LMFDB - Embedded newform 496.2.bg.c.289.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [496,2,Mod(49,496)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(496, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([0, 0, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("496.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 496 = 2^{4} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	496.bg (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.96057994026$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.1
Root			$-1.03739i$ of defining polynomial
Character	$\chi$	$=$	496.289
Dual form			496.2.bg.c.369.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.302431 - 2.87744i) q^{3} +(-1.48661 - 2.57489i) q^{5} +(-1.05848 - 0.224987i) q^{7} +(-5.25377 + 1.11672i) q^{9} +(1.62690 - 1.80686i) q^{11} +(2.62521 + 1.16882i) q^{13} +(-6.95951 + 5.05638i) q^{15} +(-1.22101 - 1.35606i) q^{17} +(-1.93514 + 0.861580i) q^{19} +(-0.327269 + 3.11375i) q^{21} +(0.136652 - 0.420572i) q^{23} +(-1.92005 + 3.32562i) q^{25} +(2.11998 + 6.52462i) q^{27} +(2.55579 + 1.85689i) q^{29} +(-1.15354 + 5.44696i) q^{31} +(-5.69116 - 4.13487i) q^{33} +(0.994234 + 3.05994i) q^{35} +(-1.57338 + 2.72517i) q^{37} +(2.56926 - 7.90738i) q^{39} +(0.726079 - 6.90818i) q^{41} +(7.68509 - 3.42162i) q^{43} +(10.6858 + 11.8677i) q^{45} +(-6.44144 + 4.67998i) q^{47} +(-5.32506 - 2.37087i) q^{49} +(-3.53273 + 3.92349i) q^{51} +(4.86824 - 1.03478i) q^{53} +(-7.07105 - 1.50300i) q^{55} +(3.06439 + 5.30768i) q^{57} +(-1.25580 - 11.9481i) q^{59} -14.4351 q^{61} +5.81225 q^{63} +(-0.893094 - 8.49722i) q^{65} +(-3.21879 - 5.57511i) q^{67} +(-1.25150 - 0.266015i) q^{69} +(1.64121 - 0.348850i) q^{71} +(9.60883 - 10.6717i) q^{73} +(10.1500 + 4.51905i) q^{75} +(-2.12856 + 1.54649i) q^{77} +(2.30692 + 2.56210i) q^{79} +(3.41274 - 1.51945i) q^{81} +(1.34357 - 12.7832i) q^{83} +(-1.67655 + 5.15991i) q^{85} +(4.57015 - 7.91573i) q^{87} +(0.698188 + 2.14880i) q^{89} +(-2.51576 - 1.82781i) q^{91} +(16.0222 + 1.67190i) q^{93} +(5.09528 + 3.70194i) q^{95} +(1.05463 + 3.24582i) q^{97} +(-6.52961 + 11.3096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} - 3 q^{5} - 2 q^{7} - 10 q^{9} + 7 q^{11} - 7 q^{13} - 14 q^{15} - 6 q^{17} - 16 q^{19} + 9 q^{21} - q^{23} - 13 q^{25} - 9 q^{27} - 14 q^{29} - 15 q^{31} - 13 q^{33} + 9 q^{35} - 8 q^{37}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 - 3 * q^5 - 2 * q^7 - 10 * q^9 + 7 * q^11 - 7 * q^13 - 14 * q^15 - 6 * q^17 - 16 * q^19 + 9 * q^21 - q^23 - 13 * q^25 - 9 * q^27 - 14 * q^29 - 15 * q^31 - 13 * q^33 + 9 * q^35 - 8 * q^37 + 3 * q^39 - 8 * q^41 - 23 * q^43 + 65 * q^45 - 14 * q^47 + 2 * q^49 + 42 * q^51 + 6 * q^53 + 7 * q^55 - 17 * q^57 - 4 * q^59 - 60 * q^61 + 46 * q^63 - 12 * q^65 - 13 * q^67 + 38 * q^69 + 14 * q^71 + 2 * q^73 - 13 * q^75 + 18 * q^77 - 18 * q^79 + 23 * q^81 + 16 * q^83 + 37 * q^85 - 15 * q^87 + q^89 - 8 * q^91 + 17 * q^93 + 22 * q^95 + 3 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/496\mathbb{Z}\right)^\times$.

$n$	$63$	$65$	$373$
$\chi(n)$	$1$	$e\left(\frac{7}{15}\right)$	$1$

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			0
$2$		0			0
$3$	−0.302431	−	2.87744i	−0.174609	−	1.66129i	−0.634206	−	0.773164i	$-0.718673\pi$
$3$	−0.302431	−	2.87744i	−0.174609	−	1.66129i	0.459597	−	0.888128i	$-0.347994\pi$
$4$		0			0
$5$	−1.48661	−	2.57489i	−0.664834	−	1.15153i	−0.979330	−	0.202268i	$-0.935169\pi$
$5$	−1.48661	−	2.57489i	−0.664834	−	1.15153i	0.314496	−	0.949259i	$-0.398165\pi$
$6$		0			0
$7$	−1.05848	−	0.224987i	−0.400067	−	0.0850369i	0.00348400	−	0.999994i	$-0.498891\pi$
$7$	−1.05848	−	0.224987i	−0.400067	−	0.0850369i	−0.403551	+	0.914957i	$0.632224\pi$
$8$		0			0
$9$	−5.25377	+	1.11672i	−1.75126	+	0.372241i
$10$		0			0
$11$	1.62690	−	1.80686i	0.490530	−	0.544789i	−0.446158	−	0.894954i	$-0.647208\pi$
$11$	1.62690	−	1.80686i	0.490530	−	0.544789i	0.936688	+	0.350165i	$0.113875\pi$
$12$		0			0
$13$	2.62521	+	1.16882i	0.728103	+	0.324172i	0.737097	−	0.675787i	$-0.236196\pi$
$13$	2.62521	+	1.16882i	0.728103	+	0.324172i	−0.00899389	+	0.999960i	$0.502863\pi$
$14$		0			0
$15$	−6.95951	+	5.05638i	−1.79694	+	1.30555i
$16$		0			0
$17$	−1.22101	−	1.35606i	−0.296137	−	0.328894i	0.576653	−	0.816989i	$-0.304359\pi$
$17$	−1.22101	−	1.35606i	−0.296137	−	0.328894i	−0.872790	+	0.488095i	$0.837692\pi$
$18$		0			0
$19$	−1.93514	+	0.861580i	−0.443951	+	0.197660i	−0.616523	−	0.787337i	$-0.711459\pi$
$19$	−1.93514	+	0.861580i	−0.443951	+	0.197660i	0.172571	+	0.984997i	$0.444792\pi$
$20$		0			0
$21$	−0.327269	+	3.11375i	−0.0714159	+	0.679477i
$22$		0			0
$23$	0.136652	−	0.420572i	0.0284939	−	0.0876953i	−0.935798	−	0.352536i	$-0.885319\pi$
$23$	0.136652	−	0.420572i	0.0284939	−	0.0876953i	0.964292	+	0.264841i	$0.0853194\pi$
$24$		0			0
$25$	−1.92005	+	3.32562i	−0.384010	+	0.665124i
$26$		0			0
$27$	2.11998	+	6.52462i	0.407990	+	1.25566i
$28$		0			0
$29$	2.55579	+	1.85689i	0.474599	+	0.344816i	0.799231	−	0.601024i	$-0.205240\pi$
$29$	2.55579	+	1.85689i	0.474599	+	0.344816i	−0.324632	+	0.945840i	$0.605240\pi$
$30$		0			0
$31$	−1.15354	+	5.44696i	−0.207181	+	0.978303i
$31$	−1.15354	+	5.44696i	−0.207181	+	0.978303i
$32$		0			0
$33$	−5.69116	−	4.13487i	−0.990704	−	0.719789i
$34$		0			0
$35$	0.994234	+	3.05994i	0.168056	+	0.517224i
$36$		0			0
$37$	−1.57338	+	2.72517i	−0.258661	+	0.448015i	−0.965884	−	0.258977i	$-0.916615\pi$
$37$	−1.57338	+	2.72517i	−0.258661	+	0.448015i	0.707222	+	0.706991i	$0.249948\pi$
$38$		0			0
$39$	2.56926	−	7.90738i	0.411412	−	1.26619i
$40$		0			0
$41$	0.726079	−	6.90818i	0.113395	−	1.07888i	−0.778814	−	0.627254i	$-0.784179\pi$
$41$	0.726079	−	6.90818i	0.113395	−	1.07888i	0.892209	−	0.451623i	$-0.149155\pi$
$42$		0			0
$43$	7.68509	−	3.42162i	1.17197	−	0.521793i	0.273944	−	0.961746i	$-0.411672\pi$
$43$	7.68509	−	3.42162i	1.17197	−	0.521793i	0.898021	+	0.439953i	$0.145005\pi$
$44$		0			0
$45$	10.6858	+	11.8677i	1.59294	+	1.76914i
$46$		0			0
$47$	−6.44144	+	4.67998i	−0.939580	+	0.682645i	−0.948320	−	0.317317i	$-0.897218\pi$
$47$	−6.44144	+	4.67998i	−0.939580	+	0.682645i	0.00873953	+	0.999962i	$0.497218\pi$
$48$		0			0
$49$	−5.32506	−	2.37087i	−0.760723	−	0.338696i
$50$		0			0
$51$	−3.53273	+	3.92349i	−0.494681	+	0.549399i
$52$		0			0
$53$	4.86824	−	1.03478i	0.668704	−	0.142137i	0.138964	−	0.990297i	$-0.455623\pi$
$53$	4.86824	−	1.03478i	0.668704	−	0.142137i	0.529740	+	0.848160i	$0.322289\pi$
$54$		0			0
$55$	−7.07105	−	1.50300i	−0.953460	−	0.202664i
$56$		0			0
$57$	3.06439	+	5.30768i	0.405889	+	0.703020i
$58$		0			0
$59$	−1.25580	−	11.9481i	−0.163491	−	1.55551i	−0.701559	−	0.712612i	$-0.747512\pi$
$59$	−1.25580	−	11.9481i	−0.163491	−	1.55551i	0.538068	−	0.842902i	$-0.319154\pi$
$60$		0			0
$61$	−14.4351			−1.84823			−0.924115	−	0.382115i	$-0.875196\pi$
$61$	−14.4351			−1.84823			−0.924115	+	0.382115i	$0.875196\pi$
$62$		0			0
$63$	5.81225			0.732274
$64$		0			0
$65$	−0.893094	−	8.49722i	−0.110775	−	1.05395i
$66$		0			0
$67$	−3.21879	−	5.57511i	−0.393238	−	0.681108i	0.599636	−	0.800273i	$-0.295312\pi$
$67$	−3.21879	−	5.57511i	−0.393238	−	0.681108i	−0.992875	+	0.119164i	$0.961979\pi$
$68$		0			0
$69$	−1.25150	−	0.266015i	−0.150663	−	0.0320244i
$70$		0			0
$71$	1.64121	−	0.348850i	0.194776	−	0.0414009i	−0.109491	−	0.993988i	$-0.534922\pi$
$71$	1.64121	−	0.348850i	0.194776	−	0.0414009i	0.304266	+	0.952587i	$0.401589\pi$
$72$		0			0
$73$	9.60883	−	10.6717i	1.12463	−	1.24903i	0.159514	−	0.987196i	$-0.449007\pi$
$73$	9.60883	−	10.6717i	1.12463	−	1.24903i	0.965114	−	0.261830i	$-0.0843261\pi$
$74$		0			0
$75$	10.1500	+	4.51905i	1.17202	+	0.521815i
$76$		0			0
$77$	−2.12856	+	1.54649i	−0.242572	+	0.176239i
$78$		0			0
$79$	2.30692	+	2.56210i	0.259549	+	0.288259i	0.858809	−	0.512296i	$-0.171205\pi$
$79$	2.30692	+	2.56210i	0.259549	+	0.288259i	−0.599260	+	0.800555i	$0.704538\pi$
$80$		0			0
$81$	3.41274	−	1.51945i	0.379194	−	0.168828i
$82$		0			0
$83$	1.34357	−	12.7832i	0.147476	−	1.40314i	−0.631155	−	0.775657i	$-0.717419\pi$
$83$	1.34357	−	12.7832i	0.147476	−	1.40314i	0.778631	−	0.627482i	$-0.215914\pi$
$84$		0			0
$85$	−1.67655	+	5.15991i	−0.181848	+	0.559670i
$86$		0			0
$87$	4.57015	−	7.91573i	0.489972	−	0.848656i
$88$		0			0
$89$	0.698188	+	2.14880i	0.0740078	+	0.227773i	0.981217	−	0.192907i	$-0.0617916\pi$
$89$	0.698188	+	2.14880i	0.0740078	+	0.227773i	−0.907209	+	0.420680i	$0.861792\pi$
$90$		0			0
$91$	−2.51576	−	1.82781i	−0.263724	−	0.191606i
$92$		0			0
$93$	16.0222	+	1.67190i	1.66142	+	0.173368i
$94$		0			0
$95$	5.09528	+	3.70194i	0.522765	+	0.379811i
$96$		0			0
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	0.990213	−	0.139562i	$-0.0445693\pi$
$97$	1.05463	+	3.24582i	0.107082	+	0.329563i	−0.883132	+	0.469125i	$0.844569\pi$
$98$		0			0
$99$	−6.52961	+	11.3096i	−0.656251	+	1.13666i
$100$		0			0
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	−0.176741	−	0.984257i	$-0.556555\pi$
$101$	5.47495	−	16.8502i	0.544778	−	1.67665i	0.721518	−	0.692395i	$-0.243445\pi$
$102$		0			0
$103$	0.843947	−	8.02962i	0.0831566	−	0.791182i	−0.870881	−	0.491494i	$-0.836451\pi$
$103$	0.843947	−	8.02962i	0.0831566	−	0.791182i	0.954037	−	0.299688i	$-0.0968824\pi$
$104$		0			0
$105$	8.50411	−	3.78627i	0.829916	−	0.369502i
$106$		0			0
$107$	8.13074	+	9.03010i	0.786028	+	0.872972i	0.994466	−	0.105063i	$-0.0335045\pi$
$107$	8.13074	+	9.03010i	0.786028	+	0.872972i	−0.208438	+	0.978036i	$0.566838\pi$
$108$		0			0
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	−0.563025	−	0.826440i	$-0.690363\pi$
$109$	0.511381	−	0.371540i	0.0489815	−	0.0355871i	0.612007	+	0.790853i	$0.290363\pi$
$110$		0			0
$111$	8.31735	+	3.70312i	0.789448	+	0.351485i
$112$		0			0
$113$	−7.56140	+	8.39779i	−0.711317	+	0.789998i	−0.985135	−	0.171784i	$-0.945047\pi$
$113$	−7.56140	+	8.39779i	−0.711317	+	0.789998i	0.273818	+	0.961782i	$0.411714\pi$
$114$		0			0
$115$	−1.28608	+	0.273364i	−0.119927	+	0.0254913i
$116$		0			0
$117$	−15.0975	−	3.20907i	−1.39576	−	0.296679i
$118$		0			0
$119$	0.987313	+	1.71008i	0.0905068	+	0.156762i
$120$		0			0
$121$	0.531887	+	5.06056i	0.0483533	+	0.460051i
$122$		0			0
$123$	−20.0975			−1.81213
$124$		0			0
$125$	−3.44866			−0.308458
$126$		0			0
$127$	0.0123141	+	0.117161i	0.00109270	+	0.0103963i	0.995055	−	0.0993289i	$-0.0316696\pi$
$127$	0.0123141	+	0.117161i	0.00109270	+	0.0103963i	−0.993962	+	0.109725i	$0.965003\pi$
$128$		0			0
$129$	−12.1697	−	21.0786i	−1.07149	−	1.85587i
$130$		0			0
$131$	5.65756	+	1.20255i	0.494303	+	0.105067i	0.448317	−	0.893875i	$-0.352024\pi$
$131$	5.65756	+	1.20255i	0.494303	+	0.105067i	0.0459863	+	0.998942i	$0.485357\pi$
$132$		0			0
$133$	2.24215	−	0.476583i	0.194419	−	0.0413250i
$134$		0			0
$135$	13.6486	−	15.1583i	1.17469	−	1.30462i
$136$		0			0
$137$	10.7848	+	4.80170i	0.921407	+	0.410237i	0.811931	−	0.583753i	$-0.198416\pi$
$137$	10.7848	+	4.80170i	0.921407	+	0.410237i	0.109475	+	0.993990i	$0.465083\pi$
$138$		0			0
$139$	−12.4767	+	9.06482i	−1.05826	+	0.768868i	−0.973765	−	0.227556i	$-0.926927\pi$
$139$	−12.4767	+	9.06482i	−1.05826	+	0.768868i	−0.0844915	+	0.996424i	$0.526927\pi$
$140$		0			0
$141$	15.4145	+	17.1195i	1.29813	+	1.44172i
$142$		0			0
$143$	6.38286	−	2.84183i	0.533762	−	0.237646i
$144$		0			0
$145$	0.981819	−	9.34138i	0.0815356	−	0.775759i
$146$		0			0
$147$	−5.21157	+	16.0396i	−0.429843	+	1.32292i
$148$		0			0
$149$	5.97511	−	10.3492i	0.489500	−	0.847840i	−0.510427	−	0.859921i	$-0.670512\pi$
$149$	5.97511	−	10.3492i	0.489500	−	0.847840i	0.999927	+	0.0120817i	$0.00384583\pi$
$150$		0			0
$151$	1.33561	+	4.11059i	0.108691	+	0.334515i	0.990579	−	0.136943i	$-0.0437278\pi$
$151$	1.33561	+	4.11059i	0.108691	+	0.334515i	−0.881888	+	0.471458i	$0.843728\pi$
$152$		0			0
$153$	7.92923	+	5.76092i	0.641040	+	0.465743i
$154$		0			0
$155$	15.7402	−	5.12730i	1.26428	−	0.411834i
$156$		0			0
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	0.832196	−	0.554481i	$-0.187083\pi$
$157$	7.04204	+	5.11634i	0.562016	+	0.408328i	−0.270180	+	0.962810i	$0.587083\pi$
$158$		0			0
$159$	−4.44982	−	13.6951i	−0.352893	−	1.08609i
$160$		0			0
$161$	−0.239267	+	0.414422i	−0.0188568	+	0.0326610i
$162$		0			0
$163$	−0.966575	+	2.97481i	−0.0757080	+	0.233005i	−0.981748	−	0.190187i	$-0.939091\pi$
$163$	−0.966575	+	2.97481i	−0.0757080	+	0.233005i	0.906040	+	0.423192i	$0.139091\pi$
$164$		0			0
$165$	−2.18628	+	20.8011i	−0.170202	+	1.61936i
$166$		0			0
$167$	12.2003	−	5.43194i	0.944090	−	0.420336i	0.123815	−	0.992305i	$-0.460487\pi$
$167$	12.2003	−	5.43194i	0.944090	−	0.420336i	0.820275	+	0.571969i	$0.193820\pi$
$168$		0			0
$169$	−3.17310	−	3.52408i	−0.244085	−	0.271083i
$170$		0			0
$171$	9.20462	−	6.68755i	0.703895	−	0.511410i
$172$		0			0
$173$	17.3982	+	7.74619i	1.32276	+	0.588932i	0.941960	−	0.335724i	$-0.108981\pi$
$173$	17.3982	+	7.74619i	1.32276	+	0.588932i	0.380803	+	0.924656i	$0.375648\pi$
$174$		0			0
$175$	2.78055	−	3.08811i	0.210190	−	0.233439i
$176$		0			0
$177$	−34.0002	+	7.22697i	−2.55561	+	0.543213i
$178$		0			0
$179$	−0.0775964	−	0.0164936i	−0.00579983	−	0.00123279i	0.205011	−	0.978760i	$-0.434277\pi$
$179$	−0.0775964	−	0.0164936i	−0.00579983	−	0.00123279i	−0.210811	+	0.977527i	$0.567610\pi$
$180$		0			0
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	0.823032	−	0.567995i	$-0.192281\pi$
$181$	−1.08143	−	1.87308i	−0.0803817	−	0.139225i	−0.903414	+	0.428769i	$0.858947\pi$
$182$		0			0
$183$	4.36564	+	41.5363i	0.322717	+	3.07045i
$184$		0			0
$185$	9.35601			0.687868
$186$		0			0
$187$	−4.43668			−0.324442
$188$		0			0
$189$	−0.776000	−	7.38314i	−0.0564457	−	0.537045i
$190$		0			0
$191$	−2.67085	−	4.62604i	−0.193256	−	0.334729i	0.753072	−	0.657939i	$-0.228571\pi$
$191$	−2.67085	−	4.62604i	−0.193256	−	0.334729i	−0.946327	+	0.323210i	$0.895238\pi$
$192$		0			0
$193$	2.08705	+	0.443616i	0.150229	+	0.0319322i	0.282412	−	0.959293i	$-0.408865\pi$
$193$	2.08705	+	0.443616i	0.150229	+	0.0319322i	−0.132183	+	0.991225i	$0.542199\pi$
$194$		0			0
$195$	−24.1802	+	5.13965i	−1.73158	+	0.368058i
$196$		0			0
$197$	−3.93163	+	4.36652i	−0.280117	+	0.311102i	−0.866742	−	0.498758i	$-0.833790\pi$
$197$	−3.93163	+	4.36652i	−0.280117	+	0.311102i	0.586624	+	0.809859i	$0.300456\pi$
$198$		0			0
$199$	−6.32901	−	2.81786i	−0.448652	−	0.199753i	0.169958	−	0.985451i	$-0.445637\pi$
$199$	−6.32901	−	2.81786i	−0.448652	−	0.199753i	−0.618609	+	0.785699i	$0.712304\pi$
$200$		0			0
$201$	−15.0686	+	10.9480i	−1.06286	+	0.772211i
$202$		0			0
$203$	−2.28748	−	2.54050i	−0.160549	−	0.178308i
$204$		0			0
$205$	−18.8672	+	8.40023i	−1.31774	+	0.586698i
$206$		0			0
$207$	−0.248276	+	2.36219i	−0.0172564	+	0.164184i
$208$		0			0
$209$	−1.59153	+	4.89823i	−0.110089	+	0.338818i
$210$		0			0
$211$	8.35437	−	14.4702i	0.575139	−	0.996170i	−0.420888	−	0.907113i	$-0.638281\pi$
$211$	8.35437	−	14.4702i	0.575139	−	0.996170i	0.996027	−	0.0890568i	$-0.0283853\pi$
$212$		0			0
$213$	−1.50015	−	4.61698i	−0.102788	−	0.316350i
$214$		0			0
$215$	−20.2351	−	14.7016i	−1.38002	−	1.00264i
$216$		0			0
$217$	2.44649	−	5.50596i	0.166078	−	0.373769i
$218$		0			0
$219$	−33.6132	−	24.4214i	−2.27137	−	1.65024i
$220$		0			0
$221$	−1.62040	−	4.98709i	−0.109000	−	0.335468i
$222$		0			0
$223$	−3.13078	+	5.42267i	−0.209653	+	0.363129i	−0.951605	−	0.307323i	$-0.900567\pi$
$223$	−3.13078	+	5.42267i	−0.209653	+	0.363129i	0.741952	+	0.670453i	$0.233900\pi$
$224$		0			0
$225$	6.37369	−	19.6162i	0.424912	−	1.30775i
$226$		0			0
$227$	−0.820289	+	7.80452i	−0.0544445	+	0.518004i	0.932982	+	0.359924i	$0.117197\pi$
$227$	−0.820289	+	7.80452i	−0.0544445	+	0.518004i	−0.987426	+	0.158081i	$0.949469\pi$
$228$		0			0
$229$	11.6687	−	5.19524i	0.771089	−	0.343311i	0.0168049	−	0.999859i	$-0.494651\pi$
$229$	11.6687	−	5.19524i	0.771089	−	0.343311i	0.754285	+	0.656548i	$0.227984\pi$
$230$		0			0
$231$	5.09368	+	5.65711i	0.335140	+	0.372210i
$232$		0			0
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	−0.871373	−	0.490622i	$-0.836770\pi$
$233$	−10.2887	+	7.47514i	−0.674032	+	0.489713i	0.197340	+	0.980335i	$0.436770\pi$
$234$		0			0
$235$	21.6264	+	9.62868i	1.41075	+	0.628106i
$236$		0			0
$237$	6.67460	−	7.41290i	0.433562	−	0.481520i
$238$		0			0
$239$	−24.8690	+	5.28607i	−1.60864	+	0.341928i	−0.922638	−	0.385668i	$-0.873971\pi$
$239$	−24.8690	+	5.28607i	−1.60864	+	0.341928i	−0.686006	+	0.727596i	$0.740638\pi$
$240$		0			0
$241$	−2.30939	−	0.490876i	−0.148761	−	0.0316201i	0.132929	−	0.991126i	$-0.457562\pi$
$241$	−2.30939	−	0.490876i	−0.148761	−	0.0316201i	−0.281690	+	0.959505i	$0.590895\pi$
$242$		0			0
$243$	4.88634	+	8.46339i	0.313459	+	0.542927i
$244$		0			0
$245$	1.81158	+	17.2360i	0.115738	+	1.10117i
$246$		0			0
$247$	−6.08718			−0.387318
$248$		0			0
$249$	−37.1893			−2.35677
$250$		0			0
$251$	0.246336	+	2.34373i	0.0155486	+	0.147935i	0.999542	−	0.0302716i	$-0.00963722\pi$
$251$	0.246336	+	2.34373i	0.0155486	+	0.147935i	−0.983993	+	0.178206i	$0.942971\pi$
$252$		0			0
$253$	−0.537595	−	0.931142i	−0.0337983	−	0.0585404i
$254$		0			0
$255$	15.3544	+	3.26367i	0.961528	+	0.204379i
$256$		0			0
$257$	25.4455	−	5.40862i	1.58725	−	0.337380i	0.672089	−	0.740470i	$-0.265397\pi$
$257$	25.4455	−	5.40862i	1.58725	−	0.337380i	0.915160	+	0.403090i	$0.132064\pi$
$258$		0			0
$259$	2.27851	−	2.53054i	0.141580	−	0.157240i
$260$		0			0
$261$	−15.5012	−	6.90157i	−0.959499	−	0.427196i
$262$		0			0
$263$	18.5552	−	13.4812i	1.14417	−	0.831285i	0.156471	−	0.987683i	$-0.449988\pi$
$263$	18.5552	−	13.4812i	1.14417	−	0.831285i	0.987694	+	0.156398i	$0.0499881\pi$
$264$		0			0
$265$	−9.90163	−	10.9969i	−0.608253	−	0.675533i
$266$		0			0
$267$	5.97190	−	2.65886i	0.365474	−	0.162720i
$268$		0			0
$269$	1.78193	−	16.9539i	0.108646	−	1.03370i	−0.795347	−	0.606154i	$-0.792712\pi$
$269$	1.78193	−	16.9539i	0.108646	−	1.03370i	0.903994	−	0.427546i	$-0.140622\pi$
$270$		0			0
$271$	−2.23929	+	6.89184i	−0.136027	+	0.418649i	−0.995748	−	0.0921146i	$-0.970637\pi$
$271$	−2.23929	+	6.89184i	−0.136027	+	0.418649i	0.859721	+	0.510764i	$0.170637\pi$
$272$		0			0
$273$	−4.49857	+	7.79175i	−0.272266	+	0.471578i
$274$		0			0
$275$	2.88520	+	8.87972i	0.173984	+	0.535467i
$276$		0			0
$277$	−12.2188	−	8.87748i	−0.734157	−	0.533396i	0.156719	−	0.987643i	$-0.449908\pi$
$277$	−12.2188	−	8.87748i	−0.734157	−	0.533396i	−0.890876	+	0.454247i	$0.849908\pi$
$278$		0			0
$279$	−0.0223278	−	29.9052i	−0.00133673	−	1.79038i
$280$		0			0
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	0.646181	−	0.763184i	$-0.276365\pi$
$281$	2.01209	+	1.46187i	0.120031	+	0.0872078i	−0.526150	+	0.850392i	$0.676365\pi$
$282$		0			0
$283$	1.46052	+	4.49503i	0.0868192	+	0.267202i	0.985035	−	0.172352i	$-0.0551366\pi$
$283$	1.46052	+	4.49503i	0.0868192	+	0.267202i	−0.898216	+	0.439554i	$0.855137\pi$
$284$		0			0
$285$	9.11114	−	15.7810i	0.539697	−	0.934783i
$286$		0			0
$287$	−2.32279	+	7.14881i	−0.137110	+	0.421981i
$288$		0			0
$289$	1.42893	−	13.5953i	0.0840546	−	0.799726i
$290$		0			0
$291$	9.02071	−	4.01628i	0.528804	−	0.235439i
$292$		0			0
$293$	−7.05858	−	7.83935i	−0.412367	−	0.457980i	0.500802	−	0.865562i	$-0.333039\pi$
$293$	−7.05858	−	7.83935i	−0.412367	−	0.457980i	−0.913169	+	0.407582i	$0.866372\pi$
$294$		0			0
$295$	−28.8982	+	20.9958i	−1.68252	+	1.22242i
$296$		0			0
$297$	15.2381	+	6.78443i	0.884203	+	0.393673i
$298$		0			0
$299$	0.850314	−	0.944369i	0.0491749	−	0.0546143i
$300$		0			0
$301$	−8.90432	+	1.89267i	−0.513237	+	0.109092i
$302$		0			0
$303$	−50.1411	−	10.6578i	−2.88053	−	0.612276i
$304$		0			0
$305$	21.4595	+	37.1689i	1.22877	+	2.12829i
$306$		0			0
$307$	0.276844	+	2.63399i	0.0158003	+	0.150330i	0.999578	−	0.0290645i	$-0.00925283\pi$
$307$	0.276844	+	2.63399i	0.0158003	+	0.150330i	−0.983777	+	0.179394i	$0.942586\pi$
$308$		0			0
$309$	−23.3600			−1.32890
$310$		0			0
$311$	−5.51283			−0.312604			−0.156302	−	0.987709i	$-0.549957\pi$
$311$	−5.51283			−0.312604			−0.156302	+	0.987709i	$0.549957\pi$
$312$		0			0
$313$	2.78834	+	26.5293i	0.157607	+	1.49953i	0.732201	+	0.681088i	$0.238493\pi$
$313$	2.78834	+	26.5293i	0.157607	+	1.49953i	−0.574595	+	0.818438i	$0.694840\pi$
$314$		0			0
$315$	−8.64057	−	14.9659i	−0.486841	−	0.843234i
$316$		0			0
$317$	−10.5055	−	2.23302i	−0.590050	−	0.125419i	−0.0967957	−	0.995304i	$-0.530859\pi$
$317$	−10.5055	−	2.23302i	−0.590050	−	0.125419i	−0.493254	+	0.869885i	$0.664193\pi$
$318$		0			0
$319$	7.51318	−	1.59698i	0.420657	−	0.0894135i
$320$		0			0
$321$	23.5246	−	26.1267i	1.31301	−	1.45825i
$322$		0			0
$323$	3.53117	+	1.57218i	0.196480	+	0.0874784i
$324$		0			0
$325$	−8.92758	+	6.48627i	−0.495213	+	0.359793i
$326$		0			0
$327$	−1.22374	−	1.35911i	−0.0676732	−	0.0751587i
$328$		0			0
$329$	7.87106	−	3.50442i	0.433945	−	0.193205i
$330$		0			0
$331$	2.05373	−	19.5400i	0.112883	−	1.07401i	−0.780635	−	0.624987i	$-0.785104\pi$
$331$	2.05373	−	19.5400i	0.112883	−	1.07401i	0.893518	−	0.449027i	$-0.148229\pi$
$332$		0			0
$333$	5.22289	−	16.0744i	0.286213	−	0.880872i
$334$		0			0
$335$	−9.57021	+	16.5761i	−0.522876	+	0.905649i
$336$		0			0
$337$	5.92655	+	18.2401i	0.322840	+	0.993599i	0.972406	+	0.233294i	$0.0749505\pi$
$337$	5.92655	+	18.2401i	0.322840	+	0.993599i	−0.649566	+	0.760305i	$0.725050\pi$
$338$		0			0
$339$	26.4510	+	19.2178i	1.43662	+	1.04376i
$340$		0			0
$341$	7.96520	+	10.9460i	0.431340	+	0.592757i
$342$		0			0
$343$	11.2313	+	8.15999i	0.606431	+	0.440598i
$344$		0			0
$345$	1.17554	+	3.61794i	0.0632889	+	0.194783i
$346$		0			0
$347$	5.32998	−	9.23180i	0.286128	−	0.495589i	−0.686754	−	0.726890i	$-0.740965\pi$
$347$	5.32998	−	9.23180i	0.286128	−	0.495589i	0.972882	+	0.231301i	$0.0742983\pi$
$348$		0			0
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	0.668671	+	0.743559i	$0.266864\pi$
$349$	−5.77910	+	17.7862i	−0.309348	+	0.952075i	−0.978019	+	0.208517i	$0.933136\pi$
$350$		0			0
$351$	−2.06072	+	19.6064i	−0.109993	+	1.04651i
$352$		0			0
$353$	−11.5675	+	5.15020i	−0.615678	+	0.274117i	−0.690787	−	0.723058i	$-0.742736\pi$
$353$	−11.5675	+	5.15020i	−0.615678	+	0.274117i	0.0751097	+	0.997175i	$0.476069\pi$
$354$		0			0
$355$	−3.33810	−	3.70733i	−0.177168	−	0.196765i
$356$		0			0
$357$	4.62205	−	3.35812i	0.244625	−	0.177730i
$358$		0			0
$359$	20.7175	+	9.22402i	1.09343	+	0.486825i	0.872574	−	0.488482i	$-0.162449\pi$
$359$	20.7175	+	9.22402i	1.09343	+	0.486825i	0.220853	+	0.975307i	$0.429116\pi$
$360$		0			0
$361$	−9.71104	+	10.7852i	−0.511107	+	0.567642i
$362$		0			0
$363$	14.4006	−	3.06095i	0.755837	−	0.160658i
$364$		0			0
$365$	−41.7631	−	8.87701i	−2.18598	−	0.464644i
$366$		0			0
$367$	4.35984	+	7.55147i	0.227582	+	0.394183i	0.957091	−	0.289788i	$-0.0935847\pi$
$367$	4.35984	+	7.55147i	0.227582	+	0.394183i	−0.729509	+	0.683971i	$0.760251\pi$
$368$		0			0
$369$	3.89987	+	37.1048i	0.203019	+	1.93160i
$370$		0			0
$371$	−5.38574			−0.279614
$372$		0			0
$373$	25.4134			1.31586			0.657928	−	0.753081i	$-0.271433\pi$
$373$	25.4134			1.31586			0.657928	+	0.753081i	$0.271433\pi$
$374$		0			0
$375$	1.04298	+	9.92333i	0.0538594	+	0.512438i
$376$		0			0
$377$	4.53913	+	7.86200i	0.233777	+	0.404914i
$378$		0			0
$379$	21.6150	+	4.59441i	1.11029	+	0.235999i	0.726326	−	0.687350i	$-0.241226\pi$
$379$	21.6150	+	4.59441i	1.11029	+	0.235999i	0.383961	+	0.923349i	$0.374560\pi$
$380$		0			0
$381$	0.333399	−	0.0708662i	0.0170806	−	0.00363059i
$382$		0			0
$383$	17.8274	−	19.7993i	0.910938	−	1.01170i	−0.0889398	−	0.996037i	$-0.528348\pi$
$383$	17.8274	−	19.7993i	0.910938	−	1.01170i	0.999877	−	0.0156617i	$-0.00498547\pi$
$384$		0			0
$385$	7.14640	+	3.18178i	0.364214	+	0.162159i
$386$		0			0
$387$	−36.5547	+	26.5585i	−1.85818	+	1.35005i
$388$		0			0
$389$	−8.66862	−	9.62748i	−0.439517	−	0.488133i	0.482165	−	0.876081i	$-0.339851\pi$
$389$	−8.66862	−	9.62748i	−0.439517	−	0.488133i	−0.921681	+	0.387948i	$0.873184\pi$
$390$		0			0
$391$	−0.737176	+	0.328212i	−0.0372806	+	0.0165984i
$392$		0			0
$393$	1.74925	−	16.6430i	0.0882379	−	0.839528i
$394$		0			0
$395$	3.16762	−	9.74894i	0.159380	−	0.490522i
$396$		0			0
$397$	1.46363	−	2.53508i	0.0734574	−	0.127232i	−0.826957	−	0.562265i	$-0.809930\pi$
$397$	1.46363	−	2.53508i	0.0734574	−	0.127232i	0.900414	+	0.435033i	$0.143263\pi$
$398$		0			0
$399$	−2.04944	−	6.30752i	−0.102600	−	0.315771i
$400$		0			0
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	0.807446	−	0.589942i	$-0.200849\pi$
$401$	9.93025	+	7.21475i	0.495893	+	0.360287i	−0.311553	+	0.950229i	$0.600849\pi$
$402$		0			0
$403$	−9.39479	+	12.9511i	−0.467988	+	0.645142i
$404$		0			0
$405$	−8.98586	−	6.52861i	−0.446511	−	0.324409i
$406$		0			0
$407$	2.36426	+	7.27645i	0.117192	+	0.360680i
$408$		0			0
$409$	8.59861	−	14.8932i	0.425174	−	0.736423i	−0.571263	−	0.820767i	$-0.693546\pi$
$409$	8.59861	−	14.8932i	0.425174	−	0.736423i	0.996437	+	0.0843442i	$0.0268795\pi$
$410$		0			0
$411$	10.5549	−	32.4848i	0.520637	−	1.60236i
$412$		0			0
$413$	−1.35893	+	12.9294i	−0.0668687	+	0.636213i
$414$		0			0
$415$	−34.9127	+	15.5442i	−1.71380	+	0.763032i
$416$		0			0
$417$	29.8568	+	33.1594i	1.46210	+	1.62382i
$418$		0			0
$419$	18.7251	−	13.6046i	0.914782	−	0.664628i	−0.0274378	−	0.999624i	$-0.508735\pi$
$419$	18.7251	−	13.6046i	0.914782	−	0.664628i	0.942220	+	0.334996i	$0.108735\pi$
$420$		0			0
$421$	26.6593	+	11.8695i	1.29929	+	0.578483i	0.935609	−	0.353038i	$-0.114851\pi$
$421$	26.6593	+	11.8695i	1.29929	+	0.578483i	0.363686	+	0.931522i	$0.381518\pi$
$422$		0			0
$423$	28.6156	−	31.7808i	1.39134	−	1.54524i
$424$		0			0
$425$	6.85415	−	1.45689i	0.332475	−	0.0706697i
$426$		0			0
$427$	15.2793	+	3.24771i	0.739416	+	0.157168i
$428$		0			0
$429$	−10.1076	−	17.5069i	−0.487999	−	0.845239i
$430$		0			0
$431$	3.17267	+	30.1859i	0.152822	+	1.45401i	0.755042	+	0.655676i	$0.227616\pi$
$431$	3.17267	+	30.1859i	0.152822	+	1.45401i	−0.602220	+	0.798330i	$0.705717\pi$
$432$		0			0
$433$	−13.8400			−0.665107			−0.332553	−	0.943084i	$-0.607910\pi$
$433$	−13.8400			−0.665107			−0.332553	+	0.943084i	$0.607910\pi$
$434$		0			0
$435$	−27.1762			−1.30300
$436$		0			0
$437$	0.0979154	+	0.931602i	0.00468393	+	0.0445646i
$438$		0			0
$439$	6.46006	+	11.1892i	0.308322	+	0.534029i	0.977995	−	0.208626i	$-0.0668993\pi$
$439$	6.46006	+	11.1892i	0.308322	+	0.534029i	−0.669674	+	0.742656i	$0.733566\pi$
$440$		0			0
$441$	30.6242	+	6.50938i	1.45830	+	0.309970i
$442$		0			0
$443$	23.2391	−	4.93962i	1.10412	−	0.234688i	0.380429	−	0.924810i	$-0.375776\pi$
$443$	23.2391	−	4.93962i	1.10412	−	0.234688i	0.723693	+	0.690122i	$0.242443\pi$
$444$		0			0
$445$	4.49500	−	4.99220i	0.213083	−	0.236653i
$446$		0			0
$447$	−31.5863	−	14.0631i	−1.49398	−	0.665163i
$448$		0			0
$449$	15.7054	−	11.4106i	0.741181	−	0.538500i	−0.151900	−	0.988396i	$-0.548539\pi$
$449$	15.7054	−	11.4106i	0.741181	−	0.538500i	0.893081	+	0.449896i	$0.148539\pi$
$450$		0			0
$451$	−11.3009	−	12.5509i	−0.532137	−	0.590998i
$452$		0			0
$453$	11.4241	−	5.08632i	0.536749	−	0.238976i
$454$		0			0
$455$	−0.966440	+	9.19507i	−0.0453074	+	0.431071i
$456$		0			0
$457$	7.52208	−	23.1506i	0.351868	−	1.08294i	−0.605935	−	0.795514i	$-0.707201\pi$
$457$	7.52208	−	23.1506i	0.351868	−	1.08294i	0.957803	−	0.287424i	$-0.0927990\pi$
$458$		0			0
$459$	6.25931	−	10.8414i	0.292159	−	0.506035i
$460$		0			0
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	−0.704126	−	0.710075i	$-0.748661\pi$
$461$	−11.8487	−	36.4665i	−0.551848	−	1.69841i	0.152279	−	0.988338i	$-0.451339\pi$
$462$		0			0
$463$	−5.33489	−	3.87603i	−0.247934	−	0.180134i	0.456877	−	0.889530i	$-0.348968\pi$
$463$	−5.33489	−	3.87603i	−0.247934	−	0.180134i	−0.704810	+	0.709396i	$0.748968\pi$
$464$		0			0
$465$	−19.5138	−	43.7409i	−0.904932	−	2.02843i
$466$		0			0
$467$	31.0674	+	22.5718i	1.43763	+	1.04450i	0.988532	+	0.151014i	$0.0482539\pi$
$467$	31.0674	+	22.5718i	1.43763	+	1.04450i	0.449096	+	0.893484i	$0.351746\pi$
$468$		0			0
$469$	2.15270	+	6.62532i	0.0994024	+	0.305929i
$470$		0			0
$471$	12.5922	−	21.8104i	0.580220	−	1.00497i
$472$		0			0
$473$	6.32051	−	19.4525i	0.290617	−	0.894429i
$474$		0			0
$475$	0.850274	−	8.08981i	0.0390132	−	0.371186i
$476$		0			0
$477$	−24.4210	+	10.8729i	−1.11816	+	0.497838i
$478$		0			0
$479$	−5.03531	−	5.59228i	−0.230069	−	0.255518i	0.617046	−	0.786927i	$-0.288329\pi$
$479$	−5.03531	−	5.59228i	−0.230069	−	0.255518i	−0.847115	+	0.531409i	$0.821663\pi$
$480$		0			0
$481$	−7.31567	+	5.31515i	−0.333566	+	0.242350i
$482$		0			0
$483$	1.26484	+	0.563141i	0.0575520	+	0.0256238i
$484$		0			0
$485$	6.78981	−	7.54085i	0.308310	−	0.342412i
$486$		0			0
$487$	24.4852	−	5.20450i	1.10953	−	0.235838i	0.383528	−	0.923529i	$-0.374709\pi$
$487$	24.4852	−	5.20450i	1.10953	−	0.235838i	0.726004	+	0.687691i	$0.241375\pi$
$488$		0			0
$489$	8.85217	+	1.88159i	0.400309	+	0.0850883i
$490$		0			0
$491$	−19.8550	−	34.3899i	−0.896044	−	1.55199i	−0.832507	−	0.554015i	$-0.813095\pi$
$491$	−19.8550	−	34.3899i	−0.896044	−	1.55199i	−0.0635377	−	0.997979i	$-0.520238\pi$
$492$		0			0
$493$	−0.602573	−	5.73310i	−0.0271385	−	0.258206i
$494$		0			0
$495$	38.8281			1.74519
$496$		0			0
$497$	−1.81567			−0.0814440
$498$		0			0
$499$	−2.47252	−	23.5245i	−0.110685	−	1.05310i	−0.899036	−	0.437875i	$-0.855731\pi$
$499$	−2.47252	−	23.5245i	−0.110685	−	1.05310i	0.788351	−	0.615226i	$-0.210935\pi$
$500$		0			0
$501$	−19.3199	−	33.4630i	−0.863148	−	1.49502i
$502$		0			0
$503$	−19.7453	−	4.19699i	−0.880400	−	0.187135i	−0.254532	−	0.967064i	$-0.581922\pi$
$503$	−19.7453	−	4.19699i	−0.880400	−	0.187135i	−0.625867	+	0.779930i	$0.715255\pi$
$504$		0			0
$505$	−51.5265	+	10.9523i	−2.29290	+	0.487370i
$506$		0			0
$507$	−9.18070	+	10.1962i	−0.407729	+	0.452829i
$508$		0			0
$509$	10.8155	+	4.81536i	0.479387	+	0.213437i	0.632180	−	0.774821i	$-0.282160\pi$
$509$	10.8155	+	4.81536i	0.479387	+	0.213437i	−0.152793	+	0.988258i	$0.548827\pi$
$510$		0			0
$511$	−12.5717	+	9.13389i	−0.556140	+	0.404060i
$512$		0			0
$513$	−9.72394	−	10.7995i	−0.429322	−	0.476811i
$514$		0			0
$515$	−21.9300	+	9.76388i	−0.966352	+	0.430248i
$516$		0			0
$517$	−2.02354	+	19.2526i	−0.0889950	+	0.846731i
$518$		0			0
$519$	17.0275	−	52.4051i	0.747422	−	2.30033i
$520$		0			0
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	−0.244672	−	0.969606i	$-0.578680\pi$
$521$	16.3742	−	28.3610i	0.717368	−	1.24252i	0.962039	−	0.272911i	$-0.0879865\pi$
$522$		0			0
$523$	9.11682	+	28.0587i	0.398651	+	1.22692i	0.926082	+	0.377323i	$0.123155\pi$
$523$	9.11682	+	28.0587i	0.398651	+	1.22692i	−0.527431	+	0.849598i	$0.676845\pi$
$524$		0			0
$525$	−9.72679	−	7.06693i	−0.424512	−	0.308426i
$526$		0			0
$527$	8.79490	−	5.08650i	0.383112	−	0.221571i
$528$		0			0
$529$	18.4492	+	13.4041i	0.802138	+	0.582788i
$530$		0			0
$531$	19.9404	+	61.3703i	0.865340	+	2.66324i
$532$		0			0
$533$	9.98053	−	17.2868i	0.432305	−	0.748774i
$534$		0			0
$535$	11.1643	−	34.3600i	0.482673	−	1.48551i
$536$		0			0
$537$	−0.0239919	+	0.228267i	−0.00103533	+	0.00985047i
$538$		0			0
$539$	−12.9472	+	5.76446i	−0.557675	+	0.248293i
$540$		0			0
$541$	8.87657	+	9.85843i	0.381634	+	0.423847i	0.903104	−	0.429423i	$-0.141283\pi$
$541$	8.87657	+	9.85843i	0.381634	+	0.423847i	−0.521470	+	0.853270i	$0.674616\pi$
$542$		0			0
$543$	−5.06264	+	3.67822i	−0.217258	+	0.157848i
$544$		0			0
$545$	−1.71690	−	0.764415i	−0.0735441	−	0.0327439i
$546$		0			0
$547$	−25.2689	+	28.0640i	−1.08042	+	1.19993i	−0.101684	+	0.994817i	$0.532423\pi$
$547$	−25.2689	+	28.0640i	−1.08042	+	1.19993i	−0.978738	+	0.205114i	$0.934244\pi$
$548$		0			0
$549$	75.8388	−	16.1200i	3.23672	−	0.687986i
$550$		0			0
$551$	−6.54568	−	1.39133i	−0.278855	−	0.0592725i
$552$		0			0
$553$	−1.86539	−	3.23095i	−0.0793245	−	0.137394i
$554$		0			0
$555$	−2.82955	−	26.9214i	−0.120108	−	1.14275i
$556$		0			0
$557$	−11.3637			−0.481496			−0.240748	−	0.970588i	$-0.577393\pi$
$557$	−11.3637			−0.481496			−0.240748	+	0.970588i	$0.577393\pi$
$558$		0			0
$559$	24.1743			1.02246
$560$		0			0
$561$	1.34179	+	12.7663i	0.0566505	+	0.538993i
$562$		0			0
$563$	−10.0933	−	17.4821i	−0.425381	−	0.736781i	0.571075	−	0.820898i	$-0.306526\pi$
$563$	−10.0933	−	17.4821i	−0.425381	−	0.736781i	−0.996456	+	0.0841167i	$0.973193\pi$
$564$		0			0
$565$	32.8643	+	6.98552i	1.38261	+	0.293883i
$566$		0			0
$567$	−3.95417	+	0.840485i	−0.166060	+	0.0352971i
$568$		0			0
$569$	−20.7361	+	23.0298i	−0.869304	+	0.965460i	−0.999662	−	0.0260074i	$-0.991721\pi$
$569$	−20.7361	+	23.0298i	−0.869304	+	0.965460i	0.130358	+	0.991467i	$0.458387\pi$
$570$		0			0
$571$	9.50060	+	4.22994i	0.397588	+	0.177017i	0.595784	−	0.803145i	$-0.296842\pi$
$571$	9.50060	+	4.22994i	0.397588	+	0.177017i	−0.198196	+	0.980162i	$0.563508\pi$
$572$		0			0
$573$	−12.5034	+	9.08427i	−0.522338	+	0.379501i
$574$		0			0
$575$	1.13628	+	1.26197i	0.0473863	+	0.0526279i
$576$		0			0
$577$	4.94581	−	2.20201i	0.205897	−	0.0916711i	−0.301197	−	0.953562i	$-0.597386\pi$
$577$	4.94581	−	2.20201i	0.205897	−	0.0916711i	0.507094	+	0.861891i	$0.330720\pi$
$578$		0			0
$579$	0.645291	−	6.13953i	0.0268174	−	0.255150i
$580$		0			0
$581$	−4.29819	+	13.2285i	−0.178319	+	0.548809i
$582$		0			0
$583$	6.05046	−	10.4797i	0.250585	−	0.434025i
$584$		0			0
$585$	14.1811	+	43.6451i	0.586318	+	1.80450i
$586$		0			0
$587$	−10.1635	−	7.38424i	−0.419494	−	0.304780i	0.357940	−	0.933744i	$-0.383479\pi$
$587$	−10.1635	−	7.38424i	−0.419494	−	0.304780i	−0.777434	+	0.628964i	$0.783479\pi$
$588$		0			0
$589$	−2.46073	−	11.5345i	−0.101393	−	0.475270i
$590$		0			0
$591$	13.7535	+	9.99247i	0.565741	+	0.411035i
$592$		0			0
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	0.962375	+	0.271726i	$0.0875943\pi$
$593$	8.36510	+	25.7451i	0.343513	+	1.05723i	−0.618861	+	0.785500i	$0.712406\pi$
$594$		0			0
$595$	2.93551	−	5.08445i	0.120344	−	0.208442i
$596$		0			0
$597$	−6.19413	+	19.0636i	−0.253509	+	0.780220i
$598$		0			0
$599$	−1.50051	+	14.2764i	−0.0613094	+	0.583320i	0.920139	+	0.391592i	$0.128076\pi$
$599$	−1.50051	+	14.2764i	−0.0613094	+	0.583320i	−0.981448	+	0.191727i	$0.938591\pi$
$600$		0			0
$601$	0.584684	−	0.260318i	0.0238498	−	0.0106186i	−0.394777	−	0.918777i	$-0.629178\pi$
$601$	0.584684	−	0.260318i	0.0238498	−	0.0106186i	0.418627	+	0.908158i	$0.362512\pi$
$602$		0			0
$603$	23.1366	+	25.6958i	0.942197	+	1.04642i
$604$		0			0
$605$	12.2397	−	8.89266i	0.497614	−	0.361538i
$606$		0			0
$607$	5.95432	+	2.65104i	0.241679	+	0.107602i	0.524002	−	0.851717i	$-0.324438\pi$
$607$	5.95432	+	2.65104i	0.241679	+	0.107602i	−0.282323	+	0.959319i	$0.591105\pi$
$608$		0			0
$609$	−6.61834	+	7.35041i	−0.268189	+	0.297854i
$610$		0			0
$611$	−22.3802	+	4.75706i	−0.905405	+	0.192450i
$612$		0			0
$613$	−10.2171	−	2.17170i	−0.412663	−	0.0877143i	−0.00309833	−	0.999995i	$-0.500986\pi$
$613$	−10.2171	−	2.17170i	−0.412663	−	0.0877143i	−0.409565	+	0.912281i	$0.634320\pi$
$614$		0			0
$615$	29.8772	+	51.7489i	1.20477	+	2.08672i
$616$		0			0
$617$	−2.26862	−	21.5845i	−0.0913311	−	0.868958i	−0.940262	−	0.340453i	$-0.889420\pi$
$617$	−2.26862	−	21.5845i	−0.0913311	−	0.868958i	0.848930	−	0.528505i	$-0.177247\pi$
$618$		0			0
$619$	−28.5478			−1.14743			−0.573716	−	0.819054i	$-0.694499\pi$
$619$	−28.5478			−1.14743			−0.573716	+	0.819054i	$0.694499\pi$
$620$		0			0
$621$	3.03377			0.121741
$622$		0			0
$623$	−0.255566	−	2.43155i	−0.0102390	−	0.0974178i
$624$		0			0
$625$	14.7271	+	25.5080i	0.589083	+	1.02032i
$626$		0			0
$627$	14.5757	+	3.09816i	0.582098	+	0.123729i
$628$		0			0
$629$	5.61660	−	1.19385i	0.223949	−	0.0476018i
$630$		0			0
$631$	−18.2275	+	20.2436i	−0.725624	+	0.805887i	−0.987232	−	0.159287i	$-0.949080\pi$
$631$	−18.2275	+	20.2436i	−0.725624	+	0.805887i	0.261609	+	0.965174i	$0.415747\pi$
$632$		0			0
$633$	−44.1638	−	19.6630i	−1.75535	−	0.781533i
$634$		0			0
$635$	0.283370	−	0.205880i	0.0112452	−	0.00817012i
$636$		0			0
$637$	−11.2083	−	12.4481i	−0.444089	−	0.493210i
$638$		0			0
$639$	−8.23296	+	3.66555i	−0.325691	+	0.145007i
$640$		0			0
$641$	−4.30742	+	40.9824i	−0.170133	+	1.61871i	0.492880	+	0.870097i	$0.335944\pi$
$641$	−4.30742	+	40.9824i	−0.170133	+	1.61871i	−0.663013	+	0.748608i	$0.730722\pi$
$642$		0			0
$643$	9.52156	−	29.3044i	0.375494	−	1.15565i	−0.567651	−	0.823269i	$-0.692148\pi$
$643$	9.52156	−	29.3044i	0.375494	−	1.15565i	0.943145	−	0.332382i	$-0.107852\pi$
$644$		0			0
$645$	−36.1834	+	62.6715i	−1.42472	+	2.46769i
$646$		0			0
$647$	−2.75525	−	8.47978i	−0.108320	−	0.333375i	0.882175	−	0.470921i	$-0.156078\pi$
$647$	−2.75525	−	8.47978i	−0.108320	−	0.333375i	−0.990495	+	0.137547i	$0.956078\pi$
$648$		0			0
$649$	−23.6317	−	17.1694i	−0.927623	−	0.673958i
$650$		0			0
$651$	−16.5830	−	5.37445i	−0.649938	−	0.210641i
$652$		0			0
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.244601	−	0.969624i	$-0.578657\pi$
$653$	−31.7469	−	23.0655i	−1.24235	−	0.902623i	−0.997753	+	0.0670010i	$0.978657\pi$
$654$		0			0
$655$	−5.31417	−	16.3553i	−0.207642	−	0.639056i
$656$		0			0
$657$	−38.5652	+	66.7969i	−1.50457	+	2.60600i
$658$		0			0
$659$	−10.1832	+	31.3407i	−0.396681	+	1.22086i	0.530963	+	0.847395i	$0.321830\pi$
$659$	−10.1832	+	31.3407i	−0.396681	+	1.22086i	−0.927644	+	0.373465i	$0.878170\pi$
$660$		0			0
$661$	0.0177359	−	0.168746i	0.000689846	−	0.00656345i	−0.994172	−	0.107810i	$-0.965616\pi$
$661$	0.0177359	−	0.168746i	0.000689846	−	0.00656345i	0.994861	+	0.101246i	$0.0322830\pi$
$662$		0			0
$663$	−13.8600	+	6.17087i	−0.538278	+	0.239657i
$664$		0			0
$665$	−4.56036	−	5.06479i	−0.176843	−	0.196404i
$666$		0			0
$667$	1.13021	−	0.821147i	0.0437620	−	0.0317950i
$668$		0			0
$669$	16.5503	+	7.36866i	0.639871	+	0.284889i
$670$		0			0
$671$	−23.4846	+	26.0823i	−0.906612	+	1.00689i
$672$		0			0
$673$	14.2676	−	3.03267i	0.549976	−	0.116901i	0.0754613	−	0.997149i	$-0.475957\pi$
$673$	14.2676	−	3.03267i	0.549976	−	0.116901i	0.474514	+	0.880248i	$0.342624\pi$
$674$		0			0
$675$	−25.7689	−	5.47735i	−0.991845	−	0.210823i
$676$		0			0
$677$	−7.88341	−	13.6545i	−0.302984	−	0.524784i	0.673826	−	0.738890i	$-0.264650\pi$
$677$	−7.88341	−	13.6545i	−0.302984	−	0.524784i	−0.976810	+	0.214106i	$0.931316\pi$
$678$		0			0
$679$	−0.386039	−	3.67291i	−0.0148148	−	0.140953i
$680$		0			0
$681$	22.7051			0.870063
$682$		0			0
$683$	−20.5935			−0.787988			−0.393994	−	0.919113i	$-0.628907\pi$
$683$	−20.5935			−0.787988			−0.393994	+	0.919113i	$0.628907\pi$
$684$		0			0
$685$	−3.66897	−	34.9079i	−0.140184	−	1.33376i
$686$		0			0
$687$	−18.4780	−	32.0048i	−0.704979	−	1.22106i
$688$		0			0
$689$	13.9896	+	2.97359i	0.532962	+	0.113285i
$690$		0			0
$691$	−5.82165	+	1.23743i	−0.221466	+	0.0470741i	−0.317308	−	0.948322i	$-0.602779\pi$
$691$	−5.82165	+	1.23743i	−0.221466	+	0.0470741i	0.0958421	+	0.995397i	$0.469446\pi$
$692$		0			0
$693$	9.45597	−	10.5019i	0.359203	−	0.398935i
$694$		0			0
$695$	41.8889	+	18.6502i	1.58894	+	0.707441i
$696$		0			0
$697$	−10.2545	+	7.45032i	−0.388417	+	0.282201i
$698$		0			0
$699$	24.6209	+	27.3443i	0.931248	+	1.03426i
$700$		0			0
$701$	−24.3281	+	10.8316i	−0.918859	+	0.409103i	−0.810988	−	0.585062i	$-0.801070\pi$
$701$	−24.3281	+	10.8316i	−0.918859	+	0.409103i	−0.107871	+	0.994165i	$0.534403\pi$
$702$		0			0
$703$	0.696753	−	6.62916i	0.0262785	−	0.250024i
$704$		0			0
$705$	21.1655	−	65.1407i	0.797138	−	2.45334i
$706$		0			0
$707$	−9.58617	+	16.6037i	−0.360525	+	0.624448i
$708$		0			0
$709$	−0.816662	−	2.51343i	−0.0306704	−	0.0943938i	0.934550	−	0.355833i	$-0.115803\pi$
$709$	−0.816662	−	2.51343i	−0.0306704	−	0.0943938i	−0.965220	+	0.261439i	$0.915803\pi$
$710$		0			0
$711$	−14.9812	−	10.8845i	−0.561839	−	0.408200i
$712$		0			0
$713$	2.13321	+	1.22948i	0.0798892	+	0.0460445i
$714$		0			0
$715$	−16.8063	−	12.2105i	−0.628519	−	0.456646i
$716$		0			0
$717$	22.7315	+	69.9605i	0.848925	+	2.61272i
$718$		0			0
$719$	2.59912	−	4.50181i	0.0969308	−	0.167889i	−0.813482	−	0.581590i	$-0.802431\pi$
$719$	2.59912	−	4.50181i	0.0969308	−	0.167889i	0.910413	+	0.413701i	$0.135764\pi$
$720$		0			0
$721$	−2.69986	+	8.30930i	−0.100548	+	0.309455i
$722$		0			0
$723$	−0.714035	+	6.79359i	−0.0265552	+	0.252656i
$724$		0			0
$725$	−11.0826	+	4.93428i	−0.411596	+	0.183254i
$726$		0			0
$727$	−16.1973	−	17.9889i	−0.600723	−	0.667171i	0.363705	−	0.931514i	$-0.381512\pi$
$727$	−16.1973	−	17.9889i	−0.600723	−	0.667171i	−0.964429	+	0.264343i	$0.914845\pi$
$728$		0			0
$729$	31.9419	−	23.2071i	1.18303	−	0.859524i
$730$		0			0
$731$	−14.0235	−	6.24366i	−0.518677	−	0.230930i
$732$		0			0
$733$	27.0080	−	29.9954i	0.997562	−	1.10790i	0.00340093	−	0.999994i	$-0.498917\pi$
$733$	27.0080	−	29.9954i	0.997562	−	1.10790i	0.994161	−	0.107910i	$-0.0344159\pi$
$734$		0			0
$735$	49.0478	−	10.4254i	1.80916	−	0.384548i
$736$		0			0
$737$	−15.3101	−	3.25427i	−0.563955	−	0.119872i
$738$		0			0
$739$	3.04893	+	5.28089i	0.112157	+	0.194261i	0.916640	−	0.399715i	$-0.130891\pi$
$739$	3.04893	+	5.28089i	0.112157	+	0.194261i	−0.804483	+	0.593976i	$0.797558\pi$
$740$		0			0
$741$	1.84095	+	17.5155i	0.0676292	+	0.643449i
$742$		0			0
$743$	−16.2263			−0.595284			−0.297642	−	0.954678i	$-0.596200\pi$
$743$	−16.2263			−0.595284			−0.297642	+	0.954678i	$0.596200\pi$
$744$		0			0
$745$	−35.5308			−1.30175
$746$		0			0
$747$	7.21649	+	68.6603i	0.264038	+	2.51215i
$748$		0			0
$749$	−6.57456	−	11.3875i	−0.240229	−	0.416089i
$750$		0			0
$751$	35.6481	+	7.57723i	1.30082	+	0.276497i	0.805697	−	0.592328i	$-0.201791\pi$
$751$	35.6481	+	7.57723i	1.30082	+	0.276497i	0.495119	+	0.868825i	$0.335124\pi$
$752$		0			0
$753$	6.66944	−	1.41763i	0.243048	−	0.0516614i
$754$		0			0
$755$	8.59879	−	9.54992i	0.312942	−	0.347557i
$756$		0			0
$757$	39.7960	+	17.7183i	1.44641	+	0.643984i	0.971713	−	0.236164i	$-0.0758904\pi$
$757$	39.7960	+	17.7183i	1.44641	+	0.643984i	0.474699	+	0.880148i	$0.342557\pi$
$758$		0			0
$759$	−2.51672	+	1.82851i	−0.0913512	+	0.0663705i
$760$		0			0
$761$	2.20765	+	2.45184i	0.0800272	+	0.0888792i	0.781828	−	0.623494i	$-0.214287\pi$
$761$	2.20765	+	2.45184i	0.0800272	+	0.0888792i	−0.701801	+	0.712373i	$0.747621\pi$
$762$		0			0
$763$	−0.624878	+	0.278214i	−0.0226221	+	0.0100720i
$764$		0			0
$765$	3.04605	−	28.9812i	0.110130	−	1.04782i
$766$		0			0
$767$	10.6685	−	32.8342i	0.385216	−	1.18557i
$768$		0			0
$769$	22.8568	−	39.5891i	0.824237	−	1.42762i	−0.0782634	−	0.996933i	$-0.524938\pi$
$769$	22.8568	−	39.5891i	0.824237	−	1.42762i	0.902501	−	0.430688i	$-0.141729\pi$
$770$		0			0
$771$	−23.2585	−	71.5823i	−0.837635	−	2.57798i
$772$		0			0
$773$	−24.2710	−	17.6339i	−0.872969	−	0.634249i	0.0584131	−	0.998292i	$-0.481396\pi$
$773$	−24.2710	−	17.6339i	−0.872969	−	0.634249i	−0.931382	+	0.364044i	$0.881396\pi$
$774$		0			0
$775$	−15.8997	−	14.2946i	−0.571133	−	0.513479i
$776$		0			0
$777$	−7.97058	−	5.79097i	−0.285943	−	0.207750i
$778$		0			0
$779$	4.54689	+	13.9939i	0.162909	+	0.501383i
$780$		0			0
$781$	2.03977	−	3.53298i	0.0729886	−	0.126420i
$782$		0			0
$783$	−6.69730	+	20.6122i	−0.239342	+	0.736619i
$784$		0			0
$785$	2.70523	−	25.7385i	0.0965537	−	0.918647i
$786$		0			0
$787$	39.4944	−	17.5840i	1.40782	−	0.626803i	0.444654	−	0.895702i	$-0.353327\pi$
$787$	39.4944	−	17.5840i	1.40782	−	0.626803i	0.963168	+	0.268899i	$0.0866599\pi$
$788$		0			0
$789$	−44.4030	−	49.3145i	−1.58079	−	1.75564i
$790$		0			0
$791$	9.89298	−	7.18767i	0.351754	−	0.255564i
$792$		0			0
$793$	−37.8953	−	16.8721i	−1.34570	−	0.599145i
$794$		0			0
$795$	−28.6483	+	31.8172i	−1.01605	+	1.12844i
$796$		0			0
$797$	−22.3250	+	4.74532i	−0.790792	+	0.168088i	−0.585564	−	0.810626i	$-0.699127\pi$
$797$	−22.3250	+	4.74532i	−0.790792	+	0.168088i	−0.205228	+	0.978714i	$0.565794\pi$
$798$		0			0
$799$	14.2114	+	3.02072i	0.502763	+	0.106865i
$800$		0			0
$801$	−6.06773	−	10.5096i	−0.214393	−	0.371339i
$802$		0			0
$803$	−3.64960	−	34.7236i	−0.128792	−	1.22537i
$804$		0			0
$805$	1.42279			0.0501467
$806$		0			0
$807$	−49.3229			−1.73625
$808$		0			0
$809$	2.22002	+	21.1221i	0.0780517	+	0.742613i	0.961634	+	0.274336i	$0.0884581\pi$
$809$	2.22002	+	21.1221i	0.0780517	+	0.742613i	−0.883582	+	0.468276i	$0.844875\pi$
$810$		0			0
$811$	1.06157	+	1.83869i	0.0372767	+	0.0645652i	0.884062	−	0.467370i	$-0.154798\pi$
$811$	1.06157	+	1.83869i	0.0372767	+	0.0645652i	−0.846785	+	0.531935i	$0.821465\pi$
$812$		0			0
$813$	20.5081	+	4.35913i	0.719250	+	0.152881i
$814$		0			0
$815$	9.09675	−	1.93357i	0.318645	−	0.0677301i
$816$		0			0
$817$	−11.9237	+	13.2426i	−0.417158	+	0.463301i
$818$		0			0
$819$	15.2584	+	6.79347i	0.533171	+	0.237383i
$820$		0			0
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.992171	−	0.124891i	$-0.960142\pi$
$821$	−33.8104	+	24.5647i	−1.17999	+	0.857313i	−0.187819	+	0.982204i	$0.560142\pi$
$822$		0			0
$823$	−10.9058	−	12.1121i	−0.380153	−	0.422203i	0.522454	−	0.852667i	$-0.325016\pi$
$823$	−10.9058	−	12.1121i	−0.380153	−	0.422203i	−0.902608	+	0.430464i	$0.858350\pi$
$824$		0			0
$825$	24.6783	−	10.9875i	0.859189	−	0.382535i
$826$		0			0
$827$	−3.24974	+	30.9192i	−0.113005	+	1.07517i	0.780205	+	0.625524i	$0.215115\pi$
$827$	−3.24974	+	30.9192i	−0.113005	+	1.07517i	−0.893209	+	0.449642i	$0.851552\pi$
$828$		0			0
$829$	−8.66756	+	26.6760i	−0.301037	+	0.926496i	0.680090	+	0.733129i	$0.261941\pi$
$829$	−8.66756	+	26.6760i	−0.301037	+	0.926496i	−0.981126	+	0.193367i	$0.938059\pi$
$830$		0			0
$831$	−21.8491	+	37.8437i	−0.757936	+	1.31278i
$832$		0			0
$833$	3.28688	+	10.1160i	0.113884	+	0.350498i
$834$		0			0
$835$	−32.1239	−	23.3394i	−1.11169	−	0.807692i
$836$		0			0
$837$	−37.9848	+	4.02104i	−1.31295	+	0.138988i
$838$		0			0
$839$	−18.6621	−	13.5588i	−0.644287	−	0.468102i	0.217034	−	0.976164i	$-0.430362\pi$
$839$	−18.6621	−	13.5588i	−0.644287	−	0.468102i	−0.861320	+	0.508062i	$0.830362\pi$
$840$		0			0
$841$	−5.87746	−	18.0890i	−0.202671	−	0.623757i
$842$		0			0
$843$	3.59793	−	6.23179i	0.123919	−	0.214634i
$844$		0			0
$845$	−4.35696	+	13.4093i	−0.149884	+	0.461296i
$846$		0			0
$847$	0.575568	−	5.47617i	0.0197768	−	0.188163i
$848$		0			0
$849$	12.4925	−	5.56202i	0.428741	−	0.190888i
$850$		0			0
$851$	0.931124	+	1.03412i	0.0319185	+	0.0354491i
$852$		0			0
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	−0.920007	−	0.391901i	$-0.871818\pi$
$853$	−24.2874	+	17.6458i	−0.831585	+	0.604182i	0.0884221	+	0.996083i	$0.471818\pi$
$854$		0			0
$855$	−30.9035	−	13.7591i	−1.05688	−	0.470551i
$856$		0			0
$857$	−36.5261	+	40.5663i	−1.24771	+	1.38572i	−0.355135	+	0.934815i	$0.615565\pi$
$857$	−36.5261	+	40.5663i	−1.24771	+	1.38572i	−0.892572	+	0.450904i	$0.851102\pi$
$858$		0			0
$859$	9.13238	−	1.94115i	0.311593	−	0.0662311i	−0.0494610	−	0.998776i	$-0.515750\pi$
$859$	9.13238	−	1.94115i	0.311593	−	0.0662311i	0.361054	+	0.932545i	$0.382417\pi$
$860$		0			0
$861$	21.2728	+	4.52167i	0.724974	+	0.154098i
$862$		0			0
$863$	6.65836	+	11.5326i	0.226653	+	0.392575i	0.956814	−	0.290700i	$-0.0938882\pi$
$863$	6.65836	+	11.5326i	0.226653	+	0.392575i	−0.730161	+	0.683275i	$0.760555\pi$
$864$		0			0
$865$	−5.91886	−	56.3142i	−0.201247	−	1.91474i
$866$		0			0
$867$	−39.5520			−1.34326
$868$		0			0
$869$	8.38250			0.284357
$870$		0			0
$871$	−1.93371	−	18.3980i	−0.0655213	−	0.623394i
$872$		0			0
$873$	−9.16547	−	15.8751i	−0.310204	−	0.537290i
$874$		0			0
$875$	3.65034	+	0.775903i	0.123404	+	0.0262303i
$876$		0			0
$877$	41.6359	−	8.84998i	1.40594	−	0.298843i	0.558402	−	0.829571i	$-0.311415\pi$
$877$	41.6359	−	8.84998i	1.40594	−	0.298843i	0.847542	+	0.530728i	$0.178081\pi$
$878$		0			0
$879$	−20.4225	+	22.6815i	−0.688835	+	0.765029i
$880$		0			0
$881$	−5.27402	−	2.34814i	−0.177686	−	0.0791110i	0.315966	−	0.948771i	$-0.397672\pi$
$881$	−5.27402	−	2.34814i	−0.177686	−	0.0791110i	−0.493652	+	0.869660i	$0.664338\pi$
$882$		0			0
$883$	22.0029	−	15.9860i	0.740457	−	0.537973i	−0.152397	−	0.988319i	$-0.548699\pi$
$883$	22.0029	−	15.9860i	0.740457	−	0.537973i	0.892854	+	0.450346i	$0.148699\pi$
$884$		0			0
$885$	69.1539	+	76.8032i	2.32458	+	2.58171i
$886$		0			0
$887$	6.73437	−	2.99834i	0.226118	−	0.100674i	−0.290551	−	0.956860i	$-0.593839\pi$
$887$	6.73437	−	2.99834i	0.226118	−	0.100674i	0.516669	+	0.856185i	$0.327172\pi$
$888$		0			0
$889$	0.0133254	−	0.126783i	0.000446920	−	0.00425216i
$890$		0			0
$891$	2.80677	−	8.63835i	0.0940304	−	0.289396i
$892$		0			0
$893$	8.43290	−	14.6062i	0.282196	−	0.488778i
$894$		0			0
$895$	0.0728867	+	0.224322i	0.00243633	+	0.00749826i
$896$		0			0
$897$	−2.97453	−	2.16112i	−0.0993166	−	0.0721578i
$898$		0			0
$899$	−13.0626	+	11.7793i	−0.435663	+	0.392862i
$900$		0			0
$901$	−7.34737	−	5.33818i	−0.244776	−	0.177841i
$902$		0			0
$903$	8.13900	+	25.0493i	0.270849	+	0.833588i
$904$		0			0
$905$	−3.21533	+	5.56911i	−0.106881	+	0.185123i
$906$		0			0
$907$	−5.09354	+	15.6763i	−0.169128	+	0.520523i	−0.999317	−	0.0369599i	$-0.988233\pi$
$907$	−5.09354	+	15.6763i	−0.169128	+	0.520523i	0.830189	+	0.557482i	$0.188233\pi$
$908$		0			0
$909$	−9.94714	+	94.6408i	−0.329926	+	3.13904i
$910$		0			0
$911$	−40.9333	+	18.2247i	−1.35618	+	0.603810i	−0.950648	−	0.310271i	$-0.899580\pi$
$911$	−40.9333	+	18.2247i	−1.35618	+	0.603810i	−0.405531	+	0.914081i	$0.632913\pi$
$912$		0			0
$913$	−20.9116	−	23.2247i	−0.692073	−	0.768625i
$914$		0			0
$915$	100.461	−	72.9895i	3.32115	−	2.41296i
$916$		0			0
$917$	−5.71785	−	2.54575i	−0.188820	−	0.0840681i
$918$		0			0
$919$	6.93006	−	7.69662i	0.228602	−	0.253888i	−0.617921	−	0.786240i	$-0.712025\pi$
$919$	6.93006	−	7.69662i	0.228602	−	0.253888i	0.846523	+	0.532352i	$0.178692\pi$
$920$		0			0
$921$	7.49544	−	1.59320i	0.246983	−	0.0524979i
$922$		0			0
$923$	4.71626	+	1.00247i	0.155238	+	0.0329968i
$924$		0			0
$925$	−6.04191	−	10.4649i	−0.198657	−	0.344084i
$926$		0			0
$927$	4.53296	+	43.1282i	0.148882	+	1.41652i
$928$		0			0
$929$	44.0624			1.44564			0.722820	−	0.691037i	$-0.242846\pi$
$929$	44.0624			1.44564			0.722820	+	0.691037i	$0.242846\pi$
$930$		0			0
$931$	12.3474			0.404671
$932$		0			0
$933$	1.66725	+	15.8629i	0.0545834	+	0.519327i
$934$		0			0
$935$	6.59563	+	11.4240i	0.215700	+	0.373604i
$936$		0			0
$937$	33.8116	+	7.18687i	1.10458	+	0.234785i	0.723887	−	0.689918i	$-0.242354\pi$
$937$	33.8116	+	7.18687i	1.10458	+	0.234785i	0.380689	+	0.924703i	$0.375687\pi$
$938$		0			0
$939$	75.4933	−	16.0466i	2.46363	−	0.523661i
$940$		0			0
$941$	−14.8206	+	16.4600i	−0.483138	+	0.536580i	−0.934595	−	0.355713i	$-0.884238\pi$
$941$	−14.8206	+	16.4600i	−0.483138	+	0.536580i	0.451457	+	0.892293i	$0.350905\pi$
$942$		0			0
$943$	−2.80617	−	1.24939i	−0.0913814	−	0.0406856i
$944$		0			0
$945$	−17.8572	+	12.9740i	−0.580894	+	0.422044i
$946$		0			0
$947$	18.7909	+	20.8694i	0.610622	+	0.678165i	0.966588	−	0.256334i	$-0.0825148\pi$
$947$	18.7909	+	20.8694i	0.610622	+	0.678165i	−0.355966	+	0.934499i	$0.615848\pi$
$948$		0			0
$949$	37.6985	−	16.7844i	1.22374	−	0.544846i
$950$		0			0
$951$	−3.24818	+	30.9044i	−0.105330	+	1.00214i
$952$		0			0
$953$	2.36916	−	7.29152i	0.0767446	−	0.236196i	−0.905323	−	0.424723i	$-0.860371\pi$
$953$	2.36916	−	7.29152i	0.0767446	−	0.236196i	0.982068	+	0.188527i	$0.0603715\pi$
$954$		0			0
$955$	−7.94104	+	13.7543i	−0.256966	+	0.445078i
$956$		0			0
$957$	−6.86743	−	21.1358i	−0.221992	−	0.683222i
$958$		0			0
$959$	−10.3352	−	7.50893i	−0.333740	−	0.242476i
$960$		0			0
$961$	−28.3387	−	12.5665i	−0.914152	−	0.405372i
$962$		0			0
$963$	−52.8011	−	38.3622i	−1.70149	−	1.23621i
$964$		0			0
$965$	−1.96038	−	6.03342i	−0.0631067	−	0.194223i
$966$		0			0
$967$	−0.925182	+	1.60246i	−0.0297518	+	0.0515317i	−0.880518	−	0.474013i	$-0.842805\pi$
$967$	−0.925182	+	1.60246i	−0.0297518	+	0.0515317i	0.850766	+	0.525545i	$0.176138\pi$
$968$		0			0
$969$	3.45592	−	10.6362i	0.111020	−	0.341685i
$970$		0			0
$971$	5.16072	−	49.1010i	0.165615	−	1.57573i	−0.524107	−	0.851652i	$-0.675601\pi$
$971$	5.16072	−	49.1010i	0.165615	−	1.57573i	0.689723	−	0.724074i	$-0.257732\pi$
$972$		0			0
$973$	15.2457	−	6.78784i	0.488756	−	0.217608i
$974$		0			0
$975$	21.3638	+	23.7270i	0.684191	+	0.759871i
$976$		0			0
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	−0.0220160	−	0.999758i	$-0.507008\pi$
$977$	28.8192	−	20.9383i	0.922007	−	0.669877i	0.944023	+	0.329881i	$0.107008\pi$
$978$		0			0
$979$	5.01847	+	2.23437i	0.160391	+	0.0714107i
$980$		0			0
$981$	−2.27177	+	2.52306i	−0.0725321	+	0.0805550i
$982$		0			0
$983$	−6.24409	+	1.32722i	−0.199156	+	0.0423318i	−0.306409	−	0.951900i	$-0.599128\pi$
$983$	−6.24409	+	1.32722i	−0.199156	+	0.0423318i	0.107254	+	0.994232i	$0.465794\pi$
$984$		0			0
$985$	17.0881	+	3.63220i	0.544473	+	0.115731i
$986$		0			0
$987$	−12.4642	−	21.5887i	−0.396740	−	0.687175i
$988$		0			0
$989$	−0.388855	−	3.69971i	−0.0123649	−	0.117644i
$990$		0			0
$991$	44.2919			1.40698			0.703489	−	0.710706i	$-0.251624\pi$
$991$	44.2919			1.40698			0.703489	+	0.710706i	$0.251624\pi$
$992$		0			0
$993$	−56.8463			−1.80396
$994$		0			0
$995$	2.15312	+	20.4856i	0.0682586	+	0.649437i
$996$		0			0
$997$	−2.66158	−	4.60999i	−0.0842931	−	0.146000i	0.820797	−	0.571220i	$-0.193530\pi$
$997$	−2.66158	−	4.60999i	−0.0842931	−	0.146000i	−0.905090	+	0.425221i	$0.860197\pi$
$998$		0			0
$999$	−21.1162	−	4.48839i	−0.668087	−	0.142006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	496.2.bg.c.289.1		16
4.3	odd	2		31.2.g.a.10.2	✓	16
12.11	even	2		279.2.y.c.10.1		16
20.3	even	4		775.2.ck.a.599.2		32
20.7	even	4		775.2.ck.a.599.3		32
20.19	odd	2		775.2.bl.a.351.1		16
31.28	even	15	inner	496.2.bg.c.369.1		16
124.3	even	30		961.2.g.l.338.2		16
124.7	odd	30		961.2.c.j.521.4		16
124.11	even	30		961.2.a.j.1.4		8
124.15	even	10		961.2.g.j.235.2		16
124.19	odd	30		961.2.g.s.448.1		16
124.23	even	10		961.2.g.m.547.1		16
124.27	even	10		961.2.c.i.439.4		16
124.35	odd	10		961.2.c.j.439.4		16
124.39	odd	10		961.2.g.s.547.1		16
124.43	even	30		961.2.g.m.448.1		16
124.47	odd	10		961.2.g.k.235.2		16
124.51	odd	30		961.2.a.i.1.4		8
124.55	even	30		961.2.c.i.521.4		16
124.59	odd	30		31.2.g.a.28.2	yes	16
124.67	odd	6		961.2.d.o.374.3		16
124.71	odd	30		961.2.d.p.531.2		16
124.75	even	30		961.2.d.n.388.3		16
124.79	even	30		961.2.g.n.844.1		16
124.83	even	30		961.2.d.q.628.2		16
124.87	odd	6		961.2.g.k.732.2		16
124.91	even	10		961.2.g.n.846.1		16
124.95	odd	10		961.2.g.t.846.1		16
124.99	even	6		961.2.g.j.732.2		16
124.103	odd	30		961.2.d.p.628.2		16
124.107	odd	30		961.2.g.t.844.1		16
124.111	odd	30		961.2.d.o.388.3		16
124.115	even	30		961.2.d.q.531.2		16
124.119	even	6		961.2.d.n.374.3		16
124.123	even	2		961.2.g.l.816.2		16
372.11	odd	30		8649.2.a.be.1.5		8
372.59	even	30		279.2.y.c.28.1		16
372.299	even	30		8649.2.a.bf.1.5		8
620.59	odd	30		775.2.bl.a.276.1		16
620.183	even	60		775.2.ck.a.524.3		32
620.307	even	60		775.2.ck.a.524.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.10.2	✓	16	4.3	odd	2
31.2.g.a.28.2	yes	16	124.59	odd	30
279.2.y.c.10.1		16	12.11	even	2
279.2.y.c.28.1		16	372.59	even	30
496.2.bg.c.289.1		16	1.1	even	1	trivial
496.2.bg.c.369.1		16	31.28	even	15	inner
775.2.bl.a.276.1		16	620.59	odd	30
775.2.bl.a.351.1		16	20.19	odd	2
775.2.ck.a.524.2		32	620.307	even	60
775.2.ck.a.524.3		32	620.183	even	60
775.2.ck.a.599.2		32	20.3	even	4
775.2.ck.a.599.3		32	20.7	even	4
961.2.a.i.1.4		8	124.51	odd	30
961.2.a.j.1.4		8	124.11	even	30
961.2.c.i.439.4		16	124.27	even	10
961.2.c.i.521.4		16	124.55	even	30
961.2.c.j.439.4		16	124.35	odd	10
961.2.c.j.521.4		16	124.7	odd	30
961.2.d.n.374.3		16	124.119	even	6
961.2.d.n.388.3		16	124.75	even	30
961.2.d.o.374.3		16	124.67	odd	6
961.2.d.o.388.3		16	124.111	odd	30
961.2.d.p.531.2		16	124.71	odd	30
961.2.d.p.628.2		16	124.103	odd	30
961.2.d.q.531.2		16	124.115	even	30
961.2.d.q.628.2		16	124.83	even	30
961.2.g.j.235.2		16	124.15	even	10
961.2.g.j.732.2		16	124.99	even	6
961.2.g.k.235.2		16	124.47	odd	10
961.2.g.k.732.2		16	124.87	odd	6
961.2.g.l.338.2		16	124.3	even	30
961.2.g.l.816.2		16	124.123	even	2
961.2.g.m.448.1		16	124.43	even	30
961.2.g.m.547.1		16	124.23	even	10
961.2.g.n.844.1		16	124.79	even	30
961.2.g.n.846.1		16	124.91	even	10
961.2.g.s.448.1		16	124.19	odd	30
961.2.g.s.547.1		16	124.39	odd	10
961.2.g.t.844.1		16	124.107	odd	30
961.2.g.t.846.1		16	124.95	odd	10
8649.2.a.be.1.5		8	372.11	odd	30
8649.2.a.bf.1.5		8	372.299	even	30

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:	\( N \)	\(=\)	\( 496 = 2^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	496.bg (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.302431 - 2.87744i) q^{3} +(-1.48661 - 2.57489i) q^{5} +(-1.05848 - 0.224987i) q^{7} +(-5.25377 + 1.11672i) q^{9} +(1.62690 - 1.80686i) q^{11} +(2.62521 + 1.16882i) q^{13} +(-6.95951 + 5.05638i) q^{15} +(-1.22101 - 1.35606i) q^{17} +(-1.93514 + 0.861580i) q^{19} +(-0.327269 + 3.11375i) q^{21} +(0.136652 - 0.420572i) q^{23} +(-1.92005 + 3.32562i) q^{25} +(2.11998 + 6.52462i) q^{27} +(2.55579 + 1.85689i) q^{29} +(-1.15354 + 5.44696i) q^{31} +(-5.69116 - 4.13487i) q^{33} +(0.994234 + 3.05994i) q^{35} +(-1.57338 + 2.72517i) q^{37} +(2.56926 - 7.90738i) q^{39} +(0.726079 - 6.90818i) q^{41} +(7.68509 - 3.42162i) q^{43} +(10.6858 + 11.8677i) q^{45} +(-6.44144 + 4.67998i) q^{47} +(-5.32506 - 2.37087i) q^{49} +(-3.53273 + 3.92349i) q^{51} +(4.86824 - 1.03478i) q^{53} +(-7.07105 - 1.50300i) q^{55} +(3.06439 + 5.30768i) q^{57} +(-1.25580 - 11.9481i) q^{59} -14.4351 q^{61} +5.81225 q^{63} +(-0.893094 - 8.49722i) q^{65} +(-3.21879 - 5.57511i) q^{67} +(-1.25150 - 0.266015i) q^{69} +(1.64121 - 0.348850i) q^{71} +(9.60883 - 10.6717i) q^{73} +(10.1500 + 4.51905i) q^{75} +(-2.12856 + 1.54649i) q^{77} +(2.30692 + 2.56210i) q^{79} +(3.41274 - 1.51945i) q^{81} +(1.34357 - 12.7832i) q^{83} +(-1.67655 + 5.15991i) q^{85} +(4.57015 - 7.91573i) q^{87} +(0.698188 + 2.14880i) q^{89} +(-2.51576 - 1.82781i) q^{91} +(16.0222 + 1.67190i) q^{93} +(5.09528 + 3.70194i) q^{95} +(1.05463 + 3.24582i) q^{97} +(-6.52961 + 11.3096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 3 q^{5} - 2 q^{7} - 10 q^{9} + 7 q^{11} - 7 q^{13} - 14 q^{15} - 6 q^{17} - 16 q^{19} + 9 q^{21} - q^{23} - 13 q^{25} - 9 q^{27} - 14 q^{29} - 15 q^{31} - 13 q^{33} + 9 q^{35} - 8 q^{37}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 - 3 * q^5 - 2 * q^7 - 10 * q^9 + 7 * q^11 - 7 * q^13 - 14 * q^15 - 6 * q^17 - 16 * q^19 + 9 * q^21 - q^23 - 13 * q^25 - 9 * q^27 - 14 * q^29 - 15 * q^31 - 13 * q^33 + 9 * q^35 - 8 * q^37 + 3 * q^39 - 8 * q^41 - 23 * q^43 + 65 * q^45 - 14 * q^47 + 2 * q^49 + 42 * q^51 + 6 * q^53 + 7 * q^55 - 17 * q^57 - 4 * q^59 - 60 * q^61 + 46 * q^63 - 12 * q^65 - 13 * q^67 + 38 * q^69 + 14 * q^71 + 2 * q^73 - 13 * q^75 + 18 * q^77 - 18 * q^79 + 23 * q^81 + 16 * q^83 + 37 * q^85 - 15 * q^87 + q^89 - 8 * q^91 + 17 * q^93 + 22 * q^95 + 3 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more