LMFDB - Embedded newform 507.2.t.a.4.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

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("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	507.4
Dual form			507.2.t.a.127.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.90487 + 0.0767637i) q^{2} +(0.278217 - 0.960518i) q^{3} +(1.62913 + 0.131517i) q^{4} +(2.99420 + 1.13555i) q^{5} +(0.603702 - 1.80831i) q^{6} +(-0.0821119 - 0.192724i) q^{7} +(-0.691848 - 0.0840056i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})$	\(q+(1.90487 + 0.0767637i) q^{2} +(0.278217 - 0.960518i) q^{3} +(1.62913 + 0.131517i) q^{4} +(2.99420 + 1.13555i) q^{5} +(0.603702 - 1.80831i) q^{6} +(-0.0821119 - 0.192724i) q^{7} +(-0.691848 - 0.0840056i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(5.61640 + 2.39293i) q^{10} +(0.276231 + 0.436824i) q^{11} +(0.579577 - 1.52822i) q^{12} +(3.48287 - 0.932518i) q^{13} +(-0.141618 - 0.373417i) q^{14} +(1.92376 - 2.56006i) q^{15} +(-4.53796 - 0.737491i) q^{16} +(-1.88509 + 0.803162i) q^{17} +(-1.56895 - 1.08297i) q^{18} +(-2.28582 + 1.31972i) q^{19} +(4.72860 + 2.24375i) q^{20} +(-0.207960 + 0.0252509i) q^{21} +(0.492652 + 0.853298i) q^{22} +(-0.979794 + 1.69705i) q^{23} +(-0.273173 + 0.641161i) q^{24} +(3.93322 + 3.48453i) q^{25} +(6.70601 - 1.50897i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-0.108425 - 0.324771i) q^{28} +(0.320467 - 7.95231i) q^{29} +(3.86103 - 4.72890i) q^{30} +(0.449545 + 0.507432i) q^{31} +(-7.22193 - 1.47437i) q^{32} +(0.496429 - 0.143793i) q^{33} +(-3.65251 + 1.38521i) q^{34} +(-0.0270120 - 0.670296i) q^{35} +(-1.30663 - 0.981871i) q^{36} +(-0.747206 + 0.152543i) q^{37} +(-4.45549 + 2.33842i) q^{38} +(0.0732961 - 3.60481i) q^{39} +(-1.97614 - 1.03716i) q^{40} +(-3.52212 - 1.02019i) q^{41} +(-0.398075 + 0.0321359i) q^{42} +(-2.10089 + 10.2909i) q^{43} +(0.392566 + 0.747972i) q^{44} +(-1.92376 - 2.56006i) q^{45} +(-1.99666 + 3.15746i) q^{46} +(-6.09788 + 4.20906i) q^{47} +(-1.97091 + 4.15361i) q^{48} +(4.81867 - 5.01677i) q^{49} +(7.22479 + 6.93951i) q^{50} +(0.246987 + 2.03412i) q^{51} +(5.79670 - 1.06114i) q^{52} +(0.704680 - 5.80356i) q^{53} +(-1.47672 + 1.20571i) q^{54} +(0.331055 + 1.62161i) q^{55} +(0.0406191 + 0.140233i) q^{56} +(0.631657 + 2.56273i) q^{57} +(1.22090 - 15.1235i) q^{58} +(0.994171 + 6.11738i) q^{59} +(3.47074 - 3.91766i) q^{60} +(-3.00721 + 2.25977i) q^{61} +(0.817374 + 1.00110i) q^{62} +(-0.0336041 + 0.206774i) q^{63} +(-4.71588 - 1.16236i) q^{64} +(11.4874 + 1.16283i) q^{65} +(0.956673 - 0.235799i) q^{66} +(-1.11442 - 13.8046i) q^{67} +(-3.17669 + 1.06053i) q^{68} +(1.35745 + 1.41326i) q^{69} -1.27890i q^{70} +(-5.06535 + 4.86534i) q^{71} +(0.539845 + 0.440770i) q^{72} +(-0.326547 + 0.622183i) q^{73} +(-1.43504 + 0.233217i) q^{74} +(4.44124 - 2.80847i) q^{75} +(-3.89745 + 1.84937i) q^{76} +(0.0615045 - 0.0891047i) q^{77} +(0.416338 - 6.86107i) q^{78} +(-0.803140 - 1.16355i) q^{79} +(-12.7501 - 7.36129i) q^{80} +(0.428693 + 0.903450i) q^{81} +(-6.63087 - 2.21371i) q^{82} +(-2.50825 + 10.1764i) q^{83} +(-0.342114 + 0.0137867i) q^{84} +(-6.55638 + 0.264213i) q^{85} +(-4.79190 + 19.4415i) q^{86} +(-7.54918 - 2.52029i) q^{87} +(-0.154414 - 0.325421i) q^{88} +(16.2456 + 9.37942i) q^{89} +(-3.46799 - 5.02425i) q^{90} +(-0.465704 - 0.594662i) q^{91} +(-1.81940 + 2.63586i) q^{92} +(0.612469 - 0.290620i) q^{93} +(-11.9388 + 7.54963i) q^{94} +(-8.34280 + 1.35584i) q^{95} +(-3.42543 + 6.52660i) q^{96} +(-2.00591 - 1.63777i) q^{97} +(9.56406 - 9.18640i) q^{98} -0.516835i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	1.90487	+	0.0767637i	1.34695	+	0.0542801i	0.703219	−	0.710973i	$-0.251745\pi$
$2$	1.90487	+	0.0767637i	1.34695	+	0.0542801i	0.643729	+	0.765254i	$0.277386\pi$
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$4$	1.62913	+	0.131517i	0.814565	+	0.0657585i
$5$	2.99420	+	1.13555i	1.33905	+	0.507834i	0.917053	−	0.398764i	$-0.130561\pi$
$5$	2.99420	+	1.13555i	1.33905	+	0.507834i	0.421995	+	0.906598i	$0.361330\pi$
$6$	0.603702	−	1.80831i	0.246460	−	0.738238i
$7$	−0.0821119	−	0.192724i	−0.0310354	−	0.0728427i	0.903741	−	0.428081i	$-0.140810\pi$
$7$	−0.0821119	−	0.192724i	−0.0310354	−	0.0728427i	−0.934776	+	0.355238i	$0.884400\pi$
$8$	−0.691848	−	0.0840056i	−0.244605	−	0.0297005i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	5.61640	+	2.39293i	1.77606	+	0.756710i
$11$	0.276231	+	0.436824i	0.0832867	+	0.131707i	0.884264	−	0.466987i	$-0.154661\pi$
$11$	0.276231	+	0.436824i	0.0832867	+	0.131707i	−0.800977	+	0.598695i	$0.795686\pi$
$12$	0.579577	−	1.52822i	0.167309	−	0.441159i
$13$	3.48287	−	0.932518i	0.965975	−	0.258634i
$13$	3.48287	−	0.932518i	0.965975	−	0.258634i
$14$	−0.141618	−	0.373417i	−0.0378491	−	0.0998000i
$15$	1.92376	−	2.56006i	0.496712	−	0.661004i
$16$	−4.53796	−	0.737491i	−1.13449	−	0.184373i
$17$	−1.88509	+	0.803162i	−0.457202	+	0.194795i	−0.608274	−	0.793727i	$-0.708138\pi$
$17$	−1.88509	+	0.803162i	−0.457202	+	0.194795i	0.151072	+	0.988523i	$0.451727\pi$
$18$	−1.56895	−	1.08297i	−0.369805	−	0.255258i
$19$	−2.28582	+	1.31972i	−0.524402	+	0.302764i	−0.738734	−	0.673997i	$-0.764576\pi$
$19$	−2.28582	+	1.31972i	−0.524402	+	0.302764i	0.214332	+	0.976761i	$0.431243\pi$
$20$	4.72860	+	2.24375i	1.05735	+	0.501718i
$21$	−0.207960	+	0.0252509i	−0.0453805	+	0.00551019i
$22$	0.492652	+	0.853298i	0.105034	+	0.181924i
$23$	−0.979794	+	1.69705i	−0.204301	+	0.353860i	−0.949910	−	0.312524i	$-0.898826\pi$
$23$	−0.979794	+	1.69705i	−0.204301	+	0.353860i	0.745609	+	0.666384i	$0.232159\pi$
$24$	−0.273173	+	0.641161i	−0.0557612	+	0.130876i
$25$	3.93322	+	3.48453i	0.786644	+	0.696906i
$26$	6.70601	−	1.50897i	1.31516	−	0.295933i
$27$	−0.748511	+	0.663123i	−0.144051	+	0.127618i
$28$	−0.108425	−	0.324771i	−0.0204903	−	0.0613760i
$29$	0.320467	−	7.95231i	0.0595093	−	1.47671i	−0.643456	−	0.765483i	$-0.722500\pi$
$29$	0.320467	−	7.95231i	0.0595093	−	1.47671i	0.702965	−	0.711224i	$-0.251859\pi$
$30$	3.86103	−	4.72890i	0.704924	−	0.863376i
$31$	0.449545	+	0.507432i	0.0807407	+	0.0911374i	0.787493	−	0.616324i	$-0.211379\pi$
$31$	0.449545	+	0.507432i	0.0807407	+	0.0911374i	−0.706752	+	0.707461i	$0.749840\pi$
$32$	−7.22193	−	1.47437i	−1.27667	−	0.260634i
$33$	0.496429	−	0.143793i	0.0864173	−	0.0250311i
$34$	−3.65251	+	1.38521i	−0.626401	+	0.237562i
$35$	−0.0270120	−	0.670296i	−0.00456586	−	0.113301i
$36$	−1.30663	−	0.981871i	−0.217772	−	0.163645i
$37$	−0.747206	+	0.152543i	−0.122840	+	0.0250780i	−0.261052	−	0.965325i	$-0.584069\pi$
$37$	−0.747206	+	0.152543i	−0.122840	+	0.0250780i	0.138212	+	0.990403i	$0.455864\pi$
$38$	−4.45549	+	2.33842i	−0.722776	+	0.379342i
$39$	0.0732961	−	3.60481i	0.0117368	−	0.577231i
$40$	−1.97614	−	1.03716i	−0.312455	−	0.163989i
$41$	−3.52212	−	1.02019i	−0.550063	−	0.159328i	−0.00846307	−	0.999964i	$-0.502694\pi$
$41$	−3.52212	−	1.02019i	−0.550063	−	0.159328i	−0.541600	+	0.840637i	$0.682181\pi$
$42$	−0.398075	+	0.0321359i	−0.0614243	+	0.00495868i
$43$	−2.10089	+	10.2909i	−0.320383	+	1.56934i	0.426563	+	0.904458i	$0.359724\pi$
$43$	−2.10089	+	10.2909i	−0.320383	+	1.56934i	−0.746947	+	0.664884i	$0.768481\pi$
$44$	0.392566	+	0.747972i	0.0591815	+	0.112761i
$45$	−1.92376	−	2.56006i	−0.286777	−	0.381631i
$46$	−1.99666	+	3.15746i	−0.294391	+	0.465542i
$47$	−6.09788	+	4.20906i	−0.889467	+	0.613955i	−0.922711	−	0.385493i	$-0.874031\pi$
$47$	−6.09788	+	4.20906i	−0.889467	+	0.613955i	0.0332442	+	0.999447i	$0.489416\pi$
$48$	−1.97091	+	4.15361i	−0.284477	+	0.599522i
$49$	4.81867	−	5.01677i	0.688381	−	0.716681i
$50$	7.22479	+	6.93951i	1.02174	+	0.981395i
$51$	0.246987	+	2.03412i	0.0345851	+	0.284834i
$52$	5.79670	−	1.06114i	0.803857	−	0.147153i
$53$	0.704680	−	5.80356i	0.0967952	−	0.797180i	−0.860776	−	0.508984i	$-0.830021\pi$
$53$	0.704680	−	5.80356i	0.0967952	−	0.797180i	0.957571	−	0.288197i	$-0.0930556\pi$
$54$	−1.47672	+	1.20571i	−0.200956	+	0.164076i
$55$	0.331055	+	1.62161i	0.0446394	+	0.218658i
$56$	0.0406191	+	0.140233i	0.00542796	+	0.0187395i
$57$	0.631657	+	2.56273i	0.0836651	+	0.339443i
$58$	1.22090	−	15.1235i	0.160312	−	1.98582i
$59$	0.994171	+	6.11738i	0.129430	+	0.796415i	0.967876	+	0.251430i	$0.0809007\pi$
$59$	0.994171	+	6.11738i	0.129430	+	0.796415i	−0.838446	+	0.544985i	$0.816535\pi$
$60$	3.47074	−	3.91766i	0.448071	−	0.505767i
$61$	−3.00721	+	2.25977i	−0.385033	+	0.289334i	−0.775580	−	0.631249i	$-0.782542\pi$
$61$	−3.00721	+	2.25977i	−0.385033	+	0.289334i	0.390547	+	0.920583i	$0.372286\pi$
$62$	0.817374	+	1.00110i	0.103807	+	0.127140i
$63$	−0.0336041	+	0.206774i	−0.00423372	+	0.0260511i
$64$	−4.71588	−	1.16236i	−0.589484	−	0.145295i
$65$	11.4874	+	1.16283i	1.42483	+	0.144232i
$66$	0.956673	−	0.235799i	0.117758	−	0.0290248i
$67$	−1.11442	−	13.8046i	−0.136148	−	1.68650i	−0.599539	−	0.800345i	$-0.704649\pi$
$67$	−1.11442	−	13.8046i	−0.136148	−	1.68650i	0.463391	−	0.886154i	$-0.346633\pi$
$68$	−3.17669	+	1.06053i	−0.385230	+	0.128609i
$69$	1.35745	+	1.41326i	0.163418	+	0.170137i
$70$		−	1.27890i		−	0.152858i
$71$	−5.06535	+	4.86534i	−0.601147	+	0.577409i	−0.930269	−	0.366878i	$-0.880427\pi$
$71$	−5.06535	+	4.86534i	−0.601147	+	0.577409i	0.329122	+	0.944287i	$0.393247\pi$
$72$	0.539845	+	0.440770i	0.0636214	+	0.0519452i
$73$	−0.326547	+	0.622183i	−0.0382194	+	0.0728210i	−0.903817	−	0.427920i	$-0.859247\pi$
$73$	−0.326547	+	0.622183i	−0.0382194	+	0.0728210i	0.865597	+	0.500741i	$0.166939\pi$
$74$	−1.43504	+	0.233217i	−0.166820	+	0.0271109i
$75$	4.44124	−	2.80847i	0.512831	−	0.324294i
$76$	−3.89745	+	1.84937i	−0.447069	+	0.212137i
$77$	0.0615045	−	0.0891047i	0.00700909	−	0.0101544i
$78$	0.416338	−	6.86107i	0.0471410	−	0.776863i
$79$	−0.803140	−	1.16355i	−0.0903604	−	0.130910i	0.775197	−	0.631720i	$-0.217651\pi$
$79$	−0.803140	−	1.16355i	−0.0903604	−	0.130910i	−0.865557	+	0.500810i	$0.833035\pi$
$80$	−12.7501	−	7.36129i	−1.42551	−	0.823017i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	−6.63087	−	2.21371i	−0.732257	−	0.244463i
$83$	−2.50825	+	10.1764i	−0.275316	+	1.11700i	0.656574	+	0.754261i	$0.272005\pi$
$83$	−2.50825	+	10.1764i	−0.275316	+	1.11700i	−0.931890	+	0.362740i	$0.881841\pi$
$84$	−0.342114	+	0.0137867i	−0.0373277	+	0.00150426i
$85$	−6.55638	+	0.264213i	−0.711139	+	0.0286579i
$86$	−4.79190	+	19.4415i	−0.516724	+	2.09643i
$87$	−7.54918	−	2.52029i	−0.809357	−	0.270203i
$88$	−0.154414	−	0.325421i	−0.0164606	−	0.0346900i
$89$	16.2456	+	9.37942i	1.72203	+	0.994217i	0.914713	+	0.404105i	$0.132417\pi$
$89$	16.2456	+	9.37942i	1.72203	+	0.994217i	0.807321	+	0.590112i	$0.200916\pi$
$90$	−3.46799	−	5.02425i	−0.365558	−	0.529603i
$91$	−0.465704	−	0.594662i	−0.0488190	−	0.0623375i
$92$	−1.81940	+	2.63586i	−0.189686	+	0.274808i
$93$	0.612469	−	0.290620i	0.0635101	−	0.0301359i
$94$	−11.9388	+	7.54963i	−1.23139	+	0.778684i
$95$	−8.34280	+	1.35584i	−0.855953	+	0.139106i
$96$	−3.42543	+	6.52660i	−0.349606	+	0.666119i
$97$	−2.00591	−	1.63777i	−0.203669	−	0.166291i	0.525122	−	0.851027i	$-0.324020\pi$
$97$	−2.00591	−	1.63777i	−0.203669	−	0.166291i	−0.728791	+	0.684737i	$0.759917\pi$
$98$	9.56406	−	9.18640i	0.966116	−	0.927967i
$99$		−	0.516835i		−	0.0519439i
$100$	5.94945	+	6.19403i	0.594945	+	0.619403i
$101$	−13.0348	+	4.35164i	−1.29701	+	0.433005i	−0.879600	−	0.475714i	$-0.842190\pi$
$101$	−13.0348	+	4.35164i	−1.29701	+	0.433005i	−0.417408	+	0.908719i	$0.637061\pi$
$102$	0.314332	+	3.89369i	0.0311235	+	0.385533i
$103$	4.86816	−	1.19989i	0.479674	−	0.118229i	0.00793738	−	0.999968i	$-0.497473\pi$
$103$	4.86816	−	1.19989i	0.479674	−	0.118229i	0.471737	+	0.881739i	$0.343627\pi$
$104$	−2.48796	+	0.352580i	−0.243964	+	0.0345733i
$105$	−0.651347	−	0.160543i	−0.0635649	−	0.0156674i
$106$	1.78783	−	11.0009i	0.173649	−	1.06851i
$107$	0.488682	+	0.598527i	0.0472427	+	0.0578618i	0.797686	−	0.603073i	$-0.206057\pi$
$107$	0.488682	+	0.598527i	0.0472427	+	0.0578618i	−0.750443	+	0.660935i	$0.770160\pi$
$108$	−1.30663	+	0.981871i	−0.125731	+	0.0944806i
$109$	−3.88290	+	4.38289i	−0.371915	+	0.419805i	−0.904434	−	0.426613i	$-0.859707\pi$
$109$	−3.88290	+	4.38289i	−0.371915	+	0.419805i	0.532520	+	0.846418i	$0.321245\pi$
$110$	0.506136	+	3.11438i	0.0482582	+	0.296944i
$111$	−0.0613653	+	0.760145i	−0.00582453	+	0.0721498i
$112$	0.230489	+	0.935130i	0.0217791	+	0.0883615i
$113$	−0.441288	−	1.52350i	−0.0415129	−	0.143319i	0.937085	−	0.349102i	$-0.113513\pi$
$113$	−0.441288	−	1.52350i	−0.0415129	−	0.143319i	−0.978598	+	0.205783i	$0.934026\pi$
$114$	1.00650	+	4.93017i	0.0942675	+	0.461753i
$115$	−4.86079	+	3.96872i	−0.453271	+	0.370085i
$116$	1.56795	−	12.9132i	0.145580	−	1.19896i
$117$	−3.44209	−	1.07332i	−0.318221	−	0.0992287i
$118$	1.42418	+	11.7291i	0.131106	+	1.07975i
$119$	0.309577	+	0.297353i	0.0283789	+	0.0272583i
$120$	−1.54601	+	1.60956i	−0.141130	+	0.146932i
$121$	4.60111	−	9.69663i	0.418282	−	0.881511i
$122$	−5.90181	+	4.07373i	−0.534325	+	0.368818i
$123$	−1.95983	+	3.09922i	−0.176712	+	0.279448i
$124$	0.665632	+	0.885795i	0.0597755	+	0.0795468i
$125$	0.379079	+	0.722275i	0.0339059	+	0.0646023i
$126$	−0.0798842	+	0.391299i	−0.00711665	+	0.0348597i
$127$	3.21123	−	0.259237i	0.284950	−	0.0230036i	0.0628349	−	0.998024i	$-0.479986\pi$
$127$	3.21123	−	0.259237i	0.284950	−	0.0230036i	0.222115	+	0.975020i	$0.428704\pi$
$128$	5.26585	+	1.52527i	0.465439	+	0.134816i
$129$	9.30005	+	4.88104i	0.818824	+	0.429752i
$130$	21.7927	+	3.09686i	1.91134	+	0.271613i
$131$	1.46668	−	0.769771i	0.128144	−	0.0672552i	−0.399433	−	0.916762i	$-0.630793\pi$
$131$	1.46668	−	0.769771i	0.128144	−	0.0672552i	0.527577	+	0.849507i	$0.323101\pi$
$132$	0.827659	−	0.168968i	0.0720385	−	0.0147068i
$133$	0.442033	+	0.332166i	0.0383291	+	0.0288025i
$134$	−1.06314	−	26.3815i	−0.0918412	−	2.27902i
$135$	−2.99420	+	1.13555i	−0.257700	+	0.0977327i
$136$	1.37167	−	0.397308i	0.117619	−	0.0340689i
$137$	−5.04064	−	1.02905i	−0.430651	−	0.0879180i	−0.0201898	−	0.999796i	$-0.506427\pi$
$137$	−5.04064	−	1.02905i	−0.430651	−	0.0879180i	−0.410461	+	0.911878i	$0.634632\pi$
$138$	2.47729	+	2.79628i	0.210881	+	0.238035i
$139$	4.10838	−	5.03185i	0.348468	−	0.426796i	−0.570396	−	0.821370i	$-0.693210\pi$
$139$	4.10838	−	5.03185i	0.348468	−	0.426796i	0.918864	+	0.394574i	$0.129108\pi$
$140$	0.0441492	−	1.09555i	0.00373129	−	0.0925911i
$141$	2.34634	+	7.02815i	0.197598	+	0.591877i
$142$	−10.0223	+	8.87901i	−0.841055	+	0.745110i
$143$	1.36942	+	1.26381i	0.114517	+	0.105685i
$144$	3.44128	+	3.04871i	0.286773	+	0.254059i
$145$	9.98980	−	23.4469i	0.829608	−	1.94716i
$146$	−0.669791	+	1.16011i	−0.0554323	+	0.0960115i
$147$	−3.47806	−	6.02417i	−0.286865	−	0.496865i
$148$	−1.23736	+	0.150242i	−0.101710	+	0.0123499i
$149$	5.80866	+	2.75624i	0.475864	+	0.225800i	0.651491	−	0.758657i	$-0.274144\pi$
$149$	5.80866	+	2.75624i	0.475864	+	0.225800i	−0.175627	+	0.984457i	$0.556195\pi$
$150$	8.67559	−	5.00885i	0.708359	−	0.408971i
$151$	−9.72752	−	6.71442i	−0.791615	−	0.546412i	0.102245	−	0.994759i	$-0.467397\pi$
$151$	−9.72752	−	6.71442i	−0.791615	−	0.546412i	−0.893859	+	0.448347i	$0.852013\pi$
$152$	1.69230	−	0.721022i	0.137264	−	0.0584826i
$153$	2.02252	+	0.328692i	0.163511	+	0.0265732i
$154$	0.123998	−	0.165012i	0.00999206	−	0.0132970i
$155$	0.769815	+	2.02984i	0.0618330	+	0.163040i
$156$	0.593502	−	5.86306i	0.0475182	−	0.469420i
$157$	8.52742	−	22.4850i	0.680562	−	1.79450i	0.0772180	−	0.997014i	$-0.475396\pi$
$157$	8.52742	−	22.4850i	0.680562	−	1.79450i	0.603344	−	0.797481i	$-0.293835\pi$
$158$	−1.44056	−	2.27807i	−0.114605	−	0.181233i
$159$	−5.37837	−	2.29151i	−0.426533	−	0.181729i
$160$	−19.9497	−	12.6154i	−1.57716	−	0.997338i
$161$	0.407515	+	0.0494813i	0.0321167	+	0.00389967i
$162$	0.747252	+	1.75387i	0.0587097	+	0.137797i
$163$	−1.88331	+	5.64120i	−0.147512	+	0.441853i	−0.996205	−	0.0870324i	$-0.972262\pi$
$163$	−1.88331	+	5.64120i	−0.147512	+	0.441853i	0.848693	+	0.528885i	$0.177390\pi$
$164$	−5.60382	−	2.12525i	−0.437585	−	0.165954i
$165$	1.64969	+	0.133177i	0.128429	+	0.0103678i
$166$	−5.55907	+	19.1921i	−0.431467	+	1.48960i
$167$	14.9011	+	0.600494i	1.15308	+	0.0464676i	0.609428	−	0.792841i	$-0.291399\pi$
$167$	14.9011	+	0.600494i	1.15308	+	0.0464676i	0.543655	+	0.839309i	$0.317040\pi$
$168$	0.145998			0.0112640
$169$	11.2608	−	6.49568i	0.866217	−	0.499668i
$170$	−12.5093			−0.959423
$171$	2.63729	+	0.106279i	0.201679	+	0.00812737i
$172$	−4.77605	+	16.4888i	−0.364171	+	1.25726i
$173$	15.6654	+	1.26464i	1.19102	+	0.0961490i	0.660036	−	0.751234i	$-0.270541\pi$
$173$	15.6654	+	1.26464i	1.19102	+	0.0961490i	0.530983	+	0.847383i	$0.321823\pi$
$174$	−14.1868	−	5.38033i	−1.07550	−	0.407882i
$175$	0.348587	−	1.04415i	0.0263507	−	0.0789300i
$176$	−0.931371	−	2.18601i	−0.0702047	−	0.164777i
$177$	6.15245	+	0.747043i	0.462446	+	0.0561512i
$178$	30.2259	+	19.1137i	2.26552	+	1.43263i
$179$	−0.138321	−	0.0589332i	−0.0103386	−	0.00440488i	0.386791	−	0.922167i	$-0.373583\pi$
$179$	−0.138321	−	0.0589332i	−0.0103386	−	0.00440488i	−0.397130	+	0.917762i	$0.629994\pi$
$180$	−2.79736	−	4.42367i	−0.208503	−	0.329721i
$181$	7.28768	−	19.2160i	0.541689	−	1.42832i	−0.332673	−	0.943042i	$-0.607951\pi$
$181$	7.28768	−	19.2160i	0.541689	−	1.42832i	0.874362	−	0.485274i	$-0.161280\pi$
$182$	−0.841458	−	1.16850i	−0.0623730	−	0.0866152i
$183$	1.33389	+	3.51718i	0.0986041	+	0.259998i
$184$	0.820431	−	1.09180i	0.0604830	−	0.0804882i
$185$	−2.41051	−	0.391746i	−0.177224	−	0.0288017i
$186$	1.18898	−	0.506579i	0.0871805	−	0.0371441i
$187$	−0.871561	−	0.601595i	−0.0637348	−	0.0439930i
$188$	−10.4878	+	6.05513i	−0.764901	+	0.441616i
$189$	0.189261	+	0.0898055i	0.0137667	+	0.00653239i
$190$	−15.9960	+	1.94227i	−1.16047	+	0.140907i
$191$	5.00412	+	8.66739i	0.362085	+	0.627150i	0.988304	−	0.152497i	$-0.0487315\pi$
$191$	5.00412	+	8.66739i	0.362085	+	0.627150i	−0.626218	+	0.779648i	$0.715398\pi$
$192$	−2.42851	+	4.20630i	−0.175262	+	0.303563i
$193$	3.71344	−	8.71576i	0.267299	−	0.627374i	−0.731199	−	0.682164i	$-0.761039\pi$
$193$	3.71344	−	8.71576i	0.267299	−	0.627374i	0.998498	+	0.0547904i	$0.0174491\pi$
$194$	−3.69528	−	3.27373i	−0.265305	−	0.235040i
$195$	4.31291	−	10.7103i	0.308854	−	0.766980i
$196$	8.51003	−	7.53923i	0.607859	−	0.538516i
$197$	8.45504	+	25.3259i	0.602397	+	1.80440i	0.594042	+	0.804434i	$0.297531\pi$
$197$	8.45504	+	25.3259i	0.602397	+	1.80440i	0.00835460	+	0.999965i	$0.497341\pi$
$198$	0.0396742	−	0.984505i	0.00281952	−	0.0699657i
$199$	6.47299	−	7.92797i	0.458858	−	0.561999i	−0.492410	−	0.870363i	$-0.663884\pi$
$199$	6.47299	−	7.92797i	0.458858	−	0.561999i	0.951268	+	0.308364i	$0.0997815\pi$
$200$	−2.42847	−	2.74118i	−0.171719	−	0.193830i
$201$	−13.5696	−	2.77026i	−0.957127	−	0.195399i
$202$	−25.1636	+	7.28873i	−1.77051	+	0.512833i
$203$	−1.55891	+	0.591218i	−0.109414	+	0.0414954i
$204$	0.134852	+	3.34633i	0.00944155	+	0.234290i
$205$	−9.38746	−	7.05422i	−0.655648	−	0.492688i
$206$	9.36533	−	1.91195i	0.652514	−	0.133212i
$207$	1.73513	−	0.910666i	0.120600	−	0.0632957i
$208$	−16.4929	+	1.66314i	−1.14358	+	0.115318i
$209$	−1.20790	−	0.633953i	−0.0835519	−	0.0438514i
$210$	−1.22841	−	0.355813i	−0.0847682	−	0.0245534i
$211$	14.3270	−	1.15660i	0.986312	−	0.0796234i	0.423228	−	0.906023i	$-0.360897\pi$
$211$	14.3270	−	1.15660i	0.986312	−	0.0796234i	0.563084	+	0.826400i	$0.309615\pi$
$212$	1.91128	−	9.36208i	0.131267	−	0.642990i
$213$	3.26398	+	6.21899i	0.223644	+	0.426118i
$214$	0.884932	+	1.17763i	0.0604927	+	0.0805011i
$215$	−17.9763	+	28.4273i	−1.22597	+	1.93872i
$216$	0.573562	−	0.395901i	0.0390259	−	0.0269377i
$217$	0.0608811	−	0.128304i	0.00413288	−	0.00870986i
$218$	−7.73288	+	8.05078i	−0.523737	+	0.545268i
$219$	0.506767	+	0.486756i	0.0342441	+	0.0328919i
$220$	0.326062	+	2.68536i	0.0219831	+	0.181047i
$221$	−5.81657	+	4.55519i	−0.391265	+	0.306416i
$222$	−0.175245	+	1.44327i	−0.0117616	+	0.0968659i
$223$	19.9743	−	16.3085i	1.33758	−	1.09210i	0.349703	−	0.936861i	$-0.386283\pi$
$223$	19.9743	−	16.3085i	1.33758	−	1.09210i	0.987877	−	0.155239i	$-0.0496149\pi$
$224$	0.308861	+	1.51290i	0.0206366	+	0.101085i
$225$	−1.46196	−	5.04726i	−0.0974638	−	0.336484i
$226$	−0.723647	−	2.93595i	−0.0481363	−	0.195297i
$227$	1.87401	−	23.2138i	0.124382	−	1.54075i	−0.570301	−	0.821436i	$-0.693174\pi$
$227$	1.87401	−	23.2138i	0.124382	−	1.54075i	0.694684	−	0.719315i	$-0.255544\pi$
$228$	0.692009	+	4.25810i	0.0458294	+	0.282000i
$229$	−7.96368	+	8.98914i	−0.526255	+	0.594019i	−0.950189	−	0.311674i	$-0.899110\pi$
$229$	−7.96368	+	8.98914i	−0.526255	+	0.594019i	0.423934	+	0.905693i	$0.360649\pi$
$230$	−9.56384	+	7.18676i	−0.630621	+	0.473881i
$231$	−0.0684750	−	0.0838667i	−0.00450533	−	0.00551802i
$232$	−0.889753	+	5.47487i	−0.0584152	+	0.359443i
$233$	12.2088	+	3.00920i	0.799826	+	0.197139i	0.617986	−	0.786189i	$-0.287949\pi$
$233$	12.2088	+	3.00920i	0.799826	+	0.197139i	0.181840	+	0.983328i	$0.441795\pi$
$234$	−6.47435	−	2.30877i	−0.423241	−	0.150929i
$235$	−23.0379	+	5.67833i	−1.50283	+	0.370413i
$236$	0.815094	+	10.0968i	0.0530581	+	0.657243i
$237$	−1.34106	+	0.447711i	−0.0871111	+	0.0290820i
$238$	0.566878	+	0.590183i	0.0367453	+	0.0382559i
$239$			16.4424i			1.06357i	0.846880	+	0.531784i	$0.178478\pi$
$239$			16.4424i			1.06357i	−0.846880	+	0.531784i	$0.821522\pi$
$240$	−10.6180	+	10.1987i	−0.685386	+	0.658322i
$241$	15.1941	+	12.4056i	0.978737	+	0.799114i	0.979615	−	0.200886i	$-0.0643821\pi$
$241$	15.1941	+	12.4056i	0.978737	+	0.799114i	−0.000878047		1.00000i	$0.500279\pi$
$242$	9.50887	−	18.1176i	0.611253	−	1.16465i
$243$	0.987050	−	0.160411i	0.0633193	−	0.0102904i
$244$	−5.19633	+	3.28596i	−0.332661	+	0.210362i
$245$	20.1249	−	9.54937i	1.28573	−	0.610087i
$246$	−3.97113	+	5.75318i	−0.253190	+	0.366809i
$247$	−6.73055	+	6.72797i	−0.428254	+	0.428090i
$248$	−0.268390	−	0.388830i	−0.0170428	−	0.0246907i
$249$	9.07675	+	5.24046i	0.575215	+	0.332101i
$250$	0.666653	+	1.40494i	0.0421628	+	0.0888563i
$251$	−25.3697	−	8.46965i	−1.60132	−	0.534600i	−0.630869	−	0.775890i	$-0.717301\pi$
$251$	−25.3697	−	8.46965i	−1.60132	−	0.534600i	−0.970453	+	0.241290i	$0.922430\pi$
$252$	−0.0819397	+	0.332443i	−0.00516172	+	0.0209419i
$253$	−1.01196	+	0.0407807i	−0.0636216	+	0.00256386i
$254$	6.13688	−	0.247308i	0.385062	−	0.0155175i
$255$	−1.57032	+	6.37103i	−0.0983371	+	0.398969i
$256$	19.1278	+	6.38579i	1.19549	+	0.399112i
$257$	−2.43735	−	5.13661i	−0.152038	−	0.320413i	0.813114	−	0.582105i	$-0.197771\pi$
$257$	−2.43735	−	5.13661i	−0.152038	−	0.320413i	−0.965151	+	0.261692i	$0.915719\pi$
$258$	17.3407	+	10.0117i	1.07959	+	0.623299i
$259$	0.0907532	+	0.131479i	0.00563913	+	0.00816969i
$260$	18.5615	+	3.40519i	1.15113	+	0.211181i
$261$	−4.52109	+	6.54994i	−0.279849	+	0.405431i
$262$	2.85292	−	1.35373i	0.176254	−	0.0836336i
$263$	19.3266	−	12.2214i	1.19173	−	0.753605i	0.216823	−	0.976211i	$-0.430431\pi$
$263$	19.3266	−	12.2214i	1.19173	−	0.753605i	0.974909	+	0.222606i	$0.0714563\pi$
$264$	−0.355533	+	0.0577798i	−0.0218816	+	0.00355610i
$265$	8.70020	−	16.5768i	0.534449	−	1.01831i
$266$	0.816518	+	0.666667i	0.0500640	+	0.0408760i
$267$	13.5289	−	12.9947i	0.827957	−	0.795263i
$268$		−	22.6360i		−	1.38272i
$269$	−5.36138	−	5.58179i	−0.326889	−	0.340328i	0.537396	−	0.843330i	$-0.319408\pi$
$269$	−5.36138	−	5.58179i	−0.326889	−	0.340328i	−0.864285	+	0.503002i	$0.832229\pi$
$270$	−5.79074	+	1.93323i	−0.352413	+	0.117653i
$271$	−2.05268	−	25.4270i	−0.124691	−	1.54458i	−0.692499	−	0.721418i	$-0.743490\pi$
$271$	−2.05268	−	25.4270i	−0.124691	−	1.54458i	0.567808	−	0.823161i	$-0.307792\pi$
$272$	9.14680	−	2.25448i	0.554606	−	0.136698i
$273$	−0.700750	+	0.281872i	−0.0424113	+	0.0170596i
$274$	−9.52277	−	2.34715i	−0.575292	−	0.141797i
$275$	−0.435649	+	2.68066i	−0.0262706	+	0.161650i
$276$	2.02560	+	2.48091i	0.121927	+	0.149333i
$277$	−20.3358	+	15.2814i	−1.22186	+	0.918169i	−0.998400	−	0.0565443i	$-0.981992\pi$
$277$	−20.3358	+	15.2814i	−1.22186	+	0.918169i	−0.223461	+	0.974713i	$0.571735\pi$
$278$	8.21219	−	9.26965i	0.492535	−	0.555957i
$279$	−0.108746	−	0.669143i	−0.00651047	−	0.0400605i
$280$	−0.0376204	+	0.466012i	−0.00224825	+	0.0278496i
$281$	0.425537	+	1.72647i	0.0253854	+	0.102993i	0.982268	−	0.187483i	$-0.0600328\pi$
$281$	0.425537	+	1.72647i	0.0253854	+	0.102993i	−0.956883	+	0.290475i	$0.906187\pi$
$282$	3.92998	+	13.5678i	0.234027	+	0.807954i
$283$	3.91059	+	19.1553i	0.232460	+	1.13867i	0.913632	+	0.406542i	$0.133266\pi$
$283$	3.91059	+	19.1553i	0.232460	+	1.13867i	−0.681172	+	0.732124i	$0.738529\pi$
$284$	−8.89199	+	7.26009i	−0.527643	+	0.430807i
$285$	−1.01881	+	8.39063i	−0.0603489	+	0.497018i
$286$	2.51156	+	2.51252i	0.148512	+	0.148569i
$287$	0.0925923	+	0.762566i	0.00546555	+	0.0450129i
$288$	5.31591	+	5.10600i	0.313243	+	0.300874i
$289$	−8.86781	+	9.23237i	−0.521636	+	0.543081i
$290$	20.8292	−	43.8965i	1.22313	−	2.57769i
$291$	−2.13119	+	1.47105i	−0.124933	+	0.0862347i
$292$	−0.613814	+	0.970670i	−0.0359208	+	0.0568042i
$293$	6.01425	+	8.00351i	0.351356	+	0.467570i	0.940174	−	0.340696i	$-0.110663\pi$
$293$	6.01425	+	8.00351i	0.351356	+	0.467570i	−0.588817	+	0.808266i	$0.700406\pi$
$294$	−6.16282	−	11.7423i	−0.359423	−	0.684823i
$295$	−3.96985	+	19.4456i	−0.231134	+	1.13217i
$296$	0.529768	−	0.0427673i	0.0307921	−	0.00248580i
$297$	−0.496429	−	0.143793i	−0.0288058	−	0.00834369i
$298$	10.8532	+	5.69618i	0.628707	+	0.329971i
$299$	−1.82997	+	6.82430i	−0.105830	+	0.394659i
$300$	7.60472	−	3.99127i	0.439059	−	0.230436i
$301$	2.15580	−	0.440110i	0.124258	−	0.0253675i
$302$	−18.0143	−	13.5368i	−1.03660	−	0.778958i
$303$	0.553334	+	13.7308i	0.0317882	+	0.788816i
$304$	11.3462	−	4.30305i	0.650750	−	0.246797i
$305$	−11.5703	+	3.35137i	−0.662512	+	0.191899i
$306$	3.82742	+	0.781373i	0.218799	+	0.0446681i
$307$	−1.66174	−	1.87572i	−0.0948406	−	0.107053i	0.699174	−	0.714951i	$-0.253551\pi$
$307$	−1.66174	−	1.87572i	−0.0948406	−	0.107053i	−0.794015	+	0.607898i	$0.792013\pi$
$308$	0.111918	−	0.137074i	0.00637710	−	0.00781053i
$309$	0.201888	−	5.00979i	0.0114850	−	0.284997i
$310$	1.31058	+	3.92567i	0.0744360	+	0.222963i
$311$	−19.6534	+	17.4114i	−1.11444	+	0.987308i	−0.999981	−	0.00612006i	$-0.998052\pi$
$311$	−19.6534	+	17.4114i	−1.11444	+	0.987308i	−0.114459	+	0.993428i	$0.536513\pi$
$312$	−0.353534	+	2.48782i	−0.0200149	+	0.140845i
$313$	−4.89138	−	4.33338i	−0.276477	−	0.244937i	0.513477	−	0.858103i	$-0.328357\pi$
$313$	−4.89138	−	4.33338i	−0.276477	−	0.244937i	−0.789954	+	0.613166i	$0.789896\pi$
$314$	17.9697	−	42.1764i	1.01409	−	2.38015i
$315$	−0.335420	+	0.580965i	−0.0188988	+	0.0327337i
$316$	−1.15539	−	2.00120i	−0.0649960	−	0.112576i
$317$	−21.0333	+	2.55391i	−1.18135	+	0.143442i	−0.687552	−	0.726135i	$-0.741315\pi$
$317$	−21.0333	+	2.55391i	−1.18135	+	0.143442i	−0.493797	+	0.869577i	$0.664391\pi$
$318$	−10.0692	−	4.77790i	−0.564653	−	0.267931i
$319$	3.56228	−	2.05669i	0.199450	−	0.115152i
$320$	−12.8004	−	8.83546i	−0.715562	−	0.493917i
$321$	0.710856	−	0.302867i	0.0396761	−	0.0169044i
$322$	0.772466	+	0.125538i	0.0430479	+	0.00699596i
$323$	3.24902	−	4.32367i	0.180781	−	0.240575i
$324$	0.579577	+	1.52822i	0.0321987	+	0.0849010i
$325$	16.9483	+	8.46838i	0.940122	+	0.469741i
$326$	−4.02050	+	10.6012i	−0.222675	+	0.587146i
$327$	3.12956	+	4.94900i	0.173065	+	0.273680i
$328$	2.35107	+	1.00170i	0.129816	+	0.0553095i
$329$	1.31189	+	0.829592i	0.0723271	+	0.0457369i
$330$	3.13223	+	0.380322i	0.172424	+	0.0209360i
$331$	3.62698	+	8.51282i	0.199357	+	0.467907i	0.989413	−	0.145127i	$-0.0463591\pi$
$331$	3.62698	+	8.51282i	0.199357	+	0.467907i	−0.790056	+	0.613034i	$0.789949\pi$
$332$	−5.42463	+	16.2487i	−0.297715	+	0.891766i
$333$	0.713060	+	0.270428i	0.0390755	+	0.0148194i
$334$	28.3386	+	2.28773i	1.55062	+	0.125179i
$335$	12.3390	−	42.5992i	0.674152	−	2.32744i
$336$	0.962335	+	0.0387808i	0.0524997	+	0.00211567i
$337$	−7.46936			−0.406882			−0.203441	−	0.979087i	$-0.565212\pi$
$337$	−7.46936			−0.406882			−0.203441	+	0.979087i	$0.565212\pi$
$338$	21.9491	−	11.5090i	1.19387	−	0.626008i
$339$	−1.58613			−0.0861465
$340$	−10.7159	−	0.431838i	−0.581153	−	0.0234197i
$341$	−0.0974801	+	0.336540i	−0.00527884	+	0.0182247i
$342$	5.01554	+	0.404897i	0.271210	+	0.0218943i
$343$	−2.73364	−	1.03673i	−0.147603	−	0.0559782i
$344$	2.31799	−	6.94323i	0.124978	−	0.374354i
$345$	2.45967	+	5.77305i	0.132424	+	0.310810i
$346$	29.7435	+	3.61152i	1.59902	+	0.194156i
$347$	−17.7463	−	11.2221i	−0.952674	−	0.602434i	−0.0348371	−	0.999393i	$-0.511091\pi$
$347$	−17.7463	−	11.2221i	−0.952674	−	0.602434i	−0.917836	+	0.396959i	$0.870066\pi$
$348$	−11.9671	−	5.09872i	−0.641506	−	0.273320i
$349$	−10.7803	−	17.0477i	−0.577057	−	0.912542i	−0.999980	−	0.00637665i	$-0.997970\pi$
$349$	−10.7803	−	17.0477i	−0.577057	−	0.912542i	0.422923	−	0.906166i	$-0.361004\pi$
$350$	0.744166	−	1.96221i	0.0397774	−	0.104884i
$351$	−1.98859	+	3.00757i	−0.106143	+	0.160532i
$352$	−1.35088	−	3.56198i	−0.0720022	−	0.189854i
$353$	16.0534	−	21.3632i	0.854436	−	1.13705i	−0.134822	−	0.990870i	$-0.543046\pi$
$353$	16.0534	−	21.3632i	0.854436	−	1.13705i	0.989258	−	0.146178i	$-0.0466973\pi$
$354$	11.6623	+	1.89531i	0.619843	+	0.100734i
$355$	−20.6915	+	8.81584i	−1.09819	+	0.467896i
$356$	25.2327	+	17.4169i	1.33733	+	0.923093i
$357$	0.371742	−	0.214626i	0.0196747	−	0.0113592i
$358$	−0.258961	−	0.122878i	−0.0136865	−	0.00649432i
$359$	6.97526	−	0.846950i	0.368140	−	0.0447003i	0.0656236	−	0.997844i	$-0.479096\pi$
$359$	6.97526	−	0.846950i	0.368140	−	0.0447003i	0.302516	+	0.953144i	$0.402173\pi$
$360$	1.11589	+	1.93278i	0.0588125	+	0.101866i
$361$	−6.01670	+	10.4212i	−0.316668	+	0.548486i
$362$	15.3572	−	36.0447i	0.807156	−	1.89446i
$363$	−8.03368	−	7.11722i	−0.421659	−	0.373557i
$364$	−0.680484	−	1.03003i	−0.0356670	−	0.0539882i
$365$	−1.68427	+	1.49213i	−0.0881586	+	0.0781017i
$366$	2.27090	+	6.80218i	0.118702	+	0.355556i
$367$	−0.0229027	+	0.568325i	−0.00119551	+	0.0296663i	−0.999677	−	0.0254283i	$-0.991905\pi$
$367$	−0.0229027	+	0.568325i	−0.00119551	+	0.0296663i	0.998481	+	0.0550947i	$0.0175461\pi$
$368$	5.69783	−	6.97858i	0.297020	−	0.363783i
$369$	2.43160	+	2.74471i	0.126584	+	0.142884i
$370$	−4.56164	−	0.931265i	−0.237148	−	0.0484141i
$371$	−1.17635	+	0.340733i	−0.0610729	+	0.0176900i
$372$	1.03601	−	0.392908i	0.0537148	−	0.0203713i
$373$	0.0990516	+	2.45794i	0.00512870	+	0.127267i	0.999725	+	0.0234495i	$0.00746488\pi$
$373$	0.0990516	+	2.45794i	0.00512870	+	0.127267i	−0.994596	+	0.103818i	$0.966894\pi$
$374$	−1.61403	−	1.21287i	−0.0834595	−	0.0627158i
$375$	0.799225	−	0.163163i	0.0412718	−	0.00842570i
$376$	4.57239	−	2.39977i	0.235803	−	0.123759i
$377$	−6.29953	−	27.9957i	−0.324442	−	1.44185i
$378$	0.353624	+	0.185596i	0.0181885	+	0.00954605i
$379$	30.2697	+	8.76772i	1.55485	+	0.450367i	0.940817	−	0.338914i	$-0.110060\pi$
$379$	30.2697	+	8.76772i	1.55485	+	0.450367i	0.614031	+	0.789282i	$0.289547\pi$
$380$	−13.7698	+	1.11161i	−0.706377	+	0.0570246i
$381$	0.644418	−	3.15657i	0.0330145	−	0.161716i
$382$	8.86687	+	16.8944i	0.453668	+	0.864393i
$383$	7.08227	+	9.42479i	0.361887	+	0.481585i	0.943261	−	0.332052i	$-0.107741\pi$
$383$	7.08227	+	9.42479i	0.361887	+	0.481585i	−0.581374	+	0.813637i	$0.697485\pi$
$384$	2.93010	−	4.63358i	0.149526	−	0.236457i
$385$	0.285340	−	0.196956i	0.0145423	−	0.0100378i
$386$	7.74268	−	16.3173i	0.394092	−	0.830531i
$387$	7.27577	−	7.57488i	0.369848	−	0.385053i
$388$	−3.05249	−	2.93196i	−0.154967	−	0.148847i
$389$	3.30892	+	27.2514i	0.167769	+	1.38170i	0.796764	+	0.604290i	$0.206543\pi$
$389$	3.30892	+	27.2514i	0.167769	+	1.38170i	−0.628995	+	0.777409i	$0.716534\pi$
$390$	9.03769	−	20.0707i	0.457641	−	1.01632i
$391$	0.483992	−	3.98604i	0.0244765	−	0.201582i
$392$	−3.75522	+	3.06605i	−0.189667	+	0.154859i
$393$	−0.331324	−	1.62293i	−0.0167131	−	0.0818662i
$394$	14.1617	+	48.8917i	0.713454	+	2.46313i
$395$	−1.08349	−	4.39591i	−0.0545165	−	0.221182i
$396$	0.0679726	−	0.841992i	0.00341575	−	0.0423117i
$397$	5.44948	+	33.5320i	0.273502	+	1.68292i	0.652706	+	0.757611i	$0.273634\pi$
$397$	5.44948	+	33.5320i	0.273502	+	1.68292i	−0.379204	+	0.925313i	$0.623802\pi$
$398$	12.9388	−	14.6049i	0.648563	−	0.732076i
$399$	0.442033	−	0.332166i	0.0221293	−	0.0166291i
$400$	−15.2790	−	18.7134i	−0.763950	−	0.935668i
$401$	−1.30098	+	8.00525i	−0.0649679	+	0.399763i	0.934116	+	0.356969i	$0.116190\pi$
$401$	−1.30098	+	8.00525i	−0.0649679	+	0.399763i	−0.999084	+	0.0427939i	$0.986374\pi$
$402$	−25.6357	−	6.31864i	−1.27859	−	0.315145i
$403$	2.03890	+	1.34811i	0.101565	+	0.0671542i
$404$	−21.8076	+	5.37510i	−1.08497	+	0.267421i
$405$	0.257678	+	3.19192i	0.0128041	+	0.158608i
$406$	−3.01491	+	1.00653i	−0.149628	+	0.0499531i
$407$	−0.273036	−	0.284260i	−0.0135339	−	0.0140903i
$408$		−	1.42805i		−	0.0706990i
$409$	−8.62703	+	8.28637i	−0.426579	+	0.409735i	−0.875027	−	0.484074i	$-0.839156\pi$
$409$	−8.62703	+	8.28637i	−0.426579	+	0.409735i	0.448448	+	0.893809i	$0.351977\pi$
$410$	−17.3404	−	14.1580i	−0.856381	−	0.699214i
$411$	−2.39082	+	4.55532i	−0.117930	+	0.224697i
$412$	8.08867	−	1.31454i	0.398500	−	0.0647626i
$413$	1.09733	−	0.693910i	0.0539961	−	0.0341451i
$414$	3.37511	−	1.60151i	0.165877	−	0.0787098i
$415$	−19.0660	+	27.6219i	−0.935913	+	1.35590i
$416$	−26.5280	+	1.59954i	−1.30064	+	0.0784240i
$417$	−3.69016	−	5.34612i	−0.180708	−	0.261800i
$418$	−2.25222	−	1.30032i	−0.110160	−	0.0636008i
$419$	0.00948492	+	0.0199891i	0.000463369	+	0.000976529i	0.903682	−	0.428204i	$-0.140854\pi$
$419$	0.00948492	+	0.0199891i	0.000463369	+	0.000976529i	−0.903219	+	0.429181i	$0.858802\pi$
$420$	−1.04001	−	0.347208i	−0.0507475	−	0.0169420i
$421$	7.49577	−	30.4115i	0.365321	−	1.48217i	−0.444653	−	0.895703i	$-0.646673\pi$
$421$	7.49577	−	30.4115i	0.365321	−	1.48217i	0.809975	−	0.586465i	$-0.199481\pi$
$422$	27.3799	−	1.10337i	1.33283	−	0.0537113i
$423$	7.40346	−	0.298349i	0.359969	−	0.0145062i
$424$	−0.975063	+	3.95599i	−0.0473532	+	0.192120i
$425$	−10.2131	−	3.40964i	−0.495409	−	0.165392i
$426$	5.74006	+	12.0969i	0.278107	+	0.586098i
$427$	0.682439	+	0.394006i	0.0330255	+	0.0190673i
$428$	0.717410	+	1.03935i	0.0346773	+	0.0502388i
$429$	1.59491	−	0.963741i	0.0770031	−	0.0465298i
$430$	−36.4247	+	52.7703i	−1.75656	+	2.54481i
$431$	−18.3633	+	8.71349i	−0.884528	+	0.419714i	−0.816079	−	0.577941i	$-0.803856\pi$
$431$	−18.3633	+	8.71349i	−0.884528	+	0.419714i	−0.0684495	+	0.997655i	$0.521805\pi$
$432$	3.88576	−	2.45721i	0.186954	−	0.118222i
$433$	−13.5021	+	2.19431i	−0.648871	+	0.105452i	−0.475934	−	0.879481i	$-0.657890\pi$
$433$	−13.5021	+	2.19431i	−0.648871	+	0.105452i	−0.172937	+	0.984933i	$0.555326\pi$
$434$	0.125820	−	0.239730i	0.00603955	−	0.0115074i
$435$	−19.7419	−	16.1187i	−0.946550	−	0.772834i
$436$	−6.90218	+	6.62963i	−0.330554	+	0.317502i
$437$		−	5.17220i		−	0.247420i
$438$	0.927961	+	0.966109i	0.0443397	+	0.0461625i
$439$	−9.88424	+	3.29984i	−0.471749	+	0.157493i	−0.542595	−	0.839994i	$-0.682558\pi$
$439$	−9.88424	+	3.29984i	−0.471749	+	0.157493i	0.0708463	+	0.997487i	$0.477430\pi$
$440$	−0.0928150	−	1.14972i	−0.00442478	−	0.0548108i
$441$	−6.75398	+	1.66471i	−0.321618	+	0.0792718i
$442$	−11.4295	+	8.23056i	−0.543646	+	0.391488i
$443$	6.77506	+	1.66990i	0.321893	+	0.0793394i	0.396951	−	0.917840i	$-0.370068\pi$
$443$	6.77506	+	1.66990i	0.321893	+	0.0793394i	−0.0750585	+	0.997179i	$0.523914\pi$
$444$	−0.199944	+	1.23030i	−0.00948892	+	0.0583877i
$445$	37.9919	+	46.5316i	1.80099	+	2.20581i
$446$	39.3004	−	29.5324i	1.86093	−	1.39840i
$447$	4.26349	−	4.81249i	0.201656	−	0.227623i
$448$	0.163215	+	1.00430i	0.00771120	+	0.0474489i
$449$	−1.24096	+	15.3720i	−0.0585643	+	0.725449i	0.899134	+	0.437674i	$0.144198\pi$
$449$	−1.24096	+	15.3720i	−0.0585643	+	0.725449i	−0.957698	+	0.287775i	$0.907084\pi$
$450$	−2.39739	−	9.72661i	−0.113014	−	0.458517i
$451$	−0.527272	−	1.82036i	−0.0248283	−	0.0857172i
$452$	−0.518549	−	2.54002i	−0.0243905	−	0.119472i
$453$	−9.15569	+	7.47539i	−0.430172	+	0.351225i
$454$	5.35172	−	44.0754i	0.251169	−	2.06856i
$455$	−0.719143	−	2.30937i	−0.0337139	−	0.108265i
$456$	−0.221727	−	1.82609i	−0.0103833	−	0.0855143i
$457$	12.9319	+	12.4212i	0.604928	+	0.581041i	0.931324	−	0.364192i	$-0.118655\pi$
$457$	12.9319	+	12.4212i	0.604928	+	0.581041i	−0.326396	+	0.945233i	$0.605834\pi$
$458$	−15.8598	+	16.5118i	−0.741081	+	0.771547i
$459$	0.878416	−	1.85122i	0.0410009	−	0.0864077i
$460$	−8.44082	+	5.82628i	−0.393555	+	0.271652i
$461$	12.8659	−	20.3458i	0.599224	−	0.947596i	−0.400289	−	0.916389i	$-0.631090\pi$
$461$	12.8659	−	20.3458i	0.599224	−	0.947596i	0.999513	−	0.0312074i	$-0.00993525\pi$
$462$	−0.123998	−	0.165012i	−0.00576892	−	0.00767704i
$463$	−9.31082	−	17.7403i	−0.432711	−	0.824461i	−1.00000		0.000942268i	$-0.999700\pi$
$463$	−9.31082	−	17.7403i	−0.432711	−	0.824461i	0.567289	−	0.823519i	$-0.307992\pi$
$464$	−7.31902	+	35.8510i	−0.339777	+	1.66434i
$465$	2.16387	−	0.174686i	0.100347	−	0.00810085i
$466$	23.0252	+	6.66934i	1.06662	+	0.308951i
$467$	−11.2545	−	5.90684i	−0.520798	−	0.273336i	0.183774	−	0.982969i	$-0.441169\pi$
$467$	−11.2545	−	5.90684i	−0.520798	−	0.273336i	−0.704572	+	0.709633i	$0.748861\pi$
$468$	−5.46645	−	2.20127i	−0.252687	−	0.101754i
$469$	−2.56897	+	1.34830i	−0.118624	+	0.0622586i
$470$	−44.3201	+	9.04801i	−2.04433	+	0.417354i
$471$	−19.2247	−	14.4465i	−0.885829	−	0.665657i
$472$	−0.173921	−	4.31581i	−0.00800538	−	0.198651i
$473$	−5.07563	+	1.92493i	−0.233378	+	0.0885084i
$474$	−2.58891	+	0.749888i	−0.118913	+	0.0344435i
$475$	−13.5892	−	2.77425i	−0.623515	−	0.127292i
$476$	0.465234	+	0.525141i	0.0213240	+	0.0240698i
$477$	−3.69739	+	4.52848i	−0.169292	+	0.207345i
$478$	−1.26218	+	31.3206i	−0.0577307	+	1.43257i
$479$	−5.74167	−	17.1984i	−0.262344	−	0.785815i	−0.994505	−	0.104685i	$-0.966617\pi$
$479$	−5.74167	−	17.1984i	−0.262344	−	0.785815i	0.732162	−	0.681131i	$-0.238512\pi$
$480$	−17.6677	+	15.6522i	−0.806417	+	0.714423i
$481$	−2.46018	+	1.22807i	−0.112174	+	0.0559953i
$482$	27.9905	+	24.7974i	1.27493	+	1.12949i
$483$	0.160906	−	0.377659i	0.00732146	−	0.0171841i
$484$	8.77107	−	15.1919i	0.398685	−	0.690543i
$485$	−4.14632	−	7.18163i	−0.188275	−	0.326101i
$486$	1.89252	−	0.229793i	0.0858464	−	0.0104236i
$487$	−16.5307	−	7.84394i	−0.749080	−	0.355443i	0.0155786	−	0.999879i	$-0.495041\pi$
$487$	−16.5307	−	7.84394i	−0.749080	−	0.355443i	−0.764658	+	0.644436i	$0.777092\pi$
$488$	2.27036	−	1.31079i	0.102775	−	0.0593369i
$489$	4.89451	+	3.37843i	0.221337	+	0.152778i
$490$	39.0684	−	16.6455i	1.76493	−	0.751966i
$491$	−25.9484	−	4.21703i	−1.17103	−	0.190312i	−0.456377	−	0.889786i	$-0.650853\pi$
$491$	−25.9484	−	4.21703i	−1.17103	−	0.190312i	−0.714657	+	0.699475i	$0.753417\pi$
$492$	−3.60042	+	4.79129i	−0.162319	+	0.216008i
$493$	5.78289	+	15.2482i	0.260448	+	0.686745i
$494$	−13.3373	+	12.2993i	−0.600073	+	0.553370i
$495$	0.586893	−	1.54751i	0.0263789	−	0.0695554i
$496$	−1.66579	−	2.63424i	−0.0747963	−	0.118281i
$497$	1.35359	+	0.576712i	0.0607169	+	0.0258691i
$498$	16.8878	+	10.6792i	0.756759	+	0.478545i
$499$	−38.3632	−	4.65814i	−1.71737	−	0.208527i	−0.798204	−	0.602387i	$-0.794216\pi$
$499$	−38.3632	−	4.65814i	−1.71737	−	0.208527i	−0.919170	+	0.393860i	$0.871139\pi$
$500$	0.522578	+	1.22654i	0.0233704	+	0.0548523i
$501$	4.72254	−	14.1457i	0.210987	−	0.631984i
$502$	−47.6759	−	18.0811i	−2.12788	−	0.806998i
$503$	2.93990	+	0.237333i	0.131084	+	0.0105822i	0.145834	−	0.989309i	$-0.453413\pi$
$503$	2.93990	+	0.237333i	0.131084	+	0.0105822i	−0.0147506	+	0.999891i	$0.504695\pi$
$504$	0.0406191	−	0.140233i	0.00180932	−	0.00624649i
$505$	−43.9702	−	1.77194i	−1.95665	−	0.0788503i
$506$	−1.93079			−0.0858341
$507$	−3.10626	−	12.6234i	−0.137954	−	0.560626i
$508$	5.26560			0.233623
$509$	−28.0857	−	1.13181i	−1.24488	−	0.0501668i	−0.590939	−	0.806716i	$-0.701243\pi$
$509$	−28.0857	−	1.13181i	−1.24488	−	0.0501668i	−0.653937	+	0.756549i	$0.726884\pi$
$510$	−3.48032	+	12.0154i	−0.154111	+	0.532053i
$511$	0.146723	+	0.0118447i	0.00649063	+	0.000523978i
$512$	25.6937	+	9.74434i	1.13551	+	0.430643i
$513$	0.835824	−	2.50360i	0.0369025	−	0.110537i
$514$	−4.24853	−	9.97168i	−0.187395	−	0.439832i
$515$	15.9388	+	1.93532i	0.702347	+	0.0852804i
$516$	14.5091	+	9.17497i	0.638726	+	0.403906i
$517$	−3.52304	−	1.50103i	−0.154943	−	0.0660151i
$518$	0.162780	+	0.257417i	0.00715216	+	0.0113102i
$519$	5.57310	−	14.6951i	0.244632	−	0.645042i
$520$	−7.84982	−	1.76951i	−0.344237	−	0.0775980i
$521$	7.69302	+	20.2848i	0.337037	+	0.888694i	0.991204	+	0.132344i	$0.0422503\pi$
$521$	7.69302	+	20.2848i	0.337037	+	0.888694i	−0.654167	+	0.756351i	$0.726980\pi$
$522$	−9.11490	+	12.1297i	−0.398949	+	0.530904i
$523$	−6.69288	−	1.08770i	−0.292659	−	0.0475618i	0.0123090	−	0.999924i	$-0.496082\pi$
$523$	−6.69288	−	1.08770i	−0.292659	−	0.0475618i	−0.304968	+	0.952362i	$0.598646\pi$
$524$	2.49065	−	1.06116i	0.108804	−	0.0463572i
$525$	−0.905938	−	0.625324i	−0.0395384	−	0.0272914i
$526$	37.7529	−	21.7967i	1.64611	−	0.950379i
$527$	−1.25498	−	0.595497i	−0.0546680	−	0.0259403i
$528$	−2.35882	+	0.286413i	−0.102655	+	0.0124645i
$529$	9.58001	+	16.5931i	0.416522	+	0.721437i
$530$	17.8453	−	30.9089i	0.775148	−	1.34260i
$531$	2.42927	−	5.70170i	0.105421	−	0.247433i
$532$	0.676444	+	0.599277i	0.0293276	+	0.0259820i
$533$	−13.2184	−	0.268769i	−0.572555	−	0.0116417i
$534$	26.7684	−	23.7147i	1.15838	−	1.02624i
$535$	0.783555	+	2.34703i	0.0338760	+	0.101471i
$536$	−0.388652	+	9.64430i	−0.0167872	+	0.416570i
$537$	−0.0950899	+	0.116464i	−0.00410343	+	0.00502579i
$538$	−9.78427	−	11.0442i	−0.421830	−	0.476148i
$539$	3.52251	+	0.719125i	0.151725	+	0.0309749i
$540$	−5.02729	+	1.45617i	−0.216340	+	0.0626637i
$541$	6.67486	−	2.53144i	0.286975	−	0.108835i	−0.206917	−	0.978358i	$-0.566343\pi$
$541$	6.67486	−	2.53144i	0.286975	−	0.108835i	0.493892	+	0.869523i	$0.335574\pi$
$542$	−1.95822	−	48.5927i	−0.0841127	−	2.08724i
$543$	−16.4298	−	12.3462i	−0.705070	−	0.529825i
$544$	14.7982	−	3.02107i	0.634466	−	0.129527i
$545$	−16.6032	+	8.71403i	−0.711203	+	0.373268i
$546$	−1.35648	+	0.483137i	−0.0580519	+	0.0206764i
$547$	−4.68516	−	2.45896i	−0.200323	−	0.105138i	0.361579	−	0.932342i	$-0.382238\pi$
$547$	−4.68516	−	2.45896i	−0.200323	−	0.105138i	−0.561902	+	0.827204i	$0.689930\pi$
$548$	−8.07651	−	2.33939i	−0.345012	−	0.0999338i
$549$	3.74943	−	0.302685i	0.160022	−	0.0129183i
$550$	−1.03563	+	5.07287i	−0.0441596	+	0.216308i
$551$	9.76226	+	18.6004i	0.415886	+	0.792405i
$552$	−0.820431	−	1.09180i	−0.0349199	−	0.0464699i
$553$	−0.158296	+	0.250326i	−0.00673144	+	0.0106449i
$554$	−39.9102	+	27.5480i	−1.69562	+	1.17040i
$555$	−1.04692	+	2.20635i	−0.0444394	+	0.0936542i
$556$	7.35485	−	7.65721i	0.311915	−	0.324738i
$557$	−6.47203	−	6.21647i	−0.274229	−	0.263400i	0.542975	−	0.839749i	$-0.317298\pi$
$557$	−6.47203	−	6.21647i	−0.274229	−	0.263400i	−0.817204	+	0.576348i	$0.804477\pi$
$558$	−0.155782	−	1.28298i	−0.00659477	−	0.0543129i
$559$	2.27926	+	37.8009i	0.0964025	+	1.59881i
$560$	−0.371758	+	3.06170i	−0.0157096	+	0.129380i
$561$	−0.820326	+	0.669776i	−0.0346342	+	0.0282779i
$562$	0.678063	+	3.32137i	0.0286023	+	0.140104i
$563$	3.99552	+	13.7941i	0.168391	+	0.581353i	0.999675	+	0.0255047i	$0.00811929\pi$
$563$	3.99552	+	13.7941i	0.168391	+	0.581353i	−0.831284	+	0.555848i	$0.812394\pi$
$564$	2.89818	+	11.7584i	0.122035	+	0.495116i
$565$	0.408710	−	5.06278i	0.0171946	−	0.212993i
$566$	5.97873	+	36.7886i	0.251305	+	1.54634i
$567$	0.138916	−	0.156803i	0.00583391	−	0.00658512i
$568$	3.91317	−	2.94056i	0.164193	−	0.123383i
$569$	−22.9074	−	28.0565i	−0.960330	−	1.17619i	−0.984305	−	0.176478i	$-0.943530\pi$
$569$	−22.9074	−	28.0565i	−0.960330	−	1.17619i	0.0239749	−	0.999713i	$-0.492368\pi$
$570$	−2.58479	+	15.9049i	−0.108265	+	0.666181i
$571$	−31.0054	−	7.64214i	−1.29754	−	0.319814i	−0.470718	−	0.882284i	$-0.656005\pi$
$571$	−31.0054	−	7.64214i	−1.29754	−	0.319814i	−0.826818	+	0.562470i	$0.809851\pi$
$572$	2.06475	+	2.23902i	0.0863317	+	0.0936180i
$573$	9.71742	−	2.39513i	0.405951	−	0.100058i
$574$	0.117839	+	1.45970i	0.00491851	+	0.0609266i
$575$	−9.76718	+	3.26076i	−0.407319	+	0.135983i
$576$	3.36457	+	3.50289i	0.140190	+	0.145954i
$577$			9.00430i			0.374854i	0.982279	+	0.187427i	$0.0600148\pi$
$577$			9.00430i			0.374854i	−0.982279	+	0.187427i	$0.939985\pi$
$578$	−17.6008	+	16.9058i	−0.732095	+	0.703187i
$579$	−7.33850	−	5.99170i	−0.304978	−	0.249007i
$580$	19.3584	−	36.8843i	0.803812	−	1.53154i
$581$	2.16718	−	0.352202i	0.0899100	−	0.0146118i
$582$	−4.17257	+	2.63857i	−0.172958	+	0.109372i
$583$	2.72979	−	1.29530i	0.113056	−	0.0536459i
$584$	0.278187	−	0.403024i	0.0115115	−	0.0166773i
$585$	−9.08750	−	7.12241i	−0.375722	−	0.294476i
$586$	10.8420	+	15.7073i	0.447879	+	0.648865i
$587$	−4.92868	−	2.84557i	−0.203428	−	0.117449i	0.394825	−	0.918756i	$-0.370805\pi$
$587$	−4.92868	−	2.84557i	−0.203428	−	0.117449i	−0.598254	+	0.801307i	$0.704138\pi$
$588$	−4.87393	−	10.2716i	−0.200997	−	0.423593i
$589$	−1.69724	−	0.566623i	−0.0699337	−	0.0233473i
$590$	−9.05477	+	36.7367i	−0.372779	+	1.51242i
$591$	26.6784	−	1.07510i	1.09740	−	0.0442238i
$592$	3.50329	−	0.141178i	0.143984	−	0.00580237i
$593$	−8.78365	+	35.6367i	−0.360701	+	1.46342i	0.457871	+	0.889019i	$0.348612\pi$
$593$	−8.78365	+	35.6367i	−0.360701	+	1.46342i	−0.818572	+	0.574403i	$0.805234\pi$
$594$	−0.934597	−	0.312014i	−0.0383470	−	0.0128021i
$595$	0.589277	+	1.24187i	0.0241580	+	0.0509119i
$596$	9.10057	+	5.25421i	0.372774	+	0.215221i
$597$	−5.81406	−	8.42312i	−0.237954	−	0.344735i
$598$	−4.00971	+	12.8589i	−0.163969	+	0.525841i
$599$	−18.3555	+	26.5926i	−0.749986	+	1.08654i	0.243197	+	0.969977i	$0.421804\pi$
$599$	−18.3555	+	26.5926i	−0.749986	+	1.08654i	−0.993183	+	0.116566i	$0.962811\pi$
$600$	−3.30859	+	1.56995i	−0.135073	+	0.0640928i
$601$	−12.4362	+	7.86419i	−0.507284	+	0.320787i	−0.763473	−	0.645840i	$-0.776507\pi$
$601$	−12.4362	+	7.86419i	−0.507284	+	0.320787i	0.256189	+	0.966627i	$0.417533\pi$
$602$	4.14031	−	0.672866i	0.168746	−	0.0274240i
$603$	−6.43618	+	12.2631i	−0.262102	+	0.499393i
$604$	−14.9643	−	12.2180i	−0.608890	−	0.497143i
$605$	24.7877	−	23.8089i	1.00776	−	0.967968i
$606$			26.1980i			1.06422i
$607$	−27.5992	−	28.7338i	−1.12022	−	1.16627i	−0.984475	−	0.175526i	$-0.943837\pi$
$607$	−27.5992	−	28.7338i	−1.12022	−	1.16627i	−0.135743	−	0.990744i	$-0.543342\pi$
$608$	18.4538	−	6.16077i	0.748399	−	0.249852i
$609$	0.134159	+	1.66185i	0.00543638	+	0.0673416i
$610$	−22.2971	+	5.49575i	−0.902785	+	0.222517i
$611$	−17.3131	+	20.3460i	−0.700414	+	0.823111i
$612$	3.25172	+	0.801478i	0.131443	+	0.0323978i
$613$	−1.24221	+	7.64365i	−0.0501725	+	0.308724i	−0.999992	−	0.00407555i	$-0.998703\pi$
$613$	−1.24221	+	7.64365i	−0.0501725	+	0.308724i	0.949819	+	0.312800i	$0.101267\pi$
$614$	−3.02142	−	3.70057i	−0.121935	−	0.149343i
$615$	−9.38746	+	7.05422i	−0.378539	+	0.284453i
$616$	−0.0500371	+	0.0564802i	−0.00201605	+	0.00227565i
$617$	−4.67227	−	28.7496i	−0.188098	−	1.15742i	−0.893653	−	0.448760i	$-0.851866\pi$
$617$	−4.67227	−	28.7496i	−0.188098	−	1.15742i	0.705554	−	0.708656i	$-0.250698\pi$
$618$	0.769140	−	9.52751i	0.0309393	−	0.383253i
$619$	−7.82794	−	31.7592i	−0.314631	−	1.27651i	−0.888998	−	0.457912i	$-0.848598\pi$
$619$	−7.82794	−	31.7592i	−0.314631	−	1.27651i	0.574366	−	0.818598i	$-0.305249\pi$
$620$	0.987171	+	3.40811i	0.0396457	+	0.136873i
$621$	−0.391968	−	1.91999i	−0.0157291	−	0.0770464i
$622$	−38.7737	+	31.6578i	−1.55468	+	1.26936i
$623$	0.473677	−	3.90108i	0.0189775	−	0.156294i
$624$	−2.99113	+	16.3044i	−0.119741	+	0.652699i
$625$	−2.85208	−	23.4890i	−0.114083	−	0.939559i
$626$	−8.98480	−	8.63002i	−0.359105	−	0.344925i
$627$	−0.944981	+	0.983829i	−0.0377389	+	0.0392903i
$628$	16.8494	−	35.5094i	0.672365	−	1.41698i
$629$	1.28603	−	0.887686i	0.0512776	−	0.0353944i
$630$	−0.683529	+	1.08092i	−0.0272325	+	0.0430647i
$631$	6.41091	+	8.53137i	0.255214	+	0.339628i	0.908806	−	0.417219i	$-0.136995\pi$
$631$	6.41091	+	8.53137i	0.255214	+	0.339628i	−0.653592	+	0.756847i	$0.726739\pi$
$632$	0.457907	+	0.872468i	0.0182145	+	0.0347049i
$633$	2.87509	−	14.0831i	0.114275	−	0.559755i
$634$	−40.2618	+	3.25027i	−1.59900	+	0.129085i
$635$	9.90944	+	2.87030i	0.393244	+	0.113905i
$636$	−8.46069	−	4.44051i	−0.335488	−	0.176078i
$637$	12.1046	−	21.9663i	0.479602	−	0.870335i
$638$	6.94357	−	3.64427i	0.274899	−	0.144278i
$639$	6.88154	−	1.40488i	0.272230	−	0.0555761i
$640$	14.0350	+	10.5466i	0.554782	+	0.416891i
$641$	1.04046	+	25.8189i	0.0410959	+	1.01978i	0.879844	+	0.475263i	$0.157647\pi$
$641$	1.04046	+	25.8189i	0.0410959	+	1.01978i	−0.838748	+	0.544520i	$0.816712\pi$
$642$	1.37734	−	0.522356i	0.0543592	−	0.0206157i
$643$	47.8131	−	13.8492i	1.88556	−	0.546160i	0.889563	−	0.456813i	$-0.151009\pi$
$643$	47.8131	−	13.8492i	1.88556	−	0.546160i	0.996001	−	0.0893467i	$-0.0284779\pi$
$644$	0.657388	+	0.134207i	0.0259047	+	0.00528848i
$645$	22.3036	+	25.1755i	0.878202	+	0.991285i
$646$	6.52088	−	7.98662i	0.256560	−	0.314229i
$647$	−1.73590	+	43.0758i	−0.0682451	+	1.69348i	0.496355	+	0.868120i	$0.334671\pi$
$647$	−1.73590	+	43.0758i	−0.0682451	+	1.69348i	−0.564600	+	0.825365i	$0.690970\pi$
$648$	−0.220695	−	0.661063i	−0.00866973	−	0.0259690i
$649$	−2.39760	+	2.12409i	−0.0941139	+	0.0833777i
$650$	31.6343	+	17.4322i	1.24080	+	0.683747i
$651$	−0.106300	−	0.0941739i	−0.00416624	−	0.00369097i
$652$	−3.81007	+	8.94256i	−0.149214	+	0.350218i
$653$	8.68033	−	15.0348i	0.339687	−	0.588356i	−0.644686	−	0.764447i	$-0.723012\pi$
$653$	8.68033	−	15.0348i	0.339687	−	0.588356i	0.984374	+	0.176091i	$0.0563454\pi$
$654$	5.58150	+	9.66744i	0.218254	+	0.378027i
$655$	5.26564	−	0.639365i	0.205746	−	0.0249820i
$656$	15.2309	+	7.22713i	0.594665	+	0.282172i
$657$	0.608529	−	0.351335i	0.0237410	−	0.0137069i
$658$	2.43531	+	1.68097i	0.0949382	+	0.0655311i
$659$	−13.2443	+	5.64285i	−0.515923	+	0.219814i	−0.634204	−	0.773166i	$-0.718672\pi$
$659$	−13.2443	+	5.64285i	−0.515923	+	0.219814i	0.118281	+	0.992980i	$0.462262\pi$
$660$	2.67005	+	0.433926i	0.103932	+	0.0168905i
$661$	10.3197	−	13.7330i	0.401389	−	0.534151i	−0.552817	−	0.833303i	$-0.686447\pi$
$661$	10.3197	−	13.7330i	0.401389	−	0.534151i	0.954206	+	0.299151i	$0.0967036\pi$
$662$	6.25545	+	16.4943i	0.243125	+	0.641068i
$663$	2.75707	+	6.85426i	0.107076	+	0.266197i
$664$	2.59020	−	6.82979i	0.100519	−	0.265047i
$665$	0.946345	+	1.49652i	0.0366977	+	0.0580328i
$666$	1.33753	+	0.569868i	0.0518282	+	0.0220819i
$667$	13.1815	+	8.33548i	0.510390	+	0.322751i
$668$	24.1969	+	2.93803i	0.936205	+	0.113676i
$669$	−10.1074	−	23.7230i	−0.390776	−	0.917185i
$670$	26.7743	−	80.1989i	1.03438	−	3.09835i
$671$	−1.81780	−	0.689402i	−0.0701755	−	0.0266141i
$672$	1.53910	+	0.124249i	0.0593721	+	0.00479301i
$673$	−1.25178	+	4.32163i	−0.0482524	+	0.166587i	−0.981026	−	0.193876i	$-0.937894\pi$
$673$	−1.25178	+	4.32163i	−0.0482524	+	0.166587i	0.932774	+	0.360463i	$0.117381\pi$
$674$	−14.2282	−	0.573376i	−0.548049	−	0.0220856i
$675$	−5.25473			−0.202255
$676$	19.1996	−	9.10132i	0.738447	−	0.350051i
$677$	25.5801			0.983124			0.491562	−	0.870843i	$-0.336426\pi$
$677$	25.5801			0.983124			0.491562	+	0.870843i	$0.336426\pi$
$678$	−3.02137	−	0.121757i	−0.116035	−	0.00467605i
$679$	−0.150929	+	0.521067i	−0.00579212	+	0.0199967i
$680$	4.55821	+	0.367977i	0.174799	+	0.0141113i
$681$	−21.7758	−	8.25849i	−0.834452	−	0.316466i
$682$	−0.211521	+	0.633583i	−0.00809957	+	0.0242612i
$683$	2.92301	+	6.86055i	0.111846	+	0.262512i	0.966491	−	0.256701i	$-0.0826356\pi$
$683$	2.92301	+	6.86055i	0.111846	+	0.262512i	−0.854645	+	0.519213i	$0.826225\pi$
$684$	4.28251	+	0.519991i	0.163746	+	0.0198824i
$685$	−13.9241	−	8.80510i	−0.532014	−	0.336425i
$686$	−5.12764	−	2.18469i	−0.195774	−	0.0834117i
$687$	6.41860	+	10.1502i	0.244885	+	0.387254i
$688$	17.1232	−	45.1502i	0.652816	−	1.72133i
$689$	−2.95761	−	20.8702i	−0.112676	−	0.795091i
$690$	4.24219	+	11.1857i	0.161497	+	0.425833i
$691$	21.2949	−	28.3384i	0.810096	−	1.07804i	−0.185346	−	0.982673i	$-0.559341\pi$
$691$	21.2949	−	28.3384i	0.810096	−	1.07804i	0.995442	−	0.0953688i	$-0.0304030\pi$
$692$	25.3547	+	4.12053i	0.963840	+	0.156639i
$693$	−0.0996064	+	0.0424383i	−0.00378373	+	0.00161210i
$694$	−32.9431	−	22.7390i	−1.25050	−	0.863159i
$695$	18.0152	−	10.4011i	0.683357	−	0.394536i
$696$	5.01117	+	2.37783i	0.189948	+	0.0901314i
$697$	7.45890	−	0.905674i	0.282526	−	0.0343049i
$698$	−19.2265	−	33.3012i	−0.727733	−	1.26047i
$699$	6.28710	−	10.8896i	0.237800	−	0.411881i
$700$	0.705217	−	1.65520i	0.0266547	−	0.0625608i
$701$	24.3592	+	21.5803i	0.920033	+	0.815078i	0.983126	−	0.182930i	$-0.0585580\pi$
$701$	24.3592	+	21.5803i	0.920033	+	0.815078i	−0.0630931	+	0.998008i	$0.520097\pi$
$702$	−4.01889	+	5.57639i	−0.151683	+	0.210467i
$703$	1.50666	−	1.33479i	0.0568248	−	0.0503424i
$704$	−0.794923	−	2.38109i	−0.0299598	−	0.0897406i
$705$	−0.955404	+	23.7081i	−0.0359826	+	0.892899i
$706$	32.2196	−	39.4618i	1.21260	−	1.48517i
$707$	1.90897	+	2.15479i	0.0717944	+	0.0810391i
$708$	9.92489	+	2.02618i	0.373000	+	0.0761485i
$709$	31.6849	−	9.17764i	1.18995	−	0.344673i	0.376561	−	0.926392i	$-0.377107\pi$
$709$	31.6849	−	9.17764i	1.18995	−	0.344673i	0.813390	+	0.581719i	$0.197619\pi$
$710$	−40.0915	+	15.2047i	−1.50461	+	0.570622i
$711$	0.0569287	+	1.41267i	0.00213499	+	0.0529793i
$712$	−10.4516	−	7.85386i	−0.391690	−	0.294336i
$713$	−1.30160	+	0.265724i	−0.0487453	+	0.00995143i
$714$	0.724597	−	0.380298i	0.0271174	−	0.0142323i
$715$	2.66521	+	5.33916i	0.0996730	+	0.199673i
$716$	−0.217593	−	0.114201i	−0.00813182	−	0.00426791i
$717$	15.7932	+	4.57456i	0.589808	+	0.170840i
$718$	13.3520	−	1.07788i	0.498292	−	0.0402263i
$719$	−7.69344	+	37.6850i	−0.286917	+	1.40541i	0.539325	+	0.842098i	$0.318679\pi$
$719$	−7.69344	+	37.6850i	−0.286917	+	1.40541i	−0.826242	+	0.563315i	$0.809526\pi$
$720$	6.84192	+	13.0362i	0.254983	+	0.485830i
$721$	−0.630982	−	0.839685i	−0.0234990	−	0.0312715i
$722$	−12.2610	+	19.3892i	−0.456308	+	0.721593i
$723$	16.1430	−	11.1427i	0.600366	−	0.414403i
$724$	14.3998	−	30.3470i	0.535165	−	1.12784i
$725$	28.9705	−	30.1615i	1.07594	−	1.12017i
$726$	−14.7568	−	14.1741i	−0.547676	−	0.526050i
$727$	−3.97152	−	32.7084i	−0.147295	−	1.21309i	−0.859508	−	0.511123i	$-0.829230\pi$
$727$	−3.97152	−	32.7084i	−0.147295	−	1.21309i	0.712212	−	0.701964i	$-0.247693\pi$
$728$	0.272241	+	0.450537i	0.0100899	+	0.0166980i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	−3.32285	+	2.71303i	−0.122984	+	0.100414i
$731$	−4.30485	−	21.0866i	−0.159221	−	0.779915i
$732$	1.71051	+	5.90538i	0.0632224	+	0.218269i
$733$	10.7155	+	43.4746i	0.395787	+	1.60577i	0.743881	+	0.668312i	$0.232983\pi$
$733$	10.7155	+	43.4746i	0.395787	+	1.60577i	−0.348094	+	0.937460i	$0.613171\pi$
$734$	−0.0872535	+	1.08083i	−0.00322059	+	0.0398941i
$735$	−3.57325	−	21.9871i	−0.131801	−	0.811007i
$736$	9.57809	−	10.8114i	0.353053	−	0.398515i
$737$	5.72234	−	4.30006i	0.210785	−	0.158395i
$738$	4.42120	+	5.41498i	0.162746	+	0.199328i
$739$	−0.913076	+	5.61838i	−0.0335881	+	0.206676i	−0.998420	−	0.0561919i	$-0.982104\pi$
$739$	−0.913076	+	5.61838i	−0.0335881	+	0.206676i	0.964832	+	0.262868i	$0.0846682\pi$
$740$	−3.87551	−	0.955227i	−0.142467	−	0.0351148i
$741$	4.58978	+	8.33665i	0.168610	+	0.306255i
$742$	−2.26695	+	0.558752i	−0.0832222	+	0.0205124i
$743$	2.77512	+	34.3760i	0.101809	+	1.26113i	0.822857	+	0.568249i	$0.192379\pi$
$743$	2.77512	+	34.3760i	0.101809	+	1.26113i	−0.721048	+	0.692886i	$0.756339\pi$
$744$	−0.448149	+	0.149614i	−0.0164299	+	0.00548512i
$745$	14.2624	+	14.8488i	0.522536	+	0.544017i
$746$			4.68967i			0.171701i
$747$	7.55887	−	7.26039i	0.276565	−	0.265644i
$748$	−1.34077	−	1.09470i	−0.0490232	−	0.0400262i
$749$	0.0752237	−	0.143327i	0.00274861	−	0.00523705i
$750$	1.53495	−	0.249453i	0.0560483	−	0.00910874i
$751$	8.16610	−	5.16393i	0.297985	−	0.188434i	−0.377103	−	0.926171i	$-0.623080\pi$
$751$	8.16610	−	5.16393i	0.297985	−	0.188434i	0.675088	+	0.737737i	$0.264105\pi$
$752$	30.7761	−	14.6034i	1.12229	−	0.532532i
$753$	−15.1935	+	22.0117i	−0.553684	+	0.802149i
$754$	−9.85073	−	53.8119i	−0.358743	−	1.95971i
$755$	−21.5016	−	31.1504i	−0.782523	−	1.13368i
$756$	0.296520	+	0.171196i	0.0107843	+	0.00622634i
$757$	7.92564	+	16.7029i	0.288062	+	0.607078i	0.994964	−	0.100234i	$-0.0319590\pi$
$757$	7.92564	+	16.7029i	0.288062	+	0.607078i	−0.706902	+	0.707312i	$0.749908\pi$
$758$	56.9868	+	19.0250i	2.06985	+	0.691019i
$759$	−0.242375	+	0.983355i	−0.00879766	+	0.0356935i
$760$	5.88585	−	0.237192i	0.213502	−	0.00860384i
$761$	52.5278	−	2.11680i	1.90413	−	0.0767338i	0.939845	−	0.341600i	$-0.110969\pi$
$761$	52.5278	−	2.11680i	1.90413	−	0.0767338i	0.964285	+	0.264866i	$0.0853279\pi$
$762$	1.46984	−	5.96339i	0.0532468	−	0.216031i
$763$	1.16352	+	0.388440i	0.0421223	+	0.0140625i
$764$	7.01245	+	14.7784i	0.253702	+	0.534665i
$765$	5.68260	+	3.28085i	0.205455	+	0.118619i
$766$	12.7673	+	18.4967i	0.461303	+	0.668313i
$767$	9.16714	+	20.3790i	0.331006	+	0.735842i
$768$	11.4554	−	16.5959i	0.413359	−	0.598854i
$769$	−42.1723	+	20.0110i	−1.52077	+	0.721614i	−0.991892	−	0.127083i	$-0.959438\pi$
$769$	−42.1723	+	20.0110i	−1.52077	+	0.721614i	−0.528878	+	0.848698i	$0.677387\pi$
$770$	0.558655	−	0.353272i	0.0201325	−	0.0127310i
$771$	−5.61192	+	0.912025i	−0.202108	+	0.0328458i
$772$	7.19594	−	13.7107i	0.258988	−	0.493460i
$773$	−6.20156	−	5.06341i	−0.223055	−	0.182118i	0.514328	−	0.857593i	$-0.328041\pi$
$773$	−6.20156	−	5.06341i	−0.223055	−	0.182118i	−0.737383	+	0.675475i	$0.763939\pi$
$774$	14.4409	−	13.8707i	0.519067	−	0.498570i
$775$			3.56229i			0.127961i
$776$	1.25020	+	1.30160i	0.0448796	+	0.0467246i
$777$	0.151537	−	0.0505904i	0.00543635	−	0.00181492i
$778$	4.21114	+	52.1644i	0.150977	+	1.87018i
$779$	9.39728	−	2.31622i	0.336693	−	0.0829873i
$780$	8.43487	−	16.8812i	0.302017	−	0.604445i
$781$	−3.52450	−	0.868712i	−0.126117	−	0.0310850i
$782$	1.22793	−	7.55573i	0.0439106	−	0.270192i
$783$	5.03349	+	6.16490i	0.179882	+	0.220316i
$784$	−25.5668	+	19.2122i	−0.913099	+	0.686149i
$785$	51.0656	−	57.6412i	1.82261	−	2.05730i
$786$	−0.506548	−	3.11691i	−0.0180680	−	0.111177i
$787$	−1.69882	+	21.0436i	−0.0605563	+	0.750124i	0.893223	+	0.449615i	$0.148439\pi$
$787$	−1.69882	+	21.0436i	−0.0605563	+	0.750124i	−0.953779	+	0.300509i	$0.902843\pi$
$788$	10.4436	+	42.3712i	0.372037	+	1.50941i
$789$	−6.36189	−	21.9638i	−0.226489	−	0.781932i
$790$	−1.72647	−	8.45682i	−0.0614251	−	0.300880i
$791$	−0.257380	+	0.210144i	−0.00915138	+	0.00747187i
$792$	−0.0434170	+	0.357571i	−0.00154276	+	0.0127057i
$793$	−8.36645	+	10.6748i	−0.297101	+	0.379072i
$794$	7.80653	+	64.2925i	0.277043	+	2.28166i
$795$	−13.5018	−	12.9687i	−0.478860	−	0.459951i
$796$	11.5880	−	12.0644i	0.410726	−	0.427611i
$797$	5.77163	−	12.1634i	0.204441	−	0.430851i	−0.775170	−	0.631753i	$-0.782336\pi$
$797$	5.77163	−	12.1634i	0.204441	−	0.430851i	0.979611	+	0.200901i	$0.0643871\pi$
$798$	0.867515	−	0.598802i	0.0307097	−	0.0211974i
$799$	8.11450	−	12.8320i	0.287070	−	0.453965i
$800$	−23.2680	−	30.9640i	−0.822647	−	1.09474i
$801$	−8.71767	−	16.6101i	−0.308024	−	0.586890i
$802$	−3.09271	+	15.1491i	−0.109208	+	0.534934i
$803$	−0.361986	+	0.0292226i	−0.0127742	+	0.00103124i
$804$	−21.7423	−	6.29774i	−0.766793	−	0.222104i
$805$	1.16399	+	0.610912i	0.0410254	+	0.0215318i
$806$	3.78036	+	2.72449i	0.133157	+	0.0959662i
$807$	−6.85304	+	3.59675i	−0.241239	+	0.126612i
$808$	9.38364	−	1.91568i	0.330115	−	0.0673935i
$809$	−10.8873	−	8.18129i	−0.382778	−	0.287639i	0.391884	−	0.920015i	$-0.371823\pi$
$809$	−10.8873	−	8.18129i	−0.382778	−	0.287639i	−0.774662	+	0.632376i	$0.782080\pi$
$810$	0.245820	+	6.09997i	0.00863725	+	0.214331i
$811$	30.0187	−	11.3846i	1.05410	−	0.399767i	0.234149	−	0.972201i	$-0.424770\pi$
$811$	30.0187	−	11.3846i	1.05410	−	0.399767i	0.819951	+	0.572433i	$0.194000\pi$
$812$	−2.61743	+	0.758147i	−0.0918537	+	0.0266058i
$813$	−24.9942	−	5.10260i	−0.876584	−	0.178956i
$814$	−0.498277	−	0.562439i	−0.0174646	−	0.0197135i
$815$	−12.0449	+	14.7523i	−0.421914	+	0.516751i
$816$	0.379327	−	9.41290i	0.0132791	−	0.329517i
$817$	−8.77876	−	26.2956i	−0.307130	−	0.919966i
$818$	−17.0695	+	15.1222i	−0.596820	+	0.528737i
$819$	0.0757818	+	0.751505i	0.00264803	+	0.0262597i
$820$	−14.3656	−	12.7268i	−0.501670	−	0.444441i
$821$	−10.0603	+	23.6123i	−0.351106	+	0.824076i	0.646996	+	0.762494i	$0.276025\pi$
$821$	−10.0603	+	23.6123i	−0.351106	+	0.824076i	−0.998102	+	0.0615829i	$0.980385\pi$
$822$	−4.90388	+	8.49378i	−0.171043	+	0.296254i
$823$	13.6512	+	23.6445i	0.475850	+	0.824197i	0.999617	−	0.0276648i	$-0.00880712\pi$
$823$	13.6512	+	23.6445i	0.475850	+	0.824197i	−0.523767	+	0.851862i	$0.675474\pi$
$824$	−3.46883	+	0.421192i	−0.120842	+	0.0146729i
$825$	2.45362	+	1.16425i	0.0854239	+	0.0405342i
$826$	2.14354	−	1.23757i	0.0745834	−	0.0430607i
$827$	−23.7966	−	16.4256i	−0.827491	−	0.571175i	0.0773120	−	0.997007i	$-0.475366\pi$
$827$	−23.7966	−	16.4256i	−0.827491	−	0.571175i	−0.904802	+	0.425831i	$0.859982\pi$
$828$	2.94652	−	1.25539i	0.102399	−	0.0436280i
$829$	−13.5313	−	2.19905i	−0.469961	−	0.0763762i	−0.0791813	−	0.996860i	$-0.525231\pi$
$829$	−13.5313	−	2.19905i	−0.469961	−	0.0763762i	−0.390780	+	0.920484i	$0.627795\pi$
$830$	−38.4386	+	51.1525i	−1.33422	+	1.77553i
$831$	9.02026	+	23.7845i	0.312909	+	0.825074i
$832$	−17.5087	+	0.349288i	−0.607006	+	0.0121094i
$833$	−5.05436	+	13.3272i	−0.175123	+	0.461761i
$834$	−6.61889	−	10.4669i	−0.229193	−	0.362440i
$835$	43.9351	+	18.7190i	1.52044	+	0.647797i
$836$	−1.88444	−	1.19165i	−0.0651748	−	0.0412141i
$837$	−0.672979	−	0.0817145i	−0.0232616	−	0.00282446i
$838$	0.0165331	+	0.0388047i	0.000571128	+	0.00134049i
$839$	15.9644	−	47.8191i	0.551151	−	1.65090i	−0.191709	−	0.981452i	$-0.561403\pi$
$839$	15.9644	−	47.8191i	0.551151	−	1.65090i	0.742860	−	0.669447i	$-0.233469\pi$
$840$	0.437147	+	0.165788i	0.0150830	+	0.00572022i
$841$	−34.2306	−	2.76338i	−1.18037	−	0.0952890i
$842$	16.6130	−	57.3547i	0.572521	−	1.97657i
$843$	1.77670	+	0.0715985i	0.0611927	+	0.00246598i
$844$	23.4927			0.808651
$845$	41.0934	−	6.66215i	1.41365	−	0.229185i
$846$	14.1256			0.485647
$847$	−2.24658	−	0.0905339i	−0.0771933	−	0.00311078i
$848$	−7.47788	+	25.8166i	−0.256792	+	0.886547i
$849$	19.4870	+	1.57316i	0.668793	+	0.0539906i
$850$	−19.1929	−	7.27892i	−0.658313	−	0.249665i
$851$	0.473234	−	1.41751i	0.0162223	−	0.0485916i
$852$	4.49954	+	10.5608i	0.154152	+	0.361807i
$853$	55.3538	+	6.72116i	1.89528	+	0.230128i	0.983546	−	0.180659i	$-0.0578230\pi$
$853$	55.3538	+	6.72116i	1.89528	+	0.230128i	0.911731	+	0.410787i	$0.134746\pi$
$854$	1.26971	+	0.802918i	0.0434487	+	0.0274753i
$855$	7.77590	+	3.31300i	0.265930	+	0.113302i
$856$	−0.287814	−	0.455142i	−0.00983729	−	0.0155564i
$857$	−9.93729	+	26.2025i	−0.339451	+	0.895059i	0.651233	+	0.758878i	$0.274252\pi$
$857$	−9.93729	+	26.2025i	−0.339451	+	0.895059i	−0.990684	+	0.136181i	$0.956517\pi$
$858$	3.11208	−	1.71337i	0.106245	−	0.0584935i
$859$	−13.3312	−	35.1515i	−0.454855	−	1.19935i	−0.944813	−	0.327609i	$-0.893757\pi$
$859$	−13.3312	−	35.1515i	−0.454855	−	1.19935i	0.489958	−	0.871746i	$-0.337012\pi$
$860$	−33.0244	+	43.9475i	−1.12612	+	1.49860i
$861$	0.758219	+	0.123223i	0.0258400	+	0.00419942i
$862$	−35.6486	+	15.1884i	−1.21420	+	0.517320i
$863$	5.91848	+	4.08523i	0.201467	+	0.139063i	0.664527	−	0.747264i	$-0.268633\pi$
$863$	5.91848	+	4.08523i	0.201467	+	0.139063i	−0.463060	+	0.886327i	$0.653248\pi$
$864$	6.38338	−	3.68545i	0.217167	−	0.125381i
$865$	45.4694	+	21.5755i	1.54600	+	0.733588i
$866$	−25.8883	+	3.14340i	−0.879719	+	0.106817i
$867$	6.40068	+	11.0863i	0.217379	+	0.376511i
$868$	0.116057	−	0.201017i	0.00393925	−	0.00682298i
$869$	0.286414	−	0.672239i	0.00971594	−	0.0228041i
$870$	−36.3684	−	32.2196i	−1.23300	−	1.09235i
$871$	−16.7544	−	47.0404i	−0.567702	−	1.59390i
$872$	3.05457	−	2.70611i	0.103441	−	0.0916405i
$873$	0.820040	+	2.45632i	0.0277541	+	0.0831338i
$874$	0.397037	−	9.85238i	0.0134300	−	0.333262i
$875$	0.108073	−	0.132365i	0.00365352	−	0.00447475i
$876$	0.761572	+	0.859637i	0.0257311	+	0.0290445i
$877$	49.0444	+	10.0125i	1.65611	+	0.338098i	0.934980	−	0.354700i	$-0.115417\pi$
$877$	49.0444	+	10.0125i	1.65611	+	0.338098i	0.721132	+	0.692797i	$0.243622\pi$
$878$	−19.0815	+	5.52703i	−0.643970	+	0.186528i
$879$	9.36079	−	3.55008i	0.315732	−	0.119741i
$880$	−0.306389	−	7.60297i	−0.0103284	−	0.256296i
$881$	−12.8335	−	9.64375i	−0.432372	−	0.324906i	0.362174	−	0.932110i	$-0.382035\pi$
$881$	−12.8335	−	9.64375i	−0.432372	−	0.324906i	−0.794546	+	0.607204i	$0.792291\pi$
$882$	−12.9933	+	2.65259i	−0.437506	+	0.0893175i
$883$	−31.9776	+	16.7831i	−1.07613	+	0.564797i	−0.907144	−	0.420821i	$-0.861742\pi$
$883$	−31.9776	+	16.7831i	−1.07613	+	0.564797i	−0.168987	+	0.985618i	$0.554050\pi$
$884$	−10.0750	+	6.65603i	−0.338860	+	0.223866i
$885$	17.5734	+	9.22322i	0.590723	+	0.310035i
$886$	12.7774	+	3.70103i	0.429266	+	0.124338i
$887$	−45.8582	+	3.70206i	−1.53977	+	0.124303i	−0.820992	−	0.570939i	$-0.806579\pi$
$887$	−45.8582	+	3.70206i	−1.53977	+	0.124303i	−0.718776	+	0.695242i	$0.755297\pi$
$888$	0.106312	−	0.520750i	0.00356759	−	0.0174752i
$889$	−0.313641	−	0.597593i	−0.0105192	−	0.0200426i
$890$	68.7978	+	91.5532i	2.30611	+	3.06887i
$891$	−0.276231	+	0.436824i	−0.00925408	+	0.0146342i
$892$	34.6856	−	23.9418i	1.16136	−	0.801629i
$893$	8.38385	−	17.6686i	0.280555	−	0.591257i
$894$	8.49083	−	8.83989i	0.283976	−	0.295650i
$895$	−0.347241	−	0.333529i	−0.0116070	−	0.0111486i
$896$	−0.138433	−	1.14010i	−0.00462471	−	0.0380879i
$897$	6.04573	+	3.65636i	0.201861	+	0.122082i
$898$	−3.54387	+	29.1864i	−0.118261	+	0.973964i
$899$	4.17932	−	3.41231i	0.139388	−	0.113807i
$900$	−1.71792	−	8.41491i	−0.0572639	−	0.280497i
$901$	3.33282	+	11.5062i	0.111032	+	0.383328i
$902$	−0.864649	−	3.50802i	−0.0287897	−	0.116804i
$903$	0.177048	−	2.19313i	0.00589179	−	0.0729829i
$904$	0.177321	+	1.09110i	0.00589762	+	0.0362895i
$905$	43.6416	−	49.2612i	1.45070	−	1.63750i
$906$	−18.0143	+	13.5368i	−0.598484	+	0.449731i
$907$	26.0919	+	31.9568i	0.866369	+	1.06111i	0.997564	+	0.0697524i	$0.0222209\pi$
$907$	26.0919	+	31.9568i	0.866369	+	1.06111i	−0.131196	+	0.991356i	$0.541882\pi$
$908$	6.10600	−	37.5718i	0.202635	−	1.24686i
$909$	13.3427	+	3.28867i	0.442548	+	0.109078i
$910$	−1.19260	−	4.45425i	−0.0395343	−	0.147657i
$911$	−24.3123	+	5.99244i	−0.805501	+	0.198538i	−0.620507	−	0.784201i	$-0.713073\pi$
$911$	−24.3123	+	5.99244i	−0.805501	+	0.198538i	−0.184995	+	0.982740i	$0.559227\pi$
$912$	−0.976444	−	12.0954i	−0.0323333	−	0.400520i
$913$	−5.13814	+	1.71536i	−0.170047	+	0.0567702i
$914$	23.6801	+	24.6536i	0.783268	+	0.815468i
$915$			12.0459i			0.398224i
$916$	−14.1561	+	13.5971i	−0.467731	+	0.449261i
$917$	−0.268785	−	0.219456i	−0.00887606	−	0.00724708i
$918$	1.81538	−	3.45891i	0.0599164	−	0.114161i
$919$	−36.1915	+	5.88168i	−1.19385	+	0.194019i	−0.724677	−	0.689089i	$-0.758011\pi$
$919$	−36.1915	+	5.88168i	−1.19385	+	0.194019i	−0.469170	+	0.883108i	$0.655447\pi$
$920$	3.69633	−	2.33741i	0.121864	−	0.0770623i
$921$	−2.26399	+	1.07428i	−0.0746009	+	0.0353986i
$922$	26.0697	−	37.7684i	0.858559	−	1.24384i
$923$	−13.1050	+	21.6689i	−0.431355	+	0.713240i
$924$	−0.100525	−	0.145635i	−0.00330702	−	0.00479105i
$925$	−3.47047	−	2.00368i	−0.114108	−	0.0658804i
$926$	−16.3741	−	34.5077i	−0.538087	−	1.13399i
$927$	−4.75582	−	1.58773i	−0.156202	−	0.0521478i
$928$	−14.0390	+	56.9586i	−0.460854	+	1.86976i
$929$	−55.6322	+	2.24190i	−1.82523	+	0.0735544i	−0.929012	−	0.370051i	$-0.879340\pi$
$929$	−55.6322	+	2.24190i	−1.82523	+	0.0735544i	−0.896222	+	0.443605i	$0.853699\pi$
$930$	4.13530	−	0.166647i	0.135602	−	0.00546457i
$931$	−4.39388	+	17.8267i	−0.144004	+	0.584246i
$932$	19.4940	+	6.50805i	0.638547	+	0.213178i
$933$	11.2560	+	23.7216i	0.368506	+	0.776609i
$934$	−20.9850	−	12.1157i	−0.686651	−	0.396438i
$935$	−1.92649	−	2.79100i	−0.0630029	−	0.0912754i
$936$	2.29124	+	1.03173i	0.0748915	+	0.0337232i
$937$	−20.7619	+	30.0788i	−0.678262	+	0.982632i	0.321105	+	0.947044i	$0.395946\pi$
$937$	−20.7619	+	30.0788i	−0.678262	+	0.982632i	−0.999367	+	0.0355882i	$0.988670\pi$
$938$	−4.99705	+	2.37113i	−0.163159	+	0.0774201i
$939$	−5.52316	+	3.49263i	−0.180241	+	0.113978i
$940$	−38.2785	+	6.22086i	−1.24851	+	0.202902i
$941$	23.8754	−	45.4908i	0.778317	−	1.48296i	−0.0948259	−	0.995494i	$-0.530229\pi$
$941$	23.8754	−	45.4908i	0.778317	−	1.48296i	0.873143	−	0.487465i	$-0.162078\pi$
$942$	−35.5117	−	28.9944i	−1.15703	−	0.944689i
$943$	5.18228	−	4.97765i	0.168758	−	0.162094i
$944$		−	28.4936i		−	0.927389i
$945$	0.464707	+	0.483812i	0.0151169	+	0.0157384i
$946$	−9.81618	+	3.27712i	−0.319152	+	0.106548i
$947$	−0.218863	−	2.71110i	−0.00711208	−	0.0880989i	0.992227	−	0.124437i	$-0.0397126\pi$
$947$	−0.218863	−	2.71110i	−0.00711208	−	0.0880989i	−0.999340	+	0.0363385i	$0.988431\pi$
$948$	−2.24364	+	0.553008i	−0.0728700	+	0.0179608i
$949$	−0.557124	+	2.47149i	−0.0180850	+	0.0802281i
$950$	−25.6727	−	6.32776i	−0.832933	−	0.205300i
$951$	−3.39876	+	20.9134i	−0.110212	+	0.678164i
$952$	−0.189201	−	0.231729i	−0.00613204	−	0.00751038i
$953$	−4.91255	+	3.69154i	−0.159133	+	0.119581i	−0.677326	−	0.735683i	$-0.736861\pi$
$953$	−4.91255	+	3.69154i	−0.159133	+	0.119581i	0.518193	+	0.855264i	$0.326605\pi$
$954$	−7.39068	+	8.34236i	−0.239282	+	0.270094i
$955$	5.14108	+	31.6344i	0.166362	+	1.02366i
$956$	−2.16245	+	26.7868i	−0.0699387	+	0.866346i
$957$	−0.984394	−	3.99384i	−0.0318209	−	0.129103i
$958$	−9.61694	−	33.2015i	−0.310709	−	1.07269i
$959$	0.215573	+	1.05595i	0.00696122	+	0.0340983i
$960$	−12.0479	+	9.83681i	−0.388844	+	0.317482i
$961$	3.68124	−	30.3177i	0.118750	−	0.977992i
$962$	−4.78059	+	2.15047i	−0.154132	+	0.0693339i
$963$	−0.0931371	−	0.767053i	−0.00300130	−	0.0247179i
$964$	23.1216	+	22.2086i	0.744696	+	0.715290i
$965$	21.0160	−	21.8799i	0.676528	−	0.704340i
$966$	0.335495	−	0.707041i	0.0107944	−	0.0227487i
$967$	−8.45007	+	5.83266i	−0.271736	+	0.187566i	−0.696138	−	0.717908i	$-0.745100\pi$
$967$	−8.45007	+	5.83266i	−0.271736	+	0.187566i	0.424402	+	0.905474i	$0.360484\pi$
$968$	−3.99784	+	6.32207i	−0.128495	+	0.203199i
$969$	−3.24902	−	4.32367i	−0.104374	−	0.138896i
$970$	−7.34692	−	13.9984i	−0.235895	−	0.449461i
$971$	−5.50967	+	26.9881i	−0.176814	+	0.866091i	0.790491	+	0.612474i	$0.209825\pi$
$971$	−5.50967	+	26.9881i	−0.176814	+	0.866091i	−0.967305	+	0.253617i	$0.918380\pi$
$972$	1.62913	−	0.131517i	0.0522544	−	0.00421841i
$973$	−1.30710	−	0.378607i	−0.0419038	−	0.0121376i
$974$	−30.8868	−	16.2107i	−0.989678	−	0.519423i
$975$	12.8493	−	13.9231i	0.411508	−	0.445896i
$976$	15.3131	−	8.03696i	0.490162	−	0.257257i
$977$	9.46794	−	1.93289i	0.302906	−	0.0618388i	−0.0461684	−	0.998934i	$-0.514701\pi$
$977$	9.46794	−	1.93289i	0.302906	−	0.0618388i	0.349075	+	0.937095i	$0.386496\pi$
$978$	9.06406	+	6.81120i	0.289837	+	0.217798i
$979$	0.390388	+	9.68737i	0.0124768	+	0.309610i
$980$	34.0419	−	12.9104i	1.08743	−	0.412408i
$981$	5.62430	−	1.62910i	0.179570	−	0.0520131i
$982$	−49.1047	−	10.0248i	−1.56699	−	0.319904i
$983$	−40.5636	−	45.7869i	−1.29378	−	1.46037i	−0.811496	−	0.584358i	$-0.801346\pi$
$983$	−40.5636	−	45.7869i	−1.29378	−	1.46037i	−0.482282	−	0.876016i	$-0.660192\pi$
$984$	1.61626	−	1.97956i	0.0515244	−	0.0631059i
$985$	−3.44280	+	85.4321i	−0.109697	+	2.72209i
$986$	9.84515	+	29.4898i	0.313533	+	0.939147i
$987$	1.16183	−	1.02929i	0.0369814	−	0.0327627i
$988$	−11.8498	+	10.0756i	−0.376992	+	0.320546i
$989$	−15.4057	−	13.6483i	−0.489873	−	0.433989i
$990$	1.23675	−	2.90275i	0.0393064	−	0.0922556i
$991$	19.2447	−	33.3328i	0.611328	−	1.05885i	−0.379689	−	0.925114i	$-0.623969\pi$
$991$	19.2447	−	33.3328i	0.611328	−	1.05885i	0.991017	−	0.133737i	$-0.0426976\pi$
$992$	−2.49845	−	4.32744i	−0.0793257	−	0.137396i
$993$	9.18581	−	1.11536i	0.291503	−	0.0353949i
$994$	2.53415	+	1.20247i	0.0803783	+	0.0381400i
$995$	28.3841	−	16.3875i	0.899835	−	0.519520i
$996$	14.0980	+	9.73114i	0.446712	+	0.308343i
$997$	−13.3930	+	5.70623i	−0.424161	+	0.180718i	−0.593490	−	0.804842i	$-0.702250\pi$
$997$	−13.3930	+	5.70623i	−0.424161	+	0.180718i	0.169329	+	0.985560i	$0.445840\pi$
$998$	−72.7195	−	11.8181i	−2.30190	−	0.374094i
$999$	0.458137	−	0.609670i	0.0144948	−	0.0192891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.4.12	✓	336
169.127	even	78	inner	507.2.t.a.127.12	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.4.12	✓	336	1.1	even	1	trivial
507.2.t.a.127.12	yes	336	169.127	even	78	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.90487 + 0.0767637i) q^{2} +(0.278217 - 0.960518i) q^{3} +(1.62913 + 0.131517i) q^{4} +(2.99420 + 1.13555i) q^{5} +(0.603702 - 1.80831i) q^{6} +(-0.0821119 - 0.192724i) q^{7} +(-0.691848 - 0.0840056i) q^{8} +(-0.845190 - 0.534466i) q^{9} +O(q^{10})\)	\(q+(1.90487 + 0.0767637i) q^{2} +(0.278217 - 0.960518i) q^{3} +(1.62913 + 0.131517i) q^{4} +(2.99420 + 1.13555i) q^{5} +(0.603702 - 1.80831i) q^{6} +(-0.0821119 - 0.192724i) q^{7} +(-0.691848 - 0.0840056i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(5.61640 + 2.39293i) q^{10} +(0.276231 + 0.436824i) q^{11} +(0.579577 - 1.52822i) q^{12} +(3.48287 - 0.932518i) q^{13} +(-0.141618 - 0.373417i) q^{14} +(1.92376 - 2.56006i) q^{15} +(-4.53796 - 0.737491i) q^{16} +(-1.88509 + 0.803162i) q^{17} +(-1.56895 - 1.08297i) q^{18} +(-2.28582 + 1.31972i) q^{19} +(4.72860 + 2.24375i) q^{20} +(-0.207960 + 0.0252509i) q^{21} +(0.492652 + 0.853298i) q^{22} +(-0.979794 + 1.69705i) q^{23} +(-0.273173 + 0.641161i) q^{24} +(3.93322 + 3.48453i) q^{25} +(6.70601 - 1.50897i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-0.108425 - 0.324771i) q^{28} +(0.320467 - 7.95231i) q^{29} +(3.86103 - 4.72890i) q^{30} +(0.449545 + 0.507432i) q^{31} +(-7.22193 - 1.47437i) q^{32} +(0.496429 - 0.143793i) q^{33} +(-3.65251 + 1.38521i) q^{34} +(-0.0270120 - 0.670296i) q^{35} +(-1.30663 - 0.981871i) q^{36} +(-0.747206 + 0.152543i) q^{37} +(-4.45549 + 2.33842i) q^{38} +(0.0732961 - 3.60481i) q^{39} +(-1.97614 - 1.03716i) q^{40} +(-3.52212 - 1.02019i) q^{41} +(-0.398075 + 0.0321359i) q^{42} +(-2.10089 + 10.2909i) q^{43} +(0.392566 + 0.747972i) q^{44} +(-1.92376 - 2.56006i) q^{45} +(-1.99666 + 3.15746i) q^{46} +(-6.09788 + 4.20906i) q^{47} +(-1.97091 + 4.15361i) q^{48} +(4.81867 - 5.01677i) q^{49} +(7.22479 + 6.93951i) q^{50} +(0.246987 + 2.03412i) q^{51} +(5.79670 - 1.06114i) q^{52} +(0.704680 - 5.80356i) q^{53} +(-1.47672 + 1.20571i) q^{54} +(0.331055 + 1.62161i) q^{55} +(0.0406191 + 0.140233i) q^{56} +(0.631657 + 2.56273i) q^{57} +(1.22090 - 15.1235i) q^{58} +(0.994171 + 6.11738i) q^{59} +(3.47074 - 3.91766i) q^{60} +(-3.00721 + 2.25977i) q^{61} +(0.817374 + 1.00110i) q^{62} +(-0.0336041 + 0.206774i) q^{63} +(-4.71588 - 1.16236i) q^{64} +(11.4874 + 1.16283i) q^{65} +(0.956673 - 0.235799i) q^{66} +(-1.11442 - 13.8046i) q^{67} +(-3.17669 + 1.06053i) q^{68} +(1.35745 + 1.41326i) q^{69} -1.27890i q^{70} +(-5.06535 + 4.86534i) q^{71} +(0.539845 + 0.440770i) q^{72} +(-0.326547 + 0.622183i) q^{73} +(-1.43504 + 0.233217i) q^{74} +(4.44124 - 2.80847i) q^{75} +(-3.89745 + 1.84937i) q^{76} +(0.0615045 - 0.0891047i) q^{77} +(0.416338 - 6.86107i) q^{78} +(-0.803140 - 1.16355i) q^{79} +(-12.7501 - 7.36129i) q^{80} +(0.428693 + 0.903450i) q^{81} +(-6.63087 - 2.21371i) q^{82} +(-2.50825 + 10.1764i) q^{83} +(-0.342114 + 0.0137867i) q^{84} +(-6.55638 + 0.264213i) q^{85} +(-4.79190 + 19.4415i) q^{86} +(-7.54918 - 2.52029i) q^{87} +(-0.154414 - 0.325421i) q^{88} +(16.2456 + 9.37942i) q^{89} +(-3.46799 - 5.02425i) q^{90} +(-0.465704 - 0.594662i) q^{91} +(-1.81940 + 2.63586i) q^{92} +(0.612469 - 0.290620i) q^{93} +(-11.9388 + 7.54963i) q^{94} +(-8.34280 + 1.35584i) q^{95} +(-3.42543 + 6.52660i) q^{96} +(-2.00591 - 1.63777i) q^{97} +(9.56406 - 9.18640i) q^{98} -0.516835i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9}+O(q^{10}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31} + 65 q^{32} - 13 q^{33} + 65 q^{34} - 82 q^{35} - 12 q^{36} - 73 q^{38} + 24 q^{40} - 132 q^{42} - 72 q^{43} + 39 q^{44} + 8 q^{48} + 68 q^{49} + 52 q^{50} - 8 q^{51} - 65 q^{52} + 37 q^{53} - 53 q^{55} + 14 q^{56} - 26 q^{57} + 26 q^{58} - 208 q^{59} + 78 q^{60} - 12 q^{61} - 49 q^{62} + 14 q^{64} + 52 q^{65} + 64 q^{66} - 26 q^{67} - 33 q^{68} + 4 q^{69} - 78 q^{71} + 52 q^{73} + 205 q^{74} - 8 q^{75} - 26 q^{76} - 114 q^{77} - 65 q^{78} + 28 q^{79} - 468 q^{80} + 14 q^{81} - 45 q^{82} - 78 q^{83} + 13 q^{85} + 13 q^{86} + 46 q^{87} + 26 q^{88} - 8 q^{90} - 260 q^{91} + 8 q^{92} - 25 q^{94} - 90 q^{95} - 65 q^{96} - 26 q^{97} + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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