LMFDB - Embedded newform 819.2.s.g.289.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [819,2,Mod(289,819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(819, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("819.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,44,0,0,4,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.17
Character	$\chi$	$=$	819.289
Dual form			819.2.s.g.802.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.37301 q^{2} +3.63116 q^{4} +(-0.794473 + 1.37607i) q^{5} +(2.03905 - 1.68590i) q^{7} +3.87075 q^{8} +(-1.88529 + 3.26542i) q^{10} +(1.64114 - 2.84254i) q^{11} +(3.29459 + 1.46482i) q^{13} +(4.83869 - 4.00066i) q^{14} +1.92300 q^{16} -5.95318 q^{17} +(3.57521 + 6.19244i) q^{19} +(-2.88486 + 4.99672i) q^{20} +(3.89444 - 6.74536i) q^{22} +5.54299 q^{23} +(1.23763 + 2.14363i) q^{25} +(7.81807 + 3.47603i) q^{26} +(7.40413 - 6.12178i) q^{28} +(-3.68065 - 6.37507i) q^{29} +(-4.24807 - 7.35787i) q^{31} -3.17821 q^{32} -14.1269 q^{34} +(0.699942 + 4.14528i) q^{35} -2.55484 q^{37} +(8.48399 + 14.6947i) q^{38} +(-3.07521 + 5.32642i) q^{40} +(1.54466 + 2.67543i) q^{41} +(-5.36917 + 9.29968i) q^{43} +(5.95924 - 10.3217i) q^{44} +13.1535 q^{46} +(-4.29375 + 7.43700i) q^{47} +(1.31547 - 6.87528i) q^{49} +(2.93690 + 5.08685i) q^{50} +(11.9632 + 5.31900i) q^{52} +(-5.97827 - 10.3547i) q^{53} +(2.60768 + 4.51664i) q^{55} +(7.89267 - 6.52571i) q^{56} +(-8.73420 - 15.1281i) q^{58} +1.21539 q^{59} +(-0.319227 - 0.552917i) q^{61} +(-10.0807 - 17.4603i) q^{62} -11.3879 q^{64} +(-4.63315 + 3.36981i) q^{65} +(-0.682078 + 1.18139i) q^{67} -21.6170 q^{68} +(1.66097 + 9.83677i) q^{70} +(-1.19321 + 2.06670i) q^{71} +(-0.309169 - 0.535496i) q^{73} -6.06265 q^{74} +(12.9822 + 22.4858i) q^{76} +(-1.44587 - 8.56288i) q^{77} +(7.41828 - 12.8488i) q^{79} +(-1.52777 + 2.64618i) q^{80} +(3.66549 + 6.34882i) q^{82} -10.1913 q^{83} +(4.72964 - 8.19198i) q^{85} +(-12.7411 + 22.0682i) q^{86} +(6.35245 - 11.0028i) q^{88} -8.27717 q^{89} +(9.18738 - 2.56750i) q^{91} +20.1275 q^{92} +(-10.1891 + 17.6480i) q^{94} -11.3616 q^{95} +(0.831568 - 1.44032i) q^{97} +(3.12162 - 16.3151i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) $ 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.37301			1.67797			0.838985	−	0.544155i	$-0.183150\pi$
$2$	2.37301			1.67797			0.838985	+	0.544155i	$0.183150\pi$
$3$		0			0
$3$		0			0
$4$	3.63116			1.81558
$5$	−0.794473	+	1.37607i	−0.355299	+	0.615396i	−0.987169	−	0.159678i	$-0.948954\pi$
$5$	−0.794473	+	1.37607i	−0.355299	+	0.615396i	0.631870	+	0.775074i	$0.282288\pi$
$6$		0			0
$7$	2.03905	−	1.68590i	0.770689	−	0.637211i
$7$	2.03905	−	1.68590i	0.770689	−	0.637211i
$8$	3.87075			1.36852
$9$		0			0
$10$	−1.88529	+	3.26542i	−0.596181	+	1.03262i
$11$	1.64114	−	2.84254i	0.494822	−	0.857057i	−0.505160	−	0.863026i	$-0.668566\pi$
$11$	1.64114	−	2.84254i	0.494822	−	0.857057i	0.999982	+	0.00596843i	$0.00189982\pi$
$12$		0			0
$13$	3.29459	+	1.46482i	0.913754	+	0.406269i
$13$	3.29459	+	1.46482i	0.913754	+	0.406269i
$14$	4.83869	−	4.00066i	1.29319	−	1.06922i
$15$		0			0
$16$	1.92300			0.480751
$17$	−5.95318			−1.44386			−0.721929	−	0.691967i	$-0.756744\pi$
$17$	−5.95318			−1.44386			−0.721929	+	0.691967i	$0.756744\pi$
$18$		0			0
$19$	3.57521	+	6.19244i	0.820209	+	1.42064i	0.905526	+	0.424290i	$0.139476\pi$
$19$	3.57521	+	6.19244i	0.820209	+	1.42064i	−0.0853172	+	0.996354i	$0.527190\pi$
$20$	−2.88486	+	4.99672i	−0.645074	+	1.11730i
$21$		0			0
$22$	3.89444	−	6.74536i	0.830296	−	1.43812i
$23$	5.54299			1.15579			0.577896	−	0.816110i	$-0.303874\pi$
$23$	5.54299			1.15579			0.577896	+	0.816110i	$0.303874\pi$
$24$		0			0
$25$	1.23763	+	2.14363i	0.247525	+	0.428726i
$26$	7.81807	+	3.47603i	1.53325	+	0.681706i
$27$		0			0
$28$	7.40413	−	6.12178i	1.39925	−	1.15691i
$29$	−3.68065	−	6.37507i	−0.683479	−	1.18382i	−0.973912	−	0.226925i	$-0.927133\pi$
$29$	−3.68065	−	6.37507i	−0.683479	−	1.18382i	0.290433	−	0.956895i	$-0.406201\pi$
$30$		0			0
$31$	−4.24807	−	7.35787i	−0.762976	−	1.32151i	−0.941310	−	0.337542i	$-0.890404\pi$
$31$	−4.24807	−	7.35787i	−0.762976	−	1.32151i	0.178335	−	0.983970i	$-0.442929\pi$
$32$	−3.17821			−0.561833
$33$		0			0
$34$	−14.1269			−2.42275
$35$	0.699942	+	4.14528i	0.118312	+	0.700680i
$36$		0			0
$37$	−2.55484			−0.420013			−0.210006	−	0.977700i	$-0.567348\pi$
$37$	−2.55484			−0.420013			−0.210006	+	0.977700i	$0.567348\pi$
$38$	8.48399	+	14.6947i	1.37629	+	2.38380i
$39$		0			0
$40$	−3.07521	+	5.32642i	−0.486233	+	0.842181i
$41$	1.54466	+	2.67543i	0.241236	+	0.417832i	0.961067	−	0.276317i	$-0.0891140\pi$
$41$	1.54466	+	2.67543i	0.241236	+	0.417832i	−0.719831	+	0.694149i	$0.755781\pi$
$42$		0			0
$43$	−5.36917	+	9.29968i	−0.818791	+	1.41819i	0.0877830	+	0.996140i	$0.472022\pi$
$43$	−5.36917	+	9.29968i	−0.818791	+	1.41819i	−0.906574	+	0.422048i	$0.861312\pi$
$44$	5.95924	−	10.3217i	0.898390	−	1.55606i
$45$		0			0
$46$	13.1535			1.93938
$47$	−4.29375	+	7.43700i	−0.626308	+	1.08480i	0.361978	+	0.932186i	$0.382101\pi$
$47$	−4.29375	+	7.43700i	−0.626308	+	1.08480i	−0.988286	+	0.152611i	$0.951232\pi$
$48$		0			0
$49$	1.31547	−	6.87528i	0.187925	−	0.982183i
$50$	2.93690	+	5.08685i	0.415340	+	0.719389i
$51$		0			0
$52$	11.9632	+	5.31900i	1.65899	+	0.737613i
$53$	−5.97827	−	10.3547i	−0.821179	−	1.42232i	−0.904805	−	0.425827i	$-0.859983\pi$
$53$	−5.97827	−	10.3547i	−0.821179	−	1.42232i	0.0836255	−	0.996497i	$-0.473350\pi$
$54$		0			0
$55$	2.60768	+	4.51664i	0.351620	+	0.609023i
$56$	7.89267	−	6.52571i	1.05470	−	0.872035i
$57$		0			0
$58$	−8.73420	−	15.1281i	−1.14686	−	1.98641i
$59$	1.21539			0.158231			0.0791154	−	0.996865i	$-0.474790\pi$
$59$	1.21539			0.158231			0.0791154	+	0.996865i	$0.474790\pi$
$60$		0			0
$61$	−0.319227	−	0.552917i	−0.0408728	−	0.0707938i	0.844865	−	0.534979i	$-0.179681\pi$
$61$	−0.319227	−	0.552917i	−0.0408728	−	0.0707938i	−0.885738	+	0.464185i	$0.846347\pi$
$62$	−10.0807	−	17.4603i	−1.28025	−	2.21746i
$63$		0			0
$64$	−11.3879			−1.42349
$65$	−4.63315	+	3.36981i	−0.574672	+	0.417973i
$66$		0			0
$67$	−0.682078	+	1.18139i	−0.0833291	+	0.144330i	−0.904678	−	0.426096i	$-0.859889\pi$
$67$	−0.682078	+	1.18139i	−0.0833291	+	0.144330i	0.821349	+	0.570426i	$0.193222\pi$
$68$	−21.6170			−2.62144
$69$		0			0
$70$	1.66097	+	9.83677i	0.198524	+	1.17572i
$71$	−1.19321	+	2.06670i	−0.141608	+	0.245272i	−0.928102	−	0.372325i	$-0.878561\pi$
$71$	−1.19321	+	2.06670i	−0.141608	+	0.245272i	0.786494	+	0.617598i	$0.211894\pi$
$72$		0			0
$73$	−0.309169	−	0.535496i	−0.0361855	−	0.0626751i	0.847366	−	0.531010i	$-0.178187\pi$
$73$	−0.309169	−	0.535496i	−0.0361855	−	0.0626751i	−0.883551	+	0.468335i	$0.844854\pi$
$74$	−6.06265			−0.704768
$75$		0			0
$76$	12.9822	+	22.4858i	1.48916	+	2.57929i
$77$	−1.44587	−	8.56288i	−0.164772	−	0.975831i
$78$		0			0
$79$	7.41828	−	12.8488i	0.834622	−	1.44561i	−0.0597162	−	0.998215i	$-0.519020\pi$
$79$	7.41828	−	12.8488i	0.834622	−	1.44561i	0.894338	−	0.447392i	$-0.147647\pi$
$80$	−1.52777	+	2.64618i	−0.170810	+	0.295852i
$81$		0			0
$82$	3.66549	+	6.34882i	0.404786	+	0.701110i
$83$	−10.1913			−1.11864			−0.559319	−	0.828953i	$-0.688937\pi$
$83$	−10.1913			−1.11864			−0.559319	+	0.828953i	$0.688937\pi$
$84$		0			0
$85$	4.72964	−	8.19198i	0.513002	−	0.888545i
$86$	−12.7411	+	22.0682i	−1.37391	+	2.37967i
$87$		0			0
$88$	6.35245	−	11.0028i	0.677173	−	1.17290i
$89$	−8.27717			−0.877379			−0.438689	−	0.898639i	$-0.644557\pi$
$89$	−8.27717			−0.877379			−0.438689	+	0.898639i	$0.644557\pi$
$90$		0			0
$91$	9.18738	−	2.56750i	0.963099	−	0.269147i
$92$	20.1275			2.09843
$93$		0			0
$94$	−10.1891	+	17.6480i	−1.05093	+	1.82026i
$95$	−11.3616			−1.16568
$96$		0			0
$97$	0.831568	−	1.44032i	0.0844329	−	0.146242i	−0.820717	−	0.571336i	$-0.806425\pi$
$97$	0.831568	−	1.44032i	0.0844329	−	0.146242i	0.905149	+	0.425094i	$0.139759\pi$
$98$	3.12162	−	16.3151i	0.315331	−	1.64807i
$99$		0			0
$100$	4.49402	+	7.78387i	0.449402	+	0.778387i
$101$	0.0969105	−	0.167854i	0.00964296	−	0.0167021i	−0.861164	−	0.508328i	$-0.830264\pi$
$101$	0.0969105	−	0.167854i	0.00964296	−	0.0167021i	0.870807	+	0.491626i	$0.163597\pi$
$102$		0			0
$103$	1.31879	−	2.28421i	0.129944	−	0.225070i	−0.793710	−	0.608296i	$-0.791853\pi$
$103$	1.31879	−	2.28421i	0.129944	−	0.225070i	0.923655	+	0.383225i	$0.125187\pi$
$104$	12.7525	+	5.66997i	1.25049	+	0.555986i
$105$		0			0
$106$	−14.1865	−	24.5717i	−1.37791	−	2.38662i
$107$	−3.61628			−0.349599			−0.174800	−	0.984604i	$-0.555928\pi$
$107$	−3.61628			−0.349599			−0.174800	+	0.984604i	$0.555928\pi$
$108$		0			0
$109$	−0.193567	−	0.335267i	−0.0185403	−	0.0321128i	0.856606	−	0.515970i	$-0.172569\pi$
$109$	−0.193567	−	0.335267i	−0.0185403	−	0.0321128i	−0.875147	+	0.483858i	$0.839235\pi$
$110$	6.18805	+	10.7180i	0.590007	+	1.02192i
$111$		0			0
$112$	3.92111	−	3.24200i	0.370510	−	0.306340i
$113$	5.11211	−	8.85443i	0.480907	−	0.832955i	−0.518853	−	0.854863i	$-0.673641\pi$
$113$	5.11211	−	8.85443i	0.480907	−	0.832955i	0.999760	+	0.0219083i	$0.00697418\pi$
$114$		0			0
$115$	−4.40375	+	7.62752i	−0.410652	+	0.711270i
$116$	−13.3650	−	23.1489i	−1.24091	−	2.14932i
$117$		0			0
$118$	2.88414			0.265507
$119$	−12.1389	+	10.0365i	−1.11277	+	0.920042i
$120$		0			0
$121$	0.113320	+	0.196276i	0.0103018	+	0.0178433i
$122$	−0.757528	−	1.31208i	−0.0685833	−	0.118790i
$123$		0			0
$124$	−15.4254	−	26.7176i	−1.38524	−	2.39931i
$125$	−11.8778			−1.06238
$126$		0			0
$127$	2.95916	+	5.12542i	0.262583	+	0.454807i	0.966928	−	0.255051i	$-0.0820923\pi$
$127$	2.95916	+	5.12542i	0.262583	+	0.454807i	−0.704345	+	0.709858i	$0.748759\pi$
$128$	−20.6672			−1.82674
$129$		0			0
$130$	−10.9945	+	7.99658i	−0.964282	+	0.701347i
$131$	0.623862	−	1.08056i	0.0545071	−	0.0944090i	−0.837484	−	0.546461i	$-0.815975\pi$
$131$	0.623862	−	1.08056i	0.0545071	−	0.0944090i	0.891991	+	0.452052i	$0.149308\pi$
$132$		0			0
$133$	17.7299	+	6.59927i	1.53738	+	0.572229i
$134$	−1.61858	+	2.80346i	−0.139824	+	0.242182i
$135$		0			0
$136$	−23.0433			−1.97595
$137$	1.04945			0.0896607			0.0448304	−	0.998995i	$-0.485725\pi$
$137$	1.04945			0.0896607			0.0448304	+	0.998995i	$0.485725\pi$
$138$		0			0
$139$	−1.79256	+	3.10480i	−0.152043	+	0.263346i	−0.931978	−	0.362514i	$-0.881918\pi$
$139$	−1.79256	+	3.10480i	−0.152043	+	0.263346i	0.779936	+	0.625860i	$0.215252\pi$
$140$	2.54160	+	15.0522i	0.214805	+	1.27214i
$141$		0			0
$142$	−2.83149	+	4.90429i	−0.237614	+	0.411559i
$143$	9.57069	−	6.96101i	0.800341	−	0.582109i
$144$		0			0
$145$	11.6967			0.971357
$146$	−0.733659	−	1.27074i	−0.0607181	−	0.105167i
$147$		0			0
$148$	−9.27702			−0.762567
$149$	11.2765	+	19.5315i	0.923806	+	1.60008i	0.793470	+	0.608609i	$0.208272\pi$
$149$	11.2765	+	19.5315i	0.923806	+	1.60008i	0.130336	+	0.991470i	$0.458394\pi$
$150$		0			0
$151$	−7.36849	−	12.7626i	−0.599639	−	1.03861i	−0.992874	−	0.119167i	$-0.961977\pi$
$151$	−7.36849	−	12.7626i	−0.599639	−	1.03861i	0.393235	−	0.919438i	$-0.371356\pi$
$152$	13.8388	+	23.9694i	1.12247	+	1.94418i
$153$		0			0
$154$	−3.43105	−	20.3198i	−0.276482	−	1.63741i
$155$	13.4999			1.08434
$156$		0			0
$157$	6.63722	+	11.4960i	0.529708	+	0.917481i	0.999399	+	0.0346506i	$0.0110318\pi$
$157$	6.63722	+	11.4960i	0.529708	+	0.917481i	−0.469691	+	0.882831i	$0.655635\pi$
$158$	17.6036	−	30.4904i	1.40047	−	2.42568i
$159$		0			0
$160$	2.52500	−	4.37342i	0.199619	−	0.345750i
$161$	11.3024	−	9.34493i	0.890757	−	0.736484i
$162$		0			0
$163$	2.40964	+	4.17362i	0.188738	+	0.326904i	0.944830	−	0.327562i	$-0.106227\pi$
$163$	2.40964	+	4.17362i	0.188738	+	0.326904i	−0.756092	+	0.654466i	$0.772894\pi$
$164$	5.60892	+	9.71493i	0.437983	+	0.758608i
$165$		0			0
$166$	−24.1840			−1.87704
$167$	−4.56029	−	7.89865i	−0.352886	−	0.611216i	0.633868	−	0.773441i	$-0.281466\pi$
$167$	−4.56029	−	7.89865i	−0.352886	−	0.611216i	−0.986754	+	0.162225i	$0.948133\pi$
$168$		0			0
$169$	8.70859	+	9.65197i	0.669892	+	0.742459i
$170$	11.2235	−	19.4396i	0.860801	−	1.49095i
$171$		0			0
$172$	−19.4963	+	33.7686i	−1.48658	+	2.57483i
$173$	7.84037	+	13.5799i	0.596092	+	1.03246i	0.993392	+	0.114773i	$0.0366140\pi$
$173$	7.84037	+	13.5799i	0.596092	+	1.03246i	−0.397300	+	0.917689i	$0.630053\pi$
$174$		0			0
$175$	6.13754	+	2.28446i	0.463954	+	0.172689i
$176$	3.15592	−	5.46621i	0.237886	−	0.412031i
$177$		0			0
$178$	−19.6418			−1.47221
$179$	−5.05568	+	8.75670i	−0.377879	+	0.654506i	−0.990753	−	0.135674i	$-0.956680\pi$
$179$	−5.05568	+	8.75670i	−0.377879	+	0.654506i	0.612874	+	0.790181i	$0.290013\pi$
$180$		0			0
$181$	−16.7897			−1.24797			−0.623983	−	0.781438i	$-0.714487\pi$
$181$	−16.7897			−1.24797			−0.623983	+	0.781438i	$0.714487\pi$
$182$	21.8017	−	6.09269i	1.61605	−	0.451620i
$183$		0			0
$184$	21.4555			1.58172
$185$	2.02975	−	3.51563i	0.149230	−	0.258474i
$186$		0			0
$187$	−9.77000	+	16.9221i	−0.714453	+	1.23747i
$188$	−15.5913	+	27.0049i	−1.13711	+	1.96954i
$189$		0			0
$190$	−26.9612			−1.95597
$191$	9.45382	+	16.3745i	0.684055	+	1.18482i	0.973733	+	0.227693i	$0.0731183\pi$
$191$	9.45382	+	16.3745i	0.684055	+	1.18482i	−0.289678	+	0.957124i	$0.593548\pi$
$192$		0			0
$193$	3.92508	−	6.79844i	0.282534	−	0.489362i	−0.689475	−	0.724310i	$-0.742158\pi$
$193$	3.92508	−	6.79844i	0.282534	−	0.489362i	0.972008	+	0.234947i	$0.0754918\pi$
$194$	1.97332	−	3.41788i	0.141676	−	0.245390i
$195$		0			0
$196$	4.77669	−	24.9653i	0.341192	−	1.78323i
$197$	12.5419	+	21.7232i	0.893572	+	1.54771i	0.835562	+	0.549396i	$0.185142\pi$
$197$	12.5419	+	21.7232i	0.893572	+	1.54771i	0.0580100	+	0.998316i	$0.481524\pi$
$198$		0			0
$199$	−7.78382			−0.551780			−0.275890	−	0.961189i	$-0.588973\pi$
$199$	−7.78382			−0.551780			−0.275890	+	0.961189i	$0.588973\pi$
$200$	4.79055	+	8.29747i	0.338743	+	0.586720i
$201$		0			0
$202$	0.229969	−	0.398319i	0.0161806	−	0.0280256i
$203$	−18.2528	−	6.79389i	−1.28109	−	0.476837i
$204$		0			0
$205$	−4.90877			−0.342843
$206$	3.12950	−	5.42046i	0.218043	−	0.377661i
$207$		0			0
$208$	6.33550	+	2.81686i	0.439288	+	0.195314i
$209$	23.4697			1.62343
$210$		0			0
$211$	1.17458	+	2.03443i	0.0808614	+	0.140056i	0.903620	−	0.428335i	$-0.140900\pi$
$211$	1.17458	+	2.03443i	0.0808614	+	0.140056i	−0.822759	+	0.568391i	$0.807566\pi$
$212$	−21.7081	−	37.5995i	−1.49092	−	2.58234i
$213$		0			0
$214$	−8.58147			−0.586617
$215$	−8.53132	−	14.7767i	−0.581831	−	1.00776i
$216$		0			0
$217$	−21.0667	−	7.84126i	−1.43010	−	0.532299i
$218$	−0.459335	−	0.795591i	−0.0311101	−	0.0538842i
$219$		0			0
$220$	9.46891	+	16.4006i	0.638394	+	1.10573i
$221$	−19.6133	−	8.72035i	−1.31933	−	0.586594i
$222$		0			0
$223$	−5.78913	−	10.0271i	−0.387669	−	0.671462i	0.604467	−	0.796630i	$-0.293386\pi$
$223$	−5.78913	−	10.0271i	−0.387669	−	0.671462i	−0.992136	+	0.125168i	$0.960053\pi$
$224$	−6.48053	+	5.35814i	−0.432998	+	0.358006i
$225$		0			0
$226$	12.1311	−	21.0116i	0.806947	−	1.39767i
$227$	12.9795			0.861479			0.430739	−	0.902476i	$-0.358253\pi$
$227$	12.9795			0.861479			0.430739	+	0.902476i	$0.358253\pi$
$228$		0			0
$229$	9.63048	−	16.6805i	0.636400	−	1.10228i	−0.349817	−	0.936818i	$-0.613756\pi$
$229$	9.63048	−	16.6805i	0.636400	−	1.10228i	0.986217	−	0.165459i	$-0.0529105\pi$
$230$	−10.4501	+	18.1002i	−0.689061	+	1.19349i
$231$		0			0
$232$	−14.2469	−	24.6763i	−0.935353	−	1.62008i
$233$	6.25233	−	10.8294i	0.409604	−	0.709454i	−0.585242	−	0.810859i	$-0.699000\pi$
$233$	6.25233	−	10.8294i	0.409604	−	0.709454i	0.994845	+	0.101405i	$0.0323337\pi$
$234$		0			0
$235$	−6.82254	−	11.8170i	−0.445053	−	0.770855i
$236$	4.41329			0.287281
$237$		0			0
$238$	−28.8056	+	23.8166i	−1.86719	+	1.54380i
$239$	29.7431			1.92392			0.961961	−	0.273187i	$-0.0880776\pi$
$239$	29.7431			1.92392			0.961961	+	0.273187i	$0.0880776\pi$
$240$		0			0
$241$	16.1479			1.04018			0.520090	−	0.854112i	$-0.325898\pi$
$241$	16.1479			1.04018			0.520090	+	0.854112i	$0.325898\pi$
$242$	0.268909	+	0.465764i	0.0172861	+	0.0299404i
$243$		0			0
$244$	−1.15916	−	2.00773i	−0.0742079	−	0.128532i
$245$	8.41575	+	7.27240i	0.537662	+	0.464617i
$246$		0			0
$247$	2.70800	+	25.6386i	0.172306	+	1.63134i
$248$	−16.4432	−	28.4805i	−1.04415	−	1.80851i
$249$		0			0
$250$	−28.1860			−1.78264
$251$	9.80082	−	16.9755i	0.618622	−	1.07149i	−0.371115	−	0.928587i	$-0.621024\pi$
$251$	9.80082	−	16.9755i	0.618622	−	1.07149i	0.989737	−	0.142898i	$-0.0456422\pi$
$252$		0			0
$253$	9.09682	−	15.7561i	0.571912	−	0.990580i
$254$	7.02211	+	12.1626i	0.440606	+	0.763152i
$255$		0			0
$256$	−26.2675			−1.64172
$257$	−5.97902			−0.372961			−0.186481	−	0.982459i	$-0.559708\pi$
$257$	−5.97902			−0.372961			−0.186481	+	0.982459i	$0.559708\pi$
$258$		0			0
$259$	−5.20945	+	4.30720i	−0.323699	+	0.267637i
$260$	−16.8237	+	12.2363i	−1.04336	+	0.758864i
$261$		0			0
$262$	1.48043	−	2.56418i	0.0914612	−	0.158415i
$263$	−7.49612	+	12.9837i	−0.462231	+	0.800607i	−0.999072	−	0.0430764i	$-0.986284\pi$
$263$	−7.49612	+	12.9837i	−0.462231	+	0.800607i	0.536841	+	0.843683i	$0.319617\pi$
$264$		0			0
$265$	18.9983			1.16706
$266$	42.0731	+	15.6601i	2.57967	+	0.960183i
$267$		0			0
$268$	−2.47674	+	4.28983i	−0.151291	+	0.262043i
$269$	−10.2059			−0.622263			−0.311131	−	0.950367i	$-0.600708\pi$
$269$	−10.2059			−0.622263			−0.311131	+	0.950367i	$0.600708\pi$
$270$		0			0
$271$	5.93324			0.360419			0.180209	−	0.983628i	$-0.442322\pi$
$271$	5.93324			0.360419			0.180209	+	0.983628i	$0.442322\pi$
$272$	−11.4480			−0.694137
$273$		0			0
$274$	2.49036			0.150448
$275$	8.12447			0.489924
$276$		0			0
$277$	8.37533			0.503225			0.251612	−	0.967828i	$-0.419039\pi$
$277$	8.37533			0.503225			0.251612	+	0.967828i	$0.419039\pi$
$278$	−4.25375	+	7.36771i	−0.255123	+	0.441886i
$279$		0			0
$280$	2.70930	+	16.0453i	0.161912	+	0.958893i
$281$	−13.9797			−0.833958			−0.416979	−	0.908916i	$-0.636911\pi$
$281$	−13.9797			−0.833958			−0.416979	+	0.908916i	$0.636911\pi$
$282$		0			0
$283$	8.44102	−	14.6203i	0.501766	−	0.869085i	−0.498232	−	0.867044i	$-0.666017\pi$
$283$	8.44102	−	14.6203i	0.501766	−	0.869085i	0.999998	−	0.00204071i	$-0.000649577\pi$
$284$	−4.33274	+	7.50452i	−0.257101	+	0.445311i
$285$		0			0
$286$	22.7113	−	16.5185i	1.34295	−	0.976760i
$287$	7.66016	+	2.85120i	0.452165	+	0.168301i
$288$		0			0
$289$	18.4404			1.08473
$290$	27.7563			1.62991
$291$		0			0
$292$	−1.12264	−	1.94447i	−0.0656976	−	0.113792i
$293$	14.2012	−	24.5972i	0.829643	−	1.43698i	−0.0686755	−	0.997639i	$-0.521877\pi$
$293$	14.2012	−	24.5972i	0.829643	−	1.43698i	0.898319	−	0.439345i	$-0.144789\pi$
$294$		0			0
$295$	−0.965598	+	1.67246i	−0.0562193	+	0.0973746i
$296$	−9.88915			−0.574795
$297$		0			0
$298$	26.7592	+	46.3483i	1.55012	+	2.68488i
$299$	18.2618	+	8.11949i	1.05611	+	0.469562i
$300$		0			0
$301$	4.73032	+	28.0144i	0.272651	+	1.61472i
$302$	−17.4855	−	30.2857i	−1.00618	−	1.74275i
$303$		0			0
$304$	6.87514	+	11.9081i	0.394317	+	0.682976i
$305$	1.01447			0.0580883
$306$		0			0
$307$	23.5914			1.34643			0.673217	−	0.739445i	$-0.264912\pi$
$307$	23.5914			1.34643			0.673217	+	0.739445i	$0.264912\pi$
$308$	−5.25018	−	31.0932i	−0.299157	−	1.77170i
$309$		0			0
$310$	32.0353			1.81949
$311$	3.26084	+	5.64795i	0.184905	+	0.320266i	0.943545	−	0.331245i	$-0.107469\pi$
$311$	3.26084	+	5.64795i	0.184905	+	0.320266i	−0.758639	+	0.651511i	$0.774135\pi$
$312$		0			0
$313$	−7.81661	+	13.5388i	−0.441821	+	0.765256i	−0.997825	−	0.0659236i	$-0.979001\pi$
$313$	−7.81661	+	13.5388i	−0.441821	+	0.765256i	0.556004	+	0.831180i	$0.312334\pi$
$314$	15.7502	+	27.2801i	0.888834	+	1.53951i
$315$		0			0
$316$	26.9370	−	46.6562i	1.51532	−	2.62462i
$317$	−8.89819	+	15.4121i	−0.499772	+	0.865631i	−1.00000		0.000262972i	$-0.999916\pi$
$317$	−8.89819	+	15.4121i	−0.499772	+	0.865631i	0.500228	+	0.865894i	$0.333250\pi$
$318$		0			0
$319$	−24.1618			−1.35280
$320$	9.04739	−	15.6705i	0.505764	−	0.876009i
$321$		0			0
$322$	26.8208	−	22.1756i	1.49466	−	1.23580i
$323$	−21.2839	−	36.8647i	−1.18427	−	2.05121i
$324$		0			0
$325$	0.937427	+	8.87528i	0.0519991	+	0.492312i
$326$	5.71810	+	9.90404i	0.316696	+	0.548534i
$327$		0			0
$328$	5.97901	+	10.3559i	0.330135	+	0.571811i
$329$	3.78286	+	22.4033i	0.208556	+	1.23513i
$330$		0			0
$331$	−0.820913	−	1.42186i	−0.0451215	−	0.0781527i	0.842583	−	0.538567i	$-0.181034\pi$
$331$	−0.820913	−	1.42186i	−0.0451215	−	0.0781527i	−0.887704	+	0.460414i	$0.847701\pi$
$332$	−37.0062			−2.03098
$333$		0			0
$334$	−10.8216	−	18.7436i	−0.592131	−	1.02560i
$335$	−1.08379	−	1.87717i	−0.0592135	−	0.102561i
$336$		0			0
$337$	7.89772			0.430216			0.215108	−	0.976590i	$-0.430990\pi$
$337$	7.89772			0.430216			0.215108	+	0.976590i	$0.430990\pi$
$338$	20.6655	+	22.9042i	1.12406	+	1.24582i
$339$		0			0
$340$	17.1741	−	29.7464i	0.931395	−	1.61322i
$341$	−27.8867			−1.51015
$342$		0			0
$343$	−8.90874	−	16.2368i	−0.481027	−	0.876706i
$344$	−20.7827	+	35.9968i	−1.12053	+	1.94082i
$345$		0			0
$346$	18.6052	+	32.2252i	1.00022	+	1.73244i
$347$	5.52400			0.296544			0.148272	−	0.988947i	$-0.452629\pi$
$347$	5.52400			0.296544			0.148272	+	0.988947i	$0.452629\pi$
$348$		0			0
$349$	−4.98919	−	8.64153i	−0.267065	−	0.462570i	0.701037	−	0.713124i	$-0.252721\pi$
$349$	−4.98919	−	8.64153i	−0.267065	−	0.462570i	−0.968103	+	0.250554i	$0.919387\pi$
$350$	14.5644	+	5.42104i	0.778501	+	0.289767i
$351$		0			0
$352$	−5.21588	+	9.03417i	−0.278007	+	0.481523i
$353$	5.29640	−	9.17364i	0.281899	−	0.488264i	−0.689953	−	0.723854i	$-0.742369\pi$
$353$	5.29640	−	9.17364i	0.281899	−	0.488264i	0.971852	+	0.235590i	$0.0757023\pi$
$354$		0			0
$355$	−1.89595	−	3.28387i	−0.100626	−	0.174290i
$356$	−30.0557			−1.59295
$357$		0			0
$358$	−11.9972	+	20.7797i	−0.634070	+	1.09824i
$359$	10.4330	−	18.0706i	0.550635	−	0.953728i	−0.447594	−	0.894237i	$-0.647719\pi$
$359$	10.4330	−	18.0706i	0.550635	−	0.953728i	0.998229	−	0.0594908i	$-0.0189477\pi$
$360$		0			0
$361$	−16.0642	+	27.8241i	−0.845486	+	1.46442i
$362$	−39.8420			−2.09405
$363$		0			0
$364$	33.3609	−	9.32300i	1.74858	−	0.488658i
$365$	0.982504			0.0514266
$366$		0			0
$367$	4.84685	−	8.39499i	0.253003	−	0.438215i	−0.711348	−	0.702840i	$-0.751915\pi$
$367$	4.84685	−	8.39499i	0.253003	−	0.438215i	0.964351	+	0.264625i	$0.0852483\pi$
$368$	10.6592			0.555649
$369$		0			0
$370$	4.81661	−	8.34261i	0.250403	−	0.433712i
$371$	−29.6470	−	11.0349i	−1.53919	−	0.572906i
$372$		0			0
$373$	6.21589	+	10.7662i	0.321847	+	0.557455i	0.980869	−	0.194668i	$-0.0623631\pi$
$373$	6.21589	+	10.7662i	0.321847	+	0.557455i	−0.659022	+	0.752123i	$0.729030\pi$
$374$	−23.1843	+	40.1564i	−1.19883	+	2.07644i
$375$		0			0
$376$	−16.6201	+	28.7868i	−0.857114	+	1.48456i
$377$	−2.78787	−	26.3947i	−0.143582	−	1.35940i
$378$		0			0
$379$	−13.3427	−	23.1102i	−0.685368	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$379$	−13.3427	−	23.1102i	−0.685368	−	1.18709i	0.287953	−	0.957644i	$-0.407025\pi$
$380$	−41.2559			−2.11638
$381$		0			0
$382$	22.4340	+	38.8568i	1.14782	+	1.98809i
$383$	−1.28041	−	2.21774i	−0.0654260	−	0.113321i	0.831457	−	0.555589i	$-0.187507\pi$
$383$	−1.28041	−	2.21774i	−0.0654260	−	0.113321i	−0.896883	+	0.442268i	$0.854174\pi$
$384$		0			0
$385$	12.9318	+	4.81337i	0.659066	+	0.245312i
$386$	9.31424	−	16.1327i	0.474083	−	0.821135i
$387$		0			0
$388$	3.01956	−	5.23002i	0.153295	−	0.265514i
$389$	10.0916	+	17.4792i	0.511664	+	0.886228i	0.999909	+	0.0135213i	$0.00430410\pi$
$389$	10.0916	+	17.4792i	0.511664	+	0.886228i	−0.488244	+	0.872707i	$0.662363\pi$
$390$		0			0
$391$	−32.9984			−1.66880
$392$	5.09187	−	26.6125i	0.257178	−	1.34414i
$393$		0			0
$394$	29.7620	+	51.5492i	1.49939	+	2.59701i
$395$	11.7872	+	20.4161i	0.593081	+	1.02725i
$396$		0			0
$397$	2.85126	+	4.93853i	0.143101	+	0.247858i	0.928663	−	0.370925i	$-0.120959\pi$
$397$	2.85126	+	4.93853i	0.143101	+	0.247858i	−0.785562	+	0.618783i	$0.787626\pi$
$398$	−18.4711			−0.925871
$399$		0			0
$400$	2.37996	+	4.12221i	0.118998	+	0.206111i
$401$	−5.32871			−0.266103			−0.133051	−	0.991109i	$-0.542478\pi$
$401$	−5.32871			−0.266103			−0.133051	+	0.991109i	$0.542478\pi$
$402$		0			0
$403$	−3.21765	−	30.4638i	−0.160283	−	1.51751i
$404$	0.351898	−	0.609505i	0.0175076	−	0.0303240i
$405$		0			0
$406$	−43.3139	−	16.1219i	−2.14963	−	0.800118i
$407$	−4.19285	+	7.26222i	−0.207832	+	0.359975i
$408$		0			0
$409$	−21.6886			−1.07243			−0.536216	−	0.844081i	$-0.680147\pi$
$409$	−21.6886			−1.07243			−0.536216	+	0.844081i	$0.680147\pi$
$410$	−11.6485			−0.575280
$411$		0			0
$412$	4.78874	−	8.29435i	0.235924	−	0.408633i
$413$	2.47825	−	2.04904i	0.121947	−	0.100826i
$414$		0			0
$415$	8.09669	−	14.0239i	0.397451	−	0.688405i
$416$	−10.4709	−	4.65551i	−0.513377	−	0.228255i
$417$		0			0
$418$	55.6937			2.72407
$419$	18.0347	+	31.2369i	0.881050	+	1.52602i	0.850175	+	0.526501i	$0.176496\pi$
$419$	18.0347	+	31.2369i	0.881050	+	1.52602i	0.0308759	+	0.999523i	$0.490170\pi$
$420$		0			0
$421$	17.4314			0.849552			0.424776	−	0.905298i	$-0.360353\pi$
$421$	17.4314			0.849552			0.424776	+	0.905298i	$0.360353\pi$
$422$	2.78729	+	4.82772i	0.135683	+	0.235010i
$423$		0			0
$424$	−23.1404	−	40.0804i	−1.12380	−	1.94648i
$425$	−7.36781	−	12.7614i	−0.357391	−	0.619020i
$426$		0			0
$427$	−1.58308	−	0.589242i	−0.0766108	−	0.0285154i
$428$	−13.1313			−0.634726
$429$		0			0
$430$	−20.2449	−	35.0652i	−0.976295	−	1.69099i
$431$	−0.337428	+	0.584442i	−0.0162533	+	0.0281516i	−0.874038	−	0.485858i	$-0.838507\pi$
$431$	−0.337428	+	0.584442i	−0.0162533	+	0.0281516i	0.857784	+	0.514010i	$0.171840\pi$
$432$		0			0
$433$	9.80271	−	16.9788i	0.471088	−	0.815948i	−0.528365	−	0.849017i	$-0.677195\pi$
$433$	9.80271	−	16.9788i	0.471088	−	0.815948i	0.999453	+	0.0330689i	$0.0105281\pi$
$434$	−49.9914	−	18.6074i	−2.39966	−	0.893182i
$435$		0			0
$436$	−0.702871	−	1.21741i	−0.0336614	−	0.0583033i
$437$	19.8173	+	34.3246i	0.947992	+	1.64197i
$438$		0			0
$439$	−32.0250			−1.52847			−0.764236	−	0.644937i	$-0.776884\pi$
$439$	−32.0250			−1.52847			−0.764236	+	0.644937i	$0.776884\pi$
$440$	10.0937	+	17.4828i	0.481198	+	0.833459i
$441$		0			0
$442$	−46.5424	−	20.6935i	−2.21380	−	0.984287i
$443$	8.77986	−	15.2072i	0.417144	−	0.722514i	−0.578507	−	0.815677i	$-0.696364\pi$
$443$	8.77986	−	15.2072i	0.417144	−	0.722514i	0.995651	+	0.0931630i	$0.0296978\pi$
$444$		0			0
$445$	6.57599	−	11.3899i	0.311732	−	0.539935i
$446$	−13.7376	−	23.7943i	−0.650496	−	1.12669i
$447$		0			0
$448$	−23.2206	+	19.1989i	−1.09707	+	0.907063i
$449$	2.82841	−	4.89895i	0.133481	−	0.231196i	−0.791535	−	0.611123i	$-0.790718\pi$
$449$	2.82841	−	4.89895i	0.133481	−	0.231196i	0.925016	+	0.379928i	$0.124051\pi$
$450$		0			0
$451$	10.1400			0.477475
$452$	18.5629	−	32.1519i	0.873125	−	1.51230i
$453$		0			0
$454$	30.8004			1.44553
$455$	−3.76607	+	14.6823i	−0.176556	+	0.688315i
$456$		0			0
$457$	−5.90864			−0.276394			−0.138197	−	0.990405i	$-0.544131\pi$
$457$	−5.90864			−0.276394			−0.138197	+	0.990405i	$0.544131\pi$
$458$	22.8532	−	39.5829i	1.06786	−	1.84959i
$459$		0			0
$460$	−15.9907	+	27.6968i	−0.745571	+	1.29137i
$461$	19.0332	−	32.9664i	0.886463	−	1.53540i	0.0424358	−	0.999099i	$-0.486488\pi$
$461$	19.0332	−	32.9664i	0.886463	−	1.53540i	0.844027	−	0.536300i	$-0.180178\pi$
$462$		0			0
$463$	−35.4984			−1.64975			−0.824876	−	0.565314i	$-0.808755\pi$
$463$	−35.4984			−1.64975			−0.824876	+	0.565314i	$0.808755\pi$
$464$	−7.07790	−	12.2593i	−0.328583	−	0.569123i
$465$		0			0
$466$	14.8368	−	25.6981i	0.687302	−	1.19044i
$467$	0.127466	−	0.220777i	0.00589842	−	0.0102164i	−0.863061	−	0.505099i	$-0.831456\pi$
$467$	0.127466	−	0.220777i	0.00589842	−	0.0102164i	0.868960	+	0.494883i	$0.164789\pi$
$468$		0			0
$469$	0.600921	+	3.55884i	0.0277480	+	0.164332i
$470$	−16.1899	−	28.0418i	−0.746786	−	1.29347i
$471$		0			0
$472$	4.70449			0.216542
$473$	17.6231	+	30.5241i	0.810312	+	1.40350i
$474$		0			0
$475$	−8.84954	+	15.3279i	−0.406045	+	0.703290i
$476$	−44.0781	+	36.4441i	−2.02032	+	1.67041i
$477$		0			0
$478$	70.5806			3.22828
$479$	7.59913	−	13.1621i	0.347213	−	0.601390i	−0.638540	−	0.769588i	$-0.720461\pi$
$479$	7.59913	−	13.1621i	0.347213	−	0.601390i	0.985753	+	0.168198i	$0.0537948\pi$
$480$		0			0
$481$	−8.41713	−	3.74238i	−0.383788	−	0.170638i
$482$	38.3192			1.74539
$483$		0			0
$484$	0.411483	+	0.712709i	0.0187038	+	0.0323959i
$485$	1.32132	+	2.28859i	0.0599978	+	0.103919i
$486$		0			0
$487$	0.229080			0.0103806			0.00519030	−	0.999987i	$-0.498348\pi$
$487$	0.229080			0.0103806			0.00519030	+	0.999987i	$0.498348\pi$
$488$	−1.23565	−	2.14021i	−0.0559352	−	0.0968826i
$489$		0			0
$490$	19.9706	+	17.2575i	0.902181	+	0.779613i
$491$	−7.19778	−	12.4669i	−0.324831	−	0.562624i	0.656647	−	0.754198i	$-0.271974\pi$
$491$	−7.19778	−	12.4669i	−0.324831	−	0.562624i	−0.981478	+	0.191574i	$0.938641\pi$
$492$		0			0
$493$	21.9116	+	37.9519i	0.986847	+	1.70927i
$494$	6.42611	+	60.8405i	0.289124	+	2.73734i
$495$		0			0
$496$	−8.16906	−	14.1492i	−0.366801	−	0.635319i
$497$	1.05124	+	6.22574i	0.0471543	+	0.279263i
$498$		0			0
$499$	−6.68657	+	11.5815i	−0.299332	+	0.518458i	−0.975983	−	0.217845i	$-0.930097\pi$
$499$	−6.68657	+	11.5815i	−0.299332	+	0.518458i	0.676651	+	0.736304i	$0.263430\pi$
$500$	−43.1301			−1.92884
$501$		0			0
$502$	23.2574	−	40.2830i	1.03803	−	1.79792i
$503$	−5.78251	+	10.0156i	−0.257829	+	0.446574i	−0.965660	−	0.259808i	$-0.916341\pi$
$503$	−5.78251	+	10.0156i	−0.257829	+	0.446574i	0.707831	+	0.706382i	$0.249674\pi$
$504$		0			0
$505$	0.153986	+	0.266711i	0.00685227	+	0.0118685i
$506$	21.5868	−	37.3894i	0.959650	−	1.66216i
$507$		0			0
$508$	10.7452	+	18.6112i	0.476740	+	0.825739i
$509$	29.5436			1.30950			0.654748	−	0.755848i	$-0.272775\pi$
$509$	29.5436			1.30950			0.654748	+	0.755848i	$0.272775\pi$
$510$		0			0
$511$	−1.53320	−	0.570676i	−0.0678250	−	0.0252452i
$512$	−20.9987			−0.928019
$513$		0			0
$514$	−14.1883			−0.625817
$515$	2.09549	+	3.62949i	0.0923382	+	0.159935i
$516$		0			0
$517$	14.0933	+	24.4103i	0.619822	+	1.07356i
$518$	−12.3621	+	10.2210i	−0.543158	+	0.449086i
$519$		0			0
$520$	−17.9338	+	13.0437i	−0.786449	+	0.572004i
$521$	−8.38685	−	14.5265i	−0.367435	−	0.636416i	0.621729	−	0.783233i	$-0.286431\pi$
$521$	−8.38685	−	14.5265i	−0.367435	−	0.636416i	−0.989164	+	0.146817i	$0.953097\pi$
$522$		0			0
$523$	−40.2787			−1.76127			−0.880633	−	0.473799i	$-0.842882\pi$
$523$	−40.2787			−1.76127			−0.880633	+	0.473799i	$0.842882\pi$
$524$	2.26534	−	3.92369i	0.0989619	−	0.171407i
$525$		0			0
$526$	−17.7883	+	30.8103i	−0.775609	+	1.34339i
$527$	25.2895	+	43.8027i	1.10163	+	1.90808i
$528$		0			0
$529$	7.72469			0.335856
$530$	45.0831			1.95828
$531$		0			0
$532$	64.3801	+	23.9630i	2.79123	+	1.03893i
$533$	1.16999	+	11.0771i	0.0506778	+	0.479802i
$534$		0			0
$535$	2.87304	−	4.97625i	0.124212	−	0.215142i
$536$	−2.64016	+	4.57289i	−0.114037	+	0.197519i
$537$		0			0
$538$	−24.2186			−1.04414
$539$	−17.3844	−	15.0226i	−0.748798	−	0.647068i
$540$		0			0
$541$	2.65491	−	4.59844i	0.114144	−	0.197702i	−0.803294	−	0.595583i	$-0.796921\pi$
$541$	2.65491	−	4.59844i	0.114144	−	0.197702i	0.917437	+	0.397881i	$0.130254\pi$
$542$	14.0796			0.604772
$543$		0			0
$544$	18.9204			0.811207
$545$	0.615133			0.0263494
$546$		0			0
$547$	28.9584			1.23817			0.619085	−	0.785324i	$-0.287504\pi$
$547$	28.9584			1.23817			0.619085	+	0.785324i	$0.287504\pi$
$548$	3.81073			0.162786
$549$		0			0
$550$	19.2794			0.822077
$551$	26.3182	−	45.5844i	1.12119	−	1.94196i
$552$		0			0
$553$	−6.53561	−	38.7060i	−0.277923	−	1.64594i
$554$	19.8747			0.844395
$555$		0			0
$556$	−6.50906	+	11.2740i	−0.276046	+	0.478125i
$557$	5.76960	−	9.99324i	0.244466	−	0.423427i	−0.717516	−	0.696542i	$-0.754721\pi$
$557$	5.76960	−	9.99324i	0.244466	−	0.423427i	0.961981	+	0.273115i	$0.0880541\pi$
$558$		0			0
$559$	−31.3116	+	22.7737i	−1.32434	+	0.963225i
$560$	1.34599	+	7.97139i	0.0568785	+	0.336853i
$561$		0			0
$562$	−33.1739			−1.39936
$563$	−23.9625			−1.00990			−0.504949	−	0.863149i	$-0.668489\pi$
$563$	−23.9625			−1.00990			−0.504949	+	0.863149i	$0.668489\pi$
$564$		0			0
$565$	8.12286	+	14.0692i	0.341731	+	0.591896i
$566$	20.0306	−	34.6940i	0.841948	−	1.45830i
$567$		0			0
$568$	−4.61862	+	7.99969i	−0.193793	+	0.335659i
$569$	−0.632181			−0.0265024			−0.0132512	−	0.999912i	$-0.504218\pi$
$569$	−0.632181			−0.0265024			−0.0132512	+	0.999912i	$0.504218\pi$
$570$		0			0
$571$	−1.82039	−	3.15301i	−0.0761810	−	0.131949i	0.825418	−	0.564522i	$-0.190939\pi$
$571$	−1.82039	−	3.15301i	−0.0761810	−	0.131949i	−0.901599	+	0.432572i	$0.857606\pi$
$572$	34.7527	−	25.2765i	1.45308	−	1.05686i
$573$		0			0
$574$	18.1776	+	6.76592i	0.758719	+	0.282404i
$575$	6.86014	+	11.8821i	0.286088	+	0.495519i
$576$		0			0
$577$	2.63632	+	4.56623i	0.109751	+	0.190095i	0.915669	−	0.401932i	$-0.131661\pi$
$577$	2.63632	+	4.56623i	0.109751	+	0.190095i	−0.805918	+	0.592027i	$0.798328\pi$
$578$	43.7591			1.82014
$579$		0			0
$580$	42.4726			1.76358
$581$	−20.7805	+	17.1815i	−0.862122	+	0.712808i
$582$		0			0
$583$	−39.2447			−1.62535
$584$	−1.19672	−	2.07277i	−0.0495205	−	0.0857720i
$585$		0			0
$586$	33.6995	−	58.3693i	1.39212	−	2.41121i
$587$	−1.40954	−	2.44139i	−0.0581779	−	0.100767i	0.835470	−	0.549537i	$-0.185196\pi$
$587$	−1.40954	−	2.44139i	−0.0581779	−	0.100767i	−0.893648	+	0.448770i	$0.851862\pi$
$588$		0			0
$589$	30.3755	−	52.6118i	1.25160	−	2.16783i
$590$	−2.29137	+	3.96877i	−0.0943342	+	0.163392i
$591$		0			0
$592$	−4.91296			−0.201922
$593$	7.65704	−	13.2624i	0.314437	−	0.544621i	−0.664881	−	0.746949i	$-0.731518\pi$
$593$	7.65704	−	13.2624i	0.314437	−	0.544621i	0.979318	+	0.202329i	$0.0648510\pi$
$594$		0			0
$595$	−4.16688	−	24.6776i	−0.170826	−	1.01168i
$596$	40.9467	+	70.9218i	1.67724	+	2.90507i
$597$		0			0
$598$	43.3355	+	19.2676i	1.77212	+	0.787911i
$599$	−4.16303	−	7.21058i	−0.170097	−	0.294616i	0.768357	−	0.640022i	$-0.221075\pi$
$599$	−4.16303	−	7.21058i	−0.170097	−	0.294616i	−0.938453	+	0.345406i	$0.887741\pi$
$600$		0			0
$601$	−8.31185	−	14.3965i	−0.339047	−	0.587247i	0.645207	−	0.764008i	$-0.276771\pi$
$601$	−8.31185	−	14.3965i	−0.339047	−	0.587247i	−0.984254	+	0.176761i	$0.943438\pi$
$602$	11.2251	+	66.4784i	0.457500	+	2.70946i
$603$		0			0
$604$	−26.7562	−	46.3430i	−1.08869	−	1.88567i
$605$	−0.360118			−0.0146409
$606$		0			0
$607$	17.3656	+	30.0780i	0.704846	+	1.22083i	0.966747	+	0.255734i	$0.0823172\pi$
$607$	17.3656	+	30.0780i	0.704846	+	1.22083i	−0.261901	+	0.965095i	$0.584349\pi$
$608$	−11.3627	−	19.6809i	−0.460820	−	0.798164i
$609$		0			0
$610$	2.40734			0.0974704
$611$	−25.0400	+	18.2122i	−1.01301	+	0.736788i
$612$		0			0
$613$	−1.12628	+	1.95078i	−0.0454902	+	0.0787913i	−0.887874	−	0.460087i	$-0.847818\pi$
$613$	−1.12628	+	1.95078i	−0.0454902	+	0.0787913i	0.842384	+	0.538878i	$0.181152\pi$
$614$	55.9826			2.25927
$615$		0			0
$616$	−5.59660	−	33.1448i	−0.225493	−	1.33544i
$617$	−13.5484	+	23.4666i	−0.545439	+	0.944729i	0.453140	+	0.891440i	$0.350304\pi$
$617$	−13.5484	+	23.4666i	−0.545439	+	0.944729i	−0.998579	+	0.0532893i	$0.983029\pi$
$618$		0			0
$619$	16.6208	+	28.7880i	0.668045	+	1.15709i	0.978450	+	0.206484i	$0.0662020\pi$
$619$	16.6208	+	28.7880i	0.668045	+	1.15709i	−0.310405	+	0.950604i	$0.600465\pi$
$620$	49.0203			1.96870
$621$		0			0
$622$	7.73800	+	13.4026i	0.310266	+	0.537396i
$623$	−16.8776	+	13.9545i	−0.676186	+	0.559075i
$624$		0			0
$625$	3.24843	−	5.62645i	0.129937	−	0.225058i
$626$	−18.5489	+	32.1276i	−0.741362	+	1.28408i
$627$		0			0
$628$	24.1008	+	41.7438i	0.961727	+	1.66576i
$629$	15.2094			0.606439
$630$		0			0
$631$	−20.6922	+	35.8399i	−0.823743	+	1.42677i	0.0791326	+	0.996864i	$0.474785\pi$
$631$	−20.6922	+	35.8399i	−0.823743	+	1.42677i	−0.902876	+	0.429901i	$0.858548\pi$
$632$	28.7143	−	49.7347i	1.14220	−	1.97834i
$633$		0			0
$634$	−21.1155	+	36.5731i	−0.838602	+	1.45250i
$635$	−9.40389			−0.373182
$636$		0			0
$637$	14.4050	−	20.7243i	0.570747	−	0.821126i
$638$	−57.3362			−2.26996
$639$		0			0
$640$	16.4195	−	28.4394i	0.649038	−	1.12417i
$641$	−46.0633			−1.81939			−0.909695	−	0.415276i	$-0.863685\pi$
$641$	−46.0633			−1.81939			−0.909695	+	0.415276i	$0.863685\pi$
$642$		0			0
$643$	−16.6181	+	28.7834i	−0.655353	+	1.13510i	0.326452	+	0.945214i	$0.394147\pi$
$643$	−16.6181	+	28.7834i	−0.655353	+	1.13510i	−0.981805	+	0.189891i	$0.939187\pi$
$644$	41.0410	−	33.9329i	1.61724	−	1.33714i
$645$		0			0
$646$	−50.5068	−	87.4803i	−1.98716	−	3.44187i
$647$	2.98855	−	5.17631i	0.117492	−	0.203502i	−0.801281	−	0.598288i	$-0.795848\pi$
$647$	2.98855	−	5.17631i	0.117492	−	0.203502i	0.918773	+	0.394786i	$0.129181\pi$
$648$		0			0
$649$	1.99463	−	3.45480i	0.0782962	−	0.135613i
$650$	2.22452	+	21.0611i	0.0872529	+	0.826084i
$651$		0			0
$652$	8.74980	+	15.1551i	0.342669	+	0.593520i
$653$	23.8552			0.933527			0.466764	−	0.884382i	$-0.345420\pi$
$653$	23.8552			0.933527			0.466764	+	0.884382i	$0.345420\pi$
$654$		0			0
$655$	0.991282	+	1.71695i	0.0387326	+	0.0670868i
$656$	2.97039	+	5.14487i	0.115974	+	0.200873i
$657$		0			0
$658$	8.97675	+	53.1631i	0.349950	+	2.07251i
$659$	−13.1153	+	22.7163i	−0.510899	+	0.884902i	0.489022	+	0.872272i	$0.337354\pi$
$659$	−13.1153	+	22.7163i	−0.510899	+	0.884902i	−0.999920	+	0.0126308i	$0.995979\pi$
$660$		0			0
$661$	8.31040	−	14.3940i	0.323237	−	0.559863i	−0.657917	−	0.753091i	$-0.728562\pi$
$661$	8.31040	−	14.3940i	0.323237	−	0.559863i	0.981154	+	0.193227i	$0.0618955\pi$
$662$	−1.94803	−	3.37409i	−0.0757124	−	0.131138i
$663$		0			0
$664$	−39.4479			−1.53088
$665$	−23.1669	+	19.1546i	−0.898376	+	0.742783i
$666$		0			0
$667$	−20.4018	−	35.3369i	−0.789960	−	1.36825i
$668$	−16.5591	−	28.6813i	−0.640692	−	1.10971i
$669$		0			0
$670$	−2.57183	−	4.45454i	−0.0993585	−	0.172094i
$671$	−2.09558			−0.0808991
$672$		0			0
$673$	21.2726	+	36.8451i	0.819997	+	1.42028i	0.905684	+	0.423954i	$0.139358\pi$
$673$	21.2726	+	36.8451i	0.819997	+	1.42028i	−0.0856874	+	0.996322i	$0.527309\pi$
$674$	18.7414			0.721890
$675$		0			0
$676$	31.6223	+	35.0478i	1.21624	+	1.34799i
$677$	−5.90158	+	10.2218i	−0.226816	+	0.392857i	−0.956863	−	0.290540i	$-0.906165\pi$
$677$	−5.90158	+	10.2218i	−0.226816	+	0.392857i	0.730047	+	0.683397i	$0.239498\pi$
$678$		0			0
$679$	−0.732623	−	4.33882i	−0.0281155	−	0.166509i
$680$	18.3073	−	31.7091i	0.702052	−	1.21599i
$681$		0			0
$682$	−66.1753			−2.53398
$683$	20.6901			0.791685			0.395843	−	0.918318i	$-0.370453\pi$
$683$	20.6901			0.791685			0.395843	+	0.918318i	$0.370453\pi$
$684$		0			0
$685$	−0.833761	+	1.44412i	−0.0318564	+	0.0551768i
$686$	−21.1405	−	38.5301i	−0.807148	−	1.47109i
$687$		0			0
$688$	−10.3249	+	17.8833i	−0.393635	+	0.681795i
$689$	−4.52818	−	42.8715i	−0.172510	−	1.63327i
$690$		0			0
$691$	12.4210			0.472519			0.236259	−	0.971690i	$-0.424078\pi$
$691$	12.4210			0.472519			0.236259	+	0.971690i	$0.424078\pi$
$692$	28.4696	+	49.3108i	1.08225	+	1.87452i
$693$		0			0
$694$	13.1085			0.497592
$695$	−2.84828	−	4.93336i	−0.108041	−	0.187133i
$696$		0			0
$697$	−9.19565	−	15.9273i	−0.348310	−	0.603291i
$698$	−11.8394	−	20.5064i	−0.448127	−	0.776179i
$699$		0			0
$700$	22.2864	+	8.29525i	0.842346	+	0.313531i
$701$	35.6900			1.34799			0.673996	−	0.738735i	$-0.264577\pi$
$701$	35.6900			1.34799			0.673996	+	0.738735i	$0.264577\pi$
$702$		0			0
$703$	−9.13408	−	15.8207i	−0.344498	−	0.596688i
$704$	−18.6892	+	32.3706i	−0.704374	+	1.22001i
$705$		0			0
$706$	12.5684	−	21.7691i	0.473018	−	0.819291i
$707$	−0.0853796	−	0.505645i	−0.00321103	−	0.0190167i
$708$		0			0
$709$	15.5062	+	26.8574i	0.582346	+	1.00865i	0.995201	+	0.0978556i	$0.0311983\pi$
$709$	15.5062	+	26.8574i	0.582346	+	1.00865i	−0.412855	+	0.910797i	$0.635468\pi$
$710$	−4.49909	−	7.79265i	−0.168848	−	0.292453i
$711$		0			0
$712$	−32.0389			−1.20071
$713$	−23.5470	−	40.7846i	−0.881841	−	1.52739i
$714$		0			0
$715$	1.97516	+	18.7002i	0.0738668	+	0.699349i
$716$	−18.3580	+	31.7970i	−0.686070	+	1.18831i
$717$		0			0
$718$	24.7577	−	42.8816i	0.923948	−	1.60033i
$719$	−13.5709	−	23.5054i	−0.506108	−	0.876605i	−0.999975	−	0.00706745i	$-0.997750\pi$
$719$	−13.5709	−	23.5054i	−0.506108	−	0.876605i	0.493867	−	0.869537i	$-0.335583\pi$
$720$		0			0
$721$	−1.16187	−	6.88099i	−0.0432705	−	0.256261i
$722$	−38.1205	+	66.0267i	−1.41870	+	2.45726i
$723$		0			0
$724$	−60.9660			−2.26578
$725$	9.11053	−	15.7799i	0.338356	−	0.586051i
$726$		0			0
$727$	−21.0336			−0.780095			−0.390047	−	0.920795i	$-0.627541\pi$
$727$	−21.0336			−0.780095			−0.390047	+	0.920795i	$0.627541\pi$
$728$	35.5621	−	9.93815i	1.31802	−	0.368332i
$729$		0			0
$730$	2.33149			0.0862923
$731$	31.9636	−	55.3627i	1.18222	−	2.04766i
$732$		0			0
$733$	4.49198	−	7.78034i	0.165915	−	0.287373i	−0.771065	−	0.636757i	$-0.780276\pi$
$733$	4.49198	−	7.78034i	0.165915	−	0.287373i	0.936980	+	0.349383i	$0.113609\pi$
$734$	11.5016	−	19.9214i	0.424532	−	0.735311i
$735$		0			0
$736$	−17.6167			−0.649362
$737$	2.23877	+	3.87767i	0.0824662	+	0.142836i
$738$		0			0
$739$	−5.96672	+	10.3347i	−0.219489	+	0.380167i	−0.954652	−	0.297724i	$-0.903772\pi$
$739$	−5.96672	+	10.3347i	−0.219489	+	0.380167i	0.735163	+	0.677891i	$0.237106\pi$
$740$	7.37034	−	12.7658i	0.270939	−	0.469280i
$741$		0			0
$742$	−70.3525	−	26.1860i	−2.58272	−	0.961318i
$743$	−7.76713	−	13.4531i	−0.284948	−	0.493545i	0.687648	−	0.726044i	$-0.258643\pi$
$743$	−7.76713	−	13.4531i	−0.284948	−	0.493545i	−0.972597	+	0.232499i	$0.925310\pi$
$744$		0			0
$745$	−35.8355			−1.31291
$746$	14.7504	+	25.5484i	0.540049	+	0.935392i
$747$		0			0
$748$	−35.4765	+	61.4470i	−1.29715	+	2.24673i
$749$	−7.37380	+	6.09670i	−0.269433	+	0.222769i
$750$		0			0
$751$	−36.6217			−1.33635			−0.668173	−	0.744006i	$-0.732923\pi$
$751$	−36.6217			−1.33635			−0.668173	+	0.744006i	$0.732923\pi$
$752$	−8.25690	+	14.3014i	−0.301098	+	0.521518i
$753$		0			0
$754$	−6.61562	−	62.6348i	−0.240927	−	2.28102i
$755$	23.4163			0.852205
$756$		0			0
$757$	−9.66722	−	16.7441i	−0.351361	−	0.608575i	0.635127	−	0.772408i	$-0.280948\pi$
$757$	−9.66722	−	16.7441i	−0.351361	−	0.608575i	−0.986488	+	0.163832i	$0.947614\pi$
$758$	−31.6623	−	54.8407i	−1.15003	−	1.99190i
$759$		0			0
$760$	−43.9781			−1.59525
$761$	11.0495	+	19.1383i	0.400543	+	0.693762i	0.993792	−	0.111258i	$-0.0354880\pi$
$761$	11.0495	+	19.1383i	0.400543	+	0.693762i	−0.593248	+	0.805020i	$0.702155\pi$
$762$		0			0
$763$	−0.959920	−	0.357293i	−0.0347514	−	0.0129349i
$764$	34.3283	+	59.4584i	1.24196	+	2.15113i
$765$		0			0
$766$	−3.03843	−	5.26271i	−0.109783	−	0.190149i
$767$	4.00422	+	1.78034i	0.144584	+	0.0642842i
$768$		0			0
$769$	−8.04717	−	13.9381i	−0.290188	−	0.502621i	0.683666	−	0.729795i	$-0.260385\pi$
$769$	−8.04717	−	13.9381i	−0.290188	−	0.502621i	−0.973854	+	0.227174i	$0.927051\pi$
$770$	30.6873	+	11.4222i	1.10589	+	0.411626i
$771$		0			0
$772$	14.2526	−	24.6862i	0.512962	−	0.888477i
$773$	23.9765			0.862375			0.431188	−	0.902262i	$-0.358095\pi$
$773$	23.9765			0.862375			0.431188	+	0.902262i	$0.358095\pi$
$774$		0			0
$775$	10.5150	−	18.2126i	0.377711	−	0.654215i
$776$	3.21879	−	5.57511i	0.115548	−	0.200135i
$777$		0			0
$778$	23.9474	+	41.4781i	0.858557	+	1.48706i
$779$	−11.0450	+	19.1305i	−0.395727	+	0.685420i
$780$		0			0
$781$	3.91645	+	6.78349i	0.140142	+	0.242732i
$782$	−78.3054			−2.80020
$783$		0			0
$784$	2.52966	−	13.2212i	0.0903449	−	0.472186i
$785$	−21.0924			−0.752819
$786$		0			0
$787$	−38.4905			−1.37204			−0.686019	−	0.727584i	$-0.740643\pi$
$787$	−38.4905			−1.37204			−0.686019	+	0.727584i	$0.740643\pi$
$788$	45.5416	+	78.8803i	1.62235	+	2.81000i
$789$		0			0
$790$	27.9712	+	48.4476i	0.995171	+	1.72369i
$791$	−4.50384	−	26.6732i	−0.160138	−	0.948389i
$792$		0			0
$793$	−0.241795	−	2.28924i	−0.00858640	−	0.0812935i
$794$	6.76607	+	11.7192i	0.240119	+	0.415898i
$795$		0			0
$796$	−28.2643			−1.00180
$797$	−22.8007	+	39.4919i	−0.807641	+	1.39888i	0.106853	+	0.994275i	$0.465923\pi$
$797$	−22.8007	+	39.4919i	−0.807641	+	1.39888i	−0.914494	+	0.404600i	$0.867411\pi$
$798$		0			0
$799$	25.5615	−	44.2738i	0.904300	−	1.56629i
$800$	−3.93343	−	6.81290i	−0.139068	−	0.240872i
$801$		0			0
$802$	−12.6451			−0.446512
$803$	−2.02956			−0.0716215
$804$		0			0
$805$	3.87977	+	22.9772i	0.136744	+	0.809840i
$806$	−7.63551	−	72.2908i	−0.268950	−	2.54633i
$807$		0			0
$808$	0.375117	−	0.649721i	0.0131966	−	0.0228571i
$809$	−12.4612	+	21.5835i	−0.438114	+	0.758836i	−0.997544	−	0.0700419i	$-0.977687\pi$
$809$	−12.4612	+	21.5835i	−0.438114	+	0.758836i	0.559430	+	0.828878i	$0.311020\pi$
$810$		0			0
$811$	−23.7418			−0.833689			−0.416844	−	0.908978i	$-0.636864\pi$
$811$	−23.7418			−0.833689			−0.416844	+	0.908978i	$0.636864\pi$
$812$	−66.2787	−	24.6697i	−2.32593	−	0.865737i
$813$		0			0
$814$	−9.94965	+	17.2333i	−0.348735	+	0.604027i
$815$	−7.65758			−0.268233
$816$		0			0
$817$	−76.7836			−2.68632
$818$	−51.4672			−1.79951
$819$		0			0
$820$	−17.8245			−0.622459
$821$	28.9555			1.01056			0.505278	−	0.862957i	$-0.331390\pi$
$821$	28.9555			1.01056			0.505278	+	0.862957i	$0.331390\pi$
$822$		0			0
$823$	37.2875			1.29976			0.649880	−	0.760036i	$-0.274819\pi$
$823$	37.2875			1.29976			0.649880	+	0.760036i	$0.274819\pi$
$824$	5.10472	−	8.84163i	0.177831	−	0.308013i
$825$		0			0
$826$	5.88091	−	4.86238i	0.204623	−	0.169184i
$827$	−20.7885			−0.722888			−0.361444	−	0.932394i	$-0.617716\pi$
$827$	−20.7885			−0.722888			−0.361444	+	0.932394i	$0.617716\pi$
$828$		0			0
$829$	27.9148	−	48.3498i	0.969520	−	1.67926i	0.272572	−	0.962135i	$-0.412126\pi$
$829$	27.9148	−	48.3498i	0.969520	−	1.67926i	0.696948	−	0.717122i	$-0.254541\pi$
$830$	19.2135	−	33.2788i	0.666910	−	1.15512i
$831$		0			0
$832$	−37.5185	−	16.6813i	−1.30072	−	0.578319i
$833$	−7.83124	+	40.9298i	−0.271336	+	1.41813i
$834$		0			0
$835$	14.4921			0.501520
$836$	85.2221			2.94747
$837$		0			0
$838$	42.7964	+	74.1255i	1.47838	+	2.56062i
$839$	−11.2275	+	19.4465i	−0.387615	+	0.671369i	−0.992128	−	0.125226i	$-0.960034\pi$
$839$	−11.2275	+	19.4465i	−0.387615	+	0.671369i	0.604513	+	0.796595i	$0.293368\pi$
$840$		0			0
$841$	−12.5943	+	21.8140i	−0.434287	+	0.752206i
$842$	41.3647			1.42552
$843$		0			0
$844$	4.26509	+	7.38735i	0.146810	+	0.254283i
$845$	−20.2005	+	4.31538i	−0.694918	+	0.148454i
$846$		0			0
$847$	0.561967	+	0.209171i	0.0193094	+	0.00718718i
$848$	−11.4963	−	19.9121i	−0.394783	−	0.683784i
$849$		0			0
$850$	−17.4839	−	30.2830i	−0.599692	−	1.03870i
$851$	−14.1614			−0.485448
$852$		0			0
$853$	10.8150			0.370298			0.185149	−	0.982710i	$-0.440723\pi$
$853$	10.8150			0.370298			0.185149	+	0.982710i	$0.440723\pi$
$854$	−3.75667	−	1.39828i	−0.128551	−	0.0478480i
$855$		0			0
$856$	−13.9978			−0.478433
$857$	17.7262	+	30.7026i	0.605514	+	1.04878i	0.991970	+	0.126474i	$0.0403659\pi$
$857$	17.7262	+	30.7026i	0.605514	+	1.04878i	−0.386456	+	0.922308i	$0.626301\pi$
$858$		0			0
$859$	−24.0734	+	41.6963i	−0.821373	+	1.42266i	0.0832873	+	0.996526i	$0.473458\pi$
$859$	−24.0734	+	41.6963i	−0.821373	+	1.42266i	−0.904660	+	0.426134i	$0.859875\pi$
$860$	−30.9786	−	53.6565i	−1.05636	−	1.82967i
$861$		0			0
$862$	−0.800718	+	1.38688i	−0.0272726	+	0.0472375i
$863$	2.06142	−	3.57048i	0.0701714	−	0.121540i	−0.828805	−	0.559538i	$-0.810979\pi$
$863$	2.06142	−	3.57048i	0.0701714	−	0.121540i	0.898976	+	0.437997i	$0.144312\pi$
$864$		0			0
$865$	−24.9158			−0.847164
$866$	23.2619	−	40.2908i	0.790471	−	1.36914i
$867$		0			0
$868$	−76.4965	−	28.4729i	−2.59646	−	0.966432i
$869$	−24.3489	−	42.1735i	−0.825979	−	1.43064i
$870$		0			0
$871$	−3.97770	+	2.89308i	−0.134779	+	0.0980283i
$872$	−0.749248	−	1.29774i	−0.0253728	−	0.0439469i
$873$		0			0
$874$	47.0267	+	81.4526i	1.59070	+	2.75517i
$875$	−24.2194	+	20.0247i	−0.818765	+	0.676960i
$876$		0			0
$877$	−14.4898	−	25.0971i	−0.489286	−	0.847468i	0.510638	−	0.859796i	$-0.329409\pi$
$877$	−14.4898	−	25.0971i	−0.489286	−	0.847468i	−0.999924	+	0.0123279i	$0.996076\pi$
$878$	−75.9956			−2.56473
$879$		0			0
$880$	5.01458	+	8.68552i	0.169042	+	0.292789i
$881$	−7.56041	−	13.0950i	−0.254717	−	0.441182i	0.710102	−	0.704099i	$-0.248649\pi$
$881$	−7.56041	−	13.0950i	−0.254717	−	0.441182i	−0.964819	+	0.262917i	$0.915316\pi$
$882$		0			0
$883$	−31.9151			−1.07403			−0.537014	−	0.843573i	$-0.680448\pi$
$883$	−31.9151			−1.07403			−0.537014	+	0.843573i	$0.680448\pi$
$884$	−71.2189	−	31.6650i	−2.39535	−	1.06501i
$885$		0			0
$886$	20.8347	−	36.0867i	0.699955	−	1.21236i
$887$	−48.6843			−1.63466			−0.817330	−	0.576170i	$-0.804547\pi$
$887$	−48.6843			−1.63466			−0.817330	+	0.576170i	$0.804547\pi$
$888$		0			0
$889$	14.6748	+	5.46214i	0.492178	+	0.183194i
$890$	15.6049	−	27.0284i	0.523076	−	0.905995i
$891$		0			0
$892$	−21.0213	−	36.4099i	−0.703844	−	1.21909i
$893$	−61.4042			−2.05481
$894$		0			0
$895$	−8.03320	−	13.9139i	−0.268520	−	0.465091i
$896$	−42.1415	+	34.8428i	−1.40785	+	1.16402i
$897$		0			0
$898$	6.71183	−	11.6252i	0.223977	−	0.387939i
$899$	−31.2713	+	54.1634i	−1.04296	+	1.80645i
$900$		0			0
$901$	35.5898	+	61.6433i	1.18567	+	2.05363i
$902$	24.0623			0.801189
$903$		0			0
$904$	19.7877	−	34.2733i	0.658130	−	1.13991i
$905$	13.3389	−	23.1037i	0.443401	−	0.767993i
$906$		0			0
$907$	20.7185	−	35.8854i	0.687945	−	1.19156i	−0.284556	−	0.958659i	$-0.591846\pi$
$907$	20.7185	−	35.8854i	0.687945	−	1.19156i	0.972501	−	0.232897i	$-0.0748204\pi$
$908$	47.1306			1.56408
$909$		0			0
$910$	−8.93692	+	34.8411i	−0.296256	+	1.15497i
$911$	−55.6403			−1.84344			−0.921722	−	0.387851i	$-0.873218\pi$
$911$	−55.6403			−1.84344			−0.921722	+	0.387851i	$0.873218\pi$
$912$		0			0
$913$	−16.7253	+	28.9691i	−0.553527	+	0.958737i
$914$	−14.0212			−0.463781
$915$		0			0
$916$	34.9698	−	60.5695i	1.15544	−	2.00127i
$917$	−0.549631	−	3.25509i	−0.0181504	−	0.107493i
$918$		0			0
$919$	−1.15990	−	2.00901i	−0.0382617	−	0.0662711i	0.846260	−	0.532769i	$-0.178849\pi$
$919$	−1.15990	−	2.00901i	−0.0382617	−	0.0662711i	−0.884522	+	0.466498i	$0.845515\pi$
$920$	−17.0458	+	29.5243i	−0.561985	+	0.973386i
$921$		0			0
$922$	45.1658	−	78.2295i	1.48746	−	2.57635i
$923$	−6.95848	+	5.06108i	−0.229041	+	0.166588i
$924$		0			0
$925$	−3.16193	−	5.47663i	−0.103964	−	0.180070i
$926$	−84.2380			−2.76823
$927$		0			0
$928$	11.6978	+	20.2613i	0.384001	+	0.665109i
$929$	−22.6240	−	39.1860i	−0.742270	−	1.28565i	−0.951459	−	0.307774i	$-0.900416\pi$
$929$	−22.6240	−	39.1860i	−0.742270	−	1.28565i	0.209189	−	0.977875i	$-0.432918\pi$
$930$		0			0
$931$	47.2779	−	16.4346i	1.54947	−	0.538622i
$932$	22.7032	−	39.3231i	0.743668	−	1.28807i
$933$		0			0
$934$	0.302478	−	0.523906i	0.00989737	−	0.0171427i
$935$	−15.5240	−	26.8884i	−0.507689	−	0.879343i
$936$		0			0
$937$	23.7899			0.777181			0.388590	−	0.921411i	$-0.372962\pi$
$937$	23.7899			0.777181			0.388590	+	0.921411i	$0.372962\pi$
$938$	1.42599	+	8.44516i	0.0465602	+	0.275744i
$939$		0			0
$940$	−24.7737	−	42.9094i	−0.808030	−	1.39955i
$941$	−15.7112	−	27.2127i	−0.512172	−	0.887107i	−0.999900	−	0.0141120i	$-0.995508\pi$
$941$	−15.7112	−	27.2127i	−0.512172	−	0.887107i	0.487729	−	0.872995i	$-0.337825\pi$
$942$		0			0
$943$	8.56204	+	14.8299i	0.278818	+	0.482928i
$944$	2.33721			0.0760697
$945$		0			0
$946$	41.8198	+	72.4340i	1.35968	+	2.35503i
$947$	17.7770			0.577674			0.288837	−	0.957378i	$-0.406731\pi$
$947$	17.7770			0.577674			0.288837	+	0.957378i	$0.406731\pi$
$948$		0			0
$949$	−0.234177	−	2.21711i	−0.00760169	−	0.0719706i
$950$	−21.0000	+	36.3731i	−0.681331	+	1.18010i
$951$		0			0
$952$	−46.9865	+	38.8487i	−1.52284	+	1.25910i
$953$	0.457510	−	0.792431i	0.0148202	−	0.0256694i	−0.858520	−	0.512780i	$-0.828616\pi$
$953$	0.457510	−	0.792431i	0.0148202	−	0.0256694i	0.873340	+	0.487110i	$0.161949\pi$
$954$		0			0
$955$	−30.0432			−0.972176
$956$	108.002			3.49303
$957$		0			0
$958$	18.0328	−	31.2337i	0.582613	−	1.00911i
$959$	2.13989	−	1.76927i	0.0691006	−	0.0571328i
$960$		0			0
$961$	−20.5922	+	35.6667i	−0.664263	+	1.15054i
$962$	−19.9739	−	8.88070i	−0.643985	−	0.286325i
$963$		0			0
$964$	58.6357			1.88853
$965$	6.23674	+	10.8024i	0.200768	+	0.347740i
$966$		0			0
$967$	48.9250			1.57332			0.786660	−	0.617386i	$-0.211808\pi$
$967$	48.9250			1.57332			0.786660	+	0.617386i	$0.211808\pi$
$968$	0.438634	+	0.759736i	0.0140982	+	0.0244188i
$969$		0			0
$970$	3.13549	+	5.43083i	0.100675	+	0.174373i
$971$	14.5954	+	25.2799i	0.468387	+	0.811270i	0.999347	−	0.0361265i	$-0.0115019\pi$
$971$	14.5954	+	25.2799i	0.468387	+	0.811270i	−0.530960	+	0.847397i	$0.678169\pi$
$972$		0			0
$973$	1.57927	+	9.35293i	0.0506290	+	0.299841i
$974$	0.543608			0.0174183
$975$		0			0
$976$	−0.613875	−	1.06326i	−0.0196497	−	0.0340342i
$977$	13.8084	−	23.9168i	0.441770	−	0.765168i	−0.556051	−	0.831148i	$-0.687684\pi$
$977$	13.8084	−	23.9168i	0.441770	−	0.765168i	0.997821	+	0.0659804i	$0.0210175\pi$
$978$		0			0
$979$	−13.5840	+	23.5282i	−0.434146	+	0.751964i
$980$	30.5589	+	26.4073i	0.976169	+	0.843549i
$981$		0			0
$982$	−17.0804	−	29.5841i	−0.545057	−	0.944066i
$983$	6.29829	+	10.9090i	0.200884	+	0.347942i	0.948814	−	0.315836i	$-0.102285\pi$
$983$	6.29829	+	10.9090i	0.200884	+	0.347942i	−0.747929	+	0.663778i	$0.768952\pi$
$984$		0			0
$985$	−39.8567			−1.26994
$986$	51.9963	+	90.0602i	1.65590	+	2.86810i
$987$		0			0
$988$	9.83320	+	93.0978i	0.312836	+	2.96184i
$989$	−29.7612	+	51.5480i	−0.946352	+	1.63913i
$990$		0			0
$991$	−2.04231	+	3.53738i	−0.0648760	+	0.112369i	−0.896639	−	0.442762i	$-0.853999\pi$
$991$	−2.04231	+	3.53738i	−0.0648760	+	0.112369i	0.831763	+	0.555131i	$0.187332\pi$
$992$	13.5012	+	23.3848i	0.428665	+	0.742469i
$993$		0			0
$994$	2.49459	+	14.7737i	0.0791235	+	0.468594i
$995$	6.18403	−	10.7111i	0.196047	−	0.339563i
$996$		0			0
$997$	42.0885			1.33296			0.666478	−	0.745525i	$-0.267801\pi$
$997$	42.0885			1.33296			0.666478	+	0.745525i	$0.267801\pi$
$998$	−15.8673	+	27.4829i	−0.502270	+	0.869957i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.g.289.17	yes	36
3.2	odd	2	inner	819.2.s.g.289.2	yes	36
7.4	even	3		819.2.n.g.172.2	yes	36
13.9	even	3		819.2.n.g.100.2	✓	36
21.11	odd	6		819.2.n.g.172.17	yes	36
39.35	odd	6		819.2.n.g.100.17	yes	36
91.74	even	3	inner	819.2.s.g.802.17	yes	36
273.74	odd	6	inner	819.2.s.g.802.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.n.g.100.2	✓	36	13.9	even	3
819.2.n.g.100.17	yes	36	39.35	odd	6
819.2.n.g.172.2	yes	36	7.4	even	3
819.2.n.g.172.17	yes	36	21.11	odd	6
819.2.s.g.289.2	yes	36	3.2	odd	2	inner
819.2.s.g.289.17	yes	36	1.1	even	1	trivial
819.2.s.g.802.2	yes	36	273.74	odd	6	inner
819.2.s.g.802.17	yes	36	91.74	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.37301 q^{2} +3.63116 q^{4} +(-0.794473 + 1.37607i) q^{5} +(2.03905 - 1.68590i) q^{7} +3.87075 q^{8} +(-1.88529 + 3.26542i) q^{10} +(1.64114 - 2.84254i) q^{11} +(3.29459 + 1.46482i) q^{13} +(4.83869 - 4.00066i) q^{14} +1.92300 q^{16} -5.95318 q^{17} +(3.57521 + 6.19244i) q^{19} +(-2.88486 + 4.99672i) q^{20} +(3.89444 - 6.74536i) q^{22} +5.54299 q^{23} +(1.23763 + 2.14363i) q^{25} +(7.81807 + 3.47603i) q^{26} +(7.40413 - 6.12178i) q^{28} +(-3.68065 - 6.37507i) q^{29} +(-4.24807 - 7.35787i) q^{31} -3.17821 q^{32} -14.1269 q^{34} +(0.699942 + 4.14528i) q^{35} -2.55484 q^{37} +(8.48399 + 14.6947i) q^{38} +(-3.07521 + 5.32642i) q^{40} +(1.54466 + 2.67543i) q^{41} +(-5.36917 + 9.29968i) q^{43} +(5.95924 - 10.3217i) q^{44} +13.1535 q^{46} +(-4.29375 + 7.43700i) q^{47} +(1.31547 - 6.87528i) q^{49} +(2.93690 + 5.08685i) q^{50} +(11.9632 + 5.31900i) q^{52} +(-5.97827 - 10.3547i) q^{53} +(2.60768 + 4.51664i) q^{55} +(7.89267 - 6.52571i) q^{56} +(-8.73420 - 15.1281i) q^{58} +1.21539 q^{59} +(-0.319227 - 0.552917i) q^{61} +(-10.0807 - 17.4603i) q^{62} -11.3879 q^{64} +(-4.63315 + 3.36981i) q^{65} +(-0.682078 + 1.18139i) q^{67} -21.6170 q^{68} +(1.66097 + 9.83677i) q^{70} +(-1.19321 + 2.06670i) q^{71} +(-0.309169 - 0.535496i) q^{73} -6.06265 q^{74} +(12.9822 + 22.4858i) q^{76} +(-1.44587 - 8.56288i) q^{77} +(7.41828 - 12.8488i) q^{79} +(-1.52777 + 2.64618i) q^{80} +(3.66549 + 6.34882i) q^{82} -10.1913 q^{83} +(4.72964 - 8.19198i) q^{85} +(-12.7411 + 22.0682i) q^{86} +(6.35245 - 11.0028i) q^{88} -8.27717 q^{89} +(9.18738 - 2.56750i) q^{91} +20.1275 q^{92} +(-10.1891 + 17.6480i) q^{94} -11.3616 q^{95} +(0.831568 - 1.44032i) q^{97} +(3.12162 - 16.3151i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 44 q^{4} + 4 q^{7} + 8 q^{10} + 20 q^{16} + 4 q^{19} - 10 q^{22} - 22 q^{25} + 16 q^{28} - 18 q^{31} + 8 q^{34} - 20 q^{37} + 14 q^{40} + 20 q^{43} + 8 q^{46} - 12 q^{49} + 10 q^{52} + 42 q^{55}+ \cdots + 28 q^{97}+O(q^{100}) \) 36 * q + 44 * q^4 + 4 * q^7 + 8 * q^10 + 20 * q^16 + 4 * q^19 - 10 * q^22 - 22 * q^25 + 16 * q^28 - 18 * q^31 + 8 * q^34 - 20 * q^37 + 14 * q^40 + 20 * q^43 + 8 * q^46 - 12 * q^49 + 10 * q^52 + 42 * q^55 - 12 * q^58 + 14 * q^61 - 12 * q^64 + 12 * q^67 - 24 * q^70 + 6 * q^73 + 14 * q^76 - 24 * q^79 + 38 * q^82 + 28 * q^85 - 12 * q^88 + 92 * q^91 + 28 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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