LMFDB - Embedded newform 256.2.m.a.5.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.19
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247919 - 1.39231i) q^{2} +(0.0918072 - 0.618914i) q^{3} +(-1.87707 - 0.690363i) q^{4} +(-2.56691 - 0.126104i) q^{5} +(-0.838961 - 0.281265i) q^{6} +(-3.84053 - 2.05281i) q^{7} +(-1.42656 + 2.44232i) q^{8} +(2.49620 + 0.757213i) q^{9} +O(q^{10})$	\(q+(0.247919 - 1.39231i) q^{2} +(0.0918072 - 0.618914i) q^{3} +(-1.87707 - 0.690363i) q^{4} +(-2.56691 - 0.126104i) q^{5} +(-0.838961 - 0.281265i) q^{6} +(-3.84053 - 2.05281i) q^{7} +(-1.42656 + 2.44232i) q^{8} +(2.49620 + 0.757213i) q^{9} +(-0.811964 + 3.54268i) q^{10} +(1.53483 + 2.56072i) q^{11} +(-0.599604 + 1.09837i) q^{12} +(-1.80079 + 1.98686i) q^{13} +(-3.81029 + 4.83829i) q^{14} +(-0.313709 + 1.57712i) q^{15} +(3.04680 + 2.59172i) q^{16} +(-1.12930 - 5.67736i) q^{17} +(1.67313 - 3.28776i) q^{18} +(-2.68453 - 5.67596i) q^{19} +(4.73122 + 2.00881i) q^{20} +(-1.62310 + 2.18849i) q^{21} +(3.94584 - 1.50212i) q^{22} +(-6.08313 - 4.99230i) q^{23} +(1.38062 + 1.10714i) q^{24} +(1.59721 + 0.157312i) q^{25} +(2.31989 + 2.99984i) q^{26} +(1.50036 - 3.17225i) q^{27} +(5.79177 + 6.50462i) q^{28} +(2.10125 - 0.526335i) q^{29} +(2.11807 + 0.827779i) q^{30} +(0.235466 + 0.0975331i) q^{31} +(4.36385 - 3.59956i) q^{32} +(1.72577 - 0.714838i) q^{33} +(-8.18464 + 0.164808i) q^{34} +(9.59943 + 5.75368i) q^{35} +(-4.16279 - 3.14462i) q^{36} +(0.870354 + 2.43248i) q^{37} +(-8.56827 + 2.33053i) q^{38} +(1.06437 + 1.29694i) q^{39} +(3.96985 - 6.08932i) q^{40} +(-7.02904 + 0.692300i) q^{41} +(2.64467 + 2.80243i) q^{42} +(0.618477 - 0.0917424i) q^{43} +(-1.11317 - 5.86624i) q^{44} +(-6.31203 - 2.25848i) q^{45} +(-8.45897 + 7.23194i) q^{46} +(6.81255 - 10.1957i) q^{47} +(1.88377 - 1.64777i) q^{48} +(6.64666 + 9.94743i) q^{49} +(0.615007 - 2.18482i) q^{50} +(-3.61748 + 0.177715i) q^{51} +(4.75187 - 2.48629i) q^{52} +(10.4409 + 2.61530i) q^{53} +(-4.04480 - 2.87544i) q^{54} +(-3.61687 - 6.76669i) q^{55} +(10.4924 - 6.45134i) q^{56} +(-3.75939 + 1.14040i) q^{57} +(-0.211883 - 3.05608i) q^{58} +(-1.43845 - 1.58708i) q^{59} +(1.67764 - 2.74380i) q^{60} +(6.67684 + 9.00268i) q^{61} +(0.194173 - 0.303662i) q^{62} +(-8.03230 - 8.03230i) q^{63} +(-3.92983 - 6.96824i) q^{64} +(4.87302 - 4.87302i) q^{65} +(-0.567426 - 2.58004i) q^{66} +(-7.79859 + 5.78383i) q^{67} +(-1.79967 + 11.4364i) q^{68} +(-3.64828 + 3.30660i) q^{69} +(10.3908 - 11.9390i) q^{70} +(-1.07050 - 3.52897i) q^{71} +(-5.41033 + 5.01629i) q^{72} +(-7.98527 + 4.26822i) q^{73} +(3.60255 - 0.608748i) q^{74} +(0.243998 - 0.974095i) q^{75} +(1.12058 + 12.5075i) q^{76} +(-0.637923 - 12.9852i) q^{77} +(2.06963 - 1.16040i) q^{78} +(5.32066 - 3.55515i) q^{79} +(-7.49404 - 7.03694i) q^{80} +(4.68110 + 3.12781i) q^{81} +(-0.778736 + 9.95826i) q^{82} +(1.21876 - 3.40619i) q^{83} +(4.55753 - 2.98743i) q^{84} +(2.18287 + 14.7157i) q^{85} +(0.0255983 - 0.883859i) q^{86} +(-0.132846 - 1.34881i) q^{87} +(-8.44362 + 0.0955291i) q^{88} +(8.12670 - 6.66941i) q^{89} +(-4.70938 + 8.22840i) q^{90} +(10.9946 - 3.93394i) q^{91} +(7.97198 + 13.5705i) q^{92} +(0.0819820 - 0.136779i) q^{93} +(-12.5067 - 12.0129i) q^{94} +(6.17519 + 14.9082i) q^{95} +(-1.82718 - 3.03131i) q^{96} +(-0.0441206 + 0.106517i) q^{97} +(15.4978 - 6.78807i) q^{98} +(1.89224 + 7.55425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

Coefficient data

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

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

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

$2$	0.247919	−	1.39231i	0.175305	−	0.984514i
$2$	0.247919	−	1.39231i	0.175305	−	0.984514i
$3$	0.0918072	−	0.618914i	0.0530049	−	0.357330i	−0.946405	−	0.322982i	$-0.895315\pi$
$3$	0.0918072	−	0.618914i	0.0530049	−	0.357330i	0.999410	−	0.0343478i	$-0.0109354\pi$
$4$	−1.87707	−	0.690363i	−0.938536	−	0.345181i
$5$	−2.56691	−	0.126104i	−1.14796	−	0.0563956i	−0.533823	−	0.845596i	$-0.679245\pi$
$5$	−2.56691	−	0.126104i	−1.14796	−	0.0563956i	−0.614135	+	0.789201i	$0.710495\pi$
$6$	−0.838961	−	0.281265i	−0.342504	−	0.114826i
$7$	−3.84053	−	2.05281i	−1.45158	−	0.775888i	−0.457996	−	0.888954i	$-0.651433\pi$
$7$	−3.84053	−	2.05281i	−1.45158	−	0.775888i	−0.993587	+	0.113067i	$0.963933\pi$
$8$	−1.42656	+	2.44232i	−0.504366	+	0.863490i
$9$	2.49620	+	0.757213i	0.832065	+	0.252404i
$10$	−0.811964	+	3.54268i	−0.256766	+	1.12029i
$11$	1.53483	+	2.56072i	0.462770	+	0.772085i	0.997329	−	0.0730462i	$-0.0232721\pi$
$11$	1.53483	+	2.56072i	0.462770	+	0.772085i	−0.534558	+	0.845131i	$0.679522\pi$
$12$	−0.599604	+	1.09837i	−0.173091	+	0.317071i
$13$	−1.80079	+	1.98686i	−0.499449	+	0.551057i	−0.937542	−	0.347873i	$-0.886904\pi$
$13$	−1.80079	+	1.98686i	−0.499449	+	0.551057i	0.438093	+	0.898930i	$0.355654\pi$
$14$	−3.81029	+	4.83829i	−1.01834	+	1.29309i
$15$	−0.313709	+	1.57712i	−0.0809992	+	0.407211i
$16$	3.04680	+	2.59172i	0.761700	+	0.647930i
$17$	−1.12930	−	5.67736i	−0.273895	−	1.37696i	−0.835469	−	0.549537i	$-0.814804\pi$
$17$	−1.12930	−	5.67736i	−0.273895	−	1.37696i	0.561575	−	0.827426i	$-0.310196\pi$
$18$	1.67313	−	3.28776i	0.394361	−	0.774932i
$19$	−2.68453	−	5.67596i	−0.615874	−	1.30216i	−0.935069	−	0.354466i	$-0.884663\pi$
$19$	−2.68453	−	5.67596i	−0.615874	−	1.30216i	0.319195	−	0.947689i	$-0.396587\pi$
$20$	4.73122	+	2.00881i	1.05793	+	0.449183i
$21$	−1.62310	+	2.18849i	−0.354189	+	0.477568i
$22$	3.94584	−	1.50212i	0.841255	−	0.320253i
$23$	−6.08313	−	4.99230i	−1.26842	−	1.04097i	−0.996912	−	0.0785300i	$-0.974977\pi$
$23$	−6.08313	−	4.99230i	−1.26842	−	1.04097i	−0.271509	−	0.962436i	$-0.587523\pi$
$24$	1.38062	+	1.10714i	0.281817	+	0.225994i
$25$	1.59721	+	0.157312i	0.319443	+	0.0314624i
$26$	2.31989	+	2.99984i	0.454967	+	0.588318i
$27$	1.50036	−	3.17225i	0.288745	−	0.610500i
$28$	5.79177	+	6.50462i	1.09454	+	1.22926i
$29$	2.10125	−	0.526335i	0.390192	−	0.0977380i	−0.0429192	−	0.999079i	$-0.513666\pi$
$29$	2.10125	−	0.526335i	0.390192	−	0.0977380i	0.433111	+	0.901341i	$0.357416\pi$
$30$	2.11807	+	0.827779i	0.386705	+	0.151131i
$31$	0.235466	+	0.0975331i	0.0422909	+	0.0175175i	0.403729	−	0.914879i	$-0.367714\pi$
$31$	0.235466	+	0.0975331i	0.0422909	+	0.0175175i	−0.361438	+	0.932396i	$0.617714\pi$
$32$	4.36385	−	3.59956i	0.771427	−	0.636318i
$33$	1.72577	−	0.714838i	0.300418	−	0.124437i
$34$	−8.18464	+	0.164808i	−1.40365	+	0.0282644i
$35$	9.59943	+	5.75368i	1.62260	+	0.972549i
$36$	−4.16279	−	3.14462i	−0.693798	−	0.524104i
$37$	0.870354	+	2.43248i	0.143085	+	0.399897i	0.991611	−	0.129257i	$-0.0412593\pi$
$37$	0.870354	+	2.43248i	0.143085	+	0.399897i	−0.848526	+	0.529154i	$0.822509\pi$
$38$	−8.56827	+	2.33053i	−1.38996	+	0.378061i
$39$	1.06437	+	1.29694i	0.170436	+	0.207677i
$40$	3.96985	−	6.08932i	0.627688	−	0.962806i
$41$	−7.02904	+	0.692300i	−1.09775	+	0.108119i	−0.630637	−	0.776078i	$-0.717206\pi$
$41$	−7.02904	+	0.692300i	−1.09775	+	0.108119i	−0.467114	+	0.884197i	$0.654706\pi$
$42$	2.64467	+	2.80243i	0.408082	+	0.432424i
$43$	0.618477	−	0.0917424i	0.0943169	−	0.0139906i	−0.0994052	−	0.995047i	$-0.531694\pi$
$43$	0.618477	−	0.0917424i	0.0943169	−	0.0139906i	0.193722	+	0.981056i	$0.437944\pi$
$44$	−1.11317	−	5.86624i	−0.167817	−	0.884369i
$45$	−6.31203	−	2.25848i	−0.940941	−	0.336674i
$46$	−8.45897	+	7.23194i	−1.24721	+	1.06629i
$47$	6.81255	−	10.1957i	0.993713	−	1.48720i	0.124831	−	0.992178i	$-0.460161\pi$
$47$	6.81255	−	10.1957i	0.993713	−	1.48720i	0.868882	−	0.495019i	$-0.164839\pi$
$48$	1.88377	−	1.64777i	0.271899	−	0.237835i
$49$	6.64666	+	9.94743i	0.949523	+	1.42106i
$50$	0.615007	−	2.18482i	0.0869752	−	0.308980i
$51$	−3.61748	+	0.177715i	−0.506548	+	0.0248851i
$52$	4.75187	−	2.48629i	0.658966	−	0.344786i
$53$	10.4409	+	2.61530i	1.43416	+	0.359239i	0.880716	−	0.473645i	$-0.157062\pi$
$53$	10.4409	+	2.61530i	1.43416	+	0.359239i	0.553447	+	0.832884i	$0.313312\pi$
$54$	−4.04480	−	2.87544i	−0.550427	−	0.391298i
$55$	−3.61687	−	6.76669i	−0.487699	−	0.912420i
$56$	10.4924	−	6.45134i	1.40210	−	0.862096i
$57$	−3.75939	+	1.14040i	−0.497944	+	0.151050i
$58$	−0.211883	−	3.05608i	−0.0278217	−	0.401283i
$59$	−1.43845	−	1.58708i	−0.187270	−	0.206621i	0.640079	−	0.768309i	$-0.278902\pi$
$59$	−1.43845	−	1.58708i	−0.187270	−	0.206621i	−0.827349	+	0.561689i	$0.810152\pi$
$60$	1.67764	−	2.74380i	0.216582	−	0.354222i
$61$	6.67684	+	9.00268i	0.854882	+	1.15267i	0.986885	+	0.161426i	$0.0516092\pi$
$61$	6.67684	+	9.00268i	0.854882	+	1.15267i	−0.132003	+	0.991249i	$0.542141\pi$
$62$	0.194173	−	0.303662i	0.0246600	−	0.0385651i
$63$	−8.03230	−	8.03230i	−1.01197	−	1.01197i
$64$	−3.92983	−	6.96824i	−0.491229	−	0.871030i
$65$	4.87302	−	4.87302i	0.604424	−	0.604424i
$66$	−0.567426	−	2.58004i	−0.0698453	−	0.317581i
$67$	−7.79859	+	5.78383i	−0.952750	+	0.706607i	−0.955994	−	0.293387i	$-0.905217\pi$
$67$	−7.79859	+	5.78383i	−0.952750	+	0.706607i	0.00324399	+	0.999995i	$0.498967\pi$
$68$	−1.79967	+	11.4364i	−0.218242	+	1.38687i
$69$	−3.64828	+	3.30660i	−0.439201	+	0.398068i
$70$	10.3908	−	11.9390i	1.24194	−	1.42698i
$71$	−1.07050	−	3.52897i	−0.127045	−	0.418811i	0.870225	−	0.492655i	$-0.163973\pi$
$71$	−1.07050	−	3.52897i	−0.127045	−	0.418811i	−0.997270	+	0.0738435i	$0.976473\pi$
$72$	−5.41033	+	5.01629i	−0.637614	+	0.591176i
$73$	−7.98527	+	4.26822i	−0.934606	+	0.499557i	−0.867085	−	0.498161i	$-0.834009\pi$
$73$	−7.98527	+	4.26822i	−0.934606	+	0.499557i	−0.0675209	+	0.997718i	$0.521509\pi$
$74$	3.60255	−	0.608748i	0.418788	−	0.0707655i
$75$	0.243998	−	0.974095i	0.0281745	−	0.112479i
$76$	1.12058	+	12.5075i	0.128540	+	1.43471i
$77$	−0.637923	−	12.9852i	−0.0726981	−	1.47980i
$78$	2.06963	−	1.16040i	0.234339	−	0.131390i
$79$	5.32066	−	3.55515i	0.598620	−	0.399985i	−0.219015	−	0.975721i	$-0.570284\pi$
$79$	5.32066	−	3.55515i	0.598620	−	0.399985i	0.817636	+	0.575736i	$0.195284\pi$
$80$	−7.49404	−	7.03694i	−0.837859	−	0.786753i
$81$	4.68110	+	3.12781i	0.520123	+	0.347535i
$82$	−0.778736	+	9.95826i	−0.0859970	+	1.09971i
$83$	1.21876	−	3.40619i	0.133776	−	0.373878i	−0.855912	−	0.517122i	$-0.827003\pi$
$83$	1.21876	−	3.40619i	0.133776	−	0.373878i	0.989687	+	0.143244i	$0.0457533\pi$
$84$	4.55753	−	2.98743i	0.497267	−	0.325956i
$85$	2.18287	+	14.7157i	0.236765	+	1.59614i
$86$	0.0255983	−	0.883859i	0.00276033	−	0.0953089i
$87$	−0.132846	−	1.34881i	−0.0142426	−	0.144608i
$88$	−8.44362	+	0.0955291i	−0.900093	+	0.0101834i
$89$	8.12670	−	6.66941i	0.861429	−	0.706956i	−0.0960759	−	0.995374i	$-0.530629\pi$
$89$	8.12670	−	6.66941i	0.861429	−	0.706956i	0.957505	+	0.288418i	$0.0931291\pi$
$90$	−4.70938	+	8.22840i	−0.496413	+	0.867349i
$91$	10.9946	−	3.93394i	1.15255	−	0.412389i
$92$	7.97198	+	13.5705i	0.831136	+	1.41482i
$93$	0.0819820	−	0.136779i	0.00850114	−	0.0141833i
$94$	−12.5067	−	12.0129i	−1.28996	−	1.23904i
$95$	6.17519	+	14.9082i	0.633561	+	1.52955i
$96$	−1.82718	−	3.03131i	−0.186486	−	0.309382i
$97$	−0.0441206	+	0.106517i	−0.00447977	+	0.0108151i	−0.926104	−	0.377269i	$-0.876863\pi$
$97$	−0.0441206	+	0.106517i	−0.00447977	+	0.0108151i	0.921624	+	0.388084i	$0.126863\pi$
$98$	15.4978	−	6.78807i	1.56551	−	0.685699i
$99$	1.89224	+	7.55425i	0.190177	+	0.759230i
$100$	−2.88948	−	1.39794i	−0.288948	−	0.139794i
$101$	−10.6125	−	5.01934i	−1.05598	−	0.499443i	−0.180944	−	0.983493i	$-0.557915\pi$
$101$	−10.6125	−	5.01934i	−1.05598	−	0.499443i	−0.875040	+	0.484050i	$0.839165\pi$
$102$	−0.649407	+	5.08072i	−0.0643009	+	0.503066i
$103$	−0.0217168	+	0.220494i	−0.00213982	+	0.0217259i	−0.996195	−	0.0871483i	$-0.972225\pi$
$103$	−0.0217168	+	0.220494i	−0.00213982	+	0.0217259i	0.994056	+	0.108874i	$0.0347246\pi$
$104$	−2.28362	−	7.23249i	−0.223927	−	0.709204i
$105$	4.44233	−	5.41299i	0.433527	−	0.528254i
$106$	6.22981	−	13.8886i	0.605092	−	1.34898i
$107$	−7.76506	−	5.75896i	−0.750677	−	0.556740i	0.151319	−	0.988485i	$-0.451648\pi$
$107$	−7.76506	−	5.75896i	−0.750677	−	0.556740i	−0.901996	+	0.431745i	$0.857898\pi$
$108$	−5.00629	+	4.91875i	−0.481731	+	0.473307i
$109$	−5.21683	+	2.46738i	−0.499682	+	0.236332i	−0.660743	−	0.750613i	$-0.729759\pi$
$109$	−5.21683	+	2.46738i	−0.499682	+	0.236332i	0.161061	+	0.986945i	$0.448509\pi$
$110$	−10.3180	+	3.35822i	−0.983786	+	0.320194i
$111$	1.58540	−	0.315355i	0.150479	−	0.0299322i
$112$	−6.38102	−	16.2081i	−0.602950	−	1.53152i
$113$	−2.31519	−	0.460520i	−0.217795	−	0.0433221i	0.0849866	−	0.996382i	$-0.472915\pi$
$113$	−2.31519	−	0.460520i	−0.217795	−	0.0433221i	−0.302782	+	0.953060i	$0.597915\pi$
$114$	0.655767	+	5.51698i	0.0614182	+	0.516712i
$115$	14.9853	+	13.5819i	1.39739	+	1.26652i
$116$	−4.30755	−	0.462654i	−0.399946	−	0.0429563i
$117$	−5.99960	+	3.59602i	−0.554663	+	0.332452i
$118$	−2.56634	+	1.60930i	−0.236250	+	0.148148i
$119$	−7.31742	+	24.1223i	−0.670787	+	2.21129i
$120$	−3.40430	−	3.01604i	−0.310769	−	0.275325i
$121$	0.983810	−	1.84058i	0.0894373	−	0.167325i
$122$	14.1899	−	7.06432i	1.28469	−	0.639573i
$123$	−0.216842	+	4.41393i	−0.0195520	+	0.397990i
$124$	−0.374653	−	0.345633i	−0.0336448	−	0.0310388i
$125$	8.63089	+	1.28027i	0.771970	+	0.114511i
$126$	−13.1748	+	9.19212i	−1.17371	+	0.818899i
$127$			9.83440i			0.872662i	0.899786	+	0.436331i	$0.143722\pi$
$127$			9.83440i			0.872662i	−0.899786	+	0.436331i	$0.856278\pi$
$128$	−10.6763	+	3.74400i	−0.943657	+	0.330926i
$129$		−	0.391207i		−	0.0344438i
$130$	−5.57665	−	7.99289i	−0.489105	−	0.701022i
$131$	7.38732	+	1.09581i	0.645433	+	0.0957410i	0.461419	−	0.887182i	$-0.347341\pi$
$131$	7.38732	+	1.09581i	0.645433	+	0.0957410i	0.184015	+	0.982923i	$0.441091\pi$
$132$	−3.73290	+	0.150394i	−0.324907	+	0.0130901i
$133$	−1.34163	+	27.3095i	−0.116334	+	2.36804i
$134$	6.11948	+	12.2920i	0.528643	+	1.06187i
$135$	−4.25134	+	7.95369i	−0.365897	+	0.684545i
$136$	15.4769	+	5.34102i	1.32714	+	0.457988i
$137$	4.76020	−	15.6923i	0.406691	−	1.34068i	−0.479574	−	0.877501i	$-0.659209\pi$
$137$	4.76020	−	15.6923i	0.406691	−	1.34068i	0.886265	−	0.463179i	$-0.153291\pi$
$138$	3.69935	+	5.89931i	0.314910	+	0.502183i
$139$	−8.78348	+	5.26462i	−0.745005	+	0.446539i	−0.835593	−	0.549350i	$-0.814876\pi$
$139$	−8.78348	+	5.26462i	−0.745005	+	0.446539i	0.0905875	+	0.995889i	$0.471126\pi$
$140$	−14.0467	−	17.4272i	−1.18716	−	1.47286i
$141$	−5.68482	−	5.15242i	−0.478748	−	0.433912i
$142$	−5.17882	+	0.615573i	−0.434597	+	0.0516577i
$143$	−7.85171	−	1.56180i	−0.656593	−	0.130604i
$144$	5.64292	+	8.77652i	0.470243	+	0.731376i
$145$	−5.46009	+	1.08608i	−0.453436	+	0.0901940i
$146$	3.96299	+	12.1762i	0.327980	+	1.00771i
$147$	6.76681	−	3.20046i	0.558117	−	0.263970i
$148$	0.0455737	−	5.16679i	0.00374614	−	0.424708i
$149$	−12.1752	−	9.02975i	−0.997432	−	0.739746i	−0.0317560	−	0.999496i	$-0.510110\pi$
$149$	−12.1752	−	9.02975i	−0.997432	−	0.739746i	−0.965676	+	0.259750i	$0.916360\pi$
$150$	−1.29575	−	0.581219i	−0.105798	−	0.0474563i
$151$	7.20315	−	8.77706i	0.586184	−	0.714267i	−0.392474	−	0.919763i	$-0.628381\pi$
$151$	7.20315	−	8.77706i	0.586184	−	0.714267i	0.978658	+	0.205496i	$0.0658807\pi$
$152$	17.6922	+	1.54064i	1.43502	+	0.124963i
$153$	1.48002	−	15.0269i	0.119653	−	1.21486i
$154$	−18.2377	−	2.33110i	−1.46963	−	0.187845i
$155$	−0.592120	−	0.280052i	−0.0475603	−	0.0224943i
$156$	−1.10254	−	3.16926i	−0.0882741	−	0.253744i
$157$	−2.86123	−	11.4227i	−0.228351	−	0.911627i	−0.970443	−	0.241330i	$-0.922416\pi$
$157$	−2.86123	−	11.4227i	−0.228351	−	0.911627i	0.742092	−	0.670298i	$-0.233834\pi$
$158$	−3.63079	−	8.28941i	−0.288850	−	0.659470i
$159$	2.57719	−	6.22189i	0.204385	−	0.493428i
$160$	−11.6555	+	8.68946i	−0.921451	+	0.686962i
$161$	13.1142	+	31.6605i	1.03355	+	2.49520i
$162$	5.51543	−	5.74212i	0.433333	−	0.451143i
$163$	−9.70590	+	16.1933i	−0.760225	+	1.26836i	0.197395	+	0.980324i	$0.436752\pi$
$163$	−9.70590	+	16.1933i	−0.760225	+	1.26836i	−0.957620	+	0.288035i	$0.906998\pi$
$164$	13.6720	+	3.55309i	1.06760	+	0.277450i
$165$	−4.52005	+	1.61730i	−0.351885	+	0.125907i
$166$	−4.44034	−	2.54135i	−0.344637	−	0.197247i
$167$	−8.91772	+	7.31859i	−0.690074	+	0.566329i	−0.912728	−	0.408568i	$-0.866028\pi$
$167$	−8.91772	+	7.31859i	−0.690074	+	0.566329i	0.222654	+	0.974898i	$0.428528\pi$
$168$	−3.02955	−	7.08615i	−0.233735	−	0.546708i
$169$	0.569433	+	5.78155i	0.0438026	+	0.444735i
$170$	21.0300	+	0.609071i	1.61293	+	0.0467136i
$171$	−2.40320	−	16.2011i	−0.183778	−	1.23893i
$172$	−1.22426	−	0.254766i	−0.0933491	−	0.0194258i
$173$	0.528344	−	1.47662i	0.0401692	−	0.112265i	−0.919785	−	0.392423i	$-0.871637\pi$
$173$	0.528344	−	1.47662i	0.0401692	−	0.112265i	0.959954	+	0.280158i	$0.0903868\pi$
$174$	−1.91090	−	0.149433i	−0.144865	−	0.0113285i
$175$	−5.81122	−	3.88293i	−0.439287	−	0.293522i
$176$	−1.96033	+	11.7799i	−0.147766	+	0.887940i
$177$	−1.11433	+	0.744570i	−0.0837580	+	0.0559653i
$178$	−7.27115	−	12.9684i	−0.544995	−	0.972022i
$179$	0.704792	+	14.3464i	0.0526786	+	1.07230i	0.869035	+	0.494750i	$0.164740\pi$
$179$	0.704792	+	14.3464i	0.0526786	+	1.07230i	−0.816357	+	0.577548i	$0.804010\pi$
$180$	10.2890	+	8.59692i	0.766894	+	0.640776i
$181$	4.65990	−	18.6033i	0.346367	−	1.38278i	−0.507216	−	0.861819i	$-0.669325\pi$
$181$	4.65990	−	18.6033i	0.346367	−	1.38278i	0.853583	−	0.520957i	$-0.174425\pi$
$182$	−2.75150	−	16.2833i	−0.203955	−	1.20700i
$183$	6.18486	−	3.30588i	0.457198	−	0.244378i
$184$	20.8707	−	7.73511i	1.53861	−	0.570240i
$185$	−1.92738	−	6.35371i	−0.141704	−	0.467134i
$186$	−0.170114	−	0.148055i	−0.0124734	−	0.0108559i
$187$	12.8048	−	11.6056i	0.936382	−	0.848688i
$188$	−19.8264	+	14.4349i	−1.44599	+	1.05278i
$189$	−12.2742	+	9.10317i	−0.892817	+	0.662158i
$190$	22.2879	−	4.90176i	1.61693	−	0.355611i
$191$	10.5925	−	10.5925i	0.766446	−	0.766446i	−0.211033	−	0.977479i	$-0.567683\pi$
$191$	10.5925	−	10.5925i	0.766446	−	0.766446i	0.977479	+	0.211033i	$0.0676827\pi$
$192$	−4.67353	+	1.79249i	−0.337283	+	0.129362i
$193$	−14.0041	−	14.0041i	−1.00804	−	1.00804i	−0.999967	−	0.00807185i	$-0.997431\pi$
$193$	−14.0041	−	14.0041i	−1.00804	−	1.00804i	−0.00807185	−	0.999967i	$-0.502569\pi$
$194$	0.137366	+	0.0878373i	0.00986232	+	0.00630635i
$195$	−2.56860	−	3.46336i	−0.183941	−	0.248016i
$196$	−5.60893	−	23.2607i	−0.400638	−	1.66148i
$197$	7.69016	+	8.48479i	0.547901	+	0.604516i	0.950448	−	0.310883i	$-0.100625\pi$
$197$	7.69016	+	8.48479i	0.547901	+	0.604516i	−0.402547	+	0.915399i	$0.631875\pi$
$198$	10.9870	−	0.761747i	0.780812	−	0.0541350i
$199$	−6.55163	+	1.98742i	−0.464433	+	0.140884i	−0.513824	−	0.857895i	$-0.671772\pi$
$199$	−6.55163	+	1.98742i	−0.464433	+	0.140884i	0.0493917	+	0.998779i	$0.484272\pi$
$200$	−2.66273	+	3.67649i	−0.188284	+	0.259967i
$201$	2.86372	+	5.35765i	0.201992	+	0.377900i
$202$	−9.61954	+	13.5315i	−0.676828	+	0.952076i
$203$	−9.15037	−	2.29205i	−0.642230	−	0.160870i
$204$	6.91295	+	2.16379i	0.484003	+	0.151495i
$205$	18.1302	−	0.890681i	1.26627	−	0.0622079i
$206$	0.301613	+	0.0849013i	0.0210144	+	0.00591535i
$207$	−11.4045	−	17.0680i	−0.792664	−	1.18631i
$208$	−10.6360	+	1.38643i	−0.737477	+	0.0961319i
$209$	10.4142	−	15.5860i	0.720367	−	1.07811i
$210$	−6.43524	−	7.52710i	−0.444074	−	0.519419i
$211$	−3.49843	−	1.25176i	−0.240842	−	0.0861745i	0.213702	−	0.976899i	$-0.431448\pi$
$211$	−3.49843	−	1.25176i	−0.240842	−	0.0861745i	−0.454544	+	0.890724i	$0.650198\pi$
$212$	−17.7927	−	12.1171i	−1.22201	−	0.832205i
$213$	−2.28241	+	0.338563i	−0.156388	+	0.0231979i
$214$	−9.94339	+	9.38364i	−0.679716	+	0.641452i
$215$	−1.59915	+	0.157502i	−0.109061	+	0.0107416i
$216$	5.60728	+	8.18978i	0.381527	+	0.557244i
$217$	−0.704096	−	0.857944i	−0.0477972	−	0.0582410i
$218$	2.14201	+	7.87518i	0.145075	+	0.533374i
$219$	1.90855	+	5.33405i	0.128968	+	0.360442i
$220$	2.11766	+	15.1985i	0.142772	+	1.02468i
$221$	13.3138	+	7.97997i	0.895582	+	0.536791i
$222$	−0.0460225	−	2.28555i	−0.00308883	−	0.153396i
$223$	1.79820	−	0.744841i	0.120417	−	0.0498782i	−0.321662	−	0.946855i	$-0.604241\pi$
$223$	1.79820	−	0.744841i	0.120417	−	0.0498782i	0.442078	+	0.896976i	$0.354241\pi$
$224$	−24.1487	+	4.86609i	−1.61350	+	0.325129i
$225$	3.86784	+	1.60211i	0.257856	+	0.106807i
$226$	−1.21517	+	3.10930i	−0.0808319	+	0.206828i
$227$	14.4310	−	3.61479i	0.957822	−	0.239922i	0.267608	−	0.963528i	$-0.413767\pi$
$227$	14.4310	−	3.61479i	0.957822	−	0.239922i	0.690213	+	0.723606i	$0.257517\pi$
$228$	7.84394	+	0.454732i	0.519477	+	0.0301154i
$229$	−1.41488	+	2.99150i	−0.0934976	+	0.197684i	−0.945318	−	0.326150i	$-0.894249\pi$
$229$	−1.41488	+	2.99150i	−0.0934976	+	0.197684i	0.851821	+	0.523834i	$0.175499\pi$
$230$	22.6254	−	17.4970i	1.49188	−	1.15372i
$231$	−8.09530	−	0.797317i	−0.532632	−	0.0524596i
$232$	−1.71208	+	5.88276i	−0.112404	+	0.386222i
$233$	−1.65465	−	1.35794i	−0.108400	−	0.0889613i	0.578632	−	0.815589i	$-0.303587\pi$
$233$	−1.65465	−	1.35794i	−0.108400	−	0.0889613i	−0.687032	+	0.726627i	$0.741087\pi$
$234$	3.51937	+	9.24485i	0.230069	+	0.604354i
$235$	−18.7730	+	25.3124i	−1.22461	+	1.65120i
$236$	1.60441	+	3.97212i	0.104438	+	0.258563i
$237$	−1.71186	−	3.61941i	−0.111197	−	0.235106i
$238$	31.7717	+	16.1685i	2.05945	+	1.04805i
$239$	1.64816	+	8.28585i	0.106610	+	0.535967i	0.996769	+	0.0803169i	$0.0255932\pi$
$239$	1.64816	+	8.28585i	0.106610	+	0.535967i	−0.890159	+	0.455650i	$0.849407\pi$
$240$	−5.04326	+	3.99212i	−0.325541	+	0.257690i
$241$	3.27581	−	16.4686i	0.211013	−	1.06084i	−0.719476	−	0.694517i	$-0.755618\pi$
$241$	3.27581	−	16.4686i	0.211013	−	1.06084i	0.930490	−	0.366318i	$-0.119382\pi$
$242$	−2.31876	−	1.82609i	−0.149055	−	0.117385i
$243$	9.43545	−	10.4104i	0.605284	−	0.667828i
$244$	−6.31780	−	21.5081i	−0.404456	−	1.37692i
$245$	−15.8070	−	26.3724i	−1.00987	−	1.68487i
$246$	6.09181	+	1.39621i	0.388400	+	0.0890191i
$247$	16.1116	+	4.88741i	1.02516	+	0.310979i
$248$	−0.574113	+	0.435945i	−0.0364562	+	0.0276825i
$249$	−1.99625	−	1.06702i	−0.126507	−	0.0676195i
$250$	3.92230	−	11.6995i	0.248068	−	0.739941i
$251$	−2.66599	−	0.130972i	−0.168276	−	0.00826687i	−0.0352447	−	0.999379i	$-0.511221\pi$
$251$	−2.66599	−	0.130972i	−0.168276	−	0.00826687i	−0.133031	+	0.991112i	$0.542471\pi$
$252$	9.53201	+	20.6224i	0.600460	+	1.29909i
$253$	3.44726	−	23.2395i	0.216727	−	1.46106i
$254$	13.6926	+	2.43814i	0.859148	+	0.152982i
$255$	9.30815			0.582899
$256$	2.56597	+	15.7929i	0.160373	+	0.987056i
$257$	31.4868			1.96410			0.982048	−	0.188632i	$-0.0604053\pi$
$257$	31.4868			1.96410			0.982048	+	0.188632i	$0.0604053\pi$
$258$	−0.544682	−	0.0969877i	−0.0339104	−	0.00603819i
$259$	1.65078	−	11.1287i	0.102575	−	0.691502i
$260$	−12.5112	+	5.78286i	−0.775909	+	0.358638i
$261$	5.64367	+	0.277256i	0.349334	+	0.0171617i
$262$	3.35717	−	10.0138i	0.207406	−	0.618654i
$263$	−12.8179	−	6.85131i	−0.790386	−	0.422470i	0.0262268	−	0.999656i	$-0.491651\pi$
$263$	−12.8179	−	6.85131i	−0.790386	−	0.422470i	−0.816613	+	0.577186i	$0.804151\pi$
$264$	−0.716061	+	5.23464i	−0.0440705	+	0.322170i
$265$	−26.4710	−	8.02988i	−1.62610	−	0.493272i
$266$	37.6908	+	8.63853i	2.31097	+	0.529662i
$267$	−3.38170	−	5.64203i	−0.206957	−	0.345286i
$268$	18.6315	−	5.47281i	1.13810	−	0.334305i
$269$	−2.91893	+	3.22055i	−0.177971	+	0.196360i	−0.823403	−	0.567457i	$-0.807927\pi$
$269$	−2.91893	+	3.22055i	−0.177971	+	0.196360i	0.645432	+	0.763817i	$0.276677\pi$
$270$	10.0200	+	7.89106i	0.609800	+	0.480235i
$271$	−1.20113	+	6.03850i	−0.0729636	+	0.366813i	−0.999966	−	0.00824264i	$-0.997376\pi$
$271$	−1.20113	+	6.03850i	−0.0729636	+	0.366813i	0.927002	+	0.375055i	$0.122376\pi$
$272$	11.2734	−	20.2246i	0.683550	−	1.22630i
$273$	−1.42538	−	7.16589i	−0.0862682	−	0.433699i
$274$	−20.6684	−	10.5181i	−1.24862	−	0.635421i
$275$	2.04863	+	4.33146i	0.123537	+	0.261197i
$276$	9.13083	−	3.68810i	0.549612	−	0.221998i
$277$	−5.56405	+	7.50226i	−0.334312	+	0.450767i	−0.938093	−	0.346383i	$-0.887410\pi$
$277$	−5.56405	+	7.50226i	−0.334312	+	0.450767i	0.603782	+	0.797150i	$0.293660\pi$
$278$	5.15240	+	13.5346i	0.309020	+	0.811749i
$279$	0.513915	+	0.421759i	0.0307673	+	0.0252501i
$280$	−27.7465	+	15.2369i	−1.65817	+	0.910578i
$281$	−21.9268	−	2.15960i	−1.30804	−	0.128831i	−0.580142	−	0.814515i	$-0.697003\pi$
$281$	−21.9268	−	2.15960i	−1.30804	−	0.128831i	−0.727899	+	0.685685i	$0.759503\pi$
$282$	−8.58316	+	6.63767i	−0.511120	+	0.395267i
$283$	0.183909	−	0.388844i	0.0109323	−	0.0231144i	−0.898449	−	0.439077i	$-0.855305\pi$
$283$	0.183909	−	0.388844i	0.0109323	−	0.0231144i	0.909382	+	0.415963i	$0.136555\pi$
$284$	−0.426860	+	7.36316i	−0.0253295	+	0.436923i
$285$	9.79384	−	2.45323i	0.580137	−	0.145317i
$286$	−4.12111	+	10.5448i	−0.243686	+	0.623529i
$287$	28.4164	+	11.7705i	1.67737	+	0.694788i
$288$	13.6186	−	5.68085i	0.802487	−	0.334747i
$289$	−15.2512	+	6.31725i	−0.897129	+	0.371603i
$290$	0.158501	+	7.87142i	0.00930750	+	0.462226i
$291$	0.0618740	+	0.0370859i	0.00362712	+	0.00217401i
$292$	17.9356	−	2.49902i	1.04960	−	0.146244i
$293$	−4.85195	−	13.5603i	−0.283454	−	0.792201i	−0.995899	−	0.0904728i	$-0.971162\pi$
$293$	−4.85195	−	13.5603i	−0.283454	−	0.792201i	0.712445	−	0.701728i	$-0.247588\pi$
$294$	−2.77843	−	10.2150i	−0.162041	−	0.595750i
$295$	3.49223	+	4.25530i	0.203326	+	0.247753i
$296$	−7.18250	−	1.34440i	−0.417474	−	0.0781417i
$297$	10.4260	−	1.02688i	0.604981	−	0.0595854i
$298$	−15.5907	+	14.7131i	−0.903146	+	0.852304i
$299$	20.8735	−	3.09628i	1.20714	−	0.179063i
$300$	−1.13048	+	1.66000i	−0.0652683	+	0.0958401i
$301$	−2.56361	−	0.917274i	−0.147764	−	0.0528708i
$302$	−10.4346	−	12.2050i	−0.600445	−	0.702321i
$303$	−4.08084	+	6.10741i	−0.234438	+	0.350862i
$304$	6.53129	−	24.2511i	0.374595	−	1.39089i
$305$	−16.0036	−	23.9511i	−0.916363	−	1.37143i
$306$	−20.5553	−	5.78612i	−1.17507	−	0.330771i
$307$	−2.86837	+	0.140914i	−0.163706	+	0.00804238i	−0.130756	−	0.991415i	$-0.541740\pi$
$307$	−2.86837	+	0.140914i	−0.163706	+	0.00804238i	−0.0329505	+	0.999457i	$0.510490\pi$
$308$	−7.76709	+	24.8146i	−0.442571	+	1.41394i
$309$	0.134473	+	0.0336837i	0.00764990	+	0.00191620i
$310$	−0.536718	+	0.754987i	−0.0304836	+	0.0428804i
$311$	−2.25240	−	4.21395i	−0.127722	−	0.238951i	0.809930	−	0.586527i	$-0.199505\pi$
$311$	−2.25240	−	4.21395i	−0.127722	−	0.238951i	−0.937652	+	0.347575i	$0.887005\pi$
$312$	−4.68594	+	0.749366i	−0.265289	+	0.0424245i
$313$	11.7464	−	3.56324i	0.663947	−	0.201406i	0.0597160	−	0.998215i	$-0.480980\pi$
$313$	11.7464	−	3.56324i	0.663947	−	0.201406i	0.604231	+	0.796809i	$0.293480\pi$
$314$	−16.6133	+	1.15183i	−0.937541	+	0.0650013i
$315$	19.6053	+	21.6311i	1.10463	+	1.21878i
$316$	−12.4416	+	3.00009i	−0.699894	+	0.168768i
$317$	−1.84343	−	2.48558i	−0.103538	−	0.139604i	0.748400	−	0.663248i	$-0.230822\pi$
$317$	−1.84343	−	2.48558i	−0.103538	−	0.139604i	−0.851938	+	0.523643i	$0.824572\pi$
$318$	−8.02388	−	5.13078i	−0.449957	−	0.287720i
$319$	4.57286	+	4.57286i	0.256031	+	0.256031i
$320$	9.20881	+	18.3824i	0.514788	+	1.02761i
$321$	−4.27719	+	4.27719i	−0.238729	+	0.238729i
$322$	47.3327	−	10.4099i	2.63775	−	0.580118i
$323$	−29.1929	+	21.6509i	−1.62434	+	1.20469i
$324$	−6.62744	−	9.10279i	−0.368191	−	0.505710i
$325$	−3.18880	+	2.89016i	−0.176883	+	0.160317i
$326$	20.1399	+	17.5283i	1.11545	+	0.970802i
$327$	1.04815	+	3.45529i	0.0579629	+	0.191078i
$328$	8.33655	−	18.1548i	0.460309	−	1.00243i
$329$	−47.0936	+	25.1721i	−2.59636	+	1.38778i
$330$	1.13118	+	6.69428i	0.0622694	+	0.368508i
$331$	3.43552	−	13.7153i	0.188833	−	0.753864i	−0.799386	−	0.600818i	$-0.794842\pi$
$331$	3.43552	−	13.7153i	0.188833	−	0.753864i	0.988219	−	0.153046i	$-0.0489083\pi$
$332$	−4.63920	+	5.55229i	−0.254609	+	0.304721i
$333$	0.330672	+	6.73098i	0.0181207	+	0.368855i
$334$	7.97889	+	14.2307i	0.436585	+	0.778668i
$335$	20.7477	−	13.8631i	1.13357	−	0.757425i
$336$	−10.6172	+	2.46128i	−0.579217	+	0.134274i
$337$	17.7023	+	11.8283i	0.964307	+	0.644329i	0.934777	−	0.355234i	$-0.115599\pi$
$337$	17.7023	+	11.8283i	0.964307	+	0.644329i	0.0295299	+	0.999564i	$0.490599\pi$
$338$	8.19091	+	0.640529i	0.445527	+	0.0348402i
$339$	−0.497574	+	1.39062i	−0.0270245	+	0.0755284i
$340$	6.06177	−	29.1294i	0.328746	−	1.57976i
$341$	0.111646	+	0.752658i	0.00604598	+	0.0407587i
$342$	−23.1528	−	0.670549i	−1.25196	−	0.0362591i
$343$	−2.11869	−	21.5114i	−0.114398	−	1.16151i
$344$	−0.658233	+	1.64139i	−0.0354895	+	0.0884981i
$345$	9.78178	−	8.02770i	0.526633	−	0.432197i
$346$	−1.92493	−	1.10170i	−0.103485	−	0.0592279i
$347$	−11.3220	+	4.05109i	−0.607799	+	0.217474i	−0.622758	−	0.782414i	$-0.713988\pi$
$347$	−11.3220	+	4.05109i	−0.607799	+	0.217474i	0.0149596	+	0.999888i	$0.495238\pi$
$348$	−0.681807	+	2.62353i	−0.0365487	+	0.140636i
$349$	5.79645	−	9.67079i	0.310277	−	0.517665i	−0.662605	−	0.748969i	$-0.730549\pi$
$349$	5.79645	−	9.67079i	0.310277	−	0.517665i	0.972882	+	0.231304i	$0.0742991\pi$
$350$	−6.84697	+	7.12838i	−0.365986	+	0.381028i
$351$	3.60100	+	8.69357i	0.192207	+	0.464029i
$352$	15.9152	+	5.64985i	0.848285	+	0.301138i
$353$	−8.47769	+	20.4670i	−0.451222	+	1.08935i	0.520636	+	0.853779i	$0.325695\pi$
$353$	−8.47769	+	20.4670i	−0.451222	+	1.08935i	−0.971858	+	0.235567i	$0.924305\pi$
$354$	0.760411	+	1.73609i	0.0404154	+	0.0922719i
$355$	2.30286	+	9.19354i	0.122223	+	0.487943i
$356$	−19.8587	+	6.90860i	−1.05251	+	0.366155i
$357$	14.2578	+	6.74345i	0.754605	+	0.356901i
$358$	20.1494	+	2.57545i	1.06493	+	0.136117i
$359$	−1.10144	+	11.1831i	−0.0581319	+	0.590223i	0.921356	+	0.388720i	$0.127083\pi$
$359$	−1.10144	+	11.1831i	−0.0581319	+	0.590223i	−0.979488	+	0.201503i	$0.935417\pi$
$360$	14.5204	−	12.1941i	0.765294	−	0.642686i
$361$	−12.9564	+	15.7874i	−0.681915	+	0.830916i
$362$	−24.7464	−	11.1002i	−1.30064	−	0.583412i
$363$	−1.04884	−	0.777872i	−0.0550498	−	0.0408277i
$364$	−23.3536	−	0.205990i	−1.22406	−	0.0107968i
$365$	21.0357	−	9.94916i	1.10106	−	0.520763i
$366$	−3.06947	−	9.43086i	−0.160444	−	0.492959i
$367$	−27.0240	+	5.37540i	−1.41064	+	0.280594i	−0.840882	−	0.541219i	$-0.817963\pi$
$367$	−27.0240	+	5.37540i	−1.41064	+	0.280594i	−0.569758	+	0.821813i	$0.692963\pi$
$368$	−5.59544	−	30.9763i	−0.291682	−	1.61475i
$369$	−18.0701	−	3.59436i	−0.940691	−	0.187115i
$370$	−9.32419	+	1.10830i	−0.484741	+	0.0576180i
$371$	−34.7297	−	31.4772i	−1.80308	−	1.63421i
$372$	−0.248313	+	0.200146i	−0.0128744	+	0.0103771i
$373$	32.9561	−	19.7531i	1.70640	−	1.02278i	0.800448	−	0.599402i	$-0.204595\pi$
$373$	32.9561	−	19.7531i	1.70640	−	1.02278i	0.905954	−	0.423376i	$-0.139155\pi$
$374$	−12.9841	−	20.7056i	−0.671392	−	1.07066i
$375$	1.58475	−	5.22424i	0.0818364	−	0.269778i
$376$	15.1826	+	31.1832i	0.782984	+	1.60815i
$377$	−2.73815	+	5.12271i	−0.141022	+	0.263833i
$378$	9.63145	+	19.3464i	0.495388	+	0.995071i
$379$	1.25116	−	25.4680i	0.0642679	−	1.30820i	−0.722680	−	0.691183i	$-0.757090\pi$
$379$	1.25116	−	25.4680i	0.0642679	−	1.30820i	0.786948	−	0.617020i	$-0.211660\pi$
$380$	−1.29919	−	32.2470i	−0.0666472	−	1.65423i
$381$	6.08664	+	0.902868i	0.311828	+	0.0462553i
$382$	−12.1220	−	17.3742i	−0.620215	−	0.888939i
$383$		−	5.34098i		−	0.272911i	−0.990646	−	0.136456i	$-0.956429\pi$
$383$		−	5.34098i		−	0.272911i	0.990646	−	0.136456i	$-0.0435711\pi$
$384$	1.33705	+	6.95141i	0.0682313	+	0.354738i
$385$			33.4124i			1.70285i
$386$	−22.9700	+	16.0262i	−1.16914	+	0.815714i
$387$	1.61331	+	0.239312i	0.0820091	+	0.0121649i
$388$	0.156353	−	0.169480i	0.00793761	−	0.00860405i
$389$	0.744527	−	15.1552i	0.0377490	−	0.768398i	−0.903071	−	0.429491i	$-0.858693\pi$
$389$	0.744527	−	15.1552i	0.0377490	−	0.768398i	0.940820	−	0.338907i	$-0.110057\pi$
$390$	−5.45888	+	2.71766i	−0.276421	+	0.137614i
$391$	−21.4734	+	40.1739i	−1.08596	+	2.03168i
$392$	−33.7767	+	2.04262i	−1.70598	+	0.103168i
$393$	1.35642	−	4.47151i	0.0684223	−	0.225558i
$394$	13.7200	−	8.60357i	0.691205	−	0.433442i
$395$	−14.1060	+	8.45480i	−0.709749	+	0.425407i
$396$	1.66330	−	15.4862i	0.0835839	−	0.778211i
$397$	−19.9677	−	18.0977i	−1.00215	−	0.908297i	−0.00636270	−	0.999980i	$-0.502025\pi$
$397$	−19.9677	−	18.0977i	−1.00215	−	0.908297i	−0.995788	+	0.0916831i	$0.970775\pi$
$398$	1.14283	+	9.61464i	0.0572848	+	0.481938i
$399$	16.7791	+	3.33756i	0.840004	+	0.167087i
$400$	4.45868	+	4.61883i	0.222934	+	0.230941i
$401$	20.6801	−	4.11353i	1.03272	−	0.205420i	0.350493	−	0.936565i	$-0.386014\pi$
$401$	20.6801	−	4.11353i	1.03272	−	0.205420i	0.682222	+	0.731145i	$0.261014\pi$
$402$	8.16950	−	2.65894i	0.407458	−	0.132616i
$403$	−0.617809	+	0.292202i	−0.0307753	+	0.0145556i
$404$	16.4553	+	16.7481i	0.818680	+	0.833251i
$405$	−11.6216	−	8.61913i	−0.577479	−	0.428288i
$406$	−5.45980	+	12.1719i	−0.270965	+	0.604083i
$407$	−4.89303	+	5.96218i	−0.242539	+	0.295534i
$408$	4.72652	−	9.08855i	0.233998	−	0.449950i
$409$	−2.63107	+	26.7137i	−0.130098	+	1.32091i	0.679393	+	0.733774i	$0.262243\pi$
$409$	−2.63107	+	26.7137i	−0.130098	+	1.32091i	−0.809491	+	0.587132i	$0.800257\pi$
$410$	3.25473	−	25.4638i	0.160740	−	1.25757i
$411$	−9.27513	−	4.38681i	−0.457509	−	0.216385i
$412$	0.192985	−	0.398891i	0.00950768	−	0.0196519i
$413$	2.26643	+	9.04809i	0.111524	+	0.445228i
$414$	−26.5913	+	11.6471i	−1.30689	+	0.572423i
$415$	−3.55797	+	8.58971i	−0.174654	+	0.421652i
$416$	−0.706529	+	15.1524i	−0.0346404	+	0.742909i
$417$	2.45196	+	5.91955i	0.120073	+	0.289881i
$418$	−19.1187	−	18.3639i	−0.935126	−	0.898209i
$419$	−1.16128	+	1.93747i	−0.0567321	+	0.0946518i	−0.884788	−	0.465994i	$-0.845697\pi$
$419$	−1.16128	+	1.93747i	−0.0567321	+	0.0946518i	0.828056	+	0.560645i	$0.189447\pi$
$420$	−12.0755	+	7.09376i	−0.589224	+	0.346140i
$421$	−16.2498	+	5.81427i	−0.791966	+	0.283370i	−0.701630	−	0.712541i	$-0.747544\pi$
$421$	−16.2498	+	5.81427i	−0.791966	+	0.283370i	−0.0903361	+	0.995911i	$0.528794\pi$
$422$	−2.61016	+	4.56057i	−0.127061	+	0.222005i
$423$	24.7258	−	20.2919i	1.20221	−	0.986627i
$424$	−21.2819	+	21.7690i	−1.03354	+	1.05720i
$425$	−0.910614	−	9.24562i	−0.0441713	−	0.448478i
$426$	−0.0944668	+	3.26176i	−0.00457693	+	0.158033i
$427$	−7.16186	−	48.2813i	−0.346587	−	2.33650i
$428$	10.5998	+	16.1707i	0.512361	+	0.781640i
$429$	−1.68746	+	4.71615i	−0.0814715	+	0.227698i
$430$	−0.177167	+	2.26556i	−0.00854375	+	0.109255i
$431$	−10.8608	−	7.25693i	−0.523145	−	0.349554i	0.265790	−	0.964031i	$-0.414367\pi$
$431$	−10.8608	−	7.25693i	−0.523145	−	0.349554i	−0.788935	+	0.614477i	$0.789367\pi$
$432$	12.7929	−	5.77669i	0.615498	−	0.277931i
$433$	11.5066	−	7.68849i	0.552974	−	0.369485i	−0.247468	−	0.968896i	$-0.579598\pi$
$433$	11.5066	−	7.68849i	0.552974	−	0.369485i	0.800441	+	0.599411i	$0.204598\pi$
$434$	−1.36909	+	0.767622i	−0.0657182	+	0.0368470i
$435$	0.170914	+	3.47903i	0.00819470	+	0.166807i
$436$	11.4958	−	1.02994i	0.550547	−	0.0493252i
$437$	−12.0057	+	47.9296i	−0.574313	+	2.29278i
$438$	7.89983	−	1.33489i	0.377469	−	0.0637835i
$439$	19.7478	−	10.5554i	0.942513	−	0.503784i	0.0728027	−	0.997346i	$-0.476806\pi$
$439$	19.7478	−	10.5554i	0.942513	−	0.503784i	0.869710	+	0.493563i	$0.164306\pi$
$440$	21.6861	+	0.819563i	1.03384	+	0.0390711i
$441$	9.05905	+	29.8637i	0.431383	+	1.42208i
$442$	14.4114	−	16.5586i	0.685479	−	0.787610i
$443$	14.5678	−	13.2035i	0.692136	−	0.627315i	−0.247742	−	0.968826i	$-0.579689\pi$
$443$	14.5678	−	13.2035i	0.692136	−	0.627315i	0.939878	+	0.341511i	$0.110939\pi$
$444$	−3.19362	−	0.502555i	−0.151562	−	0.0238502i
$445$	−21.7016	+	16.0950i	−1.02875	+	0.762976i
$446$	−0.591242	−	2.68832i	−0.0279961	−	0.127296i
$447$	−6.70641	+	6.70641i	−0.317202	+	0.317202i
$448$	0.788193	+	34.8289i	0.0372386	+	1.64551i
$449$	2.23582	+	2.23582i	0.105515	+	0.105515i	0.757893	−	0.652379i	$-0.226229\pi$
$449$	2.23582	+	2.23582i	0.105515	+	0.105515i	−0.652379	+	0.757893i	$0.726229\pi$
$450$	3.18955	−	4.98805i	0.150357	−	0.235139i
$451$	−12.5612	−	16.9368i	−0.591484	−	0.797524i
$452$	4.02786	+	2.46275i	0.189454	+	0.115838i
$453$	−4.77094	−	5.26393i	−0.224159	−	0.247321i
$454$	−1.45518	−	20.9887i	−0.0682951	−	0.985049i
$455$	−28.7183	+	8.71161i	−1.34634	+	0.408407i
$456$	2.57779	−	10.8085i	0.120716	−	0.506153i
$457$	5.79055	+	10.8334i	0.270871	+	0.506763i	0.980174	−	0.198140i	$-0.0634902\pi$
$457$	5.79055	+	10.8334i	0.270871	+	0.506763i	−0.709303	+	0.704904i	$0.750990\pi$
$458$	3.81433	+	2.71160i	0.178232	+	0.126705i
$459$	−19.7044	−	4.93569i	−0.919722	−	0.230378i
$460$	−18.7521	−	35.8395i	−0.874320	−	1.67103i
$461$	−12.1127	+	0.595057i	−0.564143	+	0.0277146i	−0.329142	−	0.944281i	$-0.606759\pi$
$461$	−12.1127	+	0.595057i	−0.564143	+	0.0277146i	−0.235001	+	0.971995i	$0.575509\pi$
$462$	−3.11710	+	11.0735i	−0.145020	+	0.515187i
$463$	15.6775	+	23.4630i	0.728595	+	1.09042i	0.992062	+	0.125751i	$0.0401339\pi$
$463$	15.6775	+	23.4630i	0.728595	+	1.09042i	−0.263467	+	0.964668i	$0.584866\pi$
$464$	7.76619	+	3.84221i	0.360536	+	0.178370i
$465$	−0.227689	+	0.340761i	−0.0105588	+	0.0158024i
$466$	−2.30089	+	1.96713i	−0.106587	+	0.0911256i
$467$	15.3625	+	5.49680i	0.710892	+	0.254361i	0.667407	−	0.744693i	$-0.267404\pi$
$467$	15.3625	+	5.49680i	0.710892	+	0.254361i	0.0434849	+	0.999054i	$0.486154\pi$
$468$	13.7442	−	2.60809i	0.635328	−	0.120559i
$469$	41.8238	−	6.20397i	1.93124	−	0.286473i
$470$	30.5886	+	32.4133i	1.41095	+	1.49511i
$471$	−7.33232	+	0.722171i	−0.337856	+	0.0332759i
$472$	5.92820	−	1.24907i	0.272867	−	0.0574933i
$473$	1.18419	+	1.44294i	0.0544490	+	0.0663463i
$474$	−5.46376	+	1.48612i	−0.250959	+	0.0682596i
$475$	−3.39487	−	9.48804i	−0.155768	−	0.435341i
$476$	30.3885	−	40.2276i	1.39285	−	1.84383i
$477$	24.0821	+	14.4343i	1.10264	+	0.660899i
$478$	11.9451	−	0.240530i	0.546357	−	0.0110016i
$479$	−12.7085	+	5.26402i	−0.580665	+	0.240519i	−0.653629	−	0.756815i	$-0.726754\pi$
$479$	−12.7085	+	5.26402i	−0.580665	+	0.240519i	0.0729637	+	0.997335i	$0.476754\pi$
$480$	4.30796	+	8.01152i	0.196631	+	0.365674i
$481$	−6.40033	−	2.65110i	−0.291830	−	0.120880i
$482$	−22.1173	−	8.64383i	−1.00742	−	0.393716i
$483$	20.7991	−	5.20991i	0.946393	−	0.237059i
$484$	−3.11735	+	2.77571i	−0.141698	+	0.126169i
$485$	0.126686	−	0.267855i	0.00575252	−	0.0121627i
$486$	−12.1553	−	15.7180i	−0.551377	−	0.712985i
$487$	30.9426	+	3.04758i	1.40214	+	0.138099i	0.770638	−	0.637273i	$-0.219938\pi$
$487$	30.9426	+	3.04758i	1.40214	+	0.138099i	0.631504	+	0.775372i	$0.282438\pi$
$488$	−31.5123	+	3.46408i	−1.42650	+	0.156811i
$489$	9.13120	+	7.49378i	0.412927	+	0.338880i
$490$	−40.6374	+	15.4701i	−1.83581	+	0.698866i
$491$	11.9511	−	16.1143i	0.539348	−	0.727226i	−0.446516	−	0.894776i	$-0.647335\pi$
$491$	11.9511	−	16.1143i	0.539348	−	0.727226i	0.985864	+	0.167549i	$0.0535854\pi$
$492$	3.45424	−	8.13556i	0.155729	−	0.366779i
$493$	−5.36113	−	11.3352i	−0.241453	−	0.510510i
$494$	10.7992	−	21.2208i	0.485879	−	0.954768i
$495$	−3.90459	−	19.6297i	−0.175498	−	0.882290i
$496$	0.464638	+	0.907425i	0.0208629	+	0.0407446i
$497$	−3.13299	+	15.7506i	−0.140534	+	0.706512i
$498$	−1.98053	+	2.51487i	−0.0887497	+	0.112694i
$499$	−16.3600	+	18.0505i	−0.732376	+	0.808052i	−0.987293	−	0.158911i	$-0.949202\pi$
$499$	−16.3600	+	18.0505i	−0.732376	+	0.808052i	0.254917	+	0.966963i	$0.417952\pi$
$500$	−15.3169	−	8.36160i	−0.684995	−	0.373942i
$501$	3.71086	+	6.19120i	0.165789	+	0.276602i
$502$	−0.843305	+	3.67943i	−0.0376385	+	0.164221i
$503$	24.1989	+	7.34067i	1.07898	+	0.327304i	0.779245	−	0.626719i	$-0.215603\pi$
$503$	24.1989	+	7.34067i	1.07898	+	0.327304i	0.299732	+	0.954023i	$0.403103\pi$
$504$	31.0760	−	8.15885i	1.38424	−	0.363424i
$505$	26.6084	+	14.2225i	1.18406	+	0.632893i
$506$	−31.5021	−	10.5612i	−1.40044	−	0.469502i
$507$	3.63056	+	0.178358i	0.161239	+	0.00792116i
$508$	6.78930	−	18.4599i	0.301226	−	0.819024i
$509$	1.72757	−	11.6463i	0.0765732	−	0.516214i	−0.916622	−	0.399755i	$-0.869095\pi$
$509$	1.72757	−	11.6463i	0.0765732	−	0.516214i	0.993195	−	0.116460i	$-0.0371546\pi$
$510$	2.30767	−	12.9599i	0.102185	−	0.573873i
$511$	39.4295			1.74426
$512$	22.6248	+	0.342737i	0.999885	+	0.0151470i
$513$	−22.0334			−0.972797
$514$	7.80620	−	43.8396i	0.344317	−	1.93368i
$515$	0.0835503	−	0.563250i	0.00368167	−	0.0248198i
$516$	−0.270074	+	0.734323i	−0.0118894	+	0.0323268i
$517$	36.5645	+	1.79630i	1.60810	+	0.0790011i
$518$	−15.0853	−	5.05742i	−0.662811	−	0.222210i
$519$	−0.865396	−	0.462564i	−0.0379867	−	0.0203043i
$520$	4.94979	+	18.8531i	0.217063	+	0.826765i
$521$	−10.6749	−	3.23820i	−0.467677	−	0.141868i	0.0476459	−	0.998864i	$-0.484828\pi$
$521$	−10.6749	−	3.23820i	−0.467677	−	0.141868i	−0.515323	+	0.856996i	$0.672328\pi$
$522$	1.78520	−	7.78902i	0.0781362	−	0.340916i
$523$	14.9429	+	24.9307i	0.653408	+	1.09014i	0.988968	+	0.148126i	$0.0473242\pi$
$523$	14.9429	+	24.9307i	0.653408	+	1.09014i	−0.335561	+	0.942019i	$0.608926\pi$
$524$	−13.1100	−	7.15684i	−0.572715	−	0.312648i
$525$	−2.93671	+	3.24016i	−0.128169	+	0.141412i
$526$	−12.7170	+	16.1480i	−0.554487	+	0.704085i
$527$	0.287820	−	1.44697i	0.0125376	−	0.0630309i
$528$	7.11074	+	2.29475i	0.309455	+	0.0998662i
$529$	7.59438	+	38.1795i	0.330191	+	1.65998i
$530$	−17.7428	+	34.8651i	−0.770697	+	1.51444i
$531$	−2.38889	−	5.05088i	−0.103669	−	0.219190i
$532$	21.3718	−	50.3357i	0.926586	−	2.18233i
$533$	11.2823	−	15.2124i	0.488691	−	0.658924i
$534$	−8.69386	+	3.30962i	−0.376220	+	0.143221i
$535$	19.2060	+	15.7620i	0.830348	+	0.681449i
$536$	−3.00077	−	27.2976i	−0.129613	−	1.17908i
$537$	8.94387	+	0.880895i	0.385957	+	0.0380134i
$538$	3.76035	+	4.86251i	0.162120	+	0.209637i
$539$	−15.2710	+	32.2879i	−0.657770	+	1.39074i
$540$	13.4710	−	11.9947i	0.579699	−	0.516169i
$541$	23.1835	−	5.80716i	0.996736	−	0.249669i	0.289908	−	0.957055i	$-0.406375\pi$
$541$	23.1835	−	5.80716i	0.996736	−	0.249669i	0.706828	+	0.707385i	$0.250125\pi$
$542$	8.10970	+	3.16941i	0.348341	+	0.136138i
$543$	−11.0861	−	4.59199i	−0.475748	−	0.197061i
$544$	−25.3641	−	20.7102i	−1.08748	−	0.887941i
$545$	13.7023	−	5.67568i	0.586942	−	0.243119i
$546$	−10.3305	+	0.208019i	−0.442106	+	0.00890238i
$547$	−13.4232	−	8.04554i	−0.573934	−	0.344003i	0.197509	−	0.980301i	$-0.436715\pi$
$547$	−13.4232	−	8.04554i	−0.573934	−	0.344003i	−0.771443	+	0.636298i	$0.780465\pi$
$548$	−19.7686	+	26.1692i	−0.844472	+	1.11789i
$549$	9.84976	+	27.5282i	0.420378	+	1.17488i
$550$	6.53864	−	1.77848i	0.278809	−	0.0758346i
$551$	−8.62832	−	10.5136i	−0.367579	−	0.447896i
$552$	−2.87128	−	13.6273i	−0.122210	−	0.580018i
$553$	−27.7322	+	2.73138i	−1.17929	+	0.116150i
$554$	9.06606	+	9.60686i	0.385180	+	0.408156i
$555$	−4.10935	+	0.609564i	−0.174432	+	0.0258745i
$556$	20.1217	−	3.81828i	0.853351	−	0.161931i
$557$	10.4859	+	3.75190i	0.444300	+	0.158973i	0.549528	−	0.835475i	$-0.314807\pi$
$557$	10.4859	+	3.75190i	0.444300	+	0.158973i	−0.105228	+	0.994448i	$0.533557\pi$
$558$	0.714630	−	0.610968i	0.0302527	−	0.0258644i
$559$	−0.931467	+	1.39404i	−0.0393969	+	0.0589616i
$560$	14.3356	+	42.4094i	0.605790	+	1.79212i
$561$	−6.00731	−	8.99057i	−0.253629	−	0.379582i
$562$	−8.44290	+	29.9935i	−0.356142	+	1.26520i
$563$	5.38486	−	0.264541i	0.226945	−	0.0111491i	0.0647225	−	0.997903i	$-0.479384\pi$
$563$	5.38486	−	0.264541i	0.226945	−	0.0111491i	0.162222	+	0.986754i	$0.448134\pi$
$564$	7.11378	+	13.5961i	0.299544	+	0.572497i
$565$	5.88482	+	1.47407i	0.247576	+	0.0620146i
$566$	−0.495798	−	0.352461i	−0.0208399	−	0.0148151i
$567$	−11.5571	−	21.6219i	−0.485353	−	0.908032i
$568$	10.1460	+	2.41979i	0.425716	+	0.101532i
$569$	31.8304	−	9.65565i	1.33440	−	0.404786i	0.459108	−	0.888381i	$-0.348169\pi$
$569$	31.8304	−	9.65565i	1.33440	−	0.404786i	0.875292	+	0.483595i	$0.160669\pi$
$570$	−0.987581	−	14.2443i	−0.0413652	−	0.596628i
$571$	11.0318	+	12.1717i	0.461666	+	0.509370i	0.926638	−	0.375956i	$-0.122686\pi$
$571$	11.0318	+	12.1717i	0.461666	+	0.509370i	−0.464972	+	0.885326i	$0.653936\pi$
$572$	13.6600	+	8.35214i	0.571154	+	0.349221i
$573$	−5.58337	−	7.52831i	−0.233249	−	0.314500i
$574$	23.4331	−	36.6464i	0.978080	−	1.52959i
$575$	−8.93071	−	8.93071i	−0.372437	−	0.372437i
$576$	−4.53319	−	20.3698i	−0.188883	−	0.848742i
$577$	15.1120	−	15.1120i	0.629122	−	0.629122i	−0.318725	−	0.947847i	$-0.603255\pi$
$577$	15.1120	−	15.1120i	0.629122	−	0.629122i	0.947847	+	0.318725i	$0.103255\pi$
$578$	5.01453	+	22.8006i	0.208577	+	0.948380i
$579$	−9.95303	+	7.38167i	−0.413634	+	0.306772i
$580$	10.9988	+	1.73079i	0.456699	+	0.0718673i
$581$	−11.6729	+	10.5797i	−0.484274	+	0.438921i
$582$	0.0669749	−	0.0769537i	0.00277620	−	0.00318983i
$583$	9.32795	+	30.7501i	0.386324	+	1.27354i
$584$	0.967155	−	25.5915i	0.0400211	−	1.05898i
$585$	15.8539	−	8.47410i	0.655479	−	0.350361i
$586$	−20.0831	+	3.39358i	−0.829624	+	0.140187i
$587$	−0.595084	+	2.37571i	−0.0245617	+	0.0980560i	−0.981072	−	0.193642i	$-0.937970\pi$
$587$	−0.595084	+	2.37571i	−0.0245617	+	0.0980560i	0.956511	+	0.291698i	$0.0942201\pi$
$588$	−14.9113	+	1.33595i	−0.614931	+	0.0550935i
$589$	−0.0785207	−	1.59833i	−0.00323539	−	0.0658578i
$590$	6.79050	−	3.80731i	0.279560	−	0.156745i
$591$	5.95736	−	3.98058i	0.245053	−	0.163739i
$592$	−3.65251	+	9.66698i	−0.150117	+	0.397311i
$593$	−32.7123	−	21.8577i	−1.34334	−	0.897588i	−0.344189	−	0.938900i	$-0.611846\pi$
$593$	−32.7123	−	21.8577i	−1.34334	−	0.897588i	−0.999146	+	0.0413126i	$0.986846\pi$
$594$	1.15509	−	14.7709i	0.0473937	−	0.606058i
$595$	21.8251	−	60.9971i	0.894742	−	2.50064i
$596$	16.6199	+	25.3548i	0.680779	+	1.03857i
$597$	0.628552	+	4.23735i	0.0257249	+	0.173423i
$598$	0.863935	−	29.8300i	0.0353289	−	1.21984i
$599$	−2.10365	−	21.3587i	−0.0859527	−	0.872692i	−0.937401	−	0.348253i	$-0.886775\pi$
$599$	−2.10365	−	21.3587i	−0.0859527	−	0.872692i	0.851448	−	0.524439i	$-0.175725\pi$
$600$	2.03097	+	1.98553i	0.0829141	+	0.0810589i
$601$	−12.9241	+	10.6065i	−0.527184	+	0.432649i	−0.859963	−	0.510356i	$-0.829514\pi$
$601$	−12.9241	+	10.6065i	−0.527184	+	0.432649i	0.332779	+	0.943005i	$0.392014\pi$
$602$	−1.91270	+	3.34194i	−0.0779559	+	0.136207i
$603$	−23.8464	+	8.53238i	−0.971100	+	0.347465i
$604$	−19.5802	+	11.5024i	−0.796707	+	0.468026i
$605$	−2.75746	+	4.60054i	−0.112107	+	0.187039i
$606$	7.49171	+	7.19596i	0.304330	+	0.292316i
$607$	4.97040	+	11.9996i	0.201742	+	0.487049i	0.992078	−	0.125625i	$-0.0400936\pi$
$607$	4.97040	+	11.9996i	0.201742	+	0.487049i	−0.790335	+	0.612675i	$0.790094\pi$
$608$	−32.1459	−	15.1059i	−1.30369	−	0.612626i
$609$	−2.25865	+	5.45286i	−0.0915251	+	0.220961i
$610$	−37.3150	+	16.3441i	−1.51084	+	0.661752i
$611$	7.98952	+	31.8959i	0.323221	+	1.29037i
$612$	−13.1521	+	27.1849i	−0.531644	+	1.09888i
$613$	−25.4233	−	12.0243i	−1.02684	−	0.485657i	−0.161512	−	0.986871i	$-0.551637\pi$
$613$	−25.4233	−	12.0243i	−1.02684	−	0.485657i	−0.865324	+	0.501214i	$0.832887\pi$
$614$	−0.514927	+	4.02860i	−0.0207808	+	0.162581i
$615$	1.11323	−	11.3028i	0.0448898	−	0.455774i
$616$	32.6241	+	16.9662i	1.31446	+	0.683589i
$617$	21.0537	−	25.6540i	0.847590	−	1.03279i	−0.151428	−	0.988468i	$-0.548387\pi$
$617$	21.0537	−	25.6540i	0.847590	−	1.03279i	0.999017	−	0.0443227i	$-0.0141130\pi$
$618$	0.0802368	−	0.178878i	0.00322760	−	0.00719552i
$619$	−2.62562	−	1.94729i	−0.105533	−	0.0782683i	0.541646	−	0.840607i	$-0.317801\pi$
$619$	−2.62562	−	1.94729i	−0.105533	−	0.0782683i	−0.647179	+	0.762338i	$0.724051\pi$
$620$	0.918115	+	0.934456i	0.0368724	+	0.0375286i
$621$	−24.9637	+	11.8070i	−1.00176	+	0.473797i
$622$	−6.42555	+	2.09133i	−0.257641	+	0.0838547i
$623$	−44.9019	+	8.93153i	−1.79895	+	0.357834i
$624$	−0.118382	+	6.71008i	−0.00473906	+	0.268618i
$625$	−29.8638	−	5.94028i	−1.19455	−	0.237611i
$626$	−2.04898	−	17.2381i	−0.0818936	−	0.688973i
$627$	−8.69028	−	7.87641i	−0.347056	−	0.314554i
$628$	−2.51505	+	23.4164i	−0.100361	+	0.934418i
$629$	12.8272	−	7.68831i	0.511453	−	0.306553i
$630$	34.9778	−	21.9340i	1.39355	−	0.873870i
$631$	2.32677	−	7.67035i	0.0926274	−	0.305352i	−0.898369	−	0.439242i	$-0.855247\pi$
$631$	2.32677	−	7.67035i	0.0926274	−	0.305352i	0.990996	+	0.133890i	$0.0427470\pi$
$632$	1.09255	+	18.0664i	0.0434593	+	0.718642i
$633$	−1.09591	+	2.05030i	−0.0435585	+	0.0814922i
$634$	−3.91773	+	1.95041i	−0.155593	+	0.0774608i
$635$	1.24016	−	25.2440i	0.0492142	−	1.00178i
$636$	−9.13293	+	9.89974i	−0.362144	+	0.392550i
$637$	−31.7334	−	4.70721i	−1.25732	−	0.186506i
$638$	7.50056	−	5.23316i	0.296950	−	0.207183i
$639$		−	9.61959i		−	0.380545i
$640$	27.8772	−	8.26419i	1.10194	−	0.326671i
$641$			0.476501i			0.0188207i	0.999956	+	0.00941033i	$0.00299545\pi$
$641$			0.476501i			0.0188207i	−0.999956	+	0.00941033i	$0.997005\pi$
$642$	4.89479	+	7.01559i	0.193182	+	0.276883i
$643$	−9.30251	−	1.37990i	−0.366855	−	0.0544178i	−0.0392419	−	0.999230i	$-0.512494\pi$
$643$	−9.30251	−	1.37990i	−0.366855	−	0.0544178i	−0.327613	+	0.944812i	$0.606244\pi$
$644$	−2.75909	−	68.4827i	−0.108723	−	2.69860i
$645$	−0.0493328	+	1.00419i	−0.00194248	+	0.0395401i
$646$	22.9074	+	46.0133i	0.901279	+	1.81037i
$647$	19.9741	−	37.3688i	0.785261	−	1.46912i	−0.0954330	−	0.995436i	$-0.530424\pi$
$647$	19.9741	−	37.3688i	0.785261	−	1.46912i	0.880694	−	0.473685i	$-0.157076\pi$
$648$	−14.3170	+	6.97072i	−0.562425	+	0.273836i
$649$	1.85629	−	6.11937i	0.0728658	−	0.240206i
$650$	3.23345	+	5.15634i	0.126826	+	0.202248i
$651$	−0.595634	+	0.357009i	−0.0233447	+	0.0139923i
$652$	29.3979	−	23.6954i	1.15131	−	0.927985i
$653$	−20.0902	−	18.2087i	−0.786189	−	0.712561i	0.176164	−	0.984361i	$-0.443631\pi$
$653$	−20.0902	−	18.2087i	−0.786189	−	0.712561i	−0.962354	+	0.271800i	$0.912381\pi$
$654$	5.07071	−	0.602722i	0.198280	−	0.0235683i
$655$	−18.8244	−	3.74441i	−0.735531	−	0.146306i
$656$	−23.2103	−	16.1080i	−0.906211	−	0.628912i
$657$	−23.1648	+	4.60776i	−0.903743	+	0.179766i
$658$	23.3720	+	71.8097i	0.911135	+	2.79943i
$659$	10.3145	−	4.87838i	0.401794	−	0.190035i	−0.215966	−	0.976401i	$-0.569290\pi$
$659$	10.3145	−	4.87838i	0.401794	−	0.190035i	0.617761	+	0.786366i	$0.288040\pi$
$660$	9.60098	+	0.0846855i	0.373718	+	0.00329638i
$661$	−5.37416	−	3.98575i	−0.209030	−	0.155028i	0.486119	−	0.873892i	$-0.338412\pi$
$661$	−5.37416	−	3.98575i	−0.209030	−	0.155028i	−0.695150	+	0.718865i	$0.744662\pi$
$662$	−18.2443	−	8.18361i	−0.709086	−	0.318065i
$663$	6.16121	−	7.50746i	0.239282	−	0.291566i
$664$	6.58038	+	7.83574i	0.255368	+	0.304086i
$665$	6.88770	−	69.9320i	0.267094	−	2.71185i
$666$	9.45361	+	1.20834i	0.366320	+	0.0468223i
$667$	−15.4098	−	7.28829i	−0.596669	−	0.282204i
$668$	21.7917	−	7.58105i	0.843146	−	0.293320i
$669$	−0.295904	−	1.18132i	−0.0114403	−	0.0456723i
$670$	−14.1581	−	32.3242i	−0.546975	−	1.24879i
$671$	−12.8055	+	30.9151i	−0.494350	+	1.19347i
$672$	0.794666	+	15.3927i	0.0306549	+	0.593786i
$673$	−8.47149	−	20.4520i	−0.326552	−	0.788366i	−0.998844	−	0.0480794i	$-0.984690\pi$
$673$	−8.47149	−	20.4520i	−0.326552	−	0.788366i	0.672292	−	0.740286i	$-0.265310\pi$
$674$	20.8575	−	21.7147i	0.803400	−	0.836420i
$675$	2.89543	−	4.83074i	0.111445	−	0.185935i
$676$	2.92250	−	11.2455i	0.112404	−	0.432520i
$677$	−23.5152	+	8.41389i	−0.903764	+	0.323372i	−0.747436	−	0.664333i	$-0.768716\pi$
$677$	−23.5152	+	8.41389i	−0.903764	+	0.323372i	−0.156327	+	0.987705i	$0.549966\pi$
$678$	1.81283	+	1.03754i	0.0696212	+	0.0398465i
$679$	0.388105	−	0.318509i	0.0148941	−	0.0122233i
$680$	−39.0544	−	15.6616i	−1.49767	−	0.600596i
$681$	−0.912368	−	9.26343i	−0.0349620	−	0.354975i
$682$	1.07562	+	0.0311519i	0.0411874	+	0.00119287i
$683$	7.46983	+	50.3575i	0.285825	+	1.92688i	0.367094	+	0.930184i	$0.380353\pi$
$683$	7.46983	+	50.3575i	0.285825	+	1.92688i	−0.0812692	+	0.996692i	$0.525897\pi$
$684$	−6.67363	+	32.0697i	−0.255173	+	1.22621i
$685$	−14.1979	+	39.6804i	−0.542473	+	1.51611i
$686$	−30.4758	−	2.38321i	−1.16357	−	0.0909915i
$687$	1.72159	+	1.15033i	0.0656826	+	0.0438877i
$688$	2.12215	+	1.32340i	0.0809061	+	0.0504541i
$689$	−23.9980	+	16.0350i	−0.914252	+	0.610884i
$690$	−8.75198	−	15.6095i	−0.333182	−	0.594245i
$691$	−2.24398	−	45.6774i	−0.0853652	−	1.73765i	−0.535366	−	0.844620i	$-0.679826\pi$
$691$	−2.24398	−	45.6774i	−0.0853652	−	1.73765i	0.450001	−	0.893028i	$-0.351424\pi$
$692$	−2.01114	+	2.40698i	−0.0764522	+	0.0914995i
$693$	8.24020	−	32.8967i	0.313019	−	1.24964i
$694$	2.83343	+	16.7682i	0.107556	+	0.636511i
$695$	23.2103	−	12.4062i	0.880418	−	0.470593i
$696$	3.48374	+	1.59971i	0.132051	+	0.0606370i
$697$	11.8683	+	39.1246i	0.449545	+	1.48195i
$698$	−12.0277	−	10.4680i	−0.455256	−	0.396221i
$699$	−0.992354	+	0.899417i	−0.0375343	+	0.0340191i
$700$	8.22744	+	11.3004i	0.310968	+	0.427114i
$701$	25.0246	−	18.5595i	0.945165	−	0.700982i	−0.00909546	−	0.999959i	$-0.502895\pi$
$701$	25.0246	−	18.5595i	0.945165	−	0.700982i	0.954260	+	0.298976i	$0.0966452\pi$
$702$	12.9969	−	2.85841i	0.490538	−	0.107884i
$703$	11.4702	−	11.4702i	0.432605	−	0.432605i
$704$	11.8121	−	20.7583i	0.445183	−	0.782358i
$705$	13.9427	+	13.9427i	0.525112	+	0.525112i
$706$	26.3946	+	16.8778i	0.993375	+	0.635203i
$707$	30.4539	+	41.0623i	1.14534	+	1.54431i
$708$	2.60570	−	0.628321i	0.0979280	−	0.0236137i
$709$	32.5011	+	35.8594i	1.22060	+	1.34673i	0.919476	+	0.393146i	$0.128613\pi$
$709$	32.5011	+	35.8594i	1.22060	+	1.34673i	0.301129	+	0.953584i	$0.402637\pi$
$710$	13.3712	−	0.927049i	0.501813	−	0.0347915i
$711$	15.9734	−	4.84548i	0.599049	−	0.181720i
$712$	4.69557	+	29.3623i	0.175974	+	1.10040i
$713$	−0.945455	−	1.76882i	−0.0354075	−	0.0662429i
$714$	12.9238	−	18.1795i	0.483661	−	0.680352i
$715$	19.9577	+	4.99915i	0.746376	+	0.186957i
$716$	8.58126	−	27.4157i	0.320697	−	1.02457i
$717$	5.27954	−	0.259367i	0.197168	−	0.00968624i
$718$	15.2974	+	4.30607i	0.570892	+	0.160701i
$719$	−5.48077	−	8.20255i	−0.204398	−	0.305903i	0.715081	−	0.699041i	$-0.246390\pi$
$719$	−5.48077	−	8.20255i	−0.204398	−	0.305903i	−0.919480	+	0.393138i	$0.871390\pi$
$720$	−13.3781	−	23.2401i	−0.498573	−	0.866109i
$721$	0.536035	−	0.802234i	0.0199630	−	0.0298767i
$722$	18.7689	+	21.9534i	0.698505	+	0.817019i
$723$	−9.89189	−	3.53938i	−0.367883	−	0.131631i
$724$	−21.5900	+	31.7028i	−0.802386	+	1.17823i
$725$	3.43894	−	0.510119i	0.127719	−	0.0189453i
$726$	−1.34307	+	1.26746i	−0.0498459	+	0.0470399i
$727$	−44.4388	+	4.37684i	−1.64814	+	0.162328i	−0.879024	−	0.476778i	$-0.841805\pi$
$727$	−44.4388	+	4.37684i	−1.64814	+	0.162328i	−0.769119	+	0.639106i	$0.779305\pi$
$728$	−6.07660	+	32.4644i	−0.225214	+	1.20321i
$729$	5.13783	+	6.26047i	0.190290	+	0.231869i
$730$	−8.63719	−	31.7549i	−0.319677	−	1.17530i
$731$	−1.21930	−	3.40772i	−0.0450974	−	0.126039i
$732$	−13.8917	+	1.93557i	−0.513452	+	0.0715408i
$733$	38.9303	+	23.3339i	1.43792	+	0.861859i	0.999322	−	0.0368224i	$-0.0117236\pi$
$733$	38.9303	+	23.3339i	1.43792	+	0.861859i	0.438603	+	0.898681i	$0.355474\pi$
$734$	0.784479	+	38.9585i	0.0289556	+	1.43798i
$735$	−17.7734	+	7.36199i	−0.655582	+	0.271551i
$736$	−44.5159	+	0.110978i	−1.64088	+	0.00409071i
$737$	−26.7803	−	11.0928i	−0.986465	−	0.408607i
$738$	−9.48440	+	24.2681i	−0.349125	+	0.893321i
$739$	−22.9406	+	5.74633i	−0.843885	+	0.211382i	−0.640732	−	0.767765i	$-0.721369\pi$
$739$	−22.9406	+	5.74633i	−0.843885	+	0.211382i	−0.203153	+	0.979147i	$0.565119\pi$
$740$	−0.768539	+	13.2570i	−0.0282521	+	0.487336i
$741$	4.50405	−	9.52302i	0.165461	−	0.349837i
$742$	−52.4363	+	40.5509i	−1.92500	+	1.48867i
$743$	−4.12610	−	0.406385i	−0.151372	−	0.0149088i	0.0220473	−	0.999757i	$-0.492982\pi$
$743$	−4.12610	−	0.406385i	−0.151372	−	0.0149088i	−0.173419	+	0.984848i	$0.555482\pi$
$744$	0.217105	+	0.395350i	0.00795944	+	0.0144942i
$745$	30.1140	+	24.7139i	1.10329	+	0.905448i
$746$	−19.3321	−	50.7824i	−0.707798	−	1.85928i
$747$	5.62146	−	7.57967i	0.205679	−	0.277326i
$748$	−32.0477	+	12.9446i	−1.17178	+	0.473302i
$749$	17.9999	+	38.0576i	0.657703	+	1.39060i
$750$	−6.88088	−	3.50166i	−0.251254	−	0.127863i
$751$	−1.14393	−	5.75090i	−0.0417424	−	0.209853i	0.954285	−	0.298897i	$-0.0966188\pi$
$751$	−1.14393	−	5.75090i	−0.0417424	−	0.209853i	−0.996028	+	0.0890440i	$0.971619\pi$
$752$	47.1809	−	13.4080i	1.72051	−	0.488941i
$753$	−0.325818	+	1.63800i	−0.0118735	+	0.0596919i
$754$	6.45358	+	5.08238i	0.235026	+	0.185089i
$755$	−19.5967	+	21.6216i	−0.713196	+	0.786891i
$756$	29.3241	−	8.61366i	1.06651	−	0.313276i
$757$	−1.05844	−	1.76590i	−0.0384697	−	0.0641829i	0.837893	−	0.545834i	$-0.183787\pi$
$757$	−1.05844	−	1.76590i	−0.0384697	−	0.0641829i	−0.876363	+	0.481651i	$0.840037\pi$
$758$	−35.1492	−	8.05602i	−1.27668	−	0.292608i
$759$	−14.0668	−	4.26711i	−0.510592	−	0.154886i
$760$	−45.2200	−	6.18576i	−1.64030	−	0.224381i
$761$	8.54478	+	4.56728i	0.309748	+	0.165564i	0.618945	−	0.785434i	$-0.287560\pi$
$761$	8.54478	+	4.56728i	0.309748	+	0.165564i	−0.309197	+	0.950998i	$0.600060\pi$
$762$	2.76607	−	8.25067i	0.100204	−	0.298890i
$763$	25.1005	+	1.23311i	0.908697	+	0.0446414i
$764$	−27.1955	+	12.5702i	−0.983900	+	0.454774i
$765$	−5.69405	+	38.3862i	−0.205869	+	1.38785i
$766$	−7.43632	−	1.32413i	−0.268685	−	0.0478429i
$767$	5.74366			0.207392
$768$	10.0100	−	0.138210i	0.361205	−	0.00498722i
$769$	−22.0649			−0.795680			−0.397840	−	0.917455i	$-0.630240\pi$
$769$	−22.0649			−0.795680			−0.397840	+	0.917455i	$0.630240\pi$
$770$	46.5205	+	8.28358i	1.67648	+	0.298519i
$771$	2.89072	−	19.4876i	0.104107	−	0.701830i
$772$	16.6188	+	35.9547i	0.598125	+	1.29404i
$773$	−43.4457	−	2.13435i	−1.56263	−	0.0767673i	−0.750750	−	0.660586i	$-0.770308\pi$
$773$	−43.4457	−	2.13435i	−1.56263	−	0.0767673i	−0.811884	+	0.583819i	$0.801558\pi$
$774$	0.733167	−	2.18690i	0.0263532	−	0.0786065i
$775$	0.360746	+	0.192823i	0.0129584	+	0.00692640i
$776$	−0.197207	−	0.259709i	−0.00707931	−	0.00932302i
$777$	−6.73613	−	2.04338i	−0.241657	−	0.0733059i
$778$	−20.9162	−	4.79388i	−0.749881	−	0.171869i
$779$	22.7991	+	38.0381i	0.816864	+	1.36286i
$780$	2.43048	+	8.27424i	0.0870250	+	0.296265i
$781$	7.39364	−	8.15763i	0.264565	−	0.291903i
$782$	50.6110	+	39.8576i	1.80985	+	1.42531i
$783$	1.48297	−	7.45538i	0.0529969	−	0.266434i
$784$	−5.52993	+	47.5341i	−0.197497	+	1.69765i
$785$	5.90407	+	29.6818i	0.210725	+	1.05939i
$786$	−5.88946	−	2.99713i	−0.210070	−	0.106904i
$787$	−17.3502	−	36.6840i	−0.618469	−	1.30764i	−0.933505	−	0.358564i	$-0.883267\pi$
$787$	−17.3502	−	36.6840i	−0.618469	−	1.30764i	0.315036	−	0.949080i	$-0.397983\pi$
$788$	−8.57741	−	21.2356i	−0.305558	−	0.756485i
$789$	−5.41715	+	7.30418i	−0.192856	+	0.260036i
$790$	8.27458	+	21.7360i	0.294396	+	0.773334i
$791$	7.94620	+	6.52128i	0.282534	+	0.231870i
$792$	−21.1493	−	6.15516i	−0.751507	−	0.218714i
$793$	−29.9107	−	2.94595i	−1.06216	−	0.104614i
$794$	−30.1480	+	23.3145i	−1.06991	+	0.827402i
$795$	−7.40003	+	15.6460i	−0.262452	+	0.554908i
$796$	13.6699	+	0.792479i	0.484517	+	0.0280887i
$797$	−24.3183	+	6.09141i	−0.861398	+	0.215769i	−0.648415	−	0.761287i	$-0.724568\pi$
$797$	−24.3183	+	6.09141i	−0.861398	+	0.215769i	−0.212983	+	0.977056i	$0.568318\pi$
$798$	8.80679	−	22.5343i	0.311757	−	0.797705i
$799$	−65.5781	−	27.1634i	−2.31999	−	0.960971i
$800$	7.53625	−	5.06278i	0.266447	−	0.178996i
$801$	25.3360	−	10.4945i	0.895204	−	0.370805i
$802$	−0.600323	−	29.8130i	−0.0211981	−	1.05273i
$803$	−23.1858	−	13.8970i	−0.818208	−	0.490415i
$804$	−1.67669	−	12.0337i	−0.0591325	−	0.424396i
$805$	−29.6705	−	82.9236i	−1.04575	−	2.92267i
$806$	0.253670	+	0.932626i	0.00893514	+	0.0328504i
$807$	1.72526	+	2.10224i	0.0607321	+	0.0740023i
$808$	27.3982	−	18.7587i	0.963867	−	0.659929i
$809$	21.3940	−	2.10713i	0.752175	−	0.0740827i	0.285339	−	0.958427i	$-0.407894\pi$
$809$	21.3940	−	2.10713i	0.752175	−	0.0740827i	0.466836	+	0.884344i	$0.345394\pi$
$810$	−14.8817	+	14.0440i	−0.522891	+	0.493455i
$811$	−46.9839	+	6.96940i	−1.64983	+	0.244729i	−0.905888	−	0.423518i	$-0.860795\pi$
$811$	−46.9839	+	6.96940i	−1.64983	+	0.244729i	−0.743939	+	0.668247i	$0.767045\pi$
$812$	15.5936	+	10.6194i	0.547226	+	0.372668i
$813$	3.62704	+	1.29777i	0.127206	+	0.0455149i
$814$	7.08814	+	8.29078i	0.248439	+	0.290592i
$815$	26.9562	−	40.3429i	0.944236	−	1.41315i
$816$	−11.4823	−	8.83402i	−0.401961	−	0.309253i
$817$	−2.18105	−	3.26417i	−0.0763052	−	0.114199i
$818$	36.5415	+	10.2861i	1.27764	+	0.359645i
$819$	30.4236	−	1.49461i	1.06309	−	0.0522261i
$820$	−34.6466	−	10.8446i	−1.20991	−	0.378709i
$821$	−12.5972	−	3.15543i	−0.439645	−	0.110125i	0.0168363	−	0.999858i	$-0.494641\pi$
$821$	−12.5972	−	3.15543i	−0.439645	−	0.110125i	−0.456482	+	0.889733i	$0.650891\pi$
$822$	−8.40730	+	11.8263i	−0.293238	+	0.412490i
$823$	17.4043	+	32.5611i	0.606675	+	1.13501i	0.978411	+	0.206671i	$0.0662628\pi$
$823$	17.4043	+	32.5611i	0.606675	+	1.13501i	−0.371736	+	0.928339i	$0.621237\pi$
$824$	−0.507536	−	0.367588i	−0.0176809	−	0.0128055i
$825$	2.86888	−	0.870265i	0.0998815	−	0.0302987i
$826$	13.1597	−	0.912382i	0.457884	−	0.0317458i
$827$	12.3301	+	13.6041i	0.428758	+	0.473062i	0.916563	−	0.399891i	$-0.130952\pi$
$827$	12.3301	+	13.6041i	0.428758	+	0.473062i	−0.487804	+	0.872953i	$0.662202\pi$
$828$	9.62389	+	39.9110i	0.334453	+	1.38700i
$829$	20.3382	+	27.4229i	0.706375	+	0.952437i	0.999994	−	0.00348601i	$-0.00110963\pi$
$829$	20.3382	+	27.4229i	0.706375	+	0.952437i	−0.293619	+	0.955923i	$0.594860\pi$
$830$	11.0775	+	7.08337i	0.384505	+	0.245867i
$831$	4.13243	+	4.13243i	0.143352	+	0.143352i
$832$	20.9218	+	4.74029i	0.725331	+	0.164340i
$833$	48.9691	−	48.9691i	1.69668	−	1.69668i
$834$	8.84975	−	1.94632i	0.306442	−	0.0673956i
$835$	23.8139	−	17.6616i	0.824115	−	0.611205i
$836$	−30.3082	+	22.0664i	−1.04823	+	0.763184i
$837$	0.662683	−	0.600621i	0.0229057	−	0.0207605i
$838$	2.40967	+	2.09720i	0.0832406	+	0.0724465i
$839$	6.75056	+	22.2536i	0.233055	+	0.768280i	0.992981	+	0.118271i	$0.0377350\pi$
$839$	6.75056	+	22.2536i	0.233055	+	0.768280i	−0.759926	+	0.650009i	$0.774765\pi$
$840$	6.88299	+	18.5716i	0.237486	+	0.640780i
$841$	−21.4375	+	11.4586i	−0.739224	+	0.395124i
$842$	4.06665	+	24.0663i	0.140146	+	0.829378i
$843$	−3.34964	+	13.3725i	−0.115368	+	0.460574i
$844$	5.70263	+	4.76482i	0.196293	+	0.164012i
$845$	−0.732607	−	14.9126i	−0.0252024	−	0.513007i
$846$	−22.1227	−	39.4568i	−0.760595	−	1.35655i
$847$	−7.55670	+	5.04923i	−0.259651	+	0.173493i
$848$	25.0331	+	35.0281i	0.859639	+	1.20287i
$849$	−0.223777	−	0.149523i	−0.00767999	−	0.00513161i
$850$	−13.0986	−	1.02431i	−0.449277	−	0.0351334i
$851$	6.84917	−	19.1421i	0.234786	−	0.656184i
$852$	4.51797	+	0.940180i	0.154783	+	0.0322101i
$853$	−4.98784	−	33.6253i	−0.170780	−	1.15131i	−0.889811	−	0.456329i	$-0.849164\pi$
$853$	−4.98784	−	33.6253i	−0.170780	−	1.15131i	0.719031	−	0.694978i	$-0.244586\pi$
$854$	−68.9983	−	1.99832i	−2.36107	−	0.0683812i
$855$	4.12579	+	41.8898i	0.141099	+	1.43260i
$856$	25.1426	−	10.7492i	0.859355	−	0.367401i
$857$	−6.32941	+	5.19442i	−0.216209	+	0.177438i	−0.736263	−	0.676695i	$-0.763412\pi$
$857$	−6.32941	+	5.19442i	−0.216209	+	0.177438i	0.520055	+	0.854133i	$0.325912\pi$
$858$	6.14800	+	3.51870i	0.209889	+	0.120127i
$859$	24.9985	−	8.94459i	0.852936	−	0.305186i	0.126118	−	0.992015i	$-0.459748\pi$
$859$	24.9985	−	8.94459i	0.852936	−	0.305186i	0.726818	+	0.686830i	$0.240998\pi$
$860$	3.11045	+	0.808348i	0.106065	+	0.0275644i
$861$	9.89372	−	16.5067i	0.337177	−	0.562546i
$862$	−12.7965	+	13.3225i	−0.435851	+	0.453765i
$863$	12.0757	+	29.1534i	0.411063	+	0.992393i	0.984853	+	0.173391i	$0.0554723\pi$
$863$	12.0757	+	29.1534i	0.411063	+	0.992393i	−0.573791	+	0.819002i	$0.694528\pi$
$864$	−4.87136	−	19.2439i	−0.165727	−	0.654690i
$865$	−1.54242	+	3.72373i	−0.0524439	+	0.126611i
$866$	−7.85207	−	17.9270i	−0.266824	−	0.609183i
$867$	2.50966	+	10.0191i	0.0852327	+	0.340268i
$868$	0.729347	+	2.09650i	0.0247557	+	0.0711600i
$869$	17.2701	+	8.16813i	0.585846	+	0.277085i
$870$	4.88628	+	0.624554i	0.165660	+	0.0211744i
$871$	2.55193	−	25.9102i	0.0864689	−	0.877934i
$872$	1.41602	−	16.2610i	0.0479525	−	0.550668i
$873$	−0.190790	+	0.232478i	−0.00645725	+	0.00786818i
$874$	63.7566	+	28.5984i	2.15660	+	0.967356i
$875$	−30.5190	−	22.6345i	−1.03173	−	0.765184i
$876$	0.0999362	−	11.3300i	0.00337653	−	0.382805i
$877$	−15.8420	+	7.49271i	−0.534947	+	0.253011i	−0.675885	−	0.737007i	$-0.736238\pi$
$877$	−15.8420	+	7.49271i	−0.534947	+	0.253011i	0.140938	+	0.990018i	$0.454988\pi$
$878$	−9.80061	−	30.1121i	−0.330754	−	1.01623i
$879$	−8.83810	+	1.75801i	−0.298102	+	0.0592961i
$880$	6.51749	−	29.9906i	0.219704	−	1.01098i
$881$	−19.6433	−	3.90729i	−0.661799	−	0.131640i	−0.147248	−	0.989100i	$-0.547041\pi$
$881$	−19.6433	−	3.90729i	−0.661799	−	0.131640i	−0.514551	+	0.857460i	$0.672041\pi$
$882$	43.8255	−	5.20925i	1.47568	−	0.175405i
$883$	−24.6213	−	22.3154i	−0.828571	−	0.750973i	0.142492	−	0.989796i	$-0.454489\pi$
$883$	−24.6213	−	22.3154i	−0.828571	−	0.750973i	−0.971063	+	0.238823i	$0.923239\pi$
$884$	−19.4818	−	24.1703i	−0.655245	−	0.812936i
$885$	2.95427	−	1.77072i	0.0993068	−	0.0595222i
$886$	−14.7717	−	23.5563i	−0.496266	−	0.791389i
$887$	−9.65809	+	31.8385i	−0.324287	+	1.06903i	0.631600	+	0.775295i	$0.282399\pi$
$887$	−9.65809	+	31.8385i	−0.324287	+	1.06903i	−0.955887	+	0.293736i	$0.905101\pi$
$888$	−1.49147	+	4.32192i	−0.0500506	+	0.145034i
$889$	20.1881	−	37.7693i	0.677087	−	1.26674i
$890$	17.0290	+	34.2057i	0.570814	+	1.14658i
$891$	−0.824725	+	16.7877i	−0.0276293	+	0.562408i
$892$	−3.88957	+	0.156706i	−0.130232	+	0.00524692i
$893$	−76.1590	−	11.2971i	−2.54856	−	0.378044i
$894$	7.67477	+	11.0001i	0.256683	+	0.367897i
$895$		−	36.9148i		−	1.23392i
$896$	48.6882	+	7.53735i	1.62656	+	0.251805i
$897$		−	13.2031i		−	0.440840i
$898$	3.66726	−	2.55865i	0.122378	−	0.0853834i
$899$	0.546107	+	0.0810073i	0.0182137	+	0.00270174i
$900$	−6.15418	−	5.67749i	−0.205139	−	0.189250i
$901$	3.05716	−	62.2300i	0.101849	−	2.07318i
$902$	−26.6955	+	13.2902i	−0.888863	+	0.442514i
$903$	−0.803071	+	1.50244i	−0.0267245	+	0.0499981i
$904$	4.42750	−	4.99747i	0.147257	−	0.166213i
$905$	−14.3075	+	47.1655i	−0.475598	+	1.56784i
$906$	−8.51184	+	5.33762i	−0.282787	+	0.177331i
$907$	13.4565	−	8.06552i	0.446816	−	0.267811i	−0.272950	−	0.962028i	$-0.587999\pi$
$907$	13.4565	−	8.06552i	0.446816	−	0.267811i	0.719766	+	0.694217i	$0.244249\pi$
$908$	−29.5836	−	3.17743i	−0.981767	−	0.105447i
$909$	−22.6902	−	20.5652i	−0.752586	−	0.682104i
$910$	5.00946	+	42.1447i	0.166062	+	1.39708i
$911$	57.2970	+	11.3971i	1.89833	+	0.377602i	0.998304	−	0.0582245i	$-0.0185439\pi$
$911$	57.2970	+	11.3971i	1.89833	+	0.377602i	0.900031	+	0.435827i	$0.143544\pi$
$912$	−14.4097	−	6.26873i	−0.477153	−	0.207578i
$913$	10.5929	−	2.10706i	0.350573	−	0.0697334i
$914$	16.5190	−	5.37646i	0.546401	−	0.177838i
$915$	−16.2929	+	7.70596i	−0.538626	+	0.254751i
$916$	4.72105	−	4.63849i	0.155988	−	0.153260i
$917$	−26.1218	−	19.3732i	−0.862616	−	0.639760i
$918$	−11.7571	+	26.2110i	−0.388043	+	0.865093i
$919$	19.2326	−	23.4350i	0.634426	−	0.773050i	−0.352223	−	0.935916i	$-0.614574\pi$
$919$	19.2326	−	23.4350i	0.634426	−	0.773050i	0.986648	+	0.162866i	$0.0520740\pi$
$920$	−54.5488	+	17.2235i	−1.79842	+	0.567841i
$921$	−0.176123	+	1.78821i	−0.00580345	+	0.0589235i
$922$	−2.17446	+	17.0121i	−0.0716119	+	0.560265i
$923$	8.93932	+	4.22799i	0.294241	+	0.139166i
$924$	14.6450	+	7.08532i	0.481786	+	0.233090i
$925$	1.00748	+	4.02210i	0.0331259	+	0.132246i
$926$	36.5546	−	16.0110i	1.20126	−	0.526155i
$927$	−0.221170	+	0.533952i	−0.00726418	+	0.0175373i
$928$	7.27495	−	9.86041i	0.238812	−	0.323684i
$929$	6.72205	+	16.2285i	0.220543	+	0.532438i	0.994964	−	0.100232i	$-0.0319586\pi$
$929$	6.72205	+	16.2285i	0.220543	+	0.532438i	−0.774421	+	0.632671i	$0.781959\pi$
$930$	0.417997	+	0.401495i	0.0137067	+	0.0131656i
$931$	38.6181	−	64.4304i	1.26566	−	2.11162i
$932$	2.16843	+	3.69125i	0.0710292	+	0.120911i
$933$	−2.81486	+	1.00717i	−0.0921543	+	0.0329733i
$934$	11.4619	−	20.0267i	0.375046	−	0.655293i
$935$	−34.3324	+	28.1759i	−1.12279	+	0.921450i
$936$	−0.223819	−	19.7829i	−0.00731575	−	0.646624i
$937$	−4.41192	−	44.7950i	−0.144131	−	1.46339i	−0.746614	−	0.665257i	$-0.768322\pi$
$937$	−4.41192	−	44.7950i	−0.144131	−	1.46339i	0.602483	−	0.798132i	$-0.294178\pi$
$938$	1.73105	−	59.7699i	0.0565208	−	1.95156i
$939$	−1.12693	−	7.59715i	−0.0367760	−	0.247924i
$940$	52.7129	−	34.5530i	1.71931	−	1.12700i
$941$	−6.96945	+	19.4783i	−0.227197	+	0.634974i	0.772803	+	0.634647i	$0.218854\pi$
$941$	−6.96945	+	19.4783i	−0.227197	+	0.634974i	−1.00000		0.000327709i	$0.999896\pi$
$942$	−0.812336	+	10.3879i	−0.0264673	+	0.338457i
$943$	46.2147	+	30.8797i	1.50496	+	1.00558i
$944$	−0.269386	−	8.56358i	−0.00876777	−	0.278721i
$945$	32.6548	−	21.8192i	1.06226	−	0.709779i
$946$	2.30260	−	1.29103i	0.0748640	−	0.0419749i
$947$	2.93109	+	59.6637i	0.0952476	+	1.93881i	0.288139	+	0.957588i	$0.406963\pi$
$947$	2.93109	+	59.6637i	0.0952476	+	1.93881i	−0.192892	+	0.981220i	$0.561787\pi$
$948$	0.714568	+	7.97570i	0.0232081	+	0.259039i
$949$	5.89942	−	23.5518i	0.191503	−	0.764524i
$950$	−14.0520	+	2.37446i	−0.455906	+	0.0770377i
$951$	−1.70760	+	0.912732i	−0.0553728	+	0.0295974i
$952$	−48.4756	−	52.2835i	−1.57110	−	1.69452i
$953$	−5.94218	−	19.5888i	−0.192486	−	0.634542i	−0.999058	−	0.0434052i	$-0.986179\pi$
$953$	−5.94218	−	19.5888i	−0.192486	−	0.634542i	0.806571	−	0.591137i	$-0.201321\pi$
$954$	26.0674	−	29.9513i	0.843964	−	0.969709i
$955$	−28.5258	+	25.8542i	−0.923072	+	0.836624i
$956$	2.62653	−	16.6910i	0.0849480	−	0.539824i
$957$	3.25003	−	2.41039i	0.105059	−	0.0779167i
$958$	4.17849	+	18.9992i	0.135001	+	0.613837i
$959$	−50.4948	+	50.4948i	−1.63056	+	1.63056i
$960$	12.2226	−	4.01182i	0.394482	−	0.129481i
$961$	−21.8744	−	21.8744i	−0.705625	−	0.705625i
$962$	−5.27793	+	8.25400i	−0.170167	+	0.266120i
$963$	−15.0224	−	20.2553i	−0.484089	−	0.652718i
$964$	−17.5182	+	28.6512i	−0.564224	+	0.922794i
$965$	34.1814	+	37.7134i	1.10034	+	1.21404i
$966$	−2.09732	−	30.2505i	−0.0674802	−	0.973295i
$967$	−7.15255	+	2.16970i	−0.230011	+	0.0697729i	−0.403186	−	0.915118i	$-0.632097\pi$
$967$	−7.15255	+	2.16970i	−0.230011	+	0.0697729i	0.173175	+	0.984891i	$0.444597\pi$
$968$	3.09181	+	5.02848i	0.0993746	+	0.161621i
$969$	10.7199	+	20.0556i	0.344374	+	0.644278i
$970$	−0.341530	−	0.242793i	−0.0109659	−	0.00779562i
$971$	−18.5870	−	4.65580i	−0.596486	−	0.149412i	−0.0670321	−	0.997751i	$-0.521353\pi$
$971$	−18.5870	−	4.65580i	−0.596486	−	0.149412i	−0.529453	+	0.848339i	$0.677603\pi$
$972$	−24.8980	+	13.0272i	−0.798603	+	0.417848i
$973$	44.5404	−	2.18813i	1.42790	−	0.0701483i
$974$	11.9144	−	42.3262i	0.381764	−	1.35622i
$975$	1.49601	+	2.23893i	0.0479105	+	0.0717032i
$976$	−2.98944	+	44.7339i	−0.0956895	+	1.43190i
$977$	16.9413	−	25.3544i	0.541999	−	0.811159i	−0.454842	−	0.890572i	$-0.650304\pi$
$977$	16.9413	−	25.3544i	0.541999	−	0.811159i	0.996842	+	0.0794126i	$0.0253044\pi$
$978$	12.6975	−	10.8556i	0.406021	−	0.347125i
$979$	29.5516	+	10.5737i	0.944474	+	0.337938i
$980$	11.4644	+	60.4154i	0.366215	+	1.92990i
$981$	−14.8906	+	2.20881i	−0.475419	+	0.0705218i
$982$	−19.4732	−	20.6348i	−0.621414	−	0.658482i
$983$	3.58203	−	0.352799i	0.114249	−	0.0112525i	−0.0407311	−	0.999170i	$-0.512969\pi$
$983$	3.58203	−	0.352799i	0.114249	−	0.0112525i	0.154980	+	0.987918i	$0.450469\pi$
$984$	−10.4709	−	6.82634i	−0.333799	−	0.217616i
$985$	−18.6700	−	22.7495i	−0.594876	−	0.724858i
$986$	−17.1112	+	4.65417i	−0.544932	+	0.148219i
$987$	11.2558	+	31.4579i	0.358276	+	1.00131i
$988$	−26.8686	−	20.2969i	−0.854805	−	0.645731i
$989$	−4.22028	−	2.52954i	−0.134197	−	0.0804347i
$990$	−28.2987	+	0.569831i	−0.899393	+	0.0181104i
$991$	13.5538	−	5.61417i	0.430551	−	0.178340i	−0.156874	−	0.987619i	$-0.550142\pi$
$991$	13.5538	−	5.61417i	0.430551	−	0.178340i	0.587425	+	0.809279i	$0.300142\pi$
$992$	1.37861	−	0.421953i	0.0437710	−	0.0133970i
$993$	−8.17321	−	3.38546i	−0.259369	−	0.107434i
$994$	21.1531	+	8.26699i	0.670935	+	0.262213i
$995$	17.0681	−	4.27533i	0.541095	−	0.135537i
$996$	3.01047	+	3.38100i	0.0953905	+	0.107131i
$997$	−6.76510	+	14.3036i	−0.214253	+	0.452999i	−0.982280	−	0.187417i	$-0.939988\pi$
$997$	−6.76510	+	14.3036i	−0.214253	+	0.452999i	0.768028	+	0.640417i	$0.221238\pi$
$998$	21.0760	+	27.2534i	0.667149	+	0.862690i
$999$	9.02228	+	0.888617i	0.285452	+	0.0281146i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.19	✓	992
256.205	even	64	inner	256.2.m.a.205.19	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.19	✓	992	1.1	even	1	trivial
256.2.m.a.205.19	yes	992	256.205	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247919 - 1.39231i) q^{2} +(0.0918072 - 0.618914i) q^{3} +(-1.87707 - 0.690363i) q^{4} +(-2.56691 - 0.126104i) q^{5} +(-0.838961 - 0.281265i) q^{6} +(-3.84053 - 2.05281i) q^{7} +(-1.42656 + 2.44232i) q^{8} +(2.49620 + 0.757213i) q^{9} +O(q^{10})\)	\(q+(0.247919 - 1.39231i) q^{2} +(0.0918072 - 0.618914i) q^{3} +(-1.87707 - 0.690363i) q^{4} +(-2.56691 - 0.126104i) q^{5} +(-0.838961 - 0.281265i) q^{6} +(-3.84053 - 2.05281i) q^{7} +(-1.42656 + 2.44232i) q^{8} +(2.49620 + 0.757213i) q^{9} +(-0.811964 + 3.54268i) q^{10} +(1.53483 + 2.56072i) q^{11} +(-0.599604 + 1.09837i) q^{12} +(-1.80079 + 1.98686i) q^{13} +(-3.81029 + 4.83829i) q^{14} +(-0.313709 + 1.57712i) q^{15} +(3.04680 + 2.59172i) q^{16} +(-1.12930 - 5.67736i) q^{17} +(1.67313 - 3.28776i) q^{18} +(-2.68453 - 5.67596i) q^{19} +(4.73122 + 2.00881i) q^{20} +(-1.62310 + 2.18849i) q^{21} +(3.94584 - 1.50212i) q^{22} +(-6.08313 - 4.99230i) q^{23} +(1.38062 + 1.10714i) q^{24} +(1.59721 + 0.157312i) q^{25} +(2.31989 + 2.99984i) q^{26} +(1.50036 - 3.17225i) q^{27} +(5.79177 + 6.50462i) q^{28} +(2.10125 - 0.526335i) q^{29} +(2.11807 + 0.827779i) q^{30} +(0.235466 + 0.0975331i) q^{31} +(4.36385 - 3.59956i) q^{32} +(1.72577 - 0.714838i) q^{33} +(-8.18464 + 0.164808i) q^{34} +(9.59943 + 5.75368i) q^{35} +(-4.16279 - 3.14462i) q^{36} +(0.870354 + 2.43248i) q^{37} +(-8.56827 + 2.33053i) q^{38} +(1.06437 + 1.29694i) q^{39} +(3.96985 - 6.08932i) q^{40} +(-7.02904 + 0.692300i) q^{41} +(2.64467 + 2.80243i) q^{42} +(0.618477 - 0.0917424i) q^{43} +(-1.11317 - 5.86624i) q^{44} +(-6.31203 - 2.25848i) q^{45} +(-8.45897 + 7.23194i) q^{46} +(6.81255 - 10.1957i) q^{47} +(1.88377 - 1.64777i) q^{48} +(6.64666 + 9.94743i) q^{49} +(0.615007 - 2.18482i) q^{50} +(-3.61748 + 0.177715i) q^{51} +(4.75187 - 2.48629i) q^{52} +(10.4409 + 2.61530i) q^{53} +(-4.04480 - 2.87544i) q^{54} +(-3.61687 - 6.76669i) q^{55} +(10.4924 - 6.45134i) q^{56} +(-3.75939 + 1.14040i) q^{57} +(-0.211883 - 3.05608i) q^{58} +(-1.43845 - 1.58708i) q^{59} +(1.67764 - 2.74380i) q^{60} +(6.67684 + 9.00268i) q^{61} +(0.194173 - 0.303662i) q^{62} +(-8.03230 - 8.03230i) q^{63} +(-3.92983 - 6.96824i) q^{64} +(4.87302 - 4.87302i) q^{65} +(-0.567426 - 2.58004i) q^{66} +(-7.79859 + 5.78383i) q^{67} +(-1.79967 + 11.4364i) q^{68} +(-3.64828 + 3.30660i) q^{69} +(10.3908 - 11.9390i) q^{70} +(-1.07050 - 3.52897i) q^{71} +(-5.41033 + 5.01629i) q^{72} +(-7.98527 + 4.26822i) q^{73} +(3.60255 - 0.608748i) q^{74} +(0.243998 - 0.974095i) q^{75} +(1.12058 + 12.5075i) q^{76} +(-0.637923 - 12.9852i) q^{77} +(2.06963 - 1.16040i) q^{78} +(5.32066 - 3.55515i) q^{79} +(-7.49404 - 7.03694i) q^{80} +(4.68110 + 3.12781i) q^{81} +(-0.778736 + 9.95826i) q^{82} +(1.21876 - 3.40619i) q^{83} +(4.55753 - 2.98743i) q^{84} +(2.18287 + 14.7157i) q^{85} +(0.0255983 - 0.883859i) q^{86} +(-0.132846 - 1.34881i) q^{87} +(-8.44362 + 0.0955291i) q^{88} +(8.12670 - 6.66941i) q^{89} +(-4.70938 + 8.22840i) q^{90} +(10.9946 - 3.93394i) q^{91} +(7.97198 + 13.5705i) q^{92} +(0.0819820 - 0.136779i) q^{93} +(-12.5067 - 12.0129i) q^{94} +(6.17519 + 14.9082i) q^{95} +(-1.82718 - 3.03131i) q^{96} +(-0.0441206 + 0.106517i) q^{97} +(15.4978 - 6.78807i) q^{98} +(1.89224 + 7.55425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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