LMFDB - Embedded newform 783.2.bf.a.4.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(4,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(126)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.bf (of order $126$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$3168$
Relative dimension:	$88$ over $\Q(\zeta_{126})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{126}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	783.4
Dual form			783.2.bf.a.196.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.21274 - 1.42914i) q^{2} +(1.69038 - 0.377660i) q^{3} +(2.03122 + 4.50164i) q^{4} +(1.52196 + 0.641561i) q^{5} +(-4.28010 - 1.58012i) q^{6} +(-0.818764 + 1.81457i) q^{7} +(1.15372 - 7.65445i) q^{8} +(2.71475 - 1.27677i) q^{9} +(-2.45083 - 3.59471i) q^{10} +(2.69879 + 2.38169i) q^{11} +(5.13361 + 6.84236i) q^{12} +(-1.92049 - 1.17359i) q^{13} +(4.40499 - 2.84505i) q^{14} +(2.81498 + 0.509696i) q^{15} +(-6.95647 + 7.88264i) q^{16} +(1.92349 + 1.11053i) q^{17} +(-7.83173 - 1.05458i) q^{18} +(-4.17937 + 0.313201i) q^{19} +(0.203360 + 8.15448i) q^{20} +(-0.698731 + 3.37652i) q^{21} +(-2.56795 - 9.12703i) q^{22} +(3.24111 - 6.32202i) q^{23} +(-0.940550 - 13.3746i) q^{24} +(-1.58641 - 1.62647i) q^{25} +(2.57233 + 5.34149i) q^{26} +(4.10676 - 3.18348i) q^{27} -9.83163 q^{28} +(3.53606 + 4.06156i) q^{29} +(-5.50041 - 5.15084i) q^{30} +(4.11381 + 5.43099i) q^{31} +(11.7551 - 3.30738i) q^{32} +(5.46144 + 3.00674i) q^{33} +(-2.66910 - 5.20627i) q^{34} +(-2.41029 + 2.23642i) q^{35} +(11.2618 + 9.62741i) q^{36} +(-0.227123 + 0.0891393i) q^{37} +(9.69549 + 5.27988i) q^{38} +(-3.68956 - 1.25851i) q^{39} +(6.66672 - 10.9096i) q^{40} +(0.883220 + 2.42663i) q^{41} +(6.37164 - 6.47279i) q^{42} +(4.42786 + 10.5041i) q^{43} +(-5.23971 + 16.9867i) q^{44} +(4.95087 - 0.201527i) q^{45} +(-16.2068 + 9.35701i) q^{46} +(1.53441 - 7.59031i) q^{47} +(-8.78210 + 15.9518i) q^{48} +(2.00952 + 2.27706i) q^{49} +(1.18587 + 5.86617i) q^{50} +(3.67083 + 1.15079i) q^{51} +(1.38213 - 11.0292i) q^{52} +(-1.80849 + 7.92352i) q^{53} +(-13.6369 + 1.17509i) q^{54} +(2.57945 + 5.35629i) q^{55} +(12.9449 + 8.36070i) q^{56} +(-6.94643 + 2.10781i) q^{57} +(-2.01986 - 14.0407i) q^{58} +(0.184823 - 1.04818i) q^{59} +(3.42337 + 13.7074i) q^{60} +(9.38628 + 4.23525i) q^{61} +(-1.34117 - 17.8966i) q^{62} +(0.0940557 + 5.97147i) q^{63} +(-10.6455 - 3.28369i) q^{64} +(-2.16998 - 3.01826i) q^{65} +(-7.78771 - 14.4583i) q^{66} +(-1.75605 + 5.22660i) q^{67} +(-1.09217 + 10.9146i) q^{68} +(3.09113 - 11.9106i) q^{69} +(8.52951 - 1.50398i) q^{70} +(4.44349 - 0.669748i) q^{71} +(-6.64094 - 22.2529i) q^{72} +(-7.24908 - 7.81265i) q^{73} +(0.629959 + 0.127349i) q^{74} +(-3.29589 - 2.15022i) q^{75} +(-9.89913 - 18.1779i) q^{76} +(-6.53142 + 2.94709i) q^{77} +(6.36547 + 8.05767i) q^{78} +(-2.33818 - 3.82626i) q^{79} +(-15.6447 + 7.53409i) q^{80} +(5.73970 - 6.93223i) q^{81} +(1.51365 - 6.63175i) q^{82} +(3.17110 + 3.25117i) q^{83} +(-16.6191 + 3.71301i) q^{84} +(2.21502 + 2.92423i) q^{85} +(5.21417 - 29.5710i) q^{86} +(7.51117 + 5.53014i) q^{87} +(21.3442 - 17.9099i) q^{88} +(-3.18520 - 10.3262i) q^{89} +(-11.2430 - 6.62957i) q^{90} +(3.70198 - 2.52397i) q^{91} +(35.0429 + 1.74892i) q^{92} +(9.00496 + 7.62679i) q^{93} +(-14.2429 + 14.6025i) q^{94} +(-6.56179 - 2.20464i) q^{95} +(18.6215 - 10.0302i) q^{96} +(-6.84193 - 1.92502i) q^{97} +(-1.19231 - 7.91044i) q^{98} +(10.3674 + 3.01995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) $ 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	−2.21274	−	1.42914i	−1.56465	−	1.01056i	−0.979936	−	0.199315i	$-0.936128\pi$
$2$	−2.21274	−	1.42914i	−1.56465	−	1.01056i	−0.584711	−	0.811241i	$-0.698792\pi$
$3$	1.69038	−	0.377660i	0.975939	−	0.218042i
$3$	1.69038	−	0.377660i	0.975939	−	0.218042i
$4$	2.03122	+	4.50164i	1.01561	+	2.25082i
$5$	1.52196	+	0.641561i	0.680643	+	0.286915i	0.701294	−	0.712872i	$-0.252606\pi$
$5$	1.52196	+	0.641561i	0.680643	+	0.286915i	−0.0206517	+	0.999787i	$0.506574\pi$
$6$	−4.28010	−	1.58012i	−1.74734	−	0.645083i
$7$	−0.818764	+	1.81457i	−0.309464	+	0.685842i	−0.999272	−	0.0381499i	$-0.987854\pi$
$7$	−0.818764	+	1.81457i	−0.309464	+	0.685842i	0.689808	+	0.723992i	$0.257695\pi$
$8$	1.15372	−	7.65445i	0.407903	−	2.70626i
$9$	2.71475	−	1.27677i	0.904915	−	0.425591i
$10$	−2.45083	−	3.59471i	−0.775022	−	1.13675i
$11$	2.69879	+	2.38169i	0.813715	+	0.718108i	0.962653	−	0.270739i	$-0.0872680\pi$
$11$	2.69879	+	2.38169i	0.813715	+	0.718108i	−0.148938	+	0.988847i	$0.547585\pi$
$12$	5.13361	+	6.84236i	1.48195	+	1.97522i
$13$	−1.92049	−	1.17359i	−0.532647	−	0.325494i	0.229063	−	0.973412i	$-0.426434\pi$
$13$	−1.92049	−	1.17359i	−0.532647	−	0.325494i	−0.761710	+	0.647918i	$0.775640\pi$
$14$	4.40499	−	2.84505i	1.17728	−	0.760370i
$15$	2.81498	+	0.509696i	0.726826	+	0.131603i
$16$	−6.95647	+	7.88264i	−1.73912	+	1.97066i
$17$	1.92349	+	1.11053i	0.466516	+	0.269343i	0.714780	−	0.699349i	$-0.246527\pi$
$17$	1.92349	+	1.11053i	0.466516	+	0.269343i	−0.248264	+	0.968692i	$0.579860\pi$
$18$	−7.83173	−	1.05458i	−1.84596	−	0.248568i
$19$	−4.17937	+	0.313201i	−0.958813	+	0.0718531i	−0.544934	−	0.838479i	$-0.683445\pi$
$19$	−4.17937	+	0.313201i	−0.958813	+	0.0718531i	−0.413879	+	0.910332i	$0.635826\pi$
$20$	0.203360	+	8.15448i	0.0454727	+	1.82340i
$21$	−0.698731	+	3.37652i	−0.152476	+	0.736817i
$22$	−2.56795	−	9.12703i	−0.547488	−	1.94589i
$23$	3.24111	−	6.32202i	0.675819	−	1.31823i	−0.259951	−	0.965622i	$-0.583707\pi$
$23$	3.24111	−	6.32202i	0.675819	−	1.31823i	0.935770	−	0.352611i	$-0.114706\pi$
$24$	−0.940550	−	13.3746i	−0.191989	−	2.73008i
$25$	−1.58641	−	1.62647i	−0.317283	−	0.325294i
$26$	2.57233	+	5.34149i	0.504475	+	1.04755i
$27$	4.10676	−	3.18348i	0.790346	−	0.612661i
$28$	−9.83163			−1.85800
$29$	3.53606	+	4.06156i	0.656630	+	0.754212i
$29$	3.53606	+	4.06156i	0.656630	+	0.754212i
$30$	−5.50041	−	5.15084i	−1.00423	−	0.940410i
$31$	4.11381	+	5.43099i	0.738863	+	0.975434i	0.999949	+	0.0101188i	$0.00322095\pi$
$31$	4.11381	+	5.43099i	0.738863	+	0.975434i	−0.261086	+	0.965316i	$0.584081\pi$
$32$	11.7551	−	3.30738i	2.07803	−	0.584668i
$33$	5.46144	+	3.00674i	0.950714	+	0.523406i
$34$	−2.66910	−	5.20627i	−0.457746	−	0.892868i
$35$	−2.41029	+	2.23642i	−0.407413	+	0.378024i
$36$	11.2618	+	9.62741i	1.87697	+	1.60457i
$37$	−0.227123	+	0.0891393i	−0.0373388	+	0.0146544i	−0.383937	−	0.923359i	$-0.625432\pi$
$37$	−0.227123	+	0.0891393i	−0.0373388	+	0.0146544i	0.346598	+	0.938014i	$0.387337\pi$
$38$	9.69549	+	5.27988i	1.57282	+	0.856510i
$39$	−3.68956	−	1.25851i	−0.590803	−	0.201523i
$40$	6.66672	−	10.9096i	1.05410	−	1.72496i
$41$	0.883220	+	2.42663i	0.137936	+	0.378976i	0.989357	−	0.145507i	$-0.0464812\pi$
$41$	0.883220	+	2.42663i	0.137936	+	0.378976i	−0.851421	+	0.524482i	$0.824259\pi$
$42$	6.37164	−	6.47279i	0.983165	−	0.998773i
$43$	4.42786	+	10.5041i	0.675243	+	1.60187i	0.793280	+	0.608856i	$0.208371\pi$
$43$	4.42786	+	10.5041i	0.675243	+	1.60187i	−0.118038	+	0.993009i	$0.537660\pi$
$44$	−5.23971	+	16.9867i	−0.789916	+	2.56084i
$45$	4.95087	−	0.201527i	0.738033	−	0.0300418i
$46$	−16.2068	+	9.35701i	−2.38957	+	1.37962i
$47$	1.53441	−	7.59031i	0.223817	−	1.10716i	−0.696972	−	0.717099i	$-0.745470\pi$
$47$	1.53441	−	7.59031i	0.223817	−	1.10716i	0.920789	−	0.390061i	$-0.127546\pi$
$48$	−8.78210	+	15.9518i	−1.26759	+	2.30245i
$49$	2.00952	+	2.27706i	0.287074	+	0.325294i
$50$	1.18587	+	5.86617i	0.167708	+	0.829602i
$51$	3.67083	+	1.15079i	0.514019	+	0.161143i
$52$	1.38213	−	11.0292i	0.191667	−	1.52947i
$53$	−1.80849	+	7.92352i	−0.248415	+	1.08838i	0.684707	+	0.728819i	$0.259930\pi$
$53$	−1.80849	+	7.92352i	−0.248415	+	1.08838i	−0.933122	+	0.359560i	$0.882927\pi$
$54$	−13.6369	+	1.17509i	−1.85574	+	0.159909i
$55$	2.57945	+	5.35629i	0.347813	+	0.722242i
$56$	12.9449	+	8.36070i	1.72983	+	1.11725i
$57$	−6.94643	+	2.10781i	−0.920077	+	0.279186i
$58$	−2.01986	−	14.0407i	−0.265221	−	1.84364i
$59$	0.184823	−	1.04818i	0.0240619	−	0.136462i	−0.970410	−	0.241462i	$-0.922373\pi$
$59$	0.184823	−	1.04818i	0.0240619	−	0.136462i	0.994472	+	0.105000i	$0.0334842\pi$
$60$	3.42337	+	13.7074i	0.441956	+	1.76961i
$61$	9.38628	+	4.23525i	1.20179	+	0.542268i	0.910158	−	0.414262i	$-0.135960\pi$
$61$	9.38628	+	4.23525i	1.20179	+	0.542268i	0.291632	+	0.956530i	$0.405802\pi$
$62$	−1.34117	−	17.8966i	−0.170328	−	2.27287i
$63$	0.0940557	+	5.97147i	0.0118499	+	0.752334i
$64$	−10.6455	−	3.28369i	−1.33068	−	0.410462i
$65$	−2.16998	−	3.01826i	−0.269153	−	0.374370i
$66$	−7.78771	−	14.4583i	−0.958601	−	1.77970i
$67$	−1.75605	+	5.22660i	−0.214535	+	0.638531i	0.785277	+	0.619145i	$0.212521\pi$
$67$	−1.75605	+	5.22660i	−0.214535	+	0.638531i	−0.999812	+	0.0193866i	$0.993829\pi$
$68$	−1.09217	+	10.9146i	−0.132445	+	1.32359i
$69$	3.09113	−	11.9106i	0.372128	−	1.43387i
$70$	8.52951	−	1.50398i	1.01947	−	0.179760i
$71$	4.44349	−	0.669748i	0.527345	−	0.0794845i	0.120027	−	0.992771i	$-0.461702\pi$
$71$	4.44349	−	0.669748i	0.527345	−	0.0794845i	0.407319	+	0.913286i	$0.366464\pi$
$72$	−6.64094	−	22.2529i	−0.782642	−	2.62253i
$73$	−7.24908	−	7.81265i	−0.848440	−	0.914401i	0.148783	−	0.988870i	$-0.452464\pi$
$73$	−7.24908	−	7.81265i	−0.848440	−	0.914401i	−0.997223	+	0.0744686i	$0.976274\pi$
$74$	0.629959	+	0.127349i	0.0732312	+	0.0148040i
$75$	−3.29589	−	2.15022i	−0.380576	−	0.248286i
$76$	−9.89913	−	18.1779i	−1.13551	−	2.08514i
$77$	−6.53142	+	2.94709i	−0.744324	+	0.335852i
$78$	6.36547	+	8.05767i	0.720748	+	0.912352i
$79$	−2.33818	−	3.82626i	−0.263065	−	0.430487i	0.694164	−	0.719817i	$-0.255774\pi$
$79$	−2.33818	−	3.82626i	−0.263065	−	0.430487i	−0.957230	+	0.289329i	$0.906568\pi$
$80$	−15.6447	+	7.53409i	−1.74913	+	0.842336i
$81$	5.73970	−	6.93223i	0.637744	−	0.770248i
$82$	1.51365	−	6.63175i	0.167155	−	0.732355i
$83$	3.17110	+	3.25117i	0.348074	+	0.356862i	0.867310	−	0.497768i	$-0.165847\pi$
$83$	3.17110	+	3.25117i	0.348074	+	0.356862i	−0.519236	+	0.854631i	$0.673784\pi$
$84$	−16.6191	+	3.71301i	−1.81330	+	0.405122i
$85$	2.21502	+	2.92423i	0.240252	+	0.317177i
$86$	5.21417	−	29.5710i	0.562258	−	3.18872i
$87$	7.51117	+	5.53014i	0.805281	+	0.592893i
$88$	21.3442	−	17.9099i	2.27530	−	1.90920i
$89$	−3.18520	−	10.3262i	−0.337631	−	1.09457i	−0.952140	−	0.305663i	$-0.901122\pi$
$89$	−3.18520	−	10.3262i	−0.337631	−	1.09457i	0.614509	−	0.788910i	$-0.289354\pi$
$90$	−11.2430	−	6.62957i	−1.18512	−	0.698819i
$91$	3.70198	−	2.52397i	0.388073	−	0.264583i
$92$	35.0429	+	1.74892i	3.65347	+	0.182337i
$93$	9.00496	+	7.62679i	0.933771	+	0.790862i
$94$	−14.2429	+	14.6025i	−1.46904	+	1.50613i
$95$	−6.56179	−	2.20464i	−0.673225	−	0.226192i
$96$	18.6215	−	10.0302i	1.90055	−	1.02370i
$97$	−6.84193	−	1.92502i	−0.694693	−	0.195456i	−0.0947522	−	0.995501i	$-0.530206\pi$
$97$	−6.84193	−	1.92502i	−0.694693	−	0.195456i	−0.599940	+	0.800045i	$0.704809\pi$
$98$	−1.19231	−	7.91044i	−0.120441	−	0.799075i
$99$	10.3674	+	3.01995i	1.04196	+	0.303517i
$100$	4.09943	−	10.4452i	0.409943	−	1.04452i
$101$	−3.99437	+	5.27330i	−0.397455	+	0.524713i	−0.951449	−	0.307807i	$-0.900405\pi$
$101$	−3.99437	+	5.27330i	−0.397455	+	0.524713i	0.553994	+	0.832521i	$0.313103\pi$
$102$	−6.47798	−	7.79254i	−0.641415	−	0.771577i
$103$	11.1206	−	6.05594i	1.09574	−	0.596710i	0.174092	−	0.984729i	$-0.444301\pi$
$103$	11.1206	−	6.05594i	1.09574	−	0.596710i	0.921651	+	0.388020i	$0.126841\pi$
$104$	−11.1989	+	13.3463i	−1.09814	+	1.30871i
$105$	−3.22969	+	4.69066i	−0.315185	+	0.457761i
$106$	15.3256	−	14.9481i	1.48855	−	1.45189i
$107$	11.1808	−	14.0203i	1.08089	−	1.35540i	0.150593	−	0.988596i	$-0.451882\pi$
$107$	11.1808	−	14.0203i	1.08089	−	1.35540i	0.930300	−	0.366801i	$-0.119547\pi$
$108$	22.6726	+	12.0208i	2.18167	+	1.15670i
$109$	−9.69776	+	4.67019i	−0.928877	+	0.447324i	−0.836232	−	0.548376i	$-0.815246\pi$
$109$	−9.69776	+	4.67019i	−0.928877	+	0.447324i	−0.0926448	+	0.995699i	$0.529532\pi$
$110$	1.94723	−	15.5385i	0.185661	−	1.48154i
$111$	−0.350260	+	0.236454i	−0.0332452	+	0.0224432i
$112$	−8.60788	−	19.0770i	−0.813368	−	1.80261i
$113$	−11.8981	+	3.34761i	−1.11928	+	0.314916i	−0.780006	−	0.625771i	$-0.784784\pi$
$113$	−11.8981	+	3.34761i	−1.11928	+	0.314916i	−0.339273	+	0.940688i	$0.610181\pi$
$114$	18.3830	+	5.26339i	1.72173	+	0.492962i
$115$	8.98882	−	7.54252i	0.838212	−	0.703343i
$116$	−11.1012	+	24.1680i	−1.03072	+	2.24394i
$117$	−6.71204	−	0.733959i	−0.620528	−	0.0678545i
$118$	−1.90697	+	2.05523i	−0.175551	+	0.189199i
$119$	−3.59002	+	2.58105i	−0.329097	+	0.236604i
$120$	7.14915	−	20.9591i	0.652625	−	1.91329i
$121$	0.243206	+	1.94074i	0.0221097	+	0.176431i
$122$	−14.7167	−	22.7859i	−1.33238	−	2.06293i
$123$	2.40941	+	3.76836i	0.217250	+	0.339781i
$124$	−16.0923	+	29.5504i	−1.44513	+	2.65371i
$125$	−4.38807	−	11.1806i	−0.392481	−	1.00003i
$126$	8.32596	−	13.3478i	0.741735	−	1.18911i
$127$	−19.7849	−	7.76501i	−1.75563	−	0.689033i	−0.999397	−	0.0347275i	$-0.988944\pi$
$127$	−19.7849	−	7.76501i	−1.75563	−	0.689033i	−0.756230	−	0.654305i	$-0.772961\pi$
$128$	3.16398	+	3.77069i	0.279659	+	0.333285i
$129$	11.4517	+	16.0837i	1.00827	+	1.41609i
$130$	0.488093	+	9.77987i	0.0428086	+	0.857751i
$131$	−14.8447	−	7.61044i	−1.29699	−	0.664927i	−0.336090	−	0.941830i	$-0.609105\pi$
$131$	−14.8447	−	7.61044i	−1.29699	−	0.664927i	−0.960898	+	0.276903i	$0.910692\pi$
$132$	−2.44188	+	30.6928i	−0.212539	+	2.67146i
$133$	2.85360	−	7.84019i	0.247438	−	0.679831i
$134$	11.3552	−	9.05550i	0.980943	−	0.782276i
$135$	8.29273	−	2.21040i	0.713725	−	0.190241i
$136$	10.7197	−	13.4421i	0.919205	−	1.15265i
$137$	3.78693	+	6.19704i	0.323539	+	0.529449i	0.972958	−	0.230982i	$-0.0741940\pi$
$137$	3.78693	+	6.19704i	0.323539	+	0.529449i	−0.649419	+	0.760431i	$0.724988\pi$
$138$	−23.8619	+	21.9375i	−2.03126	+	1.86745i
$139$	0.0266036	−	0.0518923i	0.00225649	−	0.00440144i	−0.888741	−	0.458410i	$-0.848419\pi$
$139$	0.0266036	−	0.0518923i	0.00225649	−	0.00440144i	0.890997	+	0.454009i	$0.150006\pi$
$140$	−14.9634	−	6.30759i	−1.26464	−	0.533089i
$141$	−0.272815	−	13.4100i	−0.0229752	−	1.12932i
$142$	−10.7895	−	4.86840i	−0.905433	−	0.408547i
$143$	−2.38787	−	7.74127i	−0.199683	−	0.647358i
$144$	−8.82071	+	30.2812i	−0.735059	+	2.52343i
$145$	2.77602	+	8.45014i	0.230536	+	0.701746i
$146$	4.87498	+	27.6474i	0.403456	+	2.28811i
$147$	4.25680	+	3.09018i	0.351095	+	0.254873i
$148$	−0.862610	−	0.841366i	−0.0709061	−	0.0691599i
$149$	4.32225	+	0.432506i	0.354092	+	0.0354323i	0.275025	−	0.961437i	$-0.411314\pi$
$149$	4.32225	+	0.432506i	0.354092	+	0.0354323i	0.0790672	+	0.996869i	$0.474806\pi$
$150$	4.21998	+	9.46818i	0.344560	+	0.773074i
$151$	1.38585	−	0.584186i	0.112779	−	0.0475404i	−0.331317	−	0.943519i	$-0.607493\pi$
$151$	1.38585	−	0.584186i	0.112779	−	0.0475404i	0.444096	+	0.895979i	$0.353525\pi$
$152$	−2.42446	+	32.3521i	−0.196649	+	2.62410i
$153$	6.63970	+	0.558940i	0.536788	+	0.0451876i
$154$	18.6642	+	2.81317i	1.50400	+	0.226692i
$155$	2.77676	+	10.9050i	0.223035	+	0.875913i
$156$	−1.82894	−	19.1654i	−0.146433	−	1.53446i
$157$	10.2535	+	1.80797i	0.818319	+	0.144292i	0.567111	−	0.823641i	$-0.308061\pi$
$157$	10.2535	+	1.80797i	0.818319	+	0.144292i	0.251208	+	0.967933i	$0.419172\pi$
$158$	−0.294476	+	11.8081i	−0.0234272	+	0.939403i
$159$	−0.0646388	+	14.0767i	−0.00512619	+	1.11636i
$160$	20.0128	+	2.50793i	1.58215	+	0.198269i
$161$	8.81804	+	11.0575i	0.694959	+	0.871450i
$162$	−22.6076	+	7.13642i	−1.77622	+	0.560690i
$163$	4.16815	−	3.32399i	0.326475	−	0.260355i	−0.446511	−	0.894778i	$-0.647334\pi$
$163$	4.16815	−	3.32399i	0.326475	−	0.260355i	0.772986	+	0.634423i	$0.218762\pi$
$164$	−9.12979	+	8.90495i	−0.712917	+	0.695360i
$165$	6.38310	+	8.07999i	0.496924	+	0.629026i
$166$	−2.37045	−	11.7260i	−0.183983	−	0.910111i
$167$	0.0675145	+	0.239961i	0.00522443	+	0.0185687i	0.965192	−	0.261544i	$-0.0842315\pi$
$167$	0.0675145	+	0.239961i	0.00522443	+	0.0185687i	−0.959967	+	0.280112i	$0.909628\pi$
$168$	25.0392	+	9.24397i	1.93182	+	0.713187i
$169$	−3.61977	−	7.06062i	−0.278444	−	0.543125i
$170$	−0.722129	−	9.63614i	−0.0553847	−	0.739058i
$171$	−10.9460	+	6.18637i	−0.837065	+	0.473084i
$172$	−38.2919	+	41.2688i	−2.91973	+	3.14672i
$173$	−0.220636	−	1.25129i	−0.0167746	−	0.0951336i	0.975271	−	0.221012i	$-0.0709361\pi$
$173$	−0.220636	−	1.25129i	−0.0167746	−	0.0951336i	−0.992046	+	0.125879i	$0.959825\pi$
$174$	−8.71694	−	22.9713i	−0.660830	−	1.74145i
$175$	4.25024	−	1.54696i	0.321288	−	0.116939i
$176$	−37.5481	+	4.70538i	−2.83029	+	0.354682i
$177$	−0.0834361	−	1.84163i	−0.00627144	−	0.138425i
$178$	−7.70953	+	27.4013i	−0.577854	+	2.05381i
$179$	−8.93274	−	8.28837i	−0.667664	−	0.619502i	0.271717	−	0.962377i	$-0.412409\pi$
$179$	−8.93274	−	8.28837i	−0.667664	−	0.619502i	−0.939381	+	0.342875i	$0.888599\pi$
$180$	10.9635	+	21.8777i	0.817171	+	1.63067i
$181$	14.2437	+	9.71118i	1.05872	+	0.721826i	0.961880	−	0.273473i	$-0.0881726\pi$
$181$	14.2437	+	9.71118i	1.05872	+	0.721826i	0.0968448	+	0.995299i	$0.469125\pi$
$182$	−11.7986	+	0.294240i	−0.874573	+	0.0218105i
$183$	17.4658	+	3.61435i	1.29111	+	0.267180i
$184$	−44.6523	−	32.1028i	−3.29181	−	2.36665i
$185$	−0.402862	−	0.0100467i	−0.0296190	−	0.000738651i
$186$	−9.02590	−	29.7455i	−0.661811	−	2.18105i
$187$	2.54616	+	7.57826i	0.186194	+	0.554177i
$188$	37.2856	−	8.51019i	2.71933	−	0.620669i
$189$	2.41417	+	10.0585i	0.175605	+	0.731649i
$190$	11.3688	+	14.2560i	0.824780	+	1.03424i
$191$	1.98061	−	5.44169i	0.143312	−	0.393747i	−0.847182	−	0.531303i	$-0.821703\pi$
$191$	1.98061	−	5.44169i	0.143312	−	0.393747i	0.990494	+	0.137556i	$0.0439248\pi$
$192$	−19.2350	−	1.53031i	−1.38816	−	0.110441i
$193$	−23.4684	+	10.5893i	−1.68929	+	0.762237i	−0.690031	+	0.723780i	$0.742403\pi$
$193$	−23.4684	+	10.5893i	−1.68929	+	0.762237i	−0.999260	+	0.0384575i	$0.987756\pi$
$194$	12.3883	+	14.0377i	0.889429	+	1.00785i
$195$	−4.80797	−	4.28249i	−0.344306	−	0.306675i
$196$	−6.16874	+	13.6713i	−0.440624	+	0.976524i
$197$	12.1763	−	11.2980i	0.867526	−	0.804946i	−0.114553	−	0.993417i	$-0.536544\pi$
$197$	12.1763	−	11.2980i	0.867526	−	0.804946i	0.982079	+	0.188471i	$0.0603531\pi$
$198$	−18.6245	−	21.4989i	−1.32358	−	1.52786i
$199$	−7.63092	+	5.20267i	−0.540941	+	0.368808i	−0.802753	−	0.596311i	$-0.796632\pi$
$199$	−7.63092	+	5.20267i	−0.540941	+	0.368808i	0.261812	+	0.965119i	$0.415680\pi$
$200$	−14.2800	+	10.2666i	−1.00975	+	0.725960i
$201$	−0.994501	+	9.49812i	−0.0701467	+	0.669945i
$202$	16.3748	−	5.95995i	1.15213	−	0.419341i
$203$	−10.2652	+	3.09097i	−0.720474	+	0.216943i
$204$	2.27583	+	18.8623i	0.159340	+	1.32062i
$205$	−0.212602	+	4.25988i	−0.0148487	+	0.297523i
$206$	−33.2618	−	2.49263i	−2.31746	−	0.173670i
$207$	0.727004	−	21.3009i	0.0505302	−	1.48051i
$208$	22.6108	−	6.97450i	1.56777	−	0.483594i
$209$	−12.0252	−	9.10872i	−0.831799	−	0.630063i
$210$	13.8501	−	5.76355i	0.955747	−	0.397723i
$211$	−16.0338	+	14.1499i	−1.10381	+	0.974118i	−0.999791	−	0.0204576i	$-0.993488\pi$
$211$	−16.0338	+	14.1499i	−1.10381	+	0.974118i	−0.104019	+	0.994575i	$0.533170\pi$
$212$	−39.3423	+	7.95321i	−2.70204	+	0.546229i
$213$	7.25824	−	2.81025i	0.497326	−	0.192555i
$214$	−44.7774	+	15.0444i	−3.06092	+	1.02841i
$215$			18.8277i			1.28404i
$216$	−19.6297	−	35.1078i	−1.33563	−	2.38878i
$217$	−13.2231	+	3.01810i	−0.897645	+	0.204882i
$218$	28.1330	+	3.52553i	1.90541	+	0.238779i
$219$	−15.2042	−	10.4686i	−1.02740	−	0.707405i
$220$	−18.8727	+	22.4916i	−1.27239	+	1.51638i
$221$	−2.39075	−	4.39015i	−0.160819	−	0.295313i
$222$	1.11296	−	0.0226423i	0.0746971	−	0.00151965i
$223$	−0.163092	−	6.53978i	−0.0109214	−	0.437936i	−0.980874	−	0.194643i	$-0.937645\pi$
$223$	−0.163092	−	6.53978i	−0.0109214	−	0.437936i	0.969953	−	0.243293i	$-0.0782278\pi$
$224$	−3.62321	+	24.0385i	−0.242086	+	1.60614i
$225$	−6.38334	−	2.38996i	−0.425556	−	0.159331i
$226$	31.1117	+	9.59668i	2.06952	+	0.638362i
$227$	−2.59804	−	0.129663i	−0.172438	−	0.00860601i	−0.0365591	−	0.999331i	$-0.511640\pi$
$227$	−2.59804	−	0.129663i	−0.172438	−	0.00860601i	−0.135879	+	0.990725i	$0.543386\pi$
$228$	−23.5983	−	26.9889i	−1.56284	−	1.78738i
$229$	11.5110	+	11.2275i	0.760670	+	0.741936i	0.971873	−	0.235506i	$-0.0756747\pi$
$229$	11.5110	+	11.2275i	0.760670	+	0.741936i	−0.211203	+	0.977442i	$0.567738\pi$
$230$	−30.6693	+	3.84336i	−2.02227	+	0.253424i
$231$	−9.92756	+	7.44834i	−0.653185	+	0.490065i
$232$	35.1686	−	22.3807i	2.30893	−	1.46937i
$233$	11.6453	−	20.1702i	0.762908	−	1.32139i	−0.178438	−	0.983951i	$-0.557104\pi$
$233$	11.6453	−	20.1702i	0.762908	−	1.32139i	0.941346	−	0.337444i	$-0.109562\pi$
$234$	13.8031	+	11.2165i	0.902337	+	0.733247i
$235$	7.20497	−	10.5677i	0.470000	−	0.689364i
$236$	5.09397	−	1.29708i	0.331589	−	0.0844330i
$237$	−5.39742	−	5.58478i	−0.350600	−	0.362770i
$238$	11.6325	−	0.580553i	0.754022	−	0.0376317i
$239$	1.70468	+	0.434066i	0.110267	+	0.0280774i	0.301491	−	0.953469i	$-0.402516\pi$
$239$	1.70468	+	0.434066i	0.110267	+	0.0280774i	−0.191224	+	0.981546i	$0.561246\pi$
$240$	−23.6001	+	18.6438i	−1.52338	+	1.20345i
$241$	−21.4478	+	13.1065i	−1.38157	+	0.844262i	−0.996891	−	0.0787871i	$-0.974895\pi$
$241$	−21.4478	+	13.1065i	−1.38157	+	0.844262i	−0.384682	+	0.923049i	$0.625689\pi$
$242$	2.23544	−	4.64194i	0.143700	−	0.298395i
$243$	7.08422	−	13.8857i	0.454453	−	0.890771i
$244$			50.8564i			3.25575i
$245$	1.59754	+	4.75483i	0.102063	+	0.303775i
$246$	0.0541008	−	11.7818i	0.00344934	−	0.751181i
$247$	8.39400	+	4.30335i	0.534097	+	0.273816i
$248$	46.3174	−	25.2231i	2.94116	−	1.60167i
$249$	6.58819	+	4.29810i	0.417510	+	0.272381i
$250$	−6.26902	+	31.0111i	−0.396488	+	1.96131i
$251$	−8.85631	+	0.663688i	−0.559005	+	0.0418916i	−0.351237	−	0.936287i	$-0.614239\pi$
$251$	−8.85631	+	0.663688i	−0.559005	+	0.0418916i	−0.207768	+	0.978178i	$0.566620\pi$
$252$	−26.6904	+	12.5528i	−1.68134	+	0.790750i
$253$	23.8042	−	9.34246i	1.49656	−	0.587355i
$254$	32.6817	+	45.4574i	2.05063	+	2.85225i
$255$	4.84857	+	4.10652i	0.303629	+	0.257160i
$256$	1.15824	+	9.24255i	0.0723901	+	0.577659i
$257$	−0.425522	−	0.0425799i	−0.0265433	−	0.00265606i	0.0862873	−	0.996270i	$-0.472500\pi$
$257$	−0.425522	−	0.0425799i	−0.0265433	−	0.00265606i	−0.112831	+	0.993614i	$0.535992\pi$
$258$	−2.35387	−	51.9553i	−0.146546	−	3.23460i
$259$	0.0242111	−	0.485115i	0.00150440	−	0.0301436i
$260$	9.17943	−	15.8992i	0.569284	−	0.986029i
$261$	14.7852	+	6.51135i	0.915181	+	0.403042i
$262$	21.9712	+	38.0552i	1.35738	+	2.35106i
$263$	12.4031	−	6.35870i	0.764808	−	0.392094i	−0.0295347	−	0.999564i	$-0.509403\pi$
$263$	12.4031	−	6.35870i	0.764808	−	0.392094i	0.794343	+	0.607469i	$0.207815\pi$
$264$	29.3159	−	38.3354i	1.80427	−	2.35938i
$265$	−7.83588	+	10.8990i	−0.481354	+	0.669523i
$266$	−17.5190	+	13.2701i	−1.07416	+	0.813645i
$267$	−9.28397	−	16.2522i	−0.568170	−	0.994619i
$268$	−27.0952	+	2.71128i	−1.65510	+	0.165618i
$269$	−0.457044	−	0.364480i	−0.0278664	−	0.0222228i	0.609458	−	0.792819i	$-0.291387\pi$
$269$	−0.457044	−	0.364480i	−0.0278664	−	0.0222228i	−0.637324	+	0.770596i	$0.719959\pi$
$270$	−21.5087	−	6.96044i	−1.30898	−	0.423599i
$271$	9.92481	−	20.6091i	0.602889	−	1.25191i	−0.346570	−	0.938024i	$-0.612654\pi$
$271$	9.92481	−	20.6091i	0.602889	−	1.25191i	0.949460	−	0.313889i	$-0.101632\pi$
$272$	−22.1346	+	7.43685i	−1.34211	+	0.450925i
$273$	5.30454	−	5.66454i	0.321045	−	0.342834i
$274$	0.476936	−	19.1245i	0.0288128	−	1.15535i
$275$	−0.407640	−	8.16784i	−0.0245816	−	0.492539i
$276$	59.8962	−	10.2780i	3.60533	−	0.618660i
$277$	0.0843748	+	0.0170567i	0.00506959	+	0.00102484i	0.200680	−	0.979657i	$-0.435685\pi$
$277$	0.0843748	+	0.0170567i	0.00506959	+	0.00102484i	−0.195611	+	0.980682i	$0.562669\pi$
$278$	−0.133028	+	0.0768040i	−0.00797851	+	0.00460640i
$279$	18.1021	+	9.49135i	1.08374	+	0.568232i
$280$	14.3378	+	21.0296i	0.856845	+	1.25676i
$281$	−8.67931	−	4.72650i	−0.517764	−	0.281959i	0.198121	−	0.980178i	$-0.436516\pi$
$281$	−8.67931	−	4.72650i	−0.517764	−	0.281959i	−0.715885	+	0.698218i	$0.753977\pi$
$282$	−18.5611	+	30.0627i	−1.10530	+	1.79021i
$283$	21.4094	−	21.9499i	1.27265	−	1.30479i	0.341628	−	0.939835i	$-0.389022\pi$
$283$	21.4094	−	21.9499i	1.27265	−	1.30479i	0.931026	−	0.364953i	$-0.118915\pi$
$284$	12.0407	+	18.6426i	0.714482	+	1.10623i
$285$	−11.9245	−	1.24856i	−0.706346	−	0.0739580i
$286$	−5.77964	+	20.5421i	−0.341757	+	1.21468i
$287$	−5.12643	−	0.384173i	−0.302604	−	0.0226770i
$288$	27.6894	−	23.9874i	1.63162	−	1.41347i
$289$	−6.03344	−	10.4502i	−0.354909	−	0.614720i
$290$	5.93383	−	22.6653i	0.348447	−	1.33095i
$291$	−12.2924	−	0.670089i	−0.720595	−	0.0392813i
$292$	20.4453	−	48.5019i	1.19647	−	2.83836i
$293$	−5.54174	+	21.7638i	−0.323752	+	1.27145i	0.569536	+	0.821967i	$0.307123\pi$
$293$	−5.54174	+	21.7638i	−0.323752	+	1.27145i	−0.893287	+	0.449486i	$0.851607\pi$
$294$	−5.00290	−	12.9213i	−0.291775	−	0.753588i
$295$	0.953769	−	1.47672i	0.0555306	−	0.0859782i
$296$	0.420275	+	1.84135i	0.0244280	+	0.107026i
$297$	18.6653	+	1.18951i	1.08307	+	0.0690223i
$298$	−8.94592	−	7.13413i	−0.518223	−	0.413269i
$299$	−13.6440	+	8.33764i	−0.789050	+	0.482178i
$300$	2.98486	−	19.2045i	0.172331	−	1.10877i
$301$	−22.6858	−	0.565750i	−1.30759	−	0.0326093i
$302$	−3.90142	−	0.687926i	−0.224502	−	0.0395857i
$303$	−4.76048	+	10.4224i	−0.273482	+	0.598750i
$304$	26.6048	−	35.1232i	1.52589	−	2.01446i
$305$	11.5684	+	12.4678i	0.662405	+	0.713903i
$306$	−13.8932	−	10.7259i	−0.794219	−	0.613157i
$307$	−22.9372	−	13.2428i	−1.30910	−	0.755806i	−0.327150	−	0.944972i	$-0.606088\pi$
$307$	−22.9372	−	13.2428i	−1.30910	−	0.755806i	−0.981945	+	0.189166i	$0.939422\pi$
$308$	−26.5335	−	23.4159i	−1.51188	−	1.33425i
$309$	16.5109	−	14.4366i	0.939271	−	0.821270i
$310$	9.44057	−	28.0984i	0.536188	−	1.59588i
$311$	−12.7703	−	4.29060i	−0.724139	−	0.243298i	−0.0677305	−	0.997704i	$-0.521576\pi$
$311$	−12.7703	−	4.29060i	−0.724139	−	0.243298i	−0.656408	+	0.754406i	$0.727925\pi$
$312$	−13.8899	+	26.7896i	−0.786363	+	1.51666i
$313$	18.1460	−	7.64919i	1.02567	−	0.432357i	0.190116	−	0.981762i	$-0.439113\pi$
$313$	18.1460	−	7.64919i	1.02567	−	0.432357i	0.835557	+	0.549404i	$0.185145\pi$
$314$	−20.1046	−	18.6543i	−1.13457	−	1.05272i
$315$	−3.68791	+	9.14870i	−0.207790	+	0.515471i
$316$	12.4751	−	18.2976i	0.701778	−	1.02932i
$317$	−15.8424	+	8.12193i	−0.889799	+	0.456173i	−0.840000	−	0.542586i	$-0.817445\pi$
$317$	−15.8424	+	8.12193i	−0.889799	+	0.456173i	−0.0497984	+	0.998759i	$0.515858\pi$
$318$	20.2607	−	31.0558i	1.13616	−	1.74152i
$319$	−0.130307	+	19.3831i	−0.00729579	+	1.08525i
$320$	−14.0953	−	11.8274i	−0.787953	−	0.661171i
$321$	13.6049	−	27.9222i	0.759352	−	1.55846i
$322$	−3.70937	−	37.0696i	−0.206715	−	2.06581i
$323$	−8.38682	−	4.03888i	−0.466655	−	0.224729i
$324$	42.8650	+	11.7572i	2.38139	+	0.653177i
$325$	1.13789	+	4.98540i	0.0631185	+	0.276540i
$326$	−13.9735	+	1.39826i	−0.773921	+	0.0774425i
$327$	−14.6291	+	11.5568i	−0.808992	+	0.639095i
$328$	19.5935	−	3.96091i	1.08187	−	0.218705i
$329$	12.5168	+	8.99897i	0.690074	+	0.496129i
$330$	−2.57672	−	27.0013i	−0.141844	−	1.48637i
$331$	17.6966	+	21.0900i	0.972694	+	1.15921i	0.987228	+	0.159317i	$0.0509291\pi$
$331$	17.6966	+	21.0900i	0.972694	+	1.15921i	−0.0145338	+	0.999894i	$0.504626\pi$
$332$	−8.19440	+	20.8790i	−0.449726	+	1.14588i
$333$	−0.502771	+	0.531976i	−0.0275517	+	0.0291521i
$334$	0.193546	−	0.627460i	0.0105904	−	0.0343331i
$335$	−6.02582	+	6.82809i	−0.329226	+	0.373058i
$336$	−21.7552	−	28.9965i	−1.18684	−	1.58189i
$337$	13.1314	−	21.4886i	0.715314	−	1.17056i	−0.263272	−	0.964722i	$-0.584802\pi$
$337$	13.1314	−	21.4886i	0.715314	−	1.17056i	0.978586	−	0.205838i	$-0.0659920\pi$
$338$	−2.08101	+	20.7965i	−0.113192	+	1.13118i
$339$	−18.8480	+	10.1522i	−1.02368	+	0.551389i
$340$	−8.66464	+	15.9109i	−0.469906	+	0.862892i
$341$	−1.83264	+	24.4549i	−0.0992432	+	1.32431i
$342$	33.0620	+	1.95459i	1.78779	+	0.105692i
$343$	−19.0933	+	5.88949i	−1.03094	+	0.318003i
$344$	85.5119	−	21.7740i	4.61049	−	1.17398i
$345$	12.3460	−	16.1444i	0.664686	−	0.869186i
$346$	−1.30006	+	3.08410i	−0.0698915	+	0.165802i
$347$	−10.4794	−	8.79325i	−0.562563	−	0.472046i	0.316606	−	0.948557i	$-0.397457\pi$
$347$	−10.4794	−	8.79325i	−0.562563	−	0.472046i	−0.879169	+	0.476511i	$0.841901\pi$
$348$	−9.63787	+	45.0455i	−0.516644	+	2.41469i
$349$	15.5251	+	5.65068i	0.831040	+	0.302474i	0.722286	−	0.691595i	$-0.243092\pi$
$349$	15.5251	+	5.65068i	0.831040	+	0.302474i	0.108754	+	0.994069i	$0.465314\pi$
$350$	−11.6155	−	2.65117i	−0.620875	−	0.141711i
$351$	−11.6231	+	1.29420i	−0.620393	+	0.0690793i
$352$	39.6018	+	19.0712i	2.11078	+	1.01650i
$353$	3.84396	−	5.95161i	0.204593	−	0.316772i	−0.722662	−	0.691201i	$-0.757082\pi$
$353$	3.84396	−	5.95161i	0.204593	−	0.316772i	0.927256	+	0.374429i	$0.122161\pi$
$354$	−2.44732	+	4.19429i	−0.130074	+	0.222924i
$355$	7.19251	+	1.83144i	0.381739	+	0.0972027i
$356$	40.0149	−	35.3134i	2.12079	−	1.87160i
$357$	−5.09373	+	5.71875i	−0.269589	+	0.302669i
$358$	7.92061	+	31.1062i	0.418617	+	1.64401i
$359$	−21.8036	−	8.55728i	−1.15075	−	0.451636i	−0.288181	−	0.957576i	$-0.593050\pi$
$359$	−21.8036	−	8.55728i	−1.15075	−	0.451636i	−0.862568	+	0.505940i	$0.831146\pi$
$360$	4.16936	−	38.1287i	0.219744	−	2.00956i
$361$	−1.41874	+	0.213841i	−0.0746705	+	0.0112548i
$362$	−17.6390	−	41.8446i	−0.927084	−	2.19930i
$363$	1.14405	+	3.18873i	0.0600471	+	0.167365i
$364$	18.8815	+	11.5383i	0.989660	+	0.604769i
$365$	−6.02054	−	16.5413i	−0.315129	−	0.865811i
$366$	−33.4820	−	32.9588i	−1.75013	−	1.72278i
$367$	−1.66671	−	0.468940i	−0.0870017	−	0.0244785i	0.227063	−	0.973880i	$-0.427088\pi$
$367$	−1.66671	−	0.468940i	−0.0870017	−	0.0244785i	−0.314065	+	0.949402i	$0.601691\pi$
$368$	27.2875	+	69.5275i	1.42246	+	3.62437i
$369$	5.49597	+	5.46001i	0.286109	+	0.284237i
$370$	0.877072	+	0.597977i	0.0455968	+	0.0310874i
$371$	−12.8970	−	9.76912i	−0.669580	−	0.507188i
$372$	−16.0421	+	56.0288i	−0.831742	+	2.90496i
$373$	0.496552	−	0.690662i	0.0257105	−	0.0357611i	−0.798886	−	0.601483i	$-0.794577\pi$
$373$	0.496552	−	0.690662i	0.0257105	−	0.0357611i	0.824596	+	0.565722i	$0.191402\pi$
$374$	5.19641	−	20.4076i	0.268700	−	1.05525i
$375$	−11.6400	−	17.2423i	−0.601086	−	0.890387i
$376$	−56.3293	−	20.5022i	−2.90496	−	1.05732i
$377$	−2.02438	−	11.9500i	−0.104261	−	0.615459i
$378$	9.03310	−	25.7071i	0.464612	−	1.32223i
$379$	−33.6036	−	7.66981i	−1.72610	−	0.393971i	−0.759551	−	0.650448i	$-0.774581\pi$
$379$	−33.6036	−	7.66981i	−1.72610	−	0.393971i	−0.966551	+	0.256476i	$0.917438\pi$
$380$	−3.40391	−	34.0169i	−0.174617	−	1.74503i
$381$	−36.3765	−	5.65382i	−1.86362	−	0.289654i
$382$	−12.1595	+	9.21050i	−0.622136	+	0.471250i
$383$	14.8709	−	0.742178i	0.759870	−	0.0379235i	0.333836	−	0.942631i	$-0.391657\pi$
$383$	14.8709	−	0.742178i	0.759870	−	0.0379235i	0.426033	+	0.904707i	$0.359911\pi$
$384$	6.77236	+	5.17898i	0.345601	+	0.264289i
$385$	−11.8313	+	0.295055i	−0.602980	+	0.0150374i
$386$	67.0632	+	10.1082i	3.41343	+	0.514491i
$387$	25.4319	+	22.8627i	1.29278	+	1.16218i
$388$	−5.23170	−	34.7100i	−0.265599	−	1.76214i
$389$	−4.77867	+	0.842609i	−0.242288	+	0.0427220i	−0.293473	−	0.955967i	$-0.594811\pi$
$389$	−4.77867	+	0.842609i	−0.242288	+	0.0427220i	0.0511852	+	0.998689i	$0.483700\pi$
$390$	4.51852	+	16.3473i	0.228804	+	0.827779i
$391$	13.2551	−	8.56103i	0.670337	−	0.432950i
$392$	19.7481	−	12.7547i	0.997428	−	0.644208i
$393$	−27.9673	−	7.25826i	−1.41076	−	0.366131i
$394$	−43.0894	+	7.59783i	−2.17081	+	0.382773i
$395$	−1.10384	−	7.32350i	−0.0555402	−	0.368485i
$396$	7.46372	+	52.8045i	0.375066	+	2.65353i
$397$	−12.6876	−	1.91235i	−0.636772	−	0.0959780i	−0.177281	−	0.984160i	$-0.556730\pi$
$397$	−12.6876	−	1.91235i	−0.636772	−	0.0959780i	−0.459491	+	0.888182i	$0.651968\pi$
$398$	24.3206	−	0.606519i	1.21908	−	0.0304020i
$399$	1.86273	−	14.3306i	0.0932531	−	0.717426i
$400$	23.8567	−	1.19064i	1.19283	−	0.0595319i
$401$	−21.2448	+	16.0923i	−1.06092	+	0.803613i	−0.981159	−	0.193201i	$-0.938113\pi$
$401$	−21.2448	+	16.0923i	−1.06092	+	0.803613i	−0.0797573	+	0.996814i	$0.525415\pi$
$402$	15.7747	−	19.5956i	0.786772	−	0.977341i
$403$	−1.52680	−	15.2581i	−0.0760553	−	0.760058i
$404$	−31.8520	−	7.27000i	−1.58469	−	0.361696i
$405$	13.1831	−	6.86824i	0.655072	−	0.341286i
$406$	27.1317	+	7.83087i	1.34652	+	0.388640i
$407$	−0.825260	−	0.300370i	−0.0409066	−	0.0148888i
$408$	13.0438	−	26.7705i	0.645763	−	1.32534i
$409$	−5.22628	+	20.5249i	−0.258423	+	1.01489i	0.696385	+	0.717668i	$0.254790\pi$
$409$	−5.22628	+	20.5249i	−0.258423	+	1.01489i	−0.954808	+	0.297222i	$0.903940\pi$
$410$	6.55840	−	9.12218i	0.323896	−	0.450513i
$411$	8.74171	+	9.04516i	0.431197	+	0.446165i
$412$	49.8500	+	37.7599i	2.45593	+	1.86030i
$413$	1.75068	+	1.19359i	0.0861452	+	0.0587328i
$414$	−32.0506	+	46.0944i	−1.57520	+	2.26541i
$415$	2.74047	+	6.98262i	0.134525	+	0.342763i
$416$	−26.4571	−	7.44387i	−1.29717	−	0.364966i
$417$	0.0253725	−	0.0977646i	0.00124250	−	0.00478755i
$418$	13.5910	+	37.3410i	0.664758	+	1.82641i
$419$	−22.2844	−	13.6177i	−1.08866	−	0.665268i	−0.142773	−	0.989755i	$-0.545602\pi$
$419$	−22.2844	−	13.6177i	−1.08866	−	0.665268i	−0.945890	+	0.324487i	$0.894808\pi$
$420$	−27.6759	−	5.01114i	−1.35044	−	0.244519i
$421$	7.68393	+	18.2284i	0.374492	+	0.888399i	0.994590	+	0.103875i	$0.0331243\pi$
$421$	7.68393	+	18.2284i	0.374492	+	0.888399i	−0.620099	+	0.784524i	$0.712907\pi$
$422$	55.7008	−	8.39555i	2.71147	−	0.408689i
$423$	−5.52556	−	22.5649i	−0.268662	−	1.09714i
$424$	58.5636	+	22.9845i	2.84410	+	1.11623i
$425$	−1.24521	−	4.89026i	−0.0604018	−	0.237213i
$426$	−20.0769	−	4.15468i	−0.972728	−	0.201295i
$427$	−15.3703	+	13.5644i	−0.743821	+	0.656426i
$428$	85.8252	+	21.8538i	4.14852	+	1.05634i
$429$	−6.95996	−	12.1839i	−0.336030	−	0.588242i
$430$	26.9074	−	41.6608i	1.29759	−	2.00906i
$431$	19.7311	+	9.50199i	0.950413	+	0.457695i	0.843831	−	0.536609i	$-0.180295\pi$
$431$	19.7311	+	9.50199i	0.950413	+	0.457695i	0.106582	+	0.994304i	$0.466009\pi$
$432$	−3.47433	+	54.5179i	−0.167159	+	2.62299i
$433$	2.21657	+	0.505918i	0.106522	+	0.0243128i	0.275449	−	0.961316i	$-0.411173\pi$
$433$	2.21657	+	0.505918i	0.106522	+	0.0243128i	−0.168928	+	0.985628i	$0.554030\pi$
$434$	33.5727	+	12.2195i	1.61154	+	0.586554i
$435$	7.88380	+	13.2355i	0.377999	+	0.634595i
$436$	−40.7218	−	34.1697i	−1.95022	−	1.63643i
$437$	−11.5657	+	27.4372i	−0.553265	+	1.31250i
$438$	18.6818	+	44.8934i	0.892653	+	2.14509i
$439$	6.89931	−	1.75678i	0.329286	−	0.0838465i	−0.0785270	−	0.996912i	$-0.525022\pi$
$439$	6.89931	−	1.75678i	0.329286	−	0.0838465i	0.407813	+	0.913065i	$0.366292\pi$
$440$	43.9754	−	13.5646i	2.09645	−	0.646668i
$441$	8.36262	+	3.61594i	0.398220	+	0.172188i
$442$	−0.984031	+	13.1310i	−0.0468056	+	0.624577i
$443$	6.85325	−	12.5847i	0.325608	−	0.597916i	−0.662967	−	0.748649i	$-0.730703\pi$
$443$	6.85325	−	12.5847i	0.325608	−	0.597916i	0.988575	+	0.150733i	$0.0481633\pi$
$444$	−1.77589	−	1.09645i	−0.0842798	−	0.0520353i
$445$	1.77711	−	17.7596i	0.0842432	−	0.841884i
$446$	−8.98540	+	14.7040i	−0.425471	+	0.696252i
$447$	7.46957	−	0.901240i	0.353299	−	0.0426272i
$448$	14.6746	−	16.6284i	0.693311	−	0.785616i
$449$	8.44582	−	27.3807i	0.398583	−	1.29217i	−0.504762	−	0.863259i	$-0.668420\pi$
$449$	8.44582	−	27.3807i	0.398583	−	1.29217i	0.903345	−	0.428915i	$-0.141104\pi$
$450$	10.7091	+	14.4111i	0.504832	+	0.679344i
$451$	−3.39586	+	8.65251i	−0.159905	+	0.407431i
$452$	−39.2374	−	46.7613i	−1.84557	−	2.19947i
$453$	2.12199	−	1.51087i	0.0996997	−	0.0709871i
$454$	5.56349	+	3.99987i	0.261107	+	0.187723i
$455$	7.25355	−	1.46634i	0.340052	−	0.0687430i
$456$	8.11985	+	55.6029i	0.380247	+	2.60384i
$457$	−29.1551	+	2.91741i	−1.36382	+	0.136471i	−0.754419	−	0.656393i	$-0.772082\pi$
$457$	−29.1551	+	2.91741i	−1.36382	+	0.136471i	−0.609400	+	0.792863i	$0.708589\pi$
$458$	−9.42521	−	41.2945i	−0.440411	−	1.92957i
$459$	11.4347	−	1.56273i	0.533725	−	0.0729418i
$460$	52.2120	+	25.1440i	2.43440	+	1.17234i
$461$	1.62425	+	16.2319i	0.0756487	+	0.755995i	0.958261	+	0.285894i	$0.0922905\pi$
$461$	1.62425	+	16.2319i	0.0756487	+	0.755995i	−0.882613	+	0.470101i	$0.844217\pi$
$462$	32.6119	−	2.29338i	1.51724	−	0.106698i
$463$	0.858265	+	0.720170i	0.0398870	+	0.0334691i	0.662513	−	0.749050i	$-0.269490\pi$
$463$	0.858265	+	0.720170i	0.0398870	+	0.0334691i	−0.622626	+	0.782519i	$0.713934\pi$
$464$	−56.6143	−	0.380601i	−2.62825	−	0.0176690i
$465$	8.81216	+	17.3849i	0.408654	+	0.806207i
$466$	−54.5941	+	27.9888i	−2.52902	+	1.29656i
$467$	−16.5980	+	24.3448i	−0.768064	+	1.12654i	0.220448	+	0.975399i	$0.429248\pi$
$467$	−16.5980	+	24.3448i	−0.768064	+	1.12654i	−0.988512	+	0.151144i	$0.951704\pi$
$468$	−10.3296	−	31.7060i	−0.477486	−	1.46561i
$469$	−8.04624	−	7.46582i	−0.371541	−	0.344740i
$470$	−31.0456	+	13.0868i	−1.43203	+	0.603649i
$471$	18.0151	−	0.816185i	0.830092	−	0.0376078i
$472$	−7.81004	−	2.62404i	−0.359486	−	0.120781i
$473$	−13.0678	+	38.8942i	−0.600857	+	1.78836i
$474$	3.96167	+	20.0714i	0.181966	+	0.921909i
$475$	7.13962	+	6.30075i	0.327588	+	0.289098i
$476$	−18.9111	−	10.9183i	−0.866788	−	0.500440i
$477$	5.20694	+	23.8194i	0.238410	+	1.09061i
$478$	−3.15169	−	3.39671i	−0.144155	−	0.155362i
$479$	−5.10086	+	6.73407i	−0.233064	+	0.307687i	−0.898678	−	0.438609i	$-0.855471\pi$
$479$	−5.10086	+	6.73407i	−0.233064	+	0.307687i	0.665614	+	0.746296i	$0.268170\pi$
$480$	34.7763	−	3.31868i	1.58731	−	0.151476i
$481$	0.540800	+	0.0953576i	0.0246584	+	0.00434793i
$482$	66.1895	+	1.65066i	3.01485	+	0.0751856i
$483$	19.0818	+	15.3611i	0.868250	+	0.698953i
$484$	−8.24252	+	5.03690i	−0.374660	+	0.228950i
$485$	−9.17815	−	7.31933i	−0.416758	−	0.332354i
$486$	−35.5203	+	20.6012i	−1.61123	+	0.934491i
$487$	−2.99793	−	13.1348i	−0.135849	−	0.595193i	−0.996321	−	0.0856962i	$-0.972689\pi$
$487$	−2.99793	−	13.1348i	−0.135849	−	0.595193i	0.860472	−	0.509497i	$-0.170169\pi$
$488$	43.2477	−	66.9605i	1.95773	−	3.03116i
$489$	5.79041	−	7.19294i	0.261851	−	0.325276i
$490$	3.26039	−	12.8043i	0.147289	−	0.578441i
$491$	15.9106	−	37.7443i	0.718033	−	1.70338i	0.00724187	−	0.999974i	$-0.497695\pi$
$491$	15.9106	−	37.7443i	0.718033	−	1.70338i	0.710792	−	0.703403i	$-0.248337\pi$
$492$	−12.0698	+	18.5007i	−0.544146	+	0.834075i
$493$	2.29112	+	11.7393i	0.103187	+	0.528711i
$494$	−12.4237	−	21.5184i	−0.558967	−	0.968160i
$495$	13.8413	+	11.2476i	0.622122	+	0.505541i
$496$	−71.4281	−	5.35280i	−3.20722	−	0.240348i
$497$	−2.42287	+	8.61138i	−0.108680	+	0.386273i
$498$	−8.43538	−	18.9261i	−0.377999	−	0.848097i
$499$	−17.9144	−	27.7369i	−0.801959	−	1.24168i	−0.966845	−	0.255363i	$-0.917805\pi$
$499$	−17.9144	−	27.7369i	−0.801959	−	1.24168i	0.164887	−	0.986313i	$-0.447274\pi$
$500$	41.4181	−	42.4638i	1.85227	−	1.89904i
$501$	0.204748	+	0.380127i	0.00914749	+	0.0169828i
$502$	20.5453	+	11.1883i	0.916979	+	0.499360i
$503$	22.8914	+	33.5755i	1.02068	+	1.49706i	0.860160	+	0.510025i	$0.170364\pi$
$503$	22.8914	+	33.5755i	1.02068	+	1.49706i	0.160517	+	0.987033i	$0.448684\pi$
$504$	45.8168	+	6.16947i	2.04084	+	0.274810i
$505$	−9.46244	+	5.46314i	−0.421073	+	0.243107i
$506$	−66.0243	−	13.3471i	−2.93514	−	0.593351i
$507$	−8.78528	−	10.5681i	−0.390168	−	0.469344i
$508$	−5.23220	−	104.837i	−0.232141	−	4.65139i
$509$	0.973910	−	39.0526i	0.0431678	−	1.73098i	−0.478726	−	0.877964i	$-0.658901\pi$
$509$	0.973910	−	39.0526i	0.0431678	−	1.73098i	0.521894	−	0.853011i	$-0.325226\pi$
$510$	−4.85985	−	16.0160i	−0.215198	−	0.709200i
$511$	20.1119	−	6.75723i	0.889697	−	0.298922i
$512$	14.9174	−	30.9763i	0.659263	−	1.36897i
$513$	−16.1666	+	14.5912i	−0.713773	+	0.644216i
$514$	0.880718	+	0.702349i	0.0388468	+	0.0309793i
$515$	20.8104	−	2.08239i	0.917014	−	0.0917611i
$516$	−49.1421	+	84.2212i	−2.16336	+	3.70763i
$517$	22.2188	−	16.8301i	0.977184	−	0.740188i
$518$	−0.746871	+	1.03883i	−0.0328156	+	0.0456437i
$519$	−0.845518	−	2.03182i	−0.0371141	−	0.0891871i
$520$	−25.6067	+	13.1278i	−1.12293	+	0.575692i
$521$	14.4628	+	25.0503i	0.633627	+	1.09747i	0.986804	+	0.161918i	$0.0517680\pi$
$521$	14.4628	+	25.0503i	0.633627	+	1.09747i	−0.353177	+	0.935556i	$0.614899\pi$
$522$	−23.4102	−	35.5381i	−1.02464	−	1.55546i
$523$	4.53552	−	7.85575i	0.198325	−	0.343508i	−0.749661	−	0.661822i	$-0.769783\pi$
$523$	4.53552	−	7.85575i	0.198325	−	0.343508i	0.947985	+	0.318314i	$0.103117\pi$
$524$	4.10662	−	82.2840i	0.179399	−	3.59459i
$525$	6.60028	−	4.22009i	0.288060	−	0.184180i
$526$	−36.5324	−	3.65562i	−1.59289	−	0.159393i
$527$	1.88162	+	15.0150i	0.0819648	+	0.654063i
$528$	−61.6934	+	22.1343i	−2.68486	+	0.963270i
$529$	−16.0371	−	22.3062i	−0.697264	−	0.969835i
$530$	32.9151	−	12.9182i	1.42974	−	0.561131i
$531$	−0.836547	−	3.08153i	−0.0363030	−	0.133727i
$532$	41.0900	−	3.07927i	1.78148	−	0.133503i
$533$	1.15164	−	5.69684i	0.0498831	−	0.246758i
$534$	−2.68365	+	49.2301i	−0.116133	+	2.13039i
$535$	26.0117	−	14.1652i	1.12459	−	0.612416i
$536$	37.9808	+	19.4716i	1.64052	+	0.841045i
$537$	−18.2299	−	10.6369i	−0.786677	−	0.459018i
$538$	0.490427	+	1.45968i	0.0211438	+	0.0629314i
$539$			10.9314i			0.470847i
$540$	26.7948	+	32.8411i	1.15306	+	1.41326i
$541$	−2.45727	+	5.10258i	−0.105646	+	0.219377i	−0.947090	−	0.320968i	$-0.895992\pi$
$541$	−2.45727	+	5.10258i	−0.105646	+	0.219377i	0.841444	+	0.540345i	$0.181706\pi$
$542$	−51.4144	+	31.4187i	−2.20844	+	1.34955i
$543$	27.7447	+	11.0363i	1.19064	+	0.473612i
$544$	26.2839	+	6.69270i	1.12691	+	0.286947i
$545$	−17.7559	+	0.886158i	−0.760577	+	0.0379588i
$546$	−19.8330	+	4.95324i	−0.848775	+	0.211979i
$547$	−28.9883	+	7.38133i	−1.23945	+	0.315603i	−0.809430	−	0.587216i	$-0.800224\pi$
$547$	−28.9883	+	7.38133i	−1.23945	+	0.315603i	−0.430021	+	0.902819i	$0.641494\pi$
$548$	−20.2048	+	29.6349i	−0.863105	+	1.26594i
$549$	30.8888	−	0.486525i	1.31830	−	0.0207644i
$550$	−10.7710	+	18.6559i	−0.459277	+	0.795491i
$551$	−16.0506	−	15.8673i	−0.683779	−	0.675968i
$552$	−87.6031	−	37.4025i	−3.72863	−	1.59195i
$553$	8.85742	−	1.10998i	0.376656	−	0.0472011i
$554$	−0.162323	−	0.158326i	−0.00689646	−	0.00672662i
$555$	−0.684782	+	0.135162i	−0.0290674	+	0.00573730i
$556$	0.287638	+	0.0143554i	0.0121986	+	0.000608805i
$557$	−41.6954	−	12.8613i	−1.76669	−	0.544952i	−0.770928	−	0.636922i	$-0.780207\pi$
$557$	−41.6954	−	12.8613i	−1.76669	−	0.544952i	−0.995762	+	0.0919701i	$0.970684\pi$
$558$	−26.4909	−	46.8724i	−1.12145	−	1.98427i
$559$	3.82384	−	25.3695i	0.161731	−	1.07302i
$560$	−0.861798	−	34.5570i	−0.0364176	−	1.46030i
$561$	7.16597	+	11.8485i	0.302548	+	0.500246i
$562$	12.4503	+	22.8625i	0.525182	+	0.964397i
$563$	13.9311	−	16.6025i	0.587127	−	0.699711i	−0.387924	−	0.921691i	$-0.626808\pi$
$563$	13.9311	−	16.6025i	0.587127	−	0.699711i	0.975051	+	0.221980i	$0.0712521\pi$
$564$	59.8127	−	28.4667i	2.51857	−	1.19866i
$565$	−20.2562	−	2.53843i	−0.852184	−	0.106792i
$566$	−78.7430	+	17.9726i	−3.30982	+	0.755444i
$567$	7.87955	+	16.0909i	0.330910	+	0.675756i
$568$		−	34.7852i		−	1.45955i
$569$	−28.5308	+	9.58582i	−1.19607	+	0.401859i	−0.845141	−	0.534543i	$-0.820484\pi$
$569$	−28.5308	+	9.58582i	−1.19607	+	0.401859i	−0.350930	+	0.936402i	$0.614135\pi$
$570$	24.6015	+	19.8045i	1.03044	+	0.829521i
$571$	37.6956	−	7.62034i	1.57751	−	0.318901i	0.671124	−	0.741345i	$-0.265812\pi$
$571$	37.6956	−	7.62034i	1.57751	−	0.318901i	0.906389	+	0.422444i	$0.138828\pi$
$572$	29.9982	−	26.4735i	1.25429	−	1.10691i
$573$	1.29288	−	9.94651i	0.0540107	−	0.415521i
$574$	10.7944	+	8.17647i	0.450551	+	0.341279i
$575$	−15.4243	+	4.75777i	−0.643238	+	0.198413i
$576$	−33.0923	+	4.67747i	−1.37885	+	0.194894i
$577$	24.4760	+	1.83422i	1.01895	+	0.0763597i	0.573715	−	0.819055i	$-0.305502\pi$
$577$	24.4760	+	1.83422i	1.01895	+	0.0763597i	0.445234	+	0.895414i	$0.353121\pi$
$578$	−1.58439	+	31.7463i	−0.0659021	+	1.32047i
$579$	−35.6712	+	26.7630i	−1.48245	+	1.11223i
$580$	−32.4008	+	29.6607i	−1.34537	+	1.23159i
$581$	−8.49585	+	3.09224i	−0.352467	+	0.128288i
$582$	26.2424	+	19.0504i	1.08778	+	0.789664i
$583$	−23.7521	+	17.0766i	−0.983712	+	0.707241i
$584$	−68.1649	+	46.4741i	−2.82069	+	1.92311i
$585$	−9.74460	−	5.42324i	−0.402890	−	0.224224i
$586$	43.3660	−	40.2377i	1.79143	−	1.66221i
$587$	−7.05590	+	15.6375i	−0.291228	+	0.645427i	−0.998080	−	0.0619337i	$-0.980273\pi$
$587$	−7.05590	+	15.6375i	−0.291228	+	0.645427i	0.706852	+	0.707361i	$0.250115\pi$
$588$	−5.26439	+	25.4394i	−0.217100	+	1.04910i
$589$	−18.8941	−	21.4097i	−0.778520	−	0.882170i
$590$	−4.22090	+	1.90454i	−0.173772	+	0.0784087i
$591$	16.3158	−	23.6963i	0.671141	−	0.974736i
$592$	0.877323	−	2.41043i	0.0360578	−	0.0990679i
$593$	15.4838	+	19.4161i	0.635845	+	0.797325i	0.990477	−	0.137681i	$-0.0439650\pi$
$593$	15.4838	+	19.4161i	0.635845	+	0.797325i	−0.354631	+	0.935006i	$0.615394\pi$
$594$	−39.6017	−	29.3075i	−1.62488	−	1.20250i
$595$	−7.11978	+	1.62504i	−0.291883	+	0.0666203i
$596$	6.83244	+	20.3357i	0.279868	+	0.832984i
$597$	−10.9343	+	11.6764i	−0.447511	+	0.477882i
$598$	42.1063	+	1.05006i	1.72185	+	0.0429403i
$599$	14.9185	+	10.7257i	0.609553	+	0.438239i	0.845834	−	0.533446i	$-0.179103\pi$
$599$	14.9185	+	10.7257i	0.609553	+	0.438239i	−0.236281	+	0.971685i	$0.575929\pi$
$600$	−20.2613	+	22.7474i	−0.827164	+	0.928660i
$601$	−10.1624	+	0.253435i	−0.414533	+	0.0103378i	−0.231656	−	0.972798i	$-0.574414\pi$
$601$	−10.1624	+	0.253435i	−0.414533	+	0.0103378i	−0.182878	+	0.983136i	$0.558541\pi$
$602$	49.3895	+	33.6732i	2.01296	+	1.37242i
$603$	1.90597	+	16.4310i	0.0776172	+	0.669121i
$604$	5.44476	+	5.05200i	0.221544	+	0.205563i
$605$	−0.874953	+	3.10977i	−0.0355719	+	0.126430i
$606$	25.4288	−	16.2587i	1.03297	−	0.660463i
$607$	−30.1567	+	3.77912i	−1.22402	+	0.153390i	−0.709884	−	0.704318i	$-0.751253\pi$
$607$	−30.1567	+	3.77912i	−1.22402	+	0.153390i	−0.514137	+	0.857708i	$0.671888\pi$
$608$	−48.0932	+	17.5045i	−1.95044	+	0.709901i
$609$	−16.1847	+	9.10164i	−0.655836	+	0.368817i
$610$	−7.77970	−	44.1209i	−0.314991	−	1.78640i
$611$	−11.8547	+	12.7763i	−0.479590	+	0.516875i
$612$	10.9705	+	31.0249i	0.443457	+	1.25411i
$613$	−3.46402	−	46.2242i	−0.139911	−	1.86698i	−0.420689	−	0.907205i	$-0.638212\pi$
$613$	−3.46402	−	46.2242i	−0.139911	−	1.86698i	0.280778	−	0.959773i	$-0.409407\pi$
$614$	31.8283	+	62.0834i	1.28449	+	2.50548i
$615$	1.24941	+	7.28109i	0.0503809	+	0.293602i
$616$	15.0229	+	53.3945i	0.605289	+	2.15133i
$617$	−0.121489	−	0.600969i	−0.00489095	−	0.0241941i	0.977652	−	0.210228i	$-0.0674207\pi$
$617$	−0.121489	−	0.600969i	−0.00489095	−	0.0241941i	−0.982543	+	0.186034i	$0.940437\pi$
$618$	−57.1663	+	8.34816i	−2.29957	+	0.335812i
$619$	−33.3059	+	32.4857i	−1.33868	+	1.30571i	−0.421722	+	0.906725i	$0.638574\pi$
$619$	−33.3059	+	32.4857i	−1.33868	+	1.30571i	−0.916957	+	0.398985i	$0.869362\pi$
$620$	−43.4503	+	34.6505i	−1.74501	+	1.39160i
$621$	−6.81556	−	36.2810i	−0.273499	−	1.45591i
$622$	22.1256	+	27.7446i	0.887155	+	1.11246i
$623$	21.3455	+	2.67494i	0.855189	+	0.107169i
$624$	35.5867	−	20.3287i	1.42461	−	0.813799i
$625$	0.211356	−	8.47513i	0.00845426	−	0.339005i
$626$	−51.0843	−	9.00753i	−2.04174	−	0.360013i
$627$	−23.7671	−	10.8557i	−0.949166	−	0.433537i
$628$	12.6883	+	49.8300i	0.506318	+	1.98843i
$629$	−0.535862	−	0.0807682i	−0.0213662	−	0.00322044i
$630$	21.2352	−	14.9732i	0.846031	−	0.596546i
$631$	2.33874	−	31.2083i	0.0931037	−	1.24238i	−0.733536	−	0.679651i	$-0.762131\pi$
$631$	2.33874	−	31.2083i	0.0931037	−	1.24238i	0.826640	−	0.562732i	$-0.190250\pi$
$632$	−31.9855	+	13.4830i	−1.27231	+	0.536325i
$633$	−21.7593	+	29.9739i	−0.864853	+	1.19136i
$634$	46.6626	+	4.66930i	1.85321	+	0.185442i
$635$	−25.1302	−	24.5113i	−0.997261	−	0.972701i
$636$	−63.4996	+	28.3019i	−2.51792	+	1.12224i
$637$	−1.18693	−	6.73141i	−0.0470278	−	0.266708i
$638$	27.9895	−	42.7036i	1.10812	−	1.69065i
$639$	11.2078	−	7.49153i	0.443375	−	0.296360i
$640$	2.39634	+	7.76874i	0.0947236	+	0.307086i
$641$	26.9377	+	12.1547i	1.06397	+	0.480083i	0.865959	−	0.500116i	$-0.166709\pi$
$641$	26.9377	+	12.1547i	1.06397	+	0.480083i	0.198015	+	0.980199i	$0.436550\pi$
$642$	−70.0090	+	42.3413i	−2.76303	+	1.67108i
$643$	−14.0157	−	5.90813i	−0.552727	−	0.232994i	0.0941902	−	0.995554i	$-0.469974\pi$
$643$	−14.0157	−	5.90813i	−0.552727	−	0.232994i	−0.646917	+	0.762560i	$0.723942\pi$
$644$	−31.8654	+	62.1558i	−1.25567	+	2.44928i
$645$	7.11044	+	31.8258i	0.279973	+	1.25314i
$646$	12.7858	+	20.9230i	0.503049	+	0.823203i
$647$	28.8803	−	36.2147i	1.13540	−	1.42375i	0.244441	−	0.969664i	$-0.421396\pi$
$647$	28.8803	−	36.2147i	1.13540	−	1.42375i	0.890959	−	0.454083i	$-0.150033\pi$
$648$	−46.4404	−	51.9321i	−1.82435	−	2.04009i
$649$	2.99525	−	2.38864i	0.117574	−	0.0937622i
$650$	4.60700	−	12.6576i	0.180701	−	0.496473i
$651$	−21.2123	+	10.0956i	−0.831375	+	0.395676i
$652$	23.4298	+	12.0118i	0.917583	+	0.470417i
$653$	2.29238	+	45.9322i	0.0897078	+	1.79747i	0.480509	+	0.876990i	$0.340452\pi$
$653$	2.29238	+	45.9322i	0.0897078	+	1.79747i	−0.390801	+	0.920475i	$0.627802\pi$
$654$	48.8869	−	4.66524i	1.91163	−	0.182425i
$655$	−17.7105	−	21.1066i	−0.692008	−	0.824703i
$656$	−25.2723	−	9.91866i	−0.986718	−	0.387258i
$657$	−29.6544	−	11.9539i	−1.15693	−	0.466367i
$658$	−14.8357	−	37.8007i	−0.578355	−	1.47363i
$659$	14.1927	−	26.0622i	0.552869	−	1.01524i	−0.440221	−	0.897889i	$-0.645100\pi$
$659$	14.1927	−	26.0622i	0.552869	−	1.01524i	0.993091	−	0.117349i	$-0.0374397\pi$
$660$	−23.4078	+	45.1467i	−0.911146	+	1.75733i
$661$	−8.21859	−	12.7249i	−0.319666	−	0.494940i	0.642914	−	0.765939i	$-0.277725\pi$
$661$	−8.21859	−	12.7249i	−0.319666	−	0.494940i	−0.962580	+	0.270999i	$0.912646\pi$
$662$	−9.01748	−	71.9578i	−0.350474	−	2.79672i
$663$	−5.69924	−	6.51811i	−0.221340	−	0.253142i
$664$	28.5445	−	20.5221i	1.10774	−	0.796411i
$665$	9.37303	−	10.1017i	0.363471	−	0.391728i
$666$	1.87277	−	0.458595i	0.0725685	−	0.0177702i
$667$	37.1380	−	9.19111i	1.43799	−	0.355881i
$668$	−0.943081	+	0.791339i	−0.0364889	+	0.0306178i
$669$	−2.74550	−	10.9931i	−0.106147	−	0.425018i
$670$	23.0919	−	6.49706i	0.892119	−	0.251003i
$671$	15.2445	+	33.7853i	0.588508	+	1.30427i
$672$	2.95376	+	42.0024i	0.113944	+	1.62028i
$673$	−0.354913	+	2.83214i	−0.0136809	+	0.109171i	−0.997577	−	0.0695699i	$-0.977837\pi$
$673$	−0.354913	+	2.83214i	−0.0136809	+	0.109171i	0.983896	+	0.178741i	$0.0572024\pi$
$674$	−59.7668	+	28.7822i	−2.30213	+	1.10865i
$675$	−11.6928	−	1.62920i	−0.450058	−	0.0627080i
$676$	24.4318	−	30.6366i	0.939686	−	1.17833i
$677$	14.9842	−	14.6151i	0.575888	−	0.561706i	−0.351318	−	0.936256i	$-0.614266\pi$
$677$	14.9842	−	14.6151i	0.575888	−	0.561706i	0.927207	+	0.374551i	$0.122203\pi$
$678$	56.2147	+	4.47238i	2.15891	+	0.171761i
$679$	9.09501	−	10.8390i	0.349034	−	0.415963i
$680$	24.9389	−	13.5810i	0.956361	−	0.520807i
$681$	−4.44063	+	0.761995i	−0.170165	+	0.0291997i
$682$	39.0047	−	51.4934i	1.49357	−	1.97178i
$683$	3.31335	−	8.44228i	0.126782	−	0.323035i	−0.853363	−	0.521317i	$-0.825441\pi$
$683$	3.31335	−	8.44228i	0.126782	−	0.323035i	0.980145	+	0.198282i	$0.0635362\pi$
$684$	−50.0826	−	36.7093i	−1.91496	−	1.40362i
$685$	1.78779	+	11.8612i	0.0683080	+	0.453194i
$686$	50.6654	+	14.2550i	1.93442	+	0.544260i
$687$	23.6981	+	14.6315i	0.904140	+	0.558227i
$688$	−113.603	−	38.1684i	−4.33106	−	1.45516i
$689$	12.7721	−	13.0946i	0.486578	−	0.498864i
$690$	−50.3912	+	18.0793i	−1.91836	+	0.688266i
$691$	1.59388	+	0.0795475i	0.0606342	+	0.00302613i	0.0801400	−	0.996784i	$-0.474463\pi$
$691$	1.59388	+	0.0795475i	0.0606342	+	0.00302613i	−0.0195058	+	0.999810i	$0.506209\pi$
$692$	5.18469	−	3.53486i	0.197092	−	0.134375i
$693$	−13.9684	+	16.3397i	−0.530615	+	0.620695i
$694$	10.6214	+	34.4338i	0.403183	+	1.30709i
$695$	0.0737818	−	0.0619103i	0.00279870	−	0.00234839i
$696$	50.9959	−	51.1136i	1.93300	−	1.93746i
$697$	−0.995974	+	5.64845i	−0.0377252	+	0.213950i
$698$	−26.2775	−	34.6911i	−0.994618	−	1.31308i
$699$	12.0674	−	38.4932i	0.456432	−	1.45595i
$700$	15.5970	+	15.9908i	0.589512	+	0.604397i
$701$	−0.745110	+	3.26454i	−0.0281424	+	0.123300i	−0.987048	−	0.160426i	$-0.948713\pi$
$701$	−0.745110	+	3.26454i	−0.0281424	+	0.123300i	0.958906	+	0.283726i	$0.0915705\pi$
$702$	27.5685	+	13.7473i	1.04050	+	0.518857i
$703$	0.921314	−	0.443681i	0.0347480	−	0.0167338i
$704$	−20.9091	−	34.2163i	−0.788042	−	1.28957i
$705$	8.18810	−	20.5845i	0.308382	−	0.775257i
$706$	−17.0114	+	7.67583i	−0.640232	+	0.288884i
$707$	−6.29832	−	11.5657i	−0.236873	−	0.434971i
$708$	8.12087	−	4.11635i	0.305201	−	0.154702i
$709$	3.21675	+	0.650281i	0.120808	+	0.0244218i	0.258173	−	0.966099i	$-0.416879\pi$
$709$	3.21675	+	0.650281i	0.120808	+	0.0244218i	−0.137366	+	0.990520i	$0.543864\pi$
$710$	−13.2978	−	14.3316i	−0.499058	−	0.537857i
$711$	−11.2328	−	7.40199i	−0.421264	−	0.277596i
$712$	−82.7160	+	12.4674i	−3.09991	+	0.467237i
$713$	47.6682	−	8.40518i	1.78519	−	0.314777i
$714$	19.4440	−	5.37448i	0.727675	−	0.201135i
$715$	1.33226	−	13.3139i	0.0498236	−	0.497911i
$716$	19.1669	−	57.0475i	0.716302	−	2.13196i
$717$	3.04549	+	0.0899446i	0.113736	+	0.00335904i
$718$	36.0162	+	50.0955i	1.34411	+	1.86955i
$719$	14.5081	+	4.47515i	0.541060	+	0.166895i	0.553226	−	0.833031i	$-0.313396\pi$
$719$	14.5081	+	4.47515i	0.541060	+	0.166895i	−0.0121660	+	0.999926i	$0.503873\pi$
$720$	−32.8520	+	40.4279i	−1.22432	+	1.50666i
$721$	1.88379	+	25.1374i	0.0701560	+	0.936167i
$722$	3.44492	+	1.55441i	0.128207	+	0.0578490i
$723$	−31.3051	+	30.2548i	−1.16425	+	1.12519i
$724$	−14.7842	+	83.8455i	−0.549451	+	3.11609i
$725$	0.996342	−	12.1946i	0.0370032	−	0.452896i
$726$	2.02566	−	8.69087i	0.0751795	−	0.322548i
$727$	12.4183	+	8.02059i	0.460570	+	0.297467i	0.752046	−	0.659111i	$-0.229067\pi$
$727$	12.4183	+	8.02059i	0.460570	+	0.297467i	−0.291476	+	0.956578i	$0.594146\pi$
$728$	−15.0485	−	31.2486i	−0.557735	−	1.15815i
$729$	6.73092	−	26.1476i	0.249294	−	0.968428i
$730$	−10.3179	+	45.2059i	−0.381884	+	1.67314i
$731$	−3.14819	+	25.1219i	−0.116440	+	0.929168i
$732$	19.2064	+	85.9665i	0.709889	+	3.17741i
$733$	9.15587	+	45.2915i	0.338180	+	1.67288i	0.680076	+	0.733142i	$0.261947\pi$
$733$	9.15587	+	45.2915i	0.338180	+	1.67288i	−0.341896	+	0.939738i	$0.611069\pi$
$734$	3.01783	+	3.41961i	0.111390	+	0.126220i
$735$	4.49615	+	7.43413i	0.165843	+	0.274212i
$736$	17.1904	−	85.0358i	0.633645	−	3.13446i
$737$	−17.1874	+	9.92313i	−0.633105	+	0.365523i
$738$	−4.35806	−	19.9361i	−0.160422	−	0.733859i
$739$	11.8513	−	38.4209i	0.435956	−	1.41333i	−0.425249	−	0.905076i	$-0.639814\pi$
$739$	11.8513	−	38.4209i	0.435956	−	1.41333i	0.861205	−	0.508258i	$-0.169710\pi$
$740$	−0.773073	−	1.83395i	−0.0284187	−	0.0674172i
$741$	15.8142	+	4.10421i	0.580950	+	0.150772i
$742$	14.5764	+	40.0483i	0.535116	+	1.47022i
$743$	−17.2708	+	28.2624i	−0.633603	+	1.03685i	0.360947	+	0.932586i	$0.382454\pi$
$743$	−17.2708	+	28.2624i	−0.633603	+	1.03685i	−0.994550	+	0.104259i	$0.966753\pi$
$744$	68.7681	−	60.1288i	2.52116	−	2.20443i
$745$	6.30083	+	3.43125i	0.230844	+	0.125711i
$746$	−2.08580	+	0.818615i	−0.0763665	+	0.0299716i
$747$	12.7597	+	4.77732i	0.466855	+	0.174793i
$748$	−28.9428	+	26.8550i	−1.05825	+	0.981916i
$749$	16.2864	+	31.7677i	0.595091	+	1.16077i
$750$	1.11462	+	54.7879i	0.0407001	+	2.00057i
$751$	19.0604	−	5.36275i	0.695522	−	0.195690i	0.0952122	−	0.995457i	$-0.469647\pi$
$751$	19.0604	−	5.36275i	0.695522	−	0.195690i	0.600310	+	0.799767i	$0.295044\pi$
$752$	49.1576	+	64.8970i	1.79259	+	2.36655i
$753$	−14.7198	+	4.46655i	−0.536421	+	0.162770i
$754$	−12.5989	+	29.3355i	−0.458824	+	1.06834i
$755$	2.48401			0.0904023
$756$	−40.3761	+	31.2988i	−1.46846	+	1.13833i
$757$	6.03800	+	12.5380i	0.219455	+	0.455702i	0.981409	−	0.191929i	$-0.0614742\pi$
$757$	6.03800	+	12.5380i	0.219455	+	0.455702i	−0.761954	+	0.647631i	$0.775760\pi$
$758$	63.3950	+	64.9957i	2.30261	+	2.36075i
$759$	36.7098	−	24.7822i	1.33248	−	0.899535i
$760$	−24.4458	+	47.6833i	−0.886743	+	1.72966i
$761$	−5.65953	−	20.1152i	−0.205158	−	0.729174i	−0.993490	−	0.113924i	$-0.963658\pi$
$761$	−5.65953	−	20.1152i	−0.205158	−	0.729174i	0.788332	−	0.615250i	$-0.210945\pi$
$762$	72.4118	+	64.4976i	2.62320	+	2.33650i
$763$	−0.534207	−	21.4210i	−0.0193396	−	0.775494i
$764$	28.5196	−	2.13725i	1.03180	−	0.0773230i
$765$	9.74678	+	5.11046i	0.352396	+	0.184769i
$766$	−33.9663	−	19.6104i	−1.22725	−	0.708554i
$767$	−1.58509	+	1.79612i	−0.0572341	+	0.0648541i
$768$	5.44840	+	15.1860i	0.196602	+	0.547976i
$769$	6.67475	−	4.31101i	0.240698	−	0.155459i	−0.416600	−	0.909090i	$-0.636779\pi$
$769$	6.67475	−	4.31101i	0.240698	−	0.155459i	0.657298	+	0.753631i	$0.271699\pi$
$770$	26.6014	+	16.2558i	0.958646	+	0.585817i
$771$	−0.735373	+	0.0887263i	−0.0264838	+	0.00319540i
$772$	−95.3388	−	84.1370i	−3.43132	−	3.02816i
$773$	6.82908	+	10.0164i	0.245625	+	0.360266i	0.929176	−	0.369637i	$-0.120518\pi$
$773$	6.82908	+	10.0164i	0.245625	+	0.360266i	−0.683551	+	0.729902i	$0.739565\pi$
$774$	−23.6004	−	86.9351i	−0.848297	−	3.12482i
$775$	2.30713	−	15.3068i	0.0828744	−	0.549836i
$776$	−22.6287	+	50.1503i	−0.812321	+	1.80029i
$777$	−0.142282	−	0.829170i	−0.00510435	−	0.0297463i
$778$	11.7782	+	4.96492i	0.422268	+	0.178001i
$779$	−4.45133	−	9.86515i	−0.159485	−	0.353456i
$780$	9.51220	−	30.3424i	0.340591	−	1.08643i
$781$	13.5872	+	8.77553i	0.486187	+	0.314013i
$782$	−41.5650			−1.48636
$783$	27.4516	+	5.42286i	0.981042	+	0.193797i
$784$	−31.9284			−1.14030
$785$	14.4455	+	9.32992i	0.515584	+	0.332999i
$786$	51.5114	+	56.0299i	1.83735	+	1.99852i
$787$	17.7226	+	39.2772i	0.631741	+	1.40008i	0.899639	+	0.436634i	$0.143830\pi$
$787$	17.7226	+	39.2772i	0.631741	+	1.40008i	−0.267898	+	0.963447i	$0.586329\pi$
$788$	75.5921	+	31.8647i	2.69286	+	1.13513i
$789$	18.5645	−	15.4328i	0.660914	−	0.549421i
$790$	−8.02381	+	17.7826i	−0.285474	+	0.632676i
$791$	3.66728	−	24.3308i	0.130394	−	0.865105i
$792$	35.0772	−	75.8726i	1.24641	−	2.69602i
$793$	−13.0558	−	19.1493i	−0.463625	−	0.680013i
$794$	25.3414	+	22.3639i	0.899333	+	0.793666i
$795$	−9.12946	+	21.3828i	−0.323788	+	0.758369i
$796$	−38.9206	−	23.7839i	−1.37950	−	0.842998i
$797$	−30.9762	+	20.0065i	−1.09723	+	0.708668i	−0.959474	−	0.281798i	$-0.909069\pi$
$797$	−30.9762	+	20.0065i	−1.09723	+	0.708668i	−0.137759	+	0.990466i	$0.543990\pi$
$798$	−24.6022	+	29.0478i	−0.870907	+	1.02828i
$799$	11.3807	−	12.8959i	0.402620	−	0.456224i
$800$	−24.0278	−	13.8725i	−0.849513	−	0.490466i
$801$	−21.8312	−	23.9662i	−0.771368	−	0.846803i
$802$	70.0076	−	5.24635i	2.47206	−	0.185255i
$803$	−0.956383	−	38.3498i	−0.0337500	−	1.35333i
$804$	−44.7772	+	14.8159i	−1.57917	+	0.522515i
$805$	6.32668	+	22.4864i	0.222986	+	0.792540i
$806$	−18.4275	+	35.9442i	−0.649082	+	1.26608i
$807$	−0.910226	−	0.443502i	−0.0320415	−	0.0156120i
$808$	35.7558	+	36.6587i	1.25789	+	1.28965i
$809$	15.9705	+	33.1630i	0.561492	+	1.16595i	0.967685	+	0.252162i	$0.0811417\pi$
$809$	15.9705	+	33.1630i	0.561492	+	1.16595i	−0.406193	+	0.913787i	$0.633144\pi$
$810$	−38.9864	−	3.64281i	−1.36984	−	0.127995i
$811$	32.4803			1.14054			0.570269	−	0.821458i	$-0.306839\pi$
$811$	32.4803			1.14054			0.570269	+	0.821458i	$0.306839\pi$
$812$	−34.7652	−	39.9317i	−1.22002	−	1.40133i
$813$	8.99345	−	38.5853i	0.315414	−	1.35325i
$814$	1.39682	+	1.84406i	0.0489584	+	0.0646341i
$815$	8.47632	−	2.38487i	0.296912	−	0.0835382i
$816$	−34.6073	+	20.9304i	−1.21150	+	0.732712i
$817$	−21.7956	−	42.5139i	−0.762531	−	1.48737i
$818$	40.8974	−	37.9472i	1.42994	−	1.32679i
$819$	6.82740	−	11.5785i	0.238569	−	0.404586i
$820$	−19.6083	+	7.69568i	−0.684751	+	0.268745i
$821$	30.0499	+	16.3643i	1.04875	+	0.571117i	0.908018	−	0.418931i	$-0.137595\pi$
$821$	30.0499	+	16.3643i	1.04875	+	0.571117i	0.140729	+	0.990048i	$0.455055\pi$
$822$	−6.41636	−	32.5078i	−0.223796	−	1.13384i
$823$	−8.30142	+	13.5847i	−0.289369	+	0.473532i	−0.964469	−	0.264194i	$-0.914894\pi$
$823$	−8.30142	+	13.5847i	−0.289369	+	0.473532i	0.675100	+	0.737726i	$0.264100\pi$
$824$	−33.5248	−	92.1088i	−1.16789	−	3.20876i
$825$	−3.77373	−	13.6528i	−0.131384	−	0.475329i
$826$	−2.16799	−	5.14308i	−0.0754340	−	0.178951i
$827$	12.1236	−	39.3038i	0.421580	−	1.36673i	−0.457142	−	0.889394i	$-0.651127\pi$
$827$	12.1236	−	39.3038i	0.421580	−	1.36673i	0.878722	−	0.477334i	$-0.158397\pi$
$828$	97.3655	−	39.9940i	3.38369	−	1.38989i
$829$	−14.8196	+	8.55610i	−0.514706	+	0.297166i	−0.734766	−	0.678321i	$-0.762708\pi$
$829$	−14.8196	+	8.55610i	−0.514706	+	0.297166i	0.220060	+	0.975486i	$0.429375\pi$
$830$	3.91518	−	19.3673i	0.135898	−	0.672248i
$831$	0.149067	−	0.00303265i	0.00517107	−	0.000105201i
$832$	16.5908	+	18.7997i	0.575183	+	0.651761i
$833$	1.33655	+	6.61155i	0.0463088	+	0.229076i
$834$	−0.195862	+	0.180067i	−0.00678216	+	0.00623521i
$835$	−0.0511950	+	0.408526i	−0.00177168	+	0.0141376i
$836$	16.5784	−	72.6349i	0.573377	−	2.51213i
$837$	34.1839	+	9.20752i	1.18157	+	0.318258i
$838$	29.8480	+	61.9800i	1.03108	+	2.14106i
$839$	−21.0543	−	13.5983i	−0.726875	−	0.469466i	0.125702	−	0.992068i	$-0.459882\pi$
$839$	−21.0543	−	13.5983i	−0.726875	−	0.469466i	−0.852576	+	0.522603i	$0.824961\pi$
$840$	32.1782	+	30.1332i	1.11025	+	1.03969i
$841$	−3.99251	+	28.7239i	−0.137673	+	0.990478i
$842$	9.04844	−	51.3163i	0.311830	−	1.76848i
$843$	−16.4563	−	4.71174i	−0.566785	−	0.162281i
$844$	−96.2657	−	43.4368i	−3.31360	−	1.49515i
$845$	−0.979335	−	13.0683i	−0.0336901	−	0.449564i
$846$	−20.0217	+	57.8271i	−0.688361	+	1.98814i
$847$	−3.72074	−	1.14770i	−0.127846	−	0.0394353i
$848$	−49.8775	−	69.3754i	−1.71280	−	2.38236i
$849$	27.9003	−	45.1891i	0.957535	−	1.55089i
$850$	−4.23354	+	12.6005i	−0.145209	+	0.432193i
$851$	−0.172591	+	1.72479i	−0.00591635	+	0.0591250i
$852$	27.3938	+	26.9657i	0.938497	+	0.923831i
$853$	−15.2099	+	2.68191i	−0.520777	+	0.0918270i	−0.427857	−	0.903847i	$-0.640731\pi$
$853$	−15.2099	+	2.68191i	−0.520777	+	0.0918270i	−0.0929201	+	0.995674i	$0.529620\pi$
$854$	53.3960	−	8.04815i	1.82717	−	0.275402i
$855$	−20.6284	+	2.39287i	−0.705477	+	0.0818345i
$856$	−94.4183	−	101.759i	−3.22715	−	3.47804i
$857$	12.7333	+	2.57408i	0.434960	+	0.0879290i	0.410687	−	0.911776i	$-0.365289\pi$
$857$	12.7333	+	2.57408i	0.434960	+	0.0879290i	0.0242727	+	0.999705i	$0.492273\pi$
$858$	−2.01186	+	36.9066i	−0.0686838	+	1.25997i
$859$	7.67868	+	14.1004i	0.261993	+	0.481100i	0.975632	−	0.219414i	$-0.0704145\pi$
$859$	7.67868	+	14.1004i	0.261993	+	0.481100i	−0.713639	+	0.700514i	$0.752954\pi$
$860$	−84.7554	+	38.2431i	−2.89013	+	1.30408i
$861$	−8.81068	+	1.28665i	−0.300267	+	0.0438489i
$862$	−30.0802	−	49.2240i	−1.02453	−	1.67658i
$863$	−25.4044	+	12.2341i	−0.864776	+	0.416454i	−0.813041	−	0.582207i	$-0.802189\pi$
$863$	−25.4044	+	12.2341i	−0.864776	+	0.416454i	−0.0517349	+	0.998661i	$0.516475\pi$
$864$	37.7465	−	51.0048i	1.28416	−	1.73522i
$865$	0.466978	−	2.04597i	0.0158777	−	0.0695649i
$866$	−4.18167	−	4.28726i	−0.142099	−	0.145687i
$867$	−14.1454	−	15.3862i	−0.480404	−	0.522544i
$868$	−40.4455	−	53.3954i	−1.37281	−	1.81236i
$869$	2.80273	−	15.8951i	0.0950761	−	0.539203i
$870$	1.47063	−	40.5539i	0.0498591	−	1.37491i
$871$	9.50633	−	7.97676i	0.322110	−	0.270282i
$872$	24.5592	+	79.6191i	0.831681	+	2.69624i
$873$	−21.0319	+	3.50965i	−0.711823	+	0.118784i
$874$	64.8037	−	44.1824i	2.19202	−	1.49449i
$875$	23.8808	+	1.19184i	0.807319	+	0.0402916i
$876$	16.2430	−	89.7079i	0.548800	−	3.03095i
$877$	−33.2707	+	34.1108i	−1.12347	+	1.15184i	−0.136552	+	0.990633i	$0.543602\pi$
$877$	−33.2707	+	34.1108i	−1.12347	+	1.15184i	−0.986921	+	0.161207i	$0.948461\pi$
$878$	−17.7771	−	5.97279i	−0.599948	−	0.201572i
$879$	−1.14833	+	38.8818i	−0.0387321	+	1.31145i
$880$	−60.1656	−	16.9280i	−2.02818	−	0.570642i
$881$	2.72852	+	18.1025i	0.0919261	+	0.609890i	0.986598	+	0.163167i	$0.0521709\pi$
$881$	2.72852	+	18.1025i	0.0919261	+	0.609890i	−0.894672	+	0.446723i	$0.852591\pi$
$882$	−13.3367	−	19.9525i	−0.449069	−	0.671837i
$883$	−0.0647915	+	0.165086i	−0.00218041	+	0.00555559i	−0.931960	−	0.362562i	$-0.881902\pi$
$883$	−0.0647915	+	0.165086i	−0.00218041	+	0.00555559i	0.929779	+	0.368117i	$0.119997\pi$
$884$	14.9067	−	19.6796i	0.501368	−	0.661897i
$885$	1.05453	−	2.85642i	0.0354477	−	0.0960175i
$886$	−33.1498	+	18.0524i	−1.11369	+	0.606483i
$887$	18.0930	−	21.5623i	0.607502	−	0.723993i	−0.371366	−	0.928487i	$-0.621110\pi$
$887$	18.0930	−	21.5623i	0.607502	−	0.723993i	0.978868	+	0.204494i	$0.0655549\pi$
$888$	1.40582	+	2.95385i	0.0471764	+	0.0991246i
$889$	30.2893	−	29.5434i	1.01587	−	0.990853i
$890$	−29.3132	+	36.7576i	−0.982582	+	1.23212i
$891$	32.0007	−	5.03843i	1.07206	−	0.168794i
$892$	29.1085	−	14.0179i	0.974624	−	0.469354i
$893$	−4.03560	+	32.2033i	−0.135046	+	1.07764i
$894$	−17.8163	−	8.68086i	−0.595865	−	0.290331i
$895$	−8.27780	−	18.3455i	−0.276696	−	0.613222i
$896$	−9.43273	+	2.65396i	−0.315125	+	0.0886626i
$897$	−19.9146	+	19.2465i	−0.664930	+	0.642623i
$898$	−57.8193	+	48.5162i	−1.92946	+	1.61901i
$899$	−7.51157	+	35.9128i	−0.250525	+	1.19776i
$900$	−2.20722	−	33.5900i	−0.0735739	−	1.11967i
$901$	−12.2779	+	13.2325i	−0.409037	+	0.440837i
$902$	19.8798	−	14.2926i	0.661926	−	0.475893i
$903$	−38.5613	+	7.61120i	−1.28324	+	0.253285i
$904$	11.8970	+	94.9357i	0.395688	+	3.15751i
$905$	15.4480	+	23.9182i	0.513510	+	0.795069i
$906$	−6.85467	+	0.310555i	−0.227731	+	0.0103175i
$907$	9.39240	−	17.2473i	0.311869	−	0.572688i	−0.674294	−	0.738463i	$-0.735552\pi$
$907$	9.39240	−	17.2473i	0.311869	−	0.572688i	0.986164	+	0.165774i	$0.0530124\pi$
$908$	−4.69349	−	11.9588i	−0.155759	−	0.396867i
$909$	−4.11089	+	19.4156i	−0.136350	+	0.643975i
$910$	−18.1459	−	7.12173i	−0.601530	−	0.236083i
$911$	−22.3758	−	26.6665i	−0.741344	−	0.883500i	0.255172	−	0.966896i	$-0.417868\pi$
$911$	−22.3758	−	26.6665i	−0.741344	−	0.883500i	−0.996517	+	0.0833958i	$0.973423\pi$
$912$	31.7075	−	69.4191i	1.04994	−	2.29870i
$913$	0.814837	+	16.3268i	0.0269672	+	0.540338i
$914$	68.6822	+	35.2113i	2.27181	+	1.16469i
$915$	24.2635	+	16.7063i	0.802128	+	0.552294i
$916$	−27.1609	+	74.6240i	−0.897422	+	2.46565i
$917$	25.9640	−	20.7056i	0.857406	−	0.683758i
$918$	−27.5354	−	12.8839i	−0.908803	−	0.425231i
$919$	3.47562	−	4.35829i	0.114650	−	0.143767i	−0.721195	−	0.692732i	$-0.756407\pi$
$919$	3.47562	−	4.35829i	0.114650	−	0.143767i	0.835845	+	0.548965i	$0.184978\pi$
$920$	−47.3632	−	77.5064i	−1.56152	−	2.55531i
$921$	−43.7738	−	13.7229i	−1.44239	−	0.452184i
$922$	19.6036	−	38.2383i	0.645612	−	1.25931i
$923$	−9.31968	−	3.92857i	−0.306761	−	0.129311i
$924$	−53.6948	−	29.5611i	−1.76643	−	0.972489i
$925$	0.505293	+	0.227997i	0.0166139	+	0.00749650i
$926$	−0.869897	−	2.82014i	−0.0285866	−	0.0926754i
$927$	22.4575	−	30.6388i	0.737600	−	1.00631i
$928$	55.0000	+	36.0491i	1.80546	+	1.18337i
$929$	5.25395	+	29.7966i	0.172377	+	0.977596i	0.941129	+	0.338049i	$0.109767\pi$
$929$	5.25395	+	29.7966i	0.172377	+	0.977596i	−0.768752	+	0.639547i	$0.779122\pi$
$930$	5.34648	−	51.0623i	0.175318	−	1.67440i
$931$	−9.11170	−	8.88730i	−0.298624	−	0.291269i
$932$	114.453	+	11.4528i	3.74904	+	0.375148i
$933$	−23.2070	−	2.42990i	−0.759764	−	0.0795512i
$934$	71.5193	−	30.1479i	2.34018	−	0.986470i
$935$	−0.986757	+	13.1674i	−0.0322704	+	0.430619i
$936$	−13.3619	+	50.5302i	−0.436747	+	1.65163i
$937$	−10.7502	−	1.62033i	−0.351194	−	0.0529340i	−0.0289237	−	0.999582i	$-0.509208\pi$
$937$	−10.7502	−	1.62033i	−0.351194	−	0.0529340i	−0.322271	+	0.946648i	$0.604446\pi$
$938$	7.13456	+	28.0192i	0.232952	+	0.914859i
$939$	27.7848	−	19.7830i	0.906723	−	0.645594i
$940$	62.2071	+	10.9688i	2.02897	+	0.357762i
$941$	0.304762	−	12.2206i	0.00993495	−	0.398379i	−0.974676	−	0.223620i	$-0.928212\pi$
$941$	0.304762	−	12.2206i	0.00993495	−	0.398379i	0.984611	−	0.174759i	$-0.0559145\pi$
$942$	−41.0292	−	23.9401i	−1.33681	−	0.780011i
$943$	18.2038	+	2.28123i	0.592798	+	0.0742872i
$944$	6.97675	+	8.74856i	0.227074	+	0.284741i
$945$	−2.77887	+	16.8575i	−0.0903967	+	0.548375i
$946$	84.5010	−	67.3873i	2.74737	−	2.19095i
$947$	15.5181	−	15.1359i	0.504270	−	0.491851i	−0.401360	−	0.915921i	$-0.631462\pi$
$947$	15.5181	−	15.1359i	0.504270	−	0.491851i	0.905630	+	0.424070i	$0.139399\pi$
$948$	14.1773	−	35.6412i	0.460458	−	1.15757i
$949$	4.75295	+	23.5115i	0.154287	+	0.763216i
$950$	−6.79348	−	24.1455i	−0.220410	−	0.783383i
$951$	−23.7123	+	19.7122i	−0.768925	+	0.639211i
$952$	15.6146	+	30.4575i	0.506073	+	0.987132i
$953$	−2.05920	−	27.4781i	−0.0667039	−	0.890102i	−0.925734	−	0.378176i	$-0.876551\pi$
$953$	−2.05920	−	27.4781i	−0.0667039	−	0.890102i	0.859030	−	0.511926i	$-0.171068\pi$
$954$	22.5196	−	60.1476i	0.729100	−	1.94735i
$955$	6.50560	−	7.01137i	0.210516	−	0.226883i
$956$	1.50858	+	8.55556i	0.0487909	+	0.276707i
$957$	7.09995	+	32.8140i	0.229509	+	1.06072i
$958$	20.9108	−	7.61092i	0.675598	−	0.245898i
$959$	−14.3456	+	1.79773i	−0.463242	+	0.0580518i
$960$	−28.2931	−	14.6695i	−0.913157	−	0.473456i
$961$	−4.17612	+	14.8428i	−0.134713	+	0.478800i
$962$	−1.06037	−	0.983882i	−0.0341878	−	0.0317216i
$963$	12.4524	−	52.3370i	0.401271	−	1.68654i
$964$	−102.566	−	69.9282i	−3.30342	−	2.25223i
$965$	−42.5117	+	1.06018i	−1.36850	+	0.0341283i
$966$	−20.2699	−	61.2607i	−0.652174	−	1.97103i
$967$	10.2991	+	7.40456i	0.331197	+	0.238115i	0.737072	−	0.675814i	$-0.236208\pi$
$967$	10.2991	+	7.40456i	0.331197	+	0.238115i	−0.405875	+	0.913929i	$0.633033\pi$
$968$	15.1359	+	0.377466i	0.486486	+	0.0121322i
$969$	−15.7022	−	3.65986i	−0.504427	−	0.117572i
$970$	9.84854	+	29.3127i	0.316217	+	0.941173i
$971$	−26.7584	+	6.10742i	−0.858717	+	0.195996i	−0.629138	−	0.777294i	$-0.716592\pi$
$971$	−26.7584	+	6.10742i	−0.858717	+	0.195996i	−0.229579	+	0.973290i	$0.573735\pi$
$972$	76.8982	+	3.68567i	2.46651	+	0.118218i
$973$	0.0723799	+	0.0907616i	0.00232039	+	0.00290968i
$974$	−12.1378	+	33.3484i	−0.388921	+	1.06855i
$975$	3.80624	+	7.99748i	0.121897	+	0.256124i
$976$	−98.6803	+	44.5263i	−3.15868	+	1.42525i
$977$	7.28830	+	8.25865i	0.233173	+	0.264218i	0.854638	−	0.519225i	$-0.173779\pi$
$977$	7.28830	+	8.25865i	0.233173	+	0.264218i	−0.621464	+	0.783443i	$0.713462\pi$
$978$	−23.0924	+	7.64082i	−0.738414	+	0.244326i
$979$	15.9976	−	35.4543i	0.511286	−	1.13313i
$980$	−18.1596	+	16.8496i	−0.580087	+	0.538242i
$981$	−20.3642	+	25.0602i	−0.650178	+	0.800112i
$982$	−89.1480	+	60.7801i	−2.84483	+	1.93957i
$983$	42.7144	−	30.7096i	1.36238	−	0.979483i	0.363526	−	0.931584i	$-0.381573\pi$
$983$	42.7144	−	30.7096i	1.36238	−	0.979483i	0.998852	−	0.0478992i	$-0.0152526\pi$
$984$	31.6245	−	14.0951i	1.00815	−	0.449335i
$985$	25.7802	−	9.38323i	0.821426	−	0.298975i
$986$	11.7075	−	29.2504i	0.372842	−	0.931522i
$987$	24.5567	+	10.4846i	0.781647	+	0.333727i
$988$	−2.32211	+	46.5278i	−0.0738761	+	1.48025i
$989$	80.7586	+	6.05202i	2.56797	+	0.192443i
$990$	−14.5529	−	44.6693i	−0.462522	−	1.41968i
$991$	47.9489	−	14.7903i	1.52315	−	0.469828i	0.583540	−	0.812085i	$-0.301667\pi$
$991$	47.9489	−	14.7903i	1.52315	−	0.469828i	0.939607	+	0.342256i	$0.111191\pi$
$992$	66.3208	+	50.2360i	2.10569	+	1.59500i
$993$	37.8788	+	28.9667i	1.20205	+	0.919232i
$994$	17.6681	−	15.5922i	0.560397	−	0.494554i
$995$	−14.9518	+	3.02257i	−0.474004	+	0.0958220i
$996$	−5.96647	+	38.3881i	−0.189055	+	1.21637i
$997$	39.3206	−	13.2110i	1.24530	−	0.418397i	0.382503	−	0.923954i	$-0.375062\pi$
$997$	39.3206	−	13.2110i	1.24530	−	0.418397i	0.862793	+	0.505557i	$0.168713\pi$
$998$			86.9769i			2.75321i
$999$	−0.648967	+	1.08912i	−0.0205324	+	0.0344581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.bf.a.4.3	✓	3168
27.7	even	9	inner	783.2.bf.a.439.3	yes	3168
29.22	even	14	inner	783.2.bf.a.544.3	yes	3168
783.196	even	126	inner	783.2.bf.a.196.3	yes	3168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.bf.a.4.3	✓	3168	1.1	even	1	trivial
783.2.bf.a.196.3	yes	3168	783.196	even	126	inner
783.2.bf.a.439.3	yes	3168	27.7	even	9	inner
783.2.bf.a.544.3	yes	3168	29.22	even	14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.bf (of order \(126\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.21274 - 1.42914i) q^{2} +(1.69038 - 0.377660i) q^{3} +(2.03122 + 4.50164i) q^{4} +(1.52196 + 0.641561i) q^{5} +(-4.28010 - 1.58012i) q^{6} +(-0.818764 + 1.81457i) q^{7} +(1.15372 - 7.65445i) q^{8} +(2.71475 - 1.27677i) q^{9} +(-2.45083 - 3.59471i) q^{10} +(2.69879 + 2.38169i) q^{11} +(5.13361 + 6.84236i) q^{12} +(-1.92049 - 1.17359i) q^{13} +(4.40499 - 2.84505i) q^{14} +(2.81498 + 0.509696i) q^{15} +(-6.95647 + 7.88264i) q^{16} +(1.92349 + 1.11053i) q^{17} +(-7.83173 - 1.05458i) q^{18} +(-4.17937 + 0.313201i) q^{19} +(0.203360 + 8.15448i) q^{20} +(-0.698731 + 3.37652i) q^{21} +(-2.56795 - 9.12703i) q^{22} +(3.24111 - 6.32202i) q^{23} +(-0.940550 - 13.3746i) q^{24} +(-1.58641 - 1.62647i) q^{25} +(2.57233 + 5.34149i) q^{26} +(4.10676 - 3.18348i) q^{27} -9.83163 q^{28} +(3.53606 + 4.06156i) q^{29} +(-5.50041 - 5.15084i) q^{30} +(4.11381 + 5.43099i) q^{31} +(11.7551 - 3.30738i) q^{32} +(5.46144 + 3.00674i) q^{33} +(-2.66910 - 5.20627i) q^{34} +(-2.41029 + 2.23642i) q^{35} +(11.2618 + 9.62741i) q^{36} +(-0.227123 + 0.0891393i) q^{37} +(9.69549 + 5.27988i) q^{38} +(-3.68956 - 1.25851i) q^{39} +(6.66672 - 10.9096i) q^{40} +(0.883220 + 2.42663i) q^{41} +(6.37164 - 6.47279i) q^{42} +(4.42786 + 10.5041i) q^{43} +(-5.23971 + 16.9867i) q^{44} +(4.95087 - 0.201527i) q^{45} +(-16.2068 + 9.35701i) q^{46} +(1.53441 - 7.59031i) q^{47} +(-8.78210 + 15.9518i) q^{48} +(2.00952 + 2.27706i) q^{49} +(1.18587 + 5.86617i) q^{50} +(3.67083 + 1.15079i) q^{51} +(1.38213 - 11.0292i) q^{52} +(-1.80849 + 7.92352i) q^{53} +(-13.6369 + 1.17509i) q^{54} +(2.57945 + 5.35629i) q^{55} +(12.9449 + 8.36070i) q^{56} +(-6.94643 + 2.10781i) q^{57} +(-2.01986 - 14.0407i) q^{58} +(0.184823 - 1.04818i) q^{59} +(3.42337 + 13.7074i) q^{60} +(9.38628 + 4.23525i) q^{61} +(-1.34117 - 17.8966i) q^{62} +(0.0940557 + 5.97147i) q^{63} +(-10.6455 - 3.28369i) q^{64} +(-2.16998 - 3.01826i) q^{65} +(-7.78771 - 14.4583i) q^{66} +(-1.75605 + 5.22660i) q^{67} +(-1.09217 + 10.9146i) q^{68} +(3.09113 - 11.9106i) q^{69} +(8.52951 - 1.50398i) q^{70} +(4.44349 - 0.669748i) q^{71} +(-6.64094 - 22.2529i) q^{72} +(-7.24908 - 7.81265i) q^{73} +(0.629959 + 0.127349i) q^{74} +(-3.29589 - 2.15022i) q^{75} +(-9.89913 - 18.1779i) q^{76} +(-6.53142 + 2.94709i) q^{77} +(6.36547 + 8.05767i) q^{78} +(-2.33818 - 3.82626i) q^{79} +(-15.6447 + 7.53409i) q^{80} +(5.73970 - 6.93223i) q^{81} +(1.51365 - 6.63175i) q^{82} +(3.17110 + 3.25117i) q^{83} +(-16.6191 + 3.71301i) q^{84} +(2.21502 + 2.92423i) q^{85} +(5.21417 - 29.5710i) q^{86} +(7.51117 + 5.53014i) q^{87} +(21.3442 - 17.9099i) q^{88} +(-3.18520 - 10.3262i) q^{89} +(-11.2430 - 6.62957i) q^{90} +(3.70198 - 2.52397i) q^{91} +(35.0429 + 1.74892i) q^{92} +(9.00496 + 7.62679i) q^{93} +(-14.2429 + 14.6025i) q^{94} +(-6.56179 - 2.20464i) q^{95} +(18.6215 - 10.0302i) q^{96} +(-6.84193 - 1.92502i) q^{97} +(-1.19231 - 7.91044i) q^{98} +(10.3674 + 3.01995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3168 q - 42 q^{2} - 42 q^{3} - 30 q^{4} - 30 q^{5} - 60 q^{6} - 30 q^{7} - 21 q^{8} - 42 q^{9} - 21 q^{10} - 42 q^{11} - 30 q^{13} - 42 q^{14} - 42 q^{15} - 18 q^{16} - 189 q^{18} - 21 q^{19} + 24 q^{20}+ \cdots - 21 q^{98}+O(q^{100}) \) 3168 * q - 42 * q^2 - 42 * q^3 - 30 * q^4 - 30 * q^5 - 60 * q^6 - 30 * q^7 - 21 * q^8 - 42 * q^9 - 21 * q^10 - 42 * q^11 - 30 * q^13 - 42 * q^14 - 42 * q^15 - 18 * q^16 - 189 * q^18 - 21 * q^19 + 24 * q^20 - 42 * q^21 - 30 * q^22 + 60 * q^23 + 60 * q^24 - 30 * q^25 - 84 * q^26 - 168 * q^27 - 144 * q^28 - 72 * q^29 - 54 * q^30 - 42 * q^31 - 42 * q^32 + 60 * q^33 - 60 * q^34 - 45 * q^35 + 60 * q^36 - 21 * q^37 - 42 * q^39 - 42 * q^40 - 30 * q^42 - 42 * q^43 - 21 * q^44 + 12 * q^45 - 42 * q^47 - 105 * q^48 - 120 * q^49 - 42 * q^50 - 57 * q^51 - 132 * q^53 - 12 * q^54 - 84 * q^55 - 126 * q^56 - 36 * q^57 - 63 * q^58 - 66 * q^59 - 42 * q^60 - 42 * q^61 + 3 * q^62 + 150 * q^63 - 237 * q^64 + 66 * q^65 - 42 * q^66 - 30 * q^67 - 126 * q^68 - 42 * q^69 - 111 * q^71 - 42 * q^72 - 21 * q^73 + 270 * q^74 - 42 * q^76 - 42 * q^77 - 66 * q^78 - 42 * q^79 - 246 * q^80 - 42 * q^81 - 60 * q^82 - 228 * q^83 - 168 * q^84 - 147 * q^85 + 36 * q^86 + 39 * q^87 - 12 * q^88 - 21 * q^89 - 42 * q^90 - 15 * q^91 + 120 * q^92 - 24 * q^93 + 96 * q^94 - 210 * q^95 - 258 * q^96 - 42 * q^97 - 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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