$361$	−6.27173	−	10.8630i	−0.330091	−	0.571734i
$362$	−3.30583	−	12.3375i	−0.173750	−	0.648445i
$363$	−2.89098	−	2.89098i	−0.151737	−	0.151737i
$364$		0			0
$365$	5.51325	+	3.18648i	0.288577	+	0.166788i
$366$	−0.274044	+	0.474658i	−0.0143245	+	0.0248108i
$367$	1.15293	+	0.308928i	0.0601827	+	0.0161259i	0.288785	−	0.957394i	$-0.406749\pi$
$367$	1.15293	+	0.308928i	0.0601827	+	0.0161259i	−0.228602	+	0.973520i	$0.573415\pi$
$368$	7.86881	+	2.10844i	0.410190	+	0.109910i
$369$	−12.7249	+	22.0402i	−0.662433	+	1.14737i
$370$	−3.51211	−	13.1317i	−0.182586	−	0.682686i
$371$		0			0
$372$	0.749327	+	0.749327i	0.0388508	+	0.0388508i
$373$	−2.67296	−	9.97563i	−0.138401	−	0.516518i	−0.999961	−	0.00886274i	$-0.997179\pi$
$373$	−2.67296	−	9.97563i	−0.138401	−	0.516518i	0.861560	−	0.507656i	$-0.169488\pi$
$374$	1.80658	+	3.12909i	0.0934160	+	0.161801i
$375$	2.17549	+	3.78020i	0.112342	+	0.195209i
$376$	9.42904	+	5.44386i	0.486266	+	0.280746i
$377$	0.369702	−	0.369702i	0.0190406	−	0.0190406i
$378$		0			0
$379$			26.7026i			1.37162i	0.727781	+	0.685810i	$0.240552\pi$
$379$			26.7026i			1.37162i	−0.727781	+	0.685810i	$0.759448\pi$
$380$	−12.1291	−	3.25602i	−0.622211	−	0.167030i
$381$	6.64435	−	3.83612i	0.340400	−	0.196530i
$382$	−0.753625	+	2.81257i	−0.0385588	+	0.143903i
$383$	−27.4401	+	7.35255i	−1.40212	+	0.375698i	−0.879107	−	0.476624i	$-0.841860\pi$
$383$	−27.4401	+	7.35255i	−1.40212	+	0.375698i	−0.523017	+	0.852322i	$0.675194\pi$
$384$	−0.390104			−0.0199074
$385$		0			0
$386$	11.0080			0.560294
$387$	−12.9859	+	3.47957i	−0.660112	+	0.176877i
$388$	1.98136	−	7.39453i	0.100588	−	0.375401i
$389$	−13.1438	+	7.58857i	−0.666417	+	0.384756i	−0.794718	−	0.606979i	$-0.792381\pi$
$389$	−13.1438	+	7.58857i	−0.666417	+	0.384756i	0.128301	+	0.991735i	$0.459048\pi$
$390$	−0.0318478	−	0.0552210i	−0.00161267	−	0.00279623i
$391$		−	40.8344i		−	2.06508i
$392$		0			0
$393$	3.06550	−	3.06550i	0.154634	−	0.154634i
$394$	−17.0434	−	9.84001i	−0.858634	−	0.495733i
$395$	−26.2095	+	26.1852i	−1.31874	+	1.31752i
$396$	−1.02638	−	1.77774i	−0.0515776	−	0.0893350i
$397$	−5.12446	−	19.1247i	−0.257189	−	0.959843i	−0.966860	−	0.255309i	$-0.917823\pi$
$397$	−5.12446	−	19.1247i	−0.257189	−	0.959843i	0.709670	−	0.704534i	$-0.248844\pi$
$398$	−4.08562	−	4.08562i	−0.204794	−	0.204794i
$399$		0			0
$400$	−4.33244	+	2.49598i	−0.216622	+	0.124799i
$401$	−0.241984	+	0.419128i	−0.0120841	+	0.0209303i	−0.872004	−	0.489498i	$-0.837180\pi$
$401$	−0.241984	+	0.419128i	−0.0120841	+	0.0209303i	0.859920	+	0.510429i	$0.170513\pi$
$402$	1.89137	+	0.506790i	0.0943328	+	0.0252764i
$403$	−0.191753	−	0.0513800i	−0.00955189	−	0.00255942i
$404$	−7.82817	+	13.5588i	−0.389466	+	0.674575i
$405$	16.5327	−	4.42171i	0.821517	−	0.219717i
$406$		0			0
$407$	−3.09849	−	3.09849i	−0.153587	−	0.153587i
$408$	0.506102	+	1.88880i	0.0250558	+	0.0935094i
$409$	−12.5170	−	21.6801i	−0.618926	−	1.07201i	−0.989682	−	0.143282i	$-0.954235\pi$
$409$	−12.5170	−	21.6801i	−0.618926	−	1.07201i	0.370756	−	0.928731i	$-0.379099\pi$
$410$	19.9829	+	0.00926441i	0.986884	+	0.000457537i
$411$	−1.22724	−	0.708547i	−0.0605352	−	0.0349500i
$412$	−9.27463	+	9.27463i	−0.456928	+	0.456928i
$413$		0			0
$414$			23.1994i			1.14019i
$415$	2.26691	−	1.30740i	0.111278	−	0.0641777i
$416$	0.0632882	−	0.0365395i	0.00310296	−	0.00179149i
$417$	1.50349	−	5.61110i	0.0736262	−	0.274777i
$418$	−3.91043	+	1.04780i	−0.191265	+	0.0512494i
$419$	12.6842			0.619665			0.309832	−	0.950791i	$-0.399727\pi$
$419$	12.6842			0.619665			0.309832	+	0.950791i	$0.399727\pi$
$420$		0			0
$421$	−0.694479			−0.0338469			−0.0169234	−	0.999857i	$-0.505387\pi$
$421$	−0.694479			−0.0338469			−0.0169234	+	0.999857i	$0.505387\pi$
$422$	−4.67942	+	1.25385i	−0.227791	+	0.0610363i
$423$	−8.02501	+	29.9497i	−0.390189	+	1.45621i
$424$	−4.29848	+	2.48173i	−0.208753	+	0.120523i
$425$	17.7057	+	17.7386i	0.858852	+	0.860446i
$426$		−	3.02895i		−	0.146753i
$427$		0			0
$428$	−9.58803	+	9.58803i	−0.463455	+	0.463455i
$429$	−0.0177963	−	0.0102747i	−0.000859213	−	0.000496067i
$430$	7.46081	+	7.46773i	0.359792	+	0.360126i
$431$	−13.2895	−	23.0180i	−0.640131	−	1.10874i	−0.985403	−	0.170236i	$-0.945547\pi$
$431$	−13.2895	−	23.0180i	−0.640131	−	1.10874i	0.345273	−	0.938502i	$-0.387786\pi$
$432$	−0.590433	−	2.20353i	−0.0284072	−	0.106017i
$433$	27.8041	+	27.8041i	1.33618	+	1.33618i	0.899727	+	0.436453i	$0.143765\pi$
$433$	27.8041	+	27.8041i	1.33618	+	1.33618i	0.436453	+	0.899727i	$0.356235\pi$
$434$		0			0
$435$	−3.12291	+	5.40325i	−0.149732	+	0.259066i
$436$	2.69285	−	4.66416i	0.128964	−	0.223373i
$437$	44.1940	+	11.8418i	2.11409	+	0.566468i
$438$	1.07308	+	0.287531i	0.0512738	+	0.0137388i
$439$	−7.17677	+	12.4305i	−0.342529	+	0.593277i	−0.984902	−	0.173115i	$-0.944617\pi$
$439$	−7.17677	+	12.4305i	−0.342529	+	0.593277i	0.642373	+	0.766392i	$0.277950\pi$
$440$	−0.806547	+	1.39549i	−0.0384506	+	0.0665272i
$441$		0			0
$442$	−0.259023	−	0.259023i	−0.0123205	−	0.0123205i
$443$	1.34738	+	5.02849i	0.0640159	+	0.238911i	0.990519	−	0.137377i	$-0.0438672\pi$
$443$	1.34738	+	5.02849i	0.0640159	+	0.238911i	−0.926503	+	0.376287i	$0.877200\pi$
$444$	−1.18574	−	2.05376i	−0.0562728	−	0.0974673i
$445$	−9.94676	−	9.95599i	−0.471522	−	0.471959i
$446$	−19.3722	−	11.1846i	−0.917301	−	0.529604i
$447$	−0.753958	+	0.753958i	−0.0356610	+	0.0356610i
$448$		0			0
$449$			17.0597i			0.805097i	0.915399	+	0.402549i	$0.131876\pi$
$449$			17.0597i			0.805097i	−0.915399	+	0.402549i	$0.868124\pi$
$450$	−10.0592	−	10.0779i	−0.474196	−	0.475076i
$451$	5.57866	−	3.22084i	0.262689	−	0.151663i
$452$	−2.45289	+	9.15432i	−0.115374	+	0.430583i
$453$	1.65116	−	0.442428i	0.0775784	−	0.0207871i
$454$	−15.4007			−0.722790
$455$		0			0
$456$	−2.19096			−0.102601
$457$	−19.9496	+	5.34547i	−0.933201	+	0.250051i	−0.693219	−	0.720727i	$-0.743808\pi$
$457$	−19.9496	+	5.34547i	−0.933201	+	0.250051i	−0.239982	+	0.970777i	$0.577142\pi$
$458$	2.53540	−	9.46225i	0.118472	−	0.442142i
$459$	−9.90299	+	5.71749i	−0.462232	+	0.266870i
$460$	15.7796	−	9.10063i	0.735730	−	0.424319i
$461$			28.2605i			1.31622i	0.752920	+	0.658112i	$0.228645\pi$
$461$			28.2605i			1.31622i	−0.752920	+	0.658112i	$0.771355\pi$
$462$		0			0
$463$	12.8242	−	12.8242i	0.595990	−	0.595990i	−0.343253	−	0.939243i	$-0.611529\pi$
$463$	12.8242	−	12.8242i	0.595990	−	0.595990i	0.939243	+	0.343253i	$0.111529\pi$
$464$	−6.19591	−	3.57721i	−0.287638	−	0.166068i
$465$	2.36958	+	0.00109858i	0.109887	+	5.09454e-5i
$466$	6.45376	+	11.1782i	0.298965	+	0.517822i
$467$	10.2453	+	38.2362i	0.474098	+	1.76936i	0.624806	+	0.780780i	$0.285178\pi$
$467$	10.2453	+	38.2362i	0.474098	+	1.76936i	−0.150708	+	0.988578i	$0.548155\pi$
$468$	0.147160	+	0.147160i	0.00680247	+	0.00680247i
$469$		0			0
$470$	23.5190	−	6.29022i	1.08485	−	0.290146i
$471$	−1.52728	+	2.64532i	−0.0703732	+	0.121890i
$472$	12.3434	+	3.30742i	0.568153	+	0.152236i
$473$	3.28690	+	0.880723i	0.151132	+	0.0404957i
$474$	−3.23175	+	5.59755i	−0.148439	+	0.257104i
$475$	−24.3325	+	14.0183i	−1.11645	+	0.643205i
$476$		0			0
$477$	−9.99498	−	9.99498i	−0.457639	−	0.457639i
$478$	−4.29566	−	16.0316i	−0.196479	−	0.733269i
$479$	6.91857	+	11.9833i	0.316118	+	0.547532i	0.979674	−	0.200594i	$-0.0642872\pi$
$479$	6.91857	+	11.9833i	0.316118	+	0.547532i	−0.663557	+	0.748126i	$0.730954\pi$
$480$	−0.617095	+	0.616523i	−0.0281664	+	0.0281403i
$481$	0.384735	+	0.222127i	0.0175424	+	0.0101281i
$482$	−2.99332	+	2.99332i	−0.136342	+	0.136342i
$483$		0			0
$484$		−	10.4804i		−	0.476383i
$485$	−8.55211	−	14.8286i	−0.388331	−	0.673330i
$486$	8.51255	−	4.91473i	0.386137	−	0.222936i
$487$	1.72056	−	6.42122i	0.0779661	−	0.290973i	−0.915923	−	0.401353i	$-0.868540\pi$
$487$	1.72056	−	6.42122i	0.0779661	−	0.290973i	0.993889	+	0.110380i	$0.0352067\pi$
$488$	−1.35710	+	0.363635i	−0.0614332	+	0.0164610i
$489$	−2.23928			−0.101264
$490$		0			0
$491$	−25.7747			−1.16320			−0.581599	−	0.813476i	$-0.697573\pi$
$491$	−25.7747			−1.16320			−0.581599	+	0.813476i	$0.697573\pi$
$492$	3.36742	−	0.902298i	0.151815	−	0.0406787i
$493$	−9.28179	+	34.6401i	−0.418031	+	1.56011i
$494$	0.355449	−	0.205219i	0.0159924	−	0.00923322i
$495$	−4.43316	−	1.19006i	−0.199256	−	0.0534894i
$496$			2.71648i			0.121973i
$497$		0			0
$498$	0.322825	−	0.322825i	0.0144661	−	0.0144661i
$499$	−4.56822	−	2.63746i	−0.204502	−	0.118069i	0.394252	−	0.919002i	$-0.371004\pi$
$499$	−4.56822	−	2.63746i	−0.204502	−	0.118069i	−0.598753	+	0.800933i	$0.704337\pi$
$500$	−2.90870	+	10.7953i	−0.130081	+	0.482782i
$501$	0.215217	+	0.372767i	0.00961518	+	0.0166540i
$502$	5.34386	+	19.9436i	0.238508	+	0.890125i
$503$	0.933931	+	0.933931i	0.0416419	+	0.0416419i	0.727621	−	0.685979i	$-0.240626\pi$
$503$	0.933931	+	0.933931i	0.0416419	+	0.0416419i	−0.685979	+	0.727621i	$0.740626\pi$
$504$		0			0
$505$	9.04523	+	33.8200i	0.402507	+	1.50497i
$506$	2.93604	−	5.08536i	0.130523	−	0.226072i
$507$	−4.89654	−	1.31202i	−0.217463	−	0.0582690i
$508$	18.9970	+	5.09023i	0.842855	+	0.225842i
$509$	−10.5661	+	18.3009i	−0.468332	+	0.811175i	−0.999345	−	0.0361887i	$-0.988478\pi$
$509$	−10.5661	+	18.3009i	−0.468332	+	0.811175i	0.531013	+	0.847364i	$0.321812\pi$
$510$	3.78565	+	2.18799i	0.167632	+	0.0968858i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.31608	−	12.3758i	−0.146409	−	0.546405i
$514$	−12.7044	−	22.0046i	−0.560365	−	0.970580i
$515$	−0.0135974	+	29.3289i	−0.000599174	+	1.29239i
$516$	1.59488	+	0.920806i	0.0702108	+	0.0405362i
$517$	5.54942	−	5.54942i	0.244063	−	0.244063i
$518$		0			0
$519$		−	0.689912i		−	0.0302838i
$520$	0.0423666	−	0.157822i	0.00185790	−	0.00692094i
$521$	−5.06985	+	2.92708i	−0.222114	+	0.128238i	−0.606929	−	0.794756i	$-0.707599\pi$
$521$	−5.06985	+	2.92708i	−0.222114	+	0.128238i	0.384815	+	0.922994i	$0.374265\pi$
$522$	5.27331	−	19.6803i	0.230806	−	0.861381i
$523$	38.5738	−	10.3358i	1.68672	−	0.451954i	0.717177	−	0.696891i	$-0.245434\pi$
$523$	38.5738	−	10.3358i	1.68672	−	0.451954i	0.969539	+	0.244936i	$0.0787670\pi$
$524$	11.1131			0.485478
$525$		0			0
$526$	−16.8042			−0.732697
$527$	13.1526	−	3.52422i	0.572935	−	0.153517i
$528$	−0.0727785	+	0.271613i	−0.00316728	+	0.0118204i
$529$	−37.5541	+	21.6818i	−1.63279	+	0.942689i
$530$	−2.87751	+	10.7191i	−0.124991	+	0.465609i
$531$			36.3919i			1.57927i
$532$		0			0
$533$	−0.461796	+	0.461796i	−0.0200026	+	0.0200026i
$534$	−2.12630	−	1.22762i	−0.0920140	−	0.0531243i
$535$	−0.0140569	+	30.3200i	−0.000607732	+	1.31085i
$536$	2.50970	+	4.34692i	0.108402	+	0.187758i
$537$	−1.46008	−	5.44909i	−0.0630070	−	0.235145i
$538$	−11.2169	−	11.2169i	−0.483594	−	0.483594i
$539$		0			0
$540$	−4.41646	−	2.55257i	−0.190054	−	0.109845i
$541$	−22.0144	+	38.1300i	−0.946472	+	1.63934i	−0.193694	+	0.981062i	$0.562047\pi$
$541$	−22.0144	+	38.1300i	−0.946472	+	1.63934i	−0.752778	+	0.658275i	$0.771286\pi$
$542$	−1.71118	−	0.458510i	−0.0735016	−	0.0196947i
$543$	−4.81291	−	1.28962i	−0.206542	−	0.0553427i
$544$	−2.50629	+	4.34102i	−0.107456	+	0.186120i
$545$	−3.11151	−	11.6339i	−0.133283	−	0.498341i
$546$		0			0
$547$	−0.954660	−	0.954660i	−0.0408183	−	0.0408183i	0.686403	−	0.727221i	$-0.259189\pi$
$547$	−0.954660	−	0.954660i	−0.0408183	−	0.0408183i	−0.727221	+	0.686403i	$0.759189\pi$
$548$	−0.940187	−	3.50882i	−0.0401628	−	0.149890i
$549$	−2.00056	−	3.46507i	−0.0853819	−	0.147886i
$550$	0.929580	+	3.48215i	0.0396374	+	0.148479i
$551$	−34.7985	−	20.0909i	−1.48246	−	0.855901i
$552$	2.24714	−	2.24714i	0.0956448	−	0.0956448i
$553$		0			0
$554$		−	2.11231i		−	0.0897436i
$555$	−5.12147	−	1.37484i	−0.217394	−	0.0583587i
$556$	12.8960	−	7.44549i	0.546911	−	0.315759i
$557$	6.64232	−	24.7895i	0.281444	−	1.05036i	−0.669955	−	0.742402i	$-0.733686\pi$
$557$	6.64232	−	24.7895i	0.281444	−	1.05036i	0.951399	−	0.307962i	$-0.0996469\pi$
$558$	−7.47243	+	2.00223i	−0.316333	+	0.0847612i
$559$	−0.344992			−0.0145916
$560$		0			0
$561$	1.40951			0.0595095
$562$	7.72286	−	2.06933i	0.325769	−	0.0872896i
$563$	5.13107	−	19.1494i	0.216249	−	0.807051i	−0.769475	−	0.638677i	$-0.779482\pi$
$563$	5.13107	−	19.1494i	0.216249	−	0.807051i	0.985723	−	0.168374i	$-0.0538515\pi$
$564$	3.67831	−	2.12367i	0.154885	−	0.0894228i
$565$	10.5874	+	18.3575i	0.445414	+	0.772307i
$566$		−	15.4645i		−	0.650021i
$567$		0			0
$568$	5.49030	−	5.49030i	0.230368	−	0.230368i
$569$	−13.3682	−	7.71815i	−0.560425	−	0.323562i	0.192891	−	0.981220i	$-0.438214\pi$
$569$	−13.3682	−	7.71815i	−0.560425	−	0.323562i	−0.753316	+	0.657659i	$0.771547\pi$
$570$	−3.46582	+	3.46261i	−0.145167	+	0.145033i
$571$	1.40422	+	2.43217i	0.0587646	+	0.101783i	0.893911	−	0.448244i	$-0.147951\pi$
$571$	1.40422	+	2.43217i	0.0587646	+	0.101783i	−0.835147	+	0.550028i	$0.814617\pi$
$572$	−0.0136337	−	0.0508817i	−0.000570054	−	0.00212747i
$573$	0.803202	+	0.803202i	0.0335542	+	0.0335542i
$574$		0			0
$575$	10.5787	−	39.3343i	0.441162	−	1.64035i
$576$	1.42391	−	2.46628i	0.0593296	−	0.102762i
$577$	36.1044	+	9.67413i	1.50304	+	0.402739i	0.914118	−	0.405448i	$-0.132884\pi$
$577$	36.1044	+	9.67413i	1.50304	+	0.402739i	0.588926	+	0.808187i	$0.299551\pi$
$578$	7.84903	+	2.10314i	0.326477	+	0.0874792i
$579$	2.14714	−	3.71896i	0.0892321	−	0.154555i
$580$	−15.4546	+	4.13337i	−0.641717	+	0.171629i
$581$		0			0
$582$	−2.11170	−	2.11170i	−0.0875329	−	0.0875329i
$583$	0.925991	+	3.45585i	0.0383506	+	0.143126i
$584$	1.42390	+	2.46626i	0.0589212	+	0.102055i
$585$	0.465360		0.000215749i	0.0192403		8.92014e-6i
$586$	−10.9007	−	6.29351i	−0.450303	−	0.259982i
$587$	11.9438	−	11.9438i	0.492972	−	0.492972i	−0.416269	−	0.909241i	$-0.636663\pi$
$587$	11.9438	−	11.9438i	0.492972	−	0.492972i	0.909241	+	0.416269i	$0.136663\pi$
$588$		0			0
$589$			15.2567i			0.628641i
$590$	24.7528	−	14.2757i	1.01906	−	0.587723i
$591$	−6.64870	+	3.83863i	−0.273491	+	0.157900i
$592$	1.57339	−	5.87196i	0.0646658	−	0.241336i
$593$	−21.8574	+	5.85667i	−0.897575	+	0.240505i	−0.677975	−	0.735085i	$-0.737142\pi$
$593$	−21.8574	+	5.85667i	−0.897575	+	0.240505i	−0.219601	+	0.975590i	$0.570475\pi$
$594$	−1.64437			−0.0674695
$595$		0			0
$596$	−2.73326			−0.111959
$597$	−2.17720	+	0.583378i	−0.0891067	+	0.0238761i
$598$	−0.154083	+	0.575044i	−0.00630091	+	0.0235153i
$599$	−17.8801	+	10.3231i	−0.730563	+	0.421791i	−0.818628	−	0.574324i	$-0.805265\pi$
$599$	−17.8801	+	10.3231i	−0.730563	+	0.421791i	0.0880654	+	0.996115i	$0.471932\pi$
$600$	−0.00180859	+	1.95052i	−7.38355e−5	+	0.0796297i
$601$		−	32.0064i		−	1.30557i	−0.757544	−	0.652784i	$-0.773601\pi$
$601$		−	32.0064i		−	1.30557i	0.757544	−	0.652784i	$-0.226399\pi$
$602$		0			0
$603$	−10.1076	+	10.1076i	−0.411614	+	0.411614i
$604$	3.79486	+	2.19096i	0.154411	+	0.0891491i
$605$	−16.5633	−	16.5787i	−0.673395	−	0.674019i
$606$	3.05380	+	5.28934i	0.124052	+	0.214865i
$607$	−5.27869	−	19.7003i	−0.214255	−	0.799612i	−0.986427	−	0.164199i	$-0.947496\pi$
$607$	−5.27869	−	19.7003i	−0.214255	−	0.799612i	0.772172	−	0.635414i	$-0.219170\pi$
$608$	−3.97136	−	3.97136i	−0.161060	−	0.161060i
$609$		0			0
$610$	−1.57207	+	2.72000i	−0.0636514	+	0.110130i
$611$	−0.397831	+	0.689064i	−0.0160945	+	0.0278766i
$612$	−13.7885	−	3.69462i	−0.557367	−	0.149346i
$613$	−8.75743	−	2.34655i	−0.353709	−	0.0947762i	0.0775891	−	0.996985i	$-0.475278\pi$
$613$	−8.75743	−	2.34655i	−0.353709	−	0.0947762i	−0.431299	+	0.902209i	$0.641944\pi$
$614$	4.35769	−	7.54773i	0.175862	−	0.304602i
$615$	3.90083	−	6.74921i	0.157297	−	0.272154i
$616$		0			0
$617$	−20.7279	−	20.7279i	−0.834475	−	0.834475i	0.153651	−	0.988125i	$-0.450897\pi$
$617$	−20.7279	−	20.7279i	−0.834475	−	0.834475i	−0.988125	+	0.153651i	$0.950897\pi$
$618$	1.32431	+	4.94238i	0.0532714	+	0.198812i
$619$	−23.9123	−	41.4174i	−0.961117	−	1.66470i	−0.719703	−	0.694282i	$-0.755722\pi$
$619$	−23.9123	−	41.4174i	−0.961117	−	1.66470i	−0.241414	−	0.970422i	$-0.577611\pi$
$620$	4.29313	+	4.29712i	0.172416	+	0.172576i
$621$	16.0942	+	9.29201i	0.645840	+	0.372876i
$622$	14.0811	−	14.0811i	0.564600	−	0.564600i
$623$		0			0
$624$		−	0.0285084i		−	0.00114125i
$625$	12.4598	+	21.6738i	0.498393	+	0.866951i
$626$	15.5478	−	8.97652i	0.621415	−	0.358774i
$627$	−0.408750	+	1.52548i	−0.0163239	+	0.0609216i
$628$	−7.56329	+	2.02658i	−0.301808	+	0.0808693i
$629$	−30.4719			−1.21500
$630$		0			0
$631$	−19.5896			−0.779848			−0.389924	−	0.920847i	$-0.627499\pi$
$631$	−19.5896			−0.779848			−0.389924	+	0.920847i	$0.627499\pi$
$632$	−16.0041	+	4.28828i	−0.636608	+	0.170579i
$633$	−0.489131	+	1.82546i	−0.0194412	+	0.0725556i
$634$	−6.09382	+	3.51827i	−0.242017	+	0.139728i
$635$	38.0954	−	21.9709i	1.51177	−	0.871887i
$636$			1.93627i			0.0767780i
$637$		0			0
$638$	−3.64658	+	3.64658i	−0.144369	+	0.144369i
$639$	19.1494	+	11.0559i	0.757537	+	0.437364i
$640$	−2.23607	−	0.00103668i	−0.0883883	−	4.09784e-5i
$641$	19.2616	+	33.3621i	0.760788	+	1.31772i	0.942445	+	0.334361i	$0.108520\pi$
$641$	19.2616	+	33.3621i	0.760788	+	1.31772i	−0.181657	+	0.983362i	$0.558146\pi$
$642$	1.36906	+	5.10939i	0.0540323	+	0.201651i
$643$	28.2487	+	28.2487i	1.11402	+	1.11402i	0.992601	+	0.121419i	$0.0387446\pi$
$643$	28.2487	+	28.2487i	1.11402	+	1.11402i	0.121419	+	0.992601i	$0.461255\pi$
$644$		0			0
$645$	3.97815	−	1.06396i	0.156639	−	0.0418936i
$646$	−14.0762	+	24.3807i	−0.553821	+	0.959246i
$647$	0.435000	+	0.116558i	0.0171016	+	0.00458237i	0.267360	−	0.963597i	$-0.413849\pi$
$647$	0.435000	+	0.116558i	0.0171016	+	0.00458237i	−0.250258	+	0.968179i	$0.580515\pi$
$648$	7.39274	+	1.98088i	0.290414	+	0.0778163i
$649$	4.60563	−	7.97718i	0.180787	−	0.313132i
$650$	−0.182404	−	0.316610i	−0.00715447	−	0.0124185i
$651$		0			0
$652$	−4.05894	−	4.05894i	−0.158960	−	0.158960i
$653$	4.28562	+	15.9942i	0.167709	+	0.625899i	0.997679	+	0.0680912i	$0.0216909\pi$
$653$	4.28562	+	15.9942i	0.167709	+	0.625899i	−0.829970	+	0.557808i	$0.811642\pi$
$654$	−1.05049	−	1.81951i	−0.0410775	−	0.0711484i
$655$	17.5795	−	17.5632i	0.686888	−	0.686251i
$656$	7.73933	+	4.46831i	0.302170	+	0.174458i
$657$	−5.73463	+	5.73463i	−0.223729	+	0.223729i
$658$		0			0
$659$			15.5720i			0.606598i	0.952896	+	0.303299i	$0.0980880\pi$
$659$			15.5720i			0.606598i	−0.952896	+	0.303299i	$0.901912\pi$
$660$	0.314132	+	0.544676i	0.0122276	+	0.0212015i
$661$	−11.9629	+	6.90678i	−0.465303	+	0.268643i	−0.714271	−	0.699869i	$-0.753242\pi$
$661$	−11.9629	+	6.90678i	−0.465303	+	0.268643i	0.248969	+	0.968512i	$0.419908\pi$
$662$	−1.60540	+	5.99142i	−0.0623955	+	0.232863i
$663$	−0.138031	+	0.0369854i	−0.00536069	+	0.00143639i
$664$	1.17031			0.0454169
$665$		0			0
$666$	17.3122			0.670833
$667$	56.2968	−	15.0847i	2.17982	−	0.584081i
$668$	−0.285576	+	1.06578i	−0.0110493	+	0.0412364i
$669$	−7.55718	+	4.36314i	−0.292178	+	0.168689i
$670$	10.8399	+	2.90993i	0.418782	+	0.112421i
$671$			1.01273i			0.0390962i
$672$		0			0
$673$	33.7173	−	33.7173i	1.29971	−	1.29971i	0.371121	−	0.928585i	$-0.378974\pi$
$673$	33.7173	−	33.7173i	1.29971	−	1.29971i	0.928585	−	0.371121i	$-0.121026\pi$
$674$	0.0671743	+	0.0387831i	0.00258746	+	0.00149387i
$675$	−11.0204	+	2.94195i	−0.424174	+	0.113236i
$676$	−6.49733	−	11.2537i	−0.249897	−	0.432835i
$677$	−0.921672	−	3.43973i	−0.0354227	−	0.132199i	0.945950	−	0.324312i	$-0.105133\pi$
$677$	−0.921672	−	3.43973i	−0.0354227	−	0.132199i	−0.981373	+	0.192113i	$0.938466\pi$
$678$	2.61426	+	2.61426i	0.100400	+	0.100400i
$679$		0			0
$680$	2.89594	+	10.8279i	0.111054	+	0.415230i
$681$	−3.00394	+	5.20297i	−0.115111	+	0.199378i
$682$	1.89137	+	0.506790i	0.0724241	+	0.0194060i
$683$	7.71128	+	2.06623i	0.295064	+	0.0790621i	0.403314	−	0.915062i	$-0.367858\pi$
$683$	7.71128	+	2.06623i	0.295064	+	0.0790621i	−0.108250	+	0.994124i	$0.534525\pi$
$684$	7.99718	−	13.8515i	0.305780	−	0.529626i
$685$	−7.03262	−	4.06463i	−0.268703	−	0.155302i
$686$		0			0
$687$	−2.70219	−	2.70219i	−0.103095	−	0.103095i
$688$	1.22184	+	4.55996i	0.0465821	+	0.173847i
$689$	−0.181362	−	0.314128i	−0.00690935	−	0.0119673i
$690$	0.00329451	−	7.10609i	0.000125420	−	0.270524i
$691$	−34.9099	−	20.1552i	−1.32803	−	0.766741i	−0.343038	−	0.939321i	$-0.611456\pi$
$691$	−34.9099	−	20.1552i	−1.32803	−	0.766741i	−0.984995	+	0.172581i	$0.944789\pi$
$692$	1.25054	−	1.25054i	0.0475384	−	0.0475384i
$693$		0			0
$694$		−	7.14460i		−	0.271205i
$695$	8.63287	−	32.1587i	0.327464	−	1.21985i
$696$	−2.41705	+	1.39549i	−0.0916181	+	0.0528957i
$697$	11.5939	−	43.2691i	0.439151	−	1.63893i
$698$	11.7843	−	3.15760i	0.446044	−	0.119517i
$699$	5.03528			0.190452
$700$		0			0
$701$	21.5782			0.814997			0.407499	−	0.913206i	$-0.366401\pi$
$701$	21.5782			0.814997			0.407499	+	0.913206i	$0.366401\pi$
$702$	0.161031	−	0.0431482i	0.00607774	−	0.00162852i
$703$	8.83670	−	32.9790i	0.333282	−	1.24383i
$704$	−0.624247	+	0.360409i	−0.0235272	+	0.0135834i
$705$	2.46235	−	9.17260i	0.0927374	−	0.345460i
$706$			21.8454i			0.822162i
$707$		0			0
$708$	3.52499	−	3.52499i	0.132477	−	0.132477i
$709$	19.2642	+	11.1222i	0.723483	+	0.417703i	0.816033	−	0.578005i	$-0.196169\pi$
$709$	19.2642	+	11.1222i	0.723483	+	0.417703i	−0.0925503	+	0.995708i	$0.529502\pi$
$710$	0.00804927	−	17.3619i	0.000302084	−	0.651579i
$711$	−23.5922	−	40.8630i	−0.884778	−	1.53248i
$712$	−1.62896	−	6.07935i	−0.0610477	−	0.227833i
$713$	−15.6479	−	15.6479i	−0.586018	−	0.586018i
$714$		0			0
$715$	−0.101981	−	0.0589416i	−0.00381386	−	0.00220429i
$716$	7.23051	−	12.5236i	0.270217	−	0.468030i
$717$	−6.25400	−	1.67575i	−0.233560	−	0.0625822i
$718$	−2.52998	−	0.677906i	−0.0944180	−	0.0252992i
$719$	16.3534	−	28.3249i	0.609879	−	1.05634i	−0.381381	−	0.924418i	$-0.624551\pi$
$719$	16.3534	−	28.3249i	0.609879	−	1.05634i	0.991260	−	0.131923i	$-0.0421153\pi$
$720$	−1.64529	−	6.15170i	−0.0613162	−	0.229260i
$721$		0			0
$722$	−8.86956	−	8.86956i	−0.330091	−	0.330091i
$723$	0.427411	+	1.59512i	0.0158956	+	0.0593231i
$724$	−6.38636	−	11.0615i	−0.237347	−	0.411098i
$725$	−17.9148	+	30.9630i	−0.665338	+	1.14994i
$726$	−3.54071	−	2.04423i	−0.131408	−	0.0758684i
$727$	−29.8873	+	29.8873i	−1.10846	+	1.10846i	−0.115106	+	0.993353i	$0.536721\pi$
$727$	−29.8873	+	29.8873i	−1.10846	+	1.10846i	−0.993353	+	0.115106i	$0.963279\pi$
$728$		0			0
$729$			19.1261i			0.708373i
$730$	6.15011	+	1.65097i	0.227626	+	0.0611053i
$731$	20.4932	−	11.8317i	0.757967	−	0.437612i
$732$	−0.141856	+	0.529412i	−0.00524313	+	0.0195676i
$733$	1.33683	−	0.358203i	0.0493770	−	0.0132305i	−0.234046	−	0.972226i	$-0.575197\pi$
$733$	1.33683	−	0.358203i	0.0493770	−	0.0132305i	0.283423	+	0.958995i	$0.408530\pi$
$734$	1.19361			0.0440568
$735$		0			0
$736$	8.14639			0.300280
$737$	3.49479	−	0.936426i	0.128732	−	0.0344937i
$738$	−6.58691	+	24.5827i	−0.242467	+	0.904900i
$739$	45.0666	−	26.0192i	1.65780	−	0.957131i	0.684073	−	0.729414i	$-0.260207\pi$
$739$	45.0666	−	26.0192i	1.65780	−	0.957131i	0.973727	−	0.227718i	$-0.0731263\pi$
$740$	−6.79118	−	11.7753i	−0.249649	−	0.432868i
$741$		−	0.160113i		−	0.00588191i
$742$		0			0
$743$	25.6024	−	25.6024i	0.939261	−	0.939261i	−0.0589973	−	0.998258i	$-0.518790\pi$
$743$	25.6024	−	25.6024i	0.939261	−	0.939261i	0.998258	+	0.0589973i	$0.0187903\pi$
$744$	0.917734	+	0.529854i	0.0336458	+	0.0194254i
$745$	−4.32367	+	4.31966i	−0.158407	+	0.158260i
$746$	−5.16377	−	8.94390i	−0.189059	−	0.327460i
$747$	0.862602	+	3.21927i	0.0315610	+	0.117787i
$748$	2.55489	+	2.55489i	0.0934160	+	0.0934160i
$749$		0			0
$750$	3.07975	+	3.08833i	0.112457	+	0.112770i
$751$	1.18594	−	2.05411i	0.0432756	−	0.0749556i	−0.843576	−	0.537009i	$-0.819554\pi$
$751$	1.18594	−	2.05411i	0.0432756	−	0.0749556i	0.886852	+	0.462054i	$0.152887\pi$
$752$	10.5167	+	2.81795i	0.383506	+	0.102760i
$753$	7.78007	+	2.08466i	0.283522	+	0.0759694i
$754$	0.261419	−	0.452791i	0.00952031	−	0.0164897i
$755$	9.46560	−	2.53160i	0.344488	−	0.0921342i
$756$		0			0
$757$	21.8819	+	21.8819i	0.795311	+	0.795311i	0.982352	−	0.187041i	$-0.0598897\pi$
$757$	21.8819	+	21.8819i	0.795311	+	0.795311i	−0.187041	+	0.982352i	$0.559890\pi$
$758$	6.91114	+	25.7927i	0.251024	+	0.936834i
$759$	−1.14536	−	1.98382i	−0.0415739	−	0.0720082i
$760$	−12.5586	−	0.00582237i	−0.455547	−	0.000211199i
$761$	6.45105	+	3.72452i	0.233850	+	0.135014i	0.612347	−	0.790589i	$-0.290226\pi$
$761$	6.45105	+	3.72452i	0.233850	+	0.135014i	−0.378497	+	0.925603i	$0.623559\pi$
$762$	5.42509	−	5.42509i	0.196530	−	0.196530i
$763$		0			0
$764$			2.91178i			0.105345i
$765$	−27.6506	+	15.9470i	−0.999711	+	0.576565i
$766$	−24.6021	+	14.2040i	−0.888911	+	0.513213i
$767$	−0.241702	+	0.902046i	−0.00872737	+	0.0325710i
$768$	−0.376812	+	0.100966i	−0.0135970	+	0.00364331i
$769$	24.2399			0.874112			0.437056	−	0.899434i	$-0.356021\pi$
$769$	24.2399			0.874112			0.437056	+	0.899434i	$0.356021\pi$
$770$		0			0
$771$	−9.91204			−0.356973
$772$	10.6329	−	2.84909i	0.382688	−	0.102541i
$773$	5.17765	−	19.3233i	0.186227	−	0.695009i	−0.808137	−	0.588994i	$-0.799524\pi$
$773$	5.17765	−	19.3233i	0.186227	−	0.695009i	0.994365	−	0.106015i	$-0.0338092\pi$
$774$	−11.6429	+	6.72202i	−0.418495	+	0.241618i
$775$	13.5824	+	0.0125941i	0.487893	+	0.000452392i
$776$		−	7.65538i		−	0.274812i
$777$		0			0
$778$	−10.7319	+	10.7319i	−0.384756	+	0.384756i
$779$	43.4668	+	25.0956i	1.55736	+	0.899143i
$780$	−0.0450548	−	0.0450966i	−0.00161322	−	0.00161472i
$781$	−2.79838	−	4.84694i	−0.100134	−	0.173437i
$782$	−10.5687	−	39.4430i	−0.377937	−	1.41048i
$783$	−11.5408	−	11.5408i	−0.412433	−	0.412433i
$784$		0			0
$785$	−8.76134	+	15.1589i	−0.312706	+	0.541043i
$786$	2.16763	−	3.75445i	0.0773170	−	0.133917i
$787$	−43.4418	−	11.6402i	−1.54853	−	0.414929i	−0.619523	−	0.784979i	$-0.712674\pi$
$787$	−43.4418	−	11.6402i	−1.54853	−	0.414929i	−0.929012	+	0.370050i	$0.879340\pi$
$788$	−19.0094	−	5.09356i	−0.677183	−	0.181451i
$789$	−3.27769	+	5.67713i	−0.116689	+	0.202111i
$790$	−18.5392	+	32.0764i	−0.659594	+	1.14123i
$791$		0			0
$792$	−1.45152	−	1.45152i	−0.0515776	−	0.0515776i
$793$	−0.0265741	−	0.0991757i	−0.000943673	−	0.00352183i
$794$	−9.89969	−	17.1468i	−0.351327	−	0.608516i
$795$	3.06009	+	3.06293i	0.108530	+	0.108631i
$796$	−5.00385	−	2.88897i	−0.177357	−	0.102397i
$797$	32.9123	−	32.9123i	1.16581	−	1.16581i	0.182630	−	0.983182i	$-0.441539\pi$
$797$	32.9123	−	32.9123i	1.16581	−	1.16581i	0.983182	−	0.182630i	$-0.0584611\pi$
$798$		0			0
$799$		−	54.5755i		−	1.93074i
$800$	−3.53881	+	3.53225i	−0.125116	+	0.124884i
$801$	15.5223	−	8.96180i	0.548453	−	0.316650i
$802$	−0.125260	+	0.467477i	−0.00442309	+	0.0165072i
$803$	1.98280	−	0.531289i	0.0699713	−	0.0187488i
$804$	1.95809			0.0690564
$805$		0			0
$806$	−0.198517			−0.00699247
$807$	−5.97738	+	1.60163i	−0.210414	+	0.0563802i
$808$	−4.05216	+	15.1229i	−0.142555	+	0.532021i
$809$	18.8351	−	10.8745i	0.662208	−	0.382326i	−0.130910	−	0.991394i	$-0.541790\pi$
$809$	18.8351	−	10.8745i	0.662208	−	0.382326i	0.793118	+	0.609068i	$0.208456\pi$
$810$	14.8250	−	8.55003i	0.520896	−	0.300417i
$811$		−	7.20763i		−	0.253094i	−0.991961	−	0.126547i	$-0.959611\pi$
$811$		−	7.20763i		−	0.253094i	0.991961	−	0.126547i	$-0.0403895\pi$
$812$		0			0
$813$	−0.488673	+	0.488673i	−0.0171385	+	0.0171385i
$814$	−3.79486	−	2.19096i	−0.133010	−	0.0767933i
$815$	−12.8355	−	0.00595076i	−0.449608	−	0.000208446i
$816$	0.977714	+	1.69345i	0.0342268	+	0.0592826i
$817$	6.86228	+	25.6104i	0.240081	+	0.895993i
$818$	−17.7017	−	17.7017i	−0.618926	−	0.618926i
$819$		0			0
$820$	19.3044	−	5.16300i	0.674138	−	0.180300i
$821$	17.8497	−	30.9167i	0.622960	−	1.07900i	−0.365971	−	0.930626i	$-0.619263\pi$
$821$	17.8497	−	30.9167i	0.622960	−	1.07900i	0.988932	−	0.148373i	$-0.0474035\pi$
$822$	−1.36881	−	0.366771i	−0.0477426	−	0.0127926i
$823$	−2.22436	−	0.596016i	−0.0775364	−	0.0207758i	0.219842	−	0.975535i	$-0.429446\pi$
$823$	−2.22436	−	0.596016i	−0.0775364	−	0.0207758i	−0.297379	+	0.954760i	$0.596112\pi$
$824$	−6.55815	+	11.3591i	−0.228464	+	0.395711i
$825$	1.35773	+	0.365151i	0.0472700	+	0.0127129i
$826$		0			0
$827$	4.11186	+	4.11186i	0.142984	+	0.142984i	0.774975	−	0.631992i	$-0.217762\pi$
$827$	4.11186	+	4.11186i	0.142984	+	0.142984i	−0.631992	+	0.774975i	$0.717762\pi$
$828$	6.00446	+	22.4089i	0.208669	+	0.778765i
$829$	−0.125674	−	0.217673i	−0.00436483	−	0.00756010i	0.863835	−	0.503775i	$-0.168056\pi$
$829$	−0.125674	−	0.217673i	−0.00436483	−	0.00756010i	−0.868200	+	0.496215i	$0.834723\pi$
$830$	1.85128	−	1.84957i	0.0642590	−	0.0641995i
$831$	−0.713624	−	0.412011i	−0.0247554	−	0.0142925i
$832$	0.0516746	−	0.0516746i	0.00179149	−	0.00179149i
$833$		0			0
$834$		−	5.80904i		−	0.201150i
$835$	1.23263	+	2.13726i	0.0426568	+	0.0739630i
$836$	−3.50600	+	2.02419i	−0.121257	+	0.0700080i
$837$	−1.60390	+	5.98583i	−0.0554388	+	0.206900i
$838$	12.2520	−	3.28292i	0.423239	−	0.113407i
$839$	−40.8277			−1.40953			−0.704765	−	0.709441i	$-0.748947\pi$
$839$	−40.8277			−1.40953			−0.704765	+	0.709441i	$0.748947\pi$
$840$		0			0
$841$	−22.1858			−0.765027
$842$	−0.670816	+	0.179745i	−0.0231178	+	0.00619441i
$843$	0.807256	−	3.01272i	0.0278034	−	0.103764i
$844$	−4.19545	+	2.42225i	−0.144413	+	0.0833771i
$845$	−28.0634	−	7.53350i	−0.965409	−	0.259160i
$846$			31.0063i			1.06602i
$847$		0			0
$848$	−3.50970	+	3.50970i	−0.120523	+	0.120523i
$849$	−5.22453	−	3.01638i	−0.179305	−	0.103522i
$850$	21.6935	+	12.5516i	0.744080	+	0.430515i
$851$	24.7614	+	42.8879i	0.848809	+	1.47018i
$852$	−0.783950	−	2.92574i	−0.0268577	−	0.100234i
$853$	13.9161	+	13.9161i	0.476477	+	0.476477i	0.904003	−	0.427526i	$-0.140615\pi$
$853$	13.9161	+	13.9161i	0.476477	+	0.476477i	−0.427526	+	0.904003i	$0.640615\pi$
$854$		0			0
$855$	−9.24051	−	34.5501i	−0.316019	−	1.18159i
$856$	−6.77976	+	11.7429i	−0.231727	+	0.401364i
$857$	34.0826	+	9.13239i	1.16424	+	0.311957i	0.788657	−	0.614833i	$-0.210777\pi$
$857$	34.0826	+	9.13239i	1.16424	+	0.311957i	0.375581	+	0.926790i	$0.377443\pi$
$858$	−0.0198492	−	0.00531857i	−0.000677640	−	0.000181573i
$859$	−2.19269	+	3.79785i	−0.0748136	+	0.129581i	−0.901005	−	0.433808i	$-0.857170\pi$
$859$	−2.19269	+	3.79785i	−0.0748136	+	0.129581i	0.826192	+	0.563389i	$0.190503\pi$
$860$	9.13938	+	5.28227i	0.311650	+	0.180124i
$861$		0			0
$862$	−18.7941	−	18.7941i	−0.640131	−	0.640131i
$863$	−2.87894	−	10.7444i	−0.0980003	−	0.365742i	0.899457	−	0.437009i	$-0.143962\pi$
$863$	−2.87894	−	10.7444i	−0.0980003	−	0.365742i	−0.997457	+	0.0712672i	$0.977296\pi$
$864$	−1.14063	−	1.97563i	−0.0388050	−	0.0672122i
$865$	0.00183340	−	3.95456i	6.23376e−5	−	0.134459i
$866$	34.0529	+	19.6605i	1.15717	+	0.668090i
$867$	2.24150	−	2.24150i	0.0761252	−	0.0761252i
$868$		0			0
$869$			11.9430i			0.405138i
$870$	−1.61803	+	6.02740i	−0.0548564	+	0.204348i
$871$	−0.317668	+	0.183406i	−0.0107638	+	0.00621447i
$872$	1.39392	−	5.20219i	0.0472042	−	0.176168i
$873$	21.0583	−	5.64255i	0.712715	−	0.190971i
$874$	45.7530			1.54762
$875$		0			0
$876$	1.11094			0.0375350
$877$	−33.9400	+	9.09420i	−1.14607	+	0.307089i	−0.781390	−	0.624043i	$-0.785489\pi$
$877$	−33.9400	+	9.09420i	−1.14607	+	0.307089i	−0.364682	+	0.931132i	$0.618822\pi$
$878$	−3.71497	+	13.8645i	−0.125374	+	0.467903i
$879$	−4.25240	+	2.45512i	−0.143430	+	0.0828093i
$880$	−0.417886	+	1.55669i	−0.0140869	+	0.0524758i
$881$		−	21.3357i		−	0.718817i	−0.933180	−	0.359409i	$-0.882978\pi$
$881$		−	21.3357i		−	0.718817i	0.933180	−	0.359409i	$-0.117022\pi$
$882$		0			0
$883$	−18.0448	+	18.0448i	−0.607256	+	0.607256i	−0.942228	−	0.334972i	$-0.891273\pi$
$883$	−18.0448	+	18.0448i	−0.607256	+	0.607256i	0.334972	+	0.942228i	$0.391273\pi$
$884$	−0.317237	−	0.183157i	−0.0106698	−	0.00616023i
$885$	0.00516795	−	11.1470i	0.000173719	−	0.374703i
$886$	2.60294	+	4.50842i	0.0874473	+	0.151463i
$887$	−4.44776	−	16.5993i	−0.149341	−	0.557349i	−0.999524	−	0.0308610i	$-0.990175\pi$
$887$	−4.44776	−	16.5993i	−0.149341	−	0.557349i	0.850182	−	0.526488i	$-0.176492\pi$
$888$	−1.67689	−	1.67689i	−0.0562728	−	0.0562728i
$889$		0			0
$890$	−12.1846	−	7.04233i	−0.408430	−	0.236060i
$891$	2.75840	−	4.77769i	0.0924100	−	0.160059i
$892$	−21.6069	−	5.78955i	−0.723453	−	0.193849i
$893$	59.0657	+	15.8266i	1.97656	+	0.529617i
$894$	−0.533129	+	0.923406i	−0.0178305	+	0.0308833i
$895$	−8.35465	−	31.2379i	−0.279265	−	1.04417i
$896$		0			0
$897$	0.164219	+	0.164219i	0.00548311	+	0.00548311i
$898$	4.41538	+	16.4784i	0.147343	+	0.549892i
$899$	9.71741	+	16.8310i	0.324094	+	0.561347i
$900$	−12.3248	−	7.13098i	−0.410827	−	0.237699i
$901$	21.5465	+	12.4399i	0.717817	+	0.414432i
$902$	4.55495	−	4.55495i	0.151663	−	0.151663i
$903$		0			0
$904$			9.47725i			0.315209i
$905$	−27.5841	−	7.40484i	−0.916926	−	0.246145i
$906$	1.48039	−	0.854705i	0.0491827	−	0.0283957i
$907$	−11.3271	+	42.2734i	−0.376111	+	1.40367i	0.475603	+	0.879660i	$0.342230\pi$
$907$	−11.3271	+	42.2734i	−0.376111	+	1.40367i	−0.851714	+	0.524007i	$0.824437\pi$
$908$	−14.8759	+	3.98599i	−0.493675	+	0.132280i
$909$	−44.5864			−1.47884
$910$		0			0
$911$	13.0194			0.431352			0.215676	−	0.976465i	$-0.430805\pi$
$911$	13.0194			0.431352			0.215676	+	0.976465i	$0.430805\pi$
$912$	−2.11631	+	0.567063i	−0.0700780	+	0.0187773i
$913$	0.218335	−	0.814839i	0.00722585	−	0.0269672i
$914$	−17.8863	+	10.3267i	−0.591626	+	0.341575i
$915$	0.612289	+	1.06165i	0.0202416	+	0.0350971i
$916$		−	9.79605i		−	0.323670i
$917$		0			0
$918$	−8.08575	+	8.08575i	−0.266870	+	0.266870i
$919$	−28.6630	−	16.5486i	−0.945505	−	0.545888i	−0.0538235	−	0.998550i	$-0.517141\pi$
$919$	−28.6630	−	16.5486i	−0.945505	−	0.545888i	−0.891682	+	0.452663i	$0.850474\pi$
$920$	12.8865	−	12.8746i	0.424857	−	0.424463i
$921$	−1.69995	−	2.94440i	−0.0560153	−	0.0970214i
$922$	7.31436	+	27.2976i	0.240886	+	0.898997i
$923$	0.401226	+	0.401226i	0.0132065	+	0.0132065i
$924$		0			0
$925$	−29.3525	−	7.89415i	−0.965104	−	0.259558i
$926$	9.06806	−	15.7063i	0.297995	−	0.516142i
$927$	−36.0801	−	9.66763i	−1.18503	−	0.317527i
$928$	−6.91064	−	1.85170i	−0.226853	−	0.0607851i
$929$	−3.96787	+	6.87256i	−0.130182	+	0.225481i	−0.923747	−	0.383004i	$-0.874889\pi$
$929$	−3.96787	+	6.87256i	−0.130182	+	0.225481i	0.793565	+	0.608486i	$0.208223\pi$
$930$	2.28912	−	0.612231i	0.0750633	−	0.0200759i
$931$		0			0
$932$	9.12700	+	9.12700i	0.298965	+	0.298965i
$933$	−2.01061	−	7.50371i	−0.0658245	−	0.245660i
$934$	19.7925	+	34.2816i	0.647630	+	1.12173i
$935$	8.07927	+	0.00374569i	0.264220	+	0.000122497i
$936$	0.180233	+	0.104058i	0.00589111	+	0.00340123i
$937$	−27.7324	+	27.7324i	−0.905979	+	0.905979i	−0.995945	−	0.0899655i	$-0.971324\pi$
$937$	−27.7324	+	27.7324i	−0.905979	+	0.905979i	0.0899655	+	0.995945i	$0.471324\pi$
$938$		0			0
$939$		−	7.00356i		−	0.228552i
$940$	21.0896	−	12.1631i	0.687868	−	0.396715i
$941$	10.7745	−	6.22064i	0.351238	−	0.202787i	−0.313993	−	0.949425i	$-0.601667\pi$
$941$	10.7745	−	6.22064i	0.351238	−	0.202787i	0.665230	+	0.746638i	$0.268333\pi$
$942$	−0.790577	+	2.95047i	−0.0257584	+	0.0961316i
$943$	−70.3205	+	18.8423i	−2.28995	+	0.613590i
$944$	12.7789			0.415917
$945$		0			0
$946$	3.40285			0.110636
$947$	45.5858	−	12.2147i	1.48134	−	0.396924i	0.574537	−	0.818479i	$-0.305182\pi$
$947$	45.5858	−	12.2147i	1.48134	−	0.396924i	0.906803	+	0.421555i	$0.138516\pi$
$948$	−1.67288	+	6.24326i	−0.0543325	+	0.202772i
$949$	−0.180232	+	0.104057i	−0.00585056	+	0.00337783i
$950$	−19.8752	+	19.8384i	−0.644837	+	0.643643i
$951$			2.74498i			0.0890122i
$952$		0			0
$953$	−2.48259	+	2.48259i	−0.0804190	+	0.0804190i	−0.746172	−	0.665753i	$-0.768110\pi$
$953$	−2.48259	+	2.48259i	−0.0804190	+	0.0804190i	0.665753	+	0.746172i	$0.268110\pi$
$954$	−12.2413	−	7.06752i	−0.396327	−	0.228819i
$955$	4.60180	+	4.60607i	0.148911	+	0.149049i
$956$	−8.29857	−	14.3735i	−0.268395	−	0.464874i
$957$	0.520688	+	1.94323i	0.0168315	+	0.0628158i
$958$	9.78434	+	9.78434i	0.316118	+	0.316118i
$959$		0			0
$960$	−0.436500	+	0.755231i	−0.0140880	+	0.0243750i
$961$	−11.8104	+	20.4562i	−0.380980	+	0.659877i
$962$	0.429116	+	0.114981i	0.0138353	+	0.00370715i
$963$	−37.2993	−	9.99431i	−1.20195	−	0.322062i
$964$	−2.11660	+	3.66606i	−0.0681711	+	0.118076i
$965$	12.3172	−	21.3113i	0.396506	−	0.686034i
$966$		0			0
$967$	19.8191	+	19.8191i	0.637341	+	0.637341i	0.949899	−	0.312558i	$-0.101186\pi$
$967$	19.8191	+	19.8191i	0.637341	+	0.637341i	−0.312558	+	0.949899i	$0.601186\pi$
$968$	−2.71253	−	10.1233i	−0.0871841	−	0.325375i
$969$	5.49119	+	9.51102i	0.176402	+	0.305538i
$970$	−12.0986	−	12.1098i	−0.388463	−	0.388823i
$971$	6.55582	+	3.78501i	0.210386	+	0.121467i	0.601491	−	0.798880i	$-0.294574\pi$
$971$	6.55582	+	3.78501i	0.210386	+	0.121467i	−0.391105	+	0.920346i	$0.627907\pi$
$972$	6.95047	−	6.95047i	0.222936	−	0.222936i
$973$		0			0
$974$		−	6.64774i		−	0.213007i
$975$	−0.142542		0.000132170i	−0.00456500		4.23283e-6i
$976$	−1.21675	+	0.702489i	−0.0389471	+	0.0224861i
$977$	−9.41317	+	35.1304i	−0.301154	+	1.12392i	0.635051	+	0.772470i	$0.280979\pi$
$977$	−9.41317	+	35.1304i	−0.301154	+	1.12392i	−0.936206	+	0.351453i	$0.885688\pi$
$978$	−2.16298	+	0.579568i	−0.0691644	+	0.0185326i
$979$	−4.53669			−0.144993
$980$		0			0
$981$	15.3375			0.489689
$982$	−24.8965	+	6.67099i	−0.794479	+	0.212880i
$983$	4.20075	−	15.6774i	0.133983	−	0.500032i	−0.866017	−	0.500015i	$-0.833328\pi$
$983$	4.20075	−	15.6774i	0.133983	−	0.500032i	1.00000		1.69533e-5i	$-5.39640e-6\pi$
$984$	3.01915	−	1.74311i	0.0962469	−	0.0555682i
$985$	−38.1204	+	21.9853i	−1.21462	+	0.700509i
$986$			35.8621i			1.14208i
$987$		0			0
$988$	0.290223	−	0.290223i	0.00923322	−	0.00923322i
$989$	−33.3053	−	19.2288i	−1.05905	−	0.611441i
$990$	−4.59011	−	0.00212806i	−0.145883	−	6.76341e-5i
$991$	−3.34812	−	5.79912i	−0.106357	−	0.184215i	0.807935	−	0.589272i	$-0.200585\pi$
$991$	−3.34812	−	5.79912i	−0.106357	−	0.184215i	−0.914292	+	0.405057i	$0.867252\pi$
$992$	0.703075	+	2.62391i	0.0223227	+	0.0833093i
$993$	1.71101	+	1.71101i	0.0542971	+	0.0542971i
$994$		0			0
$995$	−12.4812	+	3.33812i	−0.395680	+	0.105826i
$996$	0.228272	−	0.395379i	0.00723307	−	0.0125281i
$997$	50.3127	+	13.4812i	1.59342	+	0.426955i	0.943047	−	0.332661i	$-0.107946\pi$
$997$	50.3127	+	13.4812i	1.59342	+	0.426955i	0.650372	+	0.759616i	$0.274613\pi$
$998$	−5.09519	−	1.36525i	−0.161285	−	0.0432163i
$999$	6.93400	−	12.0100i	0.219382	−	0.379981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.d.117.7		32
5.3	odd	4	inner	490.2.l.d.313.3		32
7.2	even	3		490.2.g.b.97.3	yes	16
7.3	odd	6	inner	490.2.l.d.227.3		32
7.4	even	3	inner	490.2.l.d.227.2		32
7.5	odd	6		490.2.g.b.97.2	✓	16
7.6	odd	2	inner	490.2.l.d.117.6		32
35.3	even	12	inner	490.2.l.d.423.7		32
35.13	even	4	inner	490.2.l.d.313.2		32
35.18	odd	12	inner	490.2.l.d.423.6		32
35.23	odd	12		490.2.g.b.293.2	yes	16
35.33	even	12		490.2.g.b.293.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.g.b.97.2	✓	16	7.5	odd	6
490.2.g.b.97.3	yes	16	7.2	even	3
490.2.g.b.293.2	yes	16	35.23	odd	12
490.2.g.b.293.3	yes	16	35.33	even	12
490.2.l.d.117.6		32	7.6	odd	2	inner
490.2.l.d.117.7		32	1.1	even	1	trivial
490.2.l.d.227.2		32	7.4	even	3	inner
490.2.l.d.227.3		32	7.3	odd	6	inner
490.2.l.d.313.2		32	35.13	even	4	inner
490.2.l.d.313.3		32	5.3	odd	4	inner
490.2.l.d.423.6		32	35.18	odd	12	inner
490.2.l.d.423.7		32	35.3	even	12	inner

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.100966 - 0.376812i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.579738 - 2.15961i) q^{5} -0.390104i q^{6} +(0.707107 - 0.707107i) q^{8} +(2.46628 + 1.42391i) q^{9} +(0.00103668 - 2.23607i) q^{10} +(-0.360409 - 0.624247i) q^{11} +(-0.100966 - 0.376812i) q^{12} +(0.0516746 + 0.0516746i) q^{13} +(-0.755231 - 0.436500i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-4.84178 - 1.29735i) q^{17} +(2.75078 + 0.737070i) q^{18} +(2.80818 - 4.86391i) q^{19} +(-0.577736 - 2.16014i) q^{20} +(-0.509696 - 0.509696i) q^{22} +(2.10844 + 7.86881i) q^{23} +(-0.195052 - 0.337840i) q^{24} +(-4.32781 - 2.50401i) q^{25} +(0.0632882 + 0.0365395i) q^{26} +(1.61309 - 1.61309i) q^{27} -7.15442i q^{29} +(-0.842472 - 0.226158i) q^{30} +(-2.35254 + 1.35824i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-0.271613 + 0.0727785i) q^{33} -5.01258 q^{34} +2.84782 q^{36} +(5.87196 - 1.57339i) q^{37} +(1.45362 - 5.42498i) q^{38} +(0.0246890 - 0.0142542i) q^{39} +(-1.11714 - 1.93701i) q^{40} +8.93661i q^{41} +(-3.33812 + 3.33812i) q^{43} +(-0.624247 - 0.360409i) q^{44} +(4.50488 - 4.50071i) q^{45} +(4.07320 + 7.05498i) q^{46} +(2.81795 + 10.5167i) q^{47} +(-0.275845 - 0.275845i) q^{48} +(-4.82843 - 1.29857i) q^{50} +(-0.977714 + 1.69345i) q^{51} +(0.0705888 + 0.0189142i) q^{52} +(-4.79433 - 1.28464i) q^{53} +(1.14063 - 1.97563i) q^{54} +(-1.55707 + 0.416443i) q^{55} +(-1.54925 - 1.54925i) q^{57} +(-1.85170 - 6.91064i) q^{58} +(6.38944 + 11.0668i) q^{59} +(-0.872300 - 0.000404413i) q^{60} +(-1.21675 - 0.702489i) q^{61} +(-1.92084 + 1.92084i) q^{62} -1.00000i q^{64} +(0.141555 - 0.0816391i) q^{65} +(-0.243522 + 0.140597i) q^{66} +(-1.29911 + 4.84836i) q^{67} +(-4.84178 + 1.29735i) q^{68} +3.17794 q^{69} +7.76446 q^{71} +(2.75078 - 0.737070i) q^{72} +(-0.737063 + 2.75076i) q^{73} +(5.26466 - 3.03955i) q^{74} +(-1.38051 + 1.37795i) q^{75} -5.61636i q^{76} +(0.0201585 - 0.0201585i) q^{78} +(-14.3489 - 8.28432i) q^{79} +(-1.58041 - 1.58187i) q^{80} +(3.82676 + 6.62815i) q^{81} +(2.31297 + 8.63210i) q^{82} +(0.827536 + 0.827536i) q^{83} +(-5.60873 + 9.70421i) q^{85} +(-2.36041 + 4.08835i) q^{86} +(-2.69587 - 0.722356i) q^{87} +(-0.696257 - 0.186562i) q^{88} +(3.14690 - 5.45059i) q^{89} +(3.18651 - 5.51330i) q^{90} +(5.76037 + 5.76037i) q^{92} +(0.274273 + 1.02360i) q^{93} +(5.44386 + 9.42904i) q^{94} +(-8.87612 - 8.88435i) q^{95} +(-0.337840 - 0.195052i) q^{96} +(5.41317 - 5.41317i) q^{97} -2.05276i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{11} - 48 q^{15} + 16 q^{16} + 16 q^{18} + 32 q^{22} - 16 q^{23} - 32 q^{25} - 40 q^{30} - 96 q^{36} + 48 q^{37} + 32 q^{43} + 16 q^{46} - 64 q^{50} + 80 q^{51} - 32 q^{53} + 96 q^{57} - 16 q^{58}+ \cdots - 40 q^{95}+O(q^{100}) \) 32 * q + 16 * q^11 - 48 * q^15 + 16 * q^16 + 16 * q^18 + 32 * q^22 - 16 * q^23 - 32 * q^25 - 40 * q^30 - 96 * q^36 + 48 * q^37 + 32 * q^43 + 16 * q^46 - 64 * q^50 + 80 * q^51 - 32 * q^53 + 96 * q^57 - 16 * q^58 - 40 * q^60 - 32 * q^65 - 16 * q^67 + 32 * q^71 + 16 * q^72 + 112 * q^81 + 48 * q^85 - 48 * q^86 + 16 * q^88 + 32 * q^92 - 64 * q^93 - 40 * q^95

Introduction

L-functions

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