LMFDB - Embedded newform 325.3.w.e.24.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,3,Mod(24,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.24"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	325.w (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.85560859171$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			24.8
Character	$\chi$	$=$	325.24
Dual form			325.3.w.e.149.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.20214 + 0.590063i) q^{2} +(-1.83281 + 1.05817i) q^{3} +(1.03716 + 0.598805i) q^{4} +(-4.66050 + 1.24878i) q^{6} +(-1.17338 + 0.314408i) q^{7} +(-4.51768 - 4.51768i) q^{8} +(-2.26053 + 3.91536i) q^{9} +(-13.3250 - 3.57041i) q^{11} -2.53456 q^{12} +(-3.48944 + 12.5229i) q^{13} -2.76948 q^{14} +(-9.67808 - 16.7629i) q^{16} +(4.73592 - 8.20286i) q^{17} +(-7.28833 + 7.28833i) q^{18} +(-23.4493 + 6.28321i) q^{19} +(1.81790 - 1.81790i) q^{21} +(-27.2367 - 15.7251i) q^{22} +(5.80846 + 10.0605i) q^{23} +(13.0606 + 3.49956i) q^{24} +(-15.0736 + 25.5183i) q^{26} -28.6153i q^{27} +(-1.40526 - 0.376537i) q^{28} +(2.30788 + 3.99736i) q^{29} +(-21.8447 - 21.8447i) q^{31} +(-4.80701 - 17.9400i) q^{32} +(28.2003 - 7.55624i) q^{33} +(15.2694 - 15.2694i) q^{34} +(-4.68907 + 2.70724i) q^{36} +(-5.14329 + 19.1950i) q^{37} -55.3461 q^{38} +(-6.85595 - 26.6446i) q^{39} +(-14.6840 + 54.8015i) q^{41} +(5.07594 - 2.93060i) q^{42} +(35.4975 - 61.4835i) q^{43} +(-11.6821 - 11.6821i) q^{44} +(6.85471 + 25.5821i) q^{46} +(22.8093 + 22.8093i) q^{47} +(35.4762 + 20.4822i) q^{48} +(-41.1573 + 23.7622i) q^{49} +20.0457i q^{51} +(-11.1179 + 10.8988i) q^{52} -3.82249i q^{53} +(16.8848 - 63.0150i) q^{54} +(6.72137 + 3.88059i) q^{56} +(36.3294 - 36.3294i) q^{57} +(2.72358 + 10.1645i) q^{58} +(17.8214 + 66.5103i) q^{59} +(20.0377 - 34.7063i) q^{61} +(-35.2155 - 60.9950i) q^{62} +(1.42146 - 5.30495i) q^{63} +35.0818i q^{64} +66.5597 q^{66} +(56.1209 + 15.0375i) q^{67} +(9.82382 - 5.67179i) q^{68} +(-21.2916 - 12.2927i) q^{69} +(-53.0258 + 14.2082i) q^{71} +(27.9007 - 7.47597i) q^{72} +(34.0315 + 34.0315i) q^{73} +(-22.6525 + 39.2354i) q^{74} +(-28.0831 - 7.52483i) q^{76} +16.7579 q^{77} +(0.624199 - 62.7207i) q^{78} +27.0828 q^{79} +(9.93517 + 17.2082i) q^{81} +(-64.6726 + 112.016i) q^{82} +(20.0700 - 20.0700i) q^{83} +(2.97401 - 0.796885i) q^{84} +(114.450 - 114.450i) q^{86} +(-8.45980 - 4.88427i) q^{87} +(44.0679 + 76.3279i) q^{88} +(30.1805 + 8.08684i) q^{89} +(0.157156 - 15.7913i) q^{91} +13.9125i q^{92} +(63.1528 + 16.9217i) q^{93} +(36.7704 + 63.6881i) q^{94} +(27.7940 + 27.7940i) q^{96} +(46.1141 + 172.100i) q^{97} +(-104.655 + 28.0423i) q^{98} +(44.1010 - 44.1010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	2.20214	+	0.590063i	1.10107	+	0.295031i	0.763201	−	0.646161i	$-0.223627\pi$
$2$	2.20214	+	0.590063i	1.10107	+	0.295031i	0.337871	+	0.941193i	$0.390293\pi$
$3$	−1.83281	+	1.05817i	−0.610937	+	0.352725i	−0.773332	−	0.634001i	$-0.781411\pi$
$3$	−1.83281	+	1.05817i	−0.610937	+	0.352725i	0.162395	+	0.986726i	$0.448078\pi$
$4$	1.03716	+	0.598805i	0.259290	+	0.149701i
$5$		0			0
$5$		0			0
$6$	−4.66050	+	1.24878i	−0.776751	+	0.208130i
$7$	−1.17338	+	0.314408i	−0.167626	+	0.0449154i	−0.341656	−	0.939825i	$-0.610988\pi$
$7$	−1.17338	+	0.314408i	−0.167626	+	0.0449154i	0.174030	+	0.984740i	$0.444321\pi$
$8$	−4.51768	−	4.51768i	−0.564710	−	0.564710i
$9$	−2.26053	+	3.91536i	−0.251170	+	0.435040i
$10$		0			0
$11$	−13.3250	−	3.57041i	−1.21136	−	0.324583i	−0.404065	−	0.914730i	$-0.632403\pi$
$11$	−13.3250	−	3.57041i	−1.21136	−	0.324583i	−0.807296	+	0.590147i	$0.799070\pi$
$12$	−2.53456			−0.211213
$13$	−3.48944	+	12.5229i	−0.268419	+	0.963302i
$13$	−3.48944	+	12.5229i	−0.268419	+	0.963302i
$14$	−2.76948			−0.197820
$15$		0			0
$16$	−9.67808	−	16.7629i	−0.604880	−	1.04768i
$17$	4.73592	−	8.20286i	0.278584	−	0.482521i	−0.692449	−	0.721467i	$-0.743468\pi$
$17$	4.73592	−	8.20286i	0.278584	−	0.482521i	0.971033	+	0.238945i	$0.0768017\pi$
$18$	−7.28833	+	7.28833i	−0.404907	+	0.404907i
$19$	−23.4493	+	6.28321i	−1.23417	+	0.330695i	−0.816203	−	0.577766i	$-0.803925\pi$
$19$	−23.4493	+	6.28321i	−1.23417	+	0.330695i	−0.417969	+	0.908461i	$0.637258\pi$
$20$		0			0
$21$	1.81790	−	1.81790i	0.0865665	−	0.0865665i
$22$	−27.2367	−	15.7251i	−1.23803	−	0.714778i
$23$	5.80846	+	10.0605i	0.252542	+	0.437415i	0.964225	−	0.265085i	$-0.0854002\pi$
$23$	5.80846	+	10.0605i	0.252542	+	0.437415i	−0.711683	+	0.702501i	$0.752067\pi$
$24$	13.0606	+	3.49956i	0.544190	+	0.145815i
$25$		0			0
$26$	−15.0736	+	25.5183i	−0.579753	+	0.981473i
$27$		−	28.6153i		−	1.05983i
$28$	−1.40526	−	0.376537i	−0.0501877	−	0.0134478i
$29$	2.30788	+	3.99736i	0.0795819	+	0.137840i	0.903070	−	0.429494i	$-0.141308\pi$
$29$	2.30788	+	3.99736i	0.0795819	+	0.137840i	−0.823488	+	0.567334i	$0.807975\pi$
$30$		0			0
$31$	−21.8447	−	21.8447i	−0.704669	−	0.704669i	0.260740	−	0.965409i	$-0.416033\pi$
$31$	−21.8447	−	21.8447i	−0.704669	−	0.704669i	−0.965409	+	0.260740i	$0.916033\pi$
$32$	−4.80701	−	17.9400i	−0.150219	−	0.560625i
$33$	28.2003	−	7.55624i	0.854554	−	0.228977i
$34$	15.2694	−	15.2694i	0.449099	−	0.449099i
$35$		0			0
$36$	−4.68907	+	2.70724i	−0.130252	+	0.0752010i
$37$	−5.14329	+	19.1950i	−0.139008	+	0.518785i	0.860941	+	0.508704i	$0.169875\pi$
$37$	−5.14329	+	19.1950i	−0.139008	+	0.518785i	−0.999949	+	0.0100804i	$0.996791\pi$
$38$	−55.3461			−1.45648
$39$	−6.85595	−	26.6446i	−0.175794	−	0.683195i
$40$		0			0
$41$	−14.6840	+	54.8015i	−0.358147	+	1.33662i	0.518331	+	0.855180i	$0.326553\pi$
$41$	−14.6840	+	54.8015i	−0.358147	+	1.33662i	−0.876478	+	0.481442i	$0.840113\pi$
$42$	5.07594	−	2.93060i	0.120856	−	0.0697761i
$43$	35.4975	−	61.4835i	0.825523	−	1.42985i	−0.0759958	−	0.997108i	$-0.524214\pi$
$43$	35.4975	−	61.4835i	0.825523	−	1.42985i	0.901519	−	0.432740i	$-0.142453\pi$
$44$	−11.6821	−	11.6821i	−0.265503	−	0.265503i
$45$		0			0
$46$	6.85471	+	25.5821i	0.149015	+	0.556133i
$47$	22.8093	+	22.8093i	0.485303	+	0.485303i	0.906820	−	0.421517i	$-0.138502\pi$
$47$	22.8093	+	22.8093i	0.485303	+	0.485303i	−0.421517	+	0.906820i	$0.638502\pi$
$48$	35.4762	+	20.4822i	0.739088	+	0.426713i
$49$	−41.1573	+	23.7622i	−0.839944	+	0.484942i
$50$		0			0
$51$			20.0457i			0.393053i
$52$	−11.1179	+	10.8988i	−0.213806	+	0.209592i
$53$		−	3.82249i		−	0.0721224i	−0.999350	−	0.0360612i	$-0.988519\pi$
$53$		−	3.82249i		−	0.0721224i	0.999350	−	0.0360612i	$-0.0114811\pi$
$54$	16.8848	−	63.0150i	0.312682	−	1.16694i
$55$		0			0
$56$	6.72137	+	3.88059i	0.120024	+	0.0692962i
$57$	36.3294	−	36.3294i	0.637357	−	0.637357i
$58$	2.72358	+	10.1645i	0.0469583	+	0.175251i
$59$	17.8214	+	66.5103i	0.302057	+	1.12729i	0.935449	+	0.353462i	$0.114996\pi$
$59$	17.8214	+	66.5103i	0.302057	+	1.12729i	−0.633392	+	0.773831i	$0.718338\pi$
$60$		0			0
$61$	20.0377	−	34.7063i	0.328487	−	0.568955i	−0.653725	−	0.756732i	$-0.726795\pi$
$61$	20.0377	−	34.7063i	0.328487	−	0.568955i	0.982212	+	0.187777i	$0.0601281\pi$
$62$	−35.2155	−	60.9950i	−0.567992	−	0.983790i
$63$	1.42146	−	5.30495i	0.0225628	−	0.0842056i
$64$			35.0818i			0.548153i
$65$		0			0
$66$	66.5597			1.00848
$67$	56.1209	+	15.0375i	0.837625	+	0.224441i	0.652038	−	0.758187i	$-0.273914\pi$
$67$	56.1209	+	15.0375i	0.837625	+	0.224441i	0.185588	+	0.982628i	$0.440581\pi$
$68$	9.82382	−	5.67179i	0.144468	−	0.0834086i
$69$	−21.2916	−	12.2927i	−0.308574	−	0.178155i
$70$		0			0
$71$	−53.0258	+	14.2082i	−0.746842	+	0.200116i	−0.612117	−	0.790767i	$-0.709682\pi$
$71$	−53.0258	+	14.2082i	−0.746842	+	0.200116i	−0.134725	+	0.990883i	$0.543015\pi$
$72$	27.9007	−	7.47597i	0.387510	−	0.103833i
$73$	34.0315	+	34.0315i	0.466186	+	0.466186i	0.900676	−	0.434491i	$-0.143072\pi$
$73$	34.0315	+	34.0315i	0.466186	+	0.466186i	−0.434491	+	0.900676i	$0.643072\pi$
$74$	−22.6525	+	39.2354i	−0.306115	+	0.530208i
$75$		0			0
$76$	−28.0831	−	7.52483i	−0.369514	−	0.0990110i
$77$	16.7579			0.217635
$78$	0.624199	−	62.7207i	0.00800256	−	0.804112i
$79$	27.0828			0.342821			0.171410	−	0.985200i	$-0.445168\pi$
$79$	27.0828			0.342821			0.171410	+	0.985200i	$0.445168\pi$
$80$		0			0
$81$	9.93517	+	17.2082i	0.122656	+	0.212447i
$82$	−64.6726	+	112.016i	−0.788691	+	1.36605i
$83$	20.0700	−	20.0700i	0.241807	−	0.241807i	−0.575790	−	0.817598i	$-0.695305\pi$
$83$	20.0700	−	20.0700i	0.241807	−	0.241807i	0.817598	+	0.575790i	$0.195305\pi$
$84$	2.97401	−	0.796885i	0.0354049	−	0.00948672i
$85$		0			0
$86$	114.450	−	114.450i	1.33081	−	1.33081i
$87$	−8.45980	−	4.88427i	−0.0972391	−	0.0561410i
$88$	44.0679	+	76.3279i	0.500772	+	0.867363i
$89$	30.1805	+	8.08684i	0.339107	+	0.0908634i	0.424354	−	0.905496i	$-0.360501\pi$
$89$	30.1805	+	8.08684i	0.339107	+	0.0908634i	−0.0852470	+	0.996360i	$0.527168\pi$
$90$		0			0
$91$	0.157156	−	15.7913i	0.00172699	−	0.173531i
$92$			13.9125i			0.151223i
$93$	63.1528	+	16.9217i	0.679063	+	0.181954i
$94$	36.7704	+	63.6881i	0.391174	+	0.677533i
$95$		0			0
$96$	27.7940	+	27.7940i	0.289521	+	0.289521i
$97$	46.1141	+	172.100i	0.475403	+	1.77423i	0.619855	+	0.784716i	$0.287191\pi$
$97$	46.1141	+	172.100i	0.475403	+	1.77423i	−0.144452	+	0.989512i	$0.546142\pi$
$98$	−104.655	+	28.0423i	−1.06791	+	0.286146i
$99$	44.1010	−	44.1010i	0.445464	−	0.445464i
$100$		0			0
$101$	138.665	−	80.0583i	1.37292	−	0.792656i	0.381626	−	0.924317i	$-0.375364\pi$
$101$	138.665	−	80.0583i	1.37292	−	0.792656i	0.991295	+	0.131661i	$0.0420309\pi$
$102$	−11.8282	+	44.1436i	−0.115963	+	0.432780i
$103$	−199.397			−1.93589			−0.967946	−	0.251158i	$-0.919189\pi$
$103$	−199.397			−1.93589			−0.967946	+	0.251158i	$0.919189\pi$
$104$	72.3388	−	40.8104i	0.695565	−	0.392408i
$105$		0			0
$106$	2.25551	−	8.41767i	0.0212784	−	0.0794120i
$107$	−44.8915	+	25.9181i	−0.419547	+	0.242226i	−0.694883	−	0.719122i	$-0.744544\pi$
$107$	−44.8915	+	25.9181i	−0.419547	+	0.242226i	0.275337	+	0.961348i	$0.411211\pi$
$108$	17.1350	−	29.6786i	0.158657	−	0.274802i
$109$	−147.687	−	147.687i	−1.35493	−	1.35493i	−0.880051	−	0.474880i	$-0.842491\pi$
$109$	−147.687	−	147.687i	−1.35493	−	1.35493i	−0.474880	−	0.880051i	$-0.657509\pi$
$110$		0			0
$111$	−10.8850	−	40.6234i	−0.0980631	−	0.365977i
$112$	16.6265	+	16.6265i	0.148451	+	0.148451i
$113$	−126.033	−	72.7654i	−1.11534	−	0.643942i	−0.175132	−	0.984545i	$-0.556035\pi$
$113$	−126.033	−	72.7654i	−1.11534	−	0.643942i	−0.940207	+	0.340603i	$0.889369\pi$
$114$	101.439	−	58.5659i	0.889816	−	0.513736i
$115$		0			0
$116$			5.52787i			0.0476540i
$117$	−41.1438	−	41.9709i	−0.351656	−	0.358726i
$118$			156.981i			1.33035i
$119$	−2.97802	+	11.1141i	−0.0250254	+	0.0933960i
$120$		0			0
$121$	60.0178	+	34.6513i	0.496015	+	0.286374i
$122$	64.6047	−	64.6047i	0.529547	−	0.529547i
$123$	−31.0765	−	115.979i	−0.252654	−	0.942919i
$124$	−9.57576	−	35.7372i	−0.0772239	−	0.288203i
$125$		0			0
$126$	6.26051	−	10.8435i	0.0496866	−	0.0860597i
$127$	12.2543	+	21.2251i	0.0964907	+	0.167127i	0.910230	−	0.414104i	$-0.135905\pi$
$127$	12.2543	+	21.2251i	0.0964907	+	0.167127i	−0.813739	+	0.581230i	$0.802572\pi$
$128$	−39.9285	+	149.015i	−0.311941	+	1.16418i
$129$			150.250i			1.16473i
$130$		0			0
$131$	−192.400			−1.46870			−0.734351	−	0.678769i	$-0.762514\pi$
$131$	−192.400			−1.46870			−0.734351	+	0.678769i	$0.762514\pi$
$132$	33.7729	+	9.04943i	0.255855	+	0.0685563i
$133$	25.5395	−	14.7453i	0.192027	−	0.110867i
$134$	114.713	+	66.2297i	0.856068	+	0.494251i
$135$		0			0
$136$	−58.4533	+	15.6625i	−0.429803	+	0.115165i
$137$	−184.009	+	49.3051i	−1.34313	+	0.359891i	−0.857595	−	0.514325i	$-0.828043\pi$
$137$	−184.009	+	49.3051i	−1.34313	+	0.359891i	−0.485537	+	0.874216i	$0.661376\pi$
$138$	−39.6337	−	39.6337i	−0.287201	−	0.287201i
$139$	59.9212	−	103.786i	0.431087	−	0.746665i	−0.565880	−	0.824488i	$-0.691463\pi$
$139$	59.9212	−	103.786i	0.431087	−	0.746665i	0.996967	+	0.0778224i	$0.0247967\pi$
$140$		0			0
$141$	−65.9412	−	17.6689i	−0.467668	−	0.125311i
$142$	−125.154			−0.881367
$143$	91.2087	−	154.409i	0.637823	−	1.07978i
$144$	87.5105			0.607712
$145$		0			0
$146$	54.8616	+	95.0231i	0.375764	+	0.650843i
$147$	50.2890	−	87.1031i	0.342102	−	0.592538i
$148$	−16.8285	+	16.8285i	−0.113706	+	0.113706i
$149$	−276.255	+	74.0224i	−1.85406	+	0.496795i	−0.999737	−	0.0229414i	$-0.992697\pi$
$149$	−276.255	+	74.0224i	−1.85406	+	0.496795i	−0.854327	+	0.519736i	$0.826030\pi$
$150$		0			0
$151$	137.089	−	137.089i	0.907877	−	0.907877i	−0.0882233	−	0.996101i	$-0.528119\pi$
$151$	137.089	−	137.089i	0.907877	−	0.907877i	0.996101	+	0.0882233i	$0.0281189\pi$
$152$	134.322	+	77.5507i	0.883696	+	0.510202i
$153$	21.4114	+	37.0857i	0.139944	+	0.242390i
$154$	36.9033	+	9.88820i	0.239632	+	0.0642091i
$155$		0			0
$156$	8.84420	−	31.7401i	0.0566936	−	0.203462i
$157$			8.51422i			0.0542307i	0.999632	+	0.0271153i	$0.00863214\pi$
$157$			8.51422i			0.0542307i	−0.999632	+	0.0271153i	$0.991368\pi$
$158$	59.6403	+	15.9806i	0.377470	+	0.101143i
$159$	4.04486	+	7.00590i	0.0254394	+	0.0440623i
$160$		0			0
$161$	−9.97867	−	9.97867i	−0.0619793	−	0.0619793i
$162$	11.7247	+	43.7573i	0.0723750	+	0.270107i
$163$	188.232	−	50.4367i	1.15480	−	0.309427i	0.369912	−	0.929067i	$-0.379388\pi$
$163$	188.232	−	50.4367i	1.15480	−	0.309427i	0.784887	+	0.619639i	$0.212721\pi$
$164$	−48.0451	+	48.0451i	−0.292958	+	0.292958i
$165$		0			0
$166$	56.0396	−	32.3545i	0.337588	−	0.194907i
$167$	36.5920	−	136.563i	0.219114	−	0.817744i	−0.765564	−	0.643360i	$-0.777540\pi$
$167$	36.5920	−	136.563i	0.219114	−	0.817744i	0.984678	−	0.174384i	$-0.0557935\pi$
$168$	−16.4253			−0.0977699
$169$	−144.648	−	87.3961i	−0.855903	−	0.517137i
$170$		0			0
$171$	28.4068	−	106.016i	0.166122	−	0.619975i
$172$	73.6332	−	42.5121i	0.428100	−	0.247164i
$173$	50.9585	−	88.2627i	0.294558	−	0.510189i	−0.680324	−	0.732911i	$-0.738161\pi$
$173$	50.9585	−	88.2627i	0.294558	−	0.510189i	0.974882	+	0.222722i	$0.0714943\pi$
$174$	−15.7477	−	15.7477i	−0.0905039	−	0.0905039i
$175$		0			0
$176$	69.1095	+	257.920i	0.392668	+	1.46546i
$177$	−103.043	−	103.043i	−0.582162	−	0.582162i
$178$	61.6901	+	35.6168i	0.346573	+	0.200094i
$179$	57.4893	−	33.1915i	0.321169	−	0.185427i	−0.330744	−	0.943720i	$-0.607300\pi$
$179$	57.4893	−	33.1915i	0.321169	−	0.185427i	0.651914	+	0.758293i	$0.273966\pi$
$180$		0			0
$181$			116.383i			0.642999i	0.946910	+	0.321499i	$0.104187\pi$
$181$			116.383i			0.642999i	−0.946910	+	0.321499i	$0.895813\pi$
$182$	9.66395	−	34.6820i	0.0530986	−	0.190561i
$183$			84.8135i			0.463462i
$184$	19.2096	−	71.6911i	0.104400	−	0.389625i
$185$		0			0
$186$	129.087	+	74.5282i	0.694014	+	0.400689i
$187$	−92.3936	+	92.3936i	−0.494083	+	0.494083i
$188$	9.99856	+	37.3151i	0.0531838	+	0.198485i
$189$	8.99687	+	33.5768i	0.0476025	+	0.177655i
$190$		0			0
$191$	−58.4100	+	101.169i	−0.305812	+	0.529681i	−0.977442	−	0.211205i	$-0.932261\pi$
$191$	−58.4100	+	101.169i	−0.305812	+	0.529681i	0.671630	+	0.740887i	$0.265594\pi$
$192$	−37.1227	−	64.2983i	−0.193347	−	0.334887i
$193$	−58.7574	+	219.285i	−0.304442	+	1.13619i	0.628982	+	0.777420i	$0.283472\pi$
$193$	−58.7574	+	219.285i	−0.304442	+	1.13619i	−0.933424	+	0.358774i	$0.883195\pi$
$194$			406.199i			2.09381i
$195$		0			0
$196$	−56.9156			−0.290386
$197$	91.5676	+	24.5355i	0.464810	+	0.124545i	0.483621	−	0.875278i	$-0.339321\pi$
$197$	91.5676	+	24.5355i	0.464810	+	0.124545i	−0.0188108	+	0.999823i	$0.505988\pi$
$198$	123.139	−	71.0944i	0.621914	−	0.359062i
$199$	−247.382	−	142.826i	−1.24313	−	0.717719i	−0.273396	−	0.961902i	$-0.588147\pi$
$199$	−247.382	−	142.826i	−1.24313	−	0.717719i	−0.969729	+	0.244183i	$0.921480\pi$
$200$		0			0
$201$	−118.771	+	31.8247i	−0.590902	+	0.158332i
$202$	352.600	−	94.4788i	1.74554	−	0.467717i
$203$	−3.96482	−	3.96482i	−0.0195312	−	0.0195312i
$204$	−12.0035	+	20.7906i	−0.0588406	+	0.101915i
$205$		0			0
$206$	−439.101	−	117.657i	−2.13156	−	0.571149i
$207$	−52.5209			−0.253724
$208$	243.692	−	62.7047i	1.17160	−	0.301465i
$209$	334.894			1.60237
$210$		0			0
$211$	94.2417	+	163.231i	0.446643	+	0.773609i	0.998165	−	0.0605518i	$-0.0192860\pi$
$211$	94.2417	+	163.231i	0.446643	+	0.773609i	−0.551522	+	0.834160i	$0.685953\pi$
$212$	2.28892	−	3.96453i	0.0107968	−	0.0187006i
$213$	82.1515	−	82.1515i	0.385688	−	0.385688i
$214$	−114.151	+	30.5866i	−0.533415	+	0.142928i
$215$		0			0
$216$	−129.275	+	129.275i	−0.598494	+	0.598494i
$217$	32.5004	+	18.7641i	0.149772	+	0.0864706i
$218$	−238.084	−	412.374i	−1.09213	−	1.89162i
$219$	−98.3847	−	26.3621i	−0.449245	−	0.120375i
$220$		0			0
$221$	86.1981	+	87.9310i	0.390037	+	0.397878i
$222$		−	95.8814i		−	0.431898i
$223$	101.633	+	27.2326i	0.455756	+	0.122119i	0.479391	−	0.877601i	$-0.340858\pi$
$223$	101.633	+	27.2326i	0.455756	+	0.122119i	−0.0236357	+	0.999721i	$0.507524\pi$
$224$	11.2809	+	19.5392i	0.0503613	+	0.0872284i
$225$		0			0
$226$	−234.607	−	234.607i	−1.03809	−	1.03809i
$227$	−63.8236	−	238.193i	−0.281161	−	1.04931i	−0.951599	−	0.307343i	$-0.900560\pi$
$227$	−63.8236	−	238.193i	−0.281161	−	1.04931i	0.670438	−	0.741966i	$-0.266106\pi$
$228$	59.4336	−	15.9252i	0.260674	−	0.0698473i
$229$	201.491	−	201.491i	0.879872	−	0.879872i	−0.113649	−	0.993521i	$-0.536254\pi$
$229$	201.491	−	201.491i	0.879872	−	0.879872i	0.993521	+	0.113649i	$0.0362540\pi$
$230$		0			0
$231$	−30.7140	+	17.7328i	−0.132961	+	0.0767652i
$232$	7.63254	−	28.4850i	0.0328989	−	0.122780i
$233$	−348.962			−1.49769			−0.748846	−	0.662744i	$-0.769392\pi$
$233$	−348.962			−1.49769			−0.748846	+	0.662744i	$0.769392\pi$
$234$	−65.8390	−	116.703i	−0.281363	−	0.498732i
$235$		0			0
$236$	−21.3431	+	79.6534i	−0.0904367	+	0.337514i
$237$	−49.6377	+	28.6584i	−0.209442	+	0.120921i
$238$	−13.1161	+	22.7177i	−0.0551095	+	0.0954524i
$239$	−62.2768	−	62.2768i	−0.260572	−	0.260572i	0.564714	−	0.825287i	$-0.308986\pi$
$239$	−62.2768	−	62.2768i	−0.260572	−	0.260572i	−0.825287	+	0.564714i	$0.808986\pi$
$240$		0			0
$241$	48.6035	+	181.391i	0.201674	+	0.752658i	0.990438	+	0.137961i	$0.0440550\pi$
$241$	48.6035	+	181.391i	0.201674	+	0.752658i	−0.788763	+	0.614697i	$0.789278\pi$
$242$	111.721	+	111.721i	0.461658	+	0.461658i
$243$	186.616	+	107.743i	0.767965	+	0.443385i
$244$	41.5646	−	23.9973i	0.170347	−	0.0983497i
$245$		0			0
$246$		−	273.740i		−	1.11276i
$247$	3.14065	−	315.578i	0.0127152	−	1.27765i
$248$			197.375i			0.795867i
$249$	−15.5470	+	58.0221i	−0.0624377	+	0.233021i
$250$		0			0
$251$	−266.078	−	153.620i	−1.06007	−	0.612034i	−0.134621	−	0.990897i	$-0.542982\pi$
$251$	−266.078	−	153.620i	−1.06007	−	0.612034i	−0.925453	+	0.378864i	$0.876315\pi$
$252$	4.65091	−	4.65091i	0.0184560	−	0.0184560i
$253$	−41.4772	−	154.795i	−0.163942	−	0.611838i
$254$	14.4616	+	53.9715i	0.0569355	+	0.212486i
$255$		0			0
$256$	−105.693	+	183.065i	−0.412863	+	0.715100i
$257$	−15.6861	−	27.1691i	−0.0610353	−	0.105716i	0.833893	−	0.551926i	$-0.186107\pi$
$257$	−15.6861	−	27.1691i	−0.0610353	−	0.105716i	−0.894928	+	0.446210i	$0.852774\pi$
$258$	−88.6570	+	330.872i	−0.343632	+	1.28245i
$259$		−	24.1403i		−	0.0932056i
$260$		0			0
$261$	−20.8681			−0.0799545
$262$	−423.693	−	113.528i	−1.61715	−	0.433313i
$263$	−445.357	+	257.127i	−1.69337	+	0.977668i	−0.741608	+	0.670834i	$0.765936\pi$
$263$	−445.357	+	257.127i	−1.69337	+	0.977668i	−0.951763	+	0.306834i	$0.900730\pi$
$264$	−161.537	−	93.2631i	−0.611881	−	0.353269i
$265$		0			0
$266$	64.9423	−	17.4012i	0.244144	−	0.0654182i
$267$	−63.8725	+	17.1146i	−0.239223	+	0.0640996i
$268$	49.2018	+	49.2018i	0.183589	+	0.183589i
$269$	−166.095	+	287.685i	−0.617454	+	1.06946i	0.372495	+	0.928034i	$0.378502\pi$
$269$	−166.095	+	287.685i	−0.617454	+	1.06946i	−0.989949	+	0.141427i	$0.954831\pi$
$270$		0			0
$271$	59.2685	+	15.8809i	0.218703	+	0.0586013i	0.366507	−	0.930415i	$-0.380554\pi$
$271$	59.2685	+	15.8809i	0.218703	+	0.0586013i	−0.147804	+	0.989017i	$0.547220\pi$
$272$	−183.339			−0.674039
$273$	16.4219	+	29.1088i	0.0601536	+	0.106626i
$274$	−434.308			−1.58506
$275$		0			0
$276$	−14.7219	−	25.4991i	−0.0533402	−	0.0923879i
$277$	−131.174	+	227.199i	−0.473551	+	0.820214i	−0.999542	−	0.0302764i	$-0.990361\pi$
$277$	−131.174	+	227.199i	−0.473551	+	0.820214i	0.525991	+	0.850490i	$0.323695\pi$
$278$	193.196	−	193.196i	0.694948	−	0.694948i
$279$	134.911	−	36.1492i	0.483551	−	0.129567i
$280$		0			0
$281$	−43.8112	+	43.8112i	−0.155912	+	0.155912i	−0.780752	−	0.624841i	$-0.785164\pi$
$281$	−43.8112	+	43.8112i	−0.155912	+	0.155912i	0.624841	+	0.780752i	$0.285164\pi$
$282$	−134.786	−	77.8189i	−0.477966	−	0.275954i
$283$	−93.6272	−	162.167i	−0.330838	−	0.573028i	0.651838	−	0.758358i	$-0.273998\pi$
$283$	−93.6272	−	162.167i	−0.330838	−	0.573028i	−0.982676	+	0.185330i	$0.940665\pi$
$284$	−63.5042	−	17.0159i	−0.223606	−	0.0599151i
$285$		0			0
$286$	291.966	−	286.212i	1.02086	−	1.00074i
$287$		−	68.9200i		−	0.240139i
$288$	81.1079	+	21.7328i	0.281625	+	0.0754611i
$289$	99.6421	+	172.585i	0.344782	+	0.597180i
$290$		0			0
$291$	−266.630	−	266.630i	−0.916256	−	0.916256i
$292$	14.9179	+	55.6744i	0.0510888	+	0.190666i
$293$	264.910	−	70.9824i	0.904130	−	0.242261i	0.223341	−	0.974740i	$-0.428304\pi$
$293$	264.910	−	70.9824i	0.904130	−	0.242261i	0.680789	+	0.732479i	$0.261637\pi$
$294$	162.140	−	162.140i	0.551496	−	0.551496i
$295$		0			0
$296$	109.953	−	63.4813i	0.371462	−	0.214464i
$297$	−102.168	+	381.298i	−0.344001	+	1.28383i
$298$	−652.032			−2.18803
$299$	−146.256	+	37.6332i	−0.489150	+	0.125864i
$300$		0			0
$301$	−22.3214	+	83.3044i	−0.0741573	+	0.276759i
$302$	382.782	−	220.999i	1.26749	−	0.731786i
$303$	−169.431	+	293.464i	−0.559179	+	0.968527i
$304$	332.269	+	332.269i	1.09299	+	1.09299i
$305$		0			0
$306$	25.2682	+	94.3021i	0.0825757	+	0.308177i
$307$	−116.111	−	116.111i	−0.378211	−	0.378211i	0.492245	−	0.870457i	$-0.336176\pi$
$307$	−116.111	−	116.111i	−0.378211	−	0.378211i	−0.870457	+	0.492245i	$0.836176\pi$
$308$	17.3806	+	10.0347i	0.0564305	+	0.0325802i
$309$	365.457	−	210.997i	1.18271	−	0.682837i
$310$		0			0
$311$		−	419.831i		−	1.34994i	−0.737845	−	0.674970i	$-0.764157\pi$
$311$		−	419.831i		−	1.34994i	0.737845	−	0.674970i	$-0.235843\pi$
$312$	−89.3989	+	151.345i	−0.286535	+	0.485080i
$313$		−	3.61275i		−	0.0115423i	−0.999983	−	0.00577116i	$-0.998163\pi$
$313$		−	3.61275i		−	0.0115423i	0.999983	−	0.00577116i	$-0.00183703\pi$
$314$	−5.02392	+	18.7495i	−0.0159997	+	0.0597119i
$315$		0			0
$316$	28.0892	+	16.2173i	0.0888900	+	0.0513207i
$317$	−353.225	+	353.225i	−1.11428	+	1.11428i	−0.121710	+	0.992566i	$0.538838\pi$
$317$	−353.225	+	353.225i	−1.11428	+	1.11428i	−0.992566	+	0.121710i	$0.961162\pi$
$318$	4.77344	+	17.8147i	0.0150108	+	0.0560211i
$319$	−16.4801	−	61.5047i	−0.0516619	−	0.192805i
$320$		0			0
$321$	54.8518	−	95.0061i	0.170878	−	0.295969i
$322$	−16.0864	−	27.8625i	−0.0499578	−	0.0865295i
$323$	−59.5136	+	222.108i	−0.184253	+	0.687640i
$324$			23.7969i			0.0734473i
$325$		0			0
$326$	444.275			1.36281
$327$	426.962	+	114.404i	1.30570	+	0.349860i
$328$	313.913	−	181.238i	0.957053	−	0.552555i
$329$	−33.9354	−	19.5926i	−0.103147	−	0.0595521i
$330$		0			0
$331$	−453.373	+	121.481i	−1.36971	+	0.367012i	−0.867372	−	0.497660i	$-0.834193\pi$
$331$	−453.373	+	121.481i	−1.36971	+	0.367012i	−0.502336	+	0.864673i	$0.667526\pi$
$332$	32.8338	−	8.79780i	0.0988971	−	0.0264994i
$333$	−63.5289	−	63.5289i	−0.190777	−	0.190777i
$334$	161.162	−	279.140i	0.482520	−	0.835750i
$335$		0			0
$336$	−48.0670	−	12.8795i	−0.143057	−	0.0383319i
$337$	249.078			0.739104			0.369552	−	0.929210i	$-0.379511\pi$
$337$	249.078			0.739104			0.369552	+	0.929210i	$0.379511\pi$
$338$	−266.966	−	277.810i	−0.789839	−	0.821923i
$339$	307.994			0.908537
$340$		0			0
$341$	213.086	+	369.075i	0.624884	+	1.08233i
$342$	125.112	−	216.700i	0.365824	−	0.633626i
$343$	82.9122	−	82.9122i	0.241727	−	0.241727i
$344$	−438.129	+	117.396i	−1.27363	+	0.341268i
$345$		0			0
$346$	164.298	−	164.298i	0.474851	−	0.474851i
$347$	245.742	+	141.879i	0.708190	+	0.408873i	0.810390	−	0.585890i	$-0.199255\pi$
$347$	245.742	+	141.879i	0.708190	+	0.408873i	−0.102201	+	0.994764i	$0.532588\pi$
$348$	−5.84945	−	10.1315i	−0.0168088	−	0.0291136i
$349$	501.328	+	134.330i	1.43647	+	0.384901i	0.891296	−	0.453423i	$-0.149797\pi$
$349$	501.328	+	134.330i	1.43647	+	0.384901i	0.545173	+	0.838323i	$0.316464\pi$
$350$		0			0
$351$	358.347	+	99.8514i	1.02093	+	0.284477i
$352$			256.213i			0.727877i
$353$	260.425	+	69.7807i	0.737749	+	0.197679i	0.608077	−	0.793878i	$-0.291941\pi$
$353$	260.425	+	69.7807i	0.737749	+	0.197679i	0.129671	+	0.991557i	$0.458608\pi$
$354$	−166.113	−	287.717i	−0.469246	−	0.812759i
$355$		0			0
$356$	26.4596	+	26.4596i	0.0743247	+	0.0743247i
$357$	−6.30253	−	23.5214i	−0.0176541	−	0.0658862i
$358$	146.185	−	39.1701i	0.408337	−	0.109414i
$359$	−143.447	+	143.447i	−0.399574	+	0.399574i	−0.878083	−	0.478508i	$-0.841178\pi$
$359$	−143.447	+	143.447i	−0.399574	+	0.399574i	0.478508	+	0.878083i	$0.341178\pi$
$360$		0			0
$361$	197.754	−	114.173i	0.547796	−	0.316270i
$362$	−68.6731	+	256.291i	−0.189705	+	0.707988i
$363$	−146.668			−0.404045
$364$	9.61892	−	16.2840i	0.0264256	−	0.0447363i
$365$		0			0
$366$	−50.0452	+	186.771i	−0.136736	+	0.510304i
$367$	400.479	−	231.217i	1.09122	−	0.630018i	0.157321	−	0.987547i	$-0.449714\pi$
$367$	400.479	−	231.217i	1.09122	−	0.630018i	0.933902	+	0.357529i	$0.116381\pi$
$368$	112.430	−	194.734i	0.305515	−	0.529167i
$369$	−181.374	−	181.374i	−0.491528	−	0.491528i
$370$		0			0
$371$	1.20182	+	4.48525i	0.00323941	+	0.0120896i
$372$	55.3668	+	55.3668i	0.148835	+	0.148835i
$373$	13.8547	+	7.99902i	0.0371440	+	0.0214451i	0.518457	−	0.855104i	$-0.326507\pi$
$373$	13.8547	+	7.99902i	0.0371440	+	0.0214451i	−0.481313	+	0.876549i	$0.659840\pi$
$374$	−257.982	+	148.946i	−0.689791	+	0.398251i
$375$		0			0
$376$		−	206.090i		−	0.548111i
$377$	−58.1118	+	14.9528i	−0.154143	+	0.0396626i
$378$			79.2495i			0.209655i
$379$	−42.1137	+	157.170i	−0.111118	+	0.414697i	−0.998967	−	0.0454368i	$-0.985532\pi$
$379$	−42.1137	+	157.170i	−0.111118	+	0.414697i	0.887849	+	0.460134i	$0.152199\pi$
$380$		0			0
$381$	−44.9197	−	25.9344i	−0.117900	−	0.0680693i
$382$	−188.323	+	188.323i	−0.492993	+	0.492993i
$383$	140.296	+	523.591i	0.366307	+	1.36708i	0.865640	+	0.500667i	$0.166912\pi$
$383$	140.296	+	523.591i	0.366307	+	1.36708i	−0.499333	+	0.866410i	$0.666421\pi$
$384$	−84.5026	−	315.368i	−0.220059	−	0.821271i
$385$		0			0
$386$	−258.784	+	448.228i	−0.670426	+	1.16121i
$387$	160.487	+	277.971i	0.414694	+	0.718271i
$388$	−55.2267	+	206.109i	−0.142337	+	0.531208i
$389$			40.9518i			0.105274i	0.998614	+	0.0526372i	$0.0167627\pi$
$389$			40.9518i			0.105274i	−0.998614	+	0.0526372i	$0.983237\pi$
$390$		0			0
$391$	110.034			0.281416
$392$	293.285	+	78.5855i	0.748176	+	0.200473i
$393$	352.633	−	203.593i	0.897285	−	0.518048i
$394$	187.167	+	108.061i	0.475044	+	0.274267i
$395$		0			0
$396$	72.1477	−	19.3319i	0.182191	−	0.0488180i
$397$	257.363	−	68.9602i	0.648269	−	0.173703i	0.0803231	−	0.996769i	$-0.474405\pi$
$397$	257.363	−	68.9602i	0.648269	−	0.173703i	0.567946	+	0.823066i	$0.307738\pi$
$398$	−460.494	−	460.494i	−1.15702	−	1.15702i
$399$	−31.2061	+	54.0506i	−0.0782108	+	0.135465i
$400$		0			0
$401$	440.936	+	118.148i	1.09959	+	0.294634i	0.762598	−	0.646873i	$-0.223924\pi$
$401$	440.936	+	118.148i	1.09959	+	0.294634i	0.336992	+	0.941507i	$0.390590\pi$
$402$	−280.330			−0.697339
$403$	349.786	−	197.334i	0.867955	−	0.489663i
$404$	191.757			0.474646
$405$		0			0
$406$	−6.39162	−	11.0706i	−0.0157429	−	0.0272675i
$407$	137.068	−	237.410i	0.336778	−	0.583316i
$408$	90.5602	−	90.5602i	0.221961	−	0.221961i
$409$	690.126	−	184.919i	1.68735	−	0.452124i	0.717646	−	0.696408i	$-0.245220\pi$
$409$	690.126	−	184.919i	1.68735	−	0.452124i	0.969704	+	0.244284i	$0.0785530\pi$
$410$		0			0
$411$	285.081	−	285.081i	0.693627	−	0.693627i
$412$	−206.807	−	119.400i	−0.501958	−	0.289805i
$413$	−41.8227	−	72.4390i	−0.101266	−	0.175397i
$414$	−115.658	−	30.9906i	−0.279368	−	0.0748565i
$415$		0			0
$416$	241.435	+	2.40277i	0.580373	+	0.00577590i
$417$			253.628i			0.608221i
$418$	737.485	+	197.609i	1.76432	+	0.472748i
$419$	9.64146	+	16.6995i	0.0230107	+	0.0398556i	0.877301	−	0.479940i	$-0.159342\pi$
$419$	9.64146	+	16.6995i	0.0230107	+	0.0398556i	−0.854291	+	0.519795i	$0.826008\pi$
$420$		0			0
$421$	497.028	+	497.028i	1.18059	+	1.18059i	0.979592	+	0.200999i	$0.0644187\pi$
$421$	497.028	+	497.028i	1.18059	+	1.18059i	0.200999	+	0.979592i	$0.435581\pi$
$422$	111.217	+	415.068i	0.263547	+	0.983572i
$423$	−140.867	+	37.7453i	−0.333020	+	0.0892325i
$424$	−17.2688	+	17.2688i	−0.0407283	+	0.0407283i
$425$		0			0
$426$	229.384	−	132.435i	0.538460	−	0.310880i
$427$	−12.6000	+	47.0238i	−0.0295082	+	0.110126i
$428$	−62.0796			−0.145046
$429$	−3.77697	+	379.517i	−0.00880413	+	0.884655i
$430$		0			0
$431$	−150.008	+	559.839i	−0.348047	+	1.29893i	0.540964	+	0.841046i	$0.318059\pi$
$431$	−150.008	+	559.839i	−0.348047	+	1.29893i	−0.889012	+	0.457885i	$0.848607\pi$
$432$	−479.676	+	276.941i	−1.11036	+	0.641068i
$433$	286.082	−	495.509i	0.660698	−	1.14436i	−0.319734	−	0.947507i	$-0.603594\pi$
$433$	286.082	−	495.509i	0.660698	−	1.14436i	0.980432	−	0.196856i	$-0.0630731\pi$
$434$	60.4986	+	60.4986i	0.139398	+	0.139398i
$435$		0			0
$436$	−64.7396	−	241.611i	−0.148485	−	0.554155i
$437$	−199.417	−	199.417i	−0.456331	−	0.456331i
$438$	−201.102	−	116.106i	−0.459137	−	0.265083i
$439$	−206.594	+	119.277i	−0.470602	+	0.271702i	−0.716492	−	0.697596i	$-0.754253\pi$
$439$	−206.594	+	119.277i	−0.470602	+	0.271702i	0.245890	+	0.969298i	$0.420920\pi$
$440$		0			0
$441$		−	214.861i		−	0.487212i
$442$	137.936	+	244.499i	0.312072	+	0.553165i
$443$		−	110.509i		−	0.249455i	−0.992191	−	0.124728i	$-0.960194\pi$
$443$		−	110.509i		−	0.249455i	0.992191	−	0.124728i	$-0.0398057\pi$
$444$	13.0360	−	48.6510i	0.0293603	−	0.109574i
$445$		0			0
$446$	207.743	+	119.940i	0.465791	+	0.268924i
$447$	427.996	−	427.996i	0.957485	−	0.957485i
$448$	−11.0300	−	41.1644i	−0.0246205	−	0.0918849i
$449$	106.893	+	398.930i	0.238069	+	0.888486i	0.976741	+	0.214421i	$0.0687864\pi$
$449$	106.893	+	398.930i	0.238069	+	0.888486i	−0.738672	+	0.674065i	$0.764547\pi$
$450$		0			0
$451$	391.328	−	677.800i	0.867690	−	1.50288i
$452$	−87.1445	−	150.939i	−0.192798	−	0.333935i
$453$	−106.195	+	396.324i	−0.234425	+	0.874887i
$454$		−	562.195i		−	1.23832i
$455$		0			0
$456$	−328.249			−0.719844
$457$	−389.042	−	104.243i	−0.851295	−	0.228104i	−0.193313	−	0.981137i	$-0.561923\pi$
$457$	−389.042	−	104.243i	−0.851295	−	0.228104i	−0.657982	+	0.753033i	$0.728590\pi$
$458$	562.603	−	324.819i	1.22839	−	0.709212i
$459$	−234.727	−	135.520i	−0.511388	−	0.295250i
$460$		0			0
$461$	327.128	−	87.6537i	0.709605	−	0.190138i	0.114076	−	0.993472i	$-0.463609\pi$
$461$	327.128	−	87.6537i	0.709605	−	0.190138i	0.595529	+	0.803334i	$0.296943\pi$
$462$	−78.1002	+	20.9269i	−0.169048	+	0.0452963i
$463$	−27.1990	−	27.1990i	−0.0587451	−	0.0587451i	0.677124	−	0.735869i	$-0.263226\pi$
$463$	−27.1990	−	27.1990i	−0.0587451	−	0.0587451i	−0.735869	+	0.677124i	$0.763226\pi$
$464$	44.6716	−	77.3735i	0.0962750	−	0.166753i
$465$		0			0
$466$	−768.465	−	205.910i	−1.64907	−	0.441866i
$467$	−201.721			−0.431950			−0.215975	−	0.976399i	$-0.569293\pi$
$467$	−201.721			−0.431950			−0.215975	+	0.976399i	$0.569293\pi$
$468$	−17.5403	−	68.1677i	−0.0374792	−	0.145657i
$469$	−70.5793			−0.150489
$470$		0			0
$471$	−9.00953	−	15.6050i	−0.0191285	−	0.0331315i
$472$	219.961	−	380.984i	0.466019	−	0.807169i
$473$	−692.524	+	692.524i	−1.46411	+	1.46411i
$474$	−126.220	+	33.8204i	−0.266286	+	0.0713512i
$475$		0			0
$476$	−9.74387	+	9.74387i	−0.0204703	+	0.0204703i
$477$	14.9664	+	8.64087i	0.0313761	+	0.0181150i
$478$	−100.395	−	173.890i	−0.210032	−	0.363786i
$479$	−6.17022	−	1.65331i	−0.0128815	−	0.00345158i	0.252373	−	0.967630i	$-0.418789\pi$
$479$	−6.17022	−	1.65331i	−0.0128815	−	0.00345158i	−0.265254	+	0.964179i	$0.585456\pi$
$480$		0			0
$481$	−222.431	−	131.389i	−0.462434	−	0.273158i
$482$			428.127i			0.888231i
$483$	28.8482	+	7.72985i	0.0597271	+	0.0160038i
$484$	41.4987	+	71.8779i	0.0857411	+	0.148508i
$485$		0			0
$486$	347.379	+	347.379i	0.714772	+	0.714772i
$487$	−31.1660	−	116.313i	−0.0639958	−	0.238836i	0.926518	−	0.376251i	$-0.122787\pi$
$487$	−31.1660	−	116.313i	−0.0639958	−	0.238836i	−0.990513	+	0.137416i	$0.956120\pi$
$488$	−247.316	+	66.2681i	−0.506795	+	0.135795i
$489$	−291.623	+	291.623i	−0.596367	+	0.596367i
$490$		0			0
$491$	−151.464	+	87.4479i	−0.308481	+	0.178102i	−0.646247	−	0.763129i	$-0.723662\pi$
$491$	−151.464	+	87.4479i	−0.308481	+	0.178102i	0.337765	+	0.941230i	$0.390329\pi$
$492$	37.2175	−	138.898i	0.0756454	−	0.282312i
$493$	43.7197			0.0886809
$494$	193.127	−	693.096i	0.390946	−	1.40303i
$495$		0			0
$496$	−154.767	+	577.597i	−0.312030	+	1.16451i
$497$	57.7525	−	33.3434i	0.116202	−	0.0670894i
$498$	−68.4734	+	118.599i	−0.137497	+	0.238151i
$499$	−133.231	−	133.231i	−0.266995	−	0.266995i	0.560893	−	0.827888i	$-0.310458\pi$
$499$	−133.231	−	133.231i	−0.266995	−	0.266995i	−0.827888	+	0.560893i	$0.810458\pi$
$500$		0			0
$501$	77.4415	+	289.016i	0.154574	+	0.576877i
$502$	−495.297	−	495.297i	−0.986648	−	0.986648i
$503$	14.0035	+	8.08495i	0.0278400	+	0.0160735i	0.513855	−	0.857877i	$-0.328217\pi$
$503$	14.0035	+	8.08495i	0.0278400	+	0.0160735i	−0.486015	+	0.873950i	$0.661550\pi$
$504$	−30.3878	+	17.5444i	−0.0602932	+	0.0348103i
$505$		0			0
$506$		−	365.355i		−	0.722045i
$507$	357.592	+	7.11825i	0.705310	+	0.0140399i
$508$			29.3518i			0.0577791i
$509$	2.07048	−	7.72713i	0.00406774	−	0.0151810i	−0.963862	−	0.266402i	$-0.914165\pi$
$509$	2.07048	−	7.72713i	0.00406774	−	0.0151810i	0.967930	+	0.251221i	$0.0808319\pi$
$510$		0			0
$511$	−50.6319	−	29.2323i	−0.0990839	−	0.0572061i
$512$	95.5755	−	95.5755i	0.186671	−	0.186671i
$513$	179.796	+	671.008i	0.350479	+	1.30801i
$514$	−18.5115	−	69.0859i	−0.0360146	−	0.134408i
$515$		0			0
$516$	−89.9705	+	155.833i	−0.174361	+	0.302003i
$517$	−222.494	−	385.371i	−0.430356	−	0.745398i
$518$	14.2443	−	53.1603i	0.0274986	−	0.102626i
$519$			215.692i			0.415591i
$520$		0			0
$521$	−944.984			−1.81379			−0.906895	−	0.421358i	$-0.861554\pi$
$521$	−944.984			−1.81379			−0.906895	+	0.421358i	$0.861554\pi$
$522$	−45.9546	−	12.3135i	−0.0880356	−	0.0235891i
$523$	1.77856	−	1.02685i	0.00340070	−	0.00196339i	−0.498299	−	0.867005i	$-0.666042\pi$
$523$	1.77856	−	1.02685i	0.00340070	−	0.00196339i	0.501699	+	0.865042i	$0.332708\pi$
$524$	−199.550	−	115.210i	−0.380820	−	0.219867i
$525$		0			0
$526$	−1132.46	+	303.442i	−2.15297	+	0.576885i
$527$	−282.644	+	75.7343i	−0.536327	+	0.143708i
$528$	−399.589	−	399.589i	−0.756798	−	0.756798i
$529$	197.024	−	341.255i	0.372445	−	0.645094i
$530$		0			0
$531$	−300.698	−	80.5717i	−0.566285	−	0.151736i
$532$	35.3181			0.0663874
$533$	−635.036	−	375.114i	−1.19144	−	0.703778i
$534$	−150.755			−0.282313
$535$		0			0
$536$	−185.601	−	321.471i	−0.346271	−	0.599759i
$537$	−70.2447	+	121.667i	−0.130809	+	0.226569i
$538$	−535.517	+	535.517i	−0.995386	+	0.995386i
$539$	633.260	−	169.681i	1.17488	−	0.314808i
$540$		0			0
$541$	−65.8956	+	65.8956i	−0.121803	+	0.121803i	−0.765381	−	0.643578i	$-0.777449\pi$
$541$	−65.8956	+	65.8956i	−0.121803	+	0.121803i	0.643578	+	0.765381i	$0.277449\pi$
$542$	121.147	+	69.9442i	0.223518	+	0.129048i
$543$	−123.153	−	213.308i	−0.226802	−	0.392832i
$544$	−169.925	−	45.5312i	−0.312362	−	0.0836971i
$545$		0			0
$546$	18.9874	+	73.7918i	0.0347755	+	0.135150i
$547$		−	297.410i		−	0.543711i	−0.962338	−	0.271855i	$-0.912363\pi$
$547$		−	297.410i		−	0.543711i	0.962338	−	0.271855i	$-0.0876372\pi$
$548$	−220.371	−	59.0482i	−0.402137	−	0.107752i
$549$	90.5917	+	156.909i	0.165012	+	0.285810i
$550$		0			0
$551$	−79.2342	−	79.2342i	−0.143801	−	0.143801i
$552$	40.6542	+	151.723i	0.0736488	+	0.274861i
$553$	−31.7786	+	8.51505i	−0.0574658	+	0.0153979i
$554$	−422.925	+	422.925i	−0.763402	+	0.763402i
$555$		0			0
$556$	124.296	−	71.7621i	0.223553	−	0.129069i
$557$	−218.723	+	816.286i	−0.392681	+	1.46550i	0.433014	+	0.901387i	$0.357450\pi$
$557$	−218.723	+	816.286i	−0.392681	+	1.46550i	−0.825695	+	0.564117i	$0.809217\pi$
$558$	318.423			0.570651
$559$	646.087	+	659.076i	1.15579	+	1.17903i
$560$		0			0
$561$	71.5715	−	267.109i	0.127579	−	0.476129i
$562$	−122.330	+	70.6272i	−0.217669	+	0.125671i
$563$	−88.4819	+	153.255i	−0.157161	+	0.272212i	−0.933844	−	0.357681i	$-0.883568\pi$
$563$	−88.4819	+	153.255i	−0.157161	+	0.272212i	0.776683	+	0.629892i	$0.216901\pi$
$564$	−57.8114	−	57.8114i	−0.102502	−	0.102502i
$565$		0			0
$566$	−110.492	−	412.361i	−0.195215	−	0.728553i
$567$	−17.0682	−	17.0682i	−0.0301026	−	0.0301026i
$568$	303.742	+	175.365i	0.534757	+	0.308742i
$569$	−306.928	+	177.205i	−0.539416	+	0.311432i	−0.744842	−	0.667241i	$-0.767475\pi$
$569$	−306.928	+	177.205i	−0.539416	+	0.311432i	0.205426	+	0.978673i	$0.434142\pi$
$570$		0			0
$571$		−	1094.23i		−	1.91634i	−0.286193	−	0.958172i	$-0.592390\pi$
$571$		−	1094.23i		−	1.91634i	0.286193	−	0.958172i	$-0.407610\pi$
$572$	187.059	−	105.530i	0.327026	−	0.184494i
$573$		−	247.232i		−	0.431470i
$574$	40.6671	−	151.772i	0.0708486	−	0.264411i
$575$		0			0
$576$	−137.358	−	79.3036i	−0.238468	−	0.137680i
$577$	101.074	−	101.074i	0.175171	−	0.175171i	−0.614076	−	0.789247i	$-0.710471\pi$
$577$	101.074	−	101.074i	0.175171	−	0.175171i	0.789247	+	0.614076i	$0.210471\pi$
$578$	117.590	+	438.852i	0.203443	+	0.759260i
$579$	−124.351	−	464.085i	−0.214769	−	0.801528i
$580$		0			0
$581$	−17.2397	+	29.8600i	−0.0296724	+	0.0513942i
$582$	−429.830	−	744.487i	−0.738539	−	1.27919i
$583$	−13.6479	+	50.9345i	−0.0234097	+	0.0873663i
$584$		−	307.487i		−	0.526519i
$585$		0			0
$586$	625.254			1.06699
$587$	322.325	+	86.3669i	0.549106	+	0.147133i	0.522697	−	0.852519i	$-0.324926\pi$
$587$	322.325	+	86.3669i	0.549106	+	0.147133i	0.0264095	+	0.999651i	$0.491593\pi$
$588$	104.316	−	60.2266i	0.177407	−	0.102426i
$589$	649.498	+	374.988i	1.10271	+	0.636652i
$590$		0			0
$591$	−193.789	+	51.9256i	−0.327900	+	0.0878606i
$592$	371.542	−	99.5545i	0.627605	−	0.168166i
$593$	510.973	+	510.973i	0.861674	+	0.861674i	0.991533	−	0.129859i	$-0.0414524\pi$
$593$	510.973	+	510.973i	0.861674	+	0.861674i	−0.129859	+	0.991533i	$0.541452\pi$
$594$	−449.979	+	779.387i	−0.757541	+	1.31210i
$595$		0			0
$596$	−330.846	−	88.6500i	−0.555111	−	0.148742i
$597$	604.539			1.01263
$598$	−344.282	−	3.42631i	−0.575723	−	0.00572962i
$599$	−768.936			−1.28370			−0.641849	−	0.766831i	$-0.721833\pi$
$599$	−768.936			−1.28370			−0.641849	+	0.766831i	$0.721833\pi$
$600$		0			0
$601$	464.639	+	804.778i	0.773109	+	1.33906i	0.935851	+	0.352396i	$0.114633\pi$
$601$	464.639	+	804.778i	0.773109	+	1.33906i	−0.162742	+	0.986669i	$0.552034\pi$
$602$	−98.3097	+	170.277i	−0.163305	+	0.282853i
$603$	−185.741	+	185.741i	−0.308027	+	0.308027i
$604$	224.274	−	60.0939i	0.371314	−	0.0994933i
$605$		0			0
$606$	−546.274	+	546.274i	−0.901442	+	0.901442i
$607$	−153.946	−	88.8810i	−0.253618	−	0.146427i	0.367802	−	0.929904i	$-0.380111\pi$
$607$	−153.946	−	88.8810i	−0.253618	−	0.146427i	−0.621420	+	0.783478i	$0.713444\pi$
$608$	225.442	+	390.476i	0.370792	+	0.642231i
$609$	11.4623	+	3.07130i	0.0188214	+	0.00504319i
$610$		0			0
$611$	−365.230	+	206.047i	−0.597758	+	0.337229i
$612$			51.2851i			0.0837991i
$613$	−478.151	−	128.120i	−0.780018	−	0.209005i	−0.153225	−	0.988191i	$-0.548966\pi$
$613$	−478.151	−	128.120i	−0.780018	−	0.209005i	−0.626793	+	0.779186i	$0.715633\pi$
$614$	−187.180	−	324.205i	−0.304854	−	0.528022i
$615$		0			0
$616$	−75.7067	−	75.7067i	−0.122901	−	0.122901i
$617$	−214.627	−	800.999i	−0.347856	−	1.29822i	−0.889240	−	0.457440i	$-0.848766\pi$
$617$	−214.627	−	800.999i	−0.347856	−	1.29822i	0.541385	−	0.840775i	$-0.317900\pi$
$618$	929.290	−	249.002i	1.50371	−	0.402917i
$619$	−445.288	+	445.288i	−0.719366	+	0.719366i	−0.968475	−	0.249109i	$-0.919862\pi$
$619$	−445.288	+	445.288i	−0.719366	+	0.719366i	0.249109	+	0.968475i	$0.419862\pi$
$620$		0			0
$621$	287.886	−	166.211i	0.463584	−	0.267650i
$622$	247.727	−	924.529i	0.398274	−	1.48638i
$623$	−37.9559			−0.0609244
$624$	−380.289	+	372.795i	−0.609438	+	0.597427i
$625$		0			0
$626$	2.13175	−	7.95579i	0.00340535	−	0.0127089i
$627$	−613.798	+	354.377i	−0.978945	+	0.565194i
$628$	−5.09835	+	8.83061i	−0.00811840	+	0.0140615i
$629$	133.096	+	133.096i	0.211599	+	0.211599i
$630$		0			0
$631$	−14.1861	−	52.9432i	−0.0224819	−	0.0839036i	0.953773	−	0.300527i	$-0.0971624\pi$
$631$	−14.1861	−	52.9432i	−0.0224819	−	0.0839036i	−0.976255	+	0.216623i	$0.930496\pi$
$632$	−122.352	−	122.352i	−0.193594	−	0.193594i
$633$	−345.455	−	199.448i	−0.545742	−	0.315084i
$634$	−986.278	+	569.428i	−1.55564	+	0.898151i
$635$		0			0
$636$			9.68833i			0.0152332i
$637$	−153.956	−	598.326i	−0.241689	−	0.939288i
$638$		−	145.167i		−	0.227534i
$639$	64.2363	−	239.733i	0.100526	−	0.375169i
$640$		0			0
$641$	−480.364	−	277.338i	−0.749398	−	0.432665i	0.0760784	−	0.997102i	$-0.475760\pi$
$641$	−480.364	−	277.338i	−0.749398	−	0.432665i	−0.825476	+	0.564437i	$0.809093\pi$
$642$	176.851	−	176.851i	0.275469	−	0.275469i
$643$	95.3123	+	355.710i	0.148231	+	0.553204i	0.999590	+	0.0286218i	$0.00911185\pi$
$643$	95.3123	+	355.710i	0.148231	+	0.553204i	−0.851360	+	0.524582i	$0.824221\pi$
$644$	−4.37421	−	16.3248i	−0.00679224	−	0.0253490i
$645$		0			0
$646$	−262.115	+	453.997i	−0.405751	+	0.702781i
$647$	298.039	+	516.219i	0.460648	+	0.797866i	0.998993	−	0.0448587i	$-0.0142838\pi$
$647$	298.039	+	516.219i	0.460648	+	0.797866i	−0.538345	+	0.842724i	$0.680950\pi$
$648$	32.8573	−	122.625i	0.0507057	−	0.189236i
$649$		−	949.877i		−	1.46360i
$650$		0			0
$651$	−79.4229			−0.122001
$652$	225.429	+	60.4034i	0.345749	+	0.0926433i
$653$	635.999	−	367.194i	0.973965	−	0.562319i	0.0735223	−	0.997294i	$-0.476576\pi$
$653$	635.999	−	367.194i	0.973965	−	0.562319i	0.900443	+	0.434975i	$0.143243\pi$
$654$	872.727	+	503.869i	1.33444	+	0.770442i
$655$		0			0
$656$	1060.75	−	284.226i	1.61699	−	0.433272i
$657$	−210.175	+	56.3163i	−0.319901	+	0.0857173i
$658$	−63.1698	−	63.1698i	−0.0960028	−	0.0960028i
$659$	58.7650	−	101.784i	0.0891730	−	0.154452i	−0.817989	−	0.575234i	$-0.804911\pi$
$659$	58.7650	−	101.784i	0.0891730	−	0.154452i	0.907162	+	0.420782i	$0.138244\pi$
$660$		0			0
$661$	−147.166	−	39.4330i	−0.222641	−	0.0596565i	0.145774	−	0.989318i	$-0.453433\pi$
$661$	−147.166	−	39.4330i	−0.222641	−	0.0596565i	−0.368415	+	0.929661i	$0.620099\pi$
$662$	−1070.07			−1.61643
$663$	−251.031	−	69.9484i	−0.378629	−	0.105503i
$664$	−181.340			−0.273102
$665$		0			0
$666$	−102.414	−	177.386i	−0.153774	−	0.266345i
$667$	−26.8104	+	46.4370i	−0.0401955	+	0.0696206i
$668$	119.727	−	119.727i	0.179231	−	0.179231i
$669$	−215.092	+	57.6337i	−0.321513	+	0.0861490i
$670$		0			0
$671$	−390.917	+	390.917i	−0.582589	+	0.582589i
$672$	−41.3517	−	23.8744i	−0.0615353	−	0.0355274i
$673$	−238.096	−	412.395i	−0.353784	−	0.612771i	0.633125	−	0.774049i	$-0.281772\pi$
$673$	−238.096	−	412.395i	−0.353784	−	0.612771i	−0.986909	+	0.161278i	$0.948438\pi$
$674$	548.506	+	146.972i	0.813807	+	0.218059i
$675$		0			0
$676$	−97.6895	−	177.259i	−0.144511	−	0.262218i
$677$		−	781.304i		−	1.15407i	−0.816720	−	0.577034i	$-0.804210\pi$
$677$		−	781.304i		−	1.15407i	0.816720	−	0.577034i	$-0.195790\pi$
$678$	678.247	+	181.736i	1.00036	+	0.268047i
$679$	−108.219	−	187.441i	−0.159380	−	0.276055i
$680$		0			0
$681$	369.026	+	369.026i	0.541889	+	0.541889i
$682$	251.468	+	938.490i	0.368721	+	1.37608i
$683$	960.022	−	257.237i	1.40560	−	0.376628i	0.525245	−	0.850951i	$-0.323974\pi$
$683$	960.022	−	257.237i	1.40560	−	0.376628i	0.880351	+	0.474322i	$0.157307\pi$
$684$	92.9451	−	92.9451i	0.135885	−	0.135885i
$685$		0			0
$686$	231.508	−	133.661i	0.337475	−	0.194841i
$687$	−156.082	+	582.507i	−0.227194	+	0.847899i
$688$	−1374.19			−1.99737
$689$	47.8688	+	13.3384i	0.0694757	+	0.0193590i
$690$		0			0
$691$	−188.337	+	702.882i	−0.272557	+	1.01720i	0.684904	+	0.728633i	$0.259844\pi$
$691$	−188.337	+	702.882i	−0.272557	+	1.01720i	−0.957461	+	0.288563i	$0.906823\pi$
$692$	105.704	−	61.0284i	0.152752	−	0.0881913i
$693$	−37.8817	+	65.6131i	−0.0546634	+	0.0946798i
$694$	457.441	+	457.441i	0.659137	+	0.659137i
$695$		0			0
$696$	16.1531	+	60.2842i	0.0232085	+	0.0866153i
$697$	379.987	+	379.987i	0.545174	+	0.545174i
$698$	1024.73	+	591.629i	1.46810	+	0.847606i
$699$	639.582	−	369.263i	0.914996	−	0.528273i
$700$		0			0
$701$			372.113i			0.530831i	0.964134	+	0.265416i	$0.0855092\pi$
$701$			372.113i			0.530831i	−0.964134	+	0.265416i	$0.914491\pi$
$702$	730.214	+	431.335i	1.04019	+	0.614437i
$703$		−	482.426i		−	0.686239i
$704$	125.257	−	467.464i	0.177921	−	0.664011i
$705$		0			0
$706$	532.319	+	307.334i	0.753993	+	0.435318i
$707$	−137.537	+	137.537i	−0.194535	+	0.194535i
$708$	−45.1694	−	168.574i	−0.0637985	−	0.238099i
$709$	−206.076	−	769.087i	−0.290658	−	1.08475i	−0.944605	−	0.328209i	$-0.893555\pi$
$709$	−206.076	−	769.087i	−0.290658	−	1.08475i	0.653947	−	0.756540i	$-0.273112\pi$
$710$		0			0
$711$	−61.2216	+	106.039i	−0.0861064	+	0.149141i
$712$	−99.8121	−	172.880i	−0.140186	−	0.242809i
$713$	92.8857	−	346.654i	0.130274	−	0.486191i
$714$		−	55.5163i		−	0.0777539i
$715$		0			0
$716$	79.5008			0.111035
$717$	180.041	+	48.2420i	0.251104	+	0.0672831i
$718$	−400.534	+	231.249i	−0.557847	+	0.322073i
$719$	−477.727	−	275.816i	−0.664432	−	0.383610i	0.129531	−	0.991575i	$-0.458653\pi$
$719$	−477.727	−	275.816i	−0.664432	−	0.383610i	−0.793964	+	0.607965i	$0.791986\pi$
$720$		0			0
$721$	233.969	−	62.6919i	0.324507	−	0.0869513i
$722$	502.853	−	134.739i	0.696472	−	0.186619i
$723$	−281.024	−	281.024i	−0.388691	−	0.388691i
$724$	−69.6905	+	120.708i	−0.0962576	+	0.166723i
$725$		0			0
$726$	−322.985	−	86.5435i	−0.444883	−	0.119206i
$727$	1045.67			1.43834			0.719168	−	0.694836i	$-0.244523\pi$
$727$	1045.67			1.43834			0.719168	+	0.694836i	$0.244523\pi$
$728$	−72.0501	+	70.6302i	−0.0989700	+	0.0970195i
$729$	−634.875			−0.870884
$730$		0			0
$731$	−336.227	−	582.362i	−0.459954	−	0.796665i
$732$	−50.7867	+	87.9651i	−0.0693807	+	0.120171i
$733$	404.316	−	404.316i	0.551591	−	0.551591i	−0.375309	−	0.926900i	$-0.622463\pi$
$733$	404.316	−	404.316i	0.551591	−	0.551591i	0.926900	+	0.375309i	$0.122463\pi$
$734$	1018.34	−	272.865i	1.38739	−	0.371750i
$735$		0			0
$736$	152.565	−	152.565i	0.207289	−	0.207289i
$737$	−694.119	−	400.750i	−0.941816	−	0.543758i
$738$	−292.389	−	506.433i	−0.396191	−	0.686224i
$739$	−556.077	−	149.000i	−0.752472	−	0.201624i	−0.137858	−	0.990452i	$-0.544022\pi$
$739$	−556.077	−	149.000i	−0.752472	−	0.201624i	−0.614614	+	0.788828i	$0.710688\pi$
$740$		0			0
$741$	328.181	+	581.719i	0.442889	+	0.785046i
$742$			10.5863i			0.0142673i
$743$	−224.987	−	60.2851i	−0.302809	−	0.0811374i	0.104215	−	0.994555i	$-0.466767\pi$
$743$	−224.987	−	60.2851i	−0.302809	−	0.0811374i	−0.407024	+	0.913417i	$0.633434\pi$
$744$	−208.857	−	361.751i	−0.280722	−	0.486225i
$745$		0			0
$746$	25.7901	+	25.7901i	0.0345712	+	0.0345712i
$747$	33.2124	+	123.950i	0.0444610	+	0.165931i
$748$	−151.153	+	40.5012i	−0.202076	+	0.0541460i
$749$	44.5262	−	44.5262i	0.0594475	−	0.0594475i
$750$		0			0
$751$	171.987	−	99.2965i	0.229010	−	0.132219i	−0.381105	−	0.924532i	$-0.624456\pi$
$751$	171.987	−	99.2965i	0.229010	−	0.132219i	0.610115	+	0.792313i	$0.291123\pi$
$752$	161.600	−	603.100i	0.214894	−	0.801995i
$753$	650.229			0.863518
$754$	−136.794	−	1.36138i	−0.181424	−	0.00180554i
$755$		0			0
$756$	−10.7747	+	40.2118i	−0.0142523	+	0.0531903i
$757$	−349.645	+	201.868i	−0.461883	+	0.266668i	−0.712836	−	0.701331i	$-0.752589\pi$
$757$	−349.645	+	201.868i	−0.461883	+	0.266668i	0.250953	+	0.967999i	$0.419256\pi$
$758$	−185.481	+	321.262i	−0.244697	+	0.423828i
$759$	239.820	+	239.820i	0.315968	+	0.315968i
$760$		0			0
$761$	262.782	+	980.716i	0.345312	+	1.28872i	0.892248	+	0.451546i	$0.149127\pi$
$761$	262.782	+	980.716i	0.345312	+	1.28872i	−0.546936	+	0.837174i	$0.684206\pi$
$762$	−83.6167	−	83.6167i	−0.109733	−	0.109733i
$763$	219.728	+	126.860i	0.287979	+	0.166265i
$764$	−121.161	+	69.9524i	−0.158588	+	0.0915608i
$765$		0			0
$766$			1235.81i			1.61332i
$767$	−895.091	−	8.90799i	−1.16700	−	0.0116141i
$768$		−	447.366i		−	0.582508i
$769$	−143.955	+	537.249i	−0.187198	+	0.698633i	0.806951	+	0.590618i	$0.201116\pi$
$769$	−143.955	+	537.249i	−0.187198	+	0.698633i	−0.994149	+	0.108015i	$0.965551\pi$
$770$		0			0
$771$	57.4992	+	33.1972i	0.0745774	+	0.0430573i
$772$	−192.250	+	192.250i	−0.249028	+	0.249028i
$773$	121.247	+	452.500i	0.156853	+	0.585382i	0.998940	+	0.0460401i	$0.0146602\pi$
$773$	121.247	+	452.500i	0.156853	+	0.585382i	−0.842087	+	0.539342i	$0.818673\pi$
$774$	189.394	+	706.829i	0.244695	+	0.913216i
$775$		0			0
$776$	569.165	−	985.822i	0.733460	−	1.27039i
$777$	25.5446	+	44.2446i	0.0328759	+	0.0569428i
$778$	−24.1641	+	90.1817i	−0.0310593	+	0.115915i
$779$		−	1377.32i		−	1.76806i
$780$		0			0
$781$	757.296			0.969649
$782$	242.310	+	64.9267i	0.309859	+	0.0830265i
$783$	114.386	−	66.0405i	0.146086	−	0.0843429i
$784$	796.647	+	459.944i	1.01613	+	0.586664i
$785$		0			0
$786$	896.681	−	240.265i	1.14082	−	0.305681i
$787$	−255.618	+	68.4928i	−0.324801	+	0.0870302i	−0.417535	−	0.908661i	$-0.637106\pi$
$787$	−255.618	+	68.4928i	−0.324801	+	0.0870302i	0.0927342	+	0.995691i	$0.470439\pi$
$788$	80.2783	+	80.2783i	0.101876	+	0.101876i
$789$	544.170	−	942.530i	0.689696	−	1.19459i
$790$		0			0
$791$	170.764	+	45.7560i	0.215883	+	0.0578457i
$792$	−398.468			−0.503117
$793$	364.704	+	372.036i	0.459904	+	0.469150i
$794$	607.441			0.765039
$795$		0			0
$796$	−171.050	−	296.267i	−0.214887	−	0.372195i
$797$	127.501	−	220.839i	0.159977	−	0.277087i	−0.774883	−	0.632104i	$-0.782191\pi$
$797$	127.501	−	220.839i	0.159977	−	0.277087i	0.934860	+	0.355017i	$0.115525\pi$
$798$	−100.614	+	100.614i	−0.126082	+	0.126082i
$799$	295.124	−	79.0782i	0.369367	−	0.0989715i
$800$		0			0
$801$	−99.8870	+	99.8870i	−0.124703	+	0.124703i
$802$	901.289	+	520.359i	1.12380	+	0.648827i
$803$	−331.962	−	574.976i	−0.413403	−	0.716035i
$804$	−142.242	−	38.1136i	−0.176918	−	0.0474049i
$805$		0			0
$806$	886.718	−	228.162i	1.10015	−	0.283080i
$807$		−	703.030i		−	0.871165i
$808$	−988.122	−	264.766i	−1.22292	−	0.327681i
$809$	−6.95187	−	12.0410i	−0.00859316	−	0.0148838i	0.861697	−	0.507423i	$-0.169402\pi$
$809$	−6.95187	−	12.0410i	−0.00859316	−	0.0148838i	−0.870290	+	0.492540i	$0.836069\pi$
$810$		0			0
$811$	−567.998	−	567.998i	−0.700367	−	0.700367i	0.264122	−	0.964489i	$-0.414918\pi$
$811$	−567.998	−	567.998i	−0.700367	−	0.700367i	−0.964489	+	0.264122i	$0.914918\pi$
$812$	−1.73800	−	6.48631i	−0.00214040	−	0.00798807i
$813$	−125.433	+	33.6096i	−0.154284	+	0.0413403i
$814$	441.931	−	441.931i	0.542913	−	0.542913i
$815$		0			0
$816$	336.025	−	194.004i	0.411796	−	0.237750i
$817$	−446.077	+	1664.78i	−0.545993	+	2.03767i
$818$	1628.87			1.99128
$819$	61.4735	+	36.3121i	0.0750592	+	0.0443372i
$820$		0			0
$821$	395.448	−	1475.83i	0.481666	−	1.79760i	−0.112962	−	0.993599i	$-0.536034\pi$
$821$	395.448	−	1475.83i	0.481666	−	1.79760i	0.594627	−	0.804002i	$-0.297300\pi$
$822$	796.004	−	459.573i	0.968375	−	0.559091i
$823$	−189.106	+	327.542i	−0.229777	+	0.397985i	−0.957742	−	0.287629i	$-0.907133\pi$
$823$	−189.106	+	327.542i	−0.229777	+	0.397985i	0.727965	+	0.685614i	$0.240466\pi$
$824$	900.811	+	900.811i	1.09322	+	1.09322i
$825$		0			0
$826$	−49.3560	−	184.199i	−0.0597530	−	0.223001i
$827$	1072.43	+	1072.43i	1.29677	+	1.29677i	0.930516	+	0.366251i	$0.119359\pi$
$827$	1072.43	+	1072.43i	1.29677	+	1.29677i	0.366251	+	0.930516i	$0.380641\pi$
$828$	−54.4726	−	31.4497i	−0.0657881	−	0.0379828i
$829$	−1417.54	+	818.417i	−1.70994	+	0.987234i	−0.775331	+	0.631555i	$0.782417\pi$
$829$	−1417.54	+	818.417i	−1.70994	+	0.987234i	−0.934608	+	0.355679i	$0.884250\pi$
$830$		0			0
$831$		−	555.218i		−	0.668132i
$832$	−439.327	−	122.416i	−0.528037	−	0.147135i
$833$			450.143i			0.540388i
$834$	−149.656	+	558.526i	−0.179444	+	0.669695i
$835$		0			0
$836$	347.339	+	200.536i	0.415477	+	0.239876i
$837$	−625.093	+	625.093i	−0.746826	+	0.746826i
$838$	11.3781	+	42.4638i	0.0135777	+	0.0506728i
$839$	101.533	+	378.924i	0.121016	+	0.451638i	0.999666	−	0.0258276i	$-0.00822209\pi$
$839$	101.533	+	378.924i	0.121016	+	0.451638i	−0.878650	+	0.477466i	$0.841555\pi$
$840$		0			0
$841$	409.847	−	709.877i	0.487333	−	0.844086i
$842$	801.250	+	1387.81i	0.951603	+	1.64823i
$843$	33.9378	−	126.658i	0.0402583	−	0.150246i
$844$			225.730i			0.267452i
$845$		0			0
$846$	−332.483			−0.393005
$847$	−81.3186	−	21.7892i	−0.0960078	−	0.0257252i
$848$	−64.0761	+	36.9944i	−0.0755615	+	0.0436254i
$849$	343.202	+	198.148i	0.404243	+	0.233390i
$850$		0			0
$851$	−222.987	+	59.7492i	−0.262030	+	0.0702106i
$852$	134.397	−	36.0116i	0.157743	−	0.0422671i
$853$	−393.928	−	393.928i	−0.461815	−	0.461815i	0.437435	−	0.899250i	$-0.355887\pi$
$853$	−393.928	−	393.928i	−0.461815	−	0.461815i	−0.899250	+	0.437435i	$0.855887\pi$
$854$	−55.4940	+	96.1184i	−0.0649813	+	0.112551i
$855$		0			0
$856$	319.895	+	85.7157i	0.373709	+	0.100135i
$857$	−838.341			−0.978227			−0.489114	−	0.872220i	$-0.662680\pi$
$857$	−838.341			−0.978227			−0.489114	+	0.872220i	$0.662680\pi$
$858$	−232.256	+	833.523i	−0.270695	+	0.971472i
$859$	−491.289			−0.571931			−0.285966	−	0.958240i	$-0.592314\pi$
$859$	−491.289			−0.571931			−0.285966	+	0.958240i	$0.592314\pi$
$860$		0			0
$861$	72.9294	+	126.317i	0.0847031	+	0.146710i
$862$	−660.680	+	1144.33i	−0.766450	+	1.32753i
$863$	−543.438	+	543.438i	−0.629708	+	0.629708i	−0.947995	−	0.318287i	$-0.896893\pi$
$863$	−543.438	+	543.438i	−0.629708	+	0.629708i	0.318287	+	0.947995i	$0.396893\pi$
$864$	−513.358	+	137.554i	−0.594165	+	0.159206i
$865$		0			0
$866$	922.376	−	922.376i	1.06510	−	1.06510i
$867$	−365.250	−	210.877i	−0.421281	−	0.243227i
$868$	22.4721	+	38.9228i	0.0258895	+	0.0448420i
$869$	−360.878	−	96.6969i	−0.415279	−	0.111274i
$870$		0			0
$871$	−384.145	+	650.325i	−0.441039	+	0.746642i
$872$			1334.41i			1.53029i
$873$	−778.076	−	208.485i	−0.891267	−	0.238814i
$874$	−321.476	−	556.812i	−0.367821	−	0.637085i
$875$		0			0
$876$	−86.2550	−	86.2550i	−0.0984646	−	0.0984646i
$877$	−201.005	−	750.161i	−0.229196	−	0.855372i	−0.980680	−	0.195620i	$-0.937328\pi$
$877$	−201.005	−	750.161i	−0.229196	−	0.855372i	0.751484	−	0.659752i	$-0.229339\pi$
$878$	−525.331	+	140.762i	−0.598327	+	0.160321i
$879$	−410.419	+	410.419i	−0.466915	+	0.466915i
$880$		0			0
$881$	−692.313	+	399.707i	−0.785826	+	0.453697i	−0.838491	−	0.544915i	$-0.816562\pi$
$881$	−692.313	+	399.707i	−0.785826	+	0.453697i	0.0526650	+	0.998612i	$0.483228\pi$
$882$	126.781	−	473.154i	0.143743	−	0.536456i
$883$	1402.70			1.58856			0.794281	−	0.607550i	$-0.207848\pi$
$883$	1402.70			1.58856			0.794281	+	0.607550i	$0.207848\pi$
$884$	36.7477	+	142.814i	0.0415698	+	0.161555i
$885$		0			0
$886$	65.2071	−	243.356i	0.0735971	−	0.274668i
$887$	−45.8967	+	26.4985i	−0.0517438	+	0.0298743i	−0.525649	−	0.850702i	$-0.676177\pi$
$887$	−45.8967	+	26.4985i	−0.0517438	+	0.0298743i	0.473905	+	0.880576i	$0.342844\pi$
$888$	−134.349	+	232.698i	−0.151293	+	0.262048i
$889$	−21.0524	−	21.0524i	−0.0236809	−	0.0236809i
$890$		0			0
$891$	−70.9453	−	264.772i	−0.0796244	−	0.297162i
$892$	89.1032	+	89.1032i	0.0998915	+	0.0998915i
$893$	−678.176	−	391.545i	−0.759435	−	0.438460i
$894$	1195.05	−	689.964i	1.33675	−	0.771771i
$895$		0			0
$896$		−	187.406i		−	0.209158i
$897$	228.237	−	223.739i	0.254445	−	0.249430i
$898$			941.575i			1.04852i
$899$	36.9063	−	137.736i	0.0410526	−	0.153210i
$900$		0			0
$901$	−31.3553	−	18.1030i	−0.0348006	−	0.0200921i
$902$	1261.70	−	1261.70i	1.39879	−	1.39879i
$903$	−47.2398	−	176.301i	−0.0523143	−	0.195240i
$904$	240.648	+	898.109i	0.266203	+	0.993484i
$905$		0			0
$906$	−467.712	+	810.100i	−0.516238	+	0.894151i
$907$	−115.693	−	200.386i	−0.127556	−	0.220933i	0.795173	−	0.606382i	$-0.207380\pi$
$907$	−115.693	−	200.386i	−0.127556	−	0.220933i	−0.922729	+	0.385449i	$0.874046\pi$
$908$	76.4358	−	285.262i	0.0841804	−	0.314165i
$909$			723.898i			0.796367i
$910$		0			0
$911$	−1082.49			−1.18825			−0.594124	−	0.804373i	$-0.702501\pi$
$911$	−1082.49			−1.18825			−0.594124	+	0.804373i	$0.702501\pi$
$912$	−960.585	−	257.388i	−1.05327	−	0.282224i
$913$	−339.090	+	195.774i	−0.371402	+	0.214429i
$914$	−795.216	−	459.118i	−0.870039	−	0.502317i
$915$		0			0
$916$	329.632	−	88.3245i	0.359860	−	0.0964241i
$917$	225.759	−	60.4920i	0.246193	−	0.0659673i
$918$	−436.938	−	436.938i	−0.475967	−	0.475967i
$919$	158.907	−	275.235i	0.172913	−	0.299494i	−0.766524	−	0.642215i	$-0.778015\pi$
$919$	158.907	−	275.235i	0.172913	−	0.299494i	0.939437	+	0.342722i	$0.111349\pi$
$920$		0			0
$921$	335.675	+	89.9438i	0.364468	+	0.0976589i
$922$	772.104			0.837423
$923$	7.10195	−	713.617i	0.00769442	−	0.773150i
$924$	−42.4738			−0.0459674
$925$		0			0
$926$	−43.8470	−	75.9451i	−0.0473509	−	0.0820142i
$927$	450.743	−	780.710i	0.486239	−	0.842190i
$928$	60.6186	−	60.6186i	0.0653218	−	0.0653218i
$929$	324.719	−	87.0081i	0.349536	−	0.0936578i	−0.0797795	−	0.996813i	$-0.525422\pi$
$929$	324.719	−	87.0081i	0.349536	−	0.0936578i	0.429315	+	0.903155i	$0.358755\pi$
$930$		0			0
$931$	815.805	−	815.805i	0.876267	−	0.876267i
$932$	−361.930	−	208.960i	−0.388337	−	0.224206i
$933$	444.255	+	769.472i	0.476157	+	0.824728i
$934$	−444.218	−	119.028i	−0.475608	−	0.127439i
$935$		0			0
$936$	−3.73685	+	375.486i	−0.00399236	+	0.401160i
$937$			896.921i			0.957226i	0.878026	+	0.478613i	$0.158860\pi$
$937$			896.921i			0.957226i	−0.878026	+	0.478613i	$0.841140\pi$
$938$	−155.426	−	41.6462i	−0.165699	−	0.0443990i
$939$	3.82292	+	6.62149i	0.00407127	+	0.00705164i
$940$		0			0
$941$	−426.378	−	426.378i	−0.453111	−	0.453111i	0.443274	−	0.896386i	$-0.353817\pi$
$941$	−426.378	−	426.378i	−0.453111	−	0.453111i	−0.896386	+	0.443274i	$0.853817\pi$
$942$	−10.6324	−	39.6805i	−0.0112870	−	0.0421237i
$943$	−636.624	+	170.583i	−0.675106	+	0.180894i
$944$	942.431	−	942.431i	0.998338	−	0.998338i
$945$		0			0
$946$	−1933.67	+	1116.41i	−2.04405	+	1.18013i
$947$	359.653	−	1342.24i	0.379781	−	1.41736i	−0.466450	−	0.884548i	$-0.654467\pi$
$947$	359.653	−	1342.24i	0.379781	−	1.41736i	0.846231	−	0.532816i	$-0.178866\pi$
$948$	−68.6430			−0.0724083
$949$	−544.926	+	307.424i	−0.574211	+	0.323945i
$950$		0			0
$951$	273.622	−	1021.17i	0.287720	−	1.07378i
$952$	63.6638	−	36.7563i	0.0668737	−	0.0386096i
$953$	−254.103	+	440.120i	−0.266635	+	0.461826i	−0.967991	−	0.250986i	$-0.919245\pi$
$953$	−254.103	+	440.120i	−0.266635	+	0.461826i	0.701356	+	0.712812i	$0.252579\pi$
$954$	27.8595	+	27.8595i	0.0292029	+	0.0292029i
$955$		0			0
$956$	−27.2994	−	101.883i	−0.0285558	−	0.106572i
$957$	95.2877	+	95.2877i	0.0995692	+	0.0995692i
$958$	−12.6122	−	7.28163i	−0.0131651	−	0.00760087i
$959$	200.412	−	115.708i	0.208980	−	0.120655i
$960$		0			0
$961$		−	6.61540i		−	0.00688387i
$962$	−412.297	−	420.586i	−0.428583	−	0.437199i
$963$		−	234.355i		−	0.243360i
$964$	−58.2080	+	217.235i	−0.0603817	+	0.225348i
$965$		0			0
$966$	58.9668	+	34.0445i	0.0610422	+	0.0352427i
$967$	−779.562	+	779.562i	−0.806165	+	0.806165i	−0.984051	−	0.177886i	$-0.943074\pi$
$967$	−779.562	+	779.562i	−0.806165	+	0.806165i	0.177886	+	0.984051i	$0.443074\pi$
$968$	−114.598	−	427.684i	−0.118386	−	0.441823i
$969$	−125.952	−	470.058i	−0.129981	−	0.485096i
$970$		0			0
$971$	−401.009	+	694.568i	−0.412986	+	0.715312i	−0.995215	−	0.0977127i	$-0.968847\pi$
$971$	−401.009	+	694.568i	−0.412986	+	0.715312i	0.582229	+	0.813025i	$0.302181\pi$
$972$	129.033	+	223.493i	0.132751	+	0.229931i
$973$	−37.6793	+	140.621i	−0.0387249	+	0.144523i
$974$		−	274.528i		−	0.281856i
$975$		0			0
$976$	−775.706			−0.794780
$977$	−62.9250	−	16.8607i	−0.0644064	−	0.0172576i	0.226472	−	0.974018i	$-0.427281\pi$
$977$	−62.9250	−	16.8607i	−0.0644064	−	0.0172576i	−0.290878	+	0.956760i	$0.593947\pi$
$978$	−814.272	+	470.120i	−0.832589	+	0.480696i
$979$	−373.281	−	215.514i	−0.381288	−	0.220137i
$980$		0			0
$981$	912.102	−	244.397i	0.929767	−	0.249130i
$982$	−385.146	+	103.199i	−0.392205	+	0.105091i
$983$	−214.471	−	214.471i	−0.218180	−	0.218180i	0.589551	−	0.807731i	$-0.299305\pi$
$983$	−214.471	−	214.471i	−0.218180	−	0.218180i	−0.807731	+	0.589551i	$0.799305\pi$
$984$	−383.563	+	664.350i	−0.389800	+	0.675153i
$985$		0			0
$986$	96.2770	+	25.7973i	0.0976440	+	0.0261636i
$987$	82.9297			0.0840220
$988$	192.227	−	325.425i	0.194562	−	0.329377i
$989$	824.743			0.833916
$990$		0			0
$991$	95.2782	+	165.027i	0.0961435	+	0.166525i	0.910085	−	0.414421i	$-0.136016\pi$
$991$	95.2782	+	165.027i	0.0961435	+	0.166525i	−0.813942	+	0.580946i	$0.802683\pi$
$992$	−286.887	+	496.902i	−0.289200	+	0.500910i
$993$	702.400	−	702.400i	0.707351	−	0.707351i
$994$	146.854	−	39.3494i	0.147740	−	0.0395869i
$995$		0			0
$996$	−50.8686	+	50.8686i	−0.0510729	+	0.0510729i
$997$	1370.92	+	791.503i	1.37505	+	0.793885i	0.991559	−	0.129660i	$-0.0413885\pi$
$997$	1370.92	+	791.503i	1.37505	+	0.793885i	0.383491	+	0.923545i	$0.374722\pi$
$998$	−214.779	−	372.008i	−0.215209	−	0.372753i
$999$	549.272	+	147.177i	0.549822	+	0.147324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.3.w.e.24.8		40
5.2	odd	4		65.3.p.a.11.3	yes	40
5.3	odd	4		325.3.t.d.76.8		40
5.4	even	2		325.3.w.f.24.3		40
13.6	odd	12		325.3.w.f.149.3		40
65.19	odd	12	inner	325.3.w.e.149.8		40
65.32	even	12		65.3.p.a.6.3	✓	40
65.58	even	12		325.3.t.d.201.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.3.p.a.6.3	✓	40	65.32	even	12
65.3.p.a.11.3	yes	40	5.2	odd	4
325.3.t.d.76.8		40	5.3	odd	4
325.3.t.d.201.8		40	65.58	even	12
325.3.w.e.24.8		40	1.1	even	1	trivial
325.3.w.e.149.8		40	65.19	odd	12	inner
325.3.w.f.24.3		40	5.4	even	2
325.3.w.f.149.3		40	13.6	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	325.w (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.20214 + 0.590063i) q^{2} +(-1.83281 + 1.05817i) q^{3} +(1.03716 + 0.598805i) q^{4} +(-4.66050 + 1.24878i) q^{6} +(-1.17338 + 0.314408i) q^{7} +(-4.51768 - 4.51768i) q^{8} +(-2.26053 + 3.91536i) q^{9} +(-13.3250 - 3.57041i) q^{11} -2.53456 q^{12} +(-3.48944 + 12.5229i) q^{13} -2.76948 q^{14} +(-9.67808 - 16.7629i) q^{16} +(4.73592 - 8.20286i) q^{17} +(-7.28833 + 7.28833i) q^{18} +(-23.4493 + 6.28321i) q^{19} +(1.81790 - 1.81790i) q^{21} +(-27.2367 - 15.7251i) q^{22} +(5.80846 + 10.0605i) q^{23} +(13.0606 + 3.49956i) q^{24} +(-15.0736 + 25.5183i) q^{26} -28.6153i q^{27} +(-1.40526 - 0.376537i) q^{28} +(2.30788 + 3.99736i) q^{29} +(-21.8447 - 21.8447i) q^{31} +(-4.80701 - 17.9400i) q^{32} +(28.2003 - 7.55624i) q^{33} +(15.2694 - 15.2694i) q^{34} +(-4.68907 + 2.70724i) q^{36} +(-5.14329 + 19.1950i) q^{37} -55.3461 q^{38} +(-6.85595 - 26.6446i) q^{39} +(-14.6840 + 54.8015i) q^{41} +(5.07594 - 2.93060i) q^{42} +(35.4975 - 61.4835i) q^{43} +(-11.6821 - 11.6821i) q^{44} +(6.85471 + 25.5821i) q^{46} +(22.8093 + 22.8093i) q^{47} +(35.4762 + 20.4822i) q^{48} +(-41.1573 + 23.7622i) q^{49} +20.0457i q^{51} +(-11.1179 + 10.8988i) q^{52} -3.82249i q^{53} +(16.8848 - 63.0150i) q^{54} +(6.72137 + 3.88059i) q^{56} +(36.3294 - 36.3294i) q^{57} +(2.72358 + 10.1645i) q^{58} +(17.8214 + 66.5103i) q^{59} +(20.0377 - 34.7063i) q^{61} +(-35.2155 - 60.9950i) q^{62} +(1.42146 - 5.30495i) q^{63} +35.0818i q^{64} +66.5597 q^{66} +(56.1209 + 15.0375i) q^{67} +(9.82382 - 5.67179i) q^{68} +(-21.2916 - 12.2927i) q^{69} +(-53.0258 + 14.2082i) q^{71} +(27.9007 - 7.47597i) q^{72} +(34.0315 + 34.0315i) q^{73} +(-22.6525 + 39.2354i) q^{74} +(-28.0831 - 7.52483i) q^{76} +16.7579 q^{77} +(0.624199 - 62.7207i) q^{78} +27.0828 q^{79} +(9.93517 + 17.2082i) q^{81} +(-64.6726 + 112.016i) q^{82} +(20.0700 - 20.0700i) q^{83} +(2.97401 - 0.796885i) q^{84} +(114.450 - 114.450i) q^{86} +(-8.45980 - 4.88427i) q^{87} +(44.0679 + 76.3279i) q^{88} +(30.1805 + 8.08684i) q^{89} +(0.157156 - 15.7913i) q^{91} +13.9125i q^{92} +(63.1528 + 16.9217i) q^{93} +(36.7704 + 63.6881i) q^{94} +(27.7940 + 27.7940i) q^{96} +(46.1141 + 172.100i) q^{97} +(-104.655 + 28.0423i) q^{98} +(44.1010 - 44.1010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} - 12 q^{6} - 44 q^{7} + 36 q^{8} + 72 q^{9} - 12 q^{11} + 120 q^{12} - 36 q^{13} - 48 q^{14} + 128 q^{16} - 32 q^{17} + 136 q^{18} - 68 q^{19} - 48 q^{21} - 72 q^{22} - 28 q^{23} + 56 q^{24}+ \cdots + 76 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 - 12 * q^6 - 44 * q^7 + 36 * q^8 + 72 * q^9 - 12 * q^11 + 120 * q^12 - 36 * q^13 - 48 * q^14 + 128 * q^16 - 32 * q^17 + 136 * q^18 - 68 * q^19 - 48 * q^21 - 72 * q^22 - 28 * q^23 + 56 * q^24 - 84 * q^26 + 76 * q^28 - 28 * q^29 + 128 * q^31 + 84 * q^32 - 68 * q^33 + 28 * q^34 + 300 * q^36 - 260 * q^37 + 8 * q^38 + 88 * q^39 + 68 * q^41 - 480 * q^42 + 32 * q^43 + 240 * q^44 + 260 * q^46 - 152 * q^47 - 480 * q^48 + 132 * q^49 + 488 * q^52 - 152 * q^54 - 288 * q^56 + 252 * q^57 + 468 * q^58 - 492 * q^59 - 100 * q^61 - 8 * q^62 - 356 * q^63 - 456 * q^66 - 56 * q^67 + 12 * q^68 + 576 * q^69 - 132 * q^71 + 396 * q^72 - 424 * q^73 + 160 * q^74 - 992 * q^76 + 344 * q^77 + 12 * q^78 + 248 * q^79 + 248 * q^82 - 112 * q^83 - 1100 * q^84 + 852 * q^86 - 1068 * q^87 + 8 * q^88 - 168 * q^89 - 160 * q^91 - 24 * q^93 - 328 * q^94 + 124 * q^96 + 1020 * q^97 + 1404 * q^98 + 76 * q^99

Introduction

L-functions

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