LMFDB - Embedded newform 735.2.p.g.509.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(374,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("735.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.3
Character	$\chi$	$=$	735.509
Dual form			735.2.p.g.374.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10453 + 1.91310i) q^{2} +(0.216070 + 1.71852i) q^{3} +(-1.43998 - 2.49412i) q^{4} +(-0.889228 - 2.05165i) q^{5} +(-3.52637 - 1.48480i) q^{6} +1.94389 q^{8} +(-2.90663 + 0.742640i) q^{9} +(4.90720 + 0.564929i) q^{10} +(3.30554 - 1.90846i) q^{11} +(3.97506 - 3.01354i) q^{12} +6.50161 q^{13} +(3.33367 - 1.97146i) q^{15} +(0.732874 - 1.26937i) q^{16} +(2.54654 - 1.47025i) q^{17} +(1.78971 - 6.38095i) q^{18} +(-1.76224 - 1.01743i) q^{19} +(-3.83659 + 5.17218i) q^{20} +8.43180i q^{22} +(-1.50029 + 2.59858i) q^{23} +(0.420016 + 3.34061i) q^{24} +(-3.41855 + 3.64877i) q^{25} +(-7.18123 + 12.4383i) q^{26} +(-1.90428 - 4.83464i) q^{27} +2.25259i q^{29} +(0.0894567 + 8.55520i) q^{30} +(5.77216 - 3.33256i) q^{31} +(3.56285 + 6.17104i) q^{32} +(3.99395 + 5.26828i) q^{33} +6.49574i q^{34} +(6.03772 + 6.18009i) q^{36} +(-2.91560 - 1.68332i) q^{37} +(3.89289 - 2.24756i) q^{38} +(1.40480 + 11.1732i) q^{39} +(-1.72856 - 3.98818i) q^{40} +3.51094 q^{41} -7.03729i q^{43} +(-9.51983 - 5.49628i) q^{44} +(4.10829 + 5.30301i) q^{45} +(-3.31424 - 5.74043i) q^{46} +(4.34120 + 2.50639i) q^{47} +(2.33980 + 0.985185i) q^{48} +(-3.20459 - 10.5702i) q^{50} +(3.07688 + 4.05861i) q^{51} +(-9.36219 - 16.2158i) q^{52} +(-0.967113 - 1.67509i) q^{53} +(11.3525 + 1.69693i) q^{54} +(-6.85487 - 5.08477i) q^{55} +(1.36770 - 3.24827i) q^{57} +(-4.30944 - 2.48806i) q^{58} +(3.96509 + 6.86774i) q^{59} +(-9.71747 - 5.47572i) q^{60} +(11.8342 + 6.83249i) q^{61} +14.7237i q^{62} -12.8096 q^{64} +(-5.78141 - 13.3390i) q^{65} +(-14.4902 + 1.82186i) q^{66} +(-9.34121 + 5.39315i) q^{67} +(-7.33395 - 4.23426i) q^{68} +(-4.78988 - 2.01681i) q^{69} +10.9926i q^{71} +(-5.65016 + 1.44361i) q^{72} +(-1.65449 - 2.86566i) q^{73} +(6.44074 - 3.71856i) q^{74} +(-7.00913 - 5.08646i) q^{75} +5.86030i q^{76} +(-22.9271 - 9.65357i) q^{78} +(2.92489 - 5.06605i) q^{79} +(-3.25601 - 0.374839i) q^{80} +(7.89697 - 4.31716i) q^{81} +(-3.87795 + 6.71680i) q^{82} -2.66330i q^{83} +(-5.28089 - 3.91724i) q^{85} +(13.4631 + 7.77291i) q^{86} +(-3.87112 + 0.486717i) q^{87} +(6.42561 - 3.70983i) q^{88} +(6.75793 - 11.7051i) q^{89} +(-14.6830 + 2.00225i) q^{90} +8.64156 q^{92} +(6.97425 + 9.19951i) q^{93} +(-9.58999 + 5.53678i) q^{94} +(-0.520378 + 4.52022i) q^{95} +(-9.83524 + 7.45621i) q^{96} +4.46688 q^{97} +(-8.19069 + 8.00200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) $ 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.10453	+	1.91310i	−0.781022	+	1.35277i	0.150325	+	0.988637i	$0.451968\pi$
$2$	−1.10453	+	1.91310i	−0.781022	+	1.35277i	−0.931347	+	0.364133i	$0.881365\pi$
$3$	0.216070	+	1.71852i	0.124748	+	0.992188i
$3$	0.216070	+	1.71852i	0.124748	+	0.992188i
$4$	−1.43998	−	2.49412i	−0.719990	−	1.24706i
$5$	−0.889228	−	2.05165i	−0.397675	−	0.917526i
$5$	−0.889228	−	2.05165i	−0.397675	−	0.917526i
$6$	−3.52637	−	1.48480i	−1.43963	−	0.606166i
$7$		0			0
$7$		0			0
$8$	1.94389			0.687269
$9$	−2.90663	+	0.742640i	−0.968876	+	0.247547i
$10$	4.90720	+	0.564929i	1.55179	+	0.178646i
$11$	3.30554	−	1.90846i	0.996659	−	0.575421i	0.0894006	−	0.995996i	$-0.471505\pi$
$11$	3.30554	−	1.90846i	0.996659	−	0.575421i	0.907258	+	0.420575i	$0.138172\pi$
$12$	3.97506	−	3.01354i	1.14750	−	0.869934i
$13$	6.50161			1.80322			0.901611	−	0.432548i	$-0.142385\pi$
$13$	6.50161			1.80322			0.901611	+	0.432548i	$0.142385\pi$
$14$		0			0
$15$	3.33367	−	1.97146i	0.860750	−	0.509028i
$16$	0.732874	−	1.26937i	0.183218	−	0.317344i
$17$	2.54654	−	1.47025i	0.617628	−	0.356587i	−0.158317	−	0.987388i	$-0.550607\pi$
$17$	2.54654	−	1.47025i	0.617628	−	0.356587i	0.775945	+	0.630801i	$0.217274\pi$
$18$	1.78971	−	6.38095i	0.421839	−	1.50401i
$19$	−1.76224	−	1.01743i	−0.404285	−	0.233414i	0.284046	−	0.958811i	$-0.408323\pi$
$19$	−1.76224	−	1.01743i	−0.404285	−	0.233414i	−0.688331	+	0.725397i	$0.741656\pi$
$20$	−3.83659	+	5.17218i	−0.857888	+	1.15653i
$21$		0			0
$22$			8.43180i			1.79767i
$23$	−1.50029	+	2.59858i	−0.312832	+	0.541842i	−0.978974	−	0.203983i	$-0.934611\pi$
$23$	−1.50029	+	2.59858i	−0.312832	+	0.541842i	0.666142	+	0.745825i	$0.267944\pi$
$24$	0.420016	+	3.34061i	0.0857353	+	0.681900i
$25$	−3.41855	+	3.64877i	−0.683710	+	0.729754i
$26$	−7.18123	+	12.4383i	−1.40836	+	2.43934i
$27$	−1.90428	−	4.83464i	−0.366478	−	0.930427i
$28$		0			0
$29$			2.25259i			0.418296i	0.977884	+	0.209148i	$0.0670690\pi$
$29$			2.25259i			0.418296i	−0.977884	+	0.209148i	$0.932931\pi$
$30$	0.0894567	+	8.55520i	0.0163325	+	1.56196i
$31$	5.77216	−	3.33256i	1.03671	−	0.598545i	0.117810	−	0.993036i	$-0.462413\pi$
$31$	5.77216	−	3.33256i	1.03671	−	0.598545i	0.918900	+	0.394491i	$0.129079\pi$
$32$	3.56285	+	6.17104i	0.629829	+	1.09090i
$33$	3.99395	+	5.26828i	0.695257	+	0.917091i
$34$			6.49574i			1.11401i
$35$		0			0
$36$	6.03772	+	6.18009i	1.00629	+	1.03001i
$37$	−2.91560	−	1.68332i	−0.479321	−	0.276736i	0.240812	−	0.970572i	$-0.422586\pi$
$37$	−2.91560	−	1.68332i	−0.479321	−	0.276736i	−0.720134	+	0.693835i	$0.755919\pi$
$38$	3.89289	−	2.24756i	0.631510	−	0.364603i
$39$	1.40480	+	11.1732i	0.224948	+	1.78914i
$40$	−1.72856	−	3.98818i	−0.273309	−	0.630587i
$41$	3.51094			0.548317			0.274158	−	0.961685i	$-0.411601\pi$
$41$	3.51094			0.548317			0.274158	+	0.961685i	$0.411601\pi$
$42$		0			0
$43$		−	7.03729i		−	1.07318i	−0.843844	−	0.536588i	$-0.819713\pi$
$43$		−	7.03729i		−	1.07318i	0.843844	−	0.536588i	$-0.180287\pi$
$44$	−9.51983	−	5.49628i	−1.43517	−	0.828595i
$45$	4.10829	+	5.30301i	0.612428	+	0.790526i
$46$	−3.31424	−	5.74043i	−0.488658	−	0.846380i
$47$	4.34120	+	2.50639i	0.633229	+	0.365595i	0.782002	−	0.623276i	$-0.214199\pi$
$47$	4.34120	+	2.50639i	0.633229	+	0.365595i	−0.148772	+	0.988871i	$0.547532\pi$
$48$	2.33980	+	0.985185i	0.337721	+	0.142199i
$49$		0			0
$50$	−3.20459	−	10.5702i	−0.453197	−	1.49486i
$51$	3.07688	+	4.05861i	0.430850	+	0.568319i
$52$	−9.36219	−	16.2158i	−1.29830	−	2.24873i
$53$	−0.967113	−	1.67509i	−0.132843	−	0.230091i	0.791928	−	0.610614i	$-0.209077\pi$
$53$	−0.967113	−	1.67509i	−0.132843	−	0.230091i	−0.924771	+	0.380523i	$0.875744\pi$
$54$	11.3525	+	1.69693i	1.54488	+	0.230923i
$55$	−6.85487	−	5.08477i	−0.924310	−	0.685630i
$56$		0			0
$57$	1.36770	−	3.24827i	0.181157	−	0.430244i
$58$	−4.30944	−	2.48806i	−0.565858	−	0.326698i
$59$	3.96509	+	6.86774i	0.516211	+	0.894104i	0.999823	+	0.0188214i	$0.00599139\pi$
$59$	3.96509	+	6.86774i	0.516211	+	0.894104i	−0.483612	+	0.875283i	$0.660675\pi$
$60$	−9.71747	−	5.47572i	−1.25452	−	0.706912i
$61$	11.8342	+	6.83249i	1.51522	+	0.874810i	0.999841	+	0.0178455i	$0.00568070\pi$
$61$	11.8342	+	6.83249i	1.51522	+	0.874810i	0.515375	+	0.856965i	$0.327653\pi$
$62$			14.7237i			1.86991i
$63$		0			0
$64$	−12.8096			−1.60121
$65$	−5.78141	−	13.3390i	−0.717096	−	1.65450i
$66$	−14.4902	+	1.82186i	−1.78362	+	0.224255i
$67$	−9.34121	+	5.39315i	−1.14121	+	0.658878i	−0.946730	−	0.322029i	$-0.895635\pi$
$67$	−9.34121	+	5.39315i	−1.14121	+	0.658878i	−0.194480	+	0.980906i	$0.562302\pi$
$68$	−7.33395	−	4.23426i	−0.889372	−	0.513479i
$69$	−4.78988	−	2.01681i	−0.576634	−	0.242795i
$70$		0			0
$71$			10.9926i			1.30458i	0.757971	+	0.652288i	$0.226191\pi$
$71$			10.9926i			1.30458i	−0.757971	+	0.652288i	$0.773809\pi$
$72$	−5.65016	+	1.44361i	−0.665878	+	0.170131i
$73$	−1.65449	−	2.86566i	−0.193643	−	0.335400i	0.752812	−	0.658236i	$-0.228697\pi$
$73$	−1.65449	−	2.86566i	−0.193643	−	0.335400i	−0.946455	+	0.322836i	$0.895364\pi$
$74$	6.44074	−	3.71856i	0.748721	−	0.432274i
$75$	−7.00913	−	5.08646i	−0.809345	−	0.587334i
$76$			5.86030i			0.672223i
$77$		0			0
$78$	−22.9271	−	9.65357i	−2.59598	−	1.09305i
$79$	2.92489	−	5.06605i	0.329075	−	0.569975i	−0.653253	−	0.757140i	$-0.726596\pi$
$79$	2.92489	−	5.06605i	0.329075	−	0.569975i	0.982329	+	0.187164i	$0.0599296\pi$
$80$	−3.25601	−	0.374839i	−0.364032	−	0.0419082i
$81$	7.89697	−	4.31716i	0.877441	−	0.479684i
$82$	−3.87795	+	6.71680i	−0.428248	+	0.741746i
$83$		−	2.66330i		−	0.292336i	−0.989260	−	0.146168i	$-0.953306\pi$
$83$		−	2.66330i		−	0.292336i	0.989260	−	0.146168i	$-0.0466939\pi$
$84$		0			0
$85$	−5.28089	−	3.91724i	−0.572793	−	0.424884i
$86$	13.4631	+	7.77291i	1.45176	+	0.838175i
$87$	−3.87112	+	0.486717i	−0.415028	+	0.0521815i
$88$	6.42561	−	3.70983i	0.684972	−	0.395469i
$89$	6.75793	−	11.7051i	0.716339	−	1.24074i	−0.246101	−	0.969244i	$-0.579150\pi$
$89$	6.75793	−	11.7051i	0.716339	−	1.24074i	0.962441	−	0.271492i	$-0.0875170\pi$
$90$	−14.6830	+	2.00225i	−1.54772	+	0.211056i
$91$		0			0
$92$	8.64156			0.900945
$93$	6.97425	+	9.19951i	0.723196	+	0.953944i
$94$	−9.58999	+	5.53678i	−0.989132	+	0.571075i
$95$	−0.520378	+	4.52022i	−0.0533896	+	0.463765i
$96$	−9.83524	+	7.45621i	−1.00381	+	0.760997i
$97$	4.46688			0.453543			0.226771	−	0.973948i	$-0.427183\pi$
$97$	4.46688			0.453543			0.226771	+	0.973948i	$0.427183\pi$
$98$		0			0
$99$	−8.19069	+	8.00200i	−0.823195	+	0.804231i
$100$	14.0231	+	3.27211i	1.40231	+	0.327211i
$101$	−4.43523	−	7.68205i	−0.441322	−	0.764392i	0.556466	−	0.830871i	$-0.312157\pi$
$101$	−4.43523	−	7.68205i	−0.441322	−	0.764392i	−0.997788	+	0.0664781i	$0.978824\pi$
$102$	−11.1631	+	1.40353i	−1.10531	+	0.138970i
$103$	−0.661216	+	1.14526i	−0.0651516	+	0.112846i	−0.896761	−	0.442515i	$-0.854086\pi$
$103$	−0.661216	+	1.14526i	−0.0651516	+	0.112846i	0.831610	+	0.555361i	$0.187420\pi$
$104$	12.6384			1.23930
$105$		0			0
$106$	4.27283			0.415014
$107$	1.66222	−	2.87905i	0.160693	−	0.278328i	−0.774425	−	0.632666i	$-0.781960\pi$
$107$	1.66222	−	2.87905i	0.160693	−	0.278328i	0.935117	+	0.354338i	$0.115294\pi$
$108$	−9.31604	+	11.7113i	−0.896437	+	1.12692i
$109$	−6.14927	−	10.6509i	−0.588994	−	1.02017i	−0.994365	−	0.106015i	$-0.966191\pi$
$109$	−6.14927	−	10.6509i	−0.588994	−	1.02017i	0.405371	−	0.914152i	$-0.367142\pi$
$110$	17.2991	−	7.49779i	1.64941	−	0.714886i
$111$	2.26285	−	5.37423i	0.214780	−	0.510099i
$112$		0			0
$113$	20.4591			1.92463			0.962314	−	0.271941i	$-0.0876657\pi$
$113$	20.4591			1.92463			0.962314	+	0.271941i	$0.0876657\pi$
$114$	4.70362	+	6.20438i	0.440534	+	0.581094i
$115$	6.66548	+	0.767346i	0.621560	+	0.0715553i
$116$	5.61823	−	3.24369i	0.521640	−	0.301169i
$117$	−18.8978	+	4.82836i	−1.74710	+	0.446382i
$118$	−17.5183			−1.61269
$119$		0			0
$120$	6.48029	−	3.83229i	0.591567	−	0.349839i
$121$	1.78441	−	3.09068i	0.162219	−	0.280971i
$122$	−26.1425	+	15.0934i	−2.36683	+	1.36649i
$123$	0.758608	+	6.03363i	0.0684014	+	0.544034i
$124$	−16.6236	−	9.59763i	−1.49284	−	0.861893i
$125$	10.5259	+	3.76908i	0.941463	+	0.337117i
$126$		0			0
$127$		−	0.597329i		−	0.0530044i	−0.999649	−	0.0265022i	$-0.991563\pi$
$127$		−	0.597329i		−	0.0530044i	0.999649	−	0.0265022i	$-0.00843689\pi$
$128$	7.02295	−	12.1641i	0.620747	−	1.07517i
$129$	12.0937	−	1.52055i	1.06479	−	0.133877i
$130$	31.9047	+	3.67294i	2.79823	+	0.322139i
$131$	−2.90591	+	5.03319i	−0.253891	+	0.439752i	−0.964594	−	0.263741i	$-0.915044\pi$
$131$	−2.90591	+	5.03319i	−0.253891	+	0.439752i	0.710703	+	0.703492i	$0.248377\pi$
$132$	7.38852	−	17.5476i	0.643088	−	1.52732i
$133$		0			0
$134$		−	23.8276i		−	2.05839i
$135$	−8.22566	+	8.20601i	−0.707952	+	0.706261i
$136$	4.95020	−	2.85800i	0.424476	−	0.245071i
$137$	0.546844	+	0.947161i	0.0467200	+	0.0809215i	0.888440	−	0.458993i	$-0.151790\pi$
$137$	0.546844	+	0.947161i	0.0467200	+	0.0809215i	−0.841720	+	0.539915i	$0.818456\pi$
$138$	9.14894	−	6.93592i	0.778810	−	0.590425i
$139$			7.35968i			0.624240i	0.950043	+	0.312120i	$0.101039\pi$
$139$			7.35968i			0.624240i	−0.950043	+	0.312120i	$0.898961\pi$
$140$		0			0
$141$	−3.36929	+	8.00200i	−0.283745	+	0.673890i
$142$	−21.0299	−	12.1416i	−1.76479	−	1.01890i
$143$	21.4913	−	12.4080i	1.79720	−	1.03761i
$144$	−1.18750	+	4.23386i	−0.0989585	+	0.352822i
$145$	4.62153	−	2.00307i	0.383797	−	0.166346i
$146$	7.30973			0.604958
$147$		0			0
$148$			9.69579i			0.796989i
$149$	9.36993	+	5.40973i	0.767615	+	0.443183i	0.832023	−	0.554741i	$-0.187183\pi$
$149$	9.36993	+	5.40973i	0.767615	+	0.443183i	−0.0644082	+	0.997924i	$0.520516\pi$
$150$	17.4727	−	7.79105i	1.42664	−	0.636137i
$151$	4.14799	+	7.18453i	0.337559	+	0.584669i	0.983973	−	0.178318i	$-0.0570655\pi$
$151$	4.14799	+	7.18453i	0.337559	+	0.584669i	−0.646414	+	0.762987i	$0.723732\pi$
$152$	−3.42559	−	1.97777i	−0.277852	−	0.160418i
$153$	−6.30999	+	6.16463i	−0.510132	+	0.498381i
$154$		0			0
$155$	−11.9700	−	8.87905i	−0.961454	−	0.713183i
$156$	25.8443	−	19.5929i	2.06920	−	1.56868i
$157$	2.70593	+	4.68680i	0.215957	+	0.374048i	0.953568	−	0.301178i	$-0.0973797\pi$
$157$	2.70593	+	4.68680i	0.215957	+	0.374048i	−0.737612	+	0.675225i	$0.764046\pi$
$158$	6.46126	+	11.1912i	0.514030	+	0.890326i
$159$	2.66971	−	2.02394i	0.211722	−	0.160509i
$160$	9.49264	−	12.7972i	0.750459	−	1.01171i
$161$		0			0
$162$	−0.463276	+	19.8762i	−0.0363984	+	1.56162i
$163$	14.8583	+	8.57846i	1.16379	+	0.671917i	0.952210	−	0.305443i	$-0.0988046\pi$
$163$	14.8583	+	8.57846i	1.16379	+	0.671917i	0.211584	+	0.977360i	$0.432138\pi$
$164$	−5.05569	−	8.75671i	−0.394783	−	0.683784i
$165$	7.25715	−	12.8789i	0.564969	−	1.00262i
$166$	5.09518	+	2.94170i	0.395463	+	0.228320i
$167$		−	9.60588i		−	0.743325i	−0.928368	−	0.371663i	$-0.878788\pi$
$167$		−	9.60588i		−	0.743325i	0.928368	−	0.371663i	$-0.121212\pi$
$168$		0			0
$169$	29.2709			2.25161
$170$	13.3270	−	5.77619i	1.02213	−	0.443014i
$171$	5.87775	+	1.64858i	0.449483	+	0.126070i
$172$	−17.5518	+	10.1336i	−1.33832	+	0.772677i
$173$	−8.80967	−	5.08627i	−0.669787	−	0.386702i	0.126209	−	0.992004i	$-0.459719\pi$
$173$	−8.80967	−	5.08627i	−0.669787	−	0.386702i	−0.795996	+	0.605302i	$0.793052\pi$
$174$	3.34464	−	7.94346i	0.253556	−	0.602192i
$175$		0			0
$176$		−	5.59463i		−	0.421711i
$177$	−10.9456	+	8.29801i	−0.822724	+	0.623716i
$178$	14.9287	+	25.8573i	1.11895	+	1.93808i
$179$	−20.4854	+	11.8273i	−1.53115	+	0.884011i	−0.531843	+	0.846843i	$0.678500\pi$
$179$	−20.4854	+	11.8273i	−1.53115	+	0.884011i	−0.999309	+	0.0371678i	$0.988166\pi$
$180$	7.31048	−	17.8828i	0.544891	−	1.33291i
$181$		−	15.6330i		−	1.16199i	−0.813906	−	0.580997i	$-0.802663\pi$
$181$		−	15.6330i		−	1.16199i	0.813906	−	0.580997i	$-0.197337\pi$
$182$		0			0
$183$	−9.18476	+	21.8136i	−0.678957	+	1.61251i
$184$	−2.91640	+	5.05135i	−0.215000	+	0.372391i
$185$	−0.860958	+	7.47864i	−0.0632989	+	0.549841i
$186$	−25.3029	+	3.18134i	−1.85530	+	0.233267i
$187$	5.61181	−	9.71993i	0.410376	−	0.710792i
$188$		−	14.4366i		−	1.05290i
$189$		0			0
$190$	−8.07288	−	5.98826i	−0.585668	−	0.434434i
$191$	−9.33503	−	5.38958i	−0.675459	−	0.389976i	0.122683	−	0.992446i	$-0.460850\pi$
$191$	−9.33503	−	5.38958i	−0.675459	−	0.389976i	−0.798142	+	0.602470i	$0.794183\pi$
$192$	−2.76778	−	22.0136i	−0.199747	−	1.58870i
$193$	1.59886	−	0.923104i	0.115089	−	0.0664465i	−0.441351	−	0.897335i	$-0.645500\pi$
$193$	1.59886	−	0.923104i	0.115089	−	0.0664465i	0.556439	+	0.830888i	$0.312167\pi$
$194$	−4.93381	+	8.54561i	−0.354227	+	0.613539i
$195$	21.6742	−	12.8176i	1.55212	−	0.917890i
$196$		0			0
$197$	−8.09941			−0.577059			−0.288530	−	0.957471i	$-0.593166\pi$
$197$	−8.09941			−0.577059			−0.288530	+	0.957471i	$0.593166\pi$
$198$	−6.26180	−	24.5081i	−0.445006	−	1.74172i
$199$	−8.74922	+	5.05137i	−0.620216	+	0.358082i	−0.776953	−	0.629559i	$-0.783236\pi$
$199$	−8.74922	+	5.05137i	−0.620216	+	0.358082i	0.156737	+	0.987640i	$0.449902\pi$
$200$	−6.64528	+	7.09281i	−0.469892	+	0.501537i
$201$	−11.2866	−	14.8878i	−0.796094	−	1.05010i
$202$	19.5954			1.37873
$203$		0			0
$204$	5.69201	−	13.5184i	0.398521	−	0.946480i
$205$	−3.12203	−	7.20323i	−0.218052	−	0.503095i
$206$	−1.46067	−	2.52995i	−0.101770	−	0.176270i
$207$	2.43098	−	8.66729i	0.168965	−	0.602418i
$208$	4.76486	−	8.25298i	0.330383	−	0.572241i
$209$	−7.76686			−0.537245
$210$		0			0
$211$	10.6818			0.735367			0.367684	−	0.929951i	$-0.380151\pi$
$211$	10.6818			0.735367			0.367684	+	0.929951i	$0.380151\pi$
$212$	−2.78525	+	4.82419i	−0.191292	+	0.331327i
$213$	−18.8909	+	2.37516i	−1.29439	+	0.162743i
$214$	3.67195	+	6.36000i	0.251009	+	0.434761i
$215$	−14.4381	+	6.25775i	−0.984668	+	0.426775i
$216$	−3.70170	−	9.39800i	−0.251869	−	0.639453i
$217$		0			0
$218$	27.1683			1.84007
$219$	4.56720	−	3.46245i	0.308623	−	0.233971i
$220$	−2.81115	+	24.4188i	−0.189528	+	1.64632i
$221$	16.5566	−	9.55898i	1.11372	−	0.643006i
$222$	7.78207	+	10.2651i	0.522299	+	0.688947i
$223$	−4.13183			−0.276688			−0.138344	−	0.990384i	$-0.544178\pi$
$223$	−4.13183			−0.276688			−0.138344	+	0.990384i	$0.544178\pi$
$224$		0			0
$225$	7.22672	−	13.1444i	0.481782	−	0.876291i
$226$	−22.5977	+	39.1404i	−1.50318	+	2.60358i
$227$	6.21430	−	3.58783i	0.412458	−	0.238132i	−0.279388	−	0.960178i	$-0.590131\pi$
$227$	6.21430	−	3.58783i	0.412458	−	0.238132i	0.691845	+	0.722046i	$0.256798\pi$
$228$	−10.0711	+	1.26623i	−0.666972	+	0.0838584i
$229$	−9.05093	−	5.22556i	−0.598102	−	0.345315i	0.170192	−	0.985411i	$-0.445561\pi$
$229$	−9.05093	−	5.22556i	−0.598102	−	0.345315i	−0.768295	+	0.640096i	$0.778894\pi$
$230$	−8.83025	+	11.9042i	−0.582250	+	0.784941i
$231$		0			0
$232$			4.37879i			0.287481i
$233$	1.95072	−	3.37875i	0.127796	−	0.221349i	−0.795026	−	0.606575i	$-0.792543\pi$
$233$	1.95072	−	3.37875i	0.127796	−	0.221349i	0.922822	+	0.385226i	$0.125876\pi$
$234$	11.6360	−	41.4865i	0.760670	−	2.71206i
$235$	1.28193	−	11.1354i	0.0836240	−	0.726393i
$236$	11.4193	−	19.7788i	0.743334	−	1.28749i
$237$	9.33810	+	3.93186i	0.606574	+	0.255402i
$238$		0			0
$239$			23.7873i			1.53867i	0.638844	+	0.769336i	$0.279413\pi$
$239$			23.7873i			1.53867i	−0.638844	+	0.769336i	$0.720587\pi$
$240$	−0.0593559	−	5.67650i	−0.00383141	−	0.366417i
$241$	−11.5030	+	6.64126i	−0.740974	+	0.427801i	−0.822423	−	0.568876i	$-0.807378\pi$
$241$	−11.5030	+	6.64126i	−0.740974	+	0.427801i	0.0814495	+	0.996677i	$0.474045\pi$
$242$	3.94187	+	6.82752i	0.253393	+	0.438889i
$243$	9.12542	+	12.6383i	0.585396	+	0.810747i
$244$		−	39.3546i		−	2.51942i
$245$		0			0
$246$	−12.3809	−	5.21303i	−0.789375	−	0.332371i
$247$	−11.4574	−	6.61492i	−0.729015	−	0.420897i
$248$	11.2204	−	6.47812i	0.712498	−	0.411361i
$249$	4.57694	−	0.575459i	0.290052	−	0.0364682i
$250$	−18.8368	+	15.9740i	−1.19134	+	1.01029i
$251$	9.12747			0.576121			0.288060	−	0.957612i	$-0.406990\pi$
$251$	9.12747			0.576121			0.288060	+	0.957612i	$0.406990\pi$
$252$		0			0
$253$			11.4530i			0.720041i
$254$	1.14275	+	0.659769i	0.0717027	+	0.0413976i
$255$	5.59081	−	9.92172i	0.350110	−	0.621322i
$256$	2.70450	+	4.68433i	0.169031	+	0.292770i
$257$	−5.79051	−	3.34315i	−0.361202	−	0.208540i	0.308406	−	0.951255i	$-0.400205\pi$
$257$	−5.79051	−	3.34315i	−0.361202	−	0.208540i	−0.669608	+	0.742715i	$0.733538\pi$
$258$	−10.4489	+	24.8161i	−0.650523	+	1.54498i
$259$		0			0
$260$	−24.9440	+	33.6275i	−1.54696	+	2.08549i
$261$	−1.67287	−	6.54744i	−0.103548	−	0.405277i
$262$	−6.41935	−	11.1186i	−0.396588	−	0.686911i
$263$	−12.0642	−	20.8958i	−0.743908	−	1.28849i	−0.950703	−	0.310103i	$-0.899637\pi$
$263$	−12.0642	−	20.8958i	−0.743908	−	1.28849i	0.206795	−	0.978384i	$-0.433697\pi$
$264$	7.76379	+	10.2410i	0.477828	+	0.630288i
$265$	−2.57672	+	3.47371i	−0.158286	+	0.213389i
$266$		0			0
$267$	21.5756	+	9.08453i	1.32041	+	0.555964i
$268$	26.9023	+	15.5321i	1.64332	+	0.948771i
$269$	−9.50393	−	16.4613i	−0.579465	−	1.00366i	−0.995541	−	0.0943328i	$-0.969928\pi$
$269$	−9.50393	−	16.4613i	−0.579465	−	1.00366i	0.416076	−	0.909330i	$-0.363405\pi$
$270$	−6.61345	−	24.8003i	−0.402482	−	1.50930i
$271$	10.2612	+	5.92429i	0.623321	+	0.359875i	0.778161	−	0.628065i	$-0.216153\pi$
$271$	10.2612	+	5.92429i	0.623321	+	0.359875i	−0.154840	+	0.987940i	$0.549486\pi$
$272$		−	4.31002i		−	0.261334i
$273$		0			0
$274$	−2.41603			−0.145957
$275$	−4.33664	+	18.5853i	−0.261509	+	1.12074i
$276$	1.86718	+	14.8507i	0.112391	+	0.893907i
$277$	14.3051	−	8.25906i	0.859511	−	0.496239i	−0.00433762	−	0.999991i	$-0.501381\pi$
$277$	14.3051	−	8.25906i	0.859511	−	0.496239i	0.863848	+	0.503752i	$0.168047\pi$
$278$	−14.0798	−	8.12900i	−0.844452	−	0.487545i
$279$	−14.3026	+	13.9731i	−0.856275	+	0.836550i
$280$		0			0
$281$		−	10.1076i		−	0.602968i	−0.953471	−	0.301484i	$-0.902518\pi$
$281$		−	10.1076i		−	0.602968i	0.953471	−	0.301484i	$-0.0974820\pi$
$282$	−11.5872	−	15.2843i	−0.690007	−	0.910165i
$283$	−3.00101	−	5.19791i	−0.178392	−	0.308984i	0.762938	−	0.646472i	$-0.223756\pi$
$283$	−3.00101	−	5.19791i	−0.178392	−	0.308984i	−0.941330	+	0.337488i	$0.890423\pi$
$284$	27.4167	−	15.8291i	1.62688	−	0.939282i
$285$	−7.88053	+	0.0824021i	−0.466802	+	0.00488108i
$286$			54.8203i			3.24159i
$287$		0			0
$288$	−14.9388	−	15.2910i	−0.880275	−	0.901031i
$289$	−4.17674	+	7.23433i	−0.245691	+	0.425549i
$290$	−1.27255	+	11.0539i	−0.0747269	+	0.649109i
$291$	0.965157	+	7.67642i	0.0565785	+	0.450000i
$292$	−4.76486	+	8.25298i	−0.278842	+	0.482969i
$293$			3.55369i			0.207609i	0.994598	+	0.103805i	$0.0331016\pi$
$293$			3.55369i			0.207609i	−0.994598	+	0.103805i	$0.966898\pi$
$294$		0			0
$295$	10.5643	−	14.2420i	0.615080	−	0.829200i
$296$	−5.66760	−	3.27219i	−0.329422	−	0.190192i
$297$	−15.5214	−	12.3469i	−0.900641	−	0.716438i
$298$	−20.6988	+	11.9504i	−1.19905	+	0.692271i
$299$	−9.75431	+	16.8950i	−0.564106	+	0.977061i
$300$	−2.59322	+	24.8060i	−0.149720	+	1.43218i
$301$		0			0
$302$	−18.3264			−1.05456
$303$	12.2434	−	9.28190i	0.703367	−	0.533231i
$304$	−2.58299	+	1.49129i	−0.148145	+	0.0855314i
$305$	3.49457	−	30.3553i	0.200099	−	1.73814i
$306$	−4.82400	−	18.8807i	−0.275770	−	1.07934i
$307$	−29.0345			−1.65709			−0.828544	−	0.559923i	$-0.810831\pi$
$307$	−29.0345			−1.65709			−0.828544	+	0.559923i	$0.810831\pi$
$308$		0			0
$309$	−2.11102	−	0.888858i	−0.120092	−	0.0505654i
$310$	30.2078	−	13.0927i	1.71569	−	0.743614i
$311$	4.32216	+	7.48620i	0.245087	+	0.424503i	0.962156	−	0.272499i	$-0.0878501\pi$
$311$	4.32216	+	7.48620i	0.245087	+	0.424503i	−0.717069	+	0.697002i	$0.754517\pi$
$312$	2.73078	+	21.7194i	0.154600	+	1.22962i
$313$	−5.42607	+	9.39824i	−0.306700	+	0.531220i	−0.977638	−	0.210293i	$-0.932558\pi$
$313$	−5.42607	+	9.39824i	−0.306700	+	0.531220i	0.670938	+	0.741513i	$0.265891\pi$
$314$	−11.9551			−0.674667
$315$		0			0
$316$	−16.8471			−0.947724
$317$	4.67046	−	8.08947i	0.262319	−	0.454350i	−0.704539	−	0.709665i	$-0.748846\pi$
$317$	4.67046	−	8.08947i	0.262319	−	0.454350i	0.966858	+	0.255316i	$0.0821794\pi$
$318$	0.923229	+	7.34294i	0.0517721	+	0.411772i
$319$	4.29897	+	7.44604i	0.240696	+	0.416898i
$320$	11.3907	+	26.2809i	0.636759	+	1.46915i
$321$	5.30686	+	2.23448i	0.296200	+	0.124717i
$322$		0			0
$323$	−5.98348			−0.332930
$324$	−22.1390	−	13.4794i	−1.22994	−	0.748853i
$325$	−22.2261	+	23.7229i	−1.23288	+	1.31591i
$326$	−32.8230	+	18.9504i	−1.81790	+	1.04956i
$327$	16.9750	−	12.8690i	0.938722	−	0.711656i
$328$	6.82488			0.376841
$329$		0			0
$330$	16.6229	+	28.1088i	0.915062	+	1.54734i
$331$	−1.45459	+	2.51942i	−0.0799515	+	0.138480i	−0.903229	−	0.429159i	$-0.858810\pi$
$331$	−1.45459	+	2.51942i	−0.0799515	+	0.138480i	0.823277	+	0.567639i	$0.192143\pi$
$332$	−6.64260	+	3.83511i	−0.364560	+	0.210479i
$333$	9.72466	+	2.72755i	0.532908	+	0.149469i
$334$	18.3771	+	10.6100i	1.00555	+	0.580553i
$335$	19.3713	+	14.3692i	1.05837	+	0.785071i
$336$		0			0
$337$		−	15.2910i		−	0.832954i	−0.909146	−	0.416477i	$-0.863265\pi$
$337$		−	15.2910i		−	0.832954i	0.909146	−	0.416477i	$-0.136735\pi$
$338$	−32.3307	+	55.9983i	−1.75856	+	3.04591i
$339$	4.42059	+	35.1593i	0.240093	+	1.90959i
$340$	−2.16567	+	18.8119i	−0.117450	+	1.02022i
$341$	12.7201	−	22.0318i	0.688830	−	1.19309i
$342$	−9.64606	+	9.42384i	−0.521599	+	0.509583i
$343$		0			0
$344$		−	13.6797i		−	0.737561i
$345$	0.121510	+	11.6206i	0.00654185	+	0.625631i
$346$	19.4611	−	11.2359i	1.04624	−	0.604045i
$347$	15.7892	+	27.3477i	0.847609	+	1.46810i	0.883336	+	0.468739i	$0.155292\pi$
$347$	15.7892	+	27.3477i	0.847609	+	1.46810i	−0.0357279	+	0.999362i	$0.511375\pi$
$348$	6.78827	+	8.95418i	0.363890	+	0.479995i
$349$			8.25024i			0.441625i	0.975316	+	0.220813i	$0.0708709\pi$
$349$			8.25024i			0.441625i	−0.975316	+	0.220813i	$0.929129\pi$
$350$		0			0
$351$	−12.3809	−	31.4329i	−0.660842	−	1.67777i
$352$	23.5543	+	13.5991i	1.25545	+	0.724834i
$353$	−3.71360	+	2.14405i	−0.197655	+	0.114116i	−0.595561	−	0.803310i	$-0.703070\pi$
$353$	−3.71360	+	2.14405i	−0.197655	+	0.114116i	0.397906	+	0.917426i	$0.369737\pi$
$354$	−3.78517	−	30.1055i	−0.201180	−	1.60009i
$355$	22.5529	−	9.77488i	1.19698	−	0.518797i
$356$	−38.9252			−2.06303
$357$		0			0
$358$		−	52.2543i		−	2.76173i
$359$	6.17938	+	3.56767i	0.326135	+	0.188294i	0.654124	−	0.756387i	$-0.273037\pi$
$359$	6.17938	+	3.56767i	0.326135	+	0.188294i	−0.327989	+	0.944682i	$0.606371\pi$
$360$	7.98607	+	10.3085i	0.420903	+	0.543304i
$361$	−7.42968	−	12.8686i	−0.391036	−	0.677294i
$362$	29.9076	+	17.2672i	1.57191	+	0.907542i
$363$	5.69696	+	2.39874i	0.299013	+	0.125901i
$364$		0			0
$365$	−4.40811	+	5.94265i	−0.230731	+	0.311053i
$366$	−31.5869	−	41.6653i	−1.65107	−	2.17788i
$367$	−12.1957	−	21.1235i	−0.636609	−	1.10264i	−0.986172	−	0.165726i	$-0.947003\pi$
$367$	−12.1957	−	21.1235i	−0.636609	−	1.10264i	0.349563	−	0.936913i	$-0.386330\pi$
$368$	2.19905	+	3.80886i	0.114633	+	0.198551i
$369$	−10.2050	+	2.60737i	−0.531251	+	0.135734i
$370$	−13.3565	−	9.90750i	−0.694370	−	0.515067i
$371$		0			0
$372$	12.9019	−	30.6417i	0.668931	−	1.58870i
$373$	−19.0999	−	11.0273i	−0.988956	−	0.570974i	−0.0839940	−	0.996466i	$-0.526768\pi$
$373$	−19.0999	−	11.0273i	−0.988956	−	0.570974i	−0.904962	+	0.425492i	$0.860101\pi$
$374$	12.3968	+	21.4719i	0.641025	+	1.11029i
$375$	−4.20293	+	18.9033i	−0.217038	+	0.976163i
$376$	8.43881	+	4.87215i	0.435199	+	0.251262i
$377$			14.6455i			0.754280i
$378$		0			0
$379$	1.15801			0.0594828			0.0297414	−	0.999558i	$-0.490532\pi$
$379$	1.15801			0.0594828			0.0297414	+	0.999558i	$0.490532\pi$
$380$	12.0233	−	5.21114i	0.616782	−	0.267326i
$381$	1.02652	−	0.129065i	0.0525903	−	0.00661218i
$382$	20.6217	−	11.9059i	1.05510	−	0.609160i
$383$	−1.84403	−	1.06465i	−0.0942255	−	0.0544011i	0.452147	−	0.891944i	$-0.350658\pi$
$383$	−1.84403	−	1.06465i	−0.0942255	−	0.0544011i	−0.546372	+	0.837542i	$0.683992\pi$
$384$	22.4217	+	9.44079i	1.14420	+	0.481773i
$385$		0			0
$386$			4.07839i			0.207585i
$387$	5.22618	+	20.4548i	0.265662	+	1.03978i
$388$	−6.43222	−	11.1409i	−0.326546	−	0.565595i
$389$	−20.9207	+	12.0785i	−1.06072	+	0.612406i	−0.925631	−	0.378427i	$-0.876465\pi$
$389$	−20.9207	+	12.0785i	−1.06072	+	0.612406i	−0.135088	+	0.990834i	$0.543132\pi$
$390$	0.581612	+	55.6226i	0.0294511	+	2.81656i
$391$			8.82320i			0.446208i
$392$		0			0
$393$	−9.27752	−	3.90635i	−0.467989	−	0.197049i
$394$	8.94606	−	15.4950i	0.450696	−	0.780628i
$395$	−12.9947	−	1.49598i	−0.653832	−	0.0752707i
$396$	31.7524	+	8.90582i	1.59562	+	0.447534i
$397$	6.00792	−	10.4060i	0.301529	−	0.522263i	−0.674954	−	0.737860i	$-0.735836\pi$
$397$	6.00792	−	10.4060i	0.301529	−	0.522263i	0.976482	+	0.215597i	$0.0691697\pi$
$398$		−	22.3176i		−	1.11868i
$399$		0			0
$400$	2.12629	+	7.01351i	0.106315	+	0.350675i
$401$	−26.6997	−	15.4151i	−1.33332	−	0.769792i	−0.347513	−	0.937675i	$-0.612974\pi$
$401$	−26.6997	−	15.4151i	−1.33332	−	0.769792i	−0.985807	+	0.167883i	$0.946307\pi$
$402$	40.9482	−	5.14842i	2.04231	−	0.256780i
$403$	37.5283	−	21.6670i	1.86942	−	1.07931i
$404$	−12.7733	+	22.1240i	−0.635495	+	1.10071i
$405$	−15.8795	−	12.3629i	−0.789059	−	0.614317i
$406$		0			0
$407$	−12.8502			−0.636959
$408$	5.98112	+	7.88949i	0.296109	+	0.390588i
$409$	13.5699	−	7.83456i	0.670986	−	0.387394i	−0.125464	−	0.992098i	$-0.540042\pi$
$409$	13.5699	−	7.83456i	0.670986	−	0.387394i	0.796450	+	0.604704i	$0.206709\pi$
$410$	17.2289	+	1.98343i	0.850875	+	0.0979547i
$411$	−1.50956	+	1.14442i	−0.0744611	+	0.0564498i
$412$	3.80855			0.187634
$413$		0			0
$414$	13.8963	+	14.2240i	0.682968	+	0.699072i
$415$	−5.46417	+	2.36828i	−0.268226	+	0.116254i
$416$	23.1643	+	40.1217i	1.13572	+	1.96713i
$417$	−12.6478	+	1.59020i	−0.619363	+	0.0778726i
$418$	8.57874	−	14.8588i	0.419600	−	0.726769i
$419$	−19.5975			−0.957399			−0.478699	−	0.877979i	$-0.658892\pi$
$419$	−19.5975			−0.957399			−0.478699	+	0.877979i	$0.658892\pi$
$420$		0			0
$421$	−32.5791			−1.58781			−0.793903	−	0.608044i	$-0.791954\pi$
$421$	−32.5791			−1.58781			−0.793903	+	0.608044i	$0.791954\pi$
$422$	−11.7984	+	20.4355i	−0.574338	+	0.994782i
$423$	−14.4796	−	4.06120i	−0.704023	−	0.197462i
$424$	−1.87996	−	3.25619i	−0.0912990	−	0.158134i
$425$	−3.34089	+	14.3179i	−0.162057	+	0.694518i
$426$	16.3217	−	38.7638i	0.790789	−	1.87811i
$427$		0			0
$428$	−9.57425			−0.462789
$429$	25.9671	+	34.2523i	1.25370	+	1.65372i
$430$	3.97557	−	34.5334i	0.191719	−	1.66535i
$431$	−24.1528	+	13.9447i	−1.16340	+	0.671690i	−0.952117	−	0.305734i	$-0.901098\pi$
$431$	−24.1528	+	13.9447i	−1.16340	+	0.671690i	−0.211285	+	0.977425i	$0.567765\pi$
$432$	−7.53256	−	1.12594i	−0.362410	−	0.0541717i
$433$	3.47350			0.166926			0.0834629	−	0.996511i	$-0.473402\pi$
$433$	3.47350			0.166926			0.0834629	+	0.996511i	$0.473402\pi$
$434$		0			0
$435$	4.44088	+	7.50940i	0.212924	+	0.360048i
$436$	−17.7097	+	30.6740i	−0.848139	+	1.46902i
$437$	5.28774	−	3.05288i	0.252947	−	0.146039i
$438$	1.57941	+	12.5619i	0.0754672	+	0.600232i
$439$	−3.41910	−	1.97402i	−0.163185	−	0.0942147i	0.416184	−	0.909281i	$-0.363367\pi$
$439$	−3.41910	−	1.97402i	−0.163185	−	0.0942147i	−0.579368	+	0.815066i	$0.696701\pi$
$440$	−13.3251	−	9.88423i	−0.635249	−	0.471212i
$441$		0			0
$442$			42.2328i			2.00881i
$443$	8.01539	−	13.8831i	0.380823	−	0.659604i	−0.610357	−	0.792126i	$-0.708974\pi$
$443$	8.01539	−	13.8831i	0.380823	−	0.659604i	0.991180	+	0.132522i	$0.0423075\pi$
$444$	−16.6624	+	2.09497i	−0.790764	+	0.0994227i
$445$	−30.0241	−	3.45644i	−1.42328	−	0.163851i
$446$	4.56373	−	7.90462i	0.216099	−	0.374295i
$447$	−7.27218	+	17.2713i	−0.343962	+	0.816905i
$448$		0			0
$449$			21.1001i			0.995777i	0.867241	+	0.497889i	$0.165891\pi$
$449$			21.1001i			0.995777i	−0.867241	+	0.497889i	$0.834109\pi$
$450$	17.1644	+	28.3439i	0.809138	+	1.33614i
$451$	11.6056	−	6.70048i	0.546485	−	0.315513i
$452$	−29.4607	−	51.0274i	−1.38571	−	2.40013i
$453$	−11.4505	+	8.68077i	−0.537992	+	0.407858i
$454$			15.8515i			0.743947i
$455$		0			0
$456$	2.65867	−	6.31429i	0.124503	−	0.295694i
$457$	8.31969	+	4.80338i	0.389179	+	0.224692i	0.681804	−	0.731535i	$-0.261196\pi$
$457$	8.31969	+	4.80338i	0.389179	+	0.224692i	−0.292625	+	0.956227i	$0.594529\pi$
$458$	19.9941	−	11.5436i	0.934262	−	0.539397i
$459$	−11.9574	−	9.51186i	−0.558126	−	0.443975i
$460$	−7.68432	−	17.7295i	−0.358283	−	0.826641i
$461$	−24.5367			−1.14279			−0.571393	−	0.820676i	$-0.693597\pi$
$461$	−24.5367			−1.14279			−0.571393	+	0.820676i	$0.693597\pi$
$462$		0			0
$463$			14.5875i			0.677937i	0.940798	+	0.338968i	$0.110078\pi$
$463$			14.5875i			0.677937i	−0.940798	+	0.338968i	$0.889922\pi$
$464$	2.85938	+	1.65086i	0.132743	+	0.0766395i
$465$	12.6725	−	22.4892i	0.587672	−	1.04291i
$466$	4.30927	+	7.46387i	0.199623	+	0.345757i
$467$	15.5179	+	8.95926i	0.718083	+	0.414585i	0.814047	−	0.580800i	$-0.197260\pi$
$467$	15.5179	+	8.95926i	0.718083	+	0.414585i	−0.0959639	+	0.995385i	$0.530593\pi$
$468$	39.2549	+	40.1805i	1.81456	+	1.85735i
$469$		0			0
$470$	19.8872	+	14.7519i	0.917330	+	0.680452i
$471$	−7.46970	+	5.66287i	−0.344186	+	0.260931i
$472$	7.70770	+	13.3501i	0.354776	+	0.614490i
$473$	−13.4304	−	23.2621i	−0.617529	−	1.06959i
$474$	−17.8363	+	13.5219i	−0.819247	+	0.621081i
$475$	9.73665	−	2.95187i	0.446748	−	0.135441i
$476$		0			0
$477$	4.05503	+	4.15064i	0.185667	+	0.190045i
$478$	−45.5076	−	26.2738i	−2.08147	−	1.20174i
$479$	1.48248	+	2.56774i	0.0677364	+	0.117323i	0.897905	−	0.440190i	$-0.145089\pi$
$479$	1.48248	+	2.56774i	0.0677364	+	0.117323i	−0.830168	+	0.557513i	$0.811756\pi$
$480$	24.0433	+	13.5482i	1.09742	+	0.618389i
$481$	−18.9561	−	10.9443i	−0.864322	−	0.499017i
$482$		−	29.3419i		−	1.33649i
$483$		0			0
$484$	−10.2780			−0.467184
$485$	−3.97207	−	9.16448i	−0.180362	−	0.416138i
$486$	−34.2577	+	3.49849i	−1.55396	+	0.158695i
$487$	−28.8004	+	16.6279i	−1.30507	+	0.753482i	−0.981269	−	0.192644i	$-0.938294\pi$
$487$	−28.8004	+	16.6279i	−1.30507	+	0.753482i	−0.323800	+	0.946125i	$0.604961\pi$
$488$	23.0044	+	13.2816i	1.04136	+	0.601230i
$489$	−11.5318	+	27.3879i	−0.521487	+	1.23852i
$490$		0			0
$491$		−	25.4892i		−	1.15031i	−0.818043	−	0.575157i	$-0.804941\pi$
$491$		−	25.4892i		−	1.15031i	0.818043	−	0.575157i	$-0.195059\pi$
$492$	13.9562	−	10.5804i	0.629194	−	0.477000i
$493$	3.31187	+	5.73632i	0.149159	+	0.258351i
$494$	25.3101	−	14.6128i	1.13875	−	0.657460i
$495$	23.7007	+	9.68883i	1.06527	+	0.435481i
$496$		−	9.76937i		−	0.438658i
$497$		0			0
$498$	−3.95447	+	9.39179i	−0.177204	+	0.420856i
$499$	16.8358	−	29.1604i	0.753673	−	1.30540i	−0.192358	−	0.981325i	$-0.561613\pi$
$499$	16.8358	−	29.1604i	0.753673	−	1.30540i	0.946031	−	0.324076i	$-0.105053\pi$
$500$	−5.75651	−	31.6802i	−0.257439	−	1.41678i
$501$	16.5079	−	2.07554i	0.737519	−	0.0927283i
$502$	−10.0816	+	17.4618i	−0.449963	+	0.779358i
$503$		−	35.2418i		−	1.57135i	−0.618637	−	0.785677i	$-0.712315\pi$
$503$		−	35.2418i		−	1.57135i	0.618637	−	0.785677i	$-0.287685\pi$
$504$		0			0
$505$	−11.8170	+	15.9306i	−0.525848	+	0.708904i
$506$	−21.9107	−	12.6502i	−0.974050	−	0.562368i
$507$	6.32456	+	50.3027i	0.280884	+	2.23402i
$508$	−1.48981	+	0.860142i	−0.0660996	+	0.0381626i
$509$	11.5914	−	20.0770i	0.513782	−	0.889896i	−0.486090	−	0.873908i	$-0.661577\pi$
$509$	11.5914	−	20.0770i	0.513782	−	0.889896i	0.999872	−	0.0159875i	$-0.00508920\pi$
$510$	12.8061	+	21.6547i	0.567062	+	0.958884i
$511$		0			0
$512$	16.1430			0.713426
$513$	−1.56311	+	10.4572i	−0.0690129	+	0.461698i
$514$	12.7916	−	7.38523i	0.564213	−	0.325749i
$515$	2.93765	+	0.338189i	0.129448	+	0.0149024i
$516$	−21.2072	−	27.9737i	−0.933593	−	1.23147i
$517$	19.1334			0.841484
$518$		0			0
$519$	6.83735	−	16.2386i	0.300126	−	0.712795i
$520$	−11.2384	−	25.9296i	−0.492837	−	1.13709i
$521$	−7.18762	−	12.4493i	−0.314895	−	0.545415i	0.664520	−	0.747271i	$-0.268636\pi$
$521$	−7.18762	−	12.4493i	−0.314895	−	0.545415i	−0.979415	+	0.201856i	$0.935303\pi$
$522$	14.3737	+	4.03149i	0.629119	+	0.176454i
$523$	−12.6242	+	21.8658i	−0.552018	+	0.956124i	0.446110	+	0.894978i	$0.352809\pi$
$523$	−12.6242	+	21.8658i	−0.552018	+	0.956124i	−0.998129	+	0.0611461i	$0.980524\pi$
$524$	16.7378			0.731195
$525$		0			0
$526$	53.3010			2.32403
$527$	9.79936	−	16.9730i	0.426867	−	0.739355i
$528$	9.61448	−	1.20883i	0.418417	−	0.0526075i
$529$	6.99825	+	12.1213i	0.304272	+	0.527014i
$530$	−3.79952	−	8.76636i	−0.165040	−	0.380786i
$531$	−16.6253	−	17.0173i	−0.721477	−	0.738489i
$532$		0			0
$533$	22.8268			0.988737
$534$	−41.2106	+	31.2422i	−1.78336	+	1.35198i
$535$	−7.38490	−	0.850166i	−0.319277	−	0.0367559i
$536$	−18.1583	+	10.4837i	−0.784318	+	0.452826i
$537$	−24.7517	−	32.6491i	−1.06811	−	1.40891i
$538$	41.9896			1.81030
$539$		0			0
$540$	32.3115	+	8.69928i	1.39047	+	0.374357i
$541$	−7.88973	+	13.6654i	−0.339206	+	0.587522i	−0.984284	−	0.176595i	$-0.943492\pi$
$541$	−7.88973	+	13.6654i	−0.339206	+	0.587522i	0.645078	+	0.764117i	$0.276825\pi$
$542$	−22.6676	+	13.0871i	−0.973655	+	0.562140i
$543$	26.8657	−	3.37782i	1.15292	−	0.144956i
$544$	18.1459	+	10.4766i	0.778000	+	0.449179i
$545$	−16.3837	+	22.0872i	−0.701802	+	0.946112i
$546$		0			0
$547$			8.23195i			0.351973i	0.984393	+	0.175986i	$0.0563115\pi$
$547$			8.23195i			0.351973i	−0.984393	+	0.175986i	$0.943689\pi$
$548$	1.57489	−	2.72779i	0.0672759	−	0.116525i
$549$	−39.4717	−	11.0709i	−1.68461	−	0.472496i
$550$	−30.7657	−	28.8245i	−1.31185	−	1.22908i
$551$	2.29185	−	3.96960i	0.0976360	−	0.169111i
$552$	−9.31100	−	3.92045i	−0.396303	−	0.166865i
$553$		0			0
$554$			36.4896i			1.55029i
$555$	−13.0382	+	0.136333i	−0.553442	+	0.00578702i
$556$	18.3559	−	10.5978i	0.778464	−	0.449446i
$557$	−14.4676	−	25.0586i	−0.613011	−	1.06177i	−0.990730	−	0.135845i	$-0.956625\pi$
$557$	−14.4676	−	25.0586i	−0.613011	−	1.06177i	0.377719	−	0.925920i	$-0.376708\pi$
$558$	−10.9344	−	42.7962i	−0.462889	−	1.81171i
$559$		−	45.7537i		−	1.93518i
$560$		0			0
$561$	17.9164	+	7.54382i	0.756433	+	0.318500i
$562$	19.3369	+	11.1641i	0.815677	+	0.470931i
$563$	−5.39368	+	3.11404i	−0.227316	+	0.131241i	−0.609333	−	0.792914i	$-0.708563\pi$
$563$	−5.39368	+	3.11404i	−0.227316	+	0.131241i	0.382017	+	0.924155i	$0.375230\pi$
$564$	24.8097	−	3.11932i	1.04467	−	0.131347i
$565$	−18.1928	−	41.9749i	−0.765376	−	1.76590i
$566$	13.2589			0.557312
$567$		0			0
$568$			21.3683i			0.896594i
$569$	−8.56862	−	4.94710i	−0.359215	−	0.207393i	0.309521	−	0.950893i	$-0.399831\pi$
$569$	−8.56862	−	4.94710i	−0.359215	−	0.207393i	−0.668736	+	0.743500i	$0.733165\pi$
$570$	8.54665	−	15.1673i	0.357980	−	0.635288i
$571$	−9.60472	−	16.6359i	−0.401945	−	0.696189i	0.592015	−	0.805927i	$-0.298332\pi$
$571$	−9.60472	−	16.6359i	−0.401945	−	0.696189i	−0.993961	+	0.109737i	$0.964999\pi$
$572$	−61.8942	−	35.7347i	−2.58793	−	1.49414i
$573$	7.24509	−	17.2070i	0.302668	−	0.718831i
$574$		0			0
$575$	−4.35281	−	14.3576i	−0.181525	−	0.598753i
$576$	37.2329	−	9.51296i	1.55137	−	0.396373i
$577$	19.0377	+	32.9742i	0.792549	+	1.37273i	0.924384	+	0.381463i	$0.124580\pi$
$577$	19.0377	+	32.9742i	0.792549	+	1.37273i	−0.131835	+	0.991272i	$0.542087\pi$
$578$	−9.22669	−	15.9811i	−0.383780	−	0.664726i
$579$	1.93184	+	2.54823i	0.0802845	+	0.105901i
$580$	−11.6508	−	8.64228i	−0.483773	−	0.358851i
$581$		0			0
$582$	−15.7519	−	6.63241i	−0.652935	−	0.274922i
$583$	−6.39367	−	3.69139i	−0.264799	−	0.152882i
$584$	−3.21614	−	5.57052i	−0.133085	−	0.230510i
$585$	26.7105	+	34.4781i	1.10434	+	1.42549i
$586$	−6.79859	−	3.92517i	−0.280847	−	0.162147i
$587$			11.9232i			0.492124i	0.969254	+	0.246062i	$0.0791367\pi$
$587$			11.9232i			0.492124i	−0.969254	+	0.246062i	$0.920863\pi$
$588$		0			0
$589$	−13.5625			−0.558835
$590$	15.5777	+	35.9414i	0.641326	+	1.47968i
$591$	−1.75004	−	13.9190i	−0.0719869	−	0.572552i
$592$	−4.27353	+	2.46732i	−0.175641	+	0.101406i
$593$	14.5994	+	8.42896i	0.599525	+	0.346136i	0.768855	−	0.639424i	$-0.220827\pi$
$593$	14.5994	+	8.42896i	0.599525	+	0.346136i	−0.169330	+	0.985559i	$0.554160\pi$
$594$	40.7647	−	16.0565i	1.67260	−	0.658806i
$595$		0			0
$596$		−	31.1596i		−	1.27635i
$597$	−10.5713	−	13.9443i	−0.432655	−	0.570701i
$598$	−21.5479	−	37.3220i	−0.881159	−	1.52621i
$599$	−11.7736	+	6.79751i	−0.481058	+	0.277739i	−0.720857	−	0.693084i	$-0.756252\pi$
$599$	−11.7736	+	6.79751i	−0.481058	+	0.277739i	0.239800	+	0.970822i	$0.422918\pi$
$600$	−13.6250	−	9.88751i	−0.556237	−	0.403656i
$601$			46.2155i			1.88517i	0.333966	+	0.942585i	$0.391613\pi$
$601$			46.2155i			1.88517i	−0.333966	+	0.942585i	$0.608387\pi$
$602$		0			0
$603$	23.1462	−	22.6130i	0.942588	−	0.920874i
$604$	11.9461	−	20.6912i	0.486078	−	0.841912i
$605$	−7.92775	−	0.912661i	−0.322309	−	0.0371049i
$606$	4.23398	+	33.6751i	0.171994	+	1.36796i
$607$	−4.37164	+	7.57190i	−0.177439	+	0.307334i	−0.941003	−	0.338399i	$-0.890115\pi$
$607$	−4.37164	+	7.57190i	−0.177439	+	0.307334i	0.763563	+	0.645733i	$0.223448\pi$
$608$		−	14.4998i		−	0.588044i
$609$		0			0
$610$	54.2130	+	40.2139i	2.19502	+	1.62821i
$611$	28.2248	+	16.2956i	1.14185	+	0.659249i
$612$	24.4616	+	6.86092i	0.988801	+	0.277336i
$613$	−21.0938	+	12.1785i	−0.851970	+	0.491885i	−0.861315	−	0.508071i	$-0.830359\pi$
$613$	−21.0938	+	12.1785i	−0.851970	+	0.491885i	0.00934480	+	0.999956i	$0.497025\pi$
$614$	32.0696	−	55.5461i	1.29422	−	2.24166i
$615$	11.7043	−	6.92167i	0.471964	−	0.279109i
$616$		0			0
$617$	−25.3125			−1.01904			−0.509522	−	0.860458i	$-0.670178\pi$
$617$	−25.3125			−1.01904			−0.509522	+	0.860458i	$0.670178\pi$
$618$	4.03217	−	3.05684i	0.162198	−	0.122964i
$619$	26.2018	−	15.1276i	1.05314	−	0.608029i	0.129612	−	0.991565i	$-0.458627\pi$
$619$	26.2018	−	15.1276i	1.05314	−	0.608029i	0.923526	+	0.383535i	$0.125294\pi$
$620$	−4.90885	+	42.6403i	−0.197144	+	1.71247i
$621$	15.4202	+	2.30495i	0.618790	+	0.0924944i
$622$	−19.0958			−0.765673
$623$		0			0
$624$	15.2125	+	6.40529i	0.608986	+	0.256417i
$625$	−1.62705	−	24.9470i	−0.0650820	−	0.997880i
$626$	−11.9865	−	20.7613i	−0.479079	−	0.829788i
$627$	−1.67818	−	13.3475i	−0.0670202	−	0.533048i
$628$	7.79296	−	13.4978i	0.310973	−	0.538621i
$629$	−9.89959			−0.394723
$630$		0			0
$631$	−5.90652			−0.235135			−0.117568	−	0.993065i	$-0.537510\pi$
$631$	−5.90652			−0.235135			−0.117568	+	0.993065i	$0.537510\pi$
$632$	5.68566	−	9.84784i	0.226163	−	0.391726i
$633$	2.30802	+	18.3569i	0.0917355	+	0.729623i
$634$	10.3173	+	17.8701i	0.409754	+	0.709714i
$635$	−1.22551	+	0.531161i	−0.0486329	+	0.0210785i
$636$	−8.89228	−	3.74415i	−0.352602	−	0.148465i
$637$		0			0
$638$	−18.9934			−0.751956
$639$	−8.16352	−	31.9513i	−0.322944	−	1.26397i
$640$	−31.2015	−	3.59199i	−1.23335	−	0.141986i
$641$	0.111457	−	0.0643495i	0.00440227	−	0.00254165i	−0.497797	−	0.867293i	$-0.665858\pi$
$641$	0.111457	−	0.0643495i	0.00440227	−	0.00254165i	0.502200	+	0.864752i	$0.332524\pi$
$642$	−10.1364	+	7.68452i	−0.400052	+	0.303284i
$643$	0.150563			0.00593763			0.00296881	−	0.999996i	$-0.499055\pi$
$643$	0.150563			0.00593763			0.00296881	+	0.999996i	$0.499055\pi$
$644$		0			0
$645$	−13.8737	−	23.4600i	−0.546277	−	0.923737i
$646$	6.60894	−	11.4470i	0.260025	−	0.450377i
$647$	35.8147	−	20.6776i	1.40802	−	0.812920i	0.412822	−	0.910812i	$-0.364543\pi$
$647$	35.8147	−	20.6776i	1.40802	−	0.812920i	0.995197	+	0.0978912i	$0.0312097\pi$
$648$	15.3508	−	8.39208i	0.603038	−	0.329672i
$649$	26.2136	+	15.1344i	1.02897	+	0.594078i
$650$	−20.8350	−	68.7235i	−0.817214	−	2.69556i
$651$		0			0
$652$		−	49.4113i		−	1.93509i
$653$	14.7304	−	25.5138i	0.576446	−	0.998433i	−0.419437	−	0.907784i	$-0.637773\pi$
$653$	14.7304	−	25.5138i	0.576446	−	0.998433i	0.995883	−	0.0906487i	$-0.0288940\pi$
$654$	5.87024	+	46.6892i	0.229545	+	1.82569i
$655$	12.9104	+	1.48627i	0.504450	+	0.0580734i
$656$	2.57308	−	4.45670i	0.100462	−	0.174005i
$657$	6.93713	+	7.10071i	0.270643	+	0.277025i
$658$		0			0
$659$		−	22.4678i		−	0.875220i	−0.899165	−	0.437610i	$-0.855825\pi$
$659$		−	22.4678i		−	0.875220i	0.899165	−	0.437610i	$-0.144175\pi$
$660$	−42.5717	+	0.445147i	−1.65710	+	0.0173273i
$661$	20.3164	−	11.7297i	0.790218	−	0.456233i	−0.0498213	−	0.998758i	$-0.515865\pi$
$661$	20.3164	−	11.7297i	0.790218	−	0.456233i	0.840039	+	0.542526i	$0.182532\pi$
$662$	−3.21328	−	5.56557i	−0.124888	−	0.216312i
$663$	20.0047	+	26.3875i	0.776918	+	1.02481i
$664$		−	5.17717i		−	0.200913i
$665$		0			0
$666$	−15.9593	+	15.5916i	−0.618409	+	0.604163i
$667$	−5.85354	−	3.37954i	−0.226650	−	0.130856i
$668$	−23.9582	+	13.8323i	−0.926971	+	0.535187i
$669$	−0.892762	−	7.10063i	−0.0345162	−	0.274526i
$670$	−48.8860	+	21.1882i	−1.88863	+	0.818570i
$671$	52.1580			2.01354
$672$		0			0
$673$			44.5504i			1.71729i	0.512570	+	0.858645i	$0.328693\pi$
$673$			44.5504i			1.71729i	−0.512570	+	0.858645i	$0.671307\pi$
$674$	29.2533	+	16.8894i	1.12680	+	0.650555i
$675$	24.1503	+	9.57918i	0.929547	+	0.368703i
$676$	−42.1496	−	73.0052i	−1.62114	−	2.80789i
$677$	39.5783	+	22.8505i	1.52112	+	0.878217i	0.999689	+	0.0249214i	$0.00793355\pi$
$677$	39.5783	+	22.8505i	1.52112	+	0.878217i	0.521427	+	0.853296i	$0.325400\pi$
$678$	−72.1462	−	30.3776i	−2.77076	−	1.16664i
$679$		0			0
$680$	−10.2655	−	7.61467i	−0.393663	−	0.292009i
$681$	7.50848	+	9.90418i	0.287725	+	0.379529i
$682$	28.0994	+	48.6697i	1.07598	+	1.86366i
$683$	19.3444	+	33.5055i	0.740192	+	1.28205i	0.952407	+	0.304828i	$0.0985990\pi$
$683$	19.3444	+	33.5055i	0.740192	+	1.28205i	−0.212215	+	0.977223i	$0.568068\pi$
$684$	−4.35210	−	17.0337i	−0.166407	−	0.651300i
$685$	1.45698	−	1.96418i	0.0556682	−	0.0750473i
$686$		0			0
$687$	7.02460	−	16.6833i	0.268005	−	0.636508i
$688$	−8.93296	−	5.15745i	−0.340566	−	0.196626i
$689$	−6.28779	−	10.8908i	−0.239546	−	0.414905i
$690$	−22.3656	−	12.6028i	−0.851443	−	0.479782i
$691$	16.6768	+	9.62834i	0.634415	+	0.366279i	0.782460	−	0.622701i	$-0.213965\pi$
$691$	16.6768	+	9.62834i	0.634415	+	0.366279i	−0.148045	+	0.988981i	$0.547298\pi$
$692$			29.2965i			1.11369i
$693$		0			0
$694$	−69.7587			−2.64800
$695$	15.0995	−	6.54443i	0.572756	−	0.248244i
$696$	−7.52504	+	0.946123i	−0.285236	+	0.0358627i
$697$	8.94077	−	5.16195i	0.338656	−	0.195523i
$698$	−15.7836	−	9.11265i	−0.597417	−	0.344919i
$699$	6.22794	+	2.62231i	0.235562	+	0.0991849i
$700$		0			0
$701$		−	6.75777i		−	0.255238i	−0.991823	−	0.127619i	$-0.959267\pi$
$701$		−	6.75777i		−	0.255238i	0.991823	−	0.127619i	$-0.0407334\pi$
$702$	73.8096	+	11.0328i	2.78576	+	0.416405i
$703$	3.42531	+	5.93282i	0.129188	+	0.223760i
$704$	−42.3428	+	24.4466i	−1.59586	+	0.921367i
$705$	19.4134	−	0.202994i	0.731150	−	0.00764521i
$706$		−	9.47268i		−	0.356509i
$707$		0			0
$708$	36.4577	+	15.3507i	1.37016	+	0.576916i
$709$	−2.44586	+	4.23635i	−0.0918561	+	0.159099i	−0.908292	−	0.418336i	$-0.862613\pi$
$709$	−2.44586	+	4.23635i	−0.0918561	+	0.159099i	0.816436	+	0.577436i	$0.195947\pi$
$710$	−6.21001	+	53.9427i	−0.233057	+	2.02443i
$711$	−4.73930	+	16.8973i	−0.177738	+	0.633697i
$712$	13.1367	−	22.7534i	0.492318	−	0.852719i
$713$			19.9992i			0.748977i
$714$		0			0
$715$	−44.5677	−	33.0592i	−1.66674	−	1.23634i
$716$	58.9972	+	34.0620i	2.20483	+	1.27296i
$717$	−40.8790	+	5.13971i	−1.52665	+	0.191946i
$718$	−13.6506	+	7.88121i	−0.509438	+	0.294124i
$719$	−19.0108	+	32.9277i	−0.708985	+	1.22800i	0.256249	+	0.966611i	$0.417513\pi$
$719$	−19.0108	+	32.9277i	−0.708985	+	1.22800i	−0.965234	+	0.261387i	$0.915820\pi$
$720$	9.74237	−	1.32852i	0.363077	−	0.0495112i
$721$		0			0
$722$	32.8253			1.22163
$723$	−13.8986	−	18.3332i	−0.516894	−	0.681818i
$724$	−38.9906	+	22.5112i	−1.44907	+	0.836624i
$725$	−8.21919	−	7.70059i	−0.305253	−	0.285993i
$726$	−10.8815	+	8.24940i	−0.403851	+	0.306164i
$727$	18.6502			0.691699			0.345849	−	0.938290i	$-0.387591\pi$
$727$	18.6502			0.691699			0.345849	+	0.938290i	$0.387591\pi$
$728$		0			0
$729$	−19.7475	+	18.4130i	−0.731387	+	0.681962i
$730$	−6.50002	−	14.9970i	−0.240576	−	0.555065i
$731$	−10.3466	−	17.9208i	−0.382681	−	0.662824i
$732$	67.6317	−	8.50333i	2.49974	−	0.314292i
$733$	−18.7967	+	32.5568i	−0.694271	+	1.20251i	0.276155	+	0.961113i	$0.410940\pi$
$733$	−18.7967	+	32.5568i	−0.694271	+	1.20251i	−0.970426	+	0.241399i	$0.922394\pi$
$734$	53.8821			1.98882
$735$		0			0
$736$	−21.3813			−0.788124
$737$	−20.5852	+	35.6546i	−0.758264	+	1.31335i
$738$	6.28358	−	22.4032i	0.231302	−	0.824672i
$739$	24.7189	+	42.8144i	0.909300	+	1.57495i	0.815039	+	0.579406i	$0.196715\pi$
$739$	24.7189	+	42.8144i	0.909300	+	1.57495i	0.0942603	+	0.995548i	$0.469951\pi$
$740$	19.8924	−	8.62177i	0.731259	−	0.316942i
$741$	8.89228	−	21.1190i	0.326666	−	0.775826i
$742$		0			0
$743$	−42.7477			−1.56826			−0.784131	−	0.620596i	$-0.786891\pi$
$743$	−42.7477			−1.56826			−0.784131	+	0.620596i	$0.786891\pi$
$744$	13.5572	+	17.8828i	0.497030	+	0.655616i
$745$	2.76689	−	24.0343i	0.101371	−	0.880550i
$746$	42.1929	−	24.3601i	1.54479	−	0.891886i
$747$	1.97788	+	7.74123i	0.0723667	+	0.283237i
$748$	−32.3236			−1.18187
$749$		0			0
$750$	−31.5218	−	28.9200i	−1.15101	−	1.05601i
$751$	−2.79526	+	4.84152i	−0.102000	+	0.176670i	−0.912509	−	0.409057i	$-0.865858\pi$
$751$	−2.79526	+	4.84152i	−0.102000	+	0.176670i	0.810508	+	0.585727i	$0.199191\pi$
$752$	6.36310	−	3.67374i	0.232039	−	0.133968i
$753$	1.97217	+	15.6857i	0.0718698	+	0.571620i
$754$	−28.0183	−	16.1764i	−1.02037	−	0.589109i
$755$	11.0517	−	14.8989i	0.402211	−	0.542227i
$756$		0			0
$757$		−	42.9931i		−	1.56261i	−0.624150	−	0.781305i	$-0.714555\pi$
$757$		−	42.9931i		−	1.56261i	0.624150	−	0.781305i	$-0.285445\pi$
$758$	−1.27906	+	2.21539i	−0.0464574	+	0.0804666i
$759$	−19.6822	+	2.47464i	−0.714417	+	0.0898237i
$760$	−1.01156	+	8.78681i	−0.0366930	+	0.318731i
$761$	−24.5715	+	42.5591i	−0.890716	+	1.54277i	−0.0516970	+	0.998663i	$0.516463\pi$
$761$	−24.5715	+	42.5591i	−0.890716	+	1.54277i	−0.839019	+	0.544102i	$0.816870\pi$
$762$	−0.886912	+	2.10640i	−0.0321294	+	0.0763068i
$763$		0			0
$764$			31.0436i			1.12312i
$765$	18.2587	+	7.46414i	0.660144	+	0.269867i
$766$	4.07358	−	2.35188i	0.147184	−	0.0849769i
$767$	25.7795	+	44.6514i	0.930843	+	1.61227i
$768$	−7.46575	+	5.65988i	−0.269397	+	0.204233i
$769$			27.0203i			0.974376i	0.873297	+	0.487188i	$0.161977\pi$
$769$			27.0203i			0.974376i	−0.873297	+	0.487188i	$0.838023\pi$
$770$		0			0
$771$	4.49412	−	10.6735i	0.161852	−	0.384395i
$772$	−4.60466	−	2.65850i	−0.165725	−	0.0956816i
$773$	−45.8267	+	26.4581i	−1.64827	+	0.951631i	−0.670515	+	0.741896i	$0.733927\pi$
$773$	−45.8267	+	26.4581i	−1.64827	+	0.951631i	−0.977758	+	0.209735i	$0.932740\pi$
$774$	−44.9046	−	12.5947i	−1.61406	−	0.452708i
$775$	−7.57267	+	32.4538i	−0.272018	+	1.16577i
$776$	8.68312			0.311706
$777$		0			0
$778$		−	53.3645i		−	1.91321i
$779$	−6.18711	−	3.57213i	−0.221676	−	0.127985i
$780$	−63.1792	−	35.6010i	−2.26218	−	1.27472i
$781$	20.9788	+	36.3364i	0.750681	+	1.30022i
$782$	−16.8797	−	9.74550i	−0.603617	−	0.348499i
$783$	10.8905	−	4.28956i	0.389193	−	0.153296i
$784$		0			0
$785$	7.20950	−	9.71926i	0.257318	−	0.346895i
$786$	17.7206	−	13.4342i	0.632072	−	0.479181i
$787$	−8.37879	−	14.5125i	−0.298672	−	0.517315i	0.677161	−	0.735835i	$-0.263210\pi$
$787$	−8.37879	−	14.5125i	−0.298672	−	0.517315i	−0.975832	+	0.218521i	$0.929877\pi$
$788$	11.6630	+	20.2009i	0.415477	+	0.719627i
$789$	33.3031	−	25.2475i	1.18562	−	0.898833i
$790$	17.2150	−	23.2078i	0.612481	−	0.825697i
$791$		0			0
$792$	−15.9218	+	15.5550i	−0.565756	+	0.552723i
$793$	76.9414	+	44.4222i	2.73227	+	1.57748i
$794$	13.2719	+	22.9876i	0.471001	+	0.815798i
$795$	−6.52640	−	3.67758i	−0.231468	−	0.130430i
$796$	25.1974	+	14.5477i	0.893099	+	0.515631i
$797$		−	55.9724i		−	1.98264i	−0.131462	−	0.991321i	$-0.541967\pi$
$797$		−	55.9724i		−	1.98264i	0.131462	−	0.991321i	$-0.458033\pi$
$798$		0			0
$799$	14.7401			0.521466
$800$	−34.6965	−	8.09598i	−1.22671	−	0.286236i
$801$	−10.9501	+	39.0410i	−0.386904	+	1.37945i
$802$	58.9813	−	34.0529i	2.08270	−	1.20245i
$803$	−10.9380	−	6.31503i	−0.385992	−	0.222853i
$804$	−20.8794	+	49.5882i	−0.736359	+	1.74884i
$805$		0			0
$806$			95.7274i			3.37186i
$807$	26.2356	−	19.8895i	0.923536	−	0.700143i
$808$	−8.62160	−	14.9331i	−0.303307	−	0.525343i
$809$	36.4604	−	21.0504i	1.28188	−	0.740094i	0.304689	−	0.952452i	$-0.401447\pi$
$809$	36.4604	−	21.0504i	1.28188	−	0.740094i	0.977192	+	0.212358i	$0.0681142\pi$
$810$	41.1909	−	16.7240i	1.44730	−	0.587620i
$811$			1.35051i			0.0474227i	0.999719	+	0.0237113i	$0.00754826\pi$
$811$			1.35051i			0.0474227i	−0.999719	+	0.0237113i	$0.992452\pi$
$812$		0			0
$813$	−7.96388	+	18.9141i	−0.279306	+	0.663346i
$814$	14.1934	−	24.5837i	0.497479	−	0.861659i
$815$	4.38758	−	38.1123i	0.153690	−	1.33502i
$816$	7.40686	−	0.931265i	0.259292	−	0.0326008i
$817$	−7.15993	+	12.4014i	−0.250494	+	0.433869i
$818$			34.6141i			1.21025i
$819$		0			0
$820$	−13.4701	+	18.1592i	−0.470395	+	0.634147i
$821$	9.82457	+	5.67222i	0.342880	+	0.197962i	0.661545	−	0.749906i	$-0.269901\pi$
$821$	9.82457	+	5.67222i	0.342880	+	0.197962i	−0.318665	+	0.947867i	$0.603235\pi$
$822$	−0.522030	−	4.15199i	−0.0182079	−	0.144817i
$823$	−26.1348	+	15.0889i	−0.911002	+	0.525967i	−0.880754	−	0.473575i	$-0.842963\pi$
$823$	−26.1348	+	15.0889i	−0.911002	+	0.525967i	−0.0302488	+	0.999542i	$0.509630\pi$
$824$	−1.28533	+	2.22626i	−0.0447766	+	0.0775554i
$825$	−32.8763	−	3.43689i	−1.14460	−	0.119657i
$826$		0			0
$827$	−34.7911			−1.20981			−0.604903	−	0.796299i	$-0.706788\pi$
$827$	−34.7911			−1.20981			−0.604903	+	0.796299i	$0.706788\pi$
$828$	−25.1178	+	6.41757i	−0.872904	+	0.223026i
$829$	3.50678	−	2.02464i	0.121796	−	0.0703187i	−0.437864	−	0.899041i	$-0.644265\pi$
$829$	3.50678	−	2.02464i	0.121796	−	0.0703187i	0.559660	+	0.828722i	$0.310932\pi$
$830$	1.50458	−	13.0694i	0.0522246	−	0.453645i
$831$	17.2843	+	22.7991i	0.599585	+	0.790892i
$832$	−83.2833			−2.88733
$833$		0			0
$834$	10.9276	−	25.9529i	0.378393	−	0.898676i
$835$	−19.7079	+	8.54181i	−0.682021	+	0.295602i
$836$	11.1841	+	19.3715i	0.386811	+	0.669977i
$837$	−27.1035	−	21.5602i	−0.936834	−	0.745229i
$838$	21.6460	−	37.4920i	0.747749	−	1.29514i
$839$	−25.8653			−0.892969			−0.446485	−	0.894791i	$-0.647324\pi$
$839$	−25.8653			−0.892969			−0.446485	+	0.894791i	$0.647324\pi$
$840$		0			0
$841$	23.9258			0.825029
$842$	35.9846	−	62.3272i	1.24011	−	2.14794i
$843$	17.3701	−	2.18394i	0.598258	−	0.0752190i
$844$	−15.3816	−	26.6417i	−0.529457	−	0.917047i
$845$	−26.0285	−	60.0537i	−0.895408	−	2.06591i
$846$	23.7627	−	23.2153i	0.816978	−	0.798158i
$847$		0			0
$848$	−2.83509			−0.0973573
$849$	8.28429	−	6.28042i	0.284316	−	0.215543i
$850$	−23.7015	−	22.2060i	−0.812953	−	0.761660i
$851$	8.74849	−	5.05094i	0.299894	−	0.173144i
$852$	33.1265	+	43.6961i	1.13490	+	1.49700i
$853$	−37.5709			−1.28640			−0.643201	−	0.765697i	$-0.722394\pi$
$853$	−37.5709			−1.28640			−0.643201	+	0.765697i	$0.722394\pi$
$854$		0			0
$855$	−1.84435	−	13.5250i	−0.0630755	−	0.462547i
$856$	3.23117	−	5.59655i	0.110439	−	0.191286i
$857$	19.8563	−	11.4640i	0.678278	−	0.391604i	−0.120928	−	0.992661i	$-0.538587\pi$
$857$	19.8563	−	11.4640i	0.678278	−	0.391604i	0.799206	+	0.601057i	$0.205254\pi$
$858$	−94.2098	+	11.8450i	−3.21627	+	0.404382i
$859$	−16.2512	−	9.38264i	−0.554484	−	0.320132i	0.196444	−	0.980515i	$-0.437060\pi$
$859$	−16.2512	−	9.38264i	−0.554484	−	0.320132i	−0.750929	+	0.660383i	$0.770394\pi$
$860$	36.3981	+	26.9992i	1.24117	+	0.920666i
$861$		0			0
$862$		−	61.6092i		−	2.09842i
$863$	−4.23086	+	7.32807i	−0.144020	+	0.249450i	−0.929007	−	0.370062i	$-0.879336\pi$
$863$	−4.23086	+	7.32807i	−0.144020	+	0.249450i	0.784987	+	0.619512i	$0.212670\pi$
$864$	23.0501	−	28.9765i	0.784180	−	0.985800i
$865$	−2.60144	+	22.5972i	−0.0884517	+	0.768329i
$866$	−3.83659	+	6.64517i	−0.130373	+	0.225812i
$867$	−13.3348	−	5.61470i	−0.452874	−	0.190685i
$868$		0			0
$869$		−	22.3281i		−	0.757428i
$870$	−19.2714	+	0.201509i	−0.653360	+	0.00683181i
$871$	−60.7329	+	35.0641i	−2.05785	+	1.18810i
$872$	−11.9535	−	20.7041i	−0.404797	−	0.701129i
$873$	−12.9836	+	3.31728i	−0.439427	+	0.112273i
$874$			13.4880i			0.456238i
$875$		0			0
$876$	−15.2125	−	6.40529i	−0.513981	−	0.216415i
$877$	3.27867	+	1.89294i	0.110713	+	0.0639201i	0.554334	−	0.832294i	$-0.312973\pi$
$877$	3.27867	+	1.89294i	0.110713	+	0.0639201i	−0.443621	+	0.896214i	$0.646306\pi$
$878$	7.55301	−	4.36073i	0.254902	−	0.147168i
$879$	−6.10710	+	0.767845i	−0.205987	+	0.0258988i
$880$	−11.4782	+	4.97490i	−0.386931	+	0.167704i
$881$	−54.6531			−1.84131			−0.920654	−	0.390379i	$-0.872344\pi$
$881$	−54.6531			−1.84131			−0.920654	+	0.390379i	$0.872344\pi$
$882$		0			0
$883$			28.1492i			0.947295i	0.880715	+	0.473647i	$0.157063\pi$
$883$			28.1492i			0.947295i	−0.880715	+	0.473647i	$0.842937\pi$
$884$	−47.6824	−	27.5295i	−1.60373	−	0.925916i
$885$	26.7578	+	15.0778i	0.899453	+	0.506834i
$886$	17.7065	+	30.6686i	0.594862	+	1.03033i
$887$	−26.0011	−	15.0117i	−0.873032	−	0.504045i	−0.00467726	−	0.999989i	$-0.501489\pi$
$887$	−26.0011	−	15.0117i	−0.873032	−	0.504045i	−0.868355	+	0.495944i	$0.834822\pi$
$888$	4.39873	−	10.4469i	0.147612	−	0.350575i
$889$		0			0
$890$	39.7751	−	53.6215i	1.33326	−	1.79740i
$891$	17.8647	−	29.3416i	0.598489	−	0.982980i
$892$	5.94975	+	10.3053i	0.199212	+	0.345046i
$893$	−5.10015	−	8.83371i	−0.170670	−	0.295609i
$894$	−25.0095	−	32.9892i	−0.836442	−	1.10332i
$895$	42.4816	+	31.5118i	1.42000	+	1.05332i
$896$		0			0
$897$	−31.1420	−	13.1125i	−1.03980	−	0.437814i
$898$	−40.3668	−	23.3058i	−1.34706	−	0.777724i
$899$	7.50689	+	13.0023i	0.250369	+	0.433651i
$900$	−43.1900	+	0.903323i	−1.43967	+	0.0301108i
$901$	−4.92559	−	2.84379i	−0.164095	−	0.0947404i
$902$			29.6036i			0.985691i
$903$		0			0
$904$	39.7702			1.32274
$905$	−32.0735	+	13.9013i	−1.06616	+	0.462095i
$906$	−3.95977	−	31.4942i	−0.131555	−	1.04633i
$907$	16.8295	−	9.71653i	0.558815	−	0.322632i	−0.193855	−	0.981030i	$-0.562099\pi$
$907$	16.8295	−	9.71653i	0.558815	−	0.322632i	0.752670	+	0.658398i	$0.228766\pi$
$908$	−17.8969	−	10.3328i	−0.593931	−	0.342906i
$909$	18.5966	+	19.0351i	0.616809	+	0.631354i
$910$		0			0
$911$			53.2832i			1.76535i	0.469982	+	0.882676i	$0.344261\pi$
$911$			53.2832i			1.76535i	−0.469982	+	0.882676i	$0.655739\pi$
$912$	−3.12092	−	4.11670i	−0.103344	−	0.136318i
$913$	−5.08280	−	8.80366i	−0.168216	−	0.291359i
$914$	−18.3787	+	10.6110i	−0.607914	+	0.350979i
$915$	52.9213	−	0.553367i	1.74952	−	0.0182938i
$916$			30.0988i			0.994493i
$917$		0			0
$918$	31.4046	−	12.3697i	1.03650	−	0.408261i
$919$	−22.5064	+	38.9822i	−0.742416	+	1.28590i	0.208976	+	0.977921i	$0.432987\pi$
$919$	−22.5064	+	38.9822i	−0.742416	+	1.28590i	−0.951392	+	0.307982i	$0.900346\pi$
$920$	12.9570	+	1.49163i	0.427178	+	0.0491777i
$921$	−6.27348	−	49.8965i	−0.206718	−	1.64414i
$922$	27.1015	−	46.9412i	0.892541	−	1.54593i
$923$			71.4693i			2.35244i
$924$		0			0
$925$	16.1092	−	4.88383i	0.529666	−	0.160579i
$926$	−27.9073	−	16.1123i	−0.917092	−	0.529483i
$927$	1.07139	−	3.81989i	0.0351892	−	0.125462i
$928$	−13.9008	+	8.02565i	−0.456317	+	0.263455i
$929$	21.3495	−	36.9785i	0.700455	−	1.21322i	−0.267852	−	0.963460i	$-0.586314\pi$
$929$	21.3495	−	36.9785i	0.700455	−	1.21322i	0.968307	−	0.249764i	$-0.0803530\pi$
$930$	29.0270	+	49.0838i	0.951834	+	1.60952i
$931$		0			0
$932$	−11.2360			−0.368048
$933$	−11.9313	+	9.04526i	−0.390613	+	0.296128i
$934$	−34.2800	+	19.7916i	−1.12168	+	0.647600i
$935$	−24.9321	−	2.87024i	−0.815366	−	0.0938668i
$936$	−36.7351	+	9.38579i	−1.20073	+	0.306784i
$937$	26.4685			0.864688			0.432344	−	0.901709i	$-0.357687\pi$
$937$	26.4685			0.864688			0.432344	+	0.901709i	$0.357687\pi$
$938$		0			0
$939$	−17.3235	−	7.29415i	−0.565330	−	0.238036i
$940$	−29.6189	+	12.8375i	−0.966063	+	0.418711i
$941$	−15.8545	−	27.4609i	−0.516843	−	0.895199i	−0.999809	−	0.0195596i	$-0.993774\pi$
$941$	−15.8545	−	27.4609i	−0.516843	−	0.895199i	0.482965	−	0.875640i	$-0.339560\pi$
$942$	−2.58314	−	20.5451i	−0.0841633	−	0.669397i
$943$	−5.26744	+	9.12347i	−0.171531	+	0.297101i
$944$	11.6237			0.378318
$945$		0			0
$946$	59.3370			1.92921
$947$	−5.97276	+	10.3451i	−0.194089	+	0.336171i	−0.946601	−	0.322406i	$-0.895508\pi$
$947$	−5.97276	+	10.3451i	−0.194089	+	0.336171i	0.752513	+	0.658578i	$0.228842\pi$
$948$	−3.64015	−	28.9521i	−0.118227	−	0.940321i
$949$	−10.7568	−	18.6314i	−0.349181	−	0.604800i
$950$	−5.10720	+	21.8877i	−0.165699	+	0.710130i
$951$	14.9111	+	6.27839i	0.483524	+	0.203591i
$952$		0			0
$953$	−1.76384			−0.0571364			−0.0285682	−	0.999592i	$-0.509095\pi$
$953$	−1.76384			−0.0571364			−0.0285682	+	0.999592i	$0.509095\pi$
$954$	−12.4195	+	3.17318i	−0.402097	+	0.102735i
$955$	−2.75658	+	23.9448i	−0.0892008	+	0.774835i
$956$	59.3284	−	34.2532i	1.91882	−	1.10783i
$957$	−11.8673	+	8.99673i	−0.383615	+	0.290823i
$958$	−6.54980			−0.211614
$959$		0			0
$960$	−42.7031	+	25.2536i	−1.37824	+	0.815058i
$961$	6.71186	−	11.6253i	0.216511	−	0.375009i
$962$	41.8752	−	24.1766i	1.35011	−	0.779486i
$963$	−2.69336	+	9.60275i	−0.0867922	+	0.309444i
$964$	33.1282	+	19.1266i	1.06699	+	0.616026i
$965$	−3.31564	−	2.45946i	−0.106734	−	0.0791728i
$966$		0			0
$967$			53.4014i			1.71727i	0.512584	+	0.858637i	$0.328688\pi$
$967$			53.4014i			1.71727i	−0.512584	+	0.858637i	$0.671312\pi$
$968$	3.46869	−	6.00795i	0.111488	−	0.193103i
$969$	−1.29285	−	10.2827i	−0.0415323	−	0.330329i
$970$	21.9199	+	2.52347i	0.703805	+	0.0810236i
$971$	−23.9577	+	41.4959i	−0.768838	+	1.33167i	0.169356	+	0.985555i	$0.445831\pi$
$971$	−23.9577	+	41.4959i	−0.768838	+	1.33167i	−0.938193	+	0.346111i	$0.887502\pi$
$972$	18.3810	−	40.9588i	0.589571	−	1.31375i
$973$		0			0
$974$		−	73.4642i		−	2.35394i
$975$	−45.5706	−	33.0702i	−1.45943	−	1.05909i
$976$	17.3460	−	10.0147i	0.555231	−	0.320563i
$977$	4.07411	+	7.05657i	0.130342	+	0.225760i	0.923809	−	0.382855i	$-0.125059\pi$
$977$	4.07411	+	7.05657i	0.130342	+	0.225760i	−0.793466	+	0.608614i	$0.791726\pi$
$978$	−39.6586	−	52.3124i	−1.26814	−	1.67277i
$979$		−	51.5889i		−	1.64879i
$980$		0			0
$981$	25.7834	+	26.3914i	0.823201	+	0.842612i
$982$	48.7636	+	28.1537i	1.55611	+	0.898420i
$983$	−12.6460	+	7.30116i	−0.403344	+	0.232871i	−0.687926	−	0.725781i	$-0.741479\pi$
$983$	−12.6460	+	7.30116i	−0.403344	+	0.232871i	0.284582	+	0.958652i	$0.408145\pi$
$984$	1.47465	+	11.7287i	0.0470101	+	0.373897i
$985$	7.20222	+	16.6172i	0.229482	+	0.529467i
$986$	−14.6322			−0.465986
$987$		0			0
$988$			38.1014i			1.21217i
$989$	18.2870	+	10.5580i	0.581492	+	0.335725i
$990$	−44.7139	+	34.6403i	−1.42110	+	1.10094i
$991$	−7.84118	−	13.5813i	−0.249083	−	0.431425i	0.714188	−	0.699953i	$-0.246796\pi$
$991$	−7.84118	−	13.5813i	−0.249083	−	0.431425i	−0.963272	+	0.268529i	$0.913463\pi$
$992$	41.1307	+	23.7468i	1.30590	+	0.753962i
$993$	−4.64398	−	1.95537i	−0.147372	−	0.0620519i
$994$		0			0
$995$	18.1437	+	13.4585i	0.575194	+	0.426664i
$996$	−8.02597	−	10.5868i	−0.254313	−	0.335455i
$997$	13.5211	+	23.4192i	0.428218	+	0.741695i	0.996715	−	0.0809903i	$-0.0258083\pi$
$997$	13.5211	+	23.4192i	0.428218	+	0.741695i	−0.568497	+	0.822685i	$0.692475\pi$
$998$	37.1913	+	64.4173i	1.17727	+	2.03909i
$999$	−2.58614	+	17.3014i	−0.0818219	+	0.547391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.g.509.3		64
3.2	odd	2	inner	735.2.p.g.509.32		64
5.4	even	2	inner	735.2.p.g.509.30		64
7.2	even	3		735.2.g.c.734.29	yes	32
7.3	odd	6	inner	735.2.p.g.374.1		64
7.4	even	3	inner	735.2.p.g.374.4		64
7.5	odd	6		735.2.g.c.734.32	yes	32
7.6	odd	2	inner	735.2.p.g.509.2		64
15.14	odd	2	inner	735.2.p.g.509.1		64
21.2	odd	6		735.2.g.c.734.2	yes	32
21.5	even	6		735.2.g.c.734.3	yes	32
21.11	odd	6	inner	735.2.p.g.374.31		64
21.17	even	6	inner	735.2.p.g.374.30		64
21.20	even	2	inner	735.2.p.g.509.29		64
35.4	even	6	inner	735.2.p.g.374.29		64
35.9	even	6		735.2.g.c.734.4	yes	32
35.19	odd	6		735.2.g.c.734.1	✓	32
35.24	odd	6	inner	735.2.p.g.374.32		64
35.34	odd	2	inner	735.2.p.g.509.31		64
105.44	odd	6		735.2.g.c.734.31	yes	32
105.59	even	6	inner	735.2.p.g.374.3		64
105.74	odd	6	inner	735.2.p.g.374.2		64
105.89	even	6		735.2.g.c.734.30	yes	32
105.104	even	2	inner	735.2.p.g.509.4		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.1	✓	32	35.19	odd	6
735.2.g.c.734.2	yes	32	21.2	odd	6
735.2.g.c.734.3	yes	32	21.5	even	6
735.2.g.c.734.4	yes	32	35.9	even	6
735.2.g.c.734.29	yes	32	7.2	even	3
735.2.g.c.734.30	yes	32	105.89	even	6
735.2.g.c.734.31	yes	32	105.44	odd	6
735.2.g.c.734.32	yes	32	7.5	odd	6
735.2.p.g.374.1		64	7.3	odd	6	inner
735.2.p.g.374.2		64	105.74	odd	6	inner
735.2.p.g.374.3		64	105.59	even	6	inner
735.2.p.g.374.4		64	7.4	even	3	inner
735.2.p.g.374.29		64	35.4	even	6	inner
735.2.p.g.374.30		64	21.17	even	6	inner
735.2.p.g.374.31		64	21.11	odd	6	inner
735.2.p.g.374.32		64	35.24	odd	6	inner
735.2.p.g.509.1		64	15.14	odd	2	inner
735.2.p.g.509.2		64	7.6	odd	2	inner
735.2.p.g.509.3		64	1.1	even	1	trivial
735.2.p.g.509.4		64	105.104	even	2	inner
735.2.p.g.509.29		64	21.20	even	2	inner
735.2.p.g.509.30		64	5.4	even	2	inner
735.2.p.g.509.31		64	35.34	odd	2	inner
735.2.p.g.509.32		64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10453 + 1.91310i) q^{2} +(0.216070 + 1.71852i) q^{3} +(-1.43998 - 2.49412i) q^{4} +(-0.889228 - 2.05165i) q^{5} +(-3.52637 - 1.48480i) q^{6} +1.94389 q^{8} +(-2.90663 + 0.742640i) q^{9} +(4.90720 + 0.564929i) q^{10} +(3.30554 - 1.90846i) q^{11} +(3.97506 - 3.01354i) q^{12} +6.50161 q^{13} +(3.33367 - 1.97146i) q^{15} +(0.732874 - 1.26937i) q^{16} +(2.54654 - 1.47025i) q^{17} +(1.78971 - 6.38095i) q^{18} +(-1.76224 - 1.01743i) q^{19} +(-3.83659 + 5.17218i) q^{20} +8.43180i q^{22} +(-1.50029 + 2.59858i) q^{23} +(0.420016 + 3.34061i) q^{24} +(-3.41855 + 3.64877i) q^{25} +(-7.18123 + 12.4383i) q^{26} +(-1.90428 - 4.83464i) q^{27} +2.25259i q^{29} +(0.0894567 + 8.55520i) q^{30} +(5.77216 - 3.33256i) q^{31} +(3.56285 + 6.17104i) q^{32} +(3.99395 + 5.26828i) q^{33} +6.49574i q^{34} +(6.03772 + 6.18009i) q^{36} +(-2.91560 - 1.68332i) q^{37} +(3.89289 - 2.24756i) q^{38} +(1.40480 + 11.1732i) q^{39} +(-1.72856 - 3.98818i) q^{40} +3.51094 q^{41} -7.03729i q^{43} +(-9.51983 - 5.49628i) q^{44} +(4.10829 + 5.30301i) q^{45} +(-3.31424 - 5.74043i) q^{46} +(4.34120 + 2.50639i) q^{47} +(2.33980 + 0.985185i) q^{48} +(-3.20459 - 10.5702i) q^{50} +(3.07688 + 4.05861i) q^{51} +(-9.36219 - 16.2158i) q^{52} +(-0.967113 - 1.67509i) q^{53} +(11.3525 + 1.69693i) q^{54} +(-6.85487 - 5.08477i) q^{55} +(1.36770 - 3.24827i) q^{57} +(-4.30944 - 2.48806i) q^{58} +(3.96509 + 6.86774i) q^{59} +(-9.71747 - 5.47572i) q^{60} +(11.8342 + 6.83249i) q^{61} +14.7237i q^{62} -12.8096 q^{64} +(-5.78141 - 13.3390i) q^{65} +(-14.4902 + 1.82186i) q^{66} +(-9.34121 + 5.39315i) q^{67} +(-7.33395 - 4.23426i) q^{68} +(-4.78988 - 2.01681i) q^{69} +10.9926i q^{71} +(-5.65016 + 1.44361i) q^{72} +(-1.65449 - 2.86566i) q^{73} +(6.44074 - 3.71856i) q^{74} +(-7.00913 - 5.08646i) q^{75} +5.86030i q^{76} +(-22.9271 - 9.65357i) q^{78} +(2.92489 - 5.06605i) q^{79} +(-3.25601 - 0.374839i) q^{80} +(7.89697 - 4.31716i) q^{81} +(-3.87795 + 6.71680i) q^{82} -2.66330i q^{83} +(-5.28089 - 3.91724i) q^{85} +(13.4631 + 7.77291i) q^{86} +(-3.87112 + 0.486717i) q^{87} +(6.42561 - 3.70983i) q^{88} +(6.75793 - 11.7051i) q^{89} +(-14.6830 + 2.00225i) q^{90} +8.64156 q^{92} +(6.97425 + 9.19951i) q^{93} +(-9.58999 + 5.53678i) q^{94} +(-0.520378 + 4.52022i) q^{95} +(-9.83524 + 7.45621i) q^{96} +4.46688 q^{97} +(-8.19069 + 8.00200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) \) 64 * q - 16 * q^4 - 40 * q^9 + 32 * q^15 + 16 * q^16 - 64 * q^25 - 56 * q^30 - 32 * q^36 + 56 * q^39 + 32 * q^46 + 40 * q^51 - 8 * q^60 - 352 * q^64 - 48 * q^79 + 40 * q^81 - 128 * q^85 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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