LMFDB - Embedded newform 804.2.j.b.775.6

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			775.6
Character	$\chi$	$=$	804.775
Dual form			804.2.j.b.499.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09599 - 0.893755i) q^{2} +1.00000 q^{3} +(0.402402 + 1.95910i) q^{4} +0.0336703i q^{5} +(-1.09599 - 0.893755i) q^{6} +(-0.290483 - 0.503131i) q^{7} +(1.30993 - 2.50681i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.09599 - 0.893755i) q^{2} +1.00000 q^{3} +(0.402402 + 1.95910i) q^{4} +0.0336703i q^{5} +(-1.09599 - 0.893755i) q^{6} +(-0.290483 - 0.503131i) q^{7} +(1.30993 - 2.50681i) q^{8} +1.00000 q^{9} +(0.0300931 - 0.0369025i) q^{10} +(-0.647185 - 1.12096i) q^{11} +(0.402402 + 1.95910i) q^{12} +(-5.63171 - 3.25147i) q^{13} +(-0.131309 + 0.811049i) q^{14} +0.0336703i q^{15} +(-3.67614 + 1.57669i) q^{16} +(1.55273 - 2.68940i) q^{17} +(-1.09599 - 0.893755i) q^{18} +(-4.41614 - 2.54966i) q^{19} +(-0.0659636 + 0.0135490i) 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} +(3.26630 + 8.59696i) q^{26} +1.00000 q^{27} +(0.868793 - 0.771546i) q^{28} +(-3.50641 - 6.07327i) q^{29} +(0.0300931 - 0.0369025i) q^{30} +(-4.12899 - 7.15162i) q^{31} +(5.43821 + 1.55753i) q^{32} +(-0.647185 - 1.12096i) q^{33} +(-4.10545 + 1.55981i) q^{34} +(0.0169406 - 0.00978066i) q^{35} +(0.402402 + 1.95910i) q^{36} +(-1.39784 + 2.42113i) q^{37} +(2.56129 + 6.74137i) 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} +(1.93564 - 1.71898i) q^{44} +0.0336703i q^{45} +(-3.50842 - 9.23423i) q^{46} +(0.0521219 - 0.0300926i) q^{47} +(-3.67614 + 1.57669i) q^{48} +(3.33124 - 5.76988i) q^{49} +(-5.47872 - 4.46776i) q^{50} +(1.55273 - 2.68940i) q^{51} +(4.10374 - 12.3415i) q^{52} -9.39508i q^{53} +(-1.09599 - 0.893755i) q^{54} +(0.0377430 - 0.0217910i) q^{55} +(-1.64177 + 0.0691207i) q^{56} +(-4.41614 - 2.54966i) q^{57} +(-1.58502 + 9.79013i) q^{58} +12.8681i q^{59} +(-0.0659636 + 0.0135490i) 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} +(3.69592 - 1.40421i) q^{74} +4.99887 q^{75} +(3.21798 - 9.67766i) q^{76} +(-0.375993 + 0.651238i) q^{77} +(3.26630 + 8.59696i) q^{78} +(7.77159 + 13.4608i) q^{79} +(-0.0530878 - 0.123777i) q^{80} +1.00000 q^{81} +(-13.5224 - 2.18927i) q^{82} +(-9.69727 - 5.59872i) q^{83} +(0.868793 - 0.771546i) q^{84} +(0.0905531 + 0.0522808i) q^{85} +(0.658509 + 0.536998i) q^{86} +(-3.50641 - 6.07327i) q^{87} +(-3.65779 + 0.153998i) q^{88} -3.69655 q^{89} +(0.0300931 - 0.0369025i) 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} +(5.43821 + 1.55753i) q^{96} +(-9.48849 - 5.47818i) q^{97} +(-8.80787 + 3.34643i) 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} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 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} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) $ 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * 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 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.09599	−	0.893755i	−0.774984	−	0.631981i
$2$	−1.09599	−	0.893755i	−0.774984	−	0.631981i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.402402	+	1.95910i	0.201201	+	0.979550i
$5$			0.0336703i			0.0150578i	0.999972	+	0.00752892i	$0.00239655\pi$
$5$			0.0336703i			0.0150578i	−0.999972	+	0.00752892i	$0.997603\pi$
$6$	−1.09599	−	0.893755i	−0.447437	−	0.364874i
$7$	−0.290483	−	0.503131i	−0.109792	−	0.190166i	0.805894	−	0.592060i	$-0.201685\pi$
$7$	−0.290483	−	0.503131i	−0.109792	−	0.190166i	−0.915686	+	0.401894i	$0.868352\pi$
$8$	1.30993	−	2.50681i	0.463129	−	0.886291i
$9$	1.00000			0.333333
$10$	0.0300931	−	0.0369025i	0.00951626	−	0.0116696i
$11$	−0.647185	−	1.12096i	−0.195134	−	0.337982i	0.751811	−	0.659379i	$-0.229181\pi$
$11$	−0.647185	−	1.12096i	−0.195134	−	0.337982i	−0.946944	+	0.321398i	$0.895847\pi$
$12$	0.402402	+	1.95910i	0.116164	+	0.565543i
$13$	−5.63171	−	3.25147i	−1.56196	−	0.901795i	−0.997059	−	0.0766335i	$-0.975583\pi$
$13$	−5.63171	−	3.25147i	−1.56196	−	0.901795i	−0.564896	−	0.825162i	$-0.691084\pi$
$14$	−0.131309	+	0.811049i	−0.0350938	+	0.216762i
$15$			0.0336703i			0.00869365i
$16$	−3.67614	+	1.57669i	−0.919036	+	0.394173i
$17$	1.55273	−	2.68940i	0.376592	−	0.652276i	−0.613972	−	0.789328i	$-0.710429\pi$
$17$	1.55273	−	2.68940i	0.376592	−	0.652276i	0.990564	+	0.137052i	$0.0437627\pi$
$18$	−1.09599	−	0.893755i	−0.258328	−	0.210660i
$19$	−4.41614	−	2.54966i	−1.01313	−	0.584933i	−0.101026	−	0.994884i	$-0.532212\pi$
$19$	−4.41614	−	2.54966i	−1.01313	−	0.584933i	−0.912107	+	0.409951i	$0.865546\pi$
$20$	−0.0659636	+	0.0135490i	−0.0147499	+	0.00302965i
$21$	−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	$-0.0736745\pi$
$23$	6.04917	+	3.49249i	1.26134	+	0.728235i	0.288006	+	0.957629i	$0.407008\pi$
$24$	1.30993	−	2.50681i	0.267388	−	0.511700i
$25$	4.99887			0.999773
$26$	3.26630	+	8.59696i	0.640574	+	1.68600i
$27$	1.00000			0.192450
$28$	0.868793	−	0.771546i	0.164187	−	0.145809i
$29$	−3.50641	−	6.07327i	−0.651123	−	1.12778i	−0.982851	−	0.184403i	$-0.940965\pi$
$29$	−3.50641	−	6.07327i	−0.651123	−	1.12778i	0.331728	−	0.943375i	$-0.392369\pi$
$30$	0.0300931	−	0.0369025i	0.00549421	−	0.00673744i
$31$	−4.12899	−	7.15162i	−0.741588	−	1.28447i	−0.951772	−	0.306807i	$-0.900740\pi$
$31$	−4.12899	−	7.15162i	−0.741588	−	1.28447i	0.210184	−	0.977662i	$-0.432594\pi$
$32$	5.43821	+	1.55753i	0.961348	+	0.275335i
$33$	−0.647185	−	1.12096i	−0.112661	−	0.195134i
$34$	−4.10545	+	1.55981i	−0.704078	+	0.267505i
$35$	0.0169406	−	0.00978066i	0.00286348	−	0.00165323i
$36$	0.402402	+	1.95910i	0.0670671	+	0.326517i
$37$	−1.39784	+	2.42113i	−0.229803	+	0.398031i	−0.957750	−	0.287603i	$-0.907142\pi$
$37$	−1.39784	+	2.42113i	−0.229803	+	0.398031i	0.727946	+	0.685634i	$0.240475\pi$
$38$	2.56129	+	6.74137i	0.415496	+	1.09359i
$39$	−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	0.327963	−	0.944691i	$-0.393638\pi$
$41$	8.38854	−	4.84313i	1.31007	−	0.756369i	0.982107	+	0.188321i	$0.0603047\pi$
$42$	−0.131309	+	0.811049i	−0.0202614	+	0.125148i
$43$	−0.600833			−0.0916262			−0.0458131	−	0.998950i	$-0.514588\pi$
$43$	−0.600833			−0.0916262			−0.0458131	+	0.998950i	$0.514588\pi$
$44$	1.93564	−	1.71898i	0.291809	−	0.259146i
$45$			0.0336703i			0.00501928i
$46$	−3.50842	−	9.23423i	−0.517288	−	1.36151i
$47$	0.0521219	−	0.0300926i	0.00760277	−	0.00438946i	−0.496194	−	0.868212i	$-0.665269\pi$
$47$	0.0521219	−	0.0300926i	0.00760277	−	0.00438946i	0.503797	+	0.863822i	$0.331936\pi$
$48$	−3.67614	+	1.57669i	−0.530606	+	0.227576i
$49$	3.33124	−	5.76988i	0.475891	−	0.824268i
$50$	−5.47872	−	4.46776i	−0.774809	−	0.631837i
$51$	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	$-0.776750\pi$
$53$		−	9.39508i		−	1.29051i	0.763966	−	0.645257i	$-0.223250\pi$
$54$	−1.09599	−	0.893755i	−0.149146	−	0.121625i
$55$	0.0377430	−	0.0217910i	0.00508927	−	0.00293829i
$56$	−1.64177	+	0.0691207i	−0.219390	+	0.00923664i
$57$	−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	$0.683932\pi$
$60$	−0.0659636	+	0.0135490i	−0.00851586	+	0.00174917i
$61$	−3.76809	−	2.17551i	−0.482455	−	0.278545i	0.238984	−	0.971023i	$-0.423186\pi$
$61$	−3.76809	−	2.17551i	−0.482455	−	0.278545i	−0.721439	+	0.692478i	$0.756519\pi$
$62$	−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	$-0.538158\pi$
$71$	5.73337	−	3.31016i	0.680426	−	0.392844i	0.800015	+	0.599979i	$0.204825\pi$
$72$	1.30993	−	2.50681i	0.154376	−	0.295430i
$73$	1.38269	−	2.39489i	0.161832	−	0.280301i	−0.773694	−	0.633560i	$-0.781593\pi$
$73$	1.38269	−	2.39489i	0.161832	−	0.280301i	0.935526	+	0.353259i	$0.114927\pi$
$74$	3.69592	−	1.40421i	0.429642	−	0.163236i
$75$	4.99887			0.577219
$76$	3.21798	−	9.67766i	0.369127	−	1.11010i
$77$	−0.375993	+	0.651238i	−0.0428483	+	0.0742155i
$78$	3.26630	+	8.59696i	0.369835	+	0.973414i
$79$	7.77159	+	13.4608i	0.874372	+	1.51446i	0.857430	+	0.514601i	$0.172060\pi$
$79$	7.77159	+	13.4608i	0.874372	+	1.51446i	0.0169424	+	0.999856i	$0.494607\pi$
$80$	−0.0530878	−	0.123777i	−0.00593539	−	0.0138387i
$81$	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	$-0.543991\pi$
$83$	−9.69727	−	5.59872i	−1.06441	−	0.614539i	−0.926650	+	0.375926i	$0.877325\pi$
$84$	0.868793	−	0.771546i	0.0947931	−	0.0841826i
$85$	0.0905531	+	0.0522808i	0.00982186	+	0.00567065i
$86$	0.658509	+	0.536998i	0.0710089	+	0.0579060i
$87$	−3.50641	−	6.07327i	−0.375926	−	0.651123i
$88$	−3.65779	+	0.153998i	−0.389922	+	0.0164163i
$89$	−3.69655			−0.391833			−0.195917	−	0.980621i	$-0.562768\pi$
$89$	−3.69655			−0.391833			−0.195917	+	0.980621i	$0.562768\pi$
$90$	0.0300931	−	0.0369025i	0.00317209	−	0.00388986i
$91$			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
$96$	5.43821	+	1.55753i	0.555035	+	0.158965i
$97$	−9.48849	−	5.47818i	−0.963410	−	0.556225i	−0.0661894	−	0.997807i	$-0.521084\pi$
$97$	−9.48849	−	5.47818i	−0.963410	−	0.556225i	−0.897221	+	0.441582i	$0.854417\pi$
$98$	−8.80787	+	3.34643i	−0.889730	+	0.338041i
$99$	−0.647185	−	1.12096i	−0.0650446	−	0.112661i
$100$	2.01156	+	9.79328i	0.201156	+	0.979328i
$101$	−1.66284	+	0.960039i	−0.165458	+	0.0955275i	−0.580443	−	0.814301i	$-0.697120\pi$
$101$	−1.66284	+	0.960039i	−0.165458	+	0.0955275i	0.414984	+	0.909829i	$0.363787\pi$
$102$	−4.10545	+	1.55981i	−0.406500	+	0.154444i
$103$	−14.2972	+	8.25451i	−1.40875	+	0.813341i	−0.995268	−	0.0971715i	$-0.969020\pi$
$103$	−14.2972	+	8.25451i	−1.40875	+	0.813341i	−0.413481	+	0.910513i	$0.635687\pi$
$104$	−15.5279	+	9.85844i	−1.52264	+	0.966700i
$105$	0.0169406	−	0.00978066i	0.00165323	−	0.000954495i
$106$	−8.39691	+	10.2969i	−0.815580	+	1.00013i
$107$		−	10.4831i		−	1.01344i	−0.862112	−	0.506718i	$-0.830858\pi$
$107$		−	10.4831i		−	1.01344i	0.862112	−	0.506718i	$-0.169142\pi$
$108$	0.402402	+	1.95910i	0.0387212	+	0.188514i
$109$		−	10.9590i		−	1.04968i	−0.851200	−	0.524842i	$-0.824124\pi$
$109$		−	10.9590i		−	1.04968i	0.851200	−	0.524842i	$-0.175876\pi$
$110$	−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	−0.440734	−	0.897638i	$-0.645282\pi$
$113$	1.23603	−	0.713621i	0.116276	−	0.0671318i	0.557010	+	0.830506i	$0.311949\pi$
$114$	2.56129	+	6.74137i	0.239887	+	0.631387i
$115$	−0.117593	+	0.203678i	−0.0109656	+	0.0189930i
$116$	10.4872	−	9.31330i	0.973708	−	0.864718i
$117$	−5.63171	−	3.25147i	−0.520652	−	0.300598i
$118$	11.5010	−	14.1034i	1.05875	−	1.29832i
$119$	−1.80416			−0.165387
$120$	0.0844051	+	0.0441057i	0.00770510	+	0.00402628i
$121$	4.66230	−	8.07534i	0.423846	−	0.734122i
$122$	2.18543	+	5.75210i	0.197860	+	0.520770i
$123$	8.38854	−	4.84313i	0.756369	−	0.436690i
$124$	12.3492	−	10.9669i	1.10899	−	0.984859i
$125$			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	$-0.830926\pi$
$127$	−9.63148	+	5.56074i	−0.854655	+	0.493435i	0.00756354	+	0.999971i	$0.497592\pi$
$128$	−0.863010	+	11.2807i	−0.0762800	+	0.997086i
$129$	−0.600833			−0.0529004
$130$	−0.289463	+	0.109977i	−0.0253876	+	0.00964565i
$131$			15.9231i			1.39120i	0.718427	+	0.695602i	$0.244862\pi$
$131$			15.9231i			1.39120i	−0.718427	+	0.695602i	$0.755138\pi$
$132$	1.93564	−	1.71898i	0.168476	−	0.149618i
$133$			2.96253i			0.256884i
$134$	10.7677	−	4.24929i	0.930188	−	0.367083i
$135$			0.0336703i			0.00289788i
$136$	−4.70786	−	7.41531i	−0.403696	−	0.635857i
$137$			15.1721i			1.29624i	0.761537	+	0.648121i	$0.224445\pi$
$137$			15.1721i			1.29624i	−0.761537	+	0.648121i	$0.775555\pi$
$138$	−3.50842	−	9.23423i	−0.298656	−	0.786069i
$139$	20.0111			1.69732			0.848660	−	0.528939i	$-0.177410\pi$
$139$	20.0111			1.69732			0.848660	+	0.528939i	$0.177410\pi$
$140$	0.0259782	+	0.0292526i	0.00219556	+	0.00247229i
$141$	0.0521219	−	0.0300926i	0.00438946	−	0.00253426i
$142$	−9.24221	−	1.49631i	−0.775589	−	0.125568i
$143$			8.41721i			0.703883i
$144$	−3.67614	+	1.57669i	−0.306345	+	0.131391i
$145$	0.204489	−	0.118062i	0.0169819	−	0.00980450i
$146$	−3.65586	+	1.38900i	−0.302562	+	0.114954i
$147$	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	$0.231767\pi$
$150$	−5.47872	−	4.46776i	−0.447336	−	0.364791i
$151$	−14.7006	−	8.48742i	−1.19632	−	0.690697i	−0.236588	−	0.971610i	$-0.576029\pi$
$151$	−14.7006	−	8.48742i	−1.19632	−	0.690697i	−0.959733	+	0.280913i	$0.909363\pi$
$152$	−12.1763	+	7.73056i	−0.987632	+	0.627031i
$153$	1.55273	−	2.68940i	0.125531	−	0.217425i
$154$	0.994133	−	0.377707i	0.0801095	−	0.0304365i
$155$	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	0.493106	+	0.869969i	$0.335861\pi$
$157$	−6.35096	+	11.0002i	−0.506862	+	0.877911i	−0.999968	+	0.00794180i	$0.997472\pi$
$158$	3.51304	−	21.6988i	0.279483	−	1.72627i
$159$		−	9.39508i		−	0.745079i
$160$	−0.0524426	+	0.183106i	−0.00414595	+	0.0144758i
$161$		−	4.05804i		−	0.319818i
$162$	−1.09599	−	0.893755i	−0.0861094	−	0.0702201i
$163$	16.5094	−	9.53171i	1.29312	−	0.746581i	0.313911	−	0.949452i	$-0.398361\pi$
$163$	16.5094	−	9.53171i	1.29312	−	0.746581i	0.979205	+	0.202871i	$0.0650273\pi$
$164$	12.8637	+	14.4851i	1.00449	+	1.13110i
$165$	0.0377430	−	0.0217910i	0.00293829	−	0.00169642i
$166$	5.62425	+	14.8031i	0.436527	+	1.14895i
$167$	−4.42047	+	2.55216i	−0.342066	+	0.197492i	−0.661185	−	0.750222i	$-0.729946\pi$
$167$	−4.42047	+	2.55216i	−0.342066	+	0.197492i	0.319119	+	0.947715i	$0.396613\pi$
$168$	−1.64177	+	0.0691207i	−0.126665	+	0.00533278i
$169$	14.6441	+	25.3643i	1.12647	+	1.95110i
$170$	−0.0525193	−	0.138232i	−0.00402804	−	0.0106019i
$171$	−4.41614	−	2.54966i	−0.337711	−	0.194978i
$172$	−0.241777	−	1.17709i	−0.0184353	−	0.0897525i
$173$	−1.42698	+	2.47160i	−0.108491	+	0.187913i	−0.915159	−	0.403092i	$-0.867935\pi$
$173$	−1.42698	+	2.47160i	−0.108491	+	0.187913i	0.806668	+	0.591005i	$0.201269\pi$
$174$	−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
$178$	4.05139	+	3.30381i	0.303664	+	0.247631i
$179$	9.47559			0.708239			0.354119	−	0.935200i	$-0.384781\pi$
$179$	9.47559			0.708239			0.354119	+	0.935200i	$0.384781\pi$
$180$	−0.0659636	+	0.0135490i	−0.00491663	+	0.00100988i
$181$	10.0742	+	17.4490i	0.748807	+	1.29697i	0.948395	+	0.317091i	$0.102706\pi$
$181$	10.0742	+	17.4490i	0.748807	+	1.29697i	−0.199588	+	0.979880i	$0.563960\pi$
$182$	3.37660	−	4.14065i	0.250290	−	0.306925i
$183$	−3.76809	−	2.17551i	−0.278545	−	0.160818i
$184$	16.6790	−	10.5892i	1.22959	−	0.780647i
$185$	−0.0815202	−	0.0470657i	−0.00599348	−	0.00346034i
$186$	−1.86645	+	11.5284i	−0.136855	+	0.845306i
$187$	−4.01961			−0.293943
$188$	0.0799284	+	0.0900027i	0.00582938	+	0.00656412i
$189$	−0.290483	−	0.503131i	−0.0211295	−	0.0365974i
$190$	−0.226984	+	0.0862395i	−0.0164672	+	0.00625647i
$191$	10.6294	−	18.4107i	0.769117	−	1.33215i	−0.168925	−	0.985629i	$-0.554030\pi$
$191$	10.6294	−	18.4107i	0.769117	−	1.33215i	0.938042	−	0.346521i	$-0.112637\pi$
$192$	−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	$0.199869\pi$
$194$	5.50317	+	14.4844i	0.395104	+	1.03992i
$195$	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	−0.661544	−	0.749907i	$-0.730098\pi$
$197$	−4.81251	+	2.77851i	−0.342877	+	0.197960i	0.318666	+	0.947867i	$0.396765\pi$
$198$	−0.292552	+	1.80699i	−0.0207907	+	0.128417i
$199$	0.320038	+	0.184774i	0.0226869	+	0.0130983i	0.511301	−	0.859402i	$-0.329164\pi$
$199$	0.320038	+	0.184774i	0.0226869	+	0.0130983i	−0.488614	+	0.872500i	$0.662497\pi$
$200$	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
$208$	25.8296	+	3.07340i	1.79096	+	0.213102i
$209$			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	$-0.338813\pi$
$211$	−0.433107	−	0.250054i	−0.0298163	−	0.0172145i	−0.514834	+	0.857290i	$0.672146\pi$
$212$	18.4059	−	3.78060i	1.26412	−	0.259653i
$213$	5.73337	−	3.31016i	0.392844	−	0.226809i
$214$	−9.36930	+	11.4894i	−0.640472	+	0.785398i
$215$		−	0.0202303i		−	0.00137969i
$216$	1.30993	−	2.50681i	0.0891292	−	0.170567i
$217$	−2.39880	+	4.15485i	−0.162841	+	0.282049i
$218$	−9.79469	+	12.0110i	−0.663380	+	0.813489i
$219$	1.38269	−	2.39489i	0.0934335	−	0.161832i
$220$	0.0578785	+	0.0651737i	0.00390217	+	0.00439401i
$221$	−17.4890	+	10.0973i	−1.17644	+	0.679217i
$222$	3.69592	−	1.40421i	0.248054	−	0.0942446i
$223$			6.50721i			0.435755i	0.975976	+	0.217877i	$0.0699133\pi$
$223$			6.50721i			0.435755i	−0.975976	+	0.217877i	$0.930087\pi$
$224$	−0.796065	−	3.18857i	−0.0531893	−	0.213045i
$225$	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	$-0.484354\pi$
$227$	14.1426	−	8.16526i	0.938680	−	0.541947i	0.889546	+	0.456845i	$0.151021\pi$
$228$	3.21798	−	9.67766i	0.213116	−	0.640919i
$229$	−3.26867	−	1.88717i	−0.216000	−	0.124707i	0.388097	−	0.921619i	$-0.373133\pi$
$229$	−3.26867	−	1.88717i	−0.216000	−	0.124707i	−0.604097	+	0.796911i	$0.706466\pi$
$230$	0.310920	−	0.118130i	0.0205014	−	0.00778924i
$231$	−0.375993	+	0.651238i	−0.0247385	+	0.0428483i
$232$	−19.8177	+	0.834353i	−1.30109	+	0.0547779i
$233$	8.93565	−	5.15900i	0.585394	−	0.337977i	−0.177880	−	0.984052i	$-0.556924\pi$
$233$	8.93565	−	5.15900i	0.585394	−	0.337977i	0.763274	+	0.646075i	$0.223591\pi$
$234$	3.26630	+	8.59696i	0.213525	+	0.562001i
$235$	0.00101323	+	0.00175496i	6.60957e−5	+	0.000114481i
$236$	−25.2100	+	5.17817i	−1.64103	+	0.337070i
$237$	7.77159	+	13.4608i	0.504819	+	0.874372i
$238$	1.97735	+	1.61248i	0.128173	+	0.104522i
$239$	0.0287339	+	0.0497686i	0.00185864	+	0.00321926i	0.866953	−	0.498390i	$-0.166075\pi$
$239$	0.0287339	+	0.0497686i	0.00185864	+	0.00321926i	−0.865095	+	0.501609i	$0.832742\pi$
$240$	−0.0530878	−	0.123777i	−0.00342680	−	0.00798977i
$241$	−27.0880			−1.74489			−0.872447	−	0.488709i	$-0.837468\pi$
$241$	−27.0880			−1.74489			−0.872447	+	0.488709i	$0.837468\pi$
$242$	−12.3272	+	4.68356i	−0.792425	+	0.301071i
$243$	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
$248$	−23.3364	+	0.982497i	−1.48186	+	0.0623886i
$249$	−9.69727	−	5.59872i	−0.614539	−	0.354804i
$250$	0.300896	−	0.368983i	0.0190304	−	0.0233365i
$251$	−5.47501	+	9.48300i	−0.345580	+	0.598562i	−0.985459	−	0.169914i	$-0.945651\pi$
$251$	−5.47501	+	9.48300i	−0.345580	+	0.598562i	0.639879	+	0.768476i	$0.278984\pi$
$252$	0.868793	−	0.771546i	0.0547288	−	0.0486028i
$253$		−	9.04115i		−	0.568413i
$254$	15.5260	+	2.51366i	0.974186	+	0.157721i
$255$	0.0905531	+	0.0522808i	0.00567065	+	0.00327395i
$256$	11.0281	−	11.5923i	0.689255	−	0.724519i
$257$	−1.67704	−	2.90472i	−0.104611	−	0.181192i	0.808968	−	0.587852i	$-0.200026\pi$
$257$	−1.67704	−	2.90472i	−0.104611	−	0.181192i	−0.913579	+	0.406661i	$0.866693\pi$
$258$	0.658509	+	0.536998i	0.0409970	+	0.0334320i
$259$	1.62419			0.100922
$260$	0.415542	+	0.138174i	0.0257708	+	0.00856921i
$261$	−3.50641	−	6.07327i	−0.217041	−	0.375926i
$262$	14.2313	−	17.4516i	0.879214	−	1.07816i
$263$		−	17.4454i		−	1.07573i	−0.843030	−	0.537866i	$-0.819231\pi$
$263$		−	17.4454i		−	1.07573i	0.843030	−	0.537866i	$-0.180769\pi$
$264$	−3.65779	+	0.153998i	−0.225122	+	0.00947795i
$265$	0.316336			0.0194324
$266$	2.64778	−	3.24692i	0.162346	−	0.199081i
$267$	−3.69655			−0.226225
$268$	−15.5992	−	4.96651i	−0.952870	−	0.303378i
$269$	−1.54282			−0.0940675			−0.0470337	−	0.998893i	$-0.514977\pi$
$269$	−1.54282			−0.0940675			−0.0470337	+	0.998893i	$0.514977\pi$
$270$	0.0300931	−	0.0369025i	0.00183140	−	0.00224581i
$271$	−3.75720			−0.228234			−0.114117	−	0.993467i	$-0.536404\pi$
$271$	−3.75720			−0.228234			−0.114117	+	0.993467i	$0.536404\pi$
$272$	−1.46769	+	12.3348i	−0.0889917	+	0.747907i
$273$			3.77799i			0.228654i
$274$	13.5602	−	16.6285i	0.819200	−	1.00457i
$275$	−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	$0.255959\pi$
$278$	−21.9320	−	17.8850i	−1.31540	−	1.07267i
$279$	−4.12899	−	7.15162i	−0.247196	−	0.428156i
$280$	−0.00232732	−	0.0552788i	−0.000139084	−	0.00330354i
$281$	20.2191	+	11.6735i	1.20617	+	0.696383i	0.961921	−	0.273329i	$-0.0881246\pi$
$281$	20.2191	+	11.6735i	1.20617	+	0.696383i	0.244251	+	0.969712i	$0.421458\pi$
$282$	−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	$0.617139\pi$
$284$	8.79206	+	9.90023i	0.521713	+	0.587470i
$285$	0.0858480	−	0.148693i	0.00508520	−	0.00880782i
$286$	7.52293	−	9.22521i	0.444840	−	0.545498i
$287$	−4.87346	−	2.81369i	−0.287671	−	0.166087i
$288$	5.43821	+	1.55753i	0.320449	+	0.0917783i
$289$	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	$0.674371\pi$
$294$	−8.80787	+	3.34643i	−0.513686	+	0.195168i
$295$	−0.433274			−0.0252262
$296$	4.23824	+	6.67561i	0.246343	+	0.388012i
$297$	−0.647185	−	1.12096i	−0.0375535	−	0.0650446i
$298$	−19.9719	−	16.2866i	−1.15694	−	0.943457i
$299$	−22.7115	−	39.3374i	−1.31344	−	2.27494i
$300$	2.01156	+	9.79328i	0.116137	+	0.565415i
$301$	0.174532	+	0.302298i	0.0100598	+	0.0174242i
$302$	8.52613	+	22.4409i	0.490624	+	1.29133i
$303$	−1.66284	+	0.960039i	−0.0955275	+	0.0551528i
$304$	20.2544	+	2.41002i	1.16167	+	0.138224i
$305$	0.0732501	−	0.126873i	0.00419429	−	0.00726473i
$306$	−4.10545	+	1.55981i	−0.234693	+	0.0891683i
$307$	16.3376	+	9.43255i	0.932439	+	0.538344i	0.887582	−	0.460650i	$-0.152384\pi$
$307$	16.3376	+	9.43255i	0.932439	+	0.538344i	0.0448568	+	0.998993i	$0.485717\pi$
$308$	−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	$-0.0939571\pi$
$311$	33.7450			1.91350			0.956751	+	0.290907i	$0.0939571\pi$
$312$	−15.5279	+	9.85844i	−0.879096	+	0.558124i
$313$		−	2.93093i		−	0.165666i	−0.996563	−	0.0828331i	$-0.973603\pi$
$313$		−	2.93093i		−	0.165666i	0.996563	−	0.0828331i	$-0.0263968\pi$
$314$	16.7921	−	6.37993i	0.947633	−	0.360040i
$315$	0.0169406	−	0.00978066i	0.000954495	−	0.000551078i
$316$	−23.2437	+	20.6420i	−1.30756	+	1.16120i
$317$	−3.65620	+	6.33272i	−0.205352	+	0.355681i	−0.950245	−	0.311504i	$-0.899167\pi$
$317$	−3.65620	+	6.33272i	−0.205352	+	0.355681i	0.744892	+	0.667185i	$0.232501\pi$
$318$	−8.39691	+	10.2969i	−0.470875	+	0.577424i
$319$	−4.53859	+	7.86107i	−0.254112	+	0.440135i
$320$	0.221129	−	0.153812i	0.0123615	−	0.00859838i
$321$		−	10.4831i		−	0.585108i
$322$	−3.62689	+	4.44758i	−0.202119	+	0.247854i
$323$	−13.7141	+	7.91786i	−0.763075	+	0.440561i
$324$	0.402402	+	1.95910i	0.0223557	+	0.108839i
$325$	−28.1522	−	16.2537i	−1.56160	−	0.901591i
$326$	−26.6132	−	4.30868i	−1.47397	−	0.238636i
$327$		−	10.9590i		−	0.606035i
$328$	−1.15243	−	27.3726i	−0.0636321	−	1.51140i
$329$	−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	$-0.301495\pi$
$331$	−7.47789	−	12.9521i	−0.411022	−	0.711911i	−0.995002	+	0.0998572i	$0.968161\pi$
$332$	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	0.638360	−	0.769738i	$-0.279613\pi$
$337$	5.34071	+	3.08346i	0.290927	+	0.167967i	−0.347433	+	0.937705i	$0.612946\pi$
$338$	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
$342$	2.56129	+	6.74137i	0.138499	+	0.364531i
$343$	−7.93743			−0.428581
$344$	−0.787047	+	1.50618i	−0.0424348	+	0.0812075i
$345$	−0.117593	+	0.203678i	−0.00633101	+	0.0109656i
$346$	3.77297	−	1.43349i	0.202836	−	0.0770649i
$347$	1.38541	+	2.39960i	0.0743727	+	0.128817i	0.900813	−	0.434207i	$-0.142971\pi$
$347$	1.38541	+	2.39960i	0.0743727	+	0.128817i	−0.826441	+	0.563024i	$0.809638\pi$
$348$	10.4872	−	9.31330i	0.562171	−	0.499245i
$349$	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
$352$	−1.77360	−	7.10401i	−0.0945333	−	0.378645i
$353$	−25.1526	−	14.5218i	−1.33874	−	0.772919i	−0.352116	−	0.935956i	$-0.614538\pi$
$353$	−25.1526	−	14.5218i	−1.33874	−	0.772919i	−0.986620	+	0.163037i	$0.947871\pi$
$354$	11.5010	−	14.1034i	0.611269	−	0.749586i
$355$	0.111454	+	0.193045i	0.00591538	+	0.0102457i
$356$	−1.48750	−	7.24190i	−0.0788373	−	0.383820i
$357$	−1.80416			−0.0954864
$358$	−10.3852	−	8.46886i	−0.548874	−	0.447593i
$359$			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
$364$	−7.40145	+	1.52027i	−0.387942	+	0.0796838i
$365$	0.0806368	+	0.0465557i	0.00422072	+	0.00243683i
$366$	2.18543	+	5.75210i	0.114234	+	0.300667i
$367$	−1.44405	−	2.50118i	−0.0753790	−	0.130560i	0.825872	−	0.563858i	$-0.190683\pi$
$367$	−1.44405	−	2.50118i	−0.0753790	−	0.130560i	−0.901251	+	0.433297i	$0.857350\pi$
$368$	−27.7442	−	3.30122i	−1.44627	−	0.172088i
$369$	8.38854	−	4.84313i	0.436690	−	0.252123i
$370$	0.0472803	+	0.124443i	0.00245799	+	0.00646947i
$371$	−4.72696	+	2.72911i	−0.245412	+	0.141688i
$372$	12.3492	−	10.9669i	0.640277	−	0.568609i
$373$	−17.1124	+	9.87985i	−0.886046	+	0.511559i	−0.872647	−	0.488351i	$-0.837599\pi$
$373$	−17.1124	+	9.87985i	−0.886046	+	0.511559i	−0.0133992	+	0.999910i	$0.504265\pi$
$374$	4.40546	+	3.59255i	0.227801	+	0.185766i
$375$			0.336665i			0.0173853i
$376$	−0.00716057	−	0.170079i	−0.000369278	−	0.00877115i
$377$			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	$-0.941827\pi$
$379$	−6.50776	+	11.2718i	−0.334281	+	0.578992i	0.649065	+	0.760733i	$0.275160\pi$
$380$	0.325850	+	0.108350i	0.0167158	+	0.00555826i
$381$	−9.63148	+	5.56074i	−0.493435	+	0.284885i
$382$	−28.1044	+	10.6779i	−1.43795	+	0.546328i
$383$	7.34539	−	12.7226i	0.375332	−	0.650094i	−0.615045	−	0.788492i	$-0.710862\pi$
$383$	7.34539	−	12.7226i	0.375332	−	0.650094i	0.990377	+	0.138399i	$0.0441955\pi$
$384$	−0.863010	+	11.2807i	−0.0440403	+	0.575668i
$385$	−0.0219274	−	0.0126598i	−0.00111752	−	0.000645203i
$386$	−24.6436	−	20.0962i	−1.25432	−	1.02287i
$387$	−0.600833			−0.0305421
$388$	6.91412	−	20.7933i	0.351011	−	1.05562i
$389$	1.64530	−	2.84974i	0.0834200	−	0.144488i	−0.821297	−	0.570501i	$-0.806749\pi$
$389$	1.64530	−	2.84974i	0.0834200	−	0.144488i	0.904717	+	0.426013i	$0.140082\pi$
$390$	−0.289463	+	0.109977i	−0.0146575	+	0.00556892i
$391$	18.7854	−	10.8458i	0.950019	−	0.548494i
$392$	−10.1003	−	15.9089i	−0.510142	−	0.803520i
$393$			15.9231i			0.803212i
$394$	7.75778	+	1.25599i	0.390832	+	0.0632757i
$395$	−0.453229	+	0.261672i	−0.0228044	+	0.0131662i
$396$	1.93564	−	1.71898i	0.0972696	−	0.0863818i
$397$	−9.67527			−0.485588			−0.242794	−	0.970078i	$-0.578064\pi$
$397$	−9.67527			−0.485588			−0.242794	+	0.970078i	$0.578064\pi$
$398$	−0.185617	−	0.488547i	−0.00930413	−	0.0244887i
$399$			2.96253i			0.148312i
$400$	−18.3766	+	7.88168i	−0.918828	+	0.394084i
$401$		−	23.3294i		−	1.16501i	−0.812826	−	0.582506i	$-0.802072\pi$
$401$		−	23.3294i		−	1.16501i	0.812826	−	0.582506i	$-0.197928\pi$
$402$	10.7677	−	4.24929i	0.537044	−	0.211935i
$403$			53.7011i			2.67504i
$404$	−2.54994	−	2.87134i	−0.126864	−	0.142855i
$405$			0.0336703i			0.00167309i
$406$	5.38614	−	2.04639i	0.267310	−	0.101561i
$407$	3.61864			0.179369
$408$	−4.70786	−	7.41531i	−0.233074	−	0.367112i
$409$	−13.9774	+	8.06985i	−0.691138	+	0.399029i	−0.804038	−	0.594578i	$-0.797319\pi$
$409$	−13.9774	+	8.06985i	−0.691138	+	0.399029i	0.112900	+	0.993606i	$0.463986\pi$
$410$	0.0737135	−	0.455302i	0.00364045	−	0.0224858i
$411$			15.1721i			0.748386i
$412$	−21.9247	−	24.6881i	−1.08015	−	1.21629i
$413$	6.47436	−	3.73797i	0.318582	−	0.183934i
$414$	−3.50842	−	9.23423i	−0.172429	−	0.453837i
$415$	0.188511	−	0.326510i	0.00925363	−	0.0160278i
$416$	−25.5622	−	26.4537i	−1.25329	−	1.29700i
$417$	20.0111			0.979948
$418$	5.89916	−	7.23401i	0.288537	−	0.353827i
$419$	28.3115	+	16.3457i	1.38311	+	0.798538i	0.992526	−	0.122030i	$-0.0389403\pi$
$419$	28.3115	+	16.3457i	1.38311	+	0.798538i	0.390582	+	0.920568i	$0.372274\pi$
$420$	0.0259782	+	0.0292526i	0.00126761	+	0.00142738i
$421$	11.3203	−	19.6073i	0.551716	−	0.955601i	−0.446435	−	0.894816i	$-0.647306\pi$
$421$	11.3203	−	19.6073i	0.551716	−	0.955601i	0.998151	−	0.0607843i	$-0.0193602\pi$
$422$	0.251195	+	0.661150i	0.0122280	+	0.0321843i
$423$	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
$428$	20.5374	−	4.21841i	0.992712	−	0.203905i
$429$			8.41721i			0.406387i
$430$	−0.0180809	+	0.0221722i	−0.000871939	+	0.00106924i
$431$	−18.2121	+	10.5148i	−0.877246	+	0.506478i	−0.869749	−	0.493494i	$-0.835720\pi$
$431$	−18.2121	+	10.5148i	−0.877246	+	0.506478i	−0.00749646	+	0.999972i	$0.502386\pi$
$432$	−3.67614	+	1.57669i	−0.176869	+	0.0758587i
$433$	8.01567	−	4.62785i	0.385209	−	0.222400i	−0.294873	−	0.955536i	$-0.595277\pi$
$433$	8.01567	−	4.62785i	0.385209	−	0.222400i	0.680082	+	0.733136i	$0.261944\pi$
$434$	6.34249	−	2.40974i	0.304449	−	0.115671i
$435$	0.204489	−	0.118062i	0.00980450	−	0.00566063i
$436$	21.4698	−	4.40994i	1.02822	−	0.211198i
$437$	−17.8093	−	30.8467i	−0.851936	−	1.47560i
$438$	−3.65586	+	1.38900i	−0.174684	+	0.0663688i
$439$	−7.01941	−	4.05266i	−0.335018	−	0.193423i	0.323049	−	0.946382i	$-0.395292\pi$
$439$	−7.01941	−	4.05266i	−0.335018	−	0.193423i	−0.658067	+	0.752960i	$0.728626\pi$
$440$	−0.00518518	−	0.123159i	−0.000247194	−	0.00587138i
$441$	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	−0.983451	−	0.181175i	$-0.942010\pi$
$443$	−13.6520	−	23.6460i	−0.648627	−	1.12346i	0.334824	−	0.942281i	$-0.391323\pi$
$444$	−5.30572	−	1.76424i	−0.251799	−	0.0837270i
$445$		−	0.124464i		−	0.00590016i
$446$	5.81585	−	7.13186i	0.275389	−	0.337703i
$447$	18.2226			0.861902
$448$	−1.97732	+	4.20614i	−0.0934195	+	0.198721i
$449$	11.1672	+	19.3421i	0.527012	+	0.912812i	0.999504	+	0.0314771i	$0.0100211\pi$
$449$	11.1672	+	19.3421i	0.527012	+	0.912812i	−0.472492	+	0.881335i	$0.656646\pi$
$450$	−5.47872	−	4.46776i	−0.258270	−	0.210612i
$451$	−10.8579	−	6.26880i	−0.511278	−	0.295186i
$452$	1.89543	+	2.13434i	0.0891537	+	0.100391i
$453$	−14.7006	−	8.48742i	−0.690697	−	0.398774i
$454$	−22.7980	−	3.69100i	−1.06996	−	0.173227i
$455$	−0.127206			−0.00596351
$456$	−12.1763	+	7.73056i	−0.570209	+	0.362017i
$457$	4.11035	+	7.11934i	0.192274	+	0.333029i	0.946004	−	0.324156i	$-0.105080\pi$
$457$	4.11035	+	7.11934i	0.192274	+	0.333029i	−0.753729	+	0.657185i	$0.771747\pi$
$458$	1.89577	+	4.98971i	0.0885836	+	0.233154i
$459$	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	$0.595106\pi$
$462$	0.994133	−	0.377707i	0.0462513	−	0.0175725i
$463$	−10.1530	+	17.5855i	−0.471849	+	0.817266i	−0.999481	−	0.0322069i	$-0.989746\pi$
$463$	−10.1530	+	17.5855i	−0.471849	+	0.817266i	0.527633	+	0.849473i	$0.323080\pi$
$464$	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	$-0.391058\pi$
$467$	−6.75063	−	3.89748i	−0.312382	−	0.180354i	−0.647992	+	0.761647i	$0.724391\pi$
$468$	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
$476$	−0.725999	−	3.53453i	−0.0332761	−	0.162005i
$477$		−	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	$-0.451689\pi$
$479$	−13.7726	−	7.95160i	−0.629285	−	0.363318i	−0.780475	+	0.625187i	$0.785023\pi$
$480$	−0.0524426	+	0.183106i	−0.00239366	+	0.00835762i
$481$	15.7444	−	9.09006i	0.717885	−	0.414471i
$482$	29.6883	+	24.2101i	1.35226	+	1.10274i
$483$		−	4.05804i		−	0.184647i
$484$	17.6965	+	5.88438i	0.804388	+	0.267472i
$485$	0.184452	−	0.319481i	0.00837555	−	0.0145069i
$486$	−1.09599	−	0.893755i	−0.0497153	−	0.0405416i
$487$	15.9471	−	27.6212i	0.722631	−	1.25163i	−0.237310	−	0.971434i	$-0.576266\pi$
$487$	15.9471	−	27.6212i	0.722631	−	1.25163i	0.959942	−	0.280200i	$-0.0904009\pi$
$488$	−10.3895	+	6.59613i	−0.470311	+	0.298593i
$489$	16.5094	−	9.53171i	0.746581	−	0.431039i
$490$	−0.112675	−	0.296564i	−0.00509016	−	0.0133974i
$491$		−	27.0586i		−	1.22114i	−0.791963	−	0.610569i	$-0.790941\pi$
$491$		−	27.0586i		−	1.22114i	0.791963	−	0.610569i	$-0.209059\pi$
$492$	12.8637	+	14.4851i	0.579942	+	0.653039i
$493$	−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
$498$	5.62425	+	14.8031i	0.252029	+	0.663345i
$499$	5.10385	−	8.84013i	0.228480	−	0.395739i	−0.728878	−	0.684644i	$-0.759958\pi$
$499$	5.10385	−	8.84013i	0.228480	−	0.395739i	0.957358	+	0.288905i	$0.0932912\pi$
$500$	−0.659561	+	0.135475i	−0.0294965	+	0.00605862i
$501$	−4.42047	+	2.55216i	−0.197492	+	0.114022i
$502$	14.4761	−	5.49998i	0.646098	−	0.245476i
$503$	−11.4439	−	19.8214i	−0.510257	−	0.883790i	−0.999929	−	0.0118841i	$-0.996217\pi$
$503$	−11.4439	−	19.8214i	−0.510257	−	0.883790i	0.489673	−	0.871906i	$-0.337116\pi$
$504$	−1.64177	+	0.0691207i	−0.0731300	+	0.00307888i
$505$	−0.0323249	−	0.0559883i	−0.00143844	−	0.00249145i
$506$	−8.08058	+	9.90904i	−0.359226	+	0.440511i
$507$	14.6441	+	25.3643i	0.650368	+	1.12647i
$508$	−14.7698	−	16.6314i	−0.655302	−	0.737898i
$509$	34.4774			1.52818			0.764091	−	0.645108i	$-0.223188\pi$
$509$	34.4774			1.52818			0.764091	+	0.645108i	$0.223188\pi$
$510$	−0.0525193	−	0.138232i	−0.00232559	−	0.00612101i
$511$	−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
$516$	−0.241777	−	1.17709i	−0.0106436	−	0.0518186i
$517$	−0.0674651	−	0.0389510i	−0.00296711	−	0.00171306i
$518$	−1.78010	−	1.45163i	−0.0782133	−	0.0637810i
$519$	−1.42698	+	2.47160i	−0.0626375	+	0.108491i
$520$	−0.331937	−	0.522831i	−0.0145564	−	0.0229277i
$521$		−	2.43259i		−	0.106574i	−0.998579	−	0.0532868i	$-0.983030\pi$
$521$		−	2.43259i		−	0.106574i	0.998579	−	0.0532868i	$-0.0169697\pi$
$522$	−1.58502	+	9.79013i	−0.0693746	+	0.428503i
$523$	−10.3927	−	6.00025i	−0.454443	−	0.262373i	0.255262	−	0.966872i	$-0.417838\pi$
$523$	−10.3927	−	6.00025i	−0.454443	−	0.262373i	−0.709705	+	0.704499i	$0.751172\pi$
$524$	−31.1949	+	6.40748i	−1.36275	+	0.279912i
$525$	−1.45209	−	2.51509i	−0.0633742	−	0.109767i
$526$	−15.5920	+	19.1201i	−0.679841	+	0.833675i
$527$	−25.6448			−1.11710
$528$	4.14655	+	3.10039i	0.180456	+	0.134927i
$529$	12.8950	+	22.3348i	0.560651	+	0.971076i
$530$	−0.346702	−	0.282727i	−0.0150598	−	0.0122809i
$531$			12.8681i			0.558429i
$532$	−5.80390	+	1.19213i	−0.251631	+	0.0516854i
$533$	−62.9891			−2.72836
$534$	4.05139	+	3.30381i	0.175321	+	0.142970i
$535$	0.352969			0.0152602
$536$	12.6577	+	19.3851i	0.546731	+	0.837308i
$537$	9.47559			0.408902
$538$	1.69092	+	1.37890i	0.0729008	+	0.0594488i
$539$	−8.62372			−0.371450
$540$	−0.0659636	+	0.0135490i	−0.00283862	+	0.000583057i
$541$		−	12.3771i		−	0.532132i	−0.963955	−	0.266066i	$-0.914276\pi$
$541$		−	12.3771i		−	0.532132i	0.963955	−	0.266066i	$-0.0857240\pi$
$542$	4.11787	+	3.35802i	0.176878	+	0.144239i
$543$	10.0742	+	17.4490i	0.432324	+	0.748807i
$544$	12.6329	−	12.2071i	0.541630	−	0.523375i
$545$	0.368994			0.0158060
$546$	3.37660	−	4.14065i	0.144505	−	0.177203i
$547$	2.98453	+	5.16936i	0.127609	+	0.221026i	0.922750	−	0.385399i	$-0.125936\pi$
$547$	2.98453	+	5.16936i	0.127609	+	0.221026i	−0.795141	+	0.606425i	$0.792603\pi$
$548$	−29.7237	+	6.10530i	−1.26973	+	0.260805i
$549$	−3.76809	−	2.17551i	−0.160818	−	0.0928485i
$550$	−1.46243	+	9.03289i	−0.0623580	+	0.385164i
$551$			35.7606i			1.52345i
$552$	16.6790	−	10.5892i	0.709904	−	0.450707i
$553$	4.51503	−	7.82026i	0.191999	−	0.332551i
$554$	−25.3092	−	20.6390i	−1.07528	−	0.876868i
$555$	−0.0815202	−	0.0470657i	−0.00346034	−	0.00199783i
$556$	8.05251	+	39.2038i	0.341503	+	1.66261i
$557$	0.755373	+	1.30835i	0.0320062	+	0.0554364i	0.881585	−	0.472026i	$-0.156477\pi$
$557$	0.755373	+	1.30835i	0.0320062	+	0.0554364i	−0.849579	+	0.527462i	$0.823144\pi$
$558$	−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
$562$	−11.7268	−	30.8650i	−0.494663	−	1.30196i
$563$	21.8950			0.922765			0.461382	−	0.887201i	$-0.347354\pi$
$563$	21.8950			0.922765			0.461382	+	0.887201i	$0.347354\pi$
$564$	0.0799284	+	0.0900027i	0.00336559	+	0.00378980i
$565$	0.0240279	+	0.0416175i	0.00101086	+	0.00175086i
$566$	28.0573	−	34.4061i	1.17934	−	1.44619i
$567$	−0.290483	−	0.503131i	−0.0121991	−	0.0211295i
$568$	−0.787657	−	18.7085i	−0.0330493	−	0.784993i
$569$	11.7957	+	20.4307i	0.494500	+	0.856500i	0.999980	−	0.00633879i	$-0.00201771\pi$
$569$	11.7957	+	20.4307i	0.494500	+	0.856500i	−0.505480	+	0.862839i	$0.668684\pi$
$570$	−0.226984	+	0.0862395i	−0.00950732	+	0.00361218i
$571$	26.1342	−	15.0886i	1.09368	−	0.631438i	0.159128	−	0.987258i	$-0.449132\pi$
$571$	26.1342	−	15.0886i	1.09368	−	0.631438i	0.934554	+	0.355820i	$0.115798\pi$
$572$	−16.4902	+	3.38711i	−0.689488	+	0.141622i
$573$	10.6294	−	18.4107i	0.444050	−	0.769117i
$574$	2.82652	+	7.43946i	0.117977	+	0.310517i
$575$	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	−0.203992	−	0.978973i	$-0.565392\pi$
$577$	13.0151	−	7.51429i	0.541827	−	0.312824i	0.745819	+	0.666149i	$0.232058\pi$
$578$	1.66263	−	10.2695i	0.0691561	−	0.427153i
$579$	22.4851			0.934451
$580$	0.313582	+	0.353106i	0.0130208	+	0.0146619i
$581$			6.50533i			0.269887i
$582$	5.50317	+	14.4844i	0.228114	+	0.600399i
$583$	−10.5315	+	6.08036i	−0.436170	+	0.251823i
$584$	−4.19231	−	6.60327i	−0.173479	−	0.273245i
$585$	0.109478	−	0.189622i	0.00452636	−	0.00783989i
$586$	19.5413	+	15.9354i	0.807242	+	0.658286i
$587$	−6.40054	+	11.0861i	−0.264179	+	0.457571i	−0.967348	−	0.253452i	$-0.918434\pi$
$587$	−6.40054	+	11.0861i	−0.264179	+	0.457571i	0.703170	+	0.711022i	$0.251767\pi$
$588$	12.6443	+	4.20442i	0.521441	+	0.173387i
$589$			42.1101i			1.73512i
$590$	0.474866	+	0.387241i	0.0195499	+	0.0159425i
$591$	−4.81251	+	2.77851i	−0.197960	+	0.114292i
$592$	1.32128	−	11.1044i	0.0543044	−	0.456387i
$593$	9.92187	+	5.72839i	0.407442	+	0.235237i	0.689690	−	0.724105i	$-0.257747\pi$
$593$	9.92187	+	5.72839i	0.407442	+	0.235237i	−0.282248	+	0.959341i	$0.591080\pi$
$594$	−0.292552	+	1.80699i	−0.0120035	+	0.0741416i
$595$		−	0.0607468i		−	0.00249037i
$596$	7.33284	+	35.7000i	0.300365	+	1.46233i
$597$	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	$-0.313287\pi$
$599$	−10.8790	−	18.8430i	−0.444504	−	0.769903i	−0.998018	+	0.0629368i	$0.979953\pi$
$600$	6.54815	−	12.5312i	0.267327	−	0.511584i
$601$	−3.60069	+	6.23658i	−0.146875	+	0.254395i	−0.930071	−	0.367380i	$-0.880255\pi$
$601$	−3.60069	+	6.23658i	−0.146875	+	0.254395i	0.783196	+	0.621775i	$0.213588\pi$
$602$	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	$-0.758501\pi$
$607$	−12.1414	+	7.00982i	−0.492803	+	0.284520i	0.232934	+	0.972493i	$0.425167\pi$
$608$	−20.0447	−	20.7439i	−0.812921	−	0.841275i
$609$	−2.03710	+	3.52836i	−0.0825475	+	0.142977i
$610$	−0.193675	+	0.0735842i	−0.00784167	+	0.00297934i
$611$	−0.391381			−0.0158336
$612$	5.89363	+	1.95973i	0.238236	+	0.0792172i
$613$	−14.5446	+	25.1920i	−0.587452	+	1.01750i	0.407113	+	0.913378i	$0.366535\pi$
$613$	−14.5446	+	25.1920i	−0.587452	+	1.01750i	−0.994565	+	0.104118i	$0.966798\pi$
$614$	−9.47556	−	24.9399i	−0.382403	−	1.00649i
$615$	0.163070	+	0.282445i	0.00657561	+	0.0113893i
$616$	1.14001	+	1.79562i	0.0459322	+	0.0723474i
$617$	−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	$-0.256059\pi$
$619$	10.3590	+	5.98075i	0.416362	+	0.240387i	−0.277158	+	0.960824i	$0.589392\pi$
$620$	0.369260	+	0.415802i	0.0148298	+	0.0166990i
$621$	6.04917	+	3.49249i	0.242745	+	0.140149i
$622$	−36.9843	−	30.1598i	−1.48293	−	1.20930i
$623$	1.07378	+	1.85985i	0.0430202	+	0.0745132i
$624$	25.8296	+	3.07340i	1.03401	+	0.123034i
$625$	24.9830			0.999320
$626$	−2.61954	+	3.21228i	−0.104698	+	0.128389i
$627$			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	$-0.738138\pi$
$631$	7.40094	−	12.8188i	0.294627	−	0.510309i	0.974898	+	0.222652i	$0.0714713\pi$
$632$	43.9238	−	1.84926i	1.74720	−	0.0735595i
$633$	−0.433107	−	0.250054i	−0.0172145	−	0.00993877i
$634$	9.66707	−	3.67287i	0.383928	−	0.145868i
$635$	−0.187232	−	0.324295i	−0.00743007	−	0.0128693i
$636$	18.4059	−	3.78060i	0.729842	−	0.149911i
$637$	−37.5212	+	21.6628i	−1.48664	+	0.858313i
$638$	12.0001	−	4.55929i	0.475090	−	0.180504i
$639$	5.73337	−	3.31016i	0.226809	−	0.130948i
$640$	−0.379827	−	0.0290578i	−0.0150140	−	0.00114861i
$641$	28.6337	−	16.5317i	1.13096	−	0.652962i	0.186786	−	0.982401i	$-0.440193\pi$
$641$	28.6337	−	16.5317i	1.13096	−	0.652962i	0.944177	+	0.329439i	$0.106859\pi$
$642$	−9.36930	+	11.4894i	−0.369777	+	0.453450i
$643$			1.83327i			0.0722970i	0.999346	+	0.0361485i	$0.0115089\pi$
$643$			1.83327i			0.0722970i	−0.999346	+	0.0361485i	$0.988491\pi$
$644$	7.95010	−	1.63296i	0.313278	−	0.0643478i
$645$		−	0.0202303i		−	0.000796566i
$646$	22.1072	+	3.57916i	0.869797	+	0.140820i
$647$	−16.1402	+	27.9556i	−0.634536	+	1.09905i	0.352077	+	0.935971i	$0.385476\pi$
$647$	−16.1402	+	27.9556i	−0.634536	+	1.09905i	−0.986613	+	0.163078i	$0.947858\pi$
$648$	1.30993	−	2.50681i	0.0514588	−	0.0984768i
$649$	14.4246	−	8.32806i	0.566216	−	0.326905i
$650$	16.3278	+	42.9751i	0.640429	+	1.68562i
$651$	−2.39880	+	4.15485i	−0.0940164	+	0.162841i
$652$	25.3170	+	28.5080i	0.991490	+	1.11646i
$653$	36.6937	+	21.1851i	1.43593	+	0.829037i	0.997564	−	0.0697579i	$-0.0222227\pi$
$653$	36.6937	+	21.1851i	1.43593	+	0.829037i	0.438370	+	0.898795i	$0.355556\pi$
$654$	−9.79469	+	12.0110i	−0.383003	+	0.469668i
$655$	−0.536135			−0.0209485
$656$	−23.2014	+	31.0302i	−0.905861	+	1.21153i
$657$	1.38269	−	2.39489i	0.0539439	−	0.0934335i
$658$	0.0175625	+	0.0462249i	0.000684658	+	0.00180203i
$659$	11.7346	−	6.77500i	0.457117	−	0.263916i	−0.253714	−	0.967279i	$-0.581652\pi$
$659$	11.7346	−	6.77500i	0.457117	−	0.263916i	0.710831	+	0.703363i	$0.248319\pi$
$660$	0.0578785	+	0.0651737i	0.00225292	+	0.00253688i
$661$		−	16.7562i		−	0.651741i	−0.945414	−	0.325870i	$-0.894343\pi$
$661$		−	16.7562i		−	0.651741i	0.945414	−	0.325870i	$-0.105657\pi$
$662$	−3.38028	+	20.8788i	−0.131378	+	0.811478i
$663$	−17.4890	+	10.0973i	−0.679217	+	0.392146i
$664$	−26.7376	+	16.9753i	−1.03762	+	0.658769i
$665$	−0.0997495			−0.00386812
$666$	3.69592	−	1.40421i	0.143214	−	0.0544122i
$667$		−	48.9843i		−	1.89668i
$668$	−6.77875	−	7.63315i	−0.262278	−	0.295336i
$669$			6.50721i			0.251583i
$670$	0.143075	+	0.362552i	0.00552747	+	0.0140066i
$671$			5.63183i			0.217414i
$672$	−0.796065	−	3.18857i	−0.0307089	−	0.123002i
$673$		−	33.2782i		−	1.28278i	−0.767215	−	0.641390i	$-0.778358\pi$
$673$		−	33.2782i		−	1.28278i	0.767215	−	0.641390i	$-0.221642\pi$
$674$	−3.09753	−	8.15275i	−0.119312	−	0.314032i
$675$	4.99887			0.192406
$676$	−43.7985	+	38.8959i	−1.68456	+	1.49600i
$677$	12.8802	−	7.43641i	0.495028	−	0.285804i	−0.231630	−	0.972804i	$-0.574406\pi$
$677$	12.8802	−	7.43641i	0.495028	−	0.285804i	0.726658	+	0.687000i	$0.241073\pi$
$678$	−1.99248	−	0.322583i	−0.0765207	−	0.0123887i
$679$			6.36528i			0.244277i
$680$	0.249676	−	0.158515i	0.00957464	−	0.00607878i
$681$	14.1426	−	8.16526i	0.541947	−	0.312893i
$682$	14.1308	−	5.36881i	0.541097	−	0.205583i
$683$	13.9939	−	24.2381i	0.535461	−	0.927446i	−0.463680	−	0.886003i	$-0.653471\pi$
$683$	13.9939	−	24.2381i	0.535461	−	0.927446i	0.999141	−	0.0414431i	$-0.0131955\pi$
$684$	3.21798	−	9.67766i	0.123042	−	0.370034i
$685$	−0.510851			−0.0195186
$686$	8.69937	+	7.09413i	0.332144	+	0.270855i
$687$	−3.26867	−	1.88717i	−0.124707	−	0.0719999i
$688$	2.20875	−	0.947330i	0.0842078	−	0.0361166i
$689$	−30.5478	+	52.9104i	−1.16378	+	2.01573i
$690$	0.310920	−	0.118130i	0.0118365	−	0.00449712i
$691$	−9.34141	+	5.39326i	−0.355364	+	0.205169i	−0.667045	−	0.745017i	$-0.732441\pi$
$691$	−9.34141	+	5.39326i	−0.355364	+	0.205169i	0.311681	+	0.950187i	$0.399108\pi$
$692$	−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
$696$	−19.8177	+	0.834353i	−0.751187	+	0.0316261i
$697$		−	30.0802i		−	1.13937i
$698$	−0.544879	−	0.444335i	−0.0206240	−	0.0168183i
$699$	8.93565	−	5.15900i	0.337977	−	0.195131i
$700$	4.34298	−	3.85686i	0.164149	−	0.145775i
$701$	−13.2670	+	7.65968i	−0.501086	+	0.289302i	−0.729162	−	0.684341i	$-0.760090\pi$
$701$	−13.2670	+	7.65968i	−0.501086	+	0.289302i	0.228076	+	0.973643i	$0.426757\pi$
$702$	3.26630	+	8.59696i	0.123278	+	0.324471i
$703$	12.3461	−	7.12803i	0.465642	−	0.268839i
$704$	−4.40539	+	9.37112i	−0.166035	+	0.353187i
$705$	0.00101323	+	0.00175496i	3.81604e−5	+	6.60957e-5i
$706$	14.5881	+	38.3961i	0.549029	+	1.44506i
$707$	0.966051	+	0.557750i	0.0363321	+	0.0209763i
$708$	−25.2100	+	5.17817i	−0.947448	+	0.194607i
$709$	16.4180	−	28.4369i	0.616592	−	1.06797i	−0.373511	−	0.927626i	$-0.621846\pi$
$709$	16.4180	−	28.4369i	0.616592	−	1.06797i	0.990103	−	0.140343i	$-0.0448206\pi$
$710$	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
$714$	1.97735	+	1.61248i	0.0740005	+	0.0603456i
$715$	−0.283411			−0.0105990
$716$	3.81300	+	18.5636i	0.142498	+	0.693755i
$717$	0.0287339	+	0.0497686i	0.00107309	+	0.00185864i
$718$	7.69616	−	9.43763i	0.287218	−	0.352209i
$719$	26.9853	+	15.5800i	1.00638	+	0.581035i	0.910130	−	0.414322i	$-0.135981\pi$
$719$	26.9853	+	15.5800i	1.00638	+	0.581035i	0.0962520	+	0.995357i	$0.469315\pi$
$720$	−0.0530878	−	0.123777i	−0.00197846	−	0.00461290i
$721$	8.30621	+	4.79559i	0.309339	+	0.178597i
$722$	1.58283	−	9.77659i	0.0589068	−	0.363847i
$723$	−27.0880			−1.00741
$724$	−30.1304	+	26.7578i	−1.11979	+	0.994446i
$725$	−17.5281	−	30.3595i	−0.650975	−	1.12752i
$726$	−12.3272	+	4.68356i	−0.457507	+	0.173823i
$727$	16.2116	−	28.0793i	0.601254	−	1.04140i	−0.391377	−	0.920230i	$-0.628001\pi$
$727$	16.2116	−	28.0793i	0.601254	−	1.04140i	0.992631	−	0.121173i	$-0.0386655\pi$
$728$	9.47069	+	4.94888i	0.351007	+	0.183418i
$729$	1.00000			0.0370370
$730$	−0.0467680	−	0.123094i	−0.00173096	−	0.00455592i
$731$	−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	−0.305783	−	0.952101i	$-0.598918\pi$
$733$	9.90553	−	5.71896i	0.365869	−	0.211235i	0.671652	+	0.740866i	$0.265585\pi$
$734$	−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	$-0.856210\pi$
$739$	−1.95205	+	3.38104i	−0.0718072	+	0.124374i	0.827886	+	0.560896i	$0.189543\pi$
$740$	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	$-0.304319\pi$
$743$	4.29756	+	2.48119i	0.157662	+	0.0910262i	−0.419093	+	0.907943i	$0.637652\pi$
$744$	−23.3364	+	0.982497i	−0.855554	+	0.0360201i
$745$			0.613563i			0.0224792i
$746$	27.5852	+	4.46605i	1.00997	+	0.163514i
$747$	−9.69727	−	5.59872i	−0.354804	−	0.204846i
$748$	−1.61750	−	7.87481i	−0.0591416	−	0.287932i
$749$	−5.27436	+	3.04515i	−0.192721	+	0.111267i
$750$	0.300896	−	0.368983i	0.0109872	−	0.0134733i
$751$		−	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
$754$	40.7587	−	49.9815i	1.48434	−	1.82022i
$755$	0.285774	−	0.494976i	0.0104004	−	0.0180140i
$756$	0.868793	−	0.771546i	0.0315977	−	0.0280609i
$757$	−34.5407	+	19.9421i	−1.25540	+	0.724808i	−0.972178	−	0.234245i	$-0.924738\pi$
$757$	−34.5407	+	19.9421i	−1.25540	+	0.724808i	−0.283227	+	0.959053i	$0.591405\pi$
$758$	17.2067	−	6.53743i	0.624974	−	0.237450i
$759$		−	9.04115i		−	0.328173i
$760$	−0.260291	−	0.409982i	−0.00944174	−	0.0148716i
$761$	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
$766$	−19.4214	+	7.37888i	−0.701723	+	0.266610i
$767$	41.8403	−	72.4696i	1.51077	−	2.61673i
$768$	11.0281	−	11.5923i	0.397942	−	0.418301i
$769$	−0.974909	+	0.562864i	−0.0351561	+	0.0202974i	−0.517475	−	0.855698i	$-0.673128\pi$
$769$	−0.974909	+	0.562864i	−0.0351561	+	0.0202974i	0.482319	+	0.875996i	$0.339795\pi$
$770$	0.0127175	+	0.0334728i	0.000458308	+	0.00120628i
$771$	−1.67704	−	2.90472i	−0.0603972	−	0.104611i
$772$	9.04808	+	44.0507i	0.325647	+	1.58542i
$773$	−19.6192	−	33.9814i	−0.705653	−	1.22223i	−0.966455	−	0.256835i	$-0.917320\pi$
$773$	−19.6192	−	33.9814i	−0.705653	−	1.22223i	0.260802	−	0.965392i	$-0.416013\pi$
$774$	0.658509	+	0.536998i	0.0236696	+	0.0193020i
$775$	−20.6403	−	35.7500i	−0.741420	−	1.28418i
$776$	−26.1620	+	16.6098i	−0.939160	+	0.596258i
$777$	1.62419			0.0582676
$778$	−4.35021	+	1.65280i	−0.155963	+	0.0592559i
$779$	−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
$784$	−3.14880	+	26.4632i	−0.112457	+	0.945116i
$785$	−0.370380	−	0.213839i	−0.0132194	−	0.00763225i
$786$	14.2313	−	17.4516i	0.507615	−	0.622477i
$787$	−2.64924	+	4.58862i	−0.0944352	+	0.163567i	−0.909373	−	0.415982i	$-0.863438\pi$
$787$	−2.64924	+	4.58862i	−0.0944352	+	0.163567i	0.814938	+	0.579549i	$0.196771\pi$
$788$	−7.37994	−	8.31011i	−0.262899	−	0.296036i
$789$		−	17.4454i		−	0.621074i
$790$	0.730607	+	0.118285i	0.0259938	+	0.00420841i
$791$	−0.718090	−	0.414589i	−0.0255323	−	0.0147411i
$792$	−3.65779	+	0.153998i	−0.129974	+	0.00547210i
$793$	14.1472	+	24.5037i	0.502382	+	0.870151i
$794$	10.6040	+	8.64732i	0.376323	+	0.306882i
$795$	0.316336			0.0112193
$796$	−0.233207	+	0.701341i	−0.00826580	+	0.0248584i
$797$	7.23936	+	12.5389i	0.256431	+	0.444152i	0.965283	−	0.261205i	$-0.0841199\pi$
$797$	7.23936	+	12.5389i	0.256431	+	0.444152i	−0.708852	+	0.705357i	$0.750787\pi$
$798$	2.64778	−	3.24692i	0.0937304	−	0.114940i
$799$		−	0.186902i		−	0.00661213i
$800$	27.1849	+	7.78588i	0.961130	+	0.275273i
$801$	−3.69655			−0.130611
$802$	−20.8507	+	25.5688i	−0.736265	+	0.902867i
$803$	−3.57943			−0.126315
$804$	−15.5992	−	4.96651i	−0.550140	−	0.175155i
$805$	0.136635			0.00481577
$806$	47.9957	−	58.8561i	1.69058	−	2.07312i
$807$	−1.54282			−0.0543099
$808$	0.228442	+	5.42600i	0.00803657	+	0.190886i
$809$		−	20.7162i		−	0.728343i	−0.931332	−	0.364171i	$-0.881352\pi$
$809$		−	20.7162i		−	0.728343i	0.931332	−	0.364171i	$-0.118648\pi$
$810$	0.0300931	−	0.0369025i	0.00105736	−	0.00129662i
$811$	7.56677	+	13.1060i	0.265705	+	0.460215i	0.967748	−	0.251920i	$-0.0810619\pi$
$811$	7.56677	+	13.1060i	0.265705	+	0.460215i	−0.702043	+	0.712135i	$0.747729\pi$
$812$	−7.73215	−	2.57106i	−0.271345	−	0.0902267i
$813$	−3.75720			−0.131771
$814$	−3.96601	−	3.23418i	−0.139009	−	0.113358i
$815$	0.320936	+	0.555877i	0.0112419	+	0.0194715i
$816$	−1.46769	+	12.3348i	−0.0513794	+	0.431804i
$817$	2.65337	+	1.53192i	0.0928296	+	0.0535952i
$818$	22.5316	+	3.64787i	0.787799	+	0.127545i
$819$			3.77799i			0.132014i
$820$	−0.487718	+	0.433126i	−0.0170319	+	0.0151254i
$821$	−8.61254	+	14.9174i	−0.300580	+	0.520619i	−0.976267	−	0.216569i	$-0.930513\pi$
$821$	−8.61254	+	14.9174i	−0.300580	+	0.520619i	0.675688	+	0.737188i	$0.263847\pi$
$822$	13.5602	−	16.6285i	0.472965	−	0.579987i
$823$	−25.1095	−	14.4970i	−0.875261	−	0.505332i	−0.00616775	−	0.999981i	$-0.501963\pi$
$823$	−25.1095	−	14.4970i	−0.875261	−	0.505332i	−0.869093	+	0.494649i	$0.835297\pi$
$824$	1.96417	+	46.6532i	0.0684251	+	1.62524i
$825$	−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	$-0.527333\pi$
$827$	−28.5125	−	16.4617i	−0.991478	−	0.572430i	−0.905716	+	0.423885i	$0.860666\pi$
$828$	−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	$0.573511\pi$
$830$	−0.498427	+	0.189371i	−0.0173007	+	0.00657315i
$831$	23.0925			0.801069
$832$	4.37278	+	51.8394i	0.151599	+	1.79721i
$833$	−10.3450	−	17.9181i	−0.358433	−	0.620825i
$834$	−21.9320	−	17.8850i	−0.759444	−	0.619308i
$835$	−0.0859321	−	0.148839i	−0.00297380	−	0.00515078i
$836$	−12.9309	+	2.65602i	−0.447224	+	0.0918605i
$837$	−4.12899	−	7.15162i	−0.142719	−	0.247196i
$838$	−16.4202	−	43.2183i	−0.567227	−	1.49295i
$839$	3.33831	−	1.92737i	0.115251	−	0.0665403i	−0.441266	−	0.897376i	$-0.645471\pi$
$839$	3.33831	−	1.92737i	0.115251	−	0.0665403i	0.556517	+	0.830836i	$0.312137\pi$
$840$	−0.00232732	−	0.0552788i	−8.03001e−5	−	0.00190730i
$841$	−10.0898	+	17.4760i	−0.347923	+	0.602620i
$842$	−29.9311	+	11.3719i	−1.03149	+	0.391901i
$843$	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
$848$	14.8132	+	34.5377i	0.508686	+	1.18603i
$849$			31.3926i			1.07739i
$850$	−20.5226	+	7.79727i	−0.703918	+	0.267444i
$851$	−16.9115	+	9.76388i	−0.579720	+	0.334701i
$852$	8.79206	+	9.90023i	0.301211	+	0.339176i
$853$	26.9985	−	46.7627i	0.924410	−	1.60113i	0.131904	−	0.991263i	$-0.457891\pi$
$853$	26.9985	−	46.7627i	0.924410	−	1.60113i	0.792507	−	0.609863i	$-0.208776\pi$
$854$	2.25923	−	2.77044i	0.0773092	−	0.0948027i
$855$	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	$0.118989\pi$
$857$			21.3803i			0.730337i	−0.930941	+	0.365169i	$0.881011\pi$
$858$	7.52293	−	9.22521i	0.256829	−	0.314943i
$859$	8.86149	−	5.11618i	0.302350	−	0.174562i	−0.341148	−	0.940010i	$-0.610816\pi$
$859$	8.86149	−	5.11618i	0.302350	−	0.174562i	0.643498	+	0.765448i	$0.277482\pi$
$860$	0.0396331	−	0.00814071i	0.00135148	−	0.000277596i
$861$	−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	$0.808235\pi$
$864$	5.43821	+	1.55753i	0.185012	+	0.0529882i
$865$	−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	−0.476362	−	0.879249i	$-0.658045\pi$
$877$	15.4962	−	26.8403i	0.523271	−	0.906332i	0.999633	−	0.0270830i	$-0.00862185\pi$
$878$	4.07114	+	10.7153i	0.137394	+	0.361625i
$879$	−17.8297			−0.601382
$880$	−0.104391	+	0.139616i	−0.00351903	+	0.00470645i
$881$	15.3376	−	26.5656i	0.516738	−	0.895017i	−0.483073	−	0.875580i	$-0.660479\pi$
$881$	15.3376	−	26.5656i	0.516738	−	0.895017i	0.999811	−	0.0194367i	$-0.00618729\pi$
$882$	−8.80787	+	3.34643i	−0.296577	+	0.112680i
$883$	−5.88367	−	10.1908i	−0.198001	−	0.342948i	0.749879	−	0.661575i	$-0.230112\pi$
$883$	−5.88367	−	10.1908i	−0.198001	−	0.342948i	−0.947880	+	0.318627i	$0.896778\pi$
$884$	−26.8192	−	30.1996i	−0.902028	−	1.01572i
$885$	−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	$-0.0798239\pi$
$887$	36.8760	+	21.2903i	1.23817	+	0.714860i	0.269453	+	0.963014i	$0.413157\pi$
$888$	4.23824	+	6.67561i	0.142226	+	0.224019i
$889$	5.59556	+	3.23060i	0.187669	+	0.108351i
$890$	−0.111240	+	0.136412i	−0.00372879	+	0.00457253i
$891$	−0.647185	−	1.12096i	−0.0216815	−	0.0375535i
$892$	−12.7483	+	2.61852i	−0.426844	+	0.0876744i
$893$	−0.306904			−0.0102701
$894$	−19.9719	−	16.2866i	−0.667960	−	0.544705i
$895$			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
$900$	2.01156	+	9.79328i	0.0670518	+	0.326443i
$901$	−25.2672	−	14.5880i	−0.841771	−	0.485997i
$902$	6.29739	+	16.5749i	0.209680	+	0.551882i
$903$	0.174532	+	0.302298i	0.00580806	+	0.0100598i
$904$	−0.169807	−	4.03328i	−0.00564769	−	0.134145i
$905$	−0.587513	+	0.339201i	−0.0195296	+	0.0112754i
$906$	8.52613	+	22.4409i	0.283262	+	0.745550i
$907$	1.80339	−	1.04119i	0.0598805	−	0.0345720i	−0.469761	−	0.882794i	$-0.655660\pi$
$907$	1.80339	−	1.04119i	0.0598805	−	0.0345720i	0.529641	+	0.848222i	$0.322327\pi$
$908$	21.6876	+	24.4211i	0.719728	+	0.810444i
$909$	−1.66284	+	0.960039i	−0.0551528	+	0.0318425i
$910$	0.139417	+	0.113691i	0.00462163	+	0.00376882i
$911$			5.87683i			0.194708i	0.995250	+	0.0973540i	$0.0310379\pi$
$911$			5.87683i			0.194708i	−0.995250	+	0.0973540i	$0.968962\pi$
$912$	20.2544	+	2.41002i	0.670691	+	0.0798039i
$913$			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
$918$	−4.10545	+	1.55981i	−0.135500	+	0.0514813i
$919$	2.13927	−	3.70532i	0.0705679	−	0.122227i	−0.828582	−	0.559867i	$-0.810852\pi$
$919$	2.13927	−	3.70532i	0.0705679	−	0.122227i	0.899150	+	0.437640i	$0.144186\pi$
$920$	0.356543	+	0.561587i	0.0117549	+	0.0185150i
$921$	16.3376	+	9.43255i	0.538344	+	0.310813i
$922$	13.8536	+	11.2973i	0.456245	+	0.372057i
$923$	−43.0516			−1.41706
$924$	−1.42714	−	0.474547i	−0.0469495	−	0.0156115i
$925$	−6.98761	+	12.1029i	−0.229751	+	0.397941i
$926$	26.8447	−	10.1993i	0.882171	−	0.335169i
$927$	−14.2972	+	8.25451i	−0.469583	+	0.271114i
$928$	−9.60926	−	38.4890i	−0.315439	−	1.26346i
$929$			24.1754i			0.793168i	0.917998	+	0.396584i	$0.129804\pi$
$929$			24.1754i			0.793168i	−0.917998	+	0.396584i	$0.870196\pi$
$930$	−0.388166	−	0.0628442i	−0.0127285	−	0.00206074i
$931$	−29.4225	+	16.9871i	−0.964282	+	0.556729i
$932$	13.7027	+	15.4298i	0.448848	+	0.505421i
$933$	33.7450			1.10476
$934$	3.91525	+	10.3050i	0.128111	+	0.337190i
$935$		−	0.135342i		−	0.00442614i
$936$	−15.5279	+	9.85844i	−0.507547	+	0.322233i
$937$		−	1.69843i		−	0.0554852i	−0.999615	−	0.0277426i	$-0.991168\pi$
$937$		−	1.69843i		−	0.0554852i	0.999615	−	0.0277426i	$-0.00883188\pi$
$938$	−5.26579	−	4.18322i	−0.171934	−	0.136587i
$939$		−	2.93093i		−	0.0956474i
$940$	−0.00303042	+	0.00269122i	−9.88415e−5	+	8.77778e-5i
$941$		−	37.5905i		−	1.22541i	−0.790310	−	0.612707i	$-0.790080\pi$
$941$		−	37.5905i		−	1.22541i	0.790310	−	0.612707i	$-0.209920\pi$
$942$	16.7921	−	6.37993i	0.547116	−	0.207869i
$943$	67.6583			2.20326
$944$	−20.2891	−	47.3051i	−0.660353	−	1.53965i
$945$	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	$-0.106972\pi$
$948$	−23.2437	+	20.6420i	−0.754921	+	0.670420i
$949$	−15.5738	+	8.99155i	−0.505548	+	0.291878i
$950$	12.8035	+	33.6992i	0.415402	+	1.09335i
$951$	−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	$0.721586\pi$
$954$	−8.39691	+	10.2969i	−0.271860	+	0.333376i
$955$	0.619894	+	0.357896i	0.0200593	+	0.0115812i
$956$	−0.0859391	+	0.0763196i	−0.00277947	+	0.00246835i
$957$	−4.53859	+	7.86107i	−0.146712	+	0.254112i
$958$	7.98786	+	21.0242i	0.258076	+	0.679261i
$959$	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
$964$	−10.9003	−	53.0682i	−0.351075	−	1.70921i
$965$			0.757083i			0.0243714i
$966$	−3.62689	+	4.44758i	−0.116693	+	0.143099i
$967$	−33.5165	+	19.3507i	−1.07782	+	0.622278i	−0.930307	−	0.366783i	$-0.880459\pi$
$967$	−33.5165	+	19.3507i	−1.07782	+	0.622278i	−0.147510	+	0.989061i	$0.547126\pi$
$968$	−14.1361	−	22.2656i	−0.454351	−	0.715644i
$969$	−13.7141	+	7.91786i	−0.440561	+	0.254358i
$970$	−0.487696	+	0.185294i	−0.0156590	+	0.00594942i
$971$	38.0062	−	21.9429i	1.21968	−	0.704180i	0.254827	−	0.966987i	$-0.417981\pi$
$971$	38.0062	−	21.9429i	1.21968	−	0.704180i	0.964849	+	0.262807i	$0.0846482\pi$
$972$	0.402402	+	1.95910i	0.0129071	+	0.0628382i
$973$	−5.81288	−	10.0682i	−0.186353	−	0.322772i
$974$	−42.1645	+	16.0198i	−1.35104	+	0.513308i
$975$	−28.1522	−	16.2537i	−0.901591	−	0.520534i
$976$	17.2822	+	2.05636i	0.553189	+	0.0658226i
$977$	−12.2697	+	21.2517i	−0.392543	+	0.679904i	−0.992784	−	0.119915i	$-0.961738\pi$
$977$	−12.2697	+	21.2517i	−0.392543	+	0.679904i	0.600242	+	0.799819i	$0.295071\pi$
$978$	−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
$982$	−24.1838	+	29.6561i	−0.771736	+	0.946363i
$983$	0.107433			0.00342657			0.00171329	−	0.999999i	$-0.499455\pi$
$983$	0.107433			0.00342657			0.00171329	+	0.999999i	$0.499455\pi$
$984$	−1.15243	−	27.3726i	−0.0367380	−	0.872607i
$985$	−0.0935532	−	0.162039i	−0.00298085	−	0.00516299i
$986$	23.8685	+	19.4642i	0.760128	+	0.619865i
$987$	−0.0302811	−	0.0174828i	−0.000963857	−	0.000556483i
$988$	−49.5893	+	44.0386i	−1.57765	+	1.40106i
$989$	−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	$-0.670673\pi$
$991$	−32.1640			−1.02172			−0.510861	+	0.859663i	$0.670673\pi$
$992$	−11.3154	−	45.3230i	−0.359265	−	1.43901i
$993$	−7.47789	−	12.9521i	−0.237304	−	0.411022i
$994$	1.93186	+	5.08470i	0.0612749	+	0.161277i
$995$	−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	$0.236152\pi$
$998$	−13.4947	+	5.12713i	−0.427167	+	0.162296i
$999$	−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.b.775.6	yes	68
4.3	odd	2		804.2.j.a.775.5	yes	68
67.30	odd	6		804.2.j.a.499.5	✓	68
268.231	even	6	inner	804.2.j.b.499.6	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.5	✓	68	67.30	odd	6
804.2.j.a.775.5	yes	68	4.3	odd	2
804.2.j.b.499.6	yes	68	268.231	even	6	inner
804.2.j.b.775.6	yes	68	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.09599 - 0.893755i) q^{2} +1.00000 q^{3} +(0.402402 + 1.95910i) q^{4} +0.0336703i q^{5} +(-1.09599 - 0.893755i) q^{6} +(-0.290483 - 0.503131i) q^{7} +(1.30993 - 2.50681i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.09599 - 0.893755i) q^{2} +1.00000 q^{3} +(0.402402 + 1.95910i) q^{4} +0.0336703i q^{5} +(-1.09599 - 0.893755i) q^{6} +(-0.290483 - 0.503131i) q^{7} +(1.30993 - 2.50681i) q^{8} +1.00000 q^{9} +(0.0300931 - 0.0369025i) q^{10} +(-0.647185 - 1.12096i) q^{11} +(0.402402 + 1.95910i) q^{12} +(-5.63171 - 3.25147i) q^{13} +(-0.131309 + 0.811049i) q^{14} +0.0336703i q^{15} +(-3.67614 + 1.57669i) q^{16} +(1.55273 - 2.68940i) q^{17} +(-1.09599 - 0.893755i) q^{18} +(-4.41614 - 2.54966i) q^{19} +(-0.0659636 + 0.0135490i) 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} +(3.26630 + 8.59696i) q^{26} +1.00000 q^{27} +(0.868793 - 0.771546i) q^{28} +(-3.50641 - 6.07327i) q^{29} +(0.0300931 - 0.0369025i) q^{30} +(-4.12899 - 7.15162i) q^{31} +(5.43821 + 1.55753i) q^{32} +(-0.647185 - 1.12096i) q^{33} +(-4.10545 + 1.55981i) q^{34} +(0.0169406 - 0.00978066i) q^{35} +(0.402402 + 1.95910i) q^{36} +(-1.39784 + 2.42113i) q^{37} +(2.56129 + 6.74137i) 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} +(1.93564 - 1.71898i) q^{44} +0.0336703i q^{45} +(-3.50842 - 9.23423i) q^{46} +(0.0521219 - 0.0300926i) q^{47} +(-3.67614 + 1.57669i) q^{48} +(3.33124 - 5.76988i) q^{49} +(-5.47872 - 4.46776i) q^{50} +(1.55273 - 2.68940i) q^{51} +(4.10374 - 12.3415i) q^{52} -9.39508i q^{53} +(-1.09599 - 0.893755i) q^{54} +(0.0377430 - 0.0217910i) q^{55} +(-1.64177 + 0.0691207i) q^{56} +(-4.41614 - 2.54966i) q^{57} +(-1.58502 + 9.79013i) q^{58} +12.8681i q^{59} +(-0.0659636 + 0.0135490i) 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} +(3.69592 - 1.40421i) q^{74} +4.99887 q^{75} +(3.21798 - 9.67766i) q^{76} +(-0.375993 + 0.651238i) q^{77} +(3.26630 + 8.59696i) q^{78} +(7.77159 + 13.4608i) q^{79} +(-0.0530878 - 0.123777i) q^{80} +1.00000 q^{81} +(-13.5224 - 2.18927i) q^{82} +(-9.69727 - 5.59872i) q^{83} +(0.868793 - 0.771546i) q^{84} +(0.0905531 + 0.0522808i) q^{85} +(0.658509 + 0.536998i) q^{86} +(-3.50641 - 6.07327i) q^{87} +(-3.65779 + 0.153998i) q^{88} -3.69655 q^{89} +(0.0300931 - 0.0369025i) 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} +(5.43821 + 1.55753i) q^{96} +(-9.48849 - 5.47818i) q^{97} +(-8.80787 + 3.34643i) 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	\( 68 q + 68 q^{3} - 2 q^{4} - 4 q^{7} + 6 q^{8} + 68 q^{9} - 6 q^{10} - 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 12 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - 19 q^{26} + 68 q^{27} - 7 q^{28} - 8 q^{29} - 6 q^{30} - 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} + 4 q^{38} + 6 q^{39} + 18 q^{40} + 10 q^{42} + 4 q^{43} - 5 q^{44} + 16 q^{46} - 2 q^{48} - 46 q^{49} + 27 q^{50} + 28 q^{52} - 17 q^{56} - 4 q^{58} - 12 q^{60} + 6 q^{61} - 34 q^{62} - 4 q^{63} + 16 q^{64} - 22 q^{66} + 18 q^{67} + 34 q^{68} - 56 q^{70} + 36 q^{71} + 6 q^{72} + 6 q^{73} + 11 q^{74} - 68 q^{75} + 14 q^{76} - 4 q^{77} - 19 q^{78} - 6 q^{79} - 25 q^{80} + 68 q^{81} - 26 q^{82} - 12 q^{83} - 7 q^{84} - 33 q^{86} - 8 q^{87} + 22 q^{88} - 6 q^{90} + 10 q^{92} - 2 q^{93} + 16 q^{94} - 20 q^{95} + 15 q^{96} + 18 q^{97} - 32 q^{98}+O(q^{100}) \) 68 * q + 68 * q^3 - 2 * q^4 - 4 * q^7 + 6 * q^8 + 68 * q^9 - 6 * q^10 - 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 12 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - 19 * q^26 + 68 * q^27 - 7 * q^28 - 8 * q^29 - 6 * q^30 - 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 + 4 * q^38 + 6 * q^39 + 18 * q^40 + 10 * q^42 + 4 * q^43 - 5 * q^44 + 16 * q^46 - 2 * q^48 - 46 * q^49 + 27 * q^50 + 28 * q^52 - 17 * q^56 - 4 * q^58 - 12 * 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 + 11 * q^74 - 68 * q^75 + 14 * q^76 - 4 * q^77 - 19 * q^78 - 6 * q^79 - 25 * q^80 + 68 * q^81 - 26 * q^82 - 12 * q^83 - 7 * q^84 - 33 * q^86 - 8 * q^87 + 22 * q^88 - 6 * q^90 + 10 * q^92 - 2 * q^93 + 16 * q^94 - 20 * q^95 + 15 * q^96 + 18 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more