LMFDB - Embedded newform 120.2.w.c.53.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.12
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.864261 + 1.11940i) q^{2} +(-0.170116 - 1.72368i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 - 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(-2.94212 + 0.586449i) q^{9} +O(q^{10})$	\(q+(0.864261 + 1.11940i) q^{2} +(-0.170116 - 1.72368i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 - 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(-2.94212 + 0.586449i) q^{9} +(-0.801547 + 3.05901i) q^{10} +0.510276 q^{11} +(3.42125 + 0.543207i) q^{12} +(-0.750647 + 0.750647i) q^{13} +(4.10544 + 0.528041i) q^{14} +(2.81946 - 2.65531i) q^{15} +(-3.48771 - 1.95854i) q^{16} +(-3.14698 - 3.14698i) q^{17} +(-3.19923 - 2.78656i) q^{18} -6.01198 q^{19} +(-4.11699 + 1.74653i) q^{20} +(-3.91945 - 3.21529i) q^{21} +(0.441012 + 0.571203i) q^{22} +(2.54575 - 2.54575i) q^{23} +(2.34878 + 4.29921i) q^{24} +(-1.26945 + 4.83617i) q^{25} +(-1.48903 - 0.191519i) q^{26} +(1.51135 + 4.97150i) q^{27} +(2.95708 + 5.05199i) q^{28} -5.10739i q^{29} +(5.40909 + 0.861223i) q^{30} -4.56672 q^{31} +(-0.821906 - 5.59683i) q^{32} +(-0.0868061 - 0.879551i) q^{33} +(0.802913 - 6.24253i) q^{34} +(6.49090 + 0.837710i) q^{35} +(0.354305 - 5.98953i) q^{36} +(6.76263 + 6.76263i) q^{37} +(-5.19592 - 6.72981i) q^{38} +(1.42157 + 1.16618i) q^{39} +(-5.51322 - 3.09910i) q^{40} +4.24355i q^{41} +(0.211772 - 7.16627i) q^{42} +(5.95972 - 5.95972i) q^{43} +(-0.258254 + 0.987336i) q^{44} +(-5.05652 - 4.40813i) q^{45} +(5.04990 + 0.649518i) q^{46} +(3.33849 + 3.33849i) q^{47} +(-2.78257 + 6.34486i) q^{48} -1.56672i q^{49} +(-6.51073 + 2.75869i) q^{50} +(-4.88902 + 5.95972i) q^{51} +(-1.07252 - 1.83234i) q^{52} +(5.75871 + 5.75871i) q^{53} +(-4.25889 + 5.98848i) q^{54} +(0.696910 + 0.903452i) q^{55} +(-3.09950 + 7.67638i) q^{56} +(1.02273 + 10.3627i) q^{57} +(5.71720 - 4.41411i) q^{58} -1.16514i q^{59} +(3.71082 + 6.79925i) q^{60} +4.92929i q^{61} +(-3.94684 - 5.11198i) q^{62} +(-4.87536 + 7.30283i) q^{63} +(5.55474 - 5.75716i) q^{64} +(-2.35423 - 0.303835i) q^{65} +(0.909545 - 0.857332i) q^{66} +(-7.98415 - 7.98415i) q^{67} +(7.68180 - 4.49639i) q^{68} +(-4.82112 - 3.95497i) q^{69} +(4.67210 + 7.98991i) q^{70} +5.09150i q^{71} +(7.01088 - 4.77991i) q^{72} +(-3.20654 - 3.20654i) q^{73} +(-1.72540 + 13.4148i) q^{74} +(8.55194 + 1.36541i) q^{75} +(3.04271 - 11.6326i) q^{76} +(1.05608 - 1.05608i) q^{77} +(-0.0768090 + 2.59918i) q^{78} +7.31215i q^{79} +(-1.29572 - 8.84992i) q^{80} +(8.31215 - 3.45081i) q^{81} +(-4.75023 + 3.66754i) q^{82} +(-4.77995 - 4.77995i) q^{83} +(8.20494 - 5.95647i) q^{84} +(1.27378 - 9.86975i) q^{85} +(11.8220 + 1.52055i) q^{86} +(-8.80349 + 0.868848i) q^{87} +(-1.32842 + 0.564226i) q^{88} +12.6431 q^{89} +(0.564297 - 9.47004i) q^{90} +3.10712i q^{91} +(3.63736 + 6.21420i) q^{92} +(0.776871 + 7.87155i) q^{93} +(-0.851777 + 6.62243i) q^{94} +(-8.21087 - 10.6443i) q^{95} +(-9.50730 + 2.36881i) q^{96} +(10.8789 - 10.8789i) q^{97} +(1.75378 - 1.35405i) q^{98} +(-1.50129 + 0.299251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.864261	+	1.11940i	0.611125	+	0.791534i
$2$	0.864261	+	1.11940i	0.611125	+	0.791534i
$3$	−0.170116	−	1.72368i	−0.0982164	−	0.995165i
$3$	−0.170116	−	1.72368i	−0.0982164	−	0.995165i
$4$	−0.506107	+	1.93490i	−0.253054	+	0.967452i
$5$	1.36575	+	1.77052i	0.610783	+	0.791798i
$5$	1.36575	+	1.77052i	0.610783	+	0.791798i
$6$	1.78246	−	1.68013i	0.727685	−	0.685911i
$7$	2.06963	−	2.06963i	0.782246	−	0.782246i	−0.197964	−	0.980209i	$-0.563433\pi$
$7$	2.06963	−	2.06963i	0.782246	−	0.782246i	0.980209	+	0.197964i	$0.0634328\pi$
$8$	−2.60334	+	1.10573i	−0.920419	+	0.390933i
$9$	−2.94212	+	0.586449i	−0.980707	+	0.195483i
$10$	−0.801547	+	3.05901i	−0.253471	+	0.967343i
$11$	0.510276			0.153854			0.0769270	−	0.997037i	$-0.475489\pi$
$11$	0.510276			0.153854			0.0769270	+	0.997037i	$0.475489\pi$
$12$	3.42125	+	0.543207i	0.987629	+	0.156810i
$13$	−0.750647	+	0.750647i	−0.208192	+	0.208192i	−0.803499	−	0.595307i	$-0.797031\pi$
$13$	−0.750647	+	0.750647i	−0.208192	+	0.208192i	0.595307	+	0.803499i	$0.297031\pi$
$14$	4.10544	+	0.528041i	1.09722	+	0.141125i
$15$	2.81946	−	2.65531i	0.727981	−	0.685597i
$16$	−3.48771	−	1.95854i	−0.871928	−	0.489635i
$17$	−3.14698	−	3.14698i	−0.763254	−	0.763254i	0.213656	−	0.976909i	$-0.431463\pi$
$17$	−3.14698	−	3.14698i	−0.763254	−	0.763254i	−0.976909	+	0.213656i	$0.931463\pi$
$18$	−3.19923	−	2.78656i	−0.754066	−	0.656799i
$19$	−6.01198			−1.37924			−0.689622	−	0.724170i	$-0.742223\pi$
$19$	−6.01198			−1.37924			−0.689622	+	0.724170i	$0.742223\pi$
$20$	−4.11699	+	1.74653i	−0.920588	+	0.390536i
$21$	−3.91945	−	3.21529i	−0.855293	−	0.701634i
$22$	0.441012	+	0.571203i	0.0940240	+	0.121781i
$23$	2.54575	−	2.54575i	0.530825	−	0.530825i	−0.389993	−	0.920818i	$-0.627522\pi$
$23$	2.54575	−	2.54575i	0.530825	−	0.530825i	0.920818	+	0.389993i	$0.127522\pi$
$24$	2.34878	+	4.29921i	0.479443	+	0.877573i
$25$	−1.26945	+	4.83617i	−0.253889	+	0.967233i
$26$	−1.48903	−	0.191519i	−0.292023	−	0.0375599i
$27$	1.51135	+	4.97150i	0.290859	+	0.956766i
$28$	2.95708	+	5.05199i	0.558835	+	0.954736i
$29$		−	5.10739i		−	0.948418i	−0.880412	−	0.474209i	$-0.842734\pi$
$29$		−	5.10739i		−	0.948418i	0.880412	−	0.474209i	$-0.157266\pi$
$30$	5.40909	+	0.861223i	0.987561	+	0.157237i
$31$	−4.56672			−0.820207			−0.410104	−	0.912039i	$-0.634507\pi$
$31$	−4.56672			−0.820207			−0.410104	+	0.912039i	$0.634507\pi$
$32$	−0.821906	−	5.59683i	−0.145294	−	0.989389i
$33$	−0.0868061	−	0.879551i	−0.0151110	−	0.153110i
$34$	0.802913	−	6.24253i	0.137699	−	1.07058i
$35$	6.49090	+	0.837710i	1.09716	+	0.141599i
$36$	0.354305	−	5.98953i	0.0590509	−	0.998255i
$37$	6.76263	+	6.76263i	1.11177	+	1.11177i	0.992911	+	0.118858i	$0.0379234\pi$
$37$	6.76263	+	6.76263i	1.11177	+	1.11177i	0.118858	+	0.992911i	$0.462077\pi$
$38$	−5.19592	−	6.72981i	−0.842890	−	1.09172i
$39$	1.42157	+	1.16618i	0.227633	+	0.186738i
$40$	−5.51322	−	3.09910i	−0.871716	−	0.490011i
$41$			4.24355i			0.662732i	0.943502	+	0.331366i	$0.107509\pi$
$41$			4.24355i			0.662732i	−0.943502	+	0.331366i	$0.892491\pi$
$42$	0.211772	−	7.16627i	0.0326771	−	1.10578i
$43$	5.95972	−	5.95972i	0.908848	−	0.908848i	−0.0873310	−	0.996179i	$-0.527834\pi$
$43$	5.95972	−	5.95972i	0.908848	−	0.908848i	0.996179	+	0.0873310i	$0.0278338\pi$
$44$	−0.258254	+	0.987336i	−0.0389333	+	0.148846i
$45$	−5.05652	−	4.40813i	−0.753782	−	0.657125i
$46$	5.04990	+	0.649518i	0.744567	+	0.0957661i
$47$	3.33849	+	3.33849i	0.486969	+	0.486969i	0.907349	−	0.420379i	$-0.138103\pi$
$47$	3.33849	+	3.33849i	0.486969	+	0.486969i	−0.420379	+	0.907349i	$0.638103\pi$
$48$	−2.78257	+	6.34486i	−0.401630	+	0.915802i
$49$		−	1.56672i		−	0.223817i
$50$	−6.51073	+	2.75869i	−0.920756	+	0.390138i
$51$	−4.88902	+	5.95972i	−0.684599	+	0.834527i
$52$	−1.07252	−	1.83234i	−0.148732	−	0.254100i
$53$	5.75871	+	5.75871i	0.791019	+	0.791019i	0.981660	−	0.190641i	$-0.0610565\pi$
$53$	5.75871	+	5.75871i	0.791019	+	0.791019i	−0.190641	+	0.981660i	$0.561057\pi$
$54$	−4.25889	+	5.98848i	−0.579562	+	0.814928i
$55$	0.696910	+	0.903452i	0.0939714	+	0.121821i
$56$	−3.09950	+	7.67638i	−0.414188	+	1.02580i
$57$	1.02273	+	10.3627i	0.135464	+	1.37257i
$58$	5.71720	−	4.41411i	0.750706	−	0.579602i
$59$		−	1.16514i		−	0.151689i	−0.997120	−	0.0758444i	$-0.975835\pi$
$59$		−	1.16514i		−	0.151689i	0.997120	−	0.0758444i	$-0.0241652\pi$
$60$	3.71082	+	6.79925i	0.479064	+	0.877780i
$61$			4.92929i			0.631131i	0.948904	+	0.315565i	$0.102194\pi$
$61$			4.92929i			0.631131i	−0.948904	+	0.315565i	$0.897806\pi$
$62$	−3.94684	−	5.11198i	−0.501249	−	0.649222i
$63$	−4.87536	+	7.30283i	−0.614238	+	0.920070i
$64$	5.55474	−	5.75716i	0.694342	−	0.719645i
$65$	−2.35423	−	0.303835i	−0.292006	−	0.0376861i
$66$	0.909545	−	0.857332i	0.111957	−	0.105530i
$67$	−7.98415	−	7.98415i	−0.975419	−	0.975419i	0.0242864	−	0.999705i	$-0.492269\pi$
$67$	−7.98415	−	7.98415i	−0.975419	−	0.975419i	−0.999705	+	0.0242864i	$0.992269\pi$
$68$	7.68180	−	4.49639i	0.931555	−	0.545267i
$69$	−4.82112	−	3.95497i	−0.580395	−	0.476123i
$70$	4.67210	+	7.98991i	0.558423	+	0.954977i
$71$			5.09150i			0.604250i	0.953268	+	0.302125i	$0.0976959\pi$
$71$			5.09150i			0.604250i	−0.953268	+	0.302125i	$0.902304\pi$
$72$	7.01088	−	4.77991i	0.826241	−	0.563317i
$73$	−3.20654	−	3.20654i	−0.375297	−	0.375297i	0.494105	−	0.869402i	$-0.335496\pi$
$73$	−3.20654	−	3.20654i	−0.375297	−	0.375297i	−0.869402	+	0.494105i	$0.835496\pi$
$74$	−1.72540	+	13.4148i	−0.200574	+	1.55943i
$75$	8.55194	+	1.36541i	0.987493	+	0.157664i
$76$	3.04271	−	11.6326i	0.349023	−	1.33435i
$77$	1.05608	−	1.05608i	0.120352	−	0.120352i
$78$	−0.0768090	+	2.59918i	−0.00869691	+	0.294300i
$79$			7.31215i			0.822682i	0.911482	+	0.411341i	$0.134939\pi$
$79$			7.31215i			0.822682i	−0.911482	+	0.411341i	$0.865061\pi$
$80$	−1.29572	−	8.84992i	−0.144866	−	0.989451i
$81$	8.31215	−	3.45081i	0.923573	−	0.383423i
$82$	−4.75023	+	3.66754i	−0.524575	+	0.405012i
$83$	−4.77995	−	4.77995i	−0.524668	−	0.524668i	0.394310	−	0.918978i	$-0.370984\pi$
$83$	−4.77995	−	4.77995i	−0.524668	−	0.524668i	−0.918978	+	0.394310i	$0.870984\pi$
$84$	8.20494	−	5.95647i	0.895233	−	0.649904i
$85$	1.27378	−	9.86975i	0.138161	−	1.07052i
$86$	11.8220	+	1.52055i	1.27480	+	0.163965i
$87$	−8.80349	+	0.868848i	−0.943833	+	0.0931502i
$88$	−1.32842	+	0.564226i	−0.141610	+	0.0601467i
$89$	12.6431			1.34017			0.670083	−	0.742286i	$-0.266259\pi$
$89$	12.6431			1.34017			0.670083	+	0.742286i	$0.266259\pi$
$90$	0.564297	−	9.47004i	0.0594821	−	0.998229i
$91$			3.10712i			0.325715i
$92$	3.63736	+	6.21420i	0.379221	+	0.647875i
$93$	0.776871	+	7.87155i	0.0805578	+	0.816241i
$94$	−0.851777	+	6.62243i	−0.0878541	+	0.683052i
$95$	−8.21087	−	10.6443i	−0.842418	−	1.09208i
$96$	−9.50730	+	2.36881i	−0.970335	+	0.241766i
$97$	10.8789	−	10.8789i	1.10458	−	1.10458i	0.110732	−	0.993850i	$-0.464680\pi$
$97$	10.8789	−	10.8789i	1.10458	−	1.10458i	0.993850	−	0.110732i	$-0.0353195\pi$
$98$	1.75378	−	1.35405i	0.177159	−	0.136780i
$99$	−1.50129	+	0.299251i	−0.150886	+	0.0300759i
$100$	−8.71504	−	4.90388i	−0.871504	−	0.490388i
$101$	−6.41002			−0.637821			−0.318911	−	0.947785i	$-0.603317\pi$
$101$	−6.41002			−0.637821			−0.318911	+	0.947785i	$0.603317\pi$
$102$	−10.8967	−	0.322010i	−1.07893	−	0.0318838i
$103$	−1.86309	−	1.86309i	−0.183575	−	0.183575i	0.609336	−	0.792912i	$-0.291436\pi$
$103$	−1.86309	−	1.86309i	−0.183575	−	0.183575i	−0.792912	+	0.609336i	$0.791436\pi$
$104$	1.12418	−	2.78420i	0.110235	−	0.273013i
$105$	0.339736	−	11.3307i	0.0331548	−	1.10577i
$106$	−1.46927	+	11.4233i	−0.142708	+	1.10953i
$107$	−10.0319	+	10.0319i	−0.969824	+	0.969824i	−0.999558	−	0.0297341i	$-0.990534\pi$
$107$	−10.0319	+	10.0319i	−0.969824	+	0.969824i	0.0297341	+	0.999558i	$0.490534\pi$
$108$	−10.3843	+	0.408206i	−0.999228	+	0.0392797i
$109$	12.6448			1.21115			0.605577	−	0.795786i	$-0.292942\pi$
$109$	12.6448			1.21115			0.605577	+	0.795786i	$0.292942\pi$
$110$	−0.409011	+	1.56094i	−0.0389976	+	0.148830i
$111$	10.5062	−	12.8070i	0.997200	−	1.21559i
$112$	−11.2717	+	3.16482i	−1.06508	+	0.299047i
$113$	1.88933	−	1.88933i	0.177733	−	0.177733i	−0.612634	−	0.790367i	$-0.709890\pi$
$113$	1.88933	−	1.88933i	0.177733	−	0.177733i	0.790367	+	0.612634i	$0.209890\pi$
$114$	−10.7161	+	10.1009i	−1.00365	+	0.946039i
$115$	7.98415	+	1.03043i	0.744525	+	0.0960878i
$116$	9.88231	+	2.58489i	0.917549	+	0.240001i
$117$	1.76828	−	2.64871i	0.163477	−	0.244874i
$118$	1.30426	−	1.00699i	0.120067	−	0.0927008i
$119$	−13.0261			−1.19410
$120$	−4.40396	+	10.0302i	−0.402025	+	0.915629i
$121$	−10.7396			−0.976329
$122$	−5.51784	+	4.26019i	−0.499562	+	0.385700i
$123$	7.31452	−	0.721896i	0.659528	−	0.0650912i
$124$	2.31125	−	8.83617i	0.207556	−	0.793511i
$125$	−10.2963	+	4.35743i	−0.920925	+	0.389740i
$126$	−12.3884	+	0.854070i	−1.10364	+	0.0760866i
$127$	0.964015	−	0.964015i	0.0855425	−	0.0855425i	−0.663041	−	0.748583i	$-0.730734\pi$
$127$	0.964015	−	0.964015i	0.0855425	−	0.0855425i	0.748583	+	0.663041i	$0.230734\pi$
$128$	11.2453	+	1.24228i	0.993953	+	0.109803i
$129$	−11.2865	−	9.25878i	−0.993718	−	0.815190i
$130$	−1.69456	−	2.89791i	−0.148622	−	0.254164i
$131$	7.59234			0.663346			0.331673	−	0.943395i	$-0.392387\pi$
$131$	7.59234			0.663346			0.331673	+	0.943395i	$0.392387\pi$
$132$	1.74578	+	0.277186i	0.151951	+	0.0241259i
$133$	−12.4426	+	12.4426i	−1.07891	+	1.07891i
$134$	2.03706	−	15.8378i	0.175975	−	1.36818i
$135$	−6.73799	+	9.46570i	−0.579914	+	0.814678i
$136$	11.6723	+	4.71295i	1.00089	+	0.404132i
$137$	0.713542	+	0.713542i	0.0609620	+	0.0609620i	0.736931	−	0.675968i	$-0.236274\pi$
$137$	0.713542	+	0.713542i	0.0609620	+	0.0609620i	−0.675968	+	0.736931i	$0.736274\pi$
$138$	0.260491	−	8.81488i	0.0221744	−	0.750373i
$139$	−9.01457			−0.764606			−0.382303	−	0.924037i	$-0.624869\pi$
$139$	−9.01457			−0.764606			−0.382303	+	0.924037i	$0.624869\pi$
$140$	−4.90598	+	12.1353i	−0.414631	+	1.02562i
$141$	5.18655	−	6.32241i	0.436787	−	0.532443i
$142$	−5.69942	+	4.40038i	−0.478284	+	0.369272i
$143$	−0.383038	+	0.383038i	−0.0320312	+	0.0320312i
$144$	11.4099	+	3.71689i	0.950821	+	0.309741i
$145$	9.04271	−	6.97542i	0.750956	−	0.579277i
$146$	0.818111	−	6.36069i	0.0677073	−	0.526414i
$147$	−2.70052	+	0.266524i	−0.222735	+	0.0219825i
$148$	−16.5077	+	9.66243i	−1.35692	+	0.794247i
$149$		−	13.1573i		−	1.07789i	−0.842341	−	0.538944i	$-0.818823\pi$
$149$		−	13.1573i		−	1.07789i	0.842341	−	0.538944i	$-0.181177\pi$
$150$	5.86267	+	10.7531i	0.478685	+	0.877987i
$151$	2.75982			0.224591			0.112295	−	0.993675i	$-0.464180\pi$
$151$	2.75982			0.224591			0.112295	+	0.993675i	$0.464180\pi$
$152$	15.6512	−	6.64761i	1.26948	−	0.539192i
$153$	11.1043	+	7.41324i	0.897731	+	0.599325i
$154$	2.09491	+	0.269447i	0.168812	+	0.0217126i
$155$	−6.23700	−	8.08545i	−0.500968	−	0.649439i
$156$	−2.97591	+	2.16039i	−0.238263	+	0.172970i
$157$	−4.38090	−	4.38090i	−0.349634	−	0.349634i	0.510339	−	0.859973i	$-0.329520\pi$
$157$	−4.38090	−	4.38090i	−0.349634	−	0.349634i	−0.859973	+	0.510339i	$0.829520\pi$
$158$	−8.18522	+	6.31961i	−0.651181	+	0.502761i
$159$	8.94650	−	10.9058i	0.709504	−	0.864886i
$160$	8.78675	−	9.09907i	0.694653	−	0.719345i
$161$		−	10.5375i		−	0.830472i
$162$	11.0467	+	6.32222i	0.867911	+	0.496720i
$163$	−0.470868	+	0.470868i	−0.0368812	+	0.0368812i	−0.725307	−	0.688426i	$-0.758302\pi$
$163$	−0.470868	+	0.470868i	−0.0368812	+	0.0368812i	0.688426	+	0.725307i	$0.258302\pi$
$164$	−8.21087	−	2.14769i	−0.641162	−	0.167707i
$165$	1.43870	−	1.35494i	0.112003	−	0.105482i
$166$	1.21955	−	9.48180i	0.0946553	−	0.735930i
$167$	−0.495354	−	0.495354i	−0.0383316	−	0.0383316i	0.687681	−	0.726013i	$-0.258629\pi$
$167$	−0.495354	−	0.495354i	−0.0383316	−	0.0383316i	−0.726013	+	0.687681i	$0.758629\pi$
$168$	13.7589	+	4.03666i	1.06152	+	0.311435i
$169$			11.8731i			0.913312i
$170$	12.1491	−	7.10417i	0.931791	−	0.544865i
$171$	17.6880	−	3.52572i	1.35263	−	0.269619i
$172$	8.51523	+	14.5477i	0.649280	+	1.10925i
$173$	−2.32674	−	2.32674i	−0.176899	−	0.176899i	0.613104	−	0.790002i	$-0.289921\pi$
$173$	−2.32674	−	2.32674i	−0.176899	−	0.176899i	−0.790002	+	0.613104i	$0.789921\pi$
$174$	−8.58109	−	9.10370i	−0.650531	−	0.690150i
$175$	7.38178	+	12.6363i	0.558010	+	0.955218i
$176$	−1.77970	−	0.999395i	−0.134150	−	0.0753323i
$177$	−2.00833	+	0.198209i	−0.150955	+	0.0148983i
$178$	10.9269	+	14.1527i	0.819008	+	1.06079i
$179$			13.9141i			1.03999i	0.854169	+	0.519996i	$0.174066\pi$
$179$			13.9141i			1.03999i	−0.854169	+	0.519996i	$0.825934\pi$
$180$	11.0884	−	7.55291i	0.826484	−	0.562960i
$181$		−	5.80972i		−	0.431833i	−0.976412	−	0.215917i	$-0.930726\pi$
$181$		−	5.80972i		−	0.431833i	0.976412	−	0.215917i	$-0.0692740\pi$
$182$	−3.47811	+	2.68536i	−0.257814	+	0.199052i
$183$	8.49650	−	0.838550i	0.628079	−	0.0619874i
$184$	−3.81254	+	9.44235i	−0.281064	+	0.696099i
$185$	−2.73727	+	21.2094i	−0.201248	+	1.55935i
$186$	−8.13998	+	7.67270i	−0.596852	+	0.562589i
$187$	−1.60583	−	1.60583i	−0.117430	−	0.117430i
$188$	−8.14930	+	4.77003i	−0.594349	+	0.347890i
$189$	13.4171	+	7.16122i	0.975950	+	0.520902i
$190$	4.81889	−	18.3907i	0.349599	−	1.33420i
$191$			13.8456i			1.00183i	0.865497	+	0.500914i	$0.167003\pi$
$191$			13.8456i			1.00183i	−0.865497	+	0.500914i	$0.832997\pi$
$192$	−10.8684	−	8.59519i	−0.784361	−	0.620304i
$193$	4.57254	+	4.57254i	0.329138	+	0.329138i	0.852259	−	0.523120i	$-0.175232\pi$
$193$	4.57254	+	4.57254i	0.329138	+	0.329138i	−0.523120	+	0.852259i	$0.675232\pi$
$194$	21.5800	+	2.77562i	1.54935	+	0.199278i
$195$	−0.123221	+	4.10962i	−0.00882405	+	0.294296i
$196$	3.03145	+	0.792928i	0.216532	+	0.0566377i
$197$	−3.85757	+	3.85757i	−0.274840	+	0.274840i	−0.831045	−	0.556205i	$-0.812257\pi$
$197$	−3.85757	+	3.85757i	−0.274840	+	0.274840i	0.556205	+	0.831045i	$0.312257\pi$
$198$	−1.63249	−	1.42192i	−0.116016	−	0.101051i
$199$		−	5.91833i		−	0.419540i	−0.977751	−	0.209770i	$-0.932729\pi$
$199$		−	5.91833i		−	0.419540i	0.977751	−	0.209770i	$-0.0672714\pi$
$200$	−2.04268	−	13.9938i	−0.144439	−	0.989514i
$201$	−12.4039	+	15.1203i	−0.874900	+	1.06650i
$202$	−5.53993	−	7.17537i	−0.389788	−	0.504858i
$203$	−10.5704	−	10.5704i	−0.741896	−	0.741896i
$204$	−9.05712	−	12.4760i	−0.634125	−	0.873497i
$205$	−7.51328	+	5.79564i	−0.524750	+	0.404785i
$206$	0.475344	−	3.69573i	0.0331188	−	0.257494i
$207$	−5.99695	+	8.98285i	−0.416817	+	0.624351i
$208$	4.08821	−	1.14787i	0.283467	−	0.0795904i
$209$	−3.06777			−0.212202
$210$	12.9772	−	9.41240i	0.895513	−	0.649517i
$211$			6.95372i			0.478714i	0.970932	+	0.239357i	$0.0769366\pi$
$211$			6.95372i			0.478714i	−0.970932	+	0.239357i	$0.923063\pi$
$212$	−14.0571	+	8.22802i	−0.965444	+	0.565103i
$213$	8.77609	−	0.866144i	0.601328	−	0.0593472i
$214$	−19.8999	−	2.55953i	−1.36033	−	0.174966i
$215$	18.6913	+	2.41228i	1.27473	+	0.164516i
$216$	−9.43167	−	11.2714i	−0.641744	−	0.766919i
$217$	−9.45141	+	9.45141i	−0.641604	+	0.641604i
$218$	10.9284	+	14.1546i	0.740166	+	0.958671i
$219$	−4.98156	+	6.07252i	−0.336622	+	0.410343i
$220$	−2.10080	+	0.891212i	−0.141636	+	0.0600855i
$221$	4.72454			0.317807
$222$	23.4162	+	0.691978i	1.57159	+	0.0464425i
$223$	−16.7218	−	16.7218i	−1.11977	−	1.11977i	−0.991774	−	0.127998i	$-0.959145\pi$
$223$	−16.7218	−	16.7218i	−1.11977	−	1.11977i	−0.127998	−	0.991774i	$-0.540855\pi$
$224$	−13.2844	−	9.88231i	−0.887601	−	0.660290i
$225$	0.898700	−	14.9731i	0.0599133	−	0.998204i
$226$	3.74778	+	0.482039i	0.249298	+	0.0320647i
$227$	12.4814	−	12.4814i	0.828416	−	0.828416i	−0.158881	−	0.987298i	$-0.550789\pi$
$227$	12.4814	−	12.4814i	0.828416	−	0.828416i	0.987298	+	0.158881i	$0.0507887\pi$
$228$	−20.5685	−	3.26575i	−1.36218	−	0.216280i
$229$	1.09678			0.0724770			0.0362385	−	0.999343i	$-0.488462\pi$
$229$	1.09678			0.0724770			0.0362385	+	0.999343i	$0.488462\pi$
$230$	5.74692	+	9.82800i	0.378941	+	0.648039i
$231$	−2.00000	−	1.64069i	−0.131590	−	0.107949i
$232$	5.64737	+	13.2963i	0.370768	+	0.872942i
$233$	−6.98082	+	6.98082i	−0.457329	+	0.457329i	−0.897778	−	0.440449i	$-0.854819\pi$
$233$	−6.98082	+	6.98082i	−0.457329	+	0.457329i	0.440449	+	0.897778i	$0.354819\pi$
$234$	4.49322	−	0.309768i	0.293731	−	0.0202502i
$235$	−1.35130	+	10.4704i	−0.0881492	+	0.683014i
$236$	2.25444	+	0.589688i	0.146752	+	0.0383854i
$237$	12.6038	−	1.24391i	0.818704	−	0.0808008i
$238$	−11.2580	−	14.5814i	−0.729746	−	0.945174i
$239$	12.3210			0.796976			0.398488	−	0.917173i	$-0.369535\pi$
$239$	12.3210			0.796976			0.398488	+	0.917173i	$0.369535\pi$
$240$	−15.0340	+	3.73892i	−0.970439	+	0.241346i
$241$	−7.03833			−0.453379			−0.226689	−	0.973967i	$-0.572790\pi$
$241$	−7.03833			−0.453379			−0.226689	+	0.973967i	$0.572790\pi$
$242$	−9.28183	−	12.0219i	−0.596659	−	0.772798i
$243$	−7.36211	−	13.7404i	−0.472279	−	0.881449i
$244$	−9.53771	−	2.49475i	−0.610589	−	0.159710i
$245$	2.77390	−	2.13975i	0.177218	−	0.136704i
$246$	7.12974	+	7.56395i	0.454575	+	0.482260i
$247$	4.51288	−	4.51288i	0.287148	−	0.287148i
$248$	11.8887	−	5.04954i	0.754934	−	0.320646i
$249$	−7.42595	+	9.05224i	−0.470600	+	0.573662i
$250$	−13.7763	−	7.75966i	−0.871292	−	0.490764i
$251$	−9.92262			−0.626311			−0.313155	−	0.949702i	$-0.601386\pi$
$251$	−9.92262			−0.626311			−0.313155	+	0.949702i	$0.601386\pi$
$252$	−11.6628	−	13.1294i	−0.734688	−	0.827073i
$253$	1.29904	−	1.29904i	0.0816696	−	0.0816696i
$254$	1.91228	+	0.245957i	0.119987	+	0.0154327i
$255$	−17.2289	−	0.516586i	−1.07892	−	0.0323499i
$256$	8.32826	+	13.6616i	0.520516	+	0.853852i
$257$	−14.5324	−	14.5324i	−0.906508	−	0.906508i	0.0894809	−	0.995989i	$-0.471479\pi$
$257$	−14.5324	−	14.5324i	−0.906508	−	0.906508i	−0.995989	+	0.0894809i	$0.971479\pi$
$258$	0.609821	−	20.6361i	0.0379658	−	1.28474i
$259$	27.9923			1.73935
$260$	1.77938	−	4.40144i	0.110353	−	0.272966i
$261$	2.99522	+	15.0266i	0.185400	+	0.930120i
$262$	6.56176	+	8.49885i	0.405387	+	0.525061i
$263$	10.8634	−	10.8634i	0.669867	−	0.669867i	−0.287818	−	0.957685i	$-0.592930\pi$
$263$	10.8634	−	10.8634i	0.669867	−	0.669867i	0.957685	+	0.287818i	$0.0929298\pi$
$264$	1.19853	+	2.19379i	0.0737643	+	0.135018i
$265$	−2.33092	+	18.0608i	−0.143187	+	1.10947i
$266$	−24.6818	−	3.17457i	−1.51334	−	0.194646i
$267$	−2.15079	−	21.7926i	−0.131626	−	1.33369i
$268$	19.4894	−	11.4077i	1.19050	−	0.696838i
$269$			32.3280i			1.97108i	0.169455	+	0.985538i	$0.445799\pi$
$269$			32.3280i			1.97108i	−0.169455	+	0.985538i	$0.554201\pi$
$270$	−16.4193	+	0.638338i	−0.999245	+	0.0388480i
$271$	0.306338			0.0186087			0.00930434	−	0.999957i	$-0.497038\pi$
$271$	0.306338			0.0186087			0.00930434	+	0.999957i	$0.497038\pi$
$272$	4.81227	+	17.1392i	0.291787	+	1.03922i
$273$	5.35567	−	0.528571i	0.324140	−	0.0319905i
$274$	−0.182052	+	1.41543i	−0.0109982	+	0.0855090i
$275$	−0.647769	+	2.46778i	−0.0390619	+	0.148813i
$276$	10.0925	−	7.32676i	0.607497	−	0.441019i
$277$	−6.97897	−	6.97897i	−0.419326	−	0.419326i	0.465645	−	0.884971i	$-0.345822\pi$
$277$	−6.97897	−	6.97897i	−0.419326	−	0.419326i	−0.884971	+	0.465645i	$0.845822\pi$
$278$	−7.79094	−	10.0909i	−0.467270	−	0.605212i
$279$	13.4358	−	2.67815i	0.804383	−	0.160337i
$280$	−17.8243	+	4.99632i	−1.06521	+	0.298587i
$281$		−	15.4596i		−	0.922240i	−0.887338	−	0.461120i	$-0.847448\pi$
$281$		−	15.4596i		−	0.922240i	0.887338	−	0.461120i	$-0.152552\pi$
$282$	11.5598	+	0.341607i	0.688378	+	0.0203424i
$283$	−8.86458	+	8.86458i	−0.526945	+	0.526945i	−0.919660	−	0.392715i	$-0.871536\pi$
$283$	−8.86458	+	8.86458i	−0.526945	+	0.526945i	0.392715	+	0.919660i	$0.371536\pi$
$284$	−9.85156	−	2.57684i	−0.584583	−	0.152908i
$285$	−16.9505	+	15.9637i	−1.00406	+	0.945605i
$286$	−0.759816	−	0.0977275i	−0.0449289	−	0.00577875i
$287$	8.78258	+	8.78258i	0.518419	+	0.518419i
$288$	5.70040	+	15.9845i	0.335899	+	0.941898i
$289$			2.80690i			0.165112i
$290$	15.6235	+	4.09381i	0.917446	+	0.240397i
$291$	−20.6023	−	16.9010i	−1.20773	−	0.990754i
$292$	7.82720	−	4.58150i	0.458053	−	0.268112i
$293$	−1.49638	−	1.49638i	−0.0874192	−	0.0874192i	0.662045	−	0.749464i	$-0.269689\pi$
$293$	−1.49638	−	1.49638i	−0.0874192	−	0.0874192i	−0.749464	+	0.662045i	$0.769689\pi$
$294$	−2.63230	−	2.79261i	−0.153519	−	0.162868i
$295$	2.06291	−	1.59130i	0.120107	−	0.0926489i
$296$	−25.0830	−	10.1278i	−1.45792	−	0.588666i
$297$	0.771206	+	2.53684i	0.0447499	+	0.147202i
$298$	14.7283	−	11.3713i	0.853186	−	0.658724i
$299$			3.82192i			0.221027i
$300$	−6.97013	+	15.8561i	−0.402421	+	0.915455i
$301$		−	24.6688i		−	1.42189i
$302$	2.38520	+	3.08933i	0.137253	+	0.177771i
$303$	1.09045	+	11.0488i	0.0626445	+	0.634738i
$304$	20.9681	+	11.7747i	1.20260	+	0.675325i
$305$	−8.72738	+	6.73218i	−0.499728	+	0.385484i
$306$	1.29866	+	18.8371i	0.0742393	+	1.07685i
$307$	12.4948	+	12.4948i	0.713118	+	0.713118i	0.967186	−	0.254068i	$-0.0817688\pi$
$307$	12.4948	+	12.4948i	0.713118	+	0.713118i	−0.254068	+	0.967186i	$0.581769\pi$
$308$	1.50893	+	2.57791i	0.0859791	+	0.146890i
$309$	−2.89442	+	3.52830i	−0.164658	+	0.200718i
$310$	3.66044	−	13.9696i	0.207899	−	0.793421i
$311$		−	0.224632i		−	0.0127377i	−0.999980	−	0.00636886i	$-0.997973\pi$
$311$		−	0.224632i		−	0.0127377i	0.999980	−	0.00636886i	$-0.00202728\pi$
$312$	−4.99030	−	1.46408i	−0.282520	−	0.0828874i
$313$	−12.0383	−	12.0383i	−0.680447	−	0.680447i	0.279654	−	0.960101i	$-0.409780\pi$
$313$	−12.0383	−	12.0383i	−0.680447	−	0.680447i	−0.960101	+	0.279654i	$0.909780\pi$
$314$	1.11774	−	8.69022i	0.0630775	−	0.490417i
$315$	−19.5883	+	1.34194i	−1.10368	+	0.0756098i
$316$	−14.1483	−	3.70073i	−0.795905	−	0.208183i
$317$	20.2257	−	20.2257i	1.13599	−	1.13599i	0.146829	−	0.989162i	$-0.453093\pi$
$317$	20.2257	−	20.2257i	1.13599	−	1.13599i	0.989162	−	0.146829i	$-0.0469068\pi$
$318$	19.9400	+	0.589252i	1.11818	+	0.0330436i
$319$		−	2.60618i		−	0.145918i
$320$	17.7795	+	1.97190i	0.993906	+	0.110233i
$321$	18.9984	+	15.5852i	1.06039	+	0.869882i
$322$	11.7957	−	9.10715i	0.657347	−	0.507522i
$323$	18.9196	+	18.9196i	1.05271	+	1.05271i
$324$	2.47015	+	17.8297i	0.137230	+	0.990539i
$325$	−2.67735	−	4.58316i	−0.148513	−	0.254228i
$326$	−0.934042	−	0.120136i	−0.0517318	−	0.00665374i
$327$	−2.15109	−	21.7956i	−0.118955	−	1.20530i
$328$	−4.69221	−	11.0474i	−0.259084	−	0.609991i
$329$	13.8189			0.761860
$330$	2.76013	+	0.439461i	0.151940	+	0.0241916i
$331$		−	12.3308i		−	0.677760i	−0.940830	−	0.338880i	$-0.889952\pi$
$331$		−	12.3308i		−	0.677760i	0.940830	−	0.338880i	$-0.110048\pi$
$332$	11.6679	−	6.82959i	0.640361	−	0.374822i
$333$	−23.8624	−	15.9305i	−1.30765	−	0.872988i
$334$	0.126384	−	0.982613i	0.00691540	−	0.0537662i
$335$	3.23169	−	25.0404i	0.176566	−	1.36810i
$336$	7.37262	+	18.8904i	0.402209	+	1.03056i
$337$	10.6723	−	10.6723i	0.581359	−	0.581359i	−0.353918	−	0.935277i	$-0.615151\pi$
$337$	10.6723	−	10.6723i	0.581359	−	0.581359i	0.935277	+	0.353918i	$0.115151\pi$
$338$	−13.2907	+	10.2614i	−0.722918	+	0.558147i
$339$	−3.57799	−	2.93518i	−0.194330	−	0.159417i
$340$	18.4524	+	7.45980i	1.00072	+	0.404564i
$341$	−2.33029			−0.126192
$342$	19.2337	+	16.7528i	1.04004	+	0.905886i
$343$	11.2449	+	11.2449i	0.607166	+	0.607166i
$344$	−8.92534	+	22.1050i	−0.481222	+	1.19182i
$345$	0.417893	−	13.9374i	0.0224986	−	0.750363i
$346$	0.593640	−	4.61546i	0.0319143	−	0.248129i
$347$	8.00457	−	8.00457i	0.429708	−	0.429708i	−0.458821	−	0.888529i	$-0.651728\pi$
$347$	8.00457	−	8.00457i	0.429708	−	0.429708i	0.888529	+	0.458821i	$0.151728\pi$
$348$	2.77437	−	17.4736i	0.148722	−	0.936685i
$349$	−13.9579			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$349$	−13.9579			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$350$	−7.76533	+	19.1843i	−0.415074	+	1.02544i
$351$	−4.86633	−	2.59735i	−0.259746	−	0.138636i
$352$	−0.419399	−	2.85593i	−0.0223541	−	0.152221i
$353$	−11.8744	+	11.8744i	−0.632008	+	0.632008i	−0.948571	−	0.316563i	$-0.897471\pi$
$353$	−11.8744	+	11.8744i	−0.632008	+	0.632008i	0.316563	+	0.948571i	$0.397471\pi$
$354$	−1.95760	−	2.07682i	−0.104045	−	0.110382i
$355$	−9.01457	+	6.95372i	−0.478444	+	0.369065i
$356$	−6.39876	+	24.4632i	−0.339134	+	1.29655i
$357$	2.21595	+	22.4528i	0.117281	+	1.18833i
$358$	−15.5755	+	12.0254i	−0.823189	+	0.635564i
$359$	−33.8765			−1.78793			−0.893967	−	0.448133i	$-0.852089\pi$
$359$	−33.8765			−1.78793			−0.893967	+	0.448133i	$0.852089\pi$
$360$	18.0380	+	5.88471i	0.950687	+	0.310152i
$361$	17.1439			0.902313
$362$	6.50340	−	5.02112i	0.341811	−	0.263904i
$363$	1.82698	+	18.5116i	0.0958915	+	0.971608i
$364$	−6.01198	−	1.57254i	−0.315114	−	0.0824233i
$365$	1.29789	−	10.0566i	0.0679347	−	0.526385i
$366$	8.28186	+	8.78625i	0.432900	+	0.459265i
$367$	10.7900	−	10.7900i	0.563233	−	0.563233i	−0.366992	−	0.930224i	$-0.619612\pi$
$367$	10.7900	−	10.7900i	0.563233	−	0.563233i	0.930224	+	0.366992i	$0.119612\pi$
$368$	−13.8648	+	3.89289i	−0.722752	+	0.202931i
$369$	−2.48863	−	12.4851i	−0.129553	−	0.649946i
$370$	−26.1075	+	15.2664i	−1.35726	+	0.793660i
$371$	23.8368			1.23754
$372$	−15.6239	−	2.48067i	−0.810060	−	0.128617i
$373$	25.8380	−	25.8380i	1.33784	−	1.33784i	0.439697	−	0.898146i	$-0.355086\pi$
$373$	25.8380	−	25.8380i	1.33784	−	1.33784i	0.898146	−	0.439697i	$-0.144914\pi$
$374$	0.409708	−	3.18541i	0.0211855	−	0.164714i
$375$	9.26235	+	17.0061i	0.478306	+	0.878193i
$376$	−12.3827	−	4.99977i	−0.638588	−	0.257843i
$377$	3.83385	+	3.83385i	0.197453	+	0.197453i
$378$	3.57960	+	21.2082i	0.184115	+	1.09083i
$379$	12.2262			0.628019			0.314010	−	0.949420i	$-0.398328\pi$
$379$	12.2262			0.628019			0.314010	+	0.949420i	$0.398328\pi$
$380$	24.7513	−	10.5001i	1.26971	−	0.538644i
$381$	−1.82564	−	1.49766i	−0.0935306	−	0.0767272i
$382$	−15.4987	+	11.9662i	−0.792982	+	0.612242i
$383$	−21.6256	+	21.6256i	−1.10501	+	1.10501i	−0.111219	+	0.993796i	$0.535475\pi$
$383$	−21.6256	+	21.6256i	−1.10501	+	1.10501i	−0.993796	+	0.111219i	$0.964525\pi$
$384$	0.228292	−	19.5946i	0.0116500	−	0.999932i
$385$	3.31215	+	0.427464i	0.168803	+	0.0217856i
$386$	−1.16663	+	9.07035i	−0.0593798	+	0.461669i
$387$	−14.0391	+	21.0293i	−0.713649	+	1.06898i
$388$	15.5437	+	26.5555i	0.789112	+	1.34815i
$389$		−	6.63941i		−	0.336632i	−0.985733	−	0.168316i	$-0.946167\pi$
$389$		−	6.63941i		−	0.336632i	0.985733	−	0.168316i	$-0.0538328\pi$
$390$	−4.70680	+	3.41385i	−0.238338	+	0.172867i
$391$	−16.0228			−0.810309
$392$	1.73236	+	4.07870i	0.0874975	+	0.206006i
$393$	−1.29158	−	13.0867i	−0.0651514	−	0.660138i
$394$	−7.65210	−	0.984213i	−0.385507	−	0.0495839i
$395$	−12.9463	+	9.98658i	−0.651398	+	0.502480i
$396$	0.180794	−	3.05631i	0.00908522	−	0.153586i
$397$	−14.0596	−	14.0596i	−0.705629	−	0.705629i	0.259984	−	0.965613i	$-0.416283\pi$
$397$	−14.0596	−	14.0596i	−0.705629	−	0.705629i	−0.965613	+	0.259984i	$0.916283\pi$
$398$	6.62498	−	5.11498i	0.332080	−	0.256391i
$399$	23.5636	+	19.3303i	1.17966	+	0.967725i
$400$	13.8993	−	14.3809i	0.694964	−	0.719045i
$401$		−	18.1176i		−	0.904751i	−0.891827	−	0.452376i	$-0.850577\pi$
$401$		−	18.1176i		−	0.904751i	0.891827	−	0.452376i	$-0.149423\pi$
$402$	−27.6458	−	0.816968i	−1.37885	−	0.0407466i
$403$	3.42800	−	3.42800i	0.170761	−	0.170761i
$404$	3.24416	−	12.4028i	0.161403	−	0.617062i
$405$	17.4620	+	10.0038i	0.867696	+	0.497095i
$406$	2.69691	−	20.9681i	0.133845	−	1.04063i
$407$	3.45081	+	3.45081i	0.171050	+	0.171050i
$408$	6.13795	−	20.9211i	0.303874	−	1.03575i
$409$		−	26.3245i		−	1.30166i	−0.759223	−	0.650831i	$-0.774421\pi$
$409$		−	26.3245i		−	1.30166i	0.759223	−	0.650831i	$-0.225579\pi$
$410$	−12.9811	−	3.40141i	−0.641089	−	0.167984i
$411$	1.10853	−	1.35130i	0.0546798	−	0.0666548i
$412$	4.54782	−	2.66197i	0.224055	−	0.131146i
$413$	−2.41142	−	2.41142i	−0.118658	−	0.118658i
$414$	−15.2383	+	1.05055i	−0.748923	+	0.0516317i
$415$	1.93475	−	14.9912i	0.0949732	−	0.735890i
$416$	4.81820	+	3.58428i	0.236232	+	0.175734i
$417$	1.53352	+	15.5382i	0.0750969	+	0.760909i
$418$	−2.65135	−	3.43406i	−0.129682	−	0.167965i
$419$		−	12.7809i		−	0.624385i	−0.950019	−	0.312193i	$-0.898937\pi$
$419$		−	12.7809i		−	0.624385i	0.950019	−	0.312193i	$-0.101063\pi$
$420$	21.7519	+	6.39192i	1.06139	+	0.311894i
$421$			26.3792i			1.28564i	0.766017	+	0.642821i	$0.222236\pi$
$421$			26.3792i			1.28564i	−0.766017	+	0.642821i	$0.777764\pi$
$422$	−7.78398	+	6.00983i	−0.378918	+	0.292554i
$423$	−11.7801	−	7.86440i	−0.572769	−	0.382380i
$424$	−21.3594	−	8.62431i	−1.03730	−	0.418833i
$425$	19.2142	−	11.2244i	0.932026	−	0.544462i
$426$	8.55439	+	9.07537i	0.414462	+	0.439703i
$427$	10.2018	+	10.2018i	0.493700	+	0.493700i
$428$	−14.3336	−	24.4881i	−0.692841	−	1.18368i
$429$	0.725393	+	0.595072i	0.0350223	+	0.0287303i
$430$	13.4538	+	23.0078i	0.648801	+	1.10954i
$431$		−	28.6818i		−	1.38155i	−0.723068	−	0.690777i	$-0.757269\pi$
$431$		−	28.6818i		−	1.38155i	0.723068	−	0.690777i	$-0.242731\pi$
$432$	4.46572	−	20.2992i	0.214857	−	0.976646i
$433$	−2.25457	−	2.25457i	−0.108347	−	0.108347i	0.650855	−	0.759202i	$-0.274411\pi$
$433$	−2.25457	−	2.25457i	−0.108347	−	0.108347i	−0.759202	+	0.650855i	$0.774411\pi$
$434$	−18.7484	−	2.41142i	−0.899951	−	0.115752i
$435$	−13.5617	−	14.4001i	−0.650233	−	0.690431i
$436$	−6.39964	+	24.4665i	−0.306487	+	1.17173i
$437$	−15.3050	+	15.3050i	−0.732137	+	0.732137i
$438$	−11.1029	−	0.328105i	−0.530519	−	0.0156775i
$439$			11.8510i			0.565620i	0.959176	+	0.282810i	$0.0912665\pi$
$439$			11.8510i			0.565620i	−0.959176	+	0.282810i	$0.908733\pi$
$440$	−2.81326	−	1.58140i	−0.134117	−	0.0753902i
$441$	0.918802	+	4.60948i	0.0437525	+	0.219499i
$442$	4.08323	+	5.28864i	0.194219	+	0.251555i
$443$	−1.66807	−	1.66807i	−0.0792526	−	0.0792526i	0.666369	−	0.745622i	$-0.267847\pi$
$443$	−1.66807	−	1.66807i	−0.0792526	−	0.0792526i	−0.745622	+	0.666369i	$0.767847\pi$
$444$	19.4631	+	26.8101i	0.923679	+	1.27235i
$445$	17.2673	+	22.3848i	0.818550	+	1.06114i
$446$	4.26636	−	33.1703i	0.202018	−	1.57066i
$447$	−22.6789	+	2.23827i	−1.07268	+	0.105866i
$448$	−0.418930	−	23.4114i	−0.0197926	−	1.10609i
$449$	34.3414			1.62067			0.810336	−	0.585966i	$-0.199285\pi$
$449$	34.3414			1.62067			0.810336	+	0.585966i	$0.199285\pi$
$450$	17.5375	−	11.9346i	0.826727	−	0.562603i
$451$			2.16539i			0.101964i
$452$	2.69946	+	4.61186i	0.126972	+	0.216924i
$453$	−0.469488	−	4.75703i	−0.0220585	−	0.223505i
$454$	24.7588	+	3.18447i	1.16199	+	0.149455i
$455$	−5.50120	+	4.24355i	−0.257900	+	0.198941i
$456$	−14.1208	−	25.8468i	−0.661269	−	1.21039i
$457$	−4.61474	+	4.61474i	−0.215869	+	0.215869i	−0.806755	−	0.590886i	$-0.798778\pi$
$457$	−4.61474	+	4.61474i	−0.215869	+	0.215869i	0.590886	+	0.806755i	$0.298778\pi$
$458$	0.947900	+	1.22773i	0.0442925	+	0.0573680i
$459$	10.8890	−	20.4014i	0.508255	−	0.952254i
$460$	−6.03461	+	14.9271i	−0.281365	+	0.695977i
$461$	20.6452			0.961543			0.480772	−	0.876846i	$-0.340357\pi$
$461$	20.6452			0.961543			0.480772	+	0.876846i	$0.340357\pi$
$462$	0.108062	−	3.65678i	0.00502751	−	0.170129i
$463$	27.1817	+	27.1817i	1.26324	+	1.26324i	0.949512	+	0.313730i	$0.101579\pi$
$463$	27.1817	+	27.1817i	1.26324	+	1.26324i	0.313730	+	0.949512i	$0.398421\pi$
$464$	−10.0030	+	17.8131i	−0.464378	+	0.826952i
$465$	−12.8757	+	12.1260i	−0.597095	+	0.562332i
$466$	−13.8476	−	1.78107i	−0.641476	−	0.0825067i
$467$	6.39901	−	6.39901i	0.296111	−	0.296111i	−0.543378	−	0.839488i	$-0.682855\pi$
$467$	6.39901	−	6.39901i	0.296111	−	0.296111i	0.839488	+	0.543378i	$0.182855\pi$
$468$	4.23007	+	4.76198i	0.195535	+	0.220123i
$469$	−33.0484			−1.52603
$470$	−12.8884	+	7.53651i	−0.594499	+	0.347633i
$471$	−6.80600	+	8.29652i	−0.313604	+	0.382283i
$472$	1.28833	+	3.03326i	0.0593002	+	0.139617i
$473$	3.04110	−	3.04110i	0.139830	−	0.139830i
$474$	12.2854	+	13.0336i	0.564287	+	0.598653i
$475$	7.63189	−	29.0750i	0.350175	−	1.33405i
$476$	6.59262	−	25.2043i	0.302172	−	1.15524i
$477$	−20.3200	−	13.5656i	−0.930389	−	0.621127i
$478$	10.6485	+	13.7921i	0.487052	+	0.630834i
$479$	−35.9113			−1.64083			−0.820414	−	0.571770i	$-0.806257\pi$
$479$	−35.9113			−1.64083			−0.820414	+	0.571770i	$0.806257\pi$
$480$	−17.1786	−	13.5976i	−0.784093	−	0.620643i
$481$	−10.1527			−0.462923
$482$	−6.08295	−	7.87870i	−0.277071	−	0.358865i
$483$	−18.1632	+	1.79260i	−0.826456	+	0.0815660i
$484$	5.43540	−	20.7801i	0.247064	−	0.944552i
$485$	34.1190	+	4.40337i	1.54927	+	0.199947i
$486$	9.01824	−	20.1164i	0.409076	−	0.912501i
$487$	−23.9090	+	23.9090i	−1.08342	+	1.08342i	−0.0872343	+	0.996188i	$0.527803\pi$
$487$	−23.9090	+	23.9090i	−1.08342	+	1.08342i	−0.996188	+	0.0872343i	$0.972197\pi$
$488$	−5.45044	−	12.8326i	−0.246730	−	0.580905i
$489$	0.891726	+	0.731522i	0.0403252	+	0.0330806i
$490$	4.79261	+	1.25580i	0.216508	+	0.0567312i
$491$	−30.9507			−1.39678			−0.698392	−	0.715715i	$-0.746101\pi$
$491$	−30.9507			−1.39678			−0.698392	+	0.715715i	$0.746101\pi$
$492$	−2.30513	+	14.5182i	−0.103923	+	0.654533i
$493$	−16.0728	+	16.0728i	−0.723884	+	0.723884i
$494$	8.95201	+	1.15141i	0.402770	+	0.0518043i
$495$	−2.58022	−	2.24936i	−0.115972	−	0.101101i
$496$	15.9274	+	8.94409i	0.715161	+	0.401602i
$497$	10.5375	+	10.5375i	0.472672	+	0.472672i
$498$	−16.5510	−	0.489103i	−0.741669	−	0.0219172i
$499$	−19.9194			−0.891716			−0.445858	−	0.895104i	$-0.647101\pi$
$499$	−19.9194			−0.891716			−0.445858	+	0.895104i	$0.647101\pi$
$500$	−3.22020	−	22.1276i	−0.144012	−	0.989576i
$501$	−0.769562	+	0.938097i	−0.0343815	+	0.0419111i
$502$	−8.57573	−	11.1074i	−0.382754	−	0.495746i
$503$	14.6687	−	14.6687i	0.654047	−	0.654047i	−0.299918	−	0.953965i	$-0.596959\pi$
$503$	14.6687	−	14.6687i	0.654047	−	0.654047i	0.953965	+	0.299918i	$0.0969593\pi$
$504$	4.61729	−	24.4025i	0.205671	−	1.08698i
$505$	−8.75450	−	11.3490i	−0.389570	−	0.505026i
$506$	2.57684	+	0.331433i	0.114555	+	0.0147340i
$507$	20.4653	−	2.01979i	0.908896	−	0.0897022i
$508$	1.37738	+	2.35317i	0.0611114	+	0.104405i
$509$			4.85493i			0.215191i	0.994195	+	0.107595i	$0.0343151\pi$
$509$			4.85493i			0.215191i	−0.994195	+	0.107595i	$0.965685\pi$
$510$	−14.3120	−	19.7325i	−0.633748	−	0.873771i
$511$	−13.2727			−0.587149
$512$	−8.09503	+	21.1298i	−0.357753	+	0.933816i
$513$	−9.08621	−	29.8886i	−0.401166	−	1.31961i
$514$	3.70778	−	28.8274i	0.163543	−	1.27152i
$515$	0.754110	−	5.84314i	0.0332301	−	0.257479i
$516$	23.6270	−	17.1523i	1.04012	−	0.755088i
$517$	1.70355	+	1.70355i	0.0749222	+	0.0749222i
$518$	24.1926	+	31.3345i	1.06296	+	1.37676i
$519$	−3.61473	+	4.40636i	−0.158669	+	0.193418i
$520$	6.46481	−	1.81215i	0.283501	−	0.0794680i
$521$			15.0499i			0.659346i	0.944095	+	0.329673i	$0.106939\pi$
$521$			15.0499i			0.659346i	−0.944095	+	0.329673i	$0.893061\pi$
$522$	−14.2321	+	16.3397i	−0.622920	+	0.715170i
$523$	−15.6997	+	15.6997i	−0.686499	+	0.686499i	−0.961456	−	0.274957i	$-0.911336\pi$
$523$	−15.6997	+	15.6997i	−0.686499	+	0.686499i	0.274957	+	0.961456i	$0.411336\pi$
$524$	−3.84254	+	14.6904i	−0.167862	+	0.641755i
$525$	20.5252	−	14.8734i	0.895794	−	0.649130i
$526$	21.5493	+	2.77167i	0.939596	+	0.120851i
$527$	14.3714	+	14.3714i	0.626026	+	0.626026i
$528$	−1.41988	+	3.23763i	−0.0617923	+	0.140900i
$529$			10.0383i			0.436449i
$530$	−22.2318	+	13.0000i	−0.965688	+	0.564686i
$531$	0.683298	+	3.42800i	0.0296526	+	0.148762i
$532$	−17.7779	−	30.3725i	−0.770770	−	1.31681i
$533$	−3.18541	−	3.18541i	−0.137976	−	0.137976i
$534$	22.5358	−	21.2421i	0.975218	−	0.919235i
$535$	−31.4628	−	4.06056i	−1.36026	−	0.175553i
$536$	29.6137	+	11.9572i	1.27912	+	0.516470i
$537$	23.9835	−	2.36701i	1.03496	−	0.102144i
$538$	−36.1880	+	27.9399i	−1.56017	+	1.20457i
$539$		−	0.799460i		−	0.0344352i
$540$	−14.9051	−	17.8280i	−0.641413	−	0.767196i
$541$		−	1.45079i		−	0.0623742i	−0.999514	−	0.0311871i	$-0.990071\pi$
$541$		−	1.45079i		−	0.0623742i	0.999514	−	0.0311871i	$-0.00992877\pi$
$542$	0.264756	+	0.342914i	0.0113722	+	0.0147294i
$543$	−10.0141	+	0.988326i	−0.429745	+	0.0424131i
$544$	−15.0266	+	20.1996i	−0.644258	+	0.866050i
$545$	17.2697	+	22.3879i	0.739752	+	0.958990i
$546$	5.22038	+	5.53831i	0.223412	+	0.237018i
$547$	1.86763	+	1.86763i	0.0798541	+	0.0798541i	0.745906	−	0.666052i	$-0.232017\pi$
$547$	1.86763	+	1.86763i	0.0798541	+	0.0798541i	−0.666052	+	0.745906i	$0.732017\pi$
$548$	−1.74177	+	1.01951i	−0.0744045	+	0.0435512i
$549$	−2.89078	−	14.5026i	−0.123375	−	0.618955i
$550$	−3.32227	+	1.40769i	−0.141662	+	0.0600243i
$551$			30.7055i			1.30810i
$552$	16.9241	+	4.96530i	0.720339	+	0.211337i
$553$	15.1334	+	15.1334i	0.643539	+	0.643539i
$554$	1.78060	−	13.8439i	0.0756505	−	0.588171i
$555$	37.0238	+	1.11011i	1.57157	+	0.0471214i
$556$	4.56234	−	17.4423i	0.193486	−	0.739720i
$557$	−22.6188	+	22.6188i	−0.958389	+	0.958389i	−0.999168	−	0.0407789i	$-0.987016\pi$
$557$	−22.6188	+	22.6188i	−0.958389	+	0.958389i	0.0407789	+	0.999168i	$0.487016\pi$
$558$	14.6100	+	12.7254i	0.618490	+	0.538711i
$559$			8.94729i			0.378430i
$560$	−20.9977	−	15.6344i	−0.887315	−	0.660673i
$561$	−2.49475	+	3.04110i	−0.105328	+	0.128395i
$562$	17.3054	−	13.3611i	0.729985	−	0.563604i
$563$	26.6638	+	26.6638i	1.12375	+	1.12375i	0.991173	+	0.132574i	$0.0423241\pi$
$563$	26.6638	+	26.6638i	1.12375	+	1.12375i	0.132574	+	0.991173i	$0.457676\pi$
$564$	9.60832	+	13.2353i	0.404583	+	0.557307i
$565$	5.92543	+	0.764730i	0.249285	+	0.0321724i
$566$	−17.5843	−	2.26169i	−0.739123	−	0.0950660i
$567$	10.0612	−	24.3450i	0.422530	−	1.02239i
$568$	−5.62980	−	13.2549i	−0.236221	−	0.556163i
$569$	−29.3180			−1.22907			−0.614537	−	0.788888i	$-0.710657\pi$
$569$	−29.3180			−1.22907			−0.614537	+	0.788888i	$0.710657\pi$
$570$	−32.5194	−	5.17766i	−1.36209	−	0.216868i
$571$			28.4036i			1.18865i	0.804224	+	0.594326i	$0.202581\pi$
$571$			28.4036i			1.18865i	−0.804224	+	0.594326i	$0.797419\pi$
$572$	−0.547283	−	0.934999i	−0.0228831	−	0.0390943i
$573$	23.8652	−	2.35535i	0.996985	−	0.0983960i
$574$	−2.24077	+	17.4216i	−0.0935280	+	0.727165i
$575$	9.07997	+	15.5434i	0.378661	+	0.648203i
$576$	−12.9664	+	20.1958i	−0.540268	+	0.841493i
$577$	−18.9787	+	18.9787i	−0.790092	+	0.790092i	−0.981509	−	0.191417i	$-0.938692\pi$
$577$	−18.9787	+	18.9787i	−0.790092	+	0.790092i	0.191417	+	0.981509i	$0.438692\pi$
$578$	−3.14204	+	2.42590i	−0.130692	+	0.100904i
$579$	7.10371	−	8.65943i	0.295220	−	0.359874i
$580$	8.92020	+	21.0271i	0.370391	+	0.873102i
$581$	−19.7855			−0.820839
$582$	1.11317	−	37.6691i	0.0461423	−	1.56143i
$583$	2.93853	+	2.93853i	0.121702	+	0.121702i
$584$	11.8933	+	4.80216i	0.492147	+	0.198715i
$585$	7.10461	−	0.486718i	0.293740	−	0.0201233i
$586$	0.381782	−	2.96830i	0.0157713	−	0.122619i
$587$	−11.2326	+	11.2326i	−0.463619	+	0.463619i	−0.899840	−	0.436220i	$-0.856317\pi$
$587$	−11.2326	+	11.2326i	−0.463619	+	0.463619i	0.436220	+	0.899840i	$0.356317\pi$
$588$	0.851053	−	5.36013i	0.0350968	−	0.221048i
$589$	27.4550			1.13127
$590$	3.56418	+	0.933918i	0.146735	+	0.0384488i
$591$	7.30543	+	5.99297i	0.300505	+	0.246518i
$592$	−10.3412	−	36.8310i	−0.425022	−	1.51374i
$593$	0.161070	−	0.161070i	0.00661435	−	0.00661435i	−0.703792	−	0.710406i	$-0.748511\pi$
$593$	0.161070	−	0.161070i	0.00661435	−	0.00661435i	0.710406	+	0.703792i	$0.248511\pi$
$594$	−2.17321	+	3.05578i	−0.0891679	+	0.125380i
$595$	−17.7905	−	23.0630i	−0.729338	−	0.945489i
$596$	25.4581	+	6.65901i	1.04281	+	0.272764i
$597$	−10.2013	+	1.00680i	−0.417511	+	0.0412057i
$598$	−4.27825	+	3.30313i	−0.174951	+	0.135075i
$599$	15.6557			0.639673			0.319837	−	0.947473i	$-0.396372\pi$
$599$	15.6557			0.639673			0.319837	+	0.947473i	$0.396372\pi$
$600$	−23.7734	+	5.90149i	−0.970543	+	0.240927i
$601$	29.1506			1.18908			0.594540	−	0.804066i	$-0.297334\pi$
$601$	29.1506			1.18908			0.594540	+	0.804066i	$0.297334\pi$
$602$	27.6142	−	21.3203i	1.12547	−	0.868949i
$603$	28.1726	+	18.8080i	1.14728	+	0.765922i
$604$	−1.39676	+	5.33998i	−0.0568335	+	0.217281i
$605$	−14.6676	−	19.0147i	−0.596325	−	0.773056i
$606$	−11.4256	+	10.7697i	−0.464133	+	0.437489i
$607$	18.7872	−	18.7872i	0.762550	−	0.762550i	−0.214232	−	0.976783i	$-0.568725\pi$
$607$	18.7872	−	18.7872i	0.762550	−	0.762550i	0.976783	+	0.214232i	$0.0687250\pi$
$608$	4.94129	+	33.6480i	0.200396	+	1.36461i
$609$	−16.4217	+	20.0181i	−0.665443	+	0.811176i
$610$	−15.0787	−	3.95106i	−0.610520	−	0.159974i
$611$	−5.01206			−0.202766
$612$	−19.9639	+	17.7339i	−0.806992	+	0.716851i
$613$	29.5115	−	29.5115i	1.19196	−	1.19196i	0.215443	−	0.976516i	$-0.430880\pi$
$613$	29.5115	−	29.5115i	1.19196	−	1.19196i	0.976516	−	0.215443i	$-0.0691195\pi$
$614$	−3.18791	+	24.7855i	−0.128654	+	1.00026i
$615$	11.2679	+	11.9645i	0.454367	+	0.482456i
$616$	−1.58160	+	3.91708i	−0.0637245	+	0.157823i
$617$	−29.7517	−	29.7517i	−1.19776	−	1.19776i	−0.974836	−	0.222923i	$-0.928440\pi$
$617$	−29.7517	−	29.7517i	−1.19776	−	1.19776i	−0.222923	−	0.974836i	$-0.571560\pi$
$618$	−6.45111	−	0.190638i	−0.259502	−	0.00766859i
$619$	12.4498			0.500402			0.250201	−	0.968194i	$-0.419503\pi$
$619$	12.4498			0.500402			0.250201	+	0.968194i	$0.419503\pi$
$620$	18.8012	−	7.97590i	0.755073	−	0.320320i
$621$	16.5037	+	8.80867i	0.662271	+	0.353480i
$622$	0.251453	−	0.194141i	0.0100823	−	0.00778433i
$623$	26.1665	−	26.1665i	1.04834	−	1.04834i
$624$	−2.67403	−	6.85148i	−0.107047	−	0.274279i
$625$	−21.7770	−	12.2785i	−0.871080	−	0.491140i
$626$	3.07144	−	23.8799i	0.122759	−	0.954434i
$627$	0.521877	+	5.28785i	0.0208417	+	0.211176i
$628$	10.6938	−	6.25942i	0.426730	−	0.249778i
$629$		−	42.5637i		−	1.69712i
$630$	−18.4316	−	20.7673i	−0.734331	−	0.827390i
$631$	43.7481			1.74158			0.870791	−	0.491653i	$-0.163607\pi$
$631$	43.7481			1.74158			0.870791	+	0.491653i	$0.163607\pi$
$632$	−8.08524	−	19.0360i	−0.321614	−	0.757212i
$633$	11.9860	−	1.18294i	0.476399	−	0.0470176i
$634$	40.1210	+	5.16036i	1.59341	+	0.204944i
$635$	3.02341	+	0.390198i	0.119980	+	0.0154845i
$636$	16.5738	+	22.8301i	0.657193	+	0.905273i
$637$	1.17605	+	1.17605i	0.0465969	+	0.0465969i
$638$	2.91735	−	2.25242i	0.115499	−	0.0891741i
$639$	−2.98590	−	14.9798i	−0.118121	−	0.592592i
$640$	13.1588	+	21.6066i	0.520147	+	0.854077i
$641$			13.3935i			0.529013i	0.964384	+	0.264506i	$0.0852090\pi$
$641$			13.3935i			0.529013i	−0.964384	+	0.264506i	$0.914791\pi$
$642$	−1.02651	+	34.7365i	−0.0405129	+	1.37094i
$643$	−12.4335	+	12.4335i	−0.490331	+	0.490331i	−0.908410	−	0.418080i	$-0.862703\pi$
$643$	−12.4335	+	12.4335i	−0.490331	+	0.490331i	0.418080	+	0.908410i	$0.362703\pi$
$644$	20.3891	+	5.33311i	0.803442	+	0.210154i
$645$	0.978306	−	32.6281i	0.0385208	−	1.28473i
$646$	−4.82710	+	37.5300i	−0.189920	+	1.47660i
$647$	0.352589	+	0.352589i	0.0138617	+	0.0138617i	0.714004	−	0.700142i	$-0.246880\pi$
$647$	0.352589	+	0.352589i	0.0138617	+	0.0138617i	−0.700142	+	0.714004i	$0.746880\pi$
$648$	−17.8237	+	18.1746i	−0.700181	+	0.713965i
$649$		−	0.594545i		−	0.0233380i
$650$	2.81646	−	6.95807i	0.110471	−	0.272918i
$651$	17.8990	+	14.6833i	0.701517	+	0.575485i
$652$	−0.672775	−	1.14939i	−0.0263479	−	0.0450138i
$653$	−10.5497	−	10.5497i	−0.412841	−	0.412841i	0.469886	−	0.882727i	$-0.344295\pi$
$653$	−10.5497	−	10.5497i	−0.412841	−	0.412841i	−0.882727	+	0.469886i	$0.844295\pi$
$654$	22.5389	−	21.2450i	0.881339	−	0.830745i
$655$	10.3692	+	13.4423i	0.405160	+	0.525236i
$656$	8.31116	−	14.8003i	0.324496	−	0.577854i
$657$	11.3145	+	7.55356i	0.441421	+	0.294692i
$658$	11.9431	+	15.4688i	0.465591	+	0.603038i
$659$		−	30.8600i		−	1.20213i	−0.799199	−	0.601067i	$-0.794742\pi$
$659$		−	30.8600i		−	1.20213i	0.799199	−	0.601067i	$-0.205258\pi$
$660$	1.89354	+	3.46950i	0.0737060	+	0.135050i
$661$			44.1992i			1.71915i	0.511009	+	0.859575i	$0.329272\pi$
$661$			44.1992i			1.71915i	−0.511009	+	0.859575i	$0.670728\pi$
$662$	13.8030	−	10.6570i	0.536470	−	0.414196i
$663$	−0.803718	−	8.14357i	−0.0312138	−	0.316270i
$664$	17.7292	+	7.15852i	0.688025	+	0.277804i
$665$	−39.0232	−	5.03630i	−1.51326	−	0.195299i
$666$	−2.79072	−	40.4797i	−0.108138	−	1.56856i
$667$	−13.0021	−	13.0021i	−0.503444	−	0.503444i
$668$	1.20916	−	0.707760i	0.0467840	−	0.0273841i
$669$	−25.9783	+	31.6675i	−1.00438	+	1.22434i
$670$	30.8232	−	18.0239i	1.19081	−	0.696323i
$671$			2.51530i			0.0971021i
$672$	−14.7740	+	24.5791i	−0.569920	+	0.948160i
$673$	13.1276	+	13.1276i	0.506033	+	0.506033i	0.913306	−	0.407274i	$-0.133520\pi$
$673$	13.1276	+	13.1276i	0.506033	+	0.506033i	−0.407274	+	0.913306i	$0.633520\pi$
$674$	21.1703	+	2.72292i	0.815448	+	0.104883i
$675$	−25.9616	+	0.998085i	−0.999262	+	0.0384163i
$676$	−22.9732	−	6.00904i	−0.883586	−	0.231117i
$677$	−23.1658	+	23.1658i	−0.890334	+	0.890334i	−0.994554	−	0.104220i	$-0.966765\pi$
$677$	−23.1658	+	23.1658i	−0.890334	+	0.890334i	0.104220	+	0.994554i	$0.466765\pi$
$678$	0.193323	−	6.54196i	0.00742452	−	0.251242i
$679$		−	45.0304i		−	1.72811i
$680$	7.59716	+	27.1028i	0.291338	+	1.03934i
$681$	−23.6371	−	19.3905i	−0.905775	−	0.743047i
$682$	−2.01398	−	2.60852i	−0.0771192	−	0.0998855i
$683$	−14.8655	−	14.8655i	−0.568814	−	0.568814i	0.362982	−	0.931796i	$-0.381759\pi$
$683$	−14.8655	−	14.8655i	−0.568814	−	0.568814i	−0.931796	+	0.362982i	$0.881759\pi$
$684$	−2.13008	+	36.0090i	−0.0814455	+	1.37684i
$685$	−0.288816	+	2.23786i	−0.0110351	+	0.0855042i
$686$	−2.86899	+	22.3060i	−0.109539	+	0.851647i
$687$	−0.186579	−	1.89049i	−0.00711843	−	0.0721266i
$688$	−32.4581	+	9.11344i	−1.23745	+	0.347447i
$689$	−8.64552			−0.329368
$690$	15.9626	−	11.5777i	0.607688	−	0.440757i
$691$		−	47.2699i		−	1.79823i	−0.437710	−	0.899116i	$-0.644210\pi$
$691$		−	47.2699i		−	1.79823i	0.437710	−	0.899116i	$-0.355790\pi$
$692$	5.67960	−	3.32444i	0.215906	−	0.126376i
$693$	−2.48778	+	3.72646i	−0.0945031	+	0.141557i
$694$	15.8783	+	2.04227i	0.602733	+	0.0775235i
$695$	−12.3117	−	15.9604i	−0.467008	−	0.605414i
$696$	21.9577	−	11.9961i	0.832306	−	0.454713i
$697$	13.3544	−	13.3544i	0.505833	−	0.505833i
$698$	−12.0633	−	15.6245i	−0.456603	−	0.591396i
$699$	13.2202	+	10.8451i	0.500035	+	0.410201i
$700$	−28.1861	+	7.88770i	−1.06533	+	0.298127i
$701$	−7.65973			−0.289304			−0.144652	−	0.989483i	$-0.546206\pi$
$701$	−7.65973			−0.289304			−0.144652	+	0.989483i	$0.546206\pi$
$702$	−1.29831	−	7.69216i	−0.0490015	−	0.290322i
$703$	−40.6568	−	40.6568i	−1.53340	−	1.53340i
$704$	2.83445	−	2.93774i	0.106827	−	0.110720i
$705$	18.2775	+	0.548024i	0.688369	+	0.0206398i
$706$	−23.5547	−	3.02960i	−0.886492	−	0.114021i
$707$	−13.2664	+	13.2664i	−0.498933	+	0.498933i
$708$	0.632915	−	3.98625i	0.0237864	−	0.149812i
$709$	−43.9829			−1.65181			−0.825906	−	0.563808i	$-0.809336\pi$
$709$	−43.9829			−1.65181			−0.825906	+	0.563808i	$0.809336\pi$
$710$	−15.5749	−	4.08108i	−0.584516	−	0.153160i
$711$	−4.28821	−	21.5132i	−0.160820	−	0.806810i
$712$	−32.9143	+	13.9798i	−1.23351	+	0.523915i
$713$	−11.6257	+	11.6257i	−0.435387	+	0.435387i
$714$	−23.2185	+	21.8856i	−0.868931	+	0.819050i
$715$	−1.20131	−	0.155040i	−0.0449264	−	0.00579816i
$716$	−26.9225	−	7.04204i	−1.00614	−	0.263174i
$717$	−2.09599	−	21.2373i	−0.0782762	−	0.793123i
$718$	−29.2781	−	37.9213i	−1.09265	−	1.41521i
$719$	14.6227			0.545333			0.272666	−	0.962109i	$-0.412094\pi$
$719$	14.6227			0.545333			0.272666	+	0.962109i	$0.412094\pi$
$720$	9.00221	+	25.2777i	0.335493	+	0.942043i
$721$	−7.71179			−0.287202
$722$	14.8168	+	19.1909i	0.551425	+	0.714212i
$723$	1.19733	+	12.1318i	0.0445292	+	0.451186i
$724$	11.2413	+	2.94034i	0.417778	+	0.109277i
$725$	24.7002	+	6.48356i	0.917342	+	0.240793i
$726$	−19.1429	+	18.0440i	−0.710460	+	0.669675i
$727$	−22.1109	+	22.1109i	−0.820048	+	0.820048i	−0.986115	−	0.166067i	$-0.946893\pi$
$727$	−22.1109	+	22.1109i	−0.820048	+	0.820048i	0.166067	+	0.986115i	$0.446893\pi$
$728$	−3.43563	−	8.08889i	−0.127333	−	0.299794i
$729$	−22.4316	+	15.0274i	−0.830802	+	0.556569i
$730$	12.3790	−	7.23864i	0.458168	−	0.267914i
$731$	−37.5102			−1.38736
$732$	−2.67763	+	16.8643i	−0.0989679	+	0.623323i
$733$	8.64610	−	8.64610i	0.319351	−	0.319351i	−0.529167	−	0.848518i	$-0.677495\pi$
$733$	8.64610	−	8.64610i	0.319351	−	0.319351i	0.848518	+	0.529167i	$0.177495\pi$
$734$	21.4037	+	2.75294i	0.790023	+	0.101613i
$735$	−4.16012	−	4.41730i	−0.153448	−	0.162935i
$736$	−16.3405	−	12.1557i	−0.602318	−	0.448067i
$737$	−4.07412	−	4.07412i	−0.150072	−	0.150072i
$738$	11.8249	−	13.5761i	0.435282	−	0.499743i
$739$	−29.8509			−1.09808			−0.549041	−	0.835796i	$-0.685007\pi$
$739$	−29.8509			−1.09808			−0.549041	+	0.835796i	$0.685007\pi$
$740$	−39.6528	−	16.0306i	−1.45767	−	0.589296i
$741$	−8.54646	−	7.01103i	−0.313962	−	0.257557i
$742$	20.6012	+	26.6828i	0.756293	+	0.979558i
$743$	−6.78930	+	6.78930i	−0.249075	+	0.249075i	−0.820591	−	0.571516i	$-0.806356\pi$
$743$	−6.78930	+	6.78930i	−0.249075	+	0.249075i	0.571516	+	0.820591i	$0.306356\pi$
$744$	−10.7262	−	19.6333i	−0.393243	−	0.719791i
$745$	23.2952	−	17.9696i	0.853470	−	0.658355i
$746$	51.2539	+	6.59227i	1.87654	+	0.241360i
$747$	16.8664	+	11.2600i	0.617110	+	0.411982i
$748$	3.91984	−	2.29440i	0.143324	−	0.0838916i
$749$			41.5247i			1.51728i
$750$	−11.0316	+	25.0660i	−0.402816	+	0.915281i
$751$	22.5357			0.822339			0.411170	−	0.911559i	$-0.365120\pi$
$751$	22.5357			0.822339			0.411170	+	0.911559i	$0.365120\pi$
$752$	−5.10513	−	18.1823i	−0.186165	−	0.663039i
$753$	1.68800	+	17.1034i	0.0615140	+	0.623282i
$754$	−0.978161	+	7.60505i	−0.0356225	+	0.276959i
$755$	3.76922	+	4.88630i	0.137176	+	0.177831i
$756$	−20.6468	+	22.3364i	−0.750916	+	0.812368i
$757$	33.9790	+	33.9790i	1.23499	+	1.23499i	0.962025	+	0.272963i	$0.0880035\pi$
$757$	33.9790	+	33.9790i	1.23499	+	1.23499i	0.272963	+	0.962025i	$0.411996\pi$
$758$	10.5666	+	13.6860i	0.383798	+	0.497099i
$759$	−2.46010	−	2.01813i	−0.0892961	−	0.0732535i
$760$	33.1454	+	18.6318i	1.20231	+	0.675845i
$761$		−	34.4290i		−	1.24805i	−0.781404	−	0.624025i	$-0.785496\pi$
$761$		−	34.4290i		−	1.24805i	0.781404	−	0.624025i	$-0.214504\pi$
$762$	0.0986416	−	3.33799i	0.00357341	−	0.120923i
$763$	26.1701	−	26.1701i	0.947421	−	0.947421i
$764$	−26.7898	−	7.00733i	−0.969222	−	0.253516i
$765$	2.04049	+	29.7850i	0.0737741	+	1.07688i
$766$	−42.8977	−	5.51751i	−1.54996	−	0.199356i
$767$	0.874612	+	0.874612i	0.0315804	+	0.0315804i
$768$	22.1315	−	16.6793i	0.798600	−	0.601862i
$769$			14.8941i			0.537094i	0.963267	+	0.268547i	$0.0865434\pi$
$769$			14.8941i			0.537094i	−0.963267	+	0.268547i	$0.913457\pi$
$770$	2.38406	+	4.07706i	0.0859156	+	0.146927i
$771$	−22.5770	+	27.5214i	−0.813091	+	0.991159i
$772$	−11.1616	+	6.53323i	−0.401715	+	0.235136i
$773$	7.32969	+	7.32969i	0.263631	+	0.263631i	0.826527	−	0.562897i	$-0.190313\pi$
$773$	7.32969	+	7.32969i	0.263631	+	0.263631i	−0.562897	+	0.826527i	$0.690313\pi$
$774$	−35.6736	+	2.45939i	−1.28226	+	0.0884008i
$775$	5.79721	−	22.0854i	0.208242	−	0.793332i
$776$	−16.2923	+	40.3504i	−0.584861	+	1.44850i
$777$	−4.76193	−	48.2496i	−0.170833	−	1.73094i
$778$	7.43215	−	5.73818i	0.266455	−	0.205724i
$779$		−	25.5122i		−	0.914069i
$780$	−7.88935	−	2.31833i	−0.282484	−	0.0830095i
$781$			2.59807i			0.0929663i
$782$	−13.8479	−	17.9359i	−0.495199	−	0.641387i
$783$	25.3914	−	7.71905i	0.907414	−	0.275856i
$784$	−3.06848	+	5.46427i	−0.109589	+	0.195152i
$785$	1.77323	−	13.7397i	0.0632893	−	0.490390i
$786$	13.5330	−	12.7561i	0.482707	−	0.454996i
$787$	4.66068	+	4.66068i	0.166135	+	0.166135i	0.785278	−	0.619143i	$-0.212520\pi$
$787$	4.66068	+	4.66068i	0.166135	+	0.166135i	−0.619143	+	0.785278i	$0.712520\pi$
$788$	−5.51168	−	9.41637i	−0.196346	−	0.335444i
$789$	−20.5731	−	16.8770i	−0.732421	−	0.600837i
$790$	−22.3679	−	5.86104i	−0.795815	−	0.208526i
$791$		−	7.82040i		−	0.278061i
$792$	3.57749	−	2.43907i	0.127120	−	0.0866687i
$793$	−3.70016	−	3.70016i	−0.131396	−	0.131396i
$794$	3.58713	−	27.8894i	0.127303	−	0.989757i
$795$	31.5276	+	0.945310i	1.11817	+	0.0335267i
$796$	11.4514	+	2.99531i	0.405884	+	0.106166i
$797$	27.8720	−	27.8720i	0.987276	−	0.987276i	−0.0126440	−	0.999920i	$-0.504025\pi$
$797$	27.8720	−	27.8720i	0.987276	−	0.987276i	0.999920	+	0.0126440i	$0.00402483\pi$
$798$	−1.27317	+	43.0835i	−0.0450697	+	1.52514i
$799$		−	21.0123i		−	0.743362i
$800$	28.1106	+	3.13000i	0.993858	+	0.110662i
$801$	−37.1975	+	7.41454i	−1.31431	+	0.261980i
$802$	20.2809	−	15.6584i	0.716142	−	0.552916i
$803$	−1.63622	−	1.63622i	−0.0577410	−	0.0577410i
$804$	−22.9787	−	31.6528i	−0.810396	−	1.11631i
$805$	18.6568	−	14.3916i	0.657566	−	0.507238i
$806$	6.79998	+	0.874612i	0.239519	+	0.0308069i
$807$	55.7231	−	5.49951i	1.96155	−	0.193592i
$808$	16.6875	−	7.08773i	0.587063	−	0.249346i
$809$	18.8285			0.661975			0.330988	−	0.943635i	$-0.392618\pi$
$809$	18.8285			0.661975			0.330988	+	0.943635i	$0.392618\pi$
$810$	3.89347	+	28.1929i	0.136802	+	0.990598i
$811$		−	37.4113i		−	1.31369i	−0.754026	−	0.656845i	$-0.771891\pi$
$811$		−	37.4113i		−	1.31369i	0.754026	−	0.656845i	$-0.228109\pi$
$812$	25.8025	−	15.1030i	0.905489	−	0.530010i
$813$	−0.0521129	−	0.528027i	−0.00182768	−	0.0185187i
$814$	−0.880433	+	6.84523i	−0.0308592	+	0.239925i
$815$	−1.47677	−	0.190590i	−0.0517289	−	0.00667609i
$816$	28.7238	−	11.2104i	1.00553	−	0.392444i
$817$	−35.8297	+	35.8297i	−1.25352	+	1.25352i
$818$	29.4676	−	22.7512i	1.03031	−	0.795477i
$819$	−1.82217	−	9.14153i	−0.0636717	−	0.319431i
$820$	−7.41149	−	17.4707i	−0.258820	−	0.610103i
$821$	−14.3129			−0.499523			−0.249761	−	0.968307i	$-0.580352\pi$
$821$	−14.3129			−0.499523			−0.249761	+	0.968307i	$0.580352\pi$
$822$	2.47070	+	0.0730123i	0.0861757	+	0.00254660i
$823$	10.8660	+	10.8660i	0.378766	+	0.378766i	0.870657	−	0.491891i	$-0.163694\pi$
$823$	10.8660	+	10.8660i	0.378766	+	0.378766i	−0.491891	+	0.870657i	$0.663694\pi$
$824$	6.91031	+	2.79018i	0.240732	+	0.0972006i
$825$	4.36385	+	0.696735i	0.151930	+	0.0242572i
$826$	0.615244	−	4.78343i	0.0214071	−	0.166437i
$827$	2.49596	−	2.49596i	0.0867932	−	0.0867932i	−0.662377	−	0.749170i	$-0.730452\pi$
$827$	2.49596	−	2.49596i	0.0867932	−	0.0867932i	0.749170	+	0.662377i	$0.230452\pi$
$828$	−14.3459	−	16.1498i	−0.498553	−	0.561245i
$829$	49.1212			1.70605			0.853026	−	0.521869i	$-0.174765\pi$
$829$	49.1212			1.70605			0.853026	+	0.521869i	$0.174765\pi$
$830$	18.4533	−	10.7906i	0.640522	−	0.374546i
$831$	−10.8423	+	13.2167i	−0.376114	+	0.458483i
$832$	0.151945	+	8.49125i	0.00526773	+	0.294381i
$833$	−4.93043	+	4.93043i	−0.170829	+	0.170829i
$834$	−16.0681	+	15.1457i	−0.556392	+	0.524452i
$835$	0.200501	−	1.55356i	0.00693863	−	0.0537632i
$836$	1.55262	−	5.93585i	0.0536985	−	0.205296i
$837$	−6.90191	−	22.7034i	−0.238565	−	0.784746i
$838$	14.3069	−	11.0460i	0.494223	−	0.381577i
$839$	26.9749			0.931277			0.465638	−	0.884975i	$-0.345825\pi$
$839$	26.9749			0.931277			0.465638	+	0.884975i	$0.345825\pi$
$840$	11.6442	+	29.8734i	0.401764	+	1.03073i
$841$	2.91458			0.100503
$842$	−29.5288	+	22.7985i	−1.01763	+	0.785687i
$843$	−26.6473	+	2.62992i	−0.917782	+	0.0905792i
$844$	−13.4548	−	3.51933i	−0.463133	−	0.121140i
$845$	−21.0214	+	16.2156i	−0.723159	+	0.557835i
$846$	−1.37769	−	19.9835i	−0.0473660	−	0.687048i
$847$	−22.2270	+	22.2270i	−0.763729	+	0.763729i
$848$	−8.80606	−	31.3634i	−0.302401	−	1.07702i
$849$	16.7877	+	13.7717i	0.576151	+	0.472642i
$850$	29.1706	+	11.8076i	1.00054	+	0.404997i
$851$	34.4319			1.18031
$852$	−2.76574	+	17.4193i	−0.0947526	+	0.596774i
$853$	−16.4190	+	16.4190i	−0.562174	+	0.562174i	−0.929925	−	0.367750i	$-0.880128\pi$
$853$	−16.4190	+	16.4190i	−0.562174	+	0.562174i	0.367750	+	0.929925i	$0.380128\pi$
$854$	−2.60287	+	20.2369i	−0.0890683	+	0.692492i
$855$	30.3997	+	26.5016i	1.03965	+	0.906335i
$856$	15.0239	−	37.2091i	0.513508	−	1.27178i
$857$	24.4641	+	24.4641i	0.835678	+	0.835678i	0.988287	−	0.152608i	$-0.0487673\pi$
$857$	24.4641	+	24.4641i	0.835678	+	0.835678i	−0.152608	+	0.988287i	$0.548767\pi$
$858$	−0.0391938	+	1.32630i	−0.00133806	+	0.0452792i
$859$	−1.68121			−0.0573622			−0.0286811	−	0.999589i	$-0.509131\pi$
$859$	−1.68121			−0.0573622			−0.0286811	+	0.999589i	$0.509131\pi$
$860$	−14.1273	+	34.9449i	−0.481737	+	1.19161i
$861$	13.6443	−	16.6324i	0.464995	−	0.566830i
$862$	32.1064	−	24.7886i	1.09355	−	0.844302i
$863$	−23.0950	+	23.0950i	−0.786161	+	0.786161i	−0.980863	−	0.194701i	$-0.937626\pi$
$863$	−23.0950	+	23.0950i	−0.786161	+	0.786161i	0.194701	+	0.980863i	$0.437626\pi$
$864$	26.5824	−	12.5449i	0.904353	−	0.426785i
$865$	0.941779	−	7.29727i	0.0320215	−	0.248115i
$866$	0.575226	−	4.47229i	0.0195470	−	0.151975i
$867$	4.83819	−	0.477499i	0.164314	−	0.0162167i
$868$	−13.5042	−	23.0710i	−0.458361	−	0.783081i
$869$			3.73122i			0.126573i
$870$	4.39860	−	27.6263i	0.149126	−	0.936621i
$871$	11.9866			0.406149
$872$	−32.9188	+	13.9817i	−1.11477	+	0.473481i
$873$	−25.6271	+	38.3869i	−0.867345	+	1.29920i
$874$	−30.3599	−	3.90489i	−1.02694	−	0.132085i
$875$	−12.2912	+	30.3277i	−0.415517	+	1.02526i
$876$	−9.22855	−	12.7122i	−0.311804	−	0.429505i
$877$	14.2900	+	14.2900i	0.482539	+	0.482539i	0.905942	−	0.423403i	$-0.139164\pi$
$877$	14.2900	+	14.2900i	0.482539	+	0.482539i	−0.423403	+	0.905942i	$0.639164\pi$
$878$	−13.2660	+	10.2424i	−0.447707	+	0.345664i
$879$	−2.32471	+	2.83382i	−0.0784105	+	0.0955825i
$880$	−0.661178	−	4.51590i	−0.0222883	−	0.152231i
$881$			45.2886i			1.52581i	0.646509	+	0.762906i	$0.276228\pi$
$881$			45.2886i			1.52581i	−0.646509	+	0.762906i	$0.723772\pi$
$882$	−4.36576	+	5.01230i	−0.147003	+	0.168773i
$883$	−3.68252	+	3.68252i	−0.123927	+	0.123927i	−0.766350	−	0.642423i	$-0.777929\pi$
$883$	−3.68252	+	3.68252i	−0.123927	+	0.123927i	0.642423	+	0.766350i	$0.277929\pi$
$884$	−2.39112	+	9.14153i	−0.0804221	+	0.307463i
$885$	−3.09381	−	3.28508i	−0.103997	−	0.110427i
$886$	0.425589	−	3.30889i	0.0142980	−	0.111164i
$887$	−14.7506	−	14.7506i	−0.495277	−	0.495277i	0.414687	−	0.909964i	$-0.363891\pi$
$887$	−14.7506	−	14.7506i	−0.495277	−	0.495277i	−0.909964	+	0.414687i	$0.863891\pi$
$888$	−13.1900	+	44.9579i	−0.442628	+	1.50869i
$889$		−	3.99030i		−	0.133830i
$890$	−10.1340	+	38.6753i	−0.339694	+	1.29640i
$891$	4.24150	−	1.76087i	0.142095	−	0.0589912i
$892$	40.8180	−	23.8920i	1.36669	−	0.799964i
$893$	−20.0710	−	20.0710i	−0.671649	−	0.671649i
$894$	−22.1060	−	23.4523i	−0.739336	−	0.784363i
$895$	−24.6352	+	19.0032i	−0.823463	+	0.635209i
$896$	25.8446	−	20.7025i	0.863409	−	0.691623i
$897$	6.58775	−	0.650169i	0.219959	−	0.0217085i
$898$	29.6799	+	38.4417i	0.990432	+	1.28282i
$899$			23.3240i			0.777899i
$900$	28.5166	+	9.31687i	0.950553	+	0.310562i
$901$		−	36.2450i		−	1.20750i
$902$	−2.42393	+	1.87146i	−0.0807080	+	0.0623127i
$903$	−42.5210	+	4.19655i	−1.41501	+	0.139653i
$904$	−2.82948	+	7.00763i	−0.0941070	+	0.233070i
$905$	10.2862	−	7.93464i	0.341925	−	0.263756i
$906$	4.91925	−	4.63686i	0.163431	−	0.154049i
$907$	8.08868	+	8.08868i	0.268580	+	0.268580i	0.828528	−	0.559948i	$-0.189179\pi$
$907$	8.08868	+	8.08868i	0.268580	+	0.268580i	−0.559948	+	0.828528i	$0.689179\pi$
$908$	17.8333	+	30.4671i	0.591820	+	1.01109i
$909$	18.8591	−	3.75915i	0.625516	−	0.124683i
$910$	−9.50470	−	2.49050i	−0.315078	−	0.0825594i
$911$			38.7011i			1.28222i	0.767448	+	0.641112i	$0.221527\pi$
$911$			38.7011i			1.28222i	−0.767448	+	0.641112i	$0.778473\pi$
$912$	16.7288	−	38.1452i	0.553945	−	1.26311i
$913$	−2.43910	−	2.43910i	−0.0807223	−	0.0807223i
$914$	−9.15408	−	1.17740i	−0.302790	−	0.0389448i
$915$	13.0888	+	13.8979i	0.432702	+	0.459451i
$916$	−0.555086	+	2.12216i	−0.0183406	+	0.0701180i
$917$	15.7133	−	15.7133i	0.518899	−	0.518899i
$918$	32.2482	−	5.44296i	1.06435	−	0.179644i
$919$			39.9611i			1.31819i	0.752058	+	0.659097i	$0.229061\pi$
$919$			39.9611i			1.31819i	−0.752058	+	0.659097i	$0.770939\pi$
$920$	−21.9248	+	6.14573i	−0.722839	+	0.202619i
$921$	19.4115	−	23.6626i	0.639630	−	0.779710i
$922$	17.8428	+	23.1102i	0.587623	+	0.761094i
$923$	−3.82192	−	3.82192i	−0.125800	−	0.125800i
$924$	4.18679	−	3.03945i	0.137735	−	0.0999904i
$925$	−41.2900	+	24.1204i	−1.35761	+	0.793074i
$926$	−6.93510	+	53.9193i	−0.227901	+	1.77190i
$927$	6.57403	+	4.38882i	0.215920	+	0.144148i
$928$	−28.5852	+	4.19779i	−0.938354	+	0.137799i
$929$	−0.568113			−0.0186392			−0.00931959	−	0.999957i	$-0.502967\pi$
$929$	−0.568113			−0.0186392			−0.00931959	+	0.999957i	$0.502967\pi$
$930$	−24.7018	−	3.93296i	−0.810004	−	0.128967i
$931$			9.41909i			0.308698i
$932$	−9.97418	−	17.0403i	−0.326715	−	0.558173i
$933$	−0.387193	+	0.0382135i	−0.0126761	+	0.00125105i
$934$	12.6935	+	1.63263i	0.415343	+	0.0534213i
$935$	0.649980	−	5.03630i	0.0212566	−	0.164705i
$936$	−1.67468	+	8.85073i	−0.0547386	+	0.289295i
$937$	18.2630	−	18.2630i	0.596626	−	0.596626i	−0.342787	−	0.939413i	$-0.611371\pi$
$937$	18.2630	−	18.2630i	0.596626	−	0.596626i	0.939413	+	0.342787i	$0.111371\pi$
$938$	−28.5624	−	36.9944i	−0.932597	−	1.20791i
$939$	−18.7023	+	22.7981i	−0.610326	+	0.743988i
$940$	−19.5753	−	7.91379i	−0.638477	−	0.258119i
$941$	22.3971			0.730125			0.365063	−	0.930983i	$-0.381048\pi$
$941$	22.3971			0.730125			0.365063	+	0.930983i	$0.381048\pi$
$942$	−15.1693	−	0.448270i	−0.494242	−	0.0146054i
$943$	10.8030	+	10.8030i	0.351795	+	0.351795i
$944$	−2.28198	+	4.06369i	−0.0742721	+	0.132262i
$945$	5.64535	+	33.5356i	0.183643	+	1.09091i
$946$	6.03251	+	0.775901i	0.196134	+	0.0252267i
$947$	15.7486	−	15.7486i	0.511761	−	0.511761i	−0.403305	−	0.915066i	$-0.632139\pi$
$947$	15.7486	−	15.7486i	0.511761	−	0.511761i	0.915066	+	0.403305i	$0.132139\pi$
$948$	−3.97201	+	25.0167i	−0.129005	+	0.812504i
$949$	4.81396			0.156268
$950$	39.1424	−	16.5852i	1.26995	−	0.538095i
$951$	−38.3034	−	31.4219i	−1.24207	−	1.01893i
$952$	33.9114	−	14.4033i	1.09908	−	0.466815i
$953$	33.3609	−	33.3609i	1.08067	−	1.08067i	0.0842194	−	0.996447i	$-0.473160\pi$
$953$	33.3609	−	33.3609i	1.08067	−	1.08067i	0.996447	−	0.0842194i	$-0.0268396\pi$
$954$	−2.37644	−	34.4704i	−0.0769400	−	1.11602i
$955$	−24.5138	+	18.9096i	−0.793246	+	0.611900i
$956$	−6.23572	+	23.8399i	−0.201678	+	0.771037i
$957$	−4.49221	+	0.443352i	−0.145213	+	0.0143315i
$958$	−31.0367	−	40.1990i	−1.00275	−	1.29877i
$959$	2.95353			0.0953746
$960$	0.374346	−	30.9816i	0.0120820	−	0.999927i
$961$	−10.1451			−0.327260
$962$	−8.77458	−	11.3649i	−0.282904	−	0.366420i
$963$	23.6319	−	35.3984i	0.761529	−	1.14070i
$964$	3.56215	−	13.6185i	0.114729	−	0.438622i
$965$	−1.85080	+	14.3407i	−0.0595793	+	0.461643i
$966$	−17.7044	−	18.7826i	−0.569630	−	0.604322i
$967$	−8.01398	+	8.01398i	−0.257712	+	0.257712i	−0.824123	−	0.566411i	$-0.808332\pi$
$967$	−8.01398	+	8.01398i	−0.257712	+	0.257712i	0.566411	+	0.824123i	$0.308332\pi$
$968$	27.9589	−	11.8751i	0.898632	−	0.381679i
$969$	29.3927	−	35.8297i	0.944229	−	1.15102i
$970$	24.5586	+	41.9985i	0.788530	+	1.34849i
$971$	43.4981			1.39592			0.697961	−	0.716136i	$-0.254091\pi$
$971$	43.4981			1.39592			0.697961	+	0.716136i	$0.254091\pi$
$972$	30.3124	−	7.29085i	0.972272	−	0.233854i
$973$	−18.6568	+	18.6568i	−0.598110	+	0.598110i
$974$	−47.4274	−	6.10011i	−1.51967	−	0.195460i
$975$	−7.44443	+	5.39455i	−0.238413	+	0.172764i
$976$	9.65420	−	17.1919i	0.309024	−	0.550301i
$977$	39.7367	+	39.7367i	1.27129	+	1.27129i	0.945411	+	0.325880i	$0.105661\pi$
$977$	39.7367	+	39.7367i	1.27129	+	1.27129i	0.325880	+	0.945411i	$0.394339\pi$
$978$	−0.0481810	+	1.63042i	−0.00154066	+	0.0521352i
$979$	6.45147			0.206190
$980$	2.73632	+	6.45017i	0.0874085	+	0.206043i
$981$	−37.2026	+	7.41555i	−1.18779	+	0.236760i
$982$	−26.7495	−	34.6462i	−0.853609	−	1.10560i
$983$	−9.14087	+	9.14087i	−0.291548	+	0.291548i	−0.837692	−	0.546143i	$-0.816095\pi$
$983$	−9.14087	+	9.14087i	−0.291548	+	0.291548i	0.546143	+	0.837692i	$0.316095\pi$
$984$	−18.2439	+	9.96719i	−0.581596	+	0.317742i
$985$	−12.0984	−	1.56140i	−0.385486	−	0.0497504i
$986$	−31.8830	−	4.10079i	−1.01536	−	0.130596i
$987$	−2.35081	−	23.8193i	−0.0748271	−	0.758176i
$988$	6.44799	+	11.0160i	0.205138	+	0.350465i
$989$		−	30.3439i		−	0.964879i
$990$	0.287947	−	4.83233i	0.00915156	−	0.153582i
$991$	−23.1823			−0.736409			−0.368205	−	0.929745i	$-0.620027\pi$
$991$	−23.1823			−0.736409			−0.368205	+	0.929745i	$0.620027\pi$
$992$	3.75342	+	25.5591i	0.119171	+	0.811503i
$993$	−21.2542	+	2.09766i	−0.674483	+	0.0665671i
$994$	−2.68852	+	20.9028i	−0.0852747	+	0.662997i
$995$	10.4785	−	8.08297i	0.332191	−	0.256247i
$996$	−13.7569	−	18.9499i	−0.435904	−	0.600451i
$997$	3.70273	+	3.70273i	0.117267	+	0.117267i	0.763305	−	0.646038i	$-0.223575\pi$
$997$	3.70273	+	3.70273i	0.117267	+	0.117267i	−0.646038	+	0.763305i	$0.723575\pi$
$998$	−17.2156	−	22.2978i	−0.544949	−	0.705824i
$999$	−23.3997	+	43.8411i	−0.740334	+	1.38707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.w.c.53.12	yes	32
3.2	odd	2	inner	120.2.w.c.53.5	yes	32
4.3	odd	2		480.2.bi.c.113.9		32
5.2	odd	4	inner	120.2.w.c.77.4	yes	32
5.3	odd	4		600.2.w.j.557.13		32
5.4	even	2		600.2.w.j.293.5		32
8.3	odd	2		480.2.bi.c.113.8		32
8.5	even	2	inner	120.2.w.c.53.13	yes	32
12.11	even	2		480.2.bi.c.113.1		32
15.2	even	4	inner	120.2.w.c.77.13	yes	32
15.8	even	4		600.2.w.j.557.4		32
15.14	odd	2		600.2.w.j.293.12		32
20.7	even	4		480.2.bi.c.17.16		32
24.5	odd	2	inner	120.2.w.c.53.4	✓	32
24.11	even	2		480.2.bi.c.113.16		32
40.13	odd	4		600.2.w.j.557.12		32
40.27	even	4		480.2.bi.c.17.1		32
40.29	even	2		600.2.w.j.293.4		32
40.37	odd	4	inner	120.2.w.c.77.5	yes	32
60.47	odd	4		480.2.bi.c.17.8		32
120.29	odd	2		600.2.w.j.293.13		32
120.53	even	4		600.2.w.j.557.5		32
120.77	even	4	inner	120.2.w.c.77.12	yes	32
120.107	odd	4		480.2.bi.c.17.9		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.4	✓	32	24.5	odd	2	inner
120.2.w.c.53.5	yes	32	3.2	odd	2	inner
120.2.w.c.53.12	yes	32	1.1	even	1	trivial
120.2.w.c.53.13	yes	32	8.5	even	2	inner
120.2.w.c.77.4	yes	32	5.2	odd	4	inner
120.2.w.c.77.5	yes	32	40.37	odd	4	inner
120.2.w.c.77.12	yes	32	120.77	even	4	inner
120.2.w.c.77.13	yes	32	15.2	even	4	inner
480.2.bi.c.17.1		32	40.27	even	4
480.2.bi.c.17.8		32	60.47	odd	4
480.2.bi.c.17.9		32	120.107	odd	4
480.2.bi.c.17.16		32	20.7	even	4
480.2.bi.c.113.1		32	12.11	even	2
480.2.bi.c.113.8		32	8.3	odd	2
480.2.bi.c.113.9		32	4.3	odd	2
480.2.bi.c.113.16		32	24.11	even	2
600.2.w.j.293.4		32	40.29	even	2
600.2.w.j.293.5		32	5.4	even	2
600.2.w.j.293.12		32	15.14	odd	2
600.2.w.j.293.13		32	120.29	odd	2
600.2.w.j.557.4		32	15.8	even	4
600.2.w.j.557.5		32	120.53	even	4
600.2.w.j.557.12		32	40.13	odd	4
600.2.w.j.557.13		32	5.3	odd	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.864261 + 1.11940i) q^{2} +(-0.170116 - 1.72368i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 - 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(-2.94212 + 0.586449i) q^{9} +O(q^{10})\)	\(q+(0.864261 + 1.11940i) q^{2} +(-0.170116 - 1.72368i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(1.36575 + 1.77052i) q^{5} +(1.78246 - 1.68013i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(-2.94212 + 0.586449i) q^{9} +(-0.801547 + 3.05901i) q^{10} +0.510276 q^{11} +(3.42125 + 0.543207i) q^{12} +(-0.750647 + 0.750647i) q^{13} +(4.10544 + 0.528041i) q^{14} +(2.81946 - 2.65531i) q^{15} +(-3.48771 - 1.95854i) q^{16} +(-3.14698 - 3.14698i) q^{17} +(-3.19923 - 2.78656i) q^{18} -6.01198 q^{19} +(-4.11699 + 1.74653i) q^{20} +(-3.91945 - 3.21529i) q^{21} +(0.441012 + 0.571203i) q^{22} +(2.54575 - 2.54575i) q^{23} +(2.34878 + 4.29921i) q^{24} +(-1.26945 + 4.83617i) q^{25} +(-1.48903 - 0.191519i) q^{26} +(1.51135 + 4.97150i) q^{27} +(2.95708 + 5.05199i) q^{28} -5.10739i q^{29} +(5.40909 + 0.861223i) q^{30} -4.56672 q^{31} +(-0.821906 - 5.59683i) q^{32} +(-0.0868061 - 0.879551i) q^{33} +(0.802913 - 6.24253i) q^{34} +(6.49090 + 0.837710i) q^{35} +(0.354305 - 5.98953i) q^{36} +(6.76263 + 6.76263i) q^{37} +(-5.19592 - 6.72981i) q^{38} +(1.42157 + 1.16618i) q^{39} +(-5.51322 - 3.09910i) q^{40} +4.24355i q^{41} +(0.211772 - 7.16627i) q^{42} +(5.95972 - 5.95972i) q^{43} +(-0.258254 + 0.987336i) q^{44} +(-5.05652 - 4.40813i) q^{45} +(5.04990 + 0.649518i) q^{46} +(3.33849 + 3.33849i) q^{47} +(-2.78257 + 6.34486i) q^{48} -1.56672i q^{49} +(-6.51073 + 2.75869i) q^{50} +(-4.88902 + 5.95972i) q^{51} +(-1.07252 - 1.83234i) q^{52} +(5.75871 + 5.75871i) q^{53} +(-4.25889 + 5.98848i) q^{54} +(0.696910 + 0.903452i) q^{55} +(-3.09950 + 7.67638i) q^{56} +(1.02273 + 10.3627i) q^{57} +(5.71720 - 4.41411i) q^{58} -1.16514i q^{59} +(3.71082 + 6.79925i) q^{60} +4.92929i q^{61} +(-3.94684 - 5.11198i) q^{62} +(-4.87536 + 7.30283i) q^{63} +(5.55474 - 5.75716i) q^{64} +(-2.35423 - 0.303835i) q^{65} +(0.909545 - 0.857332i) q^{66} +(-7.98415 - 7.98415i) q^{67} +(7.68180 - 4.49639i) q^{68} +(-4.82112 - 3.95497i) q^{69} +(4.67210 + 7.98991i) q^{70} +5.09150i q^{71} +(7.01088 - 4.77991i) q^{72} +(-3.20654 - 3.20654i) q^{73} +(-1.72540 + 13.4148i) q^{74} +(8.55194 + 1.36541i) q^{75} +(3.04271 - 11.6326i) q^{76} +(1.05608 - 1.05608i) q^{77} +(-0.0768090 + 2.59918i) q^{78} +7.31215i q^{79} +(-1.29572 - 8.84992i) q^{80} +(8.31215 - 3.45081i) q^{81} +(-4.75023 + 3.66754i) q^{82} +(-4.77995 - 4.77995i) q^{83} +(8.20494 - 5.95647i) q^{84} +(1.27378 - 9.86975i) q^{85} +(11.8220 + 1.52055i) q^{86} +(-8.80349 + 0.868848i) q^{87} +(-1.32842 + 0.564226i) q^{88} +12.6431 q^{89} +(0.564297 - 9.47004i) q^{90} +3.10712i q^{91} +(3.63736 + 6.21420i) q^{92} +(0.776871 + 7.87155i) q^{93} +(-0.851777 + 6.62243i) q^{94} +(-8.21087 - 10.6443i) q^{95} +(-9.50730 + 2.36881i) q^{96} +(10.8789 - 10.8789i) q^{97} +(1.75378 - 1.35405i) q^{98} +(-1.50129 + 0.299251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more