LMFDB - Embedded newform 429.2.bb.b.25.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(25,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("429.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bb (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	429.25
Dual form			429.2.bb.b.103.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20071 + 1.65263i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.671457 + 2.06653i) q^{4} +(0.326611 - 0.449541i) q^{5} +(1.20071 - 1.65263i) q^{6} +(1.66332 + 0.540445i) q^{7} +(-0.335871 + 0.109131i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.20071 + 1.65263i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.671457 + 2.06653i) q^{4} +(0.326611 - 0.449541i) q^{5} +(1.20071 - 1.65263i) q^{6} +(1.66332 + 0.540445i) q^{7} +(-0.335871 + 0.109131i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.13509 q^{10} +(2.67252 + 1.96408i) q^{11} +2.17288 q^{12} +(-2.52783 - 2.57100i) q^{13} +(1.10400 + 3.39777i) q^{14} +(-0.528467 - 0.171709i) q^{15} +(2.93216 + 2.13034i) q^{16} +(2.64009 + 1.91814i) q^{17} +(-1.94278 - 0.631249i) q^{18} +(4.43660 - 1.44154i) q^{19} +(0.709686 + 0.976799i) q^{20} -1.74892i q^{21} +(-0.0369839 + 6.77498i) q^{22} -7.23590 q^{23} +(0.207580 + 0.285709i) q^{24} +(1.44967 + 4.46163i) q^{25} +(1.21374 - 7.26459i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.23370 + 3.07442i) q^{28} +(0.239923 - 0.738408i) q^{29} +(-0.350761 - 1.07953i) q^{30} +(-2.06463 - 2.84171i) q^{31} +8.11000i q^{32} +(1.04210 - 3.14866i) q^{33} +6.66621i q^{34} +(0.786210 - 0.571215i) q^{35} +(-0.671457 - 2.06653i) q^{36} +(-9.62714 - 3.12805i) q^{37} +(7.70938 + 5.60119i) q^{38} +(-1.66403 + 3.19860i) q^{39} +(-0.0606401 + 0.186631i) q^{40} +(6.91760 - 2.24767i) q^{41} +(2.89031 - 2.09994i) q^{42} -4.74303 q^{43} +(-5.85332 + 4.20406i) q^{44} +0.555663i q^{45} +(-8.68819 - 11.9583i) q^{46} +(-6.42057 + 2.08617i) q^{47} +(1.11999 - 3.44696i) q^{48} +(-3.18857 - 2.31663i) q^{49} +(-5.63280 + 7.75288i) q^{50} +(1.00842 - 3.10361i) q^{51} +(7.01040 - 3.49753i) q^{52} +(4.43963 - 3.22558i) q^{53} +2.04276i q^{54} +(1.75581 - 0.559919i) q^{55} -0.617640 q^{56} +(-2.74197 - 3.77399i) q^{57} +(1.50839 - 0.490106i) q^{58} +(4.32029 + 1.40375i) q^{59} +(0.709686 - 0.976799i) q^{60} +(-10.5963 - 7.69867i) q^{61} +(2.21729 - 6.82412i) q^{62} +(-1.66332 + 0.540445i) q^{63} +(-7.53851 + 5.47705i) q^{64} +(-1.98139 + 0.296647i) q^{65} +(6.45482 - 2.05841i) q^{66} -6.03187i q^{67} +(-5.73660 + 4.16788i) q^{68} +(2.23602 + 6.88175i) q^{69} +(1.88801 + 0.613453i) q^{70} +(7.32587 - 10.0832i) q^{71} +(0.207580 - 0.285709i) q^{72} +(-4.41261 - 1.43374i) q^{73} +(-6.38986 - 19.6660i) q^{74} +(3.79529 - 2.75744i) q^{75} +10.1363i q^{76} +(3.38378 + 4.71125i) q^{77} +(-7.28410 + 1.09055i) q^{78} +(-12.8043 + 9.30285i) q^{79} +(1.91535 - 0.622335i) q^{80} +(0.309017 - 0.951057i) q^{81} +(12.0206 + 8.73346i) q^{82} +(5.50333 - 7.57469i) q^{83} +(3.61420 + 1.17432i) q^{84} +(1.72456 - 0.560344i) q^{85} +(-5.69499 - 7.83848i) q^{86} -0.776408 q^{87} +(-1.11196 - 0.368022i) q^{88} +4.88260i q^{89} +(-0.918305 + 0.667188i) q^{90} +(-2.81511 - 5.64256i) q^{91} +(4.85860 - 14.9532i) q^{92} +(-2.06463 + 2.84171i) q^{93} +(-11.1569 - 8.10595i) q^{94} +(0.801009 - 2.46525i) q^{95} +(7.71307 - 2.50613i) q^{96} +(8.10855 + 11.1605i) q^{97} -8.05112i q^{98} +(-3.31658 - 0.0181048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	$ 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) $ 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.20071	+	1.65263i	0.849027	+	1.16859i	0.984076	+	0.177747i	$0.0568809\pi$
$2$	1.20071	+	1.65263i	0.849027	+	1.16859i	−0.135049	+	0.990839i	$0.543119\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.671457	+	2.06653i	−0.335729	+	1.03327i
$5$	0.326611	−	0.449541i	0.146065	−	0.201041i	−0.729716	−	0.683751i	$-0.760348\pi$
$5$	0.326611	−	0.449541i	0.146065	−	0.201041i	0.875780	+	0.482710i	$0.160348\pi$
$6$	1.20071	−	1.65263i	0.490186	−	0.674683i
$7$	1.66332	+	0.540445i	0.628676	+	0.204269i	0.605988	−	0.795474i	$-0.292778\pi$
$7$	1.66332	+	0.540445i	0.628676	+	0.204269i	0.0226873	+	0.999743i	$0.492778\pi$
$8$	−0.335871	+	0.109131i	−0.118748	+	0.0385836i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.13509			0.358946
$11$	2.67252	+	1.96408i	0.805796	+	0.592193i
$11$	2.67252	+	1.96408i	0.805796	+	0.592193i
$12$	2.17288			0.627257
$13$	−2.52783	−	2.57100i	−0.701095	−	0.713068i
$13$	−2.52783	−	2.57100i	−0.701095	−	0.713068i
$14$	1.10400	+	3.39777i	0.295057	+	0.908092i
$15$	−0.528467	−	0.171709i	−0.136450	−	0.0443352i
$16$	2.93216	+	2.13034i	0.733040	+	0.532585i
$17$	2.64009	+	1.91814i	0.640316	+	0.465216i	0.859959	−	0.510364i	$-0.170489\pi$
$17$	2.64009	+	1.91814i	0.640316	+	0.465216i	−0.219643	+	0.975580i	$0.570489\pi$
$18$	−1.94278	−	0.631249i	−0.457918	−	0.148787i
$19$	4.43660	−	1.44154i	1.01783	−	0.330711i	0.247859	−	0.968796i	$-0.420273\pi$
$19$	4.43660	−	1.44154i	1.01783	−	0.330711i	0.769966	+	0.638085i	$0.220273\pi$
$20$	0.709686	+	0.976799i	0.158691	+	0.218419i
$21$		−	1.74892i		−	0.381645i
$22$	−0.0369839	+	6.77498i	−0.00788499	+	1.44443i
$23$	−7.23590			−1.50879			−0.754394	−	0.656421i	$-0.772069\pi$
$23$	−7.23590			−1.50879			−0.754394	+	0.656421i	$0.772069\pi$
$24$	0.207580	+	0.285709i	0.0423720	+	0.0583200i
$25$	1.44967	+	4.46163i	0.289934	+	0.892327i
$26$	1.21374	−	7.26459i	0.238033	−	1.42470i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−2.23370	+	3.07442i	−0.422129	+	0.581010i
$29$	0.239923	−	0.738408i	0.0445526	−	0.137119i	−0.926306	−	0.376772i	$-0.877034\pi$
$29$	0.239923	−	0.738408i	0.0445526	−	0.137119i	0.970858	+	0.239654i	$0.0770339\pi$
$30$	−0.350761	−	1.07953i	−0.0640400	−	0.197095i
$31$	−2.06463	−	2.84171i	−0.370818	−	0.510387i	0.582305	−	0.812970i	$-0.302151\pi$
$31$	−2.06463	−	2.84171i	−0.370818	−	0.510387i	−0.953123	+	0.302583i	$0.902151\pi$
$32$			8.11000i			1.43366i
$33$	1.04210	−	3.14866i	0.181406	−	0.548111i
$34$			6.66621i			1.14325i
$35$	0.786210	−	0.571215i	0.132894	−	0.0965529i
$36$	−0.671457	−	2.06653i	−0.111910	−	0.344422i
$37$	−9.62714	−	3.12805i	−1.58269	−	0.514248i	−0.619944	−	0.784646i	$-0.712845\pi$
$37$	−9.62714	−	3.12805i	−1.58269	−	0.514248i	−0.962749	+	0.270398i	$0.912845\pi$
$38$	7.70938	+	5.60119i	1.25063	+	0.908633i
$39$	−1.66403	+	3.19860i	−0.266458	+	0.512185i
$40$	−0.0606401	+	0.186631i	−0.00958804	+	0.0295089i
$41$	6.91760	−	2.24767i	1.08035	−	0.351026i	0.285839	−	0.958278i	$-0.407728\pi$
$41$	6.91760	−	2.24767i	1.08035	−	0.351026i	0.794510	+	0.607251i	$0.207728\pi$
$42$	2.89031	−	2.09994i	0.445985	−	0.324027i
$43$	−4.74303			−0.723306			−0.361653	−	0.932313i	$-0.617787\pi$
$43$	−4.74303			−0.723306			−0.361653	+	0.932313i	$0.617787\pi$
$44$	−5.85332	+	4.20406i	−0.882422	+	0.633786i
$45$			0.555663i			0.0828334i
$46$	−8.68819	−	11.9583i	−1.28100	−	1.76315i
$47$	−6.42057	+	2.08617i	−0.936536	+	0.304299i	−0.737233	−	0.675639i	$-0.763868\pi$
$47$	−6.42057	+	2.08617i	−0.936536	+	0.304299i	−0.199303	+	0.979938i	$0.563868\pi$
$48$	1.11999	−	3.44696i	0.161656	−	0.497526i
$49$	−3.18857	−	2.31663i	−0.455510	−	0.330947i
$50$	−5.63280	+	7.75288i	−0.796598	+	1.09642i
$51$	1.00842	−	3.10361i	0.141208	−	0.434592i
$52$	7.01040	−	3.49753i	0.972167	−	0.485020i
$53$	4.43963	−	3.22558i	0.609830	−	0.443067i	−0.239525	−	0.970890i	$-0.576992\pi$
$53$	4.43963	−	3.22558i	0.609830	−	0.443067i	0.849354	+	0.527823i	$0.176992\pi$
$54$			2.04276i			0.277985i
$55$	1.75581	−	0.559919i	0.236753	−	0.0754995i
$56$	−0.617640			−0.0825356
$57$	−2.74197	−	3.77399i	−0.363182	−	0.499878i
$58$	1.50839	−	0.490106i	0.198062	−	0.0643541i
$59$	4.32029	+	1.40375i	0.562453	+	0.182752i	0.576425	−	0.817150i	$-0.304447\pi$
$59$	4.32029	+	1.40375i	0.562453	+	0.182752i	−0.0139715	+	0.999902i	$0.504447\pi$
$60$	0.709686	−	0.976799i	0.0916201	−	0.126104i
$61$	−10.5963	−	7.69867i	−1.35672	−	0.985714i	−0.998646	−	0.0520203i	$-0.983434\pi$
$61$	−10.5963	−	7.69867i	−1.35672	−	0.985714i	−0.358073	−	0.933694i	$-0.616566\pi$
$62$	2.21729	−	6.82412i	0.281596	−	0.866665i
$63$	−1.66332	+	0.540445i	−0.209559	+	0.0680897i
$64$	−7.53851	+	5.47705i	−0.942313	+	0.684631i
$65$	−1.98139	+	0.296647i	−0.245761	+	0.0367945i
$66$	6.45482	−	2.05841i	0.794533	−	0.253373i
$67$		−	6.03187i		−	0.736910i	−0.929646	−	0.368455i	$-0.879887\pi$
$67$		−	6.03187i		−	0.736910i	0.929646	−	0.368455i	$-0.120113\pi$
$68$	−5.73660	+	4.16788i	−0.695665	+	0.505430i
$69$	2.23602	+	6.88175i	0.269185	+	0.828465i
$70$	1.88801	+	0.613453i	0.225661	+	0.0733216i
$71$	7.32587	−	10.0832i	0.869421	−	1.19666i	−0.109819	−	0.993952i	$-0.535027\pi$
$71$	7.32587	−	10.0832i	0.869421	−	1.19666i	0.979240	−	0.202704i	$-0.0649730\pi$
$72$	0.207580	−	0.285709i	0.0244635	−	0.0336711i
$73$	−4.41261	−	1.43374i	−0.516457	−	0.167807i	0.0391799	−	0.999232i	$-0.487525\pi$
$73$	−4.41261	−	1.43374i	−0.516457	−	0.167807i	−0.555637	+	0.831425i	$0.687525\pi$
$74$	−6.38986	−	19.6660i	−0.742806	−	2.28612i
$75$	3.79529	−	2.75744i	0.438243	−	0.318402i
$76$			10.1363i			1.16271i
$77$	3.38378	+	4.71125i	0.385618	+	0.536896i
$78$	−7.28410	+	1.09055i	−0.824762	+	0.123481i
$79$	−12.8043	+	9.30285i	−1.44059	+	1.04665i	−0.452675	+	0.891676i	$0.649530\pi$
$79$	−12.8043	+	9.30285i	−1.44059	+	1.04665i	−0.987918	+	0.154976i	$0.950470\pi$
$80$	1.91535	−	0.622335i	0.214143	−	0.0695791i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	12.0206	+	8.73346i	1.32745	+	0.964449i
$83$	5.50333	−	7.57469i	0.604069	−	0.831430i	−0.392004	−	0.919964i	$-0.628218\pi$
$83$	5.50333	−	7.57469i	0.604069	−	0.831430i	0.996073	+	0.0885335i	$0.0282180\pi$
$84$	3.61420	+	1.17432i	0.394341	+	0.128129i
$85$	1.72456	−	0.560344i	0.187055	−	0.0607778i
$86$	−5.69499	−	7.83848i	−0.614107	−	0.845245i
$87$	−0.776408			−0.0832397
$88$	−1.11196	−	0.368022i	−0.118536	−	0.0392313i
$89$			4.88260i			0.517555i	0.965937	+	0.258777i	$0.0833196\pi$
$89$			4.88260i			0.517555i	−0.965937	+	0.258777i	$0.916680\pi$
$90$	−0.918305	+	0.667188i	−0.0967979	+	0.0703278i
$91$	−2.81511	−	5.64256i	−0.295103	−	0.591501i
$92$	4.85860	−	14.9532i	0.506544	−	1.55898i
$93$	−2.06463	+	2.84171i	−0.214092	+	0.294672i
$94$	−11.1569	−	8.10595i	−1.15074	−	0.836064i
$95$	0.801009	−	2.46525i	0.0821818	−	0.252930i
$96$	7.71307	−	2.50613i	0.787212	−	0.255781i
$97$	8.10855	+	11.1605i	0.823299	+	1.13317i	0.989133	+	0.147020i	$0.0469682\pi$
$97$	8.10855	+	11.1605i	0.823299	+	1.13317i	−0.165835	+	0.986154i	$0.553032\pi$
$98$		−	8.05112i		−	0.813286i
$99$	−3.31658	−	0.0181048i	−0.333328	−	0.00181960i
$100$	−10.1935			−1.01935
$101$	−14.2701	+	10.3679i	−1.41993	+	1.03164i	−0.428149	+	0.903708i	$0.640834\pi$
$101$	−14.2701	+	10.3679i	−1.41993	+	1.03164i	−0.991783	+	0.127932i	$0.959166\pi$
$102$	6.33994	−	2.05997i	0.627748	−	0.203968i
$103$	0.468057	−	1.44053i	0.0461191	−	0.141940i	−0.925345	−	0.379125i	$-0.876225\pi$
$103$	0.468057	−	1.44053i	0.0461191	−	0.141940i	0.971464	+	0.237185i	$0.0762249\pi$
$104$	1.12960	+	0.587660i	0.110766	+	0.0576248i
$105$	−0.786210	−	0.571215i	−0.0767262	−	0.0557449i
$106$	10.6614	+	3.46409i	1.03552	+	0.336462i
$107$	3.14102	+	9.66707i	0.303654	+	0.934551i	0.980176	+	0.198129i	$0.0634864\pi$
$107$	3.14102	+	9.66707i	0.303654	+	0.934551i	−0.676522	+	0.736423i	$0.736514\pi$
$108$	−1.75790	+	1.27719i	−0.169154	+	0.122897i
$109$			6.87790i			0.658783i	0.944193	+	0.329392i	$0.106844\pi$
$109$			6.87790i			0.658783i	−0.944193	+	0.329392i	$0.893156\pi$
$110$	3.03355	+	2.22940i	0.289238	+	0.212565i
$111$			10.1226i			0.960792i
$112$	3.72579	+	5.12811i	0.352054	+	0.484561i
$113$	2.31570	+	7.12699i	0.217843	+	0.670451i	0.998940	+	0.0460408i	$0.0146604\pi$
$113$	2.31570	+	7.12699i	0.217843	+	0.670451i	−0.781097	+	0.624410i	$0.785340\pi$
$114$	2.94472	−	9.06292i	0.275798	−	0.848820i
$115$	−2.36332	+	3.25283i	−0.220381	+	0.303328i
$116$	1.36485	+	0.991619i	0.126723	+	0.0920695i
$117$	3.55626	+	0.594164i	0.328776	+	0.0549305i
$118$	2.86752	+	8.82532i	0.263977	+	0.812437i
$119$	3.35466	+	4.61730i	0.307521	+	0.423267i
$120$	0.196235			0.0179138
$121$	3.28477	+	10.4981i	0.298615	+	0.954374i
$122$		−	26.7556i		−	2.42234i
$123$	−4.27531	−	5.88447i	−0.385492	−	0.530584i
$124$	7.25880	−	2.35853i	0.651860	−	0.211802i
$125$	5.12150	+	1.66408i	0.458081	+	0.148839i
$126$	−2.89031	−	2.09994i	−0.257490	−	0.187077i
$127$	−14.9680	−	10.8749i	−1.32820	−	0.964992i	−0.999791	−	0.0204553i	$-0.993488\pi$
$127$	−14.9680	−	10.8749i	−1.32820	−	0.964992i	−0.328406	−	0.944536i	$-0.606512\pi$
$128$	−2.67693	−	0.869786i	−0.236609	−	0.0768790i
$129$	1.46568	+	4.51089i	0.129046	+	0.397162i
$130$	−2.86931	−	2.91832i	−0.251655	−	0.255953i
$131$	−2.84921			−0.248937			−0.124468	−	0.992224i	$-0.539723\pi$
$131$	−2.84921			−0.248937			−0.124468	+	0.992224i	$0.539723\pi$
$132$	5.80708	+	4.26772i	0.505441	+	0.371457i
$133$	8.15855			0.707436
$134$	9.96844	−	7.24250i	0.861142	−	0.625656i
$135$	0.528467	−	0.171709i	0.0454832	−	0.0147784i
$136$	−1.09606	−	0.356130i	−0.0939861	−	0.0305379i
$137$	0.608491	−	0.837516i	0.0519869	−	0.0715538i	−0.782232	−	0.622987i	$-0.785919\pi$
$137$	0.608491	−	0.837516i	0.0519869	−	0.0715538i	0.834219	+	0.551433i	$0.185919\pi$
$138$	−8.68819	+	11.9583i	−0.739587	+	1.01795i
$139$	6.96269	−	21.4290i	0.590568	−	1.81758i	0.0149102	−	0.999889i	$-0.495254\pi$
$139$	6.96269	−	21.4290i	0.590568	−	1.81758i	0.575657	−	0.817691i	$-0.304746\pi$
$140$	0.652528	+	2.00827i	0.0551487	+	0.169730i
$141$	3.96813	+	5.46166i	0.334177	+	0.459955i
$142$	25.4600			2.13656
$143$	−1.70603	−	11.8359i	−0.142665	−	0.989771i
$144$	−3.62435			−0.302029
$145$	−0.253583	−	0.349027i	−0.0210589	−	0.0289851i
$146$	−2.92880	−	9.01391i	−0.242389	−	0.745997i
$147$	−1.21792	+	3.74839i	−0.100453	+	0.309162i
$148$	12.9284	−	17.7945i	1.06271	−	1.46270i
$149$	4.31973	−	5.94560i	0.353886	−	0.487082i	−0.594547	−	0.804061i	$-0.702668\pi$
$149$	4.31973	−	5.94560i	0.353886	−	0.487082i	0.948433	+	0.316979i	$0.102668\pi$
$150$	9.11406	+	2.96134i	0.744160	+	0.241792i
$151$	−3.37925	+	1.09799i	−0.275000	+	0.0893528i	−0.443270	−	0.896388i	$-0.646182\pi$
$151$	−3.37925	+	1.09799i	−0.275000	+	0.0893528i	0.168270	+	0.985741i	$0.446182\pi$
$152$	−1.33281	+	0.968340i	−0.108105	+	0.0785428i
$153$	−3.26333			−0.263824
$154$	−3.72302	+	11.2490i	−0.300010	+	0.906467i
$155$	−1.95179			−0.156772
$156$	−5.49268	−	5.58649i	−0.439766	−	0.447277i
$157$	1.42104	+	4.37351i	0.113411	+	0.349044i	0.991612	−	0.129248i	$-0.0412562\pi$
$157$	1.42104	+	4.37351i	0.113411	+	0.349044i	−0.878201	+	0.478292i	$0.841256\pi$
$158$	−30.7483	−	9.99074i	−2.44621	−	0.794820i
$159$	−4.43963	−	3.22558i	−0.352085	−	0.255805i
$160$	3.64578	+	2.64881i	0.288224	+	0.209407i
$161$	−12.0356	−	3.91061i	−0.948539	−	0.308199i
$162$	1.94278	−	0.631249i	0.152639	−	0.0495956i
$163$	−8.73432	−	12.0218i	−0.684124	−	0.941617i	0.315850	−	0.948809i	$-0.397710\pi$
$163$	−8.73432	−	12.0218i	−0.684124	−	0.941617i	−0.999974	+	0.00719272i	$0.997710\pi$
$164$			15.8047i			1.23414i
$165$	−1.07509	−	1.49685i	−0.0836956	−	0.116530i
$166$	19.1260			1.48447
$167$	0.140142	+	0.192889i	0.0108445	+	0.0149262i	0.814405	−	0.580297i	$-0.197064\pi$
$167$	0.140142	+	0.192889i	0.0108445	+	0.0149262i	−0.803560	+	0.595223i	$0.797064\pi$
$168$	0.190861	+	0.587410i	0.0147253	+	0.0453197i
$169$	−0.220128	+	12.9981i	−0.0169329	+	0.999857i
$170$	2.99673	+	2.17725i	0.229839	+	0.166988i
$171$	−2.74197	+	3.77399i	−0.209683	+	0.288605i
$172$	3.18474	−	9.80164i	0.242834	−	0.747368i
$173$	0.943690	+	2.90438i	0.0717474	+	0.220816i	0.980500	−	0.196520i	$-0.0629640\pi$
$173$	0.943690	+	2.90438i	0.0717474	+	0.220816i	−0.908752	+	0.417336i	$0.862964\pi$
$174$	−0.932238	−	1.28312i	−0.0706728	−	0.0972727i
$175$			8.20459i			0.620209i
$176$	3.65211	+	11.4524i	0.275288	+	0.863256i
$177$		−	4.54262i		−	0.341444i
$178$	−8.06913	+	5.86257i	−0.604807	+	0.439418i
$179$	1.15967	+	3.56909i	0.0866775	+	0.266766i	0.984996	−	0.172580i	$-0.0552103\pi$
$179$	1.15967	+	3.56909i	0.0866775	+	0.266766i	−0.898318	+	0.439346i	$0.855210\pi$
$180$	−1.14830	−	0.373104i	−0.0855889	−	0.0278095i
$181$	6.88898	+	5.00514i	0.512054	+	0.372029i	0.813602	−	0.581422i	$-0.197503\pi$
$181$	6.88898	+	5.00514i	0.512054	+	0.372029i	−0.301548	+	0.953451i	$0.597503\pi$
$182$	5.94494	−	11.4274i	0.440669	−	0.847054i
$183$	−4.04743	+	12.4567i	−0.299195	+	0.920827i
$184$	2.43033	−	0.789661i	0.179166	−	0.0582146i
$185$	−4.55051	+	3.30614i	−0.334560	+	0.243072i
$186$	−7.17531			−0.526119
$187$	3.28832	+	10.3116i	0.240466	+	0.754060i
$188$		−	14.6691i		−	1.06985i
$189$	1.02799	+	1.41490i	0.0747751	+	0.102919i
$190$	5.03593	−	1.63627i	0.365345	−	0.118708i
$191$	6.56687	−	20.2108i	0.475162	−	1.46240i	−0.370577	−	0.928802i	$-0.620840\pi$
$191$	6.56687	−	20.2108i	0.475162	−	1.46240i	0.845739	−	0.533597i	$-0.179160\pi$
$192$	7.53851	+	5.47705i	0.544045	+	0.395272i
$193$	−8.37418	+	11.5261i	−0.602787	+	0.829665i	−0.995960	−	0.0897995i	$-0.971377\pi$
$193$	−8.37418	+	11.5261i	−0.602787	+	0.829665i	0.393173	+	0.919465i	$0.371377\pi$
$194$	−8.70813	+	26.8009i	−0.625208	+	1.92419i
$195$	0.894410	+	1.79274i	0.0640501	+	0.128381i
$196$	6.92838	−	5.03376i	0.494884	−	0.359555i
$197$			24.4257i			1.74026i	0.492823	+	0.870130i	$0.335965\pi$
$197$			24.4257i			1.74026i	−0.492823	+	0.870130i	$0.664035\pi$
$198$	−3.95231	−	5.50281i	−0.280879	−	0.391068i
$199$	4.65604			0.330058			0.165029	−	0.986289i	$-0.447228\pi$
$199$	4.65604			0.330058			0.165029	+	0.986289i	$0.447228\pi$
$200$	−0.973805	−	1.34033i	−0.0688584	−	0.0947755i
$201$	−5.73665	+	1.86395i	−0.404632	+	0.131473i
$202$	−34.2685	−	11.1345i	−2.41112	−	0.783421i
$203$	0.798138	−	1.09854i	0.0560183	−	0.0771026i
$204$	5.73660	+	4.16788i	0.401642	+	0.291810i
$205$	1.24894	−	3.84386i	0.0872301	−	0.268467i
$206$	2.94267	−	0.956130i	0.205025	−	0.0666168i
$207$	5.85396	−	4.25315i	0.406879	−	0.295615i
$208$	−1.93490	−	12.9237i	−0.134161	−	0.896100i
$209$	14.6882	+	4.86129i	1.01600	+	0.336263i
$210$		−	1.98518i		−	0.136990i
$211$	−1.60728	+	1.16776i	−0.110650	+	0.0803917i	−0.641734	−	0.766927i	$-0.721785\pi$
$211$	−1.60728	+	1.16776i	−0.110650	+	0.0803917i	0.531084	+	0.847319i	$0.321785\pi$
$212$	3.68474	+	11.3405i	0.253069	+	0.778867i
$213$	−11.8535	−	3.85144i	−0.812189	−	0.263896i
$214$	−12.2047	+	16.7983i	−0.834293	+	1.14831i
$215$	−1.54912	+	2.13219i	−0.105649	+	0.145414i
$216$	−0.335871	−	0.109131i	−0.0228531	−	0.00742542i
$217$	−1.89834	−	5.84249i	−0.128868	−	0.396614i
$218$	−11.3666	+	8.25834i	−0.769845	+	0.559325i
$219$			4.63969i			0.313521i
$220$	−0.0218596	+	4.00440i	−0.00147377	+	0.269977i
$221$	−1.74216	−	11.6364i	−0.117191	−	0.782749i
$222$	−16.7289	+	12.1542i	−1.12277	+	0.815739i
$223$	15.9467	−	5.18140i	1.06787	−	0.346972i	0.278212	−	0.960520i	$-0.410258\pi$
$223$	15.9467	−	5.18140i	1.06787	−	0.346972i	0.789658	+	0.613548i	$0.210258\pi$
$224$	−4.38301	+	13.4895i	−0.292852	+	0.901306i
$225$	−3.79529	−	2.75744i	−0.253019	−	0.183829i
$226$	−8.99780	+	12.3844i	−0.598525	+	0.823799i
$227$	−23.4772	−	7.62821i	−1.55824	−	0.506302i	−0.601901	−	0.798570i	$-0.705590\pi$
$227$	−23.4772	−	7.62821i	−1.55824	−	0.506302i	−0.956336	+	0.292268i	$0.905590\pi$
$228$	9.64020	−	3.13229i	0.638438	−	0.207441i
$229$	11.9014	+	16.3809i	0.786469	+	1.08248i	0.994539	+	0.104367i	$0.0332818\pi$
$229$	11.9014	+	16.3809i	0.786469	+	1.08248i	−0.208070	+	0.978114i	$0.566718\pi$
$230$	−8.21338			−0.541574
$231$	3.43502	−	4.67402i	0.226007	−	0.307528i
$232$			0.274193i			0.0180016i
$233$	−14.9438	+	10.8573i	−0.979001	+	0.711286i	−0.957485	−	0.288483i	$-0.906849\pi$
$233$	−14.9438	+	10.8573i	−0.979001	+	0.711286i	−0.0215159	+	0.999769i	$0.506849\pi$
$234$	3.28809	+	6.59059i	0.214949	+	0.430841i
$235$	−1.15921	+	3.56767i	−0.0756183	+	0.232729i
$236$	−5.80177	+	7.98546i	−0.377663	+	0.519809i
$237$	12.8043	+	9.30285i	0.831727	+	0.604285i
$238$	−3.60272	+	11.0880i	−0.233530	+	0.718730i
$239$	−1.42296	+	0.462348i	−0.0920437	+	0.0299068i	−0.354677	−	0.934989i	$-0.615409\pi$
$239$	−1.42296	+	0.462348i	−0.0920437	+	0.0299068i	0.262633	+	0.964896i	$0.415409\pi$
$240$	−1.18375	−	1.62929i	−0.0764108	−	0.105170i
$241$		−	6.58825i		−	0.424387i	−0.977228	−	0.212193i	$-0.931939\pi$
$241$		−	6.58825i		−	0.424387i	0.977228	−	0.212193i	$-0.0680607\pi$
$242$	−13.4054	+	18.0337i	−0.861735	+	1.15925i
$243$	−1.00000			−0.0641500
$244$	23.0245	−	16.7283i	1.47399	−	1.07092i
$245$	−2.08284	+	0.676756i	−0.133068	+	0.0432363i
$246$	4.59145	−	14.1310i	0.292740	−	0.900961i
$247$	−14.9212	−	7.76254i	−0.949411	−	0.493919i
$248$	1.00357	+	0.729134i	0.0637265	+	0.0463000i
$249$	−8.90458	−	2.89327i	−0.564305	−	0.183354i
$250$	3.39931	+	10.4620i	0.214991	+	0.661676i
$251$	18.3927	−	13.3631i	1.16094	−	0.843469i	0.171039	−	0.985264i	$-0.445288\pi$
$251$	18.3927	−	13.3631i	1.16094	−	0.843469i	0.989896	+	0.141796i	$0.0452876\pi$
$252$		−	3.80019i		−	0.239389i
$253$	−19.3381	−	14.2119i	−1.21578	−	0.893494i
$254$		−	37.7942i		−	2.37142i
$255$	−1.06584	−	1.46700i	−0.0667453	−	0.0918671i
$256$	3.98214	+	12.2558i	0.248884	+	0.765985i
$257$	−4.55945	+	14.0325i	−0.284410	+	0.875325i	0.702164	+	0.712015i	$0.252217\pi$
$257$	−4.55945	+	14.0325i	−0.284410	+	0.875325i	−0.986575	+	0.163310i	$0.947783\pi$
$258$	−5.69499	+	7.83848i	−0.354555	+	0.488002i
$259$	−14.3225	−	10.4059i	−0.889955	−	0.646590i
$260$	0.717387	−	4.29379i	0.0444905	−	0.266290i
$261$	0.239923	+	0.738408i	0.0148509	+	0.0457063i
$262$	−3.42106	−	4.70869i	−0.211354	−	0.290904i
$263$	−0.378443			−0.0233358			−0.0116679	−	0.999932i	$-0.503714\pi$
$263$	−0.378443			−0.0233358			−0.0116679	+	0.999932i	$0.503714\pi$
$264$	−0.00639382	+	1.17127i	−0.000393512	+	0.0720865i
$265$		−	3.04930i		−	0.187317i
$266$	9.79602	+	13.4831i	0.600632	+	0.826700i
$267$	4.64363	−	1.50881i	0.284185	−	0.0923375i
$268$	12.4650	+	4.05014i	0.761424	+	0.247402i
$269$	10.9173	+	7.93188i	0.665640	+	0.483615i	0.868563	−	0.495579i	$-0.165044\pi$
$269$	10.9173	+	7.93188i	0.665640	+	0.483615i	−0.202923	+	0.979195i	$0.565044\pi$
$270$	0.918305	+	0.667188i	0.0558863	+	0.0406038i
$271$	7.39699	+	2.40343i	0.449335	+	0.145998i	0.524938	−	0.851140i	$-0.324088\pi$
$271$	7.39699	+	2.40343i	0.449335	+	0.145998i	−0.0756035	+	0.997138i	$0.524088\pi$
$272$	3.65488	+	11.2486i	0.221610	+	0.682045i
$273$	−4.49647	+	4.42097i	−0.272139	+	0.267569i
$274$	2.11472			0.127755
$275$	−4.88873	+	14.7711i	−0.294801	+	0.890731i
$276$	−15.7227			−0.946398
$277$	22.6216	−	16.4355i	1.35920	−	0.987516i	0.360704	−	0.932680i	$-0.382537\pi$
$277$	22.6216	−	16.4355i	1.35920	−	0.987516i	0.998495	−	0.0548355i	$-0.0174634\pi$
$278$	43.7743	−	14.2231i	2.62541	−	0.853046i
$279$	3.34063	+	1.08544i	0.199999	+	0.0649835i
$280$	−0.201728	+	0.277654i	−0.0120555	+	0.0165930i
$281$	3.14517	−	4.32895i	0.187625	−	0.258244i	−0.704834	−	0.709372i	$-0.748979\pi$
$281$	3.14517	−	4.32895i	0.187625	−	0.258244i	0.892459	+	0.451129i	$0.148979\pi$
$282$	−4.26155	+	13.1157i	−0.253771	+	0.781028i
$283$	1.85139	+	5.69798i	0.110053	+	0.338710i	0.990883	−	0.134723i	$-0.0430146\pi$
$283$	1.85139	+	5.69798i	0.110053	+	0.338710i	−0.880830	+	0.473433i	$0.843015\pi$
$284$	15.9183	+	21.9096i	0.944575	+	1.30010i
$285$	−2.59212			−0.153544
$286$	17.5120	−	17.0309i	1.03551	−	1.00706i
$287$	12.7209			0.750893
$288$	−4.76694	−	6.56113i	−0.280894	−	0.386618i
$289$	−1.96247	−	6.03986i	−0.115439	−	0.355286i
$290$	0.272334	−	0.838158i	0.0159920	−	0.0492183i
$291$	8.10855	−	11.1605i	0.475332	−	0.654238i
$292$	5.92576	−	8.15610i	0.346779	−	0.477300i
$293$	16.1760	+	5.25592i	0.945015	+	0.307054i	0.740688	−	0.671849i	$-0.234500\pi$
$293$	16.1760	+	5.25592i	0.945015	+	0.307054i	0.204326	+	0.978903i	$0.434500\pi$
$294$	−7.65707	+	2.48793i	−0.446569	+	0.145099i
$295$	2.04209	−	1.48367i	0.118895	−	0.0863824i
$296$	3.57484			0.207783
$297$	1.00766	+	3.15985i	0.0584703	+	0.183353i
$298$	15.0126			0.869656
$299$	18.2911	+	18.6035i	1.05780	+	1.07587i
$300$	3.14997	+	9.69460i	0.181863	+	0.559718i
$301$	−7.88918	−	2.56335i	−0.454725	−	0.147749i
$302$	−5.87206	−	4.26630i	−0.337899	−	0.245498i
$303$	14.2701	+	10.3679i	0.819798	+	0.595618i
$304$	16.0798	+	5.22464i	0.922238	+	0.299653i
$305$	−6.92174	+	2.24901i	−0.396337	+	0.128778i
$306$	−3.91830	−	5.39308i	−0.223994	−	0.308302i
$307$			0.708494i			0.0404359i	0.999796	+	0.0202180i	$0.00643601\pi$
$307$			0.708494i			0.0404359i	−0.999796	+	0.0202180i	$0.993564\pi$
$308$	−12.0080	+	3.82930i	−0.684220	+	0.218194i
$309$	−1.51467			−0.0861663
$310$	−2.34353	−	3.22559i	−0.133104	−	0.183201i
$311$	3.08126	+	9.48313i	0.174722	+	0.537739i	0.999621	−	0.0275417i	$-0.00876790\pi$
$311$	3.08126	+	9.48313i	0.174722	+	0.537739i	−0.824899	+	0.565281i	$0.808768\pi$
$312$	0.209832	−	1.25591i	0.0118794	−	0.0711020i
$313$	−2.44200	−	1.77421i	−0.138030	−	0.100285i	0.516628	−	0.856210i	$-0.327187\pi$
$313$	−2.44200	−	1.77421i	−0.138030	−	0.100285i	−0.654657	+	0.755926i	$0.727187\pi$
$314$	−5.52154	+	7.59975i	−0.311599	+	0.428879i
$315$	−0.300305	+	0.924245i	−0.0169203	+	0.0520753i
$316$	−10.6271	−	32.7069i	−0.597822	−	1.83991i
$317$	3.90945	+	5.38090i	0.219577	+	0.302221i	0.904568	−	0.426330i	$-0.140194\pi$
$317$	3.90945	+	5.38090i	0.219577	+	0.302221i	−0.684991	+	0.728552i	$0.740194\pi$
$318$		−	11.2100i		−	0.628627i
$319$	2.09149	−	1.50218i	0.117101	−	0.0841062i
$320$			5.17773i			0.289444i
$321$	8.22330	−	5.97458i	0.458980	−	0.333469i
$322$	−7.98844	−	24.5859i	−0.445178	−	1.37012i
$323$	14.4781	+	4.70421i	0.805582	+	0.261749i
$324$	1.75790	+	1.27719i	0.0976610	+	0.0709549i
$325$	7.80635	−	15.0054i	0.433018	−	0.832348i
$326$	9.38017	−	28.8692i	0.519519	−	1.59892i
$327$	6.54127	−	2.12539i	0.361733	−	0.117534i
$328$	−2.07813	+	1.50985i	−0.114746	+	0.0833675i
$329$	−11.8069			−0.650936
$330$	1.18287	−	3.57400i	0.0651149	−	0.196742i
$331$			9.59326i			0.527293i	0.964619	+	0.263647i	$0.0849253\pi$
$331$			9.59326i			0.527293i	−0.964619	+	0.263647i	$0.915075\pi$
$332$	11.9581	+	16.4589i	0.656285	+	0.903299i
$333$	9.62714	−	3.12805i	0.527564	−	0.171416i
$334$	−0.150505	+	0.463207i	−0.00823527	+	0.0253456i
$335$	−2.71157	−	1.97007i	−0.148149	−	0.107636i
$336$	3.72579	−	5.12811i	0.203258	−	0.279761i
$337$	8.50770	−	26.1840i	0.463444	−	1.42633i	−0.397485	−	0.917609i	$-0.630117\pi$
$337$	8.50770	−	26.1840i	0.463444	−	1.42633i	0.860929	−	0.508725i	$-0.169883\pi$
$338$	−21.7454	+	15.2432i	−1.18279	+	0.829118i
$339$	6.06258	−	4.40472i	0.329274	−	0.239232i
$340$			3.94011i			0.213682i
$341$	0.0635941	−	11.6496i	0.00344382	−	0.630863i
$342$	−9.52931			−0.515286
$343$	−11.2475	−	15.4809i	−0.607309	−	0.835888i
$344$	1.59305	−	0.517612i	0.0858913	−	0.0279078i
$345$	3.82393	+	1.24247i	0.205874	+	0.0668924i
$346$	−3.66677	+	5.04688i	−0.197127	+	0.271322i
$347$	12.2994	+	8.93605i	0.660267	+	0.479712i	0.866753	−	0.498737i	$-0.166203\pi$
$347$	12.2994	+	8.93605i	0.660267	+	0.479712i	−0.206486	+	0.978450i	$0.566203\pi$
$348$	0.521325	−	1.60447i	0.0279459	−	0.0860088i
$349$	13.5092	−	4.38941i	0.723131	−	0.234960i	0.0757511	−	0.997127i	$-0.475865\pi$
$349$	13.5092	−	4.38941i	0.723131	−	0.234960i	0.647380	+	0.762167i	$0.275865\pi$
$350$	−13.5592	+	9.85130i	−0.724767	+	0.526574i
$351$	−0.533861	−	3.56581i	−0.0284954	−	0.190329i
$352$	−15.9287	+	21.6742i	−0.849002	+	1.15524i
$353$		−	11.0667i		−	0.589022i	−0.955648	−	0.294511i	$-0.904843\pi$
$353$		−	11.0667i		−	0.589022i	0.955648	−	0.294511i	$-0.0951568\pi$
$354$	7.50727	−	5.45435i	0.399007	−	0.289895i
$355$	−2.14010	−	6.58656i	−0.113585	−	0.349578i
$356$	−10.0901	−	3.27846i	−0.534772	−	0.173758i
$357$	3.35466	−	4.61730i	0.177548	−	0.244373i
$358$	−4.50596	+	6.20192i	−0.238147	+	0.327782i
$359$	−2.26890	−	0.737211i	−0.119748	−	0.0389085i	0.248530	−	0.968624i	$-0.420053\pi$
$359$	−2.26890	−	0.737211i	−0.119748	−	0.0389085i	−0.368278	+	0.929716i	$0.620053\pi$
$360$	−0.0606401	−	0.186631i	−0.00319601	−	0.00983631i
$361$	2.23404	−	1.62312i	0.117581	−	0.0854274i
$362$			17.3946i			0.914242i
$363$	8.96924	−	6.36810i	0.470763	−	0.334238i
$364$	13.5508	−	2.02877i	0.710252	−	0.106337i
$365$	−2.08573	+	1.51537i	−0.109172	+	0.0793182i
$366$	−25.4461	+	8.26794i	−1.33009	+	0.432172i
$367$	4.46276	−	13.7350i	0.232954	−	0.716960i	−0.764432	−	0.644705i	$-0.776980\pi$
$367$	4.46276	−	13.7350i	0.232954	−	0.716960i	0.997386	−	0.0722553i	$-0.0230196\pi$
$368$	−21.2168	−	15.4149i	−1.10600	−	0.803558i
$369$	−4.27531	+	5.88447i	−0.222564	+	0.306333i
$370$	−10.9277	−	3.55061i	−0.568102	−	0.184587i
$371$	9.12776	−	2.96579i	0.473890	−	0.153976i
$372$	−4.48619	−	6.17471i	−0.232598	−	0.320144i
$373$	18.0009			0.932053			0.466026	−	0.884771i	$-0.345685\pi$
$373$	18.0009			0.932053			0.466026	+	0.884771i	$0.345685\pi$
$374$	−13.0930	+	17.8156i	−0.677022	+	0.921223i
$375$		−	5.38506i		−	0.278083i
$376$	1.92881	−	1.40137i	0.0994710	−	0.0722699i
$377$	−2.50494	+	1.24973i	−0.129011	+	0.0643642i
$378$	−1.10400	+	3.39777i	−0.0567837	+	0.174762i
$379$	7.40316	−	10.1896i	0.380275	−	0.523403i	−0.575383	−	0.817884i	$-0.695147\pi$
$379$	7.40316	−	10.1896i	0.380275	−	0.523403i	0.955657	+	0.294481i	$0.0951468\pi$
$380$	4.55668	+	3.31062i	0.233753	+	0.169831i
$381$	−5.71728	+	17.5960i	−0.292905	+	0.901469i
$382$	41.2858	−	13.4146i	2.11236	−	0.686349i
$383$	1.29473	+	1.78204i	0.0661574	+	0.0910578i	0.840814	−	0.541325i	$-0.182077\pi$
$383$	1.29473	+	1.78204i	0.0661574	+	0.0910578i	−0.774656	+	0.632383i	$0.782077\pi$
$384$			2.81469i			0.143636i
$385$	3.22308	+	0.0175944i	0.164263	+	0.000896696i
$386$	−29.1033			−1.48132
$387$	3.83720	−	2.78789i	0.195056	−	0.141716i
$388$	−28.5080	+	9.26282i	−1.44728	+	0.470248i
$389$	−1.15156	+	3.54414i	−0.0583864	+	0.179695i	−0.975996	−	0.217787i	$-0.930116\pi$
$389$	−1.15156	+	3.54414i	−0.0583864	+	0.179695i	0.917610	+	0.397482i	$0.130116\pi$
$390$	−1.88882	+	3.63069i	−0.0956440	+	0.183847i
$391$	−19.1034	−	13.8794i	−0.966101	−	0.701913i
$392$	1.32376	+	0.430117i	0.0668601	+	0.0217242i
$393$	0.880454	+	2.70976i	0.0444130	+	0.136689i
$394$	−40.3667	+	29.3281i	−2.03364	+	1.47753i
$395$			8.79445i			0.442497i
$396$	2.26435	−	6.84166i	0.113788	−	0.343806i
$397$		−	0.555298i		−	0.0278696i	−0.999903	−	0.0139348i	$-0.995564\pi$
$397$		−	0.555298i		−	0.0278696i	0.999903	−	0.0139348i	$-0.00443573\pi$
$398$	5.59054	+	7.69471i	0.280228	+	0.385701i
$399$	−2.52113	−	7.75924i	−0.126214	−	0.388448i
$400$	−5.25412	+	16.1705i	−0.262706	+	0.808526i
$401$	0.235467	−	0.324093i	0.0117587	−	0.0161844i	−0.803097	−	0.595848i	$-0.796816\pi$
$401$	0.235467	−	0.324093i	0.0117587	−	0.0161844i	0.814856	+	0.579664i	$0.196816\pi$
$402$	−9.96844	−	7.24250i	−0.497181	−	0.361223i
$403$	−2.08703	+	12.4915i	−0.103962	+	0.622248i
$404$	−11.8437	−	36.4513i	−0.589248	−	1.81352i
$405$	−0.326611	−	0.449541i	−0.0162294	−	0.0223379i
$406$	2.77381			0.137662
$407$	−19.5850	−	27.2683i	−0.970794	−	1.35164i
$408$			1.15246i			0.0570554i
$409$	−11.5968	−	15.9616i	−0.573423	−	0.789249i	0.419532	−	0.907740i	$-0.362194\pi$
$409$	−11.5968	−	15.9616i	−0.573423	−	0.789249i	−0.992955	+	0.118492i	$0.962194\pi$
$410$	7.85209	−	2.55130i	0.387787	−	0.126000i
$411$	−0.984559	−	0.319902i	−0.0485647	−	0.0157796i
$412$	2.66263	+	1.93451i	0.131178	+	0.0953066i
$413$	6.42737	+	4.66976i	0.316270	+	0.229784i
$414$	14.0578	+	4.56765i	0.690902	+	0.224488i
$415$	−1.60769	−	4.94795i	−0.0789182	−	0.242885i
$416$	20.8508	−	20.5007i	1.02230	−	1.00513i
$417$	−22.5317			−1.10338
$418$	9.60230	+	30.1112i	0.469664	+	1.47278i
$419$	25.2033			1.23126			0.615631	−	0.788034i	$-0.288901\pi$
$419$	25.2033			1.23126			0.615631	+	0.788034i	$0.288901\pi$
$420$	1.70834	−	1.24118i	0.0833585	−	0.0605635i
$421$	9.52619	−	3.09525i	0.464278	−	0.150853i	−0.0675314	−	0.997717i	$-0.521512\pi$
$421$	9.52619	−	3.09525i	0.464278	−	0.150853i	0.531809	+	0.846864i	$0.321512\pi$
$422$	−3.85974	−	1.25411i	−0.187889	−	0.0610489i
$423$	3.96813	−	5.46166i	0.192937	−	0.265555i
$424$	−1.13913	+	1.56788i	−0.0553210	+	0.0761429i
$425$	−4.73076	+	14.5598i	−0.229475	+	0.706253i
$426$	−7.86758	−	24.2139i	−0.381185	−	1.17317i
$427$	−13.4643	−	18.5321i	−0.651585	−	0.896830i
$428$	−22.0864			−1.06759
$429$	−10.7295	+	5.28004i	−0.518023	+	0.254923i
$430$	−5.38376			−0.259628
$431$	−11.6706	−	16.0632i	−0.562153	−	0.773738i	0.429445	−	0.903093i	$-0.358709\pi$
$431$	−11.6706	−	16.0632i	−0.562153	−	0.773738i	−0.991598	+	0.129355i	$0.958709\pi$
$432$	1.11999	+	3.44696i	0.0538853	+	0.165842i
$433$	−7.50539	+	23.0992i	−0.360686	+	1.11008i	0.591953	+	0.805973i	$0.298357\pi$
$433$	−7.50539	+	23.0992i	−0.360686	+	1.11008i	−0.952639	+	0.304104i	$0.901643\pi$
$434$	7.37613	−	10.1524i	0.354066	−	0.487330i
$435$	−0.253583	+	0.349027i	−0.0121584	+	0.0167346i
$436$	−14.2134	−	4.61822i	−0.680699	−	0.221172i
$437$	−32.1028	+	10.4308i	−1.53568	+	0.498974i
$438$	−7.66769	+	5.57091i	−0.366377	+	0.266188i
$439$	8.99214			0.429172			0.214586	−	0.976705i	$-0.431160\pi$
$439$	8.99214			0.429172			0.214586	+	0.976705i	$0.431160\pi$
$440$	−0.528620	+	0.379674i	−0.0252010	+	0.0181002i
$441$	3.94129			0.187680
$442$	17.1389	−	16.8511i	0.815212	−	0.801523i
$443$	−4.64658	−	14.3007i	−0.220766	−	0.679447i	−0.998694	−	0.0510936i	$-0.983729\pi$
$443$	−4.64658	−	14.3007i	−0.220766	−	0.679447i	0.777928	−	0.628353i	$-0.216271\pi$
$444$	−20.9186	−	6.79688i	−0.992755	−	0.322566i
$445$	2.19493	+	1.59471i	0.104050	+	0.0755965i
$446$	27.7102	+	20.1327i	1.31212	+	0.953309i
$447$	−6.98947	−	2.27102i	−0.330590	−	0.107415i
$448$	−15.4990	+	5.03593i	−0.732258	+	0.237925i
$449$	−0.167679	−	0.230790i	−0.00791326	−	0.0108917i	0.805042	−	0.593218i	$-0.202143\pi$
$449$	−0.167679	−	0.230790i	−0.00791326	−	0.0108917i	−0.812955	+	0.582326i	$0.802143\pi$
$450$		−	9.58309i		−	0.451751i
$451$	22.9021	+	7.57980i	1.07842	+	0.356919i
$452$	−16.2830			−0.765890
$453$	2.08849	+	2.87456i	0.0981260	+	0.135059i
$454$	−15.5826	−	47.9584i	−0.731329	−	2.25080i
$455$	−3.45600	−	0.577414i	−0.162020	−	0.0270696i
$456$	1.33281	+	0.968340i	0.0624144	+	0.0453467i
$457$	0.678326	−	0.933636i	0.0317308	−	0.0436736i	−0.792857	−	0.609408i	$-0.791407\pi$
$457$	0.678326	−	0.933636i	0.0317308	−	0.0436736i	0.824588	+	0.565734i	$0.191407\pi$
$458$	−12.7815	+	39.3373i	−0.597239	+	1.83811i
$459$	1.00842	+	3.10361i	0.0470692	+	0.144864i
$460$	−5.13521	−	7.06802i	−0.239431	−	0.329548i
$461$		−	10.9062i		−	0.507954i	−0.967210	−	0.253977i	$-0.918261\pi$
$461$		−	10.9062i		−	0.507954i	0.967210	−	0.253977i	$-0.0817387\pi$
$462$	11.8489	+	0.0646818i	0.551260	+	0.00300927i
$463$			16.4974i			0.766699i	0.923603	+	0.383349i	$0.125229\pi$
$463$			16.4974i			0.766699i	−0.923603	+	0.383349i	$0.874771\pi$
$464$	2.27655	−	1.65401i	0.105686	−	0.0767856i
$465$	0.603138	+	1.85627i	0.0279698	+	0.0860823i
$466$	−35.8862	−	11.6601i	−1.66240	−	0.540146i
$467$	−25.9587	−	18.8601i	−1.20122	−	0.872741i	−0.206820	−	0.978379i	$-0.566311\pi$
$467$	−25.9587	−	18.8601i	−1.20122	−	0.872741i	−0.994405	+	0.105638i	$0.966311\pi$
$468$	−3.61573	+	6.95017i	−0.167137	+	0.321272i
$469$	3.25989	−	10.0329i	0.150528	−	0.463277i
$470$	−7.28791	+	2.36798i	−0.336166	+	0.109227i
$471$	3.72033	−	2.70298i	0.171424	−	0.124547i
$472$	−1.60425			−0.0738416
$473$	−12.6759	−	9.31570i	−0.582837	−	0.428337i
$474$			32.3307i			1.48500i
$475$	12.8632	+	17.7047i	0.590205	+	0.812348i
$476$	−11.7943	+	3.83220i	−0.540591	+	0.175649i
$477$	−1.69579	+	5.21909i	−0.0776447	+	0.238966i
$478$	−2.47265	−	1.79649i	−0.113096	−	0.0821693i
$479$	−3.24265	+	4.46313i	−0.148160	+	0.203925i	−0.876646	−	0.481136i	$-0.840224\pi$
$479$	−3.24265	+	4.46313i	−0.148160	+	0.203925i	0.728486	+	0.685061i	$0.240224\pi$
$480$	1.39256	−	4.28587i	0.0635615	−	0.195622i
$481$	16.2936	+	32.6586i	0.742923	+	1.48910i
$482$	10.8879	−	7.91056i	0.495932	−	0.360316i
$483$			12.6550i			0.575822i
$484$	−23.9003	−	0.260946i	−1.08638	−	0.0118612i
$485$	7.66543			0.348069
$486$	−1.20071	−	1.65263i	−0.0544651	−	0.0749648i
$487$	−0.167168	+	0.0543163i	−0.00757512	+	0.00246131i	−0.312802	−	0.949818i	$-0.601268\pi$
$487$	−0.167168	+	0.0543163i	−0.00757512	+	0.00246131i	0.305227	+	0.952280i	$0.401268\pi$
$488$	4.39915	+	1.42937i	0.199140	+	0.0647046i
$489$	−8.73432	+	12.0218i	−0.394979	+	0.543643i
$490$	−3.61931	−	2.62958i	−0.163504	−	0.118792i
$491$	−5.97823	+	18.3991i	−0.269794	+	0.830340i	0.720756	+	0.693188i	$0.243795\pi$
$491$	−5.97823	+	18.3991i	−0.269794	+	0.830340i	−0.990550	+	0.137151i	$0.956205\pi$
$492$	15.0311	−	4.88391i	0.677656	−	0.220184i
$493$	2.04979	−	1.48926i	0.0923177	−	0.0670727i
$494$	−5.08733	−	33.9797i	−0.228890	−	1.52882i
$495$	−1.09137	+	1.48502i	−0.0490533	+	0.0667468i
$496$		−	12.7307i		−	0.571626i
$497$	17.6347	−	12.8123i	0.791024	−	0.574712i
$498$	−5.91027	−	18.1899i	−0.264846	−	0.815111i
$499$	−25.6285	−	8.32721i	−1.14729	−	0.372777i	−0.327168	−	0.944966i	$-0.606094\pi$
$499$	−25.6285	−	8.32721i	−1.14729	−	0.372777i	−0.820122	+	0.572189i	$0.806094\pi$
$500$	−6.87774	+	9.46639i	−0.307582	+	0.423350i
$501$	0.140142	−	0.192889i	0.00626110	−	0.00861767i
$502$	44.1684	+	14.3512i	1.97133	+	0.640524i
$503$	6.42312	+	19.7683i	0.286393	+	0.881427i	0.985978	+	0.166877i	$0.0533683\pi$
$503$	6.42312	+	19.7683i	0.286393	+	0.881427i	−0.699585	+	0.714550i	$0.746632\pi$
$504$	0.499681	−	0.363039i	0.0222576	−	0.0161711i
$505$			9.80126i			0.436150i
$506$	0.267612	−	49.0230i	0.0118968	−	2.17934i
$507$	12.4300	−	3.80729i	0.552035	−	0.169088i
$508$	32.5237	−	23.6299i	1.44301	−	1.04841i
$509$	34.0039	−	11.0485i	1.50720	−	0.489718i	0.565089	−	0.825030i	$-0.308842\pi$
$509$	34.0039	−	11.0485i	1.50720	−	0.489718i	0.942107	+	0.335312i	$0.108842\pi$
$510$	1.14465	−	3.52287i	0.0506860	−	0.155995i
$511$	−6.56472	−	4.76955i	−0.290406	−	0.210992i
$512$	−18.7817	+	25.8508i	−0.830043	+	1.14246i
$513$	4.43660	+	1.44154i	0.195881	+	0.0636454i
$514$	−28.6651	+	9.31387i	−1.26437	+	0.410817i
$515$	−0.494706	−	0.680904i	−0.0217993	−	0.0300042i
$516$	−10.3060			−0.453699
$517$	−21.2565	−	7.03518i	−0.934861	−	0.309407i
$518$		−	36.1642i		−	1.58896i
$519$	2.47061	−	1.79501i	0.108448	−	0.0787920i
$520$	0.633117	−	0.315866i	0.0277640	−	0.0138516i
$521$	1.26186	−	3.88362i	0.0552833	−	0.170144i	−0.919602	−	0.392850i	$-0.871489\pi$
$521$	1.26186	−	3.88362i	0.0552833	−	0.170144i	0.974886	+	0.222706i	$0.0714890\pi$
$522$	−0.932238	+	1.28312i	−0.0408029	+	0.0561604i
$523$	14.0148	+	10.1823i	0.612824	+	0.445243i	0.850408	−	0.526125i	$-0.176355\pi$
$523$	14.0148	+	10.1823i	0.612824	+	0.445243i	−0.237584	+	0.971367i	$0.576355\pi$
$524$	1.91312	−	5.88799i	0.0835751	−	0.257218i
$525$	7.80303	−	2.53536i	0.340552	−	0.110652i
$526$	−0.454398	−	0.625426i	−0.0198127	−	0.0272699i
$527$		−	11.4626i		−	0.499319i
$528$	9.76330	−	7.01234i	0.424893	−	0.305173i
$529$	29.3582			1.27644
$530$	5.03937	−	3.66131i	0.218896	−	0.159037i
$531$	−4.32029	+	1.40375i	−0.187484	+	0.0609174i
$532$	−5.47812	+	16.8599i	−0.237506	+	0.730970i
$533$	−23.2653	−	12.1035i	−1.00773	−	0.524259i
$534$	8.06913	+	5.86257i	0.349186	+	0.253698i
$535$	5.37164	+	1.74535i	0.232236	+	0.0754581i
$536$	0.658264	+	2.02593i	0.0284327	+	0.0875067i
$537$	3.03605	−	2.20582i	0.131015	−	0.0951880i
$538$			27.5661i			1.18846i
$539$	−3.97148	−	12.4539i	−0.171064	−	0.536426i
$540$			1.20739i			0.0519578i
$541$	2.30755	+	3.17608i	0.0992095	+	0.136550i	0.855736	−	0.517413i	$-0.173105\pi$
$541$	2.30755	+	3.17608i	0.0992095	+	0.136550i	−0.756526	+	0.653963i	$0.773105\pi$
$542$	4.90963	+	15.1103i	0.210887	+	0.649043i
$543$	2.63136	−	8.09848i	0.112922	−	0.347539i
$544$	−15.5561	+	21.4111i	−0.666962	+	0.917994i
$545$	3.09190	+	2.24639i	0.132442	+	0.0962250i
$546$	−12.7052	−	2.12272i	−0.543731	−	0.0908442i
$547$	−0.618641	−	1.90398i	−0.0264512	−	0.0814084i	0.936959	−	0.349438i	$-0.113627\pi$
$547$	−0.618641	−	1.90398i	−0.0264512	−	0.0814084i	−0.963411	+	0.268030i	$0.913627\pi$
$548$	1.32218	+	1.81982i	0.0564806	+	0.0777389i
$549$	13.0978			0.558999
$550$	−30.2811	+	9.65649i	−1.29119	+	0.411754i
$551$		−	3.62188i		−	0.154297i
$552$	−1.50202	−	2.06736i	−0.0639304	−	0.0879926i
$553$	−26.3253	+	8.55360i	−1.11946	+	0.363736i
$554$	54.3237	+	17.6509i	2.30799	+	0.749913i
$555$	4.55051	+	3.30614i	0.193158	+	0.140338i
$556$	39.6085	+	28.7772i	1.67977	+	1.22043i
$557$	−29.5991	−	9.61732i	−1.25415	−	0.407499i	−0.394745	−	0.918791i	$-0.629167\pi$
$557$	−29.5991	−	9.61732i	−1.25415	−	0.407499i	−0.859407	+	0.511292i	$0.829167\pi$
$558$	2.21729	+	6.82412i	0.0938655	+	0.288888i
$559$	11.9896	+	12.1944i	0.507106	+	0.515767i
$560$	3.52218			0.148839
$561$	8.79078	−	6.31385i	0.371147	−	0.266571i
$562$	10.9306			0.461078
$563$	31.8653	−	23.1515i	1.34296	−	0.975718i	0.343632	−	0.939104i	$-0.388343\pi$
$563$	31.8653	−	23.1515i	1.34296	−	0.975718i	0.999329	−	0.0366140i	$-0.0116572\pi$
$564$	−13.9511	+	4.53300i	−0.587448	+	0.190874i
$565$	3.96020	+	1.28675i	0.166607	+	0.0541339i
$566$	−7.19368	+	9.90125i	−0.302373	+	0.416181i
$567$	1.02799	−	1.41490i	0.0431714	−	0.0594204i
$568$	−1.36016	+	4.18613i	−0.0570709	+	0.175646i
$569$	8.29497	+	25.5293i	0.347743	+	1.07024i	0.960099	+	0.279661i	$0.0902222\pi$
$569$	8.29497	+	25.5293i	0.347743	+	1.07024i	−0.612355	+	0.790583i	$0.709778\pi$
$570$	−3.11237	−	4.28382i	−0.130363	−	0.179429i
$571$	−0.532964			−0.0223039			−0.0111519	−	0.999938i	$-0.503550\pi$
$571$	−0.532964			−0.0223039			−0.0111519	+	0.999938i	$0.503550\pi$
$572$	25.6049	+	4.42176i	1.07059	+	0.184883i
$573$	−21.2508			−0.887767
$574$	15.2741	+	21.0230i	0.637528	+	0.877482i
$575$	−10.4897	−	32.2839i	−0.437450	−	1.34633i
$576$	2.87945	−	8.86205i	0.119977	−	0.369252i
$577$	23.0312	−	31.6997i	0.958800	−	1.31968i	0.0112949	−	0.999936i	$-0.496405\pi$
$577$	23.0312	−	31.6997i	0.958800	−	1.31968i	0.947506	−	0.319739i	$-0.103595\pi$
$578$	7.62531	−	10.4953i	0.317171	−	0.436548i
$579$	13.5497	+	4.40257i	0.563107	+	0.182965i
$580$	0.891546	−	0.289681i	0.0370194	−	0.0120283i
$581$	13.2475	−	9.62488i	0.549599	−	0.399307i
$582$	28.1801			1.16810
$583$	18.2003	+	0.0993535i	0.753780	+	0.00411480i
$584$	1.63853			0.0678029
$585$	1.42861	−	1.40462i	0.0590658	−	0.0580740i
$586$	10.7366	+	33.0438i	0.443524	+	1.36503i
$587$	−21.6850	−	7.04588i	−0.895035	−	0.290815i	−0.174849	−	0.984595i	$-0.555944\pi$
$587$	−21.6850	−	7.04588i	−0.895035	−	0.290815i	−0.720186	+	0.693781i	$0.755944\pi$
$588$	−6.92838	−	5.03376i	−0.285722	−	0.207589i
$589$	−13.2563	−	9.63130i	−0.546218	−	0.396851i
$590$	4.90390	+	1.59337i	0.201891	+	0.0655982i
$591$	23.2302	−	7.54796i	0.955564	−	0.310481i
$592$	−21.5645	−	29.6810i	−0.886296	−	1.21988i
$593$		−	33.4190i		−	1.37235i	−0.727435	−	0.686176i	$-0.759288\pi$
$593$		−	33.4190i		−	1.37235i	0.727435	−	0.686176i	$-0.240712\pi$
$594$	−4.01215	+	5.45933i	−0.164621	+	0.223999i
$595$	3.17133			0.130012
$596$	9.38626	+	12.9191i	0.384476	+	0.529186i
$597$	−1.43880	−	4.42816i	−0.0588860	−	0.181232i
$598$	−8.78247	+	52.5658i	−0.359142	+	2.14958i
$599$	17.7360	+	12.8859i	0.724673	+	0.526506i	0.887874	−	0.460087i	$-0.152182\pi$
$599$	17.7360	+	12.8859i	0.724673	+	0.526506i	−0.163201	+	0.986593i	$0.552182\pi$
$600$	−0.973805	+	1.34033i	−0.0397554	+	0.0547186i
$601$	−3.93003	+	12.0954i	−0.160309	+	0.493381i	−0.998660	−	0.0517499i	$-0.983520\pi$
$601$	−3.93003	+	12.0954i	−0.160309	+	0.493381i	0.838351	+	0.545131i	$0.183520\pi$
$602$	−5.23632	−	16.1157i	−0.213416	−	0.656828i
$603$	3.54544	+	4.87988i	0.144382	+	0.198724i
$604$		−	7.72059i		−	0.314146i
$605$	5.79217	+	1.95215i	0.235485	+	0.0793664i
$606$			36.0320i			1.46370i
$607$	−30.3669	+	22.0629i	−1.23256	+	0.895504i	−0.997079	−	0.0763756i	$-0.975665\pi$
$607$	−30.3669	+	22.0629i	−1.23256	+	0.895504i	−0.235477	+	0.971880i	$0.575665\pi$
$608$	11.6909	+	35.9808i	0.474127	+	1.45921i
$609$	−1.29141	−	0.419606i	−0.0523308	−	0.0170033i
$610$	−12.0277	−	8.73867i	−0.486989	−	0.353818i
$611$	21.5937	+	11.2338i	0.873586	+	0.454472i
$612$	2.19119	−	6.74378i	0.0885734	−	0.272601i
$613$	43.4544	−	14.1192i	1.75511	−	0.570269i	0.758433	−	0.651751i	$-0.225965\pi$
$613$	43.4544	−	14.1192i	1.75511	−	0.570269i	0.996675	+	0.0814822i	$0.0259654\pi$
$614$	−1.17088	+	0.850693i	−0.0472528	+	0.0343312i
$615$	−4.04167			−0.162976
$616$	−1.65066	−	1.21309i	−0.0665069	−	0.0488770i
$617$			36.4958i			1.46927i	0.678465	+	0.734633i	$0.262646\pi$
$617$			36.4958i			1.46927i	−0.678465	+	0.734633i	$0.737354\pi$
$618$	−1.81867	−	2.50318i	−0.0731576	−	0.100693i
$619$	−31.1293	+	10.1145i	−1.25119	+	0.406537i	−0.858348	−	0.513067i	$-0.828509\pi$
$619$	−31.1293	+	10.1145i	−1.25119	+	0.406537i	−0.392845	+	0.919605i	$0.628509\pi$
$620$	1.31055	−	4.03345i	0.0526328	−	0.161987i
$621$	−5.85396	−	4.25315i	−0.234911	−	0.170673i
$622$	−11.9724	+	16.4786i	−0.480050	+	0.660733i
$623$	−2.63878	+	8.12132i	−0.105720	+	0.325374i
$624$	−11.6933	+	5.83385i	−0.468106	+	0.233541i
$625$	−16.5557	+	12.0284i	−0.662226	+	0.481135i
$626$		−	6.16603i		−	0.246444i
$627$	0.0844575	−	15.4715i	0.00337291	−	0.617874i
$628$	−9.99217			−0.398731
$629$	−19.4165	−	26.7245i	−0.774186	−	1.06558i
$630$	−1.88801	+	0.613453i	−0.0752203	+	0.0244405i
$631$	39.6005	+	12.8670i	1.57647	+	0.512227i	0.961145	−	0.276045i	$-0.0890238\pi$
$631$	39.6005	+	12.8670i	1.57647	+	0.512227i	0.615327	+	0.788272i	$0.289024\pi$
$632$	3.28535	−	4.52190i	0.130684	−	0.179871i
$633$	1.60728	+	1.16776i	0.0638836	+	0.0464142i
$634$	−4.19853	+	12.9217i	−0.166745	+	0.513188i
$635$	−9.77743	+	3.17688i	−0.388005	+	0.126071i
$636$	9.64678	−	7.00880i	0.382520	−	0.277917i
$637$	2.10410	+	14.0539i	0.0833674	+	0.556835i
$638$	4.99382	+	1.65278i	0.197707	+	0.0654344i
$639$			12.4635i			0.493049i
$640$	−1.26532	+	0.919307i	−0.0500160	+	0.0363388i
$641$	−11.3926	−	35.0627i	−0.449979	−	1.38489i	−0.876929	−	0.480619i	$-0.840412\pi$
$641$	−11.3926	−	35.0627i	−0.449979	−	1.38489i	0.426950	−	0.904275i	$-0.359588\pi$
$642$	19.7475	+	6.41637i	0.779373	+	0.253234i
$643$	16.2931	−	22.4255i	0.642535	−	0.884374i	−0.356212	−	0.934405i	$-0.615932\pi$
$643$	16.2931	−	22.4255i	0.642535	−	0.884374i	0.998748	+	0.0500312i	$0.0159321\pi$
$644$	16.1628	−	22.2462i	0.636903	−	0.876622i
$645$	2.50654	+	0.814423i	0.0986948	+	0.0320679i
$646$	9.60959	+	29.5753i	0.378084	+	1.16362i
$647$	−30.8994	+	22.4497i	−1.21478	+	0.882591i	−0.995656	−	0.0931060i	$-0.970320\pi$
$647$	−30.8994	+	22.4497i	−1.21478	+	0.882591i	−0.219126	+	0.975697i	$0.570320\pi$
$648$			0.353155i			0.0138733i
$649$	8.78900	+	12.2369i	0.344998	+	0.480342i
$650$	34.1715	−	5.11603i	1.34032	−	0.200667i
$651$	−4.96992	+	3.61086i	−0.194787	+	0.141521i
$652$	30.7081	−	9.97766i	1.20262	−	0.390755i
$653$	−14.6164	+	44.9845i	−0.571982	+	1.76038i	0.0742507	+	0.997240i	$0.476343\pi$
$653$	−14.6164	+	44.9845i	−0.571982	+	1.76038i	−0.646233	+	0.763140i	$0.723657\pi$
$654$	11.3666	+	8.25834i	0.444470	+	0.322927i
$655$	−0.930582	+	1.28084i	−0.0363608	+	0.0500464i
$656$	25.0718	+	8.14633i	0.978890	+	0.318061i
$657$	4.41261	−	1.43374i	0.172152	−	0.0559357i
$658$	−14.1766	−	19.5125i	−0.552663	−	0.760675i
$659$	41.0225			1.59801			0.799005	−	0.601324i	$-0.205360\pi$
$659$	41.0225			1.59801			0.799005	+	0.601324i	$0.205360\pi$
$660$	3.81516	−	1.21664i	0.148505	−	0.0473576i
$661$			37.1589i			1.44531i	0.691207	+	0.722656i	$0.257079\pi$
$661$			37.1589i			1.44531i	−0.691207	+	0.722656i	$0.742921\pi$
$662$	−15.8541	+	11.5187i	−0.616187	+	0.447686i
$663$	−10.5285	+	5.25274i	−0.408894	+	0.204000i
$664$	−1.02177	+	3.14470i	−0.0396526	+	0.122038i
$665$	2.66467	−	3.66760i	0.103331	−	0.142223i
$666$	16.7289	+	12.1542i	0.648231	+	0.470967i
$667$	−1.73606	+	5.34304i	−0.0672205	+	0.206883i
$668$	−0.492712	+	0.160092i	−0.0190636	+	0.00619414i
$669$	−9.85560	−	13.5651i	−0.381040	−	0.524456i
$670$		−	6.84670i		−	0.264511i
$671$	−13.1981	−	41.3869i	−0.509506	−	1.59772i
$672$	14.1837			0.547149
$673$	−9.51376	+	6.91215i	−0.366729	+	0.266444i	−0.755853	−	0.654741i	$-0.772778\pi$
$673$	−9.51376	+	6.91215i	−0.366729	+	0.266444i	0.389124	+	0.921185i	$0.372778\pi$
$674$	53.4877	−	17.3792i	2.06027	−	0.669422i
$675$	−1.44967	+	4.46163i	−0.0557979	+	0.171728i
$676$	−26.7133	−	9.18259i	−1.02743	−	0.353177i
$677$	−17.3343	−	12.5941i	−0.666212	−	0.484032i	0.202543	−	0.979273i	$-0.435079\pi$
$677$	−17.3343	−	12.5941i	−0.666212	−	0.484032i	−0.868755	+	0.495242i	$0.835079\pi$
$678$	14.5587	+	4.73042i	0.559125	+	0.181671i
$679$	7.45549	+	22.9457i	0.286116	+	0.880573i
$680$	−0.518079	+	0.376406i	−0.0198674	+	0.0144345i
$681$			24.6854i			0.945947i
$682$	19.3289	−	13.8827i	0.740142	−	0.531596i
$683$			23.0840i			0.883283i	0.897192	+	0.441642i	$0.145604\pi$
$683$			23.0840i			0.883283i	−0.897192	+	0.441642i	$0.854396\pi$
$684$	−5.95797	−	8.20044i	−0.227809	−	0.313552i
$685$	−0.177758	−	0.547083i	−0.00679178	−	0.0209030i
$686$	12.0792	−	37.1760i	0.461186	−	1.41938i
$687$	11.9014	−	16.3809i	0.454068	−	0.624971i
$688$	−13.9073	−	10.1043i	−0.530212	−	0.385222i
$689$	−19.5156	−	3.26058i	−0.743485	−	0.124218i
$690$	2.53807	+	7.81139i	0.0966228	+	0.297374i
$691$	15.0429	+	20.7048i	0.572260	+	0.787648i	0.992820	−	0.119616i	$-0.0381665\pi$
$691$	15.0429	+	20.7048i	0.572260	+	0.787648i	−0.420560	+	0.907265i	$0.638166\pi$
$692$	−6.63564			−0.252249
$693$	−5.50674	−	1.82254i	−0.209184	−	0.0692326i
$694$			31.0560i			1.17887i
$695$	−7.35910	−	10.1289i	−0.279147	−	0.384212i
$696$	0.260773	−	0.0847302i	0.00988456	−	0.00321169i
$697$	22.5744	+	7.33487i	0.855067	+	0.277828i
$698$	23.4747	+	17.0553i	0.888529	+	0.645554i
$699$	14.9438	+	10.8573i	0.565226	+	0.410661i
$700$	−16.9551	−	5.50903i	−0.640841	−	0.208222i
$701$	9.25490	+	28.4837i	0.349553	+	1.07581i	0.959101	+	0.283064i	$0.0913509\pi$
$701$	9.25490	+	28.4837i	0.349553	+	1.07581i	−0.609548	+	0.792749i	$0.708649\pi$
$702$	5.25195	−	5.16376i	0.198222	−	0.194894i
$703$	−47.2209			−1.78097
$704$	−30.9042	−	0.168703i	−1.16475	−	0.00635822i
$705$	3.75127			0.141281
$706$	18.2892	−	13.2879i	0.688323	−	0.500096i
$707$	−29.3391	+	9.53284i	−1.10341	+	0.358519i
$708$	9.38747	+	3.05017i	0.352803	+	0.114633i
$709$	−15.1866	+	20.9025i	−0.570344	+	0.785011i	−0.992595	−	0.121467i	$-0.961240\pi$
$709$	−15.1866	+	20.9025i	−0.570344	+	0.785011i	0.422251	+	0.906479i	$0.361240\pi$
$710$	8.31551	−	11.4453i	0.312076	−	0.429535i
$711$	4.89080	−	15.0523i	0.183419	−	0.564506i
$712$	−0.532843	−	1.63992i	−0.0199691	−	0.0614587i
$713$	14.9394	+	20.5623i	0.559486	+	0.770066i
$714$	11.6586			0.436314
$715$	−5.87795	−	3.09881i	−0.219823	−	0.115889i
$716$	−8.15430			−0.304740
$717$	0.879439	+	1.21044i	0.0328432	+	0.0452048i
$718$	−1.50595	−	4.63483i	−0.0562015	−	0.172970i
$719$	−6.69676	+	20.6105i	−0.249747	+	0.768643i	0.745072	+	0.666984i	$0.232415\pi$
$719$	−6.69676	+	20.6105i	−0.249747	+	0.768643i	−0.994819	+	0.101659i	$0.967585\pi$
$720$	−1.18375	+	1.62929i	−0.0441158	+	0.0607202i
$721$	1.55706	−	2.14311i	0.0579879	−	0.0798134i
$722$	5.36484	+	1.74314i	0.199659	+	0.0648730i
$723$	−6.26580	+	2.03588i	−0.233028	+	0.0757153i
$724$	−14.9689	+	10.8756i	−0.556316	+	0.404187i
$725$	3.64232			0.135272
$726$	21.2935	+	7.17663i	0.790277	+	0.266350i
$727$	−38.0308			−1.41049			−0.705243	−	0.708966i	$-0.749162\pi$
$727$	−38.0308			−1.41049			−0.705243	+	0.708966i	$0.749162\pi$
$728$	1.56129	+	1.58795i	0.0578652	+	0.0588535i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−5.00870	−	1.62743i	−0.185380	−	0.0602337i
$731$	−12.5220	−	9.09779i	−0.463144	−	0.336494i
$732$	−23.0245	−	16.7283i	−0.851011	−	0.618296i
$733$	−32.4343	−	10.5385i	−1.19799	−	0.389250i	−0.358967	−	0.933350i	$-0.616871\pi$
$733$	−32.4343	−	10.5385i	−1.19799	−	0.389250i	−0.839020	+	0.544100i	$0.816871\pi$
$734$	28.0573	−	9.11637i	1.03561	−	0.336491i
$735$	1.28727	+	1.77177i	0.0474815	+	0.0653527i
$736$		−	58.6831i		−	2.16309i
$737$	11.8471	−	16.1203i	0.436393	−	0.593799i
$738$	−14.8582			−0.546939
$739$	−30.1885	−	41.5509i	−1.11050	−	1.52847i	−0.820677	−	0.571393i	$-0.806403\pi$
$739$	−30.1885	−	41.5509i	−1.11050	−	1.52847i	−0.289824	−	0.957080i	$-0.593597\pi$
$740$	−3.77677	−	11.6237i	−0.138837	−	0.427296i
$741$	−2.77172	+	16.5896i	−0.101822	+	0.609435i
$742$	15.8611	+	11.5238i	0.582280	+	0.423051i
$743$	−17.2564	+	23.7514i	−0.633075	+	0.871353i	−0.998223	−	0.0595969i	$-0.981018\pi$
$743$	−17.2564	+	23.7514i	−0.633075	+	0.871353i	0.365148	+	0.930950i	$0.381018\pi$
$744$	0.383328	−	1.17976i	0.0140535	−	0.0432522i
$745$	−1.26192	−	3.88379i	−0.0462331	−	0.142291i
$746$	21.6138	+	29.7489i	0.791338	+	1.08918i
$747$			9.36283i			0.342568i
$748$	−23.5173	−	0.128378i	−0.859876	−	0.00469397i
$749$			17.7770i			0.649557i
$750$	8.89952	−	6.46588i	0.324964	−	0.236100i
$751$	−2.47427	−	7.61503i	−0.0902875	−	0.277876i	0.895709	−	0.444640i	$-0.146668\pi$
$751$	−2.47427	−	7.61503i	−0.0902875	−	0.277876i	−0.985997	+	0.166763i	$0.946668\pi$
$752$	−23.2704	−	7.56100i	−0.848583	−	0.275721i
$753$	−18.3927	−	13.3631i	−0.670266	−	0.486977i
$754$	−5.07303	−	2.63918i	−0.184749	−	0.0961132i
$755$	−0.610110	+	1.87773i	−0.0222042	+	0.0683375i
$756$	−3.61420	+	1.17432i	−0.131447	+	0.0427097i
$757$	12.5788	−	9.13902i	0.457184	−	0.332163i	−0.335242	−	0.942132i	$-0.608818\pi$
$757$	12.5788	−	9.13902i	0.457184	−	0.332163i	0.792425	+	0.609969i	$0.208818\pi$
$758$	25.7286			0.934505
$759$	−7.54051	+	22.7834i	−0.273703	+	0.826983i
$760$			0.915421i			0.0332058i
$761$	1.48115	+	2.03863i	0.0536918	+	0.0739004i	0.835019	−	0.550222i	$-0.185457\pi$
$761$	1.48115	+	2.03863i	0.0536918	+	0.0739004i	−0.781327	+	0.624122i	$0.785457\pi$
$762$	−35.9444	+	11.6790i	−1.30213	+	0.423087i
$763$	−3.71713	+	11.4401i	−0.134569	+	0.414161i
$764$	37.3568	+	27.1413i	1.35152	+	0.981938i
$765$	−1.06584	+	1.46700i	−0.0385354	+	0.0530395i
$766$	−1.39046	+	4.27940i	−0.0502394	+	0.154621i
$767$	−7.31192	−	14.6559i	−0.264018	−	0.529194i
$768$	10.4254	−	7.57448i	0.376193	−	0.273320i
$769$			32.0441i			1.15554i	0.816200	+	0.577770i	$0.196077\pi$
$769$			32.0441i			1.15554i	−0.816200	+	0.577770i	$0.803923\pi$
$770$	3.84089	+	5.34768i	0.138416	+	0.192717i
$771$	14.7547			0.531377
$772$	−18.1961	−	25.0448i	−0.654892	−	0.901382i
$773$	−10.9593	+	3.56091i	−0.394180	+	0.128077i	−0.499399	−	0.866372i	$-0.666446\pi$
$773$	−10.9593	+	3.56091i	−0.394180	+	0.128077i	0.105219	+	0.994449i	$0.466446\pi$
$774$	9.21469	+	2.99403i	0.331215	+	0.107618i
$775$	9.68565	−	13.3312i	0.347919	−	0.478869i
$776$	−3.94138	−	2.86358i	−0.141487	−	0.102797i
$777$	−5.47070	+	16.8371i	−0.196260	+	0.604027i
$778$	−7.23984	+	2.35237i	−0.259561	+	0.0843364i
$779$	27.4505	−	19.9440i	0.983517	−	0.714567i
$780$	−4.30532	+	0.644578i	−0.154155	+	0.0230796i
$781$	39.3828	−	12.5590i	1.40923	−	0.449396i
$782$		−	48.2360i		−	1.72492i
$783$	0.628127	−	0.456361i	0.0224474	−	0.0163090i
$784$	−4.41419	−	13.5855i	−0.157649	−	0.485195i
$785$	2.43020	+	0.789619i	0.0867375	+	0.0281827i
$786$	−3.42106	+	4.70869i	−0.122025	+	0.167953i
$787$	9.05105	−	12.4577i	0.322635	−	0.444069i	−0.616634	−	0.787250i	$-0.711504\pi$
$787$	9.05105	−	12.4577i	0.322635	−	0.444069i	0.939269	+	0.343181i	$0.111504\pi$
$788$	−50.4765	−	16.4008i	−1.79815	−	0.584255i
$789$	0.116945	+	0.359920i	0.00416336	+	0.0128135i
$790$	−14.5340	+	10.5595i	−0.517096	+	0.375692i
$791$			13.1060i			0.465994i
$792$	1.11592	−	0.355860i	0.0396524	−	0.0126449i
$793$	6.99238	+	46.7041i	0.248307	+	1.65851i
$794$	0.917703	−	0.666750i	0.0325681	−	0.0236621i
$795$	−2.90006	+	0.942286i	−0.102854	+	0.0334194i
$796$	−3.12633	+	9.62186i	−0.110810	+	0.341038i
$797$	−32.2840	−	23.4557i	−1.14356	−	0.830843i	−0.155947	−	0.987765i	$-0.549843\pi$
$797$	−32.2840	−	23.4557i	−1.14356	−	0.830843i	−0.987611	+	0.156922i	$0.949843\pi$
$798$	9.79602	−	13.4831i	0.346775	−	0.477295i
$799$	−20.9524	−	6.80785i	−0.741243	−	0.240845i
$800$	−36.1838	+	11.7568i	−1.27929	+	0.415667i
$801$	−2.86992	−	3.95011i	−0.101404	−	0.139570i
$802$	0.818332			0.0288963
$803$	−8.97681	−	12.4984i	−0.316785	−	0.441060i
$804$		−	13.1065i		−	0.462232i
$805$	−5.68893	+	4.13325i	−0.200509	+	0.145678i
$806$	−23.1498	+	11.5496i	−0.815417	+	0.406816i
$807$	4.17004	−	12.8341i	0.146792	−	0.451780i
$808$	3.66147	−	5.03957i	0.128810	−	0.177292i
$809$	−38.7122	−	28.1261i	−1.36105	−	0.988859i	−0.998377	−	0.0569421i	$-0.981865\pi$
$809$	−38.7122	−	28.1261i	−1.36105	−	0.988859i	−0.362671	−	0.931917i	$-0.618135\pi$
$810$	0.350761	−	1.07953i	0.0123245	−	0.0379309i
$811$	10.7404	−	3.48978i	0.377148	−	0.122543i	−0.114308	−	0.993445i	$-0.536465\pi$
$811$	10.7404	−	3.48978i	0.377148	−	0.122543i	0.491456	+	0.870903i	$0.336465\pi$
$812$	1.73426	+	2.38700i	0.0608606	+	0.0837674i
$813$		−	7.77765i		−	0.272774i
$814$	21.5485	−	65.1080i	0.755275	−	2.28203i
$815$	−8.25699			−0.289230
$816$	9.56860	−	6.95200i	0.334968	−	0.243369i
$817$	−21.0429	+	6.83726i	−0.736199	+	0.239206i
$818$	12.4543	−	38.3303i	0.435453	−	1.34019i
$819$	5.59408	+	2.91025i	0.195473	+	0.101692i
$820$	7.10484	+	5.16197i	0.248112	+	0.180264i
$821$	2.56632	+	0.833848i	0.0895652	+	0.0291015i	0.353457	−	0.935451i	$-0.385006\pi$
$821$	2.56632	+	0.833848i	0.0895652	+	0.0291015i	−0.263892	+	0.964552i	$0.585006\pi$
$822$	−0.653485	−	2.01122i	−0.0227929	−	0.0701493i
$823$	9.35922	−	6.79987i	0.326242	−	0.237029i	−0.412592	−	0.910916i	$-0.635377\pi$
$823$	9.35922	−	6.79987i	0.326242	−	0.237029i	0.738834	+	0.673887i	$0.235377\pi$
$824$			0.534912i			0.0186345i
$825$	15.5588	+	0.0849341i	0.541690	+	0.00295703i
$826$			16.2291i			0.564681i
$827$	20.8202	+	28.6566i	0.723989	+	0.996486i	0.999382	+	0.0351541i	$0.0111922\pi$
$827$	20.8202	+	28.6566i	0.723989	+	0.996486i	−0.275392	+	0.961332i	$0.588808\pi$
$828$	4.85860	+	14.9532i	0.168848	+	0.519660i
$829$	7.84393	−	24.1411i	0.272431	−	0.838456i	−0.717457	−	0.696603i	$-0.754694\pi$
$829$	7.84393	−	24.1411i	0.272431	−	0.838456i	0.989888	−	0.141853i	$-0.0453061\pi$
$830$	6.24677	−	8.59794i	0.216828	−	0.298439i
$831$	−22.6216	−	16.4355i	−0.784734	−	0.570143i
$832$	33.1376	+	5.53648i	1.14884	+	0.191943i
$833$	−3.97449	−	12.2322i	−0.137708	−	0.423821i
$834$	−27.0540	−	37.2366i	−0.936803	−	1.28940i
$835$	0.132484			0.00458479
$836$	−19.9085	+	27.0895i	−0.688551	+	0.936910i
$837$		−	3.51255i		−	0.121412i
$838$	30.2618	+	41.6518i	1.04538	+	1.43884i
$839$	32.6170	−	10.5979i	1.12607	−	0.365881i	0.313986	−	0.949428i	$-0.398336\pi$
$839$	32.6170	−	10.5979i	1.12607	−	0.365881i	0.812079	+	0.583547i	$0.198336\pi$
$840$	0.326402	+	0.106054i	0.0112619	+	0.00365923i
$841$	22.9738	+	16.6914i	0.792200	+	0.575567i
$842$	16.5534	+	12.0268i	0.570469	+	0.414470i
$843$	−5.08899	−	1.65351i	−0.175274	−	0.0569500i
$844$	−1.33399	−	4.10560i	−0.0459178	−	0.141320i
$845$	5.77130	+	4.34428i	0.198539	+	0.149448i
$846$	13.7907			0.474133
$847$	−0.210031	+	19.2369i	−0.00721676	+	0.660989i
$848$	19.8893			0.683000
$849$	4.84699	−	3.52154i	0.166348	−	0.120859i
$850$	−29.7422	+	9.66382i	−1.02015	+	0.331466i
$851$	69.6610	+	22.6342i	2.38795	+	0.775892i
$852$	15.9183	−	21.9096i	0.545350	−	0.750610i
$853$	6.77183	−	9.32063i	0.231863	−	0.319132i	−0.677193	−	0.735805i	$-0.736804\pi$
$853$	6.77183	−	9.32063i	0.231863	−	0.319132i	0.909057	+	0.416673i	$0.136804\pi$
$854$	14.4600	−	44.5032i	0.494809	−	1.52287i
$855$	0.801009	+	2.46525i	0.0273939	+	0.0843099i
$856$	−2.10995	−	2.90410i	−0.0721168	−	0.0992602i
$857$	−41.3502			−1.41250			−0.706248	−	0.707964i	$-0.749614\pi$
$857$	−41.3502			−1.41250			−0.706248	+	0.707964i	$0.749614\pi$
$858$	−21.6089	−	11.3920i	−0.737715	−	0.388918i
$859$	−8.66846			−0.295764			−0.147882	−	0.989005i	$-0.547246\pi$
$859$	−8.66846			−0.295764			−0.147882	+	0.989005i	$0.547246\pi$
$860$	−3.36606	−	4.63299i	−0.114782	−	0.157984i
$861$	−3.93098	−	12.0983i	−0.133968	−	0.412310i
$862$	12.5336	−	38.5744i	0.426895	−	1.31385i
$863$	−14.6464	+	20.1591i	−0.498571	+	0.686224i	−0.981940	−	0.189193i	$-0.939413\pi$
$863$	−14.6464	+	20.1591i	−0.498571	+	0.686224i	0.483369	+	0.875417i	$0.339413\pi$
$864$	−4.76694	+	6.56113i	−0.162175	+	0.223214i
$865$	1.61386	+	0.524374i	0.0548728	+	0.0178292i
$866$	−47.1862	+	15.3317i	−1.60345	+	0.520993i
$867$	−5.13781	+	3.73284i	−0.174489	+	0.126774i
$868$	13.3484			0.453073
$869$	−52.4913	−	0.286544i	−1.78064	−	0.00972035i
$870$	−0.881291			−0.0298786
$871$	−15.5080	+	15.2475i	−0.525467	+	0.516643i
$872$	−0.750592	−	2.31009i	−0.0254183	−	0.0782294i
$873$	−13.1199	−	4.26292i	−0.444042	−	0.144278i
$874$	−55.7843	−	40.5296i	−1.88693	−	1.37094i
$875$	7.61935	+	5.53578i	0.257581	+	0.187144i
$876$	−9.58807	−	3.11535i	−0.323951	−	0.105258i
$877$	−43.7086	+	14.2018i	−1.47594	+	0.479561i	−0.932896	−	0.360146i	$-0.882727\pi$
$877$	−43.7086	+	14.2018i	−1.47594	+	0.479561i	−0.543040	+	0.839707i	$0.682727\pi$
$878$	10.7969	+	14.8607i	0.364378	+	0.501524i
$879$		−	17.0085i		−	0.573682i
$880$	6.34113	+	2.09870i	0.213760	+	0.0707471i
$881$	−12.9930			−0.437747			−0.218873	−	0.975753i	$-0.570238\pi$
$881$	−12.9930			−0.437747			−0.218873	+	0.975753i	$0.570238\pi$
$882$	4.73233	+	6.51349i	0.159346	+	0.219321i
$883$	10.8234	+	33.3110i	0.364237	+	1.12100i	0.950458	+	0.310854i	$0.100615\pi$
$883$	10.8234	+	33.3110i	0.364237	+	1.12100i	−0.586221	+	0.810151i	$0.699385\pi$
$884$	25.2168	+	4.21311i	0.848133	+	0.141702i
$885$	−2.04209	−	1.48367i	−0.0686442	−	0.0498729i
$886$	18.0546	−	24.8500i	0.606556	−	0.834852i
$887$	12.9256	−	39.7810i	0.434000	−	1.33571i	−0.460108	−	0.887863i	$-0.652189\pi$
$887$	12.9256	−	39.7810i	0.434000	−	1.33571i	0.894108	−	0.447851i	$-0.147811\pi$
$888$	−1.10469	−	3.39988i	−0.0370709	−	0.114092i
$889$	−19.0193	−	26.1778i	−0.637887	−	0.877976i
$890$			5.54218i			0.185774i
$891$	2.69381	−	1.93479i	0.0902459	−	0.0648178i
$892$			36.4335i			1.21988i
$893$	−25.4782	+	18.5110i	−0.852595	+	0.619446i
$894$	−4.63915	−	14.2778i	−0.155156	−	0.477522i
$895$	1.98321	+	0.644384i	0.0662914	+	0.0215394i
$896$	−3.98251	−	2.89346i	−0.133046	−	0.0966639i
$897$	12.0407	−	23.1447i	0.402028	−	0.772779i
$898$	0.180078	−	0.554223i	0.00600928	−	0.0184947i
$899$	−2.59370	+	0.842743i	−0.0865046	+	0.0281070i
$900$	8.24672	−	5.99159i	0.274891	−	0.199720i
$901$	17.9081			0.596605
$902$	14.9720	+	46.9497i	0.498515	+	1.56326i
$903$			8.29518i			0.276046i
$904$	−1.55555	−	2.14103i	−0.0517368	−	0.0712096i
$905$	4.50003	−	1.46215i	0.149586	−	0.0486034i
$906$	−2.24293	+	6.90301i	−0.0745162	+	0.229337i
$907$	33.6825	+	24.4718i	1.11841	+	0.812572i	0.983967	−	0.178349i	$-0.0570756\pi$
$907$	33.6825	+	24.4718i	1.11841	+	0.812572i	0.134443	+	0.990921i	$0.457076\pi$
$908$	31.5279	−	43.3944i	1.04629	−	1.44009i
$909$	5.45071	−	16.7756i	0.180789	−	0.556410i
$910$	−3.19539	−	6.40480i	−0.105926	−	0.212317i
$911$	−22.7700	+	16.5433i	−0.754402	+	0.548105i	−0.897188	−	0.441648i	$-0.854394\pi$
$911$	−22.7700	+	16.5433i	−0.754402	+	0.548105i	0.142786	+	0.989754i	$0.454394\pi$
$912$		−	16.9073i		−	0.559856i
$913$	29.5851	−	9.43454i	0.979124	−	0.312238i
$914$	2.35743			0.0779767
$915$	4.27787	+	5.88798i	0.141422	+	0.194651i
$916$	−41.8430	+	13.5956i	−1.38253	+	0.449212i
$917$	−4.73915	−	1.53984i	−0.156500	−	0.0508501i
$918$	−3.91830	+	5.39308i	−0.129323	+	0.177998i
$919$	−35.4759	−	25.7747i	−1.17024	−	0.850230i	−0.179204	−	0.983812i	$-0.557352\pi$
$919$	−35.4759	−	25.7747i	−1.17024	−	0.850230i	−0.991038	+	0.133582i	$0.957352\pi$
$920$	0.438785	−	1.35044i	0.0144663	−	0.0445228i
$921$	0.673818	−	0.218937i	0.0222031	−	0.00721421i
$922$	18.0240	−	13.0952i	0.593587	−	0.431266i
$923$	−44.4425	+	6.65378i	−1.46284	+	0.219012i
$924$	7.35256	+	10.2370i	0.241881	+	0.336772i
$925$		−	47.4874i		−	1.56138i
$926$	−27.2641	+	19.8085i	−0.895953	+	0.650948i
$927$	0.468057	+	1.44053i	0.0153730	+	0.0473133i
$928$	5.98849	+	1.94578i	0.196582	+	0.0638733i
$929$	−0.243122	+	0.334629i	−0.00797658	+	0.0109788i	−0.812987	−	0.582282i	$-0.802160\pi$
$929$	−0.243122	+	0.334629i	−0.00797658	+	0.0109788i	0.805010	+	0.593261i	$0.202160\pi$
$930$	−2.34353	+	3.22559i	−0.0768474	+	0.105771i
$931$	−17.4859	−	5.68151i	−0.573077	−	0.186204i
$932$	−12.4029	−	38.1721i	−0.406269	−	1.25037i
$933$	8.06683	−	5.86090i	0.264096	−	0.191877i
$934$		−	65.5455i		−	2.14471i
$935$	5.70949	+	1.88965i	0.186720	+	0.0617980i
$936$	−1.25928	+	0.188536i	−0.0411610	+	0.00616248i
$937$	−44.2912	+	32.1794i	−1.44693	+	1.05126i	−0.460394	+	0.887715i	$0.652292\pi$
$937$	−44.2912	+	32.1794i	−1.44693	+	1.05126i	−0.986536	+	0.163542i	$0.947708\pi$
$938$	20.4949	−	6.65919i	0.669181	−	0.217430i
$939$	−0.932760	+	2.87074i	−0.0304395	+	0.0936830i
$940$	−6.59435	−	4.79108i	−0.215084	−	0.156268i
$941$	−6.96013	+	9.57980i	−0.226894	+	0.312293i	−0.907252	−	0.420587i	$-0.861824\pi$
$941$	−6.96013	+	9.57980i	−0.226894	+	0.312293i	0.680358	+	0.732880i	$0.261824\pi$
$942$	8.93404	+	2.90285i	0.291087	+	0.0945799i
$943$	−50.0551	+	16.2639i	−1.63002	+	0.529625i
$944$	9.67732	+	13.3197i	0.314970	+	0.433519i
$945$	0.971809			0.0316129
$946$	0.175416	−	32.1340i	0.00570326	−	1.04476i
$947$		−	31.1294i		−	1.01157i	−0.862659	−	0.505786i	$-0.831203\pi$
$947$		−	31.1294i		−	1.01157i	0.862659	−	0.505786i	$-0.168797\pi$
$948$	−27.8222	+	20.2140i	−0.903622	+	0.656520i
$949$	7.46817	+	14.9691i	0.242427	+	0.485918i
$950$	−13.8144	+	42.5163i	−0.448198	+	1.37941i
$951$	3.90945	−	5.38090i	0.126773	−	0.174488i
$952$	−1.63062	−	1.18472i	−0.0528488	−	0.0383969i
$953$	−4.88340	+	15.0296i	−0.158189	+	0.486855i	−0.998470	−	0.0552955i	$-0.982390\pi$
$953$	−4.88340	+	15.0296i	−0.158189	+	0.486855i	0.840281	+	0.542151i	$0.182390\pi$
$954$	−10.6614	+	3.46409i	−0.345175	+	0.112154i
$955$	−6.94075	−	9.55312i	−0.224597	−	0.309132i
$956$		−	3.25104i		−	0.105146i
$957$	−2.07497	−	1.52493i	−0.0670742	−	0.0492939i
$958$	−11.2694			−0.364097
$959$	1.46475	−	1.06420i	0.0472991	−	0.0343648i
$960$	4.92431	−	1.60001i	0.158931	−	0.0516400i
$961$	5.76687	−	17.7486i	0.186028	−	0.572536i
$962$	−34.4088	+	66.1406i	−1.10938	+	2.13246i
$963$	−8.22330	−	5.97458i	−0.264992	−	0.192528i
$964$	13.6148	+	4.42373i	0.438505	+	0.142479i
$965$	2.44634	+	7.52908i	0.0787506	+	0.242370i
$966$	−20.9140	+	15.1949i	−0.672897	+	0.488889i
$967$			21.4780i			0.690687i	0.938476	+	0.345344i	$0.112238\pi$
$967$			21.4780i			0.690687i	−0.938476	+	0.345344i	$0.887762\pi$
$968$	−2.24893	−	3.16754i	−0.0722833	−	0.101808i
$969$		−	15.2231i		−	0.489038i
$970$	9.20392	+	12.6681i	0.295520	+	0.406749i
$971$	13.1998	+	40.6247i	0.423600	+	1.30371i	0.904328	+	0.426838i	$0.140372\pi$
$971$	13.1998	+	40.6247i	0.423600	+	1.30371i	−0.480728	+	0.876870i	$0.659628\pi$
$972$	0.671457	−	2.06653i	0.0215370	−	0.0662841i
$973$	23.1623	−	31.8802i	0.742551	−	1.02203i
$974$	−0.290485	−	0.211050i	−0.00930774	−	0.00676247i
$975$	−16.6833	−	2.78736i	−0.534292	−	0.0892671i
$976$	−14.6693	−	45.1475i	−0.469553	−	1.44514i
$977$	24.6959	+	33.9910i	0.790093	+	1.08747i	0.994097	+	0.108499i	$0.0346045\pi$
$977$	24.6959	+	33.9910i	0.790093	+	1.08747i	−0.204004	+	0.978970i	$0.565395\pi$
$978$	−30.3549			−0.970641
$979$	−9.58982	+	13.0489i	−0.306492	+	0.417044i
$980$		−	4.75867i		−	0.152010i
$981$	−4.04273	−	5.56434i	−0.129074	−	0.177656i
$982$	−37.5850	+	12.2121i	−1.19939	+	0.389704i
$983$	19.7319	+	6.41129i	0.629351	+	0.204488i	0.606287	−	0.795246i	$-0.292658\pi$
$983$	19.7319	+	6.41129i	0.629351	+	0.204488i	0.0230633	+	0.999734i	$0.492658\pi$
$984$	2.07813	+	1.50985i	0.0662484	+	0.0481323i
$985$	10.9804	+	7.97769i	0.349863	+	0.254190i
$986$	4.92238	+	1.59938i	0.156761	+	0.0509346i
$987$	3.64854	+	11.2290i	0.116134	+	0.357424i
$988$	26.0605	−	25.6229i	0.829094	−	0.815172i
$989$	34.3201			1.09132
$990$	−3.76460	−	0.0205506i	−0.119647	−	0.000653140i
$991$	−20.9534			−0.665607			−0.332804	−	0.942996i	$-0.607995\pi$
$991$	−20.9534			−0.665607			−0.332804	+	0.942996i	$0.607995\pi$
$992$	23.0463	−	16.7441i	0.731720	−	0.531626i
$993$	9.12373	−	2.96448i	0.289533	−	0.0940749i
$994$	42.3482	+	13.7597i	1.34320	+	0.436433i
$995$	1.52071	−	2.09308i	0.0482098	−	0.0663551i
$996$	11.9581	−	16.4589i	0.378907	−	0.521520i
$997$	1.98514	−	6.10963i	0.0628700	−	0.193494i	−0.914688	−	0.404161i	$-0.867564\pi$
$997$	1.98514	−	6.10963i	0.0628700	−	0.193494i	0.977558	+	0.210667i	$0.0675636\pi$
$998$	−17.0105	−	52.3530i	−0.538458	−	1.65720i
$999$	−5.94990	−	8.18934i	−0.188247	−	0.259099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bb.b.25.12	yes	56
11.4	even	5	inner	429.2.bb.b.103.3	yes	56
13.12	even	2	inner	429.2.bb.b.25.3	✓	56
143.103	even	10	inner	429.2.bb.b.103.12	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bb.b.25.3	✓	56	13.12	even	2	inner
429.2.bb.b.25.12	yes	56	1.1	even	1	trivial
429.2.bb.b.103.3	yes	56	11.4	even	5	inner
429.2.bb.b.103.12	yes	56	143.103	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.20071 + 1.65263i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.671457 + 2.06653i) q^{4} +(0.326611 - 0.449541i) q^{5} +(1.20071 - 1.65263i) q^{6} +(1.66332 + 0.540445i) q^{7} +(-0.335871 + 0.109131i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.20071 + 1.65263i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.671457 + 2.06653i) q^{4} +(0.326611 - 0.449541i) q^{5} +(1.20071 - 1.65263i) q^{6} +(1.66332 + 0.540445i) q^{7} +(-0.335871 + 0.109131i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.13509 q^{10} +(2.67252 + 1.96408i) q^{11} +2.17288 q^{12} +(-2.52783 - 2.57100i) q^{13} +(1.10400 + 3.39777i) q^{14} +(-0.528467 - 0.171709i) q^{15} +(2.93216 + 2.13034i) q^{16} +(2.64009 + 1.91814i) q^{17} +(-1.94278 - 0.631249i) q^{18} +(4.43660 - 1.44154i) q^{19} +(0.709686 + 0.976799i) q^{20} -1.74892i q^{21} +(-0.0369839 + 6.77498i) q^{22} -7.23590 q^{23} +(0.207580 + 0.285709i) q^{24} +(1.44967 + 4.46163i) q^{25} +(1.21374 - 7.26459i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.23370 + 3.07442i) q^{28} +(0.239923 - 0.738408i) q^{29} +(-0.350761 - 1.07953i) q^{30} +(-2.06463 - 2.84171i) q^{31} +8.11000i q^{32} +(1.04210 - 3.14866i) q^{33} +6.66621i q^{34} +(0.786210 - 0.571215i) q^{35} +(-0.671457 - 2.06653i) q^{36} +(-9.62714 - 3.12805i) q^{37} +(7.70938 + 5.60119i) q^{38} +(-1.66403 + 3.19860i) q^{39} +(-0.0606401 + 0.186631i) q^{40} +(6.91760 - 2.24767i) q^{41} +(2.89031 - 2.09994i) q^{42} -4.74303 q^{43} +(-5.85332 + 4.20406i) q^{44} +0.555663i q^{45} +(-8.68819 - 11.9583i) q^{46} +(-6.42057 + 2.08617i) q^{47} +(1.11999 - 3.44696i) q^{48} +(-3.18857 - 2.31663i) q^{49} +(-5.63280 + 7.75288i) q^{50} +(1.00842 - 3.10361i) q^{51} +(7.01040 - 3.49753i) q^{52} +(4.43963 - 3.22558i) q^{53} +2.04276i q^{54} +(1.75581 - 0.559919i) q^{55} -0.617640 q^{56} +(-2.74197 - 3.77399i) q^{57} +(1.50839 - 0.490106i) q^{58} +(4.32029 + 1.40375i) q^{59} +(0.709686 - 0.976799i) q^{60} +(-10.5963 - 7.69867i) q^{61} +(2.21729 - 6.82412i) q^{62} +(-1.66332 + 0.540445i) q^{63} +(-7.53851 + 5.47705i) q^{64} +(-1.98139 + 0.296647i) q^{65} +(6.45482 - 2.05841i) q^{66} -6.03187i q^{67} +(-5.73660 + 4.16788i) q^{68} +(2.23602 + 6.88175i) q^{69} +(1.88801 + 0.613453i) q^{70} +(7.32587 - 10.0832i) q^{71} +(0.207580 - 0.285709i) q^{72} +(-4.41261 - 1.43374i) q^{73} +(-6.38986 - 19.6660i) q^{74} +(3.79529 - 2.75744i) q^{75} +10.1363i q^{76} +(3.38378 + 4.71125i) q^{77} +(-7.28410 + 1.09055i) q^{78} +(-12.8043 + 9.30285i) q^{79} +(1.91535 - 0.622335i) q^{80} +(0.309017 - 0.951057i) q^{81} +(12.0206 + 8.73346i) q^{82} +(5.50333 - 7.57469i) q^{83} +(3.61420 + 1.17432i) q^{84} +(1.72456 - 0.560344i) q^{85} +(-5.69499 - 7.83848i) q^{86} -0.776408 q^{87} +(-1.11196 - 0.368022i) q^{88} +4.88260i q^{89} +(-0.918305 + 0.667188i) q^{90} +(-2.81511 - 5.64256i) q^{91} +(4.85860 - 14.9532i) q^{92} +(-2.06463 + 2.84171i) q^{93} +(-11.1569 - 8.10595i) q^{94} +(0.801009 - 2.46525i) q^{95} +(7.71307 - 2.50613i) q^{96} +(8.10855 + 11.1605i) q^{97} -8.05112i q^{98} +(-3.31658 - 0.0181048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9}+O(q^{10}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9	\( 56 q + 14 q^{3} + 20 q^{4} - 14 q^{9} + 60 q^{12} - 3 q^{13} - 42 q^{14} - 16 q^{16} - 6 q^{17} - 40 q^{22} + 12 q^{23} + 4 q^{25} - 24 q^{26} + 14 q^{27} - 22 q^{29} - 10 q^{30} - 10 q^{35} + 20 q^{36} - 26 q^{38} + 3 q^{39} - 18 q^{42} + 6 q^{48} - 14 q^{49} - 24 q^{51} + 39 q^{52} + 10 q^{53} - 64 q^{55} - 20 q^{56} + 2 q^{61} - 8 q^{62} + 24 q^{64} - 58 q^{65} + 30 q^{66} + 18 q^{68} - 2 q^{69} - 86 q^{74} - 14 q^{75} + 52 q^{77} + 14 q^{78} - 24 q^{79} - 14 q^{81} + 62 q^{82} - 28 q^{87} - 46 q^{88} - 10 q^{90} - 19 q^{91} + 58 q^{92} + 86 q^{94} + 156 q^{95}+O(q^{100}) \) 56 * q + 14 * q^3 + 20 * q^4 - 14 * q^9 + 60 * q^12 - 3 * q^13 - 42 * q^14 - 16 * q^16 - 6 * q^17 - 40 * q^22 + 12 * q^23 + 4 * q^25 - 24 * q^26 + 14 * q^27 - 22 * q^29 - 10 * q^30 - 10 * q^35 + 20 * q^36 - 26 * q^38 + 3 * q^39 - 18 * q^42 + 6 * q^48 - 14 * q^49 - 24 * q^51 + 39 * q^52 + 10 * q^53 - 64 * q^55 - 20 * q^56 + 2 * q^61 - 8 * q^62 + 24 * q^64 - 58 * q^65 + 30 * q^66 + 18 * q^68 - 2 * q^69 - 86 * q^74 - 14 * q^75 + 52 * q^77 + 14 * q^78 - 24 * q^79 - 14 * q^81 + 62 * q^82 - 28 * q^87 - 46 * q^88 - 10 * q^90 - 19 * q^91 + 58 * q^92 + 86 * q^94 + 156 * q^95

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