LMFDB - Embedded newform 261.2.x.a.14.18

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			14.18
Character	$\chi$	$=$	261.14
Dual form			261.2.x.a.56.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.440888 + 0.597382i) q^{2} +(-1.69814 - 0.341073i) q^{3} +(0.427027 - 1.38439i) q^{4} +(1.23035 + 3.13488i) q^{5} +(-0.544938 - 1.16481i) q^{6} +(-0.830544 + 0.256189i) q^{7} +(2.41687 - 0.845700i) q^{8} +(2.76734 + 1.15838i) q^{9} +(-1.33028 + 2.11712i) q^{10} +(0.0111101 + 0.0587183i) q^{11} +(-1.19733 + 2.20523i) q^{12} +(1.79467 + 0.134492i) q^{13} +(-0.519220 - 0.383202i) q^{14} +(-1.02008 - 5.74310i) q^{15} +(-0.823252 - 0.561284i) q^{16} +(5.44064 + 5.44064i) q^{17} +(0.528094 + 2.16387i) q^{18} +(2.53419 + 1.59233i) q^{19} +(4.86529 - 0.364603i) q^{20} +(1.49776 - 0.151768i) q^{21} +(-0.0301790 + 0.0325252i) q^{22} +(0.279450 + 1.85403i) q^{23} +(-4.39263 + 0.611786i) q^{24} +(-4.64846 + 4.31314i) q^{25} +(0.710907 + 1.13140i) q^{26} +(-4.30423 - 2.91095i) q^{27} +1.25920i q^{28} +(-1.96460 - 5.01401i) q^{29} +(2.98108 - 3.14144i) q^{30} +(-4.01875 - 1.75336i) q^{31} +(-0.219146 - 5.85681i) q^{32} +(0.00116073 - 0.103501i) q^{33} +(-0.851428 + 5.64886i) q^{34} +(-1.82498 - 2.28846i) q^{35} +(2.78537 - 3.33641i) q^{36} +(1.07993 + 3.08626i) q^{37} +(0.166060 + 2.21592i) q^{38} +(-3.00173 - 0.840500i) q^{39} +(5.62477 + 6.53610i) q^{40} +(-2.62812 - 9.80827i) q^{41} +(0.751007 + 0.827821i) q^{42} +(-3.70531 - 8.49265i) q^{43} +(0.0860332 + 0.00969361i) q^{44} +(-0.226576 + 10.1005i) q^{45} +(-0.984358 + 0.984358i) q^{46} +(-4.74327 + 0.897475i) q^{47} +(1.20656 + 1.23393i) q^{48} +(-5.15950 + 3.51769i) q^{49} +(-4.62605 - 0.875296i) q^{50} +(-7.38330 - 11.0946i) q^{51} +(0.952563 - 2.42709i) q^{52} +(0.384864 + 0.306918i) q^{53} +(-0.158737 - 3.85467i) q^{54} +(-0.170406 + 0.107073i) q^{55} +(-1.79066 + 1.32157i) q^{56} +(-3.76029 - 3.56834i) q^{57} +(2.12911 - 3.38424i) q^{58} +(3.68450 + 2.12725i) q^{59} +(-8.38628 - 1.04027i) q^{60} +(-1.05228 + 1.99102i) q^{61} +(-0.724392 - 3.17377i) q^{62} +(-2.59516 - 0.253121i) q^{63} +(1.84412 - 1.47064i) q^{64} +(1.78646 + 5.79156i) q^{65} +(0.0623414 - 0.0449390i) q^{66} +(3.05194 + 4.47638i) q^{67} +(9.85526 - 5.20865i) q^{68} +(0.157814 - 3.24371i) q^{69} +(0.562470 - 2.09917i) q^{70} +(2.03947 - 0.982158i) q^{71} +(7.66795 + 0.459308i) q^{72} +(1.38053 - 12.2525i) q^{73} +(-1.36755 + 2.00583i) q^{74} +(9.36482 - 5.73885i) q^{75} +(3.28657 - 2.82833i) q^{76} +(-0.0242704 - 0.0459219i) q^{77} +(-0.821327 - 2.16375i) q^{78} +(-9.75009 - 8.39063i) q^{79} +(0.746670 - 3.27137i) q^{80} +(6.31633 + 6.41124i) q^{81} +(4.70058 - 5.89434i) q^{82} +(11.2628 + 12.1384i) q^{83} +(0.429477 - 2.13829i) q^{84} +(-10.3619 + 23.7497i) q^{85} +(3.43973 - 5.95779i) q^{86} +(1.62602 + 9.18456i) q^{87} +(0.0765098 + 0.132519i) q^{88} +(-8.37231 + 0.943332i) q^{89} +(-6.13375 + 4.31784i) q^{90} +(-1.52501 + 0.348074i) q^{91} +(2.68603 + 0.404854i) q^{92} +(6.22637 + 4.34814i) q^{93} +(-2.62739 - 2.43786i) q^{94} +(-1.87384 + 9.90350i) q^{95} +(-1.62546 + 10.0204i) q^{96} +(5.55101 + 0.207704i) q^{97} +(-4.37617 - 1.53129i) q^{98} +(-0.0372724 + 0.175363i) 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.440888	+	0.597382i	0.311755	+	0.422413i	0.932260	−	0.361790i	$-0.117834\pi$
$2$	0.440888	+	0.597382i	0.311755	+	0.422413i	−0.620505	+	0.784203i	$0.713072\pi$
$3$	−1.69814	−	0.341073i	−0.980420	−	0.196918i
$3$	−1.69814	−	0.341073i	−0.980420	−	0.196918i
$4$	0.427027	−	1.38439i	0.213514	−	0.692194i
$5$	1.23035	+	3.13488i	0.550229	+	1.40196i	0.887611	+	0.460594i	$0.152364\pi$
$5$	1.23035	+	3.13488i	0.550229	+	1.40196i	−0.337382	+	0.941368i	$0.609541\pi$
$6$	−0.544938	−	1.16481i	−0.222470	−	0.475533i
$7$	−0.830544	+	0.256189i	−0.313916	+	0.0968303i	−0.447710	−	0.894179i	$-0.647760\pi$
$7$	−0.830544	+	0.256189i	−0.313916	+	0.0968303i	0.133794	+	0.991009i	$0.457284\pi$
$8$	2.41687	−	0.845700i	0.854494	−	0.299000i
$9$	2.76734	+	1.15838i	0.922446	+	0.386125i
$10$	−1.33028	+	2.11712i	−0.420670	+	0.669493i
$11$	0.0111101	+	0.0587183i	0.00334982	+	0.0177042i	0.984202	−	0.177052i	$-0.0566561\pi$
$11$	0.0111101	+	0.0587183i	0.00334982	+	0.0177042i	−0.980852	+	0.194756i	$0.937608\pi$
$12$	−1.19733	+	2.20523i	−0.345639	+	0.636596i
$13$	1.79467	+	0.134492i	0.497753	+	0.0373014i	0.321242	−	0.946997i	$-0.395900\pi$
$13$	1.79467	+	0.134492i	0.497753	+	0.0373014i	0.176511	+	0.984299i	$0.443519\pi$
$14$	−0.519220	−	0.383202i	−0.138767	−	0.102415i
$15$	−1.02008	−	5.74310i	−0.263384	−	1.48286i
$16$	−0.823252	−	0.561284i	−0.205813	−	0.140321i
$17$	5.44064	+	5.44064i	1.31955	+	1.31955i	0.914132	+	0.405417i	$0.132874\pi$
$17$	5.44064	+	5.44064i	1.31955	+	1.31955i	0.405417	+	0.914132i	$0.367126\pi$
$18$	0.528094	+	2.16387i	0.124473	+	0.510030i
$19$	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	$0.567022\pi$
$20$	4.86529	−	0.364603i	1.08791	−	0.0815277i
$21$	1.49776	−	0.151768i	0.326837	−	0.0331185i
$22$	−0.0301790	+	0.0325252i	−0.00643417	+	0.00693439i
$23$	0.279450	+	1.85403i	0.0582693	+	0.386592i	0.998889	+	0.0471290i	$0.0150072\pi$
$23$	0.279450	+	1.85403i	0.0582693	+	0.386592i	−0.940619	+	0.339463i	$0.889755\pi$
$24$	−4.39263	+	0.611786i	−0.896641	+	0.124880i
$25$	−4.64846	+	4.31314i	−0.929693	+	0.862629i
$26$	0.710907	+	1.13140i	0.139420	+	0.221886i
$27$	−4.30423	−	2.91095i	−0.828350	−	0.560212i
$28$			1.25920i			0.237966i
$29$	−1.96460	−	5.01401i	−0.364817	−	0.931079i
$29$	−1.96460	−	5.01401i	−0.364817	−	0.931079i
$30$	2.98108	−	3.14144i	0.544269	−	0.573546i
$31$	−4.01875	−	1.75336i	−0.721789	−	0.314913i	0.00669364	−	0.999978i	$-0.497869\pi$
$31$	−4.01875	−	1.75336i	−0.721789	−	0.314913i	−0.728483	+	0.685064i	$0.759774\pi$
$32$	−0.219146	−	5.85681i	−0.0387399	−	1.03535i
$33$	0.00116073	−	0.103501i	0.000202057	−	0.0180172i
$34$	−0.851428	+	5.64886i	−0.146019	+	0.968771i
$35$	−1.82498	−	2.28846i	−0.308478	−	0.386820i
$36$	2.78537	−	3.33641i	0.464228	−	0.556069i
$37$	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	$0.806240\pi$
$38$	0.166060	+	2.21592i	0.0269385	+	0.359470i
$39$	−3.00173	−	0.840500i	−0.480661	−	0.134588i
$40$	5.62477	+	6.53610i	0.889355	+	1.03345i
$41$	−2.62812	−	9.80827i	−0.410443	−	1.53179i	−0.793791	−	0.608190i	$-0.791896\pi$
$41$	−2.62812	−	9.80827i	−0.410443	−	1.53179i	0.383348	−	0.923604i	$-0.374771\pi$
$42$	0.751007	+	0.827821i	0.115883	+	0.127736i
$43$	−3.70531	−	8.49265i	−0.565054	−	1.29512i	−0.931183	−	0.364553i	$-0.881222\pi$
$43$	−3.70531	−	8.49265i	−0.565054	−	1.29512i	0.366129	−	0.930564i	$-0.380683\pi$
$44$	0.0860332	+	0.00969361i	0.0129700	+	0.00146137i
$45$	−0.226576	+	10.1005i	−0.0337759	+	1.50569i
$46$	−0.984358	+	0.984358i	−0.145136	+	0.145136i
$47$	−4.74327	+	0.897475i	−0.691877	+	0.130910i	−0.519946	−	0.854199i	$-0.674048\pi$
$47$	−4.74327	+	0.897475i	−0.691877	+	0.130910i	−0.171931	+	0.985109i	$0.555000\pi$
$48$	1.20656	+	1.23393i	0.174151	+	0.178102i
$49$	−5.15950	+	3.51769i	−0.737071	+	0.502527i
$50$	−4.62605	−	0.875296i	−0.654222	−	0.123786i
$51$	−7.38330	−	11.0946i	−1.03387	−	1.55356i
$52$	0.952563	−	2.42709i	0.132097	−	0.336577i
$53$	0.384864	+	0.306918i	0.0528651	+	0.0421585i	0.649566	−	0.760305i	$-0.274951\pi$
$53$	0.384864	+	0.306918i	0.0528651	+	0.0421585i	−0.596701	+	0.802464i	$0.703522\pi$
$54$	−0.158737	−	3.85467i	−0.0216014	−	0.524555i
$55$	−0.170406	+	0.107073i	−0.0229775	+	0.0144377i
$56$	−1.79066	+	1.32157i	−0.239287	+	0.176602i
$57$	−3.76029	−	3.56834i	−0.498063	−	0.472639i
$58$	2.12911	−	3.38424i	0.279566	−	0.444372i
$59$	3.68450	+	2.12725i	0.479682	+	0.276944i	0.720284	−	0.693680i	$-0.244012\pi$
$59$	3.68450	+	2.12725i	0.479682	+	0.276944i	−0.240602	+	0.970624i	$0.577345\pi$
$60$	−8.38628	−	1.04027i	−1.08266	−	0.134298i
$61$	−1.05228	+	1.99102i	−0.134731	+	0.254924i	−0.942245	−	0.334925i	$-0.891289\pi$
$61$	−1.05228	+	1.99102i	−0.134731	+	0.254924i	0.807514	+	0.589849i	$0.200813\pi$
$62$	−0.724392	−	3.17377i	−0.0919979	−	0.403069i
$63$	−2.59516	−	0.253121i	−0.326960	−	0.0318902i
$64$	1.84412	−	1.47064i	0.230515	−	0.183830i
$65$	1.78646	+	5.79156i	0.221583	+	0.718354i
$66$	0.0623414	−	0.0449390i	0.00767370	−	0.00553161i
$67$	3.05194	+	4.47638i	0.372854	+	0.546876i	0.966108	−	0.258139i	$-0.0831093\pi$
$67$	3.05194	+	4.47638i	0.372854	+	0.546876i	−0.593254	+	0.805016i	$0.702157\pi$
$68$	9.85526	−	5.20865i	1.19513	−	0.631642i
$69$	0.157814	−	3.24371i	0.0189986	−	0.390497i
$70$	0.562470	−	2.09917i	0.0672280	−	0.250898i
$71$	2.03947	−	0.982158i	0.242041	−	0.116561i	−0.308931	−	0.951084i	$-0.599971\pi$
$71$	2.03947	−	0.982158i	0.242041	−	0.116561i	0.550972	+	0.834524i	$0.314257\pi$
$72$	7.66795	+	0.459308i	0.903676	+	0.0541300i
$73$	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	$-0.220861\pi$
$74$	−1.36755	+	2.00583i	−0.158974	+	0.233172i
$75$	9.36482	−	5.73885i	1.08136	−	0.662665i
$76$	3.28657	−	2.82833i	0.376996	−	0.324431i
$77$	−0.0242704	−	0.0459219i	−0.00276587	−	0.00523328i
$78$	−0.821327	−	2.16375i	−0.0929970	−	0.244996i
$79$	−9.75009	−	8.39063i	−1.09697	−	0.944020i	−0.0982794	−	0.995159i	$-0.531334\pi$
$79$	−9.75009	−	8.39063i	−1.09697	−	0.944020i	−0.998692	+	0.0511390i	$0.983715\pi$
$80$	0.746670	−	3.27137i	0.0834802	−	0.365751i
$81$	6.31633	+	6.41124i	0.701814	+	0.712360i
$82$	4.70058	−	5.89434i	0.519092	−	0.650921i
$83$	11.2628	+	12.1384i	1.23625	+	1.33236i	0.924014	+	0.382358i	$0.124888\pi$
$83$	11.2628	+	12.1384i	1.23625	+	1.33236i	0.312237	+	0.950004i	$0.398922\pi$
$84$	0.429477	−	2.13829i	0.0468598	−	0.233306i
$85$	−10.3619	+	23.7497i	−1.12390	+	2.57601i
$86$	3.43973	−	5.95779i	0.370916	−	0.642445i
$87$	1.62602	+	9.18456i	0.174327	+	0.984688i
$88$	0.0765098	+	0.132519i	0.00815597	+	0.0141266i
$89$	−8.37231	+	0.943332i	−0.887463	+	0.0999930i	−0.543913	−	0.839142i	$-0.683058\pi$
$89$	−8.37231	+	0.943332i	−0.887463	+	0.0999930i	−0.343550	+	0.939135i	$0.611629\pi$
$90$	−6.13375	+	4.31784i	−0.646554	+	0.455140i
$91$	−1.52501	+	0.348074i	−0.159865	+	0.0364880i
$92$	2.68603	+	0.404854i	0.280038	+	0.0422089i
$93$	6.22637	+	4.34814i	0.645644	+	0.450881i
$94$	−2.62739	−	2.43786i	−0.270994	−	0.251446i
$95$	−1.87384	+	9.90350i	−0.192252	+	1.01608i
$96$	−1.62546	+	10.0204i	−0.165897	+	1.02270i
$97$	5.55101	+	0.207704i	0.563620	+	0.0210892i	0.317683	−	0.948197i	$-0.397095\pi$
$97$	5.55101	+	0.207704i	0.563620	+	0.0210892i	0.245936	+	0.969286i	$0.420905\pi$
$98$	−4.37617	−	1.53129i	−0.442060	−	0.154683i
$99$	−0.0372724	+	0.175363i	−0.00374602	+	0.0176246i
$100$	3.98604	+	8.27711i	0.398604	+	0.827711i
$101$	9.54256	−	4.16338i	0.949520	−	0.414271i	0.132695	−	0.991157i	$-0.457637\pi$
$101$	9.54256	−	4.16338i	0.949520	−	0.414271i	0.816825	+	0.576885i	$0.195732\pi$
$102$	3.37251	−	9.30213i	0.333928	−	0.921049i
$103$	0.389086	−	5.19200i	0.0383378	−	0.511583i	−0.944670	−	0.328021i	$-0.893618\pi$
$103$	0.389086	−	5.19200i	0.0383378	−	0.511583i	0.983008	−	0.183562i	$-0.0587627\pi$
$104$	4.45124	−	1.19270i	0.436480	−	0.116954i
$105$	2.31854	+	4.50856i	0.226266	+	0.439991i
$106$	−0.0136658	+	0.365228i	−0.00132734	+	0.0354740i
$107$	−0.0373946	+	0.0776508i	−0.00361508	+	0.00750678i	−0.902769	−	0.430127i	$-0.858469\pi$
$107$	−0.0373946	+	0.0776508i	−0.00361508	+	0.00750678i	0.899154	+	0.437633i	$0.144183\pi$
$108$	−5.86790	+	4.71567i	−0.564639	+	0.453766i
$109$	−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	$0.785700\pi$
$110$	−0.139093	−	0.0545901i	−0.0132620	−	0.00520496i
$111$	−0.781228	−	5.60922i	−0.0741509	−	0.532404i
$112$	0.827542	+	0.255263i	0.0781954	+	0.0241201i
$113$	−13.4631	+	0.503755i	−1.26651	+	0.0473893i	−0.662178	−	0.749347i	$-0.730368\pi$
$113$	−13.4631	+	0.503755i	−1.26651	+	0.0473893i	−0.604328	+	0.796736i	$0.706558\pi$
$114$	0.473797	−	3.81957i	0.0443751	−	0.357736i
$115$	−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
$119$	−5.91252	−	3.12486i	−0.542000	−	0.286456i
$120$	−7.32235	−	13.0177i	−0.668436	−	1.18834i
$121$	10.2363	−	4.01745i	0.930572	−	0.365222i
$122$	−1.65334	+	0.249201i	−0.149686	+	0.0225616i
$123$	1.11757	+	17.5522i	0.100768	+	1.58263i
$124$	−4.14345	+	4.81478i	−0.372093	+	0.432380i
$125$	−4.06958	−	1.95980i	−0.363994	−	0.175290i
$126$	−0.992966	−	1.66190i	−0.0884604	−	0.148054i
$127$	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	$-0.148388\pi$
$128$	−9.63081	−	2.58057i	−0.851251	−	0.228092i
$129$	3.39551	+	15.6855i	0.298958	+	1.38103i
$130$	−2.67215	+	3.62063i	−0.234363	+	0.317550i
$131$	−5.70030	+	7.72364i	−0.498038	+	0.674817i	−0.979452	−	0.201676i	$-0.935361\pi$
$131$	−5.70030	+	7.72364i	−0.498038	+	0.674817i	0.481414	+	0.876493i	$0.340123\pi$
$132$	−0.142790	−	0.0458046i	−0.0124283	−	0.00398678i
$133$	−2.51269	−	0.673274i	−0.217878	−	0.0583802i
$134$	−1.32854	+	3.79676i	−0.114769	+	0.327990i
$135$	3.82976	−	17.0747i	0.329613	−	1.46956i
$136$	17.7505	+	8.54818i	1.52209	+	0.733001i
$137$	−6.03970	+	7.01826i	−0.516006	+	0.599610i	−0.954163	−	0.299288i	$-0.903251\pi$
$137$	−6.03970	+	7.01826i	−0.516006	+	0.599610i	0.438156	+	0.898899i	$0.355632\pi$
$138$	2.00731	−	1.33584i	0.170874	−	0.113714i
$139$	−15.5058	+	2.33713i	−1.31519	+	0.198232i	−0.768902	−	0.639367i	$-0.779196\pi$
$139$	−15.5058	+	2.33713i	−1.31519	+	0.198232i	−0.546285	+	0.837600i	$0.683958\pi$
$140$	−3.94743	+	1.54925i	−0.333619	+	0.130936i
$141$	8.36083	+	0.0937639i	0.704109	+	0.00789634i
$142$	1.48590	+	0.785323i	0.124694	+	0.0659028i
$143$	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
$147$	9.96133	−	4.21375i	0.821596	−	0.347544i
$148$	4.73374	−	0.177124i	0.389111	−	0.0145595i
$149$	7.54689	+	2.32791i	0.618265	+	0.190710i	0.588038	−	0.808833i	$-0.299901\pi$
$149$	7.54689	+	2.32791i	0.618265	+	0.190710i	0.0302276	+	0.999543i	$0.490377\pi$
$150$	7.55713	+	3.06419i	0.617037	+	0.250190i
$151$	−4.63079	−	1.81745i	−0.376848	−	0.147902i	0.169354	−	0.985555i	$-0.445832\pi$
$151$	−4.63079	−	1.81745i	−0.376848	−	0.147902i	−0.546202	+	0.837653i	$0.683927\pi$
$152$	7.47144	+	1.70531i	0.606014	+	0.138319i
$153$	8.75379	+	21.3584i	0.707702	+	1.72672i
$154$	0.0167324	−	0.0347451i	0.00134833	−	0.00279984i
$155$	0.552114	−	14.7556i	0.0443469	−	1.18520i
$156$	−2.44540	+	3.79664i	−0.195788	+	0.303974i
$157$	13.3439	−	3.57549i	1.06496	−	0.285355i	0.316539	−	0.948580i	$-0.397479\pi$
$157$	13.3439	−	3.57549i	1.06496	−	0.285355i	0.748420	+	0.663225i	$0.230813\pi$
$158$	0.713715	−	9.52386i	0.0567801	−	0.757678i
$159$	−0.548870	−	0.652456i	−0.0435282	−	0.0517431i
$160$	18.0908	−	7.89292i	1.43020	−	0.623990i
$161$	−0.707078	−	1.46826i	−0.0557255	−	0.115715i
$162$	−1.04517	+	6.59990i	−0.0821160	+	0.518537i
$163$	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	$0.318298\pi$
$164$	−14.7007	−	0.550062i	−1.14793	−	0.0429526i
$165$	0.325892	−	0.123704i	0.0253706	−	0.00963033i
$166$	−2.28563	+	12.0799i	−0.177400	+	0.937580i
$167$	12.6547	+	11.7418i	0.979249	+	0.908611i	0.995828	−	0.0912520i	$-0.0290869\pi$
$167$	12.6547	+	11.7418i	0.979249	+	0.908611i	−0.0165785	+	0.999863i	$0.505277\pi$
$168$	3.49154	−	1.63346i	0.269378	−	0.126024i
$169$	−9.65204	−	1.45481i	−0.742465	−	0.111909i
$170$	−18.7561	+	4.28095i	−1.43852	+	0.328334i
$171$	5.16843	+	7.34207i	0.395240	+	0.561462i
$172$	−13.3394	+	1.50299i	−1.01712	+	0.114602i
$173$	−0.536737	−	0.929655i	−0.0408073	−	0.0706804i	0.844900	−	0.534924i	$-0.179660\pi$
$173$	−0.536737	−	0.929655i	−0.0408073	−	0.0706804i	−0.885708	+	0.464243i	$0.846326\pi$
$174$	−4.76980	+	5.02072i	−0.361598	+	0.380620i
$175$	2.75578	−	4.77314i	0.208317	−	0.360816i
$176$	0.0238112	−	0.0545759i	0.00179484	−	0.00411381i
$177$	−5.53125	−	4.86904i	−0.415754	−	0.365980i
$178$	−4.25478	−	4.58556i	−0.318909	−	0.343703i
$179$	2.34746	−	2.94362i	0.175458	−	0.220017i	−0.686325	−	0.727295i	$-0.740777\pi$
$179$	2.34746	−	2.94362i	0.175458	−	0.220017i	0.861782	+	0.507279i	$0.169348\pi$
$180$	13.8862	+	4.62685i	1.03502	+	0.344865i
$181$	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	$-0.111616\pi$
$182$	−0.880292	−	0.757553i	−0.0652516	−	0.0561536i
$183$	2.46600	−	3.02211i	0.182292	−	0.223401i
$184$	2.24335	+	4.24462i	0.165382	+	0.312918i
$185$	−8.34636	+	7.18263i	−0.613637	+	0.528077i
$186$	0.147631	+	5.63656i	0.0108248	+	0.413293i
$187$	−0.259019	+	0.379911i	−0.0189413	+	0.0277818i
$188$	−0.783051	+	6.94977i	−0.0571099	+	0.506864i
$189$	4.32061	+	1.31497i	0.314278	+	0.0956502i
$190$	−6.74233	+	3.24694i	−0.489140	+	0.235558i
$191$	6.88266	−	25.6865i	0.498012	−	1.85861i	−0.0144485	−	0.999896i	$-0.504599\pi$
$191$	6.88266	−	25.6865i	0.498012	−	1.85861i	0.512461	−	0.858711i	$-0.328734\pi$
$192$	−3.63317	+	1.86837i	−0.262201	+	0.134838i
$193$	−21.4814	+	11.3533i	−1.54627	+	0.817225i	−0.999795	−	0.0202533i	$-0.993553\pi$
$193$	−21.4814	+	11.3533i	−1.54627	+	0.817225i	−0.546470	+	0.837478i	$0.684029\pi$
$194$	2.32330	+	3.40765i	0.166803	+	0.244655i
$195$	−1.05831	−	10.4442i	−0.0757872	−	0.747923i
$196$	2.66660	+	8.64490i	0.190471	+	0.617493i
$197$	−12.1479	+	9.68762i	−0.865502	+	0.690215i	−0.952020	−	0.306036i	$-0.900997\pi$
$197$	−12.1479	+	9.68762i	−0.865502	+	0.690215i	0.0865184	+	0.996250i	$0.472426\pi$
$198$	−0.121192	+	0.0550496i	−0.00861273	+	0.00391221i
$199$	−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	$-0.264253\pi$
$200$	−7.58712	+	14.3555i	−0.536490	+	1.01509i
$201$	−3.65585	−	8.64244i	−0.257864	−	0.609590i
$202$	6.69433	+	3.86497i	0.471011	+	0.271939i
$203$	2.91622	+	3.66105i	0.204679	+	0.256956i
$204$	−18.5121	+	5.48365i	−1.29611	+	0.383932i
$205$	27.5143	−	20.3064i	1.92168	−	1.41826i
$206$	3.27315	−	2.05666i	0.228051	−	0.143294i
$207$	−1.37433	+	5.45444i	−0.0955226	+	0.379109i
$208$	−1.40198	−	1.11804i	−0.0972098	−	0.0775222i
$209$	−0.0653441	+	0.166494i	−0.00451994	+	0.0115166i
$210$	−1.67112	+	3.37283i	−0.115318	+	0.232747i
$211$	15.8480	+	2.99860i	1.09102	+	0.206432i	0.700137	−	0.714009i	$-0.253122\pi$
$211$	15.8480	+	2.99860i	1.09102	+	0.206432i	0.390883	+	0.920441i	$0.372170\pi$
$212$	0.589241	−	0.401738i	0.0404693	−	0.0275915i
$213$	−3.79829	+	0.972231i	−0.260255	+	0.0666162i
$214$	−0.0628741	+	0.0118964i	−0.00429798	+	0.000813222i
$215$	22.0646	−	22.0646i	1.50480	−	1.50480i
$216$	−12.8646	−	3.39530i	−0.875323	−	0.231021i
$217$	3.78694	+	0.426686i	0.257074	+	0.0289653i
$218$	−3.86514	−	8.85899i	−0.261780	−	0.600006i
$219$	−6.52332	+	20.3356i	−0.440805	+	1.37415i
$220$	0.0754626	+	0.281630i	0.00508769	+	0.0189875i
$221$	9.03244	+	10.4959i	0.607588	+	0.706030i
$222$	3.00642	−	2.93973i	0.201777	−	0.197302i
$223$	−0.662700	−	8.84312i	−0.0443777	−	0.592179i	−0.974421	−	0.224730i	$-0.927850\pi$
$223$	−0.662700	−	8.84312i	−0.0443777	−	0.592179i	0.930043	−	0.367450i	$-0.119769\pi$
$224$	1.68246	+	4.80819i	0.112414	+	0.321261i
$225$	−17.8601	+	6.55126i	−1.19067	+	0.436751i
$226$	−6.23667	−	7.82054i	−0.414857	−	0.520215i
$227$	−2.42816	+	16.1098i	−0.161163	+	1.06925i	0.751263	+	0.660003i	$0.229445\pi$
$227$	−2.42816	+	16.1098i	−0.161163	+	1.06925i	−0.912426	+	0.409242i	$0.865793\pi$
$228$	−6.54572	+	3.68192i	−0.433501	+	0.243841i
$229$	−0.851010	−	22.7437i	−0.0562363	−	1.50295i	−0.686821	−	0.726826i	$-0.740994\pi$
$229$	−0.851010	−	22.7437i	−0.0562363	−	1.50295i	0.630585	−	0.776120i	$-0.282815\pi$
$230$	−4.29695	−	1.87474i	−0.283333	−	0.123617i
$231$	0.0255518	+	0.0862596i	0.00168118	+	0.00567546i
$232$	−8.98854	−	10.4568i	−0.590127	−	0.686521i
$233$		−	4.06185i		−	0.266101i	−0.991109	−	0.133050i	$-0.957523\pi$
$233$		−	4.06185i		−	0.266101i	0.991109	−	0.133050i	$-0.0424772\pi$
$234$	0.656731	+	3.95447i	0.0429319	+	0.258512i
$235$	−8.64936	−	13.7654i	−0.564222	−	0.897955i
$236$	4.51832	−	4.19239i	0.294118	−	0.272901i
$237$	13.6952	+	17.5739i	0.889597	+	1.14155i
$238$	−0.740026	−	4.90975i	−0.0479688	−	0.318252i
$239$	−18.7198	+	20.1751i	−1.21088	+	1.30502i	−0.271382	+	0.962472i	$0.587481\pi$
$239$	−18.7198	+	20.1751i	−1.21088	+	1.30502i	−0.939500	+	0.342549i	$0.888710\pi$
$240$	−2.38372	+	5.30057i	−0.153869	+	0.342151i
$241$	5.74393	−	0.430448i	0.369999	−	0.0277276i	0.111567	−	0.993757i	$-0.464413\pi$
$241$	5.74393	−	0.430448i	0.369999	−	0.0277276i	0.258432	+	0.966029i	$0.416794\pi$
$242$	6.91301	+	4.34373i	0.444385	+	0.279226i
$243$	−8.53929	−	13.0415i	−0.547796	−	0.836612i
$244$	2.30699	+	2.30699i	0.147690	+	0.147690i
$245$	−17.3755	−	11.8464i	−1.11008	−	0.756841i
$246$	−9.99263	+	8.40616i	−0.637107	+	0.535957i
$247$	4.33388	+	3.19855i	0.275758	+	0.203519i
$248$	−11.1956	−	0.838997i	−0.710923	−	0.0532763i
$249$	−14.9857	−	24.4541i	−0.949679	−	1.54971i
$250$	−0.623476	−	3.29515i	−0.0394321	−	0.208403i
$251$	0.839018	−	1.33529i	0.0529583	−	0.0842827i	−0.819196	−	0.573514i	$-0.805580\pi$
$251$	0.839018	−	1.33529i	0.0529583	−	0.0842827i	0.872154	+	0.489231i	$0.162723\pi$
$252$	−1.45862	+	3.48462i	−0.0918845	+	0.219510i
$253$	−0.105761	+	0.0370073i	−0.00664912	+	0.00232663i
$254$	11.5019	−	3.54788i	0.721696	−	0.222614i
$255$	25.6962	−	36.7960i	1.60916	−	2.30426i
$256$	−4.42800	−	11.2824i	−0.276750	−	0.705148i
$257$	1.75792	−	5.69903i	0.109656	−	0.355496i	−0.884068	−	0.467359i	$-0.845206\pi$
$257$	1.75792	−	5.69903i	0.109656	−	0.355496i	0.993724	+	0.111863i	$0.0356818\pi$
$258$	−7.87318	+	8.94395i	−0.490163	+	0.556826i
$259$	−1.68759	−	2.28661i	−0.104862	−	0.142083i
$260$	8.78063			0.544552
$261$	0.371400	−	16.1512i	0.0229891	−	0.999736i
$262$	−7.12716			−0.440318
$263$	1.58819	+	2.15192i	0.0979318	+	0.132693i	0.850824	−	0.525451i	$-0.176104\pi$
$263$	1.58819	+	2.15192i	0.0979318	+	0.132693i	−0.752892	+	0.658144i	$0.771342\pi$
$264$	−0.0847255	−	0.251130i	−0.00521450	−	0.0154560i
$265$	−0.488636	+	1.58412i	−0.0300167	+	0.0973117i
$266$	−0.705615	−	1.79788i	−0.0432640	−	0.110235i
$267$	14.5391	+	1.25366i	0.889777	+	0.0767226i
$268$	7.50030	−	2.31354i	0.458154	−	0.141322i
$269$	−6.19633	+	2.16819i	−0.377797	+	0.132197i	−0.512496	−	0.858690i	$-0.671279\pi$
$269$	−6.19633	+	2.16819i	−0.377797	+	0.132197i	0.134699	+	0.990887i	$0.456993\pi$
$270$	11.8886	−	5.24022i	0.723520	−	0.318910i
$271$	−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	$0.317051\pi$
$272$	−1.42528	−	7.53276i	−0.0864200	−	0.456741i
$273$	2.70840	−	0.0709375i	0.163920	−	0.00429333i
$274$	−6.85542	−	0.513743i	−0.414151	−	0.0310363i
$275$	−0.304905	−	0.225030i	−0.0183865	−	0.0135698i
$276$	−4.42316	−	1.60363i	−0.266243	−	0.0965270i
$277$	−9.53249	−	6.49914i	−0.572752	−	0.390495i	0.242025	−	0.970270i	$-0.422188\pi$
$277$	−9.53249	−	6.49914i	−0.572752	−	0.390495i	−0.814777	+	0.579774i	$0.803141\pi$
$278$	−8.23249	−	8.23249i	−0.493752	−	0.493752i
$279$	−9.09019	−	9.50738i	−0.544216	−	0.569192i
$280$	−6.34610	−	3.98752i	−0.379252	−	0.238300i
$281$	3.54713	−	0.265821i	0.211604	−	0.0158575i	0.0314937	−	0.999504i	$-0.489974\pi$
$281$	3.54713	−	0.265821i	0.211604	−	0.0158575i	0.180110	+	0.983646i	$0.442355\pi$
$282$	3.63018	+	5.03595i	0.216174	+	0.299886i
$283$	−1.46915	+	1.58337i	−0.0873321	+	0.0941216i	−0.775206	−	0.631709i	$-0.782354\pi$
$283$	−1.46915	+	1.58337i	−0.0873321	+	0.0941216i	0.687874	+	0.725830i	$0.258544\pi$
$284$	−0.488778	−	3.24283i	−0.0290036	−	0.192426i
$285$	6.55986	−	16.1784i	0.388572	−	0.958325i
$286$	−0.0585357	+	0.0543132i	−0.00346129	+	0.00321161i
$287$	4.69554	+	7.47291i	0.277169	+	0.441112i
$288$	6.17793	−	16.4616i	0.364038	−	0.970010i
$289$			42.2011i			2.48242i
$290$	13.2287	+	2.51073i	0.776819	+	0.147435i
$291$	−9.35554	−	2.24601i	−0.548431	−	0.131663i
$292$	−16.3727	−	7.14334i	−0.958140	−	0.418032i
$293$	−0.427434	−	11.4234i	−0.0249709	−	0.667363i	−0.954430	−	0.298436i	$-0.903535\pi$
$293$	−0.427434	−	11.4234i	−0.0249709	−	0.667363i	0.929459	−	0.368926i	$-0.120275\pi$
$294$	6.90905	+	4.09293i	0.402944	+	0.238704i
$295$	−2.13544	+	14.1677i	−0.124330	+	0.824878i
$296$	5.22010	+	6.54580i	0.303412	+	0.380467i
$297$	0.123105	−	0.285078i	0.00714329	−	0.0165419i
$298$	1.93668	+	5.53473i	0.112189	+	0.320618i
$299$	0.252169	+	3.36496i	0.0145833	+	0.194601i
$300$	−3.94575	−	15.4152i	−0.227808	−	0.889996i
$301$	5.25314	+	6.10426i	0.302786	+	0.351844i
$302$	−0.955947	−	3.56764i	−0.0550086	−	0.205295i
$303$	−17.6246	+	3.81528i	−1.01251	+	0.219182i
$304$	−1.19252	−	2.73329i	−0.0683958	−	0.156765i
$305$	−7.53628	−	0.849135i	−0.431526	−	0.0486213i
$306$	−8.89969	+	14.6460i	−0.508761	+	0.837258i
$307$	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	$0.114154\pi$
$308$	−0.0739378	+	0.0139898i	−0.00421300	+	0.000797142i
$309$	−2.43157	+	8.68402i	−0.138327	+	0.494017i
$310$	9.05813	−	6.17573i	0.514467	−	0.350758i
$311$	−25.8150	−	4.88446i	−1.46383	−	0.276973i	−0.607882	−	0.794027i	$-0.707981\pi$
$311$	−25.8150	−	4.88446i	−1.46383	−	0.276973i	−0.855952	+	0.517054i	$0.827028\pi$
$312$	−7.96561	+	0.507182i	−0.450964	+	0.0287135i
$313$	−12.4736	+	31.7823i	−0.705051	+	1.79644i	−0.108135	+	0.994136i	$0.534488\pi$
$313$	−12.4736	+	31.7823i	−0.705051	+	1.79644i	−0.596916	+	0.802304i	$0.703607\pi$
$314$	8.01910	+	6.39502i	0.452544	+	0.360892i
$315$	−2.39945	−	8.44695i	−0.135194	−	0.475932i
$316$	−15.7794	+	9.91488i	−0.887663	+	0.557756i
$317$	−15.5838	+	11.5014i	−0.875276	+	0.645983i	−0.935934	−	0.352176i	$-0.885442\pi$
$317$	−15.5838	+	11.5014i	−0.875276	+	0.645983i	0.0606581	+	0.998159i	$0.480680\pi$
$318$	0.147776	−	0.615545i	0.00828684	−	0.0345181i
$319$	0.272587	−	0.171064i	0.0152620	−	0.00957775i
$320$	6.87920	+	3.97171i	0.384559	+	0.222025i
$321$	0.0899858	−	0.119107i	0.00502252	−	0.00664792i
$322$	0.565371	−	1.06974i	0.0315069	−	0.0596140i
$323$	5.12427	+	22.4509i	0.285122	+	1.24920i
$324$	11.5729	−	6.00648i	0.642938	−	0.333693i
$325$	−8.92255	+	7.11550i	−0.494934	+	0.394697i
$326$	4.40295	+	14.2740i	0.243857	+	0.790565i
$327$	20.5643	+	9.24798i	1.13721	+	0.511414i
$328$	−14.6467	−	21.4827i	−0.808728	−	1.18619i
$329$	3.70957	−	1.96057i	0.204515	−	0.108090i
$330$	0.217580	+	0.140142i	0.0119774	+	0.00771458i
$331$	−8.36012	+	31.2004i	−0.459514	+	1.71493i	0.214953	+	0.976624i	$0.431040\pi$
$331$	−8.36012	+	31.2004i	−0.459514	+	1.71493i	−0.674467	+	0.738305i	$0.735627\pi$
$332$	21.6138	−	10.4086i	1.18621	−	0.571248i
$333$	−0.586520	+	9.79168i	−0.0321411	+	0.536581i
$334$	−1.43506	+	12.7365i	−0.0785231	+	0.696912i
$335$	−10.2780	+	15.0750i	−0.561545	+	0.823635i
$336$	−1.31822	−	0.715724i	−0.0719146	−	0.0390459i
$337$	1.77132	−	1.52435i	0.0964902	−	0.0830365i	−0.602720	−	0.797953i	$-0.705916\pi$
$337$	1.77132	−	1.52435i	0.0964902	−	0.0830365i	0.699210	+	0.714916i	$0.253535\pi$
$338$	−3.38639	−	6.40737i	−0.184195	−	0.348515i
$339$	23.0341	+	3.73646i	1.25104	+	0.202937i
$340$	28.4539	+	24.4866i	1.54313	+	1.32797i
$341$	0.0583057	−	0.255454i	0.00315743	−	0.0138336i
$342$	−2.10732	+	6.32456i	−0.113951	+	0.341993i
$343$	7.17738	−	9.00015i	0.387542	−	0.485963i
$344$	−16.1375	−	17.3921i	−0.870075	−	0.937718i
$345$	10.3628	−	3.49617i	0.557915	−	0.188227i
$346$	0.318719	−	0.730511i	0.0171344	−	0.0392725i
$347$	15.4822	−	26.8160i	0.831128	−	1.43956i	−0.0660157	−	0.997819i	$-0.521029\pi$
$347$	15.4822	−	26.8160i	0.831128	−	1.43956i	0.897144	−	0.441738i	$-0.145638\pi$
$348$	13.4093	+	1.67102i	0.718816	+	0.0895758i
$349$	1.57067	+	2.72048i	0.0840759	+	0.145624i	0.904997	−	0.425418i	$-0.139873\pi$
$349$	1.57067	+	2.72048i	0.0840759	+	0.145624i	−0.820921	+	0.571042i	$0.806540\pi$
$350$	4.06638	−	0.458171i	0.217357	−	0.0244903i
$351$	−7.33318	−	5.80308i	−0.391416	−	0.309745i
$352$	0.341467	−	0.0779376i	0.0182002	−	0.00415409i
$353$	2.38359	+	0.359269i	0.126866	+	0.0191220i	0.212168	−	0.977233i	$-0.431948\pi$
$353$	2.38359	+	0.359269i	0.126866	+	0.0191220i	−0.0853023	+	0.996355i	$0.527186\pi$
$354$	0.470020	−	5.45097i	0.0249813	−	0.289716i
$355$	5.58822	+	5.18511i	0.296592	+	0.275197i
$356$	−2.26926	+	11.9933i	−0.120271	+	0.635646i
$357$	8.97447	+	7.32304i	0.474979	+	0.387576i
$358$	2.79344	+	0.104523i	0.147638	+	0.00552421i
$359$	−0.332555	−	0.116366i	−0.0175516	−	0.00614157i	0.321489	−	0.946913i	$-0.395817\pi$
$359$	−0.332555	−	0.116366i	−0.0175516	−	0.00614157i	−0.339041	+	0.940772i	$0.610102\pi$
$360$	7.99438	+	24.6032i	0.421341	+	1.29670i
$361$	−4.35722	−	9.04787i	−0.229328	−	0.476203i
$362$	9.95878	−	4.34497i	0.523422	−	0.228367i
$363$	−18.7529	+	3.33086i	−0.984270	+	0.174825i
$364$	−0.169352	+	2.25984i	−0.00887645	+	0.118448i
$365$	40.1087	−	10.7471i	2.09939	−	0.562529i
$366$	2.89259	+	0.140732i	0.151198	+	0.00735616i
$367$	−0.580080	+	15.5030i	−0.0302799	+	0.809249i	0.898578	+	0.438813i	$0.144601\pi$
$367$	−0.580080	+	15.5030i	−0.0302799	+	0.809249i	−0.928858	+	0.370435i	$0.879209\pi$
$368$	0.810579	−	1.68318i	0.0422543	−	0.0877421i
$369$	4.08877	−	30.1872i	0.212853	−	1.57148i
$370$	−7.97059	−	1.81923i	−0.414371	−	0.0945775i
$371$	−0.398275	−	0.156312i	−0.0206774	−	0.00811529i
$372$	8.67833	−	6.76293i	0.449951	−	0.350642i
$373$	6.36675	+	1.96388i	0.329658	+	0.101686i	0.455166	−	0.890407i	$-0.349580\pi$
$373$	6.36675	+	1.96388i	0.329658	+	0.101686i	−0.125508	+	0.992093i	$0.540056\pi$
$374$	−0.341151	+	0.0127650i	−0.0176405	+	0.000660060i
$375$	6.24226	+	4.71604i	0.322349	+	0.243535i
$376$	−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	$0.981168\pi$
$380$	12.9101	+	6.82319i	0.662274	+	0.350022i
$381$	−14.3117	+	24.1589i	−0.733212	+	1.23770i
$382$	18.3791	−	7.21327i	0.940358	−	0.369063i
$383$	−21.9818	+	3.31322i	−1.12322	+	0.169298i	−0.684280	−	0.729220i	$-0.739883\pi$
$383$	−21.9818	+	3.31322i	−1.12322	+	0.169298i	−0.438938	+	0.898517i	$0.644645\pi$
$384$	15.4743	+	7.66696i	0.789668	+	0.391253i
$385$	0.114098	−	0.132585i	0.00581500	−	0.00675715i
$386$	−16.2531	−	7.82710i	−0.827263	−	0.398389i
$387$	−0.416152	−	27.7942i	−0.0211542	−	1.41286i
$388$	2.65798	−	7.59606i	0.134938	−	0.385631i
$389$	30.7807	+	8.24766i	1.56064	+	0.418173i	0.932867	−	0.360221i	$-0.117299\pi$
$389$	30.7807	+	8.24766i	1.56064	+	0.418173i	0.627776	+	0.778394i	$0.283965\pi$
$390$	5.77257	−	5.23693i	0.292305	−	0.265182i
$391$	−8.56672	+	11.6075i	−0.433238	+	0.587016i
$392$	−9.49495	+	12.8652i	−0.479567	+	0.649791i
$393$	12.3142	−	11.1716i	0.621170	−	0.563532i
$394$	−11.1431	−	2.98578i	−0.561380	−	0.150421i
$395$	14.3076	−	40.8888i	0.719894	−	2.05734i
$396$	0.226854	+	0.126484i	0.0113998	+	0.00635607i
$397$	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	$0.476792\pi$
$398$	7.78013	−	9.04067i	0.389982	−	0.453168i
$399$	4.03726	+	2.00032i	0.202116	+	0.100141i
$400$	6.24776	−	0.941698i	0.312388	−	0.0470849i
$401$	22.4180	−	8.79842i	1.11950	−	0.439372i	0.267840	−	0.963463i	$-0.413690\pi$
$401$	22.4180	−	8.79842i	1.11950	−	0.439372i	0.851662	+	0.524091i	$0.175595\pi$
$402$	3.55102	−	5.99429i	0.177109	−	0.298968i
$403$	−6.97653	−	3.68720i	−0.347526	−	0.183673i
$404$	−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
$408$	−27.2272	−	20.5702i	−1.34795	−	1.01838i
$409$	23.0110	−	0.861010i	1.13782	−	0.0425742i	0.538169	−	0.842837i	$-0.319116\pi$
$409$	23.0110	−	0.861010i	1.13782	−	0.0425742i	0.599650	+	0.800263i	$0.295307\pi$
$410$	24.2614	+	7.48366i	1.19819	+	0.369592i
$411$	12.6500	−	9.85799i	0.623977	−	0.486259i
$412$	−7.02159	−	2.75577i	−0.345929	−	0.135767i
$413$	−3.60512	−	0.822846i	−0.177396	−	0.0404896i
$414$	−3.86431	+	1.58380i	−0.189920	+	0.0778393i
$415$	−24.1953	+	50.2420i	−1.18770	+	2.46628i
$416$	0.394398	−	10.5405i	0.0193370	−	0.516792i
$417$	27.1281	+	1.31985i	1.32847	+	0.0646333i
$418$	−0.128270	+	0.0343699i	−0.00627389	+	0.00168108i
$419$	−0.108209	+	1.44395i	−0.00528636	+	0.0705416i	−0.999223	−	0.0394125i	$-0.987451\pi$
$419$	−0.108209	+	1.44395i	−0.00528636	+	0.0705416i	0.993937	+	0.109954i	$0.0350704\pi$
$420$	7.23168	−	1.28448i	0.352870	−	0.0626763i
$421$	16.6739	−	7.27473i	0.812634	−	0.354549i	0.0478657	−	0.998854i	$-0.484758\pi$
$421$	16.6739	−	7.27473i	0.812634	−	0.354549i	0.764769	+	0.644305i	$0.222853\pi$
$422$	5.19588	+	10.7893i	0.252931	+	0.525217i
$423$	−14.1658	−	3.01087i	−0.688767	−	0.146394i
$424$	1.18973	+	0.416304i	0.0577783	+	0.0202175i
$425$	−48.7569	−	1.82435i	−2.36506	−	0.0884941i
$426$	−2.25542	−	1.84039i	−0.109275	−	0.0891670i
$427$	0.363891	−	1.92321i	0.0176099	−	0.0930707i
$428$	0.0915303	+	0.0849277i	0.00442428	+	0.00410513i
$429$	0.0160032	−	0.185594i	0.000772642	−	0.00896058i
$430$	22.9091	+	3.45299i	1.10477	+	0.166518i
$431$	21.4473	−	4.89521i	1.03308	−	0.235794i	0.327819	−	0.944741i	$-0.393687\pi$
$431$	21.4473	−	4.89521i	1.03308	−	0.235794i	0.705262	+	0.708947i	$0.250829\pi$
$432$	1.90960	+	4.81234i	0.0918757	+	0.231534i
$433$	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
$435$	−26.7919	+	16.3976i	−1.28457	+	0.786205i
$436$	−9.43002	+	16.3333i	−0.451616	+	0.782222i
$437$	−2.24406	+	5.14343i	−0.107348	+	0.246044i
$438$	−15.0242	+	5.06881i	−0.717883	+	0.242197i
$439$	3.09788	+	3.33872i	0.147854	+	0.159348i	0.802636	−	0.596469i	$-0.203430\pi$
$439$	3.09788	+	3.33872i	0.147854	+	0.159348i	−0.654782	+	0.755818i	$0.727240\pi$
$440$	−0.321297	+	0.402894i	−0.0153172	+	0.0192072i
$441$	−18.3529	+	3.75799i	−0.873947	+	0.178952i
$442$	−2.28776	+	10.0233i	−0.108818	+	0.476762i
$443$	21.6898	+	18.6656i	1.03051	+	0.886827i	0.993652	−	0.112493i	$-0.0358836\pi$
$443$	21.6898	+	18.6656i	1.03051	+	0.886827i	0.0368595	+	0.999320i	$0.488265\pi$
$444$	−8.09895	−	1.31377i	−0.384359	−	0.0623486i
$445$	−13.2581	−	25.0856i	−0.628495	−	1.18917i
$446$	4.99055	−	4.29471i	0.236309	−	0.203361i
$447$	−12.0217	−	6.52714i	−0.568606	−	0.308723i
$448$	−1.15486	+	1.69387i	−0.0545622	+	0.0800281i
$449$	−1.58124	+	14.0339i	−0.0746232	+	0.662299i	0.899600	+	0.436714i	$0.143858\pi$
$449$	−1.58124	+	14.0339i	−0.0746232	+	0.662299i	−0.974224	+	0.225585i	$0.927571\pi$
$450$	−11.7879	−	7.78095i	−0.555688	−	0.366797i
$451$	0.546726	−	0.263289i	0.0257443	−	0.0123978i
$452$	−5.05173	+	18.8533i	−0.237614	+	0.886786i
$453$	7.24383	+	4.66571i	0.340345	+	0.219214i
$454$	−10.6943	+	5.65208i	−0.501907	+	0.265265i
$455$	−2.96747	−	4.35248i	−0.139117	−	0.204047i
$456$	−12.1059	−	5.44415i	−0.566911	−	0.254946i
$457$	−2.42197	−	7.85182i	−0.113295	−	0.367293i	0.881112	−	0.472907i	$-0.156795\pi$
$457$	−2.42197	−	7.85182i	−0.113295	−	0.367293i	−0.994407	+	0.105614i	$0.966319\pi$
$458$	13.2115	−	10.5358i	0.617333	−	0.492306i
$459$	−7.58036	−	39.2552i	−0.353821	−	1.83227i
$460$	2.03559	+	8.91849i	0.0949098	+	0.415827i
$461$	2.75442	−	5.21162i	0.128286	−	0.242730i	−0.811603	−	0.584210i	$-0.801404\pi$
$461$	2.75442	−	5.21162i	0.128286	−	0.242730i	0.939889	+	0.341480i	$0.110928\pi$
$462$	−0.0402645	+	0.0532950i	−0.00187327	+	0.00247951i
$463$	−14.8973	−	8.60095i	−0.692335	−	0.399720i	0.112151	−	0.993691i	$-0.464226\pi$
$463$	−14.8973	−	8.60095i	−0.692335	−	0.399720i	−0.804486	+	0.593971i	$0.797559\pi$
$464$	−1.19692	+	5.23050i	−0.0555658	+	0.242820i
$465$	−5.97028	+	24.8687i	−0.276865	+	1.15326i
$466$	2.42648	−	1.79082i	0.112404	−	0.0829582i
$467$	−20.8949	+	13.1291i	−0.966901	+	0.607544i	−0.920235	−	0.391366i	$-0.872002\pi$
$467$	−20.8949	+	13.1291i	−0.966901	+	0.607544i	−0.0466660	+	0.998911i	$0.514860\pi$
$468$	5.44755	−	5.61316i	0.251813	−	0.259468i
$469$	−3.68157	−	2.93596i	−0.169999	−	0.135570i
$470$	4.40979	−	11.2360i	0.203409	−	0.518277i
$471$	−23.8793	+	1.52043i	−1.10030	+	0.0700576i
$472$	10.7040	+	2.02530i	0.492691	+	0.0932222i
$473$	0.457507	−	0.311923i	0.0210362	−	0.0143422i
$474$	−4.46032	+	15.9294i	−0.204869	+	0.731661i
$475$	−18.6480	+	3.52840i	−0.855631	+	0.161894i
$476$	−6.85083	+	6.85083i	−0.314007	+	0.314007i
$477$	0.709521	+	1.29516i	0.0324867	+	0.0593015i
$478$	−20.3056	−	2.28789i	−0.928756	−	0.104646i
$479$	12.7128	+	29.1380i	0.580863	+	1.33135i	0.920481	+	0.390788i	$0.127797\pi$
$479$	12.7128	+	29.1380i	0.580863	+	1.33135i	−0.339618	+	0.940563i	$0.610298\pi$
$480$	−33.4127	+	7.23300i	−1.52507	+	0.330140i
$481$	1.52304	+	5.68406i	0.0694447	+	0.259171i
$482$	2.78957	+	3.24154i	0.127062	+	0.147648i
$483$	0.699931	+	2.73447i	0.0318479	+	0.124423i
$484$	−1.19053	−	15.8865i	−0.0541151	−	0.722116i
$485$	6.17856	+	17.6573i	0.280554	+	0.801777i
$486$	4.02588	−	10.8511i	0.182618	−	0.492214i
$487$	−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	$0.904488\pi$
$488$	−0.859431	+	5.70195i	−0.0389046	+	0.258115i
$489$	−29.9814	−	17.7610i	−1.35581	−	0.803180i
$490$	−0.583815	−	15.6028i	−0.0263741	−	0.704862i
$491$	2.48126	+	1.08256i	0.111978	+	0.0488554i	0.455134	−	0.890423i	$-0.349591\pi$
$491$	2.48126	+	1.08256i	0.111978	+	0.0488554i	−0.343156	+	0.939278i	$0.611496\pi$
$492$	24.7762	+	5.94810i	1.11700	+	0.268161i
$493$	16.5908	−	37.9681i	0.747211	−	1.71000i
$494$			3.99918i			0.179932i
$495$	−0.595601	+	0.0989133i	−0.0267703	+	0.00444582i
$496$	2.32431	+	3.69912i	0.104365	+	0.166095i
$497$	−1.44225	+	1.33822i	−0.0646939	+	0.0600272i
$498$	8.00143	−	19.7337i	0.358553	−	0.884288i
$499$	1.21474	+	8.05929i	0.0543793	+	0.360783i	0.999427	+	0.0338505i	$0.0107770\pi$
$499$	1.21474	+	8.05929i	0.0543793	+	0.360783i	−0.945048	+	0.326933i	$0.893985\pi$
$500$	−4.45095	+	4.79698i	−0.199052	+	0.214528i
$501$	−17.4846	−	24.2554i	−0.781153	−	1.08365i
$502$	1.16759	−	0.0874989i	0.0521122	−	0.00390527i
$503$	12.1893	+	7.65903i	0.543493	+	0.341499i	0.775634	−	0.631183i	$-0.217430\pi$
$503$	12.1893	+	7.65903i	0.543493	+	0.341499i	−0.232141	+	0.972682i	$0.574573\pi$
$504$	−6.48624	+	1.58297i	−0.288920	+	0.0705110i
$505$	24.7924	+	24.7924i	1.10325	+	1.10325i
$506$	−0.0687361	−	0.0468635i	−0.00305569	−	0.00208334i
$507$	15.8943	+	5.76251i	0.705890	+	0.255922i
$508$	−18.8976	−	13.9471i	−0.838445	−	0.618800i
$509$	−4.59993	−	0.344717i	−0.203889	−	0.0152793i	−0.0276057	−	0.999619i	$-0.508788\pi$
$509$	−4.59993	−	0.344717i	−0.203889	−	0.0152793i	−0.176283	+	0.984340i	$0.556407\pi$
$510$	33.3105	−	0.872458i	1.47501	−	0.0386331i
$511$	1.99237	+	10.5299i	0.0881373	+	0.465817i
$512$	−5.82167	+	9.26514i	−0.257284	+	0.409465i
$513$	−6.27252	−	14.2306i	−0.276939	−	0.628299i
$514$	4.17955	−	1.46249i	0.184352	−	0.0645075i
$515$	16.7550	−	5.16824i	0.738314	−	0.227740i
$516$	23.1647	+	1.99742i	1.01977	+	0.0879315i
$517$	−0.105396	−	0.268546i	−0.00463533	−	0.0118106i
$518$	0.621939	−	2.01628i	0.0273264	−	0.0885902i
$519$	0.594372	+	1.76175i	0.0260900	+	0.0773321i
$520$	9.21557	+	12.4867i	0.404129	+	0.547576i
$521$	−23.7321			−1.03972			−0.519860	−	0.854251i	$-0.674016\pi$
$521$	−23.7321			−1.03972			−0.519860	+	0.854251i	$0.674016\pi$
$522$	9.81220	−	6.89902i	0.429468	−	0.301962i
$523$	−0.761512			−0.0332986			−0.0166493	−	0.999861i	$-0.505300\pi$
$523$	−0.761512			−0.0332986			−0.0166493	+	0.999861i	$0.505300\pi$
$524$	8.25833	+	11.1896i	0.360767	+	0.488821i
$525$	−6.30767	+	7.16553i	−0.275289	+	0.312729i
$526$	−0.585305	+	1.89751i	−0.0255205	+	0.0827354i
$527$	−12.3252	−	31.4040i	−0.536892	−	1.36798i
$528$	−0.0590490	+	0.0845560i	−0.00256978	+	0.00367983i
$529$	18.6188	−	5.74315i	0.809515	−	0.249702i
$530$	−1.16176	+	0.406517i	−0.0504636	+	0.0176580i
$531$	7.73212	+	10.1549i	0.335545	+	0.440683i
$532$	−2.00506	+	3.19103i	−0.0869304	+	0.138349i
$533$	−3.39748	−	17.9561i	−0.147161	−	0.777765i
$534$	5.66119	+	9.23811i	0.244984	+	0.399772i
$535$	−0.289435	−	0.0216901i	−0.0125133	−	0.000937746i
$536$	11.1618	+	8.23781i	0.482118	+	0.355819i
$537$	−4.99030	+	4.19802i	−0.215347	+	0.181158i
$538$	−4.02713	−	2.74565i	−0.173622	−	0.118373i
$539$	−0.263875	−	0.263875i	−0.0113659	−	0.0113659i
$540$	−22.0026	−	12.5932i	−0.946843	−	0.541927i
$541$	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	$0.670573\pi$
$542$	−10.2736	+	0.769897i	−0.441287	+	0.0330699i
$543$	−10.3961	+	23.1172i	−0.446138	+	0.992055i
$544$	30.6725	−	33.0571i	1.31507	−	1.41731i
$545$	−6.53414	−	43.3512i	−0.279892	−	1.85696i
$546$	1.23648	+	1.58667i	0.0529163	+	0.0679033i
$547$	−11.8819	+	11.0248i	−0.508035	+	0.471388i	−0.892048	−	0.451940i	$-0.850732\pi$
$547$	−11.8819	+	11.0248i	−0.508035	+	0.471388i	0.384013	+	0.923328i	$0.374542\pi$
$548$	7.13688	+	11.3583i	0.304872	+	0.485201i
$549$	−5.21837	+	4.29088i	−0.222715	+	0.183130i
$550$		−	0.281358i		−	0.0119972i
$551$	3.00533	−	15.8347i	0.128031	−	0.674583i
$552$	−2.36179	−	7.97310i	−0.100524	−	0.339357i
$553$	10.2475	+	4.47093i	0.435767	+	0.190123i
$554$	−0.320290	−	8.55993i	−0.0136078	−	0.363677i
$555$	16.6231	−	9.35037i	0.705610	−	0.396901i
$556$	−3.38592	+	22.4641i	−0.143595	+	0.952689i
$557$	−2.67720	−	3.35710i	−0.113437	−	0.142245i	0.721871	−	0.692027i	$-0.243282\pi$
$557$	−2.67720	−	3.35710i	−0.113437	−	0.142245i	−0.835308	+	0.549782i	$0.814711\pi$
$558$	1.67178	−	9.62201i	0.0707721	−	0.407332i
$559$	−5.50761	−	15.7399i	−0.232947	−	0.665725i
$560$	0.217948	+	2.90831i	0.00920997	+	0.122899i
$561$	0.569427	−	0.556797i	0.0240412	−	0.0235080i
$562$	1.72268	+	2.00180i	0.0726671	+	0.0844407i
$563$	10.0693	+	37.5791i	0.424370	+	1.58377i	0.765295	+	0.643680i	$0.222593\pi$
$563$	10.0693	+	37.5791i	0.424370	+	1.58377i	−0.340924	+	0.940091i	$0.610740\pi$
$564$	3.70010	−	11.5346i	0.155803	−	0.485694i
$565$	−18.1436	−	41.5856i	−0.763307	−	1.74952i
$566$	−1.59361	−	0.179557i	−0.0669844	−	0.00754733i
$567$	−6.88848	−	3.70664i	−0.289289	−	0.155664i
$568$	4.09853	−	4.09853i	0.171971	−	0.171971i
$569$	−4.13815	+	0.782980i	−0.173480	+	0.0328242i	−0.271926	−	0.962318i	$-0.587661\pi$
$569$	−4.13815	+	0.782980i	−0.173480	+	0.0328242i	0.0984456	+	0.995142i	$0.468613\pi$
$570$	12.5568	−	3.21412i	0.525949	−	0.134625i
$571$	−15.3112	+	10.4390i	−0.640754	+	0.436859i	−0.839625	−	0.543167i	$-0.817225\pi$
$571$	−15.3112	+	10.4390i	−0.640754	+	0.436859i	0.198871	+	0.980026i	$0.436273\pi$
$572$	0.153098	+	0.0289676i	0.00640133	+	0.00121120i
$573$	−20.4487	+	41.2716i	−0.854255	+	1.72415i
$574$	−2.39398	+	6.09975i	−0.0999226	+	0.254599i
$575$	−9.29571	−	7.41308i	−0.387658	−	0.309147i
$576$	6.80687	−	1.93357i	0.283619	−	0.0805653i
$577$	−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	$0.520642\pi$
$578$	−25.2102	+	18.6060i	−1.04861	+	0.773907i
$579$	40.3507	−	11.9527i	1.67692	−	0.496736i
$580$	−11.3865	−	23.6783i	−0.472797	−	0.983189i
$581$	−12.4640	−	7.19608i	−0.517093	−	0.298544i
$582$	−2.78302	−	6.57907i	−0.115360	−	0.272711i
$583$	−0.0137459	+	0.0260084i	−0.000569295	+	0.00107716i
$584$	−7.02540	−	30.7803i	−0.290713	−	1.27370i
$585$	−1.76507	+	18.0966i	−0.0729765	+	0.748202i
$586$	6.63569	−	5.29179i	0.274118	−	0.218602i
$587$	−0.752116	−	2.43830i	−0.0310432	−	0.100639i	0.938725	−	0.344666i	$-0.112008\pi$
$587$	−0.752116	−	2.43830i	−0.0310432	−	0.100639i	−0.969769	+	0.244026i	$0.921532\pi$
$588$	−1.57971	−	15.5897i	−0.0651462	−	0.642909i
$589$	−7.39232	−	10.8425i	−0.304595	−	0.446759i
$590$	−9.40506	+	4.97072i	−0.387200	+	0.204641i
$591$	23.9330	−	12.3076i	0.984471	−	0.506267i
$592$	0.843213	−	3.14691i	0.0346559	−	0.129337i
$593$	6.23061	−	3.00050i	0.255861	−	0.123216i	−0.301557	−	0.953448i	$-0.597506\pi$
$593$	6.23061	−	3.00050i	0.255861	−	0.123216i	0.557418	+	0.830232i	$0.311792\pi$
$594$	0.224576	−	0.0521466i	0.00921447	−	0.00213960i
$595$	2.52159	−	22.3797i	0.103375	−	0.917480i
$596$	6.44545	−	9.45375i	0.264016	−	0.387240i
$597$	0.728533	+	27.8154i	0.0298169	+	1.13841i
$598$	−1.89899	+	1.63421i	−0.0776554	+	0.0668279i
$599$	−13.6637	−	25.8530i	−0.558285	−	1.05633i	−0.988158	−	0.153437i	$-0.950966\pi$
$599$	−13.6637	−	25.8530i	−0.558285	−	1.05633i	0.429874	−	0.902889i	$-0.358558\pi$
$600$	17.7802	−	21.7899i	0.725875	−	0.889569i
$601$	28.4634	+	24.4948i	1.16105	+	0.999163i	0.999925	+	0.0122285i	$0.00389256\pi$
$601$	28.4634	+	24.4948i	1.16105	+	0.999163i	0.161123	+	0.986934i	$0.448488\pi$
$602$	−1.33053	+	5.82943i	−0.0542284	+	0.237590i
$603$	3.26043	+	15.9229i	0.132775	+	0.648433i
$604$	−4.49353	+	5.63471i	−0.182839	+	0.229273i
$605$	25.1884	+	27.1467i	1.02406	+	1.10367i
$606$	−10.0497	−	8.84651i	−0.408239	−	0.359365i
$607$	−14.0013	+	32.0914i	−0.568297	+	1.30255i	0.360776	+	0.932653i	$0.382512\pi$
$607$	−14.0013	+	32.0914i	−0.568297	+	1.30255i	−0.929072	+	0.369898i	$0.879393\pi$
$608$	8.77064	−	15.1912i	0.355696	−	0.616084i
$609$	−3.70346	−	7.21161i	−0.150072	−	0.292229i
$610$	−2.81540	−	4.87641i	−0.113992	−	0.197440i
$611$	−8.63332	+	0.972741i	−0.349267	+	0.0393529i
$612$	33.3064	−	2.99802i	1.34633	−	0.121188i
$613$	−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	$0.448054\pi$
$614$	10.6495	+	1.60515i	0.429777	+	0.0647785i
$615$	−53.6490	+	25.0988i	−2.16333	+	1.01208i
$616$	−0.0974946	−	0.0904618i	−0.00392817	−	0.00364481i
$617$	5.11049	−	27.0096i	0.205741	−	1.08737i	−0.715571	−	0.698540i	$-0.753833\pi$
$617$	5.11049	−	27.0096i	0.205741	−	1.08737i	0.921312	−	0.388825i	$-0.127119\pi$
$618$	−6.25973	+	2.37610i	−0.251803	+	0.0955809i
$619$	−10.0209	−	0.374956i	−0.402775	−	0.0150708i	−0.164763	−	0.986333i	$-0.552686\pi$
$619$	−10.0209	−	0.374956i	−0.402775	−	0.0150708i	−0.238011	+	0.971262i	$0.576496\pi$
$620$	−20.1917	−	7.06536i	−0.810916	−	0.283752i
$621$	4.19416	−	8.79363i	0.168306	−	0.352876i
$622$	−8.46364	−	17.5749i	−0.339361	−	0.704691i
$623$	6.71190	−	2.92837i	0.268907	−	0.117323i
$624$	1.99942	+	2.37676i	0.0800409	+	0.0951467i
$625$	−1.23266	+	16.4487i	−0.0493064	+	0.657948i
$626$	−24.4856	+	6.56091i	−0.978643	+	0.262227i
$627$	0.167750	−	0.260443i	0.00669928	−	0.0104011i
$628$	0.748346	−	20.0000i	0.0298622	−	0.798085i
$629$	−10.9157	+	22.6667i	−0.435238	+	0.903781i
$630$	3.98817	−	5.15755i	0.158892	−	0.205482i
$631$	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	$0.521352\pi$
$632$	−30.6607	−	12.0334i	−1.21962	−	0.478664i
$633$	−25.8893	−	10.4973i	−1.02901	−	0.417232i
$634$	−13.7415	−	4.23868i	−0.545743	−	0.168340i
$635$	54.5582	−	2.04142i	2.16508	−	0.0810114i
$636$	−1.13763	+	0.481232i	−0.0451101	+	0.0190821i
$637$	−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
$641$	−33.1556	−	17.5232i	−1.30957	−	0.692126i	−0.340808	−	0.940133i	$-0.610701\pi$
$641$	−33.1556	−	17.5232i	−1.30957	−	0.692126i	−0.968758	+	0.248007i	$0.920224\pi$
$642$	0.110826	+	0.00124288i	0.00437397	+	4.90526e-5i
$643$	−18.9852	+	7.45113i	−0.748702	+	0.293844i	−0.708848	−	0.705361i	$-0.750785\pi$
$643$	−18.9852	+	7.45113i	−0.748702	+	0.293844i	−0.0398546	+	0.999205i	$0.512689\pi$
$644$	−2.33458	+	0.351882i	−0.0919955	+	0.0138661i
$645$	−44.9944	+	29.9431i	−1.77165	+	1.17901i
$646$	−11.1525	+	12.9595i	−0.438791	+	0.509884i
$647$	27.2706	+	13.1328i	1.07212	+	0.516305i	0.884789	−	0.465992i	$-0.154302\pi$
$647$	27.2706	+	13.1328i	1.07212	+	0.516305i	0.187330	+	0.982297i	$0.440017\pi$
$648$	20.6878	+	10.1534i	0.812692	+	0.398864i
$649$	−0.0839732	+	0.239982i	−0.00329624	+	0.00942010i
$650$	−8.18452	−	2.19304i	−0.321023	−	0.0860180i
$651$	−6.28522	−	2.01619i	−0.246337	−	0.0790209i
$652$	17.3084	−	23.4521i	0.677851	−	0.918455i
$653$	−17.1321	+	23.2131i	−0.670429	+	0.908400i	−0.999353	−	0.0359567i	$-0.988552\pi$
$653$	−17.1321	+	23.2131i	−0.670429	+	0.908400i	0.328924	+	0.944356i	$0.393314\pi$
$654$	3.54197	+	16.3621i	0.138502	+	0.639807i
$655$	−31.2261	−	8.36700i	−1.22010	−	0.326926i
$656$	−3.34162	+	9.54980i	−0.130468	+	0.372857i
$657$	18.0134	−	32.3077i	0.702770	−	1.26044i
$658$	2.80672	+	1.35164i	0.109417	+	0.0526925i
$659$	−8.94031	+	10.3888i	−0.348265	+	0.404691i	−0.904596	−	0.426269i	$-0.859828\pi$
$659$	−8.94031	+	10.3888i	−0.348265	+	0.404691i	0.556331	+	0.830961i	$0.312209\pi$
$660$	−0.0320895	−	0.503985i	−0.00124908	−	0.0196176i
$661$	38.0871	−	5.74071i	1.48142	−	0.223288i	0.641970	−	0.766730i	$-0.278117\pi$
$661$	38.0871	−	5.74071i	1.48142	−	0.223288i	0.839447	+	0.543442i	$0.182879\pi$
$662$	−22.3245	+	8.76170i	−0.867664	+	0.340533i
$663$	−11.7585	−	20.9042i	−0.456661	−	0.811851i
$664$	37.4862	+	19.8120i	1.45475	+	0.768856i
$665$	−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
$669$	−1.89079	+	15.2429i	−0.0731022	+	0.589323i
$670$	−13.5370	+	0.506517i	−0.522979	+	0.0195685i
$671$	−0.128600	−	0.0396679i	−0.00496455	−	0.00153136i
$672$	−1.21710	−	8.73881i	−0.0469508	−	0.337107i
$673$	14.0805	+	5.52620i	0.542764	+	0.213019i	0.620853	−	0.783927i	$-0.286786\pi$
$673$	14.0805	+	5.52620i	0.542764	+	0.213019i	−0.0780885	+	0.996946i	$0.524882\pi$
$674$	1.69157	+	0.386091i	0.0651570	+	0.0148717i
$675$	32.5634	−	5.03334i	1.25337	−	0.193733i
$676$	−6.13570	+	12.7409i	−0.235989	+	0.490035i
$677$	−0.823016	+	21.9956i	−0.0316311	+	0.845358i	0.889692	+	0.456561i	$0.150919\pi$
$677$	−0.823016	+	21.9956i	−0.0316311	+	0.845358i	−0.921323	+	0.388797i	$0.872891\pi$
$678$	7.92336	+	15.4075i	0.304295	+	0.591722i
$679$	−4.66357	+	1.24960i	−0.178971	+	0.0479553i
$680$	−4.95823	+	66.1629i	−0.190139	+	2.53723i
$681$	9.61797	−	26.5285i	0.368561	−	1.01657i
$682$	0.178310	−	0.0777959i	0.00682785	−	0.00297896i
$683$	−0.542211	−	1.12591i	−0.0207471	−	0.0430819i	0.890338	−	0.455301i	$-0.150468\pi$
$683$	−0.542211	−	1.12591i	−0.0207471	−	0.0430819i	−0.911085	+	0.412219i	$0.864754\pi$
$684$	12.3713	−	4.01985i	0.473030	−	0.153703i
$685$	−29.4324	−	10.2988i	−1.12455	−	0.393498i
$686$	8.54096	+	0.319580i	0.326095	+	0.0122016i
$687$	−6.31213	+	38.9122i	−0.240823	+	1.48459i
$688$	−1.71639	+	9.07132i	−0.0654366	+	0.345841i
$689$	0.649426	+	0.602579i	0.0247412	+	0.0229564i
$690$	6.65739	+	4.64914i	0.253443	+	0.176990i
$691$	45.3978	+	6.84261i	1.72701	+	0.260305i	0.936128	−	0.351660i	$-0.114383\pi$
$691$	45.3978	+	6.84261i	1.72701	+	0.260305i	0.790884	+	0.611966i	$0.209621\pi$
$692$	−1.51620	+	0.346064i	−0.0576374	+	0.0131554i
$693$	−0.0139697	−	0.155196i	−0.000530664	−	0.00589539i
$694$	22.8453	−	2.57405i	0.867196	−	0.0977095i
$695$	−26.4042	−	45.7334i	−1.00157	−	1.73477i
$696$	11.6973	+	20.8228i	0.443384	+	0.789286i
$697$	39.0646	−	67.6619i	1.47968	−	2.56288i
$698$	−0.932676	+	2.13772i	−0.0353023	+	0.0809137i
$699$	−1.38539	+	6.89758i	−0.0524001	+	0.260890i
$700$	−5.43109	−	5.85332i	−0.205276	−	0.221235i
$701$	−11.1141	+	13.9367i	−0.419775	+	0.526381i	−0.946088	−	0.323910i	$-0.895003\pi$
$701$	−11.1141	+	13.9367i	−0.419775	+	0.526381i	0.526313	+	0.850291i	$0.323574\pi$
$702$	0.233542	−	6.93922i	0.00881446	−	0.261904i
$703$	−2.17762	+	9.54076i	−0.0821303	+	0.359836i
$704$	0.106842	+	0.0919448i	0.00402675	+	0.00346530i
$705$	9.99281	+	26.3256i	0.376351	+	0.991478i
$706$	0.836277	+	1.58231i	0.0314737	+	0.0595512i
$707$	−6.85891	+	5.90257i	−0.257956	+	0.221989i
$708$	−9.10264	+	5.57818i	−0.342098	+	0.209641i
$709$	27.8859	−	40.9010i	1.04728	−	1.53607i	0.219019	−	0.975721i	$-0.429714\pi$
$709$	27.8859	−	40.9010i	1.04728	−	1.53607i	0.828256	−	0.560350i	$-0.189333\pi$
$710$	−0.633713	+	5.62435i	−0.0237828	+	0.211078i
$711$	−17.2623	−	34.5140i	−0.647387	−	1.29438i
$712$	−19.4370	+	9.36038i	−0.728433	+	0.350795i
$713$	2.12775	−	7.94086i	0.0796847	−	0.297388i
$714$	−0.417916	+	8.58984i	−0.0156401	+	0.321467i
$715$	−0.320223	+	0.169243i	−0.0119756	+	0.00632931i
$716$	−3.07269	−	4.50680i	−0.114832	−	0.168427i
$717$	38.6699	−	27.8753i	1.44416	−	1.04102i
$718$	−0.0771046	−	0.249967i	−0.00287752	−	0.00932869i
$719$	−12.7662	+	10.1807i	−0.476100	+	0.379677i	−0.831936	−	0.554871i	$-0.812767\pi$
$719$	−12.7662	+	10.1807i	−0.476100	+	0.379677i	0.355837	+	0.934548i	$0.384196\pi$
$720$	5.85577	−	8.18808i	0.218232	−	0.305152i
$721$	1.00698	+	4.41186i	0.0375019	+	0.164306i
$722$	3.48399	−	6.59203i	0.129661	−	0.245330i
$723$	−9.90079	−	1.22814i	−0.368214	−	0.0456749i
$724$	−18.3610	−	10.6007i	−0.682379	−	0.393972i
$725$	30.7585	+	14.8339i	1.14234	+	0.550916i
$726$	−10.2577	−	9.73409i	−0.380699	−	0.361266i
$727$	−4.29450	+	3.16949i	−0.159274	+	0.117550i	−0.670542	−	0.741872i	$-0.733938\pi$
$727$	−4.29450	+	3.16949i	−0.159274	+	0.117550i	0.511267	+	0.859422i	$0.329176\pi$
$728$	−3.39139	+	2.13095i	−0.125693	+	0.0789783i
$729$	10.0528	+	25.0588i	0.372326	+	0.928102i
$730$	24.1036	+	19.2220i	0.892114	+	0.711437i
$731$	26.0462	−	66.3647i	0.963354	−	2.45459i
$732$	−3.13073	−	4.70443i	−0.115715	−	0.173881i
$733$	13.8126	+	2.61349i	0.510180	+	0.0965313i	0.434627	−	0.900610i	$-0.356880\pi$
$733$	13.8126	+	2.61349i	0.510180	+	0.0965313i	0.0755531	+	0.997142i	$0.475928\pi$
$734$	−9.51695	+	6.48855i	−0.351277	+	0.239497i
$735$	25.4655	+	26.0432i	0.939310	+	0.960618i
$736$	10.7974	−	2.04299i	0.397999	−	0.0753055i
$737$	−0.228938	+	0.228938i	−0.00843303	+	0.00843303i
$738$	19.8360	−	10.8666i	0.730172	−	0.400005i
$739$	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	$0.494339\pi$
$740$	6.37942	+	14.6218i	0.234512	+	0.537507i
$741$	−6.26858	−	6.90974i	−0.230282	−	0.253836i
$742$	−0.0822172	−	0.306839i	−0.00301829	−	0.0112644i
$743$	−4.28448	−	4.97865i	−0.157182	−	0.182649i	0.673859	−	0.738860i	$-0.264636\pi$
$743$	−4.28448	−	4.97865i	−0.157182	−	0.182649i	−0.831041	+	0.556211i	$0.812255\pi$
$744$	18.7256	+	5.24325i	0.686512	+	0.192227i
$745$	1.98761	+	26.5228i	0.0728202	+	0.971719i
$746$	1.63384	+	4.66923i	0.0598190	+	0.170953i
$747$	17.1071	+	46.6376i	0.625917	+	1.70638i
$748$	0.415336	+	0.520815i	0.0151862	+	0.0190429i
$749$	0.0111646	−	0.0740725i	0.000407947	−	0.00270655i
$750$	−0.0651377	+	5.80826i	−0.00237849	+	0.212088i
$751$	1.52710	+	40.8125i	0.0557245	+	1.48927i	0.694286	+	0.719699i	$0.255720\pi$
$751$	1.52710	+	40.8125i	0.0557245	+	1.48927i	−0.638562	+	0.769571i	$0.720470\pi$
$752$	4.40865	+	1.92347i	0.160767	+	0.0701418i
$753$	−1.88020	+	1.98134i	−0.0685182	+	0.0722040i
$754$	4.27622	−	5.78725i	0.155731	−	0.210759i
$755$		−	16.7531i		−	0.609707i
$756$	3.66545	−	5.41987i	0.133311	−	0.197119i
$757$	−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	$-0.494620\pi$
$758$	1.12339	−	1.04235i	0.0408033	−	0.0378599i
$759$	0.192218	−	0.0267713i	0.00697708	−	0.000971738i
$760$	3.84655	+	25.5202i	0.139529	+	0.925716i
$761$	−18.9647	+	20.4391i	−0.687469	+	0.740916i	−0.976290	−	0.216468i	$-0.930546\pi$
$761$	−18.9647	+	20.4391i	−0.687469	+	0.740916i	0.288821	+	0.957383i	$0.406737\pi$
$762$	−20.7419	+	2.10179i	−0.751401	+	0.0761397i
$763$	11.2832	−	0.845557i	0.408478	−	0.0306112i
$764$	−32.6209	−	20.4971i	−1.18018	−	0.741559i
$765$	−56.1858	+	53.7204i	−2.03140	+	1.94227i
$766$	−11.6708	−	11.6708i	−0.421682	−	0.421682i
$767$	6.32638	+	4.31325i	0.228432	+	0.155743i
$768$	3.67125	+	20.6693i	0.132475	+	0.745838i
$769$	24.5146	+	18.0926i	0.884020	+	0.652437i	0.938200	−	0.346095i	$-0.112492\pi$
$769$	24.5146	+	18.0926i	0.884020	+	0.652437i	−0.0541794	+	0.998531i	$0.517254\pi$
$770$	0.129509	+	0.00970532i	0.00466716	+	0.000349756i
$771$	−4.92897	+	9.07816i	−0.177513	+	0.326942i
$772$	6.54416	+	34.5867i	0.235530	+	1.24480i
$773$	−10.0360	+	15.9723i	−0.360971	+	0.574482i	−0.976999	−	0.213242i	$-0.931598\pi$
$773$	−10.0360	+	15.9723i	−0.360971	+	0.574482i	0.616028	+	0.787724i	$0.288741\pi$
$774$	16.4203	−	12.5027i	0.590215	−	0.449401i
$775$	26.2435	−	9.18301i	0.942695	−	0.329863i
$776$	13.5917	−	4.19250i	0.487915	−	0.150502i
$777$	2.08587	+	4.45857i	0.0748300	+	0.159950i
$778$	8.64384	+	22.0241i	0.309897	+	0.789604i
$779$	8.95790	−	29.0408i	0.320950	−	1.04050i
$780$	−14.9107	−	2.99483i	−0.533889	−	0.107232i
$781$	0.0803294	+	0.108842i	0.00287441	+	0.00389469i
$782$	−10.7111			−0.383027
$783$	−6.13943	+	27.3003i	−0.219405	+	0.975634i
$784$	6.22199			0.222214
$785$	27.6264	+	37.4324i	0.986028	+	1.33602i
$786$	12.1029	+	2.43088i	0.431696	+	0.0867066i
$787$	13.8998	−	45.0619i	0.495473	−	1.60628i	−0.270030	−	0.962852i	$-0.587034\pi$
$787$	13.8998	−	45.0619i	0.495473	−	1.60628i	0.765503	−	0.643432i	$-0.222490\pi$
$788$	8.22395	+	20.9543i	0.292966	+	0.746465i
$789$	−1.96300	−	4.19594i	−0.0698846	−	0.149379i
$790$	30.7343	−	9.48028i	1.09348	−	0.337293i
$791$	11.0527	−	3.86750i	0.392988	−	0.137512i
$792$	0.0582218	+	0.455352i	0.00206882	+	0.0161802i
$793$	−2.15628	+	3.43170i	−0.0765717	+	0.121863i
$794$	2.74126	+	14.4879i	0.0972836	+	0.514156i
$795$	1.37007	−	2.52339i	0.0485914	−	0.0894955i
$796$	−23.2088	−	1.73926i	−0.822613	−	0.0616463i
$797$	0.127672	+	0.0942263i	0.00452238	+	0.00333767i	0.596079	−	0.802926i	$-0.296724\pi$
$797$	0.127672	+	0.0942263i	0.00452238	+	0.00333767i	−0.591557	+	0.806263i	$0.701486\pi$
$798$	0.585024	+	3.29371i	0.0207096	+	0.116596i
$799$	−30.6893	−	20.9236i	−1.08571	−	0.740223i
$800$	26.2799	+	26.2799i	0.929136	+	0.929136i
$801$	−24.2617	−	7.08776i	−0.857247	−	0.250434i
$802$	15.1399	+	9.51300i	0.534607	+	0.335916i
$803$	0.734784	−	0.0550645i	0.0259300	−	0.00194318i
$804$	−13.5256	+	1.37056i	−0.477012	+	0.0483358i
$805$	3.73287	−	4.02308i	0.131567	−	0.141795i
$806$	−0.873199	−	5.79330i	−0.0307571	−	0.204060i
$807$	11.2617	−	1.56849i	0.396432	−	0.0552133i
$808$	19.5422	−	18.1325i	0.687492	−	0.637899i
$809$	−19.0410	−	30.3035i	−0.669445	−	1.06542i	−0.992875	−	0.119164i	$-0.961979\pi$
$809$	−19.0410	−	30.3035i	−0.669445	−	1.06542i	0.323429	−	0.946252i	$-0.395164\pi$
$810$	−21.9758	+	4.84372i	−0.772152	+	0.170191i
$811$		−	20.9637i		−	0.736134i	−0.929799	−	0.368067i	$-0.880020\pi$
$811$		−	20.9637i		−	0.736134i	0.929799	−	0.368067i	$-0.119980\pi$
$812$	6.31362	−	2.47382i	0.221565	−	0.0868139i
$813$	16.5437	−	17.4337i	0.580215	−	0.611426i
$814$	−0.132972	−	0.0580152i	−0.00466067	−	0.00203343i
$815$	2.53343	+	67.7073i	0.0887421	+	2.37168i
$816$	−0.148906	+	13.2778i	−0.00521275	+	0.464815i
$817$	4.13321	−	27.4220i	0.144603	−	0.959376i
$818$	10.6596	+	13.3667i	0.372705	+	0.467357i
$819$	−4.62342	−	0.803298i	−0.161555	−	0.0280695i
$820$	−16.3627	−	46.7618i	−0.571409	−	1.63299i
$821$	−1.94072	−	25.8971i	−0.0677315	−	0.903814i	−0.922795	−	0.385291i	$-0.874101\pi$
$821$	−1.94072	−	25.8971i	−0.0677315	−	0.903814i	0.855064	−	0.518523i	$-0.173518\pi$
$822$	11.4662	+	3.21060i	0.399930	+	0.111983i
$823$	−9.77976	−	11.3643i	−0.340901	−	0.396134i	0.561185	−	0.827690i	$-0.310346\pi$
$823$	−9.77976	−	11.3643i	−0.340901	−	0.396134i	−0.902086	+	0.431556i	$0.857965\pi$
$824$	−3.45050	−	12.8775i	−0.120204	−	0.448607i
$825$	0.441019	+	0.486127i	0.0153543	+	0.0169248i
$826$	−1.09790	−	2.51642i	−0.0382009	−	0.0875574i
$827$	−3.07861	−	0.346876i	−0.107054	−	0.0120621i	0.0582751	−	0.998301i	$-0.481440\pi$
$827$	−3.07861	−	0.346876i	−0.107054	−	0.0120621i	−0.165329	+	0.986239i	$0.552869\pi$
$828$	6.96418	+	4.23180i	0.242022	+	0.147065i
$829$	−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	$0.277065\pi$
$830$	−40.6811	+	7.69728i	−1.41206	+	0.267176i
$831$	13.9708	+	14.2877i	0.484641	+	0.495635i
$832$	3.50739	−	2.39129i	0.121597	−	0.0829032i
$833$	−47.2095	−	8.93251i	−1.63571	−	0.309493i
$834$	11.1720	+	16.7878i	0.386855	+	0.581313i
$835$	−21.2396	+	54.1175i	−0.735026	+	1.87281i
$836$	0.202589	+	0.161559i	0.00700667	+	0.00558764i
$837$	12.1937	+	19.2452i	0.421475	+	0.665213i
$838$	−0.910299	+	0.571979i	−0.0314458	+	0.0197587i
$839$	−39.7757	+	29.3558i	−1.37321	+	1.01347i	−0.377024	+	0.926204i	$0.623052\pi$
$839$	−39.7757	+	29.3558i	−1.37321	+	1.01347i	−0.996185	+	0.0872701i	$0.972186\pi$
$840$	9.41652	+	8.93584i	0.324901	+	0.308316i
$841$	−21.2807	+	19.7011i	−0.733817	+	0.679347i
$842$	11.6971	+	6.75333i	0.403109	+	0.232735i
$843$	−6.11418	−	0.758429i	−0.210583	−	0.0261217i
$844$	10.9187	−	20.6593i	0.375838	−	0.711121i
$845$	−7.31473	−	32.0479i	−0.251634	−	1.10248i
$846$	−4.44691	−	9.78989i	−0.152888	−	0.336583i
$847$	−7.47246	+	5.95909i	−0.256757	+	0.204757i
$848$	−0.144571	−	0.468689i	−0.00496460	−	0.0160948i
$849$	3.03487	−	2.18769i	0.104156	−	0.0750814i
$850$	−20.4065	−	29.9308i	−0.699937	−	1.02662i
$851$	−5.42023	+	2.86467i	−0.185803	+	0.0981997i
$852$	−0.276028	+	5.67348i	−0.00945658	+	0.194370i
$853$	3.43375	−	12.8149i	0.117569	−	0.438774i	−0.881897	−	0.471442i	$-0.843734\pi$
$853$	3.43375	−	12.8149i	0.117569	−	0.438774i	0.999466	+	0.0326677i	$0.0104003\pi$
$854$	1.30933	−	0.630539i	0.0448043	−	0.0215766i
$855$	−16.6575	+	25.2357i	−0.569676	+	0.863044i
$856$	−0.0247088	+	0.219297i	−0.000844530	+	0.00749541i
$857$	31.4488	−	46.1269i	1.07427	−	1.57566i	0.288154	−	0.957584i	$-0.406959\pi$
$857$	31.4488	−	46.1269i	1.07427	−	1.57566i	0.786116	−	0.618079i	$-0.212089\pi$
$858$	0.117926	−	0.0722663i	0.00402594	−	0.00246713i
$859$	2.27983	−	1.96195i	0.0777868	−	0.0669409i	−0.612535	−	0.790444i	$-0.709850\pi$
$859$	2.27983	−	1.96195i	0.0777868	−	0.0669409i	0.690322	+	0.723503i	$0.257469\pi$
$860$	−21.1238	−	39.9682i	−0.720316	−	1.36290i
$861$	−5.42486	−	14.2915i	−0.184879	−	0.487054i
$862$	12.3802	+	10.6540i	0.421671	+	0.362877i
$863$	6.45872	−	28.2975i	0.219858	−	0.963259i	−0.737725	−	0.675101i	$-0.764100\pi$
$863$	6.45872	−	28.2975i	0.219858	−	0.963259i	0.957583	−	0.288158i	$-0.0930428\pi$
$864$	−16.1056	+	25.8470i	−0.547923	+	0.879332i
$865$	2.25398	−	2.82641i	0.0766378	−	0.0961007i
$866$	1.57423	+	1.69661i	0.0534944	+	0.0576532i
$867$	14.3936	−	71.6633i	0.488834	−	2.43381i
$868$	2.20783	−	5.06039i	0.0749385	−	0.171761i
$869$	0.384359	−	0.665729i	0.0130385	−	0.0225833i
$870$	−21.6079	−	8.77552i	−0.732576	−	0.297518i
$871$	4.87520	+	8.44409i	0.165190	+	0.286117i
$872$	−33.1241	+	3.73219i	−1.12172	+	0.126388i
$873$	15.1209	+	7.00495i	0.511766	+	0.237082i
$874$	−4.06197	+	0.927119i	−0.137398	+	0.0313603i
$875$	3.88204	+	0.585124i	0.131237	+	0.0197808i
$876$	25.3667	+	17.7147i	0.857062	+	0.598523i
$877$	30.4756	+	28.2772i	1.02909	+	0.954854i	0.999001	−	0.0446935i	$-0.0142311\pi$
$877$	30.4756	+	28.2772i	1.02909	+	0.954854i	0.0300869	+	0.999547i	$0.490422\pi$
$878$	−0.628674	+	3.32262i	−0.0212167	+	0.112133i
$879$	−3.17037	+	19.5443i	−0.106934	+	0.659213i
$880$	0.200385	+	0.00749788i	0.00675498	+	0.000252753i
$881$	4.02085	+	1.40695i	0.135466	+	0.0474015i	0.397160	−	0.917749i	$-0.369996\pi$
$881$	4.02085	+	1.40695i	0.135466	+	0.0474015i	−0.261695	+	0.965151i	$0.584281\pi$
$882$	−10.3365	−	9.30684i	−0.348049	−	0.313378i
$883$	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	$0.667564\pi$
$884$	18.3875	−	8.02237i	0.618438	−	0.269822i
$885$	8.45851	−	23.3304i	0.284330	−	0.784244i
$886$	−1.58771	+	21.1865i	−0.0533401	+	0.711775i
$887$	−44.2908	+	11.8677i	−1.48714	+	0.398478i	−0.908770	−	0.417297i	$-0.862978\pi$
$887$	−44.2908	+	11.8677i	−1.48714	+	0.398478i	−0.578370	+	0.815775i	$0.696311\pi$
$888$	−6.63185	−	12.8961i	−0.222550	−	0.432765i
$889$	−0.526868	+	14.0808i	−0.0176706	+	0.472256i
$890$	9.14033	−	18.9801i	0.306385	−	0.636214i
$891$	−0.306282	+	0.442113i	−0.0102608	+	0.0148114i
$892$	−12.5253	−	2.85882i	−0.419378	−	0.0957203i
$893$	−13.4494	−	5.27850i	−0.450067	−	0.176638i
$894$	−1.40101	−	10.0593i	−0.0468569	−	0.336433i
$895$	12.1161	+	3.73733i	0.404997	+	0.124925i
$896$	8.65993	−	0.324032i	0.289308	−	0.0108251i
$897$	0.719478	−	5.80017i	0.0240227	−	0.193662i
$898$	−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
$902$	0.398329	+	0.210523i	0.0132629	+	0.00700966i
$903$	−6.83856	−	12.1576i	−0.227573	−	0.404579i
$904$	−32.1127	+	12.6033i	−1.06805	+	0.419179i
$905$	48.7330	−	7.34532i	1.61994	−	0.244167i
$906$	0.406504	+	6.38440i	0.0135052	+	0.212107i
$907$	−12.0793	+	14.0364i	−0.401086	+	0.466070i	−0.921803	−	0.387659i	$-0.873284\pi$
$907$	−12.0793	+	14.0364i	−0.401086	+	0.466070i	0.520717	+	0.853729i	$0.325665\pi$
$908$	21.2653	+	10.2408i	0.705715	+	0.339854i
$909$	31.2303	−	0.467599i	1.03584	−	0.0155093i
$910$	1.29177	−	3.69167i	0.0428218	−	0.122378i
$911$	30.1812	+	8.08704i	0.999949	+	0.267936i	0.721424	−	0.692493i	$-0.243488\pi$
$911$	30.1812	+	8.08704i	0.999949	+	0.267936i	0.278525	+	0.960429i	$0.410154\pi$
$912$	1.09282	+	5.04824i	0.0361867	+	0.167164i
$913$	−0.587615	+	0.796190i	−0.0194472	+	0.0263500i
$914$	3.62272	−	4.90862i	0.119829	−	0.162363i
$915$	12.5080	+	4.01237i	0.413502	+	0.132645i
$916$	−31.8495	−	8.53405i	−1.05234	−	0.281973i
$917$	2.75564	−	7.87518i	0.0909994	−	0.260061i
$918$	20.1083	−	21.8355i	0.663671	−	0.720680i
$919$	−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	$0.692836\pi$
$920$	−10.5463	+	12.2550i	−0.347701	+	0.404036i
$921$	−20.9160	+	13.9193i	−0.689206	+	0.458657i
$922$	4.32773	−	0.652300i	0.142526	−	0.0214823i
$923$	3.79228	−	1.48836i	0.124824	−	0.0489899i
$924$	0.130328	+	0.00146158i	0.00428748	+	4.80826e-5i
$925$	−18.3315	−	9.68847i	−0.602735	−	0.318555i
$926$	−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	−0.845856	−	0.533411i	$-0.820910\pi$
$929$	−24.5920	+	14.1982i	−0.806837	+	0.465827i	0.0390196	+	0.999238i	$0.487577\pi$
$930$	−17.4883	+	7.39776i	−0.573465	+	0.242582i
$931$	−18.6765	+	0.698824i	−0.612096	+	0.0229030i
$932$	−5.62318	−	1.73452i	−0.184193	−	0.0568161i
$933$	42.1715	+	17.0993i	1.38063	+	0.559805i
$934$	−17.0554	−	6.69377i	−0.558071	−	0.219027i
$935$	−1.50966	−	0.344570i	−0.0493712	−	0.0112686i
$936$	13.6997	+	1.85559i	0.447788	+	0.0606517i
$937$	−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	$0.744014\pi$
$938$	0.130726	−	3.49373i	0.00426837	−	0.114074i
$939$	32.0220	−	49.7162i	1.04500	−	1.62243i
$940$	−22.7501	+	6.09588i	−0.742028	+	0.198826i
$941$	−0.499197	+	6.66132i	−0.0162733	+	0.217153i	0.983139	+	0.182862i	$0.0585362\pi$
$941$	−0.499197	+	6.66132i	−0.0162733	+	0.217153i	−0.999412	+	0.0342906i	$0.989083\pi$
$942$	−11.4364	−	13.5947i	−0.372617	−	0.442940i
$943$	17.4504	−	7.61353i	0.568263	−	0.247931i
$944$	−1.83929	−	3.81932i	−0.0598636	−	0.124308i
$945$	1.19358	+	15.1625i	0.0388271	+	0.493235i
$946$	0.388047	+	0.135784i	0.0126165	+	0.00441471i
$947$	−7.16926	−	0.268255i	−0.232970	−	0.00871711i	−0.0793485	−	0.996847i	$-0.525284\pi$
$947$	−7.16926	−	0.268255i	−0.232970	−	0.00871711i	−0.153621	+	0.988130i	$0.549094\pi$
$948$	30.1773	−	11.4549i	0.980115	−	0.372038i
$949$	4.12546	−	21.8036i	0.133918	−	0.707774i
$950$	−10.3295	−	9.58438i	−0.335133	−	0.310958i
$951$	30.3863	−	14.2157i	0.985344	−	0.460977i
$952$	−16.9325	−	2.55217i	−0.548786	−	0.0827162i
$953$	29.6114	−	6.75861i	0.959208	−	0.218933i	0.285871	−	0.958268i	$-0.407717\pi$
$953$	29.6114	−	6.75861i	0.959208	−	0.218933i	0.673337	+	0.739335i	$0.264860\pi$
$954$	−0.460889	+	0.994878i	−0.0149218	+	0.0322104i
$955$	88.9921	−	10.0270i	2.87972	−	0.324466i
$956$	19.9363	+	34.5308i	0.644787	+	1.11680i
$957$	−0.521236	+	0.197518i	−0.0168492	+	0.00638486i
$958$	−11.8016	+	20.4410i	−0.381293	+	0.660420i
$959$	3.21824	−	7.37628i	0.103922	−	0.238193i
$960$	−10.3272	−	9.09081i	−0.333308	−	0.293405i
$961$	−8.00928	−	8.63195i	−0.258364	−	0.278450i
$962$	−2.72407	+	3.41587i	−0.0878275	+	0.110132i
$963$	−0.193432	+	0.171569i	−0.00623327	+	0.00552873i
$964$	1.85691	−	8.13564i	0.0598069	−	0.262031i
$965$	−62.0208	−	53.3732i	−1.99652	−	1.71814i
$966$	−1.32494	+	1.62372i	−0.0426291	+	0.0522425i
$967$	−8.84658	−	16.7386i	−0.284487	−	0.538276i	0.699911	−	0.714230i	$-0.253223\pi$
$967$	−8.84658	−	16.7386i	−0.284487	−	0.538276i	−0.984398	+	0.175954i	$0.943699\pi$
$968$	21.3423	−	18.3665i	0.685966	−	0.590321i
$969$	−1.04433	−	39.8725i	−0.0335486	−	1.28089i
$970$	−7.82411	+	11.4759i	−0.251217	+	0.368468i
$971$	−1.97299	+	17.5108i	−0.0633162	+	0.561947i	0.921504	+	0.388369i	$0.126961\pi$
$971$	−1.97299	+	17.5108i	−0.0633162	+	0.561947i	−0.984820	+	0.173578i	$0.944467\pi$
$972$	−21.7010	+	6.25263i	−0.696060	+	0.200553i
$973$	12.2795	−	5.91351i	0.393663	−	0.189578i
$974$	3.09177	−	11.5387i	0.0990669	−	0.369723i
$975$	17.5786	−	9.03985i	0.562966	−	0.289507i
$976$	1.98382	−	1.04848i	0.0635005	−	0.0335610i
$977$	−19.9124	−	29.2061i	−0.637053	−	0.934385i	−0.999997	−	0.00257402i	$-0.999181\pi$
$977$	−19.9124	−	29.2061i	−0.637053	−	0.934385i	0.362944	−	0.931811i	$-0.381772\pi$
$978$	−2.60834	−	25.7410i	−0.0834055	−	0.823106i
$979$	−0.148408	−	0.481127i	−0.00474314	−	0.0153769i
$980$	−23.8199	+	18.9957i	−0.760898	+	0.606796i
$981$	−31.7667	−	22.7182i	−1.01423	−	0.725338i
$982$	0.447255	+	1.95955i	0.0142725	+	0.0625318i
$983$	−7.30440	+	13.8206i	−0.232974	+	0.440809i	−0.972689	−	0.232112i	$-0.925437\pi$
$983$	−7.30440	+	13.8206i	−0.232974	+	0.440809i	0.739715	+	0.672920i	$0.234960\pi$
$984$	17.5449	+	41.4762i	0.559311	+	1.32221i
$985$	−45.3157	−	26.1630i	−1.44388	−	0.833624i
$986$	29.9962	−	6.82867i	0.955273	−	0.217469i
$987$	−6.96806	+	2.06408i	−0.221796	+	0.0657003i
$988$	6.27871	−	4.63390i	0.199752	−	0.147424i
$989$	14.7102	−	9.24302i	0.467756	−	0.293911i
$990$	−0.321682	−	0.312192i	−0.0102237	−	0.00992210i
$991$	−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	$0.813572\pi$
$992$	−9.38841	+	23.9213i	−0.298082	+	0.759502i
$993$	24.8382	−	50.1311i	0.788218	−	1.59086i
$994$	−1.43530	−	0.271573i	−0.0455249	−	0.00861378i
$995$	44.7003	−	30.4761i	1.41709	−	0.966158i
$996$	−40.2532	+	10.3034i	−1.27547	+	0.326477i
$997$	9.99866	−	1.89185i	0.316661	−	0.0599154i	−0.0251517	−	0.999684i	$-0.508007\pi$
$997$	9.99866	−	1.89185i	0.316661	−	0.0599154i	0.341812	+	0.939768i	$0.388959\pi$
$998$	−4.27891	+	4.27891i	−0.135447	+	0.135447i
$999$	4.33567	−	16.4276i	0.137174	−	0.519746i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.18	✓	672	1.1	even	1	trivial
261.2.x.a.56.18	yes	672	261.56	even	84	inner
261.2.x.a.101.11	yes	672	9.2	odd	6	inner
261.2.x.a.230.11	yes	672	29.27	odd	28	inner
783.2.be.a.143.11		672	261.259	odd	84
783.2.be.a.449.11		672	3.2	odd	2
783.2.be.a.665.18		672	87.56	even	28
783.2.be.a.710.18		672	9.7	even	3

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+(0.440888 + 0.597382i) q^{2} +(-1.69814 - 0.341073i) q^{3} +(0.427027 - 1.38439i) q^{4} +(1.23035 + 3.13488i) q^{5} +(-0.544938 - 1.16481i) q^{6} +(-0.830544 + 0.256189i) q^{7} +(2.41687 - 0.845700i) q^{8} +(2.76734 + 1.15838i) q^{9} +(-1.33028 + 2.11712i) q^{10} +(0.0111101 + 0.0587183i) q^{11} +(-1.19733 + 2.20523i) q^{12} +(1.79467 + 0.134492i) q^{13} +(-0.519220 - 0.383202i) q^{14} +(-1.02008 - 5.74310i) q^{15} +(-0.823252 - 0.561284i) q^{16} +(5.44064 + 5.44064i) q^{17} +(0.528094 + 2.16387i) q^{18} +(2.53419 + 1.59233i) q^{19} +(4.86529 - 0.364603i) q^{20} +(1.49776 - 0.151768i) q^{21} +(-0.0301790 + 0.0325252i) q^{22} +(0.279450 + 1.85403i) q^{23} +(-4.39263 + 0.611786i) q^{24} +(-4.64846 + 4.31314i) q^{25} +(0.710907 + 1.13140i) q^{26} +(-4.30423 - 2.91095i) q^{27} +1.25920i q^{28} +(-1.96460 - 5.01401i) q^{29} +(2.98108 - 3.14144i) q^{30} +(-4.01875 - 1.75336i) q^{31} +(-0.219146 - 5.85681i) q^{32} +(0.00116073 - 0.103501i) q^{33} +(-0.851428 + 5.64886i) q^{34} +(-1.82498 - 2.28846i) q^{35} +(2.78537 - 3.33641i) q^{36} +(1.07993 + 3.08626i) q^{37} +(0.166060 + 2.21592i) q^{38} +(-3.00173 - 0.840500i) q^{39} +(5.62477 + 6.53610i) q^{40} +(-2.62812 - 9.80827i) q^{41} +(0.751007 + 0.827821i) q^{42} +(-3.70531 - 8.49265i) q^{43} +(0.0860332 + 0.00969361i) q^{44} +(-0.226576 + 10.1005i) q^{45} +(-0.984358 + 0.984358i) q^{46} +(-4.74327 + 0.897475i) q^{47} +(1.20656 + 1.23393i) q^{48} +(-5.15950 + 3.51769i) q^{49} +(-4.62605 - 0.875296i) q^{50} +(-7.38330 - 11.0946i) q^{51} +(0.952563 - 2.42709i) q^{52} +(0.384864 + 0.306918i) q^{53} +(-0.158737 - 3.85467i) q^{54} +(-0.170406 + 0.107073i) q^{55} +(-1.79066 + 1.32157i) q^{56} +(-3.76029 - 3.56834i) q^{57} +(2.12911 - 3.38424i) q^{58} +(3.68450 + 2.12725i) q^{59} +(-8.38628 - 1.04027i) q^{60} +(-1.05228 + 1.99102i) q^{61} +(-0.724392 - 3.17377i) q^{62} +(-2.59516 - 0.253121i) q^{63} +(1.84412 - 1.47064i) q^{64} +(1.78646 + 5.79156i) q^{65} +(0.0623414 - 0.0449390i) q^{66} +(3.05194 + 4.47638i) q^{67} +(9.85526 - 5.20865i) q^{68} +(0.157814 - 3.24371i) q^{69} +(0.562470 - 2.09917i) q^{70} +(2.03947 - 0.982158i) q^{71} +(7.66795 + 0.459308i) q^{72} +(1.38053 - 12.2525i) q^{73} +(-1.36755 + 2.00583i) q^{74} +(9.36482 - 5.73885i) q^{75} +(3.28657 - 2.82833i) q^{76} +(-0.0242704 - 0.0459219i) q^{77} +(-0.821327 - 2.16375i) q^{78} +(-9.75009 - 8.39063i) q^{79} +(0.746670 - 3.27137i) q^{80} +(6.31633 + 6.41124i) q^{81} +(4.70058 - 5.89434i) q^{82} +(11.2628 + 12.1384i) q^{83} +(0.429477 - 2.13829i) q^{84} +(-10.3619 + 23.7497i) q^{85} +(3.43973 - 5.95779i) q^{86} +(1.62602 + 9.18456i) q^{87} +(0.0765098 + 0.132519i) q^{88} +(-8.37231 + 0.943332i) q^{89} +(-6.13375 + 4.31784i) q^{90} +(-1.52501 + 0.348074i) q^{91} +(2.68603 + 0.404854i) q^{92} +(6.22637 + 4.34814i) q^{93} +(-2.62739 - 2.43786i) q^{94} +(-1.87384 + 9.90350i) q^{95} +(-1.62546 + 10.0204i) q^{96} +(5.55101 + 0.207704i) q^{97} +(-4.37617 - 1.53129i) q^{98} +(-0.0372724 + 0.175363i) 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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