LMFDB - Embedded newform 804.2.j.a.499.12

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			499.12
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.717914 + 1.21844i) q^{2} -1.00000 q^{3} +(-0.969198 - 1.74947i) q^{4} +0.567637i q^{5} +(0.717914 - 1.21844i) q^{6} +(-1.03281 + 1.78888i) q^{7} +(2.82743 + 0.0750601i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.717914 + 1.21844i) q^{2} -1.00000 q^{3} +(-0.969198 - 1.74947i) q^{4} +0.567637i q^{5} +(0.717914 - 1.21844i) q^{6} +(-1.03281 + 1.78888i) q^{7} +(2.82743 + 0.0750601i) q^{8} +1.00000 q^{9} +(-0.691633 - 0.407515i) q^{10} +(0.251452 - 0.435527i) q^{11} +(0.969198 + 1.74947i) q^{12} +(3.90313 - 2.25347i) q^{13} +(-1.43817 - 2.54268i) q^{14} -0.567637i q^{15} +(-2.12131 + 3.39117i) q^{16} +(-2.27908 - 3.94748i) q^{17} +(-0.717914 + 1.21844i) q^{18} +(4.21365 - 2.43275i) q^{19} +(0.993066 - 0.550153i) q^{20} +(1.03281 - 1.78888i) q^{21} +(0.350144 + 0.619050i) q^{22} +(-4.01670 + 2.31904i) q^{23} +(-2.82743 - 0.0750601i) q^{24} +4.67779 q^{25} +(-0.0563878 + 6.37353i) q^{26} -1.00000 q^{27} +(4.13059 + 0.0730939i) q^{28} +(-0.433527 + 0.750890i) q^{29} +(0.691633 + 0.407515i) q^{30} +(-4.20035 + 7.27522i) q^{31} +(-2.60903 - 5.01926i) q^{32} +(-0.251452 + 0.435527i) q^{33} +(6.44595 + 0.0570286i) q^{34} +(-1.01543 - 0.586261i) q^{35} +(-0.969198 - 1.74947i) q^{36} +(-0.346835 - 0.600736i) q^{37} +(-0.0608739 + 6.88058i) q^{38} +(-3.90313 + 2.25347i) q^{39} +(-0.0426070 + 1.60496i) q^{40} +(8.12044 + 4.68834i) q^{41} +(1.43817 + 2.54268i) q^{42} +8.56474 q^{43} +(-1.00565 - 0.0177957i) q^{44} +0.567637i q^{45} +(0.0580286 - 6.55898i) q^{46} +(7.71589 + 4.45477i) q^{47} +(2.12131 - 3.39117i) q^{48} +(1.36661 + 2.36705i) q^{49} +(-3.35825 + 5.69961i) q^{50} +(2.27908 + 3.94748i) q^{51} +(-7.72529 - 4.64435i) q^{52} +14.4612i q^{53} +(0.717914 - 1.21844i) q^{54} +(0.247222 + 0.142733i) q^{55} +(-3.05447 + 4.98040i) q^{56} +(-4.21365 + 2.43275i) q^{57} +(-0.603681 - 1.06730i) q^{58} +7.96043i q^{59} +(-0.993066 + 0.550153i) q^{60} +(7.38094 - 4.26139i) q^{61} +(-5.84894 - 10.3409i) q^{62} +(-1.03281 + 1.78888i) q^{63} +(7.98873 + 0.424455i) q^{64} +(1.27915 + 2.21556i) q^{65} +(-0.350144 - 0.619050i) q^{66} +(-6.54149 + 4.92025i) q^{67} +(-4.69713 + 7.81307i) q^{68} +(4.01670 - 2.31904i) q^{69} +(1.44332 - 0.816361i) q^{70} +(-4.35912 - 2.51674i) q^{71} +(2.82743 + 0.0750601i) q^{72} +(-3.10591 - 5.37959i) q^{73} +(0.980959 + 0.00867873i) q^{74} -4.67779 q^{75} +(-8.33989 - 5.01384i) q^{76} +(0.519403 + 0.899632i) q^{77} +(0.0563878 - 6.37353i) q^{78} +(4.84032 - 8.38369i) q^{79} +(-1.92496 - 1.20413i) q^{80} +1.00000 q^{81} +(-11.5422 + 6.52846i) q^{82} +(-6.79123 + 3.92092i) q^{83} +(-4.13059 - 0.0730939i) q^{84} +(2.24074 - 1.29369i) q^{85} +(-6.14875 + 10.4356i) q^{86} +(0.433527 - 0.750890i) q^{87} +(0.743653 - 1.21255i) q^{88} +10.6280 q^{89} +(-0.691633 - 0.407515i) q^{90} +9.30961i q^{91} +(7.95007 + 4.77949i) q^{92} +(4.20035 - 7.27522i) q^{93} +(-10.9672 + 6.20321i) q^{94} +(1.38092 + 2.39182i) q^{95} +(2.60903 + 5.01926i) q^{96} +(9.20546 - 5.31478i) q^{97} +(-3.86522 - 0.0341963i) q^{98} +(0.251452 - 0.435527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.717914	+	1.21844i	−0.507642	+	0.861568i
$2$	−0.717914	+	1.21844i	−0.507642	+	0.861568i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.969198	−	1.74947i	−0.484599	−	0.874736i
$5$			0.567637i			0.253855i	0.991912	+	0.126928i	$0.0405116\pi$
$5$			0.567637i			0.253855i	−0.991912	+	0.126928i	$0.959488\pi$
$6$	0.717914	−	1.21844i	0.293087	−	0.497427i
$7$	−1.03281	+	1.78888i	−0.390365	+	0.676132i	−0.992498	−	0.122264i	$-0.960984\pi$
$7$	−1.03281	+	1.78888i	−0.390365	+	0.676132i	0.602133	+	0.798396i	$0.294318\pi$
$8$	2.82743	+	0.0750601i	0.999648	+	0.0265378i
$9$	1.00000			0.333333
$10$	−0.691633	−	0.407515i	−0.218714	−	0.128868i
$11$	0.251452	−	0.435527i	0.0758156	−	0.131316i	−0.825625	−	0.564219i	$-0.809177\pi$
$11$	0.251452	−	0.435527i	0.0758156	−	0.131316i	0.901441	+	0.432903i	$0.142511\pi$
$12$	0.969198	+	1.74947i	0.279783	+	0.505029i
$13$	3.90313	−	2.25347i	1.08253	−	0.625000i	0.150954	−	0.988541i	$-0.451765\pi$
$13$	3.90313	−	2.25347i	1.08253	−	0.625000i	0.931578	+	0.363540i	$0.118432\pi$
$14$	−1.43817	−	2.54268i	−0.384368	−	0.679559i
$15$		−	0.567637i		−	0.146563i
$16$	−2.12131	+	3.39117i	−0.530327	+	0.847793i
$17$	−2.27908	−	3.94748i	−0.552758	−	0.957404i	−0.998074	−	0.0620311i	$-0.980242\pi$
$17$	−2.27908	−	3.94748i	−0.552758	−	0.957404i	0.445317	−	0.895373i	$-0.353091\pi$
$18$	−0.717914	+	1.21844i	−0.169214	+	0.287189i
$19$	4.21365	−	2.43275i	0.966676	−	0.558111i	0.0684551	−	0.997654i	$-0.478193\pi$
$19$	4.21365	−	2.43275i	0.966676	−	0.558111i	0.898221	+	0.439543i	$0.144860\pi$
$20$	0.993066	−	0.550153i	0.222056	−	0.123018i
$21$	1.03281	−	1.78888i	0.225377	−	0.390365i
$22$	0.350144	+	0.619050i	0.0746509	+	0.131982i
$23$	−4.01670	+	2.31904i	−0.837539	+	0.483553i	−0.856427	−	0.516268i	$-0.827321\pi$
$23$	−4.01670	+	2.31904i	−0.837539	+	0.483553i	0.0188878	+	0.999822i	$0.493987\pi$
$24$	−2.82743	−	0.0750601i	−0.577147	−	0.0153216i
$25$	4.67779			0.935558
$26$	−0.0563878	+	6.37353i	−0.0110586	+	1.24995i
$27$	−1.00000			−0.192450
$28$	4.13059	+	0.0730939i	0.780607	+	0.0138134i
$29$	−0.433527	+	0.750890i	−0.0805039	+	0.139437i	−0.903466	−	0.428659i	$-0.858986\pi$
$29$	−0.433527	+	0.750890i	−0.0805039	+	0.139437i	0.822963	+	0.568096i	$0.192320\pi$
$30$	0.691633	+	0.407515i	0.126274	+	0.0744017i
$31$	−4.20035	+	7.27522i	−0.754405	+	1.30667i	0.191265	+	0.981539i	$0.438741\pi$
$31$	−4.20035	+	7.27522i	−0.754405	+	1.30667i	−0.945670	+	0.325129i	$0.894592\pi$
$32$	−2.60903	−	5.01926i	−0.461215	−	0.887288i
$33$	−0.251452	+	0.435527i	−0.0437721	+	0.0758156i
$34$	6.44595	+	0.0570286i	1.10547	+	0.00978032i
$35$	−1.01543	−	0.586261i	−0.171640	−	0.0990961i
$36$	−0.969198	−	1.74947i	−0.161533	−	0.291579i
$37$	−0.346835	−	0.600736i	−0.0570193	−	0.0987603i	0.836107	−	0.548567i	$-0.184826\pi$
$37$	−0.346835	−	0.600736i	−0.0570193	−	0.0987603i	−0.893126	+	0.449806i	$0.851493\pi$
$38$	−0.0608739	+	6.88058i	−0.00987504	+	1.11618i
$39$	−3.90313	+	2.25347i	−0.625000	+	0.360844i
$40$	−0.0426070	+	1.60496i	−0.00673675	+	0.253766i
$41$	8.12044	+	4.68834i	1.26820	+	0.732196i	0.974647	−	0.223747i	$-0.0718290\pi$
$41$	8.12044	+	4.68834i	1.26820	+	0.732196i	0.293553	+	0.955943i	$0.405162\pi$
$42$	1.43817	+	2.54268i	0.221915	+	0.392343i
$43$	8.56474			1.30611			0.653055	−	0.757310i	$-0.273487\pi$
$43$	8.56474			1.30611			0.653055	+	0.757310i	$0.273487\pi$
$44$	−1.00565	−	0.0177957i	−0.151607	−	0.00268281i
$45$			0.567637i			0.0846184i
$46$	0.0580286	−	6.55898i	0.00855585	−	0.967069i
$47$	7.71589	+	4.45477i	1.12548	+	0.649795i	0.942794	−	0.333377i	$-0.108188\pi$
$47$	7.71589	+	4.45477i	1.12548	+	0.649795i	0.182684	+	0.983172i	$0.441521\pi$
$48$	2.12131	−	3.39117i	0.306185	−	0.489473i
$49$	1.36661	+	2.36705i	0.195231	+	0.338149i
$50$	−3.35825	+	5.69961i	−0.474928	+	0.806047i
$51$	2.27908	+	3.94748i	0.319135	+	0.552758i
$52$	−7.72529	−	4.64435i	−1.07130	−	0.644056i
$53$			14.4612i			1.98639i	0.116443	+	0.993197i	$0.462851\pi$
$53$			14.4612i			1.98639i	−0.116443	+	0.993197i	$0.537149\pi$
$54$	0.717914	−	1.21844i	0.0976958	−	0.165809i
$55$	0.247222	+	0.142733i	0.0333353	+	0.0192462i
$56$	−3.05447	+	4.98040i	−0.408170	+	0.665534i
$57$	−4.21365	+	2.43275i	−0.558111	+	0.322225i
$58$	−0.603681	−	1.06730i	−0.0792671	−	0.140144i
$59$			7.96043i			1.03636i	0.855272	+	0.518180i	$0.173390\pi$
$59$			7.96043i			1.03636i	−0.855272	+	0.518180i	$0.826610\pi$
$60$	−0.993066	+	0.550153i	−0.128204	+	0.0710245i
$61$	7.38094	−	4.26139i	0.945032	−	0.545615i	0.0534981	−	0.998568i	$-0.482963\pi$
$61$	7.38094	−	4.26139i	0.945032	−	0.545615i	0.891534	+	0.452953i	$0.149630\pi$
$62$	−5.84894	−	10.3409i	−0.742816	−	1.31329i
$63$	−1.03281	+	1.78888i	−0.130122	+	0.225377i
$64$	7.98873	+	0.424455i	0.998591	+	0.0530568i
$65$	1.27915	+	2.21556i	0.158660	+	0.274807i
$66$	−0.350144	−	0.619050i	−0.0430997	−	0.0761998i
$67$	−6.54149	+	4.92025i	−0.799170	+	0.601105i
$67$	−6.54149	+	4.92025i	−0.799170	+	0.601105i
$68$	−4.69713	+	7.81307i	−0.569610	+	0.947474i
$69$	4.01670	−	2.31904i	0.483553	−	0.279180i
$70$	1.44332	−	0.816361i	0.172510	−	0.0975738i
$71$	−4.35912	−	2.51674i	−0.517332	−	0.298682i	0.218510	−	0.975835i	$-0.429880\pi$
$71$	−4.35912	−	2.51674i	−0.517332	−	0.298682i	−0.735842	+	0.677153i	$0.763214\pi$
$72$	2.82743	+	0.0750601i	0.333216	+	0.00884592i
$73$	−3.10591	−	5.37959i	−0.363519	−	0.629634i	0.625018	−	0.780610i	$-0.285092\pi$
$73$	−3.10591	−	5.37959i	−0.363519	−	0.629634i	−0.988537	+	0.150976i	$0.951758\pi$
$74$	0.980959	+	0.00867873i	0.114034	+	0.00100888i
$75$	−4.67779			−0.540144
$76$	−8.33989	−	5.01384i	−0.956650	−	0.575127i
$77$	0.519403	+	0.899632i	0.0591914	+	0.102523i
$78$	0.0563878	−	6.37353i	0.00638467	−	0.721660i
$79$	4.84032	−	8.38369i	0.544579	−	0.943238i	−0.454054	−	0.890974i	$-0.650023\pi$
$79$	4.84032	−	8.38369i	0.544579	−	0.943238i	0.998633	−	0.0522644i	$-0.0166439\pi$
$80$	−1.92496	−	1.20413i	−0.215217	−	0.134626i
$81$	1.00000			0.111111
$82$	−11.5422	+	6.52846i	−1.27463	+	0.720947i
$83$	−6.79123	+	3.92092i	−0.745434	+	0.430377i	−0.824042	−	0.566529i	$-0.808286\pi$
$83$	−6.79123	+	3.92092i	−0.745434	+	0.430377i	0.0786075	+	0.996906i	$0.474953\pi$
$84$	−4.13059	−	0.0730939i	−0.450684	−	0.00797520i
$85$	2.24074	−	1.29369i	0.243042	−	0.140320i
$86$	−6.14875	+	10.4356i	−0.663037	+	1.12530i
$87$	0.433527	−	0.750890i	0.0464789	−	0.0805039i
$88$	0.743653	−	1.21255i	0.0792737	−	0.129258i
$89$	10.6280			1.12656			0.563281	−	0.826265i	$-0.309539\pi$
$89$	10.6280			1.12656			0.563281	+	0.826265i	$0.309539\pi$
$90$	−0.691633	−	0.407515i	−0.0729045	−	0.0429559i
$91$			9.30961i			0.975913i
$92$	7.95007	+	4.77949i	0.828853	+	0.498296i
$93$	4.20035	−	7.27522i	0.435556	−	0.754405i
$94$	−10.9672	+	6.20321i	−1.13118	+	0.639813i
$95$	1.38092	+	2.39182i	0.141679	+	0.245396i
$96$	2.60903	+	5.01926i	0.266283	+	0.512276i
$97$	9.20546	−	5.31478i	0.934673	−	0.539634i	0.0463866	−	0.998924i	$-0.485229\pi$
$97$	9.20546	−	5.31478i	0.934673	−	0.539634i	0.888286	+	0.459290i	$0.151896\pi$
$98$	−3.86522	−	0.0341963i	−0.390446	−	0.00345435i
$99$	0.251452	−	0.435527i	0.0252719	−	0.0437721i
$100$	−4.53370	−	8.18366i	−0.453370	−	0.818366i
$101$	−9.18807	−	5.30473i	−0.914247	−	0.527841i	−0.0324517	−	0.999473i	$-0.510332\pi$
$101$	−9.18807	−	5.30473i	−0.914247	−	0.527841i	−0.881795	+	0.471633i	$0.843665\pi$
$102$	−6.44595	−	0.0570286i	−0.638245	−	0.00564667i
$103$	−3.59279	−	2.07430i	−0.354009	−	0.204387i	0.312441	−	0.949937i	$-0.398853\pi$
$103$	−3.59279	−	2.07430i	−0.354009	−	0.204387i	−0.666449	+	0.745550i	$0.732187\pi$
$104$	11.2050	−	6.07856i	1.09874	−	0.596052i
$105$	1.01543	+	0.586261i	0.0990961	+	0.0572132i
$106$	−17.6201	−	10.3819i	−1.71141	−	1.00838i
$107$			5.03323i			0.486581i	0.969953	+	0.243291i	$0.0782269\pi$
$107$			5.03323i			0.486581i	−0.969953	+	0.243291i	$0.921773\pi$
$108$	0.969198	+	1.74947i	0.0932611	+	0.168343i
$109$			2.83143i			0.271202i	0.990764	+	0.135601i	$0.0432965\pi$
$109$			2.83143i			0.271202i	−0.990764	+	0.135601i	$0.956703\pi$
$110$	−0.351396	+	0.198755i	−0.0335043	+	0.0189505i
$111$	0.346835	+	0.600736i	0.0329201	+	0.0570193i
$112$	−3.87548	−	7.29719i	−0.366199	−	0.689520i
$113$	−7.14336	−	4.12422i	−0.671991	−	0.387974i	0.124839	−	0.992177i	$-0.460158\pi$
$113$	−7.14336	−	4.12422i	−0.671991	−	0.387974i	−0.796831	+	0.604203i	$0.793492\pi$
$114$	0.0608739	−	6.88058i	0.00570136	−	0.644426i
$115$	−1.31637	−	2.28003i	−0.122753	−	0.212614i
$116$	1.73383	+	0.0306815i	0.160983	+	0.00284871i
$117$	3.90313	−	2.25347i	0.360844	−	0.208333i
$118$	−9.69932	−	5.71491i	−0.892895	−	0.526100i
$119$	9.41540			0.863108
$120$	0.0426070	−	1.60496i	0.00388946	−	0.146512i
$121$	5.37354	+	9.30725i	0.488504	+	0.846114i
$122$	−0.106631	+	12.0526i	−0.00965394	+	1.09119i
$123$	−8.12044	−	4.68834i	−0.732196	−	0.422733i
$124$	16.7988	+	0.297267i	1.50857	+	0.0266954i
$125$			5.49348i			0.491351i
$126$	−1.43817	−	2.54268i	−0.128123	−	0.226520i
$127$	−10.1229	−	5.84445i	−0.898261	−	0.518611i	−0.0216255	−	0.999766i	$-0.506884\pi$
$127$	−10.1229	−	5.84445i	−0.898261	−	0.518611i	−0.876636	+	0.481155i	$0.840217\pi$
$128$	−6.25240	+	9.42908i	−0.552639	+	0.833421i
$129$	−8.56474			−0.754083
$130$	−3.61785	−	0.0320079i	−0.317307	−	0.00280727i
$131$		−	6.99256i		−	0.610943i	−0.952201	−	0.305471i	$-0.901186\pi$
$131$		−	6.99256i		−	0.610943i	0.952201	−	0.305471i	$-0.0988141\pi$
$132$	1.00565	+	0.0177957i	0.0875306	+	0.00154892i
$133$			10.0503i			0.871467i
$134$	−1.29881	−	11.5027i	−0.112200	−	0.993686i
$135$		−	0.567637i		−	0.0488545i
$136$	−6.14764	−	11.3323i	−0.527156	−	0.971736i
$137$		−	14.5906i		−	1.24656i	−0.781998	−	0.623282i	$-0.785799\pi$
$137$		−	14.5906i		−	1.24656i	0.781998	−	0.623282i	$-0.214201\pi$
$138$	−0.0580286	+	6.55898i	−0.00493972	+	0.558338i
$139$	20.5318			1.74149			0.870743	−	0.491738i	$-0.163638\pi$
$139$	20.5318			1.74149			0.870743	+	0.491738i	$0.163638\pi$
$140$	−0.0414908	+	2.34468i	−0.00350662	+	0.198161i
$141$	−7.71589	−	4.45477i	−0.649795	−	0.375159i
$142$	6.19597	−	3.50453i	0.519954	−	0.294093i
$143$		−	2.26656i		−	0.189539i
$144$	−2.12131	+	3.39117i	−0.176776	+	0.282598i
$145$	−0.426233	−	0.246086i	−0.0353968	−	0.0204363i
$146$	8.78450	+	0.0777181i	0.727010	+	0.00643200i
$147$	−1.36661	−	2.36705i	−0.112716	−	0.195231i
$148$	−0.714819	+	1.18901i	−0.0587577	+	0.0977360i
$149$	−7.52955			−0.616845			−0.308422	−	0.951249i	$-0.599801\pi$
$149$	−7.52955			−0.616845			−0.308422	+	0.951249i	$0.599801\pi$
$150$	3.35825	−	5.69961i	0.274200	−	0.465371i
$151$	15.9680	−	9.21910i	1.29945	−	0.750240i	0.319144	−	0.947706i	$-0.396605\pi$
$151$	15.9680	−	9.21910i	1.29945	−	0.750240i	0.980310	+	0.197466i	$0.0632713\pi$
$152$	12.0964	−	6.56215i	0.981147	−	0.532261i
$153$	−2.27908	−	3.94748i	−0.184253	−	0.319135i
$154$	−1.46904	−	0.0129968i	−0.118378	−	0.00104732i
$155$	−4.12969	−	2.38428i	−0.331704	−	0.191510i
$156$	7.72529	+	4.64435i	0.618518	+	0.371846i
$157$	7.24765	+	12.5533i	0.578425	+	1.00186i	0.995660	+	0.0930634i	$0.0296659\pi$
$157$	7.24765	+	12.5533i	0.578425	+	1.00186i	−0.417235	+	0.908799i	$0.637001\pi$
$158$	6.74009	+	11.9164i	0.536213	+	0.948019i
$159$		−	14.4612i		−	1.14685i
$160$	2.84912	−	1.48098i	0.225243	−	0.117082i
$161$		−	9.58050i		−	0.755049i
$162$	−0.717914	+	1.21844i	−0.0564047	+	0.0957298i
$163$	4.97065	+	2.86980i	0.389331	+	0.224780i	0.681870	−	0.731473i	$-0.261167\pi$
$163$	4.97065	+	2.86980i	0.389331	+	0.224780i	−0.292539	+	0.956254i	$0.594500\pi$
$164$	0.331803	−	18.7504i	0.0259095	−	1.46416i
$165$	−0.247222	−	0.142733i	−0.0192462	−	0.0111118i
$166$	0.0981118	−	11.0896i	0.00761495	−	0.860720i
$167$	−8.12255	−	4.68956i	−0.628542	−	0.362889i	0.151645	−	0.988435i	$-0.451543\pi$
$167$	−8.12255	−	4.68956i	−0.628542	−	0.362889i	−0.780187	+	0.625546i	$0.784876\pi$
$168$	3.05447	−	4.98040i	0.235657	−	0.384246i
$169$	3.65626	−	6.33283i	0.281251	−	0.487141i
$170$	−0.0323716	+	3.65897i	−0.00248279	+	0.280630i
$171$	4.21365	−	2.43275i	0.322225	−	0.186037i
$172$	−8.30093	−	14.9838i	−0.632940	−	1.14250i
$173$	6.21674	+	10.7677i	0.472650	+	0.818654i	0.999510	−	0.0312980i	$-0.00996410\pi$
$173$	6.21674	+	10.7677i	0.472650	+	0.818654i	−0.526860	+	0.849952i	$0.676631\pi$
$174$	0.603681	+	1.06730i	0.0457649	+	0.0809119i
$175$	−4.83126	+	8.36798i	−0.365209	+	0.632560i
$176$	0.943541	+	1.77660i	0.0711221	+	0.133917i
$177$		−	7.96043i		−	0.598343i
$178$	−7.62997	+	12.9496i	−0.571891	+	0.970611i
$179$	20.9617			1.56675			0.783377	−	0.621547i	$-0.213496\pi$
$179$	20.9617			1.56675			0.783377	+	0.621547i	$0.213496\pi$
$180$	0.993066	−	0.550153i	0.0740188	−	0.0410060i
$181$	−4.79979	+	8.31348i	−0.356765	+	0.617936i	−0.987418	−	0.158129i	$-0.949454\pi$
$181$	−4.79979	+	8.31348i	−0.356765	+	0.617936i	0.630653	+	0.776065i	$0.282787\pi$
$182$	−11.3432	−	6.68350i	−0.840815	−	0.495414i
$183$	−7.38094	+	4.26139i	−0.545615	+	0.315011i
$184$	−11.5310	+	6.25543i	−0.850077	+	0.461157i
$185$	0.341000	−	0.196876i	0.0250708	−	0.0144746i
$186$	5.84894	+	10.3409i	0.428865	+	0.758229i
$187$	−2.29231			−0.167630
$188$	0.315273	−	17.8163i	0.0229936	−	1.29939i
$189$	1.03281	−	1.78888i	0.0751257	−	0.130122i
$190$	−3.90568	−	0.0345543i	−0.283348	−	0.00250683i
$191$	2.48806	+	4.30945i	0.180030	+	0.311821i	0.941890	−	0.335920i	$-0.109047\pi$
$191$	2.48806	+	4.30945i	0.180030	+	0.311821i	−0.761861	+	0.647741i	$0.775714\pi$
$192$	−7.98873	−	0.424455i	−0.576537	−	0.0306324i
$193$	−21.8223			−1.57081			−0.785403	−	0.618985i	$-0.787544\pi$
$193$	−21.8223			−1.57081			−0.785403	+	0.618985i	$0.787544\pi$
$194$	−0.132990	+	15.0319i	−0.00954811	+	1.07923i
$195$	−1.27915	−	2.21556i	−0.0916022	−	0.158660i
$196$	2.81656	−	4.68499i	0.201183	−	0.334642i
$197$	19.2043	+	11.0876i	1.36825	+	0.789958i	0.990704	−	0.136034i	$-0.0434356\pi$
$197$	19.2043	+	11.0876i	1.36825	+	0.789958i	0.377543	+	0.925992i	$0.376769\pi$
$198$	0.350144	+	0.619050i	0.0248836	+	0.0439940i
$199$	15.0830	−	8.70816i	1.06920	−	0.617305i	0.141240	−	0.989975i	$-0.454891\pi$
$199$	15.0830	−	8.70816i	1.06920	−	0.617305i	0.927964	+	0.372670i	$0.121558\pi$
$200$	13.2261	+	0.351115i	0.935228	+	0.0248276i
$201$	6.54149	−	4.92025i	0.461401	−	0.347048i
$202$	13.0597	−	7.38678i	0.918881	−	0.519732i
$203$	−0.895500	−	1.55105i	−0.0628518	−	0.108862i
$204$	4.69713	−	7.81307i	0.328865	−	0.547025i
$205$	−2.66128	+	4.60947i	−0.185872	+	0.321939i
$206$	5.10673	−	2.88844i	0.355803	−	0.201247i
$207$	−4.01670	+	2.31904i	−0.279180	+	0.161184i
$208$	−0.637831	+	18.0165i	−0.0442256	+	1.24922i
$209$		−	2.44688i		−	0.169254i
$210$	−1.44332	+	0.816361i	−0.0995984	+	0.0563343i
$211$	17.0716	−	9.85630i	1.17526	−	0.678536i	0.220345	−	0.975422i	$-0.429282\pi$
$211$	17.0716	−	9.85630i	1.17526	−	0.678536i	0.954913	+	0.296886i	$0.0959482\pi$
$212$	25.2994	−	14.0157i	1.73757	−	0.962605i
$213$	4.35912	+	2.51674i	0.298682	+	0.172444i
$214$	−6.13270	−	3.61343i	−0.419223	−	0.247009i
$215$			4.86167i			0.331563i
$216$	−2.82743	−	0.0750601i	−0.192382	−	0.00510720i
$217$	−8.67631	−	15.0278i	−0.588986	−	1.02015i
$218$	−3.44994	−	2.03273i	−0.233659	−	0.137674i
$219$	3.10591	+	5.37959i	0.209878	+	0.363519i
$220$	0.0101015	−	0.570844i	0.000681045	−	0.0384863i
$221$	−17.7911	−	10.2717i	−1.19676	−	0.690947i
$222$	−0.980959	−	0.00867873i	−0.0658376	−	0.000582478i
$223$			4.69841i			0.314629i	0.987549	+	0.157315i	$0.0502836\pi$
$223$			4.69841i			0.314629i	−0.987549	+	0.157315i	$0.949716\pi$
$224$	11.6735	+	0.516710i	0.779966	+	0.0345242i
$225$	4.67779			0.311853
$226$	10.1534	−	5.74293i	0.675397	−	0.382014i
$227$	−11.2279	−	6.48243i	−0.745222	−	0.430254i	0.0787430	−	0.996895i	$-0.474909\pi$
$227$	−11.2279	−	6.48243i	−0.745222	−	0.430254i	−0.823965	+	0.566641i	$0.808243\pi$
$228$	8.33989	+	5.01384i	0.552322	+	0.332050i
$229$	−19.2661	+	11.1233i	−1.27314	+	0.735048i	−0.975578	−	0.219654i	$-0.929507\pi$
$229$	−19.2661	+	11.1233i	−1.27314	+	0.735048i	−0.297563	+	0.954702i	$0.596174\pi$
$230$	3.72312	+	0.0329392i	0.245496	+	0.00217195i
$231$	−0.519403	−	0.899632i	−0.0341742	−	0.0591914i
$232$	−1.28213	+	2.09055i	−0.0841759	+	0.137251i
$233$	−11.9482	−	6.89831i	−0.782754	−	0.451923i	0.0546516	−	0.998505i	$-0.482595\pi$
$233$	−11.9482	−	6.89831i	−0.782754	−	0.451923i	−0.837405	+	0.546582i	$0.815929\pi$
$234$	−0.0563878	+	6.37353i	−0.00368619	+	0.416651i
$235$	−2.52869	+	4.37983i	−0.164954	+	0.285708i
$236$	13.9266	−	7.71524i	0.906542	−	0.502219i
$237$	−4.84032	+	8.38369i	−0.314413	+	0.544579i
$238$	−6.75945	+	11.4721i	−0.438150	+	0.743627i
$239$	10.8958	−	18.8721i	0.704790	−	1.22073i	−0.261977	−	0.965074i	$-0.584375\pi$
$239$	10.8958	−	18.8721i	0.704790	−	1.22073i	0.966767	−	0.255658i	$-0.0822921\pi$
$240$	1.92496	+	1.20413i	0.124255	+	0.0777266i
$241$	−3.30840			−0.213113			−0.106557	−	0.994307i	$-0.533983\pi$
$241$	−3.30840			−0.213113			−0.106557	+	0.994307i	$0.533983\pi$
$242$	−15.1981	−	0.134460i	−0.976970	−	0.00864344i
$243$	−1.00000			−0.0641500
$244$	−14.6088	−	8.78262i	−0.935231	−	0.562250i
$245$	−1.34362	+	0.775742i	−0.0858410	+	0.0495603i
$246$	11.5422	−	6.52846i	0.735907	−	0.416239i
$247$	10.9643	−	18.9907i	0.697639	−	1.20835i
$248$	−12.4223	+	20.2549i	−0.788815	+	1.28619i
$249$	6.79123	−	3.92092i	0.430377	−	0.248478i
$250$	−6.69348	−	3.94384i	−0.423333	−	0.249431i
$251$	2.25380	+	3.90370i	0.142259	+	0.246400i	0.928347	−	0.371715i	$-0.121230\pi$
$251$	2.25380	+	3.90370i	0.142259	+	0.246400i	−0.786088	+	0.618115i	$0.787897\pi$
$252$	4.13059	+	0.0730939i	0.260202	+	0.00460448i
$253$			2.33251i			0.146644i
$254$	14.3885	−	8.13833i	0.902814	−	0.510644i
$255$	−2.24074	+	1.29369i	−0.140320	+	0.0810140i
$256$	−7.00009	−	14.3874i	−0.437506	−	0.899216i
$257$	−5.15090	+	8.92162i	−0.321304	+	0.556516i	−0.980757	−	0.195230i	$-0.937455\pi$
$257$	−5.15090	+	8.92162i	−0.321304	+	0.556516i	0.659453	+	0.751746i	$0.270788\pi$
$258$	6.14875	−	10.4356i	0.382804	−	0.649694i
$259$	1.43286			0.0890333
$260$	2.63631	−	4.38516i	0.163497	−	0.271956i
$261$	−0.433527	+	0.750890i	−0.0268346	+	0.0464789i
$262$	8.52002	+	5.02006i	0.526369	+	0.310140i
$263$		−	7.32912i		−	0.451933i	−0.974135	−	0.225966i	$-0.927446\pi$
$263$		−	7.32912i		−	0.451933i	0.974135	−	0.225966i	$-0.0725539\pi$
$264$	−0.743653	+	1.21255i	−0.0457687	+	0.0746272i
$265$	−8.20870			−0.504257
$266$	−12.2456	−	7.21522i	−0.750829	−	0.442394i
$267$	−10.6280			−0.650421
$268$	14.9479	+	6.67546i	0.913085	+	0.407768i
$269$	−3.52992			−0.215223			−0.107611	−	0.994193i	$-0.534320\pi$
$269$	−3.52992			−0.215223			−0.107611	+	0.994193i	$0.534320\pi$
$270$	0.691633	+	0.407515i	0.0420914	+	0.0248006i
$271$	3.15572			0.191697			0.0958483	−	0.995396i	$-0.469444\pi$
$271$	3.15572			0.191697			0.0958483	+	0.995396i	$0.469444\pi$
$272$	18.2212	+	0.645079i	1.10482	+	0.0391136i
$273$		−	9.30961i		−	0.563443i
$274$	17.7778	+	10.4748i	1.07400	+	0.632808i
$275$	1.17624	−	2.03730i	0.0709298	−	0.122854i
$276$	−7.95007	−	4.77949i	−0.478538	−	0.287692i
$277$	−4.91436			−0.295275			−0.147638	−	0.989042i	$-0.547167\pi$
$277$	−4.91436			−0.295275			−0.147638	+	0.989042i	$0.547167\pi$
$278$	−14.7401	+	25.0168i	−0.884052	+	1.50041i
$279$	−4.20035	+	7.27522i	−0.251468	+	0.435556i
$280$	−2.82706	−	1.73383i	−0.168949	−	0.103616i
$281$	−0.219861	+	0.126937i	−0.0131158	+	0.00757241i	−0.506544	−	0.862214i	$-0.669077\pi$
$281$	−0.219861	+	0.126937i	−0.0131158	+	0.00757241i	0.493428	+	0.869787i	$0.335744\pi$
$282$	10.9672	−	6.20321i	0.653088	−	0.369396i
$283$		−	9.68330i		−	0.575612i	−0.957689	−	0.287806i	$-0.907074\pi$
$283$		−	9.68330i		−	0.575612i	0.957689	−	0.287806i	$-0.0929259\pi$
$284$	−0.178115	+	10.0654i	−0.0105692	+	0.597270i
$285$	−1.38092	−	2.39182i	−0.0817986	−	0.141679i
$286$	2.76167	+	1.62719i	0.163301	+	0.0962180i
$287$	−16.7737	+	9.68431i	−0.990121	+	0.571647i
$288$	−2.60903	−	5.01926i	−0.153738	−	0.295763i
$289$	−1.88839	+	3.27079i	−0.111082	+	0.192400i
$290$	0.605840	−	0.342672i	0.0355762	−	0.0201224i
$291$	−9.20546	+	5.31478i	−0.539634	+	0.311558i
$292$	−6.40121	+	10.6476i	−0.374602	+	0.623104i
$293$	−1.34689			−0.0786864			−0.0393432	−	0.999226i	$-0.512527\pi$
$293$	−1.34689			−0.0786864			−0.0393432	+	0.999226i	$0.512527\pi$
$294$	3.86522	+	0.0341963i	0.225424	+	0.00199437i
$295$	−4.51864			−0.263085
$296$	−0.935560	−	1.72457i	−0.0543783	−	0.100239i
$297$	−0.251452	+	0.435527i	−0.0145907	+	0.0252719i
$298$	5.40557	−	9.17432i	0.313136	−	0.531454i
$299$	−10.4518	+	18.1030i	−0.604442	+	1.04692i
$300$	4.53370	+	8.18366i	0.261754	+	0.472484i
$301$	−8.84573	+	15.3213i	−0.509860	+	0.883103i
$302$	−0.230686	+	26.0745i	−0.0132745	+	1.50042i
$303$	9.18807	+	5.30473i	0.527841	+	0.304749i
$304$	−0.688574	+	19.4498i	−0.0394924	+	1.11552i
$305$	2.41892	+	4.18970i	0.138507	+	0.239901i
$306$	6.44595	+	0.0570286i	0.368491	+	0.00326011i
$307$	5.07786	−	2.93171i	0.289809	−	0.167321i	−0.348047	−	0.937477i	$-0.613155\pi$
$307$	5.07786	−	2.93171i	0.289809	−	0.167321i	0.637856	+	0.770156i	$0.279822\pi$
$308$	1.07048	−	1.78060i	0.0609961	−	0.101459i
$309$	3.59279	+	2.07430i	0.204387	+	0.118003i
$310$	5.86986	−	3.32008i	0.333386	−	0.188568i
$311$	−19.1012			−1.08313			−0.541563	−	0.840660i	$-0.682167\pi$
$311$	−19.1012			−1.08313			−0.541563	+	0.840660i	$0.682167\pi$
$312$	−11.2050	+	6.07856i	−0.634356	+	0.344131i
$313$			14.8429i			0.838968i	0.907763	+	0.419484i	$0.137789\pi$
$313$			14.8429i			0.838968i	−0.907763	+	0.419484i	$0.862211\pi$
$314$	−20.4986	−	0.181355i	−1.15681	−	0.0102345i
$315$	−1.01543	−	0.586261i	−0.0572132	−	0.0330320i
$316$	−19.3583	−	0.342559i	−1.08899	−	0.0192705i
$317$	−16.1773	−	28.0199i	−0.908608	−	1.57376i	−0.815999	−	0.578053i	$-0.803813\pi$
$317$	−16.1773	−	28.0199i	−0.908608	−	1.57376i	−0.0926086	−	0.995703i	$-0.529521\pi$
$318$	17.6201	+	10.3819i	0.988086	+	0.582187i
$319$	0.218022	+	0.377625i	0.0122069	+	0.0211430i
$320$	−0.240936	+	4.53470i	−0.0134688	+	0.253498i
$321$		−	5.03323i		−	0.280928i
$322$	11.6733	+	6.87798i	0.650526	+	0.383295i
$323$	−19.2065	−	11.0888i	−1.06868	−	0.617000i
$324$	−0.969198	−	1.74947i	−0.0538443	−	0.0971929i
$325$	18.2580	−	10.5413i	1.01277	−	0.584724i
$326$	−7.06519	+	3.99617i	−0.391304	+	0.221327i
$327$		−	2.83143i		−	0.156579i
$328$	22.6081	+	13.8655i	1.24832	+	0.765593i
$329$	−15.9381	+	9.20184i	−0.878694	+	0.507314i
$330$	0.351396	−	0.198755i	0.0193437	−	0.0109411i
$331$	−7.43209	+	12.8728i	−0.408505	+	0.707551i	−0.994722	−	0.102603i	$-0.967283\pi$
$331$	−7.43209	+	12.8728i	−0.408505	+	0.707551i	0.586218	+	0.810154i	$0.300616\pi$
$332$	13.4416	+	8.08092i	0.737703	+	0.443498i
$333$	−0.346835	−	0.600736i	−0.0190064	−	0.0329201i
$334$	11.5452	−	6.53015i	0.631728	−	0.357314i
$335$	−2.79292	−	3.71320i	−0.152594	−	0.202874i
$336$	3.87548	+	7.29719i	0.211425	+	0.398094i
$337$	12.2525	−	7.07401i	0.667439	−	0.385346i	−0.127667	−	0.991817i	$-0.540749\pi$
$337$	12.2525	−	7.07401i	0.667439	−	0.385346i	0.795105	+	0.606471i	$0.207415\pi$
$338$	5.09130	+	9.00137i	0.276930	+	0.489610i
$339$	7.14336	+	4.12422i	0.387974	+	0.223997i
$340$	−4.43499	−	2.66627i	−0.240521	−	0.144599i
$341$	2.11237	+	3.65873i	0.114391	+	0.198131i
$342$	−0.0608739	+	6.88058i	−0.00329168	+	0.372059i
$343$	−20.1051			−1.08557
$344$	24.2162	+	0.642871i	1.30565	+	0.0346613i
$345$	1.31637	+	2.28003i	0.0708712	+	0.122753i
$346$	−17.5829	−	0.155559i	−0.945263	−	0.00836293i
$347$	−2.10226	+	3.64122i	−0.112855	+	0.195471i	−0.916920	−	0.399070i	$-0.869333\pi$
$347$	−2.10226	+	3.64122i	−0.112855	+	0.195471i	0.804065	+	0.594541i	$0.202666\pi$
$348$	−1.73383	−	0.0306815i	−0.0929433	−	0.00164470i
$349$	−0.844089			−0.0451831			−0.0225915	−	0.999745i	$-0.507192\pi$
$349$	−0.844089			−0.0451831			−0.0225915	+	0.999745i	$0.507192\pi$
$350$	−6.72747	−	11.8941i	−0.359598	−	0.635766i
$351$	−3.90313	+	2.25347i	−0.208333	+	0.120281i
$352$	−2.84207	−	0.125800i	−0.151483	−	0.00670519i
$353$	23.0822	−	13.3265i	1.22854	−	0.709300i	0.261818	−	0.965117i	$-0.415678\pi$
$353$	23.0822	−	13.3265i	1.22854	−	0.709300i	0.966725	+	0.255817i	$0.0823446\pi$
$354$	9.69932	+	5.71491i	0.515513	+	0.303744i
$355$	1.42859	−	2.47440i	0.0758219	−	0.131327i
$356$	−10.3006	−	18.5933i	−0.545931	−	0.985446i
$357$	−9.41540			−0.498316
$358$	−15.0487	+	25.5406i	−0.795350	+	1.34986i
$359$		−	16.8556i		−	0.889605i	−0.895629	−	0.444803i	$-0.853274\pi$
$359$		−	16.8556i		−	0.889605i	0.895629	−	0.444803i	$-0.146726\pi$
$360$	−0.0426070	+	1.60496i	−0.00224558	+	0.0845886i
$361$	2.33654	−	4.04700i	0.122976	−	0.213000i
$362$	−6.68365	−	11.8166i	−0.351285	−	0.621068i
$363$	−5.37354	−	9.30725i	−0.282038	−	0.488504i
$364$	16.2869	−	9.02286i	0.853666	−	0.472926i
$365$	3.05366	−	1.76303i	0.159836	−	0.0922813i
$366$	0.106631	−	12.0526i	0.00557370	−	0.629997i
$367$	−4.32877	+	7.49765i	−0.225960	+	0.391374i	−0.956607	−	0.291381i	$-0.905885\pi$
$367$	−4.32877	+	7.49765i	−0.225960	+	0.391374i	0.730647	+	0.682755i	$0.239219\pi$
$368$	0.656390	−	18.5407i	0.0342167	−	0.966501i
$369$	8.12044	+	4.68834i	0.422733	+	0.244065i
$370$	−0.00492637	+	0.556829i	−0.000256110	+	0.0289482i
$371$	−25.8692	−	14.9356i	−1.34306	−	0.775419i
$372$	−16.7988	−	0.297267i	−0.870975	−	0.0154126i
$373$	8.48203	+	4.89711i	0.439183	+	0.253562i	0.703251	−	0.710942i	$-0.251731\pi$
$373$	8.48203	+	4.89711i	0.439183	+	0.253562i	−0.264068	+	0.964504i	$0.585064\pi$
$374$	1.64568	−	2.79305i	0.0850963	−	0.144425i
$375$		−	5.49348i		−	0.283682i
$376$	21.4818	+	13.1747i	1.10784	+	0.679434i
$377$			3.90776i			0.201260i
$378$	1.43817	+	2.54268i	0.0739716	+	0.130781i
$379$	−18.0207	−	31.2128i	−0.925661	−	1.60329i	−0.790494	−	0.612469i	$-0.790176\pi$
$379$	−18.0207	−	31.2128i	−0.925661	−	1.60329i	−0.135167	−	0.990823i	$-0.543157\pi$
$380$	2.84604	−	4.73403i	0.145999	−	0.242851i
$381$	10.1229	+	5.84445i	0.518611	+	0.299420i
$382$	−7.03703	−	0.0622579i	−0.360046	−	0.00318539i
$383$	7.95385	+	13.7765i	0.406423	+	0.703945i	0.994486	−	0.104870i	$-0.0334427\pi$
$383$	7.95385	+	13.7765i	0.406423	+	0.703945i	−0.588063	+	0.808815i	$0.700109\pi$
$384$	6.25240	−	9.42908i	0.319066	−	0.481176i
$385$	−0.510665	+	0.294833i	−0.0260259	+	0.0150261i
$386$	15.6666	−	26.5892i	0.797407	−	1.35336i
$387$	8.56474			0.435370
$388$	−18.2200	−	10.9536i	−0.924979	−	0.556086i
$389$	15.4391	+	26.7414i	0.782795	+	1.35584i	0.930307	+	0.366781i	$0.119540\pi$
$389$	15.4391	+	26.7414i	0.782795	+	1.35584i	−0.147512	+	0.989060i	$0.547127\pi$
$390$	3.61785	+	0.0320079i	0.183197	+	0.00162078i
$391$	18.3087	+	10.5706i	0.925912	+	0.534576i
$392$	3.68634	+	6.79524i	0.186188	+	0.343211i
$393$			6.99256i			0.352728i
$394$	−27.2966	+	15.4393i	−1.37518	+	0.777822i
$395$	4.75889	+	2.74755i	0.239446	+	0.138244i
$396$	−1.00565	−	0.0177957i	−0.0505358	−	0.000894270i
$397$	−27.7523			−1.39285			−0.696423	−	0.717631i	$-0.745226\pi$
$397$	−27.7523			−1.39285			−0.696423	+	0.717631i	$0.745226\pi$
$398$	−0.217901	+	24.6294i	−0.0109224	+	1.23456i
$399$		−	10.0503i		−	0.503142i
$400$	−9.92303	+	15.8632i	−0.496152	+	0.793159i
$401$		−	30.4324i		−	1.51972i	−0.650086	−	0.759860i	$-0.725267\pi$
$401$		−	30.4324i		−	1.51972i	0.650086	−	0.759860i	$-0.274733\pi$
$402$	1.29881	+	11.5027i	0.0647789	+	0.573705i
$403$			37.8615i			1.88601i
$404$	−0.375427	+	21.2156i	−0.0186782	+	1.05552i
$405$			0.567637i			0.0282061i
$406$	2.53276	+	0.0224078i	0.125699	+	0.00111208i
$407$	−0.348849			−0.0172918
$408$	6.14764	+	11.3323i	0.304353	+	0.561032i
$409$	−30.8839	−	17.8308i	−1.52711	−	0.881678i	−0.999481	−	0.0322035i	$-0.989748\pi$
$409$	−30.8839	−	17.8308i	−1.52711	−	0.881678i	−0.527630	−	0.849474i	$-0.676919\pi$
$410$	−3.70580	−	6.55181i	−0.183016	−	0.323571i
$411$			14.5906i			0.719704i
$412$	−0.146802	+	8.29591i	−0.00723244	+	0.408710i
$413$	−14.2402	−	8.22160i	−0.700716	−	0.404559i
$414$	0.0580286	−	6.55898i	0.00285195	−	0.322356i
$415$	−2.22566	−	3.85496i	−0.109253	−	0.189232i
$416$	−21.4941	−	13.7114i	−1.05384	−	0.672259i
$417$	−20.5318			−1.00545
$418$	2.98137	+	1.75665i	0.145824	+	0.0859204i
$419$	−10.8492	+	6.26380i	−0.530019	+	0.306007i	−0.741024	−	0.671478i	$-0.765660\pi$
$419$	−10.8492	+	6.26380i	−0.530019	+	0.306007i	0.211005	+	0.977485i	$0.432326\pi$
$420$	0.0414908	−	2.34468i	0.00202455	−	0.114408i
$421$	5.47166	+	9.47719i	0.266672	+	0.461890i	0.968000	−	0.250949i	$-0.0807425\pi$
$421$	5.47166	+	9.47719i	0.266672	+	0.461890i	−0.701328	+	0.712839i	$0.747409\pi$
$422$	−0.246631	+	27.8767i	−0.0120058	+	1.35702i
$423$	7.71589	+	4.45477i	0.375159	+	0.216598i
$424$	−1.08546	+	40.8880i	−0.0527145	+	1.98570i
$425$	−10.6610	−	18.4655i	−0.517137	−	0.895707i
$426$	−6.19597	+	3.50453i	−0.300196	+	0.169795i
$427$			17.6048i			0.851955i
$428$	8.80551	−	4.87820i	0.425630	−	0.235797i
$429$			2.26656i			0.109430i
$430$	−5.92366	−	3.49026i	−0.285664	−	0.168315i
$431$	23.1169	+	13.3466i	1.11350	+	0.642882i	0.939735	−	0.341905i	$-0.111072\pi$
$431$	23.1169	+	13.3466i	1.11350	+	0.642882i	0.173769	+	0.984786i	$0.444405\pi$
$432$	2.12131	−	3.39117i	0.102062	−	0.163158i
$433$	24.8881	+	14.3691i	1.19604	+	0.690536i	0.959671	−	0.281126i	$-0.0907080\pi$
$433$	24.8881	+	14.3691i	1.19604	+	0.690536i	0.236373	+	0.971662i	$0.424041\pi$
$434$	24.5394	+	0.217104i	1.17793	+	0.0104213i
$435$	0.426233	+	0.246086i	0.0204363	+	0.0117989i
$436$	4.95352	−	2.74422i	0.237230	−	0.131424i
$437$	−11.2833	+	19.5432i	−0.539753	+	0.934880i
$438$	−8.78450	−	0.0777181i	−0.419739	−	0.00371352i
$439$	5.89975	−	3.40622i	0.281580	−	0.162570i	−0.352559	−	0.935790i	$-0.614688\pi$
$439$	5.89975	−	3.40622i	0.281580	−	0.162570i	0.634138	+	0.773220i	$0.281355\pi$
$440$	0.688288	+	0.422125i	0.0328129	+	0.0201240i
$441$	1.36661	+	2.36705i	0.0650769	+	0.112716i
$442$	25.2879	−	14.3032i	1.20282	−	0.680333i
$443$	−2.14957	+	3.72316i	−0.102129	+	0.176893i	−0.912562	−	0.408939i	$-0.865899\pi$
$443$	−2.14957	+	3.72316i	−0.102129	+	0.176893i	0.810433	+	0.585832i	$0.199232\pi$
$444$	0.714819	−	1.18901i	0.0339238	−	0.0564279i
$445$			6.03284i			0.285984i
$446$	−5.72474	−	3.37306i	−0.271074	−	0.159719i
$447$	7.52955			0.356136
$448$	−9.01013	+	13.8525i	−0.425688	+	0.654468i
$449$	−2.34265	+	4.05758i	−0.110556	+	0.191489i	−0.915995	−	0.401190i	$-0.868597\pi$
$449$	−2.34265	+	4.05758i	−0.110556	+	0.191489i	0.805438	+	0.592680i	$0.201930\pi$
$450$	−3.35825	+	5.69961i	−0.158309	+	0.268682i
$451$	4.08380	−	2.35778i	0.192299	−	0.111024i
$452$	−0.291880	+	16.4943i	−0.0137289	+	0.775827i
$453$	−15.9680	+	9.21910i	−0.750240	+	0.433151i
$454$	15.9591	−	9.02671i	0.748999	−	0.423644i
$455$	−5.28449			−0.247741
$456$	−12.0964	+	6.56215i	−0.566466	+	0.307301i
$457$	−19.9700	+	34.5891i	−0.934159	+	1.61801i	−0.158033	+	0.987434i	$0.550515\pi$
$457$	−19.9700	+	34.5891i	−0.934159	+	1.61801i	−0.776127	+	0.630577i	$0.782818\pi$
$458$	0.278334	−	31.4602i	0.0130057	−	1.47004i
$459$	2.27908	+	3.94748i	0.106378	+	0.184253i
$460$	−2.71302	+	4.51276i	−0.126495	+	0.210409i
$461$	17.3662			0.808822			0.404411	−	0.914577i	$-0.367476\pi$
$461$	17.3662			0.808822			0.404411	+	0.914577i	$0.367476\pi$
$462$	1.46904	+	0.0129968i	0.0683457	+	0.000604668i
$463$	8.53232	+	14.7784i	0.396531	+	0.686811i	0.993295	−	0.115605i	$-0.0368807\pi$
$463$	8.53232	+	14.7784i	0.396531	+	0.686811i	−0.596765	+	0.802416i	$0.703547\pi$
$464$	−1.62675	−	3.06303i	−0.0755201	−	0.142198i
$465$	4.12969	+	2.38428i	0.191510	+	0.110568i
$466$	16.9830	−	9.60581i	0.786721	−	0.444981i
$467$	20.9631	−	12.1030i	0.970055	−	0.560061i	0.0708017	−	0.997490i	$-0.477444\pi$
$467$	20.9631	−	12.1030i	0.970055	−	0.560061i	0.899253	+	0.437429i	$0.144111\pi$
$468$	−7.72529	−	4.64435i	−0.357102	−	0.214685i
$469$	−2.04562	−	16.7836i	−0.0944580	−	0.774994i
$470$	−3.52118	−	6.22541i	−0.162420	−	0.287157i
$471$	−7.24765	−	12.5533i	−0.333954	−	0.578425i
$472$	−0.597511	+	22.5076i	−0.0275027	+	1.03600i
$473$	2.15362	−	3.73018i	0.0990235	−	0.171514i
$474$	−6.74009	−	11.9164i	−0.309583	−	0.547339i
$475$	19.7105	−	11.3799i	0.904381	−	0.522145i
$476$	−9.12539	−	16.4720i	−0.418262	−	0.754992i
$477$			14.4612i			0.662132i
$478$	15.1723	+	26.8244i	0.693963	+	1.22692i
$479$	−28.8135	+	16.6355i	−1.31652	+	0.760095i	−0.983168	−	0.182706i	$-0.941514\pi$
$479$	−28.8135	+	16.6355i	−1.31652	+	0.760095i	−0.333356	+	0.942801i	$0.608181\pi$
$480$	−2.84912	+	1.48098i	−0.130044	+	0.0675972i
$481$	−2.70748	−	1.56316i	−0.123450	−	0.0712742i
$482$	2.37515	−	4.03110i	0.108185	−	0.183611i
$483$			9.58050i			0.435928i
$484$	11.0748	−	18.4214i	0.503398	−	0.837338i
$485$	3.01687	+	5.22537i	0.136989	+	0.237272i
$486$	0.717914	−	1.21844i	0.0325653	−	0.0552696i
$487$	−7.54173	−	13.0627i	−0.341749	−	0.591926i	0.643009	−	0.765859i	$-0.277686\pi$
$487$	−7.54173	−	13.0627i	−0.341749	−	0.591926i	−0.984758	+	0.173933i	$0.944352\pi$
$488$	21.1890	−	11.4948i	0.959179	−	0.520344i
$489$	−4.97065	−	2.86980i	−0.224780	−	0.129777i
$490$	0.0194111	−	2.19404i	0.000876905	−	0.0991167i
$491$		−	17.2830i		−	0.779969i	−0.920821	−	0.389985i	$-0.872480\pi$
$491$		−	17.2830i		−	0.779969i	0.920821	−	0.389985i	$-0.127520\pi$
$492$	−0.331803	+	18.7504i	−0.0149588	+	0.845334i
$493$	3.95216			0.177996
$494$	15.2676	+	26.9930i	0.686922	+	1.21447i
$495$	0.247222	+	0.142733i	0.0111118	+	0.00641539i
$496$	−15.7613	−	29.6771i	−0.707702	−	1.33254i
$497$	9.00427	−	5.19862i	0.403897	−	0.233190i
$498$	−0.0981118	+	11.0896i	−0.00439650	+	0.496937i
$499$	2.30235	+	3.98778i	0.103067	+	0.178518i	0.912947	−	0.408078i	$-0.133801\pi$
$499$	2.30235	+	3.98778i	0.103067	+	0.178518i	−0.809880	+	0.586596i	$0.800468\pi$
$500$	9.61068	−	5.32427i	0.429803	−	0.238108i
$501$	8.12255	+	4.68956i	0.362889	+	0.209514i
$502$	−6.37447	−	0.0563962i	−0.284507	−	0.00251708i
$503$	−3.09904	+	5.36769i	−0.138179	+	0.239334i	−0.926807	−	0.375537i	$-0.877458\pi$
$503$	−3.09904	+	5.36769i	−0.138179	+	0.239334i	0.788628	+	0.614870i	$0.210792\pi$
$504$	−3.05447	+	4.98040i	−0.136057	+	0.221845i
$505$	3.01117	−	5.21549i	0.133995	−	0.232086i
$506$	−2.84202	−	1.67454i	−0.126343	−	0.0744424i
$507$	−3.65626	+	6.33283i	−0.162380	+	0.281251i
$508$	−0.413624	+	23.3741i	−0.0183516	+	1.03706i
$509$	−11.5141			−0.510354			−0.255177	−	0.966894i	$-0.582134\pi$
$509$	−11.5141			−0.510354			−0.255177	+	0.966894i	$0.582134\pi$
$510$	0.0323716	−	3.65897i	0.00143344	−	0.162022i
$511$	12.8312			0.567621
$512$	22.5557	+	1.79975i	0.996832	+	0.0795385i
$513$	−4.21365	+	2.43275i	−0.186037	+	0.107408i
$514$	−7.17257	−	12.6810i	−0.316368	−	0.559336i
$515$	1.17745	−	2.03940i	0.0518847	−	0.0898669i
$516$	8.30093	+	14.9838i	0.365428	+	0.659624i
$517$	3.88035	−	2.24032i	0.170657	−	0.0985291i
$518$	−1.02867	+	1.74585i	−0.0451970	+	0.0767083i
$519$	−6.21674	−	10.7677i	−0.272885	−	0.472650i
$520$	3.45042	+	6.36036i	0.151311	+	0.278920i
$521$			0.906106i			0.0396972i	0.999803	+	0.0198486i	$0.00631842\pi$
$521$			0.906106i			0.0396972i	−0.999803	+	0.0198486i	$0.993682\pi$
$522$	−0.603681	−	1.06730i	−0.0264224	−	0.0467145i
$523$	−3.05551	+	1.76410i	−0.133608	+	0.0771386i	−0.565314	−	0.824876i	$-0.691245\pi$
$523$	−3.05551	+	1.76410i	−0.133608	+	0.0771386i	0.431706	+	0.902014i	$0.357912\pi$
$524$	−12.2333	+	6.77718i	−0.534414	+	0.296062i
$525$	4.83126	−	8.36798i	0.210853	−	0.365209i
$526$	8.93010	+	5.26168i	0.389371	+	0.229420i
$527$	38.2917			1.66801
$528$	−0.943541	−	1.77660i	−0.0410623	−	0.0773168i
$529$	−0.744097	+	1.28881i	−0.0323520	+	0.0560354i
$530$	5.89315	−	10.0018i	0.255982	−	0.434451i
$531$			7.96043i			0.345453i
$532$	17.5826	−	9.74069i	0.762304	−	0.422312i
$533$	42.2601			1.83049
$534$	7.62997	−	12.9496i	0.330181	−	0.560382i
$535$	−2.85705			−0.123521
$536$	−18.8649	+	13.4207i	−0.814841	+	0.579685i
$537$	−20.9617			−0.904566
$538$	2.53418	−	4.30100i	0.109256	−	0.185429i
$539$	1.37455			0.0592061
$540$	−0.993066	+	0.550153i	−0.0427348	+	0.0236748i
$541$		−	41.5109i		−	1.78469i	−0.451352	−	0.892346i	$-0.649058\pi$
$541$		−	41.5109i		−	1.78469i	0.451352	−	0.892346i	$-0.350942\pi$
$542$	−2.26554	+	3.84506i	−0.0973132	+	0.165160i
$543$	4.79979	−	8.31348i	0.205979	−	0.356765i
$544$	−13.8673	+	21.7384i	−0.594554	+	0.932025i
$545$	−1.60723			−0.0688461
$546$	11.3432	+	6.68350i	0.485445	+	0.286028i
$547$	−7.82240	+	13.5488i	−0.334462	+	0.579304i	−0.983381	−	0.181552i	$-0.941888\pi$
$547$	−7.82240	+	13.5488i	−0.334462	+	0.579304i	0.648920	+	0.760857i	$0.275221\pi$
$548$	−25.5259	+	14.1412i	−1.09041	+	0.604083i
$549$	7.38094	−	4.26139i	0.315011	−	0.181872i
$550$	1.63790	+	2.89579i	0.0698402	+	0.123477i
$551$			4.21865i			0.179720i
$552$	11.5310	−	6.25543i	0.490792	−	0.266249i
$553$	9.99825	+	17.3175i	0.425169	+	0.736414i
$554$	3.52809	−	5.98785i	0.149894	−	0.254400i
$555$	−0.341000	+	0.196876i	−0.0144746	+	0.00835694i
$556$	−19.8994	−	35.9199i	−0.843923	−	1.52334i
$557$	−6.31743	+	10.9421i	−0.267678	+	0.463632i	−0.968262	−	0.249938i	$-0.919590\pi$
$557$	−6.31743	+	10.9421i	−0.267678	+	0.463632i	0.700584	+	0.713570i	$0.252923\pi$
$558$	−5.84894	−	10.3409i	−0.247605	−	0.437764i
$559$	33.4293	−	19.3004i	1.41391	−	0.816320i
$560$	4.14216	−	2.19987i	0.175038	−	0.0929614i
$561$	2.29231			0.0967815
$562$	0.00317630	−	0.359017i	0.000133984	−	0.0151442i
$563$	16.5374			0.696969			0.348484	−	0.937315i	$-0.386696\pi$
$563$	16.5374			0.696969			0.348484	+	0.937315i	$0.386696\pi$
$564$	−0.315273	+	17.8163i	−0.0132754	+	0.750201i
$565$	2.34106	−	4.05484i	0.0984893	−	0.170588i
$566$	11.7985	+	6.95178i	0.495929	+	0.292205i
$567$	−1.03281	+	1.78888i	−0.0433739	+	0.0751257i
$568$	−12.1362	−	7.44310i	−0.509224	−	0.312305i
$569$	15.0544	−	26.0750i	0.631115	−	1.09312i	−0.356209	−	0.934406i	$-0.615931\pi$
$569$	15.0544	−	26.0750i	0.631115	−	1.09312i	0.987324	−	0.158717i	$-0.0507356\pi$
$570$	3.90568	+	0.0345543i	0.163591	+	0.00144732i
$571$	−17.1865	−	9.92262i	−0.719232	−	0.415249i	0.0952382	−	0.995455i	$-0.469639\pi$
$571$	−17.1865	−	9.92262i	−0.719232	−	0.415249i	−0.814470	+	0.580206i	$0.802972\pi$
$572$	−3.96528	+	2.19674i	−0.165797	+	0.0918504i
$573$	−2.48806	−	4.30945i	−0.103940	−	0.180030i
$574$	0.242327	−	27.3903i	0.0101145	−	1.14325i
$575$	−18.7893	+	10.8480i	−0.783566	+	0.452392i
$576$	7.98873	+	0.424455i	0.332864	+	0.0176856i
$577$	−15.7427	−	9.08907i	−0.655379	−	0.378383i	0.135135	−	0.990827i	$-0.456853\pi$
$577$	−15.7427	−	9.08907i	−0.655379	−	0.378383i	−0.790514	+	0.612444i	$0.790186\pi$
$578$	−2.62956	−	4.64905i	−0.109375	−	0.193375i
$579$	21.8223			0.906905
$580$	−0.0174160	+	0.984190i	−0.000723160	+	0.0408663i
$581$		−	16.1982i		−	0.672016i
$582$	0.132990	−	15.0319i	0.00551261	−	0.623091i
$583$	6.29823	+	3.63629i	0.260846	+	0.150600i
$584$	−8.37795	−	15.4436i	−0.346682	−	0.639059i
$585$	1.27915	+	2.21556i	0.0528865	+	0.0916022i
$586$	0.966955	−	1.64111i	0.0399445	−	0.0677937i
$587$	−19.8016	−	34.2974i	−0.817300	−	1.41561i	−0.907664	−	0.419697i	$-0.862136\pi$
$587$	−19.8016	−	34.2974i	−0.817300	−	1.41561i	0.0903640	−	0.995909i	$-0.471197\pi$
$588$	−2.81656	+	4.68499i	−0.116153	+	0.193206i
$589$			40.8736i			1.68417i
$590$	3.24400	−	5.50570i	0.133553	−	0.226666i
$591$	−19.2043	−	11.0876i	−0.789958	−	0.456082i
$592$	2.77294	+	0.0981694i	0.113967	+	0.00403474i
$593$	19.2570	−	11.1181i	0.790792	−	0.456564i	−0.0494492	−	0.998777i	$-0.515747\pi$
$593$	19.2570	−	11.1181i	0.790792	−	0.456564i	0.840241	+	0.542213i	$0.182413\pi$
$594$	−0.350144	−	0.619050i	−0.0143666	−	0.0253999i
$595$			5.34454i			0.219105i
$596$	7.29763	+	13.1727i	0.298923	+	0.539577i
$597$	−15.0830	+	8.70816i	−0.617305	+	0.356401i
$598$	−14.5540	−	25.7313i	−0.595157	−	1.05223i
$599$	0.873519	−	1.51298i	0.0356910	−	0.0618187i	−0.847628	−	0.530591i	$-0.821970\pi$
$599$	0.873519	−	1.51298i	0.0356910	−	0.0618187i	0.883319	+	0.468772i	$0.155303\pi$
$600$	−13.2261	−	0.351115i	−0.539954	−	0.0143342i
$601$	−1.37648	−	2.38413i	−0.0561478	−	0.0972508i	0.836585	−	0.547837i	$-0.184548\pi$
$601$	−1.37648	−	2.38413i	−0.0561478	−	0.0972508i	−0.892733	+	0.450586i	$0.851215\pi$
$602$	−12.3176	−	21.7774i	−0.502027	−	0.887579i
$603$	−6.54149	+	4.92025i	−0.266390	+	0.200368i
$604$	−31.6047	−	19.0004i	−1.28598	−	0.773114i
$605$	−5.28314	+	3.05023i	−0.214790	+	0.124009i
$606$	−13.0597	+	7.38678i	−0.530516	+	0.300067i
$607$	6.24508	+	3.60560i	0.253480	+	0.146347i	0.621357	−	0.783528i	$-0.286582\pi$
$607$	6.24508	+	3.60560i	0.253480	+	0.146347i	−0.367877	+	0.929875i	$0.619915\pi$
$608$	−23.2041	−	14.8023i	−0.941051	−	0.600312i
$609$	0.895500	+	1.55105i	0.0362875	+	0.0628518i
$610$	−6.84148	−	0.0605279i	−0.277003	−	0.00245070i
$611$	40.1548			1.62449
$612$	−4.69713	+	7.81307i	−0.189870	+	0.315825i
$613$	22.5754	+	39.1017i	0.911810	+	1.57930i	0.811506	+	0.584344i	$0.198648\pi$
$613$	22.5754	+	39.1017i	0.911810	+	1.57930i	0.100304	+	0.994957i	$0.468019\pi$
$614$	−0.0733591	+	8.29179i	−0.00296053	+	0.334629i
$615$	2.66128	−	4.60947i	0.107313	−	0.185872i
$616$	1.40105	+	2.58263i	0.0564499	+	0.104057i
$617$	−30.6940			−1.23569			−0.617847	−	0.786299i	$-0.711995\pi$
$617$	−30.6940			−1.23569			−0.617847	+	0.786299i	$0.711995\pi$
$618$	−5.10673	+	2.88844i	−0.205423	+	0.116190i
$619$	−6.23764	+	3.60131i	−0.250712	+	0.144749i	−0.620090	−	0.784530i	$-0.712904\pi$
$619$	−6.23764	+	3.60131i	−0.250712	+	0.144749i	0.369378	+	0.929279i	$0.379571\pi$
$620$	−0.168740	+	9.53561i	−0.00677676	+	0.382959i
$621$	4.01670	−	2.31904i	0.161184	−	0.0930599i
$622$	13.7130	−	23.2736i	0.549841	−	0.933188i
$623$	−10.9767	+	19.0121i	−0.439771	+	0.761705i
$624$	0.637831	−	18.0165i	0.0255337	−	0.721236i
$625$	20.2706			0.810825
$626$	−18.0851	−	10.6559i	−0.722828	−	0.425895i
$627$			2.44688i			0.0977188i
$628$	14.9372	−	24.8462i	0.596061	−	0.991471i
$629$	−1.58093	+	2.73825i	−0.0630357	+	0.109181i
$630$	1.44332	−	0.816361i	0.0575032	−	0.0325246i
$631$	−7.04131	−	12.1959i	−0.280310	−	0.485511i	0.691151	−	0.722710i	$-0.257104\pi$
$631$	−7.04131	−	12.1959i	−0.280310	−	0.485511i	−0.971461	+	0.237199i	$0.923771\pi$
$632$	14.3150	−	23.3410i	0.569419	−	0.928454i
$633$	−17.0716	+	9.85630i	−0.678536	+	0.391753i
$634$	45.7545	+	0.404799i	1.81714	+	0.0160766i
$635$	3.31753	−	5.74613i	0.131652	−	0.228028i
$636$	−25.2994	+	14.0157i	−1.00319	+	0.555760i
$637$	10.6681	+	6.15925i	0.422687	+	0.244038i
$638$	−0.616635	−	0.00545549i	−0.0244128	−	0.000215985i
$639$	−4.35912	−	2.51674i	−0.172444	−	0.0995606i
$640$	−5.35230	−	3.54910i	−0.211568	−	0.140290i
$641$	−9.05911	−	5.23028i	−0.357813	−	0.206584i	0.310308	−	0.950636i	$-0.399568\pi$
$641$	−9.05911	−	5.23028i	−0.357813	−	0.206584i	−0.668121	+	0.744053i	$0.732901\pi$
$642$	6.13270	+	3.61343i	0.242038	+	0.142611i
$643$			12.9178i			0.509427i	0.967017	+	0.254713i	$0.0819811\pi$
$643$			12.9178i			0.509427i	−0.967017	+	0.254713i	$0.918019\pi$
$644$	−16.7608	+	9.28540i	−0.660469	+	0.365896i
$645$		−	4.86167i		−	0.191428i
$646$	27.2997	−	15.4411i	1.07409	−	0.607522i
$647$	−9.11408	−	15.7861i	−0.358312	−	0.620614i	0.629367	−	0.777108i	$-0.283314\pi$
$647$	−9.11408	−	15.7861i	−0.358312	−	0.620614i	−0.987679	+	0.156494i	$0.949981\pi$
$648$	2.82743	+	0.0750601i	0.111072	+	0.00294864i
$649$	3.46699	+	2.00166i	0.136091	+	0.0785722i
$650$	−0.263770	+	29.8140i	−0.0103459	+	1.16940i
$651$	8.67631	+	15.0278i	0.340051	+	0.588986i
$652$	0.203102	−	11.4774i	0.00795408	−	0.449490i
$653$	12.1302	−	7.00335i	0.474690	−	0.274062i	−0.243511	−	0.969898i	$-0.578299\pi$
$653$	12.1302	−	7.00335i	0.474690	−	0.274062i	0.718201	+	0.695836i	$0.244966\pi$
$654$	3.44994	+	2.03273i	0.134903	+	0.0794859i
$655$	3.96924			0.155091
$656$	−33.1249	+	17.5924i	−1.29331	+	0.686868i
$657$	−3.10591	−	5.37959i	−0.121173	−	0.209878i
$658$	0.230255	−	26.0257i	0.00897626	−	1.01459i
$659$	−14.6230	−	8.44257i	−0.569630	−	0.328876i	0.187372	−	0.982289i	$-0.440003\pi$
$659$	−14.6230	−	8.44257i	−0.569630	−	0.328876i	−0.757001	+	0.653413i	$0.773336\pi$
$660$	−0.0101015	+	0.570844i	−0.000393202	+	0.0222201i
$661$			10.6171i			0.412957i	0.978451	+	0.206479i	$0.0662004\pi$
$661$			10.6171i			0.412957i	−0.978451	+	0.206479i	$0.933800\pi$
$662$	−10.3491	−	18.2971i	−0.402229	−	0.711137i
$663$	17.7911	+	10.2717i	0.690947	+	0.398919i
$664$	−19.4960	+	10.5764i	−0.756593	+	0.410443i
$665$	−5.70490			−0.221227
$666$	0.980959	+	0.00867873i	0.0380114	+	0.000336294i
$667$		−	4.02146i		−	0.155712i
$668$	−0.331889	+	18.7553i	−0.0128412	+	0.725664i
$669$		−	4.69841i		−	0.181651i
$670$	6.52939	−	0.737254i	0.252252	−	0.0284826i
$671$		−	4.28613i		−	0.165464i
$672$	−11.6735	−	0.516710i	−0.450314	−	0.0199325i
$673$		−	41.9851i		−	1.61841i	−0.587529	−	0.809203i	$-0.699899\pi$
$673$		−	41.9851i		−	1.61841i	0.587529	−	0.809203i	$-0.300101\pi$
$674$	−0.177011	+	20.0075i	−0.00681819	+	0.770662i
$675$	−4.67779			−0.180048
$676$	−14.6228	−	0.258761i	−0.562414	−	0.00995235i
$677$	−14.1927	−	8.19415i	−0.545469	−	0.314927i	0.201823	−	0.979422i	$-0.435313\pi$
$677$	−14.1927	−	8.19415i	−0.545469	−	0.314927i	−0.747293	+	0.664495i	$0.768647\pi$
$678$	−10.1534	+	5.74293i	−0.389941	+	0.220556i
$679$			21.9566i			0.842616i
$680$	6.43263	−	3.48963i	0.246680	−	0.133821i
$681$	11.2279	+	6.48243i	0.430254	+	0.248407i
$682$	−5.97445	−	0.0528571i	−0.228774	−	0.00202400i
$683$	−8.84052	−	15.3122i	−0.338273	−	0.585906i	0.645835	−	0.763477i	$-0.276509\pi$
$683$	−8.84052	−	15.3122i	−0.338273	−	0.585906i	−0.984108	+	0.177571i	$0.943176\pi$
$684$	−8.33989	−	5.01384i	−0.318883	−	0.191709i
$685$	8.28220			0.316447
$686$	14.4337	−	24.4969i	0.551083	−	0.935296i
$687$	19.2661	−	11.1233i	0.735048	−	0.424380i
$688$	−18.1685	+	29.0445i	−0.692666	+	1.10731i
$689$	32.5878	+	56.4438i	1.24150	+	2.15034i
$690$	−3.72312	−	0.0329392i	−0.141737	−	0.00125397i
$691$	−27.6376	−	15.9566i	−1.05139	−	0.607018i	−0.128349	−	0.991729i	$-0.540968\pi$
$691$	−27.6376	−	15.9566i	−1.05139	−	0.607018i	−0.923037	+	0.384711i	$0.874301\pi$
$692$	12.8126	−	21.3121i	0.487061	−	0.810163i
$693$	0.519403	+	0.899632i	0.0197305	+	0.0341742i
$694$	−2.92737	−	5.17557i	−0.111122	−	0.196462i
$695$			11.6546i			0.442085i
$696$	1.28213	−	2.09055i	0.0485990	−	0.0792421i
$697$		−	42.7404i		−	1.61891i
$698$	0.605984	−	1.02847i	0.0229368	−	0.0389283i
$699$	11.9482	+	6.89831i	0.451923	+	0.260918i
$700$	19.3220	+	0.341918i	0.730303	+	0.0129233i
$701$	30.6740	+	17.7096i	1.15854	+	0.668883i	0.950954	−	0.309334i	$-0.100106\pi$
$701$	30.6740	+	17.7096i	1.15854	+	0.668883i	0.207586	+	0.978217i	$0.433439\pi$
$702$	0.0563878	−	6.37353i	0.00212822	−	0.240553i
$703$	−2.92288	−	1.68752i	−0.110238	−	0.0636462i
$704$	2.19364	−	3.37258i	0.0826760	−	0.127109i
$705$	2.52869	−	4.37983i	0.0952361	−	0.164954i
$706$	−0.333465	+	37.6917i	−0.0125501	+	1.41854i
$707$	18.9790	−	10.9575i	0.713780	−	0.412101i
$708$	−13.9266	+	7.71524i	−0.523392	+	0.289956i
$709$	−8.88087	−	15.3821i	−0.333528	−	0.577687i	0.649673	−	0.760214i	$-0.274906\pi$
$709$	−8.88087	−	15.3821i	−0.333528	−	0.577687i	−0.983201	+	0.182526i	$0.941573\pi$
$710$	1.98930	+	3.51707i	0.0746571	+	0.131993i
$711$	4.84032	−	8.38369i	0.181526	−	0.314413i
$712$	30.0499	+	0.797737i	1.12617	+	0.0298965i
$713$		−	38.9631i		−	1.45918i
$714$	6.75945	−	11.4721i	0.252966	−	0.429333i
$715$	1.28658			0.0481155
$716$	−20.3161	−	36.6720i	−0.759247	−	1.37050i
$717$	−10.8958	+	18.8721i	−0.406911	+	0.704790i
$718$	20.5376	+	12.1009i	0.766455	+	0.451601i
$719$	5.68667	−	3.28320i	0.212077	−	0.122443i	−0.390199	−	0.920730i	$-0.627594\pi$
$719$	5.68667	−	3.28320i	0.212077	−	0.122443i	0.602276	+	0.798288i	$0.294261\pi$
$720$	−1.92496	−	1.20413i	−0.0717389	−	0.0448755i
$721$	7.42134	−	4.28471i	0.276385	−	0.159571i
$722$	3.25360	+	5.75233i	0.121086	+	0.214080i
$723$	3.30840			0.123041
$724$	19.1961	+	0.339691i	0.713419	+	0.0126245i
$725$	−2.02795	+	3.51250i	−0.0753160	+	0.130451i
$726$	15.1981	+	0.134460i	0.564054	+	0.00499029i
$727$	−21.8417	−	37.8310i	−0.810065	−	1.40307i	−0.912818	−	0.408367i	$-0.866098\pi$
$727$	−21.8417	−	37.8310i	−0.810065	−	1.40307i	0.102753	−	0.994707i	$-0.467235\pi$
$728$	−0.698781	+	26.3223i	−0.0258985	+	0.975569i
$729$	1.00000			0.0370370
$730$	−0.0441157	+	4.98641i	−0.00163280	+	0.184555i
$731$	−19.5197	−	33.8091i	−0.721963	−	1.25048i
$732$	14.6088	+	8.78262i	0.539956	+	0.324615i
$733$	−1.69271	−	0.977289i	−0.0625218	−	0.0360970i	0.468413	−	0.883510i	$-0.344826\pi$
$733$	−1.69271	−	0.977289i	−0.0625218	−	0.0360970i	−0.530935	+	0.847413i	$0.678159\pi$
$734$	−6.02776	−	10.6570i	−0.222489	−	0.393358i
$735$	1.34362	−	0.775742i	0.0495603	−	0.0286137i
$736$	22.1195	+	14.1104i	0.815337	+	0.520117i
$737$	0.498036	+	4.08620i	0.0183454	+	0.150517i
$738$	−11.5422	+	6.52846i	−0.424876	+	0.240316i
$739$	10.5730	+	18.3129i	0.388933	+	0.673652i	0.992306	−	0.123807i	$-0.0395104\pi$
$739$	10.5730	+	18.3129i	0.388933	+	0.673652i	−0.603373	+	0.797459i	$0.706177\pi$
$740$	−0.674927	−	0.405758i	−0.0248108	−	0.0149160i
$741$	−10.9643	+	18.9907i	−0.402782	+	0.697639i
$742$	36.7701	−	20.7977i	1.34987	−	0.763506i
$743$	−39.0412	+	22.5404i	−1.43228	+	0.826928i	−0.997295	−	0.0735085i	$-0.976580\pi$
$743$	−39.0412	+	22.5404i	−1.43228	+	0.826928i	−0.434987	+	0.900437i	$0.643247\pi$
$744$	12.4223	−	20.2549i	0.455423	−	0.742581i
$745$		−	4.27406i		−	0.156589i
$746$	−12.0562	+	6.81916i	−0.441409	+	0.249667i
$747$	−6.79123	+	3.92092i	−0.248478	+	0.143459i
$748$	2.22171	+	4.01034i	0.0812336	+	0.146632i
$749$	−9.00383	−	5.19837i	−0.328993	−	0.189944i
$750$	6.69348	+	3.94384i	0.244411	+	0.144009i
$751$		−	10.7942i		−	0.393884i	−0.980415	−	0.196942i	$-0.936899\pi$
$751$		−	10.7942i		−	0.393884i	0.980415	−	0.196942i	$-0.0631011\pi$
$752$	−31.4747	+	16.7160i	−1.14776	+	0.609568i
$753$	−2.25380	−	3.90370i	−0.0821332	−	0.142259i
$754$	−4.76137	−	2.80544i	−0.173399	−	0.102168i
$755$	5.23311	+	9.06401i	0.190452	+	0.329873i
$756$	−4.13059	−	0.0730939i	−0.150228	−	0.00265840i
$757$	6.66198	+	3.84629i	0.242134	+	0.139796i	0.616157	−	0.787623i	$-0.288689\pi$
$757$	6.66198	+	3.84629i	0.242134	+	0.139796i	−0.374023	+	0.927419i	$0.622022\pi$
$758$	50.9682	+	0.450926i	1.85125	+	0.0163784i
$759$		−	2.33251i		−	0.0846647i
$760$	3.72492	+	6.86637i	0.135117	+	0.249069i
$761$	−17.2468			−0.625197			−0.312598	−	0.949885i	$-0.601199\pi$
$761$	−17.2468			−0.625197			−0.312598	+	0.949885i	$0.601199\pi$
$762$	−14.3885	+	8.13833i	−0.521240	+	0.294821i
$763$	−5.06508	−	2.92433i	−0.183368	−	0.105868i
$764$	5.12784	−	8.52951i	0.185519	−	0.308587i
$765$	2.24074	−	1.29369i	0.0810140	−	0.0467735i
$766$	−22.4960	−	0.199026i	−0.812814	−	0.00719112i
$767$	17.9386	+	31.0706i	0.647726	+	1.12189i
$768$	7.00009	+	14.3874i	0.252594	+	0.519162i
$769$	−35.3176	−	20.3906i	−1.27358	−	0.735304i	−0.297923	−	0.954590i	$-0.596294\pi$
$769$	−35.3176	−	20.3906i	−1.27358	−	0.735304i	−0.975661	+	0.219286i	$0.929627\pi$
$770$	0.00737749	−	0.833880i	0.000265866	−	0.0300509i
$771$	5.15090	−	8.92162i	0.185505	−	0.321304i
$772$	21.1502	+	38.1776i	0.761211	+	1.37404i
$773$	6.37842	−	11.0477i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$773$	6.37842	−	11.0477i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929852\pi$
$774$	−6.14875	+	10.4356i	−0.221012	+	0.375101i
$775$	−19.6483	+	34.0319i	−0.705789	+	1.22246i
$776$	26.4267	−	14.3362i	0.948665	−	0.514640i
$777$	−1.43286			−0.0514034
$778$	−43.6668	−	0.386328i	−1.56553	−	0.0138505i
$779$	45.6222			1.63459
$780$	−2.63631	+	4.38516i	−0.0943950	+	0.157014i
$781$	−2.19222	+	1.26568i	−0.0784436	+	0.0452895i
$782$	−26.0237	+	14.7194i	−0.930605	+	0.526363i
$783$	0.433527	−	0.750890i	0.0154930	−	0.0268346i
$784$	−10.9261	−	0.386812i	−0.390217	−	0.0138147i
$785$	−7.12572	+	4.11404i	−0.254328	+	0.146836i
$786$	−8.52002	−	5.02006i	−0.303899	−	0.179060i
$787$	−13.0709	−	22.6395i	−0.465928	−	0.807011i	0.533315	−	0.845917i	$-0.320946\pi$
$787$	−13.0709	−	22.6395i	−0.465928	−	0.807011i	−0.999243	+	0.0389057i	$0.987613\pi$
$788$	0.784691	−	44.3434i	0.0279535	−	1.57967i
$789$			7.32912i			0.260923i
$790$	−6.76421	+	3.82593i	−0.240660	+	0.136120i
$791$	14.7555	−	8.51906i	0.524643	−	0.302903i
$792$	0.743653	−	1.21255i	0.0264246	−	0.0430861i
$793$	19.2058	−	33.2655i	0.682019	−	1.18129i
$794$	19.9237	−	33.8145i	0.707067	−	1.20003i
$795$	8.20870			0.291133
$796$	−29.8531	−	17.9473i	−1.05811	−	0.636126i
$797$	−24.0620	+	41.6765i	−0.852318	+	1.47626i	0.0267926	+	0.999641i	$0.491471\pi$
$797$	−24.0620	+	41.6765i	−0.852318	+	1.47626i	−0.879111	+	0.476617i	$0.841863\pi$
$798$	12.2456	+	7.21522i	0.433491	+	0.255416i
$799$		−	40.6111i		−	1.43672i
$800$	−12.2045	−	23.4790i	−0.431493	−	0.830109i
$801$	10.6280			0.375521
$802$	37.0801	+	21.8478i	1.30934	+	0.771474i
$803$	−3.12395			−0.110242
$804$	−14.9479	−	6.67546i	−0.527170	−	0.235425i
$805$	5.43825			0.191673
$806$	−46.1320	−	27.1813i	−1.62493	−	0.957420i
$807$	3.52992			0.124259
$808$	−25.5805	−	15.6884i	−0.899917	−	0.551917i
$809$		−	31.5695i		−	1.10992i	−0.831876	−	0.554962i	$-0.812733\pi$
$809$		−	31.5695i		−	1.10992i	0.831876	−	0.554962i	$-0.187267\pi$
$810$	−0.691633	−	0.407515i	−0.0243015	−	0.0143186i
$811$	−11.3567	+	19.6704i	−0.398788	+	0.690721i	−0.993577	−	0.113161i	$-0.963902\pi$
$811$	−11.3567	+	19.6704i	−0.398788	+	0.690721i	0.594788	+	0.803882i	$0.297236\pi$
$812$	−1.84560	+	3.06993i	−0.0647680	+	0.107733i
$813$	−3.15572			−0.110676
$814$	0.250444	−	0.425052i	0.00877804	−	0.0148981i
$815$	−1.62901	+	2.82153i	−0.0570617	+	0.0988337i
$816$	−18.2212	−	0.645079i	−0.637870	−	0.0225823i
$817$	36.0888	−	20.8359i	1.26259	−	0.728955i
$818$	43.8978	−	24.8292i	1.53485	−	0.868133i
$819$			9.30961i			0.325304i
$820$	10.6434	+	0.188344i	0.371685	+	0.00657725i
$821$	−7.34108	−	12.7151i	−0.256206	−	0.443761i	0.709017	−	0.705192i	$-0.249139\pi$
$821$	−7.34108	−	12.7151i	−0.256206	−	0.443761i	−0.965222	+	0.261431i	$0.915806\pi$
$822$	−17.7778	−	10.4748i	−0.620074	−	0.365352i
$823$	−5.91436	+	3.41466i	−0.206162	+	0.119027i	−0.599526	−	0.800355i	$-0.704644\pi$
$823$	−5.91436	+	3.41466i	−0.206162	+	0.119027i	0.393365	+	0.919383i	$0.371311\pi$
$824$	−10.0027	−	6.13462i	−0.348460	−	0.213710i
$825$	−1.17624	+	2.03730i	−0.0409513	+	0.0709298i
$826$	20.2408	−	11.4485i	0.704268	−	0.398344i
$827$	7.63475	−	4.40792i	0.265486	−	0.153278i	−0.361348	−	0.932431i	$-0.617684\pi$
$827$	7.63475	−	4.40792i	0.265486	−	0.153278i	0.626835	+	0.779152i	$0.284350\pi$
$828$	7.95007	+	4.77949i	0.276284	+	0.166099i
$829$	3.92127			0.136191			0.0680957	−	0.997679i	$-0.478308\pi$
$829$	3.92127			0.136191			0.0680957	+	0.997679i	$0.478308\pi$
$830$	6.29487	+	0.0556919i	0.218498	+	0.00193310i
$831$	4.91436			0.170477
$832$	32.1375	−	16.3457i	1.11417	−	0.566684i
$833$	6.22924	−	10.7894i	0.215830	−	0.373829i
$834$	14.7401	−	25.0168i	0.510407	−	0.866262i
$835$	2.66197	−	4.61066i	0.0921212	−	0.159559i
$836$	−4.28074	+	2.37151i	−0.148053	+	0.0820203i
$837$	4.20035	−	7.27522i	0.145185	−	0.251468i
$838$	0.156737	−	17.7160i	0.00541439	−	0.611990i
$839$	27.3826	+	15.8094i	0.945353	+	0.545800i	0.891634	−	0.452757i	$-0.149559\pi$
$839$	27.3826	+	15.8094i	0.945353	+	0.545800i	0.0537184	+	0.998556i	$0.482893\pi$
$840$	2.82706	+	1.73383i	0.0975429	+	0.0598228i
$841$	14.1241	+	24.4637i	0.487038	+	0.843575i
$842$	−15.4756	−	0.136916i	−0.533324	−	0.00471842i
$843$	0.219861	−	0.126937i	0.00757241	−	0.00437193i
$844$	−33.7891	−	20.3136i	−1.16307	−	0.699223i
$845$	3.59475	+	2.07543i	0.123663	+	0.0713970i
$846$	−10.9672	+	6.20321i	−0.377061	+	0.213271i
$847$	−22.1994			−0.762779
$848$	−49.0403	−	30.6766i	−1.68405	−	1.05344i
$849$			9.68330i			0.332330i
$850$	30.1528	+	0.266768i	1.03423	+	0.00915005i
$851$	2.78626	+	1.60865i	0.0955118	+	0.0551438i
$852$	0.178115	−	10.0654i	0.00610210	−	0.344834i
$853$	25.8580	+	44.7873i	0.885360	+	1.53349i	0.845300	+	0.534292i	$0.179422\pi$
$853$	25.8580	+	44.7873i	0.885360	+	1.53349i	0.0400603	+	0.999197i	$0.487245\pi$
$854$	−21.4504	−	12.6387i	−0.734017	−	0.432488i
$855$	1.38092	+	2.39182i	0.0472265	+	0.0817986i
$856$	−0.377795	+	14.2311i	−0.0129128	+	0.486410i
$857$		−	42.2264i		−	1.44242i	−0.692714	−	0.721212i	$-0.743585\pi$
$857$		−	42.2264i		−	1.44242i	0.692714	−	0.721212i	$-0.256415\pi$
$858$	−2.76167	−	1.62719i	−0.0942817	−	0.0555515i
$859$	7.66460	+	4.42516i	0.261513	+	0.150984i	0.625024	−	0.780605i	$-0.285089\pi$
$859$	7.66460	+	4.42516i	0.261513	+	0.150984i	−0.363512	+	0.931590i	$0.618422\pi$
$860$	8.50536	−	4.71192i	0.290030	−	0.160675i
$861$	16.7737	−	9.68431i	0.571647	−	0.330040i
$862$	−32.8580	+	18.5849i	−1.11915	+	0.633005i
$863$			38.0295i			1.29454i	0.762261	+	0.647269i	$0.224089\pi$
$863$			38.0295i			1.29454i	−0.762261	+	0.647269i	$0.775911\pi$
$864$	2.60903	+	5.01926i	0.0887609	+	0.170759i
$865$	−6.11216	+	3.52886i	−0.207820	+	0.119985i
$866$	−35.3754	+	20.0088i	−1.20211	+	0.679928i
$867$	1.88839	−	3.27079i	0.0641332	−	0.111082i
$868$	−17.8817	+	29.7439i	−0.606944	+	1.00957i
$869$	−2.43422	−	4.21619i	−0.0825751	−	0.143024i
$870$	−0.605840	+	0.342672i	−0.0205399	+	0.0116177i
$871$	−14.4446	+	33.9454i	−0.489437	+	1.15020i
$872$	−0.212528	+	8.00568i	−0.00719710	+	0.271107i
$873$	9.20546	−	5.31478i	0.311558	−	0.179878i
$874$	−15.7118	−	27.7784i	−0.531461	−	0.939618i
$875$	−9.82715	−	5.67371i	−0.332218	−	0.191806i
$876$	6.40121	−	10.6476i	0.216277	−	0.359749i
$877$	0.732342	+	1.26845i	0.0247294	+	0.0428326i	0.878125	−	0.478431i	$-0.158794\pi$
$877$	0.732342	+	1.26845i	0.0247294	+	0.0428326i	−0.853396	+	0.521263i	$0.825461\pi$
$878$	−0.0852327	+	9.63387i	−0.00287646	+	0.325127i
$879$	1.34689			0.0454296
$880$	−1.00847	+	0.535589i	−0.0339954	+	0.0180547i
$881$	17.0588	+	29.5467i	0.574725	+	0.995454i	0.996071	+	0.0885537i	$0.0282245\pi$
$881$	17.0588	+	29.5467i	0.574725	+	0.995454i	−0.421346	+	0.906900i	$0.638442\pi$
$882$	−3.86522	−	0.0341963i	−0.130149	−	0.00115145i
$883$	−24.4683	+	42.3803i	−0.823422	+	1.42621i	0.0796966	+	0.996819i	$0.474605\pi$
$883$	−24.4683	+	42.3803i	−0.823422	+	1.42621i	−0.903119	+	0.429390i	$0.858728\pi$
$884$	−0.726947	+	41.0803i	−0.0244499	+	1.38168i
$885$	4.51864			0.151892
$886$	−2.99325	−	5.29203i	−0.100560	−	0.177789i
$887$	−27.0340	+	15.6081i	−0.907714	+	0.524069i	−0.879695	−	0.475539i	$-0.842253\pi$
$887$	−27.0340	+	15.6081i	−0.907714	+	0.524069i	−0.0280187	+	0.999607i	$0.508920\pi$
$888$	0.935560	+	1.72457i	0.0313953	+	0.0578728i
$889$	20.9100	−	12.0724i	0.701299	−	0.404895i
$890$	−7.35066	−	4.33106i	−0.246395	−	0.145177i
$891$	0.251452	−	0.435527i	0.00842395	−	0.0145907i
$892$	8.21975	−	4.55369i	0.275217	−	0.152469i
$893$	43.3493			1.45063
$894$	−5.40557	+	9.17432i	−0.180789	+	0.306835i
$895$			11.8987i			0.397729i
$896$	−10.4099	−	20.9232i	−0.347771	−	0.698995i
$897$	10.4518	−	18.1030i	0.348975	−	0.604442i
$898$	−3.26211	−	5.76738i	−0.108858	−	0.192460i
$899$	−3.64193	−	6.30800i	−0.121465	−	0.210384i
$900$	−4.53370	−	8.18366i	−0.151123	−	0.272789i
$901$	57.0852	−	32.9581i	1.90178	−	1.09799i
$902$	−0.0589980	+	6.66855i	−0.00196442	+	0.222039i
$903$	8.84573	−	15.3213i	0.294368	−	0.509860i
$904$	−19.8878	−	12.1971i	−0.661459	−	0.405671i
$905$	−4.71904	−	2.72454i	−0.156866	−	0.0905668i
$906$	0.230686	−	26.0745i	0.00766404	−	0.866269i
$907$	4.08998	+	2.36135i	0.135806	+	0.0784074i	0.566364	−	0.824156i	$-0.308350\pi$
$907$	4.08998	+	2.36135i	0.135806	+	0.0784074i	−0.430558	+	0.902563i	$0.641683\pi$
$908$	−0.458775	+	25.9257i	−0.0152250	+	0.860373i
$909$	−9.18807	−	5.30473i	−0.304749	−	0.175947i
$910$	3.79381	−	6.43884i	0.125763	−	0.213445i
$911$			15.5917i			0.516576i	0.966068	+	0.258288i	$0.0831584\pi$
$911$			15.5917i			0.516576i	−0.966068	+	0.258288i	$0.916842\pi$
$912$	0.688574	−	19.4498i	0.0228010	−	0.644047i
$913$			3.94369i			0.130517i
$914$	−27.8080	−	49.1643i	−0.919808	−	1.62621i
$915$	−2.41892	−	4.18970i	−0.0799671	−	0.138507i
$916$	38.1326	+	22.9249i	1.25994	+	0.757458i
$917$	12.5088	+	7.22197i	0.413078	+	0.238491i
$918$	−6.44595	−	0.0570286i	−0.212748	−	0.00188222i
$919$	−4.70137	−	8.14301i	−0.155084	−	0.268613i	0.778006	−	0.628257i	$-0.216231\pi$
$919$	−4.70137	−	8.14301i	−0.155084	−	0.268613i	−0.933090	+	0.359644i	$0.882898\pi$
$920$	−3.55082	−	6.54543i	−0.117067	−	0.215796i
$921$	−5.07786	+	2.93171i	−0.167321	+	0.0966030i
$922$	−12.4674	+	21.1596i	−0.410592	+	0.696856i
$923$	−22.6856			−0.746705
$924$	−1.07048	+	1.78060i	−0.0352161	+	0.0585775i
$925$	−1.62242	−	2.81011i	−0.0533448	−	0.0923960i
$926$	−24.1321	−	0.213501i	−0.793030	−	0.00701609i
$927$	−3.59279	−	2.07430i	−0.118003	−	0.0681290i
$928$	4.90000	+	0.216892i	0.160850	+	0.00711982i
$929$			46.0965i			1.51238i	0.654354	+	0.756189i	$0.272941\pi$
$929$			46.0965i			1.51238i	−0.654354	+	0.756189i	$0.727059\pi$
$930$	−5.86986	+	3.32008i	−0.192480	+	0.108870i
$931$	11.5169	+	6.64926i	0.377450	+	0.217921i
$932$	−0.488207	+	27.5889i	−0.0159918	+	0.903705i
$933$	19.1012			0.625344
$934$	−0.302850	+	34.2312i	−0.00990955	+	1.12008i
$935$		−	1.30120i		−	0.0425539i
$936$	11.2050	−	6.07856i	0.366246	−	0.198684i
$937$		−	51.8263i		−	1.69309i	−0.532315	−	0.846546i	$-0.678678\pi$
$937$		−	51.8263i		−	1.69309i	0.532315	−	0.846546i	$-0.321322\pi$
$938$	21.9184	+	9.55671i	0.715661	+	0.312038i
$939$		−	14.8429i		−	0.484378i
$940$	10.1132	+	0.178961i	0.329856	+	0.00583706i
$941$			49.4762i			1.61288i	0.591316	+	0.806440i	$0.298608\pi$
$941$			49.4762i			1.61288i	−0.591316	+	0.806440i	$0.701392\pi$
$942$	20.4986	+	0.181355i	0.667882	+	0.00590888i
$943$	−43.4898			−1.41622
$944$	−26.9952	−	16.8865i	−0.878619	−	0.549610i
$945$	1.01543	+	0.586261i	0.0330320	+	0.0190711i
$946$	2.99889	+	5.30201i	0.0975023	+	0.172383i
$947$		−	29.9429i		−	0.973015i	−0.873676	−	0.486507i	$-0.838271\pi$
$947$		−	29.9429i		−	0.973015i	0.873676	−	0.486507i	$-0.161729\pi$
$948$	19.3583	+	0.342559i	0.628727	+	0.0111258i
$949$	−24.2455	−	13.9982i	−0.787043	−	0.454399i
$950$	−0.284755	+	32.1859i	−0.00923867	+	1.04425i
$951$	16.1773	+	28.0199i	0.524585	+	0.908608i
$952$	26.6214	+	0.706721i	0.862805	+	0.0229050i
$953$	−41.5955			−1.34741			−0.673705	−	0.739001i	$-0.735298\pi$
$953$	−41.5955			−1.34741			−0.673705	+	0.739001i	$0.735298\pi$
$954$	−17.6201	−	10.3819i	−0.570471	−	0.336126i
$955$	−2.44621	+	1.41232i	−0.0791574	+	0.0457015i
$956$	−43.5763	−	0.771117i	−1.40936	−	0.0249397i
$957$	−0.218022	−	0.377625i	−0.00704765	−	0.0122069i
$958$	0.416264	−	47.0504i	0.0134489	−	1.52013i
$959$	26.1009	+	15.0693i	0.842841	+	0.486614i
$960$	0.240936	−	4.53470i	0.00777619	−	0.146357i
$961$	−19.7859	−	34.2701i	−0.638254	−	1.10549i
$962$	3.84836	−	2.17669i	0.124076	−	0.0701792i
$963$			5.03323i			0.162194i
$964$	3.20650	+	5.78796i	0.103274	+	0.186418i
$965$		−	12.3872i		−	0.398757i
$966$	−11.6733	−	6.87798i	−0.375581	−	0.221295i
$967$	−3.19424	−	1.84419i	−0.102720	−	0.0593052i	0.447760	−	0.894154i	$-0.352222\pi$
$967$	−3.19424	−	1.84419i	−0.102720	−	0.0593052i	−0.550480	+	0.834848i	$0.685555\pi$
$968$	14.4947	+	26.7189i	0.465878	+	0.858780i
$969$	19.2065	+	11.0888i	0.617000	+	0.356225i
$970$	−8.53265	−	0.0754900i	−0.273967	−	0.00242384i
$971$	−8.92628	−	5.15359i	−0.286458	−	0.165387i	0.349885	−	0.936792i	$-0.386220\pi$
$971$	−8.92628	−	5.15359i	−0.286458	−	0.165387i	−0.636343	+	0.771406i	$0.719554\pi$
$972$	0.969198	+	1.74947i	0.0310870	+	0.0561144i
$973$	−21.2054	+	36.7289i	−0.679815	+	1.17747i
$974$	21.3304	+	0.188714i	0.683470	+	0.00604679i
$975$	−18.2580	+	10.5413i	−0.584724	+	0.337590i
$976$	−1.20616	+	34.0698i	−0.0386082	+	1.09055i
$977$	−10.3662	−	17.9548i	−0.331645	−	0.574425i	0.651190	−	0.758915i	$-0.274270\pi$
$977$	−10.3662	−	17.9548i	−0.331645	−	0.574425i	−0.982834	+	0.184490i	$0.940937\pi$
$978$	7.06519	−	3.99617i	0.225920	−	0.127783i
$979$	2.67242	−	4.62877i	0.0854110	−	0.147936i
$980$	2.65938	+	1.59879i	0.0849507	+	0.0510713i
$981$			2.83143i			0.0904007i
$982$	21.0583	+	12.4077i	0.671997	+	0.395945i
$983$	−21.4317			−0.683567			−0.341783	−	0.939779i	$-0.611031\pi$
$983$	−21.4317			−0.683567			−0.341783	+	0.939779i	$0.611031\pi$
$984$	−22.6081	−	13.8655i	−0.720719	−	0.442015i
$985$	−6.29373	+	10.9011i	−0.200535	+	0.347337i
$986$	−2.83731	+	4.81548i	−0.0903585	+	0.153356i
$987$	15.9381	−	9.20184i	0.507314	−	0.292898i
$988$	−43.8502	−	0.775963i	−1.39506	−	0.0246867i
$989$	−34.4020	+	19.8620i	−1.09392	+	0.631574i
$990$	−0.351396	+	0.198755i	−0.0111681	+	0.00631684i
$991$	−27.3814			−0.869800			−0.434900	−	0.900479i	$-0.643216\pi$
$991$	−27.3814			−0.869800			−0.434900	+	0.900479i	$0.643216\pi$
$992$	47.4750	+	2.10142i	1.50733	+	0.0667202i
$993$	7.43209	−	12.8728i	0.235850	−	0.408505i
$994$	−0.130083	+	14.7033i	−0.00412599	+	0.466361i
$995$	4.94308	+	8.56166i	0.156706	+	0.271423i
$996$	−13.4416	−	8.08092i	−0.425913	−	0.256054i
$997$	−28.0470			−0.888256			−0.444128	−	0.895963i	$-0.646486\pi$
$997$	−28.0470			−0.888256			−0.444128	+	0.895963i	$0.646486\pi$
$998$	−6.51177	−	0.0576109i	−0.206126	−	0.00182364i
$999$	0.346835	+	0.600736i	0.0109734	+	0.0190064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.12	✓	68
4.3	odd	2		804.2.j.b.499.1	yes	68
67.38	odd	6		804.2.j.b.775.1	yes	68
268.239	even	6	inner	804.2.j.a.775.12	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.12	✓	68	1.1	even	1	trivial
804.2.j.a.775.12	yes	68	268.239	even	6	inner
804.2.j.b.499.1	yes	68	4.3	odd	2
804.2.j.b.775.1	yes	68	67.38	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.717914 + 1.21844i) q^{2} -1.00000 q^{3} +(-0.969198 - 1.74947i) q^{4} +0.567637i q^{5} +(0.717914 - 1.21844i) q^{6} +(-1.03281 + 1.78888i) q^{7} +(2.82743 + 0.0750601i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.717914 + 1.21844i) q^{2} -1.00000 q^{3} +(-0.969198 - 1.74947i) q^{4} +0.567637i q^{5} +(0.717914 - 1.21844i) q^{6} +(-1.03281 + 1.78888i) q^{7} +(2.82743 + 0.0750601i) q^{8} +1.00000 q^{9} +(-0.691633 - 0.407515i) q^{10} +(0.251452 - 0.435527i) q^{11} +(0.969198 + 1.74947i) q^{12} +(3.90313 - 2.25347i) q^{13} +(-1.43817 - 2.54268i) q^{14} -0.567637i q^{15} +(-2.12131 + 3.39117i) q^{16} +(-2.27908 - 3.94748i) q^{17} +(-0.717914 + 1.21844i) q^{18} +(4.21365 - 2.43275i) q^{19} +(0.993066 - 0.550153i) q^{20} +(1.03281 - 1.78888i) q^{21} +(0.350144 + 0.619050i) q^{22} +(-4.01670 + 2.31904i) q^{23} +(-2.82743 - 0.0750601i) q^{24} +4.67779 q^{25} +(-0.0563878 + 6.37353i) q^{26} -1.00000 q^{27} +(4.13059 + 0.0730939i) q^{28} +(-0.433527 + 0.750890i) q^{29} +(0.691633 + 0.407515i) q^{30} +(-4.20035 + 7.27522i) q^{31} +(-2.60903 - 5.01926i) q^{32} +(-0.251452 + 0.435527i) q^{33} +(6.44595 + 0.0570286i) q^{34} +(-1.01543 - 0.586261i) q^{35} +(-0.969198 - 1.74947i) q^{36} +(-0.346835 - 0.600736i) q^{37} +(-0.0608739 + 6.88058i) q^{38} +(-3.90313 + 2.25347i) q^{39} +(-0.0426070 + 1.60496i) q^{40} +(8.12044 + 4.68834i) q^{41} +(1.43817 + 2.54268i) q^{42} +8.56474 q^{43} +(-1.00565 - 0.0177957i) q^{44} +0.567637i q^{45} +(0.0580286 - 6.55898i) q^{46} +(7.71589 + 4.45477i) q^{47} +(2.12131 - 3.39117i) q^{48} +(1.36661 + 2.36705i) q^{49} +(-3.35825 + 5.69961i) q^{50} +(2.27908 + 3.94748i) q^{51} +(-7.72529 - 4.64435i) q^{52} +14.4612i q^{53} +(0.717914 - 1.21844i) q^{54} +(0.247222 + 0.142733i) q^{55} +(-3.05447 + 4.98040i) q^{56} +(-4.21365 + 2.43275i) q^{57} +(-0.603681 - 1.06730i) q^{58} +7.96043i q^{59} +(-0.993066 + 0.550153i) q^{60} +(7.38094 - 4.26139i) q^{61} +(-5.84894 - 10.3409i) q^{62} +(-1.03281 + 1.78888i) q^{63} +(7.98873 + 0.424455i) q^{64} +(1.27915 + 2.21556i) q^{65} +(-0.350144 - 0.619050i) q^{66} +(-6.54149 + 4.92025i) q^{67} +(-4.69713 + 7.81307i) q^{68} +(4.01670 - 2.31904i) q^{69} +(1.44332 - 0.816361i) q^{70} +(-4.35912 - 2.51674i) q^{71} +(2.82743 + 0.0750601i) q^{72} +(-3.10591 - 5.37959i) q^{73} +(0.980959 + 0.00867873i) q^{74} -4.67779 q^{75} +(-8.33989 - 5.01384i) q^{76} +(0.519403 + 0.899632i) q^{77} +(0.0563878 - 6.37353i) q^{78} +(4.84032 - 8.38369i) q^{79} +(-1.92496 - 1.20413i) q^{80} +1.00000 q^{81} +(-11.5422 + 6.52846i) q^{82} +(-6.79123 + 3.92092i) q^{83} +(-4.13059 - 0.0730939i) q^{84} +(2.24074 - 1.29369i) q^{85} +(-6.14875 + 10.4356i) q^{86} +(0.433527 - 0.750890i) q^{87} +(0.743653 - 1.21255i) q^{88} +10.6280 q^{89} +(-0.691633 - 0.407515i) q^{90} +9.30961i q^{91} +(7.95007 + 4.77949i) q^{92} +(4.20035 - 7.27522i) q^{93} +(-10.9672 + 6.20321i) q^{94} +(1.38092 + 2.39182i) q^{95} +(2.60903 + 5.01926i) q^{96} +(9.20546 - 5.31478i) q^{97} +(-3.86522 - 0.0341963i) q^{98} +(0.251452 - 0.435527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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