LMFDB - Embedded newform 845.2.v.a.389.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(64,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([13, 1]))

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

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

chi := DirichletCharacter("845.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.v (of order $26$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$1056$
Relative dimension:	$88$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			389.50
Character	$\chi$	$=$	845.389
Dual form			845.2.v.a.454.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258334 + 0.228864i) q^{2} +(2.76530 + 1.04874i) q^{3} +(-0.226716 - 1.86717i) q^{4} +(0.690181 - 2.12689i) q^{5} +(0.474353 + 0.903805i) q^{6} +(0.206669 - 0.299412i) q^{7} +(0.760874 - 1.10232i) q^{8} +(4.30150 + 3.81080i) q^{9} +O(q^{10})$	\(q+(0.258334 + 0.228864i) q^{2} +(2.76530 + 1.04874i) q^{3} +(-0.226716 - 1.86717i) q^{4} +(0.690181 - 2.12689i) q^{5} +(0.474353 + 0.903805i) q^{6} +(0.206669 - 0.299412i) q^{7} +(0.760874 - 1.10232i) q^{8} +(4.30150 + 3.81080i) q^{9} +(0.665066 - 0.391491i) q^{10} +(2.89686 + 3.26988i) q^{11} +(1.33124 - 5.40105i) q^{12} +(-1.67441 - 3.19317i) q^{13} +(0.121915 - 0.0300492i) q^{14} +(4.13911 - 5.15766i) q^{15} +(-3.20362 + 0.789621i) q^{16} +(-3.43541 - 2.37129i) q^{17} +(0.239070 + 1.96892i) q^{18} +3.53706i q^{19} +(-4.12774 - 0.806486i) q^{20} +(0.885508 - 0.611222i) q^{21} +1.50771i q^{22} +0.126756i q^{23} +(3.26009 - 2.25028i) q^{24} +(-4.04730 - 2.93587i) q^{25} +(0.298247 - 1.20812i) q^{26} +(3.77517 + 7.19298i) q^{27} +(-0.605908 - 0.318005i) q^{28} +(4.57877 + 4.05644i) q^{29} +(2.24968 - 0.385108i) q^{30} +(0.196901 + 0.375164i) q^{31} +(-3.38031 - 1.77412i) q^{32} +(4.58143 + 12.0802i) q^{33} +(-0.344780 - 1.39883i) q^{34} +(-0.494177 - 0.646210i) q^{35} +(6.14019 - 8.89561i) q^{36} +(-2.02449 + 1.06253i) q^{37} +(-0.809507 + 0.913745i) q^{38} +(-1.28143 - 10.5861i) q^{39} +(-1.81936 - 2.37909i) q^{40} +(-2.47702 - 0.939409i) q^{41} +(0.368644 + 0.0447615i) q^{42} +(0.0775596 - 0.147777i) q^{43} +(5.44866 - 6.15026i) q^{44} +(11.0740 - 6.51867i) q^{45} +(-0.0290100 + 0.0327455i) q^{46} +(1.36941 - 11.2781i) q^{47} +(-9.68707 - 1.17622i) q^{48} +(2.43530 + 6.42136i) q^{49} +(-0.373641 - 1.68472i) q^{50} +(-7.01307 - 10.1602i) q^{51} +(-5.58259 + 3.85034i) q^{52} +(9.67646 + 6.67918i) q^{53} +(-0.670961 + 2.72220i) q^{54} +(8.95402 - 3.90449i) q^{55} +(-0.172798 - 0.455630i) q^{56} +(-3.70946 + 9.78104i) q^{57} +(0.254480 + 2.09584i) q^{58} +(-1.79941 + 7.30051i) q^{59} +(-10.5686 - 6.55910i) q^{60} +(2.37143 + 3.43561i) q^{61} +(-0.0349953 + 0.141982i) q^{62} +(2.02999 - 0.500347i) q^{63} +(1.87282 + 4.93821i) q^{64} +(-7.94717 + 1.35741i) q^{65} +(-1.58120 + 4.16927i) q^{66} +(1.10234 - 9.07860i) q^{67} +(-3.64875 + 6.95210i) q^{68} +(-0.132934 + 0.350519i) q^{69} +(0.0202317 - 0.280038i) q^{70} +(-13.6384 - 5.17236i) q^{71} +(7.47361 - 1.84208i) q^{72} +(-6.79031 + 6.01569i) q^{73} +(-0.766170 - 0.188844i) q^{74} +(-8.11304 - 12.3631i) q^{75} +(6.60430 - 0.801907i) q^{76} +(1.57773 - 0.191571i) q^{77} +(2.09175 - 3.02803i) q^{78} +(-1.17584 + 9.68388i) q^{79} +(-0.531640 + 7.35872i) q^{80} +(0.817825 + 6.73539i) q^{81} +(-0.424902 - 0.809583i) q^{82} +(3.50885 + 9.25208i) q^{83} +(-1.34201 - 1.51482i) q^{84} +(-7.41452 + 5.67011i) q^{85} +(0.0538573 - 0.0204254i) q^{86} +(8.40753 + 16.0192i) q^{87} +(5.80859 - 0.705290i) q^{88} +1.30688i q^{89} +(4.35268 + 0.850435i) q^{90} +(-1.30212 - 0.158593i) q^{91} +(0.236675 - 0.0287376i) q^{92} +(0.151042 + 1.24394i) q^{93} +(2.93492 - 2.60011i) q^{94} +(7.52293 + 2.44121i) q^{95} +(-7.48697 - 8.45105i) q^{96} +(-3.08083 + 0.759356i) q^{97} +(-0.840498 + 2.21621i) q^{98} +25.1047i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1056 q - 106 q^{4} - 13 q^{5} - 26 q^{6} + 62 q^{9}+O(q^{10}) $ 1056 * q - 106 * q^4 - 13 * q^5 - 26 * q^6 + 62 * q^9	$ 1056 q - 106 q^{4} - 13 q^{5} - 26 q^{6} + 62 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 65 q^{15} - 98 q^{16} - 13 q^{20} - 26 q^{21} - 26 q^{24} - 3 q^{25} - 14 q^{26} - 54 q^{29} - 45 q^{30} + 26 q^{31} - 26 q^{34} - 17 q^{35} + 54 q^{36} - 146 q^{39} + 120 q^{40} - 26 q^{41} + 26 q^{44} - 78 q^{45} + 26 q^{46} - 164 q^{49} - 13 q^{50} - 164 q^{51} - 26 q^{54} - 119 q^{55} - 26 q^{56} - 130 q^{59} - 117 q^{60} - 54 q^{61} - 122 q^{64} - q^{65} + 140 q^{66} + 88 q^{69} - 26 q^{71} - 176 q^{74} - 65 q^{75} + 156 q^{76} - 26 q^{79} - 58 q^{81} + 468 q^{84} + 143 q^{85} + 130 q^{86} - 19 q^{90} - 26 q^{91} - 142 q^{94} + 70 q^{95} - 26 q^{96}+O(q^{100}) $ 1056 * q - 106 * q^4 - 13 * q^5 - 26 * q^6 + 62 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 65 * q^15 - 98 * q^16 - 13 * q^20 - 26 * q^21 - 26 * q^24 - 3 * q^25 - 14 * q^26 - 54 * q^29 - 45 * q^30 + 26 * q^31 - 26 * q^34 - 17 * q^35 + 54 * q^36 - 146 * q^39 + 120 * q^40 - 26 * q^41 + 26 * q^44 - 78 * q^45 + 26 * q^46 - 164 * q^49 - 13 * q^50 - 164 * q^51 - 26 * q^54 - 119 * q^55 - 26 * q^56 - 130 * q^59 - 117 * q^60 - 54 * q^61 - 122 * q^64 - q^65 + 140 * q^66 + 88 * q^69 - 26 * q^71 - 176 * q^74 - 65 * q^75 + 156 * q^76 - 26 * q^79 - 58 * q^81 + 468 * q^84 + 143 * q^85 + 130 * q^86 - 19 * q^90 - 26 * q^91 - 142 * q^94 + 70 * q^95 - 26 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{19}{26}\right)$	$-1$

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 $

$2$	0.258334	+	0.228864i	0.182670	+	0.161832i	0.749502	−	0.662002i	$-0.230293\pi$
$2$	0.258334	+	0.228864i	0.182670	+	0.161832i	−0.566832	+	0.823833i	$0.691831\pi$
$3$	2.76530	+	1.04874i	1.59655	+	0.605491i	0.982908	−	0.184096i	$-0.0589358\pi$
$3$	2.76530	+	1.04874i	1.59655	+	0.605491i	0.613639	+	0.789587i	$0.289705\pi$
$4$	−0.226716	−	1.86717i	−0.113358	−	0.933585i
$5$	0.690181	−	2.12689i	0.308658	−	0.951173i
$5$	0.690181	−	2.12689i	0.308658	−	0.951173i
$6$	0.474353	+	0.903805i	0.193654	+	0.368977i
$7$	0.206669	−	0.299412i	0.0781136	−	0.113167i	−0.781980	−	0.623304i	$-0.785790\pi$
$7$	0.206669	−	0.299412i	0.0781136	−	0.113167i	0.860093	+	0.510137i	$0.170405\pi$
$8$	0.760874	−	1.10232i	0.269010	−	0.389728i
$9$	4.30150	+	3.81080i	1.43383	+	1.27027i
$10$	0.665066	−	0.391491i	0.210312	−	0.123800i
$11$	2.89686	+	3.26988i	0.873436	+	0.985905i	0.999982	−	0.00605554i	$-0.00192755\pi$
$11$	2.89686	+	3.26988i	0.873436	+	0.985905i	−0.126546	+	0.991961i	$0.540389\pi$
$12$	1.33124	−	5.40105i	0.384296	−	1.55915i
$13$	−1.67441	−	3.19317i	−0.464397	−	0.885627i
$13$	−1.67441	−	3.19317i	−0.464397	−	0.885627i
$14$	0.121915	−	0.0300492i	0.0325830	−	0.00803099i
$15$	4.13911	−	5.15766i	1.06871	−	1.33170i
$16$	−3.20362	+	0.789621i	−0.800904	+	0.197405i
$17$	−3.43541	−	2.37129i	−0.833209	−	0.575123i	0.0732995	−	0.997310i	$-0.476647\pi$
$17$	−3.43541	−	2.37129i	−0.833209	−	0.575123i	−0.906509	+	0.422187i	$0.861262\pi$
$18$	0.239070	+	1.96892i	0.0563494	+	0.464079i
$19$			3.53706i			0.811458i	0.913994	+	0.405729i	$0.132982\pi$
$19$			3.53706i			0.811458i	−0.913994	+	0.405729i	$0.867018\pi$
$20$	−4.12774	−	0.806486i	−0.922990	−	0.180336i
$21$	0.885508	−	0.611222i	0.193234	−	0.133380i
$22$			1.50771i			0.321445i
$23$			0.126756i			0.0264305i	0.999913	+	0.0132152i	$0.00420667\pi$
$23$			0.126756i			0.0264305i	−0.999913	+	0.0132152i	$0.995793\pi$
$24$	3.26009	−	2.25028i	0.665463	−	0.459336i
$25$	−4.04730	−	2.93587i	−0.809460	−	0.587175i
$26$	0.298247	−	1.20812i	0.0584911	−	0.236932i
$27$	3.77517	+	7.19298i	0.726531	+	1.38429i
$28$	−0.605908	−	0.318005i	−0.114506	−	0.0600973i
$29$	4.57877	+	4.05644i	0.850256	+	0.753261i	0.970913	−	0.239433i	$-0.0769615\pi$
$29$	4.57877	+	4.05644i	0.850256	+	0.753261i	−0.120657	+	0.992694i	$0.538500\pi$
$30$	2.24968	−	0.385108i	0.410734	−	0.0703107i
$31$	0.196901	+	0.375164i	0.0353645	+	0.0673815i	0.902497	−	0.430696i	$-0.141732\pi$
$31$	0.196901	+	0.375164i	0.0353645	+	0.0673815i	−0.867133	+	0.498077i	$0.834040\pi$
$32$	−3.38031	−	1.77412i	−0.597559	−	0.313623i
$33$	4.58143	+	12.0802i	0.797525	+	2.10290i
$34$	−0.344780	−	1.39883i	−0.0591294	−	0.239897i
$35$	−0.494177	−	0.646210i	−0.0835311	−	0.109229i
$36$	6.14019	−	8.89561i	1.02337	−	1.48260i
$37$	−2.02449	+	1.06253i	−0.332823	+	0.174679i	−0.622854	−	0.782338i	$-0.714027\pi$
$37$	−2.02449	+	1.06253i	−0.332823	+	0.174679i	0.290030	+	0.957017i	$0.406335\pi$
$38$	−0.809507	+	0.913745i	−0.131319	+	0.148229i
$39$	−1.28143	−	10.5861i	−0.205192	−	1.69513i
$40$	−1.81936	−	2.37909i	−0.287667	−	0.376167i
$41$	−2.47702	−	0.939409i	−0.386845	−	0.146711i	0.153512	−	0.988147i	$-0.450942\pi$
$41$	−2.47702	−	0.939409i	−0.386845	−	0.146711i	−0.540357	+	0.841436i	$0.681711\pi$
$42$	0.368644	+	0.0447615i	0.0568830	+	0.00690685i
$43$	0.0775596	−	0.147777i	0.0118277	−	0.0225358i	−0.879470	−	0.475953i	$-0.842103\pi$
$43$	0.0775596	−	0.147777i	0.0118277	−	0.0225358i	0.891298	+	0.453418i	$0.149795\pi$
$44$	5.44866	−	6.15026i	0.821416	−	0.927187i
$45$	11.0740	−	6.51867i	1.65081	−	0.971746i
$46$	−0.0290100	+	0.0327455i	−0.00427729	+	0.00482806i
$47$	1.36941	−	11.2781i	0.199749	−	1.64508i	−0.455914	−	0.890024i	$-0.650687\pi$
$47$	1.36941	−	11.2781i	0.199749	−	1.64508i	0.655662	−	0.755054i	$-0.272390\pi$
$48$	−9.68707	−	1.17622i	−1.39821	−	0.169773i
$49$	2.43530	+	6.42136i	0.347900	+	0.917336i
$50$	−0.373641	−	1.68472i	−0.0528408	−	0.238255i
$51$	−7.01307	−	10.1602i	−0.982026	−	1.42271i
$52$	−5.58259	+	3.85034i	−0.774166	+	0.533947i
$53$	9.67646	+	6.67918i	1.32916	+	0.917456i	0.999644	−	0.0266922i	$-0.00849740\pi$
$53$	9.67646	+	6.67918i	1.32916	+	0.917456i	0.329521	+	0.944148i	$0.393113\pi$
$54$	−0.670961	+	2.72220i	−0.0913063	+	0.370444i
$55$	8.95402	−	3.90449i	1.20736	−	0.526481i
$56$	−0.172798	−	0.455630i	−0.0230910	−	0.0608861i
$57$	−3.70946	+	9.78104i	−0.491330	+	1.29553i
$58$	0.254480	+	2.09584i	0.0334149	+	0.275197i
$59$	−1.79941	+	7.30051i	−0.234264	+	0.950446i	0.729562	+	0.683914i	$0.239724\pi$
$59$	−1.79941	+	7.30051i	−0.234264	+	0.950446i	−0.963826	+	0.266532i	$0.914122\pi$
$60$	−10.5686	−	6.55910i	−1.36441	−	0.846776i
$61$	2.37143	+	3.43561i	0.303630	+	0.439884i	0.944865	−	0.327460i	$-0.106193\pi$
$61$	2.37143	+	3.43561i	0.303630	+	0.439884i	−0.641235	+	0.767345i	$0.721577\pi$
$62$	−0.0349953	+	0.141982i	−0.00444441	+	0.0180317i
$63$	2.02999	−	0.500347i	0.255754	−	0.0630378i
$64$	1.87282	+	4.93821i	0.234102	+	0.617277i
$65$	−7.94717	+	1.35741i	−0.985725	+	0.168366i
$66$	−1.58120	+	4.16927i	−0.194632	+	0.513202i
$67$	1.10234	−	9.07860i	0.134672	−	1.10913i	−0.756029	−	0.654538i	$-0.772863\pi$
$67$	1.10234	−	9.07860i	0.134672	−	1.10913i	0.890701	−	0.454589i	$-0.150214\pi$
$68$	−3.64875	+	6.95210i	−0.442475	+	0.843066i
$69$	−0.132934	+	0.350519i	−0.0160034	+	0.0421975i
$70$	0.0202317	−	0.280038i	0.00241815	−	0.0334709i
$71$	−13.6384	−	5.17236i	−1.61858	−	0.613846i	−0.631687	−	0.775224i	$-0.717637\pi$
$71$	−13.6384	−	5.17236i	−1.61858	−	0.613846i	−0.986893	+	0.161378i	$0.948406\pi$
$72$	7.47361	−	1.84208i	0.880773	−	0.217091i
$73$	−6.79031	+	6.01569i	−0.794746	+	0.704083i	−0.959332	−	0.282279i	$-0.908910\pi$
$73$	−6.79031	+	6.01569i	−0.794746	+	0.704083i	0.164586	+	0.986363i	$0.447371\pi$
$74$	−0.766170	−	0.188844i	−0.0890655	−	0.0219527i
$75$	−8.11304	−	12.3631i	−0.936813	−	1.42757i
$76$	6.60430	−	0.801907i	0.757565	−	0.0919850i
$77$	1.57773	−	0.191571i	0.179799	−	0.0218316i
$78$	2.09175	−	3.02803i	0.236844	−	0.342857i
$79$	−1.17584	+	9.68388i	−0.132292	+	1.08952i	0.763738	+	0.645527i	$0.223362\pi$
$79$	−1.17584	+	9.68388i	−0.132292	+	1.08952i	−0.896030	+	0.443994i	$0.853561\pi$
$80$	−0.531640	+	7.35872i	−0.0594391	+	0.822729i
$81$	0.817825	+	6.73539i	0.0908694	+	0.748377i
$82$	−0.424902	−	0.809583i	−0.0469226	−	0.0894035i
$83$	3.50885	+	9.25208i	0.385146	+	1.01555i	0.977698	+	0.210015i	$0.0673514\pi$
$83$	3.50885	+	9.25208i	0.385146	+	1.01555i	−0.592552	+	0.805532i	$0.701879\pi$
$84$	−1.34201	−	1.51482i	−0.146426	−	0.165280i
$85$	−7.41452	+	5.67011i	−0.804218	+	0.615010i
$86$	0.0538573	−	0.0204254i	0.00580758	−	0.00220253i
$87$	8.40753	+	16.0192i	0.901382	+	1.71744i
$88$	5.80859	−	0.705290i	0.619197	−	0.0751842i
$89$			1.30688i			0.138529i	0.997598	+	0.0692643i	$0.0220652\pi$
$89$			1.30688i			0.138529i	−0.997598	+	0.0692643i	$0.977935\pi$
$90$	4.35268	+	0.850435i	0.458812	+	0.0896438i
$91$	−1.30212	−	0.158593i	−0.136500	−	0.0166251i
$92$	0.236675	−	0.0287376i	0.0246751	−	0.00299610i
$93$	0.151042	+	1.24394i	0.0156623	+	0.128991i
$94$	2.93492	−	2.60011i	0.302714	−	0.268181i
$95$	7.52293	+	2.44121i	0.771837	+	0.250463i
$96$	−7.48697	−	8.45105i	−0.764136	−	0.862531i
$97$	−3.08083	+	0.759356i	−0.312811	+	0.0771009i	−0.392596	−	0.919711i	$-0.628423\pi$
$97$	−3.08083	+	0.759356i	−0.312811	+	0.0771009i	0.0797850	+	0.996812i	$0.474577\pi$
$98$	−0.840498	+	2.21621i	−0.0849031	+	0.223871i
$99$			25.1047i			2.52312i
$100$	−4.56419	+	8.22261i	−0.456419	+	0.822261i
$101$	14.9853	+	7.86492i	1.49110	+	0.782588i	0.996261	−	0.0863977i	$-0.0275356\pi$
$101$	14.9853	+	7.86492i	1.49110	+	0.782588i	0.494837	+	0.868986i	$0.335228\pi$
$102$	0.513587	−	4.22977i	0.0508527	−	0.418810i
$103$	2.76191	+	1.04746i	0.272139	+	0.103209i	0.486900	−	0.873458i	$-0.338128\pi$
$103$	2.76191	+	1.04746i	0.272139	+	0.103209i	−0.214760	+	0.976667i	$0.568897\pi$
$104$	−4.79390	−	0.583878i	−0.470081	−	0.0572540i
$105$	−0.688840	−	2.30523i	−0.0672239	−	0.224967i
$106$	0.971138	+	3.94006i	0.0943252	+	0.382693i
$107$	−0.489636	+	1.98653i	−0.0473349	+	0.192045i	−0.989849	−	0.142120i	$-0.954608\pi$
$107$	−0.489636	+	1.98653i	−0.0473349	+	0.192045i	0.942515	+	0.334165i	$0.108454\pi$
$108$	12.5746	−	8.67964i	1.20999	−	0.835199i
$109$	2.80134	−	5.33752i	0.268320	−	0.511241i	−0.713596	−	0.700557i	$-0.752935\pi$
$109$	2.80134	−	5.33752i	0.268320	−	0.511241i	0.981916	+	0.189316i	$0.0606271\pi$
$110$	3.20673	+	1.04059i	0.305750	+	0.0992166i
$111$	−6.71263	+	0.815061i	−0.637135	+	0.0773622i
$112$	−0.425667	+	1.12239i	−0.0402218	+	0.106056i
$113$	−5.03231	+	1.90850i	−0.473400	+	0.179537i	−0.579754	−	0.814791i	$-0.696852\pi$
$113$	−5.03231	+	1.90850i	−0.473400	+	0.179537i	0.106354	+	0.994328i	$0.466082\pi$
$114$	−3.19681	+	1.67782i	−0.299409	+	0.157142i
$115$	0.269596	+	0.0874847i	0.0251400	+	0.00815799i
$116$	6.53598	−	9.46900i	0.606851	−	0.879175i
$117$	4.96608	−	20.1163i	0.459114	−	1.85975i
$118$	−2.13568	+	1.47415i	−0.196605	+	0.135707i
$119$	−1.41999	+	0.538530i	−0.130170	+	0.0493669i
$120$	−2.53604	−	8.48694i	−0.231507	−	0.774748i
$121$	−0.974405	+	8.02495i	−0.0885823	+	0.729541i
$122$	−0.173666	+	1.43027i	−0.0157230	+	0.129491i
$123$	−5.86450	−	5.19550i	−0.528784	−	0.468462i
$124$	0.655855	−	0.452704i	0.0588975	−	0.0406540i
$125$	−9.03764	+	6.58187i	−0.808351	+	0.588701i
$126$	0.638927	+	0.335335i	0.0569201	+	0.0298740i
$127$	−8.70210	−	1.05663i	−0.772186	−	0.0937604i	−0.275047	−	0.961431i	$-0.588693\pi$
$127$	−8.70210	−	1.05663i	−0.772186	−	0.0937604i	−0.497140	+	0.867670i	$0.665616\pi$
$128$	−3.35384	+	8.84335i	−0.296440	+	0.781649i
$129$	0.369456	−	0.327309i	0.0325288	−	0.0288180i
$130$	−2.36369	−	1.46816i	−0.207309	−	0.128766i
$131$	−10.2325	−	9.06523i	−0.894021	−	0.792033i	0.0848756	−	0.996392i	$-0.472951\pi$
$131$	−10.2325	−	9.06523i	−0.894021	−	0.792033i	−0.978896	+	0.204358i	$0.934489\pi$
$132$	21.5172	−	11.2931i	1.87283	−	0.982938i
$133$	1.05904	+	0.731002i	0.0918303	+	0.0633859i
$134$	2.36254	−	2.09303i	0.204092	−	0.180810i
$135$	17.9042	−	3.06490i	1.54095	−	0.263785i
$136$	−5.22783	+	1.98265i	−0.448283	+	0.170011i
$137$	−14.3655	−	7.53960i	−1.22733	−	0.644152i	−0.278650	−	0.960393i	$-0.589887\pi$
$137$	−14.3655	−	7.53960i	−1.22733	−	0.644152i	−0.948679	+	0.316241i	$0.897579\pi$
$138$	−0.114563	+	0.0601272i	−0.00975224	+	0.00511837i
$139$	5.33779	−	1.31565i	0.452745	−	0.111592i	−0.00634785	−	0.999980i	$-0.502021\pi$
$139$	5.33779	−	1.31565i	0.452745	−	0.111592i	0.459093	+	0.888388i	$0.348174\pi$
$140$	−1.09455	+	1.06922i	−0.0925061	+	0.0903654i
$141$	15.6146	−	29.7512i	1.31499	−	2.50550i
$142$	−2.33950	−	4.45754i	−0.196326	−	0.374069i
$143$	5.59077	−	14.7253i	0.467524	−	1.23139i
$144$	−16.7895	−	8.81178i	−1.39912	−	0.734315i
$145$	11.7878	−	6.93886i	0.978920	−	0.576241i
$146$	−3.13095			−0.259119
$147$			20.3110i			1.67522i
$148$	2.44291	+	3.53917i	0.200806	+	0.290918i
$149$	−21.5820	−	2.62053i	−1.76807	−	0.214683i	−0.829199	−	0.558953i	$-0.811203\pi$
$149$	−21.5820	−	2.62053i	−1.76807	−	0.214683i	−0.938870	+	0.344271i	$0.888126\pi$
$150$	0.733605	−	5.05061i	0.0598986	−	0.412381i
$151$	−10.4810	+	1.27263i	−0.852935	+	0.103565i	−0.535315	−	0.844653i	$-0.679807\pi$
$151$	−10.4810	+	1.27263i	−0.852935	+	0.103565i	−0.317621	+	0.948218i	$0.602884\pi$
$152$	3.89896	+	2.69126i	0.316248	+	0.218290i
$153$	−5.74090	−	23.2918i	−0.464125	−	1.88303i
$154$	0.451426	+	0.311597i	0.0363770	+	0.0251092i
$155$	0.933829	−	0.159856i	0.0750070	−	0.0128399i
$156$	−19.4755	+	4.79268i	−1.55929	+	0.383721i
$157$	−0.653666	+	2.65203i	−0.0521683	+	0.211655i	−0.991241	−	0.132062i	$-0.957840\pi$
$157$	−0.653666	+	2.65203i	−0.0521683	+	0.211655i	0.939073	+	0.343717i	$0.111686\pi$
$158$	−2.52005	+	2.23257i	−0.200485	+	0.177614i
$159$	19.7536	+	28.6180i	1.56656	+	2.26956i
$160$	−6.10638	+	5.96507i	−0.482752	+	0.471580i
$161$	0.0379523	+	0.0261966i	0.00299106	+	0.00206458i
$162$	−1.33022	+	1.92715i	−0.104512	+	0.151412i
$163$	19.7554	−	10.3684i	1.54736	−	0.812118i	0.547663	−	0.836699i	$-0.315518\pi$
$163$	19.7554	−	10.3684i	1.54736	−	0.812118i	0.999698	+	0.0245813i	$0.00782526\pi$
$164$	−1.19246	+	4.83799i	−0.0931153	+	0.377784i
$165$	28.8553	−	1.40664i	2.24639	−	0.109507i
$166$	−1.21101	+	3.19318i	−0.0939929	+	0.247839i
$167$	−10.9923	−	9.73829i	−0.850606	−	0.753572i	0.120374	−	0.992729i	$-0.461590\pi$
$167$	−10.9923	−	9.73829i	−0.850606	−	0.753572i	−0.970981	+	0.239157i	$0.923129\pi$
$168$		−	1.44117i		−	0.111189i
$169$	−7.39273	+	10.6933i	−0.568671	+	0.822565i
$170$	−3.21311	−	0.232135i	−0.246435	−	0.0178040i
$171$	−13.4790	+	15.2147i	−1.03077	+	1.16350i
$172$	−0.293510	−	0.111314i	−0.0223799	−	0.00848758i
$173$	23.6182	−	2.86777i	1.79566	−	0.218032i	0.846403	−	0.532542i	$-0.178763\pi$
$173$	23.6182	−	2.86777i	1.79566	−	0.218032i	0.949254	+	0.314510i	$0.101840\pi$
$174$	−1.49427	+	6.06250i	−0.113280	+	0.459597i
$175$	−1.71549	+	0.605056i	−0.129679	+	0.0457380i
$176$	−11.8624	−	8.18802i	−0.894161	−	0.617195i
$177$	−12.6323	+	18.3010i	−0.949499	+	1.37559i
$178$	−0.299097	+	0.337611i	−0.0224183	+	0.0253050i
$179$	−6.65498	−	9.64141i	−0.497417	−	0.720633i	0.491207	−	0.871043i	$-0.336556\pi$
$179$	−6.65498	−	9.64141i	−0.497417	−	0.720633i	−0.988624	+	0.150410i	$0.951941\pi$
$180$	−14.6821	−	19.1991i	−1.09434	−	1.43101i
$181$	16.9210	+	4.17066i	1.25773	+	0.310003i	0.811202	−	0.584766i	$-0.198814\pi$
$181$	16.9210	+	4.17066i	1.25773	+	0.310003i	0.446529	+	0.894769i	$0.352660\pi$
$182$	−0.300087	−	0.338980i	−0.0222439	−	0.0251268i
$183$	2.95465	+	11.9875i	0.218414	+	0.886142i
$184$	0.139725	+	0.0964455i	0.0103007	+	0.00711006i
$185$	0.862626	+	5.03919i	0.0634215	+	0.370489i
$186$	−0.245674	+	0.355921i	−0.0180137	+	0.0260974i
$187$	−2.19806	−	18.1027i	−0.160738	−	1.32380i
$188$	−21.3686			−1.55846
$189$	2.93388	+	0.356237i	0.213408	+	0.0259124i
$190$	1.38473	+	2.35238i	0.100459	+	0.170660i
$191$	−1.75946			−0.127310			−0.0636549	−	0.997972i	$-0.520276\pi$
$191$	−1.75946			−0.127310			−0.0636549	+	0.997972i	$0.520276\pi$
$192$			15.6197i			1.12726i
$193$	2.46690	+	3.57393i	0.177572	+	0.257257i	0.901656	−	0.432455i	$-0.142353\pi$
$193$	2.46690	+	3.57393i	0.177572	+	0.257257i	−0.724084	+	0.689712i	$0.757737\pi$
$194$	−0.969673	−	0.508924i	−0.0696185	−	0.0365386i
$195$	−23.3999	−	4.58087i	−1.67570	−	0.328043i
$196$	11.4376	−	6.00294i	0.816975	−	0.428781i
$197$	16.5607	+	8.69174i	1.17990	+	0.619261i	0.936501	−	0.350665i	$-0.114044\pi$
$197$	16.5607	+	8.69174i	1.17990	+	0.619261i	0.243401	+	0.969926i	$0.421737\pi$
$198$	−5.74558	+	6.48542i	−0.408320	+	0.460899i
$199$	24.3185	−	5.99398i	1.72389	−	0.424902i	0.751781	−	0.659413i	$-0.229195\pi$
$199$	24.3185	−	5.99398i	1.72389	−	0.424902i	0.972113	+	0.234512i	$0.0753491\pi$
$200$	−6.31575	+	2.22758i	−0.446591	+	0.157514i
$201$	12.5694	−	23.9490i	0.886577	−	1.68923i
$202$	2.07123	+	5.46139i	0.145731	+	0.384262i
$203$	2.16084	−	0.532598i	0.151661	−	0.0373811i
$204$	−17.3808	+	15.3981i	−1.21690	+	1.07808i
$205$	−3.70761	+	4.61998i	−0.258950	+	0.322673i
$206$	0.473772	+	0.902697i	0.0330093	+	0.0628939i
$207$	−0.483042	+	0.545242i	−0.0335738	+	0.0378969i
$208$	7.88555	+	8.90756i	0.546765	+	0.617628i
$209$	−11.5658	+	10.2464i	−0.800020	+	0.708756i
$210$	0.349634	−	0.753171i	0.0241270	−	0.0519738i
$211$	−0.881369	+	7.25872i	−0.0606759	+	0.499711i	0.930413	+	0.366512i	$0.119448\pi$
$211$	−0.881369	+	7.25872i	−0.0606759	+	0.499711i	−0.991089	+	0.133199i	$0.957475\pi$
$212$	10.2774	−	19.5819i	0.705852	−	1.34489i
$213$	−32.2898	−	28.6063i	−2.21246	−	1.96007i
$214$	−0.581136	+	0.401130i	−0.0397257	+	0.0274206i
$215$	−0.260776	−	0.266954i	−0.0177848	−	0.0182061i
$216$	10.8014	+	1.31152i	0.734940	+	0.0892379i
$217$	0.153022	+	0.0185802i	0.0103878	+	0.00126131i
$218$	1.94525	−	0.737736i	0.131749	−	0.0499658i
$219$	−25.0862	+	9.51392i	−1.69517	+	0.642891i
$220$	−9.32036	−	15.8335i	−0.628378	−	1.06749i
$221$	−1.81968	+	14.9404i	−0.122405	+	1.00500i
$222$	−1.92064	−	1.32572i	−0.128905	−	0.0889768i
$223$	−19.2576	−	4.74658i	−1.28959	−	0.317855i	−0.465869	−	0.884854i	$-0.654258\pi$
$223$	−19.2576	−	4.74658i	−1.28959	−	0.317855i	−0.823718	+	0.566999i	$0.808104\pi$
$224$	−1.22980	+	0.645448i	−0.0821694	+	0.0431258i
$225$	−6.22146	−	28.0521i	−0.414764	−	1.87014i
$226$	−1.73681	−	0.658685i	−0.115531	−	0.0438151i
$227$	1.25075	+	10.3009i	0.0830153	+	0.683693i	0.973501	+	0.228682i	$0.0734415\pi$
$227$	1.25075	+	10.3009i	0.0830153	+	0.683693i	−0.890486	+	0.455011i	$0.849635\pi$
$228$	19.1039	+	4.70868i	1.26518	+	0.311840i
$229$	−2.39501	+	4.56331i	−0.158267	+	0.301552i	−0.951658	−	0.307160i	$-0.900621\pi$
$229$	−2.39501	+	4.56331i	−0.158267	+	0.301552i	0.793391	+	0.608712i	$0.208314\pi$
$230$	0.0496239	+	0.0843013i	0.00327210	+	0.00555866i
$231$	4.56381	+	1.12488i	0.300277	+	0.0740116i
$232$	7.95535	−	1.96082i	0.522294	−	0.128734i
$233$	−18.5149	+	7.02178i	−1.21295	+	0.460012i	−0.876368	−	0.481641i	$-0.840041\pi$
$233$	−18.5149	+	7.02178i	−1.21295	+	0.460012i	−0.336584	+	0.941653i	$0.609272\pi$
$234$	5.88681	−	4.06017i	0.384833	−	0.265421i
$235$	−23.0421	−	10.6965i	−1.50310	−	0.697762i
$236$	14.0393	+	1.70467i	0.913878	+	0.110965i
$237$	−13.4074	+	25.5457i	−0.870905	+	1.65937i
$238$	−0.490082	−	0.185863i	−0.0317673	−	0.0120477i
$239$		−	12.8158i		−	0.828988i	−0.910052	−	0.414494i	$-0.863959\pi$
$239$		−	12.8158i		−	0.828988i	0.910052	−	0.414494i	$-0.136041\pi$
$240$	−9.18753	+	19.7915i	−0.593052	+	1.27754i
$241$	1.31759	+	5.34566i	0.0848732	+	0.344344i	0.997991	−	0.0633510i	$-0.0201788\pi$
$241$	1.31759	+	5.34566i	0.0848732	+	0.344344i	−0.913118	+	0.407695i	$0.866333\pi$
$242$	−2.08835	+	1.85011i	−0.134244	+	0.118930i
$243$	1.03008	−	4.17920i	0.0660797	−	0.268096i
$244$	5.87723	−	5.20677i	0.376251	−	0.333329i
$245$	15.3383	−	0.747713i	0.979928	−	0.0477696i
$246$	−0.325939	−	2.68435i	−0.0207811	−	0.171148i
$247$	11.2945	−	5.92248i	0.718649	−	0.376838i
$248$	0.563367	+	0.0684051i	0.0357738	+	0.00434373i
$249$			29.2647i			1.85457i
$250$	−3.84109	−	0.368069i	−0.242932	−	0.0232787i
$251$	1.70728	−	0.896051i	0.107763	−	0.0565582i	−0.409981	−	0.912094i	$-0.634465\pi$
$251$	1.70728	−	0.896051i	0.107763	−	0.0565582i	0.517743	+	0.855536i	$0.326772\pi$
$252$	−1.39446	−	3.67689i	−0.0878429	−	0.231623i
$253$	−0.414477	+	0.367195i	−0.0260580	+	0.0230853i
$254$	−2.00623	−	2.26456i	−0.125882	−	0.142091i
$255$	−26.4499	+	7.90365i	−1.65635	+	0.494946i
$256$	6.46259	−	3.39183i	0.403912	−	0.211989i
$257$	−2.17463	+	0.264048i	−0.135650	+	0.0164708i	−0.188080	−	0.982154i	$-0.560226\pi$
$257$	−2.17463	+	0.264048i	−0.135650	+	0.0164708i	0.0524302	+	0.998625i	$0.483303\pi$
$258$	0.170353			0.0106057
$259$	−0.100264	+	0.825748i	−0.00623010	+	0.0513095i
$260$	4.33626	+	14.5310i	0.268923	+	0.901172i
$261$	4.23733	+	34.8975i	0.262284	+	2.16010i
$262$	−0.568707	−	4.68372i	−0.0351348	−	0.289361i
$263$	−20.4541	−	23.0879i	−1.26125	−	1.42366i	−0.862072	−	0.506786i	$-0.830833\pi$
$263$	−20.4541	−	23.0879i	−1.26125	−	1.42366i	−0.399180	−	0.916873i	$-0.630705\pi$
$264$	16.8022	+	4.14136i	1.03410	+	0.254883i
$265$	20.8844	−	15.9709i	1.28292	−	0.981085i
$266$	0.106286	+	0.431219i	0.00651681	+	0.0264397i
$267$	−1.37057	+	3.61390i	−0.0838777	+	0.221167i
$268$	−17.2012			−1.05073
$269$	8.20928	−	21.6461i	0.500529	−	1.31979i	−0.412153	−	0.911115i	$-0.635223\pi$
$269$	8.20928	−	21.6461i	0.500529	−	1.31979i	0.912682	−	0.408671i	$-0.134008\pi$
$270$	5.32672	+	3.30587i	0.324174	+	0.201189i
$271$	28.6501	+	3.47875i	1.74037	+	0.211319i	0.928195	−	0.372094i	$-0.121360\pi$
$271$	28.6501	+	3.47875i	1.74037	+	0.211319i	0.812176	+	0.583413i	$0.198283\pi$
$272$	12.8782	+	4.88404i	0.780853	+	0.296138i
$273$	−3.43444	−	1.80415i	−0.207862	−	0.109192i
$274$	−1.98556	−	5.23549i	−0.119952	−	0.316288i
$275$	−2.12452	−	21.7390i	−0.128113	−	1.31091i
$276$	0.684617	+	0.168743i	0.0412091	+	0.0101571i
$277$	−21.7331	+	15.0013i	−1.30582	+	0.901341i	−0.998732	−	0.0503404i	$-0.983969\pi$
$277$	−21.7331	+	15.0013i	−1.30582	+	0.901341i	−0.307086	+	0.951682i	$0.599354\pi$
$278$	1.68004	+	0.881753i	0.100762	+	0.0528840i
$279$	−0.582703	+	2.36412i	−0.0348855	+	0.141536i
$280$	−1.08833	+	0.0530542i	−0.0650404	+	0.00317060i
$281$	−18.6457	−	7.07137i	−1.11231	−	0.421842i	−0.271098	−	0.962552i	$-0.587387\pi$
$281$	−18.6457	−	7.07137i	−1.11231	−	0.421842i	−0.841209	+	0.540709i	$0.818156\pi$
$282$	10.8428	−	4.11212i	0.645678	−	0.244873i
$283$	−4.85604	−	9.25240i	−0.288661	−	0.549998i	0.697339	−	0.716741i	$-0.254367\pi$
$283$	−4.85604	−	9.25240i	−0.288661	−	0.549998i	−0.986000	+	0.166743i	$0.946675\pi$
$284$	−6.56564	+	26.6379i	−0.389599	+	1.58067i
$285$	18.2430	+	14.6403i	1.08062	+	0.867216i
$286$	4.81438	−	2.52452i	0.284680	−	0.149278i
$287$	−0.793193	+	0.547502i	−0.0468207	+	0.0323180i
$288$	−7.77958	−	20.5131i	−0.458416	−	1.20874i
$289$	0.150729	+	0.397439i	0.00886639	+	0.0233787i
$290$	4.63324	+	0.905253i	0.272073	+	0.0531583i
$291$	−9.31578	−	1.13114i	−0.546101	−	0.0663086i
$292$	12.7718	+	11.3148i	0.747413	+	0.662150i
$293$	−10.7938	−	15.6375i	−0.630580	−	0.913553i	0.369296	−	0.929312i	$-0.379599\pi$
$293$	−10.7938	−	15.6375i	−0.630580	−	0.913553i	−0.999876	+	0.0157587i	$0.994984\pi$
$294$	−4.64846	+	5.24703i	−0.271104	+	0.306013i
$295$	14.2854	+	8.86582i	0.831731	+	0.516188i
$296$	−0.369132	+	3.04008i	−0.0214554	+	0.176701i
$297$	−12.5840	+	33.1814i	−0.730200	+	1.92538i
$298$	−4.97564	−	5.61634i	−0.288231	−	0.325346i
$299$	0.404755	−	0.212241i	0.0234076	−	0.0122742i
$300$	−21.2447	+	17.9513i	−1.22657	+	1.03642i
$301$	−0.0282172	−	0.0537633i	−0.00162641	−	0.00309886i
$302$	−2.99887	−	2.06997i	−0.172566	−	0.119114i
$303$	33.1907	+	37.4646i	1.90676	+	2.15228i
$304$	−2.79294	−	11.3314i	−0.160186	−	0.649900i
$305$	8.94386	−	2.67257i	0.512124	−	0.153031i
$306$	3.84758	−	7.33096i	0.219952	−	0.419083i
$307$	3.20995	−	1.68471i	0.183202	−	0.0961517i	−0.370629	−	0.928781i	$-0.620858\pi$
$307$	3.20995	−	1.68471i	0.183202	−	0.0961517i	0.553831	+	0.832629i	$0.313166\pi$
$308$	−0.715393	−	2.90246i	−0.0407633	−	0.165383i
$309$	6.53901	+	5.79306i	0.371991	+	0.329556i
$310$	0.277826	+	0.172424i	0.0157794	+	0.00979302i
$311$	−15.4095	+	8.08751i	−0.873790	+	0.458600i	−0.841109	−	0.540865i	$-0.818097\pi$
$311$	−15.4095	+	8.08751i	−0.873790	+	0.458600i	−0.0326809	+	0.999466i	$0.510405\pi$
$312$	−12.6442	−	6.64216i	−0.715840	−	0.376038i
$313$	−5.50288	+	10.4849i	−0.311041	+	0.592639i	−0.989923	−	0.141608i	$-0.954773\pi$
$313$	−5.50288	+	10.4849i	−0.311041	+	0.592639i	0.678882	+	0.734248i	$0.262465\pi$
$314$	−0.775819	+	0.535510i	−0.0437820	+	0.0302205i
$315$	0.336876	−	4.66288i	0.0189808	−	0.262724i
$316$	18.3480			1.03216
$317$	−7.79016	−	11.2860i	−0.437539	−	0.633884i	0.540737	−	0.841192i	$-0.318145\pi$
$317$	−7.79016	−	11.2860i	−0.437539	−	0.633884i	−0.978276	+	0.207307i	$0.933530\pi$
$318$	−1.44661	+	11.9139i	−0.0811220	+	0.668100i
$319$			26.7229i			1.49620i
$320$	11.7956	−	0.575013i	0.659395	−	0.0321442i
$321$	−3.43735	+	4.97986i	−0.191854	+	0.277949i
$322$	0.00380893	+	0.0154534i	0.000212263	+	0.000861186i
$323$	8.38741	−	12.1513i	0.466688	−	0.676114i
$324$	12.3907	−	3.05404i	0.688373	−	0.169669i
$325$	−2.59793	+	17.8396i	−0.144107	+	0.989562i
$326$	7.47646	+	1.84278i	0.414083	+	0.102062i
$327$	13.3442	−	11.8220i	0.737938	−	0.653756i
$328$	−2.92022	+	2.01569i	−0.161242	+	0.111298i
$329$	−3.09378	−	2.74085i	−0.170566	−	0.151108i
$330$	7.77626	+	6.24058i	0.428069	+	0.343532i
$331$	−20.9420	−	14.4552i	−1.15107	−	0.794529i	−0.169484	−	0.985533i	$-0.554210\pi$
$331$	−20.9420	−	14.4552i	−1.15107	−	0.794529i	−0.981589	+	0.191004i	$0.938826\pi$
$332$	16.4797	−	8.64921i	0.904441	−	0.474687i
$333$	−12.7574	−	3.14442i	−0.699102	−	0.172313i
$334$	−0.610931	−	5.03147i	−0.0334287	−	0.275310i
$335$	−18.5483	−	8.61043i	−1.01340	−	0.470438i
$336$	−2.35420	+	2.65734i	−0.128432	+	0.144970i
$337$		−	3.70208i		−	0.201665i	−0.994903	−	0.100833i	$-0.967849\pi$
$337$		−	3.70208i		−	0.201665i	0.994903	−	0.100833i	$-0.0321506\pi$
$338$	−4.35712	+	1.07053i	−0.236996	+	0.0582290i
$339$	−15.9174			−0.864514
$340$	12.2681	+	12.5587i	0.665328	+	0.681090i
$341$	−0.656345	+	1.73064i	−0.0355431	+	0.0937194i
$342$	−6.96420	+	0.845606i	−0.376581	+	0.0457252i
$343$	4.89862	+	1.20740i	0.264501	+	0.0651935i
$344$	−0.103884	−	0.197935i	−0.00560107	−	0.0106720i
$345$	0.653766	+	0.524658i	0.0351976	+	0.0282466i
$346$	6.75772	+	4.66452i	0.363297	+	0.250766i
$347$	1.08256	−	1.22196i	0.0581148	−	0.0655980i	−0.718734	−	0.695285i	$-0.755278\pi$
$347$	1.08256	−	1.22196i	0.0581148	−	0.0655980i	0.776849	+	0.629687i	$0.216817\pi$
$348$	28.0045	−	19.3301i	1.50120	−	1.03620i
$349$	17.1810	+	19.3933i	0.919677	+	1.03810i	0.999148	+	0.0412640i	$0.0131385\pi$
$349$	17.1810	+	19.3933i	0.919677	+	1.03810i	−0.0794709	+	0.996837i	$0.525323\pi$
$350$	−0.581646	−	0.236307i	−0.0310903	−	0.0126312i
$351$	16.6473	−	24.0987i	0.888566	−	1.28630i
$352$	−3.99111	−	16.1926i	−0.212727	−	0.863067i
$353$	2.74134	−	3.97152i	0.145907	−	0.211383i	−0.743216	−	0.669052i	$-0.766700\pi$
$353$	2.74134	−	3.97152i	0.145907	−	0.211383i	0.889122	+	0.457669i	$0.151316\pi$
$354$	−7.45180	+	1.83670i	−0.396059	+	0.0976197i
$355$	−20.4140	+	25.4375i	−1.08346	+	1.35008i
$356$	2.44016	−	0.296289i	0.129328	−	0.0157033i
$357$	−4.49147			−0.237714
$358$	0.487363	−	4.01380i	0.0257579	−	0.212136i
$359$	18.6779	−	12.8924i	0.985783	−	0.680437i	0.0379753	−	0.999279i	$-0.487909\pi$
$359$	18.6779	−	12.8924i	0.985783	−	0.680437i	0.947808	+	0.318842i	$0.103294\pi$
$360$	1.24024	−	17.1669i	0.0653666	−	0.904775i
$361$	6.48919			0.341537
$362$	3.41677	+	4.95005i	0.179582	+	0.260169i
$363$	−11.1106	+	21.1695i	−0.583156	+	1.11111i
$364$	−0.000909524		2.46724i	−4.76720e−5		0.129319i
$365$	8.10816	+	18.5941i	0.424400	+	0.973262i
$366$	−1.98022	+	3.77300i	−0.103508	+	0.197218i
$367$	1.82676	−	2.06199i	0.0953562	−	0.107635i	−0.698895	−	0.715224i	$-0.746325\pi$
$367$	1.82676	−	2.06199i	0.0953562	−	0.107635i	0.794252	+	0.607589i	$0.207863\pi$
$368$	−0.100089	−	0.406078i	−0.00521752	−	0.0211683i
$369$	−7.07500	−	13.4803i	−0.368310	−	0.701755i
$370$	−0.930446	+	1.49922i	−0.0483716	+	0.0779408i
$371$	3.99965	−	1.51687i	0.207652	−	0.0787519i
$372$	2.28840	−	0.564041i	0.118648	−	0.0292442i
$373$	16.7727	+	18.9324i	0.868456	+	0.980284i	0.999939	−	0.0110342i	$-0.00351235\pi$
$373$	16.7727	+	18.9324i	0.868456	+	0.980284i	−0.131483	+	0.991318i	$0.541974\pi$
$374$	3.57522	−	5.17960i	0.184870	−	0.267831i
$375$	−31.8945	+	8.72273i	−1.64702	+	0.450440i
$376$	−11.3901	−	10.0907i	−0.587398	−	0.520390i
$377$	5.28619	−	21.4129i	0.272253	−	1.10282i
$378$	0.676391	+	0.763488i	0.0347898	+	0.0392696i
$379$	−6.40349	−	2.42852i	−0.328925	−	0.124745i	0.184614	−	0.982811i	$-0.440897\pi$
$379$	−6.40349	−	2.42852i	−0.328925	−	0.124745i	−0.513539	+	0.858066i	$0.671666\pi$
$380$	2.85259	−	14.6001i	0.146335	−	0.748967i
$381$	−22.9558	−	12.0481i	−1.17606	−	0.617245i
$382$	−0.454528	−	0.402677i	−0.0232557	−	0.0206027i
$383$	8.95011	+	12.9665i	0.457329	+	0.662556i	0.982029	−	0.188732i	$-0.0604377\pi$
$383$	8.95011	+	12.9665i	0.457329	+	0.662556i	−0.524699	+	0.851288i	$0.675822\pi$
$384$	−18.5487	+	20.9372i	−0.946562	+	1.06845i
$385$	0.681469	−	3.48788i	0.0347309	−	0.177759i
$386$	−0.180658	+	1.48785i	−0.00919526	+	0.0757298i
$387$	0.896772	−	0.340101i	0.0455855	−	0.0172883i
$388$	2.11632	+	5.58027i	0.107440	+	0.283295i
$389$	−12.8351	−	18.5949i	−0.650768	−	0.942800i	−0.999983	−	0.00575742i	$-0.998167\pi$
$389$	−12.8351	−	18.5949i	−0.650768	−	0.942800i	0.349216	−	0.937042i	$-0.386448\pi$
$390$	−4.99660	−	6.53880i	−0.253012	−	0.331105i
$391$	0.300576	−	0.435459i	0.0152008	−	0.0220221i
$392$	8.93132	+	2.20137i	0.451100	+	0.111186i
$393$	−18.7890	−	35.7994i	−0.947778	−	1.80584i
$394$	2.28898	+	6.03553i	0.115317	+	0.304066i
$395$	19.7850	+	9.18449i	0.995490	+	0.462122i
$396$	46.8748	−	5.69163i	2.35555	−	0.286015i
$397$	4.64835	+	1.14572i	0.233294	+	0.0575018i	0.354229	−	0.935159i	$-0.384743\pi$
$397$	4.64835	+	1.14572i	0.233294	+	0.0575018i	−0.120935	+	0.992660i	$0.538589\pi$
$398$	7.65412	+	4.01719i	0.383666	+	0.201364i
$399$	2.16193	+	3.13210i	0.108232	+	0.156801i
$400$	15.2842	+	6.20958i	0.764212	+	0.310479i
$401$	−4.56557	−	18.5232i	−0.227994	−	0.925007i	−0.967706	−	0.252083i	$-0.918884\pi$
$401$	−4.56557	−	18.5232i	−0.227994	−	0.925007i	0.739712	−	0.672924i	$-0.234962\pi$
$402$	8.72818	−	3.31016i	0.435322	−	0.165096i
$403$	0.868272	−	1.25692i	0.0432517	−	0.0626115i
$404$	11.2877	−	29.7633i	0.561585	−	1.48078i
$405$	14.8899	+	2.90921i	0.739883	+	0.144560i
$406$	0.680111	+	0.356950i	0.0337534	+	0.0177151i
$407$	−9.33900	−	3.54181i	−0.462917	−	0.175561i
$408$	−16.5358			−0.818645
$409$	18.6968	+	7.09074i	0.924495	+	0.350615i	0.770488	−	0.637455i	$-0.220013\pi$
$409$	18.6968	+	7.09074i	0.924495	+	0.350615i	0.154007	+	0.988070i	$0.450782\pi$
$410$	−2.01515	+	0.344960i	−0.0995212	+	0.0170364i
$411$	−31.8179	−	35.9150i	−1.56946	−	1.77155i
$412$	1.32961	−	5.39444i	0.0655051	−	0.265765i
$413$	1.81398	+	2.04756i	0.0892600	+	0.100754i
$414$	−0.249573	+	0.0303037i	−0.0122658	+	0.00148934i
$415$	22.0999	−	1.07733i	1.08484	−	0.0528839i
$416$	−0.00507415	+	13.7645i	−0.000248781	+	0.674861i
$417$	16.1404	+	1.95979i	0.790397	+	0.0959716i
$418$	−5.33286			−0.260839
$419$	0.228255	+	1.87985i	0.0111510	+	0.0918366i	0.997222	−	0.0744894i	$-0.0237327\pi$
$419$	0.228255	+	1.87985i	0.0111510	+	0.0918366i	−0.986071	+	0.166326i	$0.946810\pi$
$420$	−4.14809	+	1.80881i	−0.202406	+	0.0882611i
$421$	24.7124	−	9.37216i	1.20441	−	0.456771i	0.330939	−	0.943652i	$-0.392635\pi$
$421$	24.7124	−	9.37216i	1.20441	−	0.456771i	0.873468	+	0.486881i	$0.161865\pi$
$422$	−1.88895	+	1.67346i	−0.0919527	+	0.0814630i
$423$	48.8690	−	43.2942i	2.37609	−	2.10504i
$424$	14.7251	−	5.58451i	0.715116	−	0.271208i
$425$	6.94233	+	19.6833i	0.336752	+	0.954778i
$426$	−1.79461	−	14.7800i	−0.0869493	−	0.716092i
$427$	1.51876			0.0734981
$428$	3.82020	+	0.463857i	0.184656	+	0.0224214i
$429$	30.9032	−	34.8566i	1.49202	−	1.68289i
$430$	−0.00627123	−	0.128646i	−0.000302425	−	0.00620384i
$431$	21.9634	−	2.66684i	1.05794	−	0.128457i	0.426971	−	0.904265i	$-0.359581\pi$
$431$	21.9634	−	2.66684i	1.05794	−	0.128457i	0.630969	+	0.775808i	$0.282658\pi$
$432$	−17.7739	−	20.0626i	−0.855148	−	0.965263i
$433$	5.43325	−	22.0436i	0.261105	−	1.05935i	−0.683188	−	0.730242i	$-0.739407\pi$
$433$	5.43325	−	22.0436i	0.261105	−	1.05935i	0.944294	−	0.329104i	$-0.106747\pi$
$434$	0.0352785	+	0.0398212i	0.00169342	+	0.00191148i
$435$	39.8738	−	6.82573i	1.91180	−	0.327268i
$436$	−10.6012	−	4.02049i	−0.507703	−	0.192547i
$437$	−0.448345			−0.0214472
$438$	−8.65802	−	3.28355i	−0.413696	−	0.156894i
$439$	−17.7473	−	9.31451i	−0.847033	−	0.444557i	−0.0153990	−	0.999881i	$-0.504902\pi$
$439$	−17.7473	−	9.31451i	−0.847033	−	0.444557i	−0.831634	+	0.555324i	$0.812594\pi$
$440$	2.50890	−	12.8410i	0.119607	−	0.612170i
$441$	−13.9950	+	36.9019i	−0.666431	+	1.75723i
$442$	−3.88940	+	3.44315i	−0.185000	+	0.163774i
$443$	36.5640	−	13.8669i	1.73721	−	0.658835i	0.737345	−	0.675516i	$-0.236079\pi$
$443$	36.5640	−	13.8669i	1.73721	−	0.658835i	0.999861	+	0.0166808i	$0.00530990\pi$
$444$	3.04372	+	12.3488i	0.144448	+	0.586050i
$445$	2.77958	+	0.901980i	0.131765	+	0.0427579i
$446$	−3.88859	−	5.63359i	−0.184130	−	0.266758i
$447$	−56.9326	−	29.8805i	−2.69282	−	1.41330i
$448$	1.86561	+	0.459833i	0.0881420	+	0.0217250i
$449$	6.72696	−	0.816801i	0.317465	−	0.0385472i	0.0397467	−	0.999210i	$-0.487345\pi$
$449$	6.72696	−	0.816801i	0.317465	−	0.0385472i	0.277718	+	0.960663i	$0.410422\pi$
$450$	4.81291	−	8.67070i	0.226883	−	0.408741i
$451$	−4.10382	−	10.8209i	−0.193241	−	0.509535i
$452$	4.70441	+	8.96350i	0.221277	+	0.421608i
$453$	−30.3179	−	7.47269i	−1.42446	−	0.351098i
$454$	−2.03439	+	2.94732i	−0.0954786	+	0.138325i
$455$	−1.23601	+	2.66001i	−0.0579451	+	0.124703i
$456$	7.95937	+	11.5311i	0.372732	+	0.539995i
$457$	−0.612884	−	1.61604i	−0.0286695	−	0.0755953i	0.919917	−	0.392113i	$-0.128256\pi$
$457$	−0.612884	−	1.61604i	−0.0286695	−	0.0755953i	−0.948587	+	0.316517i	$0.897486\pi$
$458$	−1.66309	+	0.630728i	−0.0777113	+	0.0294720i
$459$	4.08741	−	33.6629i	0.190784	−	1.57125i
$460$	0.102227	−	0.523216i	0.00476637	−	0.0243951i
$461$	−13.9114	+	15.7027i	−0.647919	+	0.731350i	−0.977068	−	0.212929i	$-0.931700\pi$
$461$	−13.9114	+	15.7027i	−0.647919	+	0.731350i	0.329149	+	0.944278i	$0.393238\pi$
$462$	0.921545	+	1.33509i	0.0428742	+	0.0621140i
$463$	−5.54686	−	4.91409i	−0.257784	−	0.228377i	0.524325	−	0.851518i	$-0.324318\pi$
$463$	−5.54686	−	4.91409i	−0.257784	−	0.228377i	−0.782109	+	0.623141i	$0.785856\pi$
$464$	−17.8717	−	9.37978i	−0.829672	−	0.435445i
$465$	2.74997	+	0.537294i	0.127527	+	0.0249164i
$466$	−6.39008	−	2.42344i	−0.296015	−	0.112264i
$467$	25.5621	+	28.8537i	1.18287	+	1.33519i	0.929943	+	0.367703i	$0.119856\pi$
$467$	25.5621	+	28.8537i	1.18287	+	1.33519i	0.252930	+	0.967485i	$0.418606\pi$
$468$	−38.6864	−	4.71185i	−1.78828	−	0.217805i
$469$	−2.49042	−	2.20632i	−0.114997	−	0.101878i
$470$	−3.50452	−	8.03679i	−0.161651	−	0.370709i
$471$	−4.58887	+	6.64813i	−0.211444	+	0.306330i
$472$	6.67835	+	7.53830i	0.307396	+	0.346978i
$473$	0.707893	−	0.174480i	0.0325490	−	0.00802260i
$474$	−9.31010	+	3.53085i	−0.427627	+	0.162177i
$475$	10.3844	−	14.3156i	0.476467	−	0.656843i
$476$	1.32746	+	2.52926i	0.0608440	+	0.115929i
$477$	16.1703	+	65.6056i	0.740388	+	3.00387i
$478$	2.93309	−	3.31077i	0.134156	−	0.151431i
$479$	4.75173	−	9.05366i	0.217112	−	0.413673i	−0.752403	−	0.658703i	$-0.771106\pi$
$479$	4.75173	−	9.05366i	0.217112	−	0.413673i	0.969515	+	0.245030i	$0.0787979\pi$
$480$	−23.1418	+	10.0912i	−1.05627	+	0.460598i
$481$	6.78266	+	4.68543i	0.309263	+	0.213637i
$482$	−0.883053	+	1.68252i	−0.0402220	+	0.0766365i
$483$	0.0774762	+	0.112244i	0.00352529	+	0.00510726i
$484$	15.2049			0.691130
$485$	−0.511263	+	7.07667i	−0.0232152	+	0.321335i
$486$	1.22258	−	0.843883i	0.0554571	−	0.0382793i
$487$	3.12520	−	25.7383i	0.141616	−	1.16631i	−0.732559	−	0.680703i	$-0.761674\pi$
$487$	3.12520	−	25.7383i	0.141616	−	1.16631i	0.874175	−	0.485610i	$-0.161403\pi$
$488$	5.59149			0.253115
$489$	65.5034	−	7.95355i	2.96216	−	0.359672i
$490$	4.13354	+	3.31723i	0.186734	+	0.149857i
$491$	−23.5380	+	5.80160i	−1.06226	+	0.261823i	−0.731463	−	0.681881i	$-0.761162\pi$
$491$	−23.5380	+	5.80160i	−1.06226	+	0.261823i	−0.330793	+	0.943703i	$0.607316\pi$
$492$	−8.37130	+	12.1279i	−0.377408	+	0.546769i
$493$	−6.11096	−	24.7931i	−0.275224	−	1.11663i
$494$	4.27319	+	1.05492i	0.192260	+	0.0474630i
$495$	53.3949	+	17.3268i	2.39992	+	0.778782i
$496$	−0.927034	−	1.04640i	−0.0416250	−	0.0469850i
$497$	−4.36730	+	3.01453i	−0.195900	+	0.135220i
$498$	−6.69764	+	7.56007i	−0.300128	+	0.338775i
$499$	19.4220	+	13.4060i	0.869446	+	0.600135i	0.917068	−	0.398730i	$-0.130549\pi$
$499$	19.4220	+	13.4060i	0.869446	+	0.600135i	−0.0476222	+	0.998865i	$0.515164\pi$
$500$	14.3385	+	15.3826i	0.641235	+	0.687931i
$501$	−20.1840	−	38.4573i	−0.901753	−	1.71815i
$502$	0.646124	+	0.159255i	0.0288379	+	0.00710791i
$503$	−13.2246	+	1.60576i	−0.589657	+	0.0715974i	−0.409927	−	0.912119i	$-0.634446\pi$
$503$	−13.2246	+	1.60576i	−0.589657	+	0.0715974i	−0.179731	+	0.983716i	$0.557523\pi$
$504$	0.993024	−	2.61839i	0.0442328	−	0.116632i
$505$	27.0704	−	26.4439i	1.20462	−	1.17674i
$506$	−0.191112			−0.00849595
$507$	−31.6577	+	21.8173i	−1.40597	+	0.968939i
$508$			16.4879i			0.731530i
$509$	−6.39699	+	7.22070i	−0.283541	+	0.320052i	−0.872975	−	0.487765i	$-0.837812\pi$
$509$	−6.39699	+	7.22070i	−0.283541	+	0.320052i	0.589434	+	0.807817i	$0.299351\pi$
$510$	−8.64178	−	4.01165i	−0.382664	−	0.177639i
$511$	0.397822	+	3.27636i	0.0175986	+	0.144938i
$512$	20.8120	+	5.12971i	0.919771	+	0.226703i
$513$	−25.4420	+	13.3530i	−1.12329	+	0.589549i
$514$	−0.622213	−	0.429482i	−0.0274446	−	0.0189437i
$515$	4.13404	−	5.15134i	0.182167	−	0.226995i
$516$	−0.694903	−	0.615631i	−0.0305914	−	0.0271016i
$517$	40.8450	−	28.1932i	1.79636	−	1.23994i
$518$	−0.214886	+	0.190372i	−0.00944154	+	0.00836448i
$519$	68.3189	+	16.8391i	2.99887	+	0.739155i
$520$	−4.55050	+	9.79311i	−0.199553	+	0.429456i
$521$	−2.30057	+	0.567041i	−0.100790	+	0.0248425i	−0.289388	−	0.957212i	$-0.593452\pi$
$521$	−2.30057	+	0.567041i	−0.100790	+	0.0248425i	0.188598	+	0.982054i	$0.439606\pi$
$522$	−6.89216	+	9.98501i	−0.301661	+	0.437032i
$523$	9.92507	+	40.2676i	0.433993	+	1.76078i	0.626438	+	0.779471i	$0.284512\pi$
$523$	9.92507	+	40.2676i	0.433993	+	1.76078i	−0.192445	+	0.981308i	$0.561642\pi$
$524$	−14.6065	+	21.1611i	−0.638086	+	0.924428i
$525$	−5.37839	−	0.125939i	−0.234732	−	0.00549642i
$526$		−	10.6456i		−	0.464170i
$527$	0.213187	−	1.75575i	0.00928657	−	0.0764818i
$528$	−24.2160	−	35.0829i	−1.05387	−	1.52679i
$529$	22.9839			0.999301
$530$	9.05033	+	0.653852i	0.393121	+	0.0284015i
$531$	−35.5610	+	24.5460i	−1.54321	+	1.06520i
$532$	1.12480	−	2.14314i	0.0487664	−	0.0929167i
$533$	1.14784	+	9.48250i	0.0497183	+	0.410733i
$534$	−1.18116	+	0.619921i	−0.0511138	+	0.0268266i
$535$	3.88719	+	2.41247i	0.168058	+	0.104300i
$536$	−9.16875	−	8.12280i	−0.396030	−	0.350852i
$537$	−8.29170	−	33.6407i	−0.357813	−	1.45171i
$538$	7.07476	−	3.71312i	0.305015	−	0.160084i
$539$	−13.9423	+	26.5649i	−0.600539	+	1.14423i
$540$	−9.78186	−	32.7354i	−0.420944	−	1.40871i
$541$	−0.542544	−	2.20119i	−0.0233258	−	0.0946365i	0.958125	−	0.286350i	$-0.0924419\pi$
$541$	−0.542544	−	2.20119i	−0.0233258	−	0.0946365i	−0.981451	+	0.191713i	$0.938596\pi$
$542$	6.60515	+	7.45567i	0.283716	+	0.320249i
$543$	42.4178	+	29.2789i	1.82032	+	1.25648i
$544$	7.40578	+	14.1105i	0.317520	+	0.604984i
$545$	−9.41886	−	9.64199i	−0.403460	−	0.413018i
$546$	−0.474329	−	1.25209i	−0.0202994	−	0.0535847i
$547$	12.6666	+	14.2976i	0.541585	+	0.611323i	0.954049	−	0.299651i	$-0.0968702\pi$
$547$	12.6666	+	14.2976i	0.541585	+	0.611323i	−0.412464	+	0.910974i	$0.635332\pi$
$548$	−10.8208	+	28.5322i	−0.462243	+	1.21884i
$549$	−2.89170	+	23.8153i	−0.123415	+	1.01641i
$550$	4.42644	−	6.10216i	0.188744	−	0.260197i
$551$	−14.3479	+	16.1954i	−0.611240	+	0.689947i
$552$	0.285237	+	0.413237i	0.0121405	+	0.0175885i
$553$	2.65646	+	2.35342i	0.112964	+	0.100078i
$554$	−9.04769	−	1.09859i	−0.384399	−	0.0466745i
$555$	−2.89938	+	14.8396i	−0.123072	+	0.629904i
$556$	−3.66670	−	9.66828i	−0.155503	−	0.410026i
$557$	−6.03226	−	15.9058i	−0.255595	−	0.673949i	−0.999981	−	0.00619894i	$-0.998027\pi$
$557$	−6.03226	−	15.9058i	−0.255595	−	0.673949i	0.744386	−	0.667750i	$-0.232742\pi$
$558$	−0.691595	+	0.477374i	−0.0292776	+	0.0202088i
$559$	−0.601745		0.000221827i	−0.0254511		9.38230e-6i
$560$	2.09341	+	1.68000i	0.0884629	+	0.0709929i
$561$	12.9067	−	52.3645i	0.544921	−	2.21083i
$562$	−3.19843	−	6.09411i	−0.134918	−	0.257064i
$563$	1.65093	−	0.626116i	0.0695784	−	0.0263876i	−0.319570	−	0.947563i	$-0.603538\pi$
$563$	1.65093	−	0.626116i	0.0695784	−	0.0263876i	0.389149	+	0.921175i	$0.372769\pi$
$564$	−59.0906	−	22.4101i	−2.48816	−	0.943635i
$565$	0.585971	+	12.0204i	0.0246520	+	0.505701i
$566$	0.863064	−	3.50159i	0.0362773	−	0.147183i
$567$	2.18568	+	1.14713i	0.0917898	+	0.0481750i
$568$	−16.0787	+	11.0983i	−0.674646	+	0.465675i
$569$	−30.2371	−	7.45278i	−1.26761	−	0.312437i	−0.452508	−	0.891760i	$-0.649471\pi$
$569$	−30.2371	−	7.45278i	−1.26761	−	0.312437i	−0.815098	+	0.579323i	$0.803317\pi$
$570$	1.36215	+	7.95726i	0.0570542	+	0.333293i
$571$	2.30672	+	6.08232i	0.0965333	+	0.254537i	0.974581	−	0.224036i	$-0.0719233\pi$
$571$	2.30672	+	6.08232i	0.0965333	+	0.254537i	−0.878048	+	0.478573i	$0.841154\pi$
$572$	−28.7621	−	7.10047i	−1.20260	−	0.296886i
$573$	−4.86543	−	1.84521i	−0.203256	−	0.0770849i
$574$	−0.330213	−	0.0400951i	−0.0137828	−	0.00167354i
$575$	0.372140	−	0.513021i	0.0155193	−	0.0213944i
$576$	−10.7626	+	28.3787i	−0.448442	+	1.18244i
$577$	−11.4618			−0.477161			−0.238580	−	0.971123i	$-0.576682\pi$
$577$	−11.4618			−0.477161			−0.238580	+	0.971123i	$0.576682\pi$
$578$	−0.0520212	+	0.137169i	−0.00216380	+	0.00570546i
$579$	3.07361	+	12.4701i	0.127735	+	0.518241i
$580$	−15.6285	−	20.4366i	−0.648938	−	0.848584i
$581$	3.49535	+	0.861528i	0.145012	+	0.0357422i
$582$	−2.14771	−	2.42426i	−0.0890254	−	0.100489i
$583$	6.19125	+	50.9895i	0.256415	+	2.11177i
$584$	1.46462	+	12.0623i	0.0606066	+	0.499140i
$585$	−39.3576	−	24.4462i	−1.62723	−	1.01072i
$586$	0.790460	−	6.51002i	0.0326536	−	0.268927i
$587$	−32.7563			−1.35200			−0.675999	−	0.736902i	$-0.736288\pi$
$587$	−32.7563			−1.35200			−0.675999	+	0.736902i	$0.736288\pi$
$588$	37.9241	−	4.60481i	1.56396	−	0.189899i
$589$	−1.32698	+	0.696452i	−0.0546772	+	0.0286968i
$590$	1.66135	+	5.55978i	0.0683968	+	0.228892i
$591$	36.6800	+	41.4032i	1.50881	+	1.70310i
$592$	5.64668	−	5.00252i	0.232077	−	0.205602i
$593$	1.94398	+	5.12586i	0.0798298	+	0.210494i	0.968989	−	0.247104i	$-0.0794790\pi$
$593$	1.94398	+	5.12586i	0.0798298	+	0.210494i	−0.889159	+	0.457598i	$0.848710\pi$
$594$	−10.8449	+	5.69186i	−0.444973	+	0.233540i
$595$	0.165345	+	3.39183i	0.00677850	+	0.139052i
$596$			40.8915i			1.67498i
$597$	73.5341	+	8.92866i	3.00955	+	0.365426i
$598$	0.153137	+	0.0378047i	0.00626222	+	0.00154595i
$599$	−4.92721	−	40.5792i	−0.201320	−	1.65802i	−0.646748	−	0.762704i	$-0.723871\pi$
$599$	−4.92721	−	40.5792i	−0.201320	−	1.65802i	0.445428	−	0.895318i	$-0.353052\pi$
$600$	−19.8011	−	0.463657i	−0.808377	−	0.0189287i
$601$	17.4706	−	15.4776i	0.712640	−	0.631344i	−0.226846	−	0.973931i	$-0.572841\pi$
$601$	17.4706	−	15.4776i	0.712640	−	0.631344i	0.939486	+	0.342586i	$0.111303\pi$
$602$	0.00501504	−	0.0203468i	0.000204398	−	0.000829274i
$603$	39.3384	−	34.8508i	1.60199	−	1.41923i
$604$	4.75243	+	19.2814i	0.193374	+	0.784548i
$605$	16.3957	+	7.61112i	0.666578	+	0.309436i
$606$			17.2746i			0.701732i
$607$	−31.8964	−	12.0967i	−1.29463	−	0.490990i	−0.391433	−	0.920207i	$-0.628020\pi$
$607$	−31.8964	−	12.0967i	−1.29463	−	0.490990i	−0.903202	+	0.429217i	$0.858790\pi$
$608$	6.27518	−	11.9564i	0.254492	−	0.484894i
$609$	6.53392	+	0.793362i	0.264768	+	0.0321486i
$610$	2.92217	+	1.35651i	0.118315	+	0.0549237i
$611$	−38.3059	+	14.5113i	−1.54969	+	0.587066i
$612$	−42.1882	+	15.9999i	−1.70535	+	0.646756i
$613$	8.48532	−	2.09144i	0.342719	−	0.0844726i	−0.0641996	−	0.997937i	$-0.520449\pi$
$613$	8.48532	−	2.09144i	0.342719	−	0.0844726i	0.406919	+	0.913464i	$0.366603\pi$
$614$	1.21481	+	0.299424i	0.0490259	+	0.0120838i
$615$	−15.0978	+	8.88731i	−0.608802	+	0.358371i
$616$	0.989283	−	1.88492i	0.0398594	−	0.0759457i
$617$	−14.4052	−	3.55056i	−0.579930	−	0.142940i	−0.0615708	−	0.998103i	$-0.519611\pi$
$617$	−14.4052	−	3.55056i	−0.579930	−	0.142940i	−0.518360	+	0.855163i	$0.673457\pi$
$618$	0.363427	+	2.99309i	0.0146192	+	0.120400i
$619$	−4.35240	−	1.65065i	−0.174938	−	0.0663451i	0.265581	−	0.964089i	$-0.414436\pi$
$619$	−4.35240	−	1.65065i	−0.174938	−	0.0663451i	−0.440519	+	0.897743i	$0.645205\pi$
$620$	−0.510192	−	1.70738i	−0.0204898	−	0.0685699i
$621$	−0.911755	+	0.478526i	−0.0365875	+	0.0192026i
$622$	−5.83174	−	1.43739i	−0.233831	−	0.0576342i
$623$	0.391294	+	0.270091i	0.0156769	+	0.0108210i
$624$	12.4642	+	32.9020i	0.498968	+	1.31713i
$625$	7.76130	+	23.7647i	0.310452	+	0.950589i
$626$	−3.82119	+	1.44919i	−0.152726	+	0.0579212i
$627$	−42.7286	+	16.2048i	−1.70642	+	0.647158i
$628$	5.09999	+	0.619250i	0.203512	+	0.0247108i
$629$	9.47451	+	1.15041i	0.377773	+	0.0458700i
$630$	1.15419	−	1.12748i	0.0459842	−	0.0449201i
$631$	29.4718	−	20.3429i	1.17325	−	0.809838i	0.188207	−	0.982129i	$-0.439732\pi$
$631$	29.4718	−	20.3429i	1.17325	−	0.809838i	0.985046	+	0.172291i	$0.0551170\pi$
$632$	9.78004	+	8.66436i	0.389029	+	0.344650i
$633$	−10.0498	+	19.1482i	−0.399442	+	0.761074i
$634$	0.570495	−	4.69845i	0.0226573	−	0.186599i
$635$	−8.25334	+	17.7791i	−0.327524	+	0.705543i
$636$	48.9563	−	43.3715i	1.94124	−	1.71979i
$637$	16.4268	−	18.5283i	0.650855	−	0.734118i
$638$	−6.11593	+	6.90346i	−0.242132	+	0.273311i
$639$	−38.9547	−	74.2221i	−1.54103	−	2.93618i
$640$	16.4940	+	13.2367i	0.651985	+	0.523228i
$641$	−22.6857	+	20.0978i	−0.896031	+	0.793814i	−0.979237	−	0.202718i	$-0.935022\pi$
$641$	−22.6857	+	20.0978i	−0.896031	+	0.793814i	0.0832062	+	0.996532i	$0.473484\pi$
$642$	−2.02770	+	0.499783i	−0.0800269	+	0.0197248i
$643$	−0.0344130	−	0.0907397i	−0.00135712	−	0.00357842i	0.934336	−	0.356393i	$-0.115994\pi$
$643$	−0.0344130	−	0.0907397i	−0.00135712	−	0.00357842i	−0.935693	+	0.352815i	$0.885224\pi$
$644$	0.0403091	−	0.0768027i	0.00158840	−	0.00302645i
$645$	−0.441159	−	1.01169i	−0.0173706	−	0.0398354i
$646$	4.94775	−	1.21951i	0.194666	−	0.0479810i
$647$	7.56010	−	8.53359i	0.297218	−	0.335490i	−0.580863	−	0.814001i	$-0.697285\pi$
$647$	7.56010	−	8.53359i	0.297218	−	0.335490i	0.878081	+	0.478511i	$0.158823\pi$
$648$	8.04680	+	4.22328i	0.316108	+	0.165906i
$649$	−29.0844	+	15.2647i	−1.14166	+	0.599191i
$650$	−4.75398	+	4.01401i	−0.186466	+	0.157442i
$651$	0.403666	+	0.211860i	0.0158209	+	0.00830346i
$652$	−23.8385	−	34.5360i	−0.933587	−	1.35253i
$653$		−	1.78627i		−	0.0699022i	−0.999389	−	0.0349511i	$-0.988872\pi$
$653$		−	1.78627i		−	0.0699022i	0.999389	−	0.0349511i	$-0.0111275\pi$
$654$	6.15290			0.240597
$655$	−26.3430	+	15.5068i	−1.02931	+	0.605901i
$656$	8.67719	+	1.05360i	0.338787	+	0.0411362i
$657$	−52.1331			−2.03391
$658$	−0.171947	−	1.41611i	−0.00670320	−	0.0552058i
$659$	21.3497	−	30.9303i	0.831665	−	1.20488i	−0.144856	−	0.989453i	$-0.546272\pi$
$659$	21.3497	−	30.9303i	0.831665	−	1.20488i	0.976521	−	0.215422i	$-0.0691128\pi$
$660$	−9.16840	−	53.5590i	−0.356879	−	2.08478i
$661$	−20.3142	−	14.0219i	−0.790131	−	0.545388i	0.103268	−	0.994654i	$-0.467070\pi$
$661$	−20.3142	−	14.0219i	−0.790131	−	0.545388i	−0.893398	+	0.449266i	$0.851686\pi$
$662$	−2.10175	−	8.52714i	−0.0816869	−	0.331417i
$663$	−20.7005	+	39.4062i	−0.803942	+	1.53041i
$664$	12.8685	+	3.17180i	0.499395	+	0.123090i
$665$	2.28569	−	1.74793i	0.0886351	−	0.0677819i
$666$	−2.57604	−	3.73203i	−0.0998194	−	0.144613i
$667$	−0.514179	+	0.580388i	−0.0199091	+	0.0224727i
$668$	−15.6909	+	22.7322i	−0.607100	+	0.879537i
$669$	−48.2752	−	33.3220i	−1.86643	−	1.28830i
$670$	−2.82106	−	6.46943i	−0.108987	−	0.249936i
$671$	−4.36432	+	17.7068i	−0.168483	+	0.683562i
$672$	−4.07767	+	0.495119i	−0.157300	+	0.0190996i
$673$	26.0880	+	9.89389i	1.00562	+	0.381381i	0.801778	−	0.597622i	$-0.203888\pi$
$673$	26.0880	+	9.89389i	1.00562	+	0.381381i	0.203842	+	0.979004i	$0.434657\pi$
$674$	0.847274	−	0.956375i	0.0326358	−	0.0368382i
$675$	5.83843	−	40.1956i	0.224721	−	1.54713i
$676$	21.6423	+	11.3791i	0.832398	+	0.437659i
$677$			37.9590i			1.45888i	0.684043	+	0.729442i	$0.260220\pi$
$677$			37.9590i			1.45888i	−0.684043	+	0.729442i	$0.739780\pi$
$678$	−4.11201	−	3.64292i	−0.157921	−	0.139906i
$679$	−0.409352	+	1.07937i	−0.0157095	+	0.0414225i
$680$	0.608737	+	12.4874i	0.0233440	+	0.478870i
$681$	−7.34423	+	29.7967i	−0.281432	+	1.14181i
$682$	−0.565639	+	0.296870i	−0.0216594	+	0.0113677i
$683$	−0.949886	+	1.37615i	−0.0363464	+	0.0526568i	−0.840736	−	0.541446i	$-0.817877\pi$
$683$	−0.949886	+	1.37615i	−0.0363464	+	0.0526568i	0.804389	+	0.594102i	$0.202493\pi$
$684$	31.4643	+	21.7182i	1.20307	+	0.830418i
$685$	−25.9507	+	25.3501i	−0.991524	+	0.968579i
$686$	0.989151	+	1.43303i	0.0377660	+	0.0547134i
$687$	−11.4087	+	10.1072i	−0.435267	+	0.385613i
$688$	−0.131783	+	0.534665i	−0.00502418	+	0.0203839i
$689$	5.12546	−	42.0823i	0.195264	−	1.60321i
$690$	0.0488148	+	0.285161i	0.00185835	+	0.0108559i
$691$	3.00625	+	2.07506i	0.114363	+	0.0789391i	0.623873	−	0.781525i	$-0.285558\pi$
$691$	3.00625	+	2.07506i	0.114363	+	0.0789391i	−0.509510	+	0.860465i	$0.670173\pi$
$692$	−10.7092	−	43.4490i	−0.407103	−	1.65168i
$693$	7.51666	+	5.18837i	0.285534	+	0.197090i
$694$	0.559324	−	0.0679143i	0.0212317	−	0.00257799i
$695$	0.885805	−	12.2609i	0.0336005	−	0.465083i
$696$	24.0553	+	2.92084i	0.911814	+	0.110714i
$697$	6.28196	+	9.10098i	0.237946	+	0.344724i
$698$			8.94208i			0.338463i
$699$	−58.5633			−2.21507
$700$	1.51867	+	3.06593i	0.0574004	+	0.115881i
$701$	14.8560	+	7.79706i	0.561105	+	0.294491i	0.721332	−	0.692590i	$-0.243530\pi$
$701$	14.8560	+	7.79706i	0.561105	+	0.294491i	−0.160227	+	0.987080i	$0.551223\pi$
$702$	9.81591	−	2.41557i	0.370478	−	0.0911697i
$703$	−3.75824	−	7.16073i	−0.141745	−	0.270072i
$704$	−10.7221	+	20.4292i	−0.404103	+	0.769954i
$705$	−52.5005	−	53.7442i	−1.97728	−	2.02412i
$706$	1.61712	−	0.398585i	0.0608612	−	0.0150009i
$707$	5.45186	−	2.86136i	0.205038	−	0.107612i
$708$	37.0350	+	19.4375i	1.39186	+	0.730505i
$709$	29.7377	−	11.2780i	1.11682	−	0.423555i	0.273991	−	0.961732i	$-0.411656\pi$
$709$	29.7377	−	11.2780i	1.11682	−	0.423555i	0.842832	+	0.538177i	$0.180887\pi$
$710$	−11.0954	+	1.89934i	−0.416402	+	0.0712810i
$711$	−41.9612	+	37.1743i	−1.57367	+	1.39415i
$712$	1.44059	+	0.994368i	0.0539884	+	0.0372655i
$713$	−0.0475544	+	0.0249585i	−0.00178093	+	0.000934702i
$714$	−1.16030	−	1.02794i	−0.0434232	−	0.0384696i
$715$	−27.4604	−	22.0540i	−1.02696	−	0.824774i
$716$	−16.4934	+	14.6118i	−0.616386	+	0.546070i
$717$	13.4405	−	35.4397i	0.501944	−	1.32352i
$718$	7.77577	+	0.944150i	0.290189	+	0.0352354i
$719$	−11.2351	−	5.89663i	−0.418998	−	0.219907i	0.242029	−	0.970269i	$-0.422187\pi$
$719$	−11.2351	−	5.89663i	−0.418998	−	0.219907i	−0.661027	+	0.750362i	$0.729879\pi$
$720$	−30.3294	+	29.6276i	−1.13031	+	1.10415i
$721$	0.884423	−	0.610473i	0.0329376	−	0.0227352i
$722$	1.67638	+	1.48515i	0.0623885	+	0.0552714i
$723$	−1.96268	+	16.1642i	−0.0729930	+	0.601152i
$724$	3.95107	−	32.5400i	0.146840	−	1.20934i
$725$	−6.62248	−	29.8603i	−0.245953	−	1.10898i
$726$	−7.71520	+	2.92599i	−0.286338	+	0.108594i
$727$	9.79553	−	6.76137i	0.363296	−	0.250765i	−0.372407	−	0.928070i	$-0.621467\pi$
$727$	9.79553	−	6.76137i	0.363296	−	0.250765i	0.735703	+	0.677304i	$0.236852\pi$
$728$	−1.16557	+	1.31468i	−0.0431990	+	0.0487254i
$729$	18.7941	−	27.2280i	0.696078	−	1.00844i
$730$	−2.16092	+	6.65918i	−0.0799793	+	0.246467i
$731$	−0.616872	+	0.323759i	−0.0228158	+	0.0119747i
$732$	21.7128	−	8.23460i	0.802530	−	0.304359i
$733$	−0.283264	+	0.746906i	−0.0104626	+	0.0275876i	−0.940146	−	0.340773i	$-0.889311\pi$
$733$	−0.283264	+	0.746906i	−0.0104626	+	0.0275876i	0.929683	+	0.368360i	$0.120081\pi$
$734$	0.943832	−	0.114602i	0.0348375	−	0.00423003i
$735$	43.1992	+	14.0182i	1.59343	+	0.517071i
$736$	0.224881	−	0.428475i	0.00828922	−	0.0157938i
$737$	32.8792	−	22.6949i	1.21112	−	0.835977i
$738$	1.25744	−	5.10164i	0.0462870	−	0.187794i
$739$	1.48487	+	6.02437i	0.0546220	+	0.221610i	0.991909	−	0.126947i	$-0.0405178\pi$
$739$	1.48487	+	6.02437i	0.0546220	+	0.221610i	−0.937287	+	0.348557i	$0.886672\pi$
$740$	9.21346	−	2.75313i	0.338694	−	0.101207i
$741$	37.4437	−	4.53248i	1.37553	−	0.166505i
$742$	1.38041	+	0.523519i	0.0506763	+	0.0192190i
$743$	−3.53086	+	29.0792i	−0.129535	+	1.06681i	0.772459	+	0.635064i	$0.219026\pi$
$743$	−3.53086	+	29.0792i	−0.129535	+	1.06681i	−0.901994	+	0.431749i	$0.857897\pi$
$744$	1.48614	+	0.779986i	0.0544845	+	0.0285957i
$745$	−20.4691	+	44.0939i	−0.749929	+	1.61548i
$746$			8.72957i			0.319612i
$747$	−20.1645	+	53.1694i	−0.737780	+	1.94537i
$748$	−33.3024	+	8.20831i	−1.21766	+	0.300126i
$749$	0.493599	+	0.557158i	0.0180357	+	0.0203581i
$750$	−10.2358	−	5.04613i	−0.373757	−	0.184259i
$751$	−8.60870	+	7.62665i	−0.314136	+	0.278300i	−0.805427	−	0.592695i	$-0.798064\pi$
$751$	−8.60870	+	7.62665i	−0.314136	+	0.278300i	0.491291	+	0.870996i	$0.336525\pi$
$752$	4.51835	+	37.2120i	0.164767	+	1.35698i
$753$	5.66087	−	0.687355i	0.206294	−	0.0250486i
$754$	6.26626	−	4.32188i	0.228204	−	0.157394i
$755$	−4.52707	+	23.1703i	−0.164757	+	0.843255i
$756$		−	5.55881i		−	0.202172i
$757$	48.1495	−	5.84641i	1.75003	−	0.212492i	0.818083	−	0.575100i	$-0.195037\pi$
$757$	48.1495	−	5.84641i	1.75003	−	0.212492i	0.931942	+	0.362608i	$0.118114\pi$
$758$	−1.09844	−	2.09290i	−0.0398971	−	0.0760176i
$759$	−1.53125	+	0.580725i	−0.0555807	+	0.0210790i
$760$	8.41499	−	6.43520i	0.305244	−	0.233429i
$761$	26.7752	+	30.2229i	0.970599	+	1.09558i	0.995392	+	0.0958877i	$0.0305690\pi$
$761$	26.7752	+	30.2229i	0.970599	+	1.09558i	−0.0247927	+	0.999693i	$0.507893\pi$
$762$	−3.17289	−	8.36621i	−0.114942	−	0.303076i
$763$	−1.01916	−	1.94186i	−0.0368962	−	0.0702999i
$764$	0.398896	+	3.28521i	0.0144316	+	0.118855i
$765$	−53.5012	−	3.86526i	−1.93434	−	0.139749i
$766$	−0.655442	+	5.39805i	−0.0236821	+	0.195039i
$767$	26.3248	−	6.47818i	0.950532	−	0.233913i
$768$	21.4282	−	2.60185i	0.773222	−	0.0938862i
$769$	−28.6127	+	3.47421i	−1.03180	+	0.125283i	−0.618881	−	0.785485i	$-0.712414\pi$
$769$	−28.6127	+	3.47421i	−1.03180	+	0.125283i	−0.412919	+	0.910768i	$0.635491\pi$
$770$	0.974298	−	0.745075i	0.0351113	−	0.0268506i
$771$	−6.29042	−	1.55045i	−0.226544	−	0.0558381i
$772$	6.11385	−	5.41639i	0.220042	−	0.194940i
$773$	−13.1596	+	3.24354i	−0.473316	+	0.116662i	−0.468756	−	0.883328i	$-0.655298\pi$
$773$	−13.1596	+	3.24354i	−0.473316	+	0.116662i	−0.00456007	+	0.999990i	$0.501452\pi$
$774$	0.309504	+	0.117379i	0.0111249	+	0.00421912i
$775$	0.304515	−	2.09648i	0.0109385	−	0.0753078i
$776$	−1.50707	+	3.97382i	−0.0541007	+	0.142652i
$777$	−1.14325	+	2.17829i	−0.0410140	+	0.0781457i
$778$	0.939954	−	7.74122i	0.0336990	−	0.277536i
$779$	3.32275	−	8.76136i	0.119050	−	0.313908i
$780$	−3.24816	+	44.7301i	−0.116303	+	1.60160i
$781$	−22.5955	−	59.5795i	−0.808531	−	2.13192i
$782$	0.177310	−	0.0437031i	0.00634060	−	0.00156282i
$783$	−11.8922	+	48.2487i	−0.424994	+	1.72427i
$784$	−12.8722	−	18.6486i	−0.459721	−	0.666022i
$785$	5.18942	+	3.22065i	0.185218	+	0.114950i
$786$	3.33936	−	13.5483i	0.119111	−	0.483253i
$787$	−4.34458	−	35.7808i	−0.154868	−	1.27545i	−0.838209	−	0.545350i	$-0.816397\pi$
$787$	−4.34458	−	35.7808i	−0.154868	−	1.27545i	0.683341	−	0.730099i	$-0.260526\pi$
$788$	12.4744	−	32.8922i	0.444381	−	1.17174i
$789$	−32.3485	−	85.2959i	−1.15164	−	3.03661i
$790$	3.00914	+	6.90075i	0.107060	+	0.245518i
$791$	−0.468595	+	1.90116i	−0.0166613	+	0.0675976i
$792$	27.6734	+	19.1015i	0.983330	+	0.678744i
$793$	6.99976	−	13.3250i	0.248569	−	0.473184i
$794$	0.938616	+	1.35982i	0.0333102	+	0.0482582i
$795$	74.5009	−	22.2621i	2.64228	−	0.789555i
$796$	−16.7052	−	44.0479i	−0.592099	−	1.56124i
$797$	34.7255	+	4.21644i	1.23004	+	0.149354i	0.709638	−	0.704567i	$-0.248859\pi$
$797$	34.7255	+	4.21644i	1.23004	+	0.149354i	0.520403	+	0.853921i	$0.325782\pi$
$798$	−0.158324	+	1.30392i	−0.00560462	+	0.0461582i
$799$	−31.4481	+	35.4976i	−1.11255	+	1.25581i
$800$	8.47253	+	17.1046i	0.299549	+	0.604737i
$801$	−4.98024	+	5.62153i	−0.175968	+	0.198627i
$802$	3.05987	−	5.83009i	0.108048	−	0.205868i
$803$	−39.3412	−	4.77688i	−1.38832	−	0.168572i
$804$	−47.5665	−	18.0396i	−1.67754	−	0.636208i
$805$	0.0819112	−	0.0626400i	0.00288699	−	0.00220777i
$806$	0.511968	−	0.125989i	0.0180333	−	0.00443776i
$807$	45.4023	−	51.2486i	1.59824	−	1.80404i
$808$	20.0716	−	10.5344i	0.706116	−	0.370598i
$809$	4.23360	−	6.13343i	0.148846	−	0.215640i	−0.741468	−	0.670989i	$-0.765870\pi$
$809$	4.23360	−	6.13343i	0.148846	−	0.215640i	0.890313	+	0.455349i	$0.150485\pi$
$810$	3.18075	+	4.15931i	0.111760	+	0.146143i
$811$	9.71971	+	39.4344i	0.341305	+	1.38473i	0.851358	+	0.524586i	$0.175780\pi$
$811$	9.71971	+	39.4344i	0.341305	+	1.38473i	−0.510052	+	0.860143i	$0.670374\pi$
$812$	−1.48435	−	3.91390i	−0.0520904	−	0.137351i
$813$	75.5779	+	39.6663i	2.65063	+	1.39116i
$814$	−1.60199	−	3.05234i	−0.0561497	−	0.106984i
$815$	−8.41769	−	49.1736i	−0.294859	−	1.72247i
$816$	30.4899	+	27.0117i	1.06736	+	0.945598i
$817$	0.522698	+	0.274333i	0.0182869	+	0.00959770i
$818$	3.20720	+	6.11081i	0.112137	+	0.213659i
$819$	−4.99672	−	5.64432i	−0.174599	−	0.197228i
$820$	9.46685	+	5.87531i	0.330597	+	0.205175i
$821$	−22.9729	+	15.8570i	−0.801758	+	0.553414i	−0.896995	−	0.442041i	$-0.854255\pi$
$821$	−22.9729	+	15.8570i	−0.801758	+	0.553414i	0.0952367	+	0.995455i	$0.469639\pi$
$822$		−	16.5601i		−	0.577598i
$823$			55.4836i			1.93404i	0.254705	+	0.967019i	$0.418022\pi$
$823$			55.4836i			1.93404i	−0.254705	+	0.967019i	$0.581978\pi$
$824$	3.25610	−	2.24752i	0.113431	−	0.0782961i
$825$	16.9236	−	62.3429i	0.589205	−	2.17050i
$826$			0.944110i			0.0328498i
$827$	−3.97231	−	32.7149i	−0.138131	−	1.13761i	−0.882658	−	0.470016i	$-0.844248\pi$
$827$	−3.97231	−	32.7149i	−0.138131	−	1.13761i	0.744527	−	0.667592i	$-0.232675\pi$
$828$	1.12757	+	0.778308i	0.0391859	+	0.0270481i
$829$	−15.3188	+	3.77575i	−0.532045	+	0.131137i	−0.496181	−	0.868219i	$-0.665265\pi$
$829$	−15.3188	+	3.77575i	−0.532045	+	0.131137i	−0.0358645	+	0.999357i	$0.511418\pi$
$830$	5.95572	+	4.77956i	0.206726	+	0.165901i
$831$	−75.8312	+	18.6907i	−2.63055	+	0.648373i
$832$	12.6327	−	14.2488i	0.437961	−	0.493989i
$833$	6.86066	−	27.8348i	0.237708	−	0.964418i
$834$	3.72108	+	4.20024i	0.128851	+	0.145442i
$835$	−28.2989	+	16.6581i	−0.979323	+	0.576478i
$836$	21.7539	+	19.2722i	0.752373	+	0.666544i
$837$	−1.95521	+	2.83261i	−0.0675820	+	0.0979095i
$838$	−0.371264	+	0.537869i	−0.0128251	+	0.0185804i
$839$	11.0492	+	21.0525i	0.381460	+	0.726811i	0.998176	−	0.0603746i	$-0.0192295\pi$
$839$	11.0492	+	21.0525i	0.381460	+	0.726811i	−0.616716	+	0.787186i	$0.711537\pi$
$840$	−3.06521	−	0.994670i	−0.105760	−	0.0343194i
$841$	1.01490	+	8.35843i	0.0349965	+	0.288222i
$842$	8.52901	+	3.23463i	0.293929	+	0.111473i
$843$	−44.1448	−	39.1089i	−1.52043	−	1.34698i
$844$	13.7531			0.473401
$845$	17.6412	+	23.1038i	0.606876	+	0.794796i
$846$	22.5331			0.774702
$847$	2.20139	+	1.95026i	0.0756405	+	0.0670117i
$848$	−36.2737	−	13.7568i	−1.24564	−	0.472411i
$849$	−3.72503	−	30.6784i	−0.127843	−	1.05288i
$850$	−2.71135	+	6.67372i	−0.0929987	+	0.228907i
$851$	−0.134683	−	0.256616i	−0.00461686	−	0.00879669i
$852$	−46.0922	+	66.7760i	−1.57909	+	2.28771i
$853$	20.2825	−	29.3842i	0.694458	−	1.00610i	−0.304112	−	0.952636i	$-0.598360\pi$
$853$	20.2825	−	29.3842i	0.694458	−	1.00610i	0.998570	−	0.0534602i	$-0.0170250\pi$
$854$	0.392349	+	0.347591i	0.0134259	+	0.0118943i
$855$	23.0569	+	39.1693i	0.788531	+	1.33956i
$856$	1.81724	+	2.05124i	0.0621119	+	0.0701098i
$857$	11.5046	−	46.6760i	0.392989	−	1.59442i	−0.357747	−	0.933819i	$-0.616455\pi$
$857$	11.5046	−	46.6760i	0.392989	−	1.59442i	0.750736	−	0.660602i	$-0.229699\pi$
$858$	15.9608	−	1.93202i	0.544892	−	0.0659580i
$859$	−39.7158	+	9.78907i	−1.35509	+	0.333999i	−0.848958	−	0.528460i	$-0.822770\pi$
$859$	−39.7158	+	9.78907i	−1.35509	+	0.333999i	−0.506128	+	0.862459i	$0.668924\pi$
$860$	−0.439326	+	0.547435i	−0.0149809	+	0.0186674i
$861$	−2.76761	+	0.682153i	−0.0943197	+	0.0232477i
$862$	6.28425	+	4.33770i	0.214042	+	0.147743i
$863$	−3.15150	−	25.9549i	−0.107278	−	0.883515i	−0.942639	−	0.333813i	$-0.891664\pi$
$863$	−3.15150	−	25.9549i	−0.107278	−	0.883515i	0.835361	−	0.549702i	$-0.185259\pi$
$864$		−	31.0121i		−	1.05505i
$865$	10.2014	−	52.2125i	0.346858	−	1.77528i
$866$	6.44858	−	4.45114i	0.219132	−	0.151256i
$867$			1.25711i			0.0426938i
$868$		−	0.289931i		−	0.00984089i
$869$	−35.0713	+	24.2080i	−1.18971	+	0.821200i
$870$	11.8629	+	7.36237i	0.402191	+	0.249608i
$871$	−30.8353	+	11.6813i	−1.04482	+	0.395806i
$872$	−3.75216	−	7.14915i	−0.127064	−	0.242101i
$873$	−16.1459	−	8.47404i	−0.546457	−	0.286803i
$874$	−0.115823	−	0.102610i	−0.00391777	−	0.00347084i
$875$	0.102890	+	4.06625i	0.00347833	+	0.137464i
$876$	23.4515	+	44.6832i	0.792354	+	1.50970i
$877$	−24.6738	−	12.9498i	−0.833176	−	0.437285i	−0.00651112	−	0.999979i	$-0.502073\pi$
$877$	−24.6738	−	12.9498i	−0.833176	−	0.437285i	−0.826665	+	0.562694i	$0.809765\pi$
$878$	−2.45298	−	6.46799i	−0.0827842	−	0.218284i
$879$	−13.4484	−	54.5623i	−0.453603	−	1.84034i
$880$	−25.6022	+	19.5788i	−0.863049	+	0.660000i
$881$	−11.3690	+	16.4709i	−0.383033	+	0.554919i	−0.966319	−	0.257348i	$-0.917151\pi$
$881$	−11.3690	+	16.4709i	−0.383033	+	0.554919i	0.583286	+	0.812267i	$0.301767\pi$
$882$	−12.0609	+	6.33007i	−0.406113	+	0.213144i
$883$	−12.6054	+	14.2286i	−0.424207	+	0.478831i	−0.921292	−	0.388871i	$-0.872865\pi$
$883$	−12.6054	+	14.2286i	−0.424207	+	0.478831i	0.497085	+	0.867702i	$0.334404\pi$
$884$	28.3088	+	0.0104357i	0.952127	+	0.000350992i
$885$	30.2056	+	39.4984i	1.01535	+	1.32772i
$886$	12.6194	+	4.78589i	0.423956	+	0.160785i
$887$	−25.4400	−	3.08897i	−0.854190	−	0.103717i	−0.318284	−	0.947995i	$-0.603107\pi$
$887$	−25.4400	−	3.08897i	−0.854190	−	0.103717i	−0.535906	+	0.844278i	$0.680030\pi$
$888$	−4.20901	+	8.01961i	−0.141245	+	0.269120i
$889$	−2.11482	+	2.38714i	−0.0709289	+	0.0800621i
$890$	0.511630	+	0.869159i	0.0171499	+	0.0291343i
$891$	−19.6548	+	22.1857i	−0.658460	+	0.743248i
$892$	−4.49667	+	37.0334i	−0.150560	+	1.23997i
$893$	39.8913	+	4.84368i	1.33491	+	0.162088i
$894$	−7.86906	−	20.7490i	−0.263181	−	0.693951i
$895$	−25.0993	+	7.50009i	−0.838978	+	0.250700i
$896$	1.95467	+	2.83183i	0.0653009	+	0.0946047i
$897$	1.34185	−	0.162429i	0.0448032	−	0.00542334i
$898$	1.92474	+	1.32855i	0.0642295	+	0.0443344i
$899$	−0.620263	+	2.51651i	−0.0206869	+	0.0839302i
$900$	−50.9676	+	17.9764i	−1.69892	+	0.599212i
$901$	−17.4043	−	45.8914i	−0.579822	−	1.52887i
$902$	1.41636	−	3.73462i	0.0471595	−	0.124349i
$903$	−0.0216452	−	0.178264i	−0.000720307	−	0.00593226i
$904$	−1.72518	+	6.99934i	−0.0573787	+	0.232794i
$905$	20.5491	−	33.1106i	0.683075	−	1.10063i
$906$	−6.12193	−	8.86914i	−0.203387	−	0.294657i
$907$	−8.00610	+	32.4820i	−0.265838	+	1.07855i	0.674491	+	0.738283i	$0.264363\pi$
$907$	−8.00610	+	32.4820i	−0.265838	+	1.07855i	−0.940330	+	0.340265i	$0.889483\pi$
$908$	18.9499	−	4.67073i	0.628875	−	0.155004i
$909$	34.4879	+	90.9371i	1.14389	+	3.01619i
$910$	−0.928086	+	0.404294i	−0.0307657	+	0.0134022i
$911$	15.0039	−	39.5620i	0.497101	−	1.31075i	−0.418339	−	0.908291i	$-0.637388\pi$
$911$	15.0039	−	39.5620i	0.497101	−	1.31075i	0.915440	−	0.402455i	$-0.131843\pi$
$912$	4.16038	−	34.2638i	0.137764	−	1.13459i
$913$	−20.0885	+	38.2755i	−0.664833	+	1.26673i
$914$	0.211526	−	0.557747i	0.00699664	−	0.0184486i
$915$	27.5353	+	1.98932i	0.910289	+	0.0657650i
$916$	9.06347	+	3.43732i	0.299465	+	0.113572i
$917$	−4.82899	+	1.19024i	−0.159467	+	0.0393051i
$918$	8.76015	−	7.76081i	0.289128	−	0.256145i
$919$	16.3745	+	4.03595i	0.540144	+	0.133134i	0.499943	−	0.866058i	$-0.333354\pi$
$919$	16.3745	+	4.03595i	0.540144	+	0.133134i	0.0402007	+	0.999192i	$0.487200\pi$
$920$	0.301565	−	0.230616i	0.00994229	−	0.00760317i
$921$	10.6433	−	1.29233i	0.350709	−	0.0425838i
$922$	−7.18760	+	0.872732i	−0.236711	+	0.0287419i
$923$	6.31996	+	52.2104i	0.208024	+	1.71853i
$924$	1.06565	−	8.77644i	0.0350574	−	0.288724i
$925$	11.3132	+	1.64324i	0.371974	+	0.0540295i
$926$	−0.308285	−	2.53896i	−0.0101309	−	0.0834353i
$927$	7.88873	+	15.0307i	0.259100	+	0.493674i
$928$	−8.28104	−	21.8353i	−0.271838	−	0.716779i
$929$	−11.1184	−	12.5501i	−0.364782	−	0.411754i	0.537250	−	0.843423i	$-0.319463\pi$
$929$	−11.1184	−	12.5501i	−0.364782	−	0.411754i	−0.902032	+	0.431669i	$0.857925\pi$
$930$	0.587444	+	0.768171i	0.0192630	+	0.0251893i
$931$	−22.7127	+	8.61380i	−0.744380	+	0.282306i
$932$	17.3085	+	32.9786i	0.566958	+	1.08025i
$933$	−51.0935	+	6.20387i	−1.67273	+	0.203106i
$934$			13.3042i			0.435325i
$935$	−40.0194	−	7.81908i	−1.30877	−	0.255711i
$936$	−18.3959	−	20.7801i	−0.601290	−	0.679220i
$937$	8.92007	−	1.08309i	0.291406	−	0.0353831i	0.0264717	−	0.999650i	$-0.491573\pi$
$937$	8.92007	−	1.08309i	0.291406	−	0.0353831i	0.264934	+	0.964266i	$0.414650\pi$
$938$	−0.138413	−	1.13994i	−0.00451936	−	0.0372203i
$939$	−26.2130	+	23.2227i	−0.855429	+	0.757844i
$940$	−14.7482	+	45.4486i	−0.481033	+	1.48237i
$941$	10.0481	+	11.3420i	0.327559	+	0.369737i	0.889101	−	0.457710i	$-0.151330\pi$
$941$	10.0481	+	11.3420i	0.327559	+	0.369737i	−0.561543	+	0.827448i	$0.689792\pi$
$942$	−2.70698	+	0.667212i	−0.0881983	+	0.0217389i
$943$	0.119076	−	0.313977i	0.00387764	−	0.0102245i
$944$		−	24.8089i		−	0.807461i
$945$	2.78258	−	5.99416i	0.0905173	−	0.194990i
$946$	0.222805	+	0.116937i	0.00724403	+	0.00380196i
$947$	4.06190	−	33.4528i	0.131994	−	1.08707i	−0.764690	−	0.644398i	$-0.777108\pi$
$947$	4.06190	−	33.4528i	0.131994	−	1.08707i	0.896684	−	0.442671i	$-0.145969\pi$
$948$	50.7378	+	19.2423i	1.64789	+	0.624961i
$949$	30.5789	+	11.6099i	0.992633	+	0.376875i
$950$	5.95896	−	1.32159i	0.193334	−	0.0428781i
$951$	−9.70606	−	39.3790i	−0.314740	−	1.27695i
$952$	−0.486801	+	1.97503i	−0.0157773	+	0.0640110i
$953$	12.0538	−	8.32012i	0.390460	−	0.269515i	−0.356619	−	0.934250i	$-0.616071\pi$
$953$	12.0538	−	8.32012i	0.390460	−	0.269515i	0.747080	+	0.664735i	$0.231455\pi$
$954$	−10.8374	+	20.6490i	−0.350875	+	0.668536i
$955$	−1.21434	+	3.74217i	−0.0392952	+	0.121094i
$956$	−23.9294	+	2.90555i	−0.773931	+	0.0939722i
$957$	−28.0254	+	73.8970i	−0.905934	+	2.38875i
$958$	3.29960	−	1.25137i	0.106605	−	0.0404300i
$959$	−5.22635	+	2.74300i	−0.168768	+	0.0885762i
$960$	33.2214	+	10.7804i	1.07222	+	0.347937i
$961$	17.5080	−	25.3648i	0.564775	−	0.818218i
$962$	0.679868	+	2.76272i	0.0219198	+	0.0890736i
$963$	−9.67644	+	6.67917i	−0.311819	+	0.215233i
$964$	9.68254	−	3.67210i	0.311854	−	0.118270i
$965$	9.30395	−	2.78017i	0.299505	−	0.0894969i
$966$	−0.00567380	+	0.0467279i	−0.000182552	+	0.00150345i
$967$	−1.19102	+	9.80895i	−0.0383007	+	0.315434i	0.960950	+	0.276723i	$0.0892484\pi$
$967$	−1.19102	+	9.80895i	−0.0383007	+	0.315434i	−0.999250	+	0.0387115i	$0.987675\pi$
$968$	8.10464	+	7.18008i	0.260493	+	0.230777i
$969$	35.9372	−	24.8057i	1.15447	−	0.796873i
$970$	−1.75167	+	1.71114i	−0.0562429	+	0.0549413i
$971$	37.8731	+	19.8773i	1.21541	+	0.637894i	0.945697	−	0.325048i	$-0.105380\pi$
$971$	37.8731	+	19.8773i	1.21541	+	0.637894i	0.269708	+	0.962942i	$0.413073\pi$
$972$	−8.03681	−	0.975846i	−0.257781	−	0.0313003i
$973$	0.709236	−	1.87010i	0.0227371	−	0.0599527i
$974$	6.69793	−	5.93384i	0.214615	−	0.190133i
$975$	−25.8931	+	46.6073i	−0.829244	+	1.49263i
$976$	−10.3100	−	9.13384i	−0.330014	−	0.292367i
$977$	1.19720	−	0.628337i	0.0383017	−	0.0201023i	−0.445464	−	0.895300i	$-0.646961\pi$
$977$	1.19720	−	0.628337i	0.0383017	−	0.0201023i	0.483765	+	0.875198i	$0.339269\pi$
$978$	18.7421	+	12.9367i	0.599305	+	0.413670i
$979$	−4.27332	+	3.78583i	−0.136576	+	0.120996i
$980$	−4.87354	−	28.4697i	−0.155679	−	0.909431i
$981$	32.3902	−	12.2840i	1.03414	−	0.392197i
$982$	−7.40846	−	3.88826i	−0.236414	−	0.124079i
$983$	−0.0896324	+	0.0470427i	−0.00285883	+	0.00150043i	−0.466152	−	0.884705i	$-0.654360\pi$
$983$	−0.0896324	+	0.0470427i	−0.00285883	+	0.00150043i	0.463293	+	0.886205i	$0.346668\pi$
$984$	−10.1892	+	2.51142i	−0.324821	+	0.0800611i
$985$	29.9162	−	29.2239i	0.953210	−	0.931152i
$986$	4.09559	−	7.80350i	0.130430	−	0.248514i
$987$	−5.68079	−	10.8238i	−0.180822	−	0.344527i
$988$	−13.6189	−	19.7460i	−0.433275	−	0.628203i
$989$	0.0187317	+	0.00983116i	0.000595634	+	0.000312613i
$990$	9.82827	+	16.6963i	0.312363	+	0.530644i
$991$	−40.1498			−1.27540			−0.637700	−	0.770285i	$-0.720114\pi$
$991$	−40.1498			−1.27540			−0.637700	+	0.770285i	$0.720114\pi$
$992$		−	1.61750i		−	0.0513556i
$993$	−42.7511	−	61.9356i	−1.35666	−	1.96547i
$994$	−1.81814	−	0.220763i	−0.0576680	−	0.00700216i
$995$	4.03565	−	55.8597i	0.127939	−	1.77087i
$996$	54.6421	−	6.63475i	1.73140	−	0.210230i
$997$	−24.7128	−	17.0580i	−0.782663	−	0.540233i	0.108403	−	0.994107i	$-0.465426\pi$
$997$	−24.7128	−	17.0580i	−0.782663	−	0.540233i	−0.891066	+	0.453874i	$0.850042\pi$
$998$	1.94920	+	7.90823i	0.0617010	+	0.250331i
$999$	−15.2855	−	10.5508i	−0.483613	−	0.333814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.v.a.389.50	yes	1056
5.4	even	2	inner	845.2.v.a.389.39	✓	1056
169.116	even	26	inner	845.2.v.a.454.39	yes	1056
845.454	even	26	inner	845.2.v.a.454.50	yes	1056

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.v.a.389.39	✓	1056	5.4	even	2	inner
845.2.v.a.389.50	yes	1056	1.1	even	1	trivial
845.2.v.a.454.39	yes	1056	169.116	even	26	inner
845.2.v.a.454.50	yes	1056	845.454	even	26	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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.v (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258334 + 0.228864i) q^{2} +(2.76530 + 1.04874i) q^{3} +(-0.226716 - 1.86717i) q^{4} +(0.690181 - 2.12689i) q^{5} +(0.474353 + 0.903805i) q^{6} +(0.206669 - 0.299412i) q^{7} +(0.760874 - 1.10232i) q^{8} +(4.30150 + 3.81080i) q^{9} +O(q^{10})\)	\(q+(0.258334 + 0.228864i) q^{2} +(2.76530 + 1.04874i) q^{3} +(-0.226716 - 1.86717i) q^{4} +(0.690181 - 2.12689i) q^{5} +(0.474353 + 0.903805i) q^{6} +(0.206669 - 0.299412i) q^{7} +(0.760874 - 1.10232i) q^{8} +(4.30150 + 3.81080i) q^{9} +(0.665066 - 0.391491i) q^{10} +(2.89686 + 3.26988i) q^{11} +(1.33124 - 5.40105i) q^{12} +(-1.67441 - 3.19317i) q^{13} +(0.121915 - 0.0300492i) q^{14} +(4.13911 - 5.15766i) q^{15} +(-3.20362 + 0.789621i) q^{16} +(-3.43541 - 2.37129i) q^{17} +(0.239070 + 1.96892i) q^{18} +3.53706i q^{19} +(-4.12774 - 0.806486i) q^{20} +(0.885508 - 0.611222i) q^{21} +1.50771i q^{22} +0.126756i q^{23} +(3.26009 - 2.25028i) q^{24} +(-4.04730 - 2.93587i) q^{25} +(0.298247 - 1.20812i) q^{26} +(3.77517 + 7.19298i) q^{27} +(-0.605908 - 0.318005i) q^{28} +(4.57877 + 4.05644i) q^{29} +(2.24968 - 0.385108i) q^{30} +(0.196901 + 0.375164i) q^{31} +(-3.38031 - 1.77412i) q^{32} +(4.58143 + 12.0802i) q^{33} +(-0.344780 - 1.39883i) q^{34} +(-0.494177 - 0.646210i) q^{35} +(6.14019 - 8.89561i) q^{36} +(-2.02449 + 1.06253i) q^{37} +(-0.809507 + 0.913745i) q^{38} +(-1.28143 - 10.5861i) q^{39} +(-1.81936 - 2.37909i) q^{40} +(-2.47702 - 0.939409i) q^{41} +(0.368644 + 0.0447615i) q^{42} +(0.0775596 - 0.147777i) q^{43} +(5.44866 - 6.15026i) q^{44} +(11.0740 - 6.51867i) q^{45} +(-0.0290100 + 0.0327455i) q^{46} +(1.36941 - 11.2781i) q^{47} +(-9.68707 - 1.17622i) q^{48} +(2.43530 + 6.42136i) q^{49} +(-0.373641 - 1.68472i) q^{50} +(-7.01307 - 10.1602i) q^{51} +(-5.58259 + 3.85034i) q^{52} +(9.67646 + 6.67918i) q^{53} +(-0.670961 + 2.72220i) q^{54} +(8.95402 - 3.90449i) q^{55} +(-0.172798 - 0.455630i) q^{56} +(-3.70946 + 9.78104i) q^{57} +(0.254480 + 2.09584i) q^{58} +(-1.79941 + 7.30051i) q^{59} +(-10.5686 - 6.55910i) q^{60} +(2.37143 + 3.43561i) q^{61} +(-0.0349953 + 0.141982i) q^{62} +(2.02999 - 0.500347i) q^{63} +(1.87282 + 4.93821i) q^{64} +(-7.94717 + 1.35741i) q^{65} +(-1.58120 + 4.16927i) q^{66} +(1.10234 - 9.07860i) q^{67} +(-3.64875 + 6.95210i) q^{68} +(-0.132934 + 0.350519i) q^{69} +(0.0202317 - 0.280038i) q^{70} +(-13.6384 - 5.17236i) q^{71} +(7.47361 - 1.84208i) q^{72} +(-6.79031 + 6.01569i) q^{73} +(-0.766170 - 0.188844i) q^{74} +(-8.11304 - 12.3631i) q^{75} +(6.60430 - 0.801907i) q^{76} +(1.57773 - 0.191571i) q^{77} +(2.09175 - 3.02803i) q^{78} +(-1.17584 + 9.68388i) q^{79} +(-0.531640 + 7.35872i) q^{80} +(0.817825 + 6.73539i) q^{81} +(-0.424902 - 0.809583i) q^{82} +(3.50885 + 9.25208i) q^{83} +(-1.34201 - 1.51482i) q^{84} +(-7.41452 + 5.67011i) q^{85} +(0.0538573 - 0.0204254i) q^{86} +(8.40753 + 16.0192i) q^{87} +(5.80859 - 0.705290i) q^{88} +1.30688i q^{89} +(4.35268 + 0.850435i) q^{90} +(-1.30212 - 0.158593i) q^{91} +(0.236675 - 0.0287376i) q^{92} +(0.151042 + 1.24394i) q^{93} +(2.93492 - 2.60011i) q^{94} +(7.52293 + 2.44121i) q^{95} +(-7.48697 - 8.45105i) q^{96} +(-3.08083 + 0.759356i) q^{97} +(-0.840498 + 2.21621i) q^{98} +25.1047i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1056 q - 106 q^{4} - 13 q^{5} - 26 q^{6} + 62 q^{9}+O(q^{10}) \) 1056 * q - 106 * q^4 - 13 * q^5 - 26 * q^6 + 62 * q^9	\( 1056 q - 106 q^{4} - 13 q^{5} - 26 q^{6} + 62 q^{9} - 13 q^{10} - 26 q^{11} - 26 q^{14} - 65 q^{15} - 98 q^{16} - 13 q^{20} - 26 q^{21} - 26 q^{24} - 3 q^{25} - 14 q^{26} - 54 q^{29} - 45 q^{30} + 26 q^{31} - 26 q^{34} - 17 q^{35} + 54 q^{36} - 146 q^{39} + 120 q^{40} - 26 q^{41} + 26 q^{44} - 78 q^{45} + 26 q^{46} - 164 q^{49} - 13 q^{50} - 164 q^{51} - 26 q^{54} - 119 q^{55} - 26 q^{56} - 130 q^{59} - 117 q^{60} - 54 q^{61} - 122 q^{64} - q^{65} + 140 q^{66} + 88 q^{69} - 26 q^{71} - 176 q^{74} - 65 q^{75} + 156 q^{76} - 26 q^{79} - 58 q^{81} + 468 q^{84} + 143 q^{85} + 130 q^{86} - 19 q^{90} - 26 q^{91} - 142 q^{94} + 70 q^{95} - 26 q^{96}+O(q^{100}) \) 1056 * q - 106 * q^4 - 13 * q^5 - 26 * q^6 + 62 * q^9 - 13 * q^10 - 26 * q^11 - 26 * q^14 - 65 * q^15 - 98 * q^16 - 13 * q^20 - 26 * q^21 - 26 * q^24 - 3 * q^25 - 14 * q^26 - 54 * q^29 - 45 * q^30 + 26 * q^31 - 26 * q^34 - 17 * q^35 + 54 * q^36 - 146 * q^39 + 120 * q^40 - 26 * q^41 + 26 * q^44 - 78 * q^45 + 26 * q^46 - 164 * q^49 - 13 * q^50 - 164 * q^51 - 26 * q^54 - 119 * q^55 - 26 * q^56 - 130 * q^59 - 117 * q^60 - 54 * q^61 - 122 * q^64 - q^65 + 140 * q^66 + 88 * q^69 - 26 * q^71 - 176 * q^74 - 65 * q^75 + 156 * q^76 - 26 * q^79 - 58 * q^81 + 468 * q^84 + 143 * q^85 + 130 * q^86 - 19 * q^90 - 26 * q^91 - 142 * q^94 + 70 * q^95 - 26 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more