LMFDB - Embedded newform 570.2.bi.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	570.47
Dual form			570.2.bi.a.473.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(-0.117004 - 1.72809i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.38333 + 1.75682i) q^{5} +(-0.895350 + 1.48268i) q^{6} +(3.58580 - 0.960813i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.97262 + 0.404389i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.117004 - 1.72809i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.38333 + 1.75682i) q^{5} +(-0.895350 + 1.48268i) q^{6} +(3.58580 - 0.960813i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.97262 + 0.404389i) q^{9} +(-0.125487 - 2.23254i) q^{10} +(-0.985310 + 0.568869i) q^{11} +(1.58386 - 0.700991i) q^{12} +(-0.355267 + 0.0310819i) q^{13} +(-3.48842 - 1.26968i) q^{14} +(2.87409 - 2.59608i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(6.65708 + 4.66134i) q^{17} +(2.66698 + 1.37377i) q^{18} +(4.31033 + 0.648900i) q^{19} +(-1.17774 + 1.90077i) q^{20} +(-2.07993 - 6.08418i) q^{21} +(1.13341 + 0.0991604i) q^{22} +(-1.89325 - 0.882836i) q^{23} +(-1.69949 - 0.334246i) q^{24} +(-1.17281 + 4.86051i) q^{25} +(0.308846 + 0.178312i) q^{26} +(1.04663 + 5.08965i) q^{27} +(2.12929 + 3.04093i) q^{28} +(-0.296793 + 1.68320i) q^{29} +(-3.84336 + 0.478071i) q^{30} +(3.86929 - 6.70181i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.09835 + 1.63615i) q^{33} +(-2.77953 - 7.63668i) q^{34} +(6.64831 + 4.97048i) q^{35} +(-1.39670 - 2.65504i) q^{36} +(-1.54472 - 1.54472i) q^{37} +(-3.15862 - 3.00385i) q^{38} +(0.0952803 + 0.610299i) q^{39} +(2.05499 - 0.881494i) q^{40} +(-5.26338 - 6.27265i) q^{41} +(-1.78597 + 6.17687i) q^{42} +(6.10707 - 2.84777i) q^{43} +(-0.871558 - 0.731324i) q^{44} +(-4.82255 - 4.66295i) q^{45} +(1.04448 + 1.80910i) q^{46} +(-3.94092 - 5.62822i) q^{47} +(1.20043 + 1.24859i) q^{48} +(5.87264 - 3.39057i) q^{49} +(3.74858 - 3.30880i) q^{50} +(7.27632 - 12.0495i) q^{51} +(-0.150716 - 0.323212i) q^{52} +(-0.545961 - 0.254586i) q^{53} +(2.06195 - 4.76952i) q^{54} +(-2.36241 - 0.944077i) q^{55} -3.71230i q^{56} +(0.617032 - 7.52458i) q^{57} +(1.20856 - 1.20856i) q^{58} +(-0.869469 - 4.93100i) q^{59} +(3.42251 + 1.81285i) q^{60} +(-4.37353 + 1.59184i) q^{61} +(-7.01354 + 3.27047i) q^{62} +(-10.2707 + 4.30619i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.546056 - 0.581143i) q^{65} +(0.0387447 - 1.97024i) q^{66} +(-12.4111 + 8.69035i) q^{67} +(-2.10337 + 7.84988i) q^{68} +(-1.30411 + 3.37501i) q^{69} +(-2.59503 - 7.88489i) q^{70} +(1.54985 - 4.25818i) q^{71} +(-0.378761 + 2.97599i) q^{72} +(-0.138143 + 1.57899i) q^{73} +(0.379344 + 2.15137i) q^{74} +(8.53664 + 1.45802i) q^{75} +(0.864453 + 4.27232i) q^{76} +(-2.98655 + 2.98655i) q^{77} +(0.272004 - 0.554578i) q^{78} +(5.07293 + 6.04568i) q^{79} +(-2.18895 - 0.456614i) q^{80} +(8.67294 - 2.40419i) q^{81} +(0.713663 + 8.15720i) q^{82} +(7.42853 - 1.99047i) q^{83} +(5.00589 - 4.03541i) q^{84} +(1.01981 + 18.1434i) q^{85} +(-6.63603 - 1.17011i) q^{86} +(2.94345 + 0.315945i) q^{87} +(0.294468 + 1.09897i) q^{88} +(-9.90948 - 8.31504i) q^{89} +(1.27584 + 6.58576i) q^{90} +(-1.24405 + 0.452799i) q^{91} +(0.182066 - 2.08102i) q^{92} +(-12.0341 - 5.90236i) q^{93} +6.87079i q^{94} +(4.82260 + 8.47010i) q^{95} +(-0.267173 - 1.71132i) q^{96} +(7.12433 - 10.1746i) q^{97} +(-6.75533 - 0.591015i) q^{98} +(2.69891 - 2.08948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	−0.117004	−	1.72809i	−0.0675525	−	0.997716i
$3$	−0.117004	−	1.72809i	−0.0675525	−	0.997716i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	1.38333	+	1.75682i	0.618643	+	0.785672i
$5$	1.38333	+	1.75682i	0.618643	+	0.785672i
$6$	−0.895350	+	1.48268i	−0.365525	+	0.605303i
$7$	3.58580	−	0.960813i	1.35531	−	0.363153i	0.493215	−	0.869907i	$-0.335822\pi$
$7$	3.58580	−	0.960813i	1.35531	−	0.363153i	0.862091	+	0.506754i	$0.169155\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	−2.97262	+	0.404389i	−0.990873	+	0.134796i
$10$	−0.125487	−	2.23254i	−0.0396825	−	0.705992i
$11$	−0.985310	+	0.568869i	−0.297082	+	0.171521i	−0.641131	−	0.767431i	$-0.721535\pi$
$11$	−0.985310	+	0.568869i	−0.297082	+	0.171521i	0.344049	+	0.938952i	$0.388201\pi$
$12$	1.58386	−	0.700991i	0.457221	−	0.202359i
$13$	−0.355267	+	0.0310819i	−0.0985335	+	0.00862056i	−0.136316	−	0.990665i	$-0.543526\pi$
$13$	−0.355267	+	0.0310819i	−0.0985335	+	0.00862056i	0.0377824	+	0.999286i	$0.487971\pi$
$14$	−3.48842	−	1.26968i	−0.932319	−	0.339336i
$15$	2.87409	−	2.59608i	0.742087	−	0.670304i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	6.65708	+	4.66134i	1.61458	+	1.13054i	0.904551	+	0.426366i	$0.140206\pi$
$17$	6.65708	+	4.66134i	1.61458	+	1.13054i	0.710028	+	0.704174i	$0.248682\pi$
$18$	2.66698	+	1.37377i	0.628612	+	0.323800i
$19$	4.31033	+	0.648900i	0.988857	+	0.148868i
$19$	4.31033	+	0.648900i	0.988857	+	0.148868i
$20$	−1.17774	+	1.90077i	−0.263351	+	0.425025i
$21$	−2.07993	−	6.08418i	−0.453878	−	1.32768i
$22$	1.13341	+	0.0991604i	0.241644	+	0.0211411i
$23$	−1.89325	−	0.882836i	−0.394769	−	0.184084i	0.215089	−	0.976594i	$-0.430996\pi$
$23$	−1.89325	−	0.882836i	−0.394769	−	0.184084i	−0.609858	+	0.792510i	$0.708774\pi$
$24$	−1.69949	−	0.334246i	−0.346908	−	0.0682277i
$25$	−1.17281	+	4.86051i	−0.234562	+	0.972101i
$26$	0.308846	+	0.178312i	0.0605697	+	0.0349699i
$27$	1.04663	+	5.08965i	0.201425	+	0.979504i
$28$	2.12929	+	3.04093i	0.402397	+	0.574683i
$29$	−0.296793	+	1.68320i	−0.0551130	+	0.312562i	−0.999885	−	0.0151669i	$-0.995172\pi$
$29$	−0.296793	+	1.68320i	−0.0551130	+	0.312562i	0.944772	+	0.327729i	$0.106283\pi$
$30$	−3.84336	+	0.478071i	−0.701699	+	0.0872834i
$31$	3.86929	−	6.70181i	0.694945	−	1.20368i	−0.275254	−	0.961372i	$-0.588762\pi$
$31$	3.86929	−	6.70181i	0.694945	−	1.20368i	0.970199	−	0.242309i	$-0.0779048\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	1.09835	+	1.63615i	0.191197	+	0.284817i
$34$	−2.77953	−	7.63668i	−0.476685	−	1.30968i
$35$	6.64831	+	4.97048i	1.12377	+	0.840164i
$36$	−1.39670	−	2.65504i	−0.232783	−	0.442507i
$37$	−1.54472	−	1.54472i	−0.253950	−	0.253950i	0.568638	−	0.822588i	$-0.307470\pi$
$37$	−1.54472	−	1.54472i	−0.253950	−	0.253950i	−0.822588	+	0.568638i	$0.807470\pi$
$38$	−3.15862	−	3.00385i	−0.512396	−	0.487289i
$39$	0.0952803	+	0.610299i	0.0152571	+	0.0977261i
$40$	2.05499	−	0.881494i	0.324922	−	0.139376i
$41$	−5.26338	−	6.27265i	−0.822001	−	0.979623i	0.177989	−	0.984032i	$-0.443041\pi$
$41$	−5.26338	−	6.27265i	−0.822001	−	0.979623i	−0.999990	+	0.00440949i	$0.998596\pi$
$42$	−1.78597	+	6.17687i	−0.275581	+	0.953112i
$43$	6.10707	−	2.84777i	0.931319	−	0.434281i	0.103091	−	0.994672i	$-0.467127\pi$
$43$	6.10707	−	2.84777i	0.931319	−	0.434281i	0.828228	+	0.560391i	$0.189349\pi$
$44$	−0.871558	−	0.731324i	−0.131392	−	0.110251i
$45$	−4.82255	−	4.66295i	−0.718903	−	0.695111i
$46$	1.04448	+	1.80910i	0.154001	+	0.266737i
$47$	−3.94092	−	5.62822i	−0.574842	−	0.820960i	0.421463	−	0.906846i	$-0.361517\pi$
$47$	−3.94092	−	5.62822i	−0.574842	−	0.820960i	−0.996305	+	0.0858858i	$0.972628\pi$
$48$	1.20043	+	1.24859i	0.173267	+	0.180218i
$49$	5.87264	−	3.39057i	0.838948	−	0.484367i
$50$	3.74858	−	3.30880i	0.530129	−	0.467935i
$51$	7.27632	−	12.0495i	1.01889	−	1.68726i
$52$	−0.150716	−	0.323212i	−0.0209006	−	0.0448214i
$53$	−0.545961	−	0.254586i	−0.0749935	−	0.0349700i	0.384760	−	0.923017i	$-0.374284\pi$
$53$	−0.545961	−	0.254586i	−0.0749935	−	0.0349700i	−0.459753	+	0.888047i	$0.652062\pi$
$54$	2.06195	−	4.76952i	0.280596	−	0.649050i
$55$	−2.36241	−	0.944077i	−0.318547	−	0.127299i
$56$		−	3.71230i		−	0.496076i
$57$	0.617032	−	7.52458i	0.0817280	−	0.996655i
$58$	1.20856	−	1.20856i	0.158692	−	0.158692i
$59$	−0.869469	−	4.93100i	−0.113195	−	0.641962i	−0.987628	−	0.156815i	$-0.949877\pi$
$59$	−0.869469	−	4.93100i	−0.113195	−	0.641962i	0.874433	−	0.485147i	$-0.161234\pi$
$60$	3.42251	+	1.81285i	0.441844	+	0.234038i
$61$	−4.37353	+	1.59184i	−0.559974	+	0.203814i	−0.606472	−	0.795105i	$-0.707416\pi$
$61$	−4.37353	+	1.59184i	−0.559974	+	0.203814i	0.0464986	+	0.998918i	$0.485194\pi$
$62$	−7.01354	+	3.27047i	−0.890720	+	0.415350i
$63$	−10.2707	+	4.30619i	−1.29398	+	0.542529i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−0.546056	−	0.581143i	−0.0677300	−	0.0720820i
$66$	0.0387447	−	1.97024i	0.00476915	−	0.242520i
$67$	−12.4111	+	8.69035i	−1.51626	+	1.06170i	−0.540895	+	0.841090i	$0.681914\pi$
$67$	−12.4111	+	8.69035i	−1.51626	+	1.06170i	−0.975363	+	0.220605i	$0.929197\pi$
$68$	−2.10337	+	7.84988i	−0.255071	+	0.951937i
$69$	−1.30411	+	3.37501i	−0.156996	+	0.406303i
$70$	−2.59503	−	7.88489i	−0.310165	−	0.942425i
$71$	1.54985	−	4.25818i	0.183933	−	0.505353i	−0.813117	−	0.582100i	$-0.802231\pi$
$71$	1.54985	−	4.25818i	0.183933	−	0.505353i	0.997051	+	0.0767471i	$0.0244534\pi$
$72$	−0.378761	+	2.97599i	−0.0446374	+	0.350724i
$73$	−0.138143	+	1.57899i	−0.0161685	+	0.184806i	0.983816	+	0.179183i	$0.0573455\pi$
$73$	−0.138143	+	1.57899i	−0.0161685	+	0.184806i	−0.999984	+	0.00562316i	$0.998210\pi$
$74$	0.379344	+	2.15137i	0.0440979	+	0.250092i
$75$	8.53664	+	1.45802i	0.985726	+	0.168358i
$76$	0.864453	+	4.27232i	0.0991595	+	0.490069i
$77$	−2.98655	+	2.98655i	−0.340349	+	0.340349i
$78$	0.272004	−	0.554578i	0.0307984	−	0.0627936i
$79$	5.07293	+	6.04568i	0.570749	+	0.680192i	0.971785	−	0.235870i	$-0.0757941\pi$
$79$	5.07293	+	6.04568i	0.570749	+	0.680192i	−0.401036	+	0.916062i	$0.631350\pi$
$80$	−2.18895	−	0.456614i	−0.244732	−	0.0510510i
$81$	8.67294	−	2.40419i	0.963660	−	0.267132i
$82$	0.713663	+	8.15720i	0.0788109	+	0.900812i
$83$	7.42853	−	1.99047i	0.815387	−	0.218482i	0.173058	−	0.984912i	$-0.444635\pi$
$83$	7.42853	−	1.99047i	0.815387	−	0.218482i	0.642329	+	0.766429i	$0.277968\pi$
$84$	5.00589	−	4.03541i	0.546187	−	0.440299i
$85$	1.01981	+	18.1434i	0.110614	+	1.96793i
$86$	−6.63603	−	1.17011i	−0.715582	−	0.126176i
$87$	2.94345	+	0.315945i	0.315571	+	0.0338728i
$88$	0.294468	+	1.09897i	0.0313904	+	0.117151i
$89$	−9.90948	−	8.31504i	−1.05040	−	0.881393i	−0.0572673	−	0.998359i	$-0.518239\pi$
$89$	−9.90948	−	8.31504i	−1.05040	−	0.881393i	−0.993136	+	0.116966i	$0.962683\pi$
$90$	1.27584	+	6.58576i	0.134486	+	0.694200i
$91$	−1.24405	+	0.452799i	−0.130412	+	0.0474662i
$92$	0.182066	−	2.08102i	0.0189816	−	0.216961i
$93$	−12.0341	−	5.90236i	−1.24788	−	0.612046i
$94$			6.87079i			0.708667i
$95$	4.82260	+	8.47010i	0.494788	+	0.869014i
$96$	−0.267173	−	1.71132i	−0.0272682	−	0.174661i
$97$	7.12433	−	10.1746i	0.723366	−	1.03307i	−0.274084	−	0.961706i	$-0.588375\pi$
$97$	7.12433	−	10.1746i	0.723366	−	1.03307i	0.997450	−	0.0713682i	$-0.0227365\pi$
$98$	−6.75533	−	0.591015i	−0.682392	−	0.0597015i
$99$	2.69891	−	2.08948i	0.271251	−	0.210001i
$100$	−4.96851	+	0.560311i	−0.496851	+	0.0560311i
$101$	4.10312	−	4.88991i	0.408275	−	0.486564i	−0.522249	−	0.852793i	$-0.674907\pi$
$101$	4.10312	−	4.88991i	0.408275	−	0.486564i	0.930525	+	0.366229i	$0.119351\pi$
$102$	−12.8717	+	5.69681i	−1.27449	+	0.564068i
$103$	15.8694	+	4.25219i	1.56366	+	0.418981i	0.933819	−	0.357745i	$-0.116454\pi$
$103$	15.8694	+	4.25219i	1.56366	+	0.418981i	0.629839	+	0.776726i	$0.283121\pi$
$104$	−0.0619272	+	0.351207i	−0.00607246	+	0.0344386i
$105$	7.81157	−	12.0705i	0.762331	−	1.17796i
$106$	0.301201	+	0.521695i	0.0292552	+	0.0506715i
$107$	4.43858	+	16.5650i	0.429094	+	1.60140i	0.754817	+	0.655936i	$0.227726\pi$
$107$	4.43858	+	16.5650i	0.429094	+	1.60140i	−0.325722	+	0.945465i	$0.605607\pi$
$108$	−4.42474	+	2.72428i	−0.425771	+	0.262144i
$109$	−4.14541	+	11.3894i	−0.397058	+	1.09091i	0.566652	+	0.823958i	$0.308239\pi$
$109$	−4.14541	+	11.3894i	−0.397058	+	1.09091i	−0.963710	+	0.266951i	$0.913984\pi$
$110$	1.39367	+	2.12836i	0.132881	+	0.202931i
$111$	−2.48868	+	2.85015i	−0.236215	+	0.270524i
$112$	−2.12929	+	3.04093i	−0.201199	+	0.287341i
$113$	−5.94915	−	5.94915i	−0.559649	−	0.559649i	0.369559	−	0.929207i	$-0.379509\pi$
$113$	−5.94915	−	5.94915i	−0.559649	−	0.559649i	−0.929207	+	0.369559i	$0.879509\pi$
$114$	−4.82136	+	5.80986i	−0.451562	+	0.544143i
$115$	−1.06800	−	4.54734i	−0.0995916	−	0.424042i
$116$	−1.68320	+	0.296793i	−0.156281	+	0.0275565i
$117$	1.04351	−	0.236061i	0.0964722	−	0.0218238i
$118$	−2.11608	+	4.53795i	−0.194801	+	0.417752i
$119$	28.3496	+	10.3184i	2.59881	+	0.945888i
$120$	−1.76375	−	3.44807i	−0.161007	−	0.314764i
$121$	−4.85278	+	8.40525i	−0.441161	+	0.764114i
$122$	4.49563	+	1.20460i	0.407015	+	0.109059i
$123$	−10.2239	+	9.82954i	−0.921857	+	0.886300i
$124$	7.62102	+	1.34379i	0.684388	+	0.120676i
$125$	−10.1614	+	4.66326i	−0.908863	+	0.417095i
$126$	10.8832	+	2.36360i	0.969551	+	0.210566i
$127$	0.760127	+	8.68829i	0.0674504	+	0.770961i	0.952316	+	0.305114i	$0.0986947\pi$
$127$	0.760127	+	8.68829i	0.0674504	+	0.770961i	−0.884865	+	0.465847i	$0.845750\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	−5.63577	−	10.2204i	−0.496202	−	0.899855i
$130$	0.113973	+	0.789250i	0.00999611	+	0.0692218i
$131$	−21.5416	+	3.79836i	−1.88210	+	0.331864i	−0.992236	−	0.124368i	$-0.960310\pi$
$131$	−21.5416	+	3.79836i	−1.88210	+	0.331864i	−0.889861	+	0.456233i	$0.849199\pi$
$132$	−1.16182	+	1.59170i	−0.101124	+	0.138540i
$133$	16.0795	−	1.81459i	1.39427	−	0.157345i
$134$	15.1512			1.30886
$135$	−7.49375	+	8.87940i	−0.644959	+	0.764217i
$136$	6.22548	−	5.22380i	0.533831	−	0.447937i
$137$	−3.96382	+	8.50044i	−0.338652	+	0.726242i	−0.999710	−	0.0240932i	$-0.992330\pi$
$137$	−3.96382	+	8.50044i	−0.338652	+	0.726242i	0.661058	+	0.750335i	$0.270108\pi$
$138$	3.00408	−	2.01664i	0.255725	−	0.171668i
$139$	1.94398	−	2.31674i	0.164886	−	0.196504i	−0.677274	−	0.735731i	$-0.736839\pi$
$139$	1.94398	−	2.31674i	0.164886	−	0.196504i	0.842161	+	0.539227i	$0.181283\pi$
$140$	−2.39686	+	7.94737i	−0.202572	+	0.671676i
$141$	−9.26499	+	7.46881i	−0.780253	+	0.628987i
$142$	−3.71195	+	2.59914i	−0.311500	+	0.218115i
$143$	0.332367	−	0.232726i	0.0277939	−	0.0194615i
$144$	2.01722	−	2.22054i	0.168102	−	0.185045i
$145$	−3.36763	+	1.80700i	−0.279666	+	0.150063i
$146$	1.01883	−	1.21419i	0.0843189	−	0.100487i
$147$	−6.54635	−	9.75176i	−0.539933	−	0.804311i
$148$	0.923234	−	1.97988i	0.0758894	−	0.162745i
$149$	10.2664	−	8.61450i	0.841053	−	0.705727i	−0.116747	−	0.993162i	$-0.537247\pi$
$149$	10.2664	−	8.61450i	0.841053	−	0.705727i	0.957800	+	0.287434i	$0.0928023\pi$
$150$	−6.15652	−	6.09076i	−0.502677	−	0.497308i
$151$	−22.1628			−1.80359			−0.901793	−	0.432167i	$-0.857749\pi$
$151$	−22.1628			−1.80359			−0.901793	+	0.432167i	$0.857749\pi$
$152$	1.74238	−	3.99551i	0.141326	−	0.324079i
$153$	−21.6740	−	11.1643i	−1.75224	−	0.902582i
$154$	4.15945	−	0.733424i	0.335178	−	0.0591010i
$155$	17.1264	−	2.47316i	1.37562	−	0.198649i
$156$	−0.540906	+	0.298269i	−0.0433071	+	0.0238806i
$157$	−1.78949	−	3.83756i	−0.142817	−	0.306271i	0.821868	−	0.569677i	$-0.192932\pi$
$157$	−1.78949	−	3.83756i	−0.142817	−	0.306271i	−0.964685	+	0.263406i	$0.915154\pi$
$158$	−0.687840	−	7.86204i	−0.0547216	−	0.625471i
$159$	−0.376068	+	0.973259i	−0.0298242	+	0.0771845i
$160$	1.53118	+	1.62957i	0.121050	+	0.128829i
$161$	−7.63705	−	1.34662i	−0.601884	−	0.106128i
$162$	−8.48344	−	3.00519i	−0.666522	−	0.236110i
$163$	−2.51081	−	0.672770i	−0.196662	−	0.0526954i	0.159144	−	0.987255i	$-0.449127\pi$
$163$	−2.51081	−	0.672770i	−0.196662	−	0.0526954i	−0.355805	+	0.934560i	$0.615793\pi$
$164$	4.09418	−	7.09133i	0.319702	−	0.553740i
$165$	−1.35504	+	4.19292i	−0.105490	+	0.326418i
$166$	−7.22678	−	2.63033i	−0.560907	−	0.204153i
$167$	−0.130978	+	0.280883i	−0.0101354	+	0.0217354i	−0.911310	−	0.411720i	$-0.864928\pi$
$167$	−0.130978	+	0.280883i	−0.0101354	+	0.0217354i	0.901175	+	0.433456i	$0.142706\pi$
$168$	−6.41520	+	0.434355i	−0.494943	+	0.0335112i
$169$	−12.6773	+	2.23534i	−0.975173	+	0.171949i
$170$	9.57126	−	15.4472i	0.734082	−	1.18474i
$171$	−13.0754	−	0.185882i	−0.999899	−	0.0142147i
$172$	4.76477	+	4.76477i	0.363310	+	0.363310i
$173$	−2.60082	+	3.71435i	−0.197737	+	0.282397i	−0.905759	−	0.423793i	$-0.860699\pi$
$173$	−2.60082	+	3.71435i	−0.197737	+	0.282397i	0.708023	+	0.706190i	$0.249587\pi$
$174$	−2.22991	−	1.94710i	−0.169049	−	0.147609i
$175$	0.464575	+	18.5557i	0.0351186	+	1.40268i
$176$	0.389129	−	1.06912i	0.0293317	−	0.0805883i
$177$	−8.41951	+	2.07947i	−0.632849	+	0.156303i
$178$	3.34806	+	12.4951i	0.250948	+	0.936550i
$179$	−0.792845	−	1.37325i	−0.0592600	−	0.102641i	0.834873	−	0.550442i	$-0.185541\pi$
$179$	−0.792845	−	1.37325i	−0.0592600	−	0.102641i	−0.894133	+	0.447801i	$0.852207\pi$
$180$	2.73233	−	6.12653i	0.203656	−	0.456645i
$181$	1.89493	−	10.7467i	0.140849	−	0.798794i	−0.829758	−	0.558123i	$-0.811522\pi$
$181$	1.89493	−	10.7467i	0.140849	−	0.798794i	0.970607	−	0.240670i	$-0.0773673\pi$
$182$	1.27878	+	0.342649i	0.0947898	+	0.0253989i
$183$	3.26257	+	7.37163i	0.241176	+	0.544926i
$184$	−1.34276	+	1.60024i	−0.0989898	+	0.117971i
$185$	0.576934	−	4.85063i	0.0424170	−	0.356625i
$186$	6.47229	+	11.7374i	0.474571	+	0.860628i
$187$	−9.21098	−	0.805856i	−0.673573	−	0.0589300i
$188$	3.94092	−	5.62822i	0.287421	−	0.410480i
$189$	8.64322	+	17.2449i	0.628702	+	1.25438i
$190$	0.907807	−	9.70443i	0.0658592	−	0.704033i
$191$			6.74756i			0.488236i	0.969745	+	0.244118i	$0.0784985\pi$
$191$			6.74756i			0.488236i	−0.969745	+	0.244118i	$0.921502\pi$
$192$	−0.762718	+	1.55508i	−0.0550445	+	0.112228i
$193$	0.592365	−	6.77077i	0.0426394	−	0.487371i	−0.944611	−	0.328193i	$-0.893560\pi$
$193$	0.592365	−	6.77077i	0.0426394	−	0.487371i	0.987250	−	0.159177i	$-0.0508842\pi$
$194$	−11.6718	+	4.24820i	−0.837988	+	0.305003i
$195$	−0.940380	+	1.01163i	−0.0673420	+	0.0724446i
$196$	5.19465	+	4.35883i	0.371047	+	0.311345i
$197$	3.75830	+	14.0262i	0.267768	+	0.999323i	0.960534	+	0.278161i	$0.0897250\pi$
$197$	3.75830	+	14.0262i	0.267768	+	0.999323i	−0.692766	+	0.721162i	$0.743608\pi$
$198$	−3.40929	+	0.163572i	−0.242288	+	0.0116246i
$199$	−21.3336	−	3.76170i	−1.51230	−	0.266660i	−0.644899	−	0.764268i	$-0.723101\pi$
$199$	−21.3336	−	3.76170i	−1.51230	−	0.266660i	−0.867402	+	0.497608i	$0.834212\pi$
$200$	4.39134	+	2.39084i	0.310515	+	0.169058i
$201$	16.4699	+	20.4308i	1.16170	+	1.44107i
$202$	−6.16581	+	1.65212i	−0.433825	+	0.116243i
$203$	0.552996	+	6.32077i	0.0388127	+	0.443631i
$204$	13.8114	+	2.71635i	0.966994	+	0.190182i
$205$	3.73892	−	17.9239i	0.261137	−	1.25186i
$206$	−10.5605	−	12.5855i	−0.735784	−	0.876874i
$207$	5.98491	+	1.85873i	0.415980	+	0.129190i
$208$	0.252172	−	0.252172i	0.0174850	−	0.0174850i
$209$	−4.61615	+	1.81265i	−0.319306	+	0.125383i
$210$	−13.3222	+	5.40702i	−0.919320	+	0.373120i
$211$	−1.43113	−	8.11634i	−0.0985231	−	0.558752i	−0.993611	−	0.112862i	$-0.963998\pi$
$211$	−1.43113	−	8.11634i	−0.0985231	−	0.558752i	0.895088	−	0.445890i	$-0.147113\pi$
$212$	0.0525027	−	0.600109i	0.00360590	−	0.0412156i
$213$	−7.53987	−	2.18006i	−0.516624	−	0.149375i
$214$	5.86543	−	16.1151i	0.400953	−	1.10161i
$215$	13.4511	+	6.78959i	0.917356	+	0.463046i
$216$	5.18712	+	0.306330i	0.352938	+	0.0208431i
$217$	7.43533	−	27.7490i	0.504743	−	1.88373i
$218$	9.92843	−	6.95196i	0.672438	−	0.470846i
$219$	2.74480	+	0.0539765i	0.185476	+	0.00364739i
$220$	0.0791518	−	2.54283i	0.00533642	−	0.171437i
$221$	−2.50993	−	1.44911i	−0.168836	−	0.0974774i
$222$	3.67338	−	0.907263i	0.246541	−	0.0608915i
$223$	−1.22781	+	0.572538i	−0.0822203	+	0.0383400i	−0.463293	−	0.886205i	$-0.653332\pi$
$223$	−1.22781	+	0.572538i	−0.0822203	+	0.0383400i	0.381073	+	0.924545i	$0.375555\pi$
$224$	3.48842	−	1.26968i	0.233080	−	0.0848340i
$225$	1.52078	−	14.9227i	0.101385	−	0.994847i
$226$	1.46097	+	8.28555i	0.0971820	+	0.551146i
$227$	−3.92467	+	3.92467i	−0.260490	+	0.260490i	−0.825253	−	0.564763i	$-0.808967\pi$
$227$	−3.92467	+	3.92467i	−0.260490	+	0.260490i	0.564763	+	0.825253i	$0.308967\pi$
$228$	7.28183	−	1.99374i	0.482251	−	0.132038i
$229$			8.08188i			0.534066i	0.963687	+	0.267033i	$0.0860432\pi$
$229$			8.08188i			0.534066i	−0.963687	+	0.267033i	$0.913957\pi$
$230$	−1.73339	+	4.33754i	−0.114296	+	0.286009i
$231$	5.51048	+	4.81160i	0.362563	+	0.316580i
$232$	1.54903	+	0.722323i	0.101699	+	0.0474228i
$233$	−7.39421	−	15.8569i	−0.484411	−	1.03882i	−0.984907	−	0.173084i	$-0.944627\pi$
$233$	−7.39421	−	15.8569i	−0.484411	−	1.03882i	0.500496	−	0.865739i	$-0.333151\pi$
$234$	−0.990189	−	0.405161i	−0.0647307	−	0.0264862i
$235$	4.43616	−	14.7091i	0.289383	−	0.959519i
$236$	4.33625	−	2.50354i	0.282266	−	0.162966i
$237$	9.85395	−	9.47387i	0.640083	−	0.615394i
$238$	−17.3043	−	24.7130i	−1.12167	−	1.60191i
$239$	−8.84835	−	15.3258i	−0.572352	−	0.991343i	−0.996324	−	0.0856676i	$-0.972698\pi$
$239$	−8.84835	−	15.3258i	−0.572352	−	0.991343i	0.423972	−	0.905676i	$-0.360636\pi$
$240$	−0.532955	+	3.83614i	−0.0344021	+	0.247622i
$241$	8.77067	+	7.35947i	0.564969	+	0.474065i	0.879972	−	0.475025i	$-0.157561\pi$
$241$	8.77067	+	7.35947i	0.564969	+	0.474065i	−0.315003	+	0.949091i	$0.602006\pi$
$242$	8.79622	−	4.10174i	0.565442	−	0.263670i
$243$	−5.16944	−	14.7064i	−0.331620	−	0.943413i
$244$	−2.99167	−	3.56534i	−0.191522	−	0.228247i
$245$	14.0804	+	5.62688i	0.899563	+	0.359488i
$246$	14.0129	−	2.18770i	0.893431	−	0.139483i
$247$	−1.55149	−	0.0965599i	−0.0987188	−	0.00614396i
$248$	−5.47201	−	5.47201i	−0.347473	−	0.347473i
$249$	−4.30889	−	12.6043i	−0.273065	−	0.798765i
$250$	10.9985	+	2.00842i	0.695604	+	0.127023i
$251$	7.87944	+	21.6486i	0.497346	+	1.36645i	0.893830	+	0.448405i	$0.148008\pi$
$251$	7.87944	+	21.6486i	0.497346	+	1.36645i	−0.396484	+	0.918041i	$0.629770\pi$
$252$	−7.55928	−	8.17848i	−0.476190	−	0.515196i
$253$	2.36765	−	0.207143i	0.148853	−	0.0130230i
$254$	4.36074	−	7.55302i	0.273617	−	0.473919i
$255$	31.2342	−	3.88518i	1.95596	−	0.243300i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	12.3202	+	17.5950i	0.768511	+	1.09755i	0.992415	+	0.122936i	$0.0392311\pi$
$257$	12.3202	+	17.5950i	0.768511	+	1.09755i	−0.223903	+	0.974611i	$0.571880\pi$
$258$	−1.24562	+	11.6046i	−0.0775488	+	0.722471i
$259$	−7.02323	−	4.05486i	−0.436402	−	0.251957i
$260$	0.359334	−	0.711888i	0.0222849	−	0.0441494i
$261$	0.201586	−	5.12352i	0.0124779	−	0.317138i
$262$	19.8245	+	9.24431i	1.22476	+	0.571115i
$263$	21.8091	+	1.90805i	1.34481	+	0.117655i	0.736710	−	0.676209i	$-0.236378\pi$
$263$	21.8091	+	1.90805i	1.34481	+	0.117655i	0.608095	+	0.793864i	$0.291934\pi$
$264$	1.86467	−	0.637454i	0.114763	−	0.0392326i
$265$	−0.307982	−	1.31133i	−0.0189192	−	0.0805543i
$266$	−14.2123	−	7.73637i	−0.871414	−	0.474347i
$267$	−13.2097	+	18.0974i	−0.808422	+	1.10754i
$268$	−12.4111	−	8.69035i	−0.758129	−	0.530848i
$269$	−11.4670	+	9.62194i	−0.699154	+	0.586660i	−0.921533	−	0.388300i	$-0.873062\pi$
$269$	−11.4670	+	9.62194i	−0.699154	+	0.586660i	0.222379	+	0.974960i	$0.428618\pi$
$270$	11.2315	−	2.97534i	0.683529	−	0.181073i
$271$	14.5152	+	5.28308i	0.881733	+	0.320924i	0.742909	−	0.669393i	$-0.233446\pi$
$271$	14.5152	+	5.28308i	0.881733	+	0.320924i	0.138824	+	0.990317i	$0.455668\pi$
$272$	−8.09587	+	0.708296i	−0.490884	+	0.0429468i
$273$	0.928039	+	2.09686i	0.0561675	+	0.126908i
$274$	8.12263	−	4.68960i	0.490706	−	0.283309i
$275$	−1.60941	−	5.45628i	−0.0970511	−	0.329026i
$276$	−3.61750	−	0.0711381i	−0.217748	−	0.00428201i
$277$	−0.805090	+	3.00464i	−0.0483732	+	0.180531i	−0.985886	−	0.167421i	$-0.946456\pi$
$277$	−0.805090	+	3.00464i	−0.0483732	+	0.180531i	0.937512	+	0.347952i	$0.113123\pi$
$278$	−2.92124	+	0.782745i	−0.175205	+	0.0469459i
$279$	−8.79180	+	21.4866i	−0.526351	+	1.28637i
$280$	6.52182	−	5.13532i	0.389753	−	0.306894i
$281$	0.416472	+	1.14425i	0.0248446	+	0.0682601i	0.951495	−	0.307664i	$-0.0995474\pi$
$281$	0.416472	+	1.14425i	0.0248446	+	0.0682601i	−0.926650	+	0.375925i	$0.877325\pi$
$282$	11.8734	−	0.803912i	0.707049	−	0.0478723i
$283$	−9.89528	−	6.92875i	−0.588213	−	0.411871i	0.241225	−	0.970469i	$-0.422451\pi$
$283$	−9.89528	−	6.92875i	−0.588213	−	0.411871i	−0.829439	+	0.558598i	$0.811340\pi$
$284$	4.53146			0.268893
$285$	14.0729	−	9.32494i	0.833604	−	0.552362i
$286$	−0.405745			−0.0239922
$287$	−24.9003	−	17.4354i	−1.46982	−	1.02918i
$288$	−2.92606	+	0.661931i	−0.172420	+	0.0390047i
$289$	16.7743	+	46.0870i	0.986722	+	2.71100i
$290$	3.79505	+	0.451384i	0.222853	+	0.0265062i
$291$	−18.4162	−	11.1210i	−1.07958	−	0.651927i
$292$	−1.53101	+	0.410233i	−0.0895955	+	0.0240071i
$293$	−3.68843	+	13.7654i	−0.215480	+	0.804184i	0.770517	+	0.637420i	$0.219998\pi$
$293$	−3.68843	+	13.7654i	−0.215480	+	0.804184i	−0.985997	+	0.166764i	$0.946668\pi$
$294$	−0.230926	+	11.7430i	−0.0134679	+	0.684866i
$295$	7.46011	−	8.34869i	0.434344	−	0.486080i
$296$	−1.89188	+	1.09228i	−0.109963	+	0.0634874i
$297$	−3.92660	−	4.41949i	−0.227845	−	0.256445i
$298$	−13.3508	+	1.16804i	−0.773390	+	0.0676629i
$299$	0.700049	+	0.254797i	0.0404849	+	0.0147353i
$300$	1.54961	+	8.52049i	0.0894666	+	0.491931i
$301$	19.1626	−	16.0793i	1.10451	−	0.926795i
$302$	18.1547	+	12.7121i	1.04469	+	0.731498i
$303$	−8.93030	−	6.51843i	−0.513032	−	0.374474i
$304$	−3.71901	+	2.27354i	−0.213300	+	0.130396i
$305$	−8.84660	−	5.48147i	−0.506555	−	0.313868i
$306$	11.3507	+	21.5770i	0.648874	+	1.23347i
$307$	24.9637	+	2.18404i	1.42475	+	0.124650i	0.773301	−	0.634039i	$-0.218604\pi$
$307$	24.9637	+	2.18404i	1.42475	+	0.124650i	0.651453	+	0.758689i	$0.274160\pi$
$308$	−3.82790	−	1.78498i	−0.218115	−	0.101709i
$309$	5.49140	−	27.9213i	0.312395	−	1.58839i
$310$	−15.4476	−	7.79738i	−0.877367	−	0.442861i
$311$	−18.8421	−	10.8785i	−1.06844	−	0.616862i	−0.140683	−	0.990055i	$-0.544930\pi$
$311$	−18.8421	−	10.8785i	−1.06844	−	0.616862i	−0.927754	+	0.373192i	$0.878263\pi$
$312$	0.614164	+	0.0659233i	0.0347702	+	0.00373217i
$313$	−8.52085	−	12.1690i	−0.481627	−	0.687835i	0.502645	−	0.864493i	$-0.332360\pi$
$313$	−8.52085	−	12.1690i	−0.481627	−	0.687835i	−0.984272	+	0.176658i	$0.943471\pi$
$314$	−0.735276	+	4.16996i	−0.0414940	+	0.235324i
$315$	−21.7729	−	12.0868i	−1.22676	−	0.681016i
$316$	−3.94604	+	6.83474i	−0.221982	+	0.384484i
$317$	−2.89035	+	0.252873i	−0.162338	+	0.0142028i	−0.168035	−	0.985781i	$-0.553742\pi$
$317$	−2.89035	+	0.252873i	−0.162338	+	0.0142028i	0.00569681	+	0.999984i	$0.498187\pi$
$318$	0.866296	−	0.581544i	0.0485795	−	0.0326113i
$319$	−0.665085	−	1.82731i	−0.0372376	−	0.102310i
$320$	−0.319589	−	2.21311i	−0.0178655	−	0.123717i
$321$	28.1066	−	9.60847i	1.56876	−	0.536293i
$322$	5.48352	+	5.48352i	0.305584	+	0.305584i
$323$	25.6694	+	24.4117i	1.42829	+	1.35830i
$324$	5.22552	+	7.32761i	0.290307	+	0.407090i
$325$	0.265587	−	1.76323i	0.0147321	−	0.0978066i
$326$	1.67085	+	1.99124i	0.0925399	+	0.110285i
$327$	20.1670	+	5.83105i	1.11524	+	0.322458i
$328$	−7.42117	+	3.46055i	−0.409766	+	0.191077i
$329$	−19.5390	−	16.3952i	−1.07722	−	0.903896i
$330$	3.51495	−	2.65742i	0.193491	−	0.146286i
$331$	−9.98458	−	17.2938i	−0.548802	−	0.950553i	−0.998357	−	0.0573006i	$-0.981751\pi$
$331$	−9.98458	−	17.2938i	−0.548802	−	0.950553i	0.449555	−	0.893253i	$-0.351583\pi$
$332$	4.41114	+	6.29975i	0.242092	+	0.345744i
$333$	5.21652	+	3.96719i	0.285863	+	0.217400i
$334$	0.268398	−	0.154960i	0.0146861	−	0.00847903i
$335$	−32.4360	−	9.78244i	−1.77217	−	0.534472i
$336$	5.50416	+	3.32380i	0.300276	+	0.181328i
$337$	−8.85599	−	18.9917i	−0.482416	−	1.03455i	−0.985401	−	0.170250i	$-0.945543\pi$
$337$	−8.85599	−	18.9917i	−0.482416	−	1.03455i	0.502985	−	0.864295i	$-0.332235\pi$
$338$	11.6667	+	5.44029i	0.634587	+	0.295913i
$339$	−9.58461	+	10.9768i	−0.520565	+	0.596176i
$340$	−16.7004	+	7.16372i	−0.905709	+	0.388507i
$341$			8.80449i			0.476790i
$342$	10.6041	+	7.65199i	0.573404	+	0.413772i
$343$	−0.574516	+	0.574516i	−0.0310210	+	0.0310210i
$344$	−1.17011	−	6.63603i	−0.0630882	−	0.357791i
$345$	−7.73327	+	2.37767i	−0.416345	+	0.128009i
$346$	4.26093	−	1.55085i	0.229069	−	0.0833743i
$347$	−14.2327	+	6.63684i	−0.764054	+	0.356284i	−0.765265	−	0.643715i	$-0.777392\pi$
$347$	−14.2327	+	6.63684i	−0.764054	+	0.356284i	0.00121152	+	0.999999i	$0.499614\pi$
$348$	0.709827	+	2.87399i	0.0380507	+	0.154062i
$349$	−14.2631	−	8.23481i	−0.763487	−	0.440799i	0.0670596	−	0.997749i	$-0.478638\pi$
$349$	−14.2631	−	8.23481i	−0.763487	−	0.440799i	−0.830546	+	0.556950i	$0.811972\pi$
$350$	10.2625	−	15.4664i	0.548555	−	0.826713i
$351$	−0.530030	−	1.77566i	−0.0282909	−	0.0947775i
$352$	−0.931981	+	0.652580i	−0.0496747	+	0.0347826i
$353$	4.70787	−	17.5700i	0.250575	−	0.935158i	−0.719924	−	0.694053i	$-0.755823\pi$
$353$	4.70787	−	17.5700i	0.250575	−	0.935158i	0.970499	−	0.241105i	$-0.0775099\pi$
$354$	8.08959	+	3.12583i	0.429957	+	0.166136i
$355$	9.62479	−	3.16765i	0.510831	−	0.168122i
$356$	4.42434	−	12.1558i	0.234490	−	0.644255i
$357$	14.5142	−	50.1981i	0.768171	−	2.65677i
$358$	−0.138202	+	1.57966i	−0.00730421	+	0.0834874i
$359$	−2.73445	−	15.5079i	−0.144319	−	0.818474i	−0.967911	−	0.251292i	$-0.919145\pi$
$359$	−2.73445	−	15.5079i	−0.144319	−	0.818474i	0.823592	−	0.567182i	$-0.191966\pi$
$360$	−5.75223	+	3.45136i	−0.303169	+	0.181903i
$361$	18.1579	+	5.59394i	0.955677	+	0.294418i
$362$	−7.71627	+	7.71627i	−0.405558	+	0.405558i
$363$	15.0929	+	7.40260i	0.792170	+	0.388536i
$364$	−0.850984	−	1.01416i	−0.0446037	−	0.0531566i
$365$	−2.96509	+	1.94156i	−0.155200	+	0.101626i
$366$	1.55565	−	7.90982i	0.0813154	−	0.413453i
$367$	−1.19845	−	13.6983i	−0.0625584	−	0.715045i	−0.961108	−	0.276173i	$-0.910934\pi$
$367$	−1.19845	−	13.6983i	−0.0625584	−	0.715045i	0.898550	−	0.438872i	$-0.144622\pi$
$368$	2.01779	−	0.540665i	0.105184	−	0.0281841i
$369$	18.1826	+	16.5177i	0.946549	+	0.859879i
$370$	−3.25480	+	3.64249i	−0.169209	+	0.189364i
$371$	−2.20232	−	0.388328i	−0.114339	−	0.0201610i
$372$	1.43051	−	13.3271i	0.0741682	−	0.690976i
$373$	−0.736322	−	2.74799i	−0.0381253	−	0.142286i	0.944240	−	0.329259i	$-0.106799\pi$
$373$	−0.736322	−	2.74799i	−0.0381253	−	0.142286i	−0.982365	+	0.186973i	$0.940132\pi$
$374$	7.08297	+	5.94332i	0.366252	+	0.307322i
$375$	9.24749	+	17.0142i	0.477538	+	0.878611i
$376$	−6.45643	+	2.34995i	−0.332965	+	0.121189i
$377$	0.0531240	−	0.607210i	0.00273602	−	0.0312729i
$378$	2.81114	−	19.0837i	0.144589	−	0.981560i
$379$		−	10.4276i		−	0.535628i	−0.963471	−	0.267814i	$-0.913699\pi$
$379$		−	10.4276i		−	0.535628i	0.963471	−	0.267814i	$-0.0863012\pi$
$380$	−6.30986	+	7.42870i	−0.323689	+	0.381084i
$381$	14.9252	−	2.33014i	0.764644	−	0.119377i
$382$	3.87024	−	5.52728i	0.198019	−	0.282800i
$383$	10.2282	+	0.894851i	0.522636	+	0.0457247i	0.345422	−	0.938448i	$-0.387736\pi$
$383$	10.2282	+	0.894851i	0.522636	+	0.0457247i	0.177214	+	0.984172i	$0.443291\pi$
$384$	1.51674	−	0.836366i	0.0774007	−	0.0426806i
$385$	−9.37820	−	1.11544i	−0.477957	−	0.0568483i
$386$	−4.36879	+	5.20652i	−0.222366	+	0.265005i
$387$	−17.0024	+	10.9350i	−0.864279	+	0.555856i
$388$	11.9977	+	3.21476i	0.609089	+	0.163205i
$389$	−1.52051	+	8.62326i	−0.0770931	+	0.437217i	0.921691	+	0.387924i	$0.126808\pi$
$389$	−1.52051	+	8.62326i	−0.0770931	+	0.437217i	−0.998784	+	0.0492926i	$0.984303\pi$
$390$	1.35056	−	0.289302i	0.0683884	−	0.0146494i
$391$	−8.48830	−	14.7022i	−0.429272	−	0.743521i
$392$	−1.75509	−	6.55007i	−0.0886453	−	0.330829i
$393$	9.08439	+	36.7815i	0.458247	+	1.85538i
$394$	4.96646	−	13.6452i	0.250207	−	0.687437i
$395$	−3.60363	+	17.2754i	−0.181318	+	0.869218i
$396$	2.88655	+	1.82150i	0.145055	+	0.0915338i
$397$	−18.5755	+	26.5286i	−0.932279	+	1.33143i	0.0111774	+	0.999938i	$0.496442\pi$
$397$	−18.5755	+	26.5286i	−0.932279	+	1.33143i	−0.943457	+	0.331495i	$0.892447\pi$
$398$	15.3179	+	15.3179i	0.767815	+	0.767815i
$399$	−5.01715	−	27.5745i	−0.251172	−	1.38045i
$400$	−2.22585	−	4.47723i	−0.111292	−	0.223862i
$401$	−11.6779	+	2.05913i	−0.583166	+	0.102828i	−0.457445	−	0.889238i	$-0.651235\pi$
$401$	−11.6779	+	2.05913i	−0.583166	+	0.102828i	−0.125721	+	0.992066i	$0.540124\pi$
$402$	−1.77275	−	26.1826i	−0.0884169	−	1.30587i
$403$	−1.16633	+	2.50120i	−0.0580990	+	0.124594i
$404$	5.99836	+	2.18322i	0.298429	+	0.108619i
$405$	16.2212	+	11.9110i	0.806040	+	0.591861i
$406$	3.17246	−	5.49486i	0.157446	−	0.272705i
$407$	2.40076	+	0.643283i	0.119002	+	0.0318864i
$408$	−9.75563	−	10.1470i	−0.482976	−	0.502352i
$409$	−28.6970	−	5.06005i	−1.41897	−	0.250203i	−0.589058	−	0.808091i	$-0.700501\pi$
$409$	−28.6970	−	5.06005i	−1.41897	−	0.250203i	−0.829917	+	0.557887i	$0.811612\pi$
$410$	−13.3435	+	12.5379i	−0.658987	+	0.619201i
$411$	15.1534	+	5.85527i	0.747460	+	0.288819i
$412$	1.43190	+	16.3667i	0.0705447	+	0.806329i
$413$	−7.85551	−	16.8462i	−0.386545	−	0.828948i
$414$	−3.83643	−	4.95539i	−0.188550	−	0.243544i
$415$	13.7730	+	10.2971i	0.676089	+	0.505464i
$416$	−0.351207	+	0.0619272i	−0.0172193	+	0.00303623i
$417$	−4.23101	−	3.08831i	−0.207193	−	0.151235i
$418$	4.82102	+	1.16288i	0.235804	+	0.0568785i
$419$	25.7944			1.26014			0.630070	−	0.776539i	$-0.283026\pi$
$419$	25.7944			1.26014			0.630070	+	0.776539i	$0.283026\pi$
$420$	14.0143	+	3.21213i	0.683825	+	0.156736i
$421$	−16.1849	+	13.5808i	−0.788805	+	0.661886i	−0.945449	−	0.325769i	$-0.894377\pi$
$421$	−16.1849	+	13.5808i	−0.788805	+	0.661886i	0.156644	+	0.987655i	$0.449932\pi$
$422$	−3.48303	+	7.46938i	−0.169551	+	0.363604i
$423$	13.9908	+	15.1369i	0.680258	+	0.735981i
$424$	−0.387216	+	0.461466i	−0.0188049	+	0.0224108i
$425$	−30.4639	+	26.8899i	−1.47772	+	1.30435i
$426$	4.92587	+	6.11050i	0.238659	+	0.296055i
$427$	−14.1532	+	9.91016i	−0.684920	+	0.479586i
$428$	−14.0479	+	9.83648i	−0.679033	+	0.475464i
$429$	−0.441061	−	0.547132i	−0.0212946	−	0.0264158i
$430$	−7.12413	−	13.2769i	−0.343556	−	0.640271i
$431$	22.0518	−	26.2803i	1.06220	−	1.26588i	0.0995733	−	0.995030i	$-0.468252\pi$
$431$	22.0518	−	26.2803i	1.06220	−	1.26588i	0.962623	−	0.270846i	$-0.0873033\pi$
$432$	−4.07333	−	3.22614i	−0.195978	−	0.155218i
$433$	2.47491	−	5.30746i	0.118936	−	0.255060i	−0.837822	−	0.545943i	$-0.816171\pi$
$433$	2.47491	−	5.30746i	0.118936	−	0.255060i	0.956759	+	0.290883i	$0.0939491\pi$
$434$	−22.0069	+	18.4659i	−1.05636	+	0.886394i
$435$	3.51669	+	5.60815i	0.168613	+	0.268890i
$436$	−12.1204			−0.580461
$437$	−7.58765	−	5.03384i	−0.362966	−	0.240801i
$438$	−2.21745	−	1.61857i	−0.105954	−	0.0773381i
$439$	16.6923	−	2.94331i	0.796681	−	0.140476i	0.239532	−	0.970889i	$-0.423006\pi$
$439$	16.6923	−	2.94331i	0.796681	−	0.140476i	0.557149	+	0.830412i	$0.311895\pi$
$440$	−1.52334	+	2.03756i	−0.0726226	+	0.0971370i
$441$	−16.0860	+	12.4537i	−0.766000	+	0.593033i
$442$	1.22484	+	2.62667i	0.0582596	+	0.124938i
$443$	−0.439341	−	5.02169i	−0.0208737	−	0.238588i	−0.999463	−	0.0327653i	$-0.989569\pi$
$443$	−0.439341	−	5.02169i	−0.0208737	−	0.238588i	0.978589	−	0.205822i	$-0.0659870\pi$
$444$	−3.52944	−	1.36378i	−0.167500	−	0.0647222i
$445$	0.899944	−	28.9116i	0.0426615	−	1.37054i
$446$	1.33416	+	0.235248i	0.0631742	+	0.0111393i
$447$	−16.0879	−	16.7333i	−0.760931	−	0.791458i
$448$	−3.58580	−	0.960813i	−0.169413	−	0.0453941i
$449$	7.25692	−	12.5693i	0.342475	−	0.593184i	−0.642417	−	0.766356i	$-0.722068\pi$
$449$	7.25692	−	12.5693i	0.342475	−	0.593184i	0.984892	+	0.173171i	$0.0554014\pi$
$450$	−9.80506	+	11.3517i	−0.462215	+	0.535124i
$451$	8.75438	+	3.18633i	0.412227	+	0.150039i
$452$	3.55564	−	7.62510i	0.167243	−	0.358654i
$453$	2.59315	+	38.2995i	0.121837	+	1.79947i
$454$	5.46600	−	0.963804i	0.256532	−	0.0452336i
$455$	−2.51642	−	1.55921i	−0.117972	−	0.0730968i
$456$	−7.10848	−	2.54351i	−0.332885	−	0.119111i
$457$	−10.1352	−	10.1352i	−0.474105	−	0.474105i	0.429135	−	0.903240i	$-0.358818\pi$
$457$	−10.1352	−	10.1352i	−0.474105	−	0.474105i	−0.903240	+	0.429135i	$0.858818\pi$
$458$	4.63558	−	6.62029i	0.216606	−	0.309346i
$459$	−16.7571	+	38.7609i	−0.782153	+	1.80920i
$460$	3.90782	−	2.55887i	0.182203	−	0.119308i
$461$	10.8409	−	29.7850i	0.504909	−	1.38723i	−0.381519	−	0.924361i	$-0.624599\pi$
$461$	10.8409	−	29.7850i	0.504909	−	1.38723i	0.886428	−	0.462866i	$-0.153179\pi$
$462$	−1.75410	−	7.10212i	−0.0816081	−	0.330420i
$463$	−7.69359	−	28.7129i	−0.357551	−	1.33440i	−0.877243	−	0.480046i	$-0.840620\pi$
$463$	−7.69359	−	28.7129i	−0.357551	−	1.33440i	0.519692	−	0.854354i	$-0.326047\pi$
$464$	−0.854581	−	1.48018i	−0.0396729	−	0.0687155i
$465$	−6.27772	−	29.3066i	−0.291122	−	1.35906i
$466$	−3.03818	+	17.2304i	−0.140741	+	0.798182i
$467$	25.9493	+	6.95310i	1.20079	+	0.321751i	0.803143	−	0.595787i	$-0.203160\pi$
$467$	25.9493	+	6.95310i	1.20079	+	0.321751i	0.397648	+	0.917538i	$0.369826\pi$
$468$	0.578725	+	0.899837i	0.0267516	+	0.0415950i
$469$	−36.1540	+	43.0866i	−1.66944	+	1.98956i
$470$	−12.0707	+	9.50455i	−0.556780	+	0.438412i
$471$	−6.42230	+	3.54141i	−0.295924	+	0.163180i
$472$	−4.98802	−	0.436395i	−0.229592	−	0.0200867i
$473$	−4.39735	+	6.28006i	−0.202190	+	0.288757i
$474$	−13.5059	+	2.10855i	−0.620345	+	0.0968487i
$475$	−8.20917	+	20.1893i	−0.376663	+	0.926350i
$476$			30.1690i			1.38280i
$477$	1.72589	+	0.536006i	0.0790229	+	0.0245420i
$478$	−1.54237	+	17.6294i	−0.0705463	+	0.806348i
$479$	−6.53515	+	2.37860i	−0.298599	+	0.108681i	−0.486975	−	0.873416i	$-0.661900\pi$
$479$	−6.53515	+	2.37860i	−0.298599	+	0.108681i	0.188376	+	0.982097i	$0.439678\pi$
$480$	2.63689	−	2.83669i	0.120357	−	0.129477i
$481$	0.596800	+	0.500774i	0.0272117	+	0.0228334i
$482$	−2.96330	−	11.0592i	−0.134975	−	0.503732i
$483$	−1.43351	+	13.3551i	−0.0652272	+	0.607678i
$484$	−9.55810	−	1.68535i	−0.434459	−	0.0766069i
$485$	27.7302	−	1.55866i	1.25916	−	0.0707752i
$486$	−4.20066	+	15.0118i	−0.190546	+	0.680950i
$487$	−11.7170	+	3.13955i	−0.530947	+	0.142267i	−0.514325	−	0.857595i	$-0.671958\pi$
$487$	−11.7170	+	3.13955i	−0.530947	+	0.142267i	−0.0166214	+	0.999862i	$0.505291\pi$
$488$	0.405642	+	4.63651i	0.0183625	+	0.209885i
$489$	−0.868834	+	4.41763i	−0.0392900	+	0.199772i
$490$	−8.30653	−	12.6854i	−0.375251	−	0.573070i
$491$	−5.96251	−	7.10584i	−0.269084	−	0.320682i	0.614534	−	0.788891i	$-0.289344\pi$
$491$	−5.96251	−	7.10584i	−0.269084	−	0.320682i	−0.883618	+	0.468208i	$0.844900\pi$
$492$	−12.7335	−	6.24541i	−0.574071	−	0.281565i
$493$	−9.82171	+	9.82171i	−0.442348	+	0.442348i
$494$	1.21552	+	0.968994i	0.0546889	+	0.0435971i
$495$	7.40431	+	1.85105i	0.332799	+	0.0831985i
$496$	1.34379	+	7.62102i	0.0603380	+	0.342194i
$497$	1.46614	−	16.7581i	0.0657656	−	0.751704i
$498$	−3.69990	+	12.7963i	−0.165796	+	0.573417i
$499$	−9.01014	+	24.7552i	−0.403349	+	1.10819i	0.557272	+	0.830330i	$0.311848\pi$
$499$	−9.01014	+	24.7552i	−0.403349	+	1.10819i	−0.960621	+	0.277863i	$0.910374\pi$
$500$	−7.85744	−	7.95366i	−0.351395	−	0.355698i
$501$	0.500717	+	0.193477i	0.0223704	+	0.00864394i
$502$	5.96266	−	22.2529i	0.266126	−	0.993198i
$503$	32.6618	−	22.8700i	1.45632	−	1.01972i	0.465422	−	0.885089i	$-0.345902\pi$
$503$	32.6618	−	22.8700i	1.45632	−	1.01972i	0.990895	−	0.134636i	$-0.0429865\pi$
$504$	1.50121	+	11.0352i	0.0668693	+	0.491549i
$505$	14.2666	+	0.444084i	0.634856	+	0.0197615i
$506$	−2.05828	−	1.18835i	−0.0915018	−	0.0528286i
$507$	5.34618	+	21.6459i	0.237432	+	0.961330i
$508$	−7.90435	+	3.68586i	−0.350699	+	0.163533i
$509$	−15.7038	+	5.71572i	−0.696059	+	0.253345i	−0.665727	−	0.746195i	$-0.731879\pi$
$509$	−15.7038	+	5.71572i	−0.696059	+	0.253345i	−0.0303320	+	0.999540i	$0.509656\pi$
$510$	−27.8140	−	14.7327i	−1.23163	−	0.652373i
$511$	1.02175	+	5.79466i	0.0451998	+	0.256341i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.20866	+	22.6172i	0.0533634	+	0.998575i
$514$		−	21.4796i		−	0.947423i
$515$	14.4823	+	33.7618i	0.638164	+	1.48772i
$516$	7.67647	−	8.79147i	0.337938	−	0.387023i
$517$	7.08475	+	3.30367i	0.311587	+	0.145295i
$518$	3.42732	+	7.34990i	0.150588	+	0.322936i
$519$	6.72306	+	4.05986i	0.295110	+	0.178208i
$520$	−0.702671	+	0.377039i	−0.0308142	+	0.0165343i
$521$	−32.9209	+	19.0069i	−1.44229	+	0.832707i	−0.998002	−	0.0631765i	$-0.979877\pi$
$521$	−32.9209	+	19.0069i	−1.44229	+	0.832707i	−0.444289	+	0.895884i	$0.646544\pi$
$522$	−3.10386	+	4.08132i	−0.135852	+	0.178634i
$523$	2.37611	+	3.39343i	0.103900	+	0.148384i	0.867735	−	0.497027i	$-0.165575\pi$
$523$	2.37611	+	3.39343i	0.103900	+	0.148384i	−0.763835	+	0.645411i	$0.776686\pi$
$524$	−10.9369	−	18.9433i	−0.477783	−	0.827544i
$525$	32.0116	−	2.97392i	1.39710	−	0.129793i
$526$	−16.7705	−	14.0722i	−0.731230	−	0.613575i
$527$	56.9976	−	26.5784i	2.48285	−	1.15777i
$528$	−1.89308	−	0.547360i	−0.0823856	−	0.0238208i
$529$	−11.9791	−	14.2762i	−0.520832	−	0.620703i
$530$	−0.499863	+	1.25083i	−0.0217127	+	0.0543325i
$531$	4.57865	+	14.3064i	0.198696	+	0.620845i
$532$	7.20466	+	14.4891i	0.312361	+	0.628183i
$533$	2.06487	+	2.06487i	0.0894395	+	0.0894395i
$534$	21.2010	−	7.24775i	0.917458	−	0.313641i
$535$	−22.9617	+	30.7126i	−0.992721	+	1.32782i
$536$	5.18200	+	14.2374i	0.223828	+	0.614964i
$537$	−2.28034	+	1.53079i	−0.0984038	+	0.0660584i
$538$	14.9121	−	1.30464i	0.642907	−	0.0562471i
$539$	−3.85758	+	6.68152i	−0.166158	+	0.287794i
$540$	−10.9069	−	4.00489i	−0.469359	−	0.172343i
$541$	−0.434002	+	2.46135i	−0.0186592	+	0.105822i	−0.992715	−	0.120487i	$-0.961555\pi$
$541$	−0.434002	+	2.46135i	−0.0186592	+	0.105822i	0.974056	+	0.226308i	$0.0726657\pi$
$542$	−8.85986	−	12.6532i	−0.380564	−	0.543501i
$543$	−18.7930	−	2.01721i	−0.806484	−	0.0865666i
$544$	7.03801	+	4.06340i	0.301752	+	0.174217i
$545$	−25.7436	+	8.47258i	−1.10273	+	0.362925i
$546$	0.442507	−	2.24995i	0.0189376	−	0.0962891i
$547$	−23.2651	−	10.8487i	−0.994743	−	0.463856i	−0.144079	−	0.989566i	$-0.546022\pi$
$547$	−23.2651	−	10.8487i	−0.994743	−	0.463856i	−0.850664	+	0.525710i	$0.823800\pi$
$548$	−9.34351	−	0.817451i	−0.399135	−	0.0349198i
$549$	12.3571	−	6.50053i	0.527390	−	0.277436i
$550$	−1.81124	+	5.39264i	−0.0772316	+	0.229943i
$551$	−2.37150	+	7.06254i	−0.101029	+	0.300874i
$552$	2.92248	+	2.13318i	0.124389	+	0.0907944i
$553$	23.9993	+	16.8045i	1.02055	+	0.714599i
$554$	2.38288	−	1.99947i	0.101239	−	0.0849495i
$555$	−8.44985	−	0.429451i	−0.358676	−	0.0182292i
$556$	2.84191	+	1.03437i	0.120524	+	0.0438671i
$557$	38.5480	−	3.37251i	1.63333	−	0.142898i	0.766753	−	0.641942i	$-0.221871\pi$
$557$	38.5480	−	3.37251i	1.63333	−	0.142898i	0.866576	+	0.499044i	$0.166316\pi$
$558$	19.5260	−	12.5581i	0.826603	−	0.531625i
$559$	−2.08113	+	1.20154i	−0.0880223	+	0.0508197i
$560$	−8.28786	+	0.465845i	−0.350226	+	0.0196856i
$561$	−0.314870	+	16.0117i	−0.0132938	+	0.676016i
$562$	0.315159	−	1.17619i	0.0132942	−	0.0496146i
$563$	−19.3384	+	5.18171i	−0.815017	+	0.218383i	−0.642167	−	0.766565i	$-0.721964\pi$
$563$	−19.3384	+	5.18171i	−0.815017	+	0.218383i	−0.172850	+	0.984948i	$0.555298\pi$
$564$	−10.1872	−	6.15176i	−0.428958	−	0.259036i
$565$	2.22194	−	18.6812i	0.0934777	−	0.785923i
$566$	4.13157	+	11.3514i	0.173663	+	0.477135i
$567$	28.7895	−	16.9540i	1.20904	−	0.712002i
$568$	−3.71195	−	2.59914i	−0.155750	−	0.109057i
$569$	−18.3540			−0.769440			−0.384720	−	0.923033i	$-0.625702\pi$
$569$	−18.3540			−0.769440			−0.384720	+	0.923033i	$0.625702\pi$
$570$	−16.8764	−	0.433315i	−0.706874	−	0.0181496i
$571$	−9.20521			−0.385226			−0.192613	−	0.981275i	$-0.561696\pi$
$571$	−9.20521			−0.385226			−0.192613	+	0.981275i	$0.561696\pi$
$572$	0.332367	+	0.232726i	0.0138970	+	0.00973076i
$573$	11.6604	−	0.789494i	0.487121	−	0.0329816i
$574$	10.3966	+	28.5644i	0.433945	+	1.19226i
$575$	6.51145	−	8.16674i	0.271546	−	0.340577i
$576$	2.77656	+	1.13610i	0.115690	+	0.0473374i
$577$	24.8637	−	6.66220i	1.03509	−	0.277351i	0.299012	−	0.954249i	$-0.403343\pi$
$577$	24.8637	−	6.66220i	1.03509	−	0.277351i	0.736077	+	0.676898i	$0.236676\pi$
$578$	12.6937	−	47.3736i	0.527989	−	1.97048i
$579$	−11.7698	−	0.231454i	−0.489138	−	0.00961889i
$580$	−2.84982	−	2.54650i	−0.118332	−	0.105738i
$581$	24.7248	−	14.2749i	1.02576	−	0.592221i
$582$	8.70694	+	19.6729i	0.360914	+	0.815470i
$583$	0.682767	−	0.0597344i	0.0282773	−	0.00247394i
$584$	1.48943	+	0.542108i	0.0616330	+	0.0224326i
$585$	1.85823	+	1.50670i	0.0768282	+	0.0622943i
$586$	10.9169	−	9.16036i	0.450973	−	0.378411i
$587$	−24.7430	−	17.3252i	−1.02125	−	0.715089i	−0.0621274	−	0.998068i	$-0.519789\pi$
$587$	−24.7430	−	17.3252i	−1.02125	−	0.715089i	−0.959126	+	0.282979i	$0.908677\pi$
$588$	6.92467	−	9.48685i	0.285569	−	0.391231i
$589$	21.0267	−	26.3762i	0.866391	−	1.08681i
$590$	−10.8996	+	2.55991i	−0.448728	+	0.105390i
$591$	23.7988	−	8.13582i	0.978952	−	0.334663i
$592$	2.17624	+	0.190397i	0.0894431	+	0.00782526i
$593$	−0.0896149	−	0.0417881i	−0.00368004	−	0.00171603i	0.420777	−	0.907164i	$-0.361757\pi$
$593$	−0.0896149	−	0.0417881i	−0.00368004	−	0.00171603i	−0.424457	+	0.905448i	$0.639535\pi$
$594$	0.681570	+	5.87244i	0.0279652	+	0.240949i
$595$	21.0893	+	64.0789i	0.864575	+	2.62698i
$596$	11.6063	+	6.70089i	0.475412	+	0.274479i
$597$	−4.00443	+	37.3067i	−0.163891	+	1.52686i
$598$	−0.427301	−	0.610249i	−0.0174736	−	0.0249550i
$599$	0.740792	−	4.20124i	0.0302679	−	0.171658i	−0.965927	−	0.258816i	$-0.916668\pi$
$599$	0.740792	−	4.20124i	0.0302679	−	0.171658i	0.996194	+	0.0871584i	$0.0277786\pi$
$600$	3.61779	−	7.86839i	0.147696	−	0.321226i
$601$	−5.47528	+	9.48346i	−0.223341	+	0.386839i	−0.955821	−	0.293951i	$-0.905030\pi$
$601$	−5.47528	+	9.48346i	−0.223341	+	0.386839i	0.732479	+	0.680789i	$0.238363\pi$
$602$	−24.9197	+	2.18020i	−1.01565	+	0.0888581i
$603$	33.3792	−	30.8520i	1.35931	−	1.25639i
$604$	−7.58014	−	20.8263i	−0.308432	−	0.847409i
$605$	−21.4795	+	3.10178i	−0.873265	+	0.126105i
$606$	3.57645	+	10.4618i	0.145284	+	0.424982i
$607$	26.5540	+	26.5540i	1.07779	+	1.07779i	0.996707	+	0.0810857i	$0.0258387\pi$
$607$	26.5540	+	26.5540i	1.07779	+	1.07779i	0.0810857	+	0.996707i	$0.474161\pi$
$608$	4.35048	+	0.270761i	0.176435	+	0.0109808i
$609$	10.8582	−	1.69519i	0.439996	−	0.0686924i
$610$	4.10267	+	9.56435i	0.166112	+	0.387249i
$611$	1.57502	+	1.87703i	0.0637183	+	0.0759366i
$612$	3.07811	−	24.1853i	0.124425	−	0.977632i
$613$	14.8246	−	6.91281i	0.598759	−	0.279206i	−0.0995156	−	0.995036i	$-0.531729\pi$
$613$	14.8246	−	6.91281i	0.598759	−	0.279206i	0.698274	+	0.715830i	$0.253952\pi$
$614$	−19.1964	−	16.1077i	−0.774702	−	0.650052i
$615$	−31.4117	−	4.36402i	−1.26664	−	0.175974i
$616$	2.11181	+	3.65776i	0.0850873	+	0.147375i
$617$	−19.0541	−	27.2121i	−0.767090	−	1.09552i	−0.992618	−	0.121281i	$-0.961300\pi$
$617$	−19.0541	−	27.2121i	−0.767090	−	1.09552i	0.225528	−	0.974237i	$-0.427589\pi$
$618$	−20.5133	+	19.7221i	−0.825167	+	0.793339i
$619$	26.4267	−	15.2575i	1.06218	−	0.613250i	0.136146	−	0.990689i	$-0.456528\pi$
$619$	26.4267	−	15.2575i	1.06218	−	0.613250i	0.926035	+	0.377439i	$0.123195\pi$
$620$	8.18157	+	15.2476i	0.328580	+	0.612360i
$621$	2.51179	−	10.5600i	0.100795	−	0.423757i
$622$	9.19489	+	19.7185i	0.368682	+	0.790640i
$623$	−43.5226	−	20.2949i	−1.74370	−	0.813100i
$624$	−0.465282	−	0.406271i	−0.0186262	−	0.0162639i
$625$	−22.2490	−	11.4009i	−0.889962	−	0.456036i
$626$			14.8557i			0.593751i
$627$	3.67253	+	7.76505i	0.146667	+	0.310106i
$628$	2.99409	−	2.99409i	0.119477	−	0.119477i
$629$	−3.08285	−	17.4837i	−0.122921	−	0.697122i
$630$	10.9026	+	22.3894i	0.434370	+	0.892014i
$631$	7.68644	−	2.79764i	0.305992	−	0.111372i	−0.184460	−	0.982840i	$-0.559054\pi$
$631$	7.68644	−	2.79764i	0.305992	−	0.111372i	0.490453	+	0.871468i	$0.336831\pi$
$632$	7.15265	−	3.33533i	0.284517	−	0.132673i
$633$	−13.8584	+	3.42278i	−0.550820	+	0.136043i
$634$	2.51268	+	1.45070i	0.0997912	+	0.0576145i
$635$	−14.2122	+	13.3542i	−0.563995	+	0.529944i
$636$	−1.04319	−	0.0205143i	−0.0413651	−	0.000813444i
$637$	−1.98097	+	1.38709i	−0.0784889	+	0.0549585i
$638$	−0.503294	+	1.87832i	−0.0199256	+	0.0743634i
$639$	−2.88515	+	13.2847i	−0.114135	+	0.525534i
$640$	−1.00760	+	1.99618i	−0.0398288	+	0.0789061i
$641$	−12.0247	+	33.0376i	−0.474948	+	1.30491i	0.438785	+	0.898592i	$0.355409\pi$
$641$	−12.0247	+	33.0376i	−0.474948	+	1.30491i	−0.913733	+	0.406316i	$0.866813\pi$
$642$	−28.5348	−	8.25048i	−1.12618	−	0.325620i
$643$	−2.48371	+	28.3889i	−0.0979478	+	1.11955i	0.775075	+	0.631869i	$0.217712\pi$
$643$	−2.48371	+	28.3889i	−0.0979478	+	1.11955i	−0.873023	+	0.487679i	$0.837844\pi$
$644$	−1.34662	−	7.63705i	−0.0530642	−	0.300942i
$645$	10.1592	−	24.0392i	0.400019	−	0.946541i
$646$	−7.02523	−	34.7203i	−0.276404	−	1.36605i
$647$	22.0191	−	22.0191i	0.865660	−	0.865660i	−0.126329	−	0.991988i	$-0.540319\pi$
$647$	22.0191	−	22.0191i	0.865660	−	0.865660i	0.991988	+	0.126329i	$0.0403195\pi$
$648$	−0.0775489	−	8.99967i	−0.00304641	−	0.353540i
$649$	3.66179	+	4.36395i	0.143738	+	0.171300i
$650$	−1.22891	+	1.29202i	−0.0482016	+	0.0506772i
$651$	−48.8229	−	9.60219i	−1.91352	−	0.376340i
$652$	−0.226551	−	2.58949i	−0.00887243	−	0.101412i
$653$	46.7275	−	12.5206i	1.82859	−	0.489969i	0.830807	−	0.556560i	$-0.187879\pi$
$653$	46.7275	−	12.5206i	1.82859	−	0.489969i	0.997780	+	0.0665913i	$0.0212124\pi$
$654$	−13.1753	−	16.3438i	−0.515195	−	0.639095i
$655$	−36.4721	−	32.5902i	−1.42508	−	1.27341i
$656$	8.06396	+	1.42189i	0.314845	+	0.0555156i
$657$	−0.227877	−	4.74959i	−0.00889034	−	0.185299i
$658$	6.60154	+	24.6373i	0.257355	+	0.960461i
$659$	3.29343	+	2.76351i	0.128294	+	0.107651i	0.704677	−	0.709528i	$-0.251092\pi$
$659$	3.29343	+	2.76351i	0.128294	+	0.107651i	−0.576383	+	0.817180i	$0.695536\pi$
$660$	−4.40351	+	0.160740i	−0.171406	+	0.00625681i
$661$	−16.1738	+	5.88679i	−0.629089	+	0.228970i	−0.636835	−	0.771000i	$-0.719757\pi$
$661$	−16.1738	+	5.88679i	−0.629089	+	0.228970i	0.00774562	+	0.999970i	$0.497534\pi$
$662$	−1.74043	+	19.8932i	−0.0676436	+	0.773170i
$663$	−2.21052	+	4.50694i	−0.0858495	+	0.175035i
$664$		−	7.69058i		−	0.298452i
$665$	25.4311	+	25.7385i	0.986174	+	0.998095i
$666$	−1.99764	−	6.24180i	−0.0774069	−	0.241865i
$667$	2.04789	−	2.92469i	0.0792945	−	0.113244i
$668$	−0.308741	−	0.0270113i	−0.0119455	−	0.00104510i
$669$	1.13306	+	2.05478i	0.0438066	+	0.0794425i
$670$	20.9590	+	26.6178i	0.809718	+	1.02834i
$671$	3.40374	−	4.05642i	0.131400	−	0.156596i
$672$	−2.60229	−	5.87975i	−0.100385	−	0.226816i
$673$	21.7836	+	5.83689i	0.839695	+	0.224996i	0.652939	−	0.757411i	$-0.273536\pi$
$673$	21.7836	+	5.83689i	0.839695	+	0.224996i	0.186756	+	0.982406i	$0.440203\pi$
$674$	−3.63881	+	20.6367i	−0.140162	+	0.794896i
$675$	−25.9658	−	0.882027i	−0.999424	−	0.0339492i
$676$	−6.43641	−	11.1482i	−0.247554	−	0.428776i
$677$	2.89285	+	10.7963i	0.111181	+	0.414934i	0.998973	−	0.0453116i	$-0.0144281\pi$
$677$	2.89285	+	10.7963i	0.111181	+	0.414934i	−0.887792	+	0.460245i	$0.847761\pi$
$678$	14.1473	−	3.49413i	0.543323	−	0.134191i
$679$	15.7706	−	43.3292i	0.605218	−	1.66282i
$680$	17.7891	+	3.71080i	0.682182	+	0.142303i
$681$	7.24141	+	6.32300i	0.277491	+	0.242298i
$682$	5.05005	−	7.21221i	0.193376	−	0.276170i
$683$	−5.94931	−	5.94931i	−0.227644	−	0.227644i	0.584064	−	0.811708i	$-0.301462\pi$
$683$	−5.94931	−	5.94931i	−0.227644	−	0.227644i	−0.811708	+	0.584064i	$0.801462\pi$
$684$	−4.29737	−	12.3504i	−0.164314	−	0.472230i
$685$	−20.4170	+	4.79519i	−0.780093	+	0.183215i
$686$	0.800145	−	0.141087i	0.0305497	−	0.00538673i
$687$	13.9663	−	0.945616i	0.532846	−	0.0360775i
$688$	−2.84777	+	6.10707i	−0.108570	+	0.232830i
$689$	0.201875	+	0.0734765i	0.00769083	+	0.00279923i
$690$	7.69850	+	2.48795i	0.293077	+	0.0947147i
$691$	−2.89809	+	5.01964i	−0.110249	+	0.190956i	−0.915870	−	0.401474i	$-0.868498\pi$
$691$	−2.89809	+	5.01964i	−0.110249	+	0.190956i	0.805622	+	0.592430i	$0.201831\pi$
$692$	−4.37988	−	1.17359i	−0.166498	−	0.0446131i
$693$	7.67015	−	10.0856i	0.291365	−	0.383121i
$694$	15.4655	+	2.72699i	0.587063	+	0.103515i
$695$	6.75926	+	0.210399i	0.256393	+	0.00798087i
$696$	1.06700	−	2.76138i	0.0404445	−	0.104670i
$697$	−5.79979	−	66.2919i	−0.219683	−	2.51098i
$698$	6.96036	+	14.9265i	0.263454	+	0.564978i
$699$	−26.5371	+	14.6332i	−1.00373	+	0.553479i
$700$	−17.2777	+	6.78297i	−0.653037	+	0.256372i
$701$	−33.6138	+	5.92702i	−1.26958	+	0.223860i	−0.767548	−	0.640991i	$-0.778523\pi$
$701$	−33.6138	+	5.92702i	−1.26958	+	0.223860i	−0.502027	+	0.864852i	$0.667412\pi$
$702$	−0.584299	+	1.75855i	−0.0220530	+	0.0663720i
$703$	−5.65586	−	7.66060i	−0.213315	−	0.288925i
$704$	1.13774			0.0428801
$705$	−25.9378	−	5.94507i	−0.976876	−	0.223904i
$706$	−13.9342	+	11.6922i	−0.524421	+	0.440042i
$707$	10.0147	−	21.4766i	0.376641	−	0.807709i
$708$	−4.83371	−	7.20053i	−0.181662	−	0.270612i
$709$	−24.7591	+	29.5068i	−0.929848	+	1.10815i	0.0640609	+	0.997946i	$0.479595\pi$
$709$	−24.7591	+	29.5068i	−0.929848	+	1.10815i	−0.993909	+	0.110204i	$0.964850\pi$
$710$	−9.70106	−	2.92576i	−0.364074	−	0.109802i
$711$	−17.5247	−	15.9201i	−0.657227	−	0.597049i
$712$	−10.5965	+	7.41973i	−0.397120	+	0.278066i
$713$	−13.2421	+	9.27224i	−0.495922	+	0.347248i
$714$	−40.6818	+	32.7949i	−1.52248	+	1.22732i
$715$	0.868630	+	0.261972i	0.0324849	+	0.00979719i
$716$	1.01926	−	1.21471i	0.0380916	−	0.0453958i
$717$	−25.4491	+	17.0840i	−0.950415	+	0.638013i
$718$	−6.65501	+	14.2717i	−0.248363	+	0.532616i
$719$	37.5155	−	31.4792i	1.39909	−	1.17398i	0.437589	−	0.899175i	$-0.355832\pi$
$719$	37.5155	−	31.4792i	1.39909	−	1.17398i	0.961501	−	0.274801i	$-0.0886120\pi$
$720$	6.69157	+	0.472151i	0.249380	+	0.0175960i
$721$	60.9901			2.27139
$722$	−11.6655	−	14.9972i	−0.434145	−	0.558138i
$723$	11.6917	−	16.0176i	0.434817	−	0.595703i
$724$	10.7467	−	1.89493i	0.399397	−	0.0704244i
$725$	−7.83310	−	3.41663i	−0.290914	−	0.126890i
$726$	−8.11740	−	14.7208i	−0.301265	−	0.546339i
$727$	−0.294012	−	0.630511i	−0.0109043	−	0.0233844i	0.900780	−	0.434275i	$-0.142995\pi$
$727$	−0.294012	−	0.630511i	−0.0109043	−	0.0233844i	−0.911685	+	0.410891i	$0.865218\pi$
$728$	0.115385	+	1.31886i	0.00427646	+	0.0488801i
$729$	−24.8091	+	10.6540i	−0.918856	+	0.394592i
$730$	3.54249	+	0.110269i	0.131113	+	0.00408123i
$731$	53.9296	+	9.50925i	1.99466	+	0.351712i
$732$	−5.81120	+	5.58705i	−0.214788	+	0.206503i
$733$	−30.5993	−	8.19905i	−1.13021	−	0.302839i	−0.355202	−	0.934790i	$-0.615588\pi$
$733$	−30.5993	−	8.19905i	−1.13021	−	0.302839i	−0.775009	+	0.631951i	$0.782255\pi$
$734$	−6.87531	+	11.9084i	−0.253772	+	0.439547i
$735$	8.07631	−	24.9906i	0.297899	−	0.921792i
$736$	−1.96299	−	0.714469i	−0.0723567	−	0.0263357i
$737$	7.28512	−	15.6230i	0.268351	−	0.575480i
$738$	−5.42013	−	23.9597i	−0.199518	−	0.881967i
$739$	30.4568	−	5.37036i	1.12037	−	0.197552i	0.417368	−	0.908738i	$-0.362953\pi$
$739$	30.4568	−	5.37036i	1.12037	−	0.197552i	0.703004	+	0.711186i	$0.251842\pi$
$740$	4.75542	−	1.11687i	0.174813	−	0.0410570i
$741$	0.0146664	+	2.69242i	0.000538785	+	0.0989084i
$742$	1.58130	+	1.58130i	0.0580512	+	0.0580512i
$743$	−15.2221	+	21.7394i	−0.558445	+	0.797543i	−0.994759	−	0.102252i	$-0.967395\pi$
$743$	−15.2221	+	21.7394i	−0.558445	+	0.797543i	0.436313	+	0.899795i	$0.356284\pi$
$744$	−8.81589	+	10.0964i	−0.323206	+	0.370152i
$745$	29.3358	+	6.11944i	1.07478	+	0.224199i
$746$	−0.973024	+	2.67336i	−0.0356249	+	0.0978787i
$747$	−21.2773	+	8.92092i	−0.778495	+	0.326400i
$748$	−2.39308	−	8.93111i	−0.0874998	−	0.326554i
$749$	31.8318	+	55.1342i	1.16311	+	2.01456i
$750$	2.18387	−	19.2414i	0.0797435	−	0.702596i
$751$	−6.39488	+	36.2672i	−0.233352	+	1.32341i	0.612703	+	0.790313i	$0.290082\pi$
$751$	−6.39488	+	36.2672i	−0.233352	+	1.32341i	−0.846056	+	0.533095i	$0.821029\pi$
$752$	6.63667	+	1.77829i	0.242014	+	0.0648476i
$753$	36.4889	−	16.1494i	1.32973	−	0.588517i
$754$	−0.391798	+	0.466926i	−0.0142684	+	0.0170045i
$755$	−30.6585	−	38.9361i	−1.11578	−	1.41703i
$756$	−13.2487	+	14.0201i	−0.481851	+	0.509905i
$757$	−45.7924	−	4.00632i	−1.66435	−	0.145612i	−0.784267	−	0.620424i	$-0.786961\pi$
$757$	−45.7924	−	4.00632i	−1.66435	−	0.145612i	−0.880088	+	0.474812i	$0.842516\pi$
$758$	−5.98100	+	8.54175i	−0.217240	+	0.310250i
$759$	−0.634988	−	4.06729i	−0.0230486	−	0.147633i
$760$	9.42967	−	2.46605i	0.342050	−	0.0894530i
$761$		−	0.785430i		−	0.0284718i	−0.999899	−	0.0142359i	$-0.995468\pi$
$761$		−	0.785430i		−	0.0284718i	0.999899	−	0.0142359i	$-0.00453158\pi$
$762$	−13.5626	−	6.65203i	−0.491320	−	0.240978i
$763$	−3.92152	+	44.8232i	−0.141969	+	1.62271i
$764$	−6.34063	+	2.30780i	−0.229396	+	0.0834933i
$765$	−10.3685	−	53.5211i	−0.374874	−	1.93506i
$766$	−7.86518	−	6.59967i	−0.284180	−	0.238456i
$767$	0.462159	+	1.72480i	0.0166876	+	0.0622789i
$768$	−1.72216	−	0.184854i	−0.0621430	−	0.00667033i
$769$	−9.52834	−	1.68010i	−0.343601	−	0.0605861i	−0.000814872	−	1.00000i	$-0.500259\pi$
$769$	−9.52834	−	1.68010i	−0.343601	−	0.0605861i	−0.342786	+	0.939414i	$0.611370\pi$
$770$	7.04238	+	6.29283i	0.253790	+	0.226778i
$771$	28.9644	−	23.3491i	1.04313	−	0.840898i
$772$	6.56504	−	1.75910i	0.236281	−	0.0633113i
$773$	3.70290	+	42.3243i	0.133184	+	1.52230i	0.709285	+	0.704922i	$0.249018\pi$
$773$	3.70290	+	42.3243i	0.133184	+	1.52230i	−0.576101	+	0.817379i	$0.695426\pi$
$774$	20.1996	+	0.794756i	0.726059	+	0.0285669i
$775$	28.0363	+	26.6667i	1.00709	+	0.957895i
$776$	−7.98400	−	9.51496i	−0.286609	−	0.341567i
$777$	−6.18543	+	12.6112i	−0.221901	+	0.452425i
$778$	6.19163	−	6.19163i	0.221981	−	0.221981i
$779$	−18.6166	−	30.4526i	−0.667007	−	1.09108i
$780$	−1.27225	−	0.537669i	−0.0455540	−	0.0192516i
$781$	0.895263	+	5.07729i	0.0320350	+	0.181680i
$782$	−1.47961	+	16.9120i	−0.0529107	+	0.604772i
$783$	−8.87751	+	0.251115i	−0.317256	+	0.00897412i
$784$	−2.31929	+	6.37218i	−0.0828316	+	0.227578i
$785$	4.26645	−	8.45241i	0.152276	−	0.301679i
$786$	13.6555	−	35.3402i	0.487075	−	1.26054i
$787$	7.13801	−	26.6394i	0.254442	−	0.949592i	−0.713957	−	0.700189i	$-0.753099\pi$
$787$	7.13801	−	26.6394i	0.254442	−	0.949592i	0.968400	−	0.249403i	$-0.0802344\pi$
$788$	−11.8949	+	8.32888i	−0.423737	+	0.296704i
$789$	0.745527	−	37.9114i	0.0265415	−	1.34968i
$790$	12.8607	−	12.0842i	0.457562	−	0.429936i
$791$	−27.0485	−	15.6164i	−0.961733	−	0.555257i
$792$	−1.31975	−	3.14774i	−0.0468954	−	0.111850i
$793$	1.50430	−	0.701465i	0.0534192	−	0.0249098i
$794$	30.4324	−	11.0765i	1.08000	−	0.393090i
$795$	−2.23006	+	0.685654i	−0.0790922	+	0.0243176i
$796$	−3.76170	−	21.3336i	−0.133330	−	0.756151i
$797$	1.32092	−	1.32092i	0.0467895	−	0.0467895i	−0.683325	−	0.730114i	$-0.739467\pi$
$797$	1.32092	−	1.32092i	0.0467895	−	0.0467895i	0.730114	+	0.683325i	$0.239467\pi$
$798$	−11.7063	+	25.4654i	−0.414397	+	0.901466i
$799$		−	55.8374i		−	1.97539i
$800$	−0.744725	+	4.94423i	−0.0263300	+	0.174805i
$801$	32.8196	+	20.7102i	1.15963	+	0.731758i
$802$	10.7470	+	5.01142i	0.379491	+	0.176960i
$803$	−0.762122	−	1.63438i	−0.0268947	−	0.0576759i
$804$	−13.5656	+	22.4644i	−0.478422	+	0.792257i
$805$	−8.19878	−	15.2797i	−0.288969	−	0.538539i
$806$	2.39003	−	1.37988i	0.0841852	−	0.0486044i
$807$	17.9693	+	18.6902i	0.632549	+	0.657927i
$808$	−3.66132	−	5.22891i	−0.128805	−	0.183952i
$809$	12.0019	+	20.7879i	0.421963	+	0.730862i	0.996131	−	0.0878755i	$-0.0280078\pi$
$809$	12.0019	+	20.7879i	0.421963	+	0.730862i	−0.574168	+	0.818737i	$0.694674\pi$
$810$	−6.45581	−	19.0610i	−0.226834	−	0.669736i
$811$	−17.9294	−	15.0445i	−0.629586	−	0.528285i	0.271214	−	0.962519i	$-0.412575\pi$
$811$	−17.9294	−	15.0445i	−0.629586	−	0.528285i	−0.900800	+	0.434234i	$0.857019\pi$
$812$	−5.75044	+	2.68148i	−0.201801	+	0.0941014i
$813$	7.43133	−	25.7017i	0.260628	−	0.901398i
$814$	−1.59762	−	1.90397i	−0.0559965	−	0.0667341i
$815$	−2.29134	−	5.34169i	−0.0802622	−	0.187111i
$816$	2.17125	+	13.9075i	0.0760091	+	0.486861i
$817$	28.1714	−	8.31196i	0.985592	−	0.290799i
$818$	20.6049	+	20.6049i	0.720432	+	0.720432i
$819$	3.51500	−	1.84908i	0.122824	−	0.0646121i
$820$	18.1218	−	2.61691i	0.632839	−	0.0913863i
$821$	12.3065	+	33.8118i	0.429500	+	1.18004i	0.946117	+	0.323824i	$0.104969\pi$
$821$	12.3065	+	33.8118i	0.429500	+	1.18004i	−0.516618	+	0.856216i	$0.672809\pi$
$822$	−9.05446	−	13.4880i	−0.315810	−	0.470447i
$823$	30.2689	−	2.64819i	1.05511	−	0.0923100i	0.453622	−	0.891194i	$-0.350131\pi$
$823$	30.2689	−	2.64819i	1.05511	−	0.0923100i	0.601485	+	0.798884i	$0.294576\pi$
$824$	8.21461	−	14.2281i	0.286169	−	0.495660i
$825$	−9.24066	+	3.41962i	−0.321719	+	0.119056i
$826$	−3.22773	+	18.3053i	−0.112307	+	0.636924i
$827$	−15.6930	−	22.4120i	−0.545700	−	0.779340i	0.447683	−	0.894192i	$-0.352249\pi$
$827$	−15.6930	−	22.4120i	−0.545700	−	0.779340i	−0.993383	+	0.114852i	$0.963361\pi$
$828$	0.300330	+	6.25970i	0.0104372	+	0.217540i
$829$	25.5504	+	14.7515i	0.887401	+	0.512341i	0.873092	−	0.487556i	$-0.162112\pi$
$829$	25.5504	+	14.7515i	0.887401	+	0.512341i	0.0143098	+	0.999898i	$0.495445\pi$
$830$	−5.37599	−	16.3347i	−0.186603	−	0.566987i
$831$	5.28649	+	1.03972i	0.183386	+	0.0360673i
$832$	0.323212	+	0.150716i	0.0112053	+	0.00522514i
$833$	54.8992	+	4.80305i	1.90214	+	0.166416i
$834$	1.69446	+	4.95660i	0.0586742	+	0.171633i
$835$	−0.674645	+	0.158449i	−0.0233470	+	0.00548335i
$836$	−3.28215	−	3.71780i	−0.113515	−	0.128583i
$837$	38.1596	+	12.6790i	1.31899	+	0.438251i
$838$	−21.1295	−	14.7951i	−0.729908	−	0.511087i
$839$	24.9330	−	20.9213i	0.860784	−	0.722284i	−0.101353	−	0.994851i	$-0.532317\pi$
$839$	24.9330	−	20.9213i	0.860784	−	0.722284i	0.962137	+	0.272567i	$0.0878726\pi$
$840$	−9.63740	−	10.6695i	−0.332522	−	0.368132i
$841$	24.5060	+	8.91946i	0.845035	+	0.307568i
$842$	21.0475	−	1.84142i	0.725345	−	0.0634595i
$843$	1.92864	−	0.853585i	0.0664258	−	0.0293990i
$844$	7.13739	−	4.12078i	0.245679	−	0.141843i
$845$	−21.4639	−	19.1794i	−0.738380	−	0.659791i
$846$	−2.77847	−	20.4242i	−0.0955258	−	0.702200i
$847$	−9.32522	+	34.8022i	−0.320418	+	1.19582i
$848$	0.581875	−	0.155913i	0.0199817	−	0.00535407i
$849$	−10.8157	+	17.9107i	−0.371195	+	0.614693i
$850$	40.3780	−	4.55353i	1.38495	−	0.156185i
$851$	1.56080	+	4.28826i	0.0535035	+	0.147000i
$852$	−0.530201	−	7.83079i	−0.0181644	−	0.268278i
$853$	−5.33410	−	3.73498i	−0.182636	−	0.127883i	0.478683	−	0.877988i	$-0.341114\pi$
$853$	−5.33410	−	3.73498i	−0.182636	−	0.127883i	−0.661319	+	0.750104i	$0.730003\pi$
$854$	17.2778			0.591235
$855$	−17.7610	−	23.2282i	−0.607412	−	0.794387i
$856$	17.1494			0.586154
$857$	14.4735	+	10.1345i	0.494406	+	0.346187i	0.794038	−	0.607868i	$-0.207975\pi$
$857$	14.4735	+	10.1345i	0.494406	+	0.346187i	−0.299632	+	0.954055i	$0.596864\pi$
$858$	0.0474740	+	0.701166i	0.00162074	+	0.0239374i
$859$	−0.563760	−	1.54892i	−0.0192352	−	0.0528484i	0.929703	−	0.368309i	$-0.120063\pi$
$859$	−0.563760	−	1.54892i	−0.0192352	−	0.0528484i	−0.948939	+	0.315461i	$0.897841\pi$
$860$	−1.77959	+	14.9621i	−0.0606835	+	0.510202i
$861$	−27.2165	+	45.0700i	−0.927536	+	1.53598i
$862$	−33.1375	+	8.87916i	−1.12867	+	0.302426i
$863$	8.72695	−	32.5694i	0.297069	−	1.10868i	−0.642492	−	0.766293i	$-0.722099\pi$
$863$	8.72695	−	32.5694i	0.297069	−	1.10868i	0.939560	−	0.342383i	$-0.111234\pi$
$864$	1.48624	+	4.97906i	0.0505630	+	0.169391i
$865$	−10.1232	+	0.569007i	−0.344200	+	0.0193468i
$866$	−5.07156	+	2.92807i	−0.172339	+	0.0994997i
$867$	77.6799	−	34.3799i	2.63815	−	1.16760i
$868$	28.6186	−	2.50380i	0.971378	−	0.0849846i
$869$	−8.43761	−	3.07104i	−0.286226	−	0.104178i
$870$	0.335996	−	6.61102i	0.0113913	−	0.224135i
$871$	4.13915	−	3.47316i	0.140250	−	0.117684i
$872$	9.92843	+	6.95196i	0.336219	+	0.235423i
$873$	−17.0634	+	33.1262i	−0.577510	+	1.12115i
$874$	3.32814	+	8.47557i	0.112576	+	0.286691i
$875$	−31.9562	+	26.4847i	−1.08032	+	0.895347i
$876$	0.888056	+	2.59773i	0.0300046	+	0.0877691i
$877$	56.4426	+	4.93809i	1.90593	+	0.166747i	0.978361	−	0.206904i	$-0.0663387\pi$
$877$	56.4426	+	4.93809i	1.90593	+	0.166747i	0.927569	+	0.373651i	$0.121894\pi$
$878$	−15.3618	−	7.16331i	−0.518434	−	0.241750i
$879$	24.2195	+	4.76334i	0.816903	+	0.160664i
$880$	2.41655	−	0.795320i	0.0814618	−	0.0268102i
$881$	−22.0886	−	12.7529i	−0.744184	−	0.429655i	0.0794047	−	0.996842i	$-0.474698\pi$
$881$	−22.0886	−	12.7529i	−0.744184	−	0.429655i	−0.823589	+	0.567188i	$0.808031\pi$
$882$	20.3200	−	0.974921i	0.684211	−	0.0328273i
$883$	−23.3250	−	33.3115i	−0.784947	−	1.12102i	−0.989833	−	0.142235i	$-0.954571\pi$
$883$	−23.3250	−	33.3115i	−0.784947	−	1.12102i	0.204885	−	0.978786i	$-0.434318\pi$
$884$	0.503269	−	2.85418i	0.0169268	−	0.0959965i
$885$	−15.3002	−	11.9149i	−0.514310	−	0.400516i
$886$	−2.52044	+	4.36553i	−0.0846758	+	0.146663i
$887$	−18.1818	+	1.59070i	−0.610484	+	0.0534104i	−0.388206	−	0.921573i	$-0.626905\pi$
$887$	−18.1818	+	1.59070i	−0.610484	+	0.0534104i	−0.222278	+	0.974983i	$0.571349\pi$
$888$	2.10892	+	3.14155i	0.0707707	+	0.105423i
$889$	11.0735	+	30.4242i	0.371393	+	1.02039i
$890$	−17.3202	+	23.1668i	−0.580574	+	0.776553i
$891$	−7.17787	+	7.30264i	−0.240468	+	0.244648i
$892$	−0.957946	−	0.957946i	−0.0320744	−	0.0320744i
$893$	−13.3345	−	26.8167i	−0.446222	−	0.897388i
$894$	3.58059	+	22.9348i	0.119753	+	0.767053i
$895$	1.31578	−	3.29254i	0.0439817	−	0.110057i
$896$	2.38622	+	2.84378i	0.0797179	+	0.0950041i
$897$	0.358405	−	1.23956i	0.0119668	−	0.0413878i
$898$	−13.1540	+	6.13381i	−0.438955	+	0.204688i
$899$	10.1321	+	8.50183i	0.337924	+	0.283552i
$900$	14.5429	−	3.67480i	0.484763	−	0.122493i
$901$	−2.44779	−	4.23970i	−0.0815478	−	0.141245i
$902$	−5.34356	−	7.63139i	−0.177921	−	0.254098i
$903$	−30.0286	−	31.2334i	−0.999290	−	1.03938i
$904$	−7.28619	+	4.20668i	−0.242335	+	0.139912i
$905$	21.5012	−	11.5371i	0.714725	−	0.383507i
$906$	19.8435	−	32.8605i	0.659256	−	1.09172i
$907$	−5.48634	−	11.7655i	−0.182171	−	0.390667i	0.793922	−	0.608019i	$-0.208036\pi$
$907$	−5.48634	−	11.7655i	−0.182171	−	0.390667i	−0.976093	+	0.217353i	$0.930258\pi$
$908$	−5.03030	−	2.34567i	−0.166936	−	0.0778437i
$909$	−10.2196	+	16.1951i	−0.338962	+	0.537157i
$910$	1.16701	+	2.72059i	0.0386859	+	0.0901866i
$911$		−	40.9461i		−	1.35661i	−0.734783	−	0.678303i	$-0.762716\pi$
$911$		−	40.9461i		−	1.35661i	0.734783	−	0.678303i	$-0.237284\pi$
$912$	4.36403	+	6.16078i	0.144508	+	0.204004i
$913$	−6.18709	+	6.18709i	−0.204763	+	0.204763i
$914$	2.48896	+	14.1156i	0.0823275	+	0.466903i
$915$	−8.43740	+	15.9291i	−0.278932	+	0.526600i
$916$	−7.59448	+	2.76417i	−0.250929	+	0.0913306i
$917$	−73.5943	+	34.3176i	−2.43030	+	1.13327i
$918$	35.9589	−	22.1396i	1.18682	−	0.730716i
$919$	25.7895	+	14.8896i	0.850716	+	0.491161i	0.860892	−	0.508787i	$-0.169906\pi$
$919$	25.7895	+	14.8896i	0.850716	+	0.491161i	−0.0101763	+	0.999948i	$0.503239\pi$
$920$	−4.66881	−	0.145328i	−0.153926	−	0.00479133i
$921$	0.853366	−	43.3952i	0.0281194	−	1.42992i
$922$	−25.9643	+	18.1804i	−0.855089	+	0.598740i
$923$	−0.418259	+	1.56096i	−0.0137672	+	0.0513798i
$924$	−2.63673	+	6.82382i	−0.0867421	+	0.224487i
$925$	9.31975	−	5.69644i	0.306432	−	0.187298i
$926$	−10.1668	+	27.9331i	−0.334102	+	0.917937i
$927$	−48.8932	−	6.22274i	−1.60586	−	0.204382i
$928$	−0.148963	+	1.70266i	−0.00488996	+	0.0558925i
$929$	8.55155	+	48.4982i	0.280567	+	1.59118i	0.720703	+	0.693244i	$0.243819\pi$
$929$	8.55155	+	48.4982i	0.280567	+	1.59118i	−0.440136	+	0.897931i	$0.645070\pi$
$930$	−11.6672	+	27.6073i	−0.382581	+	0.905279i
$931$	27.5131	−	10.8037i	0.901706	−	0.354077i
$932$	12.3717	−	12.3717i	0.405248	−	0.405248i
$933$	−16.5944	+	33.8337i	−0.543278	+	1.10767i
$934$	−17.2683	−	20.5796i	−0.565036	−	0.673384i
$935$	−11.3261	−	17.2968i	−0.370402	−	0.565665i
$936$	0.0420618	−	1.06905i	0.00137483	−	0.0349429i
$937$	1.06744	+	12.2009i	0.0348717	+	0.398585i	0.993492	+	0.113899i	$0.0363340\pi$
$937$	1.06744	+	12.2009i	0.0348717	+	0.398585i	−0.958621	+	0.284687i	$0.908110\pi$
$938$	54.3291	−	14.5574i	1.77391	−	0.475317i
$939$	−20.0323	+	16.1487i	−0.653728	+	0.526992i
$940$	15.3393	−	0.862195i	0.500314	−	0.0281217i
$941$	27.0055	+	4.76179i	0.880354	+	0.155230i	0.595514	−	0.803345i	$-0.296949\pi$
$941$	27.0055	+	4.76179i	0.880354	+	0.155230i	0.284840	+	0.958575i	$0.408060\pi$
$942$	7.29211	+	0.782723i	0.237590	+	0.0255025i
$943$	4.42716	+	16.5224i	0.144168	+	0.538042i
$944$	3.83564	+	3.21848i	0.124839	+	0.104753i
$945$	−18.3397	+	39.0399i	−0.596589	+	1.26997i
$946$	7.20419	−	2.62211i	0.234228	−	0.0852522i
$947$	−3.81431	+	43.5977i	−0.123948	+	1.41674i	0.638468	+	0.769649i	$0.279569\pi$
$947$	−3.81431	+	43.5977i	−0.123948	+	1.41674i	−0.762416	+	0.647087i	$0.775987\pi$
$948$	12.2728	+	6.01943i	0.398601	+	0.195502i
$949$		−	0.565256i		−	0.0183490i
$950$	18.3047	−	11.8296i	0.593883	−	0.383801i
$951$	0.775172	+	4.96521i	0.0251367	+	0.161008i
$952$	17.3043	−	24.7130i	0.560834	−	0.800954i
$953$	−59.6943	−	5.22258i	−1.93369	−	0.169176i	−0.945844	−	0.324621i	$-0.894763\pi$
$953$	−59.6943	−	5.22258i	−1.93369	−	0.169176i	−0.987845	+	0.155445i	$0.950319\pi$
$954$	−1.10632	−	1.42900i	−0.0358185	−	0.0462655i
$955$	−11.8542	+	9.33409i	−0.383594	+	0.302044i
$956$	11.3752	−	13.5565i	0.367901	−	0.438447i
$957$	−3.07994	+	1.36313i	−0.0995603	+	0.0440638i
$958$	6.71759	+	1.79997i	0.217036	+	0.0581545i
$959$	−6.04615	+	34.2894i	−0.195240	+	1.10726i
$960$	−3.78707	+	0.811223i	−0.122227	+	0.0261821i
$961$	−14.4428	−	25.0157i	−0.465898	−	0.806960i
$962$	−0.201637	−	0.752521i	−0.00650105	−	0.0242622i
$963$	−19.8929	−	47.4466i	−0.641041	−	1.52895i
$964$	−3.91589	+	10.7588i	−0.126122	+	0.346518i
$965$	12.7144	−	8.32551i	0.409292	−	0.268008i
$966$	8.83444	−	10.1176i	0.284243	−	0.325529i
$967$	−15.5136	+	22.1557i	−0.498884	+	0.712479i	−0.987075	−	0.160257i	$-0.948768\pi$
$967$	−15.5136	+	22.1557i	−0.498884	+	0.712479i	0.488192	+	0.872736i	$0.337657\pi$
$968$	6.86286	+	6.86286i	0.220581	+	0.220581i
$969$	39.1822	−	47.2155i	1.25871	−	1.51678i
$970$	−23.6093	−	14.6286i	−0.758047	−	0.469696i
$971$	−2.95310	+	0.520711i	−0.0947695	+	0.0167104i	−0.220832	−	0.975312i	$-0.570877\pi$
$971$	−2.95310	+	0.520711i	−0.0947695	+	0.0167104i	0.126062	+	0.992022i	$0.459766\pi$
$972$	12.0514	−	9.88756i	0.386549	−	0.317143i
$973$	4.74477	−	10.1752i	0.152110	−	0.326202i
$974$	11.3988	+	4.14881i	0.365240	+	0.132936i
$975$	−3.07811	−	0.252654i	−0.0985783	−	0.00809140i
$976$	2.32711	−	4.03067i	0.0744889	−	0.129019i
$977$	18.1792	+	4.87110i	0.581604	+	0.155840i	0.537613	−	0.843192i	$-0.319326\pi$
$977$	18.1792	+	4.87110i	0.581604	+	0.155840i	0.0439907	+	0.999032i	$0.485993\pi$
$978$	3.24556	−	3.12037i	0.103782	−	0.0997785i
$979$	14.4941	+	2.55570i	0.463233	+	0.0816805i
$980$	−0.471760	+	15.1557i	−0.0150698	+	0.484132i
$981$	7.71697	−	35.5328i	0.246384	−	1.13447i
$982$	0.808459	+	9.24072i	0.0257989	+	0.294883i
$983$	13.3845	+	28.7031i	0.426899	+	0.915488i	0.995667	+	0.0929897i	$0.0296424\pi$
$983$	13.3845	+	28.7031i	0.426899	+	0.915488i	−0.568768	+	0.822498i	$0.692580\pi$
$984$	6.84847	+	12.4196i	0.218321	+	0.395922i
$985$	−19.4425	+	26.0054i	−0.619488	+	0.828602i
$986$	13.6790	−	2.41197i	0.435627	−	0.0768129i
$987$	−26.0463	+	35.6836i	−0.829062	+	1.13582i
$988$	−0.439904	−	1.49095i	−0.0139952	−	0.0474334i
$989$	−14.0763			−0.447600
$990$	−5.00354	−	5.76323i	−0.159023	−	0.183167i
$991$	5.17980	−	4.34637i	0.164542	−	0.138067i	−0.556799	−	0.830647i	$-0.687971\pi$
$991$	5.17980	−	4.34637i	0.164542	−	0.138067i	0.721341	+	0.692580i	$0.243526\pi$
$992$	3.27047	−	7.01354i	0.103837	−	0.222680i
$993$	−28.7171	+	19.2777i	−0.911309	+	0.611761i
$994$	−10.8130	+	12.8865i	−0.342969	+	0.408735i
$995$	−22.9028	−	42.6829i	−0.726067	−	1.35314i
$996$	10.3704	−	8.35996i	0.328600	−	0.264895i
$997$	−4.36779	+	3.05836i	−0.138329	+	0.0968592i	−0.640693	−	0.767797i	$-0.721353\pi$
$997$	−4.36779	+	3.05836i	−0.138329	+	0.0968592i	0.502364	+	0.864656i	$0.332464\pi$
$998$	21.5796	−	15.1102i	0.683092	−	0.478306i
$999$	6.24531	−	9.47881i	0.197593	−	0.299896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.47.10	yes	480
3.2	odd	2	inner	570.2.bi.a.47.32	yes	480
5.3	odd	4	inner	570.2.bi.a.503.19	yes	480
15.8	even	4	inner	570.2.bi.a.503.39	yes	480
19.17	even	9	inner	570.2.bi.a.17.39	yes	480
57.17	odd	18	inner	570.2.bi.a.17.19	✓	480
95.93	odd	36	inner	570.2.bi.a.473.32	yes	480
285.188	even	36	inner	570.2.bi.a.473.10	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.19	✓	480	57.17	odd	18	inner
570.2.bi.a.17.39	yes	480	19.17	even	9	inner
570.2.bi.a.47.10	yes	480	1.1	even	1	trivial
570.2.bi.a.47.32	yes	480	3.2	odd	2	inner
570.2.bi.a.473.10	yes	480	285.188	even	36	inner
570.2.bi.a.473.32	yes	480	95.93	odd	36	inner
570.2.bi.a.503.19	yes	480	5.3	odd	4	inner
570.2.bi.a.503.39	yes	480	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.117004 - 1.72809i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.38333 + 1.75682i) q^{5} +(-0.895350 + 1.48268i) q^{6} +(3.58580 - 0.960813i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.97262 + 0.404389i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(-0.117004 - 1.72809i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.38333 + 1.75682i) q^{5} +(-0.895350 + 1.48268i) q^{6} +(3.58580 - 0.960813i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.97262 + 0.404389i) q^{9} +(-0.125487 - 2.23254i) q^{10} +(-0.985310 + 0.568869i) q^{11} +(1.58386 - 0.700991i) q^{12} +(-0.355267 + 0.0310819i) q^{13} +(-3.48842 - 1.26968i) q^{14} +(2.87409 - 2.59608i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(6.65708 + 4.66134i) q^{17} +(2.66698 + 1.37377i) q^{18} +(4.31033 + 0.648900i) q^{19} +(-1.17774 + 1.90077i) q^{20} +(-2.07993 - 6.08418i) q^{21} +(1.13341 + 0.0991604i) q^{22} +(-1.89325 - 0.882836i) q^{23} +(-1.69949 - 0.334246i) q^{24} +(-1.17281 + 4.86051i) q^{25} +(0.308846 + 0.178312i) q^{26} +(1.04663 + 5.08965i) q^{27} +(2.12929 + 3.04093i) q^{28} +(-0.296793 + 1.68320i) q^{29} +(-3.84336 + 0.478071i) q^{30} +(3.86929 - 6.70181i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.09835 + 1.63615i) q^{33} +(-2.77953 - 7.63668i) q^{34} +(6.64831 + 4.97048i) q^{35} +(-1.39670 - 2.65504i) q^{36} +(-1.54472 - 1.54472i) q^{37} +(-3.15862 - 3.00385i) q^{38} +(0.0952803 + 0.610299i) q^{39} +(2.05499 - 0.881494i) q^{40} +(-5.26338 - 6.27265i) q^{41} +(-1.78597 + 6.17687i) q^{42} +(6.10707 - 2.84777i) q^{43} +(-0.871558 - 0.731324i) q^{44} +(-4.82255 - 4.66295i) q^{45} +(1.04448 + 1.80910i) q^{46} +(-3.94092 - 5.62822i) q^{47} +(1.20043 + 1.24859i) q^{48} +(5.87264 - 3.39057i) q^{49} +(3.74858 - 3.30880i) q^{50} +(7.27632 - 12.0495i) q^{51} +(-0.150716 - 0.323212i) q^{52} +(-0.545961 - 0.254586i) q^{53} +(2.06195 - 4.76952i) q^{54} +(-2.36241 - 0.944077i) q^{55} -3.71230i q^{56} +(0.617032 - 7.52458i) q^{57} +(1.20856 - 1.20856i) q^{58} +(-0.869469 - 4.93100i) q^{59} +(3.42251 + 1.81285i) q^{60} +(-4.37353 + 1.59184i) q^{61} +(-7.01354 + 3.27047i) q^{62} +(-10.2707 + 4.30619i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.546056 - 0.581143i) q^{65} +(0.0387447 - 1.97024i) q^{66} +(-12.4111 + 8.69035i) q^{67} +(-2.10337 + 7.84988i) q^{68} +(-1.30411 + 3.37501i) q^{69} +(-2.59503 - 7.88489i) q^{70} +(1.54985 - 4.25818i) q^{71} +(-0.378761 + 2.97599i) q^{72} +(-0.138143 + 1.57899i) q^{73} +(0.379344 + 2.15137i) q^{74} +(8.53664 + 1.45802i) q^{75} +(0.864453 + 4.27232i) q^{76} +(-2.98655 + 2.98655i) q^{77} +(0.272004 - 0.554578i) q^{78} +(5.07293 + 6.04568i) q^{79} +(-2.18895 - 0.456614i) q^{80} +(8.67294 - 2.40419i) q^{81} +(0.713663 + 8.15720i) q^{82} +(7.42853 - 1.99047i) q^{83} +(5.00589 - 4.03541i) q^{84} +(1.01981 + 18.1434i) q^{85} +(-6.63603 - 1.17011i) q^{86} +(2.94345 + 0.315945i) q^{87} +(0.294468 + 1.09897i) q^{88} +(-9.90948 - 8.31504i) q^{89} +(1.27584 + 6.58576i) q^{90} +(-1.24405 + 0.452799i) q^{91} +(0.182066 - 2.08102i) q^{92} +(-12.0341 - 5.90236i) q^{93} +6.87079i q^{94} +(4.82260 + 8.47010i) q^{95} +(-0.267173 - 1.71132i) q^{96} +(7.12433 - 10.1746i) q^{97} +(-6.75533 - 0.591015i) q^{98} +(2.69891 - 2.08948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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