LMFDB - Embedded newform 936.2.bk.c.277.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(277,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4, 1]))

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

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

chi := DirichletCharacter("936.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$160$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			277.18
Character	$\chi$	$=$	936.277
Dual form			936.2.bk.c.517.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32766 + 0.487152i) q^{2} +(1.69136 + 0.373231i) q^{3} +(1.52537 - 1.29354i) q^{4} +(1.73390 + 3.00321i) q^{5} +(-2.42737 + 0.328425i) q^{6} -2.47808i q^{7} +(-1.39502 + 2.46047i) q^{8} +(2.72140 + 1.26253i) q^{9} +(-3.76505 - 3.14257i) q^{10} +(-1.61523 - 2.79767i) q^{11} +(3.06273 - 1.61854i) q^{12} +(-3.34184 - 1.35355i) q^{13} +(1.20720 + 3.29004i) q^{14} +(1.81176 + 5.72665i) q^{15} +(0.653486 - 3.94626i) q^{16} +(2.89335 + 5.01142i) q^{17} +(-4.22814 - 0.350485i) q^{18} +(2.26334 + 3.92023i) q^{19} +(6.52962 + 2.33811i) q^{20} +(0.924894 - 4.19132i) q^{21} +(3.50737 + 2.92749i) q^{22} +9.31152 q^{23} +(-3.27780 + 3.64088i) q^{24} +(-3.51284 + 6.08441i) q^{25} +(5.09622 + 0.169075i) q^{26} +(4.13165 + 3.15111i) q^{27} +(-3.20550 - 3.77997i) q^{28} +(-3.40526 + 1.96603i) q^{29} +(-5.19516 - 6.72045i) q^{30} +(5.59979 - 3.23304i) q^{31} +(1.05482 + 5.55764i) q^{32} +(-1.68777 - 5.33472i) q^{33} +(-6.28271 - 5.24397i) q^{34} +(7.44217 - 4.29674i) q^{35} +(5.78427 - 1.59442i) q^{36} +(-1.66110 + 2.87710i) q^{37} +(-4.91470 - 4.10214i) q^{38} +(-5.14707 - 3.53662i) q^{39} +(-9.80813 + 0.0766956i) q^{40} +2.56416i q^{41} +(0.813862 + 6.01521i) q^{42} +9.40931i q^{43} +(-6.08273 - 2.17809i) q^{44} +(0.926984 + 10.3620i) q^{45} +(-12.3625 + 4.53612i) q^{46} +(-7.93235 - 4.57974i) q^{47} +(2.57814 - 6.43064i) q^{48} +0.859143 q^{49} +(1.69982 - 9.78932i) q^{50} +(3.02327 + 9.55601i) q^{51} +(-6.84841 + 2.25816i) q^{52} +0.880344i q^{53} +(-7.02049 - 2.17087i) q^{54} +(5.60131 - 9.70176i) q^{55} +(6.09724 + 3.45696i) q^{56} +(2.36498 + 7.47526i) q^{57} +(3.56327 - 4.26909i) q^{58} +(4.67229 - 8.09265i) q^{59} +(10.1713 + 6.39164i) q^{60} -12.6184i q^{61} +(-5.85964 + 7.02033i) q^{62} +(3.12866 - 6.74383i) q^{63} +(-4.10786 - 6.86480i) q^{64} +(-1.72943 - 12.3832i) q^{65} +(4.83960 + 6.26049i) q^{66} -3.65076 q^{67} +(10.8959 + 3.90159i) q^{68} +(15.7491 + 3.47535i) q^{69} +(-7.78752 + 9.33008i) q^{70} +(-3.31472 + 1.91375i) q^{71} +(-6.90283 + 4.93467i) q^{72} -6.92009i q^{73} +(0.803786 - 4.62902i) q^{74} +(-8.21236 + 8.97983i) q^{75} +(8.52342 + 3.05205i) q^{76} +(-6.93283 + 4.00267i) q^{77} +(8.55643 + 2.18803i) q^{78} +(-5.76983 + 9.99363i) q^{79} +(12.9845 - 4.87987i) q^{80} +(5.81201 + 6.87172i) q^{81} +(-1.24913 - 3.40433i) q^{82} +(-1.07422 + 1.86061i) q^{83} +(-4.01085 - 7.58969i) q^{84} +(-10.0336 + 17.3786i) q^{85} +(-4.58376 - 12.4924i) q^{86} +(-6.49329 + 2.05431i) q^{87} +(9.13686 - 0.0714465i) q^{88} +(-1.67046 - 0.964443i) q^{89} +(-6.27860 - 13.3057i) q^{90} +(-3.35420 + 8.28133i) q^{91} +(14.2035 - 12.0449i) q^{92} +(10.6779 - 3.37822i) q^{93} +(12.7625 + 2.21609i) q^{94} +(-7.84884 + 13.5946i) q^{95} +(-0.290202 + 9.79366i) q^{96} -5.53007i q^{97} +(-1.14065 + 0.418533i) q^{98} +(-0.863541 - 9.65285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 3 q^{2} + q^{4} - 3 q^{6} + 10 q^{9} + 8 q^{10} - 7 q^{12} + 2 q^{14} + 24 q^{15} - 15 q^{16} + 8 q^{17} - 6 q^{18} + q^{22} + 20 q^{23} + 12 q^{24} - 144 q^{25} - 20 q^{26} - 6 q^{28} + 7 q^{30}+ \cdots - 99 q^{98}+O(q^{100}) $ 320 * q - 3 * q^2 + q^4 - 3 * q^6 + 10 * q^9 + 8 * q^10 - 7 * q^12 + 2 * q^14 + 24 * q^15 - 15 * q^16 + 8 * q^17 - 6 * q^18 + q^22 + 20 * q^23 + 12 * q^24 - 144 * q^25 - 20 * q^26 - 6 * q^28 + 7 * q^30 + 12 * q^31 - 3 * q^32 + 18 * q^33 - 30 * q^34 + 39 * q^36 - 10 * q^38 + 44 * q^39 - 28 * q^40 + 10 * q^42 - 30 * q^46 - 12 * q^47 - 8 * q^48 - 316 * q^49 - 56 * q^52 + 36 * q^54 + 14 * q^55 + 52 * q^56 + 36 * q^57 - 3 * q^58 + 3 * q^60 - q^62 - 42 * q^63 - 26 * q^64 + 66 * q^65 + 50 * q^66 - 12 * q^68 + 3 * q^70 - 48 * q^71 + 21 * q^72 + 26 * q^74 + 35 * q^78 + 32 * q^79 - 48 * q^80 + 34 * q^81 - 23 * q^82 + 120 * q^84 + 42 * q^86 - 2 * q^87 + 13 * q^88 - 72 * q^89 + 109 * q^90 - 28 * q^92 + 130 * q^94 + 112 * q^95 - 15 * q^96 - 99 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.32766	+	0.487152i	−0.938798	+	0.344468i
$2$	−1.32766	+	0.487152i	−0.938798	+	0.344468i
$3$	1.69136	+	0.373231i	0.976507	+	0.215485i
$3$	1.69136	+	0.373231i	0.976507	+	0.215485i
$4$	1.52537	−	1.29354i	0.762683	−	0.646772i
$5$	1.73390	+	3.00321i	0.775425	+	1.34308i	0.934555	+	0.355818i	$0.115798\pi$
$5$	1.73390	+	3.00321i	0.775425	+	1.34308i	−0.159131	+	0.987258i	$0.550869\pi$
$6$	−2.42737	+	0.328425i	−0.990971	+	0.134079i
$7$		−	2.47808i		−	0.936624i	−0.883563	−	0.468312i	$-0.844862\pi$
$7$		−	2.47808i		−	0.936624i	0.883563	−	0.468312i	$-0.155138\pi$
$8$	−1.39502	+	2.46047i	−0.493213	+	0.869909i
$9$	2.72140	+	1.26253i	0.907133	+	0.420845i
$10$	−3.76505	−	3.14257i	−1.19061	−	0.993767i
$11$	−1.61523	−	2.79767i	−0.487011	−	0.843528i	0.512877	−	0.858462i	$-0.328580\pi$
$11$	−1.61523	−	2.79767i	−0.487011	−	0.843528i	−0.999888	+	0.0149338i	$0.995246\pi$
$12$	3.06273	−	1.61854i	0.884135	−	0.467231i
$13$	−3.34184	−	1.35355i	−0.926860	−	0.375408i
$13$	−3.34184	−	1.35355i	−0.926860	−	0.375408i
$14$	1.20720	+	3.29004i	0.322637	+	0.879301i
$15$	1.81176	+	5.72665i	0.467796	+	1.47861i
$16$	0.653486	−	3.94626i	0.163371	−	0.986565i
$17$	2.89335	+	5.01142i	0.701740	+	1.21545i	0.967855	+	0.251508i	$0.0809264\pi$
$17$	2.89335	+	5.01142i	0.701740	+	1.21545i	−0.266115	+	0.963941i	$0.585740\pi$
$18$	−4.22814	−	0.350485i	−0.996582	−	0.0826100i
$19$	2.26334	+	3.92023i	0.519247	+	0.899362i	0.999750	+	0.0223687i	$0.00712076\pi$
$19$	2.26334	+	3.92023i	0.519247	+	0.899362i	−0.480503	+	0.876993i	$0.659546\pi$
$20$	6.52962	+	2.33811i	1.46007	+	0.522818i
$21$	0.924894	−	4.19132i	0.201828	−	0.914620i
$22$	3.50737	+	2.92749i	0.747774	+	0.624143i
$23$	9.31152			1.94159			0.970793	−	0.239918i	$-0.0771207\pi$
$23$	9.31152			1.94159			0.970793	+	0.239918i	$0.0771207\pi$
$24$	−3.27780	+	3.64088i	−0.669078	+	0.743192i
$25$	−3.51284	+	6.08441i	−0.702567	+	1.21688i
$26$	5.09622	+	0.169075i	0.999450	+	0.0331584i
$27$	4.13165	+	3.15111i	0.795136	+	0.606431i
$28$	−3.20550	−	3.77997i	−0.605783	−	0.714348i
$29$	−3.40526	+	1.96603i	−0.632340	+	0.365082i	−0.781658	−	0.623708i	$-0.785626\pi$
$29$	−3.40526	+	1.96603i	−0.632340	+	0.365082i	0.149318	+	0.988789i	$0.452292\pi$
$30$	−5.19516	−	6.72045i	−0.948501	−	1.22698i
$31$	5.59979	−	3.23304i	1.00575	−	0.580671i	0.0958069	−	0.995400i	$-0.469457\pi$
$31$	5.59979	−	3.23304i	1.00575	−	0.580671i	0.909945	+	0.414729i	$0.136124\pi$
$32$	1.05482	+	5.55764i	0.186467	+	0.982461i
$33$	−1.68777	−	5.33472i	−0.293802	−	0.928655i
$34$	−6.28271	−	5.24397i	−1.07748	−	0.899334i
$35$	7.44217	−	4.29674i	1.25796	−	0.726282i
$36$	5.78427	−	1.59442i	0.964046	−	0.265737i
$37$	−1.66110	+	2.87710i	−0.273082	+	0.472993i	−0.969650	−	0.244499i	$-0.921377\pi$
$37$	−1.66110	+	2.87710i	−0.273082	+	0.472993i	0.696567	+	0.717492i	$0.254710\pi$
$38$	−4.91470	−	4.10214i	−0.797269	−	0.665455i
$39$	−5.14707	−	3.53662i	−0.824190	−	0.566313i
$40$	−9.80813	+	0.0766956i	−1.55080	+	0.0121266i
$41$			2.56416i			0.400454i	0.979750	+	0.200227i	$0.0641679\pi$
$41$			2.56416i			0.400454i	−0.979750	+	0.200227i	$0.935832\pi$
$42$	0.813862	+	6.01521i	0.125582	+	0.928167i
$43$			9.40931i			1.43491i	0.696607	+	0.717453i	$0.254692\pi$
$43$			9.40931i			1.43491i	−0.696607	+	0.717453i	$0.745308\pi$
$44$	−6.08273	−	2.17809i	−0.917006	−	0.328359i
$45$	0.926984	+	10.3620i	0.138187	+	1.54468i
$46$	−12.3625	+	4.53612i	−1.82276	+	0.668815i
$47$	−7.93235	−	4.57974i	−1.15705	−	0.668024i	−0.206456	−	0.978456i	$-0.566193\pi$
$47$	−7.93235	−	4.57974i	−1.15705	−	0.668024i	−0.950596	+	0.310431i	$0.899526\pi$
$48$	2.57814	−	6.43064i	0.372123	−	0.928183i
$49$	0.859143			0.122735
$50$	1.69982	−	9.78932i	0.240391	−	1.38442i
$51$	3.02327	+	9.55601i	0.423343	+	1.33811i
$52$	−6.84841	+	2.25816i	−0.949704	+	0.313150i
$53$			0.880344i			0.120925i	0.998170	+	0.0604623i	$0.0192575\pi$
$53$			0.880344i			0.120925i	−0.998170	+	0.0604623i	$0.980743\pi$
$54$	−7.02049	−	2.17087i	−0.955368	−	0.295418i
$55$	5.60131	−	9.70176i	0.755281	−	1.30819i
$56$	6.09724	+	3.45696i	0.814778	+	0.461955i
$57$	2.36498	+	7.47526i	0.313249	+	0.990123i
$58$	3.56327	−	4.26909i	0.467881	−	0.560559i
$59$	4.67229	−	8.09265i	0.608281	−	1.05357i	−0.383243	−	0.923648i	$-0.625193\pi$
$59$	4.67229	−	8.09265i	0.608281	−	1.05357i	0.991524	−	0.129926i	$-0.0414739\pi$
$60$	10.1713	+	6.39164i	1.31311	+	0.825158i
$61$		−	12.6184i		−	1.61562i	−0.589443	−	0.807810i	$-0.700653\pi$
$61$		−	12.6184i		−	1.61562i	0.589443	−	0.807810i	$-0.299347\pi$
$62$	−5.85964	+	7.02033i	−0.744175	+	0.891583i
$63$	3.12866	−	6.74383i	0.394174	−	0.849642i
$64$	−4.10786	−	6.86480i	−0.513482	−	0.858100i
$65$	−1.72943	−	12.3832i	−0.214509	−	1.53594i
$66$	4.83960	+	6.26049i	0.595713	+	0.770614i
$67$	−3.65076			−0.446012			−0.223006	−	0.974817i	$-0.571587\pi$
$67$	−3.65076			−0.446012			−0.223006	+	0.974817i	$0.571587\pi$
$68$	10.8959	+	3.90159i	1.32132	+	0.473137i
$69$	15.7491	+	3.47535i	1.89597	+	0.418382i
$70$	−7.78752	+	9.33008i	−0.930786	+	1.11516i
$71$	−3.31472	+	1.91375i	−0.393385	+	0.227121i	−0.683626	−	0.729833i	$-0.739598\pi$
$71$	−3.31472	+	1.91375i	−0.393385	+	0.227121i	0.290241	+	0.956954i	$0.406265\pi$
$72$	−6.90283	+	4.93467i	−0.813506	+	0.581556i
$73$		−	6.92009i		−	0.809935i	−0.914331	−	0.404968i	$-0.867283\pi$
$73$		−	6.92009i		−	0.809935i	0.914331	−	0.404968i	$-0.132717\pi$
$74$	0.803786	−	4.62902i	0.0934383	−	0.538113i
$75$	−8.21236	+	8.97983i	−0.948281	+	1.03690i
$76$	8.52342	+	3.05205i	0.977703	+	0.350094i
$77$	−6.93283	+	4.00267i	−0.790069	+	0.456147i
$78$	8.55643	+	2.18803i	0.968825	+	0.247746i
$79$	−5.76983	+	9.99363i	−0.649156	+	1.12437i	0.334169	+	0.942513i	$0.391545\pi$
$79$	−5.76983	+	9.99363i	−0.649156	+	1.12437i	−0.983325	+	0.181858i	$0.941789\pi$
$80$	12.9845	−	4.87987i	1.45171	−	0.545587i
$81$	5.81201	+	6.87172i	0.645779	+	0.763524i
$82$	−1.24913	−	3.40433i	−0.137944	−	0.375945i
$83$	−1.07422	+	1.86061i	−0.117911	+	0.204228i	−0.918940	−	0.394398i	$-0.870953\pi$
$83$	−1.07422	+	1.86061i	−0.117911	+	0.204228i	0.801029	+	0.598626i	$0.204286\pi$
$84$	−4.01085	−	7.58969i	−0.437620	−	0.828103i
$85$	−10.0336	+	17.3786i	−1.08829	+	1.88498i
$86$	−4.58376	−	12.4924i	−0.494280	−	1.34709i
$87$	−6.49329	+	2.05431i	−0.696154	+	0.220245i
$88$	9.13686	−	0.0714465i	0.973993	−	0.00761623i
$89$	−1.67046	−	0.964443i	−0.177069	−	0.102231i	0.408846	−	0.912603i	$-0.365931\pi$
$89$	−1.67046	−	0.964443i	−0.177069	−	0.102231i	−0.585915	+	0.810373i	$0.699265\pi$
$90$	−6.27860	−	13.3057i	−0.661823	−	1.40254i
$91$	−3.35420	+	8.28133i	−0.351616	+	0.868119i
$92$	14.2035	−	12.0449i	1.48082	−	1.25576i
$93$	10.6779	−	3.37822i	1.10725	−	0.350305i
$94$	12.7625	+	2.21609i	1.31635	+	0.228572i
$95$	−7.84884	+	13.5946i	−0.805274	+	1.39477i
$96$	−0.290202	+	9.79366i	−0.0296187	+	0.999561i
$97$		−	5.53007i		−	0.561494i	−0.959782	−	0.280747i	$-0.909418\pi$
$97$		−	5.53007i		−	0.561494i	0.959782	−	0.280747i	$-0.0905822\pi$
$98$	−1.14065	+	0.418533i	−0.115223	+	0.0422782i
$99$	−0.863541	−	9.65285i	−0.0867891	−	0.970148i
$100$	2.51209	+	13.8250i	0.251209	+	1.38250i
$101$	1.66684	−	0.962348i	0.165856	−	0.0957572i	−0.414774	−	0.909924i	$-0.636139\pi$
$101$	1.66684	−	0.962348i	0.165856	−	0.0957572i	0.580631	+	0.814167i	$0.302806\pi$
$102$	−8.66911	−	11.2143i	−0.858370	−	1.11039i
$103$	−3.97929	−	6.89234i	−0.392091	−	0.679122i	0.600634	−	0.799524i	$-0.294915\pi$
$103$	−3.97929	−	6.89234i	−0.392091	−	0.679122i	−0.992725	+	0.120402i	$0.961582\pi$
$104$	7.99230	−	6.33428i	0.783710	−	0.621127i
$105$	14.1911	−	4.48969i	1.38491	−	0.438149i
$106$	−0.428861	−	1.16880i	−0.0416547	−	0.113524i
$107$	6.79754	+	3.92456i	0.657143	+	0.379401i	0.791187	−	0.611574i	$-0.209463\pi$
$107$	6.79754	+	3.92456i	0.657143	+	0.379401i	−0.134045	+	0.990975i	$0.542797\pi$
$108$	10.3784	−	0.537870i	0.998660	−	0.0517566i
$109$	−15.9905			−1.53161			−0.765804	−	0.643074i	$-0.777659\pi$
$109$	−15.9905			−1.53161			−0.765804	+	0.643074i	$0.777659\pi$
$110$	−2.71042	+	15.6093i	−0.258428	+	1.48829i
$111$	−3.88333	+	4.24624i	−0.368590	+	0.403036i
$112$	−9.77913	−	1.61939i	−0.924041	−	0.153018i
$113$	4.92497	−	8.53031i	0.463303	−	0.802464i	−0.535821	−	0.844332i	$-0.679998\pi$
$113$	4.92497	−	8.53031i	0.463303	−	0.802464i	0.999123	+	0.0418682i	$0.0133310\pi$
$114$	−6.78148	−	8.77251i	−0.635144	−	0.821621i
$115$	16.1453	+	27.9644i	1.50555	+	2.60770i
$116$	−2.65112	+	7.40376i	−0.246150	+	0.687422i
$117$	−7.38557	−	7.90274i	−0.682796	−	0.730609i
$118$	−2.26087	+	13.0204i	−0.208130	+	1.19863i
$119$	12.4187	−	7.16993i	1.13842	−	0.657267i
$120$	−16.6177	−	3.53098i	−1.51698	−	0.322333i
$121$	0.282043	−	0.488512i	0.0256402	−	0.0444102i
$122$	6.14707	+	16.7529i	0.556530	+	1.51674i
$123$	−0.957022	+	4.33691i	−0.0862917	+	0.391046i
$124$	4.35965	−	12.1751i	0.391508	−	1.09336i
$125$	−7.02463			−0.628302
$126$	−0.868527	+	10.4776i	−0.0773746	+	0.933423i
$127$	6.28218	−	10.8811i	0.557453	−	0.965537i	−0.440255	−	0.897873i	$-0.645112\pi$
$127$	6.28218	−	10.8811i	0.557453	−	0.965537i	0.997708	−	0.0676643i	$-0.0215547\pi$
$128$	8.79804	+	7.11298i	0.777644	+	0.628705i
$129$	−3.51184	+	15.9145i	−0.309201	+	1.40120i
$130$	8.32857	+	15.5982i	0.730464	+	1.36805i
$131$	−14.2283	+	8.21474i	−1.24314	+	0.717725i	−0.969731	−	0.244174i	$-0.921483\pi$
$131$	−14.2283	+	8.21474i	−1.24314	+	0.717725i	−0.273405	+	0.961899i	$0.588150\pi$
$132$	−9.47515	−	5.95420i	−0.824706	−	0.518246i
$133$	9.71462	−	5.60874i	0.842364	−	0.486339i
$134$	4.84698	−	1.77848i	0.418715	−	0.153637i
$135$	−2.29957	+	17.8719i	−0.197915	+	1.53817i
$136$	−16.3667	+	0.127981i	−1.40344	+	0.0109743i
$137$			13.6048i			1.16233i	0.813784	+	0.581167i	$0.197404\pi$
$137$			13.6048i			1.16233i	−0.813784	+	0.581167i	$0.802596\pi$
$138$	−22.6025	+	3.05814i	−1.92405	+	0.260326i
$139$	4.57934	+	2.64388i	0.388415	+	0.224251i	0.681473	−	0.731843i	$-0.261340\pi$
$139$	4.57934	+	2.64388i	0.388415	+	0.224251i	−0.293058	+	0.956095i	$0.594673\pi$
$140$	5.79402	−	16.1809i	0.489684	−	1.36753i
$141$	−11.7072	−	10.7066i	−0.985921	−	0.901658i
$142$	3.46854	−	4.15559i	0.291073	−	0.348729i
$143$	1.61106	+	11.5357i	0.134724	+	0.964660i
$144$	6.76068	−	9.91429i	0.563390	−	0.826191i
$145$	−11.8088	−	6.81779i	−0.980664	−	0.566187i
$146$	3.37113	+	9.18753i	0.278997	+	0.760365i
$147$	1.45312	+	0.320659i	0.119851	+	0.0264475i
$148$	1.18788	+	6.53734i	0.0976431	+	0.537366i
$149$	−0.534032	+	0.924970i	−0.0437496	+	0.0757765i	−0.887071	−	0.461633i	$-0.847264\pi$
$149$	−0.534032	+	0.924970i	−0.0437496	+	0.0757765i	0.843321	+	0.537410i	$0.180597\pi$
$150$	6.52869	−	15.9228i	0.533065	−	1.30009i
$151$	−11.4326	−	6.60064i	−0.930376	−	0.537153i	−0.0434454	−	0.999056i	$-0.513833\pi$
$151$	−11.4326	−	6.60064i	−0.930376	−	0.537153i	−0.886930	+	0.461903i	$0.847167\pi$
$152$	−12.8030	+	0.100114i	−1.03846	+	0.00812035i
$153$	1.54685	+	17.2910i	0.125055	+	1.39790i
$154$	7.25454	−	8.69153i	0.584587	−	0.700383i
$155$	19.4190	+	11.2116i	1.55977	+	0.900534i
$156$	−12.4259	+	1.26332i	−0.994872	+	0.101146i
$157$	−2.61930	+	1.51225i	−0.209043	+	0.120691i	−0.600867	−	0.799349i	$-0.705178\pi$
$157$	−2.61930	+	1.51225i	−0.209043	+	0.120691i	0.391824	+	0.920040i	$0.371844\pi$
$158$	2.79196	−	16.0789i	0.222116	−	1.27917i
$159$	−0.328571	+	1.48898i	−0.0260574	+	0.118084i
$160$	−14.8618	+	12.8042i	−1.17493	+	1.01226i
$161$		−	23.0746i		−	1.81854i
$162$	−11.0639	−	6.29198i	−0.869266	−	0.494345i
$163$	−4.67579	−	8.09871i	−0.366236	−	0.634340i	0.622737	−	0.782431i	$-0.286020\pi$
$163$	−4.67579	−	8.09871i	−0.366236	−	0.634340i	−0.988974	+	0.148091i	$0.952687\pi$
$164$	3.31685	+	3.91128i	0.259002	+	0.305419i
$165$	13.0948	−	14.3186i	1.01943	−	1.11470i
$166$	0.519805	−	2.99356i	0.0403447	−	0.232346i
$167$		−	17.5854i		−	1.36080i	−0.732840	−	0.680401i	$-0.761805\pi$
$167$		−	17.5854i		−	1.36080i	0.732840	−	0.680401i	$-0.238195\pi$
$168$	9.02238	+	8.12263i	0.696092	+	0.626675i
$169$	9.33579	+	9.04671i	0.718138	+	0.695901i
$170$	4.85513	−	27.9608i	0.372372	−	2.14450i
$171$	1.21004	+	13.5260i	0.0925337	+	1.03436i
$172$	12.1714	+	14.3526i	0.928057	+	1.09438i
$173$		−	12.3624i		−	0.939893i	−0.882695	−	0.469946i	$-0.844273\pi$
$173$		−	12.3624i		−	0.939893i	0.882695	−	0.469946i	$-0.155727\pi$
$174$	7.62013	−	5.89065i	0.577681	−	0.446569i
$175$	15.0776	+	8.70507i	1.13976	+	0.658042i
$176$	−12.0958	+	4.54589i	−0.911759	+	0.342660i
$177$	10.9230	−	11.9437i	0.821020	−	0.897747i
$178$	2.68764	+	0.466684i	0.201447	+	0.0349794i
$179$	−5.18937	−	2.99608i	−0.387871	−	0.223938i	0.293366	−	0.956000i	$-0.405225\pi$
$179$	−5.18937	−	2.99608i	−0.387871	−	0.223938i	−0.681237	+	0.732063i	$0.738558\pi$
$180$	14.8177	+	14.6068i	1.10445	+	1.08873i
$181$		−	3.71126i		−	0.275855i	−0.990442	−	0.137928i	$-0.955956\pi$
$181$		−	3.71126i		−	0.275855i	0.990442	−	0.137928i	$-0.0440442\pi$
$182$	0.418981	−	12.6288i	0.0310569	−	0.936109i
$183$	4.70957	−	21.3422i	0.348142	−	1.57766i
$184$	−12.9897	+	22.9107i	−0.957615	+	1.68900i
$185$	−11.5207			−0.847020
$186$	−12.5310	+	9.68691i	−0.918815	+	0.710278i
$187$	9.34686	−	16.1892i	0.683510	−	1.18387i
$188$	−18.0238	+	3.27506i	−1.31452	+	0.238858i
$189$	7.80869	−	10.2385i	0.567999	−	0.744744i
$190$	3.79797	−	21.8726i	0.275534	−	1.58680i
$191$	−8.40882			−0.608441			−0.304220	−	0.952602i	$-0.598396\pi$
$191$	−8.40882			−0.608441			−0.304220	+	0.952602i	$0.598396\pi$
$192$	−4.38571	−	13.1440i	−0.316511	−	0.948589i
$193$			10.9838i			0.790634i	0.918545	+	0.395317i	$0.129365\pi$
$193$			10.9838i			0.790634i	−0.918545	+	0.395317i	$0.870635\pi$
$194$	2.69399	+	7.34206i	0.193417	+	0.527129i
$195$	1.69669	−	21.5899i	0.121503	−	1.54608i
$196$	1.31051	−	1.11134i	0.0936077	−	0.0793814i
$197$	−8.98236	+	15.5579i	−0.639966	+	1.10845i	0.345473	+	0.938429i	$0.387718\pi$
$197$	−8.98236	+	15.5579i	−0.639966	+	1.10845i	−0.985440	+	0.170026i	$0.945615\pi$
$198$	5.84889	+	12.3950i	0.415663	+	0.880877i
$199$	−9.16906	−	15.8813i	−0.649977	−	1.12579i	−0.983128	−	0.182920i	$-0.941445\pi$
$199$	−9.16906	−	15.8813i	−0.649977	−	1.12579i	0.333150	−	0.942874i	$-0.391888\pi$
$200$	−10.0701	−	17.1311i	−0.712061	−	1.21135i
$201$	−6.17476	−	1.36258i	−0.435534	−	0.0961088i
$202$	−1.74418	+	2.08967i	−0.122720	+	0.147029i
$203$	4.87196	+	8.43848i	0.341944	+	0.592265i
$204$	16.9727	+	10.6657i	1.18833	+	0.746747i
$205$	−7.70069	+	4.44600i	−0.537840	+	0.310522i
$206$	8.64076	+	7.21216i	0.602030	+	0.502495i
$207$	25.3403	+	11.7561i	1.76128	+	0.817107i
$208$	−7.52531	+	12.3032i	−0.521786	+	0.853076i
$209$	7.31166	−	12.6642i	0.505758	−	0.875998i
$210$	−16.6538	+	12.8740i	−1.14922	+	0.888390i
$211$		−	23.2309i		−	1.59928i	−0.600479	−	0.799640i	$-0.705024\pi$
$211$		−	23.2309i		−	1.59928i	0.600479	−	0.799640i	$-0.294976\pi$
$212$	1.13876	+	1.34285i	0.0782106	+	0.0922271i
$213$	−6.32066	+	1.99969i	−0.433084	+	0.137017i
$214$	−10.9367	−	1.89905i	−0.747616	−	0.129817i
$215$	−28.2581	+	16.3148i	−1.92719	+	1.11266i
$216$	−13.5169	+	5.76995i	−0.919711	+	0.392596i
$217$	−8.01172	−	13.8767i	−0.543871	−	0.942012i
$218$	21.2299	−	7.78978i	1.43787	−	0.527590i
$219$	2.58279	−	11.7044i	0.174529	−	0.790907i
$220$	−4.00560	−	22.0443i	−0.270058	−	1.48623i
$221$	−2.88588	−	20.6637i	−0.194125	−	1.38999i
$222$	3.08718	−	7.52934i	0.207198	−	0.505336i
$223$	13.3317	−	7.69704i	0.892754	−	0.515432i	0.0179119	−	0.999840i	$-0.494298\pi$
$223$	13.3317	−	7.69704i	0.892754	−	0.515432i	0.874842	+	0.484408i	$0.160965\pi$
$224$	13.7722	−	2.61392i	0.920197	−	0.174650i
$225$	−17.2416	+	12.1230i	−1.14944	+	0.808201i
$226$	−2.38314	+	13.7246i	−0.158524	+	0.912944i
$227$	15.7516			1.04547			0.522736	−	0.852495i	$-0.324911\pi$
$227$	15.7516			1.04547			0.522736	+	0.852495i	$0.324911\pi$
$228$	13.2770	+	8.34331i	0.879294	+	0.552549i
$229$	−1.45486	−	2.51989i	−0.0961398	−	0.166519i	0.813944	−	0.580943i	$-0.197316\pi$
$229$	−1.45486	−	2.51989i	−0.0961398	−	0.166519i	−0.910084	+	0.414424i	$0.863983\pi$
$230$	−35.0584	−	29.2621i	−2.31168	−	1.92948i
$231$	−13.2198	+	4.18241i	−0.869801	+	0.275182i
$232$	−0.0869631	−	11.1212i	−0.00570941	−	0.730141i
$233$	3.96547			0.259787			0.129893	−	0.991528i	$-0.458537\pi$
$233$	3.96547			0.259787			0.129893	+	0.991528i	$0.458537\pi$
$234$	13.6554	+	6.89427i	0.892679	+	0.450693i
$235$		−	31.7633i		−	2.07201i
$236$	−3.34124	−	18.3881i	−0.217496	−	1.19696i
$237$	−13.4888	+	14.7494i	−0.876191	+	0.958074i
$238$	−12.9950	+	15.5690i	−0.842338	+	1.00919i
$239$	−0.567210	+	0.327479i	−0.0366898	+	0.0211828i	−0.518233	−	0.855240i	$-0.673410\pi$
$239$	−0.567210	+	0.327479i	−0.0366898	+	0.0211828i	0.481543	+	0.876423i	$0.340077\pi$
$240$	23.7828	−	3.40741i	1.53517	−	0.219947i
$241$		−	19.4144i		−	1.25059i	−0.780388	−	0.625296i	$-0.784978\pi$
$241$		−	19.4144i		−	1.25059i	0.780388	−	0.625296i	$-0.215022\pi$
$242$	−0.136477	+	0.785976i	−0.00877310	+	0.0505245i
$243$	7.26547	+	13.7918i	0.466080	+	0.884743i
$244$	−16.3225	−	19.2477i	−1.04494	−	1.23221i
$245$	1.48967	+	2.58019i	0.0951716	+	0.164842i
$246$	−0.842133	−	6.22416i	−0.0536925	−	0.396838i
$247$	−2.25750	−	16.1643i	−0.143641	−	1.02851i
$248$	0.143007	+	18.2883i	0.00908095	+	1.16131i
$249$	−2.51133	+	2.74602i	−0.159149	+	0.174022i
$250$	9.32633	−	3.42206i	0.589849	−	0.216430i
$251$	−3.39275	+	1.95881i	−0.214149	+	0.123639i	−0.603238	−	0.797561i	$-0.706123\pi$
$251$	−3.39275	+	1.95881i	−0.214149	+	0.123639i	0.389089	+	0.921200i	$0.372790\pi$
$252$	−3.95109	−	14.3339i	−0.248895	−	0.902949i
$253$	−15.0403	−	26.0505i	−0.945574	−	1.63778i
$254$	−3.03988	+	17.5067i	−0.190739	+	1.09847i
$255$	−23.4566	+	25.6487i	−1.46891	+	1.60618i
$256$	−15.1459	−	5.15765i	−0.946620	−	0.322353i
$257$	−22.0055			−1.37266			−0.686331	−	0.727289i	$-0.740780\pi$
$257$	−22.0055			−1.37266			−0.686331	+	0.727289i	$0.740780\pi$
$258$	−3.09025	−	22.8399i	−0.192391	−	1.42195i
$259$	7.12967	+	4.11632i	0.443016	+	0.255776i
$260$	−18.6562	−	16.6518i	−1.15701	−	1.03270i
$261$	−11.7492	+	1.05108i	−0.727259	+	0.0650604i
$262$	14.8886	−	17.8377i	0.919820	−	1.10202i
$263$	6.88445	+	11.9242i	0.424513	+	0.735279i	0.996375	−	0.0850715i	$-0.0271119\pi$
$263$	6.88445	+	11.9242i	0.424513	+	0.735279i	−0.571861	+	0.820350i	$0.693779\pi$
$264$	15.4804	+	3.28931i	0.952752	+	0.202443i
$265$	−2.64385	+	1.52643i	−0.162411	+	0.0937679i
$266$	−10.1654	+	12.1790i	−0.623281	+	0.746742i
$267$	−2.46540	−	2.25469i	−0.150880	−	0.137985i
$268$	−5.56875	+	4.72243i	−0.340166	+	0.288468i
$269$	16.2392	−	9.37568i	0.990119	−	0.571646i	0.0848092	−	0.996397i	$-0.472972\pi$
$269$	16.2392	−	9.37568i	0.990119	−	0.571646i	0.905310	+	0.424752i	$0.139639\pi$
$270$	−5.65329	−	24.8481i	−0.344048	−	1.51221i
$271$	13.4204	+	7.74827i	0.815231	+	0.470674i	0.848769	−	0.528763i	$-0.177344\pi$
$271$	13.4204	+	7.74827i	0.815231	+	0.470674i	−0.0335379	+	0.999437i	$0.510677\pi$
$272$	21.6671	−	8.14300i	1.31376	−	0.493742i
$273$	−8.76401	+	12.7548i	−0.530422	+	0.771957i
$274$	−6.62759	−	18.0625i	−0.400387	−	1.09120i
$275$	22.6962			1.36863
$276$	28.5187	−	15.0710i	1.71662	−	0.907169i
$277$		−	14.1614i		−	0.850877i	−0.904987	−	0.425439i	$-0.860120\pi$
$277$		−	14.1614i		−	0.850877i	0.904987	−	0.425439i	$-0.139880\pi$
$278$	−7.36779	−	1.27935i	−0.441891	−	0.0767302i
$279$	19.3211	−	1.72846i	1.15672	−	0.103480i
$280$	0.190058	+	24.3053i	0.0113581	+	1.45252i
$281$	−13.8622	−	8.00333i	−0.826948	−	0.477439i	0.0258583	−	0.999666i	$-0.491768\pi$
$281$	−13.8622	−	8.00333i	−0.826948	−	0.477439i	−0.852807	+	0.522227i	$0.825101\pi$
$282$	20.7589	+	8.51156i	1.23617	+	0.506856i
$283$			1.68465i			0.100142i	0.998746	+	0.0500709i	$0.0159447\pi$
$283$			1.68465i			0.100142i	−0.998746	+	0.0500709i	$0.984055\pi$
$284$	−2.58064	+	7.20691i	−0.153133	+	0.427652i
$285$	−18.3491	+	20.0639i	−1.08691	+	1.18848i
$286$	−7.75856	−	14.5306i	−0.458773	−	0.859213i
$287$	6.35417			0.375075
$288$	−4.14613	+	16.4563i	−0.244313	+	0.969696i
$289$	−8.24292	+	14.2772i	−0.484877	+	0.839832i
$290$	18.9993	+	3.29906i	1.11568	+	0.193727i
$291$	2.06399	−	9.35335i	0.120993	−	0.548303i
$292$	−8.95144	−	10.5557i	−0.523844	−	0.617724i
$293$	−13.8222	+	23.9407i	−0.807500	+	1.39863i	0.107089	+	0.994249i	$0.465847\pi$
$293$	−13.8222	+	23.9407i	−0.807500	+	1.39863i	−0.914590	+	0.404382i	$0.867486\pi$
$294$	−2.08546	+	0.282164i	−0.121627	+	0.0164562i
$295$	32.4052			1.88670
$296$	−4.76178	−	8.10069i	−0.276773	−	0.470843i
$297$	2.14218	−	16.6487i	0.124302	−	0.966058i
$298$	0.258412	−	1.48820i	0.0149694	−	0.0862092i
$299$	−31.1176	−	12.6036i	−1.79958	−	0.728887i
$300$	−0.911047	+	24.3206i	−0.0525993	+	1.40415i
$301$	23.3170			1.34397
$302$	18.3942	+	3.19398i	1.05847	+	0.183793i
$303$	3.17840	−	1.00556i	0.182594	−	0.0577681i
$304$	16.9493	−	6.36993i	0.972109	−	0.365340i
$305$	37.8956	−	21.8791i	2.16990	−	1.25279i
$306$	−10.4770	−	22.2031i	−0.598933	−	1.26927i
$307$	8.87098			0.506293			0.253147	−	0.967428i	$-0.418534\pi$
$307$	8.87098			0.506293			0.253147	+	0.967428i	$0.418534\pi$
$308$	−5.39747	+	15.0735i	−0.307549	+	0.858890i
$309$	−4.15798	−	13.1426i	−0.236539	−	0.747657i
$310$	−31.2435	−	5.42515i	−1.77451	−	0.308128i
$311$	−0.568456	−	0.984595i	−0.0322342	−	0.0558313i	0.849458	−	0.527656i	$-0.176929\pi$
$311$	−0.568456	−	0.984595i	−0.0322342	−	0.0558313i	−0.881692	+	0.471825i	$0.843596\pi$
$312$	15.8820	−	7.73058i	0.899142	−	0.437658i
$313$	−1.30693	+	2.26368i	−0.0738722	+	0.127950i	−0.900595	−	0.434659i	$-0.856869\pi$
$313$	−1.30693	+	2.26368i	−0.0738722	+	0.127950i	0.826723	+	0.562609i	$0.190202\pi$
$314$	2.74085	−	3.28376i	0.154675	−	0.185313i
$315$	25.6779	−	2.29714i	1.44679	−	0.129429i
$316$	4.12611	+	22.7075i	0.232112	+	1.27740i
$317$	−4.28834	+	7.42763i	−0.240857	+	0.417177i	−0.960959	−	0.276692i	$-0.910762\pi$
$317$	−4.28834	+	7.42763i	−0.240857	+	0.417177i	0.720101	+	0.693869i	$0.244095\pi$
$318$	−0.289127	−	2.13692i	−0.0162134	−	0.119833i
$319$	11.0006	+	6.35118i	0.615913	+	0.355598i
$320$	13.4938	−	24.2396i	0.754327	−	1.35504i
$321$	10.0323	+	9.17489i	0.559949	+	0.512092i
$322$	11.2409	+	30.6353i	0.626428	+	1.70724i
$323$	−13.0973	+	22.6852i	−0.728752	+	1.26224i
$324$	17.7543	+	2.96380i	0.986351	+	0.164655i
$325$	19.9749	−	15.5783i	1.10801	−	0.864130i
$326$	10.1532	+	8.47452i	0.562332	+	0.469360i
$327$	−27.0456	−	5.96813i	−1.49563	−	0.330038i
$328$	−6.30904	−	3.57704i	−0.348358	−	0.197509i
$329$	−11.3490	+	19.6570i	−0.625688	+	1.08372i
$330$	−10.4102	+	25.3894i	−0.573061	+	1.39764i
$331$	−1.74541			−0.0959365			−0.0479682	−	0.998849i	$-0.515275\pi$
$331$	−1.74541			−0.0959365			−0.0479682	+	0.998849i	$0.515275\pi$
$332$	0.768196	+	4.22766i	0.0421602	+	0.232023i
$333$	−8.15294	+	5.73255i	−0.446779	+	0.314142i
$334$	8.56678	+	23.3475i	0.468753	+	1.27752i
$335$	−6.33007	−	10.9640i	−0.345849	−	0.599027i
$336$	−15.9356	−	6.38884i	−0.869359	−	0.348540i
$337$	−13.1942	−	22.8530i	−0.718734	−	1.24488i	−0.961502	−	0.274799i	$-0.911389\pi$
$337$	−13.1942	−	22.8530i	−0.718734	−	1.24488i	0.242768	−	0.970084i	$-0.421945\pi$
$338$	−16.8019	−	7.46302i	−0.913902	−	0.405935i
$339$	11.5137	−	12.5897i	0.625337	−	0.683777i
$340$	7.17518	+	39.4877i	0.389129	+	2.14152i
$341$	−18.0899	−	10.4442i	−0.979625	−	0.565587i
$342$	−8.19575	−	17.3685i	−0.443176	−	0.939183i
$343$		−	19.4755i		−	1.05158i
$344$	−23.1514	−	13.1261i	−1.24824	−	0.707714i
$345$	16.8703	+	53.3238i	0.908265	+	2.87086i
$346$	6.02234	+	16.4130i	0.323763	+	0.882370i
$347$	12.3044	+	7.10397i	0.660537	+	0.381361i	0.792482	−	0.609896i	$-0.208789\pi$
$347$	12.3044	+	7.10397i	0.660537	+	0.381361i	−0.131945	+	0.991257i	$0.542122\pi$
$348$	−7.24731	+	11.5329i	−0.388497	+	0.618231i
$349$	8.54404	+	14.7987i	0.457352	+	0.792157i	0.998820	−	0.0485644i	$-0.0154646\pi$
$349$	8.54404	+	14.7987i	0.457352	+	0.792157i	−0.541468	+	0.840721i	$0.682131\pi$
$350$	−24.2587	−	4.21229i	−1.29668	−	0.225156i
$351$	−9.54211	−	16.1229i	−0.509320	−	0.860577i
$352$	13.8446	−	11.9279i	0.737922	−	0.635760i
$353$	−11.9875	+	6.92098i	−0.638030	+	0.368367i	−0.783855	−	0.620944i	$-0.786750\pi$
$353$	−11.9875	+	6.92098i	−0.638030	+	0.368367i	0.145825	+	0.989310i	$0.453416\pi$
$354$	−8.68357	+	21.1784i	−0.461526	+	1.12562i
$355$	−11.4948	−	6.63653i	−0.610081	−	0.352230i
$356$	−3.79562	+	0.689691i	−0.201167	+	0.0365535i
$357$	23.6805	−	7.49190i	1.25331	−	0.396513i
$358$	8.34927	+	1.44977i	0.441272	+	0.0766228i
$359$			8.43809i			0.445345i	0.974893	+	0.222673i	$0.0714781\pi$
$359$			8.43809i			0.445345i	−0.974893	+	0.222673i	$0.928522\pi$
$360$	−26.7887	−	12.1744i	−1.41189	−	0.641647i
$361$	−0.745452	+	1.29116i	−0.0392343	+	0.0679559i
$362$	1.80794	+	4.92729i	0.0950234	+	0.258973i
$363$	0.659364	−	0.720983i	0.0346076	−	0.0378418i
$364$	5.59588	+	16.9709i	0.293304	+	0.889516i
$365$	20.7825	−	11.9988i	1.08780	−	0.628044i
$366$	4.14420	+	30.6295i	0.216621	+	1.60103i
$367$	12.7365	+	22.0603i	0.664842	+	1.15154i	0.979328	+	0.202279i	$0.0648347\pi$
$367$	12.7365	+	22.0603i	0.664842	+	1.15154i	−0.314486	+	0.949262i	$0.601832\pi$
$368$	6.08494	−	36.7457i	0.317200	−	1.91550i
$369$	−3.23734	+	6.97809i	−0.168529	+	0.363265i
$370$	15.2956	−	5.61233i	0.795180	−	0.291771i
$371$	2.18156			0.113261
$372$	11.9179	−	18.9654i	0.617913	−	0.983310i
$373$	−9.34774	−	5.39692i	−0.484008	−	0.279442i	0.238077	−	0.971246i	$-0.423483\pi$
$373$	−9.34774	−	5.39692i	−0.484008	−	0.279442i	−0.722085	+	0.691804i	$0.756816\pi$
$374$	−4.52285	+	26.0472i	−0.233871	+	1.34687i
$375$	−11.8812	−	2.62181i	−0.613542	−	0.135390i
$376$	22.3341	−	13.1285i	1.15179	−	0.677051i
$377$	14.0409	−	1.96095i	0.723145	−	0.100994i
$378$	−5.37957	+	17.3973i	−0.276695	+	0.894821i
$379$	4.88143	−	8.45489i	0.250742	−	0.434299i	−0.712988	−	0.701176i	$-0.752659\pi$
$379$	4.88143	−	8.45489i	0.250742	−	0.434299i	0.963730	+	0.266878i	$0.0859920\pi$
$380$	5.61285	+	30.8895i	0.287933	+	1.58460i
$381$	14.6866	−	16.0591i	0.752416	−	0.822731i
$382$	11.1641	−	4.09637i	0.571203	−	0.209588i
$383$	7.38723	+	4.26502i	0.377470	+	0.217932i	0.676717	−	0.736243i	$-0.263402\pi$
$383$	7.38723	+	4.26502i	0.377470	+	0.217932i	−0.299247	+	0.954176i	$0.596735\pi$
$384$	12.2259	+	15.3143i	0.623899	+	0.781505i
$385$	−24.0417	−	13.8805i	−1.22528	−	0.707415i
$386$	−5.35080	−	14.5828i	−0.272348	−	0.742246i
$387$	−11.8796	+	25.6065i	−0.603873	+	1.30165i
$388$	−7.15340	−	8.43539i	−0.363159	−	0.428242i
$389$	−29.9066	−	17.2666i	−1.51633	−	0.875451i	−0.999816	−	0.0191691i	$-0.993898\pi$
$389$	−29.9066	−	17.2666i	−1.51633	−	0.875451i	−0.516509	−	0.856282i	$-0.672769\pi$
$390$	8.26491	+	29.4906i	0.418510	+	1.49331i
$391$	26.9415	+	46.6640i	1.36249	+	2.35990i
$392$	−1.19852	+	2.11390i	−0.0605344	+	0.106768i
$393$	−27.1312	+	8.58362i	−1.36859	+	0.432987i
$394$	4.34647	−	25.0314i	0.218972	−	1.26106i
$395$	−40.0173			−2.01349
$396$	−13.8036	−	13.6071i	−0.693657	−	0.683783i
$397$	8.25485	+	14.2978i	0.414299	+	0.717587i	0.995355	−	0.0962767i	$-0.0306934\pi$
$397$	8.25485	+	14.2978i	0.414299	+	0.717587i	−0.581055	+	0.813864i	$0.697360\pi$
$398$	19.9100	+	16.6182i	0.997998	+	0.832996i
$399$	18.5243	−	5.86060i	0.927373	−	0.293397i
$400$	21.7151	+	17.8386i	1.08575	+	0.891932i
$401$			1.04298i			0.0520840i	0.999661	+	0.0260420i	$0.00829036\pi$
$401$			1.04298i			0.0520840i	−0.999661	+	0.0260420i	$0.991710\pi$
$402$	8.86176	−	1.19900i	0.441985	−	0.0598008i
$403$	−23.0897	+	3.22470i	−1.15018	+	0.160634i
$404$	1.29770	−	3.62406i	0.0645628	−	0.180304i
$405$	−10.5597	+	29.3696i	−0.524718	+	1.45939i
$406$	−10.5791	−	8.83006i	−0.525033	−	0.438228i
$407$	10.7322			0.531977
$408$	−27.7298	−	5.89211i	−1.37283	−	0.291703i
$409$	−28.2628	−	16.3175i	−1.39751	−	0.806851i	−0.403375	−	0.915035i	$-0.632163\pi$
$409$	−28.2628	−	16.3175i	−1.39751	−	0.806851i	−0.994131	+	0.108184i	$0.965496\pi$
$410$	8.05803	−	9.65418i	0.397958	−	0.476786i
$411$	−5.07772	+	23.0106i	−0.250466	+	1.13503i
$412$	−14.9854	−	5.36595i	−0.738279	−	0.264361i
$413$	−20.0542	−	11.5783i	−0.986803	−	0.569731i
$414$	−39.3704	−	3.26355i	−1.93495	−	0.160394i
$415$	−7.45039			−0.365725
$416$	3.99752	−	20.0005i	0.195994	−	0.980605i
$417$	6.75854	+	6.18091i	0.330967	+	0.302681i
$418$	−3.53803	+	20.3756i	−0.173051	+	0.996603i
$419$		−	2.36999i		−	0.115782i	−0.998323	−	0.0578909i	$-0.981562\pi$
$419$		−	2.36999i		−	0.115782i	0.998323	−	0.0578909i	$-0.0184375\pi$
$420$	15.8390	−	25.2052i	0.772863	−	1.22989i
$421$	−8.22286	+	14.2424i	−0.400758	+	0.694133i	−0.993818	−	0.111026i	$-0.964586\pi$
$421$	−8.22286	+	14.2424i	−0.400758	+	0.694133i	0.593060	+	0.805158i	$0.297920\pi$
$422$	11.3170	+	30.8427i	0.550901	+	1.50140i
$423$	−15.8050	−	22.4782i	−0.768465	−	1.09293i
$424$	−2.16606	−	1.22809i	−0.105193	−	0.0596415i
$425$	−40.6554			−1.97208
$426$	7.41753	−	5.73403i	0.359381	−	0.277815i
$427$	−31.2693			−1.51323
$428$	15.4453	−	2.80652i	0.746578	−	0.135658i
$429$	−1.58057	+	20.1122i	−0.0763107	+	0.971028i
$430$	29.5694	−	35.4265i	1.42596	−	1.70842i
$431$	−28.5426	−	16.4791i	−1.37485	−	0.793770i	−0.383316	−	0.923617i	$-0.625218\pi$
$431$	−28.5426	−	16.4791i	−1.37485	−	0.793770i	−0.991534	+	0.129848i	$0.958551\pi$
$432$	15.1351	−	14.2453i	0.728186	−	0.685379i
$433$	16.8792	+	29.2356i	0.811161	+	1.40497i	0.912052	+	0.410075i	$0.134497\pi$
$433$	16.8792	+	29.2356i	0.811161	+	1.40497i	−0.100891	+	0.994897i	$0.532169\pi$
$434$	17.3969	+	14.5206i	0.835078	+	0.697013i
$435$	−17.4283	−	15.9387i	−0.835621	−	0.764204i
$436$	−24.3913	+	20.6844i	−1.16813	+	0.990601i
$437$	21.0752	+	36.5033i	1.00816	+	1.74619i
$438$	2.27273	+	16.7976i	0.108595	+	0.802622i
$439$	11.4565	+	19.8433i	0.546790	+	0.947068i	0.998492	+	0.0548990i	$0.0174837\pi$
$439$	11.4565	+	19.8433i	0.546790	+	0.947068i	−0.451702	+	0.892169i	$0.649183\pi$
$440$	16.0570	+	27.3160i	0.765487	+	1.30224i
$441$	2.33807	+	1.08470i	0.111337	+	0.0516523i
$442$	13.8978	+	26.0285i	0.661052	+	1.23805i
$443$	−18.2287	−	10.5244i	−0.866072	−	0.500027i	−3.11954e−5	−	1.00000i	$-0.500010\pi$
$443$	−18.2287	−	10.5244i	−0.866072	−	0.500027i	−0.866041	+	0.499973i	$0.833343\pi$
$444$	−0.430802	+	11.5003i	−0.0204450	+	0.545782i
$445$		−	6.68900i		−	0.317089i
$446$	−13.9503	+	16.7136i	−0.660566	+	0.791412i
$447$	−1.24847	+	1.36514i	−0.0590505	+	0.0645689i
$448$	−17.0115	+	10.1796i	−0.803718	+	0.480940i
$449$	22.3680	−	12.9142i	1.05561	−	0.609457i	0.131396	−	0.991330i	$-0.458054\pi$
$449$	22.3680	−	12.9142i	1.05561	−	0.609457i	0.924215	+	0.381873i	$0.124721\pi$
$450$	16.9853	−	24.4945i	0.800692	−	1.15468i
$451$	7.17365	−	4.14171i	0.337794	−	0.195025i
$452$	−3.52194	−	19.3825i	−0.165658	−	0.911677i
$453$	−16.8732	−	15.4311i	−0.792770	−	0.725015i
$454$	−20.9128	+	7.67343i	−0.981487	+	0.360132i
$455$	−30.6864	+	4.28565i	−1.43860	+	0.200914i
$456$	−21.6919	−	4.60915i	−1.01582	−	0.215843i
$457$	−13.2887	+	7.67221i	−0.621617	+	0.358891i	−0.777498	−	0.628885i	$-0.783512\pi$
$457$	−13.2887	+	7.67221i	−0.621617	+	0.358891i	0.155881	+	0.987776i	$0.450178\pi$
$458$	3.15913	+	2.63682i	0.147616	+	0.123211i
$459$	−3.83726	+	29.8227i	−0.179108	+	1.39200i
$460$	60.8007	+	21.7714i	2.83485	+	1.01510i
$461$	5.39432			0.251238			0.125619	−	0.992079i	$-0.459908\pi$
$461$	5.39432			0.251238			0.125619	+	0.992079i	$0.459908\pi$
$462$	15.5140	−	11.9929i	0.721775	−	0.557959i
$463$	26.5313	−	15.3179i	1.23301	−	0.711882i	0.265358	−	0.964150i	$-0.414510\pi$
$463$	26.5313	−	15.3179i	1.23301	−	0.711882i	0.967657	+	0.252269i	$0.0811766\pi$
$464$	5.53316	+	14.7228i	0.256870	+	0.683488i
$465$	28.6600	+	26.2105i	1.32908	+	1.21548i
$466$	−5.26480	+	1.93179i	−0.243887	+	0.0894883i
$467$			17.6196i			0.815340i	0.913129	+	0.407670i	$0.133659\pi$
$467$			17.6196i			0.815340i	−0.913129	+	0.407670i	$0.866341\pi$
$468$	−21.4883	−	2.50102i	−0.993295	−	0.115610i
$469$			9.04687i			0.417746i
$470$	15.4736	+	42.1709i	0.713742	+	1.94520i
$471$	−4.99460	+	1.58016i	−0.230139	+	0.0728101i
$472$	13.3938	+	22.7854i	0.616501	+	1.04878i
$473$	26.3241	−	15.1982i	1.21038	−	0.698815i
$474$	10.7234	−	26.1532i	0.492540	−	1.20126i
$475$	−31.8030			−1.45922
$476$	9.66842	−	27.0009i	0.443151	−	1.23758i
$477$	−1.11146	+	2.39577i	−0.0508905	+	0.109695i
$478$	0.593530	−	0.711098i	0.0271474	−	0.0325249i
$479$	−3.53413	+	2.04043i	−0.161478	+	0.0932296i	−0.578562	−	0.815639i	$-0.696386\pi$
$479$	−3.53413	+	2.04043i	−0.161478	+	0.0932296i	0.417083	+	0.908868i	$0.363052\pi$
$480$	−29.9156	+	16.1097i	−1.36545	+	0.735304i
$481$	9.44542	−	7.36644i	0.430674	−	0.335881i
$482$	9.45776	+	25.7757i	0.430789	+	1.17405i
$483$	8.61217	−	39.0275i	0.391867	−	1.77581i
$484$	−0.201694	−	1.11000i	−0.00916790	−	0.0504543i
$485$	16.6080	−	9.58861i	0.754129	−	0.435396i
$486$	−16.3648	−	14.7714i	−0.742321	−	0.670045i
$487$	9.27754	−	5.35639i	0.420405	−	0.242721i	−0.274845	−	0.961488i	$-0.588627\pi$
$487$	9.27754	−	5.35639i	0.420405	−	0.242721i	0.695251	+	0.718767i	$0.255293\pi$
$488$	31.0472	+	17.6029i	1.40544	+	0.796845i
$489$	−4.88576	−	15.4430i	−0.220942	−	0.698356i
$490$	−3.23472	−	2.69992i	−0.146130	−	0.121970i
$491$		−	2.04088i		−	0.0921037i	−0.998939	−	0.0460519i	$-0.985336\pi$
$491$		−	2.04088i		−	0.0921037i	0.998939	−	0.0460519i	$-0.0146640\pi$
$492$	4.15018	+	7.85333i	0.187104	+	0.354055i
$493$	−19.7052	−	11.3768i	−0.887476	−	0.512385i
$494$	10.8717	+	20.3610i	0.489140	+	0.916085i
$495$	27.4922	−	19.3305i	1.23568	−	0.868841i
$496$	−9.09903	−	24.2110i	−0.408559	−	1.08710i
$497$	4.74243	+	8.21413i	0.212727	+	0.368454i
$498$	1.99647	−	4.86919i	0.0894638	−	0.218194i
$499$	−14.1779	−	24.5568i	−0.634689	−	1.09931i	−0.986581	−	0.163273i	$-0.947795\pi$
$499$	−14.1779	−	24.5568i	−0.634689	−	1.09931i	0.351891	−	0.936041i	$-0.385539\pi$
$500$	−10.7151	+	9.08668i	−0.479196	+	0.406368i
$501$	6.56343	−	29.7433i	0.293232	−	1.32883i
$502$	3.55019	−	4.25342i	0.158453	−	0.189839i
$503$	3.15519	+	5.46495i	0.140683	+	0.243670i	0.927754	−	0.373192i	$-0.121737\pi$
$503$	3.15519	+	5.46495i	0.140683	+	0.243670i	−0.787071	+	0.616862i	$0.788404\pi$
$504$	12.2285	+	17.1057i	0.544700	+	0.761950i
$505$	5.78026	+	3.33724i	0.257218	+	0.148505i
$506$	32.6589	+	27.2594i	1.45187	+	1.21183i
$507$	12.4137	+	18.7856i	0.551311	+	0.834300i
$508$	−4.49250	−	24.7239i	−0.199322	−	1.09694i
$509$	17.2739			0.765653			0.382826	−	0.923820i	$-0.374951\pi$
$509$	17.2739			0.765653			0.382826	+	0.923820i	$0.374951\pi$
$510$	18.6476	−	45.4797i	0.825730	−	2.01388i
$511$	−17.1485			−0.758605
$512$	22.6212	−	0.530752i	0.999725	−	0.0234562i
$513$	−3.00173	+	23.3290i	−0.132530	+	1.03000i
$514$	29.2158	−	10.7200i	1.28865	−	0.472839i
$515$	13.7994	−	23.9013i	0.608075	−	1.05322i
$516$	15.2293	+	28.8182i	0.670433	+	1.26865i
$517$			29.5894i			1.30134i
$518$	−11.4711	−	1.99184i	−0.504010	−	0.0875166i
$519$	4.61401	−	20.9092i	0.202533	−	0.917812i
$520$	32.8810	+	13.0195i	1.44193	+	0.570944i
$521$	−44.4327			−1.94663			−0.973315	−	0.229472i	$-0.926300\pi$
$521$	−44.4327			−1.94663			−0.973315	+	0.229472i	$0.926300\pi$
$522$	15.0870	−	7.11914i	0.660338	−	0.311596i
$523$	6.45773	+	3.72837i	0.282377	+	0.163030i	0.634499	−	0.772924i	$-0.281206\pi$
$523$	6.45773	+	3.72837i	0.282377	+	0.163030i	−0.352122	+	0.935954i	$0.614540\pi$
$524$	−11.0773	+	30.9355i	−0.483914	+	1.35142i
$525$	22.2527	+	20.3508i	0.971187	+	0.888184i
$526$	−14.9491	−	12.4775i	−0.651812	−	0.544047i
$527$	32.4043	+	18.7086i	1.41155	+	0.814960i
$528$	−22.1551	+	3.17420i	−0.964177	+	0.138139i
$529$	63.7044			2.76976
$530$	2.76654	−	3.31454i	0.120171	−	0.143974i
$531$	22.9324	−	16.1244i	0.995183	−	0.699739i
$532$	7.56320	−	21.1217i	0.327906	−	0.915740i
$533$	3.47072	−	8.56900i	0.150334	−	0.371165i
$534$	4.37159	+	1.79244i	0.189177	+	0.0775665i
$535$			27.2192i			1.17679i
$536$	5.09288	−	8.98261i	0.219979	−	0.387990i
$537$	−7.65886	−	7.00428i	−0.330504	−	0.302257i
$538$	−16.9927	+	20.3587i	−0.732608	+	0.877724i
$539$	−1.38772	−	2.40360i	−0.0597732	−	0.103530i
$540$	19.6104	+	30.2358i	0.843898	+	1.30114i
$541$	−8.28455			−0.356181			−0.178090	−	0.984014i	$-0.556992\pi$
$541$	−8.28455			−0.356181			−0.178090	+	0.984014i	$0.556992\pi$
$542$	−21.5923	−	3.74931i	−0.927470	−	0.161047i
$543$	1.38515	−	6.27707i	0.0594427	−	0.269375i
$544$	−24.7997	+	21.3663i	−1.06328	+	0.916074i
$545$	−27.7259	−	48.0226i	−1.18765	−	2.05706i
$546$	5.42211	−	21.2035i	0.232045	−	0.907425i
$547$	8.87764	+	5.12551i	0.379581	+	0.219151i	0.677636	−	0.735398i	$-0.263005\pi$
$547$	8.87764	+	5.12551i	0.379581	+	0.219151i	−0.298055	+	0.954549i	$0.596338\pi$
$548$	17.5984	+	20.7523i	0.751766	+	0.886493i
$549$	15.9312	−	34.3397i	0.679925	−	1.46558i
$550$	−30.1329	+	11.0565i	−1.28487	+	0.471450i
$551$	−15.4145	−	8.89958i	−0.656681	−	0.379135i
$552$	−30.5213	+	33.9022i	−1.29907	+	1.44297i
$553$	24.7650	+	14.2981i	1.05311	+	0.608016i
$554$	6.89876	+	18.8016i	0.293100	+	0.798802i
$555$	−19.4857	−	4.29988i	−0.827121	−	0.182520i
$556$	10.4052	−	1.89069i	0.441277	−	0.0801831i
$557$	10.3163	−	17.8684i	0.437117	−	0.757109i	−0.560348	−	0.828257i	$-0.689333\pi$
$557$	10.3163	−	17.8684i	0.437117	−	0.757109i	0.997466	+	0.0711475i	$0.0226661\pi$
$558$	−24.8098	+	11.7071i	−1.05028	+	0.495601i
$559$	12.7360	−	31.4444i	0.538675	−	1.32996i
$560$	−12.0927	−	32.1766i	−0.511010	−	1.35971i
$561$	21.8512	−	23.8933i	0.922560	−	1.00878i
$562$	22.3031	+	3.87273i	0.940800	+	0.163361i
$563$	−3.30298	−	1.90698i	−0.139204	−	0.0803695i	0.428781	−	0.903409i	$-0.358943\pi$
$563$	−3.30298	−	1.90698i	−0.139204	−	0.0803695i	−0.567985	+	0.823039i	$0.692277\pi$
$564$	−31.7072	−	1.18775i	−1.33511	−	0.0500132i
$565$	34.1577			1.43703
$566$	−0.820679	−	2.23664i	−0.0344957	−	0.0940130i
$567$	17.0286	−	14.4026i	0.715136	−	0.604852i
$568$	−0.0846510	−	10.8255i	−0.00355188	−	0.454228i
$569$	−8.26526	−	14.3159i	−0.346498	−	0.600152i	0.639127	−	0.769101i	$-0.279296\pi$
$569$	−8.26526	−	14.3159i	−0.346498	−	0.600152i	−0.985625	+	0.168949i	$0.945963\pi$
$570$	14.5872	−	35.5769i	0.610992	−	1.49015i
$571$	−0.0104374	+	0.00602605i	−0.000436793	+	0.000252183i	−0.500218	−	0.865899i	$-0.666747\pi$
$571$	−0.0104374	+	0.00602605i	−0.000436793	+	0.000252183i	0.499782	+	0.866151i	$0.333414\pi$
$572$	17.3793	+	15.5121i	0.726667	+	0.648594i
$573$	−14.2223	−	3.13843i	−0.594147	−	0.131110i
$574$	−8.43618	+	3.09545i	−0.352119	+	0.129201i
$575$	−32.7098	+	56.6551i	−1.36409	+	2.36268i
$576$	−2.51206	−	23.8682i	−0.104669	−	0.994507i
$577$			27.4629i			1.14330i	0.820499	+	0.571648i	$0.193696\pi$
$577$			27.4629i			1.14330i	−0.820499	+	0.571648i	$0.806304\pi$
$578$	3.98866	−	22.9708i	0.165906	−	0.955458i
$579$	−4.09951	+	18.5776i	−0.170370	+	0.772060i
$580$	−26.8318	+	4.87553i	−1.11413	+	0.202445i
$581$	4.61072	+	2.66200i	0.191285	+	0.110439i
$582$	1.81622	+	13.4236i	0.0752846	+	0.556424i
$583$	2.46291	−	1.42196i	0.102003	−	0.0588916i
$584$	17.0267	+	9.65364i	0.704570	+	0.399470i
$585$	10.9277	−	35.8830i	0.451806	−	1.48358i
$586$	6.68841	−	38.5187i	0.276296	−	1.59119i
$587$	7.77033	+	13.4586i	0.320716	+	0.555496i	0.980636	−	0.195840i	$-0.0627433\pi$
$587$	7.77033	+	13.4586i	0.320716	+	0.555496i	−0.659920	+	0.751336i	$0.729410\pi$
$588$	2.63133	−	1.39055i	0.108514	−	0.0573455i
$589$	25.3485	+	14.6350i	1.04447	+	0.603023i
$590$	−43.0231	+	15.7863i	−1.77123	+	0.649910i
$591$	−20.9991	+	22.9615i	−0.863787	+	0.944511i
$592$	10.2683	+	8.43526i	0.422024	+	0.346687i
$593$			10.4922i			0.430861i	0.976519	+	0.215431i	$0.0691155\pi$
$593$			10.4922i			0.430861i	−0.976519	+	0.215431i	$0.930884\pi$
$594$	5.26637	+	23.1475i	0.216082	+	0.949752i
$595$	43.0656	+	24.8639i	1.76552	+	1.01932i
$596$	0.381896	+	2.10171i	0.0156431	+	0.0860895i
$597$	−9.58080	−	30.2831i	−0.392116	−	1.23941i
$598$	47.4535	+	1.57435i	1.94052	+	0.0643798i
$599$	−5.23291	−	9.06367i	−0.213811	−	0.370331i	0.739093	−	0.673603i	$-0.235254\pi$
$599$	−5.23291	−	9.06367i	−0.213811	−	0.370331i	−0.952904	+	0.303272i	$0.901921\pi$
$600$	−10.6383	−	32.7333i	−0.434305	−	1.33633i
$601$	11.1060	+	19.2362i	0.453025	+	0.784663i	0.998572	−	0.0534175i	$-0.0170114\pi$
$601$	11.1060	+	19.2362i	0.453025	+	0.784663i	−0.545547	+	0.838080i	$0.683678\pi$
$602$	−30.9570	+	11.3589i	−1.26171	+	0.462954i
$603$	−9.93518	−	4.60922i	−0.404592	−	0.187702i
$604$	−25.9772	+	4.72024i	−1.05700	+	0.192064i
$605$	1.95614			0.0795283
$606$	−3.72997	+	2.88341i	−0.151520	+	0.117130i
$607$	14.8834	−	25.7788i	0.604099	−	1.04633i	−0.388094	−	0.921620i	$-0.626866\pi$
$607$	14.8834	−	25.7788i	0.604099	−	1.04633i	0.992193	−	0.124711i	$-0.0398003\pi$
$608$	−19.3998	+	16.7140i	−0.786765	+	0.677841i
$609$	5.09074	+	16.0909i	0.206287	+	0.652035i
$610$	−39.6541	+	47.5089i	−1.60555	+	1.92358i
$611$	20.3097	+	26.0416i	0.821643	+	1.05353i
$612$	24.7262	+	24.3742i	0.999499	+	0.985270i
$613$	−12.3164	+	21.3326i	−0.497453	+	0.861614i	−0.999996	−	0.00293837i	$-0.999065\pi$
$613$	−12.3164	+	21.3326i	−0.497453	+	0.861614i	0.502543	+	0.864552i	$0.332398\pi$
$614$	−11.7776	+	4.32151i	−0.475307	+	0.174402i
$615$	−14.6840	+	4.64565i	−0.592117	+	0.187331i
$616$	−0.177050	−	22.6418i	−0.00713354	−	0.912265i
$617$	32.8727	+	18.9791i	1.32341	+	0.764069i	0.984270	−	0.176669i	$-0.0565321\pi$
$617$	32.8727	+	18.9791i	1.32341	+	0.764069i	0.339136	+	0.940737i	$0.389865\pi$
$618$	11.9228	+	15.4234i	0.479607	+	0.620419i
$619$	−6.20697	+	10.7508i	−0.249479	+	0.432110i	−0.963381	−	0.268135i	$-0.913593\pi$
$619$	−6.20697	+	10.7508i	−0.249479	+	0.432110i	0.713902	+	0.700245i	$0.246926\pi$
$620$	44.1237	−	8.01759i	1.77205	−	0.321994i
$621$	38.4719	+	29.3416i	1.54382	+	1.17744i
$622$	1.23436	+	1.03028i	0.0494935	+	0.0413106i
$623$	−2.38996	+	4.13954i	−0.0957518	+	0.165847i
$624$	−17.3200	+	18.0005i	−0.693353	+	0.720598i
$625$	5.38415	+	9.32562i	0.215366	+	0.373025i
$626$	0.632411	−	3.64207i	0.0252762	−	0.145566i
$627$	17.0933	−	18.6907i	0.682641	−	0.746436i
$628$	−2.03923	+	5.69493i	−0.0813740	+	0.227252i
$629$	−19.2245			−0.766531
$630$	−32.9725	+	15.5589i	−1.31366	+	0.619879i
$631$	−16.8053	+	9.70255i	−0.669009	+	0.386252i	−0.795701	−	0.605690i	$-0.792897\pi$
$631$	−16.8053	+	9.70255i	−0.669009	+	0.386252i	0.126692	+	0.991942i	$0.459564\pi$
$632$	−16.5401	−	28.1378i	−0.657928	−	1.11926i
$633$	8.67048	−	39.2918i	0.344621	−	1.56171i
$634$	2.07508	−	11.9504i	0.0824121	−	0.474613i
$635$	43.5707			1.72905
$636$	1.42487	+	2.69626i	0.0564997	+	0.106914i
$637$	−2.87112	−	1.16290i	−0.113758	−	0.0460756i
$638$	−17.6990	−	3.07327i	−0.700710	−	0.121672i
$639$	−11.4369	+	1.02314i	−0.452435	+	0.0404747i
$640$	−6.10681	+	38.7556i	−0.241393	+	1.53195i
$641$	−36.1624			−1.42833			−0.714165	−	0.699978i	$-0.753193\pi$
$641$	−36.1624			−1.42833			−0.714165	+	0.699978i	$0.753193\pi$
$642$	−17.7891	−	7.29388i	−0.702079	−	0.287867i
$643$	5.12680	−	8.87989i	0.202181	−	0.350189i	−0.747050	−	0.664768i	$-0.768530\pi$
$643$	5.12680	−	8.87989i	0.202181	−	0.350189i	0.949231	+	0.314580i	$0.101864\pi$
$644$	−29.8481	−	35.1973i	−1.17618	−	1.38697i
$645$	−53.8838	+	17.0475i	−2.12167	+	0.671243i
$646$	6.33763	−	36.4986i	0.249351	−	1.43602i
$647$	18.0258	−	31.2216i	0.708667	−	1.22745i	−0.256684	−	0.966495i	$-0.582630\pi$
$647$	18.0258	−	31.2216i	0.708667	−	1.22745i	0.965352	−	0.260952i	$-0.0840366\pi$
$648$	−25.0155	+	4.71413i	−0.982703	+	0.185189i
$649$	−30.1874			−1.18496
$650$	−18.9309	+	30.4135i	−0.742531	+	1.19292i
$651$	−8.37149	−	26.4607i	−0.328104	−	1.03708i
$652$	−17.6083	−	6.30515i	−0.689596	−	0.246929i
$653$		−	1.17273i		−	0.0458924i	−0.999737	−	0.0229462i	$-0.992695\pi$
$653$		−	1.17273i		−	0.0458924i	0.999737	−	0.0229462i	$-0.00730464\pi$
$654$	38.8148	−	5.25167i	1.51778	−	0.205356i
$655$	−49.3411	−	28.4871i	−1.92792	−	1.11308i
$656$	10.1188	+	1.67564i	0.395074	+	0.0654227i
$657$	8.73685	−	18.8323i	0.340857	−	0.734719i
$658$	5.49164	−	31.6264i	0.214086	−	1.23293i
$659$		−	36.2805i		−	1.41329i	−0.707570	−	0.706644i	$-0.750208\pi$
$659$		−	36.2805i		−	1.41329i	0.707570	−	0.706644i	$-0.249792\pi$
$660$	1.45269	−	38.7798i	0.0565459	−	1.50950i
$661$	−23.0870			−0.897979			−0.448989	−	0.893537i	$-0.648216\pi$
$661$	−23.0870			−0.897979			−0.448989	+	0.893537i	$0.648216\pi$
$662$	2.31731	−	0.850280i	0.0900650	−	0.0330471i
$663$	2.83126	−	36.0268i	0.109957	−	1.39917i
$664$	−3.07942	−	5.23867i	−0.119505	−	0.203300i
$665$	33.6884	+	19.4500i	1.30638	+	0.754239i
$666$	8.03172	−	11.5826i	0.311223	−	0.448817i
$667$	−31.7081	+	18.3067i	−1.22774	+	0.708838i
$668$	−22.7476	−	26.8243i	−0.880130	−	1.03786i
$669$	25.4214	−	8.04268i	0.982849	−	0.310948i
$670$	13.7453	+	11.4728i	0.531028	+	0.443232i
$671$	−35.3020	+	20.3816i	−1.36282	+	0.786825i
$672$	24.2694	+	0.719143i	0.936213	+	0.0277416i
$673$	−15.7338	−	27.2518i	−0.606495	−	1.05048i	−0.991813	−	0.127696i	$-0.959242\pi$
$673$	−15.7338	−	27.2518i	−0.606495	−	1.05048i	0.385319	−	0.922784i	$-0.374092\pi$
$674$	28.6503	+	23.9135i	1.10357	+	0.921113i
$675$	−33.6864	+	14.0693i	−1.29659	+	0.541528i
$676$	25.9428	+	1.72329i	0.997801	+	0.0662803i
$677$	−12.4540	−	7.19033i	−0.478647	−	0.276347i	0.241206	−	0.970474i	$-0.422457\pi$
$677$	−12.4540	−	7.19033i	−0.478647	−	0.276347i	−0.719852	+	0.694127i	$0.755791\pi$
$678$	−9.15318	+	22.3237i	−0.351526	+	0.857337i
$679$	−13.7039			−0.525909
$680$	−28.7627	−	48.9308i	−1.10300	−	1.87641i
$681$	26.6417	+	5.87899i	1.02091	+	0.225283i
$682$	29.1052	+	5.05385i	1.11450	+	0.193522i
$683$	6.67003	+	11.5528i	0.255222	+	0.442057i	0.964956	−	0.262413i	$-0.0845182\pi$
$683$	6.67003	+	11.5528i	0.255222	+	0.442057i	−0.709734	+	0.704470i	$0.751185\pi$
$684$	19.3423	+	19.0669i	0.739571	+	0.729043i
$685$	−40.8580	+	23.5894i	−1.56110	+	0.901303i
$686$	9.48755	+	25.8569i	0.362236	+	0.987222i
$687$	−1.52019	−	4.80504i	−0.0579989	−	0.183324i
$688$	37.1316	+	6.14885i	1.41563	+	0.234423i
$689$	1.19159	−	2.94197i	0.0453960	−	0.112080i
$690$	−48.3748	−	62.5776i	−1.84160	−	2.38229i
$691$	−24.5029	−	42.4403i	−0.932135	−	1.61451i	−0.779664	−	0.626197i	$-0.784610\pi$
$691$	−24.5029	−	42.4403i	−0.932135	−	1.61451i	−0.152471	−	0.988308i	$-0.548723\pi$
$692$	−15.9913	−	18.8571i	−0.607897	−	0.716841i
$693$	−23.9205	+	2.13992i	−0.908664	+	0.0812888i
$694$	−19.7968	−	3.43754i	−0.751478	−	0.130487i
$695$			18.3370i			0.695560i
$696$	4.00368	−	18.8424i	0.151759	−	0.714218i
$697$	−12.8501	+	7.41899i	−0.486731	+	0.281014i
$698$	−18.5528	−	15.4854i	−0.702234	−	0.586132i
$699$	6.70704	+	1.48004i	0.253684	+	0.0559801i
$700$	34.2593	−	6.22515i	1.29488	−	0.235289i
$701$			16.3530i			0.617644i	0.951120	+	0.308822i	$0.0999348\pi$
$701$			16.3530i			0.617644i	−0.951120	+	0.308822i	$0.900065\pi$
$702$	20.5230	+	16.7573i	0.774590	+	0.632463i
$703$	−15.0385			−0.567189
$704$	−12.5703	+	22.5807i	−0.473760	+	0.851041i
$705$	11.8550	−	53.7232i	0.446487	−	2.02333i
$706$	12.5438	−	15.0284i	0.472091	−	0.565603i
$707$	−2.38477	−	4.13055i	−0.0896886	−	0.155345i
$708$	1.21175	−	32.3479i	0.0455404	−	1.21571i
$709$	36.1754			1.35860			0.679299	−	0.733862i	$-0.262284\pi$
$709$	36.1754			1.35860			0.679299	+	0.733862i	$0.262284\pi$
$710$	18.4942	+	3.21134i	0.694075	+	0.120520i
$711$	−28.3193	+	19.9120i	−1.06206	+	0.746760i
$712$	4.70331	−	2.76472i	0.176264	−	0.103612i
$713$	52.1426	−	30.1045i	1.95275	−	1.12742i
$714$	−27.7900	+	21.4827i	−1.04001	+	0.803970i
$715$	−31.8505	+	24.8401i	−1.19114	+	0.928966i
$716$	−11.7913	+	2.14255i	−0.440660	+	0.0800710i
$717$	−1.08158	+	0.342184i	−0.0403924	+	0.0127791i
$718$	−4.11063	−	11.2029i	−0.153407	−	0.418089i
$719$	6.87375	+	11.9057i	0.256348	+	0.444007i	0.965261	−	0.261289i	$-0.0841475\pi$
$719$	6.87375	+	11.9057i	0.256348	+	0.444007i	−0.708913	+	0.705296i	$0.750814\pi$
$720$	41.4970	+	3.11332i	1.54650	+	0.116027i
$721$	−17.0797	+	9.86098i	−0.636082	+	0.367242i
$722$	0.360716	−	2.07737i	0.0134245	−	0.0773118i
$723$	7.24605	−	32.8368i	0.269484	−	1.22121i
$724$	−4.80067	−	5.66102i	−0.178416	−	0.210390i
$725$		−	27.6253i		−	1.02598i
$726$	−0.524183	+	1.27843i	−0.0194543	+	0.0474470i
$727$	11.0537	−	19.1456i	0.409959	−	0.710070i	−0.584926	−	0.811087i	$-0.698876\pi$
$727$	11.0537	−	19.1456i	0.409959	−	0.710070i	0.994885	+	0.101017i	$0.0322097\pi$
$728$	−15.6968	−	19.8055i	−0.581763	−	0.734042i
$729$	7.14101	+	26.0385i	0.264482	+	0.964391i
$730$	−21.7468	+	26.0545i	−0.804887	+	0.964320i
$731$	−47.1540	+	27.2244i	−1.74406	+	1.00693i
$732$	−20.4233	−	38.6468i	−0.754868	−	1.42843i
$733$	9.59754	+	16.6234i	0.354493	+	0.614000i	0.987031	−	0.160529i	$-0.0513200\pi$
$733$	9.59754	+	16.6234i	0.354493	+	0.614000i	−0.632538	+	0.774530i	$0.717987\pi$
$734$	−27.6566	−	23.0840i	−1.02082	−	0.852047i
$735$	1.55656	+	4.92001i	0.0574148	+	0.181477i
$736$	9.82197	+	51.7501i	0.362043	+	1.90753i
$737$	5.89684	+	10.2136i	0.217213	+	0.376224i
$738$	0.898697	−	10.8416i	0.0330815	−	0.399085i
$739$	16.5572	−	28.6779i	0.609067	−	1.05493i	−0.382328	−	0.924027i	$-0.624877\pi$
$739$	16.5572	−	28.6779i	0.609067	−	1.05493i	0.991395	−	0.130908i	$-0.0417892\pi$
$740$	−17.5733	+	14.9026i	−0.646008	+	0.547829i
$741$	2.21477	−	28.1823i	0.0813617	−	1.03530i
$742$	−2.89637	+	1.06275i	−0.106329	+	0.0390148i
$743$			27.7545i			1.01822i	0.860703	+	0.509108i	$0.170024\pi$
$743$			27.7545i			1.01822i	−0.860703	+	0.509108i	$0.829976\pi$
$744$	−6.58387	+	30.9854i	−0.241376	+	1.13598i
$745$	−3.70384			−0.135698
$746$	15.0397	+	2.61151i	0.550644	+	0.0956142i
$747$	−5.27247	+	3.70721i	−0.192909	+	0.135640i
$748$	−6.68411	−	36.7851i	−0.244395	−	1.34500i
$749$	9.72535	−	16.8448i	0.355357	−	0.615496i
$750$	17.0514	−	2.30707i	0.622629	−	0.0842422i
$751$	−12.3755			−0.451589			−0.225794	−	0.974175i	$-0.572498\pi$
$751$	−12.3755			−0.451589			−0.225794	+	0.974175i	$0.572498\pi$
$752$	−23.2565	+	28.3103i	−0.848078	+	1.03237i
$753$	−6.46946	+	2.04677i	−0.235760	+	0.0745884i
$754$	−17.6863	+	9.44354i	−0.644098	+	0.343914i
$755$		−	45.7795i		−	1.66609i
$756$	−1.33288	−	25.7184i	−0.0484765	−	0.935369i
$757$	18.7677	+	10.8355i	0.682123	+	0.393824i	0.800654	−	0.599127i	$-0.204485\pi$
$757$	18.7677	+	10.8355i	0.682123	+	0.393824i	−0.118532	+	0.992950i	$0.537819\pi$
$758$	−2.36207	+	13.6032i	−0.0857944	+	0.494091i
$759$	−15.7157	−	49.6743i	−0.570443	−	1.80306i
$760$	−22.4998	−	38.2765i	−0.816155	−	1.38844i
$761$	−12.9278	−	7.46389i	−0.468634	−	0.270566i	0.247034	−	0.969007i	$-0.420544\pi$
$761$	−12.9278	−	7.46389i	−0.468634	−	0.270566i	−0.715668	+	0.698441i	$0.753877\pi$
$762$	−11.6756	+	28.4756i	−0.422961	+	1.03156i
$763$			39.6256i			1.43454i
$764$	−12.8265	+	10.8772i	−0.464047	+	0.393522i
$765$	−49.2465	+	34.6265i	−1.78051	+	1.25192i
$766$	−11.8855	−	2.06380i	−0.429439	−	0.0745681i
$767$	−26.5679	+	20.7202i	−0.959311	+	0.748161i
$768$	−23.6922	−	14.3764i	−0.854919	−	0.518762i
$769$		−	26.0700i		−	0.940110i	−0.882637	−	0.470055i	$-0.844234\pi$
$769$		−	26.0700i		−	0.940110i	0.882637	−	0.470055i	$-0.155766\pi$
$770$	38.6811	+	6.71661i	1.39397	+	0.242050i
$771$	−37.2191	−	8.21311i	−1.34041	−	0.295788i
$772$	14.2081	+	16.7544i	0.511360	+	0.603003i
$773$	−1.52365	−	2.63904i	−0.0548020	−	0.0949198i	0.837323	−	0.546709i	$-0.184119\pi$
$773$	−1.52365	−	2.63904i	−0.0548020	−	0.0949198i	−0.892125	+	0.451789i	$0.850786\pi$
$774$	3.29782	−	39.7839i	0.118538	−	1.43000i
$775$			45.4286i			1.63184i
$776$	13.6066	+	7.71455i	0.488449	+	0.276936i
$777$	10.5225	+	9.62319i	0.377493	+	0.345230i
$778$	48.1173	+	8.35512i	1.72509	+	0.299545i
$779$	−10.0521	+	5.80357i	−0.360153	+	0.207934i
$780$	−25.3394	−	35.1272i	−0.907295	−	1.25776i
$781$	10.7081	+	6.18232i	0.383166	+	0.221221i
$782$	−58.5016	−	48.8294i	−2.09201	−	1.74613i
$783$	−20.2645	−	2.60741i	−0.724193	−	0.0931814i
$784$	0.561438	−	3.39040i	0.0200513	−	0.121086i
$785$	−9.08323	−	5.24420i	−0.324194	−	0.187174i
$786$	31.8396	−	24.6132i	1.13568	−	0.877923i
$787$	−0.328788	+	0.569478i	−0.0117200	+	0.0202997i	−0.871826	−	0.489816i	$-0.837064\pi$
$787$	−0.328788	+	0.569478i	−0.0117200	+	0.0202997i	0.860106	+	0.510116i	$0.170397\pi$
$788$	6.42345	+	35.3506i	0.228826	+	1.25931i
$789$	7.19360	+	22.7376i	0.256099	+	0.809481i
$790$	53.1294	−	19.4945i	1.89026	−	0.693582i
$791$	−21.1387	−	12.2045i	−0.751607	−	0.433941i
$792$	24.9552	+	11.3412i	0.886746	+	0.402991i
$793$	−17.0797	+	42.1687i	−0.606516	+	1.49745i
$794$	−17.9249	−	14.9613i	−0.636129	−	0.530957i
$795$	−5.04142	+	1.59498i	−0.178801	+	0.0565679i
$796$	−34.5293	−	12.3642i	−1.22386	−	0.438237i
$797$	21.4193	+	12.3664i	0.758709	+	0.438041i	0.828832	−	0.559497i	$-0.189006\pi$
$797$	21.4193	+	12.3664i	0.758709	+	0.438041i	−0.0701227	+	0.997538i	$0.522339\pi$
$798$	−21.7389	+	16.8050i	−0.769550	+	0.594891i
$799$		−	53.0032i		−	1.87512i
$800$	−37.5204	−	13.1051i	−1.32655	−	0.463336i
$801$	−3.32835	−	4.73365i	−0.117602	−	0.167255i
$802$	−0.508090	−	1.38473i	−0.0179413	−	0.0488964i
$803$	−19.3601	+	11.1776i	−0.683203	+	0.394447i
$804$	−11.1813	+	5.90889i	−0.394335	+	0.208391i
$805$	69.2979	−	40.0092i	2.44243	−	1.41014i
$806$	29.0844	−	15.5295i	1.02445	−	0.547003i
$807$	30.9656	−	9.79670i	1.09004	−	0.344860i
$808$	0.0425675	+	5.44370i	0.00149752	+	0.191509i
$809$	20.1523	−	34.9048i	0.708516	−	1.22719i	−0.256891	−	0.966440i	$-0.582698\pi$
$809$	20.1523	−	34.9048i	0.708516	−	1.22719i	0.965407	−	0.260746i	$-0.0839685\pi$
$810$	−0.287684	−	44.1370i	−0.0101082	−	1.55082i
$811$	10.0090			0.351463			0.175731	−	0.984438i	$-0.443771\pi$
$811$	10.0090			0.351463			0.175731	+	0.984438i	$0.443771\pi$
$812$	18.3471	+	6.56968i	0.643856	+	0.230551i
$813$	19.8068	+	18.1140i	0.694656	+	0.635287i
$814$	−14.2488	+	5.22822i	−0.499419	+	0.183249i
$815$	16.2147	−	28.0847i	0.567977	−	0.983766i
$816$	39.6861	−	5.68591i	1.38929	−	0.199047i
$817$	−36.8866	+	21.2965i	−1.29050	+	0.745070i
$818$	45.4725	+	7.89588i	1.58991	+	0.276073i
$819$	−19.5836	+	18.3020i	−0.684306	+	0.639524i
$820$	−5.99528	+	16.7430i	−0.209364	+	0.584689i
$821$	22.6959	+	39.3104i	0.792092	+	1.37194i	0.924669	+	0.380771i	$0.124341\pi$
$821$	22.6959	+	39.3104i	0.792092	+	1.37194i	−0.132578	+	0.991173i	$0.542325\pi$
$822$	−4.46815	−	33.0239i	−0.155845	−	1.15184i
$823$	−24.5095	+	42.4517i	−0.854348	+	1.47977i	0.0229000	+	0.999738i	$0.492710\pi$
$823$	−24.5095	+	42.4517i	−0.854348	+	1.47977i	−0.877248	+	0.480037i	$0.840623\pi$
$824$	22.5096	−	0.176016i	0.784159	−	0.00613180i
$825$	38.3874	+	8.47092i	1.33648	+	0.294919i
$826$	32.2656	+	5.60261i	1.12266	+	0.194940i
$827$	19.6361			0.682814			0.341407	−	0.939916i	$-0.389097\pi$
$827$	19.6361			0.682814			0.341407	+	0.939916i	$0.389097\pi$
$828$	53.8604	−	14.8465i	1.87178	−	0.515951i
$829$	−9.37055	−	5.41009i	−0.325453	−	0.187900i	0.328368	−	0.944550i	$-0.393501\pi$
$829$	−9.37055	−	5.41009i	−0.325453	−	0.187900i	−0.653820	+	0.756650i	$0.726835\pi$
$830$	9.89159	−	3.62947i	0.343342	−	0.125981i
$831$	5.28548	−	23.9521i	0.183351	−	0.830888i
$832$	4.43593	+	28.5013i	0.153788	+	0.988104i
$833$	2.48580	+	4.30553i	0.0861279	+	0.149178i
$834$	−11.9841	−	4.91372i	−0.414975	−	0.170148i
$835$	52.8127	−	30.4915i	1.82766	−	1.05520i
$836$	−5.22870	−	28.7754i	−0.180838	−	0.995219i
$837$	33.3240	+	4.28778i	1.15185	+	0.148207i
$838$	1.15455	+	3.14655i	0.0398831	+	0.108696i
$839$			34.7941i			1.20123i	0.799539	+	0.600614i	$0.205077\pi$
$839$			34.7941i			1.20123i	−0.799539	+	0.600614i	$0.794923\pi$
$840$	−8.75003	+	41.1799i	−0.301905	+	1.42084i
$841$	−6.76949	+	11.7251i	−0.233431	+	0.404314i
$842$	3.97896	−	22.9149i	0.137124	−	0.789699i
$843$	−20.4588	−	18.7103i	−0.704640	−	0.644417i
$844$	−30.0502	−	35.4356i	−1.03437	−	1.21974i
$845$	−10.9818	+	43.7234i	−0.377785	+	1.50413i
$846$	31.9339	+	22.1440i	1.09791	+	0.761325i
$847$	−1.21057	−	0.698923i	−0.0415957	−	0.0240153i
$848$	3.47406	+	0.575292i	0.119300	+	0.0197556i
$849$	−0.628762	+	2.84935i	−0.0215791	+	0.0977893i
$850$	53.9766	−	19.8054i	1.85138	−	0.679318i
$851$	−15.4673	+	26.7902i	−0.530213	+	0.918356i
$852$	−7.05463	+	11.2263i	−0.241688	+	0.384607i
$853$	17.2851	−	29.9386i	0.591829	−	1.02508i	−0.402157	−	0.915571i	$-0.631739\pi$
$853$	17.2851	−	29.9386i	0.591829	−	1.02508i	0.993986	−	0.109507i	$-0.0349273\pi$
$854$	41.5151	−	15.2329i	1.42062	−	0.521259i
$855$	−38.5234	+	27.0868i	−1.31747	+	0.926350i
$856$	−19.1389	+	11.2503i	−0.654156	+	0.384528i
$857$	−15.2062	+	26.3379i	−0.519435	+	0.899687i	0.480310	+	0.877099i	$0.340524\pi$
$857$	−15.2062	+	26.3379i	−0.519435	+	0.899687i	−0.999745	+	0.0225884i	$0.992809\pi$
$858$	−7.69925	−	27.4722i	−0.262848	−	0.937886i
$859$	−13.6621	+	7.88781i	−0.466144	+	0.269129i	−0.714624	−	0.699508i	$-0.753402\pi$
$859$	−13.6621	+	7.88781i	−0.466144	+	0.269129i	0.248480	+	0.968637i	$0.420069\pi$
$860$	−22.0000	+	61.4392i	−0.750194	+	2.09506i
$861$	10.7472	+	2.37157i	0.366263	+	0.0808229i
$862$	45.9227	+	7.97405i	1.56413	+	0.271597i
$863$			21.3563i			0.726978i	0.931599	+	0.363489i	$0.118414\pi$
$863$			21.3563i			0.726978i	−0.931599	+	0.363489i	$0.881586\pi$
$864$	−13.1546	+	26.2861i	−0.447528	+	0.894270i
$865$	37.1267	−	21.4351i	1.26235	−	0.728816i
$866$	−36.6520	−	30.5922i	−1.24548	−	1.03957i
$867$	−19.2704	+	21.0713i	−0.654457	+	0.715619i
$868$	−30.1709	−	10.8035i	−1.02407	−	0.366696i
$869$	37.2785			1.26459
$870$	30.9034	+	12.6710i	1.04772	+	0.429588i
$871$	12.2003	+	4.94150i	0.413390	+	0.167436i
$872$	22.3070	−	39.3441i	0.755409	−	1.33236i
$873$	6.98191	−	15.0495i	0.236302	−	0.509350i
$874$	−45.7633	−	38.1972i	−1.54797	−	1.29204i
$875$			17.4076i			0.588483i
$876$	−11.2004	−	21.1944i	−0.378427	−	0.716092i
$877$	−0.810307	+	1.40349i	−0.0273621	+	0.0473926i	−0.879382	−	0.476117i	$-0.842044\pi$
$877$	−0.810307	+	1.40349i	−0.0273621	+	0.0473926i	0.852020	+	0.523509i	$0.175377\pi$
$878$	−24.8771	−	20.7641i	−0.839560	−	0.700754i
$879$	−32.3137	+	35.3335i	−1.08991	+	1.19177i
$880$	−34.6253	−	28.4442i	−1.16722	−	0.958854i
$881$	−4.20922	+	7.29058i	−0.141812	+	0.245626i	−0.928179	−	0.372134i	$-0.878626\pi$
$881$	−4.20922	+	7.29058i	−0.141812	+	0.245626i	0.786367	+	0.617760i	$0.211960\pi$
$882$	−3.63258	−	0.301117i	−0.122315	−	0.0101391i
$883$		−	46.4706i		−	1.56386i	−0.623366	−	0.781930i	$-0.714235\pi$
$883$		−	46.4706i		−	1.56386i	0.623366	−	0.781930i	$-0.285765\pi$
$884$	−31.1314	−	27.7867i	−1.04706	−	0.934567i
$885$	54.8089	+	12.0946i	1.84238	+	0.406556i
$886$	29.3285	+	5.09262i	0.985310	+	0.171090i
$887$	−11.4755			−0.385311			−0.192655	−	0.981266i	$-0.561710\pi$
$887$	−11.4755			−0.385311			−0.192655	+	0.981266i	$0.561710\pi$
$888$	−5.03045	−	15.4784i	−0.168811	−	0.519422i
$889$	−26.9641	−	15.5677i	−0.904346	−	0.522124i
$890$	3.25856	+	8.88072i	0.109227	+	0.297683i
$891$	9.83702	−	27.3595i	0.329553	−	0.916578i
$892$	10.3792	−	28.9859i	0.347522	−	0.970520i
$893$		−	41.4621i		−	1.38748i
$894$	0.992510	−	2.42064i	0.0331945	−	0.0809582i
$895$		−	20.7797i		−	0.694587i
$896$	17.6265	−	21.8022i	0.588860	−	0.728361i
$897$	−47.9270	−	32.9313i	−1.60024	−	1.09954i
$898$	−23.4060	+	28.0422i	−0.781067	+	0.935782i
$899$	−12.7125	+	22.0187i	−0.423985	+	0.734363i
$900$	−10.6181	+	40.7948i	−0.353937	+	1.35983i
$901$	−4.41178	+	2.54714i	−0.146978	+	0.0848575i
$902$	−7.50654	+	8.99344i	−0.249940	+	0.299449i
$903$	39.4374	+	8.70261i	1.31239	+	0.289605i
$904$	14.1182	+	24.0177i	0.469563	+	0.798816i
$905$	11.1457	−	6.43495i	0.370495	−	0.213905i
$906$	29.9191	+	12.2674i	0.993996	+	0.407559i
$907$	−1.87557	+	1.08286i	−0.0622772	+	0.0359558i	−0.530815	−	0.847488i	$-0.678114\pi$
$907$	−1.87557	+	1.08286i	−0.0622772	+	0.0359558i	0.468538	+	0.883443i	$0.344781\pi$
$908$	24.0270	−	20.3754i	0.797364	−	0.676182i
$909$	5.75112	−	0.514494i	0.190753	−	0.0170647i
$910$	38.6534	−	20.6388i	1.28135	−	0.684171i
$911$	−11.4781	+	19.8807i	−0.380287	+	0.658676i	−0.991103	−	0.133096i	$-0.957508\pi$
$911$	−11.4781	+	19.8807i	−0.380287	+	0.658676i	0.610816	+	0.791772i	$0.290841\pi$
$912$	31.0448	−	4.44785i	1.02800	−	0.147283i
$913$	6.94048			0.229696
$914$	13.9053	−	16.6597i	0.459947	−	0.551054i
$915$	72.2611	−	22.8616i	2.38888	−	0.755780i
$916$	−5.47879	−	1.96183i	−0.181024	−	0.0648207i
$917$	20.3567	+	35.2589i	0.672239	+	1.16435i
$918$	−9.43359	−	41.4637i	−0.311355	−	1.36851i
$919$	7.78149	+	13.4779i	0.256688	+	0.444596i	0.965353	−	0.260949i	$-0.0840355\pi$
$919$	7.78149	+	13.4779i	0.256688	+	0.444596i	−0.708665	+	0.705545i	$0.750702\pi$
$920$	−91.3286	+	0.714153i	−3.01102	+	0.0235449i
$921$	15.0040	+	3.31092i	0.494399	+	0.109099i
$922$	−7.16182	+	2.62785i	−0.235862	+	0.0865436i
$923$	13.6676	−	1.90881i	0.449876	−	0.0628294i
$924$	−14.7549	+	23.4801i	−0.485402	+	0.772440i
$925$	−11.6703	−	20.2136i	−0.383717	−	0.664618i
$926$	−27.7625	+	33.2617i	−0.912331	+	1.09305i
$927$	−2.12742	−	23.7808i	−0.0698737	−	0.781063i
$928$	−14.5184	−	16.8514i	−0.476589	−	0.553174i
$929$			8.96352i			0.294083i	0.989130	+	0.147042i	$0.0469752\pi$
$929$			8.96352i			0.294083i	−0.989130	+	0.147042i	$0.953025\pi$
$930$	−50.8193	−	20.8369i	−1.66643	−	0.683270i
$931$	1.94454	+	3.36804i	0.0637296	+	0.110383i
$932$	6.04880	−	5.12951i	0.198135	−	0.168023i
$933$	−0.593983	−	1.87747i	−0.0194461	−	0.0614656i
$934$	−8.58344	−	23.3929i	−0.280859	−	0.765439i
$935$	64.8262			2.12004
$936$	29.7475	−	7.14753i	0.972327	−	0.233624i
$937$	29.3164			0.957727			0.478863	−	0.877889i	$-0.341049\pi$
$937$	29.3164			0.957727			0.478863	+	0.877889i	$0.341049\pi$
$938$	−4.40720	−	12.0112i	−0.143900	−	0.392179i
$939$	−3.05537	+	3.34090i	−0.0997082	+	0.109026i
$940$	−41.0873	−	48.4507i	−1.34012	−	1.58029i
$941$	−14.6283	−	25.3370i	−0.476870	−	0.825964i	0.522778	−	0.852469i	$-0.324896\pi$
$941$	−14.6283	−	25.3370i	−0.476870	−	0.825964i	−0.999649	+	0.0265049i	$0.991562\pi$
$942$	5.86136	−	4.53105i	0.190973	−	0.147630i
$943$			23.8762i			0.777516i
$944$	−28.8824	−	23.7265i	−0.940043	−	0.772232i
$945$	44.2879	+	5.69850i	1.44069	+	0.185372i
$946$	−27.5456	+	33.0019i	−0.895586	+	1.07299i
$947$	−20.5907	−	35.6641i	−0.669107	−	1.15893i	−0.978154	−	0.207880i	$-0.933344\pi$
$947$	−20.5907	−	35.6641i	−0.669107	−	1.15893i	0.309048	−	0.951047i	$-0.399990\pi$
$948$	−1.49639	+	39.9465i	−0.0486006	+	1.29740i
$949$	−9.36670	+	23.1258i	−0.304056	+	0.750696i
$950$	42.2236	−	15.4929i	1.36992	−	0.502656i
$951$	−10.0253	+	10.9623i	−0.325094	+	0.355475i
$952$	0.317147	+	40.5580i	0.0102788	+	1.31449i
$953$	8.28198	+	14.3448i	0.268280	+	0.464674i	0.968418	−	0.249334i	$-0.0802115\pi$
$953$	8.28198	+	14.3448i	0.268280	+	0.464674i	−0.700138	+	0.714008i	$0.746878\pi$
$954$	0.308547	−	3.72222i	0.00998958	−	0.120511i
$955$	−14.5801	−	25.2534i	−0.471800	−	0.817181i
$956$	−0.441595	+	1.23324i	−0.0142822	+	0.0398857i
$957$	16.2355	+	14.8479i	0.524818	+	0.479964i
$958$	3.69813	−	4.43066i	0.119481	−	0.143148i
$959$	33.7137			1.08867
$960$	31.8699	−	35.9617i	1.02860	−	1.16066i
$961$	5.40510	−	9.36191i	0.174358	−	0.301997i
$962$	−8.95175	+	14.3815i	−0.288616	+	0.463678i
$963$	13.5439	+	19.2624i	0.436446	+	0.620723i
$964$	−25.1134	−	29.6141i	−0.808848	−	0.953805i
$965$	−32.9867	+	19.0449i	−1.06188	+	0.613077i
$966$	7.57829	+	56.0108i	0.243828	+	1.80212i
$967$	33.3862	−	19.2755i	1.07363	−	0.619860i	0.144458	−	0.989511i	$-0.453856\pi$
$967$	33.3862	−	19.2755i	1.07363	−	0.619860i	0.929171	+	0.369651i	$0.120523\pi$
$968$	0.808517	+	1.37544i	0.0259867	+	0.0442084i
$969$	−30.6190	+	33.4805i	−0.983624	+	1.07555i
$970$	−17.3786	+	20.8210i	−0.557994	+	0.668523i
$971$	−18.9283	+	10.9282i	−0.607437	+	0.350704i	−0.771962	−	0.635669i	$-0.780724\pi$
$971$	−18.9283	+	10.9282i	−0.607437	+	0.350704i	0.164525	+	0.986373i	$0.447391\pi$
$972$	28.9228	+	11.6393i	0.927698	+	0.373331i
$973$	6.55175	−	11.3480i	0.210039	−	0.363799i
$974$	−9.70805	+	11.6310i	−0.311066	+	0.372682i
$975$	39.5991	−	18.8933i	1.26818	−	0.605070i
$976$	−49.7954	−	8.24594i	−1.59391	−	0.263946i
$977$			20.6143i			0.659511i	0.944066	+	0.329755i	$0.106966\pi$
$977$			20.6143i			0.659511i	−0.944066	+	0.329755i	$0.893034\pi$
$978$	14.0097	+	18.1229i	0.447981	+	0.579508i
$979$			6.23120i			0.199150i
$980$	5.60988	+	2.00877i	0.179201	+	0.0641679i
$981$	−43.5164	−	20.1885i	−1.38937	−	0.644569i
$982$	0.994219	+	2.70960i	0.0317268	+	0.0864668i
$983$	26.5424	+	15.3242i	0.846570	+	0.488768i	0.859492	−	0.511149i	$-0.170780\pi$
$983$	26.5424	+	15.3242i	0.846570	+	0.488768i	−0.0129218	+	0.999917i	$0.504113\pi$
$984$	−9.33579	−	8.40479i	−0.297614	−	0.267935i
$985$	−62.2981			−1.98498
$986$	31.7040	+	5.50511i	1.00966	+	0.175318i
$987$	−26.5317	+	29.0112i	−0.844515	+	0.923437i
$988$	−24.3528	−	21.7363i	−0.774766	−	0.691525i
$989$			87.6150i			2.78599i
$990$	−27.0835	+	39.0572i	−0.860769	+	1.24132i
$991$	5.07716	−	8.79391i	0.161281	−	0.279348i	−0.774047	−	0.633128i	$-0.781771\pi$
$991$	5.07716	−	8.79391i	0.161281	−	0.279348i	0.935329	+	0.353780i	$0.115104\pi$
$992$	23.8748	+	27.7113i	0.758027	+	0.879836i
$993$	−2.95212	−	0.651441i	−0.0936827	−	0.0206729i
$994$	−10.2979	−	8.59529i	−0.326628	−	0.272626i
$995$	31.7965	−	55.0732i	1.00802	−	1.74594i
$996$	−0.278597	+	7.43721i	−0.00882770	+	0.235657i
$997$			30.8988i			0.978574i	0.872123	+	0.489287i	$0.162743\pi$
$997$			30.8988i			0.978574i	−0.872123	+	0.489287i	$0.837257\pi$
$998$	30.7863	+	25.6963i	0.974524	+	0.813404i
$999$	−15.9291	+	6.65287i	−0.503975	+	0.210488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.bk.c.277.18	✓	320
8.5	even	2	inner	936.2.bk.c.277.38	yes	320
9.4	even	3		936.2.ca.c.589.90	yes	320
13.10	even	6		936.2.ca.c.205.71	yes	320
72.13	even	6		936.2.ca.c.589.71	yes	320
104.101	even	6		936.2.ca.c.205.90	yes	320
117.49	even	6	inner	936.2.bk.c.517.38	yes	320
936.517	even	6	inner	936.2.bk.c.517.18	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.bk.c.277.18	✓	320	1.1	even	1	trivial
936.2.bk.c.277.38	yes	320	8.5	even	2	inner
936.2.bk.c.517.18	yes	320	936.517	even	6	inner
936.2.bk.c.517.38	yes	320	117.49	even	6	inner
936.2.ca.c.205.71	yes	320	13.10	even	6
936.2.ca.c.205.90	yes	320	104.101	even	6
936.2.ca.c.589.71	yes	320	72.13	even	6
936.2.ca.c.589.90	yes	320	9.4	even	3

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32766 + 0.487152i) q^{2} +(1.69136 + 0.373231i) q^{3} +(1.52537 - 1.29354i) q^{4} +(1.73390 + 3.00321i) q^{5} +(-2.42737 + 0.328425i) q^{6} -2.47808i q^{7} +(-1.39502 + 2.46047i) q^{8} +(2.72140 + 1.26253i) q^{9} +(-3.76505 - 3.14257i) q^{10} +(-1.61523 - 2.79767i) q^{11} +(3.06273 - 1.61854i) q^{12} +(-3.34184 - 1.35355i) q^{13} +(1.20720 + 3.29004i) q^{14} +(1.81176 + 5.72665i) q^{15} +(0.653486 - 3.94626i) q^{16} +(2.89335 + 5.01142i) q^{17} +(-4.22814 - 0.350485i) q^{18} +(2.26334 + 3.92023i) q^{19} +(6.52962 + 2.33811i) q^{20} +(0.924894 - 4.19132i) q^{21} +(3.50737 + 2.92749i) q^{22} +9.31152 q^{23} +(-3.27780 + 3.64088i) q^{24} +(-3.51284 + 6.08441i) q^{25} +(5.09622 + 0.169075i) q^{26} +(4.13165 + 3.15111i) q^{27} +(-3.20550 - 3.77997i) q^{28} +(-3.40526 + 1.96603i) q^{29} +(-5.19516 - 6.72045i) q^{30} +(5.59979 - 3.23304i) q^{31} +(1.05482 + 5.55764i) q^{32} +(-1.68777 - 5.33472i) q^{33} +(-6.28271 - 5.24397i) q^{34} +(7.44217 - 4.29674i) q^{35} +(5.78427 - 1.59442i) q^{36} +(-1.66110 + 2.87710i) q^{37} +(-4.91470 - 4.10214i) q^{38} +(-5.14707 - 3.53662i) q^{39} +(-9.80813 + 0.0766956i) q^{40} +2.56416i q^{41} +(0.813862 + 6.01521i) q^{42} +9.40931i q^{43} +(-6.08273 - 2.17809i) q^{44} +(0.926984 + 10.3620i) q^{45} +(-12.3625 + 4.53612i) q^{46} +(-7.93235 - 4.57974i) q^{47} +(2.57814 - 6.43064i) q^{48} +0.859143 q^{49} +(1.69982 - 9.78932i) q^{50} +(3.02327 + 9.55601i) q^{51} +(-6.84841 + 2.25816i) q^{52} +0.880344i q^{53} +(-7.02049 - 2.17087i) q^{54} +(5.60131 - 9.70176i) q^{55} +(6.09724 + 3.45696i) q^{56} +(2.36498 + 7.47526i) q^{57} +(3.56327 - 4.26909i) q^{58} +(4.67229 - 8.09265i) q^{59} +(10.1713 + 6.39164i) q^{60} -12.6184i q^{61} +(-5.85964 + 7.02033i) q^{62} +(3.12866 - 6.74383i) q^{63} +(-4.10786 - 6.86480i) q^{64} +(-1.72943 - 12.3832i) q^{65} +(4.83960 + 6.26049i) q^{66} -3.65076 q^{67} +(10.8959 + 3.90159i) q^{68} +(15.7491 + 3.47535i) q^{69} +(-7.78752 + 9.33008i) q^{70} +(-3.31472 + 1.91375i) q^{71} +(-6.90283 + 4.93467i) q^{72} -6.92009i q^{73} +(0.803786 - 4.62902i) q^{74} +(-8.21236 + 8.97983i) q^{75} +(8.52342 + 3.05205i) q^{76} +(-6.93283 + 4.00267i) q^{77} +(8.55643 + 2.18803i) q^{78} +(-5.76983 + 9.99363i) q^{79} +(12.9845 - 4.87987i) q^{80} +(5.81201 + 6.87172i) q^{81} +(-1.24913 - 3.40433i) q^{82} +(-1.07422 + 1.86061i) q^{83} +(-4.01085 - 7.58969i) q^{84} +(-10.0336 + 17.3786i) q^{85} +(-4.58376 - 12.4924i) q^{86} +(-6.49329 + 2.05431i) q^{87} +(9.13686 - 0.0714465i) q^{88} +(-1.67046 - 0.964443i) q^{89} +(-6.27860 - 13.3057i) q^{90} +(-3.35420 + 8.28133i) q^{91} +(14.2035 - 12.0449i) q^{92} +(10.6779 - 3.37822i) q^{93} +(12.7625 + 2.21609i) q^{94} +(-7.84884 + 13.5946i) q^{95} +(-0.290202 + 9.79366i) q^{96} -5.53007i q^{97} +(-1.14065 + 0.418533i) q^{98} +(-0.863541 - 9.65285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 3 q^{2} + q^{4} - 3 q^{6} + 10 q^{9} + 8 q^{10} - 7 q^{12} + 2 q^{14} + 24 q^{15} - 15 q^{16} + 8 q^{17} - 6 q^{18} + q^{22} + 20 q^{23} + 12 q^{24} - 144 q^{25} - 20 q^{26} - 6 q^{28} + 7 q^{30}+ \cdots - 99 q^{98}+O(q^{100}) \) 320 * q - 3 * q^2 + q^4 - 3 * q^6 + 10 * q^9 + 8 * q^10 - 7 * q^12 + 2 * q^14 + 24 * q^15 - 15 * q^16 + 8 * q^17 - 6 * q^18 + q^22 + 20 * q^23 + 12 * q^24 - 144 * q^25 - 20 * q^26 - 6 * q^28 + 7 * q^30 + 12 * q^31 - 3 * q^32 + 18 * q^33 - 30 * q^34 + 39 * q^36 - 10 * q^38 + 44 * q^39 - 28 * q^40 + 10 * q^42 - 30 * q^46 - 12 * q^47 - 8 * q^48 - 316 * q^49 - 56 * q^52 + 36 * q^54 + 14 * q^55 + 52 * q^56 + 36 * q^57 - 3 * q^58 + 3 * q^60 - q^62 - 42 * q^63 - 26 * q^64 + 66 * q^65 + 50 * q^66 - 12 * q^68 + 3 * q^70 - 48 * q^71 + 21 * q^72 + 26 * q^74 + 35 * q^78 + 32 * q^79 - 48 * q^80 + 34 * q^81 - 23 * q^82 + 120 * q^84 + 42 * q^86 - 2 * q^87 + 13 * q^88 - 72 * q^89 + 109 * q^90 - 28 * q^92 + 130 * q^94 + 112 * q^95 - 15 * q^96 - 99 * q^98

Introduction

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