LMFDB - Embedded newform 735.2.g.c.734.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(734,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.734"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			734.3
Character	$\chi$	$=$	735.734
Dual form			735.2.g.c.734.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.20906 q^{2} +(1.59632 - 0.672139i) q^{3} +2.87996 q^{4} +(-1.33217 + 1.79592i) q^{5} +(-3.52637 + 1.48480i) q^{6} -1.94389 q^{8} +(2.09646 - 2.14589i) q^{9} +(2.94284 - 3.96730i) q^{10} -3.81691i q^{11} +(4.59733 - 1.93573i) q^{12} -6.50161 q^{13} +(-0.919457 + 3.76226i) q^{15} -1.46575 q^{16} +2.94050i q^{17} +(-4.63121 + 4.74041i) q^{18} -2.03485i q^{19} +(-3.83659 + 5.17218i) q^{20} +8.43180i q^{22} -3.00058 q^{23} +(-3.10306 + 1.30656i) q^{24} +(-1.45065 - 4.78494i) q^{25} +14.3625 q^{26} +(1.90428 - 4.83464i) q^{27} -2.25259i q^{29} +(2.03114 - 8.31107i) q^{30} -6.66511i q^{31} +7.12571 q^{32} +(-2.56549 - 6.09300i) q^{33} -6.49574i q^{34} +(6.03772 - 6.18009i) q^{36} +3.36664i q^{37} +4.49512i q^{38} +(-10.3786 + 4.36998i) q^{39} +(2.58959 - 3.49107i) q^{40} +3.51094 q^{41} -7.03729i q^{43} -10.9926i q^{44} +(1.06101 + 6.62376i) q^{45} +6.62848 q^{46} -5.01279i q^{47} +(-2.33980 + 0.985185i) q^{48} +(3.20459 + 10.5702i) q^{50} +(1.97642 + 4.69396i) q^{51} -18.7244 q^{52} -1.93423 q^{53} +(-4.20667 + 10.6800i) q^{54} +(6.85487 + 5.08477i) q^{55} +(-1.36770 - 3.24827i) q^{57} +4.97612i q^{58} -7.93019 q^{59} +(-2.64800 + 10.8352i) q^{60} +13.6650i q^{61} +14.7237i q^{62} -12.8096 q^{64} +(8.66124 - 11.6764i) q^{65} +(5.66734 + 13.4598i) q^{66} -10.7863i q^{67} +8.46851i q^{68} +(-4.78988 + 2.01681i) q^{69} -10.9926i q^{71} +(-4.07528 + 4.17138i) q^{72} -3.30897 q^{73} -7.43712i q^{74} +(-5.53184 - 6.66324i) q^{75} -5.86030i q^{76} +(22.9271 - 9.65357i) q^{78} -5.84977 q^{79} +(1.95262 - 2.63236i) q^{80} +(-0.209716 - 8.99756i) q^{81} -7.75589 q^{82} -2.66330i q^{83} +(-5.28089 - 3.91724i) q^{85} +15.5458i q^{86} +(-1.51405 - 3.59585i) q^{87} +7.41965i q^{88} -13.5159 q^{89} +(-2.34385 - 14.6323i) q^{90} -8.64156 q^{92} +(-4.47988 - 10.6396i) q^{93} +11.0736i q^{94} +(3.65444 + 2.71077i) q^{95} +(11.3749 - 4.78946i) q^{96} -4.46688 q^{97} +(-8.19069 - 8.00200i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

Character values

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

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−2.20906			−1.56204			−0.781022	−	0.624504i	$-0.785301\pi$
$2$	−2.20906			−1.56204			−0.781022	+	0.624504i	$0.785301\pi$
$3$	1.59632	−	0.672139i	0.921634	−	0.388059i
$3$	1.59632	−	0.672139i	0.921634	−	0.388059i
$4$	2.87996			1.43998
$5$	−1.33217	+	1.79592i	−0.595764	+	0.803160i
$5$	−1.33217	+	1.79592i	−0.595764	+	0.803160i
$6$	−3.52637	+	1.48480i	−1.43963	+	0.606166i
$7$		0			0
$7$		0			0
$8$	−1.94389			−0.687269
$9$	2.09646	−	2.14589i	0.698820	−	0.715298i
$10$	2.94284	−	3.96730i	0.930609	−	1.25457i
$11$		−	3.81691i		−	1.15084i	−0.817857	−	0.575421i	$-0.804838\pi$
$11$		−	3.81691i		−	1.15084i	0.817857	−	0.575421i	$-0.195162\pi$
$12$	4.59733	−	1.93573i	1.32714	−	0.558798i
$13$	−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
$15$	−0.919457	+	3.76226i	−0.237403	+	0.971411i
$16$	−1.46575			−0.366437
$17$			2.94050i			0.713175i	0.934262	+	0.356587i	$0.116060\pi$
$17$			2.94050i			0.713175i	−0.934262	+	0.356587i	$0.883940\pi$
$18$	−4.63121	+	4.74041i	−1.09159	+	1.11733i
$19$		−	2.03485i		−	0.466828i	−0.972377	−	0.233414i	$-0.925010\pi$
$19$		−	2.03485i		−	0.466828i	0.972377	−	0.233414i	$-0.0749897\pi$
$20$	−3.83659	+	5.17218i	−0.857888	+	1.15653i
$21$		0			0
$22$			8.43180i			1.79767i
$23$	−3.00058			−0.625665			−0.312832	−	0.949808i	$-0.601278\pi$
$23$	−3.00058			−0.625665			−0.312832	+	0.949808i	$0.601278\pi$
$24$	−3.10306	+	1.30656i	−0.633410	+	0.266701i
$25$	−1.45065	−	4.78494i	−0.290131	−	0.956987i
$26$	14.3625			2.81671
$27$	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	$-0.0670690\pi$
$30$	2.03114	−	8.31107i	0.370834	−	1.51739i
$31$		−	6.66511i		−	1.19709i	−0.801089	−	0.598545i	$-0.795746\pi$
$31$		−	6.66511i		−	1.19709i	0.801089	−	0.598545i	$-0.204254\pi$
$32$	7.12571			1.25966
$33$	−2.56549	−	6.09300i	−0.446595	−	1.06066i
$34$		−	6.49574i		−	1.11401i
$35$		0			0
$36$	6.03772	−	6.18009i	1.00629	−	1.03001i
$37$			3.36664i			0.553472i	0.960946	+	0.276736i	$0.0892528\pi$
$37$			3.36664i			0.553472i	−0.960946	+	0.276736i	$0.910747\pi$
$38$			4.49512i			0.729205i
$39$	−10.3786	+	4.36998i	−1.66191	+	0.699757i
$40$	2.58959	−	3.49107i	0.409450	−	0.551986i
$41$	3.51094			0.548317			0.274158	−	0.961685i	$-0.411601\pi$
$41$	3.51094			0.548317			0.274158	+	0.961685i	$0.411601\pi$
$42$		0			0
$43$		−	7.03729i		−	1.07318i	−0.843844	−	0.536588i	$-0.819713\pi$
$43$		−	7.03729i		−	1.07318i	0.843844	−	0.536588i	$-0.180287\pi$
$44$		−	10.9926i		−	1.65719i
$45$	1.06101	+	6.62376i	0.158167	+	0.987412i
$46$	6.62848			0.977316
$47$		−	5.01279i		−	0.731190i	−0.930774	−	0.365595i	$-0.880865\pi$
$47$		−	5.01279i		−	0.731190i	0.930774	−	0.365595i	$-0.119135\pi$
$48$	−2.33980	+	0.985185i	−0.337721	+	0.142199i
$49$		0			0
$50$	3.20459	+	10.5702i	0.453197	+	1.49486i
$51$	1.97642	+	4.69396i	0.276754	+	0.657286i
$52$	−18.7244			−2.59660
$53$	−1.93423			−0.265686			−0.132843	−	0.991137i	$-0.542411\pi$
$53$	−1.93423			−0.265686			−0.132843	+	0.991137i	$0.542411\pi$
$54$	−4.20667	+	10.6800i	−0.572455	+	1.45337i
$55$	6.85487	+	5.08477i	0.924310	+	0.685630i
$56$		0			0
$57$	−1.36770	−	3.24827i	−0.181157	−	0.430244i
$58$			4.97612i			0.653396i
$59$	−7.93019			−1.03242			−0.516211	−	0.856461i	$-0.672658\pi$
$59$	−7.93019			−1.03242			−0.516211	+	0.856461i	$0.672658\pi$
$60$	−2.64800	+	10.8352i	−0.341855	+	1.39881i
$61$			13.6650i			1.74962i	0.484466	+	0.874810i	$0.339014\pi$
$61$			13.6650i			1.74962i	−0.484466	+	0.874810i	$0.660986\pi$
$62$			14.7237i			1.86991i
$63$		0			0
$64$	−12.8096			−1.60121
$65$	8.66124	−	11.6764i	1.07429	−	1.44828i
$66$	5.66734	+	13.4598i	0.697601	+	1.65679i
$67$		−	10.7863i		−	1.31776i	−0.752250	−	0.658878i	$-0.771031\pi$
$67$		−	10.7863i		−	1.31776i	0.752250	−	0.658878i	$-0.228969\pi$
$68$			8.46851i			1.02696i
$69$	−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	$-0.226191\pi$
$72$	−4.07528	+	4.17138i	−0.480277	+	0.491602i
$73$	−3.30897			−0.387286			−0.193643	−	0.981072i	$-0.562030\pi$
$73$	−3.30897			−0.387286			−0.193643	+	0.981072i	$0.562030\pi$
$74$		−	7.43712i		−	0.864548i
$75$	−5.53184	−	6.66324i	−0.638762	−	0.769404i
$76$		−	5.86030i		−	0.672223i
$77$		0			0
$78$	22.9271	−	9.65357i	2.59598	−	1.09305i
$79$	−5.84977			−0.658151			−0.329075	−	0.944304i	$-0.606737\pi$
$79$	−5.84977			−0.658151			−0.329075	+	0.944304i	$0.606737\pi$
$80$	1.95262	−	2.63236i	0.218310	−	0.294307i
$81$	−0.209716	−	8.99756i	−0.0233018	−	0.999728i
$82$	−7.75589			−0.856495
$83$		−	2.66330i		−	0.292336i	−0.989260	−	0.146168i	$-0.953306\pi$
$83$		−	2.66330i		−	0.292336i	0.989260	−	0.146168i	$-0.0466939\pi$
$84$		0			0
$85$	−5.28089	−	3.91724i	−0.572793	−	0.424884i
$86$			15.5458i			1.67635i
$87$	−1.51405	−	3.59585i	−0.162324	−	0.385516i
$88$			7.41965i			0.790938i
$89$	−13.5159			−1.43268			−0.716339	−	0.697752i	$-0.754184\pi$
$89$	−13.5159			−1.43268			−0.716339	+	0.697752i	$0.754184\pi$
$90$	−2.34385	−	14.6323i	−0.247063	−	1.54238i
$91$		0			0
$92$	−8.64156			−0.900945
$93$	−4.47988	−	10.6396i	−0.464542	−	1.10328i
$94$			11.0736i			1.14215i
$95$	3.65444	+	2.71077i	0.374937	+	0.278119i
$96$	11.3749	−	4.78946i	1.16094	−	0.488822i
$97$	−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
$100$	−4.17782	−	13.7804i	−0.417782	−	1.37804i
$101$	8.87047			0.882644			0.441322	−	0.897349i	$-0.354510\pi$
$101$	8.87047			0.882644			0.441322	+	0.897349i	$0.354510\pi$
$102$	−4.36604	−	10.3693i	−0.432302	−	1.02671i
$103$	−1.32243			−0.130303			−0.0651516	−	0.997875i	$-0.520753\pi$
$103$	−1.32243			−0.130303			−0.0651516	+	0.997875i	$0.520753\pi$
$104$	12.6384			1.23930
$105$		0			0
$106$	4.27283			0.415014
$107$	3.32444			0.321386			0.160693	−	0.987004i	$-0.448627\pi$
$107$	3.32444			0.321386			0.160693	+	0.987004i	$0.448627\pi$
$108$	5.48424	−	13.9236i	0.527722	−	1.33980i
$109$	12.2985			1.17799			0.588994	−	0.808138i	$-0.299524\pi$
$109$	12.2985			1.17799			0.588994	+	0.808138i	$0.299524\pi$
$110$	−15.1428	−	11.2326i	−1.44381	−	1.07098i
$111$	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	$0.912334\pi$
$114$	3.02135	+	7.17564i	0.282975	+	0.672061i
$115$	3.99728	−	5.38881i	0.372749	−	0.502509i
$116$		−	6.48737i		−	0.602338i
$117$	−13.6304	+	13.9518i	−1.26013	+	1.28984i
$118$	17.5183			1.61269
$119$		0			0
$120$	1.78732	−	7.31342i	0.163160	−	0.667620i
$121$	−3.56881			−0.324438
$122$		−	30.1868i		−	2.73298i
$123$	5.60458	−	2.35984i	0.505348	−	0.212780i
$124$		−	19.1953i		−	1.72379i
$125$	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	$-0.00843689\pi$
$128$	14.0459			1.24149
$129$	−4.73004	−	11.2338i	−0.416456	−	0.989077i
$130$	−19.1332	+	25.7938i	−1.67810	+	2.26227i
$131$	5.81183			0.507782			0.253891	−	0.967233i	$-0.418290\pi$
$131$	5.81183			0.507782			0.253891	+	0.967233i	$0.418290\pi$
$132$	−7.38852	−	17.5476i	−0.643088	−	1.52732i
$133$		0			0
$134$			23.8276i			2.05839i
$135$	6.14580	+	9.86048i	0.528946	+	0.848655i
$136$		−	5.71600i		−	0.490143i
$137$	1.09369			0.0934400			0.0467200	−	0.998908i	$-0.485123\pi$
$137$	1.09369			0.0934400			0.0467200	+	0.998908i	$0.485123\pi$
$138$	10.5812	−	4.45526i	0.900728	−	0.379257i
$139$		−	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
$142$			24.2833i			2.03781i
$143$			24.8161i			2.07522i
$144$	−3.07288	+	3.14534i	−0.256073	+	0.262111i
$145$	4.04547	+	3.00083i	0.335958	+	0.249205i
$146$	7.30973			0.604958
$147$		0			0
$148$			9.69579i			0.796989i
$149$			10.8195i			0.886365i	0.896431	+	0.443183i	$0.146151\pi$
$149$			10.8195i			0.886365i	−0.896431	+	0.443183i	$0.853849\pi$
$150$	12.2202	+	14.7195i	0.997774	+	1.20184i
$151$	−8.29599			−0.675118			−0.337559	−	0.941304i	$-0.609601\pi$
$151$	−8.29599			−0.675118			−0.337559	+	0.941304i	$0.609601\pi$
$152$			3.95553i			0.320836i
$153$	6.30999	+	6.16463i	0.510132	+	0.498381i
$154$		0			0
$155$	11.9700	+	8.87905i	0.961454	+	0.713183i
$156$	−29.8901	+	12.5854i	−2.39312	+	1.00764i
$157$	5.41185			0.431913			0.215957	−	0.976403i	$-0.430713\pi$
$157$	5.41185			0.431913			0.215957	+	0.976403i	$0.430713\pi$
$158$	12.9225			1.02806
$159$	−3.08764	+	1.30007i	−0.244866	+	0.103102i
$160$	−9.49264	+	12.7972i	−0.750459	+	1.01171i
$161$		0			0
$162$	0.463276	+	19.8762i	0.0363984	+	1.56162i
$163$		−	17.1569i		−	1.34383i	−0.740627	−	0.671917i	$-0.765471\pi$
$163$		−	17.1569i		−	1.34383i	0.740627	−	0.671917i	$-0.234529\pi$
$164$	10.1114			0.789566
$165$	14.3602	+	3.50949i	1.11794	+	0.273213i
$166$			5.88341i			0.456641i
$167$		−	9.60588i		−	0.743325i	−0.928368	−	0.371663i	$-0.878788\pi$
$167$		−	9.60588i		−	0.743325i	0.928368	−	0.371663i	$-0.121212\pi$
$168$		0			0
$169$	29.2709			2.25161
$170$	11.6658	+	8.65342i	0.894728	+	0.663687i
$171$	−4.36658	−	4.26599i	−0.333921	−	0.326228i
$172$		−	20.2671i		−	1.54535i
$173$			10.1725i			0.773403i	0.922205	+	0.386702i	$0.126386\pi$
$173$			10.1725i			0.773403i	−0.922205	+	0.386702i	$0.873614\pi$
$174$	3.34464	+	7.94346i	0.253556	+	0.602192i
$175$		0			0
$176$			5.59463i			0.421711i
$177$	−12.6591	+	5.33019i	−0.951516	+	0.400641i
$178$	29.8574			2.23791
$179$			23.6545i			1.76802i	0.467466	+	0.884011i	$0.345167\pi$
$179$			23.6545i			1.76802i	−0.467466	+	0.884011i	$0.654833\pi$
$180$	3.05568	+	19.0762i	0.227757	+	1.42185i
$181$			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
$184$	5.83280			0.430000
$185$	−6.04622	−	4.48493i	−0.444527	−	0.329739i
$186$	9.89634	+	23.5036i	0.725635	+	1.72337i
$187$	11.2236			0.820752
$188$		−	14.4366i		−	1.05290i
$189$		0			0
$190$	−8.07288	−	5.98826i	−0.585668	−	0.434434i
$191$		−	10.7792i		−	0.779953i	−0.920825	−	0.389976i	$-0.872483\pi$
$191$		−	10.7792i		−	0.779953i	0.920825	−	0.389976i	$-0.127517\pi$
$192$	−20.4483	+	8.60986i	−1.47573	+	0.621363i
$193$			1.84621i			0.132893i	0.997790	+	0.0664465i	$0.0211662\pi$
$193$			1.84621i			0.132893i	−0.997790	+	0.0664465i	$0.978834\pi$
$194$	9.86762			0.708454
$195$	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	$0.406834\pi$
$198$	18.0937	+	17.6769i	1.28587	+	1.25624i
$199$			10.1027i			0.716164i	0.933690	+	0.358082i	$0.116569\pi$
$199$			10.1027i			0.716164i	−0.933690	+	0.358082i	$0.883431\pi$
$200$	2.81991	+	9.30138i	0.199398	+	0.657707i
$201$	−7.24988	−	17.2184i	−0.511367	−	1.21449i
$202$	−19.5954			−1.37873
$203$		0			0
$204$	5.69201	+	13.5184i	0.398521	+	0.946480i
$205$	−4.67717	+	6.30537i	−0.326667	+	0.440386i
$206$	2.92134			0.203539
$207$	−6.29060	+	6.43893i	−0.437227	+	0.447537i
$208$	9.52972			0.660767
$209$	−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	$0.380151\pi$
$212$	−5.57050			−0.382583
$213$	−7.38852	−	17.5476i	−0.506253	−	1.20234i
$214$	−7.34390			−0.502018
$215$	12.6384	+	9.37486i	0.861932	+	0.639360i
$216$	−3.70170	+	9.39800i	−0.251869	+	0.639453i
$217$		0			0
$218$	−27.1683			−1.84007
$219$	−5.28217	+	2.22409i	−0.356936	+	0.150290i
$220$	19.7417	+	14.6439i	1.33099	+	0.987294i
$221$		−	19.1180i		−	1.28601i
$222$	−4.99878	−	11.8720i	−0.335496	−	0.796797i
$223$	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
$225$	−13.3092	−	6.91848i	−0.887280	−	0.461232i
$226$	45.1954			3.00635
$227$			7.17565i			0.476265i	0.971233	+	0.238132i	$0.0765352\pi$
$227$			7.17565i			0.476265i	−0.971233	+	0.238132i	$0.923465\pi$
$228$	−3.93894	−	9.35490i	−0.260862	−	0.619544i
$229$		−	10.4511i		−	0.690629i	−0.938487	−	0.345315i	$-0.887772\pi$
$229$		−	10.4511i		−	0.690629i	0.938487	−	0.345315i	$-0.112228\pi$
$230$	−8.83025	+	11.9042i	−0.582250	+	0.784941i
$231$		0			0
$232$			4.37879i			0.287481i
$233$	3.90144			0.255592			0.127796	−	0.991800i	$-0.459210\pi$
$233$	3.90144			0.255592			0.127796	+	0.991800i	$0.459210\pi$
$234$	30.1103	−	30.8203i	1.96837	−	2.01479i
$235$	9.00256	+	6.67788i	0.587262	+	0.435617i
$236$	−22.8386			−1.48667
$237$	−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	$-0.279413\pi$
$240$	1.34769	−	5.51452i	0.0869932	−	0.355961i
$241$			13.2825i			0.855603i	0.903873	+	0.427801i	$0.140712\pi$
$241$			13.2825i			0.855603i	−0.903873	+	0.427801i	$0.859288\pi$
$242$	7.88374			0.506786
$243$	−6.38238	−	14.2220i	−0.409430	−	0.912342i
$244$			39.3546i			2.51942i
$245$		0			0
$246$	−12.3809	+	5.21303i	−0.789375	+	0.332371i
$247$			13.2298i			0.841794i
$248$			12.9562i			0.822722i
$249$	−1.79011	−	4.25148i	−0.113444	−	0.269427i
$250$	−23.2523	−	8.32615i	−1.47061	−	0.526592i
$251$	9.12747			0.576121			0.288060	−	0.957612i	$-0.406990\pi$
$251$	9.12747			0.576121			0.288060	+	0.957612i	$0.406990\pi$
$252$		0			0
$253$			11.4530i			0.720041i
$254$			1.31954i			0.0827951i
$255$	−11.0629	−	2.70366i	−0.692786	−	0.169310i
$256$	−5.40900			−0.338062
$257$			6.68630i			0.417080i	0.978014	+	0.208540i	$0.0668712\pi$
$257$			6.68630i			0.417080i	−0.978014	+	0.208540i	$0.933129\pi$
$258$	10.4489	+	24.8161i	0.650523	+	1.54498i
$259$		0			0
$260$	24.9440	−	33.6275i	1.54696	−	2.08549i
$261$	−4.83382	−	4.72247i	−0.299206	−	0.292313i
$262$	−12.8387			−0.793177
$263$	−24.1283			−1.48782			−0.743908	−	0.668282i	$-0.767030\pi$
$263$	−24.1283			−1.48782			−0.743908	+	0.668282i	$0.767030\pi$
$264$	4.98704	+	11.8441i	0.306931	+	0.728955i
$265$	2.57672	−	3.47371i	0.158286	−	0.213389i
$266$		0			0
$267$	−21.5756	+	9.08453i	−1.32041	+	0.555964i
$268$		−	31.0641i		−	1.89754i
$269$	19.0079			1.15893			0.579465	−	0.814997i	$-0.303262\pi$
$269$	19.0079			1.15893			0.579465	+	0.814997i	$0.303262\pi$
$270$	−13.5765	−	21.7824i	−0.826237	−	1.32564i
$271$			11.8486i			0.719750i	0.933001	+	0.359875i	$0.117181\pi$
$271$			11.8486i			0.719750i	−0.933001	+	0.359875i	$0.882819\pi$
$272$		−	4.31002i		−	0.261334i
$273$		0			0
$274$	−2.41603			−0.145957
$275$	−18.2637	+	5.53702i	−1.10134	+	0.333895i
$276$	−13.7947	+	5.80833i	−0.830342	+	0.349620i
$277$			16.5181i			0.992478i	0.868186	+	0.496239i	$0.165286\pi$
$277$			16.5181i			0.992478i	−0.868186	+	0.496239i	$0.834714\pi$
$278$			16.2580i			0.975090i
$279$	−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	$0.902518\pi$
$282$	7.44297	+	17.6769i	0.443222	+	1.05265i
$283$	−6.00203			−0.356784			−0.178392	−	0.983960i	$-0.557089\pi$
$283$	−6.00203			−0.356784			−0.178392	+	0.983960i	$0.557089\pi$
$284$		−	31.6581i		−	1.87856i
$285$	7.65565	+	1.87096i	0.453482	+	0.110826i
$286$		−	54.8203i		−	3.24159i
$287$		0			0
$288$	14.9388	−	15.2910i	0.880275	−	0.901031i
$289$	8.35349			0.491382
$290$	−8.93670	−	6.62903i	−0.524781	−	0.389270i
$291$	−7.13056	+	3.00236i	−0.418001	+	0.176002i
$292$	−9.52972			−0.557684
$293$			3.55369i			0.207609i	0.994598	+	0.103805i	$0.0331016\pi$
$293$			3.55369i			0.207609i	−0.994598	+	0.103805i	$0.966898\pi$
$294$		0			0
$295$	10.5643	−	14.2420i	0.615080	−	0.829200i
$296$		−	6.54438i		−	0.380384i
$297$	−18.4534	−	7.26846i	−1.07077	−	0.421759i
$298$		−	23.9009i		−	1.38454i
$299$	19.5086			1.12821
$300$	−15.9315	−	19.1899i	−0.919805	−	1.10793i
$301$		0			0
$302$	18.3264			1.05456
$303$	14.1601	−	5.96218i	0.813475	−	0.342518i
$304$			2.98258i			0.171063i
$305$	−24.5412	−	18.2040i	−1.40522	−	1.04236i
$306$	−13.9392	−	13.6181i	−0.796849	−	0.778492i
$307$	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
$310$	−26.4425	−	19.6144i	−1.50183	−	1.11402i
$311$	−8.64432			−0.490174			−0.245087	−	0.969501i	$-0.578817\pi$
$311$	−8.64432			−0.490174			−0.245087	+	0.969501i	$0.578817\pi$
$312$	20.1749	−	8.49476i	1.14218	−	0.480921i
$313$	−10.8521			−0.613400			−0.306700	−	0.951806i	$-0.599225\pi$
$313$	−10.8521			−0.613400			−0.306700	+	0.951806i	$0.599225\pi$
$314$	−11.9551			−0.674667
$315$		0			0
$316$	−16.8471			−0.947724
$317$	9.34091			0.524638			0.262319	−	0.964981i	$-0.415513\pi$
$317$	9.34091			0.524638			0.262319	+	0.964981i	$0.415513\pi$
$318$	6.82079	−	2.87193i	0.382491	−	0.161050i
$319$	−8.59794			−0.481392
$320$	17.0646	−	23.0051i	0.953940	−	1.28602i
$321$	5.30686	−	2.23448i	0.296200	−	0.124717i
$322$		0			0
$323$	5.98348			0.332930
$324$	−0.603973	−	25.9126i	−0.0335541	−	1.43959i
$325$	9.43158	+	31.1098i	0.523170	+	1.72566i
$326$			37.9007i			2.09913i
$327$	19.6324	−	8.26633i	1.08567	−	0.457129i
$328$	−6.82488			−0.376841
$329$		0			0
$330$	−31.7226	−	7.75268i	−1.74627	−	0.426771i
$331$	2.90918			0.159903			0.0799515	−	0.996799i	$-0.474523\pi$
$331$	2.90918			0.159903			0.0799515	+	0.996799i	$0.474523\pi$
$332$		−	7.67021i		−	0.420958i
$333$	7.22445	+	7.05803i	0.395898	+	0.386777i
$334$			21.2200i			1.16111i
$335$	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	$-0.136735\pi$
$338$	−64.6613			−3.51711
$339$	−32.6592	+	13.7513i	−1.77380	+	0.746870i
$340$	−15.2088	−	11.2815i	−0.824811	−	0.611824i
$341$	−25.4401			−1.37766
$342$	9.64606	+	9.42384i	0.521599	+	0.509583i
$343$		0			0
$344$			13.6797i			0.737561i
$345$	2.75891	−	11.2890i	0.148535	−	0.607778i
$346$		−	22.4718i		−	1.20809i
$347$	31.5784			1.69522			0.847609	−	0.530622i	$-0.178042\pi$
$347$	31.5784			1.69522			0.847609	+	0.530622i	$0.178042\pi$
$348$	−4.36041	−	10.3559i	−0.233743	−	0.555135i
$349$		−	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
$352$		−	27.1982i		−	1.44967i
$353$		−	4.28810i		−	0.228232i	−0.993467	−	0.114116i	$-0.963596\pi$
$353$		−	4.28810i		−	0.228232i	0.993467	−	0.114116i	$-0.0364036\pi$
$354$	27.9647	−	11.7747i	1.48631	−	0.625819i
$355$	19.7417	+	14.6439i	1.04778	+	0.777220i
$356$	−38.9252			−2.06303
$357$		0			0
$358$		−	52.2543i		−	2.76173i
$359$			7.13534i			0.376589i	0.982113	+	0.188294i	$0.0602959\pi$
$359$			7.13534i			0.376589i	−0.982113	+	0.188294i	$0.939704\pi$
$360$	−2.06249	−	12.8759i	−0.108703	−	0.678618i
$361$	14.8594			0.782072
$362$		−	34.5343i		−	1.81508i
$363$	−5.69696	+	2.39874i	−0.299013	+	0.125901i
$364$		0			0
$365$	4.40811	−	5.94265i	0.230731	−	0.311053i
$366$	−20.2897	−	48.1877i	−1.06056	−	2.51881i
$367$	−24.3914			−1.27322			−0.636609	−	0.771187i	$-0.719664\pi$
$367$	−24.3914			−1.27322			−0.636609	+	0.771187i	$0.719664\pi$
$368$	4.39810			0.229267
$369$	7.36055	−	7.53411i	0.383175	−	0.392210i
$370$	13.3565	+	9.90750i	0.694370	+	0.515067i
$371$		0			0
$372$	−12.9019	−	30.6417i	−0.668931	−	1.58870i
$373$			22.0547i			1.14195i	0.820968	+	0.570974i	$0.193434\pi$
$373$			22.0547i			1.14195i	−0.820968	+	0.570974i	$0.806566\pi$
$374$	−24.7937			−1.28205
$375$	19.3360	−	1.05819i	0.998506	−	0.0546447i
$376$			9.74430i			0.502524i
$377$			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	$0.490532\pi$
$380$	10.5246	+	7.80691i	0.539902	+	0.400486i
$381$	−0.401488	−	0.953527i	−0.0205688	−	0.0488506i
$382$			23.8118i			1.21832i
$383$			2.12930i			0.108802i	0.998519	+	0.0544011i	$0.0173250\pi$
$383$			2.12930i			0.108802i	−0.998519	+	0.0544011i	$0.982675\pi$
$384$	22.4217	−	9.44079i	1.14420	−	0.481773i
$385$		0			0
$386$		−	4.07839i		−	0.207585i
$387$	−15.1013	−	14.7534i	−0.767641	−	0.749957i
$388$	−12.8644			−0.653093
$389$			24.1571i			1.22481i	0.790543	+	0.612406i	$0.209798\pi$
$389$			24.1571i			1.22481i	−0.790543	+	0.612406i	$0.790202\pi$
$390$	−13.2057	+	54.0353i	−0.668695	+	2.73619i
$391$		−	8.82320i		−	0.446208i
$392$		0			0
$393$	9.27752	−	3.90635i	0.467989	−	0.197049i
$394$	−17.8921			−0.901392
$395$	7.79288	−	10.5057i	0.392103	−	0.528600i
$396$	−23.5889	−	23.0454i	−1.18538	−	1.15808i
$397$	12.0158			0.603058			0.301529	−	0.953457i	$-0.402503\pi$
$397$	12.0158			0.603058			0.301529	+	0.953457i	$0.402503\pi$
$398$		−	22.3176i		−	1.11868i
$399$		0			0
$400$	2.12629	+	7.01351i	0.106315	+	0.350675i
$401$		−	30.8302i		−	1.53958i	−0.638294	−	0.769792i	$-0.720360\pi$
$401$		−	30.8302i		−	1.53958i	0.638294	−	0.769792i	$-0.279640\pi$
$402$	16.0155	+	38.0364i	0.798778	+	1.89708i
$403$			43.3340i			2.15862i
$404$	25.5466			1.27099
$405$	16.4383	+	11.6096i	0.816824	+	0.576887i
$406$		0			0
$407$	12.8502			0.636959
$408$	−3.84194	−	9.12455i	−0.190204	−	0.451732i
$409$		−	15.6691i		−	0.774788i	−0.921914	−	0.387394i	$-0.873375\pi$
$409$		−	15.6691i		−	0.774788i	0.921914	−	0.387394i	$-0.126625\pi$
$410$	10.3322	−	13.9290i	0.510269	−	0.687902i
$411$	1.74587	−	0.735110i	0.0861176	−	0.0362603i
$412$	−3.80855			−0.187634
$413$		0			0
$414$	13.8963	−	14.2240i	0.682968	−	0.699072i
$415$	4.78308	+	3.54797i	0.234792	+	0.174163i
$416$	−46.3286			−2.27144
$417$	−4.94672	−	11.7484i	−0.242242	−	0.575321i
$418$	17.1575			0.839200
$419$	−19.5975			−0.957399			−0.478699	−	0.877979i	$-0.658892\pi$
$419$	−19.5975			−0.957399			−0.478699	+	0.877979i	$0.658892\pi$
$420$		0			0
$421$	−32.5791			−1.58781			−0.793903	−	0.608044i	$-0.791954\pi$
$421$	−32.5791			−1.58781			−0.793903	+	0.608044i	$0.791954\pi$
$422$	−23.5968			−1.14868
$423$	−10.7569	−	10.5091i	−0.523019	−	0.510970i
$424$	3.75992			0.182598
$425$	14.0701	−	4.26564i	0.682499	−	0.206914i
$426$	16.3217	+	38.7638i	0.790789	+	1.87811i
$427$		0			0
$428$	9.57425			0.462789
$429$	16.6798	+	39.6143i	0.805310	+	1.91260i
$430$	−27.9190	−	20.7097i	−1.34638	−	0.998708i
$431$			27.8893i			1.34338i	0.740832	+	0.671690i	$0.234431\pi$
$431$			27.8893i			1.34338i	−0.740832	+	0.671690i	$0.765569\pi$
$432$	−2.79119	+	7.08636i	−0.134291	+	0.340943i
$433$	−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
$435$	8.47483	+	2.07116i	0.406337	+	0.0993046i
$436$	35.4193			1.69628
$437$			6.10575i			0.292078i
$438$	11.6687	−	4.91315i	0.557550	−	0.234760i
$439$		−	3.94804i		−	0.188429i	−0.995552	−	0.0942147i	$-0.969966\pi$
$439$		−	3.94804i		−	0.188429i	0.995552	−	0.0942147i	$-0.0300340\pi$
$440$	−13.3251	−	9.88423i	−0.635249	−	0.471212i
$441$		0			0
$442$			42.2328i			2.00881i
$443$	16.0308			0.761646			0.380823	−	0.924648i	$-0.375641\pi$
$443$	16.0308			0.761646			0.380823	+	0.924648i	$0.375641\pi$
$444$	6.51692	+	15.4776i	0.309279	+	0.734533i
$445$	18.0054	−	24.2734i	0.853538	−	1.15067i
$446$	−9.12747			−0.432198
$447$	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	$-0.165891\pi$
$450$	29.4009	+	15.2833i	1.38597	+	0.720464i
$451$		−	13.4010i		−	0.631026i
$452$	−58.9213			−2.77143
$453$	−13.2430	+	5.57605i	−0.622212	+	0.261986i
$454$		−	15.8515i		−	0.743947i
$455$		0			0
$456$	2.65867	+	6.31429i	0.124503	+	0.295694i
$457$		−	9.60675i		−	0.449385i	−0.974430	−	0.224692i	$-0.927862\pi$
$457$		−	9.60675i		−	0.449385i	0.974430	−	0.224692i	$-0.0721378\pi$
$458$			23.0872i			1.07879i
$459$	14.2162	+	5.59952i	0.663557	+	0.261363i
$460$	11.5120	−	15.5195i	0.536751	−	0.723603i
$461$	−24.5367			−1.14279			−0.571393	−	0.820676i	$-0.693597\pi$
$461$	−24.5367			−1.14279			−0.571393	+	0.820676i	$0.693597\pi$
$462$		0			0
$463$			14.5875i			0.677937i	0.940798	+	0.338968i	$0.110078\pi$
$463$			14.5875i			0.677937i	−0.940798	+	0.338968i	$0.889922\pi$
$464$			3.30173i			0.153279i
$465$	25.0759	+	6.12829i	1.16287	+	0.284192i
$466$	−8.61854			−0.399246
$467$		−	17.9185i		−	0.829170i	−0.910010	−	0.414585i	$-0.863927\pi$
$467$		−	17.9185i		−	0.829170i	0.910010	−	0.414585i	$-0.136073\pi$
$468$	−39.2549	+	40.1805i	−1.81456	+	1.85735i
$469$		0			0
$470$	−19.8872	−	14.7519i	−0.917330	−	0.680452i
$471$	8.63904	−	3.63752i	0.398066	−	0.167608i
$472$	15.4154			0.709552
$473$	−26.8607			−1.23506
$474$	20.6284	−	8.68572i	0.947496	−	0.398949i
$475$	−9.73665	+	2.95187i	−0.446748	+	0.135441i
$476$		0			0
$477$	−4.05503	+	4.15064i	−0.185667	+	0.190045i
$478$			52.5477i			2.40347i
$479$	−2.96497			−0.135473			−0.0677364	−	0.997703i	$-0.521578\pi$
$479$	−2.96497			−0.135473			−0.0677364	+	0.997703i	$0.521578\pi$
$480$	−6.55178	+	26.8088i	−0.299047	+	1.22365i
$481$		−	21.8886i		−	0.998034i
$482$		−	29.3419i		−	1.33649i
$483$		0			0
$484$	−10.2780			−0.467184
$485$	5.95064	−	8.02215i	0.270204	−	0.364267i
$486$	14.0991	+	31.4173i	0.639547	+	1.42512i
$487$		−	33.2558i		−	1.50696i	−0.657469	−	0.753482i	$-0.728373\pi$
$487$		−	33.2558i		−	1.50696i	0.657469	−	0.753482i	$-0.271627\pi$
$488$		−	26.5632i		−	1.20246i
$489$	−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	$0.804941\pi$
$492$	16.1410	−	6.79624i	0.727691	−	0.306398i
$493$	6.62373			0.298318
$494$		−	29.2255i		−	1.31492i
$495$	25.2823	−	4.04980i	1.13636	−	0.182025i
$496$			9.76937i			0.438658i
$497$		0			0
$498$	3.95447	+	9.39179i	0.177204	+	0.420856i
$499$	−33.6716			−1.50735			−0.753673	−	0.657249i	$-0.771720\pi$
$499$	−33.6716			−1.50735			−0.753673	+	0.657249i	$0.771720\pi$
$500$	30.3141	+	10.8548i	1.35569	+	0.485442i
$501$	−6.45648	−	15.3340i	−0.288454	−	0.685074i
$502$	−20.1632			−0.899926
$503$		−	35.2418i		−	1.57135i	−0.618637	−	0.785677i	$-0.712315\pi$
$503$		−	35.2418i		−	1.57135i	0.618637	−	0.785677i	$-0.287685\pi$
$504$		0			0
$505$	−11.8170	+	15.9306i	−0.525848	+	0.708904i
$506$		−	25.3003i		−	1.12474i
$507$	46.7257	−	19.6741i	2.07516	−	0.873758i
$508$		−	1.72028i		−	0.0763252i
$509$	−23.1829			−1.02756			−0.513782	−	0.857921i	$-0.671756\pi$
$509$	−23.1829			−1.02756			−0.513782	+	0.857921i	$0.671756\pi$
$510$	24.4387	+	5.97256i	1.08216	+	0.264469i
$511$		0			0
$512$	−16.1430			−0.713426
$513$	−9.83779	−	3.87493i	−0.434349	−	0.171082i
$514$		−	14.7705i		−	0.651497i
$515$	1.76170	−	2.37498i	0.0776299	−	0.104654i
$516$	−13.6223	−	32.3528i	−0.599689	−	1.42425i
$517$	−19.1334			−0.841484
$518$		0			0
$519$	6.83735	+	16.2386i	0.300126	+	0.712795i
$520$	−16.8365	+	22.6976i	−0.738329	+	0.995354i
$521$	14.3752			0.629791			0.314895	−	0.949126i	$-0.398031\pi$
$521$	14.3752			0.629791			0.314895	+	0.949126i	$0.398031\pi$
$522$	10.6782	+	10.4322i	0.467373	+	0.456606i
$523$	−25.2484			−1.10404			−0.552018	−	0.833832i	$-0.686142\pi$
$523$	−25.2484			−1.10404			−0.552018	+	0.833832i	$0.686142\pi$
$524$	16.7378			0.731195
$525$		0			0
$526$	53.3010			2.32403
$527$	19.5987			0.853734
$528$	3.76037	+	8.93080i	0.163649	+	0.388663i
$529$	−13.9965			−0.608543
$530$	−5.69213	+	7.67366i	−0.247250	+	0.333322i
$531$	−16.6253	+	17.0173i	−0.721477	+	0.738489i
$532$		0			0
$533$	−22.8268			−0.988737
$534$	47.6619	−	20.0683i	2.06253	−	0.868441i
$535$	−4.42871	+	5.97042i	−0.191470	+	0.258124i
$536$			20.9674i			0.905652i
$537$	15.8991	+	37.7601i	0.686097	+	1.62947i
$538$	−41.9896			−1.81030
$539$		0			0
$540$	17.6997	+	28.3978i	0.761673	+	1.22205i
$541$	15.7795			0.678412			0.339206	−	0.940712i	$-0.389842\pi$
$541$	15.7795			0.678412			0.339206	+	0.940712i	$0.389842\pi$
$542$		−	26.1742i		−	1.12428i
$543$	10.5076	+	24.9553i	0.450922	+	1.07093i
$544$			20.9531i			0.898357i
$545$	−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	$0.943689\pi$
$548$	3.14978			0.134552
$549$	29.3236	+	28.6481i	1.25150	+	1.22267i
$550$	40.3456	−	12.2316i	1.72034	−	0.521558i
$551$	−4.58370			−0.195272
$552$	9.31100	−	3.92045i	0.396303	−	0.166865i
$553$		0			0
$554$		−	36.4896i		−	1.55029i
$555$	−12.6662	−	3.09548i	−0.537649	−	0.131396i
$556$		−	21.1956i		−	0.898893i
$557$	−28.9351			−1.22602			−0.613011	−	0.790075i	$-0.710042\pi$
$557$	−28.9351			−1.22602			−0.613011	+	0.790075i	$0.710042\pi$
$558$	31.5954	+	30.8675i	1.33754	+	1.30673i
$559$			45.7537i			1.93518i
$560$		0			0
$561$	17.9164	−	7.54382i	0.756433	−	0.318500i
$562$		−	22.3283i		−	0.941862i
$563$		−	6.22808i		−	0.262482i	−0.991350	−	0.131241i	$-0.958104\pi$
$563$		−	6.22808i		−	0.262482i	0.991350	−	0.131241i	$-0.0418962\pi$
$564$	−9.70342	−	23.0454i	−0.408588	−	0.970388i
$565$	27.2549	−	36.7428i	1.14662	−	1.54578i
$566$	13.2589			0.557312
$567$		0			0
$568$			21.3683i			0.896594i
$569$		−	9.89419i		−	0.414786i	−0.978258	−	0.207393i	$-0.933502\pi$
$569$		−	9.89419i		−	0.414786i	0.978258	−	0.207393i	$-0.0664979\pi$
$570$	−16.9118	−	4.13307i	−0.708358	−	0.173115i
$571$	19.2094			0.803890			0.401945	−	0.915664i	$-0.368334\pi$
$571$	19.2094			0.803890			0.401945	+	0.915664i	$0.368334\pi$
$572$			71.4693i			2.98828i
$573$	−7.24509	−	17.2070i	−0.302668	−	0.718831i
$574$		0			0
$575$	4.35281	+	14.3576i	0.181525	+	0.598753i
$576$	−26.8549	+	27.4881i	−1.11895	+	1.14534i
$577$	38.0753			1.58510			0.792549	−	0.609809i	$-0.208754\pi$
$577$	38.0753			1.58510			0.792549	+	0.609809i	$0.208754\pi$
$578$	−18.4534			−0.767560
$579$	1.24091	+	2.94713i	0.0515704	+	0.122479i
$580$	11.6508	+	8.64228i	0.483773	+	0.358851i
$581$		0			0
$582$	15.7519	−	6.63241i	0.652935	−	0.274922i
$583$			7.38277i			0.305763i
$584$	6.43228			0.266170
$585$	−6.89830	−	43.0651i	−0.285210	−	1.78052i
$586$		−	7.85033i		−	0.324294i
$587$			11.9232i			0.492124i	0.969254	+	0.246062i	$0.0791367\pi$
$587$			11.9232i			0.492124i	−0.969254	+	0.246062i	$0.920863\pi$
$588$		0			0
$589$	−13.5625			−0.558835
$590$	−23.3373	+	31.4614i	−0.960782	+	1.29525i
$591$	12.9292	−	5.44393i	0.531838	−	0.223933i
$592$		−	4.93465i		−	0.202813i
$593$		−	16.8579i		−	0.692272i	−0.938184	−	0.346136i	$-0.887494\pi$
$593$		−	16.8579i		−	0.692272i	0.938184	−	0.346136i	$-0.112506\pi$
$594$	40.7647	+	16.0565i	1.67260	+	0.658806i
$595$		0			0
$596$			31.1596i			1.27635i
$597$	6.79044	+	16.1272i	0.277914	+	0.660041i
$598$	−43.0958			−1.76232
$599$			13.5950i			0.555477i	0.960657	+	0.277739i	$0.0895849\pi$
$599$			13.5950i			0.555477i	−0.960657	+	0.277739i	$0.910415\pi$
$600$	10.7533	+	12.9526i	0.439001	+	0.528787i
$601$		−	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
$604$	−23.8921			−0.972156
$605$	4.75426	−	6.40930i	0.193288	−	0.260575i
$606$	−31.2805	+	13.1708i	−1.27068	+	0.535029i
$607$	−8.74327			−0.354878			−0.177439	−	0.984132i	$-0.556781\pi$
$607$	−8.74327			−0.354878			−0.177439	+	0.984132i	$0.556781\pi$
$608$		−	14.4998i		−	0.588044i
$609$		0			0
$610$	54.2130	+	40.2139i	2.19502	+	1.62821i
$611$			32.5912i			1.31850i
$612$	18.1725	+	17.7539i	0.734581	+	0.717658i
$613$		−	24.3570i		−	0.983771i	−0.870660	−	0.491885i	$-0.836308\pi$
$613$		−	24.3570i		−	0.983771i	0.870660	−	0.491885i	$-0.163692\pi$
$614$	−64.1391			−2.58845
$615$	−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	$0.329822\pi$
$618$	4.66338	−	1.96354i	0.187589	−	0.0789853i
$619$		−	30.2552i		−	1.21606i	−0.793915	−	0.608029i	$-0.791960\pi$
$619$		−	30.2552i		−	1.21606i	0.793915	−	0.608029i	$-0.208040\pi$
$620$	34.4731	+	25.5713i	1.38447	+	1.02697i
$621$	−5.71394	+	14.5067i	−0.229293	+	0.582135i
$622$	19.0958			0.765673
$623$		0			0
$624$	15.2125	−	6.40529i	0.608986	−	0.256417i
$625$	−20.7912	+	13.8826i	−0.831648	+	0.555303i
$626$	23.9731			0.958157
$627$	−12.3984	+	5.22041i	−0.495143	+	0.208483i
$628$	15.5859			0.621946
$629$	−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	$0.537510\pi$
$632$	11.3713			0.452326
$633$	17.0516	−	7.17967i	0.677740	−	0.285366i
$634$	−20.6347			−0.819507
$635$	1.07275	+	0.795743i	0.0425710	+	0.0315781i
$636$	−8.89228	+	3.74415i	−0.352602	+	0.148465i
$637$		0			0
$638$	18.9934			0.751956
$639$	−23.5889	−	23.0454i	−0.933161	−	0.911664i
$640$	−18.7115	+	25.2253i	−0.739637	+	0.997118i
$641$		−	0.128699i		−	0.00508330i	−0.999997	−	0.00254165i	$-0.999191\pi$
$641$		−	0.128699i		−	0.00508330i	0.999997	−	0.00254165i	$-0.000809034\pi$
$642$	−11.7232	+	4.93612i	−0.462677	+	0.194813i
$643$	−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
$645$	26.4761	+	6.47049i	1.04250	+	0.254775i
$646$	−13.2179			−0.520051
$647$			41.3552i			1.62584i	0.582375	+	0.812920i	$0.302124\pi$
$647$			41.3552i			1.62584i	−0.582375	+	0.812920i	$0.697876\pi$
$648$	0.407664	+	17.4903i	0.0160146	+	0.687082i
$649$			30.2688i			1.18816i
$650$	−20.8350	−	68.7235i	−0.817214	−	2.69556i
$651$		0			0
$652$		−	49.4113i		−	1.93509i
$653$	29.4608			1.15289			0.576446	−	0.817136i	$-0.304439\pi$
$653$	29.4608			1.15289			0.576446	+	0.817136i	$0.304439\pi$
$654$	−43.3692	+	18.2608i	−1.69587	+	0.714056i
$655$	−7.74233	+	10.4376i	−0.302518	+	0.407830i
$656$	−5.14615			−0.200924
$657$	−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	$0.855825\pi$
$660$	41.3569	+	10.1072i	1.60981	+	0.393422i
$661$		−	23.4594i		−	0.912465i	−0.889861	−	0.456233i	$-0.849198\pi$
$661$		−	23.4594i		−	0.912465i	0.889861	−	0.456233i	$-0.150802\pi$
$662$	−6.42656			−0.249776
$663$	−12.8499	−	30.5183i	−0.499049	−	1.18523i
$664$			5.17717i			0.200913i
$665$		0			0
$666$	−15.9593	−	15.5916i	−0.618409	−	0.604163i
$667$			6.75909i			0.261713i
$668$		−	27.6646i		−	1.07037i
$669$	6.59571	−	2.77716i	0.255005	−	0.107371i
$670$	−42.7925	−	31.7424i	−1.65322	−	1.22632i
$671$	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	$0.671307\pi$
$674$			33.7788i			1.30111i
$675$	−25.8959	−	2.09846i	−0.996733	−	0.0807697i
$676$	84.2991			3.24227
$677$		−	45.7011i		−	1.75643i	−0.478262	−	0.878217i	$-0.658733\pi$
$677$		−	45.7011i		−	1.75643i	0.478262	−	0.878217i	$-0.341267\pi$
$678$	72.1462	−	30.3776i	2.77076	−	1.16664i
$679$		0			0
$680$	10.2655	+	7.61467i	0.393663	+	0.292009i
$681$	4.82303	+	11.4546i	0.184819	+	0.438942i
$682$	56.1989			2.15197
$683$	38.6888			1.48038			0.740192	−	0.672395i	$-0.234734\pi$
$683$	38.6888			1.48038			0.740192	+	0.672395i	$0.234734\pi$
$684$	−12.5756	−	12.2859i	−0.480839	−	0.469763i
$685$	−1.45698	+	1.96418i	−0.0556682	+	0.0750473i
$686$		0			0
$687$	−7.02460	−	16.6833i	−0.268005	−	0.636508i
$688$			10.3149i			0.393252i
$689$	12.5756			0.479092
$690$	−6.09460	+	24.9381i	−0.232018	+	0.949376i
$691$			19.2567i			0.732559i	0.930505	+	0.366279i	$0.119369\pi$
$691$			19.2567i			0.732559i	−0.930505	+	0.366279i	$0.880631\pi$
$692$			29.2965i			1.11369i
$693$		0			0
$694$	−69.7587			−2.64800
$695$	13.2174	+	9.80433i	0.501364	+	0.371899i
$696$	2.94315	+	6.98994i	0.111560	+	0.264953i
$697$			10.3239i			0.391046i
$698$			18.2253i			0.689838i
$699$	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	$0.959267\pi$
$702$	27.3501	−	69.4373i	1.03226	−	2.62074i
$703$	6.85063			0.258376
$704$			48.8933i			1.84273i
$705$	18.8594	+	4.60904i	0.710286	+	0.173587i
$706$			9.47268i			0.356509i
$707$		0			0
$708$	−36.4577	+	15.3507i	−1.37016	+	0.576916i
$709$	4.89171			0.183712			0.0918561	−	0.995772i	$-0.470720\pi$
$709$	4.89171			0.183712			0.0918561	+	0.995772i	$0.470720\pi$
$710$	−43.6108	−	32.3494i	−1.63668	−	1.21405i
$711$	−12.2638	+	12.5530i	−0.459929	+	0.470774i
$712$	26.2733			0.984635
$713$			19.9992i			0.748977i
$714$		0			0
$715$	−44.5677	−	33.0592i	−1.66674	−	1.23634i
$716$			68.1241i			2.54592i
$717$	−15.9884	−	37.9721i	−0.597096	−	1.41809i
$718$		−	15.7624i		−	0.588248i
$719$	38.0217			1.41797			0.708985	−	0.705224i	$-0.249154\pi$
$719$	38.0217			1.41797			0.708985	+	0.705224i	$0.249154\pi$
$720$	−1.55518	−	9.70876i	−0.0579581	−	0.361824i
$721$		0			0
$722$	−32.8253			−1.22163
$723$	8.92770	+	21.2031i	0.332025	+	0.788553i
$724$			45.0225i			1.67325i
$725$	−10.7785	+	3.26773i	−0.400304	+	0.121360i
$726$	12.5849	−	5.29896i	0.467071	−	0.196663i
$727$	−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
$730$	−9.73780	+	13.1277i	−0.360412	+	0.485878i
$731$	20.6931			0.765363
$732$	26.4517	+	62.8224i	0.977684	+	2.32198i
$733$	−37.5933			−1.38854			−0.694271	−	0.719714i	$-0.744273\pi$
$733$	−37.5933			−1.38854			−0.694271	+	0.719714i	$0.744273\pi$
$734$	53.8821			1.98882
$735$		0			0
$736$	−21.3813			−0.788124
$737$	−41.1703			−1.51653
$738$	−16.2599	+	16.6433i	−0.598536	+	0.612649i
$739$	−49.4378			−1.81860			−0.909300	−	0.416142i	$-0.863382\pi$
$739$	−49.4378			−1.81860			−0.909300	+	0.416142i	$0.863382\pi$
$740$	−17.4129	−	12.9164i	−0.640110	−	0.474818i
$741$	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	$0.213109\pi$
$744$	8.70839	+	20.6823i	0.319265	+	0.758249i
$745$	−19.4309	−	14.4134i	−0.711893	−	0.528065i
$746$		−	48.7202i		−	1.78377i
$747$	−5.71517	−	5.58351i	−0.209107	−	0.204290i
$748$	32.3236			1.18187
$749$		0			0
$750$	−42.7144	+	2.33761i	−1.55971	+	0.0853575i
$751$	5.59051			0.204001			0.102000	−	0.994784i	$-0.467476\pi$
$751$	5.59051			0.204001			0.102000	+	0.994784i	$0.467476\pi$
$752$			7.34748i			0.267935i
$753$	14.5703	−	6.13492i	0.530973	−	0.223569i
$754$		−	32.3528i		−	1.17822i
$755$	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	$-0.285445\pi$
$758$	−2.55811			−0.0929148
$759$	7.69798	+	18.2826i	0.279419	+	0.663615i
$760$	−7.10382	−	5.26944i	−0.257683	−	0.191143i
$761$	49.1430			1.78143			0.890716	−	0.454561i	$-0.150204\pi$
$761$	49.1430			1.78143			0.890716	+	0.454561i	$0.150204\pi$
$762$	0.886912	+	2.10640i	0.0321294	+	0.0763068i
$763$		0			0
$764$		−	31.0436i		−	1.12312i
$765$	−19.4771	+	3.11991i	−0.704198	+	0.112800i
$766$		−	4.70376i		−	0.169954i
$767$	51.5590			1.86169
$768$	−8.63447	+	3.63559i	−0.311570	+	0.131188i
$769$		−	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
$772$			5.31701i			0.191363i
$773$		−	52.9162i		−	1.90326i	−0.307244	−	0.951631i	$-0.599407\pi$
$773$		−	52.9162i		−	1.90326i	0.307244	−	0.951631i	$-0.400593\pi$
$774$	33.3597	+	32.5912i	1.19909	+	1.17147i
$775$	−31.8921	+	9.66877i	−1.14560	+	0.347312i
$776$	8.68312			0.311706
$777$		0			0
$778$		−	53.3645i		−	1.91321i
$779$		−	7.14426i		−	0.255970i
$780$	17.2163	−	70.4460i	0.616441	−	2.52237i
$781$	−41.9576			−1.50136
$782$			19.4910i			0.696997i
$783$	−10.8905	−	4.28956i	−0.389193	−	0.153296i
$784$		0			0
$785$	−7.20950	+	9.71926i	−0.257318	+	0.346895i
$786$	−20.4946	+	8.62938i	−0.731019	+	0.307800i
$787$	−16.7576			−0.597344			−0.298672	−	0.954356i	$-0.596544\pi$
$787$	−16.7576			−0.597344			−0.298672	+	0.954356i	$0.596544\pi$
$788$	23.3260			0.830954
$789$	−38.5165	+	16.2176i	−1.37122	+	0.577361i
$790$	−17.2150	+	23.2078i	−0.612481	+	0.825697i
$791$		0			0
$792$	15.9218	+	15.5550i	0.565756	+	0.552723i
$793$		−	88.8443i		−	3.15495i
$794$	−26.5437			−0.942002
$795$	1.77844	−	7.27706i	0.0630747	−	0.258091i
$796$			29.0955i			1.03126i
$797$		−	55.9724i		−	1.98264i	−0.131462	−	0.991321i	$-0.541967\pi$
$797$		−	55.9724i		−	1.98264i	0.131462	−	0.991321i	$-0.458033\pi$
$798$		0			0
$799$	14.7401			0.521466
$800$	−10.3369	−	34.0960i	−0.365466	−	1.20548i
$801$	−28.3355	+	29.0036i	−1.00118	+	1.02479i
$802$			68.1058i			2.40490i
$803$			12.6301i			0.445705i
$804$	−20.8794	−	49.5882i	−0.736359	−	1.74884i
$805$		0			0
$806$		−	95.7274i		−	3.37186i
$807$	30.3426	−	12.7759i	1.06811	−	0.449734i
$808$	−17.2432			−0.606614
$809$		−	42.1009i		−	1.48019i	−0.672503	−	0.740094i	$-0.734781\pi$
$809$		−	42.1009i		−	1.48019i	0.672503	−	0.740094i	$-0.265219\pi$
$810$	−36.3132	−	25.6464i	−1.27591	−	0.901123i
$811$		−	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
$814$	−28.3868			−0.994958
$815$	30.8124	+	22.8559i	1.07931	+	0.800608i
$816$	−2.89693	−	6.88016i	−0.101413	−	0.240854i
$817$	−14.3199			−0.500989
$818$			34.6141i			1.21025i
$819$		0			0
$820$	−13.4701	+	18.1592i	−0.470395	+	0.634147i
$821$			11.3444i			0.395923i	0.980210	+	0.197962i	$0.0634322\pi$
$821$			11.3444i			0.395923i	−0.980210	+	0.197962i	$0.936568\pi$
$822$	−3.85674	+	1.62390i	−0.134519	+	0.0566402i
$823$		−	30.1779i		−	1.05193i	−0.850505	−	0.525967i	$-0.823703\pi$
$823$		−	30.1779i		−	1.05193i	0.850505	−	0.525967i	$-0.176297\pi$
$824$	2.57066			0.0895533
$825$	−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	$0.293212\pi$
$828$	−18.1167	+	18.5439i	−0.629598	+	0.644444i
$829$		−	4.04928i		−	0.140637i	−0.997525	−	0.0703187i	$-0.977598\pi$
$829$		−	4.04928i		−	0.140637i	0.997525	−	0.0703187i	$-0.0224016\pi$
$830$	−10.5661	−	7.83769i	−0.366756	−	0.272050i
$831$	11.1025	+	26.3682i	0.385140	+	0.914701i
$832$	83.2833			2.88733
$833$		0			0
$834$	10.9276	+	25.9529i	0.378393	+	0.898676i
$835$	17.2514	+	12.7967i	0.597009	+	0.442846i
$836$	−22.3683			−0.773622
$837$	−32.2234	−	12.6922i	−1.11380	−	0.438707i
$838$	43.2920			1.49550
$839$	−25.8653			−0.892969			−0.446485	−	0.894791i	$-0.647324\pi$
$839$	−25.8653			−0.892969			−0.446485	+	0.894791i	$0.647324\pi$
$840$		0			0
$841$	23.9258			0.825029
$842$	71.9692			2.48022
$843$	6.79370	+	16.1349i	0.233987	+	0.555716i
$844$	30.7632			1.05891
$845$	−38.9938	+	52.5682i	−1.34143	+	1.80840i
$846$	23.7627	+	23.2153i	0.816978	+	0.798158i
$847$		0			0
$848$	2.83509			0.0973573
$849$	−9.58114	+	4.03420i	−0.328824	+	0.138453i
$850$	−31.0817	+	9.42307i	−1.06609	+	0.323209i
$851$		−	10.1019i		−	0.346288i
$852$	−21.2787	−	50.5364i	−0.728995	−	1.73135i
$853$	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
$855$	13.4784	−	2.15901i	0.460952	−	0.0738366i
$856$	−6.46234			−0.220878
$857$			22.9281i			0.783208i	0.920134	+	0.391604i	$0.128080\pi$
$857$			22.9281i			0.783208i	−0.920134	+	0.391604i	$0.871920\pi$
$858$	−36.8468	−	87.5106i	−1.25793	−	2.98756i
$859$		−	18.7653i		−	0.640263i	−0.947373	−	0.320132i	$-0.896273\pi$
$859$		−	18.7653i		−	0.640263i	0.947373	−	0.320132i	$-0.103727\pi$
$860$	36.3981	+	26.9992i	1.24117	+	0.920666i
$861$		0			0
$862$		−	61.6092i		−	2.09842i
$863$	−8.46172			−0.288040			−0.144020	−	0.989575i	$-0.546003\pi$
$863$	−8.46172			−0.288040			−0.144020	+	0.989575i	$0.546003\pi$
$864$	13.5693	−	34.4502i	0.461638	−	1.17202i
$865$	−18.2690	−	13.5515i	−0.621166	−	0.460766i
$866$	7.67319			0.260746
$867$	13.3348	−	5.61470i	0.452874	−	0.190685i
$868$		0			0
$869$			22.3281i			0.757428i
$870$	−18.7214	−	4.57533i	−0.634716	−	0.155118i
$871$			70.1283i			2.37621i
$872$	−23.9070			−0.809594
$873$	−9.36463	+	9.58544i	−0.316945	+	0.324418i
$874$		−	13.4880i		−	0.456238i
$875$		0			0
$876$	−15.2125	+	6.40529i	−0.513981	+	0.216415i
$877$		−	3.78589i		−	0.127840i	−0.997955	−	0.0639201i	$-0.979640\pi$
$877$		−	3.78589i		−	0.127840i	0.997955	−	0.0639201i	$-0.0203603\pi$
$878$			8.72146i			0.294335i
$879$	2.38857	+	5.67282i	0.0805646	+	0.191340i
$880$	−10.0475	−	7.45299i	−0.338701	−	0.251240i
$881$	−54.6531			−1.84131			−0.920654	−	0.390379i	$-0.872344\pi$
$881$	−54.6531			−1.84131			−0.920654	+	0.390379i	$0.872344\pi$
$882$		0			0
$883$			28.1492i			0.947295i	0.880715	+	0.473647i	$0.157063\pi$
$883$			28.1492i			0.947295i	−0.880715	+	0.473647i	$0.842937\pi$
$884$		−	55.0589i		−	1.85183i
$885$	7.29147	−	29.8354i	0.245100	−	1.00291i
$886$	−35.4130			−1.18972
$887$			30.0235i			1.00809i	0.863677	+	0.504045i	$0.168155\pi$
$887$			30.0235i			1.00809i	−0.863677	+	0.504045i	$0.831845\pi$
$888$	−4.39873	−	10.4469i	−0.147612	−	0.350575i
$889$		0			0
$890$	−39.7751	+	53.6215i	−1.33326	+	1.79740i
$891$	−34.3429	+	0.800467i	−1.15053	+	0.0268166i
$892$	11.8995			0.398425
$893$	−10.2003			−0.341340
$894$	−16.0647	−	38.1534i	−0.537284	−	1.27604i
$895$	−42.4816	−	31.5118i	−1.42000	−	1.05332i
$896$		0			0
$897$	31.1420	−	13.1125i	1.03980	−	0.437814i
$898$			46.6116i			1.55545i
$899$	−15.0138			−0.500737
$900$	−38.3300	−	19.9249i	−1.27767	−	0.664165i
$901$		−	5.68758i		−	0.189481i
$902$			29.6036i			0.985691i
$903$		0			0
$904$	39.7702			1.32274
$905$	−28.0756	−	20.8258i	−0.933266	−	0.692274i
$906$	29.2547	−	12.3179i	0.971922	−	0.409233i
$907$			19.4331i			0.645264i	0.946524	+	0.322632i	$0.104568\pi$
$907$			19.4331i			0.645264i	−0.946524	+	0.322632i	$0.895432\pi$
$908$			20.6656i			0.685812i
$909$	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	$-0.344261\pi$
$912$	2.00471	+	4.76115i	0.0663826	+	0.157657i
$913$	−10.1656			−0.336432
$914$			21.2219i			0.701959i
$915$	−51.4112	−	12.5644i	−1.69960	−	0.415365i
$916$		−	30.0988i		−	0.994493i
$917$		0			0
$918$	−31.4046	−	12.3697i	−1.03650	−	0.408261i
$919$	45.0127			1.48483			0.742416	−	0.669939i	$-0.233680\pi$
$919$	45.0127			1.48483			0.742416	+	0.669939i	$0.233680\pi$
$920$	−7.77028	+	10.4752i	−0.256178	+	0.345358i
$921$	46.3484	−	19.5152i	1.52723	−	0.643049i
$922$	54.2030			1.78508
$923$			71.4693i			2.35244i
$924$		0			0
$925$	16.1092	−	4.88383i	0.529666	−	0.160579i
$926$		−	32.2246i		−	1.05897i
$927$	−2.77243	+	2.83780i	−0.0910584	+	0.0932056i
$928$		−	16.0513i		−	0.526910i
$929$	−42.6990			−1.40091			−0.700455	−	0.713696i	$-0.747020\pi$
$929$	−42.6990			−1.40091			−0.700455	+	0.713696i	$0.747020\pi$
$930$	−55.3942	−	13.5378i	−1.81645	−	0.443921i
$931$		0			0
$932$	11.2360			0.368048
$933$	−13.7991	+	5.81018i	−0.451761	+	0.190217i
$934$			39.5832i			1.29520i
$935$	−14.9517	+	20.1567i	−0.488974	+	0.659195i
$936$	26.4959	−	27.1207i	0.866046	−	0.886467i
$937$	−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
$940$	25.9270	+	19.2320i	0.845646	+	0.627280i
$941$	31.7091			1.03369			0.516843	−	0.856080i	$-0.327107\pi$
$941$	31.7091			1.03369			0.516843	+	0.856080i	$0.327107\pi$
$942$	−19.0842	+	8.03550i	−0.621796	+	0.261811i
$943$	−10.5349			−0.343063
$944$	11.6237			0.378318
$945$		0			0
$946$	59.3370			1.92921
$947$	−11.9455			−0.388177			−0.194089	−	0.980984i	$-0.562175\pi$
$947$	−11.9455			−0.388177			−0.194089	+	0.980984i	$0.562175\pi$
$948$	−26.8933	+	11.3236i	−0.873455	+	0.367773i
$949$	21.5137			0.698363
$950$	21.5089	−	6.52087i	0.697840	−	0.211565i
$951$	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	$0.490905\pi$
$954$	8.95781	−	9.16903i	0.290020	−	0.296858i
$955$	19.3585	+	14.3597i	0.626426	+	0.464668i
$956$		−	68.5065i		−	2.21566i
$957$	−13.7250	+	5.77901i	−0.443668	+	0.186809i
$958$	6.54980			0.211614
$959$		0			0
$960$	11.7779	−	48.1932i	0.380131	−	1.55543i
$961$	−13.4237			−0.433023
$962$			48.3533i			1.55897i
$963$	6.96955	−	7.13389i	0.224591	−	0.229886i
$964$			38.2532i			1.23205i
$965$	−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	$0.671312\pi$
$968$	6.93738			0.222976
$969$	9.55154	−	4.02173i	0.306840	−	0.129197i
$970$	−13.1453	+	17.7214i	−0.422071	+	0.569001i
$971$	47.9153			1.53768			0.768838	−	0.639444i	$-0.220835\pi$
$971$	47.9153			1.53768			0.768838	+	0.639444i	$0.220835\pi$
$972$	−18.3810	−	40.9588i	−0.589571	−	1.31375i
$973$		0			0
$974$			73.4642i			2.35394i
$975$	35.9659	+	43.3218i	1.15183	+	1.38741i
$976$		−	20.0294i		−	0.641125i
$977$	8.14823			0.260685			0.130342	−	0.991469i	$-0.458392\pi$
$977$	8.14823			0.260685			0.130342	+	0.991469i	$0.458392\pi$
$978$	25.4745	+	60.5016i	0.814586	+	1.93463i
$979$			51.5889i			1.64879i
$980$		0			0
$981$	25.7834	−	26.3914i	0.823201	−	0.842612i
$982$		−	56.3073i		−	1.79684i
$983$		−	14.6023i		−	0.465742i	−0.972508	−	0.232871i	$-0.925188\pi$
$983$		−	14.6023i		−	0.465742i	0.972508	−	0.232871i	$-0.0748120\pi$
$984$	−10.8947	+	4.58727i	−0.347310	+	0.146237i
$985$	−10.7898	+	14.5459i	−0.343791	+	0.463471i
$986$	−14.6322			−0.465986
$987$		0			0
$988$			38.1014i			1.21217i
$989$			21.1160i			0.671449i
$990$	−55.8503	+	8.94626i	−1.77504	+	0.284331i
$991$	15.6824			0.498166			0.249083	−	0.968482i	$-0.419871\pi$
$991$	15.6824			0.498166			0.249083	+	0.968482i	$0.419871\pi$
$992$		−	47.4936i		−	1.50792i
$993$	4.64398	−	1.95537i	0.147372	−	0.0620519i
$994$		0			0
$995$	−18.1437	−	13.4585i	−0.575194	−	0.426664i
$996$	−5.15544	−	12.2441i	−0.163357	−	0.387969i
$997$	27.0422			0.856436			0.428218	−	0.903676i	$-0.359142\pi$
$997$	27.0422			0.856436			0.428218	+	0.903676i	$0.359142\pi$
$998$	74.3826			2.35454
$999$	16.2765	+	6.41102i	0.514965	+	0.202836i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.20906 q^{2} +(1.59632 - 0.672139i) q^{3} +2.87996 q^{4} +(-1.33217 + 1.79592i) q^{5} +(-3.52637 + 1.48480i) q^{6} -1.94389 q^{8} +(2.09646 - 2.14589i) q^{9} +(2.94284 - 3.96730i) q^{10} -3.81691i q^{11} +(4.59733 - 1.93573i) q^{12} -6.50161 q^{13} +(-0.919457 + 3.76226i) q^{15} -1.46575 q^{16} +2.94050i q^{17} +(-4.63121 + 4.74041i) q^{18} -2.03485i q^{19} +(-3.83659 + 5.17218i) q^{20} +8.43180i q^{22} -3.00058 q^{23} +(-3.10306 + 1.30656i) q^{24} +(-1.45065 - 4.78494i) q^{25} +14.3625 q^{26} +(1.90428 - 4.83464i) q^{27} -2.25259i q^{29} +(2.03114 - 8.31107i) q^{30} -6.66511i q^{31} +7.12571 q^{32} +(-2.56549 - 6.09300i) q^{33} -6.49574i q^{34} +(6.03772 - 6.18009i) q^{36} +3.36664i q^{37} +4.49512i q^{38} +(-10.3786 + 4.36998i) q^{39} +(2.58959 - 3.49107i) q^{40} +3.51094 q^{41} -7.03729i q^{43} -10.9926i q^{44} +(1.06101 + 6.62376i) q^{45} +6.62848 q^{46} -5.01279i q^{47} +(-2.33980 + 0.985185i) q^{48} +(3.20459 + 10.5702i) q^{50} +(1.97642 + 4.69396i) q^{51} -18.7244 q^{52} -1.93423 q^{53} +(-4.20667 + 10.6800i) q^{54} +(6.85487 + 5.08477i) q^{55} +(-1.36770 - 3.24827i) q^{57} +4.97612i q^{58} -7.93019 q^{59} +(-2.64800 + 10.8352i) q^{60} +13.6650i q^{61} +14.7237i q^{62} -12.8096 q^{64} +(8.66124 - 11.6764i) q^{65} +(5.66734 + 13.4598i) q^{66} -10.7863i q^{67} +8.46851i q^{68} +(-4.78988 + 2.01681i) q^{69} -10.9926i q^{71} +(-4.07528 + 4.17138i) q^{72} -3.30897 q^{73} -7.43712i q^{74} +(-5.53184 - 6.66324i) q^{75} -5.86030i q^{76} +(22.9271 - 9.65357i) q^{78} -5.84977 q^{79} +(1.95262 - 2.63236i) q^{80} +(-0.209716 - 8.99756i) q^{81} -7.75589 q^{82} -2.66330i q^{83} +(-5.28089 - 3.91724i) q^{85} +15.5458i q^{86} +(-1.51405 - 3.59585i) q^{87} +7.41965i q^{88} -13.5159 q^{89} +(-2.34385 - 14.6323i) q^{90} -8.64156 q^{92} +(-4.47988 - 10.6396i) q^{93} +11.0736i q^{94} +(3.65444 + 2.71077i) q^{95} +(11.3749 - 4.78946i) q^{96} -4.46688 q^{97} +(-8.19069 - 8.00200i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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