LMFDB - Embedded newform 405.3.l.n.28.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,3,Mod(28,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.28"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			28.2
Character	$\chi$	$=$	405.28
Dual form			405.3.l.n.217.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.78913 - 0.747344i) q^{2} +(3.75659 + 2.16887i) q^{4} +(4.50635 - 2.16628i) q^{5} +(-11.5096 - 3.08399i) q^{7} +(-0.689596 - 0.689596i) q^{8} +(-14.1877 + 2.67423i) q^{10} +(6.14980 + 10.6518i) q^{11} +(-0.906368 + 0.242861i) q^{13} +(29.7970 + 17.2033i) q^{14} +(-7.26748 - 12.5876i) q^{16} +(7.47753 - 7.47753i) q^{17} +25.0163i q^{19} +(21.6269 + 1.63586i) q^{20} +(-9.19203 - 34.3051i) q^{22} +(-24.7385 + 6.62867i) q^{23} +(15.6144 - 19.5241i) q^{25} +2.70947 q^{26} +(-36.5482 - 36.5482i) q^{28} +(2.93013 - 1.69171i) q^{29} +(-14.4414 + 25.0133i) q^{31} +(11.8723 + 44.3078i) q^{32} +(-26.4441 + 15.2675i) q^{34} +(-58.5472 + 11.0355i) q^{35} +(-2.59583 + 2.59583i) q^{37} +(18.6958 - 69.7736i) q^{38} +(-4.60142 - 1.61370i) q^{40} +(11.6697 - 20.2125i) q^{41} +(-4.25843 + 15.8927i) q^{43} +53.3525i q^{44} +73.9528 q^{46} +(66.9844 + 17.9484i) q^{47} +(80.5250 + 46.4912i) q^{49} +(-58.1418 + 42.7857i) q^{50} +(-3.93159 - 1.05347i) q^{52} +(27.6894 + 27.6894i) q^{53} +(50.7879 + 34.6784i) q^{55} +(5.81027 + 10.0637i) q^{56} +(-9.43678 + 2.52858i) q^{58} +(75.9971 + 43.8770i) q^{59} +(39.5244 + 68.4583i) q^{61} +(58.9725 - 58.9725i) q^{62} -74.3129i q^{64} +(-3.55831 + 3.05786i) q^{65} +(-16.5841 - 61.8926i) q^{67} +(44.3078 - 11.8723i) q^{68} +(171.543 + 12.9755i) q^{70} +88.7641 q^{71} +(12.8174 + 12.8174i) q^{73} +(9.18007 - 5.30012i) q^{74} +(-54.2571 + 93.9761i) q^{76} +(-37.9319 - 141.564i) q^{77} +(-26.2915 + 15.1794i) q^{79} +(-60.0182 - 40.9810i) q^{80} +(-47.6540 + 47.6540i) q^{82} +(-39.3035 + 146.683i) q^{83} +(17.4980 - 49.8948i) q^{85} +(23.7546 - 41.1442i) q^{86} +(3.10454 - 11.5863i) q^{88} +117.891i q^{89} +11.1809 q^{91} +(-107.309 - 28.7535i) q^{92} +(-173.414 - 100.121i) q^{94} +(54.1923 + 112.732i) q^{95} +(-18.4817 - 4.95215i) q^{97} +(-189.850 - 189.850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{7} + 80 q^{10} - 40 q^{13} + 152 q^{16} + 136 q^{22} + 32 q^{25} - 224 q^{28} - 200 q^{31} + 32 q^{37} + 48 q^{40} - 136 q^{43} + 304 q^{46} - 640 q^{52} + 496 q^{55} - 48 q^{58} + 280 q^{61}+ \cdots - 448 q^{97}+O(q^{100}) $ 32 * q - 16 * q^7 + 80 * q^10 - 40 * q^13 + 152 * q^16 + 136 * q^22 + 32 * q^25 - 224 * q^28 - 200 * q^31 + 32 * q^37 + 48 * q^40 - 136 * q^43 + 304 * q^46 - 640 * q^52 + 496 * q^55 - 48 * q^58 + 280 * q^61 + 344 * q^67 + 696 * q^70 - 1552 * q^73 - 144 * q^76 - 1760 * q^82 + 176 * q^85 - 1200 * q^88 + 304 * q^91 - 448 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.78913	−	0.747344i	−1.39456	−	0.373672i	−0.518173	−	0.855276i	$-0.673388\pi$
$2$	−2.78913	−	0.747344i	−1.39456	−	0.373672i	−0.876389	+	0.481604i	$0.840054\pi$
$3$		0			0
$3$		0			0
$4$	3.75659	+	2.16887i	0.939149	+	0.542218i
$5$	4.50635	−	2.16628i	0.901271	−	0.433256i
$5$	4.50635	−	2.16628i	0.901271	−	0.433256i
$6$		0			0
$7$	−11.5096	−	3.08399i	−1.64423	−	0.440570i	−0.686242	−	0.727374i	$-0.740741\pi$
$7$	−11.5096	−	3.08399i	−1.64423	−	0.440570i	−0.957989	+	0.286803i	$0.907407\pi$
$8$	−0.689596	−	0.689596i	−0.0861995	−	0.0861995i
$9$		0			0
$10$	−14.1877	+	2.67423i	−1.41877	+	0.267423i
$11$	6.14980	+	10.6518i	0.559073	+	0.968342i	0.997574	+	0.0696117i	$0.0221760\pi$
$11$	6.14980	+	10.6518i	0.559073	+	0.968342i	−0.438502	+	0.898730i	$0.644491\pi$
$12$		0			0
$13$	−0.906368	+	0.242861i	−0.0697206	+	0.0186816i	−0.293511	−	0.955956i	$-0.594824\pi$
$13$	−0.906368	+	0.242861i	−0.0697206	+	0.0186816i	0.223790	+	0.974637i	$0.428157\pi$
$14$	29.7970	+	17.2033i	2.12835	+	1.22881i
$15$		0			0
$16$	−7.26748	−	12.5876i	−0.454218	−	0.786728i
$17$	7.47753	−	7.47753i	0.439855	−	0.439855i	−0.452108	−	0.891963i	$-0.649328\pi$
$17$	7.47753	−	7.47753i	0.439855	−	0.439855i	0.891963	+	0.452108i	$0.149328\pi$
$18$		0			0
$19$			25.0163i			1.31665i	0.752735	+	0.658323i	$0.228734\pi$
$19$			25.0163i			1.31665i	−0.752735	+	0.658323i	$0.771266\pi$
$20$	21.6269	+	1.63586i	1.08135	+	0.0817929i
$21$		0			0
$22$	−9.19203	−	34.3051i	−0.417819	−	1.55932i
$23$	−24.7385	+	6.62867i	−1.07559	+	0.288203i	−0.752788	−	0.658264i	$-0.771291\pi$
$23$	−24.7385	+	6.62867i	−1.07559	+	0.288203i	−0.322801	+	0.946467i	$0.604625\pi$
$24$		0			0
$25$	15.6144	−	19.5241i	0.624578	−	0.780962i
$26$	2.70947			0.104211
$27$		0			0
$28$	−36.5482	−	36.5482i	−1.30529	−	1.30529i
$29$	2.93013	−	1.69171i	0.101039	−	0.0583348i	−0.448629	−	0.893718i	$-0.648088\pi$
$29$	2.93013	−	1.69171i	0.101039	−	0.0583348i	0.549668	+	0.835383i	$0.314754\pi$
$30$		0			0
$31$	−14.4414	+	25.0133i	−0.465853	+	0.806881i	−0.999240	−	0.0389908i	$-0.987586\pi$
$31$	−14.4414	+	25.0133i	−0.465853	+	0.806881i	0.533387	+	0.845871i	$0.320919\pi$
$32$	11.8723	+	44.3078i	0.371008	+	1.38462i
$33$		0			0
$34$	−26.4441	+	15.2675i	−0.777766	+	0.449044i
$35$	−58.5472	+	11.0355i	−1.67278	+	0.315300i
$36$		0			0
$37$	−2.59583	+	2.59583i	−0.0701575	+	0.0701575i	−0.741315	−	0.671157i	$-0.765797\pi$
$37$	−2.59583	+	2.59583i	−0.0701575	+	0.0701575i	0.671157	+	0.741315i	$0.265797\pi$
$38$	18.6958	−	69.7736i	0.491994	−	1.83615i
$39$		0			0
$40$	−4.60142	−	1.61370i	−0.115036	−	0.0403426i
$41$	11.6697	−	20.2125i	0.284627	−	0.492989i	−0.687891	−	0.725814i	$-0.741463\pi$
$41$	11.6697	−	20.2125i	0.284627	−	0.492989i	0.972519	+	0.232825i	$0.0747968\pi$
$42$		0			0
$43$	−4.25843	+	15.8927i	−0.0990334	+	0.369598i	−0.997600	−	0.0692394i	$-0.977943\pi$
$43$	−4.25843	+	15.8927i	−0.0990334	+	0.369598i	0.898567	+	0.438837i	$0.144609\pi$
$44$			53.3525i			1.21256i
$45$		0			0
$46$	73.9528			1.60767
$47$	66.9844	+	17.9484i	1.42520	+	0.381881i	0.887326	−	0.461143i	$-0.152561\pi$
$47$	66.9844	+	17.9484i	1.42520	+	0.381881i	0.537875	+	0.843025i	$0.319227\pi$
$48$		0			0
$49$	80.5250	+	46.4912i	1.64337	+	0.948799i
$50$	−58.1418	+	42.7857i	−1.16284	+	0.855714i
$51$		0			0
$52$	−3.93159	−	1.05347i	−0.0756075	−	0.0202590i
$53$	27.6894	+	27.6894i	0.522442	+	0.522442i	0.918308	−	0.395866i	$-0.129556\pi$
$53$	27.6894	+	27.6894i	0.522442	+	0.522442i	−0.395866	+	0.918308i	$0.629556\pi$
$54$		0			0
$55$	50.7879	+	34.6784i	0.923416	+	0.630517i
$56$	5.81027	+	10.0637i	0.103755	+	0.179709i
$57$		0			0
$58$	−9.43678	+	2.52858i	−0.162703	+	0.0435962i
$59$	75.9971	+	43.8770i	1.28809	+	0.743677i	0.978313	−	0.207133i	$-0.0664132\pi$
$59$	75.9971	+	43.8770i	1.28809	+	0.743677i	0.309774	+	0.950810i	$0.399747\pi$
$60$		0			0
$61$	39.5244	+	68.4583i	0.647942	+	1.12227i	0.983614	+	0.180289i	$0.0577032\pi$
$61$	39.5244	+	68.4583i	0.647942	+	1.12227i	−0.335672	+	0.941979i	$0.608963\pi$
$62$	58.9725	−	58.9725i	0.951169	−	0.951169i
$63$		0			0
$64$		−	74.3129i		−	1.16114i
$65$	−3.55831	+	3.05786i	−0.0547432	+	0.0470441i
$66$		0			0
$67$	−16.5841	−	61.8926i	−0.247523	−	0.923769i	−0.972098	−	0.234574i	$-0.924631\pi$
$67$	−16.5841	−	61.8926i	−0.247523	−	0.923769i	0.724575	−	0.689196i	$-0.242036\pi$
$68$	44.3078	−	11.8723i	0.651586	−	0.174592i
$69$		0			0
$70$	171.543	+	12.9755i	2.45061	+	0.185364i
$71$	88.7641			1.25020			0.625099	−	0.780546i	$-0.285059\pi$
$71$	88.7641			1.25020			0.625099	+	0.780546i	$0.285059\pi$
$72$		0			0
$73$	12.8174	+	12.8174i	0.175581	+	0.175581i	0.789426	−	0.613845i	$-0.210378\pi$
$73$	12.8174	+	12.8174i	0.175581	+	0.175581i	−0.613845	+	0.789426i	$0.710378\pi$
$74$	9.18007	−	5.30012i	0.124055	−	0.0716232i
$75$		0			0
$76$	−54.2571	+	93.9761i	−0.713909	+	1.23653i
$77$	−37.9319	−	141.564i	−0.492622	−	1.83849i
$78$		0			0
$79$	−26.2915	+	15.1794i	−0.332804	+	0.192144i	−0.657085	−	0.753816i	$-0.728211\pi$
$79$	−26.2915	+	15.1794i	−0.332804	+	0.192144i	0.324281	+	0.945961i	$0.394878\pi$
$80$	−60.0182	−	40.9810i	−0.750228	−	0.512262i
$81$		0			0
$82$	−47.6540	+	47.6540i	−0.581147	+	0.581147i
$83$	−39.3035	+	146.683i	−0.473536	+	1.76726i	0.153372	+	0.988168i	$0.450987\pi$
$83$	−39.3035	+	146.683i	−0.473536	+	1.76726i	−0.626909	+	0.779093i	$0.715680\pi$
$84$		0			0
$85$	17.4980	−	49.8948i	0.205858	−	0.586998i
$86$	23.7546	−	41.1442i	0.276216	−	0.478421i
$87$		0			0
$88$	3.10454	−	11.5863i	0.0352788	−	0.131662i
$89$			117.891i			1.32462i	0.749231	+	0.662309i	$0.230423\pi$
$89$			117.891i			1.32462i	−0.749231	+	0.662309i	$0.769577\pi$
$90$		0			0
$91$	11.1809			0.122867
$92$	−107.309	−	28.7535i	−1.16641	−	0.312538i
$93$		0			0
$94$	−173.414	−	100.121i	−1.84483	−	1.06511i
$95$	54.1923	+	112.732i	0.570445	+	1.18666i
$96$		0			0
$97$	−18.4817	−	4.95215i	−0.190533	−	0.0510531i	0.162291	−	0.986743i	$-0.448112\pi$
$97$	−18.4817	−	4.95215i	−0.190533	−	0.0510531i	−0.352824	+	0.935690i	$0.614778\pi$
$98$	−189.850	−	189.850i	−1.93724	−	1.93724i
$99$		0			0
$100$	101.002	−	39.4783i	1.01002	−	0.394783i
$101$	−9.82532	−	17.0179i	−0.0972804	−	0.168495i	0.813278	−	0.581876i	$-0.197681\pi$
$101$	−9.82532	−	17.0179i	−0.0972804	−	0.168495i	−0.910558	+	0.413381i	$0.864348\pi$
$102$		0			0
$103$	165.589	−	44.3694i	1.60766	−	0.430770i	0.660314	−	0.750990i	$-0.270423\pi$
$103$	165.589	−	44.3694i	1.60766	−	0.430770i	0.947343	+	0.320219i	$0.103757\pi$
$104$	0.792503	+	0.457552i	0.00762022	+	0.00439954i
$105$		0			0
$106$	−56.5358	−	97.9229i	−0.533357	−	0.923801i
$107$	10.5840	−	10.5840i	0.0989155	−	0.0989155i	−0.655917	−	0.754833i	$-0.727718\pi$
$107$	10.5840	−	10.5840i	0.0989155	−	0.0989155i	0.754833	+	0.655917i	$0.227718\pi$
$108$		0			0
$109$			9.08051i			0.0833075i	0.999132	+	0.0416537i	$0.0132626\pi$
$109$			9.08051i			0.0833075i	−0.999132	+	0.0416537i	$0.986737\pi$
$110$	−115.737	−	134.678i	−1.05216	−	1.22435i
$111$		0			0
$112$	44.8257	+	167.292i	0.400230	+	1.49368i
$113$	−148.642	+	39.8284i	−1.31541	+	0.352464i	−0.847258	−	0.531182i	$-0.821748\pi$
$113$	−148.642	+	39.8284i	−1.31541	+	0.352464i	−0.468155	+	0.883646i	$0.655081\pi$
$114$		0			0
$115$	−97.1211	+	83.4618i	−0.844531	+	0.725755i
$116$	14.6764			0.126521
$117$		0			0
$118$	−179.174	−	179.174i	−1.51843	−	1.51843i
$119$	−109.124	+	63.0029i	−0.917010	+	0.529436i
$120$		0			0
$121$	−15.1400	+	26.2233i	−0.125124	+	0.216722i
$122$	−59.0767	−	220.477i	−0.484235	−	1.80719i
$123$		0			0
$124$	−108.501	+	62.6432i	−0.875010	+	0.505187i
$125$	28.0696	−	121.808i	0.224557	−	0.974461i
$126$		0			0
$127$	−115.169	+	115.169i	−0.906841	+	0.906841i	−0.996016	−	0.0891750i	$-0.971577\pi$
$127$	−115.169	+	115.169i	−0.906841	+	0.906841i	0.0891750	+	0.996016i	$0.471577\pi$
$128$	−8.04831	+	30.0367i	−0.0628774	+	0.234662i
$129$		0			0
$130$	12.2099	−	5.86949i	0.0939219	−	0.0451499i
$131$	9.42889	−	16.3313i	0.0719762	−	0.124667i	−0.827791	−	0.561036i	$-0.810403\pi$
$131$	9.42889	−	16.3313i	0.0719762	−	0.124667i	0.899767	+	0.436370i	$0.143736\pi$
$132$		0			0
$133$	77.1500	−	287.928i	0.580076	−	2.16487i
$134$			185.020i			1.38075i
$135$		0			0
$136$	−10.3129			−0.0758305
$137$	73.0600	+	19.5764i	0.533284	+	0.142893i	0.515405	−	0.856947i	$-0.327642\pi$
$137$	73.0600	+	19.5764i	0.533284	+	0.142893i	0.0178799	+	0.999840i	$0.494308\pi$
$138$		0			0
$139$	38.9303	+	22.4764i	0.280074	+	0.161701i	0.633457	−	0.773778i	$-0.281635\pi$
$139$	38.9303	+	22.4764i	0.280074	+	0.161701i	−0.353383	+	0.935479i	$0.614969\pi$
$140$	−243.873	−	85.5254i	−1.74195	−	0.610896i
$141$		0			0
$142$	−247.574	−	66.3373i	−1.74348	−	0.467164i
$143$	−8.16088	−	8.16088i	−0.0570691	−	0.0570691i
$144$		0			0
$145$	9.53947	−	13.9709i	0.0657894	−	0.0963512i
$146$	−26.1703	−	45.3283i	−0.179249	−	0.310468i
$147$		0			0
$148$	−15.3815	+	4.12146i	−0.103929	+	0.0278477i
$149$	−142.228	−	82.1151i	−0.954547	−	0.551108i	−0.0600567	−	0.998195i	$-0.519128\pi$
$149$	−142.228	−	82.1151i	−0.954547	−	0.551108i	−0.894491	+	0.447087i	$0.852461\pi$
$150$		0			0
$151$	−19.2011	−	33.2572i	−0.127159	−	0.220247i	0.795416	−	0.606064i	$-0.207253\pi$
$151$	−19.2011	−	33.2572i	−0.127159	−	0.220247i	−0.922575	+	0.385818i	$0.873919\pi$
$152$	17.2511	−	17.2511i	0.113494	−	0.113494i
$153$		0			0
$154$			423.187i			2.74797i
$155$	−10.8924	+	144.003i	−0.0702733	+	0.929052i
$156$		0			0
$157$	−16.8614	−	62.9277i	−0.107398	−	0.400814i	0.891208	−	0.453594i	$-0.149858\pi$
$157$	−16.8614	−	62.9277i	−0.107398	−	0.400814i	−0.998606	+	0.0527803i	$0.983192\pi$
$158$	84.6745	−	22.6885i	0.535915	−	0.143598i
$159$		0			0
$160$	149.484	+	173.948i	0.934274	+	1.08718i
$161$	305.174			1.89549
$162$		0			0
$163$	20.9849	+	20.9849i	0.128742	+	0.128742i	0.768542	−	0.639800i	$-0.220983\pi$
$163$	20.9849	+	20.9849i	0.128742	+	0.128742i	−0.639800	+	0.768542i	$0.720983\pi$
$164$	87.6768	−	50.6202i	0.534615	−	0.308660i
$165$		0			0
$166$	219.245	−	379.743i	1.32075	−	2.28761i
$167$	24.2968	+	90.6768i	0.145490	+	0.542975i	0.999733	+	0.0231017i	$0.00735415\pi$
$167$	24.2968	+	90.6768i	0.145490	+	0.542975i	−0.854243	+	0.519873i	$0.825979\pi$
$168$		0			0
$169$	−145.596	+	84.0598i	−0.861513	+	0.497395i
$170$	−86.0926	+	126.086i	−0.506427	+	0.741682i
$171$		0			0
$172$	−50.4664	+	50.4664i	−0.293409	+	0.293409i
$173$	51.5809	−	192.502i	0.298155	−	1.11273i	−0.640524	−	0.767938i	$-0.721283\pi$
$173$	51.5809	−	192.502i	0.298155	−	1.11273i	0.938679	−	0.344792i	$-0.112051\pi$
$174$		0			0
$175$	−239.928	+	176.560i	−1.37102	+	1.00891i
$176$	89.3871	−	154.823i	0.507881	−	0.879676i
$177$		0			0
$178$	88.1051	−	328.813i	0.494973	−	1.84726i
$179$		−	45.6130i		−	0.254821i	−0.991850	−	0.127411i	$-0.959333\pi$
$179$		−	45.6130i		−	0.254821i	0.991850	−	0.127411i	$-0.0406666\pi$
$180$		0			0
$181$	−104.793			−0.578968			−0.289484	−	0.957183i	$-0.593484\pi$
$181$	−104.793			−0.578968			−0.289484	+	0.957183i	$0.593484\pi$
$182$	−31.1850	−	8.35600i	−0.171346	−	0.0459121i
$183$		0			0
$184$	21.6307	+	12.4885i	0.117558	+	0.0678722i
$185$	−6.07443	+	17.3210i	−0.0328347	+	0.0936271i
$186$		0			0
$187$	125.634	+	33.6636i	0.671840	+	0.180019i
$188$	212.706	+	212.706i	1.13141	+	1.13141i
$189$		0			0
$190$	−66.8994	−	354.925i	−0.352102	−	1.86802i
$191$	−50.6473	−	87.7237i	−0.265169	−	0.459286i	0.702439	−	0.711744i	$-0.252094\pi$
$191$	−50.6473	−	87.7237i	−0.265169	−	0.459286i	−0.967608	+	0.252458i	$0.918761\pi$
$192$		0			0
$193$	−273.261	+	73.2202i	−1.41586	+	0.379379i	−0.884014	−	0.467461i	$-0.845169\pi$
$193$	−273.261	+	73.2202i	−1.41586	+	0.379379i	−0.531848	+	0.846840i	$0.678502\pi$
$194$	47.8468	+	27.6243i	0.246633	+	0.142394i
$195$		0			0
$196$	201.667	+	349.297i	1.02891	+	1.78213i
$197$	5.26310	−	5.26310i	0.0267163	−	0.0267163i	−0.693622	−	0.720339i	$-0.743986\pi$
$197$	5.26310	−	5.26310i	0.0267163	−	0.0267163i	0.720339	+	0.693622i	$0.243986\pi$
$198$		0			0
$199$		−	141.070i		−	0.708895i	−0.935076	−	0.354448i	$-0.884669\pi$
$199$		−	141.070i		−	0.708895i	0.935076	−	0.354448i	$-0.115331\pi$
$200$	−24.2314	+	2.69605i	−0.121157	+	0.0134803i
$201$		0			0
$202$	14.6858	+	54.8081i	0.0727019	+	0.271327i
$203$	−38.9419	+	10.4344i	−0.191832	+	0.0514012i
$204$		0			0
$205$	8.80182	−	116.365i	0.0429357	−	0.567633i
$206$	−495.007			−2.40295
$207$		0			0
$208$	9.64406	+	9.64406i	0.0463657	+	0.0463657i
$209$	−266.468	+	153.845i	−1.27496	+	0.736101i
$210$		0			0
$211$	22.5534	−	39.0637i	0.106888	−	0.185136i	−0.807620	−	0.589703i	$-0.799245\pi$
$211$	22.5534	−	39.0637i	0.106888	−	0.185136i	0.914508	+	0.404568i	$0.132578\pi$
$212$	43.9632	+	164.073i	0.207374	+	0.773929i
$213$		0			0
$214$	−37.4298	+	21.6101i	−0.174906	+	0.100982i
$215$	15.2380	+	80.8431i	0.0708746	+	0.376014i
$216$		0			0
$217$	243.356	−	243.356i	1.12146	−	1.12146i
$218$	6.78627	−	25.3267i	0.0311297	−	0.116177i
$219$		0			0
$220$	115.576	+	240.425i	0.525348	+	1.09284i
$221$	−4.96140	+	8.59339i	−0.0224498	+	0.0388841i
$222$		0			0
$223$	−1.45246	+	5.42064i	−0.00651326	+	0.0243078i	−0.969106	−	0.246645i	$-0.920672\pi$
$223$	−1.45246	+	5.42064i	−0.00651326	+	0.0243078i	0.962593	+	0.270952i	$0.0873386\pi$
$224$		−	546.580i		−	2.44009i
$225$		0			0
$226$	444.346			1.96613
$227$	−73.4236	−	19.6738i	−0.323452	−	0.0866686i	0.0934396	−	0.995625i	$-0.470214\pi$
$227$	−73.4236	−	19.6738i	−0.323452	−	0.0866686i	−0.416891	+	0.908956i	$0.636880\pi$
$228$		0			0
$229$	−47.7957	−	27.5948i	−0.208715	−	0.120502i	0.391999	−	0.919966i	$-0.371784\pi$
$229$	−47.7957	−	27.5948i	−0.208715	−	0.120502i	−0.600714	+	0.799464i	$0.705117\pi$
$230$	333.257	−	160.203i	1.44895	−	0.696533i
$231$		0			0
$232$	−3.18720	−	0.854007i	−0.0137379	−	0.00368107i
$233$	96.4842	+	96.4842i	0.414095	+	0.414095i	0.883162	−	0.469067i	$-0.155410\pi$
$233$	96.4842	+	96.4842i	0.414095	+	0.414095i	−0.469067	+	0.883162i	$0.655410\pi$
$234$		0			0
$235$	340.737	−	64.2252i	1.44994	−	0.273299i
$236$	190.327	+	329.656i	0.806470	+	1.39685i
$237$		0			0
$238$	351.446	−	94.1696i	1.47666	−	0.395671i
$239$	127.675	+	73.7133i	0.534206	+	0.308424i	0.742727	−	0.669594i	$-0.233532\pi$
$239$	127.675	+	73.7133i	0.534206	+	0.308424i	−0.208522	+	0.978018i	$0.566865\pi$
$240$		0			0
$241$	179.499	+	310.901i	0.744809	+	1.29005i	0.950284	+	0.311384i	$0.100793\pi$
$241$	179.499	+	310.901i	0.744809	+	1.29005i	−0.205475	+	0.978662i	$0.565874\pi$
$242$	61.8253	−	61.8253i	0.255476	−	0.255476i
$243$		0			0
$244$			342.894i			1.40530i
$245$	463.587	+	35.0657i	1.89219	+	0.143125i
$246$		0			0
$247$	−6.07547	−	22.6740i	−0.0245970	−	0.0917974i
$248$	27.2078	−	7.29031i	0.109709	−	0.0293964i
$249$		0			0
$250$	−169.322	+	318.759i	−0.677287	+	1.27504i
$251$	−154.041			−0.613710			−0.306855	−	0.951756i	$-0.599277\pi$
$251$	−154.041			−0.613710			−0.306855	+	0.951756i	$0.599277\pi$
$252$		0			0
$253$	−222.744	−	222.744i	−0.880411	−	0.880411i
$254$	407.291	−	235.150i	1.60351	−	0.925785i
$255$		0			0
$256$	−103.730	+	179.666i	−0.405197	+	0.701821i
$257$	89.3689	+	333.529i	0.347739	+	1.29778i	0.889380	+	0.457169i	$0.151137\pi$
$257$	89.3689	+	333.529i	0.347739	+	1.29778i	−0.541641	+	0.840610i	$0.682197\pi$
$258$		0			0
$259$	37.8825	−	21.8715i	0.146265	−	0.0844459i
$260$	−19.9992	+	3.76964i	−0.0769202	+	0.0144986i
$261$		0			0
$262$	−38.5035	+	38.5035i	−0.146960	+	0.146960i
$263$	−67.4597	+	251.763i	−0.256501	+	0.957274i	0.710748	+	0.703446i	$0.248356\pi$
$263$	−67.4597	+	251.763i	−0.256501	+	0.957274i	−0.967249	+	0.253828i	$0.918310\pi$
$264$		0			0
$265$	184.762	+	64.7953i	0.697213	+	0.244511i
$266$	−430.362	+	745.409i	−1.61790	+	2.80229i
$267$		0			0
$268$	71.9374	−	268.474i	0.268423	−	1.00177i
$269$		−	194.835i		−	0.724296i	−0.932121	−	0.362148i	$-0.882044\pi$
$269$		−	194.835i		−	0.724296i	0.932121	−	0.362148i	$-0.117956\pi$
$270$		0			0
$271$	−307.130			−1.13332			−0.566661	−	0.823951i	$-0.691765\pi$
$271$	−307.130			−1.13332			−0.566661	+	0.823951i	$0.691765\pi$
$272$	−148.467	−	39.7817i	−0.545836	−	0.146256i
$273$		0			0
$274$	−189.143	−	109.202i	−0.690303	−	0.398547i
$275$	303.991	+	46.2524i	1.10542	+	0.168190i
$276$		0			0
$277$	102.569	+	27.4833i	0.370285	+	0.0992175i	0.439163	−	0.898408i	$-0.355275\pi$
$277$	102.569	+	27.4833i	0.370285	+	0.0992175i	−0.0688778	+	0.997625i	$0.521942\pi$
$278$	−91.7838	−	91.7838i	−0.330157	−	0.330157i
$279$		0			0
$280$	47.9839	+	32.7639i	0.171371	+	0.117014i
$281$	0.574798	+	0.995579i	0.00204554	+	0.00354299i	0.867046	−	0.498227i	$-0.166016\pi$
$281$	0.574798	+	0.995579i	0.00204554	+	0.00354299i	−0.865001	+	0.501770i	$0.832682\pi$
$282$		0			0
$283$	−309.889	+	83.0344i	−1.09501	+	0.293408i	−0.760732	−	0.649066i	$-0.775160\pi$
$283$	−309.889	+	83.0344i	−1.09501	+	0.293408i	−0.334280	+	0.942474i	$0.608493\pi$
$284$	333.451	+	192.518i	1.17412	+	0.677880i
$285$		0			0
$286$	16.6627	+	28.8607i	0.0582613	+	0.100911i
$287$	−196.649	+	196.649i	−0.685189	+	0.685189i
$288$		0			0
$289$			177.173i			0.613056i
$290$	−37.0478	+	31.8374i	−0.127751	+	0.109784i
$291$		0			0
$292$	20.3505	+	75.9490i	0.0696934	+	0.260099i
$293$	−99.3033	+	26.6082i	−0.338919	+	0.0908131i	−0.424264	−	0.905538i	$-0.639467\pi$
$293$	−99.3033	+	26.6082i	−0.338919	+	0.0908131i	0.0853454	+	0.996351i	$0.472801\pi$
$294$		0			0
$295$	437.520	+	33.0939i	1.48312	+	0.112183i
$296$	3.58015			0.0120951
$297$		0			0
$298$	335.322	+	335.322i	1.12524	+	1.12524i
$299$	20.8124	−	12.0160i	0.0696066	−	0.0401874i
$300$		0			0
$301$	98.0259	−	169.786i	0.325667	−	0.564073i
$302$	28.6996	+	107.108i	0.0950319	+	0.354664i
$303$		0			0
$304$	314.896	−	181.805i	1.03584	−	0.598044i
$305$	326.411	+	222.876i	1.07020	+	0.730742i
$306$		0			0
$307$	−74.6079	+	74.6079i	−0.243023	+	0.243023i	−0.818099	−	0.575077i	$-0.804972\pi$
$307$	−74.6079	+	74.6079i	−0.243023	+	0.243023i	0.575077	+	0.818099i	$0.304972\pi$
$308$	164.539	−	614.067i	0.534216	−	1.99372i
$309$		0			0
$310$	138.000	−	393.502i	0.445161	−	1.26936i
$311$	298.630	−	517.242i	0.960225	−	1.66316i	0.238295	−	0.971193i	$-0.423411\pi$
$311$	298.630	−	517.242i	0.960225	−	1.66316i	0.721930	−	0.691966i	$-0.243255\pi$
$312$		0			0
$313$	−43.8958	+	163.821i	−0.140242	+	0.523391i	0.859679	+	0.510835i	$0.170664\pi$
$313$	−43.8958	+	163.821i	−0.140242	+	0.523391i	−0.999921	+	0.0125563i	$0.996003\pi$
$314$			188.115i			0.599091i
$315$		0			0
$316$	−131.689			−0.416736
$317$	394.769	+	105.778i	1.24533	+	0.333685i	0.820530	−	0.571603i	$-0.193678\pi$
$317$	394.769	+	105.778i	1.24533	+	0.333685i	0.424798	+	0.905288i	$0.360345\pi$
$318$		0			0
$319$	36.0394	+	20.8073i	0.112976	+	0.0652268i
$320$	−160.983	−	334.880i	−0.503071	−	1.04650i
$321$		0			0
$322$	−851.168	−	228.070i	−2.64338	−	0.708292i
$323$	187.060	+	187.060i	0.579133	+	0.579133i
$324$		0			0
$325$	−9.41081	+	21.4881i	−0.0289564	+	0.0661173i
$326$	−42.8466	−	74.2126i	−0.131431	−	0.227646i
$327$		0			0
$328$	−21.9859	+	5.89110i	−0.0670301	+	0.0179607i
$329$	−715.612	−	413.159i	−2.17511	−	1.25580i
$330$		0			0
$331$	−210.145	−	363.982i	−0.634879	−	1.09964i	−0.986541	−	0.163516i	$-0.947716\pi$
$331$	−210.145	−	363.982i	−0.634879	−	1.09964i	0.351661	−	0.936127i	$-0.385617\pi$
$332$	−465.783	+	465.783i	−1.40296	+	1.40296i
$333$		0			0
$334$		−	271.067i		−	0.811578i
$335$	−208.810	−	242.984i	−0.623314	−	0.725325i
$336$		0			0
$337$	−75.2392	−	280.796i	−0.223262	−	0.833224i	−0.983094	−	0.183104i	$-0.941385\pi$
$337$	−75.2392	−	280.796i	−0.223262	−	0.833224i	0.759832	−	0.650120i	$-0.225281\pi$
$338$	468.906	−	125.643i	1.38730	−	0.371725i
$339$		0			0
$340$	173.948	−	149.484i	0.511612	−	0.439658i
$341$	−355.248			−1.04178
$342$		0			0
$343$	−370.578	−	370.578i	−1.08040	−	1.08040i
$344$	13.8961	−	8.02293i	0.0403957	−	0.0233225i
$345$		0			0
$346$	−287.731	+	498.365i	−0.831592	+	1.44036i
$347$	142.089	+	530.282i	0.409477	+	1.52819i	0.795646	+	0.605762i	$0.207132\pi$
$347$	142.089	+	530.282i	0.409477	+	1.52819i	−0.386168	+	0.922428i	$0.626202\pi$
$348$		0			0
$349$	−377.101	+	217.720i	−1.08052	+	0.623838i	−0.931036	−	0.364926i	$-0.881094\pi$
$349$	−377.101	+	217.720i	−1.08052	+	0.623838i	−0.149483	+	0.988764i	$0.547761\pi$
$350$	801.141	−	313.138i	2.28897	−	0.894680i
$351$		0			0
$352$	−398.945	+	398.945i	−1.13337	+	1.13337i
$353$	−86.1412	+	321.483i	−0.244026	+	0.910718i	0.729844	+	0.683613i	$0.239593\pi$
$353$	−86.1412	+	321.483i	−0.244026	+	0.910718i	−0.973870	+	0.227104i	$0.927074\pi$
$354$		0			0
$355$	400.002	−	192.288i	1.12677	−	0.541656i
$356$	−255.690	+	442.869i	−0.718231	+	1.24401i
$357$		0			0
$358$	−34.0886	+	127.220i	−0.0952196	+	0.355364i
$359$		−	114.922i		−	0.320116i	−0.987108	−	0.160058i	$-0.948832\pi$
$359$		−	114.922i		−	0.320116i	0.987108	−	0.160058i	$-0.0511682\pi$
$360$		0			0
$361$	−264.815			−0.733559
$362$	292.281	+	78.3166i	0.807407	+	0.216344i
$363$		0			0
$364$	42.0022	+	24.2500i	0.115391	+	0.0666209i
$365$	85.5258	+	29.9936i	0.234317	+	0.0821743i
$366$		0			0
$367$	−505.064	−	135.331i	−1.37620	−	0.368750i	−0.506458	−	0.862265i	$-0.669045\pi$
$367$	−505.064	−	135.331i	−1.37620	−	0.368750i	−0.869738	+	0.493515i	$0.835712\pi$
$368$	263.226	+	263.226i	0.715289	+	0.715289i
$369$		0			0
$370$	29.8871	−	43.7708i	0.0807759	−	0.118299i
$371$	−233.301	−	404.089i	−0.628843	−	1.08919i
$372$		0			0
$373$	−205.720	+	55.1226i	−0.551529	+	0.147782i	−0.523812	−	0.851834i	$-0.675491\pi$
$373$	−205.720	+	55.1226i	−0.551529	+	0.147782i	−0.0277173	+	0.999616i	$0.508824\pi$
$374$	−325.251	−	187.784i	−0.869656	−	0.502096i
$375$		0			0
$376$	−33.8150	−	58.5693i	−0.0899336	−	0.155770i
$377$	−2.24492	+	2.24492i	−0.00595470	+	0.00595470i
$378$		0			0
$379$		−	672.519i		−	1.77446i	−0.461331	−	0.887228i	$-0.652628\pi$
$379$		−	672.519i		−	1.77446i	0.461331	−	0.887228i	$-0.347372\pi$
$380$	−40.9231	+	541.026i	−0.107692	+	1.42375i
$381$		0			0
$382$	75.7019	+	282.523i	0.198173	+	0.739590i
$383$	294.108	−	78.8060i	0.767906	−	0.205760i	0.146460	−	0.989217i	$-0.453212\pi$
$383$	294.108	−	78.8060i	0.767906	−	0.205760i	0.621446	+	0.783457i	$0.286545\pi$
$384$		0			0
$385$	−477.601	−	555.765i	−1.24052	−	1.44354i
$386$	816.881			2.11627
$387$		0			0
$388$	−58.6876	−	58.6876i	−0.151257	−	0.151257i
$389$	616.350	−	355.850i	1.58445	−	0.914780i	0.590247	−	0.807223i	$-0.299030\pi$
$389$	616.350	−	355.850i	1.58445	−	0.914780i	0.994199	−	0.107558i	$-0.0343031\pi$
$390$		0			0
$391$	−135.417	+	234.549i	−0.346335	+	0.599870i
$392$	−23.4696	−	87.5898i	−0.0598715	−	0.223443i
$393$		0			0
$394$	−18.6128	+	10.7461i	−0.0472406	+	0.0272744i
$395$	−85.5959	+	125.359i	−0.216699	+	0.317363i
$396$		0			0
$397$	−41.4605	+	41.4605i	−0.104435	+	0.104435i	−0.757393	−	0.652959i	$-0.773527\pi$
$397$	−41.4605	+	41.4605i	−0.104435	+	0.104435i	0.652959	+	0.757393i	$0.273527\pi$
$398$	−105.428	+	393.462i	−0.264894	+	0.988599i
$399$		0			0
$400$	−359.240	−	54.6584i	−0.898099	−	0.136646i
$401$	83.1858	−	144.082i	0.207446	−	0.359307i	−0.743463	−	0.668777i	$-0.766818\pi$
$401$	83.1858	−	144.082i	0.207446	−	0.359307i	0.950909	+	0.309470i	$0.100152\pi$
$402$		0			0
$403$	7.01451	−	26.1785i	0.0174057	−	0.0649591i
$404$		−	85.2394i		−	0.210989i
$405$		0			0
$406$	116.412			0.286729
$407$	−43.6140	−	11.6863i	−0.107160	−	0.0287133i
$408$		0			0
$409$	20.5577	+	11.8690i	0.0502632	+	0.0290195i	0.524921	−	0.851151i	$-0.324095\pi$
$409$	20.5577	+	11.8690i	0.0502632	+	0.0290195i	−0.474658	+	0.880170i	$0.657428\pi$
$410$	−111.514	+	317.978i	−0.271985	+	0.775556i
$411$		0			0
$412$	718.281	+	192.463i	1.74340	+	0.467143i
$413$	−739.382	−	739.382i	−1.79027	−	1.79027i
$414$		0			0
$415$	140.640	+	746.147i	0.338893	+	1.79794i
$416$	−21.5213	−	37.2759i	−0.0517338	−	0.0896056i
$417$		0			0
$418$	858.187	−	229.950i	2.05308	−	0.550121i
$419$	−432.642	−	249.786i	−1.03256	−	0.596147i	−0.114841	−	0.993384i	$-0.536636\pi$
$419$	−432.642	−	249.786i	−1.03256	−	0.596147i	−0.917716	+	0.397236i	$0.869969\pi$
$420$		0			0
$421$	1.90482	+	3.29924i	0.00452450	+	0.00783667i	0.868279	−	0.496077i	$-0.165226\pi$
$421$	1.90482	+	3.29924i	0.00452450	+	0.00783667i	−0.863754	+	0.503913i	$0.831893\pi$
$422$	−92.0983	+	92.0983i	−0.218242	+	0.218242i
$423$		0			0
$424$		−	38.1890i		−	0.0900685i
$425$	−29.2342	−	262.749i	−0.0687865	−	0.618234i
$426$		0			0
$427$	−243.786	−	909.822i	−0.570928	−	2.13073i
$428$	62.7149	−	16.8044i	0.146530	−	0.0392626i
$429$		0			0
$430$	17.9168	−	236.869i	0.0416669	−	0.550859i
$431$	−767.834			−1.78152			−0.890759	−	0.454477i	$-0.849826\pi$
$431$	−767.834			−1.78152			−0.890759	+	0.454477i	$0.849826\pi$
$432$		0			0
$433$	367.840	+	367.840i	0.849516	+	0.849516i	0.990073	−	0.140557i	$-0.0448893\pi$
$433$	367.840	+	367.840i	0.849516	+	0.849516i	−0.140557	+	0.990073i	$0.544889\pi$
$434$	−860.622	+	496.880i	−1.98300	+	1.14489i
$435$		0			0
$436$	−19.6945	+	34.1118i	−0.0451708	+	0.0782381i
$437$	−165.825	−	618.867i	−0.379462	−	1.41617i
$438$		0			0
$439$	119.042	−	68.7289i	0.271166	−	0.156558i	−0.358251	−	0.933625i	$-0.616627\pi$
$439$	119.042	−	68.7289i	0.271166	−	0.156558i	0.629418	+	0.777067i	$0.283294\pi$
$440$	−11.1090	−	58.9372i	−0.0252478	−	0.133948i
$441$		0			0
$442$	20.2602	−	20.2602i	0.0458375	−	0.0458375i
$443$	−114.403	+	426.956i	−0.258245	+	0.963783i	0.708011	+	0.706201i	$0.249592\pi$
$443$	−114.403	+	426.956i	−0.258245	+	0.963783i	−0.966256	+	0.257582i	$0.917074\pi$
$444$		0			0
$445$	255.385	+	531.259i	0.573899	+	1.19384i
$446$	8.10216	−	14.0334i	0.0181663	−	0.0314649i
$447$		0			0
$448$	−229.181	+	855.314i	−0.511564	+	1.90918i
$449$		−	827.291i		−	1.84252i	−0.388949	−	0.921259i	$-0.627162\pi$
$449$		−	827.291i		−	1.84252i	0.388949	−	0.921259i	$-0.372838\pi$
$450$		0			0
$451$	287.066			0.636509
$452$	−644.769	−	172.765i	−1.42648	−	0.382224i
$453$		0			0
$454$	190.084	+	109.745i	0.418688	+	0.241730i
$455$	50.3852	−	24.2210i	0.110737	−	0.0532331i
$456$		0			0
$457$	855.367	+	229.195i	1.87170	+	0.501521i	0.999933	+	0.0116012i	$0.00369286\pi$
$457$	855.367	+	229.195i	1.87170	+	0.501521i	0.871768	+	0.489919i	$0.162974\pi$
$458$	112.685	+	112.685i	0.246038	+	0.246038i
$459$		0			0
$460$	−545.862	+	102.889i	−1.18666	+	0.223672i
$461$	−130.919	−	226.759i	−0.283990	−	0.491885i	0.688374	−	0.725356i	$-0.258325\pi$
$461$	−130.919	−	226.759i	−0.283990	−	0.491885i	−0.972364	+	0.233471i	$0.924992\pi$
$462$		0			0
$463$	−162.814	+	43.6260i	−0.351651	+	0.0942246i	−0.430321	−	0.902676i	$-0.641599\pi$
$463$	−162.814	+	43.6260i	−0.351651	+	0.0942246i	0.0786695	+	0.996901i	$0.474933\pi$
$464$	−42.5893	−	24.5889i	−0.0917872	−	0.0529934i
$465$		0			0
$466$	−197.000	−	341.213i	−0.422746	−	0.732217i
$467$	−63.7603	+	63.7603i	−0.136532	+	0.136532i	−0.772070	−	0.635538i	$-0.780778\pi$
$467$	−63.7603	+	63.7603i	−0.136532	+	0.136532i	0.635538	+	0.772070i	$0.280778\pi$
$468$		0			0
$469$			763.505i			1.62794i
$470$	−998.356	−	75.5155i	−2.12416	−	0.160671i
$471$		0			0
$472$	−22.1499	−	82.6647i	−0.0469278	−	0.175137i
$473$	−195.474	+	52.3770i	−0.413264	+	0.110734i
$474$		0			0
$475$	488.420	+	390.616i	1.02825	+	0.822349i
$476$	−546.580			−1.14828
$477$		0			0
$478$	−301.013	−	301.013i	−0.629734	−	0.629734i
$479$	33.6305	−	19.4166i	0.0702099	−	0.0405357i	−0.464484	−	0.885581i	$-0.653760\pi$
$479$	33.6305	−	19.4166i	0.0702099	−	0.0405357i	0.534694	+	0.845046i	$0.320427\pi$
$480$		0			0
$481$	1.72235	−	2.98320i	0.00358077	−	0.00620208i
$482$	−268.295	−	1001.29i	−0.556628	−	2.07736i
$483$		0			0
$484$	−113.750	+	65.6736i	−0.235021	+	0.135689i
$485$	−94.0127	+	17.7204i	−0.193841	+	0.0365369i
$486$		0			0
$487$	394.799	−	394.799i	0.810676	−	0.810676i	−0.174059	−	0.984735i	$-0.555688\pi$
$487$	394.799	−	394.799i	0.810676	−	0.810676i	0.984735	+	0.174059i	$0.0556883\pi$
$488$	19.9527	−	74.4644i	0.0408867	−	0.152591i
$489$		0			0
$490$	−1266.80	−	444.262i	−2.58530	−	0.906656i
$491$	−230.371	+	399.015i	−0.469188	+	0.812658i	−0.999380	−	0.0352201i	$-0.988787\pi$
$491$	−230.371	+	399.015i	−0.469188	+	0.812658i	0.530191	+	0.847878i	$0.322120\pi$
$492$		0			0
$493$	9.26030	−	34.5599i	0.0187836	−	0.0701012i
$494$			67.7810i			0.137209i
$495$		0			0
$496$	419.811			0.846394
$497$	−1021.64	−	273.748i	−2.05561	−	0.550800i
$498$		0			0
$499$	736.679	+	425.322i	1.47631	+	0.852349i	0.999643	−	0.0267345i	$-0.00851087\pi$
$499$	736.679	+	425.322i	1.47631	+	0.852349i	0.476669	+	0.879083i	$0.341844\pi$
$500$	369.631	−	396.703i	0.739262	−	0.793405i
$501$		0			0
$502$	429.640	+	115.122i	0.855857	+	0.229326i
$503$	196.093	+	196.093i	0.389847	+	0.389847i	0.874633	−	0.484786i	$-0.161103\pi$
$503$	196.093	+	196.093i	0.389847	+	0.389847i	−0.484786	+	0.874633i	$0.661103\pi$
$504$		0			0
$505$	−81.1420	−	55.4045i	−0.160677	−	0.109712i
$506$	454.795	+	787.728i	0.898804	+	1.55677i
$507$		0			0
$508$	−682.429	+	182.856i	−1.34336	+	0.359953i
$509$	338.026	+	195.159i	0.664098	+	0.383417i	0.793837	−	0.608131i	$-0.208080\pi$
$509$	338.026	+	195.159i	0.664098	+	0.383417i	−0.129738	+	0.991548i	$0.541414\pi$
$510$		0			0
$511$	−107.995	−	187.052i	−0.211340	−	0.366051i
$512$	511.543	−	511.543i	0.999108	−	0.999108i
$513$		0			0
$514$		−	997.044i		−	1.93977i
$515$	650.085	−	558.656i	1.26230	−	1.08477i
$516$		0			0
$517$	220.758	+	823.881i	0.426999	+	1.59358i
$518$	−122.005	+	32.6910i	−0.235530	+	0.0631101i
$519$		0			0
$520$	4.56249	+	0.345106i	0.00877401	+	0.000663665i
$521$	679.963			1.30511			0.652556	−	0.757741i	$-0.273697\pi$
$521$	679.963			1.30511			0.652556	+	0.757741i	$0.273697\pi$
$522$		0			0
$523$	442.612	+	442.612i	0.846295	+	0.846295i	0.989669	−	0.143374i	$-0.0457951\pi$
$523$	442.612	+	442.612i	0.846295	+	0.846295i	−0.143374	+	0.989669i	$0.545795\pi$
$524$	70.8410	−	40.9001i	0.135193	−	0.0780536i
$525$		0			0
$526$	376.307	−	651.783i	0.715413	−	1.23913i
$527$	79.0514	+	295.024i	0.150003	+	0.559818i
$528$		0			0
$529$	109.929	−	63.4674i	0.207805	−	0.119976i
$530$	−466.899	−	318.803i	−0.880941	−	0.601514i
$531$		0			0
$532$	914.300	−	914.300i	1.71861	−	1.71861i
$533$	−5.66823	+	21.1541i	−0.0106346	+	0.0396888i
$534$		0			0
$535$	24.7672	−	70.6229i	0.0462939	−	0.132005i
$536$	−31.2445	+	54.1171i	−0.0582921	+	0.100965i
$537$		0			0
$538$	−145.609	+	543.421i	−0.270649	+	1.01008i
$539$			1143.64i			2.12179i
$540$		0			0
$541$	780.447			1.44260			0.721300	−	0.692623i	$-0.243545\pi$
$541$	780.447			1.44260			0.721300	+	0.692623i	$0.243545\pi$
$542$	856.624	+	229.532i	1.58049	+	0.423490i
$543$		0			0
$544$	420.088	+	242.538i	0.772221	+	0.445842i
$545$	19.6709	+	40.9200i	0.0360935	+	0.0750826i
$546$		0			0
$547$	335.470	+	89.8890i	0.613291	+	0.164331i	0.552076	−	0.833794i	$-0.313836\pi$
$547$	335.470	+	89.8890i	0.613291	+	0.164331i	0.0612152	+	0.998125i	$0.480502\pi$
$548$	231.998	+	231.998i	0.423354	+	0.423354i
$549$		0			0
$550$	−813.304	−	356.190i	−1.47873	−	0.647618i
$551$	42.3203	+	73.3009i	0.0768063	+	0.133032i
$552$		0			0
$553$	349.418	−	93.6263i	0.631859	−	0.169306i
$554$	−265.538	−	153.308i	−0.479311	−	0.276730i
$555$		0			0
$556$	97.4968	+	168.869i	0.175354	+	0.303722i
$557$	670.322	−	670.322i	1.20345	−	1.20345i	0.230341	−	0.973110i	$-0.426016\pi$
$557$	670.322	−	670.322i	1.20345	−	1.20345i	0.973110	−	0.230341i	$-0.0739840\pi$
$558$		0			0
$559$		−	15.4388i		−	0.0276187i
$560$	564.402	+	656.771i	1.00786	+	1.17281i
$561$		0			0
$562$	−0.859143	−	3.20637i	−0.00152872	−	0.00570528i
$563$	−420.955	+	112.795i	−0.747700	+	0.200346i	−0.612498	−	0.790472i	$-0.709835\pi$
$563$	−420.955	+	112.795i	−0.747700	+	0.200346i	−0.135202	+	0.990818i	$0.543168\pi$
$564$		0			0
$565$	−583.552	+	501.481i	−1.03284	+	0.887576i
$566$	926.373			1.63670
$567$		0			0
$568$	−61.2113	−	61.2113i	−0.107766	−	0.107766i
$569$	−670.282	+	386.987i	−1.17800	+	0.680118i	−0.955551	−	0.294826i	$-0.904738\pi$
$569$	−670.282	+	386.987i	−1.17800	+	0.680118i	−0.222448	+	0.974944i	$0.571405\pi$
$570$		0			0
$571$	−233.901	+	405.128i	−0.409633	+	0.709506i	−0.994849	−	0.101372i	$-0.967677\pi$
$571$	−233.901	+	405.128i	−0.409633	+	0.709506i	0.585215	+	0.810878i	$0.301010\pi$
$572$	−12.9572	−	48.3570i	−0.0226525	−	0.0845402i
$573$		0			0
$574$	695.444	−	401.515i	1.21158	−	0.699503i
$575$	−256.860	+	586.500i	−0.446713	+	1.02000i
$576$		0			0
$577$	272.029	−	272.029i	0.471454	−	0.471454i	−0.430931	−	0.902385i	$-0.641815\pi$
$577$	272.029	−	272.029i	0.471454	−	0.471454i	0.902385	+	0.430931i	$0.141815\pi$
$578$	132.409	−	494.158i	0.229082	−	0.854945i
$579$		0			0
$580$	66.1370	−	31.7932i	0.114029	−	0.0548159i
$581$	904.737	−	1567.05i	1.55721	−	2.69716i
$582$		0			0
$583$	−124.657	+	465.226i	−0.213820	+	0.797986i
$584$		−	17.6776i		−	0.0302699i
$585$		0			0
$586$	296.855			0.506578
$587$	136.489	+	36.5721i	0.232520	+	0.0623034i	0.373197	−	0.927752i	$-0.378261\pi$
$587$	136.489	+	36.5721i	0.232520	+	0.0623034i	−0.140678	+	0.990055i	$0.544928\pi$
$588$		0			0
$589$	−625.740	−	361.271i	−1.06238	−	0.613363i
$590$	−1195.57	−	419.281i	−2.02638	−	0.710646i
$591$		0			0
$592$	51.5405	+	13.8102i	0.0870617	+	0.0233281i
$593$	94.3094	+	94.3094i	0.159038	+	0.159038i	0.782140	−	0.623102i	$-0.214128\pi$
$593$	94.3094	+	94.3094i	0.159038	+	0.159038i	−0.623102	+	0.782140i	$0.714128\pi$
$594$		0			0
$595$	−355.270	+	520.307i	−0.597093	+	0.874465i
$596$	−356.194	−	616.946i	−0.597641	−	1.03514i
$597$		0			0
$598$	−67.0285	+	17.9602i	−0.112088	+	0.0300338i
$599$	723.537	+	417.734i	1.20791	+	0.697386i	0.962302	−	0.271984i	$-0.0876797\pi$
$599$	723.537	+	417.734i	1.20791	+	0.697386i	0.245606	+	0.969370i	$0.421013\pi$
$600$		0			0
$601$	−179.809	−	311.438i	−0.299183	−	0.518200i	0.676766	−	0.736198i	$-0.263381\pi$
$601$	−179.809	−	311.438i	−0.299183	−	0.518200i	−0.975949	+	0.217998i	$0.930047\pi$
$602$	−400.295	+	400.295i	−0.664942	+	0.664942i
$603$		0			0
$604$		−	166.579i		−	0.275793i
$605$	−11.4193	+	150.969i	−0.0188748	+	0.249536i
$606$		0			0
$607$	133.400	+	497.854i	0.219769	+	0.820188i	0.984433	+	0.175759i	$0.0562380\pi$
$607$	133.400	+	497.854i	0.219769	+	0.820188i	−0.764665	+	0.644428i	$0.777095\pi$
$608$	−1108.42	+	297.000i	−1.82306	+	0.488486i
$609$		0			0
$610$	−743.836	−	865.571i	−1.21940	−	1.41897i
$611$	−65.0715			−0.106500
$612$		0			0
$613$	−470.150	−	470.150i	−0.766965	−	0.766965i	0.210606	−	0.977571i	$-0.432456\pi$
$613$	−470.150	−	470.150i	−0.766965	−	0.766965i	−0.977571	+	0.210606i	$0.932456\pi$
$614$	263.849	−	152.333i	0.429721	−	0.248099i
$615$		0			0
$616$	−71.4640	+	123.779i	−0.116013	+	0.200940i
$617$	65.6036	+	244.836i	0.106327	+	0.396817i	0.998492	−	0.0548918i	$-0.0174814\pi$
$617$	65.6036	+	244.836i	0.106327	+	0.396817i	−0.892166	+	0.451708i	$0.850815\pi$
$618$		0			0
$619$	−88.9466	+	51.3534i	−0.143694	+	0.0829618i	−0.570123	−	0.821559i	$-0.693105\pi$
$619$	−88.9466	+	51.3534i	−0.143694	+	0.0829618i	0.426429	+	0.904521i	$0.359771\pi$
$620$	−353.242	+	517.337i	−0.569745	+	0.834414i
$621$		0			0
$622$	−1219.47	+	1219.47i	−1.96057	+	1.96057i
$623$	363.575	−	1356.88i	0.583587	−	2.17798i
$624$		0			0
$625$	−137.378	−	609.715i	−0.219805	−	0.975544i
$626$	244.862	−	424.113i	0.391153	−	0.677497i
$627$		0			0
$628$	73.1406	−	272.964i	0.116466	−	0.434657i
$629$			38.8208i			0.0617183i
$630$		0			0
$631$	−1201.04			−1.90339			−0.951696	−	0.307042i	$-0.900661\pi$
$631$	−1201.04			−1.90339			−0.951696	+	0.307042i	$0.900661\pi$
$632$	28.5981	+	7.66285i	0.0452502	+	0.0121248i
$633$		0			0
$634$	−1022.01	−	590.056i	−1.61200	−	0.930688i
$635$	−269.503	+	768.479i	−0.424415	+	1.21020i
$636$		0			0
$637$	−84.2762	−	22.5817i	−0.132302	−	0.0354501i
$638$	−84.9681	−	84.9681i	−0.133179	−	0.133179i
$639$		0			0
$640$	28.7994	+	152.791i	0.0449991	+	0.238736i
$641$	−285.201	−	493.982i	−0.444931	−	0.770643i	0.553117	−	0.833104i	$-0.313438\pi$
$641$	−285.201	−	493.982i	−0.444931	−	0.770643i	−0.998047	+	0.0624611i	$0.980105\pi$
$642$		0			0
$643$	856.111	−	229.394i	1.33143	−	0.356756i	0.478183	−	0.878260i	$-0.341296\pi$
$643$	856.111	−	229.394i	1.33143	−	0.356756i	0.853249	+	0.521504i	$0.174629\pi$
$644$	1146.41	+	661.883i	1.78015	+	1.02777i
$645$		0			0
$646$	−381.936	−	661.532i	−0.591232	−	1.02404i
$647$	−254.010	+	254.010i	−0.392596	+	0.392596i	−0.875612	−	0.483016i	$-0.839541\pi$
$647$	−254.010	+	254.010i	−0.392596	+	0.392596i	0.483016	+	0.875612i	$0.339541\pi$
$648$		0			0
$649$			1079.34i			1.66308i
$650$	42.3070	−	52.9000i	0.0650876	−	0.0813845i
$651$		0			0
$652$	33.3183	+	124.346i	0.0511017	+	0.190714i
$653$	−295.968	+	79.3045i	−0.453244	+	0.121446i	−0.478217	−	0.878242i	$-0.658717\pi$
$653$	−295.968	+	79.3045i	−0.453244	+	0.121446i	0.0249729	+	0.999688i	$0.492050\pi$
$654$		0			0
$655$	7.11168	−	94.0203i	0.0108575	−	0.143542i
$656$	−339.238			−0.517131
$657$		0			0
$658$	1687.16	+	1687.16i	2.56407	+	2.56407i
$659$	−344.367	+	198.821i	−0.522561	+	0.301701i	−0.737982	−	0.674821i	$-0.764221\pi$
$659$	−344.367	+	198.821i	−0.522561	+	0.301701i	0.215421	+	0.976521i	$0.430888\pi$
$660$		0			0
$661$	347.289	−	601.522i	0.525399	−	0.910019i	−0.474163	−	0.880437i	$-0.657249\pi$
$661$	347.289	−	601.522i	0.525399	−	0.910019i	0.999562	−	0.0295815i	$-0.00941745\pi$
$662$	314.101	+	1172.24i	0.474473	+	1.77076i
$663$		0			0
$664$	128.255	−	74.0482i	0.193156	−	0.111518i
$665$	−276.067	−	1464.63i	−0.415139	−	2.20246i
$666$		0			0
$667$	−61.2733	+	61.2733i	−0.0918640	+	0.0918640i
$668$	−105.393	+	393.333i	−0.157774	+	0.588821i
$669$		0			0
$670$	400.806	+	833.766i	0.598217	+	1.24443i
$671$	−486.135	+	842.010i	−0.724493	+	1.25486i
$672$		0			0
$673$	−43.7189	+	163.161i	−0.0649612	+	0.242439i	−0.990770	−	0.135554i	$-0.956719\pi$
$673$	−43.7189	+	163.161i	−0.0649612	+	0.242439i	0.925809	+	0.377992i	$0.123385\pi$
$674$			839.406i			1.24541i
$675$		0			0
$676$	−729.259			−1.07879
$677$	252.537	+	67.6670i	0.373023	+	0.0999513i	0.440460	−	0.897772i	$-0.354815\pi$
$677$	252.537	+	67.6670i	0.373023	+	0.0999513i	−0.0674366	+	0.997724i	$0.521482\pi$
$678$		0			0
$679$	197.445	+	113.995i	0.290787	+	0.167886i
$680$	−46.4738	+	22.3407i	−0.0683438	+	0.0328540i
$681$		0			0
$682$	990.830	+	265.492i	1.45283	+	0.389285i
$683$	−545.616	−	545.616i	−0.798852	−	0.798852i	0.184062	−	0.982915i	$-0.441075\pi$
$683$	−545.616	−	545.616i	−0.798852	−	0.798852i	−0.982915	+	0.184062i	$0.941075\pi$
$684$		0			0
$685$	371.642	−	70.0505i	0.542543	−	0.102263i
$686$	756.640	+	1310.54i	1.10297	+	1.91041i
$687$		0			0
$688$	231.000	−	61.8962i	0.335755	−	0.0899654i
$689$	−31.8215	−	18.3722i	−0.0461851	−	0.0266650i
$690$		0			0
$691$	−178.080	−	308.443i	−0.257713	−	0.446372i	0.707916	−	0.706297i	$-0.249636\pi$
$691$	−178.080	−	308.443i	−0.257713	−	0.446372i	−0.965629	+	0.259925i	$0.916302\pi$
$692$	611.281	−	611.281i	0.883355	−	0.883355i
$693$		0			0
$694$		−	1585.21i		−	2.28417i
$695$	224.124	+	16.9527i	0.322480	+	0.0243924i
$696$		0			0
$697$	−63.8792	−	238.401i	−0.0916488	−	0.342038i
$698$	1214.49	−	325.423i	1.73996	−	0.466222i
$699$		0			0
$700$	−1284.25	+	142.889i	−1.83464	+	0.204128i
$701$	−357.763			−0.510361			−0.255180	−	0.966893i	$-0.582135\pi$
$701$	−357.763			−0.510361			−0.255180	+	0.966893i	$0.582135\pi$
$702$		0			0
$703$	−64.9380	−	64.9380i	−0.0923727	−	0.0923727i
$704$	791.564	−	457.010i	1.12438	−	0.649161i
$705$		0			0
$706$	480.517	−	832.280i	0.680619	−	1.17887i
$707$	60.6024	+	226.171i	0.0857177	+	0.319903i
$708$		0			0
$709$	324.344	−	187.260i	0.457467	−	0.264119i	−0.253511	−	0.967332i	$-0.581586\pi$
$709$	324.344	−	187.260i	0.457467	−	0.264119i	0.710979	+	0.703213i	$0.248252\pi$
$710$	−1259.36	+	237.376i	−1.77375	+	0.334332i
$711$		0			0
$712$	81.2971	−	81.2971i	0.114181	−	0.114181i
$713$	191.455	−	714.520i	0.268520	−	1.00213i
$714$		0			0
$715$	−54.4545	−	19.0970i	−0.0761602	−	0.0267091i
$716$	98.9288	−	171.350i	0.138169	−	0.239315i
$717$		0			0
$718$	−85.8861	+	320.531i	−0.119619	+	0.446422i
$719$			889.235i			1.23677i	0.785877	+	0.618383i	$0.212212\pi$
$719$			889.235i			1.23677i	−0.785877	+	0.618383i	$0.787788\pi$
$720$		0			0
$721$	−2042.70			−2.83314
$722$	738.601	+	197.908i	1.02299	+	0.274110i
$723$		0			0
$724$	−393.666	−	227.283i	−0.543737	−	0.313927i
$725$	12.7233	−	83.6231i	0.0175493	−	0.115342i
$726$		0			0
$727$	−433.617	−	116.187i	−0.596447	−	0.159818i	−0.0520491	−	0.998645i	$-0.516575\pi$
$727$	−433.617	−	116.187i	−0.596447	−	0.159818i	−0.544398	+	0.838827i	$0.683242\pi$
$728$	−7.71032	−	7.71032i	−0.0105911	−	0.0105911i
$729$		0			0
$730$	−216.127	−	147.573i	−0.296064	−	0.202155i
$731$	86.9955	+	150.681i	0.119009	+	0.206129i
$732$		0			0
$733$	−664.342	+	178.010i	−0.906333	+	0.242851i	−0.681734	−	0.731600i	$-0.738774\pi$
$733$	−664.342	+	178.010i	−0.906333	+	0.242851i	−0.224599	+	0.974451i	$0.572107\pi$
$734$	1307.55	+	754.912i	1.78140	+	1.02849i
$735$		0			0
$736$	−587.404	−	1017.41i	−0.798104	−	1.38236i
$737$	557.276	−	557.276i	0.756141	−	0.756141i
$738$		0			0
$739$		−	337.793i		−	0.457095i	−0.973533	−	0.228547i	$-0.926602\pi$
$739$		−	337.793i		−	0.457095i	0.973533	−	0.228547i	$-0.0733976\pi$
$740$	−60.3862	+	51.8934i	−0.0816030	+	0.0701262i
$741$		0			0
$742$	348.712	+	1301.41i	0.469962	+	1.75392i
$743$	−101.468	+	27.1883i	−0.136565	+	0.0365926i	−0.326454	−	0.945213i	$-0.605854\pi$
$743$	−101.468	+	27.1883i	−0.136565	+	0.0365926i	0.189889	+	0.981806i	$0.439187\pi$
$744$		0			0
$745$	−818.812	−	61.9348i	−1.09908	−	0.0831340i
$746$	614.975			0.824364
$747$		0			0
$748$	398.945	+	398.945i	0.533349	+	0.533349i
$749$	−154.458	+	89.1765i	−0.206219	+	0.119061i
$750$		0			0
$751$	−370.192	+	641.191i	−0.492932	+	0.853783i	−0.999967	−	0.00814279i	$-0.997408\pi$
$751$	−370.192	+	641.191i	−0.492932	+	0.853783i	0.507035	+	0.861925i	$0.330741\pi$
$752$	−260.880	−	973.616i	−0.346914	−	1.29470i
$753$		0			0
$754$	7.93910	−	4.58364i	0.0105293	−	0.00607910i
$755$	−158.571	−	108.274i	−0.210028	−	0.143409i
$756$		0			0
$757$	957.088	−	957.088i	1.26432	−	1.26432i	0.315337	−	0.948980i	$-0.397882\pi$
$757$	957.088	−	957.088i	1.26432	−	1.26432i	0.948980	−	0.315337i	$-0.102118\pi$
$758$	−502.603	+	1875.74i	−0.663065	+	2.47459i
$759$		0			0
$760$	40.3689	−	115.110i	0.0531169	−	0.151461i
$761$	−202.869	+	351.380i	−0.266582	+	0.461734i	−0.967977	−	0.251039i	$-0.919228\pi$
$761$	−202.869	+	351.380i	−0.266582	+	0.461734i	0.701395	+	0.712773i	$0.252561\pi$
$762$		0			0
$763$	28.0042	−	104.513i	0.0367028	−	0.136977i
$764$		−	439.390i		−	0.575118i
$765$		0			0
$766$	−879.199			−1.14778
$767$	−79.5374	−	21.3120i	−0.103699	−	0.0277861i
$768$		0			0
$769$	731.602	+	422.391i	0.951368	+	0.549273i	0.893506	−	0.449052i	$-0.148238\pi$
$769$	731.602	+	422.391i	0.951368	+	0.549273i	0.0578626	+	0.998325i	$0.481571\pi$
$770$	916.742	+	1907.03i	1.19057	+	2.47666i
$771$		0			0
$772$	−1185.34	−	317.610i	−1.53541	−	0.411412i
$773$	−501.313	−	501.313i	−0.648529	−	0.648529i	0.304108	−	0.952637i	$-0.401642\pi$
$773$	−501.313	−	501.313i	−0.648529	−	0.648529i	−0.952637	+	0.304108i	$0.901642\pi$
$774$		0			0
$775$	262.866	+	672.524i	0.339182	+	0.867773i
$776$	9.32990	+	16.1599i	0.0120231	+	0.0208246i
$777$		0			0
$778$	−1985.02	+	531.884i	−2.55144	+	0.683655i
$779$	505.643	+	291.933i	0.649092	+	0.374754i
$780$		0			0
$781$	545.881	+	945.494i	0.698951	+	1.21062i
$782$	552.984	−	552.984i	0.707141	−	0.707141i
$783$		0			0
$784$		−	1351.49i		−	1.72384i
$785$	−212.303	−	247.048i	−0.270449	−	0.314711i
$786$		0			0
$787$	−263.430	−	983.133i	−0.334726	−	1.24922i	−0.904165	−	0.427183i	$-0.859506\pi$
$787$	−263.430	−	983.133i	−0.334726	−	1.24922i	0.569439	−	0.822034i	$-0.307161\pi$
$788$	31.1863	−	8.35636i	0.0395766	−	0.0106045i
$789$		0			0
$790$	332.424	−	285.671i	0.420789	−	0.361609i
$791$	1833.64			2.31813
$792$		0			0
$793$	−52.4495	−	52.4495i	−0.0661406	−	0.0661406i
$794$	146.624	−	84.6533i	0.184665	−	0.106616i
$795$		0			0
$796$	305.963	−	529.943i	0.384376	−	0.665758i
$797$	−369.343	−	1378.41i	−0.463416	−	1.72949i	−0.662087	−	0.749427i	$-0.730329\pi$
$797$	−369.343	−	1378.41i	−0.463416	−	1.72949i	0.198670	−	0.980066i	$-0.436338\pi$
$798$		0			0
$799$	635.088	−	366.668i	0.794854	−	0.458909i
$800$	1050.45	+	460.048i	1.31306	+	0.575060i
$801$		0			0
$802$	−339.695	+	339.695i	−0.423559	+	0.423559i
$803$	−57.7035	+	215.352i	−0.0718599	+	0.268185i
$804$		0			0
$805$	1375.22	−	661.093i	1.70835	−	0.821233i
$806$	−39.1287	+	67.7729i	−0.0485468	+	0.0840855i
$807$		0			0
$808$	−4.96001	+	18.5110i	−0.00613862	+	0.0229097i
$809$		−	549.873i		−	0.679694i	−0.940481	−	0.339847i	$-0.889625\pi$
$809$		−	549.873i		−	0.679694i	0.940481	−	0.339847i	$-0.110375\pi$
$810$		0			0
$811$	1542.32			1.90175			0.950876	−	0.309573i	$-0.100186\pi$
$811$	1542.32			1.90175			0.950876	+	0.309573i	$0.100186\pi$
$812$	−168.920	−	45.2619i	−0.208029	−	0.0557413i
$813$		0			0
$814$	112.911	+	65.1893i	0.138711	+	0.0800851i
$815$	140.025	+	49.1063i	0.171810	+	0.0602531i
$816$		0			0
$817$	−397.576	−	106.530i	−0.486629	−	0.130392i
$818$	−48.4677	−	48.4677i	−0.0592514	−	0.0592514i
$819$		0			0
$820$	285.445	−	418.045i	0.348104	−	0.509811i
$821$	405.012	+	701.501i	0.493316	+	0.854448i	0.999970	−	0.00770144i	$-0.00245147\pi$
$821$	405.012	+	701.501i	0.493316	+	0.854448i	−0.506655	+	0.862149i	$0.669118\pi$
$822$		0			0
$823$	79.3084	−	21.2506i	0.0963650	−	0.0258209i	−0.210314	−	0.977634i	$-0.567449\pi$
$823$	79.3084	−	21.2506i	0.0963650	−	0.0258209i	0.306679	+	0.951813i	$0.400782\pi$
$824$	−144.786	−	83.5923i	−0.175711	−	0.101447i
$825$		0			0
$826$	1509.66	+	2614.80i	1.82767	+	3.16562i
$827$	−924.549	+	924.549i	−1.11796	+	1.11796i	−0.125915	+	0.992041i	$0.540187\pi$
$827$	−924.549	+	924.549i	−1.11796	+	1.11796i	−0.992041	+	0.125915i	$0.959813\pi$
$828$		0			0
$829$			114.907i			0.138610i	0.997596	+	0.0693048i	$0.0220781\pi$
$829$			114.907i			0.138610i	−0.997596	+	0.0693048i	$0.977922\pi$
$830$	165.364	−	2186.20i	0.199234	−	2.63398i
$831$		0			0
$832$	18.0477	+	67.3549i	0.0216919	+	0.0809554i
$833$	949.767	−	254.489i	1.14018	−	0.305509i
$834$		0			0
$835$	305.921	+	355.988i	0.366373	+	0.426333i
$836$	−1334.68			−1.59651
$837$		0			0
$838$	1020.02	+	1020.02i	1.21720	+	1.21720i
$839$	661.782	−	382.080i	0.788774	−	0.455399i	−0.0507566	−	0.998711i	$-0.516163\pi$
$839$	661.782	−	382.080i	0.788774	−	0.455399i	0.839531	+	0.543312i	$0.182830\pi$
$840$		0			0
$841$	−414.776	+	718.414i	−0.493194	+	0.854237i
$842$	−2.84711	−	10.6255i	−0.00338136	−	0.0126194i
$843$		0			0
$844$	169.448	−	97.8309i	0.200768	−	0.115913i
$845$	−474.009	+	694.204i	−0.560957	+	0.821544i
$846$		0			0
$847$	255.128	−	255.128i	0.301214	−	0.301214i
$848$	147.312	−	549.777i	0.173717	−	0.648322i
$849$		0			0
$850$	−114.826	+	754.689i	−0.135089	+	0.887869i
$851$	47.0101	−	81.4239i	0.0552410	−	0.0956803i
$852$		0			0
$853$	190.285	−	710.152i	0.223077	−	0.832534i	−0.760089	−	0.649819i	$-0.774845\pi$
$853$	190.285	−	710.152i	0.223077	−	0.832534i	0.983166	−	0.182715i	$-0.0584887\pi$
$854$			2719.80i			3.18478i
$855$		0			0
$856$	−14.5973			−0.0170529
$857$	694.443	+	186.075i	0.810319	+	0.217124i	0.640109	−	0.768284i	$-0.278889\pi$
$857$	694.443	+	186.075i	0.810319	+	0.217124i	0.170209	+	0.985408i	$0.445556\pi$
$858$		0			0
$859$	−1043.29	−	602.342i	−1.21454	−	0.701213i	−0.250792	−	0.968041i	$-0.580691\pi$
$859$	−1043.29	−	602.342i	−1.21454	−	0.701213i	−0.963744	+	0.266828i	$0.914025\pi$
$860$	−118.095	+	336.744i	−0.137320	+	0.391563i
$861$		0			0
$862$	2141.58	+	573.836i	2.48444	+	0.665703i
$863$	214.571	+	214.571i	0.248634	+	0.248634i	0.820410	−	0.571776i	$-0.193745\pi$
$863$	214.571	+	214.571i	0.248634	+	0.248634i	−0.571776	+	0.820410i	$0.693745\pi$
$864$		0			0
$865$	−184.573	−	979.223i	−0.213379	−	1.13205i
$866$	−751.049	−	1300.86i	−0.867263	−	1.50214i
$867$		0			0
$868$	1442.00	−	386.382i	1.66129	−	0.445141i
$869$	−323.375	−	186.701i	−0.372123	−	0.214845i
$870$		0			0
$871$	30.0625	+	52.0698i	0.0345150	+	0.0597817i
$872$	6.26188	−	6.26188i	0.00718106	−	0.00718106i
$873$		0			0
$874$			1850.02i			2.11673i
$875$	−698.724	+	1315.39i	−0.798542	+	1.50331i
$876$		0			0
$877$	−81.8801	−	305.581i	−0.0933638	−	0.348438i	0.903402	−	0.428794i	$-0.141061\pi$
$877$	−81.8801	−	305.581i	−0.0933638	−	0.348438i	−0.996766	+	0.0803551i	$0.974395\pi$
$878$	−383.387	+	102.728i	−0.436660	+	0.117003i
$879$		0			0
$880$	67.4197	−	891.325i	0.0766133	−	1.01287i
$881$	435.585			0.494421			0.247211	−	0.968962i	$-0.420486\pi$
$881$	435.585			0.494421			0.247211	+	0.968962i	$0.420486\pi$
$882$		0			0
$883$	−434.695	−	434.695i	−0.492293	−	0.492293i	0.416735	−	0.909028i	$-0.363174\pi$
$883$	−434.695	−	434.695i	−0.492293	−	0.492293i	−0.909028	+	0.416735i	$0.863174\pi$
$884$	−37.2759	+	21.5213i	−0.0421673	+	0.0243453i
$885$		0			0
$886$	638.166	−	1105.34i	0.720277	−	1.24756i
$887$	−148.261	−	553.319i	−0.167149	−	0.623810i	−0.997756	−	0.0669506i	$-0.978673\pi$
$887$	−148.261	−	553.319i	−0.167149	−	0.623810i	0.830607	−	0.556859i	$-0.187994\pi$
$888$		0			0
$889$	1680.73	−	970.369i	1.89058	−	1.09153i
$890$	−315.268	−	1672.61i	−0.354234	−	1.87933i
$891$		0			0
$892$	−17.2130	+	17.2130i	−0.0192970	+	0.0192970i
$893$	−449.003	+	1675.70i	−0.502803	+	1.87649i
$894$		0			0
$895$	−98.8106	−	205.548i	−0.110403	−	0.229663i
$896$	185.266	−	320.890i	0.206770	−	0.358136i
$897$		0			0
$898$	−618.271	+	2307.42i	−0.688497	+	2.56951i
$899$			97.7228i			0.108702i
$900$		0			0
$901$	414.097			0.459597
$902$	−800.662	−	214.537i	−0.887652	−	0.237846i
$903$		0			0
$904$	129.968	+	75.0371i	0.143770	+	0.0830057i
$905$	−472.235	+	227.012i	−0.521807	+	0.250842i
$906$		0			0
$907$	−764.884	−	204.950i	−0.843312	−	0.225965i	−0.188799	−	0.982016i	$-0.560459\pi$
$907$	−764.884	−	204.950i	−0.843312	−	0.225965i	−0.654513	+	0.756051i	$0.727126\pi$
$908$	−233.153	−	233.153i	−0.256776	−	0.256776i
$909$		0			0
$910$	−158.632	+	29.9004i	−0.174321	+	0.0328576i
$911$	−472.743	−	818.815i	−0.518928	−	0.898809i	−0.999758	−	0.0219955i	$-0.992998\pi$
$911$	−472.743	−	818.815i	−0.518928	−	0.898809i	0.480830	−	0.876814i	$-0.340335\pi$
$912$		0			0
$913$	−1804.14	+	483.417i	−1.97605	+	0.529482i
$914$	−2214.44	−	1278.51i	−2.42280	−	1.39880i
$915$		0			0
$916$	−119.699	−	207.325i	−0.130676	−	0.226338i
$917$	−158.889	+	158.889i	−0.173270	+	0.173270i
$918$		0			0
$919$			825.147i			0.897875i	0.893563	+	0.448937i	$0.148197\pi$
$919$			825.147i			0.897875i	−0.893563	+	0.448937i	$0.851803\pi$
$920$	124.529	+	9.41937i	0.135358	+	0.0102384i
$921$		0			0
$922$	195.684	+	730.302i	0.212238	+	0.792084i
$923$	−80.4529	+	21.5573i	−0.0871646	+	0.0233557i
$924$		0			0
$925$	10.1487	+	91.2136i	0.0109716	+	0.0986093i
$926$	486.714			0.525609
$927$		0			0
$928$	109.743	+	109.743i	0.118258	+	0.118258i
$929$	799.415	−	461.543i	0.860511	−	0.496817i	−0.00367207	−	0.999993i	$-0.501169\pi$
$929$	799.415	−	461.543i	0.860511	−	0.496817i	0.864184	+	0.503177i	$0.167836\pi$
$930$		0			0
$931$	−1163.04	+	2014.44i	−1.24923	+	2.16374i
$932$	153.190	+	571.714i	0.164367	+	0.613427i
$933$		0			0
$934$	225.486	−	130.185i	0.241420	−	0.139384i
$935$	639.077	−	120.459i	0.683505	−	0.128833i
$936$		0			0
$937$	967.522	−	967.522i	1.03257	−	1.03257i	0.0331234	−	0.999451i	$-0.489455\pi$
$937$	967.522	−	967.522i	1.03257	−	1.03257i	0.999451	−	0.0331234i	$-0.0105454\pi$
$938$	570.601	−	2129.51i	0.608316	−	2.27027i
$939$		0			0
$940$	1419.31	+	497.746i	1.50990	+	0.529517i
$941$	−405.942	+	703.113i	−0.431395	+	0.747197i	−0.996994	−	0.0774830i	$-0.975312\pi$
$941$	−405.942	+	703.113i	−0.431395	+	0.747197i	0.565599	+	0.824680i	$0.308645\pi$
$942$		0			0
$943$	−154.709	+	577.384i	−0.164061	+	0.612284i
$944$		−	1275.50i		−	1.35117i
$945$		0			0
$946$	584.344			0.617700
$947$	1191.67	+	319.307i	1.25836	+	0.337177i	0.825562	−	0.564312i	$-0.190858\pi$
$947$	1191.67	+	319.307i	1.25836	+	0.337177i	0.432802	+	0.901489i	$0.357525\pi$
$948$		0			0
$949$	−14.7301	−	8.50444i	−0.0155217	−	0.00896147i
$950$	−1070.34	−	1454.49i	−1.12667	−	1.53105i
$951$		0			0
$952$	118.698	+	31.8050i	0.124683	+	0.0334087i
$953$	719.749	+	719.749i	0.755245	+	0.755245i	0.975453	−	0.220208i	$-0.0706736\pi$
$953$	719.749	+	719.749i	0.755245	+	0.755245i	−0.220208	+	0.975453i	$0.570674\pi$
$954$		0			0
$955$	−418.269	−	285.598i	−0.437978	−	0.299055i
$956$	319.749	+	553.822i	0.334466	+	0.579312i
$957$		0			0
$958$	−108.311	+	29.0218i	−0.113059	+	0.0302941i
$959$	−780.519	−	450.633i	−0.813888	−	0.469899i
$960$		0			0
$961$	63.3899	+	109.795i	0.0659625	+	0.114250i
$962$	−7.03333	+	7.03333i	−0.00731116	+	0.00731116i
$963$		0			0
$964$			1557.24i			1.61539i
$965$	−1072.80	+	921.917i	−1.11171	+	0.955354i
$966$		0			0
$967$	−383.836	−	1432.50i	−0.396935	−	1.48138i	−0.818460	−	0.574564i	$-0.805172\pi$
$967$	−383.836	−	1432.50i	−0.396935	−	1.48138i	0.421525	−	0.906817i	$-0.361495\pi$
$968$	28.5240	−	7.64298i	0.0294669	−	0.00789564i
$969$		0			0
$970$	275.457	+	20.8355i	0.283976	+	0.0214799i
$971$	−798.883			−0.822742			−0.411371	−	0.911468i	$-0.634950\pi$
$971$	−798.883			−0.822742			−0.411371	+	0.911468i	$0.634950\pi$
$972$		0			0
$973$	−378.755	−	378.755i	−0.389266	−	0.389266i
$974$	−1396.20	+	806.094i	−1.43347	+	0.827612i
$975$		0			0
$976$	574.486	−	995.039i	0.588613	−	1.01951i
$977$	110.728	+	413.244i	0.113335	+	0.422972i	0.999157	−	0.0410533i	$-0.0130713\pi$
$977$	110.728	+	413.244i	0.113335	+	0.422972i	−0.885822	+	0.464025i	$0.846405\pi$
$978$		0			0
$979$	−1255.75	+	725.006i	−1.28268	+	0.740558i
$980$	1665.46	+	1137.19i	1.69945	+	1.16040i
$981$		0			0
$982$	940.736	−	940.736i	0.957980	−	0.957980i
$983$	111.413	−	415.799i	0.113340	−	0.422990i	−0.885817	−	0.464034i	$-0.846402\pi$
$983$	111.413	−	415.799i	0.113340	−	0.422990i	0.999157	+	0.0410437i	$0.0130683\pi$
$984$		0			0
$985$	12.3160	−	35.1188i	0.0125036	−	0.0356536i
$986$	−51.6563	+	89.4713i	−0.0523897	+	0.0907417i
$987$		0			0
$988$	26.3538	−	98.3538i	0.0266739	−	0.0995484i
$989$		−	421.390i		−	0.426077i
$990$		0			0
$991$	575.226			0.580450			0.290225	−	0.956958i	$-0.406270\pi$
$991$	575.226			0.580450			0.290225	+	0.956958i	$0.406270\pi$
$992$	−1279.74	−	342.905i	−1.29006	−	0.345670i
$993$		0			0
$994$	2644.90	+	1527.03i	2.66086	+	1.53625i
$995$	−305.598	−	635.712i	−0.307133	−	0.638907i
$996$		0			0
$997$	−398.810	−	106.861i	−0.400010	−	0.107182i	0.0532048	−	0.998584i	$-0.483056\pi$
$997$	−398.810	−	106.861i	−0.400010	−	0.107182i	−0.453215	+	0.891401i	$0.649723\pi$
$998$	−1736.83	−	1736.83i	−1.74031	−	1.74031i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.n.28.2		32
3.2	odd	2	inner	405.3.l.n.28.7		32
5.2	odd	4	inner	405.3.l.n.352.7		32
9.2	odd	6	inner	405.3.l.n.298.2		32
9.4	even	3		135.3.g.b.28.7	yes	16
9.5	odd	6		135.3.g.b.28.2	✓	16
9.7	even	3	inner	405.3.l.n.298.7		32
15.2	even	4	inner	405.3.l.n.352.2		32
45.2	even	12	inner	405.3.l.n.217.7		32
45.4	even	6		675.3.g.j.568.2		16
45.7	odd	12	inner	405.3.l.n.217.2		32
45.13	odd	12		675.3.g.j.82.2		16
45.14	odd	6		675.3.g.j.568.7		16
45.22	odd	12		135.3.g.b.82.7	yes	16
45.23	even	12		675.3.g.j.82.7		16
45.32	even	12		135.3.g.b.82.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.b.28.2	✓	16	9.5	odd	6
135.3.g.b.28.7	yes	16	9.4	even	3
135.3.g.b.82.2	yes	16	45.32	even	12
135.3.g.b.82.7	yes	16	45.22	odd	12
405.3.l.n.28.2		32	1.1	even	1	trivial
405.3.l.n.28.7		32	3.2	odd	2	inner
405.3.l.n.217.2		32	45.7	odd	12	inner
405.3.l.n.217.7		32	45.2	even	12	inner
405.3.l.n.298.2		32	9.2	odd	6	inner
405.3.l.n.298.7		32	9.7	even	3	inner
405.3.l.n.352.2		32	15.2	even	4	inner
405.3.l.n.352.7		32	5.2	odd	4	inner
675.3.g.j.82.2		16	45.13	odd	12
675.3.g.j.82.7		16	45.23	even	12
675.3.g.j.568.2		16	45.4	even	6
675.3.g.j.568.7		16	45.14	odd	6

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.78913 - 0.747344i) q^{2} +(3.75659 + 2.16887i) q^{4} +(4.50635 - 2.16628i) q^{5} +(-11.5096 - 3.08399i) q^{7} +(-0.689596 - 0.689596i) q^{8} +(-14.1877 + 2.67423i) q^{10} +(6.14980 + 10.6518i) q^{11} +(-0.906368 + 0.242861i) q^{13} +(29.7970 + 17.2033i) q^{14} +(-7.26748 - 12.5876i) q^{16} +(7.47753 - 7.47753i) q^{17} +25.0163i q^{19} +(21.6269 + 1.63586i) q^{20} +(-9.19203 - 34.3051i) q^{22} +(-24.7385 + 6.62867i) q^{23} +(15.6144 - 19.5241i) q^{25} +2.70947 q^{26} +(-36.5482 - 36.5482i) q^{28} +(2.93013 - 1.69171i) q^{29} +(-14.4414 + 25.0133i) q^{31} +(11.8723 + 44.3078i) q^{32} +(-26.4441 + 15.2675i) q^{34} +(-58.5472 + 11.0355i) q^{35} +(-2.59583 + 2.59583i) q^{37} +(18.6958 - 69.7736i) q^{38} +(-4.60142 - 1.61370i) q^{40} +(11.6697 - 20.2125i) q^{41} +(-4.25843 + 15.8927i) q^{43} +53.3525i q^{44} +73.9528 q^{46} +(66.9844 + 17.9484i) q^{47} +(80.5250 + 46.4912i) q^{49} +(-58.1418 + 42.7857i) q^{50} +(-3.93159 - 1.05347i) q^{52} +(27.6894 + 27.6894i) q^{53} +(50.7879 + 34.6784i) q^{55} +(5.81027 + 10.0637i) q^{56} +(-9.43678 + 2.52858i) q^{58} +(75.9971 + 43.8770i) q^{59} +(39.5244 + 68.4583i) q^{61} +(58.9725 - 58.9725i) q^{62} -74.3129i q^{64} +(-3.55831 + 3.05786i) q^{65} +(-16.5841 - 61.8926i) q^{67} +(44.3078 - 11.8723i) q^{68} +(171.543 + 12.9755i) q^{70} +88.7641 q^{71} +(12.8174 + 12.8174i) q^{73} +(9.18007 - 5.30012i) q^{74} +(-54.2571 + 93.9761i) q^{76} +(-37.9319 - 141.564i) q^{77} +(-26.2915 + 15.1794i) q^{79} +(-60.0182 - 40.9810i) q^{80} +(-47.6540 + 47.6540i) q^{82} +(-39.3035 + 146.683i) q^{83} +(17.4980 - 49.8948i) q^{85} +(23.7546 - 41.1442i) q^{86} +(3.10454 - 11.5863i) q^{88} +117.891i q^{89} +11.1809 q^{91} +(-107.309 - 28.7535i) q^{92} +(-173.414 - 100.121i) q^{94} +(54.1923 + 112.732i) q^{95} +(-18.4817 - 4.95215i) q^{97} +(-189.850 - 189.850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{7} + 80 q^{10} - 40 q^{13} + 152 q^{16} + 136 q^{22} + 32 q^{25} - 224 q^{28} - 200 q^{31} + 32 q^{37} + 48 q^{40} - 136 q^{43} + 304 q^{46} - 640 q^{52} + 496 q^{55} - 48 q^{58} + 280 q^{61}+ \cdots - 448 q^{97}+O(q^{100}) \) 32 * q - 16 * q^7 + 80 * q^10 - 40 * q^13 + 152 * q^16 + 136 * q^22 + 32 * q^25 - 224 * q^28 - 200 * q^31 + 32 * q^37 + 48 * q^40 - 136 * q^43 + 304 * q^46 - 640 * q^52 + 496 * q^55 - 48 * q^58 + 280 * q^61 + 344 * q^67 + 696 * q^70 - 1552 * q^73 - 144 * q^76 - 1760 * q^82 + 176 * q^85 - 1200 * q^88 + 304 * q^91 - 448 * q^97

Introduction

L-functions

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