LMFDB - Embedded newform 600.2.w.j.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, 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("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			557.4
Character	$\chi$	$=$	600.557
Dual form			600.2.w.j.293.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11940 + 0.864261i) q^{2} +(-0.170116 + 1.72368i) q^{3} +(0.506107 - 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 - 2.06963i) q^{7} +(1.10573 + 2.60334i) q^{8} +(-2.94212 - 0.586449i) q^{9} +O(q^{10})$	\(q+(-1.11940 + 0.864261i) q^{2} +(-0.170116 + 1.72368i) q^{3} +(0.506107 - 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 - 2.06963i) q^{7} +(1.10573 + 2.60334i) q^{8} +(-2.94212 - 0.586449i) q^{9} -0.510276 q^{11} +(3.24905 + 1.20152i) q^{12} +(-0.750647 - 0.750647i) q^{13} +(4.10544 + 0.528041i) q^{14} +(-3.48771 - 1.95854i) q^{16} +(3.14698 - 3.14698i) q^{17} +(3.80025 - 1.88629i) q^{18} +6.01198 q^{19} +(3.91945 - 3.21529i) q^{21} +(0.571203 - 0.441012i) q^{22} +(-2.54575 - 2.54575i) q^{23} +(-4.67541 + 1.46305i) q^{24} +(1.48903 + 0.191519i) q^{26} +(1.51135 - 4.97150i) q^{27} +(-5.05199 + 2.95708i) q^{28} -5.10739i q^{29} -4.56672 q^{31} +(5.59683 - 0.821906i) q^{32} +(0.0868061 - 0.879551i) q^{33} +(-0.802913 + 6.24253i) q^{34} +(-2.62375 + 5.39592i) q^{36} +(6.76263 - 6.76263i) q^{37} +(-6.72981 + 5.19592i) q^{38} +(1.42157 - 1.16618i) q^{39} -4.24355i q^{41} +(-1.60857 + 6.98662i) q^{42} +(5.95972 + 5.95972i) q^{43} +(-0.258254 + 0.987336i) q^{44} +(5.04990 + 0.649518i) q^{46} +(-3.33849 + 3.33849i) q^{47} +(3.96920 - 5.67851i) q^{48} +1.56672i q^{49} +(4.88902 + 5.95972i) q^{51} +(-1.83234 + 1.07252i) q^{52} +(5.75871 - 5.75871i) q^{53} +(2.60487 + 6.87129i) q^{54} +(3.09950 - 7.67638i) q^{56} +(-1.02273 + 10.3627i) q^{57} +(4.41411 + 5.71720i) q^{58} -1.16514i q^{59} +4.92929i q^{61} +(5.11198 - 3.94684i) q^{62} +(4.87536 + 7.30283i) q^{63} +(-5.55474 + 5.75716i) q^{64} +(0.662991 + 1.05959i) q^{66} +(-7.98415 + 7.98415i) q^{67} +(-4.49639 - 7.68180i) q^{68} +(4.82112 - 3.95497i) q^{69} -5.09150i q^{71} +(-1.72645 - 8.30779i) q^{72} +(3.20654 - 3.20654i) q^{73} +(-1.72540 + 13.4148i) q^{74} +(3.04271 - 11.6326i) q^{76} +(1.05608 + 1.05608i) q^{77} +(-0.583424 + 2.53402i) q^{78} -7.31215i q^{79} +(8.31215 + 3.45081i) q^{81} +(3.66754 + 4.75023i) q^{82} +(-4.77995 + 4.77995i) q^{83} +(-4.23762 - 9.21104i) q^{84} +(-11.8220 - 1.52055i) q^{86} +(8.80349 + 0.868848i) q^{87} +(-0.564226 - 1.32842i) q^{88} +12.6431 q^{89} +3.10712i q^{91} +(-6.21420 + 3.63736i) q^{92} +(0.776871 - 7.87155i) q^{93} +(0.851777 - 6.62243i) q^{94} +(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} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$5$		0			0
$5$		0			0
$6$	−1.29928	−	2.07651i	−0.530428	−	0.847730i
$7$	−2.06963	−	2.06963i	−0.782246	−	0.782246i	0.197964	−	0.980209i	$-0.436567\pi$
$7$	−2.06963	−	2.06963i	−0.782246	−	0.782246i	−0.980209	+	0.197964i	$0.936567\pi$
$8$	1.10573	+	2.60334i	0.390933	+	0.920419i
$9$	−2.94212	−	0.586449i	−0.980707	−	0.195483i
$10$		0			0
$11$	−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	$-0.297031\pi$
$13$	−0.750647	−	0.750647i	−0.208192	−	0.208192i	−0.803499	+	0.595307i	$0.797031\pi$
$14$	4.10544	+	0.528041i	1.09722	+	0.141125i
$15$		0			0
$16$	−3.48771	−	1.95854i	−0.871928	−	0.489635i
$17$	3.14698	−	3.14698i	0.763254	−	0.763254i	−0.213656	−	0.976909i	$-0.568537\pi$
$17$	3.14698	−	3.14698i	0.763254	−	0.763254i	0.976909	+	0.213656i	$0.0685370\pi$
$18$	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	$0.257777\pi$
$20$		0			0
$21$	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	$-0.372478\pi$
$23$	−2.54575	−	2.54575i	−0.530825	−	0.530825i	−0.920818	+	0.389993i	$0.872478\pi$
$24$	−4.67541	+	1.46305i	−0.954365	+	0.298643i
$25$		0			0
$26$	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	$-0.842734\pi$
$29$		−	5.10739i		−	0.948418i	0.880412	−	0.474209i	$-0.157266\pi$
$30$		0			0
$31$	−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
$35$		0			0
$36$	−2.62375	+	5.39592i	−0.437292	+	0.899320i
$37$	6.76263	−	6.76263i	1.11177	−	1.11177i	0.118858	−	0.992911i	$-0.462077\pi$
$37$	6.76263	−	6.76263i	1.11177	−	1.11177i	0.992911	−	0.118858i	$-0.0379234\pi$
$38$	−6.72981	+	5.19592i	−1.09172	+	0.842890i
$39$	1.42157	−	1.16618i	0.227633	−	0.186738i
$40$		0			0
$41$		−	4.24355i		−	0.662732i	−0.943502	−	0.331366i	$-0.892491\pi$
$41$		−	4.24355i		−	0.662732i	0.943502	−	0.331366i	$-0.107509\pi$
$42$	−1.60857	+	6.98662i	−0.248208	+	1.07806i
$43$	5.95972	+	5.95972i	0.908848	+	0.908848i	0.996179	−	0.0873310i	$-0.0278338\pi$
$43$	5.95972	+	5.95972i	0.908848	+	0.908848i	−0.0873310	+	0.996179i	$0.527834\pi$
$44$	−0.258254	+	0.987336i	−0.0389333	+	0.148846i
$45$		0			0
$46$	5.04990	+	0.649518i	0.744567	+	0.0957661i
$47$	−3.33849	+	3.33849i	−0.486969	+	0.486969i	−0.907349	−	0.420379i	$-0.861897\pi$
$47$	−3.33849	+	3.33849i	−0.486969	+	0.486969i	0.420379	+	0.907349i	$0.361897\pi$
$48$	3.96920	−	5.67851i	0.572905	−	0.819622i
$49$			1.56672i			0.223817i
$50$		0			0
$51$	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	$-0.561057\pi$
$53$	5.75871	−	5.75871i	0.791019	−	0.791019i	0.981660	+	0.190641i	$0.0610565\pi$
$54$	2.60487	+	6.87129i	0.354478	+	0.935064i
$55$		0			0
$56$	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	$-0.975835\pi$
$59$		−	1.16514i		−	0.151689i	0.997120	−	0.0758444i	$-0.0241652\pi$
$60$		0			0
$61$			4.92929i			0.631131i	0.948904	+	0.315565i	$0.102194\pi$
$61$			4.92929i			0.631131i	−0.948904	+	0.315565i	$0.897806\pi$
$62$	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
$65$		0			0
$66$	0.662991	+	1.05959i	0.0816085	+	0.130427i
$67$	−7.98415	+	7.98415i	−0.975419	+	0.975419i	−0.999705	−	0.0242864i	$-0.992269\pi$
$67$	−7.98415	+	7.98415i	−0.975419	+	0.975419i	0.0242864	+	0.999705i	$0.492269\pi$
$68$	−4.49639	−	7.68180i	−0.545267	−	0.931555i
$69$	4.82112	−	3.95497i	0.580395	−	0.476123i
$70$		0			0
$71$		−	5.09150i		−	0.604250i	−0.953268	−	0.302125i	$-0.902304\pi$
$71$		−	5.09150i		−	0.604250i	0.953268	−	0.302125i	$-0.0976959\pi$
$72$	−1.72645	−	8.30779i	−0.203465	−	0.979082i
$73$	3.20654	−	3.20654i	0.375297	−	0.375297i	−0.494105	−	0.869402i	$-0.664504\pi$
$73$	3.20654	−	3.20654i	0.375297	−	0.375297i	0.869402	+	0.494105i	$0.164504\pi$
$74$	−1.72540	+	13.4148i	−0.200574	+	1.55943i
$75$		0			0
$76$	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	$-0.865061\pi$
$79$		−	7.31215i		−	0.822682i	0.911482	−	0.411341i	$-0.134939\pi$
$80$		0			0
$81$	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	$-0.870984\pi$
$83$	−4.77995	+	4.77995i	−0.524668	+	0.524668i	0.394310	+	0.918978i	$0.370984\pi$
$84$	−4.23762	−	9.21104i	−0.462363	−	1.00501i
$85$		0			0
$86$	−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	$0.266259\pi$
$90$		0			0
$91$			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
$95$		0			0
$96$	0.464592	+	9.78694i	0.0474172	+	0.998875i
$97$	−10.8789	−	10.8789i	−1.10458	−	1.10458i	−0.993850	−	0.110732i	$-0.964680\pi$
$97$	−10.8789	−	10.8789i	−1.10458	−	1.10458i	−0.110732	−	0.993850i	$-0.535320\pi$
$98$	−1.35405	−	1.75378i	−0.136780	−	0.177159i
$99$	1.50129	+	0.299251i	0.150886	+	0.0300759i
$100$		0			0
$101$	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	$-0.708564\pi$
$103$	1.86309	−	1.86309i	0.183575	−	0.183575i	0.792912	+	0.609336i	$0.208564\pi$
$104$	1.12418	−	2.78420i	0.110235	−	0.273013i
$105$		0			0
$106$	−1.46927	+	11.4233i	−0.142708	+	1.10953i
$107$	−10.0319	−	10.0319i	−0.969824	−	0.969824i	0.0297341	−	0.999558i	$-0.490534\pi$
$107$	−10.0319	−	10.0319i	−0.969824	−	0.969824i	−0.999558	+	0.0297341i	$0.990534\pi$
$108$	−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			0
$111$	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	$-0.290110\pi$
$113$	−1.88933	−	1.88933i	−0.177733	−	0.177733i	−0.790367	+	0.612634i	$0.790110\pi$
$114$	−7.81124	−	12.4839i	−0.731590	−	1.16923i
$115$		0			0
$116$	−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
$120$		0			0
$121$	−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
$125$		0			0
$126$	−11.7690	−	3.96119i	−1.04847	−	0.352891i
$127$	−0.964015	−	0.964015i	−0.0855425	−	0.0855425i	0.663041	−	0.748583i	$-0.269266\pi$
$127$	−0.964015	−	0.964015i	−0.0855425	−	0.0855425i	−0.748583	+	0.663041i	$0.769266\pi$
$128$	1.24228	−	11.2453i	0.109803	−	0.993953i
$129$	−11.2865	+	9.25878i	−0.993718	+	0.815190i
$130$		0			0
$131$	−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
$135$		0			0
$136$	11.6723	+	4.71295i	1.00089	+	0.404132i
$137$	−0.713542	+	0.713542i	−0.0609620	+	0.0609620i	−0.736931	−	0.675968i	$-0.763726\pi$
$137$	−0.713542	+	0.713542i	−0.0609620	+	0.0609620i	0.675968	+	0.736931i	$0.263726\pi$
$138$	−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	$0.375131\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$	−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	$-0.818823\pi$
$149$		−	13.1573i		−	1.07789i	0.842341	−	0.538944i	$-0.181177\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−1.53697	−	3.34081i	−0.123056	−	0.267479i
$157$	−4.38090	+	4.38090i	−0.349634	+	0.349634i	−0.859973	−	0.510339i	$-0.829520\pi$
$157$	−4.38090	+	4.38090i	−0.349634	+	0.349634i	0.510339	+	0.859973i	$0.329520\pi$
$158$	6.31961	+	8.18522i	0.502761	+	0.651181i
$159$	8.94650	+	10.9058i	0.709504	+	0.864886i
$160$		0			0
$161$			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	$-0.258302\pi$
$163$	−0.470868	−	0.470868i	−0.0368812	−	0.0368812i	−0.725307	+	0.688426i	$0.758302\pi$
$164$	−8.21087	−	2.14769i	−0.641162	−	0.167707i
$165$		0			0
$166$	1.21955	−	9.48180i	0.0946553	−	0.735930i
$167$	0.495354	−	0.495354i	0.0383316	−	0.0383316i	−0.687681	−	0.726013i	$-0.741371\pi$
$167$	0.495354	−	0.495354i	0.0383316	−	0.0383316i	0.726013	+	0.687681i	$0.241371\pi$
$168$	12.7043	+	6.64841i	0.980160	+	0.512936i
$169$		−	11.8731i		−	0.913312i
$170$		0			0
$171$	−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	$-0.789921\pi$
$173$	−2.32674	+	2.32674i	−0.176899	+	0.176899i	0.613104	+	0.790002i	$0.289921\pi$
$174$	−10.6055	+	6.63592i	−0.804002	+	0.503068i
$175$		0			0
$176$	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	$0.174066\pi$
$179$			13.9141i			1.03999i	−0.854169	+	0.519996i	$0.825934\pi$
$180$		0			0
$181$		−	5.80972i		−	0.431833i	−0.976412	−	0.215917i	$-0.930726\pi$
$181$		−	5.80972i		−	0.431833i	0.976412	−	0.215917i	$-0.0692740\pi$
$182$	−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
$185$		0			0
$186$	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			0
$191$		−	13.8456i		−	1.00183i	−0.865497	−	0.500914i	$-0.832997\pi$
$191$		−	13.8456i		−	1.00183i	0.865497	−	0.500914i	$-0.167003\pi$
$192$	−8.97853	−	10.5540i	−0.647969	−	0.761666i
$193$	−4.57254	+	4.57254i	−0.329138	+	0.329138i	−0.852259	−	0.523120i	$-0.824768\pi$
$193$	−4.57254	+	4.57254i	−0.329138	+	0.329138i	0.523120	+	0.852259i	$0.324768\pi$
$194$	21.5800	+	2.77562i	1.54935	+	0.199278i
$195$		0			0
$196$	3.03145	+	0.792928i	0.216532	+	0.0566377i
$197$	−3.85757	−	3.85757i	−0.274840	−	0.274840i	0.556205	−	0.831045i	$-0.312257\pi$
$197$	−3.85757	−	3.85757i	−0.274840	−	0.274840i	−0.831045	+	0.556205i	$0.812257\pi$
$198$	−1.93918	+	0.962528i	−0.137811	+	0.0684039i
$199$			5.91833i			0.419540i	0.977751	+	0.209770i	$0.0672714\pi$
$199$			5.91833i			0.419540i	−0.977751	+	0.209770i	$0.932729\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	−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
$210$		0			0
$211$			6.95372i			0.478714i	0.970932	+	0.239357i	$0.0769366\pi$
$211$			6.95372i			0.478714i	−0.970932	+	0.239357i	$0.923063\pi$
$212$	−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
$215$		0			0
$216$	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
$220$		0			0
$221$	−4.72454			−0.317807
$222$	−22.8292	−	5.25610i	−1.53219	−	0.352766i
$223$	16.7218	−	16.7218i	1.11977	−	1.11977i	0.127998	−	0.991774i	$-0.459145\pi$
$223$	16.7218	−	16.7218i	1.11977	−	1.11977i	0.991774	−	0.127998i	$-0.0408550\pi$
$224$	−13.2844	−	9.88231i	−0.887601	−	0.660290i
$225$		0			0
$226$	3.74778	+	0.482039i	0.249298	+	0.0320647i
$227$	12.4814	+	12.4814i	0.828416	+	0.828416i	0.987298	−	0.158881i	$-0.0507887\pi$
$227$	12.4814	+	12.4814i	0.828416	+	0.828416i	−0.158881	+	0.987298i	$0.550789\pi$
$228$	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	$0.511538\pi$
$230$		0			0
$231$	−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	$-0.145181\pi$
$233$	6.98082	+	6.98082i	0.457329	+	0.457329i	−0.440449	+	0.897778i	$0.645181\pi$
$234$	−4.26859	−	1.43671i	−0.279046	−	0.0939207i
$235$		0			0
$236$	−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	$0.369535\pi$
$240$		0			0
$241$	−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
$245$		0			0
$246$	−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
$250$		0			0
$251$	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
$255$		0			0
$256$	8.32826	+	13.6616i	0.520516	+	0.853852i
$257$	14.5324	−	14.5324i	0.906508	−	0.906508i	−0.0894809	−	0.995989i	$-0.528521\pi$
$257$	14.5324	−	14.5324i	0.906508	−	0.906508i	0.995989	+	0.0894809i	$0.0285208\pi$
$258$	4.63206	−	20.1187i	0.288379	−	1.25254i
$259$	−27.9923			−1.73935
$260$		0			0
$261$	−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	$-0.407070\pi$
$263$	−10.8634	−	10.8634i	−0.669867	−	0.669867i	−0.957685	+	0.287818i	$0.907070\pi$
$264$	2.38575	−	0.746557i	0.146833	−	0.0459474i
$265$		0			0
$266$	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	$0.445799\pi$
$269$			32.3280i			1.97108i	−0.169455	+	0.985538i	$0.554201\pi$
$270$		0			0
$271$	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			0
$276$	−5.21250	−	11.3300i	−0.313755	−	0.681989i
$277$	−6.97897	+	6.97897i	−0.419326	+	0.419326i	−0.884971	−	0.465645i	$-0.845822\pi$
$277$	−6.97897	+	6.97897i	−0.419326	+	0.419326i	0.465645	+	0.884971i	$0.345822\pi$
$278$	−10.0909	+	7.79094i	−0.605212	+	0.467270i
$279$	13.4358	+	2.67815i	0.804383	+	0.160337i
$280$		0			0
$281$			15.4596i			0.922240i	0.887338	+	0.461120i	$0.152552\pi$
$281$			15.4596i			0.922240i	−0.887338	+	0.461120i	$0.847448\pi$
$282$	11.2700	+	2.59477i	0.671121	+	0.154516i
$283$	−8.86458	−	8.86458i	−0.526945	−	0.526945i	0.392715	−	0.919660i	$-0.371536\pi$
$283$	−8.86458	−	8.86458i	−0.526945	−	0.526945i	−0.919660	+	0.392715i	$0.871536\pi$
$284$	−9.85156	−	2.57684i	−0.584583	−	0.152908i
$285$		0			0
$286$	−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
$290$		0			0
$291$	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	$-0.769689\pi$
$293$	−1.49638	+	1.49638i	−0.0874192	+	0.0874192i	0.662045	+	0.749464i	$0.269689\pi$
$294$	3.25330	−	2.03560i	0.189736	−	0.118719i
$295$		0			0
$296$	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
$300$		0			0
$301$		−	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
$305$		0			0
$306$	6.02319	−	17.8954i	0.344323	−	1.02301i
$307$	12.4948	−	12.4948i	0.713118	−	0.713118i	−0.254068	−	0.967186i	$-0.581769\pi$
$307$	12.4948	−	12.4948i	0.713118	−	0.713118i	0.967186	+	0.254068i	$0.0817688\pi$
$308$	2.57791	−	1.50893i	0.146890	−	0.0859791i
$309$	2.89442	+	3.52830i	0.164658	+	0.200718i
$310$		0			0
$311$			0.224632i			0.0127377i	0.999980	+	0.00636886i	$0.00202728\pi$
$311$			0.224632i			0.0127377i	−0.999980	+	0.00636886i	$0.997973\pi$
$312$	4.60782	+	2.41136i	0.260866	+	0.136516i
$313$	12.0383	−	12.0383i	0.680447	−	0.680447i	−0.279654	−	0.960101i	$-0.590220\pi$
$313$	12.0383	−	12.0383i	0.680447	−	0.680447i	0.960101	+	0.279654i	$0.0902198\pi$
$314$	1.11774	−	8.69022i	0.0630775	−	0.490417i
$315$		0			0
$316$	−14.1483	−	3.70073i	−0.795905	−	0.208183i
$317$	20.2257	+	20.2257i	1.13599	+	1.13599i	0.989162	+	0.146829i	$0.0469068\pi$
$317$	20.2257	+	20.2257i	1.13599	+	1.13599i	0.146829	+	0.989162i	$0.453093\pi$
$318$	−19.4401	−	4.47582i	−1.09015	−	0.250992i
$319$			2.60618i			0.145918i
$320$		0			0
$321$	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
$325$		0			0
$326$	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
$330$		0			0
$331$		−	12.3308i		−	0.677760i	−0.940830	−	0.338880i	$-0.889952\pi$
$331$		−	12.3308i		−	0.677760i	0.940830	−	0.338880i	$-0.110048\pi$
$332$	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
$335$		0			0
$336$	−19.9672	+	3.53763i	−1.08930	+	0.192993i
$337$	−10.6723	−	10.6723i	−0.581359	−	0.581359i	0.353918	−	0.935277i	$-0.384849\pi$
$337$	−10.6723	−	10.6723i	−0.581359	−	0.581359i	−0.935277	+	0.353918i	$0.884849\pi$
$338$	10.2614	+	13.2907i	0.558147	+	0.722918i
$339$	3.57799	−	2.93518i	0.194330	−	0.159417i
$340$		0			0
$341$	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			0
$346$	0.593640	−	4.61546i	0.0319143	−	0.248129i
$347$	8.00457	+	8.00457i	0.429708	+	0.429708i	0.888529	−	0.458821i	$-0.151728\pi$
$347$	8.00457	+	8.00457i	0.429708	+	0.429708i	−0.458821	+	0.888529i	$0.651728\pi$
$348$	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	$0.378132\pi$
$350$		0			0
$351$	−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	$-0.102529\pi$
$353$	11.8744	+	11.8744i	0.632008	+	0.632008i	−0.316563	+	0.948571i	$0.602529\pi$
$354$	−2.41943	+	1.51385i	−0.128591	+	0.0804600i
$355$		0			0
$356$	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	$0.852089\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	10.2357	−	6.40452i	0.535029	−	0.334770i
$367$	−10.7900	−	10.7900i	−0.563233	−	0.563233i	0.366992	−	0.930224i	$-0.380388\pi$
$367$	−10.7900	−	10.7900i	−0.563233	−	0.563233i	−0.930224	+	0.366992i	$0.880388\pi$
$368$	3.89289	+	13.8648i	0.202931	+	0.722752i
$369$	−2.48863	+	12.4851i	−0.129553	+	0.649946i
$370$		0			0
$371$	−23.8368			−1.23754
$372$	−14.8375	−	5.48702i	−0.769289	−	0.284489i
$373$	25.8380	+	25.8380i	1.33784	+	1.33784i	0.898146	+	0.439697i	$0.144914\pi$
$373$	25.8380	+	25.8380i	1.33784	+	1.33784i	0.439697	+	0.898146i	$0.355086\pi$
$374$	0.409708	−	3.18541i	0.0211855	−	0.164714i
$375$		0			0
$376$	−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	$0.601672\pi$
$380$		0			0
$381$	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	0.993796	+	0.111219i	$0.0354754\pi$
$383$	21.6256	+	21.6256i	1.10501	+	1.10501i	0.111219	+	0.993796i	$0.464525\pi$
$384$	19.1719	+	4.05430i	0.978363	+	0.206895i
$385$		0			0
$386$	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	$-0.946167\pi$
$389$		−	6.63941i		−	0.336632i	0.985733	−	0.168316i	$-0.0538328\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	1.33884	−	2.75341i	0.0672792	−	0.138364i
$397$	−14.0596	+	14.0596i	−0.705629	+	0.705629i	−0.965613	−	0.259984i	$-0.916283\pi$
$397$	−14.0596	+	14.0596i	−0.705629	+	0.705629i	0.259984	+	0.965613i	$0.416283\pi$
$398$	−5.11498	−	6.62498i	−0.256391	−	0.332080i
$399$	23.5636	−	19.3303i	1.17966	−	0.967725i
$400$		0			0
$401$			18.1176i			0.904751i	0.891827	+	0.452376i	$0.149423\pi$
$401$			18.1176i			0.904751i	−0.891827	+	0.452376i	$0.850577\pi$
$402$	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
$405$		0			0
$406$	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	$0.225579\pi$
$409$			26.3245i			1.30166i	−0.759223	+	0.650831i	$0.774421\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	−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	$-0.898937\pi$
$419$		−	12.7809i		−	0.624385i	0.950019	−	0.312193i	$-0.101063\pi$
$420$		0			0
$421$			26.3792i			1.28564i	0.766017	+	0.642821i	$0.222236\pi$
$421$			26.3792i			1.28564i	−0.766017	+	0.642821i	$0.777764\pi$
$422$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$			28.6818i			1.38155i	0.723068	+	0.690777i	$0.242731\pi$
$431$			28.6818i			1.38155i	−0.723068	+	0.690777i	$0.757269\pi$
$432$	−15.0080	+	14.3791i	−0.722074	+	0.691816i
$433$	2.25457	−	2.25457i	0.108347	−	0.108347i	−0.650855	−	0.759202i	$-0.725589\pi$
$433$	2.25457	−	2.25457i	0.108347	−	0.108347i	0.759202	+	0.650855i	$0.225589\pi$
$434$	−18.7484	−	2.41142i	−0.899951	−	0.115752i
$435$		0			0
$436$	−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	$-0.908733\pi$
$439$		−	11.8510i		−	0.565620i	0.959176	−	0.282810i	$-0.0912665\pi$
$440$		0			0
$441$	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	$-0.767847\pi$
$443$	−1.66807	+	1.66807i	−0.0792526	+	0.0792526i	0.666369	+	0.745622i	$0.267847\pi$
$444$	30.0976	−	13.8467i	1.42837	−	0.657135i
$445$		0			0
$446$	−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	$0.199285\pi$
$450$		0			0
$451$			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
$455$		0			0
$456$	−28.1085	+	8.79580i	−1.31630	+	0.411901i
$457$	4.61474	+	4.61474i	0.215869	+	0.215869i	0.806755	−	0.590886i	$-0.201222\pi$
$457$	4.61474	+	4.61474i	0.215869	+	0.215869i	−0.590886	+	0.806755i	$0.701222\pi$
$458$	1.22773	−	0.947900i	0.0573680	−	0.0442925i
$459$	−10.8890	−	20.4014i	−0.508255	−	0.952254i
$460$		0			0
$461$	−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	−0.313730	+	0.949512i	$0.601579\pi$
$463$	−27.1817	+	27.1817i	−1.26324	+	1.26324i	−0.949512	+	0.313730i	$0.898421\pi$
$464$	−10.0030	+	17.8131i	−0.464378	+	0.826952i
$465$		0			0
$466$	−13.8476	−	1.78107i	−0.641476	−	0.0825067i
$467$	6.39901	+	6.39901i	0.296111	+	0.296111i	0.839488	−	0.543378i	$-0.182855\pi$
$467$	6.39901	+	6.39901i	0.296111	+	0.296111i	−0.543378	+	0.839488i	$0.682855\pi$
$468$	6.01994	−	2.08092i	0.278272	−	0.0961905i
$469$	33.0484			1.52603
$470$		0			0
$471$	−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
$475$		0			0
$476$	−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	$0.806257\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	−3.63418	−	21.7438i	−0.164850	−	0.986319i
$487$	23.9090	+	23.9090i	1.08342	+	1.08342i	0.996188	+	0.0872343i	$0.0278029\pi$
$487$	23.9090	+	23.9090i	1.08342	+	1.08342i	0.0872343	+	0.996188i	$0.472197\pi$
$488$	−12.8326	+	5.45044i	−0.580905	+	0.246730i
$489$	0.891726	−	0.731522i	0.0403252	−	0.0330806i
$490$		0			0
$491$	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
$495$		0			0
$496$	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	$0.352899\pi$
$500$		0			0
$501$	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	$-0.403041\pi$
$503$	−14.6687	−	14.6687i	−0.654047	−	0.654047i	−0.953965	+	0.299918i	$0.903041\pi$
$504$	−13.6209	+	20.7671i	−0.606724	+	0.925042i
$505$		0			0
$506$	−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	$0.0343151\pi$
$509$			4.85493i			0.215191i	−0.994195	+	0.107595i	$0.965685\pi$
$510$		0			0
$511$	−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			0
$516$	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
$520$		0			0
$521$		−	15.0499i		−	0.659346i	−0.944095	−	0.329673i	$-0.893061\pi$
$521$		−	15.0499i		−	0.659346i	0.944095	−	0.329673i	$-0.106939\pi$
$522$	−9.63401	−	19.4094i	−0.421669	−	0.849525i
$523$	−15.6997	−	15.6997i	−0.686499	−	0.686499i	0.274957	−	0.961456i	$-0.411336\pi$
$523$	−15.6997	−	15.6997i	−0.686499	−	0.686499i	−0.961456	+	0.274957i	$0.911336\pi$
$524$	−3.84254	+	14.6904i	−0.167862	+	0.641755i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		0			0
$541$		−	1.45079i		−	0.0623742i	−0.999514	−	0.0311871i	$-0.990071\pi$
$541$		−	1.45079i		−	0.0623742i	0.999514	−	0.0311871i	$-0.00992877\pi$
$542$	−0.342914	+	0.264756i	−0.0147294	+	0.0113722i
$543$	10.0141	+	0.988326i	0.429745	+	0.0424131i
$544$	15.0266	−	20.1996i	0.644258	−	0.866050i
$545$		0			0
$546$	6.45196	−	4.03702i	0.276118	−	0.172768i
$547$	1.86763	−	1.86763i	0.0798541	−	0.0798541i	−0.666052	−	0.745906i	$-0.732017\pi$
$547$	1.86763	−	1.86763i	0.0798541	−	0.0798541i	0.745906	+	0.666052i	$0.232017\pi$
$548$	1.01951	+	1.74177i	0.0435512	+	0.0744045i
$549$	2.89078	−	14.5026i	0.123375	−	0.618955i
$550$		0			0
$551$		−	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
$555$		0			0
$556$	4.56234	−	17.4423i	0.193486	−	0.739720i
$557$	−22.6188	−	22.6188i	−0.958389	−	0.958389i	0.0407789	−	0.999168i	$-0.487016\pi$
$557$	−22.6188	−	22.6188i	−0.958389	−	0.958389i	−0.999168	+	0.0407789i	$0.987016\pi$
$558$	−17.3547	+	8.61415i	−0.734682	+	0.364666i
$559$		−	8.94729i		−	0.378430i
$560$		0			0
$561$	−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	0.132574	−	0.991173i	$-0.457676\pi$
$563$	26.6638	−	26.6638i	1.12375	−	1.12375i	0.991173	−	0.132574i	$-0.0423241\pi$
$564$	−14.8582	+	6.83567i	−0.625644	+	0.287833i
$565$		0			0
$566$	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	$0.710657\pi$
$570$		0			0
$571$			28.4036i			1.18865i	0.804224	+	0.594326i	$0.202581\pi$
$571$			28.4036i			1.18865i	−0.804224	+	0.594326i	$0.797419\pi$
$572$	0.934999	−	0.547283i	0.0390943	−	0.0228831i
$573$	23.8652	+	2.35535i	0.996985	+	0.0983960i
$574$	2.24077	−	17.4216i	0.0935280	−	0.727165i
$575$		0			0
$576$	19.7190	−	13.6807i	0.821625	−	0.570028i
$577$	18.9787	+	18.9787i	0.790092	+	0.790092i	0.981509	−	0.191417i	$-0.0613081\pi$
$577$	18.9787	+	18.9787i	0.790092	+	0.790092i	−0.191417	+	0.981509i	$0.561308\pi$
$578$	2.42590	+	3.14204i	0.100904	+	0.130692i
$579$	−7.10371	−	8.65943i	−0.295220	−	0.359874i
$580$		0			0
$581$	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
$585$		0			0
$586$	0.381782	−	2.96830i	0.0157713	−	0.122619i
$587$	−11.2326	−	11.2326i	−0.463619	−	0.463619i	0.436220	−	0.899840i	$-0.356317\pi$
$587$	−11.2326	−	11.2326i	−0.463619	−	0.463619i	−0.899840	+	0.436220i	$0.856317\pi$
$588$	−1.88245	+	5.09035i	−0.0776309	+	0.209923i
$589$	−27.4550			−1.13127
$590$		0			0
$591$	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	$-0.251489\pi$
$593$	−0.161070	−	0.161070i	−0.00661435	−	0.00661435i	−0.710406	+	0.703792i	$0.751489\pi$
$594$	−1.32920	−	3.50626i	−0.0545378	−	0.143863i
$595$		0			0
$596$	−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	$0.396372\pi$
$600$		0			0
$601$	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
$605$		0			0
$606$	−8.32841	−	13.3105i	−0.338318	−	0.540700i
$607$	−18.7872	−	18.7872i	−0.762550	−	0.762550i	0.214232	−	0.976783i	$-0.431275\pi$
$607$	−18.7872	−	18.7872i	−0.762550	−	0.762550i	−0.976783	+	0.214232i	$0.931275\pi$
$608$	33.6480	−	4.94129i	1.36461	−	0.200396i
$609$	−16.4217	−	20.0181i	−0.665443	−	0.811176i
$610$		0			0
$611$	5.01206			0.202766
$612$	8.72394	+	25.2377i	0.352644	+	1.02017i
$613$	29.5115	+	29.5115i	1.19196	+	1.19196i	0.976516	+	0.215443i	$0.0691195\pi$
$613$	29.5115	+	29.5115i	1.19196	+	1.19196i	0.215443	+	0.976516i	$0.430880\pi$
$614$	−3.18791	+	24.7855i	−0.128654	+	1.00026i
$615$		0			0
$616$	−1.58160	+	3.91708i	−0.0637245	+	0.157823i
$617$	29.7517	−	29.7517i	1.19776	−	1.19776i	0.222923	−	0.974836i	$-0.428440\pi$
$617$	29.7517	−	29.7517i	1.19776	−	1.19776i	0.974836	−	0.222923i	$-0.0715598\pi$
$618$	−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	$0.580497\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	−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
$630$		0			0
$631$	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
$635$		0			0
$636$	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
$640$		0			0
$641$		−	13.3935i		−	0.529013i	−0.964384	−	0.264506i	$-0.914791\pi$
$641$		−	13.3935i		−	0.529013i	0.964384	−	0.264506i	$-0.0852090\pi$
$642$	−7.79709	+	33.8656i	−0.307727	+	1.33657i
$643$	−12.4335	−	12.4335i	−0.490331	−	0.490331i	0.418080	−	0.908410i	$-0.362703\pi$
$643$	−12.4335	−	12.4335i	−0.490331	−	0.490331i	−0.908410	+	0.418080i	$0.862703\pi$
$644$	20.3891	+	5.33311i	0.803442	+	0.210154i
$645$		0			0
$646$	−4.82710	+	37.5300i	−0.189920	+	1.47660i
$647$	−0.352589	+	0.352589i	−0.0138617	+	0.0138617i	−0.714004	−	0.700142i	$-0.753120\pi$
$647$	−0.352589	+	0.352589i	−0.0138617	+	0.0138617i	0.700142	+	0.714004i	$0.253120\pi$
$648$	0.207341	+	25.4550i	0.00814512	+	0.999967i
$649$			0.594545i			0.0233380i
$650$		0			0
$651$	−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	$-0.844295\pi$
$653$	−10.5497	+	10.5497i	−0.412841	+	0.412841i	0.469886	+	0.882727i	$0.344295\pi$
$654$	16.4291	+	26.2571i	0.642431	+	1.02673i
$655$		0			0
$656$	−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	$-0.794742\pi$
$659$		−	30.8600i		−	1.20213i	0.799199	−	0.601067i	$-0.205258\pi$
$660$		0			0
$661$			44.1992i			1.71915i	0.511009	+	0.859575i	$0.329272\pi$
$661$			44.1992i			1.71915i	−0.511009	+	0.859575i	$0.670728\pi$
$662$	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
$665$		0			0
$666$	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
$670$		0			0
$671$		−	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	$-0.866480\pi$
$673$	−13.1276	+	13.1276i	−0.506033	+	0.506033i	0.407274	+	0.913306i	$0.366480\pi$
$674$	21.1703	+	2.72292i	0.815448	+	0.104883i
$675$		0			0
$676$	−22.9732	−	6.00904i	−0.883586	−	0.231117i
$677$	−23.1658	−	23.1658i	−0.890334	−	0.890334i	0.104220	−	0.994554i	$-0.466765\pi$
$677$	−23.1658	−	23.1658i	−0.890334	−	0.890334i	−0.994554	+	0.104220i	$0.966765\pi$
$678$	−1.46844	+	6.37795i	−0.0563949	+	0.244944i
$679$			45.0304i			1.72811i
$680$		0			0
$681$	−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	$-0.881759\pi$
$683$	−14.8655	+	14.8655i	−0.568814	+	0.568814i	0.362982	+	0.931796i	$0.381759\pi$
$684$	−15.7740	+	32.4402i	−0.603132	+	1.24038i
$685$		0			0
$686$	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
$690$		0			0
$691$		−	47.2699i		−	1.79823i	−0.437710	−	0.899116i	$-0.644210\pi$
$691$		−	47.2699i		−	1.79823i	0.437710	−	0.899116i	$-0.355790\pi$
$692$	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
$695$		0			0
$696$	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
$700$		0			0
$701$	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
$705$		0			0
$706$	−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	$0.190664\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	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	$0.412094\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	13.9538	+	22.3009i	0.517872	+	0.827663i
$727$	22.1109	+	22.1109i	0.820048	+	0.820048i	0.986115	−	0.166067i	$-0.0531067\pi$
$727$	22.1109	+	22.1109i	0.820048	+	0.820048i	−0.166067	+	0.986115i	$0.553107\pi$
$728$	−8.08889	+	3.43563i	−0.299794	+	0.127333i
$729$	−22.4316	−	15.0274i	−0.830802	−	0.556569i
$730$		0			0
$731$	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	$-0.177495\pi$
$733$	8.64610	+	8.64610i	0.319351	+	0.319351i	−0.529167	+	0.848518i	$0.677495\pi$
$734$	21.4037	+	2.75294i	0.790023	+	0.101613i
$735$		0			0
$736$	−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	$0.314993\pi$
$740$		0			0
$741$	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	$-0.193644\pi$
$743$	6.78930	+	6.78930i	0.249075	+	0.249075i	−0.571516	+	0.820591i	$0.693644\pi$
$744$	21.3513	−	6.68132i	0.782777	−	0.244949i
$745$		0			0
$746$	−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
$750$		0			0
$751$	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
$755$		0			0
$756$	7.06580	+	29.5851i	0.256981	+	1.07600i
$757$	33.9790	−	33.9790i	1.23499	−	1.23499i	0.272963	−	0.962025i	$-0.411996\pi$
$757$	33.9790	−	33.9790i	1.23499	−	1.23499i	0.962025	−	0.272963i	$-0.0880035\pi$
$758$	13.6860	−	10.5666i	0.497099	−	0.383798i
$759$	−2.46010	+	2.01813i	−0.0892961	+	0.0732535i
$760$		0			0
$761$			34.4290i			1.24805i	0.781404	+	0.624025i	$0.214504\pi$
$761$			34.4290i			1.24805i	−0.781404	+	0.624025i	$0.785496\pi$
$762$	−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
$765$		0			0
$766$	−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	$-0.913457\pi$
$769$		−	14.8941i		−	0.537094i	0.963267	−	0.268547i	$-0.0865434\pi$
$770$		0			0
$771$	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	$-0.690313\pi$
$773$	7.32969	−	7.32969i	0.263631	−	0.263631i	0.826527	+	0.562897i	$0.190313\pi$
$774$	33.8902	+	11.4067i	1.21816	+	0.410005i
$775$		0			0
$776$	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
$780$		0			0
$781$			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
$785$		0			0
$786$	9.86456	+	15.7655i	0.351857	+	0.562338i
$787$	4.66068	−	4.66068i	0.166135	−	0.166135i	−0.619143	−	0.785278i	$-0.712520\pi$
$787$	4.66068	−	4.66068i	0.166135	−	0.166135i	0.785278	+	0.619143i	$0.212520\pi$
$788$	−9.41637	+	5.51168i	−0.335444	+	0.196346i
$789$	20.5731	−	16.8770i	0.732421	−	0.600837i
$790$		0			0
$791$			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
$795$		0			0
$796$	11.4514	+	2.99531i	0.405884	+	0.106166i
$797$	27.8720	+	27.8720i	0.987276	+	0.987276i	0.999920	−	0.0126440i	$-0.00402483\pi$
$797$	27.8720	+	27.8720i	0.987276	+	0.987276i	−0.0126440	+	0.999920i	$0.504025\pi$
$798$	−9.67071	+	42.0034i	−0.342339	+	1.48691i
$799$			21.0123i			0.743362i
$800$		0			0
$801$	−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
$805$		0			0
$806$	−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	$0.392618\pi$
$810$		0			0
$811$		−	37.4113i		−	1.31369i	−0.754026	−	0.656845i	$-0.771891\pi$
$811$		−	37.4113i		−	1.31369i	0.754026	−	0.656845i	$-0.228109\pi$
$812$	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
$815$		0			0
$816$	−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
$820$		0			0
$821$	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	$-0.836306\pi$
$823$	−10.8660	+	10.8660i	−0.378766	+	0.378766i	0.491891	+	0.870657i	$0.336306\pi$
$824$	6.91031	+	2.79018i	0.240732	+	0.0972006i
$825$		0			0
$826$	0.615244	−	4.78343i	0.0214071	−	0.166437i
$827$	2.49596	+	2.49596i	0.0867932	+	0.0867932i	0.749170	−	0.662377i	$-0.230452\pi$
$827$	2.49596	+	2.49596i	0.0867932	+	0.0867932i	−0.662377	+	0.749170i	$0.730452\pi$
$828$	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	$0.825235\pi$
$830$		0			0
$831$	−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			0
$836$	−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	$0.345825\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−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
$850$		0			0
$851$	−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	$-0.380128\pi$
$853$	−16.4190	−	16.4190i	−0.562174	−	0.562174i	−0.929925	+	0.367750i	$0.880128\pi$
$854$	−2.60287	+	20.2369i	−0.0890683	+	0.692492i
$855$		0			0
$856$	15.0239	−	37.2091i	0.513508	−	1.27178i
$857$	−24.4641	+	24.4641i	−0.835678	+	0.835678i	−0.988287	−	0.152608i	$-0.951233\pi$
$857$	−24.4641	+	24.4641i	−0.835678	+	0.835678i	0.152608	+	0.988287i	$0.451233\pi$
$858$	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	$0.490869\pi$
$860$		0			0
$861$	−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	$-0.0623737\pi$
$863$	23.0950	+	23.0950i	0.786161	+	0.786161i	−0.194701	+	0.980863i	$0.562374\pi$
$864$	4.37266	−	29.0668i	0.148761	−	0.988873i
$865$		0			0
$866$	−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
$870$		0			0
$871$	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
$875$		0			0
$876$	14.2710	−	6.56549i	0.482171	−	0.221827i
$877$	14.2900	−	14.2900i	0.482539	−	0.482539i	−0.423403	−	0.905942i	$-0.639164\pi$
$877$	14.2900	−	14.2900i	0.482539	−	0.482539i	0.905942	+	0.423403i	$0.139164\pi$
$878$	10.2424	+	13.2660i	0.345664	+	0.447707i
$879$	−2.32471	−	2.83382i	−0.0784105	−	0.0955825i
$880$		0			0
$881$		−	45.2886i		−	1.52581i	−0.646509	−	0.762906i	$-0.723772\pi$
$881$		−	45.2886i		−	1.52581i	0.646509	−	0.762906i	$-0.276228\pi$
$882$	2.95529	+	5.95393i	0.0995096	+	0.200479i
$883$	−3.68252	−	3.68252i	−0.123927	−	0.123927i	0.642423	−	0.766350i	$-0.277929\pi$
$883$	−3.68252	−	3.68252i	−0.123927	−	0.123927i	−0.766350	+	0.642423i	$0.777929\pi$
$884$	−2.39112	+	9.14153i	−0.0804221	+	0.307463i
$885$		0			0
$886$	0.425589	−	3.30889i	0.0142980	−	0.111164i
$887$	14.7506	−	14.7506i	0.495277	−	0.495277i	−0.414687	−	0.909964i	$-0.636109\pi$
$887$	14.7506	−	14.7506i	0.495277	−	0.495277i	0.909964	+	0.414687i	$0.136109\pi$
$888$	−21.7241	+	41.5121i	−0.729012	+	1.39306i
$889$			3.99030i			0.133830i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−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
$900$		0			0
$901$		−	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
$905$		0			0
$906$	−3.58577	−	5.73077i	−0.119129	−	0.190392i
$907$	8.08868	−	8.08868i	0.268580	−	0.268580i	−0.559948	−	0.828528i	$-0.689179\pi$
$907$	8.08868	−	8.08868i	0.268580	−	0.268580i	0.828528	+	0.559948i	$0.189179\pi$
$908$	30.4671	−	17.8333i	1.01109	−	0.591820i
$909$	−18.8591	−	3.75915i	−0.625516	−	0.124683i
$910$		0			0
$911$		−	38.7011i		−	1.28222i	−0.767448	−	0.641112i	$-0.778473\pi$
$911$		−	38.7011i		−	1.28222i	0.767448	−	0.641112i	$-0.221527\pi$
$912$	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
$915$		0			0
$916$	−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	$-0.770939\pi$
$919$		−	39.9611i		−	1.31819i	0.752058	−	0.659097i	$-0.229061\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	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	$0.502967\pi$
$930$		0			0
$931$			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			0
$936$	−4.94026	+	7.53218i	−0.161477	+	0.246197i
$937$	−18.2630	−	18.2630i	−0.596626	−	0.596626i	0.342787	−	0.939413i	$-0.388629\pi$
$937$	−18.2630	−	18.2630i	−0.596626	−	0.596626i	−0.939413	+	0.342787i	$0.888629\pi$
$938$	−36.9944	+	28.5624i	−1.20791	+	0.932597i
$939$	18.7023	+	22.7981i	0.610326	+	0.743988i
$940$		0			0
$941$	−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
$945$		0			0
$946$	6.03251	+	0.775901i	0.196134	+	0.0252267i
$947$	15.7486	+	15.7486i	0.511761	+	0.511761i	0.915066	−	0.403305i	$-0.132139\pi$
$947$	15.7486	+	15.7486i	0.511761	+	0.511761i	−0.403305	+	0.915066i	$0.632139\pi$
$948$	8.78572	−	23.7576i	0.285347	−	0.771610i
$949$	−4.81396			−0.156268
$950$		0			0
$951$	−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	−0.996447	−	0.0842194i	$-0.973160\pi$
$953$	−33.3609	−	33.3609i	−1.08067	−	1.08067i	−0.0842194	−	0.996447i	$-0.526840\pi$
$954$	11.0220	−	32.7471i	0.356849	−	1.06023i
$955$		0			0
$956$	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
$960$		0			0
$961$	−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
$965$		0			0
$966$	21.8812	−	13.6912i	0.704016	−	0.440506i
$967$	8.01398	+	8.01398i	0.257712	+	0.257712i	0.824123	−	0.566411i	$-0.191668\pi$
$967$	8.01398	+	8.01398i	0.257712	+	0.257712i	−0.566411	+	0.824123i	$0.691668\pi$
$968$	−11.8751	−	27.9589i	−0.381679	−	0.898632i
$969$	29.3927	+	35.8297i	0.944229	+	1.15102i
$970$		0			0
$971$	−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
$975$		0			0
$976$	9.65420	−	17.1919i	0.309024	−	0.550301i
$977$	−39.7367	+	39.7367i	−1.27129	+	1.27129i	−0.325880	+	0.945411i	$0.605661\pi$
$977$	−39.7367	+	39.7367i	−1.27129	+	1.27129i	−0.945411	+	0.325880i	$0.894339\pi$
$978$	−0.365972	+	1.58955i	−0.0117025	+	0.0508282i
$979$	−6.45147			−0.206190
$980$		0			0
$981$	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	$-0.183905\pi$
$983$	9.14087	+	9.14087i	0.291548	+	0.291548i	−0.546143	+	0.837692i	$0.683905\pi$
$984$	6.20851	+	19.8404i	0.197920	+	0.632488i
$985$		0			0
$986$	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			0
$991$	−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
$995$		0			0
$996$	−21.2735	+	9.78710i	−0.674078	+	0.310116i
$997$	3.70273	−	3.70273i	0.117267	−	0.117267i	−0.646038	−	0.763305i	$-0.723575\pi$
$997$	3.70273	−	3.70273i	0.117267	−	0.117267i	0.763305	+	0.646038i	$0.223575\pi$
$998$	−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	600.2.w.j.557.4		32
3.2	odd	2	inner	600.2.w.j.557.13		32
5.2	odd	4		120.2.w.c.53.5	yes	32
5.3	odd	4	inner	600.2.w.j.293.12		32
5.4	even	2		120.2.w.c.77.13	yes	32
8.5	even	2	inner	600.2.w.j.557.5		32
15.2	even	4		120.2.w.c.53.12	yes	32
15.8	even	4	inner	600.2.w.j.293.5		32
15.14	odd	2		120.2.w.c.77.4	yes	32
20.7	even	4		480.2.bi.c.113.1		32
20.19	odd	2		480.2.bi.c.17.8		32
24.5	odd	2	inner	600.2.w.j.557.12		32
40.13	odd	4	inner	600.2.w.j.293.13		32
40.19	odd	2		480.2.bi.c.17.9		32
40.27	even	4		480.2.bi.c.113.16		32
40.29	even	2		120.2.w.c.77.12	yes	32
40.37	odd	4		120.2.w.c.53.4	✓	32
60.47	odd	4		480.2.bi.c.113.9		32
60.59	even	2		480.2.bi.c.17.16		32
120.29	odd	2		120.2.w.c.77.5	yes	32
120.53	even	4	inner	600.2.w.j.293.4		32
120.59	even	2		480.2.bi.c.17.1		32
120.77	even	4		120.2.w.c.53.13	yes	32
120.107	odd	4		480.2.bi.c.113.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.4	✓	32	40.37	odd	4
120.2.w.c.53.5	yes	32	5.2	odd	4
120.2.w.c.53.12	yes	32	15.2	even	4
120.2.w.c.53.13	yes	32	120.77	even	4
120.2.w.c.77.4	yes	32	15.14	odd	2
120.2.w.c.77.5	yes	32	120.29	odd	2
120.2.w.c.77.12	yes	32	40.29	even	2
120.2.w.c.77.13	yes	32	5.4	even	2
480.2.bi.c.17.1		32	120.59	even	2
480.2.bi.c.17.8		32	20.19	odd	2
480.2.bi.c.17.9		32	40.19	odd	2
480.2.bi.c.17.16		32	60.59	even	2
480.2.bi.c.113.1		32	20.7	even	4
480.2.bi.c.113.8		32	120.107	odd	4
480.2.bi.c.113.9		32	60.47	odd	4
480.2.bi.c.113.16		32	40.27	even	4
600.2.w.j.293.4		32	120.53	even	4	inner
600.2.w.j.293.5		32	15.8	even	4	inner
600.2.w.j.293.12		32	5.3	odd	4	inner
600.2.w.j.293.13		32	40.13	odd	4	inner
600.2.w.j.557.4		32	1.1	even	1	trivial
600.2.w.j.557.5		32	8.5	even	2	inner
600.2.w.j.557.12		32	24.5	odd	2	inner
600.2.w.j.557.13		32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11940 + 0.864261i) q^{2} +(-0.170116 + 1.72368i) q^{3} +(0.506107 - 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 - 2.06963i) q^{7} +(1.10573 + 2.60334i) q^{8} +(-2.94212 - 0.586449i) q^{9} +O(q^{10})\)	\(q+(-1.11940 + 0.864261i) q^{2} +(-0.170116 + 1.72368i) q^{3} +(0.506107 - 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 - 2.06963i) q^{7} +(1.10573 + 2.60334i) q^{8} +(-2.94212 - 0.586449i) q^{9} -0.510276 q^{11} +(3.24905 + 1.20152i) q^{12} +(-0.750647 - 0.750647i) q^{13} +(4.10544 + 0.528041i) q^{14} +(-3.48771 - 1.95854i) q^{16} +(3.14698 - 3.14698i) q^{17} +(3.80025 - 1.88629i) q^{18} +6.01198 q^{19} +(3.91945 - 3.21529i) q^{21} +(0.571203 - 0.441012i) q^{22} +(-2.54575 - 2.54575i) q^{23} +(-4.67541 + 1.46305i) q^{24} +(1.48903 + 0.191519i) q^{26} +(1.51135 - 4.97150i) q^{27} +(-5.05199 + 2.95708i) q^{28} -5.10739i q^{29} -4.56672 q^{31} +(5.59683 - 0.821906i) q^{32} +(0.0868061 - 0.879551i) q^{33} +(-0.802913 + 6.24253i) q^{34} +(-2.62375 + 5.39592i) q^{36} +(6.76263 - 6.76263i) q^{37} +(-6.72981 + 5.19592i) q^{38} +(1.42157 - 1.16618i) q^{39} -4.24355i q^{41} +(-1.60857 + 6.98662i) q^{42} +(5.95972 + 5.95972i) q^{43} +(-0.258254 + 0.987336i) q^{44} +(5.04990 + 0.649518i) q^{46} +(-3.33849 + 3.33849i) q^{47} +(3.96920 - 5.67851i) q^{48} +1.56672i q^{49} +(4.88902 + 5.95972i) q^{51} +(-1.83234 + 1.07252i) q^{52} +(5.75871 - 5.75871i) q^{53} +(2.60487 + 6.87129i) q^{54} +(3.09950 - 7.67638i) q^{56} +(-1.02273 + 10.3627i) q^{57} +(4.41411 + 5.71720i) q^{58} -1.16514i q^{59} +4.92929i q^{61} +(5.11198 - 3.94684i) q^{62} +(4.87536 + 7.30283i) q^{63} +(-5.55474 + 5.75716i) q^{64} +(0.662991 + 1.05959i) q^{66} +(-7.98415 + 7.98415i) q^{67} +(-4.49639 - 7.68180i) q^{68} +(4.82112 - 3.95497i) q^{69} -5.09150i q^{71} +(-1.72645 - 8.30779i) q^{72} +(3.20654 - 3.20654i) q^{73} +(-1.72540 + 13.4148i) q^{74} +(3.04271 - 11.6326i) q^{76} +(1.05608 + 1.05608i) q^{77} +(-0.583424 + 2.53402i) q^{78} -7.31215i q^{79} +(8.31215 + 3.45081i) q^{81} +(3.66754 + 4.75023i) q^{82} +(-4.77995 + 4.77995i) q^{83} +(-4.23762 - 9.21104i) q^{84} +(-11.8220 - 1.52055i) q^{86} +(8.80349 + 0.868848i) q^{87} +(-0.564226 - 1.32842i) q^{88} +12.6431 q^{89} +3.10712i q^{91} +(-6.21420 + 3.63736i) q^{92} +(0.776871 - 7.87155i) q^{93} +(0.851777 - 6.62243i) q^{94} +(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	\( 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

Introduction

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