LMFDB - Embedded newform 490.2.l.d.117.6

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			117.6
Character	$\chi$	$=$	490.117
Dual form			490.2.l.d.423.6

$q$-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	−0.988928	−	0.148396i	$-0.952589\pi$
$3$	−0.100966	+	0.376812i	−0.0582930	+	0.217552i	0.930635	+	0.365949i	$0.119255\pi$
$4$	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	0.699904	−	0.714236i	$-0.253226\pi$
$13$	−0.0516746	−	0.0516746i	−0.0143320	−	0.0143320i	−0.714236	+	0.699904i	$0.753226\pi$
$14$		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	0.792665	−	0.609658i	$-0.208693\pi$
$17$	4.84178	+	1.29735i	1.17430	+	0.314654i	0.381639	+	0.924312i	$0.375360\pi$
$18$	2.75078	+	0.737070i	0.648365	+	0.173729i
$19$	−2.80818	+	4.86391i	−0.644240	+	1.11586i	0.340236	+	0.940340i	$0.389493\pi$
$19$	−2.80818	+	4.86391i	−0.644240	+	1.11586i	−0.984476	+	0.175517i	$0.943840\pi$
$20$	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	−0.273630	−	0.961835i	$-0.588224\pi$
$31$	2.35254	−	1.35824i	0.422528	−	0.243947i	0.696158	+	0.717888i	$0.254891\pi$
$32$	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	$-0.754148\pi$
$41$		−	8.93661i		−	1.39566i	0.716261	−	0.697832i	$-0.245852\pi$
$42$		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	$-0.791292\pi$
$47$	−2.81795	−	10.5167i	−0.411040	−	1.53402i	0.381597	−	0.924329i	$-0.375374\pi$
$48$	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	$-0.853958\pi$
$59$	−6.38944	−	11.0668i	−0.831834	−	1.44078i	0.0647485	−	0.997902i	$-0.479375\pi$
$60$	−0.872300		0.000404413i	−0.112613		5.22096e-5i
$61$	1.21675	+	0.702489i	0.155788	+	0.0899445i	0.575868	−	0.817543i	$-0.304664\pi$
$61$	1.21675	+	0.702489i	0.155788	+	0.0899445i	−0.420079	+	0.907487i	$0.637998\pi$
$62$	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	−0.909284	−	0.416175i	$-0.863370\pi$
$73$	0.737063	−	2.75076i	0.0862667	−	0.321952i	0.995551	+	0.0942238i	$0.0300369\pi$
$74$	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	0.660230	−	0.751064i	$-0.270459\pi$
$83$	−0.827536	−	0.827536i	−0.0908339	−	0.0908339i	−0.751064	+	0.660230i	$0.770459\pi$
$84$		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	−0.983209	−	0.182482i	$-0.941587\pi$
$89$	−3.14690	+	5.45059i	−0.333571	+	0.577762i	0.649638	+	0.760243i	$0.274920\pi$
$90$	−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	−0.926332	−	0.376708i	$-0.877056\pi$
$97$	−5.41317	+	5.41317i	−0.549625	+	0.549625i	0.376708	+	0.926332i	$0.377056\pi$
$98$		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	0.361021	−	0.932558i	$-0.382428\pi$
$101$	13.5588	−	7.82817i	1.34915	−	0.778932i	0.988129	+	0.153625i	$0.0490948\pi$
$102$	−0.506102	+	1.88880i	−0.0501115	+	0.187019i
$103$	12.6694	−	3.39475i	1.24835	−	0.334495i	0.426652	−	0.904416i	$-0.359693\pi$
$103$	12.6694	−	3.39475i	1.24835	−	0.334495i	0.821699	+	0.569922i	$0.193026\pi$
$104$	−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	0.0166879	−	0.999861i	$-0.494688\pi$
$131$	−9.62423	−	5.55655i	−0.840873	−	0.485478i	−0.857561	+	0.514383i	$0.828021\pi$
$132$	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	$-0.717568\pi$
$139$	−14.8910			−1.26304			−0.631518	+	0.775361i	$0.717568\pi$
$140$		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	0.547669	−	0.836695i	$-0.315515\pi$
$157$	7.56329	+	2.02658i	0.603616	+	0.161739i	0.0559476	+	0.998434i	$0.482182\pi$
$158$	−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	−0.676275	−	0.736649i	$-0.736407\pi$
$167$	0.780209	−	0.780209i	0.0603743	−	0.0603743i	0.736649	+	0.676275i	$0.236407\pi$
$168$		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	−0.323172	−	0.946340i	$-0.604749\pi$
$173$	−1.70827	+	0.457730i	−0.129877	+	0.0348006i	0.193295	+	0.981141i	$0.438083\pi$
$174$	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	$0.157442\pi$
$181$			12.7727i			0.949389i	−0.880151	+	0.474695i	$0.842558\pi$
$182$		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	0.950067	−	0.312046i	$-0.101014\pi$
$199$	2.88897	+	5.00385i	0.204794	+	0.354713i	−0.745273	+	0.666759i	$0.767681\pi$
$200$	−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	$0.0194528\pi$
$223$	15.8173	+	15.8173i	1.05921	+	1.05921i	0.0610748	+	0.998133i	$0.480547\pi$
$224$		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	0.716137	−	0.697960i	$-0.245909\pi$
$227$	14.8759	+	3.98599i	0.987350	+	0.264560i	0.271213	+	0.962519i	$0.412575\pi$
$228$	−2.11631	−	0.567063i	−0.140156	−	0.0375547i
$229$	−4.89802	+	8.48363i	−0.323670	+	0.560614i	−0.981242	−	0.192778i	$-0.938250\pi$
$229$	−4.89802	+	8.48363i	−0.323670	+	0.560614i	0.657572	+	0.753392i	$0.271584\pi$
$230$	−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	−0.377255	−	0.926109i	$-0.623132\pi$
$241$	3.66606	−	2.11660i	0.236151	−	0.136342i	0.613407	+	0.789767i	$0.289799\pi$
$242$	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	$-0.774091\pi$
$251$		−	20.6471i		−	1.30323i	0.758548	−	0.651617i	$-0.225909\pi$
$252$		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	$0.207875\pi$
$257$	6.57626	+	24.5429i	0.410216	+	1.53095i	−0.384014	+	0.923327i	$0.625459\pi$
$258$	−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	0.999822	−	0.0188421i	$-0.00599797\pi$
$269$	7.93152	+	13.7378i	0.483594	+	0.837609i	−0.516229	+	0.856451i	$0.672665\pi$
$270$	−3.60531	−	3.60866i	−0.219412	−	0.219616i
$271$	1.53420	+	0.885773i	0.0931963	+	0.0538069i	0.545874	−	0.837867i	$-0.316198\pi$
$271$	1.53420	+	0.885773i	0.0931963	+	0.0538069i	−0.452678	+	0.891674i	$0.649531\pi$
$272$	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	$0.235353\pi$
$283$	−4.00251	+	14.9376i	−0.237924	+	0.887945i	−0.976809	+	0.214113i	$0.931314\pi$
$284$	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	0.917561	−	0.397596i	$-0.130155\pi$
$293$	8.90037	+	8.90037i	0.519965	+	0.519965i	−0.397596	+	0.917561i	$0.630155\pi$
$294$		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	−0.860751	−	0.509027i	$-0.830005\pi$
$307$	−6.16270	+	6.16270i	−0.351724	+	0.351724i	0.509027	+	0.860751i	$0.330005\pi$
$308$		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	−0.901640	−	0.432486i	$-0.857636\pi$
$311$	−17.2457	+	9.95683i	−0.977916	+	0.564600i	−0.0762760	+	0.997087i	$0.524303\pi$
$312$	0.00737852	−	0.0275370i	0.000417726	−	0.00155898i
$313$	−17.3413	+	4.64659i	−0.980188	+	0.262641i	−0.713124	−	0.701038i	$-0.752720\pi$
$313$	−17.3413	+	4.64659i	−0.980188	+	0.262641i	−0.267064	+	0.963679i	$0.586054\pi$
$314$	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	$-0.605878\pi$
$349$	−12.2000			−0.653054			−0.326527	+	0.945188i	$0.605878\pi$
$350$		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	$-0.719189\pi$
$353$	5.65400	−	21.1010i	0.300932	−	1.12309i	0.936391	−	0.350959i	$-0.114144\pi$
$354$	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	0.228602	−	0.973520i	$-0.426585\pi$
$367$	−1.15293	−	0.308928i	−0.0601827	−	0.0161259i	−0.288785	+	0.957394i	$0.593251\pi$
$368$	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	0.523017	−	0.852322i	$-0.324806\pi$
$383$	27.4401	−	7.35255i	1.40212	−	0.375698i	0.879107	+	0.476624i	$0.158140\pi$
$384$	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	$0.0821772\pi$
$397$	5.12446	+	19.1247i	0.257189	+	0.959843i	−0.709670	+	0.704534i	$0.751156\pi$
$398$	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	$0.0457654\pi$
$409$	12.5170	+	21.6801i	0.618926	+	1.07201i	−0.370756	+	0.928731i	$0.620901\pi$
$410$	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	$-0.600273\pi$
$419$	−12.6842			−0.619665			−0.309832	+	0.950791i	$0.600273\pi$
$420$		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	$-0.856235\pi$
$433$	−27.8041	−	27.8041i	−1.33618	−	1.33618i	−0.436453	−	0.899727i	$-0.643765\pi$
$434$		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	−0.642373	−	0.766392i	$-0.722050\pi$
$439$	7.17677	−	12.4305i	0.342529	−	0.593277i	0.984902	+	0.173115i	$0.0553833\pi$
$440$	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	$-0.771355\pi$
$461$		−	28.2605i		−	1.31622i	0.752920	−	0.658112i	$-0.228645\pi$
$462$		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	$-0.714822\pi$
$467$	−10.2453	−	38.2362i	−0.474098	−	1.76936i	0.150708	−	0.988578i	$-0.451845\pi$
$468$	−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	0.663557	−	0.748126i	$-0.269046\pi$
$479$	−6.91857	−	11.9833i	−0.316118	−	0.547532i	−0.979674	+	0.200594i	$0.935713\pi$
$480$	−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	0.685979	−	0.727621i	$-0.259374\pi$
$503$	−0.933931	−	0.933931i	−0.0416419	−	0.0416419i	−0.727621	+	0.685979i	$0.759374\pi$
$504$		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	−0.531013	−	0.847364i	$-0.678188\pi$
$509$	10.5661	−	18.3009i	0.468332	−	0.811175i	0.999345	+	0.0361887i	$0.0115218\pi$
$510$	−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	−0.384815	−	0.922994i	$-0.625735\pi$
$521$	5.06985	−	2.92708i	0.222114	−	0.128238i	0.606929	+	0.794756i	$0.292401\pi$
$522$	5.27331	−	19.6803i	0.230806	−	0.861381i
$523$	−38.5738	+	10.3358i	−1.68672	+	0.451954i	−0.969539	−	0.244936i	$-0.921233\pi$
$523$	−38.5738	+	10.3358i	−1.68672	+	0.451954i	−0.717177	+	0.696891i	$0.754566\pi$
$524$	−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	$0.220518\pi$
$563$	−5.13107	+	19.1494i	−0.216249	+	0.807051i	−0.985723	+	0.168374i	$0.946149\pi$
$564$	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	−0.588926	−	0.808187i	$-0.700449\pi$
$577$	−36.1044	−	9.67413i	−1.50304	−	0.402739i	−0.914118	+	0.405448i	$0.867116\pi$
$578$	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	−0.909241	−	0.416269i	$-0.863337\pi$
$587$	−11.9438	+	11.9438i	−0.492972	+	0.492972i	0.416269	+	0.909241i	$0.363337\pi$
$588$		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	0.219601	−	0.975590i	$-0.429525\pi$
$593$	21.8574	−	5.85667i	0.897575	−	0.240505i	0.677975	+	0.735085i	$0.262858\pi$
$594$	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	$0.226399\pi$
$601$			32.0064i			1.30557i	−0.757544	+	0.652784i	$0.773601\pi$
$602$		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	$0.0525038\pi$
$607$	5.27869	+	19.7003i	0.214255	+	0.799612i	−0.772172	+	0.635414i	$0.780830\pi$
$608$	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	$0.244278\pi$
$619$	23.9123	+	41.4174i	0.961117	+	1.66470i	0.241414	+	0.970422i	$0.422389\pi$
$620$	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	$-0.961255\pi$
$643$	−28.2487	−	28.2487i	−1.11402	−	1.11402i	−0.121419	−	0.992601i	$-0.538745\pi$
$644$		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	0.250258	−	0.968179i	$-0.419485\pi$
$647$	−0.435000	−	0.116558i	−0.0171016	−	0.00458237i	−0.267360	+	0.963597i	$0.586151\pi$
$648$	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	−0.248969	−	0.968512i	$-0.580092\pi$
$661$	11.9629	−	6.90678i	0.465303	−	0.268643i	0.714271	+	0.699869i	$0.246758\pi$
$662$	−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	0.981373	−	0.192113i	$-0.0615339\pi$
$677$	0.921672	+	3.43973i	0.0354227	+	0.132199i	−0.945950	+	0.324312i	$0.894867\pi$
$678$	−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	0.984995	−	0.172581i	$-0.0552106\pi$
$691$	34.9099	+	20.1552i	1.32803	+	0.766741i	0.343038	+	0.939321i	$0.388544\pi$
$692$	−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	$0.375449\pi$
$719$	−16.3534	+	28.3249i	−0.609879	+	1.05634i	−0.991260	+	0.131923i	$0.957885\pi$
$720$	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	$-0.463279\pi$
$727$	29.8873	−	29.8873i	1.10846	−	1.10846i	0.993353	−	0.115106i	$-0.0367208\pi$
$728$		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	−0.283423	−	0.958995i	$-0.591470\pi$
$733$	−1.33683	+	0.358203i	−0.0493770	+	0.0132305i	0.234046	+	0.972226i	$0.424803\pi$
$734$	−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	0.378497	−	0.925603i	$-0.376441\pi$
$761$	−6.45105	−	3.72452i	−0.233850	−	0.135014i	−0.612347	+	0.790589i	$0.709774\pi$
$762$	−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	$-0.643979\pi$
$769$	−24.2399			−0.874112			−0.437056	+	0.899434i	$0.643979\pi$
$770$		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	$0.200476\pi$
$773$	−5.17765	+	19.3233i	−0.186227	+	0.695009i	−0.994365	+	0.106015i	$0.966191\pi$
$774$	−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	0.929012	−	0.370050i	$-0.120660\pi$
$787$	43.4418	+	11.6402i	1.54853	+	0.414929i	0.619523	+	0.784979i	$0.287326\pi$
$788$	−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	$0.558461\pi$
$797$	−32.9123	+	32.9123i	−1.16581	+	1.16581i	−0.983182	+	0.182630i	$0.941539\pi$
$798$		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	$0.0403895\pi$
$811$			7.20763i			0.253094i	−0.991961	+	0.126547i	$0.959611\pi$
$812$		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	0.868200	−	0.496215i	$-0.165277\pi$
$829$	0.125674	+	0.217673i	0.00436483	+	0.00756010i	−0.863835	+	0.503775i	$0.831944\pi$
$830$	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	$-0.251053\pi$
$839$	40.8277			1.40953			0.704765	+	0.709441i	$0.251053\pi$
$840$		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	0.427526	−	0.904003i	$-0.359385\pi$
$853$	−13.9161	−	13.9161i	−0.476477	−	0.476477i	−0.904003	+	0.427526i	$0.859385\pi$
$854$		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	−0.375581	−	0.926790i	$-0.622557\pi$
$857$	−34.0826	−	9.13239i	−1.16424	−	0.311957i	−0.788657	+	0.614833i	$0.789223\pi$
$858$	−0.0198492	−	0.00531857i	−0.000677640	−	0.000181573i
$859$	2.19269	−	3.79785i	0.0748136	−	0.129581i	−0.826192	−	0.563389i	$-0.809497\pi$
$859$	2.19269	−	3.79785i	0.0748136	−	0.129581i	0.901005	+	0.433808i	$0.142830\pi$
$860$	−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	$0.117022\pi$
$881$			21.3357i			0.718817i	−0.933180	+	0.359409i	$0.882978\pi$
$882$		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	$0.00982491\pi$
$887$	4.44776	+	16.5993i	0.149341	+	0.557349i	−0.850182	+	0.526488i	$0.823508\pi$
$888$	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	−0.793565	−	0.608486i	$-0.791777\pi$
$929$	3.96787	−	6.87256i	0.130182	−	0.225481i	0.923747	+	0.383004i	$0.125111\pi$
$930$	−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	−0.0899655	−	0.995945i	$-0.528676\pi$
$937$	27.7324	−	27.7324i	0.905979	−	0.905979i	0.995945	+	0.0899655i	$0.0286757\pi$
$938$		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	−0.665230	−	0.746638i	$-0.731667\pi$
$941$	−10.7745	+	6.22064i	−0.351238	+	0.202787i	0.313993	+	0.949425i	$0.398333\pi$
$942$	−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	0.391105	−	0.920346i	$-0.372093\pi$
$971$	−6.55582	−	3.78501i	−0.210386	−	0.121467i	−0.601491	+	0.798880i	$0.705426\pi$
$972$	−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	$0.166672\pi$
$983$	−4.20075	+	15.6774i	−0.133983	+	0.500032i	−1.00000		1.69533e-5i	$0.999995\pi$
$984$	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	−0.650372	−	0.759616i	$-0.725387\pi$
$997$	−50.3127	−	13.4812i	−1.59342	−	0.426955i	−0.943047	+	0.332661i	$0.892054\pi$
$998$	−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.117.6		32
5.3	odd	4	inner	490.2.l.d.313.2		32
7.2	even	3		490.2.g.b.97.2	✓	16
7.3	odd	6	inner	490.2.l.d.227.2		32
7.4	even	3	inner	490.2.l.d.227.3		32
7.5	odd	6		490.2.g.b.97.3	yes	16
7.6	odd	2	inner	490.2.l.d.117.7		32
35.3	even	12	inner	490.2.l.d.423.6		32
35.13	even	4	inner	490.2.l.d.313.3		32
35.18	odd	12	inner	490.2.l.d.423.7		32
35.23	odd	12		490.2.g.b.293.3	yes	16
35.33	even	12		490.2.g.b.293.2	yes	16

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

Modular forms

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