LMFDB - Embedded newform 930.2.z.d.349.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.1
Character	$\chi$	$=$	930.349
Dual form			930.2.z.d.469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.22153 - 0.254605i) q^{5} +1.00000 q^{6} +(-2.23337 + 3.07398i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.22153 - 0.254605i) q^{5} +1.00000 q^{6} +(-2.23337 + 3.07398i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.03412 + 0.928633i) q^{10} +(-2.25898 - 1.64124i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-3.92297 + 1.27465i) q^{13} +(3.07398 - 2.23337i) q^{14} +(2.19147 - 0.444346i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.619828 - 0.853119i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(0.925860 - 2.84950i) q^{19} +(-1.64760 - 1.51176i) q^{20} +(1.17415 - 3.61367i) q^{21} +(1.64124 + 2.25898i) q^{22} +(0.909616 + 1.25198i) q^{23} +(0.809017 + 0.587785i) q^{24} +(4.87035 + 1.13122i) q^{25} +4.12485 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-3.61367 + 1.17415i) q^{28} +(0.0548603 - 0.168843i) q^{29} +(-2.22153 - 0.254605i) q^{30} +(2.85866 + 4.77787i) q^{31} -1.00000i q^{32} +(2.65559 + 0.862852i) q^{33} +(0.325863 + 1.00290i) q^{34} +(5.74415 - 6.26029i) q^{35} +1.00000 q^{36} +2.89249i q^{37} +(-1.76109 + 2.42393i) q^{38} +(3.33708 - 2.42453i) q^{39} +(1.09980 + 1.94690i) q^{40} +(2.53639 - 7.80619i) q^{41} +(-2.23337 + 3.07398i) q^{42} +(-1.12153 - 0.364406i) q^{43} +(-0.862852 - 2.65559i) q^{44} +(-1.94690 + 1.09980i) q^{45} +(-0.478214 - 1.47179i) q^{46} +(8.77722 - 2.85189i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-2.29825 - 7.07328i) q^{49} +(-4.28241 - 2.58088i) q^{50} +(0.853119 + 0.619828i) q^{51} +(-3.92297 - 1.27465i) q^{52} +(-4.06597 - 5.59633i) q^{53} +(0.809017 - 0.587785i) q^{54} +(4.60051 + 4.22121i) q^{55} +3.79964 q^{56} +2.99615i q^{57} +(-0.104350 + 0.143626i) q^{58} +(3.06277 + 9.42624i) q^{59} +(2.03412 + 0.928633i) q^{60} +2.03663 q^{61} +(-1.24230 - 5.42740i) q^{62} +3.79964i q^{63} +(-0.309017 + 0.951057i) q^{64} +(9.03951 - 1.83286i) q^{65} +(-2.25898 - 1.64124i) q^{66} -9.47387i q^{67} -1.05451i q^{68} +(-1.25198 - 0.909616i) q^{69} +(-7.39754 + 4.17885i) q^{70} +(10.1170 - 7.35045i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(3.27719 - 4.51066i) q^{73} +(0.893829 - 2.75092i) q^{74} +(-4.98155 + 0.429166i) q^{75} +(2.42393 - 1.76109i) q^{76} +(10.0903 - 3.27853i) q^{77} +(-3.92297 + 1.27465i) q^{78} +(-10.2272 + 7.43050i) q^{79} +(-0.444346 - 2.19147i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.82449 + 6.64034i) q^{82} +(2.80822 + 0.912446i) q^{83} +(3.07398 - 2.23337i) q^{84} +(1.15975 + 2.05304i) q^{85} +(0.954028 + 0.693142i) q^{86} +0.177532i q^{87} +2.79225i q^{88} +(-7.02461 - 5.10368i) q^{89} +(2.19147 - 0.444346i) q^{90} +(4.84321 - 14.9059i) q^{91} +1.54753i q^{92} +(-4.19519 - 3.66065i) q^{93} -9.22892 q^{94} +(-2.78232 + 6.09452i) q^{95} +(0.309017 + 0.951057i) q^{96} +(3.10053 - 4.26752i) q^{97} +7.43728i q^{98} -2.79225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−2.22153	−	0.254605i	−0.993497	−	0.113863i
$5$	−2.22153	−	0.254605i	−0.993497	−	0.113863i
$6$	1.00000			0.408248
$7$	−2.23337	+	3.07398i	−0.844136	+	1.16185i	0.140989	+	0.990011i	$0.454972\pi$
$7$	−2.23337	+	3.07398i	−0.844136	+	1.16185i	−0.985124	+	0.171842i	$0.945028\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	2.03412	+	0.928633i	0.643245	+	0.293659i
$11$	−2.25898	−	1.64124i	−0.681107	−	0.494853i	0.192618	−	0.981274i	$-0.438302\pi$
$11$	−2.25898	−	1.64124i	−0.681107	−	0.494853i	−0.873725	+	0.486421i	$0.838302\pi$
$12$	−0.951057	−	0.309017i	−0.274546	−	0.0892055i
$13$	−3.92297	+	1.27465i	−1.08804	+	0.353524i	−0.797487	−	0.603336i	$-0.793838\pi$
$13$	−3.92297	+	1.27465i	−1.08804	+	0.353524i	−0.290549	+	0.956860i	$0.593838\pi$
$14$	3.07398	−	2.23337i	0.821554	−	0.596894i
$15$	2.19147	−	0.444346i	0.565836	−	0.114730i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.619828	−	0.853119i	−0.150330	−	0.206912i	0.727210	−	0.686415i	$-0.240817\pi$
$17$	−0.619828	−	0.853119i	−0.150330	−	0.206912i	−0.877540	+	0.479504i	$0.840817\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	0.925860	−	2.84950i	0.212407	−	0.653721i	−0.786921	−	0.617054i	$-0.788326\pi$
$19$	0.925860	−	2.84950i	0.212407	−	0.653721i	0.999328	−	0.0366668i	$-0.0116740\pi$
$20$	−1.64760	−	1.51176i	−0.368414	−	0.338040i
$21$	1.17415	−	3.61367i	0.256221	−	0.788568i
$22$	1.64124	+	2.25898i	0.349914	+	0.481615i
$23$	0.909616	+	1.25198i	0.189668	+	0.261056i	0.893252	−	0.449557i	$-0.148418\pi$
$23$	0.909616	+	1.25198i	0.189668	+	0.261056i	−0.703584	+	0.710612i	$0.748418\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	4.87035	+	1.13122i	0.974071	+	0.226244i
$26$	4.12485			0.808950
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	−3.61367	+	1.17415i	−0.682920	+	0.221894i
$29$	0.0548603	−	0.168843i	0.0101873	−	0.0313533i	−0.945834	−	0.324652i	$-0.894753\pi$
$29$	0.0548603	−	0.168843i	0.0101873	−	0.0313533i	0.956021	+	0.293298i	$0.0947529\pi$
$30$	−2.22153	−	0.254605i	−0.405593	−	0.0464842i
$31$	2.85866	+	4.77787i	0.513430	+	0.858131i
$31$	2.85866	+	4.77787i	0.513430	+	0.858131i
$32$		−	1.00000i		−	0.176777i
$33$	2.65559	+	0.862852i	0.462278	+	0.150203i
$34$	0.325863	+	1.00290i	0.0558850	+	0.171996i
$35$	5.74415	−	6.26029i	0.970938	−	1.05818i
$36$	1.00000			0.166667
$37$			2.89249i			0.475523i	0.971324	+	0.237761i	$0.0764136\pi$
$37$			2.89249i			0.475523i	−0.971324	+	0.237761i	$0.923586\pi$
$38$	−1.76109	+	2.42393i	−0.285687	+	0.393214i
$39$	3.33708	−	2.42453i	0.534360	−	0.388235i
$40$	1.09980	+	1.94690i	0.173894	+	0.307833i
$41$	2.53639	−	7.80619i	0.396117	−	1.21912i	−0.531972	−	0.846762i	$-0.678549\pi$
$41$	2.53639	−	7.80619i	0.396117	−	1.21912i	0.928088	−	0.372360i	$-0.121451\pi$
$42$	−2.23337	+	3.07398i	−0.344617	+	0.474325i
$43$	−1.12153	−	0.364406i	−0.171031	−	0.0555714i	0.222250	−	0.974990i	$-0.428660\pi$
$43$	−1.12153	−	0.364406i	−0.171031	−	0.0555714i	−0.393281	+	0.919418i	$0.628660\pi$
$44$	−0.862852	−	2.65559i	−0.130080	−	0.400345i
$45$	−1.94690	+	1.09980i	−0.290227	+	0.163949i
$46$	−0.478214	−	1.47179i	−0.0705088	−	0.217004i
$47$	8.77722	−	2.85189i	1.28029	−	0.415991i	0.411607	−	0.911361i	$-0.364968\pi$
$47$	8.77722	−	2.85189i	1.28029	−	0.415991i	0.868682	+	0.495370i	$0.164968\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	−2.29825	−	7.07328i	−0.328321	−	1.01047i
$50$	−4.28241	−	2.58088i	−0.605625	−	0.364991i
$51$	0.853119	+	0.619828i	0.119461	+	0.0867932i
$52$	−3.92297	−	1.27465i	−0.544018	−	0.176762i
$53$	−4.06597	−	5.59633i	−0.558504	−	0.768715i	0.432631	−	0.901571i	$-0.357585\pi$
$53$	−4.06597	−	5.59633i	−0.558504	−	0.768715i	−0.991135	+	0.132856i	$0.957585\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	4.60051	+	4.22121i	0.620332	+	0.569188i
$56$	3.79964			0.507749
$57$			2.99615i			0.396849i
$58$	−0.104350	+	0.143626i	−0.0137019	+	0.0188590i
$59$	3.06277	+	9.42624i	0.398739	+	1.22719i	0.926011	+	0.377496i	$0.123215\pi$
$59$	3.06277	+	9.42624i	0.398739	+	1.22719i	−0.527272	+	0.849696i	$0.676785\pi$
$60$	2.03412	+	0.928633i	0.262604	+	0.119886i
$61$	2.03663			0.260763			0.130382	−	0.991464i	$-0.458380\pi$
$61$	2.03663			0.260763			0.130382	+	0.991464i	$0.458380\pi$
$62$	−1.24230	−	5.42740i	−0.157772	−	0.689281i
$63$			3.79964i			0.478710i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	9.03951	−	1.83286i	1.12121	−	0.227338i
$66$	−2.25898	−	1.64124i	−0.278061	−	0.202023i
$67$		−	9.47387i		−	1.15742i	−0.815534	−	0.578709i	$-0.803557\pi$
$67$		−	9.47387i		−	1.15742i	0.815534	−	0.578709i	$-0.196443\pi$
$68$		−	1.05451i		−	0.127879i
$69$	−1.25198	−	0.909616i	−0.150721	−	0.109505i
$70$	−7.39754	+	4.17885i	−0.884175	+	0.499468i
$71$	10.1170	−	7.35045i	1.20067	−	0.872338i	0.206320	−	0.978485i	$-0.433851\pi$
$71$	10.1170	−	7.35045i	1.20067	−	0.872338i	0.994350	+	0.106147i	$0.0338514\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	3.27719	−	4.51066i	0.383566	−	0.527933i	−0.572959	−	0.819584i	$-0.694205\pi$
$73$	3.27719	−	4.51066i	0.383566	−	0.527933i	0.956525	+	0.291651i	$0.0942045\pi$
$74$	0.893829	−	2.75092i	0.103905	−	0.319788i
$75$	−4.98155	+	0.429166i	−0.575220	+	0.0495559i
$76$	2.42393	−	1.76109i	0.278044	−	0.202011i
$77$	10.0903	−	3.27853i	1.14989	−	0.373623i
$78$	−3.92297	+	1.27465i	−0.444189	+	0.144326i
$79$	−10.2272	+	7.43050i	−1.15065	+	0.835996i	−0.988567	−	0.150781i	$-0.951821\pi$
$79$	−10.2272	+	7.43050i	−1.15065	+	0.835996i	−0.162083	+	0.986777i	$0.551821\pi$
$80$	−0.444346	−	2.19147i	−0.0496794	−	0.245014i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−4.82449	+	6.64034i	−0.532776	+	0.733303i
$83$	2.80822	+	0.912446i	0.308242	+	0.100154i	0.459054	−	0.888409i	$-0.348189\pi$
$83$	2.80822	+	0.912446i	0.308242	+	0.100154i	−0.150811	+	0.988563i	$0.548189\pi$
$84$	3.07398	−	2.23337i	0.335398	−	0.243681i
$85$	1.15975	+	2.05304i	0.125793	+	0.222683i
$86$	0.954028	+	0.693142i	0.102876	+	0.0747434i
$87$			0.177532i			0.0190334i
$88$			2.79225i			0.297655i
$89$	−7.02461	−	5.10368i	−0.744607	−	0.540989i	0.149543	−	0.988755i	$-0.452220\pi$
$89$	−7.02461	−	5.10368i	−0.744607	−	0.540989i	−0.894151	+	0.447766i	$0.852220\pi$
$90$	2.19147	−	0.444346i	0.231002	−	0.0468382i
$91$	4.84321	−	14.9059i	0.507707	−	1.56256i
$92$			1.54753i			0.161341i
$93$	−4.19519	−	3.66065i	−0.435021	−	0.379592i
$94$	−9.22892			−0.951890
$95$	−2.78232	+	6.09452i	−0.285460	+	0.625284i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	3.10053	−	4.26752i	0.314811	−	0.433301i	−0.622063	−	0.782967i	$-0.713705\pi$
$97$	3.10053	−	4.26752i	0.314811	−	0.433301i	0.936874	+	0.349667i	$0.113705\pi$
$98$			7.43728i			0.751279i
$99$	−2.79225			−0.280632
$100$	3.27528	+	3.77790i	0.327528	+	0.377790i
$101$	0.734808	−	0.533869i	0.0731162	−	0.0531220i	−0.550627	−	0.834752i	$-0.685611\pi$
$101$	0.734808	−	0.533869i	0.0731162	−	0.0531220i	0.623743	+	0.781630i	$0.285611\pi$
$102$	−0.619828	−	0.853119i	−0.0613721	−	0.0844714i
$103$	16.9192	+	5.49738i	1.66710	+	0.541673i	0.982341	−	0.187099i	$-0.0599087\pi$
$103$	16.9192	+	5.49738i	1.66710	+	0.541673i	0.684756	+	0.728772i	$0.259909\pi$
$104$	3.33708	+	2.42453i	0.327227	+	0.237745i
$105$	−3.52847	+	7.72893i	−0.344344	+	0.754266i
$106$	2.13761	+	6.57888i	0.207623	+	0.638997i
$107$	−6.51743	−	8.97048i	−0.630064	−	0.867209i	0.367973	−	0.929837i	$-0.380052\pi$
$107$	−6.51743	−	8.97048i	−0.630064	−	0.867209i	−0.998037	+	0.0626277i	$0.980052\pi$
$108$	−0.951057	+	0.309017i	−0.0915155	+	0.0297352i
$109$	−1.23178	−	3.79102i	−0.117983	−	0.363114i	0.874575	−	0.484891i	$-0.161141\pi$
$109$	−1.23178	−	3.79102i	−0.117983	−	0.363114i	−0.992557	+	0.121777i	$0.961141\pi$
$110$	−3.07092	−	5.43624i	−0.292800	−	0.518325i
$111$	−0.893829	−	2.75092i	−0.0848385	−	0.261106i
$112$	−3.61367	−	1.17415i	−0.341460	−	0.110947i
$113$	1.27154	−	1.75013i	0.119617	−	0.164638i	−0.745010	−	0.667054i	$-0.767555\pi$
$113$	1.27154	−	1.75013i	0.119617	−	0.164638i	0.864626	+	0.502415i	$0.167555\pi$
$114$	0.925860	−	2.84950i	0.0867147	−	0.266880i
$115$	−1.70198	−	3.01290i	−0.158710	−	0.280954i
$116$	0.143626	−	0.104350i	0.0133353	−	0.00968869i
$117$	−2.42453	+	3.33708i	−0.224148	+	0.308513i
$118$		−	9.91134i		−	0.912413i
$119$	4.00677			0.367300
$120$	−1.64760	−	1.51176i	−0.150405	−	0.138004i
$121$	−0.989889	−	3.04656i	−0.0899899	−	0.276960i
$122$	−1.93695	−	0.629352i	−0.175363	−	0.0569789i
$123$			8.20791i			0.740083i
$124$	−0.495661	+	5.54566i	−0.0445117	+	0.498015i
$125$	−10.5316	−	3.75305i	−0.941975	−	0.335683i
$126$	1.17415	−	3.61367i	0.104602	−	0.321932i
$127$	15.5734	−	5.06011i	1.38192	−	0.449012i	0.478619	−	0.878023i	$-0.341138\pi$
$127$	15.5734	−	5.06011i	1.38192	−	0.449012i	0.903299	+	0.429011i	$0.141138\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	1.17924			0.103827
$130$	−9.16347	−	1.05021i	−0.803689	−	0.0921092i
$131$	3.28268	+	2.38500i	0.286809	+	0.208379i	0.721882	−	0.692016i	$-0.243277\pi$
$131$	3.28268	+	2.38500i	0.286809	+	0.208379i	−0.435073	+	0.900395i	$0.643277\pi$
$132$	1.64124	+	2.25898i	0.142852	+	0.196619i
$133$	6.69151	+	9.21008i	0.580228	+	0.798615i
$134$	−2.92759	+	9.01019i	−0.252905	+	0.778362i
$135$	1.51176	−	1.64760i	0.130112	−	0.141803i
$136$	−0.325863	+	1.00290i	−0.0279425	+	0.0859981i
$137$	4.87577	−	1.58424i	0.416566	−	0.135350i	−0.0932327	−	0.995644i	$-0.529720\pi$
$137$	4.87577	−	1.58424i	0.416566	−	0.135350i	0.509798	+	0.860294i	$0.329720\pi$
$138$	0.909616	+	1.25198i	0.0774317	+	0.106576i
$139$	4.79098	+	14.7451i	0.406366	+	1.25066i	0.919750	+	0.392506i	$0.128392\pi$
$139$	4.79098	+	14.7451i	0.406366	+	1.25066i	−0.513384	+	0.858159i	$0.671608\pi$
$140$	8.32682	−	1.68836i	0.703744	−	0.142692i
$141$	−7.46635	+	5.42462i	−0.628780	+	0.456835i
$142$	−11.8933	+	3.86436i	−0.998062	+	0.324290i
$143$	10.9539	+	3.55914i	0.916011	+	0.297630i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−0.164862	+	0.361120i	−0.0136910	+	0.0299894i
$146$	−4.51066	+	3.27719i	−0.373305	+	0.271222i
$147$	4.37152	+	6.01689i	0.360557	+	0.496265i
$148$	−1.70016	+	2.34007i	−0.139753	+	0.192353i
$149$	−14.2016			−1.16344			−0.581718	−	0.813390i	$-0.697619\pi$
$149$	−14.2016			−1.16344			−0.581718	+	0.813390i	$0.697619\pi$
$150$	4.87035	+	1.13122i	0.397663	+	0.0923638i
$151$	0.450501	+	0.327308i	0.0366612	+	0.0266360i	0.605965	−	0.795491i	$-0.292787\pi$
$151$	0.450501	+	0.327308i	0.0366612	+	0.0266360i	−0.569304	+	0.822127i	$0.692787\pi$
$152$	−2.84950	+	0.925860i	−0.231125	+	0.0750971i
$153$	−1.00290	−	0.325863i	−0.0810798	−	0.0263444i
$154$	−10.6095			−0.854942
$155$	−5.13411	−	11.3420i	−0.412382	−	0.911011i
$156$	4.12485			0.330253
$157$	−7.33507	−	2.38331i	−0.585402	−	0.190209i	0.00131706	−	0.999999i	$-0.499581\pi$
$157$	−7.33507	−	2.38331i	−0.585402	−	0.190209i	−0.586719	+	0.809790i	$0.699581\pi$
$158$	12.0228	−	3.90644i	0.956483	−	0.310780i
$159$	5.59633	+	4.06597i	0.443818	+	0.322452i
$160$	−0.254605	+	2.22153i	−0.0201283	+	0.175627i
$161$	−5.88007			−0.463414
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−8.83625	−	12.1621i	−0.692109	−	0.952606i	−0.999999	−	0.00118409i	$-0.999623\pi$
$163$	−8.83625	−	12.1621i	−0.692109	−	0.952606i	0.307891	−	0.951422i	$-0.400377\pi$
$164$	6.64034	−	4.82449i	0.518524	−	0.376729i
$165$	−5.67977	−	2.59297i	−0.442169	−	0.201863i
$166$	−2.38882	−	1.73558i	−0.185408	−	0.134707i
$167$	−5.70922	−	1.85504i	−0.441793	−	0.143547i	0.0796699	−	0.996821i	$-0.474613\pi$
$167$	−5.70922	−	1.85504i	−0.441793	−	0.143547i	−0.521463	+	0.853274i	$0.674613\pi$
$168$	−3.61367	+	1.17415i	−0.278801	+	0.0905880i
$169$	3.24773	−	2.35961i	0.249825	−	0.181509i
$170$	−0.468569	−	2.31094i	−0.0359376	−	0.177241i
$171$	−0.925860	−	2.84950i	−0.0708023	−	0.217907i
$172$	−0.693142	−	0.954028i	−0.0528516	−	0.0727440i
$173$	−17.3989	+	5.65325i	−1.32282	+	0.429809i	−0.883461	−	0.468505i	$-0.844793\pi$
$173$	−17.3989	+	5.65325i	−1.32282	+	0.429809i	−0.439354	+	0.898314i	$0.644793\pi$
$174$	0.0548603	−	0.168843i	0.00415895	−	0.0127999i
$175$	−14.3547	+	12.4449i	−1.08511	+	0.940746i
$176$	0.862852	−	2.65559i	0.0650399	−	0.200172i
$177$	−5.82574	−	8.01844i	−0.437889	−	0.602703i
$178$	5.10368	+	7.02461i	0.382537	+	0.526517i
$179$	9.64462	+	7.00723i	0.720873	+	0.523745i	0.886663	−	0.462416i	$-0.153017\pi$
$179$	9.64462	+	7.00723i	0.720873	+	0.523745i	−0.165790	+	0.986161i	$0.553017\pi$
$180$	−2.22153	−	0.254605i	−0.165583	−	0.0189771i
$181$	20.6601			1.53566			0.767828	−	0.640656i	$-0.221338\pi$
$181$	20.6601			1.53566			0.767828	+	0.640656i	$0.221338\pi$
$182$	−9.21234	+	12.6797i	−0.682864	+	0.939882i
$183$	−1.93695	+	0.629352i	−0.143183	+	0.0465231i
$184$	0.478214	−	1.47179i	0.0352544	−	0.108502i
$185$	0.736442	−	6.42574i	0.0541443	−	0.472430i
$186$	2.85866	+	4.77787i	0.209607	+	0.350331i
$187$			2.94446i			0.215321i
$188$	8.77722	+	2.85189i	0.640145	+	0.207996i
$189$	−1.17415	−	3.61367i	−0.0854071	−	0.262856i
$190$	4.52945	−	4.93645i	0.328601	−	0.358127i
$191$	0.250971			0.0181596			0.00907981	−	0.999959i	$-0.497110\pi$
$191$	0.250971			0.0181596			0.00907981	+	0.999959i	$0.497110\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−5.81033	+	7.99723i	−0.418237	+	0.575653i	−0.965203	−	0.261501i	$-0.915782\pi$
$193$	−5.81033	+	7.99723i	−0.418237	+	0.575653i	0.546967	+	0.837154i	$0.315782\pi$
$194$	−4.26752	+	3.10053i	−0.306390	+	0.222605i
$195$	−8.03070	+	4.53652i	−0.575090	+	0.324867i
$196$	2.29825	−	7.07328i	0.164160	−	0.505234i
$197$	0.815546	−	1.12250i	0.0581053	−	0.0799751i	−0.778976	−	0.627054i	$-0.784260\pi$
$197$	0.815546	−	1.12250i	0.0581053	−	0.0799751i	0.837081	+	0.547079i	$0.184260\pi$
$198$	2.65559	+	0.862852i	0.188724	+	0.0613202i
$199$	−3.46976	−	10.6788i	−0.245965	−	0.757001i	−0.995476	−	0.0950100i	$-0.969712\pi$
$199$	−3.46976	−	10.6788i	−0.245965	−	0.757001i	0.749512	−	0.661991i	$-0.230288\pi$
$200$	−1.94754	−	4.60511i	−0.137712	−	0.325631i
$201$	2.92759	+	9.01019i	0.206496	+	0.635530i
$202$	−0.863819	+	0.280672i	−0.0607781	+	0.0197480i
$203$	0.396494	+	0.545728i	0.0278284	+	0.0383026i
$204$	0.325863	+	1.00290i	0.0228149	+	0.0702172i
$205$	−7.62214	+	16.6959i	−0.532353	+	1.16609i
$206$	−14.3923	−	10.4566i	−1.00276	−	0.728548i
$207$	1.47179	+	0.478214i	0.102296	+	0.0332381i
$208$	−2.42453	−	3.33708i	−0.168111	−	0.231385i
$209$	−6.76822	+	4.91740i	−0.468168	+	0.340144i
$210$	5.74415	−	6.26029i	0.396384	−	0.432001i
$211$	−16.0394			−1.10420			−0.552098	−	0.833779i	$-0.686173\pi$
$211$	−16.0394			−1.10420			−0.552098	+	0.833779i	$0.686173\pi$
$212$		−	6.91744i		−	0.475092i
$213$	−7.35045	+	10.1170i	−0.503644	+	0.693207i
$214$	3.42642	+	10.5454i	0.234225	+	0.720871i
$215$	2.39872	+	1.09508i	0.163592	+	0.0746841i
$216$	1.00000			0.0680414
$217$	−21.0715	−	1.88333i	−1.43043	−	0.127849i
$218$			3.98612i			0.269974i
$219$	−1.72292	+	5.30260i	−0.116424	+	0.358317i
$220$	1.24072	+	6.11914i	0.0836496	+	0.412552i
$221$	3.51899	+	2.55670i	0.236713	+	0.171982i
$222$			2.89249i			0.194131i
$223$			8.97686i			0.601135i	0.953761	+	0.300568i	$0.0971761\pi$
$223$			8.97686i			0.601135i	−0.953761	+	0.300568i	$0.902824\pi$
$224$	3.07398	+	2.23337i	0.205389	+	0.149224i
$225$	4.60511	−	1.94754i	0.307008	−	0.129836i
$226$	−1.75013	+	1.27154i	−0.116417	+	0.0845818i
$227$	14.7250	+	4.78445i	0.977334	+	0.317555i	0.753773	−	0.657135i	$-0.228232\pi$
$227$	14.7250	+	4.78445i	0.977334	+	0.317555i	0.223561	+	0.974690i	$0.428232\pi$
$228$	−1.76109	+	2.42393i	−0.116631	+	0.160529i
$229$	−1.65436	+	5.09158i	−0.109323	+	0.336461i	−0.990721	−	0.135913i	$-0.956603\pi$
$229$	−1.65436	+	5.09158i	−0.109323	+	0.336461i	0.881398	+	0.472375i	$0.156603\pi$
$230$	0.687639	+	3.39138i	0.0453416	+	0.223621i
$231$	−8.58330	+	6.23613i	−0.564740	+	0.410308i
$232$	−0.168843	+	0.0548603i	−0.0110851	+	0.00360175i
$233$	−21.2277	+	6.89729i	−1.39067	+	0.451857i	−0.906163	−	0.422929i	$-0.861002\pi$
$233$	−21.2277	+	6.89729i	−1.39067	+	0.451857i	−0.484509	+	0.874786i	$0.661002\pi$
$234$	3.33708	−	2.42453i	0.218152	−	0.158496i
$235$	−20.2249	+	4.10083i	−1.31933	+	0.267509i
$236$	−3.06277	+	9.42624i	−0.199369	+	0.613596i
$237$	7.43050	−	10.2272i	0.482663	−	0.664328i
$238$	−3.81067	−	1.23816i	−0.247009	−	0.0802581i
$239$	−23.8933	+	17.3595i	−1.54553	+	1.12289i	−0.598781	+	0.800913i	$0.704348\pi$
$239$	−23.8933	+	17.3595i	−1.54553	+	1.12289i	−0.946747	+	0.321979i	$0.895652\pi$
$240$	1.09980	+	1.94690i	0.0709918	+	0.125672i
$241$	16.5135	+	11.9978i	1.06373	+	0.772844i	0.974775	−	0.223192i	$-0.0716476\pi$
$241$	16.5135	+	11.9978i	1.06373	+	0.772844i	0.0889539	+	0.996036i	$0.471648\pi$
$242$			3.20335i			0.205919i
$243$			1.00000i			0.0641500i
$244$	1.64767	+	1.19710i	0.105481	+	0.0766364i
$245$	3.30473	+	16.2986i	0.211131	+	1.04128i
$246$	2.53639	−	7.80619i	0.161714	−	0.497705i
$247$			12.3587i			0.786363i
$248$	2.18510	−	5.12107i	0.138754	−	0.325188i
$249$	−2.95274			−0.187122
$250$	8.85639	+	6.82381i	0.560127	+	0.431576i
$251$	−1.94190	−	5.97655i	−0.122571	−	0.377236i	0.870879	−	0.491497i	$-0.163550\pi$
$251$	−1.94190	−	5.97655i	−0.122571	−	0.377236i	−0.993451	+	0.114261i	$0.963550\pi$
$252$	−2.23337	+	3.07398i	−0.140689	+	0.193642i
$253$		−	4.32109i		−	0.271665i
$254$	−16.3749			−1.02745
$255$	−1.73742	−	1.59417i	−0.108801	−	0.0998309i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	0.398075	+	0.547904i	0.0248313	+	0.0341773i	0.821252	−	0.570565i	$-0.193276\pi$
$257$	0.398075	+	0.547904i	0.0248313	+	0.0341773i	−0.796421	+	0.604743i	$0.793276\pi$
$258$	−1.12153	−	0.364406i	−0.0698232	−	0.0226869i
$259$	−8.89145	−	6.46001i	−0.552488	−	0.401406i
$260$	8.39044	+	3.83047i	0.520353	+	0.237556i
$261$	−0.0548603	−	0.168843i	−0.00339577	−	0.0104511i
$262$	−2.38500	−	3.28268i	−0.147346	−	0.202804i
$263$	17.0256	−	5.53194i	1.04984	−	0.341114i	0.267235	−	0.963631i	$-0.413890\pi$
$263$	17.0256	−	5.53194i	1.04984	−	0.341114i	0.782606	+	0.622518i	$0.213890\pi$
$264$	−0.862852	−	2.65559i	−0.0531049	−	0.163440i
$265$	7.60781	+	13.4676i	0.467344	+	0.827308i
$266$	−3.51794	−	10.8271i	−0.215698	−	0.663852i
$267$	8.25793	+	2.68316i	0.505377	+	0.164207i
$268$	5.56860	−	7.66452i	0.340157	−	0.468185i
$269$	−9.53862	+	29.3568i	−0.581580	+	1.78992i	0.0310124	+	0.999519i	$0.490127\pi$
$269$	−9.53862	+	29.3568i	−0.581580	+	1.78992i	−0.612592	+	0.790399i	$0.709873\pi$
$270$	−1.94690	+	1.09980i	−0.118485	+	0.0669317i
$271$	14.9117	−	10.8340i	0.905822	−	0.658118i	−0.0341328	−	0.999417i	$-0.510867\pi$
$271$	14.9117	−	10.8340i	0.905822	−	0.658118i	0.939955	+	0.341299i	$0.110867\pi$
$272$	0.619828	−	0.853119i	0.0375826	−	0.0517280i
$273$			15.6730i			0.948571i
$274$	−5.12669			−0.309715
$275$	−9.14541	−	10.5488i	−0.551489	−	0.636119i
$276$	−0.478214	−	1.47179i	−0.0287851	−	0.0885914i
$277$	18.3367	+	5.95797i	1.10175	+	0.357980i	0.802775	−	0.596282i	$-0.203356\pi$
$277$	18.3367	+	5.95797i	1.10175	+	0.357980i	0.298973	+	0.954261i	$0.403356\pi$
$278$		−	15.5039i		−	0.929864i
$279$	5.12107	+	2.18510i	0.306590	+	0.130819i
$280$	−8.44100	−	0.967406i	−0.504446	−	0.0578136i
$281$	−1.14187	+	3.51431i	−0.0681181	+	0.209646i	−0.979321	−	0.202311i	$-0.935155\pi$
$281$	−1.14187	+	3.51431i	−0.0681181	+	0.209646i	0.911203	+	0.411957i	$0.135155\pi$
$282$	8.77722	−	2.85189i	0.522676	−	0.169828i
$283$	15.8457	−	21.8097i	0.941929	−	1.29645i	−0.0130919	−	0.999914i	$-0.504167\pi$
$283$	15.8457	−	21.8097i	0.941929	−	1.29645i	0.955021	−	0.296539i	$-0.0958326\pi$
$284$	12.5053			0.742055
$285$	0.762832	−	6.65601i	0.0451863	−	0.394268i
$286$	−9.31795	−	6.76989i	−0.550982	−	0.400312i
$287$	18.3313	+	25.2309i	1.08206	+	1.48933i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	4.90966	−	15.1104i	0.288804	−	0.888846i
$290$	0.268385	−	0.292501i	0.0157601	−	0.0171762i
$291$	−1.63005	+	5.01677i	−0.0955550	+	0.294088i
$292$	5.30260	−	1.72292i	0.310311	−	0.100826i
$293$	−13.7913	−	18.9821i	−0.805695	−	1.10894i	−0.991973	−	0.126447i	$-0.959643\pi$
$293$	−13.7913	−	18.9821i	−0.805695	−	1.10894i	0.186279	−	0.982497i	$-0.440357\pi$
$294$	−2.29825	−	7.07328i	−0.134036	−	0.412522i
$295$	−4.40406	−	21.7204i	−0.256414	−	1.26461i
$296$	2.34007	−	1.70016i	0.136014	−	0.0988200i
$297$	2.65559	−	0.862852i	0.154093	−	0.0500678i
$298$	13.5065	+	4.38852i	0.782409	+	0.254220i
$299$	−5.16423	−	3.75203i	−0.298655	−	0.216986i
$300$	−4.28241	−	2.58088i	−0.247245	−	0.149007i
$301$	3.62497	−	2.63369i	0.208940	−	0.151803i
$302$	−0.327308	−	0.450501i	−0.0188345	−	0.0259234i
$303$	−0.533869	+	0.734808i	−0.0306700	+	0.0422136i
$304$	2.99615			0.171841
$305$	−4.52442	−	0.518535i	−0.259068	−	0.0296912i
$306$	0.853119	+	0.619828i	0.0487696	+	0.0354332i
$307$	16.1092	−	5.23418i	0.919398	−	0.298730i	0.189178	−	0.981943i	$-0.439418\pi$
$307$	16.1092	−	5.23418i	0.919398	−	0.298730i	0.730220	+	0.683212i	$0.239418\pi$
$308$	10.0903	+	3.27853i	0.574947	+	0.186812i
$309$	−17.7899			−1.01203
$310$	1.37796	+	12.3734i	0.0782630	+	0.702762i
$311$	29.4541			1.67019			0.835093	−	0.550109i	$-0.185414\pi$
$311$	29.4541			1.67019			0.835093	+	0.550109i	$0.185414\pi$
$312$	−3.92297	−	1.27465i	−0.222094	−	0.0721628i
$313$	−22.8958	+	7.43930i	−1.29415	+	0.420494i	−0.873542	−	0.486749i	$-0.838183\pi$
$313$	−22.8958	+	7.43930i	−1.29415	+	0.420494i	−0.420606	+	0.907243i	$0.638183\pi$
$314$	6.23958	+	4.53332i	0.352120	+	0.255830i
$315$	0.967406	−	8.44100i	0.0545072	−	0.475597i
$316$	−12.6415			−0.711141
$317$	6.76388	−	9.30968i	0.379897	−	0.522884i	−0.575660	−	0.817689i	$-0.695255\pi$
$317$	6.76388	−	9.30968i	0.379897	−	0.522884i	0.955557	+	0.294805i	$0.0952548\pi$
$318$	−4.06597	−	5.59633i	−0.228008	−	0.313826i
$319$	−0.401040	+	0.291372i	−0.0224539	+	0.0163137i
$320$	0.928633	−	2.03412i	0.0519121	−	0.113711i
$321$	8.97048	+	6.51743i	0.500683	+	0.363768i
$322$	5.59228	+	1.81704i	0.311645	+	0.101260i
$323$	−3.00484	+	0.976332i	−0.167194	+	0.0543246i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−20.5482	+	1.77025i	−1.13981	+	0.0981957i
$326$	4.64549	+	14.2974i	0.257290	+	0.791857i
$327$	2.34298	+	3.22484i	0.129567	+	0.178334i
$328$	−7.80619	+	2.53639i	−0.431025	+	0.140048i
$329$	−10.8362	+	33.3503i	−0.597417	+	1.83866i
$330$	4.60051	+	4.22121i	0.253250	+	0.232370i
$331$	5.47249	−	16.8426i	0.300795	−	0.925753i	−0.680417	−	0.732825i	$-0.738202\pi$
$331$	5.47249	−	16.8426i	0.300795	−	0.925753i	0.981213	−	0.192928i	$-0.0617985\pi$
$332$	1.73558	+	2.38882i	0.0952521	+	0.131103i
$333$	1.70016	+	2.34007i	0.0931684	+	0.128235i
$334$	4.85655	+	3.52849i	0.265739	+	0.193070i
$335$	−2.41209	+	21.0465i	−0.131787	+	1.14989i
$336$	3.79964			0.207287
$337$	4.59814	−	6.32879i	0.250477	−	0.344751i	−0.665202	−	0.746664i	$-0.731654\pi$
$337$	4.59814	−	6.32879i	0.250477	−	0.344751i	0.915678	+	0.401912i	$0.131654\pi$
$338$	−3.81794	+	1.24052i	−0.207668	+	0.0674755i
$339$	−0.668490	+	2.05740i	−0.0363074	+	0.111743i
$340$	−0.268484	+	2.34263i	−0.0145606	+	0.127047i
$341$	1.38401	−	15.4849i	0.0749483	−	0.838552i
$342$			2.99615i			0.162013i
$343$	1.58019	+	0.513436i	0.0853225	+	0.0277230i
$344$	0.364406	+	1.12153i	0.0196475	+	0.0604687i
$345$	2.54971	+	2.33950i	0.137272	+	0.125954i
$346$	18.2943			0.983508
$347$		−	35.1565i		−	1.88730i	−0.330942	−	0.943651i	$-0.607366\pi$
$347$		−	35.1565i		−	1.88730i	0.330942	−	0.943651i	$-0.392634\pi$
$348$	−0.104350	+	0.143626i	−0.00559377	+	0.00769916i
$349$	22.3474	−	16.2363i	1.19623	−	0.869112i	0.202321	−	0.979319i	$-0.435152\pi$
$349$	22.3474	−	16.2363i	1.19623	−	0.869112i	0.993909	+	0.110208i	$0.0351515\pi$
$350$	17.4978	−	7.39997i	0.935296	−	0.395545i
$351$	1.27465	−	3.92297i	0.0680358	−	0.209393i
$352$	−1.64124	+	2.25898i	−0.0874785	+	0.120404i
$353$	−19.5705	−	6.35886i	−1.04164	−	0.338448i	−0.262255	−	0.964999i	$-0.584466\pi$
$353$	−19.5705	−	6.35886i	−1.04164	−	0.338448i	−0.779380	+	0.626551i	$0.784466\pi$
$354$	3.06277	+	9.42624i	0.162784	+	0.500999i
$355$	−24.3467	+	13.7534i	−1.29219	+	0.729953i
$356$	−2.68316	−	8.25793i	−0.142207	−	0.437669i
$357$	−3.81067	+	1.23816i	−0.201682	+	0.0655305i
$358$	−7.00723	−	9.64462i	−0.370343	−	0.509734i
$359$	−8.81606	−	27.1330i	−0.465294	−	1.43203i	−0.858613	−	0.512625i	$-0.828673\pi$
$359$	−8.81606	−	27.1330i	−0.465294	−	1.43203i	0.393319	−	0.919402i	$-0.371327\pi$
$360$	2.03412	+	0.928633i	0.107208	+	0.0489432i
$361$	8.10887	+	5.89144i	0.426783	+	0.310076i
$362$	−19.6490	−	6.38433i	−1.03273	−	0.335553i
$363$	1.88288	+	2.59156i	0.0988256	+	0.136022i
$364$	12.6797	−	9.21234i	0.664597	−	0.482858i
$365$	−8.42880	+	9.18617i	−0.441183	+	0.480826i
$366$	2.03663			0.106456
$367$			31.6916i			1.65429i	0.561990	+	0.827144i	$0.310036\pi$
$367$			31.6916i			1.65429i	−0.561990	+	0.827144i	$0.689964\pi$
$368$	−0.909616	+	1.25198i	−0.0474170	+	0.0652639i
$369$	−2.53639	−	7.80619i	−0.132039	−	0.406374i
$370$	−2.68606	+	5.88367i	−0.139642	+	0.305878i
$371$	26.2838			1.36459
$372$	−1.24230	−	5.42740i	−0.0644103	−	0.281398i
$373$		−	10.9341i		−	0.566144i	−0.959099	−	0.283072i	$-0.908646\pi$
$373$		−	10.9341i		−	0.566144i	0.959099	−	0.283072i	$-0.0913536\pi$
$374$	0.909890	−	2.80035i	0.0470493	−	0.144803i
$375$	11.1759	+	0.314921i	0.577121	+	0.0162624i
$376$	−7.46635	−	5.42462i	−0.385048	−	0.279753i
$377$			0.732292i			0.0377149i
$378$			3.79964i			0.195433i
$379$	−10.8636	−	7.89283i	−0.558023	−	0.405428i	0.272712	−	0.962096i	$-0.412079\pi$
$379$	−10.8636	−	7.89283i	−0.558023	−	0.405428i	−0.830735	+	0.556668i	$0.812079\pi$
$380$	−5.83321	+	3.29516i	−0.299237	+	0.169038i
$381$	−13.2475	+	9.62491i	−0.678692	+	0.493099i
$382$	−0.238688	−	0.0775543i	−0.0122123	−	0.00396802i
$383$	−6.07824	+	8.36599i	−0.310584	+	0.427482i	−0.935563	−	0.353159i	$-0.885107\pi$
$383$	−6.07824	+	8.36599i	−0.310584	+	0.427482i	0.624979	+	0.780641i	$0.285107\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−23.2505	+	4.71431i	−1.18496	+	0.240263i
$386$	7.99723	−	5.81033i	0.407048	−	0.295738i
$387$	−1.12153	+	0.364406i	−0.0570104	+	0.0185238i
$388$	5.01677	−	1.63005i	0.254688	−	0.0827531i
$389$	10.1537	−	7.37706i	0.514811	−	0.374032i	−0.299835	−	0.953991i	$-0.596932\pi$
$389$	10.1537	−	7.37706i	0.514811	−	0.374032i	0.814645	+	0.579959i	$0.196932\pi$
$390$	9.03951	−	1.83286i	0.457733	−	0.0928105i
$391$	0.504283	−	1.55202i	0.0255027	−	0.0784892i
$392$	−4.37152	+	6.01689i	−0.220795	+	0.303899i
$393$	−3.85902	−	1.25387i	−0.194662	−	0.0632494i
$394$	−1.12250	+	0.815546i	−0.0565509	+	0.0410866i
$395$	24.6118	−	13.9031i	1.23836	−	0.699543i
$396$	−2.25898	−	1.64124i	−0.113518	−	0.0824755i
$397$		−	5.62932i		−	0.282527i	−0.989972	−	0.141264i	$-0.954883\pi$
$397$		−	5.62932i		−	0.282527i	0.989972	−	0.141264i	$-0.0451165\pi$
$398$			11.2284i			0.562827i
$399$	−9.21008	−	6.69151i	−0.461080	−	0.334995i
$400$	0.429166	+	4.98155i	0.0214583	+	0.249077i
$401$	6.63765	−	20.4286i	0.331469	−	1.02016i	−0.636967	−	0.770891i	$-0.719811\pi$
$401$	6.63765	−	20.4286i	0.331469	−	1.02016i	0.968435	−	0.249264i	$-0.0801888\pi$
$402$		−	9.47387i		−	0.472514i
$403$	−17.3045	−	15.0997i	−0.862001	−	0.752168i
$404$	0.908273			0.0451883
$405$	−0.928633	+	2.03412i	−0.0461441	+	0.101076i
$406$	−0.208449	−	0.641541i	−0.0103452	−	0.0318392i
$407$	4.74728	−	6.53407i	0.235314	−	0.323882i
$408$		−	1.05451i		−	0.0522062i
$409$	18.2271			0.901271			0.450635	−	0.892708i	$-0.351197\pi$
$409$	18.2271			0.901271			0.450635	+	0.892708i	$0.351197\pi$
$410$	12.4084	−	13.5234i	0.612807	−	0.667871i
$411$	−4.14758	+	3.01339i	−0.204585	+	0.148640i
$412$	10.4566	+	14.3923i	0.515161	+	0.709059i
$413$	−35.8163	−	11.6374i	−1.76241	−	0.572641i
$414$	−1.25198	−	0.909616i	−0.0615314	−	0.0447052i
$415$	−6.00622	−	2.74201i	−0.294834	−	0.134600i
$416$	1.27465	+	3.92297i	0.0624948	+	0.192339i
$417$	−9.11299	−	12.5430i	−0.446265	−	0.614231i
$418$	7.95652	−	2.58523i	0.389166	−	0.126448i
$419$	8.92352	+	27.4638i	0.435942	+	1.34169i	0.892118	+	0.451803i	$0.149219\pi$
$419$	8.92352	+	27.4638i	0.435942	+	1.34169i	−0.456176	+	0.889890i	$0.650781\pi$
$420$	−7.39754	+	4.17885i	−0.360963	+	0.203907i
$421$	−10.6658	−	32.8259i	−0.519819	−	1.59984i	−0.774339	−	0.632771i	$-0.781918\pi$
$421$	−10.6658	−	32.8259i	−0.519819	−	1.59984i	0.254520	−	0.967067i	$-0.418082\pi$
$422$	15.2543	+	4.95644i	0.742570	+	0.241276i
$423$	5.42462	−	7.46635i	0.263754	−	0.363026i
$424$	−2.13761	+	6.57888i	−0.103811	+	0.319498i
$425$	−2.05371	−	4.85616i	−0.0996197	−	0.235558i
$426$	10.1170	−	7.35045i	0.490171	−	0.356130i
$427$	−4.54855	+	6.26054i	−0.220120	+	0.302969i
$428$		−	11.0881i		−	0.535965i
$429$	−11.5176			−0.556076
$430$	−1.94292	−	1.78273i	−0.0936960	−	0.0859710i
$431$	−6.37406	−	19.6174i	−0.307028	−	0.944935i	−0.978913	−	0.204279i	$-0.934515\pi$
$431$	−6.37406	−	19.6174i	−0.307028	−	0.944935i	0.671885	−	0.740656i	$-0.265485\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$		−	38.9035i		−	1.86958i	−0.355195	−	0.934792i	$-0.615586\pi$
$433$		−	38.9035i		−	1.86958i	0.355195	−	0.934792i	$-0.384414\pi$
$434$	19.4582	+	8.30261i	0.934024	+	0.398538i
$435$	0.0452004	−	0.394391i	0.00216719	−	0.0189096i
$436$	1.23178	−	3.79102i	0.0589915	−	0.181557i
$437$	4.40970	−	1.43280i	0.210944	−	0.0685400i
$438$	3.27719	−	4.51066i	0.156590	−	0.215528i
$439$	5.25358			0.250740			0.125370	−	0.992110i	$-0.459988\pi$
$439$	5.25358			0.250740			0.125370	+	0.992110i	$0.459988\pi$
$440$	0.710919	−	6.20305i	0.0338918	−	0.295719i
$441$	−6.01689	−	4.37152i	−0.286518	−	0.208168i
$442$	−2.55670	−	3.51899i	−0.121610	−	0.167381i
$443$	17.4071	+	23.9588i	0.827037	+	1.13832i	0.988467	+	0.151434i	$0.0483892\pi$
$443$	17.4071	+	23.9588i	0.827037	+	1.13832i	−0.161431	+	0.986884i	$0.551611\pi$
$444$	0.893829	−	2.75092i	0.0424192	−	0.130553i
$445$	14.3059	+	13.1265i	0.678166	+	0.622254i
$446$	2.77400	−	8.53750i	0.131353	−	0.404262i
$447$	13.5065	−	4.38852i	0.638835	−	0.207570i
$448$	−2.23337	−	3.07398i	−0.105517	−	0.145232i
$449$	−8.26674	−	25.4424i	−0.390132	−	1.20070i	−0.932689	−	0.360683i	$-0.882544\pi$
$449$	−8.26674	−	25.4424i	−0.390132	−	1.20070i	0.542557	−	0.840019i	$-0.317456\pi$
$450$	−4.98155	+	0.429166i	−0.234832	+	0.0202311i
$451$	−18.5415	+	13.4712i	−0.873085	+	0.634333i
$452$	2.05740	−	0.668490i	0.0967720	−	0.0314431i
$453$	−0.529596	−	0.172076i	−0.0248826	−	0.00808484i
$454$	−12.5259	−	9.10057i	−0.587868	−	0.427111i
$455$	−14.5544	+	31.8807i	−0.682322	+	1.49459i
$456$	2.42393	−	1.76109i	0.113511	−	0.0824706i
$457$	−12.9314	−	17.7985i	−0.604905	−	0.832581i	0.391241	−	0.920288i	$-0.372046\pi$
$457$	−12.9314	−	17.7985i	−0.604905	−	0.832581i	−0.996146	+	0.0877076i	$0.972046\pi$
$458$	3.14677	−	4.33116i	0.147039	−	0.202382i
$459$	1.05451			0.0492205
$460$	0.394009	−	3.43788i	0.0183708	−	0.160292i
$461$	−17.6696	−	12.8377i	−0.822956	−	0.597913i	0.0946016	−	0.995515i	$-0.469842\pi$
$461$	−17.6696	−	12.8377i	−0.822956	−	0.597913i	−0.917558	+	0.397603i	$0.869842\pi$
$462$	10.0903	−	3.27853i	0.469442	−	0.152531i
$463$	38.4335	+	12.4878i	1.78616	+	0.580358i	0.999322	−	0.0368047i	$-0.0117179\pi$
$463$	38.4335	+	12.4878i	1.78616	+	0.580358i	0.786836	+	0.617163i	$0.211718\pi$
$464$	0.177532			0.00824170
$465$	8.38770	+	9.20035i	0.388970	+	0.426656i
$466$	22.3201			1.03396
$467$	−2.05847	−	0.668839i	−0.0952548	−	0.0309502i	0.261002	−	0.965338i	$-0.415947\pi$
$467$	−2.05847	−	0.668839i	−0.0952548	−	0.0309502i	−0.356257	+	0.934388i	$0.615947\pi$
$468$	−3.92297	+	1.27465i	−0.181339	+	0.0589207i
$469$	29.1225	+	21.1587i	1.34475	+	0.977018i
$470$	20.5023	+	2.34972i	0.945699	+	0.108385i
$471$	7.71255			0.355375
$472$	5.82574	−	8.01844i	0.268151	−	0.369079i
$473$	1.93542	+	2.66388i	0.0889909	+	0.122486i
$474$	−10.2272	+	7.43050i	−0.469751	+	0.341294i
$475$	7.73268	−	12.8307i	0.354800	−	0.588714i
$476$	3.24155	+	2.35512i	0.148576	+	0.107947i
$477$	−6.57888	−	2.13761i	−0.301226	−	0.0978743i
$478$	28.0882	−	9.12642i	1.28473	−	0.417433i
$479$	19.2635	−	13.9957i	0.880171	−	0.639482i	−0.0531256	−	0.998588i	$-0.516918\pi$
$479$	19.2635	−	13.9957i	0.880171	−	0.639482i	0.933297	+	0.359106i	$0.116918\pi$
$480$	−0.444346	−	2.19147i	−0.0202815	−	0.100027i
$481$	−3.68691	−	11.3472i	−0.168109	−	0.517386i
$482$	−11.9978	−	16.5135i	−0.546483	−	0.752170i
$483$	5.59228	−	1.81704i	0.254457	−	0.0826782i
$484$	0.989889	−	3.04656i	0.0449949	−	0.138480i
$485$	−7.97444	+	8.69099i	−0.362101	+	0.394638i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−6.64089	−	9.14040i	−0.300927	−	0.414191i	0.631598	−	0.775296i	$-0.282399\pi$
$487$	−6.64089	−	9.14040i	−0.300927	−	0.414191i	−0.932525	+	0.361105i	$0.882399\pi$
$488$	−1.19710	−	1.64767i	−0.0541902	−	0.0745863i
$489$	12.1621	+	8.83625i	0.549987	+	0.399589i
$490$	1.89357	−	16.5221i	0.0855426	−	0.746393i
$491$	41.9276			1.89217			0.946084	−	0.323922i	$-0.105001\pi$
$491$	41.9276			1.89217			0.946084	+	0.323922i	$0.105001\pi$
$492$	−4.82449	+	6.64034i	−0.217505	+	0.299370i
$493$	−0.178047	+	0.0578509i	−0.00801882	+	0.00260547i
$494$	3.81904	−	11.7538i	0.171827	−	0.528828i
$495$	6.20305	+	0.710919i	0.278806	+	0.0319535i
$496$	−3.66065	+	4.19519i	−0.164368	+	0.188370i
$497$			47.5158i			2.13137i
$498$	2.80822	+	0.912446i	0.125839	+	0.0408877i
$499$	0.401638	+	1.23611i	0.0179798	+	0.0553360i	0.959644	−	0.281218i	$-0.0907385\pi$
$499$	0.401638	+	1.23611i	0.0179798	+	0.0553360i	−0.941664	+	0.336554i	$0.890738\pi$
$500$	−6.31425	−	9.22660i	−0.282382	−	0.412626i
$501$	6.00303			0.268195
$502$			6.28411i			0.280474i
$503$	−5.29036	+	7.28155i	−0.235885	+	0.324668i	−0.910506	−	0.413496i	$-0.864307\pi$
$503$	−5.29036	+	7.28155i	−0.235885	+	0.324668i	0.674620	+	0.738165i	$0.264307\pi$
$504$	3.07398	−	2.23337i	0.136926	−	0.0994824i
$505$	−1.76832	+	0.998919i	−0.0786893	+	0.0444513i
$506$	−1.33529	+	4.10960i	−0.0593609	+	0.182694i
$507$	−2.35961	+	3.24773i	−0.104794	+	0.144237i
$508$	15.5734	+	5.06011i	0.690959	+	0.224506i
$509$	2.20308	+	6.78040i	0.0976500	+	0.300536i	0.987935	−	0.154868i	$-0.0494951\pi$
$509$	2.20308	+	6.78040i	0.0976500	+	0.300536i	−0.890285	+	0.455403i	$0.849495\pi$
$510$	1.15975	+	2.05304i	0.0513548	+	0.0909100i
$511$	6.54648	+	20.1480i	0.289599	+	0.891295i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	1.76109	+	2.42393i	0.0777540	+	0.107019i
$514$	−0.209281	−	0.644100i	−0.00923097	−	0.0284100i
$515$	−36.1868	−	16.5203i	−1.59458	−	0.727970i
$516$	0.954028	+	0.693142i	0.0419987	+	0.0305139i
$517$	−24.5082	−	7.96319i	−1.07787	−	0.350221i
$518$	6.46001	+	8.89145i	0.283837	+	0.390668i
$519$	14.8004	−	10.7531i	0.649666	−	0.472010i
$520$	−6.79611	−	6.23579i	−0.298029	−	0.273457i
$521$	3.51280			0.153899			0.0769494	−	0.997035i	$-0.475482\pi$
$521$	3.51280			0.153899			0.0769494	+	0.997035i	$0.475482\pi$
$522$			0.177532i			0.00777035i
$523$	20.0849	−	27.6445i	0.878251	−	1.20881i	−0.0986518	−	0.995122i	$-0.531453\pi$
$523$	20.0849	−	27.6445i	0.878251	−	1.20881i	0.976902	−	0.213686i	$-0.0685470\pi$
$524$	1.25387	+	3.85902i	0.0547756	+	0.168582i
$525$	9.80641	−	16.2716i	0.427987	−	0.710153i
$526$	−17.9017			−0.780552
$527$	2.30422	−	5.40023i	0.100373	−	0.235238i
$528$			2.79225i			0.121517i
$529$	6.36734	−	19.5967i	0.276841	−	0.852029i
$530$	−3.07374	−	15.1594i	−0.133515	−	0.658482i
$531$	8.01844	+	5.82574i	0.347971	+	0.252815i
$532$			11.3843i			0.493571i
$533$			33.8564i			1.46649i
$534$	−7.02461	−	5.10368i	−0.303985	−	0.220858i
$535$	12.1947	+	21.5875i	0.527224	+	0.933310i
$536$	−7.66452	+	5.56860i	−0.331057	+	0.240527i
$537$	−11.3379	−	3.68392i	−0.489268	−	0.158973i
$538$	18.1435	−	24.9724i	0.782223	−	1.07664i
$539$	−6.41728	+	19.7503i	−0.276412	+	0.850708i
$540$	2.19147	−	0.444346i	0.0943060	−	0.0191216i
$541$	0.0364161	−	0.0264578i	0.00156565	−	0.00113751i	−0.587002	−	0.809585i	$-0.699692\pi$
$541$	0.0364161	−	0.0264578i	0.00156565	−	0.00113751i	0.588568	+	0.808448i	$0.299692\pi$
$542$	−17.5298	+	5.69577i	−0.752968	+	0.244654i
$543$	−19.6490	+	6.38433i	−0.843218	+	0.273978i
$544$	−0.853119	+	0.619828i	−0.0365772	+	0.0265749i
$545$	1.77121	+	8.73547i	0.0758705	+	0.374186i
$546$	4.84321	−	14.9059i	0.207270	−	0.637913i
$547$	2.52162	−	3.47072i	0.107817	−	0.148397i	−0.751699	−	0.659507i	$-0.770765\pi$
$547$	2.52162	−	3.47072i	0.107817	−	0.148397i	0.859516	+	0.511109i	$0.170765\pi$
$548$	4.87577	+	1.58424i	0.208283	+	0.0676752i
$549$	1.64767	−	1.19710i	0.0703207	−	0.0510910i
$550$	5.43803	+	12.8586i	0.231878	+	0.548294i
$551$	−0.430324	−	0.312649i	−0.0183324	−	0.0133193i
$552$			1.54753i			0.0658673i
$553$		−	48.0332i		−	2.04258i
$554$	−15.5982	−	11.3327i	−0.662703	−	0.481482i
$555$	1.28527	+	6.33882i	0.0545565	+	0.269068i
$556$	−4.79098	+	14.7451i	−0.203183	+	0.625332i
$557$			18.4404i			0.781345i	0.920530	+	0.390672i	$0.127757\pi$
$557$			18.4404i			0.781345i	−0.920530	+	0.390672i	$0.872243\pi$
$558$	−4.19519	−	3.66065i	−0.177597	−	0.154968i
$559$	4.86421			0.205734
$560$	7.72893	+	3.52847i	0.326607	+	0.149105i
$561$	−0.909890	−	2.80035i	−0.0384156	−	0.118231i
$562$	2.17196	−	2.98945i	0.0916187	−	0.126102i
$563$			34.3651i			1.44832i	0.689634	+	0.724158i	$0.257771\pi$
$563$			34.3651i			1.44832i	−0.689634	+	0.724158i	$0.742229\pi$
$564$	−9.22892			−0.388607
$565$	−3.27036	+	3.56422i	−0.137585	+	0.149948i
$566$	−21.8097	+	15.8457i	−0.916731	+	0.666044i
$567$	2.23337	+	3.07398i	0.0937929	+	0.129095i
$568$	−11.8933	−	3.86436i	−0.499031	−	0.162145i
$569$	−17.2247	−	12.5145i	−0.722097	−	0.524634i	0.164956	−	0.986301i	$-0.447252\pi$
$569$	−17.2247	−	12.5145i	−0.722097	−	0.524634i	−0.887054	+	0.461666i	$0.847252\pi$
$570$	−2.78232	+	6.09452i	−0.116538	+	0.255271i
$571$	5.77031	+	17.7592i	0.241480	+	0.743198i	0.996196	+	0.0871464i	$0.0277748\pi$
$571$	5.77031	+	17.7592i	0.241480	+	0.743198i	−0.754716	+	0.656052i	$0.772225\pi$
$572$	6.76989	+	9.31795i	0.283063	+	0.389603i
$573$	−0.238688	+	0.0775543i	−0.00997132	+	0.00323988i
$574$	−9.63736	−	29.6607i	−0.402255	−	1.23802i
$575$	3.01389	+	7.12656i	0.125688	+	0.297198i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	0.988412	+	0.321154i	0.0411481	+	0.0133698i	0.329519	−	0.944149i	$-0.393114\pi$
$577$	0.988412	+	0.321154i	0.0411481	+	0.0133698i	−0.288371	+	0.957519i	$0.593114\pi$
$578$	−9.33873	+	12.8537i	−0.388440	+	0.534642i
$579$	3.05467	−	9.40131i	0.126948	−	0.390705i
$580$	−0.345637	+	0.195249i	−0.0143518	+	0.00810729i
$581$	−9.07664	+	6.59457i	−0.376563	+	0.273589i
$582$	3.10053	−	4.26752i	0.128521	−	0.176894i
$583$			19.3152i			0.799954i
$584$	−5.57549			−0.230715
$585$	6.23579	−	6.79611i	0.257818	−	0.280984i
$586$	7.25050	+	22.3148i	0.299515	+	0.921814i
$587$	−41.9333	−	13.6250i	−1.73077	−	0.562362i	−0.737211	−	0.675662i	$-0.763858\pi$
$587$	−41.9333	−	13.6250i	−1.73077	−	0.562362i	−0.993561	+	0.113300i	$0.963858\pi$
$588$			7.43728i			0.306708i
$589$	16.2613	−	3.72211i	0.670034	−	0.153367i
$590$	−2.52347	+	22.0183i	−0.103890	+	0.906479i
$591$	−0.428758	+	1.31958i	−0.0176368	+	0.0542803i
$592$	−2.75092	+	0.893829i	−0.113062	+	0.0367361i
$593$	−18.7349	+	25.7864i	−0.769352	+	1.05892i	0.227026	+	0.973889i	$0.427100\pi$
$593$	−18.7349	+	25.7864i	−0.769352	+	1.05892i	−0.996378	+	0.0850335i	$0.972900\pi$
$594$	−2.79225			−0.114567
$595$	−8.90115	−	1.02014i	−0.364912	−	0.0418218i
$596$	−11.4893	−	8.34746i	−0.470620	−	0.341925i
$597$	6.59987	+	9.08394i	0.270115	+	0.371781i
$598$	3.75203	+	5.16423i	0.153432	+	0.211181i
$599$	0.435098	−	1.33909i	0.0177776	−	0.0547138i	−0.941774	−	0.336246i	$-0.890843\pi$
$599$	0.435098	−	1.33909i	0.0177776	−	0.0547138i	0.959552	+	0.281532i	$0.0908426\pi$
$600$	3.27528	+	3.77790i	0.133713	+	0.154232i
$601$	−10.6004	+	32.6248i	−0.432401	+	1.33079i	0.463326	+	0.886188i	$0.346656\pi$
$601$	−10.6004	+	32.6248i	−0.432401	+	1.33079i	−0.895727	+	0.444605i	$0.853344\pi$
$602$	−4.26140	+	1.38461i	−0.173682	+	0.0564326i
$603$	−5.56860	−	7.66452i	−0.226771	−	0.312124i
$604$	0.172076	+	0.529596i	0.00700167	+	0.0215489i
$605$	1.42339	+	7.02005i	0.0578692	+	0.285406i
$606$	0.734808	−	0.533869i	0.0298495	−	0.0216870i
$607$	−0.988575	+	0.321208i	−0.0401250	+	0.0130374i	−0.329011	−	0.944326i	$-0.606715\pi$
$607$	−0.988575	+	0.321208i	−0.0401250	+	0.0130374i	0.288886	+	0.957364i	$0.406715\pi$
$608$	−2.84950	−	0.925860i	−0.115563	−	0.0375486i
$609$	−0.545728	−	0.396494i	−0.0221140	−	0.0160668i
$610$	4.14274	+	1.89128i	0.167735	+	0.0765756i
$611$	−30.7976	+	22.3758i	−1.24594	+	0.905227i
$612$	−0.619828	−	0.853119i	−0.0250550	−	0.0344853i
$613$	24.0307	−	33.0754i	0.970590	−	1.33590i	0.0288412	−	0.999584i	$-0.490818\pi$
$613$	24.0307	−	33.0754i	0.970590	−	1.33590i	0.941748	−	0.336318i	$-0.109182\pi$
$614$	−16.9382			−0.683569
$615$	2.08977	−	18.2341i	0.0842678	−	0.735270i
$616$	−8.58330	−	6.23613i	−0.345831	−	0.251261i
$617$	27.8317	−	9.04306i	1.12046	−	0.364060i	0.310517	−	0.950568i	$-0.399498\pi$
$617$	27.8317	−	9.04306i	1.12046	−	0.364060i	0.809943	+	0.586508i	$0.199498\pi$
$618$	16.9192	+	5.49738i	0.680590	+	0.221137i
$619$	32.8381			1.31987			0.659937	−	0.751321i	$-0.270583\pi$
$619$	32.8381			1.31987			0.659937	+	0.751321i	$0.270583\pi$
$620$	2.51307	−	12.1936i	0.100927	−	0.489708i
$621$	−1.54753			−0.0621003
$622$	−28.0125	−	9.10180i	−1.12320	−	0.364949i
$623$	31.3772	−	10.1951i	1.25710	−	0.408456i
$624$	3.33708	+	2.42453i	0.133590	+	0.0970588i
$625$	22.4407	+	11.0189i	0.897627	+	0.440756i
$626$	24.0741			0.962194
$627$	4.91740	−	6.76822i	0.196382	−	0.270297i
$628$	−4.53332	−	6.23958i	−0.180899	−	0.248986i
$629$	2.46764	−	1.79285i	0.0983913	−	0.0714854i
$630$	−3.52847	+	7.72893i	−0.140578	+	0.307928i
$631$	−10.3435	−	7.51499i	−0.411768	−	0.299167i	0.362549	−	0.931965i	$-0.381906\pi$
$631$	−10.3435	−	7.51499i	−0.411768	−	0.299167i	−0.774317	+	0.632798i	$0.781906\pi$
$632$	12.0228	+	3.90644i	0.478241	+	0.155390i
$633$	15.2543	−	4.95644i	0.606306	−	0.197001i
$634$	−9.30968	+	6.76388i	−0.369735	+	0.268628i
$635$	−35.8851	+	7.27610i	−1.42406	+	0.288743i
$636$	2.13761	+	6.57888i	0.0847616	+	0.260869i
$637$	18.0319	+	24.8188i	0.714450	+	0.983356i
$638$	0.471450	−	0.153184i	0.0186649	−	0.00606459i
$639$	3.86436	−	11.8933i	0.152872	−	0.470491i
$640$	−1.51176	+	1.64760i	−0.0597575	+	0.0651271i
$641$	−12.5128	+	38.5103i	−0.494225	+	1.52107i	0.323937	+	0.946079i	$0.394993\pi$
$641$	−12.5128	+	38.5103i	−0.494225	+	1.52107i	−0.818162	+	0.574988i	$0.805007\pi$
$642$	−6.51743	−	8.97048i	−0.257223	−	0.354037i
$643$	−20.4378	−	28.1302i	−0.805987	−	1.10935i	−0.991930	−	0.126786i	$-0.959534\pi$
$643$	−20.4378	−	28.1302i	−0.805987	−	1.10935i	0.185943	−	0.982561i	$-0.440466\pi$
$644$	−4.75707	−	3.45622i	−0.187455	−	0.136194i
$645$	−2.61972	−	0.300241i	−0.103151	−	0.0118220i
$646$	3.15948			0.124308
$647$	−3.97572	+	5.47212i	−0.156302	+	0.215131i	−0.879985	−	0.475001i	$-0.842448\pi$
$647$	−3.97572	+	5.47212i	−0.156302	+	0.215131i	0.723683	+	0.690132i	$0.242448\pi$
$648$	−0.951057	+	0.309017i	−0.0373610	+	0.0121393i
$649$	8.55202	−	26.3204i	0.335696	−	1.03317i
$650$	20.0895	+	4.66612i	0.787975	+	0.183020i
$651$	20.6222	−	4.72030i	0.808247	−	0.185003i
$652$		−	15.0331i		−	0.588743i
$653$	13.2295	+	4.29853i	0.517711	+	0.168214i	0.556206	−	0.831044i	$-0.312257\pi$
$653$	13.2295	+	4.29853i	0.517711	+	0.168214i	−0.0384955	+	0.999259i	$0.512257\pi$
$654$	−1.23178	−	3.79102i	−0.0481663	−	0.148241i
$655$	−6.68532	−	6.13413i	−0.261217	−	0.239680i
$656$	8.20791			0.320465
$657$		−	5.57549i		−	0.217521i
$658$	20.6116	−	28.3695i	0.803525	−	1.10596i
$659$	−3.40677	+	2.47516i	−0.132709	+	0.0964187i	−0.652159	−	0.758082i	$-0.726137\pi$
$659$	−3.40677	+	2.47516i	−0.132709	+	0.0964187i	0.519450	+	0.854501i	$0.326137\pi$
$660$	−3.07092	−	5.43624i	−0.119535	−	0.211605i
$661$	9.74097	−	29.9796i	0.378880	−	1.16607i	−0.561944	−	0.827175i	$-0.689946\pi$
$661$	9.74097	−	29.9796i	0.378880	−	1.16607i	0.940824	−	0.338897i	$-0.110054\pi$
$662$	−10.4093	+	14.3272i	−0.404569	+	0.556841i
$663$	−4.13682	−	1.34414i	−0.160661	−	0.0522019i
$664$	−0.912446	−	2.80822i	−0.0354098	−	0.108980i
$665$	−12.5204	−	22.1641i	−0.485522	−	0.859487i
$666$	−0.893829	−	2.75092i	−0.0346352	−	0.106596i
$667$	0.261289	−	0.0848980i	0.0101172	−	0.00328726i
$668$	−3.52849	−	4.85655i	−0.136521	−	0.187906i
$669$	−2.77400	−	8.53750i	−0.107249	−	0.330079i
$670$	8.79775	−	19.2710i	0.339887	−	0.744503i
$671$	−4.60069	−	3.34260i	−0.177608	−	0.129040i
$672$	−3.61367	−	1.17415i	−0.139401	−	0.0452940i
$673$	16.5827	+	22.8241i	0.639214	+	0.879803i	0.998573	−	0.0533963i	$-0.0170047\pi$
$673$	16.5827	+	22.8241i	0.639214	+	0.879803i	−0.359359	+	0.933199i	$0.617005\pi$
$674$	−6.32879	+	4.59814i	−0.243776	+	0.177114i
$675$	−3.77790	+	3.27528i	−0.145411	+	0.126066i
$676$	4.01442			0.154401
$677$		−	18.3279i		−	0.704400i	−0.935925	−	0.352200i	$-0.885434\pi$
$677$		−	18.3279i		−	0.704400i	0.935925	−	0.352200i	$-0.114566\pi$
$678$	1.27154	−	1.75013i	0.0488334	−	0.0672133i
$679$	6.19359	+	19.0619i	0.237688	+	0.731529i
$680$	0.979256	−	2.14501i	0.0375527	−	0.0822572i
$681$	−15.4828			−0.593303
$682$	−6.10135	+	14.2993i	−0.233633	+	0.547548i
$683$			24.2863i			0.929288i	0.885498	+	0.464644i	$0.153818\pi$
$683$			24.2863i			0.929288i	−0.885498	+	0.464644i	$0.846182\pi$
$684$	0.925860	−	2.84950i	0.0354011	−	0.108953i
$685$	−11.2350	+	2.27802i	−0.429268	+	0.0870388i
$686$	−1.34419	−	0.976614i	−0.0513215	−	0.0372873i
$687$		−	5.35361i		−	0.204253i
$688$		−	1.17924i		−	0.0449582i
$689$	23.0840	+	16.7715i	0.879431	+	0.638944i
$690$	−1.70198	−	3.01290i	−0.0647931	−	0.114699i
$691$	−22.1080	+	16.0624i	−0.841026	+	0.611041i	−0.922657	−	0.385621i	$-0.873987\pi$
$691$	−22.1080	+	16.0624i	−0.841026	+	0.611041i	0.0816308	+	0.996663i	$0.473987\pi$
$692$	−17.3989	−	5.65325i	−0.661408	−	0.214904i
$693$	6.23613	−	8.58330i	0.236891	−	0.326053i
$694$	−10.8640	+	33.4359i	−0.412391	+	1.26921i
$695$	−6.88911	−	33.9765i	−0.261319	−	1.28880i
$696$	0.143626	−	0.104350i	0.00544413	−	0.00395539i
$697$	−8.23173	+	2.67465i	−0.311799	+	0.101310i
$698$	−26.2710	+	8.53595i	−0.994371	+	0.323091i
$699$	18.0573	−	13.1194i	0.682992	−	0.496222i
$700$	−18.9281	+	1.63068i	−0.715415	+	0.0616339i
$701$	12.3336	−	37.9590i	0.465835	−	1.43369i	−0.392095	−	0.919925i	$-0.628250\pi$
$701$	12.3336	−	37.9590i	0.465835	−	1.43369i	0.857930	−	0.513767i	$-0.171750\pi$
$702$	−2.42453	+	3.33708i	−0.0915079	+	0.125950i
$703$	8.24216	+	2.67804i	0.310859	+	0.101004i
$704$	2.25898	−	1.64124i	0.0851384	−	0.0618567i
$705$	17.9678	−	10.1500i	0.676707	−	0.382270i
$706$	16.6477	+	12.0953i	0.626544	+	0.455211i
$707$			3.45111i			0.129792i
$708$		−	9.91134i		−	0.372491i
$709$	−19.2230	−	13.9663i	−0.721934	−	0.524516i	0.165068	−	0.986282i	$-0.447216\pi$
$709$	−19.2230	−	13.9663i	−0.721934	−	0.524516i	−0.887001	+	0.461767i	$0.847216\pi$
$710$	27.4051	−	5.55669i	1.02850	−	0.208539i
$711$	−3.90644	+	12.0228i	−0.146503	+	0.450890i
$712$			8.68290i			0.325405i
$713$	−3.38152	+	7.92501i	−0.126639	+	0.296794i
$714$	4.00677			0.149950
$715$	−23.4282	−	10.6956i	−0.876165	−	0.399994i
$716$	3.68392	+	11.3379i	0.137674	+	0.423718i
$717$	17.3595	−	23.8933i	0.648302	−	0.892311i
$718$			28.5294i			1.06471i
$719$	−9.60684			−0.358275			−0.179137	−	0.983824i	$-0.557331\pi$
$719$	−9.60684			−0.358275			−0.179137	+	0.983824i	$0.557331\pi$
$720$	−1.64760	−	1.51176i	−0.0614024	−	0.0563400i
$721$	−54.6857	+	39.7315i	−2.03660	+	1.47968i
$722$	−5.89144	−	8.10887i	−0.219257	−	0.301781i
$723$	−19.4128	−	6.30760i	−0.721969	−	0.234582i
$724$	16.7144	+	12.1437i	0.621186	+	0.451318i
$725$	0.458187	−	0.760264i	0.0170166	−	0.0282355i
$726$	−0.989889	−	3.04656i	−0.0367382	−	0.113069i
$727$	28.2138	+	38.8330i	1.04639	+	1.44024i	0.891895	+	0.452242i	$0.149376\pi$
$727$	28.2138	+	38.8330i	1.04639	+	1.44024i	0.154497	+	0.987993i	$0.450624\pi$
$728$	−14.9059	+	4.84321i	−0.552449	+	0.179501i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	10.8549	−	6.13193i	0.401760	−	0.226953i
$731$	0.384271	+	1.18267i	0.0142128	+	0.0437425i
$732$	−1.93695	−	0.629352i	−0.0715917	−	0.0232615i
$733$	18.5482	−	25.5294i	0.685094	−	0.942950i	−0.314887	−	0.949129i	$-0.601967\pi$
$733$	18.5482	−	25.5294i	0.685094	−	0.942950i	0.999981	+	0.00617864i	$0.00196673\pi$
$734$	9.79324	−	30.1405i	0.361475	−	1.11251i
$735$	−8.17953	−	14.4797i	−0.301706	−	0.534091i
$736$	1.25198	−	0.909616i	0.0461486	−	0.0335289i
$737$	−15.5489	+	21.4013i	−0.572752	+	0.788325i
$738$			8.20791i			0.302138i
$739$	−17.5022			−0.643830			−0.321915	−	0.946769i	$-0.604327\pi$
$739$	−17.5022			−0.643830			−0.321915	+	0.946769i	$0.604327\pi$
$740$	4.37275	−	4.76567i	0.160746	−	0.175189i
$741$	−3.81904	−	11.7538i	−0.140296	−	0.431786i
$742$	−24.9974	−	8.12214i	−0.917683	−	0.298173i
$743$		−	8.96969i		−	0.329066i	−0.986372	−	0.164533i	$-0.947388\pi$
$743$		−	8.96969i		−	0.329066i	0.986372	−	0.164533i	$-0.0526117\pi$
$744$	−0.495661	+	5.54566i	−0.0181718	+	0.203314i
$745$	31.5491	+	3.61578i	1.15587	+	0.132472i
$746$	−3.37881	+	10.3989i	−0.123707	+	0.380731i
$747$	2.80822	−	0.912446i	0.102747	−	0.0333847i
$748$	−1.73071	+	2.38212i	−0.0632811	+	0.0870990i
$749$	42.1309			1.53943
$750$	−10.5316	−	3.75305i	−0.384560	−	0.137042i
$751$	−21.6859	−	15.7558i	−0.791331	−	0.574936i	0.117027	−	0.993129i	$-0.462664\pi$
$751$	−21.6859	−	15.7558i	−0.791331	−	0.574936i	−0.908358	+	0.418193i	$0.862664\pi$
$752$	5.42462	+	7.46635i	0.197816	+	0.272270i
$753$	3.69371	+	5.08395i	0.134606	+	0.185270i
$754$	0.226291	−	0.696451i	0.00824102	−	0.0253632i
$755$	−0.917465	−	0.841823i	−0.0333900	−	0.0306371i
$756$	1.17415	−	3.61367i	0.0427036	−	0.131428i
$757$	0.0989335	−	0.0321454i	0.00359580	−	0.00116835i	−0.307219	−	0.951639i	$-0.599398\pi$
$757$	0.0989335	−	0.0321454i	0.00359580	−	0.00116835i	0.310814	+	0.950471i	$0.399398\pi$
$758$	7.89283	+	10.8636i	0.286681	+	0.394582i
$759$	1.33529	+	4.10960i	0.0484680	+	0.149169i
$760$	6.56597	−	1.33132i	0.238173	−	0.0482922i
$761$	−10.9997	+	7.99174i	−0.398738	+	0.289700i	−0.769027	−	0.639216i	$-0.779259\pi$
$761$	−10.9997	+	7.99174i	−0.398738	+	0.289700i	0.370289	+	0.928917i	$0.379259\pi$
$762$	15.5734	−	5.06011i	0.564166	−	0.183309i
$763$	14.4045	+	4.68032i	0.521479	+	0.169439i
$764$	0.203040	+	0.147517i	0.00734572	+	0.00533698i
$765$	2.14501	+	0.979256i	0.0775529	+	0.0354051i
$766$	8.36599	−	6.07824i	0.302275	−	0.219616i
$767$	−24.0303	−	33.0749i	−0.867684	−	1.19427i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	23.5895			0.850657			0.425329	−	0.905039i	$-0.360159\pi$
$769$	23.5895			0.850657			0.425329	+	0.905039i	$0.360159\pi$
$770$	23.5694	+	2.70124i	0.849382	+	0.0973459i
$771$	−0.547904	−	0.398075i	−0.0197323	−	0.0143363i
$772$	−9.40131	+	3.05467i	−0.338360	+	0.109940i
$773$	33.2741	+	10.8114i	1.19679	+	0.388860i	0.838578	−	0.544782i	$-0.183387\pi$
$773$	33.2741	+	10.8114i	1.19679	+	0.388860i	0.358209	+	0.933641i	$0.383387\pi$
$774$	1.17924			0.0423870
$775$	8.51784	+	26.5037i	0.305970	+	0.952041i
$776$	−5.27494			−0.189359
$777$	10.4525	+	3.39623i	0.374982	+	0.121839i
$778$	−11.9363	+	3.87835i	−0.427938	+	0.139046i
$779$	−19.8954	−	14.4549i	−0.712828	−	0.517900i
$780$	−9.16347	−	1.05021i	−0.328105	−	0.0376034i
$781$	−34.9180			−1.24946
$782$	−0.959203	+	1.32023i	−0.0343010	+	0.0472113i
$783$	0.104350	+	0.143626i	0.00372918	+	0.00513278i
$784$	6.01689	−	4.37152i	0.214889	−	0.156126i
$785$	15.6882	+	7.16212i	0.559937	+	0.255627i
$786$	3.28268	+	2.38500i	0.117089	+	0.0850703i
$787$	−19.1914	−	6.23567i	−0.684100	−	0.222278i	−0.0537105	−	0.998557i	$-0.517105\pi$
$787$	−19.1914	−	6.23567i	−0.684100	−	0.222278i	−0.630390	+	0.776279i	$0.717105\pi$
$788$	1.31958	−	0.428758i	0.0470082	−	0.0152739i
$789$	−14.4828	+	10.5224i	−0.515601	+	0.374606i
$790$	−27.7036	+	5.61721i	−0.985648	+	0.199851i
$791$	2.54002	+	7.81739i	0.0903128	+	0.277954i
$792$	1.64124	+	2.25898i	0.0583190	+	0.0802692i
$793$	−7.98963	+	2.59599i	−0.283720	+	0.0921862i
$794$	−1.73955	+	5.35380i	−0.0617345	+	0.189999i
$795$	−11.3972	−	10.4575i	−0.404216	−	0.370890i
$796$	3.46976	−	10.6788i	0.122982	−	0.378500i
$797$	19.0765	+	26.2565i	0.675723	+	0.930053i	0.999873	−	0.0159529i	$-0.00507818\pi$
$797$	19.0765	+	26.2565i	0.675723	+	0.930053i	−0.324150	+	0.946006i	$0.605078\pi$
$798$	6.69151	+	9.21008i	0.236877	+	0.326033i
$799$	−7.87337	−	5.72034i	−0.278540	−	0.202371i
$800$	1.13122	−	4.87035i	0.0399947	−	0.172193i
$801$	−8.68290			−0.306795
$802$	−12.6256	+	17.3776i	−0.445824	+	0.613625i
$803$	−14.8062	+	4.81082i	−0.522499	+	0.169770i
$804$	−2.92759	+	9.01019i	−0.103248	+	0.317765i
$805$	13.0627	+	1.49709i	0.460400	+	0.0527656i
$806$	11.7915	+	19.7080i	0.415339	+	0.694186i
$807$		−	30.8676i		−	1.08659i
$808$	−0.863819	−	0.280672i	−0.0303890	−	0.00987400i
$809$	1.09230	+	3.36174i	0.0384031	+	0.118192i	0.968420	−	0.249324i	$-0.0802083\pi$
$809$	1.09230	+	3.36174i	0.0384031	+	0.118192i	−0.930017	+	0.367516i	$0.880208\pi$
$810$	1.51176	−	1.64760i	0.0531178	−	0.0578907i
$811$	−41.8876			−1.47087			−0.735437	−	0.677593i	$-0.763023\pi$
$811$	−41.8876			−1.47087			−0.735437	+	0.677593i	$0.763023\pi$
$812$			0.674556i			0.0236723i
$813$	−10.8340	+	14.9117i	−0.379965	+	0.522977i
$814$	−6.53407	+	4.74728i	−0.229019	+	0.166392i
$815$	16.5334	+	29.2681i	0.579141	+	1.02522i
$816$	−0.325863	+	1.00290i	−0.0114075	+	0.0351086i
$817$	−2.07675	+	2.85841i	−0.0726564	+	0.100003i
$818$	−17.3350	−	5.63247i	−0.606103	−	0.196935i
$819$	−4.84321	−	14.9059i	−0.169236	−	0.520854i
$820$	−15.9800	+	9.02707i	−0.558047	+	0.315239i
$821$	−10.9146	−	33.5917i	−0.380923	−	1.17236i	−0.939395	−	0.342837i	$-0.888612\pi$
$821$	−10.9146	−	33.5917i	−0.380923	−	1.17236i	0.558472	−	0.829523i	$-0.311388\pi$
$822$	4.87577	−	1.58424i	0.170062	−	0.0552565i
$823$	21.8890	+	30.1277i	0.763004	+	1.05019i	0.996958	+	0.0779375i	$0.0248335\pi$
$823$	21.8890	+	30.1277i	0.763004	+	1.05019i	−0.233954	+	0.972248i	$0.575167\pi$
$824$	−5.49738	−	16.9192i	−0.191510	−	0.589408i
$825$	11.9576	+	7.20645i	0.416309	+	0.250896i
$826$	30.4672	+	22.1357i	1.06009	+	0.770200i
$827$	41.0471	+	13.3370i	1.42735	+	0.463773i	0.917928	−	0.396746i	$-0.129861\pi$
$827$	41.0471	+	13.3370i	1.42735	+	0.463773i	0.509418	+	0.860519i	$0.329861\pi$
$828$	0.909616	+	1.25198i	0.0316114	+	0.0435093i
$829$	−32.0715	+	23.3013i	−1.11389	+	0.809289i	−0.983272	−	0.182144i	$-0.941696\pi$
$829$	−32.0715	+	23.3013i	−1.11389	+	0.809289i	−0.130619	+	0.991433i	$0.541696\pi$
$830$	4.86493	+	4.46383i	0.168864	+	0.154942i
$831$	−19.2804			−0.668830
$832$		−	4.12485i		−	0.143004i
$833$	−4.60983	+	6.34489i	−0.159721	+	0.219837i
$834$	4.79098	+	14.7451i	0.165898	+	0.510582i
$835$	12.2109	+	5.57461i	0.422575	+	0.192917i
$836$	−8.36598			−0.289344
$837$	−5.54566	−	0.495661i	−0.191686	−	0.0171325i
$838$		−	28.8771i		−	0.997543i
$839$	11.3649	−	34.9775i	0.392359	−	1.20756i	−0.538640	−	0.842536i	$-0.681062\pi$
$839$	11.3649	−	34.9775i	0.392359	−	1.20756i	0.930999	−	0.365022i	$-0.118938\pi$
$840$	8.32682	−	1.68836i	0.287302	−	0.0582538i
$841$	23.4360	+	17.0272i	0.808138	+	0.587146i
$842$			34.5152i			1.18947i
$843$		−	3.69516i		−	0.127268i
$844$	−12.9761	−	9.42771i	−0.446657	−	0.324515i
$845$	−7.81568	+	4.41506i	−0.268868	+	0.151883i
$846$	−7.46635	+	5.42462i	−0.256698	+	0.186502i
$847$	11.5759	+	3.76122i	0.397751	+	0.129237i
$848$	4.06597	−	5.59633i	0.139626	−	0.192179i
$849$	−8.33057	+	25.6389i	−0.285905	+	0.879924i
$850$	0.452562	+	5.25311i	0.0155227	+	0.180180i
$851$	−3.62134	+	2.63106i	−0.124138	+	0.0901915i
$852$	−11.8933	+	3.86436i	−0.407457	+	0.132391i
$853$	−17.9756	+	5.84063i	−0.615473	+	0.199979i	−0.600129	−	0.799903i	$-0.704884\pi$
$853$	−17.9756	+	5.84063i	−0.615473	+	0.199979i	−0.0153438	+	0.999882i	$0.504884\pi$
$854$	6.26054	−	4.54855i	0.214231	−	0.155648i
$855$	1.33132	+	6.56597i	0.0455303	+	0.224552i
$856$	−3.42642	+	10.5454i	−0.117113	+	0.360435i
$857$	21.0438	−	28.9643i	0.718842	−	0.989401i	−0.280720	−	0.959790i	$-0.590573\pi$
$857$	21.0438	−	28.9643i	0.718842	−	0.989401i	0.999561	−	0.0296112i	$-0.00942693\pi$
$858$	10.9539	+	3.55914i	0.373960	+	0.121507i
$859$	−35.1400	+	25.5307i	−1.19896	+	0.871095i	−0.994182	−	0.107713i	$-0.965647\pi$
$859$	−35.1400	+	25.5307i	−1.19896	+	0.871095i	−0.204778	+	0.978808i	$0.565647\pi$
$860$	1.29693	+	2.29588i	0.0442250	+	0.0782887i
$861$	−25.2309	−	18.3313i	−0.859868	−	0.624730i
$862$			20.6269i			0.702555i
$863$		−	32.5518i		−	1.10808i	−0.832491	−	0.554038i	$-0.813086\pi$
$863$		−	32.5518i		−	1.10808i	0.832491	−	0.554038i	$-0.186914\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	40.0915	−	8.12900i	1.36315	−	0.276394i
$866$	−12.0219	+	36.9995i	−0.408519	+	1.25729i
$867$			15.8880i			0.539585i
$868$	−15.9402	−	13.9092i	−0.541046	−	0.472108i
$869$	35.2983			1.19741
$870$	−0.164862	+	0.361120i	−0.00558933	+	0.0122431i
$871$	12.0759	+	37.1657i	0.409175	+	1.25931i
$872$	−2.34298	+	3.22484i	−0.0793434	+	0.109207i
$873$		−	5.27494i		−	0.178530i
$874$	−4.63663			−0.156836
$875$	35.0578	−	23.9919i	1.18517	−	0.811075i
$876$	−4.51066	+	3.27719i	−0.152401	+	0.110726i
$877$	18.4454	+	25.3879i	0.622856	+	0.857287i	0.997557	−	0.0698585i	$-0.0222548\pi$
$877$	18.4454	+	25.3879i	0.622856	+	0.857287i	−0.374701	+	0.927146i	$0.622255\pi$
$878$	−4.99645	−	1.62344i	−0.168622	−	0.0547886i
$879$	18.9821	+	13.7913i	0.640249	+	0.465168i
$880$	−2.59297	+	5.67977i	−0.0874091	+	0.191465i
$881$	4.08492	+	12.5721i	0.137624	+	0.423564i	0.995989	−	0.0894760i	$-0.0285192\pi$
$881$	4.08492	+	12.5721i	0.137624	+	0.423564i	−0.858365	+	0.513040i	$0.828519\pi$
$882$	4.37152	+	6.01689i	0.147197	+	0.202599i
$883$	14.4078	−	4.68138i	0.484861	−	0.157541i	−0.0563782	−	0.998409i	$-0.517955\pi$
$883$	14.4078	−	4.68138i	0.484861	−	0.157541i	0.541239	+	0.840868i	$0.317955\pi$
$884$	1.34414	+	4.13682i	0.0452082	+	0.139136i
$885$	10.9005	+	19.2964i	0.366416	+	0.648642i
$886$	−9.15146	−	28.1653i	−0.307449	−	0.946232i
$887$	−50.4200	−	16.3824i	−1.69294	−	0.550068i	−0.705586	−	0.708624i	$-0.749316\pi$
$887$	−50.4200	−	16.3824i	−1.69294	−	0.550068i	−0.987350	+	0.158555i	$0.949316\pi$
$888$	−1.70016	+	2.34007i	−0.0570538	+	0.0785278i
$889$	−19.2266	+	59.1734i	−0.644840	+	1.98461i
$890$	−9.54946	−	16.9048i	−0.320098	−	0.566649i
$891$	−2.25898	+	1.64124i	−0.0756786	+	0.0549837i
$892$	−5.27647	+	7.26243i	−0.176669	+	0.243164i
$893$		−	27.6512i		−	0.925311i
$894$	−14.2016			−0.474971
$895$	−19.6417	−	18.0223i	−0.656550	−	0.602419i
$896$	1.17415	+	3.61367i	0.0392257	+	0.120724i
$897$	6.07092	+	1.97256i	0.202702	+	0.0658619i
$898$			26.7517i			0.892717i
$899$	0.963535	−	0.220548i	0.0321357	−	0.00735568i
$900$	4.87035	+	1.13122i	0.162345	+	0.0377074i
$901$	−2.25414	+	6.93752i	−0.0750961	+	0.231122i
$902$	21.7968	−	7.08222i	0.725755	−	0.235812i
$903$	−2.63369	+	3.62497i	−0.0876438	+	0.120631i
$904$	−2.16328			−0.0719496
$905$	−45.8970	−	5.26017i	−1.52567	−	0.174854i
$906$	0.450501	+	0.327308i	0.0149669	+	0.0108741i
$907$	7.66074	+	10.5441i	0.254371	+	0.350111i	0.917036	−	0.398804i	$-0.130575\pi$
$907$	7.66074	+	10.5441i	0.254371	+	0.350111i	−0.662665	+	0.748916i	$0.730575\pi$
$908$	9.10057	+	12.5259i	0.302013	+	0.415685i
$909$	0.280672	−	0.863819i	0.00930930	−	0.0286511i
$910$	23.6938	−	25.8228i	0.785440	−	0.856016i
$911$	−14.6845	+	45.1943i	−0.486520	+	1.49735i	0.343248	+	0.939245i	$0.388473\pi$
$911$	−14.6845	+	45.1943i	−0.486520	+	1.49735i	−0.829768	+	0.558109i	$0.811527\pi$
$912$	−2.84950	+	0.925860i	−0.0943565	+	0.0306583i
$913$	−4.84616	−	6.67017i	−0.160384	−	0.220750i
$914$	6.79844	+	20.9234i	0.224872	+	0.692086i
$915$	4.46322	−	0.904967i	0.147549	−	0.0299173i
$916$	−4.33116	+	3.14677i	−0.143106	+	0.103972i
$917$	−14.6629	+	4.76426i	−0.484211	+	0.157330i
$918$	−1.00290	−	0.325863i	−0.0331007	−	0.0107551i
$919$	−43.0808	−	31.3000i	−1.42111	−	1.03249i	−0.991588	−	0.129435i	$-0.958684\pi$
$919$	−43.0808	−	31.3000i	−1.42111	−	1.03249i	−0.429517	−	0.903059i	$-0.641316\pi$
$920$	−1.43709	+	3.14786i	−0.0473794	+	0.103782i
$921$	−13.7033	+	9.95600i	−0.451538	+	0.328061i
$922$	12.8377	+	17.6696i	0.422788	+	0.581918i
$923$	−30.3195	+	41.7312i	−0.997979	+	1.37360i
$924$	−10.6095			−0.349028
$925$	−3.27205	+	14.0875i	−0.107584	+	0.463193i
$926$	−32.6935	−	23.7532i	−1.07438	−	0.780580i
$927$	16.9192	−	5.49738i	0.555699	−	0.180558i
$928$	−0.168843	−	0.0548603i	−0.00554253	−	0.00180088i
$929$	34.5221			1.13263			0.566316	−	0.824188i	$-0.308368\pi$
$929$	34.5221			1.13263			0.566316	+	0.824188i	$0.308368\pi$
$930$	−5.13411	−	11.3420i	−0.168354	−	0.371919i
$931$	−22.2832			−0.730302
$932$	−21.2277	−	6.89729i	−0.695336	−	0.225928i
$933$	−28.0125	+	9.10180i	−0.917087	+	0.297980i
$934$	1.75104	+	1.27221i	0.0572959	+	0.0416279i
$935$	0.749674	−	6.54120i	0.0245170	−	0.213920i
$936$	4.12485			0.134825
$937$	24.9761	−	34.3767i	0.815934	−	1.12304i	−0.174447	−	0.984667i	$-0.555814\pi$
$937$	24.9761	−	34.3767i	0.815934	−	1.12304i	0.990381	−	0.138370i	$-0.0441863\pi$
$938$	−21.1587	−	29.1225i	−0.690856	−	0.950882i
$939$	19.4763	−	14.1504i	0.635586	−	0.461781i
$940$	−18.7727	−	8.57027i	−0.612299	−	0.279531i
$941$	11.7083	+	8.50656i	0.381679	+	0.277306i	0.762037	−	0.647533i	$-0.224199\pi$
$941$	11.7083	+	8.50656i	0.381679	+	0.277306i	−0.380358	+	0.924839i	$0.624199\pi$
$942$	−7.33507	−	2.38331i	−0.238989	−	0.0776524i
$943$	12.0803	−	3.92514i	0.393390	−	0.127820i
$944$	−8.01844	+	5.82574i	−0.260978	+	0.189612i
$945$	1.68836	+	8.32682i	0.0549222	+	0.270871i
$946$	−1.01751	−	3.13158i	−0.0330822	−	0.101817i
$947$	−12.6054	−	17.3498i	−0.409619	−	0.563792i	0.553507	−	0.832845i	$-0.313289\pi$
$947$	−12.6054	−	17.3498i	−0.409619	−	0.563792i	−0.963125	+	0.269053i	$0.913289\pi$
$948$	12.0228	−	3.90644i	0.390482	−	0.126875i
$949$	−7.10680	+	21.8725i	−0.230696	+	0.710010i
$950$	−11.3191	+	9.81322i	−0.367241	+	0.318383i
$951$	−3.55598	+	10.9442i	−0.115311	+	0.354890i
$952$	−2.35512	−	3.24155i	−0.0763300	−	0.105059i
$953$	−27.0492	−	37.2300i	−0.876210	−	1.20600i	−0.977456	−	0.211138i	$-0.932283\pi$
$953$	−27.0492	−	37.2300i	−0.876210	−	1.20600i	0.101246	−	0.994861i	$-0.467717\pi$
$954$	5.59633	+	4.06597i	0.181188	+	0.131641i
$955$	−0.557538	−	0.0638984i	−0.0180415	−	0.00206770i
$956$	−29.5337			−0.955189
$957$	0.291372	−	0.401040i	0.00941873	−	0.0129638i
$958$	−22.6456	+	7.35800i	−0.731646	+	0.237726i
$959$	−6.01953	+	18.5262i	−0.194381	+	0.598242i
$960$	−0.254605	+	2.22153i	−0.00821733	+	0.0716994i
$961$	−14.6562	+	27.3166i	−0.472779	+	0.881181i
$962$			11.9311i			0.384674i
$963$	−10.5454	−	3.42642i	−0.339822	−	0.110415i
$964$	6.30760	+	19.4128i	0.203154	+	0.625244i
$965$	14.9439	−	16.2867i	0.481062	−	0.524288i
$966$	−5.88007			−0.189188
$967$			7.97697i			0.256522i	0.991740	+	0.128261i	$0.0409395\pi$
$967$			7.97697i			0.256522i	−0.991740	+	0.128261i	$0.959060\pi$
$968$	−1.88288	+	2.59156i	−0.0605181	+	0.0832960i
$969$	2.55607	−	1.85709i	0.0821128	−	0.0596584i
$970$	10.2698	−	5.80138i	0.329744	−	0.186271i
$971$	15.2693	−	46.9940i	0.490014	−	1.50811i	−0.334571	−	0.942371i	$-0.608591\pi$
$971$	15.2693	−	46.9940i	0.490014	−	1.50811i	0.824585	−	0.565738i	$-0.191409\pi$
$972$	−0.587785	+	0.809017i	−0.0188532	+	0.0259492i
$973$	−56.0262	−	18.2040i	−1.79612	−	0.583594i
$974$	3.49132	+	10.7452i	0.111869	+	0.344298i
$975$	18.9954	−	8.03333i	0.608340	−	0.257273i
$976$	0.629352	+	1.93695i	0.0201451	+	0.0620002i
$977$	−0.612429	+	0.198990i	−0.0195934	+	0.00636627i	−0.318797	−	0.947823i	$-0.603279\pi$
$977$	−0.612429	+	0.198990i	−0.0195934	+	0.00636627i	0.299204	+	0.954189i	$0.403279\pi$
$978$	−8.83625	−	12.1621i	−0.282552	−	0.388900i
$979$	7.49206	+	23.0582i	0.239447	+	0.736943i
$980$	−6.90650	+	15.1283i	−0.220620	+	0.483256i
$981$	−3.22484	−	2.34298i	−0.102961	−	0.0748056i
$982$	−39.8756	−	12.9564i	−1.27248	−	0.413454i
$983$	23.1076	+	31.8049i	0.737018	+	1.01442i	0.998785	+	0.0492871i	$0.0156949\pi$
$983$	23.1076	+	31.8049i	0.737018	+	1.01442i	−0.261767	+	0.965131i	$0.584305\pi$
$984$	6.64034	−	4.82449i	0.211686	−	0.153799i
$985$	−2.09755	+	2.28603i	−0.0668336	+	0.0728389i
$986$	0.187209			0.00596196
$987$		−	35.0666i		−	1.11618i
$988$	−7.26424	+	9.99837i	−0.231106	+	0.318090i
$989$	−0.563930	−	1.73560i	−0.0179319	−	0.0551888i
$990$	−5.67977	−	2.59297i	−0.180515	−	0.0824101i
$991$	6.87994			0.218548			0.109274	−	0.994012i	$-0.465147\pi$
$991$	6.87994			0.218548			0.109274	+	0.994012i	$0.465147\pi$
$992$	4.77787	−	2.85866i	0.151698	−	0.0907625i
$993$			17.7094i			0.561989i
$994$	14.6832	−	45.1902i	0.465722	−	1.43335i
$995$	4.98928	+	24.6067i	0.158171	+	0.780084i
$996$	−2.38882	−	1.73558i	−0.0756925	−	0.0549938i
$997$			0.386834i			0.0122511i	0.999981	+	0.00612557i	$0.00194984\pi$
$997$			0.386834i			0.0122511i	−0.999981	+	0.00612557i	$0.998050\pi$
$998$		−	1.29973i		−	0.0411421i
$999$	−2.34007	−	1.70016i	−0.0740367	−	0.0537908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.349.1	✓	72
5.4	even	2	inner	930.2.z.d.349.10	yes	72
31.4	even	5	inner	930.2.z.d.469.10	yes	72
155.4	even	10	inner	930.2.z.d.469.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.349.1	✓	72	1.1	even	1	trivial
930.2.z.d.349.10	yes	72	5.4	even	2	inner
930.2.z.d.469.1	yes	72	155.4	even	10	inner
930.2.z.d.469.10	yes	72	31.4	even	5	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.22153 - 0.254605i) q^{5} +1.00000 q^{6} +(-2.23337 + 3.07398i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.22153 - 0.254605i) q^{5} +1.00000 q^{6} +(-2.23337 + 3.07398i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.03412 + 0.928633i) q^{10} +(-2.25898 - 1.64124i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-3.92297 + 1.27465i) q^{13} +(3.07398 - 2.23337i) q^{14} +(2.19147 - 0.444346i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.619828 - 0.853119i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(0.925860 - 2.84950i) q^{19} +(-1.64760 - 1.51176i) q^{20} +(1.17415 - 3.61367i) q^{21} +(1.64124 + 2.25898i) q^{22} +(0.909616 + 1.25198i) q^{23} +(0.809017 + 0.587785i) q^{24} +(4.87035 + 1.13122i) q^{25} +4.12485 q^{26} +(-0.587785 + 0.809017i) q^{27} +(-3.61367 + 1.17415i) q^{28} +(0.0548603 - 0.168843i) q^{29} +(-2.22153 - 0.254605i) q^{30} +(2.85866 + 4.77787i) q^{31} -1.00000i q^{32} +(2.65559 + 0.862852i) q^{33} +(0.325863 + 1.00290i) q^{34} +(5.74415 - 6.26029i) q^{35} +1.00000 q^{36} +2.89249i q^{37} +(-1.76109 + 2.42393i) q^{38} +(3.33708 - 2.42453i) q^{39} +(1.09980 + 1.94690i) q^{40} +(2.53639 - 7.80619i) q^{41} +(-2.23337 + 3.07398i) q^{42} +(-1.12153 - 0.364406i) q^{43} +(-0.862852 - 2.65559i) q^{44} +(-1.94690 + 1.09980i) q^{45} +(-0.478214 - 1.47179i) q^{46} +(8.77722 - 2.85189i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(-2.29825 - 7.07328i) q^{49} +(-4.28241 - 2.58088i) q^{50} +(0.853119 + 0.619828i) q^{51} +(-3.92297 - 1.27465i) q^{52} +(-4.06597 - 5.59633i) q^{53} +(0.809017 - 0.587785i) q^{54} +(4.60051 + 4.22121i) q^{55} +3.79964 q^{56} +2.99615i q^{57} +(-0.104350 + 0.143626i) q^{58} +(3.06277 + 9.42624i) q^{59} +(2.03412 + 0.928633i) q^{60} +2.03663 q^{61} +(-1.24230 - 5.42740i) q^{62} +3.79964i q^{63} +(-0.309017 + 0.951057i) q^{64} +(9.03951 - 1.83286i) q^{65} +(-2.25898 - 1.64124i) q^{66} -9.47387i q^{67} -1.05451i q^{68} +(-1.25198 - 0.909616i) q^{69} +(-7.39754 + 4.17885i) q^{70} +(10.1170 - 7.35045i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(3.27719 - 4.51066i) q^{73} +(0.893829 - 2.75092i) q^{74} +(-4.98155 + 0.429166i) q^{75} +(2.42393 - 1.76109i) q^{76} +(10.0903 - 3.27853i) q^{77} +(-3.92297 + 1.27465i) q^{78} +(-10.2272 + 7.43050i) q^{79} +(-0.444346 - 2.19147i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-4.82449 + 6.64034i) q^{82} +(2.80822 + 0.912446i) q^{83} +(3.07398 - 2.23337i) q^{84} +(1.15975 + 2.05304i) q^{85} +(0.954028 + 0.693142i) q^{86} +0.177532i q^{87} +2.79225i q^{88} +(-7.02461 - 5.10368i) q^{89} +(2.19147 - 0.444346i) q^{90} +(4.84321 - 14.9059i) q^{91} +1.54753i q^{92} +(-4.19519 - 3.66065i) q^{93} -9.22892 q^{94} +(-2.78232 + 6.09452i) q^{95} +(0.309017 + 0.951057i) q^{96} +(3.10053 - 4.26752i) q^{97} +7.43728i q^{98} -2.79225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

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