LMFDB - Embedded newform 770.2.bi.a.27.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(27,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 10, 8]))

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

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

chi := DirichletCharacter("770.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bi (of order $20$, degree $8$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$48$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.6
Character	$\chi$	$=$	770.27
Dual form			770.2.bi.a.713.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.355652 - 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.77729 + 1.35692i) q^{5} +(2.16222 + 0.702547i) q^{6} +(2.50760 - 0.843757i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.355652 - 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.77729 + 1.35692i) q^{5} +(2.16222 + 0.702547i) q^{6} +(2.50760 - 0.843757i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +(-0.402154 - 2.19961i) q^{10} +(3.25893 - 0.615938i) q^{11} +(-1.60760 + 1.60760i) q^{12} +(-1.70240 + 3.34115i) q^{13} +(-0.386635 + 2.61735i) q^{14} +(3.67906 + 3.50831i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.00301 + 1.96852i) q^{17} +(0.339267 - 2.14205i) q^{18} +(-1.06821 - 0.776101i) q^{19} +(2.14244 + 0.640279i) q^{20} +(-2.78649 - 5.33074i) q^{21} +(-0.930718 + 3.18336i) q^{22} +(5.27438 - 5.27438i) q^{23} +(-0.702547 - 2.16222i) q^{24} +(1.31752 - 4.82329i) q^{25} +(-2.20411 - 3.03370i) q^{26} +(-0.857967 - 1.68385i) q^{27} +(-2.15655 - 1.53275i) q^{28} +(2.67785 + 3.68574i) q^{29} +(-4.79619 + 1.68533i) q^{30} +(4.48012 - 1.45568i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.54213 - 7.09886i) q^{33} -2.20932 q^{34} +(-3.31183 + 4.90223i) q^{35} +(1.75456 + 1.27476i) q^{36} +(-10.5411 - 1.66954i) q^{37} +(1.17647 - 0.599441i) q^{38} +(8.10802 + 2.63445i) q^{39} +(-1.54314 + 1.61825i) q^{40} +(3.61181 - 4.97123i) q^{41} +(6.01476 - 0.0626770i) q^{42} +(4.46086 - 4.46086i) q^{43} +(-2.41385 - 2.27449i) q^{44} +(2.75646 - 3.98990i) q^{45} +(2.30499 + 7.09402i) q^{46} +(2.46747 - 0.390810i) q^{47} +(2.24550 + 0.355652i) q^{48} +(5.57615 - 4.23162i) q^{49} +(3.69944 + 3.36365i) q^{50} +(4.06359 - 2.95237i) q^{51} +(3.70370 - 0.586608i) q^{52} +(-3.08166 - 1.57019i) q^{53} +1.88983 q^{54} +(-4.95628 + 5.51682i) q^{55} +(2.34474 - 1.22564i) q^{56} +(-1.36282 + 2.67469i) q^{57} +(-4.49974 + 0.712688i) q^{58} +(10.0708 - 7.31690i) q^{59} +(0.675782 - 5.03856i) q^{60} +(2.86642 + 0.931357i) q^{61} +(-0.736912 + 4.65268i) q^{62} +(-4.60673 + 3.42089i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-1.50802 - 8.24823i) q^{65} +(7.47924 + 0.957759i) q^{66} +(-7.09875 - 7.09875i) q^{67} +(1.00301 - 1.96852i) q^{68} +(-13.7195 - 9.96777i) q^{69} +(-2.86438 - 5.17642i) q^{70} +(-0.538759 + 1.65813i) q^{71} +(-1.93237 + 0.984592i) q^{72} +(2.99166 + 0.473832i) q^{73} +(6.27312 - 8.63421i) q^{74} +(-11.2993 - 1.24308i) q^{75} +1.32038i q^{76} +(7.65240 - 4.29427i) q^{77} +(-6.02828 + 6.02828i) q^{78} +(-8.50897 + 2.76473i) q^{79} +(-0.741297 - 2.10962i) q^{80} +(-8.73963 + 6.34971i) q^{81} +(2.78967 + 5.47503i) q^{82} +(12.5881 - 6.41398i) q^{83} +(-2.67480 + 5.38764i) q^{84} +(-4.45377 - 2.13762i) q^{85} +(1.94947 + 5.99984i) q^{86} +(7.32394 - 7.32394i) q^{87} +(3.12245 - 1.11816i) q^{88} +14.2547 q^{89} +(2.30362 + 4.26740i) q^{90} +(-1.44983 + 9.81470i) q^{91} +(-7.36727 - 1.16686i) q^{92} +(-4.86209 - 9.54238i) q^{93} +(-0.771996 + 2.37596i) q^{94} +(2.95163 - 0.0701237i) q^{95} +(-1.33632 + 1.83929i) q^{96} +(-0.802798 - 0.409046i) q^{97} +(1.23888 + 6.88950i) q^{98} +(-6.30909 + 3.45451i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 4 q^{7}+O(q^{10}) $ 384 * q - 4 * q^7	$ 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) $ 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.355652	−	2.24550i	−0.205336	−	1.29644i	−0.847879	−	0.530190i	$-0.822121\pi$
$3$	−0.355652	−	2.24550i	−0.205336	−	1.29644i	0.642543	−	0.766249i	$-0.277879\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−1.77729	+	1.35692i	−0.794828	+	0.606834i
$5$	−1.77729	+	1.35692i	−0.794828	+	0.606834i
$6$	2.16222	+	0.702547i	0.882721	+	0.286813i
$7$	2.50760	−	0.843757i	0.947785	−	0.318910i
$7$	2.50760	−	0.843757i	0.947785	−	0.318910i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−2.06261	+	0.670181i	−0.687535	+	0.223394i
$10$	−0.402154	−	2.19961i	−0.127172	−	0.695577i
$11$	3.25893	−	0.615938i	0.982604	−	0.185712i
$11$	3.25893	−	0.615938i	0.982604	−	0.185712i
$12$	−1.60760	+	1.60760i	−0.464074	+	0.464074i
$13$	−1.70240	+	3.34115i	−0.472161	+	0.926669i	0.524980	+	0.851114i	$0.324073\pi$
$13$	−1.70240	+	3.34115i	−0.472161	+	0.926669i	−0.997142	+	0.0755546i	$0.975927\pi$
$14$	−0.386635	+	2.61735i	−0.103333	+	0.699516i
$15$	3.67906	+	3.50831i	0.949930	+	0.905842i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	1.00301	+	1.96852i	0.243266	+	0.477437i	0.980065	−	0.198675i	$-0.0636638\pi$
$17$	1.00301	+	1.96852i	0.243266	+	0.477437i	−0.736799	+	0.676111i	$0.763664\pi$
$18$	0.339267	−	2.14205i	0.0799661	−	0.504886i
$19$	−1.06821	−	0.776101i	−0.245064	−	0.178050i	0.458472	−	0.888709i	$-0.348397\pi$
$19$	−1.06821	−	0.776101i	−0.245064	−	0.178050i	−0.703537	+	0.710659i	$0.748397\pi$
$20$	2.14244	+	0.640279i	0.479064	+	0.143171i
$21$	−2.78649	−	5.33074i	−0.608062	−	1.16326i
$22$	−0.930718	+	3.18336i	−0.198430	+	0.678694i
$23$	5.27438	−	5.27438i	1.09978	−	1.09978i	0.105349	−	0.994435i	$-0.466404\pi$
$23$	5.27438	−	5.27438i	1.09978	−	1.09978i	0.994435	−	0.105349i	$-0.0335959\pi$
$24$	−0.702547	−	2.16222i	−0.143407	−	0.441361i
$25$	1.31752	−	4.82329i	0.263504	−	0.964658i
$26$	−2.20411	−	3.03370i	−0.432262	−	0.594958i
$27$	−0.857967	−	1.68385i	−0.165116	−	0.324058i
$28$	−2.15655	−	1.53275i	−0.407549	−	0.289662i
$29$	2.67785	+	3.68574i	0.497264	+	0.684425i	0.981707	−	0.190398i	$-0.0609778\pi$
$29$	2.67785	+	3.68574i	0.497264	+	0.684425i	−0.484443	+	0.874823i	$0.660978\pi$
$30$	−4.79619	+	1.68533i	−0.875660	+	0.307698i
$31$	4.48012	−	1.45568i	0.804653	−	0.261448i	0.122322	−	0.992491i	$-0.460966\pi$
$31$	4.48012	−	1.45568i	0.804653	−	0.261448i	0.682332	+	0.731043i	$0.260966\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.54213	−	7.09886i	−0.442529	−	1.23575i
$34$	−2.20932			−0.378896
$35$	−3.31183	+	4.90223i	−0.559801	+	0.828627i
$36$	1.75456	+	1.27476i	0.292426	+	0.212460i
$37$	−10.5411	−	1.66954i	−1.73294	−	0.274471i	−0.791383	−	0.611320i	$-0.790639\pi$
$37$	−10.5411	−	1.66954i	−1.73294	−	0.274471i	−0.941559	+	0.336849i	$0.890639\pi$
$38$	1.17647	−	0.599441i	0.190848	−	0.0972421i
$39$	8.10802	+	2.63445i	1.29832	+	0.421850i
$40$	−1.54314	+	1.61825i	−0.243992	+	0.255867i
$41$	3.61181	−	4.97123i	0.564070	−	0.776375i	−0.427767	−	0.903889i	$-0.640700\pi$
$41$	3.61181	−	4.97123i	0.564070	−	0.776375i	0.991837	+	0.127514i	$0.0406997\pi$
$42$	6.01476	−	0.0626770i	0.928098	−	0.00967128i
$43$	4.46086	−	4.46086i	0.680274	−	0.680274i	−0.279787	−	0.960062i	$-0.590264\pi$
$43$	4.46086	−	4.46086i	0.680274	−	0.680274i	0.960062	+	0.279787i	$0.0902640\pi$
$44$	−2.41385	−	2.27449i	−0.363902	−	0.342892i
$45$	2.75646	−	3.98990i	0.410909	−	0.594779i
$46$	2.30499	+	7.09402i	0.339852	+	1.04596i
$47$	2.46747	−	0.390810i	0.359918	−	0.0570054i	0.0261431	−	0.999658i	$-0.491677\pi$
$47$	2.46747	−	0.390810i	0.359918	−	0.0570054i	0.333775	+	0.942653i	$0.391677\pi$
$48$	2.24550	+	0.355652i	0.324110	+	0.0513339i
$49$	5.57615	−	4.23162i	0.796593	−	0.604517i
$50$	3.69944	+	3.36365i	0.523180	+	0.475692i
$51$	4.06359	−	2.95237i	0.569016	−	0.413414i
$52$	3.70370	−	0.586608i	0.513610	−	0.0813479i
$53$	−3.08166	−	1.57019i	−0.423299	−	0.215682i	0.229347	−	0.973345i	$-0.426341\pi$
$53$	−3.08166	−	1.57019i	−0.423299	−	0.215682i	−0.652646	+	0.757663i	$0.726341\pi$
$54$	1.88983			0.257174
$55$	−4.95628	+	5.51682i	−0.668305	+	0.743887i
$56$	2.34474	−	1.22564i	0.313329	−	0.163784i
$57$	−1.36282	+	2.67469i	−0.180510	+	0.354271i
$58$	−4.49974	+	0.712688i	−0.590844	+	0.0935806i
$59$	10.0708	−	7.31690i	1.31111	−	0.952579i	0.311115	−	0.950372i	$-0.399298\pi$
$59$	10.0708	−	7.31690i	1.31111	−	0.952579i	0.999998	−	0.00220683i	$-0.000702457\pi$
$60$	0.675782	−	5.03856i	0.0872431	−	0.650475i
$61$	2.86642	+	0.931357i	0.367008	+	0.119248i	0.486714	−	0.873561i	$-0.338195\pi$
$61$	2.86642	+	0.931357i	0.367008	+	0.119248i	−0.119706	+	0.992809i	$0.538195\pi$
$62$	−0.736912	+	4.65268i	−0.0935879	+	0.590891i
$63$	−4.60673	+	3.42089i	−0.580393	+	0.430991i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	−1.50802	−	8.24823i	−0.187047	−	1.02307i
$66$	7.47924	+	0.957759i	0.920630	+	0.117892i
$67$	−7.09875	−	7.09875i	−0.867250	−	0.867250i	0.124917	−	0.992167i	$-0.460134\pi$
$67$	−7.09875	−	7.09875i	−0.867250	−	0.867250i	−0.992167	+	0.124917i	$0.960134\pi$
$68$	1.00301	−	1.96852i	0.121633	−	0.238718i
$69$	−13.7195	−	9.96777i	−1.65163	−	1.19998i
$70$	−2.86438	−	5.17642i	−0.342359	−	0.618701i
$71$	−0.538759	+	1.65813i	−0.0639389	+	0.196784i	−0.977923	−	0.208967i	$-0.932990\pi$
$71$	−0.538759	+	1.65813i	−0.0639389	+	0.196784i	0.913984	+	0.405751i	$0.132990\pi$
$72$	−1.93237	+	0.984592i	−0.227732	+	0.116035i
$73$	2.99166	+	0.473832i	0.350147	+	0.0554578i	0.329031	−	0.944319i	$-0.393278\pi$
$73$	2.99166	+	0.473832i	0.350147	+	0.0554578i	0.0211162	+	0.999777i	$0.493278\pi$
$74$	6.27312	−	8.63421i	0.729235	−	1.00371i
$75$	−11.2993	−	1.24308i	−1.30473	−	0.143538i
$76$			1.32038i			0.151458i
$77$	7.65240	−	4.29427i	0.872072	−	0.489378i
$78$	−6.02828	+	6.02828i	−0.682568	+	0.682568i
$79$	−8.50897	+	2.76473i	−0.957334	+	0.311057i	−0.745692	−	0.666291i	$-0.767881\pi$
$79$	−8.50897	+	2.76473i	−0.957334	+	0.311057i	−0.211642	+	0.977347i	$0.567881\pi$
$80$	−0.741297	−	2.10962i	−0.0828796	−	0.235862i
$81$	−8.73963	+	6.34971i	−0.971070	+	0.705523i
$82$	2.78967	+	5.47503i	0.308067	+	0.604616i
$83$	12.5881	−	6.41398i	1.38173	−	0.704026i	0.404169	−	0.914684i	$-0.367561\pi$
$83$	12.5881	−	6.41398i	1.38173	−	0.704026i	0.977560	+	0.210658i	$0.0675608\pi$
$84$	−2.67480	+	5.38764i	−0.291844	+	0.587840i
$85$	−4.45377	−	2.13762i	−0.483080	−	0.231858i
$86$	1.94947	+	5.99984i	0.210216	+	0.646979i
$87$	7.32394	−	7.32394i	0.785209	−	0.785209i
$88$	3.12245	−	1.11816i	0.332855	−	0.119197i
$89$	14.2547			1.51099			0.755496	−	0.655153i	$-0.227396\pi$
$89$	14.2547			1.51099			0.755496	+	0.655153i	$0.227396\pi$
$90$	2.30362	+	4.26740i	0.242823	+	0.449824i
$91$	−1.44983	+	9.81470i	−0.151983	+	1.02886i
$92$	−7.36727	−	1.16686i	−0.768090	−	0.121654i
$93$	−4.86209	−	9.54238i	−0.504175	−	0.989499i
$94$	−0.771996	+	2.37596i	−0.0796253	+	0.245061i
$95$	2.95163	−	0.0701237i	0.302831	−	0.00719454i
$96$	−1.33632	+	1.83929i	−0.136388	+	0.187722i
$97$	−0.802798	−	0.409046i	−0.0815118	−	0.0415323i	0.412759	−	0.910840i	$-0.364565\pi$
$97$	−0.802798	−	0.409046i	−0.0815118	−	0.0415323i	−0.494271	+	0.869308i	$0.664565\pi$
$98$	1.23888	+	6.88950i	0.125146	+	0.695944i
$99$	−6.30909	+	3.45451i	−0.634088	+	0.347191i
$100$	−4.67654	+	1.76916i	−0.467654	+	0.176916i
$101$	−5.08501	+	1.65222i	−0.505977	+	0.164402i	−0.550872	−	0.834590i	$-0.685705\pi$
$101$	−5.08501	+	1.65222i	−0.505977	+	0.164402i	0.0448947	+	0.998992i	$0.485705\pi$
$102$	0.785750	+	4.96103i	0.0778009	+	0.491215i
$103$	−15.4800	−	2.45178i	−1.52529	−	0.241581i	−0.663238	−	0.748409i	$-0.730818\pi$
$103$	−15.4800	−	2.45178i	−1.52529	−	0.241581i	−0.862047	+	0.506827i	$0.830818\pi$
$104$	−1.15877	+	3.56633i	−0.113627	+	0.349708i
$105$	12.1858	+	5.69321i	1.18921	+	0.555601i
$106$	2.79809	−	2.03293i	0.271775	−	0.197456i
$107$	1.74338	+	11.0073i	0.168539	+	1.06411i	0.916401	+	0.400261i	$0.131080\pi$
$107$	1.74338	+	11.0073i	0.168539	+	1.06411i	−0.747862	+	0.663854i	$0.768920\pi$
$108$	−0.857967	+	1.68385i	−0.0825579	+	0.162029i
$109$			14.2651i			1.36635i	0.730254	+	0.683175i	$0.239401\pi$
$109$			14.2651i			1.36635i	−0.730254	+	0.683175i	$0.760599\pi$
$110$	−2.66541	−	6.92066i	−0.254137	−	0.659859i
$111$			24.2637i			2.30301i
$112$	0.0275687	+	2.64561i	0.00260499	+	0.249986i
$113$	2.37812	−	0.376657i	0.223714	−	0.0354329i	−0.0435708	−	0.999050i	$-0.513873\pi$
$113$	2.37812	−	0.376657i	0.223714	−	0.0354329i	0.267285	+	0.963617i	$0.413873\pi$
$114$	−1.76446	−	2.42857i	−0.165256	−	0.227456i
$115$	−2.21718	+	16.5310i	−0.206753	+	1.54153i
$116$	1.40783	−	4.33285i	0.130714	−	0.402295i
$117$	1.27221	−	8.03240i	0.117616	−	0.742595i
$118$	1.94734	+	12.2950i	0.179267	+	1.13185i
$119$	4.17611	+	4.08997i	0.382823	+	0.374927i
$120$	4.18259	+	2.88958i	0.381816	+	0.263782i
$121$	10.2412	−	4.01460i	0.931022	−	0.364963i
$122$	−2.13117	+	2.13117i	−0.192947	+	0.192947i
$123$	−12.4474	−	6.34228i	−1.12235	−	0.571864i
$124$	−3.81102	−	2.76887i	−0.342239	−	0.248651i
$125$	4.20322	+	10.3602i	0.375947	+	0.926641i
$126$	−0.956622	−	5.65767i	−0.0852227	−	0.504025i
$127$	12.8210	−	6.53263i	1.13768	−	0.579677i	0.219410	−	0.975633i	$-0.429587\pi$
$127$	12.8210	−	6.53263i	1.13768	−	0.579677i	0.918269	+	0.395956i	$0.129587\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−11.6034	−	8.43034i	−1.02162	−	0.742250i
$130$	8.03385	+	2.40096i	0.704615	+	0.210578i
$131$			13.8360i			1.20886i	0.796659	+	0.604429i	$0.206599\pi$
$131$			13.8360i			1.20886i	−0.796659	+	0.604429i	$0.793401\pi$
$132$	−4.24887	+	6.22923i	−0.369817	+	0.542185i
$133$	−3.33349	−	1.04484i	−0.289050	−	0.0905993i
$134$	9.54780	−	3.10227i	0.824804	−	0.267995i
$135$	3.80972	+	1.82850i	0.327888	+	0.157373i
$136$	1.29861	+	1.78738i	0.111355	+	0.153267i
$137$	−9.12611	+	4.64999i	−0.779697	+	0.397275i	−0.798077	−	0.602556i	$-0.794149\pi$
$137$	−9.12611	+	4.64999i	−0.779697	+	0.397275i	0.0183802	+	0.999831i	$0.494149\pi$
$138$	15.1098	−	7.69885i	1.28624	−	0.655370i
$139$	−12.3649	+	8.98366i	−1.04878	+	0.761984i	−0.971980	−	0.235062i	$-0.924471\pi$
$139$	−12.3649	+	8.98366i	−1.04878	+	0.761984i	−0.0768009	+	0.997046i	$0.524471\pi$
$140$	5.91263	−	0.202133i	0.499708	−	0.0170833i
$141$	−1.75512	−	5.40172i	−0.147808	−	0.454907i
$142$	−1.23281	−	1.23281i	−0.103455	−	0.103455i
$143$	−3.49007	+	11.9372i	−0.291854	+	0.998235i
$144$		−	2.16875i		−	0.180729i
$145$	−9.76058	−	2.91700i	−0.810572	−	0.242244i
$146$	−1.78037	+	2.45047i	−0.147345	+	0.202802i
$147$	−11.4853	−	11.0162i	−0.947288	−	0.908605i
$148$	4.84520	+	9.50924i	0.398273	+	0.781655i
$149$	18.5619	+	6.03113i	1.52065	+	0.494089i	0.945961	−	0.324282i	$-0.105123\pi$
$149$	18.5619	+	6.03113i	1.52065	+	0.494089i	0.574690	+	0.818371i	$0.305123\pi$
$150$	6.23735	−	9.50338i	0.509278	−	0.775948i
$151$	−2.32500	−	1.68921i	−0.189206	−	0.137466i	0.489150	−	0.872200i	$-0.337307\pi$
$151$	−2.32500	−	1.68921i	−0.189206	−	0.137466i	−0.678356	+	0.734734i	$0.737307\pi$
$152$	−1.17647	−	0.599441i	−0.0954242	−	0.0486211i
$153$	−3.38808	−	3.38808i	−0.273910	−	0.273910i
$154$	0.352109	+	8.76790i	0.0283737	+	0.706537i
$155$	−5.98723	+	8.66634i	−0.480906	+	0.696097i
$156$	−2.63445	−	8.10802i	−0.210925	−	0.649161i
$157$	−2.53240	+	0.401092i	−0.202107	+	0.0320107i	−0.256667	−	0.966500i	$-0.582624\pi$
$157$	−2.53240	+	0.401092i	−0.202107	+	0.0320107i	0.0545599	+	0.998511i	$0.482624\pi$
$158$	1.39960	−	8.83671i	0.111346	−	0.703011i
$159$	−2.42985	+	7.47831i	−0.192700	+	0.593069i
$160$	2.21622	+	0.297245i	0.175208	+	0.0234992i
$161$	8.77576	−	17.6763i	0.691626	−	1.39309i
$162$	−1.68993	−	10.6698i	−0.132773	−	0.838296i
$163$	0.638438	+	0.325300i	0.0500063	+	0.0254795i	0.478815	−	0.877916i	$-0.341067\pi$
$163$	0.638438	+	0.325300i	0.0500063	+	0.0254795i	−0.428809	+	0.903395i	$0.641067\pi$
$164$	−6.14477			−0.479826
$165$	14.1507	+	9.16726i	1.10163	+	0.713670i
$166$			14.1280i			1.09655i
$167$	−18.5659	−	9.45979i	−1.43667	−	0.732020i	−0.449739	−	0.893160i	$-0.648483\pi$
$167$	−18.5659	−	9.45979i	−1.43667	−	0.732020i	−0.986932	+	0.161140i	$0.948483\pi$
$168$	−3.58609	−	4.82920i	−0.276673	−	0.372581i
$169$	−0.623920	−	0.858753i	−0.0479939	−	0.0660579i
$170$	3.92661	−	2.99788i	0.301157	−	0.229927i
$171$	2.72343	+	0.884895i	0.208266	+	0.0676696i
$172$	−6.23094	−	0.986883i	−0.475104	−	0.0752492i
$173$	−0.208321	−	1.31529i	−0.0158383	−	0.0999994i	0.978503	−	0.206234i	$-0.0661207\pi$
$173$	−0.208321	−	1.31529i	−0.0158383	−	0.0999994i	−0.994341	+	0.106234i	$0.966121\pi$
$174$	3.20068	+	9.85068i	0.242643	+	0.746778i
$175$	−0.765867	−	13.2066i	−0.0578941	−	0.998323i
$176$	−0.421273	+	3.28976i	−0.0317546	+	0.247975i
$177$	−20.0118	−	20.0118i	−1.50418	−	1.50418i
$178$	−6.47149	+	12.7010i	−0.485058	+	0.951981i
$179$	−10.4410	+	14.3709i	−0.780401	+	1.07413i	0.214837	+	0.976650i	$0.431078\pi$
$179$	−10.4410	+	14.3709i	−0.780401	+	1.07413i	−0.995238	+	0.0974793i	$0.968922\pi$
$180$	−4.84811	+	0.115179i	−0.361357	+	0.00858497i
$181$	10.5540	+	3.42920i	0.784471	+	0.254890i	0.673748	−	0.738961i	$-0.264683\pi$
$181$	10.5540	+	3.42920i	0.784471	+	0.254890i	0.110723	+	0.993851i	$0.464683\pi$
$182$	−8.08675	−	5.74759i	−0.599430	−	0.426040i
$183$	1.07191	−	6.76779i	0.0792380	−	0.500289i
$184$	4.38435	−	6.03454i	0.323218	−	0.444872i
$185$	21.0000	−	11.3362i	1.54395	−	0.833451i
$186$	10.7097			0.785271
$187$	4.48123	+	5.79748i	0.327700	+	0.423954i
$188$	−1.76652	−	1.76652i	−0.128836	−	0.128836i
$189$	−3.57221	−	3.49852i	−0.259840	−	0.254480i
$190$	−1.27753	+	2.66176i	−0.0926819	+	0.193104i
$191$	−2.32756	+	1.69107i	−0.168416	+	0.122362i	−0.668801	−	0.743442i	$-0.733192\pi$
$191$	−2.32756	+	1.69107i	−0.168416	+	0.122362i	0.500384	+	0.865803i	$0.333192\pi$
$192$	−1.03214	−	2.02569i	−0.0744885	−	0.146192i
$193$	−5.82405	−	11.4303i	−0.419225	−	0.822775i	−0.999962	−	0.00868384i	$-0.997236\pi$
$193$	−5.82405	−	11.4303i	−0.419225	−	0.822775i	0.580738	−	0.814091i	$-0.302764\pi$
$194$	0.728925	−	0.529595i	0.0523338	−	0.0380227i
$195$	−17.9850	+	6.31976i	−1.28794	+	0.452568i
$196$	−6.70103	−	2.02392i	−0.478645	−	0.144565i
$197$	−5.41938	−	5.41938i	−0.386114	−	0.386114i	0.487185	−	0.873299i	$-0.338024\pi$
$197$	−5.41938	−	5.41938i	−0.386114	−	0.386114i	−0.873299	+	0.487185i	$0.838024\pi$
$198$	−0.213722	−	7.18976i	−0.0151885	−	0.510954i
$199$	9.45633			0.670342			0.335171	−	0.942157i	$-0.391206\pi$
$199$	9.45633			0.670342			0.335171	+	0.942157i	$0.391206\pi$
$200$	0.546771	−	4.97001i	0.0386625	−	0.351433i
$201$	−13.4155	+	18.4649i	−0.946260	+	1.30241i
$202$	0.836407	−	5.28087i	0.0588494	−	0.371561i
$203$	9.82485	+	6.98292i	0.689569	+	0.490105i
$204$	−4.77703	−	1.55215i	−0.334459	−	0.108672i
$205$	0.326341	+	13.7363i	0.0227926	+	0.959382i
$206$	9.21231	−	12.6797i	0.641852	−	0.883433i
$207$	−7.34417	+	14.4138i	−0.510455	+	1.00182i
$208$	−2.65155	−	2.65155i	−0.183852	−	0.183852i
$209$	−3.95925	−	1.87131i	−0.273867	−	0.129441i
$210$	−10.6049	+	8.27296i	−0.731809	+	0.570888i
$211$	−5.52230	−	16.9959i	−0.380171	−	1.17005i	−0.939923	−	0.341385i	$-0.889104\pi$
$211$	−5.52230	−	16.9959i	−0.380171	−	1.17005i	0.559753	−	0.828660i	$-0.310896\pi$
$212$	0.541049	+	3.41605i	0.0371594	+	0.234615i
$213$	3.91494	+	0.620065i	0.268247	+	0.0424862i
$214$	−10.5990	−	3.44384i	−0.724536	−	0.235416i
$215$	−1.87520	+	13.9813i	−0.127888	+	0.953515i
$216$	−1.11082	−	1.52891i	−0.0755815	−	0.104029i
$217$	10.0061	−	7.43040i	0.679260	−	0.504408i
$218$	−12.7103	−	6.47623i	−0.860851	−	0.438626i
$219$		−	6.88628i		−	0.465332i
$220$	7.37643	+	0.767014i	0.497319	+	0.0517120i
$221$	−8.28466			−0.557287
$222$	−21.6192	−	11.0155i	−1.45098	−	0.739312i
$223$	2.67758	+	16.9056i	0.179304	+	1.13208i	0.899051	+	0.437844i	$0.144258\pi$
$223$	2.67758	+	16.9056i	0.179304	+	1.13208i	−0.719747	+	0.694237i	$0.755742\pi$
$224$	−2.36977	−	1.17652i	−0.158337	−	0.0786093i
$225$	0.514953	+	10.8315i	0.0343302	+	0.722102i
$226$	−0.744039	+	2.28992i	−0.0494927	+	0.152323i
$227$	4.25095	−	26.8395i	0.282146	−	1.78140i	−0.285757	−	0.958302i	$-0.592245\pi$
$227$	4.25095	−	26.8395i	0.282146	−	1.78140i	0.567902	−	0.823096i	$-0.307755\pi$
$228$	2.96491	−	0.469596i	0.196356	−	0.0310998i
$229$	6.20030	+	19.0826i	0.409727	+	1.26101i	0.916883	+	0.399156i	$0.130697\pi$
$229$	6.20030	+	19.0826i	0.409727	+	1.26101i	−0.507156	+	0.861855i	$0.669303\pi$
$230$	−13.7227	−	9.48045i	−0.904847	−	0.625122i
$231$	−12.3644	−	15.6562i	−0.813516	−	1.03010i
$232$	3.22146	+	3.22146i	0.211499	+	0.211499i
$233$	9.35155	+	4.76485i	0.612641	+	0.312156i	0.732638	−	0.680618i	$-0.238289\pi$
$233$	9.35155	+	4.76485i	0.612641	+	0.312156i	−0.119998	+	0.992774i	$0.538289\pi$
$234$	6.57935	+	4.78018i	0.430105	+	0.312490i
$235$	−3.85512	+	4.04275i	−0.251480	+	0.263720i
$236$	−11.8390	−	3.84672i	−0.770653	−	0.250400i
$237$	9.23443	+	18.1236i	0.599841	+	1.17725i
$238$	−5.54011	+	1.86413i	−0.359112	+	0.120834i
$239$	2.41807	−	3.32818i	0.156412	−	0.215282i	−0.723618	−	0.690200i	$-0.757522\pi$
$239$	2.41807	−	3.32818i	0.156412	−	0.215282i	0.880030	+	0.474918i	$0.157522\pi$
$240$	−4.47349	+	2.41487i	−0.288763	+	0.155879i
$241$		−	12.5326i		−	0.807298i	−0.914914	−	0.403649i	$-0.867742\pi$
$241$		−	12.5326i		−	0.807298i	0.914914	−	0.403649i	$-0.132258\pi$
$242$	−1.07239	+	10.9476i	−0.0689361	+	0.703738i
$243$	13.3576	+	13.3576i	0.856889	+	0.856889i
$244$	−0.931357	−	2.86642i	−0.0596241	−	0.183504i
$245$	−4.16846	+	15.0872i	−0.266313	+	0.963887i
$246$	11.3020	−	8.21140i	0.720591	−	0.523540i
$247$	4.41160	−	2.24782i	0.280703	−	0.143025i
$248$	4.19724	−	2.13860i	0.266525	−	0.135801i
$249$	−18.8796	−	25.9855i	−1.19645	−	1.64677i
$250$	−11.1392	−	0.958321i	−0.704504	−	0.0606096i
$251$	−5.14466	+	1.67160i	−0.324728	+	0.105511i	−0.466845	−	0.884339i	$-0.654609\pi$
$251$	−5.14466	+	1.67160i	−0.324728	+	0.105511i	0.142116	+	0.989850i	$0.454609\pi$
$252$	5.47532	+	1.71617i	0.344913	+	0.108109i
$253$	13.9401	−	20.4375i	0.876409	−	1.28490i
$254$			14.3893i			0.902868i
$255$	−3.21604	+	10.7612i	−0.201396	+	0.673892i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.92289	+	18.4544i	−0.182325	+	1.15115i	0.711483	+	0.702703i	$0.248024\pi$
$257$	−2.92289	+	18.4544i	−0.182325	+	1.15115i	−0.893808	+	0.448450i	$0.851976\pi$
$258$	12.7793	−	6.51138i	0.795605	−	0.405381i
$259$	−27.8415	+	4.70756i	−1.72999	+	0.292513i
$260$	−5.78656	+	6.06820i	−0.358867	+	0.376334i
$261$	−7.99346	−	5.80759i	−0.494783	−	0.359481i
$262$	−12.3280	−	6.28142i	−0.761625	−	0.388067i
$263$	−8.73314	+	8.73314i	−0.538509	+	0.538509i	−0.923091	−	0.384582i	$-0.874346\pi$
$263$	−8.73314	+	8.73314i	−0.538509	+	0.538509i	0.384582	+	0.923091i	$0.374346\pi$
$264$	−3.62134	−	6.61378i	−0.222878	−	0.407050i
$265$	7.60764	−	1.39090i	0.467333	−	0.0854426i
$266$	2.44433	−	2.49581i	0.149872	−	0.153028i
$267$	−5.06970	−	32.0088i	−0.310261	−	1.95891i
$268$	−1.57047	+	9.91555i	−0.0959316	+	0.605689i
$269$	3.30063	−	10.1583i	0.201243	−	0.619361i	−0.798604	−	0.601857i	$-0.794428\pi$
$269$	3.30063	−	10.1583i	0.201243	−	0.619361i	0.999847	−	0.0175047i	$-0.00557220\pi$
$270$	−3.35878	+	2.56436i	−0.204409	+	0.156062i
$271$	−5.27285	−	7.25745i	−0.320303	−	0.440859i	0.618257	−	0.785976i	$-0.287839\pi$
$271$	−5.27285	−	7.25745i	−0.320303	−	0.440859i	−0.938560	+	0.345117i	$0.887839\pi$
$272$	−2.18212	+	0.345614i	−0.132311	+	0.0209559i
$273$	22.5545	−	0.235030i	1.36506	−	0.0142247i
$274$		−	10.2425i		−	0.618771i
$275$	1.32286	−	16.5303i	0.0797714	−	0.996813i
$276$			16.9582i			1.02076i
$277$	−3.62809	+	7.12052i	−0.217991	+	0.427831i	−0.973942	−	0.226797i	$-0.927175\pi$
$277$	−3.62809	+	7.12052i	−0.217991	+	0.427831i	0.755951	+	0.654628i	$0.227175\pi$
$278$	−2.39093	−	15.0957i	−0.143399	−	0.905383i
$279$	−8.26515	+	6.00498i	−0.494821	+	0.359509i
$280$	−2.50417	+	5.35995i	−0.149653	+	0.320319i
$281$	−4.08033	+	12.5579i	−0.243412	+	0.749144i	0.752482	+	0.658613i	$0.228857\pi$
$281$	−4.08033	+	12.5579i	−0.243412	+	0.749144i	−0.995894	+	0.0905314i	$0.971143\pi$
$282$	5.60977	+	0.888501i	0.334057	+	0.0529095i
$283$	1.42862	+	9.01995i	0.0849226	+	0.536180i	0.993069	+	0.117529i	$0.0374972\pi$
$283$	1.42862	+	9.01995i	0.0849226	+	0.536180i	−0.908147	+	0.418652i	$0.862503\pi$
$284$	1.65813	−	0.538759i	0.0983919	−	0.0319695i
$285$	−1.20722	−	6.60294i	−0.0715093	−	0.391124i
$286$	−9.05163	−	8.52903i	−0.535234	−	0.504332i
$287$	4.86247	−	15.5134i	0.287023	−	0.915724i
$288$	1.93237	+	0.984592i	0.113866	+	0.0580177i
$289$	7.12331	−	9.80439i	0.419018	−	0.576729i
$290$	7.03028	−	7.37245i	0.412832	−	0.432925i
$291$	−0.632995	+	1.94816i	−0.0371068	+	0.114203i
$292$	−1.37511	−	2.69881i	−0.0804724	−	0.157936i
$293$	−8.43221	−	1.33553i	−0.492615	−	0.0780225i	−0.0948152	−	0.995495i	$-0.530226\pi$
$293$	−8.43221	−	1.33553i	−0.492615	−	0.0780225i	−0.397799	+	0.917472i	$0.630226\pi$
$294$	15.0297	−	5.23217i	0.876553	−	0.305146i
$295$	−7.97035	+	26.6696i	−0.464052	+	1.55277i
$296$	−10.6725			−0.620325
$297$	−3.83320	−	4.95911i	−0.222425	−	0.287757i
$298$	−13.8007	+	13.8007i	−0.799453	+	0.799453i
$299$	8.64339	+	26.6016i	0.499860	+	1.53841i
$300$	5.63587	+	9.87197i	0.325387	+	0.569958i
$301$	7.42218	−	14.9499i	0.427807	−	0.861700i
$302$	2.56063	−	1.30470i	0.147348	−	0.0750773i
$303$	5.51855	+	10.8308i	0.317032	+	0.622211i
$304$	1.06821	−	0.776101i	0.0612661	−	0.0445124i
$305$	−6.35825	+	2.23422i	−0.364072	+	0.127931i
$306$	4.55696	−	1.48065i	0.260504	−	0.0846429i
$307$	−12.4274	+	12.4274i	−0.709272	+	0.709272i	−0.966382	−	0.257110i	$-0.917230\pi$
$307$	−12.4274	+	12.4274i	−0.709272	+	0.709272i	0.257110	+	0.966382i	$0.417230\pi$
$308$	−7.97211	−	3.66681i	−0.454253	−	0.208936i
$309$			35.6322i			2.02704i
$310$	−5.00362	−	9.26909i	−0.284187	−	0.526449i
$311$	12.9019	−	17.7580i	0.731602	−	1.00696i	−0.267456	−	0.963570i	$-0.586183\pi$
$311$	12.9019	−	17.7580i	0.731602	−	1.00696i	0.999058	−	0.0433934i	$-0.0138169\pi$
$312$	8.42031	+	1.33365i	0.476706	+	0.0755029i
$313$	11.9862	−	6.10725i	0.677498	−	0.345202i	−0.0811514	−	0.996702i	$-0.525860\pi$
$313$	11.9862	−	6.10725i	0.677498	−	0.345202i	0.758649	+	0.651499i	$0.225860\pi$
$314$	0.792309	−	2.43847i	0.0447126	−	0.137611i
$315$	3.54561	−	12.3309i	0.199772	−	0.694766i
$316$	7.23816	+	5.25883i	0.407178	+	0.295832i
$317$	−6.67856	+	13.1074i	−0.375105	+	0.736185i	−0.998971	−	0.0453460i	$-0.985561\pi$
$317$	−6.67856	+	13.1074i	−0.375105	+	0.736185i	0.623866	+	0.781531i	$0.285561\pi$
$318$	−5.56010	−	5.56010i	−0.311795	−	0.311795i
$319$	10.9971	+	10.3622i	0.615720	+	0.580171i
$320$	−1.27099	+	1.83972i	−0.0710506	+	0.102844i
$321$	24.0968	−	7.82953i	1.34495	−	0.437002i
$322$	11.7656	+	15.8441i	0.655673	+	0.882960i
$323$	0.456343	−	2.88123i	0.0253916	−	0.160316i
$324$	10.2740	+	3.33824i	0.570780	+	0.185458i
$325$	13.8724	+	12.6132i	0.769502	+	0.699656i
$326$	−0.579689	+	0.421169i	−0.0321060	+	0.0233264i
$327$	32.0323	−	5.07342i	1.77139	−	0.280561i
$328$	2.78967	−	5.47503i	0.154034	−	0.302308i
$329$	5.85770	−	3.06194i	0.322945	−	0.168810i
$330$	−14.5924	+	8.44653i	−0.803284	+	0.464966i
$331$	11.7363			0.645086			0.322543	−	0.946555i	$-0.395462\pi$
$331$	11.7363			0.645086			0.322543	+	0.946555i	$0.395462\pi$
$332$	−12.5881	−	6.41398i	−0.690864	−	0.352013i
$333$	22.8610	−	3.62082i	1.25277	−	0.198420i
$334$	16.8575	−	12.2477i	0.922399	−	0.670162i
$335$	22.2490	+	2.98408i	1.21559	+	0.163038i
$336$	5.93090	−	1.00282i	0.323557	−	0.0547084i
$337$	5.08535	+	0.805441i	0.277017	+	0.0438752i	0.293397	−	0.955991i	$-0.405214\pi$
$337$	5.08535	+	0.805441i	0.277017	+	0.0438752i	−0.0163802	+	0.999866i	$0.505214\pi$
$338$	1.04841	−	0.166052i	0.0570259	−	0.00903201i
$339$	−1.69156	−	5.20610i	−0.0918732	−	0.282757i
$340$	0.888489	+	4.85964i	0.0481851	+	0.263551i
$341$	13.7038	−	7.50343i	0.742101	−	0.406334i
$342$	−2.02486	+	2.02486i	−0.109492	+	0.109492i
$343$	10.4123	−	15.3161i	0.562212	−	0.826993i
$344$	3.70811	−	5.10377i	0.199928	−	0.275177i
$345$	37.9089	−	0.900626i	2.04095	−	0.0484881i
$346$	1.26650	+	0.411512i	0.0680877	+	0.0221230i
$347$	25.4525	−	12.9687i	1.36636	−	0.696196i	0.391745	−	0.920074i	$-0.371871\pi$
$347$	25.4525	−	12.9687i	1.36636	−	0.696196i	0.974617	+	0.223877i	$0.0718715\pi$
$348$	−10.2301	−	1.62029i	−0.548391	−	0.0868566i
$349$	−17.7813	−	12.9189i	−0.951812	−	0.691532i	−0.000577532	−	1.00000i	$-0.500184\pi$
$349$	−17.7813	−	12.9189i	−0.951812	−	0.691532i	−0.951235	+	0.308468i	$0.900184\pi$
$350$	12.1148	+	5.31326i	0.647565	+	0.284006i
$351$	7.08662			0.378256
$352$	−2.73995	−	1.86888i	−0.146040	−	0.0996115i
$353$	13.9970	+	13.9970i	0.744983	+	0.744983i	0.973532	−	0.228550i	$-0.0733983\pi$
$353$	13.9970	+	13.9970i	0.744983	+	0.744983i	−0.228550	+	0.973532i	$0.573398\pi$
$354$	26.9158	−	8.74548i	1.43056	−	0.464817i
$355$	−1.29242	−	3.67803i	−0.0685947	−	0.195210i
$356$	−8.37869	−	11.5323i	−0.444069	−	0.611209i
$357$	7.69878	−	10.8321i	0.407463	−	0.573293i
$358$	−8.06440	−	15.8273i	−0.426217	−	0.836498i
$359$	19.3895	+	26.6874i	1.02334	+	1.40851i	0.909835	+	0.414970i	$0.136208\pi$
$359$	19.3895	+	26.6874i	1.02334	+	1.40851i	0.113505	+	0.993537i	$0.463792\pi$
$360$	2.09837	−	4.37199i	0.110594	−	0.230424i
$361$	−5.33258	−	16.4120i	−0.280662	−	0.863789i
$362$	−7.84684	+	7.84684i	−0.412421	+	0.412421i
$363$	−12.6571	−	21.5689i	−0.664325	−	1.13207i
$364$	8.79245	−	4.59600i	0.460849	−	0.240896i
$365$	−5.96000	+	3.21731i	−0.311960	+	0.168402i
$366$	5.54351	+	4.02759i	0.289764	+	0.210526i
$367$	−4.07290	+	25.7153i	−0.212603	+	1.34233i	0.618315	+	0.785931i	$0.287816\pi$
$367$	−4.07290	+	25.7153i	−0.212603	+	1.34233i	−0.830918	+	0.556395i	$0.812184\pi$
$368$	3.38636	+	6.64611i	0.176526	+	0.346452i
$369$	−4.11811	+	12.6742i	−0.214380	+	0.659795i
$370$	0.566801	+	23.8576i	0.0294666	+	1.24030i
$371$	−9.05245	−	1.33723i	−0.469980	−	0.0694255i
$372$	−4.86209	+	9.54238i	−0.252088	+	0.494750i
$373$	8.16155	−	8.16155i	0.422589	−	0.422589i	−0.463505	−	0.886094i	$-0.653408\pi$
$373$	8.16155	−	8.16155i	0.422589	−	0.422589i	0.886094	+	0.463505i	$0.153408\pi$
$374$	−7.20003	+	1.36081i	−0.372305	+	0.0703656i
$375$	21.7688	−	13.1229i	1.12414	−	0.677665i
$376$	2.37596	−	0.771996i	0.122531	−	0.0398127i
$377$	−16.8734	+	2.67248i	−0.869024	+	0.137640i
$378$	4.73896	−	1.59456i	0.243746	−	0.0820154i
$379$	−30.1989	−	9.81223i	−1.55122	−	0.504021i	−0.596772	−	0.802411i	$-0.703550\pi$
$379$	−30.1989	−	9.81223i	−1.55122	−	0.504021i	−0.954444	+	0.298391i	$0.903550\pi$
$380$	−1.79166	−	2.34670i	−0.0919100	−	0.120383i
$381$	−19.2288	−	26.4662i	−0.985122	−	1.35590i
$382$	−0.450065	−	2.84160i	−0.0230274	−	0.145389i
$383$	−0.0984998	+	0.193317i	−0.00503310	+	0.00987802i	−0.893509	−	0.449045i	$-0.851764\pi$
$383$	−0.0984998	+	0.193317i	−0.00503310	+	0.00987802i	0.888476	+	0.458923i	$0.151764\pi$
$384$	2.27349			0.116018
$385$	−7.77354	+	18.0159i	−0.396176	+	0.918175i
$386$	12.8286			0.652958
$387$	−6.21141	+	12.1906i	−0.315744	+	0.619682i
$388$	0.140948	+	0.889908i	0.00715553	+	0.0451782i
$389$	7.77266	+	10.6982i	0.394090	+	0.542418i	0.959248	−	0.282564i	$-0.0911851\pi$
$389$	7.77266	+	10.6982i	0.394090	+	0.542418i	−0.565159	+	0.824982i	$0.691185\pi$
$390$	2.53409	−	18.8939i	0.128319	−	0.956730i
$391$	15.6730	+	5.09246i	0.792617	+	0.257537i
$392$	4.84553	−	5.05182i	0.244736	−	0.255155i
$393$	31.0688	−	4.92081i	1.56721	−	0.248222i
$394$	7.28904	−	2.36835i	0.367217	−	0.119316i
$395$	11.3714	−	16.4597i	0.572156	−	0.828180i
$396$	6.50315	+	3.07365i	0.326796	+	0.154457i
$397$	−15.2405	+	15.2405i	−0.764898	+	0.764898i	−0.977203	−	0.212306i	$-0.931903\pi$
$397$	−15.2405	+	15.2405i	−0.764898	+	0.764898i	0.212306	+	0.977203i	$0.431903\pi$
$398$	−4.29309	+	8.42565i	−0.215193	+	0.422340i
$399$	−1.16063	+	7.85695i	−0.0581041	+	0.393339i
$400$	4.18009	+	2.74352i	0.209004	+	0.137176i
$401$	−1.04993	+	3.23134i	−0.0524308	+	0.161366i	−0.973843	−	0.227220i	$-0.927036\pi$
$401$	−1.04993	+	3.23134i	−0.0524308	+	0.161366i	0.921413	+	0.388586i	$0.127036\pi$
$402$	−10.3618	−	20.3362i	−0.516801	−	1.01428i
$403$	−2.76332	+	17.4469i	−0.137651	+	0.869093i
$404$	4.32557	+	3.14271i	0.215205	+	0.156356i
$405$	6.91679	−	23.1443i	0.343698	−	1.15005i
$406$	−10.6822	+	5.58382i	−0.530150	+	0.277121i
$407$	−35.3809	+	1.05173i	−1.75377	+	0.0521323i
$408$	3.55171	−	3.55171i	0.175836	−	0.175836i
$409$	6.55498	+	20.1742i	0.324123	+	0.997548i	0.971835	+	0.235663i	$0.0757261\pi$
$409$	6.55498	+	20.1742i	0.324123	+	0.997548i	−0.647712	+	0.761885i	$0.724274\pi$
$410$	−12.3873	−	5.94536i	−0.611763	−	0.293620i
$411$	13.6873	+	18.8389i	0.675143	+	0.929254i
$412$	7.11535	+	13.9647i	0.350548	+	0.687990i
$413$	19.0800	−	26.8452i	0.938866	−	1.32097i
$414$	−9.50856	−	13.0874i	−0.467320	−	0.643211i
$415$	−13.6695	+	28.4806i	−0.671010	+	1.39806i
$416$	3.56633	−	1.15877i	0.174854	−	0.0568135i
$417$	24.5704	+	24.5704i	1.20322	+	1.20322i
$418$	3.46481	−	2.67817i	0.169469	−	0.130993i
$419$	−30.4673			−1.48843			−0.744214	−	0.667942i	$-0.767176\pi$
$419$	−30.4673			−1.48843			−0.744214	+	0.667942i	$0.767176\pi$
$420$	−2.55673	−	13.2049i	−0.124755	−	0.644333i
$421$	4.49476	+	3.26563i	0.219061	+	0.159157i	0.691904	−	0.721990i	$-0.256772\pi$
$421$	4.49476	+	3.26563i	0.219061	+	0.159157i	−0.472843	+	0.881147i	$0.656772\pi$
$422$	17.6505	+	2.79557i	0.859214	+	0.136086i
$423$	−4.82751	+	2.45974i	−0.234722	+	0.119597i
$424$	−3.28936	−	1.06878i	−0.159745	−	0.0519044i
$425$	10.8162	−	2.24425i	0.524665	−	0.108862i
$426$	−2.32983	+	3.20673i	−0.112881	+	0.155367i
$427$	7.97369	−	0.0830902i	0.385874	−	0.00402102i
$428$	7.88035	−	7.88035i	0.380911	−	0.380911i
$429$	28.0461	+	3.59146i	1.35408	+	0.173398i
$430$	−11.6061	−	8.01818i	−0.559695	−	0.386671i
$431$	−9.62443	−	29.6210i	−0.463592	−	1.42679i	−0.860744	−	0.509038i	$-0.830001\pi$
$431$	−9.62443	−	29.6210i	−0.463592	−	1.42679i	0.397152	−	0.917753i	$-0.369999\pi$
$432$	1.86657	−	0.295635i	0.0898053	−	0.0142238i
$433$	−15.4202	−	2.44232i	−0.741048	−	0.117370i	−0.225514	−	0.974240i	$-0.572406\pi$
$433$	−15.4202	−	2.44232i	−0.741048	−	0.117370i	−0.515534	+	0.856869i	$0.672406\pi$
$434$	2.07785	+	12.2888i	0.0997399	+	0.589884i
$435$	−3.07875	+	22.9548i	−0.147615	+	1.10060i
$436$	11.5407	−	8.38483i	0.552700	−	0.401560i
$437$	−9.72760	+	1.54070i	−0.465334	+	0.0737017i
$438$	6.13572	+	3.12631i	0.293176	+	0.149381i
$439$	8.21650			0.392152			0.196076	−	0.980589i	$-0.437180\pi$
$439$	8.21650			0.392152			0.196076	+	0.980589i	$0.437180\pi$
$440$	−4.03224	+	6.22423i	−0.192230	+	0.296728i
$441$	−8.66544	+	12.4652i	−0.412640	+	0.593580i
$442$	3.76116	−	7.38169i	0.178900	−	0.351111i
$443$	−24.6688	+	3.90715i	−1.17205	+	0.185634i	−0.711948	−	0.702232i	$-0.752187\pi$
$443$	−24.6688	+	3.90715i	−1.17205	+	0.185634i	−0.460102	+	0.887866i	$0.652187\pi$
$444$	19.6298	−	14.2619i	0.931588	−	0.676838i
$445$	−25.3347	+	19.3425i	−1.20098	+	0.916922i
$446$	−16.2786	−	5.28923i	−0.770813	−	0.250452i
$447$	6.94131	−	43.8257i	0.328313	−	2.07289i
$448$	2.12414	−	1.57735i	0.100356	−	0.0745229i
$449$	−37.4247	+	12.1600i	−1.76618	+	0.573868i	−0.997811	−	0.0661353i	$-0.978933\pi$
$449$	−37.4247	+	12.1600i	−1.76618	+	0.573868i	−0.768372	+	0.640003i	$0.778933\pi$
$450$	−9.88474	−	4.45858i	−0.465971	−	0.210180i
$451$	8.70866	−	18.4255i	0.410075	−	0.867624i
$452$	−1.70254	−	1.70254i	−0.0800809	−	0.0800809i
$453$	−2.96623	+	5.82156i	−0.139366	+	0.273521i
$454$	21.9842	+	15.9725i	1.03177	+	0.749626i
$455$	−10.7410	−	19.4109i	−0.503547	−	0.909996i
$456$	−0.927630	+	2.85495i	−0.0434402	+	0.133695i
$457$	−29.0631	+	14.8084i	−1.35952	+	0.692708i	−0.973265	−	0.229686i	$-0.926230\pi$
$457$	−29.0631	+	14.8084i	−1.35952	+	0.692708i	−0.386251	+	0.922394i	$0.626230\pi$
$458$	−19.8176	−	3.13879i	−0.926014	−	0.146666i
$459$	2.45415	−	3.37785i	0.114550	−	0.157665i
$460$	14.6771	−	7.92296i	0.684324	−	0.369410i
$461$			11.8146i			0.550261i	0.961407	+	0.275130i	$0.0887210\pi$
$461$			11.8146i			0.550261i	−0.961407	+	0.275130i	$0.911279\pi$
$462$	19.5631	−	3.90898i	0.910156	−	0.181862i
$463$	−24.6801	+	24.6801i	−1.14698	+	1.14698i	−0.159840	+	0.987143i	$0.551098\pi$
$463$	−24.6801	+	24.6801i	−1.14698	+	1.14698i	−0.987143	+	0.159840i	$0.948902\pi$
$464$	−4.33285	+	1.40783i	−0.201147	+	0.0653568i
$465$	21.5896	+	10.3621i	1.00119	+	0.480531i
$466$	−8.49103	+	6.16910i	−0.393339	+	0.285778i
$467$	−10.0720	−	19.7673i	−0.466075	−	0.914723i	−0.997703	−	0.0677452i	$-0.978420\pi$
$467$	−10.0720	−	19.7673i	−0.466075	−	0.914723i	0.531628	−	0.846978i	$-0.321580\pi$
$468$	−7.24613	+	3.69209i	−0.334952	+	0.170667i
$469$	−23.7905	−	11.8112i	−1.09854	−	0.545392i
$470$	−1.85193	−	5.27031i	−0.0854233	−	0.243101i
$471$	1.80130	+	5.54385i	0.0829997	+	0.255447i
$472$	8.80224	−	8.80224i	0.405156	−	0.405156i
$473$	11.7900	−	17.2852i	0.542105	−	0.794776i
$474$	−20.3406			−0.934274
$475$	−5.15075	+	4.12976i	−0.236333	+	0.189487i
$476$	0.854202	−	5.78257i	0.0391523	−	0.265044i
$477$	7.40857	+	1.17340i	0.339215	+	0.0537264i
$478$	1.86765	+	3.66548i	0.0854245	+	0.167655i
$479$	5.06865	−	15.5997i	0.231593	−	0.712769i	−0.765962	−	0.642885i	$-0.777737\pi$
$479$	5.06865	−	15.5997i	0.231593	−	0.712769i	0.997555	−	0.0698837i	$-0.0222628\pi$
$480$	−0.120742	−	5.08224i	−0.00551109	−	0.231972i
$481$	23.5233	−	32.3771i	1.07257	−	1.47627i
$482$	11.1667	+	5.68970i	0.508627	+	0.259159i
$483$	−42.8133	−	13.4193i	−1.94807	−	0.610600i
$484$	−9.26753	−	5.92562i	−0.421251	−	0.269346i
$485$	1.98185	−	0.362341i	0.0899911	−	0.0164531i
$486$	−17.9659	+	5.83748i	−0.814950	+	0.264793i
$487$	−2.93405	−	18.5249i	−0.132954	−	0.839441i	−0.960548	−	0.278114i	$-0.910291\pi$
$487$	−2.93405	−	18.5249i	−0.132954	−	0.839441i	0.827594	−	0.561327i	$-0.189709\pi$
$488$	2.97683	+	0.471483i	0.134755	+	0.0213431i
$489$	0.503400	−	1.54930i	0.0227645	−	0.0700620i
$490$	−11.5504	−	10.5636i	−0.521792	−	0.477214i
$491$	7.68190	−	5.58123i	0.346679	−	0.251877i	−0.400795	−	0.916168i	$-0.631266\pi$
$491$	7.68190	−	5.58123i	0.346679	−	0.251877i	0.747475	+	0.664290i	$0.231266\pi$
$492$	2.18540	+	13.7981i	0.0985255	+	0.622066i
$493$	−4.56955	+	8.96824i	−0.205802	+	0.403909i
$494$			4.95125i			0.222767i
$495$	6.52559	−	14.7006i	0.293303	−	0.660744i
$496$			4.71068i			0.211516i
$497$	0.0480649	+	4.61251i	0.00215601	+	0.206900i
$498$	31.7244	−	5.02465i	1.42161	−	0.225160i
$499$	20.3783	+	28.0484i	0.912259	+	1.25562i	0.966389	+	0.257084i	$0.0827616\pi$
$499$	20.3783	+	28.0484i	0.912259	+	1.25562i	−0.0541297	+	0.998534i	$0.517238\pi$
$500$	5.91096	−	9.49002i	0.264346	−	0.424407i
$501$	−14.6389	+	45.0540i	−0.654020	+	2.01287i
$502$	0.846220	−	5.34282i	0.0377686	−	0.238462i
$503$	5.15210	+	32.5291i	0.229721	+	1.45040i	0.785393	+	0.618998i	$0.212461\pi$
$503$	5.15210	+	32.5291i	0.229721	+	1.45040i	−0.555672	+	0.831402i	$0.687539\pi$
$504$	−4.01486	+	4.09942i	−0.178836	+	0.182603i
$505$	6.79560	−	9.83644i	0.302400	−	0.437716i
$506$	11.8813	+	21.6992i	0.528187	+	0.964647i
$507$	−1.70643	+	1.70643i	−0.0757852	+	0.0757852i
$508$	−12.8210	−	6.53263i	−0.568840	−	0.289838i
$509$	−24.2814	−	17.6415i	−1.07625	−	0.781944i	−0.0992275	−	0.995065i	$-0.531637\pi$
$509$	−24.2814	−	17.6415i	−1.07625	−	0.781944i	−0.977026	+	0.213121i	$0.931637\pi$
$510$	−8.12824	−	7.75099i	−0.359925	−	0.343220i
$511$	7.90169	−	1.33605i	0.349550	−	0.0591033i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−0.390351	+	2.46458i	−0.0172344	+	0.108814i
$514$	−15.1160	−	10.9824i	−0.666739	−	0.484414i
$515$	30.8392	−	16.6476i	1.35894	−	0.733580i
$516$			14.3425i			0.631395i
$517$	7.80061	−	2.79343i	0.343070	−	0.122855i
$518$	8.44532	−	26.9442i	0.371066	−	1.18386i
$519$	−2.87938	+	0.935569i	−0.126391	+	0.0410669i
$520$	−2.77976	−	7.91077i	−0.121901	−	0.346910i
$521$	0.593964	+	0.817521i	0.0260220	+	0.0358162i	0.821830	−	0.569733i	$-0.192953\pi$
$521$	0.593964	+	0.817521i	0.0260220	+	0.0358162i	−0.795808	+	0.605549i	$0.792953\pi$
$522$	8.80355	−	4.48563i	0.385321	−	0.196331i
$523$	15.6062	−	7.95175i	0.682411	−	0.347706i	−0.0781779	−	0.996939i	$-0.524910\pi$
$523$	15.6062	−	7.95175i	0.682411	−	0.347706i	0.760589	+	0.649234i	$0.224910\pi$
$524$	11.1936	−	8.13261i	0.488994	−	0.355275i
$525$	−29.3829	+	6.41669i	−1.28238	+	0.280048i
$526$	−3.81652	−	11.7461i	−0.166408	−	0.512152i
$527$	7.35915	+	7.35915i	0.320569	+	0.320569i
$528$	7.53698	−	0.224043i	0.328005	−	0.00975023i
$529$		−	32.6382i		−	1.41905i
$530$	−2.21449	+	7.40991i	−0.0961913	+	0.321866i
$531$	−15.8685	+	21.8412i	−0.688636	+	0.947826i
$532$	1.11408	+	3.31099i	0.0483015	+	0.143550i
$533$	10.4609	+	20.5306i	0.453111	+	0.889280i
$534$	30.8217	+	10.0146i	1.33378	+	0.433373i
$535$	−18.0345	−	17.1975i	−0.779701	−	0.743513i
$536$	−8.12184	−	5.90086i	−0.350810	−	0.254878i
$537$	35.9831	+	18.3343i	1.55279	+	0.791185i
$538$	7.55264	+	7.55264i	0.325618	+	0.325618i
$539$	15.5659	−	17.2251i	0.670469	−	0.741938i
$540$	−0.760005	−	4.15689i	−0.0327054	−	0.178884i
$541$	5.87035	+	18.0671i	0.252386	+	0.776764i	0.994333	+	0.106306i	$0.0339024\pi$
$541$	5.87035	+	18.0671i	0.252386	+	0.776764i	−0.741947	+	0.670458i	$0.766098\pi$
$542$	8.86026	−	1.40333i	0.380581	−	0.0602780i
$543$	3.94671	−	24.9185i	0.169370	−	1.06936i
$544$	0.682718	−	2.10119i	0.0292713	−	0.0900878i
$545$	−19.3567	−	25.3533i	−0.829148	−	1.08601i
$546$	−10.0301	+	20.2029i	−0.429250	+	0.864606i
$547$	−2.06589	−	13.0435i	−0.0883309	−	0.557700i	−0.991673	−	0.128779i	$-0.958894\pi$
$547$	−2.06589	−	13.0435i	−0.0883309	−	0.557700i	0.903342	−	0.428920i	$-0.141106\pi$
$548$	9.12611	+	4.64999i	0.389848	+	0.198638i
$549$	−6.53648			−0.278970
$550$	14.1280	+	8.68326i	0.602421	+	0.370256i
$551$		−	6.01543i		−	0.256266i
$552$	−15.1098	−	7.69885i	−0.643118	−	0.327685i
$553$	−19.0044	+	14.1124i	−0.808147	+	0.600118i
$554$	−4.69731	−	6.46530i	−0.199570	−	0.274684i
$555$	−32.9240	−	43.1237i	−1.39755	−	1.83050i
$556$	14.5359	+	4.72299i	0.616458	+	0.200299i
$557$	2.34219	+	0.370967i	0.0992418	+	0.0157184i	0.205858	−	0.978582i	$-0.434002\pi$
$557$	2.34219	+	0.370967i	0.0992418	+	0.0157184i	−0.106616	+	0.994300i	$0.534002\pi$
$558$	−1.59818	−	10.0905i	−0.0676563	−	0.427165i
$559$	7.31023	+	22.4986i	0.309190	+	0.951589i
$560$	−3.63888	−	4.66460i	−0.153771	−	0.197115i
$561$	11.4245	−	12.1245i	0.482341	−	0.511896i
$562$	−9.33679	−	9.33679i	−0.393849	−	0.393849i
$563$	−10.2070	+	20.0324i	−0.430174	+	0.844265i	0.569576	+	0.821938i	$0.307107\pi$
$563$	−10.2070	+	20.0324i	−0.430174	+	0.844265i	−0.999751	+	0.0223264i	$0.992893\pi$
$564$	−3.33844	+	4.59497i	−0.140574	+	0.193483i
$565$	−3.71551	+	3.89635i	−0.156313	+	0.163921i
$566$	−8.68542	−	2.82206i	−0.365075	−	0.118620i
$567$	−16.5579	+	23.2967i	−0.695366	+	0.978368i
$568$	−0.272737	+	1.72200i	−0.0114438	+	0.0722534i
$569$	5.02039	−	6.90997i	0.210466	−	0.289681i	−0.690713	−	0.723129i	$-0.742703\pi$
$569$	5.02039	−	6.90997i	0.210466	−	0.289681i	0.901179	+	0.433448i	$0.142703\pi$
$570$	6.43133	+	1.92204i	0.269379	+	0.0805052i
$571$	12.6265			0.528402			0.264201	−	0.964468i	$-0.414892\pi$
$571$	12.6265			0.528402			0.264201	+	0.964468i	$0.414892\pi$
$572$	11.7088	−	4.19296i	0.489568	−	0.175317i
$573$	4.62510	+	4.62510i	0.193216	+	0.193216i
$574$	11.6150	+	11.3754i	0.484800	+	0.474800i
$575$	−18.4908	−	32.3890i	−0.771118	−	1.35071i
$576$	−1.75456	+	1.27476i	−0.0731065	+	0.0531150i
$577$	−0.332521	−	0.652609i	−0.0138430	−	0.0271685i	0.883981	−	0.467522i	$-0.154853\pi$
$577$	−0.332521	−	0.652609i	−0.0138430	−	0.0271685i	−0.897824	+	0.440353i	$0.854853\pi$
$578$	5.50186	+	10.7980i	0.228847	+	0.449138i
$579$	−23.5955	+	17.1431i	−0.980595	+	0.712444i
$580$	3.37722	+	9.61104i	0.140232	+	0.399077i
$581$	26.1542	−	26.7051i	1.08506	−	1.10791i
$582$	−1.44845	−	1.44845i	−0.0600401	−	0.0600401i
$583$	−11.0101	−	3.21901i	−0.455990	−	0.133318i
$584$	3.02895			0.125339
$585$	8.63826	+	16.0022i	0.357148	+	0.661609i
$586$	5.01811	−	6.90683i	0.207296	−	0.285319i
$587$	−5.33401	+	33.6776i	−0.220158	+	1.39002i	0.591694	+	0.806162i	$0.298459\pi$
$587$	−5.33401	+	33.6776i	−0.220158	+	1.39002i	−0.811853	+	0.583863i	$0.801541\pi$
$588$	−2.16147	+	15.7670i	−0.0891375	+	0.650218i
$589$	−5.91547	−	1.92205i	−0.243743	−	0.0791967i
$590$	−20.1443	−	19.2094i	−0.829329	−	0.790838i
$591$	−10.2418	+	14.0966i	−0.421291	+	0.579857i
$592$	4.84520	−	9.50924i	0.199136	−	0.390827i
$593$	1.60358	+	1.60358i	0.0658510	+	0.0658510i	0.739265	−	0.673414i	$-0.235173\pi$
$593$	1.60358	+	1.60358i	0.0658510	+	0.0658510i	−0.673414	+	0.739265i	$0.735173\pi$
$594$	6.15884	−	1.16402i	0.252700	−	0.0477604i
$595$	−12.9719	−	1.60241i	−0.531797	−	0.0656924i
$596$	−6.03113	−	18.5619i	−0.247045	−	0.760325i
$597$	−3.36316	−	21.2342i	−0.137645	−	0.869057i
$598$	−27.6262	−	4.37557i	−1.12972	−	0.178930i
$599$	12.1287	+	3.94085i	0.495564	+	0.161019i	0.546127	−	0.837702i	$-0.316102\pi$
$599$	12.1287	+	3.94085i	0.495564	+	0.161019i	−0.0505629	+	0.998721i	$0.516102\pi$
$600$	−11.3546	+	0.539822i	−0.463550	+	0.0220381i
$601$	−13.0966	−	18.0259i	−0.534221	−	0.735293i	0.453545	−	0.891233i	$-0.350159\pi$
$601$	−13.0966	−	18.0259i	−0.534221	−	0.735293i	−0.987766	+	0.155941i	$0.950159\pi$
$602$	9.95090	+	13.4003i	0.405568	+	0.546157i
$603$	19.3994	+	9.88447i	0.790003	+	0.402527i
$604$			2.87386i			0.116936i
$605$	−12.7542	+	21.0317i	−0.518530	+	0.855059i
$606$	−12.1557			−0.493790
$607$	25.1086	+	12.7935i	1.01913	+	0.519270i	0.881983	−	0.471281i	$-0.156208\pi$
$607$	25.1086	+	12.7935i	1.01913	+	0.519270i	0.137142	+	0.990551i	$0.456208\pi$
$608$	0.206553	+	1.30413i	0.00837684	+	0.0528893i
$609$	12.1859	−	24.5452i	0.493798	−	0.994621i
$610$	0.895876	−	6.67956i	0.0362730	−	0.270447i
$611$	−2.89488	+	8.90952i	−0.117114	+	0.360441i
$612$	−0.749551	+	4.73248i	−0.0302988	+	0.191299i
$613$	−12.6841	+	2.00897i	−0.512307	+	0.0811415i	−0.407236	−	0.913323i	$-0.633507\pi$
$613$	−12.6841	+	2.00897i	−0.512307	+	0.0811415i	−0.105072	+	0.994465i	$0.533507\pi$
$614$	−5.43099	−	16.7149i	−0.219177	−	0.674557i
$615$	30.7287	−	5.61813i	1.23910	−	0.226545i
$616$	6.88641	−	5.43850i	0.277462	−	0.219124i
$617$	7.71190	+	7.71190i	0.310469	+	0.310469i	0.845091	−	0.534622i	$-0.179546\pi$
$617$	7.71190	+	7.71190i	0.310469	+	0.310469i	−0.534622	+	0.845091i	$0.679546\pi$
$618$	−31.7485	−	16.1767i	−1.27711	−	0.650721i
$619$	−26.0112	−	18.8983i	−1.04548	−	0.759586i	−0.0741322	−	0.997248i	$-0.523619\pi$
$619$	−26.0112	−	18.8983i	−1.04548	−	0.759586i	−0.971348	+	0.237663i	$0.923619\pi$
$620$	10.5304	−	0.250178i	0.422912	−	0.0100474i
$621$	−13.4065	−	4.35605i	−0.537986	−	0.174802i
$622$	9.96513	+	19.5577i	0.399565	+	0.784191i
$623$	35.7451	−	12.0275i	1.43210	−	0.481871i
$624$	−5.01103	+	6.89709i	−0.200602	+	0.276105i
$625$	−21.5283	−	12.7096i	−0.861131	−	0.508383i
$626$			13.4524i			0.537665i
$627$	−2.79390	+	9.55603i	−0.111577	+	0.381631i
$628$	1.81300	+	1.81300i	0.0723464	+	0.0723464i
$629$	−7.28629	−	22.4249i	−0.290523	−	0.894139i
$630$	9.37722	+	8.75726i	0.373597	+	0.348898i
$631$	−21.5068	+	15.6256i	−0.856173	+	0.622046i	−0.926841	−	0.375453i	$-0.877487\pi$
$631$	−21.5068	+	15.6256i	−0.856173	+	0.622046i	0.0706678	+	0.997500i	$0.477487\pi$
$632$	−7.97171	+	4.06179i	−0.317098	+	0.161569i
$633$	−36.2002	+	18.4449i	−1.43883	+	0.733120i
$634$	−8.64678	−	11.9013i	−0.343408	−	0.472660i
$635$	−13.9224	+	29.0075i	−0.552492	+	1.15113i
$636$	7.47831	−	2.42985i	0.296534	−	0.0963499i
$637$	4.64563	+	25.8347i	0.184066	+	1.02361i
$638$	−14.2254	+	5.09416i	−0.563187	+	0.201680i
$639$		−	3.78113i		−	0.149579i
$640$	−1.06219	−	1.96768i	−0.0419866	−	0.0777793i
$641$	−35.8563	−	26.0511i	−1.41624	−	1.02896i	−0.992378	−	0.123231i	$-0.960674\pi$
$641$	−35.8563	−	26.0511i	−1.41624	−	1.02896i	−0.423861	−	0.905727i	$-0.639326\pi$
$642$	−3.96356	+	25.0249i	−0.156429	+	0.987656i
$643$	−29.7745	+	15.1709i	−1.17419	+	0.598281i	−0.928596	−	0.371091i	$-0.878984\pi$
$643$	−29.7745	+	15.1709i	−1.17419	+	0.598281i	−0.245596	+	0.969372i	$0.578984\pi$
$644$	−19.4587	+	3.29016i	−0.766781	+	0.129650i
$645$	32.0619	−	0.761714i	1.26243	−	0.0299924i
$646$	2.36002	+	1.71466i	0.0928539	+	0.0674623i
$647$	−23.5130	−	11.9804i	−0.924390	−	0.471000i	−0.0740620	−	0.997254i	$-0.523596\pi$
$647$	−23.5130	−	11.9804i	−0.924390	−	0.471000i	−0.850328	+	0.526254i	$0.823596\pi$
$648$	−7.63871	+	7.63871i	−0.300077	+	0.300077i
$649$	28.3134	−	30.0483i	1.11140	−	1.17950i
$650$	−17.5364	+	6.63412i	−0.687834	+	0.260212i
$651$	−20.2436	−	19.8261i	−0.793411	−	0.777046i
$652$	−0.112091	−	0.707714i	−0.00438982	−	0.0277162i
$653$	0.297806	−	1.88027i	0.0116540	−	0.0735807i	−0.981176	−	0.193116i	$-0.938141\pi$
$653$	0.297806	−	1.88027i	0.0116540	−	0.0735807i	0.992830	+	0.119536i	$0.0381406\pi$
$654$	−10.0219	+	30.8443i	−0.391888	+	1.20611i
$655$	−18.7744	−	24.5906i	−0.733577	−	0.960835i
$656$	3.61181	+	4.97123i	0.141017	+	0.194094i
$657$	−6.48816	+	1.02762i	−0.253127	+	0.0400914i
$658$	0.0688729	+	6.60934i	0.00268495	+	0.257659i
$659$		−	14.3763i		−	0.560020i	−0.959997	−	0.280010i	$-0.909662\pi$
$659$		−	14.3763i		−	0.560020i	0.959997	−	0.280010i	$-0.0903378\pi$
$660$	−0.901114	−	16.8365i	−0.0350758	−	0.655362i
$661$			17.9296i			0.697382i	0.937238	+	0.348691i	$0.113374\pi$
$661$			17.9296i			0.697382i	−0.937238	+	0.348691i	$0.886626\pi$
$662$	−5.32818	+	10.4571i	−0.207085	+	0.406428i
$663$	2.94646	+	18.6032i	0.114431	+	0.722488i
$664$	11.4298	−	8.30423i	0.443562	−	0.322267i
$665$	7.34235	−	2.66630i	0.284724	−	0.103395i
$666$	−7.15249	+	22.0131i	−0.277153	+	0.852990i
$667$	33.5640	+	5.31601i	1.29960	+	0.205837i
$668$	3.25962	+	20.5804i	0.126119	+	0.796281i
$669$	37.0091	−	12.0250i	1.43086	−	0.464913i
$670$	−12.7597	+	18.4693i	−0.492949	+	0.713529i
$671$	9.91513	+	1.26969i	0.382769	+	0.0490158i
$672$	−1.79905	+	5.73974i	−0.0694000	+	0.221415i
$673$	8.00921	+	4.08090i	0.308732	+	0.157307i	0.601491	−	0.798879i	$-0.294573\pi$
$673$	8.00921	+	4.08090i	0.308732	+	0.157307i	−0.292759	+	0.956186i	$0.594573\pi$
$674$	−3.02636	+	4.16542i	−0.116571	+	0.160446i
$675$	−9.25211	+	1.91971i	−0.356114	+	0.0738897i
$676$	−0.328014	+	1.00952i	−0.0126159	+	0.0388279i
$677$	−2.00912	−	3.94313i	−0.0772169	−	0.151547i	0.849170	−	0.528119i	$-0.177103\pi$
$677$	−2.00912	−	3.94313i	−0.0772169	−	0.151547i	−0.926387	+	0.376572i	$0.877103\pi$
$678$	5.40662	+	0.856325i	0.207640	+	0.0328870i
$679$	−2.35823	−	0.348358i	−0.0905007	−	0.0133688i
$680$	−4.73334	−	1.41458i	−0.181515	−	0.0542468i
$681$	−61.7798			−2.36741
$682$	0.464218	+	15.6166i	0.0177758	+	0.597992i
$683$	23.8779	−	23.8779i	0.913663	−	0.913663i	−0.0828948	−	0.996558i	$-0.526417\pi$
$683$	23.8779	−	23.8779i	0.913663	−	0.913663i	0.996558	+	0.0828948i	$0.0264166\pi$
$684$	−0.884895	−	2.72343i	−0.0338348	−	0.104133i
$685$	9.91008	−	20.6478i	0.378645	−	0.788912i
$686$	8.91968	+	16.2308i	0.340555	+	0.619695i
$687$	40.6447	−	20.7095i	1.55069	−	0.790117i
$688$	2.86405	+	5.62101i	0.109191	+	0.214299i
$689$	10.4925	−	7.62322i	0.399731	−	0.290422i
$690$	−16.4078	+	34.1860i	−0.624636	+	1.30144i
$691$	−26.9051	+	8.74198i	−1.02352	+	0.332561i	−0.772224	−	0.635350i	$-0.780856\pi$
$691$	−26.9051	+	8.74198i	−1.02352	+	0.332561i	−0.251293	+	0.967911i	$0.580856\pi$
$692$	−0.941641	+	0.941641i	−0.0357958	+	0.0357958i
$693$	−12.9059	+	13.9859i	−0.490256	+	0.531280i
$694$			28.5660i			1.08435i
$695$	9.78597	−	32.7449i	0.371203	−	1.24208i
$696$	6.08806	−	8.37949i	0.230767	−	0.317624i
$697$	13.4087	+	2.12372i	0.507889	+	0.0804417i
$698$	19.5834	−	9.97822i	0.741241	−	0.377681i
$699$	7.37357	−	22.6935i	0.278894	−	0.858348i
$700$	−10.2342	+	8.38223i	−0.386815	+	0.316818i
$701$	10.0725	+	7.31813i	0.380435	+	0.276402i	0.761525	−	0.648136i	$-0.224451\pi$
$701$	10.0725	+	7.31813i	0.380435	+	0.276402i	−0.381090	+	0.924538i	$0.624451\pi$
$702$	−3.21726	+	6.31423i	−0.121428	+	0.238315i
$703$	9.96436	+	9.96436i	0.375813	+	0.375813i
$704$	2.90909	−	1.59286i	0.109640	−	0.0600330i
$705$	10.4491	+	7.21885i	0.393535	+	0.271878i
$706$	−18.8259	+	6.11689i	−0.708521	+	0.230212i
$707$	−11.3571	+	8.43362i	−0.427128	+	0.317179i
$708$	−4.42725	+	27.9525i	−0.166386	+	1.05052i
$709$	−13.8353	−	4.49536i	−0.519596	−	0.168827i	0.0374661	−	0.999298i	$-0.488071\pi$
$709$	−13.8353	−	4.49536i	−0.519596	−	0.168827i	−0.557062	+	0.830471i	$0.688071\pi$
$710$	3.86390	+	0.518234i	0.145010	+	0.0194490i
$711$	15.6978	−	11.4051i	0.588712	−	0.427725i
$712$	14.0792	−	2.22992i	0.527639	−	0.0835699i
$713$	15.9520	−	31.3076i	0.597409	−	1.17248i
$714$	6.15625	+	11.7773i	0.230392	+	0.440755i
$715$	−9.99494	−	25.9515i	−0.373790	−	0.970533i
$716$	17.7634			0.663848
$717$	−8.33342	−	4.24609i	−0.311217	−	0.158573i
$718$	−32.5813	+	5.16037i	−1.21592	+	0.192583i
$719$	5.24533	−	3.81095i	0.195618	−	0.142125i	−0.485665	−	0.874145i	$-0.661422\pi$
$719$	5.24533	−	3.81095i	0.195618	−	0.142125i	0.681283	+	0.732020i	$0.261422\pi$
$720$	2.94283	+	3.85450i	0.109673	+	0.143649i
$721$	−40.8863	+	6.91322i	−1.52269	+	0.257462i
$722$	17.0441	+	2.69953i	0.634317	+	0.100466i
$723$	−28.1420	+	4.45726i	−1.04661	+	0.165767i
$724$	−3.42920	−	10.5540i	−0.127445	−	0.392236i
$725$	21.3055	−	8.06000i	0.791267	−	0.299341i
$726$	24.9642	−	1.48548i	0.926509	−	0.0551313i
$727$	12.2594	−	12.2594i	0.454676	−	0.454676i	−0.442227	−	0.896903i	$-0.645812\pi$
$727$	12.2594	−	12.2594i	0.454676	−	0.454676i	0.896903	+	0.442227i	$0.145812\pi$
$728$	0.103379	+	9.92067i	0.00383147	+	0.367684i
$729$	6.19465	−	8.52621i	0.229432	−	0.315785i
$730$	−0.160863	−	6.77102i	−0.00595382	−	0.250607i
$731$	13.2556	+	4.30700i	0.490276	+	0.159300i
$732$	−6.10531	+	3.11081i	−0.225659	+	0.114979i
$733$	−37.6493	−	5.96307i	−1.39061	−	0.220251i	−0.584200	−	0.811609i	$-0.698592\pi$
$733$	−37.6493	−	5.96307i	−1.39061	−	0.220251i	−0.806409	+	0.591359i	$0.798592\pi$
$734$	−21.0634	−	15.3035i	−0.777464	−	0.564861i
$735$	35.3608	+	3.99447i	1.30430	+	0.147338i
$736$	−7.45910			−0.274946
$737$	−27.5067	−	18.7619i	−1.01322	−	0.691105i
$738$	−9.42325	−	9.42325i	−0.346875	−	0.346875i
$739$	10.1407	−	3.29493i	0.373033	−	0.121206i	−0.116499	−	0.993191i	$-0.537167\pi$
$739$	10.1407	−	3.29493i	0.373033	−	0.121206i	0.489533	+	0.871985i	$0.337167\pi$
$740$	−21.5146	−	10.3261i	−0.790894	−	0.379596i
$741$	−6.61647	−	9.10679i	−0.243062	−	0.334546i
$742$	5.30121	−	7.45870i	0.194613	−	0.273818i
$743$	14.4775	+	28.4136i	0.531126	+	1.04239i	0.988229	+	0.152980i	$0.0488870\pi$
$743$	14.4775	+	28.4136i	0.531126	+	1.04239i	−0.457103	+	0.889414i	$0.651113\pi$
$744$	−6.29499	−	8.66430i	−0.230785	−	0.317649i
$745$	−41.1737	+	14.4680i	−1.50849	+	0.530067i
$746$	3.56673	+	10.9773i	0.130587	+	0.401906i
$747$	−21.6658	+	21.6658i	−0.792712	+	0.792712i
$748$	2.05626	−	7.03306i	0.0751842	−	0.257154i
$749$	13.6592	+	26.1309i	0.499096	+	0.954803i
$750$	1.80977	+	25.3539i	0.0660834	+	0.925792i
$751$	32.5501	+	23.6490i	1.18777	+	0.862966i	0.993027	−	0.117889i	$-0.0376126\pi$
$751$	32.5501	+	23.6490i	1.18777	+	0.862966i	0.194744	+	0.980854i	$0.437613\pi$
$752$	−0.390810	+	2.46747i	−0.0142514	+	0.0899795i
$753$	5.58329	+	10.9578i	0.203466	+	0.399325i
$754$	5.27916	−	16.2476i	0.192256	−	0.591702i
$755$	6.42433	−	0.152627i	0.233805	−	0.00555466i
$756$	−0.730676	+	4.94636i	−0.0265744	+	0.179897i
$757$	11.1575	−	21.8978i	0.405525	−	0.795887i	−0.594441	−	0.804139i	$-0.702627\pi$
$757$	11.1575	−	21.8978i	0.405525	−	0.795887i	0.999966	+	0.00825181i	$0.00262666\pi$
$758$	22.4528	−	22.4528i	0.815522	−	0.815522i
$759$	−50.8503	−	24.0339i	−1.84575	−	0.872376i
$760$	2.90432	−	0.530997i	0.105351	−	0.0192613i
$761$	−0.730863	+	0.237472i	−0.0264938	+	0.00860835i	−0.322234	−	0.946660i	$-0.604434\pi$
$761$	−0.730863	+	0.237472i	−0.0264938	+	0.00860835i	0.295740	+	0.955268i	$0.404434\pi$
$762$	32.3112	−	5.11760i	1.17051	−	0.185391i
$763$	12.0363	+	35.7713i	0.435743	+	1.29501i
$764$	2.73621	+	0.889049i	0.0989926	+	0.0321647i
$765$	10.6190	+	1.42424i	0.383930	+	0.0514935i
$766$	−0.127528	−	0.175528i	−0.00460779	−	0.00634208i
$767$	7.30224	+	46.1045i	0.263669	+	1.66474i
$768$	−1.03214	+	2.02569i	−0.0372442	+	0.0730959i
$769$	42.1629			1.52043			0.760217	−	0.649670i	$-0.225093\pi$
$769$	42.1629			1.52043			0.760217	+	0.649670i	$0.225093\pi$
$770$	−12.5232	−	15.1053i	−0.451303	−	0.544358i
$771$	42.4788			1.52984
$772$	−5.82405	+	11.4303i	−0.209612	+	0.411387i
$773$	7.72274	+	48.7594i	0.277768	+	1.75376i	0.593432	+	0.804884i	$0.297773\pi$
$773$	7.72274	+	48.7594i	0.277768	+	1.75376i	−0.315664	+	0.948871i	$0.602227\pi$
$774$	−8.04196	−	11.0688i	−0.289062	−	0.397860i
$775$	−1.11851	−	23.5268i	−0.0401782	−	0.845108i
$776$	−0.856903	−	0.278425i	−0.0307610	−	0.00999486i
$777$	20.4727	+	60.8438i	0.734454	+	2.18276i
$778$	−13.0608	+	2.06863i	−0.468254	+	0.0741641i
$779$	−7.71635	+	2.50719i	−0.276467	+	0.0898295i
$780$	15.6841	+	10.8355i	0.561582	+	0.387975i
$781$	−0.734472	+	5.73557i	−0.0262815	+	0.205235i
$782$	−11.6528	+	11.6528i	−0.416704	+	0.416704i
$783$	3.90875	−	7.67135i	0.139687	−	0.274152i
$784$	2.30138	+	6.61087i	0.0821922	+	0.236103i
$785$	3.95655	−	4.14913i	0.141215	−	0.148089i
$786$	−9.72045	+	29.9165i	−0.346717	+	1.06708i
$787$	6.33787	+	12.4388i	0.225921	+	0.443395i	0.975945	−	0.218016i	$-0.0699583\pi$
$787$	6.33787	+	12.4388i	0.225921	+	0.443395i	−0.750025	+	0.661410i	$0.769958\pi$
$788$	−1.19894	+	7.56980i	−0.0427104	+	0.269663i
$789$	22.7162	+	16.5043i	0.808719	+	0.587569i
$790$	9.50324	+	17.6045i	0.338110	+	0.626341i
$791$	5.64557	−	2.95106i	0.200733	−	0.104928i
$792$	−5.69101	+	4.39894i	−0.202221	+	0.156309i
$793$	−7.99161	+	7.99161i	−0.283791	+	0.283791i
$794$	−6.66033	−	20.4984i	−0.236366	−	0.727461i
$795$	−5.82894	−	16.5883i	−0.206731	−	0.588325i
$796$	−5.55829	−	7.65033i	−0.197008	−	0.271159i
$797$	0.192634	+	0.378065i	0.00682344	+	0.0133918i	0.894393	−	0.447282i	$-0.147608\pi$
$797$	0.192634	+	0.378065i	0.00682344	+	0.0133918i	−0.887570	+	0.460674i	$0.847608\pi$
$798$	−6.47368	−	4.60111i	−0.229166	−	0.162877i
$799$	3.24422	+	4.46529i	0.114772	+	0.157971i
$800$	−4.34221	+	2.47895i	−0.153520	+	0.0876443i
$801$	−29.4018	+	9.55321i	−1.03886	+	0.337546i
$802$	−2.40249	−	2.40249i	−0.0848349	−	0.0848349i
$803$	10.0415	−	0.298491i	0.354355	−	0.0105335i
$804$	22.8239			0.804936
$805$	8.38837	+	43.3240i	0.295651	+	1.52697i
$806$	−14.2908	−	10.3829i	−0.503372	−	0.365721i
$807$	−23.9843	−	3.79874i	−0.844287	−	0.133722i
$808$	−4.76394	+	2.42735i	−0.167595	+	0.0853938i
$809$	−44.5618	−	14.4790i	−1.56671	−	0.509055i	−0.608120	−	0.793845i	$-0.708076\pi$
$809$	−44.5618	−	14.4790i	−1.56671	−	0.509055i	−0.958590	+	0.284790i	$0.908076\pi$
$810$	17.4815	+	16.6702i	0.614239	+	0.585730i
$811$	−20.5189	+	28.2419i	−0.720517	+	0.991707i	0.278989	+	0.960294i	$0.410001\pi$
$811$	−20.5189	+	28.2419i	−0.720517	+	0.991707i	−0.999506	+	0.0314128i	$0.989999\pi$
$812$	−0.125598	−	12.0529i	−0.00440763	−	0.422975i
$813$	−14.4213	+	14.4213i	−0.505777	+	0.505777i
$814$	15.1255	−	32.0021i	0.530149	−	1.12167i
$815$	−1.57610	+	0.288158i	−0.0552082	+	0.0100937i
$816$	1.55215	+	4.77703i	0.0543362	+	0.167230i
$817$	−8.22721	+	1.30306i	−0.287834	+	0.0455884i
$818$	−20.9512	−	3.31835i	−0.732542	−	0.116023i
$819$	−3.58720	−	21.2155i	−0.125347	−	0.741329i
$820$	10.9210	−	8.33798i	0.381380	−	0.291175i
$821$	−24.1688	+	17.5597i	−0.843498	+	0.612837i	−0.923346	−	0.383970i	$-0.874557\pi$
$821$	−24.1688	+	17.5597i	−0.843498	+	0.612837i	0.0798478	+	0.996807i	$0.474557\pi$
$822$	−22.9995	+	3.64276i	−0.802199	+	0.127056i
$823$	25.8423	+	13.1673i	0.900806	+	0.458984i	0.842118	−	0.539293i	$-0.181308\pi$
$823$	25.8423	+	13.1673i	0.900806	+	0.458984i	0.0586878	+	0.998276i	$0.481308\pi$
$824$	−15.6729			−0.545992
$825$	−37.5892	+	2.90855i	−1.30869	+	0.101263i
$826$	15.2571	+	29.1879i	0.530864	+	1.01558i
$827$	7.44051	−	14.6028i	0.258732	−	0.507790i	−0.724701	−	0.689064i	$-0.758022\pi$
$827$	7.44051	−	14.6028i	0.258732	−	0.507790i	0.983433	+	0.181274i	$0.0580220\pi$
$828$	15.9778	−	2.53063i	0.555266	−	0.0879455i
$829$	22.8514	−	16.6025i	0.793661	−	0.576628i	−0.115387	−	0.993321i	$-0.536811\pi$
$829$	22.8514	−	16.6025i	0.793661	−	0.576628i	0.909048	+	0.416692i	$0.136811\pi$
$830$	−19.1706	−	25.1096i	−0.665422	−	0.871566i
$831$	17.2795	+	5.61444i	0.599418	+	0.194763i
$832$	−0.586608	+	3.70370i	−0.0203370	+	0.128403i
$833$	13.9230	+	6.73241i	0.482402	+	0.233264i
$834$	−33.0471	+	10.7377i	−1.14433	+	0.371815i
$835$	45.8332	−	8.37968i	1.58612	−	0.289991i
$836$	0.813273	+	4.30303i	0.0281276	+	0.148823i
$837$	−6.29495	−	6.29495i	−0.217585	−	0.217585i
$838$	13.8319	−	27.1466i	0.477815	−	0.937764i
$839$	8.37629	+	6.08573i	0.289182	+	0.210103i	0.722912	−	0.690940i	$-0.242803\pi$
$839$	8.37629	+	6.08573i	0.289182	+	0.210103i	−0.433731	+	0.901043i	$0.642803\pi$
$840$	12.9264	+	3.71684i	0.446003	+	0.128243i
$841$	2.54767	−	7.84093i	0.0878508	−	0.270377i
$842$	−4.95028	+	2.52229i	−0.170598	+	0.0869239i
$843$	29.6500	+	4.69610i	1.02120	+	0.161742i
$844$	−10.5040	+	14.4576i	−0.361564	+	0.497650i
$845$	2.27415	+	0.679641i	0.0782331	+	0.0233804i
$846$		−	5.41804i		−	0.186276i
$847$	22.2936	−	18.7081i	0.766018	−	0.642819i
$848$	2.44562	−	2.44562i	0.0839830	−	0.0839830i
$849$	19.7462	−	6.41593i	0.677688	−	0.220194i
$850$	−2.91083	+	10.6562i	−0.0998406	+	0.365505i
$851$	−64.4034	+	46.7918i	−2.20772	+	1.60400i
$852$	−1.79950	−	3.53172i	−0.0616499	−	0.120995i
$853$	−7.33831	+	3.73905i	−0.251259	+	0.128023i	−0.575085	−	0.818094i	$-0.695031\pi$
$853$	−7.33831	+	3.73905i	−0.251259	+	0.128023i	0.323826	+	0.946117i	$0.395031\pi$
$854$	−3.54595	+	7.14233i	−0.121340	+	0.244406i
$855$	−6.04105	+	2.12276i	−0.206600	+	0.0725970i
$856$	3.44384	+	10.5990i	0.117708	+	0.362268i
$857$	−28.7616	+	28.7616i	−0.982478	+	0.982478i	−0.999849	−	0.0173714i	$-0.994470\pi$
$857$	−28.7616	+	28.7616i	−0.982478	+	0.982478i	0.0173714	+	0.999849i	$0.494470\pi$
$858$	−15.9327	+	23.3588i	−0.543933	+	0.797456i
$859$	−29.5993			−1.00991			−0.504957	−	0.863145i	$-0.668492\pi$
$859$	−29.5993			−1.00991			−0.504957	+	0.863145i	$0.668492\pi$
$860$	12.4133	−	6.70092i	0.423290	−	0.228500i
$861$	−36.5646	−	5.40132i	−1.24612	−	0.184076i
$862$	30.7619	+	4.87220i	1.04775	+	0.165948i
$863$	−2.40325	−	4.71664i	−0.0818075	−	0.160556i	0.846479	−	0.532422i	$-0.178718\pi$
$863$	−2.40325	−	4.71664i	−0.0818075	−	0.160556i	−0.928286	+	0.371866i	$0.878718\pi$
$864$	−0.583991	+	1.79734i	−0.0198678	+	0.0611467i
$865$	2.15499	+	2.05497i	0.0732718	+	0.0698711i
$866$	9.17675	−	12.6307i	0.311839	−	0.429209i
$867$	−24.5492	−	12.5084i	−0.833733	−	0.424808i
$868$	−11.8928	−	3.72764i	−0.403667	−	0.126524i
$869$	−26.0272	+	14.2511i	−0.882913	+	0.483434i
$870$	−19.0552	−	13.1644i	−0.646030	−	0.446316i
$871$	35.8029	−	11.6331i	1.21314	−	0.394172i
$872$	2.23156	+	14.0895i	0.0755700	+	0.477130i
$873$	1.92999	+	0.305680i	0.0653202	+	0.0103457i
$874$	3.04346	−	9.36682i	0.102947	−	0.316837i
$875$	19.2815	+	22.4327i	0.651832	+	0.758363i
$876$	−5.57112	+	4.04765i	−0.188231	+	0.136758i
$877$	−3.87745	−	24.4813i	−0.130932	−	0.826673i	−0.962506	−	0.271259i	$-0.912560\pi$
$877$	−3.87745	−	24.4813i	−0.130932	−	0.826673i	0.831574	−	0.555414i	$-0.187440\pi$
$878$	−3.73021	+	7.32096i	−0.125889	+	0.247070i
$879$			19.4095i			0.654666i
$880$	−3.71523	−	6.41849i	−0.125240	−	0.216367i
$881$		−	42.8494i		−	1.44363i	−0.692084	−	0.721817i	$-0.743307\pi$
$881$		−	42.8494i		−	1.44363i	0.692084	−	0.721817i	$-0.256693\pi$
$882$	−7.17253	−	13.3800i	−0.241512	−	0.450529i
$883$	−16.3057	+	2.58256i	−0.548729	+	0.0869102i	−0.424642	−	0.905361i	$-0.639600\pi$
$883$	−16.3057	+	2.58256i	−0.548729	+	0.0869102i	−0.124087	+	0.992271i	$0.539600\pi$
$884$	4.86960	+	6.70243i	0.163782	+	0.225427i
$885$	62.7212	+	8.41231i	2.10835	+	0.282777i
$886$	7.71810	−	23.7539i	0.259295	−	0.798027i
$887$	0.404297	−	2.55263i	0.0135750	−	0.0857090i	−0.979971	−	0.199142i	$-0.936185\pi$
$887$	0.404297	−	2.55263i	0.0135750	−	0.0857090i	0.993546	+	0.113433i	$0.0361846\pi$
$888$	3.79569	+	23.9650i	0.127375	+	0.804213i
$889$	26.6380	−	27.1990i	0.893411	−	0.912227i
$890$	−5.73258	−	31.3547i	−0.192156	−	1.05101i
$891$	−24.5708	+	26.0763i	−0.823153	+	0.873590i
$892$	12.1031	−	12.1031i	0.405240	−	0.405240i
$893$	−2.93909	−	1.49754i	−0.0983529	−	0.0501133i
$894$	35.8977	+	26.0812i	1.20060	+	0.872286i
$895$	−0.943389	−	39.7089i	−0.0315340	−	1.32732i
$896$	0.441093	+	2.60872i	0.0147359	+	0.0871513i
$897$	56.6599	−	28.8696i	1.89182	−	0.963929i
$898$	6.15581	−	38.8662i	0.205422	−	1.29698i
$899$	17.3623	+	12.6145i	0.579066	+	0.420716i
$900$	8.46020	−	6.78322i	0.282007	−	0.226107i
$901$		−	7.64124i		−	0.254567i
$902$	12.4636	+	16.1245i	0.414993	+	0.536887i
$903$	−36.2098	−	11.3495i	−1.20499	−	0.377688i
$904$	2.28992	−	0.744039i	0.0761615	−	0.0247464i
$905$	−23.4106	+	8.22626i	−0.778196	+	0.273450i
$906$	−3.84040	−	5.28586i	−0.127589	−	0.175611i
$907$	17.5208	−	8.92728i	0.581768	−	0.296426i	−0.138232	−	0.990400i	$-0.544142\pi$
$907$	17.5208	−	8.92728i	0.581768	−	0.296426i	0.720000	+	0.693974i	$0.244142\pi$
$908$	−24.2122	+	12.3368i	−0.803511	+	0.409409i
$909$	9.38108	−	6.81575i	0.311151	−	0.226064i
$910$	22.1715	−	0.757970i	0.734979	−	0.0251265i
$911$	6.27139	+	19.3013i	0.207780	+	0.639482i	0.999588	+	0.0287112i	$0.00914032\pi$
$911$	6.27139	+	19.3013i	0.207780	+	0.639482i	−0.791807	+	0.610771i	$0.790860\pi$
$912$	−2.12264	−	2.12264i	−0.0702878	−	0.0702878i
$913$	37.0733	−	28.6562i	1.22695	−	0.948383i
$914$		−	32.6183i		−	1.07892i
$915$	7.27827	+	13.4828i	0.240612	+	0.445729i
$916$	11.7937	−	16.2326i	0.389674	−	0.536340i
$917$	11.6742	+	34.6952i	0.385517	+	1.14574i
$918$	1.89553	+	3.72018i	0.0625617	+	0.122784i
$919$	−17.5970	−	5.71760i	−0.580470	−	0.188606i	0.00404107	−	0.999992i	$-0.498714\pi$
$919$	−17.5970	−	5.71760i	−0.580470	−	0.188606i	−0.584511	+	0.811386i	$0.698714\pi$
$920$	0.396143	+	16.6743i	0.0130604	+	0.549737i
$921$	32.3256	+	23.4860i	1.06517	+	0.773889i
$922$	−10.5269	−	5.36372i	−0.346685	−	0.176645i
$923$	−4.62288	−	4.62288i	−0.152164	−	0.152164i
$924$	−5.39852	+	19.2055i	−0.177598	+	0.631813i
$925$	−21.9408	+	48.6430i	−0.721408	+	1.59937i
$926$	−10.7856	−	33.1947i	−0.354437	−	1.09085i
$927$	33.5722	−	5.31731i	1.10265	−	0.174643i
$928$	0.712688	−	4.49974i	0.0233951	−	0.147711i
$929$	−12.4265	+	38.2449i	−0.407701	+	1.25477i	0.510918	+	0.859630i	$0.329306\pi$
$929$	−12.4265	+	38.2449i	−0.407701	+	1.25477i	−0.918619	+	0.395145i	$0.870694\pi$
$930$	−19.0342	+	14.5322i	−0.624156	+	0.476529i
$931$	−9.24066	+	0.192606i	−0.302850	+	0.00631242i
$932$	−1.64186	−	10.3663i	−0.0537808	−	0.339559i
$933$	−44.4641	−	22.6556i	−1.45569	−	0.741711i
$934$	22.1854			0.725928
$935$	−15.8312	−	4.22312i	−0.517735	−	0.138111i
$936$		−	8.13252i		−	0.265820i
$937$	−1.70329	−	0.867871i	−0.0556442	−	0.0283521i	0.425947	−	0.904748i	$-0.359941\pi$
$937$	−1.70329	−	0.867871i	−0.0556442	−	0.0283521i	−0.481591	+	0.876396i	$0.659941\pi$
$938$	21.3245	−	15.8353i	0.696270	−	0.517040i
$939$	−17.9767	−	24.7428i	−0.586648	−	0.807452i
$940$	5.53664	+	0.742586i	0.180585	+	0.0242205i
$941$	−39.0758	−	12.6965i	−1.27384	−	0.413894i	−0.407430	−	0.913236i	$-0.633575\pi$
$941$	−39.0758	−	12.6965i	−1.27384	−	0.413894i	−0.866405	+	0.499342i	$0.833575\pi$
$942$	−5.75738	−	0.911879i	−0.187585	−	0.0297106i
$943$	−7.17009	−	45.2702i	−0.233490	−	1.47420i
$944$	3.84672	+	11.8390i	0.125200	+	0.385326i
$945$	11.0961	+	1.37069i	0.360955	+	0.0445884i
$946$	10.0487	+	18.3523i	0.326712	+	0.596685i
$947$	−9.02216	−	9.02216i	−0.293181	−	0.293181i	0.545155	−	0.838336i	$-0.316471\pi$
$947$	−9.02216	−	9.02216i	−0.293181	−	0.293181i	−0.838336	+	0.545155i	$0.816471\pi$
$948$	9.23443	−	18.1236i	0.299920	−	0.588627i
$949$	−6.67615	+	9.18893i	−0.216717	+	0.298285i
$950$	−1.34125	−	6.46423i	−0.0435161	−	0.209727i
$951$	31.8079	+	10.3350i	1.03144	+	0.335136i
$952$	4.76451	+	3.38633i	0.154419	+	0.109752i
$953$	−3.17570	+	20.0506i	−0.102871	+	0.649502i	0.881337	+	0.472488i	$0.156644\pi$
$953$	−3.17570	+	20.0506i	−0.102871	+	0.649502i	−0.984208	+	0.177014i	$0.943356\pi$
$954$	−4.40893	+	6.06837i	−0.142744	+	0.196471i
$955$	1.84210	−	6.16384i	0.0596088	−	0.199457i
$956$	−4.11386			−0.133052
$957$	19.3571	−	28.3793i	0.625727	−	0.917373i
$958$	11.5983	+	11.5983i	0.374725	+	0.374725i
$959$	−18.9612	+	19.3605i	−0.612290	+	0.625185i
$960$	4.58313	+	2.19971i	0.147920	+	0.0709953i
$961$	−7.12706	+	5.17811i	−0.229905	+	0.167036i
$962$	18.1688	+	35.6584i	0.585787	+	1.14967i
$963$	−10.9728	−	21.5353i	−0.353593	−	0.693966i
$964$	−10.1391	+	7.36650i	−0.326559	+	0.237259i
$965$	25.8611	+	12.4123i	0.832499	+	0.399565i
$966$	31.3935	−	32.0547i	1.01007	−	1.03134i
$967$	−21.3536	−	21.3536i	−0.686685	−	0.686685i	0.274813	−	0.961498i	$-0.411384\pi$
$967$	−21.3536	−	21.3536i	−0.686685	−	0.686685i	−0.961498	+	0.274813i	$0.911384\pi$
$968$	9.48713	−	5.56725i	0.304928	−	0.178938i
$969$	−6.63211			−0.213054
$970$	−0.576892	+	1.93034i	−0.0185229	+	0.0619795i
$971$	−16.4522	+	22.6445i	−0.527977	+	0.726697i	−0.986820	−	0.161820i	$-0.948264\pi$
$971$	−16.4522	+	22.6445i	−0.527977	+	0.726697i	0.458844	+	0.888517i	$0.348264\pi$
$972$	2.95512	−	18.6579i	0.0947856	−	0.598453i
$973$	−23.4264	+	32.9605i	−0.751015	+	1.05666i
$974$	17.8378	+	5.79585i	0.571560	+	0.185711i
$975$	23.3892	−	35.6364i	0.749055	−	1.14128i
$976$	−1.77155	+	2.43833i	−0.0567058	+	0.0780489i
$977$	23.6595	−	46.4344i	0.756934	−	1.48557i	−0.113636	−	0.993522i	$-0.536250\pi$
$977$	23.6595	−	46.4344i	0.756934	−	1.48557i	0.870570	−	0.492044i	$-0.163750\pi$
$978$	1.15190	+	1.15190i	0.0368338	+	0.0368338i
$979$	46.4550	−	8.78000i	1.48471	−	0.280610i
$980$	14.6560	−	5.49569i	0.468168	−	0.175553i
$981$	−9.56021	−	29.4233i	−0.305234	−	0.939414i
$982$	1.48540	+	9.37845i	0.0474010	+	0.299278i
$983$	−19.7187	−	3.12314i	−0.628930	−	0.0996127i	−0.166171	−	0.986097i	$-0.553140\pi$
$983$	−19.7187	−	3.12314i	−0.628930	−	0.0996127i	−0.462759	+	0.886484i	$0.653140\pi$
$984$	−13.2863	−	4.31699i	−0.423553	−	0.137621i
$985$	16.9855	+	2.27813i	0.541202	+	0.0725872i
$986$	−5.91623	−	8.14299i	−0.188411	−	0.259326i
$987$	−8.95889	−	12.0645i	−0.285165	−	0.384016i
$988$	−4.41160	−	2.24782i	−0.140352	−	0.0715127i
$989$		−	47.0565i		−	1.49631i
$990$	10.1358	+	12.4883i	0.322137	+	0.396904i
$991$	48.9871			1.55613			0.778064	−	0.628185i	$-0.216202\pi$
$991$	48.9871			1.55613			0.778064	+	0.628185i	$0.216202\pi$
$992$	−4.19724	−	2.13860i	−0.133263	−	0.0679007i
$993$	−4.17404	−	26.3539i	−0.132459	−	0.836315i
$994$	−4.13160	−	2.05121i	−0.131046	−	0.0650605i
$995$	−16.8066	+	12.8315i	−0.532807	+	0.406786i
$996$	−9.92558	+	30.5478i	−0.314504	+	0.967944i
$997$	5.45404	−	34.4354i	0.172731	−	1.09058i	−0.737155	−	0.675723i	$-0.763831\pi$
$997$	5.45404	−	34.4354i	0.172731	−	1.09058i	0.909886	−	0.414858i	$-0.136169\pi$
$998$	−34.2429	+	5.42353i	−1.08394	+	0.171679i
$999$	6.23263	+	19.1821i	0.197192	+	0.606893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bi.a.27.6	✓	384
5.3	odd	4	inner	770.2.bi.a.643.43	yes	384
7.6	odd	2	inner	770.2.bi.a.27.19	yes	384
11.9	even	5	inner	770.2.bi.a.97.30	yes	384
35.13	even	4	inner	770.2.bi.a.643.30	yes	384
55.53	odd	20	inner	770.2.bi.a.713.19	yes	384
77.20	odd	10	inner	770.2.bi.a.97.43	yes	384
385.328	even	20	inner	770.2.bi.a.713.6	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bi.a.27.6	✓	384	1.1	even	1	trivial
770.2.bi.a.27.19	yes	384	7.6	odd	2	inner
770.2.bi.a.97.30	yes	384	11.9	even	5	inner
770.2.bi.a.97.43	yes	384	77.20	odd	10	inner
770.2.bi.a.643.30	yes	384	35.13	even	4	inner
770.2.bi.a.643.43	yes	384	5.3	odd	4	inner
770.2.bi.a.713.6	yes	384	385.328	even	20	inner
770.2.bi.a.713.19	yes	384	55.53	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.355652 - 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.77729 + 1.35692i) q^{5} +(2.16222 + 0.702547i) q^{6} +(2.50760 - 0.843757i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.355652 - 2.24550i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.77729 + 1.35692i) q^{5} +(2.16222 + 0.702547i) q^{6} +(2.50760 - 0.843757i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.06261 + 0.670181i) q^{9} +(-0.402154 - 2.19961i) q^{10} +(3.25893 - 0.615938i) q^{11} +(-1.60760 + 1.60760i) q^{12} +(-1.70240 + 3.34115i) q^{13} +(-0.386635 + 2.61735i) q^{14} +(3.67906 + 3.50831i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.00301 + 1.96852i) q^{17} +(0.339267 - 2.14205i) q^{18} +(-1.06821 - 0.776101i) q^{19} +(2.14244 + 0.640279i) q^{20} +(-2.78649 - 5.33074i) q^{21} +(-0.930718 + 3.18336i) q^{22} +(5.27438 - 5.27438i) q^{23} +(-0.702547 - 2.16222i) q^{24} +(1.31752 - 4.82329i) q^{25} +(-2.20411 - 3.03370i) q^{26} +(-0.857967 - 1.68385i) q^{27} +(-2.15655 - 1.53275i) q^{28} +(2.67785 + 3.68574i) q^{29} +(-4.79619 + 1.68533i) q^{30} +(4.48012 - 1.45568i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.54213 - 7.09886i) q^{33} -2.20932 q^{34} +(-3.31183 + 4.90223i) q^{35} +(1.75456 + 1.27476i) q^{36} +(-10.5411 - 1.66954i) q^{37} +(1.17647 - 0.599441i) q^{38} +(8.10802 + 2.63445i) q^{39} +(-1.54314 + 1.61825i) q^{40} +(3.61181 - 4.97123i) q^{41} +(6.01476 - 0.0626770i) q^{42} +(4.46086 - 4.46086i) q^{43} +(-2.41385 - 2.27449i) q^{44} +(2.75646 - 3.98990i) q^{45} +(2.30499 + 7.09402i) q^{46} +(2.46747 - 0.390810i) q^{47} +(2.24550 + 0.355652i) q^{48} +(5.57615 - 4.23162i) q^{49} +(3.69944 + 3.36365i) q^{50} +(4.06359 - 2.95237i) q^{51} +(3.70370 - 0.586608i) q^{52} +(-3.08166 - 1.57019i) q^{53} +1.88983 q^{54} +(-4.95628 + 5.51682i) q^{55} +(2.34474 - 1.22564i) q^{56} +(-1.36282 + 2.67469i) q^{57} +(-4.49974 + 0.712688i) q^{58} +(10.0708 - 7.31690i) q^{59} +(0.675782 - 5.03856i) q^{60} +(2.86642 + 0.931357i) q^{61} +(-0.736912 + 4.65268i) q^{62} +(-4.60673 + 3.42089i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-1.50802 - 8.24823i) q^{65} +(7.47924 + 0.957759i) q^{66} +(-7.09875 - 7.09875i) q^{67} +(1.00301 - 1.96852i) q^{68} +(-13.7195 - 9.96777i) q^{69} +(-2.86438 - 5.17642i) q^{70} +(-0.538759 + 1.65813i) q^{71} +(-1.93237 + 0.984592i) q^{72} +(2.99166 + 0.473832i) q^{73} +(6.27312 - 8.63421i) q^{74} +(-11.2993 - 1.24308i) q^{75} +1.32038i q^{76} +(7.65240 - 4.29427i) q^{77} +(-6.02828 + 6.02828i) q^{78} +(-8.50897 + 2.76473i) q^{79} +(-0.741297 - 2.10962i) q^{80} +(-8.73963 + 6.34971i) q^{81} +(2.78967 + 5.47503i) q^{82} +(12.5881 - 6.41398i) q^{83} +(-2.67480 + 5.38764i) q^{84} +(-4.45377 - 2.13762i) q^{85} +(1.94947 + 5.99984i) q^{86} +(7.32394 - 7.32394i) q^{87} +(3.12245 - 1.11816i) q^{88} +14.2547 q^{89} +(2.30362 + 4.26740i) q^{90} +(-1.44983 + 9.81470i) q^{91} +(-7.36727 - 1.16686i) q^{92} +(-4.86209 - 9.54238i) q^{93} +(-0.771996 + 2.37596i) q^{94} +(2.95163 - 0.0701237i) q^{95} +(-1.33632 + 1.83929i) q^{96} +(-0.802798 - 0.409046i) q^{97} +(1.23888 + 6.88950i) q^{98} +(-6.30909 + 3.45451i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 4 q^{7}+O(q^{10}) \) 384 * q - 4 * q^7	\( 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) \) 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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