LMFDB - Embedded newform 120.2.w.c.53.13

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			53.13
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11940 + 0.864261i) q^{2} +(0.170116 + 1.72368i) q^{3} +(0.506107 + 1.93490i) q^{4} +(-1.36575 - 1.77052i) q^{5} +(-1.29928 + 2.07651i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(-2.94212 + 0.586449i) q^{9} +O(q^{10})$	\(q+(1.11940 + 0.864261i) q^{2} +(0.170116 + 1.72368i) q^{3} +(0.506107 + 1.93490i) q^{4} +(-1.36575 - 1.77052i) q^{5} +(-1.29928 + 2.07651i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(-2.94212 + 0.586449i) q^{9} +(0.00136610 - 3.16228i) q^{10} -0.510276 q^{11} +(-3.24905 + 1.20152i) 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} +(-3.80025 - 1.88629i) q^{18} +6.01198 q^{19} +(2.73456 - 3.53867i) q^{20} +(3.91945 + 3.21529i) q^{21} +(-0.571203 - 0.441012i) q^{22} +(2.54575 - 2.54575i) q^{23} +(-4.67541 - 1.46305i) q^{24} +(-1.26945 + 4.83617i) q^{25} +(1.48903 - 0.191519i) q^{26} +(-1.51135 - 4.97150i) q^{27} +(5.05199 + 2.95708i) q^{28} +5.10739i q^{29} +(5.45098 - 0.535599i) q^{30} -4.56672 q^{31} +(-5.59683 - 0.821906i) q^{32} +(-0.0868061 - 0.879551i) q^{33} +(-0.802913 - 6.24253i) q^{34} +(-6.49090 - 0.837710i) q^{35} +(-2.62375 - 5.39592i) q^{36} +(-6.76263 - 6.76263i) q^{37} +(6.72981 + 5.19592i) q^{38} +(1.42157 + 1.16618i) q^{39} +(6.11940 - 1.59781i) q^{40} +4.24355i q^{41} +(1.60857 + 6.98662i) 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} +(-3.96920 - 5.67851i) q^{48} -1.56672i q^{49} +(-5.60073 + 4.31647i) q^{50} +(4.88902 - 5.95972i) q^{51} +(1.83234 + 1.07252i) q^{52} +(-5.75871 - 5.75871i) q^{53} +(2.60487 - 6.87129i) q^{54} +(0.696910 + 0.903452i) q^{55} +(3.09950 + 7.67638i) q^{56} +(1.02273 + 10.3627i) q^{57} +(-4.41411 + 5.71720i) q^{58} +1.16514i q^{59} +(6.56471 + 4.11151i) q^{60} -4.92929i q^{61} +(-5.11198 - 3.94684i) q^{62} +(-4.87536 + 7.30283i) q^{63} +(-5.55474 - 5.75716i) q^{64} +(-2.35423 - 0.303835i) q^{65} +(0.662991 - 1.05959i) q^{66} +(7.98415 + 7.98415i) q^{67} +(4.49639 - 7.68180i) q^{68} +(4.82112 + 3.95497i) q^{69} +(-6.54191 - 6.54756i) q^{70} +5.09150i q^{71} +(1.72645 - 8.30779i) 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} +(0.583424 + 2.53402i) q^{78} +7.31215i q^{79} +(8.23097 + 3.50017i) q^{80} +(8.31215 - 3.45081i) q^{81} +(-3.66754 + 4.75023i) q^{82} +(4.77995 + 4.77995i) q^{83} +(-4.23762 + 9.21104i) q^{84} +(-1.27378 + 9.86975i) q^{85} +(-11.8220 + 1.52055i) q^{86} +(-8.80349 + 0.868848i) q^{87} +(0.564226 - 1.32842i) q^{88} +12.6431 q^{89} +(1.85050 + 9.30460i) q^{90} -3.10712i q^{91} +(6.21420 + 3.63736i) q^{92} +(-0.776871 - 7.87155i) q^{93} +(0.851777 + 6.62243i) q^{94} +(-8.21087 - 10.6443i) q^{95} +(0.464592 - 9.78694i) q^{96} +(10.8789 - 10.8789i) q^{97} +(1.35405 - 1.75378i) 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 $

$2$	1.11940	+	0.864261i	0.791534	+	0.611125i
$2$	1.11940	+	0.864261i	0.791534	+	0.611125i
$3$	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
$6$	−1.29928	+	2.07651i	−0.530428	+	0.847730i
$7$	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	$0.0634328\pi$
$8$	−1.10573	+	2.60334i	−0.390933	+	0.920419i
$9$	−2.94212	+	0.586449i	−0.980707	+	0.195483i
$10$	0.00136610	−	3.16228i	0.000431999	−	1.00000i
$11$	−0.510276			−0.153854			−0.0769270	−	0.997037i	$-0.524511\pi$
$11$	−0.510276			−0.153854			−0.0769270	+	0.997037i	$0.524511\pi$
$12$	−3.24905	+	1.20152i	−0.937921	+	0.346850i
$13$	0.750647	−	0.750647i	0.208192	−	0.208192i	−0.595307	−	0.803499i	$-0.702969\pi$
$13$	0.750647	−	0.750647i	0.208192	−	0.208192i	0.803499	+	0.595307i	$0.202969\pi$
$14$	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	$0.931463\pi$
$18$	−3.80025	−	1.88629i	−0.895728	−	0.444603i
$19$	6.01198			1.37924			0.689622	−	0.724170i	$-0.257777\pi$
$19$	6.01198			1.37924			0.689622	+	0.724170i	$0.257777\pi$
$20$	2.73456	−	3.53867i	0.611466	−	0.791270i
$21$	3.91945	+	3.21529i	0.855293	+	0.701634i
$22$	−0.571203	−	0.441012i	−0.121781	−	0.0940240i
$23$	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	$0.127522\pi$
$24$	−4.67541	−	1.46305i	−0.954365	−	0.298643i
$25$	−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
$28$	5.05199	+	2.95708i	0.954736	+	0.558835i
$29$			5.10739i			0.948418i	0.880412	+	0.474209i	$0.157266\pi$
$29$			5.10739i			0.948418i	−0.880412	+	0.474209i	$0.842734\pi$
$30$	5.45098	−	0.535599i	0.995207	−	0.0977865i
$31$	−4.56672			−0.820207			−0.410104	−	0.912039i	$-0.634507\pi$
$31$	−4.56672			−0.820207			−0.410104	+	0.912039i	$0.634507\pi$
$32$	−5.59683	−	0.821906i	−0.989389	−	0.145294i
$33$	−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
$36$	−2.62375	−	5.39592i	−0.437292	−	0.899320i
$37$	−6.76263	−	6.76263i	−1.11177	−	1.11177i	−0.992911	−	0.118858i	$-0.962077\pi$
$37$	−6.76263	−	6.76263i	−1.11177	−	1.11177i	−0.118858	−	0.992911i	$-0.537923\pi$
$38$	6.72981	+	5.19592i	1.09172	+	0.842890i
$39$	1.42157	+	1.16618i	0.227633	+	0.186738i
$40$	6.11940	−	1.59781i	0.967561	−	0.252636i
$41$			4.24355i			0.662732i	0.943502	+	0.331366i	$0.107509\pi$
$41$			4.24355i			0.662732i	−0.943502	+	0.331366i	$0.892491\pi$
$42$	1.60857	+	6.98662i	0.248208	+	1.07806i
$43$	−5.95972	+	5.95972i	−0.908848	+	0.908848i	−0.996179	−	0.0873310i	$-0.972166\pi$
$43$	−5.95972	+	5.95972i	−0.908848	+	0.908848i	0.0873310	+	0.996179i	$0.472166\pi$
$44$	−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	$0.638103\pi$
$48$	−3.96920	−	5.67851i	−0.572905	−	0.819622i
$49$		−	1.56672i		−	0.223817i
$50$	−5.60073	+	4.31647i	−0.792062	+	0.610440i
$51$	4.88902	−	5.95972i	0.684599	−	0.834527i
$52$	1.83234	+	1.07252i	0.254100	+	0.148732i
$53$	−5.75871	−	5.75871i	−0.791019	−	0.791019i	0.190641	−	0.981660i	$-0.438943\pi$
$53$	−5.75871	−	5.75871i	−0.791019	−	0.791019i	−0.981660	+	0.190641i	$0.938943\pi$
$54$	2.60487	−	6.87129i	0.354478	−	0.935064i
$55$	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
$58$	−4.41411	+	5.71720i	−0.579602	+	0.750706i
$59$			1.16514i			0.151689i	0.997120	+	0.0758444i	$0.0241652\pi$
$59$			1.16514i			0.151689i	−0.997120	+	0.0758444i	$0.975835\pi$
$60$	6.56471	+	4.11151i	0.847501	+	0.530794i
$61$		−	4.92929i		−	0.631131i	−0.948904	−	0.315565i	$-0.897806\pi$
$61$		−	4.92929i		−	0.631131i	0.948904	−	0.315565i	$-0.102194\pi$
$62$	−5.11198	−	3.94684i	−0.649222	−	0.501249i
$63$	−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
$66$	0.662991	−	1.05959i	0.0816085	−	0.130427i
$67$	7.98415	+	7.98415i	0.975419	+	0.975419i	0.999705	−	0.0242864i	$-0.00773136\pi$
$67$	7.98415	+	7.98415i	0.975419	+	0.975419i	−0.0242864	+	0.999705i	$0.507731\pi$
$68$	4.49639	−	7.68180i	0.545267	−	0.931555i
$69$	4.82112	+	3.95497i	0.580395	+	0.476123i
$70$	−6.54191	−	6.54756i	−0.781908	−	0.782584i
$71$			5.09150i			0.604250i	0.953268	+	0.302125i	$0.0976959\pi$
$71$			5.09150i			0.604250i	−0.953268	+	0.302125i	$0.902304\pi$
$72$	1.72645	−	8.30779i	0.203465	−	0.979082i
$73$	−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
$78$	0.583424	+	2.53402i	0.0660597	+	0.286922i
$79$			7.31215i			0.822682i	0.911482	+	0.411341i	$0.134939\pi$
$79$			7.31215i			0.822682i	−0.911482	+	0.411341i	$0.865061\pi$
$80$	8.23097	+	3.50017i	0.920250	+	0.391331i
$81$	8.31215	−	3.45081i	0.923573	−	0.383423i
$82$	−3.66754	+	4.75023i	−0.405012	+	0.524575i
$83$	4.77995	+	4.77995i	0.524668	+	0.524668i	0.918978	−	0.394310i	$-0.129016\pi$
$83$	4.77995	+	4.77995i	0.524668	+	0.524668i	−0.394310	+	0.918978i	$0.629016\pi$
$84$	−4.23762	+	9.21104i	−0.462363	+	1.00501i
$85$	−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
$88$	0.564226	−	1.32842i	0.0601467	−	0.141610i
$89$	12.6431			1.34017			0.670083	−	0.742286i	$-0.266259\pi$
$89$	12.6431			1.34017			0.670083	+	0.742286i	$0.266259\pi$
$90$	1.85050	+	9.30460i	0.195059	+	0.980791i
$91$		−	3.10712i		−	0.325715i
$92$	6.21420	+	3.63736i	0.647875	+	0.379221i
$93$	−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
$96$	0.464592	−	9.78694i	0.0474172	−	0.998875i
$97$	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	$-0.0353195\pi$
$98$	1.35405	−	1.75378i	0.136780	−	0.177159i
$99$	1.50129	−	0.299251i	0.150886	−	0.0300759i
$100$	−10.0000	−	0.00863998i	−1.00000	−	0.000863998i
$101$	6.41002			0.637821			0.318911	−	0.947785i	$-0.396683\pi$
$101$	6.41002			0.637821			0.318911	+	0.947785i	$0.396683\pi$
$102$	10.6235	−	2.44592i	1.05188	−	0.242182i
$103$	−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	−0.0297341	−	0.999558i	$-0.509466\pi$
$107$	10.0319	−	10.0319i	0.969824	−	0.969824i	0.999558	+	0.0297341i	$0.00946607\pi$
$108$	8.85447	−	5.44043i	0.852022	−	0.523506i
$109$	−12.6448			−1.21115			−0.605577	−	0.795786i	$-0.707058\pi$
$109$	−12.6448			−1.21115			−0.605577	+	0.795786i	$0.707058\pi$
$110$	−0.000697089		1.61364i	−6.64648e−5		0.153854i
$111$	10.5062	−	12.8070i	0.997200	−	1.21559i
$112$	−3.16482	+	11.2717i	−0.299047	+	1.06508i
$113$	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	$0.209890\pi$
$114$	−7.81124	+	12.4839i	−0.731590	+	1.16923i
$115$	−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
$118$	−1.00699	+	1.30426i	−0.0927008	+	0.120067i
$119$	−13.0261			−1.19410
$120$	3.79511	+	10.2760i	0.346445	+	0.938070i
$121$	−10.7396			−0.976329
$122$	4.26019	−	5.51784i	0.385700	−	0.499562i
$123$	−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
$126$	−11.7690	+	3.96119i	−1.04847	+	0.352891i
$127$	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	$0.230734\pi$
$128$	−1.24228	−	11.2453i	−0.109803	−	0.993953i
$129$	−11.2865	−	9.25878i	−0.993718	−	0.815190i
$130$	−2.37273	−	2.37478i	−0.208102	−	0.208282i
$131$	−7.59234			−0.663346			−0.331673	−	0.943395i	$-0.607613\pi$
$131$	−7.59234			−0.663346			−0.331673	+	0.943395i	$0.607613\pi$
$132$	1.65791	−	0.613109i	0.144303	−	0.0533643i
$133$	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	$0.736274\pi$
$138$	1.97863	+	8.59390i	0.168432	+	0.731561i
$139$	9.01457			0.764606			0.382303	−	0.924037i	$-0.375131\pi$
$139$	9.01457			0.764606			0.382303	+	0.924037i	$0.375131\pi$
$140$	−1.66420	−	12.9833i	−0.140651	−	1.09729i
$141$	−5.18655	+	6.32241i	−0.436787	+	0.532443i
$142$	−4.40038	+	5.69942i	−0.369272	+	0.478284i
$143$	−0.383038	+	0.383038i	−0.0320312	+	0.0320312i
$144$	9.11269	−	7.80762i	0.759390	−	0.650635i
$145$	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
$148$	9.66243	−	16.5077i	0.794247	−	1.35692i
$149$			13.1573i			1.07789i	0.842341	+	0.538944i	$0.181177\pi$
$149$			13.1573i			1.07789i	−0.842341	+	0.538944i	$0.818823\pi$
$150$	−8.39296	−	8.91954i	−0.685283	−	0.728277i
$151$	2.75982			0.224591			0.112295	−	0.993675i	$-0.464180\pi$
$151$	2.75982			0.224591			0.112295	+	0.993675i	$0.464180\pi$
$152$	−6.64761	+	15.6512i	−0.539192	+	1.26948i
$153$	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
$156$	−1.53697	+	3.34081i	−0.123056	+	0.267479i
$157$	4.38090	+	4.38090i	0.349634	+	0.349634i	0.859973	−	0.510339i	$-0.170480\pi$
$157$	4.38090	+	4.38090i	0.349634	+	0.349634i	−0.510339	+	0.859973i	$0.670480\pi$
$158$	−6.31961	+	8.18522i	−0.502761	+	0.651181i
$159$	8.94650	−	10.9058i	0.709504	−	0.864886i
$160$	6.18868	+	11.0318i	0.489258	+	0.872139i
$161$		−	10.5375i		−	0.830472i
$162$	12.2870	+	3.32104i	0.965359	+	0.260925i
$163$	0.470868	−	0.470868i	0.0368812	−	0.0368812i	−0.688426	−	0.725307i	$-0.741698\pi$
$163$	0.470868	−	0.470868i	0.0368812	−	0.0368812i	0.725307	+	0.688426i	$0.241698\pi$
$164$	−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	$0.758629\pi$
$168$	−12.7043	+	6.64841i	−0.980160	+	0.512936i
$169$			11.8731i			0.913312i
$170$	−9.95591	+	9.94731i	−0.763583	+	0.762924i
$171$	−17.6880	+	3.52572i	−1.35263	+	0.269619i
$172$	−14.5477	−	8.51523i	−1.10925	−	0.649280i
$173$	2.32674	+	2.32674i	0.176899	+	0.176899i	0.790002	−	0.613104i	$-0.210079\pi$
$173$	2.32674	+	2.32674i	0.176899	+	0.176899i	−0.613104	+	0.790002i	$0.710079\pi$
$174$	−10.6055	−	6.63592i	−0.804002	−	0.503068i
$175$	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
$178$	14.1527	+	10.9269i	1.06079	+	0.819008i
$179$		−	13.9141i		−	1.03999i	−0.854169	−	0.519996i	$-0.825934\pi$
$179$		−	13.9141i		−	1.03999i	0.854169	−	0.519996i	$-0.174066\pi$
$180$	−5.97016	+	12.0149i	−0.444989	+	0.895536i
$181$			5.80972i			0.431833i	0.976412	+	0.215917i	$0.0692740\pi$
$181$			5.80972i			0.431833i	−0.976412	+	0.215917i	$0.930726\pi$
$182$	2.68536	−	3.47811i	0.199052	−	0.257814i
$183$	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
$186$	5.93344	−	9.48282i	0.435061	−	0.695314i
$187$	1.60583	+	1.60583i	0.117430	+	0.117430i
$188$	−4.77003	+	8.14930i	−0.347890	+	0.594349i
$189$	−13.4171	−	7.16122i	−0.975950	−	0.520902i
$190$	0.00821298	−	19.0116i	0.000595832	−	1.37924i
$191$			13.8456i			1.00183i	0.865497	+	0.500914i	$0.167003\pi$
$191$			13.8456i			1.00183i	−0.865497	+	0.500914i	$0.832997\pi$
$192$	8.97853	−	10.5540i	0.647969	−	0.761666i
$193$	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	−0.556205	−	0.831045i	$-0.687743\pi$
$197$	3.85757	−	3.85757i	0.274840	−	0.274840i	0.831045	+	0.556205i	$0.187743\pi$
$198$	1.93918	+	0.962528i	0.137811	+	0.0684039i
$199$		−	5.91833i		−	0.419540i	−0.977751	−	0.209770i	$-0.932729\pi$
$199$		−	5.91833i		−	0.419540i	0.977751	−	0.209770i	$-0.0672714\pi$
$200$	−11.1865	−	8.65227i	−0.791006	−	0.611808i
$201$	−12.4039	+	15.1203i	−0.874900	+	1.06650i
$202$	7.17537	+	5.53993i	0.504858	+	0.389788i
$203$	10.5704	+	10.5704i	0.741896	+	0.741896i
$204$	14.0058	+	6.44352i	0.980606	+	0.451137i
$205$	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
$208$	−1.14787	+	4.08821i	−0.0795904	+	0.283467i
$209$	−3.06777			−0.212202
$210$	10.1730	−	12.3900i	0.702004	−	0.854990i
$211$		−	6.95372i		−	0.478714i	−0.970932	−	0.239357i	$-0.923063\pi$
$211$		−	6.95372i		−	0.478714i	0.970932	−	0.239357i	$-0.0769366\pi$
$212$	8.22802	−	14.0571i	0.565103	−	0.965444i
$213$	−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
$216$	14.6136	+	1.56256i	0.994332	+	0.106319i
$217$	−9.45141	+	9.45141i	−0.641604	+	0.641604i
$218$	−14.1546	−	10.9284i	−0.958671	−	0.740166i
$219$	4.98156	−	6.07252i	0.336622	−	0.410343i
$220$	−1.39538	+	1.80570i	−0.0940766	+	0.121740i
$221$	−4.72454			−0.317807
$222$	22.8292	−	5.25610i	1.53219	−	0.352766i
$223$	−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	−0.987298	−	0.158881i	$-0.949211\pi$
$227$	−12.4814	+	12.4814i	−0.828416	+	0.828416i	0.158881	+	0.987298i	$0.449211\pi$
$228$	−19.5332	+	7.22354i	−1.29362	+	0.478390i
$229$	−1.09678			−0.0724770			−0.0362385	−	0.999343i	$-0.511538\pi$
$229$	−1.09678			−0.0724770			−0.0362385	+	0.999343i	$0.511538\pi$
$230$	−8.04689	−	8.05384i	−0.530596	−	0.531055i
$231$	−2.00000	−	1.64069i	−0.131590	−	0.107949i
$232$	−13.2963	−	5.64737i	−0.872942	−	0.370768i
$233$	−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	$0.354819\pi$
$234$	−4.26859	+	1.43671i	−0.279046	+	0.0939207i
$235$	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
$238$	−14.5814	−	11.2580i	−0.945174	−	0.729746i
$239$	12.3210			0.796976			0.398488	−	0.917173i	$-0.369535\pi$
$239$	12.3210			0.796976			0.398488	+	0.917173i	$0.369535\pi$
$240$	−4.63294	+	14.7830i	−0.299055	+	0.954236i
$241$	−7.03833			−0.453379			−0.226689	−	0.973967i	$-0.572790\pi$
$241$	−7.03833			−0.453379			−0.226689	+	0.973967i	$0.572790\pi$
$242$	−12.0219	−	9.28183i	−0.772798	−	0.596659i
$243$	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
$246$	−8.81177	−	5.51356i	−0.561818	−	0.351532i
$247$	4.51288	−	4.51288i	0.287148	−	0.287148i
$248$	5.04954	−	11.8887i	0.320646	−	0.754934i
$249$	−7.42595	+	9.05224i	−0.470600	+	0.573662i
$250$	15.2916	+	4.02095i	0.967123	+	0.254307i
$251$	9.92262			0.626311			0.313155	−	0.949702i	$-0.398614\pi$
$251$	9.92262			0.626311			0.313155	+	0.949702i	$0.398614\pi$
$252$	−16.5977	−	5.73735i	−1.04556	−	0.361419i
$253$	−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	$0.971479\pi$
$258$	−4.63206	−	20.1187i	−0.288379	−	1.25254i
$259$	−27.9923			−1.73935
$260$	−0.603601	−	4.70898i	−0.0374338	−	0.292039i
$261$	−2.99522	−	15.0266i	−0.185400	−	0.930120i
$262$	−8.49885	−	6.56176i	−0.525061	−	0.405387i
$263$	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	$0.0929298\pi$
$264$	2.38575	+	0.746557i	0.146833	+	0.0459474i
$265$	−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
$268$	−11.4077	+	19.4894i	−0.696838	+	1.19050i
$269$		−	32.3280i		−	1.97108i	−0.169455	−	0.985538i	$-0.554201\pi$
$269$		−	32.3280i		−	1.97108i	0.169455	−	0.985538i	$-0.445799\pi$
$270$	−15.7233	+	4.77252i	−0.956891	+	0.290446i
$271$	0.306338			0.0186087			0.00930434	−	0.999957i	$-0.497038\pi$
$271$	0.306338			0.0186087			0.00930434	+	0.999957i	$0.497038\pi$
$272$	17.1392	+	4.81227i	1.03922	+	0.291787i
$273$	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
$276$	−5.21250	+	11.3300i	−0.313755	+	0.681989i
$277$	6.97897	+	6.97897i	0.419326	+	0.419326i	0.884971	−	0.465645i	$-0.154178\pi$
$277$	6.97897	+	6.97897i	0.419326	+	0.419326i	−0.465645	+	0.884971i	$0.654178\pi$
$278$	10.0909	+	7.79094i	0.605212	+	0.467270i
$279$	13.4358	−	2.67815i	0.804383	−	0.160337i
$280$	9.35801	−	15.9717i	0.559248	−	0.954494i
$281$		−	15.4596i		−	0.922240i	−0.887338	−	0.461120i	$-0.847448\pi$
$281$		−	15.4596i		−	0.922240i	0.887338	−	0.461120i	$-0.152552\pi$
$282$	−11.2700	+	2.59477i	−0.671121	+	0.154516i
$283$	8.86458	−	8.86458i	0.526945	−	0.526945i	−0.392715	−	0.919660i	$-0.628464\pi$
$283$	8.86458	−	8.86458i	0.526945	−	0.526945i	0.919660	+	0.392715i	$0.128464\pi$
$284$	−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
$288$	16.9485	−	0.864107i	0.998703	−	0.0509180i
$289$			2.80690i			0.165112i
$290$	16.1510	+	0.00697721i	0.948418	+	0.000409716i
$291$	20.6023	+	16.9010i	1.20773	+	0.990754i
$292$	4.58150	−	7.82720i	0.268112	−	0.458053i
$293$	1.49638	+	1.49638i	0.0874192	+	0.0874192i	0.749464	−	0.662045i	$-0.230311\pi$
$293$	1.49638	+	1.49638i	0.0874192	+	0.0874192i	−0.662045	+	0.749464i	$0.730311\pi$
$294$	3.25330	+	2.03560i	0.189736	+	0.118719i
$295$	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
$298$	−11.3713	+	14.7283i	−0.658724	+	0.853186i
$299$		−	3.82192i		−	0.221027i
$300$	−1.68627	−	17.2382i	−0.0973566	−	0.995250i
$301$			24.6688i			1.42189i
$302$	3.08933	+	2.38520i	0.177771	+	0.137253i
$303$	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
$306$	6.02319	+	17.8954i	0.344323	+	1.02301i
$307$	−12.4948	−	12.4948i	−0.713118	−	0.713118i	0.254068	−	0.967186i	$-0.418231\pi$
$307$	−12.4948	−	12.4948i	−0.713118	−	0.713118i	−0.967186	+	0.254068i	$0.918231\pi$
$308$	−2.57791	−	1.50893i	−0.146890	−	0.0859791i
$309$	2.89442	−	3.52830i	0.164658	−	0.200718i
$310$	−0.00623860	+	14.4412i	−0.000354329	+	0.820207i
$311$		−	0.224632i		−	0.0127377i	−0.999980	−	0.00636886i	$-0.997973\pi$
$311$		−	0.224632i		−	0.0127377i	0.999980	−	0.00636886i	$-0.00202728\pi$
$312$	−4.60782	+	2.41136i	−0.260866	+	0.136516i
$313$	−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	$0.546907\pi$
$317$	−20.2257	+	20.2257i	−1.13599	+	1.13599i	−0.989162	+	0.146829i	$0.953093\pi$
$318$	19.4401	−	4.47582i	1.09015	−	0.250992i
$319$		−	2.60618i		−	0.145918i
$320$	−2.60674	+	17.6976i	−0.145721	+	0.989326i
$321$	18.9984	+	15.5852i	1.06039	+	0.869882i
$322$	9.10715	−	11.7957i	0.507522	−	0.657347i
$323$	−18.9196	−	18.9196i	−1.05271	−	1.05271i
$324$	10.8838	+	14.3367i	0.604657	+	0.796486i
$325$	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
$328$	−11.0474	−	4.69221i	−0.609991	−	0.259084i
$329$	13.8189			0.761860
$330$	−2.78150	+	0.273303i	−0.153117	+	0.0150449i
$331$			12.3308i			0.677760i	0.940830	+	0.338880i	$0.110048\pi$
$331$			12.3308i			0.677760i	−0.940830	+	0.338880i	$0.889952\pi$
$332$	−6.82959	+	11.6679i	−0.374822	+	0.640361i
$333$	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
$336$	−19.9672	−	3.53763i	−1.08930	−	0.192993i
$337$	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	$0.115151\pi$
$338$	−10.2614	+	13.2907i	−0.558147	+	0.722918i
$339$	3.57799	+	2.93518i	0.194330	+	0.159417i
$340$	−19.7417	+	2.53051i	−1.07064	+	0.137236i
$341$	2.33029			0.126192
$342$	−22.8470	−	11.3403i	−1.23543	−	0.613215i
$343$	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	−0.888529	−	0.458821i	$-0.848272\pi$
$347$	−8.00457	+	8.00457i	−0.429708	+	0.429708i	0.458821	+	0.888529i	$0.348272\pi$
$348$	−6.13664	−	16.5942i	−0.328959	−	0.889541i
$349$	13.9579			0.747152			0.373576	−	0.927600i	$-0.378132\pi$
$349$	13.9579			0.747152			0.373576	+	0.927600i	$0.378132\pi$
$350$	−2.65794	+	20.5249i	−0.142073	+	1.09710i
$351$	−4.86633	−	2.59735i	−0.259746	−	0.138636i
$352$	2.85593	+	0.419399i	0.152221	+	0.0223541i
$353$	−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	$0.397471\pi$
$354$	−2.41943	−	1.51385i	−0.128591	−	0.0804600i
$355$	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
$358$	12.0254	−	15.5755i	0.635564	−	0.823189i
$359$	−33.8765			−1.78793			−0.893967	−	0.448133i	$-0.852089\pi$
$359$	−33.8765			−1.78793			−0.893967	+	0.448133i	$0.852089\pi$
$360$	−17.0670	+	8.28966i	−0.899508	+	0.436903i
$361$	17.1439			0.902313
$362$	−5.02112	+	6.50340i	−0.263904	+	0.341811i
$363$	−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
$366$	10.2357	+	6.40452i	0.535029	+	0.334770i
$367$	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	$0.119612\pi$
$368$	−3.89289	+	13.8648i	−0.202931	+	0.722752i
$369$	−2.48863	−	12.4851i	−0.129553	−	0.649946i
$370$	−21.3946	+	21.3761i	−1.11225	+	1.11129i
$371$	−23.8368			−1.23754
$372$	14.8375	−	5.48702i	0.769289	−	0.284489i
$373$	−25.8380	+	25.8380i	−1.33784	+	1.33784i	−0.439697	+	0.898146i	$0.644914\pi$
$373$	−25.8380	+	25.8380i	−1.33784	+	1.33784i	−0.898146	+	0.439697i	$0.855086\pi$
$374$	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
$378$	−8.82991	−	19.6121i	−0.454162	−	1.00874i
$379$	−12.2262			−0.628019			−0.314010	−	0.949420i	$-0.601672\pi$
$379$	−12.2262			−0.628019			−0.314010	+	0.949420i	$0.601672\pi$
$380$	16.4401	−	21.2744i	0.843361	−	1.09135i
$381$	1.82564	+	1.49766i	0.0935306	+	0.0767272i
$382$	−11.9662	+	15.4987i	−0.612242	+	0.792982i
$383$	−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	$0.964525\pi$
$384$	19.1719	−	4.05430i	0.978363	−	0.206895i
$385$	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
$388$	26.5555	+	15.5437i	1.34815	+	0.789112i
$389$			6.63941i			0.336632i	0.985733	+	0.168316i	$0.0538328\pi$
$389$			6.63941i			0.336632i	−0.985733	+	0.168316i	$0.946167\pi$
$390$	3.68971	−	4.49381i	0.186836	−	0.227553i
$391$	−16.0228			−0.810309
$392$	4.07870	+	1.73236i	0.206006	+	0.0874975i
$393$	−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
$396$	1.33884	+	2.75341i	0.0672792	+	0.138364i
$397$	14.0596	+	14.0596i	0.705629	+	0.705629i	0.965613	−	0.259984i	$-0.0837172\pi$
$397$	14.0596	+	14.0596i	0.705629	+	0.705629i	−0.259984	+	0.965613i	$0.583717\pi$
$398$	5.11498	−	6.62498i	0.256391	−	0.332080i
$399$	23.5636	+	19.3303i	1.17966	+	0.967725i
$400$	−5.04435	−	19.3534i	−0.252218	−	0.967671i
$401$		−	18.1176i		−	0.904751i	−0.891827	−	0.452376i	$-0.850577\pi$
$401$		−	18.1176i		−	0.904751i	0.891827	−	0.452376i	$-0.149423\pi$
$402$	−26.9528	+	6.20550i	−1.34428	+	0.309502i
$403$	−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
$408$	10.1092	+	19.3176i	0.500482	+	0.956363i
$409$		−	26.3245i		−	1.30166i	−0.759223	−	0.650831i	$-0.774421\pi$
$409$		−	26.3245i		−	1.30166i	0.759223	−	0.650831i	$-0.225579\pi$
$410$	13.4193	+	0.00579713i	0.662732	+	0.000286300i
$411$	−1.10853	+	1.35130i	−0.0546798	+	0.0666548i
$412$	2.66197	−	4.54782i	0.131146	−	0.224055i
$413$	2.41142	+	2.41142i	0.118658	+	0.118658i
$414$	−14.4765	+	4.87247i	−0.711481	+	0.239469i
$415$	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
$418$	−3.43406	−	2.65135i	−0.167965	−	0.129682i
$419$			12.7809i			0.624385i	0.950019	+	0.312193i	$0.101063\pi$
$419$			12.7809i			0.624385i	−0.950019	+	0.312193i	$0.898937\pi$
$420$	22.0958	−	5.07721i	1.07817	−	0.247742i
$421$		−	26.3792i		−	1.28564i	−0.766017	−	0.642821i	$-0.777764\pi$
$421$		−	26.3792i		−	1.28564i	0.766017	−	0.642821i	$-0.222236\pi$
$422$	6.00983	−	7.78398i	0.292554	−	0.378918i
$423$	−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
$426$	−10.5725	−	6.61527i	−0.512240	−	0.320511i
$427$	−10.2018	−	10.2018i	−0.493700	−	0.493700i
$428$	24.4881	+	14.3336i	1.18368	+	0.692841i
$429$	−0.725393	−	0.595072i	−0.0350223	−	0.0287303i
$430$	18.8381	+	18.8544i	0.908456	+	0.909241i
$431$		−	28.6818i		−	1.38155i	−0.723068	−	0.690777i	$-0.757269\pi$
$431$		−	28.6818i		−	1.38155i	0.723068	−	0.690777i	$-0.242731\pi$
$432$	15.0080	+	14.3791i	0.722074	+	0.691816i
$433$	−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
$438$	10.8246	−	2.49221i	0.517219	−	0.119082i
$439$			11.8510i			0.565620i	0.959176	+	0.282810i	$0.0912665\pi$
$439$			11.8510i			0.565620i	−0.959176	+	0.282810i	$0.908733\pi$
$440$	−3.12258	+	0.815323i	−0.148863	+	0.0388690i
$441$	0.918802	+	4.60948i	0.0437525	+	0.219499i
$442$	−5.28864	−	4.08323i	−0.251555	−	0.194219i
$443$	1.66807	+	1.66807i	0.0792526	+	0.0792526i	0.745622	−	0.666369i	$-0.232153\pi$
$443$	1.66807	+	1.66807i	0.0792526	+	0.0792526i	−0.666369	+	0.745622i	$0.732153\pi$
$444$	30.0976	+	13.8467i	1.42837	+	0.657135i
$445$	−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
$448$	−23.4114	−	0.418930i	−1.10609	−	0.0197926i
$449$	34.3414			1.62067			0.810336	−	0.585966i	$-0.199285\pi$
$449$	34.3414			1.62067			0.810336	+	0.585966i	$0.199285\pi$
$450$	13.9466	−	15.9841i	0.657450	−	0.753498i
$451$		−	2.16539i		−	0.101964i
$452$	4.61186	+	2.69946i	0.216924	+	0.126972i
$453$	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
$456$	−28.1085	−	8.79580i	−1.31630	−	0.411901i
$457$	−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	$0.298778\pi$
$458$	−1.22773	−	0.947900i	−0.0573680	−	0.0442925i
$459$	−10.8890	+	20.4014i	−0.508255	+	0.952254i
$460$	−2.04706	−	15.9701i	−0.0954445	−	0.744608i
$461$	−20.6452			−0.961543			−0.480772	−	0.876846i	$-0.659643\pi$
$461$	−20.6452			−0.961543			−0.480772	+	0.876846i	$0.659643\pi$
$462$	−0.820816	−	3.56510i	−0.0381878	−	0.165864i
$463$	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	−0.839488	−	0.543378i	$-0.817145\pi$
$467$	−6.39901	+	6.39901i	−0.296111	+	0.296111i	0.543378	+	0.839488i	$0.317145\pi$
$468$	−6.01994	−	2.08092i	−0.278272	−	0.0961905i
$469$	33.0484			1.52603
$470$	10.5618	−	10.5527i	0.487180	−	0.486759i
$471$	−6.80600	+	8.29652i	−0.313604	+	0.382283i
$472$	−3.03326	−	1.28833i	−0.139617	−	0.0593002i
$473$	3.04110	−	3.04110i	0.139830	−	0.139830i
$474$	−15.1837	−	9.50052i	−0.697412	−	0.436373i
$475$	−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
$478$	13.7921	+	10.6485i	0.630834	+	0.487052i
$479$	−35.9113			−1.64083			−0.820414	−	0.571770i	$-0.806257\pi$
$479$	−35.9113			−1.64083			−0.820414	+	0.571770i	$0.806257\pi$
$480$	−17.9624	+	12.5440i	−0.819869	+	0.572551i
$481$	−10.1527			−0.462923
$482$	−7.87870	−	6.08295i	−0.358865	−	0.277071i
$483$	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
$486$	−3.63418	+	21.7438i	−0.164850	+	0.986319i
$487$	−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	$0.972197\pi$
$488$	12.8326	+	5.45044i	0.580905	+	0.246730i
$489$	0.891726	+	0.731522i	0.0403252	+	0.0330806i
$490$	−4.95440	−	0.00214030i	−0.223817	−	9.66888e-5i
$491$	30.9507			1.39678			0.698392	−	0.715715i	$-0.253899\pi$
$491$	30.9507			1.39678			0.698392	+	0.715715i	$0.253899\pi$
$492$	−5.09873	−	13.7875i	−0.229868	−	0.621590i
$493$	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
$498$	−16.1361	+	3.71511i	−0.723076	+	0.166478i
$499$	19.9194			0.891716			0.445858	−	0.895104i	$-0.352899\pi$
$499$	19.9194			0.891716			0.445858	+	0.895104i	$0.352899\pi$
$500$	13.6422	+	17.7169i	0.610098	+	0.792326i
$501$	0.769562	−	0.938097i	0.0343815	−	0.0419111i
$502$	11.1074	+	8.57573i	0.495746	+	0.382754i
$503$	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	$0.0969593\pi$
$504$	−13.6209	−	20.7671i	−0.606724	−	0.925042i
$505$	−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
$508$	2.35317	+	1.37738i	0.104405	+	0.0611114i
$509$		−	4.85493i		−	0.215191i	−0.994195	−	0.107595i	$-0.965685\pi$
$509$		−	4.85493i		−	0.215191i	0.994195	−	0.107595i	$-0.0343151\pi$
$510$	−18.8396	−	15.4686i	−0.834231	−	0.684960i
$511$	−13.2727			−0.587149
$512$	21.1298	−	8.09503i	0.933816	−	0.357753i
$513$	−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
$516$	12.2027	−	26.5242i	0.537194	−	1.16766i
$517$	−1.70355	−	1.70355i	−0.0749222	−	0.0749222i
$518$	−31.3345	−	24.1926i	−1.37676	−	1.06296i
$519$	−3.61473	+	4.40636i	−0.158669	+	0.193418i
$520$	3.39412	−	5.79290i	0.148842	−	0.254035i
$521$			15.0499i			0.659346i	0.944095	+	0.329673i	$0.106939\pi$
$521$			15.0499i			0.659346i	−0.944095	+	0.329673i	$0.893061\pi$
$522$	9.63401	−	19.4094i	0.421669	−	0.849525i
$523$	15.6997	−	15.6997i	0.686499	−	0.686499i	−0.274957	−	0.961456i	$-0.588664\pi$
$523$	15.6997	−	15.6997i	0.686499	−	0.686499i	0.961456	+	0.274957i	$0.0886637\pi$
$524$	−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
$528$	2.02539	+	2.89761i	0.0881437	+	0.126102i
$529$			10.0383i			0.436449i
$530$	−18.2185	+	18.2028i	−0.791361	+	0.790677i
$531$	−0.683298	−	3.42800i	−0.0296526	−	0.148762i
$532$	30.3725	+	17.7779i	1.31681	+	0.770770i
$533$	3.18541	+	3.18541i	0.137976	+	0.137976i
$534$	−16.4269	+	26.2535i	−0.710862	+	1.13610i
$535$	−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
$538$	27.9399	−	36.1880i	1.20457	−	1.56017i
$539$			0.799460i			0.0344352i
$540$	−21.7254	−	8.24670i	−0.934911	−	0.354882i
$541$			1.45079i			0.0623742i	0.999514	+	0.0311871i	$0.00992877\pi$
$541$			1.45079i			0.0623742i	−0.999514	+	0.0311871i	$0.990071\pi$
$542$	0.342914	+	0.264756i	0.0147294	+	0.0113722i
$543$	−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
$546$	6.45196	+	4.03702i	0.276118	+	0.172768i
$547$	−1.86763	−	1.86763i	−0.0798541	−	0.0798541i	0.666052	−	0.745906i	$-0.267983\pi$
$547$	−1.86763	−	1.86763i	−0.0798541	−	0.0798541i	−0.745906	+	0.666052i	$0.767983\pi$
$548$	−1.01951	+	1.74177i	−0.0435512	+	0.0744045i
$549$	2.89078	+	14.5026i	0.123375	+	0.618955i
$550$	2.85792	−	2.20259i	0.121862	−	0.0939188i
$551$			30.7055i			1.30810i
$552$	−15.6270	+	8.17788i	−0.665128	+	0.348074i
$553$	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	−0.0407789	−	0.999168i	$-0.512984\pi$
$557$	22.6188	−	22.6188i	0.958389	−	0.958389i	0.999168	+	0.0407789i	$0.0129839\pi$
$558$	17.3547	+	8.61415i	0.734682	+	0.364666i
$559$			8.94729i			0.378430i
$560$	24.2791	−	9.79099i	1.02598	−	0.413745i
$561$	−2.49475	+	3.04110i	−0.105328	+	0.128395i
$562$	13.3611	−	17.3054i	0.563604	−	0.729985i
$563$	−26.6638	−	26.6638i	−1.12375	−	1.12375i	−0.991173	−	0.132574i	$-0.957676\pi$
$563$	−26.6638	−	26.6638i	−1.12375	−	1.12375i	−0.132574	−	0.991173i	$-0.542324\pi$
$564$	−14.8582	−	6.83567i	−0.625644	−	0.287833i
$565$	−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
$568$	−13.2549	−	5.62980i	−0.556163	−	0.236221i
$569$	−29.3180			−1.22907			−0.614537	−	0.788888i	$-0.710657\pi$
$569$	−29.3180			−1.22907			−0.614537	+	0.788888i	$0.710657\pi$
$570$	32.7712	−	3.22001i	1.37263	−	0.134871i
$571$		−	28.4036i		−	1.18865i	−0.804224	−	0.594326i	$-0.797419\pi$
$571$		−	28.4036i		−	1.18865i	0.804224	−	0.594326i	$-0.202581\pi$
$572$	−0.934999	−	0.547283i	−0.0390943	−	0.0228831i
$573$	−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
$576$	19.7190	+	13.6807i	0.821625	+	0.570028i
$577$	−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	$0.438692\pi$
$578$	−2.42590	+	3.14204i	−0.100904	+	0.130692i
$579$	−7.10371	+	8.65943i	−0.295220	+	0.359874i
$580$	18.0734	+	13.9665i	0.750455	+	0.579926i
$581$	19.7855			0.820839
$582$	8.45536	+	36.7247i	0.350486	+	1.52229i
$583$	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	−0.436220	−	0.899840i	$-0.643683\pi$
$587$	11.2326	−	11.2326i	0.463619	−	0.463619i	0.899840	+	0.436220i	$0.143683\pi$
$588$	1.88245	+	5.09035i	0.0776309	+	0.209923i
$589$	−27.4550			−1.13127
$590$	3.68451	+	0.00159170i	0.151689	+	6.55295e-5i
$591$	7.30543	+	5.99297i	0.300505	+	0.246518i
$592$	36.8310	+	10.3412i	1.51374	+	0.425022i
$593$	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	$0.248511\pi$
$594$	−1.32920	+	3.50626i	−0.0545378	+	0.143863i
$595$	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
$598$	3.30313	−	4.27825i	0.135075	−	0.174951i
$599$	15.6557			0.639673			0.319837	−	0.947473i	$-0.396372\pi$
$599$	15.6557			0.639673			0.319837	+	0.947473i	$0.396372\pi$
$600$	13.0107	−	20.7538i	0.531160	−	0.847271i
$601$	29.1506			1.18908			0.594540	−	0.804066i	$-0.297334\pi$
$601$	29.1506			1.18908			0.594540	+	0.804066i	$0.297334\pi$
$602$	−21.3203	+	27.6142i	−0.868949	+	1.12547i
$603$	−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
$606$	−8.32841	+	13.3105i	−0.338318	+	0.540700i
$607$	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	$0.0687250\pi$
$608$	−33.6480	−	4.94129i	−1.36461	−	0.200396i
$609$	−16.4217	+	20.0181i	−0.665443	+	0.811176i
$610$	−15.5878	−	0.00673391i	−0.631131	−	0.000272648i
$611$	5.01206			0.202766
$612$	−8.72394	+	25.2377i	−0.352644	+	1.02017i
$613$	−29.5115	+	29.5115i	−1.19196	+	1.19196i	−0.215443	+	0.976516i	$0.569120\pi$
$613$	−29.5115	+	29.5115i	−1.19196	+	1.19196i	−0.976516	+	0.215443i	$0.930880\pi$
$614$	−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	$-0.571560\pi$
$618$	6.28938	−	1.44804i	0.252996	−	0.0582488i
$619$	−12.4498			−0.500402			−0.250201	−	0.968194i	$-0.580497\pi$
$619$	−12.4498			−0.500402			−0.250201	+	0.968194i	$0.580497\pi$
$620$	−12.4880	+	16.1601i	−0.501529	+	0.649006i
$621$	−16.5037	−	8.80867i	−0.662271	−	0.353480i
$622$	0.194141	−	0.251453i	0.00778433	−	0.0100823i
$623$	26.1665	−	26.1665i	1.04834	−	1.04834i
$624$	−7.24203	−	1.28309i	−0.289913	−	0.0513646i
$625$	−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
$628$	−6.25942	+	10.6938i	−0.249778	+	0.426730i
$629$			42.5637i			1.69712i
$630$	23.0869	+	15.4272i	0.919804	+	0.614636i
$631$	43.7481			1.74158			0.870791	−	0.491653i	$-0.163607\pi$
$631$	43.7481			1.74158			0.870791	+	0.491653i	$0.163607\pi$
$632$	−19.0360	−	8.08524i	−0.757212	−	0.321614i
$633$	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
$636$	25.6296	+	11.7911i	1.01628	+	0.467548i
$637$	−1.17605	−	1.17605i	−0.0465969	−	0.0465969i
$638$	2.25242	−	2.91735i	0.0891741	−	0.115499i
$639$	−2.98590	−	14.9798i	−0.118121	−	0.592592i
$640$	−18.2133	+	17.5578i	−0.719945	+	0.694032i
$641$			13.3935i			0.529013i	0.964384	+	0.264506i	$0.0852090\pi$
$641$			13.3935i			0.529013i	−0.964384	+	0.264506i	$0.914791\pi$
$642$	7.79709	+	33.8656i	0.307727	+	1.33657i
$643$	12.4335	−	12.4335i	0.490331	−	0.490331i	−0.418080	−	0.908410i	$-0.637297\pi$
$643$	12.4335	−	12.4335i	0.490331	−	0.490331i	0.908410	+	0.418080i	$0.137297\pi$
$644$	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	$0.746880\pi$
$648$	−0.207341	+	25.4550i	−0.00814512	+	0.999967i
$649$		−	0.594545i		−	0.0233380i
$650$	−0.964026	+	7.44431i	−0.0378122	+	0.291990i
$651$	−17.8990	−	14.6833i	−0.701517	−	0.575485i
$652$	1.14939	+	0.672775i	0.0450138	+	0.0263479i
$653$	10.5497	+	10.5497i	0.412841	+	0.412841i	0.882727	−	0.469886i	$-0.155705\pi$
$653$	10.5497	+	10.5497i	0.412841	+	0.412841i	−0.469886	+	0.882727i	$0.655705\pi$
$654$	16.4291	−	26.2571i	0.642431	−	1.02673i
$655$	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
$658$	15.4688	+	11.9431i	0.603038	+	0.465591i
$659$			30.8600i			1.20213i	0.799199	+	0.601067i	$0.205258\pi$
$659$			30.8600i			1.20213i	−0.799199	+	0.601067i	$0.794742\pi$
$660$	−3.34982	−	2.09801i	−0.130391	−	0.0816649i
$661$		−	44.1992i		−	1.71915i	−0.511009	−	0.859575i	$-0.670728\pi$
$661$		−	44.1992i		−	1.71915i	0.511009	−	0.859575i	$-0.329272\pi$
$662$	−10.6570	+	13.8030i	−0.414196	+	0.536470i
$663$	−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
$666$	12.9434	+	38.4560i	0.501547	+	1.49014i
$667$	13.0021	+	13.0021i	0.503444	+	0.503444i
$668$	0.707760	−	1.20916i	0.0273841	−	0.0467840i
$669$	25.9783	−	31.6675i	1.00438	−	1.22434i
$670$	25.2590	−	25.2372i	0.975840	−	0.974997i
$671$			2.51530i			0.0971021i
$672$	−19.2938	−	21.2169i	−0.744274	−	0.818458i
$673$	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	−0.104220	−	0.994554i	$-0.533235\pi$
$677$	23.1658	−	23.1658i	0.890334	−	0.890334i	0.994554	+	0.104220i	$0.0332347\pi$
$678$	1.46844	+	6.37795i	0.0563949	+	0.244944i
$679$		−	45.0304i		−	1.72811i
$680$	−24.2858	−	14.2293i	−0.931320	−	0.545670i
$681$	−23.6371	−	19.3905i	−0.905775	−	0.743047i
$682$	2.60852	+	2.01398i	0.0998855	+	0.0771192i
$683$	14.8655	+	14.8655i	0.568814	+	0.568814i	0.931796	−	0.362982i	$-0.118241\pi$
$683$	14.8655	+	14.8655i	0.568814	+	0.568814i	−0.362982	+	0.931796i	$0.618241\pi$
$684$	−15.7740	−	32.4402i	−0.603132	−	1.24038i
$685$	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
$688$	9.11344	−	32.4581i	0.347447	−	1.23745i
$689$	−8.64552			−0.329368
$690$	12.5133	−	15.2403i	0.476374	−	0.580189i
$691$			47.2699i			1.79823i	0.437710	+	0.899116i	$0.355790\pi$
$691$			47.2699i			1.79823i	−0.437710	+	0.899116i	$0.644210\pi$
$692$	−3.32444	+	5.67960i	−0.126376	+	0.215906i
$693$	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
$696$	7.47234	−	23.8792i	0.283238	−	0.905137i
$697$	13.3544	−	13.3544i	0.505833	−	0.505833i
$698$	15.6245	+	12.0633i	0.591396	+	0.456603i
$699$	−13.2202	−	10.8451i	−0.500035	−	0.410201i
$700$	−20.7142	+	20.6784i	−0.782921	+	0.781570i
$701$	7.65973			0.289304			0.144652	−	0.989483i	$-0.453794\pi$
$701$	7.65973			0.289304			0.144652	+	0.989483i	$0.453794\pi$
$702$	−3.20258	−	7.11325i	−0.120874	−	0.268473i
$703$	−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
$708$	−1.39995	−	3.78562i	−0.0526133	−	0.142272i
$709$	43.9829			1.65181			0.825906	−	0.563808i	$-0.190664\pi$
$709$	43.9829			1.65181			0.825906	+	0.563808i	$0.190664\pi$
$710$	16.1007	+	0.00695550i	0.604250	+	0.000261035i
$711$	−4.28821	−	21.5132i	−0.160820	−	0.806810i
$712$	−13.9798	+	32.9143i	−0.523915	+	1.23351i
$713$	−11.6257	+	11.6257i	−0.435387	+	0.435387i
$714$	16.9246	−	27.0488i	0.633386	−	1.01228i
$715$	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
$718$	−37.9213	−	29.2781i	−1.41521	−	1.09265i
$719$	14.6227			0.545333			0.272666	−	0.962109i	$-0.412094\pi$
$719$	14.6227			0.545333			0.272666	+	0.962109i	$0.412094\pi$
$720$	−26.2692	−	5.47088i	−0.978994	−	0.203888i
$721$	−7.71179			−0.287202
$722$	19.1909	+	14.8168i	0.714212	+	0.551425i
$723$	−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
$726$	13.9538	−	22.3009i	0.517872	−	0.827663i
$727$	−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	$0.446893\pi$
$728$	8.08889	+	3.43563i	0.299794	+	0.127333i
$729$	−22.4316	+	15.0274i	−0.830802	+	0.556569i
$730$	−10.1444	+	10.1356i	−0.375459	+	0.375135i
$731$	37.5102			1.38736
$732$	5.92266	+	16.0155i	0.218908	+	0.591951i
$733$	−8.64610	+	8.64610i	−0.319351	+	0.319351i	−0.848518	−	0.529167i	$-0.822505\pi$
$733$	−8.64610	+	8.64610i	−0.319351	+	0.319351i	0.529167	+	0.848518i	$0.322505\pi$
$734$	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
$738$	8.00457	−	16.1266i	0.294652	−	0.593628i
$739$	29.8509			1.09808			0.549041	−	0.835796i	$-0.314993\pi$
$739$	29.8509			1.09808			0.549041	+	0.835796i	$0.314993\pi$
$740$	−42.4235	+	5.43788i	−1.55952	+	0.199901i
$741$	8.54646	+	7.01103i	0.313962	+	0.257557i
$742$	−26.6828	−	20.6012i	−0.979558	−	0.756293i
$743$	−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	$0.306356\pi$
$744$	21.3513	+	6.68132i	0.782777	+	0.244949i
$745$	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
$748$	−2.29440	+	3.91984i	−0.0838916	+	0.143324i
$749$		−	41.5247i		−	1.51728i
$750$	−4.32948	+	27.0417i	−0.158090	+	0.987425i
$751$	22.5357			0.822339			0.411170	−	0.911559i	$-0.365120\pi$
$751$	22.5357			0.822339			0.411170	+	0.911559i	$0.365120\pi$
$752$	−18.1823	−	5.10513i	−0.663039	−	0.186165i
$753$	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
$756$	7.06580	−	29.5851i	0.256981	−	1.07600i
$757$	−33.9790	−	33.9790i	−1.23499	−	1.23499i	−0.962025	−	0.272963i	$-0.911996\pi$
$757$	−33.9790	−	33.9790i	−1.23499	−	1.23499i	−0.272963	−	0.962025i	$-0.588004\pi$
$758$	−13.6860	−	10.5666i	−0.497099	−	0.383798i
$759$	−2.46010	−	2.01813i	−0.0892961	−	0.0732535i
$760$	36.7897	−	9.60599i	1.33450	−	0.348446i
$761$		−	34.4290i		−	1.24805i	−0.781404	−	0.624025i	$-0.785496\pi$
$761$		−	34.4290i		−	1.24805i	0.781404	−	0.624025i	$-0.214504\pi$
$762$	0.749259	+	3.25431i	0.0271428	+	0.117891i
$763$	−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
$768$	24.9650	+	12.0312i	0.900847	+	0.434137i
$769$			14.8941i			0.537094i	0.963267	+	0.268547i	$0.0865434\pi$
$769$			14.8941i			0.537094i	−0.963267	+	0.268547i	$0.913457\pi$
$770$	3.33818	+	3.34107i	0.120300	+	0.120404i
$771$	22.5770	−	27.5214i	0.813091	−	0.991159i
$772$	−6.53323	+	11.1616i	−0.235136	+	0.401715i
$773$	−7.32969	−	7.32969i	−0.263631	−	0.263631i	0.562897	−	0.826527i	$-0.309687\pi$
$773$	−7.32969	−	7.32969i	−0.263631	−	0.263631i	−0.826527	+	0.562897i	$0.809687\pi$
$774$	33.8902	−	11.4067i	1.21816	−	0.410005i
$775$	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
$778$	−5.73818	+	7.43215i	−0.205724	+	0.266455i
$779$			25.5122i			0.914069i
$780$	8.01408	−	1.84149i	0.286950	−	0.0659358i
$781$		−	2.59807i		−	0.0929663i
$782$	−17.9359	−	13.8479i	−0.641387	−	0.495199i
$783$	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
$786$	9.86456	−	15.7655i	0.351857	−	0.562338i
$787$	−4.66068	−	4.66068i	−0.166135	−	0.166135i	0.619143	−	0.785278i	$-0.287480\pi$
$787$	−4.66068	−	4.66068i	−0.166135	−	0.166135i	−0.785278	+	0.619143i	$0.787480\pi$
$788$	9.41637	+	5.51168i	0.335444	+	0.196346i
$789$	20.5731	+	16.8770i	0.732421	+	0.600837i
$790$	23.1231	+	0.00998914i	0.822682	+	0.000355398i
$791$		−	7.82040i		−	0.278061i
$792$	−0.880969	+	4.23927i	−0.0313039	+	0.150636i
$793$	−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	−0.999920	−	0.0126440i	$-0.995975\pi$
$797$	−27.8720	+	27.8720i	−0.987276	+	0.987276i	0.0126440	+	0.999920i	$0.495975\pi$
$798$	9.67071	+	42.0034i	0.342339	+	1.48691i
$799$		−	21.0123i		−	0.743362i
$800$	11.0797	−	26.0238i	0.391728	−	0.920081i
$801$	−37.1975	+	7.41454i	−1.31431	+	0.261980i
$802$	15.6584	−	20.2809i	0.552916	−	0.716142i
$803$	1.63622	+	1.63622i	0.0577410	+	0.0577410i
$804$	−35.5340	−	16.3478i	−1.25319	−	0.576542i
$805$	−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
$808$	−7.08773	+	16.6875i	−0.249346	+	0.587063i
$809$	18.8285			0.661975			0.330988	−	0.943635i	$-0.392618\pi$
$809$	18.8285			0.661975			0.330988	+	0.943635i	$0.392618\pi$
$810$	−10.9011	−	26.2901i	−0.383024	−	0.923738i
$811$			37.4113i			1.31369i	0.754026	+	0.656845i	$0.228109\pi$
$811$			37.4113i			1.31369i	−0.754026	+	0.656845i	$0.771891\pi$
$812$	−15.1030	+	25.8025i	−0.530010	+	0.905489i
$813$	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
$816$	−5.37914	+	30.3611i	−0.188308	+	1.06285i
$817$	−35.8297	+	35.8297i	−1.25352	+	1.25352i
$818$	22.7512	−	29.4676i	0.795477	−	1.03031i
$819$	1.82217	+	9.14153i	0.0636717	+	0.319431i
$820$	15.0165	+	11.6043i	0.524400	+	0.405238i
$821$	14.3129			0.499523			0.249761	−	0.968307i	$-0.419648\pi$
$821$	14.3129			0.499523			0.249761	+	0.968307i	$0.419648\pi$
$822$	−2.40877	+	0.554585i	−0.0840153	+	0.0193434i
$823$	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	−0.749170	−	0.662377i	$-0.769548\pi$
$827$	−2.49596	+	2.49596i	−0.0867932	+	0.0867932i	0.662377	+	0.749170i	$0.269548\pi$
$828$	−20.4161	−	7.05724i	−0.709507	−	0.245256i
$829$	−49.1212			−1.70605			−0.853026	−	0.521869i	$-0.825235\pi$
$829$	−49.1212			−1.70605			−0.853026	+	0.521869i	$0.825235\pi$
$830$	15.1221	−	15.1090i	0.524895	−	0.524441i
$831$	−10.8423	+	13.2167i	−0.376114	+	0.458483i
$832$	−8.49125	−	0.151945i	−0.294381	−	0.00526773i
$833$	−4.93043	+	4.93043i	−0.170829	+	0.170829i
$834$	−11.7124	+	18.7188i	−0.405569	+	0.648179i
$835$	−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
$838$	−11.0460	+	14.3069i	−0.381577	+	0.494223i
$839$	26.9749			0.931277			0.465638	−	0.884975i	$-0.345825\pi$
$839$	26.9749			0.931277			0.465638	+	0.884975i	$0.345825\pi$
$840$	29.1221	+	13.4131i	1.00481	+	0.462797i
$841$	2.91458			0.100503
$842$	22.7985	−	29.5288i	0.785687	−	1.01763i
$843$	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
$846$	−6.38975	−	18.9845i	−0.219684	−	0.652700i
$847$	−22.2270	+	22.2270i	−0.763729	+	0.763729i
$848$	31.3634	+	8.80606i	1.07702	+	0.302401i
$849$	16.7877	+	13.7717i	0.576151	+	0.472642i
$850$	31.2092	+	4.04153i	1.07047	+	0.138623i
$851$	−34.4319			−1.18031
$852$	−6.11755	−	16.5425i	−0.209584	−	0.566738i
$853$	16.4190	−	16.4190i	0.562174	−	0.562174i	−0.367750	−	0.929925i	$-0.619872\pi$
$853$	16.4190	−	16.4190i	0.562174	−	0.562174i	0.929925	+	0.367750i	$0.119872\pi$
$854$	−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	$0.548767\pi$
$858$	−0.297707	−	1.29305i	−0.0101636	−	0.0441441i
$859$	1.68121			0.0573622			0.0286811	−	0.999589i	$-0.490869\pi$
$859$	1.68121			0.0573622			0.0286811	+	0.999589i	$0.490869\pi$
$860$	4.79225	+	37.3867i	0.163415	+	1.27488i
$861$	−13.6443	+	16.6324i	−0.464995	+	0.566830i
$862$	24.7886	−	32.1064i	0.844302	−	1.09355i
$863$	−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	$0.437626\pi$
$864$	4.37266	+	29.0668i	0.148761	+	0.988873i
$865$	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
$868$	−23.0710	−	13.5042i	−0.783081	−	0.458361i
$869$		−	3.73122i		−	0.126573i
$870$	2.73551	+	27.8402i	0.0927425	+	0.943873i
$871$	11.9866			0.406149
$872$	13.9817	−	32.9188i	0.473481	−	1.11477i
$873$	−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
$876$	14.2710	+	6.56549i	0.482171	+	0.221827i
$877$	−14.2900	−	14.2900i	−0.482539	−	0.482539i	0.423403	−	0.905942i	$-0.360836\pi$
$877$	−14.2900	−	14.2900i	−0.482539	−	0.482539i	−0.905942	+	0.423403i	$0.860836\pi$
$878$	−10.2424	+	13.2660i	−0.345664	+	0.447707i
$879$	−2.32471	+	2.83382i	−0.0784105	+	0.0955825i
$880$	−4.20007	−	1.78605i	−0.141584	−	0.0602078i
$881$			45.2886i			1.52581i	0.646509	+	0.762906i	$0.276228\pi$
$881$			45.2886i			1.52581i	−0.646509	+	0.762906i	$0.723772\pi$
$882$	−2.95529	+	5.95393i	−0.0995096	+	0.200479i
$883$	3.68252	−	3.68252i	0.123927	−	0.123927i	−0.642423	−	0.766350i	$-0.722071\pi$
$883$	3.68252	−	3.68252i	0.123927	−	0.123927i	0.766350	+	0.642423i	$0.222071\pi$
$884$	−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	$0.863891\pi$
$888$	21.7241	+	41.5121i	0.729012	+	1.39306i
$889$		−	3.99030i		−	0.133830i
$890$	0.0172717	−	39.9810i	0.000578950	−	1.34017i
$891$	−4.24150	+	1.76087i	−0.142095	+	0.0589912i
$892$	23.8920	−	40.8180i	0.799964	−	1.36669i
$893$	20.0710	+	20.0710i	0.671649	+	0.671649i
$894$	−27.3212	−	17.0950i	−0.913758	−	0.571742i
$895$	−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
$898$	38.4417	+	29.6799i	1.28282	+	0.990432i
$899$		−	23.3240i		−	0.777899i
$900$	29.4263	−	5.83907i	0.980876	−	0.194636i
$901$			36.2450i			1.20750i
$902$	1.87146	−	2.42393i	0.0623127	−	0.0807080i
$903$	−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
$906$	−3.58577	+	5.73077i	−0.119129	+	0.190392i
$907$	−8.08868	−	8.08868i	−0.268580	−	0.268580i	0.559948	−	0.828528i	$-0.310821\pi$
$907$	−8.08868	−	8.08868i	−0.268580	−	0.268580i	−0.828528	+	0.559948i	$0.810821\pi$
$908$	−30.4671	−	17.8333i	−1.01109	−	0.591820i
$909$	−18.8591	+	3.75915i	−0.625516	+	0.124683i
$910$	−9.82558	−	0.00424464i	−0.325715	−	0.000140709i
$911$			38.7011i			1.28222i	0.767448	+	0.641112i	$0.221527\pi$
$911$			38.7011i			1.28222i	−0.767448	+	0.641112i	$0.778473\pi$
$912$	−23.8628	−	34.1391i	−0.790175	−	1.13046i
$913$	−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
$918$	−29.8212	+	13.4263i	−0.984248	+	0.443135i
$919$			39.9611i			1.31819i	0.752058	+	0.659097i	$0.229061\pi$
$919$			39.9611i			1.31819i	−0.752058	+	0.659097i	$0.770939\pi$
$920$	11.5108	−	19.6461i	0.379501	−	0.647711i
$921$	19.4115	−	23.6626i	0.639630	−	0.779710i
$922$	−23.1102	−	17.8428i	−0.761094	−	0.587623i
$923$	3.82192	+	3.82192i	0.125800	+	0.125800i
$924$	2.16236	−	4.70017i	0.0711364	−	0.154624i
$925$	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
$928$	4.19779	−	28.5852i	0.137799	−	0.938354i
$929$	−0.568113			−0.0186392			−0.00931959	−	0.999957i	$-0.502967\pi$
$929$	−0.568113			−0.0186392			−0.00931959	+	0.999957i	$0.502967\pi$
$930$	−24.8931	+	2.44593i	−0.816276	+	0.0802052i
$931$		−	9.41909i		−	0.308698i
$932$	−17.0403	−	9.97418i	−0.558173	−	0.326715i
$933$	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
$936$	−4.94026	−	7.53218i	−0.161477	−	0.246197i
$937$	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	$0.111371\pi$
$938$	36.9944	+	28.5624i	1.20791	+	0.932597i
$939$	18.7023	−	22.7981i	0.610326	−	0.743988i
$940$	20.9431	−	2.68451i	0.683090	−	0.0875590i
$941$	−22.3971			−0.730125			−0.365063	−	0.930983i	$-0.618952\pi$
$941$	−22.3971			−0.730125			−0.365063	+	0.930983i	$0.618952\pi$
$942$	−14.7890	+	3.40496i	−0.481851	+	0.110940i
$943$	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	−0.915066	−	0.403305i	$-0.867861\pi$
$947$	−15.7486	+	15.7486i	−0.511761	+	0.511761i	0.403305	+	0.915066i	$0.367861\pi$
$948$	−8.78572	−	23.7576i	−0.285347	−	0.771610i
$949$	−4.81396			−0.156268
$950$	−33.6715	+	25.9505i	−1.09245	+	0.841946i
$951$	−38.3034	−	31.4219i	−1.24207	−	1.01893i
$952$	14.4033	−	33.9114i	0.466815	−	1.09908i
$953$	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	$-0.0268396\pi$
$954$	11.0220	+	32.7471i	0.356849	+	1.06023i
$955$	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
$958$	−40.1990	−	31.0367i	−1.29877	−	1.00275i
$959$	2.95353			0.0953746
$960$	−30.9484	−	1.48254i	−0.998855	−	0.0478487i
$961$	−10.1451			−0.327260
$962$	−11.3649	−	8.77458i	−0.366420	−	0.282904i
$963$	−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
$966$	21.8812	+	13.6912i	0.704016	+	0.440506i
$967$	−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	$0.308332\pi$
$968$	11.8751	−	27.9589i	0.381679	−	0.898632i
$969$	29.3927	−	35.8297i	0.944229	−	1.15102i
$970$	−34.3872	−	34.4169i	−1.10411	−	1.10506i
$971$	−43.4981			−1.39592			−0.697961	−	0.716136i	$-0.745909\pi$
$971$	−43.4981			−1.39592			−0.697961	+	0.716136i	$0.745909\pi$
$972$	−22.8604	+	21.1991i	−0.733248	+	0.679962i
$973$	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	$0.394339\pi$
$978$	0.365972	+	1.58955i	0.0117025	+	0.0508282i
$979$	−6.45147			−0.206190
$980$	−5.54410	−	4.28429i	−0.177100	−	0.136857i
$981$	37.2026	−	7.41555i	1.18779	−	0.236760i
$982$	34.6462	+	26.7495i	1.10560	+	0.853609i
$983$	−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	$0.316095\pi$
$984$	6.20851	−	19.8404i	0.197920	−	0.632488i
$985$	−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
$988$	11.0160	+	6.44799i	0.350465	+	0.205138i
$989$			30.3439i			0.964879i
$990$	−0.944264	−	4.74792i	−0.0300107	−	0.150899i
$991$	−23.1823			−0.736409			−0.368205	−	0.929745i	$-0.620027\pi$
$991$	−23.1823			−0.736409			−0.368205	+	0.929745i	$0.620027\pi$
$992$	25.5591	+	3.75342i	0.811503	+	0.119171i
$993$	−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
$996$	−21.2735	−	9.78710i	−0.674078	−	0.310116i
$997$	−3.70273	−	3.70273i	−0.117267	−	0.117267i	0.646038	−	0.763305i	$-0.276425\pi$
$997$	−3.70273	−	3.70273i	−0.117267	−	0.117267i	−0.763305	+	0.646038i	$0.776425\pi$
$998$	22.2978	+	17.2156i	0.705824	+	0.544949i
$999$	−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.53.13	yes	32
3.2	odd	2	inner	120.2.w.c.53.4	✓	32
4.3	odd	2		480.2.bi.c.113.8		32
5.2	odd	4	inner	120.2.w.c.77.5	yes	32
5.3	odd	4		600.2.w.j.557.12		32
5.4	even	2		600.2.w.j.293.4		32
8.3	odd	2		480.2.bi.c.113.9		32
8.5	even	2	inner	120.2.w.c.53.12	yes	32
12.11	even	2		480.2.bi.c.113.16		32
15.2	even	4	inner	120.2.w.c.77.12	yes	32
15.8	even	4		600.2.w.j.557.5		32
15.14	odd	2		600.2.w.j.293.13		32
20.7	even	4		480.2.bi.c.17.1		32
24.5	odd	2	inner	120.2.w.c.53.5	yes	32
24.11	even	2		480.2.bi.c.113.1		32
40.13	odd	4		600.2.w.j.557.13		32
40.27	even	4		480.2.bi.c.17.16		32
40.29	even	2		600.2.w.j.293.5		32
40.37	odd	4	inner	120.2.w.c.77.4	yes	32
60.47	odd	4		480.2.bi.c.17.9		32
120.29	odd	2		600.2.w.j.293.12		32
120.53	even	4		600.2.w.j.557.4		32
120.77	even	4	inner	120.2.w.c.77.13	yes	32
120.107	odd	4		480.2.bi.c.17.8		32

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

\(f(q)\)	\(=\)	\(q+(1.11940 + 0.864261i) q^{2} +(0.170116 + 1.72368i) q^{3} +(0.506107 + 1.93490i) q^{4} +(-1.36575 - 1.77052i) q^{5} +(-1.29928 + 2.07651i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(-2.94212 + 0.586449i) q^{9} +O(q^{10})\)	\(q+(1.11940 + 0.864261i) q^{2} +(0.170116 + 1.72368i) q^{3} +(0.506107 + 1.93490i) q^{4} +(-1.36575 - 1.77052i) q^{5} +(-1.29928 + 2.07651i) q^{6} +(2.06963 - 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(-2.94212 + 0.586449i) q^{9} +(0.00136610 - 3.16228i) q^{10} -0.510276 q^{11} +(-3.24905 + 1.20152i) 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} +(-3.80025 - 1.88629i) q^{18} +6.01198 q^{19} +(2.73456 - 3.53867i) q^{20} +(3.91945 + 3.21529i) q^{21} +(-0.571203 - 0.441012i) q^{22} +(2.54575 - 2.54575i) q^{23} +(-4.67541 - 1.46305i) q^{24} +(-1.26945 + 4.83617i) q^{25} +(1.48903 - 0.191519i) q^{26} +(-1.51135 - 4.97150i) q^{27} +(5.05199 + 2.95708i) q^{28} +5.10739i q^{29} +(5.45098 - 0.535599i) q^{30} -4.56672 q^{31} +(-5.59683 - 0.821906i) q^{32} +(-0.0868061 - 0.879551i) q^{33} +(-0.802913 - 6.24253i) q^{34} +(-6.49090 - 0.837710i) q^{35} +(-2.62375 - 5.39592i) q^{36} +(-6.76263 - 6.76263i) q^{37} +(6.72981 + 5.19592i) q^{38} +(1.42157 + 1.16618i) q^{39} +(6.11940 - 1.59781i) q^{40} +4.24355i q^{41} +(1.60857 + 6.98662i) 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} +(-3.96920 - 5.67851i) q^{48} -1.56672i q^{49} +(-5.60073 + 4.31647i) q^{50} +(4.88902 - 5.95972i) q^{51} +(1.83234 + 1.07252i) q^{52} +(-5.75871 - 5.75871i) q^{53} +(2.60487 - 6.87129i) q^{54} +(0.696910 + 0.903452i) q^{55} +(3.09950 + 7.67638i) q^{56} +(1.02273 + 10.3627i) q^{57} +(-4.41411 + 5.71720i) q^{58} +1.16514i q^{59} +(6.56471 + 4.11151i) q^{60} -4.92929i q^{61} +(-5.11198 - 3.94684i) q^{62} +(-4.87536 + 7.30283i) q^{63} +(-5.55474 - 5.75716i) q^{64} +(-2.35423 - 0.303835i) q^{65} +(0.662991 - 1.05959i) q^{66} +(7.98415 + 7.98415i) q^{67} +(4.49639 - 7.68180i) q^{68} +(4.82112 + 3.95497i) q^{69} +(-6.54191 - 6.54756i) q^{70} +5.09150i q^{71} +(1.72645 - 8.30779i) 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} +(0.583424 + 2.53402i) q^{78} +7.31215i q^{79} +(8.23097 + 3.50017i) q^{80} +(8.31215 - 3.45081i) q^{81} +(-3.66754 + 4.75023i) q^{82} +(4.77995 + 4.77995i) q^{83} +(-4.23762 + 9.21104i) q^{84} +(-1.27378 + 9.86975i) q^{85} +(-11.8220 + 1.52055i) q^{86} +(-8.80349 + 0.868848i) q^{87} +(0.564226 - 1.32842i) q^{88} +12.6431 q^{89} +(1.85050 + 9.30460i) q^{90} -3.10712i q^{91} +(6.21420 + 3.63736i) q^{92} +(-0.776871 - 7.87155i) q^{93} +(0.851777 + 6.62243i) q^{94} +(-8.21087 - 10.6443i) q^{95} +(0.464592 - 9.78694i) q^{96} +(10.8789 - 10.8789i) q^{97} +(1.35405 - 1.75378i) 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

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