LMFDB - Embedded newform 220.3.q.a.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(29,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.q (of order $10$, degree $4$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	220.29
Dual form			220.3.q.a.129.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.914119 + 0.297015i) q^{3} +(-2.13757 - 4.52004i) q^{5} +(-1.31985 - 4.06207i) q^{7} +(-6.53376 - 4.74705i) q^{9} +(-4.47784 + 10.0473i) q^{11} +(-12.1628 - 8.83682i) q^{13} +(-0.611469 - 4.76675i) q^{15} +(1.04632 - 0.760193i) q^{17} +(-0.958233 - 0.311349i) q^{19} -4.10523i q^{21} -41.0620i q^{23} +(-15.8616 + 19.3238i) q^{25} +(-9.64730 - 13.2784i) q^{27} +(41.4155 - 13.4567i) q^{29} +(13.1808 + 9.57644i) q^{31} +(-7.07750 + 7.85447i) q^{33} +(-15.5395 + 14.6487i) q^{35} +(-10.7632 + 3.49717i) q^{37} +(-8.49362 - 11.6905i) q^{39} +(-55.1488 - 17.9189i) q^{41} +43.5352 q^{43} +(-7.49054 + 39.6800i) q^{45} +(10.9380 + 3.55398i) q^{47} +(24.8834 - 18.0789i) q^{49} +(1.18225 - 0.384135i) q^{51} +(-28.8912 + 39.7654i) q^{53} +(54.9861 - 1.23680i) q^{55} +(-0.783464 - 0.569220i) q^{57} +(-24.8092 - 76.3547i) q^{59} +(33.4826 + 46.0848i) q^{61} +(-10.6593 + 32.8060i) q^{63} +(-13.9439 + 73.8659i) q^{65} +57.7942i q^{67} +(12.1960 - 37.5355i) q^{69} +(18.7185 - 13.5998i) q^{71} +(29.5919 + 91.0744i) q^{73} +(-20.2389 + 12.9531i) q^{75} +(46.7230 + 4.92838i) q^{77} +(40.5651 - 55.8330i) q^{79} +(17.5862 + 54.1246i) q^{81} +(98.7827 - 71.7698i) q^{83} +(-5.67267 - 3.10443i) q^{85} +41.8556 q^{87} +43.8574 q^{89} +(-19.8427 + 61.0696i) q^{91} +(9.20451 + 12.6689i) q^{93} +(0.640978 + 4.99679i) q^{95} +(-80.2155 + 110.407i) q^{97} +(76.9524 - 44.3903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 5 q^{5} + 20 q^{9} - 23 q^{15} - 7 q^{25} - 74 q^{31} + 155 q^{35} + 80 q^{39} - 20 q^{41} + 12 q^{45} + 102 q^{49} + 220 q^{51} - 69 q^{55} + 40 q^{59} - 290 q^{61} - 234 q^{69} - 406 q^{71} + 153 q^{75}+ \cdots - 382 q^{99}+O(q^{100}) $ 48 * q + 5 * q^5 + 20 * q^9 - 23 * q^15 - 7 * q^25 - 74 * q^31 + 155 * q^35 + 80 * q^39 - 20 * q^41 + 12 * q^45 + 102 * q^49 + 220 * q^51 - 69 * q^55 + 40 * q^59 - 290 * q^61 - 234 * q^69 - 406 * q^71 + 153 * q^75 - 280 * q^79 + 230 * q^81 - 465 * q^85 - 636 * q^89 + 512 * q^91 - 495 * q^95 - 382 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.914119	+	0.297015i	0.304706	+	0.0990051i	0.457379	−	0.889272i	$-0.348788\pi$
$3$	0.914119	+	0.297015i	0.304706	+	0.0990051i	−0.152673	+	0.988277i	$0.548788\pi$
$4$		0			0
$5$	−2.13757	−	4.52004i	−0.427514	−	0.904009i
$5$	−2.13757	−	4.52004i	−0.427514	−	0.904009i
$6$		0			0
$7$	−1.31985	−	4.06207i	−0.188550	−	0.580296i	0.811442	−	0.584433i	$-0.198683\pi$
$7$	−1.31985	−	4.06207i	−0.188550	−	0.580296i	−0.999991	+	0.00413726i	$0.998683\pi$
$8$		0			0
$9$	−6.53376	−	4.74705i	−0.725973	−	0.527450i
$10$		0			0
$11$	−4.47784	+	10.0473i	−0.407077	+	0.913394i
$11$	−4.47784	+	10.0473i	−0.407077	+	0.913394i
$12$		0			0
$13$	−12.1628	−	8.83682i	−0.935603	−	0.679755i	0.0117552	−	0.999931i	$-0.496258\pi$
$13$	−12.1628	−	8.83682i	−0.935603	−	0.679755i	−0.947358	+	0.320176i	$0.896258\pi$
$14$		0			0
$15$	−0.611469	−	4.76675i	−0.0407646	−	0.317783i
$16$		0			0
$17$	1.04632	−	0.760193i	0.0615480	−	0.0447172i	−0.556586	−	0.830790i	$-0.687889\pi$
$17$	1.04632	−	0.760193i	0.0615480	−	0.0447172i	0.618134	+	0.786073i	$0.287889\pi$
$18$		0			0
$19$	−0.958233	−	0.311349i	−0.0504333	−	0.0163868i	0.283692	−	0.958916i	$-0.408441\pi$
$19$	−0.958233	−	0.311349i	−0.0504333	−	0.0163868i	−0.334125	+	0.942529i	$0.608441\pi$
$20$		0			0
$21$		−	4.10523i		−	0.195487i
$22$		0			0
$23$		−	41.0620i		−	1.78530i	−0.450747	−	0.892652i	$-0.648842\pi$
$23$		−	41.0620i		−	1.78530i	0.450747	−	0.892652i	$-0.351158\pi$
$24$		0			0
$25$	−15.8616	+	19.3238i	−0.634464	+	0.772952i
$26$		0			0
$27$	−9.64730	−	13.2784i	−0.357307	−	0.491791i
$28$		0			0
$29$	41.4155	−	13.4567i	1.42812	−	0.464025i	0.509948	−	0.860205i	$-0.329665\pi$
$29$	41.4155	−	13.4567i	1.42812	−	0.464025i	0.918173	+	0.396181i	$0.129665\pi$
$30$		0			0
$31$	13.1808	+	9.57644i	0.425188	+	0.308917i	0.779722	−	0.626126i	$-0.215360\pi$
$31$	13.1808	+	9.57644i	0.425188	+	0.308917i	−0.354534	+	0.935043i	$0.615360\pi$
$32$		0			0
$33$	−7.07750	+	7.85447i	−0.214470	+	0.238014i
$34$		0			0
$35$	−15.5395	+	14.6487i	−0.443985	+	0.418535i
$36$		0			0
$37$	−10.7632	+	3.49717i	−0.290897	+	0.0945180i	−0.450830	−	0.892610i	$-0.648872\pi$
$37$	−10.7632	+	3.49717i	−0.290897	+	0.0945180i	0.159934	+	0.987128i	$0.448872\pi$
$38$		0			0
$39$	−8.49362	−	11.6905i	−0.217785	−	0.299755i
$40$		0			0
$41$	−55.1488	−	17.9189i	−1.34509	−	0.437047i	−0.454053	−	0.890974i	$-0.650022\pi$
$41$	−55.1488	−	17.9189i	−1.34509	−	0.437047i	−0.891039	+	0.453928i	$0.850022\pi$
$42$		0			0
$43$	43.5352			1.01245			0.506223	−	0.862403i	$-0.331041\pi$
$43$	43.5352			1.01245			0.506223	+	0.862403i	$0.331041\pi$
$44$		0			0
$45$	−7.49054	+	39.6800i	−0.166456	+	0.881778i
$46$		0			0
$47$	10.9380	+	3.55398i	0.232724	+	0.0756165i	0.423057	−	0.906103i	$-0.360957\pi$
$47$	10.9380	+	3.55398i	0.232724	+	0.0756165i	−0.190333	+	0.981719i	$0.560957\pi$
$48$		0			0
$49$	24.8834	−	18.0789i	0.507825	−	0.368956i
$50$		0			0
$51$	1.18225	−	0.384135i	0.0231813	−	0.00753206i
$52$		0			0
$53$	−28.8912	+	39.7654i	−0.545117	+	0.750290i	−0.989340	−	0.145627i	$-0.953480\pi$
$53$	−28.8912	+	39.7654i	−0.545117	+	0.750290i	0.444222	+	0.895917i	$0.353480\pi$
$54$		0			0
$55$	54.9861	−	1.23680i	0.999747	−	0.0224873i
$56$		0			0
$57$	−0.783464	−	0.569220i	−0.0137450	−	0.00998632i
$58$		0			0
$59$	−24.8092	−	76.3547i	−0.420494	−	1.29415i	−0.907243	−	0.420606i	$-0.861817\pi$
$59$	−24.8092	−	76.3547i	−0.420494	−	1.29415i	0.486749	−	0.873542i	$-0.338183\pi$
$60$		0			0
$61$	33.4826	+	46.0848i	0.548894	+	0.755488i	0.989862	−	0.142035i	$-0.0453645\pi$
$61$	33.4826	+	46.0848i	0.548894	+	0.755488i	−0.440967	+	0.897523i	$0.645365\pi$
$62$		0			0
$63$	−10.6593	+	32.8060i	−0.169195	+	0.520730i
$64$		0			0
$65$	−13.9439	+	73.8659i	−0.214522	+	1.13640i
$66$		0			0
$67$			57.7942i			0.862600i	0.902209	+	0.431300i	$0.141945\pi$
$67$			57.7942i			0.862600i	−0.902209	+	0.431300i	$0.858055\pi$
$68$		0			0
$69$	12.1960	−	37.5355i	0.176754	−	0.543993i
$70$		0			0
$71$	18.7185	−	13.5998i	0.263640	−	0.191546i	−0.448110	−	0.893978i	$-0.647903\pi$
$71$	18.7185	−	13.5998i	0.263640	−	0.191546i	0.711750	+	0.702433i	$0.247903\pi$
$72$		0			0
$73$	29.5919	+	91.0744i	0.405368	+	1.24759i	0.920588	+	0.390536i	$0.127710\pi$
$73$	29.5919	+	91.0744i	0.405368	+	1.24759i	−0.515220	+	0.857058i	$0.672290\pi$
$74$		0			0
$75$	−20.2389	+	12.9531i	−0.269852	+	0.172708i
$76$		0			0
$77$	46.7230	+	4.92838i	0.606793	+	0.0640049i
$78$		0			0
$79$	40.5651	−	55.8330i	0.513482	−	0.706747i	−0.471020	−	0.882123i	$-0.656114\pi$
$79$	40.5651	−	55.8330i	0.513482	−	0.706747i	0.984502	+	0.175375i	$0.0561139\pi$
$80$		0			0
$81$	17.5862	+	54.1246i	0.217113	+	0.668205i
$82$		0			0
$83$	98.7827	−	71.7698i	1.19015	−	0.864697i	0.196872	−	0.980429i	$-0.436922\pi$
$83$	98.7827	−	71.7698i	1.19015	−	0.864697i	0.993280	+	0.115733i	$0.0369215\pi$
$84$		0			0
$85$	−5.67267	−	3.10443i	−0.0667373	−	0.0365227i
$86$		0			0
$87$	41.8556			0.481098
$88$		0			0
$89$	43.8574			0.492780			0.246390	−	0.969171i	$-0.420756\pi$
$89$	43.8574			0.492780			0.246390	+	0.969171i	$0.420756\pi$
$90$		0			0
$91$	−19.8427	+	61.0696i	−0.218052	+	0.671094i
$92$		0			0
$93$	9.20451	+	12.6689i	0.0989732	+	0.136225i
$94$		0			0
$95$	0.640978	+	4.99679i	0.00674714	+	0.0525978i
$96$		0			0
$97$	−80.2155	+	110.407i	−0.826964	+	1.13822i	0.161516	+	0.986870i	$0.448362\pi$
$97$	−80.2155	+	110.407i	−0.826964	+	1.13822i	−0.988480	+	0.151348i	$0.951638\pi$
$98$		0			0
$99$	76.9524	−	44.3903i	0.777297	−	0.448387i
$100$		0			0
$101$	−52.7600	+	72.6179i	−0.522376	+	0.718989i	−0.985945	−	0.167072i	$-0.946569\pi$
$101$	−52.7600	+	72.6179i	−0.522376	+	0.718989i	0.463568	+	0.886061i	$0.346569\pi$
$102$		0			0
$103$	−62.0354	+	20.1565i	−0.602285	+	0.195694i	−0.594259	−	0.804273i	$-0.702555\pi$
$103$	−62.0354	+	20.1565i	−0.602285	+	0.195694i	−0.00802580	+	0.999968i	$0.502555\pi$
$104$		0			0
$105$	−18.5558	+	8.77521i	−0.176722	+	0.0835735i
$106$		0			0
$107$	44.6896	−	137.540i	0.417660	−	1.28542i	−0.492191	−	0.870487i	$-0.663804\pi$
$107$	44.6896	−	137.540i	0.417660	−	1.28542i	0.909850	−	0.414937i	$-0.136196\pi$
$108$		0			0
$109$		−	172.365i		−	1.58133i	−0.612247	−	0.790667i	$-0.709734\pi$
$109$		−	172.365i		−	1.58133i	0.612247	−	0.790667i	$-0.290266\pi$
$110$		0			0
$111$	−10.8775			−0.0979959
$112$		0			0
$113$	−134.881	−	43.8254i	−1.19363	−	0.387835i	−0.356218	−	0.934403i	$-0.615934\pi$
$113$	−134.881	−	43.8254i	−1.19363	−	0.387835i	−0.837415	+	0.546568i	$0.815934\pi$
$114$		0			0
$115$	−185.602	+	87.7728i	−1.61393	+	0.763241i
$116$		0			0
$117$	37.5202	+	115.475i	0.320685	+	0.986968i
$118$		0			0
$119$	−4.46893	−	3.24687i	−0.0375541	−	0.0272846i
$120$		0			0
$121$	−80.8978	−	89.9808i	−0.668577	−	0.743643i
$122$		0			0
$123$	−45.0904	−	32.7601i	−0.366588	−	0.266342i
$124$		0			0
$125$	121.250	+	30.3892i	0.969998	+	0.243114i
$126$		0			0
$127$	54.0994	−	39.3055i	0.425979	−	0.309492i	−0.354060	−	0.935223i	$-0.615199\pi$
$127$	54.0994	−	39.3055i	0.425979	−	0.309492i	0.780039	+	0.625731i	$0.215199\pi$
$128$		0			0
$129$	39.7963	+	12.9306i	0.308499	+	0.100237i
$130$		0			0
$131$		−	47.9864i		−	0.366309i	−0.983084	−	0.183154i	$-0.941369\pi$
$131$		−	47.9864i		−	0.366309i	0.983084	−	0.183154i	$-0.0586308\pi$
$132$		0			0
$133$			4.30335i			0.0323560i
$134$		0			0
$135$	−39.3971	+	71.9896i	−0.291830	+	0.533257i
$136$		0			0
$137$	−139.941	−	192.612i	−1.02146	−	1.40593i	−0.911172	−	0.412026i	$-0.864821\pi$
$137$	−139.941	−	192.612i	−1.02146	−	1.40593i	−0.110293	−	0.993899i	$-0.535179\pi$
$138$		0			0
$139$	56.5353	−	18.3694i	0.406729	−	0.132154i	−0.0985054	−	0.995137i	$-0.531406\pi$
$139$	56.5353	−	18.3694i	0.406729	−	0.132154i	0.505234	+	0.862982i	$0.331406\pi$
$140$		0			0
$141$	8.94307	+	6.49752i	0.0634260	+	0.0460817i
$142$		0			0
$143$	143.250	−	82.6342i	1.00175	−	0.577862i
$144$		0			0
$145$	−149.353	−	158.435i	−1.03002	−	1.09266i
$146$		0			0
$147$	28.1161	−	9.13548i	0.191266	−	0.0621461i
$148$		0			0
$149$	−28.0581	−	38.6187i	−0.188310	−	0.259186i	0.704415	−	0.709788i	$-0.251209\pi$
$149$	−28.0581	−	38.6187i	−0.188310	−	0.259186i	−0.892725	+	0.450602i	$0.851209\pi$
$150$		0			0
$151$	107.583	+	34.9557i	0.712467	+	0.231495i	0.642754	−	0.766073i	$-0.277792\pi$
$151$	107.583	+	34.9557i	0.712467	+	0.231495i	0.0697129	+	0.997567i	$0.477792\pi$
$152$		0			0
$153$	−10.4450			−0.0682683
$154$		0			0
$155$	15.1110	−	80.0482i	0.0974903	−	0.516440i
$156$		0			0
$157$	−19.3068	−	6.27317i	−0.122974	−	0.0399565i	0.246884	−	0.969045i	$-0.420593\pi$
$157$	−19.3068	−	6.27317i	−0.122974	−	0.0399565i	−0.369857	+	0.929089i	$0.620593\pi$
$158$		0			0
$159$	−38.2210	+	27.7691i	−0.240383	+	0.174649i
$160$		0			0
$161$	−166.797	+	54.1955i	−1.03600	+	0.336618i
$162$		0			0
$163$	−138.897	+	191.175i	−0.852126	+	1.17285i	0.131264	+	0.991347i	$0.458096\pi$
$163$	−138.897	+	191.175i	−0.852126	+	1.17285i	−0.983390	+	0.181503i	$0.941904\pi$
$164$		0			0
$165$	50.6312	+	15.2011i	0.306856	+	0.0921281i
$166$		0			0
$167$	−253.976	−	184.524i	−1.52081	−	1.10494i	−0.961083	−	0.276261i	$-0.910905\pi$
$167$	−253.976	−	184.524i	−1.52081	−	1.10494i	−0.559731	−	0.828674i	$-0.689095\pi$
$168$		0			0
$169$	17.6214	+	54.2331i	0.104269	+	0.320906i
$170$		0			0
$171$	4.78287	+	6.58306i	0.0279700	+	0.0384974i
$172$		0			0
$173$	49.7200	−	153.023i	0.287399	−	0.884523i	−0.698270	−	0.715834i	$-0.746047\pi$
$173$	49.7200	−	153.023i	0.287399	−	0.884523i	0.985669	−	0.168689i	$-0.0539534\pi$
$174$		0			0
$175$	99.4296	+	38.9265i	0.568169	+	0.222437i
$176$		0			0
$177$		−	77.1661i		−	0.435966i
$178$		0			0
$179$	60.7656	−	187.017i	0.339473	−	1.04479i	−0.625004	−	0.780621i	$-0.714903\pi$
$179$	60.7656	−	187.017i	0.339473	−	1.04479i	0.964477	−	0.264168i	$-0.0850972\pi$
$180$		0			0
$181$	60.3506	−	43.8473i	0.333429	−	0.242250i	−0.408455	−	0.912778i	$-0.633932\pi$
$181$	60.3506	−	43.8473i	0.333429	−	0.242250i	0.741884	+	0.670528i	$0.233932\pi$
$182$		0			0
$183$	16.9192	+	52.0718i	0.0924544	+	0.284546i
$184$		0			0
$185$	38.8144	+	41.1746i	0.209807	+	0.222565i
$186$		0			0
$187$	2.95267	+	13.9167i	0.0157897	+	0.0744209i
$188$		0			0
$189$	−41.2047	+	56.7134i	−0.218014	+	0.300071i
$190$		0			0
$191$	33.4581	+	102.974i	0.175173	+	0.539129i	0.999641	−	0.0267802i	$-0.00852543\pi$
$191$	33.4581	+	102.974i	0.175173	+	0.539129i	−0.824468	+	0.565909i	$0.808525\pi$
$192$		0			0
$193$	87.3140	−	63.4373i	0.452404	−	0.328691i	−0.338140	−	0.941096i	$-0.609798\pi$
$193$	87.3140	−	63.4373i	0.452404	−	0.328691i	0.790544	+	0.612405i	$0.209798\pi$
$194$		0			0
$195$	−34.6857	+	63.3807i	−0.177875	+	0.325029i
$196$		0			0
$197$	296.778			1.50649			0.753243	−	0.657742i	$-0.228488\pi$
$197$	296.778			1.50649			0.753243	+	0.657742i	$0.228488\pi$
$198$		0			0
$199$	−286.494			−1.43967			−0.719835	−	0.694146i	$-0.755782\pi$
$199$	−286.494			−1.43967			−0.719835	+	0.694146i	$0.755782\pi$
$200$		0			0
$201$	−17.1658	+	52.8308i	−0.0854018	+	0.262840i
$202$		0			0
$203$	−109.324	−	150.472i	−0.538543	−	0.741241i
$204$		0			0
$205$	36.8899	+	287.578i	0.179951	+	1.40282i
$206$		0			0
$207$	−194.923	+	268.289i	−0.941659	+	1.29608i
$208$		0			0
$209$	7.41905	−	8.23352i	0.0354978	−	0.0393948i
$210$		0			0
$211$	49.3979	−	67.9904i	0.234113	−	0.322229i	−0.675755	−	0.737126i	$-0.736182\pi$
$211$	49.3979	−	67.9904i	0.234113	−	0.322229i	0.909868	+	0.414897i	$0.136182\pi$
$212$		0			0
$213$	21.1502	−	6.87213i	0.0992969	−	0.0322635i
$214$		0			0
$215$	−93.0594	−	196.781i	−0.432834	−	0.915260i
$216$		0			0
$217$	21.5035	−	66.1809i	0.0990944	−	0.304981i
$218$		0			0
$219$			92.0421i			0.420283i
$220$		0			0
$221$	−19.4439			−0.0879812
$222$		0			0
$223$	−45.2745	−	14.7106i	−0.203025	−	0.0659667i	0.205739	−	0.978607i	$-0.434040\pi$
$223$	−45.2745	−	14.7106i	−0.203025	−	0.0659667i	−0.408764	+	0.912640i	$0.634040\pi$
$224$		0			0
$225$	195.367	−	50.9612i	0.868298	−	0.226494i
$226$		0			0
$227$	104.489	+	321.585i	0.460305	+	1.41667i	0.864792	+	0.502130i	$0.167450\pi$
$227$	104.489	+	321.585i	0.460305	+	1.41667i	−0.404487	+	0.914544i	$0.632550\pi$
$228$		0			0
$229$	127.052	+	92.3084i	0.554810	+	0.403093i	0.829556	−	0.558424i	$-0.188594\pi$
$229$	127.052	+	92.3084i	0.554810	+	0.403093i	−0.274746	+	0.961517i	$0.588594\pi$
$230$		0			0
$231$	41.2466	+	18.3826i	0.178557	+	0.0795783i
$232$		0			0
$233$	−126.628	−	92.0004i	−0.543466	−	0.394851i	0.281904	−	0.959443i	$-0.409034\pi$
$233$	−126.628	−	92.0004i	−0.543466	−	0.394851i	−0.825371	+	0.564591i	$0.809034\pi$
$234$		0			0
$235$	−7.31662	−	57.0372i	−0.0311345	−	0.242711i
$236$		0			0
$237$	53.6646	−	38.9896i	0.226433	−	0.164513i
$238$		0			0
$239$	154.190	+	50.0994i	0.645147	+	0.209621i	0.613273	−	0.789871i	$-0.289853\pi$
$239$	154.190	+	50.0994i	0.645147	+	0.209621i	0.0318738	+	0.999492i	$0.489853\pi$
$240$		0			0
$241$		−	58.3751i		−	0.242220i	−0.992639	−	0.121110i	$-0.961355\pi$
$241$		−	58.3751i		−	0.242220i	0.992639	−	0.121110i	$-0.0386454\pi$
$242$		0			0
$243$			202.416i			0.832989i
$244$		0			0
$245$	−134.907	−	73.8293i	−0.550642	−	0.301344i
$246$		0			0
$247$	8.90351	+	12.2546i	0.0360466	+	0.0496139i
$248$		0			0
$249$	111.616	−	36.2662i	0.448257	−	0.145647i
$250$		0			0
$251$	216.567	+	157.345i	0.862817	+	0.626873i	0.928650	−	0.370957i	$-0.120970\pi$
$251$	216.567	+	157.345i	0.862817	+	0.626873i	−0.0658327	+	0.997831i	$0.520970\pi$
$252$		0			0
$253$	412.563	+	183.869i	1.63069	+	0.726755i
$254$		0			0
$255$	−4.26344	−	4.52269i	−0.0167194	−	0.0177360i
$256$		0			0
$257$	−31.3465	+	10.1851i	−0.121971	+	0.0396308i	−0.369366	−	0.929284i	$-0.620425\pi$
$257$	−31.3465	+	10.1851i	−0.121971	+	0.0396308i	0.247396	+	0.968915i	$0.420425\pi$
$258$		0			0
$259$	28.4115	+	39.1051i	0.109697	+	0.150985i
$260$		0			0
$261$	−334.479	−	108.679i	−1.28153	−	0.416393i
$262$		0			0
$263$	253.267			0.962993			0.481496	−	0.876448i	$-0.340093\pi$
$263$	253.267			0.962993			0.481496	+	0.876448i	$0.340093\pi$
$264$		0			0
$265$	241.498	+	45.5885i	0.911314	+	0.172032i
$266$		0			0
$267$	40.0909	+	13.0263i	0.150153	+	0.0487877i
$268$		0			0
$269$	−83.0056	+	60.3071i	−0.308571	+	0.224190i	−0.731283	−	0.682074i	$-0.761078\pi$
$269$	−83.0056	+	60.3071i	−0.308571	+	0.224190i	0.422712	+	0.906264i	$0.361078\pi$
$270$		0			0
$271$	307.806	−	100.012i	1.13581	−	0.369049i	0.320032	−	0.947407i	$-0.396306\pi$
$271$	307.806	−	100.012i	1.13581	−	0.369049i	0.815783	+	0.578358i	$0.196306\pi$
$272$		0			0
$273$	−36.2772	+	49.9313i	−0.132884	+	0.182898i
$274$		0			0
$275$	−123.127	−	245.896i	−0.447734	−	0.894167i
$276$		0			0
$277$	207.659	+	150.873i	0.749670	+	0.544667i	0.895724	−	0.444610i	$-0.146658\pi$
$277$	207.659	+	150.873i	0.749670	+	0.544667i	−0.146055	+	0.989277i	$0.546658\pi$
$278$		0			0
$279$	−40.6605	−	125.140i	−0.145737	−	0.448531i
$280$		0			0
$281$	−173.801	−	239.216i	−0.618508	−	0.851304i	0.378735	−	0.925505i	$-0.376359\pi$
$281$	−173.801	−	239.216i	−0.618508	−	0.851304i	−0.997243	+	0.0742014i	$0.976359\pi$
$282$		0			0
$283$	−93.0519	+	286.384i	−0.328805	+	1.01196i	0.640888	+	0.767634i	$0.278566\pi$
$283$	−93.0519	+	286.384i	−0.328805	+	1.01196i	−0.969693	+	0.244325i	$0.921434\pi$
$284$		0			0
$285$	−0.898192	+	4.75804i	−0.00315155	+	0.0166949i
$286$		0			0
$287$			247.668i			0.862956i
$288$		0			0
$289$	−88.7890	+	273.265i	−0.307228	+	0.945552i
$290$		0			0
$291$	−106.119	+	77.1001i	−0.364671	+	0.264949i
$292$		0			0
$293$	28.3875	+	87.3679i	0.0968858	+	0.298184i	0.987741	−	0.156104i	$-0.0498936\pi$
$293$	28.3875	+	87.3679i	0.0968858	+	0.298184i	−0.890855	+	0.454288i	$0.849894\pi$
$294$		0			0
$295$	−292.096	+	275.352i	−0.990155	+	0.933396i
$296$		0			0
$297$	176.611	−	37.4712i	0.594651	−	0.126166i
$298$		0			0
$299$	−362.857	+	499.430i	−1.21357	+	1.67034i
$300$		0			0
$301$	−57.4598	−	176.843i	−0.190896	−	0.587518i
$302$		0			0
$303$	−69.7976	+	50.7109i	−0.230355	+	0.167363i
$304$		0			0
$305$	136.734	−	249.852i	0.448308	−	0.819187i
$306$		0			0
$307$	−248.939			−0.810876			−0.405438	−	0.914123i	$-0.632881\pi$
$307$	−248.939			−0.810876			−0.405438	+	0.914123i	$0.632881\pi$
$308$		0			0
$309$	−62.6945			−0.202895
$310$		0			0
$311$	91.8030	−	282.541i	0.295186	−	0.908491i	−0.687972	−	0.725737i	$-0.741499\pi$
$311$	91.8030	−	282.541i	0.295186	−	0.908491i	0.983159	−	0.182754i	$-0.0585011\pi$
$312$		0			0
$313$	−258.778	−	356.178i	−0.826768	−	1.13795i	−0.988516	−	0.151116i	$-0.951713\pi$
$313$	−258.778	−	356.178i	−0.826768	−	1.13795i	0.161749	−	0.986832i	$-0.448287\pi$
$314$		0			0
$315$	171.069	−	21.9444i	0.543078	−	0.0696649i
$316$		0			0
$317$	−66.1411	+	91.0354i	−0.208647	+	0.287178i	−0.900496	−	0.434864i	$-0.856796\pi$
$317$	−66.1411	+	91.0354i	−0.208647	+	0.287178i	0.691849	+	0.722042i	$0.256796\pi$
$318$		0			0
$319$	−50.2481	+	476.372i	−0.157518	+	1.49333i
$320$		0			0
$321$	81.7032	−	112.455i	0.254527	−	0.350327i
$322$		0			0
$323$	−1.23930	+	0.402673i	−0.00383684	+	0.00124667i
$324$		0			0
$325$	363.683	−	94.8662i	1.11903	−	0.291896i
$326$		0			0
$327$	51.1952	−	157.562i	0.156560	−	0.481842i
$328$		0			0
$329$		−	49.1217i		−	0.149306i
$330$		0			0
$331$	581.742			1.75753			0.878765	−	0.477255i	$-0.158368\pi$
$331$	581.742			1.75753			0.878765	+	0.477255i	$0.158368\pi$
$332$		0			0
$333$	86.9252	+	28.2437i	0.261037	+	0.0848159i
$334$		0			0
$335$	261.232	−	123.539i	0.779798	−	0.368773i
$336$		0			0
$337$	−28.0866	−	86.4418i	−0.0833431	−	0.256504i	0.900698	−	0.434446i	$-0.143056\pi$
$337$	−28.0866	−	86.4418i	−0.0833431	−	0.256504i	−0.984041	+	0.177942i	$0.943056\pi$
$338$		0			0
$339$	−110.280	−	80.1232i	−0.325310	−	0.236352i
$340$		0			0
$341$	−155.239	+	89.5504i	−0.455247	+	0.262611i
$342$		0			0
$343$	−275.595	−	200.231i	−0.803483	−	0.583765i
$344$		0			0
$345$	−195.732	+	25.1081i	−0.567340	+	0.0727772i
$346$		0			0
$347$	333.877	−	242.576i	0.962181	−	0.699065i	0.00852470	−	0.999964i	$-0.497286\pi$
$347$	333.877	−	242.576i	0.962181	−	0.699065i	0.953656	+	0.300898i	$0.0972865\pi$
$348$		0			0
$349$	−45.2387	−	14.6989i	−0.129624	−	0.0421173i	0.243487	−	0.969904i	$-0.421709\pi$
$349$	−45.2387	−	14.6989i	−0.129624	−	0.0421173i	−0.373110	+	0.927787i	$0.621709\pi$
$350$		0			0
$351$			246.754i			0.703003i
$352$		0			0
$353$		−	357.561i		−	1.01292i	−0.862263	−	0.506460i	$-0.830954\pi$
$353$		−	357.561i		−	1.01292i	0.862263	−	0.506460i	$-0.169046\pi$
$354$		0			0
$355$	−101.483	−	55.5379i	−0.285869	−	0.156445i
$356$		0			0
$357$	−3.12077	−	4.29537i	−0.00874165	−	0.0120318i
$358$		0			0
$359$	−320.274	+	104.063i	−0.892129	+	0.289870i	−0.718985	−	0.695026i	$-0.755393\pi$
$359$	−320.274	+	104.063i	−0.892129	+	0.289870i	−0.173145	+	0.984896i	$0.555393\pi$
$360$		0			0
$361$	−291.234	−	211.594i	−0.806742	−	0.586132i
$362$		0			0
$363$	−47.2246	−	106.281i	−0.130095	−	0.292785i
$364$		0			0
$365$	348.406	−	328.434i	0.954536	−	0.899819i
$366$		0			0
$367$	−130.509	+	42.4049i	−0.355610	+	0.115545i	−0.481374	−	0.876516i	$-0.659862\pi$
$367$	−130.509	+	42.4049i	−0.355610	+	0.115545i	0.125764	+	0.992060i	$0.459862\pi$
$368$		0			0
$369$	275.267	+	378.872i	0.745980	+	1.02675i
$370$		0			0
$371$	199.662	+	64.8740i	0.538172	+	0.174863i
$372$		0			0
$373$	431.773			1.15757			0.578784	−	0.815481i	$-0.303527\pi$
$373$	431.773			1.15757			0.578784	+	0.815481i	$0.303527\pi$
$374$		0			0
$375$	101.811	+	63.7924i	0.271495	+	0.170113i
$376$		0			0
$377$	−622.645	−	202.309i	−1.65158	−	0.536630i
$378$		0			0
$379$	−116.541	+	84.6720i	−0.307496	+	0.223409i	−0.730821	−	0.682569i	$-0.760863\pi$
$379$	−116.541	+	84.6720i	−0.307496	+	0.223409i	0.423325	+	0.905978i	$0.360863\pi$
$380$		0			0
$381$	61.1276	−	19.8616i	0.160440	−	0.0521301i
$382$		0			0
$383$	−103.078	+	141.874i	−0.269132	+	0.370428i	−0.922096	−	0.386960i	$-0.873525\pi$
$383$	−103.078	+	141.874i	−0.269132	+	0.370428i	0.652965	+	0.757388i	$0.273525\pi$
$384$		0			0
$385$	−77.5972	−	221.725i	−0.201551	−	0.575909i
$386$		0			0
$387$	−284.448	−	206.664i	−0.735008	−	0.534015i
$388$		0			0
$389$	−18.5717	−	57.1577i	−0.0477421	−	0.146935i	0.924344	−	0.381561i	$-0.124613\pi$
$389$	−18.5717	−	57.1577i	−0.0477421	−	0.146935i	−0.972086	+	0.234626i	$0.924613\pi$
$390$		0			0
$391$	−31.2150	−	42.9638i	−0.0798338	−	0.109882i
$392$		0			0
$393$	14.2527	−	43.8653i	0.0362664	−	0.111617i
$394$		0			0
$395$	−339.078	−	64.0091i	−0.858427	−	0.162048i
$396$		0			0
$397$		−	343.378i		−	0.864931i	−0.901650	−	0.432466i	$-0.857644\pi$
$397$		−	343.378i		−	0.864931i	0.901650	−	0.432466i	$-0.142356\pi$
$398$		0			0
$399$	−1.27816	+	3.93377i	−0.00320341	+	0.00985908i
$400$		0			0
$401$	−195.989	+	142.394i	−0.488751	+	0.355098i	−0.804704	−	0.593677i	$-0.797676\pi$
$401$	−195.989	+	142.394i	−0.488751	+	0.355098i	0.315953	+	0.948775i	$0.397676\pi$
$402$		0			0
$403$	−75.6911	−	232.953i	−0.187819	−	0.578048i
$404$		0			0
$405$	207.054	−	195.185i	0.511245	−	0.481939i
$406$		0			0
$407$	13.0586	−	123.801i	0.0320850	−	0.304179i
$408$		0			0
$409$	−401.623	+	552.787i	−0.981964	+	1.35156i	−0.0461996	+	0.998932i	$0.514711\pi$
$409$	−401.623	+	552.787i	−0.981964	+	1.35156i	−0.935765	+	0.352625i	$0.885289\pi$
$410$		0			0
$411$	−70.7138	−	217.635i	−0.172053	−	0.529525i
$412$		0			0
$413$	−277.414	+	201.553i	−0.671705	+	0.488022i
$414$		0			0
$415$	−535.557	−	293.089i	−1.29050	−	0.706239i
$416$		0			0
$417$	57.1360			0.137017
$418$		0			0
$419$	−419.951			−1.00227			−0.501135	−	0.865369i	$-0.667084\pi$
$419$	−419.951			−1.00227			−0.501135	+	0.865369i	$0.667084\pi$
$420$		0			0
$421$	−50.0794	+	154.129i	−0.118953	+	0.366101i	−0.992751	−	0.120189i	$-0.961650\pi$
$421$	−50.0794	+	154.129i	−0.118953	+	0.366101i	0.873798	+	0.486290i	$0.161650\pi$
$422$		0			0
$423$	−54.5954	−	75.1441i	−0.129067	−	0.177646i
$424$		0			0
$425$	−1.90643	+	32.2767i	−0.00448572	+	0.0759451i
$426$		0			0
$427$	143.008	−	196.833i	0.334913	−	0.460968i
$428$		0			0
$429$	155.491	−	32.9901i	0.362450	−	0.0769001i
$430$		0			0
$431$	23.4210	−	32.2363i	0.0543412	−	0.0747942i	−0.780982	−	0.624554i	$-0.785281\pi$
$431$	23.4210	−	32.2363i	0.0543412	−	0.0747942i	0.835323	+	0.549760i	$0.185281\pi$
$432$		0			0
$433$	−236.160	+	76.7332i	−0.545405	+	0.177213i	−0.568744	−	0.822515i	$-0.692570\pi$
$433$	−236.160	+	76.7332i	−0.545405	+	0.177213i	0.0233386	+	0.999728i	$0.492570\pi$
$434$		0			0
$435$	−89.4691	−	189.189i	−0.205676	−	0.434917i
$436$		0			0
$437$	−12.7846	+	39.3470i	−0.0292554	+	0.0900388i
$438$		0			0
$439$		−	442.313i		−	1.00755i	−0.863836	−	0.503773i	$-0.831945\pi$
$439$		−	442.313i		−	1.00755i	0.863836	−	0.503773i	$-0.168055\pi$
$440$		0			0
$441$	−248.403			−0.563273
$442$		0			0
$443$	301.307	+	97.9005i	0.680150	+	0.220994i	0.628661	−	0.777679i	$-0.283603\pi$
$443$	301.307	+	97.9005i	0.680150	+	0.220994i	0.0514892	+	0.998674i	$0.483603\pi$
$444$		0			0
$445$	−93.7482	−	198.237i	−0.210670	−	0.445477i
$446$		0			0
$447$	−14.1781	−	43.6358i	−0.0317184	−	0.0976193i
$448$		0			0
$449$	400.851	+	291.235i	0.892765	+	0.648631i	0.936597	−	0.350407i	$-0.113957\pi$
$449$	400.851	+	291.235i	0.892765	+	0.648631i	−0.0438328	+	0.999039i	$0.513957\pi$
$450$		0			0
$451$	426.985	−	473.860i	0.946752	−	1.05069i
$452$		0			0
$453$	87.9609	+	63.9073i	0.194174	+	0.141076i
$454$		0			0
$455$	318.452	−	40.8504i	0.699895	−	0.0897812i
$456$		0			0
$457$	−415.704	+	302.027i	−0.909637	+	0.660890i	−0.940923	−	0.338620i	$-0.890040\pi$
$457$	−415.704	+	302.027i	−0.909637	+	0.660890i	0.0312859	+	0.999510i	$0.490040\pi$
$458$		0			0
$459$	−20.1882	−	6.55955i	−0.0439831	−	0.0142910i
$460$		0			0
$461$			563.523i			1.22239i	0.791479	+	0.611196i	$0.209311\pi$
$461$			563.523i			1.22239i	−0.791479	+	0.611196i	$0.790689\pi$
$462$		0			0
$463$		−	62.4020i		−	0.134778i	−0.997727	−	0.0673888i	$-0.978533\pi$
$463$		−	62.4020i		−	0.134778i	0.997727	−	0.0673888i	$-0.0214668\pi$
$464$		0			0
$465$	37.5888	−	68.6855i	0.0808362	−	0.147711i
$466$		0			0
$467$	41.7495	+	57.4633i	0.0893994	+	0.123048i	0.851374	−	0.524559i	$-0.175770\pi$
$467$	41.7495	+	57.4633i	0.0893994	+	0.123048i	−0.761975	+	0.647607i	$0.775770\pi$
$468$		0			0
$469$	234.764	−	76.2795i	0.500563	−	0.162643i
$470$		0			0
$471$	−15.7855	−	11.4689i	−0.0335149	−	0.0243500i
$472$		0			0
$473$	−194.944	+	437.412i	−0.412143	+	0.924762i
$474$		0			0
$475$	21.2156	−	13.5782i	0.0446644	−	0.0285857i
$476$		0			0
$477$	377.536	−	122.669i	0.791481	−	0.257168i
$478$		0			0
$479$	364.475	+	501.657i	0.760908	+	1.04730i	0.997138	+	0.0756030i	$0.0240882\pi$
$479$	364.475	+	501.657i	0.760908	+	1.04730i	−0.236230	+	0.971697i	$0.575912\pi$
$480$		0			0
$481$	161.815	+	52.5768i	0.336413	+	0.109307i
$482$		0			0
$483$	−168.569			−0.349004
$484$		0			0
$485$	670.511	+	126.575i	1.38250	+	0.260979i
$486$		0			0
$487$	636.038	+	206.661i	1.30603	+	0.424356i	0.877676	−	0.479254i	$-0.159093\pi$
$487$	636.038	+	206.661i	1.30603	+	0.424356i	0.428356	+	0.903610i	$0.359093\pi$
$488$		0			0
$489$	−183.750	+	133.502i	−0.375767	+	0.273010i
$490$		0			0
$491$	−70.3857	+	22.8697i	−0.143352	+	0.0465778i	−0.379814	−	0.925063i	$-0.624012\pi$
$491$	−70.3857	+	22.8697i	−0.143352	+	0.0465778i	0.236462	+	0.971641i	$0.424012\pi$
$492$		0			0
$493$	33.1040	−	45.5637i	0.0671480	−	0.0924213i
$494$		0			0
$495$	−365.137	−	252.941i	−0.737650	−	0.510992i
$496$		0			0
$497$	−79.9486	−	58.0861i	−0.160862	−	0.116873i
$498$		0			0
$499$	112.583	+	346.494i	0.225617	+	0.694377i	0.998228	+	0.0594979i	$0.0189500\pi$
$499$	112.583	+	346.494i	0.225617	+	0.694377i	−0.772612	+	0.634879i	$0.781050\pi$
$500$		0			0
$501$	−177.358	−	244.112i	−0.354007	−	0.487249i
$502$		0			0
$503$	−57.0752	+	175.659i	−0.113470	+	0.349224i	−0.991625	−	0.129152i	$-0.958774\pi$
$503$	−57.0752	+	175.659i	−0.113470	+	0.349224i	0.878155	+	0.478376i	$0.158774\pi$
$504$		0			0
$505$	441.014	+	83.2519i	0.873296	+	0.164855i
$506$		0			0
$507$			54.8094i			0.108105i
$508$		0			0
$509$	191.374	−	588.989i	0.375981	−	1.15715i	−0.566834	−	0.823832i	$-0.691832\pi$
$509$	191.374	−	588.989i	0.375981	−	1.15715i	0.942815	−	0.333317i	$-0.108168\pi$
$510$		0			0
$511$	330.894	−	240.408i	0.647542	−	0.470467i
$512$		0			0
$513$	5.11016	+	15.7275i	0.00996132	+	0.0306578i
$514$		0			0
$515$	223.713	+	237.317i	0.434394	+	0.460809i
$516$		0			0
$517$	−84.6867	+	93.9837i	−0.163804	+	0.181787i
$518$		0			0
$519$	90.9001	−	125.113i	0.175145	−	0.241066i
$520$		0			0
$521$	−47.0758	−	144.884i	−0.0903566	−	0.278089i	0.895659	−	0.444741i	$-0.146704\pi$
$521$	−47.0758	−	144.884i	−0.0903566	−	0.278089i	−0.986016	+	0.166652i	$0.946704\pi$
$522$		0			0
$523$	461.681	−	335.431i	0.882755	−	0.641359i	−0.0512241	−	0.998687i	$-0.516312\pi$
$523$	461.681	−	335.431i	0.882755	−	0.641359i	0.933979	+	0.357328i	$0.116312\pi$
$524$		0			0
$525$	79.3287	+	65.1156i	0.151102	+	0.124030i
$526$		0			0
$527$	21.0712			0.0399834
$528$		0			0
$529$	−1157.09			−2.18731
$530$		0			0
$531$	−200.363	+	616.654i	−0.377331	+	1.16131i
$532$		0			0
$533$	512.419	+	705.285i	0.961387	+	1.32324i
$534$		0			0
$535$	−717.216	+	92.0030i	−1.34059	+	0.171968i
$536$		0			0
$537$	111.094	−	152.908i	0.206879	−	0.284744i
$538$		0			0
$539$	70.2203	+	330.966i	0.130279	+	0.614037i
$540$		0			0
$541$	425.162	−	585.185i	0.785881	−	1.08167i	−0.208728	−	0.977974i	$-0.566932\pi$
$541$	425.162	−	585.185i	0.785881	−	1.08167i	0.994609	−	0.103698i	$-0.0330677\pi$
$542$		0			0
$543$	68.1910	−	22.1566i	0.125582	−	0.0408040i
$544$		0			0
$545$	−779.099	+	368.443i	−1.42954	+	0.676041i
$546$		0			0
$547$	−304.021	+	935.680i	−0.555797	+	1.71057i	0.138033	+	0.990428i	$0.455922\pi$
$547$	−304.021	+	935.680i	−0.555797	+	1.71057i	−0.693830	+	0.720139i	$0.744078\pi$
$548$		0			0
$549$		−	460.050i		−	0.837979i
$550$		0			0
$551$	−43.8755			−0.0796288
$552$		0			0
$553$	−280.337	−	91.0872i	−0.506939	−	0.164715i
$554$		0			0
$555$	23.2515	+	49.1670i	0.0418946	+	0.0885891i
$556$		0			0
$557$	179.275	+	551.752i	0.321858	+	0.990578i	0.972839	+	0.231483i	$0.0743579\pi$
$557$	179.275	+	551.752i	0.321858	+	0.990578i	−0.650981	+	0.759094i	$0.725642\pi$
$558$		0			0
$559$	−529.511	−	384.713i	−0.947247	−	0.688216i
$560$		0			0
$561$	−1.43438	+	13.5985i	−0.00255683	+	0.0242398i
$562$		0			0
$563$	758.285	+	550.926i	1.34687	+	0.978555i	0.999161	+	0.0409508i	$0.0130387\pi$
$563$	758.285	+	550.926i	1.34687	+	0.978555i	0.347704	+	0.937604i	$0.386961\pi$
$564$		0			0
$565$	90.2238	+	703.346i	0.159688	+	1.24486i
$566$		0			0
$567$	196.647	−	142.872i	0.346820	−	0.251980i
$568$		0			0
$569$	645.256	+	209.656i	1.13402	+	0.368465i	0.815101	−	0.579318i	$-0.196681\pi$
$569$	645.256	+	209.656i	1.13402	+	0.368465i	0.318916	+	0.947783i	$0.396681\pi$
$570$		0			0
$571$		−	278.056i		−	0.486964i	−0.969905	−	0.243482i	$-0.921710\pi$
$571$		−	278.056i		−	0.486964i	0.969905	−	0.243482i	$-0.0782896\pi$
$572$		0			0
$573$			104.068i			0.181619i
$574$		0			0
$575$	793.474	+	651.309i	1.37995	+	1.13271i
$576$		0			0
$577$	384.907	+	529.779i	0.667084	+	0.918162i	0.999690	−	0.0249041i	$-0.00792803\pi$
$577$	384.907	+	529.779i	0.667084	+	0.918162i	−0.332606	+	0.943066i	$0.607928\pi$
$578$		0			0
$579$	98.6573	−	32.0557i	0.170392	−	0.0553639i
$580$		0			0
$581$	−421.912	−	306.537i	−0.726183	−	0.527603i
$582$		0			0
$583$	−270.165	−	468.343i	−0.463405	−	0.803332i
$584$		0			0
$585$	441.751	−	416.429i	0.755131	−	0.711845i
$586$		0			0
$587$	329.847	−	107.174i	0.561920	−	0.182579i	−0.0142650	−	0.999898i	$-0.504541\pi$
$587$	329.847	−	107.174i	0.561920	−	0.182579i	0.576185	+	0.817319i	$0.304541\pi$
$588$		0			0
$589$	−9.64870	−	13.2803i	−0.0163815	−	0.0225472i
$590$		0			0
$591$	271.290	+	88.1476i	0.459036	+	0.149150i
$592$		0			0
$593$	−1009.02			−1.70156			−0.850778	−	0.525525i	$-0.823869\pi$
$593$	−1009.02			−1.70156			−0.850778	+	0.525525i	$0.823869\pi$
$594$		0			0
$595$	−5.12335	+	27.1402i	−0.00861067	+	0.0456137i
$596$		0			0
$597$	−261.890	−	85.0932i	−0.438677	−	0.142535i
$598$		0			0
$599$	442.754	−	321.680i	0.739156	−	0.537028i	−0.153291	−	0.988181i	$-0.548987\pi$
$599$	442.754	−	321.680i	0.739156	−	0.537028i	0.892447	+	0.451153i	$0.148987\pi$
$600$		0			0
$601$	−54.8311	+	17.8157i	−0.0912331	+	0.0296434i	−0.354278	−	0.935140i	$-0.615273\pi$
$601$	−54.8311	+	17.8157i	−0.0912331	+	0.0296434i	0.263045	+	0.964784i	$0.415273\pi$
$602$		0			0
$603$	274.352	−	377.613i	0.454979	−	0.626224i
$604$		0			0
$605$	−233.793	+	558.002i	−0.386434	+	0.922317i
$606$		0			0
$607$	134.438	+	97.6753i	0.221480	+	0.160915i	0.692993	−	0.720945i	$-0.256292\pi$
$607$	134.438	+	97.6753i	0.221480	+	0.160915i	−0.471513	+	0.881859i	$0.656292\pi$
$608$		0			0
$609$	−55.2429	−	170.020i	−0.0907109	−	0.279179i
$610$		0			0
$611$	−101.631	−	139.884i	−0.166336	−	0.228942i
$612$		0			0
$613$	114.099	−	351.162i	0.186133	−	0.572858i	−0.813833	−	0.581099i	$-0.802623\pi$
$613$	114.099	−	351.162i	0.186133	−	0.572858i	0.999966	+	0.00824040i	$0.00262303\pi$
$614$		0			0
$615$	−51.6933	+	273.837i	−0.0840541	+	0.445264i
$616$		0			0
$617$			616.728i			0.999560i	0.866152	+	0.499780i	$0.166586\pi$
$617$			616.728i			0.999560i	−0.866152	+	0.499780i	$0.833414\pi$
$618$		0			0
$619$	174.888	−	538.249i	0.282533	−	0.869546i	−0.704595	−	0.709610i	$-0.748871\pi$
$619$	174.888	−	538.249i	0.282533	−	0.869546i	0.987127	−	0.159936i	$-0.0511289\pi$
$620$		0			0
$621$	−545.236	+	396.137i	−0.877997	+	0.637902i
$622$		0			0
$623$	−57.8851	−	178.152i	−0.0929134	−	0.285958i
$624$		0			0
$625$	−121.819	−	613.013i	−0.194910	−	0.980821i
$626$		0			0
$627$	9.22738	−	5.32285i	0.0147167	−	0.00848939i
$628$		0			0
$629$	−8.60315	+	11.8412i	−0.0136775	+	0.0188255i
$630$		0			0
$631$	331.356	+	1019.81i	0.525129	+	1.61618i	0.764060	+	0.645145i	$0.223203\pi$
$631$	331.356	+	1019.81i	0.525129	+	1.61618i	−0.238931	+	0.971036i	$0.576797\pi$
$632$		0			0
$633$	65.3498	−	47.4794i	0.103238	−	0.0750069i
$634$		0			0
$635$	−293.304	−	160.513i	−0.461896	−	0.252777i
$636$		0			0
$637$	−462.412			−0.725922
$638$		0			0
$639$	−186.861			−0.292427
$640$		0			0
$641$	−122.164	+	375.981i	−0.190583	+	0.586554i	−1.00000		0.000680333i	$-0.999783\pi$
$641$	−122.164	+	375.981i	−0.190583	+	0.586554i	0.809417	+	0.587235i	$0.199783\pi$
$642$		0			0
$643$	−35.8968	−	49.4077i	−0.0558271	−	0.0768394i	0.780191	−	0.625542i	$-0.215122\pi$
$643$	−35.8968	−	49.4077i	−0.0558271	−	0.0768394i	−0.836018	+	0.548702i	$0.815122\pi$
$644$		0			0
$645$	−26.6204	−	207.521i	−0.0412720	−	0.321739i
$646$		0			0
$647$	321.833	−	442.965i	0.497423	−	0.684644i	−0.484312	−	0.874895i	$-0.660930\pi$
$647$	321.833	−	442.965i	0.497423	−	0.684644i	0.981735	+	0.190251i	$0.0609302\pi$
$648$		0			0
$649$	878.253	+	92.6388i	1.35324	+	0.142741i
$650$		0			0
$651$	39.3135	−	54.1104i	0.0603894	−	0.0831189i
$652$		0			0
$653$	−487.975	+	158.553i	−0.747282	+	0.242807i	−0.657811	−	0.753183i	$-0.728518\pi$
$653$	−487.975	+	158.553i	−0.747282	+	0.242807i	−0.0894710	+	0.995989i	$0.528518\pi$
$654$		0			0
$655$	−216.901	+	102.574i	−0.331146	+	0.156602i
$656$		0			0
$657$	238.989	−	735.532i	0.363758	−	1.11953i
$658$		0			0
$659$		−	1150.26i		−	1.74546i	−0.488206	−	0.872729i	$-0.662348\pi$
$659$		−	1150.26i		−	1.74546i	0.488206	−	0.872729i	$-0.337652\pi$
$660$		0			0
$661$	611.853			0.925648			0.462824	−	0.886450i	$-0.346836\pi$
$661$	611.853			0.925648			0.462824	+	0.886450i	$0.346836\pi$
$662$		0			0
$663$	−17.7740	−	5.77512i	−0.0268084	−	0.00871059i
$664$		0			0
$665$	19.4513	−	9.19869i	0.0292501	−	0.0138326i
$666$		0			0
$667$	−552.559	−	1700.60i	−0.828424	−	2.54963i
$668$		0			0
$669$	−37.0170	−	26.8944i	−0.0553319	−	0.0402010i
$670$		0			0
$671$	−612.959	+	130.050i	−0.913501	+	0.193815i
$672$		0			0
$673$	1030.45	+	748.663i	1.53112	+	1.11243i	0.955610	+	0.294635i	$0.0951982\pi$
$673$	1030.45	+	748.663i	1.53112	+	1.11243i	0.575514	+	0.817792i	$0.304802\pi$
$674$		0			0
$675$	409.610	+	24.1937i	0.606830	+	0.0358426i
$676$		0			0
$677$	−1080.77	+	785.228i	−1.59642	+	1.15986i	−0.702448	+	0.711735i	$0.747909\pi$
$677$	−1080.77	+	785.228i	−1.59642	+	1.15986i	−0.893969	+	0.448129i	$0.852091\pi$
$678$		0			0
$679$	554.354	+	180.121i	0.816427	+	0.265273i
$680$		0			0
$681$			325.002i			0.477242i
$682$		0			0
$683$			387.608i			0.567508i	0.958897	+	0.283754i	$0.0915798\pi$
$683$			387.608i			0.567508i	−0.958897	+	0.283754i	$0.908420\pi$
$684$		0			0
$685$	−571.481	+	1044.26i	−0.834279	+	1.52447i
$686$		0			0
$687$	88.7233	+	122.117i	0.129146	+	0.177754i
$688$		0			0
$689$	702.799	−	228.353i	1.02003	−	0.331427i
$690$		0			0
$691$	743.792	+	540.397i	1.07640	+	0.782050i	0.977052	−	0.213002i	$-0.0683242\pi$
$691$	743.792	+	540.397i	1.07640	+	0.782050i	0.0993482	+	0.995053i	$0.468324\pi$
$692$		0			0
$693$	−281.882	−	253.998i	−0.406756	−	0.366519i
$694$		0			0
$695$	−203.879	−	216.276i	−0.293351	−	0.311189i
$696$		0			0
$697$	−71.3248	+	23.1748i	−0.102331	+	0.0332494i
$698$		0			0
$699$	−88.4273	−	121.710i	−0.126505	−	0.174120i
$700$		0			0
$701$	−914.052	−	296.994i	−1.30393	−	0.423671i	−0.426980	−	0.904261i	$-0.640423\pi$
$701$	−914.052	−	296.994i	−1.30393	−	0.423671i	−0.876946	+	0.480590i	$0.840423\pi$
$702$		0			0
$703$	11.4025			0.0162197
$704$		0			0
$705$	10.2527	−	54.3119i	0.0145428	−	0.0770382i
$706$		0			0
$707$	364.614	+	118.470i	0.515720	+	0.167568i
$708$		0			0
$709$	177.278	−	128.800i	0.250039	−	0.181664i	−0.455705	−	0.890131i	$-0.650613\pi$
$709$	177.278	−	128.800i	0.250039	−	0.181664i	0.705744	+	0.708467i	$0.250613\pi$
$710$		0			0
$711$	−530.085	+	172.235i	−0.745548	+	0.242243i
$712$		0			0
$713$	393.227	−	541.231i	0.551511	−	0.759090i
$714$		0			0
$715$	−679.716	−	470.859i	−0.950652	−	0.658544i
$716$		0			0
$717$	126.068	+	91.5937i	0.175827	+	0.127746i
$718$		0			0
$719$	−380.993	−	1172.58i	−0.529893	−	1.63084i	−0.754431	−	0.656379i	$-0.772087\pi$
$719$	−380.993	−	1172.58i	−0.529893	−	1.63084i	0.224538	−	0.974465i	$-0.427913\pi$
$720$		0			0
$721$	163.754	+	225.389i	0.227121	+	0.312605i
$722$		0			0
$723$	17.3383	−	53.3618i	0.0239811	−	0.0738061i
$724$		0			0
$725$	−396.882	+	1013.75i	−0.547423	+	1.39828i
$726$		0			0
$727$		−	890.664i		−	1.22512i	−0.790423	−	0.612561i	$-0.790139\pi$
$727$		−	890.664i		−	1.22512i	0.790423	−	0.612561i	$-0.209861\pi$
$728$		0			0
$729$	98.1546	−	302.089i	0.134643	−	0.414388i
$730$		0			0
$731$	45.5515	−	33.0951i	0.0623140	−	0.0452738i
$732$		0			0
$733$	−306.920	−	944.601i	−0.418717	−	1.28868i	−0.908884	−	0.417050i	$-0.863064\pi$
$733$	−306.920	−	944.601i	−0.418717	−	1.28868i	0.490167	−	0.871629i	$-0.336936\pi$
$734$		0			0
$735$	−101.393	−	107.558i	−0.137949	−	0.146338i
$736$		0			0
$737$	−580.678	−	258.793i	−0.787894	−	0.351144i
$738$		0			0
$739$	−306.583	+	421.976i	−0.414862	+	0.571009i	−0.964396	−	0.264463i	$-0.914805\pi$
$739$	−306.583	+	421.976i	−0.414862	+	0.571009i	0.549534	+	0.835472i	$0.314805\pi$
$740$		0			0
$741$	4.49906	+	13.8467i	0.00607160	+	0.0186865i
$742$		0			0
$743$	354.813	−	257.787i	0.477541	−	0.346954i	−0.322832	−	0.946456i	$-0.604635\pi$
$743$	354.813	−	257.787i	0.477541	−	0.346954i	0.800373	+	0.599502i	$0.204635\pi$
$744$		0			0
$745$	−114.582	+	209.374i	−0.153802	+	0.281039i
$746$		0			0
$747$	−986.117			−1.32010
$748$		0			0
$749$	−617.682			−0.824676
$750$		0			0
$751$	278.184	−	856.163i	0.370418	−	1.14003i	−0.576099	−	0.817380i	$-0.695426\pi$
$751$	278.184	−	856.163i	0.370418	−	1.14003i	0.946518	−	0.322651i	$-0.104574\pi$
$752$		0			0
$753$	151.234	+	208.156i	0.200842	+	0.276436i
$754$		0			0
$755$	−71.9637	−	560.998i	−0.0953162	−	0.743044i
$756$		0			0
$757$	833.954	−	1147.84i	1.10166	−	1.51630i	0.268487	−	0.963283i	$-0.413476\pi$
$757$	833.954	−	1147.84i	1.10166	−	1.51630i	0.833170	−	0.553017i	$-0.186524\pi$
$758$		0			0
$759$	322.520	+	290.616i	0.424928	+	0.382893i
$760$		0			0
$761$	−172.382	+	237.263i	−0.226520	+	0.311778i	−0.907116	−	0.420881i	$-0.861721\pi$
$761$	−172.382	+	237.263i	−0.226520	+	0.311778i	0.680596	+	0.732659i	$0.261721\pi$
$762$		0			0
$763$	−700.160	+	227.496i	−0.917641	+	0.298160i
$764$		0			0
$765$	22.3270	+	47.2121i	0.0291856	+	0.0617151i
$766$		0			0
$767$	−372.983	+	1147.92i	−0.486289	+	1.49664i
$768$		0			0
$769$		−	538.221i		−	0.699897i	−0.936769	−	0.349949i	$-0.886199\pi$
$769$		−	538.221i		−	0.699897i	0.936769	−	0.349949i	$-0.113801\pi$
$770$		0			0
$771$	−31.6796			−0.0410890
$772$		0			0
$773$	−428.301	−	139.163i	−0.554076	−	0.180030i	0.0185777	−	0.999827i	$-0.494086\pi$
$773$	−428.301	−	139.163i	−0.554076	−	0.180030i	−0.572654	+	0.819797i	$0.694086\pi$
$774$		0			0
$775$	−394.122	+	102.806i	−0.508545	+	0.132653i
$776$		0			0
$777$	14.3567	+	44.1853i	0.0184771	+	0.0568666i
$778$		0			0
$779$	47.2664	+	34.3410i	0.0606757	+	0.0440835i
$780$		0			0
$781$	52.8229	+	248.968i	0.0676350	+	0.318781i
$782$		0			0
$783$	−578.231	−	420.109i	−0.738481	−	0.536538i
$784$		0			0
$785$	12.9147	+	100.677i	0.0164518	+	0.128251i
$786$		0			0
$787$	412.227	−	299.500i	0.523795	−	0.380560i	−0.294236	−	0.955733i	$-0.595065\pi$
$787$	412.227	−	299.500i	0.523795	−	0.380560i	0.818032	+	0.575173i	$0.195065\pi$
$788$		0			0
$789$	231.516	+	75.2242i	0.293430	+	0.0953412i
$790$		0			0
$791$			605.737i			0.765787i
$792$		0			0
$793$		−	856.401i		−	1.07995i
$794$		0			0
$795$	207.218	+	113.402i	0.260651	+	0.142644i
$796$		0			0
$797$	121.019	+	166.568i	0.151843	+	0.208994i	0.878161	−	0.478364i	$-0.158770\pi$
$797$	121.019	+	166.568i	0.151843	+	0.208994i	−0.726318	+	0.687358i	$0.758770\pi$
$798$		0			0
$799$	14.1463	−	4.59642i	0.0177050	−	0.00575271i
$800$		0			0
$801$	−286.554	−	208.193i	−0.357745	−	0.259917i
$802$		0			0
$803$	−1047.56	−	110.498i	−1.30456	−	0.137606i
$804$		0			0
$805$	601.505	+	638.082i	0.747212	+	0.792648i
$806$		0			0
$807$	−93.7892	+	30.4740i	−0.116220	+	0.0377620i
$808$		0			0
$809$	223.593	+	307.749i	0.276382	+	0.380407i	0.924531	−	0.381106i	$-0.124457\pi$
$809$	223.593	+	307.749i	0.276382	+	0.380407i	−0.648149	+	0.761513i	$0.724457\pi$
$810$		0			0
$811$	−797.193	−	259.024i	−0.982976	−	0.319388i	−0.226933	−	0.973910i	$-0.572870\pi$
$811$	−797.193	−	259.024i	−0.982976	−	0.319388i	−0.756043	+	0.654522i	$0.772870\pi$
$812$		0			0
$813$	311.076			0.382628
$814$		0			0
$815$	1161.02	+	219.170i	1.42456	+	0.268920i
$816$		0			0
$817$	−41.7169	−	13.5546i	−0.0510610	−	0.0165907i
$818$		0			0
$819$	419.548	−	304.819i	0.512268	−	0.372185i
$820$		0			0
$821$	−598.485	+	194.460i	−0.728971	+	0.236857i	−0.649908	−	0.760013i	$-0.725193\pi$
$821$	−598.485	+	194.460i	−0.728971	+	0.236857i	−0.0790628	+	0.996870i	$0.525193\pi$
$822$		0			0
$823$	307.672	−	423.474i	0.373842	−	0.514549i	−0.580098	−	0.814547i	$-0.696986\pi$
$823$	307.672	−	423.474i	0.373842	−	0.514549i	0.953940	+	0.299997i	$0.0969858\pi$
$824$		0			0
$825$	−39.5178	−	261.349i	−0.0479004	−	0.316786i
$826$		0			0
$827$	846.428	+	614.966i	1.02349	+	0.743610i	0.966996	−	0.254793i	$-0.0820072\pi$
$827$	846.428	+	614.966i	1.02349	+	0.743610i	0.0564959	+	0.998403i	$0.482007\pi$
$828$		0			0
$829$	−502.733	−	1547.25i	−0.606433	−	1.86641i	−0.486621	−	0.873613i	$-0.661771\pi$
$829$	−502.733	−	1547.25i	−0.606433	−	1.86641i	−0.119812	−	0.992797i	$-0.538229\pi$
$830$		0			0
$831$	145.013	+	199.593i	0.174504	+	0.240185i
$832$		0			0
$833$	12.2925	−	37.8324i	0.0147569	−	0.0454170i
$834$		0			0
$835$	−291.167	+	1542.42i	−0.348703	+	1.84720i
$836$		0			0
$837$		−	267.407i		−	0.319482i
$838$		0			0
$839$	425.628	−	1309.95i	0.507303	−	1.56132i	−0.289560	−	0.957160i	$-0.593509\pi$
$839$	425.628	−	1309.95i	0.507303	−	1.56132i	0.796863	−	0.604159i	$-0.206491\pi$
$840$		0			0
$841$	853.777	−	620.305i	1.01519	−	0.737581i
$842$		0			0
$843$	−87.8238	−	270.294i	−0.104180	−	0.320633i
$844$		0			0
$845$	207.469	−	195.576i	0.245526	−	0.231451i
$846$		0			0
$847$	−258.736	+	447.374i	−0.305473	+	0.528186i
$848$		0			0
$849$	−170.121	+	234.152i	−0.200378	+	0.275797i
$850$		0			0
$851$	143.601	+	441.957i	0.168743	+	0.519339i
$852$		0			0
$853$	−1116.69	+	811.322i	−1.30913	+	0.951139i	−0.309131	+	0.951020i	$0.600038\pi$
$853$	−1116.69	+	811.322i	−1.30913	+	0.951139i	−1.00000		0.000119552i	$0.999962\pi$
$854$		0			0
$855$	19.5320	−	35.6906i	0.0228445	−	0.0417433i
$856$		0			0
$857$	505.150			0.589439			0.294720	−	0.955584i	$-0.404774\pi$
$857$	505.150			0.589439			0.294720	+	0.955584i	$0.404774\pi$
$858$		0			0
$859$	−862.922			−1.00457			−0.502283	−	0.864703i	$-0.667506\pi$
$859$	−862.922			−1.00457			−0.502283	+	0.864703i	$0.667506\pi$
$860$		0			0
$861$	−73.5613	+	226.399i	−0.0854371	+	0.262948i
$862$		0			0
$863$	546.796	+	752.600i	0.633599	+	0.872074i	0.998254	−	0.0590686i	$-0.0188131\pi$
$863$	546.796	+	752.600i	0.633599	+	0.872074i	−0.364655	+	0.931143i	$0.618813\pi$
$864$		0			0
$865$	−797.949	+	102.359i	−0.922484	+	0.118334i
$866$		0			0
$867$	−162.328	+	223.425i	−0.187229	+	0.257699i
$868$		0			0
$869$	379.329	+	657.583i	0.436512	+	0.756712i
$870$		0			0
$871$	510.717	−	702.942i	0.586357	−	0.807051i
$872$		0			0
$873$	1048.22	−	340.586i	1.20071	−	0.390133i
$874$		0			0
$875$	−36.5878	−	532.634i	−0.0418147	−	0.608725i
$876$		0			0
$877$	68.0553	−	209.453i	0.0776002	−	0.238829i	−0.904730	−	0.425986i	$-0.859927\pi$
$877$	68.0553	−	209.453i	0.0776002	−	0.238829i	0.982330	+	0.187157i	$0.0599273\pi$
$878$		0			0
$879$			88.2962i			0.100451i
$880$		0			0
$881$	960.629			1.09038			0.545192	−	0.838311i	$-0.316457\pi$
$881$	960.629			1.09038			0.545192	+	0.838311i	$0.316457\pi$
$882$		0			0
$883$	1493.76	+	485.353i	1.69169	+	0.549664i	0.987122	−	0.159970i	$-0.0511397\pi$
$883$	1493.76	+	485.353i	1.69169	+	0.549664i	0.704571	+	0.709634i	$0.251140\pi$
$884$		0			0
$885$	−348.794	+	164.948i	−0.394118	+	0.186382i
$886$		0			0
$887$	−166.789	−	513.323i	−0.188037	−	0.578718i	0.811951	−	0.583726i	$-0.198406\pi$
$887$	−166.789	−	513.323i	−0.188037	−	0.578718i	−0.999987	+	0.00500809i	$0.998406\pi$
$888$		0			0
$889$	−231.065	−	167.878i	−0.259915	−	0.188839i
$890$		0			0
$891$	−622.556	−	65.6677i	−0.698716	−	0.0737011i
$892$		0			0
$893$	−9.37465	−	6.81108i	−0.0104979	−	0.00762719i
$894$		0			0
$895$	−975.217	+	125.099i	−1.08963	+	0.139775i
$896$		0			0
$897$	−480.033	+	348.765i	−0.535154	+	0.388812i
$898$		0			0
$899$	674.758	+	219.242i	0.750565	+	0.243873i
$900$		0			0
$901$			63.5700i			0.0705549i
$902$		0			0
$903$		−	178.722i		−	0.197920i
$904$		0			0
$905$	−327.195	−	179.061i	−0.361542	−	0.197857i
$906$		0			0
$907$	−20.1600	−	27.7479i	−0.0222272	−	0.0305931i	0.797759	−	0.602977i	$-0.206019\pi$
$907$	−20.1600	−	27.7479i	−0.0222272	−	0.0305931i	−0.819986	+	0.572384i	$0.806019\pi$
$908$		0			0
$909$	689.442	−	224.013i	0.758462	−	0.246439i
$910$		0			0
$911$	−544.545	−	395.635i	−0.597744	−	0.434286i	0.247333	−	0.968930i	$-0.420446\pi$
$911$	−544.545	−	395.635i	−0.597744	−	0.434286i	−0.845077	+	0.534644i	$0.820446\pi$
$912$		0			0
$913$	278.762	+	1313.88i	0.305325	+	1.43908i
$914$		0			0
$915$	199.201	−	187.782i	0.217706	−	0.205227i
$916$		0			0
$917$	−194.924	+	63.3347i	−0.212567	+	0.0690673i
$918$		0			0
$919$	811.651	+	1117.14i	0.883189	+	1.21561i	0.975527	+	0.219878i	$0.0705660\pi$
$919$	811.651	+	1117.14i	0.883189	+	1.21561i	−0.0923378	+	0.995728i	$0.529434\pi$
$920$		0			0
$921$	−227.560	−	73.9387i	−0.247079	−	0.0802809i
$922$		0			0
$923$	−347.848			−0.376867
$924$		0			0
$925$	103.143	−	263.456i	0.111506	−	0.284817i
$926$		0			0
$927$	501.008	+	162.787i	0.540462	+	0.175607i
$928$		0			0
$929$	−273.826	+	198.946i	−0.294754	+	0.214151i	−0.725327	−	0.688404i	$-0.758311\pi$
$929$	−273.826	+	198.946i	−0.294754	+	0.214151i	0.430573	+	0.902556i	$0.358311\pi$
$930$		0			0
$931$	−29.4729	+	9.57634i	−0.0316573	+	0.0102861i
$932$		0			0
$933$	167.838	−	231.009i	0.179890	−	0.247598i
$934$		0			0
$935$	56.5926	−	43.0941i	0.0605268	−	0.0460900i
$936$		0			0
$937$	943.696	+	685.635i	1.00715	+	0.731734i	0.963609	−	0.267317i	$-0.0861372\pi$
$937$	943.696	+	685.635i	1.00715	+	0.731734i	0.0435375	+	0.999052i	$0.486137\pi$
$938$		0			0
$939$	−130.764	−	402.450i	−0.139259	−	0.428594i
$940$		0			0
$941$	552.765	+	760.816i	0.587423	+	0.808519i	0.994485	−	0.104882i	$-0.0334465\pi$
$941$	552.765	+	760.816i	0.587423	+	0.808519i	−0.407061	+	0.913401i	$0.633446\pi$
$942$		0			0
$943$	−735.786	+	2264.52i	−0.780261	+	2.40140i
$944$		0			0
$945$	344.425	+	65.0184i	0.364471	+	0.0688025i
$946$		0			0
$947$			1015.36i			1.07219i	0.844158	+	0.536094i	$0.180101\pi$
$947$			1015.36i			1.07219i	−0.844158	+	0.536094i	$0.819899\pi$
$948$		0			0
$949$	444.887	−	1369.22i	0.468795	−	1.44280i
$950$		0			0
$951$	−87.4997	+	63.5723i	−0.0920081	+	0.0668478i
$952$		0			0
$953$	309.621	+	952.916i	0.324891	+	0.999911i	0.971490	+	0.237081i	$0.0761908\pi$
$953$	309.621	+	952.916i	0.324891	+	0.999911i	−0.646599	+	0.762830i	$0.723809\pi$
$954$		0			0
$955$	393.926	−	371.345i	0.412488	−	0.388843i
$956$		0			0
$957$	−187.423	+	420.537i	−0.195844	+	0.439432i
$958$		0			0
$959$	−597.703	+	822.667i	−0.623256	+	0.857838i
$960$		0			0
$961$	−214.939	−	661.514i	−0.223662	−	0.688361i
$962$		0			0
$963$	−944.902	+	686.512i	−0.981207	+	0.712889i
$964$		0			0
$965$	−473.379	−	259.061i	−0.490548	−	0.268458i
$966$		0			0
$967$	232.078			0.239998			0.119999	−	0.992774i	$-0.461711\pi$
$967$	232.078			0.239998			0.119999	+	0.992774i	$0.461711\pi$
$968$		0			0
$969$	−1.25247			−0.00129254
$970$		0			0
$971$	−419.736	+	1291.82i	−0.432272	+	1.33040i	0.463584	+	0.886053i	$0.346563\pi$
$971$	−419.736	+	1291.82i	−0.432272	+	1.33040i	−0.895856	+	0.444344i	$0.853437\pi$
$972$		0			0
$973$	−149.236	−	205.406i	−0.153377	−	0.211105i
$974$		0			0
$975$	360.627	+	21.3005i	0.369873	+	0.0218467i
$976$		0			0
$977$	664.629	−	914.784i	0.680276	−	0.936319i	−0.319661	−	0.947532i	$-0.603569\pi$
$977$	664.629	−	914.784i	0.680276	−	0.936319i	0.999937	+	0.0112126i	$0.00356914\pi$
$978$		0			0
$979$	−196.387	+	440.650i	−0.200599	+	0.450102i
$980$		0			0
$981$	−818.227	+	1126.19i	−0.834075	+	1.14801i
$982$		0			0
$983$	1218.75	−	395.995i	1.23982	−	0.402843i	0.385560	−	0.922683i	$-0.374008\pi$
$983$	1218.75	−	395.995i	1.23982	−	0.402843i	0.854264	+	0.519839i	$0.174008\pi$
$984$		0			0
$985$	−634.383	−	1341.45i	−0.644044	−	1.36188i
$986$		0			0
$987$	14.5899	−	44.9031i	0.0147821	−	0.0454945i
$988$		0			0
$989$		−	1787.64i		−	1.80752i
$990$		0			0
$991$	631.835			0.637573			0.318786	−	0.947827i	$-0.396725\pi$
$991$	631.835			0.637573			0.318786	+	0.947827i	$0.396725\pi$
$992$		0			0
$993$	531.782	+	172.786i	0.535531	+	0.174004i
$994$		0			0
$995$	612.401	+	1294.97i	0.615478	+	1.30147i
$996$		0			0
$997$	−135.041	−	415.614i	−0.135448	−	0.416865i	0.860212	−	0.509937i	$-0.170331\pi$
$997$	−135.041	−	415.614i	−0.135448	−	0.416865i	−0.995659	+	0.0930720i	$0.970331\pi$
$998$		0			0
$999$	150.272	+	109.179i	0.150423	+	0.109288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.q.a.29.8	yes	48
5.4	even	2	inner	220.3.q.a.29.5	✓	48
11.8	odd	10	inner	220.3.q.a.129.5	yes	48
55.19	odd	10	inner	220.3.q.a.129.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.q.a.29.5	✓	48	5.4	even	2	inner
220.3.q.a.29.8	yes	48	1.1	even	1	trivial
220.3.q.a.129.5	yes	48	11.8	odd	10	inner
220.3.q.a.129.8	yes	48	55.19	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.914119 + 0.297015i) q^{3} +(-2.13757 - 4.52004i) q^{5} +(-1.31985 - 4.06207i) q^{7} +(-6.53376 - 4.74705i) q^{9} +(-4.47784 + 10.0473i) q^{11} +(-12.1628 - 8.83682i) q^{13} +(-0.611469 - 4.76675i) q^{15} +(1.04632 - 0.760193i) q^{17} +(-0.958233 - 0.311349i) q^{19} -4.10523i q^{21} -41.0620i q^{23} +(-15.8616 + 19.3238i) q^{25} +(-9.64730 - 13.2784i) q^{27} +(41.4155 - 13.4567i) q^{29} +(13.1808 + 9.57644i) q^{31} +(-7.07750 + 7.85447i) q^{33} +(-15.5395 + 14.6487i) q^{35} +(-10.7632 + 3.49717i) q^{37} +(-8.49362 - 11.6905i) q^{39} +(-55.1488 - 17.9189i) q^{41} +43.5352 q^{43} +(-7.49054 + 39.6800i) q^{45} +(10.9380 + 3.55398i) q^{47} +(24.8834 - 18.0789i) q^{49} +(1.18225 - 0.384135i) q^{51} +(-28.8912 + 39.7654i) q^{53} +(54.9861 - 1.23680i) q^{55} +(-0.783464 - 0.569220i) q^{57} +(-24.8092 - 76.3547i) q^{59} +(33.4826 + 46.0848i) q^{61} +(-10.6593 + 32.8060i) q^{63} +(-13.9439 + 73.8659i) q^{65} +57.7942i q^{67} +(12.1960 - 37.5355i) q^{69} +(18.7185 - 13.5998i) q^{71} +(29.5919 + 91.0744i) q^{73} +(-20.2389 + 12.9531i) q^{75} +(46.7230 + 4.92838i) q^{77} +(40.5651 - 55.8330i) q^{79} +(17.5862 + 54.1246i) q^{81} +(98.7827 - 71.7698i) q^{83} +(-5.67267 - 3.10443i) q^{85} +41.8556 q^{87} +43.8574 q^{89} +(-19.8427 + 61.0696i) q^{91} +(9.20451 + 12.6689i) q^{93} +(0.640978 + 4.99679i) q^{95} +(-80.2155 + 110.407i) q^{97} +(76.9524 - 44.3903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 5 q^{5} + 20 q^{9} - 23 q^{15} - 7 q^{25} - 74 q^{31} + 155 q^{35} + 80 q^{39} - 20 q^{41} + 12 q^{45} + 102 q^{49} + 220 q^{51} - 69 q^{55} + 40 q^{59} - 290 q^{61} - 234 q^{69} - 406 q^{71} + 153 q^{75}+ \cdots - 382 q^{99}+O(q^{100}) \) 48 * q + 5 * q^5 + 20 * q^9 - 23 * q^15 - 7 * q^25 - 74 * q^31 + 155 * q^35 + 80 * q^39 - 20 * q^41 + 12 * q^45 + 102 * q^49 + 220 * q^51 - 69 * q^55 + 40 * q^59 - 290 * q^61 - 234 * q^69 - 406 * q^71 + 153 * q^75 - 280 * q^79 + 230 * q^81 - 465 * q^85 - 636 * q^89 + 512 * q^91 - 495 * q^95 - 382 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more