LMFDB - Embedded newform 600.2.w.j.293.13

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			293.13
Character	$\chi$	$=$	600.293
Dual form			600.2.w.j.557.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11940 + 0.864261i) q^{2} +(1.72368 + 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.78246 + 1.68013i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +O(q^{10})$	\(q+(1.11940 + 0.864261i) q^{2} +(1.72368 + 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.78246 + 1.68013i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +0.510276 q^{11} +(0.543207 + 3.42125i) 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} +(2.78656 + 3.19923i) q^{18} +6.01198 q^{19} +(-3.91945 + 3.21529i) q^{21} +(0.571203 + 0.441012i) q^{22} +(2.54575 - 2.54575i) q^{23} +(-2.34878 + 4.29921i) q^{24} +(-1.48903 + 0.191519i) q^{26} +(4.97150 + 1.51135i) q^{27} +(-5.05199 - 2.95708i) q^{28} -5.10739i q^{29} -4.56672 q^{31} +(-5.59683 - 0.821906i) q^{32} +(0.879551 + 0.0868061i) q^{33} +(-0.802913 - 6.24253i) q^{34} +(0.354305 + 5.98953i) q^{36} +(6.76263 + 6.76263i) q^{37} +(6.72981 + 5.19592i) q^{38} +(-1.42157 + 1.16618i) q^{39} -4.24355i q^{41} +(-7.16627 + 0.211772i) 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} +(-6.34486 + 2.78257i) q^{48} -1.56672i q^{49} +(-4.88902 - 5.95972i) q^{51} +(-1.83234 - 1.07252i) q^{52} +(-5.75871 - 5.75871i) q^{53} +(4.25889 + 5.98848i) q^{54} +(-3.09950 - 7.67638i) q^{56} +(10.3627 + 1.02273i) q^{57} +(4.41411 - 5.71720i) q^{58} -1.16514i q^{59} -4.92929i q^{61} +(-5.11198 - 3.94684i) q^{62} +(-7.30283 + 4.87536i) q^{63} +(-5.55474 - 5.75716i) q^{64} +(0.909545 + 0.857332i) q^{66} +(-7.98415 - 7.98415i) q^{67} +(4.49639 - 7.68180i) q^{68} +(4.82112 - 3.95497i) q^{69} -5.09150i q^{71} +(-4.77991 + 7.01088i) 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} +(-2.59918 + 0.0768090i) q^{78} +7.31215i q^{79} +(8.31215 + 3.45081i) q^{81} +(3.66754 - 4.75023i) q^{82} +(4.77995 + 4.77995i) q^{83} +(-8.20494 - 5.95647i) q^{84} +(11.8220 - 1.52055i) q^{86} +(0.868848 - 8.80349i) q^{87} +(-0.564226 + 1.32842i) q^{88} -12.6431 q^{89} -3.10712i q^{91} +(6.21420 + 3.63736i) q^{92} +(-7.87155 - 0.776871i) q^{93} +(0.851777 + 6.62243i) q^{94} +(-9.50730 - 2.36881i) 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 $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.72368	+	0.170116i	0.995165	+	0.0982164i
$3$	1.72368	+	0.170116i	0.995165	+	0.0982164i
$4$	0.506107	+	1.93490i	0.253054	+	0.967452i
$5$		0			0
$5$		0			0
$6$	1.78246	+	1.68013i	0.727685	+	0.685911i
$7$	−2.06963	+	2.06963i	−0.782246	+	0.782246i	−0.980209	−	0.197964i	$-0.936567\pi$
$7$	−2.06963	+	2.06963i	−0.782246	+	0.782246i	0.197964	+	0.980209i	$0.436567\pi$
$8$	−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	$-0.475489\pi$
$11$	0.510276			0.153854			0.0769270	+	0.997037i	$0.475489\pi$
$12$	0.543207	+	3.42125i	0.156810	+	0.987629i
$13$	−0.750647	+	0.750647i	−0.208192	+	0.208192i	−0.803499	−	0.595307i	$-0.797031\pi$
$13$	−0.750647	+	0.750647i	−0.208192	+	0.208192i	0.595307	+	0.803499i	$0.297031\pi$
$14$	−4.10544	+	0.528041i	−1.09722	+	0.141125i
$15$		0			0
$16$	−3.48771	+	1.95854i	−0.871928	+	0.489635i
$17$	−3.14698	−	3.14698i	−0.763254	−	0.763254i	0.213656	−	0.976909i	$-0.431463\pi$
$17$	−3.14698	−	3.14698i	−0.763254	−	0.763254i	−0.976909	+	0.213656i	$0.931463\pi$
$18$	2.78656	+	3.19923i	0.656799	+	0.754066i
$19$	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	$-0.627522\pi$
$23$	2.54575	−	2.54575i	0.530825	−	0.530825i	0.920818	+	0.389993i	$0.127522\pi$
$24$	−2.34878	+	4.29921i	−0.479443	+	0.877573i
$25$		0			0
$26$	−1.48903	+	0.191519i	−0.292023	+	0.0375599i
$27$	4.97150	+	1.51135i	0.956766	+	0.290859i
$28$	−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
$33$	0.879551	+	0.0868061i	0.153110	+	0.0151110i
$34$	−0.802913	−	6.24253i	−0.137699	−	1.07058i
$35$		0			0
$36$	0.354305	+	5.98953i	0.0590509	+	0.998255i
$37$	6.76263	+	6.76263i	1.11177	+	1.11177i	0.992911	+	0.118858i	$0.0379234\pi$
$37$	6.76263	+	6.76263i	1.11177	+	1.11177i	0.118858	+	0.992911i	$0.462077\pi$
$38$	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	$-0.107509\pi$
$42$	−7.16627	+	0.211772i	−1.10578	+	0.0326771i
$43$	5.95972	−	5.95972i	0.908848	−	0.908848i	−0.0873310	−	0.996179i	$-0.527834\pi$
$43$	5.95972	−	5.95972i	0.908848	−	0.908848i	0.996179	+	0.0873310i	$0.0278338\pi$
$44$	0.258254	+	0.987336i	0.0389333	+	0.148846i
$45$		0			0
$46$	5.04990	−	0.649518i	0.744567	−	0.0957661i
$47$	3.33849	+	3.33849i	0.486969	+	0.486969i	0.907349	−	0.420379i	$-0.138103\pi$
$47$	3.33849	+	3.33849i	0.486969	+	0.486969i	−0.420379	+	0.907349i	$0.638103\pi$
$48$	−6.34486	+	2.78257i	−0.915802	+	0.401630i
$49$		−	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	$-0.438943\pi$
$53$	−5.75871	−	5.75871i	−0.791019	−	0.791019i	−0.981660	+	0.190641i	$0.938943\pi$
$54$	4.25889	+	5.98848i	0.579562	+	0.814928i
$55$		0			0
$56$	−3.09950	−	7.67638i	−0.414188	−	1.02580i
$57$	10.3627	+	1.02273i	1.37257	+	0.135464i
$58$	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	$-0.897806\pi$
$61$		−	4.92929i		−	0.631131i	0.948904	−	0.315565i	$-0.102194\pi$
$62$	−5.11198	−	3.94684i	−0.649222	−	0.501249i
$63$	−7.30283	+	4.87536i	−0.920070	+	0.614238i
$64$	−5.55474	−	5.75716i	−0.694342	−	0.719645i
$65$		0			0
$66$	0.909545	+	0.857332i	0.111957	+	0.105530i
$67$	−7.98415	−	7.98415i	−0.975419	−	0.975419i	0.0242864	−	0.999705i	$-0.492269\pi$
$67$	−7.98415	−	7.98415i	−0.975419	−	0.975419i	−0.999705	+	0.0242864i	$0.992269\pi$
$68$	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	$-0.0976959\pi$
$72$	−4.77991	+	7.01088i	−0.563317	+	0.826241i
$73$	3.20654	+	3.20654i	0.375297	+	0.375297i	0.869402	−	0.494105i	$-0.164504\pi$
$73$	3.20654	+	3.20654i	0.375297	+	0.375297i	−0.494105	+	0.869402i	$0.664504\pi$
$74$	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
$78$	−2.59918	+	0.0768090i	−0.294300	+	0.00869691i
$79$			7.31215i			0.822682i	0.911482	+	0.411341i	$0.134939\pi$
$79$			7.31215i			0.822682i	−0.911482	+	0.411341i	$0.865061\pi$
$80$		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	$-0.129016\pi$
$83$	4.77995	+	4.77995i	0.524668	+	0.524668i	−0.394310	+	0.918978i	$0.629016\pi$
$84$	−8.20494	−	5.95647i	−0.895233	−	0.649904i
$85$		0			0
$86$	11.8220	−	1.52055i	1.27480	−	0.163965i
$87$	0.868848	−	8.80349i	0.0931502	−	0.943833i
$88$	−0.564226	+	1.32842i	−0.0601467	+	0.141610i
$89$	−12.6431			−1.34017			−0.670083	−	0.742286i	$-0.733741\pi$
$89$	−12.6431			−1.34017			−0.670083	+	0.742286i	$0.733741\pi$
$90$		0			0
$91$		−	3.10712i		−	0.325715i
$92$	6.21420	+	3.63736i	0.647875	+	0.379221i
$93$	−7.87155	−	0.776871i	−0.816241	−	0.0805578i
$94$	0.851777	+	6.62243i	0.0878541	+	0.683052i
$95$		0			0
$96$	−9.50730	−	2.36881i	−0.970335	−	0.241766i
$97$	−10.8789	+	10.8789i	−1.10458	+	1.10458i	−0.110732	+	0.993850i	$0.535320\pi$
$97$	−10.8789	+	10.8789i	−1.10458	+	1.10458i	−0.993850	+	0.110732i	$0.964680\pi$
$98$	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	$-0.603317\pi$
$101$	−6.41002			−0.637821			−0.318911	+	0.947785i	$0.603317\pi$
$102$	−0.322010	−	10.8967i	−0.0318838	−	1.07893i
$103$	1.86309	+	1.86309i	0.183575	+	0.183575i	0.792912	−	0.609336i	$-0.208564\pi$
$103$	1.86309	+	1.86309i	0.183575	+	0.183575i	−0.609336	+	0.792912i	$0.708564\pi$
$104$	−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	$-0.509466\pi$
$107$	10.0319	−	10.0319i	0.969824	−	0.969824i	0.999558	+	0.0297341i	$0.00946607\pi$
$108$	−0.408206	+	10.3843i	−0.0392797	+	0.999228i
$109$	−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	$-0.709890\pi$
$113$	1.88933	−	1.88933i	0.177733	−	0.177733i	0.790367	+	0.612634i	$0.209890\pi$
$114$	10.7161	+	10.1009i	1.00365	+	0.946039i
$115$		0			0
$116$	9.88231	−	2.58489i	0.917549	−	0.240001i
$117$	−2.64871	+	1.76828i	−0.244874	+	0.163477i
$118$	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
$123$	0.721896	−	7.31452i	0.0650912	−	0.659528i
$124$	−2.31125	−	8.83617i	−0.207556	−	0.793511i
$125$		0			0
$126$	−12.3884	−	0.854070i	−1.10364	−	0.0760866i
$127$	−0.964015	+	0.964015i	−0.0855425	+	0.0855425i	−0.748583	−	0.663041i	$-0.769266\pi$
$127$	−0.964015	+	0.964015i	−0.0855425	+	0.0855425i	0.663041	+	0.748583i	$0.269266\pi$
$128$	−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	$-0.392387\pi$
$131$	7.59234			0.663346			0.331673	+	0.943395i	$0.392387\pi$
$132$	0.277186	+	1.74578i	0.0241259	+	0.151951i
$133$	−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	$-0.236274\pi$
$137$	0.713542	+	0.713542i	0.0609620	+	0.0609620i	−0.675968	+	0.736931i	$0.736274\pi$
$138$	8.81488	−	0.260491i	0.750373	−	0.0221744i
$139$	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
$144$	−11.4099	+	3.71689i	−0.950821	+	0.309741i
$145$		0			0
$146$	0.818111	+	6.36069i	0.0677073	+	0.526414i
$147$	0.266524	−	2.70052i	0.0219825	−	0.222735i
$148$	−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
$153$	−7.41324	−	11.1043i	−0.599325	−	0.897731i
$154$	−2.09491	+	0.269447i	−0.168812	+	0.0217126i
$155$		0			0
$156$	−2.97591	−	2.16039i	−0.238263	−	0.172970i
$157$	−4.38090	−	4.38090i	−0.349634	−	0.349634i	0.510339	−	0.859973i	$-0.329520\pi$
$157$	−4.38090	−	4.38090i	−0.349634	−	0.349634i	−0.859973	+	0.510339i	$0.829520\pi$
$158$	−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
$162$	6.32222	+	11.0467i	0.496720	+	0.867911i
$163$	−0.470868	+	0.470868i	−0.0368812	+	0.0368812i	−0.725307	−	0.688426i	$-0.758302\pi$
$163$	−0.470868	+	0.470868i	−0.0368812	+	0.0368812i	0.688426	+	0.725307i	$0.258302\pi$
$164$	8.21087	−	2.14769i	0.641162	−	0.167707i
$165$		0			0
$166$	1.21955	+	9.48180i	0.0946553	+	0.735930i
$167$	−0.495354	−	0.495354i	−0.0383316	−	0.0383316i	0.687681	−	0.726013i	$-0.258629\pi$
$167$	−0.495354	−	0.495354i	−0.0383316	−	0.0383316i	−0.726013	+	0.687681i	$0.758629\pi$
$168$	−4.03666	−	13.7589i	−0.311435	−	1.06152i
$169$			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	$-0.210079\pi$
$173$	2.32674	+	2.32674i	0.176899	+	0.176899i	−0.613104	+	0.790002i	$0.710079\pi$
$174$	8.58109	−	9.10370i	0.650531	−	0.690150i
$175$		0			0
$176$	−1.77970	+	0.999395i	−0.134150	+	0.0753323i
$177$	0.198209	−	2.00833i	0.0148983	−	0.150955i
$178$	−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	$0.0692740\pi$
$181$			5.80972i			0.431833i	−0.976412	+	0.215917i	$0.930726\pi$
$182$	2.68536	−	3.47811i	0.199052	−	0.257814i
$183$	0.838550	−	8.49650i	0.0619874	−	0.628079i
$184$	3.81254	+	9.44235i	0.281064	+	0.696099i
$185$		0			0
$186$	−8.13998	−	7.67270i	−0.596852	−	0.562589i
$187$	−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	$-0.167003\pi$
$192$	−8.59519	−	10.8684i	−0.620304	−	0.784361i
$193$	−4.57254	−	4.57254i	−0.329138	−	0.329138i	0.523120	−	0.852259i	$-0.324768\pi$
$193$	−4.57254	−	4.57254i	−0.329138	−	0.329138i	−0.852259	+	0.523120i	$0.824768\pi$
$194$	−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	$-0.687743\pi$
$197$	3.85757	−	3.85757i	0.274840	−	0.274840i	0.831045	+	0.556205i	$0.187743\pi$
$198$	1.42192	+	1.63249i	0.101051	+	0.116016i
$199$		−	5.91833i		−	0.419540i	−0.977751	−	0.209770i	$-0.932729\pi$
$199$		−	5.91833i		−	0.419540i	0.977751	−	0.209770i	$-0.0672714\pi$
$200$		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
$204$	9.05712	−	12.4760i	0.634125	−	0.873497i
$205$		0			0
$206$	0.475344	+	3.69573i	0.0331188	+	0.257494i
$207$	8.98285	−	5.99695i	0.624351	−	0.416817i
$208$	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	$-0.923063\pi$
$211$		−	6.95372i		−	0.478714i	0.970932	−	0.239357i	$-0.0769366\pi$
$212$	8.22802	−	14.0571i	0.565103	−	0.965444i
$213$	0.866144	−	8.77609i	0.0593472	−	0.601328i
$214$	19.8999	−	2.55953i	1.36033	−	0.174966i
$215$		0			0
$216$	−9.43167	+	11.2714i	−0.641744	+	0.766919i
$217$	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
$222$	0.691978	+	23.4162i	0.0464425	+	1.57159i
$223$	16.7218	+	16.7218i	1.11977	+	1.11977i	0.991774	+	0.127998i	$0.0408550\pi$
$223$	16.7218	+	16.7218i	1.11977	+	1.11977i	0.127998	+	0.991774i	$0.459145\pi$
$224$	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	$-0.949211\pi$
$227$	−12.4814	+	12.4814i	−0.828416	+	0.828416i	0.158881	+	0.987298i	$0.449211\pi$
$228$	3.26575	+	20.5685i	0.216280	+	1.36218i
$229$	−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	$-0.854819\pi$
$233$	−6.98082	+	6.98082i	−0.457329	+	0.457329i	0.440449	+	0.897778i	$0.354819\pi$
$234$	−4.49322	−	0.309768i	−0.293731	−	0.0202502i
$235$		0			0
$236$	2.25444	−	0.589688i	0.146752	−	0.0383854i
$237$	−1.24391	+	12.6038i	−0.0808008	+	0.818704i
$238$	14.5814	+	11.2580i	0.945174	+	0.729746i
$239$	−12.3210			−0.796976			−0.398488	−	0.917173i	$-0.630465\pi$
$239$	−12.3210			−0.796976			−0.398488	+	0.917173i	$0.630465\pi$
$240$		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
$243$	13.7404	+	7.36211i	0.881449	+	0.472279i
$244$	9.53771	−	2.49475i	0.610589	−	0.159710i
$245$		0			0
$246$	7.12974	−	7.56395i	0.454575	−	0.482260i
$247$	−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	$-0.601386\pi$
$251$	−9.92262			−0.626311			−0.313155	+	0.949702i	$0.601386\pi$
$252$	−13.1294	−	11.6628i	−0.827073	−	0.734688i
$253$	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	$-0.471479\pi$
$257$	−14.5324	−	14.5324i	−0.906508	−	0.906508i	−0.995989	+	0.0894809i	$0.971479\pi$
$258$	20.6361	−	0.609821i	1.28474	−	0.0379658i
$259$	−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	$-0.592930\pi$
$263$	10.8634	−	10.8634i	0.669867	−	0.669867i	0.957685	+	0.287818i	$0.0929298\pi$
$264$	−1.19853	+	2.19379i	−0.0737643	+	0.135018i
$265$		0			0
$266$	−24.6818	+	3.17457i	−1.51334	+	0.194646i
$267$	−21.7926	−	2.15079i	−1.33369	−	0.131626i
$268$	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
$273$	0.528571	−	5.35567i	0.0319905	−	0.324140i
$274$	0.182052	+	1.41543i	0.0109982	+	0.0855090i
$275$		0			0
$276$	10.0925	+	7.32676i	0.607497	+	0.441019i
$277$	−6.97897	−	6.97897i	−0.419326	−	0.419326i	0.465645	−	0.884971i	$-0.345822\pi$
$277$	−6.97897	−	6.97897i	−0.419326	−	0.419326i	−0.884971	+	0.465645i	$0.845822\pi$
$278$	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	$0.847448\pi$
$282$	0.341607	+	11.5598i	0.0203424	+	0.688378i
$283$	−8.86458	+	8.86458i	−0.526945	+	0.526945i	−0.919660	−	0.392715i	$-0.871536\pi$
$283$	−8.86458	+	8.86458i	−0.526945	+	0.526945i	0.392715	+	0.919660i	$0.371536\pi$
$284$	9.85156	−	2.57684i	0.584583	−	0.152908i
$285$		0			0
$286$	−0.759816	+	0.0977275i	−0.0449289	+	0.00577875i
$287$	8.78258	+	8.78258i	0.518419	+	0.518419i
$288$	−15.9845	−	5.70040i	−0.941898	−	0.335899i
$289$			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	$-0.230311\pi$
$293$	1.49638	+	1.49638i	0.0874192	+	0.0874192i	−0.662045	+	0.749464i	$0.730311\pi$
$294$	2.63230	−	2.79261i	0.153519	−	0.162868i
$295$		0			0
$296$	−25.0830	+	10.1278i	−1.45792	+	0.588666i
$297$	2.53684	+	0.771206i	0.147202	+	0.0447499i
$298$	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
$303$	−11.0488	−	1.09045i	−0.634738	−	0.0626445i
$304$	−20.9681	+	11.7747i	−1.20260	+	0.675325i
$305$		0			0
$306$	1.29866	−	18.8371i	0.0742393	−	1.07685i
$307$	12.4948	+	12.4948i	0.713118	+	0.713118i	0.967186	−	0.254068i	$-0.0817688\pi$
$307$	12.4948	+	12.4948i	0.713118	+	0.713118i	−0.254068	+	0.967186i	$0.581769\pi$
$308$	−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	$0.997973\pi$
$312$	−1.46408	−	4.99030i	−0.0828874	−	0.282520i
$313$	12.0383	+	12.0383i	0.680447	+	0.680447i	0.960101	−	0.279654i	$-0.0902198\pi$
$313$	12.0383	+	12.0383i	0.680447	+	0.680447i	−0.279654	+	0.960101i	$0.590220\pi$
$314$	−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	−0.146829	+	0.989162i	$0.546907\pi$
$317$	−20.2257	+	20.2257i	−1.13599	+	1.13599i	−0.989162	+	0.146829i	$0.953093\pi$
$318$	−0.589252	−	19.9400i	−0.0330436	−	1.11818i
$319$		−	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
$324$	−2.47015	+	17.8297i	−0.137230	+	0.990539i
$325$		0			0
$326$	−0.934042	+	0.120136i	−0.0517318	+	0.00665374i
$327$	−21.7956	−	2.15109i	−1.20530	−	0.118955i
$328$	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	$0.110048\pi$
$331$			12.3308i			0.677760i	−0.940830	+	0.338880i	$0.889952\pi$
$332$	−6.82959	+	11.6679i	−0.374822	+	0.640361i
$333$	15.9305	+	23.8624i	0.872988	+	1.30765i
$334$	−0.126384	−	0.982613i	−0.00691540	−	0.0537662i
$335$		0			0
$336$	7.37262	−	18.8904i	0.402209	−	1.03056i
$337$	−10.6723	+	10.6723i	−0.581359	+	0.581359i	−0.935277	−	0.353918i	$-0.884849\pi$
$337$	−10.6723	+	10.6723i	−0.581359	+	0.581359i	0.353918	+	0.935277i	$0.384849\pi$
$338$	−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
$342$	16.7528	+	19.2337i	0.905886	+	1.04004i
$343$	−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	$-0.848272\pi$
$347$	−8.00457	+	8.00457i	−0.429708	+	0.429708i	0.458821	+	0.888529i	$0.348272\pi$
$348$	17.4736	−	2.77437i	0.936685	−	0.148722i
$349$	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	$-0.897471\pi$
$353$	−11.8744	+	11.8744i	−0.632008	+	0.632008i	0.316563	+	0.948571i	$0.397471\pi$
$354$	1.95760	−	2.07682i	0.104045	−	0.110382i
$355$		0			0
$356$	−6.39876	−	24.4632i	−0.339134	−	1.29655i
$357$	22.4528	+	2.21595i	1.18833	+	0.117281i
$358$	−12.0254	+	15.5755i	−0.635564	+	0.823189i
$359$	33.8765			1.78793			0.893967	−	0.448133i	$-0.147911\pi$
$359$	33.8765			1.78793			0.893967	+	0.448133i	$0.147911\pi$
$360$		0			0
$361$	17.1439			0.902313
$362$	−5.02112	+	6.50340i	−0.263904	+	0.341811i
$363$	−18.5116	−	1.82698i	−0.971608	−	0.0958915i
$364$	6.01198	−	1.57254i	0.315114	−	0.0824233i
$365$		0			0
$366$	8.28186	−	8.78625i	0.432900	−	0.459265i
$367$	−10.7900	+	10.7900i	−0.563233	+	0.563233i	−0.930224	−	0.366992i	$-0.880388\pi$
$367$	−10.7900	+	10.7900i	−0.563233	+	0.563233i	0.366992	+	0.930224i	$0.380388\pi$
$368$	−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
$372$	−2.48067	−	15.6239i	−0.128617	−	0.810060i
$373$	25.8380	−	25.8380i	1.33784	−	1.33784i	0.439697	−	0.898146i	$-0.355086\pi$
$373$	25.8380	−	25.8380i	1.33784	−	1.33784i	0.898146	−	0.439697i	$-0.144914\pi$
$374$	−0.409708	−	3.18541i	−0.0211855	−	0.164714i
$375$		0			0
$376$	−12.3827	+	4.99977i	−0.638588	+	0.257843i
$377$	3.83385	+	3.83385i	0.197453	+	0.197453i
$378$	−21.2082	−	3.57960i	−1.09083	−	0.184115i
$379$	−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	−0.111219	+	0.993796i	$0.535475\pi$
$383$	−21.6256	+	21.6256i	−1.10501	+	1.10501i	−0.993796	+	0.111219i	$0.964525\pi$
$384$	−0.228292	−	19.5946i	−0.0116500	−	0.999932i
$385$		0			0
$386$	−1.16663	−	9.07035i	−0.0593798	−	0.461669i
$387$	21.0293	−	14.0391i	1.06898	−	0.713649i
$388$	−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
$393$	13.0867	+	1.29158i	0.660138	+	0.0651514i
$394$	7.65210	−	0.984213i	0.385507	−	0.0495839i
$395$		0			0
$396$	0.180794	+	3.05631i	0.00908522	+	0.153586i
$397$	−14.0596	−	14.0596i	−0.705629	−	0.705629i	0.259984	−	0.965613i	$-0.416283\pi$
$397$	−14.0596	−	14.0596i	−0.705629	−	0.705629i	−0.965613	+	0.259984i	$0.916283\pi$
$398$	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	$0.850577\pi$
$402$	−0.816968	−	27.6458i	−0.0407466	−	1.37885i
$403$	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
$408$	20.9211	−	6.13795i	1.03575	−	0.303874i
$409$		−	26.3245i		−	1.30166i	−0.759223	−	0.650831i	$-0.774421\pi$
$409$		−	26.3245i		−	1.30166i	0.759223	−	0.650831i	$-0.225579\pi$
$410$		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
$414$	15.2383	+	1.05055i	0.748923	+	0.0516317i
$415$		0			0
$416$	4.81820	−	3.58428i	0.236232	−	0.175734i
$417$	15.5382	+	1.53352i	0.760909	+	0.0750969i
$418$	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	$-0.777764\pi$
$421$		−	26.3792i		−	1.28564i	0.766017	−	0.642821i	$-0.222236\pi$
$422$	6.00983	−	7.78398i	0.292554	−	0.378918i
$423$	7.86440	+	11.7801i	0.382380	+	0.572769i
$424$	21.3594	−	8.62431i	1.03730	−	0.418833i
$425$		0			0
$426$	8.55439	−	9.07537i	0.414462	−	0.439703i
$427$	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	$0.757269\pi$
$432$	−20.2992	+	4.46572i	−0.976646	+	0.214857i
$433$	2.25457	+	2.25457i	0.108347	+	0.108347i	0.759202	−	0.650855i	$-0.225589\pi$
$433$	2.25457	+	2.25457i	0.108347	+	0.108347i	−0.650855	+	0.759202i	$0.725589\pi$
$434$	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
$438$	0.328105	+	11.1029i	0.0156775	+	0.530519i
$439$			11.8510i			0.565620i	0.959176	+	0.282810i	$0.0912665\pi$
$439$			11.8510i			0.565620i	−0.959176	+	0.282810i	$0.908733\pi$
$440$		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	$-0.232153\pi$
$443$	1.66807	+	1.66807i	0.0792526	+	0.0792526i	−0.666369	+	0.745622i	$0.732153\pi$
$444$	−19.4631	+	26.8101i	−0.923679	+	1.27235i
$445$		0			0
$446$	4.26636	+	33.1703i	0.202018	+	1.57066i
$447$	2.23827	−	22.6789i	0.105866	−	1.07268i
$448$	23.4114	+	0.418930i	1.10609	+	0.0197926i
$449$	−34.3414			−1.62067			−0.810336	−	0.585966i	$-0.800715\pi$
$449$	−34.3414			−1.62067			−0.810336	+	0.585966i	$0.800715\pi$
$450$		0			0
$451$		−	2.16539i		−	0.101964i
$452$	4.61186	+	2.69946i	0.216924	+	0.126972i
$453$	4.75703	+	0.469488i	0.223505	+	0.0220585i
$454$	−24.7588	+	3.18447i	−1.16199	+	0.149455i
$455$		0			0
$456$	−14.1208	+	25.8468i	−0.661269	+	1.21039i
$457$	4.61474	−	4.61474i	0.215869	−	0.215869i	−0.590886	−	0.806755i	$-0.701222\pi$
$457$	4.61474	−	4.61474i	0.215869	−	0.215869i	0.806755	+	0.590886i	$0.201222\pi$
$458$	−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	$-0.340357\pi$
$461$	20.6452			0.961543			0.480772	+	0.876846i	$0.340357\pi$
$462$	−3.65678	+	0.108062i	−0.170129	+	0.00502751i
$463$	−27.1817	−	27.1817i	−1.26324	−	1.26324i	−0.949512	−	0.313730i	$-0.898421\pi$
$463$	−27.1817	−	27.1817i	−1.26324	−	1.26324i	−0.313730	−	0.949512i	$-0.601579\pi$
$464$	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	$-0.817145\pi$
$467$	−6.39901	+	6.39901i	−0.296111	+	0.296111i	0.543378	+	0.839488i	$0.317145\pi$
$468$	−4.76198	−	4.23007i	−0.220123	−	0.195535i
$469$	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
$474$	−12.2854	+	13.0336i	−0.564287	+	0.598653i
$475$		0			0
$476$	6.59262	+	25.2043i	0.302172	+	1.15524i
$477$	−13.5656	−	20.3200i	−0.621127	−	0.930389i
$478$	−13.7921	−	10.6485i	−0.630834	−	0.487052i
$479$	35.9113			1.64083			0.820414	−	0.571770i	$-0.193743\pi$
$479$	35.9113			1.64083			0.820414	+	0.571770i	$0.193743\pi$
$480$		0			0
$481$	−10.1527			−0.462923
$482$	−7.87870	−	6.08295i	−0.358865	−	0.277071i
$483$	−1.79260	+	18.1632i	−0.0815660	+	0.826456i
$484$	−5.43540	−	20.7801i	−0.247064	−	0.944552i
$485$		0			0
$486$	9.01824	+	20.1164i	0.409076	+	0.912501i
$487$	23.9090	−	23.9090i	1.08342	−	1.08342i	0.0872343	−	0.996188i	$-0.472197\pi$
$487$	23.9090	−	23.9090i	1.08342	−	1.08342i	0.996188	−	0.0872343i	$-0.0278029\pi$
$488$	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	$-0.746101\pi$
$491$	−30.9507			−1.39678			−0.698392	+	0.715715i	$0.746101\pi$
$492$	14.5182	−	2.30513i	0.654533	−	0.103923i
$493$	−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
$498$	0.489103	+	16.5510i	0.0219172	+	0.741669i
$499$	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	$-0.596959\pi$
$503$	14.6687	−	14.6687i	0.654047	−	0.654047i	0.953965	+	0.299918i	$0.0969593\pi$
$504$	−4.61729	−	24.4025i	−0.205671	−	1.08698i
$505$		0			0
$506$	2.57684	−	0.331433i	0.114555	−	0.0147340i
$507$	−2.01979	+	20.4653i	−0.0897022	+	0.908896i
$508$	−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
$513$	29.8886	+	9.08621i	1.31961	+	0.401166i
$514$	−3.70778	−	28.8274i	−0.163543	−	1.27152i
$515$		0			0
$516$	23.6270	+	17.1523i	1.04012	+	0.755088i
$517$	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	$-0.106939\pi$
$522$	16.3397	−	14.2321i	0.715170	−	0.622920i
$523$	−15.6997	+	15.6997i	−0.686499	+	0.686499i	−0.961456	−	0.274957i	$-0.911336\pi$
$523$	−15.6997	+	15.6997i	−0.686499	+	0.686499i	0.274957	+	0.961456i	$0.411336\pi$
$524$	3.84254	+	14.6904i	0.167862	+	0.641755i
$525$		0			0
$526$	21.5493	−	2.77167i	0.939596	−	0.120851i
$527$	14.3714	+	14.3714i	0.626026	+	0.626026i
$528$	−3.23763	+	1.41988i	−0.140900	+	0.0617923i
$529$			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
$534$	−22.5358	−	21.2421i	−0.975218	−	0.919235i
$535$		0			0
$536$	29.6137	−	11.9572i	1.27912	−	0.516470i
$537$	−2.36701	+	23.9835i	−0.102144	+	1.03496i
$538$	−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	$0.00992877\pi$
$541$			1.45079i			0.0623742i	−0.999514	+	0.0311871i	$0.990071\pi$
$542$	0.342914	+	0.264756i	0.0147294	+	0.0113722i
$543$	−0.988326	+	10.0141i	−0.0424131	+	0.429745i
$544$	15.0266	+	20.1996i	0.644258	+	0.866050i
$545$		0			0
$546$	5.22038	−	5.53831i	0.223412	−	0.237018i
$547$	1.86763	+	1.86763i	0.0798541	+	0.0798541i	0.745906	−	0.666052i	$-0.232017\pi$
$547$	1.86763	+	1.86763i	0.0798541	+	0.0798541i	−0.666052	+	0.745906i	$0.732017\pi$
$548$	−1.01951	+	1.74177i	−0.0435512	+	0.0744045i
$549$	2.89078	−	14.5026i	0.123375	−	0.618955i
$550$		0			0
$551$		−	30.7055i		−	1.30810i
$552$	4.96530	+	16.9241i	0.211337	+	0.720339i
$553$	−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	$-0.512984\pi$
$557$	22.6188	−	22.6188i	0.958389	−	0.958389i	0.999168	+	0.0407789i	$0.0129839\pi$
$558$	−12.7254	−	14.6100i	−0.538711	−	0.618490i
$559$			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	−0.991173	−	0.132574i	$-0.957676\pi$
$563$	−26.6638	−	26.6638i	−1.12375	−	1.12375i	−0.132574	−	0.991173i	$-0.542324\pi$
$564$	−9.60832	+	13.2353i	−0.404583	+	0.557307i
$565$		0			0
$566$	−17.5843	+	2.26169i	−0.739123	+	0.0950660i
$567$	−24.3450	+	10.0612i	−1.02239	+	0.422530i
$568$	13.2549	+	5.62980i	0.556163	+	0.236221i
$569$	29.3180			1.22907			0.614537	−	0.788888i	$-0.289343\pi$
$569$	29.3180			1.22907			0.614537	+	0.788888i	$0.289343\pi$
$570$		0			0
$571$		−	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
$573$	2.35535	−	23.8652i	0.0983960	−	0.996985i
$574$	2.24077	+	17.4216i	0.0935280	+	0.727165i
$575$		0			0
$576$	−12.9664	−	20.1958i	−0.540268	−	0.841493i
$577$	18.9787	−	18.9787i	0.790092	−	0.790092i	−0.191417	−	0.981509i	$-0.561308\pi$
$577$	18.9787	−	18.9787i	0.790092	−	0.790092i	0.981509	+	0.191417i	$0.0613081\pi$
$578$	−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
$582$	−37.6691	+	1.11317i	−1.56143	+	0.0461423i
$583$	−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	$-0.643683\pi$
$587$	11.2326	−	11.2326i	0.463619	−	0.463619i	0.899840	+	0.436220i	$0.143683\pi$
$588$	5.36013	−	0.851053i	0.221048	−	0.0350968i
$589$	−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	$-0.748511\pi$
$593$	0.161070	−	0.161070i	0.00661435	−	0.00661435i	0.710406	+	0.703792i	$0.248511\pi$
$594$	2.17321	+	3.05578i	0.0891679	+	0.125380i
$595$		0			0
$596$	25.4581	−	6.65901i	1.04281	−	0.272764i
$597$	1.00680	−	10.2013i	0.0412057	−	0.417511i
$598$	−3.30313	+	4.27825i	−0.135075	+	0.174951i
$599$	−15.6557			−0.639673			−0.319837	−	0.947473i	$-0.603628\pi$
$599$	−15.6557			−0.639673			−0.319837	+	0.947473i	$0.603628\pi$
$600$		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
$603$	−18.8080	−	28.1726i	−0.765922	−	1.14728i
$604$	1.39676	+	5.33998i	0.0568335	+	0.217281i
$605$		0			0
$606$	−11.4256	−	10.7697i	−0.464133	−	0.437489i
$607$	−18.7872	+	18.7872i	−0.762550	+	0.762550i	−0.976783	−	0.214232i	$-0.931275\pi$
$607$	−18.7872	+	18.7872i	−0.762550	+	0.762550i	0.214232	+	0.976783i	$0.431275\pi$
$608$	−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
$612$	17.7339	−	19.9639i	0.716851	−	0.806992i
$613$	29.5115	−	29.5115i	1.19196	−	1.19196i	0.215443	−	0.976516i	$-0.430880\pi$
$613$	29.5115	−	29.5115i	1.19196	−	1.19196i	0.976516	−	0.215443i	$-0.0691195\pi$
$614$	3.18791	+	24.7855i	0.128654	+	1.00026i
$615$		0			0
$616$	−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	$-0.571560\pi$
$618$	0.190638	+	6.45111i	0.00766859	+	0.259502i
$619$	−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
$624$	2.67403	−	6.85148i	0.107047	−	0.274279i
$625$		0			0
$626$	3.07144	+	23.8799i	0.122759	+	0.954434i
$627$	5.28785	+	0.521877i	0.211176	+	0.0208417i
$628$	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
$633$	1.18294	−	11.9860i	0.0470176	−	0.476399i
$634$	−40.1210	+	5.16036i	−1.59341	+	0.204944i
$635$		0			0
$636$	16.5738	−	22.8301i	0.657193	−	0.905273i
$637$	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	$-0.0852090\pi$
$642$	34.7365	−	1.02651i	1.37094	−	0.0405129i
$643$	−12.4335	+	12.4335i	−0.490331	+	0.490331i	−0.908410	−	0.418080i	$-0.862703\pi$
$643$	−12.4335	+	12.4335i	−0.490331	+	0.490331i	0.418080	+	0.908410i	$0.362703\pi$
$644$	−20.3891	+	5.33311i	−0.803442	+	0.210154i
$645$		0			0
$646$	−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	$0.746880\pi$
$648$	−18.1746	+	17.8237i	−0.713965	+	0.700181i
$649$		−	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	$-0.155705\pi$
$653$	10.5497	+	10.5497i	0.412841	+	0.412841i	−0.469886	+	0.882727i	$0.655705\pi$
$654$	−22.5389	−	21.2450i	−0.881339	−	0.830745i
$655$		0			0
$656$	8.31116	+	14.8003i	0.324496	+	0.577854i
$657$	7.55356	+	11.3145i	0.294692	+	0.441421i
$658$	−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	$-0.670728\pi$
$661$		−	44.1992i		−	1.71915i	0.511009	−	0.859575i	$-0.329272\pi$
$662$	−10.6570	+	13.8030i	−0.414196	+	0.536470i
$663$	8.14357	+	0.803718i	0.316270	+	0.0312138i
$664$	−17.7292	+	7.15852i	−0.688025	+	0.277804i
$665$		0			0
$666$	−2.79072	+	40.4797i	−0.108138	+	1.56856i
$667$	−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
$672$	24.5791	−	14.7740i	0.948160	−	0.569920i
$673$	−13.1276	−	13.1276i	−0.506033	−	0.506033i	0.407274	−	0.913306i	$-0.366480\pi$
$673$	−13.1276	−	13.1276i	−0.506033	−	0.506033i	−0.913306	+	0.407274i	$0.866480\pi$
$674$	−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	$-0.533235\pi$
$677$	23.1658	−	23.1658i	0.890334	−	0.890334i	0.994554	+	0.104220i	$0.0332347\pi$
$678$	6.54196	−	0.193323i	0.251242	−	0.00742452i
$679$		−	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	$-0.118241\pi$
$683$	14.8655	+	14.8655i	0.568814	+	0.568814i	−0.362982	+	0.931796i	$0.618241\pi$
$684$	2.13008	+	36.0090i	0.0814455	+	1.37684i
$685$		0			0
$686$	−2.86899	−	22.3060i	−0.109539	−	0.851647i
$687$	−1.89049	−	0.186579i	−0.0721266	−	0.00711843i
$688$	−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	$0.355790\pi$
$691$			47.2699i			1.79823i	−0.437710	+	0.899116i	$0.644210\pi$
$692$	−3.32444	+	5.67960i	−0.126376	+	0.215906i
$693$	−3.72646	+	2.48778i	−0.141557	+	0.0945031i
$694$	−15.8783	+	2.04227i	−0.602733	+	0.0775235i
$695$		0			0
$696$	21.9577	+	11.9961i	0.832306	+	0.454713i
$697$	−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	$-0.546206\pi$
$701$	−7.65973			−0.289304			−0.144652	+	0.989483i	$0.546206\pi$
$702$	−7.69216	−	1.29831i	−0.290322	−	0.0490015i
$703$	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
$708$	3.98625	−	0.632915i	0.149812	−	0.0237864i
$709$	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
$714$	23.2185	+	21.8856i	0.868931	+	0.819050i
$715$		0			0
$716$	−26.9225	+	7.04204i	−1.00614	+	0.263174i
$717$	−21.2373	−	2.09599i	−0.793123	−	0.0782762i
$718$	37.9213	+	29.2781i	1.41521	+	1.09265i
$719$	−14.6227			−0.545333			−0.272666	−	0.962109i	$-0.587906\pi$
$719$	−14.6227			−0.545333			−0.272666	+	0.962109i	$0.587906\pi$
$720$		0			0
$721$	−7.71179			−0.287202
$722$	19.1909	+	14.8168i	0.714212	+	0.551425i
$723$	−12.1318	−	1.19733i	−0.451186	−	0.0445292i
$724$	−11.2413	+	2.94034i	−0.417778	+	0.109277i
$725$		0			0
$726$	−19.1429	−	18.0440i	−0.710460	−	0.669675i
$727$	22.1109	−	22.1109i	0.820048	−	0.820048i	−0.166067	−	0.986115i	$-0.553107\pi$
$727$	22.1109	−	22.1109i	0.820048	−	0.820048i	0.986115	+	0.166067i	$0.0531067\pi$
$728$	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
$732$	16.8643	−	2.67763i	0.623323	−	0.0989679i
$733$	8.64610	−	8.64610i	0.319351	−	0.319351i	−0.529167	−	0.848518i	$-0.677495\pi$
$733$	8.64610	−	8.64610i	0.319351	−	0.319351i	0.848518	+	0.529167i	$0.177495\pi$
$734$	−21.4037	+	2.75294i	−0.790023	+	0.101613i
$735$		0			0
$736$	−16.3405	+	12.1557i	−0.602318	+	0.448067i
$737$	−4.07412	−	4.07412i	−0.150072	−	0.150072i
$738$	13.5761	−	11.8249i	0.499743	−	0.435282i
$739$	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	$-0.806356\pi$
$743$	−6.78930	+	6.78930i	−0.249075	+	0.249075i	0.571516	+	0.820591i	$0.306356\pi$
$744$	10.7262	−	19.6333i	0.393243	−	0.719791i
$745$		0			0
$746$	51.2539	−	6.59227i	1.87654	−	0.241360i
$747$	11.2600	+	16.8664i	0.411982	+	0.617110i
$748$	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
$753$	−17.1034	−	1.68800i	−0.623282	−	0.0615140i
$754$	0.978161	+	7.60505i	0.0356225	+	0.276959i
$755$		0			0
$756$	−20.6468	−	22.3364i	−0.750916	−	0.812368i
$757$	33.9790	+	33.9790i	1.23499	+	1.23499i	0.962025	+	0.272963i	$0.0880035\pi$
$757$	33.9790	+	33.9790i	1.23499	+	1.23499i	0.272963	+	0.962025i	$0.411996\pi$
$758$	−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	$0.785496\pi$
$762$	−3.33799	+	0.0986416i	−0.120923	+	0.00357341i
$763$	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
$768$	16.6793	−	22.1315i	0.601862	−	0.798600i
$769$			14.8941i			0.537094i	0.963267	+	0.268547i	$0.0865434\pi$
$769$			14.8941i			0.537094i	−0.963267	+	0.268547i	$0.913457\pi$
$770$		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	$-0.309687\pi$
$773$	−7.32969	−	7.32969i	−0.263631	−	0.263631i	−0.826527	+	0.562897i	$0.809687\pi$
$774$	35.6736	+	2.45939i	1.28226	+	0.0884008i
$775$		0			0
$776$	−16.2923	−	40.3504i	−0.584861	−	1.44850i
$777$	−48.2496	−	4.76193i	−1.73094	−	0.170833i
$778$	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
$783$	7.71905	−	25.3914i	0.275856	−	0.907414i
$784$	3.06848	+	5.46427i	0.109589	+	0.195152i
$785$		0			0
$786$	13.5330	+	12.7561i	0.482707	+	0.454996i
$787$	4.66068	+	4.66068i	0.166135	+	0.166135i	0.785278	−	0.619143i	$-0.212520\pi$
$787$	4.66068	+	4.66068i	0.166135	+	0.166135i	−0.619143	+	0.785278i	$0.712520\pi$
$788$	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
$792$	−2.43907	+	3.57749i	−0.0866687	+	0.127120i
$793$	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	$-0.995975\pi$
$797$	−27.8720	+	27.8720i	−0.987276	+	0.987276i	0.0126440	+	0.999920i	$0.495975\pi$
$798$	−43.0835	+	1.27317i	−1.52514	+	0.0450697i
$799$		−	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
$804$	22.9787	−	31.6528i	0.810396	−	1.11631i
$805$		0			0
$806$	6.79998	−	0.874612i	0.239519	−	0.0308069i
$807$	−5.49951	+	55.7231i	−0.193592	+	1.96155i
$808$	7.08773	−	16.6875i	0.249346	−	0.587063i
$809$	−18.8285			−0.661975			−0.330988	−	0.943635i	$-0.607382\pi$
$809$	−18.8285			−0.661975			−0.330988	+	0.943635i	$0.607382\pi$
$810$		0			0
$811$			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
$813$	0.528027	+	0.0521129i	0.0185187	+	0.00182768i
$814$	0.880433	+	6.84523i	0.0308592	+	0.239925i
$815$		0			0
$816$	28.7238	+	11.2104i	1.00553	+	0.392444i
$817$	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	$-0.580352\pi$
$821$	−14.3129			−0.499523			−0.249761	+	0.968307i	$0.580352\pi$
$822$	0.0730123	+	2.47070i	0.00254660	+	0.0861757i
$823$	−10.8660	−	10.8660i	−0.378766	−	0.378766i	0.491891	−	0.870657i	$-0.336306\pi$
$823$	−10.8660	−	10.8660i	−0.378766	−	0.378766i	−0.870657	+	0.491891i	$0.836306\pi$
$824$	−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	$-0.769548\pi$
$827$	−2.49596	+	2.49596i	−0.0867932	+	0.0867932i	0.662377	+	0.749170i	$0.269548\pi$
$828$	16.1498	+	14.3459i	0.561245	+	0.498553i
$829$	−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
$834$	16.0681	+	15.1457i	0.556392	+	0.524452i
$835$		0			0
$836$	1.55262	+	5.93585i	0.0536985	+	0.205296i
$837$	−22.7034	−	6.90191i	−0.784746	−	0.238565i
$838$	11.0460	−	14.3069i	0.381577	−	0.494223i
$839$	−26.9749			−0.931277			−0.465638	−	0.884975i	$-0.654175\pi$
$839$	−26.9749			−0.931277			−0.465638	+	0.884975i	$0.654175\pi$
$840$		0			0
$841$	2.91458			0.100503
$842$	22.7985	−	29.5288i	0.785687	−	1.01763i
$843$	−2.62992	+	26.6473i	−0.0905792	+	0.917782i
$844$	13.4548	−	3.51933i	0.463133	−	0.121140i
$845$		0			0
$846$	−1.37769	+	19.9835i	−0.0473660	+	0.687048i
$847$	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
$852$	17.4193	−	2.76574i	0.596774	−	0.0947526i
$853$	−16.4190	+	16.4190i	−0.562174	+	0.562174i	−0.929925	−	0.367750i	$-0.880128\pi$
$853$	−16.4190	+	16.4190i	−0.562174	+	0.562174i	0.367750	+	0.929925i	$0.380128\pi$
$854$	2.60287	+	20.2369i	0.0890683	+	0.692492i
$855$		0			0
$856$	15.0239	+	37.2091i	0.513508	+	1.27178i
$857$	24.4641	+	24.4641i	0.835678	+	0.835678i	0.988287	−	0.152608i	$-0.0487673\pi$
$857$	24.4641	+	24.4641i	0.835678	+	0.835678i	−0.152608	+	0.988287i	$0.548767\pi$
$858$	−1.32630	+	0.0391938i	−0.0452792	+	0.00133806i
$859$	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	$-0.937626\pi$
$863$	−23.0950	+	23.0950i	−0.786161	+	0.786161i	0.194701	+	0.980863i	$0.437626\pi$
$864$	−26.5824	−	12.5449i	−0.904353	−	0.426785i
$865$		0			0
$866$	0.575226	+	4.47229i	0.0195470	+	0.151975i
$867$	−0.477499	+	4.83819i	−0.0162167	+	0.164314i
$868$	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
$873$	−38.3869	+	25.6271i	−1.29920	+	0.867345i
$874$	30.3599	−	3.90489i	1.02694	−	0.132085i
$875$		0			0
$876$	−9.22855	+	12.7122i	−0.311804	+	0.429505i
$877$	14.2900	+	14.2900i	0.482539	+	0.482539i	0.905942	−	0.423403i	$-0.139164\pi$
$877$	14.2900	+	14.2900i	0.482539	+	0.482539i	−0.423403	+	0.905942i	$0.639164\pi$
$878$	−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	$-0.276228\pi$
$882$	5.01230	−	4.36576i	0.168773	−	0.147003i
$883$	−3.68252	+	3.68252i	−0.123927	+	0.123927i	−0.766350	−	0.642423i	$-0.777929\pi$
$883$	−3.68252	+	3.68252i	−0.123927	+	0.123927i	0.642423	+	0.766350i	$0.277929\pi$
$884$	2.39112	+	9.14153i	0.0804221	+	0.307463i
$885$		0			0
$886$	0.425589	+	3.30889i	0.0142980	+	0.111164i
$887$	−14.7506	−	14.7506i	−0.495277	−	0.495277i	0.414687	−	0.909964i	$-0.363891\pi$
$887$	−14.7506	−	14.7506i	−0.495277	−	0.495277i	−0.909964	+	0.414687i	$0.863891\pi$
$888$	−44.9579	+	13.1900i	−1.50869	+	0.442628i
$889$		−	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
$894$	22.1060	−	23.4523i	0.739336	−	0.784363i
$895$		0			0
$896$	25.8446	+	20.7025i	0.863409	+	0.691623i
$897$	−0.650169	+	6.58775i	−0.0217085	+	0.219959i
$898$	−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
$903$	−4.19655	+	42.5210i	−0.139653	+	1.41501i
$904$	2.82948	+	7.00763i	0.0941070	+	0.233070i
$905$		0			0
$906$	4.91925	+	4.63686i	0.163431	+	0.154049i
$907$	8.08868	+	8.08868i	0.268580	+	0.268580i	0.828528	−	0.559948i	$-0.189179\pi$
$907$	8.08868	+	8.08868i	0.268580	+	0.268580i	−0.559948	+	0.828528i	$0.689179\pi$
$908$	−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	$-0.221527\pi$
$912$	−38.1452	+	16.7288i	−1.26311	+	0.553945i
$913$	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
$918$	5.44296	−	32.2482i	0.179644	−	1.06435i
$919$			39.9611i			1.31819i	0.752058	+	0.659097i	$0.229061\pi$
$919$			39.9611i			1.31819i	−0.752058	+	0.659097i	$0.770939\pi$
$920$		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
$924$	−4.18679	−	3.03945i	−0.137735	−	0.0999904i
$925$		0			0
$926$	−6.93510	−	53.9193i	−0.227901	−	1.77190i
$927$	4.38882	+	6.57403i	0.144148	+	0.215920i
$928$	−4.19779	+	28.5852i	−0.137799	+	0.938354i
$929$	0.568113			0.0186392			0.00931959	−	0.999957i	$-0.497033\pi$
$929$	0.568113			0.0186392			0.00931959	+	0.999957i	$0.497033\pi$
$930$		0			0
$931$		−	9.41909i		−	0.308698i
$932$	−17.0403	−	9.97418i	−0.558173	−	0.326715i
$933$	−0.0382135	+	0.387193i	−0.00125105	+	0.0126761i
$934$	−12.6935	+	1.63263i	−0.415343	+	0.0534213i
$935$		0			0
$936$	−1.67468	−	8.85073i	−0.0547386	−	0.289295i
$937$	−18.2630	+	18.2630i	−0.596626	+	0.596626i	−0.939413	−	0.342787i	$-0.888629\pi$
$937$	−18.2630	+	18.2630i	−0.596626	+	0.596626i	0.342787	+	0.939413i	$0.388629\pi$
$938$	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	$-0.381048\pi$
$941$	22.3971			0.730125			0.365063	+	0.930983i	$0.381048\pi$
$942$	−0.448270	−	15.1693i	−0.0146054	−	0.494242i
$943$	−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	$-0.867861\pi$
$947$	−15.7486	+	15.7486i	−0.511761	+	0.511761i	0.403305	+	0.915066i	$0.367861\pi$
$948$	−25.0167	+	3.97201i	−0.812504	+	0.129005i
$949$	−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	0.0842194	−	0.996447i	$-0.473160\pi$
$953$	33.3609	−	33.3609i	1.08067	−	1.08067i	0.996447	−	0.0842194i	$-0.0268396\pi$
$954$	2.37644	−	34.4704i	0.0769400	−	1.11602i
$955$		0			0
$956$	−6.23572	−	23.8399i	−0.201678	−	0.771037i
$957$	0.443352	−	4.49221i	0.0143315	−	0.145213i
$958$	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
$963$	35.3984	−	23.6319i	1.14070	−	0.761529i
$964$	−3.56215	−	13.6185i	−0.114729	−	0.438622i
$965$		0			0
$966$	−17.7044	+	18.7826i	−0.569630	+	0.604322i
$967$	8.01398	−	8.01398i	0.257712	−	0.257712i	−0.566411	−	0.824123i	$-0.691668\pi$
$967$	8.01398	−	8.01398i	0.257712	−	0.257712i	0.824123	+	0.566411i	$0.191668\pi$
$968$	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	$-0.254091\pi$
$971$	43.4981			1.39592			0.697961	+	0.716136i	$0.254091\pi$
$972$	−7.29085	+	30.3124i	−0.233854	+	0.972272i
$973$	−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	0.945411	+	0.325880i	$0.105661\pi$
$977$	39.7367	+	39.7367i	1.27129	+	1.27129i	0.325880	+	0.945411i	$0.394339\pi$
$978$	−1.63042	+	0.0481810i	−0.0521352	+	0.00154066i
$979$	−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	$-0.816095\pi$
$983$	−9.14087	+	9.14087i	−0.291548	+	0.291548i	0.546143	+	0.837692i	$0.316095\pi$
$984$	18.2439	+	9.96719i	0.581596	+	0.317742i
$985$		0			0
$986$	−31.8830	+	4.10079i	−1.01536	+	0.130596i
$987$	−23.8193	−	2.35081i	−0.758176	−	0.0748271i
$988$	−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
$993$	−2.09766	+	21.2542i	−0.0665671	+	0.674483i
$994$	2.68852	+	20.9028i	0.0852747	+	0.662997i
$995$		0			0
$996$	−13.7569	+	18.9499i	−0.435904	+	0.600451i
$997$	3.70273	+	3.70273i	0.117267	+	0.117267i	0.763305	−	0.646038i	$-0.223575\pi$
$997$	3.70273	+	3.70273i	0.117267	+	0.117267i	−0.646038	+	0.763305i	$0.723575\pi$
$998$	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.293.13		32
3.2	odd	2	inner	600.2.w.j.293.4		32
5.2	odd	4	inner	600.2.w.j.557.5		32
5.3	odd	4		120.2.w.c.77.12	yes	32
5.4	even	2		120.2.w.c.53.4	✓	32
8.5	even	2	inner	600.2.w.j.293.12		32
15.2	even	4	inner	600.2.w.j.557.12		32
15.8	even	4		120.2.w.c.77.5	yes	32
15.14	odd	2		120.2.w.c.53.13	yes	32
20.3	even	4		480.2.bi.c.17.9		32
20.19	odd	2		480.2.bi.c.113.16		32
24.5	odd	2	inner	600.2.w.j.293.5		32
40.3	even	4		480.2.bi.c.17.8		32
40.13	odd	4		120.2.w.c.77.13	yes	32
40.19	odd	2		480.2.bi.c.113.1		32
40.29	even	2		120.2.w.c.53.5	yes	32
40.37	odd	4	inner	600.2.w.j.557.4		32
60.23	odd	4		480.2.bi.c.17.1		32
60.59	even	2		480.2.bi.c.113.8		32
120.29	odd	2		120.2.w.c.53.12	yes	32
120.53	even	4		120.2.w.c.77.4	yes	32
120.59	even	2		480.2.bi.c.113.9		32
120.77	even	4	inner	600.2.w.j.557.13		32
120.83	odd	4		480.2.bi.c.17.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.4	✓	32	5.4	even	2
120.2.w.c.53.5	yes	32	40.29	even	2
120.2.w.c.53.12	yes	32	120.29	odd	2
120.2.w.c.53.13	yes	32	15.14	odd	2
120.2.w.c.77.4	yes	32	120.53	even	4
120.2.w.c.77.5	yes	32	15.8	even	4
120.2.w.c.77.12	yes	32	5.3	odd	4
120.2.w.c.77.13	yes	32	40.13	odd	4
480.2.bi.c.17.1		32	60.23	odd	4
480.2.bi.c.17.8		32	40.3	even	4
480.2.bi.c.17.9		32	20.3	even	4
480.2.bi.c.17.16		32	120.83	odd	4
480.2.bi.c.113.1		32	40.19	odd	2
480.2.bi.c.113.8		32	60.59	even	2
480.2.bi.c.113.9		32	120.59	even	2
480.2.bi.c.113.16		32	20.19	odd	2
600.2.w.j.293.4		32	3.2	odd	2	inner
600.2.w.j.293.5		32	24.5	odd	2	inner
600.2.w.j.293.12		32	8.5	even	2	inner
600.2.w.j.293.13		32	1.1	even	1	trivial
600.2.w.j.557.4		32	40.37	odd	4	inner
600.2.w.j.557.5		32	5.2	odd	4	inner
600.2.w.j.557.12		32	15.2	even	4	inner
600.2.w.j.557.13		32	120.77	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.11940 + 0.864261i) q^{2} +(1.72368 + 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.78246 + 1.68013i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +O(q^{10})\)	\(q+(1.11940 + 0.864261i) q^{2} +(1.72368 + 0.170116i) q^{3} +(0.506107 + 1.93490i) q^{4} +(1.78246 + 1.68013i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-1.10573 + 2.60334i) q^{8} +(2.94212 + 0.586449i) q^{9} +0.510276 q^{11} +(0.543207 + 3.42125i) 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} +(2.78656 + 3.19923i) q^{18} +6.01198 q^{19} +(-3.91945 + 3.21529i) q^{21} +(0.571203 + 0.441012i) q^{22} +(2.54575 - 2.54575i) q^{23} +(-2.34878 + 4.29921i) q^{24} +(-1.48903 + 0.191519i) q^{26} +(4.97150 + 1.51135i) q^{27} +(-5.05199 - 2.95708i) q^{28} -5.10739i q^{29} -4.56672 q^{31} +(-5.59683 - 0.821906i) q^{32} +(0.879551 + 0.0868061i) q^{33} +(-0.802913 - 6.24253i) q^{34} +(0.354305 + 5.98953i) q^{36} +(6.76263 + 6.76263i) q^{37} +(6.72981 + 5.19592i) q^{38} +(-1.42157 + 1.16618i) q^{39} -4.24355i q^{41} +(-7.16627 + 0.211772i) 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} +(-6.34486 + 2.78257i) q^{48} -1.56672i q^{49} +(-4.88902 - 5.95972i) q^{51} +(-1.83234 - 1.07252i) q^{52} +(-5.75871 - 5.75871i) q^{53} +(4.25889 + 5.98848i) q^{54} +(-3.09950 - 7.67638i) q^{56} +(10.3627 + 1.02273i) q^{57} +(4.41411 - 5.71720i) q^{58} -1.16514i q^{59} -4.92929i q^{61} +(-5.11198 - 3.94684i) q^{62} +(-7.30283 + 4.87536i) q^{63} +(-5.55474 - 5.75716i) q^{64} +(0.909545 + 0.857332i) q^{66} +(-7.98415 - 7.98415i) q^{67} +(4.49639 - 7.68180i) q^{68} +(4.82112 - 3.95497i) q^{69} -5.09150i q^{71} +(-4.77991 + 7.01088i) 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} +(-2.59918 + 0.0768090i) q^{78} +7.31215i q^{79} +(8.31215 + 3.45081i) q^{81} +(3.66754 - 4.75023i) q^{82} +(4.77995 + 4.77995i) q^{83} +(-8.20494 - 5.95647i) q^{84} +(11.8220 - 1.52055i) q^{86} +(0.868848 - 8.80349i) q^{87} +(-0.564226 + 1.32842i) q^{88} -12.6431 q^{89} -3.10712i q^{91} +(6.21420 + 3.63736i) q^{92} +(-7.87155 - 0.776871i) q^{93} +(0.851777 + 6.62243i) q^{94} +(-9.50730 - 2.36881i) 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

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