LMFDB - Embedded newform 205.2.y.a.112.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [205,2,Mod(7,205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("205.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(205, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([10, 39])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 205 = 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	205.y (of order $40$, degree $16$, 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:	$1.63693324144$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$19$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			112.2
Character	$\chi$	$=$	205.112
Dual form			205.2.y.a.108.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10435 - 1.52890i) q^{2} +(-0.747373 - 1.80432i) q^{3} +(1.47272 + 4.53255i) q^{4} +(2.11855 + 0.715379i) q^{5} +(-1.18589 + 4.93957i) q^{6} +(1.94149 - 3.16823i) q^{7} +(2.22313 - 6.84209i) q^{8} +(-0.575677 + 0.575677i) q^{9} +(-3.36441 - 4.74445i) q^{10} +(3.21770 - 3.76745i) q^{11} +(7.07750 - 6.04476i) q^{12} +(-1.20276 + 5.00984i) q^{13} +(-8.92948 + 3.69871i) q^{14} +(-0.292573 - 4.35718i) q^{15} +(-7.42785 + 5.39665i) q^{16} +(0.576370 + 0.492267i) q^{17} +(2.09158 - 0.331273i) q^{18} +(-1.90588 + 3.11011i) q^{19} +(-0.122478 + 10.6560i) q^{20} +(-7.16751 - 1.13522i) q^{21} +(-12.5312 + 3.00848i) q^{22} +(-0.598816 - 3.78077i) q^{23} +(-14.0068 + 1.10236i) q^{24} +(3.97647 + 3.03112i) q^{25} +(10.1906 - 8.70356i) q^{26} +(-3.94400 - 1.63366i) q^{27} +(17.2194 + 4.13402i) q^{28} +(0.227041 - 2.88483i) q^{29} +(-6.04602 + 9.61634i) q^{30} +(-2.23568 - 0.726417i) q^{31} +9.49331 q^{32} +(-9.20250 - 2.99007i) q^{33} +(-0.460258 - 1.91711i) q^{34} +(6.37963 - 5.32313i) q^{35} +(-3.45709 - 1.76148i) q^{36} +(-1.20130 + 2.35768i) q^{37} +(8.76567 - 3.63086i) q^{38} +(9.93826 - 1.57407i) q^{39} +(9.60448 - 12.9049i) q^{40} +(-1.17022 - 6.29528i) q^{41} +(13.3473 + 13.3473i) q^{42} +(-2.41665 + 3.32623i) q^{43} +(21.8149 + 9.03604i) q^{44} +(-1.63142 + 0.807770i) q^{45} +(-4.52030 + 8.87159i) q^{46} +(-3.38048 + 2.07156i) q^{47} +(15.2886 + 9.36889i) q^{48} +(-3.09035 - 6.06515i) q^{49} +(-3.73359 - 12.4582i) q^{50} +(0.457442 - 1.40786i) q^{51} +(-24.4787 + 1.92652i) q^{52} +(2.36792 + 2.77248i) q^{53} +(5.80186 + 9.46777i) q^{54} +(9.51200 - 5.67963i) q^{55} +(-17.3611 - 20.3273i) q^{56} +(7.03603 + 1.11440i) q^{57} +(-4.88838 + 5.72356i) q^{58} +(-6.59416 + 9.07609i) q^{59} +(19.3183 - 7.74300i) q^{60} +(0.774296 - 4.88871i) q^{61} +(3.59404 + 4.94677i) q^{62} +(0.706203 + 2.94155i) q^{63} +(-5.12153 - 3.72101i) q^{64} +(-6.13203 + 9.75315i) q^{65} +(14.7937 + 20.3618i) q^{66} +(15.2367 + 1.19915i) q^{67} +(-1.38240 + 3.33740i) q^{68} +(-6.37418 + 3.90610i) q^{69} +(-21.5635 + 1.44793i) q^{70} +(10.1468 + 8.66618i) q^{71} +(2.65903 + 5.21863i) q^{72} -3.64388i q^{73} +(6.13259 - 3.12471i) q^{74} +(2.49721 - 9.44019i) q^{75} +(-16.9036 - 4.05819i) q^{76} +(-5.68899 - 17.5089i) q^{77} +(-23.3201 - 11.8822i) q^{78} +(0.896947 - 2.16542i) q^{79} +(-19.5969 + 6.11932i) q^{80} +10.7796i q^{81} +(-7.16229 + 15.0366i) q^{82} +(2.09482 - 2.09482i) q^{83} +(-5.41026 - 34.1590i) q^{84} +(0.868909 + 1.45521i) q^{85} +(10.1709 - 3.30474i) q^{86} +(-5.37483 + 1.74639i) q^{87} +(-18.6238 - 30.3913i) q^{88} +(-5.77183 + 1.38569i) q^{89} +(4.66808 + 0.794452i) q^{90} +(13.5372 + 13.5372i) q^{91} +(16.2547 - 8.28217i) q^{92} +(0.360201 + 4.57679i) q^{93} +(10.2809 + 0.809125i) q^{94} +(-6.26260 + 5.22548i) q^{95} +(-7.09504 - 17.1289i) q^{96} +(-0.0502119 + 0.638003i) q^{97} +(-2.76983 + 17.4880i) q^{98} +(0.316474 + 4.02119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) $ 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/205\mathbb{Z}\right)^\times$.

$n$	$6$	$42$
$\chi(n)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−2.10435	−	1.52890i	−1.48800	−	1.08109i	−0.974868	−	0.222784i	$-0.928486\pi$
$2$	−2.10435	−	1.52890i	−1.48800	−	1.08109i	−0.513131	−	0.858310i	$-0.671514\pi$
$3$	−0.747373	−	1.80432i	−0.431496	−	1.04172i	−0.978805	−	0.204793i	$-0.934348\pi$
$3$	−0.747373	−	1.80432i	−0.431496	−	1.04172i	0.547309	−	0.836930i	$-0.315652\pi$
$4$	1.47272	+	4.53255i	0.736358	+	2.26628i
$5$	2.11855	+	0.715379i	0.947442	+	0.319927i
$5$	2.11855	+	0.715379i	0.947442	+	0.319927i
$6$	−1.18589	+	4.93957i	−0.484136	+	2.01657i
$7$	1.94149	−	3.16823i	0.733816	−	1.19748i	−0.240140	−	0.970738i	$-0.577193\pi$
$7$	1.94149	−	3.16823i	0.733816	−	1.19748i	0.973955	−	0.226740i	$-0.0728068\pi$
$8$	2.22313	−	6.84209i	0.785995	−	2.41904i
$9$	−0.575677	+	0.575677i	−0.191892	+	0.191892i
$10$	−3.36441	−	4.74445i	−1.06392	−	1.50033i
$11$	3.21770	−	3.76745i	0.970174	−	1.13593i	−0.0205156	−	0.999790i	$-0.506531\pi$
$11$	3.21770	−	3.76745i	0.970174	−	1.13593i	0.990690	−	0.136139i	$-0.0434692\pi$
$12$	7.07750	−	6.04476i	2.04310	−	1.74497i
$13$	−1.20276	+	5.00984i	−0.333585	+	1.38948i	0.513531	+	0.858071i	$0.328337\pi$
$13$	−1.20276	+	5.00984i	−0.333585	+	1.38948i	−0.847115	+	0.531409i	$0.821663\pi$
$14$	−8.92948	+	3.69871i	−2.38650	+	0.988522i
$15$	−0.292573	−	4.35718i	−0.0755419	−	1.12502i
$16$	−7.42785	+	5.39665i	−1.85696	+	1.34916i
$17$	0.576370	+	0.492267i	0.139790	+	0.119392i	0.716594	−	0.697491i	$-0.245700\pi$
$17$	0.576370	+	0.492267i	0.139790	+	0.119392i	−0.576804	+	0.816883i	$0.695700\pi$
$18$	2.09158	−	0.331273i	0.492989	−	0.0780818i
$19$	−1.90588	+	3.11011i	−0.437238	+	0.713508i	−0.993036	−	0.117809i	$-0.962413\pi$
$19$	−1.90588	+	3.11011i	−0.437238	+	0.713508i	0.555798	+	0.831317i	$0.312413\pi$
$20$	−0.122478	+	10.6560i	−0.0273868	+	2.38275i
$21$	−7.16751	−	1.13522i	−1.56408	−	0.247726i
$22$	−12.5312	+	3.00848i	−2.67166	+	0.641410i
$23$	−0.598816	−	3.78077i	−0.124862	−	0.788346i	−0.968055	−	0.250736i	$-0.919327\pi$
$23$	−0.598816	−	3.78077i	−0.124862	−	0.788346i	0.843194	−	0.537610i	$-0.180673\pi$
$24$	−14.0068	+	1.10236i	−2.85913	+	0.225018i
$25$	3.97647	+	3.03112i	0.795293	+	0.606225i
$26$	10.1906	−	8.70356i	1.99853	−	1.70691i
$27$	−3.94400	−	1.63366i	−0.759024	−	0.314398i
$28$	17.2194	+	4.13402i	3.25417	+	0.781257i
$29$	0.227041	−	2.88483i	0.0421604	−	0.535699i	−0.939181	−	0.343424i	$-0.888413\pi$
$29$	0.227041	−	2.88483i	0.0421604	−	0.535699i	0.981341	−	0.192275i	$-0.0615867\pi$
$30$	−6.04602	+	9.61634i	−1.10385	+	1.75570i
$31$	−2.23568	−	0.726417i	−0.401540	−	0.130468i	0.101283	−	0.994858i	$-0.467705\pi$
$31$	−2.23568	−	0.726417i	−0.401540	−	0.130468i	−0.502823	+	0.864389i	$0.667705\pi$
$32$	9.49331			1.67820
$33$	−9.20250	−	2.99007i	−1.60195	−	0.520505i
$34$	−0.460258	−	1.91711i	−0.0789336	−	0.328782i
$35$	6.37963	−	5.32313i	1.07835	−	0.899774i
$36$	−3.45709	−	1.76148i	−0.576182	−	0.293580i
$37$	−1.20130	+	2.35768i	−0.197492	+	0.387600i	−0.968421	−	0.249322i	$-0.919792\pi$
$37$	−1.20130	+	2.35768i	−0.197492	+	0.387600i	0.770929	+	0.636921i	$0.219792\pi$
$38$	8.76567	−	3.63086i	1.42198	−	0.589003i
$39$	9.93826	−	1.57407i	1.59139	−	0.252052i
$40$	9.60448	−	12.9049i	1.51860	−	2.04044i
$41$	−1.17022	−	6.29528i	−0.182758	−	0.983158i
$41$	−1.17022	−	6.29528i	−0.182758	−	0.983158i
$42$	13.3473	+	13.3473i	2.05953	+	2.05953i
$43$	−2.41665	+	3.32623i	−0.368535	+	0.507246i	−0.952502	−	0.304532i	$-0.901500\pi$
$43$	−2.41665	+	3.32623i	−0.368535	+	0.507246i	0.583967	+	0.811778i	$0.301500\pi$
$44$	21.8149	+	9.03604i	3.28872	+	1.36223i
$45$	−1.63142	+	0.807770i	−0.243198	+	0.120415i
$46$	−4.52030	+	8.87159i	−0.666482	+	1.30805i
$47$	−3.38048	+	2.07156i	−0.493094	+	0.302168i	−0.746725	−	0.665133i	$-0.768375\pi$
$47$	−3.38048	+	2.07156i	−0.493094	+	0.302168i	0.253631	+	0.967301i	$0.418375\pi$
$48$	15.2886	+	9.36889i	2.20673	+	1.35228i
$49$	−3.09035	−	6.06515i	−0.441479	−	0.866450i
$50$	−3.73359	−	12.4582i	−0.528009	−	1.76185i
$51$	0.457442	−	1.40786i	0.0640547	−	0.197140i
$52$	−24.4787	+	1.92652i	−3.39459	+	0.267160i
$53$	2.36792	+	2.77248i	0.325259	+	0.380829i	0.898808	−	0.438342i	$-0.144434\pi$
$53$	2.36792	+	2.77248i	0.325259	+	0.380829i	−0.573550	+	0.819171i	$0.694434\pi$
$54$	5.80186	+	9.46777i	0.789533	+	1.28840i
$55$	9.51200	−	5.67963i	1.28260	−	0.765841i
$56$	−17.3611	−	20.3273i	−2.31998	−	2.71634i
$57$	7.03603	+	1.11440i	0.931945	+	0.147606i
$58$	−4.88838	+	5.72356i	−0.641876	+	0.751540i
$59$	−6.59416	+	9.07609i	−0.858487	+	1.18161i	0.123441	+	0.992352i	$0.460607\pi$
$59$	−6.59416	+	9.07609i	−0.858487	+	1.18161i	−0.981928	+	0.189254i	$0.939393\pi$
$60$	19.3183	−	7.74300i	2.49398	−	0.999617i
$61$	0.774296	−	4.88871i	0.0991385	−	0.625936i	−0.887223	−	0.461341i	$-0.847368\pi$
$61$	0.774296	−	4.88871i	0.0991385	−	0.625936i	0.986361	−	0.164594i	$-0.0526315\pi$
$62$	3.59404	+	4.94677i	0.456443	+	0.628240i
$63$	0.706203	+	2.94155i	0.0889733	+	0.370600i
$64$	−5.12153	−	3.72101i	−0.640191	−	0.465126i
$65$	−6.13203	+	9.75315i	−0.760585	+	1.20973i
$66$	14.7937	+	20.3618i	1.82098	+	2.50637i
$67$	15.2367	+	1.19915i	1.86146	+	0.146500i	0.958840	−	0.283946i	$-0.0916436\pi$
$67$	15.2367	+	1.19915i	1.86146	+	0.146500i	0.902616	+	0.430446i	$0.141644\pi$
$68$	−1.38240	+	3.33740i	−0.167640	+	0.404719i
$69$	−6.37418	+	3.90610i	−0.767361	+	0.470240i
$70$	−21.5635	+	1.44793i	−2.57733	+	0.173060i
$71$	10.1468	+	8.66618i	1.20420	+	1.02849i	0.998758	+	0.0498171i	$0.0158639\pi$
$71$	10.1468	+	8.66618i	1.20420	+	1.02849i	0.205444	+	0.978669i	$0.434136\pi$
$72$	2.65903	+	5.21863i	0.313369	+	0.615022i
$73$		−	3.64388i		−	0.426484i	−0.976999	−	0.213242i	$-0.931598\pi$
$73$		−	3.64388i		−	0.426484i	0.976999	−	0.213242i	$-0.0684023\pi$
$74$	6.13259	−	3.12471i	0.712899	−	0.363240i
$75$	2.49721	−	9.44019i	0.288353	−	1.09006i
$76$	−16.9036	−	4.05819i	−1.93897	−	0.465506i
$77$	−5.68899	−	17.5089i	−0.648320	−	1.99532i
$78$	−23.3201	−	11.8822i	−2.64049	−	1.34539i
$79$	0.896947	−	2.16542i	0.100914	−	0.243629i	−0.865356	−	0.501157i	$-0.832908\pi$
$79$	0.896947	−	2.16542i	0.100914	−	0.243629i	0.966271	+	0.257528i	$0.0829080\pi$
$80$	−19.5969	+	6.11932i	−2.19100	+	0.684160i
$81$			10.7796i			1.19773i
$82$	−7.16229	+	15.0366i	−0.790943	+	1.66052i
$83$	2.09482	−	2.09482i	0.229936	−	0.229936i	−0.582730	−	0.812666i	$-0.698015\pi$
$83$	2.09482	−	2.09482i	0.229936	−	0.229936i	0.812666	+	0.582730i	$0.198015\pi$
$84$	−5.41026	−	34.1590i	−0.590307	−	3.72705i
$85$	0.868909	+	1.45521i	0.0942464	+	0.157840i
$86$	10.1709	−	3.30474i	1.09676	−	0.356359i
$87$	−5.37483	+	1.74639i	−0.576242	+	0.187232i
$88$	−18.6238	−	30.3913i	−1.98531	−	3.23973i
$89$	−5.77183	+	1.38569i	−0.611813	+	0.146883i	−0.527499	−	0.849556i	$-0.676870\pi$
$89$	−5.77183	+	1.38569i	−0.611813	+	0.146883i	−0.0843145	+	0.996439i	$0.526870\pi$
$90$	4.66808	+	0.794452i	0.492059	+	0.0837426i
$91$	13.5372	+	13.5372i	1.41908	+	1.41908i
$92$	16.2547	−	8.28217i	1.69467	−	0.863476i
$93$	0.360201	+	4.57679i	0.0373511	+	0.474591i
$94$	10.2809	+	0.809125i	1.06040	+	0.0834549i
$95$	−6.26260	+	5.22548i	−0.642529	+	0.536123i
$96$	−7.09504	−	17.1289i	−0.724135	−	1.74822i
$97$	−0.0502119	+	0.638003i	−0.00509825	+	0.0647794i	−0.998940	−	0.0460280i	$-0.985344\pi$
$97$	−0.0502119	+	0.638003i	−0.00509825	+	0.0647794i	0.993842	+	0.110807i	$0.0353437\pi$
$98$	−2.76983	+	17.4880i	−0.279795	+	1.76656i
$99$	0.316474	+	4.02119i	0.0318069	+	0.404145i
$100$	−7.88253	+	22.4875i	−0.788253	+	2.24875i
$101$	0.150289	+	0.0920972i	0.0149543	+	0.00916401i	0.529956	−	0.848025i	$-0.322209\pi$
$101$	0.150289	+	0.0920972i	0.0149543	+	0.00916401i	−0.515001	+	0.857189i	$0.672209\pi$
$102$	−3.11509	+	2.26325i	−0.308440	+	0.224095i
$103$	−1.75773	+	1.27707i	−0.173195	+	0.125833i	−0.671006	−	0.741452i	$-0.734137\pi$
$103$	−1.75773	+	1.27707i	−0.173195	+	0.125833i	0.497811	+	0.867286i	$0.334137\pi$
$104$	31.6039	+	19.3669i	3.09902	+	1.89908i
$105$	−14.3726	−	7.53251i	−1.40262	−	0.735098i
$106$	−0.744091	−	9.45457i	−0.0722725	−	0.918309i
$107$	0.744332	−	4.69952i	0.0719573	−	0.454320i	−0.925232	−	0.379401i	$-0.876130\pi$
$107$	0.744332	−	4.69952i	0.0719573	−	0.454320i	0.997190	−	0.0749193i	$-0.0238699\pi$
$108$	1.59625	−	20.2823i	0.153600	−	1.95167i
$109$	3.51381	+	8.48308i	0.336562	+	0.812532i	0.998041	+	0.0625681i	$0.0199290\pi$
$109$	3.51381	+	8.48308i	0.336562	+	0.812532i	−0.661479	+	0.749964i	$0.730071\pi$
$110$	−28.7001	−	2.59097i	−2.73645	−	0.247039i
$111$	5.15182	+	0.405457i	0.488989	+	0.0384842i
$112$	2.67670	+	34.0107i	0.252924	+	3.21371i
$113$	0.0374005	−	0.0190565i	0.00351834	−	0.00179268i	−0.452230	−	0.891901i	$-0.649372\pi$
$113$	0.0374005	−	0.0190565i	0.00351834	−	0.00179268i	0.455749	+	0.890108i	$0.349372\pi$
$114$	−13.1025	−	13.1025i	−1.22716	−	1.22716i
$115$	1.43607	−	8.43812i	0.133914	−	0.786859i
$116$	13.4100	−	3.21946i	1.24509	−	0.298919i
$117$	−2.19165	−	3.57645i	−0.202618	−	0.330643i
$118$	27.7528	−	9.01744i	2.55486	−	0.830123i
$119$	2.67863	−	0.870341i	0.245550	−	0.0797840i
$120$	−30.4627	−	7.68477i	−2.78085	−	0.701521i
$121$	−2.11926	−	13.3805i	−0.192660	−	1.21641i
$122$	−9.10373	+	9.10373i	−0.824213	+	0.824213i
$123$	−10.4841	+	6.81638i	−0.945319	+	0.614612i
$124$		−	11.2032i		−	1.00607i
$125$	6.25592	+	9.26625i	0.559547	+	0.828799i
$126$	3.01123	−	7.26976i	0.268262	−	0.647641i
$127$	−0.548188	−	0.279316i	−0.0486438	−	0.0247853i	0.429499	−	0.903067i	$-0.358690\pi$
$127$	−0.548188	−	0.279316i	−0.0486438	−	0.0247853i	−0.478143	+	0.878282i	$0.658690\pi$
$128$	−0.778751	−	2.39675i	−0.0688325	−	0.211845i
$129$	7.80772	+	1.87447i	0.687431	+	0.165038i
$130$	27.8155	−	11.1488i	2.43958	−	0.977812i
$131$	−15.1282	+	7.70819i	−1.32176	+	0.673468i	−0.965373	−	0.260872i	$-0.915990\pi$
$131$	−15.1282	+	7.70819i	−1.32176	+	0.673468i	−0.356382	+	0.934340i	$0.615990\pi$
$132$		−	46.1144i		−	4.01374i
$133$	6.15329	+	12.0765i	0.533558	+	1.04717i
$134$	−30.2299	−	25.8188i	−2.61147	−	2.23040i
$135$	−7.18687	−	6.28244i	−0.618547	−	0.540706i
$136$	4.64948	−	2.84920i	0.398689	−	0.244317i
$137$	−7.19671	+	17.3744i	−0.614856	+	1.48439i	0.242751	+	0.970089i	$0.421950\pi$
$137$	−7.19671	+	17.3744i	−0.614856	+	1.48439i	−0.857607	+	0.514305i	$0.828050\pi$
$138$	19.3855	+	1.52567i	1.65021	+	0.129874i
$139$	−11.7822	−	16.2168i	−0.999353	−	1.37549i	−0.925721	−	0.378206i	$-0.876541\pi$
$139$	−11.7822	−	16.2168i	−0.999353	−	1.37549i	−0.0736318	−	0.997285i	$-0.523459\pi$
$140$	33.5228	+	21.0765i	2.83319	+	1.78129i
$141$	6.26424	+	4.55123i	0.527544	+	0.383283i
$142$	−8.10267	−	33.7501i	−0.679961	−	2.83224i
$143$	15.0042	+	20.6515i	1.25471	+	1.72697i
$144$	1.16931	−	7.38276i	0.0974429	−	0.615230i
$145$	2.54474	−	5.94922i	0.211329	−	0.494055i
$146$	−5.57112	+	7.66799i	−0.461069	+	0.634608i
$147$	−8.63382	+	10.1089i	−0.712105	+	0.833768i
$148$	−12.4555	−	1.97275i	−1.02383	−	0.162159i
$149$	5.16901	+	6.05213i	0.423462	+	0.495810i	0.930591	−	0.366060i	$-0.119293\pi$
$149$	5.16901	+	6.05213i	0.423462	+	0.495810i	−0.507130	+	0.861870i	$0.669293\pi$
$150$	−19.6881	+	16.0475i	−1.60753	+	1.31027i
$151$	4.50666	+	7.35421i	0.366747	+	0.598477i	0.981779	−	0.190025i	$-0.0608569\pi$
$151$	4.50666	+	7.35421i	0.366747	+	0.598477i	−0.615032	+	0.788502i	$0.710857\pi$
$152$	17.0426	+	19.9544i	1.38234	+	1.61851i
$153$	−0.615189	+	0.0484164i	−0.0497351	+	0.00391424i
$154$	−14.7977	+	45.5427i	−1.19243	+	3.66994i
$155$	−4.21673	−	3.13831i	−0.338696	−	0.252075i
$156$	21.7708	+	42.7275i	1.74306	+	3.42094i
$157$	17.8717	+	10.9518i	1.42632	+	0.874049i	0.999541	−	0.0303071i	$-0.00964853\pi$
$157$	17.8717	+	10.9518i	1.42632	+	0.874049i	0.426778	+	0.904356i	$0.359649\pi$
$158$	−5.19820	+	3.18546i	−0.413546	+	0.253421i
$159$	3.23271	−	6.34456i	0.256371	−	0.503156i
$160$	20.1120	+	6.79131i	1.58999	+	0.536900i
$161$	−13.1410	−	5.44316i	−1.03565	−	0.428981i
$162$	16.4809	−	22.6840i	1.29486	−	1.78222i
$163$	3.38791	+	3.38791i	0.265361	+	0.265361i	0.827228	−	0.561867i	$-0.189917\pi$
$163$	3.38791	+	3.38791i	0.265361	+	0.265361i	−0.561867	+	0.827228i	$0.689917\pi$
$164$	26.8103	−	14.5753i	2.09353	−	1.13814i
$165$	−17.3569	−	12.9179i	−1.35123	−	1.00566i
$166$	−7.61098	+	1.20546i	−0.590727	+	0.0935619i
$167$	−5.60015	+	2.31966i	−0.433353	+	0.179501i	−0.588686	−	0.808362i	$-0.700355\pi$
$167$	−5.60015	+	2.31966i	−0.433353	+	0.179501i	0.155334	+	0.987862i	$0.450355\pi$
$168$	−23.7016	+	46.5170i	−1.82862	+	3.58887i
$169$	−12.0688	−	6.14937i	−0.928371	−	0.473029i
$170$	0.396384	−	4.39075i	0.0304013	−	0.336755i
$171$	−0.693248	−	2.88759i	−0.0530140	−	0.220819i
$172$	−18.6354	−	6.05500i	−1.42093	−	0.461689i
$173$	−5.91876			−0.449995			−0.224998	−	0.974359i	$-0.572237\pi$
$173$	−5.91876			−0.449995			−0.224998	+	0.974359i	$0.572237\pi$
$174$	13.9806	+	4.54256i	1.05986	+	0.344371i
$175$	17.3236	−	6.71345i	1.30954	−	0.507489i
$176$	−3.56903	+	45.3488i	−0.269026	+	3.41830i
$177$	21.3045	+	5.11475i	1.60134	+	0.384448i
$178$	14.2645	+	5.90856i	1.06917	+	0.442865i
$179$	10.7805	−	9.20739i	0.805770	−	0.688192i	−0.147915	−	0.989000i	$-0.547256\pi$
$179$	10.7805	−	9.20739i	0.805770	−	0.688192i	0.953685	+	0.300808i	$0.0972562\pi$
$180$	−6.06389	−	6.20490i	−0.451975	−	0.462486i
$181$	16.9733	−	1.33583i	1.26162	−	0.0992915i	0.570054	−	0.821607i	$-0.306922\pi$
$181$	16.9733	−	1.33583i	1.26162	−	0.0992915i	0.691564	+	0.722316i	$0.256922\pi$
$182$	−7.78997	−	49.1839i	−0.577431	−	3.64576i
$183$	−9.39948	+	2.25662i	−0.694830	+	0.166814i
$184$	−27.1996	−	4.30800i	−2.00518	−	0.317590i
$185$	−4.23163	+	4.13546i	−0.311116	+	0.304045i
$186$	6.23945	−	10.1819i	0.457499	−	0.746570i
$187$	3.70918	−	0.587476i	0.271242	−	0.0429605i
$188$	−14.3680	−	12.2714i	−1.04789	−	0.894983i
$189$	−12.8331	+	9.32377i	−0.933469	+	0.678205i
$190$	21.1679	−	1.42137i	1.53568	−	0.103117i
$191$	22.4059	−	9.28082i	1.62123	−	0.671537i	0.627024	−	0.779000i	$-0.284273\pi$
$191$	22.4059	−	9.28082i	1.62123	−	0.671537i	0.994209	+	0.107463i	$0.0342728\pi$
$192$	−2.88619	+	12.0219i	−0.208293	+	0.867602i
$193$	−6.01279	+	5.13541i	−0.432810	+	0.369655i	−0.838998	−	0.544135i	$-0.816858\pi$
$193$	−6.01279	+	5.13541i	−0.432810	+	0.369655i	0.406188	+	0.913790i	$0.366858\pi$
$194$	1.08111	−	1.26581i	0.0776188	−	0.0908800i
$195$	22.1807	+	3.77489i	1.58839	+	0.270326i
$196$	22.9394	−	22.9394i	1.63853	−	1.63853i
$197$	2.33237	−	7.17830i	0.166175	−	0.511433i	−0.832946	−	0.553354i	$-0.813348\pi$
$197$	2.33237	−	7.17830i	0.166175	−	0.511433i	0.999121	+	0.0419209i	$0.0133478\pi$
$198$	5.48202	−	8.94584i	0.389590	−	0.635753i
$199$	−1.25801	+	5.23998i	−0.0891779	+	0.371453i	−0.999057	−	0.0434211i	$-0.986174\pi$
$199$	−1.25801	+	5.23998i	−0.0891779	+	0.371453i	0.909879	+	0.414874i	$0.136174\pi$
$200$	29.5794	−	20.4687i	2.09158	−	1.44736i
$201$	−9.22383	−	28.3880i	−0.650599	−	2.00234i
$202$	−0.175453	−	0.423581i	−0.0123448	−	0.0298031i
$203$	−8.69900	−	6.32019i	−0.610550	−	0.443590i
$204$	7.05489			0.493941
$205$	2.02434	−	14.1740i	0.141386	−	0.989955i
$206$	5.65139			0.393751
$207$	2.52123	+	1.83178i	0.175237	+	0.127317i
$208$	−18.1025	−	43.7032i	−1.25518	−	3.03027i
$209$	5.58462	+	17.1877i	0.386297	+	1.18890i
$210$	18.7285	+	37.8252i	1.29239	+	2.61019i
$211$	−1.55954	+	6.49594i	−0.107363	+	0.447199i	−0.999994	−	0.00358980i	$-0.998857\pi$
$211$	−1.55954	+	6.49594i	−0.107363	+	0.447199i	0.892631	+	0.450789i	$0.148857\pi$
$212$	−9.07913	+	14.8158i	−0.623557	+	1.01755i
$213$	8.05310	−	24.7849i	0.551790	−	1.69823i
$214$	−8.75143	+	8.75143i	−0.598235	+	0.598235i
$215$	−7.49929	+	5.31795i	−0.511448	+	0.362681i
$216$	−19.9457	+	23.3534i	−1.35713	+	1.58900i
$217$	−6.64202	+	5.67282i	−0.450890	+	0.385096i
$218$	5.57549	−	23.2236i	0.377620	−	1.57290i
$219$	−6.57472	+	2.72334i	−0.444278	+	0.184026i
$220$	39.7517	+	34.7492i	2.68006	+	2.34279i
$221$	−3.15941	+	2.29545i	−0.212525	+	0.154408i
$222$	−10.2213	−	8.72982i	−0.686009	−	0.585907i
$223$	−22.8766	+	3.62330i	−1.53193	+	0.242634i	−0.864728	−	0.502241i	$-0.832509\pi$
$223$	−22.8766	+	3.62330i	−1.53193	+	0.242634i	−0.667204	+	0.744875i	$0.732509\pi$
$224$	18.4312	−	30.0770i	1.23149	−	2.00960i
$225$	−4.03411	+	0.544211i	−0.268940	+	0.0362808i
$226$	−0.107839	−	0.0170800i	−0.00717335	−	0.00113615i
$227$	0.377254	−	0.0905707i	0.0250392	−	0.00601139i	−0.220906	−	0.975295i	$-0.570902\pi$
$227$	0.377254	−	0.0905707i	0.0250392	−	0.00601139i	0.245946	+	0.969284i	$0.420902\pi$
$228$	5.31101	+	33.5324i	0.351730	+	2.22074i
$229$	13.3409	−	1.04995i	0.881593	−	0.0693829i	0.370424	−	0.928863i	$-0.379213\pi$
$229$	13.3409	−	1.04995i	0.881593	−	0.0693829i	0.511169	+	0.859480i	$0.329213\pi$
$230$	−15.9230	+	15.5611i	−1.04993	+	1.02607i
$231$	−27.3398	+	23.3504i	−1.79883	+	1.53634i
$232$	−19.2335	−	7.96677i	−1.26274	−	0.523044i
$233$	−5.99384	−	1.43899i	−0.392670	−	0.0942716i	0.0323024	−	0.999478i	$-0.489716\pi$
$233$	−5.99384	−	1.43899i	−0.392670	−	0.0942716i	−0.424972	+	0.905207i	$0.639716\pi$
$234$	−0.856031	+	10.8769i	−0.0559605	+	0.711045i
$235$	−8.64365	+	1.97037i	−0.563850	+	0.128533i
$236$	−50.8492	−	16.5219i	−3.31000	−	1.07548i
$237$	−4.57746			−0.297338
$238$	−6.96744	−	2.26386i	−0.451632	−	0.146744i
$239$	−5.77542	−	24.0564i	−0.373581	−	1.55608i	−0.770023	−	0.638016i	$-0.779755\pi$
$239$	−5.77542	−	24.0564i	−0.373581	−	1.55608i	0.396442	−	0.918060i	$-0.370245\pi$
$240$	25.6874	+	30.7856i	1.65811	+	1.98720i
$241$	−14.3301	−	7.30156i	−0.923084	−	0.470335i	−0.0732075	−	0.997317i	$-0.523324\pi$
$241$	−14.3301	−	7.30156i	−0.923084	−	0.470335i	−0.849876	+	0.526982i	$0.823324\pi$
$242$	−15.9977	+	31.3973i	−1.02837	+	2.01830i
$243$	7.61778	−	3.15539i	0.488681	−	0.202418i
$244$	23.2987	−	3.69015i	1.49154	−	0.236238i
$245$	−2.20816	−	15.0601i	−0.141074	−	0.962153i
$246$	32.4837	+	1.68509i	2.07109	+	0.107437i
$247$	−13.2889	−	13.2889i	−0.845550	−	0.845550i
$248$	−9.94042	+	13.6818i	−0.631217	+	0.868796i
$249$	−5.34532	−	2.21410i	−0.338746	−	0.140313i
$250$	1.00252	−	29.0641i	0.0634052	−	1.83817i
$251$	−6.52197	+	12.8001i	−0.411663	+	0.807934i	−1.00000		0.000681826i	$-0.999783\pi$
$251$	−6.52197	+	12.8001i	−0.411663	+	0.807934i	0.588337	+	0.808616i	$0.299783\pi$
$252$	−12.2927	+	7.53297i	−0.774367	+	0.474533i
$253$	−16.1707	−	9.90941i	−1.01664	−	0.622999i
$254$	0.726533	+	1.42590i	0.0455867	+	0.0894689i
$255$	1.97627	−	2.65537i	0.123759	−	0.166286i
$256$	−5.93812	+	18.2757i	−0.371133	+	1.14223i
$257$	11.7332	−	0.923419i	0.731894	−	0.0576013i	0.292965	−	0.956123i	$-0.405358\pi$
$257$	11.7332	−	0.923419i	0.731894	−	0.0576013i	0.438929	+	0.898522i	$0.355358\pi$
$258$	−13.5643	−	15.8817i	−0.844475	−	0.988754i
$259$	5.13735	+	8.38340i	0.319220	+	0.520919i
$260$	−53.2374	−	13.4301i	−3.30165	−	0.832902i
$261$	1.53003	+	1.79143i	0.0947062	+	0.110887i
$262$	43.6200	+	6.90873i	2.69485	+	0.426823i
$263$	5.79813	−	6.78873i	0.357528	−	0.418611i	−0.552269	−	0.833666i	$-0.686238\pi$
$263$	5.79813	−	6.78873i	0.357528	−	0.418611i	0.909796	+	0.415055i	$0.136238\pi$
$264$	−40.9167	+	56.3170i	−2.51825	+	3.46607i
$265$	3.03317	+	7.56758i	0.186326	+	0.464873i
$266$	5.51510	−	34.8210i	0.338152	−	2.13501i
$267$	6.81395	+	9.37859i	0.417007	+	0.573961i
$268$	17.0041	+	70.8271i	1.03869	+	4.32645i
$269$	0.303360	+	0.220404i	0.0184962	+	0.0134383i	0.596995	−	0.802245i	$-0.296361\pi$
$269$	0.303360	+	0.220404i	0.0184962	+	0.0134383i	−0.578499	+	0.815683i	$0.696361\pi$
$270$	5.51845	+	24.2084i	0.335842	+	1.47328i
$271$	−3.65526	−	5.03103i	−0.222041	−	0.305613i	0.683434	−	0.730012i	$-0.260486\pi$
$271$	−3.65526	−	5.03103i	−0.222041	−	0.305613i	−0.905475	+	0.424399i	$0.860486\pi$
$272$	−6.93778	−	0.546015i	−0.420665	−	0.0331070i
$273$	14.3081	−	34.5427i	0.865964	−	2.09062i
$274$	41.7080	−	25.5587i	2.51967	−	1.54406i
$275$	24.2147	−	5.22787i	1.46020	−	0.315252i
$276$	−27.0920	−	23.1387i	−1.63075	−	1.39279i
$277$	13.0447	+	25.6017i	0.783782	+	1.53826i	0.841705	+	0.539938i	$0.181552\pi$
$277$	13.0447	+	25.6017i	0.783782	+	1.53826i	−0.0579226	+	0.998321i	$0.518448\pi$
$278$			52.1396i			3.12712i
$279$	1.70521	−	0.868849i	0.102088	−	0.0520166i
$280$	−22.2386	−	55.4840i	−1.32901	−	3.31580i
$281$	−20.0207	−	4.80655i	−1.19434	−	0.286735i	−0.412934	−	0.910761i	$-0.635496\pi$
$281$	−20.0207	−	4.80655i	−1.19434	−	0.286735i	−0.781403	+	0.624026i	$0.785496\pi$
$282$	−6.22376	−	19.1548i	−0.370619	−	1.14065i
$283$	17.0913	+	8.70845i	1.01597	+	0.517664i	0.880965	−	0.473181i	$-0.156894\pi$
$283$	17.0913	+	8.70845i	1.01597	+	0.517664i	0.135007	+	0.990845i	$0.456894\pi$
$284$	−24.3366	+	58.7537i	−1.44411	+	3.48639i
$285$	14.1089	+	7.39433i	0.835741	+	0.438002i
$286$		−	66.3979i		−	3.92619i
$287$	−22.2169	−	8.51472i	−1.31142	−	0.502608i
$288$	−5.46508	+	5.46508i	−0.322033	+	0.322033i
$289$	−2.56951	−	16.2232i	−0.151148	−	0.954309i
$290$	−14.4508	+	8.62857i	−0.848578	+	0.506687i
$291$	1.18869	−	0.386228i	0.0696821	−	0.0226411i
$292$	16.5161	−	5.36640i	0.966531	−	0.314045i
$293$	−11.8430	−	19.3261i	−0.691877	−	1.12904i	−0.984932	−	0.172944i	$-0.944672\pi$
$293$	−11.8430	−	19.3261i	−0.691877	−	1.12904i	0.293055	−	0.956096i	$-0.405328\pi$
$294$	33.6240	−	8.07242i	1.96099	−	0.470793i
$295$	−20.4629	+	14.5108i	−1.19139	+	0.844850i
$296$	13.4608	+	13.4608i	0.782393	+	0.782393i
$297$	−18.8454	+	9.60220i	−1.09352	+	0.557176i
$298$	−1.62430	−	20.6387i	−0.0940932	−	1.19557i
$299$	19.6613	+	1.54738i	1.13704	+	0.0894873i
$300$	46.4659	−	2.58399i	2.68271	−	0.149187i
$301$	5.84636	+	14.1144i	0.336978	+	0.813538i
$302$	1.76025	−	22.3660i	0.101291	−	1.28702i
$303$	0.0538507	−	0.340000i	0.00309364	−	0.0195325i
$304$	−2.62760	−	33.3868i	−0.150703	−	1.91486i
$305$	5.13766	−	9.80304i	0.294182	−	0.561321i
$306$	1.36860	+	0.838677i	0.0782374	+	0.0479440i
$307$	8.47024	−	6.15399i	0.483422	−	0.351227i	−0.319227	−	0.947678i	$-0.603423\pi$
$307$	8.47024	−	6.15399i	0.483422	−	0.351227i	0.802649	+	0.596451i	$0.203423\pi$
$308$	70.9818	−	51.5713i	4.04456	−	2.93855i
$309$	3.61792	+	2.21706i	0.205816	+	0.126124i
$310$	4.07531	+	13.0510i	0.231462	+	0.741249i
$311$	−0.920916	−	11.7013i	−0.0522203	−	0.663522i	−0.966205	−	0.257774i	$-0.917011\pi$
$311$	−0.920916	−	11.7013i	−0.0522203	−	0.663522i	0.913985	−	0.405748i	$-0.132989\pi$
$312$	11.3241	−	71.4978i	0.641103	−	4.04776i
$313$	−1.49478	+	18.9930i	−0.0844899	+	1.07355i	0.797826	+	0.602888i	$0.205983\pi$
$313$	−1.49478	+	18.9930i	−0.0844899	+	1.07355i	−0.882316	+	0.470658i	$0.844017\pi$
$314$	−20.8641	−	50.3705i	−1.17743	−	2.84257i
$315$	−0.608198	+	6.73701i	−0.0342681	+	0.379587i
$316$	11.1358	+	0.876409i	0.626440	+	0.0493019i
$317$	0.113706	+	1.44477i	0.00638635	+	0.0811463i	0.999285	−	0.0378210i	$-0.0120417\pi$
$317$	0.113706	+	1.44477i	0.00638635	+	0.0811463i	−0.992898	+	0.118967i	$0.962042\pi$
$318$	−16.5029	+	8.40866i	−0.925438	+	0.471534i
$319$	−10.1379	−	10.1379i	−0.567613	−	0.567613i
$320$	−8.18826	−	11.5470i	−0.457738	−	0.645495i
$321$	−9.03573	+	2.16929i	−0.504325	+	0.121078i
$322$	19.3311	+	31.5455i	1.07728	+	1.75796i
$323$	−2.62949	+	0.854375i	−0.146309	+	0.0475387i
$324$	−48.8590	+	15.8753i	−2.71439	+	0.881959i
$325$	−19.9682	+	16.2758i	−1.10764	+	0.902817i
$326$	−1.94957	−	12.3091i	−0.107977	−	0.681738i
$327$	12.6800	−	12.6800i	0.701208	−	0.701208i
$328$	−45.6744	−	5.98846i	−2.52195	−	0.330657i
$329$			14.7321i			0.812205i
$330$	16.7748	+	53.7206i	0.923421	+	2.95722i
$331$	−6.95902	+	16.8006i	−0.382502	+	0.923443i	0.608978	+	0.793187i	$0.291580\pi$
$331$	−6.95902	+	16.8006i	−0.382502	+	0.923443i	−0.991480	+	0.130256i	$0.958420\pi$
$332$	12.5799	+	6.40980i	0.690414	+	0.351783i
$333$	−0.665701	−	2.04882i	−0.0364802	−	0.112275i
$334$	15.3312	+	3.68069i	0.838885	+	0.201398i
$335$	31.4217	+	13.4405i	1.71675	+	0.734331i
$336$	59.3656	−	30.2483i	3.23866	−	1.65018i
$337$		−	11.0990i		−	0.604599i	−0.953213	−	0.302300i	$-0.902246\pi$
$337$		−	11.0990i		−	0.604599i	0.953213	−	0.302300i	$-0.0977543\pi$
$338$	15.9952	+	31.3924i	0.870026	+	1.70752i
$339$	−0.0623361	−	0.0532400i	−0.00338563	−	0.00289160i
$340$	−5.31617	+	6.08149i	−0.288310	+	0.329815i
$341$	−9.93050	+	6.08542i	−0.537767	+	0.329544i
$342$	−2.95599	+	7.13639i	−0.159842	+	0.385892i
$343$	0.714641	+	0.0562435i	0.0385870	+	0.00303686i
$344$	17.3858	+	23.9296i	0.937382	+	1.29020i
$345$	−16.2983	+	3.71530i	−0.877473	+	0.200025i
$346$	12.4551	+	9.04918i	0.669592	+	0.486487i
$347$	6.57836	+	27.4008i	0.353145	+	1.47095i	0.812636	+	0.582771i	$0.198032\pi$
$347$	6.57836	+	27.4008i	0.353145	+	1.47095i	−0.459492	+	0.888182i	$0.651968\pi$
$348$	−15.8312	−	21.7898i	−0.848641	−	1.16805i
$349$	−2.17406	+	13.7265i	−0.116375	+	0.734761i	0.858633	+	0.512591i	$0.171314\pi$
$349$	−2.17406	+	13.7265i	−0.116375	+	0.734761i	−0.975008	+	0.222170i	$0.928686\pi$
$350$	−46.7190	−	12.3586i	−2.49724	−	0.660593i
$351$	12.9281	−	17.7940i	0.690049	−	0.949771i
$352$	30.5467	−	35.7655i	1.62814	−	1.90631i
$353$	34.9274	+	5.53196i	1.85900	+	0.294437i	0.982401	−	0.186784i	$-0.0598064\pi$
$353$	34.9274	+	5.53196i	1.85900	+	0.294437i	0.876600	+	0.481221i	$0.159806\pi$
$354$	−37.0121	−	43.3355i	−1.96717	−	2.30326i
$355$	15.2968	+	25.6185i	0.811872	+	1.35969i
$356$	−14.7810	−	24.1204i	−0.783392	−	1.27838i
$357$	−3.57231	−	4.18264i	−0.189067	−	0.221369i
$358$	−36.7630	+	2.89331i	−1.94299	+	0.152916i
$359$	5.77279	−	17.7668i	0.304676	−	0.937697i	−0.675122	−	0.737706i	$-0.735909\pi$
$359$	5.77279	−	17.7668i	0.304676	−	0.937697i	0.979798	−	0.199990i	$-0.0640911\pi$
$360$	1.89997	+	12.9581i	0.100137	+	0.682953i
$361$	2.58540	+	5.07414i	0.136074	+	0.267060i
$362$	−37.7601	−	23.1394i	−1.98463	−	1.21618i
$363$	−22.5588	+	13.8240i	−1.18403	+	0.725574i
$364$	−41.4216	+	81.2945i	−2.17108	+	4.26099i
$365$	2.60675	−	7.71972i	0.136444	−	0.404069i
$366$	23.2299	+	9.62215i	1.21425	+	0.502958i
$367$	2.02175	−	2.78270i	0.105534	−	0.145256i	−0.752983	−	0.658040i	$-0.771386\pi$
$367$	2.02175	−	2.78270i	0.105534	−	0.145256i	0.858518	+	0.512784i	$0.171386\pi$
$368$	24.8514	+	24.8514i	1.29547	+	1.29547i
$369$	4.29772	+	2.95038i	0.223730	+	0.153591i
$370$	15.2275	−	2.23272i	0.791641	−	0.116073i
$371$	13.3811	−	2.11937i	0.694715	−	0.110032i
$372$	−20.2141	+	8.37294i	−1.04805	+	0.434117i
$373$	3.10143	−	6.08690i	0.160586	−	0.315168i	−0.796668	−	0.604418i	$-0.793406\pi$
$373$	3.10143	−	6.08690i	0.160586	−	0.315168i	0.957254	+	0.289250i	$0.0934059\pi$
$374$	−8.70359	−	4.43470i	−0.450052	−	0.229313i
$375$	12.0438	−	18.2130i	0.621937	−	0.940516i
$376$	6.65856	+	27.7349i	0.343389	+	1.43032i
$377$	14.1795	+	4.60718i	0.730279	+	0.237282i
$378$	41.2604			2.12220
$379$	11.9704	+	3.88941i	0.614877	+	0.199786i	0.599864	−	0.800102i	$-0.295221\pi$
$379$	11.9704	+	3.88941i	0.614877	+	0.199786i	0.0150124	+	0.999887i	$0.495221\pi$
$380$	−32.9078	−	20.6899i	−1.68814	−	1.06137i
$381$	−0.0942735	+	1.19786i	−0.00482978	+	0.0613681i
$382$	−61.3392	−	14.7262i	−3.13839	−	0.753460i
$383$	−10.0715	−	4.17175i	−0.514630	−	0.213167i	0.110227	−	0.993906i	$-0.464842\pi$
$383$	−10.0715	−	4.17175i	−0.514630	−	0.213167i	−0.624856	+	0.780740i	$0.714842\pi$
$384$	−3.74248	+	3.19638i	−0.190983	+	0.163115i
$385$	0.473122	−	41.1632i	0.0241125	−	2.09787i
$386$	20.5045	−	1.61374i	1.04365	−	0.0821372i
$387$	−0.523626	−	3.30604i	−0.0266174	−	0.168056i
$388$	−2.96573	+	0.712009i	−0.150562	+	0.0361468i
$389$	−17.6384	−	2.79365i	−0.894303	−	0.141644i	−0.307667	−	0.951494i	$-0.599548\pi$
$389$	−17.6384	−	2.79365i	−0.894303	−	0.141644i	−0.586636	+	0.809850i	$0.699548\pi$
$390$	−40.9045	−	41.8557i	−2.07128	−	2.11945i
$391$	1.51601	−	2.47390i	0.0766679	−	0.125111i
$392$	−48.3685	+	7.66082i	−2.44298	+	0.386930i
$393$	25.2144	+	21.5352i	1.27190	+	1.08631i
$394$	−15.8830	+	11.5397i	−0.800175	+	0.581361i
$395$	3.44932	−	3.94588i	0.173554	−	0.198539i
$396$	−17.7602	+	7.35651i	−0.892483	+	0.369678i
$397$	1.28504	−	5.35257i	0.0644942	−	0.268638i	−0.930801	−	0.365526i	$-0.880889\pi$
$397$	1.28504	−	5.35257i	0.0644942	−	0.268638i	0.995295	+	0.0968885i	$0.0308890\pi$
$398$	10.6587	−	9.10338i	0.534272	−	0.456311i
$399$	17.1911	−	20.1282i	0.860630	−	1.00767i
$400$	−45.8945	−	1.05514i	−2.29472	−	0.0527572i
$401$	−8.09569	+	8.09569i	−0.404280	+	0.404280i	−0.879738	−	0.475459i	$-0.842282\pi$
$401$	−8.09569	+	8.09569i	−0.404280	+	0.404280i	0.475459	+	0.879738i	$0.342282\pi$
$402$	−23.9923	+	73.8406i	−1.19663	+	3.68283i
$403$	6.32822	−	10.3267i	0.315231	−	0.514410i
$404$	−0.196103	+	0.816826i	−0.00975647	+	0.0406386i
$405$	−7.71148	+	22.8370i	−0.383187	+	1.13478i
$406$	8.64279	+	26.5998i	0.428934	+	1.32012i
$407$	5.01701	+	12.1121i	0.248684	+	0.600376i
$408$	−8.61576	−	6.25972i	−0.426544	−	0.309902i
$409$	16.6890			0.825219			0.412610	−	0.910908i	$-0.364617\pi$
$409$	16.6890			0.825219			0.412610	+	0.910908i	$0.364617\pi$
$410$	−25.9305	+	26.7320i	−1.28062	+	1.32020i
$411$	36.7275			1.81164
$412$	−8.37702	−	6.08626i	−0.412706	−	0.299849i
$413$	15.9526	+	38.5130i	0.784977	+	1.89510i
$414$	−2.50494	−	7.70940i	−0.123111	−	0.378896i
$415$	5.93655	−	2.93937i	0.291414	−	0.144288i
$416$	−11.4181	+	47.5600i	−0.559821	+	2.33182i
$417$	−20.4546	+	33.3788i	−1.00167	+	1.63457i
$418$	14.5263	−	44.7072i	0.710503	−	2.18670i
$419$	−27.2416	+	27.2416i	−1.33084	+	1.33084i	−0.426220	+	0.904620i	$0.640155\pi$
$419$	−27.2416	+	27.2416i	−1.33084	+	1.33084i	−0.904620	+	0.426220i	$0.859845\pi$
$420$	12.9748	−	76.2378i	0.633104	−	3.72002i
$421$	−11.2744	+	13.2006i	−0.549480	+	0.643358i	−0.963754	−	0.266794i	$-0.914036\pi$
$421$	−11.2744	+	13.2006i	−0.549480	+	0.643358i	0.414274	+	0.910152i	$0.364036\pi$
$422$	13.2134	−	11.2854i	0.643221	−	0.549362i
$423$	0.753514	−	3.13861i	0.0366371	−	0.152605i
$424$	24.2337	−	10.0379i	1.17689	−	0.487485i
$425$	0.799795	+	3.70453i	0.0387958	+	0.179696i
$426$	−54.8401	+	39.8437i	−2.65701	+	1.93043i
$427$	−13.9853	−	11.9446i	−0.676795	−	0.578037i
$428$	22.3970	−	3.54734i	1.08260	−	0.171467i
$429$	26.0482	−	42.5067i	1.25762	−	2.05224i
$430$	23.9117	+	0.274837i	1.15313	+	0.0132538i
$431$	−28.4815	−	4.51102i	−1.37190	−	0.217288i	−0.573399	−	0.819276i	$-0.694376\pi$
$431$	−28.4815	−	4.51102i	−1.37190	−	0.217288i	−0.798505	+	0.601988i	$0.794376\pi$
$432$	38.1118	−	9.14982i	1.83365	−	0.440221i
$433$	−3.04201	−	19.2065i	−0.146190	−	0.923006i	−0.946332	−	0.323196i	$-0.895243\pi$
$433$	−3.04201	−	19.2065i	−0.146190	−	0.923006i	0.800142	−	0.599810i	$-0.204757\pi$
$434$	22.6503	−	1.78262i	1.08725	−	0.0855683i
$435$	−12.6361	−	0.145237i	−0.605857	−	0.00696360i
$436$	−33.2752	+	28.4197i	−1.59359	+	1.36106i
$437$	12.8999	+	5.34331i	0.617086	+	0.255605i
$438$	17.9992	+	4.32123i	0.860035	+	0.206476i
$439$	0.255463	−	3.24597i	0.0121926	−	0.154922i	−0.987807	−	0.155683i	$-0.950242\pi$
$439$	0.255463	−	3.24597i	0.0121926	−	0.154922i	1.00000		0.000761029i	$0.000242243\pi$
$440$	−17.7141	−	77.7085i	−0.844487	−	3.70461i
$441$	5.27061	+	1.71252i	0.250981	+	0.0815488i
$442$	10.1580			0.483167
$443$	−13.7424	−	4.46516i	−0.652919	−	0.212146i	−0.0362183	−	0.999344i	$-0.511531\pi$
$443$	−13.7424	−	4.46516i	−0.652919	−	0.212146i	−0.616701	+	0.787198i	$0.711531\pi$
$444$	5.74941	+	23.9480i	0.272855	+	1.13652i
$445$	−13.2192	−	1.19339i	−0.626650	−	0.0565722i
$446$	53.6800	+	27.3513i	2.54182	+	1.29512i
$447$	7.05679	−	13.8497i	0.333775	−	0.655070i
$448$	−21.7324	+	9.00187i	−1.02676	+	0.425298i
$449$	14.3743	−	2.27666i	0.678363	−	0.107442i	0.192260	−	0.981344i	$-0.438418\pi$
$449$	14.3743	−	2.27666i	0.678363	−	0.107442i	0.486103	+	0.873902i	$0.338418\pi$
$450$	9.32121	+	5.02253i	0.439406	+	0.236764i
$451$	−27.4826	−	15.8476i	−1.29410	−	0.746234i
$452$	0.141455	+	0.141455i	0.00665348	+	0.00665348i
$453$	9.90117	−	13.6278i	0.465198	−	0.640290i
$454$	−0.932348	−	0.386191i	−0.0437572	−	0.0181248i
$455$	18.9949	+	38.3634i	0.890496	+	1.79850i
$456$	23.2668	−	45.6637i	1.08957	−	2.13840i
$457$	−30.5667	+	18.7313i	−1.42985	+	0.876213i	−0.999648	−	0.0265198i	$-0.991557\pi$
$457$	−30.5667	+	18.7313i	−1.42985	+	0.876213i	−0.430202	+	0.902733i	$0.641557\pi$
$458$	−29.6792	−	18.1874i	−1.38682	−	0.849843i
$459$	−1.46901	−	2.88310i	−0.0685675	−	0.134571i
$460$	40.3612	−	5.91790i	1.88185	−	0.275924i
$461$	5.34130	−	16.4388i	0.248769	−	0.765633i	−0.746224	−	0.665695i	$-0.768135\pi$
$461$	5.34130	−	16.4388i	0.248769	−	0.765633i	0.994994	−	0.0999386i	$-0.0318646\pi$
$462$	93.2329	−	7.33759i	4.33759	−	0.341376i
$463$	−21.3989	−	25.0548i	−0.994489	−	1.16440i	−0.986389	−	0.164430i	$-0.947421\pi$
$463$	−21.3989	−	25.0548i	−0.994489	−	1.16440i	−0.00810075	−	0.999967i	$-0.502579\pi$
$464$	13.8820	+	22.6533i	0.644454	+	1.05165i
$465$	−2.51103	+	9.95381i	−0.116446	+	0.461597i
$466$	10.4131	+	12.1921i	0.482375	+	0.564789i
$467$	1.94069	+	0.307375i	0.0898045	+	0.0142236i	0.201175	−	0.979555i	$-0.435524\pi$
$467$	1.94069	+	0.307375i	0.0898045	+	0.0142236i	−0.111370	+	0.993779i	$0.535524\pi$
$468$	12.9828	−	15.2009i	0.600129	−	0.702661i
$469$	33.3811	−	45.9452i	1.54140	−	2.12155i
$470$	21.2017	+	9.06892i	0.977964	+	0.418318i
$471$	6.40370	−	40.4314i	0.295067	−	1.86298i
$472$	47.4397	+	65.2952i	2.18359	+	3.00545i
$473$	4.75534	+	19.8074i	0.218651	+	0.910746i
$474$	9.63257	+	6.99847i	0.442439	+	0.321450i
$475$	−17.0058	+	6.59030i	−0.780279	+	0.302383i
$476$	7.88973	+	10.8593i	0.361625	+	0.497735i
$477$	−2.95921	−	0.232895i	−0.135493	−	0.0106635i
$478$	−24.6262	+	59.4530i	−1.12638	+	2.71932i
$479$	−26.5032	+	16.2412i	−1.21096	+	0.742078i	−0.973360	−	0.229284i	$-0.926362\pi$
$479$	−26.5032	+	16.2412i	−1.21096	+	0.742078i	−0.237602	+	0.971362i	$0.576362\pi$
$480$	−2.77748	−	41.3641i	−0.126774	−	1.88800i
$481$	−10.3667	−	8.85402i	−0.472682	−	0.403708i
$482$	18.9922	+	37.2743i	0.865071	+	1.69780i
$483$			27.7785i			1.26397i
$484$	57.5267	−	29.3113i	2.61485	−	1.33233i
$485$	−0.562790	+	1.31572i	−0.0255550	+	0.0597437i
$486$	−20.8547	−	5.00678i	−0.945989	−	0.227112i
$487$	−10.5786	−	32.5575i	−0.479361	−	1.47532i	−0.839985	−	0.542609i	$-0.817436\pi$
$487$	−10.5786	−	32.5575i	−0.479361	−	1.47532i	0.360625	−	0.932711i	$-0.382564\pi$
$488$	−31.7276	−	16.1660i	−1.43624	−	0.731802i
$489$	3.58083	−	8.64489i	0.161931	−	0.390935i
$490$	−18.3786	+	35.0677i	−0.830259	+	1.58420i
$491$			12.6420i			0.570527i	0.958449	+	0.285264i	$0.0920812\pi$
$491$			12.6420i			0.570527i	−0.958449	+	0.285264i	$0.907919\pi$
$492$	−46.3357	−	37.4812i	−2.08897	−	1.68978i
$493$	1.55096	−	1.55096i	0.0698519	−	0.0698519i
$494$	7.64707	+	48.2817i	0.344058	+	2.17230i
$495$	−2.20621	+	8.74547i	−0.0991617	+	0.393080i
$496$	20.5265	−	6.66947i	0.921668	−	0.299468i
$497$	47.1564	−	15.3220i	2.11525	−	0.687287i
$498$	7.86328	+	12.8317i	0.352362	+	0.575002i
$499$	7.98073	−	1.91600i	0.357267	−	0.0857721i	−0.0508390	−	0.998707i	$-0.516190\pi$
$499$	7.98073	−	1.91600i	0.357267	−	0.0857721i	0.408106	+	0.912935i	$0.366190\pi$
$500$	−32.7866	+	42.0019i	−1.46626	+	1.87838i
$501$	8.37080	+	8.37080i	0.373980	+	0.373980i
$502$	33.2945	−	16.9644i	1.48601	−	0.757158i
$503$	2.18603	+	27.7762i	0.0974704	+	1.23848i	0.830008	+	0.557752i	$0.188336\pi$
$503$	2.18603	+	27.7762i	0.0974704	+	1.23848i	−0.732537	+	0.680727i	$0.761664\pi$
$504$	21.6963	+	1.70754i	0.966431	+	0.0760597i
$505$	0.252510	+	0.302626i	0.0112365	+	0.0134667i
$506$	18.8783	+	45.5762i	0.839241	+	2.02611i
$507$	−2.07551	+	26.3719i	−0.0921767	+	1.17122i
$508$	0.458688	−	2.89604i	0.0203510	−	0.128491i
$509$	0.0899359	+	1.14274i	0.00398634	+	0.0506512i	0.998589	−	0.0531082i	$-0.0169128\pi$
$509$	0.0899359	+	1.14274i	0.00398634	+	0.0506512i	−0.994602	+	0.103759i	$0.966913\pi$
$510$	−8.21855	+	2.56632i	−0.363923	+	0.113639i
$511$	−11.5447	−	7.07457i	−0.510705	−	0.312961i
$512$	36.3599	−	26.4170i	1.60690	−	1.16748i
$513$	12.5977	−	9.15273i	0.556200	−	0.404103i
$514$	−26.1025	−	15.9956i	−1.15133	−	0.705536i
$515$	−4.63742	+	1.44808i	−0.204349	+	0.0638100i
$516$	3.00243	+	38.1495i	0.132175	+	1.67944i
$517$	−3.07289	+	19.4015i	−0.135145	+	0.853275i
$518$	2.00658	−	25.4961i	0.0881643	−	1.12023i
$519$	4.42352	+	10.6793i	0.194171	+	0.468770i
$520$	53.0996	+	63.6384i	2.32857	+	2.79073i
$521$	−33.7154	−	2.65346i	−1.47710	−	0.116250i	−0.685848	−	0.727745i	$-0.740569\pi$
$521$	−33.7154	−	2.65346i	−1.47710	−	0.116250i	−0.791249	+	0.611494i	$0.790569\pi$
$522$	−0.480792	−	6.10904i	−0.0210437	−	0.267386i
$523$	−6.73063	+	3.42943i	−0.294310	+	0.149958i	−0.594911	−	0.803792i	$-0.702813\pi$
$523$	−6.73063	+	3.42943i	−0.294310	+	0.149958i	0.300601	+	0.953750i	$0.402813\pi$
$524$	−57.2173	−	57.2173i	−2.49955	−	2.49955i
$525$	−25.0604	−	26.2398i	−1.09372	−	1.14520i
$526$	−22.5806	+	5.42111i	−0.984559	+	0.236372i
$527$	−0.930990	−	1.51924i	−0.0405545	−	0.0661790i
$528$	84.4911	−	27.4528i	3.67700	−	1.19473i
$529$	7.93862	−	2.57942i	0.345158	−	0.112148i
$530$	5.18721	−	20.5622i	0.225318	−	0.893166i
$531$	−1.42879	−	9.02100i	−0.0620040	−	0.391478i
$532$	−45.6754	+	45.6754i	−1.98028	+	1.98028i
$533$	32.9459	+	1.70906i	1.42704	+	0.0740278i
$534$		−	30.1537i		−	1.30488i
$535$	4.93884	−	9.42368i	0.213525	−	0.407421i
$536$	42.0778	−	101.585i	1.81748	−	4.38780i
$537$	−24.6701	−	12.5700i	−1.06459	−	0.542437i
$538$	−0.301400	−	0.927614i	−0.0129943	−	0.0399923i
$539$	−32.7940	−	7.87314i	−1.41254	−	0.339120i
$540$	17.8913	−	41.8271i	0.769919	−	1.79995i
$541$	−2.24205	+	1.14238i	−0.0963931	+	0.0491147i	−0.501522	−	0.865145i	$-0.667227\pi$
$541$	−2.24205	+	1.14238i	−0.0963931	+	0.0491147i	0.405129	+	0.914259i	$0.367227\pi$
$542$			16.1756i			0.694800i
$543$	−15.0957	−	29.6269i	−0.647817	−	1.27141i
$544$	5.47166	+	4.67324i	0.234596	+	0.200363i
$545$	1.37554	+	20.4855i	0.0589218	+	0.877502i
$546$	−82.9215	+	50.8143i	−3.54871	+	2.17465i
$547$	−0.230968	+	0.557605i	−0.00987547	+	0.0238415i	−0.928740	−	0.370731i	$-0.879107\pi$
$547$	−0.230968	+	0.557605i	−0.00987547	+	0.0238415i	0.918865	+	0.394572i	$0.129107\pi$
$548$	−89.3491	−	7.03192i	−3.81680	−	0.300389i
$549$	2.36857	+	3.26006i	0.101088	+	0.139136i
$550$	−58.9490	−	26.0206i	−2.51359	−	1.10952i
$551$	8.53942	+	6.20425i	0.363791	+	0.264310i
$552$	12.5553	+	52.2965i	0.534388	+	2.22589i
$553$	−5.11913	−	7.04588i	−0.217688	−	0.299621i
$554$	11.6918	−	73.8190i	0.496736	−	3.13627i
$555$	10.6243	+	4.54448i	0.450976	+	0.192902i
$556$	56.1517	−	77.2862i	2.38136	−	3.27767i
$557$	20.0108	−	23.4297i	0.847885	−	0.992746i	−0.152105	−	0.988364i	$-0.548605\pi$
$557$	20.0108	−	23.4297i	0.847885	−	0.992746i	0.999990	−	0.00438188i	$-0.00139480\pi$
$558$	−4.91674	−	0.778735i	−0.208142	−	0.0329665i
$559$	−13.7573	−	16.1077i	−0.581870	−	0.681282i
$560$	−18.6598	+	73.9680i	−0.788521	+	3.12572i
$561$	−3.83213	−	6.25347i	−0.161793	−	0.264022i
$562$	34.7819	+	40.7243i	1.46718	+	1.71785i
$563$	23.6947	−	1.86481i	0.998611	−	0.0785924i	0.431396	−	0.902162i	$-0.358021\pi$
$563$	23.6947	−	1.86481i	0.998611	−	0.0785924i	0.567215	+	0.823570i	$0.308021\pi$
$564$	−11.4033	+	35.0957i	−0.480164	+	1.47779i
$565$	0.0928672	−	0.0136165i	0.00390695	−	0.000572852i
$566$	−22.6517	−	44.4565i	−0.952122	−	1.86864i
$567$	34.1522	+	20.9285i	1.43426	+	0.878914i
$568$	81.8524	−	50.1592i	3.43445	−	2.10463i
$569$	−10.8563	+	21.3068i	−0.455121	+	0.893226i	0.543432	+	0.839453i	$0.317125\pi$
$569$	−10.8563	+	21.3068i	−0.455121	+	0.893226i	−0.998553	+	0.0537726i	$0.982875\pi$
$570$	−18.3849	−	37.1314i	−0.770060	−	1.55526i
$571$	36.6176	+	15.1675i	1.53240	+	0.634741i	0.980029	−	0.198857i	$-0.0637230\pi$
$571$	36.6176	+	15.1675i	1.53240	+	0.634741i	0.552372	+	0.833598i	$0.313723\pi$
$572$	−71.5072	+	98.4212i	−2.98987	+	4.11520i
$573$	−33.4911	−	33.4911i	−1.39911	−	1.39911i
$574$	33.7339	+	51.8853i	1.40803	+	2.16565i
$575$	9.07883	−	16.8492i	0.378613	−	0.702661i
$576$	5.09044	−	0.806247i	0.212102	−	0.0335936i
$577$	−29.0893	+	12.0492i	−1.21100	+	0.501614i	−0.894539	−	0.446990i	$-0.852496\pi$
$577$	−29.0893	+	12.0492i	−1.21100	+	0.501614i	−0.316465	+	0.948604i	$0.602496\pi$
$578$	−19.3966	+	38.0679i	−0.806790	+	1.58341i
$579$	13.7597	+	7.01092i	0.571834	+	0.291364i
$580$	30.7128	+	2.77267i	1.27528	+	0.115129i
$581$	−2.56979	−	10.7039i	−0.106613	−	0.444074i
$582$	−3.09191	−	1.00462i	−0.128164	−	0.0416430i
$583$	18.0644			0.748152
$584$	−24.9317	−	8.10081i	−1.03168	−	0.335214i
$585$	−2.08460	−	9.14473i	−0.0861874	−	0.378088i
$586$	−4.62573	+	58.7755i	−0.191087	+	2.42799i
$587$	−36.8153	−	8.83858i	−1.51953	−	0.364807i	−0.614075	−	0.789248i	$-0.710471\pi$
$587$	−36.8153	−	8.83858i	−1.51953	−	0.364807i	−0.905456	+	0.424441i	$0.860471\pi$
$588$	−58.5343	−	24.2457i	−2.41392	−	0.999876i
$589$	6.52017	−	5.56876i	0.268659	−	0.229457i
$590$	65.2465	+	0.749931i	2.68616	+	0.0308742i
$591$	−14.6951	+	1.15653i	−0.604475	+	0.0475732i
$592$	−3.80050	−	23.9954i	−0.156200	−	0.986206i
$593$	−12.0060	+	2.88239i	−0.493029	+	0.118366i	−0.472333	−	0.881420i	$-0.656588\pi$
$593$	−12.0060	+	2.88239i	−0.493029	+	0.118366i	−0.0206955	+	0.999786i	$0.506588\pi$
$594$	54.3380	+	8.60629i	2.22951	+	0.353120i
$595$	6.29743	+	0.0723814i	0.258169	+	0.00296735i
$596$	−19.8191	+	32.3419i	−0.811824	+	1.32478i
$597$	10.3948	−	1.64637i	0.425431	−	0.0673816i
$598$	−39.0085	−	33.3164i	−1.59517	−	1.36241i
$599$	2.55806	−	1.85854i	0.104520	−	0.0759380i	−0.534298	−	0.845296i	$-0.679424\pi$
$599$	2.55806	−	1.85854i	0.104520	−	0.0759380i	0.638817	+	0.769358i	$0.279424\pi$
$600$	−59.0390	−	38.0729i	−2.41026	−	1.55432i
$601$	24.8361	−	10.2874i	1.01308	−	0.419633i	0.186505	−	0.982454i	$-0.440284\pi$
$601$	24.8361	−	10.2874i	1.01308	−	0.419633i	0.826579	+	0.562821i	$0.190284\pi$
$602$	9.27664	−	38.6400i	0.378088	−	1.57485i
$603$	−9.46173	+	8.08108i	−0.385311	+	0.329087i
$604$	−26.6963	+	31.2574i	−1.08626	+	1.27184i
$605$	5.08237	−	29.8632i	0.206628	−	1.21411i
$606$	−0.633146	+	0.633146i	−0.0257198	+	0.0257198i
$607$	9.64927	−	29.6974i	0.391652	−	1.20538i	−0.539887	−	0.841738i	$-0.681533\pi$
$607$	9.64927	−	29.6974i	0.391652	−	1.20538i	0.931539	−	0.363642i	$-0.118467\pi$
$608$	−18.0931	+	29.5252i	−0.733772	+	1.19741i
$609$	−4.90224	+	20.4193i	−0.198649	+	0.827432i
$610$	−25.7993	+	12.7741i	−1.04458	+	0.517206i
$611$	−6.31230	−	19.4273i	−0.255368	−	0.785943i
$612$	−1.12545	−	2.71708i	−0.0454936	−	0.109831i
$613$	−32.2579	−	23.4368i	−1.30289	−	0.946602i	−0.302906	−	0.953020i	$-0.597957\pi$
$613$	−32.2579	−	23.4368i	−1.30289	−	0.946602i	−0.999979	+	0.00641849i	$0.997957\pi$
$614$	−27.2332			−1.09904
$615$	−27.0873	+	6.94070i	−1.09227	+	0.279876i
$616$	−132.445			−5.33635
$617$	−12.1913	−	8.85749i	−0.490803	−	0.356589i	0.314690	−	0.949195i	$-0.398099\pi$
$617$	−12.1913	−	8.85749i	−0.490803	−	0.356589i	−0.805493	+	0.592605i	$0.798099\pi$
$618$	−4.22369	−	10.1969i	−0.169902	−	0.410179i
$619$	−11.4537	−	35.2509i	−0.460364	−	1.41685i	−0.864721	−	0.502253i	$-0.832504\pi$
$619$	−11.4537	−	35.2509i	−0.460364	−	1.41685i	0.404356	−	0.914601i	$-0.367496\pi$
$620$	8.01450	−	23.7344i	0.321870	−	0.953196i
$621$	−3.81477	+	15.8897i	−0.153081	+	0.637630i
$622$	−15.9522	+	26.0317i	−0.639627	+	1.04378i
$623$	−6.81578	+	20.9768i	−0.273068	+	0.840418i
$624$	−65.3252	+	65.3252i	−2.61510	+	2.61510i
$625$	6.62457	+	24.1063i	0.264983	+	0.964253i
$626$	32.1839	−	37.6825i	1.28633	−	1.50609i
$627$	26.8383	−	22.9221i	1.07182	−	0.915419i
$628$	−23.3197	+	97.1335i	−0.930557	+	3.87605i
$629$	−1.85300	+	0.767536i	−0.0738838	+	0.0306037i
$630$	11.5801	−	13.2471i	0.461361	−	0.527778i
$631$	12.4739	−	9.06285i	0.496580	−	0.360786i	−0.311129	−	0.950368i	$-0.600707\pi$
$631$	12.4739	−	9.06285i	0.496580	−	0.360786i	0.807709	+	0.589581i	$0.200707\pi$
$632$	−12.8220	−	10.9510i	−0.510030	−	0.435607i
$633$	12.8863	−	2.04099i	0.512185	−	0.0811221i
$634$	1.96963	−	3.21414i	0.0782239	−	0.127650i
$635$	−0.961544	−	0.983905i	−0.0381577	−	0.0390451i
$636$	33.5179	+	5.30872i	1.32907	+	0.210504i
$637$	34.1024	−	8.18726i	1.35119	−	0.324391i
$638$	5.83384	+	36.8334i	0.230964	+	1.45825i
$639$	−10.8302	+	0.852354i	−0.428436	+	0.0337186i
$640$	0.0647644	−	5.63472i	0.00256004	−	0.222732i
$641$	18.4000	−	15.7151i	0.726757	−	0.620709i	−0.207115	−	0.978317i	$-0.566407\pi$
$641$	18.4000	−	15.7151i	0.726757	−	0.620709i	0.933872	+	0.357607i	$0.116407\pi$
$642$	22.3309	+	9.24978i	0.881332	+	0.365060i
$643$	−25.1777	−	6.04464i	−0.992912	−	0.238377i	−0.295730	−	0.955271i	$-0.595563\pi$
$643$	−25.1777	−	6.04464i	−0.992912	−	0.238377i	−0.697182	+	0.716894i	$0.745563\pi$
$644$	5.31853	−	67.5784i	0.209580	−	2.66296i
$645$	15.2000	+	9.55662i	0.598501	+	0.376291i
$646$	6.83962	+	2.22233i	0.269101	+	0.0874363i
$647$	−4.69016			−0.184389			−0.0921946	−	0.995741i	$-0.529388\pi$
$647$	−4.69016			−0.184389			−0.0921946	+	0.995741i	$0.529388\pi$
$648$	73.7548	+	23.9644i	2.89736	+	0.941410i
$649$	12.9756	+	54.0473i	0.509338	+	2.12154i
$650$	66.9040	−	3.72056i	2.62419	−	0.145932i
$651$	15.1996	+	7.74460i	0.595721	+	0.303535i
$652$	−10.3664	+	20.3453i	−0.405981	+	0.796783i
$653$	22.7199	−	9.41090i	0.889099	−	0.368277i	0.109080	−	0.994033i	$-0.465209\pi$
$653$	22.7199	−	9.41090i	0.889099	−	0.368277i	0.780019	+	0.625756i	$0.215209\pi$
$654$	−46.0697	+	7.29673i	−1.80147	+	0.285325i
$655$	−37.5640	+	5.50778i	−1.46775	+	0.215207i
$656$	42.6657	+	40.4451i	1.66581	+	1.57912i
$657$	2.09770	+	2.09770i	0.0818390	+	0.0818390i
$658$	22.5238	−	31.0014i	0.878070	−	1.20856i
$659$	−40.5581	−	16.7997i	−1.57992	−	0.654424i	−0.591519	−	0.806291i	$-0.701472\pi$
$659$	−40.5581	−	16.7997i	−1.57992	−	0.654424i	−0.988401	+	0.151867i	$0.951472\pi$
$660$	32.9892	−	97.6953i	1.28410	−	3.80279i
$661$	−18.3522	+	36.0183i	−0.713820	+	1.40095i	0.193751	+	0.981051i	$0.437935\pi$
$661$	−18.3522	+	36.0183i	−0.713820	+	1.40095i	−0.907571	+	0.419899i	$0.862065\pi$
$662$	40.3306	−	24.7146i	1.56749	−	0.960560i
$663$	6.50298	+	3.98503i	0.252555	+	0.154766i
$664$	−9.67587	−	18.9900i	−0.375496	−	0.736953i
$665$	4.39674	+	29.9866i	0.170498	+	1.16283i
$666$	−1.73157	+	5.32921i	−0.0670969	+	0.206503i
$667$	−11.0428	+	0.869090i	−0.427580	+	0.0336513i
$668$	−18.7614	−	21.9668i	−0.725901	−	0.849920i
$669$	23.6350	+	38.5687i	0.913780	+	1.49115i
$670$	−45.5732	−	76.3240i	−1.76065	−	2.94866i
$671$	−15.9265	−	18.6475i	−0.614836	−	0.719881i
$672$	−68.0434	−	10.7770i	−2.62483	−	0.415733i
$673$	14.4289	−	16.8941i	0.556193	−	0.651218i	−0.409069	−	0.912504i	$-0.634146\pi$
$673$	14.4289	−	16.8941i	0.556193	−	0.651218i	0.965262	+	0.261285i	$0.0841464\pi$
$674$	−16.9692	+	23.3561i	−0.653629	+	0.899643i
$675$	−10.7314	−	18.4510i	−0.413051	−	0.710178i
$676$	10.0984	−	63.7589i	0.388400	−	2.45226i
$677$	4.77970	+	6.57869i	0.183699	+	0.252840i	0.890928	−	0.454145i	$-0.150055\pi$
$677$	4.77970	+	6.57869i	0.183699	+	0.252840i	−0.707229	+	0.706984i	$0.750055\pi$
$678$	0.0497782	+	0.207341i	0.00191172	+	0.00796289i
$679$	1.92385	+	1.39776i	0.0738307	+	0.0536412i
$680$	11.8884	−	2.71003i	0.455899	−	0.103925i
$681$	−0.445368	−	0.612997i	−0.0170665	−	0.0234901i
$682$	30.2012	+	2.37689i	1.15646	+	0.0910157i
$683$	6.16206	−	14.8765i	0.235785	−	0.569235i	−0.761054	−	0.648689i	$-0.775318\pi$
$683$	6.16206	−	14.8765i	0.235785	−	0.569235i	0.996839	+	0.0794542i	$0.0253177\pi$
$684$	12.0672	−	7.39478i	0.461401	−	0.282747i
$685$	−27.6758	+	31.6600i	−1.05744	+	1.20967i
$686$	−1.41786	−	1.21097i	−0.0541342	−	0.0462350i
$687$	−11.8651	−	23.2866i	−0.452682	−	0.888438i
$688$		−	37.7485i		−	1.43915i
$689$	−16.7377	+	8.52829i	−0.637656	+	0.324902i
$690$	39.9777	+	17.1002i	1.52192	+	0.650994i
$691$	−13.4233	−	3.22264i	−0.510645	−	0.122595i	−0.0300683	−	0.999548i	$-0.509572\pi$
$691$	−13.4233	−	3.22264i	−0.510645	−	0.122595i	−0.480576	+	0.876953i	$0.659572\pi$
$692$	−8.71666	−	26.8271i	−0.331358	−	1.01981i
$693$	13.3545	+	6.80445i	0.507295	+	0.258480i
$694$	28.0499	−	67.7185i	1.06476	−	2.57056i
$695$	−13.3600	−	42.7848i	−0.506772	−	1.62292i
$696$			40.6575i			1.54112i
$697$	2.42448	−	4.20447i	0.0918336	−	0.159256i
$698$	25.5614	−	25.5614i	0.967511	−	0.967511i
$699$	1.88323	+	11.8903i	0.0712304	+	0.449731i
$700$	55.9418	+	68.6331i	2.11440	+	2.59409i
$701$	−13.0857	+	4.25180i	−0.494239	+	0.160588i	−0.545523	−	0.838096i	$-0.683669\pi$
$701$	−13.0857	+	4.25180i	−0.494239	+	0.160588i	0.0512834	+	0.998684i	$0.483669\pi$
$702$	−54.4103	+	17.6790i	−2.05358	+	0.667250i
$703$	−5.04311	−	8.22961i	−0.190205	−	0.310386i
$704$	−30.4983	+	7.32199i	−1.14945	+	0.275958i
$705$	10.0152	+	14.1233i	0.377195	+	0.531914i
$706$	−65.0417	−	65.0417i	−2.44788	−	2.44788i
$707$	0.583570	−	0.297344i	0.0219474	−	0.0111828i
$708$	8.19255	+	104.096i	0.307895	+	3.91217i
$709$	−10.9723	−	0.863538i	−0.412073	−	0.0324308i	−0.129271	−	0.991609i	$-0.541264\pi$
$709$	−10.9723	−	0.863538i	−0.412073	−	0.0324308i	−0.282802	+	0.959178i	$0.591264\pi$
$710$	6.97820	−	77.2975i	0.261887	−	2.90092i
$711$	0.730231	+	1.76293i	0.0273858	+	0.0661152i
$712$	−3.35049	+	42.5720i	−0.125565	+	1.59545i
$713$	−1.40766	+	8.88760i	−0.0527172	+	0.332843i
$714$	1.12256	+	14.2634i	0.0420106	+	0.533795i
$715$	17.0134	+	54.4849i	0.636266	+	2.03762i
$716$	57.6096	+	35.3032i	2.15297	+	1.31934i
$717$	−39.0889	+	28.3998i	−1.45980	+	1.06061i
$718$	−39.3116	+	28.5616i	−1.46710	+	1.06591i
$719$	−21.8988	−	13.4196i	−0.816688	−	0.500467i	0.0503368	−	0.998732i	$-0.483971\pi$
$719$	−21.8988	−	13.4196i	−0.816688	−	0.500467i	−0.867025	+	0.498265i	$0.833971\pi$
$720$	7.75872	−	14.8042i	0.289150	−	0.551720i
$721$	0.633416	+	8.04832i	0.0235897	+	0.299735i
$722$	2.31726	−	14.6306i	0.0862394	−	0.544494i
$723$	−2.46439	+	31.3131i	−0.0916517	+	1.16455i
$724$	31.0516	+	74.9653i	1.15402	+	2.78606i
$725$	9.64709	−	10.7832i	0.358284	−	0.400479i
$726$	68.6071	+	5.39949i	2.54625	+	0.200394i
$727$	1.13105	+	14.3713i	0.0419483	+	0.533004i	0.981610	+	0.190898i	$0.0611400\pi$
$727$	1.13105	+	14.3713i	0.0419483	+	0.533004i	−0.939662	+	0.342105i	$0.888860\pi$
$728$	122.718	−	62.5277i	4.54821	−	2.31743i
$729$	11.4803	+	11.4803i	0.425196	+	0.425196i
$730$	−17.2882	+	12.2595i	−0.639865	+	0.453745i
$731$	−3.03028	+	0.727505i	−0.112079	+	0.0269077i
$732$	−24.0710	−	39.2803i	−0.889690	−	1.45184i
$733$	23.0190	−	7.47932i	0.850225	−	0.276255i	0.148685	−	0.988885i	$-0.452496\pi$
$733$	23.0190	−	7.47932i	0.850225	−	0.276255i	0.701540	+	0.712630i	$0.252496\pi$
$734$	−8.50892	+	2.76472i	−0.314070	+	0.102047i
$735$	−25.5228	+	15.2397i	−0.941424	+	0.562125i
$736$	−5.68474	−	35.8921i	−0.209542	−	1.32300i
$737$	53.5449	−	53.5449i	1.97235	−	1.97235i
$738$	−4.53306	−	12.7794i	−0.166864	−	0.470416i
$739$			20.8612i			0.767393i	0.923459	+	0.383696i	$0.125349\pi$
$739$			20.8612i			0.767393i	−0.923459	+	0.383696i	$0.874651\pi$
$740$	−24.9762	−	13.0897i	−0.918144	−	0.481188i
$741$	−14.0456	+	33.9091i	−0.515978	+	1.24568i
$742$	−31.3989	−	15.9985i	−1.15269	−	0.587325i
$743$	10.1837	+	31.3421i	0.373603	+	1.14983i	0.944416	+	0.328752i	$0.106628\pi$
$743$	10.1837	+	31.3421i	0.373603	+	1.14983i	−0.570814	+	0.821080i	$0.693372\pi$
$744$	32.1155	+	7.71026i	1.17741	+	0.282672i
$745$	6.62121	+	16.5195i	0.242582	+	0.605228i
$746$	−15.8327	+	8.06718i	−0.579678	+	0.295361i
$747$			2.41187i			0.0882458i
$748$	8.12533	+	15.9469i	0.297092	+	0.583075i
$749$	−13.4441	−	11.4823i	−0.491235	−	0.419555i
$750$	−53.1901	+	19.9128i	−1.94223	+	0.727114i
$751$	5.04689	−	3.09274i	0.184164	−	0.112856i	−0.427361	−	0.904081i	$-0.640557\pi$
$751$	5.04689	−	3.09274i	0.184164	−	0.112856i	0.611524	+	0.791226i	$0.290557\pi$
$752$	13.9302	−	33.6305i	0.507983	−	1.22638i
$753$	27.9698	+	2.20127i	1.01927	+	0.0802187i
$754$	−22.7946	−	31.3741i	−0.830130	−	1.14258i
$755$	4.28653	+	18.8042i	0.156003	+	0.684355i
$756$	−61.1600	−	44.4353i	−2.22437	−	1.61610i
$757$	−3.35434	−	13.9718i	−0.121916	−	0.507815i	−0.999592	−	0.0285615i	$-0.990907\pi$
$757$	−3.35434	−	13.9718i	−0.121916	−	0.507815i	0.877676	−	0.479254i	$-0.159093\pi$
$758$	−19.2433	−	26.4861i	−0.698949	−	0.962020i
$759$	−5.79419	+	36.5831i	−0.210316	+	1.32788i
$760$	21.8307	+	54.4661i	0.791881	+	1.97569i
$761$	−20.3292	+	27.9808i	−0.736935	+	1.01430i	0.261855	+	0.965107i	$0.415666\pi$
$761$	−20.3292	+	27.9808i	−0.736935	+	1.01430i	−0.998789	+	0.0491960i	$0.984334\pi$
$762$	2.02979	−	2.37658i	0.0735314	−	0.0860942i
$763$	33.6984	+	5.33730i	1.21996	+	0.193223i
$764$	75.0634	+	87.8879i	2.71570	+	3.17967i
$765$	−1.33794	−	0.337521i	−0.0483734	−	0.0122031i
$766$	14.8158	+	24.1771i	0.535315	+	0.873555i
$767$	−37.5386	−	43.9521i	−1.35544	−	1.58702i
$768$	37.4131	−	2.94448i	1.35003	−	0.106250i
$769$	10.8678	−	33.4476i	0.391902	−	1.20615i	−0.539446	−	0.842020i	$-0.681366\pi$
$769$	10.8678	−	33.4476i	0.391902	−	1.20615i	0.931348	−	0.364130i	$-0.118634\pi$
$770$	−63.9299	+	85.8983i	−2.30387	+	3.09556i
$771$	−10.4352	−	20.4802i	−0.375814	−	0.737576i
$772$	−32.1316	−	19.6903i	−1.15644	−	0.708669i
$773$	24.4215	−	14.9655i	0.878382	−	0.538273i	−0.00865992	−	0.999963i	$-0.502757\pi$
$773$	24.4215	−	14.9655i	0.878382	−	0.538273i	0.887042	+	0.461690i	$0.152757\pi$
$774$	−3.95271	+	7.75763i	−0.142077	+	0.278842i
$775$	−6.68825	−	9.66520i	−0.240249	−	0.347184i
$776$	4.25364	+	1.76192i	0.152697	+	0.0632491i
$777$	11.2868	−	15.5349i	0.404912	−	0.557313i
$778$	32.8462	+	32.8462i	1.17759	+	1.17759i
$779$	21.8093	+	8.35852i	0.781400	+	0.299475i
$780$	15.5560	+	106.095i	0.556993	+	3.79880i
$781$	65.2987	−	10.3423i	2.33657	−	0.370077i
$782$	−6.97256	+	2.88813i	−0.249338	+	0.103279i
$783$	−5.60828	+	11.0069i	−0.200423	+	0.393353i
$784$	55.6861	+	28.3735i	1.98879	+	1.01334i
$785$	30.0274	+	35.9869i	1.07172	+	1.28443i
$786$	−20.1349	−	83.8678i	−0.718187	−	2.99146i
$787$	51.8178	+	16.8366i	1.84711	+	0.600161i	0.997331	+	0.0730176i	$0.0232629\pi$
$787$	51.8178	+	16.8366i	1.84711	+	0.600161i	0.849776	+	0.527144i	$0.176737\pi$
$788$	35.9710			1.28141
$789$	−16.5824	−	5.38795i	−0.590349	−	0.191816i
$790$	−13.2914	+	3.02986i	−0.472888	+	0.107798i
$791$	0.0122374	−	0.155491i	0.000435113	−	0.00552864i
$792$	28.2169	+	6.77427i	1.00264	+	0.240713i
$793$	23.5604	+	9.75904i	0.836654	+	0.346554i
$794$	−10.8877	+	9.29898i	−0.386390	+	0.330008i
$795$	11.3874	−	11.1286i	0.403870	−	0.394691i
$796$	−25.6032	+	2.01502i	−0.907482	+	0.0714204i
$797$	−0.429949	−	2.71459i	−0.0152296	−	0.0961558i	0.978903	−	0.204327i	$-0.0655006\pi$
$797$	−0.429949	−	2.71459i	−0.0152296	−	0.0961558i	−0.994132	+	0.108171i	$0.965501\pi$
$798$	−66.9499	+	16.0733i	−2.37000	+	0.568987i
$799$	−2.96817	−	0.470112i	−0.105006	−	0.0166314i
$800$	37.7498	+	28.7754i	1.33466	+	1.01736i
$801$	2.52500	−	4.12042i	0.0892164	−	0.145588i
$802$	29.4136	−	4.65866i	1.03863	−	0.164503i
$803$	−13.7281	−	11.7249i	−0.484455	−	0.413764i
$804$	115.086	−	83.6150i	4.05878	−	2.94887i
$805$	−23.9458	−	20.9324i	−0.843978	−	0.737769i
$806$	−29.1053	+	12.0558i	−1.02519	+	0.424647i
$807$	0.170956	−	0.712083i	0.00601793	−	0.0250665i
$808$	0.964249	−	0.823546i	0.0339222	−	0.0289723i
$809$	−13.9183	+	16.2962i	−0.489341	+	0.572945i	−0.949050	−	0.315124i	$-0.897954\pi$
$809$	−13.9183	+	16.2962i	−0.489341	+	0.572945i	0.459709	+	0.888070i	$0.347954\pi$
$810$	51.1431	−	36.2670i	1.79699	−	1.27429i
$811$	9.62551	−	9.62551i	0.337997	−	0.337997i	−0.517616	−	0.855613i	$-0.673180\pi$
$811$	9.62551	−	9.62551i	0.337997	−	0.337997i	0.855613	+	0.517616i	$0.173180\pi$
$812$	15.8355	−	48.7365i	0.555716	−	1.71032i
$813$	−6.34574	+	10.3553i	−0.222555	+	0.363176i
$814$	7.96068	−	33.1586i	0.279022	−	1.16221i
$815$	4.75379	+	9.60107i	0.166518	+	0.336311i
$816$	4.19992	+	12.9260i	0.147027	+	0.452502i
$817$	−5.73911	−	13.8554i	−0.200786	−	0.484740i
$818$	−35.1195	−	25.5158i	−1.22792	−	0.892140i
$819$	−15.5861			−0.544622
$820$	67.2257	−	11.6988i	2.34762	−	0.408541i
$821$	44.2878			1.54566			0.772828	−	0.634616i	$-0.218842\pi$
$821$	44.2878			1.54566			0.772828	+	0.634616i	$0.218842\pi$
$822$	−77.2875	−	56.1527i	−2.69571	−	1.95855i
$823$	−3.83199	−	9.25125i	−0.133575	−	0.322478i	0.842913	−	0.538049i	$-0.180839\pi$
$823$	−3.83199	−	9.25125i	−0.133575	−	0.322478i	−0.976488	+	0.215571i	$0.930839\pi$
$824$	4.83014	+	14.8656i	0.168266	+	0.517869i
$825$	−27.5301	−	39.7838i	−0.958476	−	1.38510i
$826$	25.3126	−	105.435i	0.880739	−	3.66854i
$827$	−22.4148	+	36.5776i	−0.779438	+	1.27193i	0.178211	+	0.983992i	$0.442969\pi$
$827$	−22.4148	+	36.5776i	−0.779438	+	1.27193i	−0.957650	+	0.287936i	$0.907031\pi$
$828$	−4.58959	+	14.1253i	−0.159499	+	0.490888i
$829$	−28.4770	+	28.4770i	−0.989049	+	0.989049i	−0.999941	−	0.0108921i	$-0.996533\pi$
$829$	−28.4770	+	28.4770i	−0.989049	+	0.989049i	0.0108921	+	0.999941i	$0.496533\pi$
$830$	−16.9866	−	2.89091i	−0.589612	−	0.100345i
$831$	36.4444	−	42.6709i	1.26424	−	1.48024i
$832$	24.8016	−	21.1826i	0.859842	−	0.734374i
$833$	1.20449	−	5.01705i	0.0417330	−	0.173830i
$834$	94.0764	−	38.9677i	3.25760	−	1.34934i
$835$	−13.5236	+	0.908071i	−0.468004	+	0.0314251i
$836$	−69.6797	+	50.6252i	−2.40992	+	1.75091i
$837$	7.63082	+	6.51734i	0.263760	+	0.225272i
$838$	98.9755	−	15.6762i	3.41905	−	0.541524i
$839$	4.05089	−	6.61045i	0.139852	−	0.228218i	−0.775044	−	0.631907i	$-0.782272\pi$
$839$	4.05089	−	6.61045i	0.139852	−	0.228218i	0.914896	+	0.403689i	$0.132272\pi$
$840$	−83.4902	+	81.5928i	−2.88069	+	2.81522i
$841$	20.3723	+	3.22665i	0.702492	+	0.111264i
$842$	43.9076	−	10.5413i	1.51316	−	0.363277i
$843$	6.29041	+	39.7161i	0.216653	+	1.36789i
$844$	−31.7400	+	2.49799i	−1.09254	+	0.0859844i
$845$	−21.1692	−	21.6615i	−0.728243	−	0.745178i
$846$	−6.38428	+	5.45269i	−0.219496	+	0.187467i
$847$	−46.5070	−	19.2638i	−1.59800	−	0.661913i
$848$	−32.5506	−	7.81472i	−1.11779	−	0.268358i
$849$	2.93924	−	37.3466i	0.100874	−	1.28173i
$850$	3.98080	−	9.01843i	0.136540	−	0.309330i
$851$	9.63320	+	3.13002i	0.330222	+	0.107296i
$852$	124.199			4.25498
$853$	−20.2558	−	6.58151i	−0.693545	−	0.225346i	−0.0590291	−	0.998256i	$-0.518800\pi$
$853$	−20.2558	−	6.58151i	−0.693545	−	0.225346i	−0.634516	+	0.772910i	$0.718800\pi$
$854$	11.1679	+	46.5176i	0.382157	+	1.59180i
$855$	0.597041	−	6.61342i	0.0204184	−	0.226174i
$856$	−30.4998	−	15.5404i	−1.04246	−	0.531161i
$857$	9.82600	−	19.2846i	0.335650	−	0.658750i	−0.660067	−	0.751207i	$-0.729472\pi$
$857$	9.82600	−	19.2846i	0.335650	−	0.658750i	0.995717	+	0.0924569i	$0.0294720\pi$
$858$	−119.803	+	49.6240i	−4.09000	+	1.69413i
$859$	−46.8046	+	7.41311i	−1.59695	+	0.252932i	−0.890552	−	0.454882i	$-0.849682\pi$
$859$	−46.8046	+	7.41311i	−1.59695	+	0.252932i	−0.706399	+	0.707814i	$0.749682\pi$
$860$	−35.1482	−	26.1591i	−1.19854	−	0.892019i
$861$	1.24104	+	46.4500i	0.0422945	+	1.58301i
$862$	53.0380	+	53.0380i	1.80648	+	1.80648i
$863$	4.64585	−	6.39446i	0.158146	−	0.217670i	−0.722590	−	0.691277i	$-0.757048\pi$
$863$	4.64585	−	6.39446i	0.158146	−	0.217670i	0.880736	+	0.473607i	$0.157048\pi$
$864$	−37.4417	−	15.5088i	−1.27379	−	0.527622i
$865$	−12.5392	−	4.23416i	−0.426344	−	0.143966i
$866$	−22.9634	+	45.0681i	−0.780327	+	1.53148i
$867$	−27.3515	+	16.7610i	−0.928906	+	0.569234i
$868$	−35.4942	−	21.7509i	−1.20475	−	0.738272i
$869$	−5.27200	−	10.3469i	−0.178840	−	0.350994i
$870$	26.3688	+	19.6250i	0.893986	+	0.665350i
$871$	−24.3336	+	74.8911i	−0.824512	+	2.53759i
$872$	65.8536	−	5.18279i	2.23008	−	0.175511i
$873$	−0.338378	−	0.396189i	−0.0114523	−	0.0134090i
$874$	−18.9765	−	30.9668i	−0.641889	−	1.04747i
$875$	41.5035	−	1.82982i	1.40307	−	0.0618593i
$876$	−22.0264	−	25.7896i	−0.744202	−	0.871349i
$877$	−26.5073	−	4.19835i	−0.895089	−	0.141768i	−0.308091	−	0.951357i	$-0.599690\pi$
$877$	−26.5073	−	4.19835i	−0.895089	−	0.141768i	−0.586998	+	0.809589i	$0.699690\pi$
$878$	−5.50034	+	6.44007i	−0.185628	+	0.217342i
$879$	−26.0192	+	35.8123i	−0.877605	+	1.20792i
$880$	−40.0027	+	93.5203i	−1.34849	+	3.15257i
$881$	−8.59779	+	54.2843i	−0.289667	+	1.82888i	0.228428	+	0.973561i	$0.426641\pi$
$881$	−8.59779	+	54.2843i	−0.289667	+	1.82888i	−0.518095	+	0.855323i	$0.673359\pi$
$882$	−8.47292	−	11.6620i	−0.285298	−	0.392679i
$883$	−4.76127	−	19.8321i	−0.160230	−	0.667404i	−0.993431	−	0.114434i	$-0.963494\pi$
$883$	−4.76127	−	19.8321i	−0.160230	−	0.667404i	0.833201	−	0.552970i	$-0.186506\pi$
$884$	−15.0572	−	10.9397i	−0.506427	−	0.367941i
$885$	41.4755	+	26.0766i	1.39418	+	0.876554i
$886$	22.0919	+	30.4069i	0.742193	+	1.02154i
$887$	−53.8938	−	4.24153i	−1.80958	−	0.142417i	−0.871846	−	0.489780i	$-0.837077\pi$
$887$	−53.8938	−	4.24153i	−1.80958	−	0.142417i	−0.937731	+	0.347363i	$0.887077\pi$
$888$	14.2273	−	34.3478i	0.477438	−	1.15264i
$889$	−1.94924	+	1.19450i	−0.0653754	+	0.0400621i
$890$	25.9932	+	22.7221i	0.871294	+	0.761647i
$891$	40.6115	+	34.6855i	1.36054	+	1.16201i
$892$	−50.1136	−	98.3534i	−1.67793	−	3.29312i
$893$		−	14.4618i		−	0.483946i
$894$	−36.0248	+	18.3555i	−1.20485	+	0.613901i
$895$	29.4257	−	11.7941i	0.983592	−	0.394235i
$896$	−9.10539	−	2.18601i	−0.304190	−	0.0730295i
$897$	−11.9024	−	36.6317i	−0.397409	−	1.22310i
$898$	−33.7292	−	17.1859i	−1.12556	−	0.573501i
$899$	−2.60318	+	6.28463i	−0.0868209	+	0.209604i
$900$	−8.40776	−	17.4833i	−0.280259	−	0.582778i
$901$			2.76362i			0.0920696i
$902$	33.6035	+	75.3669i	1.11887	+	2.50944i
$903$	21.0974	−	21.0974i	0.702077	−	0.702077i
$904$	−0.0472401	−	0.298262i	−0.00157118	−	0.00992006i
$905$	36.9144	+	9.31235i	1.22708	+	0.309553i
$906$	−41.6710	+	13.5397i	−1.38443	+	0.449828i
$907$	−7.41009	+	2.40768i	−0.246048	+	0.0799458i	−0.429445	−	0.903093i	$-0.641291\pi$
$907$	−7.41009	+	2.40768i	−0.246048	+	0.0799458i	0.183397	+	0.983039i	$0.441291\pi$
$908$	0.966105	+	1.57654i	0.0320613	+	0.0523193i
$909$	−0.139536	+	0.0334996i	−0.00462812	+	0.00111111i
$910$	18.6817	−	109.771i	0.619294	−	3.63888i
$911$	−3.70639	−	3.70639i	−0.122798	−	0.122798i	0.643037	−	0.765835i	$-0.277674\pi$
$911$	−3.70639	−	3.70639i	−0.122798	−	0.122798i	−0.765835	+	0.643037i	$0.777674\pi$
$912$	−58.2766	+	29.6934i	−1.92973	+	0.983247i
$913$	−1.15161	−	14.6326i	−0.0381128	−	0.484269i
$914$	92.9612	+	7.31621i	3.07488	+	0.241999i
$915$	−21.5276	−	1.94345i	−0.711679	−	0.0642484i
$916$	24.4064	+	58.9222i	0.806409	+	1.94684i
$917$	−4.94994	+	62.8950i	−0.163461	+	2.07698i
$918$	−1.31665	+	8.31300i	−0.0434559	+	0.274370i
$919$	−2.08117	−	26.4437i	−0.0686513	−	0.872298i	−0.930773	−	0.365597i	$-0.880865\pi$
$919$	−2.08117	−	26.4437i	−0.0686513	−	0.872298i	0.862122	−	0.506701i	$-0.169135\pi$
$920$	−54.5418	−	28.5847i	−1.79819	−	0.942411i
$921$	−17.4342	−	10.6837i	−0.574476	−	0.352039i
$922$	−36.3733	+	26.4267i	−1.19789	+	0.870318i
$923$	−55.6203	+	40.4105i	−1.83076	+	1.33013i
$924$	−146.101	−	89.5307i	−4.80637	−	2.94534i
$925$	−11.9233	+	5.73394i	−0.392037	+	0.188531i
$926$	6.72434	+	85.4408i	0.220975	+	2.80776i
$927$	0.276708	−	1.74706i	0.00908827	−	0.0573811i
$928$	2.15537	−	27.3866i	0.0707534	−	0.899008i
$929$	4.03605	+	9.74389i	0.132419	+	0.319687i	0.976156	−	0.217069i	$-0.0696497\pi$
$929$	4.03605	+	9.74389i	0.132419	+	0.319687i	−0.843738	+	0.536756i	$0.819650\pi$
$930$	20.5024	−	17.1072i	0.672302	−	0.560966i
$931$	24.7531	+	1.94811i	0.811251	+	0.0638468i
$932$	−2.30491	−	29.2866i	−0.0754998	−	0.959316i
$933$	−20.4247	+	10.4069i	−0.668674	+	0.340706i
$934$	−3.61395	−	3.61395i	−0.118252	−	0.118252i
$935$	8.27833	+	1.40887i	0.270730	+	0.0460751i
$936$	−29.3427	+	7.04456i	−0.959096	+	0.230259i
$937$	13.1439	+	21.4489i	0.429393	+	0.700706i	0.992031	−	0.125998i	$-0.0402131\pi$
$937$	13.1439	+	21.4489i	0.429393	+	0.700706i	−0.562637	+	0.826704i	$0.690213\pi$
$938$	−140.491	+	45.6483i	−4.58719	+	1.49047i
$939$	35.3865	−	11.4978i	1.15480	−	0.375216i
$940$	−21.6605	−	36.2760i	−0.706486	−	1.18319i
$941$	−1.25197	−	7.90460i	−0.0408129	−	0.257683i	0.958842	−	0.283939i	$-0.0916413\pi$
$941$	−1.25197	−	7.90460i	−0.0408129	−	0.257683i	−0.999655	+	0.0262565i	$0.991641\pi$
$942$	−75.2910	+	75.2910i	−2.45311	+	2.45311i
$943$	−23.1003	+	8.19406i	−0.752249	+	0.266835i
$944$		−	103.002i		−	3.35244i
$945$	−33.8575	+	10.5723i	−1.10138	+	0.343918i
$946$	20.2766	−	48.9521i	0.659250	−	1.59157i
$947$	36.8727	+	18.7876i	1.19820	+	0.610515i	0.935145	−	0.354265i	$-0.115269\pi$
$947$	36.8727	+	18.7876i	1.19820	+	0.610515i	0.263058	+	0.964780i	$0.415269\pi$
$948$	−6.74130	−	20.7476i	−0.218947	−	0.673850i
$949$	18.2553	+	4.38270i	0.592591	+	0.142269i
$950$	45.8620	+	12.1318i	1.48796	+	0.393609i
$951$	2.52184	−	1.28494i	0.0817763	−	0.0416671i
$952$		−	20.2623i		−	0.656705i
$953$	−11.5826	−	22.7321i	−0.375197	−	0.736366i	0.623779	−	0.781601i	$-0.285597\pi$
$953$	−11.5826	−	22.7321i	−0.375197	−	0.736366i	−0.998976	+	0.0452344i	$0.985597\pi$
$954$	5.87113	+	5.01442i	0.190085	+	0.162348i
$955$	54.1072	−	3.63314i	1.75087	−	0.117566i
$956$	100.531	−	61.6056i	3.25141	−	1.99247i
$957$	−10.7152	+	25.8687i	−0.346373	+	0.836218i
$958$	80.6031	+	6.34360i	2.60417	+	0.204952i
$959$	41.0737	+	56.5331i	1.32634	+	1.82555i
$960$	−14.7147	+	23.4041i	−0.474915	+	0.755365i
$961$	−20.6089	−	14.9733i	−0.664804	−	0.483009i
$962$	8.27830	+	34.4816i	0.266903	+	1.11173i
$963$	2.27691	+	3.13390i	0.0733725	+	0.100989i
$964$	11.9905	−	75.7052i	0.386189	−	2.43830i
$965$	−16.4121	+	6.57817i	−0.528325	+	0.211759i
$966$	42.4706	−	58.4557i	1.36647	−	1.88078i
$967$	−16.0013	+	18.7351i	−0.514566	+	0.602479i	−0.955475	−	0.295073i	$-0.904656\pi$
$967$	−16.0013	+	18.7351i	−0.514566	+	0.602479i	0.440909	+	0.897552i	$0.354656\pi$
$968$	−96.2618	−	15.2464i	−3.09397	−	0.490037i
$969$	3.50678	+	4.10591i	0.112654	+	0.131901i
$970$	3.19590	−	1.90828i	0.102614	−	0.0612711i
$971$	−6.38651	−	10.4218i	−0.204953	−	0.334453i	0.733604	−	0.679577i	$-0.237837\pi$
$971$	−6.38651	−	10.4218i	−0.204953	−	0.334453i	−0.938557	+	0.345124i	$0.887837\pi$
$972$	25.5208	+	29.8810i	0.818580	+	0.958434i
$973$	−74.2536	+	5.84389i	−2.38046	+	0.187346i
$974$	−27.5161	+	84.6858i	−0.881672	+	2.71351i
$975$	44.2903	+	23.8649i	1.41843	+	0.764288i
$976$	20.6313	+	40.4912i	0.660392	+	1.29609i
$977$	−10.8442	−	6.64535i	−0.346937	−	0.212603i	0.338102	−	0.941109i	$-0.390215\pi$
$977$	−10.8442	−	6.64535i	−0.346937	−	0.212603i	−0.685039	+	0.728506i	$0.740215\pi$
$978$	−20.7525	+	12.7171i	−0.663591	+	0.406649i
$979$	−13.3515	+	26.2038i	−0.426716	+	0.837478i
$980$	65.0086	−	32.1878i	2.07662	−	1.02820i
$981$	−6.90633	−	2.86069i	−0.220502	−	0.0913350i
$982$	19.3284	−	26.6033i	0.616794	−	0.848944i
$983$	18.5229	+	18.5229i	0.590789	+	0.590789i	0.937845	−	0.347056i	$-0.112818\pi$
$983$	18.5229	+	18.5229i	0.590789	+	0.590789i	−0.347056	+	0.937845i	$0.612818\pi$
$984$	23.3307	+	86.8868i	0.743757	+	2.76985i
$985$	10.0764	−	13.5390i	0.321062	−	0.431389i
$986$	−5.63503	+	0.892501i	−0.179456	+	0.0284230i
$987$	26.5813	−	11.0103i	0.846093	−	0.350463i
$988$	40.6618	−	79.8032i	1.29362	−	2.53888i
$989$	14.0229	+	7.14500i	0.445901	+	0.227198i
$990$	18.0136	−	15.0304i	0.572509	−	0.477699i
$991$	−8.25583	−	34.3880i	−0.262255	−	1.09237i	−0.935605	−	0.353047i	$-0.885145\pi$
$991$	−8.25583	−	34.3880i	−0.262255	−	1.09237i	0.673350	−	0.739323i	$-0.264855\pi$
$992$	−21.2240	−	6.89610i	−0.673863	−	0.218951i
$993$	35.5145			1.12702
$994$	−122.659	−	39.8544i	−3.89051	−	1.26410i
$995$	−6.41372	+	10.2012i	−0.203329	+	0.323400i
$996$	2.16341	−	27.4887i	0.0685502	−	0.871013i
$997$	−0.753300	−	0.180851i	−0.0238573	−	0.00572762i	0.221499	−	0.975161i	$-0.428905\pi$
$997$	−0.753300	−	0.180851i	−0.0238573	−	0.00572762i	−0.245356	+	0.969433i	$0.578905\pi$
$998$	−19.7236	−	8.16979i	−0.624340	−	0.258610i
$999$	8.58956	−	7.33618i	0.271762	−	0.232106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	205.2.y.a.112.2	yes	304
5.3	odd	4		205.2.bb.a.153.2	yes	304
41.26	odd	40		205.2.bb.a.67.2	yes	304
205.108	even	40	inner	205.2.y.a.108.2	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
205.2.y.a.108.2	✓	304	205.108	even	40	inner
205.2.y.a.112.2	yes	304	1.1	even	1	trivial
205.2.bb.a.67.2	yes	304	41.26	odd	40
205.2.bb.a.153.2	yes	304	5.3	odd	4

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:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.y (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10435 - 1.52890i) q^{2} +(-0.747373 - 1.80432i) q^{3} +(1.47272 + 4.53255i) q^{4} +(2.11855 + 0.715379i) q^{5} +(-1.18589 + 4.93957i) q^{6} +(1.94149 - 3.16823i) q^{7} +(2.22313 - 6.84209i) q^{8} +(-0.575677 + 0.575677i) q^{9} +(-3.36441 - 4.74445i) q^{10} +(3.21770 - 3.76745i) q^{11} +(7.07750 - 6.04476i) q^{12} +(-1.20276 + 5.00984i) q^{13} +(-8.92948 + 3.69871i) q^{14} +(-0.292573 - 4.35718i) q^{15} +(-7.42785 + 5.39665i) q^{16} +(0.576370 + 0.492267i) q^{17} +(2.09158 - 0.331273i) q^{18} +(-1.90588 + 3.11011i) q^{19} +(-0.122478 + 10.6560i) q^{20} +(-7.16751 - 1.13522i) q^{21} +(-12.5312 + 3.00848i) q^{22} +(-0.598816 - 3.78077i) q^{23} +(-14.0068 + 1.10236i) q^{24} +(3.97647 + 3.03112i) q^{25} +(10.1906 - 8.70356i) q^{26} +(-3.94400 - 1.63366i) q^{27} +(17.2194 + 4.13402i) q^{28} +(0.227041 - 2.88483i) q^{29} +(-6.04602 + 9.61634i) q^{30} +(-2.23568 - 0.726417i) q^{31} +9.49331 q^{32} +(-9.20250 - 2.99007i) q^{33} +(-0.460258 - 1.91711i) q^{34} +(6.37963 - 5.32313i) q^{35} +(-3.45709 - 1.76148i) q^{36} +(-1.20130 + 2.35768i) q^{37} +(8.76567 - 3.63086i) q^{38} +(9.93826 - 1.57407i) q^{39} +(9.60448 - 12.9049i) q^{40} +(-1.17022 - 6.29528i) q^{41} +(13.3473 + 13.3473i) q^{42} +(-2.41665 + 3.32623i) q^{43} +(21.8149 + 9.03604i) q^{44} +(-1.63142 + 0.807770i) q^{45} +(-4.52030 + 8.87159i) q^{46} +(-3.38048 + 2.07156i) q^{47} +(15.2886 + 9.36889i) q^{48} +(-3.09035 - 6.06515i) q^{49} +(-3.73359 - 12.4582i) q^{50} +(0.457442 - 1.40786i) q^{51} +(-24.4787 + 1.92652i) q^{52} +(2.36792 + 2.77248i) q^{53} +(5.80186 + 9.46777i) q^{54} +(9.51200 - 5.67963i) q^{55} +(-17.3611 - 20.3273i) q^{56} +(7.03603 + 1.11440i) q^{57} +(-4.88838 + 5.72356i) q^{58} +(-6.59416 + 9.07609i) q^{59} +(19.3183 - 7.74300i) q^{60} +(0.774296 - 4.88871i) q^{61} +(3.59404 + 4.94677i) q^{62} +(0.706203 + 2.94155i) q^{63} +(-5.12153 - 3.72101i) q^{64} +(-6.13203 + 9.75315i) q^{65} +(14.7937 + 20.3618i) q^{66} +(15.2367 + 1.19915i) q^{67} +(-1.38240 + 3.33740i) q^{68} +(-6.37418 + 3.90610i) q^{69} +(-21.5635 + 1.44793i) q^{70} +(10.1468 + 8.66618i) q^{71} +(2.65903 + 5.21863i) q^{72} -3.64388i q^{73} +(6.13259 - 3.12471i) q^{74} +(2.49721 - 9.44019i) q^{75} +(-16.9036 - 4.05819i) q^{76} +(-5.68899 - 17.5089i) q^{77} +(-23.3201 - 11.8822i) q^{78} +(0.896947 - 2.16542i) q^{79} +(-19.5969 + 6.11932i) q^{80} +10.7796i q^{81} +(-7.16229 + 15.0366i) q^{82} +(2.09482 - 2.09482i) q^{83} +(-5.41026 - 34.1590i) q^{84} +(0.868909 + 1.45521i) q^{85} +(10.1709 - 3.30474i) q^{86} +(-5.37483 + 1.74639i) q^{87} +(-18.6238 - 30.3913i) q^{88} +(-5.77183 + 1.38569i) q^{89} +(4.66808 + 0.794452i) q^{90} +(13.5372 + 13.5372i) q^{91} +(16.2547 - 8.28217i) q^{92} +(0.360201 + 4.57679i) q^{93} +(10.2809 + 0.809125i) q^{94} +(-6.26260 + 5.22548i) q^{95} +(-7.09504 - 17.1289i) q^{96} +(-0.0502119 + 0.638003i) q^{97} +(-2.76983 + 17.4880i) q^{98} +(0.316474 + 4.02119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) \) 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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