LMFDB - Embedded newform 405.3.l.n.217.7

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			217.7
Character	$\chi$	$=$	405.217
Dual form			405.3.l.n.28.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.78913 - 0.747344i) q^{2} +(3.75659 - 2.16887i) q^{4} +(-4.50635 - 2.16628i) q^{5} +(-11.5096 + 3.08399i) q^{7} +(0.689596 - 0.689596i) q^{8} +(-14.1877 - 2.67423i) q^{10} +(-6.14980 + 10.6518i) q^{11} +(-0.906368 - 0.242861i) q^{13} +(-29.7970 + 17.2033i) q^{14} +(-7.26748 + 12.5876i) q^{16} +(-7.47753 - 7.47753i) q^{17} -25.0163i q^{19} +(-21.6269 + 1.63586i) q^{20} +(-9.19203 + 34.3051i) q^{22} +(24.7385 + 6.62867i) q^{23} +(15.6144 + 19.5241i) q^{25} -2.70947 q^{26} +(-36.5482 + 36.5482i) q^{28} +(-2.93013 - 1.69171i) q^{29} +(-14.4414 - 25.0133i) q^{31} +(-11.8723 + 44.3078i) q^{32} +(-26.4441 - 15.2675i) q^{34} +(58.5472 + 11.0355i) q^{35} +(-2.59583 - 2.59583i) q^{37} +(-18.6958 - 69.7736i) q^{38} +(-4.60142 + 1.61370i) q^{40} +(-11.6697 - 20.2125i) q^{41} +(-4.25843 - 15.8927i) q^{43} +53.3525i q^{44} +73.9528 q^{46} +(-66.9844 + 17.9484i) q^{47} +(80.5250 - 46.4912i) q^{49} +(58.1418 + 42.7857i) q^{50} +(-3.93159 + 1.05347i) q^{52} +(-27.6894 + 27.6894i) q^{53} +(50.7879 - 34.6784i) q^{55} +(-5.81027 + 10.0637i) q^{56} +(-9.43678 - 2.52858i) q^{58} +(-75.9971 + 43.8770i) q^{59} +(39.5244 - 68.4583i) q^{61} +(-58.9725 - 58.9725i) q^{62} +74.3129i q^{64} +(3.55831 + 3.05786i) q^{65} +(-16.5841 + 61.8926i) q^{67} +(-44.3078 - 11.8723i) q^{68} +(171.543 - 12.9755i) q^{70} -88.7641 q^{71} +(12.8174 - 12.8174i) q^{73} +(-9.18007 - 5.30012i) q^{74} +(-54.2571 - 93.9761i) q^{76} +(37.9319 - 141.564i) q^{77} +(-26.2915 - 15.1794i) q^{79} +(60.0182 - 40.9810i) q^{80} +(-47.6540 - 47.6540i) q^{82} +(39.3035 + 146.683i) q^{83} +(17.4980 + 49.8948i) q^{85} +(-23.7546 - 41.1442i) q^{86} +(3.10454 + 11.5863i) q^{88} +117.891i q^{89} +11.1809 q^{91} +(107.309 - 28.7535i) q^{92} +(-173.414 + 100.121i) q^{94} +(-54.1923 + 112.732i) q^{95} +(-18.4817 + 4.95215i) q^{97} +(189.850 - 189.850i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.326612\pi$
$2$	2.78913	−	0.747344i	1.39456	−	0.373672i	0.876389	+	0.481604i	$0.159946\pi$
$3$		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	−0.957989	−	0.286803i	$-0.907407\pi$
$7$	−11.5096	+	3.08399i	−1.64423	+	0.440570i	−0.686242	+	0.727374i	$0.740741\pi$
$8$	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	0.438502	+	0.898730i	$0.355509\pi$
$11$	−6.14980	+	10.6518i	−0.559073	+	0.968342i	−0.997574	+	0.0696117i	$0.977824\pi$
$12$		0			0
$13$	−0.906368	−	0.242861i	−0.0697206	−	0.0186816i	0.223790	−	0.974637i	$-0.428157\pi$
$13$	−0.906368	−	0.242861i	−0.0697206	−	0.0186816i	−0.293511	+	0.955956i	$0.594824\pi$
$14$	−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	$-0.350672\pi$
$17$	−7.47753	−	7.47753i	−0.439855	−	0.439855i	−0.891963	+	0.452108i	$0.850672\pi$
$18$		0			0
$19$		−	25.0163i		−	1.31665i	−0.752735	−	0.658323i	$-0.771266\pi$
$19$		−	25.0163i		−	1.31665i	0.752735	−	0.658323i	$-0.228734\pi$
$20$	−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	$-0.228709\pi$
$23$	24.7385	+	6.62867i	1.07559	+	0.288203i	0.322801	+	0.946467i	$0.395375\pi$
$24$		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	$-0.351912\pi$
$29$	−2.93013	−	1.69171i	−0.101039	−	0.0583348i	−0.549668	+	0.835383i	$0.685246\pi$
$30$		0			0
$31$	−14.4414	−	25.0133i	−0.465853	−	0.806881i	0.533387	−	0.845871i	$-0.320919\pi$
$31$	−14.4414	−	25.0133i	−0.465853	−	0.806881i	−0.999240	+	0.0389908i	$0.987586\pi$
$32$	−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	0.671157	−	0.741315i	$-0.265797\pi$
$37$	−2.59583	−	2.59583i	−0.0701575	−	0.0701575i	−0.741315	+	0.671157i	$0.765797\pi$
$38$	−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	$-0.258537\pi$
$41$	−11.6697	−	20.2125i	−0.284627	−	0.492989i	−0.972519	+	0.232825i	$0.925203\pi$
$42$		0			0
$43$	−4.25843	−	15.8927i	−0.0990334	−	0.369598i	0.898567	−	0.438837i	$-0.144609\pi$
$43$	−4.25843	−	15.8927i	−0.0990334	−	0.369598i	−0.997600	+	0.0692394i	$0.977943\pi$
$44$			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	$-0.847439\pi$
$47$	−66.9844	+	17.9484i	−1.42520	+	0.381881i	−0.537875	+	0.843025i	$0.680773\pi$
$48$		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	$-0.870444\pi$
$53$	−27.6894	+	27.6894i	−0.522442	+	0.522442i	0.395866	+	0.918308i	$0.370444\pi$
$54$		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	$-0.933587\pi$
$59$	−75.9971	+	43.8770i	−1.28809	+	0.743677i	−0.309774	+	0.950810i	$0.600253\pi$
$60$		0			0
$61$	39.5244	−	68.4583i	0.647942	−	1.12227i	−0.335672	−	0.941979i	$-0.608963\pi$
$61$	39.5244	−	68.4583i	0.647942	−	1.12227i	0.983614	−	0.180289i	$-0.0577032\pi$
$62$	−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	0.724575	+	0.689196i	$0.242036\pi$
$67$	−16.5841	+	61.8926i	−0.247523	+	0.923769i	−0.972098	+	0.234574i	$0.924631\pi$
$68$	−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	$-0.714941\pi$
$71$	−88.7641			−1.25020			−0.625099	+	0.780546i	$0.714941\pi$
$72$		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
$77$	37.9319	−	141.564i	0.492622	−	1.83849i
$78$		0			0
$79$	−26.2915	−	15.1794i	−0.332804	−	0.192144i	0.324281	−	0.945961i	$-0.394878\pi$
$79$	−26.2915	−	15.1794i	−0.332804	−	0.192144i	−0.657085	+	0.753816i	$0.728211\pi$
$80$	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	0.626909	+	0.779093i	$0.284320\pi$
$83$	39.3035	+	146.683i	0.473536	+	1.76726i	−0.153372	+	0.988168i	$0.549013\pi$
$84$		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	−0.352824	−	0.935690i	$-0.614778\pi$
$97$	−18.4817	+	4.95215i	−0.190533	+	0.0510531i	0.162291	+	0.986743i	$0.448112\pi$
$98$	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	$-0.802319\pi$
$101$	9.82532	−	17.0179i	0.0972804	−	0.168495i	0.910558	+	0.413381i	$0.135652\pi$
$102$		0			0
$103$	165.589	+	44.3694i	1.60766	+	0.430770i	0.947343	−	0.320219i	$-0.103757\pi$
$103$	165.589	+	44.3694i	1.60766	+	0.430770i	0.660314	+	0.750990i	$0.270423\pi$
$104$	−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	$-0.272282\pi$
$107$	−10.5840	−	10.5840i	−0.0989155	−	0.0989155i	−0.754833	+	0.655917i	$0.772282\pi$
$108$		0			0
$109$		−	9.08051i		−	0.0833075i	−0.999132	−	0.0416537i	$-0.986737\pi$
$109$		−	9.08051i		−	0.0833075i	0.999132	−	0.0416537i	$-0.0132626\pi$
$110$	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	$-0.178252\pi$
$113$	148.642	+	39.8284i	1.31541	+	0.352464i	0.468155	+	0.883646i	$0.344919\pi$
$114$		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	0.0891750	−	0.996016i	$-0.471577\pi$
$127$	−115.169	−	115.169i	−0.906841	−	0.906841i	−0.996016	+	0.0891750i	$0.971577\pi$
$128$	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	$-0.189597\pi$
$131$	−9.42889	−	16.3313i	−0.0719762	−	0.124667i	−0.899767	+	0.436370i	$0.856264\pi$
$132$		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	$-0.672358\pi$
$137$	−73.0600	+	19.5764i	−0.533284	+	0.142893i	−0.0178799	+	0.999840i	$0.505692\pi$
$138$		0			0
$139$	38.9303	−	22.4764i	0.280074	−	0.161701i	−0.353383	−	0.935479i	$-0.614969\pi$
$139$	38.9303	−	22.4764i	0.280074	−	0.161701i	0.633457	+	0.773778i	$0.281635\pi$
$140$	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	$-0.480872\pi$
$149$	142.228	−	82.1151i	0.954547	−	0.551108i	0.894491	+	0.447087i	$0.147539\pi$
$150$		0			0
$151$	−19.2011	+	33.2572i	−0.127159	+	0.220247i	−0.922575	−	0.385818i	$-0.873919\pi$
$151$	−19.2011	+	33.2572i	−0.127159	+	0.220247i	0.795416	+	0.606064i	$0.207253\pi$
$152$	−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	−0.998606	−	0.0527803i	$-0.983192\pi$
$157$	−16.8614	+	62.9277i	−0.107398	+	0.400814i	0.891208	+	0.453594i	$0.149858\pi$
$158$	−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	−0.639800	−	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
$167$	−24.2968	+	90.6768i	−0.145490	+	0.542975i	0.854243	+	0.519873i	$0.174021\pi$
$167$	−24.2968	+	90.6768i	−0.145490	+	0.542975i	−0.999733	+	0.0231017i	$0.992646\pi$
$168$		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	−0.938679	−	0.344792i	$-0.887949\pi$
$173$	−51.5809	−	192.502i	−0.298155	−	1.11273i	0.640524	−	0.767938i	$-0.278717\pi$
$174$		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	$-0.747906\pi$
$191$	50.6473	−	87.7237i	0.265169	−	0.459286i	0.967608	+	0.252458i	$0.0812389\pi$
$192$		0			0
$193$	−273.261	−	73.2202i	−1.41586	−	0.379379i	−0.531848	−	0.846840i	$-0.678502\pi$
$193$	−273.261	−	73.2202i	−1.41586	−	0.379379i	−0.884014	+	0.467461i	$0.845169\pi$
$194$	−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	$-0.256014\pi$
$197$	−5.26310	−	5.26310i	−0.0267163	−	0.0267163i	−0.720339	+	0.693622i	$0.756014\pi$
$198$		0			0
$199$			141.070i			0.708895i	0.935076	+	0.354448i	$0.115331\pi$
$199$			141.070i			0.708895i	−0.935076	+	0.354448i	$0.884669\pi$
$200$	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	0.914508	−	0.404568i	$-0.132578\pi$
$211$	22.5534	+	39.0637i	0.106888	+	0.185136i	−0.807620	+	0.589703i	$0.799245\pi$
$212$	−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	0.962593	−	0.270952i	$-0.0873386\pi$
$223$	−1.45246	−	5.42064i	−0.00651326	−	0.0243078i	−0.969106	+	0.246645i	$0.920672\pi$
$224$		−	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	$-0.529786\pi$
$227$	73.4236	−	19.6738i	0.323452	−	0.0866686i	0.416891	+	0.908956i	$0.363120\pi$
$228$		0			0
$229$	−47.7957	+	27.5948i	−0.208715	+	0.120502i	−0.600714	−	0.799464i	$-0.705117\pi$
$229$	−47.7957	+	27.5948i	−0.208715	+	0.120502i	0.391999	+	0.919966i	$0.371784\pi$
$230$	−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	$-0.844590\pi$
$233$	−96.4842	+	96.4842i	−0.414095	+	0.414095i	0.469067	+	0.883162i	$0.344590\pi$
$234$		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	$-0.766468\pi$
$239$	−127.675	+	73.7133i	−0.534206	+	0.308424i	0.208522	+	0.978018i	$0.433135\pi$
$240$		0			0
$241$	179.499	−	310.901i	0.744809	−	1.29005i	−0.205475	−	0.978662i	$-0.565874\pi$
$241$	179.499	−	310.901i	0.744809	−	1.29005i	0.950284	−	0.311384i	$-0.100793\pi$
$242$	−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	$-0.400723\pi$
$251$	154.041			0.613710			0.306855	+	0.951756i	$0.400723\pi$
$252$		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	0.541641	+	0.840610i	$0.317803\pi$
$257$	−89.3689	+	333.529i	−0.347739	+	1.29778i	−0.889380	+	0.457169i	$0.848863\pi$
$258$		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	0.967249	+	0.253828i	$0.0816897\pi$
$263$	67.4597	+	251.763i	0.256501	+	0.957274i	−0.710748	+	0.703446i	$0.751644\pi$
$264$		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	−0.0688778	−	0.997625i	$-0.521942\pi$
$277$	102.569	−	27.4833i	0.370285	−	0.0992175i	0.439163	+	0.898408i	$0.355275\pi$
$278$	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	$-0.833984\pi$
$281$	−0.574798	+	0.995579i	−0.00204554	+	0.00354299i	0.865001	+	0.501770i	$0.167318\pi$
$282$		0			0
$283$	−309.889	−	83.0344i	−1.09501	−	0.293408i	−0.334280	−	0.942474i	$-0.608493\pi$
$283$	−309.889	−	83.0344i	−1.09501	−	0.293408i	−0.760732	+	0.649066i	$0.775160\pi$
$284$	−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	$-0.360533\pi$
$293$	99.3033	+	26.6082i	0.338919	+	0.0908131i	−0.0853454	+	0.996351i	$0.527199\pi$
$294$		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	0.575077	−	0.818099i	$-0.304972\pi$
$307$	−74.6079	−	74.6079i	−0.243023	−	0.243023i	−0.818099	+	0.575077i	$0.804972\pi$
$308$	−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	−0.721930	−	0.691966i	$-0.756745\pi$
$311$	−298.630	−	517.242i	−0.960225	−	1.66316i	−0.238295	−	0.971193i	$-0.576589\pi$
$312$		0			0
$313$	−43.8958	−	163.821i	−0.140242	−	0.523391i	−0.999921	−	0.0125563i	$-0.996003\pi$
$313$	−43.8958	−	163.821i	−0.140242	−	0.523391i	0.859679	−	0.510835i	$-0.170664\pi$
$314$			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	$-0.806322\pi$
$317$	−394.769	+	105.778i	−1.24533	+	0.333685i	−0.424798	+	0.905288i	$0.639655\pi$
$318$		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	0.351661	+	0.936127i	$0.385617\pi$
$331$	−210.145	+	363.982i	−0.634879	+	1.09964i	−0.986541	+	0.163516i	$0.947716\pi$
$332$	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	0.759832	+	0.650120i	$0.225281\pi$
$337$	−75.2392	+	280.796i	−0.223262	+	0.833224i	−0.983094	+	0.183104i	$0.941385\pi$
$338$	−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	0.386168	+	0.922428i	$0.373798\pi$
$347$	−142.089	+	530.282i	−0.409477	+	1.52819i	−0.795646	+	0.605762i	$0.792868\pi$
$348$		0			0
$349$	−377.101	−	217.720i	−1.08052	−	0.623838i	−0.149483	−	0.988764i	$-0.547761\pi$
$349$	−377.101	−	217.720i	−1.08052	−	0.623838i	−0.931036	+	0.364926i	$0.881094\pi$
$350$	−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	0.973870	+	0.227104i	$0.0729259\pi$
$353$	86.1412	+	321.483i	0.244026	+	0.910718i	−0.729844	+	0.683613i	$0.760407\pi$
$354$		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	−0.869738	−	0.493515i	$-0.835712\pi$
$367$	−505.064	+	135.331i	−1.37620	+	0.368750i	−0.506458	+	0.862265i	$0.669045\pi$
$368$	−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	−0.0277173	−	0.999616i	$-0.508824\pi$
$373$	−205.720	−	55.1226i	−0.551529	−	0.147782i	−0.523812	+	0.851834i	$0.675491\pi$
$374$	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	$0.652628\pi$
$380$	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	$-0.546788\pi$
$383$	−294.108	−	78.8060i	−0.767906	−	0.205760i	−0.621446	+	0.783457i	$0.713455\pi$
$384$		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	−0.994199	−	0.107558i	$-0.965697\pi$
$389$	−616.350	−	355.850i	−1.58445	−	0.914780i	−0.590247	−	0.807223i	$-0.700970\pi$
$390$		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	0.652959	−	0.757393i	$-0.273527\pi$
$397$	−41.4605	−	41.4605i	−0.104435	−	0.104435i	−0.757393	+	0.652959i	$0.773527\pi$
$398$	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	$-0.233182\pi$
$401$	−83.1858	−	144.082i	−0.207446	−	0.359307i	−0.950909	+	0.309470i	$0.899848\pi$
$402$		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	−0.474658	−	0.880170i	$-0.657428\pi$
$409$	20.5577	−	11.8690i	0.0502632	−	0.0290195i	0.524921	+	0.851151i	$0.324095\pi$
$410$	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	$-0.463364\pi$
$419$	432.642	−	249.786i	1.03256	−	0.596147i	0.917716	+	0.397236i	$0.130031\pi$
$420$		0			0
$421$	1.90482	−	3.29924i	0.00452450	−	0.00783667i	−0.863754	−	0.503913i	$-0.831893\pi$
$421$	1.90482	−	3.29924i	0.00452450	−	0.00783667i	0.868279	+	0.496077i	$0.165226\pi$
$422$	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	$-0.150174\pi$
$431$	767.834			1.78152			0.890759	+	0.454477i	$0.150174\pi$
$432$		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
$437$	165.825	−	618.867i	0.379462	−	1.41617i
$438$		0			0
$439$	119.042	+	68.7289i	0.271166	+	0.156558i	0.629418	−	0.777067i	$-0.283294\pi$
$439$	119.042	+	68.7289i	0.271166	+	0.156558i	−0.358251	+	0.933625i	$0.616627\pi$
$440$	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	0.966256	+	0.257582i	$0.0829258\pi$
$443$	114.403	+	426.956i	0.258245	+	0.963783i	−0.708011	+	0.706201i	$0.750408\pi$
$444$		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	0.871768	−	0.489919i	$-0.162974\pi$
$457$	855.367	−	229.195i	1.87170	−	0.501521i	0.999933	−	0.0116012i	$-0.00369286\pi$
$458$	−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	$-0.741675\pi$
$461$	130.919	−	226.759i	0.283990	−	0.491885i	0.972364	+	0.233471i	$0.0750084\pi$
$462$		0			0
$463$	−162.814	−	43.6260i	−0.351651	−	0.0942246i	0.0786695	−	0.996901i	$-0.474933\pi$
$463$	−162.814	−	43.6260i	−0.351651	−	0.0942246i	−0.430321	+	0.902676i	$0.641599\pi$
$464$	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	$-0.219222\pi$
$467$	63.7603	+	63.7603i	0.136532	+	0.136532i	−0.635538	+	0.772070i	$0.719222\pi$
$468$		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	$-0.346240\pi$
$479$	−33.6305	−	19.4166i	−0.0702099	−	0.0405357i	−0.534694	+	0.845046i	$0.679573\pi$
$480$		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	0.984735	−	0.174059i	$-0.0556883\pi$
$487$	394.799	+	394.799i	0.810676	+	0.810676i	−0.174059	+	0.984735i	$0.555688\pi$
$488$	−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	$-0.0112132\pi$
$491$	230.371	+	399.015i	0.469188	+	0.812658i	−0.530191	+	0.847878i	$0.677880\pi$
$492$		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	0.476669	−	0.879083i	$-0.341844\pi$
$499$	736.679	−	425.322i	1.47631	−	0.852349i	0.999643	+	0.0267345i	$0.00851087\pi$
$500$	−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	$-0.838897\pi$
$503$	−196.093	+	196.093i	−0.389847	+	0.389847i	0.484786	+	0.874633i	$0.338897\pi$
$504$		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	$-0.791920\pi$
$509$	−338.026	+	195.159i	−0.664098	+	0.383417i	0.129738	+	0.991548i	$0.458586\pi$
$510$		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	$-0.726303\pi$
$521$	−679.963			−1.30511			−0.652556	+	0.757741i	$0.726303\pi$
$522$		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
$527$	−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	0.0612152	−	0.998125i	$-0.480502\pi$
$547$	335.470	−	89.8890i	0.613291	−	0.164331i	0.552076	+	0.833794i	$0.313836\pi$
$548$	−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	−0.973110	−	0.230341i	$-0.926016\pi$
$557$	−670.322	−	670.322i	−1.20345	−	1.20345i	−0.230341	−	0.973110i	$-0.573984\pi$
$558$		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	$-0.290165\pi$
$563$	420.955	+	112.795i	0.747700	+	0.200346i	0.135202	+	0.990818i	$0.456832\pi$
$564$		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	$-0.0952618\pi$
$569$	670.282	+	386.987i	1.17800	+	0.680118i	0.222448	+	0.974944i	$0.428595\pi$
$570$		0			0
$571$	−233.901	−	405.128i	−0.409633	−	0.709506i	0.585215	−	0.810878i	$-0.301010\pi$
$571$	−233.901	−	405.128i	−0.409633	−	0.709506i	−0.994849	+	0.101372i	$0.967677\pi$
$572$	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	0.902385	−	0.430931i	$-0.141815\pi$
$577$	272.029	+	272.029i	0.471454	+	0.471454i	−0.430931	+	0.902385i	$0.641815\pi$
$578$	−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	$-0.621739\pi$
$587$	−136.489	+	36.5721i	−0.232520	+	0.0623034i	0.140678	+	0.990055i	$0.455072\pi$
$588$		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	$-0.785872\pi$
$593$	−94.3094	+	94.3094i	−0.159038	+	0.159038i	0.623102	+	0.782140i	$0.285872\pi$
$594$		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	$-0.912320\pi$
$599$	−723.537	+	417.734i	−1.20791	+	0.697386i	−0.245606	+	0.969370i	$0.578987\pi$
$600$		0			0
$601$	−179.809	+	311.438i	−0.299183	+	0.518200i	−0.975949	−	0.217998i	$-0.930047\pi$
$601$	−179.809	+	311.438i	−0.299183	+	0.518200i	0.676766	+	0.736198i	$0.263381\pi$
$602$	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	−0.764665	−	0.644428i	$-0.777095\pi$
$607$	133.400	−	497.854i	0.219769	−	0.820188i	0.984433	−	0.175759i	$-0.0562380\pi$
$608$	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	−0.977571	−	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
$617$	−65.6036	+	244.836i	−0.106327	+	0.396817i	−0.998492	−	0.0548918i	$-0.982519\pi$
$617$	−65.6036	+	244.836i	−0.106327	+	0.396817i	0.892166	+	0.451708i	$0.149185\pi$
$618$		0			0
$619$	−88.9466	−	51.3534i	−0.143694	−	0.0829618i	0.426429	−	0.904521i	$-0.359771\pi$
$619$	−88.9466	−	51.3534i	−0.143694	−	0.0829618i	−0.570123	+	0.821559i	$0.693105\pi$
$620$	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	$-0.686562\pi$
$641$	285.201	−	493.982i	0.444931	−	0.770643i	0.998047	+	0.0624611i	$0.0198949\pi$
$642$		0			0
$643$	856.111	+	229.394i	1.33143	+	0.356756i	0.853249	−	0.521504i	$-0.174629\pi$
$643$	856.111	+	229.394i	1.33143	+	0.356756i	0.478183	+	0.878260i	$0.341296\pi$
$644$	−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	$-0.160459\pi$
$647$	254.010	+	254.010i	0.392596	+	0.392596i	−0.483016	+	0.875612i	$0.660459\pi$
$648$		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	$-0.341283\pi$
$653$	295.968	+	79.3045i	0.453244	+	0.121446i	−0.0249729	+	0.999688i	$0.507950\pi$
$654$		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	$-0.235779\pi$
$659$	344.367	+	198.821i	0.522561	+	0.301701i	−0.215421	+	0.976521i	$0.569112\pi$
$660$		0			0
$661$	347.289	+	601.522i	0.525399	+	0.910019i	0.999562	+	0.0295815i	$0.00941745\pi$
$661$	347.289	+	601.522i	0.525399	+	0.910019i	−0.474163	+	0.880437i	$0.657249\pi$
$662$	−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	0.925809	−	0.377992i	$-0.123385\pi$
$673$	−43.7189	−	163.161i	−0.0649612	−	0.242439i	−0.990770	+	0.135554i	$0.956719\pi$
$674$			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	$-0.645185\pi$
$677$	−252.537	+	67.6670i	−0.373023	+	0.0999513i	0.0674366	+	0.997724i	$0.478518\pi$
$678$		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	$-0.558925\pi$
$683$	545.616	−	545.616i	0.798852	−	0.798852i	0.982915	+	0.184062i	$0.0589248\pi$
$684$		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	−0.965629	−	0.259925i	$-0.916302\pi$
$691$	−178.080	+	308.443i	−0.257713	+	0.446372i	0.707916	+	0.706297i	$0.249636\pi$
$692$	−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	$-0.417865\pi$
$701$	357.763			0.510361			0.255180	+	0.966893i	$0.417865\pi$
$702$		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	0.710979	−	0.703213i	$-0.248252\pi$
$709$	324.344	+	187.260i	0.457467	+	0.264119i	−0.253511	+	0.967332i	$0.581586\pi$
$710$	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	−0.544398	−	0.838827i	$-0.683242\pi$
$727$	−433.617	+	116.187i	−0.596447	+	0.159818i	−0.0520491	+	0.998645i	$0.516575\pi$
$728$	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	−0.224599	−	0.974451i	$-0.572107\pi$
$733$	−664.342	−	178.010i	−0.906333	−	0.242851i	−0.681734	+	0.731600i	$0.738774\pi$
$734$	−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	$0.926602\pi$
$740$	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	$-0.394146\pi$
$743$	101.468	+	27.1883i	0.136565	+	0.0365926i	−0.189889	+	0.981806i	$0.560813\pi$
$744$		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	0.507035	−	0.861925i	$-0.330741\pi$
$751$	−370.192	−	641.191i	−0.492932	−	0.853783i	−0.999967	+	0.00814279i	$0.997408\pi$
$752$	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	0.948980	+	0.315337i	$0.102118\pi$
$757$	957.088	+	957.088i	1.26432	+	1.26432i	0.315337	+	0.948980i	$0.397882\pi$
$758$	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	$-0.0807722\pi$
$761$	202.869	+	351.380i	0.266582	+	0.461734i	−0.701395	+	0.712773i	$0.747439\pi$
$762$		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	0.0578626	−	0.998325i	$-0.481571\pi$
$769$	731.602	−	422.391i	0.951368	−	0.549273i	0.893506	+	0.449052i	$0.148238\pi$
$770$	−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	$-0.598358\pi$
$773$	501.313	−	501.313i	0.648529	−	0.648529i	0.952637	+	0.304108i	$0.0983585\pi$
$774$		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	0.569439	+	0.822034i	$0.307161\pi$
$787$	−263.430	+	983.133i	−0.334726	+	1.24922i	−0.904165	+	0.427183i	$0.859506\pi$
$788$	−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	−0.198670	−	0.980066i	$-0.563662\pi$
$797$	369.343	−	1378.41i	0.463416	−	1.72949i	0.662087	−	0.749427i	$-0.269671\pi$
$798$		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	$-0.997549\pi$
$821$	−405.012	+	701.501i	−0.493316	+	0.854448i	0.506655	+	0.862149i	$0.330882\pi$
$822$		0			0
$823$	79.3084	+	21.2506i	0.0963650	+	0.0258209i	0.306679	−	0.951813i	$-0.400782\pi$
$823$	79.3084	+	21.2506i	0.0963650	+	0.0258209i	−0.210314	+	0.977634i	$0.567449\pi$
$824$	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	$0.0401866\pi$
$827$	924.549	+	924.549i	1.11796	+	1.11796i	0.125915	+	0.992041i	$0.459813\pi$
$828$		0			0
$829$		−	114.907i		−	0.138610i	−0.997596	−	0.0693048i	$-0.977922\pi$
$829$		−	114.907i		−	0.138610i	0.997596	−	0.0693048i	$-0.0220781\pi$
$830$	−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	$-0.483837\pi$
$839$	−661.782	−	382.080i	−0.788774	−	0.455399i	−0.839531	+	0.543312i	$0.817170\pi$
$840$		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	0.983166	+	0.182715i	$0.0584887\pi$
$853$	190.285	+	710.152i	0.223077	+	0.832534i	−0.760089	+	0.649819i	$0.774845\pi$
$854$			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	$-0.721111\pi$
$857$	−694.443	+	186.075i	−0.810319	+	0.217124i	−0.170209	+	0.985408i	$0.554444\pi$
$858$		0			0
$859$	−1043.29	+	602.342i	−1.21454	+	0.701213i	−0.963744	−	0.266828i	$-0.914025\pi$
$859$	−1043.29	+	602.342i	−1.21454	+	0.701213i	−0.250792	+	0.968041i	$0.580691\pi$
$860$	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	$-0.806255\pi$
$863$	−214.571	+	214.571i	−0.248634	+	0.248634i	0.571776	+	0.820410i	$0.306255\pi$
$864$		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	−0.996766	−	0.0803551i	$-0.974395\pi$
$877$	−81.8801	+	305.581i	−0.0933638	+	0.348438i	0.903402	+	0.428794i	$0.141061\pi$
$878$	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	$-0.579514\pi$
$881$	−435.585			−0.494421			−0.247211	+	0.968962i	$0.579514\pi$
$882$		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
$887$	148.261	−	553.319i	0.167149	−	0.623810i	−0.830607	−	0.556859i	$-0.812006\pi$
$887$	148.261	−	553.319i	0.167149	−	0.623810i	0.997756	−	0.0669506i	$-0.0213270\pi$
$888$		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	−0.654513	−	0.756051i	$-0.727126\pi$
$907$	−764.884	+	204.950i	−0.843312	+	0.225965i	−0.188799	+	0.982016i	$0.560459\pi$
$908$	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	−0.480830	−	0.876814i	$-0.659665\pi$
$911$	472.743	−	818.815i	0.518928	−	0.898809i	0.999758	−	0.0219955i	$-0.00700196\pi$
$912$		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	$-0.851803\pi$
$919$		−	825.147i		−	0.897875i	0.893563	−	0.448937i	$-0.148197\pi$
$920$	−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	$-0.498831\pi$
$929$	−799.415	−	461.543i	−0.860511	−	0.496817i	−0.864184	+	0.503177i	$0.832164\pi$
$930$		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	0.999451	+	0.0331234i	$0.0105454\pi$
$937$	967.522	+	967.522i	1.03257	+	1.03257i	0.0331234	+	0.999451i	$0.489455\pi$
$938$	−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	$-0.0246884\pi$
$941$	405.942	+	703.113i	0.431395	+	0.747197i	−0.565599	+	0.824680i	$0.691355\pi$
$942$		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	$-0.809142\pi$
$947$	−1191.67	+	319.307i	−1.25836	+	0.337177i	−0.432802	+	0.901489i	$0.642475\pi$
$948$		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	$-0.929326\pi$
$953$	−719.749	+	719.749i	−0.755245	+	0.755245i	0.220208	+	0.975453i	$0.429326\pi$
$954$		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	0.421525	+	0.906817i	$0.361495\pi$
$967$	−383.836	+	1432.50i	−0.396935	+	1.48138i	−0.818460	+	0.574564i	$0.805172\pi$
$968$	−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	$-0.365050\pi$
$971$	798.883			0.822742			0.411371	+	0.911468i	$0.365050\pi$
$972$		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	$-0.986929\pi$
$977$	−110.728	+	413.244i	−0.113335	+	0.422972i	0.885822	+	0.464025i	$0.153595\pi$
$978$		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	$-0.153598\pi$
$983$	−111.413	−	415.799i	−0.113340	−	0.422990i	−0.999157	+	0.0410437i	$0.986932\pi$
$984$		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	−0.453215	−	0.891401i	$-0.649723\pi$
$997$	−398.810	+	106.861i	−0.400010	+	0.107182i	0.0532048	+	0.998584i	$0.483056\pi$
$998$	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.217.7		32
3.2	odd	2	inner	405.3.l.n.217.2		32
5.3	odd	4	inner	405.3.l.n.298.2		32
9.2	odd	6		135.3.g.b.82.7	yes	16
9.4	even	3	inner	405.3.l.n.352.2		32
9.5	odd	6	inner	405.3.l.n.352.7		32
9.7	even	3		135.3.g.b.82.2	yes	16
15.8	even	4	inner	405.3.l.n.298.7		32
45.2	even	12		675.3.g.j.568.2		16
45.7	odd	12		675.3.g.j.568.7		16
45.13	odd	12	inner	405.3.l.n.28.7		32
45.23	even	12	inner	405.3.l.n.28.2		32
45.29	odd	6		675.3.g.j.82.2		16
45.34	even	6		675.3.g.j.82.7		16
45.38	even	12		135.3.g.b.28.7	yes	16
45.43	odd	12		135.3.g.b.28.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.b.28.2	✓	16	45.43	odd	12
135.3.g.b.28.7	yes	16	45.38	even	12
135.3.g.b.82.2	yes	16	9.7	even	3
135.3.g.b.82.7	yes	16	9.2	odd	6
405.3.l.n.28.2		32	45.23	even	12	inner
405.3.l.n.28.7		32	45.13	odd	12	inner
405.3.l.n.217.2		32	3.2	odd	2	inner
405.3.l.n.217.7		32	1.1	even	1	trivial
405.3.l.n.298.2		32	5.3	odd	4	inner
405.3.l.n.298.7		32	15.8	even	4	inner
405.3.l.n.352.2		32	9.4	even	3	inner
405.3.l.n.352.7		32	9.5	odd	6	inner
675.3.g.j.82.2		16	45.29	odd	6
675.3.g.j.82.7		16	45.34	even	6
675.3.g.j.568.2		16	45.2	even	12
675.3.g.j.568.7		16	45.7	odd	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)

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