LMFDB - Embedded newform 600.2.w.j.293.12

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			293.12
Character	$\chi$	$=$	600.293
Dual form			600.2.w.j.557.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.864261 + 1.11940i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(2.94212 + 0.586449i) q^{9} +O(q^{10})$	\(q+(0.864261 + 1.11940i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(2.94212 + 0.586449i) q^{9} -0.510276 q^{11} +(1.20152 - 3.24905i) 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} +(1.88629 + 3.80025i) q^{18} -6.01198 q^{19} +(3.91945 - 3.21529i) q^{21} +(-0.441012 - 0.571203i) q^{22} +(2.54575 - 2.54575i) q^{23} +(4.67541 - 1.46305i) q^{24} +(1.48903 + 0.191519i) q^{26} +(-4.97150 - 1.51135i) q^{27} +(-2.95708 - 5.05199i) q^{28} +5.10739i q^{29} -4.56672 q^{31} +(-0.821906 - 5.59683i) q^{32} +(0.879551 + 0.0868061i) q^{33} +(0.802913 - 6.24253i) q^{34} +(-2.62375 + 5.39592i) q^{36} +(-6.76263 - 6.76263i) q^{37} +(-5.19592 - 6.72981i) q^{38} +(-1.42157 + 1.16618i) q^{39} -4.24355i q^{41} +(6.98662 + 1.60857i) 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} +(5.67851 + 3.96920i) q^{48} -1.56672i q^{49} +(4.88902 + 5.95972i) q^{51} +(1.07252 + 1.83234i) q^{52} +(5.75871 + 5.75871i) q^{53} +(-2.60487 - 6.87129i) q^{54} +(3.09950 - 7.67638i) q^{56} +(10.3627 + 1.02273i) q^{57} +(-5.71720 + 4.41411i) q^{58} +1.16514i q^{59} +4.92929i q^{61} +(-3.94684 - 5.11198i) q^{62} +(-7.30283 + 4.87536i) q^{63} +(5.55474 - 5.75716i) q^{64} +(0.662991 + 1.05959i) q^{66} +(7.98415 + 7.98415i) q^{67} +(7.68180 - 4.49639i) q^{68} +(-4.82112 + 3.95497i) q^{69} -5.09150i q^{71} +(-8.30779 + 1.72645i) 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} +(-2.53402 - 0.583424i) q^{78} +7.31215i q^{79} +(8.31215 + 3.45081i) q^{81} +(4.75023 - 3.66754i) q^{82} +(-4.77995 - 4.77995i) q^{83} +(4.23762 + 9.21104i) q^{84} +(-11.8220 - 1.52055i) q^{86} +(0.868848 - 8.80349i) q^{87} +(1.32842 - 0.564226i) q^{88} -12.6431 q^{89} +3.10712i q^{91} +(3.63736 + 6.21420i) q^{92} +(7.87155 + 0.776871i) q^{93} +(-0.851777 + 6.62243i) q^{94} +(0.464592 + 9.78694i) q^{96} +(-10.8789 + 10.8789i) q^{97} +(1.75378 - 1.35405i) q^{98} +(-1.50129 - 0.299251i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 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 $

$2$	0.864261	+	1.11940i	0.611125	+	0.791534i
$2$	0.864261	+	1.11940i	0.611125	+	0.791534i
$3$	−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
$6$	−1.29928	−	2.07651i	−0.530428	−	0.847730i
$7$	−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	$0.436567\pi$
$8$	−2.60334	+	1.10573i	−0.920419	+	0.390933i
$9$	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	$0.524511\pi$
$12$	1.20152	−	3.24905i	0.346850	−	0.937921i
$13$	0.750647	−	0.750647i	0.208192	−	0.208192i	−0.595307	−	0.803499i	$-0.702969\pi$
$13$	0.750647	−	0.750647i	0.208192	−	0.208192i	0.803499	+	0.595307i	$0.202969\pi$
$14$	−4.10544	−	0.528041i	−1.09722	−	0.141125i
$15$		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	$0.931463\pi$
$18$	1.88629	+	3.80025i	0.444603	+	0.895728i
$19$	−6.01198			−1.37924			−0.689622	−	0.724170i	$-0.742223\pi$
$19$	−6.01198			−1.37924			−0.689622	+	0.724170i	$0.742223\pi$
$20$		0			0
$21$	3.91945	−	3.21529i	0.855293	−	0.701634i
$22$	−0.441012	−	0.571203i	−0.0940240	−	0.121781i
$23$	2.54575	−	2.54575i	0.530825	−	0.530825i	−0.389993	−	0.920818i	$-0.627522\pi$
$23$	2.54575	−	2.54575i	0.530825	−	0.530825i	0.920818	+	0.389993i	$0.127522\pi$
$24$	4.67541	−	1.46305i	0.954365	−	0.298643i
$25$		0			0
$26$	1.48903	+	0.191519i	0.292023	+	0.0375599i
$27$	−4.97150	−	1.51135i	−0.956766	−	0.290859i
$28$	−2.95708	−	5.05199i	−0.558835	−	0.954736i
$29$			5.10739i			0.948418i	0.880412	+	0.474209i	$0.157266\pi$
$29$			5.10739i			0.948418i	−0.880412	+	0.474209i	$0.842734\pi$
$30$		0			0
$31$	−4.56672			−0.820207			−0.410104	−	0.912039i	$-0.634507\pi$
$31$	−4.56672			−0.820207			−0.410104	+	0.912039i	$0.634507\pi$
$32$	−0.821906	−	5.59683i	−0.145294	−	0.989389i
$33$	0.879551	+	0.0868061i	0.153110	+	0.0151110i
$34$	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	−0.992911	−	0.118858i	$-0.962077\pi$
$37$	−6.76263	−	6.76263i	−1.11177	−	1.11177i	−0.118858	−	0.992911i	$-0.537923\pi$
$38$	−5.19592	−	6.72981i	−0.842890	−	1.09172i
$39$	−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	$-0.107509\pi$
$42$	6.98662	+	1.60857i	1.07806	+	0.248208i
$43$	−5.95972	+	5.95972i	−0.908848	+	0.908848i	−0.996179	−	0.0873310i	$-0.972166\pi$
$43$	−5.95972	+	5.95972i	−0.908848	+	0.908848i	0.0873310	+	0.996179i	$0.472166\pi$
$44$	0.258254	−	0.987336i	0.0389333	−	0.148846i
$45$		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	$0.638103\pi$
$48$	5.67851	+	3.96920i	0.819622	+	0.572905i
$49$		−	1.56672i		−	0.223817i
$50$		0			0
$51$	4.88902	+	5.95972i	0.684599	+	0.834527i
$52$	1.07252	+	1.83234i	0.148732	+	0.254100i
$53$	5.75871	+	5.75871i	0.791019	+	0.791019i	0.981660	−	0.190641i	$-0.0610565\pi$
$53$	5.75871	+	5.75871i	0.791019	+	0.791019i	−0.190641	+	0.981660i	$0.561057\pi$
$54$	−2.60487	−	6.87129i	−0.354478	−	0.935064i
$55$		0			0
$56$	3.09950	−	7.67638i	0.414188	−	1.02580i
$57$	10.3627	+	1.02273i	1.37257	+	0.135464i
$58$	−5.71720	+	4.41411i	−0.750706	+	0.579602i
$59$			1.16514i			0.151689i	0.997120	+	0.0758444i	$0.0241652\pi$
$59$			1.16514i			0.151689i	−0.997120	+	0.0758444i	$0.975835\pi$
$60$		0			0
$61$			4.92929i			0.631131i	0.948904	+	0.315565i	$0.102194\pi$
$61$			4.92929i			0.631131i	−0.948904	+	0.315565i	$0.897806\pi$
$62$	−3.94684	−	5.11198i	−0.501249	−	0.649222i
$63$	−7.30283	+	4.87536i	−0.920070	+	0.614238i
$64$	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	$-0.00773136\pi$
$67$	7.98415	+	7.98415i	0.975419	+	0.975419i	−0.0242864	+	0.999705i	$0.507731\pi$
$68$	7.68180	−	4.49639i	0.931555	−	0.545267i
$69$	−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	$-0.0976959\pi$
$72$	−8.30779	+	1.72645i	−0.979082	+	0.203465i
$73$	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
$78$	−2.53402	−	0.583424i	−0.286922	−	0.0660597i
$79$			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
$82$	4.75023	−	3.66754i	0.524575	−	0.405012i
$83$	−4.77995	−	4.77995i	−0.524668	−	0.524668i	0.394310	−	0.918978i	$-0.370984\pi$
$83$	−4.77995	−	4.77995i	−0.524668	−	0.524668i	−0.918978	+	0.394310i	$0.870984\pi$
$84$	4.23762	+	9.21104i	0.462363	+	1.00501i
$85$		0			0
$86$	−11.8220	−	1.52055i	−1.27480	−	0.163965i
$87$	0.868848	−	8.80349i	0.0931502	−	0.943833i
$88$	1.32842	−	0.564226i	0.141610	−	0.0601467i
$89$	−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
$92$	3.63736	+	6.21420i	0.379221	+	0.647875i
$93$	7.87155	+	0.776871i	0.816241	+	0.0805578i
$94$	−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	−0.110732	+	0.993850i	$0.535320\pi$
$97$	−10.8789	+	10.8789i	−1.10458	+	1.10458i	−0.993850	+	0.110732i	$0.964680\pi$
$98$	1.75378	−	1.35405i	0.177159	−	0.136780i
$99$	−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	$0.396683\pi$
$102$	−2.44592	+	10.6235i	−0.242182	+	1.05188i
$103$	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	−0.999558	−	0.0297341i	$-0.990534\pi$
$107$	−10.0319	+	10.0319i	−0.969824	+	0.969824i	0.0297341	+	0.999558i	$0.490534\pi$
$108$	5.44043	−	8.85447i	0.523506	−	0.852022i
$109$	12.6448			1.21115			0.605577	−	0.795786i	$-0.292942\pi$
$109$	12.6448			1.21115			0.605577	+	0.795786i	$0.292942\pi$
$110$		0			0
$111$	10.5062	+	12.8070i	0.997200	+	1.21559i
$112$	11.2717	−	3.16482i	1.06508	−	0.299047i
$113$	1.88933	−	1.88933i	0.177733	−	0.177733i	−0.612634	−	0.790367i	$-0.709890\pi$
$113$	1.88933	−	1.88933i	0.177733	−	0.177733i	0.790367	+	0.612634i	$0.209890\pi$
$114$	7.81124	+	12.4839i	0.731590	+	1.16923i
$115$		0			0
$116$	−9.88231	−	2.58489i	−0.917549	−	0.240001i
$117$	2.64871	−	1.76828i	0.244874	−	0.163477i
$118$	−1.30426	+	1.00699i	−0.120067	+	0.0927008i
$119$	13.0261			1.19410
$120$		0			0
$121$	−10.7396			−0.976329
$122$	−5.51784	+	4.26019i	−0.499562	+	0.385700i
$123$	−0.721896	+	7.31452i	−0.0650912	+	0.659528i
$124$	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	−0.748583	−	0.663041i	$-0.769266\pi$
$127$	−0.964015	+	0.964015i	−0.0855425	+	0.0855425i	0.663041	+	0.748583i	$0.269266\pi$
$128$	11.2453	+	1.24228i	0.993953	+	0.109803i
$129$	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	$0.607613\pi$
$132$	−0.613109	+	1.65791i	−0.0533643	+	0.144303i
$133$	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	$0.736274\pi$
$138$	−8.59390	−	1.97863i	−0.731561	−	0.168432i
$139$	−9.01457			−0.764606			−0.382303	−	0.924037i	$-0.624869\pi$
$139$	−9.01457			−0.764606			−0.382303	+	0.924037i	$0.624869\pi$
$140$		0			0
$141$	−5.18655	−	6.32241i	−0.436787	−	0.532443i
$142$	5.69942	−	4.40038i	0.478284	−	0.369272i
$143$	−0.383038	+	0.383038i	−0.0320312	+	0.0320312i
$144$	−9.11269	−	7.80762i	−0.759390	−	0.650635i
$145$		0			0
$146$	−0.818111	+	6.36069i	−0.0677073	+	0.526414i
$147$	−0.266524	+	2.70052i	−0.0219825	+	0.222735i
$148$	16.5077	−	9.66243i	1.35692	−	0.794247i
$149$			13.1573i			1.07789i	0.842341	+	0.538944i	$0.181177\pi$
$149$			13.1573i			1.07789i	−0.842341	+	0.538944i	$0.818823\pi$
$150$		0			0
$151$	2.75982			0.224591			0.112295	−	0.993675i	$-0.464180\pi$
$151$	2.75982			0.224591			0.112295	+	0.993675i	$0.464180\pi$
$152$	15.6512	−	6.64761i	1.26948	−	0.539192i
$153$	−7.41324	−	11.1043i	−0.599325	−	0.897731i
$154$	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	$-0.170480\pi$
$157$	4.38090	+	4.38090i	0.349634	+	0.349634i	−0.510339	+	0.859973i	$0.670480\pi$
$158$	−8.18522	+	6.31961i	−0.651181	+	0.502761i
$159$	−8.94650	−	10.9058i	−0.709504	−	0.864886i
$160$		0			0
$161$			10.5375i			0.830472i
$162$	3.32104	+	12.2870i	0.260925	+	0.965359i
$163$	0.470868	−	0.470868i	0.0368812	−	0.0368812i	−0.688426	−	0.725307i	$-0.741698\pi$
$163$	0.470868	−	0.470868i	0.0368812	−	0.0368812i	0.725307	+	0.688426i	$0.241698\pi$
$164$	8.21087	+	2.14769i	0.641162	+	0.167707i
$165$		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	$0.758629\pi$
$168$	−6.64841	+	12.7043i	−0.512936	+	0.980160i
$169$			11.8731i			0.913312i
$170$		0			0
$171$	−17.6880	−	3.52572i	−1.35263	−	0.269619i
$172$	−8.51523	−	14.5477i	−0.649280	−	1.10925i
$173$	−2.32674	−	2.32674i	−0.176899	−	0.176899i	0.613104	−	0.790002i	$-0.289921\pi$
$173$	−2.32674	−	2.32674i	−0.176899	−	0.176899i	−0.790002	+	0.613104i	$0.789921\pi$
$174$	10.6055	−	6.63592i	0.804002	−	0.503068i
$175$		0			0
$176$	1.77970	+	0.999395i	0.134150	+	0.0753323i
$177$	0.198209	−	2.00833i	0.0148983	−	0.150955i
$178$	−10.9269	−	14.1527i	−0.819008	−	1.06079i
$179$		−	13.9141i		−	1.03999i	−0.854169	−	0.519996i	$-0.825934\pi$
$179$		−	13.9141i		−	1.03999i	0.854169	−	0.519996i	$-0.174066\pi$
$180$		0			0
$181$		−	5.80972i		−	0.431833i	−0.976412	−	0.215917i	$-0.930726\pi$
$181$		−	5.80972i		−	0.431833i	0.976412	−	0.215917i	$-0.0692740\pi$
$182$	−3.47811	+	2.68536i	−0.257814	+	0.199052i
$183$	0.838550	−	8.49650i	0.0619874	−	0.628079i
$184$	−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
$188$	−8.14930	+	4.77003i	−0.594349	+	0.347890i
$189$	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	$-0.167003\pi$
$192$	−10.5540	+	8.97853i	−0.761666	+	0.647969i
$193$	−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	−0.831045	−	0.556205i	$-0.812257\pi$
$197$	−3.85757	+	3.85757i	−0.274840	+	0.274840i	0.556205	+	0.831045i	$0.312257\pi$
$198$	−0.962528	−	1.93918i	−0.0684039	−	0.137811i
$199$		−	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
$202$	5.53993	+	7.17537i	0.389788	+	0.504858i
$203$	−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
$207$	8.98285	−	5.99695i	0.624351	−	0.416817i
$208$	−4.08821	+	1.14787i	−0.283467	+	0.0795904i
$209$	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	$0.923063\pi$
$212$	−14.0571	+	8.22802i	−0.965444	+	0.565103i
$213$	−0.866144	+	8.77609i	−0.0593472	+	0.601328i
$214$	−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
$218$	10.9284	+	14.1546i	0.740166	+	0.958671i
$219$	−4.98156	−	6.07252i	−0.336622	−	0.410343i
$220$		0			0
$221$	−4.72454			−0.317807
$222$	−5.25610	+	22.8292i	−0.352766	+	1.53219i
$223$	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	−0.158881	−	0.987298i	$-0.550789\pi$
$227$	12.4814	−	12.4814i	0.828416	−	0.828416i	0.987298	+	0.158881i	$0.0507887\pi$
$228$	−7.22354	+	19.5332i	−0.478390	+	1.29362i
$229$	1.09678			0.0724770			0.0362385	−	0.999343i	$-0.488462\pi$
$229$	1.09678			0.0724770			0.0362385	+	0.999343i	$0.488462\pi$
$230$		0			0
$231$	−2.00000	+	1.64069i	−0.131590	+	0.107949i
$232$	−5.64737	−	13.2963i	−0.370768	−	0.872942i
$233$	−6.98082	+	6.98082i	−0.457329	+	0.457329i	−0.897778	−	0.440449i	$-0.854819\pi$
$233$	−6.98082	+	6.98082i	−0.457329	+	0.457329i	0.440449	+	0.897778i	$0.354819\pi$
$234$	4.26859	+	1.43671i	0.279046	+	0.0939207i
$235$		0			0
$236$	−2.25444	−	0.589688i	−0.146752	−	0.0383854i
$237$	1.24391	−	12.6038i	0.0808008	−	0.818704i
$238$	11.2580	+	14.5814i	0.729746	+	0.945174i
$239$	−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	$0.572790\pi$
$242$	−9.28183	−	12.0219i	−0.596659	−	0.772798i
$243$	−13.7404	−	7.36211i	−0.881449	−	0.472279i
$244$	−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
$248$	11.8887	−	5.04954i	0.754934	−	0.320646i
$249$	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	$0.398614\pi$
$252$	−5.73735	−	16.5977i	−0.361419	−	1.04556i
$253$	−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	$0.971479\pi$
$258$	20.1187	+	4.63206i	1.25254	+	0.288379i
$259$	27.9923			1.73935
$260$		0			0
$261$	−2.99522	+	15.0266i	−0.185400	+	0.930120i
$262$	−6.56176	−	8.49885i	−0.405387	−	0.525061i
$263$	10.8634	−	10.8634i	0.669867	−	0.669867i	−0.287818	−	0.957685i	$-0.592930\pi$
$263$	10.8634	−	10.8634i	0.669867	−	0.669867i	0.957685	+	0.287818i	$0.0929298\pi$
$264$	−2.38575	+	0.746557i	−0.146833	+	0.0459474i
$265$		0			0
$266$	24.6818	+	3.17457i	1.51334	+	0.194646i
$267$	21.7926	+	2.15079i	1.33369	+	0.131626i
$268$	−19.4894	+	11.4077i	−1.19050	+	0.696838i
$269$		−	32.3280i		−	1.97108i	−0.169455	−	0.985538i	$-0.554201\pi$
$269$		−	32.3280i		−	1.97108i	0.169455	−	0.985538i	$-0.445799\pi$
$270$		0			0
$271$	0.306338			0.0186087			0.00930434	−	0.999957i	$-0.497038\pi$
$271$	0.306338			0.0186087			0.00930434	+	0.999957i	$0.497038\pi$
$272$	4.81227	+	17.1392i	0.291787	+	1.03922i
$273$	0.528571	−	5.35567i	0.0319905	−	0.324140i
$274$	−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	$-0.154178\pi$
$277$	6.97897	+	6.97897i	0.419326	+	0.419326i	−0.465645	+	0.884971i	$0.654178\pi$
$278$	−7.79094	−	10.0909i	−0.467270	−	0.605212i
$279$	−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	$0.847448\pi$
$282$	2.59477	−	11.2700i	0.154516	−	0.671121i
$283$	8.86458	−	8.86458i	0.526945	−	0.526945i	−0.392715	−	0.919660i	$-0.628464\pi$
$283$	8.86458	−	8.86458i	0.526945	−	0.526945i	0.919660	+	0.392715i	$0.128464\pi$
$284$	9.85156	+	2.57684i	0.584583	+	0.152908i
$285$		0			0
$286$	−0.759816	−	0.0977275i	−0.0449289	−	0.00577875i
$287$	8.78258	+	8.78258i	0.518419	+	0.518419i
$288$	0.864107	−	16.9485i	0.0509180	−	0.998703i
$289$			2.80690i			0.165112i
$290$		0			0
$291$	20.6023	−	16.9010i	1.20773	−	0.990754i
$292$	−7.82720	+	4.58150i	−0.458053	+	0.268112i
$293$	−1.49638	−	1.49638i	−0.0874192	−	0.0874192i	0.662045	−	0.749464i	$-0.269689\pi$
$293$	−1.49638	−	1.49638i	−0.0874192	−	0.0874192i	−0.749464	+	0.662045i	$0.769689\pi$
$294$	−3.25330	+	2.03560i	−0.189736	+	0.118719i
$295$		0			0
$296$	25.0830	+	10.1278i	1.45792	+	0.588666i
$297$	2.53684	+	0.771206i	0.147202	+	0.0447499i
$298$	−14.7283	+	11.3713i	−0.853186	+	0.658724i
$299$		−	3.82192i		−	0.221027i
$300$		0			0
$301$		−	24.6688i		−	1.42189i
$302$	2.38520	+	3.08933i	0.137253	+	0.177771i
$303$	−11.0488	−	1.09045i	−0.634738	−	0.0626445i
$304$	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	$-0.418231\pi$
$307$	−12.4948	−	12.4948i	−0.713118	−	0.713118i	−0.967186	+	0.254068i	$0.918231\pi$
$308$	1.50893	+	2.57791i	0.0859791	+	0.146890i
$309$	−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	$0.997973\pi$
$312$	2.41136	−	4.60782i	0.136516	−	0.260866i
$313$	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	$-0.453093\pi$
$317$	20.2257	−	20.2257i	1.13599	−	1.13599i	0.989162	−	0.146829i	$-0.0469068\pi$
$318$	4.47582	−	19.4401i	0.250992	−	1.09015i
$319$		−	2.60618i		−	0.145918i
$320$		0			0
$321$	18.9984	−	15.5852i	1.06039	−	0.869882i
$322$	−11.7957	+	9.10715i	−0.657347	+	0.507522i
$323$	18.9196	+	18.9196i	1.05271	+	1.05271i
$324$	−10.8838	+	14.3367i	−0.604657	+	0.796486i
$325$		0			0
$326$	0.934042	+	0.120136i	0.0517318	+	0.00665374i
$327$	−21.7956	−	2.15109i	−1.20530	−	0.118955i
$328$	4.69221	+	11.0474i	0.259084	+	0.609991i
$329$	−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	$-0.110048\pi$
$332$	11.6679	−	6.82959i	0.640361	−	0.374822i
$333$	−15.9305	−	23.8624i	−0.872988	−	1.30765i
$334$	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	−0.935277	−	0.353918i	$-0.884849\pi$
$337$	−10.6723	+	10.6723i	−0.581359	+	0.581359i	0.353918	+	0.935277i	$0.384849\pi$
$338$	−13.2907	+	10.2614i	−0.722918	+	0.558147i
$339$	−3.57799	+	2.93518i	−0.194330	+	0.159417i
$340$		0			0
$341$	2.33029			0.126192
$342$	−11.3403	−	22.8470i	−0.613215	−	1.23543i
$343$	−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	−0.458821	−	0.888529i	$-0.651728\pi$
$347$	8.00457	−	8.00457i	0.429708	−	0.429708i	0.888529	+	0.458821i	$0.151728\pi$
$348$	16.5942	+	6.13664i	0.889541	+	0.328959i
$349$	−13.9579			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$349$	−13.9579			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$350$		0			0
$351$	−4.86633	+	2.59735i	−0.259746	+	0.138636i
$352$	0.419399	+	2.85593i	0.0223541	+	0.152221i
$353$	−11.8744	+	11.8744i	−0.632008	+	0.632008i	−0.948571	−	0.316563i	$-0.897471\pi$
$353$	−11.8744	+	11.8744i	−0.632008	+	0.632008i	0.316563	+	0.948571i	$0.397471\pi$
$354$	2.41943	−	1.51385i	0.128591	−	0.0804600i
$355$		0			0
$356$	6.39876	−	24.4632i	0.339134	−	1.29655i
$357$	−22.4528	−	2.21595i	−1.18833	−	0.117281i
$358$	15.5755	−	12.0254i	0.823189	−	0.635564i
$359$	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
$362$	6.50340	−	5.02112i	0.341811	−	0.263904i
$363$	18.5116	+	1.82698i	0.971608	+	0.0958915i
$364$	−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	−0.930224	−	0.366992i	$-0.880388\pi$
$367$	−10.7900	+	10.7900i	−0.563233	+	0.563233i	0.366992	+	0.930224i	$0.380388\pi$
$368$	−13.8648	+	3.89289i	−0.722752	+	0.202931i
$369$	2.48863	−	12.4851i	0.129553	−	0.649946i
$370$		0			0
$371$	−23.8368			−1.23754
$372$	−5.48702	+	14.8375i	−0.284489	+	0.769289i
$373$	−25.8380	+	25.8380i	−1.33784	+	1.33784i	−0.439697	+	0.898146i	$0.644914\pi$
$373$	−25.8380	+	25.8380i	−1.33784	+	1.33784i	−0.898146	+	0.439697i	$0.855086\pi$
$374$	−0.409708	+	3.18541i	−0.0211855	+	0.164714i
$375$		0			0
$376$	−12.3827	−	4.99977i	−0.638588	−	0.257843i
$377$	3.83385	+	3.83385i	0.197453	+	0.197453i
$378$	19.6121	+	8.82991i	1.00874	+	0.454162i
$379$	12.2262			0.628019			0.314010	−	0.949420i	$-0.398328\pi$
$379$	12.2262			0.628019			0.314010	+	0.949420i	$0.398328\pi$
$380$		0			0
$381$	1.82564	−	1.49766i	0.0935306	−	0.0767272i
$382$	15.4987	−	11.9662i	0.792982	−	0.612242i
$383$	−21.6256	+	21.6256i	−1.10501	+	1.10501i	−0.111219	+	0.993796i	$0.535475\pi$
$383$	−21.6256	+	21.6256i	−1.10501	+	1.10501i	−0.993796	+	0.111219i	$0.964525\pi$
$384$	−19.1719	−	4.05430i	−0.978363	−	0.206895i
$385$		0			0
$386$	1.16663	−	9.07035i	0.0593798	−	0.461669i
$387$	−21.0293	+	14.0391i	−1.06898	+	0.713649i
$388$	−15.5437	−	26.5555i	−0.789112	−	1.34815i
$389$			6.63941i			0.336632i	0.985733	+	0.168316i	$0.0538328\pi$
$389$			6.63941i			0.336632i	−0.985733	+	0.168316i	$0.946167\pi$
$390$		0			0
$391$	−16.0228			−0.810309
$392$	1.73236	+	4.07870i	0.0874975	+	0.206006i
$393$	13.0867	+	1.29158i	0.660138	+	0.0651514i
$394$	−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	$-0.0837172\pi$
$397$	14.0596	+	14.0596i	0.705629	+	0.705629i	−0.259984	+	0.965613i	$0.583717\pi$
$398$	6.62498	−	5.11498i	0.332080	−	0.256391i
$399$	−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	$0.850577\pi$
$402$	6.20550	−	26.9528i	0.309502	−	1.34428i
$403$	−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
$408$	−19.3176	−	10.1092i	−0.956363	−	0.500482i
$409$		−	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
$412$	−4.54782	+	2.66197i	−0.224055	+	0.131146i
$413$	−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
$417$	15.5382	+	1.53352i	0.760909	+	0.0750969i
$418$	2.65135	+	3.43406i	0.129682	+	0.167965i
$419$			12.7809i			0.624385i	0.950019	+	0.312193i	$0.101063\pi$
$419$			12.7809i			0.624385i	−0.950019	+	0.312193i	$0.898937\pi$
$420$		0			0
$421$			26.3792i			1.28564i	0.766017	+	0.642821i	$0.222236\pi$
$421$			26.3792i			1.28564i	−0.766017	+	0.642821i	$0.777764\pi$
$422$	−7.78398	+	6.00983i	−0.378918	+	0.292554i
$423$	7.86440	+	11.7801i	0.382380	+	0.572769i
$424$	−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
$428$	−14.3336	−	24.4881i	−0.692841	−	1.18368i
$429$	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	$0.757269\pi$
$432$	14.3791	+	15.0080i	0.691816	+	0.722074i
$433$	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
$438$	2.49221	−	10.8246i	0.119082	−	0.517219i
$439$			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
$442$	−4.08323	−	5.28864i	−0.194219	−	0.251555i
$443$	−1.66807	−	1.66807i	−0.0792526	−	0.0792526i	0.666369	−	0.745622i	$-0.267847\pi$
$443$	−1.66807	−	1.66807i	−0.0792526	−	0.0792526i	−0.745622	+	0.666369i	$0.767847\pi$
$444$	−30.0976	+	13.8467i	−1.42837	+	0.657135i
$445$		0			0
$446$	−4.26636	+	33.1703i	−0.202018	+	1.57066i
$447$	2.23827	−	22.6789i	0.105866	−	1.07268i
$448$	0.418930	+	23.4114i	0.0197926	+	1.10609i
$449$	−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
$452$	2.69946	+	4.61186i	0.126972	+	0.216924i
$453$	−4.75703	−	0.469488i	−0.223505	−	0.0220585i
$454$	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	−0.590886	−	0.806755i	$-0.701222\pi$
$457$	4.61474	−	4.61474i	0.215869	−	0.215869i	0.806755	+	0.590886i	$0.201222\pi$
$458$	0.947900	+	1.22773i	0.0442925	+	0.0573680i
$459$	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	$0.659643\pi$
$462$	−3.56510	−	0.820816i	−0.165864	−	0.0381878i
$463$	−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	−0.543378	−	0.839488i	$-0.682855\pi$
$467$	6.39901	−	6.39901i	0.296111	−	0.296111i	0.839488	+	0.543378i	$0.182855\pi$
$468$	2.08092	+	6.01994i	0.0961905	+	0.278272i
$469$	−33.0484			−1.52603
$470$		0			0
$471$	−6.80600	−	8.29652i	−0.313604	−	0.382283i
$472$	−1.28833	−	3.03326i	−0.0593002	−	0.139617i
$473$	3.04110	−	3.04110i	0.139830	−	0.139830i
$474$	15.1837	−	9.50052i	0.697412	−	0.436373i
$475$		0			0
$476$	−6.59262	+	25.2043i	−0.302172	+	1.15524i
$477$	13.5656	+	20.3200i	0.621127	+	0.930389i
$478$	−10.6485	−	13.7921i	−0.487052	−	0.630834i
$479$	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
$482$	−6.08295	−	7.87870i	−0.277071	−	0.358865i
$483$	1.79260	−	18.1632i	0.0815660	−	0.826456i
$484$	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	0.0872343	−	0.996188i	$-0.472197\pi$
$487$	23.9090	−	23.9090i	1.08342	−	1.08342i	0.996188	−	0.0872343i	$-0.0278029\pi$
$488$	−5.45044	−	12.8326i	−0.246730	−	0.580905i
$489$	−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	$0.253899\pi$
$492$	−13.7875	−	5.09873i	−0.621590	−	0.229868i
$493$	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
$498$	−3.71511	+	16.1361i	−0.166478	+	0.723076i
$499$	−19.9194			−0.891716			−0.445858	−	0.895104i	$-0.647101\pi$
$499$	−19.9194			−0.891716			−0.445858	+	0.895104i	$0.647101\pi$
$500$		0			0
$501$	0.769562	+	0.938097i	0.0343815	+	0.0419111i
$502$	8.57573	+	11.1074i	0.382754	+	0.495746i
$503$	14.6687	−	14.6687i	0.654047	−	0.654047i	−0.299918	−	0.953965i	$-0.596959\pi$
$503$	14.6687	−	14.6687i	0.654047	−	0.654047i	0.953965	+	0.299918i	$0.0969593\pi$
$504$	13.6209	−	20.7671i	0.606724	−	0.925042i
$505$		0			0
$506$	−2.57684	−	0.331433i	−0.114555	−	0.0147340i
$507$	2.01979	−	20.4653i	0.0897022	−	0.908896i
$508$	−1.37738	−	2.35317i	−0.0611114	−	0.104405i
$509$		−	4.85493i		−	0.215191i	−0.994195	−	0.107595i	$-0.965685\pi$
$509$		−	4.85493i		−	0.215191i	0.994195	−	0.107595i	$-0.0343151\pi$
$510$		0			0
$511$	−13.2727			−0.587149
$512$	−8.09503	+	21.1298i	−0.357753	+	0.933816i
$513$	29.8886	+	9.08621i	1.31961	+	0.401166i
$514$	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
$518$	24.1926	+	31.3345i	1.06296	+	1.37676i
$519$	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	$-0.106939\pi$
$522$	−19.4094	+	9.63401i	−0.849525	+	0.421669i
$523$	15.6997	−	15.6997i	0.686499	−	0.686499i	−0.274957	−	0.961456i	$-0.588664\pi$
$523$	15.6997	−	15.6997i	0.686499	−	0.686499i	0.961456	+	0.274957i	$0.0886637\pi$
$524$	3.84254	−	14.6904i	0.167862	−	0.641755i
$525$		0			0
$526$	21.5493	+	2.77167i	0.939596	+	0.120851i
$527$	14.3714	+	14.3714i	0.626026	+	0.626026i
$528$	−2.89761	−	2.02539i	−0.126102	−	0.0881437i
$529$			10.0383i			0.436449i
$530$		0			0
$531$	−0.683298	+	3.42800i	−0.0296526	+	0.148762i
$532$	17.7779	+	30.3725i	0.770770	+	1.31681i
$533$	−3.18541	−	3.18541i	−0.137976	−	0.137976i
$534$	16.4269	+	26.2535i	0.710862	+	1.13610i
$535$		0			0
$536$	−29.6137	−	11.9572i	−1.27912	−	0.516470i
$537$	−2.36701	+	23.9835i	−0.102144	+	1.03496i
$538$	36.1880	−	27.9399i	1.56017	−	1.20457i
$539$			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	$-0.00992877\pi$
$542$	0.264756	+	0.342914i	0.0113722	+	0.0147294i
$543$	−0.988326	+	10.0141i	−0.0424131	+	0.429745i
$544$	−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	$-0.267983\pi$
$547$	−1.86763	−	1.86763i	−0.0798541	−	0.0798541i	−0.745906	+	0.666052i	$0.767983\pi$
$548$	−1.74177	+	1.01951i	−0.0744045	+	0.0435512i
$549$	−2.89078	+	14.5026i	−0.123375	+	0.618955i
$550$		0			0
$551$		−	30.7055i		−	1.30810i
$552$	8.17788	−	15.6270i	0.348074	−	0.665128i
$553$	−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	−0.999168	−	0.0407789i	$-0.987016\pi$
$557$	−22.6188	+	22.6188i	−0.958389	+	0.958389i	0.0407789	+	0.999168i	$0.487016\pi$
$558$	−8.61415	−	17.3547i	−0.364666	−	0.734682i
$559$			8.94729i			0.378430i
$560$		0			0
$561$	−2.49475	−	3.04110i	−0.105328	−	0.128395i
$562$	−17.3054	+	13.3611i	−0.729985	+	0.563604i
$563$	26.6638	+	26.6638i	1.12375	+	1.12375i	0.991173	+	0.132574i	$0.0423241\pi$
$563$	26.6638	+	26.6638i	1.12375	+	1.12375i	0.132574	+	0.991173i	$0.457676\pi$
$564$	14.8582	−	6.83567i	0.625644	−	0.287833i
$565$		0			0
$566$	17.5843	+	2.26169i	0.739123	+	0.0950660i
$567$	−24.3450	+	10.0612i	−1.02239	+	0.422530i
$568$	5.62980	+	13.2549i	0.236221	+	0.556163i
$569$	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	$0.202581\pi$
$571$			28.4036i			1.18865i	−0.804224	+	0.594326i	$0.797419\pi$
$572$	−0.547283	−	0.934999i	−0.0228831	−	0.0390943i
$573$	−2.35535	+	23.8652i	−0.0983960	+	0.996985i
$574$	−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	−0.191417	−	0.981509i	$-0.561308\pi$
$577$	18.9787	−	18.9787i	0.790092	−	0.790092i	0.981509	+	0.191417i	$0.0613081\pi$
$578$	−3.14204	+	2.42590i	−0.130692	+	0.100904i
$579$	7.10371	+	8.65943i	0.295220	+	0.359874i
$580$		0			0
$581$	19.7855			0.820839
$582$	36.7247	+	8.45536i	1.52229	+	0.350486i
$583$	−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	−0.899840	−	0.436220i	$-0.856317\pi$
$587$	−11.2326	+	11.2326i	−0.463619	+	0.463619i	0.436220	+	0.899840i	$0.356317\pi$
$588$	−5.09035	−	1.88245i	−0.209923	−	0.0776309i
$589$	27.4550			1.13127
$590$		0			0
$591$	7.30543	−	5.99297i	0.300505	−	0.246518i
$592$	10.3412	+	36.8310i	0.425022	+	1.51374i
$593$	0.161070	−	0.161070i	0.00661435	−	0.00661435i	−0.703792	−	0.710406i	$-0.748511\pi$
$593$	0.161070	−	0.161070i	0.00661435	−	0.00661435i	0.710406	+	0.703792i	$0.248511\pi$
$594$	1.32920	+	3.50626i	0.0545378	+	0.143863i
$595$		0			0
$596$	−25.4581	−	6.65901i	−1.04281	−	0.272764i
$597$	−1.00680	+	10.2013i	−0.0412057	+	0.417511i
$598$	4.27825	−	3.30313i	0.174951	−	0.135075i
$599$	−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	$0.297334\pi$
$602$	27.6142	−	21.3203i	1.12547	−	0.868949i
$603$	18.8080	+	28.1726i	0.765922	+	1.14728i
$604$	−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	−0.976783	−	0.214232i	$-0.931275\pi$
$607$	−18.7872	+	18.7872i	−0.762550	+	0.762550i	0.214232	+	0.976783i	$0.431275\pi$
$608$	4.94129	+	33.6480i	0.200396	+	1.36461i
$609$	16.4217	+	20.0181i	0.665443	+	0.811176i
$610$		0			0
$611$	5.01206			0.202766
$612$	25.2377	−	8.72394i	1.02017	−	0.352644i
$613$	−29.5115	+	29.5115i	−1.19196	+	1.19196i	−0.215443	+	0.976516i	$0.569120\pi$
$613$	−29.5115	+	29.5115i	−1.19196	+	1.19196i	−0.976516	+	0.215443i	$0.930880\pi$
$614$	3.18791	−	24.7855i	0.128654	−	1.00026i
$615$		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	$-0.571560\pi$
$618$	1.44804	−	6.28938i	0.0582488	−	0.252996i
$619$	12.4498			0.500402			0.250201	−	0.968194i	$-0.419503\pi$
$619$	12.4498			0.500402			0.250201	+	0.968194i	$0.419503\pi$
$620$		0			0
$621$	−16.5037	+	8.80867i	−0.662271	+	0.353480i
$622$	−0.251453	+	0.194141i	−0.0100823	+	0.00778433i
$623$	26.1665	−	26.1665i	1.04834	−	1.04834i
$624$	7.24203	−	1.28309i	0.289913	−	0.0513646i
$625$		0			0
$626$	−3.07144	+	23.8799i	−0.122759	+	0.954434i
$627$	−5.28785	−	0.521877i	−0.211176	−	0.0208417i
$628$	−10.6938	+	6.25942i	−0.426730	+	0.249778i
$629$			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	$0.163607\pi$
$632$	−8.08524	−	19.0360i	−0.321614	−	0.757212i
$633$	1.18294	−	11.9860i	0.0470176	−	0.476399i
$634$	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
$638$	2.91735	−	2.25242i	0.115499	−	0.0891741i
$639$	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	$-0.0852090\pi$
$642$	33.8656	+	7.79709i	1.33657	+	0.307727i
$643$	12.4335	−	12.4335i	0.490331	−	0.490331i	−0.418080	−	0.908410i	$-0.637297\pi$
$643$	12.4335	−	12.4335i	0.490331	−	0.490331i	0.908410	+	0.418080i	$0.137297\pi$
$644$	−20.3891	−	5.33311i	−0.803442	−	0.210154i
$645$		0			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	$0.746880\pi$
$648$	−25.4550	+	0.207341i	−0.999967	+	0.00814512i
$649$		−	0.594545i		−	0.0233380i
$650$		0			0
$651$	−17.8990	+	14.6833i	−0.701517	+	0.575485i
$652$	0.672775	+	1.14939i	0.0263479	+	0.0450138i
$653$	−10.5497	−	10.5497i	−0.412841	−	0.412841i	0.469886	−	0.882727i	$-0.344295\pi$
$653$	−10.5497	−	10.5497i	−0.412841	−	0.412841i	−0.882727	+	0.469886i	$0.844295\pi$
$654$	−16.4291	−	26.2571i	−0.642431	−	1.02673i
$655$		0			0
$656$	−8.31116	+	14.8003i	−0.324496	+	0.577854i
$657$	7.55356	+	11.3145i	0.294692	+	0.441421i
$658$	−11.9431	−	15.4688i	−0.465591	−	0.603038i
$659$			30.8600i			1.20213i	0.799199	+	0.601067i	$0.205258\pi$
$659$			30.8600i			1.20213i	−0.799199	+	0.601067i	$0.794742\pi$
$660$		0			0
$661$			44.1992i			1.71915i	0.511009	+	0.859575i	$0.329272\pi$
$661$			44.1992i			1.71915i	−0.511009	+	0.859575i	$0.670728\pi$
$662$	13.8030	−	10.6570i	0.536470	−	0.414196i
$663$	8.14357	+	0.803718i	0.316270	+	0.0312138i
$664$	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
$668$	1.20916	−	0.707760i	0.0467840	−	0.0273841i
$669$	−25.9783	−	31.6675i	−1.00438	−	1.22434i
$670$		0			0
$671$		−	2.51530i		−	0.0971021i
$672$	−21.2169	−	19.2938i	−0.818458	−	0.744274i
$673$	−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	−0.994554	−	0.104220i	$-0.966765\pi$
$677$	−23.1658	+	23.1658i	−0.890334	+	0.890334i	0.104220	+	0.994554i	$0.466765\pi$
$678$	−6.37795	−	1.46844i	−0.244944	−	0.0563949i
$679$		−	45.0304i		−	1.72811i
$680$		0			0
$681$	−23.6371	+	19.3905i	−0.905775	+	0.743047i
$682$	2.01398	+	2.60852i	0.0771192	+	0.0998855i
$683$	−14.8655	−	14.8655i	−0.568814	−	0.568814i	0.362982	−	0.931796i	$-0.381759\pi$
$683$	−14.8655	−	14.8655i	−0.568814	−	0.568814i	−0.931796	+	0.362982i	$0.881759\pi$
$684$	15.7740	−	32.4402i	0.603132	−	1.24038i
$685$		0			0
$686$	2.86899	−	22.3060i	0.109539	−	0.851647i
$687$	−1.89049	−	0.186579i	−0.0721266	−	0.00711843i
$688$	32.4581	−	9.11344i	1.23745	−	0.347447i
$689$	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	$-0.355790\pi$
$692$	5.67960	−	3.32444i	0.215906	−	0.126376i
$693$	3.72646	−	2.48778i	0.141557	−	0.0945031i
$694$	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
$698$	−12.0633	−	15.6245i	−0.456603	−	0.591396i
$699$	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	$0.453794\pi$
$702$	−7.11325	−	3.20258i	−0.268473	−	0.120874i
$703$	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
$708$	3.78562	+	1.39995i	0.142272	+	0.0526133i
$709$	−43.9829			−1.65181			−0.825906	−	0.563808i	$-0.809336\pi$
$709$	−43.9829			−1.65181			−0.825906	+	0.563808i	$0.809336\pi$
$710$		0			0
$711$	−4.28821	+	21.5132i	−0.160820	+	0.806810i
$712$	32.9143	−	13.9798i	1.23351	−	0.523915i
$713$	−11.6257	+	11.6257i	−0.435387	+	0.435387i
$714$	−16.9246	−	27.0488i	−0.633386	−	1.01228i
$715$		0			0
$716$	26.9225	+	7.04204i	1.00614	+	0.263174i
$717$	21.2373	+	2.09599i	0.793123	+	0.0782762i
$718$	29.2781	+	37.9213i	1.09265	+	1.41521i
$719$	−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
$722$	14.8168	+	19.1909i	0.551425	+	0.714212i
$723$	12.1318	+	1.19733i	0.451186	+	0.0445292i
$724$	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	−0.166067	−	0.986115i	$-0.553107\pi$
$727$	22.1109	−	22.1109i	0.820048	−	0.820048i	0.986115	+	0.166067i	$0.0531067\pi$
$728$	−3.43563	−	8.08889i	−0.127333	−	0.299794i
$729$	22.4316	+	15.0274i	0.830802	+	0.556569i
$730$		0			0
$731$	37.5102			1.38736
$732$	16.0155	+	5.92266i	0.591951	+	0.218908i
$733$	−8.64610	+	8.64610i	−0.319351	+	0.319351i	−0.848518	−	0.529167i	$-0.822505\pi$
$733$	−8.64610	+	8.64610i	−0.319351	+	0.319351i	0.529167	+	0.848518i	$0.322505\pi$
$734$	−21.4037	−	2.75294i	−0.790023	−	0.101613i
$735$		0			0
$736$	−16.3405	−	12.1557i	−0.602318	−	0.448067i
$737$	−4.07412	−	4.07412i	−0.150072	−	0.150072i
$738$	16.1266	−	8.00457i	0.593628	−	0.294652i
$739$	−29.8509			−1.09808			−0.549041	−	0.835796i	$-0.685007\pi$
$739$	−29.8509			−1.09808			−0.549041	+	0.835796i	$0.685007\pi$
$740$		0			0
$741$	8.54646	−	7.01103i	0.313962	−	0.257557i
$742$	−20.6012	−	26.6828i	−0.756293	−	0.979558i
$743$	−6.78930	+	6.78930i	−0.249075	+	0.249075i	−0.820591	−	0.571516i	$-0.806356\pi$
$743$	−6.78930	+	6.78930i	−0.249075	+	0.249075i	0.571516	+	0.820591i	$0.306356\pi$
$744$	−21.3513	+	6.68132i	−0.782777	+	0.244949i
$745$		0			0
$746$	−51.2539	−	6.59227i	−1.87654	−	0.241360i
$747$	−11.2600	−	16.8664i	−0.411982	−	0.617110i
$748$	−3.91984	+	2.29440i	−0.143324	+	0.0838916i
$749$		−	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	$0.365120\pi$
$752$	−5.10513	−	18.1823i	−0.186165	−	0.663039i
$753$	−17.1034	−	1.68800i	−0.623282	−	0.0615140i
$754$	−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	−0.962025	−	0.272963i	$-0.911996\pi$
$757$	−33.9790	−	33.9790i	−1.23499	−	1.23499i	−0.272963	−	0.962025i	$-0.588004\pi$
$758$	10.5666	+	13.6860i	0.383798	+	0.497099i
$759$	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	$0.785496\pi$
$762$	3.25431	+	0.749259i	0.117891	+	0.0271428i
$763$	−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
$768$	−12.0312	−	24.9650i	−0.434137	−	0.900847i
$769$			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
$772$	11.1616	−	6.53323i	0.401715	−	0.235136i
$773$	7.32969	+	7.32969i	0.263631	+	0.263631i	0.826527	−	0.562897i	$-0.190313\pi$
$773$	7.32969	+	7.32969i	0.263631	+	0.263631i	−0.562897	+	0.826527i	$0.690313\pi$
$774$	−33.8902	−	11.4067i	−1.21816	−	0.410005i
$775$		0			0
$776$	16.2923	−	40.3504i	0.584861	−	1.44850i
$777$	−48.2496	−	4.76193i	−1.73094	−	0.170833i
$778$	−7.43215	+	5.73818i	−0.266455	+	0.205724i
$779$			25.5122i			0.914069i
$780$		0			0
$781$			2.59807i			0.0929663i
$782$	−13.8479	−	17.9359i	−0.495199	−	0.641387i
$783$	7.71905	−	25.3914i	0.275856	−	0.907414i
$784$	−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	$-0.287480\pi$
$787$	−4.66068	−	4.66068i	−0.166135	−	0.166135i	−0.785278	+	0.619143i	$0.787480\pi$
$788$	−5.51168	−	9.41637i	−0.196346	−	0.335444i
$789$	−20.5731	+	16.8770i	−0.732421	+	0.600837i
$790$		0			0
$791$			7.82040i			0.278061i
$792$	4.23927	−	0.880969i	0.150636	−	0.0313039i
$793$	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	−0.0126440	−	0.999920i	$-0.504025\pi$
$797$	27.8720	−	27.8720i	0.987276	−	0.987276i	0.999920	+	0.0126440i	$0.00402483\pi$
$798$	−42.0034	−	9.67071i	−1.48691	−	0.342339i
$799$		−	21.0123i		−	0.743362i
$800$		0			0
$801$	−37.1975	−	7.41454i	−1.31431	−	0.261980i
$802$	−20.2809	+	15.6584i	−0.716142	+	0.552916i
$803$	−1.63622	−	1.63622i	−0.0577410	−	0.0577410i
$804$	35.5340	−	16.3478i	1.25319	−	0.576542i
$805$		0			0
$806$	−6.79998	−	0.874612i	−0.239519	−	0.0308069i
$807$	−5.49951	+	55.7231i	−0.193592	+	1.96155i
$808$	−16.6875	+	7.08773i	−0.587063	+	0.249346i
$809$	−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	$-0.771891\pi$
$811$		−	37.4113i		−	1.31369i	0.754026	−	0.656845i	$-0.228109\pi$
$812$	25.8025	−	15.1030i	0.905489	−	0.530010i
$813$	−0.528027	−	0.0521129i	−0.0185187	−	0.00182768i
$814$	−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
$818$	29.4676	−	22.7512i	1.03031	−	0.795477i
$819$	−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	$0.419648\pi$
$822$	0.554585	−	2.40877i	0.0193434	−	0.0840153i
$823$	−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	−0.662377	−	0.749170i	$-0.730452\pi$
$827$	2.49596	−	2.49596i	0.0867932	−	0.0867932i	0.749170	+	0.662377i	$0.230452\pi$
$828$	7.05724	+	20.4161i	0.245256	+	0.709507i
$829$	49.1212			1.70605			0.853026	−	0.521869i	$-0.174765\pi$
$829$	49.1212			1.70605			0.853026	+	0.521869i	$0.174765\pi$
$830$		0			0
$831$	−10.8423	−	13.2167i	−0.376114	−	0.458483i
$832$	−0.151945	−	8.49125i	−0.00526773	−	0.294381i
$833$	−4.93043	+	4.93043i	−0.170829	+	0.170829i
$834$	11.7124	+	18.7188i	0.405569	+	0.648179i
$835$		0			0
$836$	−1.55262	+	5.93585i	−0.0536985	+	0.205296i
$837$	22.7034	+	6.90191i	0.784746	+	0.238565i
$838$	−14.3069	+	11.0460i	−0.494223	+	0.381577i
$839$	−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
$842$	−29.5288	+	22.7985i	−1.01763	+	0.785687i
$843$	2.62992	−	26.6473i	0.0905792	−	0.917782i
$844$	−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
$848$	−8.80606	−	31.3634i	−0.302401	−	1.07702i
$849$	−16.7877	+	13.7717i	−0.576151	+	0.472642i
$850$		0			0
$851$	−34.4319			−1.18031
$852$	−16.5425	−	6.11755i	−0.566738	−	0.209584i
$853$	16.4190	−	16.4190i	0.562174	−	0.562174i	−0.367750	−	0.929925i	$-0.619872\pi$
$853$	16.4190	−	16.4190i	0.562174	−	0.562174i	0.929925	+	0.367750i	$0.119872\pi$
$854$	2.60287	−	20.2369i	0.0890683	−	0.692492i
$855$		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	$0.548767\pi$
$858$	1.29305	+	0.297707i	0.0441441	+	0.0101636i
$859$	−1.68121			−0.0573622			−0.0286811	−	0.999589i	$-0.509131\pi$
$859$	−1.68121			−0.0573622			−0.0286811	+	0.999589i	$0.509131\pi$
$860$		0			0
$861$	−13.6443	−	16.6324i	−0.464995	−	0.566830i
$862$	−32.1064	+	24.7886i	−1.09355	+	0.844302i
$863$	−23.0950	+	23.0950i	−0.786161	+	0.786161i	−0.980863	−	0.194701i	$-0.937626\pi$
$863$	−23.0950	+	23.0950i	−0.786161	+	0.786161i	0.194701	+	0.980863i	$0.437626\pi$
$864$	−4.37266	+	29.0668i	−0.148761	+	0.988873i
$865$		0			0
$866$	−0.575226	+	4.47229i	−0.0195470	+	0.151975i
$867$	0.477499	−	4.83819i	0.0162167	−	0.164314i
$868$	13.5042	+	23.0710i	0.458361	+	0.783081i
$869$		−	3.73122i		−	0.126573i
$870$		0			0
$871$	11.9866			0.406149
$872$	−32.9188	+	13.9817i	−1.11477	+	0.473481i
$873$	−38.3869	+	25.6271i	−1.29920	+	0.867345i
$874$	−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	$-0.360836\pi$
$877$	−14.2900	−	14.2900i	−0.482539	−	0.482539i	−0.905942	+	0.423403i	$0.860836\pi$
$878$	−13.2660	+	10.2424i	−0.447707	+	0.345664i
$879$	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	$-0.276228\pi$
$882$	5.95393	−	2.95529i	0.200479	−	0.0995096i
$883$	3.68252	−	3.68252i	0.123927	−	0.123927i	−0.642423	−	0.766350i	$-0.722071\pi$
$883$	3.68252	−	3.68252i	0.123927	−	0.123927i	0.766350	+	0.642423i	$0.222071\pi$
$884$	2.39112	−	9.14153i	0.0804221	−	0.307463i
$885$		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	$0.863891\pi$
$888$	−41.5121	−	21.7241i	−1.39306	−	0.729012i
$889$		−	3.99030i		−	0.133830i
$890$		0			0
$891$	−4.24150	−	1.76087i	−0.142095	−	0.0589912i
$892$	−40.8180	+	23.8920i	−1.36669	+	0.799964i
$893$	−20.0710	−	20.0710i	−0.671649	−	0.671649i
$894$	27.3212	−	17.0950i	0.913758	−	0.571742i
$895$		0			0
$896$	−25.8446	+	20.7025i	−0.863409	+	0.691623i
$897$	−0.650169	+	6.58775i	−0.0217085	+	0.219959i
$898$	−29.6799	−	38.4417i	−0.990432	−	1.28282i
$899$		−	23.3240i		−	0.777899i
$900$		0			0
$901$		−	36.2450i		−	1.20750i
$902$	−2.42393	+	1.87146i	−0.0807080	+	0.0623127i
$903$	−4.19655	+	42.5210i	−0.139653	+	1.41501i
$904$	−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	$-0.310821\pi$
$907$	−8.08868	−	8.08868i	−0.268580	−	0.268580i	−0.828528	+	0.559948i	$0.810821\pi$
$908$	17.8333	+	30.4671i	0.591820	+	1.01109i
$909$	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	$-0.221527\pi$
$912$	−34.1391	−	23.8628i	−1.13046	−	0.790175i
$913$	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
$918$	−13.4263	+	29.8212i	−0.443135	+	0.984248i
$919$			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
$922$	−17.8428	−	23.1102i	−0.587623	−	0.761094i
$923$	−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
$927$	4.38882	+	6.57403i	0.144148	+	0.215920i
$928$	28.5852	−	4.19779i	0.938354	−	0.137799i
$929$	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
$932$	−9.97418	−	17.0403i	−0.326715	−	0.558173i
$933$	0.0382135	−	0.387193i	0.00125105	−	0.0126761i
$934$	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	−0.939413	−	0.342787i	$-0.888629\pi$
$937$	−18.2630	+	18.2630i	−0.596626	+	0.596626i	0.342787	+	0.939413i	$0.388629\pi$
$938$	−28.5624	−	36.9944i	−0.932597	−	1.20791i
$939$	−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	$0.618952\pi$
$942$	3.40496	−	14.7890i	0.110940	−	0.481851i
$943$	−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	−0.403305	−	0.915066i	$-0.632139\pi$
$947$	15.7486	−	15.7486i	0.511761	−	0.511761i	0.915066	+	0.403305i	$0.132139\pi$
$948$	23.7576	+	8.78572i	0.771610	+	0.285347i
$949$	4.81396			0.156268
$950$		0			0
$951$	−38.3034	+	31.4219i	−1.24207	+	1.01893i
$952$	−33.9114	+	14.4033i	−1.09908	+	0.466815i
$953$	33.3609	−	33.3609i	1.08067	−	1.08067i	0.0842194	−	0.996447i	$-0.473160\pi$
$953$	33.3609	−	33.3609i	1.08067	−	1.08067i	0.996447	−	0.0842194i	$-0.0268396\pi$
$954$	−11.0220	+	32.7471i	−0.356849	+	1.06023i
$955$		0			0
$956$	6.23572	−	23.8399i	0.201678	−	0.771037i
$957$	−0.443352	+	4.49221i	−0.0143315	+	0.145213i
$958$	31.0367	+	40.1990i	1.00275	+	1.29877i
$959$	−2.95353			−0.0953746
$960$		0			0
$961$	−10.1451			−0.327260
$962$	−8.77458	−	11.3649i	−0.282904	−	0.366420i
$963$	−35.3984	+	23.6319i	−1.14070	+	0.761529i
$964$	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	−0.566411	−	0.824123i	$-0.691668\pi$
$967$	8.01398	−	8.01398i	0.257712	−	0.257712i	0.824123	+	0.566411i	$0.191668\pi$
$968$	27.9589	−	11.8751i	0.898632	−	0.381679i
$969$	−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	$0.745909\pi$
$972$	21.1991	−	22.8604i	0.679962	−	0.733248i
$973$	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	$0.394339\pi$
$978$	−1.58955	−	0.365972i	−0.0508282	−	0.0117025i
$979$	6.45147			0.206190
$980$		0			0
$981$	37.2026	+	7.41555i	1.18779	+	0.236760i
$982$	26.7495	+	34.6462i	0.853609	+	1.10560i
$983$	−9.14087	+	9.14087i	−0.291548	+	0.291548i	−0.837692	−	0.546143i	$-0.816095\pi$
$983$	−9.14087	+	9.14087i	−0.291548	+	0.291548i	0.546143	+	0.837692i	$0.316095\pi$
$984$	−6.20851	−	19.8404i	−0.197920	−	0.632488i
$985$		0			0
$986$	31.8830	+	4.10079i	1.01536	+	0.130596i
$987$	23.8193	+	2.35081i	0.758176	+	0.0748271i
$988$	−6.44799	−	11.0160i	−0.205138	−	0.350465i
$989$			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	$0.620027\pi$
$992$	3.75342	+	25.5591i	0.119171	+	0.811503i
$993$	−2.09766	+	21.2542i	−0.0665671	+	0.674483i
$994$	−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	$-0.276425\pi$
$997$	−3.70273	−	3.70273i	−0.117267	−	0.117267i	−0.763305	+	0.646038i	$0.776425\pi$
$998$	−17.2156	−	22.2978i	−0.544949	−	0.705824i
$999$	23.3997	+	43.8411i	0.740334	+	1.38707i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.864261 + 1.11940i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(2.94212 + 0.586449i) q^{9} +O(q^{10})\)	\(q+(0.864261 + 1.11940i) q^{2} +(-1.72368 - 0.170116i) q^{3} +(-0.506107 + 1.93490i) q^{4} +(-1.29928 - 2.07651i) q^{6} +(-2.06963 + 2.06963i) q^{7} +(-2.60334 + 1.10573i) q^{8} +(2.94212 + 0.586449i) q^{9} -0.510276 q^{11} +(1.20152 - 3.24905i) 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} +(1.88629 + 3.80025i) q^{18} -6.01198 q^{19} +(3.91945 - 3.21529i) q^{21} +(-0.441012 - 0.571203i) q^{22} +(2.54575 - 2.54575i) q^{23} +(4.67541 - 1.46305i) q^{24} +(1.48903 + 0.191519i) q^{26} +(-4.97150 - 1.51135i) q^{27} +(-2.95708 - 5.05199i) q^{28} +5.10739i q^{29} -4.56672 q^{31} +(-0.821906 - 5.59683i) q^{32} +(0.879551 + 0.0868061i) q^{33} +(0.802913 - 6.24253i) q^{34} +(-2.62375 + 5.39592i) q^{36} +(-6.76263 - 6.76263i) q^{37} +(-5.19592 - 6.72981i) q^{38} +(-1.42157 + 1.16618i) q^{39} -4.24355i q^{41} +(6.98662 + 1.60857i) 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} +(5.67851 + 3.96920i) q^{48} -1.56672i q^{49} +(4.88902 + 5.95972i) q^{51} +(1.07252 + 1.83234i) q^{52} +(5.75871 + 5.75871i) q^{53} +(-2.60487 - 6.87129i) q^{54} +(3.09950 - 7.67638i) q^{56} +(10.3627 + 1.02273i) q^{57} +(-5.71720 + 4.41411i) q^{58} +1.16514i q^{59} +4.92929i q^{61} +(-3.94684 - 5.11198i) q^{62} +(-7.30283 + 4.87536i) q^{63} +(5.55474 - 5.75716i) q^{64} +(0.662991 + 1.05959i) q^{66} +(7.98415 + 7.98415i) q^{67} +(7.68180 - 4.49639i) q^{68} +(-4.82112 + 3.95497i) q^{69} -5.09150i q^{71} +(-8.30779 + 1.72645i) 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} +(-2.53402 - 0.583424i) q^{78} +7.31215i q^{79} +(8.31215 + 3.45081i) q^{81} +(4.75023 - 3.66754i) q^{82} +(-4.77995 - 4.77995i) q^{83} +(4.23762 + 9.21104i) q^{84} +(-11.8220 - 1.52055i) q^{86} +(0.868848 - 8.80349i) q^{87} +(1.32842 - 0.564226i) q^{88} -12.6431 q^{89} +3.10712i q^{91} +(3.63736 + 6.21420i) q^{92} +(7.87155 + 0.776871i) q^{93} +(-0.851777 + 6.62243i) q^{94} +(0.464592 + 9.78694i) q^{96} +(-10.8789 + 10.8789i) q^{97} +(1.75378 - 1.35405i) q^{98} +(-1.50129 - 0.299251i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) \) 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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