LMFDB - Embedded newform 845.2.t.e.657.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.188"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [20,-6,-2,6,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			657.1
Root			$-2.25081i$ of defining polynomial
Character	$\chi$	$=$	845.657
Dual form			845.2.t.e.418.1

$q$-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} +(0.514229 + 1.91913i) q^{3} +(1.53307 + 2.65535i) q^{4} +(-0.247944 + 2.22228i) q^{5} +(1.15743 - 4.31958i) q^{6} +(-0.638592 - 1.10607i) q^{7} -2.39966i q^{8} +(-0.820542 + 0.473740i) q^{9} +(2.98427 - 4.05275i) q^{10} +(-1.41373 - 5.27612i) q^{11} +(-4.30760 + 4.30760i) q^{12} +2.87469i q^{14} +(-4.39234 + 0.666923i) q^{15} +(0.365551 - 0.633152i) q^{16} +(-3.11179 - 0.833802i) q^{17} +2.13259 q^{18} +(-1.17707 - 0.315395i) q^{19} +(-6.28104 + 2.74852i) q^{20} +(1.79431 - 1.79431i) q^{21} +(-3.18204 + 11.8755i) q^{22} +(-0.160006 + 0.0428736i) q^{23} +(4.60524 - 1.23397i) 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} +(9.31234 + 3.64315i) 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} +(2.61634 - 1.14488i) 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} +(0.483595 - 0.129579i) q^{41} +(-5.51690 + 1.47825i) q^{42} +(1.72444 - 6.43569i) q^{43} +(11.8426 - 11.8426i) q^{44} +(-0.849334 - 1.94093i) q^{45} +(0.360144 + 0.0965002i) q^{46} -3.20027 q^{47} +(1.40308 + 0.375953i) q^{48} +(2.68440 - 4.64952i) q^{49} +(8.26642 + 7.63673i) q^{50} -6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-2.37565 - 8.86603i) q^{54} +(12.0755 - 1.83353i) q^{55} +(-2.65420 + 1.53240i) q^{56} -2.42113i q^{57} +(10.9297 + 18.9308i) q^{58} +(0.000595178 - 0.00222123i) q^{59} +(-8.50465 - 10.6407i) q^{60} +(-0.695993 - 1.20550i) q^{61} +(0.192209 + 0.717332i) q^{62} +(1.04798 + 0.605053i) q^{63} +13.0440 q^{64} -24.4270 q^{66} +(5.26055 + 3.03718i) q^{67} +(-2.55655 - 9.54117i) q^{68} +(-0.164560 - 0.285026i) q^{69} +(-6.38837 - 0.712764i) q^{70} +(3.14648 - 11.7428i) q^{71} +(1.13681 + 1.96902i) q^{72} +7.34614i q^{73} +(-2.57620 + 1.48737i) q^{74} +(-0.393034 - 9.92635i) q^{75} +(-0.967044 - 3.60906i) q^{76} +(-4.93298 + 4.93298i) q^{77} -11.1774i q^{79} +(1.31640 + 0.969342i) q^{80} +(-5.47236 + 9.47841i) q^{81} +(-1.08848 - 0.291657i) q^{82} -2.65539 q^{83} +(7.51533 + 2.01373i) q^{84} +(2.62449 - 6.70854i) q^{85} +(-10.6041 + 10.6041i) q^{86} +(4.99409 - 18.6382i) q^{87} +(-12.6609 + 3.39247i) q^{88} +(-6.96542 + 1.86638i) 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} +(0.992745 - 2.53758i) 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} - 4 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{10} - 8 q^{11} - 24 q^{12} + 8 q^{15} - 2 q^{16} + 10 q^{17} - 16 q^{19} - 12 q^{20} - 4 q^{21} + 16 q^{22} + 2 q^{23} + 28 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 4 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^10 - 8 * q^11 - 24 * q^12 + 8 * q^15 - 2 * q^16 + 10 * q^17 - 16 * q^19 - 12 * q^20 - 4 * q^21 + 16 * q^22 + 2 * q^23 + 28 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 14 * q^30 + 48 * q^32 + 18 * q^33 - 2 * q^34 - 20 * q^35 - 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 28 * q^41 - 56 * q^42 + 22 * q^43 + 36 * q^44 - 6 * q^45 + 8 * q^46 + 40 * q^47 + 28 * q^48 + 18 * q^49 + 78 * q^50 - 10 * q^53 - 12 * q^54 + 26 * q^55 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 40 * q^62 - 36 * q^63 + 20 * q^64 - 32 * q^66 + 18 * q^67 + 28 * q^68 - 16 * q^69 + 12 * q^70 - 56 * q^71 - 4 * q^72 - 18 * q^74 + 34 * q^75 - 80 * q^76 - 28 * q^77 + 110 * q^80 - 14 * q^81 - 22 * q^82 - 48 * q^83 - 32 * q^84 - 28 * q^85 - 60 * q^86 + 62 * q^87 - 50 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 + 48 * q^94 - 14 * 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.386373	−	0.922342i	$-0.626272\pi$
$2$	−1.94926	−	1.12540i	−1.37833	−	0.795780i	−0.991959	+	0.126562i	$0.959606\pi$
$3$	0.514229	+	1.91913i	0.296890	+	1.10801i	0.939705	+	0.341987i	$0.111100\pi$
$3$	0.514229	+	1.91913i	0.296890	+	1.10801i	−0.642815	+	0.766022i	$0.722233\pi$
$4$	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
$6$	1.15743	−	4.31958i	0.472518	−	1.76346i
$7$	−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
$10$	2.98427	−	4.05275i	0.943708	−	1.28159i
$11$	−1.41373	−	5.27612i	−0.426257	−	1.59081i	−0.761163	−	0.648560i	$-0.775371\pi$
$11$	−1.41373	−	5.27612i	−0.426257	−	1.59081i	0.334907	−	0.942251i	$-0.391295\pi$
$12$	−4.30760	+	4.30760i	−1.24350	+	1.24350i
$13$		0			0
$13$		0			0
$14$			2.87469i			0.768294i
$15$	−4.39234	+	0.666923i	−1.13410	+	0.172199i
$16$	0.365551	−	0.633152i	0.0913876	−	0.158288i
$17$	−3.11179	−	0.833802i	−0.754721	−	0.202227i	−0.139110	−	0.990277i	$-0.544424\pi$
$17$	−3.11179	−	0.833802i	−0.754721	−	0.202227i	−0.615611	+	0.788050i	$0.711091\pi$
$18$	2.13259			0.502657
$19$	−1.17707	−	0.315395i	−0.270039	−	0.0723567i	0.121259	−	0.992621i	$-0.461307\pi$
$19$	−1.17707	−	0.315395i	−0.270039	−	0.0723567i	−0.391297	+	0.920264i	$0.627974\pi$
$20$	−6.28104	+	2.74852i	−1.40448	+	0.614588i
$21$	1.79431	−	1.79431i	0.391551	−	0.391551i
$22$	−3.18204	+	11.8755i	−0.678413	+	2.53187i
$23$	−0.160006	+	0.0428736i	−0.0333637	+	0.00893976i	−0.275462	−	0.961312i	$-0.588831\pi$
$23$	−0.160006	+	0.0428736i	−0.0333637	+	0.00893976i	0.242099	+	0.970252i	$0.422164\pi$
$24$	4.60524	−	1.23397i	0.940042	−	0.251883i
$25$	−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	$-0.975639\pi$
$29$	−8.41068	−	4.85591i	−1.56182	−	0.901719i	−0.564751	−	0.825262i	$-0.691028\pi$
$30$	9.31234	+	3.64315i	1.70019	+	0.665145i
$31$	−0.233305	−	0.233305i	−0.0419027	−	0.0419027i	0.685845	−	0.727748i	$-0.259433\pi$
$31$	−0.233305	−	0.233305i	−0.0419027	−	0.0419027i	−0.727748	+	0.685845i	$0.759433\pi$
$32$	−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
$35$	2.61634	−	1.14488i	0.442242	−	0.193521i
$36$	−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
$41$	0.483595	−	0.129579i	0.0755249	−	0.0202368i	−0.220859	−	0.975306i	$-0.570886\pi$
$41$	0.483595	−	0.129579i	0.0755249	−	0.0202368i	0.296384	+	0.955069i	$0.404219\pi$
$42$	−5.51690	+	1.47825i	−0.851277	+	0.228099i
$43$	1.72444	−	6.43569i	0.262974	−	0.981434i	−0.700504	−	0.713648i	$-0.747041\pi$
$43$	1.72444	−	6.43569i	0.262974	−	0.981434i	0.963479	−	0.267786i	$-0.0862919\pi$
$44$	11.8426	−	11.8426i	1.78534	−	1.78534i
$45$	−0.849334	−	1.94093i	−0.126611	−	0.289337i
$46$	0.360144	+	0.0965002i	0.0531003	+	0.0142282i
$47$	−3.20027			−0.466808			−0.233404	−	0.972380i	$-0.574986\pi$
$47$	−3.20027			−0.466808			−0.233404	+	0.972380i	$0.574986\pi$
$48$	1.40308	+	0.375953i	0.202517	+	0.0542642i
$49$	2.68440	−	4.64952i	0.383486	−	0.664217i
$50$	8.26642	+	7.63673i	1.16905	+	1.08000i
$51$		−	6.40069i		−	0.896276i
$52$		0			0
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	−0.327086	−	0.944995i	$-0.606067\pi$
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	0.944995	+	0.327086i	$0.106067\pi$
$54$	−2.37565	−	8.86603i	−0.323285	−	1.20651i
$55$	12.0755	−	1.83353i	1.62827	−	0.247232i
$56$	−2.65420	+	1.53240i	−0.354682	+	0.204776i
$57$		−	2.42113i		−	0.320687i
$58$	10.9297	+	18.9308i	1.43514	+	2.48574i
$59$	0.000595178	−	0.00222123i	7.74855e−5	−	0.000289180i	−0.965887	−	0.258964i	$-0.916619\pi$
$59$	0.000595178	−	0.00222123i	7.74855e−5	−	0.000289180i	0.965965	+	0.258674i	$0.0832857\pi$
$60$	−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	$0.861736\pi$
$62$	0.192209	+	0.717332i	0.0244105	+	0.0911013i
$63$	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	0.785645	−	0.618677i	$-0.212331\pi$
$67$	5.26055	+	3.03718i	0.642678	+	0.371050i	−0.142967	+	0.989727i	$0.545664\pi$
$68$	−2.55655	−	9.54117i	−0.310027	−	1.15704i
$69$	−0.164560	−	0.285026i	−0.0198107	−	0.0343131i
$70$	−6.38837	−	0.712764i	−0.763557	−	0.0851916i
$71$	3.14648	−	11.7428i	0.373418	−	1.39361i	−0.482225	−	0.876048i	$-0.660171\pi$
$71$	3.14648	−	11.7428i	0.373418	−	1.39361i	0.855643	−	0.517567i	$-0.173162\pi$
$72$	1.13681	+	1.96902i	0.133975	+	0.232051i
$73$			7.34614i			0.859801i	0.902876	+	0.429901i	$0.141451\pi$
$73$			7.34614i			0.859801i	−0.902876	+	0.429901i	$0.858549\pi$
$74$	−2.57620	+	1.48737i	−0.299477	+	0.172903i
$75$	−0.393034	−	9.92635i	−0.0453837	−	1.14620i
$76$	−0.967044	−	3.60906i	−0.110928	−	0.413987i
$77$	−4.93298	+	4.93298i	−0.562166	+	0.562166i
$78$		0			0
$79$		−	11.1774i		−	1.25756i	−0.777584	−	0.628779i	$-0.783555\pi$
$79$		−	11.1774i		−	1.25756i	0.777584	−	0.628779i	$-0.216445\pi$
$80$	1.31640	+	0.969342i	0.147178	+	0.108376i
$81$	−5.47236	+	9.47841i	−0.608040	+	1.05316i
$82$	−1.08848	−	0.291657i	−0.120202	−	0.0322081i
$83$	−2.65539			−0.291467			−0.145733	−	0.989324i	$-0.546554\pi$
$83$	−2.65539			−0.291467			−0.145733	+	0.989324i	$0.546554\pi$
$84$	7.51533	+	2.01373i	0.819990	+	0.219716i
$85$	2.62449	−	6.70854i	0.284666	−	0.727643i
$86$	−10.6041	+	10.6041i	−1.14347	+	1.14347i
$87$	4.99409	−	18.6382i	0.535423	−	1.99823i
$88$	−12.6609	+	3.39247i	−1.34965	+	0.361639i
$89$	−6.96542	+	1.86638i	−0.738333	+	0.197836i	−0.608337	−	0.793679i	$-0.708163\pi$
$89$	−6.96542	+	1.86638i	−0.738333	+	0.197836i	−0.129996	+	0.991515i	$0.541496\pi$
$90$	−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
$95$	0.992745	−	2.53758i	0.101853	−	0.260350i
$96$	−9.05440	−	9.05440i	−0.924111	−	0.924111i
$97$	−3.62059	+	2.09035i	−0.367616	+	0.212243i	−0.672416	−	0.740173i	$-0.734743\pi$
$97$	−3.62059	+	2.09035i	−0.367616	+	0.212243i	0.304801	+	0.952416i	$0.401410\pi$
$98$	−10.4652	+	6.04207i	−1.05714	+	0.610341i
$99$	3.65954	+	3.65954i	0.367797	+	0.367797i
$100$	−4.55063	−	14.6397i	−0.455063	−	1.46397i
$101$	7.47319	+	4.31465i	0.743610	+	0.429323i	0.823380	−	0.567490i	$-0.192085\pi$
$101$	7.47319	+	4.31465i	0.743610	+	0.429323i	−0.0797704	+	0.996813i	$0.525419\pi$
$102$	−7.20336	+	12.4766i	−0.713239	+	1.23537i
$103$	1.07603	+	1.07603i	0.106025	+	0.106025i	0.758129	−	0.652104i	$-0.226114\pi$
$103$	1.07603	+	1.07603i	0.106025	+	0.106025i	−0.652104	+	0.758129i	$0.726114\pi$
$104$		0			0
$105$	3.54258	+	4.43236i	0.345720	+	0.432554i
$106$	−13.8312	+	3.70606i	−1.34340	+	0.359964i
$107$	−14.0309	+	3.75956i	−1.35642	+	0.363451i	−0.862499	−	0.506058i	$-0.831102\pi$
$107$	−14.0309	+	3.75956i	−1.35642	+	0.363451i	−0.493917	+	0.869509i	$0.664435\pi$
$108$	−3.23619	+	12.0776i	−0.311403	+	1.16217i
$109$	4.72405	−	4.72405i	0.452481	−	0.452481i	−0.443696	−	0.896177i	$-0.646333\pi$
$109$	4.72405	−	4.72405i	0.452481	−	0.452481i	0.896177	+	0.443696i	$0.146333\pi$
$110$	−25.6018	−	10.0159i	−2.44103	−	0.954974i
$111$	2.53638	+	0.679621i	0.240743	+	0.0645068i
$112$	−0.933751			−0.0882311
$113$	−11.0065	−	2.94919i	−1.03541	−	0.277437i	−0.299199	−	0.954191i	$-0.596719\pi$
$113$	−11.0065	−	2.94919i	−1.03541	−	0.277437i	−0.736209	+	0.676754i	$0.763386\pi$
$114$	−2.72475	+	4.71941i	−0.255197	+	0.442013i
$115$	−0.0556044	−	0.366209i	−0.00518514	−	0.0341492i
$116$		−	29.7777i		−	2.76479i
$117$		0			0
$118$	−0.00365994	+	0.00365994i	−0.000336925	+	0.000336925i
$119$	1.06492	+	3.97433i	0.0976210	+	0.364326i
$120$	1.60039	+	10.5401i	0.146094	+	0.962175i
$121$	−16.3126	+	9.41807i	−1.48296	+	0.856188i
$122$			3.13309i			0.283657i
$123$	0.497357	+	0.861447i	0.0448452	+	0.0776741i
$124$	0.261833	−	0.977176i	0.0235133	−	0.0877530i
$125$	3.65819	−	10.5649i	0.327199	−	0.944956i
$126$	−1.36186	−	2.35881i	−0.121324	−	0.210139i
$127$	0.135757	+	0.506651i	0.0120465	+	0.0449580i	0.971687	−	0.236270i	$-0.0759250\pi$
$127$	0.135757	+	0.506651i	0.0120465	+	0.0449580i	−0.959641	+	0.281228i	$0.909258\pi$
$128$	−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
$133$	0.402818	+	1.50334i	0.0349287	+	0.130356i
$134$	−6.83610	−	11.8405i	−0.590549	−	1.02286i
$135$	−7.12309	+	5.69316i	−0.613058	+	0.489989i
$136$	−2.00084	+	7.46723i	−0.171571	+	0.640310i
$137$	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	−0.444725	−	0.895667i	$-0.646699\pi$
$139$	1.28017	−	0.739106i	0.108583	−	0.0626902i	0.553308	+	0.832977i	$0.313365\pi$
$140$	7.05109	+	5.19211i	0.595926	+	0.438813i
$141$	−1.64567	−	6.14173i	−0.138591	−	0.517227i
$142$	−19.3487	+	19.3487i	−1.62371	+	1.62371i
$143$		0			0
$144$			0.692704i			0.0577253i
$145$	12.8766	−	17.4869i	1.06934	−	1.45221i
$146$	8.26737	−	14.3195i	0.684213	−	1.18509i
$147$	10.3034	+	2.76079i	0.849811	+	0.227706i
$148$	4.05230			0.333097
$149$	−16.6295	−	4.45586i	−1.36234	−	0.365038i	−0.497665	−	0.867369i	$-0.665809\pi$
$149$	−16.6295	−	4.45586i	−1.36234	−	0.365038i	−0.864675	+	0.502331i	$0.832476\pi$
$150$	−10.4050	+	19.7913i	−0.849567	+	1.61596i
$151$	10.0539	−	10.0539i	0.818178	−	0.818178i	−0.167666	−	0.985844i	$-0.553623\pi$
$151$	10.0539	−	10.0539i	0.818178	−	0.818178i	0.985844	+	0.167666i	$0.0536230\pi$
$152$	−0.756840	+	2.82457i	−0.0613879	+	0.229103i
$153$	2.94836	−	0.790011i	0.238361	−	0.0638686i
$154$	15.1672	−	4.06405i	1.22221	−	0.327491i
$155$	0.576314	−	0.460621i	0.0462907	−	0.0369980i
$156$		0			0
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	0.818996	−	0.573799i	$-0.194531\pi$
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	−0.573799	+	0.818996i	$0.694531\pi$
$158$	−12.5791	+	21.7876i	−1.00074	+	1.73333i
$159$	10.9463	+	6.31986i	0.868100	+	0.501198i
$160$	−5.77728	−	13.2025i	−0.456734	−	1.04375i
$161$	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	−0.154182	−	0.988043i	$-0.549274\pi$
$163$	7.97177	−	4.60251i	0.624398	−	0.360496i	0.778579	+	0.627546i	$0.215941\pi$
$164$	1.08546	+	1.08546i	0.0847602	+	0.0847602i
$165$	9.72836	+	22.2317i	0.757352	+	1.73073i
$166$	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
$171$	1.11525	−	0.298831i	0.0852854	−	0.0228522i
$172$	19.7327	−	5.28736i	1.50460	−	0.403157i
$173$	3.54983	−	13.2481i	0.269888	−	1.00724i	−0.689302	−	0.724474i	$-0.742083\pi$
$173$	3.54983	−	13.2481i	0.269888	−	1.00724i	0.959190	−	0.282762i	$-0.0912508\pi$
$174$	−30.7103	+	30.7103i	−2.32814	+	2.32814i
$175$	1.89555	+	6.09810i	0.143290	+	0.460973i
$176$	−3.85738	−	1.03358i	−0.290761	−	0.0779092i
$177$	0.00456889			0.000343419
$178$	15.6778	+	4.20086i	1.17510	+	0.314867i
$179$	−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	$0.323305\pi$
$180$	3.85177	−	5.23085i	0.287094	−	0.389885i
$181$		−	8.16619i		−	0.606988i	−0.952833	−	0.303494i	$-0.901847\pi$
$181$		−	8.16619i		−	0.606988i	0.952833	−	0.303494i	$-0.0981533\pi$
$182$		0			0
$183$	1.95560	−	1.95560i	0.144562	−	0.144562i
$184$	0.102882	+	0.383960i	0.00758455	+	0.0283059i
$185$	2.37970	+	1.75231i	0.174959	+	0.128832i
$186$	−1.27781	+	0.737745i	−0.0936937	+	0.0540941i
$187$			17.5970i			1.28682i
$188$	−4.90623	−	8.49784i	−0.357824	−	0.619769i
$189$	1.34802	−	5.03089i	0.0980542	−	0.365943i
$190$	−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	$0.654106\pi$
$192$	6.70758	+	25.0330i	0.484078	+	1.80660i
$193$	13.0743	+	7.54845i	0.941109	+	0.543349i	0.890308	−	0.455359i	$-0.150489\pi$
$193$	13.0743	+	7.54845i	0.941109	+	0.543349i	0.0508011	+	0.998709i	$0.483823\pi$
$194$	9.40995			0.675595
$195$		0			0
$196$	16.4614			1.17582
$197$	−13.3121	−	7.68576i	−0.948450	−	0.547588i	−0.0558510	−	0.998439i	$-0.517787\pi$
$197$	−13.3121	−	7.68576i	−0.948450	−	0.547588i	−0.892599	+	0.450851i	$0.851121\pi$
$198$	−3.01492	−	11.2518i	−0.214261	−	0.799633i
$199$	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
$201$	−3.12361	+	11.6575i	−0.220322	+	0.822254i
$202$	−9.71144	−	16.8207i	−0.683294	−	1.18350i
$203$			12.4038i			0.870574i
$204$	16.9961	−	9.81268i	1.18996	−	0.687025i
$205$	0.168056	+	1.10681i	0.0117375	+	0.0773031i
$206$	−0.886492	−	3.30843i	−0.0617648	−	0.230509i
$207$	0.110981	−	0.110981i	0.00771372	−	0.00771372i
$208$		0			0
$209$			6.65626i			0.460423i
$210$	−1.91720	−	12.6266i	−0.132299	−	0.871320i
$211$	−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	$0.201622\pi$
$212$	18.8414	+	5.04852i	1.29403	+	0.346734i
$213$	24.1539			1.65500
$214$	31.5808	+	8.46205i	2.15882	+	0.578454i
$215$	13.8743	+	5.42788i	0.946222	+	0.370178i
$216$	6.91961	−	6.91961i	0.470820	−	0.470820i
$217$	−0.109066	+	0.407038i	−0.00740386	+	0.0276316i
$218$	−14.5248	+	3.89192i	−0.983746	+	0.263594i
$219$	−14.0982	+	3.77760i	−0.952667	+	0.255266i
$220$	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
$225$	4.52388	−	1.40621i	0.301592	−	0.0937475i
$226$	18.1355	+	18.1355i	1.20636	+	1.20636i
$227$	23.9600	−	13.8333i	1.59028	−	0.918149i	0.597022	−	0.802225i	$-0.296350\pi$
$227$	23.9600	−	13.8333i	1.59028	−	0.918149i	0.993258	−	0.115924i	$-0.0369830\pi$
$228$	6.42896	−	3.71176i	0.425768	−	0.245817i
$229$	−12.9000	−	12.9000i	−0.852455	−	0.852455i	0.137980	−	0.990435i	$-0.455939\pi$
$229$	−12.9000	−	12.9000i	−0.852455	−	0.852455i	−0.990435	+	0.137980i	$0.955939\pi$
$230$	−0.303746	+	0.776413i	−0.0200284	+	0.0511952i
$231$	−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	−0.997246	−	0.0741712i	$-0.976369\pi$
$233$	−16.3545	−	16.3545i	−1.07142	−	1.07142i	−0.0741712	−	0.997246i	$-0.523631\pi$
$234$		0			0
$235$	0.793489	−	7.11190i	0.0517615	−	0.463929i
$236$	0.00681059	−	0.00182489i	0.000443332	−	0.000118790i
$237$	21.4509	−	5.74774i	1.39338	−	0.373356i
$238$	2.39693	−	8.94546i	0.155370	−	0.579848i
$239$	2.61794	−	2.61794i	0.169341	−	0.169341i	−0.617349	−	0.786690i	$-0.711793\pi$
$239$	2.61794	−	2.61794i	0.169341	−	0.169341i	0.786690	+	0.617349i	$0.211793\pi$
$240$	−1.18336	+	3.02481i	−0.0763854	+	0.195251i
$241$	20.1013	+	5.38613i	1.29484	+	0.346951i	0.839496	−	0.543365i	$-0.182850\pi$
$241$	20.1013	+	5.38613i	1.29484	+	0.346951i	0.455343	+	0.890316i	$0.349517\pi$
$242$	42.3965			2.72535
$243$	−9.18717	−	2.46169i	−0.589357	−	0.157918i
$244$	2.13401	−	3.69621i	0.136616	−	0.236625i
$245$	9.66694	+	7.11831i	0.617598	+	0.454772i
$246$		−	2.23891i		−	0.142748i
$247$		0			0
$248$	−0.559851	+	0.559851i	−0.0355505	+	0.0355505i
$249$	−1.36548	−	5.09603i	−0.0865336	−	0.322948i
$250$	−19.0206	+	16.4768i	−1.20297	+	1.04208i
$251$	2.05050	−	1.18386i	0.129427	−	0.0747245i	−0.433889	−	0.900966i	$-0.642859\pi$
$251$	2.05050	−	1.18386i	0.129427	−	0.0747245i	0.563315	+	0.826242i	$0.309526\pi$
$252$			3.71034i			0.233730i
$253$	0.452413	+	0.783602i	0.0284430	+	0.0492647i
$254$	0.305562	−	1.14037i	0.0191727	−	0.0715533i
$255$	14.2241	+	1.58701i	0.890749	+	0.0993827i
$256$	5.49109	+	9.51085i	0.343193	+	0.594428i
$257$	−0.225182	−	0.840391i	−0.0140465	−	0.0524221i	0.958547	−	0.284935i	$-0.0919720\pi$
$257$	−0.225182	−	0.840391i	−0.0140465	−	0.0524221i	−0.972593	+	0.232513i	$0.925305\pi$
$258$	−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
$263$	−3.93099	−	14.6707i	−0.242395	−	0.904632i	−0.974675	−	0.223627i	$-0.928210\pi$
$263$	−3.93099	−	14.6707i	−0.242395	−	0.904632i	0.732279	−	0.681004i	$-0.238457\pi$
$264$	−13.0212	−	22.5533i	−0.801398	−	1.38806i
$265$	8.88144	+	11.1122i	0.545582	+	0.682615i
$266$	0.906665	−	3.38372i	0.0555912	−	0.207469i
$267$	−7.16363	−	12.4078i	−0.438407	−	0.759343i
$268$			18.6248i			1.13769i
$269$	−21.1150	+	12.1908i	−1.28741	+	0.743285i	−0.978191	−	0.207707i	$-0.933400\pi$
$269$	−21.1150	+	12.1908i	−1.28741	+	0.743285i	−0.309216	+	0.950992i	$0.600067\pi$
$270$	20.2918	−	3.08107i	1.23492	−	0.187508i
$271$	−3.39484	−	12.6697i	−0.206222	−	0.769630i	−0.989074	−	0.147422i	$-0.952903\pi$
$271$	−3.39484	−	12.6697i	−0.206222	−	0.769630i	0.782852	−	0.622208i	$-0.213764\pi$
$272$	−1.66544	+	1.66544i	−0.100982	+	0.100982i
$273$		0			0
$274$		−	8.56086i		−	0.517181i
$275$	1.08054	+	27.2898i	0.0651591	+	1.64564i
$276$	0.504562	−	0.873927i	0.0303711	−	0.0526042i
$277$	−11.8109	−	3.16472i	−0.709647	−	0.190149i	−0.114099	−	0.993469i	$-0.536398\pi$
$277$	−11.8109	−	3.16472i	−0.709647	−	0.190149i	−0.595548	+	0.803320i	$0.703065\pi$
$278$	−3.32717			−0.199550
$279$	0.301962	+	0.0809104i	0.0180780	+	0.00484398i
$280$	−2.74733	−	6.27831i	−0.164184	−	0.375201i
$281$	6.43529	−	6.43529i	0.383897	−	0.383897i	−0.488607	−	0.872504i	$-0.662495\pi$
$281$	6.43529	−	6.43529i	0.383897	−	0.383897i	0.872504	+	0.488607i	$0.162495\pi$
$282$	−3.70409	+	13.8239i	−0.220575	+	0.823198i
$283$	−26.4212	+	7.07953i	−1.57057	+	0.420834i	−0.935992	−	0.352021i	$-0.885495\pi$
$283$	−26.4212	+	7.07953i	−1.57057	+	0.420834i	−0.634583	+	0.772855i	$0.718828\pi$
$284$	36.0050	−	9.64751i	2.13650	−	0.572474i
$285$	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
$290$	−44.7795	+	19.5951i	−2.62954	+	1.15066i
$291$	−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	−0.984002	−	0.178157i	$-0.942987\pi$
$293$	−22.6241	+	13.0620i	−1.32171	+	0.763092i	−0.337713	+	0.941249i	$0.609653\pi$
$294$	−16.9770	−	16.9770i	−0.990118	−	0.990118i
$295$	0.00478863	+	0.00187339i	0.000278805	+	0.000109073i
$296$	−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
$301$	−8.21957	+	2.20243i	−0.473768	+	0.126946i
$302$	−30.9124	+	8.28296i	−1.77881	+	0.476631i
$303$	−4.43743	+	16.5607i	−0.254924	+	0.951388i
$304$	−0.629972	+	0.629972i	−0.0361314	+	0.0361314i
$305$	2.85151	−	1.24780i	0.163277	−	0.0714485i
$306$	−6.63619	−	1.77816i	−0.379366	−	0.101651i
$307$	−14.7038			−0.839189			−0.419595	−	0.907712i	$-0.637828\pi$
$307$	−14.7038			−0.839189			−0.419595	+	0.907712i	$0.637828\pi$
$308$	−20.6614	−	5.53620i	−1.17729	−	0.315454i
$309$	−1.51172	+	2.61837i	−0.0859985	+	0.148954i
$310$	−1.64177	+	0.249283i	−0.0932462	+	0.0141583i
$311$			31.8525i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$311$			31.8525i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$312$		0			0
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	−0.959438	−	0.281919i	$-0.909029\pi$
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	0.281919	+	0.959438i	$0.409029\pi$
$314$	−2.53112	−	9.44628i	−0.142840	−	0.533084i
$315$	−1.60444	+	2.17889i	−0.0903998	+	0.122767i
$316$	29.6799	−	17.1357i	1.66963	−	0.963959i
$317$		−	15.5627i		−	0.874088i	−0.899440	−	0.437044i	$-0.856025\pi$
$317$		−	15.5627i		−	0.874088i	0.899440	−	0.437044i	$-0.143975\pi$
$318$	−14.2248	−	24.6380i	−0.797686	−	1.38163i
$319$	−13.7299	+	51.2407i	−0.768728	+	2.86893i
$320$	−3.23418	+	28.9874i	−0.180796	+	1.62044i
$321$	−14.4302	−	24.9938i	−0.805413	−	1.39502i
$322$	−0.123249	−	0.459970i	−0.00686837	−	0.0256331i
$323$	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
$328$	−0.310945	−	1.16046i	−0.0171691	−	0.0640758i
$329$	2.04367	+	3.53974i	0.112671	+	0.195152i
$330$	6.05653	−	54.2835i	0.333401	−	2.98821i
$331$	−4.41633	+	16.4820i	−0.242743	+	0.905930i	0.731761	+	0.681561i	$0.238699\pi$
$331$	−4.41633	+	16.4820i	−0.242743	+	0.905930i	−0.974504	+	0.224369i	$0.927968\pi$
$332$	−4.07089	−	7.05098i	−0.223419	−	0.386973i
$333$			1.25222i			0.0686212i
$334$	24.6361	−	14.2237i	1.34803	−	0.778284i
$335$	−8.05378	+	10.9374i	−0.440025	+	0.597571i
$336$	−0.480161	−	1.79199i	−0.0261949	−	0.0977609i
$337$	25.0560	−	25.0560i	1.36489	−	1.36489i	0.497319	−	0.867568i	$-0.334318\pi$
$337$	25.0560	−	25.0560i	1.36489	−	1.36489i	0.867568	−	0.497319i	$-0.165682\pi$
$338$		0			0
$339$		−	22.6395i		−	1.22961i
$340$	21.8370	−	3.31569i	1.18428	−	0.179818i
$341$	−0.901114	+	1.56077i	−0.0487980	+	0.0845207i
$342$	−2.51022	−	0.672610i	−0.135737	−	0.0363706i
$343$	−15.7972			−0.852971
$344$	−15.4435	−	4.13806i	−0.832655	−	0.223109i
$345$	0.674209	−	0.295027i	0.0362982	−	0.0158837i
$346$	−21.8290	+	21.8290i	−1.17354	+	1.17354i
$347$	3.33874	−	12.4604i	0.179233	−	0.668907i	−0.816559	−	0.577262i	$-0.804121\pi$
$347$	3.33874	−	12.4604i	0.179233	−	0.668907i	0.995792	−	0.0916446i	$-0.0292124\pi$
$348$	57.1472	−	15.3125i	3.06341	−	0.820838i
$349$	−25.9362	+	6.94957i	−1.38833	+	0.372002i	−0.874140	−	0.485674i	$-0.838574\pi$
$349$	−25.9362	+	6.94957i	−1.38833	+	0.372002i	−0.514191	+	0.857676i	$0.671908\pi$
$350$	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
$355$	25.3156	+	9.90391i	1.34361	+	0.525645i
$356$	−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	0.422344	−	0.906435i	$-0.361207\pi$
$359$	−9.17222	−	9.17222i	−0.484091	−	0.484091i	−0.906435	+	0.422344i	$0.861207\pi$
$360$	−4.65757	+	2.03811i	−0.245476	+	0.107418i
$361$	−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
$366$	−6.01280	+	1.61113i	−0.314294	+	0.0842149i
$367$	−14.3602	+	3.84780i	−0.749595	+	0.200853i	−0.613338	−	0.789820i	$-0.710174\pi$
$367$	−14.3602	+	3.84780i	−0.749595	+	0.200853i	−0.136256	+	0.990674i	$0.543507\pi$
$368$	−0.0313449	+	0.116981i	−0.00163397	+	0.00609805i
$369$	−0.335423	+	0.335423i	−0.0174614	+	0.0174614i
$370$	−2.66660	−	6.09382i	−0.138630	−	0.316803i
$371$	−7.84829	−	2.10294i	−0.407463	−	0.109179i
$372$	2.00997			0.104212
$373$	−5.97055	−	1.59980i	−0.309144	−	0.0828348i	0.100912	−	0.994895i	$-0.467824\pi$
$373$	−5.97055	−	1.59980i	−0.309144	−	0.0828348i	−0.410055	+	0.912061i	$0.634491\pi$
$374$	19.8037	−	34.3010i	1.02403	−	1.77366i
$375$	22.1566	+	1.58775i	1.14416	+	0.0819911i
$376$			7.67955i			0.396043i
$377$		0			0
$378$	−8.28942	+	8.28942i	−0.426362	+	0.426362i
$379$	4.72834	+	17.6464i	0.242878	+	0.906435i	0.974438	+	0.224657i	$0.0721262\pi$
$379$	4.72834	+	17.6464i	0.242878	+	0.906435i	−0.731559	+	0.681778i	$0.761207\pi$
$380$	8.26010	−	1.25420i	0.423734	−	0.0643389i
$381$	−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	$0.749048\pi$
$384$	8.46920	−	31.6075i	0.432192	−	1.61296i
$385$	−9.73936	−	12.1856i	−0.496364	−	0.621034i
$386$	−16.9901	−	29.4277i	−0.864774	−	1.49783i
$387$	1.63387	+	6.09769i	0.0830543	+	0.309963i
$388$	−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
$393$	2.62196	+	9.78529i	0.132260	+	0.493603i
$394$	17.2992	+	29.9630i	0.871519	+	1.50952i
$395$	24.8393	+	2.77138i	1.24980	+	0.139443i
$396$	−4.10703	+	15.3277i	−0.206386	+	0.770244i
$397$	−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
$400$	−2.48054	+	2.68508i	−0.124027	+	0.134254i
$401$	1.05497	+	3.93721i	0.0526828	+	0.196615i	0.987252	−	0.159168i	$-0.0508811\pi$
$401$	1.05497	+	3.93721i	0.0526828	+	0.196615i	−0.934569	+	0.355783i	$0.884214\pi$
$402$	19.2081	−	19.2081i	0.958011	−	0.958011i
$403$		0			0
$404$			26.4586i			1.31636i
$405$	−19.7068	−	14.5112i	−0.979240	−	0.721069i
$406$	13.9592	−	24.1781i	0.692786	−	1.19994i
$407$	−6.97310	−	1.86844i	−0.345644	−	0.0926149i
$408$	−15.3595			−0.760406
$409$	−6.70266	−	1.79597i	−0.331425	−	0.0888051i	0.0892692	−	0.996008i	$-0.471547\pi$
$409$	−6.70266	−	1.79597i	−0.331425	−	0.0888051i	−0.420694	+	0.907202i	$0.638214\pi$
$410$	0.918026	−	2.34659i	0.0453381	−	0.115890i
$411$	−5.34348	+	5.34348i	−0.263574	+	0.263574i
$412$	−1.20761	+	4.50687i	−0.0594948	+	0.222037i
$413$	−0.00283692		0.000760151i	−0.000139596		3.74046e-5i
$414$	−0.341229	+	0.0914320i	−0.0167705	+	0.00449364i
$415$	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	0.876599	−	0.481222i	$-0.159807\pi$
$419$	18.3846	+	10.6144i	0.898147	+	0.518546i	0.0215487	+	0.999768i	$0.493140\pi$
$420$	−6.33844	+	16.2019i	−0.309284	+	0.790570i
$421$	3.15727	+	3.15727i	0.153876	+	0.153876i	0.779847	−	0.625971i	$-0.215297\pi$
$421$	3.15727	+	3.15727i	0.153876	+	0.153876i	−0.625971	+	0.779847i	$0.715297\pi$
$422$	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
$425$	14.2575	+	7.49570i	0.691591	+	0.363595i
$426$	−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
$431$	34.6226	−	9.27711i	1.66771	−	0.446863i	0.703221	−	0.710971i	$-0.251744\pi$
$431$	34.6226	−	9.27711i	1.66771	−	0.446863i	0.964493	+	0.264109i	$0.0850777\pi$
$432$	2.87984	−	0.771651i	0.138556	−	0.0371261i
$433$	−2.09465	+	7.81733i	−0.100662	+	0.375677i	−0.997817	−	0.0660397i	$-0.978964\pi$
$433$	−2.09465	+	7.81733i	−0.100662	+	0.375677i	0.897155	+	0.441716i	$0.145630\pi$
$434$	0.670679	−	0.670679i	0.0321936	−	0.0321936i
$435$	40.1810	+	15.7195i	1.92653	+	0.753692i
$436$	19.7863	+	5.30171i	0.947590	+	0.253906i
$437$	0.201861			0.00965633
$438$	31.7323	+	8.50264i	1.51623	+	0.406272i
$439$	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	$-0.0731399\pi$
$440$	−4.39983	−	28.9772i	−0.209754	−	1.38143i
$441$			5.08683i			0.242230i
$442$		0			0
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	−0.985412	−	0.170184i	$-0.945564\pi$
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	0.170184	+	0.985412i	$0.445564\pi$
$444$	2.08381	+	7.77688i	0.0988931	+	0.369074i
$445$	−2.42058	−	15.9419i	−0.114746	−	0.755716i
$446$	23.1523	−	13.3670i	1.09629	−	0.632944i
$447$		−	34.2054i		−	1.61786i
$448$	−8.32978	−	14.4276i	−0.393545	−	0.681640i
$449$	2.37239	−	8.85389i	0.111960	−	0.417841i	−0.887081	−	0.461613i	$-0.847271\pi$
$449$	2.37239	−	8.85389i	0.111960	−	0.417841i	0.999042	+	0.0437720i	$0.0139375\pi$
$450$	−10.4008	−	2.35012i	−0.490297	−	0.110786i
$451$	−1.36735	−	2.36832i	−0.0643860	−	0.111520i
$452$	−9.04261	−	33.7475i	−0.425329	−	1.58735i
$453$	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	−0.00276341	−	0.999996i	$-0.500880\pi$
$457$	−18.6021	−	10.7399i	−0.870167	−	0.502391i	−0.867404	+	0.497605i	$0.834213\pi$
$458$	10.6277	+	39.6631i	0.496599	+	1.85333i
$459$	−6.56877	−	11.3775i	−0.306604	−	0.531054i
$460$	0.887168	−	0.709072i	0.0413644	−	0.0330607i
$461$	−1.31453	+	4.90591i	−0.0612240	+	0.228491i	−0.989758	−	0.142757i	$-0.954403\pi$
$461$	−1.31453	+	4.90591i	−0.0612240	+	0.228491i	0.928534	+	0.371248i	$0.121070\pi$
$462$	15.5989	+	27.0180i	0.725725	+	1.25699i
$463$		−	20.0793i		−	0.933163i	−0.884478	−	0.466581i	$-0.845485\pi$
$463$		−	20.0793i		−	0.933163i	0.884478	−	0.466581i	$-0.154515\pi$
$464$	−6.14905	+	3.55016i	−0.285463	+	0.164812i
$465$	1.18035	+	0.869156i	0.0547373	+	0.0403061i
$466$	13.4737	+	50.2844i	0.624156	+	2.32938i
$467$	−21.4507	+	21.4507i	−0.992618	+	0.992618i	−0.999973	−	0.00735447i	$-0.997659\pi$
$467$	−21.4507	+	21.4507i	−0.992618	+	0.992618i	0.00735447	+	0.999973i	$0.497659\pi$
$468$		0			0
$469$		−	7.75807i		−	0.358234i
$470$	−9.55047	+	12.9699i	−0.440530	+	0.598258i
$471$	−4.31627	+	7.47600i	−0.198883	+	0.344476i
$472$	−0.00533020	−	0.00142822i	−0.000245342	−	6.57392e-5i
$473$	−36.3934			−1.67337
$474$	−48.2818	−	12.9371i	−2.21766	−	0.594219i
$475$	5.39307	+	2.83533i	0.247451	+	0.130094i
$476$	−8.92064	+	8.92064i	−0.408877	+	0.408877i
$477$	−1.56007	+	5.82226i	−0.0714306	+	0.266583i
$478$	−8.04928	+	2.15680i	−0.368166	+	0.0986497i
$479$	30.0497	−	8.05179i	1.37300	−	0.367896i	0.504430	−	0.863453i	$-0.331703\pi$
$479$	30.0497	−	8.05179i	1.37300	−	0.367896i	0.868575	+	0.495557i	$0.165036\pi$
$480$	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
$485$	−3.74764	−	8.56426i	−0.170171	−	0.388883i
$486$	15.1377	+	15.1377i	0.686662	+	0.686662i
$487$	−16.8282	+	9.71579i	−0.762560	+	0.440264i	−0.830214	−	0.557445i	$-0.811782\pi$
$487$	−16.8282	+	9.71579i	−0.762560	+	0.440264i	0.0676540	+	0.997709i	$0.478449\pi$
$488$	−2.89277	+	1.67014i	−0.130950	+	0.0756039i
$489$	12.9321	+	12.9321i	0.584810	+	0.584810i
$490$	−10.8324	−	24.7546i	−0.489357	−	1.11830i
$491$	30.5824	+	17.6568i	1.38017	+	0.796839i	0.992179	−	0.124825i	$-0.0398371\pi$
$491$	30.5824	+	17.6568i	1.38017	+	0.796839i	0.387987	+	0.921665i	$0.373170\pi$
$492$	−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
$496$	−0.233002	+	0.0624327i	−0.0104621	+	0.00280331i
$497$	−14.9977	+	4.01863i	−0.672740	+	0.180260i
$498$	−3.07343	+	11.4702i	−0.137723	+	0.513991i
$499$	9.44430	−	9.44430i	0.422785	−	0.422785i	−0.463377	−	0.886161i	$-0.653362\pi$
$499$	9.44430	−	9.44430i	0.422785	−	0.422785i	0.886161	+	0.463377i	$0.153362\pi$
$500$	33.6618	−	6.48295i	1.50540	−	0.289926i
$501$	−24.2553	−	6.49919i	−1.08365	−	0.290363i
$502$	−5.32928			−0.237857
$503$	23.3052	+	6.24460i	1.03913	+	0.278433i	0.737751	−	0.675073i	$-0.235888\pi$
$503$	23.3052	+	6.24460i	1.03913	+	0.278433i	0.301375	+	0.953506i	$0.402554\pi$
$504$	1.45192	−	2.51480i	0.0646736	−	0.112018i
$505$	−11.4413	+	15.5377i	−0.509130	+	0.691419i
$506$		−	2.03659i		−	0.0905374i
$507$		0			0
$508$	−1.13721	+	1.13721i	−0.0504555	+	0.0504555i
$509$	0.963376	+	3.59537i	0.0427009	+	0.159362i	0.983984	−	0.178256i	$-0.0570455\pi$
$509$	0.963376	+	3.59537i	0.0427009	+	0.159362i	−0.941283	+	0.337618i	$0.890379\pi$
$510$	−25.9404	−	19.1014i	−1.14866	−	0.845823i
$511$	8.12538	−	4.69119i	0.359446	−	0.207526i
$512$			8.22064i			0.363304i
$513$	−2.48471	−	4.30365i	−0.109703	−	0.190011i
$514$	−0.506841	+	1.89156i	−0.0223558	+	0.0834330i
$515$	−2.65804	+	2.12445i	−0.117127	+	0.0936144i
$516$	20.2942	+	35.1506i	0.893403	+	1.54742i
$517$	4.52433	+	16.8850i	0.198980	+	0.742603i
$518$	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
$523$	0.295439	+	1.10259i	0.0129187	+	0.0482131i	0.972084	−	0.234632i	$-0.0753885\pi$
$523$	0.295439	+	1.10259i	0.0129187	+	0.0482131i	−0.959166	+	0.282845i	$0.908722\pi$
$524$	7.81683	+	13.5392i	0.341480	+	0.591461i
$525$	−10.7283	+	6.77362i	−0.468221	+	0.295625i
$526$	−8.84790	+	33.0208i	−0.385787	+	1.43978i
$527$	0.531466	+	0.920525i	0.0231510	+	0.0400987i
$528$		−	7.93430i		−	0.345296i
$529$	−19.8948	+	11.4863i	−0.864992	+	0.499403i
$530$	−4.80653	−	31.6557i	−0.208782	−	1.37503i
$531$	0.000563919		0.00210457i	2.44720e−5		9.13307e-5i
$532$	−3.37434	+	3.37434i	−0.146296	+	0.146296i
$533$		0			0
$534$			32.2479i			1.39550i
$535$	−4.87592	−	32.1127i	−0.210804	−	1.38835i
$536$	7.28818	−	12.6235i	0.314801	−	0.545252i
$537$	−24.2626	−	6.50114i	−1.04701	−	0.280545i
$538$	54.8782			2.36597
$539$	−28.3265	−	7.59005i	−1.22011	−	0.326927i
$540$	−26.0375	−	10.1863i	−1.12047	−	0.438349i
$541$	−22.3573	+	22.3573i	−0.961218	+	0.961218i	−0.999276	−	0.0380580i	$-0.987883\pi$
$541$	−22.3573	+	22.3573i	−0.961218	+	0.961218i	0.0380580	+	0.999276i	$0.487883\pi$
$542$	−7.64112	+	28.5171i	−0.328214	+	1.22491i
$543$	15.6720	−	4.19929i	0.672548	−	0.180209i
$544$	20.0551	−	5.37376i	0.859857	−	0.230398i
$545$	9.32685	+	11.6694i	0.399518	+	0.499864i
$546$		0			0
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	0.587050	−	0.809550i	$-0.300289\pi$
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	−0.809550	+	0.587050i	$0.800289\pi$
$548$	−5.83096	+	10.0995i	−0.249086	+	0.431430i
$549$	1.14218	+	0.659440i	0.0487472	+	0.0281442i
$550$	28.6058	−	54.4109i	1.21976	−	2.32009i
$551$	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
$555$	−2.13919	+	5.46804i	−0.0908035	+	0.232105i
$556$	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
$561$	−33.7709	+	9.04887i	−1.42581	+	0.382044i
$562$	−19.7863	+	5.30173i	−0.834636	+	0.223640i
$563$	−7.59751	+	28.3543i	−0.320197	+	1.19499i	0.598856	+	0.800856i	$0.295622\pi$
$563$	−7.59751	+	28.3543i	−0.320197	+	1.19499i	−0.919053	+	0.394134i	$0.871045\pi$
$564$	13.7855	−	13.7855i	0.580475	−	0.580475i
$565$	9.28293	−	23.7284i	0.390536	−	0.998259i
$566$	59.4689	+	15.9347i	2.49967	+	0.669783i
$567$	13.9784			0.587039
$568$	−28.1787	−	7.55046i	−1.18235	−	0.316810i
$569$	−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	$0.915016\pi$
$570$	−9.81226	−	7.22531i	−0.410990	−	0.302635i
$571$			33.5525i			1.40413i	0.712113	+	0.702065i	$0.247738\pi$
$571$			33.5525i			1.40413i	−0.712113	+	0.702065i	$0.752262\pi$
$572$		0			0
$573$	−20.7277	+	20.7277i	−0.865910	+	0.865910i
$574$	0.372500	+	1.39019i	0.0155478	+	0.0580253i
$575$	0.827606	−	0.0327691i	0.0345136	−	0.00136656i
$576$	−10.7031	+	6.17945i	−0.445964	+	0.257477i
$577$		−	11.0413i		−	0.459654i	−0.973232	−	0.229827i	$-0.926184\pi$
$577$		−	11.0413i		−	0.459654i	0.973232	−	0.229827i	$-0.0738160\pi$
$578$	7.45188	+	12.9070i	0.309957	+	0.536862i
$579$	−7.76326	+	28.9729i	−0.322630	+	1.20407i
$580$	66.1743	+	7.38321i	2.74774	+	0.306571i
$581$	1.69571	+	2.93706i	0.0703499	+	0.121850i
$582$	4.83886	+	18.0589i	0.200577	+	0.748565i
$583$	−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	0.857335	−	0.514758i	$-0.172118\pi$
$587$	20.3567	+	11.7529i	0.840209	+	0.485095i	−0.0171260	+	0.999853i	$0.505452\pi$
$588$	8.46495	+	31.5916i	0.349089	+	1.30282i
$589$	0.201033	+	0.348199i	0.00828342	+	0.0143473i
$590$	−0.00722594	−	0.00904086i	−0.000297487	−	0.000372206i
$591$	7.90448	−	29.4999i	0.325147	−	1.21346i
$592$	−0.483123	−	0.836794i	−0.0198563	−	0.0343920i
$593$		−	30.6582i		−	1.25898i	−0.777007	−	0.629491i	$-0.783263\pi$
$593$		−	30.6582i		−	1.25898i	0.777007	−	0.629491i	$-0.216737\pi$
$594$	−43.4198	+	25.0684i	−1.78153	+	1.02857i
$595$	−9.09612	+	1.38113i	−0.372904	+	0.0566210i
$596$	−13.6622	−	50.9882i	−0.559627	−	2.08856i
$597$	−16.0948	+	16.0948i	−0.658717	+	0.658717i
$598$		0			0
$599$			7.49378i			0.306188i	0.988212	+	0.153094i	$0.0489237\pi$
$599$			7.49378i			0.306188i	−0.988212	+	0.153094i	$0.951076\pi$
$600$	−23.8198	+	0.943146i	−0.972441	+	0.0385038i
$601$	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	$0.0738645\pi$
$602$	18.5007	+	4.95724i	0.754030	+	0.202042i
$603$	−5.75533			−0.234375
$604$	42.1101	+	11.2834i	1.71343	+	0.459113i
$605$	−16.8850	−	38.5862i	−0.686471	−	1.56875i
$606$	27.2872	−	27.2872i	1.10847	−	1.10847i
$607$	3.90296	−	14.5660i	0.158416	−	0.591218i	−0.840372	−	0.542010i	$-0.817664\pi$
$607$	3.90296	−	14.5660i	0.158416	−	0.591218i	0.998789	−	0.0492080i	$-0.0156697\pi$
$608$	7.58608	−	2.03268i	0.307656	−	0.0824363i
$609$	−23.8044	+	6.37837i	−0.964604	+	0.258465i
$610$	−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
$615$	−2.03769	+	0.891675i	−0.0821677	+	0.0359558i
$616$	11.8375	+	11.8375i	0.476945	+	0.476945i
$617$	33.6292	−	19.4158i	1.35386	−	0.781652i	0.365074	−	0.930979i	$-0.381044\pi$
$617$	33.6292	−	19.4158i	1.35386	−	0.781652i	0.988788	+	0.149326i	$0.0477105\pi$
$618$	5.89344	−	3.40258i	0.237069	−	0.136872i
$619$	14.9567	+	14.9567i	0.601159	+	0.601159i	0.940620	−	0.339461i	$-0.110245\pi$
$619$	14.9567	+	14.9567i	0.601159	+	0.601159i	−0.339461	+	0.940620i	$0.610245\pi$
$620$	2.10664	+	0.824152i	0.0846046	+	0.0330987i
$621$	−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
$626$	36.8545	−	9.87514i	1.47300	−	0.394690i
$627$	−12.7742	+	3.42284i	−0.510153	+	0.136695i
$628$	−3.44799	+	12.8681i	−0.137590	+	0.513492i
$629$	−3.01067	+	3.01067i	−0.120043	+	0.120043i
$630$	5.57959	−	2.44157i	0.222296	−	0.0972747i
$631$	−37.7256	−	10.1085i	−1.50183	−	0.402415i	−0.588119	−	0.808775i	$-0.700131\pi$
$631$	−37.7256	−	10.1085i	−1.50183	−	0.402415i	−0.913713	+	0.406360i	$0.866798\pi$
$632$	−26.8219			−1.06692
$633$	−6.11032	−	1.63726i	−0.242864	−	0.0650751i
$634$	−17.5143	+	30.3357i	−0.695582	+	1.20478i
$635$	−1.15958	+	0.176068i	−0.0460165	+	0.00698704i
$636$			38.7550i			1.53674i
$637$		0			0
$638$	84.4296	−	84.4296i	3.34260	−	3.34260i
$639$	2.98122	+	11.1261i	0.117935	+	0.440141i
$640$	21.8366	−	29.6550i	0.863168	−	1.17222i
$641$	7.55607	−	4.36250i	0.298447	−	0.172308i	−0.343298	−	0.939226i	$-0.611544\pi$
$641$	7.55607	−	4.36250i	0.298447	−	0.172308i	0.641745	+	0.766918i	$0.278211\pi$
$642$			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	$0.739089\pi$
$644$	−0.167894	+	0.626588i	−0.00661594	+	0.0246910i
$645$	−3.28220	+	29.4178i	−0.129237	+	1.15832i
$646$	−4.41809	−	7.65235i	−0.173827	−	0.301078i
$647$	−8.76765	−	32.7213i	−0.344692	−	1.28641i	−0.892972	−	0.450113i	$-0.851384\pi$
$647$	−8.76765	−	32.7213i	−0.344692	−	1.28641i	0.548280	−	0.836295i	$-0.315283\pi$
$648$	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
$653$	−5.24059	−	19.5581i	−0.205080	−	0.765369i	−0.989425	−	0.145044i	$-0.953667\pi$
$653$	−5.24059	−	19.5581i	−0.205080	−	0.765369i	0.784345	−	0.620325i	$-0.212999\pi$
$654$	−14.9382	−	25.8737i	−0.584128	−	1.01174i
$655$	−1.26422	+	11.3310i	−0.0493973	+	0.442739i
$656$	0.0947353	−	0.353557i	0.00369879	−	0.0138041i
$657$	−3.48016	−	6.02782i	−0.135774	−	0.235168i
$658$		−	9.19981i		−	0.358646i
$659$	26.2317	−	15.1449i	1.02184	−	0.589961i	0.107205	−	0.994237i	$-0.465810\pi$
$659$	26.2317	−	15.1449i	1.02184	−	0.589961i	0.914637	+	0.404276i	$0.132477\pi$
$660$	−44.1186	+	59.9148i	−1.71731	+	2.33218i
$661$	−5.66280	−	21.1339i	−0.220257	−	0.822012i	−0.984249	−	0.176786i	$-0.943430\pi$
$661$	−5.66280	−	21.1339i	−0.220257	−	0.822012i	0.763992	−	0.645226i	$-0.223237\pi$
$662$	27.1574	−	27.1574i	1.05550	−	1.05550i
$663$		0			0
$664$			6.37202i			0.247282i
$665$	−3.44071	+	0.522430i	−0.133425	+	0.0202590i
$666$	1.40925	−	2.44090i	0.0546074	−	0.0945829i
$667$	1.55395	+	0.416380i	0.0601693	+	0.0161223i
$668$	−38.7520			−1.49936
$669$	−22.7944	−	6.10774i	−0.881282	−	0.236139i
$670$	28.0078	−	12.2559i	1.08204	−	0.473488i
$671$	−5.37640	+	5.37640i	−0.207553	+	0.207553i
$672$	−4.23277	+	15.7969i	−0.163283	+	0.609379i
$673$	−0.554664	+	0.148622i	−0.0213807	+	0.00572895i	−0.269494	−	0.963002i	$-0.586856\pi$
$673$	−0.554664	+	0.148622i	−0.0213807	+	0.00572895i	0.248113	+	0.968731i	$0.420190\pi$
$674$	−77.0386	+	20.6424i	−2.96742	+	0.795117i
$675$	−10.8857	−	17.2411i	−0.418989	−	0.663610i
$676$		0			0
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	0.450111	−	0.892973i	$-0.351385\pi$
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	−0.892973	+	0.450111i	$0.851385\pi$
$678$	−25.4786	+	44.1302i	−0.978498	+	1.69481i
$679$	4.62416	+	2.66976i	0.177459	+	0.102456i
$680$	−16.0982	−	6.29788i	−0.617337	−	0.241513i
$681$	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	−0.128400	−	0.991722i	$-0.540984\pi$
$683$	17.4121	−	10.0529i	0.666256	−	0.384663i	0.794657	+	0.607059i	$0.207651\pi$
$684$	2.50325	+	2.50325i	0.0957143	+	0.0957143i
$685$	−7.79148	+	3.40948i	−0.297697	+	0.130269i
$686$	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
$691$	−41.8571	+	11.2156i	−1.59232	+	0.426661i	−0.942712	−	0.333608i	$-0.891734\pi$
$691$	−41.8571	+	11.2156i	−1.59232	+	0.426661i	−0.649608	+	0.760269i	$0.725067\pi$
$692$	40.6205	−	10.8842i	1.54416	−	0.413756i
$693$	1.71077	−	6.38467i	0.0649867	−	0.242534i
$694$	−20.5310	+	20.5310i	−0.779346	+	0.779346i
$695$	1.32509	+	3.02815i	0.0502635	+	0.114864i
$696$	−44.7253	−	11.9841i	−1.69531	−	0.454256i
$697$	−1.61289			−0.0610926
$698$	58.3773	+	15.6421i	2.20961	+	0.592064i
$699$	22.9764	−	39.7962i	0.869046	−	1.50523i
$700$	−13.2866	+	14.3821i	−0.502186	+	0.543593i
$701$			8.03468i			0.303466i	0.988422	+	0.151733i	$0.0484853\pi$
$701$			8.03468i			0.303466i	−0.988422	+	0.151733i	$0.951515\pi$
$702$		0			0
$703$	−1.13882	+	1.13882i	−0.0429514	+	0.0429514i
$704$	−18.4407	−	68.8216i	−0.695010	−	2.59381i
$705$	14.0567	−	2.13434i	0.529405	−	0.0803837i
$706$	−45.4404	+	26.2350i	−1.71017	+	0.987369i
$707$		−	11.0212i		−	0.414495i
$708$	0.00700440	+	0.0121320i	0.000263242	+	0.000455948i
$709$	5.88217	−	21.9526i	0.220910	−	0.824446i	−0.763092	−	0.646289i	$-0.776320\pi$
$709$	5.88217	−	21.9526i	0.220910	−	0.824446i	0.984002	−	0.178157i	$-0.0570134\pi$
$710$	−38.2008	−	47.7956i	−1.43365	−	1.79374i
$711$	5.29519	+	9.17153i	0.198585	+	0.343959i
$712$	4.47866	+	16.7146i	0.167845	+	0.626406i
$713$	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
$718$	7.55655	+	28.2014i	0.282008	+	1.05247i
$719$	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
$721$	0.503026	−	1.87732i	0.0187336	−	0.0699149i
$722$	19.7115	+	34.1413i	0.733585	+	1.27061i
$723$			41.3467i			1.53770i
$724$	21.6841	−	12.5193i	0.805882	−	0.465276i
$725$	35.6680	+	32.9511i	1.32468	+	1.22377i
$726$	21.8015	+	81.3643i	0.809129	+	3.01971i
$727$	−1.42786	+	1.42786i	−0.0529563	+	0.0529563i	−0.733089	−	0.680133i	$-0.761922\pi$
$727$	−1.42786	+	1.42786i	−0.0529563	+	0.0529563i	0.680133	+	0.733089i	$0.261922\pi$
$728$		0			0
$729$			13.9369i			0.516183i
$730$	29.7721	+	21.9229i	1.10191	+	0.811401i
$731$	−10.7322	+	18.5887i	−0.396945	+	0.687528i
$732$	8.19086	+	2.19473i	0.302743	+	0.0811197i
$733$	−32.1064			−1.18588			−0.592939	−	0.805247i	$-0.702033\pi$
$733$	−32.1064			−1.18588			−0.592939	+	0.805247i	$0.702033\pi$
$734$	32.3220	+	8.66065i	1.19303	+	0.319670i
$735$	−8.68992	+	22.2125i	−0.320532	+	0.819322i
$736$	0.754907	−	0.754907i	0.0278262	−	0.0278262i
$737$	8.58752	−	32.0491i	0.316325	−	1.18054i
$738$	1.03131	−	0.276339i	0.0379631	−	0.0101722i
$739$	19.8460	−	5.31771i	0.730046	−	0.195615i	0.125396	−	0.992107i	$-0.459980\pi$
$739$	19.8460	−	5.31771i	0.730046	−	0.195615i	0.604650	+	0.796492i	$0.293313\pi$
$740$	−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
$745$	14.0253	−	35.8505i	0.513849	−	1.31346i
$746$	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
$750$	−41.4020	−	28.0300i	−1.51179	−	1.02351i
$751$	−1.44204	−	0.832560i	−0.0526207	−	0.0303806i	0.473459	−	0.880816i	$-0.343005\pi$
$751$	−1.44204	−	0.832560i	−0.0526207	−	0.0303806i	−0.526080	+	0.850435i	$0.676339\pi$
$752$	−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
$756$	15.4254	−	4.13321i	0.561015	−	0.150324i
$757$	37.6990	−	10.1014i	1.37019	−	0.367143i	0.502645	−	0.864493i	$-0.332360\pi$
$757$	37.6990	−	10.1014i	1.37019	−	0.367143i	0.867550	+	0.497350i	$0.165694\pi$
$758$	10.6426	−	39.7186i	0.386556	−	1.44265i
$759$	−1.27119	+	1.27119i	−0.0461412	+	0.0461412i
$760$	−6.08932	−	2.38225i	−0.220883	−	0.0864131i
$761$	−15.7109	−	4.20973i	−0.569521	−	0.152603i	−0.0374441	−	0.999299i	$-0.511922\pi$
$761$	−15.7109	−	4.20973i	−0.569521	−	0.152603i	−0.532077	+	0.846696i	$0.678588\pi$
$762$	2.34565			0.0849739
$763$	−8.24188	−	2.20841i	−0.298376	−	0.0799496i
$764$	−22.6186	+	39.1766i	−0.818313	+	1.41736i
$765$	1.02460	+	6.74796i	0.0370443	+	0.243973i
$766$		−	23.0560i		−	0.833045i
$767$		0			0
$768$	−15.4289	+	15.4289i	−0.556741	+	0.556741i
$769$	10.3296	+	38.5504i	0.372493	+	1.39016i	0.856973	+	0.515362i	$0.172342\pi$
$769$	10.3296	+	38.5504i	0.372493	+	1.39016i	−0.484479	+	0.874803i	$0.660991\pi$
$770$	5.27082	+	34.7135i	0.189947	+	1.25099i
$771$	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	$0.712601\pi$
$774$	3.67753	−	13.7247i	0.132186	−	0.493325i
$775$	0.880735	+	1.39494i	0.0316369	+	0.0501077i
$776$	5.01612	+	8.68818i	0.180068	+	0.311887i
$777$	−0.868001	−	3.23942i	−0.0311394	−	0.116214i
$778$	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
$783$	−10.2505	−	38.2553i	−0.366322	−	1.36713i
$784$	−1.96257	−	3.39927i	−0.0700917	−	0.121402i
$785$	−7.58927	+	6.06575i	−0.270873	+	0.216496i
$786$	5.90153	−	22.0248i	0.210501	−	0.785599i
$787$	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
$790$	−45.2993	−	33.3564i	−1.61168	−	1.18677i
$791$	3.76666	+	14.0574i	0.133927	+	0.499822i
$792$	8.78163	−	8.78163i	0.312042	−	0.312042i
$793$		0			0
$794$			26.8568i			0.953111i
$795$	−16.7586	+	22.7588i	−0.594365	+	0.807171i
$796$	−17.5631	+	30.4202i	−0.622508	+	1.07822i
$797$	8.48530	+	2.27363i	0.300565	+	0.0805361i	0.405950	−	0.913895i	$-0.366941\pi$
$797$	8.48530	+	2.27363i	0.300565	+	0.0805361i	−0.105385	+	0.994432i	$0.533607\pi$
$798$	6.96002			0.246382
$799$	9.95859	+	2.66840i	0.352310	+	0.0944011i
$800$	30.7720	−	9.56524i	1.08796	−	0.338182i
$801$	4.83124	−	4.83124i	0.170703	−	0.170703i
$802$	2.37454	−	8.86190i	0.0838479	−	0.312924i
$803$	38.7592	−	10.3855i	1.36778	−	0.366496i
$804$	−35.7433	+	9.57739i	−1.26057	+	0.337768i
$805$	−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	0.514356	−	0.857577i	$-0.328031\pi$
$809$	0.820571	+	0.473757i	0.0288497	+	0.0166564i	−0.485506	+	0.874233i	$0.661365\pi$
$810$	22.0827	+	50.4642i	0.775905	+	1.77313i
$811$	−28.8041	−	28.8041i	−1.01145	−	1.01145i	−0.999934	−	0.0115151i	$-0.996335\pi$
$811$	−28.8041	−	28.8041i	−1.01145	−	1.01145i	−0.0115151	−	0.999934i	$-0.503665\pi$
$812$	−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
$815$	8.25150	+	18.8567i	0.289037	+	0.660520i
$816$	−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
$821$	1.29968	−	0.348249i	0.0453592	−	0.0121540i	−0.236068	−	0.971737i	$-0.575859\pi$
$821$	1.29968	−	0.348249i	0.0453592	−	0.0121540i	0.281427	+	0.959583i	$0.409192\pi$
$822$	16.4294	−	4.40224i	0.573041	−	0.153546i
$823$	8.55907	−	31.9429i	0.298350	−	1.11346i	−0.640169	−	0.768234i	$-0.721136\pi$
$823$	8.55907	−	31.9429i	0.298350	−	1.11346i	0.938520	−	0.345225i	$-0.112197\pi$
$824$	2.58211	−	2.58211i	0.0899520	−	0.0899520i
$825$	−51.8170	+	16.1069i	−1.80404	+	0.560771i
$826$	0.00638537	+	0.00171095i	0.000222175	+	5.95317e-5i
$827$	26.4195			0.918697			0.459349	−	0.888256i	$-0.348083\pi$
$827$	26.4195			0.918697			0.459349	+	0.888256i	$0.348083\pi$
$828$	0.464834	+	0.124552i	0.0161541	+	0.00432848i
$829$	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	$0.153061\pi$
$830$	−7.92439	+	10.7616i	−0.275060	+	0.373542i
$831$		−	24.2940i		−	0.842748i
$832$		0			0
$833$	−12.2301	+	12.2301i	−0.423747	+	0.423747i
$834$	−1.71093	−	6.38526i	−0.0592445	−	0.221104i
$835$	−22.7570	−	16.7573i	−0.787539	−	0.579909i
$836$	−17.6747	+	10.2045i	−0.611292	+	0.352929i
$837$		−	1.34551i		−	0.0465075i
$838$	−23.8909	−	41.3802i	−0.825297	−	1.42946i
$839$	13.0306	−	48.6308i	0.449866	−	1.67892i	−0.252893	−	0.967494i	$-0.581382\pi$
$839$	13.0306	−	48.6308i	0.449866	−	1.67892i	0.702759	−	0.711428i	$-0.251951\pi$
$840$	10.6361	−	8.50096i	0.366981	−	0.293311i
$841$	32.6597	+	56.5682i	1.12619	+	1.95063i
$842$	−2.60113	−	9.70754i	−0.0896408	−	0.334544i
$843$	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
$848$	−1.20379	−	4.49261i	−0.0413384	−	0.154277i
$849$	−27.1730	−	47.0651i	−0.932576	−	1.61527i
$850$	−19.3559	−	30.6565i	−0.663900	−	1.05151i
$851$	−0.0566632	+	0.211470i	−0.00194239	+	0.00724909i
$852$	37.0296	+	64.1371i	1.26861	+	2.19730i
$853$			42.9612i			1.47096i	0.677545	+	0.735481i	$0.263044\pi$
$853$			42.9612i			1.47096i	−0.677545	+	0.735481i	$0.736956\pi$
$854$	3.46543	−	2.00077i	0.118585	−	0.0684649i
$855$	0.387565	+	2.55249i	0.0132544	+	0.0872934i
$856$	9.02166	+	33.6693i	0.308354	+	1.15079i
$857$	29.0789	−	29.0789i	0.993316	−	0.993316i	−0.00666151	−	0.999978i	$-0.502120\pi$
$857$	29.0789	−	29.0789i	0.993316	−	0.993316i	0.999978	+	0.00666151i	$0.00212044\pi$
$858$		0			0
$859$		−	42.1283i		−	1.43740i	−0.695321	−	0.718700i	$-0.744738\pi$
$859$		−	42.1283i		−	1.43740i	0.695321	−	0.718700i	$-0.255262\pi$
$860$	6.85738	+	45.1625i	0.233835	+	1.54003i
$861$	0.635216	−	1.10023i	0.0216481	−	0.0374956i
$862$	−77.9289	−	20.8810i	−2.65427	−	0.711209i
$863$	−6.80768			−0.231736			−0.115868	−	0.993265i	$-0.536965\pi$
$863$	−6.80768			−0.231736			−0.115868	+	0.993265i	$0.536965\pi$
$864$	−25.3867	−	6.80234i	−0.863672	−	0.231420i
$865$	28.5609	+	11.1735i	0.971099	+	0.379910i
$866$	12.8806	−	12.8806i	0.437702	−	0.437702i
$867$	3.40497	−	12.7075i	0.115639	−	0.431570i
$868$	−1.24803	+	0.334410i	−0.0423610	+	0.0113506i
$869$	−58.9734	+	15.8019i	−2.00054	+	0.536042i
$870$	−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
$875$	−14.0217	+	2.70044i	−0.474019	+	0.0912917i
$876$	−31.6443	−	31.6443i	−1.06916	−	1.06916i
$877$	−41.2933	+	23.8407i	−1.39437	+	0.805043i	−0.993796	−	0.111219i	$-0.964524\pi$
$877$	−41.2933	+	23.8407i	−1.39437	+	0.805043i	−0.400579	+	0.916262i	$0.631191\pi$
$878$	−55.8796	+	32.2621i	−1.88585	+	1.08879i
$879$	−36.7017	−	36.7017i	−1.23792	−	1.23792i
$880$	3.25332	−	8.31591i	0.109669	−	0.280329i
$881$	−4.43737	−	2.56192i	−0.149499	−	0.0863133i	0.423385	−	0.905950i	$-0.360842\pi$
$881$	−4.43737	−	2.56192i	−0.149499	−	0.0863133i	−0.572884	+	0.819637i	$0.694175\pi$
$882$	5.72474	−	9.91554i	0.192762	−	0.333873i
$883$	−14.8283	−	14.8283i	−0.499014	−	0.499014i	0.412117	−	0.911131i	$-0.364789\pi$
$883$	−14.8283	−	14.8283i	−0.499014	−	0.499014i	−0.911131	+	0.412117i	$0.864789\pi$
$884$		0			0
$885$	−0.00113283	+	0.0101533i	−3.80796e−5	+	0.000341301i
$886$	52.7568	−	14.1361i	1.77240	−	0.474913i
$887$	10.1735	−	2.72597i	0.341592	−	0.0915293i	−0.0839449	−	0.996470i	$-0.526752\pi$
$887$	10.1735	−	2.72597i	0.341592	−	0.0915293i	0.425537	+	0.904941i	$0.360085\pi$
$888$	1.63086	−	6.08644i	0.0547280	−	0.204248i
$889$	0.473700	−	0.473700i	0.0158874	−	0.0158874i
$890$	−13.2227	+	33.7989i	−0.443226	+	1.13294i
$891$	57.7457	+	15.4729i	1.93455	+	0.518362i
$892$	−36.4179			−1.21936
$893$	3.76695	+	1.00935i	0.126056	+	0.0337767i
$894$	−38.4949	+	66.6751i	−1.28746	+	2.22995i
$895$	−22.7638	−	16.7623i	−0.760911	−	0.560301i
$896$			21.0349i			0.702725i
$897$		0			0
$898$	−14.5886	+	14.5886i	−0.486828	+	0.486828i
$899$	0.829344	+	3.09515i	0.0276602	+	0.103229i
$900$	10.6694	+	9.85667i	0.355646	+	0.328556i
$901$	−17.7490	+	10.2474i	−0.591307	+	0.341391i
$902$			6.15528i			0.204948i
$903$	−8.45347	−	14.6418i	−0.281314	−	0.487250i
$904$	−7.07704	+	26.4119i	−0.235379	+	0.878446i
$905$	18.1476	+	2.02476i	0.603245	+	0.0673053i
$906$	−31.7921	−	55.0656i	−1.05622	−	1.82943i
$907$	−5.57417	−	20.8031i	−0.185087	−	0.690755i	−0.994612	−	0.103669i	$-0.966942\pi$
$907$	−5.57417	−	20.8031i	−0.185087	−	0.690755i	0.809525	−	0.587086i	$-0.199725\pi$
$908$	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
$913$	3.75401	+	14.0102i	0.124240	+	0.463669i
$914$	24.1734	+	41.8696i	0.799586	+	1.38492i
$915$	3.86101	+	4.83077i	0.127641	+	0.159700i
$916$	14.4774	−	54.0305i	0.478347	−	1.78522i
$917$	−3.25607	−	5.63968i	−0.107525	−	0.186239i
$918$			29.5701i			0.975958i
$919$	−5.95358	+	3.43730i	−0.196390	+	0.113386i	−0.594971	−	0.803747i	$-0.702836\pi$
$919$	−5.95358	+	3.43730i	−0.196390	+	0.113386i	0.398580	+	0.917133i	$0.369503\pi$
$920$	−0.878776	+	0.133431i	−0.0289724	+	0.00439911i
$921$	−7.56111	−	28.2184i	−0.249147	−	0.929829i
$922$	8.08349	−	8.08349i	0.266216	−	0.266216i
$923$		0			0
$924$		−	42.4987i		−	1.39810i
$925$	−4.48415	+	4.85389i	−0.147438	+	0.159595i
$926$	−22.5973	+	39.1396i	−0.742593	+	1.28621i
$927$	−1.39269	−	0.373170i	−0.0457419	−	0.0122565i
$928$	62.5915			2.05467
$929$	42.9399	+	11.5057i	1.40881	+	0.377490i	0.881501	−	0.472182i	$-0.156533\pi$
$929$	42.9399	+	11.5057i	1.40881	+	0.377490i	0.527312	+	0.849672i	$0.323200\pi$
$930$	−1.32265	−	3.02257i	−0.0433714	−	0.0991141i
$931$	−4.62617	+	4.62617i	−0.151617	+	0.151617i
$932$	18.3543	−	68.4993i	0.601216	−	2.24377i
$933$	−61.1290	+	16.3795i	−2.00127	+	0.536240i
$934$	65.9535	−	17.6722i	2.15806	−	0.578252i
$935$	−39.1054	−	4.36307i	−1.27888	−	0.142688i
$936$		0			0
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	0.888738	−	0.458415i	$-0.151583\pi$
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	−0.458415	+	0.888738i	$0.651583\pi$
$938$	−8.73096	+	15.1225i	−0.285076	+	0.493766i
$939$	−29.1675	−	16.8399i	−0.951846	−	0.549548i
$940$	20.1010	−	8.79602i	0.655624	−	0.286895i
$941$	−40.0251	−	40.0251i	−1.30478	−	1.30478i	−0.925130	−	0.379650i	$-0.876045\pi$
$941$	−40.0251	−	40.0251i	−1.30478	−	1.30478i	−0.379650	−	0.925130i	$-0.623955\pi$
$942$	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
$945$	10.8458	+	4.24306i	0.352814	+	0.138027i
$946$	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
$951$	29.8668	−	8.00278i	0.968497	−	0.259508i
$952$	9.53703	−	2.55544i	0.309097	−	0.0828223i
$953$	4.62094	−	17.2456i	0.149687	−	0.558640i	−0.849815	−	0.527081i	$-0.823286\pi$
$953$	4.62094	−	17.2456i	0.149687	−	0.558640i	0.999502	−	0.0315583i	$-0.0100470\pi$
$954$	9.59336	−	9.59336i	0.310596	−	0.310596i
$955$	−30.2236	+	13.2255i	−0.978012	+	0.427969i
$956$	10.9650	+	2.93807i	0.354634	+	0.0950240i
$957$	−105.398			−3.40703
$958$	−67.6360	−	18.1230i	−2.18522	−	0.585528i
$959$	2.42886	−	4.20691i	0.0784320	−	0.135848i
$960$	−57.2935	+	8.69932i	−1.84914	+	0.280769i
$961$		−	30.8911i		−	0.996488i
$962$		0			0
$963$	9.73187	−	9.73187i	0.313605	−	0.313605i
$964$	16.5146	+	61.6333i	0.531899	+	1.98507i
$965$	−20.0165	+	27.1832i	−0.644353	+	0.875057i
$966$	0.819363	−	0.473059i	0.0263626	−	0.0152204i
$967$			23.2093i			0.746360i	0.927759	+	0.373180i	$0.121733\pi$
$967$			23.2093i			0.746360i	−0.927759	+	0.373180i	$0.878267\pi$
$968$	22.6001	+	39.1446i	0.726395	+	1.25815i
$969$	−2.01875	+	7.53407i	−0.0648515	+	0.242029i
$970$	−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	$-0.404740\pi$
$972$	−7.54788	−	28.1691i	−0.242098	−	0.903523i
$973$	−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	0.122152	−	0.992511i	$-0.461020\pi$
$977$	−21.1395	−	12.2049i	−0.676312	−	0.390469i	−0.798464	+	0.602043i	$0.794354\pi$
$978$	−10.6541	−	39.7618i	−0.340682	−	1.27144i
$979$	19.6945	+	34.1118i	0.629438	+	1.09022i
$980$	−4.08152	+	36.5819i	−0.130379	+	1.16857i
$981$	−1.63831	+	6.11424i	−0.0523071	+	0.195213i
$982$	−39.7420	−	68.8352i	−1.26822	−	2.19662i
$983$		−	4.47004i		−	0.142572i	−0.997456	−	0.0712860i	$-0.977290\pi$
$983$		−	4.47004i		−	0.142572i	0.997456	−	0.0712860i	$-0.0227103\pi$
$984$	2.06718	−	1.19349i	0.0658992	−	0.0380469i
$985$	20.3806	−	27.6776i	0.649379	−	0.881883i
$986$	−18.2264	−	68.0220i	−0.580448	−	2.16626i
$987$	−5.74230	+	5.74230i	−0.182779	+	0.182779i
$988$		0			0
$989$			1.10369i			0.0350952i
$990$	25.7522	−	3.91016i	0.818460	−	0.124273i
$991$	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	$-0.121580\pi$
$992$	2.05398	+	0.550363i	0.0652140	+	0.0174740i
$993$	−33.9020			−1.07585
$994$	33.7570	+	9.04516i	1.07071	+	0.286895i
$995$	−23.4683	+	10.2695i	−0.743995	+	0.325565i
$996$	11.4384	−	11.4384i	0.362439	−	0.362439i
$997$	−9.06967	+	33.8485i	−0.287239	+	1.07199i	0.659948	+	0.751311i	$0.270578\pi$
$997$	−9.06967	+	33.8485i	−0.287239	+	1.07199i	−0.947187	+	0.320681i	$0.896088\pi$
$998$	−29.0380	+	7.78071i	−0.919182	+	0.246294i
$999$	5.20597	−	1.39494i	0.164710	−	0.0441338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.e.657.1		20
5.3	odd	4		845.2.o.f.488.1		20
13.2	odd	12		845.2.o.f.587.1		20
13.3	even	3		845.2.t.g.427.5		20
13.4	even	6		845.2.f.e.437.1		20
13.5	odd	4		845.2.o.g.357.1		20
13.6	odd	12		845.2.k.d.577.10		20
13.7	odd	12		845.2.k.e.577.1		20
13.8	odd	4		65.2.o.a.32.5	✓	20
13.9	even	3		845.2.f.d.437.10		20
13.10	even	6		65.2.t.a.37.1	yes	20
13.11	odd	12		845.2.o.e.587.5		20
13.12	even	2		845.2.t.f.657.5		20
39.8	even	4		585.2.cf.a.487.1		20
39.23	odd	6		585.2.dp.a.37.5		20
65.3	odd	12		845.2.o.g.258.1		20
65.8	even	4		65.2.t.a.58.1	yes	20
65.18	even	4		845.2.t.g.188.5		20
65.23	odd	12		65.2.o.a.63.5	yes	20
65.28	even	12	inner	845.2.t.e.418.1		20
65.33	even	12		845.2.f.e.408.10		20
65.34	odd	4		325.2.s.b.32.1		20
65.38	odd	4		845.2.o.e.488.5		20
65.43	odd	12		845.2.k.e.268.1		20
65.47	even	4		325.2.x.b.318.5		20
65.48	odd	12		845.2.k.d.268.10		20
65.49	even	6		325.2.x.b.232.5		20
65.58	even	12		845.2.f.d.408.1		20
65.62	odd	12		325.2.s.b.193.1		20
65.63	even	12		845.2.t.f.418.5		20
195.8	odd	4		585.2.dp.a.253.5		20
195.23	even	12		585.2.cf.a.388.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.5	✓	20	13.8	odd	4
65.2.o.a.63.5	yes	20	65.23	odd	12
65.2.t.a.37.1	yes	20	13.10	even	6
65.2.t.a.58.1	yes	20	65.8	even	4
325.2.s.b.32.1		20	65.34	odd	4
325.2.s.b.193.1		20	65.62	odd	12
325.2.x.b.232.5		20	65.49	even	6
325.2.x.b.318.5		20	65.47	even	4
585.2.cf.a.388.1		20	195.23	even	12
585.2.cf.a.487.1		20	39.8	even	4
585.2.dp.a.37.5		20	39.23	odd	6
585.2.dp.a.253.5		20	195.8	odd	4
845.2.f.d.408.1		20	65.58	even	12
845.2.f.d.437.10		20	13.9	even	3
845.2.f.e.408.10		20	65.33	even	12
845.2.f.e.437.1		20	13.4	even	6
845.2.k.d.268.10		20	65.48	odd	12
845.2.k.d.577.10		20	13.6	odd	12
845.2.k.e.268.1		20	65.43	odd	12
845.2.k.e.577.1		20	13.7	odd	12
845.2.o.e.488.5		20	65.38	odd	4
845.2.o.e.587.5		20	13.11	odd	12
845.2.o.f.488.1		20	5.3	odd	4
845.2.o.f.587.1		20	13.2	odd	12
845.2.o.g.258.1		20	65.3	odd	12
845.2.o.g.357.1		20	13.5	odd	4
845.2.t.e.418.1		20	65.28	even	12	inner
845.2.t.e.657.1		20	1.1	even	1	trivial
845.2.t.f.418.5		20	65.63	even	12
845.2.t.f.657.5		20	13.12	even	2
845.2.t.g.188.5		20	65.18	even	4
845.2.t.g.427.5		20	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(0.514229 + 1.91913i) q^{3} +(1.53307 + 2.65535i) q^{4} +(-0.247944 + 2.22228i) q^{5} +(1.15743 - 4.31958i) q^{6} +(-0.638592 - 1.10607i) q^{7} -2.39966i q^{8} +(-0.820542 + 0.473740i) q^{9} +(2.98427 - 4.05275i) q^{10} +(-1.41373 - 5.27612i) q^{11} +(-4.30760 + 4.30760i) q^{12} +2.87469i q^{14} +(-4.39234 + 0.666923i) q^{15} +(0.365551 - 0.633152i) q^{16} +(-3.11179 - 0.833802i) q^{17} +2.13259 q^{18} +(-1.17707 - 0.315395i) q^{19} +(-6.28104 + 2.74852i) q^{20} +(1.79431 - 1.79431i) q^{21} +(-3.18204 + 11.8755i) q^{22} +(-0.160006 + 0.0428736i) q^{23} +(4.60524 - 1.23397i) 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} +(9.31234 + 3.64315i) 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} +(2.61634 - 1.14488i) 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} +(0.483595 - 0.129579i) q^{41} +(-5.51690 + 1.47825i) q^{42} +(1.72444 - 6.43569i) q^{43} +(11.8426 - 11.8426i) q^{44} +(-0.849334 - 1.94093i) q^{45} +(0.360144 + 0.0965002i) q^{46} -3.20027 q^{47} +(1.40308 + 0.375953i) q^{48} +(2.68440 - 4.64952i) q^{49} +(8.26642 + 7.63673i) q^{50} -6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-2.37565 - 8.86603i) q^{54} +(12.0755 - 1.83353i) q^{55} +(-2.65420 + 1.53240i) q^{56} -2.42113i q^{57} +(10.9297 + 18.9308i) q^{58} +(0.000595178 - 0.00222123i) q^{59} +(-8.50465 - 10.6407i) q^{60} +(-0.695993 - 1.20550i) q^{61} +(0.192209 + 0.717332i) q^{62} +(1.04798 + 0.605053i) q^{63} +13.0440 q^{64} -24.4270 q^{66} +(5.26055 + 3.03718i) q^{67} +(-2.55655 - 9.54117i) q^{68} +(-0.164560 - 0.285026i) q^{69} +(-6.38837 - 0.712764i) q^{70} +(3.14648 - 11.7428i) q^{71} +(1.13681 + 1.96902i) q^{72} +7.34614i q^{73} +(-2.57620 + 1.48737i) q^{74} +(-0.393034 - 9.92635i) q^{75} +(-0.967044 - 3.60906i) q^{76} +(-4.93298 + 4.93298i) q^{77} -11.1774i q^{79} +(1.31640 + 0.969342i) q^{80} +(-5.47236 + 9.47841i) q^{81} +(-1.08848 - 0.291657i) q^{82} -2.65539 q^{83} +(7.51533 + 2.01373i) q^{84} +(2.62449 - 6.70854i) q^{85} +(-10.6041 + 10.6041i) q^{86} +(4.99409 - 18.6382i) q^{87} +(-12.6609 + 3.39247i) q^{88} +(-6.96542 + 1.86638i) 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} +(0.992745 - 2.53758i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 4 q^{6} + 2 q^{7} - 12 q^{9} + 10 q^{10} - 8 q^{11} - 24 q^{12} + 8 q^{15} - 2 q^{16} + 10 q^{17} - 16 q^{19} - 12 q^{20} - 4 q^{21} + 16 q^{22} + 2 q^{23} + 28 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 4 * q^6 + 2 * q^7 - 12 * q^9 + 10 * q^10 - 8 * q^11 - 24 * q^12 + 8 * q^15 - 2 * q^16 + 10 * q^17 - 16 * q^19 - 12 * q^20 - 4 * q^21 + 16 * q^22 + 2 * q^23 + 28 * q^24 + 18 * q^25 + 4 * q^27 - 18 * q^28 - 14 * q^30 + 48 * q^32 + 18 * q^33 - 2 * q^34 - 20 * q^35 - 36 * q^36 + 4 * q^37 - 8 * q^38 - 16 * q^40 - 28 * q^41 - 56 * q^42 + 22 * q^43 + 36 * q^44 - 6 * q^45 + 8 * q^46 + 40 * q^47 + 28 * q^48 + 18 * q^49 + 78 * q^50 - 10 * q^53 - 12 * q^54 + 26 * q^55 - 8 * q^59 - 28 * q^60 - 16 * q^61 + 40 * q^62 - 36 * q^63 + 20 * q^64 - 32 * q^66 + 18 * q^67 + 28 * q^68 - 16 * q^69 + 12 * q^70 - 56 * q^71 - 4 * q^72 - 18 * q^74 + 34 * q^75 - 80 * q^76 - 28 * q^77 + 110 * q^80 - 14 * q^81 - 22 * q^82 - 48 * q^83 - 32 * q^84 - 28 * q^85 - 60 * q^86 + 62 * q^87 - 50 * q^88 + 6 * q^89 + 46 * q^90 - 8 * q^92 - 32 * q^93 + 48 * q^94 - 14 * q^95 - 56 * q^96 + 66 * q^97 - 30 * q^98 - 60 * q^99

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