LMFDB - Embedded newform 261.2.x.a.101.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.296904 + 0.680512i) q^{2} +(0.429498 - 1.67795i) q^{3} +(0.985401 + 1.06201i) q^{4} +(3.33006 + 0.501926i) q^{5} +(1.01435 + 0.790470i) q^{6} +(0.637138 + 0.591178i) q^{7} +(-2.41687 + 0.845700i) q^{8} +(-2.63106 - 1.44136i) q^{9} +(-1.33028 + 2.11712i) q^{10} +(-0.0452965 + 0.0389808i) q^{11} +(2.20523 - 1.19733i) q^{12} +(-1.01381 + 1.48699i) q^{13} +(-0.591473 + 0.258057i) q^{14} +(2.27247 - 5.37212i) q^{15} +(-0.0744600 + 0.993599i) q^{16} +(-5.44064 - 5.44064i) q^{17} +(1.76203 - 1.36252i) q^{18} +(2.53419 + 1.59233i) q^{19} +(2.74840 + 4.03116i) q^{20} +(1.26562 - 0.815179i) q^{21} +(-0.0130782 - 0.0423983i) q^{22} +(1.74536 + 0.685004i) q^{23} +(0.381004 + 4.41863i) q^{24} +(6.05952 + 1.86912i) q^{25} +(-0.710907 - 1.13140i) q^{26} +(-3.54857 + 3.79574i) q^{27} +1.25920i q^{28} +(3.35996 - 4.20840i) q^{29} +(2.98108 + 3.14144i) q^{30} +(3.52783 - 2.60366i) q^{31} +(-5.18172 - 2.73862i) q^{32} +(0.0459532 + 0.0927476i) q^{33} +(5.31777 - 2.08707i) q^{34} +(1.82498 + 2.28846i) q^{35} +(-1.06192 - 4.21453i) q^{36} +(1.07993 + 3.08626i) q^{37} +(-1.83601 + 1.25177i) q^{38} +(2.05967 + 2.33978i) q^{39} +(-8.47282 + 1.60314i) q^{40} +(-9.80827 - 2.62812i) q^{41} +(0.178971 + 1.10330i) q^{42} +(-5.50220 + 7.45521i) q^{43} +(-0.0860332 - 0.00969361i) q^{44} +(-8.03815 - 6.12041i) q^{45} +(-0.984358 + 0.984358i) q^{46} +(-3.14887 - 3.65905i) q^{47} +(1.63523 + 0.551690i) q^{48} +(-0.466657 - 6.22710i) q^{49} +(-3.07105 + 3.56863i) q^{50} +(-11.4659 + 6.79240i) q^{51} +(-2.57820 + 0.388602i) q^{52} +(-0.384864 - 0.306918i) q^{53} +(-1.52946 - 3.54181i) q^{54} +(-0.170406 + 0.107073i) q^{55} +(-2.03984 - 0.889974i) q^{56} +(3.76029 - 3.56834i) q^{57} +(1.86628 + 3.53599i) q^{58} +(3.68450 - 2.12725i) q^{59} +(7.94453 - 2.88031i) q^{60} +(2.25041 - 0.0842045i) q^{61} +(0.724392 + 3.17377i) q^{62} +(-0.824252 - 2.47377i) q^{63} +(1.84412 - 1.47064i) q^{64} +(-4.12241 + 4.44290i) q^{65} +(-0.0767595 + 0.00373454i) q^{66} +(-5.40263 + 0.404871i) q^{67} +(0.416801 - 11.1392i) q^{68} +(1.89904 - 2.63443i) q^{69} +(-2.09917 + 0.562470i) q^{70} +(-2.03947 + 0.982158i) q^{71} +(7.57790 + 1.25849i) q^{72} +(1.38053 - 12.2525i) q^{73} +(-2.42087 - 0.181419i) q^{74} +(5.73885 - 9.36482i) q^{75} +(0.806115 + 4.26042i) q^{76} +(-0.0519047 - 0.00194214i) q^{77} +(-2.20377 + 0.706934i) q^{78} +(-2.39145 + 12.6391i) q^{79} +(-0.746670 + 3.27137i) q^{80} +(4.84498 + 7.58460i) q^{81} +(4.70058 - 5.89434i) q^{82} +(-4.88077 + 15.8231i) q^{83} +(2.11287 + 0.540822i) q^{84} +(-15.3869 - 20.8485i) q^{85} +(-3.43973 - 5.95779i) q^{86} +(-5.61841 - 7.44537i) q^{87} +(0.0765098 - 0.132519i) q^{88} +(8.37231 - 0.943332i) q^{89} +(6.55157 - 3.65288i) q^{90} +(-1.52501 + 0.348074i) q^{91} +(0.992401 + 2.52860i) q^{92} +(-2.85362 - 7.03781i) q^{93} +(3.42494 - 1.05645i) q^{94} +(7.63976 + 6.57455i) q^{95} +(-6.82081 + 7.51845i) q^{96} +(-2.59563 - 4.91117i) q^{97} +(4.37617 + 1.53129i) q^{98} +(0.175363 - 0.0372724i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.296904	+	0.680512i	−0.209943	+	0.481194i	−0.989392	−	0.145271i	$-0.953594\pi$
$2$	−0.296904	+	0.680512i	−0.209943	+	0.481194i	0.779449	+	0.626466i	$0.215499\pi$
$3$	0.429498	−	1.67795i	0.247971	−	0.968767i
$3$	0.429498	−	1.67795i	0.247971	−	0.968767i
$4$	0.985401	+	1.06201i	0.492701	+	0.531005i
$5$	3.33006	+	0.501926i	1.48925	+	0.224468i	0.842691	−	0.538397i	$-0.180970\pi$
$5$	3.33006	+	0.501926i	1.48925	+	0.224468i	0.646558	+	0.762865i	$0.276208\pi$
$6$	1.01435	+	0.790470i	0.414106	+	0.322708i
$7$	0.637138	+	0.591178i	0.240816	+	0.223444i	0.791342	−	0.611373i	$-0.209383\pi$
$7$	0.637138	+	0.591178i	0.240816	+	0.223444i	−0.550527	+	0.834818i	$0.685573\pi$
$8$	−2.41687	+	0.845700i	−0.854494	+	0.299000i
$9$	−2.63106	−	1.44136i	−0.877021	−	0.480452i
$10$	−1.33028	+	2.11712i	−0.420670	+	0.669493i
$11$	−0.0452965	+	0.0389808i	−0.0136574	+	0.0117531i	−0.659090	−	0.752064i	$-0.729058\pi$
$11$	−0.0452965	+	0.0389808i	−0.0136574	+	0.0117531i	0.645432	+	0.763818i	$0.276677\pi$
$12$	2.20523	−	1.19733i	0.636596	−	0.345639i
$13$	−1.01381	+	1.48699i	−0.281180	+	0.412416i	−0.940683	−	0.339286i	$-0.889814\pi$
$13$	−1.01381	+	1.48699i	−0.281180	+	0.412416i	0.659503	+	0.751702i	$0.270767\pi$
$14$	−0.591473	+	0.258057i	−0.158078	+	0.0689686i
$15$	2.27247	−	5.37212i	0.586748	−	1.38707i
$16$	−0.0744600	+	0.993599i	−0.0186150	+	0.248400i
$17$	−5.44064	−	5.44064i	−1.31955	−	1.31955i	−0.914132	−	0.405417i	$-0.867126\pi$
$17$	−5.44064	−	5.44064i	−1.31955	−	1.31955i	−0.405417	−	0.914132i	$-0.632874\pi$
$18$	1.76203	−	1.36252i	0.415315	−	0.321150i
$19$	2.53419	+	1.59233i	0.581382	+	0.365307i	0.790387	−	0.612608i	$-0.209880\pi$
$19$	2.53419	+	1.59233i	0.581382	+	0.365307i	−0.209005	+	0.977915i	$0.567022\pi$
$20$	2.74840	+	4.03116i	0.614560	+	0.901395i
$21$	1.26562	−	0.815179i	0.276181	−	0.177887i
$22$	−0.0130782	−	0.0423983i	−0.00278827	−	0.00903935i
$23$	1.74536	+	0.685004i	0.363933	+	0.142833i	0.540259	−	0.841499i	$-0.318326\pi$
$23$	1.74536	+	0.685004i	0.363933	+	0.142833i	−0.176326	+	0.984332i	$0.556421\pi$
$24$	0.381004	+	4.41863i	0.0777722	+	0.901949i
$25$	6.05952	+	1.86912i	1.21190	+	0.373823i
$26$	−0.710907	−	1.13140i	−0.139420	−	0.221886i
$27$	−3.54857	+	3.79574i	−0.682922	+	0.730491i
$28$			1.25920i			0.237966i
$29$	3.35996	−	4.20840i	0.623930	−	0.781480i
$29$	3.35996	−	4.20840i	0.623930	−	0.781480i
$30$	2.98108	+	3.14144i	0.544269	+	0.573546i
$31$	3.52783	−	2.60366i	0.633617	−	0.467631i	−0.229042	−	0.973417i	$-0.573559\pi$
$31$	3.52783	−	2.60366i	0.633617	−	0.467631i	0.862659	+	0.505786i	$0.168797\pi$
$32$	−5.18172	−	2.73862i	−0.916007	−	0.484124i
$33$	0.0459532	+	0.0927476i	0.00799942	+	0.0161453i
$34$	5.31777	−	2.08707i	0.911990	−	0.357930i
$35$	1.82498	+	2.28846i	0.308478	+	0.386820i
$36$	−1.06192	−	4.21453i	−0.176986	−	0.702422i
$37$	1.07993	+	3.08626i	0.177539	+	0.507378i	0.997922	−	0.0644373i	$-0.0205252\pi$
$37$	1.07993	+	3.08626i	0.177539	+	0.507378i	−0.820383	+	0.571815i	$0.806240\pi$
$38$	−1.83601	+	1.25177i	−0.297841	+	0.203064i
$39$	2.05967	+	2.33978i	0.329810	+	0.374665i
$40$	−8.47282	+	1.60314i	−1.33967	+	0.253479i
$41$	−9.80827	−	2.62812i	−1.53179	−	0.410443i	−0.608190	−	0.793791i	$-0.708104\pi$
$41$	−9.80827	−	2.62812i	−1.53179	−	0.410443i	−0.923604	+	0.383348i	$0.874771\pi$
$42$	0.178971	+	1.10330i	0.0276159	+	0.170243i
$43$	−5.50220	+	7.45521i	−0.839077	+	1.13691i	0.149879	+	0.988704i	$0.452111\pi$
$43$	−5.50220	+	7.45521i	−0.839077	+	1.13691i	−0.988957	+	0.148205i	$0.952650\pi$
$44$	−0.0860332	−	0.00969361i	−0.0129700	−	0.00146137i
$45$	−8.03815	−	6.12041i	−1.19826	−	0.912377i
$46$	−0.984358	+	0.984358i	−0.145136	+	0.145136i
$47$	−3.14887	−	3.65905i	−0.459310	−	0.533728i	0.479785	−	0.877386i	$-0.340715\pi$
$47$	−3.14887	−	3.65905i	−0.459310	−	0.533728i	−0.939095	+	0.343658i	$0.888334\pi$
$48$	1.63523	+	0.551690i	0.236026	+	0.0796295i
$49$	−0.466657	−	6.22710i	−0.0666653	−	0.889586i
$50$	−3.07105	+	3.56863i	−0.434312	+	0.504680i
$51$	−11.4659	+	6.79240i	−1.60555	+	0.951126i
$52$	−2.57820	+	0.388602i	−0.357533	+	0.0538894i
$53$	−0.384864	−	0.306918i	−0.0528651	−	0.0421585i	0.596701	−	0.802464i	$-0.296478\pi$
$53$	−0.384864	−	0.306918i	−0.0528651	−	0.0421585i	−0.649566	+	0.760305i	$0.725049\pi$
$54$	−1.52946	−	3.54181i	−0.208133	−	0.481980i
$55$	−0.170406	+	0.107073i	−0.0229775	+	0.0144377i
$56$	−2.03984	−	0.889974i	−0.272585	−	0.118928i
$57$	3.76029	−	3.56834i	0.498063	−	0.472639i
$58$	1.86628	+	3.53599i	0.245054	+	0.464298i
$59$	3.68450	−	2.12725i	0.479682	−	0.276944i	−0.240602	−	0.970624i	$-0.577345\pi$
$59$	3.68450	−	2.12725i	0.479682	−	0.276944i	0.720284	+	0.693680i	$0.244012\pi$
$60$	7.94453	−	2.88031i	1.02563	−	0.371847i
$61$	2.25041	−	0.0842045i	0.288136	−	0.0107813i	0.107067	−	0.994252i	$-0.465854\pi$
$61$	2.25041	−	0.0842045i	0.288136	−	0.0107813i	0.181068	+	0.983470i	$0.442044\pi$
$62$	0.724392	+	3.17377i	0.0919979	+	0.403069i
$63$	−0.824252	−	2.47377i	−0.103846	−	0.311666i
$64$	1.84412	−	1.47064i	0.230515	−	0.183830i
$65$	−4.12241	+	4.44290i	−0.511322	+	0.551074i
$66$	−0.0767595	+	0.00373454i	−0.00944844	+	0.000459690i
$67$	−5.40263	+	0.404871i	−0.660036	+	0.0494629i	−0.400537	−	0.916281i	$-0.631176\pi$
$67$	−5.40263	+	0.404871i	−0.660036	+	0.0494629i	−0.259499	+	0.965743i	$0.583557\pi$
$68$	0.416801	−	11.1392i	0.0505445	−	1.35083i
$69$	1.89904	−	2.63443i	0.228617	−	0.317148i
$70$	−2.09917	+	0.562470i	−0.250898	+	0.0672280i
$71$	−2.03947	+	0.982158i	−0.242041	+	0.116561i	−0.550972	−	0.834524i	$-0.685743\pi$
$71$	−2.03947	+	0.982158i	−0.242041	+	0.116561i	0.308931	+	0.951084i	$0.400029\pi$
$72$	7.57790	+	1.25849i	0.893064	+	0.148314i
$73$	1.38053	−	12.2525i	0.161578	−	1.43405i	−0.607208	−	0.794543i	$-0.707711\pi$
$73$	1.38053	−	12.2525i	0.161578	−	1.43405i	0.768786	−	0.639506i	$-0.220861\pi$
$74$	−2.42087	−	0.181419i	−0.281420	−	0.0210895i
$75$	5.73885	−	9.36482i	0.662665	−	1.08136i
$76$	0.806115	+	4.26042i	0.0924677	+	0.488704i
$77$	−0.0519047	−	0.00194214i	−0.00591509	−	0.000221327i
$78$	−2.20377	+	0.706934i	−0.249528	+	0.0800445i
$79$	−2.39145	+	12.6391i	−0.269060	+	1.42201i	0.543633	+	0.839323i	$0.317048\pi$
$79$	−2.39145	+	12.6391i	−0.269060	+	1.42201i	−0.812693	+	0.582692i	$0.801999\pi$
$80$	−0.746670	+	3.27137i	−0.0834802	+	0.365751i
$81$	4.84498	+	7.58460i	0.538331	+	0.842733i
$82$	4.70058	−	5.89434i	0.519092	−	0.650921i
$83$	−4.88077	+	15.8231i	−0.535734	+	1.73681i	0.130875	+	0.991399i	$0.458221\pi$
$83$	−4.88077	+	15.8231i	−0.535734	+	1.73681i	−0.666609	+	0.745407i	$0.732255\pi$
$84$	2.11287	+	0.540822i	0.230533	+	0.0590085i
$85$	−15.3869	−	20.8485i	−1.66894	−	2.26133i
$86$	−3.43973	−	5.95779i	−0.370916	−	0.642445i
$87$	−5.61841	−	7.44537i	−0.602356	−	0.798227i
$88$	0.0765098	−	0.132519i	0.00815597	−	0.0141266i
$89$	8.37231	−	0.943332i	0.887463	−	0.0999930i	0.343550	−	0.939135i	$-0.388371\pi$
$89$	8.37231	−	0.943332i	0.887463	−	0.0999930i	0.543913	+	0.839142i	$0.316942\pi$
$90$	6.55157	−	3.65288i	0.690596	−	0.385047i
$91$	−1.52501	+	0.348074i	−0.159865	+	0.0364880i
$92$	0.992401	+	2.52860i	0.103465	+	0.263624i
$93$	−2.85362	−	7.03781i	−0.295907	−	0.729787i
$94$	3.42494	−	1.05645i	0.353256	−	0.108965i
$95$	7.63976	+	6.57455i	0.783823	+	0.674534i
$96$	−6.82081	+	7.51845i	−0.696146	+	0.767349i
$97$	−2.59563	−	4.91117i	−0.263546	−	0.498654i	0.716458	−	0.697630i	$-0.245762\pi$
$97$	−2.59563	−	4.91117i	−0.263546	−	0.498654i	−0.980004	+	0.198976i	$0.936238\pi$
$98$	4.37617	+	1.53129i	0.442060	+	0.154683i
$99$	0.175363	−	0.0372724i	0.0176246	−	0.00374602i
$100$	3.98604	+	8.27711i	0.398604	+	0.827711i
$101$	8.37687	+	6.18241i	0.833530	+	0.615173i	0.924715	−	0.380661i	$-0.124304\pi$
$101$	8.37687	+	6.18241i	0.833530	+	0.615173i	−0.0911849	+	0.995834i	$0.529065\pi$
$102$	−1.21804	−	9.81936i	−0.120604	−	0.972262i
$103$	4.30186	+	2.93296i	0.423875	+	0.288993i	0.756410	−	0.654098i	$-0.226952\pi$
$103$	4.30186	+	2.93296i	0.423875	+	0.288993i	−0.332535	+	0.943091i	$0.607904\pi$
$104$	1.19270	−	4.45124i	0.116954	−	0.436480i
$105$	4.62375	−	2.07935i	0.451232	−	0.202924i
$106$	0.323129	−	0.170779i	0.0313851	−	0.0165875i
$107$	0.0373946	−	0.0776508i	0.00361508	−	0.00750678i	−0.899154	−	0.437633i	$-0.855817\pi$
$107$	0.0373946	−	0.0776508i	0.00361508	−	0.00750678i	0.902769	+	0.430127i	$0.141531\pi$
$108$	−7.52788	−	0.0282849i	−0.724371	−	0.00272171i
$109$	−12.6917	−	2.89681i	−1.21565	−	0.277464i	−0.433844	−	0.900988i	$-0.642843\pi$
$109$	−12.6917	−	2.89681i	−1.21565	−	0.277464i	−0.781804	+	0.623524i	$0.785700\pi$
$110$	−0.0222702	−	0.147753i	−0.00212338	−	0.0140877i
$111$	5.64243	−	0.486528i	0.535556	−	0.0461792i
$112$	−0.634835	+	0.589041i	−0.0599863	+	0.0556592i
$113$	−6.29530	+	11.9113i	−0.592212	+	1.12052i	0.387830	+	0.921731i	$0.373225\pi$
$113$	−6.29530	+	11.9113i	−0.592212	+	1.12052i	−0.980042	+	0.198790i	$0.936299\pi$
$114$	1.31185	+	3.61838i	0.122866	+	0.338892i
$115$	5.46834	+	3.15715i	0.509926	+	0.294406i
$116$	7.78028	−	0.578649i	0.722381	−	0.0537262i
$117$	4.81067	−	2.45109i	0.444747	−	0.226603i
$118$	0.353673	+	3.13894i	0.0325583	+	0.288963i
$119$	−0.250054	−	6.68283i	−0.0229224	−	0.612614i
$120$	−0.949058	+	14.9056i	−0.0866368	+	1.36068i
$121$	−1.63893	+	10.8736i	−0.148994	+	0.988510i
$122$	−0.610855	+	1.55643i	−0.0553042	+	0.140913i
$123$	−8.62250	+	15.3291i	−0.777464	+	1.38217i
$124$	6.24144	+	1.18094i	0.560498	+	0.106052i
$125$	4.06958	+	1.95980i	0.363994	+	0.175290i
$126$	1.92815	+	0.173559i	0.171774	+	0.0154619i
$127$	5.35445	−	15.3021i	0.475130	−	1.35784i	−0.418164	−	0.908372i	$-0.637326\pi$
$127$	5.35445	−	15.3021i	0.475130	−	1.35784i	0.893294	−	0.449473i	$-0.148388\pi$
$128$	−2.58057	−	9.63081i	−0.228092	−	0.851251i
$129$	10.1463	+	12.4344i	0.893334	+	1.09479i
$130$	−1.79948	−	4.12446i	−0.157825	−	0.361739i
$131$	3.83871	+	8.79843i	0.335390	+	0.768722i	0.999773	+	0.0213294i	$0.00678988\pi$
$131$	3.83871	+	8.79843i	0.335390	+	0.768722i	−0.664382	+	0.747393i	$0.731305\pi$
$132$	−0.0532165	+	0.140196i	−0.00463191	+	0.0122025i
$133$	0.673274	+	2.51269i	0.0583802	+	0.217878i
$134$	1.32854	−	3.79676i	0.114769	−	0.327990i
$135$	−13.7221	+	10.8589i	−1.18101	+	0.934589i
$136$	17.7505	+	8.54818i	1.52209	+	0.733001i
$137$	−9.09784	−	1.72140i	−0.777281	−	0.147069i	−0.217890	−	0.975973i	$-0.569917\pi$
$137$	−9.09784	−	1.72140i	−0.777281	−	0.147069i	−0.559391	+	0.828904i	$0.688965\pi$
$138$	1.22893	+	2.07449i	0.104613	+	0.176592i
$139$	5.72890	−	14.5970i	0.485919	−	1.23810i	−0.452240	−	0.891896i	$-0.649375\pi$
$139$	5.72890	−	14.5970i	0.485919	−	1.23810i	0.938159	−	0.346205i	$-0.112530\pi$
$140$	−0.632023	+	4.19320i	−0.0534157	+	0.354390i
$141$	−7.49216	+	3.71210i	−0.630954	+	0.312616i
$142$	−0.0628421	−	1.67949i	−0.00527360	−	0.140940i
$143$	−0.0120418	−	0.106874i	−0.00100699	−	0.00893728i
$144$	1.62804	−	2.50690i	0.135670	−	0.208908i
$145$	13.3012	−	12.3278i	1.10460	−	1.02377i
$146$	7.92810	+	4.57729i	0.656134	+	0.378819i
$147$	−10.6492	−	1.89150i	−0.878333	−	0.156008i
$148$	−2.21347	+	4.18810i	−0.181946	+	0.344260i
$149$	5.78947	−	5.37185i	0.474292	−	0.440079i	−0.406451	−	0.913672i	$-0.633234\pi$
$149$	5.78947	−	5.37185i	0.474292	−	0.440079i	0.880743	+	0.473594i	$0.157043\pi$
$150$	4.66898	+	6.68581i	0.381221	+	0.545894i
$151$	0.741436	+	4.91911i	0.0603372	+	0.400311i	0.998530	+	0.0541985i	$0.0172604\pi$
$151$	0.741436	+	4.91911i	0.0603372	+	0.400311i	−0.938193	+	0.346113i	$0.887502\pi$
$152$	−7.47144	−	1.70531i	−0.606014	−	0.138319i
$153$	6.47276	+	22.1566i	0.523292	+	1.79125i
$154$	0.0167324	−	0.0347451i	0.00134833	−	0.00279984i
$155$	13.0547	−	6.89964i	1.04858	−	0.554192i
$156$	−0.455278	+	4.49301i	−0.0364514	+	0.359729i
$157$	−3.57549	+	13.3439i	−0.285355	+	1.06496i	0.663225	+	0.748420i	$0.269187\pi$
$157$	−3.57549	+	13.3439i	−0.285355	+	1.06496i	−0.948580	+	0.316539i	$0.897479\pi$
$158$	−7.89105	−	5.38003i	−0.627778	−	0.428012i
$159$	−0.680293	+	0.513963i	−0.0539508	+	0.0407599i
$160$	−15.8809	−	11.7206i	−1.25549	−	0.926595i
$161$	0.707078	+	1.46826i	0.0557255	+	0.115715i
$162$	−6.59990	+	1.04517i	−0.518537	+	0.0821160i
$163$	18.9901	+	6.64492i	1.48742	+	0.520471i	0.947086	−	0.320980i	$-0.104012\pi$
$163$	18.9901	+	6.64492i	1.48742	+	0.520471i	0.540334	+	0.841451i	$0.318298\pi$
$164$	−6.87399	−	13.0062i	−0.536769	−	1.01562i
$165$	0.106475	+	0.331920i	0.00828904	+	0.0258400i
$166$	−9.31865	−	8.01935i	−0.723268	−	0.622422i
$167$	16.4961	−	5.08836i	1.27650	−	0.393750i	0.418887	−	0.908038i	$-0.362420\pi$
$167$	16.4961	−	5.08836i	1.27650	−	0.393750i	0.857617	+	0.514289i	$0.171944\pi$
$168$	−2.36944	+	3.04052i	−0.182807	+	0.234581i
$169$	3.56612	+	9.08632i	0.274317	+	0.698947i
$170$	18.7561	−	4.28095i	1.43852	−	0.328334i
$171$	−4.37248	−	7.84220i	−0.334372	−	0.599708i
$172$	−13.3394	+	1.50299i	−1.01712	+	0.114602i
$173$	0.536737	−	0.929655i	0.0408073	−	0.0706804i	−0.844900	−	0.534924i	$-0.820340\pi$
$173$	0.536737	−	0.929655i	0.0408073	−	0.0706804i	0.885708	+	0.464243i	$0.153674\pi$
$174$	6.73479	−	1.61283i	0.510563	−	0.122268i
$175$	2.75578	+	4.77314i	0.208317	+	0.360816i
$176$	−0.0353585	−	0.0479090i	−0.00266525	−	0.00361128i
$177$	−1.98694	−	7.09608i	−0.149348	−	0.533374i
$178$	−1.84382	+	5.97753i	−0.138200	+	0.448035i
$179$	−2.34746	+	2.94362i	−0.175458	+	0.220017i	−0.861782	−	0.507279i	$-0.830652\pi$
$179$	−2.34746	+	2.94362i	−0.175458	+	0.220017i	0.686325	+	0.727295i	$0.259223\pi$
$180$	−1.42087	−	14.5677i	−0.105905	−	1.08581i
$181$	3.25643	−	14.2673i	0.242048	−	1.06048i	−0.697101	−	0.716973i	$-0.745527\pi$
$181$	3.25643	−	14.2673i	0.242048	−	1.06048i	0.939149	−	0.343510i	$-0.111616\pi$
$182$	0.215914	−	1.14113i	0.0160046	−	0.0845863i
$183$	0.825257	−	3.81226i	0.0610047	−	0.281810i
$184$	−4.79763	−	0.179514i	−0.353686	−	0.0132340i
$185$	2.04716	+	10.8195i	0.150510	+	0.795464i
$186$	5.63656	+	0.147631i	0.413293	+	0.0108248i
$187$	0.458522	+	0.0343615i	0.0335305	+	0.00251276i
$188$	0.783051	−	6.94977i	0.0571099	−	0.506864i
$189$	−4.50489	+	0.320578i	−0.327682	+	0.0233186i
$190$	−6.74233	+	3.24694i	−0.489140	+	0.235558i
$191$	25.6865	−	6.88266i	1.85861	−	0.498012i	0.858711	−	0.512461i	$-0.171266\pi$
$191$	25.6865	−	6.88266i	1.85861	−	0.498012i	0.999896	+	0.0144485i	$0.00459926\pi$
$192$	−1.67562	−	3.72599i	−0.120927	−	0.268900i
$193$	0.908496	−	24.2801i	0.0653950	−	1.74772i	−0.452042	−	0.891996i	$-0.649304\pi$
$193$	0.908496	−	24.2801i	0.0653950	−	1.74772i	0.517437	−	0.855721i	$-0.326886\pi$
$194$	4.11276	−	0.308209i	0.295279	−	0.0221281i
$195$	5.68441	+	8.82543i	0.407069	+	0.632002i
$196$	6.15340	−	6.63179i	0.439529	−	0.473699i
$197$	12.1479	−	9.68762i	0.865502	−	0.690215i	−0.0865184	−	0.996250i	$-0.527574\pi$
$197$	12.1479	−	9.68762i	0.865502	−	0.690215i	0.952020	+	0.306036i	$0.0990027\pi$
$198$	−0.0267017	+	0.130403i	−0.00189761	+	0.00926733i
$199$	−3.57474	−	15.6620i	−0.253407	−	1.11025i	−0.928153	−	0.372198i	$-0.878604\pi$
$199$	−3.57474	−	15.6620i	−0.253407	−	1.11025i	0.674746	−	0.738050i	$-0.264253\pi$
$200$	−16.2258	+	0.607127i	−1.14734	+	0.0429304i
$201$	−1.64106	+	9.23925i	−0.115752	+	0.651687i
$202$	−6.69433	+	3.86497i	−0.471011	+	0.271939i
$203$	4.62868	−	0.694997i	0.324869	−	0.0487792i
$204$	−18.5121	−	5.48365i	−1.29611	−	0.383932i
$205$	−31.3430	−	13.6748i	−2.18909	−	0.955091i
$206$	−3.27315	+	2.05666i	−0.228051	+	0.143294i
$207$	−3.60482	−	4.31798i	−0.250552	−	0.300120i
$208$	−1.40198	−	1.11804i	−0.0972098	−	0.0775222i
$209$	−0.176860	+	0.0266574i	−0.0122337	+	0.00184393i
$210$	0.0422107	+	3.76389i	0.00291282	+	0.259733i
$211$	−10.5208	+	12.2254i	−0.724285	+	0.841635i	−0.992566	−	0.121706i	$-0.961163\pi$
$211$	−10.5208	+	12.2254i	−0.724285	+	0.841635i	0.268281	+	0.963341i	$0.413544\pi$
$212$	−0.0532946	−	0.711167i	−0.00366029	−	0.0488432i
$213$	0.772067	+	3.84398i	0.0529011	+	0.263385i
$214$	0.0417396	+	0.0485023i	0.00285326	+	0.00331555i
$215$	−22.0646	+	22.0646i	−1.50480	+	1.50480i
$216$	5.36638	−	12.1749i	0.365136	−	0.828394i
$217$	3.78694	+	0.426686i	0.257074	+	0.0289653i
$218$	5.73954	−	7.77680i	0.388731	−	0.526711i
$219$	−19.9662	−	7.57890i	−1.34919	−	0.512134i
$220$	−0.281630	−	0.0754626i	−0.0189875	−	0.00508769i
$221$	13.6059	−	2.57438i	0.915234	−	0.173172i
$222$	−1.34417	+	3.98419i	−0.0902149	+	0.267401i
$223$	−7.32702	+	4.99548i	−0.490653	+	0.334522i	−0.783242	−	0.621716i	$-0.786436\pi$
$223$	−7.32702	+	4.99548i	−0.490653	+	0.334522i	0.292589	+	0.956238i	$0.405483\pi$
$224$	−1.68246	−	4.80819i	−0.112414	−	0.321261i
$225$	−13.2489	−	13.6517i	−0.883262	−	0.910113i
$226$	−6.23667	−	7.82054i	−0.414857	−	0.520215i
$227$	−15.1656	+	5.95205i	−1.00658	+	0.395052i	−0.810627	−	0.585563i	$-0.800874\pi$
$227$	−15.1656	+	5.95205i	−1.00658	+	0.395052i	−0.195948	+	0.980614i	$0.562778\pi$
$228$	7.49502	+	0.477219i	0.496370	+	0.0316046i
$229$	20.1221	+	10.6349i	1.32971	+	0.702771i	0.972861	−	0.231391i	$-0.0743278\pi$
$229$	20.1221	+	10.6349i	1.32971	+	0.702771i	0.356848	+	0.934163i	$0.383852\pi$
$230$	−3.77205	+	2.78390i	−0.248722	+	0.183565i
$231$	−0.0255518	+	0.0862596i	−0.00168118	+	0.00567546i
$232$	−4.56156	+	13.0127i	−0.299481	+	0.854325i
$233$			4.06185i			0.266101i	0.991109	+	0.133050i	$0.0424772\pi$
$233$			4.06185i			0.266101i	−0.991109	+	0.133050i	$0.957523\pi$
$234$	0.239687	+	4.00146i	0.0156688	+	0.261584i
$235$	−8.64936	−	13.7654i	−0.564222	−	0.897955i
$236$	5.88988	+	1.81679i	0.383398	+	0.118263i
$237$	20.1808	+	9.44124i	1.31088	+	0.613275i
$238$	4.62198	+	1.81399i	0.299599	+	0.117584i
$239$	8.11228	+	26.2994i	0.524740	+	1.70116i	0.697834	+	0.716260i	$0.254147\pi$
$239$	8.11228	+	26.2994i	0.524740	+	1.70116i	−0.173094	+	0.984905i	$0.555376\pi$
$240$	5.16852	+	2.65793i	0.333627	+	0.171568i
$241$	−3.24474	−	4.75916i	−0.209012	−	0.306565i	0.707390	−	0.706824i	$-0.249873\pi$
$241$	−3.24474	−	4.75916i	−0.209012	−	0.306565i	−0.916402	+	0.400259i	$0.868920\pi$
$242$	−6.91301	−	4.34373i	−0.444385	−	0.279226i
$243$	14.8075	−	4.87208i	0.949903	−	0.312544i
$244$	2.30699	+	2.30699i	0.147690	+	0.147690i
$245$	1.57155	−	20.9709i	0.100403	−	1.33978i
$246$	−7.87155	−	10.4190i	−0.501871	−	0.664289i
$247$	−4.93696	+	2.15397i	−0.314131	+	0.137054i
$248$	−6.32441	+	9.27620i	−0.401600	+	0.589039i
$249$	24.4541	+	14.9857i	1.54971	+	0.949679i
$250$	−2.54194	+	2.18752i	−0.160767	+	0.138351i
$251$	−0.839018	+	1.33529i	−0.0529583	+	0.0842827i	−0.872154	−	0.489231i	$-0.837277\pi$
$251$	−0.839018	+	1.33529i	−0.0529583	+	0.0842827i	0.819196	+	0.573514i	$0.194420\pi$
$252$	1.81495	−	3.31302i	0.114331	−	0.208701i
$253$	−0.105761	+	0.0370073i	−0.00664912	+	0.00232663i
$254$	8.82352	+	8.18703i	0.553637	+	0.513700i
$255$	−41.5914	+	16.8641i	−2.60456	+	1.05607i
$256$	11.9848	+	1.80642i	0.749051	+	0.112901i
$257$	−4.05655	−	4.37192i	−0.253040	−	0.272713i	0.593738	−	0.804658i	$-0.297652\pi$
$257$	−4.05655	−	4.37192i	−0.253040	−	0.272713i	−0.846779	+	0.531946i	$0.821461\pi$
$258$	−11.4743	+	3.21286i	−0.714357	+	0.200024i
$259$	−1.13646	+	2.60480i	−0.0706164	+	0.161855i
$260$	−8.78063			−0.544552
$261$	−14.9061	+	6.22966i	−0.922663	+	0.385606i
$262$	−7.12716			−0.440318
$263$	−1.06952	+	2.45137i	−0.0659495	+	0.151158i	−0.946416	−	0.322951i	$-0.895325\pi$
$263$	−1.06952	+	2.45137i	−0.0659495	+	0.151158i	0.880466	+	0.474109i	$0.157230\pi$
$264$	−0.189500	−	0.185297i	−0.0116629	−	0.0114042i
$265$	−1.12757	−	1.21523i	−0.0692660	−	0.0746510i
$266$	−1.90981	−	0.287858i	−0.117098	−	0.0176497i
$267$	2.01302	−	14.4535i	0.123195	−	0.884540i
$268$	−5.75373	−	5.33868i	−0.351465	−	0.326112i
$269$	6.19633	−	2.16819i	0.377797	−	0.132197i	−0.134699	−	0.990887i	$-0.543007\pi$
$269$	6.19633	−	2.16819i	0.377797	−	0.132197i	0.512496	+	0.858690i	$0.328721\pi$
$270$	−3.31548	−	12.5621i	−0.201774	−	0.764507i
$271$	−7.38247	+	11.7491i	−0.448453	+	0.713709i	−0.992079	−	0.125619i	$-0.959908\pi$
$271$	−7.38247	+	11.7491i	−0.448453	+	0.713709i	0.543626	+	0.839328i	$0.317051\pi$
$272$	5.81093	−	5.00071i	0.352339	−	0.303212i
$273$	−0.0709375	+	2.70840i	−0.00429333	+	0.163920i
$274$	3.87262	−	5.68009i	0.233954	−	0.343147i
$275$	−0.347335	+	0.151541i	−0.0209451	+	0.00913824i
$276$	4.66910	−	0.579176i	0.281047	−	0.0348623i
$277$	−0.862176	+	11.5049i	−0.0518032	+	0.691265i	0.909488	+	0.415730i	$0.136474\pi$
$277$	−0.862176	+	11.5049i	−0.0518032	+	0.691265i	−0.961291	+	0.275535i	$0.911145\pi$
$278$	8.23249	+	8.23249i	0.493752	+	0.493752i
$279$	−13.0347	+	1.76552i	−0.780370	+	0.105699i
$280$	−6.34610	−	3.98752i	−0.379252	−	0.238300i
$281$	2.00377	+	2.93899i	0.119535	+	0.175326i	0.881343	−	0.472478i	$-0.156640\pi$
$281$	2.00377	+	2.93899i	0.119535	+	0.175326i	−0.761808	+	0.647803i	$0.775688\pi$
$282$	−0.301676	−	6.20064i	−0.0179646	−	0.369243i
$283$	−0.636663	−	2.06401i	−0.0378457	−	0.122693i	0.934679	−	0.355493i	$-0.115687\pi$
$283$	−0.636663	−	2.06401i	−0.0378457	−	0.122693i	−0.972524	+	0.232801i	$0.925211\pi$
$284$	−3.05276	−	1.19812i	−0.181148	−	0.0710954i
$285$	14.3131	−	9.99542i	0.847832	−	0.592077i
$286$	0.0763045	+	0.0235368i	0.00451198	+	0.00139176i
$287$	−4.69554	−	7.47291i	−0.277169	−	0.441112i
$288$	9.68609	+	14.6742i	0.570759	+	0.864684i
$289$			42.2011i			2.48242i
$290$	4.44002	+	12.7118i	0.260727	+	0.746462i
$291$	−9.35554	+	2.24601i	−0.548431	+	0.131663i
$292$	14.3727	−	10.6075i	0.841097	−	0.620758i
$293$	−10.1067	−	5.34153i	−0.590438	−	0.312056i	0.145230	−	0.989398i	$-0.453608\pi$
$293$	−10.1067	−	5.34153i	−0.590438	−	0.312056i	−0.735668	+	0.677342i	$0.763132\pi$
$294$	4.44899	−	6.68533i	0.259470	−	0.389896i
$295$	13.3374	−	5.23452i	0.776531	−	0.304766i
$296$	−5.22010	−	6.54580i	−0.303412	−	0.380467i
$297$	0.0127766	−	0.310260i	0.000741376	−	0.0180031i
$298$	1.93668	+	5.53473i	0.112189	+	0.320618i
$299$	−2.78806	+	1.90086i	−0.161237	+	0.109930i
$300$	15.6006	−	3.13340i	0.900701	−	0.180907i
$301$	−7.91302	+	1.49722i	−0.456099	+	0.0862986i
$302$	−3.56764	−	0.955947i	−0.205295	−	0.0550086i
$303$	13.9717	−	11.4007i	0.802651	−	0.654951i
$304$	−1.77084	+	2.39940i	−0.101565	+	0.137615i
$305$	7.53628	+	0.849135i	0.431526	+	0.0486213i
$306$	−16.9996	−	2.17359i	−0.971802	−	0.124256i
$307$	10.2569	−	10.2569i	0.585394	−	0.585394i	−0.350987	−	0.936380i	$-0.614154\pi$
$307$	10.2569	−	10.2569i	0.585394	−	0.585394i	0.936380	+	0.350987i	$0.114154\pi$
$308$	−0.0490844	−	0.0570371i	−0.00279684	−	0.00324999i
$309$	6.76901	−	5.95862i	0.385076	−	0.338974i
$310$	0.819273	+	10.9324i	0.0465316	+	0.620921i
$311$	−17.1376	+	19.9142i	−0.971783	+	1.12923i	0.0198061	+	0.999804i	$0.493695\pi$
$311$	−17.1376	+	19.9142i	−0.971783	+	1.12923i	−0.991589	+	0.129428i	$0.958686\pi$
$312$	−6.95671	−	3.91310i	−0.393846	−	0.221536i
$313$	33.7611	−	5.08866i	1.90829	−	0.287628i	0.915015	−	0.403421i	$-0.132179\pi$
$313$	33.7611	−	5.08866i	1.90829	−	0.287628i	0.993273	+	0.115792i	$0.0369407\pi$
$314$	−8.01910	−	6.39502i	−0.452544	−	0.360892i
$315$	−1.50316	−	8.65152i	−0.0846936	−	0.487458i
$316$	−15.7794	+	9.91488i	−0.887663	+	0.557756i
$317$	−17.7524	−	7.74530i	−0.997076	−	0.435020i	−0.162974	−	0.986630i	$-0.552109\pi$
$317$	−17.7524	−	7.74530i	−0.997076	−	0.435020i	−0.834102	+	0.551611i	$0.814013\pi$
$318$	−0.147776	−	0.615545i	−0.00828684	−	0.0345181i
$319$	0.0118522	+	0.321600i	0.000663595	+	0.0180061i
$320$	6.87920	−	3.97171i	0.384559	−	0.222025i
$321$	−0.114234	−	0.0960974i	−0.00637589	−	0.00536363i
$322$	−1.20910	+	0.0452415i	−0.0673807	+	0.00252121i
$323$	−5.12427	−	22.4509i	−0.285122	−	1.24920i
$324$	−3.28067	+	12.6193i	−0.182260	+	0.701072i
$325$	−8.92255	+	7.11550i	−0.494934	+	0.394697i
$326$	−10.1602	+	10.9501i	−0.562721	+	0.606469i
$327$	−10.3118	+	20.0520i	−0.570243	+	1.10888i
$328$	25.9279	−	1.94303i	1.43163	−	0.107286i
$329$	0.156886	−	4.19287i	0.00864941	−	0.231160i
$330$	−0.257488	−	0.0260914i	−0.0141743	−	0.00143628i
$331$	31.2004	−	8.36012i	1.71493	−	0.459514i	0.738305	−	0.674467i	$-0.235627\pi$
$331$	31.2004	−	8.36012i	1.71493	−	0.459514i	0.976624	+	0.214953i	$0.0689599\pi$
$332$	−21.6138	+	10.4086i	−1.18621	+	0.571248i
$333$	1.60704	−	9.67670i	0.0880653	−	0.530280i
$334$	−1.43506	+	12.7365i	−0.0785231	+	0.696912i
$335$	−18.1943	−	1.36347i	−0.994061	−	0.0744946i
$336$	0.715724	+	1.31822i	0.0390459	+	0.0719146i
$337$	0.434462	+	2.29619i	0.0236666	+	0.125081i	0.992407	−	0.122994i	$-0.0392496\pi$
$337$	0.434462	+	2.29619i	0.0236666	+	0.125081i	−0.968741	+	0.248075i	$0.920202\pi$
$338$	−7.24214	−	0.270982i	−0.393920	−	0.0147395i
$339$	17.2828	+	15.6791i	0.938673	+	0.851573i
$340$	6.97904	−	36.8851i	0.378492	−	2.00038i
$341$	−0.0583057	+	0.255454i	−0.00315743	+	0.0138336i
$342$	6.63491	−	0.647141i	0.358775	−	0.0349934i
$343$	7.17738	−	9.00015i	0.387542	−	0.485963i
$344$	6.99324	−	22.6715i	0.377050	−	1.22237i
$345$	7.64619	−	7.81964i	0.411657	−	0.420995i
$346$	0.473282	+	0.641274i	0.0254438	+	0.0344751i
$347$	−15.4822	−	26.8160i	−0.831128	−	1.43956i	−0.897144	−	0.441738i	$-0.854362\pi$
$347$	−15.4822	−	26.8160i	−0.831128	−	1.43956i	0.0660157	−	0.997819i	$-0.478971\pi$
$348$	2.37067	−	13.3035i	0.127081	−	0.713141i
$349$	1.57067	−	2.72048i	0.0840759	−	0.145624i	−0.820921	−	0.571042i	$-0.806540\pi$
$349$	1.57067	−	2.72048i	0.0840759	−	0.145624i	0.904997	+	0.425418i	$0.139873\pi$
$350$	−4.06638	+	0.458171i	−0.217357	+	0.0244903i
$351$	−2.04664	−	9.12483i	−0.109242	−	0.487047i
$352$	0.341467	−	0.0779376i	0.0182002	−	0.00415409i
$353$	0.880661	+	2.24389i	0.0468728	+	0.119430i	0.952393	−	0.304874i	$-0.0986142\pi$
$353$	0.880661	+	2.24389i	0.0468728	+	0.119430i	−0.905520	+	0.424304i	$0.860519\pi$
$354$	5.41890	+	0.754720i	0.288011	+	0.0401129i
$355$	−7.28454	+	2.24698i	−0.386623	+	0.119258i
$356$	9.25191	+	7.96191i	0.490350	+	0.421981i
$357$	−11.3209	−	2.45068i	−0.599164	−	0.129704i
$358$	−1.30620	−	2.47145i	−0.0690348	−	0.130620i
$359$	0.332555	+	0.116366i	0.0175516	+	0.00614157i	0.339041	−	0.940772i	$-0.389898\pi$
$359$	0.332555	+	0.116366i	0.0175516	+	0.00614157i	−0.321489	+	0.946913i	$0.604183\pi$
$360$	24.6032	+	7.99438i	1.29670	+	0.421341i
$361$	−4.35722	−	9.04787i	−0.229328	−	0.476203i
$362$	8.74225	+	6.45207i	0.459482	+	0.339113i
$363$	17.5415	+	7.42025i	0.920690	+	0.389462i
$364$	−1.87241	−	1.27658i	−0.0981407	−	0.0669112i
$365$	10.7471	−	40.1087i	0.562529	−	2.09939i
$366$	2.34926	+	1.69347i	0.122798	+	0.0885192i
$367$	13.7160	−	7.24912i	0.715970	−	0.378401i	−0.0692658	−	0.997598i	$-0.522066\pi$
$367$	13.7160	−	7.24912i	0.715970	−	0.378401i	0.785236	+	0.619197i	$0.212542\pi$
$368$	−0.810579	+	1.68318i	−0.0422543	+	0.0877421i
$369$	22.0181	+	21.0520i	1.14622	+	1.09592i
$370$	−7.97059	−	1.81923i	−0.414371	−	0.0945775i
$371$	−0.0637679	−	0.423072i	−0.00331067	−	0.0219648i
$372$	4.66226	−	9.96564i	0.241727	−	0.516695i
$373$	−4.88414	+	4.53182i	−0.252891	+	0.234649i	−0.796423	−	0.604740i	$-0.793277\pi$
$373$	−4.88414	+	4.53182i	−0.252891	+	0.234649i	0.543532	+	0.839389i	$0.317087\pi$
$374$	−0.159521	+	0.301828i	−0.00824861	+	0.0156071i
$375$	5.03634	−	5.98683i	0.260075	−	0.309159i
$376$	10.7049	+	6.18047i	0.552062	+	0.318733i
$377$	2.85147	+	9.26274i	0.146858	+	0.477055i
$378$	1.11936	−	3.16081i	0.0575738	−	0.162575i
$379$	−0.231101	−	2.05108i	−0.0118709	−	0.105357i	0.986380	−	0.164485i	$-0.0525964\pi$
$379$	−0.231101	−	2.05108i	−0.0118709	−	0.105357i	−0.998250	+	0.0591287i	$0.981168\pi$
$380$	0.545997	+	14.5921i	0.0280091	+	0.748558i
$381$	−23.3765	−	15.5568i	−1.19762	−	0.796997i
$382$	−2.94268	+	19.5234i	−0.150561	+	0.998905i
$383$	−8.12156	+	20.6934i	−0.414993	+	1.05738i	0.558670	+	0.829390i	$0.311312\pi$
$383$	−8.12156	+	20.6934i	−0.414993	+	1.05738i	−0.973663	+	0.227994i	$0.926783\pi$
$384$	−17.2684	+	0.193659i	−0.881225	+	0.00988264i
$385$	−0.171871	−	0.0325198i	−0.00875936	−	0.00165736i
$386$	16.2531	+	7.82710i	0.827263	+	0.398389i
$387$	25.2223	−	11.6845i	1.28212	−	0.593957i
$388$	2.65798	−	7.59606i	0.134938	−	0.385631i
$389$	8.24766	+	30.7807i	0.418173	+	1.56064i	0.778394	+	0.627776i	$0.216035\pi$
$389$	8.24766	+	30.7807i	0.418173	+	1.56064i	−0.360221	+	0.932867i	$0.617299\pi$
$390$	−7.69353	+	1.24800i	−0.389577	+	0.0631951i
$391$	−5.76902	−	13.2227i	−0.291752	−	0.668703i
$392$	6.39411	+	14.6555i	0.322952	+	0.740213i
$393$	16.4121	−	2.66228i	0.827880	−	0.134294i
$394$	2.98578	+	11.1431i	0.150421	+	0.561380i
$395$	−14.3076	+	40.8888i	−0.719894	+	2.05734i
$396$	0.212387	+	0.149509i	0.0106728	+	0.00751311i
$397$	17.8929	+	8.61674i	0.898017	+	0.432462i	0.825172	−	0.564881i	$-0.191078\pi$
$397$	17.8929	+	8.61674i	0.898017	+	0.432462i	0.0728445	+	0.997343i	$0.476792\pi$
$398$	11.7195	+	2.21745i	0.587446	+	0.111151i
$399$	4.50535	−	0.0505260i	0.225550	−	0.00252946i
$400$	−2.30834	+	5.88156i	−0.115417	+	0.294078i
$401$	3.58935	−	23.8138i	0.179244	−	1.18920i	−0.700464	−	0.713688i	$-0.747024\pi$
$401$	3.58935	−	23.8138i	0.179244	−	1.18920i	0.879707	−	0.475515i	$-0.157738\pi$
$402$	−5.80018	−	3.85994i	−0.289287	−	0.192516i
$403$	0.295053	+	7.88545i	0.0146976	+	0.392802i
$404$	1.68880	+	14.9885i	0.0840207	+	0.745705i
$405$	12.3272	+	27.6890i	0.612542	+	1.37588i
$406$	−0.901320	+	3.35622i	−0.0447318	+	0.166566i
$407$	−0.169222	−	0.0977002i	−0.00838801	−	0.00484282i
$408$	21.9673	−	26.1131i	1.08754	−	1.29279i
$409$	−10.7598	+	20.3586i	−0.532039	+	1.00667i	0.460833	+	0.887487i	$0.347551\pi$
$409$	−10.7598	+	20.3586i	−0.532039	+	1.00667i	−0.992873	+	0.119181i	$0.961973\pi$
$410$	18.6118	−	17.2692i	0.919169	−	0.852864i
$411$	−6.79594	+	14.5264i	−0.335219	+	0.716536i
$412$	1.12423	+	7.45876i	0.0553867	+	0.367467i
$413$	3.60512	+	0.822846i	0.177396	+	0.0404896i
$414$	4.00872	−	1.17110i	0.197018	−	0.0575563i
$415$	−24.1953	+	50.2420i	−1.18770	+	2.46628i
$416$	9.32556	−	4.92870i	0.457223	−	0.241649i
$417$	−22.0325	−	15.8822i	−1.07894	−	0.777755i
$418$	0.0343699	−	0.128270i	0.00168108	−	0.00627389i
$419$	1.19639	+	0.815687i	0.0584476	+	0.0398489i	0.592191	−	0.805797i	$-0.298263\pi$
$419$	1.19639	+	0.815687i	0.0584476	+	0.0398489i	−0.533744	+	0.845646i	$0.679215\pi$
$420$	6.76454	+	2.86148i	0.330076	+	0.139626i
$421$	−14.6370	−	10.8026i	−0.713365	−	0.526488i	0.175600	−	0.984462i	$-0.443813\pi$
$421$	−14.6370	−	10.8026i	−0.713365	−	0.526488i	−0.888966	+	0.457974i	$0.848575\pi$
$422$	−5.19588	−	10.7893i	−0.252931	−	0.525217i
$423$	3.01087	+	14.1658i	0.146394	+	0.688767i
$424$	1.18973	+	0.416304i	0.0577783	+	0.0202175i
$425$	−22.7985	−	43.1369i	−1.10589	−	2.09245i
$426$	−2.84510	−	0.615892i	−0.137846	−	0.0298401i
$427$	1.48360	+	1.27674i	0.0717966	+	0.0617860i
$428$	0.119315	−	0.0368037i	0.00576729	−	0.00177897i
$429$	−0.184502	−	0.0256967i	−0.00890785	−	0.00124065i
$430$	−8.46416	−	21.5663i	−0.408178	−	1.04002i
$431$	−21.4473	+	4.89521i	−1.03308	+	0.235794i	−0.705262	−	0.708947i	$-0.749171\pi$
$431$	−21.4473	+	4.89521i	−1.03308	+	0.235794i	−0.327819	+	0.944741i	$0.606313\pi$
$432$	−3.50722	−	3.80849i	−0.168741	−	0.183236i
$433$	3.09767	−	0.349023i	0.148864	−	0.0167730i	−0.0372177	−	0.999307i	$-0.511850\pi$
$433$	3.09767	−	0.349023i	0.148864	−	0.0167730i	0.186082	+	0.982534i	$0.440421\pi$
$434$	−1.41472	+	2.45037i	−0.0679089	+	0.117622i
$435$	−14.9726	−	27.6136i	−0.717882	−	1.32397i
$436$	−9.43002	−	16.3333i	−0.451616	−	0.782222i
$437$	3.33231	+	4.51513i	0.159406	+	0.215988i
$438$	11.0856	−	11.3370i	0.529690	−	0.541705i
$439$	1.34248	−	4.35220i	0.0640729	−	0.207719i	−0.917875	−	0.396869i	$-0.870097\pi$
$439$	1.34248	−	4.35220i	0.0640729	−	0.207719i	0.981948	+	0.189149i	$0.0605730\pi$
$440$	0.321297	−	0.402894i	0.0153172	−	0.0192072i
$441$	−7.74767	+	17.0565i	−0.368937	+	0.812215i
$442$	−2.28776	+	10.0233i	−0.108818	+	0.476762i
$443$	−5.31996	+	28.1167i	−0.252759	+	1.33586i	0.594248	+	0.804282i	$0.297450\pi$
$443$	−5.31996	+	28.1167i	−0.252759	+	1.33586i	−0.847007	+	0.531581i	$0.821598\pi$
$444$	6.07675	+	5.51289i	0.288390	+	0.261630i
$445$	28.3538	+	1.06092i	1.34410	+	0.0502926i
$446$	−1.22406	−	6.46930i	−0.0579608	−	0.306330i
$447$	−6.52714	−	12.0217i	−0.308723	−	0.568606i
$448$	2.04437	+	0.153204i	0.0965874	+	0.00723823i
$449$	1.58124	−	14.0339i	0.0746232	−	0.662299i	−0.899600	−	0.436714i	$-0.856142\pi$
$449$	1.58124	−	14.0339i	0.0746232	−	0.662299i	0.974224	−	0.225585i	$-0.0724293\pi$
$450$	13.2238	−	4.96280i	0.623376	−	0.233949i
$451$	0.546726	−	0.263289i	0.0257443	−	0.0123978i
$452$	−18.8533	+	5.05173i	−0.886786	+	0.237614i
$453$	8.57248	+	0.868651i	0.402770	+	0.0408128i
$454$	0.452284	−	12.0875i	0.0212267	−	0.567297i
$455$	−5.25309	+	0.393665i	−0.246269	+	0.0184553i
$456$	−6.07040	+	11.8043i	−0.284273	+	0.552788i
$457$	−5.58889	+	6.02340i	−0.261437	+	0.281763i	−0.850106	−	0.526612i	$-0.823462\pi$
$457$	−5.58889	+	6.02340i	−0.261437	+	0.281763i	0.588668	+	0.808375i	$0.299652\pi$
$458$	−13.2115	+	10.5358i	−0.617333	+	0.492306i
$459$	39.9578	−	1.34479i	1.86507	−	0.0627694i
$460$	2.03559	+	8.91849i	0.0949098	+	0.415827i
$461$	5.89061	−	0.220411i	0.274353	−	0.0102656i	0.100139	−	0.994973i	$-0.468071\pi$
$461$	5.89061	−	0.220411i	0.274353	−	0.0102656i	0.174214	+	0.984708i	$0.444262\pi$
$462$	−0.0511142	−	0.0429991i	−0.00237805	−	0.00200050i
$463$	14.8973	−	8.60095i	0.692335	−	0.399720i	−0.112151	−	0.993691i	$-0.535774\pi$
$463$	14.8973	−	8.60095i	0.692335	−	0.399720i	0.804486	+	0.593971i	$0.202441\pi$
$464$	3.93128	+	3.65182i	0.182505	+	0.169531i
$465$	−5.97028	−	24.8687i	−0.276865	−	1.15326i
$466$	−2.76414	−	1.20598i	−0.128046	−	0.0558660i
$467$	20.8949	−	13.1291i	0.966901	−	0.607544i	0.0466660	−	0.998911i	$-0.485140\pi$
$467$	20.8949	−	13.1291i	0.966901	−	0.607544i	0.920235	+	0.391366i	$0.127998\pi$
$468$	7.34353	+	2.69368i	0.339455	+	0.124515i
$469$	−3.68157	−	2.93596i	−0.169999	−	0.135570i
$470$	11.9355	−	1.79899i	0.550545	−	0.0829813i
$471$	20.8548	+	11.7307i	0.960938	+	0.540521i
$472$	−7.10596	+	8.25728i	−0.327078	+	0.380072i
$473$	−0.0413798	−	0.552175i	−0.00190264	−	0.0253890i
$474$	−12.4166	+	10.9301i	−0.570315	+	0.502037i
$475$	12.3797	+	14.3855i	0.568020	+	0.660051i
$476$	6.85083	−	6.85083i	0.314007	−	0.314007i
$477$	0.570221	+	1.36225i	0.0261086	+	0.0623730i
$478$	−20.3056	−	2.28789i	−0.928756	−	0.104646i
$479$	−18.8779	+	25.5786i	−0.862553	+	1.16872i	0.121808	+	0.992554i	$0.461131\pi$
$479$	−18.8779	+	25.5786i	−0.862553	+	1.16872i	−0.984361	+	0.176164i	$0.943631\pi$
$480$	−26.4874	+	21.6134i	−1.20898	+	0.986511i
$481$	−5.68406	−	1.52304i	−0.259171	−	0.0694447i
$482$	4.20204	−	0.795070i	0.191398	−	0.0362144i
$483$	2.76736	−	0.555828i	0.125919	−	0.0252911i
$484$	−13.1629	+	8.97431i	−0.598313	+	0.407923i
$485$	−6.17856	−	17.6573i	−0.280554	−	0.801777i
$486$	−1.08091	+	11.5232i	−0.0490309	+	0.522705i
$487$	−10.0315	−	12.5791i	−0.454572	−	0.570016i	0.500746	−	0.865594i	$-0.333059\pi$
$487$	−10.0315	−	12.5791i	−0.454572	−	0.570016i	−0.955318	+	0.295579i	$0.904488\pi$
$488$	−5.36775	+	2.10669i	−0.242987	+	0.0953652i
$489$	19.3061	−	29.0105i	0.873052	−	1.31190i
$490$	13.8043	+	7.29580i	0.623616	+	0.329590i
$491$	2.17816	−	1.60755i	0.0982989	−	0.0725479i	−0.543562	−	0.839369i	$-0.682925\pi$
$491$	2.17816	−	1.60755i	0.0982989	−	0.0725479i	0.641861	+	0.766821i	$0.278163\pi$
$492$	−24.7762	+	5.94810i	−1.11700	+	0.268161i
$493$	−41.1767	+	4.61604i	−1.85451	+	0.207896i
$494$		−	3.99918i		−	0.179932i
$495$	0.602678	−	0.0361003i	0.0270884	−	0.00162259i
$496$	2.32431	+	3.69912i	0.104365	+	0.166095i
$497$	−1.88006	−	0.579921i	−0.0843321	−	0.0260130i
$498$	−17.4585	+	12.1920i	−0.782332	+	0.546336i
$499$	−7.58692	−	2.97765i	−0.339637	−	0.133298i	0.189392	−	0.981902i	$-0.439348\pi$
$499$	−7.58692	−	2.97765i	−0.339637	−	0.133298i	−0.529029	+	0.848604i	$0.677444\pi$
$500$	1.92883	+	6.25313i	0.0862601	+	0.279648i
$501$	−1.45301	−	29.8651i	−0.0649157	−	1.33427i
$502$	−0.659572	−	0.967414i	−0.0294381	−	0.0431778i
$503$	−12.1893	−	7.65903i	−0.543493	−	0.341499i	0.232141	−	0.972682i	$-0.425427\pi$
$503$	−12.1893	−	7.65903i	−0.543493	−	0.341499i	−0.775634	+	0.631183i	$0.782570\pi$
$504$	4.08418	+	5.28172i	0.181924	+	0.235266i
$505$	24.7924	+	24.7924i	1.10325	+	1.10325i
$506$	0.00621692	−	0.0829590i	0.000276376	−	0.00368798i
$507$	16.7781	−	2.08122i	0.745140	−	0.0924304i
$508$	21.5273	−	9.39226i	0.955119	−	0.416714i
$509$	−2.59850	+	3.81130i	−0.115177	+	0.168933i	−0.879498	−	0.475902i	$-0.842122\pi$
$509$	−2.59850	+	3.81130i	−0.115177	+	0.168933i	0.764322	+	0.644835i	$0.223074\pi$
$510$	0.872458	−	33.3105i	0.0386331	−	1.47501i
$511$	8.12300	−	6.99041i	0.359341	−	0.309238i
$512$	5.82167	−	9.26514i	0.257284	−	0.409465i
$513$	−15.0368	+	3.96861i	−0.663892	+	0.175218i
$514$	4.17955	−	1.46249i	0.184352	−	0.0645075i
$515$	12.8533	+	11.9261i	0.566386	+	0.525529i
$516$	−3.20730	+	23.0284i	−0.141193	+	1.01377i
$517$	0.285266	+	0.0429969i	0.0125460	+	0.00189100i
$518$	−1.43518	−	1.54675i	−0.0630581	−	0.0679605i
$519$	−1.32939	−	1.29990i	−0.0583538	−	0.0570595i
$520$	6.20597	−	14.2242i	0.272150	−	0.623774i
$521$	23.7321			1.03972			0.519860	−	0.854251i	$-0.325984\pi$
$521$	23.7321			1.03972			0.519860	+	0.854251i	$0.325984\pi$
$522$	0.186323	−	11.9934i	0.00815514	−	0.524936i
$523$	−0.761512			−0.0332986			−0.0166493	−	0.999861i	$-0.505300\pi$
$523$	−0.761512			−0.0332986			−0.0166493	+	0.999861i	$0.505300\pi$
$524$	−5.56135	+	12.7467i	−0.242948	+	0.556844i
$525$	9.19272	−	2.57401i	0.401203	−	0.112339i
$526$	−1.35064	−	1.45564i	−0.0588907	−	0.0634691i
$527$	−33.3592	−	5.02810i	−1.45315	−	0.219027i
$528$	−0.0955756	+	0.0387531i	−0.00415939	+	0.00168651i
$529$	−14.2831	−	13.2528i	−0.621006	−	0.576209i
$530$	1.16176	−	0.406517i	0.0504636	−	0.0176580i
$531$	−12.7603	+	0.286241i	−0.553749	+	0.0124218i
$532$	−2.00506	+	3.19103i	−0.0869304	+	0.138349i
$533$	13.8517	−	11.9203i	0.599983	−	0.516327i
$534$	9.23811	+	5.66119i	0.399772	+	0.244984i
$535$	0.163501	−	0.239813i	0.00706878	−	0.0103680i
$536$	12.7151	−	5.54753i	0.549207	−	0.239617i
$537$	3.93104	+	5.20321i	0.169637	+	0.224535i
$538$	−0.364238	+	4.86042i	−0.0157034	+	0.209548i
$539$	0.263875	+	0.263875i	0.0113659	+	0.0113659i
$540$	−25.0541	−	3.87263i	−1.07816	−	0.166652i
$541$	0.989606	+	0.621810i	0.0425465	+	0.0267337i	0.553137	−	0.833090i	$-0.313430\pi$
$541$	0.989606	+	0.621810i	0.0425465	+	0.0267337i	−0.510591	+	0.859824i	$0.670573\pi$
$542$	−5.80353	−	8.51222i	−0.249283	−	0.365631i
$543$	−22.5413	−	11.5919i	−0.967341	−	0.497458i
$544$	13.2920	+	43.0917i	0.569891	+	1.84754i
$545$	−40.8103	−	16.0169i	−1.74812	−	0.686087i
$546$	−1.82203	−	0.852408i	−0.0779758	−	0.0364797i
$547$	15.4887	+	4.77765i	0.662251	+	0.204277i	0.607618	−	0.794229i	$-0.292125\pi$
$547$	15.4887	+	4.77765i	0.662251	+	0.204277i	0.0546327	+	0.998507i	$0.482601\pi$
$548$	−7.13688	−	11.3583i	−0.304872	−	0.485201i
$549$	−6.04235	−	3.02210i	−0.257881	−	0.128980i
$550$		−	0.281358i		−	0.0119972i
$551$	15.2160	−	5.31468i	0.648221	−	0.226413i
$552$	−2.36179	+	7.97310i	−0.100524	+	0.339357i
$553$	−8.99567	+	6.63911i	−0.382535	+	0.282324i
$554$	−7.57327	−	4.00259i	−0.321757	−	0.170054i
$555$	19.0338	+	1.21191i	0.807941	+	0.0514428i
$556$	21.1474	−	8.29975i	0.896850	−	0.351988i
$557$	2.67720	+	3.35710i	0.113437	+	0.142245i	0.835308	−	0.549782i	$-0.185289\pi$
$557$	2.67720	+	3.35710i	0.113437	+	0.142245i	−0.721871	+	0.692027i	$0.756718\pi$
$558$	2.66861	−	9.39449i	0.112971	−	0.397700i
$559$	−5.50761	−	15.7399i	−0.232947	−	0.665725i
$560$	−2.40970	+	1.64290i	−0.101828	+	0.0694253i
$561$	0.254591	−	0.754621i	0.0107489	−	0.0318601i
$562$	−2.59495	+	0.490991i	−0.109461	+	0.0207112i
$563$	37.5791	+	10.0693i	1.58377	+	0.424370i	0.940091	−	0.340924i	$-0.110740\pi$
$563$	37.5791	+	10.0693i	1.58377	+	0.424370i	0.643680	+	0.765295i	$0.277407\pi$
$564$	−11.3251	−	4.29884i	−0.476872	−	0.181014i
$565$	−26.9424	+	36.5056i	−1.13347	+	1.53580i
$566$	1.59361	+	0.179557i	0.0669844	+	0.00754733i
$567$	−1.39693	+	7.69669i	−0.0586654	+	0.323230i
$568$	4.09853	−	4.09853i	0.171971	−	0.171971i
$569$	−2.74716	−	3.19225i	−0.115167	−	0.133826i	0.697429	−	0.716654i	$-0.254327\pi$
$569$	−2.74716	−	3.19225i	−0.115167	−	0.133826i	−0.812596	+	0.582828i	$0.801946\pi$
$570$	2.55239	+	12.7079i	0.106908	+	0.532275i
$571$	−1.38484	−	18.4794i	−0.0579537	−	0.773338i	−0.948163	−	0.317786i	$-0.897061\pi$
$571$	−1.38484	−	18.4794i	−0.0579537	−	0.773338i	0.890209	−	0.455553i	$-0.150558\pi$
$572$	0.101636	−	0.118103i	0.00424960	−	0.00493812i
$573$	−0.516511	−	46.0568i	−0.0215776	−	1.92405i
$574$	6.47953	−	0.976631i	0.270450	−	0.0407638i
$575$	9.29571	+	7.41308i	0.387658	+	0.309147i
$576$	−6.97172	+	1.21130i	−0.290488	+	0.0504710i
$577$	−23.8286	+	14.9725i	−0.991997	+	0.623313i	−0.927193	−	0.374585i	$-0.877785\pi$
$577$	−23.8286	+	14.9725i	−0.991997	+	0.623313i	−0.0648047	+	0.997898i	$0.520642\pi$
$578$	−28.7184	−	12.5297i	−1.19453	−	0.521166i
$579$	−40.3507	−	11.9527i	−1.67692	−	0.496736i
$580$	26.1993	+	1.97819i	1.08786	+	0.0821398i
$581$	−12.4640	+	7.19608i	−0.517093	+	0.298544i
$582$	1.24926	−	7.03340i	0.0517836	−	0.291544i
$583$	0.0293969	−	0.00109995i	0.00121749	−	4.55554e-5i
$584$	7.02540	+	30.7803i	0.290713	+	1.27370i
$585$	17.2501	−	5.74768i	0.713204	−	0.237637i
$586$	6.63569	−	5.29179i	0.274118	−	0.218602i
$587$	1.73557	−	1.87050i	0.0716347	−	0.0772039i	−0.696217	−	0.717831i	$-0.745135\pi$
$587$	1.73557	−	1.87050i	0.0716347	−	0.0772039i	0.767852	+	0.640627i	$0.221326\pi$
$588$	−8.48497	−	13.1735i	−0.349914	−	0.543265i
$589$	13.0861	−	0.980666i	0.539202	−	0.0404076i
$590$	−0.397761	+	10.6304i	−0.0163755	+	0.437646i
$591$	−11.0379	−	24.5444i	−0.454038	−	1.00962i
$592$	−3.14691	+	0.843213i	−0.129337	+	0.0346559i
$593$	−6.23061	+	3.00050i	−0.255861	+	0.123216i	−0.557418	−	0.830232i	$-0.688208\pi$
$593$	−6.23061	+	3.00050i	−0.255861	+	0.123216i	0.301557	+	0.953448i	$0.402494\pi$
$594$	0.207342	+	0.100812i	0.00850734	+	0.00413637i
$595$	2.52159	−	22.3797i	0.103375	−	0.917480i
$596$	11.4099	+	0.855055i	0.467368	+	0.0350244i
$597$	−27.8154	−	0.728533i	−1.13841	−	0.0298169i
$598$	−0.465775	−	2.46168i	−0.0190469	−	0.100666i
$599$	−29.2212	−	1.09338i	−1.19395	−	0.0446744i	−0.566988	−	0.823726i	$-0.691891\pi$
$599$	−29.2212	−	1.09338i	−1.19395	−	0.0446744i	−0.626960	+	0.779052i	$0.715701\pi$
$600$	−5.95023	+	27.4869i	−0.242917	+	1.12215i
$601$	6.98138	−	36.8975i	0.284776	−	1.50508i	−0.489372	−	0.872075i	$-0.662774\pi$
$601$	6.98138	−	36.8975i	0.284776	−	1.50508i	0.774149	−	0.633004i	$-0.218178\pi$
$602$	1.33053	−	5.82943i	0.0542284	−	0.237590i
$603$	14.7982	+	6.72187i	0.602630	+	0.273736i
$604$	−4.49353	+	5.63471i	−0.182839	+	0.229273i
$605$	−10.9155	+	35.3872i	−0.443778	+	1.43869i
$606$	3.61005	+	12.8928i	0.146648	+	0.523733i
$607$	−20.7913	−	28.1712i	−0.843893	−	1.14343i	−0.988089	−	0.153886i	$-0.950821\pi$
$607$	−20.7913	−	28.1712i	−0.843893	−	1.14343i	0.144195	−	0.989549i	$-0.453941\pi$
$608$	−8.77064	−	15.1912i	−0.355696	−	0.616084i
$609$	0.821835	−	8.06521i	0.0333024	−	0.326819i
$610$	−2.81540	+	4.87641i	−0.113992	+	0.197440i
$611$	8.63332	−	0.972741i	0.349267	−	0.0393529i
$612$	−17.1522	+	28.7073i	−0.693338	+	1.16042i
$613$	−2.95297	+	0.673995i	−0.119269	+	0.0272224i	−0.281739	−	0.959491i	$-0.590911\pi$
$613$	−2.95297	+	0.673995i	−0.119269	+	0.0272224i	0.162470	+	0.986714i	$0.448054\pi$
$614$	3.93463	+	10.0253i	0.158789	+	0.404587i
$615$	−36.4075	+	46.7189i	−1.46809	+	1.88389i
$616$	0.127090	−	0.0392019i	0.00512058	−	0.00157949i
$617$	−20.8357	−	17.9306i	−0.838816	−	0.721859i	0.123923	−	0.992292i	$-0.460452\pi$
$617$	−20.8357	−	17.9306i	−0.838816	−	0.721859i	−0.962739	+	0.270433i	$0.912833\pi$
$618$	2.04517	+	6.37553i	0.0822686	+	0.256461i
$619$	4.68574	+	8.86584i	0.188336	+	0.356348i	0.960144	−	0.279507i	$-0.0901711\pi$
$619$	4.68574	+	8.86584i	0.188336	+	0.356348i	−0.771808	+	0.635856i	$0.780647\pi$
$620$	20.1917	+	7.06536i	0.810916	+	0.283752i
$621$	−8.79363	+	4.19416i	−0.352876	+	0.168306i
$622$	−8.46364	−	17.5749i	−0.339361	−	0.704691i
$623$	5.89199	+	4.34849i	0.236058	+	0.174219i
$624$	−2.47817	+	1.87226i	−0.0992062	+	0.0749504i
$625$	−13.6287	−	9.29186i	−0.545146	−	0.371674i
$626$	−6.56091	+	24.4856i	−0.262227	+	0.978643i
$627$	−0.0312312	+	0.308212i	−0.00124726	+	0.0123088i
$628$	−17.6946	+	9.35189i	−0.706093	+	0.373181i
$629$	10.9157	−	22.6667i	0.435238	−	0.903781i
$630$	6.33376	+	1.54575i	0.252343	+	0.0615843i
$631$	7.67370	+	1.75147i	0.305485	+	0.0697250i	0.372516	−	0.928026i	$-0.378495\pi$
$631$	7.67370	+	1.75147i	0.305485	+	0.0697250i	−0.0670304	+	0.997751i	$0.521352\pi$
$632$	−4.90909	−	32.5697i	−0.195273	−	1.29555i
$633$	15.9951	+	22.9043i	0.635747	+	0.910365i
$634$	10.5415	−	9.78112i	0.418658	−	0.388458i
$635$	25.5112	−	48.2695i	1.01238	−	1.91552i
$636$	−1.21620	−	0.216019i	−0.0482253	−	0.00856571i
$637$	9.73271	+	5.61919i	0.385624	+	0.222640i
$638$	−0.222371	−	0.0874188i	−0.00880376	−	0.00346094i
$639$	6.78162	+	0.355488i	0.268277	+	0.0140629i
$640$	−3.75950	−	33.3665i	−0.148607	−	1.31893i
$641$	−1.40222	−	37.4752i	−0.0553845	−	1.48018i	−0.699159	−	0.714966i	$-0.746442\pi$
$641$	−1.40222	−	37.4752i	−0.0553845	−	1.48018i	0.643775	−	0.765215i	$-0.277367\pi$
$642$	0.0993118	−	0.0492055i	0.00391952	−	0.00194199i
$643$	3.03972	−	20.1672i	0.119875	−	0.795317i	−0.845410	−	0.534118i	$-0.820644\pi$
$643$	3.03972	−	20.1672i	0.119875	−	0.795317i	0.965285	−	0.261200i	$-0.0841180\pi$
$644$	−0.862554	+	2.19775i	−0.0339894	+	0.0866035i
$645$	27.5467	+	46.5002i	1.08465	+	1.83094i
$646$	16.7995	+	3.17864i	0.660968	+	0.125062i
$647$	−27.2706	−	13.1328i	−1.07212	−	0.516305i	−0.187330	−	0.982297i	$-0.559983\pi$
$647$	−27.2706	−	13.1328i	−1.07212	−	0.516305i	−0.884789	+	0.465992i	$0.845698\pi$
$648$	−18.1240	−	14.2336i	−0.711978	−	0.559149i
$649$	−0.0839732	+	0.239982i	−0.00329624	+	0.00942010i
$650$	−2.19304	−	8.18452i	−0.0860180	−	0.321023i
$651$	2.34245	−	6.17106i	0.0918077	−	0.241863i
$652$	11.6559	+	26.7156i	0.456480	+	1.04626i
$653$	11.5371	+	26.4434i	0.451482	+	1.03481i	0.982299	+	0.187322i	$0.0599807\pi$
$653$	11.5371	+	26.4434i	0.451482	+	1.03481i	−0.530816	+	0.847487i	$0.678115\pi$
$654$	−10.5840	−	12.9708i	−0.413867	−	0.507199i
$655$	8.36700	+	31.2261i	0.326926	+	1.22010i
$656$	3.34162	−	9.54980i	0.130468	−	0.372857i
$657$	−21.2925	+	30.2473i	−0.830700	+	1.18006i
$658$	2.80672	+	1.35164i	0.109417	+	0.0526925i
$659$	−13.4672	−	2.54812i	−0.524606	−	0.0992608i	−0.0831383	−	0.996538i	$-0.526494\pi$
$659$	−13.4672	−	2.54812i	−0.524606	−	0.0992608i	−0.441467	+	0.897277i	$0.645542\pi$
$660$	−0.247583	+	0.440152i	−0.00963714	+	0.0171329i
$661$	−14.0720	+	35.8547i	−0.547335	+	1.39459i	0.343023	+	0.939327i	$0.388549\pi$
$661$	−14.0720	+	35.8547i	−0.547335	+	1.39459i	−0.890358	+	0.455261i	$0.849546\pi$
$662$	−3.57437	+	23.7144i	−0.138922	+	0.921686i
$663$	1.52403	−	23.9358i	0.0591884	−	0.929590i
$664$	−1.58537	−	42.3700i	−0.0615244	−	1.64427i
$665$	0.980858	+	8.70536i	0.0380360	+	0.337579i
$666$	6.10797	+	3.96666i	0.236679	+	0.153705i
$667$	8.74712	−	5.04359i	0.338690	−	0.195289i
$668$	21.6592	+	12.5049i	0.838018	+	0.483830i
$669$	5.23524	+	14.4400i	0.202406	+	0.558281i
$670$	6.32983	−	11.9766i	0.244542	−	0.462697i
$671$	−0.0986534	+	0.0915370i	−0.00380847	+	0.00353375i
$672$	−8.79054	+	0.757980i	−0.339103	+	0.0292397i
$673$	−2.25443	−	14.9572i	−0.0869020	−	0.576557i	−0.989327	−	0.145711i	$-0.953453\pi$
$673$	−2.25443	−	14.9572i	−0.0869020	−	0.576557i	0.902425	−	0.430847i	$-0.141785\pi$
$674$	−1.69157	−	0.386091i	−0.0651570	−	0.0148717i
$675$	−28.5973	+	16.3677i	−1.10071	+	0.629993i
$676$	−6.13570	+	12.7409i	−0.235989	+	0.490035i
$677$	−19.4602	+	10.2850i	−0.747917	+	0.395286i	−0.797370	−	0.603491i	$-0.793776\pi$
$677$	−19.4602	+	10.2850i	−0.747917	+	0.395286i	0.0494528	+	0.998776i	$0.484252\pi$
$678$	−15.8012	+	7.10595i	−0.606840	+	0.272902i
$679$	1.24960	−	4.66357i	0.0479553	−	0.178971i
$680$	54.8197	+	37.3754i	2.10224	+	1.43328i
$681$	3.47368	+	28.0036i	0.133112	+	1.07310i
$682$	−0.156528	−	0.115523i	−0.00599378	−	0.00442361i
$683$	0.542211	+	1.12591i	0.0207471	+	0.0430819i	0.911085	−	0.412219i	$-0.135246\pi$
$683$	0.542211	+	1.12591i	0.0207471	+	0.0430819i	−0.890338	+	0.455301i	$0.849532\pi$
$684$	4.01985	−	12.3713i	0.153703	−	0.473030i
$685$	−29.4324	−	10.2988i	−1.12455	−	0.393498i
$686$	3.99371	+	7.55648i	0.152481	+	0.288508i
$687$	26.4872	−	29.1964i	1.01055	−	1.11391i
$688$	−6.99780	−	6.02209i	−0.266789	−	0.229590i
$689$	0.846562	−	0.261130i	0.0322514	−	0.00994825i
$690$	3.05117	+	7.52501i	0.116156	+	0.286472i
$691$	−16.7730	−	42.7369i	−0.638075	−	1.62579i	−0.772611	−	0.634880i	$-0.781050\pi$
$691$	−16.7730	−	42.7369i	−0.638075	−	1.62579i	0.134536	−	0.990909i	$-0.457046\pi$
$692$	1.51620	−	0.346064i	0.0576374	−	0.0131554i
$693$	0.133765	+	0.0799231i	0.00508132	+	0.00303603i
$694$	22.8453	−	2.57405i	0.867196	−	0.0977095i
$695$	26.4042	−	45.7334i	1.00157	−	1.73477i
$696$	19.8755	+	13.2430i	0.753380	+	0.501975i
$697$	39.0646	+	67.6619i	1.47968	+	2.56288i
$698$	1.38498	+	1.87658i	0.0524222	+	0.0710296i
$699$	6.81560	+	1.74456i	0.257790	+	0.0659852i
$700$	−2.35358	+	7.63012i	−0.0889570	+	0.288392i
$701$	11.1141	−	13.9367i	0.419775	−	0.526381i	−0.526313	−	0.850291i	$-0.676426\pi$
$701$	11.1141	−	13.9367i	0.419775	−	0.526381i	0.946088	+	0.323910i	$0.104997\pi$
$702$	6.81721	+	1.31644i	0.257299	+	0.0496857i
$703$	−2.17762	+	9.54076i	−0.0821303	+	0.359836i
$704$	−0.0262056	+	0.138500i	−0.000987662	+	0.00521992i
$705$	−26.8126	+	8.60103i	−1.00982	+	0.323934i
$706$	−1.78846	−	0.0669196i	−0.0673097	−	0.00251855i
$707$	1.68232	+	8.89127i	0.0632701	+	0.334391i
$708$	5.57818	−	9.10264i	0.209641	−	0.342098i
$709$	−49.3643	−	3.69934i	−1.85391	−	0.138932i	−0.899405	−	0.437116i	$-0.856000\pi$
$709$	−49.3643	−	3.69934i	−1.85391	−	0.138932i	−0.954508	+	0.298184i	$0.903619\pi$
$710$	0.633713	−	5.62435i	0.0237828	−	0.211078i
$711$	24.5096	−	29.8074i	0.919181	−	1.11787i
$712$	−19.4370	+	9.36038i	−0.728433	+	0.350795i
$713$	7.94086	−	2.12775i	0.297388	−	0.0796847i
$714$	5.02893	−	6.97637i	0.188203	−	0.261084i
$715$	0.0135429	−	0.361942i	0.000506477	−	0.0135359i
$716$	−5.43935	+	0.407623i	−0.203278	+	0.0152336i
$717$	47.6134	−	2.31651i	1.77815	−	0.0865115i
$718$	−0.177926	+	0.191758i	−0.00664012	+	0.00715635i
$719$	12.7662	−	10.1807i	0.476100	−	0.379677i	−0.355837	−	0.934548i	$-0.615804\pi$
$719$	12.7662	−	10.1807i	0.476100	−	0.379677i	0.831936	+	0.554871i	$0.187233\pi$
$720$	6.67975	−	7.53097i	0.248940	−	0.280663i
$721$	1.00698	+	4.41186i	0.0375019	+	0.164306i
$722$	7.45086	−	0.278791i	0.277292	−	0.0103755i
$723$	−9.37927	+	3.40048i	−0.348819	+	0.126465i
$724$	18.3610	−	10.6007i	0.682379	−	0.393972i
$725$	28.2258	−	19.2207i	1.04828	−	0.713841i
$726$	−10.2577	+	9.73409i	−0.380699	+	0.361266i
$727$	4.89211	+	2.13441i	0.181438	+	0.0791607i	0.488648	−	0.872481i	$-0.337490\pi$
$727$	4.89211	+	2.13441i	0.181438	+	0.0791607i	−0.307209	+	0.951642i	$0.599395\pi$
$728$	3.39139	−	2.13095i	0.125693	−	0.0789783i
$729$	−1.81533	−	26.9389i	−0.0672344	−	0.997737i
$730$	24.1036	+	19.2220i	0.892114	+	0.711437i
$731$	70.4966	−	10.6257i	2.60741	−	0.393004i
$732$	4.86186	−	2.88017i	0.179700	−	0.106454i
$733$	−9.16965	+	10.6553i	−0.338689	+	0.393563i	−0.901327	−	0.433140i	$-0.857406\pi$
$733$	−9.16965	+	10.6553i	−0.338689	+	0.393563i	0.562638	+	0.826703i	$0.309787\pi$
$734$	0.860771	+	11.4862i	0.0317717	+	0.423963i
$735$	−34.5132	−	11.6439i	−1.27304	−	0.429493i
$736$	−7.16800	−	8.32937i	−0.264216	−	0.307025i
$737$	0.228938	−	0.228938i	0.00843303	−	0.00843303i
$738$	−20.8634	+	8.73317i	−0.767991	+	0.321472i
$739$	7.00287	+	0.789034i	0.257605	+	0.0290251i	0.239822	−	0.970817i	$-0.422911\pi$
$739$	7.00287	+	0.789034i	0.257605	+	0.0290251i	0.0177824	+	0.999842i	$0.494339\pi$
$740$	−9.47312	+	12.8356i	−0.348239	+	0.471847i
$741$	1.49385	+	9.20912i	0.0548781	+	0.338306i
$742$	0.306839	+	0.0822172i	0.0112644	+	0.00301829i
$743$	−6.45388	+	1.22114i	−0.236770	+	0.0447993i	−0.302942	−	0.953009i	$-0.597969\pi$
$743$	−6.45388	+	1.22114i	−0.236770	+	0.0447993i	0.0661723	+	0.997808i	$0.478921\pi$
$744$	12.8487	+	14.5962i	0.471057	+	0.535122i
$745$	21.9756	−	14.9827i	0.805123	−	0.548924i
$746$	−1.63384	−	4.66923i	−0.0598190	−	0.170953i
$747$	35.6483	−	34.5965i	1.30430	−	1.26582i
$748$	0.415336	+	0.520815i	0.0151862	+	0.0190429i
$749$	0.0697310	−	0.0273674i	0.00254791	−	0.000999983i
$750$	2.57880	+	5.20480i	0.0941644	+	0.190053i
$751$	−36.1082	−	19.0837i	−1.31761	−	0.696376i	−0.347187	−	0.937796i	$-0.612863\pi$
$751$	−36.1082	−	19.0837i	−1.31761	−	0.696376i	−0.970421	+	0.241420i	$0.922387\pi$
$752$	3.87010	−	2.85626i	0.141128	−	0.104157i
$753$	1.88020	+	1.98134i	0.0685182	+	0.0722040i
$754$	−7.15001	−	0.809688i	−0.260388	−	0.0294871i
$755$			16.7531i			0.609707i
$756$	−4.77958	−	4.46834i	−0.173832	−	0.162512i
$757$	−24.5221	−	39.0267i	−0.891271	−	1.41845i	−0.908174	−	0.418593i	$-0.862523\pi$
$757$	−24.5221	−	39.0267i	−0.891271	−	1.41845i	0.0169024	−	0.999857i	$-0.494620\pi$
$758$	1.46440	+	0.451707i	0.0531893	+	0.0164067i
$759$	0.0166725	+	0.193356i	0.000605173	+	0.00701839i
$760$	−24.0244	−	9.42890i	−0.871458	−	0.342022i
$761$	8.21841	+	26.6434i	0.297917	+	0.965824i	0.973528	+	0.228566i	$0.0734036\pi$
$761$	8.21841	+	26.6434i	0.297917	+	0.965824i	−0.675611	+	0.737258i	$0.736120\pi$
$762$	17.5271	−	11.2891i	0.634942	−	0.408963i
$763$	−6.37386	−	9.34874i	−0.230749	−	0.338447i
$764$	32.6209	+	20.4971i	1.18018	+	0.741559i
$765$	10.4337	+	77.0316i	0.377232	+	2.78508i
$766$	−11.6708	−	11.6708i	−0.421682	−	0.421682i
$767$	−0.572196	+	7.63543i	−0.0206608	+	0.275699i
$768$	8.17855	−	19.3341i	0.295118	−	0.697660i
$769$	−27.9260	+	12.1840i	−1.00704	+	0.439366i	−0.837664	−	0.546186i	$-0.816079\pi$
$769$	−27.9260	+	12.1840i	−1.00704	+	0.439366i	−0.169373	+	0.985552i	$0.554174\pi$
$770$	0.0731593	−	0.107305i	0.00263648	−	0.00386700i
$771$	−9.07816	+	4.92897i	−0.326942	+	0.177513i
$772$	26.6809	−	22.9608i	0.960267	−	0.826377i
$773$	10.0360	−	15.9723i	0.360971	−	0.574482i	−0.616028	−	0.787724i	$-0.711259\pi$
$773$	10.0360	−	15.9723i	0.360971	−	0.574482i	0.976999	+	0.213242i	$0.0684022\pi$
$774$	0.462847	+	20.6332i	0.0166367	+	0.741646i
$775$	26.2435	−	9.18301i	0.942695	−	0.329863i
$776$	10.4267	+	9.67455i	0.374296	+	0.347296i
$777$	3.88263	+	3.02569i	0.139289	+	0.108546i
$778$	−23.3954	−	3.52629i	−0.838765	−	0.126424i
$779$	−20.6711	−	22.2782i	−0.740620	−	0.798199i
$780$	−3.77126	+	14.7335i	−0.135033	+	0.527544i
$781$	0.0540956	−	0.123988i	0.00193569	−	0.00443666i
$782$	10.7111			0.383027
$783$	4.05095	+	27.6874i	0.144769	+	0.989465i
$784$	6.22199			0.222214
$785$	−18.6042	+	42.6414i	−0.664014	+	1.52194i
$786$	−3.06110	+	11.9591i	−0.109186	+	0.426565i
$787$	32.0749	+	34.5685i	1.14335	+	1.23223i	0.968869	+	0.247573i	$0.0796330\pi$
$787$	32.0749	+	34.5685i	1.14335	+	1.23223i	0.174477	+	0.984661i	$0.444177\pi$
$788$	22.2589	+	3.35499i	0.792941	+	0.119517i
$789$	3.65393	+	2.84747i	0.130083	+	0.101373i
$790$	−23.5773	−	21.8766i	−0.838843	−	0.778333i
$791$	−11.0527	+	3.86750i	−0.392988	+	0.137512i
$792$	−0.392309	+	0.238387i	−0.0139401	+	0.00847073i
$793$	−2.15628	+	3.43170i	−0.0765717	+	0.121863i
$794$	−11.1763	+	9.61795i	−0.396631	+	0.341328i
$795$	−2.52339	+	1.37007i	−0.0894955	+	0.0485914i
$796$	13.1106	−	19.2297i	0.464694	−	0.681580i
$797$	0.145438	−	0.0634541i	0.00515169	−	0.00224766i	−0.397315	−	0.917682i	$-0.630058\pi$
$797$	0.145438	−	0.0634541i	0.00515169	−	0.00224766i	0.402466	+	0.915435i	$0.368153\pi$
$798$	−1.30327	+	3.08095i	−0.0461354	+	0.109064i
$799$	−2.77572	+	37.0395i	−0.0981981	+	1.31036i
$800$	−26.2799	−	26.2799i	−0.929136	−	0.929136i
$801$	−23.3877	−	9.58552i	−0.826365	−	0.338688i
$802$	15.1399	+	9.51300i	0.534607	+	0.335916i
$803$	0.415079	+	0.608810i	0.0146478	+	0.0214844i
$804$	−11.4293	+	7.36155i	−0.403080	+	0.259622i
$805$	1.61765	+	5.24430i	0.0570148	+	0.184837i
$806$	−5.45374	−	2.14044i	−0.192100	−	0.0753937i
$807$	−0.976811	−	11.3284i	−0.0343854	−	0.398779i
$808$	−25.4743	−	7.85778i	−0.896183	−	0.276436i
$809$	19.0410	+	30.3035i	0.669445	+	1.06542i	0.992875	+	0.119164i	$0.0380213\pi$
$809$	19.0410	+	30.3035i	0.669445	+	1.06542i	−0.323429	+	0.946252i	$0.604836\pi$
$810$	−22.5027	+	0.167803i	−0.790664	+	0.00589598i
$811$		−	20.9637i		−	0.736134i	−0.929799	−	0.368067i	$-0.880020\pi$
$811$		−	20.9637i		−	0.736134i	0.929799	−	0.368067i	$-0.119980\pi$
$812$	5.29920	+	4.23085i	0.185965	+	0.148474i
$813$	16.5437	+	17.4337i	0.580215	+	0.611426i
$814$	0.116729	−	0.0861497i	0.00409134	−	0.00301955i
$815$	59.9030	+	31.6596i	2.09831	+	1.10899i
$816$	−5.89517	−	11.8983i	−0.206372	−	0.416522i
$817$	−25.8148	+	10.1316i	−0.903145	+	0.354458i
$818$	−10.6596	−	13.3667i	−0.372705	−	0.467357i
$819$	4.51410	+	1.28228i	0.157735	+	0.0448065i
$820$	−16.3627	−	46.7618i	−0.571409	−	1.63299i
$821$	21.4572	−	14.6292i	0.748860	−	0.510564i	−0.127726	−	0.991809i	$-0.540768\pi$
$821$	21.4572	−	14.6292i	0.748860	−	0.510564i	0.876586	+	0.481246i	$0.159815\pi$
$822$	−7.86766	−	8.93768i	−0.274416	−	0.311737i
$823$	14.7316	−	2.78738i	0.513513	−	0.0971619i	0.0773045	−	0.997008i	$-0.475369\pi$
$823$	14.7316	−	2.78738i	0.513513	−	0.0971619i	0.436208	+	0.899846i	$0.356321\pi$
$824$	−12.8775	−	3.45050i	−0.448607	−	0.120204i
$825$	0.105099	+	0.647898i	0.00365906	+	0.0225569i
$826$	−1.63033	+	2.20902i	−0.0567265	+	0.0768617i
$827$	3.07861	+	0.346876i	0.107054	+	0.0120621i	0.165329	−	0.986239i	$-0.447131\pi$
$827$	3.07861	+	0.346876i	0.107054	+	0.0120621i	−0.0582751	+	0.998301i	$0.518560\pi$
$828$	1.03354	−	8.08330i	0.0359180	−	0.280914i
$829$	−3.45803	+	3.45803i	−0.120102	+	0.120102i	−0.764603	−	0.644501i	$-0.777065\pi$
$829$	−3.45803	+	3.45803i	−0.120102	+	0.120102i	0.644501	+	0.764603i	$0.277065\pi$
$830$	−27.0066	−	31.3822i	−0.937412	−	1.08929i
$831$	18.9345	+	6.38805i	0.656830	+	0.221599i
$832$	0.317229	+	4.23313i	0.0109980	+	0.146757i
$833$	−31.3405	+	36.4183i	−1.08588	+	1.26182i
$834$	17.3496	−	10.2779i	0.600767	−	0.355895i
$835$	57.4869	−	8.66476i	1.98942	−	0.299856i
$836$	−0.202589	−	0.161559i	−0.00700667	−	0.00558764i
$837$	−2.63593	+	22.6300i	−0.0911112	+	0.782207i
$838$	−0.910299	+	0.571979i	−0.0314458	+	0.0197587i
$839$	−45.3107	−	19.7688i	−1.56430	−	0.682496i	−0.573671	−	0.819086i	$-0.694481\pi$
$839$	−45.3107	−	19.7688i	−1.56430	−	0.682496i	−0.990628	+	0.136590i	$0.956386\pi$
$840$	−9.41652	+	8.93584i	−0.324901	+	0.308316i
$841$	−6.42128	−	28.2802i	−0.221424	−	0.975178i
$842$	11.6971	−	6.75333i	0.403109	−	0.232735i
$843$	5.79212	−	2.09995i	0.199491	−	0.0723260i
$844$	−23.3508	+	0.873726i	−0.803768	+	0.0300749i
$845$	7.31473	+	32.0479i	0.251634	+	1.10248i
$846$	−10.5340	−	2.15697i	−0.362165	−	0.0741580i
$847$	−7.47246	+	5.95909i	−0.256757	+	0.204757i
$848$	0.333611	−	0.359547i	0.0114562	−	0.0123469i
$849$	−3.73676	+	0.181802i	−0.128245	+	0.00623944i
$850$	36.1241	−	2.70713i	1.23905	−	0.0928537i
$851$	−0.229233	+	6.12639i	−0.00785802	+	0.210010i
$852$	−3.32155	+	4.60780i	−0.113794	+	0.157861i
$853$	−12.8149	+	3.43375i	−0.438774	+	0.117569i	−0.471442	−	0.881897i	$-0.656266\pi$
$853$	−12.8149	+	3.43375i	−0.438774	+	0.117569i	0.0326677	+	0.999466i	$0.489600\pi$
$854$	−1.30933	+	0.630539i	−0.0448043	+	0.0215766i
$855$	−10.6244	−	28.3097i	−0.363348	−	0.968170i
$856$	−0.0247088	+	0.219297i	−0.000844530	+	0.00749541i
$857$	55.6714	+	4.17200i	1.90170	+	0.142513i	0.973369	−	0.229244i	$-0.0736253\pi$
$857$	55.6714	+	4.17200i	1.90170	+	0.142513i	0.928330	+	0.371756i	$0.121244\pi$
$858$	0.0722663	−	0.117926i	0.00246713	−	0.00402594i
$859$	0.559185	+	2.95537i	0.0190792	+	0.100836i	0.990812	−	0.135249i	$-0.0431834\pi$
$859$	0.559185	+	2.95537i	0.0190792	+	0.100836i	−0.971733	+	0.236085i	$0.924136\pi$
$860$	−45.1754	−	1.69034i	−1.54047	−	0.0576402i
$861$	−14.5559	+	4.66930i	−0.496065	+	0.159129i
$862$	3.03655	−	16.0486i	0.103425	−	0.546616i
$863$	−6.45872	+	28.2975i	−0.219858	+	0.963259i	0.737725	+	0.675101i	$0.235900\pi$
$863$	−6.45872	+	28.2975i	−0.219858	+	0.963259i	−0.957583	+	0.288158i	$0.906957\pi$
$864$	28.7828	−	9.95029i	0.979209	−	0.338516i
$865$	2.25398	−	2.82641i	0.0766378	−	0.0961007i
$866$	−0.682196	+	2.21163i	−0.0231820	+	0.0751541i
$867$	70.8116	+	18.1253i	2.40489	+	0.615568i
$868$	3.27851	+	4.44223i	0.111280	+	0.150779i
$869$	−0.384359	−	0.665729i	−0.0130385	−	0.0225833i
$870$	23.2368	−	1.99046i	0.787801	−	0.0674829i
$871$	4.87520	−	8.44409i	0.165190	−	0.286117i
$872$	33.1241	−	3.73219i	1.12172	−	0.126388i
$873$	−0.249486	+	16.6628i	−0.00844384	+	0.563951i
$874$	−4.06197	+	0.927119i	−0.137398	+	0.0313603i
$875$	1.43429	+	3.65451i	0.0484878	+	0.123545i
$876$	−11.6259	−	28.6726i	−0.392802	−	0.968757i
$877$	−39.7266	+	12.2540i	−1.34147	+	0.413789i	−0.880677	−	0.473718i	$-0.842912\pi$
$877$	−39.7266	+	12.2540i	−1.34147	+	0.413789i	−0.460795	+	0.887507i	$0.652436\pi$
$878$	2.56314	+	2.20576i	0.0865017	+	0.0744407i
$879$	−13.3037	+	14.6644i	−0.448721	+	0.494617i
$880$	−0.0936992	−	0.177287i	−0.00315860	−	0.00597636i
$881$	−4.02085	−	1.40695i	−0.135466	−	0.0474015i	0.261695	−	0.965151i	$-0.415719\pi$
$881$	−4.02085	−	1.40695i	−0.135466	−	0.0474015i	−0.397160	+	0.917749i	$0.630004\pi$
$882$	−9.30684	−	10.3365i	−0.313378	−	0.348049i
$883$	14.4657	+	30.0383i	0.486808	+	1.01087i	0.989247	+	0.146255i	$0.0467221\pi$
$883$	14.4657	+	30.0383i	0.486808	+	1.01087i	−0.502438	+	0.864613i	$0.667564\pi$
$884$	16.1413	+	11.9128i	0.542891	+	0.400672i
$885$	−3.05493	−	24.6277i	−0.102690	−	0.827851i
$886$	−17.5542	−	11.9683i	−0.589745	−	0.402081i
$887$	−11.8677	+	44.2908i	−0.398478	+	1.48714i	0.417297	+	0.908770i	$0.362978\pi$
$887$	−11.8677	+	44.2908i	−0.398478	+	1.48714i	−0.815775	+	0.578370i	$0.803689\pi$
$888$	−13.2256	+	5.94768i	−0.443821	+	0.199591i
$889$	12.4578	−	6.58414i	0.417821	−	0.220825i
$890$	−9.14033	+	18.9801i	−0.306385	+	0.636214i
$891$	−0.515114	−	0.154695i	−0.0172570	−	0.00518246i
$892$	−12.5253	−	2.85882i	−0.419378	−	0.0957203i
$893$	−2.15339	−	14.2868i	−0.0720603	−	0.478089i
$894$	10.1188	−	0.872513i	0.338424	−	0.0291812i
$895$	−9.29468	+	8.62420i	−0.310687	+	0.288275i
$896$	4.04934	−	7.66173i	0.135279	−	0.255961i
$897$	1.99210	+	5.49465i	0.0665142	+	0.183461i
$898$	9.08073	+	5.24276i	0.303028	+	0.174953i
$899$	0.896149	−	23.5947i	0.0298882	−	0.786928i
$900$	1.44273	−	27.5229i	0.0480911	−	0.917430i
$901$	0.424071	+	3.76374i	0.0141279	+	0.125388i
$902$	0.0168462	+	0.450225i	0.000560918	+	0.0149909i
$903$	−0.886354	+	13.9207i	−0.0294960	+	0.463253i
$904$	5.14156	−	34.1120i	0.171006	−	1.13455i
$905$	18.0053	−	45.8767i	0.598515	−	1.52499i
$906$	−3.13633	+	5.57577i	−0.104198	+	0.185242i
$907$	18.1955	+	3.44277i	0.604171	+	0.114315i	0.478993	−	0.877819i	$-0.341002\pi$
$907$	18.1955	+	3.44277i	0.604171	+	0.114315i	0.125179	+	0.992134i	$0.460050\pi$
$908$	−21.2653	−	10.2408i	−0.705715	−	0.339854i
$909$	−13.1290	−	28.3404i	−0.435462	−	0.939991i
$910$	1.29177	−	3.69167i	0.0428218	−	0.122378i
$911$	8.08704	+	30.1812i	0.267936	+	0.999949i	0.960429	+	0.278525i	$0.0898455\pi$
$911$	8.08704	+	30.1812i	0.267936	+	0.999949i	−0.692493	+	0.721424i	$0.743488\pi$
$912$	3.26551	+	4.00192i	0.108132	+	0.132517i
$913$	−0.395713	−	0.906985i	−0.0130962	−	0.0300168i
$914$	−2.43962	−	5.59168i	−0.0806956	−	0.184956i
$915$	4.66163	−	12.2808i	0.154109	−	0.405992i
$916$	8.53405	+	31.8495i	0.281973	+	1.05234i
$917$	−2.75564	+	7.87518i	−0.0909994	+	0.260061i
$918$	−10.9485	+	27.5910i	−0.361354	+	0.910638i
$919$	−8.54177	−	4.11350i	−0.281767	−	0.135692i	0.287663	−	0.957732i	$-0.407122\pi$
$919$	−8.54177	−	4.11350i	−0.281767	−	0.135692i	−0.569430	+	0.822040i	$0.692836\pi$
$920$	−15.8863	−	3.00585i	−0.523755	−	0.0990999i
$921$	−12.8053	−	21.6160i	−0.421950	−	0.712271i
$922$	−1.59895	+	4.07407i	−0.0526588	+	0.134172i
$923$	0.607182	−	4.02839i	0.0199856	−	0.132596i
$924$	−0.116787	+	0.0578640i	−0.00384202	+	0.00190359i
$925$	0.775279	+	20.7198i	0.0254910	+	0.681262i
$926$	1.42998	+	12.6914i	0.0469921	+	0.417066i
$927$	−7.09102	−	13.9173i	−0.232900	−	0.457104i
$928$	−28.9356	+	12.6051i	−0.949857	+	0.413782i
$929$	−24.5920	−	14.1982i	−0.806837	−	0.465827i	0.0390196	−	0.999238i	$-0.487577\pi$
$929$	−24.5920	−	14.1982i	−0.806837	−	0.465827i	−0.845856	+	0.533411i	$0.820910\pi$
$930$	18.6960	+	3.32076i	0.613066	+	0.108892i
$931$	8.73303	−	16.5237i	0.286214	−	0.541543i
$932$	−4.31373	+	4.00255i	−0.141301	+	0.131108i
$933$	26.0546	+	37.3092i	0.852989	+	1.22145i
$934$	2.73075	+	18.1173i	0.0893528	+	0.592817i
$935$	1.50966	+	0.344570i	0.0493712	+	0.0112686i
$936$	−9.55390	+	9.99237i	−0.312279	+	0.326611i
$937$	−25.2327	+	52.3962i	−0.824316	+	1.71171i	−0.130630	+	0.991431i	$0.541700\pi$
$937$	−25.2327	+	52.3962i	−0.824316	+	1.71171i	−0.693686	+	0.720278i	$0.744014\pi$
$938$	3.09103	−	1.63366i	0.100926	−	0.0533407i
$939$	5.96177	−	58.8351i	0.194555	−	1.92001i
$940$	6.09588	−	22.7501i	0.198826	−	0.742028i
$941$	5.51927	+	3.76298i	0.179923	+	0.122669i	0.649933	−	0.759992i	$-0.274797\pi$
$941$	5.51927	+	3.76298i	0.179923	+	0.122669i	−0.470009	+	0.882661i	$0.655750\pi$
$942$	−14.1747	+	10.7090i	−0.461838	+	0.348919i
$943$	−15.3187	−	11.3057i	−0.498846	−	0.368165i
$944$	1.83929	+	3.81932i	0.0598636	+	0.124308i
$945$	−15.1625	−	1.19358i	−0.493235	−	0.0388271i
$946$	0.388047	+	0.135784i	0.0126165	+	0.00441471i
$947$	−3.35231	−	6.34289i	−0.108936	−	0.206116i	0.823621	−	0.567141i	$-0.191951\pi$
$947$	−3.35231	−	6.34289i	−0.108936	−	0.206116i	−0.932556	+	0.361025i	$0.882427\pi$
$948$	9.85948	+	30.7356i	0.320221	+	0.998246i
$949$	16.8197	+	14.4745i	0.545991	+	0.469864i
$950$	−13.4651	+	4.15342i	−0.436864	+	0.134755i
$951$	−20.6209	+	26.4612i	−0.668679	+	0.858062i
$952$	6.25602	+	15.9401i	0.202759	+	0.516621i
$953$	−29.6114	+	6.75861i	−0.959208	+	0.218933i	−0.673337	−	0.739335i	$-0.735140\pi$
$953$	−29.6114	+	6.75861i	−0.959208	+	0.218933i	−0.285871	+	0.958268i	$0.592283\pi$
$954$	−1.09633	−	0.0164149i	−0.0354949	−	0.000531452i
$955$	88.9921	−	10.0270i	2.87972	−	0.324466i
$956$	−19.9363	+	34.5308i	−0.644787	+	1.11680i
$957$	0.544720	+	0.118239i	0.0176083	+	0.00382213i
$958$	−11.8016	−	20.4410i	−0.381293	−	0.660420i
$959$	−4.77893	−	6.47522i	−0.154320	−	0.209096i
$960$	−3.70974	−	13.2488i	−0.119731	−	0.427604i
$961$	−3.47085	+	11.2522i	−0.111963	+	0.362975i
$962$	2.72407	−	3.41587i	0.0878275	−	0.110132i
$963$	−0.210310	+	0.150405i	−0.00677715	+	0.00484673i
$964$	1.85691	−	8.13564i	0.0598069	−	0.262031i
$965$	15.2122	−	80.3982i	0.489696	−	2.58811i
$966$	−0.443395	+	2.04825i	−0.0142660	+	0.0659014i
$967$	18.9193	+	0.707910i	0.608404	+	0.0227649i	0.339818	−	0.940491i	$-0.389634\pi$
$967$	18.9193	+	0.707910i	0.608404	+	0.0227649i	0.268585	+	0.963256i	$0.413444\pi$
$968$	−5.23472	−	27.6662i	−0.168250	−	0.889225i
$969$	−39.8725	−	1.04433i	−1.28089	−	0.0335486i
$970$	13.8504	+	1.03795i	0.444711	+	0.0333265i
$971$	1.97299	−	17.5108i	0.0633162	−	0.561947i	−0.921504	−	0.388369i	$-0.873039\pi$
$971$	1.97299	−	17.5108i	0.0633162	−	0.561947i	0.984820	−	0.173578i	$-0.0555328\pi$
$972$	19.7656	+	10.9248i	0.633981	+	0.350413i
$973$	12.2795	−	5.91351i	0.393663	−	0.189578i
$974$	11.5387	−	3.09177i	0.369723	−	0.0990669i
$975$	8.10726	+	18.0277i	0.259640	+	0.577349i
$976$	−0.0839001	+	2.24228i	−0.00268558	+	0.0717736i
$977$	−35.2494	+	2.64158i	−1.12773	+	0.0845115i	−0.625500	−	0.780224i	$-0.715105\pi$
$977$	−35.2494	+	2.64158i	−1.12773	+	0.0845115i	−0.502228	+	0.864736i	$0.667486\pi$
$978$	14.0100	+	21.7514i	0.447989	+	0.695532i
$979$	−0.342464	+	0.369089i	−0.0109452	+	0.0117961i
$980$	23.8199	−	18.9957i	0.760898	−	0.606796i
$981$	29.2174	+	25.9150i	0.932840	+	0.827402i
$982$	0.447255	+	1.95955i	0.0142725	+	0.0625318i
$983$	−15.6212	+	0.584504i	−0.498239	+	0.0186428i	−0.285330	−	0.958429i	$-0.592103\pi$
$983$	−15.6212	+	0.584504i	−0.498239	+	0.0186428i	−0.212909	+	0.977072i	$0.568294\pi$
$984$	7.87569	−	44.3404i	0.251068	−	1.41352i
$985$	45.3157	−	26.1630i	1.44388	−	0.833624i
$986$	9.08428	−	29.3918i	0.289302	−	0.936025i
$987$	−6.96806	−	2.06408i	−0.221796	−	0.0657003i
$988$	−7.15243	−	3.12057i	−0.227549	−	0.0992787i
$989$	−14.7102	+	9.24302i	−0.467756	+	0.293911i
$990$	−0.154371	+	0.420848i	−0.00490623	+	0.0133754i
$991$	−15.1061	−	12.0467i	−0.479863	−	0.382678i	0.353473	−	0.935445i	$-0.385001\pi$
$991$	−15.1061	−	12.0467i	−0.479863	−	0.382678i	−0.833336	+	0.552767i	$0.813572\pi$
$992$	−25.4106	+	3.83004i	−0.806789	+	0.121604i
$993$	−0.627388	−	55.9435i	−0.0199095	−	1.77531i
$994$	0.952839	−	1.10722i	0.0302222	−	0.0351189i
$995$	−4.04296	−	53.9496i	−0.128171	−	1.71032i
$996$	8.18215	+	40.7374i	0.259261	+	1.29081i
$997$	−6.63772	−	7.71317i	−0.210219	−	0.244278i	0.642957	−	0.765902i	$-0.277707\pi$
$997$	−6.63772	−	7.71317i	−0.210219	−	0.244278i	−0.853176	+	0.521624i	$0.825326\pi$
$998$	4.27891	−	4.27891i	0.135447	−	0.135447i
$999$	−15.5468	−	6.85267i	−0.491880	−	0.216809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.11	yes	672
3.2	odd	2		783.2.be.a.710.18		672
9.4	even	3		783.2.be.a.449.11		672
9.5	odd	6	inner	261.2.x.a.14.18	✓	672
29.27	odd	28	inner	261.2.x.a.56.18	yes	672
87.56	even	28		783.2.be.a.143.11		672
261.85	odd	84		783.2.be.a.665.18		672
261.230	even	84	inner	261.2.x.a.230.11	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.18	✓	672	9.5	odd	6	inner
261.2.x.a.56.18	yes	672	29.27	odd	28	inner
261.2.x.a.101.11	yes	672	1.1	even	1	trivial
261.2.x.a.230.11	yes	672	261.230	even	84	inner
783.2.be.a.143.11		672	87.56	even	28
783.2.be.a.449.11		672	9.4	even	3
783.2.be.a.665.18		672	261.85	odd	84
783.2.be.a.710.18		672	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.296904 + 0.680512i) q^{2} +(0.429498 - 1.67795i) q^{3} +(0.985401 + 1.06201i) q^{4} +(3.33006 + 0.501926i) q^{5} +(1.01435 + 0.790470i) q^{6} +(0.637138 + 0.591178i) q^{7} +(-2.41687 + 0.845700i) q^{8} +(-2.63106 - 1.44136i) q^{9} +(-1.33028 + 2.11712i) q^{10} +(-0.0452965 + 0.0389808i) q^{11} +(2.20523 - 1.19733i) q^{12} +(-1.01381 + 1.48699i) q^{13} +(-0.591473 + 0.258057i) q^{14} +(2.27247 - 5.37212i) q^{15} +(-0.0744600 + 0.993599i) q^{16} +(-5.44064 - 5.44064i) q^{17} +(1.76203 - 1.36252i) q^{18} +(2.53419 + 1.59233i) q^{19} +(2.74840 + 4.03116i) q^{20} +(1.26562 - 0.815179i) q^{21} +(-0.0130782 - 0.0423983i) q^{22} +(1.74536 + 0.685004i) q^{23} +(0.381004 + 4.41863i) q^{24} +(6.05952 + 1.86912i) q^{25} +(-0.710907 - 1.13140i) q^{26} +(-3.54857 + 3.79574i) q^{27} +1.25920i q^{28} +(3.35996 - 4.20840i) q^{29} +(2.98108 + 3.14144i) q^{30} +(3.52783 - 2.60366i) q^{31} +(-5.18172 - 2.73862i) q^{32} +(0.0459532 + 0.0927476i) q^{33} +(5.31777 - 2.08707i) q^{34} +(1.82498 + 2.28846i) q^{35} +(-1.06192 - 4.21453i) q^{36} +(1.07993 + 3.08626i) q^{37} +(-1.83601 + 1.25177i) q^{38} +(2.05967 + 2.33978i) q^{39} +(-8.47282 + 1.60314i) q^{40} +(-9.80827 - 2.62812i) q^{41} +(0.178971 + 1.10330i) q^{42} +(-5.50220 + 7.45521i) q^{43} +(-0.0860332 - 0.00969361i) q^{44} +(-8.03815 - 6.12041i) q^{45} +(-0.984358 + 0.984358i) q^{46} +(-3.14887 - 3.65905i) q^{47} +(1.63523 + 0.551690i) q^{48} +(-0.466657 - 6.22710i) q^{49} +(-3.07105 + 3.56863i) q^{50} +(-11.4659 + 6.79240i) q^{51} +(-2.57820 + 0.388602i) q^{52} +(-0.384864 - 0.306918i) q^{53} +(-1.52946 - 3.54181i) q^{54} +(-0.170406 + 0.107073i) q^{55} +(-2.03984 - 0.889974i) q^{56} +(3.76029 - 3.56834i) q^{57} +(1.86628 + 3.53599i) q^{58} +(3.68450 - 2.12725i) q^{59} +(7.94453 - 2.88031i) q^{60} +(2.25041 - 0.0842045i) q^{61} +(0.724392 + 3.17377i) q^{62} +(-0.824252 - 2.47377i) q^{63} +(1.84412 - 1.47064i) q^{64} +(-4.12241 + 4.44290i) q^{65} +(-0.0767595 + 0.00373454i) q^{66} +(-5.40263 + 0.404871i) q^{67} +(0.416801 - 11.1392i) q^{68} +(1.89904 - 2.63443i) q^{69} +(-2.09917 + 0.562470i) q^{70} +(-2.03947 + 0.982158i) q^{71} +(7.57790 + 1.25849i) q^{72} +(1.38053 - 12.2525i) q^{73} +(-2.42087 - 0.181419i) q^{74} +(5.73885 - 9.36482i) q^{75} +(0.806115 + 4.26042i) q^{76} +(-0.0519047 - 0.00194214i) q^{77} +(-2.20377 + 0.706934i) q^{78} +(-2.39145 + 12.6391i) q^{79} +(-0.746670 + 3.27137i) q^{80} +(4.84498 + 7.58460i) q^{81} +(4.70058 - 5.89434i) q^{82} +(-4.88077 + 15.8231i) q^{83} +(2.11287 + 0.540822i) q^{84} +(-15.3869 - 20.8485i) q^{85} +(-3.43973 - 5.95779i) q^{86} +(-5.61841 - 7.44537i) q^{87} +(0.0765098 - 0.132519i) q^{88} +(8.37231 - 0.943332i) q^{89} +(6.55157 - 3.65288i) q^{90} +(-1.52501 + 0.348074i) q^{91} +(0.992401 + 2.52860i) q^{92} +(-2.85362 - 7.03781i) q^{93} +(3.42494 - 1.05645i) q^{94} +(7.63976 + 6.57455i) q^{95} +(-6.82081 + 7.51845i) q^{96} +(-2.59563 - 4.91117i) q^{97} +(4.37617 + 1.53129i) q^{98} +(0.175363 - 0.0372724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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