LMFDB - Embedded newform 845.2.k.e.577.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
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			577.4
Root			$0.131303i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.e.268.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.131303 q^{2} +(-0.243172 + 0.243172i) q^{3} -1.98276 q^{4} +(0.813169 - 2.08297i) q^{5} +(0.0319291 - 0.0319291i) q^{6} -2.78137i q^{7} +0.522947 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} +(0.308779 + 0.704259i) q^{15} +3.89686 q^{16} +(1.71436 - 1.71436i) q^{17} -0.378379i q^{18} +(-1.34301 - 1.34301i) q^{19} +(-1.61232 + 4.13003i) 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} +5.51479i q^{28} -4.57914i q^{29} +(-0.0405435 - 0.0924710i) q^{30} +(3.87352 - 3.87352i) q^{31} -1.55756 q^{32} -1.39458 q^{33} +(-0.225100 + 0.225100i) q^{34} +(-5.79351 - 2.26173i) q^{35} -5.71379i q^{36} -7.01019i 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} +(6.00256 + 2.34334i) q^{45} +(0.740648 + 0.740648i) q^{46} -0.512375i q^{47} +(-0.947605 + 0.947605i) q^{48} -0.736030 q^{49} +(0.482867 + 0.444802i) 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} +0.653165 q^{57} +0.601253i q^{58} +(1.85697 - 1.85697i) q^{59} +(-0.612235 - 1.39638i) q^{60} -1.28353 q^{61} +(-0.508603 + 0.508603i) q^{62} +8.01518 q^{63} -7.58920 q^{64} +0.183113 q^{66} +3.61629 q^{67} +(-3.39916 + 3.39916i) q^{68} +2.74335 q^{69} +(0.760703 + 0.296970i) q^{70} +(4.54457 - 4.54457i) q^{71} +1.50699i q^{72} +9.93250 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} +(3.16880 - 8.11702i) q^{80} -7.94960 q^{81} +(0.596122 - 0.596122i) q^{82} -3.17194i q^{83} +(-1.34104 - 1.34104i) q^{84} +(-2.17689 - 4.96502i) 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} +1.88386i q^{93} +0.0672762i q^{94} +(-3.88955 + 1.70536i) q^{95} +(0.378755 - 0.378755i) q^{96} -11.7700 q^{97} +0.0966426 q^{98} +(-8.26335 + 8.26335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.131303			−0.0928450			−0.0464225	−	0.998922i	$-0.514782\pi$
$2$	−0.131303			−0.0928450			−0.0464225	+	0.998922i	$0.514782\pi$
$3$	−0.243172	+	0.243172i	−0.140395	+	0.140395i	−0.773811	−	0.633416i	$-0.781652\pi$
$3$	−0.243172	+	0.243172i	−0.140395	+	0.140395i	0.633416	+	0.773811i	$0.281652\pi$
$4$	−1.98276			−0.991380
$5$	0.813169	−	2.08297i	0.363660	−	0.931532i
$5$	0.813169	−	2.08297i	0.363660	−	0.931532i
$6$	0.0319291	−	0.0319291i	0.0130350	−	0.0130350i
$7$		−	2.78137i		−	1.05126i	−0.850713	−	0.525630i	$-0.823830\pi$
$7$		−	2.78137i		−	1.05126i	0.850713	−	0.525630i	$-0.176170\pi$
$8$	0.522947			0.184890
$9$			2.88174i			0.960578i
$10$	−0.106771	+	0.273499i	−0.0337640	+	0.0864880i
$11$	2.86749	+	2.86749i	0.864581	+	0.864581i	0.991866	−	0.127285i	$-0.0406264\pi$
$11$	2.86749	+	2.86749i	0.864581	+	0.864581i	−0.127285	+	0.991866i	$0.540626\pi$
$12$	0.482151	−	0.482151i	0.139185	−	0.139185i
$13$		0			0
$13$		0			0
$14$			0.365201i			0.0976042i
$15$	0.308779	+	0.704259i	0.0797264	+	0.181839i
$16$	3.89686			0.974214
$17$	1.71436	−	1.71436i	0.415793	−	0.415793i	−0.467958	−	0.883751i	$-0.655010\pi$
$17$	1.71436	−	1.71436i	0.415793	−	0.415793i	0.883751	+	0.467958i	$0.155010\pi$
$18$		−	0.378379i		−	0.0891849i
$19$	−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	$0.819909\pi$
$20$	−1.61232	+	4.13003i	−0.360525	+	0.923502i
$21$	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	−0.980709	−	0.195474i	$-0.937376\pi$
$23$	−5.64077	−	5.64077i	−1.17618	−	1.17618i	−0.195474	−	0.980709i	$-0.562624\pi$
$24$	−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
$28$			5.51479i			1.04220i
$29$		−	4.57914i		−	0.850325i	−0.905117	−	0.425162i	$-0.860217\pi$
$29$		−	4.57914i		−	0.850325i	0.905117	−	0.425162i	$-0.139783\pi$
$30$	−0.0405435	−	0.0924710i	−0.00740220	−	0.0168828i
$31$	3.87352	−	3.87352i	0.695704	−	0.695704i	−0.267777	−	0.963481i	$-0.586289\pi$
$31$	3.87352	−	3.87352i	0.695704	−	0.695704i	0.963481	+	0.267777i	$0.0862890\pi$
$32$	−1.55756			−0.275340
$33$	−1.39458			−0.242766
$34$	−0.225100	+	0.225100i	−0.0386043	+	0.0386043i
$35$	−5.79351	−	2.26173i	−0.979282	−	0.382301i
$36$		−	5.71379i		−	0.952298i
$37$		−	7.01019i		−	1.15247i	−0.817284	−	0.576234i	$-0.804522\pi$
$37$		−	7.01019i		−	1.15247i	0.817284	−	0.576234i	$-0.195478\pi$
$38$	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	−0.966333	−	0.257294i	$-0.917169\pi$
$41$	−4.54006	+	4.54006i	−0.709039	+	0.709039i	0.257294	+	0.966333i	$0.417169\pi$
$42$	−0.0888066	−	0.0888066i	−0.0137032	−	0.0137032i
$43$	−4.57069	−	4.57069i	−0.697023	−	0.697023i	0.266744	−	0.963767i	$-0.414052\pi$
$43$	−4.57069	−	4.57069i	−0.697023	−	0.697023i	−0.963767	+	0.266744i	$0.914052\pi$
$44$	−5.68554	−	5.68554i	−0.857128	−	0.857128i
$45$	6.00256	+	2.34334i	0.894809	+	0.349324i
$46$	0.740648	+	0.740648i	0.109203	+	0.109203i
$47$		−	0.512375i		−	0.0747376i	−0.999302	−	0.0373688i	$-0.988102\pi$
$47$		−	0.512375i		−	0.0747376i	0.999302	−	0.0373688i	$-0.0118976\pi$
$48$	−0.947605	+	0.947605i	−0.136775	+	0.136775i
$49$	−0.736030			−0.105147
$50$	0.482867	+	0.444802i	0.0682877	+	0.0629045i
$51$			0.833767i			0.116751i
$52$		0			0
$53$	−1.32662	+	1.32662i	−0.182225	+	0.182225i	−0.792325	−	0.610100i	$-0.791129\pi$
$53$	−1.32662	+	1.32662i	−0.182225	+	0.182225i	0.610100	+	0.792325i	$0.291129\pi$
$54$	0.187798	+	0.187798i	0.0255561	+	0.0255561i
$55$	8.30464	−	3.64114i	1.11980	−	0.490971i
$56$		−	1.45451i		−	0.194367i
$57$	0.653165			0.0865138
$58$			0.601253i			0.0789484i
$59$	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	$0.195317\pi$
$60$	−0.612235	−	1.39638i	−0.0790392	−	0.180271i
$61$	−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
$63$	8.01518			1.00982
$64$	−7.58920			−0.948650
$65$		0			0
$66$	0.183113			0.0225396
$67$	3.61629			0.441800			0.220900	−	0.975296i	$-0.429101\pi$
$67$	3.61629			0.441800			0.220900	+	0.975296i	$0.429101\pi$
$68$	−3.39916	+	3.39916i	−0.412209	+	0.412209i
$69$	2.74335			0.330261
$70$	0.760703	+	0.296970i	0.0909214	+	0.0354948i
$71$	4.54457	−	4.54457i	0.539341	−	0.539341i	−0.383994	−	0.923336i	$-0.625452\pi$
$71$	4.54457	−	4.54457i	0.539341	−	0.539341i	0.923336	+	0.383994i	$0.125452\pi$
$72$			1.50699i			0.177601i
$73$	9.93250			1.16251			0.581256	−	0.813721i	$-0.302562\pi$
$73$	9.93250			1.16251			0.581256	+	0.813721i	$0.302562\pi$
$74$			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	$-0.843831\pi$
$79$		−	8.37577i		−	0.942347i	0.882040	−	0.471174i	$-0.156169\pi$
$80$	3.16880	−	8.11702i	0.354283	−	0.907511i
$81$	−7.94960			−0.883289
$82$	0.596122	−	0.596122i	0.0658307	−	0.0658307i
$83$		−	3.17194i		−	0.348166i	−0.984731	−	0.174083i	$-0.944304\pi$
$83$		−	3.17194i		−	0.348166i	0.984731	−	0.174083i	$-0.0556961\pi$
$84$	−1.34104	−	1.34104i	−0.146320	−	0.146320i
$85$	−2.17689	−	4.96502i	−0.236117	−	0.538532i
$86$	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
$93$			1.88386i			0.195347i
$94$			0.0672762i			0.00693901i
$95$	−3.88955	+	1.70536i	−0.399059	+	0.174966i
$96$	0.378755	−	0.378755i	0.0386565	−	0.0386565i
$97$	−11.7700			−1.19506			−0.597531	−	0.801846i	$-0.703851\pi$
$97$	−11.7700			−1.19506			−0.597531	+	0.801846i	$0.703851\pi$
$98$	0.0966426			0.00976238
$99$	−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	$-0.0159855\pi$
$102$		−	0.109476i		−	0.0108397i
$103$	6.00002	+	6.00002i	0.591200	+	0.591200i	0.937955	−	0.346756i	$-0.112717\pi$
$103$	6.00002	+	6.00002i	0.591200	+	0.591200i	−0.346756	+	0.937955i	$0.612717\pi$
$104$		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	0.855901	−	0.517140i	$-0.173003\pi$
$107$	3.50416	+	3.50416i	0.338760	+	0.338760i	−0.517140	+	0.855901i	$0.673003\pi$
$108$	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	$0.604654\pi$
$110$	−1.09042	+	0.478091i	−0.103968	+	0.0455842i
$111$	1.70468	+	1.70468i	0.161801	+	0.161801i
$112$		−	10.8386i		−	1.02415i
$113$	5.30540	−	5.30540i	0.499090	−	0.499090i	−0.412065	−	0.911155i	$-0.635192\pi$
$113$	5.30540	−	5.30540i	0.499090	−	0.499090i	0.911155	+	0.412065i	$0.135192\pi$
$114$	−0.0857623			−0.00803237
$115$	−16.3365	+	7.16265i	−1.52338	+	0.667920i
$116$			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
$122$	0.168531			0.0152581
$123$		−	2.20803i		−	0.199091i
$124$	−7.68025	+	7.68025i	−0.689707	+	0.689707i
$125$	−10.0467	+	4.90544i	−0.898606	+	0.438756i
$126$	−1.05241			−0.0937564
$127$	−11.7016	+	11.7016i	−1.03835	+	1.03835i	−0.0391188	+	0.999235i	$0.512455\pi$
$127$	−11.7016	+	11.7016i	−1.03835	+	1.03835i	−0.999235	+	0.0391188i	$0.987545\pi$
$128$	4.11160			0.363418
$129$	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	$0.687006\pi$
$132$	2.76513			0.240673
$133$	−3.73542	+	3.73542i	−0.323902	+	0.323902i
$134$	−0.474828			−0.0410189
$135$	−4.14226	+	1.81616i	−0.356509	+	0.156310i
$136$	0.896518	−	0.896518i	0.0768758	−	0.0768758i
$137$		−	14.9451i		−	1.27684i	−0.769687	−	0.638422i	$-0.779588\pi$
$137$		−	14.9451i		−	1.27684i	0.769687	−	0.638422i	$-0.220412\pi$
$138$	−0.360209			−0.0306631
$139$		−	8.57227i		−	0.727090i	−0.931577	−	0.363545i	$-0.881566\pi$
$139$		−	8.57227i		−	0.727090i	0.931577	−	0.363545i	$-0.118434\pi$
$140$	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
$145$	−9.53820	−	3.72361i	−0.792105	−	0.309229i
$146$	−1.30416			−0.107933
$147$	0.178982	−	0.178982i	0.0147622	−	0.0147622i
$148$			13.8995i			1.14253i
$149$	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	$0.584316\pi$
$150$	−0.225583	+	0.00925629i	−0.0184188	+	0.000755773i
$151$	1.86999	+	1.86999i	0.152177	+	0.152177i	0.779090	−	0.626912i	$-0.215682\pi$
$151$	1.86999	+	1.86999i	0.152177	+	0.152177i	−0.626912	+	0.779090i	$0.715682\pi$
$152$	−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	0.163039	−	0.986620i	$-0.447870\pi$
$157$	−10.3194	−	10.3194i	−0.823581	−	0.823581i	−0.986620	+	0.163039i	$0.947870\pi$
$158$			1.09976i			0.0874922i
$159$		−	0.645192i		−	0.0511671i
$160$	−1.26656	+	3.24435i	−0.100130	+	0.256488i
$161$	−15.6891	+	15.6891i	−1.23647	+	1.23647i
$162$	1.04380			0.0820089
$163$	18.6954			1.46434			0.732170	−	0.681122i	$-0.238508\pi$
$163$	18.6954			1.46434			0.732170	+	0.681122i	$0.238508\pi$
$164$	9.00186	−	9.00186i	0.702927	−	0.702927i
$165$	−1.13403	+	2.90488i	−0.0882844	+	0.226144i
$166$			0.416484i			0.0323255i
$167$		−	20.6778i		−	1.60010i	−0.599935	−	0.800049i	$-0.704807\pi$
$167$		−	20.6778i		−	1.60010i	0.599935	−	0.800049i	$-0.295193\pi$
$168$	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	$-0.00769365\pi$
$173$	12.8312	+	12.8312i	0.975540	+	0.975540i	−0.0241680	+	0.999708i	$0.507694\pi$
$174$	−0.146208	−	0.146208i	−0.0110840	−	0.0110840i
$175$	−9.42220	+	10.2285i	−0.712252	+	0.773204i
$176$	11.1742	+	11.1742i	0.842287	+	0.842287i
$177$			0.903127i			0.0678832i
$178$	0.578360	−	0.578360i	0.0433499	−	0.0433499i
$179$	17.3622			1.29771			0.648856	−	0.760911i	$-0.275248\pi$
$179$	17.3622			1.29771			0.648856	+	0.760911i	$0.275248\pi$
$180$	−11.9016	−	4.64628i	−0.887096	−	0.346313i
$181$			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
$187$	9.83181			0.718973
$188$			1.01592i			0.0740934i
$189$	−3.97812	+	3.97812i	−0.289365	+	0.289365i
$190$	0.510708	−	0.223918i	0.0370506	−	0.0162447i
$191$	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
$193$	1.19516			0.0860298			0.0430149	−	0.999074i	$-0.486304\pi$
$193$	1.19516			0.0860298			0.0430149	+	0.999074i	$0.486304\pi$
$194$	1.54543			0.110955
$195$		0			0
$196$	1.45937			0.104241
$197$	20.1210			1.43356			0.716780	−	0.697300i	$-0.245615\pi$
$197$	20.1210			1.43356			0.716780	+	0.697300i	$0.245615\pi$
$198$	1.08500	−	1.08500i	0.0771075	−	0.0771075i
$199$	−2.17769			−0.154372			−0.0771862	−	0.997017i	$-0.524594\pi$
$199$	−2.17769			−0.154372			−0.0771862	+	0.997017i	$0.524594\pi$
$200$	−1.92314	−	1.77154i	−0.135987	−	0.125267i
$201$	−0.879379	+	0.879379i	−0.0620266	+	0.0620266i
$202$			0.132482i			0.00932143i
$203$	−12.7363			−0.893912
$204$		−	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
$210$	−0.257196	+	0.112767i	−0.0177482	+	0.00778163i
$211$	−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
$213$			2.21022i			0.151442i
$214$	−0.460106	−	0.460106i	−0.0314522	−	0.0314522i
$215$	−13.2373	+	5.80386i	−0.902779	+	0.395820i
$216$	−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
$223$		−	13.4134i		−	0.898231i	−0.893474	−	0.449115i	$-0.851739\pi$
$223$		−	13.4134i		−	0.898231i	0.893474	−	0.449115i	$-0.148261\pi$
$224$			4.33215i			0.289454i
$225$	9.76220	−	10.5976i	0.650813	−	0.706508i
$226$	−0.696612	+	0.696612i	−0.0463380	+	0.0463380i
$227$	14.6813			0.974431			0.487215	−	0.873282i	$-0.338013\pi$
$227$	14.6813			0.974431			0.487215	+	0.873282i	$0.338013\pi$
$228$	−1.29507			−0.0857681
$229$	−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
$232$		−	2.39465i		−	0.157216i
$233$	13.9459	+	13.9459i	0.913629	+	0.913629i	0.996556	−	0.0829267i	$-0.0264267\pi$
$233$	13.9459	+	13.9459i	0.913629	+	0.913629i	−0.0829267	+	0.996556i	$0.526427\pi$
$234$		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	$0.595682\pi$
$240$	1.20327	+	2.74439i	0.0776706	+	0.177150i
$241$	−5.73049	−	5.73049i	−0.369133	−	0.369133i	0.498028	−	0.867161i	$-0.334058\pi$
$241$	−5.73049	−	5.73049i	−0.369133	−	0.369133i	−0.867161	+	0.498028i	$0.834058\pi$
$242$		−	0.714943i		−	0.0459582i
$243$	6.22393	−	6.22393i	0.399265	−	0.399265i
$244$	2.54494			0.162923
$245$	−0.598517	+	1.53313i	−0.0382378	+	0.0979479i
$246$			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	$-0.0471404\pi$
$252$	−15.8922			−1.00111
$253$		−	32.3497i		−	2.03381i
$254$	1.53646	−	1.53646i	0.0964059	−	0.0964059i
$255$	1.73671	+	0.677993i	0.108757	+	0.0424576i
$256$	14.6385			0.914908
$257$	−12.2720	+	12.2720i	−0.765507	+	0.765507i	−0.977312	−	0.211805i	$-0.932066\pi$
$257$	−12.2720	+	12.2720i	−0.765507	+	0.765507i	0.211805	+	0.977312i	$0.432066\pi$
$258$	−0.291876			−0.0181714
$259$	−19.4980			−1.21154
$260$		0			0
$261$	13.1959			0.816804
$262$	1.66597			0.102924
$263$	1.71239	−	1.71239i	0.105590	−	0.105590i	−0.652338	−	0.757928i	$-0.726212\pi$
$263$	1.71239	−	1.71239i	0.105590	−	0.105590i	0.757928	+	0.652338i	$0.226212\pi$
$264$	−0.729293			−0.0448849
$265$	1.68454	+	3.84207i	0.103480	+	0.236016i
$266$	0.490470	−	0.490470i	0.0300726	−	0.0300726i
$267$		−	2.14224i		−	0.131103i
$268$	−7.17023			−0.437992
$269$			9.73216i			0.593380i	0.954974	+	0.296690i	$0.0958828\pi$
$269$			9.73216i			0.593380i	−0.954974	+	0.296690i	$0.904117\pi$
$270$	0.543890	−	0.238466i	0.0331001	−	0.0145126i
$271$	15.4981	+	15.4981i	0.941441	+	0.941441i	0.998378	−	0.0569369i	$-0.0181334\pi$
$271$	15.4981	+	15.4981i	0.941441	+	0.941441i	−0.0569369	+	0.998378i	$0.518133\pi$
$272$	6.68061	−	6.68061i	0.405071	−	0.405071i
$273$		0			0
$274$			1.96233i			0.118548i
$275$	−0.831290	−	20.2592i	−0.0501287	−	1.22167i
$276$	−5.43941			−0.327414
$277$	−12.7676	+	12.7676i	−0.767128	+	0.767128i	−0.977600	−	0.210472i	$-0.932500\pi$
$277$	−12.7676	+	12.7676i	−0.767128	+	0.767128i	0.210472	+	0.977600i	$0.432500\pi$
$278$			1.12556i			0.0675067i
$279$	11.1625	+	11.1625i	0.668278	+	0.668278i
$280$	−3.02970	−	1.18276i	−0.181059	−	0.0706835i
$281$	11.3739	+	11.3739i	0.678510	+	0.678510i	0.959663	−	0.281153i	$-0.0907168\pi$
$281$	11.3739	+	11.3739i	0.678510	+	0.678510i	−0.281153	+	0.959663i	$0.590717\pi$
$282$	−0.0163597	−	0.0163597i	−0.000974204	−	0.000974204i
$283$	−8.02927	−	8.02927i	−0.477290	−	0.477290i	0.426974	−	0.904264i	$-0.359580\pi$
$283$	−8.02927	−	8.02927i	−0.477290	−	0.477290i	−0.904264	+	0.426974i	$0.859580\pi$
$284$	−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
$288$		−	4.48848i		−	0.264486i
$289$			11.1220i			0.654232i
$290$	1.25239	+	0.488920i	0.0735429	+	0.0287104i
$291$	2.86213	−	2.86213i	0.167781	−	0.167781i
$292$	−19.6938			−1.15249
$293$	0.699613			0.0408719			0.0204359	−	0.999791i	$-0.493495\pi$
$293$	0.699613			0.0408719			0.0204359	+	0.999791i	$0.493495\pi$
$294$	−0.0235007	+	0.0235007i	−0.00137059	+	0.00137059i
$295$	−2.35798	−	5.37805i	−0.137287	−	0.313122i
$296$		−	3.66596i		−	0.213079i
$297$		−	8.20258i		−	0.475962i
$298$	−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
$305$	−1.04373	+	2.67356i	−0.0597638	+	0.153088i
$306$	−0.648678	−	0.648678i	−0.0370824	−	0.0370824i
$307$		−	14.2048i		−	0.810709i	−0.914159	−	0.405355i	$-0.867148\pi$
$307$		−	14.2048i		−	0.810709i	0.914159	−	0.405355i	$-0.132852\pi$
$308$	−15.8136	+	15.8136i	−0.901064	+	0.901064i
$309$	−2.91807			−0.166003
$310$	0.645823	+	1.47298i	0.0366803	+	0.0836598i
$311$		−	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	−0.920343	−	0.391113i	$-0.872090\pi$
$313$	−9.36303	+	9.36303i	−0.529230	+	0.529230i	0.391113	+	0.920343i	$0.372090\pi$
$314$	1.35497	+	1.35497i	0.0764653	+	0.0764653i
$315$	6.51769	−	16.6954i	0.367230	−	0.940677i
$316$			16.6071i			0.934224i
$317$	17.3024			0.971798			0.485899	−	0.874015i	$-0.338492\pi$
$317$	17.3024			0.971798			0.485899	+	0.874015i	$0.338492\pi$
$318$			0.0847154i			0.00475060i
$319$	13.1306	−	13.1306i	0.735175	−	0.735175i
$320$	−6.17130	+	15.8081i	−0.344986	+	0.883697i
$321$	−1.70423			−0.0951207
$322$	2.06002	−	2.06002i	0.114800	−	0.114800i
$323$	−4.60481			−0.256218
$324$	15.7622			0.875675
$325$		0			0
$326$	−2.45476			−0.135957
$327$	−3.16610			−0.175086
$328$	−2.37421	+	2.37421i	−0.131094	+	0.131094i
$329$	−1.42511			−0.0785686
$330$	0.148901	−	0.381418i	0.00819676	−	0.0209964i
$331$	−12.7065	+	12.7065i	−0.698412	+	0.698412i	−0.964068	−	0.265656i	$-0.914412\pi$
$331$	−12.7065	+	12.7065i	−0.698412	+	0.698412i	0.265656	+	0.964068i	$0.414412\pi$
$332$			6.28920i			0.345165i
$333$	20.2015			1.10704
$334$			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	$-0.809650\pi$
$337$	−4.83668	+	4.83668i	−0.263471	+	0.263471i	0.562992	+	0.826462i	$0.309650\pi$
$338$		0			0
$339$			2.58024i			0.140140i
$340$	4.31625	+	9.84444i	0.234082	+	0.533889i
$341$	22.2145			1.20299
$342$	−0.508168	+	0.508168i	−0.0274786	+	0.0274786i
$343$		−	17.4224i		−	0.940723i
$344$	−2.39023	−	2.39023i	−0.128872	−	0.128872i
$345$	2.23081	−	5.71432i	0.120103	−	0.307648i
$346$	−1.68477	−	1.68477i	−0.0905740	−	0.0905740i
$347$	13.1536	+	13.1536i	0.706123	+	0.706123i	0.965718	−	0.259594i	$-0.0835889\pi$
$347$	13.1536	+	13.1536i	0.706123	+	0.706123i	−0.259594	+	0.965718i	$0.583589\pi$
$348$	−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
$353$			32.7215i			1.74159i	0.491646	+	0.870795i	$0.336396\pi$
$353$			32.7215i			1.74159i	−0.491646	+	0.870795i	$0.663604\pi$
$354$		−	0.118583i		−	0.00630261i
$355$	−5.77069	−	13.1617i	−0.306277	−	0.698551i
$356$	8.73364	−	8.73364i	0.462882	−	0.462882i
$357$	2.31902			0.122735
$358$	−2.27970			−0.120486
$359$	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
$362$		−	3.27316i		−	0.172033i
$363$	−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	0.921827	−	0.387601i	$-0.126696\pi$
$367$	10.2343	+	10.2343i	0.534226	+	0.534226i	−0.387601	+	0.921827i	$0.626696\pi$
$368$	−21.9813	−	21.9813i	−1.14585	−	1.14585i
$369$	−13.0833	−	13.0833i	−0.681087	−	0.681087i
$370$	1.91728	+	0.748487i	0.0996747	+	0.0389120i
$371$	3.68982	+	3.68982i	0.191566	+	0.191566i
$372$		−	3.73524i		−	0.193663i
$373$	−7.17039	+	7.17039i	−0.371269	+	0.371269i	−0.867939	−	0.496671i	$-0.834556\pi$
$373$	−7.17039	+	7.17039i	−0.371269	+	0.371269i	0.496671	+	0.867939i	$0.334556\pi$
$374$	−1.29094			−0.0667530
$375$	1.25021	−	3.63594i	0.0645608	−	0.187759i
$376$		−	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
$382$	−0.891162			−0.0455958
$383$			12.0071i			0.613532i	0.951785	+	0.306766i	$0.0992469\pi$
$383$			12.0071i			0.613532i	−0.951785	+	0.306766i	$0.900753\pi$
$384$	−0.999825	+	0.999825i	−0.0510221	+	0.0510221i
$385$	−10.1274	−	23.0983i	−0.516138	−	1.17720i
$386$	−0.156928			−0.00798743
$387$	13.1715	−	13.1715i	0.669546	−	0.669546i
$388$	23.3371			1.18476
$389$	−7.37166			−0.373758			−0.186879	−	0.982383i	$-0.559837\pi$
$389$	−7.37166			−0.373758			−0.186879	+	0.982383i	$0.559837\pi$
$390$		0			0
$391$	−19.3406			−0.978097
$392$	−0.384904			−0.0194406
$393$	3.08536	−	3.08536i	0.155636	−	0.155636i
$394$	−2.64194			−0.133099
$395$	−17.4465	−	6.81091i	−0.877826	−	0.342694i
$396$	16.3842	−	16.3842i	0.823339	−	0.823339i
$397$			6.05477i			0.303880i	0.988390	+	0.151940i	$0.0485521\pi$
$397$			6.05477i			0.303880i	−0.988390	+	0.151940i	$0.951448\pi$
$398$	0.285937			0.0143327
$399$		−	1.81669i		−	0.0909485i
$400$	−14.3307	−	13.2010i	−0.716537	−	0.660051i
$401$	1.70733	+	1.70733i	0.0852602	+	0.0852602i	0.748451	−	0.663190i	$-0.230798\pi$
$401$	1.70733	+	1.70733i	0.0852602	+	0.0852602i	−0.663190	+	0.748451i	$0.730798\pi$
$402$	0.115465	−	0.115465i	0.00575886	−	0.00575886i
$403$		0			0
$404$			2.00058i			0.0995324i
$405$	−6.46437	+	16.5588i	−0.321217	+	0.822812i
$406$	1.67231			0.0829952
$407$	20.1017	−	20.1017i	0.996402	−	0.996402i
$408$			0.436016i			0.0215860i
$409$	−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	$0.915880\pi$
$410$	−0.756955	−	1.72645i	−0.0373834	−	0.0852634i
$411$	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
$418$			1.01131i			0.0494649i
$419$		−	30.0803i		−	1.46952i	−0.678328	−	0.734759i	$-0.737295\pi$
$419$		−	30.0803i		−	1.46952i	0.678328	−	0.734759i	$-0.262705\pi$
$420$	−3.88384	+	1.70285i	−0.189512	+	0.0830907i
$421$	9.24685	−	9.24685i	0.450664	−	0.450664i	−0.444911	−	0.895575i	$-0.646765\pi$
$421$	9.24685	−	9.24685i	0.450664	−	0.450664i	0.895575	+	0.444911i	$0.146765\pi$
$422$	2.61986			0.127533
$423$	1.47653			0.0717913
$424$	−0.693751	+	0.693751i	−0.0336915	+	0.0336915i
$425$	−12.1122	+	0.496995i	−0.587526	+	0.0241078i
$426$		−	0.290208i		−	0.0140606i
$427$			3.56998i			0.172764i
$428$	−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	−0.806372	−	0.591409i	$-0.798572\pi$
$431$	−4.46276	+	4.46276i	−0.214963	+	0.214963i	0.591409	+	0.806372i	$0.298572\pi$
$432$	−5.57356	−	5.57356i	−0.268158	−	0.268158i
$433$	8.68986	+	8.68986i	0.417608	+	0.417608i	0.884379	−	0.466770i	$-0.154583\pi$
$433$	8.68986	+	8.68986i	0.417608	+	0.417608i	−0.466770	+	0.884379i	$0.654583\pi$
$434$	1.41461	+	1.41461i	0.0679036	+	0.0679036i
$435$	3.22490	−	1.41394i	0.154622	−	0.0677934i
$436$	−12.9078	−	12.9078i	−0.618171	−	0.618171i
$437$			15.1513i			0.724783i
$438$	0.317136	−	0.317136i	0.0151533	−	0.0151533i
$439$	−34.4447			−1.64395			−0.821977	−	0.569520i	$-0.807129\pi$
$439$	−34.4447			−1.64395			−0.821977	+	0.569520i	$0.807129\pi$
$440$	4.34289	−	1.90412i	0.207039	−	0.0907754i
$441$		−	2.12104i		−	0.101002i
$442$		0			0
$443$	−5.39452	+	5.39452i	−0.256301	+	0.256301i	−0.823548	−	0.567247i	$-0.808009\pi$
$443$	−5.39452	+	5.39452i	−0.256301	+	0.256301i	0.567247	+	0.823548i	$0.308009\pi$
$444$	−3.37997	−	3.37997i	−0.160406	−	0.160406i
$445$	5.59320	+	12.7569i	0.265143	+	0.604734i
$446$			1.76122i			0.0833962i
$447$	−4.17534			−0.197487
$448$			21.1084i			0.997277i
$449$	−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	$0.987335\pi$
$450$	−1.28180	+	1.39149i	−0.0604247	+	0.0655957i
$451$	−26.0372			−1.22604
$452$	−10.5193	+	10.5193i	−0.494788	+	0.494788i
$453$	−0.909456			−0.0427300
$454$	−1.92769			−0.0904710
$455$		0			0
$456$	0.341570			0.0159955
$457$	−3.10750			−0.145363			−0.0726814	−	0.997355i	$-0.523156\pi$
$457$	−3.10750			−0.145363			−0.0726814	+	0.997355i	$0.523156\pi$
$458$	0.348319	−	0.348319i	0.0162759	−	0.0162759i
$459$	−4.90400			−0.228899
$460$	32.3913	−	14.2018i	1.51025	−	0.662163i
$461$	11.8061	−	11.8061i	0.549863	−	0.549863i	−0.376538	−	0.926401i	$-0.622886\pi$
$461$	11.8061	−	11.8061i	0.549863	−	0.549863i	0.926401	+	0.376538i	$0.122886\pi$
$462$		−	0.509304i		−	0.0236950i
$463$	15.6396			0.726832			0.363416	−	0.931627i	$-0.381610\pi$
$463$	15.6396			0.726832			0.363416	+	0.931627i	$0.381610\pi$
$464$		−	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	$-0.914283\pi$
$467$	−15.0821	+	15.0821i	−0.697916	+	0.697916i	0.266045	+	0.963961i	$0.414283\pi$
$468$		0			0
$469$		−	10.0582i		−	0.464447i
$470$	0.140134	+	0.0547069i	0.00646391	+	0.00252344i
$471$	5.01879			0.231254
$472$	0.971099	−	0.971099i	0.0446984	−	0.0446984i
$473$		−	26.2128i		−	1.20527i
$474$	−0.267430	−	0.267430i	−0.0122835	−	0.0122835i
$475$	0.389341	+	9.48854i	0.0178642	+	0.435364i
$476$	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
$483$		−	7.63028i		−	0.347190i
$484$		−	10.7961i		−	0.490733i
$485$	−9.57099	+	24.5165i	−0.434596	+	1.11324i
$486$	−0.817218	+	0.817218i	−0.0370698	+	0.0370698i
$487$	−15.2167			−0.689534			−0.344767	−	0.938688i	$-0.612042\pi$
$487$	−15.2167			−0.689534			−0.344767	+	0.938688i	$0.612042\pi$
$488$	−0.671220			−0.0303847
$489$	−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	$-0.217459\pi$
$492$			4.37799i			0.197375i
$493$	−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	$0.733117\pi$
$500$	19.9202	−	9.72631i	0.890860	−	0.434974i
$501$	5.02826	+	5.02826i	0.224646	+	0.224646i
$502$			0.613896i			0.0273995i
$503$	16.3763	−	16.3763i	0.730184	−	0.730184i	−0.240472	−	0.970656i	$-0.577302\pi$
$503$	16.3763	−	16.3763i	0.730184	−	0.730184i	0.970656	+	0.240472i	$0.0773021\pi$
$504$	4.19151			0.186705
$505$	−2.10168	−	0.820476i	−0.0935237	−	0.0365107i
$506$			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
$512$	−10.1453			−0.448362
$513$			3.84174i			0.169617i
$514$	1.61135	−	1.61135i	0.0710734	−	0.0710734i
$515$	17.3769	−	7.61882i	0.765717	−	0.335725i
$516$	−4.40752			−0.194030
$517$	1.46923	−	1.46923i	0.0646167	−	0.0646167i
$518$	2.56013			0.112486
$519$	−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	$0.291422\pi$
$522$	−1.73265			−0.0758361
$523$	−0.387298	+	0.387298i	−0.0169354	+	0.0169354i	−0.715524	−	0.698588i	$-0.753812\pi$
$523$	−0.387298	+	0.387298i	−0.0169354	+	0.0169354i	0.698588	+	0.715524i	$0.253812\pi$
$524$	25.1573			1.09900
$525$	−0.196075	−	4.77850i	−0.00855742	−	0.208551i
$526$	−0.224841	+	0.224841i	−0.00980352	+	0.00980352i
$527$		−	13.2812i		−	0.578538i
$528$	−5.43449			−0.236506
$529$			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
$535$	10.1485	−	4.44959i	0.438760	−	0.192372i
$536$	1.89113			0.0816842
$537$	−4.22200	+	4.22200i	−0.182193	+	0.182193i
$538$		−	1.27786i		−	0.0550923i
$539$	−2.11056	−	2.11056i	−0.0909082	−	0.0909082i
$540$	8.21311	−	3.60100i	0.353436	−	0.154962i
$541$	−29.7507	−	29.7507i	−1.27908	−	1.27908i	−0.941182	−	0.337899i	$-0.890284\pi$
$541$	−29.7507	−	29.7507i	−1.27908	−	1.27908i	−0.337899	−	0.941182i	$-0.609716\pi$
$542$	−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	0.333176	−	0.942864i	$-0.391880\pi$
$547$	−14.2594	−	14.2594i	−0.609688	−	0.609688i	−0.942864	+	0.333176i	$0.891880\pi$
$548$			29.6325i			1.26584i
$549$		−	3.69880i		−	0.157861i
$550$	0.109151	+	2.66008i	0.00465420	+	0.113426i
$551$	−6.14984	+	6.14984i	−0.261992	+	0.261992i
$552$	1.43463			0.0610618
$553$	−23.2961			−0.990652
$554$	1.67641	−	1.67641i	0.0712240	−	0.0712240i
$555$	4.93699	−	2.16460i	0.209564	−	0.0918822i
$556$			16.9967i			0.720823i
$557$			35.1772i			1.49051i	0.666781	+	0.745254i	$0.267672\pi$
$557$			35.1772i			1.49051i	−0.666781	+	0.745254i	$0.732328\pi$
$558$	−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	−0.955895	−	0.293708i	$-0.905111\pi$
$563$	−29.6501	−	29.6501i	−1.24960	−	1.24960i	−0.293708	−	0.955895i	$-0.594889\pi$
$564$	−0.247042	−	0.247042i	−0.0104024	−	0.0104024i
$565$	−6.73679	−	15.3652i	−0.283419	−	0.646417i
$566$	1.05426	+	1.05426i	0.0443140	+	0.0443140i
$567$			22.1108i			0.928566i
$568$	2.37657	−	2.37657i	0.0997186	−	0.0997186i
$569$	27.5482			1.15488			0.577441	−	0.816433i	$-0.304051\pi$
$569$	27.5482			1.15488			0.577441	+	0.816433i	$0.304051\pi$
$570$	−0.0697392	+	0.178640i	−0.00292105	+	0.00748241i
$571$		−	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
$577$	6.73701			0.280465			0.140233	−	0.990119i	$-0.455215\pi$
$577$	6.73701			0.280465			0.140233	+	0.990119i	$0.455215\pi$
$578$		−	1.46034i		−	0.0607422i
$579$	−0.290630	+	0.290630i	−0.0120782	+	0.0120782i
$580$	18.9120	+	7.38303i	0.785276	+	0.306564i
$581$	−8.82236			−0.366013
$582$	−0.375805	+	0.375805i	−0.0155776	+	0.0155776i
$583$	−7.60813			−0.315097
$584$	5.19417			0.214936
$585$		0			0
$586$	−0.0918611			−0.00379475
$587$	−5.19438			−0.214395			−0.107198	−	0.994238i	$-0.534188\pi$
$587$	−5.19438			−0.214395			−0.107198	+	0.994238i	$0.534188\pi$
$588$	−0.354877	+	0.354877i	−0.0146349	+	0.0146349i
$589$	−10.4044			−0.428704
$590$	0.309609	+	0.706152i	0.0127464	+	0.0290718i
$591$	−4.89285	+	4.89285i	−0.201265	+	0.201265i
$592$		−	27.3177i		−	1.12275i
$593$	−12.9267			−0.530836			−0.265418	−	0.964133i	$-0.585510\pi$
$593$	−12.9267			−0.530836			−0.265418	+	0.964133i	$0.585510\pi$
$594$			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	$0.111186\pi$
$599$			16.7523i			0.684481i	−0.939612	+	0.342241i	$0.888814\pi$
$600$	0.898442	−	0.0368656i	0.0366787	−	0.00150503i
$601$	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
$603$			10.4212i			0.424384i
$604$	−3.70774	−	3.70774i	−0.150866	−	0.150866i
$605$	11.3418	+	4.42771i	0.461108	+	0.180012i
$606$	−0.0322160	−	0.0322160i	−0.00130868	−	0.00130868i
$607$	26.4935	+	26.4935i	1.07534	+	1.07534i	0.996920	+	0.0784195i	$0.0249874\pi$
$607$	26.4935	+	26.4935i	1.07534	+	1.07534i	0.0784195	+	0.996920i	$0.475013\pi$
$608$	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
$613$		−	17.2946i		−	0.698524i	−0.937025	−	0.349262i	$-0.886432\pi$
$613$		−	17.2946i		−	0.698524i	0.937025	−	0.349262i	$-0.113568\pi$
$614$			1.86512i			0.0752703i
$615$	−4.59926	−	1.79550i	−0.185460	−	0.0724016i
$616$	4.17079	−	4.17079i	0.168046	−	0.168046i
$617$	12.1401			0.488742			0.244371	−	0.969682i	$-0.421419\pi$
$617$	12.1401			0.488742			0.244371	+	0.969682i	$0.421419\pi$
$618$	0.383150			0.0154126
$619$	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
$622$			2.82249i			0.113172i
$623$	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
$630$	−0.855790	+	2.19214i	−0.0340955	+	0.0873371i
$631$	15.3003	+	15.3003i	0.609096	+	0.609096i	0.942710	−	0.333614i	$-0.108268\pi$
$631$	15.3003	+	15.3003i	0.609096	+	0.609096i	−0.333614	+	0.942710i	$0.608268\pi$
$632$		−	4.38008i		−	0.174230i
$633$	4.85197	−	4.85197i	0.192848	−	0.192848i
$634$	−2.27185			−0.0902265
$635$	14.8587	+	33.8896i	0.589651	+	1.34487i
$636$			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	$0.647190\pi$
$642$	0.223769			0.00883148
$643$			31.6498i			1.24814i	0.781367	+	0.624072i	$0.214523\pi$
$643$			31.6498i			1.24814i	−0.781367	+	0.624072i	$0.785477\pi$
$644$	31.1077	−	31.1077i	1.22581	−	1.22581i
$645$	1.80761	−	4.63028i	0.0711747	−	0.182317i
$646$	0.604623			0.0237886
$647$	26.8607	−	26.8607i	1.05600	−	1.05600i	0.0576668	−	0.998336i	$-0.481634\pi$
$647$	26.8607	−	26.8607i	1.05600	−	1.05600i	0.998336	−	0.0576668i	$-0.0183661\pi$
$648$	−4.15722			−0.163311
$649$	10.6497			0.418038
$650$		0			0
$651$	5.23971			0.205361
$652$	−37.0685			−1.45172
$653$	1.95007	−	1.95007i	0.0763122	−	0.0763122i	−0.667920	−	0.744233i	$-0.732815\pi$
$653$	1.95007	−	1.95007i	0.0763122	−	0.0763122i	0.744233	+	0.667920i	$0.232815\pi$
$654$	0.415718			0.0162558
$655$	−10.3175	+	26.4287i	−0.403138	+	1.03265i
$656$	−17.6920	+	17.6920i	−0.690756	+	0.690756i
$657$			28.6228i			1.11668i
$658$	0.187120			0.00729470
$659$		−	2.08099i		−	0.0810639i	−0.999178	−	0.0405320i	$-0.987095\pi$
$659$		−	2.08099i		−	0.0810639i	0.999178	−	0.0405320i	$-0.0129053\pi$
$660$	2.24852	−	5.75967i	0.0875233	−	0.224195i
$661$	−26.5742	−	26.5742i	−1.03362	−	1.03362i	−0.999415	−	0.0342010i	$-0.989111\pi$
$661$	−26.5742	−	26.5742i	−1.03362	−	1.03362i	−0.0342010	−	0.999415i	$-0.510889\pi$
$662$	1.66840	−	1.66840i	0.0648440	−	0.0648440i
$663$		0			0
$664$		−	1.65876i		−	0.0643723i
$665$	4.74323	+	10.8183i	0.183934	+	0.419515i
$666$	−2.65251			−0.102783
$667$	−25.8299	+	25.8299i	−1.00014	+	1.00014i
$668$			40.9991i			1.58630i
$669$	3.26177	+	3.26177i	0.126107	+	0.126107i
$670$	−0.386116	+	0.989052i	−0.0149169	+	0.0382104i
$671$	−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	$-0.137198\pi$
$673$	12.7309	+	12.7309i	0.490741	+	0.490741i	−0.417799	+	0.908540i	$0.637198\pi$
$674$	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	0.938158	−	0.346206i	$-0.112530\pi$
$677$	15.4021	+	15.4021i	0.591952	+	0.591952i	−0.346206	+	0.938158i	$0.612530\pi$
$678$		−	0.338793i		−	0.0130113i
$679$			32.7367i			1.25632i
$680$	−1.13840	−	2.59644i	−0.0436556	−	0.0995689i
$681$	−3.57007	+	3.57007i	−0.136805	+	0.136805i
$682$	−2.91683			−0.111691
$683$	−6.16751			−0.235993			−0.117997	−	0.993014i	$-0.537647\pi$
$683$	−6.16751			−0.235993			−0.117997	+	0.993014i	$0.537647\pi$
$684$	−7.67369	+	7.67369i	−0.293411	+	0.293411i
$685$	−31.1301	−	12.1529i	−1.18942	−	0.464337i
$686$			2.28761i			0.0873414i
$687$		−	1.29017i		−	0.0492230i
$688$	−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	−0.508096	−	0.861300i	$-0.669651\pi$
$691$	9.28463	−	9.28463i	0.353204	−	0.353204i	0.861300	+	0.508096i	$0.169651\pi$
$692$	−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
$695$	−17.8558	−	6.97070i	−0.677308	−	0.264414i
$696$	0.582310	+	0.582310i	0.0220724	+	0.0220724i
$697$			15.5666i			0.589627i
$698$	0.233693	−	0.233693i	0.00884543	−	0.00884543i
$699$	−6.78252			−0.256538
$700$	18.6820	−	20.2807i	0.706112	−	0.766539i
$701$		−	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
$707$	−2.80636			−0.105544
$708$		−	1.79068i		−	0.0672980i
$709$	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	$0.237591\pi$
$710$	0.757707	+	1.72817i	0.0284362	+	0.0648569i
$711$	24.1367			0.905198
$712$	−2.30347	+	2.30347i	−0.0863262	+	0.0863262i
$713$	−43.6993			−1.63655
$714$	−0.304493			−0.0113954
$715$		0			0
$716$	−34.4251			−1.28653
$717$	−4.95537			−0.185062
$718$	−0.0918703	+	0.0918703i	−0.00342857	+	0.00342857i
$719$	6.73696			0.251246			0.125623	−	0.992078i	$-0.459907\pi$
$719$	6.73696			0.251246			0.125623	+	0.992078i	$0.459907\pi$
$720$	23.3911	+	9.13165i	0.871735	+	0.340316i
$721$	16.6883	−	16.6883i	0.621504	−	0.621504i
$722$			2.02109i			0.0752173i
$723$	2.78698			0.103649
$724$		−	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	−0.337062	+	0.941483i	$0.609433\pi$
$727$	−34.4733	+	34.4733i	−1.27854	+	1.27854i	−0.941483	+	0.337062i	$0.890567\pi$
$728$		0			0
$729$		−	20.8218i		−	0.771179i
$730$	−1.06051	+	2.71653i	−0.0392511	+	0.100543i
$731$	−15.6716			−0.579635
$732$	−0.618857	+	0.618857i	−0.0228736	+	0.0228736i
$733$			28.7555i			1.06211i	0.847338	+	0.531054i	$0.178204\pi$
$733$			28.7555i			1.06211i	−0.847338	+	0.531054i	$0.821796\pi$
$734$	−1.34379	−	1.34379i	−0.0496002	−	0.0496002i
$735$	−0.227271	−	0.518355i	−0.00838300	−	0.0191198i
$736$	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
$743$		−	52.9634i		−	1.94304i	−0.236963	−	0.971519i	$-0.576152\pi$
$743$		−	52.9634i		−	1.94304i	0.236963	−	0.971519i	$-0.423848\pi$
$744$			0.985158i			0.0361176i
$745$	24.8638	−	10.9014i	0.910940	−	0.399398i
$746$	0.941490	−	0.941490i	0.0344704	−	0.0344704i
$747$	9.14070			0.334441
$748$	−19.4941			−0.712776
$749$	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	$0.676193\pi$
$752$		−	1.99665i		−	0.0728104i
$753$	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	0.690872	−	0.722977i	$-0.257227\pi$
$757$	−0.883345	−	0.883345i	−0.0321057	−	0.0321057i	−0.722977	+	0.690872i	$0.757227\pi$
$758$	−0.0975328	−	0.0975328i	−0.00354255	−	0.00354255i
$759$	7.86654	+	7.86654i	0.285537	+	0.285537i
$760$	−2.03403	+	0.891810i	−0.0737819	+	0.0323493i
$761$	−14.4328	−	14.4328i	−0.523189	−	0.523189i	0.395344	−	0.918533i	$-0.370625\pi$
$761$	−14.4328	−	14.4328i	−0.523189	−	0.523189i	−0.918533	+	0.395344i	$0.870625\pi$
$762$			0.747246i			0.0270698i
$763$	18.1068	−	18.1068i	0.655509	−	0.655509i
$764$	−13.4572			−0.486863
$765$	14.3079	−	6.27322i	0.517302	−	0.226809i
$766$		−	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
$772$	−2.36972			−0.0852882
$773$		−	21.3836i		−	0.769114i	−0.923101	−	0.384557i	$-0.874354\pi$
$773$		−	21.3836i		−	0.769114i	0.923101	−	0.384557i	$-0.125646\pi$
$774$	−1.72945	+	1.72945i	−0.0621639	+	0.0621639i
$775$	−27.3669	+	1.12294i	−0.983047	+	0.0403372i
$776$	−6.15508			−0.220954
$777$	4.74135	−	4.74135i	0.170095	−	0.170095i
$778$	0.967919			0.0347016
$779$	12.1947			0.436921
$780$		0			0
$781$	26.0630			0.932608
$782$	2.53947			0.0908114
$783$	−6.54941	+	6.54941i	−0.234057	+	0.234057i
$784$	−2.86820			−0.102436
$785$	−29.8865	+	13.1036i	−1.06670	+	0.467688i
$786$	−0.405116	+	0.405116i	−0.0144500	+	0.0144500i
$787$			39.3828i			1.40385i	0.712252	+	0.701923i	$0.247675\pi$
$787$			39.3828i			1.40385i	−0.712252	+	0.701923i	$0.752325\pi$
$788$	−39.8950			−1.42120
$789$			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
$795$	−1.34391	−	0.524650i	−0.0476637	−	0.0186074i
$796$	4.31784			0.153042
$797$	27.6949	−	27.6949i	0.981002	−	0.981002i	−0.0188205	−	0.999823i	$-0.505991\pi$
$797$	27.6949	−	27.6949i	0.981002	−	0.981002i	0.999823	+	0.0188205i	$0.00599112\pi$
$798$			0.238537i			0.00844411i
$799$	−0.878395	−	0.878395i	−0.0310754	−	0.0310754i
$800$	5.72795	+	5.27641i	0.202514	+	0.186549i
$801$	−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
$808$		−	0.527646i		−	0.0185625i
$809$			26.7479i			0.940406i	0.882558	+	0.470203i	$0.155819\pi$
$809$			26.7479i			0.940406i	−0.882558	+	0.470203i	$0.844181\pi$
$810$	0.848789	−	2.17421i	0.0298234	−	0.0763939i
$811$	−7.93739	+	7.93739i	−0.278720	+	0.278720i	−0.832598	−	0.553878i	$-0.813147\pi$
$811$	−7.93739	+	7.93739i	−0.278720	+	0.278720i	0.553878	+	0.832598i	$0.313147\pi$
$812$	25.2530			0.886207
$813$	−7.53738			−0.264348
$814$	−2.63940	+	2.63940i	−0.0925109	+	0.0925109i
$815$	15.2025	−	38.9420i	0.532522	−	1.36408i
$816$			3.24907i			0.113740i
$817$			12.2770i			0.429517i
$818$	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	−0.290305	−	0.956934i	$-0.593757\pi$
$821$	19.1010	−	19.1010i	0.666629	−	0.666629i	0.956934	+	0.290305i	$0.0937569\pi$
$822$	−0.477182	−	0.477182i	−0.0166436	−	0.0166436i
$823$	−6.63054	−	6.63054i	−0.231126	−	0.231126i	0.582036	−	0.813163i	$-0.302256\pi$
$823$	−6.63054	−	6.63054i	−0.231126	−	0.231126i	−0.813163	+	0.582036i	$0.802256\pi$
$824$	3.13769	+	3.13769i	0.109307	+	0.109307i
$825$	5.12860	+	4.72431i	0.178555	+	0.164479i
$826$	0.678170	+	0.678170i	0.0235965	+	0.0235965i
$827$		−	45.0330i		−	1.56595i	−0.622052	−	0.782976i	$-0.713701\pi$
$827$		−	45.0330i		−	1.56595i	0.622052	−	0.782976i	$-0.286299\pi$
$828$	−32.2302	+	32.2302i	−1.12008	+	1.12008i
$829$	42.0151			1.45924			0.729622	−	0.683851i	$-0.239696\pi$
$829$	42.0151			1.45924			0.729622	+	0.683851i	$0.239696\pi$
$830$	0.867524	+	0.338672i	0.0301122	+	0.0117555i
$831$		−	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
$837$	−11.0804			−0.382993
$838$			3.94962i			0.136437i
$839$	−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	$0.279890\pi$
$840$	1.02435	−	0.449122i	0.0353434	−	0.0154962i
$841$	8.03148			0.276948
$842$	−1.21414	+	1.21414i	−0.0418419	+	0.0418419i
$843$	−5.53162			−0.190519
$844$	39.5617			1.36177
$845$		0			0
$846$	−0.193872			−0.00666546
$847$	15.1446			0.520374
$848$	−5.16964	+	5.16964i	−0.177526	+	0.177526i
$849$	3.90498			0.134019
$850$	1.59036	−	0.0652568i	0.0545488	−	0.00223829i
$851$	−39.5429	+	39.5429i	−1.35551	+	1.35551i
$852$		−	4.38234i		−	0.150136i
$853$	23.0805			0.790260			0.395130	−	0.918625i	$-0.370700\pi$
$853$	23.0805			0.790260			0.395130	+	0.918625i	$0.370700\pi$
$854$		−	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	−0.349940	+	0.936772i	$0.613798\pi$
$857$	−37.6679	+	37.6679i	−1.28671	+	1.28671i	−0.936772	+	0.349940i	$0.886202\pi$
$858$		0			0
$859$			5.08674i			0.173557i	0.996228	+	0.0867787i	$0.0276573\pi$
$859$			5.08674i			0.173557i	−0.996228	+	0.0867787i	$0.972343\pi$
$860$	26.2465	−	11.5077i	0.894997	−	0.392408i
$861$	−6.14135			−0.209297
$862$	0.585972	−	0.585972i	0.0199583	−	0.0199583i
$863$		−	45.1879i		−	1.53821i	−0.639120	−	0.769107i	$-0.720701\pi$
$863$		−	45.1879i		−	1.53821i	0.639120	−	0.769107i	$-0.279299\pi$
$864$	2.22773	+	2.22773i	0.0757891	+	0.0757891i
$865$	37.1610	−	16.2931i	1.26351	−	0.553981i
$866$	−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
$873$		−	33.9180i		−	1.14795i
$874$		−	1.98940i		−	0.0672924i
$875$	13.6439	+	27.9437i	0.461246	+	0.944669i
$876$	4.78896	−	4.78896i	0.161804	−	0.161804i
$877$	20.3282			0.686436			0.343218	−	0.939256i	$-0.388483\pi$
$877$	20.3282			0.686436			0.343218	+	0.939256i	$0.388483\pi$
$878$	4.52267			0.152633
$879$	−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	$0.812245\pi$
$882$			0.278498i			0.00937753i
$883$	−15.9555	−	15.9555i	−0.536944	−	0.536944i	0.385686	−	0.922630i	$-0.373965\pi$
$883$	−15.9555	−	15.9555i	−0.536944	−	0.536944i	−0.922630	+	0.385686i	$0.873965\pi$
$884$		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	0.699573	−	0.714561i	$-0.253374\pi$
$887$	−0.446393	−	0.446393i	−0.0149884	−	0.0149884i	−0.714561	+	0.699573i	$0.753374\pi$
$888$	0.891457	+	0.891457i	0.0299153	+	0.0299153i
$889$	32.5466	+	32.5466i	1.09158	+	1.09158i
$890$	−0.734401	−	1.67501i	−0.0246172	−	0.0561465i
$891$	−22.7954	−	22.7954i	−0.763675	−	0.763675i
$892$			26.5956i			0.890488i
$893$	−0.688126	+	0.688126i	−0.0230273	+	0.0230273i
$894$	0.548233			0.0183356
$895$	14.1184	−	36.1649i	0.471926	−	1.20886i
$896$		−	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
$902$	3.41875			0.113832
$903$		−	6.18278i		−	0.205750i
$904$	2.77444	−	2.77444i	0.0922765	−	0.0922765i
$905$	51.9250	+	20.2710i	1.72604	+	0.673830i
$906$	0.119414			0.00396726
$907$	27.6995	−	27.6995i	0.919748	−	0.919748i	−0.0772631	−	0.997011i	$-0.524618\pi$
$907$	27.6995	−	27.6995i	0.919748	−	0.919748i	0.997011	+	0.0772631i	$0.0246181\pi$
$908$	−29.1094			−0.966031
$909$	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	$0.467163\pi$
$912$	2.54529			0.0842829
$913$	9.09552	−	9.09552i	0.301018	−	0.301018i
$914$	0.408023			0.0134962
$915$	−0.396328	−	0.903940i	−0.0131022	−	0.0298833i
$916$	5.25986	−	5.25986i	0.173791	−	0.173791i
$917$			35.2900i			1.16538i
$918$	0.643907			0.0212521
$919$			22.9801i			0.758043i	0.925388	+	0.379022i	$0.123739\pi$
$919$			22.9801i			0.758043i	−0.925388	+	0.379022i	$0.876261\pi$
$920$	−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
$925$	−23.7478	+	25.7801i	−0.780823	+	0.847644i
$926$	−2.05351			−0.0674827
$927$	−17.2905	+	17.2905i	−0.567894	+	0.567894i
$928$			7.13229i			0.234129i
$929$	−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	$0.755663\pi$
$930$	−0.515234	−	0.201142i	−0.0168952	−	0.00659570i
$931$	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	0.670653	−	0.741772i	$-0.266014\pi$
$937$	−2.17699	−	2.17699i	−0.0711191	−	0.0711191i	−0.741772	+	0.670653i	$0.766014\pi$
$938$			1.32067i			0.0431215i
$939$		−	4.55365i		−	0.148603i
$940$	2.11612	+	0.826112i	0.0690203	+	0.0269448i
$941$	−22.9413	+	22.9413i	−0.747866	+	0.747866i	−0.974078	−	0.226212i	$-0.927366\pi$
$941$	−22.9413	+	22.9413i	−0.747866	+	0.747866i	0.226212	+	0.974078i	$0.427366\pi$
$942$	−0.658980			−0.0214707
$943$	51.2190			1.66792
$944$	7.23636	−	7.23636i	0.235523	−	0.235523i
$945$	5.05141	+	11.5212i	0.164322	+	0.374784i
$946$			3.44181i			0.111903i
$947$			27.2986i			0.887086i	0.896253	+	0.443543i	$0.146279\pi$
$947$			27.2986i			0.887086i	−0.896253	+	0.443543i	$0.853721\pi$
$948$	−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	$-0.216965\pi$
$953$	4.52281	+	4.52281i	0.146508	+	0.146508i	−0.630048	+	0.776556i	$0.716965\pi$
$954$	0.501965	+	0.501965i	0.0162517	+	0.0162517i
$955$	5.51905	−	14.1373i	0.178592	−	0.457472i
$956$	−20.2024	−	20.2024i	−0.653393	−	0.653393i
$957$			6.38600i			0.206430i
$958$	−3.95981	+	3.95981i	−0.127936	+	0.127936i
$959$	−41.5678			−1.34229
$960$	−2.34339	−	5.34476i	−0.0756325	−	0.172501i
$961$			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
$967$	−28.4424			−0.914647			−0.457324	−	0.889300i	$-0.651192\pi$
$967$	−28.4424			−0.914647			−0.457324	+	0.889300i	$0.651192\pi$
$968$			2.84744i			0.0915203i
$969$	1.11976	−	1.11976i	0.0359718	−	0.0359718i
$970$	1.25670	−	3.21908i	0.0403501	−	0.103358i
$971$	−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
$973$	−23.8427			−0.764361
$974$	1.99799			0.0640197
$975$		0			0
$976$	−5.00174			−0.160102
$977$	−38.0451			−1.21717			−0.608586	−	0.793488i	$-0.708263\pi$
$977$	−38.0451			−1.21717			−0.608586	+	0.793488i	$0.708263\pi$
$978$	0.596928	−	0.596928i	0.0190876	−	0.0190876i
$979$	−25.2614			−0.807357
$980$	1.18671	−	3.03982i	0.0379082	−	0.0971035i
$981$	−18.7601	+	18.7601i	−0.598965	+	0.598965i
$982$			3.67323i			0.117217i
$983$	−34.5934			−1.10336			−0.551679	−	0.834056i	$-0.686013\pi$
$983$	−34.5934			−1.10336			−0.551679	+	0.834056i	$0.686013\pi$
$984$		−	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
$990$	−1.37773	−	3.14231i	−0.0437871	−	0.0998690i
$991$	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
$993$		−	6.17972i		−	0.196107i
$994$	1.65968	+	1.65968i	0.0526420	+	0.0526420i
$995$	−1.77083	+	4.53606i	−0.0561391	+	0.143803i
$996$	−1.52936	−	1.52936i	−0.0484595	−	0.0484595i
$997$	5.20122	+	5.20122i	0.164724	+	0.164724i	0.784656	−	0.619932i	$-0.212840\pi$
$997$	5.20122	+	5.20122i	0.164724	+	0.164724i	−0.619932	+	0.784656i	$0.712840\pi$
$998$	−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.k.e.577.4		20
5.3	odd	4		845.2.f.e.408.7		20
13.2	odd	12		845.2.t.e.657.3		20
13.3	even	3		65.2.o.a.32.3	✓	20
13.4	even	6		845.2.o.f.587.3		20
13.5	odd	4		845.2.f.d.437.7		20
13.6	odd	12		845.2.t.g.427.3		20
13.7	odd	12		65.2.t.a.37.3	yes	20
13.8	odd	4		845.2.f.e.437.4		20
13.9	even	3		845.2.o.e.587.3		20
13.10	even	6		845.2.o.g.357.3		20
13.11	odd	12		845.2.t.f.657.3		20
13.12	even	2		845.2.k.d.577.7		20
39.20	even	12		585.2.dp.a.37.3		20
39.29	odd	6		585.2.cf.a.487.3		20
65.3	odd	12		65.2.t.a.58.3	yes	20
65.7	even	12		325.2.s.b.193.3		20
65.8	even	4	inner	845.2.k.e.268.4		20
65.18	even	4		845.2.k.d.268.7		20
65.23	odd	12		845.2.t.g.188.3		20
65.28	even	12		845.2.o.f.488.3		20
65.29	even	6		325.2.s.b.32.3		20
65.33	even	12		65.2.o.a.63.3	yes	20
65.38	odd	4		845.2.f.d.408.4		20
65.42	odd	12		325.2.x.b.318.3		20
65.43	odd	12		845.2.t.e.418.3		20
65.48	odd	12		845.2.t.f.418.3		20
65.58	even	12		845.2.o.g.258.3		20
65.59	odd	12		325.2.x.b.232.3		20
65.63	even	12		845.2.o.e.488.3		20
195.68	even	12		585.2.dp.a.253.3		20
195.98	odd	12		585.2.cf.a.388.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.3	✓	20	13.3	even	3
65.2.o.a.63.3	yes	20	65.33	even	12
65.2.t.a.37.3	yes	20	13.7	odd	12
65.2.t.a.58.3	yes	20	65.3	odd	12
325.2.s.b.32.3		20	65.29	even	6
325.2.s.b.193.3		20	65.7	even	12
325.2.x.b.232.3		20	65.59	odd	12
325.2.x.b.318.3		20	65.42	odd	12
585.2.cf.a.388.3		20	195.98	odd	12
585.2.cf.a.487.3		20	39.29	odd	6
585.2.dp.a.37.3		20	39.20	even	12
585.2.dp.a.253.3		20	195.68	even	12
845.2.f.d.408.4		20	65.38	odd	4
845.2.f.d.437.7		20	13.5	odd	4
845.2.f.e.408.7		20	5.3	odd	4
845.2.f.e.437.4		20	13.8	odd	4
845.2.k.d.268.7		20	65.18	even	4
845.2.k.d.577.7		20	13.12	even	2
845.2.k.e.268.4		20	65.8	even	4	inner
845.2.k.e.577.4		20	1.1	even	1	trivial
845.2.o.e.488.3		20	65.63	even	12
845.2.o.e.587.3		20	13.9	even	3
845.2.o.f.488.3		20	65.28	even	12
845.2.o.f.587.3		20	13.4	even	6
845.2.o.g.258.3		20	65.58	even	12
845.2.o.g.357.3		20	13.10	even	6
845.2.t.e.418.3		20	65.43	odd	12
845.2.t.e.657.3		20	13.2	odd	12
845.2.t.f.418.3		20	65.48	odd	12
845.2.t.f.657.3		20	13.11	odd	12
845.2.t.g.188.3		20	65.23	odd	12
845.2.t.g.427.3		20	13.6	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.131303 q^{2} +(-0.243172 + 0.243172i) q^{3} -1.98276 q^{4} +(0.813169 - 2.08297i) q^{5} +(0.0319291 - 0.0319291i) q^{6} -2.78137i q^{7} +0.522947 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} +(0.308779 + 0.704259i) q^{15} +3.89686 q^{16} +(1.71436 - 1.71436i) q^{17} -0.378379i q^{18} +(-1.34301 - 1.34301i) q^{19} +(-1.61232 + 4.13003i) 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} +5.51479i q^{28} -4.57914i q^{29} +(-0.0405435 - 0.0924710i) q^{30} +(3.87352 - 3.87352i) q^{31} -1.55756 q^{32} -1.39458 q^{33} +(-0.225100 + 0.225100i) q^{34} +(-5.79351 - 2.26173i) q^{35} -5.71379i q^{36} -7.01019i 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} +(6.00256 + 2.34334i) q^{45} +(0.740648 + 0.740648i) q^{46} -0.512375i q^{47} +(-0.947605 + 0.947605i) q^{48} -0.736030 q^{49} +(0.482867 + 0.444802i) 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} +0.653165 q^{57} +0.601253i q^{58} +(1.85697 - 1.85697i) q^{59} +(-0.612235 - 1.39638i) q^{60} -1.28353 q^{61} +(-0.508603 + 0.508603i) q^{62} +8.01518 q^{63} -7.58920 q^{64} +0.183113 q^{66} +3.61629 q^{67} +(-3.39916 + 3.39916i) q^{68} +2.74335 q^{69} +(0.760703 + 0.296970i) q^{70} +(4.54457 - 4.54457i) q^{71} +1.50699i q^{72} +9.93250 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} +(3.16880 - 8.11702i) q^{80} -7.94960 q^{81} +(0.596122 - 0.596122i) q^{82} -3.17194i q^{83} +(-1.34104 - 1.34104i) q^{84} +(-2.17689 - 4.96502i) 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} +1.88386i q^{93} +0.0672762i q^{94} +(-3.88955 + 1.70536i) q^{95} +(0.378755 - 0.378755i) q^{96} -11.7700 q^{97} +0.0966426 q^{98} +(-8.26335 + 8.26335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 4 q^{3} + 12 q^{4} - 6 q^{5} + 4 q^{6} + 12 q^{8} + 8 q^{10} + 8 q^{11} + 24 q^{12} - 24 q^{15} + 4 q^{16} + 14 q^{17} - 4 q^{19} - 22 q^{20} + 4 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{24}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q + 8 * q^2 + 4 * q^3 + 12 * q^4 - 6 * q^5 + 4 * q^6 + 12 * q^8 + 8 * q^10 + 8 * q^11 + 24 * q^12 - 24 * q^15 + 4 * q^16 + 14 * q^17 - 4 * q^19 - 22 * q^20 + 4 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 + 12 * q^32 + 36 * q^33 - 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 + 32 * q^43 + 36 * q^44 - 20 * q^45 + 4 * q^46 + 28 * q^48 + 36 * q^49 - 52 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 12 * q^57 - 8 * q^59 - 92 * q^60 + 32 * q^61 - 4 * q^62 + 64 * q^63 - 20 * q^64 - 32 * q^66 + 116 * q^67 - 50 * q^68 - 32 * q^69 + 32 * q^70 - 40 * q^71 + 72 * q^73 - 4 * q^75 - 16 * q^76 + 28 * q^77 - 34 * q^80 + 28 * q^81 + 34 * q^82 - 8 * q^84 + 60 * q^86 - 28 * q^87 + 32 * q^88 - 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 + 56 * q^96 + 44 * q^97 - 8 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more