LMFDB - Embedded newform 945.2.bq.a.719.42

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [945,2,Mod(719,945)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(945, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("945.719"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.42
Character	$\chi$	$=$	945.719
Dual form			945.2.bq.a.899.42

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.53172 q^{2} +4.40959 q^{4} +(1.09270 - 1.95090i) q^{5} +(2.57916 - 0.589845i) q^{7} +6.10041 q^{8} +(2.76640 - 4.93913i) q^{10} +(-1.23377 - 0.712319i) q^{11} +(-2.08746 + 3.61559i) q^{13} +(6.52971 - 1.49332i) q^{14} +6.62532 q^{16} +(-4.27416 + 2.46769i) q^{17} +(-4.54377 - 2.62335i) q^{19} +(4.81835 - 8.60267i) q^{20} +(-3.12356 - 1.80339i) q^{22} +(-0.238847 - 0.413696i) q^{23} +(-2.61202 - 4.26349i) q^{25} +(-5.28486 + 9.15364i) q^{26} +(11.3731 - 2.60098i) q^{28} +(1.74963 - 1.01015i) q^{29} +10.6444i q^{31} +4.57262 q^{32} +(-10.8210 + 6.24749i) q^{34} +(1.66752 - 5.67621i) q^{35} +(7.03282 + 4.06040i) q^{37} +(-11.5035 - 6.64157i) q^{38} +(6.66590 - 11.9013i) q^{40} +(-0.421048 + 0.729276i) q^{41} +(3.70789 - 2.14075i) q^{43} +(-5.44044 - 3.14104i) q^{44} +(-0.604694 - 1.04736i) q^{46} -4.94304i q^{47} +(6.30416 - 3.04261i) q^{49} +(-6.61290 - 10.7940i) q^{50} +(-9.20484 + 15.9433i) q^{52} +(2.33122 + 4.03778i) q^{53} +(-2.73781 + 1.62862i) q^{55} +(15.7339 - 3.59830i) q^{56} +(4.42958 - 2.55742i) q^{58} -0.202459 q^{59} -1.78370i q^{61} +26.9486i q^{62} -1.67406 q^{64} +(4.77268 + 8.02317i) q^{65} +2.38316i q^{67} +(-18.8473 + 10.8815i) q^{68} +(4.22169 - 14.3706i) q^{70} +11.7260i q^{71} +(-4.52420 - 7.83614i) q^{73} +(17.8051 + 10.2798i) q^{74} +(-20.0362 - 11.5679i) q^{76} +(-3.60226 - 1.10945i) q^{77} +0.452236 q^{79} +(7.23947 - 12.9253i) q^{80} +(-1.06597 + 1.84632i) q^{82} +(10.6524 - 6.15019i) q^{83} +(0.143843 + 11.0349i) q^{85} +(9.38732 - 5.41977i) q^{86} +(-7.52652 - 4.34544i) q^{88} +(1.33067 - 2.30479i) q^{89} +(-3.25126 + 10.5565i) q^{91} +(-1.05322 - 1.82423i) q^{92} -12.5144i q^{94} +(-10.0829 + 5.99791i) q^{95} +(-4.69437 - 8.13089i) q^{97} +(15.9604 - 7.70304i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 76 q^{4} + 3 q^{5} - 6 q^{10} + 12 q^{11} + 12 q^{14} + 52 q^{16} - 12 q^{19} + 6 q^{20} + q^{25} + 12 q^{26} - 6 q^{29} - 12 q^{34} - 30 q^{40} - 6 q^{41} + 84 q^{44} - 18 q^{46} - 8 q^{49} - 30 q^{50}+ \cdots + 20 q^{91}+O(q^{100}) $ 88 * q + 76 * q^4 + 3 * q^5 - 6 * q^10 + 12 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 + 6 * q^20 + q^25 + 12 * q^26 - 6 * q^29 - 12 * q^34 - 30 * q^40 - 6 * q^41 + 84 * q^44 - 18 * q^46 - 8 * q^49 - 30 * q^50 + 78 * q^56 + 12 * q^59 - 8 * q^64 + 15 * q^70 + 30 * q^74 - 48 * q^76 - 16 * q^79 + 69 * q^80 - 7 * q^85 + 12 * q^86 - 72 * q^89 + 20 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	2.53172			1.79019			0.895097	−	0.445871i	$-0.147106\pi$
$2$	2.53172			1.79019			0.895097	+	0.445871i	$0.147106\pi$
$3$		0			0
$3$		0			0
$4$	4.40959			2.20480
$5$	1.09270	−	1.95090i	0.488670	−	0.872469i
$5$	1.09270	−	1.95090i	0.488670	−	0.872469i
$6$		0			0
$7$	2.57916	−	0.589845i	0.974832	−	0.222941i
$7$	2.57916	−	0.589845i	0.974832	−	0.222941i
$8$	6.10041			2.15682
$9$		0			0
$10$	2.76640	−	4.93913i	0.874814	−	1.56189i
$11$	−1.23377	−	0.712319i	−0.371997	−	0.214772i	0.302334	−	0.953202i	$-0.402234\pi$
$11$	−1.23377	−	0.712319i	−0.371997	−	0.214772i	−0.674330	+	0.738430i	$0.735568\pi$
$12$		0			0
$13$	−2.08746	+	3.61559i	−0.578957	+	1.00278i	0.416642	+	0.909071i	$0.363207\pi$
$13$	−2.08746	+	3.61559i	−0.578957	+	1.00278i	−0.995599	+	0.0937125i	$0.970127\pi$
$14$	6.52971	−	1.49332i	1.74514	−	0.399107i
$15$		0			0
$16$	6.62532			1.65633
$17$	−4.27416	+	2.46769i	−1.03664	+	0.598502i	−0.918879	−	0.394540i	$-0.870904\pi$
$17$	−4.27416	+	2.46769i	−1.03664	+	0.598502i	−0.117758	+	0.993042i	$0.537571\pi$
$18$		0			0
$19$	−4.54377	−	2.62335i	−1.04241	−	0.601837i	−0.121896	−	0.992543i	$-0.538898\pi$
$19$	−4.54377	−	2.62335i	−1.04241	−	0.601837i	−0.920515	+	0.390706i	$0.872231\pi$
$20$	4.81835	−	8.60267i	1.07742	−	1.92362i
$21$		0			0
$22$	−3.12356	−	1.80339i	−0.665946	−	0.384484i
$23$	−0.238847	−	0.413696i	−0.0498031	−	0.0862616i	0.840049	−	0.542510i	$-0.182526\pi$
$23$	−0.238847	−	0.413696i	−0.0498031	−	0.0862616i	−0.889852	+	0.456249i	$0.849193\pi$
$24$		0			0
$25$	−2.61202	−	4.26349i	−0.522404	−	0.852698i
$26$	−5.28486	+	9.15364i	−1.03645	+	1.79518i
$27$		0			0
$28$	11.3731	−	2.60098i	2.14931	−	0.491539i
$29$	1.74963	−	1.01015i	0.324899	−	0.187580i	−0.328675	−	0.944443i	$-0.606602\pi$
$29$	1.74963	−	1.01015i	0.324899	−	0.187580i	0.653574	+	0.756863i	$0.273269\pi$
$30$		0			0
$31$			10.6444i			1.91179i	0.293703	+	0.955897i	$0.405112\pi$
$31$			10.6444i			1.91179i	−0.293703	+	0.955897i	$0.594888\pi$
$32$	4.57262			0.808333
$33$		0			0
$34$	−10.8210	+	6.24749i	−1.85578	+	1.07144i
$35$	1.66752	−	5.67621i	0.281862	−	0.959455i
$36$		0			0
$37$	7.03282	+	4.06040i	1.15619	+	0.667526i	0.950388	−	0.311068i	$-0.100687\pi$
$37$	7.03282	+	4.06040i	1.15619	+	0.667526i	0.205801	+	0.978594i	$0.434020\pi$
$38$	−11.5035	−	6.64157i	−1.86612	−	1.07740i
$39$		0			0
$40$	6.66590	−	11.9013i	1.05397	−	1.88176i
$41$	−0.421048	+	0.729276i	−0.0657566	+	0.113894i	−0.897029	−	0.441971i	$-0.854279\pi$
$41$	−0.421048	+	0.729276i	−0.0657566	+	0.113894i	0.831273	+	0.555865i	$0.187613\pi$
$42$		0			0
$43$	3.70789	−	2.14075i	0.565447	−	0.326461i	−0.189882	−	0.981807i	$-0.560810\pi$
$43$	3.70789	−	2.14075i	0.565447	−	0.326461i	0.755329	+	0.655346i	$0.227477\pi$
$44$	−5.44044	−	3.14104i	−0.820176	−	0.473529i
$45$		0			0
$46$	−0.604694	−	1.04736i	−0.0891573	−	0.154425i
$47$		−	4.94304i		−	0.721016i	−0.932756	−	0.360508i	$-0.882603\pi$
$47$		−	4.94304i		−	0.721016i	0.932756	−	0.360508i	$-0.117397\pi$
$48$		0			0
$49$	6.30416	−	3.04261i	0.900595	−	0.434659i
$50$	−6.61290	−	10.7940i	−0.935205	−	1.52650i
$51$		0			0
$52$	−9.20484	+	15.9433i	−1.27648	+	2.21093i
$53$	2.33122	+	4.03778i	0.320217	+	0.554632i	0.980533	−	0.196356i	$-0.0629108\pi$
$53$	2.33122	+	4.03778i	0.320217	+	0.554632i	−0.660316	+	0.750988i	$0.729577\pi$
$54$		0			0
$55$	−2.73781	+	1.62862i	−0.369166	+	0.219603i
$56$	15.7339	−	3.59830i	2.10254	−	0.480843i
$57$		0			0
$58$	4.42958	−	2.55742i	0.581632	−	0.335805i
$59$	−0.202459			−0.0263579			−0.0131790	−	0.999913i	$-0.504195\pi$
$59$	−0.202459			−0.0263579			−0.0131790	+	0.999913i	$0.504195\pi$
$60$		0			0
$61$		−	1.78370i		−	0.228379i	−0.993459	−	0.114189i	$-0.963573\pi$
$61$		−	1.78370i		−	0.228379i	0.993459	−	0.114189i	$-0.0364271\pi$
$62$			26.9486i			3.42248i
$63$		0			0
$64$	−1.67406			−0.209257
$65$	4.77268	+	8.02317i	0.591978	+	0.995152i
$66$		0			0
$67$			2.38316i			0.291150i	0.989347	+	0.145575i	$0.0465032\pi$
$67$			2.38316i			0.291150i	−0.989347	+	0.145575i	$0.953497\pi$
$68$	−18.8473	+	10.8815i	−2.28557	+	1.31958i
$69$		0			0
$70$	4.22169	−	14.3706i	0.504588	−	1.71761i
$71$			11.7260i			1.39162i	0.718223	+	0.695812i	$0.244956\pi$
$71$			11.7260i			1.39162i	−0.718223	+	0.695812i	$0.755044\pi$
$72$		0			0
$73$	−4.52420	−	7.83614i	−0.529517	−	0.917150i	−0.999407	−	0.0344256i	$-0.989040\pi$
$73$	−4.52420	−	7.83614i	−0.529517	−	0.917150i	0.469890	−	0.882725i	$-0.344293\pi$
$74$	17.8051	+	10.2798i	2.06980	+	1.19500i
$75$		0			0
$76$	−20.0362	−	11.5679i	−2.29831	−	1.32693i
$77$	−3.60226	−	1.10945i	−0.410516	−	0.126434i
$78$		0			0
$79$	0.452236			0.0508806			0.0254403	−	0.999676i	$-0.491901\pi$
$79$	0.452236			0.0508806			0.0254403	+	0.999676i	$0.491901\pi$
$80$	7.23947	−	12.9253i	0.809398	−	1.44510i
$81$		0			0
$82$	−1.06597	+	1.84632i	−0.117717	+	0.203892i
$83$	10.6524	−	6.15019i	1.16926	−	0.675071i	0.215752	−	0.976448i	$-0.430780\pi$
$83$	10.6524	−	6.15019i	1.16926	−	0.675071i	0.953505	+	0.301378i	$0.0974465\pi$
$84$		0			0
$85$	0.143843	+	11.0349i	0.0156019	+	1.19690i
$86$	9.38732	−	5.41977i	1.01226	−	0.584429i
$87$		0			0
$88$	−7.52652	−	4.34544i	−0.802329	−	0.463225i
$89$	1.33067	−	2.30479i	0.141051	−	0.244307i	−0.786842	−	0.617155i	$-0.788285\pi$
$89$	1.33067	−	2.30479i	0.141051	−	0.244307i	0.927893	+	0.372848i	$0.121619\pi$
$90$		0			0
$91$	−3.25126	+	10.5565i	−0.340825	+	1.10662i
$92$	−1.05322	−	1.82423i	−0.109806	−	0.190189i
$93$		0			0
$94$		−	12.5144i		−	1.29076i
$95$	−10.0829	+	5.99791i	−1.03448	+	0.615372i
$96$		0			0
$97$	−4.69437	−	8.13089i	−0.476641	−	0.825567i	0.523001	−	0.852332i	$-0.324813\pi$
$97$	−4.69437	−	8.13089i	−0.476641	−	0.825567i	−0.999642	+	0.0267656i	$0.991479\pi$
$98$	15.9604	−	7.70304i	1.61224	−	0.778125i
$99$		0			0
$100$	−11.5179	−	18.8003i	−1.15179	−	1.88003i
$101$	−9.22577	+	15.9795i	−0.917998	+	1.59002i	−0.115546	+	0.993302i	$0.536862\pi$
$101$	−9.22577	+	15.9795i	−0.917998	+	1.59002i	−0.802452	+	0.596717i	$0.796471\pi$
$102$		0			0
$103$	−9.34498	−	16.1860i	−0.920789	−	1.59485i	−0.798198	−	0.602396i	$-0.794213\pi$
$103$	−9.34498	−	16.1860i	−0.920789	−	1.59485i	−0.122591	−	0.992457i	$-0.539120\pi$
$104$	−12.7343	+	22.0565i	−1.24871	+	2.16282i
$105$		0			0
$106$	5.90198	+	10.2225i	0.573251	+	0.992900i
$107$	−0.440832	+	0.763543i	−0.0426168	+	0.0738145i	−0.886547	−	0.462639i	$-0.846903\pi$
$107$	−0.440832	+	0.763543i	−0.0426168	+	0.0738145i	0.843930	+	0.536453i	$0.180236\pi$
$108$		0			0
$109$	2.17023	+	3.75895i	0.207870	+	0.360042i	0.951043	−	0.309057i	$-0.100013\pi$
$109$	2.17023	+	3.75895i	0.207870	+	0.360042i	−0.743173	+	0.669099i	$0.766680\pi$
$110$	−6.93135	+	4.12320i	−0.660878	+	0.393132i
$111$		0			0
$112$	17.0878	−	3.90791i	1.61464	−	0.369263i
$113$	4.60460	−	7.97540i	0.433164	−	0.750262i	−0.563980	−	0.825789i	$-0.690730\pi$
$113$	4.60460	−	7.97540i	0.433164	−	0.750262i	0.997144	+	0.0755263i	$0.0240637\pi$
$114$		0			0
$115$	−1.06807	+	0.0139225i	−0.0995978	+	0.00129828i
$116$	7.71517	−	4.45436i	0.716336	−	0.413577i
$117$		0			0
$118$	−0.512569			−0.0471858
$119$	−9.56821	+	8.88566i	−0.877116	+	0.814548i
$120$		0			0
$121$	−4.48520	−	7.76860i	−0.407746	−	0.706236i
$122$		−	4.51581i		−	0.408843i
$123$		0			0
$124$			46.9375i			4.21511i
$125$	−11.1718	+	0.437080i	−0.999236	+	0.0390936i
$126$		0			0
$127$		−	8.82849i		−	0.783401i	−0.920093	−	0.391701i	$-0.871887\pi$
$127$		−	8.82849i		−	0.783401i	0.920093	−	0.391701i	$-0.128113\pi$
$128$	−13.3835			−1.18294
$129$		0			0
$130$	12.0831	+	20.3124i	1.05976	+	1.78151i
$131$	1.10536	+	1.91453i	0.0965753	+	0.167273i	0.910265	−	0.414026i	$-0.135878\pi$
$131$	1.10536	+	1.91453i	0.0965753	+	0.167273i	−0.813690	+	0.581300i	$0.802544\pi$
$132$		0			0
$133$	−13.2665	−	4.08591i	−1.15035	−	0.354294i
$134$			6.03350i			0.521215i
$135$		0			0
$136$	−26.0741	+	15.0539i	−2.23584	+	1.29086i
$137$	−2.41786	+	4.18786i	−0.206572	+	0.357793i	−0.950632	−	0.310319i	$-0.899564\pi$
$137$	−2.41786	+	4.18786i	−0.206572	+	0.357793i	0.744061	+	0.668112i	$0.232897\pi$
$138$		0			0
$139$	1.08200	+	0.624695i	0.0917743	+	0.0529859i	0.545185	−	0.838316i	$-0.316459\pi$
$139$	1.08200	+	0.624695i	0.0917743	+	0.0529859i	−0.453410	+	0.891302i	$0.649793\pi$
$140$	7.35308	−	25.0298i	0.621448	−	2.11540i
$141$		0			0
$142$			29.6870i			2.49128i
$143$	5.15090	−	2.97387i	0.430740	−	0.248688i
$144$		0			0
$145$	−0.0588822	−	4.51715i	−0.00488990	−	0.375129i
$146$	−11.4540	−	19.8389i	−0.947938	−	1.64188i
$147$		0			0
$148$	31.0119	+	17.9047i	2.54916	+	1.47176i
$149$	−2.98242	+	1.72190i	−0.244329	+	0.141063i	−0.617165	−	0.786834i	$-0.711719\pi$
$149$	−2.98242	+	1.72190i	−0.244329	+	0.141063i	0.372836	+	0.927897i	$0.378385\pi$
$150$		0			0
$151$	8.51168	−	14.7427i	0.692671	−	1.19974i	−0.278288	−	0.960498i	$-0.589767\pi$
$151$	8.51168	−	14.7427i	0.692671	−	1.19974i	0.970960	−	0.239244i	$-0.0768995\pi$
$152$	−27.7188	−	16.0035i	−2.24829	−	1.29805i
$153$		0			0
$154$	−9.11990	−	2.80882i	−0.734903	−	0.226341i
$155$	20.7662	+	11.6311i	1.66798	+	0.934235i
$156$		0			0
$157$	4.68164			0.373636			0.186818	−	0.982395i	$-0.440183\pi$
$157$	4.68164			0.373636			0.186818	+	0.982395i	$0.440183\pi$
$158$	1.14493			0.0910861
$159$		0			0
$160$	4.99649	−	8.92072i	0.395008	−	0.705245i
$161$	−0.860043	−	0.926106i	−0.0677809	−	0.0729874i
$162$		0			0
$163$	−13.9563	−	8.05767i	−1.09314	−	0.631125i	−0.158730	−	0.987322i	$-0.550740\pi$
$163$	−13.9563	−	8.05767i	−1.09314	−	0.631125i	−0.934411	+	0.356197i	$0.884073\pi$
$164$	−1.85665	+	3.21581i	−0.144980	+	0.251112i
$165$		0			0
$166$	26.9689	−	15.5705i	2.09320	−	1.20851i
$167$	9.83837	+	5.68018i	0.761316	+	0.439546i	0.829768	−	0.558108i	$-0.188473\pi$
$167$	9.83837	+	5.68018i	0.761316	+	0.439546i	−0.0684521	+	0.997654i	$0.521806\pi$
$168$		0			0
$169$	−2.21497	−	3.83644i	−0.170382	−	0.295111i
$170$	0.364169	+	27.9372i	0.0279305	+	2.14269i
$171$		0			0
$172$	16.3503	−	9.43983i	1.24670	−	0.719780i
$173$		−	13.5586i		−	1.03084i	−0.856938	−	0.515420i	$-0.827636\pi$
$173$		−	13.5586i		−	1.03084i	0.856938	−	0.515420i	$-0.172364\pi$
$174$		0			0
$175$	−9.25163	−	9.45555i	−0.699357	−	0.714772i
$176$	−8.17414	−	4.71934i	−0.616149	−	0.355734i
$177$		0			0
$178$	3.36888	−	5.83507i	0.252508	−	0.437357i
$179$	0.777342	−	0.448799i	0.0581013	−	0.0335448i	−0.470668	−	0.882310i	$-0.655987\pi$
$179$	0.777342	−	0.448799i	0.0581013	−	0.0335448i	0.528769	+	0.848766i	$0.322654\pi$
$180$		0			0
$181$			13.4784i			1.00184i	0.865493	+	0.500921i	$0.167005\pi$
$181$			13.4784i			1.00184i	−0.865493	+	0.500921i	$0.832995\pi$
$182$	−8.23127	+	26.7260i	−0.610143	+	1.98106i
$183$		0			0
$184$	−1.45707	−	2.52371i	−0.107416	−	0.186051i
$185$	15.6062	−	9.28353i	1.14739	−	0.682539i
$186$		0			0
$187$	7.03113			0.514167
$188$		−	21.7968i		−	1.58969i
$189$		0			0
$190$	−25.5269	+	15.1850i	−1.85192	+	1.10164i
$191$			1.97538i			0.142934i	0.997443	+	0.0714668i	$0.0227680\pi$
$191$			1.97538i			0.142934i	−0.997443	+	0.0714668i	$0.977232\pi$
$192$		0			0
$193$		−	16.5768i		−	1.19322i	−0.802531	−	0.596611i	$-0.796514\pi$
$193$		−	16.5768i		−	1.19322i	0.802531	−	0.596611i	$-0.203486\pi$
$194$	−11.8848	−	20.5851i	−0.853280	−	1.47792i
$195$		0			0
$196$	27.7988	−	13.4167i	1.98563	−	0.958335i
$197$	−24.5924			−1.75214			−0.876069	−	0.482186i	$-0.839843\pi$
$197$	−24.5924			−1.75214			−0.876069	+	0.482186i	$0.839843\pi$
$198$		0			0
$199$	0.627348	−	0.362200i	0.0444715	−	0.0256757i	−0.477599	−	0.878578i	$-0.658493\pi$
$199$	0.627348	−	0.362200i	0.0444715	−	0.0256757i	0.522071	+	0.852902i	$0.325160\pi$
$200$	−15.9344	−	26.0090i	−1.12673	−	1.83912i
$201$		0			0
$202$	−23.3570	+	40.4556i	−1.64339	+	2.84644i
$203$	3.91676	−	3.63736i	0.274902	−	0.255293i
$204$		0			0
$205$	0.962666	+	1.61830i	0.0672355	+	0.113027i
$206$	−23.6589	−	40.9783i	−1.64839	−	2.85510i
$207$		0			0
$208$	−13.8301	+	23.9544i	−0.958944	+	1.66094i
$209$	3.73732	+	6.47322i	0.258516	+	0.447762i
$210$		0			0
$211$	5.83962	−	10.1145i	0.402016	−	0.696312i	−0.591953	−	0.805972i	$-0.701643\pi$
$211$	5.83962	−	10.1145i	0.402016	−	0.696312i	0.993969	+	0.109660i	$0.0349763\pi$
$212$	10.2797	+	17.8050i	0.706013	+	1.22285i
$213$		0			0
$214$	−1.11606	+	1.93307i	−0.0762924	+	0.132142i
$215$	−0.124785	−	9.57291i	−0.00851029	−	0.652867i
$216$		0			0
$217$	6.27856	+	27.4537i	0.426216	+	1.86368i
$218$	5.49441	+	9.51659i	0.372128	+	0.644545i
$219$		0			0
$220$	−12.0726	+	7.18154i	−0.813935	+	0.484179i
$221$		−	20.6048i		−	1.38603i
$222$		0			0
$223$	13.2349	+	22.9235i	0.886275	+	1.53507i	0.844245	+	0.535957i	$0.180049\pi$
$223$	13.2349	+	22.9235i	0.886275	+	1.53507i	0.0420295	+	0.999116i	$0.486618\pi$
$224$	11.7935	−	2.69714i	0.787989	−	0.180210i
$225$		0			0
$226$	11.6575	−	20.1915i	0.775448	−	1.34312i
$227$	6.71384	+	3.87624i	0.445613	+	0.257275i	0.705976	−	0.708236i	$-0.250509\pi$
$227$	6.71384	+	3.87624i	0.445613	+	0.257275i	−0.260363	+	0.965511i	$0.583842\pi$
$228$		0			0
$229$	−16.0456	+	9.26392i	−1.06032	+	0.612177i	−0.925521	−	0.378696i	$-0.876373\pi$
$229$	−16.0456	+	9.26392i	−1.06032	+	0.612177i	−0.134800	+	0.990873i	$0.543039\pi$
$230$	−2.70405	+	0.0352479i	−0.178299	+	0.00232418i
$231$		0			0
$232$	10.6735	−	6.16233i	0.700748	−	0.404577i
$233$	−4.75564	+	8.23700i	−0.311552	+	0.539624i	−0.978699	−	0.205302i	$-0.934182\pi$
$233$	−4.75564	+	8.23700i	−0.311552	+	0.539624i	0.667146	+	0.744927i	$0.267516\pi$
$234$		0			0
$235$	−9.64337	−	5.40125i	−0.629064	−	0.352339i
$236$	−0.892762			−0.0581139
$237$		0			0
$238$	−24.2240	+	22.4960i	−1.57021	+	1.45820i
$239$	17.6506	+	10.1906i	1.14173	+	0.659175i	0.946857	−	0.321654i	$-0.104239\pi$
$239$	17.6506	+	10.1906i	1.14173	+	0.659175i	0.194868	+	0.980829i	$0.437572\pi$
$240$		0			0
$241$	−7.82942	−	4.52032i	−0.504337	−	0.291179i	0.226166	−	0.974089i	$-0.427381\pi$
$241$	−7.82942	−	4.52032i	−0.504337	−	0.291179i	−0.730503	+	0.682910i	$0.760714\pi$
$242$	−11.3553	−	19.6679i	−0.729944	−	1.26430i
$243$		0			0
$244$		−	7.86537i		−	0.503529i
$245$	0.952715	−	15.6235i	0.0608667	−	0.998146i
$246$		0			0
$247$	18.9699	−	10.9523i	1.20702	−	0.696875i
$248$			64.9352i			4.12339i
$249$		0			0
$250$	−28.2838	+	1.10656i	−1.78883	+	0.0699852i
$251$	4.81421			0.303871			0.151935	−	0.988390i	$-0.451449\pi$
$251$	4.81421			0.303871			0.151935	+	0.988390i	$0.451449\pi$
$252$		0			0
$253$			0.680543i			0.0427853i
$254$		−	22.3512i		−	1.40244i
$255$		0			0
$256$	−30.5351			−1.90844
$257$	0.228355	−	0.131841i	0.0142444	−	0.00822401i	−0.492861	−	0.870108i	$-0.664049\pi$
$257$	0.228355	−	0.131841i	0.0142444	−	0.00822401i	0.507105	+	0.861884i	$0.330716\pi$
$258$		0			0
$259$	20.5338	+	6.32416i	1.27591	+	0.392964i
$260$	21.0456	+	35.3789i	1.30519	+	2.19411i
$261$		0			0
$262$	2.79845	+	4.84705i	0.172889	+	0.299452i
$263$	−4.69057	+	8.12431i	−0.289233	+	0.500966i	−0.973627	−	0.228146i	$-0.926734\pi$
$263$	−4.69057	+	8.12431i	−0.289233	+	0.500966i	0.684394	+	0.729113i	$0.260067\pi$
$264$		0			0
$265$	10.4246	−	0.135888i	0.640380	−	0.00834752i
$266$	−33.5870	−	10.3444i	−2.05935	−	0.634255i
$267$		0			0
$268$			10.5088i			0.641926i
$269$	−5.85382	−	10.1391i	−0.356914	−	0.618192i	0.630530	−	0.776165i	$-0.282838\pi$
$269$	−5.85382	−	10.1391i	−0.356914	−	0.618192i	−0.987444	+	0.157972i	$0.949504\pi$
$270$		0			0
$271$	9.67252	+	5.58443i	0.587564	+	0.339230i	0.764134	−	0.645058i	$-0.223167\pi$
$271$	9.67252	+	5.58443i	0.587564	+	0.339230i	−0.176570	+	0.984288i	$0.556500\pi$
$272$	−28.3177	+	16.3492i	−1.71701	+	0.991317i
$273$		0			0
$274$	−6.12134	+	10.6025i	−0.369804	+	0.640519i
$275$	0.185674	+	7.12077i	0.0111966	+	0.429399i
$276$		0			0
$277$	−8.68920	−	5.01671i	−0.522083	−	0.301425i	0.215703	−	0.976459i	$-0.430796\pi$
$277$	−8.68920	−	5.01671i	−0.522083	−	0.301425i	−0.737787	+	0.675034i	$0.764129\pi$
$278$	2.73933	+	1.58155i	0.164294	+	0.0948551i
$279$		0			0
$280$	10.1725	−	34.6272i	0.607925	−	2.06937i
$281$	11.3034	−	6.52601i	0.674303	−	0.389309i	−0.123402	−	0.992357i	$-0.539380\pi$
$281$	11.3034	−	6.52601i	0.674303	−	0.389309i	0.797705	+	0.603048i	$0.206047\pi$
$282$		0			0
$283$	13.3399			0.792974			0.396487	−	0.918040i	$-0.370229\pi$
$283$	13.3399			0.792974			0.396487	+	0.918040i	$0.370229\pi$
$284$			51.7071i			3.06825i
$285$		0			0
$286$	13.0406	−	7.52901i	0.771108	−	0.445200i
$287$	−0.655790	+	2.12927i	−0.0387101	+	0.125687i
$288$		0			0
$289$	3.67897	−	6.37216i	0.216410	−	0.374833i
$290$	−0.149073	−	11.4361i	−0.00875388	−	0.671554i
$291$		0			0
$292$	−19.9499	−	34.5542i	−1.16748	−	2.02213i
$293$	−3.97741	−	2.29636i	−0.232363	−	0.134155i	0.379299	−	0.925274i	$-0.376165\pi$
$293$	−3.97741	−	2.29636i	−0.232363	−	0.134155i	−0.611662	+	0.791120i	$0.709499\pi$
$294$		0			0
$295$	−0.221227	+	0.394978i	−0.0128803	+	0.0229965i
$296$	42.9031	+	24.7701i	2.49369	+	1.43973i
$297$		0			0
$298$	−7.55063	+	4.35936i	−0.437396	+	0.252531i
$299$	1.99434			0.115336
$300$		0			0
$301$	8.30053	−	7.70842i	0.478435	−	0.444306i
$302$	21.5492	−	37.3243i	1.24002	−	2.14777i
$303$		0			0
$304$	−30.1039	−	17.3805i	−1.72658	−	0.996840i
$305$	−3.47981	−	1.94904i	−0.199253	−	0.111602i
$306$		0			0
$307$	−20.6137			−1.17649			−0.588244	−	0.808683i	$-0.700181\pi$
$307$	−20.6137			−1.17649			−0.588244	+	0.808683i	$0.700181\pi$
$308$	−15.8845	−	4.89223i	−0.905103	−	0.278761i
$309$		0			0
$310$	52.5741	+	29.4467i	2.98601	+	1.67246i
$311$	11.5614			0.655584			0.327792	−	0.944750i	$-0.393695\pi$
$311$	11.5614			0.655584			0.327792	+	0.944750i	$0.393695\pi$
$312$		0			0
$313$	29.0404			1.64146			0.820731	−	0.571315i	$-0.193566\pi$
$313$	29.0404			1.64146			0.820731	+	0.571315i	$0.193566\pi$
$314$	11.8526			0.668881
$315$		0			0
$316$	1.99418			0.112181
$317$	21.6855			1.21798			0.608988	−	0.793179i	$-0.291576\pi$
$317$	21.6855			1.21798			0.608988	+	0.793179i	$0.291576\pi$
$318$		0			0
$319$	−2.87820			−0.161148
$320$	−1.82924	+	3.26591i	−0.102257	+	0.182570i
$321$		0			0
$322$	−2.17739	−	2.34464i	−0.121341	−	0.130662i
$323$	25.8944			1.44080
$324$		0			0
$325$	20.8675	−	0.544119i	1.15752	−	0.0301823i
$326$	−35.3334	−	20.3997i	−1.95693	−	1.12984i
$327$		0			0
$328$	−2.56856	+	4.44888i	−0.141825	+	0.245648i
$329$	−2.91563	−	12.7489i	−0.160744	−	0.702870i
$330$		0			0
$331$	5.95239			0.327173			0.163587	−	0.986529i	$-0.447694\pi$
$331$	5.95239			0.327173			0.163587	+	0.986529i	$0.447694\pi$
$332$	46.9729	−	27.1198i	2.57797	−	1.48839i
$333$		0			0
$334$	24.9080	+	14.3806i	1.36290	+	0.786873i
$335$	4.64931	+	2.60408i	0.254019	+	0.142276i
$336$		0			0
$337$	2.43132	+	1.40373i	0.132443	+	0.0764658i	0.564757	−	0.825257i	$-0.308970\pi$
$337$	2.43132	+	1.40373i	0.132443	+	0.0764658i	−0.432315	+	0.901723i	$0.642303\pi$
$338$	−5.60768	−	9.71279i	−0.305018	−	0.528306i
$339$		0			0
$340$	0.634288	+	48.6594i	0.0343991	+	2.63893i
$341$	7.58222	−	13.1328i	0.410600	−	0.711181i
$342$		0			0
$343$	14.4648	−	11.5659i	0.781026	−	0.624499i
$344$	22.6196	−	13.0594i	1.21957	−	0.704118i
$345$		0			0
$346$		−	34.3265i		−	1.84540i
$347$	−9.89128			−0.530992			−0.265496	−	0.964112i	$-0.585536\pi$
$347$	−9.89128			−0.530992			−0.265496	+	0.964112i	$0.585536\pi$
$348$		0			0
$349$	0.279669	−	0.161467i	0.0149703	−	0.00864312i	−0.492496	−	0.870315i	$-0.663915\pi$
$349$	0.279669	−	0.161467i	0.0149703	−	0.00864312i	0.507466	+	0.861671i	$0.330582\pi$
$350$	−23.4225	−	23.9388i	−1.25199	−	1.27958i
$351$		0			0
$352$	−5.64157	−	3.25716i	−0.300697	−	0.173607i
$353$	−14.7971	−	8.54312i	−0.787571	−	0.454704i	0.0515356	−	0.998671i	$-0.483588\pi$
$353$	−14.7971	−	8.54312i	−0.787571	−	0.454704i	−0.839107	+	0.543967i	$0.816922\pi$
$354$		0			0
$355$	22.8763	+	12.8130i	1.21415	+	0.680045i
$356$	5.86771	−	10.1632i	0.310988	−	0.538647i
$357$		0			0
$358$	1.96801	−	1.13623i	0.104013	−	0.0600517i
$359$	17.2188	+	9.94126i	0.908772	+	0.524680i	0.880036	−	0.474907i	$-0.157518\pi$
$359$	17.2188	+	9.94126i	0.908772	+	0.524680i	0.0287362	+	0.999587i	$0.490852\pi$
$360$		0			0
$361$	4.26388	+	7.38525i	0.224415	+	0.388698i
$362$			34.1235i			1.79349i
$363$		0			0
$364$	−14.3367	+	46.5497i	−0.751449	+	2.43987i
$365$	−20.2311	+	0.263718i	−1.05894	+	0.0138036i
$366$		0			0
$367$	15.6841	−	27.1656i	0.818702	−	1.41803i	−0.0879374	−	0.996126i	$-0.528028\pi$
$367$	15.6841	−	27.1656i	0.818702	−	1.41803i	0.906639	−	0.421907i	$-0.138639\pi$
$368$	−1.58244	−	2.74087i	−0.0824904	−	0.142878i
$369$		0			0
$370$	39.5104	−	23.5033i	2.05405	−	1.22188i
$371$	8.39425	+	9.03905i	0.435808	+	0.469284i
$372$		0			0
$373$	−22.1887	+	12.8107i	−1.14889	+	0.663312i	−0.948616	−	0.316428i	$-0.897516\pi$
$373$	−22.1887	+	12.8107i	−1.14889	+	0.663312i	−0.200273	+	0.979740i	$0.564183\pi$
$374$	17.8008			0.920459
$375$		0			0
$376$		−	30.1545i		−	1.55510i
$377$			8.43460i			0.434404i
$378$		0			0
$379$	−5.00587			−0.257134			−0.128567	−	0.991701i	$-0.541038\pi$
$379$	−5.00587			−0.257134			−0.128567	+	0.991701i	$0.541038\pi$
$380$	−44.4613	+	26.4483i	−2.28081	+	1.35677i
$381$		0			0
$382$			5.00111i			0.255879i
$383$	19.9749	−	11.5325i	1.02067	−	0.589284i	0.106372	−	0.994326i	$-0.466077\pi$
$383$	19.9749	−	11.5325i	1.02067	−	0.589284i	0.914298	+	0.405043i	$0.132743\pi$
$384$		0			0
$385$	−6.10061	+	5.81535i	−0.310916	+	0.296378i
$386$		−	41.9677i		−	2.13610i
$387$		0			0
$388$	−20.7003	−	35.8539i	−1.05090	−	1.82021i
$389$	−14.5687	−	8.41123i	−0.738661	−	0.426466i	0.0829213	−	0.996556i	$-0.473575\pi$
$389$	−14.5687	−	8.41123i	−0.738661	−	0.426466i	−0.821582	+	0.570090i	$0.806908\pi$
$390$		0			0
$391$	2.04175	+	1.17880i	0.103256	+	0.0596146i
$392$	38.4580	−	18.5612i	1.94242	−	0.937481i
$393$		0			0
$394$	−62.2611			−3.13667
$395$	0.494158	−	0.882268i	0.0248638	−	0.0443917i
$396$		0			0
$397$	−13.0997	+	22.6893i	−0.657453	+	1.13874i	0.323820	+	0.946119i	$0.395033\pi$
$397$	−13.0997	+	22.6893i	−0.657453	+	1.13874i	−0.981273	+	0.192623i	$0.938301\pi$
$398$	1.58827	−	0.916987i	0.0796127	−	0.0459644i
$399$		0			0
$400$	−17.3055	−	28.2470i	−0.865273	−	1.41235i
$401$	−31.4306	+	18.1465i	−1.56957	+	0.906192i	−0.573352	+	0.819309i	$0.694357\pi$
$401$	−31.4306	+	18.1465i	−1.56957	+	0.906192i	−0.996219	+	0.0868828i	$0.972309\pi$
$402$		0			0
$403$	−38.4858	−	22.2198i	−1.91711	−	1.10685i
$404$	−40.6819	+	70.4631i	−2.02400	+	3.50567i
$405$		0			0
$406$	9.91612	−	9.20876i	0.492129	−	0.457023i
$407$	−5.78460	−	10.0192i	−0.286732	−	0.496634i
$408$		0			0
$409$		−	2.42575i		−	0.119945i	−0.998200	−	0.0599727i	$-0.980899\pi$
$409$		−	2.42575i		−	0.119945i	0.998200	−	0.0599727i	$-0.0191014\pi$
$410$	2.43720	+	4.09708i	0.120365	+	0.202340i
$411$		0			0
$412$	−41.2076	−	71.3736i	−2.03015	−	3.51633i
$413$	−0.522175	+	0.119420i	−0.0256946	+	0.00587626i
$414$		0			0
$415$	−0.358497	−	27.5021i	−0.0175979	−	1.35003i
$416$	−9.54516	+	16.5327i	−0.467990	+	0.810582i
$417$		0			0
$418$	9.46183	+	16.3884i	0.462793	+	0.801582i
$419$	−7.51552	+	13.0173i	−0.367157	+	0.635935i	−0.989120	−	0.147112i	$-0.953002\pi$
$419$	−7.51552	+	13.0173i	−0.367157	+	0.635935i	0.621963	+	0.783047i	$0.286336\pi$
$420$		0			0
$421$	11.1388	+	19.2929i	0.542871	+	0.940281i	0.998738	+	0.0502323i	$0.0159962\pi$
$421$	11.1388	+	19.2929i	0.542871	+	0.940281i	−0.455866	+	0.890048i	$0.650671\pi$
$422$	14.7843	−	25.6071i	0.719687	−	1.24653i
$423$		0			0
$424$	14.2214	+	24.6321i	0.690650	+	1.19624i
$425$	21.6852	+	11.7772i	1.05188	+	0.571278i
$426$		0			0
$427$	−1.05210	−	4.60044i	−0.0509149	−	0.222631i
$428$	−1.94389	+	3.36691i	−0.0939614	+	0.162746i
$429$		0			0
$430$	−0.315921	−	24.2359i	−0.0152351	−	1.16876i
$431$	−16.8829	+	9.74735i	−0.813221	+	0.469514i	−0.848073	−	0.529879i	$-0.822237\pi$
$431$	−16.8829	+	9.74735i	−0.813221	+	0.469514i	0.0348520	+	0.999392i	$0.488904\pi$
$432$		0			0
$433$	16.9416			0.814161			0.407080	−	0.913392i	$-0.366547\pi$
$433$	16.9416			0.814161			0.407080	+	0.913392i	$0.366547\pi$
$434$	15.8955	+	69.5050i	0.763010	+	3.33634i
$435$		0			0
$436$	9.56983	+	16.5754i	0.458312	+	0.793819i
$437$			2.50632i			0.119893i
$438$		0			0
$439$			1.65776i			0.0791207i	0.999217	+	0.0395604i	$0.0125957\pi$
$439$			1.65776i			0.0791207i	−0.999217	+	0.0395604i	$0.987404\pi$
$440$	−16.7017	+	9.93523i	−0.796223	+	0.473643i
$441$		0			0
$442$		−	52.1655i		−	2.48126i
$443$	36.0899			1.71468			0.857341	−	0.514749i	$-0.172115\pi$
$443$	36.0899			1.71468			0.857341	+	0.514749i	$0.172115\pi$
$444$		0			0
$445$	−3.04239	−	5.11444i	−0.144223	−	0.242448i
$446$	33.5070	+	58.0359i	1.58660	+	2.74808i
$447$		0			0
$448$	−4.31766	+	0.987434i	−0.203990	+	0.0466519i
$449$		−	26.4059i		−	1.24617i	−0.782154	−	0.623086i	$-0.785879\pi$
$449$		−	26.4059i		−	1.24617i	0.782154	−	0.623086i	$-0.214121\pi$
$450$		0			0
$451$	1.03895	−	0.599840i	0.0489224	−	0.0282454i
$452$	20.3044	−	35.1683i	0.955039	−	1.65418i
$453$		0			0
$454$	16.9975	+	9.81354i	0.797734	+	0.460572i
$455$	17.0420	+	17.8779i	0.798939	+	0.838130i
$456$		0			0
$457$			31.7898i			1.48706i	0.668700	+	0.743532i	$0.266851\pi$
$457$			31.7898i			1.48706i	−0.668700	+	0.743532i	$0.733149\pi$
$458$	−40.6229	+	23.4536i	−1.89818	+	1.09592i
$459$		0			0
$460$	−4.70974	+	0.0613927i	−0.219593	+	0.00286245i
$461$	5.79487	+	10.0370i	0.269894	+	0.467470i	0.968834	−	0.247710i	$-0.0796780\pi$
$461$	5.79487	+	10.0370i	0.269894	+	0.467470i	−0.698940	+	0.715180i	$0.746345\pi$
$462$		0			0
$463$	−25.9642	−	14.9904i	−1.20666	−	0.696664i	−0.244630	−	0.969616i	$-0.578667\pi$
$463$	−25.9642	−	14.9904i	−1.20666	−	0.696664i	−0.962028	+	0.272952i	$0.912000\pi$
$464$	11.5919	−	6.69257i	0.538139	−	0.310695i
$465$		0			0
$466$	−12.0399	+	20.8538i	−0.557739	+	0.966032i
$467$	−2.17113	−	1.25350i	−0.100468	−	0.0580052i	0.448924	−	0.893570i	$-0.351807\pi$
$467$	−2.17113	−	1.25350i	−0.100468	−	0.0580052i	−0.549392	+	0.835565i	$0.685141\pi$
$468$		0			0
$469$	1.40570	+	6.14657i	0.0649091	+	0.283822i
$470$	−24.4143	−	13.6744i	−1.12615	−	0.630755i
$471$		0			0
$472$	−1.23508			−0.0568493
$473$	−6.09959			−0.280459
$474$		0			0
$475$	0.683804	+	26.2245i	0.0313751	+	1.20326i
$476$	−42.1919	+	39.1822i	−1.93386	+	1.79591i
$477$		0			0
$478$	44.6864	+	25.7997i	2.04391	+	1.18005i
$479$	17.7777	−	30.7920i	0.812286	−	1.40692i	−0.0989748	−	0.995090i	$-0.531556\pi$
$479$	17.7777	−	30.7920i	0.812286	−	1.40692i	0.911261	−	0.411830i	$-0.135110\pi$
$480$		0			0
$481$	−29.3614	+	16.9518i	−1.33877	+	0.772937i
$482$	−19.8219	−	11.4442i	−0.902862	−	0.521267i
$483$		0			0
$484$	−19.7779	−	34.2564i	−0.898996	−	1.55711i
$485$	−20.9921	+	0.273637i	−0.953201	+	0.0124252i
$486$		0			0
$487$	15.4460	−	8.91776i	0.699926	−	0.404102i	−0.107394	−	0.994217i	$-0.534251\pi$
$487$	15.4460	−	8.91776i	0.699926	−	0.404102i	0.807320	+	0.590114i	$0.200917\pi$
$488$		−	10.8813i		−	0.492572i
$489$		0			0
$490$	2.41200	−	39.5542i	0.108963	−	1.78688i
$491$	6.13294	+	3.54085i	0.276776	+	0.159796i	0.631963	−	0.774999i	$-0.282250\pi$
$491$	6.13294	+	3.54085i	0.276776	+	0.159796i	−0.355187	+	0.934795i	$0.615583\pi$
$492$		0			0
$493$	−4.98548	+	8.63510i	−0.224535	+	0.388905i
$494$	48.0263	−	27.7280i	2.16081	−	1.24754i
$495$		0			0
$496$			70.5226i			3.16656i
$497$	6.91655	+	30.2434i	0.310250	+	1.35660i
$498$		0			0
$499$	−11.4852	−	19.8930i	−0.514149	−	0.890533i	−0.999865	−	0.0164161i	$-0.994774\pi$
$499$	−11.4852	−	19.8930i	−0.514149	−	0.890533i	0.485716	−	0.874117i	$-0.338559\pi$
$500$	−49.2630	+	1.92734i	−2.20311	+	0.0861934i
$501$		0			0
$502$	12.1882			0.543987
$503$		−	5.23692i		−	0.233503i	−0.993161	−	0.116751i	$-0.962752\pi$
$503$		−	5.23692i		−	0.233503i	0.993161	−	0.116751i	$-0.0372481\pi$
$504$		0			0
$505$	21.0934	+	35.4593i	0.938645	+	1.57792i
$506$			1.72294i			0.0765941i
$507$		0			0
$508$		−	38.9300i		−	1.72724i
$509$	4.85855	+	8.41525i	0.215351	+	0.373000i	0.953381	−	0.301769i	$-0.0975770\pi$
$509$	4.85855	+	8.41525i	0.215351	+	0.373000i	−0.738030	+	0.674768i	$0.764244\pi$
$510$		0			0
$511$	−16.2907	−	17.5421i	−0.720660	−	0.776017i
$512$	−50.5392			−2.23354
$513$		0			0
$514$	0.578131	−	0.333784i	0.0255003	−	0.0147226i
$515$	−41.7885	+	0.544724i	−1.84142	+	0.0240034i
$516$		0			0
$517$	−3.52102	+	6.09859i	−0.154854	+	0.268216i
$518$	51.9858	+	16.0110i	2.28412	+	0.703482i
$519$		0			0
$520$	29.1153	+	48.9446i	1.27679	+	2.14636i
$521$	−2.77492	−	4.80630i	−0.121571	−	0.210568i	0.798816	−	0.601575i	$-0.205460\pi$
$521$	−2.77492	−	4.80630i	−0.121571	−	0.210568i	−0.920387	+	0.391007i	$0.872127\pi$
$522$		0			0
$523$	−3.79740	+	6.57728i	−0.166049	+	0.287605i	−0.937027	−	0.349257i	$-0.886434\pi$
$523$	−3.79740	+	6.57728i	−0.166049	+	0.287605i	0.770979	+	0.636861i	$0.219768\pi$
$524$	4.87417	+	8.44230i	0.212929	+	0.368804i
$525$		0			0
$526$	−11.8752	+	20.5685i	−0.517784	+	0.896827i
$527$	−26.2671	−	45.4959i	−1.14421	−	1.98183i
$528$		0			0
$529$	11.3859	−	19.7210i	0.495039	−	0.857433i
$530$	26.3922	−	0.344029i	1.14640	−	0.0149437i
$531$		0			0
$532$	−58.4998	−	18.0172i	−2.53629	−	0.781145i
$533$	−1.75784	−	3.04467i	−0.0761405	−	0.131879i
$534$		0			0
$535$	1.00790	+	1.69434i	0.0435753	+	0.0732527i
$536$			14.5383i			0.627957i
$537$		0			0
$538$	−14.8202	−	25.6694i	−0.638945	−	1.10668i
$539$	−9.94522	−	0.736681i	−0.428371	−	0.0317311i
$540$		0			0
$541$	−16.8986	+	29.2693i	−0.726530	+	1.25839i	0.231812	+	0.972761i	$0.425535\pi$
$541$	−16.8986	+	29.2693i	−0.726530	+	1.25839i	−0.958341	+	0.285626i	$0.907799\pi$
$542$	24.4881	+	14.1382i	1.05185	+	0.607288i
$543$		0			0
$544$	−19.5441	+	11.2838i	−0.837947	+	0.483789i
$545$	9.70474	−	0.126504i	0.415705	−	0.00541883i
$546$		0			0
$547$	14.5277	−	8.38754i	0.621158	−	0.358626i	−0.156162	−	0.987731i	$-0.549912\pi$
$547$	14.5277	−	8.38754i	0.621158	−	0.358626i	0.777320	+	0.629106i	$0.216579\pi$
$548$	−10.6618	+	18.4667i	−0.455449	+	0.788860i
$549$		0			0
$550$	0.470074	+	18.0278i	0.0200440	+	0.768707i
$551$	−10.5999			−0.451571
$552$		0			0
$553$	1.16639	−	0.266749i	0.0496000	−	0.0113433i
$554$	−21.9986	−	12.7009i	−0.934631	−	0.539609i
$555$		0			0
$556$	4.77119	+	2.75465i	0.202344	+	0.116823i
$557$	3.36711	+	5.83201i	0.142669	+	0.247110i	0.928501	−	0.371330i	$-0.121098\pi$
$557$	3.36711	+	5.83201i	0.142669	+	0.247110i	−0.785832	+	0.618440i	$0.787765\pi$
$558$		0			0
$559$			17.8749i			0.756028i
$560$	11.0478	−	37.6067i	0.466856	−	1.58917i
$561$		0			0
$562$	28.6170	−	16.5220i	1.20713	−	0.696939i
$563$		−	45.8890i		−	1.93399i	−0.254795	−	0.966995i	$-0.582008\pi$
$563$		−	45.8890i		−	1.93399i	0.254795	−	0.966995i	$-0.417992\pi$
$564$		0			0
$565$	−10.5278	−	17.6978i	−0.442906	−	0.744553i
$566$	33.7728			1.41958
$567$		0			0
$568$			71.5336i			3.00148i
$569$		−	25.9763i		−	1.08898i	−0.838767	−	0.544491i	$-0.816723\pi$
$569$		−	25.9763i		−	1.08898i	0.838767	−	0.544491i	$-0.183277\pi$
$570$		0			0
$571$	−27.1543			−1.13637			−0.568187	−	0.822900i	$-0.692355\pi$
$571$	−27.1543			−1.13637			−0.568187	+	0.822900i	$0.692355\pi$
$572$	22.7134	−	13.1136i	0.949694	−	0.548306i
$573$		0			0
$574$	−1.66028	+	5.39072i	−0.0692986	+	0.225004i
$575$	−1.13991	+	2.09891i	−0.0475377	+	0.0875304i
$576$		0			0
$577$	−6.23651	−	10.8020i	−0.259629	−	0.449691i	0.706513	−	0.707700i	$-0.250267\pi$
$577$	−6.23651	−	10.8020i	−0.259629	−	0.449691i	−0.966143	+	0.258008i	$0.916934\pi$
$578$	9.31411	−	16.1325i	0.387416	−	0.671024i
$579$		0			0
$580$	−0.259647	−	19.9188i	−0.0107812	−	0.827083i
$581$	23.8467	−	22.1456i	0.989328	−	0.918755i
$582$		0			0
$583$		−	6.64228i		−	0.275095i
$584$	−27.5994	−	47.8036i	−1.14207	−	1.97813i
$585$		0			0
$586$	−10.0697	−	5.81373i	−0.415974	−	0.240163i
$587$	−14.4358	+	8.33452i	−0.595830	+	0.344002i	−0.767399	−	0.641170i	$-0.778450\pi$
$587$	−14.4358	+	8.33452i	−0.595830	+	0.344002i	0.171569	+	0.985172i	$0.445116\pi$
$588$		0			0
$589$	27.9240	−	48.3657i	1.15059	−	1.99288i
$590$	−0.560084	+	0.999972i	−0.0230583	+	0.0411682i
$591$		0			0
$592$	46.5947	+	26.9014i	1.91503	+	1.10564i
$593$	−0.329806	−	0.190413i	−0.0135435	−	0.00781934i	0.493213	−	0.869909i	$-0.335822\pi$
$593$	−0.329806	−	0.190413i	−0.0135435	−	0.00781934i	−0.506756	+	0.862089i	$0.669156\pi$
$594$		0			0
$595$	6.87988	+	28.3760i	0.282048	+	1.16330i
$596$	−13.1512	+	7.59287i	−0.538696	+	0.311016i
$597$		0			0
$598$	5.04910			0.206473
$599$		−	21.0025i		−	0.858137i	−0.903272	−	0.429069i	$-0.858842\pi$
$599$		−	21.0025i		−	0.858137i	0.903272	−	0.429069i	$-0.141158\pi$
$600$		0			0
$601$	−3.49714	+	2.01907i	−0.142651	+	0.0823597i	−0.569627	−	0.821903i	$-0.692912\pi$
$601$	−3.49714	+	2.01907i	−0.142651	+	0.0823597i	0.426976	+	0.904263i	$0.359579\pi$
$602$	21.0146	−	19.5155i	0.856491	−	0.795394i
$603$		0			0
$604$	37.5331	−	65.0092i	1.52720	−	2.64519i
$605$	−20.0567	+	0.261445i	−0.815422	+	0.0106292i
$606$		0			0
$607$	8.88367	+	15.3870i	0.360577	+	0.624538i	0.988056	−	0.154096i	$-0.0492465\pi$
$607$	8.88367	+	15.3870i	0.360577	+	0.624538i	−0.627479	+	0.778634i	$0.715913\pi$
$608$	−20.7769	−	11.9956i	−0.842615	−	0.486484i
$609$		0			0
$610$	−8.80990	−	4.93442i	−0.356702	−	0.199789i
$611$	17.8720	+	10.3184i	0.723023	+	0.417437i
$612$		0			0
$613$	12.3044	−	7.10394i	0.496969	−	0.286925i	−0.230492	−	0.973074i	$-0.574034\pi$
$613$	12.3044	−	7.10394i	0.496969	−	0.286925i	0.727461	+	0.686149i	$0.240700\pi$
$614$	−52.1881			−2.10614
$615$		0			0
$616$	−21.9752	−	6.76811i	−0.885408	−	0.272695i
$617$	−16.5509	+	28.6670i	−0.666314	+	1.15409i	0.312614	+	0.949880i	$0.398795\pi$
$617$	−16.5509	+	28.6670i	−0.666314	+	1.15409i	−0.978927	+	0.204209i	$0.934538\pi$
$618$		0			0
$619$	35.6504	+	20.5828i	1.43291	+	0.827291i	0.997342	−	0.0728641i	$-0.0232139\pi$
$619$	35.6504	+	20.5828i	1.43291	+	0.827291i	0.435569	+	0.900155i	$0.356547\pi$
$620$	91.5704	+	51.2886i	3.67756	+	2.05980i
$621$		0			0
$622$	29.2701			1.17362
$623$	2.07254	−	6.72931i	0.0830348	−	0.269604i
$624$		0			0
$625$	−11.3547	+	22.2726i	−0.454188	+	0.890906i
$626$	73.5222			2.93854
$627$		0			0
$628$	20.6441			0.823791
$629$	−40.0792			−1.59806
$630$		0			0
$631$	10.0626			0.400586			0.200293	−	0.979736i	$-0.435811\pi$
$631$	10.0626			0.400586			0.200293	+	0.979736i	$0.435811\pi$
$632$	2.75882			0.109740
$633$		0			0
$634$	54.9015			2.18042
$635$	−17.2235	−	9.64687i	−0.683493	−	0.382824i
$636$		0			0
$637$	−2.15885	+	29.1446i	−0.0855369	+	1.15475i
$638$	−7.28679			−0.288487
$639$		0			0
$640$	−14.6241	+	26.1098i	−0.578068	+	1.03208i
$641$	33.9181	+	19.5826i	1.33968	+	0.773466i	0.986760	−	0.162186i	$-0.0518545\pi$
$641$	33.9181	+	19.5826i	1.33968	+	0.773466i	0.352923	+	0.935652i	$0.385188\pi$
$642$		0			0
$643$	7.40682	−	12.8290i	0.292097	−	0.505926i	−0.682209	−	0.731157i	$-0.738980\pi$
$643$	7.40682	−	12.8290i	0.292097	−	0.505926i	0.974305	+	0.225231i	$0.0723138\pi$
$644$	−3.79244	−	4.08375i	−0.149443	−	0.160922i
$645$		0			0
$646$	65.5573			2.57932
$647$	23.0628	−	13.3153i	0.906691	−	0.523478i	0.0273261	−	0.999627i	$-0.491301\pi$
$647$	23.0628	−	13.3153i	0.906691	−	0.523478i	0.879365	+	0.476148i	$0.157967\pi$
$648$		0			0
$649$	0.249789	+	0.144216i	0.00980506	+	0.00566096i
$650$	52.8306	−	1.37756i	2.07219	−	0.0540322i
$651$		0			0
$652$	−61.5415	−	35.5310i	−2.41015	−	1.39150i
$653$	−10.6651	−	18.4725i	−0.417358	−	0.722885i	0.578315	−	0.815814i	$-0.303711\pi$
$653$	−10.6651	−	18.4725i	−0.417358	−	0.722885i	−0.995673	+	0.0929286i	$0.970377\pi$
$654$		0			0
$655$	4.94288	−	0.0644317i	0.193134	−	0.00251756i
$656$	−2.78957	+	4.83168i	−0.108915	+	0.188646i
$657$		0			0
$658$	−7.38155	−	32.2766i	−0.287763	−	1.25827i
$659$	3.91124	−	2.25816i	0.152360	−	0.0879653i	−0.421882	−	0.906651i	$-0.638630\pi$
$659$	3.91124	−	2.25816i	0.152360	−	0.0879653i	0.574242	+	0.818686i	$0.305297\pi$
$660$		0			0
$661$			33.8778i			1.31770i	0.752276	+	0.658848i	$0.228956\pi$
$661$			33.8778i			1.31770i	−0.752276	+	0.658848i	$0.771044\pi$
$662$	15.0698			0.585703
$663$		0			0
$664$	64.9842	−	37.5186i	2.52187	−	1.45601i
$665$	−22.4675	+	21.4169i	−0.871251	+	0.830512i
$666$		0			0
$667$	−0.835791	−	0.482544i	−0.0323620	−	0.0186842i
$668$	43.3832	+	25.0473i	1.67855	+	0.969109i
$669$		0			0
$670$	11.7707	+	6.59279i	0.454744	+	0.254702i
$671$	−1.27056	+	2.20068i	−0.0490495	+	0.0849561i
$672$		0			0
$673$	−0.00944408	+	0.00545254i	−0.000364043	+	0.000210180i	−0.500182	−	0.865920i	$-0.666734\pi$
$673$	−0.00944408	+	0.00545254i	−0.000364043	+	0.000210180i	0.499818	+	0.866130i	$0.333400\pi$
$674$	6.15542	+	3.55384i	0.237098	+	0.136889i
$675$		0			0
$676$	−9.76712	−	16.9172i	−0.375659	−	0.650660i
$677$		−	35.1941i		−	1.35262i	−0.736618	−	0.676309i	$-0.763578\pi$
$677$		−	35.1941i		−	1.35262i	0.736618	−	0.676309i	$-0.236422\pi$
$678$		0			0
$679$	−16.9035	−	18.2019i	−0.648697	−	0.698526i
$680$	0.877499	+	67.3174i	0.0336506	+	2.58150i
$681$		0			0
$682$	19.1960	−	33.2485i	0.735054	−	1.27315i
$683$	13.2893	+	23.0177i	0.508499	+	0.880746i	0.999952	+	0.00984199i	$0.00313285\pi$
$683$	13.2893	+	23.0177i	0.508499	+	0.880746i	−0.491452	+	0.870904i	$0.663534\pi$
$684$		0			0
$685$	5.52810	+	9.29307i	0.211218	+	0.355070i
$686$	36.6208	−	29.2815i	1.39819	−	1.11797i
$687$		0			0
$688$	24.5659	−	14.1831i	0.936567	−	0.540727i
$689$	−19.4653			−0.741568
$690$		0			0
$691$			3.28870i			0.125108i	0.998042	+	0.0625540i	$0.0199246\pi$
$691$			3.28870i			0.125108i	−0.998042	+	0.0625540i	$0.980075\pi$
$692$		−	59.7878i		−	2.27279i
$693$		0			0
$694$	−25.0419			−0.950578
$695$	2.40102	−	1.42828i	0.0910759	−	0.0541776i
$696$		0			0
$697$		−	4.15606i		−	0.157422i
$698$	0.708042	−	0.408788i	0.0267998	−	0.0154729i
$699$		0			0
$700$	−40.7959	−	41.6951i	−1.54194	−	1.57593i
$701$			39.7933i			1.50297i	0.659749	+	0.751486i	$0.270663\pi$
$701$			39.7933i			1.50297i	−0.659749	+	0.751486i	$0.729337\pi$
$702$		0			0
$703$	−21.3037	−	36.8990i	−0.803483	−	1.39167i
$704$	2.06540	+	1.19246i	0.0778428	+	0.0449426i
$705$		0			0
$706$	−37.4621	−	21.6288i	−1.40991	−	0.814009i
$707$	−14.3693	+	46.6555i	−0.540414	+	1.75466i
$708$		0			0
$709$	−3.08929			−0.116021			−0.0580103	−	0.998316i	$-0.518476\pi$
$709$	−3.08929			−0.116021			−0.0580103	+	0.998316i	$0.518476\pi$
$710$	57.9164	+	32.4390i	2.17356	+	1.21741i
$711$		0			0
$712$	8.11762	−	14.0601i	0.304221	−	0.526926i
$713$	4.40355	−	2.54239i	0.164914	−	0.0952133i
$714$		0			0
$715$	−0.173349	−	13.2984i	−0.00648287	−	0.497333i
$716$	3.42776	−	1.97902i	0.128101	−	0.0739594i
$717$		0			0
$718$	43.5931	+	25.1685i	1.62688	+	0.939279i
$719$	−10.5791	+	18.3235i	−0.394532	+	0.683350i	−0.993041	−	0.117766i	$-0.962427\pi$
$719$	−10.5791	+	18.3235i	−0.394532	+	0.683350i	0.598509	+	0.801116i	$0.295760\pi$
$720$		0			0
$721$	−33.6495	−	36.2342i	−1.25317	−	1.34943i
$722$	10.7949	+	18.6974i	0.401746	+	0.695844i
$723$		0			0
$724$			59.4343i			2.20886i
$725$	−8.87685	−	4.82101i	−0.329678	−	0.179048i
$726$		0			0
$727$	4.31669	+	7.47672i	0.160097	+	0.277296i	0.934903	−	0.354903i	$-0.115486\pi$
$727$	4.31669	+	7.47672i	0.160097	+	0.277296i	−0.774806	+	0.632199i	$0.782153\pi$
$728$	−19.8340	+	64.3987i	−0.735097	+	2.38677i
$729$		0			0
$730$	−51.2194	+	0.667659i	−1.89572	+	0.0247112i
$731$	−10.5654	+	18.2998i	−0.390776	+	0.676843i
$732$		0			0
$733$	−2.57990	−	4.46851i	−0.0952907	−	0.165048i	0.814439	−	0.580249i	$-0.197045\pi$
$733$	−2.57990	−	4.46851i	−0.0952907	−	0.165048i	−0.909730	+	0.415201i	$0.863711\pi$
$734$	39.7076	−	68.7756i	1.46564	−	2.53855i
$735$		0			0
$736$	−1.09216	−	1.89167i	−0.0402575	−	0.0697280i
$737$	1.69757	−	2.94028i	0.0625309	−	0.108307i
$738$		0			0
$739$	−7.92896	−	13.7334i	−0.291671	−	0.505190i	0.682534	−	0.730854i	$-0.260878\pi$
$739$	−7.92896	−	13.7334i	−0.291671	−	0.505190i	−0.974205	+	0.225664i	$0.927545\pi$
$740$	68.8169	−	40.9366i	2.52976	−	1.50486i
$741$		0			0
$742$	21.2519	+	22.8843i	0.780181	+	0.840110i
$743$	14.5897	−	25.2701i	0.535243	−	0.927069i	−0.463908	−	0.885883i	$-0.653553\pi$
$743$	14.5897	−	25.2701i	0.535243	−	0.927069i	0.999152	−	0.0411854i	$-0.0131134\pi$
$744$		0			0
$745$	0.100370	+	7.69991i	0.00367729	+	0.282103i
$746$	−56.1756	+	32.4330i	−2.05674	+	1.18746i
$747$		0			0
$748$	31.0044			1.13363
$749$	−0.686605	+	2.22932i	−0.0250880	+	0.0814577i
$750$		0			0
$751$	13.9911	+	24.2333i	0.510543	+	0.884287i	0.999925	+	0.0122173i	$0.00388898\pi$
$751$	13.9911	+	24.2333i	0.510543	+	0.884287i	−0.489382	+	0.872069i	$0.662778\pi$
$752$		−	32.7492i		−	1.19424i
$753$		0			0
$754$			21.3540i			0.777668i
$755$	−19.4608	−	32.7147i	−0.708250	−	1.19061i
$756$		0			0
$757$		−	12.4434i		−	0.452263i	−0.974097	−	0.226132i	$-0.927392\pi$
$757$		−	12.4434i		−	0.452263i	0.974097	−	0.226132i	$-0.0726079\pi$
$758$	−12.6734			−0.460320
$759$		0			0
$760$	−61.5095	+	36.5897i	−2.23118	+	1.32725i
$761$	10.5154	+	18.2131i	0.381181	+	0.660225i	0.991231	−	0.132138i	$-0.0421841\pi$
$761$	10.5154	+	18.2131i	0.381181	+	0.660225i	−0.610050	+	0.792363i	$0.708851\pi$
$762$		0			0
$763$	7.81457	+	8.41484i	0.282907	+	0.304638i
$764$			8.71063i			0.315140i
$765$		0			0
$766$	50.5708	−	29.1971i	1.82720	−	1.05493i
$767$	0.422625	−	0.732009i	0.0152601	−	0.0264313i
$768$		0			0
$769$	−11.8574	−	6.84585i	−0.427588	−	0.246868i	0.270731	−	0.962655i	$-0.412735\pi$
$769$	−11.8574	−	6.84585i	−0.427588	−	0.246868i	−0.698318	+	0.715787i	$0.746068\pi$
$770$	−15.4450	+	14.7228i	−0.556600	+	0.530574i
$771$		0			0
$772$		−	73.0967i		−	2.63081i
$773$	−0.308779	+	0.178273i	−0.0111060	+	0.00641205i	−0.505543	−	0.862802i	$-0.668708\pi$
$773$	−0.308779	+	0.178273i	−0.0111060	+	0.00641205i	0.494437	+	0.869214i	$0.335374\pi$
$774$		0			0
$775$	45.3824	−	27.8034i	1.63018	−	0.998729i
$776$	−28.6376	−	49.6017i	−1.02803	−	1.78060i
$777$		0			0
$778$	−36.8838	−	21.2948i	−1.32235	−	0.763457i
$779$	3.82628	−	2.20911i	0.137091	−	0.0791494i
$780$		0			0
$781$	8.35268	−	14.4673i	0.298882	−	0.517680i
$782$	5.16912	+	2.98439i	0.184847	+	0.106722i
$783$		0			0
$784$	41.7671	−	20.1583i	1.49168	−	0.719939i
$785$	5.11562	−	9.13342i	0.182584	−	0.325986i
$786$		0			0
$787$	10.5853			0.377324			0.188662	−	0.982042i	$-0.439585\pi$
$787$	10.5853			0.377324			0.188662	+	0.982042i	$0.439585\pi$
$788$	−108.443			−3.86311
$789$		0			0
$790$	1.25107	−	2.23365i	0.0445110	−	0.0794698i
$791$	7.17176	−	23.2859i	0.254998	−	0.827950i
$792$		0			0
$793$	6.44910	+	3.72339i	0.229014	+	0.132222i
$794$	−33.1646	+	57.4428i	−1.17697	+	2.03857i
$795$		0			0
$796$	2.76635	−	1.59715i	0.0980507	−	0.0566096i
$797$	32.2113	+	18.5972i	1.14098	+	0.658747i	0.946674	−	0.322193i	$-0.104420\pi$
$797$	32.2113	+	18.5972i	1.14098	+	0.658747i	0.194309	+	0.980940i	$0.437753\pi$
$798$		0			0
$799$	12.1979	+	21.1273i	0.431530	+	0.747432i
$800$	−11.9438	−	19.4953i	−0.422276	−	0.689264i
$801$		0			0
$802$	−79.5735	+	45.9418i	−2.80984	+	1.62226i
$803$			12.8907i			0.454902i
$804$		0			0
$805$	−2.74651	+	0.665903i	−0.0968017	+	0.0234700i
$806$	−97.4351	−	56.2542i	−3.43201	−	1.98147i
$807$		0			0
$808$	−56.2809	+	97.4814i	−1.97996	+	3.42938i
$809$	27.2837	−	15.7522i	0.959243	−	0.553819i	0.0633032	−	0.997994i	$-0.479836\pi$
$809$	27.2837	−	15.7522i	0.959243	−	0.553819i	0.895940	+	0.444175i	$0.146503\pi$
$810$		0			0
$811$			1.59210i			0.0559062i	0.999609	+	0.0279531i	$0.00889891\pi$
$811$			1.59210i			0.0559062i	−0.999609	+	0.0279531i	$0.991101\pi$
$812$	17.2713	−	16.0393i	0.606104	−	0.562868i
$813$		0			0
$814$	−14.6450	−	25.3658i	−0.513306	−	0.889072i
$815$	−30.9697	+	18.4227i	−1.08482	+	0.645320i
$816$		0			0
$817$	−22.4637			−0.785905
$818$		−	6.14130i		−	0.214726i
$819$		0			0
$820$	4.24496	+	7.13604i	0.148241	+	0.249201i
$821$		−	25.4155i		−	0.887006i	−0.896273	−	0.443503i	$-0.853736\pi$
$821$		−	25.4155i		−	0.887006i	0.896273	−	0.443503i	$-0.146264\pi$
$822$		0			0
$823$			19.7366i			0.687973i	0.938975	+	0.343986i	$0.111777\pi$
$823$			19.7366i			0.687973i	−0.938975	+	0.343986i	$0.888223\pi$
$824$	−57.0082	−	98.7411i	−1.98597	−	3.43981i
$825$		0			0
$826$	−1.32200	+	0.302337i	−0.0459983	+	0.0105196i
$827$	11.0429			0.383998			0.191999	−	0.981395i	$-0.438503\pi$
$827$	11.0429			0.383998			0.191999	+	0.981395i	$0.438503\pi$
$828$		0			0
$829$	−18.4118	+	10.6300i	−0.639467	+	0.369196i	−0.784409	−	0.620244i	$-0.787034\pi$
$829$	−18.4118	+	10.6300i	−0.639467	+	0.369196i	0.144942	+	0.989440i	$0.453700\pi$
$830$	−0.907614	−	69.6276i	−0.0315037	−	2.41681i
$831$		0			0
$832$	3.49452	−	6.05269i	0.121151	−	0.209839i
$833$	−19.4368	+	28.5613i	−0.673445	+	0.989592i
$834$		0			0
$835$	21.8318	−	12.9869i	0.755522	−	0.449432i
$836$	16.4800	+	28.5443i	0.569974	+	0.987225i
$837$		0			0
$838$	−19.0272	+	32.9560i	−0.657283	+	1.13845i
$839$	17.8301	+	30.8827i	0.615564	+	1.06619i	0.990285	+	0.139051i	$0.0444051\pi$
$839$	17.8301	+	30.8827i	0.615564	+	1.06619i	−0.374721	+	0.927137i	$0.622262\pi$
$840$		0			0
$841$	−12.4592	+	21.5799i	−0.429627	+	0.744136i
$842$	28.2003	+	48.8443i	0.971845	+	1.68328i
$843$		0			0
$844$	25.7503	−	44.6009i	0.886363	−	1.53523i
$845$	−9.90481	+	0.129112i	−0.340736	+	0.00444158i
$846$		0			0
$847$	−16.1503	−	17.3909i	−0.554932	−	0.597559i
$848$	15.4450	+	26.7516i	0.530385	+	0.918654i
$849$		0			0
$850$	54.9007	+	29.8165i	1.88308	+	1.02270i
$851$		−	3.87927i		−	0.132980i
$852$		0			0
$853$	12.0777	+	20.9192i	0.413534	+	0.716261i	0.995273	−	0.0971139i	$-0.0309611\pi$
$853$	12.0777	+	20.9192i	0.413534	+	0.716261i	−0.581740	+	0.813375i	$0.697628\pi$
$854$	−2.66363	−	11.6470i	−0.0911476	−	0.398553i
$855$		0			0
$856$	−2.68925	+	4.65792i	−0.0919167	+	0.159204i
$857$	−46.6132	−	26.9122i	−1.59228	−	0.919302i	−0.992915	−	0.118824i	$-0.962088\pi$
$857$	−46.6132	−	26.9122i	−1.59228	−	0.919302i	−0.599362	−	0.800478i	$-0.704579\pi$
$858$		0			0
$859$	−14.8971	+	8.60083i	−0.508282	+	0.293457i	−0.732127	−	0.681168i	$-0.761472\pi$
$859$	−14.8971	+	8.60083i	−0.508282	+	0.293457i	0.223845	+	0.974625i	$0.428139\pi$
$860$	−0.550253	−	42.2126i	−0.0187635	−	1.43944i
$861$		0			0
$862$	−42.7428	+	24.6775i	−1.45582	+	0.840521i
$863$	−14.6092	+	25.3039i	−0.497304	+	0.861356i	−0.999995	−	0.00310991i	$-0.999010\pi$
$863$	−14.6092	+	25.3039i	−0.497304	+	0.861356i	0.502691	+	0.864466i	$0.332343\pi$
$864$		0			0
$865$	−26.4514	−	14.8154i	−0.899375	−	0.503740i
$866$	42.8913			1.45751
$867$		0			0
$868$	27.6859	+	121.060i	0.939720	+	4.10903i
$869$	−0.557957	−	0.322137i	−0.0189274	−	0.0109277i
$870$		0			0
$871$	−8.61653	−	4.97476i	−0.291960	−	0.168563i
$872$	13.2393	+	22.9311i	0.448339	+	0.776545i
$873$		0			0
$874$			6.34529i			0.214633i
$875$	−28.5561	+	7.71693i	−0.965371	+	0.260880i
$876$		0			0
$877$	−28.2956	+	16.3364i	−0.955473	+	0.551643i	−0.894777	−	0.446514i	$-0.852665\pi$
$877$	−28.2956	+	16.3364i	−0.955473	+	0.551643i	−0.0606963	+	0.998156i	$0.519332\pi$
$878$			4.19699i			0.141641i
$879$		0			0
$880$	−18.1388	+	10.7901i	−0.611460	+	0.363734i
$881$	51.6741			1.74094			0.870472	−	0.492217i	$-0.163814\pi$
$881$	51.6741			1.74094			0.870472	+	0.492217i	$0.163814\pi$
$882$		0			0
$883$			18.8576i			0.634610i	0.948324	+	0.317305i	$0.102778\pi$
$883$			18.8576i			0.634610i	−0.948324	+	0.317305i	$0.897222\pi$
$884$		−	90.8587i		−	3.05591i
$885$		0			0
$886$	91.3693			3.06961
$887$	33.3082	−	19.2305i	1.11838	−	0.645697i	0.177393	−	0.984140i	$-0.443234\pi$
$887$	33.3082	−	19.2305i	1.11838	−	0.645697i	0.940987	+	0.338443i	$0.109900\pi$
$888$		0			0
$889$	−5.20744	−	22.7701i	−0.174652	−	0.763685i
$890$	−7.70246	−	12.9483i	−0.258187	−	0.434028i
$891$		0			0
$892$	58.3605	+	101.083i	1.95406	+	3.38452i
$893$	−12.9673	+	22.4600i	−0.433934	+	0.751596i
$894$		0			0
$895$	−0.0261607	−	2.00692i	−0.000874456	−	0.0670839i
$896$	−34.5182	+	7.89418i	−1.15317	+	0.263726i
$897$		0			0
$898$		−	66.8523i		−	2.23089i
$899$	10.7525	+	18.6238i	0.358615	+	0.621139i
$900$		0			0
$901$	−19.9280	−	11.5054i	−0.663897	−	0.383301i
$902$	2.63034	−	1.51863i	0.0875807	−	0.0505647i
$903$		0			0
$904$	28.0899	−	48.6532i	0.934257	−	1.61818i
$905$	26.2950	+	14.7278i	0.874076	+	0.489570i
$906$		0			0
$907$	5.68017	+	3.27945i	0.188607	+	0.108892i	0.591330	−	0.806430i	$-0.298603\pi$
$907$	5.68017	+	3.27945i	0.188607	+	0.108892i	−0.402723	+	0.915322i	$0.631936\pi$
$908$	29.6053	+	17.0926i	0.982486	+	0.567239i
$909$		0			0
$910$	43.1454	+	45.2618i	1.43026	+	1.50042i
$911$	−40.3423	+	23.2916i	−1.33660	+	0.771686i	−0.986302	−	0.164952i	$-0.947253\pi$
$911$	−40.3423	+	23.2916i	−1.33660	+	0.771686i	−0.350298	+	0.936638i	$0.613920\pi$
$912$		0			0
$913$	−17.5236			−0.579946
$914$			80.4828i			2.66213i
$915$		0			0
$916$	−70.7544	+	40.8501i	−2.33779	+	1.34972i
$917$	3.98017	+	4.28590i	0.131437	+	0.141533i
$918$		0			0
$919$	−25.8448	+	44.7644i	−0.852540	+	1.47664i	0.0263686	+	0.999652i	$0.491606\pi$
$919$	−25.8448	+	44.7644i	−0.852540	+	1.47664i	−0.878909	+	0.476990i	$0.841728\pi$
$920$	−6.51565	+	0.0849332i	−0.214814	+	0.00280016i
$921$		0			0
$922$	14.6710	+	25.4109i	0.483163	+	0.836863i
$923$	−42.3965	−	24.4776i	−1.39550	−	0.805691i
$924$		0			0
$925$	−1.05839	−	40.5902i	−0.0347996	−	1.33460i
$926$	−65.7340	−	37.9515i	−2.16015	−	1.24716i
$927$		0			0
$928$	8.00041	−	4.61904i	0.262626	−	0.151627i
$929$	−45.2591			−1.48490			−0.742452	−	0.669899i	$-0.766337\pi$
$929$	−45.2591			−1.48490			−0.742452	+	0.669899i	$0.766337\pi$
$930$		0			0
$931$	−36.6265	−	2.71307i	−1.20038	−	0.0889172i
$932$	−20.9704	+	36.3218i	−0.686909	+	1.18976i
$933$		0			0
$934$	−5.49669	−	3.17352i	−0.179857	−	0.103841i
$935$	7.68290	−	13.7170i	0.251258	−	0.448595i
$936$		0			0
$937$	16.0761			0.525184			0.262592	−	0.964907i	$-0.415423\pi$
$937$	16.0761			0.525184			0.262592	+	0.964907i	$0.415423\pi$
$938$	3.55883	+	15.5614i	0.116200	+	0.508097i
$939$		0			0
$940$	−42.5233	−	23.8173i	−1.38696	−	0.776835i
$941$	23.6483			0.770912			0.385456	−	0.922726i	$-0.374044\pi$
$941$	23.6483			0.770912			0.385456	+	0.922726i	$0.374044\pi$
$942$		0			0
$943$	0.402265			0.0130995
$944$	−1.34136			−0.0436574
$945$		0			0
$946$	−15.4424			−0.502077
$947$	−28.5396			−0.927413			−0.463707	−	0.885989i	$-0.653481\pi$
$947$	−28.5396			−0.927413			−0.463707	+	0.885989i	$0.653481\pi$
$948$		0			0
$949$	37.7763			1.22627
$950$	1.73120	+	66.3931i	0.0561675	+	2.15408i
$951$		0			0
$952$	−58.3699	+	54.2062i	−1.89178	+	1.75683i
$953$	−60.3601			−1.95525			−0.977627	−	0.210346i	$-0.932541\pi$
$953$	−60.3601			−1.95525			−0.977627	+	0.210346i	$0.932541\pi$
$954$		0			0
$955$	3.85377	+	2.15850i	0.124705	+	0.0698473i
$956$	77.8321	+	44.9364i	2.51727	+	1.45335i
$957$		0			0
$958$	45.0082	−	77.9565i	1.45415	−	2.51866i
$959$	−3.76587	+	12.2273i	−0.121606	+	0.394841i
$960$		0			0
$961$	−82.3036			−2.65495
$962$	−74.3349	+	42.9173i	−2.39665	+	1.38371i
$963$		0			0
$964$	−34.5245	−	19.9328i	−1.11196	−	0.641991i
$965$	−32.3396	−	18.1134i	−1.04105	−	0.583091i
$966$		0			0
$967$	20.6715	+	11.9347i	0.664752	+	0.383795i	0.794085	−	0.607807i	$-0.207950\pi$
$967$	20.6715	+	11.9347i	0.664752	+	0.383795i	−0.129333	+	0.991601i	$0.541284\pi$
$968$	−27.3616	−	47.3916i	−0.879434	−	1.52322i
$969$		0			0
$970$	−53.1460	+	0.692772i	−1.70642	+	0.0222436i
$971$	21.2234	−	36.7601i	0.681092	−	1.17969i	−0.293555	−	0.955942i	$-0.594839\pi$
$971$	21.2234	−	36.7601i	0.681092	−	1.17969i	0.974648	−	0.223745i	$-0.0718282\pi$
$972$		0			0
$973$	3.15914	+	0.972975i	0.101277	+	0.0311922i
$974$	39.1049	−	22.5772i	1.25300	−	0.723422i
$975$		0			0
$976$		−	11.8176i		−	0.378271i
$977$	−7.00412			−0.224082			−0.112041	−	0.993704i	$-0.535739\pi$
$977$	−7.00412			−0.224082			−0.112041	+	0.993704i	$0.535739\pi$
$978$		0			0
$979$	−3.28349	+	1.89572i	−0.104941	+	0.0605875i
$980$	4.20108	−	68.8931i	0.134199	−	2.20071i
$981$		0			0
$982$	15.5269	+	8.96444i	0.495482	+	0.286067i
$983$	−24.7050	−	14.2634i	−0.787967	−	0.454933i	0.0512794	−	0.998684i	$-0.483670\pi$
$983$	−24.7050	−	14.2634i	−0.787967	−	0.454933i	−0.839246	+	0.543751i	$0.817003\pi$
$984$		0			0
$985$	−26.8721	+	47.9774i	−0.856217	+	1.52869i
$986$	−12.6218	+	21.8616i	−0.401961	+	0.696216i
$987$		0			0
$988$	83.6493	−	48.2950i	2.66124	−	1.53647i
$989$	−1.77124	−	1.02263i	−0.0563221	−	0.0325176i
$990$		0			0
$991$	28.9247	+	50.0991i	0.918824	+	1.59145i	0.801204	+	0.598391i	$0.204193\pi$
$991$	28.9247	+	50.0991i	0.918824	+	1.59145i	0.117620	+	0.993059i	$0.462474\pi$
$992$			48.6729i			1.54536i
$993$		0			0
$994$	17.5108	+	76.5677i	0.555407	+	2.42858i
$995$	−0.0211128	−	1.61967i	−0.000669321	−	0.0513469i
$996$		0			0
$997$	−1.10662	+	1.91671i	−0.0350469	+	0.0607030i	−0.883017	−	0.469341i	$-0.844491\pi$
$997$	−1.10662	+	1.91671i	−0.0350469	+	0.0607030i	0.847970	+	0.530044i	$0.177825\pi$
$998$	−29.0773	−	50.3634i	−0.920427	−	1.59423i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.bq.a.719.42		88
3.2	odd	2		315.2.bq.a.194.3	yes	88
5.4	even	2	inner	945.2.bq.a.719.3		88
7.3	odd	6		945.2.u.a.584.3		88
9.2	odd	6		945.2.u.a.89.42		88
9.7	even	3		315.2.u.a.299.3	yes	88
15.14	odd	2		315.2.bq.a.194.42	yes	88
21.17	even	6		315.2.u.a.59.42	yes	88
35.24	odd	6		945.2.u.a.584.42		88
45.29	odd	6		945.2.u.a.89.3		88
45.34	even	6		315.2.u.a.299.42	yes	88
63.38	even	6	inner	945.2.bq.a.899.3		88
63.52	odd	6		315.2.bq.a.164.42	yes	88
105.59	even	6		315.2.u.a.59.3	✓	88
315.164	even	6	inner	945.2.bq.a.899.42		88
315.304	odd	6		315.2.bq.a.164.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.u.a.59.3	✓	88	105.59	even	6
315.2.u.a.59.42	yes	88	21.17	even	6
315.2.u.a.299.3	yes	88	9.7	even	3
315.2.u.a.299.42	yes	88	45.34	even	6
315.2.bq.a.164.3	yes	88	315.304	odd	6
315.2.bq.a.164.42	yes	88	63.52	odd	6
315.2.bq.a.194.3	yes	88	3.2	odd	2
315.2.bq.a.194.42	yes	88	15.14	odd	2
945.2.u.a.89.3		88	45.29	odd	6
945.2.u.a.89.42		88	9.2	odd	6
945.2.u.a.584.3		88	7.3	odd	6
945.2.u.a.584.42		88	35.24	odd	6
945.2.bq.a.719.3		88	5.4	even	2	inner
945.2.bq.a.719.42		88	1.1	even	1	trivial
945.2.bq.a.899.3		88	63.38	even	6	inner
945.2.bq.a.899.42		88	315.164	even	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.53172 q^{2} +4.40959 q^{4} +(1.09270 - 1.95090i) q^{5} +(2.57916 - 0.589845i) q^{7} +6.10041 q^{8} +(2.76640 - 4.93913i) q^{10} +(-1.23377 - 0.712319i) q^{11} +(-2.08746 + 3.61559i) q^{13} +(6.52971 - 1.49332i) q^{14} +6.62532 q^{16} +(-4.27416 + 2.46769i) q^{17} +(-4.54377 - 2.62335i) q^{19} +(4.81835 - 8.60267i) q^{20} +(-3.12356 - 1.80339i) q^{22} +(-0.238847 - 0.413696i) q^{23} +(-2.61202 - 4.26349i) q^{25} +(-5.28486 + 9.15364i) q^{26} +(11.3731 - 2.60098i) q^{28} +(1.74963 - 1.01015i) q^{29} +10.6444i q^{31} +4.57262 q^{32} +(-10.8210 + 6.24749i) q^{34} +(1.66752 - 5.67621i) q^{35} +(7.03282 + 4.06040i) q^{37} +(-11.5035 - 6.64157i) q^{38} +(6.66590 - 11.9013i) q^{40} +(-0.421048 + 0.729276i) q^{41} +(3.70789 - 2.14075i) q^{43} +(-5.44044 - 3.14104i) q^{44} +(-0.604694 - 1.04736i) q^{46} -4.94304i q^{47} +(6.30416 - 3.04261i) q^{49} +(-6.61290 - 10.7940i) q^{50} +(-9.20484 + 15.9433i) q^{52} +(2.33122 + 4.03778i) q^{53} +(-2.73781 + 1.62862i) q^{55} +(15.7339 - 3.59830i) q^{56} +(4.42958 - 2.55742i) q^{58} -0.202459 q^{59} -1.78370i q^{61} +26.9486i q^{62} -1.67406 q^{64} +(4.77268 + 8.02317i) q^{65} +2.38316i q^{67} +(-18.8473 + 10.8815i) q^{68} +(4.22169 - 14.3706i) q^{70} +11.7260i q^{71} +(-4.52420 - 7.83614i) q^{73} +(17.8051 + 10.2798i) q^{74} +(-20.0362 - 11.5679i) q^{76} +(-3.60226 - 1.10945i) q^{77} +0.452236 q^{79} +(7.23947 - 12.9253i) q^{80} +(-1.06597 + 1.84632i) q^{82} +(10.6524 - 6.15019i) q^{83} +(0.143843 + 11.0349i) q^{85} +(9.38732 - 5.41977i) q^{86} +(-7.52652 - 4.34544i) q^{88} +(1.33067 - 2.30479i) q^{89} +(-3.25126 + 10.5565i) q^{91} +(-1.05322 - 1.82423i) q^{92} -12.5144i q^{94} +(-10.0829 + 5.99791i) q^{95} +(-4.69437 - 8.13089i) q^{97} +(15.9604 - 7.70304i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 76 q^{4} + 3 q^{5} - 6 q^{10} + 12 q^{11} + 12 q^{14} + 52 q^{16} - 12 q^{19} + 6 q^{20} + q^{25} + 12 q^{26} - 6 q^{29} - 12 q^{34} - 30 q^{40} - 6 q^{41} + 84 q^{44} - 18 q^{46} - 8 q^{49} - 30 q^{50}+ \cdots + 20 q^{91}+O(q^{100}) \) 88 * q + 76 * q^4 + 3 * q^5 - 6 * q^10 + 12 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 + 6 * q^20 + q^25 + 12 * q^26 - 6 * q^29 - 12 * q^34 - 30 * q^40 - 6 * q^41 + 84 * q^44 - 18 * q^46 - 8 * q^49 - 30 * q^50 + 78 * q^56 + 12 * q^59 - 8 * q^64 + 15 * q^70 + 30 * q^74 - 48 * q^76 - 16 * q^79 + 69 * q^80 - 7 * q^85 + 12 * q^86 - 72 * q^89 + 20 * q^91

Introduction

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