LMFDB - Embedded newform 820.2.s.c.583.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			583.10
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36670 + 0.363517i) q^{2} +2.89040 q^{3} +(1.73571 - 0.993633i) q^{4} +(2.03850 - 0.918980i) q^{5} +(-3.95030 + 1.05071i) q^{6} +3.97005i q^{7} +(-2.01099 + 1.98895i) q^{8} +5.35442 q^{9} +(-2.45194 + 1.99699i) q^{10} +(2.11810 - 2.11810i) q^{11} +(5.01690 - 2.87200i) q^{12} -5.49792i q^{13} +(-1.44318 - 5.42584i) q^{14} +(5.89208 - 2.65622i) q^{15} +(2.02539 - 3.44932i) q^{16} -4.67818i q^{17} +(-7.31785 + 1.94642i) q^{18} +(-4.23103 + 4.23103i) q^{19} +(2.62512 - 3.62060i) q^{20} +11.4750i q^{21} +(-2.12483 + 3.66476i) q^{22} +(2.64446 - 2.64446i) q^{23} +(-5.81256 + 5.74887i) q^{24} +(3.31095 - 3.74668i) q^{25} +(1.99859 + 7.51398i) q^{26} +6.80520 q^{27} +(3.94477 + 6.89086i) q^{28} +(-5.09727 + 5.09727i) q^{29} +(-7.08709 + 5.77211i) q^{30} +3.94542i q^{31} +(-1.51420 + 5.45043i) q^{32} +(6.12215 - 6.12215i) q^{33} +(1.70060 + 6.39365i) q^{34} +(3.64839 + 8.09294i) q^{35} +(9.29372 - 5.32032i) q^{36} +(-3.93647 + 3.93647i) q^{37} +(4.24448 - 7.32057i) q^{38} -15.8912i q^{39} +(-2.27159 + 5.90253i) q^{40} +(-3.43841 + 5.40161i) q^{41} +(-4.17136 - 15.6829i) q^{42} +(-5.85200 - 5.85200i) q^{43} +(1.57179 - 5.78101i) q^{44} +(10.9150 - 4.92060i) q^{45} +(-2.65287 + 4.57548i) q^{46} +7.58708 q^{47} +(5.85418 - 9.96991i) q^{48} -8.76128 q^{49} +(-3.16308 + 6.32415i) q^{50} -13.5218i q^{51} +(-5.46291 - 9.54281i) q^{52} +6.61578i q^{53} +(-9.30064 + 2.47380i) q^{54} +(2.37125 - 6.26422i) q^{55} +(-7.89624 - 7.98371i) q^{56} +(-12.2294 + 12.2294i) q^{57} +(5.11347 - 8.81936i) q^{58} +6.92744 q^{59} +(7.58764 - 10.4650i) q^{60} +6.04740i q^{61} +(-1.43423 - 5.39219i) q^{62} +21.2573i q^{63} +(0.0881340 - 7.99951i) q^{64} +(-5.05248 - 11.2075i) q^{65} +(-6.14161 + 10.5926i) q^{66} -8.81626 q^{67} +(-4.64839 - 8.11997i) q^{68} +(7.64355 - 7.64355i) q^{69} +(-7.92816 - 9.73433i) q^{70} +(-7.87467 + 7.87467i) q^{71} +(-10.7677 + 10.6497i) q^{72} +(4.97545 - 4.97545i) q^{73} +(3.94898 - 6.81092i) q^{74} +(9.56998 - 10.8294i) q^{75} +(-3.13975 + 11.5479i) q^{76} +(8.40894 + 8.40894i) q^{77} +(5.77671 + 21.7184i) q^{78} +(1.04312 + 1.04312i) q^{79} +(0.958897 - 8.89272i) q^{80} +3.60652 q^{81} +(2.73569 - 8.63227i) q^{82} +(1.36790 - 1.36790i) q^{83} +(11.4020 + 19.9173i) q^{84} +(-4.29916 - 9.53647i) q^{85} +(10.1252 + 5.87060i) q^{86} +(-14.7332 + 14.7332i) q^{87} +(-0.0466698 + 8.47226i) q^{88} +(-4.94457 + 4.94457i) q^{89} +(-13.1287 + 10.6927i) q^{90} +21.8270 q^{91} +(1.96240 - 7.21764i) q^{92} +11.4038i q^{93} +(-10.3692 + 2.75803i) q^{94} +(-4.73671 + 12.5132i) q^{95} +(-4.37666 + 15.7539i) q^{96} -5.20787i q^{97} +(11.9740 - 3.18487i) q^{98} +(11.3412 - 11.3412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.36670	+	0.363517i	−0.966399	+	0.257045i
$2$	−1.36670	+	0.363517i	−0.966399	+	0.257045i
$3$	2.89040			1.66877			0.834387	−	0.551179i	$-0.185822\pi$
$3$	2.89040			1.66877			0.834387	+	0.551179i	$0.185822\pi$
$4$	1.73571	−	0.993633i	0.867856	−	0.496816i
$5$	2.03850	−	0.918980i	0.911644	−	0.410980i
$5$	2.03850	−	0.918980i	0.911644	−	0.410980i
$6$	−3.95030	+	1.05071i	−1.61270	+	0.428950i
$7$			3.97005i			1.50054i	0.661133	+	0.750268i	$0.270076\pi$
$7$			3.97005i			1.50054i	−0.661133	+	0.750268i	$0.729924\pi$
$8$	−2.01099	+	1.98895i	−0.710991	+	0.703201i
$9$	5.35442			1.78481
$10$	−2.45194	+	1.99699i	−0.775372	+	0.631505i
$11$	2.11810	−	2.11810i	0.638630	−	0.638630i	−0.311587	−	0.950217i	$-0.600861\pi$
$11$	2.11810	−	2.11810i	0.638630	−	0.638630i	0.950217	+	0.311587i	$0.100861\pi$
$12$	5.01690	−	2.87200i	1.44825	−	0.829074i
$13$		−	5.49792i		−	1.52485i	−0.647077	−	0.762425i	$-0.724009\pi$
$13$		−	5.49792i		−	1.52485i	0.647077	−	0.762425i	$-0.275991\pi$
$14$	−1.44318	−	5.42584i	−0.385706	−	1.45012i
$15$	5.89208	−	2.65622i	1.52133	−	0.685833i
$16$	2.02539	−	3.44932i	0.506347	−	0.862330i
$17$		−	4.67818i		−	1.13463i	−0.823502	−	0.567313i	$-0.807983\pi$
$17$		−	4.67818i		−	1.13463i	0.823502	−	0.567313i	$-0.192017\pi$
$18$	−7.31785	+	1.94642i	−1.72483	+	0.458775i
$19$	−4.23103	+	4.23103i	−0.970664	+	0.970664i	−0.999582	−	0.0289178i	$-0.990794\pi$
$19$	−4.23103	+	4.23103i	−0.970664	+	0.970664i	0.0289178	+	0.999582i	$0.490794\pi$
$20$	2.62512	−	3.62060i	0.586994	−	0.809591i
$21$			11.4750i			2.50406i
$22$	−2.12483	+	3.66476i	−0.453015	+	0.781328i
$23$	2.64446	−	2.64446i	0.551408	−	0.551408i	−0.375439	−	0.926847i	$-0.622508\pi$
$23$	2.64446	−	2.64446i	0.551408	−	0.551408i	0.926847	+	0.375439i	$0.122508\pi$
$24$	−5.81256	+	5.74887i	−1.18648	+	1.17348i
$25$	3.31095	−	3.74668i	0.662190	−	0.749336i
$26$	1.99859	+	7.51398i	0.391955	+	1.47361i
$27$	6.80520			1.30966
$28$	3.94477	+	6.89086i	0.745491	+	1.30225i
$29$	−5.09727	+	5.09727i	−0.946539	+	0.946539i	−0.998642	−	0.0521023i	$-0.983408\pi$
$29$	−5.09727	+	5.09727i	−0.946539	+	0.946539i	0.0521023	+	0.998642i	$0.483408\pi$
$30$	−7.08709	+	5.77211i	−1.29392	+	1.05384i
$31$			3.94542i			0.708619i	0.935128	+	0.354309i	$0.115284\pi$
$31$			3.94542i			0.708619i	−0.935128	+	0.354309i	$0.884716\pi$
$32$	−1.51420	+	5.45043i	−0.267676	+	0.963509i
$33$	6.12215	−	6.12215i	1.06573	−	1.06573i
$34$	1.70060	+	6.39365i	0.291650	+	1.09650i
$35$	3.64839	+	8.09294i	0.616691	+	1.36796i
$36$	9.29372	−	5.32032i	1.54895	−	0.886720i
$37$	−3.93647	+	3.93647i	−0.647151	+	0.647151i	−0.952304	−	0.305152i	$-0.901293\pi$
$37$	−3.93647	+	3.93647i	−0.647151	+	0.647151i	0.305152	+	0.952304i	$0.401293\pi$
$38$	4.24448	−	7.32057i	0.688545	−	1.18755i
$39$		−	15.8912i		−	2.54463i
$40$	−2.27159	+	5.90253i	−0.359169	+	0.933272i
$41$	−3.43841	+	5.40161i	−0.536989	+	0.843589i
$41$	−3.43841	+	5.40161i	−0.536989	+	0.843589i
$42$	−4.17136	−	15.6829i	−0.643655	−	2.41992i
$43$	−5.85200	−	5.85200i	−0.892422	−	0.892422i	0.102329	−	0.994751i	$-0.467371\pi$
$43$	−5.85200	−	5.85200i	−0.892422	−	0.892422i	−0.994751	+	0.102329i	$0.967371\pi$
$44$	1.57179	−	5.78101i	0.236957	−	0.871521i
$45$	10.9150	−	4.92060i	1.62711	−	0.733520i
$46$	−2.65287	+	4.57548i	−0.391144	+	0.674617i
$47$	7.58708			1.10669			0.553345	−	0.832952i	$-0.313351\pi$
$47$	7.58708			1.10669			0.553345	+	0.832952i	$0.313351\pi$
$48$	5.85418	−	9.96991i	0.844979	−	1.43903i
$49$	−8.76128			−1.25161
$50$	−3.16308	+	6.32415i	−0.447328	+	0.894370i
$51$		−	13.5218i		−	1.89343i
$52$	−5.46291	−	9.54281i	−0.757570	−	1.32335i
$53$			6.61578i			0.908748i	0.890811	+	0.454374i	$0.150137\pi$
$53$			6.61578i			0.908748i	−0.890811	+	0.454374i	$0.849863\pi$
$54$	−9.30064	+	2.47380i	−1.26566	+	0.336642i
$55$	2.37125	−	6.26422i	0.319739	−	0.844668i
$56$	−7.89624	−	7.98371i	−1.05518	−	1.06687i
$57$	−12.2294	+	12.2294i	−1.61982	+	1.61982i
$58$	5.11347	−	8.81936i	0.671432	−	1.15804i
$59$	6.92744			0.901876			0.450938	−	0.892555i	$-0.351090\pi$
$59$	6.92744			0.901876			0.450938	+	0.892555i	$0.351090\pi$
$60$	7.58764	−	10.4650i	0.979560	−	1.35102i
$61$			6.04740i			0.774290i	0.922019	+	0.387145i	$0.126539\pi$
$61$			6.04740i			0.774290i	−0.922019	+	0.387145i	$0.873461\pi$
$62$	−1.43423	−	5.39219i	−0.182147	−	0.684809i
$63$			21.2573i			2.67817i
$64$	0.0881340	−	7.99951i	0.0110168	−	0.999939i
$65$	−5.05248	−	11.2075i	−0.626683	−	1.39012i
$66$	−6.14161	+	10.5926i	−0.755980	+	1.30386i
$67$	−8.81626			−1.07708			−0.538539	−	0.842601i	$-0.681023\pi$
$67$	−8.81626			−1.07708			−0.538539	+	0.842601i	$0.681023\pi$
$68$	−4.64839	−	8.11997i	−0.563701	−	0.984692i
$69$	7.64355	−	7.64355i	0.920175	−	0.920175i
$70$	−7.92816	−	9.73433i	−0.947596	−	1.16347i
$71$	−7.87467	+	7.87467i	−0.934552	+	0.934552i	−0.997986	−	0.0634342i	$-0.979795\pi$
$71$	−7.87467	+	7.87467i	−0.934552	+	0.934552i	0.0634342	+	0.997986i	$0.479795\pi$
$72$	−10.7677	+	10.6497i	−1.26898	+	1.25508i
$73$	4.97545	−	4.97545i	0.582333	−	0.582333i	−0.353211	−	0.935544i	$-0.614910\pi$
$73$	4.97545	−	4.97545i	0.582333	−	0.582333i	0.935544	+	0.353211i	$0.114910\pi$
$74$	3.94898	−	6.81092i	0.459060	−	0.791754i
$75$	9.56998	−	10.8294i	1.10505	−	1.25047i
$76$	−3.13975	+	11.5479i	−0.360155	+	1.32464i
$77$	8.40894	+	8.40894i	0.958288	+	0.958288i
$78$	5.77671	+	21.7184i	0.654084	+	2.45913i
$79$	1.04312	+	1.04312i	0.117360	+	0.117360i	0.763348	−	0.645988i	$-0.223554\pi$
$79$	1.04312	+	1.04312i	0.117360	+	0.117360i	−0.645988	+	0.763348i	$0.723554\pi$
$80$	0.958897	−	8.89272i	0.107208	−	0.994237i
$81$	3.60652			0.400724
$82$	2.73569	−	8.63227i	0.302106	−	0.953274i
$83$	1.36790	−	1.36790i	0.150147	−	0.150147i	−0.628037	−	0.778184i	$-0.716141\pi$
$83$	1.36790	−	1.36790i	0.150147	−	0.150147i	0.778184	+	0.628037i	$0.216141\pi$
$84$	11.4020	+	19.9173i	1.24406	+	2.17316i
$85$	−4.29916	−	9.53647i	−0.466309	−	1.03438i
$86$	10.1252	+	5.87060i	1.09183	+	0.633043i
$87$	−14.7332	+	14.7332i	−1.57956	+	1.57956i
$88$	−0.0466698	+	8.47226i	−0.00497502	+	0.903146i
$89$	−4.94457	+	4.94457i	−0.524123	+	0.524123i	−0.918814	−	0.394691i	$-0.870852\pi$
$89$	−4.94457	+	4.94457i	−0.524123	+	0.524123i	0.394691	+	0.918814i	$0.370852\pi$
$90$	−13.1287	+	10.6927i	−1.38389	+	1.12711i
$91$	21.8270			2.28809
$92$	1.96240	−	7.21764i	0.204594	−	0.752491i
$93$			11.4038i			1.18252i
$94$	−10.3692	+	2.75803i	−1.06950	+	0.284469i
$95$	−4.73671	+	12.5132i	−0.485976	+	1.28382i
$96$	−4.37666	+	15.7539i	−0.446691	+	1.60788i
$97$		−	5.20787i		−	0.528779i	−0.964416	−	0.264389i	$-0.914830\pi$
$97$		−	5.20787i		−	0.528779i	0.964416	−	0.264389i	$-0.0851704\pi$
$98$	11.9740	−	3.18487i	1.20956	−	0.321720i
$99$	11.3412	−	11.3412i	1.13983	−	1.13983i
$100$	2.02404	−	9.79302i	0.202404	−	0.979302i
$101$	9.59727	−	9.59727i	0.954964	−	0.954964i	−0.0440648	−	0.999029i	$-0.514031\pi$
$101$	9.59727	−	9.59727i	0.954964	−	0.954964i	0.999029	+	0.0440648i	$0.0140308\pi$
$102$	4.91541	+	18.4802i	0.486698	+	1.82981i
$103$	4.49066	+	4.49066i	0.442478	+	0.442478i	0.892844	−	0.450366i	$-0.148706\pi$
$103$	4.49066	+	4.49066i	0.442478	+	0.442478i	−0.450366	+	0.892844i	$0.648706\pi$
$104$	10.9351	+	11.0562i	1.07228	+	1.08415i
$105$	10.5453	+	23.3918i	1.02912	+	2.28281i
$106$	−2.40495	−	9.04176i	−0.233589	−	0.878213i
$107$	8.17781	+	8.17781i	0.790579	+	0.790579i	0.981588	−	0.191009i	$-0.0611761\pi$
$107$	8.17781	+	8.17781i	0.790579	+	0.790579i	−0.191009	+	0.981588i	$0.561176\pi$
$108$	11.8119	−	6.76187i	1.13660	−	0.650661i
$109$	−9.10583	−	9.10583i	−0.872181	−	0.872181i	0.120529	−	0.992710i	$-0.461541\pi$
$109$	−9.10583	−	9.10583i	−0.872181	−	0.872181i	−0.992710	+	0.120529i	$0.961541\pi$
$110$	−0.963625	+	9.42327i	−0.0918780	+	0.898474i
$111$	−11.3780	+	11.3780i	−1.07995	+	1.07995i
$112$	13.6940	+	8.04089i	1.29396	+	0.759793i
$113$	−10.0574	−	10.0574i	−0.946120	−	0.946120i	0.0525011	−	0.998621i	$-0.483281\pi$
$113$	−10.0574	−	10.0574i	−0.946120	−	0.946120i	−0.998621	+	0.0525011i	$0.983281\pi$
$114$	12.2682	−	21.1594i	1.14903	−	1.98176i
$115$	2.96052	−	7.82093i	0.276070	−	0.729306i
$116$	−3.78258	+	13.9122i	−0.351203	+	1.29172i
$117$		−	29.4382i		−	2.72156i
$118$	−9.46770	+	2.51824i	−0.871572	+	0.231823i
$119$	18.5726			1.70255
$120$	−6.56579	+	17.0607i	−0.599372	+	1.55742i
$121$			2.02734i			0.184303i
$122$	−2.19833	−	8.26495i	−0.199027	−	0.748273i
$123$	−9.93838	+	15.6128i	−0.896114	+	1.40776i
$124$	3.92030	+	6.84811i	0.352053	+	0.614979i
$125$	3.30625	−	10.6803i	0.295720	−	0.955275i
$126$	−7.72737	−	29.0522i	−0.688409	−	2.58818i
$127$	−9.07050	−	9.07050i	−0.804877	−	0.804877i	0.178977	−	0.983853i	$-0.442721\pi$
$127$	−9.07050	−	9.07050i	−0.804877	−	0.804877i	−0.983853	+	0.178977i	$0.942721\pi$
$128$	2.78750	+	10.9649i	0.246383	+	0.969173i
$129$	−16.9146	−	16.9146i	−1.48925	−	1.48925i
$130$	10.9793	+	13.4806i	0.962949	+	1.18233i
$131$	0.242048			0.0211478			0.0105739	−	0.999944i	$-0.496634\pi$
$131$	0.242048			0.0211478			0.0105739	+	0.999944i	$0.496634\pi$
$132$	4.54312	−	16.7094i	0.395427	−	1.45437i
$133$	−16.7974	−	16.7974i	−1.45652	−	1.45652i
$134$	12.0491	−	3.20486i	1.04089	−	0.276857i
$135$	13.8724	−	6.25384i	1.19395	−	0.538245i
$136$	9.30468	+	9.40776i	0.797870	+	0.806709i
$137$		−	1.85162i		−	0.158195i	−0.996867	−	0.0790973i	$-0.974796\pi$
$137$		−	1.85162i		−	0.158195i	0.996867	−	0.0790973i	$-0.0252038\pi$
$138$	−7.66785	+	13.2250i	−0.652730	+	1.12578i
$139$	−7.67400			−0.650900			−0.325450	−	0.945559i	$-0.605516\pi$
$139$	−7.67400			−0.650900			−0.325450	+	0.945559i	$0.605516\pi$
$140$	14.3740	+	10.4218i	1.21482	+	0.880806i
$141$	21.9297			1.84681
$142$	7.89970	−	13.6249i	0.662928	−	1.14337i
$143$	−11.6451	−	11.6451i	−0.973815	−	0.973815i
$144$	10.8448	−	18.4691i	0.903731	−	1.53909i
$145$	−5.70649	+	15.0751i	−0.473898	+	1.25192i
$146$	−4.99127	+	8.60859i	−0.413080	+	0.712452i
$147$	−25.3236			−2.08866
$148$	−2.92117	+	10.7440i	−0.240119	+	0.883149i
$149$	14.4592	+	14.4592i	1.18455	+	1.18455i	0.978554	+	0.205993i	$0.0660423\pi$
$149$	14.4592	+	14.4592i	1.18455	+	1.18455i	0.205993	+	0.978554i	$0.433958\pi$
$150$	−9.14258	+	18.2793i	−0.746488	+	1.49250i
$151$	−10.2588	+	10.2588i	−0.834848	+	0.834848i	−0.988175	−	0.153328i	$-0.951001\pi$
$151$	−10.2588	+	10.2588i	−0.834848	+	0.834848i	0.153328	+	0.988175i	$0.451001\pi$
$152$	0.0932258	−	16.9238i	0.00756161	−	1.37271i
$153$		−	25.0489i		−	2.02509i
$154$	−14.5493	−	8.43567i	−1.17241	−	0.679766i
$155$	3.62576	+	8.04273i	0.291228	+	0.646008i
$156$	−15.7900	−	27.5825i	−1.26421	−	2.20837i
$157$	1.71893			0.137185			0.0685926	−	0.997645i	$-0.478149\pi$
$157$	1.71893			0.137185			0.0685926	+	0.997645i	$0.478149\pi$
$158$	−1.80482	−	1.04644i	−0.143584	−	0.0832501i
$159$			19.1223i			1.51649i
$160$	1.92213	+	12.5022i	0.151958	+	0.988387i
$161$	10.4986	+	10.4986i	0.827408	+	0.827408i
$162$	−4.92901	+	1.31103i	−0.387259	+	0.103004i
$163$	3.32591	−	3.32591i	0.260506	−	0.260506i	−0.564754	−	0.825259i	$-0.691029\pi$
$163$	3.32591	−	3.32591i	0.260506	−	0.260506i	0.825259	+	0.564754i	$0.191029\pi$
$164$	−0.600876	+	12.7921i	−0.0469206	+	0.998899i
$165$	6.85386	−	18.1061i	0.533572	−	1.40956i
$166$	−1.37225	+	2.36676i	−0.106507	+	0.183696i
$167$			6.72919i			0.520720i	0.965512	+	0.260360i	$0.0838413\pi$
$167$			6.72919i			0.520720i	−0.965512	+	0.260360i	$0.916159\pi$
$168$	−22.8233	−	23.0761i	−1.76085	−	1.78036i
$169$	−17.2271			−1.32516
$170$	9.34230	+	11.4706i	0.716522	+	0.879757i
$171$	−22.6547	+	22.6547i	−1.73245	+	1.73245i
$172$	−15.9721	−	4.34265i	−1.21786	−	0.331124i
$173$	0.649205	−	0.649205i	0.0493581	−	0.0493581i	−0.681997	−	0.731355i	$-0.738888\pi$
$173$	0.649205	−	0.649205i	0.0493581	−	0.0493581i	0.731355	+	0.681997i	$0.238888\pi$
$174$	14.7800	−	25.4915i	1.12047	−	1.93250i
$175$	14.8745	+	13.1446i	1.12441	+	0.993641i
$176$	−3.01602	−	11.5960i	−0.227341	−	0.874078i
$177$	20.0231			1.50503
$178$	4.96029	−	8.55515i	0.371789	−	0.641236i
$179$	10.8330	−	10.8330i	0.809700	−	0.809700i	−0.174889	−	0.984588i	$-0.555957\pi$
$179$	10.8330	−	10.8330i	0.809700	−	0.809700i	0.984588	+	0.174889i	$0.0559565\pi$
$180$	14.0560	−	19.3862i	1.04767	−	1.44496i
$181$	−2.35689	+	2.35689i	−0.175186	+	0.175186i	−0.789254	−	0.614067i	$-0.789532\pi$
$181$	−2.35689	+	2.35689i	−0.175186	+	0.175186i	0.614067	+	0.789254i	$0.289532\pi$
$182$	−29.8309	+	7.93448i	−2.21121	+	0.588143i
$183$			17.4794i			1.29211i
$184$	−0.0582676	+	10.5777i	−0.00429555	+	0.779797i
$185$	−4.40695	+	11.6420i	−0.324005	+	0.855938i
$186$	−4.14549	−	15.5856i	−0.303962	−	1.14279i
$187$	−9.90884	−	9.90884i	−0.724606	−	0.724606i
$188$	13.1690	−	7.53877i	0.960447	−	0.549821i
$189$			27.0170i			1.96520i
$190$	1.92490	−	18.8236i	0.139647	−	1.36560i
$191$	−5.54616	−	5.54616i	−0.401306	−	0.401306i	0.477387	−	0.878693i	$-0.341584\pi$
$191$	−5.54616	−	5.54616i	−0.401306	−	0.401306i	−0.878693	+	0.477387i	$0.841584\pi$
$192$	0.254743	−	23.1218i	0.0183845	−	1.66867i
$193$		−	19.5306i		−	1.40584i	−0.711267	−	0.702922i	$-0.751878\pi$
$193$		−	19.5306i		−	1.40584i	0.711267	−	0.702922i	$-0.248122\pi$
$194$	1.89315	+	7.11757i	0.135920	+	0.511012i
$195$	−14.6037	−	32.3942i	−1.04579	−	2.31980i
$196$	−15.2071	+	8.70549i	−1.08622	+	0.621821i
$197$	1.07079	+	1.07079i	0.0762910	+	0.0762910i	0.744223	−	0.667932i	$-0.232820\pi$
$197$	1.07079	+	1.07079i	0.0762910	+	0.0762910i	−0.667932	+	0.744223i	$0.732820\pi$
$198$	−11.3772	+	19.6226i	−0.808544	+	1.39452i
$199$	−4.54898	+	4.54898i	−0.322469	+	0.322469i	−0.849713	−	0.527245i	$-0.823225\pi$
$199$	−4.54898	+	4.54898i	−0.322469	+	0.322469i	0.527245	+	0.849713i	$0.323225\pi$
$200$	0.793685	+	14.1198i	0.0561220	+	0.998424i
$201$	−25.4825			−1.79740
$202$	−9.62777	+	16.6053i	−0.677408	+	1.16835i
$203$	−20.2364	−	20.2364i	−1.42032	−	1.42032i
$204$	−13.4357	−	23.4700i	−0.940689	−	1.64323i
$205$	−2.04523	+	14.1710i	−0.142845	+	0.989745i
$206$	−7.76980	−	4.50494i	−0.541347	−	0.313874i
$207$	14.1595	−	14.1595i	0.984156	−	0.984156i
$208$	−18.9641	−	11.1354i	−1.31492	−	0.772103i
$209$			17.9234i			1.23979i
$210$	−22.9156	−	28.1361i	−1.58132	−	1.94158i
$211$	−2.07424	−	2.07424i	−0.142797	−	0.142797i	0.632095	−	0.774891i	$-0.282195\pi$
$211$	−2.07424	−	2.07424i	−0.142797	−	0.142797i	−0.774891	+	0.632095i	$0.782195\pi$
$212$	6.57366	+	11.4831i	0.451481	+	0.788662i
$213$	−22.7610	+	22.7610i	−1.55956	+	1.55956i
$214$	−14.1493	−	8.20381i	−0.967229	−	0.560801i
$215$	−17.3072	−	6.55142i	−1.18034	−	0.446803i
$216$	−13.6852	+	13.5352i	−0.931158	+	0.920955i
$217$	−15.6635			−1.06331
$218$	15.7550	+	9.13478i	1.06706	+	0.618685i
$219$	14.3811	−	14.3811i	0.971781	−	0.971781i
$220$	−2.10853	−	13.2290i	−0.142157	−	0.891901i
$221$	−25.7203			−1.73013
$222$	11.4141	−	19.6863i	0.766066	−	1.32126i
$223$	−3.55858	+	3.55858i	−0.238300	+	0.238300i	−0.816146	−	0.577846i	$-0.803893\pi$
$223$	−3.55858	+	3.55858i	−0.238300	+	0.238300i	0.577846	+	0.816146i	$0.303893\pi$
$224$	−21.6385	−	6.01146i	−1.44578	−	0.401658i
$225$	17.7282	−	20.0613i	1.18188	−	1.33742i
$226$	17.4014	+	10.0894i	1.15752	+	0.671134i
$227$	6.82130			0.452746			0.226373	−	0.974041i	$-0.427313\pi$
$227$	6.82130			0.452746			0.226373	+	0.974041i	$0.427313\pi$
$228$	−9.07515	+	33.3781i	−0.601016	+	2.21052i
$229$	11.7099	+	11.7099i	0.773814	+	0.773814i	0.978771	−	0.204957i	$-0.0657054\pi$
$229$	11.7099	+	11.7099i	0.773814	+	0.773814i	−0.204957	+	0.978771i	$0.565705\pi$
$230$	−1.20309	+	11.7650i	−0.0793296	+	0.775763i
$231$	24.3052	+	24.3052i	1.59917	+	1.59917i
$232$	0.112312	−	20.3888i	0.00737367	−	1.33859i
$233$		−	7.39818i		−	0.484671i	−0.970193	−	0.242335i	$-0.922087\pi$
$233$		−	7.39818i		−	0.484671i	0.970193	−	0.242335i	$-0.0779134\pi$
$234$	10.7013	+	40.2330i	0.699563	+	2.63011i
$235$	15.4663	−	6.97237i	1.00891	−	0.454827i
$236$	12.0240	−	6.88333i	0.782698	−	0.448067i
$237$	3.01504	+	3.01504i	0.195848	+	0.195848i
$238$	−25.3831	+	6.75145i	−1.64534	+	0.437632i
$239$	6.27100	+	6.27100i	0.405637	+	0.405637i	0.880214	−	0.474577i	$-0.157399\pi$
$239$	6.27100	+	6.27100i	0.405637	+	0.405637i	−0.474577	+	0.880214i	$0.657399\pi$
$240$	2.77160	−	25.7035i	0.178906	−	1.65916i
$241$		−	22.4409i		−	1.44554i	−0.691086	−	0.722772i	$-0.742868\pi$
$241$		−	22.4409i		−	1.44554i	0.691086	−	0.722772i	$-0.257132\pi$
$242$	−0.736970	−	2.77075i	−0.0473742	−	0.178111i
$243$	−9.99133			−0.640944
$244$	6.00889	+	10.4965i	0.384680	+	0.671972i
$245$	−17.8599	+	8.05144i	−1.14102	+	0.514387i
$246$	7.90723	−	24.9507i	0.504146	−	1.59080i
$247$	23.2618	+	23.2618i	1.48012	+	1.48012i
$248$	−7.84726	−	7.93419i	−0.498301	−	0.503821i
$249$	3.95379	−	3.95379i	0.250561	−	0.250561i
$250$	−0.636172	+	15.7986i	−0.0402350	+	0.999190i
$251$	2.71865			0.171600			0.0857999	−	0.996312i	$-0.472655\pi$
$251$	2.71865			0.171600			0.0857999	+	0.996312i	$0.472655\pi$
$252$	21.1219	+	36.8965i	1.33056	+	2.32426i
$253$		−	11.2024i		−	0.704292i
$254$	15.6939	+	9.09933i	0.984722	+	0.570943i
$255$	−12.4263	−	27.5642i	−0.778164	−	1.72614i
$256$	−7.79560	−	13.9724i	−0.487225	−	0.873276i
$257$	−8.12085			−0.506565			−0.253282	−	0.967392i	$-0.581510\pi$
$257$	−8.12085			−0.506565			−0.253282	+	0.967392i	$0.581510\pi$
$258$	29.2659	+	16.9684i	1.82201	+	1.05641i
$259$	−15.6280	−	15.6280i	−0.971074	−	0.971074i
$260$	−19.9058	−	14.4327i	−1.23450	−	0.895077i
$261$	−27.2929	+	27.2929i	−1.68939	+	1.68939i
$262$	−0.330805	+	0.0879883i	−0.0204372	+	0.00543594i
$263$		−	10.8140i		−	0.666821i	−0.942782	−	0.333410i	$-0.891801\pi$
$263$		−	10.8140i		−	0.666821i	0.942782	−	0.333410i	$-0.108199\pi$
$264$	−0.134894	+	24.4882i	−0.00830218	+	1.50715i
$265$	6.07977	+	13.4863i	0.373477	+	0.828455i
$266$	29.0630	+	16.8508i	1.78197	+	1.03319i
$267$	−14.2918	+	14.2918i	−0.874643	+	0.874643i
$268$	−15.3025	+	8.76012i	−0.934748	+	0.535110i
$269$		−	19.3684i		−	1.18091i	−0.807070	−	0.590456i	$-0.798948\pi$
$269$		−	19.3684i		−	1.18091i	0.807070	−	0.590456i	$-0.201052\pi$
$270$	−16.6860	+	13.5899i	−1.01548	+	0.827058i
$271$		−	16.7811i		−	1.01938i	−0.860358	−	0.509690i	$-0.829760\pi$
$271$		−	16.7811i		−	1.01938i	0.860358	−	0.509690i	$-0.170240\pi$
$272$	−16.1365	−	9.47514i	−0.978422	−	0.574515i
$273$	63.0888			3.81831
$274$	0.673094	+	2.53060i	0.0406631	+	0.152879i
$275$	−0.922909	−	14.9487i	−0.0556535	−	0.901443i
$276$	5.67212	−	20.8619i	0.341421	−	1.25574i
$277$	−8.42934	+	8.42934i	−0.506470	+	0.506470i	−0.913441	−	0.406971i	$-0.866585\pi$
$277$	−8.42934	+	8.42934i	−0.506470	+	0.506470i	0.406971	+	0.913441i	$0.366585\pi$
$278$	10.4880	−	2.78963i	0.629030	−	0.167311i
$279$			21.1254i			1.26475i
$280$	−23.4333	−	9.01830i	−1.40041	−	0.538947i
$281$	−0.244835	+	0.244835i	−0.0146056	+	0.0146056i	−0.714372	−	0.699766i	$-0.753287\pi$
$281$	−0.244835	+	0.244835i	−0.0146056	+	0.0146056i	0.699766	+	0.714372i	$0.253287\pi$
$282$	−29.9712	+	7.97181i	−1.78476	+	0.474714i
$283$	−12.5957	+	12.5957i	−0.748736	+	0.748736i	−0.974242	−	0.225506i	$-0.927597\pi$
$283$	−12.5957	+	12.5957i	−0.748736	+	0.748736i	0.225506	+	0.974242i	$0.427597\pi$
$284$	−5.84363	+	21.4927i	−0.346756	+	1.27536i
$285$	−13.6910	+	36.1681i	−0.810985	+	2.14241i
$286$	20.1485	+	11.6821i	1.19141	+	0.690780i
$287$	−21.4446	−	13.6507i	−1.26584	−	0.805772i
$288$	−8.10768	+	29.1839i	−0.477749	+	1.71968i
$289$	−4.88539			−0.287376
$290$	2.31900	−	22.6774i	0.136176	−	1.33166i
$291$		−	15.0528i		−	0.882412i
$292$	3.69218	−	13.5797i	0.216068	−	0.794693i
$293$	11.1282			0.650117			0.325059	−	0.945694i	$-0.394616\pi$
$293$	11.1282			0.650117			0.325059	+	0.945694i	$0.394616\pi$
$294$	34.6096	−	9.20555i	2.01848	−	0.536878i
$295$	14.1216	−	6.36618i	0.822190	−	0.370653i
$296$	0.0867355	−	15.7456i	0.00504140	−	0.915196i
$297$	14.4141	−	14.4141i	0.836389	−	0.836389i
$298$	−25.0175	−	14.5052i	−1.44923	−	0.840263i
$299$	−14.5390	−	14.5390i	−0.840814	−	0.840814i
$300$	5.85028	−	28.3058i	0.337766	−	1.63423i
$301$	23.2327	−	23.2327i	1.33911	−	1.33911i
$302$	10.2914	−	17.7499i	0.592203	−	1.02139i
$303$	27.7399	−	27.7399i	1.59362	−	1.59362i
$304$	6.02469	+	23.1636i	0.345540	+	1.32853i
$305$	5.55743	+	12.3276i	0.318218	+	0.705877i
$306$	9.10570	+	34.2343i	0.520538	+	1.95704i
$307$	5.05107	−	5.05107i	0.288280	−	0.288280i	−0.548120	−	0.836400i	$-0.684656\pi$
$307$	5.05107	−	5.05107i	0.288280	−	0.288280i	0.836400	+	0.548120i	$0.184656\pi$
$308$	22.9509	+	6.24010i	1.30775	+	0.355563i
$309$	12.9798	+	12.9798i	0.738396	+	0.738396i
$310$	−7.87898	−	9.67394i	−0.447496	−	0.549443i
$311$	10.3786	+	10.3786i	0.588516	+	0.588516i	0.937229	−	0.348713i	$-0.113381\pi$
$311$	10.3786	+	10.3786i	0.588516	+	0.588516i	−0.348713	+	0.937229i	$0.613381\pi$
$312$	31.6068	+	31.9570i	1.78938	+	1.80921i
$313$	−1.55243			−0.0877483			−0.0438741	−	0.999037i	$-0.513970\pi$
$313$	−1.55243			−0.0877483			−0.0438741	+	0.999037i	$0.513970\pi$
$314$	−2.34925	+	0.624858i	−0.132576	+	0.0352628i
$315$	19.5350	+	43.3329i	1.10067	+	2.44153i
$316$	2.84704	+	0.774079i	0.160159	+	0.0435453i
$317$	−5.50774			−0.309346			−0.154673	−	0.987966i	$-0.549432\pi$
$317$	−5.50774			−0.309346			−0.154673	+	0.987966i	$0.549432\pi$
$318$	−6.95126	−	26.1343i	−0.389807	−	1.46554i
$319$			21.5930i			1.20898i
$320$	−7.17173	−	16.3880i	−0.400912	−	0.916117i
$321$	23.6371	+	23.6371i	1.31930	+	1.31930i
$322$	−18.1649	−	10.5320i	−1.01229	−	0.586926i
$323$	19.7935	+	19.7935i	1.10134	+	1.10134i
$324$	6.25987	−	3.58355i	0.347771	−	0.199086i
$325$	−20.5989	−	18.2034i	−1.14262	−	1.00974i
$326$	−3.33649	+	5.75453i	−0.184791	+	0.318714i
$327$	−26.3195	−	26.3195i	−1.45547	−	1.45547i
$328$	−3.82894	−	17.7014i	−0.211418	−	0.977396i
$329$			30.1211i			1.66063i
$330$	−2.78526	+	27.2370i	−0.153324	+	1.49935i
$331$	−5.67764	+	5.67764i	−0.312071	+	0.312071i	−0.845712	−	0.533640i	$-0.820824\pi$
$331$	−5.67764	+	5.67764i	−0.312071	+	0.312071i	0.533640	+	0.845712i	$0.320824\pi$
$332$	1.01509	−	3.73348i	0.0557104	−	0.204901i
$333$	−21.0775	+	21.0775i	−1.15504	+	1.15504i
$334$	−2.44617	−	9.19675i	−0.133849	−	0.503224i
$335$	−17.9719	+	8.10196i	−0.981912	+	0.442658i
$336$	39.5810	+	23.2414i	2.15932	+	1.26792i
$337$	−8.59922	−	8.59922i	−0.468430	−	0.468430i	0.432976	−	0.901405i	$-0.357464\pi$
$337$	−8.59922	−	8.59922i	−0.468430	−	0.468430i	−0.901405	+	0.432976i	$0.857464\pi$
$338$	23.5443	−	6.26235i	1.28064	−	0.340627i
$339$	−29.0699	−	29.0699i	−1.57886	−	1.57886i
$340$	−16.9378	−	12.2808i	−0.918583	−	0.666019i
$341$	8.35678	+	8.35678i	0.452545	+	0.452545i
$342$	22.7267	−	39.1974i	1.22892	−	2.11955i
$343$		−	6.99236i		−	0.377552i
$344$	23.4076	+	0.128942i	1.26206	+	0.00695209i
$345$	8.55710	−	22.6056i	0.460699	−	1.21705i
$346$	−0.651268	+	1.12326i	−0.0350124	+	0.0603869i
$347$	25.7265			1.38107			0.690536	−	0.723298i	$-0.257375\pi$
$347$	25.7265			1.38107			0.690536	+	0.723298i	$0.257375\pi$
$348$	−10.9332	+	40.2118i	−0.586079	+	2.15558i
$349$	5.38091			0.288034			0.144017	−	0.989575i	$-0.453998\pi$
$349$	5.38091			0.288034			0.144017	+	0.989575i	$0.453998\pi$
$350$	−25.1072	−	12.5576i	−1.34204	−	0.671231i
$351$		−	37.4145i		−	1.99704i
$352$	8.33731	+	14.7518i	0.444380	+	0.786272i
$353$	−22.1106	−	22.1106i	−1.17683	−	1.17683i	−0.980548	−	0.196281i	$-0.937113\pi$
$353$	−22.1106	−	22.1106i	−1.17683	−	1.17683i	−0.196281	−	0.980548i	$-0.562887\pi$
$354$	−27.3654	+	7.27872i	−1.45446	+	0.386859i
$355$	−8.81584	+	23.2892i	−0.467896	+	1.23606i
$356$	−3.66926	+	13.4954i	−0.194470	+	0.715257i
$357$	53.6823			2.84117
$358$	−10.8675	+	18.7435i	−0.574364	+	0.990623i
$359$	1.25683			0.0663329			0.0331664	−	0.999450i	$-0.489441\pi$
$359$	1.25683			0.0663329			0.0331664	+	0.999450i	$0.489441\pi$
$360$	−12.1630	+	31.6046i	−0.641047	+	1.66571i
$361$		−	16.8032i		−	0.884377i
$362$	2.36438	−	4.07792i	0.124269	−	0.214331i
$363$			5.85981i			0.307560i
$364$	37.8854	−	21.6880i	1.98573	−	1.13676i
$365$	5.57011	−	14.7148i	0.291553	−	0.770208i
$366$	−6.35405	−	23.8890i	−0.332131	−	1.24870i
$367$	−6.00019	+	6.00019i	−0.313207	+	0.313207i	−0.846151	−	0.532944i	$-0.821086\pi$
$367$	−6.00019	+	6.00019i	−0.313207	+	0.313207i	0.532944	+	0.846151i	$0.321086\pi$
$368$	−3.76553	−	14.4776i	−0.196292	−	0.754700i
$369$	−18.4107	+	28.9224i	−0.958421	+	1.50564i
$370$	1.79089	−	17.5131i	0.0931039	−	0.910462i
$371$	−26.2650			−1.36361
$372$	11.3312	+	19.7938i	0.587497	+	1.02626i
$373$	1.39112	+	1.39112i	0.0720293	+	0.0720293i	0.742204	−	0.670174i	$-0.233781\pi$
$373$	1.39112	+	1.39112i	0.0720293	+	0.0720293i	−0.670174	+	0.742204i	$0.733781\pi$
$374$	17.1444	+	9.94034i	0.886515	+	0.514003i
$375$	9.55639	−	30.8703i	0.493490	−	1.59414i
$376$	−15.2575	+	15.0903i	−0.786846	+	0.778225i
$377$	28.0244	+	28.0244i	1.44333	+	1.44333i
$378$	−9.82112	−	36.9240i	−0.505144	−	1.89916i
$379$	−6.38161			−0.327801			−0.163901	−	0.986477i	$-0.552408\pi$
$379$	−6.38161			−0.327801			−0.163901	+	0.986477i	$0.552408\pi$
$380$	4.21193	+	26.4258i	0.216067	+	1.35561i
$381$	−26.2174	−	26.2174i	−1.34316	−	1.34316i
$382$	9.59604	+	5.56379i	0.490976	+	0.284668i
$383$			33.1381i			1.69328i	0.532167	+	0.846640i	$0.321378\pi$
$383$			33.1381i			1.69328i	−0.532167	+	0.846640i	$0.678622\pi$
$384$	8.05700	+	31.6931i	0.411157	+	1.61733i
$385$	24.8693	+	9.41397i	1.26746	+	0.479780i
$386$	7.09970	+	26.6924i	0.361365	+	1.35861i
$387$	−31.3340	−	31.3340i	−1.59280	−	1.59280i
$388$	−5.17471	−	9.03936i	−0.262706	−	0.458904i
$389$	36.2135			1.83610			0.918050	−	0.396465i	$-0.129763\pi$
$389$	36.2135			1.83610			0.918050	+	0.396465i	$0.129763\pi$
$390$	31.7346	+	38.9643i	1.60694	+	1.97303i
$391$	−12.3713	−	12.3713i	−0.625642	−	0.625642i
$392$	17.6188	−	17.4258i	0.889884	−	0.880134i
$393$	0.699615			0.0352909
$394$	−1.85270	−	1.07420i	−0.0933378	−	0.0541173i
$395$	3.08501	+	1.16780i	0.155224	+	0.0587581i
$396$	8.41604	−	30.9539i	0.422922	−	1.55549i
$397$	7.02431			0.352540			0.176270	−	0.984342i	$-0.443597\pi$
$397$	7.02431			0.352540			0.176270	+	0.984342i	$0.443597\pi$
$398$	4.56344	−	7.87070i	0.228745	−	0.394523i
$399$	−48.5511	−	48.5511i	−2.43060	−	2.43060i
$400$	−6.21752	−	19.0090i	−0.310876	−	0.950450i
$401$		−	12.6243i		−	0.630427i	−0.949021	−	0.315213i	$-0.897924\pi$
$401$		−	12.6243i		−	0.630427i	0.949021	−	0.315213i	$-0.102076\pi$
$402$	34.8268	−	9.26332i	1.73700	−	0.462012i
$403$	21.6916			1.08054
$404$	7.12193	−	26.1942i	0.354329	−	1.30321i
$405$	7.35188	−	3.31432i	0.365318	−	0.164690i
$406$	35.0133	+	20.3007i	1.73768	+	1.00751i
$407$			16.6756i			0.826580i
$408$	26.8943	+	27.1922i	1.33146	+	1.34621i
$409$		−	3.48240i		−	0.172194i	−0.996287	−	0.0860968i	$-0.972561\pi$
$409$		−	3.48240i		−	0.172194i	0.996287	−	0.0860968i	$-0.0274394\pi$
$410$	−2.35619	−	20.1109i	−0.116364	−	0.993207i
$411$		−	5.35192i		−	0.263991i
$412$	12.2566	+	3.33243i	0.603838	+	0.164177i
$413$			27.5023i			1.35330i
$414$	−14.2045	+	24.4990i	−0.698115	+	1.20406i
$415$	1.53139	−	4.04554i	0.0751731	−	0.198588i
$416$	29.9660	+	8.32498i	1.46921	+	0.408166i
$417$	−22.1809			−1.08621
$418$	−6.51547	−	24.4959i	−0.318682	−	1.19813i
$419$		−	1.48835i		−	0.0727107i	−0.999339	−	0.0363553i	$-0.988425\pi$
$419$		−	1.48835i		−	0.0727107i	0.999339	−	0.0363553i	$-0.0115748\pi$
$420$	41.5465	+	30.1233i	2.02726	+	1.46987i
$421$	−5.39787	−	5.39787i	−0.263076	−	0.263076i	0.563226	−	0.826303i	$-0.309560\pi$
$421$	−5.39787	−	5.39787i	−0.263076	−	0.263076i	−0.826303	+	0.563226i	$0.809560\pi$
$422$	3.58887	+	2.08083i	0.174704	+	0.101293i
$423$	40.6244			1.97522
$424$	−13.1585	−	13.3042i	−0.639032	−	0.646111i
$425$	−17.5276	−	15.4892i	−0.850216	−	0.751338i
$426$	22.8333	−	39.3813i	1.10628	−	1.90803i
$427$	−24.0084			−1.16185
$428$	22.3201	+	6.06858i	1.07888	+	0.293336i
$429$	−33.6591	−	33.6591i	−1.62508	−	1.62508i
$430$	26.0352	+	2.66236i	1.25553	+	0.128390i
$431$	−27.9795			−1.34772			−0.673862	−	0.738857i	$-0.735366\pi$
$431$	−27.9795			−1.34772			−0.673862	+	0.738857i	$0.735366\pi$
$432$	13.7832	−	23.4733i	0.663143	−	1.12936i
$433$	24.8001	+	24.8001i	1.19182	+	1.19182i	0.976557	+	0.215258i	$0.0690593\pi$
$433$	24.8001	+	24.8001i	1.19182	+	1.19182i	0.215258	+	0.976557i	$0.430941\pi$
$434$	21.4072	−	5.69394i	1.02758	−	0.273318i
$435$	−16.4940	+	43.5730i	−0.790829	+	2.08916i
$436$	−24.8530	−	6.75725i	−1.19024	−	0.323613i
$437$			22.3776i			1.07046i
$438$	−14.4268	+	24.8823i	−0.689337	+	1.18892i
$439$	7.77457	+	7.77457i	0.371060	+	0.371060i	0.867863	−	0.496803i	$-0.165493\pi$
$439$	7.77457	+	7.77457i	0.371060	+	0.371060i	−0.496803	+	0.867863i	$0.665493\pi$
$440$	7.69070	+	17.3136i	0.366640	+	0.825392i
$441$	−46.9115			−2.23388
$442$	35.1518	−	9.34975i	1.67200	−	0.444722i
$443$	1.04205	+	1.04205i	0.0495091	+	0.0495091i	0.731428	−	0.681919i	$-0.238854\pi$
$443$	1.04205	+	1.04205i	0.0495091	+	0.0495091i	−0.681919	+	0.731428i	$0.738854\pi$
$444$	−8.44335	+	31.0544i	−0.400704	+	1.47378i
$445$	−5.53554	+	14.6235i	−0.262410	+	0.693218i
$446$	3.56989	−	6.15709i	0.169039	−	0.291547i
$447$	41.7930	+	41.7930i	1.97674	+	1.97674i
$448$	31.7585	+	0.349896i	1.50045	+	0.0165310i
$449$	−2.36619			−0.111667			−0.0558337	−	0.998440i	$-0.517782\pi$
$449$	−2.36619			−0.111667			−0.0558337	+	0.998440i	$0.517782\pi$
$450$	−16.9365	+	33.8621i	−0.798392	+	1.59628i
$451$	4.15824	+	18.7240i	0.195804	+	0.881679i
$452$	−27.4501	−	7.46338i	−1.29114	−	0.351048i
$453$	−29.6520	+	29.6520i	−1.39317	+	1.39317i
$454$	−9.32264	+	2.47966i	−0.437533	+	0.116376i
$455$	44.4943	−	20.0586i	2.08593	−	0.940361i
$456$	0.269460	−	48.9167i	0.0126186	−	2.29073i
$457$			9.72260i			0.454804i	0.973801	+	0.227402i	$0.0730231\pi$
$457$			9.72260i			0.454804i	−0.973801	+	0.227402i	$0.926977\pi$
$458$	−20.2607	−	11.7472i	−0.946719	−	0.548908i
$459$		−	31.8360i		−	1.48598i
$460$	−2.63252	−	16.5166i	−0.122742	−	0.770089i
$461$	34.5880			1.61092			0.805462	−	0.592647i	$-0.201917\pi$
$461$	34.5880			1.61092			0.805462	+	0.592647i	$0.201917\pi$
$462$	−42.0532	−	24.3825i	−1.95649	−	1.13438i
$463$	−22.0463			−1.02458			−0.512290	−	0.858813i	$-0.671203\pi$
$463$	−22.0463			−1.02458			−0.512290	+	0.858813i	$0.671203\pi$
$464$	7.25816	+	27.9061i	0.336952	+	1.29551i
$465$	10.4799	+	23.2467i	0.485994	+	1.07804i
$466$	2.68936	+	10.1111i	0.124582	+	0.468385i
$467$	−9.53839	−	9.53839i	−0.441384	−	0.441384i	0.451093	−	0.892477i	$-0.351034\pi$
$467$	−9.53839	−	9.53839i	−0.441384	−	0.441384i	−0.892477	+	0.451093i	$0.851034\pi$
$468$	−29.2507	−	51.0961i	−1.35211	−	2.36192i
$469$		−	35.0010i		−	1.61619i
$470$	−18.6031	+	15.1513i	−0.858096	+	0.698880i
$471$	4.96838			0.228931
$472$	−13.9310	+	13.7783i	−0.641226	+	0.634200i
$473$	−24.7902			−1.13985
$474$	−5.21666	−	3.02463i	−0.239609	−	0.138926i
$475$	1.84357	+	29.8610i	0.0845886	+	1.37012i
$476$	32.2367	−	18.4543i	1.47757	−	0.845854i
$477$			35.4236i			1.62194i
$478$	−10.8502	−	6.29094i	−0.496275	−	0.287741i
$479$	−14.2940	−	14.2940i	−0.653111	−	0.653111i	0.300630	−	0.953741i	$-0.402803\pi$
$479$	−14.2940	−	14.2940i	−0.653111	−	0.653111i	−0.953741	+	0.300630i	$0.902803\pi$
$480$	5.55573	+	36.1364i	0.253583	+	1.64939i
$481$	21.6424	+	21.6424i	0.986808	+	0.986808i
$482$	8.15763	+	30.6698i	0.371570	+	1.39697i
$483$	30.3453	+	30.3453i	1.38076	+	1.38076i
$484$	2.01443	+	3.51887i	0.0915648	+	0.159949i
$485$	−4.78593	−	10.6162i	−0.217318	−	0.482058i
$486$	13.6551	−	3.63201i	0.619408	−	0.164752i
$487$	7.77770	−	7.77770i	0.352441	−	0.352441i	−0.508576	−	0.861017i	$-0.669828\pi$
$487$	7.77770	−	7.77770i	0.352441	−	0.352441i	0.861017	+	0.508576i	$0.169828\pi$
$488$	−12.0280	−	12.1612i	−0.544481	−	0.550513i
$489$	9.61322	−	9.61322i	0.434725	−	0.434725i
$490$	21.4821	−	17.4962i	0.970464	−	0.790398i
$491$			11.7930i			0.532210i	0.963944	+	0.266105i	$0.0857369\pi$
$491$			11.7930i			0.532210i	−0.963944	+	0.266105i	$0.914263\pi$
$492$	−1.73677	+	36.9744i	−0.0782998	+	1.66694i
$493$	23.8460	+	23.8460i	1.07397	+	1.07397i
$494$	−40.2479	−	23.3358i	−1.81084	−	1.04993i
$495$	12.6966	−	33.5413i	0.570672	−	1.50757i
$496$	13.6090	+	7.99101i	0.611063	+	0.358807i
$497$	−31.2628	−	31.2628i	−1.40233	−	1.40233i
$498$	−3.96635	+	6.84089i	−0.177737	+	0.306547i
$499$	29.1074	+	29.1074i	1.30303	+	1.30303i	0.926342	+	0.376684i	$0.122936\pi$
$499$	29.1074	+	29.1074i	1.30303	+	1.30303i	0.376684	+	0.926342i	$0.377064\pi$
$500$	−4.87359	−	21.8231i	−0.217954	−	0.975959i
$501$			19.4501i			0.868964i
$502$	−3.71557	+	0.988274i	−0.165834	+	0.0441088i
$503$	23.5030			1.04795			0.523974	−	0.851734i	$-0.324449\pi$
$503$	23.5030			1.04795			0.523974	+	0.851734i	$0.324449\pi$
$504$	−42.2797	−	42.7481i	−1.88329	−	1.90415i
$505$	10.7443	−	28.3837i	0.478116	−	1.26306i
$506$	4.07227	+	15.3103i	0.181035	+	0.680627i
$507$	−49.7933			−2.21140
$508$	−24.7565	−	6.73103i	−1.09839	−	0.298641i
$509$	−27.3102	−	27.3102i	−1.21050	−	1.21050i	−0.970861	−	0.239644i	$-0.922969\pi$
$509$	−27.3102	−	27.3102i	−1.21050	−	1.21050i	−0.239644	−	0.970861i	$-0.577031\pi$
$510$	27.0030	+	33.1547i	1.19571	+	1.46812i
$511$	19.7528	+	19.7528i	0.873812	+	0.873812i
$512$	15.7334	+	16.2622i	0.695325	+	0.718695i
$513$	−28.7930	+	28.7930i	−1.27124	+	1.27124i
$514$	11.0987	−	2.95206i	0.489544	−	0.130210i
$515$	13.2810	+	5.02738i	0.585232	+	0.221533i
$516$	−46.1658	−	12.5520i	−2.03234	−	0.552570i
$517$	16.0702	−	16.0702i	0.706765	−	0.706765i
$518$	27.0397	+	15.6776i	1.18806	+	0.688836i
$519$	1.87646	−	1.87646i	0.0823675	−	0.0823675i
$520$	32.4517	+	12.4890i	1.42310	+	0.547679i
$521$	−21.4258	−	21.4258i	−0.938680	−	0.938680i	0.0595460	−	0.998226i	$-0.481035\pi$
$521$	−21.4258	−	21.4258i	−0.938680	−	0.938680i	−0.998226	+	0.0595460i	$0.981035\pi$
$522$	27.3797	−	47.2225i	1.19838	−	2.06687i
$523$	14.7430	−	14.7430i	0.644667	−	0.644667i	−0.307032	−	0.951699i	$-0.599336\pi$
$523$	14.7430	−	14.7430i	0.644667	−	0.644667i	0.951699	+	0.307032i	$0.0993360\pi$
$524$	0.420125	−	0.240506i	0.0183532	−	0.0105066i
$525$	42.9932	+	37.9933i	1.87638	+	1.65816i
$526$	3.93107	+	14.7795i	0.171403	+	0.644415i
$527$	18.4574			0.804017
$528$	−8.71751	−	33.5170i	−0.379381	−	1.45864i
$529$			9.01366i			0.391898i
$530$	−13.2117	−	16.2215i	−0.573878	−	0.704617i
$531$	37.0924			1.60967
$532$	−45.8458	−	12.4650i	−1.98767	−	0.540425i
$533$	29.6976	+	18.9041i	1.28635	+	0.818828i
$534$	14.3372	−	24.7278i	0.620432	−	1.07008i
$535$	24.1857	+	9.15521i	1.04564	+	0.395814i
$536$	17.7294	−	17.5351i	0.765793	−	0.757402i
$537$	31.3118	−	31.3118i	1.35121	−	1.35121i
$538$	7.04073	+	26.4707i	0.303547	+	1.14123i
$539$	−18.5572	+	18.5572i	−0.799317	+	0.799317i
$540$	17.8645	−	24.6389i	0.768764	−	1.06029i
$541$			13.1806i			0.566680i	0.959020	+	0.283340i	$0.0914424\pi$
$541$			13.1806i			0.566680i	−0.959020	+	0.283340i	$0.908558\pi$
$542$	6.10021	+	22.9347i	0.262026	+	0.985128i
$543$	−6.81236	+	6.81236i	−0.292346	+	0.292346i
$544$	25.4981	+	7.08372i	1.09322	+	0.303712i
$545$	−26.9303	−	10.1942i	−1.15357	−	0.436669i
$546$	−86.2232	+	22.9338i	−3.69001	+	0.981477i
$547$	6.34750			0.271400			0.135700	−	0.990750i	$-0.456672\pi$
$547$	6.34750			0.271400			0.135700	+	0.990750i	$0.456672\pi$
$548$	−1.83983	−	3.21388i	−0.0785936	−	0.137290i
$549$			32.3803i			1.38196i
$550$	6.69545	+	20.0949i	0.285495	+	0.856849i
$551$		−	43.1334i		−	1.83754i
$552$	−0.168417	+	30.5737i	−0.00716829	+	1.30130i
$553$	−4.14125	+	4.14125i	−0.176104	+	0.176104i
$554$	8.45614	−	14.5845i	0.359267	−	0.619638i
$555$	−12.7378	+	33.6501i	−0.540691	+	1.42837i
$556$	−13.3199	+	7.62514i	−0.564888	+	0.323378i
$557$		−	5.08673i		−	0.215532i	−0.994176	−	0.107766i	$-0.965630\pi$
$557$		−	5.08673i		−	0.215532i	0.994176	−	0.107766i	$-0.0343697\pi$
$558$	−7.67944	−	28.8720i	−0.325097	−	1.22225i
$559$	−32.1738	+	32.1738i	−1.36081	+	1.36081i
$560$	35.3045	+	3.80687i	1.49189	+	0.160869i
$561$	−28.6405	−	28.6405i	−1.20920	−	1.20920i
$562$	0.245613	−	0.423616i	0.0103606	−	0.0178692i
$563$	25.7047			1.08333			0.541663	−	0.840596i	$-0.317795\pi$
$563$	25.7047			1.08333			0.541663	+	0.840596i	$0.317795\pi$
$564$	38.0636	−	21.7901i	1.60277	−	0.917527i
$565$	−29.7445	−	11.2594i	−1.25136	−	0.473688i
$566$	12.6357	−	21.7932i	0.531119	−	0.916037i
$567$			14.3180i			0.601301i
$568$	0.173509	−	31.4982i	0.00728029	−	1.32164i
$569$	9.50288			0.398381			0.199191	−	0.979961i	$-0.436169\pi$
$569$	9.50288			0.398381			0.199191	+	0.979961i	$0.436169\pi$
$570$	5.56373	−	54.4076i	0.233039	−	2.27888i
$571$	−17.3201	+	17.3201i	−0.724823	+	0.724823i	−0.969584	−	0.244760i	$-0.921291\pi$
$571$	−17.3201	+	17.3201i	−0.724823	+	0.724823i	0.244760	+	0.969584i	$0.421291\pi$
$572$	−31.7836	−	8.64160i	−1.32894	−	0.361324i
$573$	−16.0306	−	16.0306i	−0.669689	−	0.669689i
$574$	34.2705	+	10.8608i	1.43042	+	0.453321i
$575$	−1.15226	−	18.6636i	−0.0480525	−	0.778327i
$576$	0.471906	−	42.8327i	0.0196628	−	1.78470i
$577$	−40.3754			−1.68085			−0.840425	−	0.541928i	$-0.817695\pi$
$577$	−40.3754			−1.68085			−0.840425	+	0.541928i	$0.817695\pi$
$578$	6.67684	−	1.77592i	0.277720	−	0.0738686i
$579$		−	56.4513i		−	2.34603i
$580$	5.07426	+	31.8361i	0.210697	+	1.32192i
$581$	5.43064	+	5.43064i	0.225301	+	0.225301i
$582$	5.47195	+	20.5726i	0.226820	+	0.852763i
$583$	14.0129	+	14.0129i	0.580354	+	0.580354i
$584$	−0.109628	+	19.9015i	−0.00453645	+	0.823530i
$585$	−27.0531	−	60.0096i	−1.11851	−	2.48109i
$586$	−15.2089	+	4.04529i	−0.628273	+	0.167109i
$587$		−	38.9892i		−	1.60926i	−0.593779	−	0.804628i	$-0.702365\pi$
$587$		−	38.9892i		−	1.60926i	0.593779	−	0.804628i	$-0.297635\pi$
$588$	−43.9545	+	25.1624i	−1.81265	+	1.03768i
$589$	−16.6932	−	16.6932i	−0.687830	−	0.687830i
$590$	−16.9857	+	13.8340i	−0.699289	+	0.569539i
$591$	3.09503	+	3.09503i	0.127312	+	0.127312i
$592$	5.60526	+	21.5510i	0.230375	+	0.885741i
$593$	−21.2839			−0.874023			−0.437012	−	0.899456i	$-0.643963\pi$
$593$	−21.2839			−0.874023			−0.437012	+	0.899456i	$0.643963\pi$
$594$	−14.4599	+	24.9394i	−0.593297	+	1.02328i
$595$	37.8602	−	17.0679i	1.55212	−	0.699714i
$596$	39.4642	+	10.7299i	1.61652	+	0.439513i
$597$	−13.1484	+	13.1484i	−0.538127	+	0.538127i
$598$	25.1556	+	14.5853i	1.02869	+	0.596435i
$599$	−22.8913			−0.935312			−0.467656	−	0.883911i	$-0.654901\pi$
$599$	−22.8913			−0.935312			−0.467656	+	0.883911i	$0.654901\pi$
$600$	2.29407	+	40.8120i	0.0936549	+	1.66614i
$601$	−22.2838	+	22.2838i	−0.908977	+	0.908977i	−0.996190	−	0.0872129i	$-0.972204\pi$
$601$	−22.2838	+	22.2838i	−0.908977	+	0.908977i	0.0872129	+	0.996190i	$0.472204\pi$
$602$	−23.3066	+	40.1975i	−0.949905	+	1.63833i
$603$	−47.2059			−1.92237
$604$	−7.61283	+	27.9997i	−0.309761	+	1.13929i
$605$	1.86308	+	4.13272i	0.0757450	+	0.168019i
$606$	−27.8281	+	47.9960i	−1.13044	+	1.94970i
$607$	11.4728	−	11.4728i	0.465666	−	0.465666i	−0.434841	−	0.900507i	$-0.643195\pi$
$607$	11.4728	−	11.4728i	0.465666	−	0.465666i	0.900507	+	0.434841i	$0.143195\pi$
$608$	−16.6543	−	29.4675i	−0.675420	−	1.19507i
$609$	−58.4913	−	58.4913i	−2.37019	−	2.37019i
$610$	−12.0766	−	14.8279i	−0.488968	−	0.600363i
$611$		−	41.7132i		−	1.68753i
$612$	−24.8894	−	43.4777i	−1.00610	−	1.75748i
$613$	11.5024	−	11.5024i	0.464577	−	0.464577i	−0.435575	−	0.900152i	$-0.643455\pi$
$613$	11.5024	−	11.5024i	0.464577	−	0.464577i	0.900152	+	0.435575i	$0.143455\pi$
$614$	−5.06713	+	8.73943i	−0.204493	+	0.352695i
$615$	−5.91153	+	40.9598i	−0.238376	+	1.65166i
$616$	−33.6353	−	0.185281i	−1.35520	−	0.00746520i
$617$	3.02791	+	3.02791i	0.121899	+	0.121899i	0.765425	−	0.643526i	$-0.222529\pi$
$617$	3.02791	+	3.02791i	0.121899	+	0.121899i	−0.643526	+	0.765425i	$0.722529\pi$
$618$	−22.4578	−	13.0211i	−0.903386	−	0.523784i
$619$	26.1115			1.04951			0.524755	−	0.851253i	$-0.324157\pi$
$619$	26.1115			1.04951			0.524755	+	0.851253i	$0.324157\pi$
$620$	14.2848	+	10.3572i	0.573691	+	0.415955i
$621$	17.9961	−	17.9961i	0.722158	−	0.722158i
$622$	−17.9572	−	10.4116i	−0.720017	−	0.417467i
$623$	−19.6302	−	19.6302i	−0.786467	−	0.786467i
$624$	−54.8138	−	32.1858i	−2.19431	−	1.28846i
$625$	−3.07519	−	24.8101i	−0.123008	−	0.992406i
$626$	2.12169	−	0.564332i	0.0847999	−	0.0225553i
$627$			51.8059i			2.06893i
$628$	2.98356	−	1.70798i	0.119057	−	0.0681559i
$629$	18.4155	+	18.4155i	0.734275	+	0.734275i
$630$	−42.4506	−	52.1216i	−1.69127	−	2.07657i
$631$		−	2.37388i		−	0.0945028i	−0.998883	−	0.0472514i	$-0.984954\pi$
$631$		−	2.37388i		−	0.0945028i	0.998883	−	0.0472514i	$-0.0150462\pi$
$632$	−4.17243	−	0.0229840i	−0.165970	−	0.000914254i
$633$	−5.99538	−	5.99538i	−0.238295	−	0.238295i
$634$	7.52741	−	2.00216i	0.298951	−	0.0795158i
$635$	−26.8258	−	10.1546i	−1.06455	−	0.402973i
$636$	19.0005	+	33.1907i	0.753419	+	1.31610i
$637$			48.1688i			1.90852i
$638$	−7.84942	−	29.5111i	−0.310762	−	1.16835i
$639$	−42.1643	+	42.1643i	−1.66799	+	1.66799i
$640$	15.7589	+	19.7903i	0.622924	+	0.782282i
$641$	23.1051	−	23.1051i	0.912595	−	0.912595i	−0.0838808	−	0.996476i	$-0.526732\pi$
$641$	23.1051	−	23.1051i	0.912595	−	0.912595i	0.996476	+	0.0838808i	$0.0267315\pi$
$642$	−40.8973	−	23.7123i	−1.61409	−	0.935849i
$643$	10.6945			0.421748			0.210874	−	0.977513i	$-0.432369\pi$
$643$	10.6945			0.421748			0.210874	+	0.977513i	$0.432369\pi$
$644$	28.6544	+	7.79081i	1.12914	+	0.307001i
$645$	−50.0246	−	18.9362i	−1.96972	−	0.745614i
$646$	−34.2470	−	19.8564i	−1.34743	−	0.781241i
$647$	−26.7516	+	26.7516i	−1.05171	+	1.05171i	−0.0531249	+	0.998588i	$0.516918\pi$
$647$	−26.7516	+	26.7516i	−1.05171	+	1.05171i	−0.998588	+	0.0531249i	$0.983082\pi$
$648$	−7.25265	+	7.17319i	−0.284911	+	0.281789i
$649$	14.6730	−	14.6730i	0.575965	−	0.575965i
$650$	34.7697	+	17.3904i	1.36378	+	0.682107i
$651$	−45.2738			−1.77442
$652$	2.46809	−	9.07756i	0.0966579	−	0.355505i
$653$		−	19.0085i		−	0.743860i	−0.928261	−	0.371930i	$-0.878696\pi$
$653$		−	19.0085i		−	0.743860i	0.928261	−	0.371930i	$-0.121304\pi$
$654$	45.5383	+	26.4032i	1.78069	+	1.03245i
$655$	0.493414	−	0.222437i	0.0192793	−	0.00869133i
$656$	11.6677	+	22.8005i	0.455549	+	0.890211i
$657$	26.6406	−	26.6406i	1.03935	−	1.03935i
$658$	−10.9495	−	41.1663i	−0.426856	−	1.60483i
$659$	5.89061	+	5.89061i	0.229466	+	0.229466i	0.812469	−	0.583004i	$-0.198123\pi$
$659$	5.89061	+	5.89061i	0.229466	+	0.229466i	−0.583004	+	0.812469i	$0.698123\pi$
$660$	−6.09451	−	38.2372i	−0.237228	−	1.48838i
$661$		−	15.8159i		−	0.615166i	−0.951521	−	0.307583i	$-0.900480\pi$
$661$		−	15.8159i		−	0.615166i	0.951521	−	0.307583i	$-0.0995202\pi$
$662$	5.69569	−	9.82352i	0.221369	−	0.381802i
$663$	−74.3419			−2.88720
$664$	−0.0301401	+	5.47153i	−0.00116966	+	0.212336i
$665$	−49.6779	−	18.8050i	−1.92643	−	0.729226i
$666$	21.1445	−	36.4685i	0.819332	−	1.41313i
$667$			26.9591i			1.04386i
$668$	6.68634	+	11.6799i	0.258702	+	0.451910i
$669$	−10.2857	+	10.2857i	−0.397669	+	0.397669i
$670$	21.6170	−	17.6060i	0.835136	−	0.680180i
$671$	12.8090	+	12.8090i	0.494485	+	0.494485i
$672$	−62.5438	−	17.3755i	−2.41268	−	0.670276i
$673$	6.60956			0.254780			0.127390	−	0.991853i	$-0.459340\pi$
$673$	6.60956			0.254780			0.127390	+	0.991853i	$0.459340\pi$
$674$	14.8785	+	8.62656i	0.573098	+	0.332283i
$675$	22.5317	−	25.4969i	0.867246	−	0.981376i
$676$	−29.9013	+	17.1174i	−1.15005	+	0.658363i
$677$	17.3019	+	17.3019i	0.664966	+	0.664966i	0.956546	−	0.291581i	$-0.0941811\pi$
$677$	17.3019	+	17.3019i	0.664966	+	0.664966i	−0.291581	+	0.956546i	$0.594181\pi$
$678$	50.2971	+	29.1623i	1.93165	+	1.11997i
$679$	20.6755			0.793452
$680$	27.6131	+	10.6269i	1.05892	+	0.407523i
$681$	19.7163			0.755530
$682$	−14.4590	−	8.38335i	−0.553664	−	0.321015i
$683$		−	26.3718i		−	1.00909i	−0.863386	−	0.504544i	$-0.831661\pi$
$683$		−	26.3718i		−	1.00909i	0.863386	−	0.504544i	$-0.168339\pi$
$684$	−16.8116	+	61.8324i	−0.642806	+	2.36422i
$685$	−1.70160	−	3.77452i	−0.0650148	−	0.144217i
$686$	2.54184	+	9.55642i	0.0970478	+	0.364866i
$687$	33.8464	+	33.8464i	1.29132	+	1.29132i
$688$	−32.0380	+	8.33284i	−1.22144	+	0.317687i
$689$	36.3731			1.38570
$690$	−3.47742	+	34.0057i	−0.132383	+	1.29457i
$691$	−5.58695	−	5.58695i	−0.212538	−	0.212538i	0.592807	−	0.805345i	$-0.298020\pi$
$691$	−5.58695	−	5.58695i	−0.212538	−	0.212538i	−0.805345	+	0.592807i	$0.798020\pi$
$692$	0.481761	−	1.77190i	0.0183138	−	0.0673576i
$693$	45.0250	+	45.0250i	1.71036	+	1.71036i
$694$	−35.1603	+	9.35201i	−1.33467	+	0.354998i
$695$	−15.6434	+	7.05225i	−0.593390	+	0.267507i
$696$	0.324628	−	58.9317i	0.0123050	−	2.23380i
$697$	25.2697	+	16.0855i	0.957158	+	0.609282i
$698$	−7.35407	+	1.95605i	−0.278356	+	0.0740376i
$699$		−	21.3837i		−	0.808805i
$700$	38.8788	+	8.03552i	1.46948	+	0.303714i
$701$	−4.86224			−0.183644			−0.0918221	−	0.995775i	$-0.529269\pi$
$701$	−4.86224			−0.183644			−0.0918221	+	0.995775i	$0.529269\pi$
$702$	13.6008	+	51.1342i	0.513328	+	1.92994i
$703$		−	33.3106i		−	1.25633i
$704$	−16.7571	−	17.1304i	−0.631556	−	0.645627i
$705$	44.7037	−	20.1530i	1.68364	−	0.759004i
$706$	38.2560	+	22.1809i	1.43978	+	0.834789i
$707$	38.1016	+	38.1016i	1.43296	+	1.43296i
$708$	34.7543	−	19.8956i	1.30615	−	0.747722i
$709$	−5.10370	+	5.10370i	−0.191673	+	0.191673i	−0.796419	−	0.604745i	$-0.793275\pi$
$709$	−5.10370	+	5.10370i	−0.191673	+	0.191673i	0.604745	+	0.796419i	$0.293275\pi$
$710$	3.58257	−	35.0339i	0.134451	−	1.31480i
$711$	5.58531	+	5.58531i	0.209466	+	0.209466i
$712$	0.108948	−	19.7780i	0.00408299	−	0.741211i
$713$	10.4335	+	10.4335i	0.390738	+	0.390738i
$714$	−73.3673	+	19.5144i	−2.74570	+	0.730308i
$715$	−34.4402	−	13.0369i	−1.28799	−	0.487554i
$716$	8.03897	−	29.5671i	0.300431	−	1.10497i
$717$	18.1257	+	18.1257i	0.676917	+	0.676917i
$718$	−1.71770	+	0.456878i	−0.0641041	+	0.0170505i
$719$	−12.2870	+	12.2870i	−0.458229	+	0.458229i	−0.898074	−	0.439845i	$-0.855034\pi$
$719$	−12.2870	+	12.2870i	−0.458229	+	0.458229i	0.439845	+	0.898074i	$0.355034\pi$
$720$	5.13433	−	47.6153i	0.191345	−	1.77452i
$721$	−17.8281	+	17.8281i	−0.663955	+	0.663955i
$722$	6.10823	+	22.9648i	0.227325	+	0.854661i
$723$		−	64.8631i		−	2.41229i
$724$	−1.74900	+	6.43276i	−0.0650010	+	0.239072i
$725$	2.22101	+	35.9747i	0.0824863	+	1.33607i
$726$	−2.13014	−	8.00858i	−0.0790569	−	0.297226i
$727$		−	41.1680i		−	1.52684i	−0.645904	−	0.763419i	$-0.723519\pi$
$727$		−	41.1680i		−	1.52684i	0.645904	−	0.763419i	$-0.276481\pi$
$728$	−43.8938	+	43.4129i	−1.62681	+	1.60899i
$729$	−39.6985			−1.47031
$730$	−2.26358	+	22.1355i	−0.0837787	+	0.819270i
$731$	−27.3767	+	27.3767i	−1.01256	+	1.01256i
$732$	17.3681	+	30.3392i	0.641943	+	1.12137i
$733$	16.8082	−	16.8082i	0.620826	−	0.620826i	−0.324916	−	0.945743i	$-0.605336\pi$
$733$	16.8082	−	16.8082i	0.620826	−	0.620826i	0.945743	+	0.324916i	$0.105336\pi$
$734$	6.01926	−	10.3816i	0.222175	−	0.383192i
$735$	−51.6221	+	23.2719i	−1.90411	+	0.858396i
$736$	10.4092	+	18.4177i	0.383688	+	0.678885i
$737$	−18.6737	+	18.6737i	−0.687854	+	0.687854i
$738$	14.6480	−	46.2207i	0.539200	−	1.70141i
$739$	52.1405			1.91802			0.959009	−	0.283374i	$-0.0914537\pi$
$739$	52.1405			1.91802			0.959009	+	0.283374i	$0.0914537\pi$
$740$	3.91870	+	24.5861i	0.144054	+	0.903802i
$741$	67.2361	+	67.2361i	2.46998	+	2.46998i
$742$	35.8962	−	9.54775i	1.31779	−	0.350509i
$743$	−5.84030	−	5.84030i	−0.214260	−	0.214260i	0.591814	−	0.806074i	$-0.298412\pi$
$743$	−5.84030	−	5.84030i	−0.214260	−	0.214260i	−0.806074	+	0.591814i	$0.798412\pi$
$744$	−22.6817	−	22.9330i	−0.831552	−	0.840764i
$745$	42.7629	+	16.1874i	1.56671	+	0.593060i
$746$	−2.40693	−	1.39554i	−0.0881238	−	0.0510943i
$747$	7.32432	−	7.32432i	0.267983	−	0.267983i
$748$	−27.0446	−	7.35314i	−0.988850	−	0.268857i
$749$	−32.4663	+	32.4663i	−1.18629	+	1.18629i
$750$	−1.83879	+	45.6642i	−0.0671432	+	1.66742i
$751$	−30.4466	+	30.4466i	−1.11101	+	1.11101i	−0.118000	+	0.993014i	$0.537648\pi$
$751$	−30.4466	+	30.4466i	−1.11101	+	1.11101i	−0.993014	+	0.118000i	$0.962352\pi$
$752$	15.3668	−	26.1703i	0.560369	−	0.954331i
$753$	7.85799			0.286361
$754$	−48.4881	−	28.1135i	−1.76583	−	1.02383i
$755$	−11.4849	+	30.3401i	−0.417978	+	1.10419i
$756$	26.8450	+	46.8937i	0.976341	+	1.70551i
$757$		−	23.8184i		−	0.865695i	−0.901467	−	0.432847i	$-0.857509\pi$
$757$		−	23.8184i		−	0.865695i	0.901467	−	0.432847i	$-0.142491\pi$
$758$	8.72171	−	2.31982i	0.316787	−	0.0842596i
$759$		−	32.3796i		−	1.17530i
$760$	−15.3626	−	34.5849i	−0.557261	−	1.25453i
$761$	−0.854509			−0.0309759			−0.0154880	−	0.999880i	$-0.504930\pi$
$761$	−0.854509			−0.0309759			−0.0154880	+	0.999880i	$0.504930\pi$
$762$	45.3616	+	26.3007i	1.64328	+	0.952774i
$763$	36.1506	−	36.1506i	1.30874	−	1.30874i
$764$	−15.1374	−	4.11569i	−0.547651	−	0.148900i
$765$	−23.0195	−	51.0622i	−0.832270	−	1.84616i
$766$	−12.0463	−	45.2897i	−0.435249	−	1.63638i
$767$		−	38.0865i		−	1.37522i
$768$	−22.5324	−	40.3859i	−0.813069	−	1.45730i
$769$		−	19.1960i		−	0.692225i	−0.938193	−	0.346112i	$-0.887502\pi$
$769$		−	19.1960i		−	0.692225i	0.938193	−	0.346112i	$-0.112498\pi$
$770$	−37.4108	−	3.82564i	−1.34819	−	0.137866i
$771$	−23.4725			−0.845342
$772$	−19.4062	−	33.8995i	−0.698446	−	1.22007i
$773$	27.6369			0.994031			0.497015	−	0.867742i	$-0.334429\pi$
$773$	27.6369			0.994031			0.497015	+	0.867742i	$0.334429\pi$
$774$	54.2145	+	31.4336i	1.94870	+	1.12986i
$775$	14.7822	+	13.0631i	0.530993	+	0.469240i
$776$	10.3582	+	10.4730i	0.371838	+	0.375957i
$777$	−45.1711	−	45.1711i	−1.62050	−	1.62050i
$778$	−49.4929	+	13.1642i	−1.77441	+	0.471960i
$779$	−8.30633	−	37.4023i	−0.297605	−	1.34008i
$780$	−57.5357	−	41.7162i	−2.06011	−	1.49368i
$781$			33.3586i			1.19367i
$782$	21.4049	+	12.4106i	0.765438	+	0.443802i
$783$	−34.6880	+	34.6880i	−1.23965	+	1.23965i
$784$	−17.7450	+	30.2204i	−0.633750	+	1.07930i
$785$	3.50403	−	1.57966i	0.125064	−	0.0563804i
$786$	−0.956160	+	0.254322i	−0.0341051	+	0.00907135i
$787$	−1.73587	+	1.73587i	−0.0618770	+	0.0618770i	−0.737368	−	0.675491i	$-0.763932\pi$
$787$	−1.73587	+	1.73587i	−0.0618770	+	0.0618770i	0.675491	+	0.737368i	$0.263932\pi$
$788$	2.92257	+	0.794614i	0.104112	+	0.0283070i
$789$		−	31.2568i		−	1.11277i
$790$	−4.64078	−	0.474567i	−0.165112	−	0.0168843i
$791$	39.9283	−	39.9283i	1.41969	−	1.41969i
$792$	−0.249889	+	45.3640i	−0.00887944	+	1.61194i
$793$	33.2481			1.18067
$794$	−9.60010	+	2.55345i	−0.340695	+	0.0906187i
$795$	17.5730	+	38.9807i	0.623249	+	1.38250i
$796$	−3.37570	+	12.4157i	−0.119649	+	0.440064i
$797$	−10.2727	+	10.2727i	−0.363877	+	0.363877i	−0.865238	−	0.501361i	$-0.832833\pi$
$797$	−10.2727	+	10.2727i	−0.363877	+	0.363877i	0.501361	+	0.865238i	$0.332833\pi$
$798$	84.0038	+	48.7055i	2.97370	+	1.72415i
$799$		−	35.4937i		−	1.25568i
$800$	15.4075	+	23.7193i	0.544739	+	0.838606i
$801$	−26.4753	+	26.4753i	−0.935458	+	0.935458i
$802$	4.58914	+	17.2535i	0.162048	+	0.609244i
$803$		−	21.0770i		−	0.743790i
$804$	−44.2303	+	25.3203i	−1.55988	+	0.892977i
$805$	31.0495	+	11.7534i	1.09435	+	0.414254i
$806$	−29.6458	+	7.88526i	−1.04423	+	0.277746i
$807$		−	55.9824i		−	1.97067i
$808$	−0.211465	+	38.3885i	−0.00743930	+	1.35050i
$809$	38.8381	−	38.8381i	1.36547	−	1.36547i	0.498697	−	0.866776i	$-0.333812\pi$
$809$	38.8381	−	38.8381i	1.36547	−	1.36547i	0.866776	−	0.498697i	$-0.166188\pi$
$810$	−8.84297	+	7.20219i	−0.310710	+	0.253059i
$811$	19.9152			0.699319			0.349659	−	0.936877i	$-0.386297\pi$
$811$	19.9152			0.699319			0.349659	+	0.936877i	$0.386297\pi$
$812$	−55.2321	−	15.0170i	−1.93827	−	0.526994i
$813$		−	48.5041i		−	1.70111i
$814$	−6.06187	−	22.7905i	−0.212468	−	0.798807i
$815$	3.72342	−	9.83632i	0.130426	−	0.344551i
$816$	−46.6411	−	27.3869i	−1.63276	−	0.958735i
$817$	49.5199			1.73248
$818$	1.26591	+	4.75938i	0.0442615	+	0.166408i
$819$	116.871			4.08380
$820$	10.5308	+	26.6290i	0.367753	+	0.929924i
$821$	21.2860			0.742887			0.371444	−	0.928455i	$-0.378863\pi$
$821$	21.2860			0.742887			0.371444	+	0.928455i	$0.378863\pi$
$822$	1.94551	+	7.31445i	0.0678575	+	0.255121i
$823$	23.2629			0.810893			0.405446	−	0.914119i	$-0.367116\pi$
$823$	23.2629			0.810893			0.405446	+	0.914119i	$0.367116\pi$
$824$	−17.9624	−	0.0989466i	−0.625749	−	0.00344697i
$825$	−2.66758	−	43.2078i	−0.0928731	−	1.50430i
$826$	−9.99753	−	37.5872i	−0.347858	−	1.30783i
$827$			12.1337i			0.421929i	0.977494	+	0.210964i	$0.0676604\pi$
$827$			12.1337i			0.421929i	−0.977494	+	0.210964i	$0.932340\pi$
$828$	10.5075	−	38.6463i	0.365161	−	1.34305i
$829$	27.7302			0.963108			0.481554	−	0.876416i	$-0.340072\pi$
$829$	27.7302			0.963108			0.481554	+	0.876416i	$0.340072\pi$
$830$	−0.622325	+	6.08571i	−0.0216012	+	0.211238i
$831$	−24.3642	+	24.3642i	−0.845184	+	0.845184i
$832$	−43.9807	−	0.484554i	−1.52476	−	0.0167989i
$833$			40.9869i			1.42011i
$834$	30.3146	−	8.06314i	1.04971	−	0.279204i
$835$	6.18399	+	13.7174i	0.214006	+	0.474712i
$836$	17.8093	+	31.1099i	0.615948	+	1.07596i
$837$			26.8494i			0.928051i
$838$	0.541040	+	2.03412i	0.0186899	+	0.0702675i
$839$	33.9785	−	33.9785i	1.17307	−	1.17307i	0.191596	−	0.981474i	$-0.438634\pi$
$839$	33.9785	−	33.9785i	1.17307	−	1.17307i	0.981474	−	0.191596i	$-0.0613663\pi$
$840$	−67.7317	−	26.0665i	−2.33697	−	0.899380i
$841$		−	22.9643i		−	0.791874i
$842$	9.33946	+	5.41503i	0.321859	+	0.186614i
$843$	−0.707670	+	0.707670i	−0.0243735	+	0.0243735i
$844$	−5.66131	−	1.53925i	−0.194870	−	0.0529832i
$845$	−35.1175	+	15.8314i	−1.20808	+	0.544617i
$846$	−55.5211	+	14.7676i	−1.90886	+	0.507722i
$847$	−8.04862			−0.276554
$848$	22.8199	+	13.3995i	0.783640	+	0.460142i
$849$	−36.4066	+	36.4066i	−1.24947	+	1.24947i
$850$	29.5855	+	14.7975i	1.01478	+	0.507549i
$851$			20.8197i			0.713689i
$852$	−16.8904	+	62.1225i	−0.578656	+	2.12828i
$853$	29.6879	−	29.6879i	1.01649	−	1.01649i	0.0166325	−	0.999862i	$-0.494705\pi$
$853$	29.6879	−	29.6879i	1.01649	−	1.01649i	0.999862	−	0.0166325i	$-0.00529452\pi$
$854$	32.8122	−	8.72747i	1.12281	−	0.298648i
$855$	−25.3623	+	67.0007i	−0.867373	+	2.29138i
$856$	−32.7107	−	0.180189i	−1.11803	−	0.00615872i
$857$	36.5526	−	36.5526i	1.24861	−	1.24861i	0.292281	−	0.956333i	$-0.405586\pi$
$857$	36.5526	−	36.5526i	1.24861	−	1.24861i	0.956333	−	0.292281i	$-0.0944141\pi$
$858$	58.2373	+	33.7661i	1.98819	+	1.15275i
$859$			52.4327i			1.78898i	0.447086	+	0.894491i	$0.352462\pi$
$859$			52.4327i			1.78898i	−0.447086	+	0.894491i	$0.647538\pi$
$860$	−36.5500	+	5.82558i	−1.24634	+	0.198651i
$861$	−61.9836	−	39.4558i	−2.11239	−	1.34465i
$862$	38.2394	−	10.1710i	1.30244	−	0.346426i
$863$	26.3665	+	26.3665i	0.897526	+	0.897526i	0.995217	−	0.0976910i	$-0.0311457\pi$
$863$	26.3665	+	26.3665i	0.897526	+	0.897526i	−0.0976910	+	0.995217i	$0.531146\pi$
$864$	−10.3045	+	37.0913i	−0.350565	+	1.26187i
$865$	0.726797	−	1.92001i	0.0247118	−	0.0652822i
$866$	−42.9094	−	24.8789i	−1.45812	−	0.845420i
$867$	−14.1207			−0.479565
$868$	−27.1873	+	15.5638i	−0.922798	+	0.528269i
$869$	4.41887			0.149900
$870$	6.70283	−	65.5468i	0.227247	−	2.22225i
$871$			48.4711i			1.64238i
$872$	36.4228	+	0.200636i	1.23343	+	0.00679441i
$873$		−	27.8851i		−	0.943767i
$874$	−8.13461	−	30.5833i	−0.275157	−	1.03450i
$875$	42.4013	+	13.1260i	1.43342	+	0.443739i
$876$	10.6719	−	39.2508i	0.360569	−	1.32616i
$877$	−22.1149	+	22.1149i	−0.746768	+	0.746768i	−0.973871	−	0.227102i	$-0.927075\pi$
$877$	−22.1149	+	22.1149i	−0.746768	+	0.746768i	0.227102	+	0.973871i	$0.427075\pi$
$878$	−13.4516	−	7.79928i	−0.453971	−	0.263213i
$879$	32.1650			1.08490
$880$	−16.8046	−	20.8667i	−0.566483	−	0.703416i
$881$			9.30681i			0.313554i	0.987634	+	0.156777i	$0.0501105\pi$
$881$			9.30681i			0.313554i	−0.987634	+	0.156777i	$0.949890\pi$
$882$	64.1137	−	17.0531i	2.15882	−	0.574208i
$883$			41.2787i			1.38914i	0.719425	+	0.694570i	$0.244405\pi$
$883$			41.2787i			1.38914i	−0.719425	+	0.694570i	$0.755595\pi$
$884$	−44.6430	+	25.5565i	−1.50151	+	0.859558i
$885$	40.8170	−	18.4008i	1.37205	−	0.618536i
$886$	−1.80296	−	1.04536i	−0.0605716	−	0.0351195i
$887$	21.8934			0.735109			0.367554	−	0.930002i	$-0.380195\pi$
$887$	21.8934			0.735109			0.367554	+	0.930002i	$0.380195\pi$
$888$	0.250700	−	45.5112i	0.00841295	−	1.52726i
$889$	36.0103	−	36.0103i	1.20775	−	1.20775i
$890$	2.24952	−	21.9981i	0.0754042	−	0.737377i
$891$	7.63895	−	7.63895i	0.255914	−	0.255914i
$892$	−2.64074	+	9.71258i	−0.0884186	+	0.325201i
$893$	−32.1011	+	32.1011i	−1.07422	+	1.07422i
$894$	−72.3107	−	41.9258i	−2.41843	−	1.40221i
$895$	12.1278	−	32.0385i	0.405387	−	1.07093i
$896$	−43.5313	+	11.0665i	−1.45428	+	0.369707i
$897$	−42.0236	−	42.0236i	−1.40313	−	1.40313i
$898$	3.23386	−	0.860148i	0.107915	−	0.0287035i
$899$	−20.1109	−	20.1109i	−0.670735	−	0.670735i
$900$	10.8375	−	52.4359i	0.361251	−	1.74786i
$901$	30.9498			1.03109
$902$	−12.4895	−	24.0784i	−0.415856	−	0.801724i
$903$	67.1519	−	67.1519i	2.23467	−	2.23467i
$904$	40.2290	+	0.221603i	1.33800	+	0.00737040i
$905$	−2.63858	+	6.97045i	−0.0877094	+	0.231706i
$906$	29.7462	−	51.3042i	0.988253	−	1.70447i
$907$	−0.978011	+	0.978011i	−0.0324743	+	0.0324743i	−0.723157	−	0.690683i	$-0.757310\pi$
$907$	−0.978011	+	0.978011i	−0.0324743	+	0.0324743i	0.690683	+	0.723157i	$0.257310\pi$
$908$	11.8398	−	6.77787i	0.392918	−	0.224931i
$909$	51.3878	−	51.3878i	1.70442	−	1.70442i
$910$	−53.5186	+	43.5884i	−1.77412	+	1.44494i
$911$	−46.5805			−1.54328			−0.771640	−	0.636060i	$-0.780563\pi$
$911$	−46.5805			−1.54328			−0.771640	+	0.636060i	$0.780563\pi$
$912$	17.4138	+	66.9522i	0.576627	+	2.21701i
$913$		−	5.79470i		−	0.191777i
$914$	−3.53432	−	13.2878i	−0.116905	−	0.439522i
$915$	16.0632	+	35.6317i	0.531033	+	1.17795i
$916$	31.9604	+	8.68969i	1.05600	+	0.287116i
$917$			0.960941i			0.0317331i
$918$	11.5729	+	43.5101i	0.381963	+	1.43605i
$919$	−32.4294	+	32.4294i	−1.06975	+	1.06975i	−0.0723701	+	0.997378i	$0.523056\pi$
$919$	−32.4294	+	32.4294i	−1.06975	+	1.06975i	−0.997378	+	0.0723701i	$0.976944\pi$
$920$	9.60190	+	21.6161i	0.316565	+	0.712663i
$921$	14.5996	−	14.5996i	0.481074	−	0.481074i
$922$	−47.2713	+	12.5733i	−1.55680	+	0.414080i
$923$	43.2943	+	43.2943i	1.42505	+	1.42505i
$924$	66.3373	+	18.0364i	2.18234	+	0.593354i
$925$	1.71522	+	27.7821i	0.0563961	+	0.913471i
$926$	30.1306	−	8.01421i	0.990154	−	0.263363i
$927$	24.0449	+	24.0449i	0.789737	+	0.789737i
$928$	−20.0640	−	35.5006i	−0.658633	−	1.16537i
$929$	30.1813	+	30.1813i	0.990218	+	0.990218i	0.999953	−	0.00973503i	$-0.00309881\pi$
$929$	30.1813	+	30.1813i	0.990218	+	0.990218i	−0.00973503	+	0.999953i	$0.503099\pi$
$930$	−22.7734	−	27.9616i	−0.746769	−	0.916896i
$931$	37.0692	−	37.0692i	1.21489	−	1.21489i
$932$	−7.35107	−	12.8411i	−0.240792	−	0.420624i
$933$	29.9983	+	29.9983i	0.982100	+	0.982100i
$934$	16.5034	+	9.56871i	0.540009	+	0.313098i
$935$	−29.3052	−	11.0931i	−0.958382	−	0.362784i
$936$	58.5511	+	59.1997i	1.91380	+	1.93500i
$937$			57.0303i			1.86310i	0.363616	+	0.931549i	$0.381542\pi$
$937$			57.0303i			1.86310i	−0.363616	+	0.931549i	$0.618458\pi$
$938$	12.7234	+	47.8357i	0.415435	+	1.56189i
$939$	−4.48713			−0.146432
$940$	19.9170	−	27.4698i	0.649620	−	0.895966i
$941$			48.5768i			1.58356i	0.610808	+	0.791778i	$0.290845\pi$
$941$			48.5768i			1.58356i	−0.610808	+	0.791778i	$0.709155\pi$
$942$	−6.79027	+	1.80609i	−0.221239	+	0.0588456i
$943$	5.19159	+	23.3771i	0.169062	+	0.761262i
$944$	14.0308	−	23.8949i	0.456662	−	0.777714i
$945$	24.8281	+	55.0741i	0.807657	+	1.79156i
$946$	33.8807	−	9.01165i	1.10155	−	0.292994i
$947$	24.4622	+	24.4622i	0.794913	+	0.794913i	0.982288	−	0.187375i	$-0.0599979\pi$
$947$	24.4622	+	24.4622i	0.794913	+	0.794913i	−0.187375	+	0.982288i	$0.559998\pi$
$948$	8.22909	+	2.23740i	0.267268	+	0.0726673i
$949$	−27.3547	−	27.3547i	−0.887970	−	0.887970i
$950$	−13.3746	−	40.1407i	−0.433928	−	1.30234i
$951$	−15.9196			−0.516228
$952$	−37.3493	+	36.9400i	−1.21050	+	1.19723i
$953$	−13.4867	−	13.4867i	−0.436876	−	0.436876i	0.454083	−	0.890959i	$-0.349967\pi$
$953$	−13.4867	−	13.4867i	−0.436876	−	0.436876i	−0.890959	+	0.454083i	$0.849967\pi$
$954$	−12.8771	−	48.4133i	−0.416911	−	1.56744i
$955$	−16.4027	−	6.20903i	−0.530777	−	0.200920i
$956$	17.1157	+	4.65358i	0.553562	+	0.150507i
$957$			62.4125i			2.01751i
$958$	24.7317	+	14.3395i	0.799045	+	0.463287i
$959$	7.35102			0.237377
$960$	−20.7292	−	47.3679i	−0.669031	−	1.52879i
$961$	15.4337			0.497860
$962$	−37.4459	−	21.7112i	−1.20730	−	0.699997i
$963$	43.7874	+	43.7874i	1.41103	+	1.41103i
$964$	−22.2980	−	38.9509i	−0.718170	−	1.25452i
$965$	−17.9482	−	39.8131i	−0.577774	−	1.28163i
$966$	−52.5037	−	30.4417i	−1.68928	−	0.979446i
$967$	36.3493			1.16891			0.584457	−	0.811425i	$-0.301308\pi$
$967$	36.3493			1.16891			0.584457	+	0.811425i	$0.301308\pi$
$968$	−4.03227	−	4.07694i	−0.129602	−	0.131038i
$969$	57.2112	+	57.2112i	1.83789	+	1.83789i
$970$	10.4001	+	12.7694i	0.333926	+	0.410000i
$971$	−40.6018	+	40.6018i	−1.30297	+	1.30297i	−0.376597	+	0.926377i	$0.622906\pi$
$971$	−40.6018	+	40.6018i	−1.30297	+	1.30297i	−0.926377	+	0.376597i	$0.877094\pi$
$972$	−17.3421	+	9.92771i	−0.556247	+	0.318432i
$973$		−	30.4662i		−	0.976700i
$974$	−7.80242	+	13.4571i	−0.250006	+	0.431192i
$975$	−59.5392	−	52.6150i	−1.90678	−	1.68503i
$976$	20.8594	+	12.2483i	0.667693	+	0.392059i
$977$	23.4482			0.750176			0.375088	−	0.926989i	$-0.377613\pi$
$977$	23.4482			0.750176			0.375088	+	0.926989i	$0.377613\pi$
$978$	−9.64378	+	16.6329i	−0.308374	+	0.531862i
$979$			20.9462i			0.669442i
$980$	−22.9994	+	31.7211i	−0.734688	+	1.01329i
$981$	−48.7564	−	48.7564i	−1.55667	−	1.55667i
$982$	−4.28695	−	16.1174i	−0.136802	−	0.514328i
$983$	5.03443	−	5.03443i	0.160573	−	0.160573i	−0.622247	−	0.782821i	$-0.713780\pi$
$983$	5.03443	−	5.03443i	0.160573	−	0.160573i	0.782821	+	0.622247i	$0.213780\pi$
$984$	−11.0672	−	51.1641i	−0.352809	−	1.63105i
$985$	3.16685	+	1.19877i	0.100904	+	0.0381961i
$986$	−41.2586	−	23.9218i	−1.31394	−	0.761824i
$987$			87.0620i			2.77121i
$988$	63.4896	+	17.2621i	2.01987	+	0.549181i
$989$	−30.9508			−0.984177
$990$	−5.15965	+	50.4561i	−0.163984	+	1.60360i
$991$	35.6129	−	35.6129i	1.13128	−	1.13128i	0.141316	−	0.989964i	$-0.454867\pi$
$991$	35.6129	−	35.6129i	1.13128	−	1.13128i	0.989964	−	0.141316i	$-0.0451335\pi$
$992$	−21.5042	−	5.97417i	−0.682760	−	0.189680i
$993$	−16.4107	+	16.4107i	−0.520777	+	0.520777i
$994$	54.0913	+	31.3622i	1.71567	+	0.994749i
$995$	−5.09267	+	13.4535i	−0.161448	+	0.426505i
$996$	2.93402	−	10.7912i	0.0929680	−	0.341934i
$997$	0.0795810			0.00252036			0.00126018	−	0.999999i	$-0.499599\pi$
$997$	0.0795810			0.00252036			0.00126018	+	0.999999i	$0.499599\pi$
$998$	−50.3619	−	29.1999i	−1.59418	−	0.924307i
$999$	−26.7885	+	26.7885i	−0.847549	+	0.847549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.583.10	yes	240
4.3	odd	2	inner	820.2.s.c.583.71	yes	240
5.2	odd	4		820.2.j.c.747.50	yes	240
20.7	even	4		820.2.j.c.747.111	yes	240
41.32	even	4		820.2.j.c.483.111	yes	240
164.155	odd	4		820.2.j.c.483.50	✓	240
205.32	odd	4	inner	820.2.s.c.647.71	yes	240
820.647	even	4	inner	820.2.s.c.647.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.50	✓	240	164.155	odd	4
820.2.j.c.483.111	yes	240	41.32	even	4
820.2.j.c.747.50	yes	240	5.2	odd	4
820.2.j.c.747.111	yes	240	20.7	even	4
820.2.s.c.583.10	yes	240	1.1	even	1	trivial
820.2.s.c.583.71	yes	240	4.3	odd	2	inner
820.2.s.c.647.10	yes	240	820.647	even	4	inner
820.2.s.c.647.71	yes	240	205.32	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36670 + 0.363517i) q^{2} +2.89040 q^{3} +(1.73571 - 0.993633i) q^{4} +(2.03850 - 0.918980i) q^{5} +(-3.95030 + 1.05071i) q^{6} +3.97005i q^{7} +(-2.01099 + 1.98895i) q^{8} +5.35442 q^{9} +(-2.45194 + 1.99699i) q^{10} +(2.11810 - 2.11810i) q^{11} +(5.01690 - 2.87200i) q^{12} -5.49792i q^{13} +(-1.44318 - 5.42584i) q^{14} +(5.89208 - 2.65622i) q^{15} +(2.02539 - 3.44932i) q^{16} -4.67818i q^{17} +(-7.31785 + 1.94642i) q^{18} +(-4.23103 + 4.23103i) q^{19} +(2.62512 - 3.62060i) q^{20} +11.4750i q^{21} +(-2.12483 + 3.66476i) q^{22} +(2.64446 - 2.64446i) q^{23} +(-5.81256 + 5.74887i) q^{24} +(3.31095 - 3.74668i) q^{25} +(1.99859 + 7.51398i) q^{26} +6.80520 q^{27} +(3.94477 + 6.89086i) q^{28} +(-5.09727 + 5.09727i) q^{29} +(-7.08709 + 5.77211i) q^{30} +3.94542i q^{31} +(-1.51420 + 5.45043i) q^{32} +(6.12215 - 6.12215i) q^{33} +(1.70060 + 6.39365i) q^{34} +(3.64839 + 8.09294i) q^{35} +(9.29372 - 5.32032i) q^{36} +(-3.93647 + 3.93647i) q^{37} +(4.24448 - 7.32057i) q^{38} -15.8912i q^{39} +(-2.27159 + 5.90253i) q^{40} +(-3.43841 + 5.40161i) q^{41} +(-4.17136 - 15.6829i) q^{42} +(-5.85200 - 5.85200i) q^{43} +(1.57179 - 5.78101i) q^{44} +(10.9150 - 4.92060i) q^{45} +(-2.65287 + 4.57548i) q^{46} +7.58708 q^{47} +(5.85418 - 9.96991i) q^{48} -8.76128 q^{49} +(-3.16308 + 6.32415i) q^{50} -13.5218i q^{51} +(-5.46291 - 9.54281i) q^{52} +6.61578i q^{53} +(-9.30064 + 2.47380i) q^{54} +(2.37125 - 6.26422i) q^{55} +(-7.89624 - 7.98371i) q^{56} +(-12.2294 + 12.2294i) q^{57} +(5.11347 - 8.81936i) q^{58} +6.92744 q^{59} +(7.58764 - 10.4650i) q^{60} +6.04740i q^{61} +(-1.43423 - 5.39219i) q^{62} +21.2573i q^{63} +(0.0881340 - 7.99951i) q^{64} +(-5.05248 - 11.2075i) q^{65} +(-6.14161 + 10.5926i) q^{66} -8.81626 q^{67} +(-4.64839 - 8.11997i) q^{68} +(7.64355 - 7.64355i) q^{69} +(-7.92816 - 9.73433i) q^{70} +(-7.87467 + 7.87467i) q^{71} +(-10.7677 + 10.6497i) q^{72} +(4.97545 - 4.97545i) q^{73} +(3.94898 - 6.81092i) q^{74} +(9.56998 - 10.8294i) q^{75} +(-3.13975 + 11.5479i) q^{76} +(8.40894 + 8.40894i) q^{77} +(5.77671 + 21.7184i) q^{78} +(1.04312 + 1.04312i) q^{79} +(0.958897 - 8.89272i) q^{80} +3.60652 q^{81} +(2.73569 - 8.63227i) q^{82} +(1.36790 - 1.36790i) q^{83} +(11.4020 + 19.9173i) q^{84} +(-4.29916 - 9.53647i) q^{85} +(10.1252 + 5.87060i) q^{86} +(-14.7332 + 14.7332i) q^{87} +(-0.0466698 + 8.47226i) q^{88} +(-4.94457 + 4.94457i) q^{89} +(-13.1287 + 10.6927i) q^{90} +21.8270 q^{91} +(1.96240 - 7.21764i) q^{92} +11.4038i q^{93} +(-10.3692 + 2.75803i) q^{94} +(-4.73671 + 12.5132i) q^{95} +(-4.37666 + 15.7539i) q^{96} -5.20787i q^{97} +(11.9740 - 3.18487i) q^{98} +(11.3412 - 11.3412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more