LMFDB - Embedded newform 460.2.s.a.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(9,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 10]))

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

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

chi := DirichletCharacter("460.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.s (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			449.1
Character	$\chi$	$=$	460.449
Dual form			460.2.s.a.209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.24344 - 0.466336i) q^{3} +(-1.87946 - 1.21146i) q^{5} +(3.45164 - 2.99087i) q^{7} +(7.42393 + 2.17986i) q^{9} +O(q^{10})$	\(q+(-3.24344 - 0.466336i) q^{3} +(-1.87946 - 1.21146i) q^{5} +(3.45164 - 2.99087i) q^{7} +(7.42393 + 2.17986i) q^{9} +(-2.75398 - 1.76988i) q^{11} +(-1.02701 - 0.889909i) q^{13} +(5.53096 + 4.80575i) q^{15} +(-4.62683 + 2.11300i) q^{17} +(-0.171142 + 0.374750i) q^{19} +(-12.5899 + 8.09106i) q^{21} +(-4.78206 + 0.363201i) q^{23} +(2.06473 + 4.55378i) q^{25} +(-14.1205 - 6.44861i) q^{27} +(1.72921 + 3.78644i) q^{29} +(-0.905801 - 6.29999i) q^{31} +(8.10702 + 7.02477i) q^{33} +(-10.1105 + 1.43968i) q^{35} +(-3.21016 + 10.9328i) q^{37} +(2.91604 + 3.36529i) q^{39} +(-1.44448 + 0.424138i) q^{41} +(-0.0389495 - 0.00560009i) q^{43} +(-11.3122 - 13.0908i) q^{45} +2.24762i q^{47} +(1.97236 - 13.7180i) q^{49} +(15.9922 - 4.69573i) q^{51} +(3.04939 - 2.64231i) q^{53} +(3.03186 + 6.66276i) q^{55} +(0.729849 - 1.13567i) q^{57} +(0.959993 - 1.10789i) q^{59} +(0.685440 + 4.76734i) q^{61} +(32.1444 - 14.6799i) q^{63} +(0.852133 + 2.91673i) q^{65} +(-0.149361 - 0.232410i) q^{67} +(15.6797 + 1.05203i) q^{69} +(-10.4268 + 6.70088i) q^{71} +(-10.5868 - 4.83484i) q^{73} +(-4.57323 - 15.7327i) q^{75} +(-14.7992 + 2.12781i) q^{77} +(-1.78449 + 2.05941i) q^{79} +(23.2645 + 14.9512i) q^{81} +(1.18219 - 4.02618i) q^{83} +(11.2558 + 1.63392i) q^{85} +(-3.84282 - 13.0875i) q^{87} +(-0.786991 + 5.47364i) q^{89} -6.20647 q^{91} +20.8560i q^{93} +(0.775649 - 0.496994i) q^{95} +(-0.0232544 - 0.0791971i) q^{97} +(-16.5873 - 19.1428i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{9}+O(q^{10}) $ 120 * q + 20 * q^9	$ 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) $ 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{10}{11}\right)$

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
$3$	−3.24344	−	0.466336i	−1.87260	−	0.269239i	−0.890136	−	0.455695i	$-0.849391\pi$
$3$	−3.24344	−	0.466336i	−1.87260	−	0.269239i	−0.982463	+	0.186456i	$0.940300\pi$
$4$		0			0
$5$	−1.87946	−	1.21146i	−0.840519	−	0.541781i
$5$	−1.87946	−	1.21146i	−0.840519	−	0.541781i
$6$		0			0
$7$	3.45164	−	2.99087i	1.30460	−	1.13044i	0.321590	−	0.946879i	$-0.395783\pi$
$7$	3.45164	−	2.99087i	1.30460	−	1.13044i	0.983008	−	0.183562i	$-0.0587627\pi$
$8$		0			0
$9$	7.42393	+	2.17986i	2.47464	+	0.726621i
$10$		0			0
$11$	−2.75398	−	1.76988i	−0.830358	−	0.533638i	0.0550339	−	0.998484i	$-0.482473\pi$
$11$	−2.75398	−	1.76988i	−0.830358	−	0.533638i	−0.885392	+	0.464846i	$0.846110\pi$
$12$		0			0
$13$	−1.02701	−	0.889909i	−0.284841	−	0.246816i	0.500707	−	0.865617i	$-0.333073\pi$
$13$	−1.02701	−	0.889909i	−0.284841	−	0.246816i	−0.785548	+	0.618801i	$0.787619\pi$
$14$		0			0
$15$	5.53096	+	4.80575i	1.42809	+	1.24084i
$16$		0			0
$17$	−4.62683	+	2.11300i	−1.12217	+	0.512478i	−0.888058	−	0.459731i	$-0.847946\pi$
$17$	−4.62683	+	2.11300i	−1.12217	+	0.512478i	−0.234113	+	0.972209i	$0.575218\pi$
$18$		0			0
$19$	−0.171142	+	0.374750i	−0.0392628	+	0.0859735i	−0.928247	−	0.371964i	$-0.878684\pi$
$19$	−0.171142	+	0.374750i	−0.0392628	+	0.0859735i	0.888984	+	0.457938i	$0.151412\pi$
$20$		0			0
$21$	−12.5899	+	8.09106i	−2.74735	+	1.76561i
$22$		0			0
$23$	−4.78206	+	0.363201i	−0.997128	+	0.0757326i
$23$	−4.78206	+	0.363201i	−0.997128	+	0.0757326i
$24$		0			0
$25$	2.06473	+	4.55378i	0.412946	+	0.910756i
$26$		0			0
$27$	−14.1205	−	6.44861i	−2.71749	−	1.24104i
$28$		0			0
$29$	1.72921	+	3.78644i	0.321106	+	0.703124i	0.999501	−	0.0315732i	$-0.0100517\pi$
$29$	1.72921	+	3.78644i	0.321106	+	0.703124i	−0.678396	+	0.734697i	$0.737324\pi$
$30$		0			0
$31$	−0.905801	−	6.29999i	−0.162687	−	1.13151i	−0.893542	−	0.448979i	$-0.851788\pi$
$31$	−0.905801	−	6.29999i	−0.162687	−	1.13151i	0.730856	−	0.682532i	$-0.239121\pi$
$32$		0			0
$33$	8.10702	+	7.02477i	1.41125	+	1.22286i
$34$		0			0
$35$	−10.1105	+	1.43968i	−1.70899	+	0.243351i
$36$		0			0
$37$	−3.21016	+	10.9328i	−0.527747	+	1.79734i	0.0723093	+	0.997382i	$0.476963\pi$
$37$	−3.21016	+	10.9328i	−0.527747	+	1.79734i	−0.600056	+	0.799958i	$0.704855\pi$
$38$		0			0
$39$	2.91604	+	3.36529i	0.466941	+	0.538878i
$40$		0			0
$41$	−1.44448	+	0.424138i	−0.225590	+	0.0662393i	−0.392574	−	0.919720i	$-0.628415\pi$
$41$	−1.44448	+	0.424138i	−0.225590	+	0.0662393i	0.166984	+	0.985960i	$0.446597\pi$
$42$		0			0
$43$	−0.0389495	−	0.00560009i	−0.00593974	−	0.000854006i	0.139344	−	0.990244i	$-0.455501\pi$
$43$	−0.0389495	−	0.00560009i	−0.00593974	−	0.000854006i	−0.145284	+	0.989390i	$0.546410\pi$
$44$		0			0
$45$	−11.3122	−	13.0908i	−1.68632	−	1.95146i
$46$		0			0
$47$			2.24762i			0.327849i	0.986473	+	0.163924i	$0.0524153\pi$
$47$			2.24762i			0.327849i	−0.986473	+	0.163924i	$0.947585\pi$
$48$		0			0
$49$	1.97236	−	13.7180i	0.281765	−	1.95972i
$50$		0			0
$51$	15.9922	−	4.69573i	2.23936	−	0.657534i
$52$		0			0
$53$	3.04939	−	2.64231i	0.418865	−	0.362949i	−0.419781	−	0.907625i	$-0.637893\pi$
$53$	3.04939	−	2.64231i	0.418865	−	0.362949i	0.838646	+	0.544677i	$0.183348\pi$
$54$		0			0
$55$	3.03186	+	6.66276i	0.408816	+	0.898406i
$56$		0			0
$57$	0.729849	−	1.13567i	0.0966708	−	0.150423i
$58$		0			0
$59$	0.959993	−	1.10789i	0.124980	−	0.144235i	−0.689811	−	0.723990i	$-0.742306\pi$
$59$	0.959993	−	1.10789i	0.124980	−	0.144235i	0.814791	+	0.579755i	$0.196852\pi$
$60$		0			0
$61$	0.685440	+	4.76734i	0.0877616	+	0.610396i	0.985476	+	0.169817i	$0.0543176\pi$
$61$	0.685440	+	4.76734i	0.0877616	+	0.610396i	−0.897714	+	0.440579i	$0.854773\pi$
$62$		0			0
$63$	32.1444	−	14.6799i	4.04982	−	1.84949i
$64$		0			0
$65$	0.852133	+	2.91673i	0.105694	+	0.361776i
$66$		0			0
$67$	−0.149361	−	0.232410i	−0.0182473	−	0.0283934i	0.832010	−	0.554761i	$-0.187190\pi$
$67$	−0.149361	−	0.232410i	−0.0182473	−	0.0283934i	−0.850257	+	0.526367i	$0.823554\pi$
$68$		0			0
$69$	15.6797	+	1.05203i	1.88761	+	0.126649i
$70$		0			0
$71$	−10.4268	+	6.70088i	−1.23743	+	0.795248i	−0.985031	−	0.172375i	$-0.944856\pi$
$71$	−10.4268	+	6.70088i	−1.23743	+	0.795248i	−0.252399	+	0.967623i	$0.581219\pi$
$72$		0			0
$73$	−10.5868	−	4.83484i	−1.23909	−	0.565875i	−0.315382	−	0.948965i	$-0.602133\pi$
$73$	−10.5868	−	4.83484i	−1.23909	−	0.565875i	−0.923711	+	0.383090i	$0.874860\pi$
$74$		0			0
$75$	−4.57323	−	15.7327i	−0.528071	−	1.81666i
$76$		0			0
$77$	−14.7992	+	2.12781i	−1.68653	+	0.242486i
$78$		0			0
$79$	−1.78449	+	2.05941i	−0.200770	+	0.231701i	−0.847202	−	0.531270i	$-0.821715\pi$
$79$	−1.78449	+	2.05941i	−0.200770	+	0.231701i	0.646432	+	0.762972i	$0.276260\pi$
$80$		0			0
$81$	23.2645	+	14.9512i	2.58494	+	1.66124i
$82$		0			0
$83$	1.18219	−	4.02618i	0.129763	−	0.441931i	−0.868822	−	0.495125i	$-0.835122\pi$
$83$	1.18219	−	4.02618i	0.129763	−	0.441931i	0.998584	+	0.0531945i	$0.0169403\pi$
$84$		0			0
$85$	11.2558	+	1.63392i	1.22086	+	0.177223i
$86$		0			0
$87$	−3.84282	−	13.0875i	−0.411994	−	1.40312i
$88$		0			0
$89$	−0.786991	+	5.47364i	−0.0834209	+	0.580205i	0.904644	+	0.426168i	$0.140137\pi$
$89$	−0.786991	+	5.47364i	−0.0834209	+	0.580205i	−0.988065	+	0.154037i	$0.950772\pi$
$90$		0			0
$91$	−6.20647			−0.650614
$92$		0			0
$93$			20.8560i			2.16267i
$94$		0			0
$95$	0.775649	−	0.496994i	0.0795799	−	0.0509905i
$96$		0			0
$97$	−0.0232544	−	0.0791971i	−0.00236112	−	0.00804124i	0.958304	−	0.285751i	$-0.0922429\pi$
$97$	−0.0232544	−	0.0791971i	−0.00236112	−	0.00804124i	−0.960665	+	0.277709i	$0.910425\pi$
$98$		0			0
$99$	−16.5873	−	19.1428i	−1.66709	−	1.92392i
$100$		0			0
$101$	−3.40719	−	1.00044i	−0.339028	−	0.0995477i	0.107787	−	0.994174i	$-0.465624\pi$
$101$	−3.40719	−	1.00044i	−0.339028	−	0.0995477i	−0.446815	+	0.894626i	$0.647442\pi$
$102$		0			0
$103$	−5.00222	+	7.78361i	−0.492883	+	0.766942i	−0.995212	−	0.0977349i	$-0.968840\pi$
$103$	−5.00222	+	7.78361i	−0.492883	+	0.766942i	0.502329	+	0.864677i	$0.332477\pi$
$104$		0			0
$105$	33.4642	+	0.0453882i	3.26578	+	0.00442943i
$106$		0			0
$107$	11.8256	−	1.70026i	1.14322	−	0.164371i	0.455426	−	0.890274i	$-0.349487\pi$
$107$	11.8256	−	1.70026i	1.14322	−	0.164371i	0.687797	+	0.725903i	$0.258578\pi$
$108$		0			0
$109$	−8.04408	−	17.6141i	−0.770483	−	1.68712i	−0.725586	−	0.688131i	$-0.758431\pi$
$109$	−8.04408	−	17.6141i	−0.770483	−	1.68712i	−0.0448972	−	0.998992i	$-0.514296\pi$
$110$		0			0
$111$	15.5103	−	33.9628i	1.47217	−	3.22361i
$112$		0			0
$113$	−0.0601617	−	0.0936134i	−0.00565953	−	0.00880641i	0.838412	−	0.545037i	$-0.183484\pi$
$113$	−0.0601617	−	0.0936134i	−0.00565953	−	0.00880641i	−0.844072	+	0.536230i	$0.819848\pi$
$114$		0			0
$115$	9.42768	+	5.11065i	0.879136	+	0.476571i
$116$		0			0
$117$	−5.68457	−	8.84537i	−0.525539	−	0.817754i
$118$		0			0
$119$	−9.65045	+	21.1315i	−0.884656	+	1.93713i
$120$		0			0
$121$	−0.117604	−	0.257517i	−0.0106913	−	0.0234106i
$122$		0			0
$123$	4.88288	−	0.702052i	0.440274	−	0.0633019i
$124$		0			0
$125$	1.63614	−	11.0600i	0.146341	−	0.989234i
$126$		0			0
$127$	−1.84643	+	2.87310i	−0.163844	+	0.254947i	−0.913462	−	0.406925i	$-0.866601\pi$
$127$	−1.84643	+	2.87310i	−0.163844	+	0.254947i	0.749617	+	0.661871i	$0.230238\pi$
$128$		0			0
$129$	0.123719	+	0.0363271i	0.0108928	+	0.00319842i
$130$		0			0
$131$	−9.33460	−	10.7727i	−0.815568	−	0.941215i	0.183559	−	0.983009i	$-0.441238\pi$
$131$	−9.33460	−	10.7727i	−0.815568	−	0.941215i	−0.999126	+	0.0417934i	$0.986693\pi$
$132$		0			0
$133$	0.530103	+	1.80537i	0.0459658	+	0.156545i
$134$		0			0
$135$	18.7267	+	29.2263i	1.61173	+	2.51540i
$136$		0			0
$137$		−	13.8462i		−	1.18296i	−0.806319	−	0.591480i	$-0.798544\pi$
$137$		−	13.8462i		−	1.18296i	0.806319	−	0.591480i	$-0.201456\pi$
$138$		0			0
$139$	−11.0823			−0.939991			−0.469995	−	0.882669i	$-0.655744\pi$
$139$	−11.0823			−0.939991			−0.469995	+	0.882669i	$0.655744\pi$
$140$		0			0
$141$	1.04815	−	7.29001i	0.0882697	−	0.613930i
$142$		0			0
$143$	1.25334	+	4.26848i	0.104809	+	0.356948i
$144$		0			0
$145$	1.33714	−	9.21132i	0.111044	−	0.764958i
$146$		0			0
$147$	−12.7944	+	43.5738i	−1.05527	+	3.59391i
$148$		0			0
$149$	16.4880	+	10.5962i	1.35075	+	0.868072i	0.997717	−	0.0675405i	$-0.0215152\pi$
$149$	16.4880	+	10.5962i	1.35075	+	0.868072i	0.353029	+	0.935612i	$0.385152\pi$
$150$		0			0
$151$	−3.88323	+	4.48148i	−0.316013	+	0.364698i	−0.891427	−	0.453164i	$-0.850295\pi$
$151$	−3.88323	+	4.48148i	−0.316013	+	0.364698i	0.575415	+	0.817862i	$0.304841\pi$
$152$		0			0
$153$	−38.9553	+	5.60093i	−3.14935	+	0.452808i
$154$		0			0
$155$	−5.92977	+	12.9379i	−0.476290	+	1.03920i
$156$		0			0
$157$	12.2350	+	5.58753i	0.976458	+	0.445933i	0.838736	−	0.544538i	$-0.183295\pi$
$157$	12.2350	+	5.58753i	0.976458	+	0.445933i	0.137721	+	0.990471i	$0.456022\pi$
$158$		0			0
$159$	−11.1227	+	7.14812i	−0.882087	+	0.566883i
$160$		0			0
$161$	−15.4197	+	15.5561i	−1.21524	+	1.22599i
$162$		0			0
$163$	2.35325	+	3.66172i	0.184321	+	0.286808i	0.921101	−	0.389324i	$-0.127291\pi$
$163$	2.35325	+	3.66172i	0.184321	+	0.286808i	−0.736780	+	0.676132i	$0.763655\pi$
$164$		0			0
$165$	−6.72658	−	23.0241i	−0.523663	−	1.79242i
$166$		0			0
$167$	1.42714	−	0.651754i	0.110436	−	0.0504343i	−0.359431	−	0.933172i	$-0.617029\pi$
$167$	1.42714	−	0.651754i	0.110436	−	0.0504343i	0.469867	+	0.882737i	$0.344302\pi$
$168$		0			0
$169$	−1.58728	−	11.0398i	−0.122099	−	0.849215i
$170$		0			0
$171$	−2.08745	+	2.40905i	−0.159632	+	0.184225i
$172$		0			0
$173$	5.83920	−	9.08597i	0.443946	−	0.690794i	−0.545105	−	0.838368i	$-0.683510\pi$
$173$	5.83920	−	9.08597i	0.443946	−	0.690794i	0.989051	+	0.147574i	$0.0471465\pi$
$174$		0			0
$175$	20.7464	+	9.54268i	1.56828	+	0.721359i
$176$		0			0
$177$	−3.63032	+	3.14569i	−0.272872	+	0.236445i
$178$		0			0
$179$	6.18881	−	1.81720i	0.462573	−	0.135824i	−0.0421384	−	0.999112i	$-0.513417\pi$
$179$	6.18881	−	1.81720i	0.462573	−	0.135824i	0.504711	+	0.863288i	$0.331599\pi$
$180$		0			0
$181$	1.38307	−	9.61948i	0.102803	−	0.715010i	−0.871603	−	0.490213i	$-0.836919\pi$
$181$	1.38307	−	9.61948i	0.102803	−	0.715010i	0.974406	−	0.224797i	$-0.0721719\pi$
$182$		0			0
$183$		−	15.7822i		−	1.16666i
$184$		0			0
$185$	19.2780	−	16.6588i	1.41735	−	1.22478i
$186$		0			0
$187$	16.4820	+	2.36975i	1.20528	+	0.173293i
$188$		0			0
$189$	−68.0258	+	19.9742i	−4.94815	+	1.45291i
$190$		0			0
$191$	−0.805843	−	0.929992i	−0.0583088	−	0.0672919i	0.725846	−	0.687857i	$-0.241449\pi$
$191$	−0.805843	−	0.929992i	−0.0583088	−	0.0672919i	−0.784155	+	0.620565i	$0.786903\pi$
$192$		0			0
$193$	−2.98759	+	10.1748i	−0.215051	+	0.732397i	0.779337	+	0.626605i	$0.215556\pi$
$193$	−2.98759	+	10.1748i	−0.215051	+	0.732397i	−0.994388	+	0.105792i	$0.966262\pi$
$194$		0			0
$195$	−1.40367	−	9.85760i	−0.100519	−	0.705918i
$196$		0			0
$197$	−12.5636	−	10.8864i	−0.895117	−	0.775623i	0.0801200	−	0.996785i	$-0.474470\pi$
$197$	−12.5636	−	10.8864i	−0.895117	−	0.775623i	−0.975237	+	0.221162i	$0.929015\pi$
$198$		0			0
$199$	−1.63206	−	11.3512i	−0.115694	−	0.804668i	−0.962211	−	0.272306i	$-0.912214\pi$
$199$	−1.63206	−	11.3512i	−0.115694	−	0.804668i	0.846517	−	0.532362i	$-0.178695\pi$
$200$		0			0
$201$	0.376062	+	0.823460i	0.0265253	+	0.0580824i
$202$		0			0
$203$	17.2933	+	7.89760i	1.21375	+	0.554303i
$204$		0			0
$205$	3.22867	+	0.952782i	0.225500	+	0.0665452i
$206$		0			0
$207$	−36.2934	−	7.72786i	−2.52257	−	0.537123i
$208$		0			0
$209$	1.13458	−	0.729153i	0.0784809	−	0.0504366i
$210$		0			0
$211$	−5.05224	+	11.0629i	−0.347811	+	0.761599i	0.652183	+	0.758061i	$0.273853\pi$
$211$	−5.05224	+	11.0629i	−0.347811	+	0.761599i	−0.999994	+	0.00353756i	$0.998874\pi$
$212$		0			0
$213$	36.9434	−	16.8715i	2.53132	−	1.15602i
$214$		0			0
$215$	0.0664197	+	0.0577109i	0.00452979	+	0.00393585i
$216$		0			0
$217$	−21.9689	−	19.0362i	−1.49135	−	1.29226i
$218$		0			0
$219$	32.0830	+	20.6185i	2.16797	+	1.39327i
$220$		0			0
$221$	6.63218	+	1.94738i	0.446128	+	0.130995i
$222$		0			0
$223$	5.99346	−	5.19336i	0.401352	−	0.347773i	−0.430677	−	0.902506i	$-0.641725\pi$
$223$	5.99346	−	5.19336i	0.401352	−	0.347773i	0.832028	+	0.554733i	$0.187180\pi$
$224$		0			0
$225$	5.40180	+	38.3078i	0.360120	+	2.55385i
$226$		0			0
$227$	−18.0435	−	2.59426i	−1.19759	−	0.172187i	−0.485473	−	0.874252i	$-0.661353\pi$
$227$	−18.0435	−	2.59426i	−1.19759	−	0.172187i	−0.712113	+	0.702065i	$0.752262\pi$
$228$		0			0
$229$	9.24820			0.611138			0.305569	−	0.952170i	$-0.401153\pi$
$229$	9.24820			0.611138			0.305569	+	0.952170i	$0.401153\pi$
$230$		0			0
$231$	48.9927			3.22348
$232$		0			0
$233$	3.86830	+	0.556178i	0.253421	+	0.0364364i	0.267854	−	0.963459i	$-0.413685\pi$
$233$	3.86830	+	0.556178i	0.253421	+	0.0364364i	−0.0144335	+	0.999896i	$0.504594\pi$
$234$		0			0
$235$	2.72290	−	4.22431i	0.177622	−	0.275563i
$236$		0			0
$237$	6.74824	−	5.84739i	0.438346	−	0.379829i
$238$		0			0
$239$	−19.6492	−	5.76951i	−1.27100	−	0.373199i	−0.424421	−	0.905465i	$-0.639522\pi$
$239$	−19.6492	−	5.76951i	−1.27100	−	0.373199i	−0.846577	+	0.532266i	$0.821341\pi$
$240$		0			0
$241$	−5.63274	−	3.61995i	−0.362837	−	0.233181i	0.346501	−	0.938050i	$-0.387370\pi$
$241$	−5.63274	−	3.61995i	−0.362837	−	0.233181i	−0.709338	+	0.704868i	$0.751006\pi$
$242$		0			0
$243$	−33.2894	−	28.8455i	−2.13552	−	1.85044i
$244$		0			0
$245$	−20.3258	+	23.3931i	−1.29857	+	1.49453i
$246$		0			0
$247$	0.509258	−	0.232570i	0.0324033	−	0.0147981i
$248$		0			0
$249$	−5.71192	+	12.5074i	−0.361978	+	0.792622i
$250$		0			0
$251$	−8.50585	+	5.46638i	−0.536884	+	0.345035i	−0.780819	−	0.624757i	$-0.785198\pi$
$251$	−8.50585	+	5.46638i	−0.536884	+	0.345035i	0.243935	+	0.969792i	$0.421562\pi$
$252$		0			0
$253$	13.8125	+	7.46341i	0.868387	+	0.469221i
$254$		0			0
$255$	−35.7454	−	10.5485i	−2.23846	−	0.660571i
$256$		0			0
$257$	0.864198	+	0.394666i	0.0539072	+	0.0246186i	0.442186	−	0.896923i	$-0.354203\pi$
$257$	0.864198	+	0.394666i	0.0539072	+	0.0246186i	−0.388279	+	0.921542i	$0.626930\pi$
$258$		0			0
$259$	21.6182	+	47.3372i	1.34329	+	2.94139i
$260$		0			0
$261$	4.58361	+	31.8797i	0.283718	+	1.97330i
$262$		0			0
$263$	−6.38861	−	5.53576i	−0.393938	−	0.341350i	0.435259	−	0.900305i	$-0.356657\pi$
$263$	−6.38861	−	5.53576i	−0.393938	−	0.341350i	−0.829198	+	0.558956i	$0.811202\pi$
$264$		0			0
$265$	−8.93224	+	1.27190i	−0.548703	+	0.0781322i
$266$		0			0
$267$	5.10511	−	17.3864i	0.312428	−	1.06403i
$268$		0			0
$269$	−8.67073	−	10.0066i	−0.528664	−	0.610111i	0.427115	−	0.904197i	$-0.359530\pi$
$269$	−8.67073	−	10.0066i	−0.528664	−	0.610111i	−0.955779	+	0.294087i	$0.904985\pi$
$270$		0			0
$271$	2.41988	−	0.710541i	0.146997	−	0.0431623i	−0.207406	−	0.978255i	$-0.566502\pi$
$271$	2.41988	−	0.710541i	0.146997	−	0.0431623i	0.354403	+	0.935093i	$0.384684\pi$
$272$		0			0
$273$	20.1303	+	2.89430i	1.21834	+	0.175171i
$274$		0			0
$275$	2.37340	−	16.1954i	0.143121	−	0.976617i
$276$		0			0
$277$		−	17.0871i		−	1.02667i	−0.858190	−	0.513333i	$-0.828411\pi$
$277$		−	17.0871i		−	1.02667i	0.858190	−	0.513333i	$-0.171589\pi$
$278$		0			0
$279$	7.00850	−	48.7452i	0.419588	−	2.91830i
$280$		0			0
$281$	7.79194	−	2.28792i	0.464828	−	0.136486i	−0.0409286	−	0.999162i	$-0.513032\pi$
$281$	7.79194	−	2.28792i	0.464828	−	0.136486i	0.505756	+	0.862676i	$0.331213\pi$
$282$		0			0
$283$	−4.14897	+	3.59510i	−0.246631	+	0.213707i	−0.769400	−	0.638768i	$-0.779445\pi$
$283$	−4.14897	+	3.59510i	−0.246631	+	0.213707i	0.522769	+	0.852474i	$0.324899\pi$
$284$		0			0
$285$	−2.74754	+	1.25026i	−0.162750	+	0.0740588i
$286$		0			0
$287$	−3.71730	+	5.78423i	−0.219425	+	0.341432i
$288$		0			0
$289$	5.81013	−	6.70525i	0.341773	−	0.394427i
$290$		0			0
$291$	0.0384916	+	0.267715i	0.00225642	+	0.0156937i
$292$		0			0
$293$	−19.3572	+	8.84012i	−1.13086	+	0.516446i	−0.890837	−	0.454322i	$-0.849881\pi$
$293$	−19.3572	+	8.84012i	−1.13086	+	0.516446i	−0.240021	+	0.970768i	$0.577154\pi$
$294$		0			0
$295$	−3.14643	+	0.919242i	−0.183192	+	0.0535203i
$296$		0			0
$297$	27.4744	+	42.7509i	1.59422	+	2.48066i
$298$		0			0
$299$	5.23444	+	3.88259i	0.302715	+	0.224536i
$300$		0			0
$301$	−0.151189	+	0.0971632i	−0.00871438	+	0.00560039i
$302$		0			0
$303$	10.5845	+	4.83377i	0.608062	+	0.277693i
$304$		0			0
$305$	4.48719	−	9.79041i	0.256936	−	0.560597i
$306$		0			0
$307$	16.7306	−	2.40550i	0.954867	−	0.137289i	0.352768	−	0.935711i	$-0.385240\pi$
$307$	16.7306	−	2.40550i	0.954867	−	0.137289i	0.602099	+	0.798422i	$0.294331\pi$
$308$		0			0
$309$	19.8542	−	22.9129i	1.12946	−	1.30347i
$310$		0			0
$311$	−15.1027	−	9.70594i	−0.856398	−	0.550373i	0.0371664	−	0.999309i	$-0.488167\pi$
$311$	−15.1027	−	9.70594i	−0.856398	−	0.550373i	−0.893564	+	0.448936i	$0.851803\pi$
$312$		0			0
$313$	4.29089	−	14.6134i	0.242535	−	0.825999i	−0.744791	−	0.667297i	$-0.767451\pi$
$313$	4.29089	−	14.6134i	0.242535	−	0.825999i	0.987327	−	0.158702i	$-0.0507308\pi$
$314$		0			0
$315$	−78.1982	−	11.3515i	−4.40597	−	0.639584i
$316$		0			0
$317$	2.99263	+	10.1920i	0.168083	+	0.572438i	0.999850	+	0.0173135i	$0.00551133\pi$
$317$	2.99263	+	10.1920i	0.168083	+	0.572438i	−0.831767	+	0.555125i	$0.812670\pi$
$318$		0			0
$319$	1.93932	−	13.4883i	0.108581	−	0.755198i
$320$		0			0
$321$	−39.1484			−2.18505
$322$		0			0
$323$		−	2.09553i		−	0.116598i
$324$		0			0
$325$	1.93195	−	6.51419i	0.107165	−	0.361342i
$326$		0			0
$327$	17.8764	+	60.8814i	0.988567	+	3.36675i
$328$		0			0
$329$	6.72232	+	7.75798i	0.370614	+	0.427711i
$330$		0			0
$331$	−26.8245	−	7.87638i	−1.47441	−	0.432925i	−0.556878	−	0.830594i	$-0.688001\pi$
$331$	−26.8245	−	7.87638i	−1.47441	−	0.432925i	−0.917529	+	0.397669i	$0.869819\pi$
$332$		0			0
$333$	−47.6640	+	74.1666i	−2.61197	+	4.06431i
$334$		0			0
$335$	−0.000837866		0.617750i	−4.57775e−5		0.0337513i
$336$		0			0
$337$	25.6774	−	3.69186i	1.39874	−	0.201108i	0.598661	−	0.801003i	$-0.295700\pi$
$337$	25.6774	−	3.69186i	1.39874	−	0.201108i	0.800079	+	0.599894i	$0.204791\pi$
$338$		0			0
$339$	0.151475	+	0.331685i	0.00822701	+	0.0180146i
$340$		0			0
$341$	−8.65565	+	18.9532i	−0.468730	+	1.02637i
$342$		0			0
$343$	−16.9365	−	26.3537i	−0.914486	−	1.42297i
$344$		0			0
$345$	−28.1948	−	20.9725i	−1.51796	−	1.12912i
$346$		0			0
$347$	−9.41077	−	14.6434i	−0.505197	−	0.786102i	0.491188	−	0.871053i	$-0.336563\pi$
$347$	−9.41077	−	14.6434i	−0.505197	−	0.786102i	−0.996385	+	0.0849519i	$0.972926\pi$
$348$		0			0
$349$	−10.3698	+	22.7067i	−0.555082	+	1.21546i	0.399286	+	0.916827i	$0.369258\pi$
$349$	−10.3698	+	22.7067i	−0.555082	+	1.21546i	−0.954368	+	0.298634i	$0.903469\pi$
$350$		0			0
$351$	8.76320	+	19.1887i	0.467745	+	1.02422i
$352$		0			0
$353$	−28.4872	+	4.09583i	−1.51622	+	0.217999i	−0.849611	−	0.527410i	$-0.823163\pi$
$353$	−28.4872	+	4.09583i	−1.51622	+	0.217999i	−0.666607	+	0.745409i	$0.732254\pi$
$354$		0			0
$355$	27.7145	+	0.0375897i	1.47093	+	0.00199506i
$356$		0			0
$357$	41.1550	−	64.0385i	2.17816	−	3.38928i
$358$		0			0
$359$	−13.4961	−	3.96280i	−0.712295	−	0.209149i	−0.0945419	−	0.995521i	$-0.530139\pi$
$359$	−13.4961	−	3.96280i	−0.712295	−	0.209149i	−0.617753	+	0.786372i	$0.711957\pi$
$360$		0			0
$361$	12.3312	+	14.2310i	0.649011	+	0.748998i
$362$		0			0
$363$	0.261352	+	0.890082i	0.0137174	+	0.0467172i
$364$		0			0
$365$	14.0403	+	21.9124i	0.734902	+	1.14695i
$366$		0			0
$367$			28.6649i			1.49630i	0.663532	+	0.748148i	$0.269057\pi$
$367$			28.6649i			1.49630i	−0.663532	+	0.748148i	$0.730943\pi$
$368$		0			0
$369$	−11.6483			−0.606387
$370$		0			0
$371$	2.62260	−	18.2406i	0.136159	−	0.947005i
$372$		0			0
$373$	−10.0321	−	34.1662i	−0.519442	−	1.76906i	−0.631522	−	0.775358i	$-0.717570\pi$
$373$	−10.0321	−	34.1662i	−0.519442	−	1.76906i	0.112080	−	0.993699i	$-0.464249\pi$
$374$		0			0
$375$	−10.4644	+	35.1093i	−0.540379	+	1.81304i
$376$		0			0
$377$	1.59367	−	5.42754i	0.0820782	−	0.279533i
$378$		0			0
$379$	24.2949	+	15.6134i	1.24794	+	0.802005i	0.986587	−	0.163237i	$-0.0521934\pi$
$379$	24.2949	+	15.6134i	1.24794	+	0.802005i	0.261358	+	0.965242i	$0.415830\pi$
$380$		0			0
$381$	7.32862	−	8.45767i	0.375456	−	0.433300i
$382$		0			0
$383$	3.46412	−	0.498066i	0.177008	−	0.0254500i	−0.0532406	−	0.998582i	$-0.516955\pi$
$383$	3.46412	−	0.498066i	0.177008	−	0.0254500i	0.230249	+	0.973132i	$0.426046\pi$
$384$		0			0
$385$	30.3923	+	13.9296i	1.54894	+	0.709916i
$386$		0			0
$387$	−0.276951	−	0.126479i	−0.0140782	−	0.00642931i
$388$		0			0
$389$	11.9826	−	7.70078i	0.607544	−	0.390445i	−0.200391	−	0.979716i	$-0.564221\pi$
$389$	11.9826	−	7.70078i	0.607544	−	0.390445i	0.807935	+	0.589271i	$0.200585\pi$
$390$		0			0
$391$	21.3583	−	11.7850i	1.08014	−	0.595991i
$392$		0			0
$393$	25.2525	+	39.2936i	1.27382	+	1.98210i
$394$		0			0
$395$	5.84876	−	1.70874i	0.294283	−	0.0859759i
$396$		0			0
$397$	−25.5233	+	11.6561i	−1.28098	+	0.585002i	−0.935467	−	0.353413i	$-0.885021\pi$
$397$	−25.5233	+	11.6561i	−1.28098	+	0.585002i	−0.345509	+	0.938415i	$0.612294\pi$
$398$		0			0
$399$	−0.877449	−	6.10279i	−0.0439274	−	0.305522i
$400$		0			0
$401$	15.4836	−	17.8691i	0.773216	−	0.892339i	−0.223384	−	0.974731i	$-0.571710\pi$
$401$	15.4836	−	17.8691i	0.773216	−	0.892339i	0.996600	+	0.0823913i	$0.0262557\pi$
$402$		0			0
$403$	−4.67615	+	7.27623i	−0.232935	+	0.362455i
$404$		0			0
$405$	−25.6119	−	56.2841i	−1.27267	−	2.79678i
$406$		0			0
$407$	28.1904	−	24.4272i	1.39735	−	1.21081i
$408$		0			0
$409$	29.1086	−	8.54707i	1.43933	−	0.422625i	0.533331	−	0.845906i	$-0.320940\pi$
$409$	29.1086	−	8.54707i	1.43933	−	0.422625i	0.905998	+	0.423281i	$0.139122\pi$
$410$		0			0
$411$	−6.45698	+	44.9093i	−0.318499	+	2.21521i
$412$		0			0
$413$		−	6.69525i		−	0.329452i
$414$		0			0
$415$	−7.09944	+	6.13486i	−0.348498	+	0.301148i
$416$		0			0
$417$	35.9448	+	5.16809i	1.76023	+	0.253082i
$418$		0			0
$419$	27.0165	−	7.93277i	1.31984	−	0.387541i	0.455407	−	0.890283i	$-0.349494\pi$
$419$	27.0165	−	7.93277i	1.31984	−	0.387541i	0.864436	+	0.502742i	$0.167675\pi$
$420$		0			0
$421$	−17.4553	−	20.1445i	−0.850719	−	0.981782i	0.149256	−	0.988799i	$-0.452312\pi$
$421$	−17.4553	−	20.1445i	−0.850719	−	0.981782i	−0.999975	+	0.00701626i	$0.997767\pi$
$422$		0			0
$423$	−4.89950	+	16.6862i	−0.238222	+	0.811310i
$424$		0			0
$425$	−19.1753	−	16.7068i	−0.930138	−	0.810397i
$426$		0			0
$427$	16.6244	+	14.4051i	0.804510	+	0.697112i
$428$		0			0
$429$	−2.07458	−	14.4290i	−0.100162	−	0.696639i
$430$		0			0
$431$	11.8342	+	25.9133i	0.570034	+	1.24820i	0.946779	+	0.321884i	$0.104316\pi$
$431$	11.8342	+	25.9133i	0.570034	+	1.24820i	−0.376745	+	0.926317i	$0.622957\pi$
$432$		0			0
$433$	−9.99822	−	4.56604i	−0.480484	−	0.219430i	0.160423	−	0.987048i	$-0.448714\pi$
$433$	−9.99822	−	4.56604i	−0.480484	−	0.219430i	−0.640907	+	0.767619i	$0.721442\pi$
$434$		0			0
$435$	−8.63250	+	29.2528i	−0.413897	+	1.40256i
$436$		0			0
$437$	0.682304	−	1.85423i	0.0326390	−	0.0887000i
$438$		0			0
$439$	15.8417	−	10.1808i	0.756083	−	0.485905i	−0.104935	−	0.994479i	$-0.533463\pi$
$439$	15.8417	−	10.1808i	0.756083	−	0.485905i	0.861018	+	0.508574i	$0.169827\pi$
$440$		0			0
$441$	44.5461	−	97.5424i	2.12124	−	4.64488i
$442$		0			0
$443$	22.6874	−	10.3610i	1.07791	−	0.492266i	0.204309	−	0.978906i	$-0.434505\pi$
$443$	22.6874	−	10.3610i	1.07791	−	0.492266i	0.873602	+	0.486641i	$0.161778\pi$
$444$		0			0
$445$	8.11021	−	9.33407i	0.384461	−	0.442478i
$446$		0			0
$447$	−48.5363	−	42.0569i	−2.29569	−	1.98922i
$448$		0			0
$449$	4.04021	+	2.59649i	0.190669	+	0.122536i	0.632493	−	0.774566i	$-0.282032\pi$
$449$	4.04021	+	2.59649i	0.190669	+	0.122536i	−0.441823	+	0.897102i	$0.645668\pi$
$450$		0			0
$451$	4.72876	+	1.38849i	0.222668	+	0.0653814i
$452$		0			0
$453$	14.6849	−	12.7245i	0.689956	−	0.597850i
$454$		0			0
$455$	11.6648	+	7.51889i	0.546854	+	0.352491i
$456$		0			0
$457$	26.3614	+	3.79020i	1.23314	+	0.177298i	0.727900	−	0.685683i	$-0.240496\pi$
$457$	26.3614	+	3.79020i	1.23314	+	0.177298i	0.505236	+	0.862981i	$0.331405\pi$
$458$		0			0
$459$	78.9590			3.68549
$460$		0			0
$461$	−39.4673			−1.83817			−0.919087	−	0.394056i	$-0.871072\pi$
$461$	−39.4673			−1.83817			−0.919087	+	0.394056i	$0.871072\pi$
$462$		0			0
$463$	−25.6850	−	3.69295i	−1.19368	−	0.171626i	−0.483310	−	0.875450i	$-0.660565\pi$
$463$	−25.6850	−	3.69295i	−1.19368	−	0.171626i	−0.710375	+	0.703824i	$0.751475\pi$
$464$		0			0
$465$	25.2662	−	39.1980i	1.17169	−	1.81776i
$466$		0			0
$467$	13.6477	−	11.8258i	0.631539	−	0.547232i	−0.279190	−	0.960236i	$-0.590066\pi$
$467$	13.6477	−	11.8258i	0.631539	−	0.547232i	0.910729	+	0.413004i	$0.135520\pi$
$468$		0			0
$469$	−1.21065	−	0.355478i	−0.0559025	−	0.0164145i
$470$		0			0
$471$	−37.0777	−	23.8284i	−1.70845	−	1.09795i
$472$		0			0
$473$	0.0973549	+	0.0843585i	0.00447638	+	0.00387881i
$474$		0			0
$475$	−2.05989	−	0.00558774i	−0.0945142	−	0.000256383i
$476$		0			0
$477$	28.3983	−	12.9691i	1.30027	−	0.593813i
$478$		0			0
$479$	13.7144	−	30.0303i	0.626625	−	1.37212i	−0.283976	−	0.958832i	$-0.591653\pi$
$479$	13.7144	−	30.0303i	0.626625	−	1.37212i	0.910601	−	0.413287i	$-0.135619\pi$
$480$		0			0
$481$	13.0261	−	8.37134i	0.593937	−	0.381700i
$482$		0			0
$483$	57.2671	−	43.2646i	2.60574	−	1.96861i
$484$		0			0
$485$	−0.0522385	+	0.177019i	−0.00237203	+	0.00803803i
$486$		0			0
$487$	−12.3443	−	5.63748i	−0.559376	−	0.255458i	0.115603	−	0.993296i	$-0.463120\pi$
$487$	−12.3443	−	5.63748i	−0.559376	−	0.255458i	−0.674979	+	0.737837i	$0.735847\pi$
$488$		0			0
$489$	−5.92501	−	12.9740i	−0.267938	−	0.586703i
$490$		0			0
$491$	0.729982	+	5.07714i	0.0329436	+	0.229128i	0.999641	−	0.0267944i	$-0.00852993\pi$
$491$	0.729982	+	5.07714i	0.0329436	+	0.229128i	−0.966697	+	0.255922i	$0.917621\pi$
$492$		0			0
$493$	−16.0015	−	13.8654i	−0.720671	−	0.624465i
$494$		0			0
$495$	7.98446	+	56.0729i	0.358875	+	2.52029i
$496$		0			0
$497$	−15.9481	+	54.3141i	−0.715368	+	2.43632i
$498$		0			0
$499$	−15.3234	−	17.6842i	−0.685972	−	0.791654i	0.300814	−	0.953683i	$-0.402742\pi$
$499$	−15.3234	−	17.6842i	−0.685972	−	0.791654i	−0.986786	+	0.162029i	$0.948196\pi$
$500$		0			0
$501$	−4.93278	+	1.44840i	−0.220381	+	0.0647096i
$502$		0			0
$503$	3.05483	+	0.439218i	0.136208	+	0.0195838i	0.210082	−	0.977684i	$-0.432627\pi$
$503$	3.05483	+	0.439218i	0.136208	+	0.0195838i	−0.0738735	+	0.997268i	$0.523536\pi$
$504$		0			0
$505$	5.19168	+	6.00797i	0.231027	+	0.267351i
$506$		0			0
$507$			36.5471i			1.62311i
$508$		0			0
$509$	−3.72029	+	25.8752i	−0.164899	+	1.14690i	0.724336	+	0.689448i	$0.242147\pi$
$509$	−3.72029	+	25.8752i	−0.164899	+	1.14690i	−0.889235	+	0.457451i	$0.848762\pi$
$510$		0			0
$511$	−51.0023	+	14.9756i	−2.25621	+	0.662482i
$512$		0			0
$513$	4.83323	−	4.18802i	0.213392	−	0.184906i
$514$		0			0
$515$	18.8310	−	8.56898i	0.829793	−	0.377594i
$516$		0			0
$517$	3.97801	−	6.18991i	0.174953	−	0.272232i
$518$		0			0
$519$	−23.1762	+	26.7468i	−1.01732	+	1.17405i
$520$		0			0
$521$	4.86647	+	33.8471i	0.213204	+	1.48287i	0.762364	+	0.647149i	$0.224039\pi$
$521$	4.86647	+	33.8471i	0.213204	+	1.48287i	−0.549160	+	0.835717i	$0.685052\pi$
$522$		0			0
$523$	−10.6312	+	4.85510i	−0.464869	+	0.212299i	−0.634059	−	0.773285i	$-0.718612\pi$
$523$	−10.6312	+	4.85510i	−0.464869	+	0.212299i	0.169189	+	0.985584i	$0.445885\pi$
$524$		0			0
$525$	−62.8397	−	40.6259i	−2.74255	−	1.77306i
$526$		0			0
$527$	17.5029	+	27.2350i	0.762437	+	1.18638i
$528$		0			0
$529$	22.7362	−	3.47370i	0.988529	−	0.151030i
$530$		0			0
$531$	9.54197	−	6.13225i	0.414086	−	0.266117i
$532$		0			0
$533$	1.86094	+	0.849864i	0.0806063	+	0.0368117i
$534$		0			0
$535$	−24.2855	−	11.1306i	−1.04995	−	0.481220i
$536$		0			0
$537$	−20.9204	+	3.00790i	−0.902783	+	0.129801i
$538$		0			0
$539$	−29.7111	+	34.2884i	−1.27975	+	1.47691i
$540$		0			0
$541$	−28.9639	−	18.6140i	−1.24526	−	0.800278i	−0.259061	−	0.965861i	$-0.583413\pi$
$541$	−28.9639	−	18.6140i	−1.24526	−	0.800278i	−0.986196	+	0.165583i	$0.947050\pi$
$542$		0			0
$543$	−8.97181	+	30.5552i	−0.385017	+	1.31125i
$544$		0			0
$545$	−6.22023	+	42.8500i	−0.266446	+	1.83549i
$546$		0			0
$547$	−5.35258	−	18.2292i	−0.228860	−	0.779425i	−0.991214	−	0.132265i	$-0.957775\pi$
$547$	−5.35258	−	18.2292i	−0.228860	−	0.779425i	0.762355	−	0.647159i	$-0.224043\pi$
$548$		0			0
$549$	−5.30349	+	36.8866i	−0.226348	+	1.57428i
$550$		0			0
$551$	−1.71491			−0.0730575
$552$		0			0
$553$			12.4455i			0.529236i
$554$		0			0
$555$	−70.2956	+	45.0416i	−2.98388	+	1.91191i
$556$		0			0
$557$	0.538064	+	1.83248i	0.0227985	+	0.0776446i	0.970107	−	0.242680i	$-0.0780263\pi$
$557$	0.538064	+	1.83248i	0.0227985	+	0.0776446i	−0.947308	+	0.320324i	$0.896208\pi$
$558$		0			0
$559$	0.0350179	+	0.0404129i	0.00148110	+	0.00170928i
$560$		0			0
$561$	−52.3531	−	15.3723i	−2.21035	−	0.649018i
$562$		0			0
$563$	12.9556	−	20.1593i	0.546012	−	0.849611i	−0.453112	−	0.891453i	$-0.649686\pi$
$563$	12.9556	−	20.1593i	0.546012	−	0.849611i	0.999124	+	0.0418423i	$0.0133227\pi$
$564$		0			0
$565$	−0.000337487		0.248826i	−1.41982e−5		0.0104682i
$566$		0			0
$567$	125.018	−	17.9748i	5.25025	−	0.754872i
$568$		0			0
$569$	9.77454	+	21.4033i	0.409770	+	0.897271i	0.996186	+	0.0872607i	$0.0278113\pi$
$569$	9.77454	+	21.4033i	0.409770	+	0.897271i	−0.586416	+	0.810010i	$0.699461\pi$
$570$		0			0
$571$	−2.28210	+	4.99709i	−0.0955027	+	0.209122i	−0.951354	−	0.308100i	$-0.900307\pi$
$571$	−2.28210	+	4.99709i	−0.0955027	+	0.209122i	0.855851	+	0.517222i	$0.173034\pi$
$572$		0			0
$573$	2.18001	+	3.39216i	0.0910713	+	0.141710i
$574$		0			0
$575$	−11.5276	−	21.0265i	−0.480734	−	0.876866i
$576$		0			0
$577$	−0.514407	−	0.800433i	−0.0214150	−	0.0333225i	0.830381	−	0.557196i	$-0.188123\pi$
$577$	−0.514407	−	0.800433i	−0.0214150	−	0.0333225i	−0.851796	+	0.523874i	$0.824486\pi$
$578$		0			0
$579$	14.4349	−	31.6080i	0.599894	−	1.31359i
$580$		0			0
$581$	−7.96125	−	17.4327i	−0.330288	−	0.723231i
$582$		0			0
$583$	−13.0745	+	1.87983i	−0.541491	+	0.0778547i
$584$		0			0
$585$	−0.0318886	+	23.5111i	−0.00131843	+	0.972066i
$586$		0			0
$587$	19.1473	−	29.7938i	0.790294	−	1.22972i	−0.179008	−	0.983848i	$-0.557289\pi$
$587$	19.1473	−	29.7938i	0.790294	−	1.22972i	0.969302	−	0.245874i	$-0.0790748\pi$
$588$		0			0
$589$	2.51594	+	0.738746i	0.103667	+	0.0304395i
$590$		0			0
$591$	35.6724	+	41.1682i	1.46737	+	1.69343i
$592$		0			0
$593$	11.2199	+	38.2115i	0.460746	+	1.56916i	0.782699	+	0.622401i	$0.213843\pi$
$593$	11.2199	+	38.2115i	0.460746	+	1.56916i	−0.321953	+	0.946756i	$0.604339\pi$
$594$		0			0
$595$	43.7376	−	28.0247i	1.79307	−	1.14890i
$596$		0			0
$597$			37.5781i			1.53797i
$598$		0			0
$599$	−13.8648			−0.566499			−0.283249	−	0.959046i	$-0.591412\pi$
$599$	−13.8648			−0.566499			−0.283249	+	0.959046i	$0.591412\pi$
$600$		0			0
$601$	3.53841	−	24.6102i	0.144335	−	1.00387i	−0.780949	−	0.624595i	$-0.785264\pi$
$601$	3.53841	−	24.6102i	0.144335	−	1.00387i	0.925284	−	0.379275i	$-0.123827\pi$
$602$		0			0
$603$	−0.602223	−	2.05098i	−0.0245244	−	0.0835225i
$604$		0			0
$605$	−0.0909394	+	0.626464i	−0.00369721	+	0.0254694i
$606$		0			0
$607$	−6.37929	+	21.7259i	−0.258927	+	0.881826i	0.722723	+	0.691138i	$0.242890\pi$
$607$	−6.37929	+	21.7259i	−0.258927	+	0.881826i	−0.981651	+	0.190688i	$0.938928\pi$
$608$		0			0
$609$	−52.4069	−	33.6799i	−2.12363	−	1.36478i
$610$		0			0
$611$	2.00018	−	2.30833i	0.0809184	−	0.0933849i
$612$		0			0
$613$	−7.27864	+	1.04651i	−0.293982	+	0.0422682i	−0.287728	−	0.957712i	$-0.592900\pi$
$613$	−7.27864	+	1.04651i	−0.293982	+	0.0422682i	−0.00625397	+	0.999980i	$0.501991\pi$
$614$		0			0
$615$	−10.0277	−	4.59593i	−0.404355	−	0.185326i
$616$		0			0
$617$	−19.4081	−	8.86340i	−0.781342	−	0.356827i	−0.0155203	−	0.999880i	$-0.504940\pi$
$617$	−19.4081	−	8.86340i	−0.781342	−	0.356827i	−0.765822	+	0.643052i	$0.777668\pi$
$618$		0			0
$619$	−37.2913	+	23.9657i	−1.49886	+	0.963261i	−0.503822	+	0.863808i	$0.668073\pi$
$619$	−37.2913	+	23.9657i	−1.49886	+	0.963261i	−0.995042	+	0.0994538i	$0.968290\pi$
$620$		0			0
$621$	69.8672	+	25.7091i	2.80367	+	1.03167i
$622$		0			0
$623$	13.6545	+	21.2468i	0.547056	+	0.851236i
$624$		0			0
$625$	−16.4738	+	18.8046i	−0.658951	+	0.752186i
$626$		0			0
$627$	−4.01998	+	1.83587i	−0.160543	+	0.0733174i
$628$		0			0
$629$	−8.24816	−	57.3672i	−0.328876	−	2.28738i
$630$		0			0
$631$	−11.9133	+	13.7487i	−0.474263	+	0.547329i	−0.941592	−	0.336755i	$-0.890671\pi$
$631$	−11.9133	+	13.7487i	−0.474263	+	0.547329i	0.467330	+	0.884083i	$0.345216\pi$
$632$		0			0
$633$	21.5456	−	33.5257i	0.856362	−	1.33253i
$634$		0			0
$635$	6.95094	−	3.16300i	0.275840	−	0.125520i
$636$		0			0
$637$	−14.2334	+	12.3333i	−0.563949	+	0.488665i
$638$		0			0
$639$	−92.0147	+	27.0179i	−3.64004	+	1.06881i
$640$		0			0
$641$	4.78332	−	33.2687i	0.188930	−	1.31404i	−0.645855	−	0.763460i	$-0.723499\pi$
$641$	4.78332	−	33.2687i	0.188930	−	1.31404i	0.834785	−	0.550576i	$-0.185592\pi$
$642$		0			0
$643$			21.9362i			0.865079i	0.901615	+	0.432539i	$0.142382\pi$
$643$			21.9362i			0.865079i	−0.901615	+	0.432539i	$0.857618\pi$
$644$		0			0
$645$	−0.188515	−	0.218156i	−0.00742279	−	0.00858987i
$646$		0			0
$647$	−39.3419	−	5.65651i	−1.54669	−	0.222380i	−0.684517	−	0.728997i	$-0.739987\pi$
$647$	−39.3419	−	5.65651i	−1.54669	−	0.222380i	−0.862171	+	0.506617i	$0.830896\pi$
$648$		0			0
$649$	−4.60464	+	1.35204i	−0.180748	+	0.0530723i
$650$		0			0
$651$	62.3775	+	71.9875i	2.44477	+	2.82141i
$652$		0			0
$653$	13.2830	−	45.2377i	0.519803	−	1.77029i	−0.110432	−	0.993884i	$-0.535223\pi$
$653$	13.2830	−	45.2377i	0.519803	−	1.77029i	0.630235	−	0.776404i	$-0.282958\pi$
$654$		0			0
$655$	4.49330	+	31.5553i	0.175568	+	1.23297i
$656$		0			0
$657$	−68.0566	−	58.9713i	−2.65514	−	2.30069i
$658$		0			0
$659$	0.0121139	+	0.0842538i	0.000471889	+	0.00328206i	0.990056	−	0.140674i	$-0.0449268\pi$
$659$	0.0121139	+	0.0842538i	0.000471889	+	0.00328206i	−0.989584	+	0.143956i	$0.954018\pi$
$660$		0			0
$661$	2.78494	+	6.09816i	0.108321	+	0.237191i	0.956028	−	0.293274i	$-0.0947447\pi$
$661$	2.78494	+	6.09816i	0.108321	+	0.237191i	−0.847707	+	0.530465i	$0.822017\pi$
$662$		0			0
$663$	−20.6029	−	9.40903i	−0.800151	−	0.365417i
$664$		0			0
$665$	1.19082	−	4.03531i	0.0461781	−	0.156483i
$666$		0			0
$667$	−9.64441	−	17.4789i	−0.373433	−	0.676786i
$668$		0			0
$669$	−21.8613	+	14.0494i	−0.845205	+	0.543180i
$670$		0			0
$671$	6.54992	−	14.3423i	0.252857	−	0.553680i
$672$		0			0
$673$	−26.8957	+	12.2828i	−1.03675	+	0.473469i	−0.859736	−	0.510739i	$-0.829372\pi$
$673$	−26.8957	+	12.2828i	−1.03675	+	0.473469i	−0.177016	+	0.984208i	$0.556645\pi$
$674$		0			0
$675$	0.210545	−	77.6162i	0.00810388	−	2.98745i
$676$		0			0
$677$	35.1675	+	30.4728i	1.35160	+	1.17117i	0.968946	+	0.247273i	$0.0795346\pi$
$677$	35.1675	+	30.4728i	1.35160	+	1.17117i	0.382652	+	0.923893i	$0.375011\pi$
$678$		0			0
$679$	−0.317133	−	0.203809i	−0.0121705	−	0.00782148i
$680$		0			0
$681$	57.3130	+	16.8286i	2.19624	+	0.644874i
$682$		0			0
$683$	−24.8760	+	21.5552i	−0.951853	+	0.824785i	−0.984626	−	0.174678i	$-0.944112\pi$
$683$	−24.8760	+	21.5552i	−0.951853	+	0.824785i	0.0327731	+	0.999463i	$0.489566\pi$
$684$		0			0
$685$	−16.7741	+	26.0234i	−0.640906	+	0.994302i
$686$		0			0
$687$	−29.9960	−	4.31277i	−1.14442	−	0.164542i
$688$		0			0
$689$	−5.48316			−0.208892
$690$		0			0
$691$	−15.0813			−0.573718			−0.286859	−	0.957973i	$-0.592611\pi$
$691$	−15.0813			−0.573718			−0.286859	+	0.957973i	$0.592611\pi$
$692$		0			0
$693$	−114.507	−	16.4636i	−4.34976	−	0.625401i
$694$		0			0
$695$	20.8288	+	13.4258i	0.790081	+	0.509270i
$696$		0			0
$697$	5.78717	−	5.01461i	0.219205	−	0.189942i
$698$		0			0
$699$	−12.2872	−	3.60785i	−0.464746	−	0.136462i
$700$		0			0
$701$	1.73691	+	1.11624i	0.0656020	+	0.0421599i	0.573031	−	0.819534i	$-0.305768\pi$
$701$	1.73691	+	1.11624i	0.0656020	+	0.0421599i	−0.507429	+	0.861694i	$0.669404\pi$
$702$		0			0
$703$	−3.54767	−	3.07407i	−0.133803	−	0.115941i
$704$		0			0
$705$	−10.8015	+	12.4315i	−0.406808	+	0.468197i
$706$		0			0
$707$	−14.7526	+	6.73729i	−0.554829	+	0.253382i
$708$		0			0
$709$	−9.44866	+	20.6897i	−0.354852	+	0.777017i	0.645065	+	0.764128i	$0.276830\pi$
$709$	−9.44866	+	20.6897i	−0.354852	+	0.777017i	−0.999917	+	0.0128897i	$0.995897\pi$
$710$		0			0
$711$	−17.7371	+	11.3990i	−0.665195	+	0.427495i
$712$		0			0
$713$	6.61976	+	29.7979i	0.247912	+	1.11594i
$714$		0			0
$715$	2.81549	−	9.54079i	0.105293	−	0.356806i
$716$		0			0
$717$	61.0403	+	27.8762i	2.27959	+	1.04105i
$718$		0			0
$719$	0.932921	+	2.04281i	0.0347921	+	0.0761840i	0.926230	−	0.376959i	$-0.123030\pi$
$719$	0.932921	+	2.04281i	0.0347921	+	0.0761840i	−0.891438	+	0.453143i	$0.850303\pi$
$720$		0			0
$721$	6.01384	+	41.8272i	0.223967	+	1.55773i
$722$		0			0
$723$	16.5813	+	14.3678i	0.616667	+	0.534345i
$724$		0			0
$725$	−13.6722	+	15.6924i	−0.507774	+	0.582801i
$726$		0			0
$727$	8.53770	−	29.0768i	0.316646	−	1.07840i	−0.635334	−	0.772237i	$-0.719138\pi$
$727$	8.53770	−	29.0768i	0.316646	−	1.07840i	0.951980	−	0.306160i	$-0.0990442\pi$
$728$		0			0
$729$	40.1909	+	46.3828i	1.48855	+	1.71788i
$730$		0			0
$731$	0.192046	−	0.0563897i	0.00710307	−	0.00208565i
$732$		0			0
$733$	−2.85650	−	0.410703i	−0.105507	−	0.0151696i	0.0893590	−	0.995999i	$-0.471518\pi$
$733$	−2.85650	−	0.410703i	−0.105507	−	0.0151696i	−0.194866	+	0.980830i	$0.562427\pi$
$734$		0			0
$735$	76.8345	−	66.3953i	2.83408	−	2.44903i
$736$		0			0
$737$			0.904405i			0.0333142i
$738$		0			0
$739$	−7.35815	+	51.1770i	−0.270674	+	1.88258i	0.170804	+	0.985305i	$0.445364\pi$
$739$	−7.35815	+	51.1770i	−0.270674	+	1.88258i	−0.441478	+	0.897272i	$0.645546\pi$
$740$		0			0
$741$	−1.76020	+	0.516842i	−0.0646626	+	0.0189867i
$742$		0			0
$743$	14.5140	−	12.5765i	0.532467	−	0.461385i	−0.346648	−	0.937995i	$-0.612680\pi$
$743$	14.5140	−	12.5765i	0.532467	−	0.461385i	0.879115	+	0.476610i	$0.158135\pi$
$744$		0			0
$745$	−18.1516	−	39.8896i	−0.665023	−	1.46144i
$746$		0			0
$747$	17.5531	−	27.3131i	0.642233	−	0.999333i
$748$		0			0
$749$	35.7324	−	41.2374i	1.30563	−	1.50678i
$750$		0			0
$751$	−4.26373	−	29.6549i	−0.155586	−	1.08212i	−0.906647	−	0.421889i	$-0.861367\pi$
$751$	−4.26373	−	29.6549i	−0.155586	−	1.08212i	0.751062	−	0.660232i	$-0.229542\pi$
$752$		0			0
$753$	30.1373	−	13.7633i	1.09827	−	0.501561i
$754$		0			0
$755$	12.7275	−	3.71839i	0.463201	−	0.135326i
$756$		0			0
$757$	16.5886	+	25.8124i	0.602923	+	0.938166i	0.999794	+	0.0202919i	$0.00645957\pi$
$757$	16.5886	+	25.8124i	0.602923	+	0.938166i	−0.396871	+	0.917874i	$0.629904\pi$
$758$		0			0
$759$	−41.3196	−	30.6484i	−1.49981	−	1.11247i
$760$		0			0
$761$	−1.39786	+	0.898349i	−0.0506723	+	0.0325651i	−0.565732	−	0.824589i	$-0.691406\pi$
$761$	−1.39786	+	0.898349i	−0.0506723	+	0.0325651i	0.515059	+	0.857154i	$0.327770\pi$
$762$		0			0
$763$	−80.4466	−	36.7387i	−2.91236	−	1.33003i
$764$		0			0
$765$	80.0002	+	36.6661i	2.89241	+	1.32567i
$766$		0			0
$767$	−1.97184	+	0.283508i	−0.0711991	+	0.0102369i
$768$		0			0
$769$	−21.8970	+	25.2705i	−0.789628	+	0.911279i	−0.997765	−	0.0668206i	$-0.978714\pi$
$769$	−21.8970	+	25.2705i	−0.789628	+	0.911279i	0.208137	+	0.978100i	$0.433260\pi$
$770$		0			0
$771$	−2.61892	−	1.68308i	−0.0943182	−	0.0606146i
$772$		0			0
$773$	4.32523	−	14.7304i	0.155568	−	0.529814i	−0.844415	−	0.535689i	$-0.820052\pi$
$773$	4.32523	−	14.7304i	0.155568	−	0.529814i	0.999983	+	0.00587481i	$0.00187002\pi$
$774$		0			0
$775$	26.8185	−	17.1326i	0.963349	−	0.615421i
$776$		0			0
$777$	−48.0422	−	163.617i	−1.72350	−	5.86972i
$778$		0			0
$779$	0.0882666	−	0.613907i	0.00316248	−	0.0219955i
$780$		0			0
$781$	40.5749			1.45188
$782$		0			0
$783$		−	64.6174i		−	2.30924i
$784$		0			0
$785$	−16.2261	−	25.3237i	−0.579133	−	0.903842i
$786$		0			0
$787$	12.0337	+	40.9831i	0.428956	+	1.46089i	0.836633	+	0.547763i	$0.184520\pi$
$787$	12.0337	+	40.9831i	0.428956	+	1.46089i	−0.407678	+	0.913126i	$0.633661\pi$
$788$		0			0
$789$	18.1395	+	20.9341i	0.645784	+	0.745274i
$790$		0			0
$791$	−0.487642	−	0.143184i	−0.0173385	−	0.00509105i
$792$		0			0
$793$	3.53855	−	5.50609i	0.125657	−	0.195527i
$794$		0			0
$795$	29.5643	+	0.0400986i	1.04854	+	0.00142215i
$796$		0			0
$797$	31.3559	−	4.50830i	1.11068	−	0.159692i	0.437536	−	0.899201i	$-0.355851\pi$
$797$	31.3559	−	4.50830i	1.11068	−	0.159692i	0.673147	+	0.739509i	$0.264942\pi$
$798$		0			0
$799$	−4.74922	−	10.3993i	−0.168015	−	0.367902i
$800$		0			0
$801$	−17.7744	+	38.9204i	−0.628026	+	1.37519i
$802$		0			0
$803$	20.5989	+	32.0524i	0.726918	+	1.13111i
$804$		0			0
$805$	47.8263	−	10.5568i	1.68565	−	0.372078i
$806$		0			0
$807$	23.4566	+	36.4991i	0.825710	+	1.28483i
$808$		0			0
$809$	9.44644	−	20.6848i	0.332119	−	0.727239i	−0.667734	−	0.744400i	$-0.732736\pi$
$809$	9.44644	−	20.6848i	0.332119	−	0.727239i	0.999853	+	0.0171610i	$0.00546279\pi$
$810$		0			0
$811$	2.63138	+	5.76191i	0.0924001	+	0.202328i	0.950189	−	0.311674i	$-0.100890\pi$
$811$	2.63138	+	5.76191i	0.0924001	+	0.202328i	−0.857789	+	0.514002i	$0.828162\pi$
$812$		0			0
$813$	−8.18008	+	1.17612i	−0.286888	+	0.0412483i
$814$		0			0
$815$	0.0132009	−	9.73292i	0.000462409	−	0.340929i
$816$		0			0
$817$	0.00876455	−	0.0136379i	0.000306633	−	0.000477130i
$818$		0			0
$819$	−46.0764	−	13.5293i	−1.61004	−	0.472750i
$820$		0			0
$821$	−3.20514	−	3.69893i	−0.111860	−	0.129094i	0.697058	−	0.717015i	$-0.254492\pi$
$821$	−3.20514	−	3.69893i	−0.111860	−	0.129094i	−0.808918	+	0.587921i	$0.799947\pi$
$822$		0			0
$823$	11.8600	+	40.3914i	0.413413	+	1.40795i	0.858659	+	0.512547i	$0.171298\pi$
$823$	11.8600	+	40.3914i	0.413413	+	1.40795i	−0.445246	+	0.895408i	$0.646884\pi$
$824$		0			0
$825$	−15.2504	+	51.4218i	−0.530952	+	1.79028i
$826$		0			0
$827$			38.6197i			1.34294i	0.741032	+	0.671470i	$0.234337\pi$
$827$			38.6197i			1.34294i	−0.741032	+	0.671470i	$0.765663\pi$
$828$		0			0
$829$	−24.4637			−0.849661			−0.424831	−	0.905273i	$-0.639666\pi$
$829$	−24.4637			−0.849661			−0.424831	+	0.905273i	$0.639666\pi$
$830$		0			0
$831$	−7.96834	+	55.4210i	−0.276418	+	1.92253i
$832$		0			0
$833$	19.8605	+	67.6386i	0.688125	+	2.34354i
$834$		0			0
$835$	−3.47183	−	0.503981i	−0.120148	−	0.0174410i
$836$		0			0
$837$	−27.8358	+	94.8001i	−0.962147	+	3.27677i
$838$		0			0
$839$	−24.3002	−	15.6168i	−0.838936	−	0.539152i	0.0491697	−	0.998790i	$-0.484342\pi$
$839$	−24.3002	−	15.6168i	−0.838936	−	0.539152i	−0.888106	+	0.459639i	$0.847979\pi$
$840$		0			0
$841$	7.64402	−	8.82167i	0.263587	−	0.304195i
$842$		0			0
$843$	−26.3396	+	3.78706i	−0.907184	+	0.130433i
$844$		0			0
$845$	−10.3910	+	22.6718i	−0.357462	+	0.779932i
$846$		0			0
$847$	−1.17612	−	0.537118i	−0.0404121	−	0.0184556i
$848$		0			0
$849$	15.1335	−	9.72568i	0.519379	−	0.333784i
$850$		0			0
$851$	11.3804	−	53.4472i	0.390114	−	1.83215i
$852$		0			0
$853$	−11.6662	−	18.1530i	−0.399444	−	0.621546i	0.582025	−	0.813171i	$-0.302261\pi$
$853$	−11.6662	−	18.1530i	−0.399444	−	0.621546i	−0.981468	+	0.191625i	$0.938624\pi$
$854$		0			0
$855$	6.84175	−	1.99884i	0.233983	−	0.0683590i
$856$		0			0
$857$	30.2994	−	13.8373i	1.03501	−	0.472672i	0.175868	−	0.984414i	$-0.443727\pi$
$857$	30.2994	−	13.8373i	1.03501	−	0.472672i	0.859139	+	0.511741i	$0.170999\pi$
$858$		0			0
$859$	4.51364	+	31.3931i	0.154003	+	1.07112i	0.909422	+	0.415875i	$0.136524\pi$
$859$	4.51364	+	31.3931i	0.154003	+	1.07112i	−0.755419	+	0.655243i	$0.772566\pi$
$860$		0			0
$861$	14.7542	−	17.0273i	0.502822	−	0.580288i
$862$		0			0
$863$	3.90431	−	6.07523i	0.132904	−	0.206803i	−0.768422	−	0.639943i	$-0.778958\pi$
$863$	3.90431	−	6.07523i	0.132904	−	0.206803i	0.901327	+	0.433140i	$0.142594\pi$
$864$		0			0
$865$	−21.9818	+	10.0028i	−0.747405	+	0.340104i
$866$		0			0
$867$	−21.9717	+	19.0386i	−0.746198	+	0.646584i
$868$		0			0
$869$	8.55935	−	2.51325i	0.290356	−	0.0852562i
$870$		0			0
$871$	−0.0534287	+	0.371605i	−0.00181036	+	0.0125914i
$872$		0			0
$873$		−	0.638645i		−	0.0216149i
$874$		0			0
$875$	−27.4315	−	43.0686i	−0.927354	−	1.45598i
$876$		0			0
$877$	34.8478	+	5.01036i	1.17673	+	0.169188i	0.702807	−	0.711381i	$-0.251930\pi$
$877$	34.8478	+	5.01036i	1.17673	+	0.169188i	0.473919	+	0.880568i	$0.342839\pi$
$878$		0			0
$879$	66.9062	−	19.6454i	2.25669	−	0.662624i
$880$		0			0
$881$	−10.5994	−	12.2323i	−0.357102	−	0.412118i	0.548565	−	0.836108i	$-0.315174\pi$
$881$	−10.5994	−	12.2323i	−0.357102	−	0.412118i	−0.905667	+	0.423990i	$0.860629\pi$
$882$		0			0
$883$	15.9678	−	54.3813i	0.537359	−	1.83008i	−0.0199905	−	0.999800i	$-0.506364\pi$
$883$	15.9678	−	54.3813i	0.537359	−	1.83008i	0.557350	−	0.830278i	$-0.311818\pi$
$884$		0			0
$885$	10.6339	−	1.51421i	0.357456	−	0.0508996i
$886$		0			0
$887$	−0.730900	−	0.633328i	−0.0245412	−	0.0212651i	0.642504	−	0.766282i	$-0.277896\pi$
$887$	−0.730900	−	0.633328i	−0.0245412	−	0.0212651i	−0.667045	+	0.745017i	$0.732441\pi$
$888$		0			0
$889$	2.21984	+	15.4394i	0.0744512	+	0.517819i
$890$		0			0
$891$	−37.6083	−	82.3506i	−1.25992	−	2.75885i
$892$		0			0
$893$	−0.842294	−	0.384663i	−0.0281863	−	0.0128723i
$894$		0			0
$895$	−13.8331	−	4.08214i	−0.462388	−	0.136451i
$896$		0			0
$897$	−15.1670	−	15.0339i	−0.506410	−	0.501968i
$898$		0			0
$899$	22.2882	−	14.3237i	0.743352	−	0.477724i
$900$		0			0
$901$	−8.52578	+	18.6689i	−0.284035	+	0.621950i
$902$		0			0
$903$	0.535682	−	0.244638i	0.0178264	−	0.00814104i
$904$		0			0
$905$	−14.2530	+	16.4039i	−0.473787	+	0.545283i
$906$		0			0
$907$	−25.7351	−	22.2996i	−0.854521	−	0.740446i	0.112904	−	0.993606i	$-0.463985\pi$
$907$	−25.7351	−	22.2996i	−0.854521	−	0.740446i	−0.967425	+	0.253160i	$0.918530\pi$
$908$		0			0
$909$	−23.1140	−	14.8544i	−0.766641	−	0.492691i
$910$		0			0
$911$	28.0801	+	8.24506i	0.930335	+	0.273171i	0.711577	−	0.702608i	$-0.247981\pi$
$911$	28.0801	+	8.24506i	0.930335	+	0.273171i	0.218758	+	0.975779i	$0.429799\pi$
$912$		0			0
$913$	−10.3816	+	8.99570i	−0.343581	+	0.297714i
$914$		0			0
$915$	−19.1195	+	29.6620i	−0.632072	+	0.980596i
$916$		0			0
$917$	−64.4394	−	9.26499i	−2.12798	−	0.305957i
$918$		0			0
$919$	−17.0303			−0.561777			−0.280888	−	0.959740i	$-0.590629\pi$
$919$	−17.0303			−0.561777			−0.280888	+	0.959740i	$0.590629\pi$
$920$		0			0
$921$	−55.3865			−1.82505
$922$		0			0
$923$	16.6716	+	2.39701i	0.548751	+	0.0788985i
$924$		0			0
$925$	−56.4136	+	7.95492i	−1.85487	+	0.261556i
$926$		0			0
$927$	−54.1034	+	46.8808i	−1.77699	+	1.53977i
$928$		0			0
$929$	−24.4559	−	7.18090i	−0.802372	−	0.235598i	−0.145263	−	0.989393i	$-0.546403\pi$
$929$	−24.4559	−	7.18090i	−0.802372	−	0.235598i	−0.657109	+	0.753795i	$0.728221\pi$
$930$		0			0
$931$	4.80328	+	3.08688i	0.157421	+	0.101168i
$932$		0			0
$933$	44.4585	+	38.5235i	1.45551	+	1.26120i
$934$		0			0
$935$	−28.1063	−	24.4211i	−0.919175	−	0.798655i
$936$		0			0
$937$	−8.61020	+	3.93215i	−0.281283	+	0.128458i	−0.551061	−	0.834465i	$-0.685777\pi$
$937$	−8.61020	+	3.93215i	−0.281283	+	0.128458i	0.269778	+	0.962923i	$0.413050\pi$
$938$		0			0
$939$	−20.7320	+	45.3967i	−0.676563	+	1.48147i
$940$		0			0
$941$	−17.2604	+	11.0926i	−0.562675	+	0.361609i	−0.790849	−	0.612011i	$-0.790361\pi$
$941$	−17.2604	+	11.0926i	−0.562675	+	0.361609i	0.228174	+	0.973620i	$0.426724\pi$
$942$		0			0
$943$	6.75355	−	2.55289i	0.219926	−	0.0831336i
$944$		0			0
$945$	152.050	+	44.8699i	4.94618	+	1.45962i
$946$		0			0
$947$	−36.2413	−	16.5509i	−1.17769	−	0.537831i	−0.272213	−	0.962237i	$-0.587756\pi$
$947$	−36.2413	−	16.5509i	−1.17769	−	0.537831i	−0.905472	+	0.424406i	$0.860483\pi$
$948$		0			0
$949$	6.57020	+	14.3867i	0.213278	+	0.467013i
$950$		0			0
$951$	−4.95354	−	34.4526i	−0.160629	−	1.11720i
$952$		0			0
$953$	25.0772	+	21.7295i	0.812329	+	0.703888i	0.958413	−	0.285385i	$-0.0921214\pi$
$953$	25.0772	+	21.7295i	0.812329	+	0.703888i	−0.146084	+	0.989272i	$0.546667\pi$
$954$		0			0
$955$	0.387900	+	2.72413i	0.0125522	+	0.0881507i
$956$		0			0
$957$	−12.5801	+	42.8440i	−0.406658	+	1.38495i
$958$		0			0
$959$	−41.4121	−	47.7921i	−1.33727	−	1.54329i
$960$		0			0
$961$	−9.12508	+	2.67937i	−0.294357	+	0.0864311i
$962$		0			0
$963$	91.4987	+	13.1555i	2.94850	+	0.423931i
$964$		0			0
$965$	17.9414	−	15.5037i	0.577554	−	0.499083i
$966$		0			0
$967$		−	27.4976i		−	0.884263i	−0.896950	−	0.442131i	$-0.854223\pi$
$967$		−	27.4976i		−	0.884263i	0.896950	−	0.442131i	$-0.145777\pi$
$968$		0			0
$969$	−0.977219	+	6.79671i	−0.0313928	+	0.218342i
$970$		0			0
$971$	29.6099	−	8.69426i	0.950228	−	0.279012i	0.230346	−	0.973109i	$-0.426014\pi$
$971$	29.6099	−	8.69426i	0.950228	−	0.279012i	0.719882	+	0.694097i	$0.244196\pi$
$972$		0			0
$973$	−38.2522	+	33.1458i	−1.22631	+	1.06260i
$974$		0			0
$975$	−9.30396	+	20.2274i	−0.297965	+	0.647797i
$976$		0			0
$977$	−2.42375	+	3.77143i	−0.0775426	+	0.120659i	−0.877859	−	0.478920i	$-0.841029\pi$
$977$	−2.42375	+	3.77143i	−0.0775426	+	0.120659i	0.800316	+	0.599578i	$0.204665\pi$
$978$		0			0
$979$	11.8550	−	13.6814i	0.378889	−	0.437261i
$980$		0			0
$981$	−21.3224	−	148.301i	−0.680773	−	4.73488i
$982$		0			0
$983$	18.0156	−	8.22745i	0.574609	−	0.262415i	−0.106846	−	0.994276i	$-0.534075\pi$
$983$	18.0156	−	8.22745i	0.574609	−	0.262415i	0.681454	+	0.731861i	$0.261348\pi$
$984$		0			0
$985$	10.4243	+	35.6808i	0.332145	+	1.13688i
$986$		0			0
$987$	−18.1856	−	28.2974i	−0.578854	−	0.900715i
$988$		0			0
$989$	0.188293	+	0.0126335i	0.00598736	+	0.000401721i
$990$		0			0
$991$	−1.84212	+	1.18386i	−0.0585170	+	0.0376066i	−0.569572	−	0.821941i	$-0.692891\pi$
$991$	−1.84212	+	1.18386i	−0.0585170	+	0.0376066i	0.511055	+	0.859548i	$0.329255\pi$
$992$		0			0
$993$	83.3305	+	38.0558i	2.64441	+	1.20766i
$994$		0			0
$995$	−10.6842	+	23.3114i	−0.338711	+	0.739019i
$996$		0			0
$997$	10.7521	−	1.54591i	0.340521	−	0.0489595i	0.0300668	−	0.999548i	$-0.490428\pi$
$997$	10.7521	−	1.54591i	0.340521	−	0.0489595i	0.310454	+	0.950588i	$0.399519\pi$
$998$		0			0
$999$	115.830	−	133.675i	3.66471	−	4.22930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.s.a.449.1	yes	120
5.4	even	2	inner	460.2.s.a.449.12	yes	120
23.2	even	11	inner	460.2.s.a.209.12	yes	120
115.94	even	22	inner	460.2.s.a.209.1	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.s.a.209.1	✓	120	115.94	even	22	inner
460.2.s.a.209.12	yes	120	23.2	even	11	inner
460.2.s.a.449.1	yes	120	1.1	even	1	trivial
460.2.s.a.449.12	yes	120	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.24344 - 0.466336i) q^{3} +(-1.87946 - 1.21146i) q^{5} +(3.45164 - 2.99087i) q^{7} +(7.42393 + 2.17986i) q^{9} +O(q^{10})\)	\(q+(-3.24344 - 0.466336i) q^{3} +(-1.87946 - 1.21146i) q^{5} +(3.45164 - 2.99087i) q^{7} +(7.42393 + 2.17986i) q^{9} +(-2.75398 - 1.76988i) q^{11} +(-1.02701 - 0.889909i) q^{13} +(5.53096 + 4.80575i) q^{15} +(-4.62683 + 2.11300i) q^{17} +(-0.171142 + 0.374750i) q^{19} +(-12.5899 + 8.09106i) q^{21} +(-4.78206 + 0.363201i) q^{23} +(2.06473 + 4.55378i) q^{25} +(-14.1205 - 6.44861i) q^{27} +(1.72921 + 3.78644i) q^{29} +(-0.905801 - 6.29999i) q^{31} +(8.10702 + 7.02477i) q^{33} +(-10.1105 + 1.43968i) q^{35} +(-3.21016 + 10.9328i) q^{37} +(2.91604 + 3.36529i) q^{39} +(-1.44448 + 0.424138i) q^{41} +(-0.0389495 - 0.00560009i) q^{43} +(-11.3122 - 13.0908i) q^{45} +2.24762i q^{47} +(1.97236 - 13.7180i) q^{49} +(15.9922 - 4.69573i) q^{51} +(3.04939 - 2.64231i) q^{53} +(3.03186 + 6.66276i) q^{55} +(0.729849 - 1.13567i) q^{57} +(0.959993 - 1.10789i) q^{59} +(0.685440 + 4.76734i) q^{61} +(32.1444 - 14.6799i) q^{63} +(0.852133 + 2.91673i) q^{65} +(-0.149361 - 0.232410i) q^{67} +(15.6797 + 1.05203i) q^{69} +(-10.4268 + 6.70088i) q^{71} +(-10.5868 - 4.83484i) q^{73} +(-4.57323 - 15.7327i) q^{75} +(-14.7992 + 2.12781i) q^{77} +(-1.78449 + 2.05941i) q^{79} +(23.2645 + 14.9512i) q^{81} +(1.18219 - 4.02618i) q^{83} +(11.2558 + 1.63392i) q^{85} +(-3.84282 - 13.0875i) q^{87} +(-0.786991 + 5.47364i) q^{89} -6.20647 q^{91} +20.8560i q^{93} +(0.775649 - 0.496994i) q^{95} +(-0.0232544 - 0.0791971i) q^{97} +(-16.5873 - 19.1428i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{9}+O(q^{10}) \) 120 * q + 20 * q^9	\( 120 q + 20 q^{9} - 4 q^{11} + 9 q^{15} + 8 q^{19} + 14 q^{25} + 10 q^{29} - 18 q^{31} + 10 q^{35} - 60 q^{39} + 2 q^{41} - 2 q^{45} - 28 q^{49} + 24 q^{51} + 6 q^{55} - 36 q^{61} + 39 q^{65} + 118 q^{69} - 76 q^{71} + 83 q^{75} + 64 q^{79} - 160 q^{81} + 38 q^{85} - 48 q^{89} - 80 q^{91} + 21 q^{95} - 142 q^{99}+O(q^{100}) \) 120 * q + 20 * q^9 - 4 * q^11 + 9 * q^15 + 8 * q^19 + 14 * q^25 + 10 * q^29 - 18 * q^31 + 10 * q^35 - 60 * q^39 + 2 * q^41 - 2 * q^45 - 28 * q^49 + 24 * q^51 + 6 * q^55 - 36 * q^61 + 39 * q^65 + 118 * q^69 - 76 * q^71 + 83 * q^75 + 64 * q^79 - 160 * q^81 + 38 * q^85 - 48 * q^89 - 80 * q^91 + 21 * q^95 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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