LMFDB - Embedded newform 280.2.bg.a.249.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(9,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bg (of order $6$, degree $2$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.8
Character	$\chi$	$=$	280.249
Dual form			280.2.bg.a.9.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.650755 + 0.375714i) q^{3} +(-1.48694 - 1.67003i) q^{5} +(-0.543003 - 2.58943i) q^{7} +(-1.21768 - 2.10908i) q^{9} +O(q^{10})$	\(q+(0.650755 + 0.375714i) q^{3} +(-1.48694 - 1.67003i) q^{5} +(-0.543003 - 2.58943i) q^{7} +(-1.21768 - 2.10908i) q^{9} +(2.63851 - 4.57003i) q^{11} +2.43536i q^{13} +(-0.340178 - 1.64545i) q^{15} +(5.30579 + 3.06330i) q^{17} +(-0.220655 - 0.382187i) q^{19} +(0.619522 - 1.88910i) q^{21} +(-2.75984 + 1.59339i) q^{23} +(-0.578031 + 4.96648i) q^{25} -4.08428i q^{27} +1.25215 q^{29} +(0.322674 - 0.558887i) q^{31} +(3.43405 - 1.98265i) q^{33} +(-3.51703 + 4.75716i) q^{35} +(-9.31074 + 5.37556i) q^{37} +(-0.914997 + 1.58482i) q^{39} +8.90154 q^{41} -10.4159i q^{43} +(-1.71163 + 5.16964i) q^{45} +(6.52112 - 3.76497i) q^{47} +(-6.41029 + 2.81214i) q^{49} +(2.30185 + 3.98692i) q^{51} +(-2.89319 - 1.67039i) q^{53} +(-11.5554 + 2.38895i) q^{55} -0.331613i q^{57} +(-4.07767 + 7.06274i) q^{59} +(1.73518 + 3.00542i) q^{61} +(-4.80011 + 4.29833i) q^{63} +(4.06713 - 3.62122i) q^{65} +(4.14517 + 2.39322i) q^{67} -2.39464 q^{69} +13.7064 q^{71} +(4.61237 + 2.66295i) q^{73} +(-2.24213 + 3.01479i) q^{75} +(-13.2665 - 4.35069i) q^{77} +(2.70220 + 4.68034i) q^{79} +(-2.11852 + 3.66938i) q^{81} +11.9379i q^{83} +(-2.77356 - 13.4158i) q^{85} +(0.814841 + 0.470448i) q^{87} +(4.30119 + 7.44987i) q^{89} +(6.30618 - 1.32241i) q^{91} +(0.419963 - 0.242466i) q^{93} +(-0.310164 + 0.936790i) q^{95} +13.6714i q^{97} -12.8514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{9}+O(q^{10}) $ 24 * q + 14 * q^9	$ 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) $ 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.650755	+	0.375714i	0.375714	+	0.216918i	0.675952	−	0.736946i	$-0.263733\pi$
$3$	0.650755	+	0.375714i	0.375714	+	0.216918i	−0.300238	+	0.953864i	$0.597066\pi$
$4$		0			0
$5$	−1.48694	−	1.67003i	−0.664979	−	0.746862i
$5$	−1.48694	−	1.67003i	−0.664979	−	0.746862i
$6$		0			0
$7$	−0.543003	−	2.58943i	−0.205236	−	0.978713i
$7$	−0.543003	−	2.58943i	−0.205236	−	0.978713i
$8$		0			0
$9$	−1.21768	−	2.10908i	−0.405893	−	0.703027i
$10$		0			0
$11$	2.63851	−	4.57003i	0.795540	−	1.37792i	−0.126956	−	0.991908i	$-0.540521\pi$
$11$	2.63851	−	4.57003i	0.795540	−	1.37792i	0.922496	−	0.386007i	$-0.126146\pi$
$12$		0			0
$13$			2.43536i			0.675446i	0.941245	+	0.337723i	$0.109657\pi$
$13$			2.43536i			0.675446i	−0.941245	+	0.337723i	$0.890343\pi$
$14$		0			0
$15$	−0.340178	−	1.64545i	−0.0878335	−	0.424853i
$16$		0			0
$17$	5.30579	+	3.06330i	1.28684	+	0.742959i	0.978090	−	0.208183i	$-0.0667549\pi$
$17$	5.30579	+	3.06330i	1.28684	+	0.742959i	0.308753	+	0.951142i	$0.400088\pi$
$18$		0			0
$19$	−0.220655	−	0.382187i	−0.0506218	−	0.0876796i	0.839604	−	0.543199i	$-0.182787\pi$
$19$	−0.220655	−	0.382187i	−0.0506218	−	0.0876796i	−0.890226	+	0.455519i	$0.849454\pi$
$20$		0			0
$21$	0.619522	−	1.88910i	0.135191	−	0.412235i
$22$		0			0
$23$	−2.75984	+	1.59339i	−0.575466	+	0.332245i	−0.759329	−	0.650707i	$-0.774473\pi$
$23$	−2.75984	+	1.59339i	−0.575466	+	0.332245i	0.183864	+	0.982952i	$0.441139\pi$
$24$		0			0
$25$	−0.578031	+	4.96648i	−0.115606	+	0.993295i
$26$		0			0
$27$		−	4.08428i		−	0.786020i
$28$		0			0
$29$	1.25215			0.232518			0.116259	−	0.993219i	$-0.462910\pi$
$29$	1.25215			0.232518			0.116259	+	0.993219i	$0.462910\pi$
$30$		0			0
$31$	0.322674	−	0.558887i	0.0579539	−	0.100379i	−0.835593	−	0.549349i	$-0.814876\pi$
$31$	0.322674	−	0.558887i	0.0579539	−	0.100379i	0.893547	+	0.448970i	$0.148209\pi$
$32$		0			0
$33$	3.43405	−	1.98265i	0.597791	−	0.345135i
$34$		0			0
$35$	−3.51703	+	4.75716i	−0.594486	+	0.804106i
$36$		0			0
$37$	−9.31074	+	5.37556i	−1.53068	+	0.883737i	−0.531346	+	0.847155i	$0.678314\pi$
$37$	−9.31074	+	5.37556i	−1.53068	+	0.883737i	−0.999331	+	0.0365820i	$0.988353\pi$
$38$		0			0
$39$	−0.914997	+	1.58482i	−0.146517	+	0.253775i
$40$		0			0
$41$	8.90154			1.39019			0.695093	−	0.718920i	$-0.255363\pi$
$41$	8.90154			1.39019			0.695093	+	0.718920i	$0.255363\pi$
$42$		0			0
$43$		−	10.4159i		−	1.58841i	−0.607651	−	0.794204i	$-0.707888\pi$
$43$		−	10.4159i		−	1.58841i	0.607651	−	0.794204i	$-0.292112\pi$
$44$		0			0
$45$	−1.71163	+	5.16964i	−0.255154	+	0.770644i
$46$		0			0
$47$	6.52112	−	3.76497i	0.951203	−	0.549177i	0.0577485	−	0.998331i	$-0.481608\pi$
$47$	6.52112	−	3.76497i	0.951203	−	0.549177i	0.893454	+	0.449154i	$0.148275\pi$
$48$		0			0
$49$	−6.41029	+	2.81214i	−0.915756	+	0.401734i
$50$		0			0
$51$	2.30185	+	3.98692i	0.322323	+	0.558280i
$52$		0			0
$53$	−2.89319	−	1.67039i	−0.397411	−	0.229445i	0.287955	−	0.957644i	$-0.407025\pi$
$53$	−2.89319	−	1.67039i	−0.397411	−	0.229445i	−0.685366	+	0.728199i	$0.740358\pi$
$54$		0			0
$55$	−11.5554	+	2.38895i	−1.55813	+	0.322126i
$56$		0			0
$57$		−	0.331613i		−	0.0439232i
$58$		0			0
$59$	−4.07767	+	7.06274i	−0.530868	+	0.919490i	0.468483	+	0.883472i	$0.344801\pi$
$59$	−4.07767	+	7.06274i	−0.530868	+	0.919490i	−0.999351	+	0.0360179i	$0.988533\pi$
$60$		0			0
$61$	1.73518	+	3.00542i	0.222167	+	0.384805i	0.955466	−	0.295102i	$-0.0953535\pi$
$61$	1.73518	+	3.00542i	0.222167	+	0.384805i	−0.733299	+	0.679907i	$0.762020\pi$
$62$		0			0
$63$	−4.80011	+	4.29833i	−0.604757	+	0.541539i
$64$		0			0
$65$	4.06713	−	3.62122i	0.504465	−	0.449158i
$66$		0			0
$67$	4.14517	+	2.39322i	0.506414	+	0.292378i	0.731358	−	0.681993i	$-0.238887\pi$
$67$	4.14517	+	2.39322i	0.506414	+	0.292378i	−0.224945	+	0.974372i	$0.572220\pi$
$68$		0			0
$69$	−2.39464			−0.288281
$70$		0			0
$71$	13.7064			1.62665			0.813326	−	0.581808i	$-0.197654\pi$
$71$	13.7064			1.62665			0.813326	+	0.581808i	$0.197654\pi$
$72$		0			0
$73$	4.61237	+	2.66295i	0.539837	+	0.311675i	0.745013	−	0.667050i	$-0.232443\pi$
$73$	4.61237	+	2.66295i	0.539837	+	0.311675i	−0.205176	+	0.978725i	$0.565777\pi$
$74$		0			0
$75$	−2.24213	+	3.01479i	−0.258899	+	0.348118i
$76$		0			0
$77$	−13.2665	−	4.35069i	−1.51186	−	0.495807i
$78$		0			0
$79$	2.70220	+	4.68034i	0.304021	+	0.526580i	0.977043	−	0.213043i	$-0.0683374\pi$
$79$	2.70220	+	4.68034i	0.304021	+	0.526580i	−0.673022	+	0.739622i	$0.735004\pi$
$80$		0			0
$81$	−2.11852	+	3.66938i	−0.235391	+	0.407708i
$82$		0			0
$83$			11.9379i			1.31036i	0.755475	+	0.655178i	$0.227406\pi$
$83$			11.9379i			1.31036i	−0.755475	+	0.655178i	$0.772594\pi$
$84$		0			0
$85$	−2.77356	−	13.4158i	−0.300835	−	1.45515i
$86$		0			0
$87$	0.814841	+	0.470448i	0.0873601	+	0.0504374i
$88$		0			0
$89$	4.30119	+	7.44987i	0.455925	+	0.789685i	0.998741	−	0.0501668i	$-0.0159753\pi$
$89$	4.30119	+	7.44987i	0.455925	+	0.789685i	−0.542816	+	0.839852i	$0.682642\pi$
$90$		0			0
$91$	6.30618	−	1.32241i	0.661068	−	0.138626i
$92$		0			0
$93$	0.419963	−	0.242466i	0.0435482	−	0.0251426i
$94$		0			0
$95$	−0.310164	+	0.936790i	−0.0318221	+	0.0961126i
$96$		0			0
$97$			13.6714i			1.38812i	0.719917	+	0.694061i	$0.244180\pi$
$97$			13.6714i			1.38812i	−0.719917	+	0.694061i	$0.755820\pi$
$98$		0			0
$99$	−12.8514			−1.29162
$100$		0			0
$101$	5.84070	−	10.1164i	0.581172	−	1.00662i	−0.414169	−	0.910200i	$-0.635928\pi$
$101$	5.84070	−	10.1164i	0.581172	−	1.00662i	0.995341	−	0.0964191i	$-0.0307389\pi$
$102$		0			0
$103$	0.390227	−	0.225297i	0.0384502	−	0.0221992i	−0.480652	−	0.876912i	$-0.659600\pi$
$103$	0.390227	−	0.225297i	0.0384502	−	0.0221992i	0.519102	+	0.854712i	$0.326267\pi$
$104$		0			0
$105$	−4.07605	+	1.77435i	−0.397782	+	0.173159i
$106$		0			0
$107$	0.400630	−	0.231304i	0.0387304	−	0.0223610i	−0.480510	−	0.876989i	$-0.659548\pi$
$107$	0.400630	−	0.231304i	0.0387304	−	0.0223610i	0.519240	+	0.854628i	$0.326215\pi$
$108$		0			0
$109$	1.20303	−	2.08371i	0.115229	−	0.199583i	−0.802642	−	0.596461i	$-0.796573\pi$
$109$	1.20303	−	2.08371i	0.115229	−	0.199583i	0.917871	+	0.396878i	$0.129906\pi$
$110$		0			0
$111$	−8.07869			−0.766795
$112$		0			0
$113$		−	13.2753i		−	1.24884i	−0.781089	−	0.624420i	$-0.785335\pi$
$113$		−	13.2753i		−	1.24884i	0.781089	−	0.624420i	$-0.214665\pi$
$114$		0			0
$115$	6.76472	+	2.23975i	0.630814	+	0.208857i
$116$		0			0
$117$	5.13636	−	2.96548i	0.474857	−	0.274159i
$118$		0			0
$119$	5.05114	−	15.4024i	0.463037	−	1.41193i
$120$		0			0
$121$	−8.42345	−	14.5898i	−0.765768	−	1.32635i
$122$		0			0
$123$	5.79272	+	3.34443i	0.522312	+	0.301557i
$124$		0			0
$125$	9.15368	−	6.41951i	0.818730	−	0.574178i
$126$		0			0
$127$		−	5.17855i		−	0.459522i	−0.973247	−	0.229761i	$-0.926205\pi$
$127$		−	5.17855i		−	0.459522i	0.973247	−	0.229761i	$-0.0737945\pi$
$128$		0			0
$129$	3.91339	−	6.77820i	0.344555	−	0.596787i
$130$		0			0
$131$	−4.57672	−	7.92711i	−0.399870	−	0.692595i	0.593840	−	0.804583i	$-0.297611\pi$
$131$	−4.57672	−	7.92711i	−0.399870	−	0.692595i	−0.993710	+	0.111989i	$0.964278\pi$
$132$		0			0
$133$	−0.869829	+	0.778900i	−0.0754237	+	0.0675392i
$134$		0			0
$135$	−6.82088	+	6.07307i	−0.587048	+	0.522686i
$136$		0			0
$137$	6.83751	+	3.94764i	0.584168	+	0.337270i	0.762788	−	0.646649i	$-0.223830\pi$
$137$	6.83751	+	3.94764i	0.584168	+	0.337270i	−0.178620	+	0.983918i	$0.557163\pi$
$138$		0			0
$139$	3.92998			0.333337			0.166668	−	0.986013i	$-0.446699\pi$
$139$	3.92998			0.333337			0.166668	+	0.986013i	$0.446699\pi$
$140$		0			0
$141$	5.65820			0.476507
$142$		0			0
$143$	11.1297	+	6.42571i	0.930708	+	0.537345i
$144$		0			0
$145$	−1.86186	−	2.09113i	−0.154619	−	0.173659i
$146$		0			0
$147$	−5.22809	−	0.578422i	−0.431206	−	0.0477075i
$148$		0			0
$149$	−3.52101	−	6.09856i	−0.288452	−	0.499614i	0.684988	−	0.728554i	$-0.259807\pi$
$149$	−3.52101	−	6.09856i	−0.288452	−	0.499614i	−0.973440	+	0.228940i	$0.926474\pi$
$150$		0			0
$151$	0.357682	−	0.619523i	0.0291077	−	0.0504161i	−0.851105	−	0.524996i	$-0.824067\pi$
$151$	0.357682	−	0.619523i	0.0291077	−	0.0504161i	0.880212	+	0.474580i	$0.157400\pi$
$152$		0			0
$153$		−	14.9205i		−	1.20625i
$154$		0			0
$155$	−1.41316	+	0.292154i	−0.113508	+	0.0234664i
$156$		0			0
$157$	−13.6359	−	7.87271i	−1.08827	−	0.628310i	−0.155151	−	0.987891i	$-0.549586\pi$
$157$	−13.6359	−	7.87271i	−1.08827	−	0.628310i	−0.933114	+	0.359580i	$0.882920\pi$
$158$		0			0
$159$	−1.25517	−	2.17403i	−0.0995418	−	0.172412i
$160$		0			0
$161$	5.62458	+	6.28118i	0.443279	+	0.495027i
$162$		0			0
$163$	−11.2091	+	6.47157i	−0.877964	+	0.506893i	−0.869987	−	0.493076i	$-0.835873\pi$
$163$	−11.2091	+	6.47157i	−0.877964	+	0.506893i	−0.00797733	+	0.999968i	$0.502539\pi$
$164$		0			0
$165$	−8.41730	−	2.78690i	−0.655286	−	0.216960i
$166$		0			0
$167$			4.70185i			0.363840i	0.983313	+	0.181920i	$0.0582312\pi$
$167$			4.70185i			0.363840i	−0.983313	+	0.181920i	$0.941769\pi$
$168$		0			0
$169$	7.06904			0.543772
$170$		0			0
$171$	−0.537375	+	0.930760i	−0.0410941	+	0.0711770i
$172$		0			0
$173$	−7.08857	+	4.09259i	−0.538934	+	0.311154i	−0.744647	−	0.667459i	$-0.767382\pi$
$173$	−7.08857	+	4.09259i	−0.538934	+	0.311154i	0.205713	+	0.978612i	$0.434049\pi$
$174$		0			0
$175$	13.1742	−	1.20004i	0.995877	−	0.0907145i
$176$		0			0
$177$	−5.30714	+	3.06408i	−0.398909	+	0.230310i
$178$		0			0
$179$	10.0971	−	17.4887i	0.754691	−	1.30716i	−0.190837	−	0.981622i	$-0.561120\pi$
$179$	10.0971	−	17.4887i	0.754691	−	1.30716i	0.945528	−	0.325542i	$-0.105547\pi$
$180$		0			0
$181$	−0.542841			−0.0403490			−0.0201745	−	0.999796i	$-0.506422\pi$
$181$	−0.542841			−0.0403490			−0.0201745	+	0.999796i	$0.506422\pi$
$182$		0			0
$183$			2.60773i			0.192769i
$184$		0			0
$185$	22.8219	+	7.55614i	1.67790	+	0.555539i
$186$		0			0
$187$	27.9987	−	16.1651i	2.04747	−	1.18211i
$188$		0			0
$189$	−10.5759	+	2.21778i	−0.769287	+	0.161319i
$190$		0			0
$191$	6.49553	+	11.2506i	0.470000	+	0.814064i	0.999412	−	0.0343014i	$-0.0109206\pi$
$191$	6.49553	+	11.2506i	0.470000	+	0.814064i	−0.529412	+	0.848365i	$0.677587\pi$
$192$		0			0
$193$	−4.18758	−	2.41770i	−0.301429	−	0.174030i	0.341656	−	0.939825i	$-0.389012\pi$
$193$	−4.18758	−	2.41770i	−0.301429	−	0.174030i	−0.643084	+	0.765795i	$0.722346\pi$
$194$		0			0
$195$	4.00725	−	0.828454i	0.286965	−	0.0593268i
$196$		0			0
$197$			16.5967i			1.18246i	0.806502	+	0.591232i	$0.201358\pi$
$197$			16.5967i			1.18246i	−0.806502	+	0.591232i	$0.798642\pi$
$198$		0			0
$199$	−7.82221	+	13.5485i	−0.554502	+	0.960425i	0.443441	+	0.896304i	$0.353758\pi$
$199$	−7.82221	+	13.5485i	−0.554502	+	0.960425i	−0.997942	+	0.0641211i	$0.979576\pi$
$200$		0			0
$201$	1.79833	+	3.11480i	0.126844	+	0.219701i
$202$		0			0
$203$	−0.679919	−	3.24234i	−0.0477210	−	0.227568i
$204$		0			0
$205$	−13.2360	−	14.8659i	−0.924445	−	1.03828i
$206$		0			0
$207$	6.72118	+	3.88048i	0.467155	+	0.269712i
$208$		0			0
$209$	−2.32880			−0.161087
$210$		0			0
$211$	−23.5521			−1.62139			−0.810697	−	0.585465i	$-0.800912\pi$
$211$	−23.5521			−1.62139			−0.810697	+	0.585465i	$0.800912\pi$
$212$		0			0
$213$	8.91953	+	5.14969i	0.611156	+	0.352851i
$214$		0			0
$215$	−17.3949	+	15.4878i	−1.18632	+	1.05626i
$216$		0			0
$217$	−1.62241	−	0.532063i	−0.110137	−	0.0361188i
$218$		0			0
$219$	2.00102	+	3.46586i	0.135216	+	0.234201i
$220$		0			0
$221$	−7.46023	+	12.9215i	−0.501829	+	0.869194i
$222$		0			0
$223$		−	21.4669i		−	1.43753i	−0.695253	−	0.718765i	$-0.744708\pi$
$223$		−	21.4669i		−	1.43753i	0.695253	−	0.718765i	$-0.255292\pi$
$224$		0			0
$225$	11.1786	−	4.82845i	0.745237	−	0.321897i
$226$		0			0
$227$	−14.3801	−	8.30234i	−0.954440	−	0.551046i	−0.0599823	−	0.998199i	$-0.519104\pi$
$227$	−14.3801	−	8.30234i	−0.954440	−	0.551046i	−0.894457	+	0.447153i	$0.852438\pi$
$228$		0			0
$229$	6.37297	+	11.0383i	0.421138	+	0.729432i	0.996051	−	0.0887822i	$-0.0282975\pi$
$229$	6.37297	+	11.0383i	0.421138	+	0.729432i	−0.574913	+	0.818214i	$0.694964\pi$
$230$		0			0
$231$	−6.99863	−	7.81564i	−0.460476	−	0.514231i
$232$		0			0
$233$	13.3431	−	7.70367i	0.874139	−	0.504684i	0.00541733	−	0.999985i	$-0.498276\pi$
$233$	13.3431	−	7.70367i	0.874139	−	0.504684i	0.868721	+	0.495301i	$0.164942\pi$
$234$		0			0
$235$	−15.9841	−	5.29222i	−1.04269	−	0.345226i
$236$		0			0
$237$			4.06101i			0.263791i
$238$		0			0
$239$	1.60666			0.103926			0.0519631	−	0.998649i	$-0.483452\pi$
$239$	1.60666			0.103926			0.0519631	+	0.998649i	$0.483452\pi$
$240$		0			0
$241$	−10.9076	+	18.8925i	−0.702620	+	1.21697i	0.264923	+	0.964269i	$0.414653\pi$
$241$	−10.9076	+	18.8925i	−0.702620	+	1.21697i	−0.967544	+	0.252704i	$0.918680\pi$
$242$		0			0
$243$	−13.3685	+	7.71833i	−0.857592	+	0.495131i
$244$		0			0
$245$	14.2281	+	6.52394i	0.908999	+	0.416799i
$246$		0			0
$247$	0.930760	−	0.537375i	0.0592229	−	0.0341923i
$248$		0			0
$249$	−4.48524	+	7.76866i	−0.284240	+	0.492319i
$250$		0			0
$251$	−8.23904			−0.520044			−0.260022	−	0.965603i	$-0.583730\pi$
$251$	−8.23904			−0.520044			−0.260022	+	0.965603i	$0.583730\pi$
$252$		0			0
$253$			16.8167i			1.05726i
$254$		0			0
$255$	3.23559	−	9.77247i	0.202620	−	0.611976i
$256$		0			0
$257$	6.33750	−	3.65896i	0.395323	−	0.228240i	−0.289141	−	0.957286i	$-0.593370\pi$
$257$	6.33750	−	3.65896i	0.395323	−	0.228240i	0.684464	+	0.729047i	$0.260036\pi$
$258$		0			0
$259$	18.9754	+	21.1906i	1.17907	+	1.31672i
$260$		0			0
$261$	−1.52471	−	2.64088i	−0.0943772	−	0.163466i
$262$		0			0
$263$	−13.7588	−	7.94362i	−0.848402	−	0.489825i	0.0117097	−	0.999931i	$-0.496273\pi$
$263$	−13.7588	−	7.94362i	−0.848402	−	0.489825i	−0.860111	+	0.510107i	$0.829606\pi$
$264$		0			0
$265$	1.51240	+	7.31550i	0.0929058	+	0.449387i
$266$		0			0
$267$			6.46406i			0.395594i
$268$		0			0
$269$	5.53887	−	9.59361i	0.337711	−	0.584932i	−0.646291	−	0.763091i	$-0.723681\pi$
$269$	5.53887	−	9.59361i	0.337711	−	0.584932i	0.984002	+	0.178159i	$0.0570141\pi$
$270$		0			0
$271$	1.41052	+	2.44310i	0.0856832	+	0.148408i	0.905682	−	0.423957i	$-0.139359\pi$
$271$	1.41052	+	2.44310i	0.0856832	+	0.148408i	−0.819999	+	0.572365i	$0.806026\pi$
$272$		0			0
$273$	4.60063	+	1.50876i	0.278443	+	0.0913142i
$274$		0			0
$275$	21.1718	+	15.7457i	1.27671	+	0.949502i
$276$		0			0
$277$	1.25529	+	0.724740i	0.0754228	+	0.0435454i	0.537237	−	0.843431i	$-0.319468\pi$
$277$	1.25529	+	0.724740i	0.0754228	+	0.0435454i	−0.461814	+	0.886977i	$0.652801\pi$
$278$		0			0
$279$	−1.57165			−0.0940923
$280$		0			0
$281$	−20.2681			−1.20909			−0.604546	−	0.796570i	$-0.706645\pi$
$281$	−20.2681			−1.20909			−0.604546	+	0.796570i	$0.706645\pi$
$282$		0			0
$283$	1.41168	+	0.815034i	0.0839157	+	0.0484487i	0.541371	−	0.840784i	$-0.317906\pi$
$283$	1.41168	+	0.815034i	0.0839157	+	0.0484487i	−0.457455	+	0.889233i	$0.651239\pi$
$284$		0			0
$285$	−0.553806	+	0.493088i	−0.0328046	+	0.0292080i
$286$		0			0
$287$	−4.83356	−	23.0499i	−0.285316	−	1.36059i
$288$		0			0
$289$	10.2676	+	17.7840i	0.603977	+	1.04612i
$290$		0			0
$291$	−5.13654	+	8.89674i	−0.301109	+	0.521536i
$292$		0			0
$293$			20.5114i			1.19829i	0.800641	+	0.599144i	$0.204493\pi$
$293$			20.5114i			1.19829i	−0.800641	+	0.599144i	$0.795507\pi$
$294$		0			0
$295$	17.8583	−	3.69200i	1.03975	−	0.214956i
$296$		0			0
$297$	−18.6653	−	10.7764i	−1.08307	−	0.625310i
$298$		0			0
$299$	−3.88048	−	6.72118i	−0.224414	−	0.388696i
$300$		0			0
$301$	−26.9712	+	5.65586i	−1.55460	+	0.325998i
$302$		0			0
$303$	7.60174	−	4.38887i	0.436709	−	0.252134i
$304$		0			0
$305$	2.43905	−	7.36669i	0.139660	−	0.421816i
$306$		0			0
$307$		−	1.58019i		−	0.0901860i	−0.998983	−	0.0450930i	$-0.985642\pi$
$307$		−	1.58019i		−	0.0901860i	0.998983	−	0.0450930i	$-0.0143584\pi$
$308$		0			0
$309$	0.338589			0.0192617
$310$		0			0
$311$	−10.4205	+	18.0489i	−0.590894	+	1.02346i	0.403219	+	0.915104i	$0.367891\pi$
$311$	−10.4205	+	18.0489i	−0.590894	+	1.02346i	−0.994112	+	0.108354i	$0.965442\pi$
$312$		0			0
$313$	−19.8921	+	11.4847i	−1.12437	+	0.649155i	−0.942513	−	0.334170i	$-0.891544\pi$
$313$	−19.8921	+	11.4847i	−1.12437	+	0.649155i	−0.181857	+	0.983325i	$0.558211\pi$
$314$		0			0
$315$	14.3158	+	1.62501i	0.806606	+	0.0915587i
$316$		0			0
$317$	17.0128	−	9.82235i	0.955534	−	0.551678i	0.0607384	−	0.998154i	$-0.480654\pi$
$317$	17.0128	−	9.82235i	0.955534	−	0.551678i	0.894796	+	0.446476i	$0.147321\pi$
$318$		0			0
$319$	3.30380	−	5.72234i	0.184977	−	0.320390i
$320$		0			0
$321$	0.347616			0.0194021
$322$		0			0
$323$		−	2.70374i		−	0.150440i
$324$		0			0
$325$	−12.0951	−	1.40771i	−0.670918	−	0.0780859i
$326$		0			0
$327$	1.56576	−	0.903990i	0.0865865	−	0.0499907i
$328$		0			0
$329$	−13.2901	−	14.8416i	−0.732708	−	0.818243i
$330$		0			0
$331$	3.47851	+	6.02496i	0.191196	+	0.331162i	0.945647	−	0.325195i	$-0.105430\pi$
$331$	3.47851	+	6.02496i	0.191196	+	0.331162i	−0.754451	+	0.656357i	$0.772097\pi$
$332$		0			0
$333$	22.6750	+	13.0914i	1.24258	+	0.717405i
$334$		0			0
$335$	−2.16686	−	10.4812i	−0.118388	−	0.572647i
$336$		0			0
$337$			31.0168i			1.68959i	0.535089	+	0.844796i	$0.320278\pi$
$337$			31.0168i			1.68959i	−0.535089	+	0.844796i	$0.679722\pi$
$338$		0			0
$339$	4.98773	−	8.63901i	0.270896	−	0.469206i
$340$		0			0
$341$	−1.70275	−	2.94926i	−0.0922093	−	0.159711i
$342$		0			0
$343$	10.7626	+	15.0720i	0.581128	+	0.813812i
$344$		0			0
$345$	3.56068	+	3.99913i	0.191700	+	0.215306i
$346$		0			0
$347$	5.03201	+	2.90523i	0.270133	+	0.155961i	0.628948	−	0.777447i	$-0.283486\pi$
$347$	5.03201	+	2.90523i	0.270133	+	0.155961i	−0.358815	+	0.933409i	$0.616819\pi$
$348$		0			0
$349$	28.0316			1.50050			0.750249	−	0.661155i	$-0.229934\pi$
$349$	28.0316			1.50050			0.750249	+	0.661155i	$0.229934\pi$
$350$		0			0
$351$	9.94667			0.530914
$352$		0			0
$353$	−28.4988	−	16.4538i	−1.51684	−	0.875748i	−0.999804	−	0.0197845i	$-0.993702\pi$
$353$	−28.4988	−	16.4538i	−1.51684	−	0.875748i	−0.517036	−	0.855964i	$-0.672965\pi$
$354$		0			0
$355$	−20.3806	−	22.8902i	−1.08169	−	1.21489i
$356$		0			0
$357$	9.07393	−	8.12538i	0.480243	−	0.430041i
$358$		0			0
$359$	−14.1684	−	24.5404i	−0.747778	−	1.29519i	−0.948885	−	0.315621i	$-0.897787\pi$
$359$	−14.1684	−	24.5404i	−0.747778	−	1.29519i	0.201107	−	0.979569i	$-0.435546\pi$
$360$		0			0
$361$	9.40262	−	16.2858i	0.494875	−	0.857148i
$362$		0			0
$363$		−	12.6592i		−	0.664437i
$364$		0			0
$365$	−2.41108	−	11.6625i	−0.126202	−	0.610441i
$366$		0			0
$367$	−20.5814	−	11.8827i	−1.07434	−	0.620271i	−0.144977	−	0.989435i	$-0.546311\pi$
$367$	−20.5814	−	11.8827i	−1.07434	−	0.620271i	−0.929364	+	0.369164i	$0.879644\pi$
$368$		0			0
$369$	−10.8392	−	18.7741i	−0.564267	−	0.977339i
$370$		0			0
$371$	−2.75434	+	8.39875i	−0.142998	+	0.436041i
$372$		0			0
$373$	7.87096	−	4.54430i	0.407543	−	0.235295i	−0.282191	−	0.959358i	$-0.591061\pi$
$373$	7.87096	−	4.54430i	0.407543	−	0.235295i	0.689733	+	0.724063i	$0.257728\pi$
$374$		0			0
$375$	8.36871	−	0.738364i	0.432158	−	0.0381290i
$376$		0			0
$377$			3.04942i			0.157053i
$378$		0			0
$379$	8.08377			0.415235			0.207618	−	0.978210i	$-0.433429\pi$
$379$	8.08377			0.415235			0.207618	+	0.978210i	$0.433429\pi$
$380$		0			0
$381$	1.94565	−	3.36997i	0.0996789	−	0.172649i
$382$		0			0
$383$	4.78796	−	2.76433i	0.244653	−	0.141251i	−0.372660	−	0.927968i	$-0.621554\pi$
$383$	4.78796	−	2.76433i	0.244653	−	0.141251i	0.617314	+	0.786717i	$0.288221\pi$
$384$		0			0
$385$	12.4606	+	28.6247i	0.635053	+	1.45885i
$386$		0			0
$387$	−21.9680	+	12.6832i	−1.11669	+	0.644723i
$388$		0			0
$389$	−11.1528	+	19.3173i	−0.565472	+	0.979426i	0.431534	+	0.902097i	$0.357972\pi$
$389$	−11.1528	+	19.3173i	−0.565472	+	0.979426i	−0.997006	+	0.0773289i	$0.975361\pi$
$390$		0			0
$391$	−19.5241			−0.987379
$392$		0			0
$393$		−	6.87815i		−	0.346957i
$394$		0			0
$395$	3.79833	−	11.4721i	0.191115	−	0.577226i
$396$		0			0
$397$	27.9034	−	16.1100i	1.40043	−	0.808539i	0.405994	−	0.913876i	$-0.366925\pi$
$397$	27.9034	−	16.1100i	1.40043	−	0.808539i	0.994437	+	0.105337i	$0.0335921\pi$
$398$		0			0
$399$	−0.858689	+	0.180067i	−0.0429882	+	0.00901463i
$400$		0			0
$401$	−2.97214	−	5.14789i	−0.148421	−	0.257073i	0.782223	−	0.622999i	$-0.214086\pi$
$401$	−2.97214	−	5.14789i	−0.148421	−	0.257073i	−0.930644	+	0.365925i	$0.880753\pi$
$402$		0			0
$403$	1.36109	+	0.785826i	0.0678007	+	0.0391448i
$404$		0			0
$405$	9.27809	−	1.91814i	0.461032	−	0.0953132i
$406$		0			0
$407$			56.7338i			2.81219i
$408$		0			0
$409$	15.2617	−	26.4341i	0.754643	−	1.30708i	−0.190909	−	0.981608i	$-0.561143\pi$
$409$	15.2617	−	26.4341i	0.754643	−	1.30708i	0.945552	−	0.325472i	$-0.105523\pi$
$410$		0			0
$411$	2.96637	+	5.13790i	0.146320	+	0.253434i
$412$		0			0
$413$	20.5027	+	6.72376i	1.00887	+	0.330855i
$414$		0			0
$415$	19.9367	−	17.7509i	0.978655	−	0.871359i
$416$		0			0
$417$	2.55746	+	1.47655i	0.125239	+	0.0723069i
$418$		0			0
$419$	−4.06306			−0.198493			−0.0992466	−	0.995063i	$-0.531643\pi$
$419$	−4.06306			−0.198493			−0.0992466	+	0.995063i	$0.531643\pi$
$420$		0			0
$421$	−2.34322			−0.114201			−0.0571007	−	0.998368i	$-0.518186\pi$
$421$	−2.34322			−0.114201			−0.0571007	+	0.998368i	$0.518186\pi$
$422$		0			0
$423$	−15.8812	−	9.16904i	−0.772173	−	0.445814i
$424$		0			0
$425$	−18.2807	+	24.5804i	−0.886745	+	1.19232i
$426$		0			0
$427$	6.84012	−	6.12509i	0.331017	−	0.296414i
$428$		0			0
$429$	4.82845	+	8.36313i	0.233120	+	0.403776i
$430$		0			0
$431$	3.21851	−	5.57462i	0.155030	−	0.268520i	−0.778040	−	0.628215i	$-0.783786\pi$
$431$	3.21851	−	5.57462i	0.155030	−	0.268520i	0.933070	+	0.359695i	$0.117119\pi$
$432$		0			0
$433$		−	22.4161i		−	1.07725i	−0.842547	−	0.538624i	$-0.818945\pi$
$433$		−	22.4161i		−	1.07725i	0.842547	−	0.538624i	$-0.181055\pi$
$434$		0			0
$435$	−0.425952	−	2.06034i	−0.0204228	−	0.0987857i
$436$		0			0
$437$	1.21795	+	0.703181i	0.0582623	+	0.0336377i
$438$		0			0
$439$	8.70385	+	15.0755i	0.415412	+	0.719515i	0.995472	−	0.0950591i	$-0.0303040\pi$
$439$	8.70385	+	15.0755i	0.415412	+	0.719515i	−0.580059	+	0.814574i	$0.696971\pi$
$440$		0			0
$441$	13.7367	+	10.0955i	0.654129	+	0.480740i
$442$		0			0
$443$	30.9059	−	17.8436i	1.46839	−	0.847773i	0.469013	−	0.883191i	$-0.344610\pi$
$443$	30.9059	−	17.8436i	1.46839	−	0.847773i	0.999373	+	0.0354180i	$0.0112763\pi$
$444$		0			0
$445$	6.04595	−	18.2606i	0.286605	−	0.865637i
$446$		0			0
$447$		−	5.29157i		−	0.250282i
$448$		0			0
$449$	5.24155			0.247364			0.123682	−	0.992322i	$-0.460530\pi$
$449$	5.24155			0.247364			0.123682	+	0.992322i	$0.460530\pi$
$450$		0			0
$451$	23.4868	−	40.6803i	1.10595	−	1.91556i
$452$		0			0
$453$	0.465527	−	0.268772i	0.0218724	−	0.0126280i
$454$		0			0
$455$	−11.5854	−	8.56521i	−0.543131	−	0.401543i
$456$		0			0
$457$	−12.9639	+	7.48473i	−0.606427	+	0.350121i	−0.771566	−	0.636150i	$-0.780526\pi$
$457$	−12.9639	+	7.48473i	−0.606427	+	0.350121i	0.165139	+	0.986270i	$0.447193\pi$
$458$		0			0
$459$	12.5114	−	21.6703i	0.583981	−	1.01148i
$460$		0			0
$461$	−9.92904			−0.462441			−0.231221	−	0.972901i	$-0.574272\pi$
$461$	−9.92904			−0.462441			−0.231221	+	0.972901i	$0.574272\pi$
$462$		0			0
$463$			3.07448i			0.142883i	0.997445	+	0.0714415i	$0.0227599\pi$
$463$			3.07448i			0.142883i	−0.997445	+	0.0714415i	$0.977240\pi$
$464$		0			0
$465$	−1.02939	−	0.340822i	−0.0477366	−	0.0158052i
$466$		0			0
$467$	−17.2722	+	9.97212i	−0.799263	+	0.461455i	−0.843213	−	0.537579i	$-0.819339\pi$
$467$	−17.2722	+	9.97212i	−0.799263	+	0.461455i	0.0439504	+	0.999034i	$0.486006\pi$
$468$		0			0
$469$	3.94623	−	12.0332i	0.182220	−	0.555640i
$470$		0			0
$471$	−5.91577	−	10.2464i	−0.272584	−	0.472130i
$472$		0			0
$473$	−47.6009	−	27.4824i	−2.18869	−	1.26364i
$474$		0			0
$475$	2.02567	−	0.874964i	0.0929439	−	0.0401461i
$476$		0			0
$477$			8.13598i			0.372521i
$478$		0			0
$479$	−20.1696	+	34.9347i	−0.921571	+	1.59621i	−0.124586	+	0.992209i	$0.539760\pi$
$479$	−20.1696	+	34.9347i	−0.921571	+	1.59621i	−0.796985	+	0.603999i	$0.793573\pi$
$480$		0			0
$481$	−13.0914	−	22.6750i	−0.596917	−	1.03389i
$482$		0			0
$483$	1.30030	+	6.20075i	0.0591655	+	0.282144i
$484$		0			0
$485$	22.8317	−	20.3285i	1.03674	−	0.923071i
$486$		0			0
$487$	5.12959	+	2.96157i	0.232444	+	0.134202i	0.611699	−	0.791091i	$-0.290486\pi$
$487$	5.12959	+	2.96157i	0.232444	+	0.134202i	−0.379255	+	0.925292i	$0.623820\pi$
$488$		0			0
$489$	−9.72584			−0.439818
$490$		0			0
$491$	−26.3855			−1.19076			−0.595380	−	0.803444i	$-0.702999\pi$
$491$	−26.3855			−1.19076			−0.595380	+	0.803444i	$0.702999\pi$
$492$		0			0
$493$	6.64362	+	3.83570i	0.299214	+	0.172751i
$494$		0			0
$495$	19.1093	+	21.4623i	0.858897	+	0.964659i
$496$		0			0
$497$	−7.44263	−	35.4918i	−0.333848	−	1.59203i
$498$		0			0
$499$	−3.01447	−	5.22122i	−0.134946	−	0.233734i	0.790631	−	0.612293i	$-0.209753\pi$
$499$	−3.01447	−	5.22122i	−0.134946	−	0.233734i	−0.925577	+	0.378559i	$0.876420\pi$
$500$		0			0
$501$	−1.76655	+	3.05976i	−0.0789237	+	0.136700i
$502$		0			0
$503$			37.5173i			1.67281i	0.548109	+	0.836407i	$0.315348\pi$
$503$			37.5173i			1.67281i	−0.548109	+	0.836407i	$0.684652\pi$
$504$		0			0
$505$	−25.5795	+	5.28827i	−1.13827	+	0.235325i
$506$		0			0
$507$	4.60022	+	2.65594i	0.204303	+	0.117954i
$508$		0			0
$509$	−7.95808	−	13.7838i	−0.352736	−	0.610956i	0.633992	−	0.773340i	$-0.281415\pi$
$509$	−7.95808	−	13.7838i	−0.352736	−	0.610956i	−0.986728	+	0.162383i	$0.948082\pi$
$510$		0			0
$511$	4.39100	−	13.3894i	0.194246	−	0.592312i
$512$		0			0
$513$	−1.56096	+	0.901218i	−0.0689179	+	0.0397898i
$514$		0			0
$515$	−0.956497	−	0.316689i	−0.0421483	−	0.0139550i
$516$		0			0
$517$		−	39.7356i		−	1.74757i
$518$		0			0
$519$	−6.15057			−0.269980
$520$		0			0
$521$	−9.69465	+	16.7916i	−0.424730	+	0.735654i	−0.996395	−	0.0848329i	$-0.972964\pi$
$521$	−9.69465	+	16.7916i	−0.424730	+	0.735654i	0.571665	+	0.820487i	$0.306298\pi$
$522$		0			0
$523$	−5.12959	+	2.96157i	−0.224301	+	0.129500i	−0.607940	−	0.793983i	$-0.708004\pi$
$523$	−5.12959	+	2.96157i	−0.224301	+	0.129500i	0.383639	+	0.923483i	$0.374671\pi$
$524$		0			0
$525$	9.02406	+	4.16880i	0.393842	+	0.181941i
$526$		0			0
$527$	3.42408	−	1.97689i	0.149155	−	0.0861148i
$528$		0			0
$529$	−6.42220	+	11.1236i	−0.279226	+	0.483634i
$530$		0			0
$531$	19.8612			0.861902
$532$		0			0
$533$			21.6784i			0.938996i
$534$		0			0
$535$	−0.981998	−	0.325132i	−0.0424555	−	0.0140567i
$536$		0			0
$537$	13.1415	−	7.58722i	0.567096	−	0.327413i
$538$		0			0
$539$	−4.06206	+	36.7151i	−0.174965	+	1.58143i
$540$		0			0
$541$	11.7171	+	20.2947i	0.503759	+	0.872536i	0.999991	+	0.00434560i	$0.00138325\pi$
$541$	11.7171	+	20.2947i	0.503759	+	0.872536i	−0.496232	+	0.868190i	$0.665283\pi$
$542$		0			0
$543$	−0.353256	−	0.203953i	−0.0151597	−	0.00875245i
$544$		0			0
$545$	−5.26870	+	1.08924i	−0.225686	+	0.0466581i
$546$		0			0
$547$			40.9760i			1.75201i	0.482306	+	0.876003i	$0.339799\pi$
$547$			40.9760i			1.75201i	−0.482306	+	0.876003i	$0.660201\pi$
$548$		0			0
$549$	4.22579	−	7.31928i	0.180352	−	0.312379i
$550$		0			0
$551$	−0.276293	−	0.478553i	−0.0117705	−	0.0203870i
$552$		0			0
$553$	10.6521	−	9.53859i	0.452974	−	0.405622i
$554$		0			0
$555$	12.0125	+	13.4917i	0.509903	+	0.572690i
$556$		0			0
$557$	−6.66687	−	3.84912i	−0.282484	−	0.163092i	0.352063	−	0.935976i	$-0.385480\pi$
$557$	−6.66687	−	3.84912i	−0.282484	−	0.163092i	−0.634548	+	0.772884i	$0.718814\pi$
$558$		0			0
$559$	25.3664			1.07288
$560$		0			0
$561$	24.2938			1.02568
$562$		0			0
$563$	20.9572	+	12.0996i	0.883240	+	0.509939i	0.871725	−	0.489995i	$-0.163001\pi$
$563$	20.9572	+	12.0996i	0.883240	+	0.509939i	0.0115147	+	0.999934i	$0.496335\pi$
$564$		0			0
$565$	−22.1703	+	19.7396i	−0.932711	+	0.830452i
$566$		0			0
$567$	10.6520	+	3.49326i	0.447340	+	0.146703i
$568$		0			0
$569$	8.15072	+	14.1175i	0.341696	+	0.591835i	0.984748	−	0.173988i	$-0.0556653\pi$
$569$	8.15072	+	14.1175i	0.341696	+	0.591835i	−0.643052	+	0.765823i	$0.722332\pi$
$570$		0			0
$571$	−15.5302	+	26.8991i	−0.649918	+	1.12569i	0.333224	+	0.942848i	$0.391863\pi$
$571$	−15.5302	+	26.8991i	−0.649918	+	1.12569i	−0.983142	+	0.182843i	$0.941470\pi$
$572$		0			0
$573$			9.76184i			0.407807i
$574$		0			0
$575$	−6.31827	−	14.6277i	−0.263490	−	0.610017i
$576$		0			0
$577$	−5.49015	−	3.16974i	−0.228558	−	0.131958i	0.381349	−	0.924431i	$-0.375460\pi$
$577$	−5.49015	−	3.16974i	−0.228558	−	0.131958i	−0.609907	+	0.792473i	$0.708793\pi$
$578$		0			0
$579$	−1.81673	−	3.14666i	−0.0755006	−	0.130771i
$580$		0			0
$581$	30.9124	−	6.48232i	1.28246	−	0.268932i
$582$		0			0
$583$	−15.2674	+	8.81466i	−0.632313	+	0.365066i
$584$		0			0
$585$	−12.5899	−	4.16842i	−0.520529	−	0.172343i
$586$		0			0
$587$			14.8548i			0.613122i	0.951851	+	0.306561i	$0.0991783\pi$
$587$			14.8548i			0.613122i	−0.951851	+	0.306561i	$0.900822\pi$
$588$		0			0
$589$	−0.284799			−0.0117349
$590$		0			0
$591$	−6.23559	+	10.8004i	−0.256498	+	0.444268i
$592$		0			0
$593$	−10.6383	+	6.14203i	−0.436863	+	0.252223i	−0.702266	−	0.711914i	$-0.747828\pi$
$593$	−10.6383	+	6.14203i	−0.436863	+	0.252223i	0.265403	+	0.964138i	$0.414495\pi$
$594$		0			0
$595$	−33.2332	+	14.4668i	−1.36243	+	0.593080i
$596$		0			0
$597$	−10.1807	+	5.87782i	−0.416668	+	0.240563i
$598$		0			0
$599$	−11.4087	+	19.7605i	−0.466148	+	0.807392i	−0.999253	−	0.0386573i	$-0.987692\pi$
$599$	−11.4087	+	19.7605i	−0.466148	+	0.807392i	0.533104	+	0.846049i	$0.321025\pi$
$600$		0			0
$601$	25.8612			1.05490			0.527450	−	0.849586i	$-0.323148\pi$
$601$	25.8612			1.05490			0.527450	+	0.849586i	$0.323148\pi$
$602$		0			0
$603$		−	11.6567i		−	0.474697i
$604$		0			0
$605$	−11.8404	+	35.7616i	−0.481380	+	1.45392i
$606$		0			0
$607$	−1.93194	+	1.11541i	−0.0784151	+	0.0452730i	−0.538695	−	0.842501i	$-0.681082\pi$
$607$	−1.93194	+	1.11541i	−0.0784151	+	0.0452730i	0.460280	+	0.887774i	$0.347749\pi$
$608$		0			0
$609$	0.775732	−	2.36543i	0.0314343	−	0.0958520i
$610$		0			0
$611$	9.16904	+	15.8812i	0.370940	+	0.642487i
$612$		0			0
$613$	17.2616	+	9.96601i	0.697191	+	0.402524i	0.806300	−	0.591506i	$-0.201466\pi$
$613$	17.2616	+	9.96601i	0.697191	+	0.402524i	−0.109109	+	0.994030i	$0.534800\pi$
$614$		0			0
$615$	−3.02811	−	14.6470i	−0.122105	−	0.590624i
$616$		0			0
$617$		−	12.1435i		−	0.488880i	−0.969664	−	0.244440i	$-0.921396\pi$
$617$		−	12.1435i		−	0.488880i	0.969664	−	0.244440i	$-0.0786040\pi$
$618$		0			0
$619$	0.465052	−	0.805494i	0.0186920	−	0.0323755i	−0.856528	−	0.516100i	$-0.827383\pi$
$619$	0.465052	−	0.805494i	0.0186920	−	0.0323755i	0.875220	+	0.483725i	$0.160716\pi$
$620$		0			0
$621$	6.50785	+	11.2719i	0.261151	+	0.452327i
$622$		0			0
$623$	16.9554	−	15.1829i	0.679302	−	0.608291i
$624$		0			0
$625$	−24.3318	−	5.74156i	−0.973270	−	0.229662i
$626$		0			0
$627$	−1.51548	−	0.874964i	−0.0605225	−	0.0349427i
$628$		0			0
$629$	−65.8678			−2.62632
$630$		0			0
$631$	35.8314			1.42643			0.713214	−	0.700947i	$-0.247239\pi$
$631$	35.8314			1.42643			0.713214	+	0.700947i	$0.247239\pi$
$632$		0			0
$633$	−15.3267	−	8.84886i	−0.609180	−	0.351711i
$634$		0			0
$635$	−8.64836	+	7.70019i	−0.343200	+	0.305573i
$636$		0			0
$637$	−6.84856	−	15.6114i	−0.271350	−	0.618544i
$638$		0			0
$639$	−16.6900	−	28.9079i	−0.660246	−	1.14358i
$640$		0			0
$641$	3.09838	−	5.36655i	0.122379	−	0.211966i	−0.798327	−	0.602225i	$-0.794281\pi$
$641$	3.09838	−	5.36655i	0.122379	−	0.211966i	0.920705	+	0.390259i	$0.127614\pi$
$642$		0			0
$643$		−	20.2885i		−	0.800102i	−0.916493	−	0.400051i	$-0.868992\pi$
$643$		−	20.2885i		−	0.800102i	0.916493	−	0.400051i	$-0.131008\pi$
$644$		0			0
$645$	−17.1388	+	3.54325i	−0.674840	+	0.139516i
$646$		0			0
$647$	−20.6270	−	11.9090i	−0.810930	−	0.468191i	0.0363487	−	0.999339i	$-0.488427\pi$
$647$	−20.6270	−	11.9090i	−0.810930	−	0.468191i	−0.847279	+	0.531148i	$0.821761\pi$
$648$		0			0
$649$	21.5180	+	37.2702i	0.844654	+	1.46298i
$650$		0			0
$651$	−0.855890	−	0.955806i	−0.0335450	−	0.0374610i
$652$		0			0
$653$	−8.60522	+	4.96823i	−0.336748	+	0.194422i	−0.658833	−	0.752289i	$-0.728950\pi$
$653$	−8.60522	+	4.96823i	−0.336748	+	0.194422i	0.322085	+	0.946711i	$0.395616\pi$
$654$		0			0
$655$	−6.43325	+	19.4304i	−0.251368	+	0.759209i
$656$		0			0
$657$		−	12.9705i		−	0.506026i
$658$		0			0
$659$	−45.4504			−1.77050			−0.885249	−	0.465118i	$-0.846012\pi$
$659$	−45.4504			−1.77050			−0.885249	+	0.465118i	$0.846012\pi$
$660$		0			0
$661$	−2.77019	+	4.79811i	−0.107748	+	0.186625i	−0.914858	−	0.403777i	$-0.867697\pi$
$661$	−2.77019	+	4.79811i	−0.107748	+	0.186625i	0.807110	+	0.590402i	$0.201031\pi$
$662$		0			0
$663$	−9.70957	+	5.60582i	−0.377088	+	0.217712i
$664$		0			0
$665$	2.59417	+	0.294467i	0.100598	+	0.0114190i
$666$		0			0
$667$	−3.45572	+	1.99516i	−0.133806	+	0.0772529i
$668$		0			0
$669$	8.06541	−	13.9697i	0.311827	−	0.540100i
$670$		0			0
$671$	18.3132			0.706972
$672$		0			0
$673$		−	9.34880i		−	0.360370i	−0.983633	−	0.180185i	$-0.942330\pi$
$673$		−	9.34880i		−	0.360370i	0.983633	−	0.180185i	$-0.0576696\pi$
$674$		0			0
$675$	20.2845	+	2.36084i	0.780749	+	0.0908688i
$676$		0			0
$677$	28.4355	−	16.4172i	1.09286	−	0.630965i	0.158526	−	0.987355i	$-0.449326\pi$
$677$	28.4355	−	16.4172i	1.09286	−	0.630965i	0.934337	+	0.356390i	$0.115992\pi$
$678$		0			0
$679$	35.4012	−	7.42362i	1.35857	−	0.284892i
$680$		0			0
$681$	−6.23861	−	10.8056i	−0.239064	−	0.414071i
$682$		0			0
$683$	−11.3356	−	6.54464i	−0.433746	−	0.250424i	0.267195	−	0.963642i	$-0.413903\pi$
$683$	−11.3356	−	6.54464i	−0.433746	−	0.250424i	−0.700941	+	0.713219i	$0.747237\pi$
$684$		0			0
$685$	−3.57426	−	17.2888i	−0.136566	−	0.660570i
$686$		0			0
$687$			9.57766i			0.365410i
$688$		0			0
$689$	4.06799	−	7.04596i	0.154978	−	0.268430i
$690$		0			0
$691$	11.4898	+	19.9009i	0.437093	+	0.757068i	0.997464	−	0.0711743i	$-0.0226746\pi$
$691$	11.4898	+	19.9009i	0.437093	+	0.757068i	−0.560371	+	0.828242i	$0.689341\pi$
$692$		0			0
$693$	6.97836	+	33.2778i	0.265086	+	1.26412i
$694$		0			0
$695$	−5.84364	−	6.56321i	−0.221662	−	0.248957i
$696$		0			0
$697$	47.2297	+	27.2681i	1.78895	+	1.03285i
$698$		0			0
$699$	11.5775			0.437901
$700$		0			0
$701$	3.12916			0.118187			0.0590934	−	0.998252i	$-0.481179\pi$
$701$	3.12916			0.118187			0.0590934	+	0.998252i	$0.481179\pi$
$702$		0			0
$703$	4.10893	+	2.37229i	0.154971	+	0.0894728i
$704$		0			0
$705$	−8.41340	−	9.44940i	−0.316867	−	0.355885i
$706$		0			0
$707$	−29.3672	−	9.63086i	−1.10447	−	0.362206i
$708$		0			0
$709$	18.9356	+	32.7974i	0.711141	+	1.23173i	0.964429	+	0.264342i	$0.0851546\pi$
$709$	18.9356	+	32.7974i	0.711141	+	1.23173i	−0.253288	+	0.967391i	$0.581512\pi$
$710$		0			0
$711$	6.58081	−	11.3983i	0.246800	−	0.427470i
$712$		0			0
$713$			2.05658i			0.0770196i
$714$		0			0
$715$	−5.81795	−	28.1415i	−0.217579	−	1.05243i
$716$		0			0
$717$	1.04554	+	0.603644i	0.0390465	+	0.0225435i
$718$		0			0
$719$	−12.9091	−	22.3592i	−0.481427	−	0.833857i	0.518345	−	0.855171i	$-0.326548\pi$
$719$	−12.9091	−	22.3592i	−0.481427	−	0.833857i	−0.999773	+	0.0213145i	$0.993215\pi$
$720$		0			0
$721$	−0.795286	−	0.888127i	−0.0296180	−	0.0330756i
$722$		0			0
$723$	−14.1964	+	8.19627i	−0.527968	+	0.304823i
$724$		0			0
$725$	−0.723780	+	6.21875i	−0.0268805	+	0.230959i
$726$		0			0
$727$			24.1385i			0.895248i	0.894222	+	0.447624i	$0.147730\pi$
$727$			24.1385i			0.895248i	−0.894222	+	0.447624i	$0.852270\pi$
$728$		0			0
$729$	1.11156			0.0411690
$730$		0			0
$731$	31.9070	−	55.2645i	1.18012	−	2.04403i
$732$		0			0
$733$	−9.44521	+	5.45320i	−0.348867	+	0.201418i	−0.664186	−	0.747567i	$-0.731222\pi$
$733$	−9.44521	+	5.45320i	−0.348867	+	0.201418i	0.315319	+	0.948986i	$0.397888\pi$
$734$		0			0
$735$	6.80786	+	9.59118i	0.251112	+	0.353776i
$736$		0			0
$737$	21.8742	−	12.6290i	0.805745	−	0.465197i
$738$		0			0
$739$	−21.8077	+	37.7720i	−0.802208	+	1.38946i	0.115952	+	0.993255i	$0.463008\pi$
$739$	−21.8077	+	37.7720i	−0.802208	+	1.38946i	−0.918160	+	0.396210i	$0.870325\pi$
$740$		0			0
$741$	0.807597			0.0296678
$742$		0			0
$743$		−	36.1676i		−	1.32686i	−0.748238	−	0.663431i	$-0.769100\pi$
$743$		−	36.1676i		−	1.32686i	0.748238	−	0.663431i	$-0.230900\pi$
$744$		0			0
$745$	−4.94929	+	14.9484i	−0.181328	+	0.547667i
$746$		0			0
$747$	25.1780	−	14.5365i	0.921215	−	0.531864i
$748$		0			0
$749$	−0.816489	−	0.911805i	−0.0298339	−	0.0333166i
$750$		0			0
$751$	−20.9582	−	36.3007i	−0.764777	−	1.32463i	−0.940364	−	0.340169i	$-0.889516\pi$
$751$	−20.9582	−	36.3007i	−0.764777	−	1.32463i	0.175587	−	0.984464i	$-0.443818\pi$
$752$		0			0
$753$	−5.36160	−	3.09552i	−0.195388	−	0.112807i
$754$		0			0
$755$	−1.56648	+	0.323851i	−0.0570099	+	0.0117862i
$756$		0			0
$757$		−	27.3777i		−	0.995060i	−0.867447	−	0.497530i	$-0.834241\pi$
$757$		−	27.3777i		−	0.995060i	0.867447	−	0.497530i	$-0.165759\pi$
$758$		0			0
$759$	−6.31827	+	10.9436i	−0.229339	+	0.397226i
$760$		0			0
$761$	7.10666	+	12.3091i	0.257616	+	0.446204i	0.965603	−	0.260022i	$-0.0837297\pi$
$761$	7.10666	+	12.3091i	0.257616	+	0.446204i	−0.707987	+	0.706226i	$0.750396\pi$
$762$		0			0
$763$	−6.04887	−	1.98370i	−0.218984	−	0.0718148i
$764$		0			0
$765$	−24.9177	+	22.1858i	−0.900900	+	0.802129i
$766$		0			0
$767$	−17.2003	−	9.93059i	−0.621066	−	0.358573i
$768$		0			0
$769$	−38.1788			−1.37676			−0.688381	−	0.725349i	$-0.741678\pi$
$769$	−38.1788			−1.37676			−0.688381	+	0.725349i	$0.741678\pi$
$770$		0			0
$771$	5.49889			0.198038
$772$		0			0
$773$	25.9658	+	14.9914i	0.933927	+	0.539203i	0.888051	−	0.459744i	$-0.152059\pi$
$773$	25.9658	+	14.9914i	0.933927	+	0.539203i	0.0458753	+	0.998947i	$0.485392\pi$
$774$		0			0
$775$	2.58918	+	1.92561i	0.0930063	+	0.0691698i
$776$		0			0
$777$	4.38675	+	20.9192i	0.157374	+	0.750472i
$778$		0			0
$779$	−1.96417	−	3.40205i	−0.0703738	−	0.121891i
$780$		0			0
$781$	36.1645	−	62.6387i	1.29407	−	2.24139i
$782$		0			0
$783$		−	5.11411i		−	0.182763i
$784$		0			0
$785$	7.12808	+	34.4787i	0.254412	+	1.23060i
$786$		0			0
$787$	−25.1825	−	14.5391i	−0.897661	−	0.518265i	−0.0212201	−	0.999775i	$-0.506755\pi$
$787$	−25.1825	−	14.5391i	−0.897661	−	0.518265i	−0.876440	+	0.481510i	$0.840088\pi$
$788$		0			0
$789$	−5.96906	−	10.3387i	−0.212504	−	0.368068i
$790$		0			0
$791$	−34.3756	+	7.20856i	−1.22226	+	0.256307i
$792$		0			0
$793$	−7.31928	+	4.22579i	−0.259915	+	0.150062i
$794$		0			0
$795$	−1.76433	+	5.32883i	−0.0625744	+	0.188994i
$796$		0			0
$797$			42.5726i			1.50800i	0.656875	+	0.753999i	$0.271878\pi$
$797$			42.5726i			1.50800i	−0.656875	+	0.753999i	$0.728122\pi$
$798$		0			0
$799$	46.1329			1.63207
$800$		0			0
$801$	10.4749	−	18.1431i	0.370113	−	0.641055i
$802$		0			0
$803$	24.3395	−	14.0524i	0.858923	−	0.495900i
$804$		0			0
$805$	2.12640	−	18.7330i	0.0749457	−	0.660250i
$806$		0			0
$807$	7.20890	−	4.16206i	0.253765	−	0.146511i
$808$		0			0
$809$	10.6887	−	18.5134i	0.375794	−	0.650895i	−0.614651	−	0.788799i	$-0.710703\pi$
$809$	10.6887	−	18.5134i	0.375794	−	0.650895i	0.990446	+	0.137904i	$0.0440366\pi$
$810$		0			0
$811$	23.3902			0.821342			0.410671	−	0.911784i	$-0.365294\pi$
$811$	23.3902			0.821342			0.410671	+	0.911784i	$0.365294\pi$
$812$		0			0
$813$			2.11981i			0.0743451i
$814$		0			0
$815$	27.4750	+	9.09675i	0.962406	+	0.318645i
$816$		0			0
$817$	−3.98081	+	2.29832i	−0.139271	+	0.0804082i
$818$		0			0
$819$	−10.4680	−	11.6900i	−0.365780	−	0.408481i
$820$		0			0
$821$	1.29822	+	2.24859i	0.0453083	+	0.0784763i	0.887790	−	0.460248i	$-0.152240\pi$
$821$	1.29822	+	2.24859i	0.0453083	+	0.0784763i	−0.842482	+	0.538725i	$0.818906\pi$
$822$		0			0
$823$	9.83049	+	5.67564i	0.342669	+	0.197840i	0.661452	−	0.749988i	$-0.269941\pi$
$823$	9.83049	+	5.67564i	0.342669	+	0.197840i	−0.318782	+	0.947828i	$0.603274\pi$
$824$		0			0
$825$	7.86178	+	18.2011i	0.273712	+	0.633682i
$826$		0			0
$827$		−	28.8025i		−	1.00156i	−0.865574	−	0.500781i	$-0.833046\pi$
$827$		−	28.8025i		−	1.00156i	0.865574	−	0.500781i	$-0.166954\pi$
$828$		0			0
$829$	−1.66584	+	2.88531i	−0.0578569	+	0.100211i	−0.893503	−	0.449057i	$-0.851760\pi$
$829$	−1.66584	+	2.88531i	−0.0578569	+	0.100211i	0.835646	+	0.549268i	$0.185093\pi$
$830$		0			0
$831$	0.544589	+	0.943256i	0.0188916	+	0.0327212i
$832$		0			0
$833$	−42.6261	−	4.71604i	−1.47691	−	0.163401i
$834$		0			0
$835$	7.85226	−	6.99136i	0.271739	−	0.241946i
$836$		0			0
$837$	−2.28265	−	1.31789i	−0.0789000	−	0.0455529i
$838$		0			0
$839$	30.6414			1.05786			0.528929	−	0.848666i	$-0.322594\pi$
$839$	30.6414			1.05786			0.528929	+	0.848666i	$0.322594\pi$
$840$		0			0
$841$	−27.4321			−0.945936
$842$		0			0
$843$	−13.1896	−	7.61499i	−0.454272	−	0.262274i
$844$		0			0
$845$	−10.5112	−	11.8055i	−0.361597	−	0.406123i
$846$		0			0
$847$	−33.2054	+	29.7343i	−1.14095	+	1.02168i
$848$		0			0
$849$	0.612439	+	1.06078i	0.0210188	+	0.0364057i
$850$		0			0
$851$	17.1308	−	29.6713i	0.587235	−	1.01712i
$852$		0			0
$853$		−	11.0513i		−	0.378390i	−0.981940	−	0.189195i	$-0.939412\pi$
$853$		−	11.0513i		−	0.378390i	0.981940	−	0.189195i	$-0.0605878\pi$
$854$		0			0
$855$	2.35344	−	0.486548i	0.0804861	−	0.0166396i
$856$		0			0
$857$	9.95009	+	5.74468i	0.339888	+	0.196235i	0.660223	−	0.751070i	$-0.270462\pi$
$857$	9.95009	+	5.74468i	0.339888	+	0.196235i	−0.320334	+	0.947305i	$0.603795\pi$
$858$		0			0
$859$	−25.3174	−	43.8510i	−0.863819	−	1.49618i	−0.868215	−	0.496188i	$-0.834733\pi$
$859$	−25.3174	−	43.8510i	−0.863819	−	1.49618i	0.00439604	−	0.999990i	$-0.498601\pi$
$860$		0			0
$861$	5.51470	−	16.8159i	0.187941	−	0.573084i
$862$		0			0
$863$	44.5101	−	25.6979i	1.51514	−	0.874766i	0.515298	−	0.857011i	$-0.327681\pi$
$863$	44.5101	−	25.6979i	1.51514	−	0.874766i	0.999842	−	0.0177551i	$-0.00565192\pi$
$864$		0			0
$865$	17.3750	+	5.75274i	0.590769	+	0.195599i
$866$		0			0
$867$			15.4307i			0.524055i
$868$		0			0
$869$	28.5191			0.967443
$870$		0			0
$871$	−5.82834	+	10.0950i	−0.197486	+	0.342055i
$872$		0			0
$873$	28.8341	−	16.6474i	0.975887	−	0.563428i
$874$		0			0
$875$	−21.5933	−	20.2170i	−0.729988	−	0.683460i
$876$		0			0
$877$	5.33546	−	3.08043i	0.180166	−	0.104019i	−0.407205	−	0.913337i	$-0.633496\pi$
$877$	5.33546	−	3.08043i	0.180166	−	0.104019i	0.587371	+	0.809318i	$0.300163\pi$
$878$		0			0
$879$	−7.70642	+	13.3479i	−0.259931	+	0.450214i
$880$		0			0
$881$	−5.10894			−0.172124			−0.0860622	−	0.996290i	$-0.527428\pi$
$881$	−5.10894			−0.172124			−0.0860622	+	0.996290i	$0.527428\pi$
$882$		0			0
$883$			7.26283i			0.244414i	0.992505	+	0.122207i	$0.0389971\pi$
$883$			7.26283i			0.244414i	−0.992505	+	0.122207i	$0.961003\pi$
$884$		0			0
$885$	13.0085	+	4.30701i	0.437276	+	0.144779i
$886$		0			0
$887$	27.0382	−	15.6105i	0.907854	−	0.524150i	0.0281142	−	0.999605i	$-0.491050\pi$
$887$	27.0382	−	15.6105i	0.907854	−	0.524150i	0.879740	+	0.475455i	$0.157716\pi$
$888$		0			0
$889$	−13.4095	+	2.81197i	−0.449740	+	0.0943105i
$890$		0			0
$891$	11.1794	+	19.3634i	0.374525	+	0.648697i
$892$		0			0
$893$	−2.87784	−	1.66152i	−0.0963033	−	0.0556007i
$894$		0			0
$895$	−44.2204	+	9.14207i	−1.47812	+	0.305586i
$896$		0			0
$897$		−	5.83180i		−	0.194718i
$898$		0			0
$899$	0.404035	−	0.699808i	0.0134753	−	0.0233399i
$900$		0			0
$901$	−10.2338	−	17.7254i	−0.340937	−	0.590520i
$902$		0			0
$903$	−19.6767	−	6.45288i	−0.654798	−	0.214738i
$904$		0			0
$905$	0.807170	+	0.906563i	0.0268312	+	0.0301352i
$906$		0			0
$907$	24.4522	+	14.1175i	0.811921	+	0.468763i	0.847623	−	0.530599i	$-0.178033\pi$
$907$	24.4522	+	14.1175i	0.811921	+	0.468763i	−0.0357012	+	0.999363i	$0.511366\pi$
$908$		0			0
$909$	−28.4484			−0.943574
$910$		0			0
$911$	48.7700			1.61582			0.807911	−	0.589304i	$-0.200598\pi$
$911$	48.7700			1.61582			0.807911	+	0.589304i	$0.200598\pi$
$912$		0			0
$913$	54.5566	+	31.4983i	1.80556	+	1.04244i
$914$		0			0
$915$	4.35500	−	3.87753i	0.143972	−	0.128187i
$916$		0			0
$917$	−18.0415	+	16.1555i	−0.595784	+	0.533503i
$918$		0			0
$919$	−21.9481	−	38.0153i	−0.724002	−	1.25401i	−0.959383	−	0.282106i	$-0.908967\pi$
$919$	−21.9481	−	38.0153i	−0.724002	−	1.25401i	0.235381	−	0.971903i	$-0.424366\pi$
$920$		0			0
$921$	0.593698	−	1.02831i	0.0195630	−	0.0338841i
$922$		0			0
$923$			33.3800i			1.09872i
$924$		0			0
$925$	−21.3157	−	49.3488i	−0.700855	−	1.62258i
$926$		0			0
$927$	−0.950341	−	0.548679i	−0.0312133	−	0.0180210i
$928$		0			0
$929$	−16.9771	−	29.4052i	−0.557000	−	0.964752i	−0.997745	−	0.0671197i	$-0.978619\pi$
$929$	−16.9771	−	29.4052i	−0.557000	−	0.964752i	0.440745	−	0.897632i	$-0.354714\pi$
$930$		0			0
$931$	2.48923	+	1.82941i	0.0815811	+	0.0599566i
$932$		0			0
$933$	−13.5624	+	7.83027i	−0.444014	+	0.256352i
$934$		0			0
$935$	−68.6286	−	22.7224i	−2.24440	−	0.743102i
$936$		0			0
$937$			16.4081i			0.536028i	0.963415	+	0.268014i	$0.0863674\pi$
$937$			16.4081i			0.536028i	−0.963415	+	0.268014i	$0.913633\pi$
$938$		0			0
$939$	−17.2599			−0.563255
$940$		0			0
$941$	−14.3702	+	24.8900i	−0.468456	+	0.811389i	−0.999350	−	0.0360487i	$-0.988523\pi$
$941$	−14.3702	+	24.8900i	−0.468456	+	0.811389i	0.530894	+	0.847438i	$0.321856\pi$
$942$		0			0
$943$	−24.5668	+	14.1836i	−0.800005	+	0.461883i
$944$		0			0
$945$	19.4295	+	14.3645i	0.632043	+	0.467277i
$946$		0			0
$947$	−5.57841	+	3.22069i	−0.181274	+	0.104659i	−0.587891	−	0.808940i	$-0.700042\pi$
$947$	−5.57841	+	3.22069i	−0.181274	+	0.104659i	0.406617	+	0.913599i	$0.366708\pi$
$948$		0			0
$949$	−6.48524	+	11.2328i	−0.210520	+	0.364631i
$950$		0			0
$951$	14.7616			0.478677
$952$		0			0
$953$		−	17.4655i		−	0.565762i	−0.959155	−	0.282881i	$-0.908710\pi$
$953$		−	17.4655i		−	0.565762i	0.959155	−	0.282881i	$-0.0912902\pi$
$954$		0			0
$955$	9.13042	−	27.5767i	0.295453	−	0.892360i
$956$		0			0
$957$	4.29993	−	2.48256i	0.138997	−	0.0802499i
$958$		0			0
$959$	6.50934	−	19.8488i	0.210198	−	0.640953i
$960$		0			0
$961$	15.2918	+	26.4861i	0.493283	+	0.854391i
$962$		0			0
$963$	−0.975678	−	0.563308i	−0.0314408	−	0.0181523i
$964$		0			0
$965$	2.18903	+	10.5884i	0.0704673	+	0.340852i
$966$		0			0
$967$		−	43.5117i		−	1.39924i	−0.714515	−	0.699620i	$-0.753352\pi$
$967$		−	43.5117i		−	1.39924i	0.714515	−	0.699620i	$-0.246648\pi$
$968$		0			0
$969$	1.01583	−	1.75947i	0.0326332	−	0.0565223i
$970$		0			0
$971$	21.9304	+	37.9846i	0.703780	+	1.21898i	0.967130	+	0.254282i	$0.0818392\pi$
$971$	21.9304	+	37.9846i	0.703780	+	1.21898i	−0.263350	+	0.964700i	$0.584827\pi$
$972$		0			0
$973$	−2.13399	−	10.1764i	−0.0684127	−	0.326241i
$974$		0			0
$975$	−7.34208	−	5.46039i	−0.235135	−	0.174872i
$976$		0			0
$977$	−1.65757	−	0.957000i	−0.0530304	−	0.0306171i	0.473250	−	0.880928i	$-0.343081\pi$
$977$	−1.65757	−	0.957000i	−0.0530304	−	0.0306171i	−0.526281	+	0.850311i	$0.676414\pi$
$978$		0			0
$979$	45.3948			1.45083
$980$		0			0
$981$	−5.85961			−0.187083
$982$		0			0
$983$	3.49101	+	2.01553i	0.111346	+	0.0642855i	0.554639	−	0.832091i	$-0.312856\pi$
$983$	3.49101	+	2.01553i	0.111346	+	0.0642855i	−0.443293	+	0.896377i	$0.646190\pi$
$984$		0			0
$985$	27.7170	−	24.6782i	0.883137	−	0.786313i
$986$		0			0
$987$	−3.07242	−	14.6515i	−0.0977963	−	0.466363i
$988$		0			0
$989$	16.5966	+	28.7461i	0.527741	+	0.914074i
$990$		0			0
$991$	−18.4129	+	31.8921i	−0.584905	+	1.01309i	0.409982	+	0.912094i	$0.365535\pi$
$991$	−18.4129	+	31.8921i	−0.584905	+	1.01309i	−0.994887	+	0.100992i	$0.967798\pi$
$992$		0			0
$993$			5.22770i			0.165896i
$994$		0			0
$995$	34.2575	−	7.08236i	1.08604	−	0.224526i
$996$		0			0
$997$	−34.4515	−	19.8906i	−1.09109	−	0.629942i	−0.157224	−	0.987563i	$-0.550255\pi$
$997$	−34.4515	−	19.8906i	−1.09109	−	0.629942i	−0.933867	+	0.357621i	$0.883588\pi$
$998$		0			0
$999$	21.9553	+	38.0277i	0.694634	+	1.20314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bg.a.249.8	yes	24
4.3	odd	2		560.2.bw.f.529.5		24
5.2	odd	4		1400.2.q.o.1201.4		12
5.3	odd	4		1400.2.q.n.1201.3		12
5.4	even	2	inner	280.2.bg.a.249.5	yes	24
7.2	even	3	inner	280.2.bg.a.9.5	✓	24
7.3	odd	6		1960.2.g.e.1569.8		12
7.4	even	3		1960.2.g.f.1569.5		12
20.19	odd	2		560.2.bw.f.529.8		24
28.23	odd	6		560.2.bw.f.289.8		24
35.2	odd	12		1400.2.q.o.401.4		12
35.3	even	12		9800.2.a.cw.1.3		6
35.4	even	6		1960.2.g.f.1569.8		12
35.9	even	6	inner	280.2.bg.a.9.8	yes	24
35.17	even	12		9800.2.a.cy.1.4		6
35.18	odd	12		9800.2.a.cx.1.4		6
35.23	odd	12		1400.2.q.n.401.3		12
35.24	odd	6		1960.2.g.e.1569.5		12
35.32	odd	12		9800.2.a.cv.1.3		6
140.79	odd	6		560.2.bw.f.289.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bg.a.9.5	✓	24	7.2	even	3	inner
280.2.bg.a.9.8	yes	24	35.9	even	6	inner
280.2.bg.a.249.5	yes	24	5.4	even	2	inner
280.2.bg.a.249.8	yes	24	1.1	even	1	trivial
560.2.bw.f.289.5		24	140.79	odd	6
560.2.bw.f.289.8		24	28.23	odd	6
560.2.bw.f.529.5		24	4.3	odd	2
560.2.bw.f.529.8		24	20.19	odd	2
1400.2.q.n.401.3		12	35.23	odd	12
1400.2.q.n.1201.3		12	5.3	odd	4
1400.2.q.o.401.4		12	35.2	odd	12
1400.2.q.o.1201.4		12	5.2	odd	4
1960.2.g.e.1569.5		12	35.24	odd	6
1960.2.g.e.1569.8		12	7.3	odd	6
1960.2.g.f.1569.5		12	7.4	even	3
1960.2.g.f.1569.8		12	35.4	even	6
9800.2.a.cv.1.3		6	35.32	odd	12
9800.2.a.cw.1.3		6	35.3	even	12
9800.2.a.cx.1.4		6	35.18	odd	12
9800.2.a.cy.1.4		6	35.17	even	12

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bg (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.650755 + 0.375714i) q^{3} +(-1.48694 - 1.67003i) q^{5} +(-0.543003 - 2.58943i) q^{7} +(-1.21768 - 2.10908i) q^{9} +O(q^{10})\)	\(q+(0.650755 + 0.375714i) q^{3} +(-1.48694 - 1.67003i) q^{5} +(-0.543003 - 2.58943i) q^{7} +(-1.21768 - 2.10908i) q^{9} +(2.63851 - 4.57003i) q^{11} +2.43536i q^{13} +(-0.340178 - 1.64545i) q^{15} +(5.30579 + 3.06330i) q^{17} +(-0.220655 - 0.382187i) q^{19} +(0.619522 - 1.88910i) q^{21} +(-2.75984 + 1.59339i) q^{23} +(-0.578031 + 4.96648i) q^{25} -4.08428i q^{27} +1.25215 q^{29} +(0.322674 - 0.558887i) q^{31} +(3.43405 - 1.98265i) q^{33} +(-3.51703 + 4.75716i) q^{35} +(-9.31074 + 5.37556i) q^{37} +(-0.914997 + 1.58482i) q^{39} +8.90154 q^{41} -10.4159i q^{43} +(-1.71163 + 5.16964i) q^{45} +(6.52112 - 3.76497i) q^{47} +(-6.41029 + 2.81214i) q^{49} +(2.30185 + 3.98692i) q^{51} +(-2.89319 - 1.67039i) q^{53} +(-11.5554 + 2.38895i) q^{55} -0.331613i q^{57} +(-4.07767 + 7.06274i) q^{59} +(1.73518 + 3.00542i) q^{61} +(-4.80011 + 4.29833i) q^{63} +(4.06713 - 3.62122i) q^{65} +(4.14517 + 2.39322i) q^{67} -2.39464 q^{69} +13.7064 q^{71} +(4.61237 + 2.66295i) q^{73} +(-2.24213 + 3.01479i) q^{75} +(-13.2665 - 4.35069i) q^{77} +(2.70220 + 4.68034i) q^{79} +(-2.11852 + 3.66938i) q^{81} +11.9379i q^{83} +(-2.77356 - 13.4158i) q^{85} +(0.814841 + 0.470448i) q^{87} +(4.30119 + 7.44987i) q^{89} +(6.30618 - 1.32241i) q^{91} +(0.419963 - 0.242466i) q^{93} +(-0.310164 + 0.936790i) q^{95} +13.6714i q^{97} -12.8514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{9}+O(q^{10}) \) 24 * q + 14 * q^9	\( 24 q + 14 q^{9} - 2 q^{11} + 12 q^{15} - 10 q^{19} - 10 q^{21} - 2 q^{25} + 12 q^{29} + 4 q^{31} - 28 q^{35} + 20 q^{39} + 24 q^{41} - 8 q^{45} - 30 q^{49} - 12 q^{55} - 48 q^{59} - 18 q^{61} - 26 q^{65} - 60 q^{69} + 16 q^{71} - 14 q^{75} - 44 q^{79} + 12 q^{81} - 44 q^{85} + 30 q^{89} + 44 q^{91} - 26 q^{95} - 44 q^{99}+O(q^{100}) \) 24 * q + 14 * q^9 - 2 * q^11 + 12 * q^15 - 10 * q^19 - 10 * q^21 - 2 * q^25 + 12 * q^29 + 4 * q^31 - 28 * q^35 + 20 * q^39 + 24 * q^41 - 8 * q^45 - 30 * q^49 - 12 * q^55 - 48 * q^59 - 18 * q^61 - 26 * q^65 - 60 * q^69 + 16 * q^71 - 14 * q^75 - 44 * q^79 + 12 * q^81 - 44 * q^85 + 30 * q^89 + 44 * q^91 - 26 * q^95 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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