LMFDB - Embedded newform 336.2.bs.a.115.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,2,Mod(19,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.31
Character	$\chi$	$=$	336.115
Dual form			336.2.bs.a.187.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39364 - 0.240374i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.88444 - 0.669989i) q^{4} +(-0.718534 + 2.68161i) q^{5} +(-1.28394 + 0.592883i) q^{6} +(-0.164584 + 2.64063i) q^{7} +(2.46517 - 1.38669i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.356785 + 3.90990i) q^{10} +(1.77791 - 0.476389i) q^{11} +(-1.64682 + 1.13489i) q^{12} +(-3.89320 + 3.89320i) q^{13} +(0.405370 + 3.71963i) q^{14} -2.77620i q^{15} +(3.10223 - 2.52511i) q^{16} +(1.76864 + 1.02112i) q^{17} +(1.08674 - 0.904988i) q^{18} +(2.09434 - 7.81618i) q^{19} +(0.442611 + 5.53474i) q^{20} +(-0.524469 - 2.59325i) q^{21} +(2.36325 - 1.09128i) q^{22} +(2.56511 + 4.44290i) q^{23} +(-2.02227 + 1.97748i) q^{24} +(-2.34460 - 1.35365i) q^{25} +(-4.48988 + 6.36153i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.45904 + 5.08637i) q^{28} +(-0.480330 - 0.480330i) q^{29} +(-0.667328 - 3.86902i) q^{30} +(3.39359 - 5.87787i) q^{31} +(3.71641 - 4.26478i) q^{32} +(-1.59403 + 0.920314i) q^{33} +(2.71028 + 0.997938i) q^{34} +(-6.96287 - 2.33873i) q^{35} +(1.29698 - 1.52245i) q^{36} +(-9.53235 - 2.55419i) q^{37} +(1.03994 - 11.3963i) q^{38} +(2.75291 - 4.76818i) q^{39} +(1.94725 + 7.60702i) q^{40} +9.53641 q^{41} +(-1.35427 - 3.48797i) q^{42} +(-3.82420 - 3.82420i) q^{43} +(3.03119 - 2.08891i) q^{44} +(0.718534 + 2.68161i) q^{45} +(4.64278 + 5.57519i) q^{46} +(-6.70468 - 11.6128i) q^{47} +(-2.34298 + 3.24198i) q^{48} +(-6.94582 - 0.869208i) q^{49} +(-3.59290 - 1.32292i) q^{50} +(-1.97266 - 0.528572i) q^{51} +(-4.72811 + 9.94491i) q^{52} +(1.17655 + 4.39093i) q^{53} +(-0.815479 + 1.15542i) q^{54} +5.10996i q^{55} +(3.25601 + 6.73783i) q^{56} +8.09191i q^{57} +(-0.784864 - 0.553946i) q^{58} +(2.40283 + 8.96747i) q^{59} +(-1.86002 - 5.23159i) q^{60} +(-1.87444 - 0.502253i) q^{61} +(3.31654 - 9.00735i) q^{62} +(1.17778 + 2.36914i) q^{63} +(4.15418 - 6.83687i) q^{64} +(-7.64264 - 13.2374i) q^{65} +(-2.00028 + 1.66575i) q^{66} +(-0.606879 - 2.26490i) q^{67} +(4.01703 + 0.739278i) q^{68} +(-3.62761 - 3.62761i) q^{69} +(-10.2659 - 1.58564i) q^{70} +4.35387 q^{71} +(1.44156 - 2.43350i) q^{72} +(-2.93679 + 5.08666i) q^{73} +(-13.8986 - 1.26827i) q^{74} +(2.61506 + 0.700703i) q^{75} +(-1.29009 - 16.1323i) q^{76} +(0.965352 + 4.77320i) q^{77} +(2.69040 - 7.30683i) q^{78} +(2.98280 - 1.72212i) q^{79} +(4.54229 + 10.1333i) q^{80} +(0.500000 - 0.866025i) q^{81} +(13.2903 - 2.29231i) q^{82} +(3.24589 + 3.24589i) q^{83} +(-2.72578 - 4.53543i) q^{84} +(-4.00907 + 4.00907i) q^{85} +(-6.24877 - 4.41030i) q^{86} +(0.588282 + 0.339645i) q^{87} +(3.72225 - 3.63979i) q^{88} +(-4.76354 - 8.25069i) q^{89} +(1.64596 + 3.56447i) q^{90} +(-9.63974 - 10.9213i) q^{91} +(7.81048 + 6.65378i) q^{92} +(-1.75665 + 6.55592i) q^{93} +(-12.1353 - 14.5724i) q^{94} +(19.4551 + 11.2324i) q^{95} +(-2.48597 + 5.08133i) q^{96} -1.26255i q^{97} +(-9.88888 + 0.458240i) q^{98} +(1.30152 - 1.30152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44}+ \cdots - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.39364	−	0.240374i	0.985449	−	0.169970i
$2$	1.39364	−	0.240374i	0.985449	−	0.169970i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.88444	−	0.669989i	0.942220	−	0.334994i
$5$	−0.718534	+	2.68161i	−0.321338	+	1.19925i	0.596604	+	0.802536i	$0.296517\pi$
$5$	−0.718534	+	2.68161i	−0.321338	+	1.19925i	−0.917942	+	0.396715i	$0.870150\pi$
$6$	−1.28394	+	0.592883i	−0.524164	+	0.242044i
$7$	−0.164584	+	2.64063i	−0.0622067	+	0.998063i
$7$	−0.164584	+	2.64063i	−0.0622067	+	0.998063i
$8$	2.46517	−	1.38669i	0.871571	−	0.490269i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−0.356785	+	3.90990i	−0.112825	+	1.23642i
$11$	1.77791	−	0.476389i	0.536060	−	0.143637i	0.0193747	−	0.999812i	$-0.493832\pi$
$11$	1.77791	−	0.476389i	0.536060	−	0.143637i	0.516685	+	0.856175i	$0.327166\pi$
$12$	−1.64682	+	1.13489i	−0.475397	+	0.327614i
$13$	−3.89320	+	3.89320i	−1.07978	+	1.07978i	−0.0832514	+	0.996529i	$0.526530\pi$
$13$	−3.89320	+	3.89320i	−1.07978	+	1.07978i	−0.996529	+	0.0832514i	$0.973470\pi$
$14$	0.405370	+	3.71963i	0.108340	+	0.994114i
$15$		−	2.77620i		−	0.716813i
$16$	3.10223	−	2.52511i	0.775558	−	0.631277i
$17$	1.76864	+	1.02112i	0.428957	+	0.247659i	0.698902	−	0.715217i	$-0.253672\pi$
$17$	1.76864	+	1.02112i	0.428957	+	0.247659i	−0.269945	+	0.962876i	$0.587006\pi$
$18$	1.08674	−	0.904988i	0.256146	−	0.213308i
$19$	2.09434	−	7.81618i	0.480474	−	1.79315i	−0.119153	−	0.992876i	$-0.538018\pi$
$19$	2.09434	−	7.81618i	0.480474	−	1.79315i	0.599628	−	0.800279i	$-0.295315\pi$
$20$	0.442611	+	5.53474i	0.0989708	+	1.23761i
$21$	−0.524469	−	2.59325i	−0.114449	−	0.565893i
$22$	2.36325	−	1.09128i	0.503846	−	0.232661i
$23$	2.56511	+	4.44290i	0.534862	+	0.926408i	0.999170	+	0.0407343i	$0.0129697\pi$
$23$	2.56511	+	4.44290i	0.534862	+	0.926408i	−0.464308	+	0.885674i	$0.653697\pi$
$24$	−2.02227	+	1.97748i	−0.412795	+	0.403650i
$25$	−2.34460	−	1.35365i	−0.468919	−	0.270731i
$26$	−4.48988	+	6.36153i	−0.880538	+	1.24760i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.45904	+	5.08637i	0.275733	+	0.961234i
$29$	−0.480330	−	0.480330i	−0.0891951	−	0.0891951i	0.661101	−	0.750297i	$-0.270089\pi$
$29$	−0.480330	−	0.480330i	−0.0891951	−	0.0891951i	−0.750297	+	0.661101i	$0.770089\pi$
$30$	−0.667328	−	3.86902i	−0.121837	−	0.706382i
$31$	3.39359	−	5.87787i	0.609507	−	1.05570i	−0.381814	−	0.924239i	$-0.624701\pi$
$31$	3.39359	−	5.87787i	0.609507	−	1.05570i	0.991322	−	0.131458i	$-0.0419660\pi$
$32$	3.71641	−	4.26478i	0.656974	−	0.753913i
$33$	−1.59403	+	0.920314i	−0.277485	+	0.160206i
$34$	2.71028	+	0.997938i	0.464810	+	0.171145i
$35$	−6.96287	−	2.33873i	−1.17694	−	0.395317i
$36$	1.29698	−	1.52245i	0.216163	−	0.253741i
$37$	−9.53235	−	2.55419i	−1.56711	−	0.419906i	−0.632204	−	0.774802i	$-0.717849\pi$
$37$	−9.53235	−	2.55419i	−1.56711	−	0.419906i	−0.934906	+	0.354897i	$0.884516\pi$
$38$	1.03994	−	11.3963i	0.168700	−	1.84873i
$39$	2.75291	−	4.76818i	0.440818	−	0.763520i
$40$	1.94725	+	7.60702i	0.307887	+	1.20277i
$41$	9.53641			1.48934			0.744669	−	0.667434i	$-0.232607\pi$
$41$	9.53641			1.48934			0.744669	+	0.667434i	$0.232607\pi$
$42$	−1.35427	−	3.48797i	−0.208968	−	0.538206i
$43$	−3.82420	−	3.82420i	−0.583184	−	0.583184i	0.352593	−	0.935777i	$-0.385300\pi$
$43$	−3.82420	−	3.82420i	−0.583184	−	0.583184i	−0.935777	+	0.352593i	$0.885300\pi$
$44$	3.03119	−	2.08891i	0.456969	−	0.314914i
$45$	0.718534	+	2.68161i	0.107113	+	0.399750i
$46$	4.64278	+	5.57519i	0.684541	+	0.822017i
$47$	−6.70468	−	11.6128i	−0.977977	−	1.69391i	−0.669737	−	0.742598i	$-0.733593\pi$
$47$	−6.70468	−	11.6128i	−0.977977	−	1.69391i	−0.308240	−	0.951309i	$-0.599740\pi$
$48$	−2.34298	+	3.24198i	−0.338180	+	0.467940i
$49$	−6.94582	−	0.869208i	−0.992261	−	0.124173i
$50$	−3.59290	−	1.32292i	−0.508112	−	0.187089i
$51$	−1.97266	−	0.528572i	−0.276227	−	0.0740148i
$52$	−4.72811	+	9.94491i	−0.655670	+	1.37911i
$53$	1.17655	+	4.39093i	0.161611	+	0.603141i	0.998448	+	0.0556887i	$0.0177354\pi$
$53$	1.17655	+	4.39093i	0.161611	+	0.603141i	−0.836837	+	0.547452i	$0.815598\pi$
$54$	−0.815479	+	1.15542i	−0.110973	+	0.157233i
$55$			5.10996i			0.689026i
$56$	3.25601	+	6.73783i	0.435102	+	0.900381i
$57$			8.09191i			1.07180i
$58$	−0.784864	−	0.553946i	−0.103058	−	0.0727367i
$59$	2.40283	+	8.96747i	0.312821	+	1.16746i	0.926001	+	0.377521i	$0.123224\pi$
$59$	2.40283	+	8.96747i	0.312821	+	1.16746i	−0.613180	+	0.789943i	$0.710110\pi$
$60$	−1.86002	−	5.23159i	−0.240128	−	0.675395i
$61$	−1.87444	−	0.502253i	−0.239997	−	0.0643070i	0.136816	−	0.990597i	$-0.456313\pi$
$61$	−1.87444	−	0.502253i	−0.239997	−	0.0643070i	−0.376812	+	0.926290i	$0.622980\pi$
$62$	3.31654	−	9.00735i	0.421201	−	1.14393i
$63$	1.17778	+	2.36914i	0.148386	+	0.298484i
$64$	4.15418	−	6.83687i	0.519272	−	0.854609i
$65$	−7.64264	−	13.2374i	−0.947953	−	1.64190i
$66$	−2.00028	+	1.66575i	−0.246217	+	0.205039i
$67$	−0.606879	−	2.26490i	−0.0741421	−	0.276702i	0.918895	−	0.394501i	$-0.129083\pi$
$67$	−0.606879	−	2.26490i	−0.0741421	−	0.276702i	−0.993037	+	0.117799i	$0.962416\pi$
$68$	4.01703	+	0.739278i	0.487136	+	0.0896506i
$69$	−3.62761	−	3.62761i	−0.436713	−	0.436713i
$70$	−10.2659	−	1.58564i	−1.22701	−	0.189521i
$71$	4.35387			0.516709			0.258355	−	0.966050i	$-0.416820\pi$
$71$	4.35387			0.516709			0.258355	+	0.966050i	$0.416820\pi$
$72$	1.44156	−	2.43350i	0.169889	−	0.286790i
$73$	−2.93679	+	5.08666i	−0.343725	+	0.595349i	−0.985121	−	0.171861i	$-0.945022\pi$
$73$	−2.93679	+	5.08666i	−0.343725	+	0.595349i	0.641396	+	0.767210i	$0.278355\pi$
$74$	−13.8986	−	1.26827i	−1.61568	−	0.147434i
$75$	2.61506	+	0.700703i	0.301961	+	0.0809102i
$76$	−1.29009	−	16.1323i	−0.147984	−	1.85050i
$77$	0.965352	+	4.77320i	0.110012	+	0.543957i
$78$	2.69040	−	7.30683i	0.304628	−	0.827336i
$79$	2.98280	−	1.72212i	0.335591	−	0.193753i	−0.322730	−	0.946491i	$-0.604601\pi$
$79$	2.98280	−	1.72212i	0.335591	−	0.193753i	0.658320	+	0.752738i	$0.271267\pi$
$80$	4.54229	+	10.1333i	0.507843	+	1.13294i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	13.2903	−	2.29231i	1.46767	−	0.253143i
$83$	3.24589	+	3.24589i	0.356283	+	0.356283i	0.862441	−	0.506158i	$-0.168935\pi$
$83$	3.24589	+	3.24589i	0.356283	+	0.356283i	−0.506158	+	0.862441i	$0.668935\pi$
$84$	−2.72578	−	4.53543i	−0.297407	−	0.494856i
$85$	−4.00907	+	4.00907i	−0.434845	+	0.434845i
$86$	−6.24877	−	4.41030i	−0.673823	−	0.475575i
$87$	0.588282	+	0.339645i	0.0630704	+	0.0364137i
$88$	3.72225	−	3.63979i	0.396793	−	0.388003i
$89$	−4.76354	−	8.25069i	−0.504934	−	0.874572i	−0.999984	−	0.00570691i	$-0.998183\pi$
$89$	−4.76354	−	8.25069i	−0.504934	−	0.874572i	0.495050	−	0.868865i	$-0.335150\pi$
$90$	1.64596	+	3.56447i	0.173500	+	0.375728i
$91$	−9.63974	−	10.9213i	−1.01052	−	1.14486i
$92$	7.81048	+	6.65378i	0.814299	+	0.693705i
$93$	−1.75665	+	6.55592i	−0.182156	+	0.679817i
$94$	−12.1353	−	14.5724i	−1.25166	−	1.50303i
$95$	19.4551	+	11.2324i	1.99605	+	1.15242i
$96$	−2.48597	+	5.08133i	−0.253723	+	0.518612i
$97$		−	1.26255i		−	0.128192i	−0.997944	−	0.0640962i	$-0.979584\pi$
$97$		−	1.26255i		−	0.128192i	0.997944	−	0.0640962i	$-0.0204164\pi$
$98$	−9.88888	+	0.458240i	−0.998928	+	0.0462892i
$99$	1.30152	−	1.30152i	0.130808	−	0.130808i
$100$	−5.32518	−	0.980026i	−0.532518	−	0.0980026i
$101$	4.38606	−	1.17524i	0.436430	−	0.116941i	−0.0339131	−	0.999425i	$-0.510797\pi$
$101$	4.38606	−	1.17524i	0.436430	−	0.116941i	0.470343	+	0.882484i	$0.344130\pi$
$102$	−2.87622	−	0.262460i	−0.284788	−	0.0259874i
$103$	7.77116	−	4.48668i	0.765715	−	0.442086i	−0.0656291	−	0.997844i	$-0.520905\pi$
$103$	7.77116	−	4.48668i	0.765715	−	0.442086i	0.831344	+	0.555759i	$0.187572\pi$
$104$	−4.19876	+	14.9961i	−0.411722	+	1.47049i
$105$	7.33092	+	0.456917i	0.715424	+	0.0445906i
$106$	2.69514	+	5.83654i	0.261775	+	0.566895i
$107$	1.13950	−	4.25268i	0.110160	−	0.411122i	−0.888719	−	0.458451i	$-0.848404\pi$
$107$	1.13950	−	4.25268i	0.110160	−	0.411122i	0.998879	+	0.0473292i	$0.0150710\pi$
$108$	−0.858747	+	1.80625i	−0.0826330	+	0.173807i
$109$	8.47257	−	2.27022i	0.811525	−	0.217447i	0.170887	−	0.985291i	$-0.445337\pi$
$109$	8.47257	−	2.27022i	0.811525	−	0.217447i	0.640638	+	0.767843i	$0.278670\pi$
$110$	1.22830	+	7.12142i	0.117114	+	0.679000i
$111$	9.86862			0.936688
$112$	6.15729	+	8.60743i	0.581809	+	0.813325i
$113$	8.52426			0.801895			0.400947	−	0.916101i	$-0.368681\pi$
$113$	8.52426			0.801895			0.400947	+	0.916101i	$0.368681\pi$
$114$	1.94509	+	11.2772i	0.182174	+	1.05620i
$115$	−13.7572	+	3.68624i	−1.28287	+	0.343743i
$116$	−1.22697	−	0.583338i	−0.113921	−	0.0541616i
$117$	−1.42501	+	5.31821i	−0.131742	+	0.491669i
$118$	5.50421	+	11.9198i	0.506704	+	1.09731i
$119$	−2.98749	+	4.50225i	−0.273863	+	0.412720i
$120$	−3.84974	−	6.84383i	−0.351431	−	0.624753i
$121$	−6.59226	+	3.80605i	−0.599297	+	0.346004i
$122$	−2.73301	−	0.249392i	−0.247435	−	0.0225789i
$123$	−9.21147	+	2.46821i	−0.830570	+	0.222551i
$124$	2.45691	−	13.3502i	0.220637	−	1.19888i
$125$	−4.50072	+	4.50072i	−0.402557	+	0.402557i
$126$	2.21088	+	3.01861i	0.196961	+	0.268919i
$127$		−	5.73788i		−	0.509155i	−0.967052	−	0.254577i	$-0.918064\pi$
$127$		−	5.73788i		−	0.509155i	0.967052	−	0.254577i	$-0.0819364\pi$
$128$	4.14600	−	10.5267i	0.366458	−	0.930435i
$129$	4.68366	+	2.70411i	0.412374	+	0.238084i
$130$	−13.8330	−	16.6111i	−1.21323	−	1.45689i
$131$	−0.00333383	+	0.0124420i	−0.000291278	+	0.00108706i	−0.966071	−	0.258275i	$-0.916846\pi$
$131$	−0.00333383	+	0.0124420i	−0.000291278	+	0.00108706i	0.965780	+	0.259363i	$0.0835124\pi$
$132$	−2.38725	+	2.80226i	−0.207784	+	0.243905i
$133$	20.2949	+	6.81678i	1.75979	+	0.591090i
$134$	−1.39019	−	3.01057i	−0.120094	−	0.260074i
$135$	−1.38810	−	2.40426i	−0.119469	−	0.206926i
$136$	5.77598	+	0.0646937i	0.495286	+	0.00554744i
$137$	12.1045	+	6.98855i	1.03416	+	0.597072i	0.918174	−	0.396178i	$-0.129664\pi$
$137$	12.1045	+	6.98855i	1.03416	+	0.597072i	0.115986	+	0.993251i	$0.462997\pi$
$138$	−5.92755	−	4.18358i	−0.504587	−	0.356130i
$139$	−0.127227	+	0.127227i	−0.0107913	+	0.0107913i	−0.712482	−	0.701691i	$-0.752429\pi$
$139$	−0.127227	+	0.127227i	−0.0107913	+	0.0107913i	0.701691	+	0.712482i	$0.252429\pi$
$140$	−14.6880	+	0.257844i	−1.24136	+	0.0217918i
$141$	9.48184	+	9.48184i	0.798515	+	0.798515i
$142$	6.06771	−	1.04656i	0.509191	−	0.0878253i
$143$	−5.06708	+	8.77644i	−0.423731	+	0.733923i
$144$	1.42406	−	3.73792i	0.118671	−	0.311494i
$145$	1.63319	−	0.942923i	0.135629	−	0.0783055i
$146$	−2.87011	+	7.79488i	−0.237532	+	0.645109i
$147$	6.93412	−	0.958122i	0.571916	−	0.0790245i
$148$	−19.6744	+	1.57336i	−1.61723	+	0.129329i
$149$	−3.20189	−	0.857943i	−0.262309	−	0.0702855i	0.125268	−	0.992123i	$-0.460021\pi$
$149$	−3.20189	−	0.857943i	−0.262309	−	0.0702855i	−0.387577	+	0.921838i	$0.626688\pi$
$150$	3.81287	+	0.347931i	0.311319	+	0.0284085i
$151$	−10.6303	+	18.4122i	−0.865081	+	1.49837i	0.00188478	+	0.999998i	$0.499400\pi$
$151$	−10.6303	+	18.4122i	−0.865081	+	1.49837i	−0.866966	+	0.498367i	$0.833933\pi$
$152$	−5.67572	−	22.1725i	−0.460361	−	1.79842i
$153$	2.04224			0.165106
$154$	2.49270	+	6.42006i	0.200868	+	0.517343i
$155$	13.3237	+	13.3237i	1.07019	+	1.07019i
$156$	1.99307	−	10.8298i	0.159573	−	0.867075i
$157$	−1.91384	−	7.14256i	−0.152741	−	0.570039i	−0.999288	−	0.0377243i	$-0.987989\pi$
$157$	−1.91384	−	7.14256i	−0.152741	−	0.570039i	0.846547	−	0.532314i	$-0.178678\pi$
$158$	3.74298	−	3.11699i	0.297775	−	0.247975i
$159$	−2.27291	−	3.93680i	−0.180254	−	0.312209i
$160$	8.76609	+	13.0303i	0.693020	+	1.03014i
$161$	−12.1542	+	6.04227i	−0.957886	+	0.476197i
$162$	0.488647	−	1.32711i	0.0383918	−	0.104268i
$163$	−7.84963	−	2.10330i	−0.614830	−	0.164743i	−0.0620537	−	0.998073i	$-0.519765\pi$
$163$	−7.84963	−	2.10330i	−0.614830	−	0.164743i	−0.552776	+	0.833330i	$0.686432\pi$
$164$	17.9708	−	6.38929i	1.40328	−	0.498920i
$165$	−1.32255	−	4.93584i	−0.102961	−	0.384255i
$166$	5.30381	+	3.74336i	0.411656	+	0.290541i
$167$		−	5.46606i		−	0.422976i	−0.977381	−	0.211488i	$-0.932169\pi$
$167$		−	5.46606i		−	0.422976i	0.977381	−	0.211488i	$-0.0678310\pi$
$168$	−4.88894	−	5.66553i	−0.377190	−	0.437105i
$169$		−	17.3140i		−	1.33185i
$170$	−4.62351	+	6.55087i	−0.354607	+	0.502429i
$171$	−2.09434	−	7.81618i	−0.160158	−	0.597718i
$172$	−9.76864	−	4.64430i	−0.744852	−	0.354125i
$173$	3.22811	+	0.864971i	0.245429	+	0.0657625i	0.379436	−	0.925218i	$-0.376118\pi$
$173$	3.22811	+	0.864971i	0.245429	+	0.0657625i	−0.134007	+	0.990980i	$0.542785\pi$
$174$	0.901492	+	0.331933i	0.0683420	+	0.0251638i
$175$	3.96038	−	5.96842i	0.299376	−	0.451170i
$176$	4.31255	−	5.96728i	0.325071	−	0.449801i
$177$	−4.64190	−	8.04001i	−0.348907	−	0.604324i
$178$	−8.62189	−	10.3534i	−0.646238	−	0.776022i
$179$	0.327333	+	1.22162i	0.0244660	+	0.0913085i	0.977079	−	0.212876i	$-0.0682829\pi$
$179$	0.327333	+	1.22162i	0.0244660	+	0.0913085i	−0.952613	+	0.304184i	$0.901616\pi$
$180$	3.15068	+	4.57192i	0.234838	+	0.340771i
$181$	13.4277	+	13.4277i	0.998072	+	0.998072i	0.999998	−	0.00192653i	$-0.000613233\pi$
$181$	13.4277	+	13.4277i	0.998072	+	0.998072i	−0.00192653	+	0.999998i	$0.500613\pi$
$182$	−16.0595	−	12.9031i	−1.19041	−	0.956441i
$183$	1.94056			0.143450
$184$	12.4844	+	7.39551i	0.920360	+	0.545204i
$185$	13.6986	−	23.7268i	1.00714	−	1.74443i
$186$	−0.872259	+	9.55881i	−0.0639571	+	0.700886i
$187$	3.63093	+	0.972904i	0.265520	+	0.0711458i
$188$	−20.4150	−	17.3916i	−1.48892	−	1.26842i
$189$	−1.75083	−	1.98358i	−0.127354	−	0.144284i
$190$	29.8133	+	10.9774i	2.16288	+	0.796381i
$191$	−17.6983	+	10.2181i	−1.28060	+	0.739358i	−0.976959	−	0.213427i	$-0.931537\pi$
$191$	−17.6983	+	10.2181i	−1.28060	+	0.739358i	−0.303646	+	0.952785i	$0.598204\pi$
$192$	−2.24311	+	7.67909i	−0.161883	+	0.554191i
$193$	−1.04540	+	1.81069i	−0.0752497	+	0.130336i	−0.901195	−	0.433414i	$-0.857309\pi$
$193$	−1.04540	+	1.81069i	−0.0752497	+	0.130336i	0.825945	+	0.563750i	$0.190642\pi$
$194$	−0.303484	−	1.75953i	−0.0217889	−	0.126327i
$195$	10.8083	+	10.8083i	0.774000	+	0.774000i
$196$	−13.6714	+	3.01565i	−0.976525	+	0.215404i
$197$	−1.32672	+	1.32672i	−0.0945247	+	0.0945247i	−0.752788	−	0.658263i	$-0.771291\pi$
$197$	−1.32672	+	1.32672i	−0.0945247	+	0.0945247i	0.658263	+	0.752788i	$0.271291\pi$
$198$	1.50099	−	2.12670i	0.106671	−	0.151138i
$199$	−6.96496	−	4.02122i	−0.493733	−	0.285057i	0.232389	−	0.972623i	$-0.425346\pi$
$199$	−6.96496	−	4.02122i	−0.493733	−	0.285057i	−0.726122	+	0.687566i	$0.758679\pi$
$200$	−7.65694	−	0.0857613i	−0.541427	−	0.00606424i
$201$	1.17240	+	2.03066i	0.0826948	+	0.143232i
$202$	5.83008	−	2.69216i	0.410203	−	0.189419i
$203$	1.34743	−	1.18932i	0.0945709	−	0.0834738i
$204$	−4.07149	+	0.325596i	−0.285061	+	0.0227962i
$205$	−6.85224	+	25.5729i	−0.478581	+	1.78609i
$206$	9.75168	−	8.12078i	0.679431	−	0.565802i
$207$	4.44290	+	2.56511i	0.308803	+	0.178287i
$208$	−2.24686	+	21.9084i	−0.155792	+	1.51907i
$209$		−	14.8942i		−	1.03025i
$210$	10.3265	−	1.12539i	0.712594	−	0.0776592i
$211$	−6.04852	+	6.04852i	−0.416398	+	0.416398i	−0.883960	−	0.467563i	$-0.845132\pi$
$211$	−6.04852	+	6.04852i	−0.416398	+	0.416398i	0.467563	+	0.883960i	$0.345132\pi$
$212$	5.15900	+	7.48617i	0.354322	+	0.514152i
$213$	−4.20552	+	1.12686i	−0.288157	+	0.0772115i
$214$	0.565816	−	6.20059i	0.0386784	−	0.423864i
$215$	13.0028	−	7.50717i	0.886784	−	0.511985i
$216$	−0.762603	+	2.72368i	−0.0518886	+	0.185323i
$217$	14.9627	+	9.92861i	1.01574	+	0.673998i
$218$	11.2620	−	5.20044i	0.762757	−	0.352219i
$219$	1.52019	−	5.67344i	0.102725	−	0.383375i
$220$	3.42361	+	9.62941i	0.230820	+	0.649215i
$221$	−10.8611	+	2.91022i	−0.730596	+	0.195763i
$222$	13.7533	−	2.37216i	0.923058	−	0.159209i
$223$	0.122649			0.00821321			0.00410660	−	0.999992i	$-0.498693\pi$
$223$	0.122649			0.00821321			0.00410660	+	0.999992i	$0.498693\pi$
$224$	10.6500	+	10.5156i	0.711585	+	0.702600i
$225$	−2.70731			−0.180487
$226$	11.8797	−	2.04901i	0.790227	−	0.136298i
$227$	−21.2753	+	5.70069i	−1.41209	+	0.378368i	−0.882670	−	0.469993i	$-0.844256\pi$
$227$	−21.2753	+	5.70069i	−1.41209	+	0.378368i	−0.529418	+	0.848361i	$0.677590\pi$
$228$	5.42149	+	15.2487i	0.359047	+	1.00987i
$229$	−1.94505	+	7.25903i	−0.128533	+	0.479690i	−0.999941	−	0.0108681i	$-0.996541\pi$
$229$	−1.94505	+	7.25903i	−0.128533	+	0.479690i	0.871408	+	0.490558i	$0.163207\pi$
$230$	−18.2865	+	8.44415i	−1.20577	+	0.556791i
$231$	−2.16785	−	4.36071i	−0.142634	−	0.286913i
$232$	−1.85017	−	0.518028i	−0.121469	−	0.0340102i
$233$	−8.81183	+	5.08751i	−0.577282	+	0.333294i	−0.760052	−	0.649862i	$-0.774827\pi$
$233$	−8.81183	+	5.08751i	−0.577282	+	0.333294i	0.182771	+	0.983156i	$0.441493\pi$
$234$	−0.707584	+	7.75419i	−0.0462562	+	0.506907i
$235$	35.9586	−	9.63508i	2.34568	−	0.628523i
$236$	10.5361	+	15.2888i	0.685841	+	0.995216i
$237$	−2.43544	+	2.43544i	−0.158199	+	0.158199i
$238$	−3.08125	+	6.99261i	−0.199728	+	0.453263i
$239$		−	7.71316i		−	0.498923i	−0.968385	−	0.249461i	$-0.919746\pi$
$239$		−	7.71316i		−	0.498923i	0.968385	−	0.249461i	$-0.0802536\pi$
$240$	−7.01021	−	8.61242i	−0.452507	−	0.555930i
$241$	−0.751865	−	0.434090i	−0.0484319	−	0.0279622i	0.475589	−	0.879668i	$-0.342235\pi$
$241$	−0.751865	−	0.434090i	−0.0484319	−	0.0279622i	−0.524020	+	0.851706i	$0.675568\pi$
$242$	−8.27234	+	6.88885i	−0.531766	+	0.442832i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−3.86877	+	0.309384i	−0.247672	+	0.0198063i
$245$	7.32169	−	18.0014i	0.467765	−	1.15007i
$246$	−12.2441	+	5.65398i	−0.780658	+	0.360485i
$247$	22.2763	+	38.5837i	1.41741	+	2.45502i
$248$	0.215003	−	19.1959i	0.0136527	−	1.21894i
$249$	−3.97539	−	2.29519i	−0.251930	−	0.145452i
$250$	−5.19051	+	7.35423i	−0.328277	+	0.465122i
$251$	−13.4432	+	13.4432i	−0.848529	+	0.848529i	−0.989950	−	0.141421i	$-0.954833\pi$
$251$	−13.4432	+	13.4432i	−0.848529	+	0.848529i	0.141421	+	0.989950i	$0.454833\pi$
$252$	3.80675	+	3.67541i	0.239803	+	0.231529i
$253$	6.67708	+	6.67708i	0.419784	+	0.419784i
$254$	−1.37924	−	7.99652i	−0.0865412	−	0.501746i
$255$	2.83484	−	4.91009i	0.177525	−	0.307482i
$256$	3.24767	−	15.6669i	0.202979	−	0.979183i
$257$	−5.20491	+	3.00506i	−0.324673	+	0.187450i	−0.653474	−	0.756949i	$-0.726689\pi$
$257$	−5.20491	+	3.00506i	−0.324673	+	0.187450i	0.328800	+	0.944399i	$0.393356\pi$
$258$	7.17732	+	2.64272i	0.446841	+	0.164528i
$259$	8.31352	−	24.7510i	0.516577	−	1.53795i
$260$	−23.2710	−	19.8247i	−1.44321	−	1.22947i
$261$	−0.656143	−	0.175813i	−0.0406142	−	0.0108826i
$262$	−0.00165540	+	0.0181410i	−0.000102271	+	0.00112076i
$263$	−3.40907	+	5.90468i	−0.210212	+	0.364098i	−0.951781	−	0.306779i	$-0.900749\pi$
$263$	−3.40907	+	5.90468i	−0.210212	+	0.364098i	0.741569	+	0.670877i	$0.234082\pi$
$264$	−2.65337	+	4.47916i	−0.163304	+	0.275673i
$265$	−12.6201			−0.775249
$266$	29.9223	+	4.62173i	1.83465	+	0.283377i
$267$	6.73666	+	6.73666i	0.412277	+	0.412277i
$268$	−2.66109	−	3.86147i	−0.162552	−	0.235877i
$269$	−5.02599	−	18.7573i	−0.306440	−	1.14365i	−0.931699	−	0.363232i	$-0.881673\pi$
$269$	−5.02599	−	18.7573i	−0.306440	−	1.14365i	0.625259	−	0.780418i	$-0.284994\pi$
$270$	−2.51243	−	3.01700i	−0.152902	−	0.183609i
$271$	5.53173	+	9.58124i	0.336029	+	0.582019i	0.983682	−	0.179916i	$-0.0575827\pi$
$271$	5.53173	+	9.58124i	0.336029	+	0.582019i	−0.647653	+	0.761935i	$0.724249\pi$
$272$	8.06516	−	1.29824i	0.489022	−	0.0787172i
$273$	12.1379	+	8.05417i	0.734619	+	0.487461i
$274$	18.5492	+	6.82988i	1.12060	+	0.412608i
$275$	−4.81335	−	1.28973i	−0.290256	−	0.0777738i
$276$	−9.26647	−	4.40556i	−0.557776	−	0.265183i
$277$	−7.21529	−	26.9278i	−0.433525	−	1.61794i	−0.744572	−	0.667542i	$-0.767347\pi$
$277$	−7.21529	−	26.9278i	−0.433525	−	1.61794i	0.311048	−	0.950394i	$-0.399320\pi$
$278$	−0.146726	+	0.207891i	−0.00880006	+	0.0124685i
$279$		−	6.78718i		−	0.406338i
$280$	−20.4078	+	3.88997i	−1.21960	+	0.232470i
$281$			9.53041i			0.568536i	0.958745	+	0.284268i	$0.0917506\pi$
$281$			9.53041i			0.568536i	−0.958745	+	0.284268i	$0.908249\pi$
$282$	15.4934	+	10.9350i	0.922620	+	0.651172i
$283$	1.91091	+	7.13162i	0.113592	+	0.423931i	0.999178	−	0.0405451i	$-0.0129094\pi$
$283$	1.91091	+	7.13162i	0.113592	+	0.423931i	−0.885586	+	0.464476i	$0.846243\pi$
$284$	8.20461	−	2.91704i	0.486854	−	0.173095i
$285$	−21.6993	−	5.81431i	−1.28536	−	0.344410i
$286$	−4.95203	+	13.4492i	−0.292820	+	0.795265i
$287$	−1.56954	+	25.1821i	−0.0926468	+	1.48645i
$288$	1.08612	−	5.55161i	0.0640000	−	0.327132i
$289$	−6.41462	−	11.1104i	−0.377331	−	0.653556i
$290$	2.04942	−	1.70667i	0.120346	−	0.100219i
$291$	0.326772	+	1.21953i	0.0191557	+	0.0714900i
$292$	−2.12619	+	11.5531i	−0.124426	+	0.676096i
$293$	−21.0562	−	21.0562i	−1.23012	−	1.23012i	−0.963919	−	0.266196i	$-0.914233\pi$
$293$	−21.0562	−	21.0562i	−1.23012	−	1.23012i	−0.266196	−	0.963919i	$-0.585767\pi$
$294$	9.43333	−	3.00206i	0.550163	−	0.175084i
$295$	−25.7737			−1.50060
$296$	−27.0408	+	6.92191i	−1.57171	+	0.402328i
$297$	−0.920314	+	1.59403i	−0.0534020	+	0.0924950i
$298$	−4.66849	−	0.426008i	−0.270439	−	0.0246780i
$299$	−27.2836	−	7.31061i	−1.57785	−	0.422784i
$300$	5.39738	−	0.431627i	0.311618	−	0.0249200i
$301$	10.7277	−	9.46888i	0.618333	−	0.545777i
$302$	−10.3889	+	28.2152i	−0.597816	+	1.62360i
$303$	−3.93244	+	2.27039i	−0.225913	+	0.130431i
$304$	−13.2396	−	29.5360i	−0.759341	−	1.69401i
$305$	2.69369	−	4.66561i	0.154240	−	0.267152i
$306$	2.84614	−	0.490903i	0.162703	−	0.0280631i
$307$	−14.7959	−	14.7959i	−0.844449	−	0.844449i	0.144985	−	0.989434i	$-0.453687\pi$
$307$	−14.7959	−	14.7959i	−0.844449	−	0.844449i	−0.989434	+	0.144985i	$0.953687\pi$
$308$	5.01714	+	8.34804i	0.285878	+	0.475674i
$309$	−6.34512	+	6.34512i	−0.360961	+	0.360961i
$310$	21.7711	+	15.3657i	1.23652	+	0.872716i
$311$	3.48684	+	2.01313i	0.197720	+	0.114154i	0.595592	−	0.803287i	$-0.296918\pi$
$311$	3.48684	+	2.01313i	0.197720	+	0.114154i	−0.397871	+	0.917441i	$0.630251\pi$
$312$	0.174412	−	15.5718i	0.00987413	−	0.881581i
$313$	−6.98128	−	12.0919i	−0.394605	−	0.683476i	0.598446	−	0.801163i	$-0.295785\pi$
$313$	−6.98128	−	12.0919i	−0.394605	−	0.683476i	−0.993051	+	0.117687i	$0.962452\pi$
$314$	−4.38409	−	9.49409i	−0.247409	−	0.535783i
$315$	−7.19938	+	1.45603i	−0.405639	+	0.0820382i
$316$	4.46710	−	5.24367i	0.251294	−	0.294979i
$317$	−0.159615	+	0.595693i	−0.00896489	+	0.0334574i	−0.970263	−	0.242052i	$-0.922180\pi$
$317$	−0.159615	+	0.595693i	−0.00896489	+	0.0334574i	0.961299	+	0.275509i	$0.0888464\pi$
$318$	−4.11392	−	4.94011i	−0.230697	−	0.277028i
$319$	−1.08281	−	0.625159i	−0.0606256	−	0.0350022i
$320$	15.3489	+	16.0524i	0.858029	+	0.897356i
$321$			4.40270i			0.245735i
$322$	−15.4861	+	11.3423i	−0.863008	+	0.632080i
$323$	11.6854	−	11.6854i	0.650193	−	0.650193i
$324$	0.361993	−	1.96697i	0.0201107	−	0.109276i
$325$	14.3980	−	3.85794i	0.798659	−	0.214000i
$326$	−11.4451	−	1.04439i	−0.633885	−	0.0578432i
$327$	−7.59630	+	4.38572i	−0.420076	+	0.242531i
$328$	23.5089	−	13.2241i	1.29806	−	0.730177i
$329$	31.7687	−	15.7933i	1.75146	−	0.870711i
$330$	−3.02961	−	6.56085i	−0.166774	−	0.361163i
$331$	6.49787	−	24.2504i	0.357155	−	1.33292i	−0.520595	−	0.853804i	$-0.674290\pi$
$331$	6.49787	−	24.2504i	0.357155	−	1.33292i	0.877751	−	0.479118i	$-0.159043\pi$
$332$	8.29139	+	3.94197i	0.455049	+	0.216344i
$333$	−9.53235	+	2.55419i	−0.522370	+	0.139969i
$334$	−1.31390	−	7.61769i	−0.0718934	−	0.416821i
$335$	6.50965			0.355660
$336$	−8.17525	−	6.72051i	−0.445997	−	0.366634i
$337$	13.5982			0.740739			0.370369	−	0.928885i	$-0.379231\pi$
$337$	13.5982			0.740739			0.370369	+	0.928885i	$0.379231\pi$
$338$	−4.16185	−	24.1295i	−0.226375	−	1.31247i
$339$	−8.23380	+	2.20624i	−0.447199	+	0.119827i
$340$	−4.86883	+	10.2409i	−0.264049	+	0.555390i
$341$	3.23334	−	12.0670i	0.175095	−	0.653465i
$342$	−4.79756	−	10.3895i	−0.259422	−	0.561799i
$343$	3.43842	−	18.1983i	0.185657	−	0.982615i
$344$	−14.7303	−	4.12433i	−0.794204	−	0.222369i
$345$	12.3344	−	7.12126i	0.664061	−	0.383396i
$346$	4.70673	+	0.429498i	0.253036	+	0.0230900i
$347$	−22.2328	+	5.95727i	−1.19352	+	0.319803i	−0.800277	−	0.599631i	$-0.795314\pi$
$347$	−22.2328	+	5.95727i	−1.19352	+	0.319803i	−0.393244	+	0.919434i	$0.628647\pi$
$348$	1.33614	+	0.245898i	0.0716246	+	0.0131815i
$349$	15.3660	−	15.3660i	0.822525	−	0.822525i	−0.163945	−	0.986470i	$-0.552422\pi$
$349$	15.3660	−	15.3660i	0.822525	−	0.822525i	0.986470	+	0.163945i	$0.0524219\pi$
$350$	4.08467	−	9.26977i	0.218335	−	0.495490i
$351$		−	5.50582i		−	0.293879i
$352$	4.57574	−	9.35284i	0.243888	−	0.498508i
$353$	5.00015	+	2.88684i	0.266131	+	0.153651i	0.627128	−	0.778916i	$-0.284230\pi$
$353$	5.00015	+	2.88684i	0.266131	+	0.153651i	−0.360997	+	0.932567i	$0.617564\pi$
$354$	−8.40173	−	10.0891i	−0.446547	−	0.536227i
$355$	−3.12841	+	11.6754i	−0.166039	+	0.619664i
$356$	−14.5045	−	12.3564i	−0.768736	−	0.654889i
$357$	1.72043	−	5.12206i	0.0910547	−	0.271088i
$358$	0.749831	+	1.62382i	0.0396298	+	0.0858214i
$359$	−15.3406	−	26.5707i	−0.809645	−	1.40235i	−0.913110	−	0.407713i	$-0.866327\pi$
$359$	−15.3406	−	26.5707i	−0.809645	−	1.40235i	0.103466	−	0.994633i	$-0.467007\pi$
$360$	5.48987	+	5.61424i	0.289342	+	0.295897i
$361$	−40.2519	−	23.2395i	−2.11852	−	1.22313i
$362$	21.9410	+	15.4856i	1.15319	+	0.813906i
$363$	5.38256	−	5.38256i	0.282511	−	0.282511i
$364$	−25.4826	−	14.1219i	−1.33565	−	0.740190i
$365$	−11.5303	−	11.5303i	−0.603521	−	0.603521i
$366$	2.70443	−	0.466460i	0.141363	−	0.0243823i
$367$	−10.9890	+	19.0335i	−0.573621	+	0.993541i	0.422569	+	0.906331i	$0.361128\pi$
$367$	−10.9890	+	19.0335i	−0.573621	+	0.993541i	−0.996190	+	0.0872102i	$0.972205\pi$
$368$	19.1763	+	7.30572i	0.999636	+	0.380837i
$369$	8.25878	−	4.76821i	0.429935	−	0.248223i
$370$	13.3876	−	36.3592i	0.695989	−	1.89023i
$371$	−11.7884	+	2.38414i	−0.612026	+	0.123779i
$372$	1.08208	+	13.5312i	0.0561034	+	0.701559i
$373$	22.7520	+	6.09639i	1.17806	+	0.315659i	0.794155	−	0.607716i	$-0.207914\pi$
$373$	22.7520	+	6.09639i	1.17806	+	0.315659i	0.383900	+	0.923375i	$0.374581\pi$
$374$	5.29405	+	0.483092i	0.273749	+	0.0249801i
$375$	3.18249	−	5.51224i	0.164343	−	0.284651i
$376$	−32.6316	−	19.3304i	−1.68285	−	0.996888i
$377$	3.74004			0.192622
$378$	−2.91682	−	2.34354i	−0.150025	−	0.120539i
$379$	12.0328	+	12.0328i	0.618085	+	0.618085i	0.945040	−	0.326955i	$-0.106022\pi$
$379$	12.0328	+	12.0328i	0.618085	+	0.618085i	−0.326955	+	0.945040i	$0.606022\pi$
$380$	44.1875	+	8.13209i	2.26677	+	0.417168i
$381$	1.48507	+	5.54237i	0.0760826	+	0.283944i
$382$	−22.2088	+	18.4946i	−1.13630	+	0.946264i
$383$	−12.2449	−	21.2088i	−0.625685	−	1.08372i	−0.988408	−	0.151821i	$-0.951486\pi$
$383$	−12.2449	−	21.2088i	−0.625685	−	1.08372i	0.362724	−	0.931897i	$-0.381847\pi$
$384$	−1.28022	+	11.2410i	−0.0653312	+	0.573642i
$385$	−13.4935	−	0.841015i	−0.687692	−	0.0428621i
$386$	−1.02167	+	2.77473i	−0.0520014	+	0.141230i
$387$	−5.22395	−	1.39975i	−0.265548	−	0.0711534i
$388$	−0.845893	−	2.37920i	−0.0429437	−	0.120785i
$389$	0.403284	+	1.50508i	0.0204473	+	0.0763104i	0.975396	−	0.220462i	$-0.0707565\pi$
$389$	0.403284	+	1.50508i	0.0204473	+	0.0763104i	−0.954948	+	0.296772i	$0.904090\pi$
$390$	17.6609	+	12.4648i	0.894295	+	0.631181i
$391$			10.4772i			0.529852i
$392$	−18.3280	+	7.48896i	−0.925704	+	0.378250i
$393$		−	0.0128809i		−	0.000649757i
$394$	−1.53005	+	2.16787i	−0.0770829	+	0.109216i
$395$	2.47480	+	9.23609i	0.124521	+	0.464718i
$396$	1.58063	−	3.32464i	0.0794298	−	0.167069i
$397$	8.49660	+	2.27666i	0.426432	+	0.114262i	0.465651	−	0.884969i	$-0.345820\pi$
$397$	8.49660	+	2.27666i	0.426432	+	0.114262i	−0.0392189	+	0.999231i	$0.512487\pi$
$398$	−10.6732	−	3.92992i	−0.535000	−	0.196989i
$399$	−21.3677	−	1.33179i	−1.06972	−	0.0666731i
$400$	−10.6916	+	1.72101i	−0.534580	+	0.0860506i
$401$	19.8143	+	34.3194i	0.989479	+	1.71383i	0.620033	+	0.784576i	$0.287119\pi$
$401$	19.8143	+	34.3194i	0.989479	+	1.71383i	0.369446	+	0.929252i	$0.379547\pi$
$402$	2.12202	+	2.54818i	0.105837	+	0.127092i
$403$	9.67181	+	36.0957i	0.481787	+	1.79805i
$404$	7.47788	−	5.15329i	0.372038	−	0.256386i
$405$	1.96307	+	1.96307i	0.0975459	+	0.0975459i
$406$	1.59194	−	1.98136i	0.0790067	−	0.0983334i
$407$	−18.1644			−0.900378
$408$	−5.59591	+	1.43244i	−0.277039	+	0.0709165i
$409$	−16.2655	+	28.1726i	−0.804276	+	1.39305i	0.112502	+	0.993651i	$0.464113\pi$
$409$	−16.2655	+	28.1726i	−0.804276	+	1.39305i	−0.916778	+	0.399396i	$0.869220\pi$
$410$	−3.40245	+	37.2864i	−0.168035	+	1.84145i
$411$	−13.5008	−	3.61754i	−0.665948	−	0.178440i
$412$	11.6383	−	13.6615i	0.573376	−	0.673052i
$413$	−24.0752	+	4.86907i	−1.18466	+	0.239591i
$414$	6.80837	+	2.50687i	0.334613	+	0.123206i
$415$	−11.0365	+	6.37191i	−0.541759	+	0.312785i
$416$	2.13491	+	31.0724i	0.104672	+	1.52345i
$417$	0.0899633	−	0.155821i	0.00440552	−	0.00763059i
$418$	−3.58018	−	20.7571i	−0.175112	−	1.01526i
$419$	13.0545	+	13.0545i	0.637755	+	0.637755i	0.950001	−	0.312246i	$-0.101081\pi$
$419$	13.0545	+	13.0545i	0.637755	+	0.637755i	−0.312246	+	0.950001i	$0.601081\pi$
$420$	14.1208	−	4.05060i	0.689025	−	0.197649i
$421$	−28.2316	+	28.2316i	−1.37593	+	1.37593i	−0.524540	+	0.851386i	$0.675763\pi$
$421$	−28.2316	+	28.2316i	−1.37593	+	1.37593i	−0.851386	+	0.524540i	$0.824237\pi$
$422$	−6.97553	+	9.88335i	−0.339563	+	0.481114i
$423$	−11.6128	−	6.70468i	−0.564636	−	0.325992i
$424$	8.98926	+	9.19290i	0.436557	+	0.446447i
$425$	−2.76449	−	4.78824i	−0.134098	−	0.232264i
$426$	−5.59009	+	2.58134i	−0.270841	+	0.125066i
$427$	1.63477	−	4.86702i	0.0791118	−	0.235532i
$428$	−0.701923	−	8.77738i	−0.0339288	−	0.424271i
$429$	2.62291	−	9.78885i	0.126635	−	0.472610i
$430$	16.3166	−	13.5878i	0.786858	−	0.655262i
$431$	13.9810	+	8.07196i	0.673443	+	0.388812i	0.797380	−	0.603478i	$-0.206219\pi$
$431$	13.9810	+	8.07196i	0.673443	+	0.388812i	−0.123937	+	0.992290i	$0.539552\pi$
$432$	−0.408088	+	3.97913i	−0.0196341	+	0.191446i
$433$			28.5121i			1.37021i	0.728447	+	0.685103i	$0.240243\pi$
$433$			28.5121i			1.37021i	−0.728447	+	0.685103i	$0.759757\pi$
$434$	23.2392	+	10.2402i	1.11552	+	0.491546i
$435$	−1.33349	+	1.33349i	−0.0639362	+	0.0639362i
$436$	14.4450	−	9.95461i	0.691791	−	0.476740i
$437$	40.0987	−	10.7444i	1.91818	−	0.513975i
$438$	0.754846	−	8.27212i	0.0360679	−	0.395257i
$439$	−13.7356	+	7.93025i	−0.655564	+	0.378490i	−0.790585	−	0.612353i	$-0.790223\pi$
$439$	−13.7356	+	7.93025i	−0.655564	+	0.378490i	0.135021	+	0.990843i	$0.456890\pi$
$440$	7.08593	+	12.5969i	0.337809	+	0.600535i
$441$	−6.44986	+	2.72016i	−0.307136	+	0.129531i
$442$	−14.4369	+	6.66651i	−0.686691	+	0.317094i
$443$	1.46322	−	5.46080i	0.0695196	−	0.259451i	−0.922415	−	0.386200i	$-0.873788\pi$
$443$	1.46322	−	5.46080i	0.0695196	−	0.259451i	0.991935	+	0.126749i	$0.0404543\pi$
$444$	18.5968	−	6.61186i	0.882566	−	0.313785i
$445$	25.5479	−	6.84553i	1.21109	−	0.324509i
$446$	0.170928	−	0.0294818i	0.00809370	−	0.00139600i
$447$	3.31484			0.156786
$448$	17.3699	+	12.0949i	0.820652	+	0.571429i
$449$	−7.40443			−0.349437			−0.174718	−	0.984618i	$-0.555901\pi$
$449$	−7.40443			−0.349437			−0.174718	+	0.984618i	$0.555901\pi$
$450$	−3.77300	+	0.650767i	−0.177861	+	0.0306775i
$451$	16.9549	−	4.54305i	0.798374	−	0.213924i
$452$	16.0635	−	5.71116i	0.755562	−	0.268630i
$453$	5.50265	−	20.5362i	0.258537	−	0.964873i
$454$	−28.2797	+	13.0587i	−1.32723	+	0.612875i
$455$	36.2130	−	18.0027i	1.69769	−	0.843979i
$456$	11.2210	+	19.9480i	0.525470	+	0.934149i
$457$	−21.1446	+	12.2078i	−0.989103	+	0.571059i	−0.905006	−	0.425399i	$-0.860134\pi$
$457$	−21.1446	+	12.2078i	−0.989103	+	0.571059i	−0.0840969	+	0.996458i	$0.526801\pi$
$458$	−0.965808	+	10.5840i	−0.0451292	+	0.494557i
$459$	−1.97266	+	0.528572i	−0.0920757	+	0.0246716i
$460$	−23.4549	+	16.1637i	−1.09359	+	0.753635i
$461$	10.6706	−	10.6706i	0.496981	−	0.496981i	−0.413516	−	0.910497i	$-0.635699\pi$
$461$	10.6706	−	10.6706i	0.496981	−	0.496981i	0.910497	+	0.413516i	$0.135699\pi$
$462$	−4.06940	−	5.55614i	−0.189326	−	0.258495i
$463$		−	20.3520i		−	0.945839i	−0.881106	−	0.472919i	$-0.843200\pi$
$463$		−	20.3520i		−	0.945839i	0.881106	−	0.472919i	$-0.156800\pi$
$464$	−2.70298	−	0.277210i	−0.125483	−	0.0128691i
$465$	−16.3182	−	9.42130i	−0.756737	−	0.436903i
$466$	−11.0576	+	9.20827i	−0.512232	+	0.426565i
$467$	−1.73154	+	6.46219i	−0.0801260	+	0.299034i	−0.994347	−	0.106182i	$-0.966137\pi$
$467$	−1.73154	+	6.46219i	−0.0801260	+	0.299034i	0.914221	+	0.405217i	$0.132804\pi$
$468$	0.877794	+	10.9766i	0.0405760	+	0.507393i
$469$	6.08065	−	1.22978i	0.280778	−	0.0567858i
$470$	47.7972	−	22.0713i	2.20472	−	1.01807i
$471$	3.69726	+	6.40385i	0.170361	+	0.295074i
$472$	18.3585	+	18.7744i	0.845018	+	0.864162i
$473$	−8.62088	−	4.97727i	−0.396389	−	0.228855i
$474$	−2.80870	+	3.97954i	−0.129008	+	0.182786i
$475$	−15.4908	+	15.4908i	−0.710766	+	0.710766i
$476$	−2.61329	+	10.4858i	−0.119780	+	0.480616i
$477$	3.21438	+	3.21438i	0.147177	+	0.147177i
$478$	−1.85405	−	10.7493i	−0.0848021	−	0.491663i
$479$	−8.38510	+	14.5234i	−0.383125	+	0.663592i	−0.991507	−	0.130052i	$-0.958486\pi$
$479$	−8.38510	+	14.5234i	−0.383125	+	0.663592i	0.608382	+	0.793644i	$0.291819\pi$
$480$	−11.8399	−	10.3175i	−0.540414	−	0.470928i
$481$	47.0553	−	27.1674i	2.14554	−	1.23873i
$482$	−1.15217	−	0.424234i	−0.0524799	−	0.0193233i
$483$	10.1762	−	8.98212i	0.463034	−	0.408701i
$484$	−9.87272	+	11.5890i	−0.448760	+	0.526773i
$485$	3.38566	+	0.907185i	0.153735	+	0.0411931i
$486$	−0.128516	+	1.40836i	−0.00582959	+	0.0638846i
$487$	10.4571	−	18.1121i	0.473854	−	0.820740i	−0.525698	−	0.850671i	$-0.676196\pi$
$487$	10.4571	−	18.1121i	0.473854	−	0.820740i	0.999552	+	0.0299319i	$0.00952903\pi$
$488$	−5.31728	+	1.36112i	−0.240702	+	0.0616150i
$489$	8.12653			0.367494
$490$	5.87668	−	26.8474i	0.265482	−	1.21284i
$491$	4.47715	+	4.47715i	0.202051	+	0.202051i	0.800878	−	0.598827i	$-0.204366\pi$
$491$	4.47715	+	4.47715i	0.202051	+	0.202051i	−0.598827	+	0.800878i	$0.704366\pi$
$492$	−15.7048	+	10.8228i	−0.708027	+	0.487928i
$493$	−0.359053	−	1.34000i	−0.0161709	−	0.0603508i
$494$	40.3195	+	48.4169i	1.81406	+	2.17838i
$495$	2.55498	+	4.42535i	0.114838	+	0.198905i
$496$	−4.31456	−	26.8037i	−0.193729	−	1.20352i
$497$	−0.716575	+	11.4969i	−0.0321428	+	0.515709i
$498$	−6.09194	−	2.24308i	−0.272986	−	0.100515i
$499$	−12.2645	−	3.28627i	−0.549036	−	0.147114i	−0.0263716	−	0.999652i	$-0.508395\pi$
$499$	−12.2645	−	3.28627i	−0.549036	−	0.147114i	−0.522665	+	0.852538i	$0.675062\pi$
$500$	−5.46591	+	11.4968i	−0.244443	+	0.514151i
$501$	1.41472	+	5.27981i	0.0632050	+	0.235884i
$502$	−15.5035	+	21.9664i	−0.691957	+	0.980406i
$503$		−	28.2260i		−	1.25853i	−0.777189	−	0.629267i	$-0.783355\pi$
$503$		−	28.2260i		−	1.25853i	0.777189	−	0.629267i	$-0.216645\pi$
$504$	6.18870	+	4.20713i	0.275667	+	0.187401i
$505$			12.6062i			0.560966i
$506$	10.9104	+	7.70042i	0.485027	+	0.342325i
$507$	4.48120	+	16.7241i	0.199017	+	0.742743i
$508$	−3.84432	−	10.8127i	−0.170564	−	0.479736i
$509$	23.9845	+	6.42663i	1.06309	+	0.284855i	0.747653	−	0.664089i	$-0.231181\pi$
$509$	23.9845	+	6.42663i	1.06309	+	0.284855i	0.315442	+	0.948945i	$0.397847\pi$
$510$	2.77048	−	7.52430i	0.122679	−	0.333182i
$511$	−12.9486	−	8.59214i	−0.572814	−	0.380094i
$512$	0.760138	−	22.6146i	0.0335937	−	0.999436i
$513$	4.04595	+	7.00780i	0.178633	+	0.309402i
$514$	−6.53141	+	5.43908i	−0.288088	+	0.239908i
$515$	6.44767	+	24.0630i	0.284118	+	1.06034i
$516$	10.6378	+	1.95774i	0.468304	+	0.0861848i
$517$	−17.4525	−	17.4525i	−0.767562	−	0.767562i
$518$	5.63651	−	36.4922i	0.247654	−	1.60338i
$519$	−3.34199			−0.146697
$520$	−37.1967	−	22.0346i	−1.63118	−	0.966282i
$521$	1.13672	−	1.96885i	0.0498004	−	0.0862568i	−0.840051	−	0.542508i	$-0.817475\pi$
$521$	1.13672	−	1.96885i	0.0498004	−	0.0862568i	0.889851	+	0.456251i	$0.150808\pi$
$522$	−0.956685	−	0.0872993i	−0.0418730	−	0.00382099i
$523$	17.4880	+	4.68590i	0.764697	+	0.204900i	0.620028	−	0.784580i	$-0.287121\pi$
$523$	17.4880	+	4.68590i	0.764697	+	0.204900i	0.144670	+	0.989480i	$0.453788\pi$
$524$	0.00205361	+	0.0256799i	8.97124e−5	+	0.00112183i
$525$	−2.28069	+	6.79007i	−0.0995375	+	0.296343i
$526$	−3.33167	+	9.04843i	−0.145268	+	0.394530i
$527$	12.0041	−	6.93054i	0.522905	−	0.301899i
$528$	−2.62116	+	6.88012i	−0.114071	+	0.299419i
$529$	−1.65956	+	2.87444i	−0.0721546	+	0.124975i
$530$	−17.5879	+	3.03356i	−0.763968	+	0.131769i
$531$	6.56464	+	6.56464i	0.284881	+	0.284881i
$532$	42.8117	−	0.751546i	1.85612	−	0.0325837i
$533$	−37.1272	+	37.1272i	−1.60816	+	1.60816i
$534$	11.0078	+	7.76913i	0.476353	+	0.336203i
$535$	10.5852	+	6.11140i	0.457640	+	0.264219i
$536$	−4.63679	−	4.74183i	−0.200279	−	0.204816i
$537$	−0.632360	−	1.09528i	−0.0272883	−	0.0472648i
$538$	−11.5132	−	24.9327i	−0.496368	−	1.07492i
$539$	−12.7631	+	1.76354i	−0.549747	+	0.0759613i
$540$	−4.22662	−	3.60068i	−0.181885	−	0.154948i
$541$	9.83611	−	36.7088i	0.422887	−	1.57824i	−0.345607	−	0.938379i	$-0.612327\pi$
$541$	9.83611	−	36.7088i	0.422887	−	1.57824i	0.768494	−	0.639857i	$-0.221006\pi$
$542$	10.0123	+	12.0231i	0.430065	+	0.516435i
$543$	−16.4455	−	9.49480i	−0.705743	−	0.407461i
$544$	10.9278	−	3.74793i	0.468527	−	0.160691i
$545$			24.3513i			1.04310i
$546$	18.8518	+	8.30694i	0.806784	+	0.355504i
$547$	17.5002	−	17.5002i	0.748254	−	0.748254i	−0.225897	−	0.974151i	$-0.572531\pi$
$547$	17.5002	−	17.5002i	0.748254	−	0.748254i	0.974151	+	0.225897i	$0.0725312\pi$
$548$	27.4925	+	5.05961i	1.17442	+	0.216136i
$549$	−1.87444	+	0.502253i	−0.0799989	+	0.0214357i
$550$	−7.01807	−	0.640412i	−0.299252	−	0.0273072i
$551$	−4.76032	+	2.74837i	−0.202797	+	0.117085i
$552$	−13.9731	−	3.91232i	−0.594733	−	0.166519i
$553$	4.05655	+	8.15988i	0.172502	+	0.346994i
$554$	−16.5282	−	35.7932i	−0.702218	−	1.52071i
$555$	−7.09094	+	26.4638i	−0.300994	+	1.12332i
$556$	−0.154512	+	0.324993i	−0.00655275	+	0.0137828i
$557$	12.5038	−	3.35039i	0.529804	−	0.141961i	0.0160062	−	0.999872i	$-0.494905\pi$
$557$	12.5038	−	3.35039i	0.529804	−	0.141961i	0.513798	+	0.857911i	$0.328238\pi$
$558$	−1.63147	−	9.45886i	−0.0690654	−	0.400426i
$559$	29.7767			1.25942
$560$	−27.5060	+	10.3267i	−1.16234	+	0.436383i
$561$	−3.75901			−0.158706
$562$	2.29087	+	13.2819i	0.0966343	+	0.560264i
$563$	41.1101	−	11.0154i	1.73259	−	0.464245i	0.751809	−	0.659381i	$-0.229181\pi$
$563$	41.1101	−	11.0154i	1.73259	−	0.464245i	0.980776	+	0.195136i	$0.0625148\pi$
$564$	24.2207	+	11.5152i	1.01988	+	0.484879i
$565$	−6.12497	+	22.8587i	−0.257680	+	0.961673i
$566$	4.37737	+	9.47954i	0.183995	+	0.398455i
$567$	2.20456	+	1.46285i	0.0925828	+	0.0614338i
$568$	10.7331	−	6.03747i	0.450349	−	0.253327i
$569$	−30.9761	+	17.8840i	−1.29858	+	0.749738i	−0.980159	−	0.198210i	$-0.936487\pi$
$569$	−30.9761	+	17.8840i	−1.29858	+	0.749738i	−0.318424	+	0.947948i	$0.603154\pi$
$570$	−31.6385	−	2.88707i	−1.32519	−	0.120926i
$571$	19.9656	−	5.34978i	0.835536	−	0.223881i	0.184409	−	0.982850i	$-0.440963\pi$
$571$	19.9656	−	5.34978i	0.835536	−	0.223881i	0.651127	+	0.758968i	$0.274296\pi$
$572$	−3.66850	+	19.9336i	−0.153387	+	0.833464i
$573$	14.4506	−	14.4506i	0.603683	−	0.603683i
$574$	3.86577	+	35.4720i	0.161354	+	1.48057i
$575$		−	13.8891i		−	0.579214i
$576$	0.179185	−	7.99799i	0.00746604	−	0.333250i
$577$	32.8375	+	18.9587i	1.36704	+	0.789263i	0.990549	−	0.137156i	$-0.0437962\pi$
$577$	32.8375	+	18.9587i	1.36704	+	0.789263i	0.376494	+	0.926419i	$0.377130\pi$
$578$	−11.6103	−	13.9420i	−0.482925	−	0.579911i
$579$	0.541140	−	2.01956i	0.0224890	−	0.0839301i
$580$	2.44590	−	2.87110i	0.101561	−	0.119216i
$581$	−9.10540	+	8.03696i	−0.377756	+	0.333429i
$582$	0.748544	+	1.62103i	0.0310281	+	0.0671939i
$583$	4.18358	+	7.24618i	0.173266	+	0.300106i
$584$	−0.186061	+	16.6119i	−0.00769928	+	0.687407i
$585$	−13.2374	−	7.64264i	−0.547301	−	0.315984i
$586$	−34.4060	−	24.2833i	−1.42130	−	1.00313i
$587$	0.303911	−	0.303911i	0.0125438	−	0.0125438i	−0.700807	−	0.713351i	$-0.747177\pi$
$587$	0.303911	−	0.303911i	0.0125438	−	0.0125438i	0.713351	+	0.700807i	$0.247177\pi$
$588$	12.4250	−	6.45130i	0.512398	−	0.266047i
$589$	−38.8352	−	38.8352i	−1.60018	−	1.60018i
$590$	−35.9192	+	6.19535i	−1.47877	+	0.255058i
$591$	0.938130	−	1.62489i	0.0385895	−	0.0668390i
$592$	−36.0211	+	16.1465i	−1.48046	+	0.663619i
$593$	−24.7998	+	14.3182i	−1.01841	+	0.587977i	−0.913642	−	0.406520i	$-0.866742\pi$
$593$	−24.7998	+	14.3182i	−1.01841	+	0.587977i	−0.104764	+	0.994497i	$0.533409\pi$
$594$	−0.899418	+	2.44272i	−0.0369036	+	0.100226i
$595$	−9.92664	−	11.2463i	−0.406953	−	0.461053i
$596$	−6.60858	+	0.528486i	−0.270698	+	0.0216476i
$597$	7.76841	+	2.08154i	0.317940	+	0.0851917i
$598$	−39.7807	−	3.63006i	−1.62675	−	0.148444i
$599$	−19.1600	+	33.1861i	−0.782856	+	1.35595i	0.147416	+	0.989075i	$0.452905\pi$
$599$	−19.1600	+	33.1861i	−0.782856	+	1.35595i	−0.930272	+	0.366872i	$0.880429\pi$
$600$	7.41823	−	1.89892i	0.302848	−	0.0775232i
$601$	−4.60200			−0.187720			−0.0938598	−	0.995585i	$-0.529921\pi$
$601$	−4.60200			−0.187720			−0.0938598	+	0.995585i	$0.529921\pi$
$602$	12.6744	−	15.7748i	0.516570	−	0.642934i
$603$	−1.65803	−	1.65803i	−0.0675200	−	0.0675200i
$604$	−7.69619	+	41.8189i	−0.313153	+	1.70159i
$605$	−5.46955	−	20.4126i	−0.222369	−	0.829892i
$606$	−4.93464	+	4.10936i	−0.200456	+	0.166931i
$607$	5.30207	+	9.18346i	0.215204	+	0.372745i	0.953336	−	0.301912i	$-0.0976249\pi$
$607$	5.30207	+	9.18346i	0.215204	+	0.372745i	−0.738131	+	0.674657i	$0.764292\pi$
$608$	−25.5508	−	37.9800i	−1.03622	−	1.54029i
$609$	−0.993697	+	1.49753i	−0.0402666	+	0.0606831i
$610$	2.63253	−	7.14966i	0.106588	−	0.289481i
$611$	71.3138	+	19.1085i	2.88505	+	0.773046i
$612$	3.84849	−	1.36828i	0.155566	−	0.0553095i
$613$	11.9321	+	44.5312i	0.481932	+	1.79860i	0.593493	+	0.804839i	$0.297748\pi$
$613$	11.9321	+	44.5312i	0.481932	+	1.79860i	−0.111561	+	0.993758i	$0.535585\pi$
$614$	−24.1767	−	17.0636i	−0.975693	−	0.688631i
$615$		−	26.4750i		−	1.06758i
$616$	8.99872	+	10.4281i	0.362569	+	0.420161i
$617$			18.7866i			0.756318i	0.925741	+	0.378159i	$0.123443\pi$
$617$			18.7866i			0.756318i	−0.925741	+	0.378159i	$0.876557\pi$
$618$	−7.31758	+	10.3680i	−0.294356	+	0.417062i
$619$	−5.97382	−	22.2946i	−0.240108	−	0.896096i	−0.975779	−	0.218757i	$-0.929800\pi$
$619$	−5.97382	−	22.2946i	−0.240108	−	0.896096i	0.735671	−	0.677339i	$-0.236867\pi$
$620$	34.0345	+	16.1810i	1.36686	+	0.649846i
$621$	−4.95541	−	1.32780i	−0.198854	−	0.0532827i
$622$	5.34329	+	1.96742i	0.214246	+	0.0788863i
$623$	22.5710	−	11.2208i	0.904288	−	0.449552i
$624$	−3.50000	−	21.7434i	−0.140112	−	0.870432i
$625$	−15.6035	−	27.0261i	−0.624140	−	1.08104i
$626$	−12.6359	−	15.1736i	−0.505034	−	0.606460i
$627$	3.85490	+	14.3867i	0.153950	+	0.574549i
$628$	−8.39196	−	12.1775i	−0.334876	−	0.485934i
$629$	−14.2511	−	14.2511i	−0.568229	−	0.568229i
$630$	−9.68332	+	3.75973i	−0.385793	+	0.149791i
$631$	10.9811			0.437151			0.218575	−	0.975820i	$-0.429859\pi$
$631$	10.9811			0.437151			0.218575	+	0.975820i	$0.429859\pi$
$632$	4.96507	−	8.38154i	0.197500	−	0.333400i
$633$	4.27695	−	7.40790i	0.169994	−	0.294437i
$634$	−0.0792564	+	0.868546i	−0.00314767	+	0.0344944i
$635$	15.3867	+	4.12287i	0.610605	+	0.163611i
$636$	−6.92078	−	5.89584i	−0.274427	−	0.233785i
$637$	30.4255	−	23.6575i	1.20550	−	0.937344i
$638$	−1.65931	−	0.610965i	−0.0656928	−	0.0241883i
$639$	3.77056	−	2.17694i	0.149161	−	0.0861182i
$640$	25.2493	+	18.6817i	0.998068	+	0.738459i
$641$	18.8302	−	32.6149i	0.743748	−	1.28821i	−0.207029	−	0.978335i	$-0.566379\pi$
$641$	18.8302	−	32.6149i	0.743748	−	1.28821i	0.950777	−	0.309875i	$-0.100287\pi$
$642$	1.05830	+	6.13576i	0.0417676	+	0.242159i
$643$	9.96576	+	9.96576i	0.393011	+	0.393011i	0.875759	−	0.482748i	$-0.160361\pi$
$643$	9.96576	+	9.96576i	0.393011	+	0.393011i	−0.482748	+	0.875759i	$0.660361\pi$
$644$	−18.8556	+	19.5295i	−0.743016	+	0.769569i
$645$	−10.6167	+	10.6167i	−0.418034	+	0.418034i
$646$	13.4763	−	19.0941i	0.530219	−	0.751246i
$647$	−26.6441	−	15.3830i	−1.04749	−	0.604768i	−0.125544	−	0.992088i	$-0.540067\pi$
$647$	−26.6441	−	15.3830i	−1.04749	−	0.604768i	−0.921945	+	0.387320i	$0.873401\pi$
$648$	0.0316777	−	2.82825i	0.00124442	−	0.111104i
$649$	8.54401	+	14.7987i	0.335382	+	0.580898i
$650$	19.1383	−	8.83748i	0.750664	−	0.346635i
$651$	−17.0226	−	5.71766i	−0.667169	−	0.224093i
$652$	−16.2013	+	1.29561i	−0.634493	+	0.0507402i
$653$	−7.07378	+	26.3997i	−0.276818	+	1.03310i	0.677794	+	0.735251i	$0.262936\pi$
$653$	−7.07378	+	26.3997i	−0.276818	+	1.03310i	−0.954613	+	0.297849i	$0.903731\pi$
$654$	−9.53225	+	7.93806i	−0.372741	+	0.310403i
$655$	−0.0309691	−	0.0178800i	−0.00121006	−	0.000698631i
$656$	29.5842	−	24.0805i	1.15507	−	0.940184i
$657$			5.87357i			0.229150i
$658$	40.4776	−	29.6464i	1.57798	−	1.15574i
$659$	−5.34039	+	5.34039i	−0.208032	+	0.208032i	−0.803431	−	0.595398i	$-0.796994\pi$
$659$	−5.34039	+	5.34039i	−0.208032	+	0.208032i	0.595398	+	0.803431i	$0.296994\pi$
$660$	−5.79923	−	8.41520i	−0.225735	−	0.327561i
$661$	−12.1632	+	3.25911i	−0.473092	+	0.126765i	−0.487484	−	0.873132i	$-0.662085\pi$
$661$	−12.1632	+	3.25911i	−0.473092	+	0.126765i	0.0143922	+	0.999896i	$0.495419\pi$
$662$	3.22649	−	35.3581i	0.125401	−	1.37423i
$663$	9.73779	−	5.62211i	0.378184	−	0.218345i
$664$	12.5027	+	3.50064i	0.485200	+	0.135851i
$665$	−32.8625	+	49.5249i	−1.27435	+	1.92049i
$666$	−12.6707	+	5.85094i	−0.490978	+	0.226719i
$667$	0.901959	−	3.36616i	0.0349240	−	0.130338i
$668$	−3.66220	−	10.3005i	−0.141695	−	0.398537i
$669$	−0.118470	+	0.0317440i	−0.00458032	+	0.00122729i
$670$	9.07208	−	1.56475i	0.350485	−	0.0604517i
$671$	−3.57184			−0.137890
$672$	−13.0088	−	7.40082i	−0.501824	−	0.285493i
$673$	−24.8040			−0.956124			−0.478062	−	0.878326i	$-0.658660\pi$
$673$	−24.8040			−0.956124			−0.478062	+	0.878326i	$0.658660\pi$
$674$	18.9509	−	3.26865i	0.729960	−	0.125904i
$675$	2.61506	−	0.700703i	0.100654	−	0.0269701i
$676$	−11.6002	−	32.6273i	−0.446162	−	1.25490i
$677$	−11.4179	+	42.6123i	−0.438827	+	1.63772i	0.292912	+	0.956140i	$0.405376\pi$
$677$	−11.4179	+	42.6123i	−0.438827	+	1.63772i	−0.731739	+	0.681585i	$0.761291\pi$
$678$	−10.9446	+	5.05389i	−0.420325	+	0.194094i
$679$	3.33392	+	0.207795i	0.127944	+	0.00797443i
$680$	−4.32372	+	15.4424i	−0.165807	+	0.592190i
$681$	19.0749	−	11.0129i	0.730951	−	0.422015i
$682$	1.60550	−	17.5942i	0.0614779	−	0.673717i
$683$	29.6672	−	7.94930i	1.13518	−	0.304171i	0.358170	−	0.933656i	$-0.383401\pi$
$683$	29.6672	−	7.94930i	1.13518	−	0.304171i	0.777013	+	0.629485i	$0.216734\pi$
$684$	−9.18341	−	13.3259i	−0.351136	−	0.509530i
$685$	−27.4381	+	27.4381i	−1.04835	+	1.04835i
$686$	0.417507	−	26.1883i	0.0159405	−	0.999873i
$687$		−	7.51510i		−	0.286719i
$688$	−21.5200	−	2.20703i	−0.820444	−	0.0841424i
$689$	−21.6753	−	12.5142i	−0.825763	−	0.476755i
$690$	15.4779	−	12.8893i	0.589233	−	0.490688i
$691$	10.1409	−	37.8465i	0.385779	−	1.43975i	−0.451155	−	0.892446i	$-0.648988\pi$
$691$	10.1409	−	37.8465i	0.385779	−	1.43975i	0.836935	−	0.547303i	$-0.184345\pi$
$692$	6.66271	−	0.532814i	0.253278	−	0.0202546i
$693$	3.22262	+	3.65104i	0.122417	+	0.138691i
$694$	−29.5525	+	13.6465i	−1.12180	+	0.518013i
$695$	−0.249757	−	0.432591i	−0.00947381	−	0.0164091i
$696$	1.92120	+	0.0215183i	0.0728229	+	0.000815651i
$697$	16.8664	+	9.73784i	0.638862	+	0.368847i
$698$	17.7210	−	25.1082i	0.670752	−	0.950361i
$699$	7.19483	−	7.19483i	0.272133	−	0.272133i
$700$	3.46432	−	13.9005i	0.130939	−	0.525391i
$701$	20.2522	+	20.2522i	0.764913	+	0.764913i	0.977206	−	0.212293i	$-0.0680931\pi$
$701$	20.2522	+	20.2522i	0.764913	+	0.764913i	−0.212293	+	0.977206i	$0.568093\pi$
$702$	−1.32346	−	7.67311i	−0.0499507	−	0.289603i
$703$	−39.9280	+	69.1573i	−1.50591	+	2.60832i
$704$	4.12873	−	14.1343i	0.155608	−	0.532708i
$705$	−32.2396	+	18.6135i	−1.21421	+	0.701027i
$706$	7.66231	+	2.82129i	0.288375	+	0.106181i
$707$	2.38150	+	11.7754i	0.0895656	+	0.442859i
$708$	−14.1341	−	12.0409i	−0.531192	−	0.452525i
$709$	33.4610	+	8.96584i	1.25665	+	0.336719i	0.824903	−	0.565274i	$-0.191230\pi$
$709$	33.4610	+	8.96584i	1.25665	+	0.336719i	0.431750	+	0.901993i	$0.357896\pi$
$710$	−1.55340	+	17.0232i	−0.0582980	+	0.638869i
$711$	1.72212	−	2.98280i	0.0645845	−	0.111864i
$712$	−23.1841	−	13.7338i	−0.868862	−	0.514698i
$713$	34.8197			1.30401
$714$	1.16644	−	7.55183i	0.0436528	−	0.282620i
$715$	−19.8941	−	19.8941i	−0.743997	−	0.743997i
$716$	1.43532	+	2.08277i	0.0536402	+	0.0778368i
$717$	1.99631	+	7.45034i	0.0745537	+	0.278238i
$718$	−27.7661	−	33.3423i	−1.03622	−	1.24432i
$719$	−15.0728	−	26.1069i	−0.562121	−	0.973622i	−0.997311	−	0.0732836i	$-0.976652\pi$
$719$	−15.0728	−	26.1069i	−0.562121	−	0.973622i	0.435190	−	0.900339i	$-0.356681\pi$
$720$	9.00040	+	6.50459i	0.335425	+	0.242412i
$721$	10.5686	+	21.2592i	0.393597	+	0.791732i
$722$	−61.6827	−	22.7118i	−2.29559	−	0.845246i
$723$	0.838597	+	0.224701i	0.0311877	+	0.00835673i
$724$	34.3001	+	16.3073i	1.27475	+	0.606055i
$725$	0.475980	+	1.77638i	0.0176774	+	0.0659731i
$726$	6.20750	−	8.79516i	0.230382	−	0.326419i
$727$		−	30.4180i		−	1.12814i	−0.825726	−	0.564071i	$-0.809234\pi$
$727$		−	30.4180i		−	1.12814i	0.825726	−	0.564071i	$-0.190766\pi$
$728$	−38.9080	−	13.5555i	−1.44203	−	0.502399i
$729$		−	1.00000i		−	0.0370370i
$730$	−18.8405	−	13.2974i	−0.697320	−	0.492159i
$731$	−2.85864	−	10.6686i	−0.105731	−	0.394592i
$732$	3.65687	−	1.30015i	0.135162	−	0.0480550i
$733$	−0.954032	−	0.255632i	−0.0352380	−	0.00944199i	0.241157	−	0.970486i	$-0.422473\pi$
$733$	−0.954032	−	0.255632i	−0.0352380	−	0.00944199i	−0.276395	+	0.961044i	$0.589140\pi$
$734$	−10.7395	+	29.1672i	−0.396402	+	1.07658i
$735$	−2.41310	+	19.2830i	−0.0890084	+	0.711265i
$736$	28.4809	+	5.57201i	1.04982	+	0.205387i
$737$	−2.15795	−	3.73768i	−0.0794892	−	0.137679i
$738$	10.3636	−	8.63034i	0.381488	−	0.317687i
$739$	1.18278	+	4.41418i	0.0435091	+	0.162378i	0.984262	−	0.176714i	$-0.0565468\pi$
$739$	1.18278	+	4.41418i	0.0435091	+	0.162378i	−0.940753	+	0.339092i	$0.889880\pi$
$740$	9.91763	−	53.8896i	0.364579	−	1.98102i
$741$	−31.5034	−	31.5034i	−1.15731	−	1.15731i
$742$	−15.8557	+	6.15627i	−0.582082	+	0.226004i
$743$	13.8598			0.508467			0.254234	−	0.967143i	$-0.418177\pi$
$743$	13.8598			0.508467			0.254234	+	0.967143i	$0.418177\pi$
$744$	4.76058	+	18.5974i	0.174531	+	0.681814i
$745$	4.60133	−	7.96974i	0.168580	−	0.291989i
$746$	33.1734	+	3.02714i	1.21457	+	0.110831i
$747$	4.43397	+	1.18808i	0.162230	+	0.0434695i
$748$	7.49410	−	0.599300i	0.274011	−	0.0219126i
$749$	11.0422	+	3.70892i	0.403473	+	0.135521i
$750$	3.11023	−	8.44704i	0.113570	−	0.308442i
$751$	−6.93018	+	4.00114i	−0.252886	+	0.146004i	−0.621085	−	0.783743i	$-0.713308\pi$
$751$	−6.93018	+	4.00114i	−0.252886	+	0.146004i	0.368199	+	0.929747i	$0.379974\pi$
$752$	−50.1231	−	19.0957i	−1.82780	−	0.696348i
$753$	9.50579	−	16.4645i	0.346410	−	0.600000i
$754$	5.21226	−	0.899011i	0.189819	−	0.0327400i
$755$	−41.7361	−	41.7361i	−1.51893	−	1.51893i
$756$	−4.62831	−	2.56491i	−0.168330	−	0.0932849i
$757$	14.3545	−	14.3545i	0.521724	−	0.521724i	−0.396368	−	0.918092i	$-0.629730\pi$
$757$	14.3545	−	14.3545i	0.521724	−	0.521724i	0.918092	+	0.396368i	$0.129730\pi$
$758$	19.6618	+	13.8770i	0.714148	+	0.504035i
$759$	−8.17772	−	4.72141i	−0.296832	−	0.171376i
$760$	63.5360	+	0.711633i	2.30469	+	0.0258136i
$761$	6.93048	+	12.0039i	0.251230	+	0.435142i	0.963865	−	0.266393i	$-0.0858317\pi$
$761$	6.93048	+	12.0039i	0.251230	+	0.435142i	−0.712635	+	0.701535i	$0.752498\pi$
$762$	3.40190	+	7.36707i	0.123238	+	0.266881i
$763$	4.60035	+	22.7465i	0.166544	+	0.823480i
$764$	−26.5054	+	31.1131i	−0.958931	+	1.12563i
$765$	−1.46742	+	5.47650i	−0.0530548	+	0.198003i
$766$	−22.1630	−	26.6139i	−0.800780	−	0.961601i
$767$	−44.2668	−	25.5575i	−1.59838	−	0.922827i
$768$	0.917892	+	15.9736i	0.0331216	+	0.576399i
$769$			17.2769i			0.623023i	0.950242	+	0.311511i	$0.100835\pi$
$769$			17.2769i			0.623023i	−0.950242	+	0.311511i	$0.899165\pi$
$770$	−19.0072	+	2.07142i	−0.684971	+	0.0746488i
$771$	4.24979	−	4.24979i	0.153053	−	0.153053i
$772$	−0.756856	+	4.11254i	−0.0272398	+	0.148014i
$773$	39.1418	−	10.4880i	1.40783	−	0.377228i	0.526683	−	0.850062i	$-0.323436\pi$
$773$	39.1418	−	10.4880i	1.40783	−	0.377228i	0.881152	+	0.472834i	$0.156769\pi$
$774$	−7.61675	−	0.695042i	−0.273778	−	0.0249828i
$775$	−15.9132	+	9.18750i	−0.571619	+	0.330025i
$776$	−1.75077	−	3.11240i	−0.0628488	−	0.111729i
$777$	−1.62421	+	26.0593i	−0.0582683	+	0.934874i
$778$	0.923812	+	2.00059i	0.0331203	+	0.0717245i
$779$	19.9725	−	74.5383i	0.715589	−	2.67061i
$780$	27.6091	+	13.1262i	0.988564	+	0.469993i
$781$	7.74079	−	2.07414i	0.276987	−	0.0742185i
$782$	2.51844	+	14.6013i	0.0900592	+	0.522143i
$783$	0.679289			0.0242758
$784$	−23.7424	+	14.8425i	−0.847943	+	0.530088i
$785$	20.5287			0.732701
$786$	−0.00309625	−	0.0179513i	−0.000110439	−	0.000640303i
$787$	−8.88638	+	2.38110i	−0.316765	+	0.0848770i	−0.413699	−	0.910414i	$-0.635763\pi$
$787$	−8.88638	+	2.38110i	−0.316765	+	0.0848770i	0.0969334	+	0.995291i	$0.469097\pi$
$788$	−1.61123	+	3.38900i	−0.0573978	+	0.120728i
$789$	1.76466	−	6.58582i	0.0628237	−	0.234461i
$790$	5.66909	+	12.2769i	0.201697	+	0.436791i
$791$	−1.40295	+	22.5094i	−0.0498833	+	0.800342i
$792$	1.40367	−	5.01328i	0.0498772	−	0.178139i
$793$	9.25293	−	5.34218i	0.328581	−	0.189706i
$794$	12.3884	+	1.13046i	0.439648	+	0.0401187i
$795$	12.1901	−	3.26633i	0.432339	−	0.115845i
$796$	−15.8192	−	2.91131i	−0.560698	−	0.103189i
$797$	16.7457	−	16.7457i	0.593164	−	0.593164i	−0.345321	−	0.938485i	$-0.612230\pi$
$797$	16.7457	−	16.7457i	0.593164	−	0.593164i	0.938485	+	0.345321i	$0.112230\pi$
$798$	−30.0989	+	3.28021i	−1.06549	+	0.116118i
$799$		−	27.3852i		−	0.968818i
$800$	−14.4865	+	4.96845i	−0.512175	+	0.175661i
$801$	−8.25069	−	4.76354i	−0.291524	−	0.168311i
$802$	35.8634	+	43.0659i	1.26638	+	1.52071i
$803$	−2.79811	+	10.4427i	−0.0987431	+	0.368514i
$804$	3.56984	+	3.04116i	0.125898	+	0.107253i
$805$	−7.46976	−	36.9344i	−0.263275	−	1.30177i
$806$	22.1555	+	47.9794i	0.780393	+	1.69000i
$807$	9.70947	+	16.8173i	0.341789	+	0.591997i
$808$	9.18272	−	8.97929i	0.323047	−	0.315890i
$809$	−9.26704	−	5.35033i	−0.325812	−	0.188107i	0.328168	−	0.944619i	$-0.393569\pi$
$809$	−9.26704	−	5.35033i	−0.325812	−	0.188107i	−0.653980	+	0.756512i	$0.726902\pi$
$810$	3.20768	+	2.26394i	0.112706	+	0.0795466i
$811$	−38.0038	+	38.0038i	−1.33449	+	1.33449i	−0.433193	+	0.901301i	$0.642613\pi$
$811$	−38.0038	+	38.0038i	−1.33449	+	1.33449i	−0.901301	+	0.433193i	$0.857387\pi$
$812$	1.74232	−	3.14396i	0.0611433	−	0.110331i
$813$	−7.82305	−	7.82305i	−0.274366	−	0.274366i
$814$	−25.3146	+	4.36627i	−0.887277	+	0.153038i
$815$	11.2805	−	19.5383i	0.395137	−	0.684397i
$816$	−7.45434	+	3.34142i	−0.260954	+	0.116973i
$817$	−37.8998	+	21.8814i	−1.32595	+	0.765535i
$818$	−15.8962	+	43.1722i	−0.555797	+	1.50948i
$819$	−13.8089	−	4.63821i	−0.482521	−	0.162072i
$820$	4.22092	+	52.7815i	0.147401	+	1.84321i
$821$	−44.0582	−	11.8054i	−1.53764	−	0.412010i	−0.612139	−	0.790750i	$-0.709691\pi$
$821$	−44.0582	−	11.8054i	−1.53764	−	0.412010i	−0.925503	+	0.378740i	$0.876357\pi$
$822$	−19.6848	−	1.79628i	−0.686587	−	0.0626523i
$823$	−3.99738	+	6.92366i	−0.139340	+	0.241344i	−0.927247	−	0.374450i	$-0.877831\pi$
$823$	−3.99738	+	6.92366i	−0.139340	+	0.241344i	0.787907	+	0.615794i	$0.211165\pi$
$824$	12.9356	−	21.8366i	0.450634	−	0.760715i
$825$	4.98314			0.173491
$826$	−32.3817	+	12.5728i	−1.12670	+	0.437463i
$827$	10.5806	+	10.5806i	0.367922	+	0.367922i	0.866719	−	0.498797i	$-0.166225\pi$
$827$	10.5806	+	10.5806i	0.367922	+	0.367922i	−0.498797	+	0.866719i	$0.666225\pi$
$828$	10.0910	+	1.85710i	0.350685	+	0.0645388i
$829$	7.55404	+	28.1921i	0.262363	+	0.979151i	0.963845	+	0.266464i	$0.0858554\pi$
$829$	7.55404	+	28.1921i	0.262363	+	0.979151i	−0.701482	+	0.712687i	$0.747478\pi$
$830$	−13.8492	+	11.5330i	−0.480712	+	0.400317i
$831$	13.9389	+	24.1428i	0.483534	+	0.837505i
$832$	10.4443	+	42.7904i	0.362090	+	1.48349i
$833$	−11.3971	−	8.62985i	−0.394885	−	0.299006i
$834$	0.0879207	−	0.238783i	0.00304445	−	0.00826837i
$835$	14.6578	+	3.92755i	0.507255	+	0.135918i
$836$	−9.97893	−	28.0672i	−0.345129	−	0.970724i
$837$	1.75665	+	6.55592i	0.0607188	+	0.226606i
$838$	21.3312	+	15.0553i	0.736875	+	0.520076i
$839$		−	28.7459i		−	0.992418i	−0.868203	−	0.496209i	$-0.834725\pi$
$839$		−	28.7459i		−	0.992418i	0.868203	−	0.496209i	$-0.165275\pi$
$840$	18.7056	−	9.03934i	0.645405	−	0.311887i
$841$		−	28.5386i		−	0.984088i
$842$	−32.5585	+	46.1308i	−1.12204	+	1.58977i
$843$	−2.46665	−	9.20567i	−0.0849560	−	0.317060i
$844$	−7.34564	+	15.4505i	−0.252847	+	0.531829i
$845$	46.4295	+	12.4407i	1.59722	+	0.427974i
$846$	−17.7957	−	6.55245i	−0.611829	−	0.225278i
$847$	−8.96537	−	18.0341i	−0.308054	−	0.619660i
$848$	14.7375	+	10.6508i	0.506087	+	0.365749i
$849$	−3.69160	−	6.39403i	−0.126695	−	0.219443i
$850$	−5.00366	−	6.00855i	−0.171624	−	0.206091i
$851$	−13.1035	−	48.9030i	−0.449183	−	1.67637i
$852$	−7.17006	+	4.94116i	−0.245642	+	0.169281i
$853$	−19.5710	−	19.5710i	−0.670099	−	0.670099i	0.287640	−	0.957739i	$-0.407129\pi$
$853$	−19.5710	−	19.5710i	−0.670099	−	0.670099i	−0.957739	+	0.287640i	$0.907129\pi$
$854$	1.10836	−	7.17581i	0.0379273	−	0.245551i
$855$	22.4648			0.768279
$856$	−3.08808	−	12.0637i	−0.105548	−	0.412330i
$857$	−1.69064	+	2.92827i	−0.0577510	+	0.100028i	−0.893456	−	0.449152i	$-0.851726\pi$
$857$	−1.69064	+	2.92827i	−0.0577510	+	0.100028i	0.835705	+	0.549179i	$0.185060\pi$
$858$	1.30240	−	14.2726i	0.0444631	−	0.487257i
$859$	26.9545	+	7.22244i	0.919676	+	0.246426i	0.687447	−	0.726235i	$-0.258731\pi$
$859$	26.9545	+	7.22244i	0.919676	+	0.246426i	0.232229	+	0.972661i	$0.425398\pi$
$860$	19.4733	−	22.8586i	0.664034	−	0.779470i
$861$	−5.00155	−	24.7303i	−0.170453	−	0.842806i
$862$	21.4248	+	7.88868i	0.729730	+	0.268690i
$863$	15.5339	−	8.96851i	0.528781	−	0.305292i	−0.211739	−	0.977326i	$-0.567913\pi$
$863$	15.5339	−	8.96851i	0.528781	−	0.305292i	0.740520	+	0.672035i	$0.234579\pi$
$864$	0.387755	+	5.64355i	0.0131917	+	0.191997i
$865$	−4.63902	+	8.03502i	−0.157732	+	0.273199i
$866$	6.85358	+	39.7355i	0.232894	+	1.35027i
$867$	9.07164	+	9.07164i	0.308089	+	0.308089i
$868$	34.8485	+	8.68501i	1.18283	+	0.294788i
$869$	4.48274	−	4.48274i	0.152067	−	0.152067i
$870$	−1.53787	+	2.17894i	−0.0521386	+	0.0738731i
$871$	11.1804	+	6.45503i	0.378835	+	0.218720i
$872$	17.7383	−	17.3453i	0.600694	−	0.587387i
$873$	−0.631274	−	1.09340i	−0.0213654	−	0.0370060i
$874$	53.3003	−	24.6125i	1.80291	−	0.832530i
$875$	−11.1440	−	12.6255i	−0.376735	−	0.426819i
$876$	−0.936425	−	11.7098i	−0.0316389	−	0.395636i
$877$	5.91972	−	22.0927i	0.199895	−	0.746017i	−0.791051	−	0.611751i	$-0.790466\pi$
$877$	5.91972	−	22.0927i	0.199895	−	0.746017i	0.990945	−	0.134266i	$-0.0428678\pi$
$878$	−17.2362	+	14.3536i	−0.581693	+	0.484409i
$879$	25.7884	+	14.8890i	0.869823	+	0.502192i
$880$	12.9032	+	15.8523i	0.434966	+	0.534380i
$881$			25.9051i			0.872766i	0.899761	+	0.436383i	$0.143741\pi$
$881$			25.9051i			0.872766i	−0.899761	+	0.436383i	$0.856259\pi$
$882$	−8.33490	+	5.34129i	−0.280651	+	0.179851i
$883$	20.8312	−	20.8312i	0.701026	−	0.701026i	−0.263605	−	0.964631i	$-0.584911\pi$
$883$	20.8312	−	20.8312i	0.701026	−	0.701026i	0.964631	+	0.263605i	$0.0849114\pi$
$884$	−18.5173	+	12.7609i	−0.622803	+	0.429197i
$885$	24.8955	−	6.67073i	0.836854	−	0.224234i
$886$	0.726555	−	7.96209i	0.0244091	−	0.267492i
$887$	1.09658	−	0.633108i	0.0368194	−	0.0212577i	−0.481477	−	0.876459i	$-0.659900\pi$
$887$	1.09658	−	0.633108i	0.0368194	−	0.0212577i	0.518297	+	0.855201i	$0.326566\pi$
$888$	24.3279	−	13.6847i	0.816390	−	0.459229i
$889$	15.1516	+	0.944361i	0.508169	+	0.0316729i
$890$	33.9589	−	15.6812i	1.13831	−	0.525636i
$891$	0.476389	−	1.77791i	0.0159596	−	0.0595622i
$892$	0.231125	−	0.0821736i	0.00773865	−	0.00275138i
$893$	−104.810	+	28.0837i	−3.50733	+	0.939786i
$894$	4.61968	−	0.796802i	0.154505	−	0.0266491i
$895$	−3.51112			−0.117364
$896$	27.1146	+	12.6805i	0.905837	+	0.423627i
$897$	28.2460			0.943108
$898$	−10.3191	+	1.77984i	−0.344352	+	0.0593939i
$899$	−4.45337	+	1.19328i	−0.148528	+	0.0397980i
$900$	−5.10176	+	1.81386i	−0.170059	+	0.0604622i
$901$	−2.40279	+	8.96735i	−0.0800487	+	0.298746i
$902$	22.5369	−	10.4069i	0.750396	−	0.346511i
$903$	−7.91141	+	11.9228i	−0.263275	+	0.396765i
$904$	21.0138	−	11.8205i	0.698908	−	0.393145i
$905$	−45.6560	+	26.3595i	−1.51766	+	0.876220i
$906$	2.73232	−	29.9426i	0.0907752	−	0.994777i
$907$	−29.5579	+	7.92002i	−0.981455	+	0.262980i	−0.713657	−	0.700495i	$-0.752963\pi$
$907$	−29.5579	+	7.92002i	−0.981455	+	0.262980i	−0.267798	+	0.963475i	$0.586296\pi$
$908$	−36.2726	+	24.9968i	−1.20375	+	0.829547i
$909$	3.21082	−	3.21082i	0.106496	−	0.106496i
$910$	46.1403	−	33.7939i	1.52954	−	1.12026i
$911$			9.20311i			0.304913i	0.988310	+	0.152456i	$0.0487184\pi$
$911$			9.20311i			0.304913i	−0.988310	+	0.152456i	$0.951282\pi$
$912$	20.4329	+	25.1030i	0.676602	+	0.831242i
$913$	7.31720	+	4.22459i	0.242164	+	0.139813i
$914$	−26.5334	+	22.0959i	−0.877648	+	0.730868i
$915$	−1.39436	+	5.20381i	−0.0460960	+	0.172033i
$916$	1.19813	+	14.9824i	0.0395875	+	0.495032i
$917$	−0.0323061	−	0.0108512i	−0.00106684	−	0.000358337i
$918$	−2.62211	+	1.21081i	−0.0865425	+	0.0399628i
$919$	−0.912455	−	1.58042i	−0.0300991	−	0.0521332i	0.850583	−	0.525840i	$-0.176249\pi$
$919$	−0.912455	−	1.58042i	−0.0300991	−	0.0521332i	−0.880683	+	0.473707i	$0.842916\pi$
$920$	−28.8023	+	28.1642i	−0.949583	+	0.928547i
$921$	18.1213	+	10.4623i	0.597116	+	0.344745i
$922$	12.3060	−	17.4359i	0.405277	−	0.574221i
$923$	−16.9505	+	16.9505i	−0.557932	+	0.557932i
$924$	−7.00682	−	6.76506i	−0.230507	−	0.222554i
$925$	18.8920	+	18.8920i	0.621166	+	0.621166i
$926$	−4.89211	−	28.3633i	−0.160765	−	0.932076i
$927$	4.48668	−	7.77116i	0.147362	−	0.255238i
$928$	−3.83360	+	0.263398i	−0.125844	+	0.00864645i
$929$	32.4848	−	18.7551i	1.06579	−	0.615335i	0.138763	−	0.990326i	$-0.455687\pi$
$929$	32.4848	−	18.7551i	1.06579	−	0.615335i	0.927029	+	0.374990i	$0.122354\pi$
$930$	−25.0062	−	9.20739i	−0.819987	−	0.301922i
$931$	−21.3408	+	52.4694i	−0.699416	+	1.71962i
$932$	−13.1968	+	15.4909i	−0.432275	+	0.507422i
$933$	−3.88906	−	1.04207i	−0.127322	−	0.0341159i
$934$	−0.859789	+	9.42215i	−0.0281331	+	0.308302i
$935$	−5.21789	+	9.03765i	−0.170643	+	0.295563i
$936$	3.86182	+	15.0864i	0.126227	+	0.493114i
$937$	−1.40264			−0.0458223			−0.0229112	−	0.999738i	$-0.507293\pi$
$937$	−1.40264			−0.0458223			−0.0229112	+	0.999738i	$0.507293\pi$
$938$	8.17860	−	3.17549i	0.267041	−	0.103683i
$939$	9.87302	+	9.87302i	0.322194	+	0.322194i
$940$	61.3065	−	42.2486i	1.99960	−	1.37800i
$941$	7.44071	+	27.7691i	0.242560	+	0.905246i	0.974594	+	0.223978i	$0.0719045\pi$
$941$	7.44071	+	27.7691i	0.242560	+	0.905246i	−0.732034	+	0.681268i	$0.761429\pi$
$942$	6.69196	+	8.03590i	0.218036	+	0.261824i
$943$	24.4619	+	42.3693i	0.796590	+	1.37973i
$944$	30.0979	+	21.7518i	0.979604	+	0.707959i
$945$	6.57722	−	3.26976i	0.213957	−	0.106365i
$946$	−13.2108	−	4.86426i	−0.429519	−	0.158151i
$947$	33.3171	+	8.92728i	1.08266	+	0.290098i	0.755685	−	0.654936i	$-0.227304\pi$
$947$	33.3171	+	8.92728i	1.08266	+	0.290098i	0.326974	+	0.945033i	$0.393971\pi$
$948$	−2.95773	+	6.22116i	−0.0960625	+	0.202054i
$949$	−8.36991	−	31.2369i	−0.271699	−	1.01399i
$950$	−17.8649	+	25.3121i	−0.579614	+	0.821233i
$951$		−	0.616707i		−	0.0199981i
$952$	−1.12146	+	15.2416i	−0.0363468	+	0.493982i
$953$		−	38.7939i		−	1.25666i	−0.777948	−	0.628329i	$-0.783739\pi$
$953$		−	38.7939i		−	1.25666i	0.777948	−	0.628329i	$-0.216261\pi$
$954$	5.25233	+	3.70702i	0.170051	+	0.120019i
$955$	−14.6841	−	54.8020i	−0.475168	−	1.77335i
$956$	−5.16773	−	14.5350i	−0.167136	−	0.470095i
$957$	1.20772	+	0.323606i	0.0390399	+	0.0104607i
$958$	−8.19472	+	22.2559i	−0.264759	+	0.719056i
$959$	−20.4464	+	30.8133i	−0.660248	+	0.995015i
$960$	−18.9806	−	11.5328i	−0.612595	−	0.372221i
$961$	−7.53294	−	13.0474i	−0.242998	−	0.420885i
$962$	59.0476	−	49.1724i	1.90377	−	1.58538i
$963$	−1.13950	−	4.25268i	−0.0367200	−	0.137041i
$964$	−1.70768	−	0.314275i	−0.0550007	−	0.0101221i
$965$	−4.10440	−	4.10440i	−0.132125	−	0.132125i
$966$	12.0229	−	14.9639i	0.386829	−	0.481456i
$967$	−22.0005			−0.707490			−0.353745	−	0.935342i	$-0.615092\pi$
$967$	−22.0005			−0.707490			−0.353745	+	0.935342i	$0.615092\pi$
$968$	−10.9733	+	18.5240i	−0.352694	+	0.595384i
$969$	−8.26282	+	14.3116i	−0.265440	+	0.459756i
$970$	4.93644	+	0.450459i	0.158500	+	0.0144634i
$971$	−48.4673	−	12.9868i	−1.55539	−	0.416765i	−0.624189	−	0.781273i	$-0.714571\pi$
$971$	−48.4673	−	12.9868i	−1.55539	−	0.416765i	−0.931200	+	0.364508i	$0.881237\pi$
$972$	0.159430	+	1.99364i	0.00511373	+	0.0639459i
$973$	−0.315021	−	0.356900i	−0.0100991	−	0.0114417i
$974$	10.2196	−	27.7553i	0.327458	−	0.889338i
$975$	−12.9089	+	7.45297i	−0.413416	+	0.238686i
$976$	−7.08317	+	3.17504i	−0.226727	+	0.101631i
$977$	21.4119	−	37.0865i	0.685027	−	1.18650i	−0.288401	−	0.957510i	$-0.593124\pi$
$977$	21.4119	−	37.0865i	0.685027	−	1.18650i	0.973428	−	0.228993i	$-0.0735432\pi$
$978$	11.3254	−	1.95341i	0.362147	−	0.0624632i
$979$	−12.3997	−	12.3997i	−0.396296	−	0.396296i
$980$	1.73654	−	38.8280i	0.0554717	−	1.24032i
$981$	6.20235	−	6.20235i	0.198026	−	0.198026i
$982$	7.31571	+	5.16332i	0.233454	+	0.164768i
$983$	23.3323	+	13.4709i	0.744185	+	0.429655i	0.823589	−	0.567187i	$-0.191968\pi$
$983$	23.3323	+	13.4709i	0.744185	+	0.429655i	−0.0794040	+	0.996843i	$0.525302\pi$
$984$	−19.2852	+	18.8580i	−0.614791	+	0.601172i
$985$	−2.60444	−	4.51102i	−0.0829844	−	0.143733i
$986$	−0.822492	−	1.78117i	−0.0261935	−	0.0567240i
$987$	−26.5986	+	23.4775i	−0.846642	+	0.747296i
$988$	67.8289	+	57.7837i	2.15793	+	1.83835i
$989$	7.18103	−	26.8000i	0.228344	−	0.852190i
$990$	4.62445	+	5.55318i	0.146975	+	0.176492i
$991$	−42.2604	−	24.3991i	−1.34245	−	0.775062i	−0.355280	−	0.934760i	$-0.615615\pi$
$991$	−42.2604	−	24.3991i	−1.34245	−	0.775062i	−0.987166	+	0.159698i	$0.948948\pi$
$992$	−12.4558	−	36.3175i	−0.395473	−	1.15308i
$993$			25.1058i			0.796710i
$994$	1.76493	+	16.1948i	0.0559801	+	0.513668i
$995$	15.7879	−	15.7879i	0.500510	−	0.500510i
$996$	−9.02913	−	1.66169i	−0.286099	−	0.0526525i
$997$	9.11898	−	2.44342i	0.288801	−	0.0773840i	−0.111510	−	0.993763i	$-0.535569\pi$
$997$	9.11898	−	2.44342i	0.288801	−	0.0773840i	0.400311	+	0.916379i	$0.368902\pi$
$998$	−17.8822	−	1.63179i	−0.566052	−	0.0516533i
$999$	8.54647	−	4.93431i	0.270398	−	0.156115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.115.31	yes	128
7.5	odd	6	inner	336.2.bs.a.19.11	✓	128
16.11	odd	4	inner	336.2.bs.a.283.11	yes	128
112.75	even	12	inner	336.2.bs.a.187.31	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.11	✓	128	7.5	odd	6	inner
336.2.bs.a.115.31	yes	128	1.1	even	1	trivial
336.2.bs.a.187.31	yes	128	112.75	even	12	inner
336.2.bs.a.283.11	yes	128	16.11	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39364 - 0.240374i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.88444 - 0.669989i) q^{4} +(-0.718534 + 2.68161i) q^{5} +(-1.28394 + 0.592883i) q^{6} +(-0.164584 + 2.64063i) q^{7} +(2.46517 - 1.38669i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.356785 + 3.90990i) q^{10} +(1.77791 - 0.476389i) q^{11} +(-1.64682 + 1.13489i) q^{12} +(-3.89320 + 3.89320i) q^{13} +(0.405370 + 3.71963i) q^{14} -2.77620i q^{15} +(3.10223 - 2.52511i) q^{16} +(1.76864 + 1.02112i) q^{17} +(1.08674 - 0.904988i) q^{18} +(2.09434 - 7.81618i) q^{19} +(0.442611 + 5.53474i) q^{20} +(-0.524469 - 2.59325i) q^{21} +(2.36325 - 1.09128i) q^{22} +(2.56511 + 4.44290i) q^{23} +(-2.02227 + 1.97748i) q^{24} +(-2.34460 - 1.35365i) q^{25} +(-4.48988 + 6.36153i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.45904 + 5.08637i) q^{28} +(-0.480330 - 0.480330i) q^{29} +(-0.667328 - 3.86902i) q^{30} +(3.39359 - 5.87787i) q^{31} +(3.71641 - 4.26478i) q^{32} +(-1.59403 + 0.920314i) q^{33} +(2.71028 + 0.997938i) q^{34} +(-6.96287 - 2.33873i) q^{35} +(1.29698 - 1.52245i) q^{36} +(-9.53235 - 2.55419i) q^{37} +(1.03994 - 11.3963i) q^{38} +(2.75291 - 4.76818i) q^{39} +(1.94725 + 7.60702i) q^{40} +9.53641 q^{41} +(-1.35427 - 3.48797i) q^{42} +(-3.82420 - 3.82420i) q^{43} +(3.03119 - 2.08891i) q^{44} +(0.718534 + 2.68161i) q^{45} +(4.64278 + 5.57519i) q^{46} +(-6.70468 - 11.6128i) q^{47} +(-2.34298 + 3.24198i) q^{48} +(-6.94582 - 0.869208i) q^{49} +(-3.59290 - 1.32292i) q^{50} +(-1.97266 - 0.528572i) q^{51} +(-4.72811 + 9.94491i) q^{52} +(1.17655 + 4.39093i) q^{53} +(-0.815479 + 1.15542i) q^{54} +5.10996i q^{55} +(3.25601 + 6.73783i) q^{56} +8.09191i q^{57} +(-0.784864 - 0.553946i) q^{58} +(2.40283 + 8.96747i) q^{59} +(-1.86002 - 5.23159i) q^{60} +(-1.87444 - 0.502253i) q^{61} +(3.31654 - 9.00735i) q^{62} +(1.17778 + 2.36914i) q^{63} +(4.15418 - 6.83687i) q^{64} +(-7.64264 - 13.2374i) q^{65} +(-2.00028 + 1.66575i) q^{66} +(-0.606879 - 2.26490i) q^{67} +(4.01703 + 0.739278i) q^{68} +(-3.62761 - 3.62761i) q^{69} +(-10.2659 - 1.58564i) q^{70} +4.35387 q^{71} +(1.44156 - 2.43350i) q^{72} +(-2.93679 + 5.08666i) q^{73} +(-13.8986 - 1.26827i) q^{74} +(2.61506 + 0.700703i) q^{75} +(-1.29009 - 16.1323i) q^{76} +(0.965352 + 4.77320i) q^{77} +(2.69040 - 7.30683i) q^{78} +(2.98280 - 1.72212i) q^{79} +(4.54229 + 10.1333i) q^{80} +(0.500000 - 0.866025i) q^{81} +(13.2903 - 2.29231i) q^{82} +(3.24589 + 3.24589i) q^{83} +(-2.72578 - 4.53543i) q^{84} +(-4.00907 + 4.00907i) q^{85} +(-6.24877 - 4.41030i) q^{86} +(0.588282 + 0.339645i) q^{87} +(3.72225 - 3.63979i) q^{88} +(-4.76354 - 8.25069i) q^{89} +(1.64596 + 3.56447i) q^{90} +(-9.63974 - 10.9213i) q^{91} +(7.81048 + 6.65378i) q^{92} +(-1.75665 + 6.55592i) q^{93} +(-12.1353 - 14.5724i) q^{94} +(19.4551 + 11.2324i) q^{95} +(-2.48597 + 5.08133i) q^{96} -1.26255i q^{97} +(-9.88888 + 0.458240i) q^{98} +(1.30152 - 1.30152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44}+ \cdots - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more