LMFDB - Embedded newform 405.3.l.n.352.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

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")

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

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			352.7
Character	$\chi$	$=$	405.352
Dual form			405.3.l.n.298.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.747344 - 2.78913i) q^{2} +(-3.75659 - 2.16887i) q^{4} +(-0.377122 - 4.98576i) q^{5} +(3.08399 - 11.5096i) q^{7} +(-0.689596 + 0.689596i) q^{8} +(-14.1877 - 2.67423i) q^{10} +(6.14980 + 10.6518i) q^{11} +(0.242861 + 0.906368i) q^{13} +(-29.7970 - 17.2033i) q^{14} +(-7.26748 - 12.5876i) q^{16} +(7.47753 + 7.47753i) q^{17} -25.0163i q^{19} +(-9.39677 + 19.5474i) q^{20} +(34.3051 - 9.19203i) q^{22} +(6.62867 + 24.7385i) q^{23} +(-24.7156 + 3.76048i) q^{25} +2.70947 q^{26} +(-36.5482 + 36.5482i) q^{28} +(-2.93013 + 1.69171i) q^{29} +(-14.4414 + 25.0133i) q^{31} +(-44.3078 + 11.8723i) q^{32} +(26.4441 - 15.2675i) q^{34} +(-58.5472 - 11.0355i) q^{35} +(-2.59583 - 2.59583i) q^{37} +(-69.7736 - 18.6958i) q^{38} +(3.69822 + 3.17810i) q^{40} +(11.6697 - 20.2125i) q^{41} +(15.8927 + 4.25843i) q^{43} -53.3525i q^{44} +73.9528 q^{46} +(-17.9484 + 66.9844i) q^{47} +(-80.5250 - 46.4912i) q^{49} +(-7.98258 + 71.7452i) q^{50} +(1.05347 - 3.93159i) q^{52} +(27.6894 - 27.6894i) q^{53} +(50.7879 - 34.6784i) q^{55} +(5.81027 + 10.0637i) q^{56} +(2.52858 + 9.43678i) q^{58} +(-75.9971 - 43.8770i) q^{59} +(39.5244 + 68.4583i) q^{61} +(58.9725 + 58.9725i) q^{62} +74.3129i q^{64} +(4.42734 - 1.55266i) q^{65} +(61.8926 - 16.5841i) q^{67} +(-11.8723 - 44.3078i) q^{68} +(-74.5343 + 155.048i) q^{70} +88.7641 q^{71} +(12.8174 - 12.8174i) q^{73} +(-9.18007 + 5.30012i) q^{74} +(-54.2571 + 93.9761i) q^{76} +(141.564 - 37.9319i) q^{77} +(26.2915 - 15.1794i) q^{79} +(-60.0182 + 40.9810i) q^{80} +(-47.6540 - 47.6540i) q^{82} +(146.683 + 39.3035i) q^{83} +(34.4612 - 40.1011i) q^{85} +(23.7546 - 41.1442i) q^{86} +(-11.5863 - 3.10454i) q^{88} -117.891i q^{89} +11.1809 q^{91} +(28.7535 - 107.309i) q^{92} +(173.414 + 100.121i) q^{94} +(-124.725 + 9.43419i) q^{95} +(4.95215 - 18.4817i) q^{97} +(-189.850 + 189.850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.747344	−	2.78913i	0.373672	−	1.39456i	−0.481604	−	0.876389i	$-0.659946\pi$
$2$	0.747344	−	2.78913i	0.373672	−	1.39456i	0.855276	−	0.518173i	$-0.173388\pi$
$3$		0			0
$3$		0			0
$4$	−3.75659	−	2.16887i	−0.939149	−	0.542218i
$5$	−0.377122	−	4.98576i	−0.0754244	−	0.997152i
$5$	−0.377122	−	4.98576i	−0.0754244	−	0.997152i
$6$		0			0
$7$	3.08399	−	11.5096i	0.440570	−	1.64423i	−0.286803	−	0.957989i	$-0.592593\pi$
$7$	3.08399	−	11.5096i	0.440570	−	1.64423i	0.727374	−	0.686242i	$-0.240741\pi$
$8$	−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
$13$	0.242861	+	0.906368i	0.0186816	+	0.0697206i	0.974637	−	0.223790i	$-0.0718430\pi$
$13$	0.242861	+	0.906368i	0.0186816	+	0.0697206i	−0.955956	+	0.293511i	$0.905176\pi$
$14$	−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	0.891963	−	0.452108i	$-0.149328\pi$
$17$	7.47753	+	7.47753i	0.439855	+	0.439855i	−0.452108	+	0.891963i	$0.649328\pi$
$18$		0			0
$19$		−	25.0163i		−	1.31665i	−0.752735	−	0.658323i	$-0.771266\pi$
$19$		−	25.0163i		−	1.31665i	0.752735	−	0.658323i	$-0.228734\pi$
$20$	−9.39677	+	19.5474i	−0.469839	+	0.977370i
$21$		0			0
$22$	34.3051	−	9.19203i	1.55932	−	0.417819i
$23$	6.62867	+	24.7385i	0.288203	+	1.07559i	0.946467	+	0.322801i	$0.104625\pi$
$23$	6.62867	+	24.7385i	0.288203	+	1.07559i	−0.658264	+	0.752788i	$0.728709\pi$
$24$		0			0
$25$	−24.7156	+	3.76048i	−0.988622	+	0.150419i
$26$	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	−0.549668	−	0.835383i	$-0.685246\pi$
$29$	−2.93013	+	1.69171i	−0.101039	+	0.0583348i	0.448629	+	0.893718i	$0.351912\pi$
$30$		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	$0.320919\pi$
$32$	−44.3078	+	11.8723i	−1.38462	+	0.371008i
$33$		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	0.671157	−	0.741315i	$-0.265797\pi$
$37$	−2.59583	−	2.59583i	−0.0701575	−	0.0701575i	−0.741315	+	0.671157i	$0.765797\pi$
$38$	−69.7736	−	18.6958i	−1.83615	−	0.491994i
$39$		0			0
$40$	3.69822	+	3.17810i	0.0924555	+	0.0794524i
$41$	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
$43$	15.8927	+	4.25843i	0.369598	+	0.0990334i	0.438837	−	0.898567i	$-0.355391\pi$
$43$	15.8927	+	4.25843i	0.369598	+	0.0990334i	−0.0692394	+	0.997600i	$0.522057\pi$
$44$		−	53.3525i		−	1.21256i
$45$		0			0
$46$	73.9528			1.60767
$47$	−17.9484	+	66.9844i	−0.381881	+	1.42520i	0.461143	+	0.887326i	$0.347439\pi$
$47$	−17.9484	+	66.9844i	−0.381881	+	1.42520i	−0.843025	+	0.537875i	$0.819227\pi$
$48$		0			0
$49$	−80.5250	−	46.4912i	−1.64337	−	0.948799i
$50$	−7.98258	+	71.7452i	−0.159652	+	1.43490i
$51$		0			0
$52$	1.05347	−	3.93159i	0.0202590	−	0.0756075i
$53$	27.6894	−	27.6894i	0.522442	−	0.522442i	−0.395866	−	0.918308i	$-0.629556\pi$
$53$	27.6894	−	27.6894i	0.522442	−	0.522442i	0.918308	+	0.395866i	$0.129556\pi$
$54$		0			0
$55$	50.7879	−	34.6784i	0.923416	−	0.630517i
$56$	5.81027	+	10.0637i	0.103755	+	0.179709i
$57$		0			0
$58$	2.52858	+	9.43678i	0.0435962	+	0.162703i
$59$	−75.9971	−	43.8770i	−1.28809	−	0.743677i	−0.309774	−	0.950810i	$-0.600253\pi$
$59$	−75.9971	−	43.8770i	−1.28809	−	0.743677i	−0.978313	+	0.207133i	$0.933587\pi$
$60$		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
$65$	4.42734	−	1.55266i	0.0681130	−	0.0238870i
$66$		0			0
$67$	61.8926	−	16.5841i	0.923769	−	0.247523i	0.234574	−	0.972098i	$-0.424631\pi$
$67$	61.8926	−	16.5841i	0.923769	−	0.247523i	0.689196	+	0.724575i	$0.257964\pi$
$68$	−11.8723	−	44.3078i	−0.174592	−	0.651586i
$69$		0			0
$70$	−74.5343	+	155.048i	−1.06478	+	2.21497i
$71$	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	−0.613845	−	0.789426i	$-0.710378\pi$
$73$	12.8174	−	12.8174i	0.175581	−	0.175581i	0.789426	+	0.613845i	$0.210378\pi$
$74$	−9.18007	+	5.30012i	−0.124055	+	0.0716232i
$75$		0			0
$76$	−54.2571	+	93.9761i	−0.713909	+	1.23653i
$77$	141.564	−	37.9319i	1.83849	−	0.492622i
$78$		0			0
$79$	26.2915	−	15.1794i	0.332804	−	0.192144i	−0.324281	−	0.945961i	$-0.605122\pi$
$79$	26.2915	−	15.1794i	0.332804	−	0.192144i	0.657085	+	0.753816i	$0.271789\pi$
$80$	−60.0182	+	40.9810i	−0.750228	+	0.512262i
$81$		0			0
$82$	−47.6540	−	47.6540i	−0.581147	−	0.581147i
$83$	146.683	+	39.3035i	1.76726	+	0.473536i	0.988168	−	0.153372i	$-0.0490134\pi$
$83$	146.683	+	39.3035i	1.76726	+	0.473536i	0.779093	+	0.626909i	$0.215680\pi$
$84$		0			0
$85$	34.4612	−	40.1011i	0.405426	−	0.471778i
$86$	23.7546	−	41.1442i	0.276216	−	0.478421i
$87$		0			0
$88$	−11.5863	−	3.10454i	−0.131662	−	0.0352788i
$89$		−	117.891i		−	1.32462i	−0.749231	−	0.662309i	$-0.769577\pi$
$89$		−	117.891i		−	1.32462i	0.749231	−	0.662309i	$-0.230423\pi$
$90$		0			0
$91$	11.1809			0.122867
$92$	28.7535	−	107.309i	0.312538	−	1.16641i
$93$		0			0
$94$	173.414	+	100.121i	1.84483	+	1.06511i
$95$	−124.725	+	9.43419i	−1.31290	+	0.0993073i
$96$		0			0
$97$	4.95215	−	18.4817i	0.0510531	−	0.190533i	−0.935690	−	0.352824i	$-0.885222\pi$
$97$	4.95215	−	18.4817i	0.0510531	−	0.190533i	0.986743	+	0.162291i	$0.0518883\pi$
$98$	−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
$103$	−44.3694	−	165.589i	−0.430770	−	1.60766i	−0.750990	−	0.660314i	$-0.770423\pi$
$103$	−44.3694	−	165.589i	−0.430770	−	1.60766i	0.320219	−	0.947343i	$-0.396243\pi$
$104$	−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	0.754833	−	0.655917i	$-0.227718\pi$
$107$	10.5840	+	10.5840i	0.0989155	+	0.0989155i	−0.655917	+	0.754833i	$0.727718\pi$
$108$		0			0
$109$		−	9.08051i		−	0.0833075i	−0.999132	−	0.0416537i	$-0.986737\pi$
$109$		−	9.08051i		−	0.0833075i	0.999132	−	0.0416537i	$-0.0132626\pi$
$110$	−58.7664	−	167.570i	−0.534240	−	1.52337i
$111$		0			0
$112$	−167.292	+	44.8257i	−1.49368	+	0.400230i
$113$	39.8284	+	148.642i	0.352464	+	1.31541i	0.883646	+	0.468155i	$0.155081\pi$
$113$	39.8284	+	148.642i	0.352464	+	1.31541i	−0.531182	+	0.847258i	$0.678252\pi$
$114$		0			0
$115$	120.841	−	42.3784i	1.05079	−	0.368508i
$116$	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
$122$	220.477	−	59.0767i	1.80719	−	0.484235i
$123$		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	0.0891750	−	0.996016i	$-0.471577\pi$
$127$	−115.169	−	115.169i	−0.906841	−	0.906841i	−0.996016	+	0.0891750i	$0.971577\pi$
$128$	30.0367	+	8.04831i	0.234662	+	0.0628774i
$129$		0			0
$130$	−1.02180	−	13.5088i	−0.00786002	−	0.103914i
$131$	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
$133$	−287.928	−	77.1500i	−2.16487	−	0.580076i
$134$		−	185.020i		−	1.38075i
$135$		0			0
$136$	−10.3129			−0.0758305
$137$	−19.5764	+	73.0600i	−0.142893	+	0.533284i	0.856947	+	0.515405i	$0.172358\pi$
$137$	−19.5764	+	73.0600i	−0.142893	+	0.533284i	−0.999840	+	0.0178799i	$0.994308\pi$
$138$		0			0
$139$	−38.9303	−	22.4764i	−0.280074	−	0.161701i	0.353383	−	0.935479i	$-0.385031\pi$
$139$	−38.9303	−	22.4764i	−0.280074	−	0.161701i	−0.633457	+	0.773778i	$0.718365\pi$
$140$	196.004	+	168.437i	1.40003	+	1.20312i
$141$		0			0
$142$	66.3373	−	247.574i	0.467164	−	1.74348i
$143$	−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
$148$	4.12146	+	15.3815i	0.0278477	+	0.103929i
$149$	142.228	+	82.1151i	0.954547	+	0.551108i	0.894491	−	0.447087i	$-0.147539\pi$
$149$	142.228	+	82.1151i	0.954547	+	0.551108i	0.0600567	+	0.998195i	$0.480872\pi$
$150$		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
$155$	130.156	+	62.5684i	0.839719	+	0.403667i
$156$		0			0
$157$	62.9277	−	16.8614i	0.400814	−	0.107398i	−0.0527803	−	0.998606i	$-0.516808\pi$
$157$	62.9277	−	16.8614i	0.400814	−	0.107398i	0.453594	+	0.891208i	$0.350142\pi$
$158$	−22.6885	−	84.6745i	−0.143598	−	0.535915i
$159$		0			0
$160$	75.9016	+	216.431i	0.474385	+	1.35269i
$161$	305.174			1.89549
$162$		0			0
$163$	20.9849	−	20.9849i	0.128742	−	0.128742i	−0.639800	−	0.768542i	$-0.720983\pi$
$163$	20.9849	−	20.9849i	0.128742	−	0.128742i	0.768542	+	0.639800i	$0.220983\pi$
$164$	−87.6768	+	50.6202i	−0.534615	+	0.308660i
$165$		0			0
$166$	219.245	−	379.743i	1.32075	−	2.28761i
$167$	−90.6768	+	24.2968i	−0.542975	+	0.145490i	−0.519873	−	0.854243i	$-0.674021\pi$
$167$	−90.6768	+	24.2968i	−0.542975	+	0.145490i	−0.0231017	+	0.999733i	$0.507354\pi$
$168$		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
$173$	−192.502	−	51.5809i	−1.11273	−	0.298155i	−0.344792	−	0.938679i	$-0.612051\pi$
$173$	−192.502	−	51.5809i	−1.11273	−	0.298155i	−0.767938	+	0.640524i	$0.778717\pi$
$174$		0			0
$175$	−32.9409	+	296.064i	−0.188234	+	1.69179i
$176$	89.3871	−	154.823i	0.507881	−	0.879676i
$177$		0			0
$178$	−328.813	−	88.1051i	−1.84726	−	0.494973i
$179$			45.6130i			0.254821i	0.991850	+	0.127411i	$0.0406666\pi$
$179$			45.6130i			0.254821i	−0.991850	+	0.127411i	$0.959333\pi$
$180$		0			0
$181$	−104.793			−0.578968			−0.289484	−	0.957183i	$-0.593484\pi$
$181$	−104.793			−0.578968			−0.289484	+	0.957183i	$0.593484\pi$
$182$	8.35600	−	31.1850i	0.0459121	−	0.171346i
$183$		0			0
$184$	−21.6307	−	12.4885i	−0.117558	−	0.0678722i
$185$	−11.9632	+	13.9211i	−0.0646661	+	0.0752493i
$186$		0			0
$187$	−33.6636	+	125.634i	−0.180019	+	0.671840i
$188$	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
$193$	73.2202	+	273.261i	0.379379	+	1.41586i	0.846840	+	0.531848i	$0.178502\pi$
$193$	73.2202	+	273.261i	0.379379	+	1.41586i	−0.467461	+	0.884014i	$0.654831\pi$
$194$	−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	0.720339	−	0.693622i	$-0.243986\pi$
$197$	5.26310	+	5.26310i	0.0267163	+	0.0267163i	−0.693622	+	0.720339i	$0.743986\pi$
$198$		0			0
$199$			141.070i			0.708895i	0.935076	+	0.354448i	$0.115331\pi$
$199$			141.070i			0.708895i	−0.935076	+	0.354448i	$0.884669\pi$
$200$	14.4505	−	19.6370i	0.0722527	−	0.0981848i
$201$		0			0
$202$	−54.8081	+	14.6858i	−0.271327	+	0.0727019i
$203$	10.4344	+	38.9419i	0.0514012	+	0.191832i
$204$		0			0
$205$	−105.176	−	50.5598i	−0.513053	−	0.246633i
$206$	−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	$0.132578\pi$
$212$	−164.073	+	43.9632i	−0.773929	+	0.207374i
$213$		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
$218$	−25.3267	−	6.78627i	−0.116177	−	0.0311297i
$219$		0			0
$220$	−266.003	+	20.1204i	−1.20910	+	0.0914563i
$221$	−4.96140	+	8.59339i	−0.0224498	+	0.0388841i
$222$		0			0
$223$	5.42064	+	1.45246i	0.0243078	+	0.00651326i	0.270952	−	0.962593i	$-0.412661\pi$
$223$	5.42064	+	1.45246i	0.0243078	+	0.00651326i	−0.246645	+	0.969106i	$0.579328\pi$
$224$			546.580i			2.44009i
$225$		0			0
$226$	444.346			1.96613
$227$	19.6738	−	73.4236i	0.0866686	−	0.323452i	−0.908956	−	0.416891i	$-0.863120\pi$
$227$	19.6738	−	73.4236i	0.0866686	−	0.323452i	0.995625	+	0.0934396i	$0.0297862\pi$
$228$		0			0
$229$	47.7957	+	27.5948i	0.208715	+	0.120502i	0.600714	−	0.799464i	$-0.294883\pi$
$229$	47.7957	+	27.5948i	0.208715	+	0.120502i	−0.391999	+	0.919966i	$0.628216\pi$
$230$	−27.8892	−	368.711i	−0.121258	−	1.60309i
$231$		0			0
$232$	0.854007	−	3.18720i	0.00368107	−	0.0137379i
$233$	96.4842	−	96.4842i	0.414095	−	0.414095i	−0.469067	−	0.883162i	$-0.655410\pi$
$233$	96.4842	−	96.4842i	0.414095	−	0.414095i	0.883162	+	0.469067i	$0.155410\pi$
$234$		0			0
$235$	340.737	+	64.2252i	1.44994	+	0.273299i
$236$	190.327	+	329.656i	0.806470	+	1.39685i
$237$		0			0
$238$	−94.1696	−	351.446i	−0.395671	−	1.47666i
$239$	−127.675	−	73.7133i	−0.534206	−	0.308424i	0.208522	−	0.978018i	$-0.433135\pi$
$239$	−127.675	−	73.7133i	−0.534206	−	0.308424i	−0.742727	+	0.669594i	$0.766468\pi$
$240$		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
$245$	−201.426	+	419.011i	−0.822146	+	1.71025i
$246$		0			0
$247$	22.6740	−	6.07547i	0.0917974	−	0.0245970i
$248$	−7.29031	−	27.2078i	−0.0293964	−	0.109709i
$249$		0			0
$250$	360.714	+	12.7425i	1.44286	+	0.0509700i
$251$	−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
$257$	−333.529	+	89.3689i	−1.29778	+	0.347739i	−0.840610	−	0.541641i	$-0.817803\pi$
$257$	−333.529	+	89.3689i	−1.29778	+	0.347739i	−0.457169	+	0.889380i	$0.651137\pi$
$258$		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
$263$	251.763	+	67.4597i	0.957274	+	0.256501i	0.703446	−	0.710748i	$-0.251644\pi$
$263$	251.763	+	67.4597i	0.957274	+	0.256501i	0.253828	+	0.967249i	$0.418310\pi$
$264$		0			0
$265$	−148.495	−	127.611i	−0.560359	−	0.481549i
$266$	−430.362	+	745.409i	−1.61790	+	2.80229i
$267$		0			0
$268$	−268.474	−	71.9374i	−1.00177	−	0.268423i
$269$			194.835i			0.724296i	0.932121	+	0.362148i	$0.117956\pi$
$269$			194.835i			0.724296i	−0.932121	+	0.362148i	$0.882044\pi$
$270$		0			0
$271$	−307.130			−1.13332			−0.566661	−	0.823951i	$-0.691765\pi$
$271$	−307.130			−1.13332			−0.566661	+	0.823951i	$0.691765\pi$
$272$	39.7817	−	148.467i	0.146256	−	0.545836i
$273$		0			0
$274$	189.143	+	109.202i	0.690303	+	0.398547i
$275$	−192.051	−	240.138i	−0.698369	−	0.873229i
$276$		0			0
$277$	−27.4833	+	102.569i	−0.0992175	+	0.370285i	−0.997625	−	0.0688778i	$-0.978058\pi$
$277$	−27.4833	+	102.569i	−0.0992175	+	0.370285i	0.898408	+	0.439163i	$0.144725\pi$
$278$	−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
$283$	83.0344	+	309.889i	0.293408	+	1.09501i	0.942474	+	0.334280i	$0.108493\pi$
$283$	83.0344	+	309.889i	0.293408	+	1.09501i	−0.649066	+	0.760732i	$0.724840\pi$
$284$	−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
$290$	46.0959	−	16.1657i	0.158951	−	0.0557438i
$291$		0			0
$292$	−75.9490	+	20.3505i	−0.260099	+	0.0696934i
$293$	26.6082	+	99.3033i	0.0908131	+	0.338919i	0.996351	−	0.0853454i	$-0.0271994\pi$
$293$	26.6082	+	99.3033i	0.0908131	+	0.338919i	−0.905538	+	0.424264i	$0.860533\pi$
$294$		0			0
$295$	−190.100	+	395.450i	−0.644406	+	1.34051i
$296$	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
$302$	−107.108	+	28.6996i	−0.354664	+	0.0950319i
$303$		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	0.575077	−	0.818099i	$-0.304972\pi$
$307$	−74.6079	−	74.6079i	−0.243023	−	0.243023i	−0.818099	+	0.575077i	$0.804972\pi$
$308$	−614.067	−	164.539i	−1.99372	−	0.534216i
$309$		0			0
$310$	271.783	−	316.262i	0.876719	−	1.02020i
$311$	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
$313$	163.821	+	43.8958i	0.523391	+	0.140242i	0.510835	−	0.859679i	$-0.329336\pi$
$313$	163.821	+	43.8958i	0.523391	+	0.140242i	0.0125563	+	0.999921i	$0.496003\pi$
$314$		−	188.115i		−	0.599091i
$315$		0			0
$316$	−131.689			−0.416736
$317$	−105.778	+	394.769i	−0.333685	+	1.24533i	0.571603	+	0.820530i	$0.306322\pi$
$317$	−105.778	+	394.769i	−0.333685	+	1.24533i	−0.905288	+	0.424798i	$0.860345\pi$
$318$		0			0
$319$	−36.0394	−	20.8073i	−0.112976	−	0.0652268i
$320$	370.506	−	28.0251i	1.15783	−	0.0875783i
$321$		0			0
$322$	228.070	−	851.168i	0.708292	−	2.64338i
$323$	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
$328$	5.89110	+	21.9859i	0.0179607	+	0.0670301i
$329$	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
$335$	−106.025	−	302.327i	−0.316493	−	0.902469i
$336$		0			0
$337$	280.796	−	75.2392i	0.833224	−	0.223262i	0.183104	−	0.983094i	$-0.441385\pi$
$337$	280.796	−	75.2392i	0.833224	−	0.223262i	0.650120	+	0.759832i	$0.274719\pi$
$338$	−125.643	−	468.906i	−0.371725	−	1.38730i
$339$		0			0
$340$	−216.431	+	75.9016i	−0.636561	+	0.223240i
$341$	−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
$347$	−530.282	+	142.089i	−1.52819	+	0.409477i	−0.922428	−	0.386168i	$-0.873798\pi$
$347$	−530.282	+	142.089i	−1.52819	+	0.409477i	−0.605762	+	0.795646i	$0.707132\pi$
$348$		0			0
$349$	377.101	−	217.720i	1.08052	−	0.623838i	0.149483	−	0.988764i	$-0.452239\pi$
$349$	377.101	−	217.720i	1.08052	−	0.623838i	0.931036	+	0.364926i	$0.118906\pi$
$350$	801.141	+	313.138i	2.28897	+	0.894680i
$351$		0			0
$352$	−398.945	−	398.945i	−1.13337	−	1.13337i
$353$	321.483	+	86.1412i	0.910718	+	0.244026i	0.683613	−	0.729844i	$-0.260407\pi$
$353$	321.483	+	86.1412i	0.910718	+	0.244026i	0.227104	+	0.973870i	$0.427074\pi$
$354$		0			0
$355$	−33.4749	−	442.556i	−0.0942954	−	1.24664i
$356$	−255.690	+	442.869i	−0.718231	+	1.24401i
$357$		0			0
$358$	127.220	+	34.0886i	0.355364	+	0.0952196i
$359$			114.922i			0.320116i	0.987108	+	0.160058i	$0.0511682\pi$
$359$			114.922i			0.320116i	−0.987108	+	0.160058i	$0.948832\pi$
$360$		0			0
$361$	−264.815			−0.733559
$362$	−78.3166	+	292.281i	−0.216344	+	0.807407i
$363$		0			0
$364$	−42.0022	−	24.2500i	−0.115391	−	0.0666209i
$365$	−68.7382	−	59.0707i	−0.188324	−	0.161838i
$366$		0			0
$367$	135.331	−	505.064i	0.368750	−	1.37620i	−0.493515	−	0.869738i	$-0.664288\pi$
$367$	135.331	−	505.064i	0.368750	−	1.37620i	0.862265	−	0.506458i	$-0.169045\pi$
$368$	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
$373$	55.1226	+	205.720i	0.147782	+	0.551529i	0.999616	+	0.0277173i	$0.00882383\pi$
$373$	55.1226	+	205.720i	0.147782	+	0.551529i	−0.851834	+	0.523812i	$0.824509\pi$
$374$	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	$0.347372\pi$
$379$			672.519i			1.77446i	−0.461331	+	0.887228i	$0.652628\pi$
$380$	489.003	+	235.072i	1.28685	+	0.618611i
$381$		0			0
$382$	−282.523	+	75.7019i	−0.739590	+	0.198173i
$383$	−78.8060	−	294.108i	−0.205760	−	0.767906i	−0.989217	−	0.146460i	$-0.953212\pi$
$383$	−78.8060	−	294.108i	−0.205760	−	0.767906i	0.783457	−	0.621446i	$-0.213455\pi$
$384$		0			0
$385$	−242.506	−	691.497i	−0.629885	−	1.79610i
$386$	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	$0.700970\pi$
$389$	−616.350	+	355.850i	−1.58445	+	0.914780i	−0.994199	+	0.107558i	$0.965697\pi$
$390$		0			0
$391$	−135.417	+	234.549i	−0.346335	+	0.599870i
$392$	87.5898	−	23.4696i	0.223443	−	0.0598715i
$393$		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	0.652959	−	0.757393i	$-0.273527\pi$
$397$	−41.4605	−	41.4605i	−0.104435	−	0.104435i	−0.757393	+	0.652959i	$0.773527\pi$
$398$	393.462	+	105.428i	0.988599	+	0.264894i
$399$		0			0
$400$	226.955	+	283.781i	0.567389	+	0.709454i
$401$	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
$403$	−26.1785	−	7.01451i	−0.0649591	−	0.0174057i
$404$			85.2394i			0.210989i
$405$		0			0
$406$	116.412			0.286729
$407$	11.6863	−	43.6140i	0.0287133	−	0.107160i
$408$		0			0
$409$	−20.5577	−	11.8690i	−0.0502632	−	0.0290195i	0.474658	−	0.880170i	$-0.342572\pi$
$409$	−20.5577	−	11.8690i	−0.0502632	−	0.0290195i	−0.524921	+	0.851151i	$0.675905\pi$
$410$	−219.620	+	255.563i	−0.535659	+	0.623324i
$411$		0			0
$412$	−192.463	+	718.281i	−0.467143	+	1.74340i
$413$	−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
$418$	−229.950	−	858.187i	−0.550121	−	2.05308i
$419$	432.642	+	249.786i	1.03256	+	0.596147i	0.917716	−	0.397236i	$-0.130031\pi$
$419$	432.642	+	249.786i	1.03256	+	0.596147i	0.114841	+	0.993384i	$0.463364\pi$
$420$		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
$425$	−212.930	−	156.692i	−0.501013	−	0.368688i
$426$		0			0
$427$	909.822	−	243.786i	2.13073	−	0.570928i
$428$	−16.8044	−	62.7149i	−0.0392626	−	0.146530i
$429$		0			0
$430$	−214.093	−	102.918i	−0.497892	−	0.239345i
$431$	−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	−0.140557	−	0.990073i	$-0.544889\pi$
$433$	367.840	−	367.840i	0.849516	−	0.849516i	0.990073	+	0.140557i	$0.0448893\pi$
$434$	860.622	−	496.880i	1.98300	−	1.14489i
$435$		0			0
$436$	−19.6945	+	34.1118i	−0.0451708	+	0.0782381i
$437$	618.867	−	165.825i	1.41617	−	0.379462i
$438$		0			0
$439$	−119.042	+	68.7289i	−0.271166	+	0.156558i	−0.629418	−	0.777067i	$-0.716706\pi$
$439$	−119.042	+	68.7289i	−0.271166	+	0.156558i	0.358251	+	0.933625i	$0.383373\pi$
$440$	−11.1090	+	58.9372i	−0.0252478	+	0.133948i
$441$		0			0
$442$	20.2602	+	20.2602i	0.0458375	+	0.0458375i
$443$	426.956	+	114.403i	0.963783	+	0.258245i	0.706201	−	0.708011i	$-0.250408\pi$
$443$	426.956	+	114.403i	0.963783	+	0.258245i	0.257582	+	0.966256i	$0.417074\pi$
$444$		0			0
$445$	−587.776	+	44.4593i	−1.32084	+	0.0999085i
$446$	8.10216	−	14.0334i	0.0181663	−	0.0314649i
$447$		0			0
$448$	855.314	+	229.181i	1.90918	+	0.511564i
$449$			827.291i			1.84252i	0.388949	+	0.921259i	$0.372838\pi$
$449$			827.291i			1.84252i	−0.388949	+	0.921259i	$0.627162\pi$
$450$		0			0
$451$	287.066			0.636509
$452$	172.765	−	644.769i	0.382224	−	1.42648i
$453$		0			0
$454$	−190.084	−	109.745i	−0.418688	−	0.241730i
$455$	−4.21658	−	55.7454i	−0.00926720	−	0.122517i
$456$		0			0
$457$	−229.195	+	855.367i	−0.501521	+	1.87170i	−0.0116012	+	0.999933i	$0.503693\pi$
$457$	−229.195	+	855.367i	−0.501521	+	1.87170i	−0.489919	+	0.871768i	$0.662974\pi$
$458$	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
$463$	43.6260	+	162.814i	0.0942246	+	0.351651i	0.996901	−	0.0786695i	$-0.0250672\pi$
$463$	43.6260	+	162.814i	0.0942246	+	0.351651i	−0.902676	+	0.430321i	$0.858401\pi$
$464$	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	0.635538	−	0.772070i	$-0.280778\pi$
$467$	−63.7603	−	63.7603i	−0.136532	−	0.136532i	−0.772070	+	0.635538i	$0.780778\pi$
$468$		0			0
$469$		−	763.505i		−	1.62794i
$470$	433.780	−	902.360i	0.922936	−	1.91991i
$471$		0			0
$472$	82.6647	−	22.1499i	0.175137	−	0.0469278i
$473$	52.3770	+	195.474i	0.110734	+	0.413264i
$474$		0			0
$475$	94.0732	+	618.292i	0.198049	+	1.30167i
$476$	−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	−0.534694	−	0.845046i	$-0.679573\pi$
$479$	−33.6305	+	19.4166i	−0.0702099	+	0.0405357i	0.464484	+	0.885581i	$0.346240\pi$
$480$		0			0
$481$	1.72235	−	2.98320i	0.00358077	−	0.00620208i
$482$	1001.29	−	268.295i	2.07736	−	0.556628i
$483$		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	0.984735	−	0.174059i	$-0.0556883\pi$
$487$	394.799	+	394.799i	0.810676	+	0.810676i	−0.174059	+	0.984735i	$0.555688\pi$
$488$	−74.4644	−	19.9527i	−0.152591	−	0.0408867i
$489$		0			0
$490$	1018.14	+	874.947i	2.07784	+	1.78561i
$491$	−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
$493$	−34.5599	−	9.26030i	−0.0701012	−	0.0187836i
$494$		−	67.7810i		−	0.137209i
$495$		0			0
$496$	419.811			0.846394
$497$	273.748	−	1021.64i	0.550800	−	2.05561i
$498$		0			0
$499$	−736.679	−	425.322i	−1.47631	−	0.852349i	−0.476669	−	0.879083i	$-0.658156\pi$
$499$	−736.679	−	425.322i	−1.47631	−	0.852349i	−0.999643	+	0.0267345i	$0.991489\pi$
$500$	158.739	−	518.461i	0.317478	−	1.03692i
$501$		0			0
$502$	−115.122	+	429.640i	−0.229326	+	0.855857i
$503$	196.093	−	196.093i	0.389847	−	0.389847i	−0.484786	−	0.874633i	$-0.661103\pi$
$503$	196.093	−	196.093i	0.389847	−	0.389847i	0.874633	+	0.484786i	$0.161103\pi$
$504$		0			0
$505$	−81.1420	+	55.4045i	−0.160677	+	0.109712i
$506$	454.795	+	787.728i	0.898804	+	1.55677i
$507$		0			0
$508$	182.856	+	682.429i	0.359953	+	1.34336i
$509$	−338.026	−	195.159i	−0.664098	−	0.383417i	0.129738	−	0.991548i	$-0.458586\pi$
$509$	−338.026	−	195.159i	−0.664098	−	0.383417i	−0.793837	+	0.608131i	$0.791920\pi$
$510$		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
$515$	−808.852	+	283.662i	−1.57059	+	0.550800i
$516$		0			0
$517$	−823.881	+	220.758i	−1.59358	+	0.426999i
$518$	32.6910	+	122.005i	0.0631101	+	0.235530i
$519$		0			0
$520$	−1.98237	+	4.12378i	−0.00381226	+	0.00793035i
$521$	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	−0.143374	−	0.989669i	$-0.545795\pi$
$523$	442.612	−	442.612i	0.846295	−	0.846295i	0.989669	+	0.143374i	$0.0457951\pi$
$524$	−70.8410	+	40.9001i	−0.135193	+	0.0780536i
$525$		0			0
$526$	376.307	−	651.783i	0.715413	−	1.23913i
$527$	−295.024	+	79.0514i	−0.559818	+	0.150003i
$528$		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
$533$	21.1541	+	5.66823i	0.0396888	+	0.0106346i
$534$		0			0
$535$	48.7776	−	56.7605i	0.0911731	−	0.106094i
$536$	−31.2445	+	54.1171i	−0.0582921	+	0.100965i
$537$		0			0
$538$	543.421	+	145.609i	1.01008	+	0.270649i
$539$		−	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	$0.243545\pi$
$542$	−229.532	+	856.624i	−0.423490	+	1.58049i
$543$		0			0
$544$	−420.088	−	242.538i	−0.772221	−	0.445842i
$545$	−45.2732	+	3.42446i	−0.0830702	+	0.00628342i
$546$		0			0
$547$	−89.8890	+	335.470i	−0.164331	+	0.613291i	0.833794	+	0.552076i	$0.186164\pi$
$547$	−89.8890	+	335.470i	−0.164331	+	0.613291i	−0.998125	+	0.0612152i	$0.980502\pi$
$548$	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
$553$	−93.6263	−	349.418i	−0.169306	−	0.631859i
$554$	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	0.973110	+	0.230341i	$0.0739840\pi$
$557$	670.322	+	670.322i	1.20345	+	1.20345i	0.230341	+	0.973110i	$0.426016\pi$
$558$		0			0
$559$			15.4388i			0.0276187i
$560$	286.580	+	817.172i	0.511749	+	1.45924i
$561$		0			0
$562$	3.20637	−	0.859143i	0.00570528	−	0.00152872i
$563$	112.795	+	420.955i	0.200346	+	0.747700i	0.990818	+	0.135202i	$0.0431684\pi$
$563$	112.795	+	420.955i	0.200346	+	0.747700i	−0.790472	+	0.612498i	$0.790165\pi$
$564$		0			0
$565$	726.071	−	254.631i	1.28508	−	0.450674i
$566$	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	0.222448	−	0.974944i	$-0.428595\pi$
$569$	670.282	−	386.987i	1.17800	−	0.680118i	0.955551	+	0.294826i	$0.0952618\pi$
$570$		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	$0.301010\pi$
$572$	48.3570	−	12.9572i	0.0845402	−	0.0226525i
$573$		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	0.902385	−	0.430931i	$-0.141815\pi$
$577$	272.029	+	272.029i	0.471454	+	0.471454i	−0.430931	+	0.902385i	$0.641815\pi$
$578$	−494.158	−	132.409i	−0.854945	−	0.229082i
$579$		0			0
$580$	−5.53479	−	73.1730i	−0.00954275	−	0.126160i
$581$	904.737	−	1567.05i	1.55721	−	2.69716i
$582$		0			0
$583$	465.226	+	124.657i	0.797986	+	0.213820i
$584$			17.6776i			0.0302699i
$585$		0			0
$586$	296.855			0.506578
$587$	−36.5721	+	136.489i	−0.0623034	+	0.232520i	−0.990055	−	0.140678i	$-0.955072\pi$
$587$	−36.5721	+	136.489i	−0.0623034	+	0.232520i	0.927752	+	0.373197i	$0.121739\pi$
$588$		0			0
$589$	625.740	+	361.271i	1.06238	+	0.613363i
$590$	960.891	+	825.749i	1.62863	+	1.39958i
$591$		0			0
$592$	−13.8102	+	51.5405i	−0.0233281	+	0.0870617i
$593$	94.3094	−	94.3094i	0.159038	−	0.159038i	−0.623102	−	0.782140i	$-0.714128\pi$
$593$	94.3094	−	94.3094i	0.159038	−	0.159038i	0.782140	+	0.623102i	$0.214128\pi$
$594$		0			0
$595$	−355.270	−	520.307i	−0.597093	−	0.874465i
$596$	−356.194	−	616.946i	−0.597641	−	1.03514i
$597$		0			0
$598$	17.9602	+	67.0285i	0.0300338	+	0.112088i
$599$	−723.537	−	417.734i	−1.20791	−	0.697386i	−0.245606	−	0.969370i	$-0.578987\pi$
$599$	−723.537	−	417.734i	−1.20791	−	0.697386i	−0.962302	+	0.271984i	$0.912320\pi$
$600$		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
$605$	136.453	+	65.5951i	0.225542	+	0.108422i
$606$		0			0
$607$	−497.854	+	133.400i	−0.820188	+	0.219769i	−0.644428	−	0.764665i	$-0.722905\pi$
$607$	−497.854	+	133.400i	−0.820188	+	0.219769i	−0.175759	+	0.984433i	$0.556238\pi$
$608$	297.000	+	1108.42i	0.488486	+	1.82306i
$609$		0			0
$610$	−377.689	−	1076.97i	−0.619162	−	1.76552i
$611$	−65.0715			−0.106500
$612$		0			0
$613$	−470.150	+	470.150i	−0.766965	+	0.766965i	−0.977571	−	0.210606i	$-0.932456\pi$
$613$	−470.150	+	470.150i	−0.766965	+	0.766965i	0.210606	+	0.977571i	$0.432456\pi$
$614$	−263.849	+	152.333i	−0.429721	+	0.248099i
$615$		0			0
$616$	−71.4640	+	123.779i	−0.116013	+	0.200940i
$617$	−244.836	+	65.6036i	−0.396817	+	0.106327i	−0.451708	−	0.892166i	$-0.649185\pi$
$617$	−244.836	+	65.6036i	−0.396817	+	0.106327i	0.0548918	+	0.998492i	$0.482519\pi$
$618$		0			0
$619$	88.9466	−	51.3534i	0.143694	−	0.0829618i	−0.426429	−	0.904521i	$-0.640229\pi$
$619$	88.9466	−	51.3534i	0.143694	−	0.0829618i	0.570123	+	0.821559i	$0.306895\pi$
$620$	−353.242	−	517.337i	−0.569745	−	0.834414i
$621$		0			0
$622$	−1219.47	−	1219.47i	−1.96057	−	1.96057i
$623$	−1356.88	−	363.575i	−2.17798	−	0.583587i
$624$		0			0
$625$	596.718	−	185.885i	0.954748	−	0.297415i
$626$	244.862	−	424.113i	0.391153	−	0.677497i
$627$		0			0
$628$	−272.964	−	73.1406i	−0.434657	−	0.116466i
$629$		−	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	$0.900661\pi$
$632$	−7.66285	+	28.5981i	−0.0121248	+	0.0452502i
$633$		0			0
$634$	1022.01	+	590.056i	1.61200	+	0.930688i
$635$	−530.771	+	617.636i	−0.835860	+	0.972656i
$636$		0			0
$637$	22.5817	−	84.2762i	0.0354501	−	0.132302i
$638$	−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
$643$	−229.394	−	856.111i	−0.356756	−	1.33143i	−0.878260	−	0.478183i	$-0.841296\pi$
$643$	−229.394	−	856.111i	−0.356756	−	1.33143i	0.521504	−	0.853249i	$-0.325371\pi$
$644$	−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	0.483016	−	0.875612i	$-0.339541\pi$
$647$	−254.010	−	254.010i	−0.392596	−	0.392596i	−0.875612	+	0.483016i	$0.839541\pi$
$648$		0			0
$649$		−	1079.34i		−	1.66308i
$650$	−66.9662	+	10.1889i	−0.103025	+	0.0156753i
$651$		0			0
$652$	−124.346	+	33.3183i	−0.190714	+	0.0511017i
$653$	79.3045	+	295.968i	0.121446	+	0.453244i	0.999688	−	0.0249729i	$-0.00794995\pi$
$653$	79.3045	+	295.968i	0.121446	+	0.453244i	−0.878242	+	0.478217i	$0.841283\pi$
$654$		0			0
$655$	−84.9798	−	40.8513i	−0.129740	−	0.0623683i
$656$	−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	−0.215421	−	0.976521i	$-0.569112\pi$
$659$	344.367	−	198.821i	0.522561	−	0.301701i	0.737982	+	0.674821i	$0.235779\pi$
$660$		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	$-0.00941745\pi$
$662$	−1172.24	+	314.101i	−1.77076	+	0.474473i
$663$		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
$668$	393.333	+	105.393i	0.588821	+	0.157774i
$669$		0			0
$670$	−922.465	+	69.7752i	−1.37681	+	0.104142i
$671$	−486.135	+	842.010i	−0.724493	+	1.25486i
$672$		0			0
$673$	163.161	+	43.7189i	0.242439	+	0.0649612i	0.377992	−	0.925809i	$-0.376615\pi$
$673$	163.161	+	43.7189i	0.242439	+	0.0649612i	−0.135554	+	0.990770i	$0.543281\pi$
$674$		−	839.406i		−	1.24541i
$675$		0			0
$676$	−729.259			−1.07879
$677$	−67.6670	+	252.537i	−0.0999513	+	0.373023i	−0.997724	−	0.0674366i	$-0.978518\pi$
$677$	−67.6670	+	252.537i	−0.0999513	+	0.373023i	0.897772	+	0.440460i	$0.145185\pi$
$678$		0			0
$679$	−197.445	−	113.995i	−0.290787	−	0.167886i
$680$	3.88924	+	51.4178i	0.00571947	+	0.0756145i
$681$		0			0
$682$	−265.492	+	990.830i	−0.389285	+	1.45283i
$683$	−545.616	+	545.616i	−0.798852	+	0.798852i	−0.982915	−	0.184062i	$-0.941075\pi$
$683$	−545.616	+	545.616i	−0.798852	+	0.798852i	0.184062	+	0.982915i	$0.441075\pi$
$684$		0			0
$685$	371.642	+	70.0505i	0.542543	+	0.102263i
$686$	756.640	+	1310.54i	1.10297	+	1.91041i
$687$		0			0
$688$	−61.8962	−	231.000i	−0.0899654	−	0.335755i
$689$	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
$695$	−97.3804	+	202.573i	−0.140116	+	0.291472i
$696$		0			0
$697$	238.401	−	63.8792i	0.342038	−	0.0916488i
$698$	−325.423	−	1214.49i	−0.466222	−	1.73996i
$699$		0			0
$700$	765.870	−	1040.75i	1.09410	−	1.48678i
$701$	−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
$707$	−226.171	+	60.6024i	−0.319903	+	0.0857177i
$708$		0			0
$709$	−324.344	+	187.260i	−0.457467	+	0.264119i	−0.710979	−	0.703213i	$-0.751748\pi$
$709$	−324.344	+	187.260i	−0.457467	+	0.264119i	0.253511	+	0.967332i	$0.418414\pi$
$710$	−1259.36	−	237.376i	−1.77375	−	0.334332i
$711$		0			0
$712$	81.2971	+	81.2971i	0.114181	+	0.114181i
$713$	−714.520	−	191.455i	−1.00213	−	0.268520i
$714$		0			0
$715$	43.7658	+	37.6105i	0.0612109	+	0.0526021i
$716$	98.9288	−	171.350i	0.138169	−	0.239315i
$717$		0			0
$718$	320.531	+	85.8861i	0.446422	+	0.119619i
$719$		−	889.235i		−	1.23677i	−0.785877	−	0.618383i	$-0.787788\pi$
$719$		−	889.235i		−	1.23677i	0.785877	−	0.618383i	$-0.212212\pi$
$720$		0			0
$721$	−2042.70			−2.83314
$722$	−197.908	+	738.601i	−0.274110	+	1.02299i
$723$		0			0
$724$	393.666	+	227.283i	0.543737	+	0.313927i
$725$	66.0581	−	52.8302i	0.0911146	−	0.0728693i
$726$		0			0
$727$	116.187	−	433.617i	0.159818	−	0.596447i	−0.838827	−	0.544398i	$-0.816758\pi$
$727$	116.187	−	433.617i	0.159818	−	0.596447i	0.998645	−	0.0520491i	$-0.0165752\pi$
$728$	−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
$733$	178.010	+	664.342i	0.242851	+	0.906333i	0.974451	+	0.224599i	$0.0721072\pi$
$733$	178.010	+	664.342i	0.242851	+	0.906333i	−0.731600	+	0.681734i	$0.761226\pi$
$734$	−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	$0.0733976\pi$
$739$			337.793i			0.457095i	−0.973533	+	0.228547i	$0.926602\pi$
$740$	75.1341	−	26.3493i	0.101533	−	0.0356072i
$741$		0			0
$742$	−1301.41	+	348.712i	−1.75392	+	0.469962i
$743$	27.1883	+	101.468i	0.0365926	+	0.136565i	0.981806	−	0.189889i	$-0.0608128\pi$
$743$	27.1883	+	101.468i	0.0365926	+	0.136565i	−0.945213	+	0.326454i	$0.894146\pi$
$744$		0			0
$745$	355.769	−	740.079i	0.477542	−	0.993395i
$746$	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	$0.330741\pi$
$752$	973.616	−	260.880i	1.29470	−	0.346914i
$753$		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	0.948980	+	0.315337i	$0.102118\pi$
$757$	957.088	+	957.088i	1.26432	+	1.26432i	0.315337	+	0.948980i	$0.397882\pi$
$758$	1875.74	+	502.603i	2.47459	+	0.663065i
$759$		0			0
$760$	79.5041	−	92.5157i	0.104611	−	0.121731i
$761$	−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
$763$	−104.513	−	28.0042i	−0.136977	−	0.0367028i
$764$			439.390i			0.575118i
$765$		0			0
$766$	−879.199			−1.14778
$767$	21.3120	−	79.5374i	0.0277861	−	0.103699i
$768$		0			0
$769$	−731.602	−	422.391i	−0.951368	−	0.549273i	−0.0578626	−	0.998325i	$-0.518429\pi$
$769$	−731.602	−	422.391i	−0.951368	−	0.549273i	−0.893506	+	0.449052i	$0.851762\pi$
$770$	−2109.91	+	159.593i	−2.74014	+	0.207264i
$771$		0			0
$772$	317.610	−	1185.34i	0.411412	−	1.53541i
$773$	−501.313	+	501.313i	−0.648529	+	0.648529i	−0.952637	−	0.304108i	$-0.901642\pi$
$773$	−501.313	+	501.313i	−0.648529	+	0.648529i	0.304108	+	0.952637i	$0.401642\pi$
$774$		0			0
$775$	262.866	−	672.524i	0.339182	−	0.867773i
$776$	9.32990	+	16.1599i	0.0120231	+	0.0208246i
$777$		0			0
$778$	531.884	+	1985.02i	0.683655	+	2.55144i
$779$	−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
$785$	−107.798	−	307.384i	−0.137323	−	0.391572i
$786$		0			0
$787$	983.133	−	263.430i	1.24922	−	0.334726i	0.427183	−	0.904165i	$-0.359506\pi$
$787$	983.133	−	263.430i	1.24922	−	0.334726i	0.822034	+	0.569439i	$0.192839\pi$
$788$	−8.35636	−	31.1863i	−0.0106045	−	0.0395766i
$789$		0			0
$790$	−413.610	+	145.052i	−0.523557	+	0.183610i
$791$	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
$797$	1378.41	−	369.343i	1.72949	−	0.463416i	0.749427	−	0.662087i	$-0.230329\pi$
$797$	1378.41	−	369.343i	1.72949	−	0.463416i	0.980066	+	0.198670i	$0.0636622\pi$
$798$		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
$803$	215.352	+	57.7035i	0.268185	+	0.0718599i
$804$		0			0
$805$	−115.088	−	1521.52i	−0.142966	−	1.89009i
$806$	−39.1287	+	67.7729i	−0.0485468	+	0.0840855i
$807$		0			0
$808$	18.5110	+	4.96001i	0.0229097	+	0.00613862i
$809$			549.873i			0.679694i	0.940481	+	0.339847i	$0.110375\pi$
$809$			549.873i			0.679694i	−0.940481	+	0.339847i	$0.889625\pi$
$810$		0			0
$811$	1542.32			1.90175			0.950876	−	0.309573i	$-0.100186\pi$
$811$	1542.32			1.90175			0.950876	+	0.309573i	$0.100186\pi$
$812$	45.2619	−	168.920i	0.0557413	−	0.208029i
$813$		0			0
$814$	−112.911	−	65.1893i	−0.138711	−	0.0800851i
$815$	−112.540	−	96.7119i	−0.138085	−	0.118665i
$816$		0			0
$817$	106.530	−	397.576i	0.130392	−	0.486629i
$818$	−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
$823$	−21.2506	−	79.3084i	−0.0258209	−	0.0963650i	0.951813	−	0.306679i	$-0.0992179\pi$
$823$	−21.2506	−	79.3084i	−0.0258209	−	0.0963650i	−0.977634	+	0.210314i	$0.932551\pi$
$824$	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	−0.992041	−	0.125915i	$-0.959813\pi$
$827$	−924.549	−	924.549i	−1.11796	−	1.11796i	−0.125915	−	0.992041i	$-0.540187\pi$
$828$		0			0
$829$		−	114.907i		−	0.138610i	−0.997596	−	0.0693048i	$-0.977922\pi$
$829$		−	114.907i		−	0.138610i	0.997596	−	0.0693048i	$-0.0220781\pi$
$830$	−1975.99	−	949.892i	−2.38071	−	1.14445i
$831$		0			0
$832$	−67.3549	+	18.0477i	−0.0809554	+	0.0216919i
$833$	−254.489	−	949.767i	−0.305509	−	1.14018i
$834$		0			0
$835$	155.334	+	442.930i	0.186029	+	0.530455i
$836$	−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	−0.839531	−	0.543312i	$-0.817170\pi$
$839$	−661.782	+	382.080i	−0.788774	+	0.455399i	0.0507566	+	0.998711i	$0.483837\pi$
$840$		0			0
$841$	−414.776	+	718.414i	−0.493194	+	0.854237i
$842$	10.6255	−	2.84711i	0.0126194	−	0.00338136i
$843$		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
$848$	−549.777	−	147.312i	−0.648322	−	0.173717i
$849$		0			0
$850$	−596.166	+	476.787i	−0.701372	+	0.560925i
$851$	47.0101	−	81.4239i	0.0552410	−	0.0956803i
$852$		0			0
$853$	−710.152	−	190.285i	−0.832534	−	0.223077i	−0.182715	−	0.983166i	$-0.558489\pi$
$853$	−710.152	−	190.285i	−0.832534	−	0.223077i	−0.649819	+	0.760089i	$0.725155\pi$
$854$		−	2719.80i		−	3.18478i
$855$		0			0
$856$	−14.5973			−0.0170529
$857$	−186.075	+	694.443i	−0.217124	+	0.810319i	0.768284	+	0.640109i	$0.221111\pi$
$857$	−186.075	+	694.443i	−0.217124	+	0.810319i	−0.985408	+	0.170209i	$0.945556\pi$
$858$		0			0
$859$	1043.29	+	602.342i	1.21454	+	0.701213i	0.963744	−	0.266828i	$-0.0859755\pi$
$859$	1043.29	+	602.342i	1.21454	+	0.701213i	0.250792	+	0.968041i	$0.419309\pi$
$860$	−232.581	+	270.645i	−0.270443	+	0.314704i
$861$		0			0
$862$	−573.836	+	2141.58i	−0.665703	+	2.48444i
$863$	214.571	−	214.571i	0.248634	−	0.248634i	−0.571776	−	0.820410i	$-0.693745\pi$
$863$	214.571	−	214.571i	0.248634	−	0.248634i	0.820410	+	0.571776i	$0.193745\pi$
$864$		0			0
$865$	−184.573	+	979.223i	−0.213379	+	1.13205i
$866$	−751.049	−	1300.86i	−0.867263	−	1.50214i
$867$		0			0
$868$	−386.382	−	1442.00i	−0.445141	−	1.66129i
$869$	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
$875$	1488.53	+	52.5833i	1.70117	+	0.0600952i
$876$		0			0
$877$	305.581	−	81.8801i	0.348438	−	0.0933638i	−0.0803551	−	0.996766i	$-0.525605\pi$
$877$	305.581	−	81.8801i	0.348438	−	0.0933638i	0.428794	+	0.903402i	$0.358939\pi$
$878$	102.728	+	383.387i	0.117003	+	0.436660i
$879$		0			0
$880$	−805.620	−	387.275i	−0.915477	−	0.440085i
$881$	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	−0.909028	−	0.416735i	$-0.863174\pi$
$883$	−434.695	+	434.695i	−0.492293	+	0.492293i	0.416735	+	0.909028i	$0.363174\pi$
$884$	37.2759	−	21.5213i	0.0421673	−	0.0243453i
$885$		0			0
$886$	638.166	−	1105.34i	0.720277	−	1.24756i
$887$	553.319	−	148.261i	0.623810	−	0.167149i	0.0669506	−	0.997756i	$-0.478673\pi$
$887$	553.319	−	148.261i	0.623810	−	0.167149i	0.556859	+	0.830607i	$0.312006\pi$
$888$		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
$893$	1675.70	+	449.003i	1.87649	+	0.502803i
$894$		0			0
$895$	227.415	−	17.2017i	0.254096	−	0.0192198i
$896$	185.266	−	320.890i	0.206770	−	0.358136i
$897$		0			0
$898$	2307.42	+	618.271i	2.56951	+	0.688497i
$899$		−	97.7228i		−	0.108702i
$900$		0			0
$901$	414.097			0.459597
$902$	214.537	−	800.662i	0.237846	−	0.887652i
$903$		0			0
$904$	−129.968	−	75.0371i	−0.143770	−	0.0830057i
$905$	39.5198	+	522.474i	0.0436683	+	0.577319i
$906$		0			0
$907$	204.950	−	764.884i	0.225965	−	0.843312i	−0.756051	−	0.654513i	$-0.772874\pi$
$907$	204.950	−	764.884i	0.225965	−	0.843312i	0.982016	−	0.188799i	$-0.0604595\pi$
$908$	−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
$913$	483.417	+	1804.14i	0.529482	+	1.97605i
$914$	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	$-0.851803\pi$
$919$		−	825.147i		−	0.897875i	0.893563	−	0.448937i	$-0.148197\pi$
$920$	−54.1072	+	112.555i	−0.0588121	+	0.122342i
$921$		0			0
$922$	−730.302	+	195.684i	−0.792084	+	0.212238i
$923$	21.5573	+	80.4529i	0.0233557	+	0.0871646i
$924$		0			0
$925$	73.9189	+	54.3958i	0.0799124	+	0.0588063i
$926$	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	−0.864184	−	0.503177i	$-0.832164\pi$
$929$	−799.415	+	461.543i	−0.860511	+	0.496817i	0.00367207	+	0.999993i	$0.498831\pi$
$930$		0			0
$931$	−1163.04	+	2014.44i	−1.24923	+	2.16374i
$932$	−571.714	+	153.190i	−0.613427	+	0.164367i
$933$		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	0.999451	+	0.0331234i	$0.0105454\pi$
$937$	967.522	+	967.522i	1.03257	+	1.03257i	0.0331234	+	0.999451i	$0.489455\pi$
$938$	−2129.51	−	570.601i	−2.27027	−	0.608316i
$939$		0			0
$940$	−1140.71	−	980.282i	−1.21353	−	1.04285i
$941$	−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
$943$	577.384	+	154.709i	0.612284	+	0.164061i
$944$			1275.50i			1.35117i
$945$		0			0
$946$	584.344			0.617700
$947$	−319.307	+	1191.67i	−0.337177	+	1.25836i	0.564312	+	0.825562i	$0.309142\pi$
$947$	−319.307	+	1191.67i	−0.337177	+	1.25836i	−0.901489	+	0.432802i	$0.857525\pi$
$948$		0			0
$949$	14.7301	+	8.50444i	0.0155217	+	0.00896147i
$950$	1794.80	+	199.694i	1.88926	+	0.210205i
$951$		0			0
$952$	−31.8050	+	118.698i	−0.0334087	+	0.124683i
$953$	719.749	−	719.749i	0.755245	−	0.755245i	−0.220208	−	0.975453i	$-0.570674\pi$
$953$	719.749	−	719.749i	0.755245	−	0.755245i	0.975453	+	0.220208i	$0.0706736\pi$
$954$		0			0
$955$	−418.269	+	285.598i	−0.437978	+	0.299055i
$956$	319.749	+	553.822i	0.334466	+	0.579312i
$957$		0			0
$958$	29.0218	+	108.311i	0.0302941	+	0.113059i
$959$	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
$965$	1334.80	−	468.111i	1.38321	−	0.485089i
$966$		0			0
$967$	1432.50	−	383.836i	1.48138	−	0.396935i	0.574564	−	0.818460i	$-0.305172\pi$
$967$	1432.50	−	383.836i	1.48138	−	0.396935i	0.906817	+	0.421525i	$0.138505\pi$
$968$	−7.64298	−	28.5240i	−0.00789564	−	0.0294669i
$969$		0			0
$970$	−119.684	+	248.970i	−0.123386	+	0.256670i
$971$	−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
$977$	−413.244	+	110.728i	−0.422972	+	0.113335i	−0.464025	−	0.885822i	$-0.653595\pi$
$977$	−413.244	+	110.728i	−0.422972	+	0.113335i	0.0410533	+	0.999157i	$0.486929\pi$
$978$		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
$983$	−415.799	−	111.413i	−0.422990	−	0.113340i	0.0410437	−	0.999157i	$-0.486932\pi$
$983$	−415.799	−	111.413i	−0.422990	−	0.113340i	−0.464034	+	0.885817i	$0.653598\pi$
$984$		0			0
$985$	24.2557	−	28.2254i	0.0246251	−	0.0286552i
$986$	−51.6563	+	89.4713i	−0.0523897	+	0.0907417i
$987$		0			0
$988$	−98.3538	−	26.3538i	−0.0995484	−	0.0266739i
$989$			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	$0.406270\pi$
$992$	342.905	−	1279.74i	0.345670	−	1.29006i
$993$		0			0
$994$	−2644.90	−	1527.03i	−2.66086	−	1.53625i
$995$	703.342	−	53.2007i	0.706876	−	0.0534680i
$996$		0			0
$997$	106.861	−	398.810i	0.107182	−	0.400010i	−0.891401	−	0.453215i	$-0.850277\pi$
$997$	106.861	−	398.810i	0.107182	−	0.400010i	0.998584	+	0.0532048i	$0.0169436\pi$
$998$	−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.352.7		32
3.2	odd	2	inner	405.3.l.n.352.2		32
5.3	odd	4	inner	405.3.l.n.28.2		32
9.2	odd	6	inner	405.3.l.n.217.7		32
9.4	even	3		135.3.g.b.82.7	yes	16
9.5	odd	6		135.3.g.b.82.2	yes	16
9.7	even	3	inner	405.3.l.n.217.2		32
15.8	even	4	inner	405.3.l.n.28.7		32
45.4	even	6		675.3.g.j.82.2		16
45.13	odd	12		135.3.g.b.28.7	yes	16
45.14	odd	6		675.3.g.j.82.7		16
45.22	odd	12		675.3.g.j.568.2		16
45.23	even	12		135.3.g.b.28.2	✓	16
45.32	even	12		675.3.g.j.568.7		16
45.38	even	12	inner	405.3.l.n.298.2		32
45.43	odd	12	inner	405.3.l.n.298.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.b.28.2	✓	16	45.23	even	12
135.3.g.b.28.7	yes	16	45.13	odd	12
135.3.g.b.82.2	yes	16	9.5	odd	6
135.3.g.b.82.7	yes	16	9.4	even	3
405.3.l.n.28.2		32	5.3	odd	4	inner
405.3.l.n.28.7		32	15.8	even	4	inner
405.3.l.n.217.2		32	9.7	even	3	inner
405.3.l.n.217.7		32	9.2	odd	6	inner
405.3.l.n.298.2		32	45.38	even	12	inner
405.3.l.n.298.7		32	45.43	odd	12	inner
405.3.l.n.352.2		32	3.2	odd	2	inner
405.3.l.n.352.7		32	1.1	even	1	trivial
675.3.g.j.82.2		16	45.4	even	6
675.3.g.j.82.7		16	45.14	odd	6
675.3.g.j.568.2		16	45.22	odd	12
675.3.g.j.568.7		16	45.32	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.747344 - 2.78913i) q^{2} +(-3.75659 - 2.16887i) q^{4} +(-0.377122 - 4.98576i) q^{5} +(3.08399 - 11.5096i) q^{7} +(-0.689596 + 0.689596i) q^{8} +(-14.1877 - 2.67423i) q^{10} +(6.14980 + 10.6518i) q^{11} +(0.242861 + 0.906368i) q^{13} +(-29.7970 - 17.2033i) q^{14} +(-7.26748 - 12.5876i) q^{16} +(7.47753 + 7.47753i) q^{17} -25.0163i q^{19} +(-9.39677 + 19.5474i) q^{20} +(34.3051 - 9.19203i) q^{22} +(6.62867 + 24.7385i) q^{23} +(-24.7156 + 3.76048i) q^{25} +2.70947 q^{26} +(-36.5482 + 36.5482i) q^{28} +(-2.93013 + 1.69171i) q^{29} +(-14.4414 + 25.0133i) q^{31} +(-44.3078 + 11.8723i) q^{32} +(26.4441 - 15.2675i) q^{34} +(-58.5472 - 11.0355i) q^{35} +(-2.59583 - 2.59583i) q^{37} +(-69.7736 - 18.6958i) q^{38} +(3.69822 + 3.17810i) q^{40} +(11.6697 - 20.2125i) q^{41} +(15.8927 + 4.25843i) q^{43} -53.3525i q^{44} +73.9528 q^{46} +(-17.9484 + 66.9844i) q^{47} +(-80.5250 - 46.4912i) q^{49} +(-7.98258 + 71.7452i) q^{50} +(1.05347 - 3.93159i) q^{52} +(27.6894 - 27.6894i) q^{53} +(50.7879 - 34.6784i) q^{55} +(5.81027 + 10.0637i) q^{56} +(2.52858 + 9.43678i) q^{58} +(-75.9971 - 43.8770i) q^{59} +(39.5244 + 68.4583i) q^{61} +(58.9725 + 58.9725i) q^{62} +74.3129i q^{64} +(4.42734 - 1.55266i) q^{65} +(61.8926 - 16.5841i) q^{67} +(-11.8723 - 44.3078i) q^{68} +(-74.5343 + 155.048i) q^{70} +88.7641 q^{71} +(12.8174 - 12.8174i) q^{73} +(-9.18007 + 5.30012i) q^{74} +(-54.2571 + 93.9761i) q^{76} +(141.564 - 37.9319i) q^{77} +(26.2915 - 15.1794i) q^{79} +(-60.0182 + 40.9810i) q^{80} +(-47.6540 - 47.6540i) q^{82} +(146.683 + 39.3035i) q^{83} +(34.4612 - 40.1011i) q^{85} +(23.7546 - 41.1442i) q^{86} +(-11.5863 - 3.10454i) q^{88} -117.891i q^{89} +11.1809 q^{91} +(28.7535 - 107.309i) q^{92} +(173.414 + 100.121i) q^{94} +(-124.725 + 9.43419i) q^{95} +(4.95215 - 18.4817i) q^{97} +(-189.850 + 189.850i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{7} + 80 q^{10} - 40 q^{13} + 152 q^{16} + 136 q^{22} + 32 q^{25} - 224 q^{28} - 200 q^{31} + 32 q^{37} + 48 q^{40} - 136 q^{43} + 304 q^{46} - 640 q^{52} + 496 q^{55} - 48 q^{58} + 280 q^{61}+ \cdots - 448 q^{97}+O(q^{100}) \) 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

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