LMFDB - Embedded newform 804.2.j.a.499.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.5
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32201 + 0.502280i) q^{2} -1.00000 q^{3} +(1.49543 - 1.32804i) q^{4} -0.0336703i q^{5} +(1.32201 - 0.502280i) q^{6} +(0.290483 - 0.503131i) q^{7} +(-1.30993 + 2.50681i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.32201 + 0.502280i) q^{2} -1.00000 q^{3} +(1.49543 - 1.32804i) q^{4} -0.0336703i q^{5} +(1.32201 - 0.502280i) q^{6} +(0.290483 - 0.503131i) q^{7} +(-1.30993 + 2.50681i) q^{8} +1.00000 q^{9} +(0.0169119 + 0.0445126i) q^{10} +(0.647185 - 1.12096i) q^{11} +(-1.49543 + 1.32804i) q^{12} +(-5.63171 + 3.25147i) q^{13} +(-0.131309 + 0.811049i) q^{14} +0.0336703i q^{15} +(0.472616 - 3.97198i) q^{16} +(1.55273 + 2.68940i) q^{17} +(-1.32201 + 0.502280i) q^{18} +(4.41614 - 2.54966i) q^{19} +(-0.0447156 - 0.0503516i) q^{20} +(-0.290483 + 0.503131i) q^{21} +(-0.292552 + 1.80699i) q^{22} +(-6.04917 + 3.49249i) q^{23} +(1.30993 - 2.50681i) q^{24} +4.99887 q^{25} +(5.81204 - 7.12718i) q^{26} -1.00000 q^{27} +(-0.233782 - 1.13817i) q^{28} +(-3.50641 + 6.07327i) q^{29} +(-0.0169119 - 0.0445126i) q^{30} +(4.12899 - 7.15162i) q^{31} +(1.37024 + 5.48839i) q^{32} +(-0.647185 + 1.12096i) q^{33} +(-3.40356 - 2.77552i) q^{34} +(-0.0169406 - 0.00978066i) q^{35} +(1.49543 - 1.32804i) q^{36} +(-1.39784 - 2.42113i) q^{37} +(-4.55755 + 5.58882i) q^{38} +(5.63171 - 3.25147i) q^{39} +(0.0844051 + 0.0441057i) q^{40} +(8.38854 + 4.84313i) q^{41} +(0.131309 - 0.811049i) q^{42} +0.600833 q^{43} +(-0.520858 - 2.53580i) q^{44} -0.0336703i q^{45} +(6.24286 - 7.65549i) q^{46} +(-0.0521219 - 0.0300926i) q^{47} +(-0.472616 + 3.97198i) q^{48} +(3.33124 + 5.76988i) q^{49} +(-6.60856 + 2.51083i) q^{50} +(-1.55273 - 2.68940i) q^{51} +(-4.10374 + 12.3415i) q^{52} +9.39508i q^{53} +(1.32201 - 0.502280i) q^{54} +(-0.0377430 - 0.0217910i) q^{55} +(0.880743 + 1.38725i) q^{56} +(-4.41614 + 2.54966i) q^{57} +(1.58502 - 9.79013i) q^{58} +12.8681i q^{59} +(0.0447156 + 0.0503516i) q^{60} +(-3.76809 + 2.17551i) q^{61} +(-1.86645 + 11.5284i) q^{62} +(0.290483 - 0.503131i) q^{63} +(-4.56819 - 6.56747i) q^{64} +(0.109478 + 0.189622i) q^{65} +(0.292552 - 1.80699i) q^{66} +(4.00175 + 7.14045i) q^{67} +(5.89363 + 1.95973i) q^{68} +(6.04917 - 3.49249i) q^{69} +(0.0273083 + 0.00442122i) q^{70} +(-5.73337 - 3.31016i) q^{71} +(-1.30993 + 2.50681i) q^{72} +(1.38269 + 2.39489i) q^{73} +(3.06404 + 2.49865i) q^{74} -4.99887 q^{75} +(3.21798 - 9.67766i) q^{76} +(-0.375993 - 0.651238i) q^{77} +(-5.81204 + 7.12718i) q^{78} +(-7.77159 + 13.4608i) q^{79} +(-0.133738 - 0.0159132i) q^{80} +1.00000 q^{81} +(-13.5224 - 2.18927i) q^{82} +(9.69727 - 5.59872i) q^{83} +(0.233782 + 1.13817i) q^{84} +(0.0905531 - 0.0522808i) q^{85} +(-0.794309 + 0.301787i) q^{86} +(3.50641 - 6.07327i) q^{87} +(1.96226 + 3.09074i) q^{88} -3.69655 q^{89} +(0.0169119 + 0.0445126i) q^{90} +3.77799i q^{91} +(-4.40794 + 13.2563i) q^{92} +(-4.12899 + 7.15162i) q^{93} +(0.0840207 + 0.0136030i) q^{94} +(-0.0858480 - 0.148693i) q^{95} +(-1.37024 - 5.48839i) q^{96} +(-9.48849 + 5.47818i) q^{97} +(-7.30203 - 5.95463i) q^{98} +(0.647185 - 1.12096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.32201	+	0.502280i	−0.934803	+	0.355166i
$2$	−1.32201	+	0.502280i	−0.934803	+	0.355166i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.49543	−	1.32804i	0.747715	−	0.664020i
$5$		−	0.0336703i		−	0.0150578i	−0.999972	−	0.00752892i	$-0.997603\pi$
$5$		−	0.0336703i		−	0.0150578i	0.999972	−	0.00752892i	$-0.00239655\pi$
$6$	1.32201	−	0.502280i	0.539709	−	0.205055i
$7$	0.290483	−	0.503131i	0.109792	−	0.190166i	−0.805894	−	0.592060i	$-0.798315\pi$
$7$	0.290483	−	0.503131i	0.109792	−	0.190166i	0.915686	+	0.401894i	$0.131648\pi$
$8$	−1.30993	+	2.50681i	−0.463129	+	0.886291i
$9$	1.00000			0.333333
$10$	0.0169119	+	0.0445126i	0.00534803	+	0.0140761i
$11$	0.647185	−	1.12096i	0.195134	−	0.337982i	−0.751811	−	0.659379i	$-0.770819\pi$
$11$	0.647185	−	1.12096i	0.195134	−	0.337982i	0.946944	+	0.321398i	$0.104153\pi$
$12$	−1.49543	+	1.32804i	−0.431693	+	0.383372i
$13$	−5.63171	+	3.25147i	−1.56196	+	0.901795i	−0.564896	+	0.825162i	$0.691084\pi$
$13$	−5.63171	+	3.25147i	−1.56196	+	0.901795i	−0.997059	+	0.0766335i	$0.975583\pi$
$14$	−0.131309	+	0.811049i	−0.0350938	+	0.216762i
$15$			0.0336703i			0.00869365i
$16$	0.472616	−	3.97198i	0.118154	−	0.992995i
$17$	1.55273	+	2.68940i	0.376592	+	0.652276i	0.990564	−	0.137052i	$-0.0437627\pi$
$17$	1.55273	+	2.68940i	0.376592	+	0.652276i	−0.613972	+	0.789328i	$0.710429\pi$
$18$	−1.32201	+	0.502280i	−0.311601	+	0.118389i
$19$	4.41614	−	2.54966i	1.01313	−	0.584933i	0.101026	−	0.994884i	$-0.467788\pi$
$19$	4.41614	−	2.54966i	1.01313	−	0.584933i	0.912107	+	0.409951i	$0.134454\pi$
$20$	−0.0447156	−	0.0503516i	−0.00999871	−	0.0112590i
$21$	−0.290483	+	0.503131i	−0.0633886	+	0.109792i
$22$	−0.292552	+	1.80699i	−0.0623722	+	0.385251i
$23$	−6.04917	+	3.49249i	−1.26134	+	0.728235i	−0.973334	−	0.229394i	$-0.926326\pi$
$23$	−6.04917	+	3.49249i	−1.26134	+	0.728235i	−0.288006	+	0.957629i	$0.592992\pi$
$24$	1.30993	−	2.50681i	0.267388	−	0.511700i
$25$	4.99887			0.999773
$26$	5.81204	−	7.12718i	1.13983	−	1.39775i
$27$	−1.00000			−0.192450
$28$	−0.233782	−	1.13817i	−0.0441806	−	0.215094i
$29$	−3.50641	+	6.07327i	−0.651123	+	1.12778i	0.331728	+	0.943375i	$0.392369\pi$
$29$	−3.50641	+	6.07327i	−0.651123	+	1.12778i	−0.982851	+	0.184403i	$0.940965\pi$
$30$	−0.0169119	−	0.0445126i	−0.00308769	−	0.00812685i
$31$	4.12899	−	7.15162i	0.741588	−	1.28447i	−0.210184	−	0.977662i	$-0.567406\pi$
$31$	4.12899	−	7.15162i	0.741588	−	1.28447i	0.951772	−	0.306807i	$-0.0992605\pi$
$32$	1.37024	+	5.48839i	0.242227	+	0.970220i
$33$	−0.647185	+	1.12096i	−0.112661	+	0.195134i
$34$	−3.40356	−	2.77552i	−0.583705	−	0.475997i
$35$	−0.0169406	−	0.00978066i	−0.00286348	−	0.00165323i
$36$	1.49543	−	1.32804i	0.249238	−	0.221340i
$37$	−1.39784	−	2.42113i	−0.229803	−	0.398031i	0.727946	−	0.685634i	$-0.240475\pi$
$37$	−1.39784	−	2.42113i	−0.229803	−	0.398031i	−0.957750	+	0.287603i	$0.907142\pi$
$38$	−4.55755	+	5.58882i	−0.739332	+	0.906627i
$39$	5.63171	−	3.25147i	0.901795	−	0.520652i
$40$	0.0844051	+	0.0441057i	0.0133456	+	0.00697372i
$41$	8.38854	+	4.84313i	1.31007	+	0.756369i	0.982107	−	0.188321i	$-0.0603047\pi$
$41$	8.38854	+	4.84313i	1.31007	+	0.756369i	0.327963	+	0.944691i	$0.393638\pi$
$42$	0.131309	−	0.811049i	0.0202614	−	0.125148i
$43$	0.600833			0.0916262			0.0458131	−	0.998950i	$-0.485412\pi$
$43$	0.600833			0.0916262			0.0458131	+	0.998950i	$0.485412\pi$
$44$	−0.520858	−	2.53580i	−0.0785223	−	0.382286i
$45$		−	0.0336703i		−	0.00501928i
$46$	6.24286	−	7.65549i	0.920460	−	1.12874i
$47$	−0.0521219	−	0.0300926i	−0.00760277	−	0.00438946i	0.496194	−	0.868212i	$-0.334731\pi$
$47$	−0.0521219	−	0.0300926i	−0.00760277	−	0.00438946i	−0.503797	+	0.863822i	$0.668064\pi$
$48$	−0.472616	+	3.97198i	−0.0682163	+	0.573306i
$49$	3.33124	+	5.76988i	0.475891	+	0.824268i
$50$	−6.60856	+	2.51083i	−0.934591	+	0.355085i
$51$	−1.55273	−	2.68940i	−0.217425	−	0.376592i
$52$	−4.10374	+	12.3415i	−0.569086	+	1.71146i
$53$			9.39508i			1.29051i	0.763966	+	0.645257i	$0.223250\pi$
$53$			9.39508i			1.29051i	−0.763966	+	0.645257i	$0.776750\pi$
$54$	1.32201	−	0.502280i	0.179903	−	0.0683517i
$55$	−0.0377430	−	0.0217910i	−0.00508927	−	0.00293829i
$56$	0.880743	+	1.38725i	0.117694	+	0.185379i
$57$	−4.41614	+	2.54966i	−0.584933	+	0.337711i
$58$	1.58502	−	9.79013i	0.208124	−	1.28551i
$59$			12.8681i			1.67529i	0.546217	+	0.837644i	$0.316068\pi$
$59$			12.8681i			1.67529i	−0.546217	+	0.837644i	$0.683932\pi$
$60$	0.0447156	+	0.0503516i	0.00577276	+	0.00650037i
$61$	−3.76809	+	2.17551i	−0.482455	+	0.278545i	−0.721439	−	0.692478i	$-0.756519\pi$
$61$	−3.76809	+	2.17551i	−0.482455	+	0.278545i	0.238984	+	0.971023i	$0.423186\pi$
$62$	−1.86645	+	11.5284i	−0.237040	+	1.46411i
$63$	0.290483	−	0.503131i	0.0365974	−	0.0633886i
$64$	−4.56819	−	6.56747i	−0.571023	−	0.820934i
$65$	0.109478	+	0.189622i	0.0135791	+	0.0235197i
$66$	0.292552	−	1.80699i	0.0360106	−	0.222425i
$67$	4.00175	+	7.14045i	0.488892	+	0.872344i
$67$	4.00175	+	7.14045i	0.488892	+	0.872344i
$68$	5.89363	+	1.95973i	0.714707	+	0.237652i
$69$	6.04917	−	3.49249i	0.728235	−	0.420446i
$70$	0.0273083	+	0.00442122i	0.00326397	+	0.000528437i
$71$	−5.73337	−	3.31016i	−0.680426	−	0.392844i	0.119590	−	0.992823i	$-0.461842\pi$
$71$	−5.73337	−	3.31016i	−0.680426	−	0.392844i	−0.800015	+	0.599979i	$0.795175\pi$
$72$	−1.30993	+	2.50681i	−0.154376	+	0.295430i
$73$	1.38269	+	2.39489i	0.161832	+	0.280301i	0.935526	−	0.353259i	$-0.114927\pi$
$73$	1.38269	+	2.39489i	0.161832	+	0.280301i	−0.773694	+	0.633560i	$0.781593\pi$
$74$	3.06404	+	2.49865i	0.356188	+	0.290462i
$75$	−4.99887			−0.577219
$76$	3.21798	−	9.67766i	0.369127	−	1.11010i
$77$	−0.375993	−	0.651238i	−0.0428483	−	0.0742155i
$78$	−5.81204	+	7.12718i	−0.658084	+	0.806994i
$79$	−7.77159	+	13.4608i	−0.874372	+	1.51446i	−0.0169424	+	0.999856i	$0.505393\pi$
$79$	−7.77159	+	13.4608i	−0.874372	+	1.51446i	−0.857430	+	0.514601i	$0.827940\pi$
$80$	−0.133738	−	0.0159132i	−0.0149524	−	0.00177915i
$81$	1.00000			0.111111
$82$	−13.5224	−	2.18927i	−1.49329	−	0.241765i
$83$	9.69727	−	5.59872i	1.06441	−	0.614539i	0.137764	−	0.990465i	$-0.456009\pi$
$83$	9.69727	−	5.59872i	1.06441	−	0.614539i	0.926650	+	0.375926i	$0.122675\pi$
$84$	0.233782	+	1.13817i	0.0255077	+	0.124185i
$85$	0.0905531	−	0.0522808i	0.00982186	−	0.00567065i
$86$	−0.794309	+	0.301787i	−0.0856525	+	0.0325425i
$87$	3.50641	−	6.07327i	0.375926	−	0.651123i
$88$	1.96226	+	3.09074i	0.209178	+	0.329474i
$89$	−3.69655			−0.391833			−0.195917	−	0.980621i	$-0.562768\pi$
$89$	−3.69655			−0.391833			−0.195917	+	0.980621i	$0.562768\pi$
$90$	0.0169119	+	0.0445126i	0.00178268	+	0.00469204i
$91$			3.77799i			0.396041i
$92$	−4.40794	+	13.2563i	−0.459559	+	1.38207i
$93$	−4.12899	+	7.15162i	−0.428156	+	0.741588i
$94$	0.0840207	+	0.0136030i	0.00866608	+	0.00140304i
$95$	−0.0858480	−	0.148693i	−0.00880782	−	0.0152556i
$96$	−1.37024	−	5.48839i	−0.139850	−	0.560157i
$97$	−9.48849	+	5.47818i	−0.963410	+	0.556225i	−0.897221	−	0.441582i	$-0.854417\pi$
$97$	−9.48849	+	5.47818i	−0.963410	+	0.556225i	−0.0661894	+	0.997807i	$0.521084\pi$
$98$	−7.30203	−	5.95463i	−0.737617	−	0.601508i
$99$	0.647185	−	1.12096i	0.0650446	−	0.112661i
$100$	7.47545	−	6.63870i	0.747545	−	0.663870i
$101$	−1.66284	−	0.960039i	−0.165458	−	0.0955275i	0.414984	−	0.909829i	$-0.363787\pi$
$101$	−1.66284	−	0.960039i	−0.165458	−	0.0955275i	−0.580443	+	0.814301i	$0.697120\pi$
$102$	3.40356	+	2.77552i	0.337002	+	0.274817i
$103$	14.2972	+	8.25451i	1.40875	+	0.813341i	0.995268	−	0.0971715i	$-0.0309795\pi$
$103$	14.2972	+	8.25451i	1.40875	+	0.813341i	0.413481	+	0.910513i	$0.364313\pi$
$104$	−0.773691	−	18.3768i	−0.0758666	−	1.80199i
$105$	0.0169406	+	0.00978066i	0.00165323	+	0.000954495i
$106$	−4.71897	−	12.4204i	−0.458346	−	1.20638i
$107$		−	10.4831i		−	1.01344i	−0.862112	−	0.506718i	$-0.830858\pi$
$107$		−	10.4831i		−	1.01344i	0.862112	−	0.506718i	$-0.169142\pi$
$108$	−1.49543	+	1.32804i	−0.143898	+	0.127791i
$109$			10.9590i			1.04968i	0.851200	+	0.524842i	$0.175876\pi$
$109$			10.9590i			1.04968i	−0.851200	+	0.524842i	$0.824124\pi$
$110$	0.0608419	+	0.00985031i	0.00580105	+	0.000939190i
$111$	1.39784	+	2.42113i	0.132677	+	0.229803i
$112$	−1.86114	−	1.39158i	−0.175861	−	0.131492i
$113$	1.23603	+	0.713621i	0.116276	+	0.0671318i	0.557010	−	0.830506i	$-0.311949\pi$
$113$	1.23603	+	0.713621i	0.116276	+	0.0671318i	−0.440734	+	0.897638i	$0.645282\pi$
$114$	4.55755	−	5.58882i	0.426854	−	0.523441i
$115$	0.117593	+	0.203678i	0.0109656	+	0.0189930i
$116$	2.82197	+	13.7388i	0.262013	+	1.27562i
$117$	−5.63171	+	3.25147i	−0.520652	+	0.300598i
$118$	−6.46341	−	17.0118i	−0.595005	−	1.56606i
$119$	1.80416			0.165387
$120$	−0.0844051	−	0.0441057i	−0.00770510	−	0.00402628i
$121$	4.66230	+	8.07534i	0.423846	+	0.734122i
$122$	3.88875	−	4.76869i	0.352071	−	0.431737i
$123$	−8.38854	−	4.84313i	−0.756369	−	0.436690i
$124$	−3.32303	−	16.1782i	−0.298417	−	1.45285i
$125$		−	0.336665i		−	0.0301123i
$126$	−0.131309	+	0.811049i	−0.0116979	+	0.0722540i
$127$	9.63148	+	5.56074i	0.854655	+	0.493435i	0.862219	−	0.506536i	$-0.169074\pi$
$127$	9.63148	+	5.56074i	0.854655	+	0.493435i	−0.00756354	+	0.999971i	$0.502408\pi$
$128$	9.33791	+	6.38776i	0.825362	+	0.564604i
$129$	−0.600833			−0.0529004
$130$	−0.239975	−	0.195693i	−0.0210472	−	0.0171634i
$131$			15.9231i			1.39120i	0.718427	+	0.695602i	$0.244862\pi$
$131$			15.9231i			1.39120i	−0.718427	+	0.695602i	$0.755138\pi$
$132$	0.520858	+	2.53580i	0.0453348	+	0.220713i
$133$		−	2.96253i		−	0.256884i
$134$	−8.87687	−	7.42975i	−0.766845	−	0.641833i
$135$			0.0336703i			0.00289788i
$136$	−8.77577	+	0.369473i	−0.752516	+	0.0316820i
$137$		−	15.1721i		−	1.29624i	−0.761537	−	0.648121i	$-0.775555\pi$
$137$		−	15.1721i		−	1.29624i	0.761537	−	0.648121i	$-0.224445\pi$
$138$	−6.24286	+	7.65549i	−0.531428	+	0.651679i
$139$	−20.0111			−1.69732			−0.848660	−	0.528939i	$-0.822590\pi$
$139$	−20.0111			−1.69732			−0.848660	+	0.528939i	$0.822590\pi$
$140$	−0.0383226	+	0.00787152i	−0.00323885	+	0.000665265i
$141$	0.0521219	+	0.0300926i	0.00438946	+	0.00253426i
$142$	9.24221	+	1.49631i	0.775589	+	0.125568i
$143$			8.41721i			0.703883i
$144$	0.472616	−	3.97198i	0.0393847	−	0.330998i
$145$	0.204489	+	0.118062i	0.0169819	+	0.00980450i
$146$	−3.03084	−	2.47157i	−0.250834	−	0.204549i
$147$	−3.33124	−	5.76988i	−0.274756	−	0.475891i
$148$	−5.30572	−	1.76424i	−0.436128	−	0.145019i
$149$	18.2226			1.49286			0.746429	−	0.665465i	$-0.231767\pi$
$149$	18.2226			1.49286			0.746429	+	0.665465i	$0.231767\pi$
$150$	6.60856	−	2.51083i	0.539587	−	0.205009i
$151$	14.7006	−	8.48742i	1.19632	−	0.690697i	0.236588	−	0.971610i	$-0.423971\pi$
$151$	14.7006	−	8.48742i	1.19632	−	0.690697i	0.959733	+	0.280913i	$0.0906374\pi$
$152$	0.606695	+	14.4103i	0.0492094	+	1.16883i
$153$	1.55273	+	2.68940i	0.125531	+	0.217425i
$154$	0.824171	+	0.672091i	0.0664136	+	0.0541586i
$155$	−0.240797	−	0.139024i	−0.0193413	−	0.0111667i
$156$	4.10374	−	12.3415i	0.328562	−	0.988109i
$157$	−6.35096	−	11.0002i	−0.506862	−	0.877911i	−0.999968	−	0.00794180i	$-0.997472\pi$
$157$	−6.35096	−	11.0002i	−0.506862	−	0.877911i	0.493106	−	0.869969i	$-0.335861\pi$
$158$	3.51304	−	21.6988i	0.279483	−	1.72627i
$159$		−	9.39508i		−	0.745079i
$160$	0.184796	−	0.0461366i	0.0146094	−	0.00364742i
$161$			4.05804i			0.319818i
$162$	−1.32201	+	0.502280i	−0.103867	+	0.0394629i
$163$	−16.5094	−	9.53171i	−1.29312	−	0.746581i	−0.313911	−	0.949452i	$-0.601639\pi$
$163$	−16.5094	−	9.53171i	−1.29312	−	0.746581i	−0.979205	+	0.202871i	$0.934973\pi$
$164$	18.9763	−	3.89777i	1.48180	−	0.304365i
$165$	0.0377430	+	0.0217910i	0.00293829	+	0.00169642i
$166$	−10.0078	+	12.2723i	−0.776754	+	0.952517i
$167$	4.42047	+	2.55216i	0.342066	+	0.197492i	0.661185	−	0.750222i	$-0.270054\pi$
$167$	4.42047	+	2.55216i	0.342066	+	0.197492i	−0.319119	+	0.947715i	$0.603387\pi$
$168$	−0.880743	−	1.38725i	−0.0679508	−	0.107029i
$169$	14.6441	−	25.3643i	1.12647	−	1.95110i
$170$	−0.0934526	+	0.114599i	−0.00716749	+	0.00878933i
$171$	4.41614	−	2.54966i	0.337711	−	0.194978i
$172$	0.898504	−	0.797931i	0.0685103	−	0.0608417i
$173$	−1.42698	−	2.47160i	−0.108491	−	0.187913i	0.806668	−	0.591005i	$-0.201269\pi$
$173$	−1.42698	−	2.47160i	−0.108491	−	0.187913i	−0.915159	+	0.403092i	$0.867935\pi$
$174$	−1.58502	+	9.79013i	−0.120160	+	0.742188i
$175$	1.45209	−	2.51509i	0.109767	−	0.190123i
$176$	−4.14655	−	3.10039i	−0.312558	−	0.233701i
$177$		−	12.8681i		−	0.967228i
$178$	4.88688	−	1.85670i	0.366287	−	0.139166i
$179$	−9.47559			−0.708239			−0.354119	−	0.935200i	$-0.615219\pi$
$179$	−9.47559			−0.708239			−0.354119	+	0.935200i	$0.615219\pi$
$180$	−0.0447156	−	0.0503516i	−0.00333290	−	0.00375299i
$181$	10.0742	−	17.4490i	0.748807	−	1.29697i	−0.199588	−	0.979880i	$-0.563960\pi$
$181$	10.0742	−	17.4490i	0.748807	−	1.29697i	0.948395	−	0.317091i	$-0.102706\pi$
$182$	−1.89761	−	4.99454i	−0.140660	−	0.370220i
$183$	3.76809	−	2.17551i	0.278545	−	0.160818i
$184$	−0.831042	−	19.7390i	−0.0612652	−	1.45518i
$185$	−0.0815202	+	0.0470657i	−0.00599348	+	0.00346034i
$186$	1.86645	−	11.5284i	0.136855	−	0.845306i
$187$	4.01961			0.293943
$188$	−0.117909	+	0.0242187i	−0.00859939	+	0.00176633i
$189$	−0.290483	+	0.503131i	−0.0211295	+	0.0365974i
$190$	0.188178	+	0.153454i	0.0136518	+	0.0111327i
$191$	−10.6294	−	18.4107i	−0.769117	−	1.33215i	−0.938042	−	0.346521i	$-0.887363\pi$
$191$	−10.6294	−	18.4107i	−0.769117	−	1.33215i	0.168925	−	0.985629i	$-0.445970\pi$
$192$	4.56819	+	6.56747i	0.329681	+	0.473966i
$193$	22.4851			1.61852			0.809258	−	0.587453i	$-0.199869\pi$
$193$	22.4851			1.61852			0.809258	+	0.587453i	$0.199869\pi$
$194$	9.79231	−	12.0081i	0.703047	−	0.862132i
$195$	−0.109478	−	0.189622i	−0.00783989	−	0.0135791i
$196$	12.6443	+	4.20442i	0.903162	+	0.300316i
$197$	−4.81251	−	2.77851i	−0.342877	−	0.197960i	0.318666	−	0.947867i	$-0.396765\pi$
$197$	−4.81251	−	2.77851i	−0.342877	−	0.197960i	−0.661544	+	0.749907i	$0.730098\pi$
$198$	−0.292552	+	1.80699i	−0.0207907	+	0.128417i
$199$	−0.320038	+	0.184774i	−0.0226869	+	0.0130983i	−0.511301	−	0.859402i	$-0.670836\pi$
$199$	−0.320038	+	0.184774i	−0.0226869	+	0.0130983i	0.488614	+	0.872500i	$0.337503\pi$
$200$	−6.54815	+	12.5312i	−0.463024	+	0.886090i
$201$	−4.00175	−	7.14045i	−0.282262	−	0.503648i
$202$	2.68050	+	0.433973i	0.188599	+	0.0305342i
$203$	2.03710	+	3.52836i	0.142977	+	0.247643i
$204$	−5.89363	−	1.95973i	−0.412636	−	0.137208i
$205$	0.163070	−	0.282445i	0.0113893	−	0.0197268i
$206$	−23.0472	−	3.73134i	−1.60577	−	0.259975i
$207$	−6.04917	+	3.49249i	−0.420446	+	0.242745i
$208$	10.2531	+	23.9057i	0.710927	+	1.65757i
$209$		−	6.60042i		−	0.456560i
$210$	−0.0273083	−	0.00442122i	−0.00188445	−	0.000305093i
$211$	0.433107	−	0.250054i	0.0298163	−	0.0172145i	−0.485018	−	0.874504i	$-0.661187\pi$
$211$	0.433107	−	0.250054i	0.0298163	−	0.0172145i	0.514834	+	0.857290i	$0.327854\pi$
$212$	12.4771	+	14.0497i	0.856928	+	0.964936i
$213$	5.73337	+	3.31016i	0.392844	+	0.226809i
$214$	5.26544	+	13.8587i	0.359938	+	0.947364i
$215$		−	0.0202303i		−	0.00137969i
$216$	1.30993	−	2.50681i	0.0891292	−	0.170567i
$217$	−2.39880	−	4.15485i	−0.162841	−	0.282049i
$218$	−5.50450	−	14.4880i	−0.372812	−	0.981248i
$219$	−1.38269	−	2.39489i	−0.0934335	−	0.161832i
$220$	−0.0853813	+	0.0175375i	−0.00575641	+	0.00118238i
$221$	−17.4890	−	10.0973i	−1.17644	−	0.679217i
$222$	−3.06404	−	2.49865i	−0.205645	−	0.167699i
$223$			6.50721i			0.435755i	0.975976	+	0.217877i	$0.0699133\pi$
$223$			6.50721i			0.435755i	−0.975976	+	0.217877i	$0.930087\pi$
$224$	3.15941	+	0.904872i	0.211097	+	0.0604593i
$225$	4.99887			0.333258
$226$	−1.99248	−	0.322583i	−0.132538	−	0.0214579i
$227$	−14.1426	−	8.16526i	−0.938680	−	0.541947i	−0.0491338	−	0.998792i	$-0.515646\pi$
$227$	−14.1426	−	8.16526i	−0.938680	−	0.541947i	−0.889546	+	0.456845i	$0.848979\pi$
$228$	−3.21798	+	9.67766i	−0.213116	+	0.640919i
$229$	−3.26867	+	1.88717i	−0.216000	+	0.124707i	−0.604097	−	0.796911i	$-0.706466\pi$
$229$	−3.26867	+	1.88717i	−0.216000	+	0.124707i	0.388097	+	0.921619i	$0.373133\pi$
$230$	−0.257763	−	0.210199i	−0.0169964	−	0.0138601i
$231$	0.375993	+	0.651238i	0.0247385	+	0.0428483i
$232$	−10.6314	−	16.7454i	−0.697986	−	1.09939i
$233$	8.93565	+	5.15900i	0.585394	+	0.337977i	0.763274	−	0.646075i	$-0.223591\pi$
$233$	8.93565	+	5.15900i	0.585394	+	0.337977i	−0.177880	+	0.984052i	$0.556924\pi$
$234$	5.81204	−	7.12718i	0.379945	−	0.465918i
$235$	−0.00101323	+	0.00175496i	−6.60957e−5	+	0.000114481i
$236$	17.0894	+	19.2434i	1.11243	+	1.25264i
$237$	7.77159	−	13.4608i	0.504819	−	0.874372i
$238$	−2.38512	+	0.906195i	−0.154605	+	0.0587399i
$239$	−0.0287339	+	0.0497686i	−0.00185864	+	0.00321926i	−0.866953	−	0.498390i	$-0.833925\pi$
$239$	−0.0287339	+	0.0497686i	−0.00185864	+	0.00321926i	0.865095	+	0.501609i	$0.167258\pi$
$240$	0.133738	+	0.0159132i	0.00863275	+	0.00102719i
$241$	−27.0880			−1.74489			−0.872447	−	0.488709i	$-0.837468\pi$
$241$	−27.0880			−1.74489			−0.872447	+	0.488709i	$0.837468\pi$
$242$	−10.2197	−	8.33392i	−0.656947	−	0.535724i
$243$	−1.00000			−0.0641500
$244$	−2.74575	+	8.25750i	−0.175779	+	0.528632i
$245$	0.194274	−	0.112164i	0.0124117	−	0.00716589i
$246$	13.5224	+	2.18927i	0.862154	+	0.139583i
$247$	−16.5803	+	28.7179i	−1.05498	+	1.82728i
$248$	12.5191	+	19.7187i	0.794962	+	1.25214i
$249$	−9.69727	+	5.59872i	−0.614539	+	0.354804i
$250$	0.169100	+	0.445075i	0.0106948	+	0.0281490i
$251$	5.47501	+	9.48300i	0.345580	+	0.598562i	0.985459	−	0.169914i	$-0.0543490\pi$
$251$	5.47501	+	9.48300i	0.345580	+	0.598562i	−0.639879	+	0.768476i	$0.721016\pi$
$252$	−0.233782	−	1.13817i	−0.0147269	−	0.0716980i
$253$			9.04115i			0.568413i
$254$	−15.5260	−	2.51366i	−0.974186	−	0.157721i
$255$	−0.0905531	+	0.0522808i	−0.00567065	+	0.00327395i
$256$	−15.5533	−	3.75445i	−0.972079	−	0.234653i
$257$	−1.67704	+	2.90472i	−0.104611	+	0.181192i	−0.913579	−	0.406661i	$-0.866693\pi$
$257$	−1.67704	+	2.90472i	−0.104611	+	0.181192i	0.808968	+	0.587852i	$0.200026\pi$
$258$	0.794309	−	0.301787i	0.0494515	−	0.0187884i
$259$	−1.62419			−0.100922
$260$	0.415542	+	0.138174i	0.0257708	+	0.00856921i
$261$	−3.50641	+	6.07327i	−0.217041	+	0.375926i
$262$	−7.99784	−	21.0505i	−0.494108	−	1.30050i
$263$		−	17.4454i		−	1.07573i	−0.843030	−	0.537866i	$-0.819231\pi$
$263$		−	17.4454i		−	1.07573i	0.843030	−	0.537866i	$-0.180769\pi$
$264$	−1.96226	−	3.09074i	−0.120769	−	0.190222i
$265$	0.316336			0.0194324
$266$	1.48802	+	3.91650i	0.0912365	+	0.240136i
$267$	3.69655			0.226225
$268$	15.4671	+	5.36354i	0.944806	+	0.327630i
$269$	−1.54282			−0.0940675			−0.0470337	−	0.998893i	$-0.514977\pi$
$269$	−1.54282			−0.0940675			−0.0470337	+	0.998893i	$0.514977\pi$
$270$	−0.0169119	−	0.0445126i	−0.00102923	−	0.00270895i
$271$	3.75720			0.228234			0.114117	−	0.993467i	$-0.463596\pi$
$271$	3.75720			0.228234			0.114117	+	0.993467i	$0.463596\pi$
$272$	11.4161	−	4.89635i	0.692203	−	0.296885i
$273$		−	3.77799i		−	0.228654i
$274$	7.62066	+	20.0577i	0.460381	+	1.21173i
$275$	3.23519	−	5.60352i	0.195089	−	0.337905i
$276$	4.40794	−	13.2563i	0.265327	−	0.797936i
$277$	23.0925			1.38749			0.693746	−	0.720220i	$-0.255959\pi$
$277$	23.0925			1.38749			0.693746	+	0.720220i	$0.255959\pi$
$278$	26.4549	−	10.0512i	1.58666	−	0.602830i
$279$	4.12899	−	7.15162i	0.247196	−	0.428156i
$280$	0.0467092	−	0.0296549i	0.00279141	−	0.00177222i
$281$	20.2191	−	11.6735i	1.20617	−	0.696383i	0.244251	−	0.969712i	$-0.421458\pi$
$281$	20.2191	−	11.6735i	1.20617	−	0.696383i	0.961921	+	0.273329i	$0.0881246\pi$
$282$	−0.0840207	−	0.0136030i	−0.00500336	−	0.000810045i
$283$			31.3926i			1.86610i	0.359752	+	0.933048i	$0.382861\pi$
$283$			31.3926i			1.86610i	−0.359752	+	0.933048i	$0.617139\pi$
$284$	−12.9699	+	2.66403i	−0.769621	+	0.158081i
$285$	0.0858480	+	0.148693i	0.00508520	+	0.00880782i
$286$	−4.22780	−	11.1277i	−0.249995	−	0.657992i
$287$	4.87346	−	2.81369i	0.287671	−	0.166087i
$288$	1.37024	+	5.48839i	0.0807424	+	0.323407i
$289$	3.67808	−	6.37062i	0.216358	−	0.374742i
$290$	−0.329637	−	0.0533683i	−0.0193570	−	0.00313389i
$291$	9.48849	−	5.47818i	0.556225	−	0.321137i
$292$	5.24823	+	1.74512i	0.307129	+	0.102125i
$293$	−17.8297			−1.04162			−0.520812	−	0.853671i	$-0.674371\pi$
$293$	−17.8297			−1.04162			−0.520812	+	0.853671i	$0.674371\pi$
$294$	7.30203	+	5.95463i	0.425863	+	0.347281i
$295$	0.433274			0.0252262
$296$	7.90037	−	0.332617i	0.459200	−	0.0193330i
$297$	−0.647185	+	1.12096i	−0.0375535	+	0.0650446i
$298$	−24.0906	+	9.15288i	−1.39553	+	0.530212i
$299$	22.7115	−	39.3374i	1.31344	−	2.27494i
$300$	−7.47545	+	6.63870i	−0.431595	+	0.383285i
$301$	0.174532	−	0.302298i	0.0100598	−	0.0174242i
$302$	−15.1714	+	18.6043i	−0.873014	+	1.07056i
$303$	1.66284	+	0.960039i	0.0955275	+	0.0551528i
$304$	−8.04007	−	18.7459i	−0.461129	−	1.07515i
$305$	0.0732501	+	0.126873i	0.00419429	+	0.00726473i
$306$	−3.40356	−	2.77552i	−0.194568	−	0.158666i
$307$	−16.3376	+	9.43255i	−0.932439	+	0.538344i	−0.887582	−	0.460650i	$-0.847616\pi$
$307$	−16.3376	+	9.43255i	−0.932439	+	0.538344i	−0.0448568	+	0.998993i	$0.514283\pi$
$308$	−1.42714	−	0.474547i	−0.0813189	−	0.0270398i
$309$	−14.2972	−	8.25451i	−0.813341	−	0.469583i
$310$	0.388166	+	0.0628442i	0.0220464	+	0.00356931i
$311$	−33.7450			−1.91350			−0.956751	−	0.290907i	$-0.906043\pi$
$311$	−33.7450			−1.91350			−0.956751	+	0.290907i	$0.906043\pi$
$312$	0.773691	+	18.3768i	0.0438016	+	1.04038i
$313$			2.93093i			0.165666i	0.996563	+	0.0828331i	$0.0263968\pi$
$313$			2.93093i			0.165666i	−0.996563	+	0.0828331i	$0.973603\pi$
$314$	13.9212	+	11.3524i	0.785620	+	0.640654i
$315$	−0.0169406	−	0.00978066i	−0.000954495	−	0.000551078i
$316$	6.25461	+	30.4506i	0.351849	+	1.71298i
$317$	−3.65620	−	6.33272i	−0.205352	−	0.355681i	0.744892	−	0.667185i	$-0.232501\pi$
$317$	−3.65620	−	6.33272i	−0.205352	−	0.355681i	−0.950245	+	0.311504i	$0.899167\pi$
$318$	4.71897	+	12.4204i	0.264626	+	0.696502i
$319$	4.53859	+	7.86107i	0.254112	+	0.440135i
$320$	−0.221129	+	0.153812i	−0.0123615	+	0.00859838i
$321$			10.4831i			0.585108i
$322$	−2.03827	−	5.36477i	−0.113588	−	0.298967i
$323$	13.7141	+	7.91786i	0.763075	+	0.440561i
$324$	1.49543	−	1.32804i	0.0830794	−	0.0737800i
$325$	−28.1522	+	16.2537i	−1.56160	+	0.901591i
$326$	26.6132	+	4.30868i	1.47397	+	0.238636i
$327$		−	10.9590i		−	0.606035i
$328$	−23.1292	+	14.6843i	−1.27709	+	0.810807i
$329$	−0.0302811	+	0.0174828i	−0.00166945	+	0.000963857i
$330$	−0.0608419	−	0.00985031i	−0.00334924	−	0.000542242i
$331$	7.47789	−	12.9521i	0.411022	−	0.711911i	−0.583980	−	0.811768i	$-0.698505\pi$
$331$	7.47789	−	12.9521i	0.411022	−	0.711911i	0.995002	+	0.0998572i	$0.0318386\pi$
$332$	7.06625	−	21.2509i	0.387811	−	1.16629i
$333$	−1.39784	−	2.42113i	−0.0766011	−	0.132677i
$334$	−7.12582	−	1.15367i	−0.389907	−	0.0631260i
$335$	0.240421	−	0.134740i	0.0131356	−	0.00736166i
$336$	1.86114	+	1.39158i	0.101534	+	0.0759170i
$337$	5.34071	−	3.08346i	0.290927	−	0.167967i	−0.347433	−	0.937705i	$-0.612946\pi$
$337$	5.34071	−	3.08346i	0.290927	−	0.167967i	0.638360	+	0.769738i	$0.279613\pi$
$338$	−6.61968	+	40.8874i	−0.360063	+	2.22398i
$339$	−1.23603	−	0.713621i	−0.0671318	−	0.0387586i
$340$	0.0659846	−	0.198440i	0.00357852	−	0.0107619i
$341$	−5.34444	−	9.25684i	−0.289418	−	0.501286i
$342$	−4.55755	+	5.58882i	−0.246444	+	0.302209i
$343$	7.93743			0.428581
$344$	−0.787047	+	1.50618i	−0.0424348	+	0.0812075i
$345$	−0.117593	−	0.203678i	−0.00633101	−	0.0109656i
$346$	3.12792	+	2.55074i	0.168158	+	0.137129i
$347$	−1.38541	+	2.39960i	−0.0743727	+	0.128817i	−0.900813	−	0.434207i	$-0.857029\pi$
$347$	−1.38541	+	2.39960i	−0.0743727	+	0.128817i	0.826441	+	0.563024i	$0.190362\pi$
$348$	−2.82197	−	13.7388i	−0.151274	−	0.736477i
$349$	0.497155			0.0266121			0.0133060	−	0.999911i	$-0.495764\pi$
$349$	0.497155			0.0266121			0.0133060	+	0.999911i	$0.495764\pi$
$350$	−0.656396	+	4.05433i	−0.0350858	+	0.216713i
$351$	5.63171	−	3.25147i	0.300598	−	0.173551i
$352$	7.03906	+	2.01602i	0.375183	+	0.107454i
$353$	−25.1526	+	14.5218i	−1.33874	+	0.772919i	−0.986620	−	0.163037i	$-0.947871\pi$
$353$	−25.1526	+	14.5218i	−1.33874	+	0.772919i	−0.352116	+	0.935956i	$0.614538\pi$
$354$	6.46341	+	17.0118i	0.343526	+	0.904168i
$355$	−0.111454	+	0.193045i	−0.00591538	+	0.0102457i
$356$	−5.52792	+	4.90916i	−0.292979	+	0.260185i
$357$	−1.80416			−0.0954864
$358$	12.5268	−	4.75940i	0.662064	−	0.251542i
$359$			8.61103i			0.454473i	0.973840	+	0.227236i	$0.0729690\pi$
$359$			8.61103i			0.454473i	−0.973840	+	0.227236i	$0.927031\pi$
$360$	0.0844051	+	0.0441057i	0.00444854	+	0.00232457i
$361$	3.50155	−	6.06487i	0.184292	−	0.319204i
$362$	−4.55389	+	28.1278i	−0.239347	+	1.47836i
$363$	−4.66230	−	8.07534i	−0.244707	−	0.423846i
$364$	5.01732	+	5.64971i	0.262979	+	0.296125i
$365$	0.0806368	−	0.0465557i	0.00422072	−	0.00243683i
$366$	−3.88875	+	4.76869i	−0.203268	+	0.249263i
$367$	1.44405	−	2.50118i	0.0753790	−	0.130560i	−0.825872	−	0.563858i	$-0.809317\pi$
$367$	1.44405	−	2.50118i	0.0753790	−	0.130560i	0.901251	+	0.433297i	$0.142650\pi$
$368$	11.0132	+	25.6778i	0.574101	+	1.33855i
$369$	8.38854	+	4.84313i	0.436690	+	0.252123i
$370$	0.0841305	−	0.103167i	0.00437373	−	0.00536342i
$371$	4.72696	+	2.72911i	0.245412	+	0.141688i
$372$	3.32303	+	16.1782i	0.172291	+	0.838801i
$373$	−17.1124	−	9.87985i	−0.886046	−	0.511559i	−0.0133992	−	0.999910i	$-0.504265\pi$
$373$	−17.1124	−	9.87985i	−0.886046	−	0.511559i	−0.872647	+	0.488351i	$0.837599\pi$
$374$	−5.31397	+	2.01897i	−0.274779	+	0.104398i
$375$			0.336665i			0.0173853i
$376$	0.143712	−	0.0912407i	0.00741140	−	0.00470538i
$377$		−	45.6039i		−	2.34872i
$378$	0.131309	−	0.811049i	0.00675380	−	0.0417159i
$379$	6.50776	+	11.2718i	0.334281	+	0.578992i	0.983346	−	0.181741i	$-0.0581732\pi$
$379$	6.50776	+	11.2718i	0.334281	+	0.578992i	−0.649065	+	0.760733i	$0.724840\pi$
$380$	−0.325850	−	0.108350i	−0.0167158	−	0.00555826i
$381$	−9.63148	−	5.56074i	−0.493435	−	0.284885i
$382$	23.2995	+	19.0002i	1.19211	+	0.972134i
$383$	−7.34539	−	12.7226i	−0.375332	−	0.650094i	0.615045	−	0.788492i	$-0.289138\pi$
$383$	−7.34539	−	12.7226i	−0.375332	−	0.650094i	−0.990377	+	0.138399i	$0.955805\pi$
$384$	−9.33791	−	6.38776i	−0.476523	−	0.325974i
$385$	−0.0219274	+	0.0126598i	−0.00111752	+	0.000645203i
$386$	−29.7256	+	11.2938i	−1.51299	+	0.574842i
$387$	0.600833			0.0305421
$388$	−6.91412	+	20.7933i	−0.351011	+	1.05562i
$389$	1.64530	+	2.84974i	0.0834200	+	0.144488i	0.904717	−	0.426013i	$-0.140082\pi$
$389$	1.64530	+	2.84974i	0.0834200	+	0.144488i	−0.821297	+	0.570501i	$0.806749\pi$
$390$	0.239975	+	0.195693i	0.0121516	+	0.00990932i
$391$	−18.7854	−	10.8458i	−0.950019	−	0.548494i
$392$	−18.8277	+	0.792672i	−0.950940	+	0.0400360i
$393$		−	15.9231i		−	0.803212i
$394$	7.75778	+	1.25599i	0.390832	+	0.0632757i
$395$	0.453229	+	0.261672i	0.0228044	+	0.0131662i
$396$	−0.520858	−	2.53580i	−0.0261741	−	0.127429i
$397$	−9.67527			−0.485588			−0.242794	−	0.970078i	$-0.578064\pi$
$397$	−9.67527			−0.485588			−0.242794	+	0.970078i	$0.578064\pi$
$398$	0.330286	−	0.405023i	0.0165557	−	0.0203020i
$399$			2.96253i			0.148312i
$400$	2.36255	−	19.8554i	0.118127	−	0.992770i
$401$			23.3294i			1.16501i	0.812826	+	0.582506i	$0.197928\pi$
$401$			23.3294i			1.16501i	−0.812826	+	0.582506i	$0.802072\pi$
$402$	8.87687	+	7.42975i	0.442738	+	0.370562i
$403$			53.7011i			2.67504i
$404$	−3.76163	+	0.772644i	−0.187148	+	0.0384405i
$405$		−	0.0336703i		−	0.00167309i
$406$	−4.46530	−	3.64134i	−0.221609	−	0.180717i
$407$	−3.61864			−0.179369
$408$	8.77577	−	0.369473i	0.434466	−	0.0182916i
$409$	−13.9774	−	8.06985i	−0.691138	−	0.399029i	0.112900	−	0.993606i	$-0.463986\pi$
$409$	−13.9774	−	8.06985i	−0.691138	−	0.399029i	−0.804038	+	0.594578i	$0.797319\pi$
$410$	−0.0737135	+	0.455302i	−0.00364045	+	0.0224858i
$411$			15.1721i			0.748386i
$412$	32.3428	−	6.64327i	1.59342	−	0.327290i
$413$	6.47436	+	3.73797i	0.318582	+	0.183934i
$414$	6.24286	−	7.65549i	0.306820	−	0.376247i
$415$	−0.188511	−	0.326510i	−0.00925363	−	0.0160278i
$416$	−25.5622	−	26.4537i	−1.25329	−	1.29700i
$417$	20.0111			0.979948
$418$	3.31526	+	8.72583i	0.162155	+	0.426794i
$419$	−28.3115	+	16.3457i	−1.38311	+	0.798538i	−0.992526	−	0.122030i	$-0.961060\pi$
$419$	−28.3115	+	16.3457i	−1.38311	+	0.798538i	−0.390582	+	0.920568i	$0.627726\pi$
$420$	0.0383226	−	0.00787152i	0.00186995	−	0.000384091i
$421$	11.3203	+	19.6073i	0.551716	+	0.955601i	0.998151	+	0.0607843i	$0.0193602\pi$
$421$	11.3203	+	19.6073i	0.551716	+	0.955601i	−0.446435	+	0.894816i	$0.647306\pi$
$422$	−0.446975	+	0.548116i	−0.0217584	+	0.0266819i
$423$	−0.0521219	−	0.0300926i	−0.00253426	−	0.00146315i
$424$	−23.5517	−	12.3069i	−1.14377	−	0.597674i
$425$	7.76187	+	13.4440i	0.376506	+	0.652128i
$426$	−9.24221	−	1.49631i	−0.447787	−	0.0724967i
$427$			2.52779i			0.122328i
$428$	−13.9219	−	15.6767i	−0.672943	−	0.757761i
$429$		−	8.41721i		−	0.406387i
$430$	0.0101613	+	0.0267446i	0.000490020	+	0.00128974i
$431$	18.2121	+	10.5148i	0.877246	+	0.506478i	0.869749	−	0.493494i	$-0.164280\pi$
$431$	18.2121	+	10.5148i	0.877246	+	0.506478i	0.00749646	+	0.999972i	$0.497614\pi$
$432$	−0.472616	+	3.97198i	−0.0227388	+	0.191102i
$433$	8.01567	+	4.62785i	0.385209	+	0.222400i	0.680082	−	0.733136i	$-0.261944\pi$
$433$	8.01567	+	4.62785i	0.385209	+	0.222400i	−0.294873	+	0.955536i	$0.595277\pi$
$434$	5.25814	+	4.28788i	0.252399	+	0.205825i
$435$	−0.204489	−	0.118062i	−0.00980450	−	0.00566063i
$436$	14.5540	+	16.3884i	0.697012	+	0.784864i
$437$	−17.8093	+	30.8467i	−0.851936	+	1.47560i
$438$	3.03084	+	2.47157i	0.144819	+	0.118096i
$439$	7.01941	−	4.05266i	0.335018	−	0.193423i	−0.323049	−	0.946382i	$-0.604708\pi$
$439$	7.01941	−	4.05266i	0.335018	−	0.193423i	0.658067	+	0.752960i	$0.271374\pi$
$440$	0.104066	−	0.0660701i	0.00496117	−	0.00314977i
$441$	3.33124	+	5.76988i	0.158630	+	0.274756i
$442$	28.1924	+	4.56434i	1.34097	+	0.217104i
$443$	13.6520	−	23.6460i	0.648627	−	1.12346i	−0.334824	−	0.942281i	$-0.608677\pi$
$443$	13.6520	−	23.6460i	0.648627	−	1.12346i	0.983451	−	0.181175i	$-0.0579900\pi$
$444$	5.30572	+	1.76424i	0.251799	+	0.0837270i
$445$			0.124464i			0.00590016i
$446$	−3.26844	−	8.60260i	−0.154765	−	0.407345i
$447$	−18.2226			−0.861902
$448$	−4.63128	+	0.390660i	−0.218807	+	0.0184569i
$449$	11.1672	−	19.3421i	0.527012	−	0.912812i	−0.472492	−	0.881335i	$-0.656646\pi$
$449$	11.1672	−	19.3421i	0.527012	−	0.912812i	0.999504	−	0.0314771i	$-0.0100211\pi$
$450$	−6.60856	+	2.51083i	−0.311530	+	0.118362i
$451$	10.8579	−	6.26880i	0.511278	−	0.295186i
$452$	2.79611	−	0.574325i	0.131518	−	0.0270140i
$453$	−14.7006	+	8.48742i	−0.690697	+	0.398774i
$454$	22.7980	+	3.69100i	1.06996	+	0.173227i
$455$	0.127206			0.00596351
$456$	−0.606695	−	14.4103i	−0.0284111	−	0.674824i
$457$	4.11035	−	7.11934i	0.192274	−	0.333029i	−0.753729	−	0.657185i	$-0.771747\pi$
$457$	4.11035	−	7.11934i	0.192274	−	0.333029i	0.946004	+	0.324156i	$0.105080\pi$
$458$	3.37333	−	4.13664i	0.157625	−	0.193293i
$459$	−1.55273	−	2.68940i	−0.0724751	−	0.125531i
$460$	0.446345	+	0.148417i	0.0208109	+	0.00691997i
$461$	−12.6403			−0.588715			−0.294358	−	0.955695i	$-0.595106\pi$
$461$	−12.6403			−0.588715			−0.294358	+	0.955695i	$0.595106\pi$
$462$	−0.824171	−	0.672091i	−0.0383439	−	0.0312685i
$463$	10.1530	+	17.5855i	0.471849	+	0.817266i	0.999481	−	0.0322069i	$-0.0102535\pi$
$463$	10.1530	+	17.5855i	0.471849	+	0.817266i	−0.527633	+	0.849473i	$0.676920\pi$
$464$	22.4657	+	16.7977i	1.04295	+	0.779814i
$465$	0.240797	+	0.139024i	0.0111667	+	0.00644711i
$466$	−14.4043	−	2.33206i	−0.667266	−	0.108030i
$467$	6.75063	−	3.89748i	0.312382	−	0.180354i	−0.335610	−	0.942001i	$-0.608942\pi$
$467$	6.75063	−	3.89748i	0.312382	−	0.180354i	0.647992	+	0.761647i	$0.275609\pi$
$468$	−4.10374	+	12.3415i	−0.189695	+	0.570485i
$469$	4.75502	+	0.0607697i	0.219567	+	0.00280609i
$470$	0.000458016	−	0.00282901i	2.11267e−5	−	0.000130492i
$471$	6.35096	+	11.0002i	0.292637	+	0.506862i
$472$	−32.2579	−	16.8563i	−1.48479	−	0.775874i
$473$	0.388851	−	0.673509i	0.0178794	−	0.0309680i
$474$	−3.51304	+	21.6988i	−0.161359	+	0.996661i
$475$	22.0757	−	12.7454i	1.01290	−	0.584800i
$476$	2.69800	−	2.39600i	0.123663	−	0.109821i
$477$			9.39508i			0.430171i
$478$	0.0129888	−	0.0802272i	0.000594093	−	0.00366951i
$479$	13.7726	−	7.95160i	0.629285	−	0.363318i	−0.151190	−	0.988505i	$-0.548311\pi$
$479$	13.7726	−	7.95160i	0.629285	−	0.363318i	0.780475	+	0.625187i	$0.214977\pi$
$480$	−0.184796	+	0.0461366i	−0.00843475	+	0.00210584i
$481$	15.7444	+	9.09006i	0.717885	+	0.414471i
$482$	35.8107	−	13.6058i	1.63113	−	0.619726i
$483$		−	4.05804i		−	0.184647i
$484$	17.6965	+	5.88438i	0.804388	+	0.267472i
$485$	0.184452	+	0.319481i	0.00837555	+	0.0145069i
$486$	1.32201	−	0.502280i	0.0599677	−	0.0227839i
$487$	−15.9471	−	27.6212i	−0.722631	−	1.25163i	−0.959942	−	0.280200i	$-0.909599\pi$
$487$	−15.9471	−	27.6212i	−0.722631	−	1.25163i	0.237310	−	0.971434i	$-0.423734\pi$
$488$	−0.517665	−	12.2956i	−0.0234336	−	0.556598i
$489$	16.5094	+	9.53171i	0.746581	+	0.431039i
$490$	−0.200494	+	0.245862i	−0.00905741	+	0.0111069i
$491$		−	27.0586i		−	1.22114i	−0.791963	−	0.610569i	$-0.790941\pi$
$491$		−	27.0586i		−	1.22114i	0.791963	−	0.610569i	$-0.209059\pi$
$492$	−18.9763	+	3.89777i	−0.855519	+	0.175725i
$493$	−21.7780			−0.980830
$494$	7.49490	−	46.2934i	0.337212	−	2.08284i
$495$	−0.0377430	−	0.0217910i	−0.00169642	−	0.000979431i
$496$	−26.4547	−	19.7802i	−1.18785	−	0.888159i
$497$	−3.33089	+	1.92309i	−0.149411	+	0.0862624i
$498$	10.0078	−	12.2723i	0.448459	−	0.549936i
$499$	−5.10385	−	8.84013i	−0.228480	−	0.395739i	0.728878	−	0.684644i	$-0.240042\pi$
$499$	−5.10385	−	8.84013i	−0.228480	−	0.395739i	−0.957358	+	0.288905i	$0.906709\pi$
$500$	−0.447105	−	0.503459i	−0.0199951	−	0.0225154i
$501$	−4.42047	−	2.55216i	−0.197492	−	0.114022i
$502$	−12.0012	−	9.78664i	−0.535638	−	0.436799i
$503$	11.4439	−	19.8214i	0.510257	−	0.883790i	−0.489673	−	0.871906i	$-0.662884\pi$
$503$	11.4439	−	19.8214i	0.510257	−	0.883790i	0.999929	−	0.0118841i	$-0.00378291\pi$
$504$	0.880743	+	1.38725i	0.0392314	+	0.0617930i
$505$	−0.0323249	+	0.0559883i	−0.00143844	+	0.00249145i
$506$	−4.54119	−	11.9525i	−0.201881	−	0.531354i
$507$	−14.6441	+	25.3643i	−0.650368	+	1.12647i
$508$	21.7881	−	4.47531i	0.966689	−	0.198560i
$509$	34.4774			1.52818			0.764091	−	0.645108i	$-0.223188\pi$
$509$	34.4774			1.52818			0.764091	+	0.645108i	$0.223188\pi$
$510$	0.0934526	−	0.114599i	0.00413815	−	0.00507452i
$511$	1.60659			0.0710714
$512$	22.4474	−	2.84868i	0.992044	−	0.125895i
$513$	−4.41614	+	2.54966i	−0.194978	+	0.112570i
$514$	0.758085	−	4.68242i	0.0334377	−	0.206533i
$515$	0.277932	−	0.481393i	0.0122472	−	0.0212127i
$516$	−0.898504	+	0.797931i	−0.0395544	+	0.0351270i
$517$	−0.0674651	+	0.0389510i	−0.00296711	+	0.00171306i
$518$	2.14720	−	0.815800i	0.0943426	−	0.0358442i
$519$	1.42698	+	2.47160i	0.0626375	+	0.108491i
$520$	−0.618754	+	0.0260504i	−0.0271341	+	0.00114239i
$521$			2.43259i			0.106574i	0.998579	+	0.0532868i	$0.0169697\pi$
$521$			2.43259i			0.106574i	−0.998579	+	0.0532868i	$0.983030\pi$
$522$	1.58502	−	9.79013i	0.0693746	−	0.428503i
$523$	10.3927	−	6.00025i	0.454443	−	0.262373i	−0.255262	−	0.966872i	$-0.582162\pi$
$523$	10.3927	−	6.00025i	0.454443	−	0.262373i	0.709705	+	0.704499i	$0.248828\pi$
$524$	21.1465	+	23.8118i	0.923788	+	1.04022i
$525$	−1.45209	+	2.51509i	−0.0633742	+	0.109767i
$526$	8.76250	+	23.0631i	0.382063	+	1.00560i
$527$	25.6448			1.11710
$528$	4.14655	+	3.10039i	0.180456	+	0.134927i
$529$	12.8950	−	22.3348i	0.560651	−	0.971076i
$530$	−0.418200	+	0.158889i	−0.0181654	+	0.00690171i
$531$			12.8681i			0.558429i
$532$	−3.93436	−	4.43026i	−0.170576	−	0.192076i
$533$	−62.9891			−2.72836
$534$	−4.88688	+	1.85670i	−0.211476	+	0.0803474i
$535$	−0.352969			−0.0152602
$536$	−23.1417	+	0.678182i	−0.999571	+	0.0292930i
$537$	9.47559			0.408902
$538$	2.03963	−	0.774929i	0.0879346	−	0.0334095i
$539$	8.62372			0.371450
$540$	0.0447156	+	0.0503516i	0.00192425	+	0.00216679i
$541$			12.3771i			0.532132i	0.963955	+	0.266066i	$0.0857240\pi$
$541$			12.3771i			0.532132i	−0.963955	+	0.266066i	$0.914276\pi$
$542$	−4.96706	+	1.88717i	−0.213354	+	0.0810608i
$543$	−10.0742	+	17.4490i	−0.432324	+	0.748807i
$544$	−12.6329	+	12.2071i	−0.541630	+	0.523375i
$545$	0.368994			0.0158060
$546$	1.89761	+	4.99454i	0.0812101	+	0.213747i
$547$	−2.98453	+	5.16936i	−0.127609	+	0.221026i	−0.922750	−	0.385399i	$-0.874064\pi$
$547$	−2.98453	+	5.16936i	−0.127609	+	0.221026i	0.795141	+	0.606425i	$0.207397\pi$
$548$	−20.1492	−	22.6888i	−0.860731	−	0.969219i
$549$	−3.76809	+	2.17551i	−0.160818	+	0.0928485i
$550$	−1.46243	+	9.03289i	−0.0623580	+	0.385164i
$551$			35.7606i			1.52345i
$552$	0.831042	+	19.7390i	0.0353715	+	0.840149i
$553$	4.51503	+	7.82026i	0.191999	+	0.332551i
$554$	−30.5285	+	11.5989i	−1.29703	+	0.492790i
$555$	0.0815202	−	0.0470657i	0.00346034	−	0.00199783i
$556$	−29.9252	+	26.5756i	−1.26911	+	1.12705i
$557$	0.755373	−	1.30835i	0.0320062	−	0.0554364i	−0.849579	−	0.527462i	$-0.823144\pi$
$557$	0.755373	−	1.30835i	0.0320062	−	0.0554364i	0.881585	+	0.472026i	$0.156477\pi$
$558$	−1.86645	+	11.5284i	−0.0790133	+	0.488037i
$559$	−3.38372	+	1.95359i	−0.143116	+	0.0826281i
$560$	−0.0468550	+	0.0626652i	−0.00197999	+	0.00264809i
$561$	−4.01961			−0.169708
$562$	−20.8665	+	25.5882i	−0.880202	+	1.07937i
$563$	−21.8950			−0.922765			−0.461382	−	0.887201i	$-0.652646\pi$
$563$	−21.8950			−0.922765			−0.461382	+	0.887201i	$0.652646\pi$
$564$	0.117909	−	0.0242187i	0.00496486	−	0.00101979i
$565$	0.0240279	−	0.0416175i	0.00101086	−	0.00175086i
$566$	−15.7679	−	41.5014i	−0.662773	−	1.74443i
$567$	0.290483	−	0.503131i	0.0121991	−	0.0211295i
$568$	15.8082	−	10.0364i	0.663299	−	0.421118i
$569$	11.7957	−	20.4307i	0.494500	−	0.856500i	−0.505480	−	0.862839i	$-0.668684\pi$
$569$	11.7957	−	20.4307i	0.494500	−	0.856500i	0.999980	+	0.00633879i	$0.00201771\pi$
$570$	−0.188178	−	0.153454i	−0.00788189	−	0.00642749i
$571$	−26.1342	−	15.0886i	−1.09368	−	0.631438i	−0.159128	−	0.987258i	$-0.550868\pi$
$571$	−26.1342	−	15.0886i	−1.09368	−	0.631438i	−0.934554	+	0.355820i	$0.884202\pi$
$572$	11.1784	+	12.5873i	0.467392	+	0.526303i
$573$	10.6294	+	18.4107i	0.444050	+	0.769117i
$574$	−5.02950	+	6.16757i	−0.209927	+	0.257430i
$575$	−30.2390	+	17.4585i	−1.26105	+	0.728069i
$576$	−4.56819	−	6.56747i	−0.190341	−	0.273645i
$577$	13.0151	+	7.51429i	0.541827	+	0.312824i	0.745819	−	0.666149i	$-0.232058\pi$
$577$	13.0151	+	7.51429i	0.541827	+	0.312824i	−0.203992	+	0.978973i	$0.565392\pi$
$578$	−1.66263	+	10.2695i	−0.0691561	+	0.427153i
$579$	−22.4851			−0.934451
$580$	0.462590	−	0.0950167i	0.0192080	−	0.00394536i
$581$		−	6.50533i		−	0.269887i
$582$	−9.79231	+	12.0081i	−0.405904	+	0.497752i
$583$	10.5315	+	6.08036i	0.436170	+	0.251823i
$584$	−7.81475	+	0.329013i	−0.323377	+	0.0136146i
$585$	0.109478	+	0.189622i	0.00452636	+	0.00783989i
$586$	23.5711	−	8.95552i	0.973713	−	0.369949i
$587$	6.40054	+	11.0861i	0.264179	+	0.457571i	0.967348	−	0.253452i	$-0.0815658\pi$
$587$	6.40054	+	11.0861i	0.264179	+	0.457571i	−0.703170	+	0.711022i	$0.748233\pi$
$588$	−12.6443	−	4.20442i	−0.521441	−	0.173387i
$589$		−	42.1101i		−	1.73512i
$590$	−0.572794	+	0.217625i	−0.0235815	+	0.00895949i
$591$	4.81251	+	2.77851i	0.197960	+	0.114292i
$592$	−10.2773	+	4.40792i	−0.422395	+	0.181165i
$593$	9.92187	−	5.72839i	0.407442	−	0.235237i	−0.282248	−	0.959341i	$-0.591080\pi$
$593$	9.92187	−	5.72839i	0.407442	−	0.235237i	0.689690	+	0.724105i	$0.257747\pi$
$594$	0.292552	−	1.80699i	0.0120035	−	0.0741416i
$595$		−	0.0607468i		−	0.00249037i
$596$	27.2507	−	24.2004i	1.11623	−	0.991288i
$597$	0.320038	−	0.184774i	0.0130983	−	0.00756231i
$598$	−10.2664	+	63.4120i	−0.419825	+	2.59311i
$599$	10.8790	−	18.8430i	0.444504	−	0.769903i	−0.553514	−	0.832840i	$-0.686713\pi$
$599$	10.8790	−	18.8430i	0.444504	−	0.769903i	0.998018	+	0.0629368i	$0.0200467\pi$
$600$	6.54815	−	12.5312i	0.267327	−	0.511584i
$601$	−3.60069	−	6.23658i	−0.146875	−	0.254395i	0.783196	−	0.621775i	$-0.213588\pi$
$601$	−3.60069	−	6.23658i	−0.146875	−	0.254395i	−0.930071	+	0.367380i	$0.880255\pi$
$602$	−0.0788948	+	0.487305i	−0.00321551	+	0.0198611i
$603$	4.00175	+	7.14045i	0.162964	+	0.290781i
$604$	10.7121	−	32.2154i	0.435870	−	1.31083i
$605$	0.271900	−	0.156981i	0.0110543	−	0.00638220i
$606$	−2.68050	−	0.433973i	−0.108888	−	0.0176289i
$607$	12.1414	+	7.00982i	0.492803	+	0.284520i	0.725736	−	0.687973i	$-0.241499\pi$
$607$	12.1414	+	7.00982i	0.492803	+	0.284520i	−0.232934	+	0.972493i	$0.574833\pi$
$608$	20.0447	+	20.7439i	0.812921	+	0.841275i
$609$	−2.03710	−	3.52836i	−0.0825475	−	0.142977i
$610$	−0.160563	−	0.130935i	−0.00650102	−	0.00530142i
$611$	0.391381			0.0158336
$612$	5.89363	+	1.95973i	0.238236	+	0.0792172i
$613$	−14.5446	−	25.1920i	−0.587452	−	1.01750i	−0.994565	−	0.104118i	$-0.966798\pi$
$613$	−14.5446	−	25.1920i	−0.587452	−	1.01750i	0.407113	−	0.913378i	$-0.366535\pi$
$614$	16.8608	−	20.6760i	0.680446	−	0.834416i
$615$	−0.163070	+	0.282445i	−0.00657561	+	0.0113893i
$616$	2.12505	−	0.0894678i	0.0856208	−	0.00360476i
$617$	−12.4273			−0.500303			−0.250151	−	0.968207i	$-0.580480\pi$
$617$	−12.4273			−0.500303			−0.250151	+	0.968207i	$0.580480\pi$
$618$	23.0472	+	3.73134i	0.927094	+	0.150097i
$619$	−10.3590	+	5.98075i	−0.416362	+	0.240387i	−0.693519	−	0.720438i	$-0.743941\pi$
$619$	−10.3590	+	5.98075i	−0.416362	+	0.240387i	0.277158	+	0.960824i	$0.410608\pi$
$620$	−0.544726	+	0.111888i	−0.0218767	+	0.00449351i
$621$	6.04917	−	3.49249i	0.242745	−	0.140149i
$622$	44.6113	−	16.9494i	1.78875	−	0.679611i
$623$	−1.07378	+	1.85985i	−0.0430202	+	0.0745132i
$624$	−10.2531	−	23.9057i	−0.410454	−	0.956996i
$625$	24.9830			0.999320
$626$	−1.47215	−	3.87473i	−0.0588389	−	0.154865i
$627$			6.60042i			0.263595i
$628$	−24.1061	−	8.01567i	−0.961939	−	0.319860i
$629$	4.34092	−	7.51870i	0.173084	−	0.299790i
$630$	0.0273083	+	0.00442122i	0.00108799	+	0.000176146i
$631$	−7.40094	−	12.8188i	−0.294627	−	0.510309i	0.680271	−	0.732961i	$-0.261862\pi$
$631$	−7.40094	−	12.8188i	−0.294627	−	0.510309i	−0.974898	+	0.222652i	$0.928529\pi$
$632$	−23.5634	−	37.1145i	−0.937303	−	1.47634i
$633$	−0.433107	+	0.250054i	−0.0172145	+	0.00993877i
$634$	8.01433	+	6.53549i	0.318290	+	0.259558i
$635$	0.187232	−	0.324295i	0.00743007	−	0.0128693i
$636$	−12.4771	−	14.0497i	−0.494747	−	0.557106i
$637$	−37.5212	−	21.6628i	−1.48664	−	0.858313i
$638$	−9.94852	−	8.11278i	−0.393866	−	0.321188i
$639$	−5.73337	−	3.31016i	−0.226809	−	0.130948i
$640$	0.215078	−	0.314411i	0.00850171	−	0.0124282i
$641$	28.6337	+	16.5317i	1.13096	+	0.652962i	0.944177	−	0.329439i	$-0.106859\pi$
$641$	28.6337	+	16.5317i	1.13096	+	0.652962i	0.186786	+	0.982401i	$0.440193\pi$
$642$	−5.26544	−	13.8587i	−0.207810	−	0.546961i
$643$			1.83327i			0.0722970i	0.999346	+	0.0361485i	$0.0115089\pi$
$643$			1.83327i			0.0722970i	−0.999346	+	0.0361485i	$0.988491\pi$
$644$	5.38924	+	6.06850i	0.212366	+	0.239133i
$645$			0.0202303i			0.000796566i
$646$	−22.1072	−	3.57916i	−0.869797	−	0.140820i
$647$	16.1402	+	27.9556i	0.634536	+	1.09905i	0.986613	+	0.163078i	$0.0521422\pi$
$647$	16.1402	+	27.9556i	0.634536	+	1.09905i	−0.352077	+	0.935971i	$0.614524\pi$
$648$	−1.30993	+	2.50681i	−0.0514588	+	0.0984768i
$649$	14.4246	+	8.32806i	0.566216	+	0.326905i
$650$	29.0536	−	35.6278i	1.13958	−	1.39744i
$651$	2.39880	+	4.15485i	0.0940164	+	0.162841i
$652$	−37.3471	+	7.67116i	−1.46263	+	0.300426i
$653$	36.6937	−	21.1851i	1.43593	−	0.829037i	0.438370	−	0.898795i	$-0.355556\pi$
$653$	36.6937	−	21.1851i	1.43593	−	0.829037i	0.997564	+	0.0697579i	$0.0222227\pi$
$654$	5.50450	+	14.4880i	0.215243	+	0.566524i
$655$	0.536135			0.0209485
$656$	23.2014	−	31.0302i	0.905861	−	1.21153i
$657$	1.38269	+	2.39489i	0.0539439	+	0.0934335i
$658$	0.0312507	−	0.0383220i	0.00121828	−	0.00149395i
$659$	−11.7346	−	6.77500i	−0.457117	−	0.263916i	0.253714	−	0.967279i	$-0.418348\pi$
$659$	−11.7346	−	6.77500i	−0.457117	−	0.263916i	−0.710831	+	0.703363i	$0.751681\pi$
$660$	0.0853813	−	0.0175375i	0.00332346	−	0.000682645i
$661$			16.7562i			0.651741i	0.945414	+	0.325870i	$0.105657\pi$
$661$			16.7562i			0.651741i	−0.945414	+	0.325870i	$0.894343\pi$
$662$	−3.38028	+	20.8788i	−0.131378	+	0.811478i
$663$	17.4890	+	10.0973i	0.679217	+	0.392146i
$664$	1.33222	+	31.6431i	0.0517002	+	1.22799i
$665$	−0.0997495			−0.00386812
$666$	3.06404	+	2.49865i	0.118729	+	0.0968208i
$667$		−	48.9843i		−	1.89668i
$668$	9.99988	−	2.05399i	0.386907	−	0.0794713i
$669$		−	6.50721i		−	0.251583i
$670$	−0.250162	+	0.298887i	−0.00966461	+	0.0115470i
$671$			5.63183i			0.217414i
$672$	−3.15941	−	0.904872i	−0.121877	−	0.0349062i
$673$			33.2782i			1.28278i	0.767215	+	0.641390i	$0.221642\pi$
$673$			33.2782i			1.28278i	−0.767215	+	0.641390i	$0.778358\pi$
$674$	−5.51172	+	6.75891i	−0.212304	+	0.260343i
$675$	−4.99887			−0.192406
$676$	−11.7856	−	57.3786i	−0.453294	−	2.20687i
$677$	12.8802	+	7.43641i	0.495028	+	0.285804i	0.726658	−	0.687000i	$-0.241073\pi$
$677$	12.8802	+	7.43641i	0.495028	+	0.285804i	−0.231630	+	0.972804i	$0.574406\pi$
$678$	1.99248	+	0.322583i	0.0765207	+	0.0123887i
$679$			6.36528i			0.244277i
$680$	0.0124403	+	0.295483i	0.000477063	+	0.0113313i
$681$	14.1426	+	8.16526i	0.541947	+	0.312893i
$682$	11.7149	+	9.55325i	0.448588	+	0.365813i
$683$	−13.9939	−	24.2381i	−0.535461	−	0.927446i	−0.999141	−	0.0414431i	$-0.986804\pi$
$683$	−13.9939	−	24.2381i	−0.535461	−	0.927446i	0.463680	−	0.886003i	$-0.346529\pi$
$684$	3.21798	−	9.67766i	0.123042	−	0.370034i
$685$	−0.510851			−0.0195186
$686$	−10.4934	+	3.98682i	−0.400639	+	0.152217i
$687$	3.26867	−	1.88717i	0.124707	−	0.0719999i
$688$	0.283964	−	2.38650i	0.0108260	−	0.0909844i
$689$	−30.5478	−	52.9104i	−1.16378	−	2.01573i
$690$	0.257763	+	0.210199i	0.00981287	+	0.00800215i
$691$	9.34141	+	5.39326i	0.355364	+	0.205169i	0.667045	−	0.745017i	$-0.267559\pi$
$691$	9.34141	+	5.39326i	0.355364	+	0.205169i	−0.311681	+	0.950187i	$0.600892\pi$
$692$	−5.41634	−	1.80102i	−0.205898	−	0.0684645i
$693$	−0.375993	−	0.651238i	−0.0142828	−	0.0247385i
$694$	0.626256	−	3.86816i	0.0237723	−	0.146833i
$695$			0.673781i			0.0255580i
$696$	10.6314	+	16.7454i	0.402982	+	0.634734i
$697$			30.0802i			1.13937i
$698$	−0.657245	+	0.249711i	−0.0248771	+	0.00945171i
$699$	−8.93565	−	5.15900i	−0.337977	−	0.195131i
$700$	−1.16865	−	5.68956i	−0.0441706	−	0.215045i
$701$	−13.2670	−	7.65968i	−0.501086	−	0.289302i	0.228076	−	0.973643i	$-0.426757\pi$
$701$	−13.2670	−	7.65968i	−0.501086	−	0.289302i	−0.729162	+	0.684341i	$0.760090\pi$
$702$	−5.81204	+	7.12718i	−0.219361	+	0.268998i
$703$	−12.3461	−	7.12803i	−0.465642	−	0.268839i
$704$	−10.3183	+	0.870376i	−0.388886	+	0.0328035i
$705$	0.00101323	−	0.00175496i	3.81604e−5	−	6.60957e-5i
$706$	25.9579	−	31.8317i	0.976940	−	1.19800i
$707$	−0.966051	+	0.557750i	−0.0363321	+	0.0209763i
$708$	−17.0894	−	19.2434i	−0.642259	−	0.723210i
$709$	16.4180	+	28.4369i	0.616592	+	1.06797i	0.990103	+	0.140343i	$0.0448206\pi$
$709$	16.4180	+	28.4369i	0.616592	+	1.06797i	−0.373511	+	0.927626i	$0.621846\pi$
$710$	0.0503814	−	0.311188i	0.00189078	−	0.0116787i
$711$	−7.77159	+	13.4608i	−0.291457	+	0.504819i
$712$	4.84220	−	9.26654i	0.181469	−	0.347278i
$713$			57.6818i			2.16020i
$714$	2.38512	−	0.906195i	0.0892610	−	0.0339135i
$715$	0.283411			0.0105990
$716$	−14.1701	+	12.5840i	−0.529560	+	0.470285i
$717$	0.0287339	−	0.0497686i	0.00107309	−	0.00185864i
$718$	−4.32515	−	11.3839i	−0.161413	−	0.424843i
$719$	−26.9853	+	15.5800i	−1.00638	+	0.581035i	−0.910130	−	0.414322i	$-0.864019\pi$
$719$	−26.9853	+	15.5800i	−1.00638	+	0.581035i	−0.0962520	+	0.995357i	$0.530685\pi$
$720$	−0.133738	−	0.0159132i	−0.00498412	−	0.000593048i
$721$	8.30621	−	4.79559i	0.309339	−	0.178597i
$722$	−1.58283	+	9.77659i	−0.0589068	+	0.363847i
$723$	27.0880			1.00741
$724$	−8.10773	−	39.4726i	−0.301322	−	1.46699i
$725$	−17.5281	+	30.3595i	−0.650975	+	1.12752i
$726$	10.2197	+	8.33392i	0.379289	+	0.309301i
$727$	−16.2116	−	28.0793i	−0.601254	−	1.04140i	−0.992631	−	0.121173i	$-0.961334\pi$
$727$	−16.2116	−	28.0793i	−0.601254	−	1.04140i	0.391377	−	0.920230i	$-0.371999\pi$
$728$	−9.47069	−	4.94888i	−0.351007	−	0.183418i
$729$	1.00000			0.0370370
$730$	−0.0832187	+	0.102049i	−0.00308006	+	0.00377702i
$731$	0.932930	+	1.61588i	0.0345057	+	0.0597656i
$732$	2.74575	−	8.25750i	0.101486	−	0.305206i
$733$	9.90553	+	5.71896i	0.365869	+	0.211235i	0.671652	−	0.740866i	$-0.265585\pi$
$733$	9.90553	+	5.71896i	0.365869	+	0.211235i	−0.305783	+	0.952101i	$0.598918\pi$
$734$	−0.652765	+	4.03190i	−0.0240940	+	0.148820i
$735$	−0.194274	+	0.112164i	−0.00716589	+	0.00413723i
$736$	−27.4570	−	28.4147i	−1.01208	−	1.04738i
$737$	10.5940	+	0.135393i	0.390236	+	0.00498726i
$738$	−13.5224	−	2.18927i	−0.497765	−	0.0805882i
$739$	1.95205	+	3.38104i	0.0718072	+	0.124374i	0.899693	−	0.436522i	$-0.143790\pi$
$739$	1.95205	+	3.38104i	0.0718072	+	0.124374i	−0.827886	+	0.560896i	$0.810457\pi$
$740$	−0.0594025	+	0.178646i	−0.00218368	+	0.00656714i
$741$	16.5803	−	28.7179i	0.609092	−	1.05498i
$742$	−7.61988	−	1.23366i	−0.279734	−	0.0452890i
$743$	−4.29756	+	2.48119i	−0.157662	+	0.0910262i	−0.576755	−	0.816917i	$-0.695681\pi$
$743$	−4.29756	+	2.48119i	−0.157662	+	0.0910262i	0.419093	+	0.907943i	$0.362348\pi$
$744$	−12.5191	−	19.7187i	−0.458972	−	0.722922i
$745$		−	0.613563i		−	0.0224792i
$746$	27.5852	+	4.46605i	1.00997	+	0.163514i
$747$	9.69727	−	5.59872i	0.354804	−	0.204846i
$748$	6.01104	−	5.33820i	0.219785	−	0.195184i
$749$	−5.27436	−	3.04515i	−0.192721	−	0.111267i
$750$	−0.169100	−	0.445075i	−0.00617467	−	0.0162519i
$751$		−	2.70734i		−	0.0987922i	−0.998779	−	0.0493961i	$-0.984270\pi$
$751$		−	2.70734i		−	0.0987922i	0.998779	−	0.0493961i	$-0.0157297\pi$
$752$	−0.144161	+	0.192805i	−0.00525701	+	0.00703088i
$753$	−5.47501	−	9.48300i	−0.199521	−	0.345580i
$754$	22.9059	+	60.2889i	0.834185	+	2.19559i
$755$	−0.285774	−	0.494976i	−0.0104004	−	0.0180140i
$756$	0.233782	+	1.13817i	0.00850257	+	0.0413949i
$757$	−34.5407	−	19.9421i	−1.25540	−	0.724808i	−0.283227	−	0.959053i	$-0.591405\pi$
$757$	−34.5407	−	19.9421i	−1.25540	−	0.724808i	−0.972178	+	0.234245i	$0.924738\pi$
$758$	−14.2649	−	11.6327i	−0.518125	−	0.422518i
$759$		−	9.04115i		−	0.328173i
$760$	0.485200	−	0.0204276i	0.0176000	−	0.000740988i
$761$	52.4392			1.90092			0.950459	−	0.310849i	$-0.100614\pi$
$761$	52.4392			1.90092			0.950459	+	0.310849i	$0.100614\pi$
$762$	15.5260	+	2.51366i	0.562447	+	0.0910602i
$763$	5.51383	+	3.18341i	0.199614	+	0.115247i
$764$	−40.3457	−	13.4156i	−1.45965	−	0.485359i
$765$	0.0905531	−	0.0522808i	0.00327395	−	0.00189022i
$766$	16.1010	+	13.1300i	0.581752	+	0.474405i
$767$	−41.8403	−	72.4696i	−1.51077	−	2.61673i
$768$	15.5533	+	3.75445i	0.561230	+	0.135477i
$769$	−0.974909	−	0.562864i	−0.0351561	−	0.0202974i	0.482319	−	0.875996i	$-0.339795\pi$
$769$	−0.974909	−	0.562864i	−0.0351561	−	0.0202974i	−0.517475	+	0.855698i	$0.673128\pi$
$770$	0.0226295	−	0.0277501i	0.000815512	−	0.00100004i
$771$	1.67704	−	2.90472i	0.0603972	−	0.104611i
$772$	33.6249	−	29.8612i	1.21019	−	1.07473i
$773$	−19.6192	+	33.9814i	−0.705653	+	1.22223i	0.260802	+	0.965392i	$0.416013\pi$
$773$	−19.6192	+	33.9814i	−0.705653	+	1.22223i	−0.966455	+	0.256835i	$0.917320\pi$
$774$	−0.794309	+	0.301787i	−0.0285508	+	0.0108475i
$775$	20.6403	−	35.7500i	0.741420	−	1.28418i
$776$	−1.30354	−	30.9619i	−0.0467943	−	1.11147i
$777$	1.62419			0.0582676
$778$	−3.60647	−	2.94099i	−0.129298	−	0.105440i
$779$	49.3933			1.76970
$780$	−0.415542	−	0.138174i	−0.0148788	−	0.00494744i
$781$	−7.42111	+	4.28458i	−0.265548	+	0.153314i
$782$	30.2822	+	4.90268i	1.08289	+	0.175320i
$783$	3.50641	−	6.07327i	0.125309	−	0.217041i
$784$	24.4922	−	10.5047i	0.874723	−	0.375167i
$785$	−0.370380	+	0.213839i	−0.0132194	+	0.00763225i
$786$	7.99784	+	21.0505i	0.285273	+	0.750846i
$787$	2.64924	+	4.58862i	0.0944352	+	0.163567i	0.909373	−	0.415982i	$-0.136562\pi$
$787$	2.64924	+	4.58862i	0.0944352	+	0.163567i	−0.814938	+	0.579549i	$0.803229\pi$
$788$	−10.8867	+	2.23615i	−0.387824	+	0.0796597i
$789$			17.4454i			0.621074i
$790$	−0.730607	−	0.118285i	−0.0259938	−	0.00420841i
$791$	0.718090	−	0.414589i	0.0255323	−	0.0147411i
$792$	1.96226	+	3.09074i	0.0697260	+	0.109825i
$793$	14.1472	−	24.5037i	0.502382	−	0.870151i
$794$	12.7908	−	4.85970i	0.453929	−	0.172464i
$795$	−0.316336			−0.0112193
$796$	−0.233207	+	0.701341i	−0.00826580	+	0.0248584i
$797$	7.23936	−	12.5389i	0.256431	−	0.444152i	−0.708852	−	0.705357i	$-0.750787\pi$
$797$	7.23936	−	12.5389i	0.256431	−	0.444152i	0.965283	+	0.261205i	$0.0841199\pi$
$798$	−1.48802	−	3.91650i	−0.0526754	−	0.138643i
$799$		−	0.186902i		−	0.00661213i
$800$	6.84966	+	27.4357i	0.242172	+	0.970000i
$801$	−3.69655			−0.130611
$802$	−11.7179	−	30.8417i	−0.413773	−	1.08906i
$803$	3.57943			0.126315
$804$	−15.4671	−	5.36354i	−0.545484	−	0.189157i
$805$	0.136635			0.00481577
$806$	−26.9730	−	70.9935i	−0.950084	−	2.50064i
$807$	1.54282			0.0543099
$808$	4.58483	−	2.91083i	0.161294	−	0.102403i
$809$			20.7162i			0.728343i	0.931332	+	0.364171i	$0.118648\pi$
$809$			20.7162i			0.728343i	−0.931332	+	0.364171i	$0.881352\pi$
$810$	0.0169119	+	0.0445126i	0.000594225	+	0.00156401i
$811$	−7.56677	+	13.1060i	−0.265705	+	0.460215i	−0.967748	−	0.251920i	$-0.918938\pi$
$811$	−7.56677	+	13.1060i	−0.265705	+	0.460215i	0.702043	+	0.712135i	$0.252271\pi$
$812$	7.73215	+	2.57106i	0.271345	+	0.0902267i
$813$	−3.75720			−0.131771
$814$	4.78389	−	1.81757i	0.167675	−	0.0637059i
$815$	−0.320936	+	0.555877i	−0.0112419	+	0.0194715i
$816$	−11.4161	+	4.89635i	−0.399643	+	0.171406i
$817$	2.65337	−	1.53192i	0.0928296	−	0.0535952i
$818$	22.5316	+	3.64787i	0.787799	+	0.127545i
$819$			3.77799i			0.132014i
$820$	−0.131239	−	0.638940i	−0.00458307	−	0.0223127i
$821$	−8.61254	−	14.9174i	−0.300580	−	0.520619i	0.675688	−	0.737188i	$-0.263847\pi$
$821$	−8.61254	−	14.9174i	−0.300580	−	0.520619i	−0.976267	+	0.216569i	$0.930513\pi$
$822$	−7.62066	−	20.0577i	−0.265801	−	0.699593i
$823$	25.1095	−	14.4970i	0.875261	−	0.505332i	0.00616775	−	0.999981i	$-0.498037\pi$
$823$	25.1095	−	14.4970i	0.875261	−	0.505332i	0.869093	+	0.494649i	$0.164703\pi$
$824$	−39.4208	+	25.0276i	−1.37329	+	0.871879i
$825$	−3.23519	+	5.60352i	−0.112635	+	0.195089i
$826$	−10.4367	−	1.68970i	−0.363139	−	0.0587922i
$827$	28.5125	−	16.4617i	0.991478	−	0.572430i	0.0857626	−	0.996316i	$-0.472667\pi$
$827$	28.5125	−	16.4617i	0.991478	−	0.572430i	0.905716	+	0.423885i	$0.139334\pi$
$828$	−4.40794	+	13.2563i	−0.153186	+	0.460689i
$829$	−13.1808			−0.457789			−0.228894	−	0.973451i	$-0.573511\pi$
$829$	−13.1808			−0.457789			−0.228894	+	0.973451i	$0.573511\pi$
$830$	0.413213	+	0.336965i	0.0143428	+	0.0116962i
$831$	−23.0925			−0.801069
$832$	47.0806	+	22.1328i	1.63223	+	0.767316i
$833$	−10.3450	+	17.9181i	−0.358433	+	0.620825i
$834$	−26.4549	+	10.0512i	−0.916059	+	0.348044i
$835$	0.0859321	−	0.148839i	0.00297380	−	0.00515078i
$836$	−8.76562	−	9.87045i	−0.303165	−	0.341377i
$837$	−4.12899	+	7.15162i	−0.142719	+	0.247196i
$838$	29.2181	−	35.8295i	1.00932	−	1.23771i
$839$	−3.33831	−	1.92737i	−0.115251	−	0.0665403i	0.441266	−	0.897376i	$-0.354529\pi$
$839$	−3.33831	−	1.92737i	−0.115251	−	0.0665403i	−0.556517	+	0.830836i	$0.687863\pi$
$840$	−0.0467092	+	0.0296549i	−0.00161162	+	0.00102319i
$841$	−10.0898	−	17.4760i	−0.347923	−	0.602620i
$842$	−24.8139	−	20.2351i	−0.855143	−	0.697348i
$843$	−20.2191	+	11.6735i	−0.696383	+	0.402057i
$844$	0.315598	−	0.949122i	0.0108633	−	0.0326701i
$845$	−0.854026	−	0.493072i	−0.0293794	−	0.0169622i
$846$	0.0840207	+	0.0136030i	0.00288869	+	0.000467680i
$847$	5.41728			0.186140
$848$	37.3171	+	4.44027i	1.28147	+	0.152480i
$849$		−	31.3926i		−	1.07739i
$850$	−17.0139	−	13.8744i	−0.583573	−	0.475889i
$851$	16.9115	+	9.76388i	0.579720	+	0.334701i
$852$	12.9699	−	2.66403i	0.444341	−	0.0912683i
$853$	26.9985	+	46.7627i	0.924410	+	1.60113i	0.792507	+	0.609863i	$0.208776\pi$
$853$	26.9985	+	46.7627i	0.924410	+	1.60113i	0.131904	+	0.991263i	$0.457891\pi$
$854$	−1.26966	−	3.34177i	−0.0434469	−	0.114353i
$855$	−0.0858480	−	0.148693i	−0.00293594	−	0.00508520i
$856$	26.2791	+	13.7320i	0.898200	+	0.469352i
$857$		−	21.3803i		−	0.730337i	−0.930941	−	0.365169i	$-0.881011\pi$
$857$		−	21.3803i		−	0.730337i	0.930941	−	0.365169i	$-0.118989\pi$
$858$	4.22780	+	11.1277i	0.144335	+	0.379892i
$859$	−8.86149	−	5.11618i	−0.302350	−	0.174562i	0.341148	−	0.940010i	$-0.389184\pi$
$859$	−8.86149	−	5.11618i	−0.302350	−	0.174562i	−0.643498	+	0.765448i	$0.722518\pi$
$860$	−0.0268666	−	0.0302529i	−0.000916144	−	0.00103162i
$861$	−4.87346	+	2.81369i	−0.166087	+	0.0958903i
$862$	−29.3580	−	4.75306i	−0.999936	−	0.161890i
$863$			33.2934i			1.13332i	0.823951	+	0.566660i	$0.191765\pi$
$863$			33.2934i			1.13332i	−0.823951	+	0.566660i	$0.808235\pi$
$864$	−1.37024	−	5.48839i	−0.0466166	−	0.186719i
$865$	−0.0832198	+	0.0480470i	−0.00282956	+	0.00163365i
$866$	−12.9213	−	2.09196i	−0.439083	−	0.0710876i
$867$	−3.67808	+	6.37062i	−0.124914	+	0.216358i
$868$	−9.10504	−	3.02757i	−0.309045	−	0.102762i
$869$	10.0593	+	17.4233i	0.341239	+	0.591043i
$870$	0.329637	+	0.0533683i	0.0111757	+	0.00180935i
$871$	−45.7537	−	27.2013i	−1.55030	−	0.921682i
$872$	−27.4722	−	14.3555i	−0.930326	−	0.486139i
$873$	−9.48849	+	5.47818i	−0.321137	+	0.185408i
$874$	8.05047	−	49.7250i	0.272311	−	1.68197i
$875$	−0.169387	−	0.0977955i	−0.00572632	−	0.00330609i
$876$	−5.24823	−	1.74512i	−0.177321	−	0.0589621i
$877$	15.4962	+	26.8403i	0.523271	+	0.906332i	0.999633	+	0.0270830i	$0.00862185\pi$
$877$	15.4962	+	26.8403i	0.523271	+	0.906332i	−0.476362	+	0.879249i	$0.658045\pi$
$878$	−7.24417	+	8.88337i	−0.244479	+	0.299799i
$879$	17.8297			0.601382
$880$	−0.104391	+	0.139616i	−0.00351903	+	0.00470645i
$881$	15.3376	+	26.5656i	0.516738	+	0.895017i	0.999811	+	0.0194367i	$0.00618729\pi$
$881$	15.3376	+	26.5656i	0.516738	+	0.895017i	−0.483073	+	0.875580i	$0.660479\pi$
$882$	−7.30203	−	5.95463i	−0.245872	−	0.200503i
$883$	5.88367	−	10.1908i	0.198001	−	0.342948i	−0.749879	−	0.661575i	$-0.769888\pi$
$883$	5.88367	−	10.1908i	0.198001	−	0.342948i	0.947880	+	0.318627i	$0.103222\pi$
$884$	−39.5632	+	8.12634i	−1.33065	+	0.273319i
$885$	−0.433274			−0.0145644
$886$	−6.17122	+	38.1174i	−0.207326	+	1.28058i
$887$	−36.8760	+	21.2903i	−1.23817	+	0.714860i	−0.968721	−	0.248154i	$-0.920176\pi$
$887$	−36.8760	+	21.2903i	−1.23817	+	0.714860i	−0.269453	+	0.963014i	$0.586843\pi$
$888$	−7.90037	+	0.332617i	−0.265119	+	0.0111619i
$889$	5.59556	−	3.23060i	0.187669	−	0.108351i
$890$	−0.0625158	−	0.164543i	−0.00209553	−	0.00551549i
$891$	0.647185	−	1.12096i	0.0216815	−	0.0375535i
$892$	8.64184	+	9.73107i	0.289350	+	0.325820i
$893$	−0.306904			−0.0102701
$894$	24.0906	−	9.15288i	0.805709	−	0.306118i
$895$			0.319046i			0.0106645i
$896$	5.92638	−	2.84266i	0.197987	−	0.0949665i
$897$	−22.7115	+	39.3374i	−0.758313	+	1.31344i
$898$	−5.04798	+	31.1796i	−0.168453	+	1.04048i
$899$	28.9558	+	50.1529i	0.965730	+	1.67269i
$900$	7.47545	−	6.63870i	0.249182	−	0.221290i
$901$	−25.2672	+	14.5880i	−0.841771	+	0.485997i
$902$	−11.2056	+	13.7411i	−0.373104	+	0.457529i
$903$	−0.174532	+	0.302298i	−0.00580806	+	0.0100598i
$904$	−3.40802	+	2.16369i	−0.113349	+	0.0719634i
$905$	−0.587513	−	0.339201i	−0.0195296	−	0.0112754i
$906$	15.1714	−	18.6043i	0.504035	−	0.618087i
$907$	−1.80339	−	1.04119i	−0.0598805	−	0.0345720i	0.469761	−	0.882794i	$-0.344340\pi$
$907$	−1.80339	−	1.04119i	−0.0598805	−	0.0345720i	−0.529641	+	0.848222i	$0.677673\pi$
$908$	−31.9931	+	6.57144i	−1.06173	+	0.218081i
$909$	−1.66284	−	0.960039i	−0.0551528	−	0.0318425i
$910$	−0.168168	+	0.0638931i	−0.00557471	+	0.00211804i
$911$			5.87683i			0.194708i	0.995250	+	0.0973540i	$0.0310379\pi$
$911$			5.87683i			0.194708i	−0.995250	+	0.0973540i	$0.968962\pi$
$912$	8.04007	+	18.7459i	0.266233	+	0.620737i
$913$		−	14.4936i		−	0.479669i
$914$	−1.85803	+	11.4764i	−0.0614582	+	0.379605i
$915$	−0.0732501	−	0.126873i	−0.00242158	−	0.00419429i
$916$	−2.38183	+	7.16304i	−0.0786978	+	0.236674i
$917$	8.01139	+	4.62538i	0.264559	+	0.152743i
$918$	3.40356	+	2.77552i	0.112334	+	0.0916057i
$919$	−2.13927	−	3.70532i	−0.0705679	−	0.122227i	0.828582	−	0.559867i	$-0.189148\pi$
$919$	−2.13927	−	3.70532i	−0.0705679	−	0.122227i	−0.899150	+	0.437640i	$0.855814\pi$
$920$	−0.664620	+	0.0279815i	−0.0219119	+	0.000922521i
$921$	16.3376	−	9.43255i	0.538344	−	0.310813i
$922$	16.7106	−	6.34895i	0.550333	−	0.209092i
$923$	43.0516			1.41706
$924$	1.42714	+	0.474547i	0.0469495	+	0.0156115i
$925$	−6.98761	−	12.1029i	−0.229751	−	0.397941i
$926$	−22.2552	−	18.1485i	−0.731351	−	0.596398i
$927$	14.2972	+	8.25451i	0.469583	+	0.271114i
$928$	−38.1371	−	10.9227i	−1.25191	−	0.358554i
$929$		−	24.1754i		−	0.793168i	−0.917998	−	0.396584i	$-0.870196\pi$
$929$		−	24.1754i		−	0.793168i	0.917998	−	0.396584i	$-0.129804\pi$
$930$	−0.388166	−	0.0628442i	−0.0127285	−	0.00206074i
$931$	29.4225	+	16.9871i	0.964282	+	0.556729i
$932$	20.2140	−	4.15199i	0.662131	−	0.136003i
$933$	33.7450			1.10476
$934$	−6.96678	+	8.54321i	−0.227960	+	0.279543i
$935$		−	0.135342i		−	0.00442614i
$936$	−0.773691	−	18.3768i	−0.0252889	−	0.600665i
$937$			1.69843i			0.0554852i	0.999615	+	0.0277426i	$0.00883188\pi$
$937$			1.69843i			0.0554852i	−0.999615	+	0.0277426i	$0.991168\pi$
$938$	−6.31672	+	2.30802i	−0.206248	+	0.0753594i
$939$		−	2.93093i		−	0.0956474i
$940$	0.000815451		0.00397003i	2.65971e−5		0.000129488i
$941$			37.5905i			1.22541i	0.790310	+	0.612707i	$0.209920\pi$
$941$			37.5905i			1.22541i	−0.790310	+	0.612707i	$0.790080\pi$
$942$	−13.9212	−	11.3524i	−0.453578	−	0.369882i
$943$	−67.6583			−2.20326
$944$	51.1120	+	6.08169i	1.66355	+	0.197942i
$945$	0.0169406	+	0.00978066i	0.000551078	+	0.000318165i
$946$	−0.175775	+	1.08570i	−0.00571493	+	0.0352991i
$947$		−	20.2963i		−	0.659543i	−0.944061	−	0.329771i	$-0.893028\pi$
$947$		−	20.2963i		−	0.659543i	0.944061	−	0.329771i	$-0.106972\pi$
$948$	−6.25461	−	30.4506i	−0.203140	−	0.988991i
$949$	−15.5738	−	8.99155i	−0.505548	−	0.291878i
$950$	−22.7826	+	27.9378i	−0.739164	+	0.906422i
$951$	3.65620	+	6.33272i	0.118560	+	0.205352i
$952$	−2.36332	+	4.52269i	−0.0765956	+	0.146581i
$953$	−39.5920			−1.28251			−0.641255	−	0.767328i	$-0.721586\pi$
$953$	−39.5920			−1.28251			−0.641255	+	0.767328i	$0.721586\pi$
$954$	−4.71897	−	12.4204i	−0.152782	−	0.402126i
$955$	−0.619894	+	0.357896i	−0.0200593	+	0.0115812i
$956$	0.0231252	+	0.112585i	0.000747922	+	0.00364127i
$957$	−4.53859	−	7.86107i	−0.146712	−	0.254112i
$958$	−14.2136	+	17.4298i	−0.459219	+	0.563131i
$959$	−7.63357	−	4.40724i	−0.246501	−	0.142317i
$960$	0.221129	−	0.153812i	0.00713691	−	0.00496428i
$961$	−18.5971	−	32.2111i	−0.599906	−	1.03907i
$962$	−25.3801	−	4.10904i	−0.818287	−	0.132481i
$963$		−	10.4831i		−	0.337812i
$964$	−40.5082	+	35.9740i	−1.30468	+	1.15864i
$965$		−	0.757083i		−	0.0243714i
$966$	2.03827	+	5.36477i	0.0655803	+	0.172609i
$967$	33.5165	+	19.3507i	1.07782	+	0.622278i	0.930307	−	0.366783i	$-0.119541\pi$
$967$	33.5165	+	19.3507i	1.07782	+	0.622278i	0.147510	+	0.989061i	$0.452874\pi$
$968$	−26.3506	+	1.10940i	−0.846941	+	0.0356575i
$969$	−13.7141	−	7.91786i	−0.440561	−	0.254358i
$970$	−0.404317	−	0.329711i	−0.0129818	−	0.0105864i
$971$	−38.0062	−	21.9429i	−1.21968	−	0.704180i	−0.254827	−	0.966987i	$-0.582019\pi$
$971$	−38.0062	−	21.9429i	−1.21968	−	0.704180i	−0.964849	+	0.262807i	$0.915352\pi$
$972$	−1.49543	+	1.32804i	−0.0479659	+	0.0425969i
$973$	−5.81288	+	10.0682i	−0.186353	+	0.322772i
$974$	34.9558	+	28.5056i	1.12006	+	0.913378i
$975$	28.1522	−	16.2537i	0.901591	−	0.520534i
$976$	6.86022	+	15.9950i	0.219590	+	0.511987i
$977$	−12.2697	−	21.2517i	−0.392543	−	0.679904i	0.600242	−	0.799819i	$-0.295071\pi$
$977$	−12.2697	−	21.2517i	−0.392543	−	0.679904i	−0.992784	+	0.119915i	$0.961738\pi$
$978$	−26.6132	−	4.30868i	−0.850997	−	0.137776i
$979$	−2.39235	+	4.14367i	−0.0764598	+	0.132432i
$980$	0.141564	−	0.425737i	0.00452210	−	0.0135997i
$981$			10.9590i			0.349895i
$982$	13.5910	+	35.7718i	0.433707	+	1.14152i
$983$	−0.107433			−0.00342657			−0.00171329	−	0.999999i	$-0.500545\pi$
$983$	−0.107433			−0.00342657			−0.00171329	+	0.999999i	$0.500545\pi$
$984$	23.1292	−	14.6843i	0.737331	−	0.468120i
$985$	−0.0935532	+	0.162039i	−0.00298085	+	0.00516299i
$986$	28.7907	−	10.9386i	0.916883	−	0.348357i
$987$	0.0302811	−	0.0174828i	0.000963857	−	0.000556483i
$988$	13.3439	+	64.9649i	0.424526	+	2.06681i
$989$	−3.63454	+	2.09841i	−0.115572	+	0.0667254i
$990$	0.0608419	+	0.00985031i	0.00193368	+	0.000313063i
$991$	32.1640			1.02172			0.510861	−	0.859663i	$-0.329327\pi$
$991$	32.1640			1.02172			0.510861	+	0.859663i	$0.329327\pi$
$992$	44.9086	+	12.8620i	1.42585	+	0.408370i
$993$	−7.47789	+	12.9521i	−0.237304	+	0.411022i
$994$	3.43755	−	4.21539i	0.109032	−	0.133704i
$995$	0.00622141	+	0.0107758i	0.000197232	+	0.000341616i
$996$	−7.06625	+	21.2509i	−0.223903	+	0.673359i
$997$	46.5541			1.47438			0.737191	−	0.675684i	$-0.236152\pi$
$997$	46.5541			1.47438			0.737191	+	0.675684i	$0.236152\pi$
$998$	11.1876	+	9.12319i	0.354136	+	0.288790i
$999$	1.39784	+	2.42113i	0.0442257	+	0.0766011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.5	✓	68
4.3	odd	2		804.2.j.b.499.6	yes	68
67.38	odd	6		804.2.j.b.775.6	yes	68
268.239	even	6	inner	804.2.j.a.775.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.5	✓	68	1.1	even	1	trivial
804.2.j.a.775.5	yes	68	268.239	even	6	inner
804.2.j.b.499.6	yes	68	4.3	odd	2
804.2.j.b.775.6	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32201 + 0.502280i) q^{2} -1.00000 q^{3} +(1.49543 - 1.32804i) q^{4} -0.0336703i q^{5} +(1.32201 - 0.502280i) q^{6} +(0.290483 - 0.503131i) q^{7} +(-1.30993 + 2.50681i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.32201 + 0.502280i) q^{2} -1.00000 q^{3} +(1.49543 - 1.32804i) q^{4} -0.0336703i q^{5} +(1.32201 - 0.502280i) q^{6} +(0.290483 - 0.503131i) q^{7} +(-1.30993 + 2.50681i) q^{8} +1.00000 q^{9} +(0.0169119 + 0.0445126i) q^{10} +(0.647185 - 1.12096i) q^{11} +(-1.49543 + 1.32804i) q^{12} +(-5.63171 + 3.25147i) q^{13} +(-0.131309 + 0.811049i) q^{14} +0.0336703i q^{15} +(0.472616 - 3.97198i) q^{16} +(1.55273 + 2.68940i) q^{17} +(-1.32201 + 0.502280i) q^{18} +(4.41614 - 2.54966i) q^{19} +(-0.0447156 - 0.0503516i) q^{20} +(-0.290483 + 0.503131i) q^{21} +(-0.292552 + 1.80699i) q^{22} +(-6.04917 + 3.49249i) q^{23} +(1.30993 - 2.50681i) q^{24} +4.99887 q^{25} +(5.81204 - 7.12718i) q^{26} -1.00000 q^{27} +(-0.233782 - 1.13817i) q^{28} +(-3.50641 + 6.07327i) q^{29} +(-0.0169119 - 0.0445126i) q^{30} +(4.12899 - 7.15162i) q^{31} +(1.37024 + 5.48839i) q^{32} +(-0.647185 + 1.12096i) q^{33} +(-3.40356 - 2.77552i) q^{34} +(-0.0169406 - 0.00978066i) q^{35} +(1.49543 - 1.32804i) q^{36} +(-1.39784 - 2.42113i) q^{37} +(-4.55755 + 5.58882i) q^{38} +(5.63171 - 3.25147i) q^{39} +(0.0844051 + 0.0441057i) q^{40} +(8.38854 + 4.84313i) q^{41} +(0.131309 - 0.811049i) q^{42} +0.600833 q^{43} +(-0.520858 - 2.53580i) q^{44} -0.0336703i q^{45} +(6.24286 - 7.65549i) q^{46} +(-0.0521219 - 0.0300926i) q^{47} +(-0.472616 + 3.97198i) q^{48} +(3.33124 + 5.76988i) q^{49} +(-6.60856 + 2.51083i) q^{50} +(-1.55273 - 2.68940i) q^{51} +(-4.10374 + 12.3415i) q^{52} +9.39508i q^{53} +(1.32201 - 0.502280i) q^{54} +(-0.0377430 - 0.0217910i) q^{55} +(0.880743 + 1.38725i) q^{56} +(-4.41614 + 2.54966i) q^{57} +(1.58502 - 9.79013i) q^{58} +12.8681i q^{59} +(0.0447156 + 0.0503516i) q^{60} +(-3.76809 + 2.17551i) q^{61} +(-1.86645 + 11.5284i) q^{62} +(0.290483 - 0.503131i) q^{63} +(-4.56819 - 6.56747i) q^{64} +(0.109478 + 0.189622i) q^{65} +(0.292552 - 1.80699i) q^{66} +(4.00175 + 7.14045i) q^{67} +(5.89363 + 1.95973i) q^{68} +(6.04917 - 3.49249i) q^{69} +(0.0273083 + 0.00442122i) q^{70} +(-5.73337 - 3.31016i) q^{71} +(-1.30993 + 2.50681i) q^{72} +(1.38269 + 2.39489i) q^{73} +(3.06404 + 2.49865i) q^{74} -4.99887 q^{75} +(3.21798 - 9.67766i) q^{76} +(-0.375993 - 0.651238i) q^{77} +(-5.81204 + 7.12718i) q^{78} +(-7.77159 + 13.4608i) q^{79} +(-0.133738 - 0.0159132i) q^{80} +1.00000 q^{81} +(-13.5224 - 2.18927i) q^{82} +(9.69727 - 5.59872i) q^{83} +(0.233782 + 1.13817i) q^{84} +(0.0905531 - 0.0522808i) q^{85} +(-0.794309 + 0.301787i) q^{86} +(3.50641 - 6.07327i) q^{87} +(1.96226 + 3.09074i) q^{88} -3.69655 q^{89} +(0.0169119 + 0.0445126i) q^{90} +3.77799i q^{91} +(-4.40794 + 13.2563i) q^{92} +(-4.12899 + 7.15162i) q^{93} +(0.0840207 + 0.0136030i) q^{94} +(-0.0858480 - 0.148693i) q^{95} +(-1.37024 - 5.48839i) q^{96} +(-9.48849 + 5.47818i) q^{97} +(-7.30203 - 5.95463i) q^{98} +(0.647185 - 1.12096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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