LMFDB - Embedded newform 1860.2.s.a.433.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.2
Character	$\chi$	$=$	1860.433
Dual form			1860.2.s.a.1177.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.61302 - 1.54861i) q^{5} +(-2.80826 + 2.80826i) q^{7} -1.00000i q^{9} -2.34265i q^{11} +(-0.590842 + 0.590842i) q^{13} +(-0.0455449 + 2.23560i) q^{15} +(3.30425 + 3.30425i) q^{17} -6.38127i q^{19} -3.97148i q^{21} +(-3.47676 + 3.47676i) q^{23} +(0.203641 - 4.99585i) q^{25} +(0.707107 + 0.707107i) q^{27} +8.33933 q^{29} +(4.99725 + 2.45509i) q^{31} +(1.65650 + 1.65650i) q^{33} +(-0.180881 + 8.87866i) q^{35} +(3.67706 + 3.67706i) q^{37} -0.835576i q^{39} +4.78580 q^{41} +(-7.19448 + 7.19448i) q^{43} +(-1.54861 - 1.61302i) q^{45} +(7.44953 - 7.44953i) q^{47} -8.77265i q^{49} -4.67291 q^{51} +(-7.23439 + 7.23439i) q^{53} +(-3.62784 - 3.77873i) q^{55} +(4.51224 + 4.51224i) q^{57} +11.9801i q^{59} +4.05315i q^{61} +(2.80826 + 2.80826i) q^{63} +(-0.0380563 + 1.86802i) q^{65} +(7.19745 - 7.19745i) q^{67} -4.91689i q^{69} +2.52995 q^{71} +(10.7663 - 10.7663i) q^{73} +(3.38860 + 3.67660i) q^{75} +(6.57877 + 6.57877i) q^{77} -3.70118 q^{79} -1.00000 q^{81} +(2.11806 - 2.11806i) q^{83} +(10.4468 + 0.212827i) q^{85} +(-5.89680 + 5.89680i) q^{87} +18.5496 q^{89} -3.31847i q^{91} +(-5.26960 + 1.79758i) q^{93} +(-9.88207 - 10.2931i) q^{95} +(1.23892 - 1.23892i) q^{97} -2.34265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.61302	−	1.54861i	0.721363	−	0.692558i
$5$	1.61302	−	1.54861i	0.721363	−	0.692558i
$6$		0			0
$7$	−2.80826	+	2.80826i	−1.06142	+	1.06142i	−0.0634366	+	0.997986i	$0.520206\pi$
$7$	−2.80826	+	2.80826i	−1.06142	+	1.06142i	−0.997986	+	0.0634366i	$0.979794\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$		−	2.34265i		−	0.706336i	−0.935560	−	0.353168i	$-0.885104\pi$
$11$		−	2.34265i		−	0.706336i	0.935560	−	0.353168i	$-0.114896\pi$
$12$		0			0
$13$	−0.590842	+	0.590842i	−0.163870	+	0.163870i	−0.784279	−	0.620409i	$-0.786967\pi$
$13$	−0.590842	+	0.590842i	−0.163870	+	0.163870i	0.620409	+	0.784279i	$0.286967\pi$
$14$		0			0
$15$	−0.0455449	+	2.23560i	−0.0117596	+	0.577230i
$16$		0			0
$17$	3.30425	+	3.30425i	0.801397	+	0.801397i	0.983314	−	0.181917i	$-0.0582301\pi$
$17$	3.30425	+	3.30425i	0.801397	+	0.801397i	−0.181917	+	0.983314i	$0.558230\pi$
$18$		0			0
$19$		−	6.38127i		−	1.46396i	−0.681324	−	0.731982i	$-0.738596\pi$
$19$		−	6.38127i		−	1.46396i	0.681324	−	0.731982i	$-0.261404\pi$
$20$		0			0
$21$		−	3.97148i		−	0.866648i
$22$		0			0
$23$	−3.47676	+	3.47676i	−0.724955	+	0.724955i	−0.969610	−	0.244655i	$-0.921325\pi$
$23$	−3.47676	+	3.47676i	−0.724955	+	0.724955i	0.244655	+	0.969610i	$0.421325\pi$
$24$		0			0
$25$	0.203641	−	4.99585i	0.0407282	−	0.999170i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	8.33933			1.54857			0.774287	−	0.632834i	$-0.218108\pi$
$29$	8.33933			1.54857			0.774287	+	0.632834i	$0.218108\pi$
$30$		0			0
$31$	4.99725	+	2.45509i	0.897533	+	0.440947i
$31$	4.99725	+	2.45509i	0.897533	+	0.440947i
$32$		0			0
$33$	1.65650	+	1.65650i	0.288360	+	0.288360i
$34$		0			0
$35$	−0.180881	+	8.87866i	−0.0305744	+	1.50077i
$36$		0			0
$37$	3.67706	+	3.67706i	0.604504	+	0.604504i	0.941505	−	0.337000i	$-0.109412\pi$
$37$	3.67706	+	3.67706i	0.604504	+	0.604504i	−0.337000	+	0.941505i	$0.609412\pi$
$38$		0			0
$39$		−	0.835576i		−	0.133799i
$40$		0			0
$41$	4.78580			0.747416			0.373708	−	0.927546i	$-0.378086\pi$
$41$	4.78580			0.747416			0.373708	+	0.927546i	$0.378086\pi$
$42$		0			0
$43$	−7.19448	+	7.19448i	−1.09715	+	1.09715i	−0.102405	+	0.994743i	$0.532654\pi$
$43$	−7.19448	+	7.19448i	−1.09715	+	1.09715i	−0.994743	+	0.102405i	$0.967346\pi$
$44$		0			0
$45$	−1.54861	−	1.61302i	−0.230853	−	0.240454i
$46$		0			0
$47$	7.44953	−	7.44953i	1.08663	−	1.08663i	0.0907523	−	0.995873i	$-0.471073\pi$
$47$	7.44953	−	7.44953i	1.08663	−	1.08663i	0.995873	−	0.0907523i	$-0.0289272\pi$
$48$		0			0
$49$		−	8.77265i		−	1.25324i
$50$		0			0
$51$	−4.67291			−0.654338
$52$		0			0
$53$	−7.23439	+	7.23439i	−0.993719	+	0.993719i	−0.999980	−	0.00626091i	$-0.998007\pi$
$53$	−7.23439	+	7.23439i	−0.993719	+	0.993719i	0.00626091	+	0.999980i	$0.498007\pi$
$54$		0			0
$55$	−3.62784	−	3.77873i	−0.489178	−	0.509524i
$56$		0			0
$57$	4.51224	+	4.51224i	0.597661	+	0.597661i
$58$		0			0
$59$			11.9801i			1.55967i	0.625984	+	0.779836i	$0.284697\pi$
$59$			11.9801i			1.55967i	−0.625984	+	0.779836i	$0.715303\pi$
$60$		0			0
$61$			4.05315i			0.518953i	0.965749	+	0.259477i	$0.0835501\pi$
$61$			4.05315i			0.518953i	−0.965749	+	0.259477i	$0.916450\pi$
$62$		0			0
$63$	2.80826	+	2.80826i	0.353807	+	0.353807i
$64$		0			0
$65$	−0.0380563	+	1.86802i	−0.00472030	+	0.231699i
$66$		0			0
$67$	7.19745	−	7.19745i	0.879309	−	0.879309i	−0.114154	−	0.993463i	$-0.536416\pi$
$67$	7.19745	−	7.19745i	0.879309	−	0.879309i	0.993463	+	0.114154i	$0.0364159\pi$
$68$		0			0
$69$		−	4.91689i		−	0.591924i
$70$		0			0
$71$	2.52995			0.300249			0.150125	−	0.988667i	$-0.452032\pi$
$71$	2.52995			0.300249			0.150125	+	0.988667i	$0.452032\pi$
$72$		0			0
$73$	10.7663	−	10.7663i	1.26010	−	1.26010i	0.309059	−	0.951043i	$-0.399986\pi$
$73$	10.7663	−	10.7663i	1.26010	−	1.26010i	0.951043	−	0.309059i	$-0.100014\pi$
$74$		0			0
$75$	3.38860	+	3.67660i	0.391282	+	0.424537i
$76$		0			0
$77$	6.57877	+	6.57877i	0.749721	+	0.749721i
$78$		0			0
$79$	−3.70118			−0.416415			−0.208208	−	0.978085i	$-0.566763\pi$
$79$	−3.70118			−0.416415			−0.208208	+	0.978085i	$0.566763\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	2.11806	−	2.11806i	0.232488	−	0.232488i	−0.581243	−	0.813730i	$-0.697433\pi$
$83$	2.11806	−	2.11806i	0.232488	−	0.232488i	0.813730	+	0.581243i	$0.197433\pi$
$84$		0			0
$85$	10.4468	+	0.212827i	1.13311	+	0.0230844i
$86$		0			0
$87$	−5.89680	+	5.89680i	−0.632203	+	0.632203i
$88$		0			0
$89$	18.5496			1.96625			0.983124	−	0.182939i	$-0.0585609\pi$
$89$	18.5496			1.96625			0.983124	+	0.182939i	$0.0585609\pi$
$90$		0			0
$91$		−	3.31847i		−	0.347870i
$92$		0			0
$93$	−5.26960	+	1.79758i	−0.546432	+	0.186401i
$94$		0			0
$95$	−9.88207	−	10.2931i	−1.01388	−	1.05605i
$96$		0			0
$97$	1.23892	−	1.23892i	0.125793	−	0.125793i	−0.641407	−	0.767200i	$-0.721649\pi$
$97$	1.23892	−	1.23892i	0.125793	−	0.125793i	0.767200	+	0.641407i	$0.221649\pi$
$98$		0			0
$99$	−2.34265			−0.235445
$100$		0			0
$101$	2.92312			0.290862			0.145431	−	0.989368i	$-0.453543\pi$
$101$	2.92312			0.290862			0.145431	+	0.989368i	$0.453543\pi$
$102$		0			0
$103$	8.02128	+	8.02128i	0.790360	+	0.790360i	0.981553	−	0.191192i	$-0.0612354\pi$
$103$	8.02128	+	8.02128i	0.790360	+	0.790360i	−0.191192	+	0.981553i	$0.561235\pi$
$104$		0			0
$105$	−6.15026	−	6.40606i	−0.600203	−	0.625167i
$106$		0			0
$107$	−4.83791	+	4.83791i	−0.467698	+	0.467698i	−0.901168	−	0.433470i	$-0.857289\pi$
$107$	−4.83791	+	4.83791i	−0.467698	+	0.467698i	0.433470	+	0.901168i	$0.357289\pi$
$108$		0			0
$109$			14.3473i			1.37422i	0.726554	+	0.687109i	$0.241121\pi$
$109$			14.3473i			1.37422i	−0.726554	+	0.687109i	$0.758879\pi$
$110$		0			0
$111$	−5.20014			−0.493576
$112$		0			0
$113$	−3.72753	−	3.72753i	−0.350657	−	0.350657i	0.509697	−	0.860354i	$-0.329757\pi$
$113$	−3.72753	−	3.72753i	−0.350657	−	0.350657i	−0.860354	+	0.509697i	$0.829757\pi$
$114$		0			0
$115$	−0.223939	+	10.9922i	−0.0208824	+	1.02503i
$116$		0			0
$117$	0.590842	+	0.590842i	0.0546233	+	0.0546233i
$118$		0			0
$119$	−18.5584			−1.70124
$120$		0			0
$121$	5.51199			0.501090
$122$		0			0
$123$	−3.38407	+	3.38407i	−0.305131	+	0.305131i
$124$		0			0
$125$	−7.40813	−	8.37375i	−0.662603	−	0.748971i
$126$		0			0
$127$	13.1600	+	13.1600i	1.16776	+	1.16776i	0.982733	+	0.185031i	$0.0592387\pi$
$127$	13.1600	+	13.1600i	1.16776	+	1.16776i	0.185031	+	0.982733i	$0.440761\pi$
$128$		0			0
$129$		−	10.1745i		−	0.895817i
$130$		0			0
$131$	−19.8630			−1.73544			−0.867719	−	0.497056i	$-0.834414\pi$
$131$	−19.8630			−1.73544			−0.867719	+	0.497056i	$0.834414\pi$
$132$		0			0
$133$	17.9203	+	17.9203i	1.55388	+	1.55388i
$134$		0			0
$135$	2.23560	+	0.0455449i	0.192410	+	0.00391988i
$136$		0			0
$137$	−4.43440	−	4.43440i	−0.378857	−	0.378857i	0.491833	−	0.870690i	$-0.336327\pi$
$137$	−4.43440	−	4.43440i	−0.378857	−	0.378857i	−0.870690	+	0.491833i	$0.836327\pi$
$138$		0			0
$139$	−4.83171			−0.409820			−0.204910	−	0.978781i	$-0.565690\pi$
$139$	−4.83171			−0.409820			−0.204910	+	0.978781i	$0.565690\pi$
$140$		0			0
$141$			10.5352i			0.887226i
$142$		0			0
$143$	1.38414	+	1.38414i	0.115747	+	0.115747i
$144$		0			0
$145$	13.4515	−	12.9143i	1.11708	−	1.07248i
$146$		0			0
$147$	6.20320	+	6.20320i	0.511631	+	0.511631i
$148$		0			0
$149$		0	0.000206065i		0	1.68815e-5i	1.00000		8.44074e-6i	$2.68677e-6\pi$
$149$		0	0.000206065i		0	1.68815e-5i	−1.00000		8.44074e-6i	$0.999997\pi$
$150$		0			0
$151$		−	20.3716i		−	1.65782i	−0.559381	−	0.828911i	$-0.688961\pi$
$151$		−	20.3716i		−	1.65782i	0.559381	−	0.828911i	$-0.311039\pi$
$152$		0			0
$153$	3.30425	−	3.30425i	0.267132	−	0.267132i
$154$		0			0
$155$	11.8626	−	3.77868i	0.952828	−	0.303511i
$156$		0			0
$157$	2.62965	−	2.62965i	0.209869	−	0.209869i	−0.594343	−	0.804212i	$-0.702588\pi$
$157$	2.62965	−	2.62965i	0.209869	−	0.209869i	0.804212	+	0.594343i	$0.202588\pi$
$158$		0			0
$159$		−	10.2310i		−	0.811369i
$160$		0			0
$161$		−	19.5273i		−	1.53897i
$162$		0			0
$163$	1.39589	+	1.39589i	0.109335	+	0.109335i	0.759658	−	0.650323i	$-0.225366\pi$
$163$	1.39589	+	1.39589i	0.109335	+	0.109335i	−0.650323	+	0.759658i	$0.725366\pi$
$164$		0			0
$165$	5.23724	+	0.106696i	0.407719	+	0.00830626i
$166$		0			0
$167$	9.88999	+	9.88999i	0.765310	+	0.765310i	0.977277	−	0.211967i	$-0.0679868\pi$
$167$	9.88999	+	9.88999i	0.765310	+	0.765310i	−0.211967	+	0.977277i	$0.567987\pi$
$168$		0			0
$169$			12.3018i			0.946293i
$170$		0			0
$171$	−6.38127			−0.487988
$172$		0			0
$173$	0.820017	+	0.820017i	0.0623448	+	0.0623448i	0.737592	−	0.675247i	$-0.235963\pi$
$173$	0.820017	+	0.820017i	0.0623448	+	0.0623448i	−0.675247	+	0.737592i	$0.735963\pi$
$174$		0			0
$175$	13.4578	+	14.6015i	1.01731	+	1.10377i
$176$		0			0
$177$	−8.47118	−	8.47118i	−0.636733	−	0.636733i
$178$		0			0
$179$	6.44016			0.481360			0.240680	−	0.970605i	$-0.422630\pi$
$179$	6.44016			0.481360			0.240680	+	0.970605i	$0.422630\pi$
$180$		0			0
$181$			17.2858i			1.28484i	0.766352	+	0.642421i	$0.222070\pi$
$181$			17.2858i			1.28484i	−0.766352	+	0.642421i	$0.777930\pi$
$182$		0			0
$183$	−2.86601	−	2.86601i	−0.211862	−	0.211862i
$184$		0			0
$185$	11.6255	+	0.236840i	0.854721	+	0.0174128i
$186$		0			0
$187$	7.74069	−	7.74069i	0.566056	−	0.566056i
$188$		0			0
$189$	−3.97148			−0.288883
$190$		0			0
$191$	3.68562			0.266682			0.133341	−	0.991070i	$-0.457429\pi$
$191$	3.68562			0.266682			0.133341	+	0.991070i	$0.457429\pi$
$192$		0			0
$193$	5.17809	+	5.17809i	0.372727	+	0.372727i	0.868470	−	0.495742i	$-0.165104\pi$
$193$	5.17809	+	5.17809i	0.372727	+	0.372727i	−0.495742	+	0.868470i	$0.665104\pi$
$194$		0			0
$195$	−1.29398	−	1.34780i	−0.0926637	−	0.0965178i
$196$		0			0
$197$	−1.71608	−	1.71608i	−0.122266	−	0.122266i	0.643326	−	0.765592i	$-0.277554\pi$
$197$	−1.71608	−	1.71608i	−0.122266	−	0.122266i	−0.765592	+	0.643326i	$0.777554\pi$
$198$		0			0
$199$	−6.90093			−0.489194			−0.244597	−	0.969625i	$-0.578656\pi$
$199$	−6.90093			−0.489194			−0.244597	+	0.969625i	$0.578656\pi$
$200$		0			0
$201$			10.1787i			0.717953i
$202$		0			0
$203$	−23.4190	+	23.4190i	−1.64369	+	1.64369i
$204$		0			0
$205$	7.71957	−	7.41131i	0.539158	−	0.517628i
$206$		0			0
$207$	3.47676	+	3.47676i	0.241652	+	0.241652i
$208$		0			0
$209$	−14.9491			−1.03405
$210$		0			0
$211$	17.5192			1.20607			0.603036	−	0.797714i	$-0.293957\pi$
$211$	17.5192			1.20607			0.603036	+	0.797714i	$0.293957\pi$
$212$		0			0
$213$	−1.78894	+	1.78894i	−0.122576	+	0.122576i
$214$		0			0
$215$	−0.463398	+	22.7462i	−0.0316035	+	1.55128i
$216$		0			0
$217$	−20.9281	+	7.13906i	−1.42069	+	0.484631i
$218$		0			0
$219$			15.2259i			1.02887i
$220$		0			0
$221$	−3.90457			−0.262650
$222$		0			0
$223$	19.4287	−	19.4287i	1.30104	−	1.30104i	0.373356	−	0.927688i	$-0.378207\pi$
$223$	19.4287	−	19.4287i	1.30104	−	1.30104i	0.927688	−	0.373356i	$-0.121793\pi$
$224$		0			0
$225$	−4.99585	−	0.203641i	−0.333057	−	0.0135761i
$226$		0			0
$227$	9.62547	−	9.62547i	0.638865	−	0.638865i	−0.311411	−	0.950275i	$-0.600802\pi$
$227$	9.62547	−	9.62547i	0.638865	−	0.638865i	0.950275	+	0.311411i	$0.100802\pi$
$228$		0			0
$229$	−0.974170			−0.0643750			−0.0321875	−	0.999482i	$-0.510247\pi$
$229$	−0.974170			−0.0643750			−0.0321875	+	0.999482i	$0.510247\pi$
$230$		0			0
$231$	−9.30379			−0.612144
$232$		0			0
$233$	−19.6144	−	19.6144i	−1.28498	−	1.28498i	−0.937796	−	0.347188i	$-0.887137\pi$
$233$	−19.6144	−	19.6144i	−1.28498	−	1.28498i	−0.347188	−	0.937796i	$-0.612863\pi$
$234$		0			0
$235$	0.479826	−	23.5526i	0.0313004	−	1.53640i
$236$		0			0
$237$	2.61713	−	2.61713i	0.170001	−	0.170001i
$238$		0			0
$239$	15.3194			0.990930			0.495465	−	0.868628i	$-0.334998\pi$
$239$	15.3194			0.990930			0.495465	+	0.868628i	$0.334998\pi$
$240$		0			0
$241$		−	27.4249i		−	1.76659i	−0.468817	−	0.883295i	$-0.655320\pi$
$241$		−	27.4249i		−	1.76659i	0.468817	−	0.883295i	$-0.344680\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−13.5854	−	14.1504i	−0.867938	−	0.904037i
$246$		0			0
$247$	3.77032	+	3.77032i	0.239900	+	0.239900i
$248$		0			0
$249$			2.99539i			0.189825i
$250$		0			0
$251$			19.7833i			1.24871i	0.781141	+	0.624355i	$0.214638\pi$
$251$			19.7833i			1.24871i	−0.781141	+	0.624355i	$0.785362\pi$
$252$		0			0
$253$	8.14484	+	8.14484i	0.512062	+	0.512062i
$254$		0			0
$255$	−7.53748	+	7.23649i	−0.472015	+	0.453167i
$256$		0			0
$257$	−12.7635	+	12.7635i	−0.796166	+	0.796166i	−0.982489	−	0.186322i	$-0.940343\pi$
$257$	−12.7635	+	12.7635i	−0.796166	+	0.796166i	0.186322	+	0.982489i	$0.440343\pi$
$258$		0			0
$259$	−20.6523			−1.28327
$260$		0			0
$261$		−	8.33933i		−	0.516192i
$262$		0			0
$263$	−5.18659	+	5.18659i	−0.319819	+	0.319819i	−0.848697	−	0.528879i	$-0.822613\pi$
$263$	−5.18659	+	5.18659i	−0.319819	+	0.319819i	0.528879	+	0.848697i	$0.322613\pi$
$264$		0			0
$265$	−0.465969	+	22.8724i	−0.0286242	+	1.40504i
$266$		0			0
$267$	−13.1165	+	13.1165i	−0.802718	+	0.802718i
$268$		0			0
$269$	−27.5691			−1.68092			−0.840458	−	0.541876i	$-0.817714\pi$
$269$	−27.5691			−1.68092			−0.840458	+	0.541876i	$0.817714\pi$
$270$		0			0
$271$			7.47354i			0.453985i	0.973896	+	0.226993i	$0.0728893\pi$
$271$			7.47354i			0.453985i	−0.973896	+	0.226993i	$0.927111\pi$
$272$		0			0
$273$	2.34651	+	2.34651i	0.142018	+	0.142018i
$274$		0			0
$275$	−11.7035	−	0.477059i	−0.705750	−	0.0287678i
$276$		0			0
$277$	−3.81276	−	3.81276i	−0.229087	−	0.229087i	0.583224	−	0.812311i	$-0.301791\pi$
$277$	−3.81276	−	3.81276i	−0.229087	−	0.229087i	−0.812311	+	0.583224i	$0.801791\pi$
$278$		0			0
$279$	2.45509	−	4.99725i	0.146982	−	0.299178i
$280$		0			0
$281$	16.7586			0.999736			0.499868	−	0.866101i	$-0.333382\pi$
$281$	16.7586			0.999736			0.499868	+	0.866101i	$0.333382\pi$
$282$		0			0
$283$	5.44856	+	5.44856i	0.323883	+	0.323883i	0.850255	−	0.526372i	$-0.176448\pi$
$283$	5.44856	+	5.44856i	0.323883	+	0.323883i	−0.526372	+	0.850255i	$0.676448\pi$
$284$		0			0
$285$	14.2660	+	0.290634i	0.845044	+	0.0172157i
$286$		0			0
$287$	−13.4398	+	13.4398i	−0.793324	+	0.793324i
$288$		0			0
$289$			4.83608i			0.284475i
$290$		0			0
$291$			1.75209i			0.102710i
$292$		0			0
$293$	−14.5237	−	14.5237i	−0.848485	−	0.848485i	0.141459	−	0.989944i	$-0.454821\pi$
$293$	−14.5237	−	14.5237i	−0.848485	−	0.848485i	−0.989944	+	0.141459i	$0.954821\pi$
$294$		0			0
$295$	18.5524	+	19.3240i	1.08016	+	1.12509i
$296$		0			0
$297$	1.65650	−	1.65650i	0.0961201	−	0.0961201i
$298$		0			0
$299$		−	4.10843i		−	0.237597i
$300$		0			0
$301$		−	40.4079i		−	2.32907i
$302$		0			0
$303$	−2.06696	+	2.06696i	−0.118744	+	0.118744i
$304$		0			0
$305$	6.27674	+	6.53780i	0.359405	+	0.374354i
$306$		0			0
$307$	2.53470	−	2.53470i	0.144663	−	0.144663i	−0.631066	−	0.775729i	$-0.717382\pi$
$307$	2.53470	−	2.53470i	0.144663	−	0.144663i	0.775729	+	0.631066i	$0.217382\pi$
$308$		0			0
$309$	−11.3438			−0.645326
$310$		0			0
$311$	−0.165410			−0.00937956			−0.00468978	−	0.999989i	$-0.501493\pi$
$311$	−0.165410			−0.00937956			−0.00468978	+	0.999989i	$0.501493\pi$
$312$		0			0
$313$	−9.84027	+	9.84027i	−0.556205	+	0.556205i	−0.928225	−	0.372020i	$-0.878665\pi$
$313$	−9.84027	+	9.84027i	−0.556205	+	0.556205i	0.372020	+	0.928225i	$0.378665\pi$
$314$		0			0
$315$	8.87866	+	0.180881i	0.500256	+	0.0101915i
$316$		0			0
$317$	1.46344	−	1.46344i	0.0821951	−	0.0821951i	−0.664814	−	0.747009i	$-0.731489\pi$
$317$	1.46344	−	1.46344i	0.0821951	−	0.0821951i	0.747009	+	0.664814i	$0.231489\pi$
$318$		0			0
$319$		−	19.5361i		−	1.09381i
$320$		0			0
$321$		−	6.84183i		−	0.381874i
$322$		0			0
$323$	21.0853	−	21.0853i	1.17322	−	1.17322i
$324$		0			0
$325$	2.83144	+	3.07208i	0.157060	+	0.170408i
$326$		0			0
$327$	−10.1450	−	10.1450i	−0.561022	−	0.561022i
$328$		0			0
$329$			41.8404i			2.30674i
$330$		0			0
$331$		−	31.2427i		−	1.71725i	−0.512601	−	0.858627i	$-0.671318\pi$
$331$		−	31.2427i		−	1.71725i	0.512601	−	0.858627i	$-0.328682\pi$
$332$		0			0
$333$	3.67706	−	3.67706i	0.201501	−	0.201501i
$334$		0			0
$335$	0.463590	−	22.7556i	0.0253286	−	1.24327i
$336$		0			0
$337$	−6.37463	−	6.37463i	−0.347248	−	0.347248i	0.511835	−	0.859084i	$-0.328966\pi$
$337$	−6.37463	−	6.37463i	−0.347248	−	0.347248i	−0.859084	+	0.511835i	$0.828966\pi$
$338$		0			0
$339$	5.27153			0.286310
$340$		0			0
$341$	5.75142	−	11.7068i	0.311457	−	0.633960i
$342$		0			0
$343$	4.97806	+	4.97806i	0.268790	+	0.268790i
$344$		0			0
$345$	−7.61432	−	7.93102i	−0.409941	−	0.426992i
$346$		0			0
$347$	−26.1547	−	26.1547i	−1.40406	−	1.40406i	−0.786617	−	0.617441i	$-0.788169\pi$
$347$	−26.1547	−	26.1547i	−1.40406	−	1.40406i	−0.617441	−	0.786617i	$-0.711831\pi$
$348$		0			0
$349$		−	22.3736i		−	1.19763i	−0.800887	−	0.598815i	$-0.795638\pi$
$349$		−	22.3736i		−	1.19763i	0.800887	−	0.598815i	$-0.204362\pi$
$350$		0			0
$351$	−0.835576			−0.0445998
$352$		0			0
$353$	−14.1703	+	14.1703i	−0.754209	+	0.754209i	−0.975262	−	0.221053i	$-0.929051\pi$
$353$	−14.1703	+	14.1703i	−0.754209	+	0.754209i	0.221053	+	0.975262i	$0.429051\pi$
$354$		0			0
$355$	4.08084	−	3.91789i	0.216589	−	0.207940i
$356$		0			0
$357$	13.1227	−	13.1227i	0.694529	−	0.694529i
$358$		0			0
$359$			21.6850i			1.14449i	0.820082	+	0.572246i	$0.193928\pi$
$359$			21.6850i			1.14449i	−0.820082	+	0.572246i	$0.806072\pi$
$360$		0			0
$361$	−21.7206			−1.14319
$362$		0			0
$363$	−3.89756	+	3.89756i	−0.204569	+	0.204569i
$364$		0			0
$365$	0.693461	−	34.0390i	0.0362974	−	1.78168i
$366$		0			0
$367$	−21.3190	−	21.3190i	−1.11284	−	1.11284i	−0.992765	−	0.120078i	$-0.961686\pi$
$367$	−21.3190	−	21.3190i	−1.11284	−	1.11284i	−0.120078	−	0.992765i	$-0.538314\pi$
$368$		0			0
$369$		−	4.78580i		−	0.249139i
$370$		0			0
$371$		−	40.6321i		−	2.10951i
$372$		0			0
$373$	−18.5794	−	18.5794i	−0.962003	−	0.962003i	0.0373012	−	0.999304i	$-0.488124\pi$
$373$	−18.5794	−	18.5794i	−0.962003	−	0.962003i	−0.999304	+	0.0373012i	$0.988124\pi$
$374$		0			0
$375$	11.1595	+	0.682796i	0.576273	+	0.0352594i
$376$		0			0
$377$	−4.92722	+	4.92722i	−0.253765	+	0.253765i
$378$		0			0
$379$			21.4565i			1.10214i	0.834458	+	0.551072i	$0.185781\pi$
$379$			21.4565i			1.10214i	−0.834458	+	0.551072i	$0.814219\pi$
$380$		0			0
$381$	−18.6111			−0.953475
$382$		0			0
$383$	10.1362	−	10.1362i	0.517936	−	0.517936i	−0.399010	−	0.916946i	$-0.630646\pi$
$383$	10.1362	−	10.1362i	0.517936	−	0.517936i	0.916946	+	0.399010i	$0.130646\pi$
$384$		0			0
$385$	20.7996	+	0.423740i	1.06005	+	0.0215958i
$386$		0			0
$387$	7.19448	+	7.19448i	0.365716	+	0.365716i
$388$		0			0
$389$	−13.1383			−0.666139			−0.333069	−	0.942902i	$-0.608084\pi$
$389$	−13.1383			−0.666139			−0.333069	+	0.942902i	$0.608084\pi$
$390$		0			0
$391$	−22.9762			−1.16195
$392$		0			0
$393$	14.0453	−	14.0453i	0.708489	−	0.708489i
$394$		0			0
$395$	−5.97006	+	5.73166i	−0.300386	+	0.288391i
$396$		0			0
$397$	18.6614	−	18.6614i	0.936591	−	0.936591i	−0.0615154	−	0.998106i	$-0.519593\pi$
$397$	18.6614	−	18.6614i	0.936591	−	0.936591i	0.998106	+	0.0615154i	$0.0195933\pi$
$398$		0			0
$399$	−25.3431			−1.26874
$400$		0			0
$401$		−	4.56354i		−	0.227892i	−0.993487	−	0.113946i	$-0.963651\pi$
$401$		−	4.56354i		−	0.227892i	0.993487	−	0.113946i	$-0.0363492\pi$
$402$		0			0
$403$	−4.40315	+	1.50202i	−0.219337	+	0.0748207i
$404$		0			0
$405$	−1.61302	+	1.54861i	−0.0801514	+	0.0769508i
$406$		0			0
$407$	8.61406	−	8.61406i	0.426983	−	0.426983i
$408$		0			0
$409$	−10.2634			−0.507495			−0.253747	−	0.967271i	$-0.581663\pi$
$409$	−10.2634			−0.507495			−0.253747	+	0.967271i	$0.581663\pi$
$410$		0			0
$411$	6.27119			0.309335
$412$		0			0
$413$	−33.6431	−	33.6431i	−1.65547	−	1.65547i
$414$		0			0
$415$	0.136425	−	6.69652i	0.00669684	−	0.328719i
$416$		0			0
$417$	3.41654	−	3.41654i	0.167309	−	0.167309i
$418$		0			0
$419$			10.7538i			0.525357i	0.964883	+	0.262678i	$0.0846058\pi$
$419$			10.7538i			0.525357i	−0.964883	+	0.262678i	$0.915394\pi$
$420$		0			0
$421$	−17.7013			−0.862707			−0.431353	−	0.902183i	$-0.641964\pi$
$421$	−17.7013			−0.862707			−0.431353	+	0.902183i	$0.641964\pi$
$422$		0			0
$423$	−7.44953	−	7.44953i	−0.362209	−	0.362209i
$424$		0			0
$425$	17.1804	−	15.8346i	0.833372	−	0.768093i
$426$		0			0
$427$	−11.3823	−	11.3823i	−0.550829	−	0.550829i
$428$		0			0
$429$	−1.95746			−0.0945072
$430$		0			0
$431$	−18.4134			−0.886944			−0.443472	−	0.896288i	$-0.646254\pi$
$431$	−18.4134			−0.886944			−0.443472	+	0.896288i	$0.646254\pi$
$432$		0			0
$433$	−4.04147	+	4.04147i	−0.194221	+	0.194221i	−0.797517	−	0.603296i	$-0.793854\pi$
$433$	−4.04147	+	4.04147i	−0.194221	+	0.194221i	0.603296	+	0.797517i	$0.293854\pi$
$434$		0			0
$435$	−0.379814	+	18.6434i	−0.0182107	+	0.893885i
$436$		0			0
$437$	22.1862	+	22.1862i	1.06131	+	1.06131i
$438$		0			0
$439$		−	23.6616i		−	1.12931i	−0.825328	−	0.564654i	$-0.809010\pi$
$439$		−	23.6616i		−	1.12931i	0.825328	−	0.564654i	$-0.190990\pi$
$440$		0			0
$441$	−8.77265			−0.417745
$442$		0			0
$443$	7.48906	+	7.48906i	0.355816	+	0.355816i	0.862268	−	0.506452i	$-0.169043\pi$
$443$	7.48906	+	7.48906i	0.355816	+	0.355816i	−0.506452	+	0.862268i	$0.669043\pi$
$444$		0			0
$445$	29.9207	−	28.7259i	1.41838	−	1.36174i
$446$		0			0
$447$	−0.000145710	0	0.000145710i	−6.89184e−6	0	6.89184e-6i
$448$		0			0
$449$	−26.9184			−1.27036			−0.635179	−	0.772365i	$-0.719074\pi$
$449$	−26.9184			−1.27036			−0.635179	+	0.772365i	$0.719074\pi$
$450$		0			0
$451$		−	11.2115i		−	0.527927i
$452$		0			0
$453$	14.4049	+	14.4049i	0.676803	+	0.676803i
$454$		0			0
$455$	−5.13901	−	5.35275i	−0.240920	−	0.250941i
$456$		0			0
$457$	9.36231	+	9.36231i	0.437950	+	0.437950i	0.891322	−	0.453371i	$-0.149779\pi$
$457$	9.36231	+	9.36231i	0.437950	+	0.437950i	−0.453371	+	0.891322i	$0.649779\pi$
$458$		0			0
$459$			4.67291i			0.218113i
$460$		0			0
$461$		−	7.72661i		−	0.359864i	−0.983679	−	0.179932i	$-0.942412\pi$
$461$		−	7.72661i		−	0.359864i	0.983679	−	0.179932i	$-0.0575878\pi$
$462$		0			0
$463$	−15.3589	+	15.3589i	−0.713789	+	0.713789i	−0.967326	−	0.253537i	$-0.918406\pi$
$463$	−15.3589	+	15.3589i	−0.713789	+	0.713789i	0.253537	+	0.967326i	$0.418406\pi$
$464$		0			0
$465$	−5.71621	+	11.0601i	−0.265083	+	0.512898i
$466$		0			0
$467$	−22.1773	+	22.1773i	−1.02624	+	1.02624i	−0.0265988	+	0.999646i	$0.508468\pi$
$467$	−22.1773	+	22.1773i	−1.02624	+	1.02624i	−0.999646	+	0.0265988i	$0.991532\pi$
$468$		0			0
$469$			40.4246i			1.86664i
$470$		0			0
$471$			3.71889i			0.171357i
$472$		0			0
$473$	16.8542	+	16.8542i	0.774955	+	0.774955i
$474$		0			0
$475$	−31.8799	−	1.29949i	−1.46275	−	0.0596246i
$476$		0			0
$477$	7.23439	+	7.23439i	0.331240	+	0.331240i
$478$		0			0
$479$		−	23.8060i		−	1.08772i	−0.839175	−	0.543862i	$-0.816962\pi$
$479$		−	23.8060i		−	1.08772i	0.839175	−	0.543862i	$-0.183038\pi$
$480$		0			0
$481$	−4.34512			−0.198120
$482$		0			0
$483$	13.8079	+	13.8079i	0.628281	+	0.628281i
$484$		0			0
$485$	0.0797990	−	3.91699i	0.00362349	−	0.177861i
$486$		0			0
$487$	3.40350	+	3.40350i	0.154227	+	0.154227i	0.780003	−	0.625776i	$-0.215218\pi$
$487$	3.40350	+	3.40350i	0.154227	+	0.154227i	−0.625776	+	0.780003i	$0.715218\pi$
$488$		0			0
$489$	−1.97409			−0.0892716
$490$		0			0
$491$		−	3.39101i		−	0.153034i	−0.997068	−	0.0765170i	$-0.975620\pi$
$491$		−	3.39101i		−	0.153034i	0.997068	−	0.0765170i	$-0.0243799\pi$
$492$		0			0
$493$	27.5552	+	27.5552i	1.24102	+	1.24102i
$494$		0			0
$495$	−3.77873	+	3.62784i	−0.169841	+	0.163059i
$496$		0			0
$497$	−7.10475	+	7.10475i	−0.318691	+	0.318691i
$498$		0			0
$499$	−11.9195			−0.533590			−0.266795	−	0.963753i	$-0.585965\pi$
$499$	−11.9195			−0.533590			−0.266795	+	0.963753i	$0.585965\pi$
$500$		0			0
$501$	−13.9866			−0.624873
$502$		0			0
$503$	13.7680	+	13.7680i	0.613886	+	0.613886i	0.943956	−	0.330070i	$-0.107072\pi$
$503$	13.7680	+	13.7680i	0.613886	+	0.613886i	−0.330070	+	0.943956i	$0.607072\pi$
$504$		0			0
$505$	4.71505	−	4.52677i	0.209817	−	0.201439i
$506$		0			0
$507$	−8.69870	−	8.69870i	−0.386323	−	0.386323i
$508$		0			0
$509$	8.50149			0.376822			0.188411	−	0.982090i	$-0.439666\pi$
$509$	8.50149			0.376822			0.188411	+	0.982090i	$0.439666\pi$
$510$		0			0
$511$			60.4692i			2.67500i
$512$		0			0
$513$	4.51224	−	4.51224i	0.199220	−	0.199220i
$514$		0			0
$515$	25.3603	+	0.516653i	1.11751	+	0.0227664i
$516$		0			0
$517$	−17.4517	−	17.4517i	−0.767523	−	0.767523i
$518$		0			0
$519$	−1.15968			−0.0509043
$520$		0			0
$521$	−13.4865			−0.590854			−0.295427	−	0.955365i	$-0.595462\pi$
$521$	−13.4865			−0.590854			−0.295427	+	0.955365i	$0.595462\pi$
$522$		0			0
$523$	−30.2304	+	30.2304i	−1.32188	+	1.32188i	−0.409635	+	0.912250i	$0.634344\pi$
$523$	−30.2304	+	30.2304i	−1.32188	+	1.32188i	−0.912250	+	0.409635i	$0.865656\pi$
$524$		0			0
$525$	−19.8409	−	0.808755i	−0.865929	−	0.0352970i
$526$		0			0
$527$	8.39993	+	24.6244i	0.365907	+	1.07265i
$528$		0			0
$529$		−	1.17577i		−	0.0511204i
$530$		0			0
$531$	11.9801			0.519890
$532$		0			0
$533$	−2.82765	+	2.82765i	−0.122479	+	0.122479i
$534$		0			0
$535$	−0.311611	+	15.2956i	−0.0134721	+	0.661288i
$536$		0			0
$537$	−4.55388	+	4.55388i	−0.196514	+	0.196514i
$538$		0			0
$539$	−20.5513			−0.885205
$540$		0			0
$541$	26.1455			1.12408			0.562041	−	0.827110i	$-0.310016\pi$
$541$	26.1455			1.12408			0.562041	+	0.827110i	$0.310016\pi$
$542$		0			0
$543$	−12.2229	−	12.2229i	−0.524535	−	0.524535i
$544$		0			0
$545$	22.2183	+	23.1424i	0.951726	+	0.991310i
$546$		0			0
$547$	12.6490	−	12.6490i	0.540831	−	0.540831i	−0.382942	−	0.923773i	$-0.625089\pi$
$547$	12.6490	−	12.6490i	0.540831	−	0.540831i	0.923773	+	0.382942i	$0.125089\pi$
$548$		0			0
$549$	4.05315			0.172984
$550$		0			0
$551$		−	53.2155i		−	2.26706i
$552$		0			0
$553$	10.3939	−	10.3939i	0.441992	−	0.441992i
$554$		0			0
$555$	−8.38791	+	8.05297i	−0.356047	+	0.341830i
$556$		0			0
$557$	20.4859	+	20.4859i	0.868017	+	0.868017i	0.992253	−	0.124235i	$-0.0396478\pi$
$557$	20.4859	+	20.4859i	0.868017	+	0.868017i	−0.124235	+	0.992253i	$0.539648\pi$
$558$		0			0
$559$		−	8.50159i		−	0.359579i
$560$		0			0
$561$			10.9470i			0.462183i
$562$		0			0
$563$	19.2280	+	19.2280i	0.810365	+	0.810365i	0.984688	−	0.174323i	$-0.0557738\pi$
$563$	19.2280	+	19.2280i	0.810365	+	0.810365i	−0.174323	+	0.984688i	$0.555774\pi$
$564$		0			0
$565$	−11.7851	−	0.240091i	−0.495801	−	0.0101007i
$566$		0			0
$567$	2.80826	−	2.80826i	0.117936	−	0.117936i
$568$		0			0
$569$	32.1659			1.34847			0.674233	−	0.738518i	$-0.264474\pi$
$569$	32.1659			1.34847			0.674233	+	0.738518i	$0.264474\pi$
$570$		0			0
$571$		−	24.2190i		−	1.01353i	−0.862084	−	0.506766i	$-0.830841\pi$
$571$		−	24.2190i		−	1.01353i	0.862084	−	0.506766i	$-0.169159\pi$
$572$		0			0
$573$	−2.60613	+	2.60613i	−0.108873	+	0.108873i
$574$		0			0
$575$	16.6614	+	18.0774i	0.694828	+	0.753880i
$576$		0			0
$577$	−7.82073	+	7.82073i	−0.325581	+	0.325581i	−0.850903	−	0.525322i	$-0.823945\pi$
$577$	−7.82073	+	7.82073i	−0.325581	+	0.325581i	0.525322	+	0.850903i	$0.323945\pi$
$578$		0			0
$579$	−7.32293			−0.304331
$580$		0			0
$581$			11.8961i			0.493535i
$582$		0			0
$583$	16.9476	+	16.9476i	0.701900	+	0.701900i
$584$		0			0
$585$	1.86802	+	0.0380563i	0.0772330	+	0.00157343i
$586$		0			0
$587$	13.1603	+	13.1603i	0.543182	+	0.543182i	0.924460	−	0.381279i	$-0.124516\pi$
$587$	13.1603	+	13.1603i	0.543182	+	0.543182i	−0.381279	+	0.924460i	$0.624516\pi$
$588$		0			0
$589$	15.6666	−	31.8888i	0.645530	−	1.31396i
$590$		0			0
$591$	2.42690			0.0998295
$592$		0			0
$593$	−29.5952	−	29.5952i	−1.21533	−	1.21533i	−0.969249	−	0.246082i	$-0.920857\pi$
$593$	−29.5952	−	29.5952i	−1.21533	−	1.21533i	−0.246082	−	0.969249i	$-0.579143\pi$
$594$		0			0
$595$	−29.9349	+	28.7396i	−1.22721	+	1.17821i
$596$		0			0
$597$	4.87970	−	4.87970i	0.199713	−	0.199713i
$598$		0			0
$599$			32.1078i			1.31189i	0.754808	+	0.655946i	$0.227730\pi$
$599$			32.1078i			1.31189i	−0.754808	+	0.655946i	$0.772270\pi$
$600$		0			0
$601$			3.91825i			0.159829i	0.996802	+	0.0799144i	$0.0254647\pi$
$601$			3.91825i			0.159829i	−0.996802	+	0.0799144i	$0.974535\pi$
$602$		0			0
$603$	−7.19745	−	7.19745i	−0.293103	−	0.293103i
$604$		0			0
$605$	8.89092	−	8.53589i	0.361467	−	0.347033i
$606$		0			0
$607$	31.9631	−	31.9631i	1.29734	−	1.29734i	0.367197	−	0.930143i	$-0.380317\pi$
$607$	31.9631	−	31.9631i	1.29734	−	1.29734i	0.930143	−	0.367197i	$-0.119683\pi$
$608$		0			0
$609$		−	33.1195i		−	1.34207i
$610$		0			0
$611$			8.80298i			0.356131i
$612$		0			0
$613$	−12.0660	+	12.0660i	−0.487339	+	0.487339i	−0.907466	−	0.420126i	$-0.861986\pi$
$613$	−12.0660	+	12.0660i	−0.487339	+	0.487339i	0.420126	+	0.907466i	$0.361986\pi$
$614$		0			0
$615$	−0.217969	+	10.6991i	−0.00878935	+	0.431431i
$616$		0			0
$617$	14.8193	−	14.8193i	0.596604	−	0.596604i	−0.342803	−	0.939407i	$-0.611376\pi$
$617$	14.8193	−	14.8193i	0.596604	−	0.596604i	0.939407	+	0.342803i	$0.111376\pi$
$618$		0			0
$619$	−11.9749			−0.481314			−0.240657	−	0.970610i	$-0.577363\pi$
$619$	−11.9749			−0.481314			−0.240657	+	0.970610i	$0.577363\pi$
$620$		0			0
$621$	−4.91689			−0.197308
$622$		0			0
$623$	−52.0920	+	52.0920i	−2.08702	+	2.08702i
$624$		0			0
$625$	−24.9171	−	2.03472i	−0.996682	−	0.0813888i
$626$		0			0
$627$	10.5706	−	10.5706i	0.422149	−	0.422149i
$628$		0			0
$629$			24.2998i			0.968896i
$630$		0			0
$631$		−	28.8804i		−	1.14971i	−0.818255	−	0.574855i	$-0.805058\pi$
$631$		−	28.8804i		−	1.14971i	0.818255	−	0.574855i	$-0.194942\pi$
$632$		0			0
$633$	−12.3880	+	12.3880i	−0.492377	+	0.492377i
$634$		0			0
$635$	41.6070	+	0.847641i	1.65113	+	0.0336376i
$636$		0			0
$637$	5.18324	+	5.18324i	0.205368	+	0.205368i
$638$		0			0
$639$		−	2.52995i		−	0.100083i
$640$		0			0
$641$		−	8.72732i		−	0.344708i	−0.985035	−	0.172354i	$-0.944863\pi$
$641$		−	8.72732i		−	0.344708i	0.985035	−	0.172354i	$-0.0551374\pi$
$642$		0			0
$643$	0.343295	−	0.343295i	0.0135382	−	0.0135382i	−0.700305	−	0.713843i	$-0.746953\pi$
$643$	0.343295	−	0.343295i	0.0135382	−	0.0135382i	0.713843	+	0.700305i	$0.246953\pi$
$644$		0			0
$645$	−15.7563	−	16.4117i	−0.620405	−	0.646209i
$646$		0			0
$647$	−9.89103	−	9.89103i	−0.388857	−	0.388857i	0.485423	−	0.874280i	$-0.338666\pi$
$647$	−9.89103	−	9.89103i	−0.388857	−	0.388857i	−0.874280	+	0.485423i	$0.838666\pi$
$648$		0			0
$649$	28.0651			1.10165
$650$		0			0
$651$	9.75034	−	19.8465i	0.382146	−	0.777845i
$652$		0			0
$653$	0.510799	+	0.510799i	0.0199891	+	0.0199891i	0.717031	−	0.697042i	$-0.245501\pi$
$653$	0.510799	+	0.510799i	0.0199891	+	0.0199891i	−0.697042	+	0.717031i	$0.745501\pi$
$654$		0			0
$655$	−32.0393	+	30.7599i	−1.25188	+	1.20189i
$656$		0			0
$657$	−10.7663	−	10.7663i	−0.420034	−	0.420034i
$658$		0			0
$659$			11.1578i			0.434647i	0.976100	+	0.217324i	$0.0697327\pi$
$659$			11.1578i			0.434647i	−0.976100	+	0.217324i	$0.930267\pi$
$660$		0			0
$661$	18.2481			0.709768			0.354884	−	0.934910i	$-0.384520\pi$
$661$	18.2481			0.709768			0.354884	+	0.934910i	$0.384520\pi$
$662$		0			0
$663$	2.76095	−	2.76095i	0.107226	−	0.107226i
$664$		0			0
$665$	56.6571	+	1.15425i	2.19707	+	0.0447598i
$666$		0			0
$667$	−28.9939	+	28.9939i	−1.12265	+	1.12265i
$668$		0			0
$669$			27.4764i			1.06230i
$670$		0			0
$671$	9.49513			0.366555
$672$		0			0
$673$	7.41450	−	7.41450i	0.285808	−	0.285808i	−0.549612	−	0.835420i	$-0.685224\pi$
$673$	7.41450	−	7.41450i	0.285808	−	0.285808i	0.835420	+	0.549612i	$0.185224\pi$
$674$		0			0
$675$	3.67660	−	3.38860i	0.141512	−	0.130427i
$676$		0			0
$677$	−1.48326	−	1.48326i	−0.0570064	−	0.0570064i	0.678029	−	0.735035i	$-0.262834\pi$
$677$	−1.48326	−	1.48326i	−0.0570064	−	0.0570064i	−0.735035	+	0.678029i	$0.762834\pi$
$678$		0			0
$679$			6.95841i			0.267039i
$680$		0			0
$681$			13.6125i			0.521631i
$682$		0			0
$683$	21.0351	+	21.0351i	0.804885	+	0.804885i	0.983855	−	0.178970i	$-0.0572764\pi$
$683$	21.0351	+	21.0351i	0.804885	+	0.804885i	−0.178970	+	0.983855i	$0.557276\pi$
$684$		0			0
$685$	−14.0199	−	0.285621i	−0.535673	−	0.0109130i
$686$		0			0
$687$	0.688842	−	0.688842i	0.0262810	−	0.0262810i
$688$		0			0
$689$		−	8.54875i		−	0.325682i
$690$		0			0
$691$	−15.3014			−0.582094			−0.291047	−	0.956709i	$-0.594004\pi$
$691$	−15.3014			−0.582094			−0.291047	+	0.956709i	$0.594004\pi$
$692$		0			0
$693$	6.57877	−	6.57877i	0.249907	−	0.249907i
$694$		0			0
$695$	−7.79363	+	7.48242i	−0.295629	+	0.283824i
$696$		0			0
$697$	15.8134	+	15.8134i	0.598977	+	0.598977i
$698$		0			0
$699$	27.7390			1.04918
$700$		0			0
$701$	−16.8005			−0.634547			−0.317273	−	0.948334i	$-0.602767\pi$
$701$	−16.8005			−0.634547			−0.317273	+	0.948334i	$0.602767\pi$
$702$		0			0
$703$	23.4643	−	23.4643i	0.884972	−	0.884972i
$704$		0			0
$705$	16.3149	+	16.9935i	0.614455	+	0.640012i
$706$		0			0
$707$	−8.20889	+	8.20889i	−0.308727	+	0.308727i
$708$		0			0
$709$	7.82240			0.293776			0.146888	−	0.989153i	$-0.453074\pi$
$709$	7.82240			0.293776			0.146888	+	0.989153i	$0.453074\pi$
$710$		0			0
$711$			3.70118i			0.138805i
$712$		0			0
$713$	−25.9100	+	8.83850i	−0.970338	+	0.331005i
$714$		0			0
$715$	4.37611	+	0.0891525i	0.163657	+	0.00333412i
$716$		0			0
$717$	−10.8325	+	10.8325i	−0.404546	+	0.404546i
$718$		0			0
$719$	17.4492			0.650746			0.325373	−	0.945586i	$-0.394510\pi$
$719$	17.4492			0.650746			0.325373	+	0.945586i	$0.394510\pi$
$720$		0			0
$721$	−45.0517			−1.67781
$722$		0			0
$723$	19.3923	+	19.3923i	0.721208	+	0.721208i
$724$		0			0
$725$	1.69823	−	41.6621i	0.0630706	−	1.54729i
$726$		0			0
$727$	31.7736	−	31.7736i	1.17842	−	1.17842i	0.198268	−	0.980148i	$-0.436468\pi$
$727$	31.7736	−	31.7736i	1.17842	−	1.17842i	0.980148	−	0.198268i	$-0.0635317\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−47.5447			−1.75850
$732$		0			0
$733$	11.9121	+	11.9121i	0.439982	+	0.439982i	0.892006	−	0.452024i	$-0.149298\pi$
$733$	11.9121	+	11.9121i	0.439982	+	0.439982i	−0.452024	+	0.892006i	$0.649298\pi$
$734$		0			0
$735$	19.6122	+	0.399550i	0.723406	+	0.0147376i
$736$		0			0
$737$	−16.8611	−	16.8611i	−0.621087	−	0.621087i
$738$		0			0
$739$	−5.48940			−0.201931			−0.100965	−	0.994890i	$-0.532193\pi$
$739$	−5.48940			−0.201931			−0.100965	+	0.994890i	$0.532193\pi$
$740$		0			0
$741$	−5.33204			−0.195877
$742$		0			0
$743$	−25.0099	+	25.0099i	−0.917524	+	0.917524i	−0.996849	−	0.0793249i	$-0.974724\pi$
$743$	−25.0099	+	25.0099i	−0.917524	+	0.917524i	0.0793249	+	0.996849i	$0.474724\pi$
$744$		0			0
$745$	0.000319113	0	0.000332386i	1.16914e−5	0	1.21777e-5i
$746$		0			0
$747$	−2.11806	−	2.11806i	−0.0774959	−	0.0774959i
$748$		0			0
$749$		−	27.1722i		−	0.992851i
$750$		0			0
$751$	48.8733			1.78341			0.891706	−	0.452615i	$-0.149509\pi$
$751$	48.8733			1.78341			0.891706	+	0.452615i	$0.149509\pi$
$752$		0			0
$753$	−13.9889	−	13.9889i	−0.509784	−	0.509784i
$754$		0			0
$755$	−31.5476	−	32.8598i	−1.14814	−	1.19589i
$756$		0			0
$757$	16.3606	+	16.3606i	0.594635	+	0.594635i	0.938880	−	0.344245i	$-0.111865\pi$
$757$	16.3606	+	16.3606i	0.594635	+	0.594635i	−0.344245	+	0.938880i	$0.611865\pi$
$758$		0			0
$759$	−11.5185			−0.418097
$760$		0			0
$761$		−	11.3566i		−	0.411677i	−0.978586	−	0.205838i	$-0.934008\pi$
$761$		−	11.3566i		−	0.411677i	0.978586	−	0.205838i	$-0.0659921\pi$
$762$		0			0
$763$	−40.2908	−	40.2908i	−1.45863	−	1.45863i
$764$		0			0
$765$	0.212827	−	10.4468i	0.00769479	−	0.377704i
$766$		0			0
$767$	−7.07832	−	7.07832i	−0.255583	−	0.255583i
$768$		0			0
$769$			45.6650i			1.64672i	0.567517	+	0.823362i	$0.307904\pi$
$769$			45.6650i			1.64672i	−0.567517	+	0.823362i	$0.692096\pi$
$770$		0			0
$771$		−	18.0503i		−	0.650067i
$772$		0			0
$773$	−26.0941	+	26.0941i	−0.938541	+	0.938541i	−0.998218	−	0.0596768i	$-0.980993\pi$
$773$	−26.0941	+	26.0941i	−0.938541	+	0.938541i	0.0596768	+	0.998218i	$0.480993\pi$
$774$		0			0
$775$	13.2829	−	24.4656i	0.477136	−	0.878829i
$776$		0			0
$777$	14.6034	−	14.6034i	0.523892	−	0.523892i
$778$		0			0
$779$		−	30.5395i		−	1.09419i
$780$		0			0
$781$		−	5.92678i		−	0.212077i
$782$		0			0
$783$	5.89680	+	5.89680i	0.210734	+	0.210734i
$784$		0			0
$785$	0.169376	−	8.31396i	0.00604530	−	0.296738i
$786$		0			0
$787$	−3.78155	−	3.78155i	−0.134798	−	0.134798i	0.636489	−	0.771286i	$-0.280386\pi$
$787$	−3.78155	−	3.78155i	−0.134798	−	0.134798i	−0.771286	+	0.636489i	$0.780386\pi$
$788$		0			0
$789$		−	7.33495i		−	0.261131i
$790$		0			0
$791$	20.9358			0.744390
$792$		0			0
$793$	−2.39477	−	2.39477i	−0.0850408	−	0.0850408i
$794$		0			0
$795$	−15.8437	−	16.5027i	−0.561919	−	0.585291i
$796$		0			0
$797$	9.39731	+	9.39731i	0.332870	+	0.332870i	0.853675	−	0.520805i	$-0.174368\pi$
$797$	9.39731	+	9.39731i	0.332870	+	0.332870i	−0.520805	+	0.853675i	$0.674368\pi$
$798$		0			0
$799$	49.2302			1.74164
$800$		0			0
$801$		−	18.5496i		−	0.655416i
$802$		0			0
$803$	−25.2217	−	25.2217i	−0.890055	−	0.890055i
$804$		0			0
$805$	−30.2401	−	31.4979i	−1.06582	−	1.11015i
$806$		0			0
$807$	19.4943	−	19.4943i	0.686231	−	0.686231i
$808$		0			0
$809$	17.9124			0.629766			0.314883	−	0.949131i	$-0.398035\pi$
$809$	17.9124			0.629766			0.314883	+	0.949131i	$0.398035\pi$
$810$		0			0
$811$	−41.0739			−1.44230			−0.721151	−	0.692778i	$-0.756386\pi$
$811$	−41.0739			−1.44230			−0.721151	+	0.692778i	$0.756386\pi$
$812$		0			0
$813$	−5.28459	−	5.28459i	−0.185339	−	0.185339i
$814$		0			0
$815$	4.41329	+	0.0899099i	0.154591	+	0.00314941i
$816$		0			0
$817$	45.9099	+	45.9099i	1.60618	+	1.60618i
$818$		0			0
$819$	−3.31847			−0.115957
$820$		0			0
$821$		−	15.5381i		−	0.542283i	−0.962540	−	0.271141i	$-0.912599\pi$
$821$		−	15.5381i		−	0.542283i	0.962540	−	0.271141i	$-0.0874011\pi$
$822$		0			0
$823$	−11.6096	+	11.6096i	−0.404684	+	0.404684i	−0.879880	−	0.475196i	$-0.842377\pi$
$823$	−11.6096	+	11.6096i	−0.404684	+	0.404684i	0.475196	+	0.879880i	$0.342377\pi$
$824$		0			0
$825$	8.61298	−	7.93832i	0.299866	−	0.276377i
$826$		0			0
$827$	−1.46239	−	1.46239i	−0.0508522	−	0.0508522i	0.681223	−	0.732076i	$-0.261448\pi$
$827$	−1.46239	−	1.46239i	−0.0508522	−	0.0508522i	−0.732076	+	0.681223i	$0.761448\pi$
$828$		0			0
$829$	35.4345			1.23069			0.615346	−	0.788257i	$-0.289016\pi$
$829$	35.4345			1.23069			0.615346	+	0.788257i	$0.289016\pi$
$830$		0			0
$831$	5.39206			0.187049
$832$		0			0
$833$	28.9870	−	28.9870i	1.00434	−	1.00434i
$834$		0			0
$835$	31.2684	+	0.637017i	1.08209	+	0.0220449i
$836$		0			0
$837$	1.79758	+	5.26960i	0.0621335	+	0.182144i
$838$		0			0
$839$			5.36395i			0.185184i	0.995704	+	0.0925921i	$0.0295152\pi$
$839$			5.36395i			0.185184i	−0.995704	+	0.0925921i	$0.970485\pi$
$840$		0			0
$841$	40.5444			1.39808
$842$		0			0
$843$	−11.8501	+	11.8501i	−0.408141	+	0.408141i
$844$		0			0
$845$	19.0507	+	19.8430i	0.655363	+	0.682621i
$846$		0			0
$847$	−15.4791	+	15.4791i	−0.531868	+	0.531868i
$848$		0			0
$849$	−7.70542			−0.264449
$850$		0			0
$851$	−25.5685			−0.876477
$852$		0			0
$853$	34.2256	+	34.2256i	1.17186	+	1.17186i	0.981766	+	0.190095i	$0.0608796\pi$
$853$	34.2256	+	34.2256i	1.17186	+	1.17186i	0.190095	+	0.981766i	$0.439120\pi$
$854$		0			0
$855$	−10.2931	+	9.88207i	−0.352016	+	0.337960i
$856$		0			0
$857$	17.9008	−	17.9008i	0.611479	−	0.611479i	−0.331852	−	0.943331i	$-0.607674\pi$
$857$	17.9008	−	17.9008i	0.611479	−	0.611479i	0.943331	+	0.331852i	$0.107674\pi$
$858$		0			0
$859$	−6.95037			−0.237144			−0.118572	−	0.992945i	$-0.537832\pi$
$859$	−6.95037			−0.237144			−0.118572	+	0.992945i	$0.537832\pi$
$860$		0			0
$861$		−	19.0067i		−	0.647746i
$862$		0			0
$863$	18.6267	−	18.6267i	0.634062	−	0.634062i	−0.315023	−	0.949084i	$-0.602012\pi$
$863$	18.6267	−	18.6267i	0.634062	−	0.634062i	0.949084	+	0.315023i	$0.102012\pi$
$864$		0			0
$865$	2.59258	+	0.0528175i	0.0881505	+	0.00179585i
$866$		0			0
$867$	−3.41962	−	3.41962i	−0.116136	−	0.116136i
$868$		0			0
$869$			8.67057i			0.294129i
$870$		0			0
$871$			8.50511i			0.288185i
$872$		0			0
$873$	−1.23892	−	1.23892i	−0.0419310	−	0.0419310i
$874$		0			0
$875$	44.3196	+	2.71171i	1.49828	+	0.0916725i
$876$		0			0
$877$	−7.89446	+	7.89446i	−0.266577	+	0.266577i	−0.827719	−	0.561142i	$-0.810362\pi$
$877$	−7.89446	+	7.89446i	−0.266577	+	0.266577i	0.561142	+	0.827719i	$0.310362\pi$
$878$		0			0
$879$	20.5397			0.692785
$880$		0			0
$881$			39.7745i			1.34004i	0.742344	+	0.670018i	$0.233714\pi$
$881$			39.7745i			1.34004i	−0.742344	+	0.670018i	$0.766286\pi$
$882$		0			0
$883$	13.3850	−	13.3850i	0.450442	−	0.450442i	−0.445059	−	0.895501i	$-0.646817\pi$
$883$	13.3850	−	13.3850i	0.450442	−	0.450442i	0.895501	+	0.445059i	$0.146817\pi$
$884$		0			0
$885$	−26.7827	−	0.545631i	−0.900290	−	0.0183412i
$886$		0			0
$887$	−5.66657	+	5.66657i	−0.190265	+	0.190265i	−0.795811	−	0.605546i	$-0.792955\pi$
$887$	−5.66657	+	5.66657i	−0.190265	+	0.190265i	0.605546	+	0.795811i	$0.292955\pi$
$888$		0			0
$889$	−73.9136			−2.47898
$890$		0			0
$891$			2.34265i			0.0784818i
$892$		0			0
$893$	−47.5375	−	47.5375i	−1.59078	−	1.59078i
$894$		0			0
$895$	10.3881	−	9.97327i	0.347235	−	0.333369i
$896$		0			0
$897$	2.90510	+	2.90510i	0.0969985	+	0.0969985i
$898$		0			0
$899$	41.6737	+	20.4738i	1.38990	+	0.682839i
$900$		0			0
$901$	−47.8084			−1.59273
$902$		0			0
$903$	28.5727	+	28.5727i	0.950841	+	0.950841i
$904$		0			0
$905$	26.7689	+	27.8823i	0.889828	+	0.926838i
$906$		0			0
$907$	14.7632	−	14.7632i	0.490205	−	0.490205i	−0.418166	−	0.908371i	$-0.637327\pi$
$907$	14.7632	−	14.7632i	0.490205	−	0.490205i	0.908371	+	0.418166i	$0.137327\pi$
$908$		0			0
$909$		−	2.92312i		−	0.0969539i
$910$		0			0
$911$			33.3950i			1.10643i	0.833040	+	0.553213i	$0.186598\pi$
$911$			33.3950i			1.10643i	−0.833040	+	0.553213i	$0.813402\pi$
$912$		0			0
$913$	−4.96188	−	4.96188i	−0.164214	−	0.164214i
$914$		0			0
$915$	−9.06125	−	0.184601i	−0.299556	−	0.00610271i
$916$		0			0
$917$	55.7804	−	55.7804i	1.84203	−	1.84203i
$918$		0			0
$919$		−	5.95382i		−	0.196398i	−0.995167	−	0.0981992i	$-0.968692\pi$
$919$		−	5.95382i		−	0.196398i	0.995167	−	0.0981992i	$-0.0313082\pi$
$920$		0			0
$921$			3.58461i			0.118117i
$922$		0			0
$923$	−1.49480	+	1.49480i	−0.0492018	+	0.0492018i
$924$		0			0
$925$	19.1188	−	17.6212i	0.628623	−	0.579382i
$926$		0			0
$927$	8.02128	−	8.02128i	0.263453	−	0.263453i
$928$		0			0
$929$	20.0037			0.656299			0.328150	−	0.944626i	$-0.393575\pi$
$929$	20.0037			0.656299			0.328150	+	0.944626i	$0.393575\pi$
$930$		0			0
$931$	−55.9806			−1.83469
$932$		0			0
$933$	0.116963	−	0.116963i	0.00382919	−	0.00382919i
$934$		0			0
$935$	0.498580	−	24.4731i	0.0163053	−	0.800358i
$936$		0			0
$937$	8.95779	−	8.95779i	0.292638	−	0.292638i	−0.545483	−	0.838122i	$-0.683654\pi$
$937$	8.95779	−	8.95779i	0.292638	−	0.292638i	0.838122	+	0.545483i	$0.183654\pi$
$938$		0			0
$939$		−	13.9162i		−	0.454139i
$940$		0			0
$941$			57.1162i			1.86193i	0.365102	+	0.930967i	$0.381034\pi$
$941$			57.1162i			1.86193i	−0.365102	+	0.930967i	$0.618966\pi$
$942$		0			0
$943$	−16.6391	+	16.6391i	−0.541843	+	0.541843i
$944$		0			0
$945$	−6.40606	+	6.15026i	−0.208389	+	0.200068i
$946$		0			0
$947$	−14.7498	−	14.7498i	−0.479304	−	0.479304i	0.425605	−	0.904909i	$-0.360061\pi$
$947$	−14.7498	−	14.7498i	−0.479304	−	0.479304i	−0.904909	+	0.425605i	$0.860061\pi$
$948$		0			0
$949$			12.7224i			0.412986i
$950$		0			0
$951$			2.06962i			0.0671120i
$952$		0			0
$953$	10.6476	−	10.6476i	0.344910	−	0.344910i	−0.513299	−	0.858210i	$-0.671577\pi$
$953$	10.6476	−	10.6476i	0.344910	−	0.344910i	0.858210	+	0.513299i	$0.171577\pi$
$954$		0			0
$955$	5.94496	−	5.70757i	0.192374	−	0.184693i
$956$		0			0
$957$	13.8141	+	13.8141i	0.446548	+	0.446548i
$958$		0			0
$959$	24.9059			0.804254
$960$		0			0
$961$	18.9451	+	24.5374i	0.611131	+	0.791529i
$962$		0			0
$963$	4.83791	+	4.83791i	0.155899	+	0.155899i
$964$		0			0
$965$	16.3712	+	0.333522i	0.527007	+	0.0107365i
$966$		0			0
$967$	−27.1563	−	27.1563i	−0.873286	−	0.873286i	0.119543	−	0.992829i	$-0.461857\pi$
$967$	−27.1563	−	27.1563i	−0.873286	−	0.873286i	−0.992829	+	0.119543i	$0.961857\pi$
$968$		0			0
$969$			29.8191i			0.957927i
$970$		0			0
$971$	29.6682			0.952097			0.476048	−	0.879419i	$-0.342069\pi$
$971$	29.6682			0.952097			0.476048	+	0.879419i	$0.342069\pi$
$972$		0			0
$973$	13.5687	−	13.5687i	0.434993	−	0.434993i
$974$		0			0
$975$	−4.17441	−	0.170157i	−0.133688	−	0.00544940i
$976$		0			0
$977$	−36.3083	+	36.3083i	−1.16161	+	1.16161i	−0.177481	+	0.984124i	$0.556795\pi$
$977$	−36.3083	+	36.3083i	−1.16161	+	1.16161i	−0.984124	+	0.177481i	$0.943205\pi$
$978$		0			0
$979$		−	43.4551i		−	1.38883i
$980$		0			0
$981$	14.3473			0.458073
$982$		0			0
$983$	15.6642	−	15.6642i	0.499610	−	0.499610i	−0.411707	−	0.911316i	$-0.635067\pi$
$983$	15.6642	−	15.6642i	0.499610	−	0.499610i	0.911316	+	0.411707i	$0.135067\pi$
$984$		0			0
$985$	−5.42560	−	0.110533i	−0.172874	−	0.00352188i
$986$		0			0
$987$	−29.5857	−	29.5857i	−0.941722	−	0.941722i
$988$		0			0
$989$		−	50.0270i		−	1.59077i
$990$		0			0
$991$			30.4752i			0.968077i	0.875047	+	0.484038i	$0.160830\pi$
$991$			30.4752i			0.968077i	−0.875047	+	0.484038i	$0.839170\pi$
$992$		0			0
$993$	22.0919	+	22.0919i	0.701066	+	0.701066i
$994$		0			0
$995$	−11.1313	+	10.6868i	−0.352886	+	0.338795i
$996$		0			0
$997$	−7.01162	+	7.01162i	−0.222060	+	0.222060i	−0.809366	−	0.587305i	$-0.800189\pi$
$997$	−7.01162	+	7.01162i	−0.222060	+	0.222060i	0.587305	+	0.809366i	$0.300189\pi$
$998$		0			0
$999$			5.20014i			0.164525i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.433.2	✓	64
5.2	odd	4	inner	1860.2.s.a.1177.30	yes	64
31.30	odd	2	inner	1860.2.s.a.433.30	yes	64
155.92	even	4	inner	1860.2.s.a.1177.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.2	✓	64	1.1	even	1	trivial
1860.2.s.a.433.30	yes	64	31.30	odd	2	inner
1860.2.s.a.1177.2	yes	64	155.92	even	4	inner
1860.2.s.a.1177.30	yes	64	5.2	odd	4	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:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.61302 - 1.54861i) q^{5} +(-2.80826 + 2.80826i) q^{7} -1.00000i q^{9} -2.34265i q^{11} +(-0.590842 + 0.590842i) q^{13} +(-0.0455449 + 2.23560i) q^{15} +(3.30425 + 3.30425i) q^{17} -6.38127i q^{19} -3.97148i q^{21} +(-3.47676 + 3.47676i) q^{23} +(0.203641 - 4.99585i) q^{25} +(0.707107 + 0.707107i) q^{27} +8.33933 q^{29} +(4.99725 + 2.45509i) q^{31} +(1.65650 + 1.65650i) q^{33} +(-0.180881 + 8.87866i) q^{35} +(3.67706 + 3.67706i) q^{37} -0.835576i q^{39} +4.78580 q^{41} +(-7.19448 + 7.19448i) q^{43} +(-1.54861 - 1.61302i) q^{45} +(7.44953 - 7.44953i) q^{47} -8.77265i q^{49} -4.67291 q^{51} +(-7.23439 + 7.23439i) q^{53} +(-3.62784 - 3.77873i) q^{55} +(4.51224 + 4.51224i) q^{57} +11.9801i q^{59} +4.05315i q^{61} +(2.80826 + 2.80826i) q^{63} +(-0.0380563 + 1.86802i) q^{65} +(7.19745 - 7.19745i) q^{67} -4.91689i q^{69} +2.52995 q^{71} +(10.7663 - 10.7663i) q^{73} +(3.38860 + 3.67660i) q^{75} +(6.57877 + 6.57877i) q^{77} -3.70118 q^{79} -1.00000 q^{81} +(2.11806 - 2.11806i) q^{83} +(10.4468 + 0.212827i) q^{85} +(-5.89680 + 5.89680i) q^{87} +18.5496 q^{89} -3.31847i q^{91} +(-5.26960 + 1.79758i) q^{93} +(-9.88207 - 10.2931i) q^{95} +(1.23892 - 1.23892i) q^{97} -2.34265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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