LMFDB - Embedded newform 845.2.t.g.188.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.t (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.5
Root			$2.25081i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.g.427.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.94926 + 1.12540i) q^{2} +(-1.91913 + 0.514229i) q^{3} +(1.53307 + 2.65535i) q^{4} +(-0.247944 - 2.22228i) q^{5} +(-4.31958 - 1.15743i) q^{6} +(-0.638592 - 1.10607i) q^{7} +2.39966i q^{8} +(0.820542 - 0.473740i) q^{9} +(2.01765 - 4.61083i) q^{10} +(5.27612 - 1.41373i) q^{11} +(-4.30760 - 4.30760i) q^{12} -2.87469i q^{14} +(1.61860 + 4.13734i) q^{15} +(0.365551 - 0.633152i) q^{16} +(0.833802 - 3.11179i) q^{17} +2.13259 q^{18} +(0.315395 - 1.17707i) q^{19} +(5.52081 - 4.06528i) q^{20} +(1.79431 + 1.79431i) q^{21} +(11.8755 + 3.18204i) q^{22} +(0.0428736 + 0.160006i) q^{23} +(-1.23397 - 4.60524i) q^{24} +(-4.87705 + 1.10200i) q^{25} +(2.88358 - 2.88358i) q^{27} +(1.95801 - 3.39137i) q^{28} +(8.41068 + 4.85591i) q^{29} +(-1.50111 + 9.88630i) q^{30} +(-0.233305 + 0.233305i) q^{31} +(5.58143 - 3.22244i) q^{32} +(-9.39857 + 5.42627i) q^{33} +(5.12732 - 5.12732i) q^{34} +(-2.29967 + 1.69337i) q^{35} +(2.51589 + 1.45255i) q^{36} +(0.660816 - 1.14457i) q^{37} +(1.93947 - 1.93947i) q^{38} +(5.33270 - 0.594981i) q^{40} +(-0.129579 - 0.483595i) q^{41} +(1.47825 + 5.51690i) q^{42} +(-6.43569 - 1.72444i) q^{43} +(11.8426 + 11.8426i) q^{44} +(-1.25623 - 1.70601i) q^{45} +(-0.0965002 + 0.360144i) q^{46} -3.20027 q^{47} +(-0.375953 + 1.40308i) q^{48} +(2.68440 - 4.64952i) q^{49} +(-10.7468 - 3.34056i) q^{50} +6.40069i q^{51} +(4.49845 + 4.49845i) q^{53} +(8.86603 - 2.37565i) q^{54} +(-4.44989 - 11.3745i) q^{55} +(2.65420 - 1.53240i) q^{56} +2.42113i q^{57} +(10.9297 + 18.9308i) q^{58} +(-0.00222123 - 0.000595178i) q^{59} +(-8.50465 + 10.6407i) q^{60} +(-0.695993 - 1.20550i) q^{61} +(-0.717332 + 0.192209i) q^{62} +(-1.04798 - 0.605053i) q^{63} +13.0440 q^{64} -24.4270 q^{66} +(-5.26055 - 3.03718i) q^{67} +(9.54117 - 2.55655i) q^{68} +(-0.164560 - 0.285026i) q^{69} +(-6.38837 + 0.712764i) q^{70} +(-11.7428 - 3.14648i) q^{71} +(1.13681 + 1.96902i) q^{72} -7.34614i q^{73} +(2.57620 - 1.48737i) q^{74} +(8.79299 - 4.62280i) q^{75} +(3.60906 - 0.967044i) q^{76} +(-4.93298 - 4.93298i) q^{77} +11.1774i q^{79} +(-1.49768 - 0.655369i) q^{80} +(-5.47236 + 9.47841i) q^{81} +(0.291657 - 1.08848i) q^{82} -2.65539 q^{83} +(-2.01373 + 7.51533i) q^{84} +(-7.12201 - 1.08139i) q^{85} +(-10.6041 - 10.6041i) q^{86} +(-18.6382 - 4.99409i) q^{87} +(3.39247 + 12.6609i) q^{88} +(1.86638 + 6.96542i) q^{89} +(-0.528764 - 4.73922i) q^{90} +(-0.359145 + 0.359145i) q^{92} +(0.327769 - 0.567713i) q^{93} +(-6.23815 - 3.60160i) q^{94} +(-2.69398 - 0.409048i) q^{95} +(-9.05440 + 9.05440i) q^{96} +(3.62059 - 2.09035i) q^{97} +(10.4652 - 6.04207i) q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 8 * q^6 + 2 * q^7 + 12 * q^9 - 2 * q^10 + 16 * q^11 - 24 * q^12 + 20 * q^15 - 2 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^21 + 16 * q^22 - 10 * q^23 - 32 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 26 * q^30 - 48 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 + 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 + 40 * q^42 + 10 * q^43 + 36 * q^44 - 4 * q^46 + 40 * q^47 - 56 * q^48 + 18 * q^49 - 36 * q^50 - 10 * q^53 + 48 * q^54 - 10 * q^55 + 16 * q^59 - 28 * q^60 - 16 * q^61 - 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 22 * q^68 - 16 * q^69 + 12 * q^70 + 16 * q^71 - 4 * q^72 + 18 * q^74 - 38 * q^75 + 64 * q^76 - 28 * q^77 + 2 * q^80 - 14 * q^81 + 56 * q^82 - 48 * q^83 + 40 * q^84 + 26 * q^85 - 60 * q^86 - 34 * q^87 + 82 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 - 48 * q^94 - 26 * q^95 - 56 * q^96 - 66 * q^97 + 30 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.94926	+	1.12540i	1.37833	+	0.795780i	0.991959	−	0.126562i	$-0.0403943\pi$
$2$	1.94926	+	1.12540i	1.37833	+	0.795780i	0.386373	+	0.922342i	$0.373728\pi$
$3$	−1.91913	+	0.514229i	−1.10801	+	0.296890i	−0.766022	−	0.642815i	$-0.777767\pi$
$3$	−1.91913	+	0.514229i	−1.10801	+	0.296890i	−0.341987	+	0.939705i	$0.611100\pi$
$4$	1.53307	+	2.65535i	0.766533	+	1.32767i
$5$	−0.247944	−	2.22228i	−0.110884	−	0.993833i
$5$	−0.247944	−	2.22228i	−0.110884	−	0.993833i
$6$	−4.31958	−	1.15743i	−1.76346	−	0.472518i
$7$	−0.638592	−	1.10607i	−0.241365	−	0.418057i	0.719738	−	0.694245i	$-0.244262\pi$
$7$	−0.638592	−	1.10607i	−0.241365	−	0.418057i	−0.961103	+	0.276189i	$0.910928\pi$
$8$			2.39966i			0.848406i
$9$	0.820542	−	0.473740i	0.273514	−	0.157913i
$10$	2.01765	−	4.61083i	0.638038	−	1.45807i
$11$	5.27612	−	1.41373i	1.59081	−	0.426257i	0.648560	−	0.761163i	$-0.275371\pi$
$11$	5.27612	−	1.41373i	1.59081	−	0.426257i	0.942251	+	0.334907i	$0.108705\pi$
$12$	−4.30760	−	4.30760i	−1.24350	−	1.24350i
$13$		0			0
$13$		0			0
$14$		−	2.87469i		−	0.768294i
$15$	1.61860	+	4.13734i	0.417920	+	1.06826i
$16$	0.365551	−	0.633152i	0.0913876	−	0.158288i
$17$	0.833802	−	3.11179i	0.202227	−	0.754721i	−0.788050	−	0.615611i	$-0.788909\pi$
$17$	0.833802	−	3.11179i	0.202227	−	0.754721i	0.990277	−	0.139110i	$-0.0444241\pi$
$18$	2.13259			0.502657
$19$	0.315395	−	1.17707i	0.0723567	−	0.270039i	−0.920264	−	0.391297i	$-0.872026\pi$
$19$	0.315395	−	1.17707i	0.0723567	−	0.270039i	0.992621	+	0.121259i	$0.0386931\pi$
$20$	5.52081	−	4.06528i	1.23449	−	0.909024i
$21$	1.79431	+	1.79431i	0.391551	+	0.391551i
$22$	11.8755	+	3.18204i	2.53187	+	0.678413i
$23$	0.0428736	+	0.160006i	0.00893976	+	0.0333637i	0.970252	−	0.242099i	$-0.0778358\pi$
$23$	0.0428736	+	0.160006i	0.00893976	+	0.0333637i	−0.961312	+	0.275462i	$0.911169\pi$
$24$	−1.23397	−	4.60524i	−0.251883	−	0.940042i
$25$	−4.87705	+	1.10200i	−0.975409	+	0.220401i
$26$		0			0
$27$	2.88358	−	2.88358i	0.554946	−	0.554946i
$28$	1.95801	−	3.39137i	0.370029	−	0.640908i
$29$	8.41068	+	4.85591i	1.56182	+	0.901719i	0.997073	+	0.0764575i	$0.0243610\pi$
$29$	8.41068	+	4.85591i	1.56182	+	0.901719i	0.564751	+	0.825262i	$0.308972\pi$
$30$	−1.50111	+	9.88630i	−0.274065	+	1.80498i
$31$	−0.233305	+	0.233305i	−0.0419027	+	0.0419027i	−0.727748	−	0.685845i	$-0.759433\pi$
$31$	−0.233305	+	0.233305i	−0.0419027	+	0.0419027i	0.685845	+	0.727748i	$0.259433\pi$
$32$	5.58143	−	3.22244i	0.986667	−	0.569652i
$33$	−9.39857	+	5.42627i	−1.63608	+	0.944592i
$34$	5.12732	−	5.12732i	0.879328	−	0.879328i
$35$	−2.29967	+	1.69337i	−0.388715	+	0.286232i
$36$	2.51589	+	1.45255i	0.419315	+	0.242091i
$37$	0.660816	−	1.14457i	0.108638	−	0.188166i	−0.806581	−	0.591124i	$-0.798685\pi$
$37$	0.660816	−	1.14457i	0.108638	−	0.188166i	0.915219	+	0.402958i	$0.132018\pi$
$38$	1.93947	−	1.93947i	0.314623	−	0.314623i
$39$		0			0
$40$	5.33270	−	0.594981i	0.843175	−	0.0940747i
$41$	−0.129579	−	0.483595i	−0.0202368	−	0.0755249i	0.955069	−	0.296384i	$-0.0957807\pi$
$41$	−0.129579	−	0.483595i	−0.0202368	−	0.0755249i	−0.975306	+	0.220859i	$0.929114\pi$
$42$	1.47825	+	5.51690i	0.228099	+	0.851277i
$43$	−6.43569	−	1.72444i	−0.981434	−	0.262974i	−0.267786	−	0.963479i	$-0.586292\pi$
$43$	−6.43569	−	1.72444i	−0.981434	−	0.262974i	−0.713648	+	0.700504i	$0.752959\pi$
$44$	11.8426	+	11.8426i	1.78534	+	1.78534i
$45$	−1.25623	−	1.70601i	−0.187268	−	0.254317i
$46$	−0.0965002	+	0.360144i	−0.0142282	+	0.0531003i
$47$	−3.20027			−0.466808			−0.233404	−	0.972380i	$-0.574986\pi$
$47$	−3.20027			−0.466808			−0.233404	+	0.972380i	$0.574986\pi$
$48$	−0.375953	+	1.40308i	−0.0542642	+	0.202517i
$49$	2.68440	−	4.64952i	0.383486	−	0.664217i
$50$	−10.7468	−	3.34056i	−1.51983	−	0.472427i
$51$			6.40069i			0.896276i
$52$		0			0
$53$	4.49845	+	4.49845i	0.617909	+	0.617909i	0.944995	−	0.327086i	$-0.106067\pi$
$53$	4.49845	+	4.49845i	0.617909	+	0.617909i	−0.327086	+	0.944995i	$0.606067\pi$
$54$	8.86603	−	2.37565i	1.20651	−	0.323285i
$55$	−4.44989	−	11.3745i	−0.600024	−	1.53374i
$56$	2.65420	−	1.53240i	0.354682	−	0.204776i
$57$			2.42113i			0.320687i
$58$	10.9297	+	18.9308i	1.43514	+	2.48574i
$59$	−0.00222123		0.000595178i	−0.000289180		7.74855e-5i	0.258674	−	0.965965i	$-0.416714\pi$
$59$	−0.00222123		0.000595178i	−0.000289180		7.74855e-5i	−0.258964	+	0.965887i	$0.583381\pi$
$60$	−8.50465	+	10.6407i	−1.09795	+	1.37371i
$61$	−0.695993	−	1.20550i	−0.0891128	−	0.154348i	0.818024	−	0.575185i	$-0.195070\pi$
$61$	−0.695993	−	1.20550i	−0.0891128	−	0.154348i	−0.907136	+	0.420837i	$0.861736\pi$
$62$	−0.717332	+	0.192209i	−0.0911013	+	0.0244105i
$63$	−1.04798	−	0.605053i	−0.132033	−	0.0762295i
$64$	13.0440			1.63050
$65$		0			0
$66$	−24.4270			−3.00675
$67$	−5.26055	−	3.03718i	−0.642678	−	0.371050i	0.142967	−	0.989727i	$-0.454336\pi$
$67$	−5.26055	−	3.03718i	−0.642678	−	0.371050i	−0.785645	+	0.618677i	$0.787669\pi$
$68$	9.54117	−	2.55655i	1.15704	−	0.310027i
$69$	−0.164560	−	0.285026i	−0.0198107	−	0.0343131i
$70$	−6.38837	+	0.712764i	−0.763557	+	0.0851916i
$71$	−11.7428	−	3.14648i	−1.39361	−	0.373418i	−0.517567	−	0.855643i	$-0.673162\pi$
$71$	−11.7428	−	3.14648i	−1.39361	−	0.373418i	−0.876048	+	0.482225i	$0.839829\pi$
$72$	1.13681	+	1.96902i	0.133975	+	0.232051i
$73$		−	7.34614i		−	0.859801i	−0.902876	−	0.429901i	$-0.858549\pi$
$73$		−	7.34614i		−	0.859801i	0.902876	−	0.429901i	$-0.141451\pi$
$74$	2.57620	−	1.48737i	0.299477	−	0.172903i
$75$	8.79299	−	4.62280i	1.01533	−	0.533795i
$76$	3.60906	−	0.967044i	0.413987	−	0.110928i
$77$	−4.93298	−	4.93298i	−0.562166	−	0.562166i
$78$		0			0
$79$			11.1774i			1.25756i	0.777584	+	0.628779i	$0.216445\pi$
$79$			11.1774i			1.25756i	−0.777584	+	0.628779i	$0.783555\pi$
$80$	−1.49768	−	0.655369i	−0.167445	−	0.0732725i
$81$	−5.47236	+	9.47841i	−0.608040	+	1.05316i
$82$	0.291657	−	1.08848i	0.0322081	−	0.120202i
$83$	−2.65539			−0.291467			−0.145733	−	0.989324i	$-0.546554\pi$
$83$	−2.65539			−0.291467			−0.145733	+	0.989324i	$0.546554\pi$
$84$	−2.01373	+	7.51533i	−0.219716	+	0.819990i
$85$	−7.12201	−	1.08139i	−0.772490	−	0.117293i
$86$	−10.6041	−	10.6041i	−1.14347	−	1.14347i
$87$	−18.6382	−	4.99409i	−1.99823	−	0.535423i
$88$	3.39247	+	12.6609i	0.361639	+	1.34965i
$89$	1.86638	+	6.96542i	0.197836	+	0.738333i	0.991515	+	0.129996i	$0.0414964\pi$
$89$	1.86638	+	6.96542i	0.197836	+	0.738333i	−0.793679	+	0.608337i	$0.791837\pi$
$90$	−0.528764	−	4.73922i	−0.0557367	−	0.499558i
$91$		0			0
$92$	−0.359145	+	0.359145i	−0.0374434	+	0.0374434i
$93$	0.327769	−	0.567713i	0.0339881	−	0.0588691i
$94$	−6.23815	−	3.60160i	−0.643416	−	0.371477i
$95$	−2.69398	−	0.409048i	−0.276397	−	0.0419675i
$96$	−9.05440	+	9.05440i	−0.924111	+	0.924111i
$97$	3.62059	−	2.09035i	0.367616	−	0.212243i	−0.304801	−	0.952416i	$-0.598590\pi$
$97$	3.62059	−	2.09035i	0.367616	−	0.212243i	0.672416	+	0.740173i	$0.265257\pi$
$98$	10.4652	−	6.04207i	1.05714	−	0.610341i
$99$	3.65954	−	3.65954i	0.367797	−	0.367797i
$100$	−10.4030	−	11.2608i	−1.04030	−	1.12608i
$101$	−7.47319	−	4.31465i	−0.743610	−	0.429323i	0.0797704	−	0.996813i	$-0.474581\pi$
$101$	−7.47319	−	4.31465i	−0.743610	−	0.429323i	−0.823380	+	0.567490i	$0.807915\pi$
$102$	−7.20336	+	12.4766i	−0.713239	+	1.23537i
$103$	1.07603	−	1.07603i	0.106025	−	0.106025i	−0.652104	−	0.758129i	$-0.726114\pi$
$103$	1.07603	−	1.07603i	0.106025	−	0.106025i	0.758129	+	0.652104i	$0.226114\pi$
$104$		0			0
$105$	3.54258	−	4.43236i	0.345720	−	0.432554i
$106$	3.70606	+	13.8312i	0.359964	+	1.34340i
$107$	3.75956	+	14.0309i	0.363451	+	1.35642i	0.869509	+	0.493917i	$0.164435\pi$
$107$	3.75956	+	14.0309i	0.363451	+	1.35642i	−0.506058	+	0.862499i	$0.668898\pi$
$108$	12.0776	+	3.23619i	1.16217	+	0.311403i
$109$	4.72405	+	4.72405i	0.452481	+	0.452481i	0.896177	−	0.443696i	$-0.146333\pi$
$109$	4.72405	+	4.72405i	0.452481	+	0.452481i	−0.443696	+	0.896177i	$0.646333\pi$
$110$	4.12691	−	27.1797i	0.393486	−	2.59149i
$111$	−0.679621	+	2.53638i	−0.0645068	+	0.240743i
$112$	−0.933751			−0.0882311
$113$	2.94919	−	11.0065i	0.277437	−	1.03541i	−0.676754	−	0.736209i	$-0.736614\pi$
$113$	2.94919	−	11.0065i	0.277437	−	1.03541i	0.954191	−	0.299199i	$-0.0967193\pi$
$114$	−2.72475	+	4.71941i	−0.255197	+	0.442013i
$115$	0.344949	−	0.134950i	0.0321666	−	0.0125841i
$116$			29.7777i			2.76479i
$117$		0			0
$118$	−0.00365994	−	0.00365994i	−0.000336925	−	0.000336925i
$119$	−3.97433	+	1.06492i	−0.364326	+	0.0976210i
$120$	−9.92818	+	3.88407i	−0.906315	+	0.354566i
$121$	16.3126	−	9.41807i	1.48296	−	0.856188i
$122$		−	3.13309i		−	0.283657i
$123$	0.497357	+	0.861447i	0.0448452	+	0.0776741i
$124$	−0.977176	−	0.261833i	−0.0877530	−	0.0235133i
$125$	3.65819	+	10.5649i	0.327199	+	0.944956i
$126$	−1.36186	−	2.35881i	−0.121324	−	0.210139i
$127$	−0.506651	+	0.135757i	−0.0449580	+	0.0120465i	−0.281228	−	0.959641i	$-0.590742\pi$
$127$	−0.506651	+	0.135757i	−0.0449580	+	0.0120465i	0.236270	+	0.971687i	$0.424075\pi$
$128$	14.2632	+	8.23486i	1.26070	+	0.727865i
$129$	13.2377			1.16551
$130$		0			0
$131$	5.09883			0.445486			0.222743	−	0.974877i	$-0.428499\pi$
$131$	5.09883			0.445486			0.222743	+	0.974877i	$0.428499\pi$
$132$	−28.8173	−	16.6377i	−2.50822	−	1.44812i
$133$	−1.50334	+	0.402818i	−0.130356	+	0.0349287i
$134$	−6.83610	−	11.8405i	−0.590549	−	1.02286i
$135$	−7.12309	−	5.69316i	−0.613058	−	0.489989i
$136$	7.46723	+	2.00084i	0.640310	+	0.171571i
$137$	1.90173	+	3.29390i	0.162476	+	0.281417i	0.935756	−	0.352648i	$-0.114719\pi$
$137$	1.90173	+	3.29390i	0.162476	+	0.281417i	−0.773280	+	0.634065i	$0.781385\pi$
$138$		−	0.740785i		−	0.0630598i
$139$	−1.28017	+	0.739106i	−0.108583	+	0.0626902i	−0.553308	−	0.832977i	$-0.686635\pi$
$139$	−1.28017	+	0.739106i	−0.108583	+	0.0626902i	0.444725	+	0.895667i	$0.353301\pi$
$140$	−8.02204	−	3.51037i	−0.677986	−	0.296680i
$141$	6.14173	−	1.64567i	0.517227	−	0.138591i
$142$	−19.3487	−	19.3487i	−1.62371	−	1.62371i
$143$		0			0
$144$		−	0.692704i		−	0.0577253i
$145$	8.70580	−	19.8949i	0.722977	−	1.65218i
$146$	8.26737	−	14.3195i	0.684213	−	1.18509i
$147$	−2.76079	+	10.3034i	−0.227706	+	0.849811i
$148$	4.05230			0.333097
$149$	4.45586	−	16.6295i	0.365038	−	1.36234i	−0.502331	−	0.864675i	$-0.667524\pi$
$149$	4.45586	−	16.6295i	0.365038	−	1.36234i	0.867369	−	0.497665i	$-0.165809\pi$
$150$	22.3423	+	0.884644i	1.82424	+	0.0722308i
$151$	10.0539	+	10.0539i	0.818178	+	0.818178i	0.985844	−	0.167666i	$-0.0536230\pi$
$151$	10.0539	+	10.0539i	0.818178	+	0.818178i	−0.167666	+	0.985844i	$0.553623\pi$
$152$	2.82457	+	0.756840i	0.229103	+	0.0613879i
$153$	−0.790011	−	2.94836i	−0.0638686	−	0.238361i
$154$	−4.06405	−	15.1672i	−0.327491	−	1.22221i
$155$	0.576314	+	0.460621i	0.0462907	+	0.0369980i
$156$		0			0
$157$	3.07230	−	3.07230i	0.245196	−	0.245196i	−0.573799	−	0.818996i	$-0.694531\pi$
$157$	3.07230	−	3.07230i	0.245196	−	0.245196i	0.818996	+	0.573799i	$0.194531\pi$
$158$	−12.5791	+	21.7876i	−1.00074	+	1.73333i
$159$	−10.9463	−	6.31986i	−0.868100	−	0.501198i
$160$	−8.54504	−	11.6045i	−0.675545	−	0.917417i
$161$	0.149600	−	0.149600i	0.0117902	−	0.0117902i
$162$	−21.3341	+	12.3172i	−1.67616	+	0.967733i
$163$	−7.97177	+	4.60251i	−0.624398	+	0.360496i	−0.778579	−	0.627546i	$-0.784059\pi$
$163$	−7.97177	+	4.60251i	−0.624398	+	0.360496i	0.154182	+	0.988043i	$0.450726\pi$
$164$	1.08546	−	1.08546i	0.0847602	−	0.0847602i
$165$	14.3890	+	19.5408i	1.12018	+	1.52125i
$166$	−5.17603	−	2.98838i	−0.401738	−	0.231944i
$167$	−6.31936	+	10.9455i	−0.489007	+	0.846985i	−0.999920	−	0.0126474i	$-0.995974\pi$
$167$	−6.31936	+	10.9455i	−0.489007	+	0.846985i	0.510913	+	0.859632i	$0.329307\pi$
$168$	−4.30574	+	4.30574i	−0.332195	+	0.332195i
$169$		0			0
$170$	−12.6656	−	10.1230i	−0.971409	−	0.776402i
$171$	−0.298831	−	1.11525i	−0.0228522	−	0.0852854i
$172$	−5.28736	−	19.7327i	−0.403157	−	1.50460i
$173$	−13.2481	−	3.54983i	−1.00724	−	0.269888i	−0.282762	−	0.959190i	$-0.591251\pi$
$173$	−13.2481	−	3.54983i	−1.00724	−	0.269888i	−0.724474	+	0.689302i	$0.757917\pi$
$174$	−30.7103	−	30.7103i	−2.32814	−	2.32814i
$175$	4.33334	+	4.69064i	0.327570	+	0.354579i
$176$	1.03358	−	3.85738i	0.0779092	−	0.290761i
$177$	0.00456889			0.000343419
$178$	−4.20086	+	15.6778i	−0.314867	+	1.17510i
$179$	−6.32126	+	10.9487i	−0.472473	+	0.818347i	−0.999504	−	0.0314989i	$-0.989972\pi$
$179$	−6.32126	+	10.9487i	−0.472473	+	0.818347i	0.527031	+	0.849846i	$0.323305\pi$
$180$	2.60417	−	5.95116i	0.194103	−	0.443573i
$181$			8.16619i			0.606988i	0.952833	+	0.303494i	$0.0981533\pi$
$181$			8.16619i			0.606988i	−0.952833	+	0.303494i	$0.901847\pi$
$182$		0			0
$183$	1.95560	+	1.95560i	0.144562	+	0.144562i
$184$	−0.383960	+	0.102882i	−0.0283059	+	0.00758455i
$185$	−2.70739	−	1.18473i	−0.199052	−	0.0871030i
$186$	1.27781	−	0.737745i	0.0936937	−	0.0540941i
$187$		−	17.5970i		−	1.28682i
$188$	−4.90623	−	8.49784i	−0.357824	−	0.619769i
$189$	−5.03089	−	1.34802i	−0.365943	−	0.0980542i
$190$	−4.79091	−	3.82916i	−0.347569	−	0.277796i
$191$	7.37692	+	12.7772i	0.533775	+	0.924526i	0.999222	+	0.0394498i	$0.0125605\pi$
$191$	7.37692	+	12.7772i	0.533775	+	0.924526i	−0.465446	+	0.885076i	$0.654106\pi$
$192$	−25.0330	+	6.70758i	−1.80660	+	0.484078i
$193$	−13.0743	−	7.54845i	−0.941109	−	0.543349i	−0.0508011	−	0.998709i	$-0.516177\pi$
$193$	−13.0743	−	7.54845i	−0.941109	−	0.543349i	−0.890308	+	0.455359i	$0.849511\pi$
$194$	9.40995			0.675595
$195$		0			0
$196$	16.4614			1.17582
$197$	13.3121	+	7.68576i	0.948450	+	0.547588i	0.892599	−	0.450851i	$-0.148879\pi$
$197$	13.3121	+	7.68576i	0.948450	+	0.547588i	0.0558510	+	0.998439i	$0.482213\pi$
$198$	11.2518	−	3.01492i	0.799633	−	0.214261i
$199$	5.72810	+	9.92136i	0.406054	+	0.703307i	0.994444	−	0.105271i	$-0.0335710\pi$
$199$	5.72810	+	9.92136i	0.406054	+	0.703307i	−0.588389	+	0.808578i	$0.700238\pi$
$200$	−2.64443	−	11.7032i	−0.186989	−	0.827544i
$201$	11.6575	+	3.12361i	0.822254	+	0.220322i
$202$	−9.71144	−	16.8207i	−0.683294	−	1.18350i
$203$		−	12.4038i		−	0.870574i
$204$	−16.9961	+	9.81268i	−1.18996	+	0.687025i
$205$	−1.04255	+	0.407865i	−0.0728152	+	0.0284865i
$206$	3.30843	−	0.886492i	0.230509	−	0.0617648i
$207$	0.110981	+	0.110981i	0.00771372	+	0.00771372i
$208$		0			0
$209$		−	6.65626i		−	0.460423i
$210$	11.8936	−	4.65297i	0.820735	−	0.321085i
$211$	−1.59195	+	2.75735i	−0.109595	+	0.189823i	−0.915606	−	0.402076i	$-0.868289\pi$
$211$	−1.59195	+	2.75735i	−0.109595	+	0.189823i	0.806011	+	0.591900i	$0.201622\pi$
$212$	−5.04852	+	18.8414i	−0.346734	+	1.29403i
$213$	24.1539			1.65500
$214$	−8.46205	+	31.5808i	−0.578454	+	2.15882i
$215$	−2.23649	+	14.7295i	−0.152527	+	1.00454i
$216$	6.91961	+	6.91961i	0.470820	+	0.470820i
$217$	0.407038	+	0.109066i	0.0276316	+	0.00740386i
$218$	3.89192	+	14.5248i	0.263594	+	0.983746i
$219$	3.77760	+	14.0982i	0.255266	+	0.952667i
$220$	23.3813	−	29.2539i	1.57636	−	1.97230i
$221$		0			0
$222$	−4.17921	+	4.17921i	−0.280490	+	0.280490i
$223$	−5.93874	+	10.2862i	−0.397688	+	0.688815i	−0.993440	−	0.114353i	$-0.963521\pi$
$223$	−5.93874	+	10.2862i	−0.397688	+	0.688815i	0.595753	+	0.803168i	$0.296854\pi$
$224$	−7.12851	−	4.11565i	−0.476294	−	0.274988i
$225$	−3.47976	+	3.21469i	−0.231984	+	0.214313i
$226$	18.1355	−	18.1355i	1.20636	−	1.20636i
$227$	−23.9600	+	13.8333i	−1.59028	+	0.918149i	−0.597022	+	0.802225i	$0.703650\pi$
$227$	−23.9600	+	13.8333i	−1.59028	+	0.918149i	−0.993258	+	0.115924i	$0.963017\pi$
$228$	−6.42896	+	3.71176i	−0.425768	+	0.245817i
$229$	−12.9000	+	12.9000i	−0.852455	+	0.852455i	−0.990435	−	0.137980i	$-0.955939\pi$
$229$	−12.9000	+	12.9000i	−0.852455	+	0.852455i	0.137980	+	0.990435i	$0.455939\pi$
$230$	0.824266	+	0.125155i	0.0543505	+	0.00825246i
$231$	12.0037	+	6.93034i	0.789786	+	0.455983i
$232$	−11.6525	+	20.1827i	−0.765024	+	1.32506i
$233$	−16.3545	+	16.3545i	−1.07142	+	1.07142i	−0.0741712	+	0.997246i	$0.523631\pi$
$233$	−16.3545	+	16.3545i	−1.07142	+	1.07142i	−0.997246	+	0.0741712i	$0.976369\pi$
$234$		0			0
$235$	0.793489	+	7.11190i	0.0517615	+	0.463929i
$236$	−0.00182489	−	0.00681059i	−0.000118790	−	0.000443332i
$237$	−5.74774	−	21.4509i	−0.373356	−	1.39338i
$238$	−8.94546	−	2.39693i	−0.579848	−	0.155370i
$239$	2.61794	+	2.61794i	0.169341	+	0.169341i	0.786690	−	0.617349i	$-0.211793\pi$
$239$	2.61794	+	2.61794i	0.169341	+	0.169341i	−0.617349	+	0.786690i	$0.711793\pi$
$240$	3.21124	+	0.487588i	0.207285	+	0.0314737i
$241$	−5.38613	+	20.1013i	−0.346951	+	1.29484i	0.543365	+	0.839496i	$0.317150\pi$
$241$	−5.38613	+	20.1013i	−0.346951	+	1.29484i	−0.890316	+	0.455343i	$0.849517\pi$
$242$	42.3965			2.72535
$243$	2.46169	−	9.18717i	0.157918	−	0.589357i
$244$	2.13401	−	3.69621i	0.136616	−	0.236625i
$245$	−10.9981	−	4.81267i	−0.702643	−	0.307470i
$246$			2.23891i			0.142748i
$247$		0			0
$248$	−0.559851	−	0.559851i	−0.0355505	−	0.0355505i
$249$	5.09603	−	1.36548i	0.322948	−	0.0865336i
$250$	−4.75905	+	24.7107i	−0.300989	+	1.56284i
$251$	−2.05050	+	1.18386i	−0.129427	+	0.0747245i	−0.563315	−	0.826242i	$-0.690474\pi$
$251$	−2.05050	+	1.18386i	−0.129427	+	0.0747245i	0.433889	+	0.900966i	$0.357141\pi$
$252$		−	3.71034i		−	0.233730i
$253$	0.452413	+	0.783602i	0.0284430	+	0.0492647i
$254$	−1.14037	−	0.305562i	−0.0715533	−	0.0191727i
$255$	14.2241	−	1.58701i	0.890749	−	0.0993827i
$256$	5.49109	+	9.51085i	0.343193	+	0.594428i
$257$	0.840391	−	0.225182i	0.0524221	−	0.0140465i	−0.232513	−	0.972593i	$-0.574695\pi$
$257$	0.840391	−	0.225182i	0.0524221	−	0.0140465i	0.284935	+	0.958547i	$0.408028\pi$
$258$	25.8036	+	14.8977i	1.60646	+	0.927492i
$259$	−1.68797			−0.104885
$260$		0			0
$261$	9.20175			0.569574
$262$	9.93892	+	5.73824i	0.614028	+	0.354509i
$263$	14.6707	−	3.93099i	0.904632	−	0.242395i	0.223627	−	0.974675i	$-0.428210\pi$
$263$	14.6707	−	3.93099i	0.904632	−	0.242395i	0.681004	+	0.732279i	$0.261543\pi$
$264$	−13.0212	−	22.5533i	−0.801398	−	1.38806i
$265$	8.88144	−	11.1122i	0.545582	−	0.682615i
$266$	−3.38372	−	0.906665i	−0.207469	−	0.0555912i
$267$	−7.16363	−	12.4078i	−0.438407	−	0.759343i
$268$		−	18.6248i		−	1.13769i
$269$	21.1150	−	12.1908i	1.28741	−	0.743285i	0.309216	−	0.950992i	$-0.399933\pi$
$269$	21.1150	−	12.1908i	1.28741	−	0.743285i	0.978191	+	0.207707i	$0.0666000\pi$
$270$	−7.47763	−	19.1138i	−0.455074	−	1.16323i
$271$	12.6697	−	3.39484i	0.769630	−	0.206222i	0.147422	−	0.989074i	$-0.452903\pi$
$271$	12.6697	−	3.39484i	0.769630	−	0.206222i	0.622208	+	0.782852i	$0.286236\pi$
$272$	−1.66544	−	1.66544i	−0.100982	−	0.100982i
$273$		0			0
$274$			8.56086i			0.517181i
$275$	−24.1740	+	12.7091i	−1.45775	+	0.766390i
$276$	0.504562	−	0.873927i	0.0303711	−	0.0526042i
$277$	3.16472	−	11.8109i	0.190149	−	0.709647i	−0.803320	−	0.595548i	$-0.796935\pi$
$277$	3.16472	−	11.8109i	0.190149	−	0.709647i	0.993469	−	0.114099i	$-0.0363982\pi$
$278$	−3.32717			−0.199550
$279$	−0.0809104	+	0.301962i	−0.00484398	+	0.0180780i
$280$	−4.06352	−	5.51841i	−0.242841	−	0.329788i
$281$	6.43529	+	6.43529i	0.383897	+	0.383897i	0.872504	−	0.488607i	$-0.162495\pi$
$281$	6.43529	+	6.43529i	0.383897	+	0.383897i	−0.488607	+	0.872504i	$0.662495\pi$
$282$	13.8239	+	3.70409i	0.823198	+	0.220575i
$283$	7.07953	+	26.4212i	0.420834	+	1.57057i	0.772855	+	0.634583i	$0.218828\pi$
$283$	7.07953	+	26.4212i	0.420834	+	1.57057i	−0.352021	+	0.935992i	$0.614505\pi$
$284$	−9.64751	−	36.0050i	−0.572474	−	2.13650i
$285$	5.38044	−	0.600307i	0.318710	−	0.0355591i
$286$		0			0
$287$	−0.452144	+	0.452144i	−0.0266892	+	0.0266892i
$288$	3.05320	−	5.28829i	0.179911	−	0.311616i
$289$	5.73440	+	3.31076i	0.337318	+	0.194750i
$290$	39.3596	−	28.9826i	2.31127	−	1.70192i
$291$	−5.87346	+	5.87346i	−0.344308	+	0.344308i
$292$	19.5066	−	11.2621i	1.14154	−	0.659066i
$293$	22.6241	−	13.0620i	1.32171	−	0.763092i	0.337713	−	0.941249i	$-0.390347\pi$
$293$	22.6241	−	13.0620i	1.32171	−	0.763092i	0.984002	+	0.178157i	$0.0570135\pi$
$294$	−16.9770	+	16.9770i	−0.990118	+	0.990118i
$295$	−0.000771909		0.00508377i	−4.49423e−5		0.000295989i
$296$	2.74657	+	1.58573i	0.159641	+	0.0921688i
$297$	11.1375	−	19.2908i	0.646265	−	1.11936i
$298$	27.4005	−	27.4005i	1.58727	−	1.58727i
$299$		0			0
$300$	25.7554	+	16.2614i	1.48699	+	0.938852i
$301$	2.20243	+	8.21957i	0.126946	+	0.473768i
$302$	8.28296	+	30.9124i	0.476631	+	1.77881i
$303$	16.5607	+	4.43743i	0.951388	+	0.254924i
$304$	−0.629972	−	0.629972i	−0.0361314	−	0.0361314i
$305$	−2.50638	+	1.84559i	−0.143515	+	0.105678i
$306$	1.77816	−	6.63619i	0.101651	−	0.379366i
$307$	−14.7038			−0.839189			−0.419595	−	0.907712i	$-0.637828\pi$
$307$	−14.7038			−0.839189			−0.419595	+	0.907712i	$0.637828\pi$
$308$	5.53620	−	20.6614i	0.315454	−	1.17729i
$309$	−1.51172	+	2.61837i	−0.0859985	+	0.148954i
$310$	0.604999	+	1.54645i	0.0343617	+	0.0878327i
$311$		−	31.8525i		−	1.80619i	−0.429440	−	0.903095i	$-0.641289\pi$
$311$		−	31.8525i		−	1.80619i	0.429440	−	0.903095i	$-0.358711\pi$
$312$		0			0
$313$	−11.9865	−	11.9865i	−0.677519	−	0.677519i	0.281919	−	0.959438i	$-0.409029\pi$
$313$	−11.9865	−	11.9865i	−0.677519	−	0.677519i	−0.959438	+	0.281919i	$0.909029\pi$
$314$	9.44628	−	2.53112i	0.533084	−	0.142840i
$315$	−1.08476	+	2.47893i	−0.0611190	+	0.139672i
$316$	−29.6799	+	17.1357i	−1.66963	+	0.963959i
$317$			15.5627i			0.874088i	0.899440	+	0.437044i	$0.143975\pi$
$317$			15.5627i			0.874088i	−0.899440	+	0.437044i	$0.856025\pi$
$318$	−14.2248	−	24.6380i	−0.797686	−	1.38163i
$319$	51.2407	+	13.7299i	2.86893	+	0.768728i
$320$	−3.23418	−	28.9874i	−0.180796	−	1.62044i
$321$	−14.4302	−	24.9938i	−0.805413	−	1.39502i
$322$	0.459970	−	0.123249i	0.0256331	−	0.00686837i
$323$	−3.39983	−	1.96289i	−0.189171	−	0.109218i
$324$	−33.5580			−1.86433
$325$		0			0
$326$	−20.7187			−1.14750
$327$	−11.4953	−	6.63680i	−0.635691	−	0.367016i
$328$	1.16046	−	0.310945i	0.0640758	−	0.0171691i
$329$	2.04367	+	3.53974i	0.112671	+	0.195152i
$330$	6.05653	+	54.2835i	0.333401	+	2.98821i
$331$	16.4820	+	4.41633i	0.905930	+	0.242743i	0.681561	−	0.731761i	$-0.261301\pi$
$331$	16.4820	+	4.41633i	0.905930	+	0.242743i	0.224369	+	0.974504i	$0.427968\pi$
$332$	−4.07089	−	7.05098i	−0.223419	−	0.386973i
$333$		−	1.25222i		−	0.0686212i
$334$	−24.6361	+	14.2237i	−1.34803	+	0.778284i
$335$	−5.44513	+	12.4435i	−0.297499	+	0.679858i
$336$	1.79199	−	0.480161i	0.0977609	−	0.0261949i
$337$	25.0560	+	25.0560i	1.36489	+	1.36489i	0.867568	+	0.497319i	$0.165682\pi$
$337$	25.0560	+	25.0560i	1.36489	+	1.36489i	0.497319	+	0.867568i	$0.334318\pi$
$338$		0			0
$339$			22.6395i			1.22961i
$340$	−8.04704	−	20.5693i	−0.436412	−	1.11552i
$341$	−0.901114	+	1.56077i	−0.0487980	+	0.0845207i
$342$	0.672610	−	2.51022i	0.0363706	−	0.135737i
$343$	−15.7972			−0.852971
$344$	4.13806	−	15.4435i	0.223109	−	0.832655i
$345$	−0.592605	+	0.436368i	−0.0319048	+	0.0234933i
$346$	−21.8290	−	21.8290i	−1.17354	−	1.17354i
$347$	−12.4604	−	3.33874i	−0.668907	−	0.179233i	−0.0916446	−	0.995792i	$-0.529212\pi$
$347$	−12.4604	−	3.33874i	−0.668907	−	0.179233i	−0.577262	+	0.816559i	$0.695879\pi$
$348$	−15.3125	−	57.1472i	−0.820838	−	3.06341i
$349$	6.94957	+	25.9362i	0.372002	+	1.38833i	0.857676	+	0.514191i	$0.171908\pi$
$349$	6.94957	+	25.9362i	0.372002	+	1.38833i	−0.485674	+	0.874140i	$0.661426\pi$
$350$	3.16792	+	14.0200i	0.169332	+	0.749402i
$351$		0			0
$352$	24.8926	−	24.8926i	1.32678	−	1.32678i
$353$	11.6558	−	20.1885i	0.620378	−	1.07453i	−0.369038	−	0.929414i	$-0.620313\pi$
$353$	11.6558	−	20.1885i	0.620378	−	1.07453i	0.989415	−	0.145111i	$-0.0463540\pi$
$354$	0.00890593	+	0.00514184i	0.000473345	+	0.000273286i
$355$	−4.08078	+	26.8759i	−0.216586	+	1.42643i
$356$	−15.6343	+	15.6343i	−0.828617	+	0.828617i
$357$	7.07964	−	4.08743i	0.374694	−	0.216330i
$358$	−24.6435	+	14.2279i	−1.30245	+	0.751970i
$359$	−9.17222	+	9.17222i	−0.484091	+	0.484091i	−0.906435	−	0.422344i	$-0.861207\pi$
$359$	−9.17222	+	9.17222i	−0.484091	+	0.484091i	0.422344	+	0.906435i	$0.361207\pi$
$360$	4.09384	−	3.01452i	0.215764	−	0.158879i
$361$	15.1685	+	8.75751i	0.798340	+	0.460922i
$362$	−9.19026	+	15.9180i	−0.483029	+	0.836631i
$363$	−26.4629	+	26.4629i	−1.38894	+	1.38894i
$364$		0			0
$365$	−16.3252	+	1.82143i	−0.854499	+	0.0953382i
$366$	1.61113	+	6.01280i	0.0842149	+	0.314294i
$367$	3.84780	+	14.3602i	0.200853	+	0.749595i	0.990674	+	0.136256i	$0.0435071\pi$
$367$	3.84780	+	14.3602i	0.200853	+	0.749595i	−0.789820	+	0.613338i	$0.789826\pi$
$368$	0.116981	+	0.0313449i	0.00609805	+	0.00163397i
$369$	−0.335423	−	0.335423i	−0.0174614	−	0.0174614i
$370$	−3.94410	−	5.35625i	−0.205044	−	0.278458i
$371$	2.10294	−	7.84829i	0.109179	−	0.407463i
$372$	2.00997			0.104212
$373$	1.59980	−	5.97055i	0.0828348	−	0.309144i	−0.912061	−	0.410055i	$-0.865509\pi$
$373$	1.59980	−	5.97055i	0.0828348	−	0.309144i	0.994895	+	0.100912i	$0.0321760\pi$
$374$	19.8037	−	34.3010i	1.02403	−	1.77366i
$375$	−12.4533	−	18.3943i	−0.643087	−	0.949877i
$376$		−	7.67955i		−	0.396043i
$377$		0			0
$378$	−8.28942	−	8.28942i	−0.426362	−	0.426362i
$379$	−17.6464	+	4.72834i	−0.906435	+	0.242878i	−0.681778	−	0.731559i	$-0.738793\pi$
$379$	−17.6464	+	4.72834i	−0.906435	+	0.242878i	−0.224657	+	0.974438i	$0.572126\pi$
$380$	−3.04389	−	7.78056i	−0.156148	−	0.399134i
$381$	0.902517	−	0.521068i	0.0462373	−	0.0266951i
$382$			33.2081i			1.69907i
$383$	5.12171	+	8.87106i	0.261707	+	0.453290i	0.966696	−	0.255929i	$-0.0823812\pi$
$383$	5.12171	+	8.87106i	0.261707	+	0.453290i	−0.704989	+	0.709219i	$0.749048\pi$
$384$	−31.6075	−	8.46920i	−1.61296	−	0.432192i
$385$	−9.73936	+	12.1856i	−0.496364	+	0.621034i
$386$	−16.9901	−	29.4277i	−0.864774	−	1.49783i
$387$	−6.09769	+	1.63387i	−0.309963	+	0.0830543i
$388$	11.1012	+	6.40929i	0.563579	+	0.325382i
$389$	−3.41200			−0.172995			−0.0864977	−	0.996252i	$-0.527568\pi$
$389$	−3.41200			−0.172995			−0.0864977	+	0.996252i	$0.527568\pi$
$390$		0			0
$391$	0.533655			0.0269881
$392$	11.1572	+	6.44164i	0.563526	+	0.325352i
$393$	−9.78529	+	2.62196i	−0.493603	+	0.132260i
$394$	17.2992	+	29.9630i	0.871519	+	1.50952i
$395$	24.8393	−	2.77138i	1.24980	−	0.139443i
$396$	15.3277	+	4.10703i	0.770244	+	0.206386i
$397$	−5.96603	−	10.3335i	−0.299426	−	0.518622i	0.676578	−	0.736371i	$-0.263462\pi$
$397$	−5.96603	−	10.3335i	−0.299426	−	0.518622i	−0.976005	+	0.217749i	$0.930129\pi$
$398$			25.7857i			1.29252i
$399$	2.67795	−	1.54612i	0.134065	−	0.0774027i
$400$	−1.08507	+	3.49075i	−0.0542536	+	0.174538i
$401$	−3.93721	+	1.05497i	−0.196615	+	0.0526828i	−0.355783	−	0.934569i	$-0.615786\pi$
$401$	−3.93721	+	1.05497i	−0.196615	+	0.0526828i	0.159168	+	0.987252i	$0.449119\pi$
$402$	19.2081	+	19.2081i	0.958011	+	0.958011i
$403$		0			0
$404$		−	26.4586i		−	1.31636i
$405$	22.4205	+	9.81100i	1.11408	+	0.487512i
$406$	13.9592	−	24.1781i	0.692786	−	1.19994i
$407$	1.86844	−	6.97310i	0.0926149	−	0.345644i
$408$	−15.3595			−0.760406
$409$	1.79597	−	6.70266i	0.0888051	−	0.331425i	−0.907202	−	0.420694i	$-0.861786\pi$
$409$	1.79597	−	6.70266i	0.0888051	−	0.331425i	0.996008	+	0.0892692i	$0.0284531\pi$
$410$	−2.49122	−	0.378261i	−0.123033	−	0.0186810i
$411$	−5.34348	−	5.34348i	−0.263574	−	0.263574i
$412$	4.50687	+	1.20761i	0.222037	+	0.0594948i
$413$	0.000760151		0.00283692i	3.74046e−5		0.000139596i
$414$	0.0914320	+	0.341229i	0.00449364	+	0.0167705i
$415$	0.658389	+	5.90102i	0.0323190	+	0.289670i
$416$		0			0
$417$	2.07674	−	2.07674i	0.101698	−	0.101698i
$418$	7.49098	−	12.9748i	0.366396	−	0.634616i
$419$	−18.3846	−	10.6144i	−0.898147	−	0.518546i	−0.0215487	−	0.999768i	$-0.506860\pi$
$419$	−18.3846	−	10.6144i	−0.898147	−	0.518546i	−0.876599	+	0.481222i	$0.840193\pi$
$420$	17.2004	+	2.61168i	0.839296	+	0.127437i
$421$	3.15727	−	3.15727i	0.153876	−	0.153876i	−0.625971	−	0.779847i	$-0.715297\pi$
$421$	3.15727	−	3.15727i	0.153876	−	0.153876i	0.779847	+	0.625971i	$0.215297\pi$
$422$	−6.20625	+	3.58318i	−0.302116	+	0.174427i
$423$	−2.62596	+	1.51610i	−0.127678	+	0.0737152i
$424$	−10.7947	+	10.7947i	−0.524238	+	0.524238i
$425$	−0.637290	+	16.0952i	−0.0309131	+	0.780733i
$426$	47.0822	+	27.1829i	2.28114	+	1.31702i
$427$	−0.888911	+	1.53964i	−0.0430174	+	0.0745084i
$428$	−31.4932	+	31.4932i	−1.52228	+	1.52228i
$429$		0			0
$430$	−20.9361	+	26.1946i	−1.00963	+	1.26321i
$431$	−9.27711	−	34.6226i	−0.446863	−	1.66771i	−0.710971	−	0.703221i	$-0.751744\pi$
$431$	−9.27711	−	34.6226i	−0.446863	−	1.66771i	0.264109	−	0.964493i	$-0.414922\pi$
$432$	−0.771651	−	2.87984i	−0.0371261	−	0.138556i
$433$	7.81733	+	2.09465i	0.375677	+	0.100662i	0.441716	−	0.897155i	$-0.354370\pi$
$433$	7.81733	+	2.09465i	0.375677	+	0.100662i	−0.0660397	+	0.997817i	$0.521036\pi$
$434$	0.670679	+	0.670679i	0.0321936	+	0.0321936i
$435$	−6.47703	+	42.6575i	−0.310550	+	2.04527i
$436$	−5.30171	+	19.7863i	−0.253906	+	0.947590i
$437$	0.201861			0.00965633
$438$	−8.50264	+	31.7323i	−0.406272	+	1.51623i
$439$	14.3336	−	24.8265i	0.684104	−	1.18490i	−0.289613	−	0.957144i	$-0.593527\pi$
$439$	14.3336	−	24.8265i	0.684104	−	1.18490i	0.973717	−	0.227759i	$-0.0731399\pi$
$440$	27.2949	−	10.6782i	1.30123	−	0.509064i
$441$		−	5.08683i		−	0.242230i
$442$		0			0
$443$	−17.1586	−	17.1586i	−0.815229	−	0.815229i	0.170184	−	0.985412i	$-0.445564\pi$
$443$	−17.1586	−	17.1586i	−0.815229	−	0.815229i	−0.985412	+	0.170184i	$0.945564\pi$
$444$	−7.77688	+	2.08381i	−0.369074	+	0.0988931i
$445$	15.0163	−	5.87465i	0.711843	−	0.278485i
$446$	−23.1523	+	13.3670i	−1.09629	+	0.632944i
$447$			34.2054i			1.61786i
$448$	−8.32978	−	14.4276i	−0.393545	−	0.681640i
$449$	−8.85389	−	2.37239i	−0.417841	−	0.111960i	0.0437720	−	0.999042i	$-0.486062\pi$
$449$	−8.85389	−	2.37239i	−0.417841	−	0.111960i	−0.461613	+	0.887081i	$0.652729\pi$
$450$	−10.4008	+	2.35012i	−0.490297	+	0.110786i
$451$	−1.36735	−	2.36832i	−0.0643860	−	0.111520i
$452$	33.7475	−	9.04261i	1.58735	−	0.425329i
$453$	−24.4648	−	14.1248i	−1.14946	−	0.663639i
$454$	−62.2722			−2.92258
$455$		0			0
$456$	−5.80989			−0.272073
$457$	18.6021	+	10.7399i	0.870167	+	0.502391i	0.867404	−	0.497605i	$-0.165787\pi$
$457$	18.6021	+	10.7399i	0.870167	+	0.502391i	0.00276341	+	0.999996i	$0.499120\pi$
$458$	−39.6631	+	10.6277i	−1.85333	+	0.496599i
$459$	−6.56877	−	11.3775i	−0.306604	−	0.531054i
$460$	0.887168	+	0.709072i	0.0413644	+	0.0330607i
$461$	4.90591	+	1.31453i	0.228491	+	0.0612240i	0.371248	−	0.928534i	$-0.378930\pi$
$461$	4.90591	+	1.31453i	0.228491	+	0.0612240i	−0.142757	+	0.989758i	$0.545597\pi$
$462$	15.5989	+	27.0180i	0.725725	+	1.25699i
$463$			20.0793i			0.933163i	0.884478	+	0.466581i	$0.154515\pi$
$463$			20.0793i			0.933163i	−0.884478	+	0.466581i	$0.845485\pi$
$464$	6.14905	−	3.55016i	0.285463	−	0.164812i
$465$	−1.34289	−	0.587633i	−0.0622748	−	0.0272508i
$466$	−50.2844	+	13.4737i	−2.32938	+	0.624156i
$467$	−21.4507	−	21.4507i	−0.992618	−	0.992618i	0.00735447	−	0.999973i	$-0.497659\pi$
$467$	−21.4507	−	21.4507i	−0.992618	−	0.992618i	−0.999973	+	0.00735447i	$0.997659\pi$
$468$		0			0
$469$			7.75807i			0.358234i
$470$	−6.45704	+	14.7559i	−0.297841	+	0.680639i
$471$	−4.31627	+	7.47600i	−0.198883	+	0.344476i
$472$	0.00142822	−	0.00533020i	6.57392e−5	−	0.000245342i
$473$	−36.3934			−1.67337
$474$	12.9371	−	48.2818i	0.594219	−	2.21766i
$475$	−0.241062	+	6.08820i	−0.0110607	+	0.279346i
$476$	−8.92064	−	8.92064i	−0.408877	−	0.408877i
$477$	5.82226	+	1.56007i	0.266583	+	0.0714306i
$478$	2.15680	+	8.04928i	0.0986497	+	0.368166i
$479$	−8.05179	−	30.0497i	−0.367896	−	1.37300i	−0.863453	−	0.504430i	$-0.831703\pi$
$479$	−8.05179	−	30.0497i	−0.367896	−	1.37300i	0.495557	−	0.868575i	$-0.334964\pi$
$480$	22.3664	+	17.8764i	1.02088	+	0.815943i
$481$		0			0
$482$	−33.1210	+	33.1210i	−1.50862	+	1.50862i
$483$	−0.210173	+	0.364031i	−0.00956321	+	0.0165640i
$484$	50.0165	+	28.8770i	2.27348	+	1.31259i
$485$	−5.54305	−	7.52768i	−0.251697	−	0.341814i
$486$	15.1377	−	15.1377i	0.686662	−	0.686662i
$487$	16.8282	−	9.71579i	0.762560	−	0.440264i	−0.0676540	−	0.997709i	$-0.521551\pi$
$487$	16.8282	−	9.71579i	0.762560	−	0.440264i	0.830214	+	0.557445i	$0.188218\pi$
$488$	2.89277	−	1.67014i	0.130950	−	0.0756039i
$489$	12.9321	−	12.9321i	0.584810	−	0.584810i
$490$	−16.0219	−	21.7584i	−0.723797	−	0.982945i
$491$	−30.5824	−	17.6568i	−1.38017	−	0.796839i	−0.387987	−	0.921665i	$-0.626830\pi$
$491$	−30.5824	−	17.6568i	−1.38017	−	0.796839i	−0.992179	+	0.124825i	$0.960163\pi$
$492$	−1.52496	+	2.64131i	−0.0687506	+	0.119079i
$493$	22.1234	−	22.1234i	0.996389	−	0.996389i
$494$		0			0
$495$	−9.03988	−	7.22515i	−0.406312	−	0.324746i
$496$	0.0624327	+	0.233002i	0.00280331	+	0.0104621i
$497$	4.01863	+	14.9977i	0.180260	+	0.672740i
$498$	11.4702	+	3.07343i	0.513991	+	0.137723i
$499$	9.44430	+	9.44430i	0.422785	+	0.422785i	0.886161	−	0.463377i	$-0.153362\pi$
$499$	9.44430	+	9.44430i	0.422785	+	0.422785i	−0.463377	+	0.886161i	$0.653362\pi$
$500$	−22.4453	+	25.9105i	−1.00378	+	1.15875i
$501$	6.49919	−	24.2553i	0.290363	−	1.08365i
$502$	−5.32928			−0.237857
$503$	−6.24460	+	23.3052i	−0.278433	+	1.03913i	0.675073	+	0.737751i	$0.264112\pi$
$503$	−6.24460	+	23.3052i	−0.278433	+	1.03913i	−0.953506	+	0.301375i	$0.902554\pi$
$504$	1.45192	−	2.51480i	0.0646736	−	0.112018i
$505$	−7.73542	+	17.6773i	−0.344221	+	0.786630i
$506$			2.03659i			0.0905374i
$507$		0			0
$508$	−1.13721	−	1.13721i	−0.0504555	−	0.0504555i
$509$	−3.59537	+	0.963376i	−0.159362	+	0.0427009i	−0.337618	−	0.941283i	$-0.609621\pi$
$509$	−3.59537	+	0.963376i	−0.159362	+	0.0427009i	0.178256	+	0.983984i	$0.442954\pi$
$510$	29.5125	+	12.9144i	1.30683	+	0.571858i
$511$	−8.12538	+	4.69119i	−0.359446	+	0.207526i
$512$		−	8.22064i		−	0.363304i
$513$	−2.48471	−	4.30365i	−0.109703	−	0.190011i
$514$	1.89156	+	0.506841i	0.0834330	+	0.0223558i
$515$	−2.65804	−	2.12445i	−0.117127	−	0.0936144i
$516$	20.2942	+	35.1506i	0.893403	+	1.54742i
$517$	−16.8850	+	4.52433i	−0.742603	+	0.198980i
$518$	−3.29028	−	1.89964i	−0.144567	−	0.0834656i
$519$	27.2503			1.19615
$520$		0			0
$521$	45.2323			1.98166			0.990832	−	0.135103i	$-0.0431364\pi$
$521$	45.2323			1.98166			0.990832	+	0.135103i	$0.0431364\pi$
$522$	17.9366	+	10.3557i	0.785062	+	0.453256i
$523$	−1.10259	+	0.295439i	−0.0482131	+	0.0129187i	−0.282845	−	0.959166i	$-0.591278\pi$
$523$	−1.10259	+	0.295439i	−0.0482131	+	0.0129187i	0.234632	+	0.972084i	$0.424612\pi$
$524$	7.81683	+	13.5392i	0.341480	+	0.591461i
$525$	−10.7283	−	6.77362i	−0.468221	−	0.295625i
$526$	33.0208	+	8.84790i	1.43978	+	0.385787i
$527$	0.531466	+	0.920525i	0.0231510	+	0.0400987i
$528$			7.93430i			0.345296i
$529$	19.8948	−	11.4863i	0.864992	−	0.499403i
$530$	29.8179	−	11.6653i	1.29521	−	0.506706i
$531$	−0.00210457		0.000563919i	−9.13307e−5		2.44720e-5i
$532$	−3.37434	−	3.37434i	−0.146296	−	0.146296i
$533$		0			0
$534$		−	32.2479i		−	1.39550i
$535$	30.2484	−	11.8337i	1.30775	−	0.511614i
$536$	7.28818	−	12.6235i	0.314801	−	0.545252i
$537$	6.50114	−	24.2626i	0.280545	−	1.04701i
$538$	54.8782			2.36597
$539$	7.59005	−	28.3265i	0.326927	−	1.22011i
$540$	4.19714	−	27.6423i	0.180616	−	1.18953i
$541$	−22.3573	−	22.3573i	−0.961218	−	0.961218i	0.0380580	−	0.999276i	$-0.487883\pi$
$541$	−22.3573	−	22.3573i	−0.961218	−	0.961218i	−0.999276	+	0.0380580i	$0.987883\pi$
$542$	28.5171	+	7.64112i	1.22491	+	0.328214i
$543$	−4.19929	−	15.6720i	−0.180209	−	0.672548i
$544$	−5.37376	−	20.0551i	−0.230398	−	0.859857i
$545$	9.32685	−	11.6694i	0.399518	−	0.499864i
$546$		0			0
$547$	−5.20384	+	5.20384i	−0.222500	+	0.222500i	−0.809550	−	0.587050i	$-0.800289\pi$
$547$	−5.20384	+	5.20384i	−0.222500	+	0.222500i	0.587050	+	0.809550i	$0.300289\pi$
$548$	−5.83096	+	10.0995i	−0.249086	+	0.431430i
$549$	−1.14218	−	0.659440i	−0.0487472	−	0.0281442i
$550$	−61.4242	−	2.43209i	−2.61914	−	0.103705i
$551$	8.36844	−	8.36844i	0.356507	−	0.356507i
$552$	0.683964	−	0.394887i	0.0291114	−	0.0168075i
$553$	12.3630	−	7.13781i	0.525730	−	0.303530i
$554$	19.4608	−	19.4608i	0.826812	−	0.826812i
$555$	5.80505	+	0.881427i	0.246411	+	0.0374145i
$556$	−3.92517	−	2.26620i	−0.166464	−	0.0961081i
$557$	3.29321	−	5.70401i	0.139538	−	0.241687i	−0.787784	−	0.615952i	$-0.788772\pi$
$557$	3.29321	−	5.70401i	0.139538	−	0.241687i	0.927322	+	0.374265i	$0.122105\pi$
$558$	−0.497544	+	0.497544i	−0.0210627	+	0.0210627i
$559$		0			0
$560$	0.231518	+	2.07505i	0.00978343	+	0.0876871i
$561$	9.04887	+	33.7709i	0.382044	+	1.42581i
$562$	5.30173	+	19.7863i	0.223640	+	0.834636i
$563$	28.3543	+	7.59751i	1.19499	+	0.320197i	0.800856	−	0.598856i	$-0.204378\pi$
$563$	28.3543	+	7.59751i	1.19499	+	0.320197i	0.394134	+	0.919053i	$0.371045\pi$
$564$	13.7855	+	13.7855i	0.580475	+	0.580475i
$565$	−25.1908	−	3.82492i	−1.05979	−	0.160916i
$566$	−15.9347	+	59.4689i	−0.669783	+	2.49967i
$567$	13.9784			0.587039
$568$	7.55046	−	28.1787i	0.316810	−	1.18235i
$569$	−16.9543	+	29.3658i	−0.710763	+	1.23108i	0.253808	+	0.967255i	$0.418317\pi$
$569$	−16.9543	+	29.3658i	−0.710763	+	1.23108i	−0.964571	+	0.263823i	$0.915016\pi$
$570$	11.1634	+	4.88501i	0.467585	+	0.204611i
$571$		−	33.5525i		−	1.40413i	−0.712113	−	0.702065i	$-0.752262\pi$
$571$		−	33.5525i		−	1.40413i	0.712113	−	0.702065i	$-0.247738\pi$
$572$		0			0
$573$	−20.7277	−	20.7277i	−0.865910	−	0.865910i
$574$	−1.39019	+	0.372500i	−0.0580253	+	0.0155478i
$575$	−0.385424	−	0.733112i	−0.0160733	−	0.0305729i
$576$	10.7031	−	6.17945i	0.445964	−	0.257477i
$577$			11.0413i			0.459654i	0.973232	+	0.229827i	$0.0738160\pi$
$577$			11.0413i			0.459654i	−0.973232	+	0.229827i	$0.926184\pi$
$578$	7.45188	+	12.9070i	0.309957	+	0.536862i
$579$	28.9729	+	7.76326i	1.20407	+	0.322630i
$580$	66.1743	−	7.38321i	2.74774	−	0.306571i
$581$	1.69571	+	2.93706i	0.0703499	+	0.121850i
$582$	−18.0589	+	4.83886i	−0.748565	+	0.200577i
$583$	30.0940	+	17.3748i	1.24636	+	0.719589i
$584$	17.6282			0.729461
$585$		0			0
$586$	58.8002			2.42902
$587$	−20.3567	−	11.7529i	−0.840209	−	0.485095i	0.0171260	−	0.999853i	$-0.494548\pi$
$587$	−20.3567	−	11.7529i	−0.840209	−	0.485095i	−0.857335	+	0.514758i	$0.827882\pi$
$588$	−31.5916	+	8.46495i	−1.30282	+	0.349089i
$589$	0.201033	+	0.348199i	0.00828342	+	0.0143473i
$590$	−0.00722594	+	0.00904086i	−0.000297487	+	0.000372206i
$591$	−29.4999	−	7.90448i	−1.21346	−	0.325147i
$592$	−0.483123	−	0.836794i	−0.0198563	−	0.0343920i
$593$			30.6582i			1.25898i	0.777007	+	0.629491i	$0.216737\pi$
$593$			30.6582i			1.25898i	−0.777007	+	0.629491i	$0.783263\pi$
$594$	43.4198	−	25.0684i	1.78153	−	1.02857i
$595$	3.35196	+	8.56804i	0.137417	+	0.351255i
$596$	50.9882	−	13.6622i	2.08856	−	0.559627i
$597$	−16.0948	−	16.0948i	−0.658717	−	0.658717i
$598$		0			0
$599$		−	7.49378i		−	0.306188i	−0.988212	−	0.153094i	$-0.951076\pi$
$599$		−	7.49378i		−	0.306188i	0.988212	−	0.153094i	$-0.0489237\pi$
$600$	11.0931	+	21.1002i	0.452875	+	0.861410i
$601$	7.04653	−	12.2049i	0.287434	−	0.497850i	−0.685763	−	0.727825i	$-0.740531\pi$
$601$	7.04653	−	12.2049i	0.287434	−	0.497850i	0.973196	+	0.229975i	$0.0738645\pi$
$602$	−4.95724	+	18.5007i	−0.202042	+	0.754030i
$603$	−5.75533			−0.234375
$604$	−11.2834	+	42.1101i	−0.459113	+	1.71343i
$605$	−24.9742	−	33.9159i	−1.01534	−	1.37888i
$606$	27.2872	+	27.2872i	1.10847	+	1.10847i
$607$	−14.5660	−	3.90296i	−0.591218	−	0.158416i	−0.0492080	−	0.998789i	$-0.515670\pi$
$607$	−14.5660	−	3.90296i	−0.591218	−	0.158416i	−0.542010	+	0.840372i	$0.682336\pi$
$608$	−2.03268	−	7.58608i	−0.0824363	−	0.307656i
$609$	6.37837	+	23.8044i	0.258465	+	0.964604i
$610$	−6.96260	+	0.776832i	−0.281908	+	0.0314530i
$611$		0			0
$612$	6.61779	−	6.61779i	0.267508	−	0.267508i
$613$	5.95807	−	10.3197i	0.240644	−	0.416808i	−0.720254	−	0.693711i	$-0.755975\pi$
$613$	5.95807	−	10.3197i	0.240644	−	0.416808i	0.960898	+	0.276903i	$0.0893080\pi$
$614$	−28.6614	−	16.5477i	−1.15668	−	0.667810i
$615$	1.79106	−	1.31886i	0.0722225	−	0.0531814i
$616$	11.8375	−	11.8375i	0.476945	−	0.476945i
$617$	−33.6292	+	19.4158i	−1.35386	+	0.781652i	−0.988788	−	0.149326i	$-0.952290\pi$
$617$	−33.6292	+	19.4158i	−1.35386	+	0.781652i	−0.365074	+	0.930979i	$0.618956\pi$
$618$	−5.89344	+	3.40258i	−0.237069	+	0.136872i
$619$	14.9567	−	14.9567i	0.601159	−	0.601159i	−0.339461	−	0.940620i	$-0.610245\pi$
$619$	14.9567	−	14.9567i	0.601159	−	0.601159i	0.940620	+	0.339461i	$0.110245\pi$
$620$	−0.339582	+	2.23648i	−0.0136379	+	0.0898191i
$621$	0.585021	+	0.337762i	0.0234761	+	0.0135539i
$622$	35.8469	−	62.0887i	1.43733	−	2.48953i
$623$	6.51241	−	6.51241i	0.260914	−	0.260914i
$624$		0			0
$625$	22.5712	−	10.7490i	0.902847	−	0.429961i
$626$	−9.87514	−	36.8545i	−0.394690	−	1.47300i
$627$	3.42284	+	12.7742i	0.136695	+	0.510153i
$628$	12.8681	+	3.44799i	0.513492	+	0.137590i
$629$	−3.01067	−	3.01067i	−0.120043	−	0.120043i
$630$	−4.90426	+	3.61128i	−0.195390	+	0.143877i
$631$	10.1085	−	37.7256i	0.402415	−	1.50183i	−0.406360	−	0.913713i	$-0.633202\pi$
$631$	10.1085	−	37.7256i	0.402415	−	1.50183i	0.808775	−	0.588119i	$-0.200131\pi$
$632$	−26.8219			−1.06692
$633$	1.63726	−	6.11032i	0.0650751	−	0.242864i
$634$	−17.5143	+	30.3357i	−0.695582	+	1.20478i
$635$	0.427310	+	1.09226i	0.0169573	+	0.0433450i
$636$		−	38.7550i		−	1.53674i
$637$		0			0
$638$	84.4296	+	84.4296i	3.34260	+	3.34260i
$639$	−11.1261	+	2.98122i	−0.440141	+	0.117935i
$640$	14.7637	−	33.7386i	0.583585	−	1.33363i
$641$	−7.55607	+	4.36250i	−0.298447	+	0.172308i	−0.641745	−	0.766918i	$-0.721789\pi$
$641$	−7.55607	+	4.36250i	−0.298447	+	0.172308i	0.343298	+	0.939226i	$0.388456\pi$
$642$		−	64.9590i		−	2.56373i
$643$	7.39852	+	12.8146i	0.291769	+	0.505359i	0.974228	−	0.225565i	$-0.0724228\pi$
$643$	7.39852	+	12.8146i	0.291769	+	0.505359i	−0.682459	+	0.730924i	$0.739089\pi$
$644$	0.626588	+	0.167894i	0.0246910	+	0.00661594i
$645$	−3.28220	−	29.4178i	−0.129237	−	1.15832i
$646$	−4.41809	−	7.65235i	−0.173827	−	0.301078i
$647$	32.7213	−	8.76765i	1.28641	−	0.344692i	0.450113	−	0.892972i	$-0.351384\pi$
$647$	32.7213	−	8.76765i	1.28641	−	0.344692i	0.836295	+	0.548280i	$0.184717\pi$
$648$	−22.7449	−	13.1318i	−0.893505	−	0.515865i
$649$	−0.0125609			−0.000493060
$650$		0			0
$651$	−0.837243			−0.0328141
$652$	−24.4425	−	14.1119i	−0.957242	−	0.552664i
$653$	19.5581	−	5.24059i	0.765369	−	0.205080i	0.145044	−	0.989425i	$-0.453667\pi$
$653$	19.5581	−	5.24059i	0.765369	−	0.205080i	0.620325	+	0.784345i	$0.287001\pi$
$654$	−14.9382	−	25.8737i	−0.584128	−	1.01174i
$655$	−1.26422	−	11.3310i	−0.0493973	−	0.442739i
$656$	−0.353557	−	0.0947353i	−0.0138041	−	0.00369879i
$657$	−3.48016	−	6.02782i	−0.135774	−	0.235168i
$658$			9.19981i			0.358646i
$659$	−26.2317	+	15.1449i	−1.02184	+	0.589961i	−0.914637	−	0.404276i	$-0.867523\pi$
$659$	−26.2317	+	15.1449i	−1.02184	+	0.589961i	−0.107205	+	0.994237i	$0.534190\pi$
$660$	−29.8284	+	68.1652i	−1.16107	+	2.65333i
$661$	21.1339	−	5.66280i	0.822012	−	0.220257i	0.176786	−	0.984249i	$-0.443430\pi$
$661$	21.1339	−	5.66280i	0.822012	−	0.220257i	0.645226	+	0.763992i	$0.276763\pi$
$662$	27.1574	+	27.1574i	1.05550	+	1.05550i
$663$		0			0
$664$		−	6.37202i		−	0.247282i
$665$	1.26792	+	3.24096i	0.0491677	+	0.125679i
$666$	1.40925	−	2.44090i	0.0546074	−	0.0945829i
$667$	−0.416380	+	1.55395i	−0.0161223	+	0.0601693i
$668$	−38.7520			−1.49936
$669$	6.10774	−	22.7944i	0.236139	−	0.881282i
$670$	−24.6179	+	18.1275i	−0.951071	+	0.700326i
$671$	−5.37640	−	5.37640i	−0.207553	−	0.207553i
$672$	15.7969	+	4.23277i	0.609379	+	0.163283i
$673$	0.148622	+	0.554664i	0.00572895	+	0.0213807i	0.968731	−	0.248113i	$-0.0798104\pi$
$673$	0.148622	+	0.554664i	0.00572895	+	0.0213807i	−0.963002	+	0.269494i	$0.913144\pi$
$674$	20.6424	+	77.0386i	0.795117	+	2.96742i
$675$	−10.8857	+	17.2411i	−0.418989	+	0.663610i
$676$		0			0
$677$	−11.5229	+	11.5229i	−0.442862	+	0.442862i	−0.892973	−	0.450111i	$-0.851385\pi$
$677$	−11.5229	+	11.5229i	−0.442862	+	0.442862i	0.450111	+	0.892973i	$0.351385\pi$
$678$	−25.4786	+	44.1302i	−0.978498	+	1.69481i
$679$	−4.62416	−	2.66976i	−0.177459	−	0.102456i
$680$	2.59496	−	17.0904i	0.0995124	−	0.655386i
$681$	38.8688	−	38.8688i	1.48946	−	1.48946i
$682$	−3.51300	+	2.02823i	−0.134520	+	0.0776650i
$683$	−17.4121	+	10.0529i	−0.666256	+	0.384663i	−0.794657	−	0.607059i	$-0.792349\pi$
$683$	−17.4121	+	10.0529i	−0.666256	+	0.384663i	0.128400	+	0.991722i	$0.459016\pi$
$684$	2.50325	−	2.50325i	0.0957143	−	0.0957143i
$685$	6.84843	−	5.04288i	0.261665	−	0.192679i
$686$	−30.7929	−	17.7783i	−1.17568	−	0.678777i
$687$	18.1232	−	31.3902i	0.691442	−	1.19761i
$688$	−3.44440	+	3.44440i	−0.131317	+	0.131317i
$689$		0			0
$690$	−1.64623	+	0.183673i	−0.0626709	+	0.00699232i
$691$	11.2156	+	41.8571i	0.426661	+	1.59232i	0.760269	+	0.649608i	$0.225067\pi$
$691$	11.2156	+	41.8571i	0.426661	+	1.59232i	−0.333608	+	0.942712i	$0.608266\pi$
$692$	−10.8842	−	40.6205i	−0.413756	−	1.54416i
$693$	−6.38467	−	1.71077i	−0.242534	−	0.0649867i
$694$	−20.5310	−	20.5310i	−0.779346	−	0.779346i
$695$	1.95991	+	2.66164i	0.0743436	+	0.100962i
$696$	11.9841	−	44.7253i	0.454256	−	1.69531i
$697$	−1.61289			−0.0610926
$698$	−15.6421	+	58.3773i	−0.592064	+	2.20961i
$699$	22.9764	−	39.7962i	0.869046	−	1.50523i
$700$	−5.81200	+	18.6976i	−0.219673	+	0.706702i
$701$		−	8.03468i		−	0.303466i	−0.988422	−	0.151733i	$-0.951515\pi$
$701$		−	8.03468i		−	0.303466i	0.988422	−	0.151733i	$-0.0484853\pi$
$702$		0			0
$703$	−1.13882	−	1.13882i	−0.0429514	−	0.0429514i
$704$	68.8216	−	18.4407i	2.59381	−	0.695010i
$705$	−5.17995	−	13.2406i	−0.195088	−	0.498670i
$706$	45.4404	−	26.2350i	1.71017	−	0.987369i
$707$			11.0212i			0.414495i
$708$	0.00700440	+	0.0121320i	0.000263242	+	0.000455948i
$709$	−21.9526	−	5.88217i	−0.824446	−	0.220910i	−0.178157	−	0.984002i	$-0.557013\pi$
$709$	−21.9526	−	5.88217i	−0.824446	−	0.220910i	−0.646289	+	0.763092i	$0.723680\pi$
$710$	−38.2008	+	47.7956i	−1.43365	+	1.79374i
$711$	5.29519	+	9.17153i	0.198585	+	0.343959i
$712$	−16.7146	+	4.47866i	−0.626406	+	0.167845i
$713$	−0.0473328	−	0.0273276i	−0.00177263	−	0.00102343i
$714$	18.4000			0.688604
$715$		0			0
$716$	−38.7636			−1.44866
$717$	−6.37039	−	3.67794i	−0.237906	−	0.137355i
$718$	−28.2014	+	7.55655i	−1.05247	+	0.282008i
$719$	21.4786	+	37.2021i	0.801018	+	1.38740i	0.918946	+	0.394382i	$0.129041\pi$
$719$	21.4786	+	37.2021i	0.801018	+	1.38740i	−0.117928	+	0.993022i	$0.537625\pi$
$720$	−1.53938	+	0.171752i	−0.0573693	+	0.00640081i
$721$	−1.87732	−	0.503026i	−0.0699149	−	0.0187336i
$722$	19.7115	+	34.1413i	0.733585	+	1.27061i
$723$		−	41.3467i		−	1.53770i
$724$	−21.6841	+	12.5193i	−0.805882	+	0.465276i
$725$	−46.3705	−	14.4139i	−1.72216	−	0.535319i
$726$	−81.3643	+	21.8015i	−3.01971	+	0.809129i
$727$	−1.42786	−	1.42786i	−0.0529563	−	0.0529563i	0.680133	−	0.733089i	$-0.261922\pi$
$727$	−1.42786	−	1.42786i	−0.0529563	−	0.0529563i	−0.733089	+	0.680133i	$0.761922\pi$
$728$		0			0
$729$		−	13.9369i		−	0.516183i
$730$	−33.8718	−	14.8220i	−1.25365	−	0.548586i
$731$	−10.7322	+	18.5887i	−0.396945	+	0.687528i
$732$	−2.19473	+	8.19086i	−0.0811197	+	0.302743i
$733$	−32.1064			−1.18588			−0.592939	−	0.805247i	$-0.702033\pi$
$733$	−32.1064			−1.18588			−0.592939	+	0.805247i	$0.702033\pi$
$734$	−8.66065	+	32.3220i	−0.319670	+	1.19303i
$735$	23.5816	+	3.58058i	0.869820	+	0.132072i
$736$	0.754907	+	0.754907i	0.0278262	+	0.0278262i
$737$	−32.0491	−	8.58752i	−1.18054	−	0.316325i
$738$	−0.276339	−	1.03131i	−0.0101722	−	0.0379631i
$739$	−5.31771	−	19.8460i	−0.195615	−	0.730046i	−0.992107	−	0.125396i	$-0.959980\pi$
$739$	−5.31771	−	19.8460i	−0.195615	−	0.730046i	0.796492	−	0.604650i	$-0.206687\pi$
$740$	−1.00474	−	9.00534i	−0.0369351	−	0.331043i
$741$		0			0
$742$	12.9317	−	12.9317i	0.474736	−	0.474736i
$743$	11.2520	−	19.4891i	0.412797	−	0.714985i	−0.582398	−	0.812904i	$-0.697885\pi$
$743$	11.2520	−	19.4891i	0.412797	−	0.714985i	0.995194	+	0.0979193i	$0.0312187\pi$
$744$	1.36232	+	0.786533i	0.0499449	+	0.0288357i
$745$	−38.0601	−	5.77897i	−1.39442	−	0.211725i
$746$	9.83771	−	9.83771i	0.360184	−	0.360184i
$747$	−2.17886	+	1.25796i	−0.0797202	+	0.0460265i
$748$	46.7261	−	26.9773i	1.70848	−	0.986389i
$749$	13.1184	−	13.1184i	0.479334	−	0.479334i
$750$	−3.57372	−	49.8702i	−0.130494	−	1.82100i
$751$	1.44204	+	0.832560i	0.0526207	+	0.0303806i	0.526080	−	0.850435i	$-0.323661\pi$
$751$	1.44204	+	0.832560i	0.0526207	+	0.0303806i	−0.473459	+	0.880816i	$0.656995\pi$
$752$	−1.16986	+	2.02626i	−0.0426605	+	0.0738901i
$753$	3.32640	−	3.32640i	0.121221	−	0.121221i
$754$		0			0
$755$	19.8498	−	24.8355i	0.722410	−	0.903855i
$756$	−4.13321	−	15.4254i	−0.150324	−	0.561015i
$757$	−10.1014	−	37.6990i	−0.367143	−	1.37019i	−0.864493	−	0.502645i	$-0.832360\pi$
$757$	−10.1014	−	37.6990i	−0.367143	−	1.37019i	0.497350	−	0.867550i	$-0.334306\pi$
$758$	−39.7186	−	10.6426i	−1.44265	−	0.386556i
$759$	−1.27119	−	1.27119i	−0.0461412	−	0.0461412i
$760$	0.981575	−	6.46463i	0.0356055	−	0.234497i
$761$	4.20973	−	15.7109i	0.152603	−	0.569521i	−0.846696	−	0.532077i	$-0.821412\pi$
$761$	4.20973	−	15.7109i	0.152603	−	0.569521i	0.999299	−	0.0374441i	$-0.0119216\pi$
$762$	2.34565			0.0849739
$763$	2.20841	−	8.24188i	0.0799496	−	0.298376i
$764$	−22.6186	+	39.1766i	−0.818313	+	1.41736i
$765$	−6.35620	+	2.48665i	−0.229809	+	0.0899052i
$766$			23.0560i			0.833045i
$767$		0			0
$768$	−15.4289	−	15.4289i	−0.556741	−	0.556741i
$769$	−38.5504	+	10.3296i	−1.39016	+	0.372493i	−0.874803	−	0.484479i	$-0.839009\pi$
$769$	−38.5504	+	10.3296i	−1.39016	+	0.372493i	−0.515362	+	0.856973i	$0.672342\pi$
$770$	−32.6982	+	12.7921i	−1.17836	+	0.460995i
$771$	−1.49702	+	0.864306i	−0.0539139	+	0.0311272i
$772$		−	46.2891i		−	1.66598i
$773$	10.2944	+	17.8304i	0.370262	+	0.641313i	0.989606	−	0.143807i	$-0.0459345\pi$
$773$	10.2944	+	17.8304i	0.370262	+	0.641313i	−0.619343	+	0.785120i	$0.712601\pi$
$774$	−13.7247	−	3.67753i	−0.493325	−	0.132186i
$775$	0.880735	−	1.39494i	0.0316369	−	0.0501077i
$776$	5.01612	+	8.68818i	0.180068	+	0.311887i
$777$	3.23942	−	0.868001i	0.116214	−	0.0311394i
$778$	−6.65087	−	3.83988i	−0.238445	−	0.137666i
$779$	−0.610095			−0.0218589
$780$		0			0
$781$	−66.4048			−2.37615
$782$	1.04023	+	0.600577i	0.0371986	+	0.0214766i
$783$	38.2553	−	10.2505i	1.36713	−	0.366322i
$784$	−1.96257	−	3.39927i	−0.0700917	−	0.121402i
$785$	−7.58927	−	6.06575i	−0.270873	−	0.216496i
$786$	−22.0248	−	5.90153i	−0.785599	−	0.210501i
$787$	14.3244	+	24.8106i	0.510611	+	0.884404i	0.999924	+	0.0122960i	$0.00391402\pi$
$787$	14.3244	+	24.8106i	0.510611	+	0.884404i	−0.489314	+	0.872108i	$0.662753\pi$
$788$			47.1311i			1.67898i
$789$	−26.1334	+	15.0881i	−0.930375	+	0.537152i
$790$	51.5371	+	22.5521i	1.83361	+	0.802369i
$791$	−14.0574	+	3.76666i	−0.499822	+	0.133927i
$792$	8.78163	+	8.78163i	0.312042	+	0.312042i
$793$		0			0
$794$		−	26.8568i		−	0.953111i
$795$	−11.3304	+	25.8927i	−0.401848	+	0.918321i
$796$	−17.5631	+	30.4202i	−0.622508	+	1.07822i
$797$	−2.27363	+	8.48530i	−0.0805361	+	0.300565i	−0.994432	−	0.105385i	$-0.966393\pi$
$797$	−2.27363	+	8.48530i	−0.0805361	+	0.300565i	0.913895	+	0.405950i	$0.133059\pi$
$798$	6.96002			0.246382
$799$	−2.66840	+	9.95859i	−0.0944011	+	0.352310i
$800$	−23.6698	+	21.8667i	−0.836852	+	0.773106i
$801$	4.83124	+	4.83124i	0.170703	+	0.170703i
$802$	−8.86190	−	2.37454i	−0.312924	−	0.0838479i
$803$	−10.3855	−	38.7592i	−0.366496	−	1.36778i
$804$	9.57739	+	35.7433i	0.337768	+	1.26057i
$805$	−0.369546	−	0.295361i	−0.0130248	−	0.0104101i
$806$		0			0
$807$	−34.2536	+	34.2536i	−1.20578	+	1.20578i
$808$	10.3537	−	17.9331i	0.364241	−	0.630884i
$809$	−0.820571	−	0.473757i	−0.0288497	−	0.0166564i	0.485506	−	0.874233i	$-0.338635\pi$
$809$	−0.820571	−	0.473757i	−0.0288497	−	0.0166564i	−0.514356	+	0.857577i	$0.671969\pi$
$810$	32.6620	+	44.3563i	1.14762	+	1.55852i
$811$	−28.8041	+	28.8041i	−1.01145	+	1.01145i	−0.0115151	+	0.999934i	$0.503665\pi$
$811$	−28.8041	+	28.8041i	−1.01145	+	1.01145i	−0.999934	+	0.0115151i	$0.996335\pi$
$812$	32.9363	−	19.0158i	1.15584	−	0.667324i
$813$	−22.5690	+	13.0302i	−0.791531	+	0.456991i
$814$	11.4896	−	11.4896i	0.402711	−	0.402711i
$815$	12.2046	+	16.5743i	0.427509	+	0.580574i
$816$	4.05261	+	2.33978i	0.141870	+	0.0819086i
$817$	−4.05958	+	7.03139i	−0.142027	+	0.245997i
$818$	11.0440	−	11.0440i	0.386145	−	0.386145i
$819$		0			0
$820$	−2.68133	−	2.14306i	−0.0936361	−	0.0748390i
$821$	−0.348249	−	1.29968i	−0.0121540	−	0.0453592i	0.959583	−	0.281427i	$-0.0908078\pi$
$821$	−0.348249	−	1.29968i	−0.0121540	−	0.0453592i	−0.971737	+	0.236068i	$0.924141\pi$
$822$	−4.40224	−	16.4294i	−0.153546	−	0.573041i
$823$	−31.9429	−	8.55907i	−1.11346	−	0.298350i	−0.345225	−	0.938520i	$-0.612197\pi$
$823$	−31.9429	−	8.55907i	−1.11346	−	0.298350i	−0.768234	+	0.640169i	$0.778864\pi$
$824$	2.58211	+	2.58211i	0.0899520	+	0.0899520i
$825$	39.8575	−	36.8214i	1.38766	−	1.28196i
$826$	−0.00171095	+	0.00638537i	−5.95317e−5	+	0.000222175i
$827$	26.4195			0.918697			0.459349	−	0.888256i	$-0.348083\pi$
$827$	26.4195			0.918697			0.459349	+	0.888256i	$0.348083\pi$
$828$	−0.124552	+	0.464834i	−0.00432848	+	0.0161541i
$829$	1.23034	−	2.13101i	0.0427314	−	0.0740130i	−0.843869	−	0.536550i	$-0.819727\pi$
$829$	1.23034	−	2.13101i	0.0427314	−	0.0740130i	0.886600	+	0.462537i	$0.153061\pi$
$830$	−5.35766	+	12.2435i	−0.185967	+	0.424980i
$831$			24.2940i			0.842748i
$832$		0			0
$833$	−12.2301	−	12.2301i	−0.423747	−	0.423747i
$834$	6.38526	−	1.71093i	0.221104	−	0.0592445i
$835$	25.8907	+	11.3295i	0.895985	+	0.392074i
$836$	17.6747	−	10.2045i	0.611292	−	0.352929i
$837$			1.34551i			0.0465075i
$838$	−23.8909	−	41.3802i	−0.825297	−	1.42946i
$839$	−48.6308	−	13.0306i	−1.67892	−	0.449866i	−0.711428	−	0.702759i	$-0.751951\pi$
$839$	−48.6308	−	13.0306i	−1.67892	−	0.449866i	−0.967494	+	0.252893i	$0.918618\pi$
$840$	10.6361	+	8.50096i	0.366981	+	0.293311i
$841$	32.6597	+	56.5682i	1.12619	+	1.95063i
$842$	9.70754	−	2.60113i	0.334544	−	0.0896408i
$843$	−15.6594	−	9.04093i	−0.539337	−	0.311386i
$844$	−9.76228			−0.336032
$845$		0			0
$846$	−6.82488			−0.234644
$847$	−20.8342	−	12.0286i	−0.715870	−	0.413308i
$848$	4.49261	−	1.20379i	0.154277	−	0.0413384i
$849$	−27.1730	−	47.0651i	−0.932576	−	1.61527i
$850$	−19.3559	+	30.6565i	−0.663900	+	1.05151i
$851$	0.211470	+	0.0566632i	0.00724909	+	0.00194239i
$852$	37.0296	+	64.1371i	1.26861	+	2.19730i
$853$		−	42.9612i		−	1.47096i	−0.677545	−	0.735481i	$-0.736956\pi$
$853$		−	42.9612i		−	1.47096i	0.677545	−	0.735481i	$-0.263044\pi$
$854$	−3.46543	+	2.00077i	−0.118585	+	0.0684649i
$855$	−2.40431	+	0.940605i	−0.0822255	+	0.0321680i
$856$	−33.6693	+	9.02166i	−1.15079	+	0.308354i
$857$	29.0789	+	29.0789i	0.993316	+	0.993316i	0.999978	−	0.00666151i	$-0.00212044\pi$
$857$	29.0789	+	29.0789i	0.993316	+	0.993316i	−0.00666151	+	0.999978i	$0.502120\pi$
$858$		0			0
$859$			42.1283i			1.43740i	0.695321	+	0.718700i	$0.255262\pi$
$859$			42.1283i			1.43740i	−0.695321	+	0.718700i	$0.744738\pi$
$860$	−42.5406	+	16.6426i	−1.45062	+	0.567508i
$861$	0.635216	−	1.10023i	0.0216481	−	0.0374956i
$862$	20.8810	−	77.9289i	0.711209	−	2.65427i
$863$	−6.80768			−0.231736			−0.115868	−	0.993265i	$-0.536965\pi$
$863$	−6.80768			−0.231736			−0.115868	+	0.993265i	$0.536965\pi$
$864$	6.80234	−	25.3867i	0.231420	−	0.863672i
$865$	−4.60391	+	30.3212i	−0.156537	+	1.03095i
$866$	12.8806	+	12.8806i	0.437702	+	0.437702i
$867$	−12.7075	−	3.40497i	−0.431570	−	0.115639i
$868$	0.334410	+	1.24803i	0.0113506	+	0.0423610i
$869$	15.8019	+	58.9734i	0.536042	+	2.00054i
$870$	−60.6323	+	75.8612i	−2.05563	+	2.57194i
$871$		0			0
$872$	−11.3361	+	11.3361i	−0.383888	+	0.383888i
$873$	1.98056	−	3.43044i	0.0670320	−	0.116103i
$874$	0.393479	+	0.227175i	0.0133096	+	0.00768432i
$875$	9.34949	−	10.7929i	0.316071	−	0.364867i
$876$	−31.6443	+	31.6443i	−1.06916	+	1.06916i
$877$	41.2933	−	23.8407i	1.39437	−	0.805043i	0.400579	−	0.916262i	$-0.368809\pi$
$877$	41.2933	−	23.8407i	1.39437	−	0.805043i	0.993796	+	0.111219i	$0.0354756\pi$
$878$	55.8796	−	32.2621i	1.88585	−	1.08879i
$879$	−36.7017	+	36.7017i	−1.23792	+	1.23792i
$880$	−8.82845	−	1.34049i	−0.297607	−	0.0451880i
$881$	4.43737	+	2.56192i	0.149499	+	0.0863133i	0.572884	−	0.819637i	$-0.305825\pi$
$881$	4.43737	+	2.56192i	0.149499	+	0.0863133i	−0.423385	+	0.905950i	$0.639158\pi$
$882$	5.72474	−	9.91554i	0.192762	−	0.333873i
$883$	−14.8283	+	14.8283i	−0.499014	+	0.499014i	−0.911131	−	0.412117i	$-0.864789\pi$
$883$	−14.8283	+	14.8283i	−0.499014	+	0.499014i	0.412117	+	0.911131i	$0.364789\pi$
$884$		0			0
$885$	−0.00113283	−	0.0101533i	−3.80796e−5	−	0.000341301i
$886$	−14.1361	−	52.7568i	−0.474913	−	1.77240i
$887$	−2.72597	−	10.1735i	−0.0915293	−	0.341592i	0.904941	−	0.425537i	$-0.139915\pi$
$887$	−2.72597	−	10.1735i	−0.0915293	−	0.341592i	−0.996470	+	0.0839449i	$0.973248\pi$
$888$	−6.08644	−	1.63086i	−0.204248	−	0.0547280i
$889$	0.473700	+	0.473700i	0.0158874	+	0.0158874i
$890$	35.8820	+	5.44825i	1.20277	+	0.182626i
$891$	−15.4729	+	57.7457i	−0.518362	+	1.93455i
$892$	−36.4179			−1.21936
$893$	−1.00935	+	3.76695i	−0.0337767	+	0.126056i
$894$	−38.4949	+	66.6751i	−1.28746	+	2.22995i
$895$	25.8985	+	11.3329i	0.865691	+	0.378818i
$896$		−	21.0349i		−	0.702725i
$897$		0			0
$898$	−14.5886	−	14.5886i	−0.486828	−	0.486828i
$899$	−3.09515	+	0.829344i	−0.103229	+	0.0276602i
$900$	−13.8708	−	4.31163i	−0.462361	−	0.143721i
$901$	17.7490	−	10.2474i	0.591307	−	0.341391i
$902$		−	6.15528i		−	0.204948i
$903$	−8.45347	−	14.6418i	−0.281314	−	0.487250i
$904$	26.4119	+	7.07704i	0.878446	+	0.235379i
$905$	18.1476	−	2.02476i	0.603245	−	0.0673053i
$906$	−31.7921	−	55.0656i	−1.05622	−	1.82943i
$907$	20.8031	−	5.57417i	0.690755	−	0.185087i	0.103669	−	0.994612i	$-0.466942\pi$
$907$	20.8031	−	5.57417i	0.690755	−	0.185087i	0.587086	+	0.809525i	$0.300275\pi$
$908$	−73.4645	−	42.4147i	−2.43800	−	1.40758i
$909$	−8.17608			−0.271184
$910$		0			0
$911$	−16.6400			−0.551309			−0.275654	−	0.961257i	$-0.588895\pi$
$911$	−16.6400			−0.551309			−0.275654	+	0.961257i	$0.588895\pi$
$912$	1.53295	+	0.885047i	0.0507609	+	0.0293068i
$913$	−14.0102	+	3.75401i	−0.463669	+	0.124240i
$914$	24.1734	+	41.8696i	0.799586	+	1.38492i
$915$	3.86101	−	4.83077i	0.127641	−	0.159700i
$916$	−54.0305	−	14.4774i	−1.78522	−	0.478347i
$917$	−3.25607	−	5.63968i	−0.107525	−	0.186239i
$918$		−	29.5701i		−	0.975958i
$919$	5.95358	−	3.43730i	0.196390	−	0.113386i	−0.398580	−	0.917133i	$-0.630497\pi$
$919$	5.95358	−	3.43730i	0.196390	−	0.113386i	0.594971	+	0.803747i	$0.297164\pi$
$920$	0.323833	+	0.827758i	0.0106765	+	0.0272904i
$921$	28.2184	−	7.56111i	0.929829	−	0.249147i
$922$	8.08349	+	8.08349i	0.266216	+	0.266216i
$923$		0			0
$924$			42.4987i			1.39810i
$925$	−1.96152	+	6.31033i	−0.0644942	+	0.207482i
$926$	−22.5973	+	39.1396i	−0.742593	+	1.28621i
$927$	0.373170	−	1.39269i	0.0122565	−	0.0457419i
$928$	62.5915			2.05467
$929$	−11.5057	+	42.9399i	−0.377490	+	1.40881i	0.472182	+	0.881501i	$0.343467\pi$
$929$	−11.5057	+	42.9399i	−0.377490	+	1.40881i	−0.849672	+	0.527312i	$0.823200\pi$
$930$	−1.95630	−	2.65674i	−0.0641497	−	0.0871178i
$931$	−4.62617	−	4.62617i	−0.151617	−	0.151617i
$932$	−68.4993	−	18.3543i	−2.24377	−	0.601216i
$933$	16.3795	+	61.1290i	0.536240	+	2.00127i
$934$	−17.6722	−	65.9535i	−0.578252	−	2.15806i
$935$	−39.1054	+	4.36307i	−1.27888	+	0.142688i
$936$		0			0
$937$	13.1724	−	13.1724i	0.430323	−	0.430323i	−0.458415	−	0.888738i	$-0.651583\pi$
$937$	13.1724	−	13.1724i	0.430323	−	0.430323i	0.888738	+	0.458415i	$0.151583\pi$
$938$	−8.73096	+	15.1225i	−0.285076	+	0.493766i
$939$	29.1675	+	16.8399i	0.951846	+	0.549548i
$940$	−17.6681	+	13.0100i	−0.576270	+	0.424339i
$941$	−40.0251	+	40.0251i	−1.30478	+	1.30478i	−0.379650	+	0.925130i	$0.623955\pi$
$941$	−40.0251	+	40.0251i	−1.30478	+	1.30478i	−0.925130	+	0.379650i	$0.876045\pi$
$942$	−16.8270	+	9.71510i	−0.548255	+	0.316535i
$943$	0.0718228	−	0.0414669i	0.00233887	−	0.00135035i
$944$	−0.00118881	+	0.00118881i	−3.86925e−5	+	3.86925e-5i
$945$	−1.74830	+	11.5143i	−0.0568723	+	0.374559i
$946$	−70.9401	−	40.9573i	−2.30646	−	1.33164i
$947$	−29.4472	+	51.0040i	−0.956904	+	1.65741i	−0.226955	+	0.973905i	$0.572877\pi$
$947$	−29.4472	+	51.0040i	−0.956904	+	1.65741i	−0.729949	+	0.683501i	$0.760456\pi$
$948$	48.1479	−	48.1479i	1.56377	−	1.56377i
$949$		0			0
$950$	−7.32157	+	11.5962i	−0.237543	+	0.376229i
$951$	−8.00278	−	29.8668i	−0.259508	−	0.968497i
$952$	−2.55544	−	9.53703i	−0.0828223	−	0.309097i
$953$	−17.2456	−	4.62094i	−0.558640	−	0.149687i	−0.0315583	−	0.999502i	$-0.510047\pi$
$953$	−17.2456	−	4.62094i	−0.558640	−	0.149687i	−0.527081	+	0.849815i	$0.676714\pi$
$954$	9.59336	+	9.59336i	0.310596	+	0.310596i
$955$	26.5654	−	19.5616i	0.859638	−	0.632999i
$956$	−2.93807	+	10.9650i	−0.0950240	+	0.354634i
$957$	−105.398			−3.40703
$958$	18.1230	−	67.6360i	0.585528	−	2.18522i
$959$	2.42886	−	4.20691i	0.0784320	−	0.135848i
$960$	21.1129	+	53.9673i	0.681417	+	1.74179i
$961$			30.8911i			0.996488i
$962$		0			0
$963$	9.73187	+	9.73187i	0.313605	+	0.313605i
$964$	−61.6333	+	16.5146i	−1.98507	+	0.531899i
$965$	−13.5331	+	30.9263i	−0.435645	+	0.995554i
$966$	−0.819363	+	0.473059i	−0.0263626	+	0.0152204i
$967$		−	23.2093i		−	0.746360i	−0.927759	−	0.373180i	$-0.878267\pi$
$967$		−	23.2093i		−	0.746360i	0.927759	−	0.373180i	$-0.121733\pi$
$968$	22.6001	+	39.1446i	0.726395	+	1.25815i
$969$	7.53407	+	2.01875i	0.242029	+	0.0648515i
$970$	−2.33314	−	20.9115i	−0.0749127	−	0.671429i
$971$	−21.1932	−	36.7078i	−0.680123	−	1.17801i	−0.974943	−	0.222455i	$-0.928593\pi$
$971$	−21.1932	−	36.7078i	−0.680123	−	1.17801i	0.294820	−	0.955553i	$-0.404740\pi$
$972$	28.1691	−	7.54788i	0.903523	−	0.242098i
$973$	1.63501	+	0.943975i	0.0524161	+	0.0302624i
$974$	43.7367			1.40141
$975$		0			0
$976$	−1.01768			−0.0325752
$977$	21.1395	+	12.2049i	0.676312	+	0.390469i	0.798464	−	0.602043i	$-0.205646\pi$
$977$	21.1395	+	12.2049i	0.676312	+	0.390469i	−0.122152	+	0.992511i	$0.538980\pi$
$978$	39.7618	−	10.6541i	1.27144	−	0.340682i
$979$	19.6945	+	34.1118i	0.629438	+	1.09022i
$980$	−4.08152	−	36.5819i	−0.130379	−	1.16857i
$981$	6.11424	+	1.63831i	0.195213	+	0.0523071i
$982$	−39.7420	−	68.8352i	−1.26822	−	2.19662i
$983$			4.47004i			0.142572i	0.997456	+	0.0712860i	$0.0227103\pi$
$983$			4.47004i			0.142572i	−0.997456	+	0.0712860i	$0.977290\pi$
$984$	−2.06718	+	1.19349i	−0.0658992	+	0.0380469i
$985$	13.7792	−	31.4889i	0.439043	−	1.00332i
$986$	68.0220	−	18.2264i	2.16626	−	0.580448i
$987$	−5.74230	−	5.74230i	−0.182779	−	0.182779i
$988$		0			0
$989$		−	1.10369i		−	0.0350952i
$990$	−9.48982	−	24.2572i	−0.301606	−	0.770944i
$991$	24.7675	−	42.8986i	0.786766	−	1.36272i	−0.141172	−	0.989985i	$-0.545087\pi$
$991$	24.7675	−	42.8986i	0.786766	−	1.36272i	0.927938	−	0.372734i	$-0.121580\pi$
$992$	−0.550363	+	2.05398i	−0.0174740	+	0.0652140i
$993$	−33.9020			−1.07585
$994$	−9.04516	+	33.7570i	−0.286895	+	1.07071i
$995$	20.6278	−	15.1894i	0.653945	−	0.481536i
$996$	11.4384	+	11.4384i	0.362439	+	0.362439i
$997$	33.8485	+	9.06967i	1.07199	+	0.287239i	0.751311	−	0.659948i	$-0.229422\pi$
$997$	33.8485	+	9.06967i	1.07199	+	0.287239i	0.320681	+	0.947187i	$0.396088\pi$
$998$	7.78071	+	29.0380i	0.246294	+	0.919182i
$999$	−1.39494	−	5.20597i	−0.0441338	−	0.164710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.g.188.5		20
5.2	odd	4		845.2.o.g.357.1		20
13.2	odd	12		65.2.o.a.63.5	yes	20
13.3	even	3		845.2.t.e.418.1		20
13.4	even	6		845.2.f.e.408.10		20
13.5	odd	4		845.2.o.e.488.5		20
13.6	odd	12		845.2.k.e.268.1		20
13.7	odd	12		845.2.k.d.268.10		20
13.8	odd	4		845.2.o.f.488.1		20
13.9	even	3		845.2.f.d.408.1		20
13.10	even	6		845.2.t.f.418.5		20
13.11	odd	12		845.2.o.g.258.1		20
13.12	even	2		65.2.t.a.58.1	yes	20
39.2	even	12		585.2.cf.a.388.1		20
39.38	odd	2		585.2.dp.a.253.5		20
65.2	even	12		65.2.t.a.37.1	yes	20
65.7	even	12		845.2.f.d.437.10		20
65.12	odd	4		65.2.o.a.32.5	✓	20
65.17	odd	12		845.2.k.e.577.1		20
65.22	odd	12		845.2.k.d.577.10		20
65.28	even	12		325.2.x.b.232.5		20
65.32	even	12		845.2.f.e.437.1		20
65.37	even	12	inner	845.2.t.g.427.5		20
65.38	odd	4		325.2.s.b.32.1		20
65.42	odd	12		845.2.o.f.587.1		20
65.47	even	4		845.2.t.e.657.1		20
65.54	odd	12		325.2.s.b.193.1		20
65.57	even	4		845.2.t.f.657.5		20
65.62	odd	12		845.2.o.e.587.5		20
65.64	even	2		325.2.x.b.318.5		20
195.2	odd	12		585.2.dp.a.37.5		20
195.77	even	4		585.2.cf.a.487.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.5	✓	20	65.12	odd	4
65.2.o.a.63.5	yes	20	13.2	odd	12
65.2.t.a.37.1	yes	20	65.2	even	12
65.2.t.a.58.1	yes	20	13.12	even	2
325.2.s.b.32.1		20	65.38	odd	4
325.2.s.b.193.1		20	65.54	odd	12
325.2.x.b.232.5		20	65.28	even	12
325.2.x.b.318.5		20	65.64	even	2
585.2.cf.a.388.1		20	39.2	even	12
585.2.cf.a.487.1		20	195.77	even	4
585.2.dp.a.37.5		20	195.2	odd	12
585.2.dp.a.253.5		20	39.38	odd	2
845.2.f.d.408.1		20	13.9	even	3
845.2.f.d.437.10		20	65.7	even	12
845.2.f.e.408.10		20	13.4	even	6
845.2.f.e.437.1		20	65.32	even	12
845.2.k.d.268.10		20	13.7	odd	12
845.2.k.d.577.10		20	65.22	odd	12
845.2.k.e.268.1		20	13.6	odd	12
845.2.k.e.577.1		20	65.17	odd	12
845.2.o.e.488.5		20	13.5	odd	4
845.2.o.e.587.5		20	65.62	odd	12
845.2.o.f.488.1		20	13.8	odd	4
845.2.o.f.587.1		20	65.42	odd	12
845.2.o.g.258.1		20	13.11	odd	12
845.2.o.g.357.1		20	5.2	odd	4
845.2.t.e.418.1		20	13.3	even	3
845.2.t.e.657.1		20	65.47	even	4
845.2.t.f.418.5		20	13.10	even	6
845.2.t.f.657.5		20	65.57	even	4
845.2.t.g.188.5		20	1.1	even	1	trivial
845.2.t.g.427.5		20	65.37	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.94926 + 1.12540i) q^{2} +(-1.91913 + 0.514229i) q^{3} +(1.53307 + 2.65535i) q^{4} +(-0.247944 - 2.22228i) q^{5} +(-4.31958 - 1.15743i) q^{6} +(-0.638592 - 1.10607i) q^{7} +2.39966i q^{8} +(0.820542 - 0.473740i) q^{9} +(2.01765 - 4.61083i) q^{10} +(5.27612 - 1.41373i) q^{11} +(-4.30760 - 4.30760i) q^{12} -2.87469i q^{14} +(1.61860 + 4.13734i) q^{15} +(0.365551 - 0.633152i) q^{16} +(0.833802 - 3.11179i) q^{17} +2.13259 q^{18} +(0.315395 - 1.17707i) q^{19} +(5.52081 - 4.06528i) q^{20} +(1.79431 + 1.79431i) q^{21} +(11.8755 + 3.18204i) q^{22} +(0.0428736 + 0.160006i) q^{23} +(-1.23397 - 4.60524i) q^{24} +(-4.87705 + 1.10200i) q^{25} +(2.88358 - 2.88358i) q^{27} +(1.95801 - 3.39137i) q^{28} +(8.41068 + 4.85591i) q^{29} +(-1.50111 + 9.88630i) q^{30} +(-0.233305 + 0.233305i) q^{31} +(5.58143 - 3.22244i) q^{32} +(-9.39857 + 5.42627i) q^{33} +(5.12732 - 5.12732i) q^{34} +(-2.29967 + 1.69337i) q^{35} +(2.51589 + 1.45255i) q^{36} +(0.660816 - 1.14457i) q^{37} +(1.93947 - 1.93947i) q^{38} +(5.33270 - 0.594981i) q^{40} +(-0.129579 - 0.483595i) q^{41} +(1.47825 + 5.51690i) q^{42} +(-6.43569 - 1.72444i) q^{43} +(11.8426 + 11.8426i) q^{44} +(-1.25623 - 1.70601i) q^{45} +(-0.0965002 + 0.360144i) q^{46} -3.20027 q^{47} +(-0.375953 + 1.40308i) q^{48} +(2.68440 - 4.64952i) q^{49} +(-10.7468 - 3.34056i) q^{50} +6.40069i q^{51} +(4.49845 + 4.49845i) q^{53} +(8.86603 - 2.37565i) q^{54} +(-4.44989 - 11.3745i) q^{55} +(2.65420 - 1.53240i) q^{56} +2.42113i q^{57} +(10.9297 + 18.9308i) q^{58} +(-0.00222123 - 0.000595178i) q^{59} +(-8.50465 + 10.6407i) q^{60} +(-0.695993 - 1.20550i) q^{61} +(-0.717332 + 0.192209i) q^{62} +(-1.04798 - 0.605053i) q^{63} +13.0440 q^{64} -24.4270 q^{66} +(-5.26055 - 3.03718i) q^{67} +(9.54117 - 2.55655i) q^{68} +(-0.164560 - 0.285026i) q^{69} +(-6.38837 + 0.712764i) q^{70} +(-11.7428 - 3.14648i) q^{71} +(1.13681 + 1.96902i) q^{72} -7.34614i q^{73} +(2.57620 - 1.48737i) q^{74} +(8.79299 - 4.62280i) q^{75} +(3.60906 - 0.967044i) q^{76} +(-4.93298 - 4.93298i) q^{77} +11.1774i q^{79} +(-1.49768 - 0.655369i) q^{80} +(-5.47236 + 9.47841i) q^{81} +(0.291657 - 1.08848i) q^{82} -2.65539 q^{83} +(-2.01373 + 7.51533i) q^{84} +(-7.12201 - 1.08139i) q^{85} +(-10.6041 - 10.6041i) q^{86} +(-18.6382 - 4.99409i) q^{87} +(3.39247 + 12.6609i) q^{88} +(1.86638 + 6.96542i) q^{89} +(-0.528764 - 4.73922i) q^{90} +(-0.359145 + 0.359145i) q^{92} +(0.327769 - 0.567713i) q^{93} +(-6.23815 - 3.60160i) q^{94} +(-2.69398 - 0.409048i) q^{95} +(-9.05440 + 9.05440i) q^{96} +(3.62059 - 2.09035i) q^{97} +(10.4652 - 6.04207i) q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 8 q^{6} + 2 q^{7} + 12 q^{9} - 2 q^{10} + 16 q^{11} - 24 q^{12} + 20 q^{15} - 2 q^{16} + 4 q^{17} + 20 q^{19} - 4 q^{21} + 16 q^{22} - 10 q^{23} - 32 q^{24} + 18 q^{25}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 8 * q^6 + 2 * q^7 + 12 * q^9 - 2 * q^10 + 16 * q^11 - 24 * q^12 + 20 * q^15 - 2 * q^16 + 4 * q^17 + 20 * q^19 - 4 * q^21 + 16 * q^22 - 10 * q^23 - 32 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 26 * q^30 - 48 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 + 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 + 40 * q^42 + 10 * q^43 + 36 * q^44 - 4 * q^46 + 40 * q^47 - 56 * q^48 + 18 * q^49 - 36 * q^50 - 10 * q^53 + 48 * q^54 - 10 * q^55 + 16 * q^59 - 28 * q^60 - 16 * q^61 - 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 22 * q^68 - 16 * q^69 + 12 * q^70 + 16 * q^71 - 4 * q^72 + 18 * q^74 - 38 * q^75 + 64 * q^76 - 28 * q^77 + 2 * q^80 - 14 * q^81 + 56 * q^82 - 48 * q^83 + 40 * q^84 + 26 * q^85 - 60 * q^86 - 34 * q^87 + 82 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 - 48 * q^94 - 26 * q^95 - 56 * q^96 - 66 * q^97 + 30 * q^98 - 60 * q^99

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