LMFDB - Embedded newform 1305.2.r.c.476.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1305,2,Mod(476,1305)] 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("1305.476"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1305, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.r (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			476.10
Character	$\chi$	$=$	1305.476
Dual form			1305.2.r.c.1061.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.251233 - 0.251233i) q^{2} +1.87376i q^{4} -1.00000 q^{5} -1.71619 q^{7} +(0.973218 + 0.973218i) q^{8} +(-0.251233 + 0.251233i) q^{10} +(-0.909719 + 0.909719i) q^{11} -7.03988i q^{13} +(-0.431163 + 0.431163i) q^{14} -3.25852 q^{16} +(-2.14351 + 2.14351i) q^{17} +(1.00494 + 1.00494i) q^{19} -1.87376i q^{20} +0.457103i q^{22} +4.56045i q^{23} +1.00000 q^{25} +(-1.76865 - 1.76865i) q^{26} -3.21573i q^{28} +(-5.36749 - 0.435991i) q^{29} +(-5.06890 - 5.06890i) q^{31} +(-2.76508 + 2.76508i) q^{32} +1.07704i q^{34} +1.71619 q^{35} +(5.64663 - 5.64663i) q^{37} +0.504949 q^{38} +(-0.973218 - 0.973218i) q^{40} +(-2.03006 - 2.03006i) q^{41} +(-1.91974 - 1.91974i) q^{43} +(-1.70460 - 1.70460i) q^{44} +(1.14574 + 1.14574i) q^{46} +(-3.96809 - 3.96809i) q^{47} -4.05470 q^{49} +(0.251233 - 0.251233i) q^{50} +13.1911 q^{52} -13.0642i q^{53} +(0.909719 - 0.909719i) q^{55} +(-1.67022 - 1.67022i) q^{56} +(-1.45803 + 1.23896i) q^{58} -4.81342i q^{59} +(2.58064 + 2.58064i) q^{61} -2.54695 q^{62} -5.12767i q^{64} +7.03988i q^{65} +3.31333i q^{67} +(-4.01643 - 4.01643i) q^{68} +(0.431163 - 0.431163i) q^{70} -5.50131 q^{71} +(5.58888 - 5.58888i) q^{73} -2.83724i q^{74} +(-1.88302 + 1.88302i) q^{76} +(1.56125 - 1.56125i) q^{77} +(-9.89566 - 9.89566i) q^{79} +3.25852 q^{80} -1.02004 q^{82} +5.54789i q^{83} +(2.14351 - 2.14351i) q^{85} -0.964604 q^{86} -1.77071 q^{88} +(-0.0286537 + 0.0286537i) q^{89} +12.0818i q^{91} -8.54520 q^{92} -1.99383 q^{94} +(-1.00494 - 1.00494i) q^{95} +(1.31577 - 1.31577i) q^{97} +(-1.01868 + 1.01868i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{5} + 8 q^{7} + 8 q^{11} - 24 q^{14} - 32 q^{16} + 16 q^{19} + 32 q^{25} - 8 q^{26} - 8 q^{29} - 8 q^{31} + 40 q^{32} - 8 q^{35} + 24 q^{37} - 24 q^{38} - 24 q^{41} + 16 q^{43} - 48 q^{44} - 64 q^{46}+ \cdots + 80 q^{98}+O(q^{100}) $ 32 * q - 32 * q^5 + 8 * q^7 + 8 * q^11 - 24 * q^14 - 32 * q^16 + 16 * q^19 + 32 * q^25 - 8 * q^26 - 8 * q^29 - 8 * q^31 + 40 * q^32 - 8 * q^35 + 24 * q^37 - 24 * q^38 - 24 * q^41 + 16 * q^43 - 48 * q^44 - 64 * q^46 - 8 * q^47 + 48 * q^49 + 40 * q^52 - 8 * q^55 + 104 * q^56 + 16 * q^58 + 16 * q^61 - 8 * q^62 + 56 * q^68 + 24 * q^70 - 48 * q^71 + 16 * q^73 - 48 * q^76 + 56 * q^77 + 32 * q^80 - 80 * q^82 - 112 * q^86 + 8 * q^88 - 32 * q^89 - 24 * q^92 - 104 * q^94 - 16 * q^95 - 72 * q^97 + 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.251233	−	0.251233i	0.177649	−	0.177649i	−0.612681	−	0.790330i	$-0.709909\pi$
$2$	0.251233	−	0.251233i	0.177649	−	0.177649i	0.790330	+	0.612681i	$0.209909\pi$
$3$		0			0
$3$		0			0
$4$			1.87376i			0.936882i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	−1.71619			−0.648658			−0.324329	−	0.945944i	$-0.605138\pi$
$7$	−1.71619			−0.648658			−0.324329	+	0.945944i	$0.605138\pi$
$8$	0.973218	+	0.973218i	0.344085	+	0.344085i
$9$		0			0
$10$	−0.251233	+	0.251233i	−0.0794469	+	0.0794469i
$11$	−0.909719	+	0.909719i	−0.274291	+	0.274291i	−0.830825	−	0.556534i	$-0.812131\pi$
$11$	−0.909719	+	0.909719i	−0.274291	+	0.274291i	0.556534	+	0.830825i	$0.312131\pi$
$12$		0			0
$13$		−	7.03988i		−	1.95251i	−0.216620	−	0.976256i	$-0.569503\pi$
$13$		−	7.03988i		−	1.95251i	0.216620	−	0.976256i	$-0.430497\pi$
$14$	−0.431163	+	0.431163i	−0.115233	+	0.115233i
$15$		0			0
$16$	−3.25852			−0.814629
$17$	−2.14351	+	2.14351i	−0.519877	+	0.519877i	−0.917534	−	0.397657i	$-0.869823\pi$
$17$	−2.14351	+	2.14351i	−0.519877	+	0.519877i	0.397657	+	0.917534i	$0.369823\pi$
$18$		0			0
$19$	1.00494	+	1.00494i	0.230549	+	0.230549i	0.812922	−	0.582373i	$-0.197876\pi$
$19$	1.00494	+	1.00494i	0.230549	+	0.230549i	−0.582373	+	0.812922i	$0.697876\pi$
$20$		−	1.87376i		−	0.418986i
$21$		0			0
$22$			0.457103i			0.0974548i
$23$			4.56045i			0.950919i	0.879738	+	0.475459i	$0.157718\pi$
$23$			4.56045i			0.950919i	−0.879738	+	0.475459i	$0.842282\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−1.76865	−	1.76865i	−0.346861	−	0.346861i
$27$		0			0
$28$		−	3.21573i		−	0.607716i
$29$	−5.36749	−	0.435991i	−0.996717	−	0.0809615i
$29$	−5.36749	−	0.435991i	−0.996717	−	0.0809615i
$30$		0			0
$31$	−5.06890	−	5.06890i	−0.910402	−	0.910402i	0.0859019	−	0.996304i	$-0.472623\pi$
$31$	−5.06890	−	5.06890i	−0.910402	−	0.910402i	−0.996304	+	0.0859019i	$0.972623\pi$
$32$	−2.76508	+	2.76508i	−0.488802	+	0.488802i
$33$		0			0
$34$			1.07704i			0.184711i
$35$	1.71619			0.290089
$36$		0			0
$37$	5.64663	−	5.64663i	0.928301	−	0.928301i	−0.0692955	−	0.997596i	$-0.522075\pi$
$37$	5.64663	−	5.64663i	0.928301	−	0.928301i	0.997596	+	0.0692955i	$0.0220751\pi$
$38$	0.504949			0.0819136
$39$		0			0
$40$	−0.973218	−	0.973218i	−0.153879	−	0.153879i
$41$	−2.03006	−	2.03006i	−0.317042	−	0.317042i	0.530588	−	0.847630i	$-0.321971\pi$
$41$	−2.03006	−	2.03006i	−0.317042	−	0.317042i	−0.847630	+	0.530588i	$0.821971\pi$
$42$		0			0
$43$	−1.91974	−	1.91974i	−0.292757	−	0.292757i	0.545411	−	0.838169i	$-0.316374\pi$
$43$	−1.91974	−	1.91974i	−0.292757	−	0.292757i	−0.838169	+	0.545411i	$0.816374\pi$
$44$	−1.70460	−	1.70460i	−0.256978	−	0.256978i
$45$		0			0
$46$	1.14574	+	1.14574i	0.168929	+	0.168929i
$47$	−3.96809	−	3.96809i	−0.578805	−	0.578805i	0.355769	−	0.934574i	$-0.384219\pi$
$47$	−3.96809	−	3.96809i	−0.578805	−	0.578805i	−0.934574	+	0.355769i	$0.884219\pi$
$48$		0			0
$49$	−4.05470			−0.579243
$50$	0.251233	−	0.251233i	0.0355297	−	0.0355297i
$51$		0			0
$52$	13.1911			1.82927
$53$		−	13.0642i		−	1.79450i	−0.441519	−	0.897252i	$-0.645560\pi$
$53$		−	13.0642i		−	1.79450i	0.441519	−	0.897252i	$-0.354440\pi$
$54$		0			0
$55$	0.909719	−	0.909719i	0.122666	−	0.122666i
$56$	−1.67022	−	1.67022i	−0.223193	−	0.223193i
$57$		0			0
$58$	−1.45803	+	1.23896i	−0.191448	+	0.162683i
$59$		−	4.81342i		−	0.626654i	−0.949645	−	0.313327i	$-0.898556\pi$
$59$		−	4.81342i		−	0.626654i	0.949645	−	0.313327i	$-0.101444\pi$
$60$		0			0
$61$	2.58064	+	2.58064i	0.330418	+	0.330418i	0.852745	−	0.522327i	$-0.174936\pi$
$61$	2.58064	+	2.58064i	0.330418	+	0.330418i	−0.522327	+	0.852745i	$0.674936\pi$
$62$	−2.54695			−0.323463
$63$		0			0
$64$		−	5.12767i		−	0.640959i
$65$			7.03988i			0.873190i
$66$		0			0
$67$			3.31333i			0.404787i	0.979304	+	0.202394i	$0.0648721\pi$
$67$			3.31333i			0.404787i	−0.979304	+	0.202394i	$0.935128\pi$
$68$	−4.01643	−	4.01643i	−0.487064	−	0.487064i
$69$		0			0
$70$	0.431163	−	0.431163i	0.0515339	−	0.0515339i
$71$	−5.50131			−0.652885			−0.326443	−	0.945217i	$-0.605850\pi$
$71$	−5.50131			−0.652885			−0.326443	+	0.945217i	$0.605850\pi$
$72$		0			0
$73$	5.58888	−	5.58888i	0.654128	−	0.654128i	−0.299856	−	0.953984i	$-0.596939\pi$
$73$	5.58888	−	5.58888i	0.654128	−	0.654128i	0.953984	+	0.299856i	$0.0969386\pi$
$74$		−	2.83724i		−	0.329823i
$75$		0			0
$76$	−1.88302	+	1.88302i	−0.215998	+	0.215998i
$77$	1.56125	−	1.56125i	0.177921	−	0.177921i
$78$		0			0
$79$	−9.89566	−	9.89566i	−1.11335	−	1.11335i	−0.992695	−	0.120654i	$-0.961501\pi$
$79$	−9.89566	−	9.89566i	−1.11335	−	1.11335i	−0.120654	−	0.992695i	$-0.538499\pi$
$80$	3.25852			0.364313
$81$		0			0
$82$	−1.02004			−0.112644
$83$			5.54789i			0.608960i	0.952519	+	0.304480i	$0.0984827\pi$
$83$			5.54789i			0.608960i	−0.952519	+	0.304480i	$0.901517\pi$
$84$		0			0
$85$	2.14351	−	2.14351i	0.232496	−	0.232496i
$86$	−0.964604			−0.104016
$87$		0			0
$88$	−1.77071			−0.188758
$89$	−0.0286537	+	0.0286537i	−0.00303729	+	0.00303729i	−0.708624	−	0.705587i	$-0.750684\pi$
$89$	−0.0286537	+	0.0286537i	−0.00303729	+	0.00303729i	0.705587	+	0.708624i	$0.250684\pi$
$90$		0			0
$91$			12.0818i			1.26651i
$92$	−8.54520			−0.890898
$93$		0			0
$94$	−1.99383			−0.205648
$95$	−1.00494	−	1.00494i	−0.103105	−	0.103105i
$96$		0			0
$97$	1.31577	−	1.31577i	0.133596	−	0.133596i	−0.637146	−	0.770743i	$-0.719885\pi$
$97$	1.31577	−	1.31577i	0.133596	−	0.133596i	0.770743	+	0.637146i	$0.219885\pi$
$98$	−1.01868	+	1.01868i	−0.102902	+	0.102902i
$99$		0			0
$100$			1.87376i			0.187376i
$101$	−7.63005	+	7.63005i	−0.759218	+	0.759218i	−0.976180	−	0.216962i	$-0.930385\pi$
$101$	−7.63005	+	7.63005i	−0.759218	+	0.759218i	0.216962	+	0.976180i	$0.430385\pi$
$102$		0			0
$103$	−9.41157			−0.927349			−0.463675	−	0.886006i	$-0.653469\pi$
$103$	−9.41157			−0.927349			−0.463675	+	0.886006i	$0.653469\pi$
$104$	6.85134	−	6.85134i	0.671829	−	0.671829i
$105$		0			0
$106$	−3.28216	−	3.28216i	−0.318791	−	0.318791i
$107$			17.2703i			1.66958i	0.550570	+	0.834789i	$0.314411\pi$
$107$			17.2703i			1.66958i	−0.550570	+	0.834789i	$0.685589\pi$
$108$		0			0
$109$			0.692336i			0.0663137i	0.999450	+	0.0331569i	$0.0105561\pi$
$109$			0.692336i			0.0663137i	−0.999450	+	0.0331569i	$0.989444\pi$
$110$		−	0.457103i		−	0.0435831i
$111$		0			0
$112$	5.59223			0.528416
$113$	1.36960	+	1.36960i	0.128841	+	0.128841i	0.768587	−	0.639746i	$-0.220960\pi$
$113$	1.36960	+	1.36960i	0.128841	+	0.128841i	−0.639746	+	0.768587i	$0.720960\pi$
$114$		0			0
$115$		−	4.56045i		−	0.425264i
$116$	0.816945	−	10.0574i	0.0758514	−	0.933806i
$117$		0			0
$118$	−1.20929	−	1.20929i	−0.111324	−	0.111324i
$119$	3.67866	−	3.67866i	0.337223	−	0.337223i
$120$		0			0
$121$			9.34482i			0.849529i
$122$	1.29669			0.117397
$123$		0			0
$124$	9.49793	−	9.49793i	0.852939	−	0.852939i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	11.2368	+	11.2368i	0.997108	+	0.997108i	0.999996	−	0.00288737i	$-0.000919079\pi$
$127$	11.2368	+	11.2368i	0.997108	+	0.997108i	−0.00288737	+	0.999996i	$0.500919\pi$
$128$	−6.81841	−	6.81841i	−0.602668	−	0.602668i
$129$		0			0
$130$	1.76865	+	1.76865i	0.155121	+	0.155121i
$131$	13.6435	+	13.6435i	1.19204	+	1.19204i	0.976494	+	0.215546i	$0.0691530\pi$
$131$	13.6435	+	13.6435i	1.19204	+	1.19204i	0.215546	+	0.976494i	$0.430847\pi$
$132$		0			0
$133$	−1.72467	−	1.72467i	−0.149548	−	0.149548i
$134$	0.832418	+	0.832418i	0.0719100	+	0.0719100i
$135$		0			0
$136$	−4.17221			−0.357764
$137$	0.0372510	−	0.0372510i	0.00318257	−	0.00318257i	−0.705514	−	0.708696i	$-0.749284\pi$
$137$	0.0372510	−	0.0372510i	0.00318257	−	0.00318257i	0.708696	+	0.705514i	$0.249284\pi$
$138$		0			0
$139$	8.16951			0.692929			0.346465	−	0.938063i	$-0.387382\pi$
$139$	8.16951			0.692929			0.346465	+	0.938063i	$0.387382\pi$
$140$			3.21573i			0.271779i
$141$		0			0
$142$	−1.38211	+	1.38211i	−0.115984	+	0.115984i
$143$	6.40431	+	6.40431i	0.535556	+	0.535556i
$144$		0			0
$145$	5.36749	+	0.435991i	0.445745	+	0.0362071i
$146$		−	2.80822i		−	0.232410i
$147$		0			0
$148$	10.5805	+	10.5805i	0.869708	+	0.869708i
$149$	−14.5910			−1.19534			−0.597670	−	0.801743i	$-0.703907\pi$
$149$	−14.5910			−1.19534			−0.597670	+	0.801743i	$0.703907\pi$
$150$		0			0
$151$		−	8.63424i		−	0.702644i	−0.936255	−	0.351322i	$-0.885732\pi$
$151$		−	8.63424i		−	0.702644i	0.936255	−	0.351322i	$-0.114268\pi$
$152$			1.95605i			0.158657i
$153$		0			0
$154$		−	0.784475i		−	0.0632148i
$155$	5.06890	+	5.06890i	0.407144	+	0.407144i
$156$		0			0
$157$	0.424954	−	0.424954i	0.0339150	−	0.0339150i	−0.689946	−	0.723861i	$-0.742366\pi$
$157$	0.424954	−	0.424954i	0.0339150	−	0.0339150i	0.723861	+	0.689946i	$0.242366\pi$
$158$	−4.97224			−0.395570
$159$		0			0
$160$	2.76508	−	2.76508i	0.218599	−	0.218599i
$161$		−	7.82658i		−	0.616821i
$162$		0			0
$163$	−2.25740	+	2.25740i	−0.176813	+	0.176813i	−0.789965	−	0.613152i	$-0.789901\pi$
$163$	−2.25740	+	2.25740i	−0.176813	+	0.176813i	0.613152	+	0.789965i	$0.289901\pi$
$164$	3.80386	−	3.80386i	0.297031	−	0.297031i
$165$		0			0
$166$	1.39381	+	1.39381i	0.108181	+	0.108181i
$167$	−9.73578			−0.753377			−0.376689	−	0.926340i	$-0.622937\pi$
$167$	−9.73578			−0.753377			−0.376689	+	0.926340i	$0.622937\pi$
$168$		0			0
$169$	−36.5599			−2.81230
$170$		−	1.07704i		−	0.0826053i
$171$		0			0
$172$	3.59714	−	3.59714i	0.274279	−	0.274279i
$173$	2.05589			0.156306			0.0781531	−	0.996941i	$-0.475098\pi$
$173$	2.05589			0.156306			0.0781531	+	0.996941i	$0.475098\pi$
$174$		0			0
$175$	−1.71619			−0.129732
$176$	2.96434	−	2.96434i	0.223445	−	0.223445i
$177$		0			0
$178$			0.0143975i			0.00107914i
$179$	−0.506207			−0.0378357			−0.0189178	−	0.999821i	$-0.506022\pi$
$179$	−0.506207			−0.0378357			−0.0189178	+	0.999821i	$0.506022\pi$
$180$		0			0
$181$	19.1979			1.42697			0.713484	−	0.700672i	$-0.247116\pi$
$181$	19.1979			1.42697			0.713484	+	0.700672i	$0.247116\pi$
$182$	3.03534	+	3.03534i	0.224994	+	0.224994i
$183$		0			0
$184$	−4.43831	+	4.43831i	−0.327196	+	0.327196i
$185$	−5.64663	+	5.64663i	−0.415149	+	0.415149i
$186$		0			0
$187$		−	3.89998i		−	0.285195i
$188$	7.43526	−	7.43526i	0.542272	−	0.542272i
$189$		0			0
$190$	−0.504949			−0.0366329
$191$	−16.1208	+	16.1208i	−1.16646	+	1.16646i	−0.183423	+	0.983034i	$0.558718\pi$
$191$	−16.1208	+	16.1208i	−1.16646	+	1.16646i	−0.983034	+	0.183423i	$0.941282\pi$
$192$		0			0
$193$	−15.7585	−	15.7585i	−1.13432	−	1.13432i	−0.989450	−	0.144875i	$-0.953722\pi$
$193$	−15.7585	−	15.7585i	−1.13432	−	1.13432i	−0.144875	−	0.989450i	$-0.546278\pi$
$194$		−	0.661131i		−	0.0474664i
$195$		0			0
$196$		−	7.59755i		−	0.542682i
$197$			20.9990i			1.49612i	0.663634	+	0.748058i	$0.269013\pi$
$197$			20.9990i			1.49612i	−0.663634	+	0.748058i	$0.730987\pi$
$198$		0			0
$199$	−4.81438			−0.341282			−0.170641	−	0.985333i	$-0.554584\pi$
$199$	−4.81438			−0.341282			−0.170641	+	0.985333i	$0.554584\pi$
$200$	0.973218	+	0.973218i	0.0688169	+	0.0688169i
$201$		0			0
$202$			3.83384i			0.269748i
$203$	9.21161	+	0.748243i	0.646528	+	0.0525163i
$204$		0			0
$205$	2.03006	+	2.03006i	0.141786	+	0.141786i
$206$	−2.36450	+	2.36450i	−0.164742	+	0.164742i
$207$		0			0
$208$			22.9396i			1.59057i
$209$	−1.82843			−0.126475
$210$		0			0
$211$	−17.6477	+	17.6477i	−1.21492	+	1.21492i	−0.245525	+	0.969390i	$0.578960\pi$
$211$	−17.6477	+	17.6477i	−1.21492	+	1.21492i	−0.969390	+	0.245525i	$0.921040\pi$
$212$	24.4792			1.68124
$213$		0			0
$214$	4.33886	+	4.33886i	0.296598	+	0.296598i
$215$	1.91974	+	1.91974i	0.130925	+	0.130925i
$216$		0			0
$217$	8.69919	+	8.69919i	0.590539	+	0.590539i
$218$	0.173938	+	0.173938i	0.0117806	+	0.0117806i
$219$		0			0
$220$	1.70460	+	1.70460i	0.114924	+	0.114924i
$221$	15.0901	+	15.0901i	1.01507	+	1.01507i
$222$		0			0
$223$	2.05201			0.137413			0.0687065	−	0.997637i	$-0.478113\pi$
$223$	2.05201			0.137413			0.0687065	+	0.997637i	$0.478113\pi$
$224$	4.74540	−	4.74540i	0.317066	−	0.317066i
$225$		0			0
$226$	0.688178			0.0457769
$227$		−	20.7569i		−	1.37768i	−0.724913	−	0.688841i	$-0.758120\pi$
$227$		−	20.7569i		−	1.37768i	0.724913	−	0.688841i	$-0.241880\pi$
$228$		0			0
$229$	−12.0703	+	12.0703i	−0.797626	+	0.797626i	−0.982721	−	0.185095i	$-0.940741\pi$
$229$	−12.0703	+	12.0703i	−0.797626	+	0.797626i	0.185095	+	0.982721i	$0.440741\pi$
$230$	−1.14574	−	1.14574i	−0.0755476	−	0.0755476i
$231$		0			0
$232$	−4.79942	−	5.64805i	−0.315097	−	0.370813i
$233$			8.71593i			0.570999i	0.958379	+	0.285500i	$0.0921596\pi$
$233$			8.71593i			0.570999i	−0.958379	+	0.285500i	$0.907840\pi$
$234$		0			0
$235$	3.96809	+	3.96809i	0.258849	+	0.258849i
$236$	9.01921			0.587101
$237$		0			0
$238$		−	1.84841i		−	0.119814i
$239$			8.12294i			0.525430i	0.964874	+	0.262715i	$0.0846178\pi$
$239$			8.12294i			0.525430i	−0.964874	+	0.262715i	$0.915382\pi$
$240$		0			0
$241$		−	18.2430i		−	1.17514i	−0.809174	−	0.587569i	$-0.800085\pi$
$241$		−	18.2430i		−	1.17514i	0.809174	−	0.587569i	$-0.199915\pi$
$242$	2.34773	+	2.34773i	0.150918	+	0.150918i
$243$		0			0
$244$	−4.83552	+	4.83552i	−0.309562	+	0.309562i
$245$	4.05470			0.259045
$246$		0			0
$247$	7.07467	−	7.07467i	0.450151	−	0.450151i
$248$		−	9.86630i		−	0.626510i
$249$		0			0
$250$	−0.251233	+	0.251233i	−0.0158894	+	0.0158894i
$251$	15.9128	−	15.9128i	1.00440	−	1.00440i	0.00441463	−	0.999990i	$-0.498595\pi$
$251$	15.9128	−	15.9128i	1.00440	−	1.00440i	0.999990	−	0.00441463i	$-0.00140523\pi$
$252$		0			0
$253$	−4.14872	−	4.14872i	−0.260828	−	0.260828i
$254$	5.64614			0.354270
$255$		0			0
$256$	6.82932			0.426833
$257$			12.6836i			0.791183i	0.918426	+	0.395592i	$0.129460\pi$
$257$			12.6836i			0.791183i	−0.918426	+	0.395592i	$0.870540\pi$
$258$		0			0
$259$	−9.69068	+	9.69068i	−0.602150	+	0.602150i
$260$	−13.1911			−0.818076
$261$		0			0
$262$	6.85541			0.423529
$263$	14.6840	−	14.6840i	0.905457	−	0.905457i	−0.0904444	−	0.995902i	$-0.528829\pi$
$263$	14.6840	−	14.6840i	0.905457	−	0.905457i	0.995902	+	0.0904444i	$0.0288287\pi$
$264$		0			0
$265$			13.0642i			0.802527i
$266$	−0.866588			−0.0531339
$267$		0			0
$268$	−6.20839			−0.379238
$269$	−18.1270	−	18.1270i	−1.10522	−	1.10522i	−0.993770	−	0.111450i	$-0.964450\pi$
$269$	−18.1270	−	18.1270i	−1.10522	−	1.10522i	−0.111450	−	0.993770i	$-0.535550\pi$
$270$		0			0
$271$	−7.19575	+	7.19575i	−0.437111	+	0.437111i	−0.891038	−	0.453928i	$-0.850022\pi$
$271$	−7.19575	+	7.19575i	−0.437111	+	0.437111i	0.453928	+	0.891038i	$0.350022\pi$
$272$	6.98466	−	6.98466i	0.423508	−	0.423508i
$273$		0			0
$274$		−	0.0187174i		−	0.00113076i
$275$	−0.909719	+	0.909719i	−0.0548581	+	0.0548581i
$276$		0			0
$277$	−5.35608			−0.321816			−0.160908	−	0.986969i	$-0.551442\pi$
$277$	−5.35608			−0.321816			−0.160908	+	0.986969i	$0.551442\pi$
$278$	2.05245	−	2.05245i	0.123098	−	0.123098i
$279$		0			0
$280$	1.67022	+	1.67022i	0.0998150	+	0.0998150i
$281$		−	6.71123i		−	0.400359i	−0.979759	−	0.200179i	$-0.935848\pi$
$281$		−	6.71123i		−	0.400359i	0.979759	−	0.200179i	$-0.0641525\pi$
$282$		0			0
$283$			9.23985i			0.549252i	0.961551	+	0.274626i	$0.0885541\pi$
$283$			9.23985i			0.549252i	−0.961551	+	0.274626i	$0.911446\pi$
$284$		−	10.3081i		−	0.611676i
$285$		0			0
$286$	3.21795			0.190282
$287$	3.48397	+	3.48397i	0.205652	+	0.205652i
$288$		0			0
$289$			7.81073i			0.459455i
$290$	1.45803	−	1.23896i	0.0856183	−	0.0727540i
$291$		0			0
$292$	10.4722	+	10.4722i	0.612841	+	0.612841i
$293$	9.25343	−	9.25343i	0.540591	−	0.540591i	−0.383111	−	0.923702i	$-0.625147\pi$
$293$	9.25343	−	9.25343i	0.540591	−	0.540591i	0.923702	+	0.383111i	$0.125147\pi$
$294$		0			0
$295$			4.81342i			0.280248i
$296$	10.9908			0.638828
$297$		0			0
$298$	−3.66574	+	3.66574i	−0.212350	+	0.212350i
$299$	32.1050			1.85668
$300$		0			0
$301$	3.29463	+	3.29463i	0.189899	+	0.189899i
$302$	−2.16921	−	2.16921i	−0.124824	−	0.124824i
$303$		0			0
$304$	−3.27462	−	3.27462i	−0.187812	−	0.187812i
$305$	−2.58064	−	2.58064i	−0.147767	−	0.147767i
$306$		0			0
$307$	10.3536	+	10.3536i	0.590911	+	0.590911i	0.937877	−	0.346967i	$-0.112788\pi$
$307$	10.3536	+	10.3536i	0.590911	+	0.590911i	−0.346967	+	0.937877i	$0.612788\pi$
$308$	2.92541	+	2.92541i	0.166691	+	0.166691i
$309$		0			0
$310$	2.54695			0.144657
$311$	19.1198	−	19.1198i	1.08418	−	1.08418i	0.0880705	−	0.996114i	$-0.471930\pi$
$311$	19.1198	−	19.1198i	1.08418	−	1.08418i	0.996114	−	0.0880705i	$-0.0280701\pi$
$312$		0			0
$313$	4.15465			0.234835			0.117417	−	0.993083i	$-0.462538\pi$
$313$	4.15465			0.234835			0.117417	+	0.993083i	$0.462538\pi$
$314$		−	0.213525i		−	0.0120499i
$315$		0			0
$316$	18.5421	−	18.5421i	1.04308	−	1.04308i
$317$	1.51248	+	1.51248i	0.0849492	+	0.0849492i	0.748305	−	0.663355i	$-0.230868\pi$
$317$	1.51248	+	1.51248i	0.0849492	+	0.0849492i	−0.663355	+	0.748305i	$0.730868\pi$
$318$		0			0
$319$	5.27953	−	4.48627i	0.295597	−	0.251183i
$320$			5.12767i			0.286646i
$321$		0			0
$322$	−1.96630	−	1.96630i	−0.109577	−	0.109577i
$323$	−4.30820			−0.239715
$324$		0			0
$325$		−	7.03988i		−	0.390502i
$326$			1.13427i			0.0628212i
$327$		0			0
$328$		−	3.95139i		−	0.218179i
$329$	6.80998	+	6.80998i	0.375446	+	0.375446i
$330$		0			0
$331$	−15.9336	+	15.9336i	−0.875791	+	0.875791i	−0.993096	−	0.117305i	$-0.962574\pi$
$331$	−15.9336	+	15.9336i	−0.875791	+	0.875791i	0.117305	+	0.993096i	$0.462574\pi$
$332$	−10.3954			−0.570524
$333$		0			0
$334$	−2.44595	+	2.44595i	−0.133837	+	0.133837i
$335$		−	3.31333i		−	0.181026i
$336$		0			0
$337$	20.8284	−	20.8284i	1.13460	−	1.13460i	0.145192	−	0.989404i	$-0.453620\pi$
$337$	20.8284	−	20.8284i	1.13460	−	1.13460i	0.989404	−	0.145192i	$-0.0463799\pi$
$338$	−9.18507	+	9.18507i	−0.499602	+	0.499602i
$339$		0			0
$340$	4.01643	+	4.01643i	0.217822	+	0.217822i
$341$	9.22255			0.499429
$342$		0			0
$343$	18.9719			1.02439
$344$		−	3.73665i		−	0.201467i
$345$		0			0
$346$	0.516507	−	0.516507i	0.0277676	−	0.0277676i
$347$	14.8892			0.799292			0.399646	−	0.916670i	$-0.369133\pi$
$347$	14.8892			0.799292			0.399646	+	0.916670i	$0.369133\pi$
$348$		0			0
$349$	−4.16209			−0.222792			−0.111396	−	0.993776i	$-0.535532\pi$
$349$	−4.16209			−0.222792			−0.111396	+	0.993776i	$0.535532\pi$
$350$	−0.431163	+	0.431163i	−0.0230466	+	0.0230466i
$351$		0			0
$352$		−	5.03090i		−	0.268148i
$353$	−14.0711			−0.748931			−0.374466	−	0.927241i	$-0.622174\pi$
$353$	−14.0711			−0.748931			−0.374466	+	0.927241i	$0.622174\pi$
$354$		0			0
$355$	5.50131			0.291979
$356$	−0.0536903	−	0.0536903i	−0.00284558	−	0.00284558i
$357$		0			0
$358$	−0.127176	+	0.127176i	−0.00672146	+	0.00672146i
$359$	6.69033	−	6.69033i	0.353102	−	0.353102i	−0.508160	−	0.861263i	$-0.669674\pi$
$359$	6.69033	−	6.69033i	0.353102	−	0.353102i	0.861263	+	0.508160i	$0.169674\pi$
$360$		0			0
$361$		−	16.9802i		−	0.893694i
$362$	4.82315	−	4.82315i	0.253499	−	0.253499i
$363$		0			0
$364$	−22.6384			−1.18657
$365$	−5.58888	+	5.58888i	−0.292535	+	0.292535i
$366$		0			0
$367$	20.3434	+	20.3434i	1.06192	+	1.06192i	0.997952	+	0.0639658i	$0.0203749\pi$
$367$	20.3434	+	20.3434i	1.06192	+	1.06192i	0.0639658	+	0.997952i	$0.479625\pi$
$368$		−	14.8603i		−	0.774646i
$369$		0			0
$370$			2.83724i			0.147501i
$371$			22.4206i			1.16402i
$372$		0			0
$373$	−24.8857			−1.28853			−0.644267	−	0.764801i	$-0.722837\pi$
$373$	−24.8857			−1.28853			−0.644267	+	0.764801i	$0.722837\pi$
$374$	−0.979805	−	0.979805i	−0.0506645	−	0.0506645i
$375$		0			0
$376$		−	7.72363i		−	0.398316i
$377$	−3.06933	+	37.7865i	−0.158078	+	1.94610i
$378$		0			0
$379$	−7.70315	−	7.70315i	−0.395684	−	0.395684i	0.481023	−	0.876708i	$-0.340265\pi$
$379$	−7.70315	−	7.70315i	−0.395684	−	0.395684i	−0.876708	+	0.481023i	$0.840265\pi$
$380$	1.88302	−	1.88302i	0.0965970	−	0.0965970i
$381$		0			0
$382$			8.10014i			0.414439i
$383$	−1.66294			−0.0849723			−0.0424861	−	0.999097i	$-0.513528\pi$
$383$	−1.66294			−0.0849723			−0.0424861	+	0.999097i	$0.513528\pi$
$384$		0			0
$385$	−1.56125	+	1.56125i	−0.0795686	+	0.0795686i
$386$	−7.91814			−0.403023
$387$		0			0
$388$	2.46544	+	2.46544i	0.125164	+	0.125164i
$389$	−3.72549	−	3.72549i	−0.188890	−	0.188890i	0.606326	−	0.795216i	$-0.292643\pi$
$389$	−3.72549	−	3.72549i	−0.188890	−	0.188890i	−0.795216	+	0.606326i	$0.792643\pi$
$390$		0			0
$391$	−9.77536	−	9.77536i	−0.494361	−	0.494361i
$392$	−3.94611	−	3.94611i	−0.199309	−	0.199309i
$393$		0			0
$394$	5.27564	+	5.27564i	0.265783	+	0.265783i
$395$	9.89566	+	9.89566i	0.497905	+	0.497905i
$396$		0			0
$397$	20.4883			1.02828			0.514139	−	0.857707i	$-0.328112\pi$
$397$	20.4883			1.02828			0.514139	+	0.857707i	$0.328112\pi$
$398$	−1.20953	+	1.20953i	−0.0606284	+	0.0606284i
$399$		0			0
$400$	−3.25852			−0.162926
$401$			30.1828i			1.50726i	0.657300	+	0.753629i	$0.271699\pi$
$401$			30.1828i			1.50726i	−0.657300	+	0.753629i	$0.728301\pi$
$402$		0			0
$403$	−35.6845	+	35.6845i	−1.77757	+	1.77757i
$404$	−14.2969	−	14.2969i	−0.711297	−	0.711297i
$405$		0			0
$406$	2.50225	−	2.12628i	0.124184	−	0.105525i
$407$			10.2737i			0.509248i
$408$		0			0
$409$	7.59438	+	7.59438i	0.375518	+	0.375518i	0.869482	−	0.493964i	$-0.164453\pi$
$409$	7.59438	+	7.59438i	0.375518	+	0.375518i	−0.493964	+	0.869482i	$0.664453\pi$
$410$	1.02004			0.0503761
$411$		0			0
$412$		−	17.6351i		−	0.868817i
$413$			8.26073i			0.406484i
$414$		0			0
$415$		−	5.54789i		−	0.272335i
$416$	19.4659	+	19.4659i	0.954393	+	0.954393i
$417$		0			0
$418$	−0.459362	+	0.459362i	−0.0224681	+	0.0224681i
$419$	18.0170			0.880187			0.440093	−	0.897952i	$-0.354945\pi$
$419$	18.0170			0.880187			0.440093	+	0.897952i	$0.354945\pi$
$420$		0			0
$421$	−21.5614	+	21.5614i	−1.05084	+	1.05084i	−0.0522021	+	0.998637i	$0.516624\pi$
$421$	−21.5614	+	21.5614i	−1.05084	+	1.05084i	−0.998637	+	0.0522021i	$0.983376\pi$
$422$			8.86736i			0.431656i
$423$		0			0
$424$	12.7143	−	12.7143i	0.617461	−	0.617461i
$425$	−2.14351	+	2.14351i	−0.103975	+	0.103975i
$426$		0			0
$427$	−4.42887	−	4.42887i	−0.214328	−	0.214328i
$428$	−32.3604			−1.56420
$429$		0			0
$430$	0.964604			0.0465174
$431$		−	39.6974i		−	1.91216i	−0.293113	−	0.956078i	$-0.594691\pi$
$431$		−	39.6974i		−	1.91216i	0.293113	−	0.956078i	$-0.405309\pi$
$432$		0			0
$433$	−4.10746	+	4.10746i	−0.197392	+	0.197392i	−0.798881	−	0.601489i	$-0.794574\pi$
$433$	−4.10746	+	4.10746i	−0.197392	+	0.197392i	0.601489	+	0.798881i	$0.294574\pi$
$434$	4.37105			0.209817
$435$		0			0
$436$	−1.29727			−0.0621281
$437$	−4.58298	+	4.58298i	−0.219234	+	0.219234i
$438$		0			0
$439$		−	3.56192i		−	0.170001i	−0.996381	−	0.0850006i	$-0.972911\pi$
$439$		−	3.56192i		−	0.170001i	0.996381	−	0.0850006i	$-0.0270892\pi$
$440$	1.77071			0.0844153
$441$		0			0
$442$	7.58225			0.360651
$443$	5.67336	+	5.67336i	0.269550	+	0.269550i	0.828919	−	0.559369i	$-0.188957\pi$
$443$	5.67336	+	5.67336i	0.269550	+	0.269550i	−0.559369	+	0.828919i	$0.688957\pi$
$444$		0			0
$445$	0.0286537	−	0.0286537i	0.00135832	−	0.00135832i
$446$	0.515534	−	0.515534i	0.0244113	−	0.0244113i
$447$		0			0
$448$			8.80005i			0.415763i
$449$	15.3009	−	15.3009i	0.722092	−	0.722092i	−0.246939	−	0.969031i	$-0.579425\pi$
$449$	15.3009	−	15.3009i	0.722092	−	0.722092i	0.969031	+	0.246939i	$0.0794247\pi$
$450$		0			0
$451$	3.69357			0.173923
$452$	−2.56630	+	2.56630i	−0.120709	+	0.120709i
$453$		0			0
$454$	−5.21481	−	5.21481i	−0.244743	−	0.244743i
$455$		−	12.0818i		−	0.566402i
$456$		0			0
$457$			7.20400i			0.336989i	0.985703	+	0.168495i	$0.0538905\pi$
$457$			7.20400i			0.336989i	−0.985703	+	0.168495i	$0.946109\pi$
$458$			6.06490i			0.283394i
$459$		0			0
$460$	8.54520			0.398422
$461$	−26.7798	−	26.7798i	−1.24726	−	1.24726i	−0.956924	−	0.290338i	$-0.906232\pi$
$461$	−26.7798	−	26.7798i	−1.24726	−	1.24726i	−0.290338	−	0.956924i	$-0.593768\pi$
$462$		0			0
$463$		−	6.58766i		−	0.306154i	−0.988214	−	0.153077i	$-0.951082\pi$
$463$		−	6.58766i		−	0.306154i	0.988214	−	0.153077i	$-0.0489183\pi$
$464$	17.4901	+	1.42069i	0.811955	+	0.0659537i
$465$		0			0
$466$	2.18973	+	2.18973i	0.101437	+	0.101437i
$467$	−26.4375	+	26.4375i	−1.22338	+	1.22338i	−0.256962	+	0.966422i	$0.582721\pi$
$467$	−26.4375	+	26.4375i	−1.22338	+	1.22338i	−0.966422	+	0.256962i	$0.917279\pi$
$468$		0			0
$469$		−	5.68629i		−	0.262569i
$470$	1.99383			0.0919685
$471$		0			0
$472$	4.68451	−	4.68451i	0.215622	−	0.215622i
$473$	3.49285			0.160601
$474$		0			0
$475$	1.00494	+	1.00494i	0.0461099	+	0.0461099i
$476$	6.89295	+	6.89295i	0.315938	+	0.315938i
$477$		0			0
$478$	2.04075	+	2.04075i	0.0933419	+	0.0933419i
$479$	−7.22083	−	7.22083i	−0.329928	−	0.329928i	0.522631	−	0.852559i	$-0.324951\pi$
$479$	−7.22083	−	7.22083i	−0.329928	−	0.329928i	−0.852559	+	0.522631i	$0.824951\pi$
$480$		0			0
$481$	−39.7516	−	39.7516i	−1.81252	−	1.81252i
$482$	−4.58326	−	4.58326i	−0.208762	−	0.208762i
$483$		0			0
$484$	−17.5100			−0.795909
$485$	−1.31577	+	1.31577i	−0.0597461	+	0.0597461i
$486$		0			0
$487$	21.3440			0.967189			0.483595	−	0.875292i	$-0.339331\pi$
$487$	21.3440			0.967189			0.483595	+	0.875292i	$0.339331\pi$
$488$			5.02306i			0.227383i
$489$		0			0
$490$	1.01868	−	1.01868i	0.0460191	−	0.0460191i
$491$	−14.3761	−	14.3761i	−0.648786	−	0.648786i	0.303913	−	0.952700i	$-0.401707\pi$
$491$	−14.3761	−	14.3761i	−0.648786	−	0.648786i	−0.952700	+	0.303913i	$0.901707\pi$
$492$		0			0
$493$	12.4398	−	10.5707i	0.560261	−	0.476081i
$494$		−	3.55478i		−	0.159937i
$495$		0			0
$496$	16.5171	+	16.5171i	0.741640	+	0.741640i
$497$	9.44127			0.423499
$498$		0			0
$499$		−	38.6232i		−	1.72901i	−0.502622	−	0.864506i	$-0.667631\pi$
$499$		−	38.6232i		−	1.72901i	0.502622	−	0.864506i	$-0.332369\pi$
$500$		−	1.87376i		−	0.0837973i
$501$		0			0
$502$		−	7.99563i		−	0.356862i
$503$	−6.89899	−	6.89899i	−0.307611	−	0.307611i	0.536371	−	0.843982i	$-0.319795\pi$
$503$	−6.89899	−	6.89899i	−0.307611	−	0.307611i	−0.843982	+	0.536371i	$0.819795\pi$
$504$		0			0
$505$	7.63005	−	7.63005i	0.339533	−	0.339533i
$506$	−2.08459			−0.0926715
$507$		0			0
$508$	−21.0552	+	21.0552i	−0.934173	+	0.934173i
$509$		−	12.5298i		−	0.555376i	−0.960671	−	0.277688i	$-0.910432\pi$
$509$		−	12.5298i		−	0.555376i	0.960671	−	0.277688i	$-0.0895681\pi$
$510$		0			0
$511$	−9.59156	+	9.59156i	−0.424306	+	0.424306i
$512$	15.3526	−	15.3526i	0.678494	−	0.678494i
$513$		0			0
$514$	3.18655	+	3.18655i	0.140553	+	0.140553i
$515$	9.41157			0.414723
$516$		0			0
$517$	7.21969			0.317521
$518$			4.86924i			0.213942i
$519$		0			0
$520$	−6.85134	+	6.85134i	−0.300451	+	0.300451i
$521$	−34.7768			−1.52360			−0.761800	−	0.647813i	$-0.775684\pi$
$521$	−34.7768			−1.52360			−0.761800	+	0.647813i	$0.775684\pi$
$522$		0			0
$523$	8.80756			0.385128			0.192564	−	0.981284i	$-0.438320\pi$
$523$	8.80756			0.385128			0.192564	+	0.981284i	$0.438320\pi$
$524$	−25.5647	+	25.5647i	−1.11680	+	1.11680i
$525$		0			0
$526$		−	7.37824i		−	0.321707i
$527$	21.7305			0.946595
$528$		0			0
$529$	2.20234			0.0957539
$530$	3.28216	+	3.28216i	0.142568	+	0.142568i
$531$		0			0
$532$	3.23162	−	3.23162i	0.140109	−	0.140109i
$533$	−14.2914	+	14.2914i	−0.619029	+	0.619029i
$534$		0			0
$535$		−	17.2703i		−	0.746658i
$536$	−3.22459	+	3.22459i	−0.139281	+	0.139281i
$537$		0			0
$538$	−9.10819			−0.392682
$539$	3.68864	−	3.68864i	0.158881	−	0.158881i
$540$		0			0
$541$	−3.51456	−	3.51456i	−0.151103	−	0.151103i	0.627508	−	0.778610i	$-0.284075\pi$
$541$	−3.51456	−	3.51456i	−0.151103	−	0.151103i	−0.778610	+	0.627508i	$0.784075\pi$
$542$			3.61562i			0.155304i
$543$		0			0
$544$		−	11.8540i		−	0.508235i
$545$		−	0.692336i		−	0.0296564i
$546$		0			0
$547$	−33.8780			−1.44852			−0.724259	−	0.689528i	$-0.757818\pi$
$547$	−33.8780			−1.44852			−0.724259	+	0.689528i	$0.757818\pi$
$548$	0.0697996	+	0.0697996i	0.00298169	+	0.00298169i
$549$		0			0
$550$			0.457103i			0.0194910i
$551$	−4.95586	−	5.83216i	−0.211127	−	0.248458i
$552$		0			0
$553$	16.9828	+	16.9828i	0.722182	+	0.722182i
$554$	−1.34563	+	1.34563i	−0.0571701	+	0.0571701i
$555$		0			0
$556$			15.3077i			0.649193i
$557$	−0.344915			−0.0146145			−0.00730725	−	0.999973i	$-0.502326\pi$
$557$	−0.344915			−0.0146145			−0.00730725	+	0.999973i	$0.502326\pi$
$558$		0			0
$559$	−13.5147	+	13.5147i	−0.571612	+	0.571612i
$560$	−5.59223			−0.236315
$561$		0			0
$562$	−1.68608	−	1.68608i	−0.0711232	−	0.0711232i
$563$	−27.5224	−	27.5224i	−1.15993	−	1.15993i	−0.984490	−	0.175442i	$-0.943865\pi$
$563$	−27.5224	−	27.5224i	−1.15993	−	1.15993i	−0.175442	−	0.984490i	$-0.556135\pi$
$564$		0			0
$565$	−1.36960	−	1.36960i	−0.0576195	−	0.0576195i
$566$	2.32136	+	2.32136i	0.0975740	+	0.0975740i
$567$		0			0
$568$	−5.35397	−	5.35397i	−0.224648	−	0.224648i
$569$	8.98926	+	8.98926i	0.376849	+	0.376849i	0.869964	−	0.493115i	$-0.164142\pi$
$569$	8.98926	+	8.98926i	0.376849	+	0.376849i	−0.493115	+	0.869964i	$0.664142\pi$
$570$		0			0
$571$	38.9090			1.62829			0.814146	−	0.580660i	$-0.197205\pi$
$571$	38.9090			1.62829			0.814146	+	0.580660i	$0.197205\pi$
$572$	−12.0002	+	12.0002i	−0.501752	+	0.501752i
$573$		0			0
$574$	1.75058			0.0730676
$575$			4.56045i			0.190184i
$576$		0			0
$577$	−24.5454	+	24.5454i	−1.02184	+	1.02184i	−0.0220806	+	0.999756i	$0.507029\pi$
$577$	−24.5454	+	24.5454i	−1.02184	+	1.02184i	−0.999756	+	0.0220806i	$0.992971\pi$
$578$	1.96232	+	1.96232i	0.0816216	+	0.0816216i
$579$		0			0
$580$	−0.816945	+	10.0574i	−0.0339218	+	0.417611i
$581$		−	9.52122i		−	0.395007i
$582$		0			0
$583$	11.8847	+	11.8847i	0.492216	+	0.492216i
$584$	10.8784			0.450151
$585$		0			0
$586$		−	4.64954i		−	0.192071i
$587$			39.4702i			1.62911i	0.580087	+	0.814554i	$0.303018\pi$
$587$			39.4702i			1.62911i	−0.580087	+	0.814554i	$0.696982\pi$
$588$		0			0
$589$		−	10.1879i		−	0.419785i
$590$	1.20929	+	1.20929i	0.0497857	+	0.0497857i
$591$		0			0
$592$	−18.3997	+	18.3997i	−0.756221	+	0.756221i
$593$	25.0604			1.02911			0.514553	−	0.857459i	$-0.327958\pi$
$593$	25.0604			1.02911			0.514553	+	0.857459i	$0.327958\pi$
$594$		0			0
$595$	−3.67866	+	3.67866i	−0.150811	+	0.150811i
$596$		−	27.3400i		−	1.11989i
$597$		0			0
$598$	8.06584	−	8.06584i	0.329837	−	0.329837i
$599$	−27.5859	+	27.5859i	−1.12713	+	1.12713i	−0.136489	+	0.990642i	$0.543582\pi$
$599$	−27.5859	+	27.5859i	−1.12713	+	1.12713i	−0.990642	+	0.136489i	$0.956418\pi$
$600$		0			0
$601$	5.81843	+	5.81843i	0.237339	+	0.237339i	0.815747	−	0.578408i	$-0.196326\pi$
$601$	5.81843	+	5.81843i	0.237339	+	0.237339i	−0.578408	+	0.815747i	$0.696326\pi$
$602$	1.65544			0.0674708
$603$		0			0
$604$	16.1785			0.658295
$605$		−	9.34482i		−	0.379921i
$606$		0			0
$607$	6.17438	−	6.17438i	0.250610	−	0.250610i	−0.570610	−	0.821221i	$-0.693293\pi$
$607$	6.17438	−	6.17438i	0.250610	−	0.250610i	0.821221	+	0.570610i	$0.193293\pi$
$608$	−5.55750			−0.225386
$609$		0			0
$610$	−1.29669			−0.0525013
$611$	−27.9349	+	27.9349i	−1.13012	+	1.13012i
$612$		0			0
$613$		−	35.9742i		−	1.45298i	−0.687175	−	0.726492i	$-0.741150\pi$
$613$		−	35.9742i		−	1.45298i	0.687175	−	0.726492i	$-0.258850\pi$
$614$	5.20233			0.209949
$615$		0			0
$616$	3.03887			0.122440
$617$	−25.9848	−	25.9848i	−1.04611	−	1.04611i	−0.998884	−	0.0472240i	$-0.984963\pi$
$617$	−25.9848	−	25.9848i	−1.04611	−	1.04611i	−0.0472240	−	0.998884i	$-0.515037\pi$
$618$		0			0
$619$	−3.81348	+	3.81348i	−0.153277	+	0.153277i	−0.779580	−	0.626303i	$-0.784567\pi$
$619$	−3.81348	+	3.81348i	−0.153277	+	0.153277i	0.626303	+	0.779580i	$0.284567\pi$
$620$	−9.49793	+	9.49793i	−0.381446	+	0.381446i
$621$		0			0
$622$		−	9.60706i		−	0.385208i
$623$	0.0491751	−	0.0491751i	0.00197016	−	0.00197016i
$624$		0			0
$625$	1.00000			0.0400000
$626$	1.04379	−	1.04379i	0.0417181	−	0.0417181i
$627$		0			0
$628$	0.796264	+	0.796264i	0.0317744	+	0.0317744i
$629$			24.2072i			0.965205i
$630$		0			0
$631$			13.9362i			0.554791i	0.960756	+	0.277395i	$0.0894712\pi$
$631$			13.9362i			0.554791i	−0.960756	+	0.277395i	$0.910529\pi$
$632$		−	19.2613i		−	0.766172i
$633$		0			0
$634$	0.759969			0.0301822
$635$	−11.2368	−	11.2368i	−0.445920	−	0.445920i
$636$		0			0
$637$			28.5446i			1.13098i
$638$	0.199293	−	2.45350i	0.00789009	−	0.0971348i
$639$		0			0
$640$	6.81841	+	6.81841i	0.269521	+	0.269521i
$641$	14.2905	−	14.2905i	0.564442	−	0.564442i	−0.366124	−	0.930566i	$-0.619315\pi$
$641$	14.2905	−	14.2905i	0.564442	−	0.564442i	0.930566	+	0.366124i	$0.119315\pi$
$642$		0			0
$643$		−	41.7056i		−	1.64471i	−0.568976	−	0.822354i	$-0.692660\pi$
$643$		−	41.7056i		−	1.64471i	0.568976	−	0.822354i	$-0.307340\pi$
$644$	14.6652			0.577888
$645$		0			0
$646$	−1.08236	+	1.08236i	−0.0425850	+	0.0425850i
$647$	13.4004			0.526825			0.263413	−	0.964683i	$-0.415152\pi$
$647$	13.4004			0.526825			0.263413	+	0.964683i	$0.415152\pi$
$648$		0			0
$649$	4.37886	+	4.37886i	0.171885	+	0.171885i
$650$	−1.76865	−	1.76865i	−0.0693723	−	0.0693723i
$651$		0			0
$652$	−4.22983	−	4.22983i	−0.165653	−	0.165653i
$653$	9.60943	+	9.60943i	0.376046	+	0.376046i	0.869673	−	0.493628i	$-0.164329\pi$
$653$	9.60943	+	9.60943i	0.376046	+	0.376046i	−0.493628	+	0.869673i	$0.664329\pi$
$654$		0			0
$655$	−13.6435	−	13.6435i	−0.533096	−	0.533096i
$656$	6.61499	+	6.61499i	0.258272	+	0.258272i
$657$		0			0
$658$	3.42179			0.133395
$659$	−16.1709	+	16.1709i	−0.629927	+	0.629927i	−0.948050	−	0.318122i	$-0.896948\pi$
$659$	−16.1709	+	16.1709i	−0.629927	+	0.629927i	0.318122	+	0.948050i	$0.396948\pi$
$660$		0			0
$661$	15.0331			0.584721			0.292360	−	0.956308i	$-0.405559\pi$
$661$	15.0331			0.584721			0.292360	+	0.956308i	$0.405559\pi$
$662$			8.00611i			0.311166i
$663$		0			0
$664$	−5.39931	+	5.39931i	−0.209534	+	0.209534i
$665$	1.72467	+	1.72467i	0.0668798	+	0.0668798i
$666$		0			0
$667$	1.98831	−	24.4781i	0.0769878	−	0.947797i
$668$		−	18.2426i		−	0.705826i
$669$		0			0
$670$	−0.832418	−	0.832418i	−0.0321591	−	0.0321591i
$671$	−4.69532			−0.181261
$672$		0			0
$673$		−	44.6231i		−	1.72009i	−0.510216	−	0.860046i	$-0.670434\pi$
$673$		−	44.6231i		−	1.72009i	0.510216	−	0.860046i	$-0.329566\pi$
$674$		−	10.4656i		−	0.403119i
$675$		0			0
$676$		−	68.5047i		−	2.63480i
$677$	−27.0906	−	27.0906i	−1.04118	−	1.04118i	−0.999115	−	0.0420619i	$-0.986607\pi$
$677$	−27.0906	−	27.0906i	−1.04118	−	1.04118i	−0.0420619	−	0.999115i	$-0.513393\pi$
$678$		0			0
$679$	−2.25811	+	2.25811i	−0.0866583	+	0.0866583i
$680$	4.17221			0.159997
$681$		0			0
$682$	2.31701	−	2.31701i	0.0887230	−	0.0887230i
$683$		−	12.0492i		−	0.461050i	−0.973066	−	0.230525i	$-0.925956\pi$
$683$		−	12.0492i		−	0.461050i	0.973066	−	0.230525i	$-0.0740443\pi$
$684$		0			0
$685$	−0.0372510	+	0.0372510i	−0.00142329	+	0.00142329i
$686$	4.76638	−	4.76638i	0.181981	−	0.181981i
$687$		0			0
$688$	6.25550	+	6.25550i	0.238489	+	0.238489i
$689$	−91.9703			−3.50379
$690$		0			0
$691$	15.3361			0.583413			0.291706	−	0.956508i	$-0.405777\pi$
$691$	15.3361			0.583413			0.291706	+	0.956508i	$0.405777\pi$
$692$			3.85225i			0.146441i
$693$		0			0
$694$	3.74065	−	3.74065i	0.141993	−	0.141993i
$695$	−8.16951			−0.309887
$696$		0			0
$697$	8.70291			0.329646
$698$	−1.04566	+	1.04566i	−0.0395786	+	0.0395786i
$699$		0			0
$700$		−	3.21573i		−	0.121543i
$701$	−18.2230			−0.688275			−0.344137	−	0.938919i	$-0.611829\pi$
$701$	−18.2230			−0.688275			−0.344137	+	0.938919i	$0.611829\pi$
$702$		0			0
$703$	11.3491			0.428038
$704$	4.66474	+	4.66474i	0.175809	+	0.175809i
$705$		0			0
$706$	−3.53514	+	3.53514i	−0.133047	+	0.133047i
$707$	13.0946	−	13.0946i	0.492473	−	0.492473i
$708$		0			0
$709$		−	18.0128i		−	0.676486i	−0.941059	−	0.338243i	$-0.890167\pi$
$709$		−	18.0128i		−	0.676486i	0.941059	−	0.338243i	$-0.109833\pi$
$710$	1.38211	−	1.38211i	0.0518697	−	0.0518697i
$711$		0			0
$712$	−0.0557726			−0.00209017
$713$	23.1165	−	23.1165i	0.865718	−	0.865718i
$714$		0			0
$715$	−6.40431	−	6.40431i	−0.239508	−	0.239508i
$716$		−	0.948511i		−	0.0354475i
$717$		0			0
$718$		−	3.36167i		−	0.125456i
$719$		−	13.9256i		−	0.519337i	−0.965698	−	0.259668i	$-0.916387\pi$
$719$		−	13.9256i		−	0.519337i	0.965698	−	0.259668i	$-0.0836132\pi$
$720$		0			0
$721$	16.1520			0.601533
$722$	−4.26599	−	4.26599i	−0.158764	−	0.158764i
$723$		0			0
$724$			35.9723i			1.33690i
$725$	−5.36749	−	0.435991i	−0.199343	−	0.0161923i
$726$		0			0
$727$	−2.54046	−	2.54046i	−0.0942206	−	0.0942206i	0.658425	−	0.752646i	$-0.271223\pi$
$727$	−2.54046	−	2.54046i	−0.0942206	−	0.0942206i	−0.752646	+	0.658425i	$0.771223\pi$
$728$	−11.7582	+	11.7582i	−0.435787	+	0.435787i
$729$		0			0
$730$			2.80822i			0.103937i
$731$	8.22996			0.304396
$732$		0			0
$733$	19.1911	−	19.1911i	0.708838	−	0.708838i	−0.257453	−	0.966291i	$-0.582883\pi$
$733$	19.1911	−	19.1911i	0.708838	−	0.708838i	0.966291	+	0.257453i	$0.0828833\pi$
$734$	10.2219			0.377297
$735$		0			0
$736$	−12.6100	−	12.6100i	−0.464811	−	0.464811i
$737$	−3.01420	−	3.01420i	−0.111029	−	0.111029i
$738$		0			0
$739$	24.2130	+	24.2130i	0.890690	+	0.890690i	0.994588	−	0.103898i	$-0.0331316\pi$
$739$	24.2130	+	24.2130i	0.890690	+	0.890690i	−0.103898	+	0.994588i	$0.533132\pi$
$740$	−10.5805	−	10.5805i	−0.388945	−	0.388945i
$741$		0			0
$742$	5.63280	+	5.63280i	0.206787	+	0.206787i
$743$	18.3277	+	18.3277i	0.672379	+	0.672379i	0.958264	−	0.285885i	$-0.0922875\pi$
$743$	18.3277	+	18.3277i	0.672379	+	0.672379i	−0.285885	+	0.958264i	$0.592288\pi$
$744$		0			0
$745$	14.5910			0.534572
$746$	−6.25212	+	6.25212i	−0.228906	+	0.228906i
$747$		0			0
$748$	7.30765			0.267194
$749$		−	29.6390i		−	1.08299i
$750$		0			0
$751$	−30.0805	+	30.0805i	−1.09765	+	1.09765i	−0.102967	+	0.994685i	$0.532834\pi$
$751$	−30.0805	+	30.0805i	−1.09765	+	1.09765i	−0.994685	+	0.102967i	$0.967166\pi$
$752$	12.9301	+	12.9301i	0.471511	+	0.471511i
$753$		0			0
$754$	8.72210	+	10.2643i	0.317640	+	0.373805i
$755$			8.63424i			0.314232i
$756$		0			0
$757$	3.90395	+	3.90395i	0.141892	+	0.141892i	0.774484	−	0.632593i	$-0.218009\pi$
$757$	3.90395	+	3.90395i	0.141892	+	0.141892i	−0.632593	+	0.774484i	$0.718009\pi$
$758$	−3.87057			−0.140586
$759$		0			0
$760$		−	1.95605i		−	0.0709536i
$761$		−	26.9077i		−	0.975403i	−0.873010	−	0.487702i	$-0.837835\pi$
$761$		−	26.9077i		−	0.975403i	0.873010	−	0.487702i	$-0.162165\pi$
$762$		0			0
$763$		−	1.18818i		−	0.0430149i
$764$	−30.2065	−	30.2065i	−1.09283	−	1.09283i
$765$		0			0
$766$	−0.417786	+	0.417786i	−0.0150952	+	0.0150952i
$767$	−33.8859			−1.22355
$768$		0			0
$769$	−16.9098	+	16.9098i	−0.609783	+	0.609783i	−0.942889	−	0.333106i	$-0.891903\pi$
$769$	−16.9098	+	16.9098i	−0.609783	+	0.609783i	0.333106	+	0.942889i	$0.391903\pi$
$770$			0.784475i			0.0282705i
$771$		0			0
$772$	29.5278	−	29.5278i	1.06273	−	1.06273i
$773$	13.3531	−	13.3531i	0.480277	−	0.480277i	−0.424943	−	0.905220i	$-0.639706\pi$
$773$	13.3531	−	13.3531i	0.480277	−	0.480277i	0.905220	+	0.424943i	$0.139706\pi$
$774$		0			0
$775$	−5.06890	−	5.06890i	−0.182080	−	0.182080i
$776$	2.56106			0.0919368
$777$		0			0
$778$	−1.87193			−0.0671121
$779$		−	4.08019i		−	0.146188i
$780$		0			0
$781$	5.00464	−	5.00464i	0.179080	−	0.179080i
$782$	−4.91179			−0.175645
$783$		0			0
$784$	13.2123			0.471868
$785$	−0.424954	+	0.424954i	−0.0151673	+	0.0151673i
$786$		0			0
$787$		−	4.95273i		−	0.176546i	−0.996096	−	0.0882730i	$-0.971865\pi$
$787$		−	4.95273i		−	0.176546i	0.996096	−	0.0882730i	$-0.0281348\pi$
$788$	−39.3471			−1.40168
$789$		0			0
$790$	4.97224			0.176904
$791$	−2.35049	−	2.35049i	−0.0835738	−	0.0835738i
$792$		0			0
$793$	18.1674	−	18.1674i	0.645145	−	0.645145i
$794$	5.14734	−	5.14734i	0.182672	−	0.182672i
$795$		0			0
$796$		−	9.02101i		−	0.319741i
$797$	7.76711	−	7.76711i	0.275125	−	0.275125i	−0.556034	−	0.831159i	$-0.687678\pi$
$797$	7.76711	−	7.76711i	0.275125	−	0.275125i	0.831159	+	0.556034i	$0.187678\pi$
$798$		0			0
$799$	17.0113			0.601815
$800$	−2.76508	+	2.76508i	−0.0977605	+	0.0977605i
$801$		0			0
$802$	7.58293	+	7.58293i	0.267763	+	0.267763i
$803$			10.1686i			0.358843i
$804$		0			0
$805$			7.82658i			0.275851i
$806$			17.9303i			0.631566i
$807$		0			0
$808$	−14.8514			−0.522470
$809$	−27.7876	−	27.7876i	−0.976961	−	0.976961i	0.0227798	−	0.999741i	$-0.492748\pi$
$809$	−27.7876	−	27.7876i	−0.976961	−	0.976961i	−0.999741	+	0.0227798i	$0.992748\pi$
$810$		0			0
$811$			35.7322i			1.25473i	0.778727	+	0.627363i	$0.215866\pi$
$811$			35.7322i			1.25473i	−0.778727	+	0.627363i	$0.784134\pi$
$812$	−1.40203	+	17.2604i	−0.0492016	+	0.605721i
$813$		0			0
$814$	2.58109	+	2.58109i	0.0904673	+	0.0904673i
$815$	2.25740	−	2.25740i	0.0790731	−	0.0790731i
$816$		0			0
$817$		−	3.85845i		−	0.134990i
$818$	3.81592			0.133421
$819$		0			0
$820$	−3.80386	+	3.80386i	−0.132836	+	0.132836i
$821$	−36.8720			−1.28684			−0.643421	−	0.765513i	$-0.722485\pi$
$821$	−36.8720			−1.28684			−0.643421	+	0.765513i	$0.722485\pi$
$822$		0			0
$823$	−19.0901	−	19.0901i	−0.665440	−	0.665440i	0.291217	−	0.956657i	$-0.405940\pi$
$823$	−19.0901	−	19.0901i	−0.665440	−	0.665440i	−0.956657	+	0.291217i	$0.905940\pi$
$824$	−9.15951	−	9.15951i	−0.319087	−	0.319087i
$825$		0			0
$826$	2.07537	+	2.07537i	0.0722114	+	0.0722114i
$827$	−24.6938	−	24.6938i	−0.858688	−	0.858688i	0.132496	−	0.991184i	$-0.457701\pi$
$827$	−24.6938	−	24.6938i	−0.858688	−	0.858688i	−0.991184	+	0.132496i	$0.957701\pi$
$828$		0			0
$829$	3.70573	+	3.70573i	0.128705	+	0.128705i	0.768525	−	0.639820i	$-0.220991\pi$
$829$	3.70573	+	3.70573i	0.128705	+	0.128705i	−0.639820	+	0.768525i	$0.720991\pi$
$830$	−1.39381	−	1.39381i	−0.0483800	−	0.0483800i
$831$		0			0
$832$	−36.0982			−1.25148
$833$	8.69129	−	8.69129i	0.301135	−	0.301135i
$834$		0			0
$835$	9.73578			0.336921
$836$		−	3.42604i		−	0.118492i
$837$		0			0
$838$	4.52646	−	4.52646i	0.156364	−	0.156364i
$839$	38.6084	+	38.6084i	1.33291	+	1.33291i	0.902757	+	0.430152i	$0.141540\pi$
$839$	38.6084	+	38.6084i	1.33291	+	1.33291i	0.430152	+	0.902757i	$0.358460\pi$
$840$		0			0
$841$	28.6198	+	4.68035i	0.986890	+	0.161392i
$842$			10.8339i			0.373360i
$843$		0			0
$844$	−33.0676	−	33.0676i	−1.13823	−	1.13823i
$845$	36.5599			1.25770
$846$		0			0
$847$		−	16.0375i		−	0.551054i
$848$			42.5699i			1.46186i
$849$		0			0
$850$			1.07704i			0.0369422i
$851$	25.7512	+	25.7512i	0.882738	+	0.882738i
$852$		0			0
$853$	−18.6713	+	18.6713i	−0.639292	+	0.639292i	−0.950381	−	0.311089i	$-0.899306\pi$
$853$	−18.6713	+	18.6713i	−0.639292	+	0.639292i	0.311089	+	0.950381i	$0.399306\pi$
$854$	−2.22536			−0.0761502
$855$		0			0
$856$	−16.8077	+	16.8077i	−0.574476	+	0.574476i
$857$			18.2164i			0.622259i	0.950368	+	0.311129i	$0.100707\pi$
$857$			18.2164i			0.622259i	−0.950368	+	0.311129i	$0.899293\pi$
$858$		0			0
$859$	−9.34433	+	9.34433i	−0.318825	+	0.318825i	−0.848316	−	0.529491i	$-0.822383\pi$
$859$	−9.34433	+	9.34433i	−0.318825	+	0.318825i	0.529491	+	0.848316i	$0.322383\pi$
$860$	−3.59714	+	3.59714i	−0.122661	+	0.122661i
$861$		0			0
$862$	−9.97330	−	9.97330i	−0.339692	−	0.339692i
$863$	53.4622			1.81987			0.909937	−	0.414745i	$-0.136129\pi$
$863$	53.4622			1.81987			0.909937	+	0.414745i	$0.136129\pi$
$864$		0			0
$865$	−2.05589			−0.0699023
$866$			2.06386i			0.0701329i
$867$		0			0
$868$	−16.3002	+	16.3002i	−0.553266	+	0.553266i
$869$	18.0045			0.610762
$870$		0			0
$871$	23.3254			0.790352
$872$	−0.673794	+	0.673794i	−0.0228175	+	0.0228175i
$873$		0			0
$874$			2.30279i			0.0778932i
$875$	1.71619			0.0580177
$876$		0			0
$877$	−33.6537			−1.13640			−0.568202	−	0.822889i	$-0.692361\pi$
$877$	−33.6537			−1.13640			−0.568202	+	0.822889i	$0.692361\pi$
$878$	−0.894873	−	0.894873i	−0.0302005	−	0.0302005i
$879$		0			0
$880$	−2.96434	+	2.96434i	−0.0999277	+	0.0999277i
$881$	−28.8814	+	28.8814i	−0.973041	+	0.973041i	−0.999646	−	0.0266053i	$-0.991530\pi$
$881$	−28.8814	+	28.8814i	−0.973041	+	0.973041i	0.0266053	+	0.999646i	$0.491530\pi$
$882$		0			0
$883$			8.99954i			0.302859i	0.988468	+	0.151429i	$0.0483876\pi$
$883$			8.99954i			0.302859i	−0.988468	+	0.151429i	$0.951612\pi$
$884$	−28.2752	+	28.2752i	−0.950998	+	0.950998i
$885$		0			0
$886$	2.85068			0.0957703
$887$	27.9050	−	27.9050i	0.936957	−	0.936957i	−0.0611708	−	0.998127i	$-0.519483\pi$
$887$	27.9050	−	27.9050i	0.936957	−	0.936957i	0.998127	+	0.0611708i	$0.0194834\pi$
$888$		0			0
$889$	−19.2845	−	19.2845i	−0.646782	−	0.646782i
$890$		−	0.0143975i		−	0.000482606i
$891$		0			0
$892$			3.84499i			0.128740i
$893$		−	7.97539i		−	0.266886i
$894$		0			0
$895$	0.506207			0.0169206
$896$	11.7017	+	11.7017i	0.390925	+	0.390925i
$897$		0			0
$898$		−	7.68817i		−	0.256558i
$899$	24.9973	+	29.4173i	0.833706	+	0.981121i
$900$		0			0
$901$	28.0032	+	28.0032i	0.932922	+	0.932922i
$902$	0.927948	−	0.927948i	0.0308973	−	0.0308973i
$903$		0			0
$904$			2.66584i			0.0886644i
$905$	−19.1979			−0.638159
$906$		0			0
$907$	−12.3263	+	12.3263i	−0.409287	+	0.409287i	−0.881490	−	0.472203i	$-0.843459\pi$
$907$	−12.3263	+	12.3263i	−0.409287	+	0.409287i	0.472203	+	0.881490i	$0.343459\pi$
$908$	38.8935			1.29072
$909$		0			0
$910$	−3.03534	−	3.03534i	−0.100621	−	0.100621i
$911$	−3.22864	−	3.22864i	−0.106970	−	0.106970i	0.651596	−	0.758566i	$-0.274100\pi$
$911$	−3.22864	−	3.22864i	−0.106970	−	0.106970i	−0.758566	+	0.651596i	$0.774100\pi$
$912$		0			0
$913$	−5.04702	−	5.04702i	−0.167032	−	0.167032i
$914$	1.80988	+	1.80988i	0.0598657	+	0.0598657i
$915$		0			0
$916$	−22.6168	−	22.6168i	−0.747281	−	0.747281i
$917$	−23.4148	−	23.4148i	−0.773226	−	0.773226i
$918$		0			0
$919$	−9.19875			−0.303439			−0.151719	−	0.988424i	$-0.548481\pi$
$919$	−9.19875			−0.303439			−0.151719	+	0.988424i	$0.548481\pi$
$920$	4.43831	−	4.43831i	0.146327	−	0.146327i
$921$		0			0
$922$	−13.4560			−0.443149
$923$			38.7286i			1.27477i
$924$		0			0
$925$	5.64663	−	5.64663i	0.185660	−	0.185660i
$926$	−1.65504	−	1.65504i	−0.0543879	−	0.0543879i
$927$		0			0
$928$	16.0471	−	13.6360i	0.526772	−	0.447624i
$929$			16.9275i			0.555373i	0.960672	+	0.277687i	$0.0895677\pi$
$929$			16.9275i			0.555373i	−0.960672	+	0.277687i	$0.910432\pi$
$930$		0			0
$931$	−4.07474	−	4.07474i	−0.133544	−	0.133544i
$932$	−16.3316			−0.534959
$933$		0			0
$934$			13.2840i			0.434665i
$935$			3.89998i			0.127543i
$936$		0			0
$937$		−	3.96008i		−	0.129370i	−0.997906	−	0.0646850i	$-0.979396\pi$
$937$		−	3.96008i		−	0.129370i	0.997906	−	0.0646850i	$-0.0206043\pi$
$938$	−1.42859	−	1.42859i	−0.0466450	−	0.0466450i
$939$		0			0
$940$	−7.43526	+	7.43526i	−0.242511	+	0.242511i
$941$	16.8068			0.547885			0.273942	−	0.961746i	$-0.411672\pi$
$941$	16.8068			0.547885			0.273942	+	0.961746i	$0.411672\pi$
$942$		0			0
$943$	9.25798	−	9.25798i	0.301481	−	0.301481i
$944$			15.6846i			0.510491i
$945$		0			0
$946$	0.877519	−	0.877519i	0.0285306	−	0.0285306i
$947$	39.1526	−	39.1526i	1.27229	−	1.27229i	0.327405	−	0.944884i	$-0.393826\pi$
$947$	39.1526	−	39.1526i	1.27229	−	1.27229i	0.944884	−	0.327405i	$-0.106174\pi$
$948$		0			0
$949$	−39.3450	−	39.3450i	−1.27719	−	1.27719i
$950$	0.504949			0.0163827
$951$		0			0
$952$	7.16029			0.232066
$953$		−	41.8117i		−	1.35441i	−0.735793	−	0.677206i	$-0.763190\pi$
$953$		−	41.8117i		−	1.35441i	0.735793	−	0.677206i	$-0.236810\pi$
$954$		0			0
$955$	16.1208	−	16.1208i	0.521656	−	0.521656i
$956$	−15.2205			−0.492265
$957$		0			0
$958$	−3.62822			−0.117223
$959$	−0.0639297	+	0.0639297i	−0.00206440	+	0.00206440i
$960$		0			0
$961$			20.3875i			0.657663i
$962$	−19.9739			−0.643983
$963$		0			0
$964$	34.1831			1.10096
$965$	15.7585	+	15.7585i	0.507285	+	0.507285i
$966$		0			0
$967$	−16.5339	+	16.5339i	−0.531694	+	0.531694i	−0.921076	−	0.389382i	$-0.872689\pi$
$967$	−16.5339	+	16.5339i	−0.531694	+	0.531694i	0.389382	+	0.921076i	$0.372689\pi$
$968$	−9.09455	+	9.09455i	−0.292310	+	0.292310i
$969$		0			0
$970$			0.661131i			0.0212276i
$971$	−20.2384	+	20.2384i	−0.649480	+	0.649480i	−0.952867	−	0.303387i	$-0.901882\pi$
$971$	−20.2384	+	20.2384i	−0.649480	+	0.649480i	0.303387	+	0.952867i	$0.401882\pi$
$972$		0			0
$973$	−14.0204			−0.449474
$974$	5.36232	−	5.36232i	0.171820	−	0.171820i
$975$		0			0
$976$	−8.40908	−	8.40908i	−0.269168	−	0.269168i
$977$			5.07782i			0.162454i	0.996696	+	0.0812269i	$0.0258838\pi$
$977$			5.07782i			0.162454i	−0.996696	+	0.0812269i	$0.974116\pi$
$978$		0			0
$979$		−	0.0521336i		−	0.00166620i
$980$			7.59755i			0.242695i
$981$		0			0
$982$	−7.22353			−0.230512
$983$	2.49804	+	2.49804i	0.0796751	+	0.0796751i	0.745821	−	0.666146i	$-0.232057\pi$
$983$	2.49804	+	2.49804i	0.0796751	+	0.0796751i	−0.666146	+	0.745821i	$0.732057\pi$
$984$		0			0
$985$		−	20.9990i		−	0.669083i
$986$	0.469581	−	5.78101i	0.0149545	−	0.184105i
$987$		0			0
$988$	13.2563	+	13.2563i	0.421738	+	0.421738i
$989$	8.75486	−	8.75486i	0.278388	−	0.278388i
$990$		0			0
$991$			2.70838i			0.0860345i	0.999074	+	0.0430173i	$0.0136970\pi$
$991$			2.70838i			0.0860345i	−0.999074	+	0.0430173i	$0.986303\pi$
$992$	28.0319			0.890013
$993$		0			0
$994$	2.37196	−	2.37196i	0.0752341	−	0.0752341i
$995$	4.81438			0.152626
$996$		0			0
$997$	−19.8721	−	19.8721i	−0.629356	−	0.629356i	0.318550	−	0.947906i	$-0.396804\pi$
$997$	−19.8721	−	19.8721i	−0.629356	−	0.629356i	−0.947906	+	0.318550i	$0.896804\pi$
$998$	−9.70344	−	9.70344i	−0.307157	−	0.307157i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.r.c.476.10	✓	32
3.2	odd	2		1305.2.r.d.476.7	yes	32
29.17	odd	4		1305.2.r.d.1061.7	yes	32
87.17	even	4	inner	1305.2.r.c.1061.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.r.c.476.10	✓	32	1.1	even	1	trivial
1305.2.r.c.1061.10	yes	32	87.17	even	4	inner
1305.2.r.d.476.7	yes	32	3.2	odd	2
1305.2.r.d.1061.7	yes	32	29.17	odd	4

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:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.251233 - 0.251233i) q^{2} +1.87376i q^{4} -1.00000 q^{5} -1.71619 q^{7} +(0.973218 + 0.973218i) q^{8} +(-0.251233 + 0.251233i) q^{10} +(-0.909719 + 0.909719i) q^{11} -7.03988i q^{13} +(-0.431163 + 0.431163i) q^{14} -3.25852 q^{16} +(-2.14351 + 2.14351i) q^{17} +(1.00494 + 1.00494i) q^{19} -1.87376i q^{20} +0.457103i q^{22} +4.56045i q^{23} +1.00000 q^{25} +(-1.76865 - 1.76865i) q^{26} -3.21573i q^{28} +(-5.36749 - 0.435991i) q^{29} +(-5.06890 - 5.06890i) q^{31} +(-2.76508 + 2.76508i) q^{32} +1.07704i q^{34} +1.71619 q^{35} +(5.64663 - 5.64663i) q^{37} +0.504949 q^{38} +(-0.973218 - 0.973218i) q^{40} +(-2.03006 - 2.03006i) q^{41} +(-1.91974 - 1.91974i) q^{43} +(-1.70460 - 1.70460i) q^{44} +(1.14574 + 1.14574i) q^{46} +(-3.96809 - 3.96809i) q^{47} -4.05470 q^{49} +(0.251233 - 0.251233i) q^{50} +13.1911 q^{52} -13.0642i q^{53} +(0.909719 - 0.909719i) q^{55} +(-1.67022 - 1.67022i) q^{56} +(-1.45803 + 1.23896i) q^{58} -4.81342i q^{59} +(2.58064 + 2.58064i) q^{61} -2.54695 q^{62} -5.12767i q^{64} +7.03988i q^{65} +3.31333i q^{67} +(-4.01643 - 4.01643i) q^{68} +(0.431163 - 0.431163i) q^{70} -5.50131 q^{71} +(5.58888 - 5.58888i) q^{73} -2.83724i q^{74} +(-1.88302 + 1.88302i) q^{76} +(1.56125 - 1.56125i) q^{77} +(-9.89566 - 9.89566i) q^{79} +3.25852 q^{80} -1.02004 q^{82} +5.54789i q^{83} +(2.14351 - 2.14351i) q^{85} -0.964604 q^{86} -1.77071 q^{88} +(-0.0286537 + 0.0286537i) q^{89} +12.0818i q^{91} -8.54520 q^{92} -1.99383 q^{94} +(-1.00494 - 1.00494i) q^{95} +(1.31577 - 1.31577i) q^{97} +(-1.01868 + 1.01868i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{5} + 8 q^{7} + 8 q^{11} - 24 q^{14} - 32 q^{16} + 16 q^{19} + 32 q^{25} - 8 q^{26} - 8 q^{29} - 8 q^{31} + 40 q^{32} - 8 q^{35} + 24 q^{37} - 24 q^{38} - 24 q^{41} + 16 q^{43} - 48 q^{44} - 64 q^{46}+ \cdots + 80 q^{98}+O(q^{100}) \) 32 * q - 32 * q^5 + 8 * q^7 + 8 * q^11 - 24 * q^14 - 32 * q^16 + 16 * q^19 + 32 * q^25 - 8 * q^26 - 8 * q^29 - 8 * q^31 + 40 * q^32 - 8 * q^35 + 24 * q^37 - 24 * q^38 - 24 * q^41 + 16 * q^43 - 48 * q^44 - 64 * q^46 - 8 * q^47 + 48 * q^49 + 40 * q^52 - 8 * q^55 + 104 * q^56 + 16 * q^58 + 16 * q^61 - 8 * q^62 + 56 * q^68 + 24 * q^70 - 48 * q^71 + 16 * q^73 - 48 * q^76 + 56 * q^77 + 32 * q^80 - 80 * q^82 - 112 * q^86 + 8 * q^88 - 32 * q^89 - 24 * q^92 - 104 * q^94 - 16 * q^95 - 72 * q^97 + 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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