LMFDB - Embedded newform 930.2.z.d.109.5

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			109.5
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.218072 + 2.22541i) q^{5} +1.00000 q^{6} +(-0.288858 - 0.0938558i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.218072 + 2.22541i) q^{5} +1.00000 q^{6} +(-0.288858 - 0.0938558i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.67221 - 1.48449i) q^{10} +(-0.702180 + 2.16109i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(-3.19120 + 4.39231i) q^{13} +(0.0938558 + 0.288858i) q^{14} +(-1.92857 - 1.13164i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.67414 - 0.543961i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(3.75245 - 2.72631i) q^{19} +(-2.18388 - 0.480291i) q^{20} +(0.245718 - 0.178524i) q^{21} +(2.16109 - 0.702180i) q^{22} +(-4.96714 + 1.61392i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.90489 + 0.970598i) q^{25} +5.42920 q^{26} +(0.951057 + 0.309017i) q^{27} +(0.178524 - 0.245718i) q^{28} +(1.15125 - 0.836430i) q^{29} +(0.218072 + 2.22541i) q^{30} +(-0.544113 - 5.54111i) q^{31} +1.00000i q^{32} +(-1.33563 - 1.83833i) q^{33} +(-1.42411 - 1.03467i) q^{34} +(0.145876 - 0.663295i) q^{35} +1.00000 q^{36} +1.08625i q^{37} +(-4.41127 - 1.43331i) q^{38} +(-1.67771 - 5.16348i) q^{39} +(0.895088 + 2.04910i) q^{40} +(-1.96576 + 1.42821i) q^{41} +(-0.288858 - 0.0938558i) q^{42} +(-3.24350 - 4.46429i) q^{43} +(-1.83833 - 1.33563i) q^{44} +(2.04910 - 0.895088i) q^{45} +(4.22530 + 3.06986i) q^{46} +(-4.58225 + 6.30692i) q^{47} +(0.951057 - 0.309017i) q^{48} +(-5.58849 - 4.06027i) q^{49} +(3.66825 + 3.39764i) q^{50} +(-0.543961 + 1.67414i) q^{51} +(-3.19120 - 4.39231i) q^{52} +(-1.73316 + 0.563139i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-4.96243 - 1.09137i) q^{55} -0.303724 q^{56} +4.63828i q^{57} +(-1.35337 - 0.439737i) q^{58} +(0.537561 + 0.390561i) q^{59} +(1.67221 - 1.48449i) q^{60} -9.71743 q^{61} +(-4.16303 + 3.69718i) q^{62} +0.303724i q^{63} +(0.809017 - 0.587785i) q^{64} +(-10.4706 - 6.14389i) q^{65} +(-0.702180 + 2.16109i) q^{66} -2.06627i q^{67} +1.76029i q^{68} +(1.61392 - 4.96714i) q^{69} +(-0.622361 + 0.271859i) q^{70} +(4.66092 + 14.3448i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-5.94843 - 1.93276i) q^{73} +(0.878797 - 0.638483i) q^{74} +(2.09779 - 4.53864i) q^{75} +(1.43331 + 4.41127i) q^{76} +(0.405661 - 0.558345i) q^{77} +(-3.19120 + 4.39231i) q^{78} +(-2.67001 - 8.21746i) q^{79} +(1.13164 - 1.92857i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(2.31089 + 0.750854i) q^{82} +(-5.70355 - 7.85026i) q^{83} +(0.0938558 + 0.288858i) q^{84} +(1.57562 + 3.60702i) q^{85} +(-1.70521 + 5.24809i) q^{86} +1.42302i q^{87} +2.27230i q^{88} +(-5.29646 + 16.3008i) q^{89} +(-1.92857 - 1.13164i) q^{90} +(1.33405 - 0.969244i) q^{91} -5.22276i q^{92} +(4.80268 + 2.81679i) q^{93} +7.79579 q^{94} +(6.88546 + 7.75620i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-14.4505 - 4.69526i) q^{97} +6.90775i q^{98} +2.27230 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.218072	+	2.22541i	0.0975247	+	0.995233i
$5$	0.218072	+	2.22541i	0.0975247	+	0.995233i
$6$	1.00000			0.408248
$7$	−0.288858	−	0.0938558i	−0.109178	−	0.0354741i	0.253918	−	0.967226i	$-0.418281\pi$
$7$	−0.288858	−	0.0938558i	−0.109178	−	0.0354741i	−0.363097	+	0.931751i	$0.618281\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	1.67221	−	1.48449i	0.528801	−	0.469436i
$11$	−0.702180	+	2.16109i	−0.211715	+	0.651592i	0.787655	+	0.616116i	$0.211295\pi$
$11$	−0.702180	+	2.16109i	−0.211715	+	0.651592i	−0.999371	+	0.0354763i	$0.988705\pi$
$12$	−0.587785	−	0.809017i	−0.169679	−	0.233543i
$13$	−3.19120	+	4.39231i	−0.885081	+	1.21821i	0.0899071	+	0.995950i	$0.471343\pi$
$13$	−3.19120	+	4.39231i	−0.885081	+	1.21821i	−0.974988	+	0.222259i	$0.928657\pi$
$14$	0.0938558	+	0.288858i	0.0250840	+	0.0772006i
$15$	−1.92857	−	1.13164i	−0.497955	−	0.292188i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.67414	−	0.543961i	0.406038	−	0.131930i	−0.0988750	−	0.995100i	$-0.531524\pi$
$17$	1.67414	−	0.543961i	0.406038	−	0.131930i	0.504913	+	0.863170i	$0.331524\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	3.75245	−	2.72631i	0.860870	−	0.625459i	−0.0672512	−	0.997736i	$-0.521423\pi$
$19$	3.75245	−	2.72631i	0.860870	−	0.625459i	0.928122	+	0.372277i	$0.121423\pi$
$20$	−2.18388	−	0.480291i	−0.488330	−	0.107396i
$21$	0.245718	−	0.178524i	0.0536200	−	0.0389572i
$22$	2.16109	−	0.702180i	0.460745	−	0.149705i
$23$	−4.96714	+	1.61392i	−1.03572	+	0.336526i	−0.777049	−	0.629440i	$-0.783284\pi$
$23$	−4.96714	+	1.61392i	−1.03572	+	0.336526i	−0.258670	+	0.965966i	$0.583284\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−4.90489	+	0.970598i	−0.980978	+	0.194120i
$26$	5.42920			1.06475
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	0.178524	−	0.245718i	0.0337379	−	0.0464363i
$29$	1.15125	−	0.836430i	0.213781	−	0.155321i	−0.475742	−	0.879585i	$-0.657820\pi$
$29$	1.15125	−	0.836430i	0.213781	−	0.155321i	0.689523	+	0.724264i	$0.257820\pi$
$30$	0.218072	+	2.22541i	0.0398143	+	0.406302i
$31$	−0.544113	−	5.54111i	−0.0977255	−	0.995213i
$31$	−0.544113	−	5.54111i	−0.0977255	−	0.995213i
$32$			1.00000i			0.176777i
$33$	−1.33563	−	1.83833i	−0.232503	−	0.320012i
$34$	−1.42411	−	1.03467i	−0.244232	−	0.177445i
$35$	0.145876	−	0.663295i	0.0246575	−	0.112117i
$36$	1.00000			0.166667
$37$			1.08625i			0.178579i	0.996006	+	0.0892894i	$0.0284596\pi$
$37$			1.08625i			0.178579i	−0.996006	+	0.0892894i	$0.971540\pi$
$38$	−4.41127	−	1.43331i	−0.715602	−	0.232513i
$39$	−1.67771	−	5.16348i	−0.268649	−	0.826818i
$40$	0.895088	+	2.04910i	0.141526	+	0.323991i
$41$	−1.96576	+	1.42821i	−0.307000	+	0.223049i	−0.730608	−	0.682797i	$-0.760763\pi$
$41$	−1.96576	+	1.42821i	−0.307000	+	0.223049i	0.423608	+	0.905846i	$0.360763\pi$
$42$	−0.288858	−	0.0938558i	−0.0445718	−	0.0144823i
$43$	−3.24350	−	4.46429i	−0.494629	−	0.680798i	0.486604	−	0.873622i	$-0.338235\pi$
$43$	−3.24350	−	4.46429i	−0.494629	−	0.680798i	−0.981233	+	0.192824i	$0.938235\pi$
$44$	−1.83833	−	1.33563i	−0.277139	−	0.201353i
$45$	2.04910	−	0.895088i	0.305462	−	0.133432i
$46$	4.22530	+	3.06986i	0.622986	+	0.452626i
$47$	−4.58225	+	6.30692i	−0.668390	+	0.919959i	−0.999723	−	0.0235545i	$-0.992502\pi$
$47$	−4.58225	+	6.30692i	−0.668390	+	0.919959i	0.331333	+	0.943514i	$0.392502\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	−5.58849	−	4.06027i	−0.798356	−	0.580039i
$50$	3.66825	+	3.39764i	0.518769	+	0.480498i
$51$	−0.543961	+	1.67414i	−0.0761697	+	0.234426i
$52$	−3.19120	−	4.39231i	−0.442540	−	0.609104i
$53$	−1.73316	+	0.563139i	−0.238068	+	0.0773531i	−0.425621	−	0.904901i	$-0.639944\pi$
$53$	−1.73316	+	0.563139i	−0.238068	+	0.0773531i	0.187553	+	0.982254i	$0.439944\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−4.96243	−	1.09137i	−0.669134	−	0.147160i
$56$	−0.303724			−0.0405868
$57$			4.63828i			0.614355i
$58$	−1.35337	−	0.439737i	−0.177707	−	0.0577404i
$59$	0.537561	+	0.390561i	0.0699845	+	0.0508467i	0.622227	−	0.782837i	$-0.286228\pi$
$59$	0.537561	+	0.390561i	0.0699845	+	0.0508467i	−0.552243	+	0.833683i	$0.686228\pi$
$60$	1.67221	−	1.48449i	0.215882	−	0.191646i
$61$	−9.71743			−1.24419			−0.622095	−	0.782942i	$-0.713718\pi$
$61$	−9.71743			−1.24419			−0.622095	+	0.782942i	$0.713718\pi$
$62$	−4.16303	+	3.69718i	−0.528706	+	0.469542i
$63$			0.303724i			0.0382656i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−10.4706	−	6.14389i	−1.29872	−	0.762056i
$66$	−0.702180	+	2.16109i	−0.0864324	+	0.266011i
$67$		−	2.06627i		−	0.252435i	−0.992003	−	0.126218i	$-0.959716\pi$
$67$		−	2.06627i		−	0.252435i	0.992003	−	0.126218i	$-0.0402838\pi$
$68$			1.76029i			0.213467i
$69$	1.61392	−	4.96714i	0.194293	−	0.597973i
$70$	−0.622361	+	0.271859i	−0.0743863	+	0.0324934i
$71$	4.66092	+	14.3448i	0.553150	+	1.70242i	0.700781	+	0.713377i	$0.252835\pi$
$71$	4.66092	+	14.3448i	0.553150	+	1.70242i	−0.147631	+	0.989043i	$0.547165\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	−5.94843	−	1.93276i	−0.696211	−	0.226213i	−0.0605323	−	0.998166i	$-0.519280\pi$
$73$	−5.94843	−	1.93276i	−0.696211	−	0.226213i	−0.635679	+	0.771953i	$0.719280\pi$
$74$	0.878797	−	0.638483i	0.102158	−	0.0742221i
$75$	2.09779	−	4.53864i	0.242232	−	0.524077i
$76$	1.43331	+	4.41127i	0.164412	+	0.506007i
$77$	0.405661	−	0.558345i	0.0462294	−	0.0636293i
$78$	−3.19120	+	4.39231i	−0.361333	+	0.497332i
$79$	−2.67001	−	8.21746i	−0.300400	−	0.924536i	−0.981354	−	0.192210i	$-0.938435\pi$
$79$	−2.67001	−	8.21746i	−0.300400	−	0.924536i	0.680954	−	0.732326i	$-0.261565\pi$
$80$	1.13164	−	1.92857i	0.126521	−	0.215621i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	2.31089	+	0.750854i	0.255195	+	0.0829180i
$83$	−5.70355	−	7.85026i	−0.626046	−	0.861678i	0.371730	−	0.928341i	$-0.378765\pi$
$83$	−5.70355	−	7.85026i	−0.626046	−	0.861678i	−0.997776	+	0.0666630i	$0.978765\pi$
$84$	0.0938558	+	0.288858i	0.0102405	+	0.0315170i
$85$	1.57562	+	3.60702i	0.170900	+	0.391236i
$86$	−1.70521	+	5.24809i	−0.183877	+	0.565916i
$87$			1.42302i			0.152564i
$88$			2.27230i			0.242228i
$89$	−5.29646	+	16.3008i	−0.561423	+	1.72788i	0.116923	+	0.993141i	$0.462697\pi$
$89$	−5.29646	+	16.3008i	−0.561423	+	1.72788i	−0.678347	+	0.734742i	$0.737303\pi$
$90$	−1.92857	−	1.13164i	−0.203289	−	0.119285i
$91$	1.33405	−	0.969244i	0.139846	−	0.101604i
$92$		−	5.22276i		−	0.544510i
$93$	4.80268	+	2.81679i	0.498014	+	0.292087i
$94$	7.79579			0.804074
$95$	6.88546	+	7.75620i	0.706434	+	0.795769i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−14.4505	−	4.69526i	−1.46723	−	0.476732i	−0.536960	−	0.843608i	$-0.680427\pi$
$97$	−14.4505	−	4.69526i	−1.46723	−	0.476732i	−0.930270	+	0.366876i	$0.880427\pi$
$98$			6.90775i			0.697788i
$99$	2.27230			0.228375
$100$	0.592601	−	4.96476i	0.0592601	−	0.496476i
$101$	5.88499	+	18.1121i	0.585578	+	1.80222i	0.596936	+	0.802289i	$0.296385\pi$
$101$	5.88499	+	18.1121i	0.585578	+	1.80222i	−0.0113578	+	0.999935i	$0.503615\pi$
$102$	1.67414	−	0.543961i	0.165764	−	0.0538601i
$103$	4.69679	+	6.46458i	0.462788	+	0.636974i	0.975084	−	0.221835i	$-0.0712048\pi$
$103$	4.69679	+	6.46458i	0.462788	+	0.636974i	−0.512296	+	0.858809i	$0.671205\pi$
$104$	−1.67771	+	5.16348i	−0.164513	+	0.506320i
$105$	0.450874	+	0.507891i	0.0440008	+	0.0495651i
$106$	1.47432	+	1.07115i	0.143198	+	0.104040i
$107$	18.5026	−	6.01185i	1.78871	−	0.581188i	0.789253	−	0.614069i	$-0.210468\pi$
$107$	18.5026	−	6.01185i	1.78871	−	0.581188i	0.999459	+	0.0328810i	$0.0104682\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	6.35457	+	4.61686i	0.608657	+	0.442215i	0.848941	−	0.528487i	$-0.177241\pi$
$109$	6.35457	+	4.61686i	0.608657	+	0.442215i	−0.240284	+	0.970703i	$0.577241\pi$
$110$	2.03391	+	4.65618i	0.193926	+	0.443949i
$111$	−0.878797	−	0.638483i	−0.0834117	−	0.0606021i
$112$	0.178524	+	0.245718i	0.0168690	+	0.0232181i
$113$	5.73635	+	1.86385i	0.539631	+	0.175337i	0.566136	−	0.824312i	$-0.308438\pi$
$113$	5.73635	+	1.86385i	0.539631	+	0.175337i	−0.0265051	+	0.999649i	$0.508438\pi$
$114$	3.75245	−	2.72631i	0.351449	−	0.255343i
$115$	−4.67482	−	10.7020i	−0.435930	−	0.997963i
$116$	0.439737	+	1.35337i	0.0408286	+	0.125657i
$117$	5.16348	+	1.67771i	0.477364	+	0.155105i
$118$		−	0.664462i		−	0.0611687i
$119$	−0.534643			−0.0490106
$120$	−2.18388	−	0.480291i	−0.199360	−	0.0438443i
$121$	4.72194	+	3.43069i	0.429268	+	0.311881i
$122$	5.71176	+	7.86157i	0.517119	+	0.711753i
$123$		−	2.42982i		−	0.219089i
$124$	5.43805	+	1.19482i	0.488352	+	0.107298i
$125$	−3.22960	−	10.7037i	−0.288864	−	0.957370i
$126$	0.245718	−	0.178524i	0.0218903	−	0.0159042i
$127$	−3.83201	+	5.27431i	−0.340036	+	0.468019i	−0.944452	−	0.328650i	$-0.893406\pi$
$127$	−3.83201	+	5.27431i	−0.340036	+	0.468019i	0.604416	+	0.796669i	$0.293406\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	5.51817			0.485848
$130$	1.18396	+	12.0822i	0.103840	+	1.05968i
$131$	0.763135	−	2.34869i	0.0666754	−	0.205206i	−0.912168	−	0.409816i	$-0.865593\pi$
$131$	0.763135	−	2.34869i	0.0666754	−	0.205206i	0.978843	+	0.204610i	$0.0655928\pi$
$132$	2.16109	−	0.702180i	0.188099	−	0.0611169i
$133$	−1.33981	+	0.435329i	−0.116176	+	0.0377478i
$134$	−1.67165	+	1.21453i	−0.144409	+	0.104919i
$135$	−0.480291	+	2.18388i	−0.0413368	+	0.187958i
$136$	1.42411	−	1.03467i	0.122116	−	0.0887226i
$137$	1.65817	−	2.28227i	0.141667	−	0.194987i	−0.732288	−	0.680995i	$-0.761547\pi$
$137$	1.65817	−	2.28227i	0.141667	−	0.194987i	0.873954	+	0.486008i	$0.161547\pi$
$138$	−4.96714	+	1.61392i	−0.422831	+	0.137386i
$139$	−1.93687	−	1.40722i	−0.164283	−	0.119359i	0.502606	−	0.864516i	$-0.332375\pi$
$139$	−1.93687	−	1.40722i	−0.164283	−	0.119359i	−0.666889	+	0.745157i	$0.732375\pi$
$140$	0.585753	+	0.343705i	0.0495052	+	0.0290484i
$141$	−2.40903	−	7.41423i	−0.202877	−	0.624391i
$142$	8.86560	−	12.2024i	0.743985	−	1.02401i
$143$	−7.25138	−	9.98067i	−0.606391	−	0.834625i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	2.11245	+	2.37959i	0.175430	+	0.197615i
$146$	1.93276	+	5.94843i	0.159957	+	0.492296i
$147$	6.56966	−	2.13461i	0.541857	−	0.176060i
$148$	−1.03309	−	0.335670i	−0.0849193	−	0.0275919i
$149$	−20.9097			−1.71299			−0.856494	−	0.516158i	$-0.827362\pi$
$149$	−20.9097			−1.71299			−0.856494	+	0.516158i	$0.827362\pi$
$150$	−4.90489	+	0.970598i	−0.400483	+	0.0792490i
$151$	−0.500273	+	1.53968i	−0.0407117	+	0.125298i	−0.969347	−	0.245697i	$-0.920983\pi$
$151$	−0.500273	+	1.53968i	−0.0407117	+	0.125298i	0.928635	+	0.370995i	$0.120983\pi$
$152$	2.72631	−	3.75245i	0.221133	−	0.304364i
$153$	−1.03467	−	1.42411i	−0.0836485	−	0.115132i
$154$	−0.690152			−0.0556140
$155$	12.2126	−	2.41923i	0.980939	−	0.194318i
$156$	5.42920			0.434684
$157$	−10.3188	−	14.2026i	−0.823530	−	1.13349i	−0.989093	−	0.147293i	$-0.952944\pi$
$157$	−10.3188	−	14.2026i	−0.823530	−	1.13349i	0.165562	−	0.986199i	$-0.447056\pi$
$158$	−5.07867	+	6.99019i	−0.404037	+	0.556109i
$159$	0.563139	−	1.73316i	0.0446598	−	0.137449i
$160$	−2.22541	+	0.218072i	−0.175934	+	0.0172401i
$161$	1.58627			0.125016
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	9.06672	−	2.94596i	0.710161	−	0.230745i	0.0684086	−	0.997657i	$-0.478208\pi$
$163$	9.06672	−	2.94596i	0.710161	−	0.230745i	0.641752	+	0.766912i	$0.278208\pi$
$164$	−0.750854	−	2.31089i	−0.0586319	−	0.180450i
$165$	3.79978	−	3.37320i	0.295812	−	0.262603i
$166$	−2.99853	+	9.22853i	−0.232731	+	0.716273i
$167$	−2.33634	−	3.21569i	−0.180791	−	0.248838i	0.708997	−	0.705212i	$-0.249148\pi$
$167$	−2.33634	−	3.21569i	−0.180791	−	0.248838i	−0.889788	+	0.456374i	$0.849148\pi$
$168$	0.178524	−	0.245718i	0.0137734	−	0.0189575i
$169$	−5.09143	−	15.6698i	−0.391648	−	1.20537i
$170$	1.99202	−	3.39486i	0.152781	−	0.260374i
$171$	−3.75245	−	2.72631i	−0.286957	−	0.208486i
$172$	5.24809	−	1.70521i	0.400163	−	0.130021i
$173$	−1.57516	+	2.16803i	−0.119757	+	0.164832i	−0.864687	−	0.502311i	$-0.832483\pi$
$173$	−1.57516	+	2.16803i	−0.119757	+	0.164832i	0.744929	+	0.667143i	$0.232483\pi$
$174$	1.15125	−	0.836430i	0.0872758	−	0.0634096i
$175$	1.50791	+	0.179987i	0.113988	+	0.0136057i
$176$	1.83833	−	1.33563i	0.138569	−	0.100677i
$177$	−0.631941	+	0.205330i	−0.0474996	+	0.0154336i
$178$	16.3008	−	5.29646i	1.22180	−	0.396986i
$179$	−0.430627	+	1.32533i	−0.0321866	+	0.0990601i	−0.965859	−	0.259068i	$-0.916585\pi$
$179$	−0.430627	+	1.32533i	−0.0321866	+	0.0990601i	0.933673	+	0.358128i	$0.116585\pi$
$180$	0.218072	+	2.22541i	0.0162541	+	0.165872i
$181$	6.27963			0.466761			0.233381	−	0.972385i	$-0.425021\pi$
$181$	6.27963			0.466761			0.233381	+	0.972385i	$0.425021\pi$
$182$	−1.56827	−	0.509562i	−0.116248	−	0.0377712i
$183$	5.71176	−	7.86157i	0.422226	−	0.581144i
$184$	−4.22530	+	3.06986i	−0.311493	+	0.226313i
$185$	−2.41736	+	0.236881i	−0.177728	+	0.0174158i
$186$	−0.544113	−	5.54111i	−0.0398963	−	0.406294i
$187$			3.99992i			0.292503i
$188$	−4.58225	−	6.30692i	−0.334195	−	0.459980i
$189$	−0.245718	−	0.178524i	−0.0178733	−	0.0129857i
$190$	2.22772	−	10.1294i	0.161616	−	0.734866i
$191$	1.83887			0.133056			0.0665280	−	0.997785i	$-0.478808\pi$
$191$	1.83887			0.133056			0.0665280	+	0.997785i	$0.478808\pi$
$192$			1.00000i			0.0721688i
$193$	15.6484	+	5.08446i	1.12639	+	0.365987i	0.812204	−	0.583373i	$-0.198267\pi$
$193$	15.6484	+	5.08446i	1.12639	+	0.365987i	0.314189	+	0.949360i	$0.398267\pi$
$194$	4.69526	+	14.4505i	0.337100	+	1.03749i
$195$	11.1250	−	4.85961i	0.796677	−	0.348004i
$196$	5.58849	−	4.06027i	0.399178	−	0.290020i
$197$	9.30909	+	3.02471i	0.663245	+	0.215501i	0.621245	−	0.783616i	$-0.286627\pi$
$197$	9.30909	+	3.02471i	0.663245	+	0.215501i	0.0419999	+	0.999118i	$0.486627\pi$
$198$	−1.33563	−	1.83833i	−0.0949188	−	0.130644i
$199$	1.89913	+	1.37980i	0.134626	+	0.0978113i	0.653060	−	0.757306i	$-0.273485\pi$
$199$	1.89913	+	1.37980i	0.134626	+	0.0978113i	−0.518434	+	0.855117i	$0.673485\pi$
$200$	−4.36490	+	2.43879i	−0.308645	+	0.172448i
$201$	1.67165	+	1.21453i	0.117909	+	0.0856660i
$202$	11.1939	−	15.4071i	0.787601	−	1.08404i
$203$	−0.411051	+	0.133559i	−0.0288501	+	0.00937398i
$204$	−1.42411	−	1.03467i	−0.0997075	−	0.0724417i
$205$	−3.60703	−	4.06317i	−0.251926	−	0.283784i
$206$	2.46925	−	7.59957i	0.172041	−	0.529487i
$207$	3.06986	+	4.22530i	0.213370	+	0.293679i
$208$	5.16348	−	1.67771i	0.358023	−	0.116329i
$209$	3.25691	+	10.0237i	0.225285	+	0.693356i
$210$	0.145876	−	0.663295i	0.0100664	−	0.0457717i
$211$	20.3840			1.40329			0.701645	−	0.712527i	$-0.252449\pi$
$211$	20.3840			1.40329			0.701645	+	0.712527i	$0.252449\pi$
$212$		−	1.82236i		−	0.125160i
$213$	−14.3448	−	4.66092i	−0.982892	−	0.319361i
$214$	−15.7392	−	11.4352i	−1.07591	−	0.781696i
$215$	9.22756	−	8.19165i	0.629315	−	0.558666i
$216$	1.00000			0.0680414
$217$	−0.362894	+	1.65166i	−0.0246348	+	0.112122i
$218$		−	7.85468i		−	0.531986i
$219$	5.06004	−	3.67633i	0.341926	−	0.248424i
$220$	2.57142	−	4.38230i	0.173365	−	0.295455i
$221$	−2.95327	+	9.08924i	−0.198659	+	0.611408i
$222$			1.08625i			0.0729045i
$223$			12.0348i			0.805910i	0.915220	+	0.402955i	$0.132017\pi$
$223$			12.0348i			0.805910i	−0.915220	+	0.402955i	$0.867983\pi$
$224$	0.0938558	−	0.288858i	0.00627100	−	0.0193002i
$225$	2.43879	+	4.36490i	0.162586	+	0.290993i
$226$	−1.86385	−	5.73635i	−0.123982	−	0.381576i
$227$	3.36001	+	4.62465i	0.223012	+	0.306949i	0.905832	−	0.423637i	$-0.139247\pi$
$227$	3.36001	+	4.62465i	0.223012	+	0.306949i	−0.682820	+	0.730586i	$0.739247\pi$
$228$	−4.41127	−	1.43331i	−0.292143	−	0.0949231i
$229$	12.8421	−	9.33030i	0.848627	−	0.616564i	−0.0761402	−	0.997097i	$-0.524260\pi$
$229$	12.8421	−	9.33030i	0.848627	−	0.616564i	0.924767	+	0.380534i	$0.124260\pi$
$230$	−5.91027	+	10.0725i	−0.389712	+	0.664159i
$231$	0.213269	+	0.656373i	0.0140320	+	0.0431862i
$232$	0.836430	−	1.15125i	0.0549143	−	0.0755831i
$233$	−8.92092	+	12.2786i	−0.584429	+	0.804397i	−0.994172	−	0.107804i	$-0.965618\pi$
$233$	−8.92092	+	12.2786i	−0.584429	+	0.804397i	0.409744	+	0.912201i	$0.365618\pi$
$234$	−1.67771	−	5.16348i	−0.109676	−	0.337547i
$235$	−15.0347	−	8.82201i	−0.980759	−	0.575485i
$236$	−0.537561	+	0.390561i	−0.0349923	+	0.0254234i
$237$	8.21746	+	2.67001i	0.533781	+	0.173436i
$238$	0.314255	+	0.432535i	0.0203701	+	0.0280371i
$239$	−3.55579	−	10.9436i	−0.230005	−	0.707883i	−0.997745	−	0.0671213i	$-0.978619\pi$
$239$	−3.55579	−	10.9436i	−0.230005	−	0.707883i	0.767740	−	0.640762i	$-0.221381\pi$
$240$	0.895088	+	2.04910i	0.0577777	+	0.132269i
$241$	−6.23775	+	19.1978i	−0.401809	+	1.23664i	0.521722	+	0.853116i	$0.325290\pi$
$241$	−6.23775	+	19.1978i	−0.401809	+	1.23664i	−0.923531	+	0.383524i	$0.874710\pi$
$242$		−	5.83664i		−	0.375194i
$243$		−	1.00000i		−	0.0641500i
$244$	3.00285	−	9.24183i	0.192238	−	0.591647i
$245$	7.81708	−	13.3221i	0.499415	−	0.851118i
$246$	−1.96576	+	1.42821i	−0.125332	+	0.0910593i
$247$			25.1821i			1.60230i
$248$	−2.22978	−	5.10177i	−0.141591	−	0.323963i
$249$	9.70345			0.614931
$250$	−6.76119	+	8.90429i	−0.427615	+	0.563157i
$251$	−7.43325	−	5.40057i	−0.469183	−	0.340881i	0.327940	−	0.944699i	$-0.393646\pi$
$251$	−7.43325	−	5.40057i	−0.469183	−	0.340881i	−0.797123	+	0.603817i	$0.793646\pi$
$252$	−0.288858	−	0.0938558i	−0.0181964	−	0.00591236i
$253$		−	11.8677i		−	0.746115i
$254$	6.51940			0.409064
$255$	−3.84427	−	0.845453i	−0.240737	−	0.0529443i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−14.3660	+	4.66780i	−0.896126	+	0.291169i	−0.720637	−	0.693312i	$-0.756151\pi$
$257$	−14.3660	+	4.66780i	−0.896126	+	0.291169i	−0.175489	+	0.984481i	$0.556151\pi$
$258$	−3.24350	−	4.46429i	−0.201931	−	0.277935i
$259$	0.101951	−	0.313773i	0.00633493	−	0.0194969i
$260$	9.07878	−	8.05957i	0.563042	−	0.499833i
$261$	−1.15125	−	0.836430i	−0.0712604	−	0.0517737i
$262$	−2.34869	+	0.763135i	−0.145103	+	0.0471467i
$263$	14.3012	−	19.6839i	0.881847	−	1.21376i	−0.0940586	−	0.995567i	$-0.529984\pi$
$263$	14.3012	−	19.6839i	0.881847	−	1.21376i	0.975906	−	0.218192i	$-0.0700159\pi$
$264$	−1.83833	−	1.33563i	−0.113141	−	0.0822021i
$265$	−1.63117	−	3.73419i	−0.100202	−	0.229390i
$266$	1.13971	+	0.828046i	0.0698799	+	0.0507707i
$267$	−10.0745	−	13.8663i	−0.616547	−	0.848604i
$268$	1.96514	+	0.638514i	0.120040	+	0.0390034i
$269$	−16.9643	+	12.3253i	−1.03433	+	0.751487i	−0.969171	−	0.246388i	$-0.920756\pi$
$269$	−16.9643	+	12.3253i	−1.03433	+	0.751487i	−0.0651619	+	0.997875i	$0.520756\pi$
$270$	2.04910	−	0.895088i	0.124704	−	0.0544733i
$271$	5.85147	+	18.0090i	0.355451	+	1.09397i	0.955747	+	0.294189i	$0.0950494\pi$
$271$	5.85147	+	18.0090i	0.355451	+	1.09397i	−0.600296	+	0.799778i	$0.704951\pi$
$272$	−1.67414	−	0.543961i	−0.101510	−	0.0329825i
$273$			1.64898i			0.0998006i
$274$	−2.82104			−0.170425
$275$	1.34657	−	11.2814i	0.0812011	−	0.680296i
$276$	4.22530	+	3.06986i	0.254333	+	0.184784i
$277$	12.3448	+	16.9912i	0.741729	+	1.02090i	0.998517	+	0.0544351i	$0.0173358\pi$
$277$	12.3448	+	16.9912i	0.741729	+	1.02090i	−0.256788	+	0.966468i	$0.582664\pi$
$278$			2.39411i			0.143589i
$279$	−5.10177	+	2.22978i	−0.305435	+	0.133493i
$280$	−0.0662336	−	0.675909i	−0.00395821	−	0.0403933i
$281$	3.71114	−	2.69630i	0.221388	−	0.160848i	−0.471563	−	0.881832i	$-0.656310\pi$
$281$	3.71114	−	2.69630i	0.221388	−	0.160848i	0.692951	+	0.720984i	$0.256310\pi$
$282$	−4.58225	+	6.30692i	−0.272869	+	0.375572i
$283$	14.0139	+	4.55340i	0.833042	+	0.270672i	0.694326	−	0.719660i	$-0.255702\pi$
$283$	14.0139	+	4.55340i	0.833042	+	0.270672i	0.138716	+	0.990332i	$0.455702\pi$
$284$	−15.0831			−0.895015
$285$	−10.3221	+	1.01148i	−0.611427	+	0.0599148i
$286$	−3.81227	+	11.7330i	−0.225425	+	0.693785i
$287$	0.701872	−	0.228052i	0.0414302	−	0.0134615i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	−11.2464	+	8.17102i	−0.661555	+	0.480648i
$290$	0.683463	−	3.10770i	0.0401343	−	0.182491i
$291$	12.2924	−	8.93092i	0.720591	−	0.523540i
$292$	3.67633	−	5.06004i	0.215141	−	0.296116i
$293$	10.3081	−	3.34932i	0.602208	−	0.195669i	0.00798293	−	0.999968i	$-0.497459\pi$
$293$	10.3081	−	3.34932i	0.602208	−	0.195669i	0.594225	+	0.804299i	$0.297459\pi$
$294$	−5.58849	−	4.06027i	−0.325927	−	0.236800i
$295$	−0.751931	+	1.28146i	−0.0437791	+	0.0746097i
$296$	0.335670	+	1.03309i	0.0195104	+	0.0600470i
$297$	−1.33563	+	1.83833i	−0.0775009	+	0.106671i
$298$	12.2904	+	16.9163i	0.711964	+	0.979934i
$299$	8.76230	−	26.9676i	0.506737	−	1.55958i
$300$	3.66825	+	3.39764i	0.211787	+	0.196163i
$301$	0.517912	+	1.59397i	0.0298520	+	0.0918749i
$302$	1.53968	−	0.500273i	0.0885988	−	0.0287875i
$303$	−18.1121	−	5.88499i	−1.04051	−	0.338084i
$304$	−4.63828			−0.266024
$305$	−2.11910	−	21.6253i	−0.121339	−	1.23826i
$306$	−0.543961	+	1.67414i	−0.0310962	+	0.0957042i
$307$	0.380957	−	0.524342i	0.0217423	−	0.0299258i	−0.798007	−	0.602648i	$-0.794112\pi$
$307$	0.380957	−	0.524342i	0.0217423	−	0.0299258i	0.819750	+	0.572722i	$0.194112\pi$
$308$	0.405661	+	0.558345i	0.0231147	+	0.0318146i
$309$	−7.99066			−0.454573
$310$	−9.13558	−	8.45820i	−0.518866	−	0.480394i
$311$	35.1025			1.99048			0.995240	−	0.0974563i	$-0.0310706\pi$
$311$	35.1025			1.99048			0.995240	+	0.0974563i	$0.0310706\pi$
$312$	−3.19120	−	4.39231i	−0.180666	−	0.248666i
$313$	10.3105	−	14.1912i	0.582783	−	0.802132i	−0.411214	−	0.911539i	$-0.634895\pi$
$313$	10.3105	−	14.1912i	0.582783	−	0.802132i	0.993997	+	0.109406i	$0.0348950\pi$
$314$	−5.42492	+	16.6962i	−0.306146	+	0.942220i
$315$	−0.675909	+	0.0662336i	−0.0380832	+	0.00373184i
$316$	8.64035			0.486057
$317$	−13.6440	−	4.43321i	−0.766324	−	0.248994i	−0.100333	−	0.994954i	$-0.531991\pi$
$317$	−13.6440	−	4.43321i	−0.766324	−	0.248994i	−0.665991	+	0.745960i	$0.731991\pi$
$318$	−1.73316	+	0.563139i	−0.0971910	+	0.0315793i
$319$	0.999216	+	3.07527i	0.0559454	+	0.172182i
$320$	1.48449	+	1.67221i	0.0829853	+	0.0934796i
$321$	−6.01185	+	18.5026i	−0.335549	+	1.03271i
$322$	−0.932389	−	1.28332i	−0.0519600	−	0.0715168i
$323$	4.79911	−	6.60541i	0.267030	−	0.367535i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	11.3893	−	24.6412i	0.631766	−	1.36685i
$326$	−7.71262	−	5.60354i	−0.427162	−	0.310352i
$327$	−7.47024	+	2.42723i	−0.413105	+	0.134226i
$328$	−1.42821	+	1.96576i	−0.0788597	+	0.108541i
$329$	1.91556	−	1.39174i	0.105608	−	0.0767289i
$330$	−4.96243	−	1.09137i	−0.273173	−	0.0600777i
$331$	0.504329	−	0.366416i	0.0277204	−	0.0201401i	−0.573839	−	0.818968i	$-0.694546\pi$
$331$	0.504329	−	0.366416i	0.0277204	−	0.0201401i	0.601559	+	0.798828i	$0.294546\pi$
$332$	9.22853	−	2.99853i	0.506482	−	0.164566i
$333$	1.03309	−	0.335670i	0.0566128	−	0.0183946i
$334$	−1.22829	+	3.78028i	−0.0672088	+	0.206847i
$335$	4.59830	−	0.450596i	0.251232	−	0.0246187i
$336$	−0.303724			−0.0165695
$337$	−9.92385	−	3.22446i	−0.540587	−	0.175647i	0.0259810	−	0.999662i	$-0.491729\pi$
$337$	−9.92385	−	3.22446i	−0.540587	−	0.175647i	−0.566568	+	0.824015i	$0.691729\pi$
$338$	−9.68447	+	13.3295i	−0.526766	+	0.725031i
$339$	−4.87963	+	3.54526i	−0.265025	+	0.192552i
$340$	−3.91737	+	0.383870i	−0.212449	+	0.0208183i
$341$	12.3569	+	2.71498i	0.669163	+	0.147025i
$342$			4.63828i			0.250809i
$343$	2.48287	+	3.41738i	0.134062	+	0.184521i
$344$	−4.46429	−	3.24350i	−0.240699	−	0.174878i
$345$	11.4059	+	2.50844i	0.614071	+	0.135050i
$346$	2.67983			0.144068
$347$			33.4765i			1.79711i	0.438857	+	0.898557i	$0.355383\pi$
$347$			33.4765i			1.79711i	−0.438857	+	0.898557i	$0.644617\pi$
$348$	−1.35337	−	0.439737i	−0.0725484	−	0.0235724i
$349$	4.33631	+	13.3458i	0.232117	+	0.714384i	0.997491	+	0.0707971i	$0.0225543\pi$
$349$	4.33631	+	13.3458i	0.232117	+	0.714384i	−0.765373	+	0.643586i	$0.777446\pi$
$350$	−0.740717	−	1.32572i	−0.0395930	−	0.0708628i
$351$	−4.39231	+	3.19120i	−0.234444	+	0.170334i
$352$	−2.16109	−	0.702180i	−0.115186	−	0.0374263i
$353$	11.4322	+	15.7351i	0.608476	+	0.837496i	0.996451	−	0.0841744i	$-0.0268253\pi$
$353$	11.4322	+	15.7351i	0.608476	+	0.837496i	−0.387975	+	0.921670i	$0.626825\pi$
$354$	0.537561	+	0.390561i	0.0285711	+	0.0207581i
$355$	−30.9067	+	13.5007i	−1.64036	+	0.716541i
$356$	−13.8663	−	10.0745i	−0.734913	−	0.533945i
$357$	0.314255	−	0.432535i	0.0166321	−	0.0228922i
$358$	1.32533	−	0.430627i	0.0700461	−	0.0227594i
$359$	14.7401	+	10.7093i	0.777952	+	0.565215i	0.904364	−	0.426763i	$-0.140346\pi$
$359$	14.7401	+	10.7093i	0.777952	+	0.565215i	−0.126412	+	0.991978i	$0.540346\pi$
$360$	1.67221	−	1.48449i	0.0881334	−	0.0782393i
$361$	0.776757	−	2.39061i	0.0408820	−	0.125822i
$362$	−3.69108	−	5.08033i	−0.193999	−	0.267016i
$363$	−5.55098	+	1.80362i	−0.291351	+	0.0946656i
$364$	0.509562	+	1.56827i	0.0267083	+	0.0821997i
$365$	3.00400	−	13.6592i	0.157237	−	0.714954i
$366$	−9.71743			−0.507938
$367$			16.1774i			0.844454i	0.906490	+	0.422227i	$0.138752\pi$
$367$			16.1774i			0.844454i	−0.906490	+	0.422227i	$0.861248\pi$
$368$	4.96714	+	1.61392i	0.258930	+	0.0841314i
$369$	1.96576	+	1.42821i	0.102333	+	0.0743496i
$370$	1.61253	+	1.81645i	0.0838313	+	0.0944326i
$371$	0.553492			0.0287359
$372$	−4.16303	+	3.69718i	−0.215843	+	0.191690i
$373$		−	12.6960i		−	0.657374i	−0.944439	−	0.328687i	$-0.893394\pi$
$373$		−	12.6960i		−	0.657374i	0.944439	−	0.328687i	$-0.106606\pi$
$374$	3.23600	−	2.35109i	0.167330	−	0.121572i
$375$	10.5578	+	3.67869i	0.545203	+	0.189967i
$376$	−2.40903	+	7.41423i	−0.124236	+	0.382360i
$377$			7.72586i			0.397902i
$378$			0.303724i			0.0156219i
$379$	1.99358	−	6.13561i	0.102403	−	0.315165i	−0.886709	−	0.462328i	$-0.847014\pi$
$379$	1.99358	−	6.13561i	0.102403	−	0.315165i	0.989112	+	0.147163i	$0.0470142\pi$
$380$	−9.50431	+	4.15167i	−0.487561	+	0.212976i
$381$	−2.01461	−	6.20032i	−0.103211	−	0.317652i
$382$	−1.08086	−	1.48768i	−0.0553016	−	0.0761162i
$383$	−14.4274	−	4.68774i	−0.737205	−	0.239532i	−0.0837384	−	0.996488i	$-0.526686\pi$
$383$	−14.4274	−	4.68774i	−0.737205	−	0.239532i	−0.653467	+	0.756955i	$0.726686\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	1.33101	+	0.781002i	0.0678345	+	0.0398036i
$386$	−5.08446	−	15.6484i	−0.258792	−	0.796480i
$387$	−3.24350	+	4.46429i	−0.164876	+	0.226933i
$388$	8.93092	−	12.2924i	0.453399	−	0.624050i
$389$	0.228664	+	0.703755i	0.0115937	+	0.0356818i	0.956686	−	0.291122i	$-0.0940285\pi$
$389$	0.228664	+	0.703755i	0.0115937	+	0.0356818i	−0.945092	+	0.326804i	$0.894028\pi$
$390$	−10.4706	−	6.14389i	−0.530200	−	0.311108i
$391$	−7.43777	+	5.40385i	−0.376144	+	0.273285i
$392$	−6.56966	−	2.13461i	−0.331818	−	0.107814i
$393$	1.45157	+	1.99791i	0.0732220	+	0.100781i
$394$	−3.02471	−	9.30909i	−0.152383	−	0.468985i
$395$	17.7049	−	7.73387i	0.890833	−	0.389133i
$396$	−0.702180	+	2.16109i	−0.0352859	+	0.108599i
$397$			24.5764i			1.23345i	0.787178	+	0.616726i	$0.211541\pi$
$397$			24.5764i			1.23345i	−0.787178	+	0.616726i	$0.788459\pi$
$398$		−	2.34745i		−	0.117667i
$399$	0.435329	−	1.33981i	0.0217937	−	0.0670742i
$400$	4.53864	+	2.09779i	0.226932	+	0.104890i
$401$	−24.4709	+	17.7791i	−1.22202	+	0.887848i	−0.996266	−	0.0863370i	$-0.972484\pi$
$401$	−24.4709	+	17.7791i	−1.22202	+	0.887848i	−0.225752	+	0.974185i	$0.572484\pi$
$402$		−	2.06627i		−	0.103056i
$403$	26.0747	+	15.2929i	1.29887	+	0.761794i
$404$	−19.0442			−0.947485
$405$	−1.48449	−	1.67221i	−0.0737647	−	0.0830930i
$406$	0.349661	+	0.254044i	0.0173534	+	0.0126080i
$407$	−2.34749	−	0.762745i	−0.116361	−	0.0378078i
$408$			1.76029i			0.0871475i
$409$	18.1509			0.897505			0.448753	−	0.893656i	$-0.351868\pi$
$409$	18.1509			0.897505			0.448753	+	0.893656i	$0.351868\pi$
$410$	−1.16702	+	5.30642i	−0.0576349	+	0.262065i
$411$	0.871749	+	2.68297i	0.0430002	+	0.132341i
$412$	−7.59957	+	2.46925i	−0.374404	+	0.121651i
$413$	−0.118623	−	0.163270i	−0.00583704	−	0.00803400i
$414$	1.61392	−	4.96714i	0.0793199	−	0.244121i
$415$	16.2263	−	14.4046i	0.796516	−	0.707096i
$416$	−4.39231	−	3.19120i	−0.215351	−	0.156462i
$417$	2.27693	−	0.739820i	0.111502	−	0.0362291i
$418$	6.19500	−	8.52669i	0.303008	−	0.417054i
$419$	18.5418	+	13.4714i	0.905826	+	0.658121i	0.939956	−	0.341296i	$-0.110866\pi$
$419$	18.5418	+	13.4714i	0.905826	+	0.658121i	−0.0341299	+	0.999417i	$0.510866\pi$
$420$	−0.622361	+	0.271859i	−0.0303681	+	0.0132654i
$421$	−5.49538	−	3.99263i	−0.267828	−	0.194589i	0.445763	−	0.895151i	$-0.352933\pi$
$421$	−5.49538	−	3.99263i	−0.267828	−	0.194589i	−0.713591	+	0.700562i	$0.752933\pi$
$422$	−11.9814	−	16.4910i	−0.583245	−	0.802768i
$423$	7.41423	+	2.40903i	0.360492	+	0.117131i
$424$	−1.47432	+	1.07115i	−0.0715991	+	0.0520198i
$425$	−7.68350	+	4.29298i	−0.372704	+	0.208240i
$426$	4.66092	+	14.3448i	0.225822	+	0.695010i
$427$	2.80696	+	0.912037i	0.135838	+	0.0441366i
$428$			19.4548i			0.940381i
$429$	12.3368			0.595625
$430$	−12.0510	−	2.65032i	−0.581151	−	0.127810i
$431$	−1.45490	−	1.05704i	−0.0700799	−	0.0509160i	0.552194	−	0.833716i	$-0.313791\pi$
$431$	−1.45490	−	1.05704i	−0.0700799	−	0.0509160i	−0.622274	+	0.782800i	$0.713791\pi$
$432$	−0.587785	−	0.809017i	−0.0282798	−	0.0389238i
$433$			14.3201i			0.688180i	0.938937	+	0.344090i	$0.111813\pi$
$433$			14.3201i			0.688180i	−0.938937	+	0.344090i	$0.888187\pi$
$434$	1.54953	−	0.677237i	0.0743798	−	0.0325084i
$435$	−3.16680	+	0.310321i	−0.151837	+	0.0148787i
$436$	−6.35457	+	4.61686i	−0.304328	+	0.221108i
$437$	−14.2389	+	19.5981i	−0.681137	+	0.937505i
$438$	−5.94843	−	1.93276i	−0.284227	−	0.0923510i
$439$	−14.0671			−0.671384			−0.335692	−	0.941972i	$-0.608970\pi$
$439$	−14.0671			−0.671384			−0.335692	+	0.941972i	$0.608970\pi$
$440$	−5.05680	+	0.495525i	−0.241074	+	0.0236232i
$441$	−2.13461	+	6.56966i	−0.101648	+	0.312841i
$442$	9.08924	−	2.95327i	0.432331	−	0.140473i
$443$	−22.3199	+	7.25219i	−1.06045	+	0.344562i	−0.786762	−	0.617256i	$-0.788244\pi$
$443$	−22.3199	+	7.25219i	−1.06045	+	0.344562i	−0.273690	+	0.961818i	$0.588244\pi$
$444$	0.878797	−	0.638483i	0.0417058	−	0.0303011i
$445$	−37.4310	−	8.23203i	−1.77440	−	0.390236i
$446$	9.73635	−	7.07388i	0.461030	−	0.334958i
$447$	12.2904	−	16.9163i	0.581316	−	0.800113i
$448$	−0.288858	+	0.0938558i	−0.0136473	+	0.00443427i
$449$	−22.0642	−	16.0306i	−1.04127	−	0.756529i	−0.0707393	−	0.997495i	$-0.522536\pi$
$449$	−22.0642	−	16.0306i	−1.04127	−	0.756529i	−0.970534	+	0.240966i	$0.922536\pi$
$450$	2.09779	−	4.53864i	0.0988908	−	0.213954i
$451$	−1.70617	−	5.25104i	−0.0803403	−	0.247262i
$452$	−3.54526	+	4.87963i	−0.166755	+	0.229519i
$453$	−0.951576	−	1.30973i	−0.0447090	−	0.0615366i
$454$	1.76646	−	5.43661i	0.0829041	−	0.255153i
$455$	2.44788	+	2.75744i	0.114759	+	0.129271i
$456$	1.43331	+	4.41127i	0.0671208	+	0.206576i
$457$	−29.1561	+	9.47341i	−1.36387	+	0.443147i	−0.897332	−	0.441356i	$-0.854498\pi$
$457$	−29.1561	+	9.47341i	−1.36387	+	0.443147i	−0.466535	+	0.884503i	$0.654498\pi$
$458$	−15.0967	−	4.90523i	−0.705424	−	0.229206i
$459$	1.76029			0.0821635
$460$	11.6228	−	1.13894i	0.541914	−	0.0531032i
$461$	−8.73595	+	26.8865i	−0.406874	+	1.25223i	0.512447	+	0.858719i	$0.328739\pi$
$461$	−8.73595	+	26.8865i	−0.406874	+	1.25223i	−0.919321	+	0.393509i	$0.871261\pi$
$462$	0.405661	−	0.558345i	0.0188731	−	0.0259765i
$463$	−3.24981	−	4.47298i	−0.151032	−	0.207877i	0.726797	−	0.686853i	$-0.241008\pi$
$463$	−3.24981	−	4.47298i	−0.151032	−	0.207877i	−0.877828	+	0.478976i	$0.841008\pi$
$464$	−1.42302			−0.0660621
$465$	−5.22118	+	11.3022i	−0.242126	+	0.524126i
$466$	15.1772			0.703069
$467$	−9.32066	−	12.8288i	−0.431308	−	0.593645i	0.536944	−	0.843618i	$-0.319578\pi$
$467$	−9.32066	−	12.8288i	−0.431308	−	0.593645i	−0.968253	+	0.249972i	$0.919578\pi$
$468$	−3.19120	+	4.39231i	−0.147513	+	0.203035i
$469$	−0.193932	+	0.596860i	−0.00895493	+	0.0275604i
$470$	1.70004	+	17.3488i	0.0784171	+	0.800241i
$471$	17.5554			0.808910
$472$	0.631941	+	0.205330i	0.0290875	+	0.00945109i
$473$	11.9252	−	3.87475i	0.548323	−	0.178161i
$474$	−2.67001	−	8.21746i	−0.122638	−	0.377440i
$475$	−15.7592	+	17.0144i	−0.723081	+	0.780673i
$476$	0.165214	−	0.508476i	0.00757256	−	0.0233059i
$477$	1.07115	+	1.47432i	0.0490448	+	0.0675043i
$478$	−6.76352	+	9.30919i	−0.309356	+	0.425792i
$479$	0.308929	+	0.950787i	0.0141153	+	0.0434426i	0.957866	−	0.287215i	$-0.0927295\pi$
$479$	0.308929	+	0.950787i	0.0141153	+	0.0434426i	−0.943751	+	0.330658i	$0.892729\pi$
$480$	1.13164	−	1.92857i	0.0516520	−	0.0880269i
$481$	−4.77116	−	3.46645i	−0.217546	−	0.158057i
$482$	19.1978	−	6.23775i	0.874436	−	0.284122i
$483$	−0.932389	+	1.28332i	−0.0424252	+	0.0583932i
$484$	−4.72194	+	3.43069i	−0.214634	+	0.155941i
$485$	7.29763	−	33.1823i	0.331368	−	1.50673i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−36.4626	+	11.8474i	−1.65228	+	0.536858i	−0.979232	−	0.202743i	$-0.935014\pi$
$487$	−36.4626	+	11.8474i	−1.65228	+	0.536858i	−0.673046	+	0.739601i	$0.735014\pi$
$488$	−9.24183	+	3.00285i	−0.418358	+	0.135933i
$489$	−2.94596	+	9.06672i	−0.133221	+	0.410011i
$490$	−15.3726	+	1.50639i	−0.694462	+	0.0680516i
$491$	19.5636			0.882891			0.441445	−	0.897288i	$-0.354466\pi$
$491$	19.5636			0.882891			0.441445	+	0.897288i	$0.354466\pi$
$492$	2.31089	+	0.750854i	0.104183	+	0.0338511i
$493$	1.47236	−	2.02653i	0.0663119	−	0.0912705i
$494$	20.3728	−	14.8017i	0.916615	−	0.665960i
$495$	0.495525	+	5.05680i	0.0222722	+	0.227286i
$496$	−2.81679	+	4.80268i	−0.126478	+	0.215647i
$497$		−	4.58108i		−	0.205490i
$498$	−5.70355	−	7.85026i	−0.255582	−	0.351779i
$499$	21.5839	+	15.6816i	0.966229	+	0.702006i	0.954589	−	0.297926i	$-0.0962948\pi$
$499$	21.5839	+	15.6816i	0.966229	+	0.702006i	0.0116399	+	0.999932i	$0.496295\pi$
$500$	11.1778	+	0.236105i	0.499888	+	0.0105589i
$501$	3.97482			0.177582
$502$			9.18800i			0.410081i
$503$	−40.0915	−	13.0265i	−1.78759	−	0.580824i	−0.788190	−	0.615431i	$-0.788982\pi$
$503$	−40.0915	−	13.0265i	−1.78759	−	0.580824i	−0.999401	+	0.0346078i	$0.988982\pi$
$504$	0.0938558	+	0.288858i	0.00418067	+	0.0128668i
$505$	−39.0235	+	17.0462i	−1.73653	+	0.758548i
$506$	−9.60115	+	6.97565i	−0.426823	+	0.310105i
$507$	15.6698	+	5.09143i	0.695921	+	0.226118i
$508$	−3.83201	−	5.27431i	−0.170018	−	0.234009i
$509$	−2.84633	−	2.06798i	−0.126161	−	0.0916614i	0.522915	−	0.852385i	$-0.324844\pi$
$509$	−2.84633	−	2.06798i	−0.126161	−	0.0916614i	−0.649076	+	0.760723i	$0.724844\pi$
$510$	1.57562	+	3.60702i	0.0697695	+	0.159722i
$511$	1.53685	+	1.11659i	0.0679864	+	0.0493950i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	4.41127	−	1.43331i	0.194762	−	0.0632821i
$514$	12.2204	+	8.87867i	0.539021	+	0.391622i
$515$	−13.3621	+	11.8620i	−0.588804	+	0.522703i
$516$	−1.70521	+	5.24809i	−0.0750676	+	0.231034i
$517$	−10.4123	−	14.3312i	−0.457930	−	0.630287i
$518$	−0.313773	+	0.101951i	−0.0137864	+	0.00447947i
$519$	−0.828113	−	2.54867i	−0.0363501	−	0.111874i
$520$	−11.8567	−	2.60759i	−0.519951	−	0.114351i
$521$	41.8369			1.83291			0.916454	−	0.400140i	$-0.131039\pi$
$521$	41.8369			1.83291			0.916454	+	0.400140i	$0.131039\pi$
$522$			1.42302i			0.0622839i
$523$	5.47680	+	1.77952i	0.239484	+	0.0778130i	0.426300	−	0.904582i	$-0.359817\pi$
$523$	5.47680	+	1.77952i	0.239484	+	0.0778130i	−0.186816	+	0.982395i	$0.559817\pi$
$524$	1.99791	+	1.45157i	0.0872793	+	0.0634121i
$525$	−1.03194	+	1.11413i	−0.0450377	+	0.0486248i
$526$	−24.3306			−1.06086
$527$	−3.92507	−	8.98062i	−0.170979	−	0.391202i
$528$			2.27230i			0.0988892i
$529$	3.46031	−	2.51406i	0.150448	−	0.109307i
$530$	−2.06225	+	3.51455i	−0.0895783	+	0.152662i
$531$	0.205330	−	0.631941i	0.00891057	−	0.0274239i
$532$		−	1.40876i		−	0.0610773i
$533$		−	13.1920i		−	0.571407i
$534$	−5.29646	+	16.3008i	−0.229200	+	0.705405i
$535$	17.4137	+	39.8648i	0.752861	+	1.72351i
$536$	−0.638514	−	1.96514i	−0.0275796	−	0.0848812i
$537$	−0.819102	−	1.12740i	−0.0353468	−	0.0486508i
$538$	19.9428	+	6.47980i	0.859794	+	0.279364i
$539$	12.6987	−	9.22617i	0.546973	−	0.397399i
$540$	−1.92857	−	1.13164i	−0.0829926	−	0.0486980i
$541$	10.3828	+	31.9549i	0.446390	+	1.37385i	0.880952	+	0.473205i	$0.156903\pi$
$541$	10.3828	+	31.9549i	0.446390	+	1.37385i	−0.434562	+	0.900642i	$0.643097\pi$
$542$	11.1302	−	15.3193i	0.478081	−	0.658022i
$543$	−3.69108	+	5.08033i	−0.158399	+	0.218018i
$544$	0.543961	+	1.67414i	0.0233221	+	0.0717781i
$545$	−8.88865	+	15.1483i	−0.380748	+	0.648882i
$546$	1.33405	−	0.969244i	0.0570921	−	0.0414798i
$547$	−31.8225	−	10.3398i	−1.36063	−	0.442096i	−0.464377	−	0.885637i	$-0.653722\pi$
$547$	−31.8225	−	10.3398i	−1.36063	−	0.442096i	−0.896254	+	0.443541i	$0.853722\pi$
$548$	1.65817	+	2.28227i	0.0708333	+	0.0974937i
$549$	3.00285	+	9.24183i	0.128159	+	0.394431i
$550$	−9.91836	+	5.54166i	−0.422920	+	0.236297i
$551$	2.03963	−	6.27732i	0.0868910	−	0.267423i
$552$		−	5.22276i		−	0.222295i
$553$			2.62428i			0.111596i
$554$	6.49006	−	19.9744i	0.275736	−	0.848629i
$555$	1.22925	−	2.09492i	0.0521786	−	0.0889243i
$556$	1.93687	−	1.40722i	0.0821417	−	0.0596794i
$557$			13.1070i			0.555361i	0.960674	+	0.277680i	$0.0895656\pi$
$557$			13.1070i			0.555361i	−0.960674	+	0.277680i	$0.910434\pi$
$558$	4.80268	+	2.81679i	0.203314	+	0.119244i
$559$	29.9592			1.26714
$560$	−0.507891	+	0.450874i	−0.0214623	+	0.0190529i
$561$	−3.23600	−	2.35109i	−0.136624	−	0.0992633i
$562$	−4.36270	−	1.41753i	−0.184030	−	0.0597948i
$563$			15.1483i			0.638426i	0.947683	+	0.319213i	$0.103419\pi$
$563$			15.1483i			0.638426i	−0.947683	+	0.319213i	$0.896581\pi$
$564$	7.79579			0.328262
$565$	−2.89690	+	13.1722i	−0.121873	+	0.554158i
$566$	−4.55340	−	14.0139i	−0.191394	−	0.589050i
$567$	0.288858	−	0.0938558i	0.0121309	−	0.00394157i
$568$	8.86560	+	12.2024i	0.371992	+	0.512003i
$569$	7.24569	−	22.2999i	0.303755	−	0.934862i	−0.676384	−	0.736549i	$-0.736454\pi$
$569$	7.24569	−	22.2999i	0.303755	−	0.934862i	0.980139	−	0.198312i	$-0.0635460\pi$
$570$	6.88546	+	7.75620i	0.288400	+	0.324871i
$571$	−26.0235	−	18.9072i	−1.08905	−	0.791242i	−0.109812	−	0.993952i	$-0.535025\pi$
$571$	−26.0235	−	18.9072i	−1.08905	−	0.791242i	−0.979239	+	0.202711i	$0.935025\pi$
$572$	11.7330	−	3.81227i	0.490580	−	0.159399i
$573$	−1.08086	+	1.48768i	−0.0451536	+	0.0621486i
$574$	−0.597048	−	0.433781i	−0.0249203	−	0.0181057i
$575$	22.7968	−	12.7372i	0.950692	−	0.531178i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−11.2554	−	15.4918i	−0.468570	−	0.644932i	0.507688	−	0.861541i	$-0.330500\pi$
$577$	−11.2554	−	15.4918i	−0.468570	−	0.644932i	−0.976258	+	0.216609i	$0.930500\pi$
$578$	13.2210	+	4.29576i	0.549920	+	0.178680i
$579$	−13.3113	+	9.67122i	−0.553198	+	0.401922i
$580$	−2.91591	+	1.27373i	−0.121077	+	0.0528887i
$581$	0.910725	+	2.80292i	0.0377832	+	0.116285i
$582$	−14.4505	−	4.69526i	−0.598994	−	0.194625i
$583$		−	4.14094i		−	0.171500i
$584$	−6.25455			−0.258815
$585$	−2.60759	+	11.8567i	−0.107811	+	0.490215i
$586$	−8.76862	−	6.37078i	−0.362229	−	0.263174i
$587$	13.0410	+	17.9494i	0.538261	+	0.740853i	0.988361	−	0.152125i	$-0.0486118\pi$
$587$	13.0410	+	17.9494i	0.538261	+	0.740853i	−0.450100	+	0.892978i	$0.648612\pi$
$588$			6.90775i			0.284871i
$589$	−17.1486	−	19.3093i	−0.706594	−	0.795626i
$590$	1.47870	−	0.144901i	0.0608771	−	0.00596546i
$591$	−7.91878	+	5.75333i	−0.325735	+	0.236661i
$592$	0.638483	−	0.878797i	0.0262415	−	0.0361183i
$593$	30.3776	+	9.87029i	1.24746	+	0.405324i	0.857010	−	0.515300i	$-0.172319\pi$
$593$	30.3776	+	9.87029i	1.24746	+	0.405324i	0.390450	+	0.920624i	$0.372319\pi$
$594$	2.27230			0.0932337
$595$	−0.116591	−	1.18980i	−0.00477975	−	0.0487770i
$596$	6.46144	−	19.8863i	0.264671	−	0.814574i
$597$	−2.23256	+	0.725403i	−0.0913726	+	0.0296888i
$598$	−26.9676	+	8.76230i	−1.10279	+	0.358317i
$599$	−21.5214	+	15.6362i	−0.879339	+	0.638877i	−0.933076	−	0.359678i	$-0.882887\pi$
$599$	−21.5214	+	15.6362i	−0.879339	+	0.638877i	0.0537377	+	0.998555i	$0.482887\pi$
$600$	0.592601	−	4.96476i	0.0241928	−	0.202685i
$601$	−12.9834	+	9.43302i	−0.529606	+	0.384781i	−0.820210	−	0.572062i	$-0.806144\pi$
$601$	−12.9834	+	9.43302i	−0.529606	+	0.384781i	0.290605	+	0.956843i	$0.406144\pi$
$602$	0.985127	−	1.35591i	0.0401508	−	0.0552628i
$603$	−1.96514	+	0.638514i	−0.0800268	+	0.0260023i
$604$	−1.30973	−	0.951576i	−0.0532923	−	0.0387191i
$605$	−6.60497	+	11.2564i	−0.268530	+	0.457637i
$606$	5.88499	+	18.1121i	0.239061	+	0.735755i
$607$	16.0043	−	22.0281i	0.649596	−	0.894092i	−0.349486	−	0.936942i	$-0.613644\pi$
$607$	16.0043	−	22.0281i	0.649596	−	0.894092i	0.999082	+	0.0428496i	$0.0136436\pi$
$608$	2.72631	+	3.75245i	0.110567	+	0.152182i
$609$	0.133559	−	0.411051i	0.00541207	−	0.0166566i
$610$	−16.2496	+	14.4254i	−0.657928	+	0.584067i
$611$	−13.0791	−	40.2534i	−0.529124	−	1.62848i
$612$	1.67414	−	0.543961i	0.0676731	−	0.0219883i
$613$	33.9519	+	11.0316i	1.37130	+	0.445564i	0.899801	−	0.436300i	$-0.143711\pi$
$613$	33.9519	+	11.0316i	1.37130	+	0.445564i	0.471504	+	0.881864i	$0.343711\pi$
$614$	−0.648122			−0.0261561
$615$	5.40733	−	0.529874i	0.218045	−	0.0213666i
$616$	0.213269	−	0.656373i	0.00859284	−	0.0264460i
$617$	2.98683	−	4.11101i	0.120245	−	0.165503i	−0.744651	−	0.667454i	$-0.767384\pi$
$617$	2.98683	−	4.11101i	0.120245	−	0.165503i	0.864896	+	0.501951i	$0.167384\pi$
$618$	4.69679	+	6.46458i	0.188933	+	0.260043i
$619$	−34.0826			−1.36989			−0.684947	−	0.728593i	$-0.740175\pi$
$619$	−34.0826			−1.36989			−0.684947	+	0.728593i	$0.740175\pi$
$620$	−1.47307	+	12.3624i	−0.0591599	+	0.496488i
$621$	−5.22276			−0.209582
$622$	−20.6327	−	28.3985i	−0.827297	−	1.13868i
$623$	3.05985	−	4.21152i	0.122590	−	0.168731i
$624$	−1.67771	+	5.16348i	−0.0671624	+	0.206704i
$625$	23.1159	−	9.52135i	0.924635	−	0.380854i
$626$	−17.5413			−0.701089
$627$	−10.0237	−	3.25691i	−0.400309	−	0.130068i
$628$	16.6962	−	5.42492i	0.666250	−	0.216478i
$629$	0.590879	+	1.81854i	0.0235599	+	0.0725098i
$630$	0.450874	+	0.507891i	0.0179632	+	0.0202349i
$631$	14.3334	−	44.1138i	0.570605	−	1.75614i	−0.0800737	−	0.996789i	$-0.525516\pi$
$631$	14.3334	−	44.1138i	0.570605	−	1.75614i	0.650679	−	0.759353i	$-0.274484\pi$
$632$	−5.07867	−	6.99019i	−0.202019	−	0.278055i
$633$	−11.9814	+	16.4910i	−0.476218	+	0.655457i
$634$	4.43321	+	13.6440i	0.176065	+	0.541873i
$635$	−12.5731	−	7.37761i	−0.498950	−	0.292771i
$636$	1.47432	+	1.07115i	0.0584605	+	0.0424740i
$637$	35.6680	−	11.5892i	1.41322	−	0.459182i
$638$	1.90062	−	2.61598i	0.0752464	−	0.103568i
$639$	12.2024	−	8.86560i	0.482721	−	0.350718i
$640$	0.480291	−	2.18388i	0.0189852	−	0.0863253i
$641$	15.9449	−	11.5846i	0.629784	−	0.457565i	−0.226542	−	0.974002i	$-0.572742\pi$
$641$	15.9449	−	11.5846i	0.629784	−	0.457565i	0.856325	+	0.516437i	$0.172742\pi$
$642$	18.5026	−	6.01185i	0.730239	−	0.237269i
$643$	−21.5139	+	6.99028i	−0.848424	+	0.275670i	−0.700786	−	0.713372i	$-0.747167\pi$
$643$	−21.5139	+	6.99028i	−0.848424	+	0.275670i	−0.147638	+	0.989041i	$0.547167\pi$
$644$	−0.490186	+	1.50864i	−0.0193160	+	0.0594486i
$645$	1.20336	+	12.2802i	0.0473821	+	0.483532i
$646$	−8.16474			−0.321237
$647$	21.8006	+	7.08343i	0.857069	+	0.278479i	0.704404	−	0.709799i	$-0.251214\pi$
$647$	21.8006	+	7.08343i	0.857069	+	0.278479i	0.152665	+	0.988278i	$0.451214\pi$
$648$	−0.587785	+	0.809017i	−0.0230904	+	0.0317812i
$649$	−1.22150	+	0.887473i	−0.0479481	+	0.0348364i
$650$	−26.6296	+	5.26957i	−1.04450	+	0.206690i
$651$	−1.12292	−	1.26441i	−0.0440108	−	0.0495562i
$652$			9.53332i			0.373354i
$653$	−12.6915	−	17.4684i	−0.496657	−	0.683589i	0.484942	−	0.874547i	$-0.338841\pi$
$653$	−12.6915	−	17.4684i	−0.496657	−	0.683589i	−0.981598	+	0.190957i	$0.938841\pi$
$654$	6.35457	+	4.61686i	0.248483	+	0.180534i
$655$	5.39321	+	1.18611i	0.210730	+	0.0463450i
$656$	2.42982			0.0948683
$657$			6.25455i			0.244013i
$658$	−2.25188	−	0.731679i	−0.0877873	−	0.0285238i
$659$	−6.31798	−	19.4447i	−0.246114	−	0.757460i	−0.995451	−	0.0952717i	$-0.969628\pi$
$659$	−6.31798	−	19.4447i	−0.246114	−	0.757460i	0.749338	−	0.662188i	$-0.230372\pi$
$660$	2.03391	+	4.65618i	0.0791698	+	0.181241i
$661$	8.66176	−	6.29314i	0.336903	−	0.244775i	−0.406451	−	0.913673i	$-0.633234\pi$
$661$	8.66176	−	6.29314i	0.336903	−	0.244775i	0.743354	+	0.668898i	$0.233234\pi$
$662$	−0.592874	−	0.192636i	−0.0230427	−	0.00748703i
$663$	−5.61746	−	7.73177i	−0.218164	−	0.300277i
$664$	−7.85026	−	5.70355i	−0.304649	−	0.221341i
$665$	−1.26096	−	2.88668i	−0.0488979	−	0.111941i
$666$	−0.878797	−	0.638483i	−0.0340527	−	0.0247407i
$667$	−4.36847	+	6.01268i	−0.169148	+	0.232812i
$668$	3.78028	−	1.22829i	0.146263	−	0.0475238i
$669$	−9.73635	−	7.07388i	−0.376429	−	0.273492i
$670$	−3.06735	−	3.45525i	−0.118502	−	0.133488i
$671$	6.82338	−	21.0002i	0.263414	−	0.810704i
$672$	0.178524	+	0.245718i	0.00688672	+	0.00947876i
$673$	−14.0425	+	4.56270i	−0.541300	+	0.175879i	−0.566890	−	0.823793i	$-0.691854\pi$
$673$	−14.0425	+	4.56270i	−0.541300	+	0.175879i	0.0255898	+	0.999673i	$0.491854\pi$
$674$	3.22446	+	9.92385i	0.124201	+	0.382253i
$675$	−4.96476	−	0.592601i	−0.191094	−	0.0228092i
$676$	16.4762			0.633700
$677$			10.0762i			0.387260i	0.981075	+	0.193630i	$0.0620262\pi$
$677$			10.0762i			0.387260i	−0.981075	+	0.193630i	$0.937974\pi$
$678$	5.73635	+	1.86385i	0.220303	+	0.0715809i
$679$	3.73348	+	2.71253i	0.143278	+	0.104097i
$680$	2.61313	+	2.94359i	0.100209	+	0.112881i
$681$	−5.71639			−0.219052
$682$	−5.06673	−	11.5928i	−0.194015	−	0.443910i
$683$		−	37.2795i		−	1.42646i	−0.700929	−	0.713231i	$-0.747231\pi$
$683$		−	37.2795i		−	1.42646i	0.700929	−	0.713231i	$-0.252769\pi$
$684$	3.75245	−	2.72631i	0.143478	−	0.104243i
$685$	5.44058	+	3.19240i	0.207874	+	0.121975i
$686$	1.30532	−	4.01737i	0.0498375	−	0.153384i
$687$			15.8737i			0.605618i
$688$			5.51817i			0.210378i
$689$	3.05739	−	9.40969i	0.116477	−	0.358481i
$690$	−4.67482	−	10.7020i	−0.177968	−	0.407417i
$691$	−12.5753	−	38.7029i	−0.478388	−	1.47233i	−0.841333	−	0.540516i	$-0.818229\pi$
$691$	−12.5753	−	38.7029i	−0.478388	−	1.47233i	0.362945	−	0.931810i	$-0.381771\pi$
$692$	−1.57516	−	2.16803i	−0.0598787	−	0.0824160i
$693$	−0.656373	−	0.213269i	−0.0249336	−	0.00810141i
$694$	27.0831	−	19.6770i	1.02806	−	0.746929i
$695$	2.70926	−	4.61721i	0.102768	−	0.175141i
$696$	0.439737	+	1.35337i	0.0166682	+	0.0512995i
$697$	−2.51407	+	3.46032i	−0.0952271	+	0.131069i
$698$	8.24815	−	11.3526i	0.312197	−	0.429702i
$699$	−4.69000	−	14.4343i	−0.177392	−	0.545957i
$700$	−0.637149	+	1.37849i	−0.0240820	+	0.0521021i
$701$	−22.6751	+	16.4744i	−0.856426	+	0.622230i	−0.926910	−	0.375283i	$-0.877546\pi$
$701$	−22.6751	+	16.4744i	−0.856426	+	0.622230i	0.0704840	+	0.997513i	$0.477546\pi$
$702$	5.16348	+	1.67771i	0.194883	+	0.0633213i
$703$	2.96146	+	4.07610i	0.111694	+	0.153733i
$704$	0.702180	+	2.16109i	0.0264644	+	0.0814491i
$705$	15.9744	−	6.97791i	0.601629	−	0.262803i
$706$	6.01028	−	18.4977i	0.226200	−	0.696171i
$707$		−	5.78418i		−	0.217536i
$708$		−	0.664462i		−	0.0249720i
$709$	−10.9524	+	33.7081i	−0.411326	+	1.26593i	0.504169	+	0.863605i	$0.331799\pi$
$709$	−10.9524	+	33.7081i	−0.411326	+	1.26593i	−0.915496	+	0.402328i	$0.868201\pi$
$710$	29.0888	+	17.0686i	1.09168	+	0.640572i
$711$	−6.99019	+	5.07867i	−0.262153	+	0.190465i
$712$			17.1397i			0.642337i
$713$	11.6456	+	26.6453i	0.436131	+	0.997875i
$714$	−0.534643			−0.0200085
$715$	20.6297	−	18.3138i	0.771509	−	0.684897i
$716$	−1.12740	−	0.819102i	−0.0421328	−	0.0306113i
$717$	10.9436	+	3.55579i	0.408697	+	0.132794i
$718$		−	18.2197i		−	0.679955i
$719$	−22.9071			−0.854289			−0.427145	−	0.904183i	$-0.640481\pi$
$719$	−22.9071			−0.854289			−0.427145	+	0.904183i	$0.640481\pi$
$720$	−2.18388	−	0.480291i	−0.0813883	−	0.0178994i
$721$	−0.749969	−	2.30817i	−0.0279303	−	0.0859607i
$722$	−2.39061	+	0.776757i	−0.0889694	+	0.0289079i
$723$	−11.8649	−	16.3306i	−0.441260	−	0.607343i
$724$	−1.94051	+	5.97229i	−0.0721186	+	0.221958i
$725$	−4.83490	+	5.22000i	−0.179564	+	0.193866i
$726$	4.72194	+	3.43069i	0.175248	+	0.127325i
$727$	−24.0202	+	7.80464i	−0.890860	+	0.289458i	−0.718459	−	0.695569i	$-0.755152\pi$
$727$	−24.0202	+	7.80464i	−0.890860	+	0.289458i	−0.172401	+	0.985027i	$0.555152\pi$
$728$	0.969244	−	1.33405i	0.0359226	−	0.0494432i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−12.8162	+	5.59837i	−0.474349	+	0.207205i
$731$	−7.85847	−	5.70951i	−0.290656	−	0.211174i
$732$	5.71176	+	7.86157i	0.211113	+	0.290572i
$733$	41.7965	+	13.5805i	1.54379	+	0.501608i	0.952419	−	0.304792i	$-0.0985870\pi$
$733$	41.7965	+	13.5805i	1.54379	+	0.501608i	0.591371	+	0.806400i	$0.298587\pi$
$734$	13.0878	−	9.50885i	0.483080	−	0.350978i
$735$	6.18304	+	14.1547i	0.228065	+	0.522103i
$736$	−1.61392	−	4.96714i	−0.0594899	−	0.183091i
$737$	4.46540	+	1.45090i	0.164485	+	0.0534444i
$738$		−	2.42982i		−	0.0894427i
$739$	19.8351			0.729648			0.364824	−	0.931077i	$-0.381129\pi$
$739$	19.8351			0.729648			0.364824	+	0.931077i	$0.381129\pi$
$740$	0.521717	−	2.37224i	0.0191787	−	0.0872053i
$741$	−20.3728	−	14.8017i	−0.748413	−	0.543754i
$742$	−0.325335	−	0.447785i	−0.0119434	−	0.0164387i
$743$			9.80345i			0.359654i	0.983698	+	0.179827i	$0.0575537\pi$
$743$			9.80345i			0.359654i	−0.983698	+	0.179827i	$0.942446\pi$
$744$	5.43805	+	1.19482i	0.199369	+	0.0438041i
$745$	−4.55981	−	46.5326i	−0.167059	−	1.70482i
$746$	−10.2713	+	7.46252i	−0.376058	+	0.273222i
$747$	−5.70355	+	7.85026i	−0.208682	+	0.287226i
$748$	−3.80415	−	1.23604i	−0.139093	−	0.0451942i
$749$	−5.90887			−0.215905
$750$	−3.22960	−	10.7037i	−0.117928	−	0.390845i
$751$	4.82026	−	14.8352i	0.175894	−	0.541345i	−0.823779	−	0.566910i	$-0.808139\pi$
$751$	4.82026	−	14.8352i	0.175894	−	0.541345i	0.999673	+	0.0255652i	$0.00813855\pi$
$752$	7.41423	−	2.40903i	0.270369	−	0.0878483i
$753$	8.73831	−	2.83925i	0.318442	−	0.103468i
$754$	6.25035	−	4.54115i	0.227624	−	0.165379i
$755$	−3.53552	−	0.777551i	−0.128671	−	0.0282980i
$756$	0.245718	−	0.178524i	0.00893666	−	0.00649286i
$757$	20.5806	−	28.3267i	0.748013	−	1.02955i	−0.250104	−	0.968219i	$-0.580465\pi$
$757$	20.5806	−	28.3267i	0.748013	−	1.02955i	0.998117	−	0.0613328i	$-0.0195351\pi$
$758$	−6.13561	+	1.99358i	−0.222855	+	0.0724101i
$759$	9.60115	+	6.97565i	0.348500	+	0.253200i
$760$	8.94526	+	5.24886i	0.324479	+	0.190396i
$761$	−13.3954	−	41.2269i	−0.485584	−	1.49447i	−0.831134	−	0.556072i	$-0.812308\pi$
$761$	−13.3954	−	41.2269i	−0.485584	−	1.49447i	0.345550	−	0.938400i	$-0.387692\pi$
$762$	−3.83201	+	5.27431i	−0.138819	+	0.191068i
$763$	−1.40225	−	1.93003i	−0.0507649	−	0.0698718i
$764$	−0.568242	+	1.74887i	−0.0205583	+	0.0632718i
$765$	2.94359	−	2.61313i	0.106426	−	0.0944780i
$766$	4.68774	+	14.4274i	0.169375	+	0.521283i
$767$	−3.43094	+	1.11478i	−0.123884	+	0.0402523i
$768$	−0.951057	−	0.309017i	−0.0343183	−	0.0111507i
$769$	−11.9683			−0.431589			−0.215795	−	0.976439i	$-0.569234\pi$
$769$	−11.9683			−0.431589			−0.215795	+	0.976439i	$0.569234\pi$
$770$	−0.150503	−	1.53587i	−0.00542374	−	0.0553489i
$771$	4.66780	−	14.3660i	0.168107	−	0.517379i
$772$	−9.67122	+	13.3113i	−0.348075	+	0.479084i
$773$	7.22735	+	9.94759i	0.259950	+	0.357790i	0.918965	−	0.394340i	$-0.129027\pi$
$773$	7.22735	+	9.94759i	0.259950	+	0.357790i	−0.659015	+	0.752130i	$0.729027\pi$
$774$	5.51817			0.198347
$775$	8.04701	+	26.6504i	0.289057	+	0.957312i
$776$	−15.1942			−0.545440
$777$	0.193922	+	0.266911i	0.00695693	+	0.00957539i
$778$	0.434944	−	0.598650i	0.0155935	−	0.0214626i
$779$	−3.48267	+	10.7186i	−0.124780	+	0.384032i
$780$	1.18396	+	12.0822i	0.0423924	+	0.432612i
$781$	−34.2733			−1.22639
$782$	8.74362	+	2.84097i	0.312671	+	0.101593i
$783$	1.35337	−	0.439737i	0.0483656	−	0.0157149i
$784$	2.13461	+	6.56966i	0.0762362	+	0.234631i
$785$	29.3564	−	26.0608i	1.04777	−	0.930148i
$786$	0.763135	−	2.34869i	0.0272201	−	0.0837750i
$787$	13.9949	+	19.2623i	0.498864	+	0.686628i	0.981992	−	0.188922i	$-0.0604994\pi$
$787$	13.9949	+	19.2623i	0.498864	+	0.686628i	−0.483128	+	0.875550i	$0.660499\pi$
$788$	−5.75333	+	7.91878i	−0.204954	+	0.282095i
$789$	7.51856	+	23.1398i	0.267668	+	0.823797i
$790$	−16.6635	−	9.77775i	−0.592862	−	0.347877i
$791$	−1.48206	−	1.07678i	−0.0526960	−	0.0382859i
$792$	2.16109	−	0.702180i	0.0767909	−	0.0249509i
$793$	31.0103	−	42.6820i	1.10121	−	1.51568i
$794$	19.8827	−	14.4456i	0.705610	−	0.512656i
$795$	3.97980	+	0.875260i	0.141149	+	0.0310423i
$796$	−1.89913	+	1.37980i	−0.0673128	+	0.0489056i
$797$	−2.83872	+	0.922356i	−0.100553	+	0.0326715i	−0.358861	−	0.933391i	$-0.616835\pi$
$797$	−2.83872	+	0.922356i	−0.100553	+	0.0326715i	0.258309	+	0.966062i	$0.416835\pi$
$798$	−1.33981	+	0.435329i	−0.0474286	+	0.0154105i
$799$	−4.24060	+	13.0512i	−0.150022	+	0.461719i
$800$	−0.970598	−	4.90489i	−0.0343158	−	0.173414i
$801$	17.1397			0.605601
$802$	28.7673	+	9.34705i	1.01581	+	0.330056i
$803$	8.35374	−	11.4979i	0.294797	−	0.405753i
$804$	−1.67165	+	1.21453i	−0.0589546	+	0.0428330i
$805$	0.345922	+	3.53011i	0.0121921	+	0.124420i
$806$	−2.95410	−	30.0838i	−0.104054	−	1.05966i
$807$		−	20.9691i		−	0.738146i
$808$	11.1939	+	15.4071i	0.393800	+	0.542020i
$809$	−16.9579	−	12.3206i	−0.596208	−	0.433171i	0.248323	−	0.968677i	$-0.420121\pi$
$809$	−16.9579	−	12.3206i	−0.596208	−	0.433171i	−0.844531	+	0.535507i	$0.820121\pi$
$810$	−0.480291	+	2.18388i	−0.0168757	+	0.0767336i
$811$	−1.51986			−0.0533696			−0.0266848	−	0.999644i	$-0.508495\pi$
$811$	−1.51986			−0.0533696			−0.0266848	+	0.999644i	$0.508495\pi$
$812$		−	0.432205i		−	0.0151674i
$813$	−18.0090	−	5.85147i	−0.631602	−	0.205220i
$814$	0.762745	+	2.34749i	0.0267342	+	0.0822794i
$815$	8.53316	+	19.5347i	0.298903	+	0.684272i
$816$	1.42411	−	1.03467i	0.0498537	−	0.0362209i
$817$	−24.3421	−	7.90923i	−0.851623	−	0.276709i
$818$	−10.6688	−	14.6844i	−0.373027	−	0.513428i
$819$	−1.33405	−	0.969244i	−0.0466155	−	0.0338681i
$820$	4.97894	−	2.17490i	0.173872	−	0.0759507i
$821$	7.34256	+	5.33468i	0.256257	+	0.186182i	0.708495	−	0.705716i	$-0.249374\pi$
$821$	7.34256	+	5.33468i	0.256257	+	0.186182i	−0.452238	+	0.891897i	$0.649374\pi$
$822$	1.65817	−	2.28227i	0.0578352	−	0.0796033i
$823$	43.1455	−	14.0188i	1.50396	−	0.488665i	0.562788	−	0.826601i	$-0.309729\pi$
$823$	43.1455	−	14.0188i	1.50396	−	0.488665i	0.941169	+	0.337936i	$0.109729\pi$
$824$	6.46458	+	4.69679i	0.225204	+	0.163620i
$825$	8.33538	+	7.72045i	0.290201	+	0.268792i
$826$	−0.0623636	+	0.191935i	−0.00216991	+	0.00667829i
$827$	−8.34757	−	11.4895i	−0.290274	−	0.399527i	0.638829	−	0.769348i	$-0.279419\pi$
$827$	−8.34757	−	11.4895i	−0.290274	−	0.399527i	−0.929103	+	0.369821i	$0.879419\pi$
$828$	−4.96714	+	1.61392i	−0.172620	+	0.0560876i
$829$	−1.70200	−	5.23822i	−0.0591129	−	0.181931i	0.917140	−	0.398566i	$-0.130492\pi$
$829$	−1.70200	−	5.23822i	−0.0591129	−	0.181931i	−0.976253	+	0.216635i	$0.930492\pi$
$830$	−21.1912	−	4.66048i	−0.735556	−	0.161768i
$831$	−21.0023			−0.728561
$832$			5.42920i			0.188224i
$833$	−11.5645	−	3.75755i	−0.400687	−	0.130191i
$834$	−1.93687	−	1.40722i	−0.0670684	−	0.0487281i
$835$	6.64675	−	5.90056i	0.230020	−	0.204197i
$836$	−10.5396			−0.364519
$837$	1.19482	−	5.43805i	0.0412989	−	0.187967i
$838$		−	22.9189i		−	0.791721i
$839$	−15.5855	+	11.3235i	−0.538072	+	0.390932i	−0.823368	−	0.567507i	$-0.807908\pi$
$839$	−15.5855	+	11.3235i	−0.538072	+	0.390932i	0.285297	+	0.958439i	$0.407908\pi$
$840$	0.585753	+	0.343705i	0.0202104	+	0.0118590i
$841$	−8.33574	+	25.6548i	−0.287439	+	0.884647i
$842$			6.79266i			0.234091i
$843$			4.58722i			0.157992i
$844$	−6.29899	+	19.3863i	−0.216820	+	0.667304i
$845$	33.7614	−	14.7477i	1.16143	−	0.507335i
$846$	−2.40903	−	7.41423i	−0.0828242	−	0.254907i
$847$	−1.04198	−	1.43417i	−0.0358029	−	0.0492785i
$848$	1.73316	+	0.563139i	0.0595171	+	0.0193383i
$849$	−11.9210	+	8.66109i	−0.409127	+	0.297248i
$850$	7.98934	+	3.69273i	0.274032	+	0.126660i
$851$	−1.75312	−	5.39556i	−0.0600963	−	0.184958i
$852$	8.86560	−	12.2024i	0.303730	−	0.418049i
$853$	14.7587	−	20.3136i	0.505327	−	0.695523i	−0.477796	−	0.878471i	$-0.658564\pi$
$853$	14.7587	−	20.3136i	0.505327	−	0.695523i	0.983123	+	0.182948i	$0.0585641\pi$
$854$	−0.912037	−	2.80696i	−0.0312093	−	0.0960522i
$855$	5.24886	−	8.94526i	0.179507	−	0.305921i
$856$	15.7392	−	11.4352i	0.537956	−	0.390848i
$857$	54.2956	+	17.6417i	1.85470	+	0.602630i	0.995915	+	0.0902995i	$0.0287824\pi$
$857$	54.2956	+	17.6417i	1.85470	+	0.602630i	0.858789	+	0.512330i	$0.171218\pi$
$858$	−7.25138	−	9.98067i	−0.247558	−	0.340734i
$859$	3.11103	+	9.57477i	0.106147	+	0.326687i	0.989998	−	0.141082i	$-0.0450580\pi$
$859$	3.11103	+	9.57477i	0.106147	+	0.326687i	−0.883851	+	0.467769i	$0.845058\pi$
$860$	4.93925	+	11.3073i	0.168427	+	0.385575i
$861$	−0.228052	+	0.701872i	−0.00777200	+	0.0239197i
$862$			1.79835i			0.0612521i
$863$			6.12108i			0.208364i	0.994558	+	0.104182i	$0.0332224\pi$
$863$			6.12108i			0.208364i	−0.994558	+	0.104182i	$0.966778\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−5.16824	−	3.03260i	−0.175726	−	0.103111i
$866$	11.5852	−	8.41715i	0.393681	−	0.286026i
$867$		−	13.9014i		−	0.472115i
$868$	−1.45869	−	0.855525i	−0.0495110	−	0.0290384i
$869$	19.6335			0.666020
$870$	2.11245	+	2.37959i	0.0716189	+	0.0806758i
$871$	9.07572	+	6.59390i	0.307519	+	0.223426i
$872$	7.47024	+	2.42723i	0.252974	+	0.0821963i
$873$			15.1942i			0.514246i
$874$	24.2246			0.819409
$875$	−0.0717107	+	3.39498i	−0.00242427	+	0.114771i
$876$	1.93276	+	5.94843i	0.0653020	+	0.200979i
$877$	−14.6451	+	4.75848i	−0.494530	+	0.160682i	−0.545655	−	0.838010i	$-0.683719\pi$
$877$	−14.6451	+	4.75848i	−0.494530	+	0.160682i	0.0511255	+	0.998692i	$0.483719\pi$
$878$	8.26841	+	11.3805i	0.279045	+	0.384073i
$879$	−3.34932	+	10.3081i	−0.112970	+	0.347685i
$880$	3.37320	+	3.79978i	0.113711	+	0.128090i
$881$	8.75559	+	6.36131i	0.294983	+	0.214318i	0.725426	−	0.688300i	$-0.241643\pi$
$881$	8.75559	+	6.36131i	0.294983	+	0.214318i	−0.430443	+	0.902618i	$0.641643\pi$
$882$	6.56966	−	2.13461i	0.221212	−	0.0718761i
$883$	1.53612	−	2.11429i	0.0516945	−	0.0711514i	−0.782387	−	0.622792i	$-0.785998\pi$
$883$	1.53612	−	2.11429i	0.0516945	−	0.0711514i	0.834082	+	0.551641i	$0.185998\pi$
$884$	−7.73177	−	5.61746i	−0.260047	−	0.188936i
$885$	−0.594752	−	1.36155i	−0.0199924	−	0.0457680i
$886$	18.9865	+	13.7945i	0.637863	+	0.463435i
$887$	−28.7125	−	39.5194i	−0.964072	−	1.32693i	−0.944985	−	0.327114i	$-0.893924\pi$
$887$	−28.7125	−	39.5194i	−0.964072	−	1.32693i	−0.0190872	−	0.999818i	$-0.506076\pi$
$888$	−1.03309	−	0.335670i	−0.0346681	−	0.0112644i
$889$	1.60193	−	1.16387i	0.0537271	−	0.0390350i
$890$	15.3415	+	35.1210i	0.514249	+	1.17726i
$891$	−0.702180	−	2.16109i	−0.0235239	−	0.0723992i
$892$	−11.4458	−	3.71896i	−0.383233	−	0.124520i
$893$			36.1590i			1.21002i
$894$	−20.9097			−0.699324
$895$	−3.04332	−	0.669304i	−0.101727	−	0.0223724i
$896$	0.245718	+	0.178524i	0.00820885	+	0.00596408i
$897$	16.6669	+	22.9400i	0.556491	+	0.765944i
$898$			27.2728i			0.910106i
$899$	−5.26116	−	5.92408i	−0.175470	−	0.197579i
$900$	−4.90489	+	0.970598i	−0.163496	+	0.0323533i
$901$	−2.59523	+	1.88555i	−0.0864597	+	0.0628166i
$902$	−3.24532	+	4.46680i	−0.108057	+	0.148728i
$903$	−1.59397	−	0.517912i	−0.0530440	−	0.0172350i
$904$	6.03156			0.200607
$905$	1.36941	+	13.9748i	0.0455208	+	0.464536i
$906$	−0.500273	+	1.53968i	−0.0166205	+	0.0511525i
$907$	49.7178	−	16.1543i	1.65085	−	0.536394i	0.671927	−	0.740617i	$-0.265467\pi$
$907$	49.7178	−	16.1543i	1.65085	−	0.536394i	0.978924	+	0.204223i	$0.0654667\pi$
$908$	−5.43661	+	1.76646i	−0.180420	+	0.0586221i
$909$	15.4071	−	11.1939i	0.511021	−	0.371279i
$910$	0.791988	−	3.60116i	0.0262541	−	0.119377i
$911$	−2.33640	+	1.69749i	−0.0774083	+	0.0562404i	−0.625816	−	0.779970i	$-0.715234\pi$
$911$	−2.33640	+	1.69749i	−0.0774083	+	0.0562404i	0.548408	+	0.836211i	$0.315234\pi$
$912$	2.72631	−	3.75245i	0.0902772	−	0.124256i
$913$	20.9700	−	6.81357i	0.694006	−	0.225496i
$914$	24.8017	+	18.0195i	0.820367	+	0.596032i
$915$	18.7408	+	10.9966i	0.619551	+	0.363537i
$916$	4.90523	+	15.0967i	0.162073	+	0.498810i
$917$	−0.440876	+	0.606814i	−0.0145590	+	0.0200388i
$918$	−1.03467	−	1.42411i	−0.0341494	−	0.0470026i
$919$	−9.44261	+	29.0614i	−0.311483	+	0.958646i	0.665695	+	0.746224i	$0.268135\pi$
$919$	−9.44261	+	29.0614i	−0.311483	+	0.958646i	−0.977178	+	0.212422i	$0.931865\pi$
$920$	−7.75311	−	8.73357i	−0.255612	−	0.287937i
$921$	0.200281	+	0.616401i	0.00659948	+	0.0203111i
$922$	26.8865	−	8.73595i	0.885459	−	0.287703i
$923$	−77.8810	−	25.3051i	−2.56348	−	0.832927i
$924$	−0.690152			−0.0227043
$925$	−1.05431	−	5.32795i	−0.0346656	−	0.175182i
$926$	−1.70853	+	5.25831i	−0.0561457	+	0.172799i
$927$	4.69679	−	6.46458i	0.154263	−	0.212325i
$928$	0.836430	+	1.15125i	0.0274572	+	0.0377916i
$929$	6.19257			0.203172			0.101586	−	0.994827i	$-0.467608\pi$
$929$	6.19257			0.203172			0.101586	+	0.994827i	$0.467608\pi$
$930$	12.2126	−	2.41923i	0.400467	−	0.0793298i
$931$	−32.0401			−1.05007
$932$	−8.92092	−	12.2786i	−0.292214	−	0.402199i
$933$	−20.6327	+	28.3985i	−0.675485	+	0.929726i
$934$	−4.90016	+	15.0811i	−0.160338	+	0.493470i
$935$	−8.90146	+	0.872270i	−0.291109	+	0.0285263i
$936$	5.42920			0.177459
$937$	−13.0183	−	4.22990i	−0.425289	−	0.138185i	0.0885491	−	0.996072i	$-0.471777\pi$
$937$	−13.0183	−	4.22990i	−0.425289	−	0.138185i	−0.513839	+	0.857887i	$0.671777\pi$
$938$	0.596860	−	0.193932i	0.0194882	−	0.00633209i
$939$	5.42055	+	16.6827i	0.176893	+	0.544420i
$940$	13.0362	−	11.5727i	0.425195	−	0.377461i
$941$	−5.08216	+	15.6413i	−0.165674	+	0.509891i	−0.999085	−	0.0427616i	$-0.986384\pi$
$941$	−5.08216	+	15.6413i	−0.165674	+	0.509891i	0.833412	+	0.552653i	$0.186384\pi$
$942$	−10.3188	−	14.2026i	−0.336205	−	0.462746i
$943$	7.45919	−	10.2667i	0.242905	−	0.334330i
$944$	−0.205330	−	0.631941i	−0.00668293	−	0.0205679i
$945$	0.343705	−	0.585753i	0.0111807	−	0.0190546i
$946$	−10.1442	−	7.37021i	−0.329817	−	0.239626i
$947$	0.452596	−	0.147057i	0.0147074	−	0.00477873i	−0.301654	−	0.953417i	$-0.597539\pi$
$947$	0.452596	−	0.147057i	0.0147074	−	0.00477873i	0.316361	+	0.948639i	$0.397539\pi$
$948$	−5.07867	+	6.99019i	−0.164947	+	0.227031i
$949$	27.4720	−	19.9595i	0.891778	−	0.647914i
$950$	23.0279	+	2.74865i	0.747125	+	0.0891779i
$951$	11.6063	−	8.43246i	0.376360	−	0.273441i
$952$	−0.508476	+	0.165214i	−0.0164798	+	0.00535461i
$953$	14.5778	−	4.73660i	0.472220	−	0.153434i	−0.0632328	−	0.997999i	$-0.520141\pi$
$953$	14.5778	−	4.73660i	0.472220	−	0.153434i	0.535453	+	0.844565i	$0.320141\pi$
$954$	0.563139	−	1.73316i	0.0182323	−	0.0561132i
$955$	0.401006	+	4.09224i	0.0129762	+	0.132422i
$956$	11.5068			0.372156
$957$	−3.07527	−	0.999216i	−0.0994094	−	0.0323001i
$958$	0.587618	−	0.808787i	0.0189851	−	0.0261307i
$959$	−0.693179	+	0.503624i	−0.0223839	+	0.0162629i
$960$	−2.22541	+	0.218072i	−0.0718248	+	0.00703824i
$961$	−30.4079	+	6.02998i	−0.980899	+	0.194515i
$962$			5.89748i			0.190142i
$963$	−11.4352	−	15.7392i	−0.368495	−	0.507190i
$964$	−16.3306	−	11.8649i	−0.525974	−	0.382143i
$965$	−7.90254	+	35.9328i	−0.254392	+	1.15672i
$966$	1.58627			0.0510375
$967$			39.0602i			1.25609i	0.778176	+	0.628046i	$0.216145\pi$
$967$			39.0602i			1.25609i	−0.778176	+	0.628046i	$0.783855\pi$
$968$	5.55098	+	1.80362i	0.178415	+	0.0579706i
$969$	2.52304	+	7.76513i	0.0810518	+	0.249452i
$970$	−31.1344	+	13.6001i	−0.999667	+	0.436674i
$971$	−3.78529	+	2.75017i	−0.121476	+	0.0882573i	−0.646864	−	0.762605i	$-0.723920\pi$
$971$	−3.78529	+	2.75017i	−0.121476	+	0.0882573i	0.525389	+	0.850862i	$0.323920\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	0.427406	+	0.588274i	0.0137020	+	0.0188592i
$974$	31.0169	+	22.5351i	0.993847	+	0.722072i
$975$	13.2407	+	23.6979i	0.424041	+	0.758940i
$976$	7.86157	+	5.71176i	0.251643	+	0.182829i
$977$	17.2546	−	23.7489i	0.552022	−	0.759793i	−0.438263	−	0.898847i	$-0.644406\pi$
$977$	17.2546	−	23.7489i	0.552022	−	0.759793i	0.990285	+	0.139054i	$0.0444061\pi$
$978$	9.06672	−	2.94596i	0.289922	−	0.0942013i
$979$	−31.5084	−	22.8922i	−1.00701	−	0.731638i
$980$	10.2545	+	11.5512i	0.327567	+	0.368991i
$981$	2.42723	−	7.47024i	0.0774954	−	0.238506i
$982$	−11.4992	−	15.8272i	−0.366953	−	0.505068i
$983$	18.3636	−	5.96670i	0.585709	−	0.190308i	−0.00114761	−	0.999999i	$-0.500365\pi$
$983$	18.3636	−	5.96670i	0.585709	−	0.190308i	0.586856	+	0.809691i	$0.300365\pi$
$984$	−0.750854	−	2.31089i	−0.0239364	−	0.0736685i
$985$	−4.70116	+	21.3761i	−0.149791	+	0.681100i
$986$	−2.50493			−0.0797733
$987$			2.36776i			0.0753668i
$988$	−23.9496	−	7.78171i	−0.761940	−	0.247569i
$989$	23.3159	+	16.9400i	0.741403	+	0.538661i
$990$	3.79978	−	3.37320i	0.120765	−	0.107207i
$991$	36.6779			1.16511			0.582556	−	0.812791i	$-0.302053\pi$
$991$	36.6779			1.16511			0.582556	+	0.812791i	$0.302053\pi$
$992$	5.54111	−	0.544113i	0.175931	−	0.0172756i
$993$			0.623384i			0.0197825i
$994$	−3.70617	+	2.69269i	−0.117553	+	0.0854070i
$995$	−2.65647	+	4.52723i	−0.0842157	+	0.143523i
$996$	−2.99853	+	9.22853i	−0.0950121	+	0.292417i
$997$		−	48.4956i		−	1.53587i	−0.640528	−	0.767935i	$-0.721284\pi$
$997$		−	48.4956i		−	1.53587i	0.640528	−	0.767935i	$-0.278716\pi$
$998$		−	26.6792i		−	0.844515i
$999$	−0.335670	+	1.03309i	−0.0106201	+	0.0326854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.109.5	✓	72
5.4	even	2	inner	930.2.z.d.109.14	yes	72
31.2	even	5	inner	930.2.z.d.529.14	yes	72
155.64	even	10	inner	930.2.z.d.529.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.5	✓	72	1.1	even	1	trivial
930.2.z.d.109.14	yes	72	5.4	even	2	inner
930.2.z.d.529.5	yes	72	155.64	even	10	inner
930.2.z.d.529.14	yes	72	31.2	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)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.218072 + 2.22541i) q^{5} +1.00000 q^{6} +(-0.288858 - 0.0938558i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.218072 + 2.22541i) q^{5} +1.00000 q^{6} +(-0.288858 - 0.0938558i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.67221 - 1.48449i) q^{10} +(-0.702180 + 2.16109i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(-3.19120 + 4.39231i) q^{13} +(0.0938558 + 0.288858i) q^{14} +(-1.92857 - 1.13164i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.67414 - 0.543961i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(3.75245 - 2.72631i) q^{19} +(-2.18388 - 0.480291i) q^{20} +(0.245718 - 0.178524i) q^{21} +(2.16109 - 0.702180i) q^{22} +(-4.96714 + 1.61392i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(-4.90489 + 0.970598i) q^{25} +5.42920 q^{26} +(0.951057 + 0.309017i) q^{27} +(0.178524 - 0.245718i) q^{28} +(1.15125 - 0.836430i) q^{29} +(0.218072 + 2.22541i) q^{30} +(-0.544113 - 5.54111i) q^{31} +1.00000i q^{32} +(-1.33563 - 1.83833i) q^{33} +(-1.42411 - 1.03467i) q^{34} +(0.145876 - 0.663295i) q^{35} +1.00000 q^{36} +1.08625i q^{37} +(-4.41127 - 1.43331i) q^{38} +(-1.67771 - 5.16348i) q^{39} +(0.895088 + 2.04910i) q^{40} +(-1.96576 + 1.42821i) q^{41} +(-0.288858 - 0.0938558i) q^{42} +(-3.24350 - 4.46429i) q^{43} +(-1.83833 - 1.33563i) q^{44} +(2.04910 - 0.895088i) q^{45} +(4.22530 + 3.06986i) q^{46} +(-4.58225 + 6.30692i) q^{47} +(0.951057 - 0.309017i) q^{48} +(-5.58849 - 4.06027i) q^{49} +(3.66825 + 3.39764i) q^{50} +(-0.543961 + 1.67414i) q^{51} +(-3.19120 - 4.39231i) q^{52} +(-1.73316 + 0.563139i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-4.96243 - 1.09137i) q^{55} -0.303724 q^{56} +4.63828i q^{57} +(-1.35337 - 0.439737i) q^{58} +(0.537561 + 0.390561i) q^{59} +(1.67221 - 1.48449i) q^{60} -9.71743 q^{61} +(-4.16303 + 3.69718i) q^{62} +0.303724i q^{63} +(0.809017 - 0.587785i) q^{64} +(-10.4706 - 6.14389i) q^{65} +(-0.702180 + 2.16109i) q^{66} -2.06627i q^{67} +1.76029i q^{68} +(1.61392 - 4.96714i) q^{69} +(-0.622361 + 0.271859i) q^{70} +(4.66092 + 14.3448i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-5.94843 - 1.93276i) q^{73} +(0.878797 - 0.638483i) q^{74} +(2.09779 - 4.53864i) q^{75} +(1.43331 + 4.41127i) q^{76} +(0.405661 - 0.558345i) q^{77} +(-3.19120 + 4.39231i) q^{78} +(-2.67001 - 8.21746i) q^{79} +(1.13164 - 1.92857i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(2.31089 + 0.750854i) q^{82} +(-5.70355 - 7.85026i) q^{83} +(0.0938558 + 0.288858i) q^{84} +(1.57562 + 3.60702i) q^{85} +(-1.70521 + 5.24809i) q^{86} +1.42302i q^{87} +2.27230i q^{88} +(-5.29646 + 16.3008i) q^{89} +(-1.92857 - 1.13164i) q^{90} +(1.33405 - 0.969244i) q^{91} -5.22276i q^{92} +(4.80268 + 2.81679i) q^{93} +7.79579 q^{94} +(6.88546 + 7.75620i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-14.4505 - 4.69526i) q^{97} +6.90775i q^{98} +2.27230 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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