LMFDB - Embedded newform 418.2.n.d.125.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			125.6
Character	$\chi$	$=$	418.125
Dual form			418.2.n.d.311.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 + 0.406737i) q^{2} +(1.27149 + 1.41213i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.245336 - 2.33422i) q^{5} +(-1.73593 - 0.772884i) q^{6} +(-0.645619 - 1.98701i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.0638446 + 0.607441i) q^{9} +O(q^{10})$	\(q+(-0.913545 + 0.406737i) q^{2} +(1.27149 + 1.41213i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.245336 - 2.33422i) q^{5} +(-1.73593 - 0.772884i) q^{6} +(-0.645619 - 1.98701i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.0638446 + 0.607441i) q^{9} +(1.17354 + 2.03263i) q^{10} +(2.86266 + 1.67487i) q^{11} +1.90021 q^{12} +(0.0367169 - 0.349338i) q^{13} +(1.39799 + 1.55263i) q^{14} +(2.98428 - 3.31438i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.738395 - 7.02536i) q^{17} +(-0.188744 - 0.580893i) q^{18} +(1.24115 - 4.17846i) q^{19} +(-1.89883 - 1.37958i) q^{20} +(1.98502 - 3.43816i) q^{21} +(-3.29640 - 0.365723i) q^{22} +(3.21470 + 5.56803i) q^{23} +(-1.73593 + 0.772884i) q^{24} +(-0.497653 + 0.105779i) q^{25} +(0.108546 + 0.334071i) q^{26} +(3.67294 - 2.66854i) q^{27} +(-1.90864 - 0.849782i) q^{28} +(-3.86772 + 4.29554i) q^{29} +(-1.37819 + 4.24165i) q^{30} +(-0.524196 - 0.380850i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.27470 + 6.17202i) q^{33} +(3.53203 + 6.11765i) q^{34} +(-4.47973 + 1.99450i) q^{35} +(0.408696 + 0.453903i) q^{36} +(0.399526 + 1.22961i) q^{37} +(0.565691 + 4.32204i) q^{38} +(0.539996 - 0.392330i) q^{39} +(2.29579 + 0.487985i) q^{40} +(4.83622 + 5.37117i) q^{41} +(-0.414982 + 3.94829i) q^{42} +(-0.0857287 + 0.148487i) q^{43} +(3.16016 - 1.00666i) q^{44} +1.43356 q^{45} +(-5.20150 - 3.77911i) q^{46} +(-4.43894 + 0.943525i) q^{47} +(1.27149 - 1.41213i) q^{48} +(2.13173 - 1.54879i) q^{49} +(0.411605 - 0.299048i) q^{50} +(8.98185 - 9.97536i) q^{51} +(-0.235041 - 0.261039i) q^{52} +(-0.426632 + 4.05913i) q^{53} +(-2.27000 + 3.93176i) q^{54} +(3.20720 - 7.09298i) q^{55} +2.08927 q^{56} +(7.47863 - 3.56020i) q^{57} +(1.78618 - 5.49731i) q^{58} +(2.06925 + 0.439833i) q^{59} +(-0.466190 - 4.43550i) q^{60} +(-12.4767 - 5.55497i) q^{61} +(0.633782 + 0.134715i) q^{62} +(1.24821 - 0.265316i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.824440 q^{65} +(-3.67488 - 5.11995i) q^{66} +(2.17191 + 3.76186i) q^{67} +(-5.71494 - 4.15215i) q^{68} +(-3.77532 + 11.6193i) q^{69} +(3.28120 - 3.64414i) q^{70} +(1.39040 + 13.2288i) q^{71} +(-0.557982 - 0.248429i) q^{72} +(-6.49287 - 1.38010i) q^{73} +(-0.865114 - 0.960807i) q^{74} +(-0.782134 - 0.568254i) q^{75} +(-2.27471 - 3.71829i) q^{76} +(1.47980 - 6.76946i) q^{77} +(-0.333736 + 0.578047i) q^{78} +(15.2769 - 6.80171i) q^{79} +(-2.29579 + 0.487985i) q^{80} +(10.2307 + 2.17461i) q^{81} +(-6.60276 - 2.93974i) q^{82} +(-10.0089 + 7.27186i) q^{83} +(-1.22681 - 3.77573i) q^{84} +(-16.2176 + 3.44715i) q^{85} +(0.0179222 - 0.170518i) q^{86} -10.9836 q^{87} +(-2.47751 + 2.20499i) q^{88} +(-5.05529 - 8.75601i) q^{89} +(-1.30963 + 0.583083i) q^{90} +(-0.717844 + 0.152583i) q^{91} +(6.28891 + 1.33675i) q^{92} +(-0.128698 - 1.22448i) q^{93} +(3.67140 - 2.66743i) q^{94} +(-10.0579 - 1.87198i) q^{95} +(-0.587196 + 1.80720i) q^{96} +(0.0508167 - 0.0226251i) q^{97} +(-1.31748 + 2.28194i) q^{98} +(-1.20015 + 1.63196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$2$	−0.913545	+	0.406737i	−0.645974	+	0.287606i
$3$	1.27149	+	1.41213i	0.734093	+	0.815293i	0.988407	−	0.151829i	$-0.0485162\pi$
$3$	1.27149	+	1.41213i	0.734093	+	0.815293i	−0.254314	+	0.967122i	$0.581850\pi$
$4$	0.669131	−	0.743145i	0.334565	−	0.371572i
$5$	−0.245336	−	2.33422i	−0.109718	−	1.04389i	−0.901408	−	0.432972i	$-0.857465\pi$
$5$	−0.245336	−	2.33422i	−0.109718	−	1.04389i	0.791690	−	0.610923i	$-0.209202\pi$
$6$	−1.73593	−	0.772884i	−0.708689	−	0.315529i
$7$	−0.645619	−	1.98701i	−0.244021	−	0.751020i	−0.995796	−	0.0915999i	$-0.970802\pi$
$7$	−0.645619	−	1.98701i	−0.244021	−	0.751020i	0.751775	−	0.659420i	$-0.229198\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.0638446	+	0.607441i	−0.0212815	+	0.202480i
$10$	1.17354	+	2.03263i	0.371105	+	0.642774i
$11$	2.86266	+	1.67487i	0.863124	+	0.504993i
$11$	2.86266	+	1.67487i	0.863124	+	0.504993i
$12$	1.90021			0.548543
$13$	0.0367169	−	0.349338i	0.0101834	−	0.0968890i	−0.988250	−	0.152849i	$-0.951155\pi$
$13$	0.0367169	−	0.349338i	0.0101834	−	0.0968890i	0.998433	+	0.0559599i	$0.0178219\pi$
$14$	1.39799	+	1.55263i	0.373629	+	0.414957i
$15$	2.98428	−	3.31438i	0.770537	−	0.855768i
$16$	−0.104528	−	0.994522i	−0.0261321	−	0.248630i
$17$	−0.738395	−	7.02536i	−0.179087	−	1.70390i	−0.602628	−	0.798022i	$-0.705880\pi$
$17$	−0.738395	−	7.02536i	−0.179087	−	1.70390i	0.423541	−	0.905877i	$-0.360787\pi$
$18$	−0.188744	−	0.580893i	−0.0444873	−	0.136918i
$19$	1.24115	−	4.17846i	0.284738	−	0.958605i
$19$	1.24115	−	4.17846i	0.284738	−	0.958605i
$20$	−1.89883	−	1.37958i	−0.424590	−	0.308483i
$21$	1.98502	−	3.43816i	0.433167	−	0.750267i
$22$	−3.29640	−	0.365723i	−0.702795	−	0.0779724i
$23$	3.21470	+	5.56803i	0.670312	+	1.16101i	0.977816	+	0.209468i	$0.0671731\pi$
$23$	3.21470	+	5.56803i	0.670312	+	1.16101i	−0.307504	+	0.951547i	$0.599494\pi$
$24$	−1.73593	+	0.772884i	−0.354344	+	0.157764i
$25$	−0.497653	+	0.105779i	−0.0995307	+	0.0211559i
$26$	0.108546	+	0.334071i	0.0212876	+	0.0655166i
$27$	3.67294	−	2.66854i	0.706857	−	0.513562i
$28$	−1.90864	−	0.849782i	−0.360699	−	0.160594i
$29$	−3.86772	+	4.29554i	−0.718217	+	0.797661i	−0.986164	−	0.165773i	$-0.946988\pi$
$29$	−3.86772	+	4.29554i	−0.718217	+	0.797661i	0.267947	+	0.963434i	$0.413655\pi$
$30$	−1.37819	+	4.24165i	−0.251623	+	0.774415i
$31$	−0.524196	−	0.380850i	−0.0941483	−	0.0684028i	0.539715	−	0.841848i	$-0.318532\pi$
$31$	−0.524196	−	0.380850i	−0.0941483	−	0.0684028i	−0.633864	+	0.773445i	$0.718532\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.27470	+	6.17202i	0.221896	+	1.07441i
$34$	3.53203	+	6.11765i	0.605738	+	1.04917i
$35$	−4.47973	+	1.99450i	−0.757212	+	0.337133i
$36$	0.408696	+	0.453903i	0.0681160	+	0.0756505i
$37$	0.399526	+	1.22961i	0.0656817	+	0.202147i	0.978511	−	0.206193i	$-0.0661076\pi$
$37$	0.399526	+	1.22961i	0.0656817	+	0.202147i	−0.912830	+	0.408341i	$0.866108\pi$
$38$	0.565691	+	4.32204i	0.0917672	+	0.701127i
$39$	0.539996	−	0.392330i	0.0864685	−	0.0628231i
$40$	2.29579	+	0.487985i	0.362996	+	0.0771572i
$41$	4.83622	+	5.37117i	0.755291	+	0.838835i	0.991122	−	0.132959i	$-0.0424478\pi$
$41$	4.83622	+	5.37117i	0.755291	+	0.838835i	−0.235831	+	0.971794i	$0.575781\pi$
$42$	−0.414982	+	3.94829i	−0.0640332	+	0.609235i
$43$	−0.0857287	+	0.148487i	−0.0130735	+	0.0226440i	−0.872488	−	0.488635i	$-0.837495\pi$
$43$	−0.0857287	+	0.148487i	−0.0130735	+	0.0226440i	0.859415	+	0.511279i	$0.170828\pi$
$44$	3.16016	−	1.00666i	0.476413	−	0.151760i
$45$	1.43356			0.213703
$46$	−5.20150	−	3.77911i	−0.766919	−	0.557199i
$47$	−4.43894	+	0.943525i	−0.647486	+	0.137627i	−0.519936	−	0.854205i	$-0.674044\pi$
$47$	−4.43894	+	0.943525i	−0.647486	+	0.137627i	−0.127549	+	0.991832i	$0.540711\pi$
$48$	1.27149	−	1.41213i	0.183523	−	0.203823i
$49$	2.13173	−	1.54879i	0.304532	−	0.221256i
$50$	0.411605	−	0.299048i	0.0582097	−	0.0422918i
$51$	8.98185	−	9.97536i	1.25771	−	1.39683i
$52$	−0.235041	−	0.261039i	−0.0325943	−	0.0361996i
$53$	−0.426632	+	4.05913i	−0.0586024	+	0.557564i	0.925348	+	0.379120i	$0.123773\pi$
$53$	−0.426632	+	4.05913i	−0.0586024	+	0.557564i	−0.983950	+	0.178445i	$0.942893\pi$
$54$	−2.27000	+	3.93176i	−0.308908	+	0.535044i
$55$	3.20720	−	7.09298i	0.432459	−	0.956417i
$56$	2.08927			0.279190
$57$	7.47863	−	3.56020i	0.990569	−	0.471560i
$58$	1.78618	−	5.49731i	0.234538	−	0.721832i
$59$	2.06925	+	0.439833i	0.269394	+	0.0572614i	0.340628	−	0.940198i	$-0.389360\pi$
$59$	2.06925	+	0.439833i	0.269394	+	0.0572614i	−0.0712342	+	0.997460i	$0.522694\pi$
$60$	−0.466190	−	4.43550i	−0.0601849	−	0.572621i
$61$	−12.4767	−	5.55497i	−1.59747	−	0.711241i	−0.601332	−	0.798999i	$-0.705363\pi$
$61$	−12.4767	−	5.55497i	−1.59747	−	0.711241i	−0.996142	+	0.0877582i	$0.972030\pi$
$62$	0.633782	+	0.134715i	0.0804905	+	0.0171088i
$63$	1.24821	−	0.265316i	0.157260	−	0.0334266i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.824440			−0.102259
$66$	−3.67488	−	5.11995i	−0.452346	−	0.630223i
$67$	2.17191	+	3.76186i	0.265341	+	0.459584i	0.967653	−	0.252285i	$-0.0811821\pi$
$67$	2.17191	+	3.76186i	0.265341	+	0.459584i	−0.702312	+	0.711869i	$0.747849\pi$
$68$	−5.71494	−	4.15215i	−0.693038	−	0.503522i
$69$	−3.77532	+	11.6193i	−0.454496	+	1.39879i
$70$	3.28120	−	3.64414i	0.392178	−	0.435558i
$71$	1.39040	+	13.2288i	0.165010	+	1.56996i	0.693141	+	0.720802i	$0.256226\pi$
$71$	1.39040	+	13.2288i	0.165010	+	1.56996i	−0.528131	+	0.849163i	$0.677107\pi$
$72$	−0.557982	−	0.248429i	−0.0657588	−	0.0292777i
$73$	−6.49287	−	1.38010i	−0.759933	−	0.161529i	−0.188383	−	0.982096i	$-0.560325\pi$
$73$	−6.49287	−	1.38010i	−0.759933	−	0.161529i	−0.571550	+	0.820567i	$0.693658\pi$
$74$	−0.865114	−	0.960807i	−0.100568	−	0.111692i
$75$	−0.782134	−	0.568254i	−0.0903130	−	0.0656163i
$76$	−2.27471	−	3.71829i	−0.260928	−	0.426517i
$77$	1.47980	−	6.76946i	0.168639	−	0.771452i
$78$	−0.333736	+	0.578047i	−0.0377881	+	0.0654510i
$79$	15.2769	−	6.80171i	1.71879	−	0.765253i	0.721437	−	0.692480i	$-0.243482\pi$
$79$	15.2769	−	6.80171i	1.71879	−	0.765253i	0.997349	−	0.0727721i	$-0.0231846\pi$
$80$	−2.29579	+	0.487985i	−0.256677	+	0.0545584i
$81$	10.2307	+	2.17461i	1.13675	+	0.241623i
$82$	−6.60276	−	2.93974i	−0.729153	−	0.324640i
$83$	−10.0089	+	7.27186i	−1.09862	+	0.798191i	−0.980833	−	0.194849i	$-0.937578\pi$
$83$	−10.0089	+	7.27186i	−1.09862	+	0.798191i	−0.117782	+	0.993039i	$0.537578\pi$
$84$	−1.22681	−	3.77573i	−0.133856	−	0.411966i
$85$	−16.2176	+	3.44715i	−1.75904	+	0.373896i
$86$	0.0179222	−	0.170518i	0.00193260	−	0.0183875i
$87$	−10.9836			−1.17757
$88$	−2.47751	+	2.20499i	−0.264103	+	0.235052i
$89$	−5.05529	−	8.75601i	−0.535859	−	0.928136i	−0.999121	−	0.0419142i	$-0.986654\pi$
$89$	−5.05529	−	8.75601i	−0.535859	−	0.928136i	0.463262	−	0.886221i	$-0.346679\pi$
$90$	−1.30963	+	0.583083i	−0.138047	+	0.0614623i
$91$	−0.717844	+	0.152583i	−0.0752506	+	0.0159950i
$92$	6.28891	+	1.33675i	0.655664	+	0.139366i
$93$	−0.128698	−	1.22448i	−0.0133453	−	0.126972i
$94$	3.67140	−	2.66743i	0.378676	−	0.275125i
$95$	−10.0579	−	1.87198i	−1.03192	−	0.192061i
$96$	−0.587196	+	1.80720i	−0.0599305	+	0.184447i
$97$	0.0508167	−	0.0226251i	0.00515965	−	0.00229723i	−0.404155	−	0.914690i	$-0.632434\pi$
$97$	0.0508167	−	0.0226251i	0.00515965	−	0.00229723i	0.409315	+	0.912393i	$0.365768\pi$
$98$	−1.31748	+	2.28194i	−0.133086	+	0.230511i
$99$	−1.20015	+	1.63196i	−0.120620	+	0.164019i
$100$	−0.254386	+	0.440609i	−0.0254386	+	0.0440609i
$101$	−1.23919	+	11.7901i	−0.123304	+	1.17316i	0.741466	+	0.670990i	$0.234131\pi$
$101$	−1.23919	+	11.7901i	−0.123304	+	1.17316i	−0.864770	+	0.502168i	$0.832536\pi$
$102$	−4.14799	+	12.7662i	−0.410712	+	1.26404i
$103$	−3.00255	−	9.24088i	−0.295850	−	0.910531i	−0.982935	−	0.183954i	$-0.941110\pi$
$103$	−3.00255	−	9.24088i	−0.295850	−	0.910531i	0.687085	−	0.726577i	$-0.258890\pi$
$104$	0.320894	+	0.142871i	0.0314663	+	0.0140097i
$105$	−8.51241	−	3.78997i	−0.830726	−	0.369863i
$106$	−1.26125	−	3.88173i	−0.122503	−	0.377027i
$107$	3.18364	−	9.79822i	0.307774	−	0.947230i	−0.670854	−	0.741590i	$-0.734072\pi$
$107$	3.18364	−	9.79822i	0.307774	−	0.947230i	0.978628	−	0.205640i	$-0.0659277\pi$
$108$	0.474559	−	4.51513i	0.0456645	−	0.434468i
$109$	−7.57480	+	13.1199i	−0.725535	+	1.25666i	0.233219	+	0.972424i	$0.425074\pi$
$109$	−7.57480	+	13.1199i	−0.725535	+	1.25666i	−0.958754	+	0.284239i	$0.908259\pi$
$110$	−0.0449512	+	7.78424i	−0.00428593	+	0.742199i
$111$	−1.22838	+	2.12762i	−0.116593	+	0.201945i
$112$	−1.90864	+	0.849782i	−0.180350	+	0.0802968i
$113$	−1.57451	+	4.84583i	−0.148117	+	0.455857i	−0.997399	−	0.0720827i	$-0.977035\pi$
$113$	−1.57451	+	4.84583i	−0.148117	+	0.455857i	0.849282	+	0.527940i	$0.177035\pi$
$114$	−5.38400	+	6.29424i	−0.504258	+	0.589510i
$115$	12.2083	−	8.86986i	1.13843	−	0.827119i
$116$	0.604197	+	5.74855i	0.0560983	+	0.533739i
$117$	0.209858	+	0.0446067i	0.0194014	+	0.00412389i
$118$	−2.06925	+	0.439833i	−0.190490	+	0.0404899i
$119$	−13.4827	+	6.00290i	−1.23596	+	0.550285i
$120$	2.22997	+	3.86241i	0.203567	+	0.352589i
$121$	5.38962	+	9.58916i	0.489965	+	0.871742i
$122$	13.6574			1.23648
$123$	−1.43559	+	13.6587i	−0.129443	+	1.23157i
$124$	−0.633782	+	0.134715i	−0.0569153	+	0.0120977i
$125$	−3.25743	−	10.0253i	−0.291353	−	0.896693i
$126$	−1.03238	+	0.750071i	−0.0919721	+	0.0668217i
$127$	−14.9057	−	6.63643i	−1.32266	−	0.588888i	−0.380730	−	0.924686i	$-0.624327\pi$
$127$	−14.9057	−	6.63643i	−1.32266	−	0.588888i	−0.941934	+	0.335798i	$0.890994\pi$
$128$	0.978148	+	0.207912i	0.0864569	+	0.0183770i
$129$	−0.318685	+	0.0677386i	−0.0280587	+	0.00596405i
$130$	0.753164	−	0.335330i	0.0660568	−	0.0294104i
$131$	1.32245	−	2.29054i	0.115543	−	0.200126i	−0.802454	−	0.596714i	$-0.796473\pi$
$131$	1.32245	−	2.29054i	0.115543	−	0.200126i	0.917997	+	0.396588i	$0.129806\pi$
$132$	5.43964	+	3.18260i	0.473460	+	0.277010i
$133$	−9.10396	+	0.231525i	−0.789414	+	0.0200758i
$134$	−3.51423	−	2.55323i	−0.303583	−	0.220566i
$135$	−7.13007	−	7.91875i	−0.613659	−	0.681538i
$136$	6.90969	+	1.46870i	0.592501	+	0.125940i
$137$	10.3370	+	4.60232i	0.883148	+	0.393203i	0.797640	−	0.603134i	$-0.206082\pi$
$137$	10.3370	+	4.60232i	0.883148	+	0.393203i	0.0855087	+	0.996337i	$0.472748\pi$
$138$	−1.27705	−	12.1503i	−0.108709	−	1.03430i
$139$	5.46427	−	6.06869i	0.463473	−	0.514739i	−0.465418	−	0.885091i	$-0.654096\pi$
$139$	5.46427	−	6.06869i	0.463473	−	0.514739i	0.928892	+	0.370351i	$0.120763\pi$
$140$	−1.51532	+	4.66367i	−0.128068	+	0.394152i
$141$	−6.97643	−	5.06867i	−0.587521	−	0.426859i
$142$	−6.65081	−	11.5195i	−0.558124	−	0.966699i
$143$	0.690205	−	0.938540i	0.0577178	−	0.0784846i
$144$	0.610787			0.0508989
$145$	10.9756	+	7.97425i	0.911475	+	0.662226i
$146$	6.49287	−	1.38010i	0.537354	−	0.114218i
$147$	4.89755	+	1.04101i	0.403943	+	0.0858608i
$148$	1.18112	+	0.525867i	0.0970872	+	0.0432260i
$149$	2.05990	+	19.5987i	0.168754	+	1.60559i	0.671401	+	0.741094i	$0.265693\pi$
$149$	2.05990	+	19.5987i	0.168754	+	1.60559i	−0.502647	+	0.864492i	$0.667641\pi$
$150$	0.945644	+	0.201003i	0.0772115	+	0.0164118i
$151$	−2.05467	+	6.32364i	−0.167207	+	0.514610i	−0.999192	−	0.0401876i	$-0.987204\pi$
$151$	−2.05467	+	6.32364i	−0.167207	+	0.514610i	0.831985	+	0.554798i	$0.187204\pi$
$152$	3.59042	+	2.47162i	0.291222	+	0.200475i
$153$	4.31463			0.348817
$154$	1.40152	+	6.78610i	0.112938	+	0.546840i
$155$	−0.760384	+	1.31702i	−0.0610755	+	0.105786i
$156$	0.0697698	−	0.663815i	0.00558605	−	0.0531477i
$157$	−6.55204	−	7.27677i	−0.522909	−	0.580750i	0.422612	−	0.906311i	$-0.361113\pi$
$157$	−6.55204	−	7.27677i	−0.522909	−	0.580750i	−0.945521	+	0.325561i	$0.894447\pi$
$158$	−11.1896	+	12.4273i	−0.890200	+	0.988667i
$159$	−6.27447	+	4.55867i	−0.497598	+	0.361526i
$160$	1.89883	−	1.37958i	0.150115	−	0.109065i
$161$	8.98827	−	9.98248i	0.708375	−	0.786730i
$162$	−10.2307	+	2.17461i	−0.803803	+	0.170854i
$163$	−9.18820	−	6.67562i	−0.719676	−	0.522875i	0.166605	−	0.986024i	$-0.446720\pi$
$163$	−9.18820	−	6.67562i	−0.719676	−	0.522875i	−0.886281	+	0.463149i	$0.846720\pi$
$164$	7.22762			0.564382
$165$	14.0941	−	4.48964i	1.09723	−	0.349518i
$166$	6.18582	−	10.7141i	0.480112	−	0.831579i
$167$	−0.784771	+	7.46660i	−0.0607274	+	0.577783i	0.921275	+	0.388913i	$0.127149\pi$
$167$	−0.784771	+	7.46660i	−0.0607274	+	0.577783i	−0.982002	+	0.188870i	$0.939517\pi$
$168$	2.65648	+	2.95032i	0.204952	+	0.227622i
$169$	12.5952	+	2.67720i	0.968864	+	0.205938i
$170$	13.4134	−	9.74541i	1.02876	−	0.747439i
$171$	2.45893	+	1.02070i	0.188039	+	0.0780545i
$172$	0.0529833	+	0.163066i	0.00403994	+	0.0124336i
$173$	−4.14701	−	4.60572i	−0.315291	−	0.350166i	0.564580	−	0.825378i	$-0.309038\pi$
$173$	−4.14701	−	4.60572i	−0.315291	−	0.350166i	−0.879871	+	0.475212i	$0.842371\pi$
$174$	10.0340	−	4.46743i	0.760677	−	0.338675i
$175$	0.531480	+	0.920550i	0.0401761	+	0.0695870i
$176$	1.36647	−	3.02205i	0.103001	−	0.227795i
$177$	2.00992	+	3.48129i	0.151075	+	0.261670i
$178$	8.17963	+	5.94285i	0.613089	+	0.445435i
$179$	−3.09250	+	9.51773i	−0.231144	+	0.711389i	0.766465	+	0.642286i	$0.222014\pi$
$179$	−3.09250	+	9.51773i	−0.231144	+	0.711389i	−0.997610	+	0.0691030i	$0.977986\pi$
$180$	0.959241	−	1.06535i	0.0714976	−	0.0794062i
$181$	15.2922	+	6.80855i	1.13666	+	0.506075i	0.886776	−	0.462200i	$-0.152940\pi$
$181$	15.2922	+	6.80855i	1.13666	+	0.506075i	0.249888	+	0.968275i	$0.419606\pi$
$182$	0.593723	−	0.431365i	0.0440097	−	0.0319749i
$183$	−8.01958	−	24.6817i	−0.592825	−	1.82453i
$184$	−6.28891	+	1.33675i	−0.463625	+	0.0985464i
$185$	2.77217	−	1.23425i	0.203814	−	0.0907439i
$186$	0.615612	+	1.06627i	0.0451388	+	0.0781827i
$187$	9.65279	−	21.3479i	0.705882	−	1.56111i
$188$	−2.26905	+	3.93011i	−0.165488	+	0.286633i
$189$	−7.67375	−	5.57531i	−0.558183	−	0.405544i
$190$	9.94980	−	2.38080i	0.721834	−	0.172721i
$191$	−3.35967	−	10.3400i	−0.243097	−	0.748175i	−0.995944	−	0.0899795i	$-0.971320\pi$
$191$	−3.35967	−	10.3400i	−0.243097	−	0.748175i	0.752847	−	0.658196i	$-0.228680\pi$
$192$	−0.198626	−	1.88980i	−0.0143346	−	0.136384i
$193$	1.69058	+	16.0848i	0.121691	+	1.15781i	0.869513	+	0.493910i	$0.164433\pi$
$193$	1.69058	+	16.0848i	0.121691	+	1.15781i	−0.747823	+	0.663899i	$0.768901\pi$
$194$	−0.0372209	+	0.0413380i	−0.00267231	+	0.00296790i
$195$	−1.04826	−	1.16422i	−0.0750678	−	0.0833712i
$196$	0.275428	−	2.62052i	0.0196734	−	0.187180i
$197$	2.45783			0.175113			0.0875566	−	0.996160i	$-0.472094\pi$
$197$	2.45783			0.175113			0.0875566	+	0.996160i	$0.472094\pi$
$198$	0.432612	−	1.97902i	0.0307444	−	0.140643i
$199$	5.59195	+	9.68554i	0.396403	+	0.686589i	0.993279	−	0.115744i	$-0.0369251\pi$
$199$	5.59195	+	9.68554i	0.396403	+	0.686589i	−0.596877	+	0.802333i	$0.703592\pi$
$200$	0.0531811	−	0.505984i	0.00376047	−	0.0357785i
$201$	−2.55068	+	7.85017i	−0.179911	+	0.553709i
$202$	−3.66341	−	11.2748i	−0.257756	−	0.793293i
$203$	11.0324	+	4.91192i	0.774320	+	0.344749i
$204$	−1.40310	−	13.3496i	−0.0982369	−	0.934661i
$205$	11.3510	−	12.6065i	0.792787	−	0.880479i
$206$	6.50157	+	7.22072i	0.452986	+	0.503092i
$207$	−3.58749	+	1.59725i	−0.249348	+	0.111017i
$208$	−0.351263			−0.0243557
$209$	10.5514	−	9.88275i	0.729853	−	0.683604i
$210$	9.31799			0.643003
$211$	14.8240	−	6.60005i	1.02052	−	0.454366i	0.172886	−	0.984942i	$-0.444691\pi$
$211$	14.8240	−	6.60005i	1.02052	−	0.454366i	0.847638	+	0.530575i	$0.178024\pi$
$212$	2.73105	+	3.03314i	0.187569	+	0.208317i
$213$	−16.9128	+	18.7836i	−1.15885	+	1.28703i
$214$	1.07690	+	10.2460i	0.0736154	+	0.700404i
$215$	0.367633	+	0.163681i	0.0250723	+	0.0111629i
$216$	1.40294	+	4.31780i	0.0954578	+	0.293789i
$217$	−0.418324	+	1.28747i	−0.0283977	+	0.0873990i
$218$	1.58357	−	15.0666i	0.107253	−	1.02044i
$219$	−6.30672	−	10.9236i	−0.426168	−	0.738145i
$220$	−3.12507	−	7.12954i	−0.210692	−	0.480674i
$221$	−2.48134			−0.166913
$222$	0.256802	−	2.44331i	0.0172354	−	0.163984i
$223$	−1.33835	−	1.48639i	−0.0896224	−	0.0995358i	0.696665	−	0.717396i	$-0.254666\pi$
$223$	−1.33835	−	1.48639i	−0.0896224	−	0.0995358i	−0.786288	+	0.617861i	$0.788000\pi$
$224$	1.39799	−	1.55263i	0.0934073	−	0.103739i
$225$	−0.0324823	−	0.309048i	−0.00216549	−	0.0206032i
$226$	−0.532594	−	5.06729i	−0.0354276	−	0.337071i
$227$	−3.92101	−	12.0676i	−0.260247	−	0.800957i	−0.992750	−	0.120194i	$-0.961648\pi$
$227$	−3.92101	−	12.0676i	−0.260247	−	0.800957i	0.732504	−	0.680763i	$-0.238352\pi$
$228$	2.35843	−	7.93995i	0.156191	−	0.525836i
$229$	13.3728	+	9.71590i	0.883699	+	0.642045i	0.934227	−	0.356678i	$-0.116091\pi$
$229$	13.3728	+	9.71590i	0.883699	+	0.642045i	−0.0505288	+	0.998723i	$0.516091\pi$
$230$	−7.54516	+	13.0686i	−0.497513	+	0.861718i
$231$	11.4409	−	6.51761i	0.752756	−	0.428827i
$232$	−2.89011	−	5.00581i	−0.189745	−	0.328648i
$233$	5.09522	−	2.26854i	0.333799	−	0.148617i	−0.232992	−	0.972479i	$-0.574851\pi$
$233$	5.09522	−	2.26854i	0.333799	−	0.148617i	0.566791	+	0.823862i	$0.308185\pi$
$234$	−0.209858	+	0.0446067i	−0.0137189	+	0.00291603i
$235$	3.29143	+	10.1300i	0.214709	+	0.660807i
$236$	1.71146	−	1.24345i	0.111406	−	0.0809416i
$237$	29.0293	+	12.9247i	1.88565	+	0.839547i
$238$	9.87550	−	10.9679i	0.640134	−	0.710940i
$239$	−2.58812	+	7.96542i	−0.167412	+	0.515240i	−0.999206	−	0.0398438i	$-0.987314\pi$
$239$	−2.58812	+	7.96542i	−0.167412	+	0.515240i	0.831794	+	0.555084i	$0.187314\pi$
$240$	−3.60816	−	2.62148i	−0.232906	−	0.169216i
$241$	−2.31844	−	4.01566i	−0.149344	−	0.258671i	0.781641	−	0.623728i	$-0.214383\pi$
$241$	−2.31844	−	4.01566i	−0.149344	−	0.258671i	−0.930985	+	0.365057i	$0.881050\pi$
$242$	−8.82392	−	6.56798i	−0.567223	−	0.422206i
$243$	3.12742	+	5.41685i	0.200624	+	0.347491i
$244$	−12.4767	+	5.55497i	−0.798737	+	0.355621i
$245$	−4.13821	−	4.59594i	−0.264380	−	0.293624i
$246$	−4.24403	−	13.0618i	−0.270589	−	0.832789i
$247$	−1.41413	−	0.587000i	−0.0899787	−	0.0373499i
$248$	0.524196	−	0.380850i	0.0332865	−	0.0241840i
$249$	−22.9949	−	4.88773i	−1.45725	−	0.309747i
$250$	7.05348	+	7.83368i	0.446101	+	0.495446i
$251$	−2.05264	+	19.5296i	−0.129562	+	1.23270i	0.715724	+	0.698383i	$0.246097\pi$
$251$	−2.05264	+	19.5296i	−0.129562	+	1.23270i	−0.845286	+	0.534314i	$0.820570\pi$
$252$	0.638049	−	1.10513i	0.0401933	−	0.0696168i
$253$	−0.123136	+	21.3236i	−0.00774149	+	1.34060i
$254$	16.3163			1.02377
$255$	−25.4882	−	18.5183i	−1.59614	−	1.15966i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−19.8965	+	22.0973i	−1.24111	+	1.37839i	−0.342572	+	0.939491i	$0.611298\pi$
$257$	−19.8965	+	22.0973i	−1.24111	+	1.37839i	−0.898536	+	0.438899i	$0.855369\pi$
$258$	0.263582	−	0.191503i	0.0164099	−	0.0119225i
$259$	2.18532	−	1.58773i	0.135789	−	0.0986565i
$260$	−0.551658	+	0.612679i	−0.0342124	+	0.0379967i
$261$	−2.36235	−	2.62366i	−0.146226	−	0.162400i
$262$	−0.276466	+	2.63040i	−0.0170802	+	0.162507i
$263$	8.16097	−	14.1352i	0.503227	−	0.871614i	−0.496766	−	0.867884i	$-0.665479\pi$
$263$	8.16097	−	14.1352i	0.503227	−	0.871614i	0.999993	−	0.00372998i	$-0.00118729\pi$
$264$	−6.26384	−	0.694949i	−0.385513	−	0.0427712i
$265$	9.57957			0.588468
$266$	8.22272	−	3.91442i	0.504167	−	0.240009i
$267$	5.93689	−	18.2719i	0.363332	−	1.11822i
$268$	4.24890	+	0.903131i	0.259543	+	0.0551675i
$269$	1.54937	+	14.7412i	0.0944665	+	0.898789i	0.934430	+	0.356146i	$0.115909\pi$
$269$	1.54937	+	14.7412i	0.0944665	+	0.898789i	−0.839964	+	0.542642i	$0.817424\pi$
$270$	9.73449	+	4.33408i	0.592422	+	0.263763i
$271$	10.6479	+	2.26329i	0.646816	+	0.137485i	0.519627	−	0.854393i	$-0.326071\pi$
$271$	10.6479	+	2.26329i	0.646816	+	0.137485i	0.127189	+	0.991878i	$0.459404\pi$
$272$	−6.90969	+	1.46870i	−0.418961	+	0.0890530i
$273$	−1.12820	−	0.819682i	−0.0682815	−	0.0496094i
$274$	−11.3152			−0.683579
$275$	−1.60178	−	0.530695i	−0.0965908	−	0.0320021i
$276$	6.10860	+	10.5804i	0.367695	+	0.636866i
$277$	11.7872	+	8.56391i	0.708225	+	0.514556i	0.882601	−	0.470124i	$-0.155791\pi$
$277$	11.7872	+	8.56391i	0.708225	+	0.514556i	−0.174376	+	0.984679i	$0.555791\pi$
$278$	−2.52350	+	7.76654i	−0.151350	+	0.465806i
$279$	0.264811	−	0.294103i	0.0158538	−	0.0176075i
$280$	−0.512573	−	4.87681i	−0.0306321	−	0.291445i
$281$	22.3375	+	9.94531i	1.33254	+	0.593287i	0.944548	−	0.328374i	$-0.106500\pi$
$281$	22.3375	+	9.94531i	1.33254	+	0.593287i	0.387997	+	0.921661i	$0.373167\pi$
$282$	8.43490	+	1.79289i	0.502291	+	0.106765i
$283$	13.2539	+	14.7200i	0.787866	+	0.875013i	0.994642	−	0.103375i	$-0.0329641\pi$
$283$	13.2539	+	14.7200i	0.787866	+	0.875013i	−0.206777	+	0.978388i	$0.566297\pi$
$284$	10.7612	+	7.81850i	0.638562	+	0.463943i
$285$	−10.1451	−	16.5833i	−0.600942	−	0.982311i
$286$	−0.248795	+	1.13813i	−0.0147115	+	0.0672990i
$287$	7.55021	−	13.0774i	0.445675	−	0.771932i
$288$	−0.557982	+	0.248429i	−0.0328794	+	0.0146388i
$289$	−32.1819	+	6.84047i	−1.89305	+	0.402381i
$290$	−13.2701	−	2.82066i	−0.779250	−	0.165635i
$291$	0.0965622	+	0.0429923i	0.00566058	+	0.00252025i
$292$	−5.37020	+	3.90168i	−0.314267	+	0.228328i
$293$	2.19123	+	6.74392i	0.128013	+	0.393984i	0.994438	−	0.105324i	$-0.0335878\pi$
$293$	2.19123	+	6.74392i	0.128013	+	0.393984i	−0.866425	+	0.499307i	$0.833588\pi$
$294$	−4.89755	+	1.04101i	−0.285631	+	0.0607128i
$295$	0.519004	−	4.93799i	0.0302176	−	0.287501i
$296$	−1.29289			−0.0751479
$297$	14.9838	−	1.48743i	0.869450	−	0.0863097i
$298$	−9.85331	−	17.0664i	−0.570787	−	0.988632i
$299$	2.06316	−	0.918578i	0.119316	−	0.0531227i
$300$	−0.945644	+	0.201003i	−0.0545968	+	0.0116049i
$301$	0.350393	+	0.0744783i	0.0201963	+	0.00429286i
$302$	−0.695017	−	6.61264i	−0.0399937	−	0.380515i
$303$	−18.2247	+	13.2410i	−1.04698	+	0.760678i
$304$	−4.28531	−	0.797578i	−0.245779	−	0.0457443i
$305$	−9.90554	+	30.4861i	−0.567190	+	1.74563i
$306$	−3.94161	+	1.75492i	−0.225327	+	0.100322i
$307$	−13.8124	+	23.9238i	−0.788317	+	1.36541i	0.138680	+	0.990337i	$0.455714\pi$
$307$	−13.8124	+	23.9238i	−0.788317	+	1.36541i	−0.926997	+	0.375068i	$0.877619\pi$
$308$	−4.04051	−	5.62936i	−0.230229	−	0.320763i
$309$	9.23162	−	15.9896i	0.525169	−	0.909619i
$310$	0.158964	−	1.51244i	0.00902853	−	0.0859007i
$311$	1.60355	−	4.93523i	0.0909291	−	0.279851i	−0.895242	−	0.445580i	$-0.852998\pi$
$311$	1.60355	−	4.93523i	0.0909291	−	0.279851i	0.986171	+	0.165729i	$0.0529976\pi$
$312$	0.206260	+	0.634803i	0.0116772	+	0.0359387i
$313$	−18.9818	−	8.45126i	−1.07292	−	0.477693i	−0.207237	−	0.978291i	$-0.566447\pi$
$313$	−18.9818	−	8.45126i	−1.07292	−	0.477693i	−0.865680	+	0.500597i	$0.833114\pi$
$314$	8.94531	+	3.98271i	0.504813	+	0.224757i
$315$	−0.925536	−	2.84851i	−0.0521481	−	0.160495i
$316$	5.16758	−	15.9042i	0.290699	−	0.894680i
$317$	2.00620	−	19.0877i	0.112680	−	1.07207i	−0.781358	−	0.624083i	$-0.785473\pi$
$317$	2.00620	−	19.0877i	0.112680	−	1.07207i	0.894038	−	0.447991i	$-0.147860\pi$
$318$	3.87784	−	6.71661i	0.217458	−	0.376649i
$319$	−18.2664	+	5.81872i	−1.02272	+	0.325786i
$320$	−1.17354	+	2.03263i	−0.0656028	+	0.113627i
$321$	17.8843	−	7.96261i	0.998205	−	0.444429i
$322$	−4.15095	+	12.7753i	−0.231323	+	0.711940i
$323$	−30.2717	−	5.63414i	−1.68436	−	0.313492i
$324$	8.46175	−	6.14782i	0.470097	−	0.341546i
$325$	0.0186805	+	0.177733i	0.00103621	+	0.00985887i
$326$	11.1091	+	2.36130i	0.615274	+	0.130781i
$327$	−28.1583	+	5.98524i	−1.55716	+	0.330984i
$328$	−6.60276	+	2.93974i	−0.364576	+	0.162320i
$329$	4.74066	+	8.21106i	0.261361	+	0.452691i
$330$	−11.0495	+	9.83409i	−0.608256	+	0.541349i
$331$	3.02000			0.165994			0.0829970	−	0.996550i	$-0.473551\pi$
$331$	3.02000			0.165994			0.0829970	+	0.996550i	$0.473551\pi$
$332$	−1.29319	+	12.3039i	−0.0709729	+	0.675262i
$333$	−0.772426	+	0.164184i	−0.0423287	+	0.00899724i
$334$	−2.32002	−	7.14027i	−0.126946	−	0.390698i
$335$	8.24816	−	5.99264i	0.450645	−	0.327413i
$336$	−3.62681	−	1.61476i	−0.197859	−	0.0880925i
$337$	−11.2273	−	2.38644i	−0.611590	−	0.129998i	−0.108305	−	0.994118i	$-0.534542\pi$
$337$	−11.2273	−	2.38644i	−0.611590	−	0.129998i	−0.503286	+	0.864120i	$0.667876\pi$
$338$	−12.5952	+	2.67720i	−0.685090	+	0.145620i
$339$	−8.84490	+	3.93800i	−0.480389	+	0.213883i
$340$	−8.28994	+	14.3586i	−0.449585	+	0.778704i
$341$	−0.862717	−	1.96820i	−0.0467188	−	0.106584i
$342$	−2.66150	+	0.0676852i	−0.143917	+	0.00366000i
$343$	−16.2855	−	11.8321i	−0.879336	−	0.638875i
$344$	−0.114727	−	0.127418i	−0.00618569	−	0.00686990i
$345$	28.0481	+	5.96181i	1.51006	+	0.320973i
$346$	5.66180	+	2.52079i	0.304380	+	0.135519i
$347$	0.688455	+	6.55021i	0.0369582	+	0.351634i	0.997337	+	0.0729349i	$0.0232365\pi$
$347$	0.688455	+	6.55021i	0.0369582	+	0.351634i	−0.960378	+	0.278699i	$0.910097\pi$
$348$	−7.34947	+	8.16241i	−0.393973	+	0.437551i
$349$	3.53521	−	10.8803i	0.189235	−	0.582406i	−0.810760	−	0.585378i	$-0.800946\pi$
$349$	3.53521	−	10.8803i	0.189235	−	0.582406i	0.999996	+	0.00297187i	$0.000945977\pi$
$350$	−0.859952	−	0.624792i	−0.0459664	−	0.0333965i
$351$	−0.797366	−	1.38108i	−0.0425602	−	0.0737165i
$352$	−0.0191520	+	3.31657i	−0.00102080	+	0.176774i
$353$	−22.1291			−1.17782			−0.588908	−	0.808200i	$-0.700442\pi$
$353$	−22.1291			−1.17782			−0.588908	+	0.808200i	$0.700442\pi$
$354$	−3.25213	−	2.36281i	−0.172849	−	0.125582i
$355$	30.5377	−	6.49099i	1.62077	−	0.344506i
$356$	−9.88963	−	2.10211i	−0.524150	−	0.111411i
$357$	−25.6200	−	11.4068i	−1.35595	−	0.603710i
$358$	−1.04607	−	9.95271i	−0.0552866	−	0.526017i
$359$	34.9011	+	7.41847i	1.84201	+	0.391532i	0.991027	−	0.133659i	$-0.0426727\pi$
$359$	34.9011	+	7.41847i	1.84201	+	0.391532i	0.850985	+	0.525191i	$0.176006\pi$
$360$	−0.442996	+	1.36340i	−0.0233479	+	0.0718575i
$361$	−15.9191	−	10.3722i	−0.837848	−	0.545903i
$362$	−16.7394			−0.879806
$363$	−6.68831	+	19.8033i	−0.351045	+	1.03941i
$364$	−0.366941	+	0.635560i	−0.0192329	+	0.0333124i
$365$	−1.62852	+	15.4944i	−0.0852409	+	0.811013i
$366$	17.3652	+	19.2860i	0.907695	+	1.00810i
$367$	−9.61918	+	10.6832i	−0.502117	+	0.557657i	−0.939912	−	0.341418i	$-0.889093\pi$
$367$	−9.61918	+	10.6832i	−0.502117	+	0.557657i	0.437795	+	0.899075i	$0.355760\pi$
$368$	5.20150	−	3.77911i	0.271147	−	0.197000i
$369$	−3.57143	+	2.59480i	−0.185921	+	0.135080i
$370$	−2.03049	+	2.25509i	−0.105560	+	0.117236i
$371$	8.34098	−	1.77293i	0.433042	−	0.0920460i
$372$	−0.996080	−	0.723695i	−0.0516444	−	0.0375218i
$373$	−9.15392			−0.473972			−0.236986	−	0.971513i	$-0.576160\pi$
$373$	−9.15392			−0.473972			−0.236986	+	0.971513i	$0.576160\pi$
$374$	−0.135291	+	23.4284i	−0.00699572	+	1.21146i
$375$	10.0153	−	17.3470i	0.517187	−	0.895795i
$376$	0.474361	−	4.51325i	0.0244633	−	0.232753i
$377$	1.35858	+	1.50886i	0.0699707	+	0.0777103i
$378$	9.27800	+	1.97210i	0.477209	+	0.101434i
$379$	−21.7339	+	15.7906i	−1.11639	+	0.811107i	−0.983659	−	0.180044i	$-0.942376\pi$
$379$	−21.7339	+	15.7906i	−1.11639	+	0.811107i	−0.132735	+	0.991152i	$0.542376\pi$
$380$	−8.12123	+	6.22192i	−0.416610	+	0.319178i
$381$	−9.58086	−	29.4869i	−0.490842	−	1.51066i
$382$	7.27486	+	8.07955i	0.372214	+	0.413386i
$383$	22.5537	−	10.0415i	1.15244	−	0.513099i	0.260598	−	0.965448i	$-0.416080\pi$
$383$	22.5537	−	10.0415i	1.15244	−	0.513099i	0.891841	+	0.452349i	$0.149414\pi$
$384$	0.950104	+	1.64563i	0.0484848	+	0.0839781i
$385$	−16.1645	−	1.79339i	−0.823817	−	0.0913994i
$386$	−8.08669	−	14.0066i	−0.411602	−	0.712915i
$387$	−0.0847235	−	0.0615552i	−0.00430674	−	0.00312903i
$388$	0.0171893	−	0.0529033i	0.000872655	−	0.00268576i
$389$	10.8510	−	12.0512i	0.550166	−	0.611022i	−0.402359	−	0.915482i	$-0.631809\pi$
$389$	10.8510	−	12.0512i	0.550166	−	0.611022i	0.952525	+	0.304460i	$0.0984761\pi$
$390$	1.43117	+	0.637197i	0.0724700	+	0.0322657i
$391$	36.7437	−	26.6958i	1.85821	−	1.35007i
$392$	0.814247	+	2.50600i	0.0411257	+	0.126572i
$393$	4.91601	−	1.04493i	0.247980	−	0.0527098i
$394$	−2.24534	+	0.999690i	−0.113119	+	0.0503637i
$395$	−19.6247	−	33.9909i	−0.987424	−	1.71027i
$396$	0.409728	+	1.98388i	0.0205896	+	0.0996938i
$397$	−6.92762	+	11.9990i	−0.347687	+	0.602212i	−0.985838	−	0.167699i	$-0.946366\pi$
$397$	−6.92762	+	11.9990i	−0.347687	+	0.602212i	0.638151	+	0.769911i	$0.279700\pi$
$398$	−9.04796	−	6.57373i	−0.453533	−	0.329511i
$399$	−11.9025	−	12.5616i	−0.595871	−	0.628866i
$400$	0.157219	+	0.483870i	0.00786095	+	0.0241935i
$401$	−3.13844	−	29.8603i	−0.156726	−	1.49115i	−0.736535	−	0.676399i	$-0.763539\pi$
$401$	−3.13844	−	29.8603i	−0.156726	−	1.49115i	0.579809	−	0.814752i	$-0.303127\pi$
$402$	−0.862795	−	8.20894i	−0.0430323	−	0.409425i
$403$	−0.152293	+	0.169138i	−0.00758623	+	0.00842536i
$404$	7.93256	+	8.81001i	0.394660	+	0.438314i
$405$	2.56605	−	24.4143i	0.127508	−	1.21316i
$406$	−12.0764			−0.599342
$407$	−0.915740	+	4.18912i	−0.0453915	+	0.207647i
$408$	6.71158	+	11.6248i	0.332273	+	0.575513i
$409$	0.433659	−	4.12599i	0.0214431	−	0.204017i	−0.978555	−	0.205986i	$-0.933960\pi$
$409$	0.433659	−	4.12599i	0.0214431	−	0.204017i	0.999998	+	0.00196860i	$0.000626626\pi$
$410$	−5.24209	+	16.1335i	−0.258889	+	0.796777i
$411$	6.64427	+	20.4489i	0.327737	+	1.00867i
$412$	−8.87641	−	3.95203i	−0.437309	−	0.194703i
$413$	−0.461995	−	4.39559i	−0.0227333	−	0.216293i
$414$	2.62767	−	2.91833i	0.129143	−	0.143428i
$415$	19.4297	+	21.5788i	0.953765	+	1.05926i
$416$	0.320894	−	0.142871i	0.0157331	−	0.00700484i
$417$	15.5175			0.759896
$418$	−5.61947	+	13.3200i	−0.274857	+	0.651501i
$419$	6.38107			0.311735			0.155868	−	0.987778i	$-0.450183\pi$
$419$	6.38107			0.311735			0.155868	+	0.987778i	$0.450183\pi$
$420$	−8.51241	+	3.78997i	−0.415363	+	0.184932i
$421$	1.04771	+	1.16360i	0.0510623	+	0.0567105i	0.768135	−	0.640288i	$-0.221185\pi$
$421$	1.04771	+	1.16360i	0.0510623	+	0.0567105i	−0.717073	+	0.696999i	$0.754518\pi$
$422$	−10.8579	+	12.0589i	−0.528553	+	0.587018i
$423$	−0.289734	−	2.75663i	−0.0140873	−	0.134032i
$424$	−3.72863	−	1.66009i	−0.181078	−	0.0806212i
$425$	1.11060	+	3.41809i	0.0538722	+	0.165801i
$426$	7.81066	−	24.0388i	0.378428	−	1.16468i
$427$	−2.98261	+	28.3777i	−0.144339	+	1.37329i
$428$	−5.15123	−	8.92219i	−0.248994	−	0.431270i
$429$	2.20293	−	0.218683i	0.106358	−	0.0105581i
$430$	−0.402424			−0.0194066
$431$	1.67734	−	15.9588i	0.0807945	−	0.768708i	−0.876852	−	0.480761i	$-0.840360\pi$
$431$	1.67734	−	15.9588i	0.0807945	−	0.768708i	0.957646	−	0.287947i	$-0.0929729\pi$
$432$	−3.03785	−	3.37388i	−0.146159	−	0.162326i
$433$	7.38064	−	8.19703i	0.354691	−	0.393924i	−0.539223	−	0.842163i	$-0.681282\pi$
$433$	7.38064	−	8.19703i	0.354691	−	0.393924i	0.893914	+	0.448239i	$0.147949\pi$
$434$	−0.141503	−	1.34631i	−0.00679234	−	0.0646248i
$435$	2.69468	+	25.6381i	0.129200	+	1.22925i
$436$	4.68149	+	14.4081i	0.224203	+	0.690024i
$437$	27.2557	−	6.52178i	1.30382	−	0.311979i
$438$	10.2045	+	7.41399i	0.487589	+	0.354254i
$439$	14.5105	−	25.1328i	0.692546	−	1.19953i	−0.278455	−	0.960449i	$-0.589822\pi$
$439$	14.5105	−	25.1328i	0.692546	−	1.19953i	0.971001	−	0.239076i	$-0.0768444\pi$
$440$	5.75474	+	5.24208i	0.274347	+	0.249906i
$441$	0.804699	+	1.39378i	0.0383190	+	0.0663705i
$442$	2.26681	−	1.00925i	0.107821	−	0.0480052i
$443$	31.4397	−	6.68272i	1.49375	−	0.317506i	0.612617	−	0.790380i	$-0.290117\pi$
$443$	31.4397	−	6.68272i	1.49375	−	0.317506i	0.881130	+	0.472874i	$0.156783\pi$
$444$	0.759182	+	2.33652i	0.0360292	+	0.110886i
$445$	−19.1982	+	13.9483i	−0.910083	+	0.661214i
$446$	1.82721	+	0.813526i	0.0865209	+	0.0385216i
$447$	−25.0567	+	27.8283i	−1.18514	+	1.31623i
$448$	−0.645619	+	1.98701i	−0.0305026	+	0.0938775i
$449$	−28.7785	−	20.9088i	−1.35814	−	0.986746i	−0.998561	−	0.0536319i	$-0.982920\pi$
$449$	−28.7785	−	20.9088i	−1.35814	−	0.986746i	−0.359579	−	0.933115i	$-0.617080\pi$
$450$	0.155375	+	0.269118i	0.00732447	+	0.0126863i
$451$	4.84843	+	23.4759i	0.228304	+	1.10543i
$452$	2.54760	+	4.41258i	0.119829	+	0.207550i
$453$	−11.5423	+	5.13896i	−0.542304	+	0.241449i
$454$	8.49038	+	9.42952i	0.398473	+	0.442549i
$455$	0.532275	+	1.63817i	0.0249534	+	0.0767987i
$456$	1.07493	+	8.21276i	0.0503382	+	0.384598i
$457$	−17.0628	+	12.3968i	−0.798164	+	0.579900i	−0.910375	−	0.413785i	$-0.864207\pi$
$457$	−17.0628	+	12.3968i	−0.798164	+	0.579900i	0.112211	+	0.993684i	$0.464207\pi$
$458$	−16.1685	−	3.43671i	−0.755502	−	0.160587i
$459$	−21.4596	−	23.8333i	−1.00165	−	1.11244i
$460$	1.57737	−	15.0076i	0.0735451	−	0.699735i
$461$	−4.30117	+	7.44984i	−0.200325	+	0.346973i	−0.948633	−	0.316378i	$-0.897533\pi$
$461$	−4.30117	+	7.44984i	−0.200325	+	0.346973i	0.748308	+	0.663351i	$0.230867\pi$
$462$	−7.80083	+	10.6076i	−0.362928	+	0.493509i
$463$	28.2928			1.31488			0.657438	−	0.753508i	$-0.271640\pi$
$463$	28.2928			1.31488			0.657438	+	0.753508i	$0.271640\pi$
$464$	4.67629	+	3.39752i	0.217091	+	0.157726i
$465$	−2.82663	+	0.600818i	−0.131082	+	0.0278623i
$466$	−3.73202	+	4.14483i	−0.172882	+	0.192005i
$467$	6.25894	−	4.54739i	0.289629	−	0.210428i	−0.433477	−	0.901165i	$-0.642714\pi$
$467$	6.25894	−	4.54739i	0.289629	−	0.210428i	0.723107	+	0.690737i	$0.242714\pi$
$468$	0.173572	−	0.126107i	0.00802336	−	0.00582931i
$469$	6.07263	−	6.74434i	0.280408	−	0.311425i
$470$	−7.12710	−	7.91545i	−0.328749	−	0.365112i
$471$	1.94492	−	18.5046i	0.0896170	−	0.852649i
$472$	−1.05774	+	1.83206i	−0.0486864	+	0.0843274i
$473$	−0.494108	+	0.281482i	−0.0227191	+	0.0129425i
$474$	−31.7765			−1.45954
$475$	−0.175665	+	2.21071i	−0.00806005	+	0.101435i
$476$	−4.56069	+	14.0364i	−0.209039	+	0.643355i
$477$	−2.43844	−	0.518307i	−0.111649	−	0.0237317i
$478$	−0.875462	−	8.32946i	−0.0400427	−	0.380981i
$479$	−29.6285	−	13.1914i	−1.35376	−	0.602733i	−0.403726	−	0.914880i	$-0.632285\pi$
$479$	−29.6285	−	13.1914i	−1.35376	−	0.602733i	−0.950034	+	0.312147i	$0.898952\pi$
$480$	4.36247	+	0.927272i	0.199119	+	0.0423240i
$481$	0.444221	−	0.0944221i	0.0202547	−	0.00430527i
$482$	3.75132	+	2.72549i	0.170868	+	0.124143i
$483$	25.5250			1.16143
$484$	10.7325	+	2.41114i	0.487841	+	0.109597i
$485$	−0.0652790	−	0.113067i	−0.00296417	−	0.00513409i
$486$	−5.06027	−	3.67650i	−0.229538	−	0.166769i
$487$	−5.66030	+	17.4206i	−0.256492	+	0.789403i	0.737039	+	0.675850i	$0.236223\pi$
$487$	−5.66030	+	17.4206i	−0.256492	+	0.789403i	−0.993532	+	0.113553i	$0.963777\pi$
$488$	9.13859	−	10.1494i	0.413685	−	0.459443i
$489$	−2.25584	−	21.4629i	−0.102013	−	0.970586i
$490$	5.64978	+	2.51544i	0.255231	+	0.113636i
$491$	38.9433	+	8.27765i	1.75749	+	0.373565i	0.970064	−	0.242849i	$-0.0780821\pi$
$491$	38.9433	+	8.27765i	1.75749	+	0.373565i	0.787422	+	0.616415i	$0.211415\pi$
$492$	9.18982	+	10.2063i	0.414309	+	0.460137i
$493$	33.0336	+	24.0003i	1.48776	+	1.08092i
$494$	1.53062	−	0.0389257i	0.0688660	−	0.00175135i
$495$	4.10380	+	2.40103i	0.184452	+	0.107918i
$496$	−0.323971	+	0.561134i	−0.0145467	+	0.0251957i
$497$	25.3880	−	11.3035i	1.13881	−	0.507030i
$498$	22.9949	−	4.88773i	1.03043	−	0.219024i
$499$	−10.6985	−	2.27404i	−0.478932	−	0.101800i	−0.0378813	−	0.999282i	$-0.512061\pi$
$499$	−10.6985	−	2.27404i	−0.478932	−	0.101800i	−0.441051	+	0.897482i	$0.645394\pi$
$500$	−9.62992	−	4.28752i	−0.430663	−	0.191744i
$501$	−11.5416	+	8.38548i	−0.515642	+	0.374636i
$502$	−6.06822	−	18.6761i	−0.270838	−	0.833554i
$503$	−4.42556	+	0.940683i	−0.197326	+	0.0419430i	−0.305514	−	0.952187i	$-0.598828\pi$
$503$	−4.42556	+	0.940683i	−0.197326	+	0.0419430i	0.108188	+	0.994130i	$0.465495\pi$
$504$	−0.133388	+	1.26911i	−0.00594160	+	0.0565305i
$505$	27.8247			1.23818
$506$	−8.56059	−	19.5301i	−0.380565	−	0.868221i
$507$	12.2341	+	21.1901i	0.543336	+	0.941086i
$508$	−14.9057	+	6.63643i	−0.661332	+	0.294444i
$509$	−19.0329	+	4.04557i	−0.843619	+	0.179317i	−0.609396	−	0.792866i	$-0.708588\pi$
$509$	−19.0329	+	4.04557i	−0.843619	+	0.179317i	−0.234223	+	0.972183i	$0.575255\pi$
$510$	30.8167	+	6.55030i	1.36459	+	0.290052i
$511$	1.44964	+	13.7924i	0.0641284	+	0.610141i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−6.59177	−	18.6593i	−0.291034	−	0.823828i
$514$	9.18857	−	28.2795i	0.405290	−	1.24736i
$515$	−20.8336	+	9.27572i	−0.918039	+	0.408737i
$516$	−0.162902	+	0.282155i	−0.00717138	+	0.0124212i
$517$	−14.2874	−	4.73366i	−0.628361	−	0.208186i
$518$	−1.35060	+	2.33931i	−0.0593420	+	0.102783i
$519$	1.23100	−	11.7122i	0.0540351	−	0.514110i
$520$	0.254766	−	0.784089i	0.0111722	−	0.0343846i
$521$	−7.78716	−	23.9664i	−0.341162	−	1.04999i	−0.963607	−	0.267324i	$-0.913861\pi$
$521$	−7.78716	−	23.9664i	−0.341162	−	1.04999i	0.622445	−	0.782664i	$-0.286139\pi$
$522$	3.22525	+	1.43598i	0.141165	+	0.0628509i
$523$	−8.22016	−	3.65985i	−0.359443	−	0.160034i	0.219067	−	0.975710i	$-0.429699\pi$
$523$	−8.22016	−	3.65985i	−0.359443	−	0.160034i	−0.578509	+	0.815676i	$0.696365\pi$
$524$	−0.817316	−	2.51544i	−0.0357046	−	0.109888i
$525$	−0.624166	+	1.92098i	−0.0272408	+	0.0838386i
$526$	−1.70611	+	16.2325i	−0.0743898	+	0.707772i
$527$	−2.28855	+	3.96388i	−0.0996907	+	0.172669i
$528$	6.00496	−	1.91287i	0.261333	−	0.0832468i
$529$	−9.16864	+	15.8805i	−0.398636	+	0.690458i
$530$	−8.75137	+	3.89636i	−0.380135	+	0.169247i
$531$	−0.399283	+	1.22887i	−0.0173274	+	0.0533283i
$532$	−5.91968	+	6.92048i	−0.256651	+	0.300041i
$533$	2.05393	−	1.49226i	0.0889654	−	0.0646371i
$534$	2.00822	+	19.1069i	0.0869042	+	0.826838i
$535$	−23.6523	−	5.02744i	−1.02258	−	0.217355i
$536$	−4.24890	+	0.903131i	−0.183524	+	0.0390093i
$537$	−17.3723	+	7.73466i	−0.749672	+	0.333775i
$538$	−7.41121	−	12.8366i	−0.319520	−	0.553425i
$539$	8.69643	−	0.863289i	0.374582	−	0.0371845i
$540$	−10.6557			−0.458550
$541$	2.03689	−	19.3797i	0.0875727	−	0.833199i	−0.859274	−	0.511515i	$-0.829085\pi$
$541$	2.03689	−	19.3797i	0.0875727	−	0.833199i	0.946847	−	0.321684i	$-0.104249\pi$
$542$	−10.6479	+	2.26329i	−0.457368	+	0.0972166i
$543$	9.82934	+	30.2516i	0.421817	+	1.29822i
$544$	5.71494	−	4.15215i	0.245026	−	0.178022i
$545$	32.4832	+	14.4625i	1.39143	+	0.619504i
$546$	1.36405	+	0.289938i	0.0583761	+	0.0124082i
$547$	36.5228	−	7.76316i	1.56160	−	0.331929i	0.655569	−	0.755135i	$-0.272429\pi$
$547$	36.5228	−	7.76316i	1.56160	−	0.331929i	0.906033	+	0.423206i	$0.139095\pi$
$548$	10.3370	−	4.60232i	0.441574	−	0.196601i
$549$	4.17088	−	7.22418i	0.178009	−	0.308321i
$550$	1.67915	−	0.166688i	0.0715992	−	0.00710760i
$551$	13.1483	+	21.4925i	0.560138	+	0.915612i
$552$	−9.88393	−	7.18109i	−0.420688	−	0.305648i
$553$	−23.3781	−	25.9641i	−0.994140	−	1.10410i
$554$	−14.2514	−	3.02923i	−0.605484	−	0.128700i
$555$	5.26770	+	2.34533i	0.223601	+	0.0995538i
$556$	−0.853603	−	8.12149i	−0.0362008	−	0.344428i
$557$	−19.2883	+	21.4218i	−0.817271	+	0.907672i	−0.997106	−	0.0760250i	$-0.975777\pi$
$557$	−19.2883	+	21.4218i	−0.817271	+	0.907672i	0.179834	+	0.983697i	$0.442444\pi$
$558$	−0.122295	+	0.376385i	−0.00517715	+	0.0159336i
$559$	0.0487243	+	0.0354003i	0.00206082	+	0.00149727i
$560$	2.45184	+	4.24671i	0.103609	+	0.179456i
$561$	42.4194	−	13.5126i	1.79095	−	0.570502i
$562$	−24.4515			−1.03142
$563$	15.5466	+	11.2953i	0.655210	+	0.476038i	0.865042	−	0.501699i	$-0.167292\pi$
$563$	15.5466	+	11.2953i	0.655210	+	0.476038i	−0.209832	+	0.977738i	$0.567292\pi$
$564$	−8.43490	+	1.79289i	−0.355173	+	0.0754944i
$565$	11.6975	+	2.48638i	0.492118	+	0.104603i
$566$	−18.0953	−	8.05652i	−0.760600	−	0.338641i
$567$	−2.28419	−	21.7326i	−0.0959268	−	0.912682i
$568$	−13.0110	−	2.76556i	−0.545927	−	0.116040i
$569$	1.04091	−	3.20358i	0.0436371	−	0.134301i	−0.926864	−	0.375396i	$-0.877507\pi$
$569$	1.04091	−	3.20358i	0.0436371	−	0.134301i	0.970501	+	0.241095i	$0.0775066\pi$
$570$	16.0130	+	11.0232i	0.670712	+	0.461713i
$571$	−38.8264			−1.62484			−0.812418	−	0.583076i	$-0.801849\pi$
$571$	−38.8264			−1.62484			−0.812418	+	0.583076i	$0.801849\pi$
$572$	−0.235634	−	1.14093i	−0.00985235	−	0.0477046i
$573$	10.3296	−	17.8914i	0.431526	−	0.747426i
$574$	−1.57842	+	15.0177i	−0.0658822	+	0.626827i
$575$	−2.18879	−	2.43090i	−0.0912789	−	0.101375i
$576$	0.408696	−	0.453903i	0.0170290	−	0.0189126i
$577$	5.13748	−	3.73260i	0.213876	−	0.155390i	−0.475690	−	0.879613i	$-0.657801\pi$
$577$	5.13748	−	3.73260i	0.213876	−	0.155390i	0.689566	+	0.724223i	$0.257801\pi$
$578$	26.6174	−	19.3386i	1.10714	−	0.804381i
$579$	−20.5642	+	22.8389i	−0.854621	+	0.949153i
$580$	13.2701	−	2.82066i	0.551013	−	0.117121i
$581$	20.9112	+	15.1929i	0.867542	+	0.630306i
$582$	−0.105701			−0.00438143
$583$	−8.01982	+	10.9053i	−0.332147	+	0.451653i
$584$	3.31896	−	5.74861i	0.137340	−	0.237879i
$585$	0.0526361	−	0.500799i	0.00217623	−	0.0207055i
$586$	−4.74479	−	5.26962i	−0.196005	−	0.217686i
$587$	−29.6947	−	6.31180i	−1.22563	−	0.260516i	−0.450765	−	0.892642i	$-0.648849\pi$
$587$	−29.6947	−	6.31180i	−1.22563	−	0.260516i	−0.774865	+	0.632127i	$0.782182\pi$
$588$	4.05072	−	2.94302i	0.167049	−	0.121368i
$589$	−2.24197	+	1.71764i	−0.0923789	+	0.0707742i
$590$	1.53433	+	4.72218i	0.0631673	+	0.194409i
$591$	3.12510	+	3.47078i	0.128549	+	0.142769i
$592$	1.18112	−	0.525867i	0.0485436	−	0.0216130i
$593$	−2.93252	−	5.07927i	−0.120424	−	0.208581i	0.799511	−	0.600652i	$-0.205092\pi$
$593$	−2.93252	−	5.07927i	−0.120424	−	0.208581i	−0.919935	+	0.392071i	$0.871759\pi$
$594$	−13.0834	+	7.45331i	−0.536819	+	0.305813i
$595$	17.3199	+	29.9990i	0.710047	+	1.22984i
$596$	15.9430	+	11.5833i	0.653051	+	0.474469i
$597$	−6.56714	+	20.2116i	−0.268775	+	0.827205i
$598$	−1.51117	+	1.67833i	−0.0617964	+	0.0686318i
$599$	−11.9537	−	5.32212i	−0.488414	−	0.217456i	0.147728	−	0.989028i	$-0.452804\pi$
$599$	−11.9537	−	5.32212i	−0.488414	−	0.217456i	−0.636142	+	0.771572i	$0.719471\pi$
$600$	0.782134	−	0.568254i	0.0319305	−	0.0231989i
$601$	1.06684	+	3.28339i	0.0435172	+	0.133932i	0.970455	−	0.241284i	$-0.0775685\pi$
$601$	1.06684	+	3.28339i	0.0435172	+	0.133932i	−0.926937	+	0.375216i	$0.877569\pi$
$602$	−0.350393	+	0.0744783i	−0.0142809	+	0.00303551i
$603$	−2.42377	+	1.07913i	−0.0987036	+	0.0439457i
$604$	3.32453	+	5.75826i	0.135273	+	0.234300i
$605$	21.0609	−	14.9331i	0.856249	−	0.607118i
$606$	11.2635	−	19.5090i	0.457549	−	0.792498i
$607$	8.92774	+	6.48638i	0.362366	+	0.263274i	0.754038	−	0.656831i	$-0.228103\pi$
$607$	8.92774	+	6.48638i	0.362366	+	0.263274i	−0.391672	+	0.920105i	$0.628103\pi$
$608$	4.23923	−	1.01437i	0.171923	−	0.0411381i
$609$	7.09123	+	21.8246i	0.287351	+	0.884375i
$610$	−3.35066	−	31.8794i	−0.135664	−	1.29076i
$611$	0.166625	+	1.58533i	0.00674094	+	0.0641358i
$612$	2.88705	−	3.20640i	0.116702	−	0.129611i
$613$	−14.0100	−	15.5597i	−0.565857	−	0.628448i	0.390516	−	0.920596i	$-0.372297\pi$
$613$	−14.0100	−	15.5597i	−0.565857	−	0.628448i	−0.956373	+	0.292148i	$0.905630\pi$
$614$	2.88758	−	27.4735i	0.116533	−	1.10874i
$615$	32.2347			1.29983
$616$	5.98086	+	3.49925i	0.240976	+	0.140989i
$617$	−18.2779	−	31.6582i	−0.735840	−	1.27451i	−0.954354	−	0.298679i	$-0.903454\pi$
$617$	−18.2779	−	31.6582i	−0.735840	−	1.27451i	0.218513	−	0.975834i	$-0.429879\pi$
$618$	−1.92994	+	18.3621i	−0.0776334	+	0.738632i
$619$	1.07851	−	3.31931i	0.0433490	−	0.133414i	−0.927040	−	0.374963i	$-0.877655\pi$
$619$	1.07851	−	3.31931i	0.0433490	−	0.133414i	0.970389	+	0.241549i	$0.0776554\pi$
$620$	0.469943	+	1.44634i	0.0188734	+	0.0580863i
$621$	26.6659	+	11.8724i	1.07007	+	0.476425i
$622$	0.542420	+	5.16078i	0.0217490	+	0.206928i
$623$	−14.1345	+	15.6980i	−0.566287	+	0.628926i
$624$	−0.446626	−	0.496028i	−0.0178793	−	0.0198570i
$625$	−24.9261	+	11.0978i	−0.997044	+	0.443912i
$626$	20.7782			0.830464
$627$	27.3716	+	2.33410i	1.09312	+	0.0932149i
$628$	−9.79186			−0.390738
$629$	8.34347	−	3.71475i	0.332676	−	0.148117i
$630$	2.00411	+	2.22579i	0.0798457	+	0.0886777i
$631$	19.3766	−	21.5199i	0.771371	−	0.856695i	−0.221589	−	0.975140i	$-0.571124\pi$
$631$	19.3766	−	21.5199i	0.771371	−	0.856695i	0.992961	+	0.118445i	$0.0377911\pi$
$632$	1.74799	+	16.6310i	0.0695314	+	0.661547i
$633$	28.1686	+	12.5415i	1.11960	+	0.498479i
$634$	5.93092	+	18.2535i	0.235547	+	0.724939i
$635$	−11.8340	+	36.4213i	−0.469617	+	1.44533i
$636$	−0.810689	+	7.71319i	−0.0321459	+	0.305848i
$637$	−0.462781	−	0.801561i	−0.0183361	−	0.0317590i
$638$	14.3205	−	12.7453i	0.566955	−	0.504591i
$639$	−8.12446			−0.321399
$640$	0.245336	−	2.33422i	0.00969777	−	0.0922681i
$641$	−28.0133	−	31.1119i	−1.10646	−	1.22885i	−0.971258	−	0.238030i	$-0.923498\pi$
$641$	−28.0133	−	31.1119i	−1.10646	−	1.22885i	−0.135202	−	0.990818i	$-0.543168\pi$
$642$	−13.0994	+	14.5484i	−0.516994	+	0.574180i
$643$	1.16209	+	11.0566i	0.0458285	+	0.436029i	0.993246	+	0.116028i	$0.0370164\pi$
$643$	1.16209	+	11.0566i	0.0458285	+	0.436029i	−0.947417	+	0.320000i	$0.896317\pi$
$644$	−1.40411	−	13.3592i	−0.0553295	−	0.526425i
$645$	0.236302	+	0.727262i	0.00930438	+	0.0286359i
$646$	29.9461	−	7.16555i	1.17822	−	0.281925i
$647$	−33.6980	−	24.4831i	−1.32481	−	0.962529i	−0.999859	−	0.0167966i	$-0.994653\pi$
$647$	−33.6980	−	24.4831i	−1.32481	−	0.962529i	−0.324948	−	0.945732i	$-0.605347\pi$
$648$	−5.22965	+	9.05802i	−0.205440	+	0.355833i
$649$	5.18689	+	4.72482i	0.203603	+	0.185465i
$650$	−0.0893561	−	0.154769i	−0.00350484	−	0.00607055i
$651$	−2.34996	+	1.04627i	−0.0921023	+	0.0410066i
$652$	−11.1091	+	2.36130i	−0.435064	+	0.0924758i
$653$	−12.3663	−	38.0595i	−0.483930	−	1.48938i	−0.833524	−	0.552483i	$-0.813681\pi$
$653$	−12.3663	−	38.0595i	−0.483930	−	1.48938i	0.349594	−	0.936901i	$-0.386319\pi$
$654$	23.2895	−	16.9208i	0.910691	−	0.661656i
$655$	−5.67107	−	2.52492i	−0.221587	−	0.0986570i
$656$	4.83622	−	5.37117i	0.188823	−	0.209709i
$657$	1.25287	−	3.85592i	0.0488789	−	0.150434i
$658$	−7.67055	−	5.57298i	−0.299029	−	0.217257i
$659$	15.2236	+	26.3681i	0.593028	+	1.02715i	0.993822	+	0.110986i	$0.0354009\pi$
$659$	15.2236	+	26.3681i	0.593028	+	1.02715i	−0.400794	+	0.916168i	$0.631266\pi$
$660$	6.09435	−	13.4781i	0.237222	−	0.524635i
$661$	1.98427	+	3.43686i	0.0771793	+	0.133678i	0.902032	−	0.431669i	$-0.142075\pi$
$661$	1.98427	+	3.43686i	0.0771793	+	0.133678i	−0.824853	+	0.565348i	$0.808742\pi$
$662$	−2.75890	+	1.22834i	−0.107228	+	0.0477409i
$663$	−3.15499	−	3.50397i	−0.122530	−	0.136083i
$664$	−3.82304	−	11.7661i	−0.148363	−	0.456614i
$665$	2.77396	+	21.1939i	0.107570	+	0.821862i
$666$	0.638866	−	0.464164i	0.0247556	−	0.0179860i
$667$	−36.3512	−	7.72669i	−1.40753	−	0.299179i
$668$	5.02365	+	5.57933i	0.194371	+	0.215871i
$669$	0.397277	−	3.77984i	0.0153596	−	0.146137i
$670$	−5.09764	+	8.82938i	−0.196939	+	0.341109i
$671$	−26.4126	−	36.7988i	−1.01965	−	1.42060i
$672$	3.97004			0.153148
$673$	26.4457	+	19.2140i	1.01941	+	0.740644i	0.966162	−	0.257938i	$-0.0830430\pi$
$673$	26.4457	+	19.2140i	1.01941	+	0.740644i	0.0532469	+	0.998581i	$0.483043\pi$
$674$	11.2273	−	2.38644i	0.432460	−	0.0919222i
$675$	−1.54557	+	1.71653i	−0.0594891	+	0.0660693i
$676$	10.4174	−	7.56868i	0.400669	−	0.291103i
$677$	−0.254221	+	0.184702i	−0.00977049	+	0.00709868i	−0.592660	−	0.805453i	$-0.701922\pi$
$677$	−0.254221	+	0.184702i	−0.00977049	+	0.00709868i	0.582889	+	0.812552i	$0.301922\pi$
$678$	6.47849	−	7.19509i	0.248805	−	0.276326i
$679$	−0.0777645	−	0.0863662i	−0.00298433	−	0.00331443i
$680$	1.73307	−	16.4891i	0.0664602	−	0.632326i
$681$	12.0555	−	20.8808i	0.461970	−	0.800155i
$682$	1.58867	+	1.44715i	0.0608334	+	0.0554141i
$683$	−21.3341			−0.816328			−0.408164	−	0.912909i	$-0.633831\pi$
$683$	−21.3341			−0.816328			−0.408164	+	0.912909i	$0.633831\pi$
$684$	2.40387	−	1.14436i	0.0919142	−	0.0437558i
$685$	8.20679	−	25.2579i	0.313565	−	0.965055i
$686$	19.6901	+	4.18526i	0.751772	+	0.159794i
$687$	3.28322	+	31.2377i	0.125263	+	1.19179i
$688$	0.156634	+	0.0697380i	0.00597162	+	0.00265874i
$689$	1.40235	+	0.298078i	0.0534251	+	0.0113559i
$690$	−28.0481	+	5.96181i	−1.06777	+	0.226962i
$691$	27.2669	+	19.8105i	1.03728	+	0.753629i	0.969753	−	0.244089i	$-0.0784888\pi$
$691$	27.2669	+	19.8105i	1.03728	+	0.753629i	0.0675279	+	0.997717i	$0.478489\pi$
$692$	−6.19761			−0.235598
$693$	4.01757	+	1.33109i	0.152615	+	0.0505638i
$694$	−3.29315	−	5.70390i	−0.125006	−	0.216517i
$695$	−15.5062	−	11.2659i	−0.588185	−	0.427341i
$696$	3.39412	−	10.4460i	0.128654	−	0.395956i
$697$	34.1633	−	37.9422i	1.29403	−	1.43716i
$698$	1.19582	+	11.3775i	0.0452626	+	0.430645i
$699$	9.68198	+	4.31069i	0.366206	+	0.163045i
$700$	1.03973	+	0.221002i	0.0392981	+	0.00835308i
$701$	−18.9624	−	21.0599i	−0.716200	−	0.795421i	0.269667	−	0.962954i	$-0.413087\pi$
$701$	−18.9624	−	21.0599i	−0.716200	−	0.795421i	−0.985866	+	0.167533i	$0.946420\pi$
$702$	1.29017	+	0.937360i	0.0486941	+	0.0353784i
$703$	5.63377	−	0.143274i	0.212482	−	0.00540367i
$704$	−1.33147	−	3.03763i	−0.0501818	−	0.114485i
$705$	−10.1198	+	17.5280i	−0.381135	+	0.660144i
$706$	20.2160	−	9.00073i	0.760838	−	0.338747i
$707$	24.2271	−	5.14963i	0.911154	−	0.193672i
$708$	3.93201	+	0.835774i	0.147774	+	0.0314103i
$709$	−22.4233	−	9.98350i	−0.842125	−	0.374938i	−0.0601052	−	0.998192i	$-0.519144\pi$
$709$	−22.4233	−	9.98350i	−0.842125	−	0.374938i	−0.782019	+	0.623254i	$0.785810\pi$
$710$	−25.2575	+	18.3506i	−0.947896	+	0.688686i
$711$	3.15629	+	9.71407i	0.118370	+	0.364306i
$712$	9.88963	−	2.10211i	0.370630	−	0.0787798i
$713$	0.435453	−	4.14306i	0.0163078	−	0.155159i
$714$	28.0446			1.04954
$715$	−2.36009	−	1.38083i	−0.0882624	−	0.0516402i
$716$	5.00377	+	8.66678i	0.187000	+	0.323893i
$717$	−14.5390	+	6.47317i	−0.542968	+	0.241745i
$718$	−34.9011	+	7.41847i	−1.30250	+	0.276855i
$719$	−32.6263	−	6.93494i	−1.21676	−	0.258629i	−0.445575	−	0.895245i	$-0.647001\pi$
$719$	−32.6263	−	6.93494i	−1.21676	−	0.258629i	−0.771181	+	0.636615i	$0.780334\pi$
$720$	−0.149848	−	1.42571i	−0.00558451	−	0.0531331i
$721$	−16.4232	+	11.9322i	−0.611634	+	0.444378i
$722$	18.7616	+	3.00056i	0.698233	+	0.111669i
$723$	2.72276	−	8.37980i	0.101261	−	0.311648i
$724$	15.2922	−	6.80855i	0.568332	−	0.253038i
$725$	1.47040	−	2.54681i	0.0546094	−	0.0945863i
$726$	−1.94466	−	20.8116i	−0.0721732	−	0.772392i
$727$	14.9904	−	25.9641i	0.555963	−	0.962957i	−0.441865	−	0.897082i	$-0.645683\pi$
$727$	14.9904	−	25.9641i	0.555963	−	0.962957i	0.997828	−	0.0658749i	$-0.0209838\pi$
$728$	0.0767115	−	0.729861i	0.00284312	−	0.0270505i
$729$	6.02349	−	18.5384i	0.223092	−	0.686607i
$730$	−4.81440	−	14.8172i	−0.178189	−	0.548409i
$731$	1.10647	+	0.492633i	0.0409244	+	0.0182207i
$732$	−23.7083	−	10.5556i	−0.876282	−	0.390146i
$733$	3.30167	+	10.1615i	0.121950	+	0.375323i	0.993333	−	0.115280i	$-0.0367765\pi$
$733$	3.30167	+	10.1615i	0.121950	+	0.375323i	−0.871383	+	0.490603i	$0.836776\pi$
$734$	4.44231	−	13.6720i	0.163969	−	0.504644i
$735$	1.22839	−	11.6874i	0.0453099	−	0.431095i
$736$	−3.21470	+	5.56803i	−0.118496	+	0.205240i
$737$	−0.0831928	+	14.4066i	−0.00306445	+	0.530673i
$738$	2.20727	−	3.82310i	0.0812506	−	0.140730i
$739$	5.50238	−	2.44982i	0.202408	−	0.0901179i	−0.303029	−	0.952981i	$-0.597998\pi$
$739$	5.50238	−	2.44982i	0.202408	−	0.0901179i	0.505437	+	0.862863i	$0.331331\pi$
$740$	0.937718	−	2.88600i	0.0344712	−	0.106091i
$741$	−0.969123	−	2.74329i	−0.0356016	−	0.100777i
$742$	−6.89875	+	5.01224i	−0.253261	+	0.184005i
$743$	−3.02678	−	28.7979i	−0.111042	−	1.05649i	−0.898153	−	0.439683i	$-0.855091\pi$
$743$	−3.02678	−	28.7979i	−0.111042	−	1.05649i	0.787111	−	0.616811i	$-0.211576\pi$
$744$	1.20432	+	0.255986i	0.0441524	+	0.00938489i
$745$	45.2422	−	9.61653i	1.65755	−	0.352323i
$746$	8.36252	−	3.72323i	0.306174	−	0.136317i
$747$	−3.77821	−	6.54406i	−0.138238	−	0.239435i
$748$	−9.40561	−	21.4580i	−0.343903	−	0.784581i
$749$	−21.5246			−0.786492
$750$	−2.09377	+	19.9208i	−0.0764535	+	0.727407i
$751$	13.2451	−	2.81533i	0.483320	−	0.102733i	0.0401935	−	0.999192i	$-0.487203\pi$
$751$	13.2451	−	2.81533i	0.483320	−	0.102733i	0.443127	+	0.896459i	$0.353869\pi$
$752$	1.40235	+	4.31599i	0.0511385	+	0.157388i
$753$	−30.1882	+	21.9330i	−1.10012	+	0.799284i
$754$	−1.85484	−	0.825827i	−0.0675492	−	0.0300748i
$755$	15.2648	+	3.24464i	0.555545	+	0.118085i
$756$	−9.27800	+	1.97210i	−0.337438	+	0.0717246i
$757$	−6.56631	+	2.92351i	−0.238656	+	0.106257i	−0.522580	−	0.852590i	$-0.675030\pi$
$757$	−6.56631	+	2.92351i	−0.238656	+	0.106257i	0.283924	+	0.958847i	$0.408364\pi$
$758$	13.4323	−	23.2654i	0.487882	−	0.845036i
$759$	−30.2682	+	26.9388i	−1.09867	+	0.977815i
$760$	4.88843	−	8.98721i	0.177322	−	0.326000i
$761$	−15.2234	−	11.0605i	−0.551849	−	0.400942i	0.276618	−	0.960980i	$-0.410786\pi$
$761$	−15.2234	−	11.0605i	−0.551849	−	0.400942i	−0.828467	+	0.560038i	$0.810786\pi$
$762$	20.7459	+	23.0407i	0.751546	+	0.834676i
$763$	30.9599	+	6.58074i	1.12082	+	0.238239i
$764$	−9.93217	−	4.42209i	−0.359333	−	0.159985i
$765$	−1.05854	−	10.0713i	−0.0382715	−	0.364129i
$766$	−16.5195	+	18.3468i	−0.596875	+	0.662897i
$767$	0.229627	−	0.706719i	0.00829135	−	0.0255182i
$768$	−1.53730	−	1.11691i	−0.0554725	−	0.0403032i
$769$	1.95682	+	3.38932i	0.0705649	+	0.122222i	0.899149	−	0.437643i	$-0.144186\pi$
$769$	1.95682	+	3.38932i	0.0705649	+	0.122222i	−0.828584	+	0.559865i	$0.810853\pi$
$770$	15.4964	−	4.93634i	0.558452	−	0.177893i
$771$	−56.5023			−2.03488
$772$	13.0845	+	9.50648i	0.470923	+	0.342146i
$773$	29.8504	−	6.34490i	1.07364	−	0.228210i	0.363020	−	0.931781i	$-0.381746\pi$
$773$	29.8504	−	6.34490i	1.07364	−	0.228210i	0.710625	+	0.703571i	$0.248412\pi$
$774$	0.102436	+	0.0217733i	0.00368197	+	0.000782626i
$775$	0.301154	+	0.134082i	0.0108178	+	0.00481638i
$776$	0.00581448	+	0.0553211i	0.000208728	+	0.00198591i
$777$	5.02068	+	1.06718i	0.180116	+	0.0382848i
$778$	−5.01118	+	15.4228i	−0.179660	+	0.552936i
$779$	28.4457	−	13.5416i	1.01917	−	0.485177i
$780$	−1.56661			−0.0560935
$781$	−18.1762	+	40.1981i	−0.650396	+	1.43840i
$782$	−22.7088	+	39.3329i	−0.812066	+	1.40654i
$783$	−2.74305	+	26.0984i	−0.0980287	+	0.932681i
$784$	−1.76313	−	1.95816i	−0.0629690	−	0.0699342i
$785$	−15.3781	+	17.0791i	−0.548869	+	0.609581i
$786$	−4.06599	+	2.95411i	−0.145029	+	0.105370i
$787$	30.4808	−	22.1456i	1.08652	−	0.789404i	0.107713	−	0.994182i	$-0.465647\pi$
$787$	30.4808	−	22.1456i	1.08652	−	0.789404i	0.978808	+	0.204778i	$0.0656472\pi$
$788$	1.64461	−	1.82652i	0.0585868	−	0.0650672i
$789$	30.3373	−	6.44839i	1.08004	−	0.229569i
$790$	31.7534	+	23.0702i	1.12973	+	0.820800i
$791$	10.6453			0.378502
$792$	−1.18122	−	1.64572i	−0.0419729	−	0.0584779i
$793$	−2.39867	+	4.15462i	−0.0851792	+	0.147535i
$794$	1.44827	−	13.7793i	0.0513971	−	0.489011i
$795$	12.1803	+	13.5276i	0.431991	+	0.479774i
$796$	10.9395	+	2.32526i	0.387740	+	0.0824167i
$797$	18.6317	−	13.5367i	0.659967	−	0.479494i	−0.206685	−	0.978408i	$-0.566267\pi$
$797$	18.6317	−	13.5367i	0.659967	−	0.479494i	0.866652	+	0.498913i	$0.166267\pi$
$798$	15.9827	+	6.63440i	0.565783	+	0.234855i
$799$	9.90629	+	30.4884i	0.350459	+	1.07860i
$800$	−0.340434	−	0.378091i	−0.0120362	−	0.0133675i
$801$	5.64151	−	2.51176i	0.199333	−	0.0887488i
$802$	15.0124	+	26.0022i	0.530106	+	0.918170i
$803$	−16.2754	−	14.8255i	−0.574345	−	0.523180i
$804$	4.12708	+	7.14831i	0.145551	+	0.252102i
$805$	−25.5065	−	18.5315i	−0.898984	−	0.653150i
$806$	0.0703315	−	0.216458i	0.00247732	−	0.00762441i
$807$	−18.8465	+	20.9312i	−0.663429	+	0.736812i
$808$	−10.8301	−	4.82188i	−0.381002	−	0.169633i
$809$	−8.57502	+	6.23012i	−0.301482	+	0.219039i	−0.728233	−	0.685330i	$-0.759658\pi$
$809$	−8.57502	+	6.23012i	−0.301482	+	0.219039i	0.426751	+	0.904369i	$0.359658\pi$
$810$	7.58599	+	23.3473i	0.266545	+	0.820340i
$811$	−39.2450	+	8.34178i	−1.37808	+	0.292920i	−0.836609	−	0.547801i	$-0.815465\pi$
$811$	−39.2450	+	8.34178i	−1.37808	+	0.292920i	−0.541469	+	0.840720i	$0.682132\pi$
$812$	11.0324	−	4.91192i	0.387160	−	0.172375i
$813$	10.3427	+	17.9140i	0.362733	+	0.628271i
$814$	−0.867299	−	4.19942i	−0.0303988	−	0.147189i
$815$	−13.3282	+	23.0851i	−0.466865	+	0.808634i
$816$	−10.8596	−	7.88994i	−0.380161	−	0.276203i
$817$	0.514044	+	0.542508i	0.0179841	+	0.0189799i
$818$	1.28202	+	3.94566i	0.0448249	+	0.137957i
$819$	−0.0468544	−	0.445790i	−0.00163722	−	0.0155772i
$820$	−1.77320	−	16.8708i	−0.0619227	−	0.589155i
$821$	−2.38638	+	2.65034i	−0.0832851	+	0.0924975i	−0.783347	−	0.621585i	$-0.786489\pi$
$821$	−2.38638	+	2.65034i	−0.0832851	+	0.0924975i	0.700062	+	0.714082i	$0.253156\pi$
$822$	−14.3872	−	15.9786i	−0.501810	−	0.557317i
$823$	3.36371	−	32.0035i	0.117251	−	1.11557i	−0.764750	−	0.644327i	$-0.777138\pi$
$823$	3.36371	−	32.0035i	0.117251	−	1.11557i	0.882002	−	0.471246i	$-0.156196\pi$
$824$	9.71644			0.338488
$825$	−1.28723	−	2.93669i	−0.0448156	−	0.102242i
$826$	2.20990	+	3.82766i	0.0768923	+	0.133181i
$827$	−0.120951	+	1.15077i	−0.00420586	+	0.0400161i	−0.996424	−	0.0844993i	$-0.973071\pi$
$827$	−0.120951	+	1.15077i	−0.00420586	+	0.0400161i	0.992218	+	0.124515i	$0.0397376\pi$
$828$	−1.21351	+	3.73480i	−0.0421723	+	0.129793i
$829$	5.24519	+	16.1430i	0.182173	+	0.560671i	0.999888	−	0.0149519i	$-0.00475953\pi$
$829$	5.24519	+	16.1430i	0.182173	+	0.560671i	−0.817715	+	0.575623i	$0.804760\pi$
$830$	−26.5268	−	11.8105i	−0.920758	−	0.409948i
$831$	2.89394	+	27.5340i	0.100390	+	0.955143i
$832$	−0.235041	+	0.261039i	−0.00814856	+	0.00904990i
$833$	−12.4549	−	13.8325i	−0.431535	−	0.479269i
$834$	−14.1760	+	6.31154i	−0.490873	+	0.218551i
$835$	17.6212			0.609807
$836$	−0.284076	−	14.4540i	−0.00982497	−	0.499903i
$837$	−2.94165			−0.101678
$838$	−5.82939	+	2.59541i	−0.201373	+	0.0896571i
$839$	−20.0791	−	22.3001i	−0.693206	−	0.769884i	0.289073	−	0.957307i	$-0.406653\pi$
$839$	−20.0791	−	22.3001i	−0.693206	−	0.769884i	−0.982279	+	0.187424i	$0.939986\pi$
$840$	6.23496	−	6.92462i	0.215126	−	0.238922i
$841$	−0.461062	−	4.38671i	−0.0158987	−	0.151266i
$842$	−1.43041	−	0.636860i	−0.0492952	−	0.0219477i
$843$	14.3578	+	44.1888i	0.494509	+	1.52194i
$844$	5.01437	−	15.4327i	0.172602	−	0.531214i
$845$	3.15910	−	30.0568i	0.108676	−	1.03399i
$846$	1.38591	+	2.40046i	0.0476485	+	0.0825296i
$847$	15.5741	−	16.9002i	0.535134	−	0.580697i
$848$	4.08149			0.140159
$849$	−3.93432	+	37.4326i	−0.135026	+	1.28468i
$850$	−2.40485	−	2.67085i	−0.0824856	−	0.0916095i
$851$	−5.56217	+	6.17742i	−0.190669	+	0.211759i
$852$	2.64204	+	25.1374i	0.0905150	+	0.861192i
$853$	−2.19009	−	20.8373i	−0.0749871	−	0.713455i	−0.965836	−	0.259155i	$-0.916556\pi$
$853$	−2.19009	−	20.8373i	−0.0749871	−	0.713455i	0.890849	−	0.454300i	$-0.150111\pi$
$854$	−8.81749	−	27.1374i	−0.301728	−	0.928624i
$855$	1.77926	−	5.99009i	0.0608495	−	0.204857i
$856$	8.33487	+	6.05563i	0.284880	+	0.206977i
$857$	−23.5767	+	40.8360i	−0.805364	+	1.39493i	0.110681	+	0.993856i	$0.464697\pi$
$857$	−23.5767	+	40.8360i	−0.805364	+	1.39493i	−0.916045	+	0.401075i	$0.868637\pi$
$858$	−1.92353	+	1.09579i	−0.0656681	+	0.0374096i
$859$	28.5731	+	49.4901i	0.974902	+	1.68858i	0.680257	+	0.732974i	$0.261868\pi$
$859$	28.5731	+	49.4901i	0.974902	+	1.68858i	0.294646	+	0.955607i	$0.404798\pi$
$860$	0.367633	−	0.163681i	0.0125362	−	0.00558146i
$861$	28.0669	−	5.96581i	0.956518	−	0.203314i
$862$	4.95871	+	15.2613i	0.168894	+	0.519803i
$863$	−42.1348	+	30.6127i	−1.43429	+	1.04207i	−0.445087	+	0.895487i	$0.646827\pi$
$863$	−42.1348	+	30.6127i	−1.43429	+	1.04207i	−0.989198	+	0.146582i	$0.953173\pi$
$864$	4.14750	+	1.84658i	0.141101	+	0.0628221i
$865$	−9.73335	+	10.8100i	−0.330944	+	0.367550i
$866$	−3.40852	+	10.4903i	−0.115826	+	0.356476i
$867$	−50.5785	−	36.7474i	−1.71774	−	1.24801i
$868$	0.676862	+	1.17236i	0.0229742	+	0.0397925i
$869$	55.1245	+	6.11586i	1.86997	+	0.207466i
$870$	−12.8897	−	22.3256i	−0.437001	−	0.756908i
$871$	1.39391	−	0.620608i	0.0472308	−	0.0210285i
$872$	−10.1371	−	11.2584i	−0.343284	−	0.381256i
$873$	0.0104990	+	0.0323126i	0.000355338	+	0.00109362i
$874$	−22.2467	+	17.0438i	−0.752506	+	0.576517i
$875$	−17.8174	+	12.9451i	−0.602338	+	0.437624i
$876$	−12.3378	−	2.62248i	−0.416856	−	0.0886054i
$877$	−12.5408	−	13.9280i	−0.423474	−	0.470316i	0.493220	−	0.869904i	$-0.335820\pi$
$877$	−12.5408	−	13.9280i	−0.423474	−	0.470316i	−0.916695	+	0.399589i	$0.869153\pi$
$878$	−3.03351	+	28.8619i	−0.102376	+	0.974043i
$879$	−6.73716	+	11.6691i	−0.227239	+	0.393589i
$880$	−7.38937	−	2.44821i	−0.249095	−	0.0825293i
$881$	−34.9509			−1.17753			−0.588764	−	0.808305i	$-0.700385\pi$
$881$	−34.9509			−1.17753			−0.588764	+	0.808305i	$0.700385\pi$
$882$	−1.30203	−	0.945981i	−0.0438417	−	0.0318528i
$883$	−10.2097	+	2.17014i	−0.343584	+	0.0730311i	−0.376472	−	0.926428i	$-0.622863\pi$
$883$	−10.2097	+	2.17014i	−0.343584	+	0.0730311i	0.0328878	+	0.999459i	$0.489530\pi$
$884$	−1.66034	+	1.84399i	−0.0558432	+	0.0620202i
$885$	7.63299	−	5.54569i	0.256580	−	0.186416i
$886$	−26.0035	+	18.8927i	−0.873606	+	0.634712i
$887$	−18.0062	+	19.9979i	−0.604590	+	0.671465i	−0.965279	−	0.261221i	$-0.915875\pi$
$887$	−18.0062	+	19.9979i	−0.604590	+	0.671465i	0.360689	+	0.932686i	$0.382542\pi$
$888$	−1.64390	−	1.82573i	−0.0551656	−	0.0612676i
$889$	−3.56328	+	33.9023i	−0.119509	+	1.13705i
$890$	11.8651	−	20.5510i	0.397721	−	0.688872i
$891$	25.6449	+	23.3603i	0.859137	+	0.782601i
$892$	−2.00013			−0.0669693
$893$	−1.56688	+	19.7190i	−0.0524337	+	0.659871i
$894$	11.5717	−	35.6139i	0.387014	−	1.19111i
$895$	22.9752	+	4.88352i	0.767975	+	0.163238i
$896$	−0.218388	−	2.07782i	−0.00729583	−	0.0694152i
$897$	3.92043	+	1.74549i	0.130899	+	0.0582802i
$898$	34.7948	+	7.39587i	1.16112	+	0.246803i
$899$	3.66340	−	0.778679i	0.122181	−	0.0259704i
$900$	−0.251403	−	0.182655i	−0.00838009	−	0.00608849i
$901$	28.8319			0.960529
$902$	−13.9778	−	19.4742i	−0.465408	−	0.648421i
$903$	0.340347	+	0.589498i	0.0113260	+	0.0196173i
$904$	−4.12211	−	2.99489i	−0.137099	−	0.0996085i
$905$	12.1409	−	37.3658i	0.403577	−	1.24208i
$906$	8.45420	−	9.38934i	0.280872	−	0.311940i
$907$	0.827442	+	7.87259i	0.0274748	+	0.261405i	0.999633	+	0.0270807i	$0.00862109\pi$
$907$	0.827442	+	7.87259i	0.0274748	+	0.261405i	−0.972158	+	0.234324i	$0.924712\pi$
$908$	−11.5917	−	5.16095i	−0.384683	−	0.171272i
$909$	−7.08267	−	1.50547i	−0.234917	−	0.0499332i
$910$	−1.15256	−	1.28005i	−0.0382071	−	0.0424332i
$911$	24.2209	+	17.5975i	0.802475	+	0.583032i	0.911639	−	0.410992i	$-0.134817\pi$
$911$	24.2209	+	17.5975i	0.802475	+	0.583032i	−0.109164	+	0.994024i	$0.534817\pi$
$912$	−4.32243	−	7.06552i	−0.143130	−	0.233963i
$913$	−40.8314	+	4.05330i	−1.35132	+	0.134145i
$914$	10.5454	−	18.2651i	0.348810	−	0.604157i
$915$	−55.6451	+	24.7748i	−1.83957	+	0.819029i
$916$	16.1685	−	3.43671i	0.534221	−	0.113552i
$917$	−5.40513	−	1.14890i	−0.178493	−	0.0379399i
$918$	29.2981	+	13.0444i	0.966983	+	0.430528i
$919$	−7.59892	+	5.52094i	−0.250665	+	0.182119i	−0.706022	−	0.708190i	$-0.749512\pi$
$919$	−7.59892	+	5.52094i	−0.250665	+	0.182119i	0.455356	+	0.890309i	$0.349512\pi$
$920$	4.66316	+	14.3517i	0.153740	+	0.473163i
$921$	−51.3459	+	10.9139i	−1.69190	+	0.359625i
$922$	0.899188	−	8.55521i	0.0296132	−	0.281751i
$923$	4.67236			0.153793
$924$	2.81193	−	12.8634i	0.0925057	−	0.423174i
$925$	−0.328893	−	0.569660i	−0.0108139	−	0.0187303i
$926$	−25.8467	+	11.5077i	−0.849376	+	0.378167i
$927$	5.80499	−	1.23389i	0.190661	−	0.0405262i
$928$	−5.65390	−	1.20177i	−0.185598	−	0.0394502i
$929$	5.42268	+	51.5933i	0.177912	+	1.69272i	0.611208	+	0.791470i	$0.290684\pi$
$929$	5.42268	+	51.5933i	0.177912	+	1.69272i	−0.433296	+	0.901252i	$0.642650\pi$
$930$	2.33788	−	1.69857i	0.0766620	−	0.0556982i
$931$	−3.82578	−	10.8296i	−0.125385	−	0.354926i
$932$	1.72352	−	5.30444i	0.0564556	−	0.173753i
$933$	9.00807	−	4.01065i	0.294911	−	0.131303i
$934$	−3.86824	+	6.69999i	−0.126573	+	0.219230i
$935$	−52.1989	−	17.2943i	−1.70709	−	0.565585i
$936$	−0.107273	+	0.185803i	−0.00350634	+	0.00607315i
$937$	3.63475	−	34.5823i	0.118742	−	1.12975i	−0.759157	−	0.650908i	$-0.774388\pi$
$937$	3.63475	−	34.5823i	0.118742	−	1.12975i	0.877899	−	0.478847i	$-0.158945\pi$
$938$	−2.80446	+	8.63123i	−0.0915687	+	0.281819i
$939$	−12.2009	−	37.5505i	−0.398161	−	1.22541i
$940$	9.73043	+	4.33227i	0.317372	+	0.141303i
$941$	−48.5715	−	21.6254i	−1.58338	−	0.704968i	−0.588740	−	0.808323i	$-0.700376\pi$
$941$	−48.5715	−	21.6254i	−1.58338	−	0.704968i	−0.994645	+	0.103355i	$0.967042\pi$
$942$	5.74975	+	17.6959i	0.187337	+	0.576564i
$943$	−14.3598	+	44.1949i	−0.467619	+	1.43918i
$944$	0.221128	−	2.10389i	0.00719710	−	0.0684758i
$945$	−11.1313	+	19.2800i	−0.362102	+	0.627180i
$946$	0.336901	−	0.458118i	0.0109536	−	0.0148947i
$947$	28.5739	−	49.4914i	0.928526	−	1.60825i	0.142735	−	0.989761i	$-0.454410\pi$
$947$	28.5739	−	49.4914i	0.928526	−	1.60825i	0.785790	−	0.618493i	$-0.212256\pi$
$948$	29.0293	−	12.9247i	0.942827	−	0.419774i
$949$	−0.720521	+	2.21754i	−0.0233891	+	0.0719843i
$950$	−0.738701	−	2.09104i	−0.0239666	−	0.0678422i
$951$	29.5052	−	21.4368i	0.956772	−	0.695135i
$952$	−1.54270	−	14.6779i	−0.0499993	−	0.475712i
$953$	−0.294734	−	0.0626478i	−0.00954739	−	0.00202936i	0.203136	−	0.979151i	$-0.434887\pi$
$953$	−0.294734	−	0.0626478i	−0.00954739	−	0.00202936i	−0.212683	+	0.977121i	$0.568220\pi$
$954$	2.43844	−	0.518307i	0.0789475	−	0.0167808i
$955$	−23.3116	+	10.3790i	−0.754344	+	0.335856i
$956$	4.18767	+	7.25326i	0.135439	+	0.234587i
$957$	−31.4423	−	18.3961i	−1.01639	−	0.594662i
$958$	32.4324			1.04784
$959$	2.47111	−	23.5111i	0.0797964	−	0.759212i
$960$	−4.36247	+	0.927272i	−0.140798	+	0.0299276i
$961$	−9.44979	−	29.0835i	−0.304832	−	0.938177i
$962$	−0.367411	+	0.266940i	−0.0118458	+	0.00860648i
$963$	5.74858	+	2.55943i	0.185246	+	0.0824766i
$964$	−4.53556	−	0.964063i	−0.146081	−	0.0310504i
$965$	37.1307	−	7.89237i	1.19528	−	0.254064i
$966$	−23.3183	+	10.3820i	−0.750253	+	0.334034i
$967$	−12.8752	+	22.3006i	−0.414039	+	0.717137i	−0.995327	−	0.0965607i	$-0.969216\pi$
$967$	−12.8752	+	22.3006i	−0.414039	+	0.717137i	0.581288	+	0.813698i	$0.302549\pi$
$968$	−10.7853	+	2.16261i	−0.346653	+	0.0695091i
$969$	−30.5339	−	49.9112i	−0.980889	−	1.60338i
$970$	0.105624	+	0.0767401i	0.00339137	+	0.00246398i
$971$	−3.95096	−	4.38799i	−0.126792	−	0.140817i	0.676406	−	0.736529i	$-0.263537\pi$
$971$	−3.95096	−	4.38799i	−0.126792	−	0.140817i	−0.803198	+	0.595712i	$0.796870\pi$
$972$	6.11815	+	1.30045i	0.196240	+	0.0417121i
$973$	−15.5864	−	6.93951i	−0.499677	−	0.222470i
$974$	−1.91466	−	18.2168i	−0.0613496	−	0.583703i
$975$	−0.227230	+	0.252365i	−0.00727719	+	0.00808214i
$976$	−4.22037	+	12.9890i	−0.135091	+	0.415767i
$977$	−15.6348	−	11.3594i	−0.500203	−	0.363418i	0.308892	−	0.951097i	$-0.400042\pi$
$977$	−15.6348	−	11.3594i	−0.500203	−	0.363418i	−0.809094	+	0.587679i	$0.800042\pi$
$978$	10.7906	+	18.6898i	0.345044	+	0.597634i
$979$	0.193638	−	33.5324i	0.00618869	−	1.07170i
$980$	−6.18445			−0.197555
$981$	−7.48598	−	5.43888i	−0.239009	−	0.173650i
$982$	−38.9433	+	8.27765i	−1.24273	+	0.264150i
$983$	47.1355	+	10.0190i	1.50339	+	0.319555i	0.884730	−	0.466104i	$-0.154343\pi$
$983$	47.1355	+	10.0190i	1.50339	+	0.319555i	0.618659	+	0.785659i	$0.287676\pi$
$984$	−12.5466	−	5.58611i	−0.399971	−	0.178079i
$985$	−0.602995	−	5.73712i	−0.0192130	−	0.182800i
$986$	−39.9395	−	8.48940i	−1.27193	−	0.270357i
$987$	−5.56739	+	17.1347i	−0.177212	+	0.545403i
$988$	−1.38246	+	0.658121i	−0.0439820	+	0.0209376i
$989$	−1.10237			−0.0350533
$990$	−4.72560	−	0.524287i	−0.150189	−	0.0166629i
$991$	2.69960	−	4.67584i	0.0857556	−	0.148533i	−0.819957	−	0.572425i	$-0.806003\pi$
$991$	2.69960	−	4.67584i	0.0857556	−	0.148533i	0.905713	+	0.423892i	$0.139336\pi$
$992$	0.0677283	−	0.644392i	0.00215038	−	0.0204595i
$993$	3.83989	+	4.26462i	0.121855	+	0.135334i
$994$	−18.5956	+	20.6525i	−0.589816	+	0.655057i
$995$	21.2363	−	15.4290i	0.673235	−	0.489134i
$996$	−19.0189	+	13.8180i	−0.602637	+	0.437841i
$997$	−9.69245	+	10.7646i	−0.306963	+	0.340917i	−0.876813	−	0.480832i	$-0.840335\pi$
$997$	−9.69245	+	10.7646i	−0.306963	+	0.340917i	0.569850	+	0.821749i	$0.307001\pi$
$998$	10.6985	−	2.27404i	0.338656	−	0.0719836i
$999$	4.74872	+	3.45014i	0.150243	+	0.109158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.d.125.6	✓	64
11.3	even	5	inner	418.2.n.d.201.3	yes	64
19.7	even	3	inner	418.2.n.d.235.3	yes	64
209.102	even	15	inner	418.2.n.d.311.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.d.125.6	✓	64	1.1	even	1	trivial
418.2.n.d.201.3	yes	64	11.3	even	5	inner
418.2.n.d.235.3	yes	64	19.7	even	3	inner
418.2.n.d.311.6	yes	64	209.102	even	15	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 + 0.406737i) q^{2} +(1.27149 + 1.41213i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.245336 - 2.33422i) q^{5} +(-1.73593 - 0.772884i) q^{6} +(-0.645619 - 1.98701i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.0638446 + 0.607441i) q^{9} +O(q^{10})\)	\(q+(-0.913545 + 0.406737i) q^{2} +(1.27149 + 1.41213i) q^{3} +(0.669131 - 0.743145i) q^{4} +(-0.245336 - 2.33422i) q^{5} +(-1.73593 - 0.772884i) q^{6} +(-0.645619 - 1.98701i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.0638446 + 0.607441i) q^{9} +(1.17354 + 2.03263i) q^{10} +(2.86266 + 1.67487i) q^{11} +1.90021 q^{12} +(0.0367169 - 0.349338i) q^{13} +(1.39799 + 1.55263i) q^{14} +(2.98428 - 3.31438i) q^{15} +(-0.104528 - 0.994522i) q^{16} +(-0.738395 - 7.02536i) q^{17} +(-0.188744 - 0.580893i) q^{18} +(1.24115 - 4.17846i) q^{19} +(-1.89883 - 1.37958i) q^{20} +(1.98502 - 3.43816i) q^{21} +(-3.29640 - 0.365723i) q^{22} +(3.21470 + 5.56803i) q^{23} +(-1.73593 + 0.772884i) q^{24} +(-0.497653 + 0.105779i) q^{25} +(0.108546 + 0.334071i) q^{26} +(3.67294 - 2.66854i) q^{27} +(-1.90864 - 0.849782i) q^{28} +(-3.86772 + 4.29554i) q^{29} +(-1.37819 + 4.24165i) q^{30} +(-0.524196 - 0.380850i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.27470 + 6.17202i) q^{33} +(3.53203 + 6.11765i) q^{34} +(-4.47973 + 1.99450i) q^{35} +(0.408696 + 0.453903i) q^{36} +(0.399526 + 1.22961i) q^{37} +(0.565691 + 4.32204i) q^{38} +(0.539996 - 0.392330i) q^{39} +(2.29579 + 0.487985i) q^{40} +(4.83622 + 5.37117i) q^{41} +(-0.414982 + 3.94829i) q^{42} +(-0.0857287 + 0.148487i) q^{43} +(3.16016 - 1.00666i) q^{44} +1.43356 q^{45} +(-5.20150 - 3.77911i) q^{46} +(-4.43894 + 0.943525i) q^{47} +(1.27149 - 1.41213i) q^{48} +(2.13173 - 1.54879i) q^{49} +(0.411605 - 0.299048i) q^{50} +(8.98185 - 9.97536i) q^{51} +(-0.235041 - 0.261039i) q^{52} +(-0.426632 + 4.05913i) q^{53} +(-2.27000 + 3.93176i) q^{54} +(3.20720 - 7.09298i) q^{55} +2.08927 q^{56} +(7.47863 - 3.56020i) q^{57} +(1.78618 - 5.49731i) q^{58} +(2.06925 + 0.439833i) q^{59} +(-0.466190 - 4.43550i) q^{60} +(-12.4767 - 5.55497i) q^{61} +(0.633782 + 0.134715i) q^{62} +(1.24821 - 0.265316i) q^{63} +(-0.809017 - 0.587785i) q^{64} -0.824440 q^{65} +(-3.67488 - 5.11995i) q^{66} +(2.17191 + 3.76186i) q^{67} +(-5.71494 - 4.15215i) q^{68} +(-3.77532 + 11.6193i) q^{69} +(3.28120 - 3.64414i) q^{70} +(1.39040 + 13.2288i) q^{71} +(-0.557982 - 0.248429i) q^{72} +(-6.49287 - 1.38010i) q^{73} +(-0.865114 - 0.960807i) q^{74} +(-0.782134 - 0.568254i) q^{75} +(-2.27471 - 3.71829i) q^{76} +(1.47980 - 6.76946i) q^{77} +(-0.333736 + 0.578047i) q^{78} +(15.2769 - 6.80171i) q^{79} +(-2.29579 + 0.487985i) q^{80} +(10.2307 + 2.17461i) q^{81} +(-6.60276 - 2.93974i) q^{82} +(-10.0089 + 7.27186i) q^{83} +(-1.22681 - 3.77573i) q^{84} +(-16.2176 + 3.44715i) q^{85} +(0.0179222 - 0.170518i) q^{86} -10.9836 q^{87} +(-2.47751 + 2.20499i) q^{88} +(-5.05529 - 8.75601i) q^{89} +(-1.30963 + 0.583083i) q^{90} +(-0.717844 + 0.152583i) q^{91} +(6.28891 + 1.33675i) q^{92} +(-0.128698 - 1.22448i) q^{93} +(3.67140 - 2.66743i) q^{94} +(-10.0579 - 1.87198i) q^{95} +(-0.587196 + 1.80720i) q^{96} +(0.0508167 - 0.0226251i) q^{97} +(-1.31748 + 2.28194i) q^{98} +(-1.20015 + 1.63196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9	\( 64 q - 8 q^{2} - 6 q^{3} + 8 q^{4} - 7 q^{5} - 4 q^{6} + 22 q^{7} + 16 q^{8} + 14 q^{9} - 8 q^{10} - 6 q^{11} - 8 q^{12} + 9 q^{13} + 11 q^{14} + 9 q^{15} + 8 q^{16} - 2 q^{17} - 12 q^{18} + 4 q^{19} + 14 q^{20} - 36 q^{21} + 7 q^{22} + 8 q^{23} - 4 q^{24} + 31 q^{25} - 12 q^{26} + 54 q^{27} + 9 q^{28} + 18 q^{29} + 18 q^{30} + 20 q^{31} + 32 q^{32} + 10 q^{33} + 2 q^{34} - 16 q^{35} - 6 q^{36} + 18 q^{37} - 31 q^{38} + 2 q^{39} - 3 q^{40} + 16 q^{41} + 6 q^{42} + 42 q^{43} - 2 q^{44} - 8 q^{45} - 24 q^{46} - 34 q^{47} - 6 q^{48} - 10 q^{49} - 58 q^{50} - 40 q^{51} - 6 q^{52} + 15 q^{53} - 28 q^{54} + 49 q^{55} + 8 q^{56} + 8 q^{57} + 36 q^{58} - 7 q^{59} + 4 q^{60} - 15 q^{61} - 37 q^{63} - 16 q^{64} - 48 q^{65} - 10 q^{66} - 14 q^{67} + 4 q^{68} - 30 q^{69} - 19 q^{70} - 4 q^{71} - 14 q^{72} + 8 q^{73} + 9 q^{74} - 96 q^{75} - 10 q^{76} - 58 q^{77} + 46 q^{78} + 12 q^{79} + 3 q^{80} - 8 q^{81} + 4 q^{82} - 6 q^{83} - 48 q^{84} + 18 q^{85} + 3 q^{86} - 244 q^{87} + 6 q^{88} - 4 q^{89} - 9 q^{90} - 33 q^{91} + 8 q^{92} + 3 q^{93} + 62 q^{94} - 49 q^{95} - 12 q^{96} - 15 q^{97} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^2 - 6 * q^3 + 8 * q^4 - 7 * q^5 - 4 * q^6 + 22 * q^7 + 16 * q^8 + 14 * q^9 - 8 * q^10 - 6 * q^11 - 8 * q^12 + 9 * q^13 + 11 * q^14 + 9 * q^15 + 8 * q^16 - 2 * q^17 - 12 * q^18 + 4 * q^19 + 14 * q^20 - 36 * q^21 + 7 * q^22 + 8 * q^23 - 4 * q^24 + 31 * q^25 - 12 * q^26 + 54 * q^27 + 9 * q^28 + 18 * q^29 + 18 * q^30 + 20 * q^31 + 32 * q^32 + 10 * q^33 + 2 * q^34 - 16 * q^35 - 6 * q^36 + 18 * q^37 - 31 * q^38 + 2 * q^39 - 3 * q^40 + 16 * q^41 + 6 * q^42 + 42 * q^43 - 2 * q^44 - 8 * q^45 - 24 * q^46 - 34 * q^47 - 6 * q^48 - 10 * q^49 - 58 * q^50 - 40 * q^51 - 6 * q^52 + 15 * q^53 - 28 * q^54 + 49 * q^55 + 8 * q^56 + 8 * q^57 + 36 * q^58 - 7 * q^59 + 4 * q^60 - 15 * q^61 - 37 * q^63 - 16 * q^64 - 48 * q^65 - 10 * q^66 - 14 * q^67 + 4 * q^68 - 30 * q^69 - 19 * q^70 - 4 * q^71 - 14 * q^72 + 8 * q^73 + 9 * q^74 - 96 * q^75 - 10 * q^76 - 58 * q^77 + 46 * q^78 + 12 * q^79 + 3 * q^80 - 8 * q^81 + 4 * q^82 - 6 * q^83 - 48 * q^84 + 18 * q^85 + 3 * q^86 - 244 * q^87 + 6 * q^88 - 4 * q^89 - 9 * q^90 - 33 * q^91 + 8 * q^92 + 3 * q^93 + 62 * q^94 - 49 * q^95 - 12 * q^96 - 15 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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