LMFDB - Embedded newform 735.2.p.g.374.1

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			374.1
Character	$\chi$	$=$	735.374
Dual form			735.2.p.g.509.1

$q$-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} +(-1.38025 + 1.04638i) q^{3} +(-1.43998 + 2.49412i) q^{4} +(-2.22140 - 0.255732i) q^{5} +(3.52637 + 1.48480i) q^{6} +1.94389 q^{8} +(0.810168 - 2.88853i) q^{9} +(1.96436 + 4.53223i) q^{10} +(-3.30554 - 1.90846i) q^{11} +(-0.622272 - 4.94927i) q^{12} -6.50161 q^{13} +(3.33367 - 1.97146i) q^{15} +(0.732874 + 1.26937i) q^{16} +(2.54654 + 1.47025i) q^{17} +(-6.42092 + 1.64054i) q^{18} +(-1.76224 + 1.01743i) q^{19} +(3.83659 - 5.17218i) q^{20} +8.43180i q^{22} +(-1.50029 - 2.59858i) q^{23} +(-2.68305 + 2.03405i) q^{24} +(4.86920 + 1.13616i) q^{25} +(7.18123 + 12.4383i) q^{26} +(1.90428 + 4.83464i) q^{27} +2.25259i q^{29} +(-7.45375 - 4.20013i) q^{30} +(5.77216 + 3.33256i) q^{31} +(3.56285 - 6.17104i) q^{32} +(6.55944 - 0.824719i) q^{33} -6.49574i q^{34} +(6.03772 + 6.18009i) q^{36} +(2.91560 - 1.68332i) q^{37} +(3.89289 + 2.24756i) q^{38} +(8.97383 - 6.80317i) q^{39} +(-4.31815 - 0.497115i) q^{40} -3.51094 q^{41} -7.03729i q^{43} +(9.51983 - 5.49628i) q^{44} +(-2.53840 + 6.20939i) 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} +(-5.05330 + 0.635352i) q^{51} +(9.36219 - 16.2158i) q^{52} +(-0.967113 + 1.67509i) q^{53} +(7.14584 - 8.98309i) 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} +(0.116625 + 11.1534i) q^{60} +(11.8342 - 6.83249i) q^{61} -14.7237i q^{62} -12.8096 q^{64} +(14.4427 + 1.66267i) q^{65} +(-8.82289 - 11.6380i) q^{66} +(9.34121 + 5.39315i) q^{67} +(-7.33395 + 4.23426i) q^{68} +(4.78988 + 2.01681i) q^{69} +10.9926i q^{71} +(1.57488 - 5.61499i) q^{72} +(1.65449 - 2.86566i) q^{73} +(-6.44074 - 3.71856i) q^{74} +(-7.90957 + 3.52686i) q^{75} -5.86030i q^{76} +(-22.9271 - 9.65357i) q^{78} +(2.92489 + 5.06605i) q^{79} +(-1.30338 - 3.00720i) q^{80} +(-7.68725 - 4.68040i) q^{81} +(3.87795 + 6.71680i) q^{82} +2.66330i q^{83} +(-5.28089 - 3.91724i) q^{85} +(-13.4631 + 7.77291i) q^{86} +(-2.35707 - 3.10913i) q^{87} +(-6.42561 - 3.70983i) q^{88} +(-6.75793 - 11.7051i) q^{89} +(14.6830 - 2.00225i) q^{90} +8.64156 q^{92} +(-11.4541 + 1.44013i) q^{93} +(-9.58999 - 5.53678i) q^{94} +(4.17481 - 1.80945i) q^{95} +(1.53965 + 12.2457i) 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	$-0.881365\pi$
$2$	−1.10453	−	1.91310i	−0.781022	−	1.35277i	0.150325	−	0.988637i	$-0.451968\pi$
$3$	−1.38025	+	1.04638i	−0.796886	+	0.604129i
$3$	−1.38025	+	1.04638i	−0.796886	+	0.604129i
$4$	−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
$9$	0.810168	−	2.88853i	0.270056	−	0.962845i
$10$	1.96436	+	4.53223i	0.621185	+	1.43322i
$11$	−3.30554	−	1.90846i	−0.996659	−	0.575421i	−0.0894006	−	0.995996i	$-0.528495\pi$
$11$	−3.30554	−	1.90846i	−0.996659	−	0.575421i	−0.907258	+	0.420575i	$0.861828\pi$
$12$	−0.622272	−	4.94927i	−0.179635	−	1.42873i
$13$	−6.50161			−1.80322			−0.901611	−	0.432548i	$-0.857615\pi$
$13$	−6.50161			−1.80322			−0.901611	+	0.432548i	$0.857615\pi$
$14$		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	0.775945	−	0.630801i	$-0.217274\pi$
$17$	2.54654	+	1.47025i	0.617628	+	0.356587i	−0.158317	+	0.987388i	$0.550607\pi$
$18$	−6.42092	+	1.64054i	−1.51343	+	0.386679i
$19$	−1.76224	+	1.01743i	−0.404285	+	0.233414i	−0.688331	−	0.725397i	$-0.741656\pi$
$19$	−1.76224	+	1.01743i	−0.404285	+	0.233414i	0.284046	+	0.958811i	$0.408323\pi$
$20$	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	0.666142	−	0.745825i	$-0.267944\pi$
$23$	−1.50029	−	2.59858i	−0.312832	−	0.541842i	−0.978974	+	0.203983i	$0.934611\pi$
$24$	−2.68305	+	2.03405i	−0.547675	+	0.415199i
$25$	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	$0.0670690\pi$
$29$			2.25259i			0.418296i	−0.977884	+	0.209148i	$0.932931\pi$
$30$	−7.45375	−	4.20013i	−1.36086	−	0.766835i
$31$	5.77216	+	3.33256i	1.03671	+	0.598545i	0.918900	−	0.394491i	$-0.129079\pi$
$31$	5.77216	+	3.33256i	1.03671	+	0.598545i	0.117810	+	0.993036i	$0.462413\pi$
$32$	3.56285	−	6.17104i	0.629829	−	1.09090i
$33$	6.55944	−	0.824719i	1.14185	−	0.143565i
$34$		−	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
$39$	8.97383	−	6.80317i	1.43696	−	1.08938i
$40$	−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
$45$	−2.53840	+	6.20939i	−0.378402	+	0.925641i
$46$	−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
$51$	−5.05330	+	0.635352i	−0.707604	+	0.0889671i
$52$	9.36219	−	16.2158i	1.29830	−	2.24873i
$53$	−0.967113	+	1.67509i	−0.132843	+	0.230091i	−0.924771	−	0.380523i	$-0.875744\pi$
$53$	−0.967113	+	1.67509i	−0.132843	+	0.230091i	0.791928	+	0.610614i	$0.209077\pi$
$54$	7.14584	−	8.98309i	0.972425	−	1.22244i
$55$	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	$0.994009\pi$
$60$	0.116625	+	11.1534i	0.0150562	+	1.43990i
$61$	11.8342	−	6.83249i	1.51522	−	0.874810i	0.515375	−	0.856965i	$-0.327653\pi$
$61$	11.8342	−	6.83249i	1.51522	−	0.874810i	0.999841	−	0.0178455i	$-0.00568070\pi$
$62$		−	14.7237i		−	1.86991i
$63$		0			0
$64$	−12.8096			−1.60121
$65$	14.4427	+	1.66267i	1.79139	+	0.206229i
$66$	−8.82289	−	11.6380i	−1.08602	−	1.43254i
$67$	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	$0.226191\pi$
$71$			10.9926i			1.30458i	−0.757971	+	0.652288i	$0.773809\pi$
$72$	1.57488	−	5.61499i	0.185601	−	0.661733i
$73$	1.65449	−	2.86566i	0.193643	−	0.335400i	−0.752812	−	0.658236i	$-0.771303\pi$
$73$	1.65449	−	2.86566i	0.193643	−	0.335400i	0.946455	+	0.322836i	$0.104636\pi$
$74$	−6.44074	−	3.71856i	−0.748721	−	0.432274i
$75$	−7.90957	+	3.52686i	−0.913318	+	0.407246i
$76$		−	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
$81$	−7.68725	−	4.68040i	−0.854139	−	0.520044i
$82$	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
$87$	−2.35707	−	3.10913i	−0.252705	−	0.333334i
$88$	−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	$-0.420850\pi$
$90$	14.6830	−	2.00225i	1.54772	−	0.211056i
$91$		0			0
$92$	8.64156			0.900945
$93$	−11.4541	+	1.44013i	−1.18774	+	0.149334i
$94$	−9.58999	−	5.53678i	−0.989132	−	0.571075i
$95$	4.17481	−	1.80945i	0.428327	−	0.185646i
$96$	1.53965	+	12.2457i	0.157140	+	1.24982i
$97$	−4.46688			−0.453543			−0.226771	−	0.973948i	$-0.572817\pi$
$97$	−4.46688			−0.453543			−0.226771	+	0.973948i	$0.572817\pi$
$98$		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	$0.0211763\pi$
$102$	6.79703	+	8.96573i	0.673006	+	0.887740i
$103$	0.661216	+	1.14526i	0.0651516	+	0.112846i	0.896761	−	0.442515i	$-0.145914\pi$
$103$	0.661216	+	1.14526i	0.0651516	+	0.112846i	−0.831610	+	0.555361i	$0.812580\pi$
$104$	−12.6384			−1.23930
$105$		0			0
$106$	4.27283			0.415014
$107$	1.66222	+	2.87905i	0.160693	+	0.278328i	0.935117	−	0.354338i	$-0.115294\pi$
$107$	1.66222	+	2.87905i	0.160693	+	0.278328i	−0.774425	+	0.632666i	$0.781960\pi$
$108$	−14.8003	−	2.21229i	−1.42416	−	0.212878i
$109$	−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	$-0.0876657\pi$
$113$	20.4591			1.92463			0.962314	+	0.271941i	$0.0876657\pi$
$114$	−7.72496	+	0.971260i	−0.723509	+	0.0909668i
$115$	2.66820	+	6.15615i	0.248811	+	0.574064i
$116$	−5.61823	−	3.24369i	−0.521640	−	0.301169i
$117$	−5.26740	+	18.7801i	−0.486971	+	1.73622i
$118$	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
$123$	4.84597	−	3.67379i	0.436946	−	0.331254i
$124$	−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
$129$	7.36370	+	9.71321i	0.648337	+	0.855200i
$130$	−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
$135$	−2.99378	−	11.2266i	−0.257664	−	0.966235i
$136$	4.95020	+	2.85800i	0.424476	+	0.245071i
$137$	0.546844	−	0.947161i	0.0467200	−	0.0809215i	−0.841720	−	0.539915i	$-0.818456\pi$
$137$	0.546844	−	0.947161i	0.0467200	−	0.0809215i	0.888440	+	0.458993i	$0.151790\pi$
$138$	−1.43221	−	11.3912i	−0.121918	−	0.969681i
$139$		−	7.35968i		−	0.624240i	−0.950043	−	0.312120i	$-0.898961\pi$
$139$		−	7.35968i		−	0.624240i	0.950043	−	0.312120i	$-0.101039\pi$
$140$		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
$144$	4.26038	−	1.08852i	0.355032	−	0.0907103i
$145$	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	−0.832023	−	0.554741i	$-0.812817\pi$
$149$	−9.36993	+	5.40973i	−0.767615	+	0.443183i	0.0644082	+	0.997924i	$0.479484\pi$
$150$	15.4836	+	11.2363i	1.26423	+	0.917441i
$151$	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
$156$	4.04577	+	32.1782i	0.323921	+	2.57632i
$157$	−2.70593	+	4.68680i	−0.215957	+	0.374048i	−0.953568	−	0.301178i	$-0.902620\pi$
$157$	−2.70593	+	4.68680i	−0.215957	+	0.374048i	0.737612	+	0.675225i	$0.235954\pi$
$158$	6.46126	−	11.1912i	0.514030	−	0.890326i
$159$	−0.417928	−	3.32401i	−0.0331438	−	0.263611i
$160$	−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
$165$	−14.7820	+	0.154567i	−1.15078	+	0.0120330i
$166$	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
$171$	1.51117	+	5.91457i	0.115562	+	0.452298i
$172$	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
$177$	−1.71347	−	13.6282i	−0.128793	−	1.02436i
$178$	−14.9287	+	25.8573i	−1.11895	+	1.93808i
$179$	20.4854	+	11.8273i	1.53115	+	0.884011i	0.999309	+	0.0371678i	$0.0118336\pi$
$179$	20.4854	+	11.8273i	1.53115	+	0.884011i	0.531843	+	0.846843i	$0.321500\pi$
$180$	−11.8317	−	15.2725i	−0.881885	−	1.13834i
$181$			15.6330i			1.16199i	0.813906	+	0.580997i	$0.197337\pi$
$181$			15.6330i			1.16199i	−0.813906	+	0.580997i	$0.802663\pi$
$182$		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
$186$	15.4066	+	20.3223i	1.12966	+	1.49010i
$187$	−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	$-0.539150\pi$
$191$	9.33503	−	5.38958i	0.675459	−	0.389976i	0.798142	+	0.602470i	$0.205817\pi$
$192$	17.6805	−	13.4038i	1.27598	−	0.967335i
$193$	−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
$195$	−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	$0.593166\pi$
$198$	24.3555	+	6.83118i	1.73087	+	0.485471i
$199$	−8.74922	−	5.05137i	−0.620216	−	0.358082i	0.156737	−	0.987640i	$-0.449902\pi$
$199$	−8.74922	−	5.05137i	−0.620216	−	0.358082i	−0.776953	+	0.629559i	$0.783236\pi$
$200$	9.46519	+	2.20858i	0.669290	+	0.156170i
$201$	−18.5365	+	2.33059i	−1.30746	+	0.164387i
$202$	−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
$207$	−8.72158	+	2.22835i	−0.606192	+	0.154881i
$208$	−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
$213$	−11.5024	−	15.1725i	−0.788133	−	1.03960i
$214$	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
$219$	0.714969	+	5.68654i	0.0483131	+	0.384261i
$220$	−22.5529	+	9.77488i	−1.52052	+	0.659023i
$221$	−16.5566	−	9.55898i	−1.11372	−	0.643006i
$222$	12.7809	−	1.60694i	0.857795	−	0.107851i
$223$	4.13183			0.276688			0.138344	−	0.990384i	$-0.455822\pi$
$223$	4.13183			0.276688			0.138344	+	0.990384i	$0.455822\pi$
$224$		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	0.691845	−	0.722046i	$-0.256798\pi$
$227$	6.21430	+	3.58783i	0.412458	+	0.238132i	−0.279388	+	0.960178i	$0.590131\pi$
$228$	6.13212	+	8.08867i	0.406109	+	0.535685i
$229$	−9.05093	+	5.22556i	−0.598102	+	0.345315i	−0.768295	−	0.640096i	$-0.778894\pi$
$229$	−9.05093	+	5.22556i	−0.598102	+	0.345315i	0.170192	+	0.985411i	$0.445561\pi$
$230$	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	0.922822	−	0.385226i	$-0.125876\pi$
$233$	1.95072	+	3.37875i	0.127796	+	0.221349i	−0.795026	+	0.606575i	$0.792543\pi$
$234$	41.7463	−	10.6661i	2.72904	−	0.697268i
$235$	−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	$0.279413\pi$
$239$			23.7873i			1.53867i	−0.638844	+	0.769336i	$0.720587\pi$
$240$	4.94567	+	2.78685i	0.319242	+	0.179890i
$241$	−11.5030	−	6.64126i	−0.740974	−	0.427801i	0.0814495	−	0.996677i	$-0.474045\pi$
$241$	−11.5030	−	6.64126i	−0.740974	−	0.427801i	−0.822423	+	0.568876i	$0.807378\pi$
$242$	3.94187	−	6.82752i	0.253393	−	0.438889i
$243$	15.5078	−	1.58370i	0.994826	−	0.101594i
$244$			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
$249$	−2.78683	−	3.67602i	−0.176608	−	0.232958i
$250$	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
$255$	11.3879	−	0.119076i	0.713136	−	0.00745684i
$256$	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
$261$	6.50669	+	1.82498i	0.402754	+	0.112963i
$262$	6.41935	−	11.1186i	0.396588	−	0.686911i
$263$	−12.0642	+	20.8958i	−0.743908	+	1.28849i	0.206795	+	0.978384i	$0.433697\pi$
$263$	−12.0642	+	20.8958i	−0.743908	+	1.28849i	−0.950703	+	0.310103i	$0.899637\pi$
$264$	12.7508	−	1.60316i	0.784759	−	0.0986678i
$265$	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	$-0.0300718\pi$
$270$	−18.1710	+	18.1276i	−1.10585	+	1.10321i
$271$	10.2612	−	5.92429i	0.623321	−	0.359875i	−0.154840	−	0.987940i	$-0.549486\pi$
$271$	10.2612	−	5.92429i	0.623321	−	0.359875i	0.778161	+	0.628065i	$0.216153\pi$
$272$			4.31002i			0.261334i
$273$		0			0
$274$	−2.41603			−0.145957
$275$	−13.9270	−	13.0483i	−0.839832	−	0.786842i
$276$	−11.9275	+	9.04238i	−0.717951	+	0.544287i
$277$	−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	$-0.902518\pi$
$281$		−	10.1076i		−	0.602968i	0.953471	−	0.301484i	$-0.0974820\pi$
$282$	19.0302	−	2.39266i	1.13323	−	0.142481i
$283$	3.00101	−	5.19791i	0.178392	−	0.308984i	−0.762938	−	0.646472i	$-0.776244\pi$
$283$	3.00101	−	5.19791i	0.178392	−	0.308984i	0.941330	+	0.337488i	$0.109577\pi$
$284$	−27.4167	−	15.8291i	−1.62688	−	0.939282i
$285$	−3.86890	+	6.86594i	−0.229174	+	0.406703i
$286$		−	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
$291$	6.16540	−	4.67406i	0.361422	−	0.273998i
$292$	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
$297$	2.93202	−	19.6153i	0.170133	−	1.13820i
$298$	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
$303$	1.91664	+	15.2441i	0.110108	+	0.875750i
$304$	−2.58299	−	1.49129i	−0.148145	−	0.0855314i
$305$	−28.0358	+	12.1513i	−1.60532	+	0.695780i
$306$	−18.7632	−	5.26264i	−1.07262	−	0.300845i
$307$	29.0345			1.65709			0.828544	−	0.559923i	$-0.189169\pi$
$307$	29.0345			1.65709			0.828544	+	0.559923i	$0.189169\pi$
$308$		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	$0.245483\pi$
$312$	17.4441	−	13.2246i	0.987580	−	0.748696i
$313$	5.42607	+	9.39824i	0.306700	+	0.531220i	0.977638	−	0.210293i	$-0.0674419\pi$
$313$	5.42607	+	9.39824i	0.306700	+	0.531220i	−0.670938	+	0.741513i	$0.734109\pi$
$314$	11.9551			0.674667
$315$		0			0
$316$	−16.8471			−0.947724
$317$	4.67046	+	8.08947i	0.262319	+	0.454350i	0.966858	−	0.255316i	$-0.0821794\pi$
$317$	4.67046	+	8.08947i	0.262319	+	0.454350i	−0.704539	+	0.709665i	$0.748846\pi$
$318$	−5.89756	+	4.47101i	−0.330719	+	0.250722i
$319$	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
$324$	22.7430	−	12.4332i	1.26350	−	0.690736i
$325$	−31.6576	−	7.38690i	−1.75605	−	0.409752i
$326$	32.8230	+	18.9504i	1.81790	+	1.04956i
$327$	−2.65734	−	21.1353i	−0.146951	−	1.16879i
$328$	−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	0.823277	−	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
$333$	−2.50020	−	9.78557i	−0.137010	−	0.536246i
$334$	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
$339$	−28.2386	+	21.4080i	−1.53371	+	1.16272i
$340$	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
$345$	−10.1245	−	5.70506i	−0.545083	−	0.307150i
$346$	19.4611	+	11.2359i	1.04624	+	0.604045i
$347$	15.7892	−	27.3477i	0.847609	−	1.46810i	−0.0357279	−	0.999362i	$-0.511375\pi$
$347$	15.7892	−	27.3477i	0.847609	−	1.46810i	0.883336	−	0.468739i	$-0.155292\pi$
$348$	11.1487	−	1.40172i	0.597632	−	0.0751403i
$349$		−	8.25024i		−	0.441625i	−0.975316	−	0.220813i	$-0.929129\pi$
$349$		−	8.25024i		−	0.441625i	0.975316	−	0.220813i	$-0.0708709\pi$
$350$		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	$0.703070\pi$
$354$	−24.1796	+	18.3308i	−1.28513	+	0.974272i
$355$	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	−0.654124	−	0.756387i	$-0.726963\pi$
$359$	−6.17938	+	3.56767i	−0.326135	+	0.188294i	0.327989	+	0.944682i	$0.393629\pi$
$360$	−4.93436	+	12.0704i	−0.260064	+	0.636164i
$361$	−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
$366$	51.8766	−	6.52245i	2.71163	−	0.340934i
$367$	12.1957	−	21.1235i	0.636609	−	1.10264i	−0.349563	−	0.936913i	$-0.613670\pi$
$367$	12.1957	−	21.1235i	0.636609	−	1.10264i	0.986172	−	0.165726i	$-0.0529969\pi$
$368$	2.19905	−	3.80886i	0.114633	−	0.198551i
$369$	−2.84445	+	10.1415i	−0.148076	+	0.527944i
$370$	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
$375$	18.4722	−	5.81182i	0.953901	−	0.300121i
$376$	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
$381$	0.625034	+	0.824462i	0.0320215	+	0.0422385i
$382$	−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
$387$	−20.3275	−	5.70139i	−1.03330	−	0.289818i
$388$	6.43222	−	11.1409i	0.326546	−	0.565595i
$389$	20.9207	+	12.0785i	1.06072	+	0.612406i	0.925631	−	0.378427i	$-0.123535\pi$
$389$	20.9207	+	12.0785i	1.06072	+	0.612406i	0.135088	+	0.990834i	$0.456868\pi$
$390$	48.4614	+	27.3076i	2.45394	+	1.38277i
$391$		−	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
$396$	−8.16352	−	31.9513i	−0.410232	−	1.60561i
$397$	−6.00792	−	10.4060i	−0.301529	−	0.522263i	0.674954	−	0.737860i	$-0.264164\pi$
$397$	−6.00792	−	10.4060i	−0.301529	−	0.522263i	−0.976482	+	0.215597i	$0.930830\pi$
$398$			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	$-0.387026\pi$
$401$	26.6997	−	15.4151i	1.33332	−	0.769792i	0.985807	+	0.167883i	$0.0536930\pi$
$402$	24.9328	+	32.8880i	1.24353	+	1.64030i
$403$	−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
$408$	−9.82306	+	1.23505i	−0.486314	+	0.0611443i
$409$	13.5699	+	7.83456i	0.670986	+	0.387394i	0.796450	−	0.604704i	$-0.206709\pi$
$409$	13.5699	+	7.83456i	0.670986	+	0.387394i	−0.125464	+	0.992098i	$0.540042\pi$
$410$	−6.89675	−	15.9124i	−0.340606	−	0.785857i
$411$	0.236313	+	1.87953i	0.0116564	+	0.0927101i
$412$	−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
$417$	7.70103	+	10.1582i	0.377121	+	0.497448i
$418$	−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
$423$	−3.72270	−	14.5703i	−0.181004	−	0.708433i
$424$	−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
$429$	−42.6469	+	5.36200i	−2.05901	+	0.258880i
$430$	31.8946	−	13.8238i	1.53809	−	0.666642i
$431$	24.1528	+	13.9447i	1.16340	+	0.671690i	0.952117	−	0.305734i	$-0.0989019\pi$
$431$	24.1528	+	13.9447i	1.16340	+	0.671690i	0.211285	+	0.977425i	$0.432235\pi$
$432$	−4.74137	+	5.96042i	−0.228119	+	0.286771i
$433$	−3.47350			−0.166926			−0.0834629	−	0.996511i	$-0.526598\pi$
$433$	−3.47350			−0.166926			−0.0834629	+	0.996511i	$0.526598\pi$
$434$		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
$438$	10.0892	−	7.64878i	0.482083	−	0.365473i
$439$	−3.41910	+	1.97402i	−0.163185	+	0.0942147i	−0.579368	−	0.815066i	$-0.696701\pi$
$439$	−3.41910	+	1.97402i	−0.163185	+	0.0942147i	0.416184	+	0.909281i	$0.363367\pi$
$440$	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	0.991180	−	0.132522i	$-0.0423075\pi$
$443$	8.01539	+	13.8831i	0.380823	+	0.659604i	−0.610357	+	0.792126i	$0.708974\pi$
$444$	−10.1455	−	13.3826i	−0.481484	−	0.635110i
$445$	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	$0.165891\pi$
$449$			21.1001i			0.995777i	−0.867241	+	0.497889i	$0.834109\pi$
$450$	−33.1287	+	0.692891i	−1.56170	+	0.0326632i
$451$	11.6056	+	6.70048i	0.546485	+	0.315513i
$452$	−29.4607	+	51.0274i	−1.38571	+	2.40013i
$453$	1.79251	+	14.2568i	0.0842195	+	0.669844i
$454$		−	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
$459$	−2.25879	+	15.1114i	−0.105431	+	0.705339i
$460$	−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
$465$	25.8125	−	0.269906i	1.19702	−	0.0125166i
$466$	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
$471$	−1.16934	−	9.30039i	−0.0538802	−	0.428539i
$472$	−7.70770	+	13.3501i	−0.354776	+	0.614490i
$473$	−13.4304	+	23.2621i	−0.617529	+	1.06959i
$474$	2.79216	+	22.2076i	0.128248	+	1.02003i
$475$	−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	$0.188244\pi$
$480$	−0.288558	−	27.5962i	−0.0131708	−	1.25959i
$481$	−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
$486$	−20.1586	−	27.9188i	−0.914414	−	1.26642i
$487$	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	$-0.804941\pi$
$491$		−	25.4892i		−	1.15031i	0.818043	−	0.575157i	$-0.195059\pi$
$492$	2.18476	+	17.3766i	0.0984966	+	0.783398i
$493$	−3.31187	+	5.73632i	−0.149159	+	0.258351i
$494$	−25.3101	−	14.6128i	−1.13875	−	0.657460i
$495$	20.2411	−	15.6810i	0.909771	−	0.704808i
$496$			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
$501$	−10.0514	−	13.2585i	−0.449064	−	0.592346i
$502$	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
$507$	−40.4011	+	30.6286i	−1.79428	+	1.36026i
$508$	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	$-0.338423\pi$
$510$	−12.8061	−	21.6547i	−0.567062	−	0.958884i
$511$		0			0
$512$	16.1430			0.713426
$513$	−8.27468	−	6.58231i	−0.365336	−	0.290616i
$514$	12.7916	+	7.38523i	0.564213	+	0.325749i
$515$	−1.17594	−	2.71317i	−0.0518183	−	0.119557i
$516$	−34.8295	+	4.37911i	−1.53328	+	0.192780i
$517$	−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	$0.0646972\pi$
$522$	−3.69547	−	14.4637i	−0.161746	−	0.633060i
$523$	12.6242	+	21.8658i	0.552018	+	0.956124i	0.998129	+	0.0611461i	$0.0194755\pi$
$523$	12.6242	+	21.8658i	0.552018	+	0.956124i	−0.446110	+	0.894978i	$0.647191\pi$
$524$	−16.7378			−0.731195
$525$		0			0
$526$	53.3010			2.32403
$527$	9.79936	+	16.9730i	0.426867	+	0.739355i
$528$	5.85412	+	7.72197i	0.254768	+	0.336056i
$529$	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
$534$	−6.45128	−	51.3106i	−0.279174	−	2.22042i
$535$	−2.95618	−	6.82059i	−0.127807	−	0.294880i
$536$	18.1583	+	10.4837i	0.784318	+	0.452826i
$537$	−40.6508	+	5.11102i	−1.75421	+	0.220557i
$538$	−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	0.645078	−	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
$543$	−16.3581	−	21.5774i	−0.701994	−	0.925977i
$544$	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
$549$	−10.1482	−	39.7190i	−0.433113	−	1.69517i
$550$	−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
$555$	6.40105	−	11.3596i	0.271709	−	0.482188i
$556$	18.3559	+	10.5978i	0.778464	+	0.449446i
$557$	−14.4676	+	25.0586i	−0.613011	+	1.06177i	0.377719	+	0.925920i	$0.376708\pi$
$557$	−14.4676	+	25.0586i	−0.613011	+	1.06177i	−0.990730	+	0.135845i	$0.956625\pi$
$558$	−42.5298	−	11.9286i	−1.80043	−	0.504980i
$559$			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	$0.708563\pi$
$564$	−15.1062	−	19.9261i	−0.636087	−	0.839041i
$565$	−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	−0.309521	−	0.950893i	$-0.600169\pi$
$569$	8.56862	−	4.94710i	0.359215	−	0.207393i	0.668736	+	0.743500i	$0.266835\pi$
$570$	17.4086	−	0.182031i	0.729165	−	0.00762446i
$571$	−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
$576$	−10.3780	+	37.0011i	−0.432415	+	1.54171i
$577$	−19.0377	+	32.9742i	−0.792549	+	1.37273i	0.131835	+	0.991272i	$0.457913\pi$
$577$	−19.0377	+	32.9742i	−0.792549	+	1.37273i	−0.924384	+	0.381463i	$0.875420\pi$
$578$	−9.22669	+	15.9811i	−0.383780	+	0.664726i
$579$	3.17275	−	0.398910i	0.131855	−	0.0165781i
$580$	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
$585$	16.5037	−	40.3710i	0.682342	−	1.66914i
$586$	−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
$591$	11.1792	−	8.47508i	0.459851	−	0.348618i
$592$	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
$597$	17.3618	−	2.18289i	0.710569	−	0.0893399i
$598$	21.5479	−	37.3220i	0.881159	−	1.52621i
$599$	11.7736	+	6.79751i	0.481058	+	0.277739i	0.720857	−	0.693084i	$-0.243748\pi$
$599$	11.7736	+	6.79751i	0.481058	+	0.277739i	−0.239800	+	0.970822i	$0.577082\pi$
$600$	−15.3753	+	6.85582i	−0.627695	+	0.279888i
$601$		−	46.2155i		−	1.88517i	−0.333966	−	0.942585i	$-0.608387\pi$
$601$		−	46.2155i		−	1.88517i	0.333966	−	0.942585i	$-0.391613\pi$
$602$		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
$606$	27.0465	−	20.5043i	1.09869	−	0.832930i
$607$	4.37164	+	7.57190i	0.177439	+	0.307334i	0.941003	−	0.338399i	$-0.109885\pi$
$607$	4.37164	+	7.57190i	0.177439	+	0.307334i	−0.763563	+	0.645733i	$0.776552\pi$
$608$			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
$612$	6.28906	+	24.6148i	0.254220	+	0.994995i
$613$	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
$615$	−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	$0.670178\pi$
$618$	0.631212	+	5.02038i	0.0253911	+	0.201949i
$619$	26.2018	+	15.1276i	1.05314	+	0.608029i	0.923526	−	0.383535i	$-0.125294\pi$
$619$	26.2018	+	15.1276i	1.05314	+	0.608029i	0.129612	+	0.991565i	$0.458627\pi$
$620$	39.3820	−	17.0690i	1.58162	−	0.685506i
$621$	9.70623	−	12.2018i	0.389498	−	0.489641i
$622$	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
$627$	−10.7202	+	8.12711i	−0.428123	+	0.324565i
$628$	−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
$633$	−14.7436	+	11.1773i	−0.586004	+	0.444257i
$634$	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
$639$	31.7524	+	8.90582i	1.25610	+	0.352309i
$640$	−12.4900	−	28.8173i	−0.493711	−	1.13910i
$641$	−0.111457	−	0.0643495i	−0.00440227	−	0.00254165i	0.497797	−	0.867293i	$-0.334142\pi$
$641$	−0.111457	−	0.0643495i	−0.00440227	−	0.00254165i	−0.502200	+	0.864752i	$0.667476\pi$
$642$	1.58679	+	12.6206i	0.0626257	+	0.498097i
$643$	−0.150563			−0.00593763			−0.00296881	−	0.999996i	$-0.500945\pi$
$643$	−0.150563			−0.00593763			−0.00296881	+	0.999996i	$0.500945\pi$
$644$		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	0.995197	−	0.0978912i	$-0.0312097\pi$
$647$	35.8147	+	20.6776i	1.40802	+	0.812920i	0.412822	+	0.910812i	$0.364543\pi$
$648$	−14.9432	−	9.09817i	−0.587023	−	0.357410i
$649$	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	$0.0288940\pi$
$653$	14.7304	+	25.5138i	0.576446	+	0.998433i	−0.419437	+	0.907784i	$0.637773\pi$
$654$	−37.4990	+	28.4284i	−1.46633	+	1.11164i
$655$	−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	$-0.855825\pi$
$659$		−	22.4678i		−	0.875220i	0.899165	−	0.437610i	$-0.144175\pi$
$660$	20.9003	−	37.0907i	0.813544	−	1.44375i
$661$	20.3164	+	11.7297i	0.790218	+	0.456233i	0.840039	−	0.542526i	$-0.182532\pi$
$661$	20.3164	+	11.7297i	0.790218	+	0.456233i	−0.0498213	+	0.998758i	$0.515865\pi$
$662$	−3.21328	+	5.56557i	−0.124888	+	0.216312i
$663$	32.8546	−	4.13081i	1.27597	−	0.160427i
$664$			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
$669$	−5.70294	+	4.32347i	−0.220489	+	0.167155i
$670$	−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
$675$	3.77936	+	25.7044i	0.145468	+	0.989363i
$676$	−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
$681$	−12.3315	+	1.55044i	−0.472545	+	0.0594130i
$682$	−28.0994	+	48.6697i	−1.07598	+	1.86366i
$683$	19.3444	−	33.5055i	0.740192	−	1.28205i	−0.212215	−	0.977223i	$-0.568068\pi$
$683$	19.3444	−	33.5055i	0.740192	−	1.28205i	0.952407	−	0.304828i	$-0.0985990\pi$
$684$	−16.9277	−	4.74783i	−0.647246	−	0.181538i
$685$	−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
$690$	0.268422	+	25.6706i	0.0102187	+	0.977262i
$691$	16.6768	−	9.62834i	0.634415	−	0.366279i	−0.148045	−	0.988981i	$-0.547298\pi$
$691$	16.6768	−	9.62834i	0.634415	−	0.366279i	0.782460	+	0.622701i	$0.213965\pi$
$692$		−	29.2965i		−	1.11369i
$693$		0			0
$694$	−69.7587			−2.64800
$695$	−1.88211	+	16.3488i	−0.0713923	+	0.620144i
$696$	−4.58189	−	6.04381i	−0.173676	−	0.229090i
$697$	−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	$-0.0407334\pi$
$702$	−46.4594	+	58.4046i	−1.75350	+	2.20434i
$703$	−3.42531	+	5.93282i	−0.129188	+	0.223760i
$704$	42.3428	+	24.4466i	1.59586	+	0.921367i
$705$	9.53089	−	16.9140i	0.358954	−	0.637017i
$706$			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
$711$	17.0031	−	4.34428i	0.637667	−	0.162923i
$712$	−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
$717$	−24.8906	−	32.8324i	−0.929557	−	1.22615i
$718$	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	$0.582487\pi$
$720$	−9.74237	+	1.32852i	−0.363077	+	0.0495112i
$721$		0			0
$722$	32.8253			1.22163
$723$	22.8263	−	2.86995i	0.848919	−	0.106735i
$724$	−38.9906	−	22.5112i	−1.44907	−	0.836624i
$725$	−2.55931	+	10.9683i	−0.0950506	+	0.407353i
$726$	1.70344	+	13.5484i	0.0632205	+	0.502827i
$727$	−18.6502			−0.691699			−0.345849	−	0.938290i	$-0.612409\pi$
$727$	−18.6502			−0.691699			−0.345849	+	0.938290i	$0.612409\pi$
$728$		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
$732$	−41.1799	−	54.3191i	−1.52205	−	2.00769i
$733$	18.7967	+	32.5568i	0.694271	+	1.20251i	0.970426	+	0.241399i	$0.0776062\pi$
$733$	18.7967	+	32.5568i	0.694271	+	1.20251i	−0.276155	+	0.961113i	$0.589060\pi$
$734$	−53.8821			−1.98882
$735$		0			0
$736$	−21.3813			−0.788124
$737$	−20.5852	−	35.6546i	−0.758264	−	1.31335i
$738$	22.5435	−	5.75984i	0.829837	−	0.212023i
$739$	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	$-0.786891\pi$
$743$	−42.7477			−1.56826			−0.784131	+	0.620596i	$0.786891\pi$
$744$	−22.2656	+	2.79945i	−0.816295	+	0.102633i
$745$	22.1978	−	9.62097i	0.813264	−	0.352485i
$746$	−42.1929	−	24.3601i	−1.54479	−	0.891886i
$747$	7.69304	+	2.15772i	0.281474	+	0.0789470i
$748$	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	0.810508	−	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
$753$	12.5982	−	9.55082i	0.459103	−	0.348051i
$754$	−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
$759$	−11.9842	−	15.8079i	−0.434998	−	0.573791i
$760$	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
$765$	−15.5935	+	12.0804i	−0.563783	+	0.436768i
$766$	4.07358	+	2.35188i	0.147184	+	0.0849769i
$767$	25.7795	−	44.6514i	0.930843	−	1.61227i
$768$	1.16872	+	9.29547i	0.0421725	+	0.335421i
$769$		−	27.0203i		−	0.974376i	−0.873297	−	0.487188i	$-0.838023\pi$
$769$		−	27.0203i		−	0.974376i	0.873297	−	0.487188i	$-0.161977\pi$
$770$		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	$-0.733927\pi$
$774$	11.5450	+	45.1859i	0.414975	+	1.62417i
$775$	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
$780$	−0.758249	−	72.5152i	−0.0271497	−	2.59646i
$781$	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
$786$	2.77405	+	22.0636i	0.0989471	+	0.786981i
$787$	8.37879	−	14.5125i	0.298672	−	0.517315i	−0.677161	−	0.735835i	$-0.736790\pi$
$787$	8.37879	−	14.5125i	0.298672	−	0.517315i	0.975832	+	0.218521i	$0.0701231\pi$
$788$	11.6630	−	20.2009i	0.415477	−	0.719627i
$789$	−5.21340	−	41.4650i	−0.185602	−	1.47619i
$790$	−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
$795$	0.0783271	+	7.49082i	0.00277798	+	0.265672i
$796$	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
$801$	−39.2856	+	10.0374i	−1.38809	+	0.354655i
$802$	−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
$807$	4.10702	+	32.6654i	0.144574	+	1.14988i
$808$	8.62160	−	14.9331i	0.303307	−	0.525343i
$809$	−36.4604	−	21.0504i	−1.28188	−	0.740094i	−0.304689	−	0.952452i	$-0.598553\pi$
$809$	−36.4604	−	21.0504i	−1.28188	−	0.740094i	−0.977192	+	0.212358i	$0.931886\pi$
$810$	6.11209	−	44.0344i	0.214757	−	1.54721i
$811$		−	1.35051i		−	0.0474227i	−0.999719	−	0.0237113i	$-0.992452\pi$
$811$		−	1.35051i		−	0.0474227i	0.999719	−	0.0237113i	$-0.00754826\pi$
$812$		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
$816$	−4.50993	−	5.94890i	−0.157879	−	0.208253i
$817$	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	$-0.730099\pi$
$821$	−9.82457	+	5.67222i	−0.342880	+	0.197962i	0.318665	+	0.947867i	$0.396765\pi$
$822$	3.33471	−	2.52809i	0.116312	−	0.0881771i
$823$	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
$825$	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	$0.706788\pi$
$828$	7.00112	−	24.9614i	0.243306	−	0.867470i
$829$	3.50678	+	2.02464i	0.121796	+	0.0703187i	0.559660	−	0.828722i	$-0.310932\pi$
$829$	3.50678	+	2.02464i	0.121796	+	0.0703187i	−0.437864	+	0.899041i	$0.644265\pi$
$830$	−12.0707	+	5.23169i	−0.418980	+	0.181595i
$831$	28.3867	−	3.56906i	0.984725	−	0.123809i
$832$	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
$837$	−5.11992	+	34.2524i	−0.176970	+	1.18394i
$838$	−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
$843$	10.5764	+	13.9510i	0.364271	+	0.480497i
$844$	−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
$849$	1.29686	+	10.3146i	0.0445080	+	0.353997i
$850$	7.38023	−	31.6291i	0.253140	−	1.08487i
$851$	−8.74849	−	5.05094i	−0.299894	−	0.173144i
$852$	54.4052	−	6.84036i	1.86389	−	0.234347i
$853$	37.5709			1.28640			0.643201	−	0.765697i	$-0.277606\pi$
$853$	37.5709			1.28640			0.643201	+	0.765697i	$0.277606\pi$
$854$		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	0.799206	−	0.601057i	$-0.205254\pi$
$857$	19.8563	+	11.4640i	0.678278	+	0.391604i	−0.120928	+	0.992661i	$0.538587\pi$
$858$	57.3630	+	75.6656i	1.95834	+	2.58318i
$859$	−16.2512	+	9.38264i	−0.554484	+	0.320132i	−0.750929	−	0.660383i	$-0.770394\pi$
$859$	−16.2512	+	9.38264i	−0.554484	+	0.320132i	0.196444	+	0.980515i	$0.437060\pi$
$860$	−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	0.784987	−	0.619512i	$-0.212670\pi$
$863$	−4.23086	−	7.32807i	−0.144020	−	0.249450i	−0.929007	+	0.370062i	$0.879336\pi$
$864$	36.6194	+	5.47373i	1.24582	+	0.186220i
$865$	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
$870$	9.46117	−	16.7902i	0.320764	−	0.569243i
$871$	−60.7329	−	35.0641i	−2.05785	−	1.18810i
$872$	−11.9535	+	20.7041i	−0.404797	+	0.701129i
$873$	−3.61892	+	12.9027i	−0.122482	+	0.436691i
$874$		−	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
$879$	3.71852	+	4.90498i	0.125423	+	0.165441i
$880$	−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
$885$	0.321135	+	30.7118i	0.0107948	+	1.03237i
$886$	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
$891$	16.4782	+	30.1420i	0.552041	+	1.00980i
$892$	−5.94975	+	10.3053i	−0.199212	+	0.345046i
$893$	−5.10015	+	8.83371i	−0.170670	+	0.295609i
$894$	−41.0742	+	5.16426i	−1.37373	+	0.172719i
$895$	−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
$900$	22.3773	+	36.9519i	0.745909	+	1.23173i
$901$	−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
$906$	25.2949	−	19.1764i	0.840367	−	0.637092i
$907$	−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	$0.344261\pi$
$911$			53.2832i			1.76535i	−0.469982	+	0.882676i	$0.655739\pi$
$912$	5.12563	−	0.644446i	0.169727	−	0.0213397i
$913$	5.08280	−	8.80366i	0.168216	−	0.291359i
$914$	18.3787	+	10.6110i	0.607914	+	0.350979i
$915$	25.9814	−	46.1079i	0.858920	−	1.52428i
$916$		−	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
$921$	−40.0749	+	30.3812i	−1.32051	+	1.00110i
$922$	−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
$927$	3.84382	−	0.982092i	0.126248	−	0.0322561i
$928$	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	$-0.413686\pi$
$930$	−29.0270	−	49.0838i	−0.951834	−	1.60952i
$931$		0			0
$932$	−11.2360			−0.368048
$933$	−1.86777	−	14.8554i	−0.0611482	−	0.486345i
$934$	−34.2800	−	19.7916i	−1.12168	−	0.647600i
$935$	9.98034	+	23.0269i	0.326392	+	0.753061i
$936$	−10.2392	+	36.5065i	−0.334680	+	1.19325i
$937$	−26.4685			−0.864688			−0.432344	−	0.901709i	$-0.642313\pi$
$937$	−26.4685			−0.864688			−0.432344	+	0.901709i	$0.642313\pi$
$938$		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	$-0.00622642\pi$
$942$	−16.5010	+	12.5096i	−0.537633	+	0.407586i
$943$	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	0.752513	−	0.658578i	$-0.228842\pi$
$947$	−5.97276	−	10.3451i	−0.194089	−	0.336171i	−0.946601	+	0.322406i	$0.895508\pi$
$948$	23.2532	−	17.6285i	0.755229	−	0.572548i
$949$	−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	$-0.509095\pi$
$953$	−1.76384			−0.0571364			−0.0285682	+	0.999592i	$0.509095\pi$
$954$	3.46171	−	12.3422i	0.112077	−	0.399594i
$955$	−22.1151	+	9.58513i	−0.715627	+	0.310167i
$956$	−59.3284	−	34.2532i	−1.91882	−	1.10783i
$957$	1.85775	+	14.7757i	0.0600527	+	0.477632i
$958$	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
$963$	9.66291	−	2.46886i	0.311383	−	0.0795580i
$964$	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
$969$	8.25869	−	6.26101i	0.265307	−	0.201133i
$970$	−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
$975$	51.4249	−	22.9302i	1.64692	−	0.734356i
$976$	17.3460	+	10.0147i	0.555231	+	0.320563i
$977$	4.07411	−	7.05657i	0.130342	−	0.225760i	−0.793466	−	0.608614i	$-0.791726\pi$
$977$	4.07411	−	7.05657i	0.130342	−	0.225760i	0.923809	+	0.382855i	$0.125059\pi$
$978$	−65.1332	+	8.18920i	−2.08273	+	0.261862i
$979$			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	$0.741479\pi$
$984$	9.42003	−	7.14143i	0.300300	−	0.227661i
$985$	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
$990$	−52.3563	−	21.4032i	−1.66399	−	0.680240i
$991$	−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
$996$	13.1814	−	1.65730i	0.417669	−	0.0525136i
$997$	−13.5211	+	23.4192i	−0.428218	+	0.741695i	−0.996715	−	0.0809903i	$-0.974192\pi$
$997$	−13.5211	+	23.4192i	−0.428218	+	0.741695i	0.568497	+	0.822685i	$0.307525\pi$
$998$	37.1913	−	64.4173i	1.17727	−	2.03909i
$999$	13.6904	+	10.8903i	0.433144	+	0.344555i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.1	✓	32	35.4	even	6
735.2.g.c.734.2	yes	32	21.17	even	6
735.2.g.c.734.3	yes	32	21.11	odd	6
735.2.g.c.734.4	yes	32	35.24	odd	6
735.2.g.c.734.29	yes	32	7.3	odd	6
735.2.g.c.734.30	yes	32	105.74	odd	6
735.2.g.c.734.31	yes	32	105.59	even	6
735.2.g.c.734.32	yes	32	7.4	even	3
735.2.p.g.374.1		64	1.1	even	1	trivial
735.2.p.g.374.2		64	105.104	even	2	inner
735.2.p.g.374.3		64	15.14	odd	2	inner
735.2.p.g.374.4		64	7.6	odd	2	inner
735.2.p.g.374.29		64	35.34	odd	2	inner
735.2.p.g.374.30		64	3.2	odd	2	inner
735.2.p.g.374.31		64	21.20	even	2	inner
735.2.p.g.374.32		64	5.4	even	2	inner
735.2.p.g.509.1		64	105.89	even	6	inner
735.2.p.g.509.2		64	7.2	even	3	inner
735.2.p.g.509.3		64	7.5	odd	6	inner
735.2.p.g.509.4		64	105.44	odd	6	inner
735.2.p.g.509.29		64	21.2	odd	6	inner
735.2.p.g.509.30		64	35.19	odd	6	inner
735.2.p.g.509.31		64	35.9	even	6	inner
735.2.p.g.509.32		64	21.5	even	6	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} +(-1.38025 + 1.04638i) q^{3} +(-1.43998 + 2.49412i) q^{4} +(-2.22140 - 0.255732i) q^{5} +(3.52637 + 1.48480i) q^{6} +1.94389 q^{8} +(0.810168 - 2.88853i) q^{9} +(1.96436 + 4.53223i) q^{10} +(-3.30554 - 1.90846i) q^{11} +(-0.622272 - 4.94927i) q^{12} -6.50161 q^{13} +(3.33367 - 1.97146i) q^{15} +(0.732874 + 1.26937i) q^{16} +(2.54654 + 1.47025i) q^{17} +(-6.42092 + 1.64054i) q^{18} +(-1.76224 + 1.01743i) q^{19} +(3.83659 - 5.17218i) q^{20} +8.43180i q^{22} +(-1.50029 - 2.59858i) q^{23} +(-2.68305 + 2.03405i) q^{24} +(4.86920 + 1.13616i) q^{25} +(7.18123 + 12.4383i) q^{26} +(1.90428 + 4.83464i) q^{27} +2.25259i q^{29} +(-7.45375 - 4.20013i) q^{30} +(5.77216 + 3.33256i) q^{31} +(3.56285 - 6.17104i) q^{32} +(6.55944 - 0.824719i) q^{33} -6.49574i q^{34} +(6.03772 + 6.18009i) q^{36} +(2.91560 - 1.68332i) q^{37} +(3.89289 + 2.24756i) q^{38} +(8.97383 - 6.80317i) q^{39} +(-4.31815 - 0.497115i) q^{40} -3.51094 q^{41} -7.03729i q^{43} +(9.51983 - 5.49628i) q^{44} +(-2.53840 + 6.20939i) 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} +(-5.05330 + 0.635352i) q^{51} +(9.36219 - 16.2158i) q^{52} +(-0.967113 + 1.67509i) q^{53} +(7.14584 - 8.98309i) 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} +(0.116625 + 11.1534i) q^{60} +(11.8342 - 6.83249i) q^{61} -14.7237i q^{62} -12.8096 q^{64} +(14.4427 + 1.66267i) q^{65} +(-8.82289 - 11.6380i) q^{66} +(9.34121 + 5.39315i) q^{67} +(-7.33395 + 4.23426i) q^{68} +(4.78988 + 2.01681i) q^{69} +10.9926i q^{71} +(1.57488 - 5.61499i) q^{72} +(1.65449 - 2.86566i) q^{73} +(-6.44074 - 3.71856i) q^{74} +(-7.90957 + 3.52686i) q^{75} -5.86030i q^{76} +(-22.9271 - 9.65357i) q^{78} +(2.92489 + 5.06605i) q^{79} +(-1.30338 - 3.00720i) q^{80} +(-7.68725 - 4.68040i) q^{81} +(3.87795 + 6.71680i) q^{82} +2.66330i q^{83} +(-5.28089 - 3.91724i) q^{85} +(-13.4631 + 7.77291i) q^{86} +(-2.35707 - 3.10913i) q^{87} +(-6.42561 - 3.70983i) q^{88} +(-6.75793 - 11.7051i) q^{89} +(14.6830 - 2.00225i) q^{90} +8.64156 q^{92} +(-11.4541 + 1.44013i) q^{93} +(-9.58999 - 5.53678i) q^{94} +(4.17481 - 1.80945i) q^{95} +(1.53965 + 12.2457i) 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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