LMFDB - Embedded newform 804.2.j.b.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.b.775.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28998 + 0.579621i) q^{2} +1.00000 q^{3} +(1.32808 - 1.49540i) q^{4} +0.235101i q^{5} +(-1.28998 + 0.579621i) q^{6} +(-1.44937 + 2.51039i) q^{7} +(-0.846427 + 2.69881i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.28998 + 0.579621i) q^{2} +1.00000 q^{3} +(1.32808 - 1.49540i) q^{4} +0.235101i q^{5} +(-1.28998 + 0.579621i) q^{6} +(-1.44937 + 2.51039i) q^{7} +(-0.846427 + 2.69881i) q^{8} +1.00000 q^{9} +(-0.136269 - 0.303274i) q^{10} +(3.19736 - 5.53800i) q^{11} +(1.32808 - 1.49540i) q^{12} +(1.73407 - 1.00116i) q^{13} +(0.414583 - 4.07842i) q^{14} +0.235101i q^{15} +(-0.472415 - 3.97201i) q^{16} +(-0.407663 - 0.706092i) q^{17} +(-1.28998 + 0.579621i) q^{18} +(3.54301 - 2.04556i) q^{19} +(0.351569 + 0.312232i) q^{20} +(-1.44937 + 2.51039i) q^{21} +(-0.914584 + 8.99714i) q^{22} +(-4.43135 + 2.55844i) q^{23} +(-0.846427 + 2.69881i) q^{24} +4.94473 q^{25} +(-1.65661 + 2.29658i) q^{26} +1.00000 q^{27} +(1.82914 + 5.50137i) q^{28} +(2.01950 - 3.49788i) q^{29} +(-0.136269 - 0.303274i) q^{30} +(-2.52900 + 4.38035i) q^{31} +(2.91166 + 4.84997i) q^{32} +(3.19736 - 5.53800i) q^{33} +(0.935141 + 0.674553i) q^{34} +(-0.590194 - 0.340748i) q^{35} +(1.32808 - 1.49540i) q^{36} +(5.72046 + 9.90813i) q^{37} +(-3.38475 + 4.69232i) q^{38} +(1.73407 - 1.00116i) q^{39} +(-0.634492 - 0.198996i) q^{40} +(2.79199 + 1.61196i) q^{41} +(0.414583 - 4.07842i) q^{42} +3.37738 q^{43} +(-4.03514 - 12.1362i) q^{44} +0.235101i q^{45} +(4.23341 - 5.86883i) q^{46} +(-2.62685 - 1.51661i) q^{47} +(-0.472415 - 3.97201i) q^{48} +(-0.701357 - 1.21479i) q^{49} +(-6.37858 + 2.86607i) q^{50} +(-0.407663 - 0.706092i) q^{51} +(0.805842 - 3.92274i) q^{52} -6.57075i q^{53} +(-1.28998 + 0.579621i) q^{54} +(1.30199 + 0.751703i) q^{55} +(-5.54826 - 6.03643i) q^{56} +(3.54301 - 2.04556i) q^{57} +(-0.577665 + 5.68274i) q^{58} -8.62896i q^{59} +(0.351569 + 0.312232i) q^{60} +(10.8670 - 6.27409i) q^{61} +(0.723402 - 7.11641i) q^{62} +(-1.44937 + 2.51039i) q^{63} +(-6.56712 - 4.56869i) q^{64} +(0.235375 + 0.407681i) q^{65} +(-0.914584 + 8.99714i) q^{66} +(6.30929 - 5.21467i) q^{67} +(-1.59730 - 0.328129i) q^{68} +(-4.43135 + 2.55844i) q^{69} +(0.958841 + 0.0974687i) q^{70} +(-1.74319 - 1.00643i) q^{71} +(-0.846427 + 2.69881i) q^{72} +(6.93381 + 12.0097i) q^{73} +(-13.1222 - 9.46555i) q^{74} +4.94473 q^{75} +(1.64648 - 8.01486i) q^{76} +(9.26834 + 16.0532i) q^{77} +(-1.65661 + 2.29658i) q^{78} +(-6.44716 + 11.1668i) q^{79} +(0.933821 - 0.111065i) q^{80} +1.00000 q^{81} +(-4.53593 - 0.461089i) q^{82} +(-4.51692 + 2.60784i) q^{83} +(1.82914 + 5.50137i) q^{84} +(0.166003 - 0.0958418i) q^{85} +(-4.35674 + 1.95760i) q^{86} +(2.01950 - 3.49788i) q^{87} +(12.2396 + 13.3166i) q^{88} +4.15475 q^{89} +(-0.136269 - 0.303274i) q^{90} +5.80424i q^{91} +(-2.05930 + 10.0244i) q^{92} +(-2.52900 + 4.38035i) q^{93} +(4.26764 + 0.433817i) q^{94} +(0.480912 + 0.832964i) q^{95} +(2.91166 + 4.84997i) q^{96} +(-4.52526 + 2.61266i) q^{97} +(1.60885 + 1.16052i) q^{98} +(3.19736 - 5.53800i) 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.28998	+	0.579621i	−0.912151	+	0.409854i
$2$	−1.28998	+	0.579621i	−0.912151	+	0.409854i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.32808	−	1.49540i	0.664039	−	0.747698i
$5$			0.235101i			0.105140i	0.998617	+	0.0525701i	$0.0167413\pi$
$5$			0.235101i			0.105140i	−0.998617	+	0.0525701i	$0.983259\pi$
$6$	−1.28998	+	0.579621i	−0.526631	+	0.236629i
$7$	−1.44937	+	2.51039i	−0.547811	+	0.948837i	0.450613	+	0.892719i	$0.351205\pi$
$7$	−1.44937	+	2.51039i	−0.547811	+	0.948837i	−0.998424	+	0.0561172i	$0.982128\pi$
$8$	−0.846427	+	2.69881i	−0.299257	+	0.954172i
$9$	1.00000			0.333333
$10$	−0.136269	−	0.303274i	−0.0430922	−	0.0959038i
$11$	3.19736	−	5.53800i	0.964041	−	1.66977i	0.251872	−	0.967761i	$-0.418954\pi$
$11$	3.19736	−	5.53800i	0.964041	−	1.66977i	0.712169	−	0.702008i	$-0.247713\pi$
$12$	1.32808	−	1.49540i	0.383383	−	0.431683i
$13$	1.73407	−	1.00116i	0.480944	−	0.277673i	−0.239866	−	0.970806i	$-0.577103\pi$
$13$	1.73407	−	1.00116i	0.480944	−	0.277673i	0.720810	+	0.693133i	$0.243770\pi$
$14$	0.414583	−	4.07842i	0.110802	−	1.09000i
$15$			0.235101i			0.0607028i
$16$	−0.472415	−	3.97201i	−0.118104	−	0.993001i
$17$	−0.407663	−	0.706092i	−0.0988727	−	0.171253i	0.812346	−	0.583176i	$-0.198190\pi$
$17$	−0.407663	−	0.706092i	−0.0988727	−	0.171253i	−0.911218	+	0.411924i	$0.864857\pi$
$18$	−1.28998	+	0.579621i	−0.304050	+	0.136618i
$19$	3.54301	−	2.04556i	0.812822	−	0.469283i	−0.0351131	−	0.999383i	$-0.511179\pi$
$19$	3.54301	−	2.04556i	0.812822	−	0.469283i	0.847935	+	0.530101i	$0.177846\pi$
$20$	0.351569	+	0.312232i	0.0786131	+	0.0698173i
$21$	−1.44937	+	2.51039i	−0.316279	+	0.547811i
$22$	−0.914584	+	8.99714i	−0.194990	+	1.91820i
$23$	−4.43135	+	2.55844i	−0.924000	+	0.533472i	−0.884909	−	0.465764i	$-0.845780\pi$
$23$	−4.43135	+	2.55844i	−0.924000	+	0.533472i	−0.0390909	+	0.999236i	$0.512446\pi$
$24$	−0.846427	+	2.69881i	−0.172776	+	0.550892i
$25$	4.94473			0.988946
$26$	−1.65661	+	2.29658i	−0.324888	+	0.450397i
$27$	1.00000			0.192450
$28$	1.82914	+	5.50137i	0.345675	+	1.03966i
$29$	2.01950	−	3.49788i	0.375013	−	0.649541i	−0.615316	−	0.788280i	$-0.710972\pi$
$29$	2.01950	−	3.49788i	0.375013	−	0.649541i	0.990329	+	0.138739i	$0.0443051\pi$
$30$	−0.136269	−	0.303274i	−0.0248793	−	0.0553701i
$31$	−2.52900	+	4.38035i	−0.454221	+	0.786734i	−0.998643	−	0.0520776i	$-0.983416\pi$
$31$	−2.52900	+	4.38035i	−0.454221	+	0.786734i	0.544422	+	0.838811i	$0.316749\pi$
$32$	2.91166	+	4.84997i	0.514714	+	0.857362i
$33$	3.19736	−	5.53800i	0.556589	−	0.964041i
$34$	0.935141	+	0.674553i	0.160375	+	0.115685i
$35$	−0.590194	−	0.340748i	−0.0997609	−	0.0575970i
$36$	1.32808	−	1.49540i	0.221346	−	0.249233i
$37$	5.72046	+	9.90813i	0.940438	+	1.62889i	0.764638	+	0.644460i	$0.222918\pi$
$37$	5.72046	+	9.90813i	0.940438	+	1.62889i	0.175800	+	0.984426i	$0.443749\pi$
$38$	−3.38475	+	4.69232i	−0.549079	+	0.761195i
$39$	1.73407	−	1.00116i	0.277673	−	0.160315i
$40$	−0.634492	−	0.198996i	−0.100322	−	0.0314640i
$41$	2.79199	+	1.61196i	0.436036	+	0.251745i	0.701915	−	0.712261i	$-0.252329\pi$
$41$	2.79199	+	1.61196i	0.436036	+	0.251745i	−0.265879	+	0.964006i	$0.585662\pi$
$42$	0.414583	−	4.07842i	0.0639715	−	0.629315i
$43$	3.37738			0.515046			0.257523	−	0.966272i	$-0.417094\pi$
$43$	3.37738			0.515046			0.257523	+	0.966272i	$0.417094\pi$
$44$	−4.03514	−	12.1362i	−0.608321	−	1.82960i
$45$			0.235101i			0.0350468i
$46$	4.23341	−	5.86883i	0.624182	−	0.865312i
$47$	−2.62685	−	1.51661i	−0.383166	−	0.221221i	0.296029	−	0.955179i	$-0.404338\pi$
$47$	−2.62685	−	1.51661i	−0.383166	−	0.221221i	−0.679195	+	0.733958i	$0.737671\pi$
$48$	−0.472415	−	3.97201i	−0.0681872	−	0.573310i
$49$	−0.701357	−	1.21479i	−0.100194	−	0.173541i
$50$	−6.37858	+	2.86607i	−0.902068	+	0.405323i
$51$	−0.407663	−	0.706092i	−0.0570842	−	0.0988727i
$52$	0.805842	−	3.92274i	0.111750	−	0.543987i
$53$		−	6.57075i		−	0.902562i	−0.892382	−	0.451281i	$-0.850967\pi$
$53$		−	6.57075i		−	0.902562i	0.892382	−	0.451281i	$-0.149033\pi$
$54$	−1.28998	+	0.579621i	−0.175544	+	0.0788765i
$55$	1.30199	+	0.751703i	0.175560	+	0.101360i
$56$	−5.54826	−	6.03643i	−0.741417	−	0.806652i
$57$	3.54301	−	2.04556i	0.469283	−	0.270941i
$58$	−0.577665	+	5.68274i	−0.0758512	+	0.746180i
$59$		−	8.62896i		−	1.12339i	−0.827343	−	0.561697i	$-0.810148\pi$
$59$		−	8.62896i		−	1.12339i	0.827343	−	0.561697i	$-0.189852\pi$
$60$	0.351569	+	0.312232i	0.0453873	+	0.0403090i
$61$	10.8670	−	6.27409i	1.39138	−	0.803315i	0.397913	−	0.917423i	$-0.369735\pi$
$61$	10.8670	−	6.27409i	1.39138	−	0.803315i	0.993468	+	0.114109i	$0.0364012\pi$
$62$	0.723402	−	7.11641i	0.0918721	−	0.903784i
$63$	−1.44937	+	2.51039i	−0.182604	+	0.316279i
$64$	−6.56712	−	4.56869i	−0.820890	−	0.571086i
$65$	0.235375	+	0.407681i	0.0291946	+	0.0505666i
$66$	−0.914584	+	8.99714i	−0.112577	+	1.10747i
$67$	6.30929	−	5.21467i	0.770803	−	0.637074i
$67$	6.30929	−	5.21467i	0.770803	−	0.637074i
$68$	−1.59730	−	0.328129i	−0.193701	−	0.0397915i
$69$	−4.43135	+	2.55844i	−0.533472	+	0.308000i
$70$	0.958841	+	0.0974687i	0.114603	+	0.0116497i
$71$	−1.74319	−	1.00643i	−0.206879	−	0.119441i	0.392981	−	0.919546i	$-0.371444\pi$
$71$	−1.74319	−	1.00643i	−0.206879	−	0.119441i	−0.599860	+	0.800105i	$0.704777\pi$
$72$	−0.846427	+	2.69881i	−0.0997524	+	0.318057i
$73$	6.93381	+	12.0097i	0.811541	+	1.40563i	0.911785	+	0.410667i	$0.134704\pi$
$73$	6.93381	+	12.0097i	0.811541	+	1.40563i	−0.100245	+	0.994963i	$0.531963\pi$
$74$	−13.1222	−	9.46555i	−1.52543	−	1.10035i
$75$	4.94473			0.570968
$76$	1.64648	−	8.01486i	0.188864	−	0.919367i
$77$	9.26834	+	16.0532i	1.05622	+	1.82944i
$78$	−1.65661	+	2.29658i	−0.187574	+	0.260037i
$79$	−6.44716	+	11.1668i	−0.725362	+	1.25636i	0.233463	+	0.972366i	$0.424994\pi$
$79$	−6.44716	+	11.1668i	−0.725362	+	1.25636i	−0.958825	+	0.283998i	$0.908339\pi$
$80$	0.933821	−	0.111065i	0.104404	−	0.0124175i
$81$	1.00000			0.111111
$82$	−4.53593	−	0.461089i	−0.500910	−	0.0509188i
$83$	−4.51692	+	2.60784i	−0.495796	+	0.286248i	−0.726976	−	0.686663i	$-0.759075\pi$
$83$	−4.51692	+	2.60784i	−0.495796	+	0.286248i	0.231180	+	0.972911i	$0.425741\pi$
$84$	1.82914	+	5.50137i	0.199575	+	0.600249i
$85$	0.166003	−	0.0958418i	0.0180055	−	0.0103955i
$86$	−4.35674	+	1.95760i	−0.469800	+	0.211094i
$87$	2.01950	−	3.49788i	0.216514	−	0.375013i
$88$	12.2396	+	13.3166i	1.30475	+	1.41955i
$89$	4.15475			0.440403			0.220202	−	0.975454i	$-0.429328\pi$
$89$	4.15475			0.440403			0.220202	+	0.975454i	$0.429328\pi$
$90$	−0.136269	−	0.303274i	−0.0143641	−	0.0319679i
$91$			5.80424i			0.608450i
$92$	−2.05930	+	10.0244i	−0.214697	+	1.04512i
$93$	−2.52900	+	4.38035i	−0.262245	+	0.454221i
$94$	4.26764	+	0.433817i	0.440174	+	0.0447448i
$95$	0.480912	+	0.832964i	0.0493405	+	0.0854603i
$96$	2.91166	+	4.84997i	0.297170	+	0.494998i
$97$	−4.52526	+	2.61266i	−0.459471	+	0.265276i	−0.711822	−	0.702360i	$-0.752130\pi$
$97$	−4.52526	+	2.61266i	−0.459471	+	0.265276i	0.252351	+	0.967636i	$0.418796\pi$
$98$	1.60885	+	1.16052i	0.162518	+	0.117231i
$99$	3.19736	−	5.53800i	0.321347	−	0.556589i
$100$	6.56699	−	7.39432i	0.656699	−	0.739432i
$101$	13.2560	+	7.65337i	1.31902	+	0.761539i	0.983572	−	0.180519i	$-0.0577776\pi$
$101$	13.2560	+	7.65337i	1.31902	+	0.761539i	0.335452	+	0.942057i	$0.391111\pi$
$102$	0.935141	+	0.674553i	0.0925928	+	0.0667907i
$103$	−12.1379	−	7.00780i	−1.19598	−	0.690499i	−0.236323	−	0.971675i	$-0.575942\pi$
$103$	−12.1379	−	7.00780i	−1.19598	−	0.690499i	−0.959656	+	0.281176i	$0.909276\pi$
$104$	1.23419	+	5.52733i	0.121022	+	0.541999i
$105$	−0.590194	−	0.340748i	−0.0575970	−	0.0332536i
$106$	3.80855	+	8.47612i	0.369919	+	0.823273i
$107$		−	1.64330i		−	0.158864i	−0.996840	−	0.0794319i	$-0.974689\pi$
$107$		−	1.64330i		−	0.158864i	0.996840	−	0.0794319i	$-0.0253106\pi$
$108$	1.32808	−	1.49540i	0.127794	−	0.143894i
$109$		−	14.4519i		−	1.38424i	−0.721781	−	0.692122i	$-0.756676\pi$
$109$		−	14.4519i		−	1.38424i	0.721781	−	0.692122i	$-0.243324\pi$
$110$	−2.11524	−	0.215019i	−0.201680	−	0.0205013i
$111$	5.72046	+	9.90813i	0.542962	+	0.940438i
$112$	10.6560	+	4.57097i	1.00689	+	0.431916i
$113$	0.874188	+	0.504713i	0.0822367	+	0.0474794i	0.540554	−	0.841309i	$-0.318214\pi$
$113$	0.874188	+	0.504713i	0.0822367	+	0.0474794i	−0.458318	+	0.888788i	$0.651548\pi$
$114$	−3.38475	+	4.69232i	−0.317011	+	0.439476i
$115$	−0.601491	−	1.04181i	−0.0560893	−	0.0971496i
$116$	−2.54866	−	7.66542i	−0.236637	−	0.711717i
$117$	1.73407	−	1.00116i	0.160315	−	0.0925577i
$118$	5.00153	+	11.1312i	0.460428	+	1.02471i
$119$	2.36342			0.216654
$120$	−0.634492	−	0.198996i	−0.0579209	−	0.0181657i
$121$	−14.9463	−	25.8877i	−1.35875	−	2.35343i
$122$	−10.3816	+	14.3922i	−0.939908	+	1.30301i
$123$	2.79199	+	1.61196i	0.251745	+	0.145345i
$124$	3.19165	+	9.59930i	0.286619	+	0.862042i
$125$			2.33801i			0.209118i
$126$	0.414583	−	4.07842i	0.0369340	−	0.363335i
$127$	−2.97285	−	1.71637i	−0.263798	−	0.152304i	0.362268	−	0.932074i	$-0.382002\pi$
$127$	−2.97285	−	1.71637i	−0.263798	−	0.152304i	−0.626066	+	0.779770i	$0.715336\pi$
$128$	11.1195	+	2.08706i	0.982838	+	0.184471i
$129$	3.37738			0.297362
$130$	−0.539928	−	0.389471i	−0.0473548	−	0.0341588i
$131$			6.21933i			0.543385i	0.962384	+	0.271693i	$0.0875834\pi$
$131$			6.21933i			0.543385i	−0.962384	+	0.271693i	$0.912417\pi$
$132$	−4.03514	−	12.1362i	−0.351214	−	1.05632i
$133$			11.8591i			1.02831i
$134$	−5.11631	+	10.3838i	−0.441982	+	0.897024i
$135$			0.235101i			0.0202343i
$136$	2.25066	−	0.502547i	0.192993	−	0.0430931i
$137$			13.3865i			1.14368i	0.820365	+	0.571841i	$0.193771\pi$
$137$			13.3865i			1.14368i	−0.820365	+	0.571841i	$0.806229\pi$
$138$	4.23341	−	5.86883i	0.360372	−	0.499588i
$139$	−13.4337			−1.13944			−0.569718	−	0.821841i	$-0.692947\pi$
$139$	−13.4337			−1.13944			−0.569718	+	0.821841i	$0.692947\pi$
$140$	−1.29338	+	0.430032i	−0.109310	+	0.0363443i
$141$	−2.62685	−	1.51661i	−0.221221	−	0.127722i
$142$	2.83202	+	0.287883i	0.237658	+	0.0241586i
$143$		−	12.8044i		−	1.07075i
$144$	−0.472415	−	3.97201i	−0.0393679	−	0.331000i
$145$	0.822355	+	0.474787i	0.0682929	+	0.0394289i
$146$	−15.9055	−	11.4733i	−1.31635	−	0.949533i
$147$	−0.701357	−	1.21479i	−0.0578470	−	0.100194i
$148$	22.4138	+	4.60442i	1.84240	+	0.378481i
$149$	−12.0870			−0.990208			−0.495104	−	0.868834i	$-0.664870\pi$
$149$	−12.0870			−0.990208			−0.495104	+	0.868834i	$0.664870\pi$
$150$	−6.37858	+	2.86607i	−0.520809	+	0.234014i
$151$	11.4766	−	6.62604i	0.933955	−	0.539219i	0.0458947	−	0.998946i	$-0.485386\pi$
$151$	11.4766	−	6.62604i	0.933955	−	0.539219i	0.888060	+	0.459727i	$0.152053\pi$
$152$	2.52166	+	11.2933i	0.204534	+	0.916008i
$153$	−0.407663	−	0.706092i	−0.0329576	−	0.0570842i
$154$	−21.2607	−	15.3362i	−1.71324	−	1.23582i
$155$	−1.02982	−	0.594569i	−0.0827174	−	0.0477569i
$156$	0.805842	−	3.92274i	0.0645190	−	0.314071i
$157$	−8.85140	−	15.3311i	−0.706419	−	1.22355i	−0.966177	−	0.257880i	$-0.916976\pi$
$157$	−8.85140	−	15.3311i	−0.706419	−	1.22355i	0.259758	−	0.965674i	$-0.416357\pi$
$158$	1.84416	−	18.1418i	0.146714	−	1.44329i
$159$		−	6.57075i		−	0.521095i
$160$	−1.14023	+	0.684534i	−0.0901433	+	0.0541172i
$161$		−	14.8325i		−	1.16897i
$162$	−1.28998	+	0.579621i	−0.101350	+	0.0455393i
$163$	−13.0435	−	7.53069i	−1.02165	−	0.589849i	−0.107068	−	0.994252i	$-0.534146\pi$
$163$	−13.0435	−	7.53069i	−1.02165	−	0.589849i	−0.914581	+	0.404402i	$0.867480\pi$
$164$	6.11850	−	2.03433i	0.477774	−	0.158854i
$165$	1.30199	+	0.751703i	0.101360	+	0.0585200i
$166$	4.31516	−	5.98216i	0.334921	−	0.464305i
$167$	−10.0484	−	5.80146i	−0.777570	−	0.448930i	0.0579983	−	0.998317i	$-0.481528\pi$
$167$	−10.0484	−	5.80146i	−0.777570	−	0.448930i	−0.835568	+	0.549386i	$0.814862\pi$
$168$	−5.54826	−	6.03643i	−0.428058	−	0.465721i
$169$	−4.49534	+	7.78615i	−0.345795	+	0.598935i
$170$	−0.158588	+	0.219852i	−0.0121631	+	0.0168619i
$171$	3.54301	−	2.04556i	0.270941	−	0.156428i
$172$	4.48543	−	5.05052i	0.342011	−	0.385099i
$173$	−3.67434	−	6.36414i	−0.279355	−	0.483857i	0.691870	−	0.722022i	$-0.256787\pi$
$173$	−3.67434	−	6.36414i	−0.279355	−	0.483857i	−0.971225	+	0.238165i	$0.923454\pi$
$174$	−0.577665	+	5.68274i	−0.0437927	+	0.430807i
$175$	−7.16675	+	12.4132i	−0.541755	+	0.938348i
$176$	−23.5074	−	10.0837i	−1.77194	−	0.760088i
$177$		−	8.62896i		−	0.648592i
$178$	−5.35954	+	2.40818i	−0.401714	+	0.180501i
$179$	−2.89766			−0.216581			−0.108291	−	0.994119i	$-0.534538\pi$
$179$	−2.89766			−0.216581			−0.108291	+	0.994119i	$0.534538\pi$
$180$	0.351569	+	0.312232i	0.0262044	+	0.0232724i
$181$	−5.46241	+	9.46117i	−0.406018	+	0.703243i	−0.994439	−	0.105311i	$-0.966416\pi$
$181$	−5.46241	+	9.46117i	−0.406018	+	0.703243i	0.588422	+	0.808554i	$0.299749\pi$
$182$	−3.36426	−	7.48733i	−0.249376	−	0.554998i
$183$	10.8670	−	6.27409i	0.803315	−	0.463794i
$184$	−3.15392	−	14.1249i	−0.232510	−	1.04130i
$185$	−2.32941	+	1.34488i	−0.171261	+	0.0988779i
$186$	0.723402	−	7.11641i	0.0530424	−	0.521800i
$187$	−5.21378			−0.381270
$188$	−5.75661	+	1.91400i	−0.419844	+	0.139593i
$189$	−1.44937	+	2.51039i	−0.105426	+	0.182604i
$190$	−1.10317	−	0.795757i	−0.0800323	−	0.0577303i
$191$	12.5615	+	21.7571i	0.908916	+	1.57429i	0.815573	+	0.578655i	$0.196422\pi$
$191$	12.5615	+	21.7571i	0.908916	+	1.57429i	0.0933432	+	0.995634i	$0.470245\pi$
$192$	−6.56712	−	4.56869i	−0.473941	−	0.329717i
$193$	7.83761			0.564164			0.282082	−	0.959390i	$-0.408975\pi$
$193$	7.83761			0.564164			0.282082	+	0.959390i	$0.408975\pi$
$194$	4.32313	−	5.99321i	0.310383	−	0.430287i
$195$	0.235375	+	0.407681i	0.0168555	+	0.0291946i
$196$	−2.74804	−	0.564525i	−0.196289	−	0.0403232i
$197$	−16.3087	−	9.41585i	−1.16195	−	0.670852i	−0.210179	−	0.977663i	$-0.567405\pi$
$197$	−16.3087	−	9.41585i	−1.16195	−	0.670852i	−0.951770	+	0.306811i	$0.900738\pi$
$198$	−0.914584	+	8.99714i	−0.0649966	+	0.639399i
$199$	3.18870	−	1.84100i	0.226041	−	0.130505i	−0.382703	−	0.923871i	$-0.625007\pi$
$199$	3.18870	−	1.84100i	0.226041	−	0.130505i	0.608744	+	0.793366i	$0.291673\pi$
$200$	−4.18535	+	13.3449i	−0.295949	+	0.943625i
$201$	6.30929	−	5.21467i	0.445023	−	0.367815i
$202$	−21.5360	−	2.18919i	−1.51527	−	0.154031i
$203$	5.85403	+	10.1395i	0.410872	+	0.711651i
$204$	−1.59730	−	0.328129i	−0.111833	−	0.0229736i
$205$	−0.378972	+	0.656399i	−0.0264686	+	0.0458449i
$206$	19.7194	+	2.00453i	1.37392	+	0.139662i
$207$	−4.43135	+	2.55844i	−0.308000	+	0.177824i
$208$	−4.79583	−	6.41476i	−0.332531	−	0.444784i
$209$		−	26.1615i		−	1.80963i
$210$	0.958841	+	0.0974687i	0.0661663	+	0.00672598i
$211$	−13.5030	+	7.79595i	−0.929583	+	0.536695i	−0.886680	−	0.462384i	$-0.846994\pi$
$211$	−13.5030	+	7.79595i	−0.929583	+	0.536695i	−0.0429036	+	0.999079i	$0.513661\pi$
$212$	−9.82587	−	8.72648i	−0.674844	−	0.599337i
$213$	−1.74319	−	1.00643i	−0.119441	−	0.0689595i
$214$	0.952492	+	2.11982i	0.0651110	+	0.144908i
$215$			0.794025i			0.0541521i
$216$	−0.846427	+	2.69881i	−0.0575921	+	0.183631i
$217$	−7.33091	−	12.6975i	−0.497655	−	0.861963i
$218$	8.37664	+	18.6426i	0.567338	+	1.26264i
$219$	6.93381	+	12.0097i	0.468543	+	0.811541i
$220$	2.85323	−	0.948665i	0.192365	−	0.0639590i
$221$	−1.41383	−	0.816275i	−0.0951045	−	0.0549086i
$222$	−13.1222	−	9.46555i	−0.880706	−	0.635286i
$223$			14.9141i			0.998722i	0.866394	+	0.499361i	$0.166432\pi$
$223$			14.9141i			0.998722i	−0.866394	+	0.499361i	$0.833568\pi$
$224$	−16.3954	+	0.279984i	−1.09546	+	0.0187072i
$225$	4.94473			0.329649
$226$	−1.42022	−	0.144370i	−0.0944719	−	0.00960332i
$227$	9.23332	+	5.33086i	0.612837	+	0.353821i	0.774075	−	0.633094i	$-0.218215\pi$
$227$	9.23332	+	5.33086i	0.612837	+	0.353821i	−0.161238	+	0.986916i	$0.551549\pi$
$228$	1.64648	−	8.01486i	0.109041	−	0.530797i
$229$	−2.06775	+	1.19381i	−0.136641	+	0.0788894i	−0.566762	−	0.823882i	$-0.691804\pi$
$229$	−2.06775	+	1.19381i	−0.136641	+	0.0788894i	0.430121	+	0.902771i	$0.358471\pi$
$230$	1.37977	+	0.995277i	0.0909791	+	0.0656267i
$231$	9.26834	+	16.0532i	0.609812	+	1.05622i
$232$	7.73075	+	8.41096i	0.507549	+	0.552206i
$233$	−21.8723	−	12.6280i	−1.43290	−	0.827288i	−0.435563	−	0.900158i	$-0.643451\pi$
$233$	−21.8723	−	12.6280i	−1.43290	−	0.827288i	−0.997341	+	0.0728705i	$0.976784\pi$
$234$	−1.65661	+	2.29658i	−0.108296	+	0.150132i
$235$	0.356557	−	0.617575i	0.0232592	−	0.0402862i
$236$	−12.9037	−	11.4599i	−0.839960	−	0.745978i
$237$	−6.44716	+	11.1668i	−0.418788	+	0.725362i
$238$	−3.04876	+	1.36989i	−0.197621	+	0.0887966i
$239$	2.77589	−	4.80799i	0.179558	−	0.311003i	−0.762171	−	0.647375i	$-0.775867\pi$
$239$	2.77589	−	4.80799i	0.179558	−	0.311003i	0.941729	+	0.336372i	$0.109200\pi$
$240$	0.933821	−	0.111065i	0.0602779	−	0.00716922i
$241$	−9.81905			−0.632501			−0.316250	−	0.948676i	$-0.602424\pi$
$241$	−9.81905			−0.632501			−0.316250	+	0.948676i	$0.602424\pi$
$242$	34.2854	+	24.7313i	2.20395	+	1.58979i
$243$	1.00000			0.0641500
$244$	5.05004	−	24.5830i	0.323296	−	1.57377i
$245$	0.285597	−	0.164890i	0.0182461	−	0.0105344i
$246$	−4.53593	−	0.461089i	−0.289200	−	0.0293980i
$247$	4.09588	−	7.09427i	0.260615	−	0.451398i
$248$	−9.68111	−	10.5329i	−0.614751	−	0.668841i
$249$	−4.51692	+	2.60784i	−0.286248	+	0.165265i
$250$	−1.35516	−	3.01598i	−0.0857080	−	0.190747i
$251$	8.15118	+	14.1183i	0.514498	+	0.891137i	0.999858	+	0.0168226i	$0.00535505\pi$
$251$	8.15118	+	14.1183i	0.514498	+	0.891137i	−0.485360	+	0.874314i	$0.661312\pi$
$252$	1.82914	+	5.50137i	0.115225	+	0.346554i
$253$			32.7210i			2.05715i
$254$	4.82975	+	0.490957i	0.303045	+	0.0308054i
$255$	0.166003	−	0.0958418i	0.0103955	−	0.00600185i
$256$	−15.5536	+	3.75287i	−0.972103	+	0.234554i
$257$	−5.29612	+	9.17315i	−0.330363	+	0.572206i	−0.982583	−	0.185824i	$-0.940505\pi$
$257$	−5.29612	+	9.17315i	−0.330363	+	0.572206i	0.652220	+	0.758030i	$0.273838\pi$
$258$	−4.35674	+	1.95760i	−0.271239	+	0.121875i
$259$	−33.1643			−2.06073
$260$	0.922240	+	0.189454i	0.0571949	+	0.0117494i
$261$	2.01950	−	3.49788i	0.125004	−	0.216514i
$262$	−3.60486	−	8.02279i	−0.222709	−	0.495650i
$263$		−	14.1911i		−	0.875058i	−0.899204	−	0.437529i	$-0.855854\pi$
$263$		−	14.1911i		−	0.875058i	0.899204	−	0.437529i	$-0.144146\pi$
$264$	12.2396	+	13.3166i	0.753298	+	0.819579i
$265$	1.54479			0.0948956
$266$	−6.87378	−	15.2979i	−0.421458	−	0.937977i
$267$	4.15475			0.254267
$268$	0.581243	−	16.3604i	0.0355051	−	0.999369i
$269$	−24.0676			−1.46743			−0.733714	−	0.679458i	$-0.762215\pi$
$269$	−24.0676			−1.46743			−0.733714	+	0.679458i	$0.762215\pi$
$270$	−0.136269	−	0.303274i	−0.00829309	−	0.0184567i
$271$	21.5190			1.30719			0.653594	−	0.756846i	$-0.273261\pi$
$271$	21.5190			1.30719			0.653594	+	0.756846i	$0.273261\pi$
$272$	−2.61202	+	1.95281i	−0.158377	+	0.118406i
$273$			5.80424i			0.351289i
$274$	−7.75907	−	17.2682i	−0.468743	−	1.04321i
$275$	15.8101	−	27.3839i	0.953384	−	1.65131i
$276$	−2.05930	+	10.0244i	−0.123955	+	0.603399i
$277$	3.85303			0.231506			0.115753	−	0.993278i	$-0.463072\pi$
$277$	3.85303			0.231506			0.115753	+	0.993278i	$0.463072\pi$
$278$	17.3292	−	7.78648i	1.03934	−	0.467002i
$279$	−2.52900	+	4.38035i	−0.151407	+	0.262245i
$280$	1.41917	−	1.30440i	0.0848116	−	0.0779528i
$281$	0.365712	−	0.211144i	0.0218165	−	0.0125958i	−0.489052	−	0.872255i	$-0.662657\pi$
$281$	0.365712	−	0.211144i	0.0218165	−	0.0125958i	0.510869	+	0.859659i	$0.329324\pi$
$282$	4.26764	+	0.433817i	0.254134	+	0.0258334i
$283$		−	29.9940i		−	1.78296i	−0.453061	−	0.891480i	$-0.649668\pi$
$283$		−	29.9940i		−	1.78296i	0.453061	−	0.891480i	$-0.350332\pi$
$284$	−3.82011	+	1.27014i	−0.226682	+	0.0753689i
$285$	0.480912	+	0.832964i	0.0284868	+	0.0493405i
$286$	7.42167	+	16.5173i	0.438853	+	0.976689i
$287$	−8.09327	+	4.67265i	−0.477731	+	0.275818i
$288$	2.91166	+	4.84997i	0.171571	+	0.285787i
$289$	8.16762	−	14.1467i	0.480448	−	0.832161i
$290$	−1.33602	−	0.135810i	−0.0784535	−	0.00797501i
$291$	−4.52526	+	2.61266i	−0.265276	+	0.153157i
$292$	27.1679	+	5.58105i	1.58988	+	0.326606i
$293$	19.8679			1.16070			0.580348	−	0.814369i	$-0.302917\pi$
$293$	19.8679			1.16070			0.580348	+	0.814369i	$0.302917\pi$
$294$	1.60885	+	1.16052i	0.0938301	+	0.0676832i
$295$	2.02868			0.118114
$296$	−31.5821	+	7.05191i	−1.83567	+	0.409884i
$297$	3.19736	−	5.53800i	0.185530	−	0.321347i
$298$	15.5920	−	7.00590i	0.903219	−	0.405841i
$299$	−5.12284	+	8.87302i	−0.296262	+	0.513140i
$300$	6.56699	−	7.39432i	0.379145	−	0.426911i
$301$	−4.89508	+	8.47853i	−0.282148	+	0.488694i
$302$	−10.9640	+	15.1995i	−0.630907	+	0.874635i
$303$	13.2560	+	7.65337i	0.761539	+	0.439675i
$304$	−9.79873	−	13.1065i	−0.561996	−	0.751709i
$305$	1.47504	+	2.55485i	0.0844607	+	0.146290i
$306$	0.935141	+	0.674553i	0.0534585	+	0.0385616i
$307$	2.56878	−	1.48308i	0.146608	−	0.0846441i	−0.424902	−	0.905240i	$-0.639691\pi$
$307$	2.56878	−	1.48308i	0.146608	−	0.0846441i	0.571510	+	0.820595i	$0.306358\pi$
$308$	36.3150	+	7.46012i	2.06924	+	0.425080i
$309$	−12.1379	−	7.00780i	−0.690499	−	0.398660i
$310$	1.67307	+	0.170072i	0.0950241	+	0.00965946i
$311$	−6.28873			−0.356601			−0.178300	−	0.983976i	$-0.557060\pi$
$311$	−6.28873			−0.356601			−0.178300	+	0.983976i	$0.557060\pi$
$312$	1.23419	+	5.52733i	0.0698722	+	0.312923i
$313$		−	2.18292i		−	0.123386i	−0.998095	−	0.0616930i	$-0.980350\pi$
$313$		−	2.18292i		−	0.123386i	0.998095	−	0.0616930i	$-0.0196500\pi$
$314$	20.3043	+	14.6463i	1.14584	+	0.826537i
$315$	−0.590194	−	0.340748i	−0.0332536	−	0.0191990i
$316$	8.13646	+	24.4714i	0.457711	+	1.37663i
$317$	6.98396	+	12.0966i	0.392259	+	0.679412i	0.992747	−	0.120222i	$-0.0383605\pi$
$317$	6.98396	+	12.0966i	0.392259	+	0.679412i	−0.600489	+	0.799633i	$0.705027\pi$
$318$	3.80855	+	8.47612i	0.213573	+	0.475317i
$319$	−12.9142	−	22.3680i	−0.723055	−	1.25237i
$320$	1.07410	−	1.54394i	0.0600441	−	0.0863086i
$321$		−	1.64330i		−	0.0917201i
$322$	8.59724	+	19.1336i	0.479106	+	1.06627i
$323$	−2.88870	−	1.66779i	−0.160732	−	0.0927985i
$324$	1.32808	−	1.49540i	0.0737821	−	0.0830775i
$325$	8.57450	−	4.95049i	0.475628	−	0.274604i
$326$	21.1908	+	2.15410i	1.17365	+	0.119305i
$327$		−	14.4519i		−	0.799193i
$328$	−6.71358	+	6.17064i	−0.370695	+	0.340717i
$329$	7.61458	−	4.39628i	0.419805	−	0.242375i
$330$	−2.11524	−	0.215019i	−0.116440	−	0.0118364i
$331$	−6.25903	+	10.8410i	−0.344027	+	0.595873i	−0.985177	−	0.171543i	$-0.945125\pi$
$331$	−6.25903	+	10.8410i	−0.344027	+	0.595873i	0.641149	+	0.767416i	$0.278458\pi$
$332$	−2.09906	+	10.2180i	−0.115201	+	0.560786i
$333$	5.72046	+	9.90813i	0.313479	+	0.542962i
$334$	16.3249	+	1.65947i	0.893257	+	0.0908020i
$335$	1.22597	+	1.48332i	0.0669821	+	0.0810424i
$336$	10.6560	+	4.57097i	0.581331	+	0.249367i
$337$	−29.1412	+	16.8247i	−1.58742	+	0.916497i	−0.593690	+	0.804694i	$0.702329\pi$
$337$	−29.1412	+	16.8247i	−1.58742	+	0.916497i	−0.993730	+	0.111803i	$0.964337\pi$
$338$	1.28586	−	12.6495i	0.0699416	−	0.688045i
$339$	0.874188	+	0.504713i	0.0474794	+	0.0274122i
$340$	0.0771435	−	0.375525i	0.00418369	−	0.0203657i
$341$	16.1722	+	28.0111i	0.875776	+	1.51689i
$342$	−3.38475	+	4.69232i	−0.183026	+	0.253732i
$343$	−16.2251			−0.876073
$344$	−2.85871	+	9.11490i	−0.154131	+	0.491443i
$345$	−0.601491	−	1.04181i	−0.0323832	−	0.0560893i
$346$	8.42861	+	6.07987i	0.453125	+	0.326856i
$347$	9.04189	−	15.6610i	0.485394	−	0.840727i	−0.514465	−	0.857511i	$-0.672009\pi$
$347$	9.04189	−	15.6610i	0.485394	−	0.840727i	0.999859	+	0.0167840i	$0.00534275\pi$
$348$	−2.54866	−	7.66542i	−0.136622	−	0.410910i
$349$	−13.5860			−0.727242			−0.363621	−	0.931547i	$-0.618460\pi$
$349$	−13.5860			−0.727242			−0.363621	+	0.931547i	$0.618460\pi$
$350$	2.05000	−	20.1667i	0.109577	−	1.07796i
$351$	1.73407	−	1.00116i	0.0925577	−	0.0534382i
$352$	36.1688	−	0.617654i	1.92780	−	0.0329210i
$353$	−19.4263	+	11.2158i	−1.03396	+	0.596955i	−0.918116	−	0.396313i	$-0.870290\pi$
$353$	−19.4263	+	11.2158i	−1.03396	+	0.596955i	−0.115841	+	0.993268i	$0.536956\pi$
$354$	5.00153	+	11.1312i	0.265828	+	0.591614i
$355$	0.236613	−	0.409825i	0.0125581	−	0.0217513i
$356$	5.51784	−	6.21300i	0.292445	−	0.329288i
$357$	2.36342			0.125085
$358$	3.73792	−	1.67955i	0.197555	−	0.0887668i
$359$		−	5.52164i		−	0.291421i	−0.989327	−	0.145710i	$-0.953453\pi$
$359$		−	5.52164i		−	0.291421i	0.989327	−	0.145710i	$-0.0465468\pi$
$360$	−0.634492	−	0.198996i	−0.0334406	−	0.0104880i
$361$	−1.13140	+	1.95964i	−0.0595472	+	0.103139i
$362$	1.56248	−	15.3708i	0.0821223	−	0.807872i
$363$	−14.9463	−	25.8877i	−0.784475	−	1.35875i
$364$	8.67964	+	7.70849i	0.454937	+	0.404035i
$365$	−2.82349	+	1.63014i	−0.147788	+	0.0853256i
$366$	−10.3816	+	14.3922i	−0.542656	+	0.752292i
$367$	−0.139450	+	0.241535i	−0.00727925	+	0.0126080i	−0.869642	−	0.493683i	$-0.835650\pi$
$367$	−0.139450	+	0.241535i	−0.00727925	+	0.0126080i	0.862363	+	0.506291i	$0.168984\pi$
$368$	12.2556	+	16.3927i	0.638866	+	0.854528i
$369$	2.79199	+	1.61196i	0.145345	+	0.0839151i
$370$	2.22536	−	3.08504i	0.115691	−	0.160384i
$371$	16.4951	+	9.52346i	0.856384	+	0.494434i
$372$	3.19165	+	9.59930i	0.165479	+	0.497700i
$373$	18.3750	+	10.6088i	0.951423	+	0.549304i	0.893523	−	0.449018i	$-0.148226\pi$
$373$	18.3750	+	10.6088i	0.951423	+	0.549304i	0.0579003	+	0.998322i	$0.481559\pi$
$374$	6.72566	−	3.02202i	0.347775	−	0.156265i
$375$			2.33801i			0.120734i
$376$	6.31649	−	5.80567i	0.325748	−	0.299405i
$377$		−	8.08743i		−	0.416524i
$378$	0.414583	−	4.07842i	0.0213238	−	0.209772i
$379$	−4.23662	−	7.33804i	−0.217621	−	0.376930i	0.736459	−	0.676482i	$-0.236496\pi$
$379$	−4.23662	−	7.33804i	−0.217621	−	0.376930i	−0.954080	+	0.299552i	$0.903163\pi$
$380$	1.88430	+	0.387088i	0.0966625	+	0.0198572i
$381$	−2.97285	−	1.71637i	−0.152304	−	0.0879325i
$382$	−28.8149	−	20.7853i	−1.47430	−	1.06347i
$383$	−1.97404	−	3.41913i	−0.100869	−	0.174710i	0.811174	−	0.584805i	$-0.198829\pi$
$383$	−1.97404	−	3.41913i	−0.100869	−	0.174710i	−0.912043	+	0.410095i	$0.865496\pi$
$384$	11.1195	+	2.08706i	0.567442	+	0.106505i
$385$	−3.77413	+	2.17899i	−0.192347	+	0.111052i
$386$	−10.1103	+	4.54285i	−0.514603	+	0.231225i
$387$	3.37738			0.171682
$388$	−2.10294	+	10.2369i	−0.106761	+	0.519699i
$389$	−10.0597	−	17.4240i	−0.510048	−	0.883430i	−0.999932	−	0.0116419i	$-0.996294\pi$
$389$	−10.0597	−	17.4240i	−0.510048	−	0.883430i	0.489884	−	0.871788i	$-0.337039\pi$
$390$	−0.539928	−	0.389471i	−0.0273403	−	0.0197216i
$391$	3.61299	+	2.08596i	0.182717	+	0.105492i
$392$	3.87212	−	0.864600i	0.195572	−	0.0436689i
$393$			6.21933i			0.313724i
$394$	26.4955	+	2.69334i	1.33482	+	0.135689i
$395$	−2.62532	−	1.51573i	−0.132094	−	0.0762647i
$396$	−4.03514	−	12.1362i	−0.202774	−	0.609868i
$397$	−25.7933			−1.29453			−0.647264	−	0.762266i	$-0.724087\pi$
$397$	−25.7933			−1.29453			−0.647264	+	0.762266i	$0.724087\pi$
$398$	−3.04627	+	4.22309i	−0.152696	+	0.211684i
$399$			11.8591i			0.593697i
$400$	−2.33596	−	19.6405i	−0.116798	−	0.982024i
$401$			1.07761i			0.0538134i	0.999638	+	0.0269067i	$0.00856571\pi$
$401$			1.07761i			0.0538134i	−0.999638	+	0.0269067i	$0.991434\pi$
$402$	−5.11631	+	10.3838i	−0.255178	+	0.517897i
$403$			10.1278i			0.504500i
$404$	29.0499	−	9.65872i	1.44528	−	0.480539i
$405$			0.235101i			0.0116823i
$406$	−13.4286	−	9.68656i	−0.666451	−	0.480736i
$407$	73.1615			3.62648
$408$	2.25066	−	0.502547i	0.111424	−	0.0248798i
$409$	17.3718	+	10.0296i	0.858982	+	0.495934i	0.863671	−	0.504055i	$-0.168159\pi$
$409$	17.3718	+	10.0296i	0.858982	+	0.495934i	−0.00468923	+	0.999989i	$0.501493\pi$
$410$	0.108402	−	1.06640i	0.00535361	−	0.0526658i
$411$			13.3865i			0.660305i
$412$	−26.5995	+	8.84400i	−1.31046	+	0.435712i
$413$	21.6620	+	12.5066i	1.06592	+	0.615408i
$414$	4.23341	−	5.86883i	0.208061	−	0.288437i
$415$	−0.613106	−	1.06193i	−0.0300962	−	0.0521281i
$416$	9.90464	+	5.49513i	0.485615	+	0.269421i
$417$	−13.4337			−0.657853
$418$	15.1638	+	33.7478i	0.741685	+	1.65066i
$419$	−31.3443	+	18.0966i	−1.53127	+	0.884078i	−0.531964	+	0.846767i	$0.678546\pi$
$419$	−31.3443	+	18.0966i	−1.53127	+	0.884078i	−0.999304	+	0.0373114i	$0.988121\pi$
$420$	−1.29338	+	0.430032i	−0.0631103	+	0.0209834i
$421$	5.64428	+	9.77618i	0.275085	+	0.476462i	0.970157	−	0.242479i	$-0.0779606\pi$
$421$	5.64428	+	9.77618i	0.275085	+	0.476462i	−0.695071	+	0.718941i	$0.744627\pi$
$422$	12.8998	−	17.8832i	0.627954	−	0.870541i
$423$	−2.62685	−	1.51661i	−0.127722	−	0.0737403i
$424$	17.7332	+	5.56166i	0.861200	+	0.270098i
$425$	−2.01578	−	3.49143i	−0.0977797	−	0.169359i
$426$	2.83202	+	0.287883i	0.137212	+	0.0139480i
$427$			36.3739i			1.76026i
$428$	−2.45738	−	2.18243i	−0.118782	−	0.105492i
$429$		−	12.8044i		−	0.618200i
$430$	−0.460234	−	1.02427i	−0.0221944	−	0.0493949i
$431$	24.1928	+	13.9677i	1.16533	+	0.672801i	0.952575	−	0.304305i	$-0.0984242\pi$
$431$	24.1928	+	13.9677i	1.16533	+	0.672801i	0.212752	+	0.977106i	$0.431757\pi$
$432$	−0.472415	−	3.97201i	−0.0227291	−	0.191103i
$433$	5.61433	+	3.24143i	0.269807	+	0.155773i	0.628800	−	0.777567i	$-0.283546\pi$
$433$	5.61433	+	3.24143i	0.269807	+	0.155773i	−0.358993	+	0.933340i	$0.616880\pi$
$434$	16.8164	+	12.1303i	0.807215	+	0.582275i
$435$	0.822355	+	0.474787i	0.0394289	+	0.0227643i
$436$	−21.6113	−	19.1933i	−1.03500	−	0.919192i
$437$	−10.4669	+	18.1291i	−0.500698	+	0.867234i
$438$	−15.9055	−	11.4733i	−0.759995	−	0.548213i
$439$	−8.75700	+	5.05586i	−0.417949	+	0.241303i	−0.694199	−	0.719783i	$-0.744241\pi$
$439$	−8.75700	+	5.05586i	−0.417949	+	0.241303i	0.276250	+	0.961086i	$0.410908\pi$
$440$	−3.13074	+	2.87755i	−0.149252	+	0.137182i
$441$	−0.701357	−	1.21479i	−0.0333980	−	0.0578470i
$442$	2.29694	+	0.233490i	0.109254	+	0.0111060i
$443$	1.33530	−	2.31281i	0.0634421	−	0.109885i	−0.832560	−	0.553935i	$-0.813126\pi$
$443$	1.33530	−	2.31281i	0.0634421	−	0.109885i	0.896002	+	0.444050i	$0.146459\pi$
$444$	22.4138	+	4.60442i	1.06371	+	0.218516i
$445$			0.976786i			0.0463041i
$446$	−8.64453	−	19.2388i	−0.409330	−	0.910985i
$447$	−12.0870			−0.571697
$448$	20.9874	−	9.86428i	0.991560	−	0.466044i
$449$	8.97459	−	15.5445i	0.423537	−	0.733588i	−0.572745	−	0.819733i	$-0.694122\pi$
$449$	8.97459	−	15.5445i	0.423537	−	0.733588i	0.996283	+	0.0861453i	$0.0274549\pi$
$450$	−6.37858	+	2.86607i	−0.300689	+	0.135108i
$451$	17.8540	−	10.3080i	0.840713	−	0.485386i
$452$	1.91574	−	0.636959i	0.0901086	−	0.0299600i
$453$	11.4766	−	6.62604i	0.539219	−	0.311318i
$454$	−15.0006	−	1.52485i	−0.704015	−	0.0715650i
$455$	−1.36458			−0.0639726
$456$	2.52166	+	11.2933i	0.118088	+	0.528858i
$457$	19.8496	−	34.3805i	0.928524	−	1.60825i	0.142731	−	0.989762i	$-0.454412\pi$
$457$	19.8496	−	34.3805i	0.928524	−	1.60825i	0.785793	−	0.618489i	$-0.212255\pi$
$458$	1.97538	−	2.73850i	0.0923036	−	0.127962i
$459$	−0.407663	−	0.706092i	−0.0190281	−	0.0329576i
$460$	−2.35675	−	0.484143i	−0.109884	−	0.0225733i
$461$	4.66725			0.217376			0.108688	−	0.994076i	$-0.465335\pi$
$461$	4.66725			0.217376			0.108688	+	0.994076i	$0.465335\pi$
$462$	−21.2607	−	15.3362i	−0.989139	−	0.713503i
$463$	−4.46536	−	7.73423i	−0.207523	−	0.359440i	0.743411	−	0.668835i	$-0.233207\pi$
$463$	−4.46536	−	7.73423i	−0.207523	−	0.359440i	−0.950934	+	0.309395i	$0.899874\pi$
$464$	−14.8477	−	6.36903i	−0.689285	−	0.295675i
$465$	−1.02982	−	0.594569i	−0.0477569	−	0.0275725i
$466$	35.5343	+	3.61215i	1.64609	+	0.167330i
$467$	−30.1132	+	17.3859i	−1.39347	+	0.804522i	−0.993698	−	0.112091i	$-0.964245\pi$
$467$	−30.1132	+	17.3859i	−1.39347	+	0.804522i	−0.399775	+	0.916613i	$0.630912\pi$
$468$	0.805842	−	3.92274i	0.0372500	−	0.181329i
$469$	3.94632	+	23.3968i	0.182224	+	1.08036i
$470$	−0.101991	+	1.00333i	−0.00470448	+	0.0462800i
$471$	−8.85140	−	15.3311i	−0.407851	−	0.706419i
$472$	23.2879	+	7.30379i	1.07191	+	0.336184i
$473$	10.7987	−	18.7039i	0.496526	−	0.860007i
$474$	1.84416	−	18.1418i	0.0847053	−	0.833281i
$475$	17.5192	−	10.1147i	0.803836	−	0.464095i
$476$	3.13881	−	3.53425i	0.143867	−	0.161992i
$477$		−	6.57075i		−	0.300854i
$478$	−0.794026	+	7.81116i	−0.0363179	+	0.357274i
$479$	−7.53961	+	4.35300i	−0.344494	+	0.198894i	−0.662257	−	0.749276i	$-0.730401\pi$
$479$	−7.53961	+	4.35300i	−0.344494	+	0.198894i	0.317764	+	0.948170i	$0.397068\pi$
$480$	−1.14023	+	0.684534i	−0.0520442	+	0.0312446i
$481$	19.8393	+	11.4542i	0.904596	+	0.522269i
$482$	12.6663	−	5.69133i	0.576936	−	0.259233i
$483$		−	14.8325i		−	0.674903i
$484$	−58.5621	−	12.0303i	−2.66192	−	0.546832i
$485$	−0.614239	−	1.06389i	−0.0278911	−	0.0483089i
$486$	−1.28998	+	0.579621i	−0.0585145	+	0.0262922i
$487$	9.23049	+	15.9877i	0.418273	+	0.724471i	0.995766	−	0.0919253i	$-0.0293021\pi$
$487$	9.23049	+	15.9877i	0.418273	+	0.724471i	−0.577493	+	0.816396i	$0.695969\pi$
$488$	7.73440	+	34.6386i	0.350120	+	1.56802i
$489$	−13.0435	−	7.53069i	−0.589849	−	0.340550i
$490$	−0.272840	+	0.378242i	−0.0123257	+	0.0170872i
$491$			2.21211i			0.0998313i	0.998753	+	0.0499157i	$0.0158953\pi$
$491$			2.21211i			0.0998313i	−0.998753	+	0.0499157i	$0.984105\pi$
$492$	6.11850	−	2.03433i	0.275843	−	0.0917145i
$493$	−3.29311			−0.148314
$494$	−1.17160	+	11.5255i	−0.0527127	+	0.518557i
$495$	1.30199	+	0.751703i	0.0585200	+	0.0337865i
$496$	18.5935	+	7.97584i	0.834873	+	0.358126i
$497$	5.05306	−	2.91739i	0.226661	−	0.130863i
$498$	4.31516	−	5.98216i	0.193367	−	0.268067i
$499$	8.34635	+	14.4563i	0.373634	+	0.647153i	0.990122	−	0.140212i	$-0.0447783\pi$
$499$	8.34635	+	14.4563i	0.373634	+	0.647153i	−0.616488	+	0.787365i	$0.711445\pi$
$500$	3.49625	+	3.10506i	0.156357	+	0.138863i
$501$	−10.0484	−	5.80146i	−0.448930	−	0.259190i
$502$	−18.6981	−	13.4876i	−0.834536	−	0.601982i
$503$	3.99543	−	6.92029i	0.178147	−	0.308560i	−0.763099	−	0.646282i	$-0.776323\pi$
$503$	3.99543	−	6.92029i	0.178147	−	0.308560i	0.941246	+	0.337722i	$0.109656\pi$
$504$	−5.54826	−	6.03643i	−0.247139	−	0.268884i
$505$	−1.79931	+	3.11650i	−0.0800684	+	0.138682i
$506$	−18.9658	−	42.2094i	−0.843133	−	1.87644i
$507$	−4.49534	+	7.78615i	−0.199645	+	0.345795i
$508$	−6.51483	+	2.16610i	−0.289049	+	0.0961053i
$509$	−23.7360			−1.05208			−0.526040	−	0.850460i	$-0.676324\pi$
$509$	−23.7360			−1.05208			−0.526040	+	0.850460i	$0.676324\pi$
$510$	−0.158588	+	0.219852i	−0.00702239	+	0.00973523i
$511$	−40.1987			−1.77828
$512$	17.8886	−	13.8563i	0.790572	−	0.612369i
$513$	3.54301	−	2.04556i	0.156428	−	0.0903135i
$514$	1.51492	−	14.9029i	0.0668202	−	0.657339i
$515$	1.64754	−	2.85362i	0.0725992	−	0.125746i
$516$	4.48543	−	5.05052i	0.197460	−	0.222337i
$517$	−16.7980	+	9.69834i	−0.738776	+	0.426532i
$518$	42.7812	−	19.2227i	1.87970	−	0.844598i
$519$	−3.67434	−	6.36414i	−0.161286	−	0.279355i
$520$	−1.29948	+	0.290159i	−0.0569859	+	0.0127243i
$521$			39.8097i			1.74410i	0.489421	+	0.872048i	$0.337208\pi$
$521$			39.8097i			1.74410i	−0.489421	+	0.872048i	$0.662792\pi$
$522$	−0.577665	+	5.68274i	−0.0252837	+	0.248727i
$523$	−11.9338	+	6.88996i	−0.521827	+	0.301277i	−0.737682	−	0.675149i	$-0.764080\pi$
$523$	−11.9338	+	6.88996i	−0.521827	+	0.301277i	0.215855	+	0.976425i	$0.430746\pi$
$524$	9.30036	+	8.25976i	0.406288	+	0.360829i
$525$	−7.16675	+	12.4132i	−0.312783	+	0.541755i
$526$	8.22543	+	18.3061i	0.358646	+	0.798185i
$527$	4.12391			0.179640
$528$	−23.5074	−	10.0837i	−1.02303	−	0.438837i
$529$	1.59123	−	2.75609i	0.0691838	−	0.119830i
$530$	−1.99274	+	0.895392i	−0.0865592	+	0.0388934i
$531$		−	8.62896i		−	0.374465i
$532$	17.7340	+	15.7498i	0.768867	+	0.682840i
$533$	6.45534			0.279612
$534$	−5.35954	+	2.40818i	−0.231930	+	0.104212i
$535$	0.386341			0.0167030
$536$	8.73304	+	21.4414i	0.377210	+	0.926128i
$537$	−2.89766			−0.125043
$538$	31.0466	−	13.9501i	1.33852	−	0.601431i
$539$	−8.96998			−0.386364
$540$	0.351569	+	0.312232i	0.0151291	+	0.0134363i
$541$		−	42.7004i		−	1.83583i	−0.396772	−	0.917917i	$-0.629870\pi$
$541$		−	42.7004i		−	1.83583i	0.396772	−	0.917917i	$-0.370130\pi$
$542$	−27.7590	+	12.4729i	−1.19235	+	0.535756i
$543$	−5.46241	+	9.46117i	−0.234414	+	0.406018i
$544$	2.23755	−	4.03306i	0.0959343	−	0.172916i
$545$	3.39766			0.145540
$546$	−3.36426	−	7.48733i	−0.143977	−	0.320428i
$547$	12.9895	−	22.4985i	0.555393	−	0.961968i	−0.442480	−	0.896778i	$-0.645901\pi$
$547$	12.9895	−	22.4985i	0.555393	−	0.961968i	0.997873	−	0.0651899i	$-0.0207653\pi$
$548$	20.0180	+	17.7783i	0.855128	+	0.759450i
$549$	10.8670	−	6.27409i	0.463794	−	0.267772i
$550$	−4.52237	+	44.4884i	−0.192834	+	1.89699i
$551$		−	16.5240i		−	0.703948i
$552$	−3.15392	−	14.1249i	−0.134240	−	0.601195i
$553$	−18.6887	−	32.3697i	−0.794722	−	1.37650i
$554$	−4.97032	+	2.23330i	−0.211169	+	0.0948838i
$555$	−2.32941	+	1.34488i	−0.0988779	+	0.0570872i
$556$	−17.8411	+	20.0888i	−0.756630	+	0.851953i
$557$	0.168437	−	0.291741i	0.00713689	−	0.0123614i	−0.862435	−	0.506168i	$-0.831062\pi$
$557$	0.168437	−	0.291741i	0.00713689	−	0.0123614i	0.869572	+	0.493807i	$0.164395\pi$
$558$	0.723402	−	7.11641i	0.0306240	−	0.301261i
$559$	5.85661	−	3.38132i	0.247708	−	0.143014i
$560$	−1.07464	+	2.50523i	−0.0454118	+	0.105865i
$561$	−5.21378			−0.220126
$562$	−0.349376	+	0.484345i	−0.0147376	+	0.0204309i
$563$	18.7645			0.790829			0.395414	−	0.918503i	$-0.370601\pi$
$563$	18.7645			0.790829			0.395414	+	0.918503i	$0.370601\pi$
$564$	−5.75661	+	1.91400i	−0.242397	+	0.0805940i
$565$	−0.118658	+	0.205522i	−0.00499199	+	0.00864639i
$566$	17.3852	+	38.6916i	0.730753	+	1.62633i
$567$	−1.44937	+	2.51039i	−0.0608679	+	0.105426i
$568$	4.19165	−	3.85266i	0.175878	−	0.161654i
$569$	−12.3169	+	21.3335i	−0.516351	+	0.894346i	0.483469	+	0.875362i	$0.339377\pi$
$569$	−12.3169	+	21.3335i	−0.516351	+	0.894346i	−0.999820	+	0.0189846i	$0.993957\pi$
$570$	−1.10317	−	0.795757i	−0.0462066	−	0.0333306i
$571$	−41.0027	−	23.6729i	−1.71591	−	0.990681i	−0.926057	−	0.377383i	$-0.876824\pi$
$571$	−41.0027	−	23.6729i	−1.71591	−	0.990681i	−0.789852	−	0.613298i	$-0.789843\pi$
$572$	−19.1476	−	17.0052i	−0.800600	−	0.711023i
$573$	12.5615	+	21.7571i	0.524763	+	0.908916i
$574$	7.73176	−	10.7186i	0.322717	−	0.447387i
$575$	−21.9118	+	12.6508i	−0.913785	+	0.527574i
$576$	−6.56712	−	4.56869i	−0.273630	−	0.190362i
$577$	7.91971	+	4.57245i	0.329702	+	0.190353i	0.655709	−	0.755014i	$-0.272370\pi$
$577$	7.91971	+	4.57245i	0.329702	+	0.190353i	−0.326007	+	0.945367i	$0.605703\pi$
$578$	−2.33629	+	22.9831i	−0.0971769	+	0.955970i
$579$	7.83761			0.325720
$580$	1.80215	−	0.599192i	0.0748301	−	0.0248801i
$581$		−	15.1189i		−	0.627239i
$582$	4.32313	−	5.99321i	0.179199	−	0.248427i
$583$	−36.3888	−	21.0091i	−1.50707	−	0.870107i
$584$	−38.2808	+	8.54767i	−1.58407	+	0.353705i
$585$	0.235375	+	0.407681i	0.00973154	+	0.0168555i
$586$	−25.6291	+	11.5159i	−1.05873	+	0.475716i
$587$	23.3621	+	40.4644i	0.964258	+	1.67014i	0.711595	+	0.702590i	$0.247973\pi$
$587$	23.3621	+	40.4644i	0.964258	+	1.67014i	0.252663	+	0.967554i	$0.418694\pi$
$588$	−2.74804	−	0.564525i	−0.113327	−	0.0232806i
$589$			20.6928i			0.852632i
$590$	−2.61694	+	1.17586i	−0.107738	+	0.0484095i
$591$	−16.3087	−	9.41585i	−0.670852	−	0.387316i
$592$	36.6527	−	27.4024i	1.50642	−	1.12623i
$593$	30.9536	−	17.8710i	1.27111	−	0.733876i	0.295913	−	0.955215i	$-0.404376\pi$
$593$	30.9536	−	17.8710i	1.27111	−	0.733876i	0.975197	+	0.221339i	$0.0710427\pi$
$594$	−0.914584	+	8.99714i	−0.0375258	+	0.369157i
$595$			0.555642i			0.0227791i
$596$	−16.0525	+	18.0749i	−0.657537	+	0.740376i
$597$	3.18870	−	1.84100i	0.130505	−	0.0753471i
$598$	1.46535	−	14.4153i	0.0599227	−	0.589485i
$599$	−1.15356	+	1.99803i	−0.0471334	+	0.0816374i	−0.888630	−	0.458626i	$-0.848342\pi$
$599$	−1.15356	+	1.99803i	−0.0471334	+	0.0816374i	0.841496	+	0.540263i	$0.181675\pi$
$600$	−4.18535	+	13.3449i	−0.170866	+	0.544802i
$601$	−11.5336	−	19.9768i	−0.470465	−	0.814869i	0.528964	−	0.848644i	$-0.322580\pi$
$601$	−11.5336	−	19.9768i	−0.470465	−	0.814869i	−0.999429	+	0.0337747i	$0.989247\pi$
$602$	1.40020	−	13.7744i	0.0570681	−	0.561403i
$603$	6.30929	−	5.21467i	0.256934	−	0.212358i
$604$	5.33332	−	25.9620i	0.217010	−	1.05638i
$605$	6.08621	−	3.51388i	0.247440	−	0.142859i
$606$	−21.5360	−	2.18919i	−0.874841	−	0.0889299i
$607$	5.92912	+	3.42318i	0.240656	+	0.138943i	0.615478	−	0.788154i	$-0.288963\pi$
$607$	5.92912	+	3.42318i	0.240656	+	0.138943i	−0.374822	+	0.927097i	$0.622296\pi$
$608$	20.2369	+	11.2275i	0.820716	+	0.455336i
$609$	5.85403	+	10.1395i	0.237217	+	0.410872i
$610$	−3.38361	−	2.44073i	−0.136999	−	0.0988222i
$611$	−6.07353			−0.245709
$612$	−1.59730	−	0.328129i	−0.0645668	−	0.0132638i
$613$	5.95910	+	10.3215i	0.240686	+	0.416880i	0.960910	−	0.276862i	$-0.0892943\pi$
$613$	5.95910	+	10.3215i	0.240686	+	0.416880i	−0.720224	+	0.693742i	$0.755961\pi$
$614$	−2.45404	+	3.40206i	−0.0990368	+	0.137296i
$615$	−0.378972	+	0.656399i	−0.0152816	+	0.0264686i
$616$	−51.1695	+	11.4256i	−2.06168	+	0.460349i
$617$	−37.6167			−1.51439			−0.757196	−	0.653188i	$-0.773431\pi$
$617$	−37.6167			−1.51439			−0.757196	+	0.653188i	$0.773431\pi$
$618$	19.7194	+	2.00453i	0.793231	+	0.0806341i
$619$	36.8629	−	21.2828i	1.48164	−	0.855427i	0.481860	−	0.876248i	$-0.339961\pi$
$619$	36.8629	−	21.2828i	1.48164	−	0.855427i	0.999783	+	0.0208212i	$0.00662808\pi$
$620$	−2.25680	+	0.750359i	−0.0906353	+	0.0301351i
$621$	−4.43135	+	2.55844i	−0.177824	+	0.102667i
$622$	8.11231	−	3.64508i	0.325274	−	0.146154i
$623$	−6.02178	+	10.4300i	−0.241258	+	0.417871i
$624$	−4.79583	−	6.41476i	−0.191987	−	0.256796i
$625$	24.1740			0.966959
$626$	1.26527	+	2.81592i	0.0505703	+	0.112547i
$627$		−	26.1615i		−	1.04479i
$628$	−34.6814	−	7.12453i	−1.38394	−	0.284300i
$629$	4.66404	−	8.07835i	0.185967	−	0.322105i
$630$	0.958841	+	0.0974687i	0.0382011	+	0.00388325i
$631$	18.3751	+	31.8266i	0.731501	+	1.26700i	0.956242	+	0.292578i	$0.0945131\pi$
$631$	18.3751	+	31.8266i	0.731501	+	1.26700i	−0.224741	+	0.974419i	$0.572154\pi$
$632$	−24.6800	−	26.8515i	−0.981718	−	1.06810i
$633$	−13.5030	+	7.79595i	−0.536695	+	0.309861i
$634$	−16.0206	−	11.5563i	−0.636259	−	0.458957i
$635$	0.403521	−	0.698919i	0.0160132	−	0.0277357i
$636$	−9.82587	−	8.72648i	−0.389621	−	0.346027i
$637$	−2.43240	−	1.40435i	−0.0963753	−	0.0556423i
$638$	29.6240	+	21.3689i	1.17282	+	0.846002i
$639$	−1.74319	−	1.00643i	−0.0689595	−	0.0398138i
$640$	−0.490668	+	2.61421i	−0.0193954	+	0.103336i
$641$	−12.3408	−	7.12498i	−0.487434	−	0.281420i	0.236076	−	0.971735i	$-0.424139\pi$
$641$	−12.3408	−	7.12498i	−0.487434	−	0.281420i	−0.723509	+	0.690315i	$0.757472\pi$
$642$	0.952492	+	2.11982i	0.0375919	+	0.0836626i
$643$		−	6.43821i		−	0.253898i	−0.991909	−	0.126949i	$-0.959481\pi$
$643$		−	6.43821i		−	0.253898i	0.991909	−	0.126949i	$-0.0405185\pi$
$644$	−22.1805	−	19.6988i	−0.874034	−	0.776240i
$645$			0.794025i			0.0312647i
$646$	4.69305	+	0.477061i	0.184646	+	0.0187697i
$647$	−9.39544	−	16.2734i	−0.369373	−	0.639772i	0.620095	−	0.784527i	$-0.287094\pi$
$647$	−9.39544	−	16.2734i	−0.369373	−	0.639772i	−0.989468	+	0.144755i	$0.953761\pi$
$648$	−0.846427	+	2.69881i	−0.0332508	+	0.106019i
$649$	−47.7871	−	27.5899i	−1.87581	−	1.08300i
$650$	−8.19149	+	11.3560i	−0.321297	+	0.445418i
$651$	−7.33091	−	12.6975i	−0.287321	−	0.497655i
$652$	−28.5842	+	9.50390i	−1.11944	+	0.372202i
$653$	5.83640	−	3.36965i	0.228396	−	0.131864i	−0.381436	−	0.924395i	$-0.624570\pi$
$653$	5.83640	−	3.36965i	0.228396	−	0.131864i	0.609832	+	0.792531i	$0.291237\pi$
$654$	8.37664	+	18.6426i	0.327553	+	0.728985i
$655$	−1.46217			−0.0571317
$656$	5.08372	−	11.8513i	0.198486	−	0.462716i
$657$	6.93381	+	12.0097i	0.270514	+	0.468543i
$658$	−7.27445	+	10.0847i	−0.283588	+	0.393141i
$659$	14.1614	+	8.17609i	0.551650	+	0.318495i	0.749787	−	0.661679i	$-0.230156\pi$
$659$	14.1614	+	8.17609i	0.551650	+	0.318495i	−0.198137	+	0.980174i	$0.563489\pi$
$660$	2.85323	−	0.948665i	0.111062	−	0.0369267i
$661$			24.3810i			0.948313i	0.880441	+	0.474156i	$0.157247\pi$
$661$			24.3810i			0.948313i	−0.880441	+	0.474156i	$0.842753\pi$
$662$	1.79035	−	17.6124i	0.0695840	−	0.684527i
$663$	−1.41383	−	0.816275i	−0.0549086	−	0.0317015i
$664$	−3.21483	−	14.3976i	−0.124759	−	0.558737i
$665$	−2.78808			−0.108117
$666$	−13.1222	−	9.46555i	−0.508476	−	0.366783i
$667$			20.6671i			0.800234i
$668$	−22.0206	+	7.32157i	−0.852001	+	0.283280i
$669$			14.9141i			0.576612i
$670$	−2.44124	−	1.20285i	−0.0943133	−	0.0464701i
$671$		−	80.2421i		−	3.09771i
$672$	−16.3954	+	0.279984i	−0.632466	+	0.0108006i
$673$		−	4.54750i		−	0.175293i	−0.996152	−	0.0876467i	$-0.972065\pi$
$673$		−	4.54750i		−	0.175293i	0.996152	−	0.0876467i	$-0.0279346\pi$
$674$	27.8395	−	38.5942i	1.07234	−	1.48659i
$675$	4.94473			0.190323
$676$	5.67322	+	17.0629i	0.218201	+	0.656266i
$677$	26.2018	+	15.1276i	1.00702	+	0.581401i	0.910317	−	0.413912i	$-0.135838\pi$
$677$	26.2018	+	15.1276i	1.00702	+	0.581401i	0.0966997	+	0.995314i	$0.469171\pi$
$678$	−1.42022	−	0.144370i	−0.0545434	−	0.00554448i
$679$		−	15.1469i		−	0.581284i
$680$	0.118149	+	0.529133i	0.00453082	+	0.0202913i
$681$	9.23332	+	5.33086i	0.353821	+	0.204279i
$682$	−37.0976	−	26.7599i	−1.42054	−	1.02469i
$683$	18.7182	+	32.4208i	0.716231	+	1.24055i	0.962483	+	0.271343i	$0.0874678\pi$
$683$	18.7182	+	32.4208i	0.716231	+	1.24055i	−0.246251	+	0.969206i	$0.579199\pi$
$684$	1.64648	−	8.01486i	0.0629546	−	0.306456i
$685$	−3.14717			−0.120247
$686$	20.9300	−	9.40441i	0.799111	−	0.359062i
$687$	−2.06775	+	1.19381i	−0.0788894	+	0.0455468i
$688$	−1.59553	−	13.4150i	−0.0608288	−	0.511441i
$689$	−6.57841	−	11.3941i	−0.250617	−	0.434082i
$690$	1.37977	+	0.995277i	0.0525268	+	0.0378896i
$691$	11.6749	+	6.74052i	0.444135	+	0.256421i	0.705350	−	0.708859i	$-0.250790\pi$
$691$	11.6749	+	6.74052i	0.444135	+	0.256421i	−0.261215	+	0.965281i	$0.584123\pi$
$692$	−14.3967	−	2.95749i	−0.547281	−	0.112427i
$693$	9.26834	+	16.0532i	0.352075	+	0.609812i
$694$	−2.58637	+	25.4432i	−0.0981773	+	0.965811i
$695$		−	3.15828i		−	0.119800i
$696$	7.73075	+	8.41096i	0.293033	+	0.318817i
$697$		−	2.62854i		−	0.0995630i
$698$	17.5256	−	7.87474i	0.663355	−	0.298063i
$699$	−21.8723	−	12.6280i	−0.827288	−	0.477635i
$700$	9.04460	+	27.2028i	0.341854	+	1.02817i
$701$	14.3736	+	8.29858i	0.542882	+	0.313433i	0.746246	−	0.665670i	$-0.231854\pi$
$701$	14.3736	+	8.29858i	0.542882	+	0.313433i	−0.203364	+	0.979103i	$0.565188\pi$
$702$	−1.65661	+	2.29658i	−0.0625248	+	0.0866789i
$703$	40.5353	+	23.4030i	1.52882	+	0.882663i
$704$	−46.2988	+	21.7609i	−1.74495	+	0.820146i
$705$	0.356557	−	0.617575i	0.0134287	−	0.0232592i
$706$	18.5585	−	25.7280i	0.698460	−	0.968284i
$707$	−38.4258	+	22.1852i	−1.44515	+	0.834359i
$708$	−12.9037	−	11.4599i	−0.484951	−	0.430691i
$709$	−7.59628	−	13.1571i	−0.285284	−	0.494127i	0.687394	−	0.726285i	$-0.258755\pi$
$709$	−7.59628	−	13.1571i	−0.285284	−	0.494127i	−0.972678	+	0.232158i	$0.925421\pi$
$710$	−0.0676815	+	0.665811i	−0.00254004	+	0.0249874i
$711$	−6.44716	+	11.1668i	−0.241787	+	0.418788i
$712$	−3.51670	+	11.2129i	−0.131794	+	0.420221i
$713$		−	25.8811i		−	0.969256i
$714$	−3.04876	+	1.36989i	−0.114097	+	0.0512668i
$715$	3.01031			0.112579
$716$	−3.84832	+	4.33315i	−0.143819	+	0.161937i
$717$	2.77589	−	4.80799i	0.103668	−	0.179558i
$718$	3.20046	+	7.12278i	0.119440	+	0.265820i
$719$	−39.1282	+	22.5907i	−1.45924	+	0.842491i	−0.998974	−	0.0452916i	$-0.985578\pi$
$719$	−39.1282	+	22.5907i	−1.45924	+	0.842491i	−0.460263	+	0.887783i	$0.652245\pi$
$720$	0.933821	−	0.111065i	0.0348015	−	0.00413915i
$721$	35.1845	−	20.3138i	1.31034	−	0.756526i
$722$	0.323628	−	3.18367i	0.0120442	−	0.118484i
$723$	−9.81905			−0.365175
$724$	6.89368	+	20.7336i	0.256202	+	0.770559i
$725$	9.98590	−	17.2961i	0.370867	−	0.642360i
$726$	34.2854	+	24.7313i	1.27245	+	0.917866i
$727$	15.7199	+	27.2277i	0.583019	+	1.00982i	0.995119	+	0.0986798i	$0.0314620\pi$
$727$	15.7199	+	27.2277i	0.583019	+	1.00982i	−0.412100	+	0.911138i	$0.635205\pi$
$728$	−15.6645	−	4.91287i	−0.580566	−	0.182083i
$729$	1.00000			0.0370370
$730$	2.69737	−	3.73940i	0.0998342	−	0.138401i
$731$	−1.37683	−	2.38474i	−0.0509240	−	0.0882029i
$732$	5.05004	−	24.5830i	0.186655	−	0.908614i
$733$	5.62826	+	3.24948i	0.207885	+	0.120022i	0.600328	−	0.799754i	$-0.295037\pi$
$733$	5.62826	+	3.24948i	0.207885	+	0.120022i	−0.392443	+	0.919776i	$0.628370\pi$
$734$	0.0398888	−	0.392403i	0.00147232	−	0.0144839i
$735$	0.285597	−	0.164890i	0.0105344	−	0.00608205i
$736$	−25.3109	−	14.0426i	−0.932974	−	0.517617i
$737$	−8.70572	−	51.6140i	−0.320679	−	1.90123i
$738$	−4.53593	−	0.461089i	−0.166970	−	0.0169729i
$739$	2.23869	+	3.87753i	0.0823517	+	0.142637i	0.904260	−	0.426983i	$-0.140424\pi$
$739$	2.23869	+	3.87753i	0.0823517	+	0.142637i	−0.821908	+	0.569620i	$0.807090\pi$
$740$	−1.08250	+	5.26950i	−0.0397936	+	0.193711i
$741$	4.09588	−	7.09427i	0.150466	−	0.260615i
$742$	−26.7983	−	2.72412i	−0.983797	−	0.100006i
$743$	5.98049	−	3.45284i	0.219403	−	0.126672i	−0.386271	−	0.922385i	$-0.626237\pi$
$743$	5.98049	−	3.45284i	0.219403	−	0.126672i	0.605674	+	0.795713i	$0.292904\pi$
$744$	−9.68111	−	10.5329i	−0.354927	−	0.386155i
$745$		−	2.84167i		−	0.104111i
$746$	−29.8525	−	3.03458i	−1.09298	−	0.111104i
$747$	−4.51692	+	2.60784i	−0.165265	+	0.0954160i
$748$	−6.92431	+	7.79667i	−0.253178	+	0.285074i
$749$	4.12532	+	2.38175i	0.150736	+	0.0870274i
$750$	−1.35516	−	3.01598i	−0.0494835	−	0.110128i
$751$		−	6.87637i		−	0.250922i	−0.992099	−	0.125461i	$-0.959959\pi$
$751$		−	6.87637i		−	0.250922i	0.992099	−	0.125461i	$-0.0400410\pi$
$752$	−4.78304	+	11.1503i	−0.174419	+	0.406611i
$753$	8.15118	+	14.1183i	0.297046	+	0.514498i
$754$	4.68765	+	10.4326i	0.170714	+	0.379933i
$755$	1.55779	+	2.69816i	0.0566936	+	0.0981963i
$756$	1.82914	+	5.50137i	0.0665252	+	0.200083i
$757$	−28.1976	−	16.2799i	−1.02486	−	0.591703i	−0.109351	−	0.994003i	$-0.534877\pi$
$757$	−28.1976	−	16.2799i	−1.02486	−	0.591703i	−0.915508	+	0.402300i	$0.868211\pi$
$758$	9.71843	+	7.01027i	0.352989	+	0.254624i
$759$			32.7210i			1.18770i
$760$	−2.65507	+	0.592845i	−0.0963094	+	0.0215048i
$761$	−13.0667			−0.473668			−0.236834	−	0.971550i	$-0.576110\pi$
$761$	−13.0667			−0.473668			−0.236834	+	0.971550i	$0.576110\pi$
$762$	4.82975	+	0.490957i	0.174963	+	0.0177855i
$763$	36.2799	+	20.9462i	1.31342	+	0.758304i
$764$	49.2181	+	10.1108i	1.78065	+	0.365795i
$765$	0.166003	−	0.0958418i	0.00600185	−	0.00346517i
$766$	4.52826	+	3.26641i	0.163613	+	0.118020i
$767$	−8.63901	−	14.9632i	−0.311937	−	0.540290i
$768$	−15.5536	+	3.75287i	−0.561244	+	0.135420i
$769$	19.3547	+	11.1744i	0.697948	+	0.402961i	0.806583	−	0.591121i	$-0.201315\pi$
$769$	19.3547	+	11.1744i	0.697948	+	0.402961i	−0.108635	+	0.994082i	$0.534648\pi$
$770$	3.60554	−	4.99841i	0.129935	−	0.180130i
$771$	−5.29612	+	9.17315i	−0.190735	+	0.330363i
$772$	10.4090	−	11.7203i	0.374627	−	0.421824i
$773$	−26.6592	+	46.1750i	−0.958864	+	1.66080i	−0.233596	+	0.972334i	$0.575049\pi$
$773$	−26.6592	+	46.1750i	−0.958864	+	1.66080i	−0.725268	+	0.688467i	$0.758284\pi$
$774$	−4.35674	+	1.95760i	−0.156600	+	0.0703646i
$775$	−12.5052	+	21.6596i	−0.449200	+	0.778037i
$776$	−3.22077	−	14.4242i	−0.115619	−	0.517800i
$777$	−33.1643			−1.18976
$778$	23.0761	+	16.6457i	0.827318	+	0.596776i
$779$	13.1894			0.472559
$780$	0.922240	+	0.189454i	0.0330215	+	0.00678354i
$781$	−11.1472	+	6.43585i	−0.398879	+	0.230293i
$782$	−5.86974	−	0.596675i	−0.209901	−	0.0213370i
$783$	2.01950	−	3.49788i	0.0721712	−	0.125004i
$784$	−4.49381	+	3.35968i	−0.160493	+	0.119988i
$785$	3.60435	−	2.08097i	0.128645	−	0.0742730i
$786$	−3.60486	−	8.02279i	−0.128581	−	0.286163i
$787$	−19.1918	−	33.2411i	−0.684113	−	1.18492i	−0.973715	−	0.227771i	$-0.926856\pi$
$787$	−19.1918	−	33.2411i	−0.684113	−	1.18492i	0.289602	−	0.957147i	$-0.406477\pi$
$788$	−35.7397	+	11.8830i	−1.27317	+	0.423315i
$789$		−	14.1911i		−	0.505215i
$790$	4.26516	+	0.433564i	0.151747	+	0.0154255i
$791$	−2.53405	+	1.46303i	−0.0901003	+	0.0520195i
$792$	12.2396	+	13.3166i	0.434917	+	0.473184i
$793$	12.5628	−	21.7594i	0.446118	−	0.772699i
$794$	33.2727	−	14.9503i	1.18081	−	0.530568i
$795$	1.54479			0.0547880
$796$	1.48183	−	7.21336i	0.0525220	−	0.255671i
$797$	17.5630	−	30.4200i	0.622113	−	1.07753i	−0.366979	−	0.930229i	$-0.619608\pi$
$797$	17.5630	−	30.4200i	0.622113	−	1.07753i	0.989092	−	0.147302i	$-0.0470589\pi$
$798$	−6.87378	−	15.2979i	−0.243329	−	0.541541i
$799$			2.47307i			0.0874909i
$800$	14.3974	+	23.9818i	0.509024	+	0.847884i
$801$	4.15475			0.146801
$802$	−0.624607	−	1.39010i	−0.0220557	−	0.0490860i
$803$	88.6796			3.12943
$804$	0.581243	−	16.3604i	0.0204989	−	0.576986i
$805$	3.48714			0.122905
$806$	−5.87027	−	13.0646i	−0.206771	−	0.460180i
$807$	−24.0676			−0.847220
$808$	−31.8752	+	29.2974i	−1.12137	+	1.03068i
$809$		−	28.0854i		−	0.987430i	−0.869624	−	0.493715i	$-0.835639\pi$
$809$		−	28.0854i		−	0.987430i	0.869624	−	0.493715i	$-0.164361\pi$
$810$	−0.136269	−	0.303274i	−0.00478802	−	0.0106560i
$811$	25.4585	−	44.0954i	0.893968	−	1.54840i	0.0588924	−	0.998264i	$-0.481243\pi$
$811$	25.4585	−	44.0954i	0.893968	−	1.54840i	0.835076	−	0.550134i	$-0.185424\pi$
$812$	22.9371	+	4.71193i	0.804935	+	0.165356i
$813$	21.5190			0.754705
$814$	−94.3767	+	42.4060i	−3.30790	+	1.48633i
$815$	1.77047	−	3.06655i	0.0620169	−	0.107416i
$816$	−2.61202	+	1.95281i	−0.0914389	+	0.0683619i
$817$	11.9661	−	6.90863i	0.418641	−	0.241702i
$818$	−28.2226	−	2.86891i	−0.986782	−	0.100309i
$819$			5.80424i			0.202817i
$820$	0.478272	+	1.43846i	0.0167020	+	0.0502333i
$821$	−5.90812	−	10.2332i	−0.206195	−	0.357140i	0.744318	−	0.667825i	$-0.232775\pi$
$821$	−5.90812	−	10.2332i	−0.206195	−	0.357140i	−0.950513	+	0.310686i	$0.899441\pi$
$822$	−7.75907	−	17.2682i	−0.270629	−	0.602298i
$823$	−22.7903	+	13.1580i	−0.794420	+	0.458659i	−0.841516	−	0.540232i	$-0.818337\pi$
$823$	−22.7903	+	13.1580i	−0.794420	+	0.458659i	0.0470961	+	0.998890i	$0.485003\pi$
$824$	29.1865	−	26.8262i	1.01676	−	0.934533i
$825$	15.8101	−	27.3839i	0.550437	−	0.953384i
$826$	−35.1926	−	3.57742i	−1.22451	−	0.124474i
$827$	−26.6710	+	15.3985i	−0.927441	+	0.535458i	−0.886001	−	0.463683i	$-0.846528\pi$
$827$	−26.6710	+	15.3985i	−0.927441	+	0.535458i	−0.0414398	+	0.999141i	$0.513194\pi$
$828$	−2.05930	+	10.0244i	−0.0715656	+	0.348373i
$829$	10.9586			0.380608			0.190304	−	0.981725i	$-0.439053\pi$
$829$	10.9586			0.380608			0.190304	+	0.981725i	$0.439053\pi$
$830$	1.40641	+	1.01450i	0.0488172	+	0.0352137i
$831$	3.85303			0.133660
$832$	−15.9619	−	1.34764i	−0.553378	−	0.0467212i
$833$	−0.571834	+	0.990446i	−0.0198129	+	0.0343169i
$834$	17.3292	−	7.78648i	0.600061	−	0.269624i
$835$	1.36393	−	2.36239i	0.0472006	−	0.0817539i
$836$	−39.1219	−	34.7446i	−1.35306	−	1.20167i
$837$	−2.52900	+	4.38035i	−0.0874149	+	0.151407i
$838$	29.9442	−	41.5120i	1.03440	−	1.43401i
$839$	10.7364	+	6.19867i	0.370662	+	0.214002i	0.673748	−	0.738961i	$-0.264683\pi$
$839$	10.7364	+	6.19867i	0.370662	+	0.214002i	−0.303086	+	0.952963i	$0.598017\pi$
$840$	1.41917	−	1.30440i	0.0489660	−	0.0450061i
$841$	6.34320	+	10.9868i	0.218731	+	0.378853i
$842$	−12.9475	−	9.33950i	−0.446199	−	0.321860i
$843$	0.365712	−	0.211144i	0.0125958	−	0.00727218i
$844$	−6.27499	+	30.5459i	−0.215994	+	1.05143i
$845$	−1.83053	−	1.05686i	−0.0629722	−	0.0363570i
$846$	4.26764	+	0.433817i	0.146725	+	0.0149149i
$847$	86.6508			2.97736
$848$	−26.0991	+	3.10412i	−0.896246	+	0.106596i
$849$		−	29.9940i		−	1.02939i
$850$	4.62402	+	3.33548i	0.158603	+	0.114406i
$851$	−50.6987	−	29.2709i	−1.73793	−	1.00339i
$852$	−3.82011	+	1.27014i	−0.130875	+	0.0435142i
$853$	23.4746	+	40.6592i	0.803756	+	1.39215i	0.917128	+	0.398593i	$0.130501\pi$
$853$	23.4746	+	40.6592i	0.803756	+	1.39215i	−0.113372	+	0.993553i	$0.536165\pi$
$854$	−21.0831	−	46.9215i	−0.721449	−	1.60562i
$855$	0.480912	+	0.832964i	0.0164468	+	0.0284868i
$856$	4.43495	+	1.39093i	0.151584	+	0.0475412i
$857$			20.6750i			0.706244i	0.935577	+	0.353122i	$0.114880\pi$
$857$			20.6750i			0.706244i	−0.935577	+	0.353122i	$0.885120\pi$
$858$	7.42167	+	16.5173i	0.253372	+	0.563892i
$859$	12.8690	+	7.42993i	0.439085	+	0.253506i	0.703210	−	0.710983i	$-0.251750\pi$
$859$	12.8690	+	7.42993i	0.439085	+	0.253506i	−0.264124	+	0.964489i	$0.585083\pi$
$860$	1.18738	+	1.05453i	0.0404894	+	0.0359591i
$861$	−8.09327	+	4.67265i	−0.275818	+	0.159244i
$862$	−39.3041	−	3.99537i	−1.33870	−	0.136083i
$863$		−	35.9948i		−	1.22528i	−0.790363	−	0.612639i	$-0.790108\pi$
$863$		−	35.9948i		−	1.22528i	0.790363	−	0.612639i	$-0.209892\pi$
$864$	2.91166	+	4.84997i	0.0990568	+	0.164999i
$865$	1.49622	−	0.863840i	0.0508728	−	0.0293714i
$866$	−9.12115	−	0.927189i	−0.309949	−	0.0315072i
$867$	8.16762	−	14.1467i	0.277387	−	0.480448i
$868$	−28.7238	−	5.90068i	−0.974950	−	0.200282i
$869$	41.2278	+	71.4086i	1.39856	+	2.42237i
$870$	−1.33602	−	0.135810i	−0.0452952	−	0.00460437i
$871$	5.72000	−	15.3592i	0.193815	−	0.520428i
$872$	39.0030	+	12.2325i	1.32081	+	0.414245i
$873$	−4.52526	+	2.61266i	−0.153157	+	0.0884252i
$874$	2.99397	−	29.4530i	0.101273	−	0.996262i
$875$	−5.86931	−	3.38865i	−0.198419	−	0.114557i
$876$	27.1679	+	5.58105i	0.917918	+	0.188566i
$877$	0.544101	+	0.942410i	0.0183730	+	0.0318229i	0.875066	−	0.484004i	$-0.160818\pi$
$877$	0.544101	+	0.942410i	0.0183730	+	0.0318229i	−0.856693	+	0.515827i	$0.827485\pi$
$878$	8.36585	−	11.5977i	0.282334	−	0.391403i
$879$	19.8679			0.670128
$880$	2.37069	−	5.52661i	0.0799159	−	0.186302i
$881$	15.3589	+	26.6025i	0.517456	+	0.896260i	0.999794	+	0.0202752i	$0.00645423\pi$
$881$	15.3589	+	26.6025i	0.517456	+	0.896260i	−0.482338	+	0.875985i	$0.660212\pi$
$882$	1.60885	+	1.16052i	0.0541728	+	0.0390769i
$883$	−4.03966	+	6.99689i	−0.135945	+	0.235464i	−0.925958	−	0.377626i	$-0.876740\pi$
$883$	−4.03966	+	6.99689i	−0.135945	+	0.235464i	0.790013	+	0.613090i	$0.210074\pi$
$884$	−3.09833	+	1.03016i	−0.104208	+	0.0346479i
$885$	2.02868			0.0681932
$886$	−0.381954	+	3.75744i	−0.0128320	+	0.126234i
$887$	−16.9765	+	9.80136i	−0.570013	+	0.329097i	−0.757155	−	0.653236i	$-0.773411\pi$
$887$	−16.9765	+	9.80136i	−0.570013	+	0.329097i	0.187141	+	0.982333i	$0.440078\pi$
$888$	−31.5821	+	7.05191i	−1.05983	+	0.236647i
$889$	8.61752	−	4.97533i	0.289022	−	0.166867i
$890$	−0.566166	−	1.26003i	−0.0189779	−	0.0422363i
$891$	3.19736	−	5.53800i	0.107116	−	0.185530i
$892$	22.3025	+	19.8071i	0.746742	+	0.663190i
$893$	−12.4093			−0.415261
$894$	15.5920	−	7.00590i	0.521474	−	0.234312i
$895$		−	0.681243i		−	0.0227714i
$896$	−21.3557	+	24.8894i	−0.713443	+	0.831497i
$897$	−5.12284	+	8.87302i	−0.171047	+	0.296262i
$898$	−2.56712	+	25.2538i	−0.0856659	+	0.842732i
$899$	10.2146	+	17.6923i	0.340677	+	0.590070i
$900$	6.56699	−	7.39432i	0.218900	−	0.246477i
$901$	−4.63956	+	2.67865i	−0.154566	+	0.0892388i
$902$	−17.0565	+	23.6457i	−0.567920	+	0.787315i
$903$	−4.89508	+	8.47853i	−0.162898	+	0.282148i
$904$	−2.10206	+	1.93206i	−0.0699134	+	0.0642594i
$905$	−2.22433	−	1.28422i	−0.0739391	−	0.0426888i
$906$	−10.9640	+	15.1995i	−0.364254	+	0.504970i
$907$	15.9454	+	9.20609i	0.529459	+	0.305683i	0.740796	−	0.671730i	$-0.234448\pi$
$907$	15.9454	+	9.20609i	0.529459	+	0.305683i	−0.211337	+	0.977413i	$0.567782\pi$
$908$	20.2343	−	6.72766i	0.671499	−	0.223265i
$909$	13.2560	+	7.65337i	0.439675	+	0.253846i
$910$	1.76028	−	0.790940i	0.0583526	−	0.0262194i
$911$		−	34.1972i		−	1.13300i	−0.824061	−	0.566501i	$-0.808297\pi$
$911$		−	34.1972i		−	1.13300i	0.824061	−	0.566501i	$-0.191703\pi$
$912$	−9.79873	−	13.1065i	−0.324468	−	0.433999i
$913$			33.3529i			1.10382i
$914$	−5.67783	+	55.8552i	−0.187806	+	1.84753i
$915$	1.47504	+	2.55485i	0.0487634	+	0.0844607i
$916$	−0.960906	+	4.67758i	−0.0317492	+	0.154551i
$917$	−15.6129	−	9.01412i	−0.515584	−	0.297673i
$918$	0.935141	+	0.674553i	0.0308643	+	0.0222636i
$919$	16.4169	+	28.4349i	0.541544	+	0.937982i	0.998816	+	0.0486547i	$0.0154934\pi$
$919$	16.4169	+	28.4349i	0.541544	+	0.937982i	−0.457272	+	0.889327i	$0.651173\pi$
$920$	3.32077	−	0.741490i	0.109483	−	0.0244462i
$921$	2.56878	−	1.48308i	0.0846441	−	0.0488693i
$922$	−6.02065	+	2.70524i	−0.198279	+	0.0890923i
$923$	−4.03042			−0.132663
$924$	36.3150	+	7.46012i	1.19468	+	0.245420i
$925$	28.2861	+	48.9930i	0.930042	+	1.61088i
$926$	10.2431	+	7.38876i	0.336610	+	0.242810i
$927$	−12.1379	−	7.00780i	−0.398660	−	0.230166i
$928$	22.8448	−	0.390120i	0.749916	−	0.0128063i
$929$		−	8.02509i		−	0.263295i	−0.991297	−	0.131647i	$-0.957973\pi$
$929$		−	8.02509i		−	0.263295i	0.991297	−	0.131647i	$-0.0420266\pi$
$930$	1.67307	+	0.170072i	0.0548622	+	0.00557689i
$931$	−4.96983	−	2.86933i	−0.162880	−	0.0940386i
$932$	−47.9320	+	15.9368i	−1.57007	+	0.522028i
$933$	−6.28873			−0.205884
$934$	28.7681	−	39.8816i	0.941321	−	1.30497i
$935$		−	1.22576i		−	0.0400868i
$936$	1.23419	+	5.52733i	0.0403407	+	0.180666i
$937$		−	56.6512i		−	1.85071i	−0.379098	−	0.925356i	$-0.623766\pi$
$937$		−	56.6512i		−	1.85071i	0.379098	−	0.925356i	$-0.376234\pi$
$938$	−18.6519	−	27.8939i	−0.609007	−	0.910768i
$939$		−	2.18292i		−	0.0712369i
$940$	−0.449983	−	1.35338i	−0.0146768	−	0.0441425i
$941$			5.86281i			0.191122i	0.995424	+	0.0955611i	$0.0304645\pi$
$941$			5.86281i			0.191122i	−0.995424	+	0.0955611i	$0.969535\pi$
$942$	20.3043	+	14.6463i	0.661550	+	0.477201i
$943$	−16.4964			−0.537196
$944$	−34.2743	+	4.07645i	−1.11553	+	0.132677i
$945$	−0.590194	−	0.340748i	−0.0191990	−	0.0110845i
$946$	−3.08890	+	30.3868i	−0.100429	+	0.987960i
$947$		−	18.7323i		−	0.608718i	−0.952557	−	0.304359i	$-0.901558\pi$
$947$		−	18.7323i		−	0.608718i	0.952557	−	0.304359i	$-0.0984423\pi$
$948$	8.13646	+	24.4714i	0.264260	+	0.794795i
$949$	24.0474	+	13.8838i	0.780611	+	0.450686i
$950$	−16.7367	+	23.2023i	−0.543009	+	0.752781i
$951$	6.98396	+	12.0966i	0.226471	+	0.392259i
$952$	−2.00046	+	6.37841i	−0.0648353	+	0.206726i
$953$	50.5704			1.63814			0.819069	−	0.573695i	$-0.194491\pi$
$953$	50.5704			1.63814			0.819069	+	0.573695i	$0.194491\pi$
$954$	3.80855	+	8.47612i	0.123306	+	0.274424i
$955$	−5.11511	+	2.95321i	−0.165521	+	0.0955637i
$956$	−3.50324	−	10.5365i	−0.113303	−	0.340773i
$957$	−12.9142	−	22.3680i	−0.417456	−	0.723055i
$958$	7.20283	−	9.98538i	0.232713	−	0.322613i
$959$	−33.6052	−	19.4019i	−1.08517	−	0.626522i
$960$	1.07410	−	1.54394i	0.0346665	−	0.0498303i
$961$	2.70836	+	4.69102i	0.0873666	+	0.151323i
$962$	−32.2314	−	3.27641i	−1.03918	−	0.105636i
$963$		−	1.64330i		−	0.0529546i
$964$	−13.0405	+	14.6834i	−0.420005	+	0.472919i
$965$			1.84263i			0.0593163i
$966$	8.59724	+	19.1336i	0.276612	+	0.615614i
$967$	14.0184	+	8.09355i	0.450803	+	0.260271i	0.708169	−	0.706043i	$-0.249521\pi$
$967$	14.0184	+	8.09355i	0.450803	+	0.260271i	−0.257366	+	0.966314i	$0.582855\pi$
$968$	82.5168	−	18.4250i	2.65219	−	0.592203i
$969$	−2.88870	−	1.66779i	−0.0927985	−	0.0535773i
$970$	1.40901	+	1.01637i	0.0452405	+	0.0326337i
$971$	−29.8129	−	17.2125i	−0.956742	−	0.552375i	−0.0615733	−	0.998103i	$-0.519612\pi$
$971$	−29.8129	−	17.2125i	−0.956742	−	0.552375i	−0.895169	+	0.445727i	$0.852945\pi$
$972$	1.32808	−	1.49540i	0.0425981	−	0.0479648i
$973$	19.4705	−	33.7239i	0.624195	−	1.08114i
$974$	−21.1739	−	15.2735i	−0.678456	−	0.489396i
$975$	8.57450	−	4.95049i	0.274604	−	0.158543i
$976$	−30.0545	−	40.2000i	−0.962020	−	1.28677i
$977$	7.64486	+	13.2413i	0.244581	+	0.423626i	0.962014	−	0.273001i	$-0.0880163\pi$
$977$	7.64486	+	13.2413i	0.244581	+	0.423626i	−0.717433	+	0.696628i	$0.754683\pi$
$978$	21.1908	+	2.15410i	0.677607	+	0.0688806i
$979$	13.2843	−	23.0090i	0.424567	−	0.735371i
$980$	0.132720	−	0.646067i	0.00423960	−	0.0206379i
$981$		−	14.4519i		−	0.461414i
$982$	−1.28219	−	2.85358i	−0.0409163	−	0.0910613i
$983$	25.5418			0.814657			0.407328	−	0.913282i	$-0.366460\pi$
$983$	25.5418			0.814657			0.407328	+	0.913282i	$0.366460\pi$
$984$	−6.71358	+	6.17064i	−0.214021	+	0.196713i
$985$	2.21367	−	3.83420i	0.0705335	−	0.122168i
$986$	4.24803	−	1.90875i	0.135285	−	0.0607871i
$987$	7.61458	−	4.39628i	0.242375	−	0.139935i
$988$	−5.16909	−	15.5467i	−0.164451	−	0.494607i
$989$	−14.9664	+	8.64083i	−0.475902	+	0.274762i
$990$	−2.11524	−	0.215019i	−0.0672266	−	0.00683376i
$991$	−41.8016			−1.32787			−0.663935	−	0.747790i	$-0.731115\pi$
$991$	−41.8016			−1.32787			−0.663935	+	0.747790i	$0.731115\pi$
$992$	−28.6081	+	0.488541i	−0.908310	+	0.0155112i
$993$	−6.25903	+	10.8410i	−0.198624	+	0.344027i
$994$	−4.82735	+	6.69222i	−0.153114	+	0.212264i
$995$	0.432820	+	0.749667i	0.0137213	+	0.0237660i
$996$	−2.09906	+	10.2180i	−0.0665114	+	0.323770i
$997$	−15.2321			−0.482405			−0.241202	−	0.970475i	$-0.577542\pi$
$997$	−15.2321			−0.482405			−0.241202	+	0.970475i	$0.577542\pi$
$998$	−19.1458	−	13.8106i	−0.606049	−	0.437166i
$999$	5.72046	+	9.90813i	0.180987	+	0.313479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.b.499.5	yes	68
4.3	odd	2		804.2.j.a.499.7	✓	68
67.38	odd	6		804.2.j.a.775.7	yes	68
268.239	even	6	inner	804.2.j.b.775.5	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.7	✓	68	4.3	odd	2
804.2.j.a.775.7	yes	68	67.38	odd	6
804.2.j.b.499.5	yes	68	1.1	even	1	trivial
804.2.j.b.775.5	yes	68	268.239	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.28998 + 0.579621i) q^{2} +1.00000 q^{3} +(1.32808 - 1.49540i) q^{4} +0.235101i q^{5} +(-1.28998 + 0.579621i) q^{6} +(-1.44937 + 2.51039i) q^{7} +(-0.846427 + 2.69881i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.28998 + 0.579621i) q^{2} +1.00000 q^{3} +(1.32808 - 1.49540i) q^{4} +0.235101i q^{5} +(-1.28998 + 0.579621i) q^{6} +(-1.44937 + 2.51039i) q^{7} +(-0.846427 + 2.69881i) q^{8} +1.00000 q^{9} +(-0.136269 - 0.303274i) q^{10} +(3.19736 - 5.53800i) q^{11} +(1.32808 - 1.49540i) q^{12} +(1.73407 - 1.00116i) q^{13} +(0.414583 - 4.07842i) q^{14} +0.235101i q^{15} +(-0.472415 - 3.97201i) q^{16} +(-0.407663 - 0.706092i) q^{17} +(-1.28998 + 0.579621i) q^{18} +(3.54301 - 2.04556i) q^{19} +(0.351569 + 0.312232i) q^{20} +(-1.44937 + 2.51039i) q^{21} +(-0.914584 + 8.99714i) q^{22} +(-4.43135 + 2.55844i) q^{23} +(-0.846427 + 2.69881i) q^{24} +4.94473 q^{25} +(-1.65661 + 2.29658i) q^{26} +1.00000 q^{27} +(1.82914 + 5.50137i) q^{28} +(2.01950 - 3.49788i) q^{29} +(-0.136269 - 0.303274i) q^{30} +(-2.52900 + 4.38035i) q^{31} +(2.91166 + 4.84997i) q^{32} +(3.19736 - 5.53800i) q^{33} +(0.935141 + 0.674553i) q^{34} +(-0.590194 - 0.340748i) q^{35} +(1.32808 - 1.49540i) q^{36} +(5.72046 + 9.90813i) q^{37} +(-3.38475 + 4.69232i) q^{38} +(1.73407 - 1.00116i) q^{39} +(-0.634492 - 0.198996i) q^{40} +(2.79199 + 1.61196i) q^{41} +(0.414583 - 4.07842i) q^{42} +3.37738 q^{43} +(-4.03514 - 12.1362i) q^{44} +0.235101i q^{45} +(4.23341 - 5.86883i) q^{46} +(-2.62685 - 1.51661i) q^{47} +(-0.472415 - 3.97201i) q^{48} +(-0.701357 - 1.21479i) q^{49} +(-6.37858 + 2.86607i) q^{50} +(-0.407663 - 0.706092i) q^{51} +(0.805842 - 3.92274i) q^{52} -6.57075i q^{53} +(-1.28998 + 0.579621i) q^{54} +(1.30199 + 0.751703i) q^{55} +(-5.54826 - 6.03643i) q^{56} +(3.54301 - 2.04556i) q^{57} +(-0.577665 + 5.68274i) q^{58} -8.62896i q^{59} +(0.351569 + 0.312232i) q^{60} +(10.8670 - 6.27409i) q^{61} +(0.723402 - 7.11641i) q^{62} +(-1.44937 + 2.51039i) q^{63} +(-6.56712 - 4.56869i) q^{64} +(0.235375 + 0.407681i) q^{65} +(-0.914584 + 8.99714i) q^{66} +(6.30929 - 5.21467i) q^{67} +(-1.59730 - 0.328129i) q^{68} +(-4.43135 + 2.55844i) q^{69} +(0.958841 + 0.0974687i) q^{70} +(-1.74319 - 1.00643i) q^{71} +(-0.846427 + 2.69881i) q^{72} +(6.93381 + 12.0097i) q^{73} +(-13.1222 - 9.46555i) q^{74} +4.94473 q^{75} +(1.64648 - 8.01486i) q^{76} +(9.26834 + 16.0532i) q^{77} +(-1.65661 + 2.29658i) q^{78} +(-6.44716 + 11.1668i) q^{79} +(0.933821 - 0.111065i) q^{80} +1.00000 q^{81} +(-4.53593 - 0.461089i) q^{82} +(-4.51692 + 2.60784i) q^{83} +(1.82914 + 5.50137i) q^{84} +(0.166003 - 0.0958418i) q^{85} +(-4.35674 + 1.95760i) q^{86} +(2.01950 - 3.49788i) q^{87} +(12.2396 + 13.3166i) q^{88} +4.15475 q^{89} +(-0.136269 - 0.303274i) q^{90} +5.80424i q^{91} +(-2.05930 + 10.0244i) q^{92} +(-2.52900 + 4.38035i) q^{93} +(4.26764 + 0.433817i) q^{94} +(0.480912 + 0.832964i) q^{95} +(2.91166 + 4.84997i) q^{96} +(-4.52526 + 2.61266i) q^{97} +(1.60885 + 1.16052i) q^{98} +(3.19736 - 5.53800i) 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

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