LMFDB - Embedded newform 1035.2.j.b.323.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(323,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1035.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1035 = 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1035.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.13
Character	$\chi$	$=$	1035.323
Dual form			1035.2.j.b.737.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221928 + 0.221928i) q^{2} -1.90150i q^{4} +(-0.110029 + 2.23336i) q^{5} +(-2.97861 + 2.97861i) q^{7} +(0.865851 - 0.865851i) q^{8} +O(q^{10})$	\(q+(0.221928 + 0.221928i) q^{2} -1.90150i q^{4} +(-0.110029 + 2.23336i) q^{5} +(-2.97861 + 2.97861i) q^{7} +(0.865851 - 0.865851i) q^{8} +(-0.520063 + 0.471226i) q^{10} -3.50722i q^{11} +(1.91351 + 1.91351i) q^{13} -1.32208 q^{14} -3.41868 q^{16} +(-2.17102 - 2.17102i) q^{17} +5.55117i q^{19} +(4.24672 + 0.209219i) q^{20} +(0.778349 - 0.778349i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-4.97579 - 0.491467i) q^{25} +0.849322i q^{26} +(5.66382 + 5.66382i) q^{28} -8.97304 q^{29} -9.28011 q^{31} +(-2.49040 - 2.49040i) q^{32} -0.963621i q^{34} +(-6.32458 - 6.98005i) q^{35} +(1.88296 - 1.88296i) q^{37} +(-1.23196 + 1.23196i) q^{38} +(1.83849 + 2.02902i) q^{40} +8.12627i q^{41} +(6.99496 + 6.99496i) q^{43} -6.66896 q^{44} -0.313853 q^{46} +(-3.77578 - 3.77578i) q^{47} -10.7443i q^{49} +(-0.995196 - 1.21334i) q^{50} +(3.63853 - 3.63853i) q^{52} +(1.93048 - 1.93048i) q^{53} +(7.83287 + 0.385894i) q^{55} +5.15807i q^{56} +(-1.99137 - 1.99137i) q^{58} -1.94095 q^{59} -10.7671 q^{61} +(-2.05951 - 2.05951i) q^{62} +5.73198i q^{64} +(-4.48409 + 4.06301i) q^{65} +(-8.02601 + 8.02601i) q^{67} +(-4.12819 + 4.12819i) q^{68} +(0.145466 - 2.95267i) q^{70} +11.2955i q^{71} +(7.05517 + 7.05517i) q^{73} +0.835763 q^{74} +10.5555 q^{76} +(10.4466 + 10.4466i) q^{77} -3.76401i q^{79} +(0.376153 - 7.63514i) q^{80} +(-1.80345 + 1.80345i) q^{82} +(1.73655 - 1.73655i) q^{83} +(5.08755 - 4.60980i) q^{85} +3.10475i q^{86} +(-3.03673 - 3.03673i) q^{88} +11.2411 q^{89} -11.3992 q^{91} +(1.34456 + 1.34456i) q^{92} -1.67590i q^{94} +(-12.3978 - 0.610788i) q^{95} +(4.47082 - 4.47082i) q^{97} +(2.38446 - 2.38446i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{7}+O(q^{10}) $ 44 * q + 12 * q^7	$ 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) $ 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	0.221928	+	0.221928i	0.156927	+	0.156927i	0.781203	−	0.624277i	$-0.214606\pi$
$2$	0.221928	+	0.221928i	0.156927	+	0.156927i	−0.624277	+	0.781203i	$0.714606\pi$
$3$		0			0
$3$		0			0
$4$		−	1.90150i		−	0.950748i
$5$	−0.110029	+	2.23336i	−0.0492063	+	0.998789i
$5$	−0.110029	+	2.23336i	−0.0492063	+	0.998789i
$6$		0			0
$7$	−2.97861	+	2.97861i	−1.12581	+	1.12581i	−0.134959	+	0.990851i	$0.543090\pi$
$7$	−2.97861	+	2.97861i	−1.12581	+	1.12581i	−0.990851	+	0.134959i	$0.956910\pi$
$8$	0.865851	−	0.865851i	0.306125	−	0.306125i
$9$		0			0
$10$	−0.520063	+	0.471226i	−0.164458	+	0.149015i
$11$		−	3.50722i		−	1.05747i	−0.848788	−	0.528733i	$-0.822667\pi$
$11$		−	3.50722i		−	1.05747i	0.848788	−	0.528733i	$-0.177333\pi$
$12$		0			0
$13$	1.91351	+	1.91351i	0.530712	+	0.530712i	0.920784	−	0.390072i	$-0.127550\pi$
$13$	1.91351	+	1.91351i	0.530712	+	0.530712i	−0.390072	+	0.920784i	$0.627550\pi$
$14$	−1.32208			−0.353339
$15$		0			0
$16$	−3.41868			−0.854670
$17$	−2.17102	−	2.17102i	−0.526550	−	0.526550i	0.392992	−	0.919542i	$-0.371440\pi$
$17$	−2.17102	−	2.17102i	−0.526550	−	0.526550i	−0.919542	+	0.392992i	$0.871440\pi$
$18$		0			0
$19$			5.55117i			1.27353i	0.771059	+	0.636763i	$0.219727\pi$
$19$			5.55117i			1.27353i	−0.771059	+	0.636763i	$0.780273\pi$
$20$	4.24672	+	0.209219i	0.949596	+	0.0467828i
$21$		0			0
$22$	0.778349	−	0.778349i	0.165945	−	0.165945i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$23$	−0.707107	+	0.707107i	−0.147442	+	0.147442i
$24$		0			0
$25$	−4.97579	−	0.491467i	−0.995157	−	0.0982934i
$26$			0.849322i			0.166566i
$27$		0			0
$28$	5.66382	+	5.66382i	1.07036	+	1.07036i
$29$	−8.97304			−1.66625			−0.833126	−	0.553083i	$-0.813451\pi$
$29$	−8.97304			−1.66625			−0.833126	+	0.553083i	$0.813451\pi$
$30$		0			0
$31$	−9.28011			−1.66676			−0.833378	−	0.552703i	$-0.813596\pi$
$31$	−9.28011			−1.66676			−0.833378	+	0.552703i	$0.813596\pi$
$32$	−2.49040	−	2.49040i	−0.440245	−	0.440245i
$33$		0			0
$34$		−	0.963621i		−	0.165260i
$35$	−6.32458	−	6.98005i	−1.06905	−	1.17984i
$36$		0			0
$37$	1.88296	−	1.88296i	0.309557	−	0.309557i	−0.535181	−	0.844738i	$-0.679756\pi$
$37$	1.88296	−	1.88296i	0.309557	−	0.309557i	0.844738	+	0.535181i	$0.179756\pi$
$38$	−1.23196	+	1.23196i	−0.199850	+	0.199850i
$39$		0			0
$40$	1.83849	+	2.02902i	0.290690	+	0.320817i
$41$			8.12627i			1.26911i	0.772877	+	0.634555i	$0.218817\pi$
$41$			8.12627i			1.26911i	−0.772877	+	0.634555i	$0.781183\pi$
$42$		0			0
$43$	6.99496	+	6.99496i	1.06672	+	1.06672i	0.997609	+	0.0691124i	$0.0220167\pi$
$43$	6.99496	+	6.99496i	1.06672	+	1.06672i	0.0691124	+	0.997609i	$0.477983\pi$
$44$	−6.66896			−1.00538
$45$		0			0
$46$	−0.313853			−0.0462752
$47$	−3.77578	−	3.77578i	−0.550755	−	0.550755i	0.375904	−	0.926659i	$-0.377332\pi$
$47$	−3.77578	−	3.77578i	−0.550755	−	0.550755i	−0.926659	+	0.375904i	$0.877332\pi$
$48$		0			0
$49$		−	10.7443i		−	1.53490i
$50$	−0.995196	−	1.21334i	−0.140742	−	0.171592i
$51$		0			0
$52$	3.63853	−	3.63853i	0.504573	−	0.504573i
$53$	1.93048	−	1.93048i	0.265172	−	0.265172i	−0.561979	−	0.827151i	$-0.689960\pi$
$53$	1.93048	−	1.93048i	0.265172	−	0.265172i	0.827151	+	0.561979i	$0.189960\pi$
$54$		0			0
$55$	7.83287	+	0.385894i	1.05618	+	0.0520340i
$56$			5.15807i			0.689276i
$57$		0			0
$58$	−1.99137	−	1.99137i	−0.261479	−	0.261479i
$59$	−1.94095			−0.252690			−0.126345	−	0.991986i	$-0.540325\pi$
$59$	−1.94095			−0.252690			−0.126345	+	0.991986i	$0.540325\pi$
$60$		0			0
$61$	−10.7671			−1.37859			−0.689294	−	0.724482i	$-0.742079\pi$
$61$	−10.7671			−1.37859			−0.689294	+	0.724482i	$0.742079\pi$
$62$	−2.05951	−	2.05951i	−0.261559	−	0.261559i
$63$		0			0
$64$			5.73198i			0.716497i
$65$	−4.48409	+	4.06301i	−0.556183	+	0.503954i
$66$		0			0
$67$	−8.02601	+	8.02601i	−0.980534	+	0.980534i	−0.999814	−	0.0192804i	$-0.993862\pi$
$67$	−8.02601	+	8.02601i	−0.980534	+	0.980534i	0.0192804	+	0.999814i	$0.493862\pi$
$68$	−4.12819	+	4.12819i	−0.500617	+	0.500617i
$69$		0			0
$70$	0.145466	−	2.95267i	0.0173865	−	0.352911i
$71$			11.2955i			1.34053i	0.742123	+	0.670264i	$0.233819\pi$
$71$			11.2955i			1.34053i	−0.742123	+	0.670264i	$0.766181\pi$
$72$		0			0
$73$	7.05517	+	7.05517i	0.825746	+	0.825746i	0.986925	−	0.161180i	$-0.0515298\pi$
$73$	7.05517	+	7.05517i	0.825746	+	0.825746i	−0.161180	+	0.986925i	$0.551530\pi$
$74$	0.835763			0.0971555
$75$		0			0
$76$	10.5555			1.21080
$77$	10.4466	+	10.4466i	1.19051	+	1.19051i
$78$		0			0
$79$		−	3.76401i		−	0.423484i	−0.977326	−	0.211742i	$-0.932086\pi$
$79$		−	3.76401i		−	0.423484i	0.977326	−	0.211742i	$-0.0679136\pi$
$80$	0.376153	−	7.63514i	0.0420551	−	0.853634i
$81$		0			0
$82$	−1.80345	+	1.80345i	−0.199157	+	0.199157i
$83$	1.73655	−	1.73655i	0.190612	−	0.190612i	−0.605349	−	0.795960i	$-0.706966\pi$
$83$	1.73655	−	1.73655i	0.190612	−	0.190612i	0.795960	+	0.605349i	$0.206966\pi$
$84$		0			0
$85$	5.08755	−	4.60980i	0.551822	−	0.500003i
$86$			3.10475i			0.334794i
$87$		0			0
$88$	−3.03673	−	3.03673i	−0.323716	−	0.323716i
$89$	11.2411			1.19155			0.595775	−	0.803151i	$-0.296845\pi$
$89$	11.2411			1.19155			0.595775	+	0.803151i	$0.296845\pi$
$90$		0			0
$91$	−11.3992			−1.19496
$92$	1.34456	+	1.34456i	0.140180	+	0.140180i
$93$		0			0
$94$		−	1.67590i		−	0.172856i
$95$	−12.3978	−	0.610788i	−1.27198	−	0.0626655i
$96$		0			0
$97$	4.47082	−	4.47082i	0.453943	−	0.453943i	−0.442718	−	0.896661i	$-0.645986\pi$
$97$	4.47082	−	4.47082i	0.453943	−	0.453943i	0.896661	+	0.442718i	$0.145986\pi$
$98$	2.38446	−	2.38446i	0.240866	−	0.240866i
$99$		0			0
$100$	−0.934523	+	9.46144i	−0.0934523	+	0.946144i
$101$		−	18.1805i		−	1.80903i	−0.426441	−	0.904515i	$-0.640233\pi$
$101$		−	18.1805i		−	1.80903i	0.426441	−	0.904515i	$-0.359767\pi$
$102$		0			0
$103$	8.16935	+	8.16935i	0.804950	+	0.804950i	0.983865	−	0.178915i	$-0.0572586\pi$
$103$	8.16935	+	8.16935i	0.804950	+	0.804950i	−0.178915	+	0.983865i	$0.557259\pi$
$104$	3.31363			0.324928
$105$		0			0
$106$	0.856856			0.0832252
$107$	−6.46191	−	6.46191i	−0.624697	−	0.624697i	0.322032	−	0.946729i	$-0.395634\pi$
$107$	−6.46191	−	6.46191i	−0.624697	−	0.624697i	−0.946729	+	0.322032i	$0.895634\pi$
$108$		0			0
$109$			10.8824i			1.04234i	0.853452	+	0.521171i	$0.174505\pi$
$109$			10.8824i			1.04234i	−0.853452	+	0.521171i	$0.825495\pi$
$110$	1.65269	+	1.82397i	0.157578	+	0.173909i
$111$		0			0
$112$	10.1829	−	10.1829i	0.962196	−	0.962196i
$113$	9.79508	−	9.79508i	0.921443	−	0.921443i	−0.0756882	−	0.997132i	$-0.524115\pi$
$113$	9.79508	−	9.79508i	0.921443	−	0.921443i	0.997132	+	0.0756882i	$0.0241154\pi$
$114$		0			0
$115$	−1.50142	−	1.65703i	−0.140008	−	0.154518i
$116$			17.0622i			1.58419i
$117$		0			0
$118$	−0.430751	−	0.430751i	−0.0396539	−	0.0396539i
$119$	12.9333			1.18559
$120$		0			0
$121$	−1.30056			−0.118233
$122$	−2.38952	−	2.38952i	−0.216337	−	0.216337i
$123$		0			0
$124$			17.6461i			1.58467i
$125$	1.64510	−	11.0586i	0.147142	−	0.989115i
$126$		0			0
$127$	−12.6998	+	12.6998i	−1.12693	+	1.12693i	−0.136255	+	0.990674i	$0.543507\pi$
$127$	−12.6998	+	12.6998i	−1.12693	+	1.12693i	−0.990674	+	0.136255i	$0.956493\pi$
$128$	−6.25289	+	6.25289i	−0.552683	+	0.552683i
$129$		0			0
$130$	−1.89684	−	0.0934497i	−0.166364	−	0.00819608i
$131$		−	17.9040i		−	1.56428i	−0.623104	−	0.782139i	$-0.714129\pi$
$131$		−	17.9040i		−	1.56428i	0.623104	−	0.782139i	$-0.285871\pi$
$132$		0			0
$133$	−16.5348	−	16.5348i	−1.43375	−	1.43375i
$134$	−3.56239			−0.307744
$135$		0			0
$136$	−3.75957			−0.322380
$137$	−8.64866	−	8.64866i	−0.738905	−	0.738905i	0.233461	−	0.972366i	$-0.424995\pi$
$137$	−8.64866	−	8.64866i	−0.738905	−	0.738905i	−0.972366	+	0.233461i	$0.924995\pi$
$138$		0			0
$139$			2.09567i			0.177753i	0.996043	+	0.0888763i	$0.0283276\pi$
$139$			2.09567i			0.177753i	−0.996043	+	0.0888763i	$0.971672\pi$
$140$	−13.2725	+	12.0262i	−1.12173	+	1.01640i
$141$		0			0
$142$	−2.50678	+	2.50678i	−0.210365	+	0.210365i
$143$	6.71109	−	6.71109i	0.561209	−	0.561209i
$144$		0			0
$145$	0.987292	−	20.0400i	0.0819901	−	1.66423i
$146$			3.13148i			0.259163i
$147$		0			0
$148$	−3.58044	−	3.58044i	−0.294311	−	0.294311i
$149$	−3.30251			−0.270552			−0.135276	−	0.990808i	$-0.543192\pi$
$149$	−3.30251			−0.270552			−0.135276	+	0.990808i	$0.543192\pi$
$150$		0			0
$151$	−8.29211			−0.674802			−0.337401	−	0.941361i	$-0.609548\pi$
$151$	−8.29211			−0.674802			−0.337401	+	0.941361i	$0.609548\pi$
$152$	4.80649	+	4.80649i	0.389858	+	0.389858i
$153$		0			0
$154$			4.63680i			0.373644i
$155$	1.02108	−	20.7258i	0.0820149	−	1.66474i
$156$		0			0
$157$	7.07685	−	7.07685i	0.564794	−	0.564794i	−0.365871	−	0.930665i	$-0.619229\pi$
$157$	7.07685	−	7.07685i	0.564794	−	0.564794i	0.930665	+	0.365871i	$0.119229\pi$
$158$	0.835338	−	0.835338i	0.0664559	−	0.0664559i
$159$		0			0
$160$	5.83598	−	5.28795i	0.461375	−	0.418049i
$161$		−	4.21240i		−	0.331983i
$162$		0			0
$163$	−9.27630	−	9.27630i	−0.726576	−	0.726576i	0.243360	−	0.969936i	$-0.421750\pi$
$163$	−9.27630	−	9.27630i	−0.726576	−	0.726576i	−0.969936	+	0.243360i	$0.921750\pi$
$164$	15.4521			1.20660
$165$		0			0
$166$	0.770780			0.0598241
$167$	8.87907	+	8.87907i	0.687083	+	0.687083i	0.961586	−	0.274503i	$-0.0885133\pi$
$167$	8.87907	+	8.87907i	0.687083	+	0.687083i	−0.274503	+	0.961586i	$0.588513\pi$
$168$		0			0
$169$		−	5.67697i		−	0.436690i
$170$	2.15211	+	0.106026i	0.165060	+	0.00813182i
$171$		0			0
$172$	13.3009	−	13.3009i	1.01418	−	1.01418i
$173$	−6.73321	+	6.73321i	−0.511917	+	0.511917i	−0.915113	−	0.403197i	$-0.867899\pi$
$173$	−6.73321	+	6.73321i	−0.511917	+	0.511917i	0.403197	+	0.915113i	$0.367899\pi$
$174$		0			0
$175$	16.2848	−	13.3571i	1.23102	−	1.00970i
$176$			11.9900i			0.903784i
$177$		0			0
$178$	2.49471	+	2.49471i	0.186986	+	0.186986i
$179$	5.57523			0.416713			0.208356	−	0.978053i	$-0.433189\pi$
$179$	5.57523			0.416713			0.208356	+	0.978053i	$0.433189\pi$
$180$		0			0
$181$	12.2190			0.908234			0.454117	−	0.890942i	$-0.349955\pi$
$181$	12.2190			0.908234			0.454117	+	0.890942i	$0.349955\pi$
$182$	−2.52980	−	2.52980i	−0.187521	−	0.187521i
$183$		0			0
$184$			1.22450i			0.0902712i
$185$	3.99815	+	4.41251i	0.293950	+	0.324414i
$186$		0			0
$187$	−7.61425	+	7.61425i	−0.556809	+	0.556809i
$188$	−7.17964	+	7.17964i	−0.523629	+	0.523629i
$189$		0			0
$190$	−2.61586	−	2.88696i	−0.189774	−	0.209442i
$191$			6.32774i			0.457859i	0.973443	+	0.228929i	$0.0735225\pi$
$191$			6.32774i			0.457859i	−0.973443	+	0.228929i	$0.926477\pi$
$192$		0			0
$193$	14.2232	+	14.2232i	1.02381	+	1.02381i	0.999710	+	0.0241005i	$0.00767218\pi$
$193$	14.2232	+	14.2232i	1.02381	+	1.02381i	0.0241005	+	0.999710i	$0.492328\pi$
$194$	1.98440			0.142472
$195$		0			0
$196$	−20.4302			−1.45930
$197$	13.1198	+	13.1198i	0.934750	+	0.934750i	0.997998	−	0.0632478i	$-0.0201459\pi$
$197$	13.1198	+	13.1198i	0.934750	+	0.934750i	−0.0632478	+	0.997998i	$0.520146\pi$
$198$		0			0
$199$			2.45827i			0.174262i	0.996197	+	0.0871310i	$0.0277699\pi$
$199$			2.45827i			0.174262i	−0.996197	+	0.0871310i	$0.972230\pi$
$200$	−4.73383	+	3.88275i	−0.334732	+	0.274552i
$201$		0			0
$202$	4.03477	−	4.03477i	0.283885	−	0.283885i
$203$	26.7272	−	26.7272i	1.87588	−	1.87588i
$204$		0			0
$205$	−18.1489	−	0.894123i	−1.26757	−	0.0624483i
$206$			3.62601i			0.252636i
$207$		0			0
$208$	−6.54167	−	6.54167i	−0.453583	−	0.453583i
$209$	19.4692			1.34671
$210$		0			0
$211$	8.55165			0.588720			0.294360	−	0.955695i	$-0.404894\pi$
$211$	8.55165			0.588720			0.294360	+	0.955695i	$0.404894\pi$
$212$	−3.67081	−	3.67081i	−0.252112	−	0.252112i
$213$		0			0
$214$		−	2.86816i		−	0.196063i
$215$	−16.3919	+	14.8526i	−1.11792	+	1.01294i
$216$		0			0
$217$	27.6419	−	27.6419i	1.87645	−	1.87645i
$218$	−2.41510	+	2.41510i	−0.163571	+	0.163571i
$219$		0			0
$220$	0.733776	−	14.8942i	0.0494712	−	1.00417i
$221$		−	8.30854i		−	0.558893i
$222$		0			0
$223$	−1.78448	−	1.78448i	−0.119498	−	0.119498i	0.644829	−	0.764327i	$-0.276929\pi$
$223$	−1.78448	−	1.78448i	−0.119498	−	0.119498i	−0.764327	+	0.644829i	$0.776929\pi$
$224$	14.8359			0.991265
$225$		0			0
$226$	4.34760			0.289198
$227$	13.2161	+	13.2161i	0.877182	+	0.877182i	0.993242	−	0.116060i	$-0.0370266\pi$
$227$	13.2161	+	13.2161i	0.877182	+	0.877182i	−0.116060	+	0.993242i	$0.537027\pi$
$228$		0			0
$229$		−	16.8703i		−	1.11482i	−0.830238	−	0.557409i	$-0.811795\pi$
$229$		−	16.8703i		−	1.11482i	0.830238	−	0.557409i	$-0.188205\pi$
$230$	0.0345329	−	0.700948i	0.00227703	−	0.0462191i
$231$		0			0
$232$	−7.76932	+	7.76932i	−0.510081	+	0.510081i
$233$	−10.0504	+	10.0504i	−0.658420	+	0.658420i	−0.955006	−	0.296586i	$-0.904152\pi$
$233$	−10.0504	+	10.0504i	−0.658420	+	0.658420i	0.296586	+	0.955006i	$0.404152\pi$
$234$		0			0
$235$	8.84812	−	8.01724i	0.577188	−	0.522987i
$236$			3.69071i			0.240245i
$237$		0			0
$238$	2.87026	+	2.87026i	0.186051	+	0.186051i
$239$	−0.415940			−0.0269049			−0.0134525	−	0.999910i	$-0.504282\pi$
$239$	−0.415940			−0.0269049			−0.0134525	+	0.999910i	$0.504282\pi$
$240$		0			0
$241$	2.78410			0.179340			0.0896699	−	0.995972i	$-0.471419\pi$
$241$	2.78410			0.179340			0.0896699	+	0.995972i	$0.471419\pi$
$242$	−0.288631	−	0.288631i	−0.0185539	−	0.0185539i
$243$		0			0
$244$			20.4736i			1.31069i
$245$	23.9958	+	1.18218i	1.53304	+	0.0755266i
$246$		0			0
$247$	−10.6222	+	10.6222i	−0.675875	+	0.675875i
$248$	−8.03519	+	8.03519i	−0.510235	+	0.510235i
$249$		0			0
$250$	2.81932	−	2.08913i	0.178309	−	0.132128i
$251$			14.8832i			0.939422i	0.882820	+	0.469711i	$0.155642\pi$
$251$			14.8832i			0.939422i	−0.882820	+	0.469711i	$0.844358\pi$
$252$		0			0
$253$	2.47998	+	2.47998i	0.155915	+	0.155915i
$254$	−5.63690			−0.353691
$255$		0			0
$256$	8.68857			0.543036
$257$	5.67216	+	5.67216i	0.353819	+	0.353819i	0.861529	−	0.507709i	$-0.169508\pi$
$257$	5.67216	+	5.67216i	0.353819	+	0.353819i	−0.507709	+	0.861529i	$0.669508\pi$
$258$		0			0
$259$			11.2172i			0.697005i
$260$	7.72580	+	8.52648i	0.479134	+	0.528790i
$261$		0			0
$262$	3.97339	−	3.97339i	0.245477	−	0.245477i
$263$	−14.3013	+	14.3013i	−0.881856	+	0.881856i	−0.993723	−	0.111867i	$-0.964317\pi$
$263$	−14.3013	+	14.3013i	−0.881856	+	0.881856i	0.111867	+	0.993723i	$0.464317\pi$
$264$		0			0
$265$	4.09905	+	4.52387i	0.251803	+	0.277899i
$266$		−	7.33907i		−	0.449987i
$267$		0			0
$268$	15.2614	+	15.2614i	0.932240	+	0.932240i
$269$	−10.3088			−0.628536			−0.314268	−	0.949334i	$-0.601759\pi$
$269$	−10.3088			−0.628536			−0.314268	+	0.949334i	$0.601759\pi$
$270$		0			0
$271$	−15.2998			−0.929400			−0.464700	−	0.885468i	$-0.653838\pi$
$271$	−15.2998			−0.929400			−0.464700	+	0.885468i	$0.653838\pi$
$272$	7.42203	+	7.42203i	0.450027	+	0.450027i
$273$		0			0
$274$		−	3.83876i		−	0.231908i
$275$	−1.72368	+	17.4512i	−0.103942	+	1.05234i
$276$		0			0
$277$	−2.21672	+	2.21672i	−0.133190	+	0.133190i	−0.770559	−	0.637369i	$-0.780023\pi$
$277$	−2.21672	+	2.21672i	−0.133190	+	0.133190i	0.637369	+	0.770559i	$0.280023\pi$
$278$	−0.465088	+	0.465088i	−0.0278941	+	0.0278941i
$279$		0			0
$280$	−11.5198	−	0.567536i	−0.688441	−	0.0339167i
$281$		−	2.19985i		−	0.131232i	−0.997845	−	0.0656161i	$-0.979099\pi$
$281$		−	2.19985i		−	0.131232i	0.997845	−	0.0656161i	$-0.0209013\pi$
$282$		0			0
$283$	7.16128	+	7.16128i	0.425694	+	0.425694i	0.887158	−	0.461465i	$-0.152676\pi$
$283$	7.16128	+	7.16128i	0.425694	+	0.425694i	−0.461465	+	0.887158i	$0.652676\pi$
$284$	21.4783			1.27450
$285$		0			0
$286$	2.97875			0.176137
$287$	−24.2050	−	24.2050i	−1.42878	−	1.42878i
$288$		0			0
$289$		−	7.57332i		−	0.445489i
$290$	4.66655	−	4.22833i	0.274029	−	0.248296i
$291$		0			0
$292$	13.4154	−	13.4154i	0.785076	−	0.785076i
$293$	10.9893	−	10.9893i	0.642001	−	0.642001i	−0.309046	−	0.951047i	$-0.600010\pi$
$293$	10.9893	−	10.9893i	0.642001	−	0.642001i	0.951047	+	0.309046i	$0.100010\pi$
$294$		0			0
$295$	0.213560	−	4.33484i	0.0124340	−	0.252384i
$296$		−	3.26073i		−	0.189526i
$297$		0			0
$298$	−0.732919	−	0.732919i	−0.0424569	−	0.0424569i
$299$	−2.70611			−0.156498
$300$		0			0
$301$	−41.6706			−2.40185
$302$	−1.84025	−	1.84025i	−0.105895	−	0.105895i
$303$		0			0
$304$		−	18.9777i		−	1.08844i
$305$	1.18469	−	24.0468i	0.0678352	−	1.37692i
$306$		0			0
$307$	7.34426	−	7.34426i	0.419159	−	0.419159i	−0.465755	−	0.884914i	$-0.654217\pi$
$307$	7.34426	−	7.34426i	0.419159	−	0.419159i	0.884914	+	0.465755i	$0.154217\pi$
$308$	19.8642	−	19.8642i	1.13187	−	1.13187i
$309$		0			0
$310$	4.82624	−	4.37303i	0.274112	−	0.248371i
$311$			10.5469i			0.598061i	0.954244	+	0.299031i	$0.0966633\pi$
$311$			10.5469i			0.598061i	−0.954244	+	0.299031i	$0.903337\pi$
$312$		0			0
$313$	1.39270	+	1.39270i	0.0787201	+	0.0787201i	0.745371	−	0.666650i	$-0.232273\pi$
$313$	1.39270	+	1.39270i	0.0787201	+	0.0787201i	−0.666650	+	0.745371i	$0.732273\pi$
$314$	3.14110			0.177263
$315$		0			0
$316$	−7.15724			−0.402626
$317$	11.2264	+	11.2264i	0.630535	+	0.630535i	0.948202	−	0.317667i	$-0.102900\pi$
$317$	11.2264	+	11.2264i	0.630535	+	0.630535i	−0.317667	+	0.948202i	$0.602900\pi$
$318$		0			0
$319$			31.4704i			1.76200i
$320$	−12.8016	−	0.630682i	−0.715629	−	0.0352562i
$321$		0			0
$322$	0.934848	−	0.934848i	0.0520971	−	0.0520971i
$323$	12.0517	−	12.0517i	0.670576	−	0.670576i
$324$		0			0
$325$	−8.58078	−	10.4616i	−0.475976	−	0.580307i
$326$		−	4.11734i		−	0.228038i
$327$		0			0
$328$	7.03614	+	7.03614i	0.388506	+	0.388506i
$329$	22.4932			1.24009
$330$		0			0
$331$	0.302201			0.0166105			0.00830523	−	0.999966i	$-0.497356\pi$
$331$	0.302201			0.0166105			0.00830523	+	0.999966i	$0.497356\pi$
$332$	−3.30205	−	3.30205i	−0.181224	−	0.181224i
$333$		0			0
$334$			3.94103i			0.215643i
$335$	−17.0419	−	18.8081i	−0.931098	−	1.02759i
$336$		0			0
$337$	−10.0492	+	10.0492i	−0.547416	+	0.547416i	−0.925692	−	0.378277i	$-0.876517\pi$
$337$	−10.0492	+	10.0492i	−0.547416	+	0.547416i	0.378277	+	0.925692i	$0.376517\pi$
$338$	1.25988	−	1.25988i	0.0685284	−	0.0685284i
$339$		0			0
$340$	−8.76552	−	9.67396i	−0.475377	−	0.524644i
$341$			32.5473i			1.76254i
$342$		0			0
$343$	11.1528	+	11.1528i	0.602193	+	0.602193i
$344$	12.1132			0.653099
$345$		0			0
$346$	−2.98858			−0.160667
$347$	−21.8137	−	21.8137i	−1.17102	−	1.17102i	−0.981966	−	0.189055i	$-0.939457\pi$
$347$	−21.8137	−	21.8137i	−1.17102	−	1.17102i	−0.189055	−	0.981966i	$-0.560543\pi$
$348$		0			0
$349$			9.03070i			0.483403i	0.970351	+	0.241701i	$0.0777054\pi$
$349$			9.03070i			0.483403i	−0.970351	+	0.241701i	$0.922295\pi$
$350$	6.57837	+	0.649756i	0.351628	+	0.0347309i
$351$		0			0
$352$	−8.73438	+	8.73438i	−0.465544	+	0.465544i
$353$	11.2530	−	11.2530i	0.598937	−	0.598937i	−0.341093	−	0.940030i	$-0.610797\pi$
$353$	11.2530	−	11.2530i	0.598937	−	0.598937i	0.940030	+	0.341093i	$0.110797\pi$
$354$		0			0
$355$	−25.2269	−	1.24283i	−1.33890	−	0.0659624i
$356$		−	21.3748i		−	1.13286i
$357$		0			0
$358$	1.23730	+	1.23730i	0.0653934	+	0.0653934i
$359$	10.8647			0.573415			0.286707	−	0.958018i	$-0.407439\pi$
$359$	10.8647			0.573415			0.286707	+	0.958018i	$0.407439\pi$
$360$		0			0
$361$	−11.8155			−0.621870
$362$	2.71175	+	2.71175i	0.142526	+	0.142526i
$363$		0			0
$364$			21.6755i			1.13611i
$365$	−16.5330	+	14.9805i	−0.865377	+	0.784113i
$366$		0			0
$367$	10.5756	−	10.5756i	0.552040	−	0.552040i	−0.374990	−	0.927029i	$-0.622354\pi$
$367$	10.5756	−	10.5756i	0.552040	−	0.552040i	0.927029	+	0.374990i	$0.122354\pi$
$368$	2.41737	−	2.41737i	0.126014	−	0.126014i
$369$		0			0
$370$	−0.0919579	+	1.86656i	−0.00478066	+	0.0970378i
$371$			11.5003i			0.597067i
$372$		0			0
$373$	15.2581	+	15.2581i	0.790036	+	0.790036i	0.981500	−	0.191464i	$-0.0613235\pi$
$373$	15.2581	+	15.2581i	0.790036	+	0.790036i	−0.191464	+	0.981500i	$0.561323\pi$
$374$	−3.37963			−0.174756
$375$		0			0
$376$	−6.53853			−0.337199
$377$	−17.1700	−	17.1700i	−0.884299	−	0.884299i
$378$		0			0
$379$		−	15.6254i		−	0.802622i	−0.915942	−	0.401311i	$-0.868555\pi$
$379$		−	15.6254i		−	0.802622i	0.915942	−	0.401311i	$-0.131445\pi$
$380$	−1.16141	+	23.5743i	−0.0595791	+	1.20934i
$381$		0			0
$382$	−1.40430	+	1.40430i	−0.0718503	+	0.0718503i
$383$	1.80133	−	1.80133i	0.0920435	−	0.0920435i	−0.659586	−	0.751629i	$-0.729268\pi$
$383$	1.80133	−	1.80133i	0.0920435	−	0.0920435i	0.751629	+	0.659586i	$0.229268\pi$
$384$		0			0
$385$	−24.4805	+	22.1817i	−1.24764	+	1.13048i
$386$			6.31306i			0.321326i
$387$		0			0
$388$	−8.50125	−	8.50125i	−0.431585	−	0.431585i
$389$	−29.9873			−1.52042			−0.760208	−	0.649680i	$-0.774903\pi$
$389$	−29.9873			−1.52042			−0.760208	+	0.649680i	$0.774903\pi$
$390$		0			0
$391$	3.07029			0.155271
$392$	−9.30295	−	9.30295i	−0.469870	−	0.469870i
$393$		0			0
$394$			5.82332i			0.293375i
$395$	8.40638	+	0.414148i	0.422971	+	0.0208381i
$396$		0			0
$397$	15.5118	−	15.5118i	0.778516	−	0.778516i	−0.201062	−	0.979578i	$-0.564439\pi$
$397$	15.5118	−	15.5118i	0.778516	−	0.778516i	0.979578	+	0.201062i	$0.0644394\pi$
$398$	−0.545559	+	0.545559i	−0.0273464	+	0.0273464i
$399$		0			0
$400$	17.0106	+	1.68017i	0.850531	+	0.0840084i
$401$			7.48422i			0.373744i	0.982384	+	0.186872i	$0.0598350\pi$
$401$			7.48422i			0.373744i	−0.982384	+	0.186872i	$0.940165\pi$
$402$		0			0
$403$	−17.7576	−	17.7576i	−0.884567	−	0.884567i
$404$	−34.5702			−1.71993
$405$		0			0
$406$	11.8630			0.588753
$407$	−6.60395	−	6.60395i	−0.327346	−	0.327346i
$408$		0			0
$409$			35.1682i			1.73895i	0.493973	+	0.869477i	$0.335544\pi$
$409$			35.1682i			1.73895i	−0.493973	+	0.869477i	$0.664456\pi$
$410$	−3.82931	−	4.22618i	−0.189116	−	0.208716i
$411$		0			0
$412$	15.5340	−	15.5340i	0.765305	−	0.765305i
$413$	5.78134	−	5.78134i	0.284481	−	0.284481i
$414$		0			0
$415$	3.68728	+	4.06942i	0.181001	+	0.199760i
$416$		−	9.53081i		−	0.467286i
$417$		0			0
$418$	4.32075	+	4.32075i	0.211335	+	0.211335i
$419$	−9.80547			−0.479028			−0.239514	−	0.970893i	$-0.576988\pi$
$419$	−9.80547			−0.479028			−0.239514	+	0.970893i	$0.576988\pi$
$420$		0			0
$421$	−15.6580			−0.763124			−0.381562	−	0.924343i	$-0.624614\pi$
$421$	−15.6580			−0.763124			−0.381562	+	0.924343i	$0.624614\pi$
$422$	1.89785	+	1.89785i	0.0923859	+	0.0923859i
$423$		0			0
$424$		−	3.34302i		−	0.162351i
$425$	9.73556	+	11.8695i	0.472244	+	0.575757i
$426$		0			0
$427$	32.0711	−	32.0711i	1.55203	−	1.55203i
$428$	−12.2873	+	12.2873i	−0.593929	+	0.593929i
$429$		0			0
$430$	−6.93403	−	0.341612i	−0.334389	−	0.0164740i
$431$			31.2520i			1.50535i	0.658390	+	0.752677i	$0.271238\pi$
$431$			31.2520i			1.50535i	−0.658390	+	0.752677i	$0.728762\pi$
$432$		0			0
$433$	−17.0556	−	17.0556i	−0.819638	−	0.819638i	0.166418	−	0.986055i	$-0.446780\pi$
$433$	−17.0556	−	17.0556i	−0.819638	−	0.819638i	−0.986055	+	0.166418i	$0.946780\pi$
$434$	12.2690			0.588931
$435$		0			0
$436$	20.6928			0.991004
$437$	−3.92527	−	3.92527i	−0.187771	−	0.187771i
$438$		0			0
$439$		−	21.7682i		−	1.03894i	−0.854489	−	0.519470i	$-0.826129\pi$
$439$		−	21.7682i		−	1.03894i	0.854489	−	0.519470i	$-0.173871\pi$
$440$	7.11623	−	6.44797i	0.339253	−	0.307395i
$441$		0			0
$442$	1.84390	−	1.84390i	0.0877053	−	0.0877053i
$443$	−19.0960	+	19.0960i	−0.907277	+	0.907277i	−0.996052	−	0.0887748i	$-0.971705\pi$
$443$	−19.0960	+	19.0960i	−0.907277	+	0.907277i	0.0887748	+	0.996052i	$0.471705\pi$
$444$		0			0
$445$	−1.23684	+	25.1053i	−0.0586318	+	1.19011i
$446$		−	0.792052i		−	0.0375048i
$447$		0			0
$448$	−17.0734	−	17.0734i	−0.806640	−	0.806640i
$449$	−0.947301			−0.0447059			−0.0223529	−	0.999750i	$-0.507116\pi$
$449$	−0.947301			−0.0447059			−0.0223529	+	0.999750i	$0.507116\pi$
$450$		0			0
$451$	28.5006			1.34204
$452$	−18.6253	−	18.6253i	−0.876060	−	0.876060i
$453$		0			0
$454$			5.86603i			0.275307i
$455$	1.25424	−	25.4585i	0.0587996	−	1.19351i
$456$		0			0
$457$	−13.1135	+	13.1135i	−0.613425	+	0.613425i	−0.943837	−	0.330412i	$-0.892812\pi$
$457$	−13.1135	+	13.1135i	−0.613425	+	0.613425i	0.330412	+	0.943837i	$0.392812\pi$
$458$	3.74398	−	3.74398i	0.174945	−	0.174945i
$459$		0			0
$460$	−3.15083	+	2.85495i	−0.146908	+	0.133113i
$461$			14.2727i			0.664746i	0.943148	+	0.332373i	$0.107849\pi$
$461$			14.2727i			0.664746i	−0.943148	+	0.332373i	$0.892151\pi$
$462$		0			0
$463$	−9.40419	−	9.40419i	−0.437050	−	0.437050i	0.453968	−	0.891018i	$-0.350008\pi$
$463$	−9.40419	−	9.40419i	−0.437050	−	0.437050i	−0.891018	+	0.453968i	$0.850008\pi$
$464$	30.6759			1.42410
$465$		0			0
$466$	−4.46091			−0.206648
$467$	4.33309	+	4.33309i	0.200511	+	0.200511i	0.800219	−	0.599708i	$-0.204716\pi$
$467$	4.33309	+	4.33309i	0.200511	+	0.200511i	−0.599708	+	0.800219i	$0.704716\pi$
$468$		0			0
$469$		−	47.8128i		−	2.20779i
$470$	3.74289	+	0.184397i	0.172647	+	0.00850562i
$471$		0			0
$472$	−1.68057	+	1.68057i	−0.0773547	+	0.0773547i
$473$	24.5328	−	24.5328i	1.12802	−	1.12802i
$474$		0			0
$475$	2.72822	−	27.6215i	0.125179	−	1.26736i
$476$		−	24.5926i		−	1.12720i
$477$		0			0
$478$	−0.0923088	−	0.0923088i	−0.00422210	−	0.00422210i
$479$	−29.9904			−1.37030			−0.685149	−	0.728403i	$-0.740263\pi$
$479$	−29.9904			−1.37030			−0.685149	+	0.728403i	$0.740263\pi$
$480$		0			0
$481$	7.20612			0.328571
$482$	0.617870	+	0.617870i	0.0281432	+	0.0281432i
$483$		0			0
$484$			2.47301i			0.112410i
$485$	9.49303	+	10.4769i	0.431056	+	0.475730i
$486$		0			0
$487$	−21.2886	+	21.2886i	−0.964680	+	0.964680i	−0.999397	−	0.0347172i	$-0.988947\pi$
$487$	−21.2886	+	21.2886i	−0.964680	+	0.964680i	0.0347172	+	0.999397i	$0.488947\pi$
$488$	−9.32272	+	9.32272i	−0.422020	+	0.422020i
$489$		0			0
$490$	5.06299	+	5.58771i	0.228723	+	0.252427i
$491$		−	9.18392i		−	0.414465i	−0.978292	−	0.207232i	$-0.933554\pi$
$491$		−	9.18392i		−	0.414465i	0.978292	−	0.207232i	$-0.0664456\pi$
$492$		0			0
$493$	19.4807	+	19.4807i	0.877366	+	0.877366i
$494$	−4.71473			−0.212126
$495$		0			0
$496$	31.7257			1.42453
$497$	−33.6449	−	33.6449i	−1.50918	−	1.50918i
$498$		0			0
$499$		−	8.06976i		−	0.361252i	−0.983552	−	0.180626i	$-0.942188\pi$
$499$		−	8.06976i		−	0.361252i	0.983552	−	0.180626i	$-0.0578124\pi$
$500$	−21.0280	−	3.12815i	−0.940399	−	0.139895i
$501$		0			0
$502$	−3.30301	+	3.30301i	−0.147420	+	0.147420i
$503$	5.84494	−	5.84494i	0.260613	−	0.260613i	−0.564690	−	0.825303i	$-0.691004\pi$
$503$	5.84494	−	5.84494i	0.260613	−	0.260613i	0.825303	+	0.564690i	$0.191004\pi$
$504$		0			0
$505$	40.6037	+	2.00038i	1.80684	+	0.0890157i
$506$			1.10075i			0.0489344i
$507$		0			0
$508$	24.1487	+	24.1487i	1.07143	+	1.07143i
$509$	−12.1386			−0.538034			−0.269017	−	0.963135i	$-0.586699\pi$
$509$	−12.1386			−0.538034			−0.269017	+	0.963135i	$0.586699\pi$
$510$		0			0
$511$	−42.0293			−1.85927
$512$	14.4340	+	14.4340i	0.637900	+	0.637900i
$513$		0			0
$514$			2.51762i			0.111047i
$515$	−19.1440	+	17.3462i	−0.843583	+	0.764366i
$516$		0			0
$517$	−13.2425	+	13.2425i	−0.582404	+	0.582404i
$518$	−2.48942	+	2.48942i	−0.109379	+	0.109379i
$519$		0			0
$520$	−0.364594	+	7.40052i	−0.0159885	+	0.324534i
$521$			1.03512i			0.0453493i	0.999743	+	0.0226747i	$0.00721819\pi$
$521$			1.03512i			0.0453493i	−0.999743	+	0.0226747i	$0.992782\pi$
$522$		0			0
$523$	13.3022	+	13.3022i	0.581664	+	0.581664i	0.935360	−	0.353696i	$-0.115075\pi$
$523$	13.3022	+	13.3022i	0.581664	+	0.581664i	−0.353696	+	0.935360i	$0.615075\pi$
$524$	−34.0444			−1.48723
$525$		0			0
$526$	−6.34771			−0.276773
$527$	20.1473	+	20.1473i	0.877631	+	0.877631i
$528$		0			0
$529$		−	1.00000i		−	0.0434783i
$530$	−0.0942787	+	1.91367i	−0.00409521	+	0.0831244i
$531$		0			0
$532$	−31.4409	+	31.4409i	−1.36313	+	1.36313i
$533$	−15.5497	+	15.5497i	−0.673532	+	0.673532i
$534$		0			0
$535$	15.1428	−	13.7208i	0.654679	−	0.593201i
$536$			13.8987i			0.600331i
$537$		0			0
$538$	−2.28780	−	2.28780i	−0.0986341	−	0.0986341i
$539$	−37.6825			−1.62310
$540$		0			0
$541$	−13.8589			−0.595840			−0.297920	−	0.954591i	$-0.596293\pi$
$541$	−13.8589			−0.595840			−0.297920	+	0.954591i	$0.596293\pi$
$542$	−3.39546	−	3.39546i	−0.145848	−	0.145848i
$543$		0			0
$544$			10.8134i			0.463623i
$545$	−24.3042	−	1.19737i	−1.04108	−	0.0512898i
$546$		0			0
$547$	−21.8630	+	21.8630i	−0.934794	+	0.934794i	−0.998000	−	0.0632062i	$-0.979867\pi$
$547$	−21.8630	+	21.8630i	−0.934794	+	0.934794i	0.0632062	+	0.998000i	$0.479867\pi$
$548$	−16.4454	+	16.4454i	−0.702512	+	0.702512i
$549$		0			0
$550$	−4.25543	+	3.49037i	−0.181452	+	0.148830i
$551$		−	49.8109i		−	2.12202i
$552$		0			0
$553$	11.2115	+	11.2115i	0.476762	+	0.476762i
$554$	−0.983906			−0.0418022
$555$		0			0
$556$	3.98491			0.168998
$557$	9.18436	+	9.18436i	0.389154	+	0.389154i	0.874386	−	0.485232i	$-0.161265\pi$
$557$	9.18436	+	9.18436i	0.389154	+	0.389154i	−0.485232	+	0.874386i	$0.661265\pi$
$558$		0			0
$559$			26.7698i			1.13224i
$560$	21.6217	+	23.8625i	0.913684	+	1.00838i
$561$		0			0
$562$	0.488209	−	0.488209i	0.0205938	−	0.0205938i
$563$	4.95515	−	4.95515i	0.208834	−	0.208834i	−0.594937	−	0.803772i	$-0.702823\pi$
$563$	4.95515	−	4.95515i	0.208834	−	0.208834i	0.803772	+	0.594937i	$0.202823\pi$
$564$		0			0
$565$	20.7982	+	22.9537i	0.874986	+	0.965668i
$566$			3.17857i			0.133605i
$567$		0			0
$568$	9.78020	+	9.78020i	0.410368	+	0.410368i
$569$	14.3121			0.599994			0.299997	−	0.953940i	$-0.403014\pi$
$569$	14.3121			0.599994			0.299997	+	0.953940i	$0.403014\pi$
$570$		0			0
$571$	8.17879			0.342272			0.171136	−	0.985247i	$-0.445256\pi$
$571$	8.17879			0.342272			0.171136	+	0.985247i	$0.445256\pi$
$572$	−12.7611	−	12.7611i	−0.533568	−	0.533568i
$573$		0			0
$574$		−	10.7435i		−	0.448427i
$575$	3.86593	−	3.17089i	0.161221	−	0.132235i
$576$		0			0
$577$	−9.14462	+	9.14462i	−0.380696	+	0.380696i	−0.871353	−	0.490657i	$-0.836757\pi$
$577$	−9.14462	+	9.14462i	−0.380696	+	0.380696i	0.490657	+	0.871353i	$0.336757\pi$
$578$	1.68073	−	1.68073i	0.0699092	−	0.0699092i
$579$		0			0
$580$	−38.1060	−	1.87733i	−1.58227	−	0.0779519i
$581$			10.3451i			0.429185i
$582$		0			0
$583$	−6.77062	−	6.77062i	−0.280410	−	0.280410i
$584$	12.2175			0.505562
$585$		0			0
$586$	4.87766			0.201494
$587$	31.9584	+	31.9584i	1.31906	+	1.31906i	0.914517	+	0.404547i	$0.132571\pi$
$587$	31.9584	+	31.9584i	1.31906	+	1.31906i	0.404547	+	0.914517i	$0.367429\pi$
$588$		0			0
$589$		−	51.5155i		−	2.12266i
$590$	1.00942	−	0.914627i	0.0415570	−	0.0376546i
$591$		0			0
$592$	−6.43724	+	6.43724i	−0.264569	+	0.264569i
$593$	28.6892	−	28.6892i	1.17812	−	1.17812i	0.197902	−	0.980222i	$-0.436587\pi$
$593$	28.6892	−	28.6892i	1.17812	−	1.17812i	0.980222	−	0.197902i	$-0.0634127\pi$
$594$		0			0
$595$	−1.42303	+	28.8847i	−0.0583386	+	1.18416i
$596$			6.27971i			0.257227i
$597$		0			0
$598$	−0.600561	−	0.600561i	−0.0245588	−	0.0245588i
$599$	−33.0173			−1.34905			−0.674525	−	0.738252i	$-0.735652\pi$
$599$	−33.0173			−1.34905			−0.674525	+	0.738252i	$0.735652\pi$
$600$		0			0
$601$	−11.8631			−0.483907			−0.241953	−	0.970288i	$-0.577788\pi$
$601$	−11.8631			−0.483907			−0.241953	+	0.970288i	$0.577788\pi$
$602$	−9.24786	−	9.24786i	−0.376915	−	0.376915i
$603$		0			0
$604$			15.7674i			0.641567i
$605$	0.143099	−	2.90462i	0.00581779	−	0.118089i
$606$		0			0
$607$	−26.8450	+	26.8450i	−1.08960	+	1.08960i	−0.0940351	+	0.995569i	$0.529977\pi$
$607$	−26.8450	+	26.8450i	−1.08960	+	1.08960i	−0.995569	+	0.0940351i	$0.970023\pi$
$608$	13.8247	−	13.8247i	0.560664	−	0.560664i
$609$		0			0
$610$	5.59958	−	5.07375i	0.226720	−	0.205430i
$611$		−	14.4500i		−	0.584584i
$612$		0			0
$613$	13.9441	+	13.9441i	0.563196	+	0.563196i	0.930214	−	0.367018i	$-0.119621\pi$
$613$	13.9441	+	13.9441i	0.563196	+	0.563196i	−0.367018	+	0.930214i	$0.619621\pi$
$614$	3.25979			0.131554
$615$		0			0
$616$	18.0905			0.728886
$617$	7.28638	+	7.28638i	0.293338	+	0.293338i	0.838398	−	0.545059i	$-0.183493\pi$
$617$	7.28638	+	7.28638i	0.293338	+	0.293338i	−0.545059	+	0.838398i	$0.683493\pi$
$618$		0			0
$619$			38.1044i			1.53155i	0.643111	+	0.765773i	$0.277643\pi$
$619$			38.1044i			1.53155i	−0.643111	+	0.765773i	$0.722357\pi$
$620$	−39.4101	−	1.94158i	−1.58275	−	0.0779755i
$621$		0			0
$622$	−2.34066	+	2.34066i	−0.0938518	+	0.0938518i
$623$	−33.4828	+	33.4828i	−1.34146	+	1.34146i
$624$		0			0
$625$	24.5169	+	4.89087i	0.980677	+	0.195635i
$626$			0.618158i			0.0247066i
$627$		0			0
$628$	−13.4566	−	13.4566i	−0.536977	−	0.536977i
$629$	−8.17591			−0.325995
$630$		0			0
$631$	29.4274			1.17149			0.585743	−	0.810497i	$-0.300803\pi$
$631$	29.4274			1.17149			0.585743	+	0.810497i	$0.300803\pi$
$632$	−3.25907	−	3.25907i	−0.129639	−	0.129639i
$633$		0			0
$634$			4.98288i			0.197896i
$635$	−26.9660	−	29.7607i	−1.07011	−	1.18102i
$636$		0			0
$637$	20.5593	−	20.5593i	0.814588	−	0.814588i
$638$	−6.98416	+	6.98416i	−0.276505	+	0.276505i
$639$		0			0
$640$	−13.2770	−	14.6529i	−0.524818	−	0.579209i
$641$		−	12.2284i		−	0.482993i	−0.970402	−	0.241496i	$-0.922362\pi$
$641$		−	12.2284i		−	0.482993i	0.970402	−	0.241496i	$-0.0776382\pi$
$642$		0			0
$643$	7.67059	+	7.67059i	0.302499	+	0.302499i	0.841991	−	0.539492i	$-0.181384\pi$
$643$	7.67059	+	7.67059i	0.302499	+	0.302499i	−0.539492	+	0.841991i	$0.681384\pi$
$644$	−8.00985			−0.315632
$645$		0			0
$646$	5.34923			0.210463
$647$	−5.99944	−	5.99944i	−0.235862	−	0.235862i	0.579272	−	0.815134i	$-0.303337\pi$
$647$	−5.99944	−	5.99944i	−0.235862	−	0.235862i	−0.815134	+	0.579272i	$0.803337\pi$
$648$		0			0
$649$			6.80733i			0.267211i
$650$	0.417414	−	4.22604i	0.0163723	−	0.165759i
$651$		0			0
$652$	−17.6388	+	17.6388i	−0.690791	+	0.690791i
$653$	−19.3650	+	19.3650i	−0.757812	+	0.757812i	−0.975924	−	0.218111i	$-0.930010\pi$
$653$	−19.3650	+	19.3650i	−0.757812	+	0.757812i	0.218111	+	0.975924i	$0.430010\pi$
$654$		0			0
$655$	39.9860	+	1.96995i	1.56238	+	0.0769724i
$656$		−	27.7811i		−	1.08467i
$657$		0			0
$658$	4.99187	+	4.99187i	0.194603	+	0.194603i
$659$	24.0672			0.937524			0.468762	−	0.883324i	$-0.344700\pi$
$659$	24.0672			0.937524			0.468762	+	0.883324i	$0.344700\pi$
$660$		0			0
$661$	−29.9105			−1.16338			−0.581691	−	0.813410i	$-0.697609\pi$
$661$	−29.9105			−1.16338			−0.581691	+	0.813410i	$0.697609\pi$
$662$	0.0670668	+	0.0670668i	0.00260663	+	0.00260663i
$663$		0			0
$664$		−	3.00720i		−	0.116702i
$665$	38.7475	−	35.1089i	1.50256	−	1.36146i
$666$		0			0
$667$	6.34490	−	6.34490i	0.245675	−	0.245675i
$668$	16.8835	−	16.8835i	0.653243	−	0.653243i
$669$		0			0
$670$	0.391965	−	7.95610i	0.0151429	−	0.307371i
$671$			37.7626i			1.45781i
$672$		0			0
$673$	−33.9352	−	33.9352i	−1.30810	−	1.30810i	−0.922782	−	0.385323i	$-0.874090\pi$
$673$	−33.9352	−	33.9352i	−1.30810	−	1.30810i	−0.385323	−	0.922782i	$-0.625910\pi$
$674$	−4.46040			−0.171808
$675$		0			0
$676$	−10.7947			−0.415182
$677$	−9.15823	−	9.15823i	−0.351979	−	0.351979i	0.508866	−	0.860846i	$-0.330065\pi$
$677$	−9.15823	−	9.15823i	−0.351979	−	0.351979i	−0.860846	+	0.508866i	$0.830065\pi$
$678$		0			0
$679$			26.6337i			1.02211i
$680$	0.413660	−	8.39646i	0.0158631	−	0.321990i
$681$		0			0
$682$	−7.22316	+	7.22316i	−0.276589	+	0.276589i
$683$	−22.7557	+	22.7557i	−0.870723	+	0.870723i	−0.992551	−	0.121828i	$-0.961124\pi$
$683$	−22.7557	+	22.7557i	−0.870723	+	0.870723i	0.121828	+	0.992551i	$0.461124\pi$
$684$		0			0
$685$	20.2672	−	18.3640i	0.774368	−	0.701651i
$686$			4.95022i			0.189000i
$687$		0			0
$688$	−23.9135	−	23.9135i	−0.911694	−	0.911694i
$689$	7.38799			0.281460
$690$		0			0
$691$	−43.1298			−1.64074			−0.820368	−	0.571836i	$-0.806231\pi$
$691$	−43.1298			−1.64074			−0.820368	+	0.571836i	$0.806231\pi$
$692$	12.8032	+	12.8032i	0.486704	+	0.486704i
$693$		0			0
$694$		−	9.68215i		−	0.367529i
$695$	−4.68039	−	0.230584i	−0.177537	−	0.00874655i
$696$		0			0
$697$	17.6423	−	17.6423i	0.668251	−	0.668251i
$698$	−2.00417	+	2.00417i	−0.0758588	+	0.0758588i
$699$		0			0
$700$	−25.3984	−	30.9656i	−0.959969	−	1.17039i
$701$			17.3741i			0.656209i	0.944641	+	0.328105i	$0.106410\pi$
$701$			17.3741i			0.656209i	−0.944641	+	0.328105i	$0.893590\pi$
$702$		0			0
$703$	10.4526	+	10.4526i	0.394229	+	0.394229i
$704$	20.1033			0.757671
$705$		0			0
$706$	4.99471			0.187978
$707$	54.1528	+	54.1528i	2.03663	+	2.03663i
$708$		0			0
$709$			29.8937i			1.12268i	0.827585	+	0.561341i	$0.189714\pi$
$709$			29.8937i			1.12268i	−0.827585	+	0.561341i	$0.810286\pi$
$710$	−5.32273	−	5.87437i	−0.199758	−	0.220461i
$711$		0			0
$712$	9.73309	−	9.73309i	0.364763	−	0.364763i
$713$	6.56203	−	6.56203i	0.245750	−	0.245750i
$714$		0			0
$715$	14.2499	+	15.7267i	0.532914	+	0.588144i
$716$		−	10.6013i		−	0.396189i
$717$		0			0
$718$	2.41117	+	2.41117i	0.0899841	+	0.0899841i
$719$	−42.8268			−1.59717			−0.798585	−	0.601882i	$-0.794418\pi$
$719$	−42.8268			−1.59717			−0.798585	+	0.601882i	$0.794418\pi$
$720$		0			0
$721$	−48.6667			−1.81244
$722$	−2.62219	−	2.62219i	−0.0975880	−	0.0975880i
$723$		0			0
$724$		−	23.2344i		−	0.863501i
$725$	44.6479	+	4.40995i	1.65818	+	0.163782i
$726$		0			0
$727$	16.7556	−	16.7556i	0.621430	−	0.621430i	−0.324467	−	0.945897i	$-0.605185\pi$
$727$	16.7556	−	16.7556i	0.621430	−	0.621430i	0.945897	+	0.324467i	$0.105185\pi$
$728$	−9.87001	+	9.87001i	−0.365807	+	0.365807i
$729$		0			0
$730$	−6.99372	−	0.344553i	−0.258849	−	0.0127525i
$731$		−	30.3724i		−	1.12337i
$732$		0			0
$733$	−14.5146	−	14.5146i	−0.536108	−	0.536108i	0.386275	−	0.922384i	$-0.373761\pi$
$733$	−14.5146	−	14.5146i	−0.536108	−	0.536108i	−0.922384	+	0.386275i	$0.873761\pi$
$734$	4.69402			0.173260
$735$		0			0
$736$	3.52196			0.129821
$737$	28.1490	+	28.1490i	1.03688	+	1.03688i
$738$		0			0
$739$		−	25.4582i		−	0.936495i	−0.883597	−	0.468248i	$-0.844886\pi$
$739$		−	25.4582i		−	0.936495i	0.883597	−	0.468248i	$-0.155114\pi$
$740$	8.39037	−	7.60246i	0.308436	−	0.279472i
$741$		0			0
$742$	−2.55224	+	2.55224i	−0.0936958	+	0.0936958i
$743$	−20.3299	+	20.3299i	−0.745831	+	0.745831i	−0.973693	−	0.227862i	$-0.926826\pi$
$743$	−20.3299	+	20.3299i	−0.745831	+	0.745831i	0.227862	+	0.973693i	$0.426826\pi$
$744$		0			0
$745$	0.363371	−	7.37569i	0.0133129	−	0.270224i
$746$			6.77241i			0.247955i
$747$		0			0
$748$	14.4785	+	14.4785i	0.529385	+	0.529385i
$749$	38.4951			1.40658
$750$		0			0
$751$	38.6336			1.40976			0.704881	−	0.709326i	$-0.251001\pi$
$751$	38.6336			1.40976			0.704881	+	0.709326i	$0.251001\pi$
$752$	12.9082	+	12.9082i	0.470713	+	0.470713i
$753$		0			0
$754$		−	7.62100i		−	0.277540i
$755$	0.912370	−	18.5193i	0.0332045	−	0.673985i
$756$		0			0
$757$	−2.97930	+	2.97930i	−0.108284	+	0.108284i	−0.759173	−	0.650889i	$-0.774396\pi$
$757$	−2.97930	+	2.97930i	−0.108284	+	0.108284i	0.650889	+	0.759173i	$0.274396\pi$
$758$	3.46771	−	3.46771i	0.125953	−	0.125953i
$759$		0			0
$760$	−11.2635	+	10.2058i	−0.408569	+	0.370202i
$761$		−	14.5624i		−	0.527885i	−0.964538	−	0.263943i	$-0.914977\pi$
$761$		−	14.5624i		−	0.527885i	0.964538	−	0.263943i	$-0.0850230\pi$
$762$		0			0
$763$	−32.4144	−	32.4144i	−1.17348	−	1.17348i
$764$	12.0322			0.435308
$765$		0			0
$766$	0.799529			0.0288882
$767$	−3.71402	−	3.71402i	−0.134106	−	0.134106i
$768$		0			0
$769$		−	24.1110i		−	0.869466i	−0.900559	−	0.434733i	$-0.856843\pi$
$769$		−	24.1110i		−	0.869466i	0.900559	−	0.434733i	$-0.143157\pi$
$770$	−10.3556	−	0.510181i	−0.373192	−	0.0183857i
$771$		0			0
$772$	27.0454	−	27.0454i	0.973385	−	0.973385i
$773$	−1.14031	+	1.14031i	−0.0410140	+	0.0410140i	−0.727316	−	0.686302i	$-0.759233\pi$
$773$	−1.14031	+	1.14031i	−0.0410140	+	0.0410140i	0.686302	+	0.727316i	$0.259233\pi$
$774$		0			0
$775$	46.1758	+	4.56087i	1.65869	+	0.163831i
$776$		−	7.74213i		−	0.277926i
$777$		0			0
$778$	−6.65502	−	6.65502i	−0.238594	−	0.238594i
$779$	−45.1103			−1.61625
$780$		0			0
$781$	39.6157			1.41756
$782$	0.681383	+	0.681383i	0.0243662	+	0.0243662i
$783$		0			0
$784$			36.7313i			1.31183i
$785$	15.0265	+	16.5838i	0.536318	+	0.591901i
$786$		0			0
$787$	−12.9435	+	12.9435i	−0.461387	+	0.461387i	−0.899110	−	0.437723i	$-0.855785\pi$
$787$	−12.9435	+	12.9435i	−0.461387	+	0.461387i	0.437723	+	0.899110i	$0.355785\pi$
$788$	24.9473	−	24.9473i	0.888712	−	0.888712i
$789$		0			0
$790$	1.77370	+	1.95752i	0.0631054	+	0.0696455i
$791$			58.3515i			2.07474i
$792$		0			0
$793$	−20.6030	−	20.6030i	−0.731633	−	0.731633i
$794$	6.88501			0.244340
$795$		0			0
$796$	4.67439			0.165679
$797$	−7.72888	−	7.72888i	−0.273771	−	0.273771i	0.556845	−	0.830616i	$-0.312012\pi$
$797$	−7.72888	−	7.72888i	−0.273771	−	0.273771i	−0.830616	+	0.556845i	$0.812012\pi$
$798$		0			0
$799$			16.3946i			0.580000i
$800$	11.1678	+	13.6157i	0.394840	+	0.481386i
$801$		0			0
$802$	−1.66096	+	1.66096i	−0.0586505	+	0.0586505i
$803$	24.7440	−	24.7440i	0.873197	−	0.873197i
$804$		0			0
$805$	9.40779	+	0.463484i	0.331581	+	0.0163357i
$806$		−	7.88180i		−	0.277624i
$807$		0			0
$808$	−15.7416	−	15.7416i	−0.553789	−	0.553789i
$809$	−32.7480			−1.15136			−0.575679	−	0.817676i	$-0.695262\pi$
$809$	−32.7480			−1.15136			−0.575679	+	0.817676i	$0.695262\pi$
$810$		0			0
$811$	37.6435			1.32184			0.660921	−	0.750456i	$-0.270166\pi$
$811$	37.6435			1.32184			0.660921	+	0.750456i	$0.270166\pi$
$812$	−50.8217	−	50.8217i	−1.78349	−	1.78349i
$813$		0			0
$814$		−	2.93120i		−	0.102739i
$815$	21.7380	−	19.6967i	0.761448	−	0.689944i
$816$		0			0
$817$	−38.8302	+	38.8302i	−1.35850	+	1.35850i
$818$	−7.80480	+	7.80480i	−0.272889	+	0.272889i
$819$		0			0
$820$	−1.70017	+	34.5100i	−0.0593725	+	1.20514i
$821$		−	31.1029i		−	1.08550i	−0.839894	−	0.542750i	$-0.817383\pi$
$821$		−	31.1029i		−	1.08550i	0.839894	−	0.542750i	$-0.182617\pi$
$822$		0			0
$823$	8.07466	+	8.07466i	0.281465	+	0.281465i	0.833693	−	0.552228i	$-0.186222\pi$
$823$	8.07466	+	8.07466i	0.281465	+	0.281465i	−0.552228	+	0.833693i	$0.686222\pi$
$824$	14.1469			0.492830
$825$		0			0
$826$	2.56608			0.0892854
$827$	−22.2387	−	22.2387i	−0.773315	−	0.773315i	0.205370	−	0.978685i	$-0.434160\pi$
$827$	−22.2387	−	22.2387i	−0.773315	−	0.773315i	−0.978685	+	0.205370i	$0.934160\pi$
$828$		0			0
$829$		−	4.45174i		−	0.154615i	−0.997007	−	0.0773077i	$-0.975368\pi$
$829$		−	4.45174i		−	0.154615i	0.997007	−	0.0773077i	$-0.0246324\pi$
$830$	−0.0848079	+	1.72143i	−0.00294372	+	0.0597517i
$831$		0			0
$832$	−10.9682	+	10.9682i	−0.380253	+	0.380253i
$833$	−23.3261	+	23.3261i	−0.808201	+	0.808201i
$834$		0			0
$835$	−20.8071	+	18.8532i	−0.720060	+	0.652442i
$836$		−	37.0205i		−	1.28038i
$837$		0			0
$838$	−2.17611	−	2.17611i	−0.0751724	−	0.0751724i
$839$	−14.5102			−0.500948			−0.250474	−	0.968123i	$-0.580586\pi$
$839$	−14.5102			−0.500948			−0.250474	+	0.968123i	$0.580586\pi$
$840$		0			0
$841$	51.5155			1.77640
$842$	−3.47494	−	3.47494i	−0.119755	−	0.119755i
$843$		0			0
$844$		−	16.2609i		−	0.559724i
$845$	12.6787	+	0.624630i	0.436161	+	0.0214879i
$846$		0			0
$847$	3.87387	−	3.87387i	0.133108	−	0.133108i
$848$	−6.59970	+	6.59970i	−0.226635	+	0.226635i
$849$		0			0
$850$	−0.473588	+	4.79478i	−0.0162439	+	0.164459i
$851$			2.66291i			0.0912834i
$852$		0			0
$853$	31.5289	+	31.5289i	1.07953	+	1.07953i	0.996551	+	0.0829779i	$0.0264431\pi$
$853$	31.5289	+	31.5289i	1.07953	+	1.07953i	0.0829779	+	0.996551i	$0.473557\pi$
$854$	14.2349			0.487110
$855$		0			0
$856$	−11.1901			−0.382470
$857$	30.8923	+	30.8923i	1.05526	+	1.05526i	0.998381	+	0.0568810i	$0.0181156\pi$
$857$	30.8923	+	30.8923i	1.05526	+	1.05526i	0.0568810	+	0.998381i	$0.481884\pi$
$858$		0			0
$859$		−	15.5140i		−	0.529331i	−0.964340	−	0.264665i	$-0.914738\pi$
$859$		−	15.5140i		−	0.529331i	0.964340	−	0.264665i	$-0.0852615\pi$
$860$	28.2422	+	31.1691i	0.963050	+	1.06286i
$861$		0			0
$862$	−6.93568	+	6.93568i	−0.236230	+	0.236230i
$863$	−20.5580	+	20.5580i	−0.699804	+	0.699804i	−0.964368	−	0.264564i	$-0.914772\pi$
$863$	−20.5580	+	20.5580i	−0.699804	+	0.699804i	0.264564	+	0.964368i	$0.414772\pi$
$864$		0			0
$865$	−14.2968	−	15.7785i	−0.486107	−	0.536486i
$866$		−	7.57021i		−	0.257246i
$867$		0			0
$868$	−52.5609	−	52.5609i	−1.78403	−	1.78403i
$869$	−13.2012			−0.447819
$870$		0			0
$871$	−30.7157			−1.04076
$872$	9.42251	+	9.42251i	0.319086	+	0.319086i
$873$		0			0
$874$		−	1.74226i		−	0.0589327i
$875$	28.0393	+	37.8396i	0.947902	+	1.27921i
$876$		0			0
$877$	20.2801	−	20.2801i	0.684809	−	0.684809i	−0.276271	−	0.961080i	$-0.589099\pi$
$877$	20.2801	−	20.2801i	0.684809	−	0.684809i	0.961080	+	0.276271i	$0.0890987\pi$
$878$	4.83097	−	4.83097i	0.163037	−	0.163037i
$879$		0			0
$880$	−26.7781	−	1.31925i	−0.902689	−	0.0444719i
$881$		−	45.8431i		−	1.54449i	−0.635324	−	0.772246i	$-0.719133\pi$
$881$		−	45.8431i		−	1.54449i	0.635324	−	0.772246i	$-0.280867\pi$
$882$		0			0
$883$	−10.8627	−	10.8627i	−0.365559	−	0.365559i	0.500295	−	0.865855i	$-0.333225\pi$
$883$	−10.8627	−	10.8627i	−0.365559	−	0.365559i	−0.865855	+	0.500295i	$0.833225\pi$
$884$	−15.7987			−0.531366
$885$		0			0
$886$	−8.47586			−0.284752
$887$	−38.7471	−	38.7471i	−1.30100	−	1.30100i	−0.927718	−	0.373283i	$-0.878232\pi$
$887$	−38.7471	−	38.7471i	−1.30100	−	1.30100i	−0.373283	−	0.927718i	$-0.621768\pi$
$888$		0			0
$889$		−	75.6559i		−	2.53742i
$890$	−5.84607	+	5.29709i	−0.195961	+	0.177559i
$891$		0			0
$892$	−3.39318	+	3.39318i	−0.113612	+	0.113612i
$893$	20.9600	−	20.9600i	0.701400	−	0.701400i
$894$		0			0
$895$	−0.613436	+	12.4515i	−0.0205049	+	0.416208i
$896$		−	37.2499i		−	1.24443i
$897$		0			0
$898$	−0.210232	−	0.210232i	−0.00701555	−	0.00701555i
$899$	83.2708			2.77724
$900$		0			0
$901$	−8.38225			−0.279253
$902$	6.32508	+	6.32508i	0.210602	+	0.210602i
$903$		0			0
$904$		−	16.9622i		−	0.564153i
$905$	−1.34444	+	27.2895i	−0.0446908	+	0.907134i
$906$		0			0
$907$	−21.8139	+	21.8139i	−0.724317	+	0.724317i	−0.969482	−	0.245164i	$-0.921158\pi$
$907$	−21.8139	+	21.8139i	−0.724317	+	0.724317i	0.245164	+	0.969482i	$0.421158\pi$
$908$	25.1303	−	25.1303i	0.833979	−	0.833979i
$909$		0			0
$910$	5.92831	−	5.37161i	0.196521	−	0.178067i
$911$		−	1.03636i		−	0.0343363i	−0.999853	−	0.0171681i	$-0.994535\pi$
$911$		−	1.03636i		−	0.0343363i	0.999853	−	0.0171681i	$-0.00546506\pi$
$912$		0			0
$913$	−6.09047	−	6.09047i	−0.201565	−	0.201565i
$914$	−5.82051			−0.192526
$915$		0			0
$916$	−32.0787			−1.05991
$917$	53.3291	+	53.3291i	1.76108	+	1.76108i
$918$		0			0
$919$		−	26.9773i		−	0.889900i	−0.895555	−	0.444950i	$-0.853221\pi$
$919$		−	26.9773i		−	0.889900i	0.895555	−	0.444950i	$-0.146779\pi$
$920$	−2.73474	−	0.134730i	−0.0901618	−	0.00444191i
$921$		0			0
$922$	−3.16751	+	3.16751i	−0.104316	+	0.104316i
$923$	−21.6140	+	21.6140i	−0.711433	+	0.711433i
$924$		0			0
$925$	−10.2946	+	8.44380i	−0.338485	+	0.277630i
$926$		−	4.17410i		−	0.137170i
$927$		0			0
$928$	22.3465	+	22.3465i	0.733559	+	0.733559i
$929$	2.18761			0.0717732			0.0358866	−	0.999356i	$-0.488574\pi$
$929$	2.18761			0.0717732			0.0358866	+	0.999356i	$0.488574\pi$
$930$		0			0
$931$	59.6434			1.95473
$932$	19.1107	+	19.1107i	0.625992	+	0.625992i
$933$		0			0
$934$			1.92327i			0.0629312i
$935$	−16.1676	−	17.8431i	−0.528736	−	0.583533i
$936$		0			0
$937$	−0.117553	+	0.117553i	−0.00384031	+	0.00384031i	−0.709024	−	0.705184i	$-0.750864\pi$
$937$	−0.117553	+	0.117553i	−0.00384031	+	0.00384031i	0.705184	+	0.709024i	$0.250864\pi$
$938$	10.6110	−	10.6110i	0.346461	−	0.346461i
$939$		0			0
$940$	−15.2447	−	16.8247i	−0.497229	−	0.548760i
$941$			57.6331i			1.87878i	0.342845	+	0.939392i	$0.388610\pi$
$941$			57.6331i			1.87878i	−0.342845	+	0.939392i	$0.611390\pi$
$942$		0			0
$943$	−5.74614	−	5.74614i	−0.187120	−	0.187120i
$944$	6.63549			0.215967
$945$		0			0
$946$	10.8890			0.354033
$947$	−35.9183	−	35.9183i	−1.16719	−	1.16719i	−0.982866	−	0.184322i	$-0.940991\pi$
$947$	−35.9183	−	35.9183i	−1.16719	−	1.16719i	−0.184322	−	0.982866i	$-0.559009\pi$
$948$		0			0
$949$			27.0003i			0.876466i
$950$	6.73544	−	5.52450i	0.218527	−	0.179239i
$951$		0			0
$952$	11.1983	−	11.1983i	0.362939	−	0.362939i
$953$	10.8426	−	10.8426i	0.351225	−	0.351225i	−0.509340	−	0.860565i	$-0.670111\pi$
$953$	10.8426	−	10.8426i	0.351225	−	0.351225i	0.860565	+	0.509340i	$0.170111\pi$
$954$		0			0
$955$	−14.1321	−	0.696232i	−0.457304	−	0.0225295i
$956$			0.790909i			0.0255798i
$957$		0			0
$958$	−6.65572	−	6.65572i	−0.215036	−	0.215036i
$959$	51.5220			1.66373
$960$		0			0
$961$	55.1204			1.77808
$962$	1.59924	+	1.59924i	0.0515616	+	0.0515616i
$963$		0			0
$964$		−	5.29396i		−	0.170507i
$965$	−33.3305	+	30.2006i	−1.07295	+	0.972192i
$966$		0			0
$967$	7.03735	−	7.03735i	0.226306	−	0.226306i	−0.584842	−	0.811148i	$-0.698843\pi$
$967$	7.03735	−	7.03735i	0.226306	−	0.226306i	0.811148	+	0.584842i	$0.198843\pi$
$968$	−1.12609	+	1.12609i	−0.0361939	+	0.0361939i
$969$		0			0
$970$	−0.218341	+	4.43188i	−0.00701050	+	0.142299i
$971$			20.1313i			0.646043i	0.946392	+	0.323021i	$0.104699\pi$
$971$			20.1313i			0.646043i	−0.946392	+	0.323021i	$0.895301\pi$
$972$		0			0
$973$	−6.24220	−	6.24220i	−0.200116	−	0.200116i
$974$	−9.44908			−0.302768
$975$		0			0
$976$	36.8093			1.17824
$977$	−23.6858	−	23.6858i	−0.757776	−	0.757776i	0.218141	−	0.975917i	$-0.430001\pi$
$977$	−23.6858	−	23.6858i	−0.757776	−	0.757776i	−0.975917	+	0.218141i	$0.930001\pi$
$978$		0			0
$979$		−	39.4248i		−	1.26002i
$980$	2.24791	−	45.6280i	0.0718068	−	1.45753i
$981$		0			0
$982$	2.03817	−	2.03817i	0.0650406	−	0.0650406i
$983$	−25.4149	+	25.4149i	−0.810610	+	0.810610i	−0.984725	−	0.174115i	$-0.944293\pi$
$983$	−25.4149	+	25.4149i	−0.810610	+	0.810610i	0.174115	+	0.984725i	$0.444293\pi$
$984$		0			0
$985$	−30.7449	+	27.8578i	−0.979613	+	0.887622i
$986$			8.64661i			0.275364i
$987$		0			0
$988$	20.1981	+	20.1981i	0.642587	+	0.642587i
$989$	−9.89237			−0.314559
$990$		0			0
$991$	−19.7854			−0.628504			−0.314252	−	0.949340i	$-0.601754\pi$
$991$	−19.7854			−0.628504			−0.314252	+	0.949340i	$0.601754\pi$
$992$	23.1112	+	23.1112i	0.733781	+	0.733781i
$993$		0			0
$994$		−	14.9335i		−	0.473661i
$995$	−5.49020	−	0.270480i	−0.174051	−	0.00857479i
$996$		0			0
$997$	−22.0218	+	22.0218i	−0.697438	+	0.697438i	−0.963857	−	0.266419i	$-0.914159\pi$
$997$	−22.0218	+	22.0218i	−0.697438	+	0.697438i	0.266419	+	0.963857i	$0.414159\pi$
$998$	1.79090	−	1.79090i	0.0566901	−	0.0566901i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.323.13	yes	44
3.2	odd	2	inner	1035.2.j.b.323.10	✓	44
5.2	odd	4	inner	1035.2.j.b.737.10	yes	44
15.2	even	4	inner	1035.2.j.b.737.13	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.10	✓	44	3.2	odd	2	inner
1035.2.j.b.323.13	yes	44	1.1	even	1	trivial
1035.2.j.b.737.10	yes	44	5.2	odd	4	inner
1035.2.j.b.737.13	yes	44	15.2	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221928 + 0.221928i) q^{2} -1.90150i q^{4} +(-0.110029 + 2.23336i) q^{5} +(-2.97861 + 2.97861i) q^{7} +(0.865851 - 0.865851i) q^{8} +O(q^{10})\)	\(q+(0.221928 + 0.221928i) q^{2} -1.90150i q^{4} +(-0.110029 + 2.23336i) q^{5} +(-2.97861 + 2.97861i) q^{7} +(0.865851 - 0.865851i) q^{8} +(-0.520063 + 0.471226i) q^{10} -3.50722i q^{11} +(1.91351 + 1.91351i) q^{13} -1.32208 q^{14} -3.41868 q^{16} +(-2.17102 - 2.17102i) q^{17} +5.55117i q^{19} +(4.24672 + 0.209219i) q^{20} +(0.778349 - 0.778349i) q^{22} +(-0.707107 + 0.707107i) q^{23} +(-4.97579 - 0.491467i) q^{25} +0.849322i q^{26} +(5.66382 + 5.66382i) q^{28} -8.97304 q^{29} -9.28011 q^{31} +(-2.49040 - 2.49040i) q^{32} -0.963621i q^{34} +(-6.32458 - 6.98005i) q^{35} +(1.88296 - 1.88296i) q^{37} +(-1.23196 + 1.23196i) q^{38} +(1.83849 + 2.02902i) q^{40} +8.12627i q^{41} +(6.99496 + 6.99496i) q^{43} -6.66896 q^{44} -0.313853 q^{46} +(-3.77578 - 3.77578i) q^{47} -10.7443i q^{49} +(-0.995196 - 1.21334i) q^{50} +(3.63853 - 3.63853i) q^{52} +(1.93048 - 1.93048i) q^{53} +(7.83287 + 0.385894i) q^{55} +5.15807i q^{56} +(-1.99137 - 1.99137i) q^{58} -1.94095 q^{59} -10.7671 q^{61} +(-2.05951 - 2.05951i) q^{62} +5.73198i q^{64} +(-4.48409 + 4.06301i) q^{65} +(-8.02601 + 8.02601i) q^{67} +(-4.12819 + 4.12819i) q^{68} +(0.145466 - 2.95267i) q^{70} +11.2955i q^{71} +(7.05517 + 7.05517i) q^{73} +0.835763 q^{74} +10.5555 q^{76} +(10.4466 + 10.4466i) q^{77} -3.76401i q^{79} +(0.376153 - 7.63514i) q^{80} +(-1.80345 + 1.80345i) q^{82} +(1.73655 - 1.73655i) q^{83} +(5.08755 - 4.60980i) q^{85} +3.10475i q^{86} +(-3.03673 - 3.03673i) q^{88} +11.2411 q^{89} -11.3992 q^{91} +(1.34456 + 1.34456i) q^{92} -1.67590i q^{94} +(-12.3978 - 0.610788i) q^{95} +(4.47082 - 4.47082i) q^{97} +(2.38446 - 2.38446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 44 * q + 12 * q^7	\( 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) \) 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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