LMFDB - Embedded newform 360.2.bs.a.113.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(113,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("360.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.10
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.416476 - 1.68123i) q^{3} +(-1.03051 + 1.98445i) q^{5} +(3.03419 + 0.813008i) q^{7} +(-2.65309 - 1.40039i) q^{9} +O(q^{10})$	\(q+(0.416476 - 1.68123i) q^{3} +(-1.03051 + 1.98445i) q^{5} +(3.03419 + 0.813008i) q^{7} +(-2.65309 - 1.40039i) q^{9} +(2.94123 - 1.69812i) q^{11} +(5.55317 - 1.48797i) q^{13} +(2.90714 + 2.55901i) q^{15} +(-2.09273 - 2.09273i) q^{17} +3.28564i q^{19} +(2.63052 - 4.76258i) q^{21} +(0.0615809 + 0.229823i) q^{23} +(-2.87608 - 4.09001i) q^{25} +(-3.45933 + 3.87724i) q^{27} +(-1.22364 - 2.11940i) q^{29} +(3.55077 - 6.15011i) q^{31} +(-1.62998 - 5.65212i) q^{33} +(-4.74015 + 5.18338i) q^{35} +(-0.726179 + 0.726179i) q^{37} +(-0.188856 - 9.95587i) q^{39} +(3.66754 + 2.11746i) q^{41} +(-1.74949 + 6.52918i) q^{43} +(5.51305 - 3.82181i) q^{45} +(-1.55773 + 5.81352i) q^{47} +(2.48313 + 1.43364i) q^{49} +(-4.38994 + 2.64679i) q^{51} +(-9.69300 + 9.69300i) q^{53} +(0.338853 + 7.58666i) q^{55} +(5.52393 + 1.36839i) q^{57} +(0.978837 - 1.69540i) q^{59} +(-0.195605 - 0.338797i) q^{61} +(-6.91146 - 6.40603i) q^{63} +(-2.76982 + 12.5533i) q^{65} +(3.75113 + 13.9994i) q^{67} +(0.412033 - 0.00781600i) q^{69} -3.49075i q^{71} +(-11.7750 - 11.7750i) q^{73} +(-8.07408 + 3.13197i) q^{75} +(10.3048 - 2.76117i) q^{77} +(11.6301 - 6.71466i) q^{79} +(5.07782 + 7.43073i) q^{81} +(7.73261 + 2.07195i) q^{83} +(6.30950 - 1.99633i) q^{85} +(-4.07283 + 1.17454i) q^{87} -16.6210 q^{89} +18.0591 q^{91} +(-8.86096 - 8.53104i) q^{93} +(-6.52019 - 3.38590i) q^{95} +(-7.49838 - 2.00919i) q^{97} +(-10.1814 + 0.386408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.416476	−	1.68123i	0.240453	−	0.970661i
$3$	0.416476	−	1.68123i	0.240453	−	0.970661i
$4$		0			0
$5$	−1.03051	+	1.98445i	−0.460860	+	0.887473i
$5$	−1.03051	+	1.98445i	−0.460860	+	0.887473i
$6$		0			0
$7$	3.03419	+	0.813008i	1.14682	+	0.307288i	0.781688	−	0.623670i	$-0.214359\pi$
$7$	3.03419	+	0.813008i	1.14682	+	0.307288i	0.365127	+	0.930958i	$0.381026\pi$
$8$		0			0
$9$	−2.65309	−	1.40039i	−0.884365	−	0.466796i
$10$		0			0
$11$	2.94123	−	1.69812i	0.886814	−	0.512002i	0.0139150	−	0.999903i	$-0.495571\pi$
$11$	2.94123	−	1.69812i	0.886814	−	0.512002i	0.872899	+	0.487901i	$0.162237\pi$
$12$		0			0
$13$	5.55317	−	1.48797i	1.54017	−	0.412688i	0.613850	−	0.789423i	$-0.289620\pi$
$13$	5.55317	−	1.48797i	1.54017	−	0.412688i	0.926321	+	0.376735i	$0.122953\pi$
$14$		0			0
$15$	2.90714	+	2.55901i	0.750620	+	0.660734i
$16$		0			0
$17$	−2.09273	−	2.09273i	−0.507561	−	0.507561i	0.406216	−	0.913777i	$-0.366848\pi$
$17$	−2.09273	−	2.09273i	−0.507561	−	0.507561i	−0.913777	+	0.406216i	$0.866848\pi$
$18$		0			0
$19$			3.28564i			0.753777i	0.926259	+	0.376889i	$0.123006\pi$
$19$			3.28564i			0.753777i	−0.926259	+	0.376889i	$0.876994\pi$
$20$		0			0
$21$	2.63052	−	4.76258i	0.574028	−	1.03928i
$22$		0			0
$23$	0.0615809	+	0.229823i	0.0128405	+	0.0479214i	0.972049	−	0.234779i	$-0.0754365\pi$
$23$	0.0615809	+	0.229823i	0.0128405	+	0.0479214i	−0.959208	+	0.282700i	$0.908770\pi$
$24$		0			0
$25$	−2.87608	−	4.09001i	−0.575216	−	0.818002i
$26$		0			0
$27$	−3.45933	+	3.87724i	−0.665749	+	0.746176i
$28$		0			0
$29$	−1.22364	−	2.11940i	−0.227224	−	0.393564i	0.729760	−	0.683703i	$-0.239632\pi$
$29$	−1.22364	−	2.11940i	−0.227224	−	0.393564i	−0.956984	+	0.290139i	$0.906298\pi$
$30$		0			0
$31$	3.55077	−	6.15011i	0.637736	−	1.10459i	−0.348192	−	0.937423i	$-0.613204\pi$
$31$	3.55077	−	6.15011i	0.637736	−	1.10459i	0.985928	−	0.167168i	$-0.0534623\pi$
$32$		0			0
$33$	−1.62998	−	5.65212i	−0.283744	−	0.983908i
$34$		0			0
$35$	−4.74015	+	5.18338i	−0.801231	+	0.876150i
$36$		0			0
$37$	−0.726179	+	0.726179i	−0.119383	+	0.119383i	−0.764274	−	0.644891i	$-0.776903\pi$
$37$	−0.726179	+	0.726179i	−0.119383	+	0.119383i	0.644891	+	0.764274i	$0.276903\pi$
$38$		0			0
$39$	−0.188856	−	9.95587i	−0.0302412	−	1.59422i
$40$		0			0
$41$	3.66754	+	2.11746i	0.572774	+	0.330691i	0.758257	−	0.651956i	$-0.226051\pi$
$41$	3.66754	+	2.11746i	0.572774	+	0.330691i	−0.185482	+	0.982648i	$0.559385\pi$
$42$		0			0
$43$	−1.74949	+	6.52918i	−0.266795	+	0.995691i	0.694348	+	0.719639i	$0.255693\pi$
$43$	−1.74949	+	6.52918i	−0.266795	+	0.995691i	−0.961143	+	0.276052i	$0.910974\pi$
$44$		0			0
$45$	5.51305	−	3.82181i	0.821837	−	0.569722i
$46$		0			0
$47$	−1.55773	+	5.81352i	−0.227218	+	0.847990i	0.754286	+	0.656546i	$0.227983\pi$
$47$	−1.55773	+	5.81352i	−0.227218	+	0.847990i	−0.981504	+	0.191443i	$0.938683\pi$
$48$		0			0
$49$	2.48313	+	1.43364i	0.354733	+	0.204805i
$50$		0			0
$51$	−4.38994	+	2.64679i	−0.614714	+	0.370625i
$52$		0			0
$53$	−9.69300	+	9.69300i	−1.33144	+	1.33144i	−0.427348	+	0.904087i	$0.640552\pi$
$53$	−9.69300	+	9.69300i	−1.33144	+	1.33144i	−0.904087	+	0.427348i	$0.859448\pi$
$54$		0			0
$55$	0.338853	+	7.58666i	0.0456909	+	1.02298i
$56$		0			0
$57$	5.52393	+	1.36839i	0.731662	+	0.181248i
$58$		0			0
$59$	0.978837	−	1.69540i	0.127434	−	0.220722i	−0.795248	−	0.606284i	$-0.792659\pi$
$59$	0.978837	−	1.69540i	0.127434	−	0.220722i	0.922682	+	0.385563i	$0.125993\pi$
$60$		0			0
$61$	−0.195605	−	0.338797i	−0.0250446	−	0.0433785i	0.853231	−	0.521532i	$-0.174639\pi$
$61$	−0.195605	−	0.338797i	−0.0250446	−	0.0433785i	−0.878276	+	0.478154i	$0.841306\pi$
$62$		0			0
$63$	−6.91146	−	6.40603i	−0.870762	−	0.807084i
$64$		0			0
$65$	−2.76982	+	12.5533i	−0.343554	+	1.55705i
$66$		0			0
$67$	3.75113	+	13.9994i	0.458274	+	1.71030i	0.678281	+	0.734802i	$0.262725\pi$
$67$	3.75113	+	13.9994i	0.458274	+	1.71030i	−0.220008	+	0.975498i	$0.570608\pi$
$68$		0			0
$69$	0.412033	−	0.00781600i	0.0496030	−	0.000940936i
$70$		0			0
$71$		−	3.49075i		−	0.414276i	−0.978312	−	0.207138i	$-0.933585\pi$
$71$		−	3.49075i		−	0.414276i	0.978312	−	0.207138i	$-0.0664150\pi$
$72$		0			0
$73$	−11.7750	−	11.7750i	−1.37815	−	1.37815i	−0.847736	−	0.530418i	$-0.822035\pi$
$73$	−11.7750	−	11.7750i	−1.37815	−	1.37815i	−0.530418	−	0.847736i	$-0.677965\pi$
$74$		0			0
$75$	−8.07408	+	3.13197i	−0.932314	+	0.361649i
$76$		0			0
$77$	10.3048	−	2.76117i	1.17434	−	0.314665i
$78$		0			0
$79$	11.6301	−	6.71466i	1.30849	−	0.755458i	0.326647	−	0.945146i	$-0.394081\pi$
$79$	11.6301	−	6.71466i	1.30849	−	0.755458i	0.981844	+	0.189688i	$0.0607478\pi$
$80$		0			0
$81$	5.07782	+	7.43073i	0.564203	+	0.825636i
$82$		0			0
$83$	7.73261	+	2.07195i	0.848765	+	0.227426i	0.656883	−	0.753992i	$-0.271874\pi$
$83$	7.73261	+	2.07195i	0.848765	+	0.227426i	0.191881	+	0.981418i	$0.438541\pi$
$84$		0			0
$85$	6.30950	−	1.99633i	0.684362	−	0.216532i
$86$		0			0
$87$	−4.07283	+	1.17454i	−0.436653	+	0.125924i
$88$		0			0
$89$	−16.6210			−1.76182			−0.880912	−	0.473280i	$-0.843070\pi$
$89$	−16.6210			−1.76182			−0.880912	+	0.473280i	$0.843070\pi$
$90$		0			0
$91$	18.0591			1.89311
$92$		0			0
$93$	−8.86096	−	8.53104i	−0.918838	−	0.884628i
$94$		0			0
$95$	−6.52019	−	3.38590i	−0.668957	−	0.347386i
$96$		0			0
$97$	−7.49838	−	2.00919i	−0.761345	−	0.204002i	−0.142801	−	0.989751i	$-0.545611\pi$
$97$	−7.49838	−	2.00919i	−0.761345	−	0.204002i	−0.618545	+	0.785750i	$0.712277\pi$
$98$		0			0
$99$	−10.1814	+	0.386408i	−1.02327	+	0.0388354i
$100$		0			0
$101$	−12.0065	+	6.93193i	−1.19469	+	0.689753i	−0.959366	−	0.282165i	$-0.908948\pi$
$101$	−12.0065	+	6.93193i	−1.19469	+	0.689753i	−0.235321	+	0.971918i	$0.575614\pi$
$102$		0			0
$103$	−13.0262	+	3.49036i	−1.28351	+	0.343915i	−0.835191	−	0.549960i	$-0.814643\pi$
$103$	−13.0262	+	3.49036i	−1.28351	+	0.343915i	−0.448317	+	0.893875i	$0.647976\pi$
$104$		0			0
$105$	6.74031	+	10.1281i	0.657787	+	0.988397i
$106$		0			0
$107$	−12.4934	−	12.4934i	−1.20778	−	1.20778i	−0.971743	−	0.236042i	$-0.924150\pi$
$107$	−12.4934	−	12.4934i	−1.20778	−	1.20778i	−0.236042	−	0.971743i	$-0.575850\pi$
$108$		0			0
$109$			7.20151i			0.689779i	0.938643	+	0.344890i	$0.112084\pi$
$109$			7.20151i			0.689779i	−0.938643	+	0.344890i	$0.887916\pi$
$110$		0			0
$111$	0.918441	+	1.52331i	0.0871745	+	0.144587i
$112$		0			0
$113$	1.13197	+	4.22456i	0.106486	+	0.397413i	0.998510	−	0.0545769i	$-0.0173810\pi$
$113$	1.13197	+	4.22456i	0.106486	+	0.397413i	−0.892023	+	0.451990i	$0.850714\pi$
$114$		0			0
$115$	−0.519532	−	0.114632i	−0.0484466	−	0.0106895i
$116$		0			0
$117$	−16.8168	−	3.82888i	−1.55471	−	0.353980i
$118$		0			0
$119$	−4.64833	−	8.05114i	−0.426111	−	0.738047i
$120$		0			0
$121$	0.267220	−	0.462839i	0.0242927	−	0.0420762i
$122$		0			0
$123$	5.08739	−	5.28413i	0.458714	−	0.476454i
$124$		0			0
$125$	11.0803	−	1.49262i	0.991048	−	0.133504i
$126$		0			0
$127$	0.679629	−	0.679629i	0.0603073	−	0.0603073i	−0.676310	−	0.736617i	$-0.736422\pi$
$127$	0.679629	−	0.679629i	0.0603073	−	0.0603073i	0.736617	+	0.676310i	$0.236422\pi$
$128$		0			0
$129$	10.2485	+	5.66055i	0.902327	+	0.498384i
$130$		0			0
$131$	5.79933	+	3.34824i	0.506690	+	0.292537i	0.731472	−	0.681872i	$-0.238834\pi$
$131$	5.79933	+	3.34824i	0.506690	+	0.292537i	−0.224782	+	0.974409i	$0.572167\pi$
$132$		0			0
$133$	−2.67125	+	9.96925i	−0.231627	+	0.864443i
$134$		0			0
$135$	−4.12930	−	10.8604i	−0.355394	−	0.934717i
$136$		0			0
$137$	1.00885	−	3.76507i	0.0861917	−	0.321672i	−0.909345	−	0.416042i	$-0.863417\pi$
$137$	1.00885	−	3.76507i	0.0861917	−	0.321672i	0.995537	+	0.0943700i	$0.0300837\pi$
$138$		0			0
$139$	−12.5402	−	7.24007i	−1.06364	−	0.614095i	−0.137205	−	0.990543i	$-0.543812\pi$
$139$	−12.5402	−	7.24007i	−1.06364	−	0.614095i	−0.926438	+	0.376448i	$0.877145\pi$
$140$		0			0
$141$	9.12513	+	5.04010i	0.768475	+	0.424453i
$142$		0			0
$143$	13.8064	−	13.8064i	1.15455	−	1.15455i
$144$		0			0
$145$	5.46683	−	0.244172i	0.453995	−	0.0202774i
$146$		0			0
$147$	3.44445	−	3.57765i	0.284093	−	0.295080i
$148$		0			0
$149$	10.2819	−	17.8088i	0.842329	−	1.45896i	−0.0455921	−	0.998960i	$-0.514517\pi$
$149$	10.2819	−	17.8088i	0.842329	−	1.45896i	0.887921	−	0.459996i	$-0.152149\pi$
$150$		0			0
$151$	−3.70859	−	6.42347i	−0.301801	−	0.522735i	0.674743	−	0.738053i	$-0.264254\pi$
$151$	−3.70859	−	6.42347i	−0.301801	−	0.522735i	−0.976544	+	0.215318i	$0.930921\pi$
$152$		0			0
$153$	2.62157	+	8.48284i	0.211942	+	0.685797i
$154$		0			0
$155$	8.54546	+	13.3841i	0.686388	+	1.07504i
$156$		0			0
$157$	0.936602	+	3.49545i	0.0747490	+	0.278967i	0.993176	−	0.116623i	$-0.0372069\pi$
$157$	0.936602	+	3.49545i	0.0747490	+	0.278967i	−0.918427	+	0.395590i	$0.870540\pi$
$158$		0			0
$159$	12.2593	+	20.3331i	0.972225	+	1.61252i
$160$		0			0
$161$			0.747392i			0.0589027i
$162$		0			0
$163$	5.27239	+	5.27239i	0.412965	+	0.412965i	0.882770	−	0.469805i	$-0.155676\pi$
$163$	5.27239	+	5.27239i	0.412965	+	0.412965i	−0.469805	+	0.882770i	$0.655676\pi$
$164$		0			0
$165$	12.8961	+	2.58997i	1.00396	+	0.201629i
$166$		0			0
$167$	10.6996	−	2.86696i	0.827963	−	0.221852i	0.180138	−	0.983641i	$-0.442346\pi$
$167$	10.6996	−	2.86696i	0.827963	−	0.221852i	0.647825	+	0.761789i	$0.275679\pi$
$168$		0			0
$169$	17.3653	−	10.0259i	1.33579	−	0.771219i
$170$		0			0
$171$	4.60117	−	8.71711i	0.351860	−	0.666614i
$172$		0			0
$173$	15.4548	+	4.14110i	1.17501	+	0.314842i	0.792944	−	0.609295i	$-0.208548\pi$
$173$	15.4548	+	4.14110i	1.17501	+	0.314842i	0.382062	+	0.924137i	$0.375214\pi$
$174$		0			0
$175$	−5.40136	−	14.7481i	−0.408304	−	1.11485i
$176$		0			0
$177$	−2.44269	−	2.35175i	−0.183604	−	0.176768i
$178$		0			0
$179$	−0.895526			−0.0669347			−0.0334674	−	0.999440i	$-0.510655\pi$
$179$	−0.895526			−0.0669347			−0.0334674	+	0.999440i	$0.510655\pi$
$180$		0			0
$181$	−22.9120			−1.70304			−0.851520	−	0.524323i	$-0.824319\pi$
$181$	−22.9120			−1.70304			−0.851520	+	0.524323i	$0.824319\pi$
$182$		0			0
$183$	−0.651062	+	0.187756i	−0.0481279	+	0.0138793i
$184$		0			0
$185$	−0.692728	−	2.18940i	−0.0509304	−	0.160968i
$186$		0			0
$187$	−9.70890	−	2.60149i	−0.709985	−	0.190240i
$188$		0			0
$189$	−13.6485	+	8.95182i	−0.992782	+	0.651149i
$190$		0			0
$191$	3.20643	−	1.85123i	0.232009	−	0.133950i	−0.379490	−	0.925196i	$-0.623900\pi$
$191$	3.20643	−	1.85123i	0.232009	−	0.133950i	0.611498	+	0.791246i	$0.290567\pi$
$192$		0			0
$193$	−14.6818	+	3.93398i	−1.05682	+	0.283174i	−0.745067	−	0.666989i	$-0.767583\pi$
$193$	−14.6818	+	3.93398i	−1.05682	+	0.283174i	−0.311753	+	0.950163i	$0.600916\pi$
$194$		0			0
$195$	19.9516	+	9.88490i	1.42876	+	0.707872i
$196$		0			0
$197$	8.12966	+	8.12966i	0.579215	+	0.579215i	0.934687	−	0.355472i	$-0.115680\pi$
$197$	8.12966	+	8.12966i	0.579215	+	0.579215i	−0.355472	+	0.934687i	$0.615680\pi$
$198$		0			0
$199$		−	1.00021i		−	0.0709033i	−0.999371	−	0.0354517i	$-0.988713\pi$
$199$		−	1.00021i		−	0.0709033i	0.999371	−	0.0354517i	$-0.0112870\pi$
$200$		0			0
$201$	25.0985	−	0.476103i	1.77031	−	0.0335817i
$202$		0			0
$203$	−1.98966	−	7.42550i	−0.139647	−	0.521168i
$204$		0			0
$205$	−7.98144	+	5.09598i	−0.557448	+	0.355919i
$206$		0			0
$207$	0.158462	−	0.695979i	0.0110138	−	0.0483739i
$208$		0			0
$209$	5.57941	+	9.66382i	0.385936	+	0.668460i
$210$		0			0
$211$	3.51802	−	6.09340i	0.242191	−	0.419487i	−0.719147	−	0.694858i	$-0.755467\pi$
$211$	3.51802	−	6.09340i	0.242191	−	0.419487i	0.961338	+	0.275371i	$0.0888007\pi$
$212$		0			0
$213$	−5.86877	−	1.45382i	−0.402122	−	0.0996139i
$214$		0			0
$215$	−11.1540	−	10.2002i	−0.760694	−	0.695647i
$216$		0			0
$217$	15.7738	−	15.7738i	1.07079	−	1.07079i
$218$		0			0
$219$	−24.7004	+	14.8925i	−1.66910	+	1.00634i
$220$		0			0
$221$	−14.7352	−	8.50736i	−0.991196	−	0.572267i
$222$		0			0
$223$	−1.78351	+	6.65615i	−0.119433	+	0.445729i	−0.999580	−	0.0289714i	$-0.990777\pi$
$223$	−1.78351	+	6.65615i	−0.119433	+	0.445729i	0.880148	+	0.474700i	$0.157443\pi$
$224$		0			0
$225$	1.90291	+	14.8788i	0.126861	+	0.991921i
$226$		0			0
$227$	−0.796434	+	2.97233i	−0.0528612	+	0.197281i	−0.987307	−	0.158826i	$-0.949229\pi$
$227$	−0.796434	+	2.97233i	−0.0528612	+	0.197281i	0.934445	+	0.356106i	$0.115896\pi$
$228$		0			0
$229$	14.3556	+	8.28819i	0.948642	+	0.547699i	0.892659	−	0.450733i	$-0.148837\pi$
$229$	14.3556	+	8.28819i	0.948642	+	0.547699i	0.0559834	+	0.998432i	$0.482171\pi$
$230$		0			0
$231$	−0.350455	−	18.4748i	−0.0230582	−	1.21555i
$232$		0			0
$233$	3.55468	−	3.55468i	0.232875	−	0.232875i	−0.581017	−	0.813892i	$-0.697345\pi$
$233$	3.55468	−	3.55468i	0.232875	−	0.232875i	0.813892	+	0.581017i	$0.197345\pi$
$234$		0			0
$235$	−9.93138	−	9.08215i	−0.647852	−	0.592454i
$236$		0			0
$237$	−6.44523	−	22.3495i	−0.418663	−	1.45175i
$238$		0			0
$239$	13.0099	−	22.5339i	0.841543	−	1.45759i	−0.0470474	−	0.998893i	$-0.514981\pi$
$239$	13.0099	−	22.5339i	0.841543	−	1.45759i	0.888590	−	0.458702i	$-0.151685\pi$
$240$		0			0
$241$	−2.12847	−	3.68662i	−0.137107	−	0.237476i	0.789293	−	0.614016i	$-0.210447\pi$
$241$	−2.12847	−	3.68662i	−0.137107	−	0.237476i	−0.926400	+	0.376540i	$0.877114\pi$
$242$		0			0
$243$	14.6076	−	5.44228i	0.937077	−	0.349123i
$244$		0			0
$245$	−5.40389	+	3.45027i	−0.345242	+	0.220430i
$246$		0			0
$247$	4.88892	+	18.2457i	0.311075	+	1.16095i
$248$		0			0
$249$	6.70388	−	12.1374i	0.424841	−	0.769177i
$250$		0			0
$251$			9.12760i			0.576129i	0.957611	+	0.288065i	$0.0930118\pi$
$251$			9.12760i			0.576129i	−0.957611	+	0.288065i	$0.906988\pi$
$252$		0			0
$253$	0.571390	+	0.571390i	0.0359230	+	0.0359230i
$254$		0			0
$255$	−0.728534	−	11.4392i	−0.0456226	−	0.716349i
$256$		0			0
$257$	−8.23321	+	2.20608i	−0.513573	+	0.137612i	−0.506292	−	0.862362i	$-0.668984\pi$
$257$	−8.23321	+	2.20608i	−0.513573	+	0.137612i	−0.00728107	+	0.999973i	$0.502318\pi$
$258$		0			0
$259$	−2.79375	+	1.61297i	−0.173595	+	0.100225i
$260$		0			0
$261$	0.278439	+	7.33655i	0.0172350	+	0.454121i
$262$		0			0
$263$	18.0955	+	4.84868i	1.11582	+	0.298983i	0.769190	−	0.639020i	$-0.220660\pi$
$263$	18.0955	+	4.84868i	1.11582	+	0.298983i	0.346628	+	0.938003i	$0.387327\pi$
$264$		0			0
$265$	−9.24649	−	29.2240i	−0.568007	−	1.79522i
$266$		0			0
$267$	−6.92226	+	27.9438i	−0.423635	+	1.71013i
$268$		0			0
$269$	5.16197			0.314731			0.157365	−	0.987540i	$-0.449700\pi$
$269$	5.16197			0.314731			0.157365	+	0.987540i	$0.449700\pi$
$270$		0			0
$271$	−3.07446			−0.186760			−0.0933800	−	0.995631i	$-0.529767\pi$
$271$	−3.07446			−0.186760			−0.0933800	+	0.995631i	$0.529767\pi$
$272$		0			0
$273$	7.52118	−	30.3615i	0.455203	−	1.83756i
$274$		0			0
$275$	−15.4045	−	7.14572i	−0.928928	−	0.430903i
$276$		0			0
$277$	5.07931	+	1.36100i	0.305186	+	0.0817744i	0.408162	−	0.912909i	$-0.366170\pi$
$277$	5.07931	+	1.36100i	0.305186	+	0.0817744i	−0.102976	+	0.994684i	$0.532836\pi$
$278$		0			0
$279$	−18.0331	+	11.3444i	−1.07961	+	0.679169i
$280$		0			0
$281$	4.86036	−	2.80613i	0.289945	−	0.167400i	−0.347972	−	0.937505i	$-0.613130\pi$
$281$	4.86036	−	2.80613i	0.289945	−	0.167400i	0.637917	+	0.770105i	$0.279796\pi$
$282$		0			0
$283$	−23.1165	+	6.19404i	−1.37413	+	0.368198i	−0.868986	−	0.494836i	$-0.835228\pi$
$283$	−23.1165	+	6.19404i	−1.37413	+	0.368198i	−0.505146	+	0.863034i	$0.668561\pi$
$284$		0			0
$285$	−8.40799	+	9.55181i	−0.498046	+	0.565800i
$286$		0			0
$287$	9.40651	+	9.40651i	0.555248	+	0.555248i
$288$		0			0
$289$		−	8.24097i		−	0.484763i
$290$		0			0
$291$	−6.50081	+	11.7698i	−0.381084	+	0.689955i
$292$		0			0
$293$	0.254720	+	0.950629i	0.0148809	+	0.0555363i	0.972967	−	0.230944i	$-0.0741814\pi$
$293$	0.254720	+	0.950629i	0.0148809	+	0.0555363i	−0.958086	+	0.286480i	$0.907515\pi$
$294$		0			0
$295$	2.35572	+	3.68958i	0.137155	+	0.214816i
$296$		0			0
$297$	−3.59067	+	17.2782i	−0.208352	+	1.00258i
$298$		0			0
$299$	0.683938	+	1.18462i	0.0395531	+	0.0685081i
$300$		0			0
$301$	−10.6166	+	18.3884i	−0.611928	+	1.05989i
$302$		0			0
$303$	6.65379	+	23.0727i	0.382250	+	1.32549i
$304$		0			0
$305$	0.873899	−	0.0390321i	0.0500393	−	0.00223497i
$306$		0			0
$307$	−2.47325	+	2.47325i	−0.141156	+	0.141156i	−0.774154	−	0.632998i	$-0.781824\pi$
$307$	−2.47325	+	2.47325i	−0.141156	+	0.141156i	0.632998	+	0.774154i	$0.281824\pi$
$308$		0			0
$309$	0.443005	+	23.3537i	0.0252017	+	1.32855i
$310$		0			0
$311$	−3.23174	−	1.86584i	−0.183255	−	0.105802i	0.405566	−	0.914066i	$-0.367074\pi$
$311$	−3.23174	−	1.86584i	−0.183255	−	0.105802i	−0.588821	+	0.808263i	$0.700408\pi$
$312$		0			0
$313$	−8.47901	+	31.6441i	−0.479262	+	1.78863i	0.125353	+	0.992112i	$0.459994\pi$
$313$	−8.47901	+	31.6441i	−0.479262	+	1.78863i	−0.604615	+	0.796518i	$0.706673\pi$
$314$		0			0
$315$	19.8348	−	7.11394i	1.11756	−	0.400825i
$316$		0			0
$317$	7.62837	−	28.4695i	0.428452	−	1.59900i	−0.327816	−	0.944742i	$-0.606313\pi$
$317$	7.62837	−	28.4695i	0.428452	−	1.59900i	0.756268	−	0.654262i	$-0.227021\pi$
$318$		0			0
$319$	−7.19800	−	4.15577i	−0.403011	−	0.232678i
$320$		0			0
$321$	−26.2076	+	15.8011i	−1.46276	+	0.881934i
$322$		0			0
$323$	6.87595	−	6.87595i	0.382588	−	0.382588i
$324$		0			0
$325$	−22.0571	−	18.4330i	−1.22351	−	1.02248i
$326$		0			0
$327$	12.1074	+	2.99926i	0.669542	+	0.165859i
$328$		0			0
$329$	−9.45288	+	16.3729i	−0.521154	+	0.902666i
$330$		0			0
$331$	−3.40386	−	5.89566i	−0.187093	−	0.324055i	0.757187	−	0.653199i	$-0.226573\pi$
$331$	−3.40386	−	5.89566i	−0.187093	−	0.324055i	−0.944280	+	0.329144i	$0.893240\pi$
$332$		0			0
$333$	2.94356	−	0.909689i	0.161306	−	0.0498507i
$334$		0			0
$335$	−31.6467	−	6.98267i	−1.72905	−	0.381504i
$336$		0			0
$337$	0.437226	+	1.63175i	0.0238172	+	0.0888871i	0.976811	−	0.214101i	$-0.0686823\pi$
$337$	0.437226	+	1.63175i	0.0238172	+	0.0888871i	−0.952994	+	0.302988i	$0.902016\pi$
$338$		0			0
$339$	7.57391	−	0.143672i	0.411358	−	0.00780320i
$340$		0			0
$341$		−	24.1185i		−	1.30609i
$342$		0			0
$343$	−9.17952	−	9.17952i	−0.495648	−	0.495648i
$344$		0			0
$345$	−0.409096	+	0.825714i	−0.0220250	+	0.0444549i
$346$		0			0
$347$	19.9343	−	5.34138i	1.07013	−	0.286740i	0.319583	−	0.947558i	$-0.396457\pi$
$347$	19.9343	−	5.34138i	1.07013	−	0.286740i	0.750546	+	0.660818i	$0.229790\pi$
$348$		0			0
$349$	−11.3107	+	6.53023i	−0.605447	+	0.349555i	−0.771182	−	0.636615i	$-0.780334\pi$
$349$	−11.3107	+	6.53023i	−0.605447	+	0.349555i	0.165734	+	0.986170i	$0.447001\pi$
$350$		0			0
$351$	−13.4410	+	26.6784i	−0.717430	+	1.42399i
$352$		0			0
$353$	−3.15999	−	0.846716i	−0.168189	−	0.0450661i	0.173742	−	0.984791i	$-0.444414\pi$
$353$	−3.15999	−	0.846716i	−0.168189	−	0.0450661i	−0.341931	+	0.939725i	$0.611081\pi$
$354$		0			0
$355$	6.92722	+	3.59727i	0.367659	+	0.190923i
$356$		0			0
$357$	−15.4718	+	4.46181i	−0.818853	+	0.236144i
$358$		0			0
$359$	−2.30629			−0.121721			−0.0608605	−	0.998146i	$-0.519384\pi$
$359$	−2.30629			−0.121721			−0.0608605	+	0.998146i	$0.519384\pi$
$360$		0			0
$361$	8.20457			0.431820
$362$		0			0
$363$	−0.666849	−	0.642021i	−0.0350005	−	0.0336974i
$364$		0			0
$365$	35.5011	−	11.2325i	1.85821	−	0.587938i
$366$		0			0
$367$	30.5823	+	8.19449i	1.59638	+	0.427749i	0.943947	−	0.330097i	$-0.107081\pi$
$367$	30.5823	+	8.19449i	1.59638	+	0.427749i	0.652434	+	0.757846i	$0.273748\pi$
$368$		0			0
$369$	−6.76508	−	10.7538i	−0.352176	−	0.559821i
$370$		0			0
$371$	−37.2908	+	21.5299i	−1.93604	+	1.11778i
$372$		0			0
$373$	20.6108	−	5.52264i	1.06719	−	0.285952i	0.317849	−	0.948141i	$-0.397039\pi$
$373$	20.6108	−	5.52264i	1.06719	−	0.285952i	0.749336	+	0.662190i	$0.230373\pi$
$374$		0			0
$375$	2.10522	−	19.2501i	0.108713	−	0.994073i
$376$		0			0
$377$	−9.94867	−	9.94867i	−0.512383	−	0.512383i
$378$		0			0
$379$			16.2658i			0.835519i	0.908558	+	0.417759i	$0.137185\pi$
$379$			16.2658i			0.835519i	−0.908558	+	0.417759i	$0.862815\pi$
$380$		0			0
$381$	−0.859566	−	1.42566i	−0.0440369	−	0.0730390i
$382$		0			0
$383$	9.17016	+	34.2235i	0.468574	+	1.74874i	0.644762	+	0.764384i	$0.276957\pi$
$383$	9.17016	+	34.2235i	0.468574	+	1.74874i	−0.176188	+	0.984356i	$0.556377\pi$
$384$		0			0
$385$	−5.13987	+	23.2948i	−0.261952	+	1.18721i
$386$		0			0
$387$	13.7850	−	14.8726i	0.700729	−	0.756015i
$388$		0			0
$389$	−4.25870	−	7.37629i	−0.215925	−	0.373993i	0.737633	−	0.675201i	$-0.235943\pi$
$389$	−4.25870	−	7.37629i	−0.215925	−	0.373993i	−0.953558	+	0.301209i	$0.902610\pi$
$390$		0			0
$391$	0.352085	−	0.609829i	0.0178057	−	0.0308404i
$392$		0			0
$393$	8.04446	−	8.35556i	0.405790	−	0.421482i
$394$		0			0
$395$	1.33988	+	29.9990i	0.0674168	+	1.50941i
$396$		0			0
$397$	0.728419	−	0.728419i	0.0365583	−	0.0365583i	−0.688591	−	0.725150i	$-0.741771\pi$
$397$	0.728419	−	0.728419i	0.0365583	−	0.0365583i	0.725150	+	0.688591i	$0.241771\pi$
$398$		0			0
$399$	15.6481	+	8.64295i	0.783386	+	0.432689i
$400$		0			0
$401$	−31.1541	−	17.9868i	−1.55576	−	0.898218i	−0.997655	−	0.0684477i	$-0.978195\pi$
$401$	−31.1541	−	17.9868i	−1.55576	−	0.898218i	−0.558105	−	0.829770i	$-0.688471\pi$
$402$		0			0
$403$	10.5668	−	39.4360i	0.526372	−	1.96445i
$404$		0			0
$405$	−19.9787	+	2.41921i	−0.992748	+	0.120212i
$406$		0			0
$407$	−0.902721	+	3.36900i	−0.0447462	+	0.166995i
$408$		0			0
$409$	6.21653	+	3.58912i	0.307388	+	0.177470i	0.645757	−	0.763543i	$-0.276542\pi$
$409$	6.21653	+	3.58912i	0.307388	+	0.177470i	−0.338369	+	0.941013i	$0.609875\pi$
$410$		0			0
$411$	−5.90981	−	3.26417i	−0.291509	−	0.161010i
$412$		0			0
$413$	4.34835	−	4.34835i	0.213968	−	0.213968i
$414$		0			0
$415$	−12.0802	+	13.2098i	−0.592996	+	0.648444i
$416$		0			0
$417$	−17.3949	+	18.0676i	−0.851834	+	0.884776i
$418$		0			0
$419$	−0.336617	+	0.583038i	−0.0164448	+	0.0284833i	−0.874131	−	0.485691i	$-0.838568\pi$
$419$	−0.336617	+	0.583038i	−0.0164448	+	0.0284833i	0.857686	+	0.514174i	$0.171901\pi$
$420$		0			0
$421$	1.48391	+	2.57020i	0.0723212	+	0.125264i	0.899918	−	0.436059i	$-0.143626\pi$
$421$	1.48391	+	2.57020i	0.0723212	+	0.125264i	−0.827597	+	0.561323i	$0.810293\pi$
$422$		0			0
$423$	12.2740	−	13.2424i	0.596782	−	0.643868i
$424$		0			0
$425$	−2.54042	+	14.5781i	−0.123229	+	0.707143i
$426$		0			0
$427$	−0.318056	−	1.18700i	−0.0153918	−	0.0574431i
$428$		0			0
$429$	−17.4617	−	28.9618i	−0.843061	−	1.39829i
$430$		0			0
$431$			28.1152i			1.35426i	0.735864	+	0.677130i	$0.236776\pi$
$431$			28.1152i			1.35426i	−0.735864	+	0.677130i	$0.763224\pi$
$432$		0			0
$433$	7.98191	+	7.98191i	0.383586	+	0.383586i	0.872392	−	0.488806i	$-0.162567\pi$
$433$	7.98191	+	7.98191i	0.383586	+	0.383586i	−0.488806	+	0.872392i	$0.662567\pi$
$434$		0			0
$435$	1.86629	−	9.29271i	0.0894820	−	0.445551i
$436$		0			0
$437$	−0.755115	+	0.202333i	−0.0361221	+	0.00967888i
$438$		0			0
$439$	12.3583	−	7.13508i	0.589830	−	0.340539i	−0.175200	−	0.984533i	$-0.556057\pi$
$439$	12.3583	−	7.13508i	0.589830	−	0.340539i	0.765030	+	0.643994i	$0.222724\pi$
$440$		0			0
$441$	−4.58034	−	7.28093i	−0.218111	−	0.346711i
$442$		0			0
$443$	10.0822	+	2.70151i	0.479019	+	0.128353i	0.490246	−	0.871584i	$-0.336907\pi$
$443$	10.0822	+	2.70151i	0.479019	+	0.128353i	−0.0112266	+	0.999937i	$0.503574\pi$
$444$		0			0
$445$	17.1282	−	32.9836i	0.811954	−	1.56357i
$446$		0			0
$447$	−25.6586	−	24.7033i	−1.21361	−	1.16843i
$448$		0			0
$449$	−3.77542			−0.178173			−0.0890866	−	0.996024i	$-0.528395\pi$
$449$	−3.77542			−0.178173			−0.0890866	+	0.996024i	$0.528395\pi$
$450$		0			0
$451$	14.3828			0.677259
$452$		0			0
$453$	−12.3439	+	3.55979i	−0.579967	+	0.167253i
$454$		0			0
$455$	−18.6101	+	35.8373i	−0.872457	+	1.68008i
$456$		0			0
$457$	−11.9147	−	3.19253i	−0.557345	−	0.149340i	−0.0308589	−	0.999524i	$-0.509824\pi$
$457$	−11.9147	−	3.19253i	−0.557345	−	0.149340i	−0.526486	+	0.850184i	$0.676491\pi$
$458$		0			0
$459$	15.3535	−	0.874575i	0.716638	−	0.0408217i
$460$		0			0
$461$	7.36613	−	4.25284i	0.343075	−	0.198074i	−0.318556	−	0.947904i	$-0.603198\pi$
$461$	7.36613	−	4.25284i	0.343075	−	0.198074i	0.661631	+	0.749830i	$0.269865\pi$
$462$		0			0
$463$	−5.70880	+	1.52967i	−0.265311	+	0.0710898i	−0.389022	−	0.921228i	$-0.627187\pi$
$463$	−5.70880	+	1.52967i	−0.265311	+	0.0710898i	0.123711	+	0.992318i	$0.460520\pi$
$464$		0			0
$465$	26.0608	−	8.79276i	1.20854	−	0.407754i
$466$		0			0
$467$	−20.0209	−	20.0209i	−0.926458	−	0.926458i	0.0710172	−	0.997475i	$-0.477375\pi$
$467$	−20.0209	−	20.0209i	−0.926458	−	0.926458i	−0.997475	+	0.0710172i	$0.977375\pi$
$468$		0			0
$469$			45.5265i			2.10222i
$470$		0			0
$471$	6.26673	−	0.118876i	0.288756	−	0.00547751i
$472$		0			0
$473$	5.94168	+	22.1747i	0.273199	+	1.01959i
$474$		0			0
$475$	13.4383	−	9.44976i	0.616591	−	0.433585i
$476$		0			0
$477$	39.2904	−	12.1425i	1.79898	−	0.555966i
$478$		0			0
$479$	7.81321	+	13.5329i	0.356995	+	0.618333i	0.987457	−	0.157887i	$-0.0504681\pi$
$479$	7.81321	+	13.5329i	0.356995	+	0.618333i	−0.630462	+	0.776220i	$0.717135\pi$
$480$		0			0
$481$	−2.95206	+	5.11313i	−0.134603	+	0.233138i
$482$		0			0
$483$	1.25654	+	0.311271i	0.0571746	+	0.0141633i
$484$		0			0
$485$	11.7143	−	12.8097i	0.531920	−	0.581657i
$486$		0			0
$487$	−5.97770	+	5.97770i	−0.270875	+	0.270875i	−0.829453	−	0.558577i	$-0.811347\pi$
$487$	−5.97770	+	5.97770i	−0.270875	+	0.270875i	0.558577	+	0.829453i	$0.311347\pi$
$488$		0			0
$489$	11.0599	−	6.66829i	0.500148	−	0.301551i
$490$		0			0
$491$	12.6264	+	7.28985i	0.569821	+	0.328986i	0.757078	−	0.653325i	$-0.226626\pi$
$491$	12.6264	+	7.28985i	0.569821	+	0.328986i	−0.187257	+	0.982311i	$0.559960\pi$
$492$		0			0
$493$	−1.87459	+	6.99608i	−0.0844275	+	0.315088i
$494$		0			0
$495$	9.72526	−	20.6026i	0.437118	−	0.926020i
$496$		0			0
$497$	2.83801	−	10.5916i	0.127302	−	0.475098i
$498$		0			0
$499$	−5.78570	−	3.34038i	−0.259004	−	0.149536i	0.364876	−	0.931056i	$-0.381111\pi$
$499$	−5.78570	−	3.34038i	−0.259004	−	0.149536i	−0.623880	+	0.781520i	$0.714445\pi$
$500$		0			0
$501$	−0.363882	−	19.1826i	−0.0162570	−	0.857016i
$502$		0			0
$503$	−14.2030	+	14.2030i	−0.633278	+	0.633278i	−0.948889	−	0.315610i	$-0.897791\pi$
$503$	−14.2030	+	14.2030i	−0.633278	+	0.633278i	0.315610	+	0.948889i	$0.397791\pi$
$504$		0			0
$505$	−1.38324	−	30.9697i	−0.0615534	−	1.37813i
$506$		0			0
$507$	−9.62357	−	33.3706i	−0.427398	−	1.48204i
$508$		0			0
$509$	−5.76147	+	9.97916i	−0.255373	+	0.442319i	−0.964997	−	0.262262i	$-0.915532\pi$
$509$	−5.76147	+	9.97916i	−0.255373	+	0.442319i	0.709624	+	0.704581i	$0.248865\pi$
$510$		0			0
$511$	−26.1543	−	45.3006i	−1.15700	−	2.00398i
$512$		0			0
$513$	−12.7392	−	11.3661i	−0.562450	−	0.501826i
$514$		0			0
$515$	6.49724	−	29.4467i	0.286303	−	1.29758i
$516$		0			0
$517$	5.29042	+	19.7441i	0.232672	+	0.868345i
$518$		0			0
$519$	13.3987	−	24.2584i	0.588138	−	1.06483i
$520$		0			0
$521$		−	0.929896i		−	0.0407395i	−0.999793	−	0.0203698i	$-0.993516\pi$
$521$		−	0.929896i		−	0.0407395i	0.999793	−	0.0203698i	$-0.00648434\pi$
$522$		0			0
$523$	−6.37455	−	6.37455i	−0.278740	−	0.278740i	0.553866	−	0.832606i	$-0.313152\pi$
$523$	−6.37455	−	6.37455i	−0.278740	−	0.278740i	−0.832606	+	0.553866i	$0.813152\pi$
$524$		0			0
$525$	−27.0446	+	2.93869i	−1.18032	+	0.128255i
$526$		0			0
$527$	−20.3013	+	5.43972i	−0.884338	+	0.236958i
$528$		0			0
$529$	19.8696	−	11.4717i	0.863894	−	0.498769i
$530$		0			0
$531$	−4.97116	+	3.12729i	−0.215730	+	0.135713i
$532$		0			0
$533$	23.5172	+	6.30141i	1.01864	+	0.272944i
$534$		0			0
$535$	37.6672	−	11.9179i	1.62850	−	0.515256i
$536$		0			0
$537$	−0.372965	+	1.50559i	−0.0160946	+	0.0649709i
$538$		0			0
$539$	9.73796			0.419444
$540$		0			0
$541$	36.6299			1.57484			0.787422	−	0.616414i	$-0.211415\pi$
$541$	36.6299			1.57484			0.787422	+	0.616414i	$0.211415\pi$
$542$		0			0
$543$	−9.54233	+	38.5205i	−0.409501	+	1.65307i
$544$		0			0
$545$	−14.2910	−	7.42126i	−0.612161	−	0.317892i
$546$		0			0
$547$	−24.8517	−	6.65899i	−1.06258	−	0.284718i	−0.315140	−	0.949045i	$-0.602052\pi$
$547$	−24.8517	−	6.65899i	−1.06258	−	0.284718i	−0.747442	+	0.664327i	$0.768718\pi$
$548$		0			0
$549$	0.0445099	+	1.17278i	0.00189964	+	0.0500532i
$550$		0			0
$551$	6.96360	−	4.02044i	0.296659	−	0.171276i
$552$		0			0
$553$	40.7471	−	10.9181i	1.73274	−	0.464287i
$554$		0			0
$555$	−3.96941	+	0.252802i	−0.168492	+	0.0107309i
$556$		0			0
$557$	12.1203	+	12.1203i	0.513554	+	0.513554i	0.915613	−	0.402060i	$-0.131706\pi$
$557$	12.1203	+	12.1203i	0.513554	+	0.513554i	−0.402060	+	0.915613i	$0.631706\pi$
$558$		0			0
$559$			38.8608i			1.64364i
$560$		0			0
$561$	−8.41724	+	15.2395i	−0.355376	+	0.643411i
$562$		0			0
$563$	−1.47668	−	5.51104i	−0.0622345	−	0.232262i	0.927802	−	0.373073i	$-0.121696\pi$
$563$	−1.47668	−	5.51104i	−0.0622345	−	0.232262i	−0.990037	+	0.140810i	$0.955029\pi$
$564$		0			0
$565$	−9.54993	−	2.10714i	−0.401769	−	0.0886479i
$566$		0			0
$567$	9.36583	+	26.6745i	0.393328	+	1.12023i
$568$		0			0
$569$	−13.0508	−	22.6046i	−0.547117	−	0.947635i	−0.998470	−	0.0552895i	$-0.982392\pi$
$569$	−13.0508	−	22.6046i	−0.547117	−	0.947635i	0.451353	−	0.892345i	$-0.350941\pi$
$570$		0			0
$571$	−13.0301	+	22.5688i	−0.545294	+	0.944477i	0.453294	+	0.891361i	$0.350249\pi$
$571$	−13.0301	+	22.5688i	−0.545294	+	0.944477i	−0.998588	+	0.0531159i	$0.983085\pi$
$572$		0			0
$573$	−1.77695	−	6.16174i	−0.0742332	−	0.257411i
$574$		0			0
$575$	0.762866	−	0.912856i	0.0318137	−	0.0380687i
$576$		0			0
$577$	15.3451	−	15.3451i	0.638825	−	0.638825i	−0.311441	−	0.950266i	$-0.600812\pi$
$577$	15.3451	−	15.3451i	0.638825	−	0.638825i	0.950266	+	0.311441i	$0.100812\pi$
$578$		0			0
$579$	0.499311	+	26.3220i	0.0207506	+	1.09390i
$580$		0			0
$581$	21.7777	+	12.5734i	0.903491	+	0.521631i
$582$		0			0
$583$	−12.0495	+	44.9692i	−0.499038	+	1.86243i
$584$		0			0
$585$	24.9282	−	29.4264i	1.03065	−	1.21663i
$586$		0			0
$587$	8.81041	−	32.8809i	0.363644	−	1.35714i	−0.505605	−	0.862765i	$-0.668731\pi$
$587$	8.81041	−	32.8809i	0.363644	−	1.35714i	0.869249	−	0.494374i	$-0.164603\pi$
$588$		0			0
$589$	20.2070	+	11.6665i	0.832616	+	0.480711i
$590$		0			0
$591$	17.0537	−	10.2821i	0.701495	−	0.422947i
$592$		0			0
$593$	−21.8483	+	21.8483i	−0.897200	+	0.897200i	−0.995188	−	0.0979873i	$-0.968760\pi$
$593$	−21.8483	+	21.8483i	−0.897200	+	0.897200i	0.0979873	+	0.995188i	$0.468760\pi$
$594$		0			0
$595$	20.7672	−	0.927555i	0.851374	−	0.0380261i
$596$		0			0
$597$	−1.68159	−	0.416566i	−0.0688231	−	0.0170489i
$598$		0			0
$599$	−1.90160	+	3.29366i	−0.0776971	+	0.134575i	−0.902256	−	0.431201i	$-0.858090\pi$
$599$	−1.90160	+	3.29366i	−0.0776971	+	0.134575i	0.824559	+	0.565776i	$0.191423\pi$
$600$		0			0
$601$	5.43898	+	9.42059i	0.221861	+	0.384274i	0.955373	−	0.295402i	$-0.0954536\pi$
$601$	5.43898	+	9.42059i	0.221861	+	0.384274i	−0.733512	+	0.679676i	$0.762120\pi$
$602$		0			0
$603$	9.65251	−	42.3948i	0.393081	−	1.72645i
$604$		0			0
$605$	0.643106	+	1.00725i	0.0261460	+	0.0409504i
$606$		0			0
$607$	−9.50370	−	35.4683i	−0.385743	−	1.43961i	−0.836992	−	0.547215i	$-0.815688\pi$
$607$	−9.50370	−	35.4683i	−0.385743	−	1.43961i	0.451249	−	0.892398i	$-0.350979\pi$
$608$		0			0
$609$	−13.3126	+	0.252532i	−0.539456	+	0.0102331i
$610$		0			0
$611$			34.6013i			1.39982i
$612$		0			0
$613$	18.5592	+	18.5592i	0.749600	+	0.749600i	0.974404	−	0.224804i	$-0.0721741\pi$
$613$	18.5592	+	18.5592i	0.749600	+	0.749600i	−0.224804	+	0.974404i	$0.572174\pi$
$614$		0			0
$615$	5.24346	+	15.5410i	0.211437	+	0.626675i
$616$		0			0
$617$	3.32138	−	0.889960i	0.133714	−	0.0358284i	−0.191342	−	0.981524i	$-0.561284\pi$
$617$	3.32138	−	0.889960i	0.133714	−	0.0358284i	0.325055	+	0.945695i	$0.394617\pi$
$618$		0			0
$619$	34.4779	−	19.9058i	1.38578	−	0.800082i	0.392946	−	0.919562i	$-0.371456\pi$
$619$	34.4779	−	19.9058i	1.38578	−	0.800082i	0.992837	+	0.119480i	$0.0381227\pi$
$620$		0			0
$621$	−1.10411	−	0.556270i	−0.0443064	−	0.0223223i
$622$		0			0
$623$	−50.4313	−	13.5130i	−2.02049	−	0.541388i
$624$		0			0
$625$	−8.45633	+	23.5264i	−0.338253	+	0.941055i
$626$		0			0
$627$	18.5708	−	5.35554i	0.741648	−	0.213880i
$628$		0			0
$629$	3.03939			0.121189
$630$		0			0
$631$	20.6099			0.820467			0.410234	−	0.911980i	$-0.365447\pi$
$631$	20.6099			0.820467			0.410234	+	0.911980i	$0.365447\pi$
$632$		0			0
$633$	−8.77925	−	8.45238i	−0.348944	−	0.335952i
$634$		0			0
$635$	0.648322	+	2.04906i	0.0257279	+	0.0813144i
$636$		0			0
$637$	15.9225	+	4.26641i	0.630871	+	0.169041i
$638$		0			0
$639$	−4.88841	+	9.26130i	−0.193383	+	0.366371i
$640$		0			0
$641$	13.1348	−	7.58339i	0.518794	−	0.299526i	−0.217647	−	0.976028i	$-0.569838\pi$
$641$	13.1348	−	7.58339i	0.518794	−	0.299526i	0.736441	+	0.676502i	$0.236505\pi$
$642$		0			0
$643$	34.2403	−	9.17467i	1.35031	−	0.361813i	0.490058	−	0.871690i	$-0.336975\pi$
$643$	34.2403	−	9.17467i	1.35031	−	0.361813i	0.860248	+	0.509876i	$0.170309\pi$
$644$		0			0
$645$	−21.7943	+	14.5043i	−0.858148	+	0.571105i
$646$		0			0
$647$	−1.01457	−	1.01457i	−0.0398869	−	0.0398869i	0.686882	−	0.726769i	$-0.258979\pi$
$647$	−1.01457	−	1.01457i	−0.0398869	−	0.0398869i	−0.726769	+	0.686882i	$0.758979\pi$
$648$		0			0
$649$		−	6.64873i		−	0.260986i
$650$		0			0
$651$	−19.9500	−	33.0888i	−0.781902	−	1.29685i
$652$		0			0
$653$	−3.56940	−	13.3212i	−0.139681	−	0.521298i	−0.999935	−	0.0114312i	$-0.996361\pi$
$653$	−3.56940	−	13.3212i	−0.139681	−	0.521298i	0.860253	−	0.509867i	$-0.170305\pi$
$654$		0			0
$655$	−12.6207	+	8.05806i	−0.493132	+	0.314854i
$656$		0			0
$657$	14.7506	+	47.7296i	0.575474	+	1.86211i
$658$		0			0
$659$	−8.41061	−	14.5676i	−0.327631	−	0.567473i	0.654410	−	0.756140i	$-0.272917\pi$
$659$	−8.41061	−	14.5676i	−0.327631	−	0.567473i	−0.982041	+	0.188666i	$0.939584\pi$
$660$		0			0
$661$	−25.1497	+	43.5606i	−0.978210	+	1.69431i	−0.309303	+	0.950964i	$0.600096\pi$
$661$	−25.1497	+	43.5606i	−0.978210	+	1.69431i	−0.668907	+	0.743346i	$0.733238\pi$
$662$		0			0
$663$	−20.4397	+	21.2302i	−0.793813	+	0.824512i
$664$		0			0
$665$	−17.0307	−	15.5744i	−0.660422	−	0.603950i
$666$		0			0
$667$	0.411735	−	0.411735i	0.0159424	−	0.0159424i
$668$		0			0
$669$	10.4478	+	5.77063i	0.403933	+	0.223105i
$670$		0			0
$671$	−1.15064	−	0.664320i	−0.0444198	−	0.0256458i
$672$		0			0
$673$	7.61500	−	28.4196i	0.293537	−	1.09549i	−0.648836	−	0.760929i	$-0.724744\pi$
$673$	7.61500	−	28.4196i	0.293537	−	1.09549i	0.942372	−	0.334566i	$-0.108590\pi$
$674$		0			0
$675$	25.8073	+	2.99744i	0.993322	+	0.115371i
$676$		0			0
$677$	−10.0801	+	37.6194i	−0.387409	+	1.44583i	0.446926	+	0.894571i	$0.352519\pi$
$677$	−10.0801	+	37.6194i	−0.387409	+	1.44583i	−0.834335	+	0.551258i	$0.814148\pi$
$678$		0			0
$679$	−21.1180	−	12.1925i	−0.810435	−	0.467905i
$680$		0			0
$681$	4.66549	+	2.57690i	0.178782	+	0.0987469i
$682$		0			0
$683$	26.6118	−	26.6118i	1.01827	−	1.01827i	0.0184430	−	0.999830i	$-0.494129\pi$
$683$	26.6118	−	26.6118i	1.01827	−	1.01827i	0.999830	−	0.0184430i	$-0.00587093\pi$
$684$		0			0
$685$	6.43196	+	5.88197i	0.245753	+	0.224739i
$686$		0			0
$687$	19.9131	−	20.6832i	0.759734	−	0.789114i
$688$		0			0
$689$	−39.4040	+	68.2497i	−1.50117	+	2.60011i
$690$		0			0
$691$	−17.5023	−	30.3149i	−0.665819	−	1.15323i	−0.979063	−	0.203560i	$-0.934749\pi$
$691$	−17.5023	−	30.3149i	−0.665819	−	1.15323i	0.313243	−	0.949673i	$-0.398584\pi$
$692$		0			0
$693$	−31.2064	−	7.10512i	−1.18543	−	0.269901i
$694$		0			0
$695$	27.2904	−	17.4243i	1.03518	−	0.660943i
$696$		0			0
$697$	−3.24391	−	12.1064i	−0.122872	−	0.458564i
$698$		0			0
$699$	−4.49580	−	7.45668i	−0.170047	−	0.282038i
$700$		0			0
$701$		−	13.1349i		−	0.496100i	−0.968747	−	0.248050i	$-0.920210\pi$
$701$		−	13.1349i		−	0.496100i	0.968747	−	0.248050i	$-0.0797897\pi$
$702$		0			0
$703$	−2.38596	−	2.38596i	−0.0899883	−	0.0899883i
$704$		0			0
$705$	−19.4054	+	12.9145i	−0.730850	+	0.486387i
$706$		0			0
$707$	−42.0656	+	11.2714i	−1.58204	+	0.423906i
$708$		0			0
$709$	−2.93501	+	1.69453i	−0.110227	+	0.0636393i	−0.554100	−	0.832450i	$-0.686937\pi$
$709$	−2.93501	+	1.69453i	−0.110227	+	0.0636393i	0.443873	+	0.896090i	$0.353604\pi$
$710$		0			0
$711$	−40.2590	+	1.52792i	−1.50983	+	0.0573016i
$712$		0			0
$713$	1.63210	+	0.437319i	0.0611224	+	0.0163777i
$714$		0			0
$715$	13.1704	+	41.6258i	0.492545	+	1.55672i
$716$		0			0
$717$	−32.4664	−	31.2576i	−1.21248	−	1.16734i
$718$		0			0
$719$	8.25562			0.307883			0.153941	−	0.988080i	$-0.450803\pi$
$719$	8.25562			0.307883			0.153941	+	0.988080i	$0.450803\pi$
$720$		0			0
$721$	−42.3616			−1.57763
$722$		0			0
$723$	−7.08453	+	2.04307i	−0.263476	+	0.0759825i
$724$		0			0
$725$	−5.14910	+	11.1003i	−0.191233	+	0.412254i
$726$		0			0
$727$	−12.7987	−	3.42941i	−0.474679	−	0.127190i	0.0135448	−	0.999908i	$-0.495688\pi$
$727$	−12.7987	−	3.42941i	−0.474679	−	0.127190i	−0.488224	+	0.872718i	$0.662355\pi$
$728$		0			0
$729$	−3.06604	−	26.8254i	−0.113557	−	0.993531i
$730$		0			0
$731$	17.3250	−	10.0026i	0.640789	−	0.369960i
$732$		0			0
$733$	−17.6204	+	4.72136i	−0.650823	+	0.174387i	−0.569101	−	0.822268i	$-0.692709\pi$
$733$	−17.6204	+	4.72136i	−0.650823	+	0.174387i	−0.0817220	+	0.996655i	$0.526042\pi$
$734$		0			0
$735$	3.55012	+	10.5222i	0.130948	+	0.388116i
$736$		0			0
$737$	34.8056	+	34.8056i	1.28208	+	1.28208i
$738$		0			0
$739$		−	36.9780i		−	1.36026i	−0.733092	−	0.680129i	$-0.761924\pi$
$739$		−	36.9780i		−	1.36026i	0.733092	−	0.680129i	$-0.238076\pi$
$740$		0			0
$741$	32.7114	−	0.620514i	1.20168	−	0.0227952i
$742$		0			0
$743$	−2.07096	−	7.72891i	−0.0759760	−	0.283546i	0.917477	−	0.397789i	$-0.130222\pi$
$743$	−2.07096	−	7.72891i	−0.0759760	−	0.283546i	−0.993453	+	0.114243i	$0.963556\pi$
$744$		0			0
$745$	24.7450	+	38.7562i	0.906588	+	1.41992i
$746$		0			0
$747$	−17.6138	−	16.3257i	−0.644456	−	0.597328i
$748$		0			0
$749$	−27.7501	−	48.0646i	−1.01397	−	1.75624i
$750$		0			0
$751$	18.6780	−	32.3513i	0.681570	−	1.18051i	−0.292932	−	0.956133i	$-0.594631\pi$
$751$	18.6780	−	32.3513i	0.681570	−	1.18051i	0.974502	−	0.224381i	$-0.0720359\pi$
$752$		0			0
$753$	15.3456	+	3.80143i	0.559226	+	0.138532i
$754$		0			0
$755$	16.5688	−	0.740035i	0.603001	−	0.0269326i
$756$		0			0
$757$	−16.4248	+	16.4248i	−0.596971	+	0.596971i	−0.939505	−	0.342535i	$-0.888715\pi$
$757$	−16.4248	+	16.4248i	−0.596971	+	0.596971i	0.342535	+	0.939505i	$0.388715\pi$
$758$		0			0
$759$	1.19861	−	0.722670i	0.0435068	−	0.0262313i
$760$		0			0
$761$	13.3436	+	7.70393i	0.483705	+	0.279267i	0.721959	−	0.691936i	$-0.243242\pi$
$761$	13.3436	+	7.70393i	0.483705	+	0.279267i	−0.238254	+	0.971203i	$0.576575\pi$
$762$		0			0
$763$	−5.85489	+	21.8507i	−0.211961	+	0.791050i
$764$		0			0
$765$	−19.5353	−	3.53931i	−0.706302	−	0.127964i
$766$		0			0
$767$	2.91295	−	10.8713i	0.105181	−	0.392540i
$768$		0			0
$769$	−40.4052	−	23.3279i	−1.45705	−	0.841227i	−0.458182	−	0.888858i	$-0.651499\pi$
$769$	−40.4052	−	23.3279i	−1.45705	−	0.841227i	−0.998865	+	0.0476316i	$0.984833\pi$
$770$		0			0
$771$	0.280001	+	14.7607i	0.0100840	+	0.531595i
$772$		0			0
$773$	−4.65902	+	4.65902i	−0.167573	+	0.167573i	−0.785912	−	0.618339i	$-0.787806\pi$
$773$	−4.65902	+	4.65902i	−0.167573	+	0.167573i	0.618339	+	0.785912i	$0.287806\pi$
$774$		0			0
$775$	−35.3663	+	3.16554i	−1.27039	+	0.113709i
$776$		0			0
$777$	1.54826	+	5.36872i	0.0555433	+	0.192602i
$778$		0			0
$779$	−6.95720	+	12.0502i	−0.249268	+	0.431744i
$780$		0			0
$781$	−5.92772	−	10.2671i	−0.212110	−	0.367386i
$782$		0			0
$783$	12.4504	+	2.58738i	0.444942	+	0.0924654i
$784$		0			0
$785$	−7.90172	−	1.74347i	−0.282024	−	0.0622271i
$786$		0			0
$787$	7.70309	+	28.7483i	0.274585	+	1.02477i	0.956119	+	0.292980i	$0.0946468\pi$
$787$	7.70309	+	28.7483i	0.274585	+	1.02477i	−0.681533	+	0.731787i	$0.738686\pi$
$788$		0			0
$789$	15.6881	−	28.4035i	0.558512	−	1.01119i
$790$		0			0
$791$			13.7384i			0.488481i
$792$		0			0
$793$	−1.59034	−	1.59034i	−0.0564748	−	0.0564748i
$794$		0			0
$795$	−52.9834	+	3.37439i	−1.87913	+	0.119677i
$796$		0			0
$797$	−28.2618	+	7.57273i	−1.00108	+	0.268240i	−0.721900	−	0.691998i	$-0.756731\pi$
$797$	−28.2618	+	7.57273i	−1.00108	+	0.268240i	−0.279185	+	0.960237i	$0.590064\pi$
$798$		0			0
$799$	15.4260	−	8.90622i	0.545734	−	0.315080i
$800$		0			0
$801$	44.0971	+	23.2759i	1.55809	+	0.822413i
$802$		0			0
$803$	−54.6281	−	14.6376i	−1.92778	−	0.516548i
$804$		0			0
$805$	−1.48316	−	0.770198i	−0.0522746	−	0.0271459i
$806$		0			0
$807$	2.14984	−	8.67847i	0.0756779	−	0.305497i
$808$		0			0
$809$	40.0053			1.40651			0.703255	−	0.710937i	$-0.251729\pi$
$809$	40.0053			1.40651			0.703255	+	0.710937i	$0.251729\pi$
$810$		0			0
$811$	6.60898			0.232073			0.116036	−	0.993245i	$-0.462981\pi$
$811$	6.60898			0.232073			0.116036	+	0.993245i	$0.462981\pi$
$812$		0			0
$813$	−1.28044	+	5.16888i	−0.0449070	+	0.181281i
$814$		0			0
$815$	−15.8961	+	5.02952i	−0.556815	+	0.176176i
$816$		0			0
$817$	−21.4525	−	5.74819i	−0.750529	−	0.201104i
$818$		0			0
$819$	−47.9124	−	25.2897i	−1.67420	−	0.883695i
$820$		0			0
$821$	−29.7026	+	17.1488i	−1.03663	+	0.598497i	−0.918876	−	0.394546i	$-0.870902\pi$
$821$	−29.7026	+	17.1488i	−1.03663	+	0.598497i	−0.117751	+	0.993043i	$0.537569\pi$
$822$		0			0
$823$	−21.5401	+	5.77164i	−0.750839	+	0.201187i	−0.613890	−	0.789391i	$-0.710396\pi$
$823$	−21.5401	+	5.77164i	−0.750839	+	0.201187i	−0.136949	+	0.990578i	$0.543730\pi$
$824$		0			0
$825$	−18.4293	+	22.9226i	−0.641624	+	0.798062i
$826$		0			0
$827$	24.5941	+	24.5941i	0.855221	+	0.855221i	0.990771	−	0.135549i	$-0.0432799\pi$
$827$	24.5941	+	24.5941i	0.855221	+	0.855221i	−0.135549	+	0.990771i	$0.543280\pi$
$828$		0			0
$829$		−	5.55712i		−	0.193007i	−0.995333	−	0.0965034i	$-0.969234\pi$
$829$		−	5.55712i		−	0.193007i	0.995333	−	0.0965034i	$-0.0307659\pi$
$830$		0			0
$831$	4.40357	−	7.97269i	0.152758	−	0.276570i
$832$		0			0
$833$	−2.19631	−	8.19674i	−0.0760977	−	0.284000i
$834$		0			0
$835$	−5.33680	+	24.1873i	−0.184687	+	0.837037i
$836$		0			0
$837$	11.5622	+	35.0424i	0.399647	+	1.21124i
$838$		0			0
$839$	16.4957	+	28.5713i	0.569493	+	0.986392i	0.996616	+	0.0821979i	$0.0261939\pi$
$839$	16.4957	+	28.5713i	0.569493	+	0.986392i	−0.427123	+	0.904194i	$0.640473\pi$
$840$		0			0
$841$	11.5054	−	19.9280i	0.396738	−	0.687171i
$842$		0			0
$843$	−2.69354	−	9.34009i	−0.0927703	−	0.321690i
$844$		0			0
$845$	2.00062	+	44.7923i	0.0688234	+	1.54090i
$846$		0			0
$847$	1.18709	−	1.18709i	0.0407888	−	0.0407888i
$848$		0			0
$849$	0.786164	+	41.4439i	0.0269811	+	1.42235i
$850$		0			0
$851$	−0.211612	−	0.122174i	−0.00725395	−	0.00418807i
$852$		0			0
$853$	13.3192	−	49.7079i	0.456040	−	1.70197i	−0.228972	−	0.973433i	$-0.573536\pi$
$853$	13.3192	−	49.7079i	0.456040	−	1.70197i	0.685012	−	0.728532i	$-0.259797\pi$
$854$		0			0
$855$	12.5571	+	18.1139i	0.429444	+	0.619482i
$856$		0			0
$857$	−5.49853	+	20.5208i	−0.187826	+	0.700977i	0.806181	+	0.591668i	$0.201530\pi$
$857$	−5.49853	+	20.5208i	−0.187826	+	0.700977i	−0.994008	+	0.109309i	$0.965136\pi$
$858$		0			0
$859$	−16.9006	−	9.75756i	−0.576640	−	0.332924i	0.183157	−	0.983084i	$-0.441368\pi$
$859$	−16.9006	−	9.75756i	−0.576640	−	0.332924i	−0.759797	+	0.650160i	$0.774702\pi$
$860$		0			0
$861$	19.7321	−	11.8969i	0.672469	−	0.405447i
$862$		0			0
$863$	−11.2268	+	11.2268i	−0.382165	+	0.382165i	−0.871882	−	0.489716i	$-0.837100\pi$
$863$	−11.2268	+	11.2268i	−0.382165	+	0.382165i	0.489716	+	0.871882i	$0.337100\pi$
$864$		0			0
$865$	−24.1442	+	26.4018i	−0.820926	+	0.897687i
$866$		0			0
$867$	−13.8550	−	3.43217i	−0.470540	−	0.116563i
$868$		0			0
$869$	22.8046	−	39.4987i	0.773592	−	1.33990i
$870$		0			0
$871$	41.6613	+	72.1595i	1.41164	+	2.44503i
$872$		0			0
$873$	17.0803	+	15.8312i	0.578080	+	0.535805i
$874$		0			0
$875$	34.8331	+	4.47944i	1.17757	+	0.151433i
$876$		0			0
$877$	6.52337	+	24.3456i	0.220279	+	0.822091i	0.984241	+	0.176831i	$0.0565845\pi$
$877$	6.52337	+	24.3456i	0.220279	+	0.822091i	−0.763963	+	0.645260i	$0.776749\pi$
$878$		0			0
$879$	1.70431	−	0.0323297i	0.0574851	−	0.00109045i
$880$		0			0
$881$		−	40.4262i		−	1.36199i	−0.732287	−	0.680997i	$-0.761547\pi$
$881$		−	40.4262i		−	1.36199i	0.732287	−	0.680997i	$-0.238453\pi$
$882$		0			0
$883$	−30.1834	−	30.1834i	−1.01575	−	1.01575i	−0.999874	−	0.0158776i	$-0.994946\pi$
$883$	−30.1834	−	30.1834i	−1.01575	−	1.01575i	−0.0158776	−	0.999874i	$-0.505054\pi$
$884$		0			0
$885$	7.18416	−	2.42389i	0.241493	−	0.0814783i
$886$		0			0
$887$	24.7478	−	6.63116i	0.830951	−	0.222653i	0.181823	−	0.983331i	$-0.441800\pi$
$887$	24.7478	−	6.63116i	0.830951	−	0.222653i	0.649129	+	0.760679i	$0.275134\pi$
$888$		0			0
$889$	2.61467	−	1.50958i	0.0876931	−	0.0506296i
$890$		0			0
$891$	27.5533	+	13.2327i	0.923070	+	0.443313i
$892$		0			0
$893$	−19.1011	−	5.11813i	−0.639195	−	0.171272i
$894$		0			0
$895$	0.922852	−	1.77713i	0.0308476	−	0.0594028i
$896$		0			0
$897$	2.27646	−	0.656495i	0.0760088	−	0.0219197i
$898$		0			0
$899$	−17.3794			−0.579636
$900$		0			0
$901$	40.5696			1.35157
$902$		0			0
$903$	26.4937	+	25.5073i	0.881654	+	0.848828i
$904$		0			0
$905$	23.6112	−	45.4678i	0.784863	−	1.51140i
$906$		0			0
$907$	−25.4617	−	6.82243i	−0.845441	−	0.226535i	−0.190002	−	0.981784i	$-0.560850\pi$
$907$	−25.4617	−	6.82243i	−0.845441	−	0.226535i	−0.655439	+	0.755248i	$0.727516\pi$
$908$		0			0
$909$	41.5617	−	1.57736i	1.37851	−	0.0523178i
$910$		0			0
$911$	16.9648	−	9.79463i	0.562069	−	0.324511i	−0.191907	−	0.981413i	$-0.561467\pi$
$911$	16.9648	−	9.79463i	0.562069	−	0.324511i	0.753975	+	0.656903i	$0.228134\pi$
$912$		0			0
$913$	26.2618	−	7.03683i	0.869139	−	0.232885i
$914$		0			0
$915$	0.298336	−	1.48548i	0.00986269	−	0.0491086i
$916$		0			0
$917$	14.8741	+	14.8741i	0.491186	+	0.491186i
$918$		0			0
$919$		−	3.89990i		−	0.128646i	−0.997929	−	0.0643230i	$-0.979511\pi$
$919$		−	3.89990i		−	0.128646i	0.997929	−	0.0643230i	$-0.0204888\pi$
$920$		0			0
$921$	3.12806	+	5.18816i	0.103073	+	0.170956i
$922$		0			0
$923$	−5.19412	−	19.3847i	−0.170967	−	0.638056i
$924$		0			0
$925$	5.05863	+	0.881530i	0.166327	+	0.0289845i
$926$		0			0
$927$	39.4476	+	8.98148i	1.29563	+	0.294990i
$928$		0			0
$929$	1.78619	+	3.09378i	0.0586031	+	0.101504i	0.893839	−	0.448389i	$-0.148002\pi$
$929$	1.78619	+	3.09378i	0.0586031	+	0.101504i	−0.835235	+	0.549892i	$0.814669\pi$
$930$		0			0
$931$	−4.71042	+	8.15868i	−0.154378	+	0.267390i
$932$		0			0
$933$	−4.48286	+	4.65623i	−0.146762	+	0.152438i
$934$		0			0
$935$	15.1677	−	16.5859i	0.496037	−	0.542418i
$936$		0			0
$937$	−8.38418	+	8.38418i	−0.273899	+	0.273899i	−0.830668	−	0.556769i	$-0.812041\pi$
$937$	−8.38418	+	8.38418i	−0.273899	+	0.273899i	0.556769	+	0.830668i	$0.312041\pi$
$938$		0			0
$939$	49.6698	+	27.4342i	1.62091	+	0.895282i
$940$		0			0
$941$	−5.27557	−	3.04585i	−0.171979	−	0.0992919i	0.411540	−	0.911392i	$-0.364991\pi$
$941$	−5.27557	−	3.04585i	−0.171979	−	0.0992919i	−0.583519	+	0.812100i	$0.698324\pi$
$942$		0			0
$943$	−0.260790	+	0.973281i	−0.00849248	+	0.0316944i
$944$		0			0
$945$	−3.69946	−	36.3097i	−0.120344	−	1.18116i
$946$		0			0
$947$	−10.6480	+	39.7391i	−0.346015	+	1.29135i	0.545407	+	0.838171i	$0.316375\pi$
$947$	−10.6480	+	39.7391i	−0.346015	+	1.29135i	−0.891422	+	0.453174i	$0.850292\pi$
$948$		0			0
$949$	−82.9090	−	47.8676i	−2.69134	−	1.55385i
$950$		0			0
$951$	−44.6868	−	24.6819i	−1.44907	−	0.800366i
$952$		0			0
$953$	11.2198	−	11.2198i	0.363445	−	0.363445i	−0.501634	−	0.865080i	$-0.667268\pi$
$953$	11.2198	−	11.2198i	0.363445	−	0.363445i	0.865080	+	0.501634i	$0.167268\pi$
$954$		0			0
$955$	0.369406	+	8.27071i	0.0119537	+	0.267634i
$956$		0			0
$957$	−9.98462	+	10.3707i	−0.322757	+	0.335239i
$958$		0			0
$959$	6.12207	−	10.6037i	0.197692	−	0.342412i
$960$		0			0
$961$	−9.71587	−	16.8284i	−0.313415	−	0.542851i
$962$		0			0
$963$	15.6506	+	50.6419i	0.504333	+	1.63191i
$964$		0			0
$965$	7.32304	−	33.1893i	0.235737	−	1.06840i
$966$		0			0
$967$	3.81915	+	14.2532i	0.122815	+	0.458354i	0.999752	−	0.0222519i	$-0.00708360\pi$
$967$	3.81915	+	14.2532i	0.122815	+	0.458354i	−0.876937	+	0.480605i	$0.840417\pi$
$968$		0			0
$969$	−8.69641	−	14.4238i	−0.279369	−	0.463358i
$970$		0			0
$971$		−	47.4037i		−	1.52126i	−0.649188	−	0.760628i	$-0.724891\pi$
$971$		−	47.4037i		−	1.52126i	0.649188	−	0.760628i	$-0.275109\pi$
$972$		0			0
$973$	−32.1630	−	32.1630i	−1.03110	−	1.03110i
$974$		0			0
$975$	−40.1764	+	29.4063i	−1.28668	+	0.941756i
$976$		0			0
$977$	49.8778	−	13.3647i	1.59573	−	0.427575i	0.651981	−	0.758235i	$-0.273938\pi$
$977$	49.8778	−	13.3647i	1.59573	−	0.427575i	0.943750	+	0.330660i	$0.107271\pi$
$978$		0			0
$979$	−48.8862	+	28.2245i	−1.56241	+	0.902058i
$980$		0			0
$981$	10.0849	−	19.1063i	0.321986	−	0.610017i
$982$		0			0
$983$	8.47712	+	2.27144i	0.270378	+	0.0724476i	0.391461	−	0.920195i	$-0.371970\pi$
$983$	8.47712	+	2.27144i	0.270378	+	0.0724476i	−0.121083	+	0.992642i	$0.538637\pi$
$984$		0			0
$985$	−24.5106	+	7.75517i	−0.780974	+	0.247100i
$986$		0			0
$987$	23.5897	+	22.7114i	0.750869	+	0.722913i
$988$		0			0
$989$	−1.60829			−0.0511407
$990$		0			0
$991$	−9.92720			−0.315348			−0.157674	−	0.987491i	$-0.550400\pi$
$991$	−9.92720			−0.315348			−0.157674	+	0.987491i	$0.550400\pi$
$992$		0			0
$993$	−11.3296	+	3.26729i	−0.359535	+	0.103684i
$994$		0			0
$995$	1.98488	+	1.03074i	0.0629248	+	0.0326765i
$996$		0			0
$997$	−21.2535	−	5.69487i	−0.673106	−	0.180358i	−0.0939527	−	0.995577i	$-0.529950\pi$
$997$	−21.2535	−	5.69487i	−0.673106	−	0.180358i	−0.579154	+	0.815218i	$0.696617\pi$
$998$		0			0
$999$	−0.303479	−	5.32767i	−0.00960164	−	0.168560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.10	✓	72
3.2	odd	2		1080.2.bt.a.233.13		72
4.3	odd	2		720.2.cu.e.113.9		72
5.2	odd	4	inner	360.2.bs.a.257.2	yes	72
9.2	odd	6	inner	360.2.bs.a.353.2	yes	72
9.7	even	3		1080.2.bt.a.953.6		72
15.2	even	4		1080.2.bt.a.17.6		72
20.7	even	4		720.2.cu.e.257.17		72
36.11	even	6		720.2.cu.e.353.17		72
45.2	even	12	inner	360.2.bs.a.137.10	yes	72
45.7	odd	12		1080.2.bt.a.737.13		72
180.47	odd	12		720.2.cu.e.497.9		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.10	✓	72	1.1	even	1	trivial
360.2.bs.a.137.10	yes	72	45.2	even	12	inner
360.2.bs.a.257.2	yes	72	5.2	odd	4	inner
360.2.bs.a.353.2	yes	72	9.2	odd	6	inner
720.2.cu.e.113.9		72	4.3	odd	2
720.2.cu.e.257.17		72	20.7	even	4
720.2.cu.e.353.17		72	36.11	even	6
720.2.cu.e.497.9		72	180.47	odd	12
1080.2.bt.a.17.6		72	15.2	even	4
1080.2.bt.a.233.13		72	3.2	odd	2
1080.2.bt.a.737.13		72	45.7	odd	12
1080.2.bt.a.953.6		72	9.7	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.416476 - 1.68123i) q^{3} +(-1.03051 + 1.98445i) q^{5} +(3.03419 + 0.813008i) q^{7} +(-2.65309 - 1.40039i) q^{9} +O(q^{10})\)	\(q+(0.416476 - 1.68123i) q^{3} +(-1.03051 + 1.98445i) q^{5} +(3.03419 + 0.813008i) q^{7} +(-2.65309 - 1.40039i) q^{9} +(2.94123 - 1.69812i) q^{11} +(5.55317 - 1.48797i) q^{13} +(2.90714 + 2.55901i) q^{15} +(-2.09273 - 2.09273i) q^{17} +3.28564i q^{19} +(2.63052 - 4.76258i) q^{21} +(0.0615809 + 0.229823i) q^{23} +(-2.87608 - 4.09001i) q^{25} +(-3.45933 + 3.87724i) q^{27} +(-1.22364 - 2.11940i) q^{29} +(3.55077 - 6.15011i) q^{31} +(-1.62998 - 5.65212i) q^{33} +(-4.74015 + 5.18338i) q^{35} +(-0.726179 + 0.726179i) q^{37} +(-0.188856 - 9.95587i) q^{39} +(3.66754 + 2.11746i) q^{41} +(-1.74949 + 6.52918i) q^{43} +(5.51305 - 3.82181i) q^{45} +(-1.55773 + 5.81352i) q^{47} +(2.48313 + 1.43364i) q^{49} +(-4.38994 + 2.64679i) q^{51} +(-9.69300 + 9.69300i) q^{53} +(0.338853 + 7.58666i) q^{55} +(5.52393 + 1.36839i) q^{57} +(0.978837 - 1.69540i) q^{59} +(-0.195605 - 0.338797i) q^{61} +(-6.91146 - 6.40603i) q^{63} +(-2.76982 + 12.5533i) q^{65} +(3.75113 + 13.9994i) q^{67} +(0.412033 - 0.00781600i) q^{69} -3.49075i q^{71} +(-11.7750 - 11.7750i) q^{73} +(-8.07408 + 3.13197i) q^{75} +(10.3048 - 2.76117i) q^{77} +(11.6301 - 6.71466i) q^{79} +(5.07782 + 7.43073i) q^{81} +(7.73261 + 2.07195i) q^{83} +(6.30950 - 1.99633i) q^{85} +(-4.07283 + 1.17454i) q^{87} -16.6210 q^{89} +18.0591 q^{91} +(-8.86096 - 8.53104i) q^{93} +(-6.52019 - 3.38590i) q^{95} +(-7.49838 - 2.00919i) q^{97} +(-10.1814 + 0.386408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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