LMFDB - Embedded newform 845.2.f.d.408.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(408,845)] 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("845.408"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,4,-12,0,-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:	$10$ over $\Q(i)$
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:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			408.4
Root			$-0.131303i$ of defining polynomial
Character	$\chi$	$=$	845.408
Dual form			845.2.f.d.437.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.131303i q^{2} +(-0.243172 - 0.243172i) q^{3} +1.98276 q^{4} +(-2.08297 + 0.813169i) q^{5} +(-0.0319291 + 0.0319291i) q^{6} +2.78137 q^{7} -0.522947i q^{8} -2.88174i q^{9} +(0.106771 + 0.273499i) q^{10} +(-2.86749 - 2.86749i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(0.704259 + 0.308779i) q^{15} +3.89686 q^{16} +(-1.71436 - 1.71436i) q^{17} -0.378379 q^{18} +(-1.34301 - 1.34301i) q^{19} +(-4.13003 + 1.61232i) q^{20} +(-0.676351 - 0.676351i) q^{21} +(-0.376509 + 0.376509i) q^{22} +(5.64077 - 5.64077i) q^{23} +(-0.127166 + 0.127166i) q^{24} +(3.67751 - 3.38761i) q^{25} +(-1.43027 + 1.43027i) q^{27} +5.51479 q^{28} +4.57914i q^{29} +(0.0405435 - 0.0924710i) q^{30} +(-3.87352 + 3.87352i) q^{31} -1.55756i q^{32} +1.39458i q^{33} +(-0.225100 + 0.225100i) q^{34} +(-5.79351 + 2.26173i) q^{35} -5.71379i q^{36} +7.01019 q^{37} +(-0.176341 + 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(4.54006 - 4.54006i) q^{41} +(-0.0888066 + 0.0888066i) q^{42} +(4.57069 - 4.57069i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(2.34334 + 6.00256i) q^{45} +(-0.740648 - 0.740648i) q^{46} +0.512375 q^{47} +(-0.947605 - 0.947605i) q^{48} +0.736030 q^{49} +(-0.444802 - 0.482867i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(0.187798 + 0.187798i) q^{54} +(8.30464 + 3.64114i) q^{55} -1.45451i q^{56} +0.653165i q^{57} +0.601253 q^{58} +(1.85697 - 1.85697i) q^{59} +(1.39638 + 0.612235i) q^{60} -1.28353 q^{61} +(0.508603 + 0.508603i) q^{62} -8.01518i q^{63} +7.58920 q^{64} +0.183113 q^{66} +3.61629i q^{67} +(-3.39916 - 3.39916i) q^{68} -2.74335 q^{69} +(0.296970 + 0.760703i) q^{70} +(-4.54457 + 4.54457i) q^{71} -1.50699 q^{72} -9.93250i q^{73} -0.920457i q^{74} +(-1.71804 - 0.0704959i) q^{75} +(-2.66287 - 2.66287i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(-8.11702 + 3.16880i) q^{80} -7.94960 q^{81} +(-0.596122 - 0.596122i) q^{82} -3.17194 q^{83} +(-1.34104 - 1.34104i) q^{84} +(4.96502 + 2.17689i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(1.11352 - 1.11352i) q^{87} +(-1.49954 + 1.49954i) q^{88} +(-4.40479 + 4.40479i) q^{89} +(0.788152 - 0.307686i) q^{90} +(11.1843 - 11.1843i) q^{92} +1.88386 q^{93} -0.0672762i q^{94} +(3.88955 + 1.70536i) q^{95} +(-0.378755 + 0.378755i) q^{96} -11.7700i q^{97} -0.0966426i q^{98} +(-8.26335 + 8.26335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Character values

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

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

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 $

$2$		−	0.131303i		−	0.0928450i	−0.998922	−	0.0464225i	$-0.985218\pi$
$2$		−	0.131303i		−	0.0928450i	0.998922	−	0.0464225i	$-0.0147820\pi$
$3$	−0.243172	−	0.243172i	−0.140395	−	0.140395i	0.633416	−	0.773811i	$-0.281652\pi$
$3$	−0.243172	−	0.243172i	−0.140395	−	0.140395i	−0.773811	+	0.633416i	$0.781652\pi$
$4$	1.98276			0.991380
$5$	−2.08297	+	0.813169i	−0.931532	+	0.363660i
$5$	−2.08297	+	0.813169i	−0.931532	+	0.363660i
$6$	−0.0319291	+	0.0319291i	−0.0130350	+	0.0130350i
$7$	2.78137			1.05126			0.525630	−	0.850713i	$-0.323830\pi$
$7$	2.78137			1.05126			0.525630	+	0.850713i	$0.323830\pi$
$8$		−	0.522947i		−	0.184890i
$9$		−	2.88174i		−	0.960578i
$10$	0.106771	+	0.273499i	0.0337640	+	0.0864880i
$11$	−2.86749	−	2.86749i	−0.864581	−	0.864581i	0.127285	−	0.991866i	$-0.459374\pi$
$11$	−2.86749	−	2.86749i	−0.864581	−	0.864581i	−0.991866	+	0.127285i	$0.959374\pi$
$12$	−0.482151	−	0.482151i	−0.139185	−	0.139185i
$13$		0			0
$13$		0			0
$14$		−	0.365201i		−	0.0976042i
$15$	0.704259	+	0.308779i	0.181839	+	0.0797264i
$16$	3.89686			0.974214
$17$	−1.71436	−	1.71436i	−0.415793	−	0.415793i	0.467958	−	0.883751i	$-0.344990\pi$
$17$	−1.71436	−	1.71436i	−0.415793	−	0.415793i	−0.883751	+	0.467958i	$0.844990\pi$
$18$	−0.378379			−0.0891849
$19$	−1.34301	−	1.34301i	−0.308108	−	0.308108i	0.536067	−	0.844175i	$-0.319909\pi$
$19$	−1.34301	−	1.34301i	−0.308108	−	0.308108i	−0.844175	+	0.536067i	$0.819909\pi$
$20$	−4.13003	+	1.61232i	−0.923502	+	0.360525i
$21$	−0.676351	−	0.676351i	−0.147592	−	0.147592i
$22$	−0.376509	+	0.376509i	−0.0802720	+	0.0802720i
$23$	5.64077	−	5.64077i	1.17618	−	1.17618i	0.195474	−	0.980709i	$-0.437376\pi$
$23$	5.64077	−	5.64077i	1.17618	−	1.17618i	0.980709	−	0.195474i	$-0.0626244\pi$
$24$	−0.127166	+	0.127166i	−0.0259576	+	0.0259576i
$25$	3.67751	−	3.38761i	0.735502	−	0.677522i
$26$		0			0
$27$	−1.43027	+	1.43027i	−0.275256	+	0.275256i
$28$	5.51479			1.04220
$29$			4.57914i			0.850325i	0.905117	+	0.425162i	$0.139783\pi$
$29$			4.57914i			0.850325i	−0.905117	+	0.425162i	$0.860217\pi$
$30$	0.0405435	−	0.0924710i	0.00740220	−	0.0168828i
$31$	−3.87352	+	3.87352i	−0.695704	+	0.695704i	−0.963481	−	0.267777i	$-0.913711\pi$
$31$	−3.87352	+	3.87352i	−0.695704	+	0.695704i	0.267777	+	0.963481i	$0.413711\pi$
$32$		−	1.55756i		−	0.275340i
$33$			1.39458i			0.242766i
$34$	−0.225100	+	0.225100i	−0.0386043	+	0.0386043i
$35$	−5.79351	+	2.26173i	−0.979282	+	0.382301i
$36$		−	5.71379i		−	0.952298i
$37$	7.01019			1.15247			0.576234	−	0.817284i	$-0.304522\pi$
$37$	7.01019			1.15247			0.576234	+	0.817284i	$0.304522\pi$
$38$	−0.176341	+	0.176341i	−0.0286063	+	0.0286063i
$39$		0			0
$40$	0.425244	+	1.08928i	0.0672370	+	0.172230i
$41$	4.54006	−	4.54006i	0.709039	−	0.709039i	−0.257294	−	0.966333i	$-0.582831\pi$
$41$	4.54006	−	4.54006i	0.709039	−	0.709039i	0.966333	+	0.257294i	$0.0828309\pi$
$42$	−0.0888066	+	0.0888066i	−0.0137032	+	0.0137032i
$43$	4.57069	−	4.57069i	0.697023	−	0.697023i	−0.266744	−	0.963767i	$-0.585948\pi$
$43$	4.57069	−	4.57069i	0.697023	−	0.697023i	0.963767	+	0.266744i	$0.0859478\pi$
$44$	−5.68554	−	5.68554i	−0.857128	−	0.857128i
$45$	2.34334	+	6.00256i	0.349324	+	0.894809i
$46$	−0.740648	−	0.740648i	−0.109203	−	0.109203i
$47$	0.512375			0.0747376			0.0373688	−	0.999302i	$-0.488102\pi$
$47$	0.512375			0.0747376			0.0373688	+	0.999302i	$0.488102\pi$
$48$	−0.947605	−	0.947605i	−0.136775	−	0.136775i
$49$	0.736030			0.105147
$50$	−0.444802	−	0.482867i	−0.0629045	−	0.0682877i
$51$			0.833767i			0.116751i
$52$		0			0
$53$	−1.32662	−	1.32662i	−0.182225	−	0.182225i	0.610100	−	0.792325i	$-0.291129\pi$
$53$	−1.32662	−	1.32662i	−0.182225	−	0.182225i	−0.792325	+	0.610100i	$0.791129\pi$
$54$	0.187798	+	0.187798i	0.0255561	+	0.0255561i
$55$	8.30464	+	3.64114i	1.11980	+	0.490971i
$56$		−	1.45451i		−	0.194367i
$57$			0.653165i			0.0865138i
$58$	0.601253			0.0789484
$59$	1.85697	−	1.85697i	0.241757	−	0.241757i	−0.575819	−	0.817577i	$-0.695317\pi$
$59$	1.85697	−	1.85697i	0.241757	−	0.241757i	0.817577	+	0.575819i	$0.195317\pi$
$60$	1.39638	+	0.612235i	0.180271	+	0.0790392i
$61$	−1.28353			−0.164340			−0.0821698	−	0.996618i	$-0.526185\pi$
$61$	−1.28353			−0.164340			−0.0821698	+	0.996618i	$0.526185\pi$
$62$	0.508603	+	0.508603i	0.0645926	+	0.0645926i
$63$		−	8.01518i		−	1.00982i
$64$	7.58920			0.948650
$65$		0			0
$66$	0.183113			0.0225396
$67$			3.61629i			0.441800i	0.975296	+	0.220900i	$0.0708995\pi$
$67$			3.61629i			0.441800i	−0.975296	+	0.220900i	$0.929101\pi$
$68$	−3.39916	−	3.39916i	−0.412209	−	0.412209i
$69$	−2.74335			−0.330261
$70$	0.296970	+	0.760703i	0.0354948	+	0.0909214i
$71$	−4.54457	+	4.54457i	−0.539341	+	0.539341i	−0.923336	−	0.383994i	$-0.874548\pi$
$71$	−4.54457	+	4.54457i	−0.539341	+	0.539341i	0.383994	+	0.923336i	$0.374548\pi$
$72$	−1.50699			−0.177601
$73$		−	9.93250i		−	1.16251i	−0.813721	−	0.581256i	$-0.802562\pi$
$73$		−	9.93250i		−	1.16251i	0.813721	−	0.581256i	$-0.197438\pi$
$74$		−	0.920457i		−	0.107001i
$75$	−1.71804	−	0.0704959i	−0.198382	−	0.00814016i
$76$	−2.66287	−	2.66287i	−0.305452	−	0.305452i
$77$	−7.97556	−	7.97556i	−0.908899	−	0.908899i
$78$		0			0
$79$			8.37577i			0.942347i	0.882040	+	0.471174i	$0.156169\pi$
$79$			8.37577i			0.942347i	−0.882040	+	0.471174i	$0.843831\pi$
$80$	−8.11702	+	3.16880i	−0.907511	+	0.354283i
$81$	−7.94960			−0.883289
$82$	−0.596122	−	0.596122i	−0.0658307	−	0.0658307i
$83$	−3.17194			−0.348166			−0.174083	−	0.984731i	$-0.555696\pi$
$83$	−3.17194			−0.348166			−0.174083	+	0.984731i	$0.555696\pi$
$84$	−1.34104	−	1.34104i	−0.146320	−	0.146320i
$85$	4.96502	+	2.17689i	0.538532	+	0.236117i
$86$	−0.600143	−	0.600143i	−0.0647151	−	0.0647151i
$87$	1.11352	−	1.11352i	0.119382	−	0.119382i
$88$	−1.49954	+	1.49954i	−0.159852	+	0.159852i
$89$	−4.40479	+	4.40479i	−0.466907	+	0.466907i	−0.900911	−	0.434004i	$-0.857100\pi$
$89$	−4.40479	+	4.40479i	−0.466907	+	0.466907i	0.434004	+	0.900911i	$0.357100\pi$
$90$	0.788152	−	0.307686i	0.0830785	−	0.0324330i
$91$		0			0
$92$	11.1843	−	11.1843i	1.16604	−	1.16604i
$93$	1.88386			0.195347
$94$		−	0.0672762i		−	0.00693901i
$95$	3.88955	+	1.70536i	0.399059	+	0.174966i
$96$	−0.378755	+	0.378755i	−0.0386565	+	0.0386565i
$97$		−	11.7700i		−	1.19506i	−0.801846	−	0.597531i	$-0.796149\pi$
$97$		−	11.7700i		−	1.19506i	0.801846	−	0.597531i	$-0.203851\pi$
$98$		−	0.0966426i		−	0.00976238i
$99$	−8.26335	+	8.26335i	−0.830498	+	0.830498i
$100$	7.29162	−	6.71682i	0.729162	−	0.671682i
$101$		−	1.00899i		−	0.100398i	−0.998739	−	0.0501989i	$-0.984014\pi$
$101$		−	1.00899i		−	0.100398i	0.998739	−	0.0501989i	$-0.0159855\pi$
$102$	0.109476			0.0108397
$103$	−6.00002	+	6.00002i	−0.591200	+	0.591200i	−0.937955	−	0.346756i	$-0.887283\pi$
$103$	−6.00002	+	6.00002i	−0.591200	+	0.591200i	0.346756	+	0.937955i	$0.387283\pi$
$104$		0			0
$105$	1.95880	+	0.858830i	0.191160	+	0.0838132i
$106$	−0.174188	+	0.174188i	−0.0169187	+	0.0169187i
$107$	3.50416	−	3.50416i	0.338760	−	0.338760i	−0.517140	−	0.855901i	$-0.673003\pi$
$107$	3.50416	−	3.50416i	0.338760	−	0.338760i	0.855901	+	0.517140i	$0.173003\pi$
$108$	−2.83588	+	2.83588i	−0.272883	+	0.272883i
$109$	6.51002	+	6.51002i	0.623546	+	0.623546i	0.946436	−	0.322890i	$-0.104654\pi$
$109$	6.51002	+	6.51002i	0.623546	+	0.623546i	−0.322890	+	0.946436i	$0.604654\pi$
$110$	0.478091	−	1.09042i	0.0455842	−	0.103968i
$111$	−1.70468	−	1.70468i	−0.161801	−	0.161801i
$112$	10.8386			1.02415
$113$	5.30540	+	5.30540i	0.499090	+	0.499090i	0.911155	−	0.412065i	$-0.135192\pi$
$113$	5.30540	+	5.30540i	0.499090	+	0.499090i	−0.412065	+	0.911155i	$0.635192\pi$
$114$	0.0857623			0.00803237
$115$	−7.16265	+	16.3365i	−0.667920	+	1.52338i
$116$			9.07933i			0.842995i
$117$		0			0
$118$	−0.243826	−	0.243826i	−0.0224460	−	0.0224460i
$119$	−4.76827	−	4.76827i	−0.437106	−	0.437106i
$120$	0.161475	−	0.368290i	0.0147406	−	0.0336201i
$121$			5.44500i			0.495000i
$122$			0.168531i			0.0152581i
$123$	−2.20803			−0.199091
$124$	−7.68025	+	7.68025i	−0.689707	+	0.689707i
$125$	−4.90544	+	10.0467i	−0.438756	+	0.898606i
$126$	−1.05241			−0.0937564
$127$	11.7016	+	11.7016i	1.03835	+	1.03835i	0.999235	+	0.0391188i	$0.0124551\pi$
$127$	11.7016	+	11.7016i	1.03835	+	1.03835i	0.0391188	+	0.999235i	$0.487545\pi$
$128$		−	4.11160i		−	0.363418i
$129$	−2.22292			−0.195718
$130$		0			0
$131$	−12.6880			−1.10856			−0.554278	−	0.832332i	$-0.687006\pi$
$131$	−12.6880			−1.10856			−0.554278	+	0.832332i	$0.687006\pi$
$132$			2.76513i			0.240673i
$133$	−3.73542	−	3.73542i	−0.323902	−	0.323902i
$134$	0.474828			0.0410189
$135$	1.81616	−	4.14226i	0.156310	−	0.356509i
$136$	−0.896518	+	0.896518i	−0.0768758	+	0.0768758i
$137$	14.9451			1.27684			0.638422	−	0.769687i	$-0.279588\pi$
$137$	14.9451			1.27684			0.638422	+	0.769687i	$0.279588\pi$
$138$			0.360209i			0.0306631i
$139$			8.57227i			0.727090i	0.931577	+	0.363545i	$0.118434\pi$
$139$			8.57227i			0.727090i	−0.931577	+	0.363545i	$0.881566\pi$
$140$	−11.4871	+	4.48446i	−0.970840	+	0.379006i
$141$	−0.124595	−	0.124595i	−0.0104928	−	0.0104928i
$142$	0.596714	+	0.596714i	0.0500751	+	0.0500751i
$143$		0			0
$144$		−	11.2297i		−	0.935809i
$145$	−3.72361	−	9.53820i	−0.309229	−	0.792105i
$146$	−1.30416			−0.107933
$147$	−0.178982	−	0.178982i	−0.0147622	−	0.0147622i
$148$	13.8995			1.14253
$149$	8.58517	+	8.58517i	0.703324	+	0.703324i	0.965123	−	0.261798i	$-0.0843155\pi$
$149$	8.58517	+	8.58517i	0.703324	+	0.703324i	−0.261798	+	0.965123i	$0.584316\pi$
$150$	−0.00925629	+	0.225583i	−0.000755773	+	0.0184188i
$151$	−1.86999	−	1.86999i	−0.152177	−	0.152177i	0.626912	−	0.779090i	$-0.284318\pi$
$151$	−1.86999	−	1.86999i	−0.152177	−	0.152177i	−0.779090	+	0.626912i	$0.784318\pi$
$152$	−0.702324	+	0.702324i	−0.0569660	+	0.0569660i
$153$	−4.94033	+	4.94033i	−0.399402	+	0.399402i
$154$	−1.04721	+	1.04721i	−0.0843867	+	0.0843867i
$155$	4.91859	−	11.2182i	0.395071	−	0.901071i
$156$		0			0
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	−0.986620	−	0.163039i	$-0.947870\pi$
$157$	−10.3194	+	10.3194i	−0.823581	+	0.823581i	0.163039	+	0.986620i	$0.447870\pi$
$158$	1.09976			0.0874922
$159$			0.645192i			0.0511671i
$160$	1.26656	+	3.24435i	0.100130	+	0.256488i
$161$	15.6891	−	15.6891i	1.23647	−	1.23647i
$162$			1.04380i			0.0820089i
$163$		−	18.6954i		−	1.46434i	−0.681122	−	0.732170i	$-0.738508\pi$
$163$		−	18.6954i		−	1.46434i	0.681122	−	0.732170i	$-0.261492\pi$
$164$	9.00186	−	9.00186i	0.702927	−	0.702927i
$165$	−1.13403	−	2.90488i	−0.0882844	−	0.226144i
$166$			0.416484i			0.0323255i
$167$	20.6778			1.60010			0.800049	−	0.599935i	$-0.204807\pi$
$167$	20.6778			1.60010			0.800049	+	0.599935i	$0.204807\pi$
$168$	−0.353695	+	0.353695i	−0.0272882	+	0.0272882i
$169$		0			0
$170$	0.285831	−	0.651920i	0.0219223	−	0.0500000i
$171$	−3.87021	+	3.87021i	−0.295962	+	0.295962i
$172$	9.06258	−	9.06258i	0.691015	−	0.691015i
$173$	−12.8312	+	12.8312i	−0.975540	+	0.975540i	−0.999708	−	0.0241680i	$-0.992306\pi$
$173$	−12.8312	+	12.8312i	−0.975540	+	0.975540i	0.0241680	+	0.999708i	$0.492306\pi$
$174$	−0.146208	−	0.146208i	−0.0110840	−	0.0110840i
$175$	10.2285	−	9.42220i	0.773204	−	0.712252i
$176$	−11.1742	−	11.1742i	−0.842287	−	0.842287i
$177$	−0.903127			−0.0678832
$178$	0.578360	+	0.578360i	0.0433499	+	0.0433499i
$179$	−17.3622			−1.29771			−0.648856	−	0.760911i	$-0.724752\pi$
$179$	−17.3622			−1.29771			−0.648856	+	0.760911i	$0.724752\pi$
$180$	4.64628	+	11.9016i	0.346313	+	0.887096i
$181$			24.9284i			1.85291i	0.376406	+	0.926455i	$0.377160\pi$
$181$			24.9284i			1.85291i	−0.376406	+	0.926455i	$0.622840\pi$
$182$		0			0
$183$	0.312119	+	0.312119i	0.0230725	+	0.0230725i
$184$	−2.94982	−	2.94982i	−0.217464	−	0.217464i
$185$	−14.6020	+	5.70047i	−1.07356	+	0.419107i
$186$		−	0.247356i		−	0.0181370i
$187$			9.83181i			0.718973i
$188$	1.01592			0.0740934
$189$	−3.97812	+	3.97812i	−0.289365	+	0.289365i
$190$	0.223918	−	0.510708i	0.0162447	−	0.0370506i
$191$	6.78709			0.491096			0.245548	−	0.969384i	$-0.421032\pi$
$191$	6.78709			0.491096			0.245548	+	0.969384i	$0.421032\pi$
$192$	−1.84548	−	1.84548i	−0.133186	−	0.133186i
$193$		−	1.19516i		−	0.0860298i	−0.999074	−	0.0430149i	$-0.986304\pi$
$193$		−	1.19516i		−	0.0860298i	0.999074	−	0.0430149i	$-0.0136963\pi$
$194$	−1.54543			−0.110955
$195$		0			0
$196$	1.45937			0.104241
$197$			20.1210i			1.43356i	0.697300	+	0.716780i	$0.254385\pi$
$197$			20.1210i			1.43356i	−0.697300	+	0.716780i	$0.745615\pi$
$198$	1.08500	+	1.08500i	0.0771075	+	0.0771075i
$199$	2.17769			0.154372			0.0771862	−	0.997017i	$-0.475406\pi$
$199$	2.17769			0.154372			0.0771862	+	0.997017i	$0.475406\pi$
$200$	−1.77154	−	1.92314i	−0.125267	−	0.135987i
$201$	0.879379	−	0.879379i	0.0620266	−	0.0620266i
$202$	−0.132482			−0.00932143
$203$			12.7363i			0.893912i
$204$			1.65316i			0.115744i
$205$	−5.76497	+	13.1486i	−0.402643	+	0.918342i
$206$	0.787818	+	0.787818i	0.0548899	+	0.0548899i
$207$	−16.2552	−	16.2552i	−1.12982	−	1.12982i
$208$		0			0
$209$			7.70215i			0.532769i
$210$	0.112767	−	0.257196i	0.00778163	−	0.0177482i
$211$	−19.9528			−1.37361			−0.686805	−	0.726842i	$-0.740987\pi$
$211$	−19.9528			−1.37361			−0.686805	+	0.726842i	$0.740987\pi$
$212$	−2.63037	−	2.63037i	−0.180654	−	0.180654i
$213$	2.21022			0.151442
$214$	−0.460106	−	0.460106i	−0.0314522	−	0.0314522i
$215$	−5.80386	+	13.2373i	−0.395820	+	0.902779i
$216$	0.747956	+	0.747956i	0.0508919	+	0.0508919i
$217$	−10.7737	+	10.7737i	−0.731366	+	0.731366i
$218$	0.854782	−	0.854782i	0.0578931	−	0.0578931i
$219$	−2.41530	+	2.41530i	−0.163211	+	0.163211i
$220$	16.4661	+	7.21950i	1.11015	+	0.486738i
$221$		0			0
$222$	−0.223829	+	0.223829i	−0.0150224	+	0.0150224i
$223$	−13.4134			−0.898231			−0.449115	−	0.893474i	$-0.648261\pi$
$223$	−13.4134			−0.898231			−0.449115	+	0.893474i	$0.648261\pi$
$224$		−	4.33215i		−	0.289454i
$225$	−9.76220	−	10.5976i	−0.650813	−	0.706508i
$226$	0.696612	−	0.696612i	0.0463380	−	0.0463380i
$227$			14.6813i			0.974431i	0.873282	+	0.487215i	$0.161987\pi$
$227$			14.6813i			0.974431i	−0.873282	+	0.487215i	$0.838013\pi$
$228$			1.29507i			0.0857681i
$229$	−2.65280	+	2.65280i	−0.175302	+	0.175302i	−0.789304	−	0.614002i	$-0.789558\pi$
$229$	−2.65280	+	2.65280i	−0.175302	+	0.175302i	0.614002	+	0.789304i	$0.289558\pi$
$230$	2.14502	+	0.940474i	0.141438	+	0.0620130i
$231$			3.87886i			0.255210i
$232$	2.39465			0.157216
$233$	−13.9459	+	13.9459i	−0.913629	+	0.913629i	−0.996556	−	0.0829267i	$-0.973573\pi$
$233$	−13.9459	+	13.9459i	−0.913629	+	0.913629i	0.0829267	+	0.996556i	$0.473573\pi$
$234$		0			0
$235$	−1.06726	+	0.416648i	−0.0696205	+	0.0271791i
$236$	3.68193	−	3.68193i	0.239673	−	0.239673i
$237$	2.03675	−	2.03675i	0.132301	−	0.132301i
$238$	−0.626086	+	0.626086i	−0.0405831	+	0.0405831i
$239$	10.1890	+	10.1890i	0.659074	+	0.659074i	0.955161	−	0.296087i	$-0.0956818\pi$
$239$	10.1890	+	10.1890i	0.659074	+	0.659074i	−0.296087	+	0.955161i	$0.595682\pi$
$240$	2.74439	+	1.20327i	0.177150	+	0.0776706i
$241$	5.73049	+	5.73049i	0.369133	+	0.369133i	0.867161	−	0.498028i	$-0.165942\pi$
$241$	5.73049	+	5.73049i	0.369133	+	0.369133i	−0.498028	+	0.867161i	$0.665942\pi$
$242$	0.714943			0.0459582
$243$	6.22393	+	6.22393i	0.399265	+	0.399265i
$244$	−2.54494			−0.162923
$245$	−1.53313	+	0.598517i	−0.0979479	+	0.0382378i
$246$			0.289920i			0.0184846i
$247$		0			0
$248$	2.02564	+	2.02564i	0.128628	+	0.128628i
$249$	0.771327	+	0.771327i	0.0488809	+	0.0488809i
$250$	1.31916	+	0.644097i	0.0834311	+	0.0407363i
$251$		−	4.67543i		−	0.295110i	−0.989054	−	0.147555i	$-0.952860\pi$
$251$		−	4.67543i		−	0.295110i	0.989054	−	0.147555i	$-0.0471404\pi$
$252$		−	15.8922i		−	1.00111i
$253$	−32.3497			−2.03381
$254$	1.53646	−	1.53646i	0.0964059	−	0.0964059i
$255$	−0.677993	−	1.73671i	−0.0424576	−	0.108757i
$256$	14.6385			0.914908
$257$	12.2720	+	12.2720i	0.765507	+	0.765507i	0.977312	−	0.211805i	$-0.0679342\pi$
$257$	12.2720	+	12.2720i	0.765507	+	0.765507i	−0.211805	+	0.977312i	$0.567934\pi$
$258$			0.291876i			0.0181714i
$259$	19.4980			1.21154
$260$		0			0
$261$	13.1959			0.816804
$262$			1.66597i			0.102924i
$263$	1.71239	+	1.71239i	0.105590	+	0.105590i	0.757928	−	0.652338i	$-0.226212\pi$
$263$	1.71239	+	1.71239i	0.105590	+	0.105590i	−0.652338	+	0.757928i	$0.726212\pi$
$264$	0.729293			0.0448849
$265$	3.84207	+	1.68454i	0.236016	+	0.103480i
$266$	−0.490470	+	0.490470i	−0.0300726	+	0.0300726i
$267$	2.14224			0.131103
$268$			7.17023i			0.437992i
$269$		−	9.73216i		−	0.593380i	−0.954974	−	0.296690i	$-0.904117\pi$
$269$		−	9.73216i		−	0.593380i	0.954974	−	0.296690i	$-0.0958828\pi$
$270$	−0.543890	−	0.238466i	−0.0331001	−	0.0145126i
$271$	−15.4981	−	15.4981i	−0.941441	−	0.941441i	0.0569369	−	0.998378i	$-0.481867\pi$
$271$	−15.4981	−	15.4981i	−0.941441	−	0.941441i	−0.998378	+	0.0569369i	$0.981867\pi$
$272$	−6.68061	−	6.68061i	−0.405071	−	0.405071i
$273$		0			0
$274$		−	1.96233i		−	0.118548i
$275$	−20.2592	−	0.831290i	−1.22167	−	0.0501287i
$276$	−5.43941			−0.327414
$277$	12.7676	+	12.7676i	0.767128	+	0.767128i	0.977600	−	0.210472i	$-0.0675000\pi$
$277$	12.7676	+	12.7676i	0.767128	+	0.767128i	−0.210472	+	0.977600i	$0.567500\pi$
$278$	1.12556			0.0675067
$279$	11.1625	+	11.1625i	0.668278	+	0.668278i
$280$	1.18276	+	3.02970i	0.0706835	+	0.181059i
$281$	−11.3739	−	11.3739i	−0.678510	−	0.678510i	0.281153	−	0.959663i	$-0.409283\pi$
$281$	−11.3739	−	11.3739i	−0.678510	−	0.678510i	−0.959663	+	0.281153i	$0.909283\pi$
$282$	−0.0163597	+	0.0163597i	−0.000974204	+	0.000974204i
$283$	8.02927	−	8.02927i	0.477290	−	0.477290i	−0.426974	−	0.904264i	$-0.640420\pi$
$283$	8.02927	−	8.02927i	0.477290	−	0.477290i	0.904264	+	0.426974i	$0.140420\pi$
$284$	−9.01079	+	9.01079i	−0.534692	+	0.534692i
$285$	−0.531134	−	1.36052i	−0.0314616	−	0.0805904i
$286$		0			0
$287$	12.6276	−	12.6276i	0.745384	−	0.745384i
$288$	−4.48848			−0.264486
$289$		−	11.1220i		−	0.654232i
$290$	−1.25239	+	0.488920i	−0.0735429	+	0.0287104i
$291$	−2.86213	+	2.86213i	−0.167781	+	0.167781i
$292$		−	19.6938i		−	1.15249i
$293$		−	0.699613i		−	0.0408719i	−0.999791	−	0.0204359i	$-0.993495\pi$
$293$		−	0.699613i		−	0.0408719i	0.999791	−	0.0204359i	$-0.00650541\pi$
$294$	−0.0235007	+	0.0235007i	−0.00137059	+	0.00137059i
$295$	−2.35798	+	5.37805i	−0.137287	+	0.313122i
$296$		−	3.66596i		−	0.213079i
$297$	8.20258			0.475962
$298$	1.12725	−	1.12725i	0.0653001	−	0.0653001i
$299$		0			0
$300$	−3.40646	−	0.139776i	−0.196672	−	0.00806999i
$301$	12.7128	−	12.7128i	0.732753	−	0.732753i
$302$	−0.245534	+	0.245534i	−0.0141289	+	0.0141289i
$303$	−0.245357	+	0.245357i	−0.0140954	+	0.0140954i
$304$	−5.23352	−	5.23352i	−0.300163	−	0.300163i
$305$	2.67356	−	1.04373i	0.153088	−	0.0597638i
$306$	0.648678	+	0.648678i	0.0370824	+	0.0370824i
$307$	14.2048			0.810709			0.405355	−	0.914159i	$-0.367148\pi$
$307$	14.2048			0.810709			0.405355	+	0.914159i	$0.367148\pi$
$308$	−15.8136	−	15.8136i	−0.901064	−	0.901064i
$309$	2.91807			0.166003
$310$	−1.47298	−	0.645823i	−0.0836598	−	0.0366803i
$311$		−	21.4961i		−	1.21893i	−0.792812	−	0.609466i	$-0.791384\pi$
$311$		−	21.4961i		−	1.21893i	0.792812	−	0.609466i	$-0.208616\pi$
$312$		0			0
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	0.391113	−	0.920343i	$-0.372090\pi$
$313$	−9.36303	−	9.36303i	−0.529230	−	0.529230i	−0.920343	+	0.391113i	$0.872090\pi$
$314$	1.35497	+	1.35497i	0.0764653	+	0.0764653i
$315$	6.51769	+	16.6954i	0.367230	+	0.940677i
$316$			16.6071i			0.934224i
$317$			17.3024i			0.971798i	0.874015	+	0.485899i	$0.161508\pi$
$317$			17.3024i			0.971798i	−0.874015	+	0.485899i	$0.838492\pi$
$318$	0.0847154			0.00475060
$319$	13.1306	−	13.1306i	0.735175	−	0.735175i
$320$	−15.8081	+	6.17130i	−0.883697	+	0.344986i
$321$	−1.70423			−0.0951207
$322$	−2.06002	−	2.06002i	−0.114800	−	0.114800i
$323$			4.60481i			0.256218i
$324$	−15.7622			−0.875675
$325$		0			0
$326$	−2.45476			−0.135957
$327$		−	3.16610i		−	0.175086i
$328$	−2.37421	−	2.37421i	−0.131094	−	0.131094i
$329$	1.42511			0.0785686
$330$	−0.381418	+	0.148901i	−0.0209964	+	0.00819676i
$331$	12.7065	−	12.7065i	0.698412	−	0.698412i	−0.265656	−	0.964068i	$-0.585588\pi$
$331$	12.7065	−	12.7065i	0.698412	−	0.698412i	0.964068	+	0.265656i	$0.0855885\pi$
$332$	−6.28920			−0.345165
$333$		−	20.2015i		−	1.10704i
$334$		−	2.71505i		−	0.148561i
$335$	−2.94065	−	7.53262i	−0.160665	−	0.411551i
$336$	−2.63564	−	2.63564i	−0.143786	−	0.143786i
$337$	4.83668	+	4.83668i	0.263471	+	0.263471i	0.826462	−	0.562992i	$-0.190350\pi$
$337$	4.83668	+	4.83668i	0.263471	+	0.263471i	−0.562992	+	0.826462i	$0.690350\pi$
$338$		0			0
$339$		−	2.58024i		−	0.140140i
$340$	9.84444	+	4.31625i	0.533889	+	0.234082i
$341$	22.2145			1.20299
$342$	0.508168	+	0.508168i	0.0274786	+	0.0274786i
$343$	−17.4224			−0.940723
$344$	−2.39023	−	2.39023i	−0.128872	−	0.128872i
$345$	5.71432	−	2.23081i	0.307648	−	0.120103i
$346$	1.68477	+	1.68477i	0.0905740	+	0.0905740i
$347$	13.1536	−	13.1536i	0.706123	−	0.706123i	−0.259594	−	0.965718i	$-0.583589\pi$
$347$	13.1536	−	13.1536i	0.706123	−	0.706123i	0.965718	+	0.259594i	$0.0835889\pi$
$348$	2.20784	−	2.20784i	0.118352	−	0.118352i
$349$	−1.77981	+	1.77981i	−0.0952710	+	0.0952710i	−0.753136	−	0.657865i	$-0.771460\pi$
$349$	−1.77981	+	1.77981i	−0.0952710	+	0.0952710i	0.657865	+	0.753136i	$0.271460\pi$
$350$	−1.23716	−	1.34303i	−0.0661290	−	0.0717881i
$351$		0			0
$352$	−4.46629	+	4.46629i	−0.238054	+	0.238054i
$353$	32.7215			1.74159			0.870795	−	0.491646i	$-0.163604\pi$
$353$	32.7215			1.74159			0.870795	+	0.491646i	$0.163604\pi$
$354$			0.118583i			0.00630261i
$355$	5.77069	−	13.1617i	0.306277	−	0.698551i
$356$	−8.73364	+	8.73364i	−0.462882	+	0.462882i
$357$			2.31902i			0.122735i
$358$			2.27970i			0.120486i
$359$	0.699684	−	0.699684i	0.0369279	−	0.0369279i	−0.688402	−	0.725330i	$-0.741687\pi$
$359$	0.699684	−	0.699684i	0.0369279	−	0.0369279i	0.725330	+	0.688402i	$0.241687\pi$
$360$	3.13902	−	1.22544i	0.165441	−	0.0645864i
$361$		−	15.3926i		−	0.810139i
$362$	3.27316			0.172033
$363$	1.32407	−	1.32407i	0.0694956	−	0.0694956i
$364$		0			0
$365$	8.07680	+	20.6891i	0.422759	+	1.08292i
$366$	0.0409820	−	0.0409820i	0.00214217	−	0.00214217i
$367$	10.2343	−	10.2343i	0.534226	−	0.534226i	−0.387601	−	0.921827i	$-0.626696\pi$
$367$	10.2343	−	10.2343i	0.534226	−	0.534226i	0.921827	+	0.387601i	$0.126696\pi$
$368$	21.9813	−	21.9813i	1.14585	−	1.14585i
$369$	−13.0833	−	13.0833i	−0.681087	−	0.681087i
$370$	0.748487	+	1.91728i	0.0389120	+	0.0996747i
$371$	−3.68982	−	3.68982i	−0.191566	−	0.191566i
$372$	3.73524			0.193663
$373$	−7.17039	−	7.17039i	−0.371269	−	0.371269i	0.496671	−	0.867939i	$-0.334556\pi$
$373$	−7.17039	−	7.17039i	−0.371269	−	0.371269i	−0.867939	+	0.496671i	$0.834556\pi$
$374$	1.29094			0.0667530
$375$	3.63594	−	1.25021i	0.187759	−	0.0645608i
$376$		−	0.267945i		−	0.0138182i
$377$		0			0
$378$	0.522337	+	0.522337i	0.0268661	+	0.0268661i
$379$	0.742810	+	0.742810i	0.0381556	+	0.0381556i	0.725927	−	0.687772i	$-0.241411\pi$
$379$	0.742810	+	0.742810i	0.0381556	+	0.0381556i	−0.687772	+	0.725927i	$0.741411\pi$
$380$	7.71204	+	3.38131i	0.395619	+	0.173458i
$381$		−	5.69102i		−	0.291560i
$382$		−	0.891162i		−	0.0455958i
$383$	12.0071			0.613532			0.306766	−	0.951785i	$-0.400753\pi$
$383$	12.0071			0.613532			0.306766	+	0.951785i	$0.400753\pi$
$384$	−0.999825	+	0.999825i	−0.0510221	+	0.0510221i
$385$	23.0983	+	10.1274i	1.17720	+	0.516138i
$386$	−0.156928			−0.00798743
$387$	−13.1715	−	13.1715i	−0.669546	−	0.669546i
$388$		−	23.3371i		−	1.18476i
$389$	7.37166			0.373758			0.186879	−	0.982383i	$-0.440163\pi$
$389$	7.37166			0.373758			0.186879	+	0.982383i	$0.440163\pi$
$390$		0			0
$391$	−19.3406			−0.978097
$392$		−	0.384904i		−	0.0194406i
$393$	3.08536	+	3.08536i	0.155636	+	0.155636i
$394$	2.64194			0.133099
$395$	−6.81091	−	17.4465i	−0.342694	−	0.877826i
$396$	−16.3842	+	16.3842i	−0.823339	+	0.823339i
$397$	−6.05477			−0.303880			−0.151940	−	0.988390i	$-0.548552\pi$
$397$	−6.05477			−0.303880			−0.151940	+	0.988390i	$0.548552\pi$
$398$		−	0.285937i		−	0.0143327i
$399$			1.81669i			0.0909485i
$400$	14.3307	−	13.2010i	0.716537	−	0.660051i
$401$	−1.70733	−	1.70733i	−0.0852602	−	0.0852602i	0.663190	−	0.748451i	$-0.269202\pi$
$401$	−1.70733	−	1.70733i	−0.0852602	−	0.0852602i	−0.748451	+	0.663190i	$0.769202\pi$
$402$	−0.115465	−	0.115465i	−0.00575886	−	0.00575886i
$403$		0			0
$404$		−	2.00058i		−	0.0995324i
$405$	16.5588	−	6.46437i	0.822812	−	0.321217i
$406$	1.67231			0.0829952
$407$	−20.1017	−	20.1017i	−0.996402	−	0.996402i
$408$	0.436016			0.0215860
$409$	−14.2391	−	14.2391i	−0.704077	−	0.704077i	0.261206	−	0.965283i	$-0.415880\pi$
$409$	−14.2391	−	14.2391i	−0.704077	−	0.704077i	−0.965283	+	0.261206i	$0.915880\pi$
$410$	1.72645	+	0.756955i	0.0852634	+	0.0373834i
$411$	−3.63422	−	3.63422i	−0.179263	−	0.179263i
$412$	−11.8966	+	11.8966i	−0.586103	+	0.586103i
$413$	5.16494	−	5.16494i	0.254150	−	0.254150i
$414$	−2.13435	+	2.13435i	−0.104898	+	0.104898i
$415$	6.60706	−	2.57933i	0.324328	−	0.126614i
$416$		0			0
$417$	2.08453	−	2.08453i	0.102080	−	0.102080i
$418$	1.01131			0.0494649
$419$			30.0803i			1.46952i	0.678328	+	0.734759i	$0.262705\pi$
$419$			30.0803i			1.46952i	−0.678328	+	0.734759i	$0.737295\pi$
$420$	3.88384	+	1.70285i	0.189512	+	0.0830907i
$421$	−9.24685	+	9.24685i	−0.450664	+	0.450664i	−0.895575	−	0.444911i	$-0.853235\pi$
$421$	−9.24685	+	9.24685i	−0.450664	+	0.450664i	0.444911	+	0.895575i	$0.353235\pi$
$422$			2.61986i			0.127533i
$423$		−	1.47653i		−	0.0717913i
$424$	−0.693751	+	0.693751i	−0.0336915	+	0.0336915i
$425$	−12.1122	−	0.496995i	−0.587526	−	0.0241078i
$426$		−	0.290208i		−	0.0140606i
$427$	−3.56998			−0.172764
$428$	6.94792	−	6.94792i	0.335840	−	0.335840i
$429$		0			0
$430$	1.73810	+	0.762061i	0.0838185	+	0.0367499i
$431$	4.46276	−	4.46276i	0.214963	−	0.214963i	−0.591409	−	0.806372i	$-0.701428\pi$
$431$	4.46276	−	4.46276i	0.214963	−	0.214963i	0.806372	+	0.591409i	$0.201428\pi$
$432$	−5.57356	+	5.57356i	−0.268158	+	0.268158i
$433$	−8.68986	+	8.68986i	−0.417608	+	0.417608i	−0.884379	−	0.466770i	$-0.845417\pi$
$433$	−8.68986	+	8.68986i	−0.417608	+	0.417608i	0.466770	+	0.884379i	$0.345417\pi$
$434$	1.41461	+	1.41461i	0.0679036	+	0.0679036i
$435$	−1.41394	+	3.22490i	−0.0677934	+	0.154622i
$436$	12.9078	+	12.9078i	0.618171	+	0.618171i
$437$	−15.1513			−0.724783
$438$	0.317136	+	0.317136i	0.0151533	+	0.0151533i
$439$	34.4447			1.64395			0.821977	−	0.569520i	$-0.192871\pi$
$439$	34.4447			1.64395			0.821977	+	0.569520i	$0.192871\pi$
$440$	1.90412	−	4.34289i	0.0907754	−	0.207039i
$441$		−	2.12104i		−	0.101002i
$442$		0			0
$443$	−5.39452	−	5.39452i	−0.256301	−	0.256301i	0.567247	−	0.823548i	$-0.308009\pi$
$443$	−5.39452	−	5.39452i	−0.256301	−	0.256301i	−0.823548	+	0.567247i	$0.808009\pi$
$444$	−3.37997	−	3.37997i	−0.160406	−	0.160406i
$445$	5.59320	−	12.7569i	0.265143	−	0.604734i
$446$			1.76122i			0.0833962i
$447$		−	4.17534i		−	0.197487i
$448$	21.1084			0.997277
$449$	−22.0157	+	22.0157i	−1.03899	+	1.03899i	−0.0397782	+	0.999209i	$0.512665\pi$
$449$	−22.0157	+	22.0157i	−1.03899	+	1.03899i	−0.999209	+	0.0397782i	$0.987335\pi$
$450$	−1.39149	+	1.28180i	−0.0655957	+	0.0604247i
$451$	−26.0372			−1.22604
$452$	10.5193	+	10.5193i	0.494788	+	0.494788i
$453$			0.909456i			0.0427300i
$454$	1.92769			0.0904710
$455$		0			0
$456$	0.341570			0.0159955
$457$		−	3.10750i		−	0.145363i	−0.997355	−	0.0726814i	$-0.976844\pi$
$457$		−	3.10750i		−	0.145363i	0.997355	−	0.0726814i	$-0.0231556\pi$
$458$	0.348319	+	0.348319i	0.0162759	+	0.0162759i
$459$	4.90400			0.228899
$460$	−14.2018	+	32.3913i	−0.662163	+	1.51025i
$461$	−11.8061	+	11.8061i	−0.549863	+	0.549863i	−0.926401	−	0.376538i	$-0.877114\pi$
$461$	−11.8061	+	11.8061i	−0.549863	+	0.549863i	0.376538	+	0.926401i	$0.377114\pi$
$462$	0.509304			0.0236950
$463$		−	15.6396i		−	0.726832i	−0.931627	−	0.363416i	$-0.881610\pi$
$463$		−	15.6396i		−	0.726832i	0.931627	−	0.363416i	$-0.118390\pi$
$464$			17.8442i			0.828398i
$465$	−3.92402	+	1.53190i	−0.181972	+	0.0710400i
$466$	1.83114	+	1.83114i	0.0848258	+	0.0848258i
$467$	15.0821	+	15.0821i	0.697916	+	0.697916i	0.963961	−	0.266045i	$-0.0857169\pi$
$467$	15.0821	+	15.0821i	0.697916	+	0.697916i	−0.266045	+	0.963961i	$0.585717\pi$
$468$		0			0
$469$			10.0582i			0.464447i
$470$	0.0547069	+	0.140134i	0.00252344	+	0.00646391i
$471$	5.01879			0.231254
$472$	−0.971099	−	0.971099i	−0.0446984	−	0.0446984i
$473$	−26.2128			−1.20527
$474$	−0.267430	−	0.267430i	−0.0122835	−	0.0122835i
$475$	−9.48854	−	0.389341i	−0.435364	−	0.0178642i
$476$	−9.45433	−	9.45433i	−0.433339	−	0.433339i
$477$	−3.82296	+	3.82296i	−0.175041	+	0.175041i
$478$	1.33785	−	1.33785i	0.0611917	−	0.0611917i
$479$	30.1579	−	30.1579i	1.37795	−	1.37795i	0.529871	−	0.848079i	$-0.322240\pi$
$479$	30.1579	−	30.1579i	1.37795	−	1.37795i	0.848079	−	0.529871i	$-0.177760\pi$
$480$	0.480942	−	1.09693i	0.0219519	−	0.0500676i
$481$		0			0
$482$	0.752428	−	0.752428i	0.0342722	−	0.0342722i
$483$	−7.63028			−0.347190
$484$			10.7961i			0.490733i
$485$	9.57099	+	24.5165i	0.434596	+	1.11324i
$486$	0.817218	−	0.817218i	0.0370698	−	0.0370698i
$487$		−	15.2167i		−	0.689534i	−0.938688	−	0.344767i	$-0.887958\pi$
$487$		−	15.2167i		−	0.689534i	0.938688	−	0.344767i	$-0.112042\pi$
$488$			0.671220i			0.0303847i
$489$	−4.54620	+	4.54620i	−0.205586	+	0.205586i
$490$	0.0785868	+	0.201303i	0.00355019	+	0.00909396i
$491$		−	27.9753i		−	1.26251i	−0.775576	−	0.631254i	$-0.782541\pi$
$491$		−	27.9753i		−	1.26251i	0.775576	−	0.631254i	$-0.217459\pi$
$492$	−4.37799			−0.197375
$493$	7.85029	−	7.85029i	0.353559	−	0.353559i
$494$		0			0
$495$	10.4928	−	23.9318i	0.471616	−	1.07565i
$496$	−15.0945	+	15.0945i	−0.677765	+	0.677765i
$497$	−12.6401	+	12.6401i	−0.566988	+	0.566988i
$498$	0.101277	−	0.101277i	0.00453834	−	0.00453834i
$499$	1.67479	+	1.67479i	0.0749740	+	0.0749740i	0.743599	−	0.668625i	$-0.233117\pi$
$499$	1.67479	+	1.67479i	0.0749740	+	0.0749740i	−0.668625	+	0.743599i	$0.733117\pi$
$500$	−9.72631	+	19.9202i	−0.434974	+	0.890860i
$501$	−5.02826	−	5.02826i	−0.224646	−	0.224646i
$502$	−0.613896			−0.0273995
$503$	16.3763	+	16.3763i	0.730184	+	0.730184i	0.970656	−	0.240472i	$-0.0773021\pi$
$503$	16.3763	+	16.3763i	0.730184	+	0.730184i	−0.240472	+	0.970656i	$0.577302\pi$
$504$	−4.19151			−0.186705
$505$	0.820476	+	2.10168i	0.0365107	+	0.0935237i
$506$			4.24760i			0.188829i
$507$		0			0
$508$	23.2016	+	23.2016i	1.02940	+	1.02940i
$509$	4.26103	+	4.26103i	0.188867	+	0.188867i	0.795206	−	0.606339i	$-0.207363\pi$
$509$	4.26103	+	4.26103i	0.188867	+	0.188867i	−0.606339	+	0.795206i	$0.707363\pi$
$510$	−0.228034	+	0.0890223i	−0.0100975	+	0.00394197i
$511$		−	27.6260i		−	1.22210i
$512$		−	10.1453i		−	0.448362i
$513$	3.84174			0.169617
$514$	1.61135	−	1.61135i	0.0710734	−	0.0710734i
$515$	7.61882	−	17.3769i	0.335725	−	0.765717i
$516$	−4.40752			−0.194030
$517$	−1.46923	−	1.46923i	−0.0646167	−	0.0646167i
$518$		−	2.56013i		−	0.112486i
$519$	6.24038			0.273922
$520$		0			0
$521$	27.8183			1.21874			0.609371	−	0.792886i	$-0.291422\pi$
$521$	27.8183			1.21874			0.609371	+	0.792886i	$0.291422\pi$
$522$		−	1.73265i		−	0.0758361i
$523$	−0.387298	−	0.387298i	−0.0169354	−	0.0169354i	0.698588	−	0.715524i	$-0.253812\pi$
$523$	−0.387298	−	0.387298i	−0.0169354	−	0.0169354i	−0.715524	+	0.698588i	$0.753812\pi$
$524$	−25.1573			−1.09900
$525$	−4.77850	−	0.196075i	−0.208551	−	0.00855742i
$526$	0.224841	−	0.224841i	0.00980352	−	0.00980352i
$527$	13.2812			0.578538
$528$			5.43449i			0.236506i
$529$		−	40.6367i		−	1.76681i
$530$	0.221184	−	0.504474i	0.00960763	−	0.0219129i
$531$	−5.35131	−	5.35131i	−0.232227	−	0.232227i
$532$	−7.40643	−	7.40643i	−0.321110	−	0.321110i
$533$		0			0
$534$		−	0.281282i		−	0.0121722i
$535$	−4.44959	+	10.1485i	−0.192372	+	0.438760i
$536$	1.89113			0.0816842
$537$	4.22200	+	4.22200i	0.182193	+	0.182193i
$538$	−1.27786			−0.0550923
$539$	−2.11056	−	2.11056i	−0.0909082	−	0.0909082i
$540$	3.60100	−	8.21311i	0.154962	−	0.353436i
$541$	29.7507	+	29.7507i	1.27908	+	1.27908i	0.941182	+	0.337899i	$0.109716\pi$
$541$	29.7507	+	29.7507i	1.27908	+	1.27908i	0.337899	+	0.941182i	$0.390284\pi$
$542$	−2.03494	+	2.03494i	−0.0874080	+	0.0874080i
$543$	6.06187	−	6.06187i	0.260140	−	0.260140i
$544$	−2.67022	+	2.67022i	−0.114485	+	0.114485i
$545$	−18.8539	−	8.26641i	−0.807612	−	0.354094i
$546$		0			0
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	−0.942864	−	0.333176i	$-0.891880\pi$
$547$	−14.2594	+	14.2594i	−0.609688	+	0.609688i	0.333176	+	0.942864i	$0.391880\pi$
$548$	29.6325			1.26584
$549$			3.69880i			0.157861i
$550$	−0.109151	+	2.66008i	−0.00465420	+	0.113426i
$551$	6.14984	−	6.14984i	0.261992	−	0.261992i
$552$			1.43463i			0.0610618i
$553$			23.2961i			0.990652i
$554$	1.67641	−	1.67641i	0.0712240	−	0.0712240i
$555$	4.93699	+	2.16460i	0.209564	+	0.0918822i
$556$			16.9967i			0.720823i
$557$	−35.1772			−1.49051			−0.745254	−	0.666781i	$-0.767672\pi$
$557$	−35.1772			−1.49051			−0.745254	+	0.666781i	$0.767672\pi$
$558$	1.46566	−	1.46566i	0.0620463	−	0.0620463i
$559$		0			0
$560$	−22.5765	+	8.81362i	−0.954030	+	0.372443i
$561$	2.39082	−	2.39082i	0.100940	−	0.100940i
$562$	−1.49342	+	1.49342i	−0.0629963	+	0.0629963i
$563$	29.6501	−	29.6501i	1.24960	−	1.24960i	0.293708	−	0.955895i	$-0.405111\pi$
$563$	29.6501	−	29.6501i	1.24960	−	1.24960i	0.955895	−	0.293708i	$-0.0948894\pi$
$564$	−0.247042	−	0.247042i	−0.0104024	−	0.0104024i
$565$	−15.3652	−	6.73679i	−0.646417	−	0.283419i
$566$	−1.05426	−	1.05426i	−0.0443140	−	0.0443140i
$567$	−22.1108			−0.928566
$568$	2.37657	+	2.37657i	0.0997186	+	0.0997186i
$569$	−27.5482			−1.15488			−0.577441	−	0.816433i	$-0.695949\pi$
$569$	−27.5482			−1.15488			−0.577441	+	0.816433i	$0.695949\pi$
$570$	−0.178640	+	0.0697392i	−0.00748241	+	0.00292105i
$571$		−	4.72029i		−	0.197538i	−0.995110	−	0.0987690i	$-0.968510\pi$
$571$		−	4.72029i		−	0.197538i	0.995110	−	0.0987690i	$-0.0314905\pi$
$572$		0			0
$573$	−1.65043	−	1.65043i	−0.0689476	−	0.0689476i
$574$	−1.65804	−	1.65804i	−0.0692052	−	0.0692052i
$575$	1.63527	−	39.8528i	0.0681955	−	1.66197i
$576$		−	21.8701i		−	0.911252i
$577$			6.73701i			0.280465i	0.990119	+	0.140233i	$0.0447851\pi$
$577$			6.73701i			0.280465i	−0.990119	+	0.140233i	$0.955215\pi$
$578$	−1.46034			−0.0607422
$579$	−0.290630	+	0.290630i	−0.0120782	+	0.0120782i
$580$	−7.38303	−	18.9120i	−0.306564	−	0.785276i
$581$	−8.82236			−0.366013
$582$	0.375805	+	0.375805i	0.0155776	+	0.0155776i
$583$			7.60813i			0.315097i
$584$	−5.19417			−0.214936
$585$		0			0
$586$	−0.0918611			−0.00379475
$587$		−	5.19438i		−	0.214395i	−0.994238	−	0.107198i	$-0.965812\pi$
$587$		−	5.19438i		−	0.214395i	0.994238	−	0.107198i	$-0.0341877\pi$
$588$	−0.354877	−	0.354877i	−0.0146349	−	0.0146349i
$589$	10.4044			0.428704
$590$	0.706152	+	0.309609i	0.0290718	+	0.0127464i
$591$	4.89285	−	4.89285i	0.201265	−	0.201265i
$592$	27.3177			1.12275
$593$			12.9267i			0.530836i	0.964133	+	0.265418i	$0.0855100\pi$
$593$			12.9267i			0.530836i	−0.964133	+	0.265418i	$0.914490\pi$
$594$		−	1.07702i		−	0.0441907i
$595$	13.8096	+	6.05474i	0.566137	+	0.248220i
$596$	17.0223	+	17.0223i	0.697262	+	0.697262i
$597$	−0.529553	−	0.529553i	−0.0216732	−	0.0216732i
$598$		0			0
$599$		−	16.7523i		−	0.684481i	−0.939612	−	0.342241i	$-0.888814\pi$
$599$		−	16.7523i		−	0.684481i	0.939612	−	0.342241i	$-0.111186\pi$
$600$	−0.0368656	+	0.898442i	−0.00150503	+	0.0366787i
$601$	12.5761			0.512988			0.256494	−	0.966546i	$-0.417433\pi$
$601$	12.5761			0.512988			0.256494	+	0.966546i	$0.417433\pi$
$602$	−1.66922	−	1.66922i	−0.0680324	−	0.0680324i
$603$	10.4212			0.424384
$604$	−3.70774	−	3.70774i	−0.150866	−	0.150866i
$605$	−4.42771	−	11.3418i	−0.180012	−	0.461108i
$606$	0.0322160	+	0.0322160i	0.00130868	+	0.00130868i
$607$	26.4935	−	26.4935i	1.07534	−	1.07534i	0.0784195	−	0.996920i	$-0.475013\pi$
$607$	26.4935	−	26.4935i	1.07534	−	1.07534i	0.996920	−	0.0784195i	$-0.0249874\pi$
$608$	−2.09182	+	2.09182i	−0.0848346	+	0.0848346i
$609$	3.09711	−	3.09711i	0.125501	−	0.125501i
$610$	−0.137044	−	0.351045i	−0.00554877	−	0.0142134i
$611$		0			0
$612$	−9.79548	+	9.79548i	−0.395959	+	0.395959i
$613$	−17.2946			−0.698524			−0.349262	−	0.937025i	$-0.613568\pi$
$613$	−17.2946			−0.698524			−0.349262	+	0.937025i	$0.613568\pi$
$614$		−	1.86512i		−	0.0752703i
$615$	4.59926	−	1.79550i	0.185460	−	0.0724016i
$616$	−4.17079	+	4.17079i	−0.168046	+	0.168046i
$617$			12.1401i			0.488742i	0.969682	+	0.244371i	$0.0785814\pi$
$617$			12.1401i			0.488742i	−0.969682	+	0.244371i	$0.921419\pi$
$618$		−	0.383150i		−	0.0154126i
$619$	2.99993	−	2.99993i	0.120577	−	0.120577i	−0.644243	−	0.764821i	$-0.722828\pi$
$619$	2.99993	−	2.99993i	0.120577	−	0.120577i	0.764821	+	0.644243i	$0.222828\pi$
$620$	9.75238	−	22.2431i	0.391665	−	0.893303i
$621$			16.1357i			0.647502i
$622$	−2.82249			−0.113172
$623$	−12.2514	+	12.2514i	−0.490840	+	0.490840i
$624$		0			0
$625$	2.04819	−	24.9160i	0.0819276	−	0.996638i
$626$	−1.22939	+	1.22939i	−0.0491363	+	0.0491363i
$627$	1.87294	−	1.87294i	0.0747982	−	0.0747982i
$628$	−20.4610	+	20.4610i	−0.816481	+	0.816481i
$629$	−12.0180	−	12.0180i	−0.479188	−	0.479188i
$630$	2.19214	−	0.855790i	0.0873371	−	0.0340955i
$631$	−15.3003	−	15.3003i	−0.609096	−	0.609096i	0.333614	−	0.942710i	$-0.391732\pi$
$631$	−15.3003	−	15.3003i	−0.609096	−	0.609096i	−0.942710	+	0.333614i	$0.891732\pi$
$632$	4.38008			0.174230
$633$	4.85197	+	4.85197i	0.192848	+	0.192848i
$634$	2.27185			0.0902265
$635$	−33.8896	−	14.8587i	−1.34487	−	0.589651i
$636$			1.27926i			0.0507260i
$637$		0			0
$638$	−1.72409	−	1.72409i	−0.0682572	−	0.0682572i
$639$	13.0963	+	13.0963i	0.518080	+	0.518080i
$640$	3.34343	+	8.56434i	0.132161	+	0.338535i
$641$			45.3182i			1.78996i	0.446106	+	0.894980i	$0.352810\pi$
$641$			45.3182i			1.78996i	−0.446106	+	0.894980i	$0.647190\pi$
$642$			0.223769i			0.00883148i
$643$	31.6498			1.24814			0.624072	−	0.781367i	$-0.285477\pi$
$643$	31.6498			1.24814			0.624072	+	0.781367i	$0.285477\pi$
$644$	31.1077	−	31.1077i	1.22581	−	1.22581i
$645$	4.63028	−	1.80761i	0.182317	−	0.0711747i
$646$	0.604623			0.0237886
$647$	−26.8607	−	26.8607i	−1.05600	−	1.05600i	−0.998336	−	0.0576668i	$-0.981634\pi$
$647$	−26.8607	−	26.8607i	−1.05600	−	1.05600i	−0.0576668	−	0.998336i	$-0.518366\pi$
$648$			4.15722i			0.163311i
$649$	−10.6497			−0.418038
$650$		0			0
$651$	5.23971			0.205361
$652$		−	37.0685i		−	1.45172i
$653$	1.95007	+	1.95007i	0.0763122	+	0.0763122i	0.744233	−	0.667920i	$-0.232815\pi$
$653$	1.95007	+	1.95007i	0.0763122	+	0.0763122i	−0.667920	+	0.744233i	$0.732815\pi$
$654$	−0.415718			−0.0162558
$655$	26.4287	−	10.3175i	1.03265	−	0.403138i
$656$	17.6920	−	17.6920i	0.690756	−	0.690756i
$657$	−28.6228			−1.11668
$658$		−	0.187120i		−	0.00729470i
$659$			2.08099i			0.0810639i	0.999178	+	0.0405320i	$0.0129053\pi$
$659$			2.08099i			0.0810639i	−0.999178	+	0.0405320i	$0.987095\pi$
$660$	−2.24852	−	5.75967i	−0.0875233	−	0.224195i
$661$	26.5742	+	26.5742i	1.03362	+	1.03362i	0.999415	+	0.0342010i	$0.0108886\pi$
$661$	26.5742	+	26.5742i	1.03362	+	1.03362i	0.0342010	+	0.999415i	$0.489111\pi$
$662$	−1.66840	−	1.66840i	−0.0648440	−	0.0648440i
$663$		0			0
$664$			1.65876i			0.0643723i
$665$	10.8183	+	4.74323i	0.419515	+	0.183934i
$666$	−2.65251			−0.102783
$667$	25.8299	+	25.8299i	1.00014	+	1.00014i
$668$	40.9991			1.58630
$669$	3.26177	+	3.26177i	0.126107	+	0.126107i
$670$	−0.989052	+	0.386116i	−0.0382104	+	0.0149169i
$671$	3.68052	+	3.68052i	0.142085	+	0.142085i
$672$	−1.05346	+	1.05346i	−0.0406380	+	0.0406380i
$673$	−12.7309	+	12.7309i	−0.490741	+	0.490741i	−0.908540	−	0.417799i	$-0.862802\pi$
$673$	−12.7309	+	12.7309i	−0.490741	+	0.490741i	0.417799	+	0.908540i	$0.362802\pi$
$674$	0.635068	−	0.635068i	0.0244619	−	0.0244619i
$675$	−0.414638	+	10.1050i	−0.0159594	+	0.388943i
$676$		0			0
$677$	15.4021	−	15.4021i	0.591952	−	0.591952i	−0.346206	−	0.938158i	$-0.612530\pi$
$677$	15.4021	−	15.4021i	0.591952	−	0.591952i	0.938158	+	0.346206i	$0.112530\pi$
$678$	−0.338793			−0.0130113
$679$		−	32.7367i		−	1.25632i
$680$	1.13840	−	2.59644i	0.0436556	−	0.0995689i
$681$	3.57007	−	3.57007i	0.136805	−	0.136805i
$682$		−	2.91683i		−	0.111691i
$683$			6.16751i			0.235993i	0.993014	+	0.117997i	$0.0376472\pi$
$683$			6.16751i			0.235993i	−0.993014	+	0.117997i	$0.962353\pi$
$684$	−7.67369	+	7.67369i	−0.293411	+	0.293411i
$685$	−31.1301	+	12.1529i	−1.18942	+	0.464337i
$686$			2.28761i			0.0873414i
$687$	1.29017			0.0492230
$688$	17.8113	−	17.8113i	0.679050	−	0.679050i
$689$		0			0
$690$	−0.292911	−	0.750304i	−0.0111509	−	0.0285636i
$691$	−9.28463	+	9.28463i	−0.353204	+	0.353204i	−0.861300	−	0.508096i	$-0.830349\pi$
$691$	−9.28463	+	9.28463i	−0.353204	+	0.353204i	0.508096	+	0.861300i	$0.330349\pi$
$692$	−25.4412	+	25.4412i	−0.967131	+	0.967131i
$693$	−22.9834	+	22.9834i	−0.873069	+	0.873069i
$694$	−1.72710	−	1.72710i	−0.0655600	−	0.0655600i
$695$	−6.97070	−	17.8558i	−0.264414	−	0.677308i
$696$	−0.582310	−	0.582310i	−0.0220724	−	0.0220724i
$697$	−15.5666			−0.589627
$698$	0.233693	+	0.233693i	0.00884543	+	0.00884543i
$699$	6.78252			0.256538
$700$	20.2807	−	18.6820i	0.766539	−	0.706112i
$701$		−	23.2292i		−	0.877354i	−0.898645	−	0.438677i	$-0.855447\pi$
$701$		−	23.2292i		−	0.877354i	0.898645	−	0.438677i	$-0.144553\pi$
$702$		0			0
$703$	−9.41478	−	9.41478i	−0.355085	−	0.355085i
$704$	−21.7620	−	21.7620i	−0.820184	−	0.820184i
$705$	0.360845	+	0.158211i	0.0135902	+	0.00595856i
$706$		−	4.29642i		−	0.161698i
$707$		−	2.80636i		−	0.105544i
$708$	−1.79068			−0.0672980
$709$	1.46763	−	1.46763i	0.0551179	−	0.0551179i	−0.679011	−	0.734128i	$-0.737591\pi$
$709$	1.46763	−	1.46763i	0.0551179	−	0.0551179i	0.734128	+	0.679011i	$0.237591\pi$
$710$	−1.72817	−	0.757707i	−0.0648569	−	0.0284362i
$711$	24.1367			0.905198
$712$	2.30347	+	2.30347i	0.0863262	+	0.0863262i
$713$			43.6993i			1.63655i
$714$	0.304493			0.0113954
$715$		0			0
$716$	−34.4251			−1.28653
$717$		−	4.95537i		−	0.185062i
$718$	−0.0918703	−	0.0918703i	−0.00342857	−	0.00342857i
$719$	−6.73696			−0.251246			−0.125623	−	0.992078i	$-0.540093\pi$
$719$	−6.73696			−0.251246			−0.125623	+	0.992078i	$0.540093\pi$
$720$	9.13165	+	23.3911i	0.340316	+	0.871735i
$721$	−16.6883	+	16.6883i	−0.621504	+	0.621504i
$722$	−2.02109			−0.0752173
$723$		−	2.78698i		−	0.103649i
$724$			49.4269i			1.83694i
$725$	15.5123	+	16.8398i	0.576114	+	0.625416i
$726$	−0.173854	−	0.173854i	−0.00645232	−	0.00645232i
$727$	34.4733	+	34.4733i	1.27854	+	1.27854i	0.941483	+	0.337062i	$0.109433\pi$
$727$	34.4733	+	34.4733i	1.27854	+	1.27854i	0.337062	+	0.941483i	$0.390567\pi$
$728$		0			0
$729$			20.8218i			0.771179i
$730$	2.71653	−	1.06051i	0.100543	−	0.0392511i
$731$	−15.6716			−0.579635
$732$	0.618857	+	0.618857i	0.0228736	+	0.0228736i
$733$	28.7555			1.06211			0.531054	−	0.847338i	$-0.321796\pi$
$733$	28.7555			1.06211			0.531054	+	0.847338i	$0.321796\pi$
$734$	−1.34379	−	1.34379i	−0.0496002	−	0.0496002i
$735$	0.518355	+	0.227271i	0.0191198	+	0.00838300i
$736$	−8.78585	−	8.78585i	−0.323851	−	0.323851i
$737$	10.3697	−	10.3697i	0.381972	−	0.381972i
$738$	−1.71787	+	1.71787i	−0.0632355	+	0.0632355i
$739$	−21.6960	+	21.6960i	−0.798100	+	0.798100i	−0.982796	−	0.184696i	$-0.940870\pi$
$739$	−21.6960	+	21.6960i	−0.798100	+	0.798100i	0.184696	+	0.982796i	$0.440870\pi$
$740$	−28.9523	+	11.3027i	−1.06431	+	0.415494i
$741$		0			0
$742$	−0.484483	+	0.484483i	−0.0177859	+	0.0177859i
$743$	−52.9634			−1.94304			−0.971519	−	0.236963i	$-0.923848\pi$
$743$	−52.9634			−1.94304			−0.971519	+	0.236963i	$0.923848\pi$
$744$		−	0.985158i		−	0.0361176i
$745$	−24.8638	−	10.9014i	−0.910940	−	0.399398i
$746$	−0.941490	+	0.941490i	−0.0344704	+	0.0344704i
$747$			9.14070i			0.334441i
$748$			19.4941i			0.712776i
$749$	9.74639	−	9.74639i	0.356125	−	0.356125i
$750$	−0.164156	−	0.477409i	−0.00599414	−	0.0174325i
$751$			46.6245i			1.70135i	0.525690	+	0.850676i	$0.323807\pi$
$751$			46.6245i			1.70135i	−0.525690	+	0.850676i	$0.676193\pi$
$752$	1.99665			0.0728104
$753$	−1.13693	+	1.13693i	−0.0414321	+	0.0414321i
$754$		0			0
$755$	5.41574	+	2.37451i	0.197099	+	0.0864172i
$756$	−7.88765	+	7.88765i	−0.286871	+	0.286871i
$757$	−0.883345	+	0.883345i	−0.0321057	+	0.0321057i	−0.722977	−	0.690872i	$-0.757227\pi$
$757$	−0.883345	+	0.883345i	−0.0321057	+	0.0321057i	0.690872	+	0.722977i	$0.257227\pi$
$758$	0.0975328	−	0.0975328i	0.00354255	−	0.00354255i
$759$	7.86654	+	7.86654i	0.285537	+	0.285537i
$760$	0.891810	−	2.03403i	0.0323493	−	0.0737819i
$761$	14.4328	+	14.4328i	0.523189	+	0.523189i	0.918533	−	0.395344i	$-0.129375\pi$
$761$	14.4328	+	14.4328i	0.523189	+	0.523189i	−0.395344	+	0.918533i	$0.629375\pi$
$762$	−0.747246			−0.0270698
$763$	18.1068	+	18.1068i	0.655509	+	0.655509i
$764$	13.4572			0.486863
$765$	6.27322	−	14.3079i	0.226809	−	0.517302i
$766$		−	1.57656i		−	0.0569633i
$767$		0			0
$768$	−3.55968	−	3.55968i	−0.128449	−	0.128449i
$769$	26.1077	+	26.1077i	0.941469	+	0.941469i	0.998379	−	0.0569104i	$-0.0181249\pi$
$769$	26.1077	+	26.1077i	0.941469	+	0.941469i	−0.0569104	+	0.998379i	$0.518125\pi$
$770$	1.32975	−	3.03287i	0.0479208	−	0.109297i
$771$		−	5.96841i		−	0.214947i
$772$		−	2.36972i		−	0.0852882i
$773$	−21.3836			−0.769114			−0.384557	−	0.923101i	$-0.625646\pi$
$773$	−21.3836			−0.769114			−0.384557	+	0.923101i	$0.625646\pi$
$774$	−1.72945	+	1.72945i	−0.0621639	+	0.0621639i
$775$	−1.12294	+	27.3669i	−0.0403372	+	0.983047i
$776$	−6.15508			−0.220954
$777$	−4.74135	−	4.74135i	−0.170095	−	0.170095i
$778$		−	0.967919i		−	0.0347016i
$779$	−12.1947			−0.436921
$780$		0			0
$781$	26.0630			0.932608
$782$			2.53947i			0.0908114i
$783$	−6.54941	−	6.54941i	−0.234057	−	0.234057i
$784$	2.86820			0.102436
$785$	13.1036	−	29.8865i	0.467688	−	1.06670i
$786$	0.405116	−	0.405116i	0.0144500	−	0.0144500i
$787$	−39.3828			−1.40385			−0.701923	−	0.712252i	$-0.747675\pi$
$787$	−39.3828			−1.40385			−0.701923	+	0.712252i	$0.747675\pi$
$788$			39.8950i			1.42120i
$789$		−	0.832807i		−	0.0296487i
$790$	−2.29076	+	0.894291i	−0.0815017	+	0.0318174i
$791$	14.7563	+	14.7563i	0.524673	+	0.524673i
$792$	4.32129	+	4.32129i	0.153550	+	0.153550i
$793$		0			0
$794$			0.795007i			0.0282138i
$795$	−0.524650	−	1.34391i	−0.0186074	−	0.0476637i
$796$	4.31784			0.153042
$797$	−27.6949	−	27.6949i	−0.981002	−	0.981002i	0.0188205	−	0.999823i	$-0.494009\pi$
$797$	−27.6949	−	27.6949i	−0.981002	−	0.981002i	−0.999823	+	0.0188205i	$0.994009\pi$
$798$	0.238537			0.00844411
$799$	−0.878395	−	0.878395i	−0.0310754	−	0.0310754i
$800$	−5.27641	−	5.72795i	−0.186549	−	0.202514i
$801$	12.6934	+	12.6934i	0.448500	+	0.448500i
$802$	−0.224177	+	0.224177i	−0.00791598	+	0.00791598i
$803$	−28.4813	+	28.4813i	−1.00508	+	1.00508i
$804$	1.74360	−	1.74360i	0.0614919	−	0.0614919i
$805$	−19.9220	+	45.4378i	−0.702158	+	1.60147i
$806$		0			0
$807$	−2.36658	+	2.36658i	−0.0833077	+	0.0833077i
$808$	−0.527646			−0.0185625
$809$		−	26.7479i		−	0.940406i	−0.882558	−	0.470203i	$-0.844181\pi$
$809$		−	26.7479i		−	0.940406i	0.882558	−	0.470203i	$-0.155819\pi$
$810$	−0.848789	−	2.17421i	−0.0298234	−	0.0763939i
$811$	7.93739	−	7.93739i	0.278720	−	0.278720i	−0.553878	−	0.832598i	$-0.686853\pi$
$811$	7.93739	−	7.93739i	0.278720	−	0.278720i	0.832598	+	0.553878i	$0.186853\pi$
$812$			25.2530i			0.886207i
$813$			7.53738i			0.264348i
$814$	−2.63940	+	2.63940i	−0.0925109	+	0.0925109i
$815$	15.2025	+	38.9420i	0.532522	+	1.36408i
$816$			3.24907i			0.113740i
$817$	−12.2770			−0.429517
$818$	−1.86963	+	1.86963i	−0.0653700	+	0.0653700i
$819$		0			0
$820$	−11.4305	+	26.0706i	−0.399172	+	0.910425i
$821$	−19.1010	+	19.1010i	−0.666629	+	0.666629i	−0.956934	−	0.290305i	$-0.906243\pi$
$821$	−19.1010	+	19.1010i	−0.666629	+	0.666629i	0.290305	+	0.956934i	$0.406243\pi$
$822$	−0.477182	+	0.477182i	−0.0166436	+	0.0166436i
$823$	6.63054	−	6.63054i	0.231126	−	0.231126i	−0.582036	−	0.813163i	$-0.697744\pi$
$823$	6.63054	−	6.63054i	0.231126	−	0.231126i	0.813163	+	0.582036i	$0.197744\pi$
$824$	3.13769	+	3.13769i	0.109307	+	0.109307i
$825$	4.72431	+	5.12860i	0.164479	+	0.178555i
$826$	−0.678170	−	0.678170i	−0.0235965	−	0.0235965i
$827$	45.0330			1.56595			0.782976	−	0.622052i	$-0.213701\pi$
$827$	45.0330			1.56595			0.782976	+	0.622052i	$0.213701\pi$
$828$	−32.2302	−	32.2302i	−1.12008	−	1.12008i
$829$	−42.0151			−1.45924			−0.729622	−	0.683851i	$-0.760304\pi$
$829$	−42.0151			−1.45924			−0.729622	+	0.683851i	$0.760304\pi$
$830$	−0.338672	−	0.867524i	−0.0117555	−	0.0301122i
$831$		−	6.20942i		−	0.215402i
$832$		0			0
$833$	−1.26182	−	1.26182i	−0.0437194	−	0.0437194i
$834$	−0.273705	−	0.273705i	−0.00947761	−	0.00947761i
$835$	−43.0712	+	16.8146i	−1.49054	+	0.581892i
$836$			15.2715i			0.528176i
$837$		−	11.0804i		−	0.382993i
$838$	3.94962			0.136437
$839$	−3.84087	+	3.84087i	−0.132602	+	0.132602i	−0.770292	−	0.637691i	$-0.779890\pi$
$839$	−3.84087	+	3.84087i	−0.132602	+	0.132602i	0.637691	+	0.770292i	$0.279890\pi$
$840$	0.449122	−	1.02435i	0.0154962	−	0.0353434i
$841$	8.03148			0.276948
$842$	1.21414	+	1.21414i	0.0418419	+	0.0418419i
$843$			5.53162i			0.190519i
$844$	−39.5617			−1.36177
$845$		0			0
$846$	−0.193872			−0.00666546
$847$			15.1446i			0.520374i
$848$	−5.16964	−	5.16964i	−0.177526	−	0.177526i
$849$	−3.90498			−0.134019
$850$	−0.0652568	+	1.59036i	−0.00223829	+	0.0545488i
$851$	39.5429	−	39.5429i	1.35551	−	1.35551i
$852$	4.38234			0.150136
$853$		−	23.0805i		−	0.790260i	−0.918625	−	0.395130i	$-0.870700\pi$
$853$		−	23.0805i		−	0.790260i	0.918625	−	0.395130i	$-0.129300\pi$
$854$			0.468748i			0.0160402i
$855$	4.91438	−	11.2086i	0.168068	−	0.383328i
$856$	−1.83249	−	1.83249i	−0.0626333	−	0.0626333i
$857$	37.6679	+	37.6679i	1.28671	+	1.28671i	0.936772	+	0.349940i	$0.113798\pi$
$857$	37.6679	+	37.6679i	1.28671	+	1.28671i	0.349940	+	0.936772i	$0.386202\pi$
$858$		0			0
$859$		−	5.08674i		−	0.173557i	−0.996228	−	0.0867787i	$-0.972343\pi$
$859$		−	5.08674i		−	0.173557i	0.996228	−	0.0867787i	$-0.0276573\pi$
$860$	−11.5077	+	26.2465i	−0.392408	+	0.894997i
$861$	−6.14135			−0.209297
$862$	−0.585972	−	0.585972i	−0.0199583	−	0.0199583i
$863$	−45.1879			−1.53821			−0.769107	−	0.639120i	$-0.779299\pi$
$863$	−45.1879			−1.53821			−0.769107	+	0.639120i	$0.779299\pi$
$864$	2.22773	+	2.22773i	0.0757891	+	0.0757891i
$865$	16.2931	−	37.1610i	0.553981	−	1.26351i
$866$	1.14100	+	1.14100i	0.0387728	+	0.0387728i
$867$	−2.70454	+	2.70454i	−0.0918511	+	0.0918511i
$868$	−21.3616	+	21.3616i	−0.725061	+	0.725061i
$869$	24.0174	−	24.0174i	0.814735	−	0.814735i
$870$	0.423437	+	0.185654i	0.0143559	+	0.00629427i
$871$		0			0
$872$	3.40439	−	3.40439i	0.115287	−	0.115287i
$873$	−33.9180			−1.14795
$874$			1.98940i			0.0672924i
$875$	−13.6439	+	27.9437i	−0.461246	+	0.944669i
$876$	−4.78896	+	4.78896i	−0.161804	+	0.161804i
$877$			20.3282i			0.686436i	0.939256	+	0.343218i	$0.111517\pi$
$877$			20.3282i			0.686436i	−0.939256	+	0.343218i	$0.888483\pi$
$878$		−	4.52267i		−	0.152633i
$879$	−0.170126	+	0.170126i	−0.00573821	+	0.00573821i
$880$	32.3620	+	14.1890i	1.09092	+	0.478310i
$881$			33.0200i			1.11247i	0.831025	+	0.556236i	$0.187755\pi$
$881$			33.0200i			1.11247i	−0.831025	+	0.556236i	$0.812245\pi$
$882$	−0.278498			−0.00937753
$883$	15.9555	−	15.9555i	0.536944	−	0.536944i	−0.385686	−	0.922630i	$-0.626035\pi$
$883$	15.9555	−	15.9555i	0.536944	−	0.536944i	0.922630	+	0.385686i	$0.126035\pi$
$884$		0			0
$885$	1.88119	−	0.734395i	0.0632353	−	0.0246864i
$886$	−0.708315	+	0.708315i	−0.0237963	+	0.0237963i
$887$	−0.446393	+	0.446393i	−0.0149884	+	0.0149884i	−0.714561	−	0.699573i	$-0.753374\pi$
$887$	−0.446393	+	0.446393i	−0.0149884	+	0.0149884i	0.699573	+	0.714561i	$0.253374\pi$
$888$	−0.891457	+	0.891457i	−0.0299153	+	0.0299153i
$889$	32.5466	+	32.5466i	1.09158	+	1.09158i
$890$	−1.67501	−	0.734401i	−0.0561465	−	0.0246172i
$891$	22.7954	+	22.7954i	0.763675	+	0.763675i
$892$	−26.5956			−0.890488
$893$	−0.688126	−	0.688126i	−0.0230273	−	0.0230273i
$894$	−0.548233			−0.0183356
$895$	36.1649	−	14.1184i	1.20886	−	0.471926i
$896$		−	11.4359i		−	0.382046i
$897$		0			0
$898$	2.89072	+	2.89072i	0.0964647	+	0.0964647i
$899$	−17.7374	−	17.7374i	−0.591575	−	0.591575i
$900$	−19.3561	−	21.0125i	−0.645203	−	0.700417i
$901$			4.54860i			0.151536i
$902$			3.41875i			0.113832i
$903$	−6.18278			−0.205750
$904$	2.77444	−	2.77444i	0.0922765	−	0.0922765i
$905$	−20.2710	−	51.9250i	−0.673830	−	1.72604i
$906$	0.119414			0.00396726
$907$	−27.6995	−	27.6995i	−0.919748	−	0.919748i	0.0772631	−	0.997011i	$-0.475382\pi$
$907$	−27.6995	−	27.6995i	−0.919748	−	0.919748i	−0.997011	+	0.0772631i	$0.975382\pi$
$908$			29.1094i			0.966031i
$909$	−2.90763			−0.0964400
$910$		0			0
$911$	6.21630			0.205955			0.102978	−	0.994684i	$-0.467163\pi$
$911$	6.21630			0.205955			0.102978	+	0.994684i	$0.467163\pi$
$912$			2.54529i			0.0842829i
$913$	9.09552	+	9.09552i	0.301018	+	0.301018i
$914$	−0.408023			−0.0134962
$915$	−0.903940	−	0.396328i	−0.0298833	−	0.0131022i
$916$	−5.25986	+	5.25986i	−0.173791	+	0.173791i
$917$	−35.2900			−1.16538
$918$		−	0.643907i		−	0.0212521i
$919$		−	22.9801i		−	0.758043i	−0.925388	−	0.379022i	$-0.876261\pi$
$919$		−	22.9801i		−	0.758043i	0.925388	−	0.379022i	$-0.123739\pi$
$920$	8.54309	+	3.74568i	0.281657	+	0.123492i
$921$	−3.45420	−	3.45420i	−0.113820	−	0.113820i
$922$	1.55017	+	1.55017i	0.0510520	+	0.0510520i
$923$		0			0
$924$			7.69084i			0.253010i
$925$	25.7801	−	23.7478i	0.847644	−	0.780823i
$926$	−2.05351			−0.0674827
$927$	17.2905	+	17.2905i	0.567894	+	0.567894i
$928$	7.13229			0.234129
$929$	−0.766865	−	0.766865i	−0.0251600	−	0.0251600i	0.694415	−	0.719575i	$-0.255663\pi$
$929$	−0.766865	−	0.766865i	−0.0251600	−	0.0251600i	−0.719575	+	0.694415i	$0.755663\pi$
$930$	0.201142	+	0.515234i	0.00659570	+	0.0168952i
$931$	−0.988497	−	0.988497i	−0.0323967	−	0.0323967i
$932$	−27.6514	+	27.6514i	−0.905753	+	0.905753i
$933$	−5.22724	+	5.22724i	−0.171132	+	0.171132i
$934$	1.98032	−	1.98032i	0.0647980	−	0.0647980i
$935$	−7.99493	−	20.4794i	−0.261462	−	0.669746i
$936$		0			0
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	−0.741772	−	0.670653i	$-0.766014\pi$
$937$	−2.17699	+	2.17699i	−0.0711191	+	0.0711191i	0.670653	+	0.741772i	$0.266014\pi$
$938$	1.32067			0.0431215
$939$			4.55365i			0.148603i
$940$	−2.11612	+	0.826112i	−0.0690203	+	0.0269448i
$941$	22.9413	−	22.9413i	0.747866	−	0.747866i	−0.226212	−	0.974078i	$-0.572634\pi$
$941$	22.9413	−	22.9413i	0.747866	−	0.747866i	0.974078	+	0.226212i	$0.0726342\pi$
$942$		−	0.658980i		−	0.0214707i
$943$		−	51.2190i		−	1.66792i
$944$	7.23636	−	7.23636i	0.235523	−	0.235523i
$945$	5.05141	−	11.5212i	0.164322	−	0.374784i
$946$			3.44181i			0.111903i
$947$	−27.2986			−0.887086			−0.443543	−	0.896253i	$-0.646279\pi$
$947$	−27.2986			−0.887086			−0.443543	+	0.896253i	$0.646279\pi$
$948$	4.03838	−	4.03838i	0.131161	−	0.131161i
$949$		0			0
$950$	−0.0511215	+	1.24587i	−0.00165860	+	0.0404214i
$951$	4.20745	−	4.20745i	0.136436	−	0.136436i
$952$	−2.49355	+	2.49355i	−0.0808164	+	0.0808164i
$953$	−4.52281	+	4.52281i	−0.146508	+	0.146508i	−0.776556	−	0.630048i	$-0.783035\pi$
$953$	−4.52281	+	4.52281i	−0.146508	+	0.146508i	0.630048	+	0.776556i	$0.283035\pi$
$954$	0.501965	+	0.501965i	0.0162517	+	0.0162517i
$955$	−14.1373	+	5.51905i	−0.457472	+	0.178592i
$956$	20.2024	+	20.2024i	0.653393	+	0.653393i
$957$	−6.38600			−0.206430
$958$	−3.95981	−	3.95981i	−0.127936	−	0.127936i
$959$	41.5678			1.34229
$960$	5.34476	+	2.34339i	0.172501	+	0.0756325i
$961$			0.991728i			0.0319912i
$962$		0			0
$963$	−10.0981	−	10.0981i	−0.325406	−	0.325406i
$964$	11.3622	+	11.3622i	0.365951	+	0.365951i
$965$	0.971870	+	2.48949i	0.0312856	+	0.0801394i
$966$			1.00188i			0.0322348i
$967$		−	28.4424i		−	0.914647i	−0.889300	−	0.457324i	$-0.848808\pi$
$967$		−	28.4424i		−	0.914647i	0.889300	−	0.457324i	$-0.151192\pi$
$968$	2.84744			0.0915203
$969$	1.11976	−	1.11976i	0.0359718	−	0.0359718i
$970$	3.21908	−	1.25670i	0.103358	−	0.0403501i
$971$	−1.23984			−0.0397884			−0.0198942	−	0.999802i	$-0.506333\pi$
$971$	−1.23984			−0.0397884			−0.0198942	+	0.999802i	$0.506333\pi$
$972$	12.3406	+	12.3406i	0.395824	+	0.395824i
$973$			23.8427i			0.764361i
$974$	−1.99799			−0.0640197
$975$		0			0
$976$	−5.00174			−0.160102
$977$		−	38.0451i		−	1.21717i	−0.793488	−	0.608586i	$-0.791737\pi$
$977$		−	38.0451i		−	1.21717i	0.793488	−	0.608586i	$-0.208263\pi$
$978$	0.596928	+	0.596928i	0.0190876	+	0.0190876i
$979$	25.2614			0.807357
$980$	−3.03982	+	1.18671i	−0.0971035	+	0.0379082i
$981$	18.7601	−	18.7601i	0.598965	−	0.598965i
$982$	−3.67323			−0.117217
$983$			34.5934i			1.10336i	0.834056	+	0.551679i	$0.186013\pi$
$983$			34.5934i			1.10336i	−0.834056	+	0.551679i	$0.813987\pi$
$984$			1.15468i			0.0368099i
$985$	−16.3618	−	41.9113i	−0.521329	−	1.33541i
$986$	−1.03076	−	1.03076i	−0.0328262	−	0.0328262i
$987$	−0.346545	−	0.346545i	−0.0110307	−	0.0110307i
$988$		0			0
$989$		−	51.5644i		−	1.63965i
$990$	−3.14231	−	1.37773i	−0.0998690	−	0.0437871i
$991$	39.4972			1.25467			0.627335	−	0.778750i	$-0.284146\pi$
$991$	39.4972			1.25467			0.627335	+	0.778750i	$0.284146\pi$
$992$	6.03324	+	6.03324i	0.191555	+	0.191555i
$993$	−6.17972			−0.196107
$994$	1.65968	+	1.65968i	0.0526420	+	0.0526420i
$995$	−4.53606	+	1.77083i	−0.143803	+	0.0561391i
$996$	1.52936	+	1.52936i	0.0484595	+	0.0484595i
$997$	5.20122	−	5.20122i	0.164724	−	0.164724i	−0.619932	−	0.784656i	$-0.712840\pi$
$997$	5.20122	−	5.20122i	0.164724	−	0.164724i	0.784656	+	0.619932i	$0.212840\pi$
$998$	0.219905	−	0.219905i	0.00696096	−	0.00696096i
$999$	−10.0265	+	10.0265i	−0.317224	+	0.317224i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.d.408.4		20
5.2	odd	4		845.2.k.d.577.7		20
13.2	odd	12		845.2.o.e.488.3		20
13.3	even	3		845.2.t.g.188.3		20
13.4	even	6		845.2.t.f.418.3		20
13.5	odd	4		845.2.k.e.268.4		20
13.6	odd	12		65.2.o.a.63.3	yes	20
13.7	odd	12		845.2.o.g.258.3		20
13.8	odd	4		845.2.k.d.268.7		20
13.9	even	3		845.2.t.e.418.3		20
13.10	even	6		65.2.t.a.58.3	yes	20
13.11	odd	12		845.2.o.f.488.3		20
13.12	even	2		845.2.f.e.408.7		20
39.23	odd	6		585.2.dp.a.253.3		20
39.32	even	12		585.2.cf.a.388.3		20
65.2	even	12		845.2.t.f.657.3		20
65.7	even	12		845.2.t.g.427.3		20
65.12	odd	4		845.2.k.e.577.4		20
65.17	odd	12		845.2.o.e.587.3		20
65.19	odd	12		325.2.s.b.193.3		20
65.22	odd	12		845.2.o.f.587.3		20
65.23	odd	12		325.2.s.b.32.3		20
65.32	even	12		65.2.t.a.37.3	yes	20
65.37	even	12		845.2.t.e.657.3		20
65.42	odd	12		845.2.o.g.357.3		20
65.47	even	4	inner	845.2.f.d.437.7		20
65.49	even	6		325.2.x.b.318.3		20
65.57	even	4		845.2.f.e.437.4		20
65.58	even	12		325.2.x.b.232.3		20
65.62	odd	12		65.2.o.a.32.3	✓	20
195.32	odd	12		585.2.dp.a.37.3		20
195.62	even	12		585.2.cf.a.487.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.3	✓	20	65.62	odd	12
65.2.o.a.63.3	yes	20	13.6	odd	12
65.2.t.a.37.3	yes	20	65.32	even	12
65.2.t.a.58.3	yes	20	13.10	even	6
325.2.s.b.32.3		20	65.23	odd	12
325.2.s.b.193.3		20	65.19	odd	12
325.2.x.b.232.3		20	65.58	even	12
325.2.x.b.318.3		20	65.49	even	6
585.2.cf.a.388.3		20	39.32	even	12
585.2.cf.a.487.3		20	195.62	even	12
585.2.dp.a.37.3		20	195.32	odd	12
585.2.dp.a.253.3		20	39.23	odd	6
845.2.f.d.408.4		20	1.1	even	1	trivial
845.2.f.d.437.7		20	65.47	even	4	inner
845.2.f.e.408.7		20	13.12	even	2
845.2.f.e.437.4		20	65.57	even	4
845.2.k.d.268.7		20	13.8	odd	4
845.2.k.d.577.7		20	5.2	odd	4
845.2.k.e.268.4		20	13.5	odd	4
845.2.k.e.577.4		20	65.12	odd	4
845.2.o.e.488.3		20	13.2	odd	12
845.2.o.e.587.3		20	65.17	odd	12
845.2.o.f.488.3		20	13.11	odd	12
845.2.o.f.587.3		20	65.22	odd	12
845.2.o.g.258.3		20	13.7	odd	12
845.2.o.g.357.3		20	65.42	odd	12
845.2.t.e.418.3		20	13.9	even	3
845.2.t.e.657.3		20	65.37	even	12
845.2.t.f.418.3		20	13.4	even	6
845.2.t.f.657.3		20	65.2	even	12
845.2.t.g.188.3		20	13.3	even	3
845.2.t.g.427.3		20	65.7	even	12

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.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.131303i q^{2} +(-0.243172 - 0.243172i) q^{3} +1.98276 q^{4} +(-2.08297 + 0.813169i) q^{5} +(-0.0319291 + 0.0319291i) q^{6} +2.78137 q^{7} -0.522947i q^{8} -2.88174i q^{9} +(0.106771 + 0.273499i) q^{10} +(-2.86749 - 2.86749i) q^{11} +(-0.482151 - 0.482151i) q^{12} -0.365201i q^{14} +(0.704259 + 0.308779i) q^{15} +3.89686 q^{16} +(-1.71436 - 1.71436i) q^{17} -0.378379 q^{18} +(-1.34301 - 1.34301i) q^{19} +(-4.13003 + 1.61232i) q^{20} +(-0.676351 - 0.676351i) q^{21} +(-0.376509 + 0.376509i) q^{22} +(5.64077 - 5.64077i) q^{23} +(-0.127166 + 0.127166i) q^{24} +(3.67751 - 3.38761i) q^{25} +(-1.43027 + 1.43027i) q^{27} +5.51479 q^{28} +4.57914i q^{29} +(0.0405435 - 0.0924710i) q^{30} +(-3.87352 + 3.87352i) q^{31} -1.55756i q^{32} +1.39458i q^{33} +(-0.225100 + 0.225100i) q^{34} +(-5.79351 + 2.26173i) q^{35} -5.71379i q^{36} +7.01019 q^{37} +(-0.176341 + 0.176341i) q^{38} +(0.425244 + 1.08928i) q^{40} +(4.54006 - 4.54006i) q^{41} +(-0.0888066 + 0.0888066i) q^{42} +(4.57069 - 4.57069i) q^{43} +(-5.68554 - 5.68554i) q^{44} +(2.34334 + 6.00256i) q^{45} +(-0.740648 - 0.740648i) q^{46} +0.512375 q^{47} +(-0.947605 - 0.947605i) q^{48} +0.736030 q^{49} +(-0.444802 - 0.482867i) q^{50} +0.833767i q^{51} +(-1.32662 - 1.32662i) q^{53} +(0.187798 + 0.187798i) q^{54} +(8.30464 + 3.64114i) q^{55} -1.45451i q^{56} +0.653165i q^{57} +0.601253 q^{58} +(1.85697 - 1.85697i) q^{59} +(1.39638 + 0.612235i) q^{60} -1.28353 q^{61} +(0.508603 + 0.508603i) q^{62} -8.01518i q^{63} +7.58920 q^{64} +0.183113 q^{66} +3.61629i q^{67} +(-3.39916 - 3.39916i) q^{68} -2.74335 q^{69} +(0.296970 + 0.760703i) q^{70} +(-4.54457 + 4.54457i) q^{71} -1.50699 q^{72} -9.93250i q^{73} -0.920457i q^{74} +(-1.71804 - 0.0704959i) q^{75} +(-2.66287 - 2.66287i) q^{76} +(-7.97556 - 7.97556i) q^{77} +8.37577i q^{79} +(-8.11702 + 3.16880i) q^{80} -7.94960 q^{81} +(-0.596122 - 0.596122i) q^{82} -3.17194 q^{83} +(-1.34104 - 1.34104i) q^{84} +(4.96502 + 2.17689i) q^{85} +(-0.600143 - 0.600143i) q^{86} +(1.11352 - 1.11352i) q^{87} +(-1.49954 + 1.49954i) q^{88} +(-4.40479 + 4.40479i) q^{89} +(0.788152 - 0.307686i) q^{90} +(11.1843 - 11.1843i) q^{92} +1.88386 q^{93} -0.0672762i q^{94} +(3.88955 + 1.70536i) q^{95} +(-0.378755 + 0.378755i) q^{96} -11.7700i q^{97} -0.0966426i q^{98} +(-8.26335 + 8.26335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

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