LMFDB - Embedded newform 735.2.p.g.374.31

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			374.31
Character	$\chi$	$=$	735.374
Dual form			735.2.p.g.509.31

$q$-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} +(-2.22140 - 0.255732i) q^{5} +(3.52637 - 1.48480i) q^{6} -1.94389 q^{8} +(-2.90663 - 0.742640i) q^{9} +(-1.96436 - 4.53223i) q^{10} +(3.30554 + 1.90846i) q^{11} +(3.97506 + 3.01354i) q^{12} +6.50161 q^{13} +(-0.919457 + 3.76226i) 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} +(4.86920 + 1.13616i) q^{25} +(7.18123 + 12.4383i) q^{26} +(-1.90428 + 4.83464i) q^{27} -2.25259i q^{29} +(-8.21317 + 2.39652i) 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} +(4.31815 + 0.497115i) q^{40} -3.51094 q^{41} -7.03729i q^{43} +(-9.51983 + 5.49628i) q^{44} +(6.26685 + 2.39302i) 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} +(-8.05952 - 7.71082i) q^{60} +(-11.8342 + 6.83249i) q^{61} -14.7237i q^{62} -12.8096 q^{64} +(-14.4427 - 1.66267i) 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} +(3.00461 - 8.12233i) q^{75} +5.86030i q^{76} +(22.9271 - 9.65357i) q^{78} +(2.92489 + 5.06605i) q^{79} +(-1.30338 - 3.00720i) 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} +(2.34385 + 14.6323i) q^{90} -8.64156 q^{92} +(-6.97425 + 9.19951i) q^{93} +(9.58999 + 5.53678i) q^{94} +(-4.17481 + 1.80945i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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	0.931347	+	0.364133i	$0.118635\pi$
$2$	1.10453	+	1.91310i	0.781022	+	1.35277i	−0.150325	+	0.988637i	$0.548032\pi$
$3$	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
$5$	−2.22140	−	0.255732i	−0.993439	−	0.114367i
$5$	−2.22140	−	0.255732i	−0.993439	−	0.114367i
$6$	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
$10$	−1.96436	−	4.53223i	−0.621185	−	1.43322i
$11$	3.30554	+	1.90846i	0.996659	+	0.575421i	0.907258	−	0.420575i	$-0.138172\pi$
$11$	3.30554	+	1.90846i	0.996659	+	0.575421i	0.0894006	+	0.995996i	$0.471505\pi$
$12$	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
$15$	−0.919457	+	3.76226i	−0.237403	+	0.971411i
$16$	0.732874	+	1.26937i	0.183218	+	0.317344i
$17$	2.54654	+	1.47025i	0.617628	+	0.356587i	0.775945	−	0.630801i	$-0.217274\pi$
$17$	2.54654	+	1.47025i	0.617628	+	0.356587i	−0.158317	+	0.987388i	$0.550607\pi$
$18$	−1.78971	−	6.38095i	−0.421839	−	1.50401i
$19$	1.76224	−	1.01743i	0.404285	−	0.233414i	−0.284046	−	0.958811i	$-0.591677\pi$
$19$	1.76224	−	1.01743i	0.404285	−	0.233414i	0.688331	+	0.725397i	$0.258344\pi$
$20$	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	$-0.0653888\pi$
$23$	1.50029	+	2.59858i	0.312832	+	0.541842i	−0.666142	+	0.745825i	$0.732056\pi$
$24$	−0.420016	+	3.34061i	−0.0857353	+	0.681900i
$25$	4.86920	+	1.13616i	0.973840	+	0.227233i
$26$	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	$-0.932931\pi$
$29$		−	2.25259i		−	0.418296i	0.977884	−	0.209148i	$-0.0670690\pi$
$30$	−8.21317	+	2.39652i	−1.49951	+	0.437542i
$31$	−5.77216	−	3.33256i	−1.03671	−	0.598545i	−0.117810	−	0.993036i	$-0.537587\pi$
$31$	−5.77216	−	3.33256i	−1.03671	−	0.598545i	−0.918900	+	0.394491i	$0.870921\pi$
$32$	−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	$-0.577414\pi$
$37$	2.91560	−	1.68332i	0.479321	−	0.276736i	0.720134	+	0.693835i	$0.244081\pi$
$38$	3.89289	+	2.24756i	0.631510	+	0.364603i
$39$	1.40480	−	11.1732i	0.224948	−	1.78914i
$40$	4.31815	+	0.497115i	0.682759	+	0.0786008i
$41$	−3.51094			−0.548317			−0.274158	−	0.961685i	$-0.588399\pi$
$41$	−3.51094			−0.548317			−0.274158	+	0.961685i	$0.588399\pi$
$42$		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
$45$	6.26685	+	2.39302i	0.934208	+	0.356730i
$46$	−3.31424	+	5.74043i	−0.488658	+	0.846380i
$47$	4.34120	−	2.50639i	0.633229	−	0.365595i	−0.148772	−	0.988871i	$-0.547532\pi$
$47$	4.34120	−	2.50639i	0.633229	−	0.365595i	0.782002	+	0.623276i	$0.214199\pi$
$48$	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	$-0.790923\pi$
$53$	0.967113	−	1.67509i	0.132843	−	0.230091i	0.924771	+	0.380523i	$0.124256\pi$
$54$	−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	0.483612	+	0.875283i	$0.339325\pi$
$59$	−3.96509	+	6.86774i	−0.516211	+	0.894104i	−0.999823	+	0.0188214i	$0.994009\pi$
$60$	−8.05952	−	7.71082i	−1.04048	−	0.995462i
$61$	−11.8342	+	6.83249i	−1.51522	+	0.874810i	−0.515375	+	0.856965i	$0.672347\pi$
$61$	−11.8342	+	6.83249i	−1.51522	+	0.874810i	−0.999841	+	0.0178455i	$0.994319\pi$
$62$		−	14.7237i		−	1.86991i
$63$		0			0
$64$	−12.8096			−1.60121
$65$	−14.4427	−	1.66267i	−1.79139	−	0.206229i
$66$	14.4902	+	1.82186i	1.78362	+	0.224255i
$67$	9.34121	+	5.39315i	1.14121	+	0.658878i	0.946730	−	0.322029i	$-0.104365\pi$
$67$	9.34121	+	5.39315i	1.14121	+	0.658878i	0.194480	+	0.980906i	$0.437698\pi$
$68$	−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	$-0.773809\pi$
$71$		−	10.9926i		−	1.30458i	0.757971	−	0.652288i	$-0.226191\pi$
$72$	5.65016	+	1.44361i	0.665878	+	0.170131i
$73$	−1.65449	+	2.86566i	−0.193643	+	0.335400i	−0.946455	−	0.322836i	$-0.895364\pi$
$73$	−1.65449	+	2.86566i	−0.193643	+	0.335400i	0.752812	+	0.658236i	$0.228697\pi$
$74$	6.44074	+	3.71856i	0.748721	+	0.432274i
$75$	3.00461	−	8.12233i	0.346942	−	0.937886i
$76$			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	0.982329	−	0.187164i	$-0.0599296\pi$
$79$	2.92489	+	5.06605i	0.329075	+	0.569975i	−0.653253	+	0.757140i	$0.726596\pi$
$80$	−1.30338	−	3.00720i	−0.145723	−	0.336215i
$81$	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	$0.0466939\pi$
$83$			2.66330i			0.292336i	−0.989260	+	0.146168i	$0.953306\pi$
$84$		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	−0.962441	−	0.271492i	$-0.912483\pi$
$89$	−6.75793	−	11.7051i	−0.716339	−	1.24074i	0.246101	−	0.969244i	$-0.420850\pi$
$90$	2.34385	+	14.6323i	0.247063	+	1.54238i
$91$		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
$95$	−4.17481	+	1.80945i	−0.428327	+	0.185646i
$96$	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
$100$	−9.84529	+	10.5083i	−0.984529	+	1.05083i
$101$	4.43523	−	7.68205i	0.441322	−	0.764392i	−0.556466	−	0.830871i	$-0.687843\pi$
$101$	4.43523	−	7.68205i	0.441322	−	0.764392i	0.997788	+	0.0664781i	$0.0211763\pi$
$102$	11.1631	+	1.40353i	1.10531	+	0.138970i
$103$	−0.661216	−	1.14526i	−0.0651516	−	0.112846i	0.831610	−	0.555361i	$-0.187420\pi$
$103$	−0.661216	−	1.14526i	−0.0651516	−	0.112846i	−0.896761	+	0.442515i	$0.854086\pi$
$104$	−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	$-0.218040\pi$
$107$	−1.66222	−	2.87905i	−0.160693	−	0.278328i	−0.935117	+	0.354338i	$0.884706\pi$
$108$	−9.31604	−	11.7113i	−0.896437	−	1.12692i
$109$	−6.14927	+	10.6509i	−0.588994	+	1.02017i	0.405371	+	0.914152i	$0.367142\pi$
$109$	−6.14927	+	10.6509i	−0.588994	+	1.02017i	−0.994365	+	0.106015i	$0.966191\pi$
$110$	2.15628	−	18.7304i	0.205593	−	1.78587i
$111$	−2.26285	−	5.37423i	−0.214780	−	0.510099i
$112$		0			0
$113$	−20.4591			−1.92463			−0.962314	−	0.271941i	$-0.912334\pi$
$113$	−20.4591			−1.92463			−0.962314	+	0.271941i	$0.912334\pi$
$114$	4.70362	−	6.20438i	0.440534	−	0.581094i
$115$	−2.66820	−	6.15615i	−0.248811	−	0.574064i
$116$	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
$120$	1.78732	−	7.31342i	0.163160	−	0.667620i
$121$	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
$130$	−12.7715	−	29.4668i	−1.12013	−	2.58441i
$131$	2.90591	+	5.03319i	0.253891	+	0.439752i	0.964594	−	0.263741i	$-0.0849563\pi$
$131$	2.90591	+	5.03319i	0.253891	+	0.439752i	−0.710703	+	0.703492i	$0.751623\pi$
$132$	7.38852	+	17.5476i	0.643088	+	1.52732i
$133$		0			0
$134$			23.8276i			2.05839i
$135$	5.46653	−	10.2527i	0.470484	−	0.882409i
$136$	−4.95020	−	2.85800i	−0.424476	−	0.245071i
$137$	−0.546844	+	0.947161i	−0.0467200	+	0.0809215i	−0.888440	−	0.458993i	$-0.848210\pi$
$137$	−0.546844	+	0.947161i	−0.0467200	+	0.0809215i	0.841720	+	0.539915i	$0.181544\pi$
$138$	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
$145$	−0.576060	+	5.00390i	−0.0478392	+	0.415551i
$146$	−7.30973			−0.604958
$147$		0			0
$148$			9.69579i			0.796989i
$149$	9.36993	−	5.40973i	0.767615	−	0.443183i	−0.0644082	−	0.997924i	$-0.520516\pi$
$149$	9.36993	−	5.40973i	0.767615	−	0.443183i	0.832023	+	0.554741i	$0.187183\pi$
$150$	18.8576	−	3.22324i	1.53971	−	0.263177i
$151$	4.14799	−	7.18453i	0.337559	−	0.584669i	−0.646414	−	0.762987i	$-0.723732\pi$
$151$	4.14799	−	7.18453i	0.337559	−	0.584669i	0.983973	+	0.178318i	$0.0570655\pi$
$152$	−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	−0.737612	−	0.675225i	$-0.764046\pi$
$157$	2.70593	−	4.68680i	0.215957	−	0.374048i	0.953568	+	0.301178i	$0.0973797\pi$
$158$	−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	$-0.901195\pi$
$163$	−14.8583	+	8.57846i	−1.16379	+	0.671917i	−0.211584	+	0.977360i	$0.567862\pi$
$164$	5.05569	−	8.75671i	0.394783	−	0.683784i
$165$	−10.2194	+	10.6816i	−0.795580	+	0.831559i
$166$	−5.09518	+	2.94170i	−0.395463	+	0.228320i
$167$			9.60588i			0.743325i	0.928368	+	0.371663i	$0.121212\pi$
$167$			9.60588i			0.743325i	−0.928368	+	0.371663i	$0.878788\pi$
$168$		0			0
$169$	29.2709			2.25161
$170$	1.66117	−	14.4296i	0.127406	−	1.10670i
$171$	−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	−0.795996	−	0.605302i	$-0.793052\pi$
$173$	−8.80967	+	5.08627i	−0.669787	+	0.386702i	0.126209	+	0.992004i	$0.459719\pi$
$174$	−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	−0.999309	−	0.0371678i	$-0.988166\pi$
$179$	−20.4854	−	11.8273i	−1.53115	−	0.884011i	−0.531843	−	0.846843i	$-0.678500\pi$
$180$	−14.9926	+	12.1844i	−1.11748	+	0.908170i
$181$		−	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
$185$	−6.90717	+	2.99371i	−0.507826	+	0.220102i
$186$	−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	−0.798142	−	0.602470i	$-0.794183\pi$
$191$	−9.33503	+	5.38958i	−0.675459	+	0.389976i	0.122683	+	0.992446i	$0.460850\pi$
$192$	−2.76778	+	22.0136i	−0.199747	+	1.58870i
$193$	−1.59886	−	0.923104i	−0.115089	−	0.0664465i	0.441351	−	0.897335i	$-0.354500\pi$
$193$	−1.59886	−	0.923104i	−0.115089	−	0.0664465i	−0.556439	+	0.830888i	$0.687833\pi$
$194$	4.93381	+	8.54561i	0.354227	+	0.613539i
$195$	−5.97795	+	24.4607i	−0.428090	+	1.75167i
$196$		0			0
$197$	8.09941			0.577059			0.288530	−	0.957471i	$-0.406834\pi$
$197$	8.09941			0.577059			0.288530	+	0.957471i	$0.406834\pi$
$198$	6.26180	−	24.5081i	0.445006	−	1.74172i
$199$	8.74922	+	5.05137i	0.620216	+	0.358082i	0.776953	−	0.629559i	$-0.216764\pi$
$199$	8.74922	+	5.05137i	0.620216	+	0.358082i	−0.156737	+	0.987640i	$0.550098\pi$
$200$	−9.46519	−	2.20858i	−0.669290	−	0.156170i
$201$	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
$205$	7.79919	+	0.897861i	0.544719	+	0.0627093i
$206$	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
$215$	−1.79966	+	15.6326i	−0.122736	+	1.06614i
$216$	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
$220$	22.5529	−	9.77488i	1.52052	−	0.659023i
$221$	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
$225$	−13.3092	−	6.91848i	−0.887280	−	0.461232i
$226$	−22.5977	−	39.1404i	−1.50318	−	2.60358i
$227$	6.21430	+	3.58783i	0.412458	+	0.238132i	0.691845	−	0.722046i	$-0.256798\pi$
$227$	6.21430	+	3.58783i	0.412458	+	0.238132i	−0.279388	+	0.960178i	$0.590131\pi$
$228$	10.0711	+	1.26623i	0.666972	+	0.0838584i
$229$	9.05093	−	5.22556i	0.598102	−	0.345315i	−0.170192	−	0.985411i	$-0.554439\pi$
$229$	9.05093	−	5.22556i	0.598102	−	0.345315i	0.768295	+	0.640096i	$0.221106\pi$
$230$	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	$-0.207457\pi$
$233$	−1.95072	−	3.37875i	−0.127796	−	0.221349i	−0.922822	+	0.385226i	$0.874124\pi$
$234$	−11.6360	−	41.4865i	−0.760670	−	2.71206i
$235$	−10.2845	+	4.45751i	−0.670886	+	0.290776i
$236$	−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	$-0.720587\pi$
$239$		−	23.7873i		−	1.53867i	0.638844	−	0.769336i	$-0.279413\pi$
$240$	−5.44956	+	1.59013i	−0.351768	+	0.102642i
$241$	11.5030	+	6.64126i	0.740974	+	0.427801i	0.822423	−	0.568876i	$-0.192622\pi$
$241$	11.5030	+	6.64126i	0.740974	+	0.427801i	−0.0814495	+	0.996677i	$0.525955\pi$
$242$	−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
$250$	−4.41551	−	24.3002i	−0.279261	−	1.53688i
$251$	−9.12747			−0.576121			−0.288060	−	0.957612i	$-0.593010\pi$
$251$	−9.12747			−0.576121			−0.288060	+	0.957612i	$0.593010\pi$
$252$		0			0
$253$			11.4530i			0.720041i
$254$	1.14275	−	0.659769i	0.0717027	−	0.0413976i
$255$	−7.87289	+	8.22893i	−0.493020	+	0.515315i
$256$	2.70450	−	4.68433i	0.169031	−	0.292770i
$257$	−5.79051	+	3.34315i	−0.361202	+	0.208540i	−0.669608	−	0.742715i	$-0.733538\pi$
$257$	−5.79051	+	3.34315i	−0.361202	+	0.208540i	0.308406	+	0.951255i	$0.400205\pi$
$258$	−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	−0.206795	−	0.978384i	$-0.566303\pi$
$263$	12.0642	−	20.8958i	0.743908	−	1.28849i	0.950703	−	0.310103i	$-0.100363\pi$
$264$	−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	−0.416076	−	0.909330i	$-0.636595\pi$
$269$	9.50393	−	16.4613i	0.579465	−	1.00366i	0.995541	−	0.0943328i	$-0.0300718\pi$
$270$	25.6524	−	0.866351i	1.56115	−	0.0527244i
$271$	−10.2612	+	5.92429i	−0.623321	+	0.359875i	−0.778161	−	0.628065i	$-0.783847\pi$
$271$	−10.2612	+	5.92429i	−0.623321	+	0.359875i	0.154840	+	0.987940i	$0.450514\pi$
$272$			4.31002i			0.261334i
$273$		0			0
$274$	−2.41603			−0.145957
$275$	13.9270	+	13.0483i	0.839832	+	0.786842i
$276$	−1.86718	+	14.8507i	−0.112391	+	0.893907i
$277$	−14.3051	−	8.25906i	−0.859511	−	0.496239i	0.00433762	−	0.999991i	$-0.498619\pi$
$277$	−14.3051	−	8.25906i	−0.859511	−	0.496239i	−0.863848	+	0.503752i	$0.831953\pi$
$278$	−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	$0.0974820\pi$
$281$			10.1076i			0.602968i	−0.953471	+	0.301484i	$0.902518\pi$
$282$	11.5872	−	15.2843i	0.690007	−	0.910165i
$283$	−3.00101	+	5.19791i	−0.178392	+	0.308984i	−0.941330	−	0.337488i	$-0.890423\pi$
$283$	−3.00101	+	5.19791i	−0.178392	+	0.308984i	0.762938	+	0.646472i	$0.223756\pi$
$284$	27.4167	+	15.8291i	1.62688	+	0.939282i
$285$	2.20753	+	7.56547i	0.130763	+	0.448140i
$286$			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
$290$	−10.2093	+	4.42490i	−0.599508	+	0.259839i
$291$	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	$-0.966898\pi$
$293$		−	3.55369i		−	0.207609i	0.994598	−	0.103805i	$-0.0331016\pi$
$294$		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
$300$	15.9315	+	19.1899i	0.919805	+	1.10793i
$301$		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
$305$	28.0358	−	12.1513i	1.60532	−	0.695780i
$306$	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
$310$	−3.76531	+	32.7071i	−0.213855	+	1.85764i
$311$	−4.32216	+	7.48620i	−0.245087	+	0.424503i	−0.962156	−	0.272499i	$-0.912150\pi$
$311$	−4.32216	+	7.48620i	−0.245087	+	0.424503i	0.717069	+	0.697002i	$0.245483\pi$
$312$	−2.73078	+	21.7194i	−0.154600	+	1.22962i
$313$	−5.42607	−	9.39824i	−0.306700	−	0.531220i	0.670938	−	0.741513i	$-0.265891\pi$
$313$	−5.42607	−	9.39824i	−0.306700	−	0.531220i	−0.977638	+	0.210293i	$0.932558\pi$
$314$	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	$-0.251154\pi$
$317$	−4.67046	−	8.08947i	−0.262319	−	0.454350i	−0.966858	+	0.255316i	$0.917821\pi$
$318$	0.923229	−	7.34294i	0.0517721	−	0.411772i
$319$	4.29897	−	7.44604i	0.240696	−	0.416898i
$320$	28.4553	+	3.27584i	1.59070	+	0.183125i
$321$	−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
$325$	31.6576	+	7.38690i	1.75605	+	0.409752i
$326$	−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
$330$	−31.7226	−	7.75268i	−1.74627	−	0.426771i
$331$	−1.45459	−	2.51942i	−0.0799515	−	0.138480i	0.823277	−	0.567639i	$-0.192143\pi$
$331$	−1.45459	−	2.51942i	−0.0799515	−	0.138480i	−0.903229	+	0.429159i	$0.858810\pi$
$332$	−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
$340$	17.3744	−	7.53043i	0.942261	−	0.408395i
$341$	−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
$345$	−11.1560	+	3.25520i	−0.600618	+	0.175254i
$346$	−19.4611	−	11.2359i	−1.04624	−	0.604045i
$347$	−15.7892	+	27.3477i	−0.847609	+	1.46810i	0.0357279	+	0.999362i	$0.488625\pi$
$347$	−15.7892	+	27.3477i	−0.847609	+	1.46810i	−0.883336	+	0.468739i	$0.844708\pi$
$348$	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	0.397906	−	0.917426i	$-0.369737\pi$
$353$	−3.71360	−	2.14405i	−0.197655	−	0.114116i	−0.595561	+	0.803310i	$0.703070\pi$
$354$	−3.78517	+	30.1055i	−0.201180	+	1.60009i
$355$	−2.81115	+	24.4188i	−0.149200	+	1.29602i
$356$	38.9252			2.06303
$357$		0			0
$358$		−	52.2543i		−	2.76173i
$359$	6.17938	−	3.56767i	0.326135	−	0.188294i	−0.327989	−	0.944682i	$-0.606371\pi$
$359$	6.17938	−	3.56767i	0.326135	−	0.188294i	0.654124	+	0.756387i	$0.273037\pi$
$360$	−12.1821	−	4.65176i	−0.642052	−	0.245169i
$361$	−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	0.349563	+	0.936913i	$0.386330\pi$
$367$	−12.1957	+	21.1235i	−0.636609	+	1.10264i	−0.986172	+	0.165726i	$0.947003\pi$
$368$	−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	$-0.473232\pi$
$373$	19.0999	−	11.0273i	0.988956	−	0.570974i	0.904962	+	0.425492i	$0.139899\pi$
$374$	−12.3968	+	21.4719i	−0.641025	+	1.11029i
$375$	−8.75157	+	17.2745i	−0.451929	+	0.892054i
$376$	−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	$0.490532\pi$
$380$	1.49867	−	13.0181i	0.0768800	−	0.667812i
$381$	−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	−0.546372	−	0.837542i	$-0.683992\pi$
$383$	−1.84403	+	1.06465i	−0.0942255	+	0.0544011i	0.452147	+	0.891944i	$0.350658\pi$
$384$	−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	−0.135088	−	0.990834i	$-0.543132\pi$
$389$	−20.9207	−	12.0785i	−1.06072	−	0.612406i	−0.925631	+	0.378427i	$0.876465\pi$
$390$	−53.3988	+	15.5812i	−2.70395	+	0.788985i
$391$			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
$395$	−5.20178	−	12.0017i	−0.261730	−	0.603871i
$396$	31.7524	−	8.90582i	1.59562	−	0.447534i
$397$	6.00792	+	10.4060i	0.301529	+	0.522263i	0.976482	−	0.215597i	$-0.0691697\pi$
$397$	6.00792	+	10.4060i	0.301529	+	0.522263i	−0.674954	+	0.737860i	$0.735836\pi$
$398$			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	−0.985807	−	0.167883i	$-0.946307\pi$
$401$	−26.6997	+	15.4151i	−1.33332	+	0.769792i	−0.347513	+	0.937675i	$0.612974\pi$
$402$	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
$405$	−16.4383	−	11.6096i	−0.816824	−	0.576887i
$406$		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	$-0.459958\pi$
$409$	−13.5699	−	7.83456i	−0.670986	−	0.387394i	−0.796450	+	0.604704i	$0.793291\pi$
$410$	6.89675	+	15.9124i	0.340606	+	0.785857i
$411$	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
$415$	0.681092	−	5.91625i	0.0334335	−	0.290417i
$416$	−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	$-0.341108\pi$
$419$	19.5975			0.957399			0.478699	+	0.877979i	$0.341108\pi$
$420$		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
$425$	10.7292	+	10.0522i	0.520442	+	0.487605i
$426$	−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
$430$	−31.8946	+	13.8238i	−1.53809	+	0.666642i
$431$	−24.1528	−	13.9447i	−1.16340	−	0.671690i	−0.211285	−	0.977425i	$-0.567765\pi$
$431$	−24.1528	−	13.9447i	−1.16340	−	0.671690i	−0.952117	+	0.305734i	$0.901098\pi$
$432$	−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
$435$	8.47483	+	2.07116i	0.406337	+	0.0993046i
$436$	−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	$-0.636633\pi$
$439$	3.41910	−	1.97402i	0.163185	−	0.0942147i	0.579368	+	0.815066i	$0.303299\pi$
$440$	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	$-0.291026\pi$
$443$	−8.01539	−	13.8831i	−0.380823	−	0.659604i	−0.991180	+	0.132522i	$0.957693\pi$
$444$	16.6624	+	2.09497i	0.790764	+	0.0994227i
$445$	12.0187	+	27.7298i	0.569740	+	1.31452i
$446$	−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	$-0.834109\pi$
$449$		−	21.1001i		−	0.995777i	0.867241	−	0.497889i	$-0.165891\pi$
$450$	−1.46466	−	33.1036i	−0.0690447	−	1.56052i
$451$	−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	$-0.738804\pi$
$457$	−8.31969	+	4.80338i	−0.389179	+	0.224692i	0.292625	+	0.956227i	$0.405471\pi$
$458$	19.9941	+	11.5436i	0.934262	+	0.539397i
$459$	−11.9574	+	9.51186i	−0.558126	+	0.443975i
$460$	19.1963	+	2.20993i	0.895034	+	0.103038i
$461$	24.5367			1.14279			0.571393	−	0.820676i	$-0.306403\pi$
$461$	24.5367			1.14279			0.571393	+	0.820676i	$0.306403\pi$
$462$		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
$465$	17.8452	−	18.6522i	0.827551	−	0.864975i
$466$	4.30927	−	7.46387i	0.199623	−	0.345757i
$467$	15.5179	−	8.95926i	0.718083	−	0.414585i	−0.0959639	−	0.995385i	$-0.530593\pi$
$467$	15.5179	−	8.95926i	0.718083	−	0.414585i	0.814047	+	0.580800i	$0.197260\pi$
$468$	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	$-0.854911\pi$
$479$	−1.48248	+	2.56774i	−0.0677364	+	0.117323i	0.830168	+	0.557513i	$0.188244\pi$
$480$	−19.9412	−	19.0784i	−0.910186	−	0.870805i
$481$	18.9561	−	10.9443i	0.864322	−	0.499017i
$482$			29.3419i			1.33649i
$483$		0			0
$484$	−10.2780			−0.467184
$485$	−9.92271	−	1.14232i	−0.450567	−	0.0518703i
$486$	34.2577	+	3.49849i	1.55396	+	0.158695i
$487$	28.8004	+	16.6279i	1.30507	+	0.753482i	0.981269	−	0.192644i	$-0.0617061\pi$
$487$	28.8004	+	16.6279i	1.30507	+	0.753482i	0.323800	+	0.946125i	$0.395039\pi$
$488$	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	$0.195059\pi$
$491$			25.4892i			1.15031i	−0.818043	+	0.575157i	$0.804941\pi$
$492$	−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
$495$	16.1484	+	19.8702i	0.725816	+	0.893101i
$496$		−	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	0.946031	+	0.324076i	$0.105053\pi$
$499$	16.8358	+	29.1604i	0.753673	+	1.30540i	−0.192358	+	0.981325i	$0.561613\pi$
$500$	24.5576	−	20.8254i	1.09825	−	0.931339i
$501$	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	$0.287685\pi$
$503$			35.2418i			1.57135i	−0.618637	+	0.785677i	$0.712315\pi$
$504$		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	−0.999872	−	0.0159875i	$-0.994911\pi$
$509$	−11.5914	−	20.0770i	−0.513782	−	0.889896i	0.486090	−	0.873908i	$-0.338423\pi$
$510$	−24.4387	−	5.97256i	−1.08216	−	0.264469i
$511$		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
$515$	1.17594	+	2.71317i	0.0518183	+	0.119557i
$516$	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
$520$	28.0749	+	3.23205i	1.23117	+	0.141735i
$521$	7.18762	−	12.4493i	0.314895	−	0.545415i	−0.664520	−	0.747271i	$-0.731364\pi$
$521$	7.18762	−	12.4493i	0.314895	−	0.545415i	0.979415	+	0.201856i	$0.0646972\pi$
$522$	−14.3737	+	4.03149i	−0.629119	+	0.176454i
$523$	−12.6242	−	21.8658i	−0.552018	−	0.956124i	−0.998129	−	0.0611461i	$-0.980524\pi$
$523$	−12.6242	−	21.8658i	−0.552018	−	0.956124i	0.446110	−	0.894978i	$-0.352809\pi$
$524$	−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
$530$	−9.49164	−	1.09270i	−0.412291	−	0.0474638i
$531$	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
$535$	2.95618	+	6.82059i	0.127807	+	0.294880i
$536$	−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
$540$	17.6997	+	28.3978i	0.761673	+	1.22205i
$541$	−7.88973	−	13.6654i	−0.339206	−	0.587522i	0.645078	−	0.764117i	$-0.276825\pi$
$541$	−7.88973	−	13.6654i	−0.339206	−	0.587522i	−0.984284	+	0.176595i	$0.943492\pi$
$542$	−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
$550$	−9.57991	+	41.0561i	−0.408489	+	1.75064i
$551$	−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
$555$	3.65232	+	12.5170i	0.155032	+	0.531316i
$556$	−18.3559	−	10.5978i	−0.778464	−	0.449446i
$557$	14.4676	−	25.0586i	0.613011	−	1.06177i	−0.377719	−	0.925920i	$-0.623292\pi$
$557$	14.4676	−	25.0586i	0.613011	−	1.06177i	0.990730	−	0.135845i	$-0.0433750\pi$
$558$	−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	0.382017	−	0.924155i	$-0.375230\pi$
$563$	−5.39368	−	3.11404i	−0.227316	−	0.131241i	−0.609333	+	0.792914i	$0.708563\pi$
$564$	24.8097	+	3.11932i	1.04467	+	0.131347i
$565$	45.4477	+	5.23204i	1.91200	+	0.220114i
$566$	−13.2589			−0.557312
$567$		0			0
$568$			21.3683i			0.896594i
$569$	−8.56862	+	4.94710i	−0.359215	+	0.207393i	−0.668736	−	0.743500i	$-0.733165\pi$
$569$	−8.56862	+	4.94710i	−0.359215	+	0.207393i	0.309521	+	0.950893i	$0.399831\pi$
$570$	−12.0353	+	12.5795i	−0.504102	+	0.526899i
$571$	−9.60472	+	16.6359i	−0.401945	+	0.696189i	−0.993961	−	0.109737i	$-0.964999\pi$
$571$	−9.60472	+	16.6359i	−0.401945	+	0.696189i	0.592015	+	0.805927i	$0.298332\pi$
$572$	−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	−0.131835	−	0.991272i	$-0.542087\pi$
$577$	19.0377	−	32.9742i	0.792549	−	1.37273i	0.924384	−	0.381463i	$-0.124580\pi$
$578$	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
$585$	40.7446	+	15.5585i	1.68458	+	0.643263i
$586$	6.79859	−	3.92517i	0.280847	−	0.162147i
$587$		−	11.9232i		−	0.492124i	−0.969254	−	0.246062i	$-0.920863\pi$
$587$		−	11.9232i		−	0.492124i	0.969254	−	0.246062i	$-0.0791367\pi$
$588$		0			0
$589$	−13.5625			−0.558835
$590$	38.9151	+	4.47999i	1.60211	+	0.184438i
$591$	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	−0.169330	−	0.985559i	$-0.554160\pi$
$593$	14.5994	−	8.42896i	0.599525	−	0.346136i	0.768855	+	0.639424i	$0.220827\pi$
$594$	−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	0.239800	−	0.970822i	$-0.422918\pi$
$599$	−11.7736	−	6.79751i	−0.481058	−	0.277739i	−0.720857	+	0.693084i	$0.756252\pi$
$600$	−5.84063	+	15.7889i	−0.238443	+	0.644580i
$601$			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
$605$	−3.17349	−	7.32196i	−0.129021	−	0.297680i
$606$	4.23398	−	33.6751i	0.171994	−	1.36796i
$607$	−4.37164	−	7.57190i	−0.177439	−	0.307334i	0.763563	−	0.645733i	$-0.223448\pi$
$607$	−4.37164	−	7.57190i	−0.177439	−	0.307334i	−0.941003	+	0.338399i	$0.890115\pi$
$608$			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	$-0.169641\pi$
$613$	21.0938	+	12.1785i	0.851970	+	0.491885i	−0.00934480	+	0.999956i	$0.502975\pi$
$614$	−32.0696	−	55.5461i	−1.29422	−	2.24166i
$615$	3.22816	−	13.2091i	0.130172	−	0.532641i
$616$		0			0
$617$	25.3125			1.01904			0.509522	−	0.860458i	$-0.329822\pi$
$617$	25.3125			1.01904			0.509522	+	0.860458i	$0.329822\pi$
$618$	−4.03217	−	3.05684i	−0.162198	−	0.122964i
$619$	−26.2018	−	15.1276i	−1.05314	−	0.608029i	−0.129612	−	0.991565i	$-0.541373\pi$
$619$	−26.2018	−	15.1276i	−1.05314	−	0.608029i	−0.923526	+	0.383535i	$0.874706\pi$
$620$	−39.3820	+	17.0690i	−1.58162	+	0.685506i
$621$	−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
$625$	22.4183	+	11.0644i	0.896730	+	0.442577i
$626$	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
$635$	−0.152756	+	1.32690i	−0.00606194	+	0.0526566i
$636$	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
$640$	12.4900	+	28.8173i	0.493711	+	1.13910i
$641$	0.111457	+	0.0643495i	0.00440227	+	0.00254165i	0.502200	−	0.864752i	$-0.332524\pi$
$641$	0.111457	+	0.0643495i	0.00440227	+	0.00254165i	−0.497797	+	0.867293i	$0.665858\pi$
$642$	−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
$645$	26.4761	+	6.47049i	1.04250	+	0.254775i
$646$	6.60894	+	11.4470i	0.260025	+	0.450377i
$647$	35.8147	+	20.6776i	1.40802	+	0.812920i	0.995197	−	0.0978912i	$-0.0312097\pi$
$647$	35.8147	+	20.6776i	1.40802	+	0.812920i	0.412822	+	0.910812i	$0.364543\pi$
$648$	−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	−0.995883	−	0.0906487i	$-0.971106\pi$
$653$	−14.7304	−	25.5138i	−0.576446	−	0.998433i	0.419437	−	0.907784i	$-0.362227\pi$
$654$	−5.87024	+	46.6892i	−0.229545	+	1.82569i
$655$	−5.16804	−	11.9238i	−0.201932	−	0.465903i
$656$	−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	$0.144175\pi$
$659$			22.4678i			0.875220i	−0.899165	+	0.437610i	$0.855825\pi$
$660$	−11.9253	−	40.8697i	−0.464193	−	1.59085i
$661$	−20.3164	−	11.7297i	−0.790218	−	0.456233i	0.0498213	−	0.998758i	$-0.484135\pi$
$661$	−20.3164	−	11.7297i	−0.790218	−	0.456233i	−0.840039	+	0.542526i	$0.817468\pi$
$662$	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
$670$	6.09349	−	52.9306i	0.235412	−	2.04489i
$671$	−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
$675$	−14.7653	+	21.3773i	−0.568315	+	0.822811i
$676$	−42.1496	+	73.0052i	−1.62114	+	2.80789i
$677$	39.5783	−	22.8505i	1.52112	−	0.878217i	0.521427	−	0.853296i	$-0.325400\pi$
$677$	39.5783	−	22.8505i	1.52112	−	0.878217i	0.999689	−	0.0249214i	$-0.00793355\pi$
$678$	−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	0.212215	+	0.977223i	$0.431932\pi$
$683$	−19.3444	+	33.5055i	−0.740192	+	1.28205i	−0.952407	+	0.304828i	$0.901401\pi$
$684$	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
$690$	−18.5497	−	17.7471i	−0.706175	−	0.675621i
$691$	−16.6768	+	9.62834i	−0.634415	+	0.366279i	−0.782460	−	0.622701i	$-0.786035\pi$
$691$	−16.6768	+	9.62834i	−0.634415	+	0.366279i	0.148045	+	0.988981i	$0.452702\pi$
$692$		−	29.2965i		−	1.11369i
$693$		0			0
$694$	−69.7587			−2.64800
$695$	1.88211	−	16.3488i	0.0713923	−	0.620144i
$696$	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	$0.0407334\pi$
$701$			6.75777i			0.255238i	−0.991823	+	0.127619i	$0.959267\pi$
$702$	−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
$705$	5.43815	+	18.6372i	0.204813	+	0.701919i
$706$		−	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	0.816436	−	0.577436i	$-0.195947\pi$
$709$	−2.44586	−	4.23635i	−0.0918561	−	0.159099i	−0.908292	+	0.418336i	$0.862613\pi$
$710$	−49.8208	+	21.5933i	−1.86974	+	0.810384i
$711$	−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	0.965234	+	0.261387i	$0.0841798\pi$
$719$	19.0108	+	32.9277i	0.708985	+	1.22800i	−0.256249	+	0.966611i	$0.582487\pi$
$720$	1.55518	+	9.70876i	0.0579581	+	0.361824i
$721$		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
$725$	2.55931	−	10.9683i	0.0950506	−	0.407353i
$726$	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
$730$	16.2378	+	1.86933i	0.600988	+	0.0691872i
$731$	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	−0.970426	−	0.241399i	$-0.922394\pi$
$733$	−18.7967	−	32.5568i	−0.694271	−	1.20251i	0.276155	−	0.961113i	$-0.410940\pi$
$734$	−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	0.0942603	−	0.995548i	$-0.469951\pi$
$739$	24.7189	−	42.8144i	0.909300	−	1.57495i	0.815039	−	0.579406i	$-0.196715\pi$
$740$	2.47953	−	21.5382i	0.0911492	−	0.791760i
$741$	−8.89228	−	21.1190i	−0.326666	−	0.775826i
$742$		0			0
$743$	42.7477			1.56826			0.784131	−	0.620596i	$-0.213109\pi$
$743$	42.7477			1.56826			0.784131	+	0.620596i	$0.213109\pi$
$744$	13.5572	−	17.8828i	0.497030	−	0.655616i
$745$	−22.1978	+	9.62097i	−0.813264	+	0.352485i
$746$	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
$750$	−42.7144	+	2.33761i	−1.55971	+	0.0853575i
$751$	−2.79526	−	4.84152i	−0.102000	−	0.176670i	0.810508	−	0.585727i	$-0.199191\pi$
$751$	−2.79526	−	4.84152i	−0.102000	−	0.176670i	−0.912509	+	0.409057i	$0.865858\pi$
$752$	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
$760$	8.11537	−	3.51737i	0.294376	−	0.127588i
$761$	24.5715	+	42.5591i	0.890716	+	1.54277i	0.839019	+	0.544102i	$0.183130\pi$
$761$	24.5715	+	42.5591i	0.890716	+	1.54277i	0.0516970	+	0.998663i	$0.483537\pi$
$762$	−0.886912	−	2.10640i	−0.0321294	−	0.0763068i
$763$		0			0
$764$		−	31.0436i		−	1.12312i
$765$	12.4405	+	15.3077i	0.449787	+	0.553453i
$766$	−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	−0.977758	−	0.209735i	$-0.932740\pi$
$773$	−45.8267	−	26.4581i	−1.64827	−	0.951631i	−0.670515	−	0.741896i	$-0.733927\pi$
$774$	−44.9046	+	12.5947i	−1.61406	+	0.452708i
$775$	−24.3195	−	22.7850i	−0.873581	−	0.818462i
$776$	−8.68312			−0.311706
$777$		0			0
$778$		−	53.3645i		−	1.91321i
$779$	−6.18711	+	3.57213i	−0.221676	+	0.127985i
$780$	−52.3999	−	50.1327i	−1.87622	−	1.79504i
$781$	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	−0.975832	−	0.218521i	$-0.929877\pi$
$787$	−8.37879	+	14.5125i	−0.298672	+	0.517315i	0.677161	+	0.735835i	$0.263210\pi$
$788$	−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
$795$	5.41290	+	5.17870i	0.191976	+	0.183670i
$796$	−25.1974	+	14.5477i	−0.893099	+	0.515631i
$797$			55.9724i			1.98264i	0.131462	+	0.991321i	$0.458033\pi$
$797$			55.9724i			1.98264i	−0.131462	+	0.991321i	$0.541967\pi$
$798$		0			0
$799$	14.7401			0.521466
$800$	−24.3596	+	26.0001i	−0.861241	+	0.919241i
$801$	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	0.977192	−	0.212358i	$-0.0681142\pi$
$809$	36.4604	+	21.0504i	1.28188	+	0.740094i	0.304689	+	0.952452i	$0.401447\pi$
$810$	4.05386	−	44.2713i	0.142438	−	1.55554i
$811$			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
$815$	35.2000	−	15.2564i	1.23300	−	0.534409i
$816$	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	−0.318665	−	0.947867i	$-0.603235\pi$
$821$	9.82457	−	5.67222i	0.342880	−	0.197962i	0.661545	+	0.749906i	$0.269901\pi$
$822$	−0.522030	+	4.15199i	−0.0182079	+	0.144817i
$823$	26.1348	+	15.0889i	0.911002	+	0.525967i	0.880754	−	0.473575i	$-0.157037\pi$
$823$	26.1348	+	15.0889i	0.911002	+	0.525967i	0.0302488	+	0.999542i	$0.490370\pi$
$824$	1.28533	+	2.22626i	0.0447766	+	0.0775554i
$825$	25.4330	−	21.1146i	0.885463	−	0.735114i
$826$		0			0
$827$	34.7911			1.20981			0.604903	−	0.796299i	$-0.293212\pi$
$827$	34.7911			1.20981			0.604903	+	0.796299i	$0.293212\pi$
$828$	25.1178	+	6.41757i	0.872904	+	0.223026i
$829$	−3.50678	−	2.02464i	−0.121796	−	0.0703187i	0.437864	−	0.899041i	$-0.355735\pi$
$829$	−3.50678	−	2.02464i	−0.121796	−	0.0703187i	−0.559660	+	0.828722i	$0.689068\pi$
$830$	12.0707	−	5.23169i	0.418980	−	0.181595i
$831$	−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
$835$	2.45653	−	21.3385i	0.0850118	−	0.738448i
$836$	−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	$-0.352676\pi$
$839$	25.8653			0.892969			0.446485	+	0.894791i	$0.352676\pi$
$840$		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
$845$	−65.0223	−	7.48552i	−2.23684	−	0.257510i
$846$	−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
$850$	−7.38023	+	31.6291i	−0.253140	+	1.08487i
$851$	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
$855$	13.4784	−	2.15901i	0.460952	−	0.0738366i
$856$	3.23117	+	5.59655i	0.110439	+	0.191286i
$857$	19.8563	+	11.4640i	0.678278	+	0.391604i	0.799206	−	0.601057i	$-0.205254\pi$
$857$	19.8563	+	11.4640i	0.678278	+	0.391604i	−0.120928	+	0.992661i	$0.538587\pi$
$858$	94.2098	+	11.8450i	3.21627	+	0.404382i
$859$	16.2512	−	9.38264i	0.554484	−	0.320132i	−0.196444	−	0.980515i	$-0.562940\pi$
$859$	16.2512	−	9.38264i	0.554484	−	0.320132i	0.750929	+	0.660383i	$0.229606\pi$
$860$	−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	$-0.120664\pi$
$863$	4.23086	+	7.32807i	0.144020	+	0.249450i	−0.784987	+	0.619512i	$0.787330\pi$
$864$	−23.0501	−	28.9765i	−0.784180	−	0.985800i
$865$	20.8705	−	9.04569i	0.709618	−	0.307563i
$866$	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
$870$	5.39837	+	18.5009i	0.183022	+	0.627240i
$871$	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	$-0.687027\pi$
$877$	−3.27867	+	1.89294i	−0.110713	+	0.0639201i	0.443621	+	0.896214i	$0.353694\pi$
$878$	7.55301	+	4.36073i	0.254902	+	0.147168i
$879$	−6.10710	−	0.767845i	−0.205987	−	0.0258988i
$880$	1.43073	−	12.4279i	0.0482298	−	0.418944i
$881$	54.6531			1.84131			0.920654	−	0.390379i	$-0.127656\pi$
$881$	54.6531			1.84131			0.920654	+	0.390379i	$0.127656\pi$
$882$		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
$885$	−22.1925	−	21.2323i	−0.745993	−	0.713716i
$886$	17.7065	−	30.6686i	0.594862	−	1.03033i
$887$	−26.0011	+	15.0117i	−0.873032	+	0.504045i	−0.868355	−	0.495944i	$-0.834822\pi$
$887$	−26.0011	+	15.0117i	−0.873032	+	0.504045i	−0.00467726	+	0.999989i	$0.501489\pi$
$888$	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
$900$	36.4205	−	23.2323i	1.21402	−	0.774408i
$901$	4.92559	−	2.84379i	0.164095	−	0.0947404i
$902$		−	29.6036i		−	0.985691i
$903$		0			0
$904$	39.7702			1.32274
$905$	−3.99787	+	34.7271i	−0.132894	+	1.15437i
$906$	3.95977	−	31.4942i	0.131555	−	1.04633i
$907$	−16.8295	−	9.71653i	−0.558815	−	0.322632i	0.193855	−	0.981030i	$-0.437901\pi$
$907$	−16.8295	−	9.71653i	−0.558815	−	0.322632i	−0.752670	+	0.658398i	$0.771234\pi$
$908$	−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	$-0.655739\pi$
$911$		−	53.2832i		−	1.76535i	0.469982	−	0.882676i	$-0.344261\pi$
$912$	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
$915$	−14.8245	−	50.8056i	−0.490084	−	1.67958i
$916$			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	−0.951392	−	0.307982i	$-0.900346\pi$
$919$	−22.5064	−	38.9822i	−0.742416	−	1.28590i	0.208976	−	0.977921i	$-0.432987\pi$
$920$	5.18669	+	11.9669i	0.171000	+	0.394536i
$921$	−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	−0.968307	−	0.249764i	$-0.919647\pi$
$929$	−21.3495	−	36.9785i	−0.700455	−	1.21322i	0.267852	−	0.963460i	$-0.413686\pi$
$930$	55.3942	+	13.5378i	1.81645	+	0.443921i
$931$		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
$935$	−9.98034	−	23.0269i	−0.326392	−	0.753061i
$936$	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
$940$	3.69191	−	32.0695i	0.120417	−	1.04599i
$941$	15.8545	−	27.4609i	0.516843	−	0.895199i	−0.482965	−	0.875640i	$-0.660440\pi$
$941$	15.8545	−	27.4609i	0.516843	−	0.895199i	0.999809	−	0.0195596i	$-0.00622642\pi$
$942$	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	$-0.104492\pi$
$947$	5.97276	+	10.3451i	0.194089	+	0.336171i	−0.752513	+	0.658578i	$0.771158\pi$
$948$	−3.64015	+	28.9521i	−0.118227	+	0.940321i
$949$	−10.7568	+	18.6314i	−0.349181	+	0.604800i
$950$	16.4017	+	15.3668i	0.532141	+	0.498565i
$951$	−14.9111	+	6.27839i	−0.483524	+	0.203591i
$952$		0			0
$953$	1.76384			0.0571364			0.0285682	−	0.999592i	$-0.490905\pi$
$953$	1.76384			0.0571364			0.0285682	+	0.999592i	$0.490905\pi$
$954$	−12.4195	−	3.17318i	−0.402097	−	0.102735i
$955$	22.1151	−	9.58513i	0.715627	−	0.310167i
$956$	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
$960$	11.7779	−	48.1932i	0.380131	−	1.55543i
$961$	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
$970$	−8.77456	−	20.2449i	−0.281734	−	0.650025i
$971$	23.9577	+	41.4959i	0.768838	+	1.33167i	0.938193	+	0.346111i	$0.112498\pi$
$971$	23.9577	+	41.4959i	0.768838	+	1.33167i	−0.169356	+	0.985555i	$0.554169\pi$
$972$	18.3810	+	40.9588i	0.589571	+	1.31375i
$973$		0			0
$974$			73.4642i			2.35394i
$975$	19.5348	−	52.8082i	0.625614	−	1.69122i
$976$	−17.3460	−	10.0147i	−0.555231	−	0.320563i
$977$	−4.07411	+	7.05657i	−0.130342	+	0.225760i	−0.923809	−	0.382855i	$-0.874941\pi$
$977$	−4.07411	+	7.05657i	−0.130342	+	0.225760i	0.793466	+	0.608614i	$0.208274\pi$
$978$	−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	0.284582	−	0.958652i	$-0.408145\pi$
$983$	−12.6460	−	7.30116i	−0.403344	−	0.232871i	−0.687926	+	0.725781i	$0.741479\pi$
$984$	1.47465	−	11.7287i	0.0470101	−	0.373897i
$985$	−17.9920	−	2.07128i	−0.573273	−	0.0659965i
$986$	14.6322			0.465986
$987$		0			0
$988$			38.1014i			1.21217i
$989$	18.2870	−	10.5580i	0.581492	−	0.335725i
$990$	−20.1774	+	52.8409i	−0.641281	+	1.67939i
$991$	−7.84118	+	13.5813i	−0.249083	+	0.431425i	−0.963272	−	0.268529i	$-0.913463\pi$
$991$	−7.84118	+	13.5813i	−0.249083	+	0.431425i	0.714188	+	0.699953i	$0.246796\pi$
$992$	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	−0.568497	−	0.822685i	$-0.692475\pi$
$997$	13.5211	−	23.4192i	0.428218	−	0.741695i	0.996715	+	0.0809903i	$0.0258083\pi$
$998$	−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.374.31		64
3.2	odd	2	inner	735.2.p.g.374.4		64
5.4	even	2	inner	735.2.p.g.374.2		64
7.2	even	3	inner	735.2.p.g.509.32		64
7.3	odd	6		735.2.g.c.734.3	yes	32
7.4	even	3		735.2.g.c.734.2	yes	32
7.5	odd	6	inner	735.2.p.g.509.29		64
7.6	odd	2	inner	735.2.p.g.374.30		64
15.14	odd	2	inner	735.2.p.g.374.29		64
21.2	odd	6	inner	735.2.p.g.509.3		64
21.5	even	6	inner	735.2.p.g.509.2		64
21.11	odd	6		735.2.g.c.734.29	yes	32
21.17	even	6		735.2.g.c.734.32	yes	32
21.20	even	2	inner	735.2.p.g.374.1		64
35.4	even	6		735.2.g.c.734.31	yes	32
35.9	even	6	inner	735.2.p.g.509.1		64
35.19	odd	6	inner	735.2.p.g.509.4		64
35.24	odd	6		735.2.g.c.734.30	yes	32
35.34	odd	2	inner	735.2.p.g.374.3		64
105.44	odd	6	inner	735.2.p.g.509.30		64
105.59	even	6		735.2.g.c.734.1	✓	32
105.74	odd	6		735.2.g.c.734.4	yes	32
105.89	even	6	inner	735.2.p.g.509.31		64
105.104	even	2	inner	735.2.p.g.374.32		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.1	✓	32	105.59	even	6
735.2.g.c.734.2	yes	32	7.4	even	3
735.2.g.c.734.3	yes	32	7.3	odd	6
735.2.g.c.734.4	yes	32	105.74	odd	6
735.2.g.c.734.29	yes	32	21.11	odd	6
735.2.g.c.734.30	yes	32	35.24	odd	6
735.2.g.c.734.31	yes	32	35.4	even	6
735.2.g.c.734.32	yes	32	21.17	even	6
735.2.p.g.374.1		64	21.20	even	2	inner
735.2.p.g.374.2		64	5.4	even	2	inner
735.2.p.g.374.3		64	35.34	odd	2	inner
735.2.p.g.374.4		64	3.2	odd	2	inner
735.2.p.g.374.29		64	15.14	odd	2	inner
735.2.p.g.374.30		64	7.6	odd	2	inner
735.2.p.g.374.31		64	1.1	even	1	trivial
735.2.p.g.374.32		64	105.104	even	2	inner
735.2.p.g.509.1		64	35.9	even	6	inner
735.2.p.g.509.2		64	21.5	even	6	inner
735.2.p.g.509.3		64	21.2	odd	6	inner
735.2.p.g.509.4		64	35.19	odd	6	inner
735.2.p.g.509.29		64	7.5	odd	6	inner
735.2.p.g.509.30		64	105.44	odd	6	inner
735.2.p.g.509.31		64	105.89	even	6	inner
735.2.p.g.509.32		64	7.2	even	3	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} +(-2.22140 - 0.255732i) q^{5} +(3.52637 - 1.48480i) q^{6} -1.94389 q^{8} +(-2.90663 - 0.742640i) q^{9} +(-1.96436 - 4.53223i) q^{10} +(3.30554 + 1.90846i) q^{11} +(3.97506 + 3.01354i) q^{12} +6.50161 q^{13} +(-0.919457 + 3.76226i) 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} +(4.86920 + 1.13616i) q^{25} +(7.18123 + 12.4383i) q^{26} +(-1.90428 + 4.83464i) q^{27} -2.25259i q^{29} +(-8.21317 + 2.39652i) 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} +(4.31815 + 0.497115i) q^{40} -3.51094 q^{41} -7.03729i q^{43} +(-9.51983 + 5.49628i) q^{44} +(6.26685 + 2.39302i) 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} +(-8.05952 - 7.71082i) q^{60} +(-11.8342 + 6.83249i) q^{61} -14.7237i q^{62} -12.8096 q^{64} +(-14.4427 - 1.66267i) 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} +(3.00461 - 8.12233i) q^{75} +5.86030i q^{76} +(22.9271 - 9.65357i) q^{78} +(2.92489 + 5.06605i) q^{79} +(-1.30338 - 3.00720i) 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} +(2.34385 + 14.6323i) q^{90} -8.64156 q^{92} +(-6.97425 + 9.19951i) q^{93} +(9.58999 + 5.53678i) q^{94} +(-4.17481 + 1.80945i) 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

Fields

Representations

Groups

Database

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