LMFDB - Embedded newform 336.2.s.c.155.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.20
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41409 - 0.0184003i) q^{2} +(-1.52146 + 0.827739i) q^{3} +(1.99932 - 0.0520394i) q^{4} +(1.23935 - 1.23935i) q^{5} +(-2.13626 + 1.19850i) q^{6} -1.00000 q^{7} +(2.82627 - 0.110377i) q^{8} +(1.62970 - 2.51875i) q^{9} +O(q^{10})$	\(q+(1.41409 - 0.0184003i) q^{2} +(-1.52146 + 0.827739i) q^{3} +(1.99932 - 0.0520394i) q^{4} +(1.23935 - 1.23935i) q^{5} +(-2.13626 + 1.19850i) q^{6} -1.00000 q^{7} +(2.82627 - 0.110377i) q^{8} +(1.62970 - 2.51875i) q^{9} +(1.72975 - 1.77536i) q^{10} +(3.57267 + 3.57267i) q^{11} +(-2.99882 + 1.73409i) q^{12} +(1.58965 - 1.58965i) q^{13} +(-1.41409 + 0.0184003i) q^{14} +(-0.859765 + 2.91147i) q^{15} +(3.99458 - 0.208087i) q^{16} +2.20802i q^{17} +(2.25820 - 3.59173i) q^{18} +(-3.76716 - 3.76716i) q^{19} +(2.41336 - 2.54235i) q^{20} +(1.52146 - 0.827739i) q^{21} +(5.11782 + 4.98635i) q^{22} +3.97123i q^{23} +(-4.20871 + 2.50735i) q^{24} +1.92804i q^{25} +(2.21866 - 2.27716i) q^{26} +(-0.394660 + 5.18114i) q^{27} +(-1.99932 + 0.0520394i) q^{28} +(-4.75337 - 4.75337i) q^{29} +(-1.16222 + 4.13292i) q^{30} -1.24630i q^{31} +(5.64489 - 0.367756i) q^{32} +(-8.39291 - 2.47844i) q^{33} +(0.0406281 + 3.12234i) q^{34} +(-1.23935 + 1.23935i) q^{35} +(3.12722 - 5.12060i) q^{36} +(-6.39946 - 6.39946i) q^{37} +(-5.39644 - 5.25780i) q^{38} +(-1.10278 + 3.73440i) q^{39} +(3.36594 - 3.63953i) q^{40} +3.93566 q^{41} +(2.13626 - 1.19850i) q^{42} +(1.19053 - 1.19053i) q^{43} +(7.32883 + 6.95699i) q^{44} +(-1.10184 - 5.14136i) q^{45} +(0.0730718 + 5.61569i) q^{46} -8.26073 q^{47} +(-5.90537 + 3.62307i) q^{48} +1.00000 q^{49} +(0.0354765 + 2.72643i) q^{50} +(-1.82766 - 3.35941i) q^{51} +(3.09549 - 3.26094i) q^{52} +(-2.18249 + 2.18249i) q^{53} +(-0.462752 + 7.33388i) q^{54} +8.85554 q^{55} +(-2.82627 + 0.110377i) q^{56} +(8.84982 + 2.61337i) q^{57} +(-6.80917 - 6.63425i) q^{58} +(-5.45245 - 5.45245i) q^{59} +(-1.56744 + 5.86572i) q^{60} +(-5.10830 + 5.10830i) q^{61} +(-0.0229323 - 1.76239i) q^{62} +(-1.62970 + 2.51875i) q^{63} +(7.97563 - 0.623910i) q^{64} -3.94024i q^{65} +(-11.9140 - 3.35032i) q^{66} +(-7.23888 - 7.23888i) q^{67} +(0.114904 + 4.41454i) q^{68} +(-3.28714 - 6.04208i) q^{69} +(-1.72975 + 1.77536i) q^{70} -6.13227i q^{71} +(4.32796 - 7.29855i) q^{72} +10.2246i q^{73} +(-9.16719 - 8.93169i) q^{74} +(-1.59591 - 2.93344i) q^{75} +(-7.72781 - 7.33573i) q^{76} +(-3.57267 - 3.57267i) q^{77} +(-1.49071 + 5.30108i) q^{78} +6.53910i q^{79} +(4.69278 - 5.20857i) q^{80} +(-3.68817 - 8.20959i) q^{81} +(5.56539 - 0.0724172i) q^{82} +(-12.3619 + 12.3619i) q^{83} +(2.99882 - 1.73409i) q^{84} +(2.73650 + 2.73650i) q^{85} +(1.66162 - 1.70543i) q^{86} +(11.1666 + 3.29753i) q^{87} +(10.4917 + 9.70299i) q^{88} -9.15394 q^{89} +(-1.65271 - 7.25009i) q^{90} +(-1.58965 + 1.58965i) q^{91} +(0.206661 + 7.93977i) q^{92} +(1.03161 + 1.89620i) q^{93} +(-11.6814 + 0.152000i) q^{94} -9.33763 q^{95} +(-8.28408 + 5.23202i) q^{96} +7.67756 q^{97} +(1.41409 - 0.0184003i) q^{98} +(14.8210 - 3.17628i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	1.41409	−	0.0184003i	0.999915	−	0.0130110i
$2$	1.41409	−	0.0184003i	0.999915	−	0.0130110i
$3$	−1.52146	+	0.827739i	−0.878417	+	0.477895i
$3$	−1.52146	+	0.827739i	−0.878417	+	0.477895i
$4$	1.99932	−	0.0520394i	0.999661	−	0.0260197i
$5$	1.23935	−	1.23935i	0.554253	−	0.554253i	−0.373413	−	0.927665i	$-0.621812\pi$
$5$	1.23935	−	1.23935i	0.554253	−	0.554253i	0.927665	+	0.373413i	$0.121812\pi$
$6$	−2.13626	+	1.19850i	−0.872125	+	0.489284i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.82627	−	0.110377i	0.999238	−	0.0390241i
$9$	1.62970	−	2.51875i	0.543233	−	0.839582i
$10$	1.72975	−	1.77536i	0.546994	−	0.561417i
$11$	3.57267	+	3.57267i	1.07720	+	1.07720i	0.996759	+	0.0804398i	$0.0256325\pi$
$11$	3.57267	+	3.57267i	1.07720	+	1.07720i	0.0804398	+	0.996759i	$0.474368\pi$
$12$	−2.99882	+	1.73409i	−0.865685	+	0.500589i
$13$	1.58965	−	1.58965i	0.440888	−	0.440888i	−0.451422	−	0.892310i	$-0.649083\pi$
$13$	1.58965	−	1.58965i	0.440888	−	0.440888i	0.892310	+	0.451422i	$0.149083\pi$
$14$	−1.41409	+	0.0184003i	−0.377932	+	0.00491768i
$15$	−0.859765	+	2.91147i	−0.221990	+	0.751740i
$16$	3.99458	−	0.208087i	0.998646	−	0.0520218i
$17$			2.20802i			0.535523i	0.963485	+	0.267761i	$0.0862839\pi$
$17$			2.20802i			0.535523i	−0.963485	+	0.267761i	$0.913716\pi$
$18$	2.25820	−	3.59173i	0.532263	−	0.846579i
$19$	−3.76716	−	3.76716i	−0.864246	−	0.864246i	0.127582	−	0.991828i	$-0.459278\pi$
$19$	−3.76716	−	3.76716i	−0.864246	−	0.864246i	−0.991828	+	0.127582i	$0.959278\pi$
$20$	2.41336	−	2.54235i	0.539643	−	0.568486i
$21$	1.52146	−	0.827739i	0.332010	−	0.180627i
$22$	5.11782	+	4.98635i	1.09112	+	1.06309i
$23$			3.97123i			0.828059i	0.910264	+	0.414029i	$0.135879\pi$
$23$			3.97123i			0.828059i	−0.910264	+	0.414029i	$0.864121\pi$
$24$	−4.20871	+	2.50735i	−0.859098	+	0.511810i
$25$			1.92804i			0.385608i
$26$	2.21866	−	2.27716i	0.435115	−	0.446587i
$27$	−0.394660	+	5.18114i	−0.0759524	+	0.997111i
$28$	−1.99932	+	0.0520394i	−0.377837	+	0.00983453i
$29$	−4.75337	−	4.75337i	−0.882679	−	0.882679i	0.111128	−	0.993806i	$-0.464554\pi$
$29$	−4.75337	−	4.75337i	−0.882679	−	0.882679i	−0.993806	+	0.111128i	$0.964554\pi$
$30$	−1.16222	+	4.13292i	−0.212191	+	0.754564i
$31$		−	1.24630i		−	0.223842i	−0.993717	−	0.111921i	$-0.964300\pi$
$31$		−	1.24630i		−	0.223842i	0.993717	−	0.111921i	$-0.0357004\pi$
$32$	5.64489	−	0.367756i	0.997885	−	0.0650108i
$33$	−8.39291	−	2.47844i	−1.46102	−	0.431442i
$34$	0.0406281	+	3.12234i	0.00696766	+	0.535477i
$35$	−1.23935	+	1.23935i	−0.209488	+	0.209488i
$36$	3.12722	−	5.12060i	0.521203	−	0.853433i
$37$	−6.39946	−	6.39946i	−1.05206	−	1.05206i	−0.998568	−	0.0534969i	$-0.982963\pi$
$37$	−6.39946	−	6.39946i	−1.05206	−	1.05206i	−0.0534969	−	0.998568i	$-0.517037\pi$
$38$	−5.39644	−	5.25780i	−0.875417	−	0.852928i
$39$	−1.10278	+	3.73440i	−0.176585	+	0.597982i
$40$	3.36594	−	3.63953i	0.532201	−	0.575460i
$41$	3.93566			0.614646			0.307323	−	0.951605i	$-0.400567\pi$
$41$	3.93566			0.614646			0.307323	+	0.951605i	$0.400567\pi$
$42$	2.13626	−	1.19850i	0.329632	−	0.184932i
$43$	1.19053	−	1.19053i	0.181554	−	0.181554i	−0.610479	−	0.792033i	$-0.709023\pi$
$43$	1.19053	−	1.19053i	0.181554	−	0.181554i	0.792033	+	0.610479i	$0.209023\pi$
$44$	7.32883	+	6.95699i	1.10486	+	1.04881i
$45$	−1.10184	−	5.14136i	−0.164253	−	0.766429i
$46$	0.0730718	+	5.61569i	0.0107738	+	0.827989i
$47$	−8.26073			−1.20495			−0.602476	−	0.798137i	$-0.705819\pi$
$47$	−8.26073			−1.20495			−0.602476	+	0.798137i	$0.705819\pi$
$48$	−5.90537	+	3.62307i	−0.852367	+	0.522945i
$49$	1.00000			0.142857
$50$	0.0354765	+	2.72643i	0.00501713	+	0.385575i
$51$	−1.82766	−	3.35941i	−0.255924	−	0.470412i
$52$	3.09549	−	3.26094i	0.429267	−	0.452211i
$53$	−2.18249	+	2.18249i	−0.299788	+	0.299788i	−0.840931	−	0.541143i	$-0.817992\pi$
$53$	−2.18249	+	2.18249i	−0.299788	+	0.299788i	0.541143	+	0.840931i	$0.317992\pi$
$54$	−0.462752	+	7.33388i	−0.0629726	+	0.998015i
$55$	8.85554			1.19408
$56$	−2.82627	+	0.110377i	−0.377677	+	0.0147497i
$57$	8.84982	+	2.61337i	1.17219	+	0.346149i
$58$	−6.80917	−	6.63425i	−0.894088	−	0.871119i
$59$	−5.45245	−	5.45245i	−0.709849	−	0.709849i	0.256654	−	0.966503i	$-0.417380\pi$
$59$	−5.45245	−	5.45245i	−0.709849	−	0.709849i	−0.966503	+	0.256654i	$0.917380\pi$
$60$	−1.56744	+	5.86572i	−0.202355	+	0.757261i
$61$	−5.10830	+	5.10830i	−0.654051	+	0.654051i	−0.953966	−	0.299915i	$-0.903042\pi$
$61$	−5.10830	+	5.10830i	−0.654051	+	0.654051i	0.299915	+	0.953966i	$0.403042\pi$
$62$	−0.0229323	−	1.76239i	−0.00291241	−	0.223824i
$63$	−1.62970	+	2.51875i	−0.205323	+	0.317332i
$64$	7.97563	−	0.623910i	0.996954	−	0.0779887i
$65$		−	3.94024i		−	0.488727i
$66$	−11.9140	−	3.35032i	−1.46651	−	0.412396i
$67$	−7.23888	−	7.23888i	−0.884371	−	0.884371i	0.109605	−	0.993975i	$-0.465041\pi$
$67$	−7.23888	−	7.23888i	−0.884371	−	0.884371i	−0.993975	+	0.109605i	$0.965041\pi$
$68$	0.114904	+	4.41454i	0.0139341	+	0.535341i
$69$	−3.28714	−	6.04208i	−0.395725	−	0.727381i
$70$	−1.72975	+	1.77536i	−0.206744	+	0.212196i
$71$		−	6.13227i		−	0.727766i	−0.931445	−	0.363883i	$-0.881451\pi$
$71$		−	6.13227i		−	0.727766i	0.931445	−	0.363883i	$-0.118549\pi$
$72$	4.32796	−	7.29855i	0.510055	−	0.860142i
$73$			10.2246i			1.19670i	0.801237	+	0.598348i	$0.204176\pi$
$73$			10.2246i			1.19670i	−0.801237	+	0.598348i	$0.795824\pi$
$74$	−9.16719	−	8.93169i	−1.06566	−	1.03829i
$75$	−1.59591	−	2.93344i	−0.184280	−	0.338725i
$76$	−7.72781	−	7.33573i	−0.886441	−	0.841466i
$77$	−3.57267	−	3.57267i	−0.407143	−	0.407143i
$78$	−1.49071	+	5.30108i	−0.168790	+	0.600229i
$79$			6.53910i			0.735706i	0.929884	+	0.367853i	$0.119907\pi$
$79$			6.53910i			0.735706i	−0.929884	+	0.367853i	$0.880093\pi$
$80$	4.69278	−	5.20857i	0.524669	−	0.582335i
$81$	−3.68817	−	8.20959i	−0.409797	−	0.912177i
$82$	5.56539	−	0.0724172i	0.614594	−	0.00799714i
$83$	−12.3619	+	12.3619i	−1.35690	+	1.35690i	−0.479183	+	0.877715i	$0.659067\pi$
$83$	−12.3619	+	12.3619i	−1.35690	+	1.35690i	−0.877715	+	0.479183i	$0.840933\pi$
$84$	2.99882	−	1.73409i	0.327198	−	0.189205i
$85$	2.73650	+	2.73650i	0.296815	+	0.296815i
$86$	1.66162	−	1.70543i	0.179177	−	0.183901i
$87$	11.1666	+	3.29753i	1.19719	+	0.353532i
$88$	10.4917	+	9.70299i	1.11842	+	1.03434i
$89$	−9.15394			−0.970316			−0.485158	−	0.874427i	$-0.661238\pi$
$89$	−9.15394			−0.970316			−0.485158	+	0.874427i	$0.661238\pi$
$90$	−1.65271	−	7.25009i	−0.174211	−	0.764227i
$91$	−1.58965	+	1.58965i	−0.166640	+	0.166640i
$92$	0.206661	+	7.93977i	0.0215459	+	0.827778i
$93$	1.03161	+	1.89620i	0.106973	+	0.196627i
$94$	−11.6814	+	0.152000i	−1.20485	+	0.0156776i
$95$	−9.33763			−0.958021
$96$	−8.28408	+	5.23202i	−0.845490	+	0.533991i
$97$	7.67756			0.779538			0.389769	−	0.920913i	$-0.372555\pi$
$97$	7.67756			0.779538			0.389769	+	0.920913i	$0.372555\pi$
$98$	1.41409	−	0.0184003i	0.142845	−	0.00185871i
$99$	14.8210	−	3.17628i	1.48957	−	0.319228i
$100$	0.100334	+	3.85477i	0.0100334	+	0.385477i
$101$	5.10294	−	5.10294i	0.507761	−	0.507761i	−0.406077	−	0.913839i	$-0.633104\pi$
$101$	5.10294	−	5.10294i	0.507761	−	0.507761i	0.913839	+	0.406077i	$0.133104\pi$
$102$	−2.64630	−	4.71690i	−0.262022	−	0.467042i
$103$	17.2234			1.69707			0.848535	−	0.529139i	$-0.177485\pi$
$103$	17.2234			1.69707			0.848535	+	0.529139i	$0.177485\pi$
$104$	4.31731	−	4.66823i	0.423347	−	0.457758i
$105$	0.859765	−	2.91147i	0.0839044	−	0.284131i
$106$	−3.04608	+	3.12640i	−0.295862	+	0.303663i
$107$	8.98275	+	8.98275i	0.868396	+	0.868396i	0.992295	−	0.123899i	$-0.0395399\pi$
$107$	8.98275	+	8.98275i	0.868396	+	0.868396i	−0.123899	+	0.992295i	$0.539540\pi$
$108$	−0.519429	+	10.3793i	−0.0499821	+	0.998750i
$109$	9.91151	−	9.91151i	0.949350	−	0.949350i	−0.0494277	−	0.998778i	$-0.515740\pi$
$109$	9.91151	−	9.91151i	0.949350	−	0.949350i	0.998778	+	0.0494277i	$0.0157397\pi$
$110$	12.5226	−	0.162944i	1.19398	−	0.0155361i
$111$	15.0336	+	4.43946i	1.42693	+	0.421375i
$112$	−3.99458	+	0.208087i	−0.377453	+	0.0196624i
$113$			14.2233i			1.33801i	0.743256	+	0.669007i	$0.233280\pi$
$113$			14.2233i			1.33801i	−0.743256	+	0.669007i	$0.766720\pi$
$114$	12.5626	+	3.53271i	1.17659	+	0.330869i
$115$	4.92173	+	4.92173i	0.458954	+	0.458954i
$116$	−9.75088	−	9.25616i	−0.905347	−	0.859413i
$117$	−1.41327	−	6.59455i	−0.130657	−	0.609667i
$118$	−7.81061	−	7.60995i	−0.719025	−	0.700553i
$119$		−	2.20802i		−	0.202409i
$120$	−2.10857	+	8.32352i	−0.192485	+	0.759830i
$121$			14.5279i			1.32072i
$122$	−7.12962	+	7.31761i	−0.645486	+	0.662506i
$123$	−5.98796	+	3.25770i	−0.539916	+	0.293737i
$124$	−0.0648569	−	2.49176i	−0.00582432	−	0.223767i
$125$	8.58624	+	8.58624i	0.767977	+	0.767977i
$126$	−2.25820	+	3.59173i	−0.201176	+	0.319977i
$127$		−	2.23296i		−	0.198143i	−0.995080	−	0.0990717i	$-0.968413\pi$
$127$		−	2.23296i		−	0.198143i	0.995080	−	0.0990717i	$-0.0315873\pi$
$128$	11.2668	−	1.02902i	0.995855	−	0.0909534i
$129$	−0.825900	+	2.79680i	−0.0727164	+	0.246244i
$130$	−0.0725016	−	5.57187i	−0.00635881	−	0.488686i
$131$	−4.97791	+	4.97791i	−0.434922	+	0.434922i	−0.890299	−	0.455377i	$-0.849505\pi$
$131$	−4.97791	+	4.97791i	−0.434922	+	0.434922i	0.455377	+	0.890299i	$0.349505\pi$
$132$	−16.9091	−	4.51845i	−1.47175	−	0.393280i
$133$	3.76716	+	3.76716i	0.326654	+	0.326654i
$134$	−10.3697	−	10.1033i	−0.895802	−	0.872789i
$135$	5.93211	+	6.91035i	0.510555	+	0.594748i
$136$	0.243714	+	6.24046i	0.0208983	+	0.535115i
$137$	−5.14127			−0.439248			−0.219624	−	0.975585i	$-0.570483\pi$
$137$	−5.14127			−0.439248			−0.219624	+	0.975585i	$0.570483\pi$
$138$	−4.75950	−	8.48358i	−0.405156	−	0.722171i
$139$	13.3617	−	13.3617i	1.13332	−	1.13332i	0.143702	−	0.989621i	$-0.454099\pi$
$139$	13.3617	−	13.3617i	1.13332	−	1.13332i	0.989621	−	0.143702i	$-0.0459006\pi$
$140$	−2.41336	+	2.54235i	−0.203966	+	0.214868i
$141$	12.5684	−	6.83772i	1.05845	−	0.575840i
$142$	−0.112835	−	8.67160i	−0.00946894	−	0.727705i
$143$	11.3585			0.949849
$144$	5.98584	−	10.4005i	0.498820	−	0.866705i
$145$	−11.7821			−0.978454
$146$	0.188135	+	14.4585i	0.0155702	+	1.19659i
$147$	−1.52146	+	0.827739i	−0.125488	+	0.0682707i
$148$	−13.1276	−	12.4616i	−1.07908	−	1.02433i
$149$	14.3514	−	14.3514i	1.17571	−	1.17571i	0.194886	−	0.980826i	$-0.437566\pi$
$149$	14.3514	−	14.3514i	1.17571	−	1.17571i	0.980826	−	0.194886i	$-0.0624336\pi$
$150$	−2.31075	−	4.11880i	−0.188672	−	0.336298i
$151$	−17.5454			−1.42782			−0.713911	−	0.700236i	$-0.753078\pi$
$151$	−17.5454			−1.42782			−0.713911	+	0.700236i	$0.753078\pi$
$152$	−11.0628	−	10.2312i	−0.897314	−	0.829861i
$153$	5.56143	+	3.59840i	0.449615	+	0.290913i
$154$	−5.11782	−	4.98635i	−0.412406	−	0.401811i
$155$	−1.54460	−	1.54460i	−0.124065	−	0.124065i
$156$	−2.01047	+	7.52365i	−0.160966	+	0.602374i
$157$	9.29740	−	9.29740i	0.742014	−	0.742014i	−0.230952	−	0.972965i	$-0.574184\pi$
$157$	9.29740	−	9.29740i	0.742014	−	0.742014i	0.972965	+	0.230952i	$0.0741839\pi$
$158$	0.120321	+	9.24690i	0.00957225	+	0.735644i
$159$	1.51404	−	5.12710i	0.120071	−	0.406606i
$160$	6.54019	−	7.45175i	0.517048	−	0.589113i
$161$		−	3.97123i		−	0.312977i
$162$	−5.36648	−	11.5413i	−0.421630	−	0.906768i
$163$	−11.6109	−	11.6109i	−0.909434	−	0.909434i	0.0867928	−	0.996226i	$-0.472338\pi$
$163$	−11.6109	−	11.6109i	−0.909434	−	0.909434i	−0.996226	+	0.0867928i	$0.972338\pi$
$164$	7.86865	−	0.204809i	0.614438	−	0.0159929i
$165$	−13.4734	+	7.33007i	−1.04890	+	0.570645i
$166$	−17.2535	+	17.7084i	−1.33913	+	1.37444i
$167$		−	4.92377i		−	0.381013i	−0.981686	−	0.190507i	$-0.938987\pi$
$167$		−	4.92377i		−	0.381013i	0.981686	−	0.190507i	$-0.0610130\pi$
$168$	4.20871	−	2.50735i	0.324709	−	0.193446i
$169$			7.94606i			0.611235i
$170$	3.92002	+	3.81931i	0.300652	+	0.292928i
$171$	−15.6279	+	3.34919i	−1.19509	+	0.256119i
$172$	2.31830	−	2.44221i	0.176769	−	0.186217i
$173$	−1.92511	−	1.92511i	−0.146363	−	0.146363i	0.630128	−	0.776491i	$-0.283002\pi$
$173$	−1.92511	−	1.92511i	−0.146363	−	0.146363i	−0.776491	+	0.630128i	$0.783002\pi$
$174$	15.8513	+	4.45754i	1.20169	+	0.337926i
$175$		−	1.92804i		−	0.145746i
$176$	15.0147	+	13.5279i	1.13178	+	1.01970i
$177$	12.8089	+	3.78250i	0.962777	+	0.284310i
$178$	−12.9445	+	0.168435i	−0.970233	+	0.0126247i
$179$	−3.30607	+	3.30607i	−0.247107	+	0.247107i	−0.819782	−	0.572675i	$-0.805906\pi$
$179$	−3.30607	+	3.30607i	−0.247107	+	0.247107i	0.572675	+	0.819782i	$0.305906\pi$
$180$	−2.47049	−	10.2219i	−0.184139	−	0.761895i
$181$	14.1503	+	14.1503i	1.05178	+	1.05178i	0.998584	+	0.0531972i	$0.0169412\pi$
$181$	14.1503	+	14.1503i	1.05178	+	1.05178i	0.0531972	+	0.998584i	$0.483059\pi$
$182$	−2.21866	+	2.27716i	−0.164458	+	0.168794i
$183$	3.54375	−	12.0004i	0.261962	−	0.887097i
$184$	0.438332	+	11.2238i	0.0323142	+	0.827428i
$185$	−15.8623			−1.16622
$186$	1.49369	+	2.66243i	0.109522	+	0.195219i
$187$	−7.88850	+	7.88850i	−0.576865	+	0.576865i
$188$	−16.5159	+	0.429884i	−1.20454	+	0.0313525i
$189$	0.394660	−	5.18114i	0.0287073	−	0.376873i
$190$	−13.2043	+	0.171815i	−0.957940	+	0.0124648i
$191$	8.46813			0.612732			0.306366	−	0.951914i	$-0.400887\pi$
$191$	8.46813			0.612732			0.306366	+	0.951914i	$0.400887\pi$
$192$	−11.6182	+	7.55100i	−0.838471	+	0.544946i
$193$	−17.2773			−1.24365			−0.621823	−	0.783158i	$-0.713608\pi$
$193$	−17.2773			−1.24365			−0.621823	+	0.783158i	$0.713608\pi$
$194$	10.8568	−	0.141269i	0.779472	−	0.0101425i
$195$	3.26149	+	5.99493i	0.233560	+	0.429306i
$196$	1.99932	−	0.0520394i	0.142809	−	0.00371710i
$197$	−16.4452	+	16.4452i	−1.17167	+	1.17167i	−0.189864	+	0.981810i	$0.560805\pi$
$197$	−16.4452	+	16.4452i	−1.17167	+	1.17167i	−0.981810	+	0.189864i	$0.939195\pi$
$198$	20.8998	−	4.76426i	1.48529	−	0.338581i
$199$	8.20937			0.581947			0.290973	−	0.956731i	$-0.406021\pi$
$199$	8.20937			0.581947			0.290973	+	0.956731i	$0.406021\pi$
$200$	0.212811	+	5.44917i	0.0150480	+	0.385314i
$201$	17.0056	+	5.02179i	1.19948	+	0.354210i
$202$	7.12214	−	7.30993i	0.501112	−	0.514325i
$203$	4.75337	+	4.75337i	0.333621	+	0.333621i
$204$	−3.82890	−	6.62144i	−0.268077	−	0.463594i
$205$	4.87764	−	4.87764i	0.340669	−	0.340669i
$206$	24.3555	−	0.316915i	1.69693	−	0.0220805i
$207$	10.0025	+	6.47190i	0.695223	+	0.449828i
$208$	6.01919	−	6.68076i	0.417355	−	0.463227i
$209$		−	26.9176i		−	1.86193i
$210$	1.16222	−	4.13292i	0.0802005	−	0.285198i
$211$	−15.5340	−	15.5340i	−1.06940	−	1.06940i	−0.997405	−	0.0719974i	$-0.977063\pi$
$211$	−15.5340	−	15.5340i	−1.06940	−	1.06940i	−0.0719974	−	0.997405i	$-0.522937\pi$
$212$	−4.24992	+	4.47707i	−0.291886	+	0.307487i
$213$	5.07591	+	9.33002i	0.347796	+	0.639282i
$214$	12.8677	+	12.5372i	0.879621	+	0.857024i
$215$		−	2.95096i		−	0.201254i
$216$	−0.543540	+	14.6869i	−0.0369832	+	0.999316i
$217$			1.24630i			0.0846045i
$218$	13.8334	−	14.1982i	0.936918	−	0.961622i
$219$	−8.46327	−	15.5563i	−0.571895	−	1.05120i
$220$	17.7051	−	0.460837i	1.19368	−	0.0310697i
$221$	3.50996	+	3.50996i	0.236106	+	0.236106i
$222$	21.3406	+	6.00119i	1.43229	+	0.402774i
$223$			4.58037i			0.306724i	0.988170	+	0.153362i	$0.0490101\pi$
$223$			4.58037i			0.306724i	−0.988170	+	0.153362i	$0.950990\pi$
$224$	−5.64489	+	0.367756i	−0.377165	+	0.0245718i
$225$	4.85624	+	3.14212i	0.323750	+	0.209475i
$226$	0.261712	+	20.1130i	0.0174088	+	1.33790i
$227$	15.9988	−	15.9988i	1.06188	−	1.06188i	0.0639247	−	0.997955i	$-0.479638\pi$
$227$	15.9988	−	15.9988i	1.06188	−	1.06188i	0.997955	−	0.0639247i	$-0.0203617\pi$
$228$	17.8296	+	4.76443i	1.18080	+	0.315532i
$229$	−4.16743	−	4.16743i	−0.275392	−	0.275392i	0.555875	−	0.831266i	$-0.312383\pi$
$229$	−4.16743	−	4.16743i	−0.275392	−	0.275392i	−0.831266	+	0.555875i	$0.812383\pi$
$230$	7.05035	+	6.86923i	0.464886	+	0.452943i
$231$	8.39291	+	2.47844i	0.552213	+	0.163070i
$232$	−13.9590	−	12.9097i	−0.916452	−	0.847560i
$233$	7.47847			0.489931			0.244966	−	0.969532i	$-0.421223\pi$
$233$	7.47847			0.489931			0.244966	+	0.969532i	$0.421223\pi$
$234$	−2.11984	−	9.29932i	−0.138578	−	0.607915i
$235$	−10.2379	+	10.2379i	−0.667847	+	0.667847i
$236$	−11.1850	−	10.6175i	−0.728079	−	0.691139i
$237$	−5.41267	−	9.94900i	−0.351590	−	0.646257i
$238$	−0.0406281	−	3.12234i	−0.00263353	−	0.202391i
$239$	3.99993			0.258734			0.129367	−	0.991597i	$-0.458705\pi$
$239$	3.99993			0.258734			0.129367	+	0.991597i	$0.458705\pi$
$240$	−2.82856	+	11.8090i	−0.182583	+	0.762270i
$241$	3.26993			0.210635			0.105317	−	0.994439i	$-0.466414\pi$
$241$	3.26993			0.210635			0.105317	+	0.994439i	$0.466414\pi$
$242$	0.267317	+	20.5438i	0.0171838	+	1.32060i
$243$	12.4068	+	9.43775i	0.795897	+	0.605432i
$244$	−9.94731	+	10.4790i	−0.636811	+	0.670848i
$245$	1.23935	−	1.23935i	0.0791789	−	0.0791789i
$246$	−8.40759	+	4.71687i	−0.536048	+	0.300736i
$247$	−11.9769			−0.762072
$248$	−0.137563	−	3.52239i	−0.00873525	−	0.223672i
$249$	8.57577	−	29.0407i	0.543467	−	1.84038i
$250$	12.2997	+	11.9838i	0.777904	+	0.757920i
$251$	3.56566	+	3.56566i	0.225062	+	0.225062i	0.810626	−	0.585564i	$-0.199127\pi$
$251$	3.56566	+	3.56566i	0.225062	+	0.225062i	−0.585564	+	0.810626i	$0.699127\pi$
$252$	−3.12722	+	5.12060i	−0.196996	+	0.322567i
$253$	−14.1879	+	14.1879i	−0.891984	+	0.891984i
$254$	−0.0410872	−	3.15762i	−0.00257804	−	0.198127i
$255$	−6.42858	−	1.89837i	−0.402573	−	0.118881i
$256$	15.9134	−	1.66244i	0.994587	−	0.103903i
$257$			17.0440i			1.06318i	0.847002	+	0.531589i	$0.178405\pi$
$257$			17.0440i			1.06318i	−0.847002	+	0.531589i	$0.821595\pi$
$258$	−1.11644	+	3.97013i	−0.0695064	+	0.247169i
$259$	6.39946	+	6.39946i	0.397643	+	0.397643i
$260$	−0.205048	−	7.87782i	−0.0127165	−	0.488562i
$261$	−19.7191	+	4.22598i	−1.22058	+	0.261582i
$262$	−6.94764	+	7.13083i	−0.429227	+	0.440544i
$263$		−	26.4446i		−	1.63064i	−0.579009	−	0.815321i	$-0.696560\pi$
$263$		−	26.4446i		−	1.63064i	0.579009	−	0.815321i	$-0.303440\pi$
$264$	−23.9942	−	6.07838i	−1.47674	−	0.374098i
$265$			5.40972i			0.332316i
$266$	5.39644	+	5.25780i	0.330877	+	0.322376i
$267$	13.9274	−	7.57707i	0.852342	−	0.463709i
$268$	−14.8496	−	14.0962i	−0.907082	−	0.861060i
$269$	11.5967	+	11.5967i	0.707061	+	0.707061i	0.965916	−	0.258855i	$-0.0833452\pi$
$269$	11.5967	+	11.5967i	0.707061	+	0.707061i	−0.258855	+	0.965916i	$0.583345\pi$
$270$	8.51571	+	9.66273i	0.518250	+	0.588055i
$271$		−	7.02845i		−	0.426948i	−0.976949	−	0.213474i	$-0.931522\pi$
$271$		−	7.02845i		−	0.426948i	0.976949	−	0.213474i	$-0.0684778\pi$
$272$	0.459460	+	8.82011i	0.0278589	+	0.534797i
$273$	1.10278	−	3.73440i	0.0667430	−	0.226016i
$274$	−7.27023	+	0.0946008i	−0.439211	+	0.00571504i
$275$	−6.88824	+	6.88824i	−0.415377	+	0.415377i
$276$	−6.88648	−	11.9090i	−0.414518	−	0.716838i
$277$	3.04438	+	3.04438i	0.182919	+	0.182919i	0.792627	−	0.609707i	$-0.208713\pi$
$277$	3.04438	+	3.04438i	0.182919	+	0.182919i	−0.609707	+	0.792627i	$0.708713\pi$
$278$	18.6488	−	19.1405i	1.11848	−	1.14797i
$279$	−3.13912	−	2.03110i	−0.187934	−	0.121599i
$280$	−3.36594	+	3.63953i	−0.201153	+	0.217503i
$281$	−9.56982			−0.570887			−0.285444	−	0.958395i	$-0.592141\pi$
$281$	−9.56982			−0.570887			−0.285444	+	0.958395i	$0.592141\pi$
$282$	17.6471	−	9.90044i	1.05087	−	0.589563i
$283$	−15.9451	+	15.9451i	−0.947839	+	0.947839i	−0.998705	−	0.0508666i	$-0.983802\pi$
$283$	−15.9451	+	15.9451i	−0.947839	+	0.947839i	0.0508666	+	0.998705i	$0.483802\pi$
$284$	−0.319120	−	12.2604i	−0.0189363	−	0.727520i
$285$	14.2069	−	7.72912i	0.841542	−	0.457834i
$286$	16.0620	−	0.209000i	0.949769	−	0.0123584i
$287$	−3.93566			−0.232315
$288$	8.27317	−	14.8174i	0.487501	−	0.873122i
$289$	12.1247			0.713216
$290$	−16.6611	+	0.216795i	−0.978371	+	0.0127306i
$291$	−11.6811	+	6.35501i	−0.684759	+	0.372537i
$292$	0.532081	+	20.4422i	0.0311377	+	1.19629i
$293$	−1.28702	+	1.28702i	−0.0751886	+	0.0751886i	−0.743701	−	0.668512i	$-0.766931\pi$
$293$	−1.28702	+	1.28702i	−0.0751886	+	0.0751886i	0.668512	+	0.743701i	$0.266931\pi$
$294$	−2.13626	+	1.19850i	−0.124589	+	0.0698977i
$295$	−13.5150			−0.786871
$296$	−18.7930	−	17.3803i	−1.09232	−	1.01021i
$297$	−19.9205	+	17.1005i	−1.15590	+	0.992272i
$298$	20.0301	−	20.5583i	1.16031	−	1.19091i
$299$	6.31285	+	6.31285i	0.365081	+	0.365081i
$300$	−3.34340	−	5.78185i	−0.193031	−	0.333815i
$301$	−1.19053	+	1.19053i	−0.0686211	+	0.0686211i
$302$	−24.8108	+	0.322840i	−1.42770	+	0.0185773i
$303$	−3.54003	+	11.9878i	−0.203369	+	0.688683i
$304$	−15.8321	−	14.2643i	−0.908035	−	0.818116i
$305$			12.6619i			0.725019i
$306$	7.93060	+	4.98614i	0.453362	+	0.285039i
$307$	6.52035	+	6.52035i	0.372136	+	0.372136i	0.868255	−	0.496119i	$-0.165242\pi$
$307$	6.52035	+	6.52035i	0.372136	+	0.372136i	−0.496119	+	0.868255i	$0.665242\pi$
$308$	−7.32883	−	6.95699i	−0.417599	−	0.396411i
$309$	−26.2047	+	14.2565i	−1.49074	+	0.811022i
$310$	−2.21263	−	2.15579i	−0.125669	−	0.122441i
$311$		−	17.8276i		−	1.01091i	−0.862852	−	0.505456i	$-0.831324\pi$
$311$		−	17.8276i		−	1.01091i	0.862852	−	0.505456i	$-0.168676\pi$
$312$	−2.70455	+	10.6761i	−0.153115	+	0.604418i
$313$		−	4.87439i		−	0.275517i	−0.990466	−	0.137758i	$-0.956010\pi$
$313$		−	4.87439i		−	0.275517i	0.990466	−	0.137758i	$-0.0439897\pi$
$314$	12.9763	−	13.3185i	0.732296	−	0.751605i
$315$	1.10184	+	5.14136i	0.0620817	+	0.289683i
$316$	0.340291	+	13.0738i	0.0191429	+	0.735457i
$317$	−4.97157	−	4.97157i	−0.279231	−	0.279231i	0.553571	−	0.832802i	$-0.313265\pi$
$317$	−4.97157	−	4.97157i	−0.279231	−	0.279231i	−0.832802	+	0.553571i	$0.813265\pi$
$318$	2.04666	−	7.27806i	0.114771	−	0.408133i
$319$		−	33.9644i		−	1.90164i
$320$	9.11133	−	10.6578i	0.509339	−	0.595790i
$321$	−21.1023	−	6.23155i	−1.17782	−	0.347811i
$322$	−0.0730718	−	5.61569i	−0.00407213	−	0.312950i
$323$	8.31795	−	8.31795i	0.462823	−	0.462823i
$324$	−7.80107	−	16.2217i	−0.433393	−	0.901205i
$325$	3.06490	+	3.06490i	0.170010	+	0.170010i
$326$	−16.6325	−	16.2052i	−0.921189	−	0.897524i
$327$	−6.87585	+	23.2841i	−0.380235	+	1.28761i
$328$	11.1232	−	0.434405i	0.614178	−	0.0239860i
$329$	8.26073			0.455429
$330$	−18.9177	+	10.6133i	−1.04139	+	0.584244i
$331$	9.97563	−	9.97563i	0.548310	−	0.548310i	−0.377642	−	0.925952i	$-0.623265\pi$
$331$	9.97563	−	9.97563i	0.548310	−	0.548310i	0.925952	+	0.377642i	$0.123265\pi$
$332$	−24.0722	+	25.3588i	−1.32113	+	1.39174i
$333$	−26.5478	+	5.68944i	−1.45481	+	0.311779i
$334$	−0.0905988	−	6.96268i	−0.00495735	−	0.380981i
$335$	−17.9430			−0.980329
$336$	5.90537	−	3.62307i	0.322164	−	0.197655i
$337$	7.16141			0.390107			0.195054	−	0.980793i	$-0.437512\pi$
$337$	7.16141			0.390107			0.195054	+	0.980793i	$0.437512\pi$
$338$	0.146210	+	11.2365i	0.00795276	+	0.611183i
$339$	−11.7732	−	21.6402i	−0.639430	−	1.17533i
$340$	5.61355	+	5.32874i	0.304437	+	0.288991i
$341$	4.45262	−	4.45262i	0.241123	−	0.241123i
$342$	−22.0376	+	5.02363i	−1.19166	+	0.271647i
$343$	−1.00000			−0.0539949
$344$	3.23336	−	3.49617i	0.174331	−	0.188501i
$345$	−11.5621	−	3.41432i	−0.622485	−	0.183821i
$346$	−2.75770	−	2.68686i	−0.148255	−	0.144446i
$347$	7.59346	+	7.59346i	0.407638	+	0.407638i	0.880914	−	0.473276i	$-0.156929\pi$
$347$	7.59346	+	7.59346i	0.407638	+	0.407638i	−0.473276	+	0.880914i	$0.656929\pi$
$348$	22.4973	+	6.01172i	1.20598	+	0.322262i
$349$	−7.63248	+	7.63248i	−0.408557	+	0.408557i	−0.881235	−	0.472678i	$-0.843287\pi$
$349$	−7.63248	+	7.63248i	−0.408557	+	0.408557i	0.472678	+	0.881235i	$0.343287\pi$
$350$	−0.0354765	−	2.72643i	−0.00189630	−	0.145734i
$351$	7.60881	+	8.86355i	0.406128	+	0.473101i
$352$	21.4812	+	18.8534i	1.14495	+	1.00489i
$353$			18.8358i			1.00253i	0.865294	+	0.501265i	$0.167132\pi$
$353$			18.8358i			1.00253i	−0.865294	+	0.501265i	$0.832868\pi$
$354$	18.1826	+	5.11312i	0.966394	+	0.271759i
$355$	−7.60000	−	7.60000i	−0.403366	−	0.403366i
$356$	−18.3017	+	0.476366i	−0.969987	+	0.0252473i
$357$	1.82766	+	3.35941i	0.0967300	+	0.177799i
$358$	−4.61426	+	4.73592i	−0.243871	+	0.250301i
$359$			15.8207i			0.834984i	0.908681	+	0.417492i	$0.137091\pi$
$359$			15.8207i			0.834984i	−0.908681	+	0.417492i	$0.862909\pi$
$360$	−3.68159	−	14.4093i	−0.194037	−	0.759435i
$361$			9.38299i			0.493842i
$362$	20.2702	+	19.7494i	1.06538	+	1.03801i
$363$	−12.0253	−	22.1036i	−0.631164	−	1.16014i
$364$	−3.09549	+	3.26094i	−0.162248	+	0.170920i
$365$	12.6718	+	12.6718i	0.663271	+	0.663271i
$366$	4.79039	−	17.0349i	0.250398	−	0.890431i
$367$		−	25.6082i		−	1.33674i	−0.743831	−	0.668368i	$-0.766993\pi$
$367$		−	25.6082i		−	1.33674i	0.743831	−	0.668368i	$-0.233007\pi$
$368$	0.826363	+	15.8634i	0.0430771	+	0.826938i
$369$	6.41393	−	9.91292i	0.333896	−	0.516046i
$370$	−22.4308	+	0.291871i	−1.16612	+	0.0151736i
$371$	2.18249	−	2.18249i	0.113309	−	0.113309i
$372$	2.16120	+	3.73744i	0.112053	+	0.193777i
$373$	−20.8264	−	20.8264i	−1.07835	−	1.07835i	−0.996658	−	0.0816898i	$-0.973968\pi$
$373$	−20.8264	−	20.8264i	−1.07835	−	1.07835i	−0.0816898	−	0.996658i	$-0.526032\pi$
$374$	−11.0099	+	11.3002i	−0.569310	+	0.584321i
$375$	−20.1708	−	5.95648i	−1.04162	−	0.307592i
$376$	−23.3471	+	0.911792i	−1.20403	+	0.0470221i
$377$	−15.1123			−0.778325
$378$	0.462752	−	7.33388i	0.0238014	−	0.377214i
$379$	7.30890	−	7.30890i	0.375433	−	0.375433i	−0.494018	−	0.869451i	$-0.664472\pi$
$379$	7.30890	−	7.30890i	0.375433	−	0.375433i	0.869451	+	0.494018i	$0.164472\pi$
$380$	−18.6689	+	0.485925i	−0.957697	+	0.0249274i
$381$	1.84831	+	3.39737i	0.0946918	+	0.174053i
$382$	11.9747	−	0.155816i	0.612681	−	0.00797224i
$383$	−15.8671			−0.810769			−0.405384	−	0.914146i	$-0.632862\pi$
$383$	−15.8671			−0.810769			−0.405384	+	0.914146i	$0.632862\pi$
$384$	−16.2903	+	10.8916i	−0.831310	+	0.555809i
$385$	−8.85554			−0.451320
$386$	−24.4317	+	0.317907i	−1.24354	+	0.0161810i
$387$	−1.05844	−	4.93885i	−0.0538036	−	0.251056i
$388$	15.3499	−	0.399536i	0.779274	−	0.0202834i
$389$	2.42160	−	2.42160i	0.122780	−	0.122780i	−0.643047	−	0.765827i	$-0.722330\pi$
$389$	2.42160	−	2.42160i	0.122780	−	0.122780i	0.765827	+	0.643047i	$0.222330\pi$
$390$	4.72236	+	8.41738i	0.239126	+	0.426231i
$391$	−8.76854			−0.443444
$392$	2.82627	−	0.110377i	0.142748	−	0.00557487i
$393$	3.45330	−	11.6941i	0.174196	−	0.589890i
$394$	−22.9525	+	23.5577i	−1.15633	+	1.18682i
$395$	8.10421	+	8.10421i	0.407767	+	0.407767i
$396$	29.4667	−	7.12168i	1.48076	−	0.357878i
$397$	−2.29467	+	2.29467i	−0.115166	+	0.115166i	−0.762341	−	0.647175i	$-0.775950\pi$
$397$	−2.29467	+	2.29467i	−0.115166	+	0.115166i	0.647175	+	0.762341i	$0.275950\pi$
$398$	11.6088	−	0.151055i	0.581897	−	0.00757169i
$399$	−8.84982	−	2.61337i	−0.443045	−	0.130832i
$400$	0.401201	+	7.70172i	0.0200600	+	0.385086i
$401$			4.57856i			0.228642i	0.993444	+	0.114321i	$0.0364693\pi$
$401$			4.57856i			0.228642i	−0.993444	+	0.114321i	$0.963531\pi$
$402$	24.1399	+	6.78837i	1.20399	+	0.338573i
$403$	−1.98118	−	1.98118i	−0.0986895	−	0.0986895i
$404$	9.93687	−	10.4680i	0.494378	−	0.520801i
$405$	−14.7455	−	5.60361i	−0.732707	−	0.278445i
$406$	6.80917	+	6.63425i	0.337934	+	0.329252i
$407$		−	45.7263i		−	2.26657i
$408$	−5.53627	−	9.29289i	−0.274086	−	0.460067i
$409$		−	34.4670i		−	1.70428i	−0.523312	−	0.852141i	$-0.675304\pi$
$409$		−	34.4670i		−	1.70428i	0.523312	−	0.852141i	$-0.324696\pi$
$410$	6.80770	−	6.98720i	0.336208	−	0.345073i
$411$	7.82225	−	4.25563i	0.385843	−	0.209915i
$412$	34.4351	−	0.896295i	1.69650	−	0.0441573i
$413$	5.45245	+	5.45245i	0.268298	+	0.268298i
$414$	14.2636	+	8.96783i	0.701017	+	0.440745i
$415$			30.6414i			1.50413i
$416$	8.38877	−	9.55797i	0.411293	−	0.468618i
$417$	−9.26932	+	31.3893i	−0.453921	+	1.53714i
$418$	−0.495292	−	38.0640i	−0.0242255	−	1.86177i
$419$	19.6092	−	19.6092i	0.957971	−	0.957971i	−0.0411805	−	0.999152i	$-0.513112\pi$
$419$	19.6092	−	19.6092i	0.957971	−	0.957971i	0.999152	+	0.0411805i	$0.0131119\pi$
$420$	1.56744	−	5.86572i	0.0764830	−	0.286218i
$421$	20.9601	+	20.9601i	1.02153	+	1.02153i	0.999763	+	0.0217712i	$0.00693054\pi$
$421$	20.9601	+	20.9601i	1.02153	+	1.02153i	0.0217712	+	0.999763i	$0.493069\pi$
$422$	−22.2523	−	21.6807i	−1.08323	−	1.05540i
$423$	−13.4625	+	20.8067i	−0.654569	+	1.01166i
$424$	−5.92741	+	6.40920i	−0.287860	+	0.311258i
$425$	−4.25714			−0.206502
$426$	7.34949	+	13.1001i	0.356084	+	0.634703i
$427$	5.10830	−	5.10830i	0.247208	−	0.247208i
$428$	18.4269	+	17.4920i	0.890697	+	0.845506i
$429$	−17.2816	+	9.40190i	−0.834363	+	0.453928i
$430$	−0.0542985	−	4.17294i	−0.00261851	−	0.201237i
$431$	28.8191			1.38817			0.694083	−	0.719895i	$-0.255810\pi$
$431$	28.8191			1.38817			0.694083	+	0.719895i	$0.255810\pi$
$432$	−0.498373	+	20.7786i	−0.0239780	+	0.999712i
$433$	29.7649			1.43041			0.715205	−	0.698915i	$-0.246333\pi$
$433$	29.7649			1.43041			0.715205	+	0.698915i	$0.246333\pi$
$434$	0.0229323	+	1.76239i	0.00110079	+	0.0845973i
$435$	17.9261	−	9.75254i	0.859490	−	0.467598i
$436$	19.3005	−	20.3321i	0.924327	−	0.973730i
$437$	14.9603	−	14.9603i	0.715646	−	0.715646i
$438$	−12.2541	−	21.8423i	−0.585523	−	1.04367i
$439$	−10.4581			−0.499137			−0.249568	−	0.968357i	$-0.580289\pi$
$439$	−10.4581			−0.499137			−0.249568	+	0.968357i	$0.580289\pi$
$440$	25.0282	−	0.977446i	1.19317	−	0.0465979i
$441$	1.62970	−	2.51875i	0.0776046	−	0.119940i
$442$	5.02800	+	4.89883i	0.239158	+	0.233014i
$443$	−19.0958	−	19.0958i	−0.907268	−	0.907268i	0.0887831	−	0.996051i	$-0.471702\pi$
$443$	−19.0958	−	19.0958i	−0.907268	−	0.907268i	−0.996051	+	0.0887831i	$0.971702\pi$
$444$	30.2881	+	8.09357i	1.43741	+	0.384104i
$445$	−11.3449	+	11.3449i	−0.537800	+	0.537800i
$446$	0.0842801	+	6.47708i	0.00399078	+	0.306698i
$447$	−9.95590	+	33.7143i	−0.470898	+	1.59463i
$448$	−7.97563	+	0.623910i	−0.376813	+	0.0294770i
$449$			26.5991i			1.25529i	0.778500	+	0.627645i	$0.215981\pi$
$449$			26.5991i			1.25529i	−0.778500	+	0.627645i	$0.784019\pi$
$450$	6.92500	+	4.35390i	0.326448	+	0.205245i
$451$	14.0608	+	14.0608i	0.662097	+	0.662097i
$452$	0.740171	+	28.4369i	0.0348147	+	1.33756i
$453$	26.6946	−	14.5230i	1.25422	−	0.682349i
$454$	22.3295	−	22.9182i	1.04797	−	1.07561i
$455$			3.94024i			0.184721i
$456$	25.3005	+	6.40928i	1.18480	+	0.300142i
$457$		−	5.10142i		−	0.238634i	−0.992856	−	0.119317i	$-0.961929\pi$
$457$		−	5.10142i		−	0.238634i	0.992856	−	0.119317i	$-0.0380705\pi$
$458$	−5.96982	−	5.81646i	−0.278951	−	0.271785i
$459$	−11.4400	−	0.871416i	−0.533976	−	0.0406742i
$460$	10.0963	+	9.58400i	0.470740	+	0.446857i
$461$	−7.89211	−	7.89211i	−0.367572	−	0.367572i	0.499019	−	0.866591i	$-0.333694\pi$
$461$	−7.89211	−	7.89211i	−0.367572	−	0.367572i	−0.866591	+	0.499019i	$0.833694\pi$
$462$	11.9140	+	3.35032i	0.554288	+	0.155871i
$463$			11.5271i			0.535708i	0.963460	+	0.267854i	$0.0863145\pi$
$463$			11.5271i			0.535708i	−0.963460	+	0.267854i	$0.913686\pi$
$464$	−19.9768	−	17.9986i	−0.927402	−	0.835565i
$465$	3.62858	+	1.07153i	0.168271	+	0.0496908i
$466$	10.5753	−	0.137606i	0.489890	−	0.00637448i
$467$	−17.4574	+	17.4574i	−0.807833	+	0.807833i	−0.984306	−	0.176472i	$-0.943531\pi$
$467$	−17.4574	+	17.4574i	−0.807833	+	0.807833i	0.176472	+	0.984306i	$0.443531\pi$
$468$	−3.16877	−	13.1111i	−0.146476	−	0.606061i
$469$	7.23888	+	7.23888i	0.334261	+	0.334261i
$470$	−14.2890	+	14.6657i	−0.659101	+	0.676480i
$471$	−6.44983	+	21.8415i	−0.297193	+	1.00640i
$472$	−16.0119	−	14.8083i	−0.737009	−	0.681607i
$473$	8.50674			0.391140
$474$	−7.83708	−	13.9692i	−0.359969	−	0.641628i
$475$	7.26324	−	7.26324i	0.333260	−	0.333260i
$476$	−0.114904	−	4.41454i	−0.00526661	−	0.202340i
$477$	1.94034	+	9.05393i	0.0888420	+	0.414551i
$478$	5.65628	−	0.0735999i	0.258712	−	0.00336638i
$479$	2.12141			0.0969295			0.0484648	−	0.998825i	$-0.484567\pi$
$479$	2.12141			0.0969295			0.0484648	+	0.998825i	$0.484567\pi$
$480$	−3.78256	+	16.7511i	−0.172650	+	0.764581i
$481$	−20.3457			−0.927686
$482$	4.62399	−	0.0601676i	0.210617	−	0.00274056i
$483$	3.28714	+	6.04208i	0.149570	+	0.274924i
$484$	0.756023	+	29.0459i	0.0343647	+	1.32027i
$485$	9.51515	−	9.51515i	0.432061	−	0.432061i
$486$	17.7181	+	13.1176i	0.803707	+	0.595025i
$487$	34.1205			1.54615			0.773073	−	0.634316i	$-0.218718\pi$
$487$	34.1205			1.54615			0.773073	+	0.634316i	$0.218718\pi$
$488$	−13.8736	+	15.0013i	−0.628029	+	0.679077i
$489$	27.2763	+	8.05474i	1.23348	+	0.364248i
$490$	1.72975	−	1.77536i	0.0781421	−	0.0802024i
$491$	2.32777	+	2.32777i	0.105051	+	0.105051i	0.757679	−	0.652628i	$-0.226334\pi$
$491$	2.32777	+	2.32777i	0.105051	+	0.105051i	−0.652628	+	0.757679i	$0.726334\pi$
$492$	−11.8023	+	6.82479i	−0.532090	+	0.307686i
$493$	10.4955	−	10.4955i	0.472694	−	0.472694i
$494$	−16.9365	+	0.220378i	−0.762007	+	0.00991529i
$495$	14.4319	−	22.3049i	0.648664	−	1.00253i
$496$	−0.259340	−	4.97846i	−0.0116447	−	0.223539i
$497$			6.13227i			0.275070i
$498$	11.5926	−	41.2240i	0.519476	−	1.84729i
$499$	16.4946	+	16.4946i	0.738401	+	0.738401i	0.972269	−	0.233867i	$-0.0751381\pi$
$499$	16.4946	+	16.4946i	0.738401	+	0.738401i	−0.233867	+	0.972269i	$0.575138\pi$
$500$	17.6135	+	16.7198i	0.787699	+	0.747734i
$501$	4.07560	+	7.49134i	0.182084	+	0.334688i
$502$	5.10779	+	4.97657i	0.227972	+	0.222115i
$503$			21.0199i			0.937231i	0.883402	+	0.468616i	$0.155247\pi$
$503$			21.0199i			0.937231i	−0.883402	+	0.468616i	$0.844753\pi$
$504$	−4.32796	+	7.29855i	−0.192783	+	0.325103i
$505$		−	12.6486i		−	0.562856i
$506$	−19.8019	+	20.3241i	−0.880303	+	0.903514i
$507$	−6.57726	−	12.0896i	−0.292106	−	0.536919i
$508$	−0.116202	−	4.46442i	−0.00515564	−	0.198076i
$509$	−15.8208	−	15.8208i	−0.701244	−	0.701244i	0.263433	−	0.964678i	$-0.415145\pi$
$509$	−15.8208	−	15.8208i	−0.701244	−	0.701244i	−0.964678	+	0.263433i	$0.915145\pi$
$510$	−9.12555	−	2.56619i	−0.404086	−	0.113633i
$511$		−	10.2246i		−	0.452308i
$512$	22.4725	−	2.64366i	0.993151	−	0.116835i
$513$	21.0049	−	18.0314i	0.927391	−	0.796108i
$514$	0.313615	+	24.1019i	0.0138330	+	1.06309i
$515$	21.3457	−	21.3457i	0.940606	−	0.940606i
$516$	−1.50570	+	5.63468i	−0.0662846	+	0.248053i
$517$	−29.5128	−	29.5128i	−1.29797	−	1.29797i
$518$	9.16719	+	8.93169i	0.402783	+	0.392436i
$519$	4.52246	+	1.33549i	0.198514	+	0.0586216i
$520$	−0.434911	−	11.1362i	−0.0190721	−	0.488355i
$521$	−9.99923			−0.438074			−0.219037	−	0.975717i	$-0.570292\pi$
$521$	−9.99923			−0.438074			−0.219037	+	0.975717i	$0.570292\pi$
$522$	−27.8069	+	6.33877i	−1.21707	+	0.277440i
$523$	−17.9456	+	17.9456i	−0.784708	+	0.784708i	−0.980621	−	0.195913i	$-0.937233\pi$
$523$	−17.9456	+	17.9456i	−0.784708	+	0.784708i	0.195913	+	0.980621i	$0.437233\pi$
$524$	−9.69341	+	10.2115i	−0.423458	+	0.446092i
$525$	1.59591	+	2.93344i	0.0696514	+	0.128026i
$526$	−0.486588	−	37.3951i	−0.0212162	−	1.63050i
$527$	2.75186			0.119873
$528$	−34.0419	−	8.15390i	−1.48148	−	0.354853i
$529$	7.22933			0.314319
$530$	0.0995403	+	7.64984i	0.00432375	+	0.332288i
$531$	−22.6192	+	4.84750i	−0.981590	+	0.210364i
$532$	7.72781	+	7.33573i	0.335043	+	0.318044i
$533$	6.25630	−	6.25630i	0.270990	−	0.270990i
$534$	19.5552	−	10.9710i	0.846236	−	0.474760i
$535$	22.2655			0.962621
$536$	−21.2581	−	19.6601i	−0.918209	−	0.849185i
$537$	2.29350	−	7.76662i	0.0989718	−	0.335154i
$538$	16.6122	+	16.1854i	0.716201	+	0.697802i
$539$	3.57267	+	3.57267i	0.153886	+	0.153886i
$540$	12.2198	+	13.5073i	0.525857	+	0.581263i
$541$	−19.7562	+	19.7562i	−0.849384	+	0.849384i	−0.990056	−	0.140672i	$-0.955074\pi$
$541$	−19.7562	+	19.7562i	−0.849384	+	0.849384i	0.140672	+	0.990056i	$0.455074\pi$
$542$	−0.129325	−	9.93888i	−0.00555500	−	0.426912i
$543$	−33.2418	−	9.81638i	−1.42654	−	0.421261i
$544$	0.812012	+	12.4640i	0.0348147	+	0.534390i
$545$		−	24.5676i		−	1.05236i
$546$	1.49071	−	5.30108i	0.0637967	−	0.226865i
$547$	13.7252	+	13.7252i	0.586847	+	0.586847i	0.936776	−	0.349929i	$-0.113794\pi$
$547$	13.7252	+	13.7252i	0.586847	+	0.586847i	−0.349929	+	0.936776i	$0.613794\pi$
$548$	−10.2791	+	0.267549i	−0.439099	+	0.0114291i
$549$	4.54153	+	21.1915i	0.193828	+	0.904432i
$550$	−9.61388	+	9.86737i	−0.409937	+	0.420746i
$551$			35.8134i			1.52570i
$552$	−9.95726	−	16.7137i	−0.423809	−	0.711384i
$553$		−	6.53910i		−	0.278071i
$554$	4.36106	+	4.24903i	0.185284	+	0.180524i
$555$	24.1339	−	13.1298i	1.02443	−	0.557331i
$556$	26.0190	−	27.4096i	1.10345	−	1.16243i
$557$	6.97099	+	6.97099i	0.295370	+	0.295370i	0.839197	−	0.543827i	$-0.183025\pi$
$557$	6.97099	+	6.97099i	0.295370	+	0.295370i	−0.543827	+	0.839197i	$0.683025\pi$
$558$	−4.47638	−	2.81440i	−0.189500	−	0.119143i
$559$		−	3.78504i		−	0.160090i
$560$	−4.69278	+	5.20857i	−0.198306	+	0.220102i
$561$	5.47245	−	18.5317i	0.231047	−	0.782408i
$562$	−13.5326	+	0.176087i	−0.570839	+	0.00742780i
$563$	12.0301	−	12.0301i	0.507009	−	0.507009i	−0.406598	−	0.913607i	$-0.633285\pi$
$563$	12.0301	−	12.0301i	0.507009	−	0.507009i	0.913607	+	0.406598i	$0.133285\pi$
$564$	24.7724	−	14.3249i	1.04311	−	0.603186i
$565$	17.6276	+	17.6276i	0.741597	+	0.741597i
$566$	−22.2545	+	22.8413i	−0.935426	+	0.960091i
$567$	3.68817	+	8.20959i	0.154889	+	0.344770i
$568$	−0.676860	−	17.3315i	−0.0284004	−	0.727212i
$569$	−5.33785			−0.223774			−0.111887	−	0.993721i	$-0.535690\pi$
$569$	−5.33785			−0.223774			−0.111887	+	0.993721i	$0.535690\pi$
$570$	19.9476	−	11.1911i	0.835514	−	0.468744i
$571$	29.1035	−	29.1035i	1.21795	−	1.21795i	0.249595	−	0.968350i	$-0.419703\pi$
$571$	29.1035	−	29.1035i	1.21795	−	1.21795i	0.968350	−	0.249595i	$-0.0802974\pi$
$572$	22.7094	−	0.591092i	0.949527	−	0.0247148i
$573$	−12.8839	+	7.00940i	−0.538235	+	0.292822i
$574$	−5.56539	+	0.0724172i	−0.232295	+	0.00302264i
$575$	−7.65669			−0.319306
$576$	11.4264	−	21.1054i	0.476100	−	0.879391i
$577$	−8.17753			−0.340435			−0.170217	−	0.985407i	$-0.554447\pi$
$577$	−8.17753			−0.340435			−0.170217	+	0.985407i	$0.554447\pi$
$578$	17.1454	−	0.223097i	0.713155	−	0.00927962i
$579$	26.2867	−	14.3011i	1.09244	−	0.594332i
$580$	−23.5563	+	0.613136i	−0.978123	+	0.0254591i
$581$	12.3619	−	12.3619i	0.512859	−	0.512859i
$582$	−16.4013	+	9.20152i	−0.679854	+	0.381415i
$583$	−15.5946			−0.645862
$584$	1.12855	+	28.8974i	0.0466999	+	1.19578i
$585$	−9.92447	−	6.42140i	−0.410327	−	0.265492i
$586$	−1.79629	+	1.84365i	−0.0742040	+	0.0761605i
$587$	25.8580	+	25.8580i	1.06727	+	1.06727i	0.997568	+	0.0697047i	$0.0222057\pi$
$587$	25.8580	+	25.8580i	1.06727	+	1.06727i	0.0697047	+	0.997568i	$0.477794\pi$
$588$	−2.99882	+	1.73409i	−0.123669	+	0.0715128i
$589$	−4.69502	+	4.69502i	−0.193455	+	0.193455i
$590$	−19.1114	+	0.248679i	−0.786805	+	0.0102380i
$591$	11.4085	−	38.6332i	0.469281	−	1.58916i
$592$	−26.8948	−	24.2315i	−1.10537	−	0.995910i
$593$		−	18.1350i		−	0.744714i	−0.928090	−	0.372357i	$-0.878550\pi$
$593$		−	18.1350i		−	0.744714i	0.928090	−	0.372357i	$-0.121450\pi$
$594$	−27.8548	+	24.5483i	−1.14290	+	1.00723i
$595$	−2.73650	−	2.73650i	−0.112185	−	0.112185i
$596$	27.9462	−	29.4399i	1.14472	−	1.20591i
$597$	−12.4902	+	6.79521i	−0.511192	+	0.278109i
$598$	9.04312	+	8.81080i	0.369801	+	0.360300i
$599$			4.71552i			0.192671i	0.995349	+	0.0963354i	$0.0307122\pi$
$599$			4.71552i			0.192671i	−0.995349	+	0.0963354i	$0.969288\pi$
$600$	−4.83427	−	8.11455i	−0.197358	−	0.331275i
$601$		−	14.1554i		−	0.577413i	−0.957418	−	0.288706i	$-0.906775\pi$
$601$		−	14.1554i		−	0.577413i	0.957418	−	0.288706i	$-0.0932251\pi$
$602$	−1.66162	+	1.70543i	−0.0677224	+	0.0695081i
$603$	−30.0301	+	6.43572i	−1.22292	+	0.262083i
$604$	−35.0789	+	0.913052i	−1.42734	+	0.0371515i
$605$	18.0051	+	18.0051i	0.732011	+	0.732011i
$606$	−4.78536	+	17.0171i	−0.194392	+	0.691271i
$607$		−	7.96072i		−	0.323116i	−0.986863	−	0.161558i	$-0.948348\pi$
$607$		−	7.96072i		−	0.323116i	0.986863	−	0.161558i	$-0.0516518\pi$
$608$	−22.6506	−	19.8798i	−0.918603	−	0.806232i
$609$	−11.1666	−	3.29753i	−0.452494	−	0.133623i
$610$	0.232983	+	17.9051i	0.00943320	+	0.724958i
$611$	−13.1316	+	13.1316i	−0.531249	+	0.531249i
$612$	11.3064	+	6.90495i	0.457033	+	0.279116i
$613$	17.7697	+	17.7697i	0.717713	+	0.717713i	0.968136	−	0.250423i	$-0.0805697\pi$
$613$	17.7697	+	17.7697i	0.717713	+	0.717713i	−0.250423	+	0.968136i	$0.580570\pi$
$614$	9.34037	+	9.10041i	0.376947	+	0.367263i
$615$	−3.38374	+	11.4586i	−0.136446	+	0.462054i
$616$	−10.4917	−	9.70299i	−0.422721	−	0.390945i
$617$	−21.7284			−0.874752			−0.437376	−	0.899279i	$-0.644092\pi$
$617$	−21.7284			−0.874752			−0.437376	+	0.899279i	$0.644092\pi$
$618$	−36.7936	+	20.6421i	−1.48006	+	0.830349i
$619$	−19.6253	+	19.6253i	−0.788807	+	0.788807i	−0.981299	−	0.192491i	$-0.938343\pi$
$619$	−19.6253	+	19.6253i	−0.788807	+	0.788807i	0.192491	+	0.981299i	$0.438343\pi$
$620$	−3.16853	−	3.00777i	−0.127251	−	0.120795i
$621$	−20.5755	−	1.56729i	−0.825667	−	0.0628930i
$622$	−0.328033	−	25.2099i	−0.0131529	−	1.01083i
$623$	9.15394			0.366745
$624$	−3.62805	+	15.1468i	−0.145238	+	0.606359i
$625$	11.6425			0.465698
$626$	−0.0896901	−	6.89284i	−0.00358474	−	0.275493i
$627$	22.2807	+	40.9541i	0.889807	+	1.63555i
$628$	18.1047	−	19.0723i	0.722455	−	0.761069i
$629$	14.1301	−	14.1301i	0.563405	−	0.563405i
$630$	1.65271	+	7.25009i	0.0658455	+	0.288851i
$631$	−26.1699			−1.04181			−0.520904	−	0.853616i	$-0.674405\pi$
$631$	−26.1699			−1.04181			−0.520904	+	0.853616i	$0.674405\pi$
$632$	0.721765	+	18.4813i	0.0287103	+	0.735146i
$633$	36.4924	+	10.7763i	1.45044	+	0.428319i
$634$	−7.12174	−	6.93879i	−0.282841	−	0.275574i
$635$	−2.76742	−	2.76742i	−0.109822	−	0.109822i
$636$	2.76025	−	10.3295i	0.109451	−	0.409592i
$637$	1.58965	−	1.58965i	0.0629840	−	0.0629840i
$638$	−0.624954	−	48.0288i	−0.0247422	−	1.90148i
$639$	−15.4456	−	9.99374i	−0.611020	−	0.395346i
$640$	12.6882	−	15.2388i	0.501544	−	0.602367i
$641$		−	19.6364i		−	0.775592i	−0.921745	−	0.387796i	$-0.873237\pi$
$641$		−	19.6364i		−	0.775592i	0.921745	−	0.387796i	$-0.126763\pi$
$642$	−29.9553	−	8.42371i	−1.18224	−	0.332457i
$643$	8.37406	+	8.37406i	0.330241	+	0.330241i	0.852678	−	0.522437i	$-0.174977\pi$
$643$	8.37406	+	8.37406i	0.330241	+	0.330241i	−0.522437	+	0.852678i	$0.674977\pi$
$644$	−0.206661	−	7.93977i	−0.00814357	−	0.312871i
$645$	2.44262	+	4.48978i	0.0961782	+	0.176785i
$646$	11.6093	−	11.9154i	0.456762	−	0.468806i
$647$			15.9115i			0.625544i	0.949828	+	0.312772i	$0.101258\pi$
$647$			15.9115i			0.625544i	−0.949828	+	0.312772i	$0.898742\pi$
$648$	−11.3299	−	22.7955i	−0.445082	−	0.895490i
$649$		−	38.9596i		−	1.52930i
$650$	4.39045	+	4.27766i	0.172208	+	0.167784i
$651$	−1.03161	−	1.89620i	−0.0404321	−	0.0743180i
$652$	−23.8181	−	22.6097i	−0.932789	−	0.885462i
$653$	7.56494	+	7.56494i	0.296039	+	0.296039i	0.839460	−	0.543421i	$-0.182871\pi$
$653$	7.56494	+	7.56494i	0.296039	+	0.296039i	−0.543421	+	0.839460i	$0.682871\pi$
$654$	−9.29466	+	33.0525i	−0.363450	+	1.29245i
$655$			12.3387i			0.482114i
$656$	15.7213	−	0.818960i	0.613814	−	0.0319750i
$657$	25.7531	+	16.6630i	1.00472	+	0.650084i
$658$	11.6814	−	0.152000i	0.455390	−	0.00592557i
$659$	−21.0236	+	21.0236i	−0.818963	+	0.818963i	−0.985958	−	0.166995i	$-0.946594\pi$
$659$	−21.0236	+	21.0236i	−0.818963	+	0.818963i	0.166995	+	0.985958i	$0.446594\pi$
$660$	−26.5562	+	15.3563i	−1.03370	+	0.597744i
$661$	18.6305	+	18.6305i	0.724643	+	0.724643i	0.969547	−	0.244904i	$-0.0787565\pi$
$661$	18.6305	+	18.6305i	0.724643	+	0.724643i	−0.244904	+	0.969547i	$0.578756\pi$
$662$	13.9229	−	14.2900i	0.541130	−	0.555398i
$663$	−8.24561	−	2.43495i	−0.320233	−	0.0945655i
$664$	−33.5737	+	36.3027i	−1.30291	+	1.40882i
$665$	9.33763			0.362098
$666$	−37.4364	+	8.53388i	−1.45063	+	0.330681i
$667$	18.8767	−	18.8767i	0.730910	−	0.730910i
$668$	−0.256230	−	9.84421i	−0.00991385	−	0.380884i
$669$	−3.79135	−	6.96887i	−0.146582	−	0.269432i
$670$	−25.3730	+	0.330156i	−0.980246	+	0.0127550i
$671$	−36.5005			−1.40909
$672$	8.28408	−	5.23202i	0.319565	−	0.201830i
$673$	48.8310			1.88230			0.941148	−	0.337995i	$-0.109749\pi$
$673$	48.8310			1.88230			0.941148	+	0.337995i	$0.109749\pi$
$674$	10.1269	−	0.131772i	0.390074	−	0.00507567i
$675$	−9.98945	−	0.760921i	−0.384494	−	0.0292879i
$676$	0.413508	+	15.8867i	0.0159042	+	0.611028i
$677$	17.2859	−	17.2859i	0.664352	−	0.664352i	−0.292051	−	0.956403i	$-0.594338\pi$
$677$	17.2859	−	17.2859i	0.664352	−	0.664352i	0.956403	+	0.292051i	$0.0943377\pi$
$678$	−17.0465	−	30.3846i	−0.654668	−	1.16691i
$679$	−7.67756			−0.294638
$680$	8.03613	+	7.43204i	0.308172	+	0.285006i
$681$	−11.0988	+	37.5845i	−0.425306	+	1.44024i
$682$	6.21449	−	6.37835i	0.237965	−	0.244240i
$683$	18.1722	+	18.1722i	0.695338	+	0.695338i	0.963401	−	0.268063i	$-0.0863835\pi$
$683$	18.1722	+	18.1722i	0.695338	+	0.695338i	−0.268063	+	0.963401i	$0.586384\pi$
$684$	−31.0708	+	7.50938i	−1.18802	+	0.287128i
$685$	−6.37181	+	6.37181i	−0.243454	+	0.243454i
$686$	−1.41409	+	0.0184003i	−0.0539904	+	0.000702526i
$687$	9.79014	+	2.89105i	0.373517	+	0.110300i
$688$	4.50794	−	5.00341i	0.171864	−	0.190753i
$689$			6.93876i			0.264346i
$690$	−16.4128	−	4.61543i	−0.624824	−	0.175706i
$691$	28.3836	+	28.3836i	1.07976	+	1.07976i	0.996530	+	0.0832314i	$0.0265241\pi$
$691$	28.3836	+	28.3836i	1.07976	+	1.07976i	0.0832314	+	0.996530i	$0.473476\pi$
$692$	−3.94909	−	3.74873i	−0.150122	−	0.142505i
$693$	−14.8210	+	3.17628i	−0.563003	+	0.120657i
$694$	10.8776	+	10.5981i	0.412907	+	0.402300i
$695$		−	33.1195i		−	1.25629i
$696$	31.9239	+	8.08717i	1.21007	+	0.306544i
$697$			8.69000i			0.329157i
$698$	−10.6526	+	10.9335i	−0.403207	+	0.413838i
$699$	−11.3782	+	6.19022i	−0.430364	+	0.234136i
$700$	−0.100334	−	3.85477i	−0.00379227	−	0.145697i
$701$	−8.31473	−	8.31473i	−0.314043	−	0.314043i	0.532431	−	0.846474i	$-0.321279\pi$
$701$	−8.31473	−	8.31473i	−0.314043	−	0.314043i	−0.846474	+	0.532431i	$0.821279\pi$
$702$	10.9227	+	12.3939i	0.412249	+	0.467777i
$703$			48.2156i			1.81849i
$704$	30.7233	+	26.2653i	1.15793	+	0.989909i
$705$	7.10228	−	24.0509i	0.267487	−	0.905809i
$706$	0.346584	+	26.6356i	0.0130439	+	1.00244i
$707$	−5.10294	+	5.10294i	−0.191916	+	0.191916i
$708$	25.8060	+	6.89587i	0.969848	+	0.259163i
$709$	−34.8067	−	34.8067i	−1.30719	−	1.30719i	−0.923434	−	0.383757i	$-0.874630\pi$
$709$	−34.8067	−	34.8067i	−1.30719	−	1.30719i	−0.383757	−	0.923434i	$-0.625370\pi$
$710$	−10.8870	−	10.6073i	−0.408580	−	0.398084i
$711$	16.4703	+	10.6568i	0.617686	+	0.399660i
$712$	−25.8715	+	1.01038i	−0.969576	+	0.0378657i
$713$	4.94935			0.185355
$714$	2.64630	+	4.71690i	0.0990352	+	0.176525i
$715$	14.0772	−	14.0772i	0.526456	−	0.526456i
$716$	−6.43785	+	6.78194i	−0.240594	+	0.253453i
$717$	−6.08575	+	3.31090i	−0.227276	+	0.123648i
$718$	0.291105	+	22.3719i	0.0108639	+	0.834914i
$719$	7.90389			0.294765			0.147383	−	0.989080i	$-0.452915\pi$
$719$	7.90389			0.294765			0.147383	+	0.989080i	$0.452915\pi$
$720$	−5.47124	−	20.3083i	−0.203901	−	0.756846i
$721$	−17.2234			−0.641432
$722$	0.172650	+	13.2684i	0.00642536	+	0.493800i
$723$	−4.97507	+	2.70665i	−0.185025	+	0.100661i
$724$	29.0273	+	27.5546i	1.07879	+	1.02406i
$725$	9.16469	−	9.16469i	0.340368	−	0.340368i
$726$	−17.4116	−	31.0353i	−0.646205	−	1.15183i
$727$	−28.1472			−1.04392			−0.521960	−	0.852970i	$-0.674799\pi$
$727$	−28.1472			−1.04392			−0.521960	+	0.852970i	$0.674799\pi$
$728$	−4.31731	+	4.66823i	−0.160010	+	0.173016i
$729$	−26.6885	−	4.08958i	−0.988462	−	0.151466i
$730$	18.1523	+	17.6859i	0.671845	+	0.654586i
$731$	2.62871	+	2.62871i	0.0972264	+	0.0972264i
$732$	6.46061	−	24.1772i	0.238791	−	0.893613i
$733$	28.6742	−	28.6742i	1.05911	−	1.05911i	0.0609673	−	0.998140i	$-0.480581\pi$
$733$	28.6742	−	28.6742i	1.05911	−	1.05911i	0.998140	−	0.0609673i	$-0.0194185\pi$
$734$	−0.471198	−	36.2124i	−0.0173922	−	1.33662i
$735$	−0.859765	+	2.91147i	−0.0317129	+	0.107391i
$736$	1.46045	+	22.4171i	0.0538327	+	0.826307i
$737$		−	51.7242i		−	1.90529i
$738$	8.88750	−	14.1358i	0.327153	−	0.520347i
$739$	1.83024	+	1.83024i	0.0673263	+	0.0673263i	0.739968	−	0.672642i	$-0.234841\pi$
$739$	1.83024	+	1.83024i	0.0673263	+	0.0673263i	−0.672642	+	0.739968i	$0.734841\pi$
$740$	−31.7139	+	0.825465i	−1.16582	+	0.0303447i
$741$	18.2224	−	9.91374i	0.669417	−	0.364190i
$742$	3.04608	−	3.12640i	0.111825	−	0.114774i
$743$		−	1.62576i		−	0.0596432i	−0.999555	−	0.0298216i	$-0.990506\pi$
$743$		−	1.62576i		−	0.0596432i	0.999555	−	0.0298216i	$-0.00949392\pi$
$744$	3.12491	+	5.24532i	0.114565	+	0.192303i
$745$		−	35.5727i		−	1.30328i
$746$	−29.8336	−	29.0672i	−1.09229	−	1.06423i
$747$	10.9904	+	51.2828i	0.402116	+	1.87634i
$748$	−15.3612	+	16.1822i	−0.561659	+	0.591679i
$749$	−8.98275	−	8.98275i	−0.328223	−	0.328223i
$750$	−28.6330	−	8.05188i	−1.04553	−	0.294013i
$751$			30.5920i			1.11632i	0.829734	+	0.558159i	$0.188492\pi$
$751$			30.5920i			1.11632i	−0.829734	+	0.558159i	$0.811508\pi$
$752$	−32.9982	+	1.71895i	−1.20332	+	0.0626838i
$753$	−8.37645	−	2.47358i	−0.305255	−	0.0901424i
$754$	−21.3703	+	0.278071i	−0.778259	+	0.0101268i
$755$	−21.7448	+	21.7448i	−0.791374	+	0.791374i
$756$	0.519429	−	10.3793i	0.0188915	−	0.377492i
$757$	−11.0220	−	11.0220i	−0.400602	−	0.400602i	0.477843	−	0.878445i	$-0.341419\pi$
$757$	−11.0220	−	11.0220i	−0.400602	−	0.400602i	−0.878445	+	0.477843i	$0.841419\pi$
$758$	10.2010	−	10.4700i	0.370517	−	0.380286i
$759$	9.84247	−	33.3302i	0.357259	−	1.20981i
$760$	−26.3907	+	1.03066i	−0.957291	+	0.0373859i
$761$	−2.53536			−0.0919066			−0.0459533	−	0.998944i	$-0.514633\pi$
$761$	−2.53536			−0.0919066			−0.0459533	+	0.998944i	$0.514633\pi$
$762$	2.67620	+	4.77019i	0.0969484	+	0.172806i
$763$	−9.91151	+	9.91151i	−0.358821	+	0.358821i
$764$	16.9305	−	0.440677i	0.612525	−	0.0159431i
$765$	11.3522	−	2.43288i	0.410440	−	0.0879610i
$766$	−22.4375	+	0.291958i	−0.810700	+	0.0105489i
$767$	−17.3349			−0.625928
$768$	−22.8356	+	15.7015i	−0.824008	+	0.566578i
$769$	−1.37099			−0.0494393			−0.0247196	−	0.999694i	$-0.507869\pi$
$769$	−1.37099			−0.0494393			−0.0247196	+	0.999694i	$0.507869\pi$
$770$	−12.5226	+	0.162944i	−0.451282	+	0.00587211i
$771$	−14.1080	−	25.9319i	−0.508088	−	0.933914i
$772$	−34.5429	+	0.899100i	−1.24322	+	0.0323593i
$773$	−3.38228	+	3.38228i	−0.121652	+	0.121652i	−0.765312	−	0.643660i	$-0.777415\pi$
$773$	−3.38228	+	3.38228i	−0.121652	+	0.121652i	0.643660	+	0.765312i	$0.277415\pi$
$774$	−1.58761	−	6.96452i	−0.0570655	−	0.250335i
$775$	2.40292			0.0863154
$776$	21.6989	−	0.847424i	0.778944	−	0.0304207i
$777$	−15.0336	−	4.43946i	−0.539328	−	0.159265i
$778$	3.37981	−	3.46892i	0.121172	−	0.124367i
$779$	−14.8263	−	14.8263i	−0.531206	−	0.531206i
$780$	6.83275	+	11.8161i	0.244652	+	0.423084i
$781$	21.9085	−	21.9085i	0.783949	−	0.783949i
$782$	−12.3995	+	0.161344i	−0.443407	+	0.00576964i
$783$	26.5039	−	22.7519i	0.947170	−	0.813087i
$784$	3.99458	−	0.208087i	0.142664	−	0.00743169i
$785$		−	23.0454i		−	0.822526i
$786$	4.66811	−	16.6001i	0.166506	−	0.592107i
$787$	37.7087	+	37.7087i	1.34417	+	1.34417i	0.891862	+	0.452308i	$0.149399\pi$
$787$	37.7087	+	37.7087i	1.34417	+	1.34417i	0.452308	+	0.891862i	$0.350601\pi$
$788$	−32.0235	+	33.7351i	−1.14079	+	1.20176i
$789$	21.8892	+	40.2344i	0.779276	+	1.43238i
$790$	11.6092	+	11.3110i	0.413038	+	0.402427i
$791$		−	14.2233i		−	0.505721i
$792$	41.5376	−	10.6129i	1.47597	−	0.377114i
$793$			16.2408i			0.576727i
$794$	−3.20266	+	3.28711i	−0.113658	+	0.116655i
$795$	−4.47783	−	8.23068i	−0.158812	−	0.291912i
$796$	16.4132	−	0.427211i	0.581750	−	0.0151421i
$797$	−11.4184	−	11.4184i	−0.404459	−	0.404459i	0.475342	−	0.879801i	$-0.342324\pi$
$797$	−11.4184	−	11.4184i	−0.404459	−	0.404459i	−0.879801	+	0.475342i	$0.842324\pi$
$798$	−12.5626	−	3.53271i	−0.444710	−	0.125057i
$799$		−	18.2398i		−	0.645278i
$800$	0.709049	+	10.8836i	0.0250687	+	0.384792i
$801$	−14.9182	+	23.0565i	−0.527107	+	0.814660i
$802$	0.0842468	+	6.47451i	0.00297486	+	0.228623i
$803$	−36.5290	+	36.5290i	−1.28908	+	1.28908i
$804$	34.2610	+	9.15522i	1.20829	+	0.322880i
$805$	−4.92173	−	4.92173i	−0.173468	−	0.173468i
$806$	−2.83803	−	2.76512i	−0.0999652	−	0.0973971i
$807$	−27.2429	−	8.04489i	−0.958995	−	0.283193i
$808$	13.8590	−	14.9855i	0.487560	−	0.527189i
$809$	10.3878			0.365216			0.182608	−	0.983186i	$-0.441546\pi$
$809$	10.3878			0.365216			0.182608	+	0.983186i	$0.441546\pi$
$810$	−20.9546	−	7.65271i	−0.736268	−	0.268889i
$811$	20.4489	−	20.4489i	0.718058	−	0.718058i	−0.250149	−	0.968207i	$-0.580480\pi$
$811$	20.4489	−	20.4489i	0.718058	−	0.718058i	0.968207	+	0.250149i	$0.0804797\pi$
$812$	9.75088	+	9.25616i	0.342189	+	0.324827i
$813$	5.81772	+	10.6935i	0.204036	+	0.375038i
$814$	−0.841376	−	64.6612i	−0.0294902	−	2.26638i
$815$	−28.7798			−1.00811
$816$	−7.99979	−	13.0391i	−0.280049	−	0.456462i
$817$	−8.96984			−0.313815
$818$	−0.634202	−	48.7395i	−0.0221743	−	1.70414i
$819$	1.41327	+	6.59455i	0.0493837	+	0.230432i
$820$	9.49815	−	10.0058i	0.331690	−	0.349418i
$821$	−11.8610	+	11.8610i	−0.413952	+	0.413952i	−0.883113	−	0.469161i	$-0.844556\pi$
$821$	−11.8610	+	11.8610i	−0.413952	+	0.413952i	0.469161	+	0.883113i	$0.344556\pi$
$822$	10.9831	−	6.16179i	0.383079	−	0.214917i
$823$	4.69616			0.163698			0.0818490	−	0.996645i	$-0.473917\pi$
$823$	4.69616			0.163698			0.0818490	+	0.996645i	$0.473917\pi$
$824$	48.6780	−	1.90106i	1.69578	−	0.0662266i
$825$	4.77854	−	16.1819i	0.166367	−	0.563380i
$826$	7.81061	+	7.60995i	0.271766	+	0.264784i
$827$	−13.0079	−	13.0079i	−0.452329	−	0.452329i	0.443798	−	0.896127i	$-0.353631\pi$
$827$	−13.0079	−	13.0079i	−0.452329	−	0.452329i	−0.896127	+	0.443798i	$0.853631\pi$
$828$	20.3351	+	12.4189i	0.706693	+	0.431587i
$829$	−20.0165	+	20.0165i	−0.695203	+	0.695203i	−0.963372	−	0.268169i	$-0.913582\pi$
$829$	−20.0165	+	20.0165i	−0.695203	+	0.695203i	0.268169	+	0.963372i	$0.413582\pi$
$830$	0.563811	+	43.3299i	0.0195702	+	1.50400i
$831$	−7.15187	−	2.11196i	−0.248096	−	0.0732632i
$832$	11.6866	−	13.6702i	0.405161	−	0.473930i
$833$			2.20802i			0.0765032i
$834$	−12.5301	+	44.5579i	−0.433882	+	1.54292i
$835$	−6.10226	−	6.10226i	−0.211177	−	0.211177i
$836$	−1.40078	−	53.8170i	−0.0484469	−	1.86130i
$837$	6.45727	+	0.491866i	0.223196	+	0.0170014i
$838$	27.3684	−	28.0900i	0.945426	−	0.970354i
$839$			35.4357i			1.22338i	0.791099	+	0.611688i	$0.209509\pi$
$839$			35.4357i			1.22338i	−0.791099	+	0.611688i	$0.790491\pi$
$840$	2.10857	−	8.32352i	0.0727526	−	0.287189i
$841$			16.1890i			0.558243i
$842$	30.0253	+	29.2539i	1.03474	+	1.00816i
$843$	14.5601	−	7.92131i	0.501477	−	0.272824i
$844$	−31.8658	−	30.2490i	−1.09687	−	1.04121i
$845$	9.84792	+	9.84792i	0.338779	+	0.338779i
$846$	−18.6544	+	29.6703i	−0.641351	+	1.02009i
$847$		−	14.5279i		−	0.499184i
$848$	−8.26398	+	9.17227i	−0.283786	+	0.314977i
$849$	11.0615	−	37.4583i	0.379630	−	1.28557i
$850$	−6.02000	+	0.0783326i	−0.206484	+	0.00268679i
$851$	25.4137	−	25.4137i	0.871172	−	0.871172i
$852$	10.6339	+	18.3896i	0.364312	+	0.630016i
$853$	4.77904	+	4.77904i	0.163631	+	0.163631i	0.784173	−	0.620542i	$-0.213087\pi$
$853$	4.77904	+	4.77904i	0.163631	+	0.163631i	−0.620542	+	0.784173i	$0.713087\pi$
$854$	7.12962	−	7.31761i	0.243971	−	0.250404i
$855$	−15.2175	+	23.5191i	−0.520428	+	0.804338i
$856$	26.3792	+	24.3962i	0.901623	+	0.833846i
$857$	−13.0169			−0.444647			−0.222324	−	0.974973i	$-0.571364\pi$
$857$	−13.0169			−0.444647			−0.222324	+	0.974973i	$0.571364\pi$
$858$	−24.2648	+	13.6132i	−0.828387	+	0.464746i
$859$	−13.5335	+	13.5335i	−0.461758	+	0.461758i	−0.899231	−	0.437473i	$-0.855873\pi$
$859$	−13.5335	+	13.5335i	−0.461758	+	0.461758i	0.437473	+	0.899231i	$0.355873\pi$
$860$	−0.153566	−	5.89992i	−0.00523657	−	0.201186i
$861$	5.98796	−	3.25770i	0.204069	−	0.111022i
$862$	40.7529	−	0.530279i	1.38805	−	0.0180614i
$863$	28.1516			0.958293			0.479146	−	0.877735i	$-0.340946\pi$
$863$	28.1516			0.958293			0.479146	+	0.877735i	$0.340946\pi$
$864$	−0.322414	+	29.3921i	−0.0109687	+	0.999940i
$865$	−4.77175			−0.162244
$866$	42.0904	−	0.547683i	1.43029	−	0.0186110i
$867$	−18.4472	+	10.0361i	−0.626501	+	0.340842i
$868$	0.0648569	+	2.49176i	0.00220139	+	0.0845759i
$869$	−23.3620	+	23.3620i	−0.792502	+	0.792502i
$870$	25.1697	−	14.1208i	0.853334	−	0.478741i
$871$	−23.0145			−0.779817
$872$	26.9186	−	29.1066i	0.911579	−	0.985674i
$873$	12.5121	−	19.3378i	0.423470	−	0.654486i
$874$	20.8799	−	21.4305i	0.706275	−	0.724897i
$875$	−8.58624	−	8.58624i	−0.290268	−	0.290268i
$876$	−17.7303	−	30.6616i	−0.599053	−	1.03596i
$877$	−31.2389	+	31.2389i	−1.05486	+	1.05486i	−0.0564564	+	0.998405i	$0.517980\pi$
$877$	−31.2389	+	31.2389i	−1.05486	+	1.05486i	−0.998405	+	0.0564564i	$0.982020\pi$
$878$	−14.7887	+	0.192431i	−0.499094	+	0.00649425i
$879$	0.892838	−	3.02347i	0.0301147	−	0.101979i
$880$	35.3742	−	1.84273i	1.19246	−	0.0621183i
$881$			36.9138i			1.24366i	0.783154	+	0.621828i	$0.213610\pi$
$881$			36.9138i			1.24366i	−0.783154	+	0.621828i	$0.786390\pi$
$882$	2.25820	−	3.59173i	0.0760375	−	0.120940i
$883$	−14.6891	−	14.6891i	−0.494329	−	0.494329i	0.415338	−	0.909667i	$-0.363663\pi$
$883$	−14.6891	−	14.6891i	−0.494329	−	0.494329i	−0.909667	+	0.415338i	$0.863663\pi$
$884$	7.20020	+	6.83489i	0.242169	+	0.229882i
$885$	20.5625	−	11.1869i	0.691201	−	0.376042i
$886$	−27.3546	−	26.6519i	−0.918996	−	0.895387i
$887$		−	8.84622i		−	0.297027i	−0.988910	−	0.148514i	$-0.952551\pi$
$887$		−	8.84622i		−	0.297027i	0.988910	−	0.148514i	$-0.0474488\pi$
$888$	42.9791	+	10.8878i	1.44229	+	0.365369i
$889$			2.23296i			0.0748912i
$890$	−15.8340	+	16.2515i	−0.530757	+	0.544752i
$891$	16.1535	−	42.5067i	0.541163	−	1.42403i
$892$	0.238360	+	9.15764i	0.00798088	+	0.306621i
$893$	31.1195	+	31.1195i	1.04137	+	1.04137i
$894$	−13.4582	+	47.8584i	−0.450111	+	1.60062i
$895$			8.19473i			0.273920i
$896$	−11.2668	+	1.02902i	−0.376398	+	0.0343772i
$897$	−14.8301	−	4.37937i	−0.495164	−	0.146223i
$898$	0.489431	+	37.6136i	0.0163325	+	1.25518i
$899$	−5.92413	+	5.92413i	−0.197581	+	0.197581i
$900$	9.87272	+	6.02940i	0.329091	+	0.200980i
$901$	−4.81897	−	4.81897i	−0.160543	−	0.160543i
$902$	20.1420	+	19.6246i	0.670655	+	0.653426i
$903$	0.825900	−	2.79680i	0.0274842	−	0.0930716i
$904$	1.56992	+	40.1989i	0.0522147	+	1.33699i
$905$	35.0742			1.16591
$906$	37.4815	−	21.0281i	1.24524	−	0.698610i
$907$	−26.6472	+	26.6472i	−0.884804	+	0.884804i	−0.994018	−	0.109214i	$-0.965167\pi$
$907$	−26.6472	+	26.6472i	−0.884804	+	0.884804i	0.109214	+	0.994018i	$0.465167\pi$
$908$	31.1542	−	32.8194i	1.03389	−	1.08915i
$909$	−4.53676	−	21.1693i	−0.150475	−	0.702140i
$910$	0.0725016	+	5.57187i	0.00240340	+	0.184706i
$911$	48.5784			1.60947			0.804737	−	0.593632i	$-0.202306\pi$
$911$	48.5784			1.60947			0.804737	+	0.593632i	$0.202306\pi$
$912$	35.8951	+	8.59779i	1.18861	+	0.284701i
$913$	−88.3301			−2.92330
$914$	−0.0938675	−	7.21388i	−0.00310486	−	0.238614i
$915$	−10.4808	−	19.2646i	−0.346483	−	0.636869i
$916$	−8.54891	−	8.11517i	−0.282464	−	0.268133i
$917$	4.97791	−	4.97791i	0.164385	−	0.164385i
$918$	−16.1933	−	1.02176i	−0.534460	−	0.0337232i
$919$	31.5660			1.04126			0.520632	−	0.853781i	$-0.325696\pi$
$919$	31.5660			1.04126			0.520632	+	0.853781i	$0.325696\pi$
$920$	14.4534	+	13.3669i	0.476514	+	0.440694i
$921$	−15.3176	−	4.52333i	−0.504733	−	0.149049i
$922$	−11.3054	−	11.0150i	−0.372324	−	0.362759i
$923$	−9.74813	−	9.74813i	−0.320864	−	0.320864i
$924$	16.9091	+	4.51845i	0.556269	+	0.148646i
$925$	12.3384	−	12.3384i	0.405685	−	0.405685i
$926$	0.212101	+	16.3003i	0.00697008	+	0.535663i
$927$	28.0689	−	43.3813i	0.921904	−	1.42483i
$928$	−28.5803	−	25.0842i	−0.938195	−	0.823428i
$929$		−	8.25723i		−	0.270911i	−0.990783	−	0.135456i	$-0.956750\pi$
$929$		−	8.25723i		−	0.270911i	0.990783	−	0.135456i	$-0.0432498\pi$
$930$	5.15086	+	1.44847i	0.168904	+	0.0474973i
$931$	−3.76716	−	3.76716i	−0.123464	−	0.123464i
$932$	14.9519	−	0.389176i	0.489765	−	0.0127479i
$933$	14.7566	+	27.1241i	0.483110	+	0.888002i
$934$	−24.3652	+	25.0077i	−0.797254	+	0.818275i
$935$			19.5532i			0.639457i
$936$	−4.72218	−	18.4820i	−0.154349	−	0.604104i
$937$		−	11.4367i		−	0.373620i	−0.982396	−	0.186810i	$-0.940185\pi$
$937$		−	11.4367i		−	0.373620i	0.982396	−	0.186810i	$-0.0598149\pi$
$938$	10.3697	+	10.1033i	0.338581	+	0.329883i
$939$	4.03472	+	7.41620i	0.131668	+	0.242018i
$940$	−19.9361	+	21.0017i	−0.650244	+	0.684998i
$941$	−38.7594	−	38.7594i	−1.26352	−	1.26352i	−0.949375	−	0.314144i	$-0.898283\pi$
$941$	−38.7594	−	38.7594i	−1.26352	−	1.26352i	−0.314144	−	0.949375i	$-0.601717\pi$
$942$	−8.71878	+	31.0046i	−0.284073	+	1.01018i
$943$			15.6294i			0.508963i
$944$	−22.9149	−	20.6457i	−0.745815	−	0.671960i
$945$	−5.93211	−	6.91035i	−0.192972	−	0.224794i
$946$	12.0293	−	0.156526i	0.391107	−	0.00508911i
$947$	−11.9692	+	11.9692i	−0.388948	+	0.388948i	−0.874312	−	0.485364i	$-0.838687\pi$
$947$	−11.9692	+	11.9692i	−0.388948	+	0.388948i	0.485364	+	0.874312i	$0.338687\pi$
$948$	−11.3394	−	19.6096i	−0.368287	−	0.636890i
$949$	16.2534	+	16.2534i	0.527609	+	0.527609i
$950$	10.1373	−	10.4045i	0.328896	−	0.337568i
$951$	11.6792	+	3.44890i	0.378725	+	0.111838i
$952$	−0.243714	−	6.24046i	−0.00789881	−	0.202254i
$953$	30.7222			0.995190			0.497595	−	0.867409i	$-0.334217\pi$
$953$	30.7222			0.995190			0.497595	+	0.867409i	$0.334217\pi$
$954$	2.91041	+	12.7674i	0.0942282	+	0.413360i
$955$	10.4950	−	10.4950i	0.339609	−	0.339609i
$956$	7.99715	−	0.208154i	0.258646	−	0.00673219i
$957$	28.1136	+	51.6756i	0.908785	+	1.67043i
$958$	2.99987	−	0.0390345i	0.0969213	−	0.00126115i
$959$	5.14127			0.166020
$960$	−5.04067	+	23.7573i	−0.162687	+	0.766763i
$961$	29.4467			0.949895
$962$	−28.7708	+	0.374367i	−0.927608	+	0.0120701i
$963$	37.2645	−	7.98611i	1.20083	−	0.257349i
$964$	6.53764	−	0.170165i	0.210563	−	0.00548065i
$965$	−21.4125	+	21.4125i	−0.689294	+	0.689294i
$966$	4.75950	+	8.48358i	0.153134	+	0.272955i
$967$	−14.1286			−0.454346			−0.227173	−	0.973854i	$-0.572948\pi$
$967$	−14.1286			−0.454346			−0.227173	+	0.973854i	$0.572948\pi$
$968$	1.60354	+	41.0597i	0.0515397	+	1.31971i
$969$	−5.77036	+	19.5405i	−0.185371	+	0.627733i
$970$	13.2802	−	13.6304i	0.426403	−	0.437646i
$971$	3.35904	+	3.35904i	0.107797	+	0.107797i	0.758948	−	0.651151i	$-0.225714\pi$
$971$	3.35904	+	3.35904i	0.107797	+	0.107797i	−0.651151	+	0.758948i	$0.725714\pi$
$972$	25.2964	+	18.2235i	0.811381	+	0.584518i
$973$	−13.3617	+	13.3617i	−0.428356	+	0.428356i
$974$	48.2496	−	0.627827i	1.54602	−	0.0201169i
$975$	−7.20007	−	2.12619i	−0.230587	−	0.0680927i
$976$	−19.3426	+	21.4685i	−0.619141	+	0.687190i
$977$		−	15.4506i		−	0.494310i	−0.968976	−	0.247155i	$-0.920504\pi$
$977$		−	15.4506i		−	0.494310i	0.968976	−	0.247155i	$-0.0794957\pi$
$978$	38.7194	+	10.8883i	1.23811	+	0.348168i
$979$	−32.7040	−	32.7040i	−1.04522	−	1.04522i
$980$	2.41336	−	2.54235i	0.0770919	−	0.0812124i
$981$	−8.81182	−	41.1173i	−0.281340	−	1.31278i
$982$	3.33451	+	3.24885i	0.106409	+	0.103675i
$983$		−	24.7893i		−	0.790655i	−0.918540	−	0.395327i	$-0.870631\pi$
$983$		−	24.7893i		−	0.790655i	0.918540	−	0.395327i	$-0.129369\pi$
$984$	−16.5640	+	9.86807i	−0.528042	+	0.314582i
$985$			40.7627i			1.29881i
$986$	14.6485	−	15.0348i	0.466504	−	0.478804i
$987$	−12.5684	+	6.83772i	−0.400056	+	0.217647i
$988$	−23.9457	+	0.623271i	−0.761814	+	0.0198289i
$989$	4.72787	+	4.72787i	0.150338	+	0.150338i
$990$	19.9976	−	31.8067i	0.635565	−	1.01088i
$991$			6.86472i			0.218065i	0.994038	+	0.109033i	$0.0347753\pi$
$991$			6.86472i			0.218065i	−0.994038	+	0.109033i	$0.965225\pi$
$992$	−0.458336	−	7.03524i	−0.0145522	−	0.223369i
$993$	−6.92033	+	23.4348i	−0.219610	+	0.743680i
$994$	0.112835	+	8.67160i	0.00357892	+	0.275046i
$995$	10.1743	−	10.1743i	0.322545	−	0.322545i
$996$	15.6345	−	58.5079i	0.495397	−	1.85389i
$997$	−42.8927	−	42.8927i	−1.35842	−	1.35842i	−0.875861	−	0.482563i	$-0.839706\pi$
$997$	−42.8927	−	42.8927i	−1.35842	−	1.35842i	−0.482563	−	0.875861i	$-0.660294\pi$
$998$	23.6285	+	23.0215i	0.747946	+	0.728732i
$999$	35.6821	−	30.6309i	1.12893	−	0.969119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.20	yes	40
3.2	odd	2	inner	336.2.s.c.155.1	✓	40
4.3	odd	2		1344.2.s.c.911.16		40
12.11	even	2		1344.2.s.c.911.8		40
16.3	odd	4	inner	336.2.s.c.323.1	yes	40
16.13	even	4		1344.2.s.c.239.8		40
48.29	odd	4		1344.2.s.c.239.16		40
48.35	even	4	inner	336.2.s.c.323.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.1	✓	40	3.2	odd	2	inner
336.2.s.c.155.20	yes	40	1.1	even	1	trivial
336.2.s.c.323.1	yes	40	16.3	odd	4	inner
336.2.s.c.323.20	yes	40	48.35	even	4	inner
1344.2.s.c.239.8		40	16.13	even	4
1344.2.s.c.239.16		40	48.29	odd	4
1344.2.s.c.911.8		40	12.11	even	2
1344.2.s.c.911.16		40	4.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41409 - 0.0184003i) q^{2} +(-1.52146 + 0.827739i) q^{3} +(1.99932 - 0.0520394i) q^{4} +(1.23935 - 1.23935i) q^{5} +(-2.13626 + 1.19850i) q^{6} -1.00000 q^{7} +(2.82627 - 0.110377i) q^{8} +(1.62970 - 2.51875i) q^{9} +O(q^{10})\)	\(q+(1.41409 - 0.0184003i) q^{2} +(-1.52146 + 0.827739i) q^{3} +(1.99932 - 0.0520394i) q^{4} +(1.23935 - 1.23935i) q^{5} +(-2.13626 + 1.19850i) q^{6} -1.00000 q^{7} +(2.82627 - 0.110377i) q^{8} +(1.62970 - 2.51875i) q^{9} +(1.72975 - 1.77536i) q^{10} +(3.57267 + 3.57267i) q^{11} +(-2.99882 + 1.73409i) q^{12} +(1.58965 - 1.58965i) q^{13} +(-1.41409 + 0.0184003i) q^{14} +(-0.859765 + 2.91147i) q^{15} +(3.99458 - 0.208087i) q^{16} +2.20802i q^{17} +(2.25820 - 3.59173i) q^{18} +(-3.76716 - 3.76716i) q^{19} +(2.41336 - 2.54235i) q^{20} +(1.52146 - 0.827739i) q^{21} +(5.11782 + 4.98635i) q^{22} +3.97123i q^{23} +(-4.20871 + 2.50735i) q^{24} +1.92804i q^{25} +(2.21866 - 2.27716i) q^{26} +(-0.394660 + 5.18114i) q^{27} +(-1.99932 + 0.0520394i) q^{28} +(-4.75337 - 4.75337i) q^{29} +(-1.16222 + 4.13292i) q^{30} -1.24630i q^{31} +(5.64489 - 0.367756i) q^{32} +(-8.39291 - 2.47844i) q^{33} +(0.0406281 + 3.12234i) q^{34} +(-1.23935 + 1.23935i) q^{35} +(3.12722 - 5.12060i) q^{36} +(-6.39946 - 6.39946i) q^{37} +(-5.39644 - 5.25780i) q^{38} +(-1.10278 + 3.73440i) q^{39} +(3.36594 - 3.63953i) q^{40} +3.93566 q^{41} +(2.13626 - 1.19850i) q^{42} +(1.19053 - 1.19053i) q^{43} +(7.32883 + 6.95699i) q^{44} +(-1.10184 - 5.14136i) q^{45} +(0.0730718 + 5.61569i) q^{46} -8.26073 q^{47} +(-5.90537 + 3.62307i) q^{48} +1.00000 q^{49} +(0.0354765 + 2.72643i) q^{50} +(-1.82766 - 3.35941i) q^{51} +(3.09549 - 3.26094i) q^{52} +(-2.18249 + 2.18249i) q^{53} +(-0.462752 + 7.33388i) q^{54} +8.85554 q^{55} +(-2.82627 + 0.110377i) q^{56} +(8.84982 + 2.61337i) q^{57} +(-6.80917 - 6.63425i) q^{58} +(-5.45245 - 5.45245i) q^{59} +(-1.56744 + 5.86572i) q^{60} +(-5.10830 + 5.10830i) q^{61} +(-0.0229323 - 1.76239i) q^{62} +(-1.62970 + 2.51875i) q^{63} +(7.97563 - 0.623910i) q^{64} -3.94024i q^{65} +(-11.9140 - 3.35032i) q^{66} +(-7.23888 - 7.23888i) q^{67} +(0.114904 + 4.41454i) q^{68} +(-3.28714 - 6.04208i) q^{69} +(-1.72975 + 1.77536i) q^{70} -6.13227i q^{71} +(4.32796 - 7.29855i) q^{72} +10.2246i q^{73} +(-9.16719 - 8.93169i) q^{74} +(-1.59591 - 2.93344i) q^{75} +(-7.72781 - 7.33573i) q^{76} +(-3.57267 - 3.57267i) q^{77} +(-1.49071 + 5.30108i) q^{78} +6.53910i q^{79} +(4.69278 - 5.20857i) q^{80} +(-3.68817 - 8.20959i) q^{81} +(5.56539 - 0.0724172i) q^{82} +(-12.3619 + 12.3619i) q^{83} +(2.99882 - 1.73409i) q^{84} +(2.73650 + 2.73650i) q^{85} +(1.66162 - 1.70543i) q^{86} +(11.1666 + 3.29753i) q^{87} +(10.4917 + 9.70299i) q^{88} -9.15394 q^{89} +(-1.65271 - 7.25009i) q^{90} +(-1.58965 + 1.58965i) q^{91} +(0.206661 + 7.93977i) q^{92} +(1.03161 + 1.89620i) q^{93} +(-11.6814 + 0.152000i) q^{94} -9.33763 q^{95} +(-8.28408 + 5.23202i) q^{96} +7.67756 q^{97} +(1.41409 - 0.0184003i) q^{98} +(14.8210 - 3.17628i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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