LMFDB - Embedded newform 220.3.x.a.37.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(37,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.37"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 5, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.x (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.2
Character	$\chi$	$=$	220.37
Dual form			220.3.x.a.113.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87775 - 3.68530i) q^{3} +(3.24376 - 3.80500i) q^{5} +(2.52559 - 4.95675i) q^{7} +(-4.76541 + 6.55902i) q^{9} +(10.8597 - 1.75112i) q^{11} +(-8.82368 + 1.39753i) q^{13} +(-20.1135 - 4.80938i) q^{15} +(-27.6325 - 4.37656i) q^{17} +(15.6008 + 5.06901i) q^{19} -23.0096 q^{21} +(-0.317508 + 0.317508i) q^{23} +(-3.95603 - 24.6850i) q^{25} +(-3.64643 - 0.577539i) q^{27} +(-10.1414 + 3.29515i) q^{29} +(0.900009 + 0.653895i) q^{31} +(-26.8453 - 36.7332i) q^{33} +(-10.6680 - 25.6884i) q^{35} +(-12.9590 + 25.4335i) q^{37} +(21.7190 + 29.8937i) q^{39} +(-3.08786 + 9.50347i) q^{41} +(27.9830 - 27.9830i) q^{43} +(9.49923 + 39.4083i) q^{45} +(50.5139 - 25.7381i) q^{47} +(10.6107 + 14.6044i) q^{49} +(35.7581 + 110.052i) q^{51} +(90.5466 - 14.3412i) q^{53} +(28.5633 - 47.0015i) q^{55} +(-10.6137 - 67.0120i) q^{57} +(2.39521 - 0.778250i) q^{59} +(-50.6854 + 36.8251i) q^{61} +(20.4760 + 40.1864i) q^{63} +(-23.3043 + 38.1073i) q^{65} +(-59.4330 - 59.4330i) q^{67} +(1.76631 + 0.573910i) q^{69} +(110.315 - 80.1487i) q^{71} +(97.5018 + 49.6796i) q^{73} +(-83.5432 + 60.9316i) q^{75} +(18.7473 - 58.2516i) q^{77} +(-23.2780 + 32.0394i) q^{79} +(27.2666 + 83.9181i) q^{81} +(-21.4857 + 135.655i) q^{83} +(-106.286 + 90.9451i) q^{85} +(31.1867 + 31.1867i) q^{87} -128.868i q^{89} +(-15.3578 + 47.2664i) q^{91} +(0.719803 - 4.54466i) q^{93} +(69.8928 - 42.9184i) q^{95} +(-16.2826 - 102.805i) q^{97} +(-40.2654 + 79.5740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.87775	−	3.68530i	−0.625918	−	1.22843i	−0.958428	−	0.285334i	$-0.907896\pi$
$3$	−1.87775	−	3.68530i	−0.625918	−	1.22843i	0.332510	−	0.943100i	$-0.392104\pi$
$4$		0			0
$5$	3.24376	−	3.80500i	0.648752	−	0.761000i
$5$	3.24376	−	3.80500i	0.648752	−	0.761000i
$6$		0			0
$7$	2.52559	−	4.95675i	0.360799	−	0.708107i	−0.637243	−	0.770663i	$-0.719925\pi$
$7$	2.52559	−	4.95675i	0.360799	−	0.708107i	0.998041	+	0.0625558i	$0.0199251\pi$
$8$		0			0
$9$	−4.76541	+	6.55902i	−0.529490	+	0.728781i
$10$		0			0
$11$	10.8597	−	1.75112i	0.987247	−	0.159193i
$11$	10.8597	−	1.75112i	0.987247	−	0.159193i
$12$		0			0
$13$	−8.82368	+	1.39753i	−0.678744	+	0.107503i	−0.486282	−	0.873802i	$-0.661647\pi$
$13$	−8.82368	+	1.39753i	−0.678744	+	0.107503i	−0.192462	+	0.981304i	$0.561647\pi$
$14$		0			0
$15$	−20.1135	−	4.80938i	−1.34090	−	0.320625i
$16$		0			0
$17$	−27.6325	−	4.37656i	−1.62544	−	0.257445i	−0.723826	−	0.689983i	$-0.757618\pi$
$17$	−27.6325	−	4.37656i	−1.62544	−	0.257445i	−0.901615	+	0.432539i	$0.857618\pi$
$18$		0			0
$19$	15.6008	+	5.06901i	0.821095	+	0.266790i	0.689290	−	0.724486i	$-0.257923\pi$
$19$	15.6008	+	5.06901i	0.821095	+	0.266790i	0.131805	+	0.991276i	$0.457923\pi$
$20$		0			0
$21$	−23.0096			−1.09569
$22$		0			0
$23$	−0.317508	+	0.317508i	−0.0138047	+	0.0138047i	−0.713975	−	0.700171i	$-0.753107\pi$
$23$	−0.317508	+	0.317508i	−0.0138047	+	0.0138047i	0.700171	+	0.713975i	$0.253107\pi$
$24$		0			0
$25$	−3.95603	−	24.6850i	−0.158241	−	0.987400i
$26$		0			0
$27$	−3.64643	−	0.577539i	−0.135053	−	0.0213903i
$28$		0			0
$29$	−10.1414	+	3.29515i	−0.349704	+	0.113626i	−0.478602	−	0.878032i	$-0.658856\pi$
$29$	−10.1414	+	3.29515i	−0.349704	+	0.113626i	0.128897	+	0.991658i	$0.458856\pi$
$30$		0			0
$31$	0.900009	+	0.653895i	0.0290326	+	0.0210934i	0.602207	−	0.798340i	$-0.294288\pi$
$31$	0.900009	+	0.653895i	0.0290326	+	0.0210934i	−0.573174	+	0.819433i	$0.694288\pi$
$32$		0			0
$33$	−26.8453	−	36.7332i	−0.813494	−	1.11313i
$34$		0			0
$35$	−10.6680	−	25.6884i	−0.304801	−	0.733954i
$36$		0			0
$37$	−12.9590	+	25.4335i	−0.350244	+	0.687392i	−0.997172	−	0.0751595i	$-0.976053\pi$
$37$	−12.9590	+	25.4335i	−0.350244	+	0.687392i	0.646928	+	0.762551i	$0.276053\pi$
$38$		0			0
$39$	21.7190	+	29.8937i	0.556898	+	0.766505i
$40$		0			0
$41$	−3.08786	+	9.50347i	−0.0753137	+	0.231792i	−0.981625	−	0.190818i	$-0.938886\pi$
$41$	−3.08786	+	9.50347i	−0.0753137	+	0.231792i	0.906312	+	0.422610i	$0.138886\pi$
$42$		0			0
$43$	27.9830	−	27.9830i	0.650768	−	0.650768i	−0.302410	−	0.953178i	$-0.597791\pi$
$43$	27.9830	−	27.9830i	0.650768	−	0.650768i	0.953178	+	0.302410i	$0.0977911\pi$
$44$		0			0
$45$	9.49923	+	39.4083i	0.211094	+	0.875740i
$46$		0			0
$47$	50.5139	−	25.7381i	1.07476	−	0.547620i	0.175256	−	0.984523i	$-0.443925\pi$
$47$	50.5139	−	25.7381i	1.07476	−	0.547620i	0.899509	+	0.436903i	$0.143925\pi$
$48$		0			0
$49$	10.6107	+	14.6044i	0.216545	+	0.298049i
$50$		0			0
$51$	35.7581	+	110.052i	0.701139	+	2.15789i
$52$		0			0
$53$	90.5466	−	14.3412i	1.70843	−	0.270588i	0.775681	−	0.631125i	$-0.217407\pi$
$53$	90.5466	−	14.3412i	1.70843	−	0.270588i	0.932745	+	0.360537i	$0.117407\pi$
$54$		0			0
$55$	28.5633	−	47.0015i	0.519333	−	0.854572i
$56$		0			0
$57$	−10.6137	−	67.0120i	−0.186204	−	1.17565i
$58$		0			0
$59$	2.39521	−	0.778250i	0.0405967	−	0.0131907i	−0.288648	−	0.957435i	$-0.593206\pi$
$59$	2.39521	−	0.778250i	0.0405967	−	0.0131907i	0.329245	+	0.944245i	$0.393206\pi$
$60$		0			0
$61$	−50.6854	+	36.8251i	−0.830908	+	0.603690i	−0.919816	−	0.392350i	$-0.871662\pi$
$61$	−50.6854	+	36.8251i	−0.830908	+	0.603690i	0.0889078	+	0.996040i	$0.471662\pi$
$62$		0			0
$63$	20.4760	+	40.1864i	0.325016	+	0.637879i
$64$		0			0
$65$	−23.3043	+	38.1073i	−0.358527	+	0.586267i
$66$		0			0
$67$	−59.4330	−	59.4330i	−0.887060	−	0.887060i	0.107179	−	0.994240i	$-0.465818\pi$
$67$	−59.4330	−	59.4330i	−0.887060	−	0.887060i	−0.994240	+	0.107179i	$0.965818\pi$
$68$		0			0
$69$	1.76631	+	0.573910i	0.0255987	+	0.00831754i
$70$		0			0
$71$	110.315	−	80.1487i	1.55374	−	1.12885i	0.612815	−	0.790226i	$-0.290037\pi$
$71$	110.315	−	80.1487i	1.55374	−	1.12885i	0.940920	−	0.338629i	$-0.109963\pi$
$72$		0			0
$73$	97.5018	+	49.6796i	1.33564	+	0.680543i	0.968358	−	0.249566i	$-0.0802880\pi$
$73$	97.5018	+	49.6796i	1.33564	+	0.680543i	0.367283	+	0.930109i	$0.380288\pi$
$74$		0			0
$75$	−83.5432	+	60.9316i	−1.11391	+	0.812421i
$76$		0			0
$77$	18.7473	−	58.2516i	0.243472	−	0.756514i
$78$		0			0
$79$	−23.2780	+	32.0394i	−0.294658	+	0.405562i	−0.930520	−	0.366240i	$-0.880645\pi$
$79$	−23.2780	+	32.0394i	−0.294658	+	0.405562i	0.635862	+	0.771803i	$0.280645\pi$
$80$		0			0
$81$	27.2666	+	83.9181i	0.336625	+	1.03603i
$82$		0			0
$83$	−21.4857	+	135.655i	−0.258863	+	1.63440i	0.425288	+	0.905058i	$0.360173\pi$
$83$	−21.4857	+	135.655i	−0.258863	+	1.63440i	−0.684151	+	0.729341i	$0.739827\pi$
$84$		0			0
$85$	−106.286	+	90.9451i	−1.25042	+	1.06994i
$86$		0			0
$87$	31.1867	+	31.1867i	0.358468	+	0.358468i
$88$		0			0
$89$		−	128.868i		−	1.44796i	−0.689823	−	0.723978i	$-0.742312\pi$
$89$		−	128.868i		−	1.44796i	0.689823	−	0.723978i	$-0.257688\pi$
$90$		0			0
$91$	−15.3578	+	47.2664i	−0.168767	+	0.519411i
$92$		0			0
$93$	0.719803	−	4.54466i	0.00773982	−	0.0488673i
$94$		0			0
$95$	69.8928	−	42.9184i	0.735714	−	0.451772i
$96$		0			0
$97$	−16.2826	−	102.805i	−0.167862	−	1.05984i	−0.917425	−	0.397908i	$-0.869736\pi$
$97$	−16.2826	−	102.805i	−0.167862	−	1.05984i	0.749563	−	0.661933i	$-0.230264\pi$
$98$		0			0
$99$	−40.2654	+	79.5740i	−0.406721	+	0.803778i
$100$		0			0
$101$	−47.2895	−	34.3578i	−0.468213	−	0.340176i	0.328532	−	0.944493i	$-0.393446\pi$
$101$	−47.2895	−	34.3578i	−0.468213	−	0.340176i	−0.796744	+	0.604317i	$0.793446\pi$
$102$		0			0
$103$	−13.9431	−	7.10435i	−0.135370	−	0.0689742i	0.384994	−	0.922919i	$-0.374204\pi$
$103$	−13.9431	−	7.10435i	−0.135370	−	0.0689742i	−0.520363	+	0.853945i	$0.674204\pi$
$104$		0			0
$105$	−74.6375	+	87.5513i	−0.710833	+	0.833822i
$106$		0			0
$107$	63.1421	−	32.1725i	0.590113	−	0.300677i	−0.133319	−	0.991073i	$-0.542564\pi$
$107$	63.1421	−	32.1725i	0.590113	−	0.300677i	0.723432	+	0.690396i	$0.242564\pi$
$108$		0			0
$109$		−	92.8038i		−	0.851411i	−0.904862	−	0.425706i	$-0.860026\pi$
$109$		−	92.8038i		−	0.851411i	0.904862	−	0.425706i	$-0.139974\pi$
$110$		0			0
$111$	118.064			1.06364
$112$		0			0
$113$	−12.0944	−	23.7367i	−0.107030	−	0.210059i	0.831279	−	0.555855i	$-0.187609\pi$
$113$	−12.0944	−	23.7367i	−0.107030	−	0.210059i	−0.938310	+	0.345796i	$0.887609\pi$
$114$		0			0
$115$	0.178197	+	2.23804i	0.00154954	+	0.0194612i
$116$		0			0
$117$	32.8820	−	64.5345i	0.281043	−	0.551577i
$118$		0			0
$119$	−91.4819	+	125.914i	−0.768755	+	1.05810i
$120$		0			0
$121$	114.867	−	38.0334i	0.949315	−	0.314326i
$122$		0			0
$123$	40.8214	−	6.46547i	0.331881	−	0.0525648i
$124$		0			0
$125$	−106.759	−	65.0196i	−0.854071	−	0.520157i
$126$		0			0
$127$	−4.11743	−	0.652137i	−0.0324207	−	0.00513494i	0.140203	−	0.990123i	$-0.455224\pi$
$127$	−4.11743	−	0.652137i	−0.0324207	−	0.00513494i	−0.172624	+	0.984988i	$0.555224\pi$
$128$		0			0
$129$	−155.671	−	50.5806i	−1.20675	−	0.392098i
$130$		0			0
$131$	191.601			1.46260			0.731300	−	0.682056i	$-0.238914\pi$
$131$	191.601			1.46260			0.731300	+	0.682056i	$0.238914\pi$
$132$		0			0
$133$	64.5270	−	64.5270i	0.485166	−	0.485166i
$134$		0			0
$135$	−14.0257	+	12.0013i	−0.103894	+	0.0888984i
$136$		0			0
$137$	171.415	+	27.1495i	1.25121	+	0.198172i	0.746656	−	0.665210i	$-0.231658\pi$
$137$	171.415	+	27.1495i	1.25121	+	0.198172i	0.504551	+	0.863382i	$0.331658\pi$
$138$		0			0
$139$	−204.129	+	66.3254i	−1.46855	+	0.477161i	−0.930670	−	0.365860i	$-0.880775\pi$
$139$	−204.129	+	66.3254i	−1.46855	+	0.477161i	−0.537881	+	0.843021i	$0.680775\pi$
$140$		0			0
$141$	−189.705	−	137.829i	−1.34543	−	0.977511i
$142$		0			0
$143$	−93.3754	+	30.6282i	−0.652975	+	0.214183i
$144$		0			0
$145$	−20.3583	+	49.2768i	−0.140402	+	0.339840i
$146$		0			0
$147$	33.8972	−	66.5271i	0.230593	−	0.452565i
$148$		0			0
$149$	127.852	+	175.973i	0.858066	+	1.18103i	0.982027	+	0.188740i	$0.0604402\pi$
$149$	127.852	+	175.973i	0.858066	+	1.18103i	−0.123961	+	0.992287i	$0.539560\pi$
$150$		0			0
$151$	69.2395	−	213.097i	0.458540	−	1.41124i	−0.408388	−	0.912808i	$-0.633909\pi$
$151$	69.2395	−	213.097i	0.458540	−	1.41124i	0.866928	−	0.498433i	$-0.166091\pi$
$152$		0			0
$153$	160.386	−	160.386i	1.04828	−	1.04828i
$154$		0			0
$155$	5.40749	−	1.30346i	0.0348870	−	0.00840939i
$156$		0			0
$157$	−33.3601	+	16.9978i	−0.212485	+	0.108266i	−0.556994	−	0.830517i	$-0.688045\pi$
$157$	−33.3601	+	16.9978i	−0.212485	+	0.108266i	0.344509	+	0.938783i	$0.388045\pi$
$158$		0			0
$159$	−222.876	−	306.762i	−1.40173	−	1.92932i
$160$		0			0
$161$	0.771913	+	2.37570i	0.00479449	+	0.0147559i
$162$		0			0
$163$	−123.119	+	19.5001i	−0.755329	+	0.119632i	−0.522211	−	0.852816i	$-0.674893\pi$
$163$	−123.119	+	19.5001i	−0.755329	+	0.119632i	−0.233118	+	0.972449i	$0.574893\pi$
$164$		0			0
$165$	−226.849	−	17.0072i	−1.37484	−	0.103074i
$166$		0			0
$167$	−25.5813	−	161.514i	−0.153182	−	0.967151i	−0.937801	−	0.347173i	$-0.887142\pi$
$167$	−25.5813	−	161.514i	−0.153182	−	0.967151i	0.784619	−	0.619978i	$-0.212858\pi$
$168$		0			0
$169$	−84.8244	+	27.5611i	−0.501919	+	0.163083i
$170$		0			0
$171$	−107.592	+	78.1701i	−0.629193	+	0.457135i
$172$		0			0
$173$	−74.8559	−	146.913i	−0.432693	−	0.849208i	−0.999675	−	0.0254781i	$-0.991889\pi$
$173$	−74.8559	−	146.913i	−0.432693	−	0.849208i	0.566982	−	0.823730i	$-0.308111\pi$
$174$		0			0
$175$	−132.349	−	42.7352i	−0.756279	−	0.244201i
$176$		0			0
$177$	−7.36569	−	7.36569i	−0.0416141	−	0.0416141i
$178$		0			0
$179$	298.726	+	97.0620i	1.66886	+	0.542246i	0.982700	−	0.185203i	$-0.0592944\pi$
$179$	298.726	+	97.0620i	1.66886	+	0.542246i	0.686161	+	0.727449i	$0.259294\pi$
$180$		0			0
$181$	−232.209	+	168.710i	−1.28292	+	0.932098i	−0.999637	−	0.0269379i	$-0.991424\pi$
$181$	−232.209	+	168.710i	−1.28292	+	0.932098i	−0.283285	+	0.959036i	$0.591424\pi$
$182$		0			0
$183$	230.886	+	117.642i	1.26167	+	0.642855i
$184$		0			0
$185$	54.7385	+	131.809i	0.295884	+	0.712482i
$186$		0			0
$187$	−307.745	+	0.859688i	−1.64570	+	0.00459726i
$188$		0			0
$189$	−12.0721	+	16.6158i	−0.0638736	+	0.0879145i
$190$		0			0
$191$	−31.0596	−	95.5917i	−0.162616	−	0.500480i	0.836237	−	0.548368i	$-0.184751\pi$
$191$	−31.0596	−	95.5917i	−0.162616	−	0.500480i	−0.998853	+	0.0478882i	$0.984751\pi$
$192$		0			0
$193$	−35.5821	+	224.657i	−0.184363	+	1.16402i	0.705809	+	0.708402i	$0.250584\pi$
$193$	−35.5821	+	224.657i	−0.184363	+	1.16402i	−0.890173	+	0.455623i	$0.849416\pi$
$194$		0			0
$195$	184.197	+	14.3271i	0.944599	+	0.0734721i
$196$		0			0
$197$	124.305	+	124.305i	0.630992	+	0.630992i	0.948317	−	0.317325i	$-0.102785\pi$
$197$	124.305	+	124.305i	0.630992	+	0.630992i	−0.317325	+	0.948317i	$0.602785\pi$
$198$		0			0
$199$			111.738i			0.561497i	0.959781	+	0.280749i	$0.0905827\pi$
$199$			111.738i			0.561497i	−0.959781	+	0.280749i	$0.909417\pi$
$200$		0			0
$201$	−107.428	+	330.629i	−0.534468	+	1.64492i
$202$		0			0
$203$	−9.27986	+	58.5907i	−0.0457136	+	0.288624i
$204$		0			0
$205$	26.1444	+	42.5763i	0.127534	+	0.207689i
$206$		0			0
$207$	−0.569487	−	3.59560i	−0.00275114	−	0.0173700i
$208$		0			0
$209$	178.297	+	27.7291i	0.853095	+	0.132675i
$210$		0			0
$211$	170.668	+	123.997i	0.808851	+	0.587665i	0.913497	−	0.406845i	$-0.133371\pi$
$211$	170.668	+	123.997i	0.808851	+	0.587665i	−0.104646	+	0.994510i	$0.533371\pi$
$212$		0			0
$213$	−502.517	−	256.045i	−2.35923	−	1.20209i
$214$		0			0
$215$	−15.7051	−	197.246i	−0.0730472	−	0.917422i
$216$		0			0
$217$	5.51425	−	2.80965i	0.0254113	−	0.0129477i
$218$		0			0
$219$		−	452.610i		−	2.06671i
$220$		0			0
$221$	249.937			1.13093
$222$		0			0
$223$	27.8065	+	54.5733i	0.124693	+	0.244723i	0.944911	−	0.327327i	$-0.106148\pi$
$223$	27.8065	+	54.5733i	0.124693	+	0.244723i	−0.820218	+	0.572051i	$0.806148\pi$
$224$		0			0
$225$	180.762	+	91.6865i	0.803385	+	0.407496i
$226$		0			0
$227$	−9.04279	+	17.7475i	−0.0398361	+	0.0781827i	−0.910067	−	0.414462i	$-0.863970\pi$
$227$	−9.04279	+	17.7475i	−0.0398361	+	0.0781827i	0.870231	+	0.492645i	$0.163970\pi$
$228$		0			0
$229$	−144.481	+	198.861i	−0.630921	+	0.868388i	−0.998091	−	0.0617661i	$-0.980327\pi$
$229$	−144.481	+	198.861i	−0.630921	+	0.868388i	0.367170	+	0.930154i	$0.380327\pi$
$230$		0			0
$231$	−249.877	+	40.2926i	−1.08172	+	0.174427i
$232$		0			0
$233$	184.602	−	29.2381i	0.792284	−	0.125485i	0.252841	−	0.967508i	$-0.418635\pi$
$233$	184.602	−	29.2381i	0.792284	−	0.125485i	0.539443	+	0.842022i	$0.318635\pi$
$234$		0			0
$235$	65.9215	−	275.694i	0.280517	−	1.17316i
$236$		0			0
$237$	161.785	+	25.6243i	0.682639	+	0.108119i
$238$		0			0
$239$	172.151	+	55.9353i	0.720298	+	0.234039i	0.646152	−	0.763209i	$-0.276377\pi$
$239$	172.151	+	55.9353i	0.720298	+	0.234039i	0.0741454	+	0.997247i	$0.476377\pi$
$240$		0			0
$241$	278.499			1.15560			0.577798	−	0.816180i	$-0.303912\pi$
$241$	278.499			1.15560			0.577798	+	0.816180i	$0.303912\pi$
$242$		0			0
$243$	234.568	−	234.568i	0.965301	−	0.965301i
$244$		0			0
$245$	89.9882	+	6.99940i	0.367299	+	0.0285690i
$246$		0			0
$247$	−144.741	−	22.9246i	−0.585994	−	0.0928123i
$248$		0			0
$249$	540.275	−	175.546i	2.16978	−	0.705003i
$250$		0			0
$251$	−95.3862	−	69.3021i	−0.380025	−	0.276104i	0.381331	−	0.924439i	$-0.375466\pi$
$251$	−95.3862	−	69.3021i	−0.380025	−	0.276104i	−0.761356	+	0.648335i	$0.775466\pi$
$252$		0			0
$253$	−2.89205	+	4.00404i	−0.0114310	+	0.0158263i
$254$		0			0
$255$	534.739	+	220.923i	2.09702	+	0.866366i
$256$		0			0
$257$	−96.8010	+	189.983i	−0.376658	+	0.739232i	−0.999055	−	0.0434692i	$-0.986159\pi$
$257$	−96.8010	+	189.983i	−0.376658	+	0.739232i	0.622397	+	0.782702i	$0.286159\pi$
$258$		0			0
$259$	93.3383	+	128.469i	0.360380	+	0.496020i
$260$		0			0
$261$	26.7151	−	82.2206i	0.102357	−	0.315022i
$262$		0			0
$263$	−222.145	+	222.145i	−0.844659	+	0.844659i	−0.989461	−	0.144802i	$-0.953745\pi$
$263$	−222.145	+	222.145i	−0.844659	+	0.844659i	0.144802	+	0.989461i	$0.453745\pi$
$264$		0			0
$265$	239.143	−	391.049i	0.902428	−	1.47566i
$266$		0			0
$267$	−474.917	+	241.982i	−1.77872	+	0.906301i
$268$		0			0
$269$	151.651	+	208.729i	0.563757	+	0.775945i	0.991798	−	0.127814i	$-0.0407962\pi$
$269$	151.651	+	208.729i	0.563757	+	0.775945i	−0.428041	+	0.903759i	$0.640796\pi$
$270$		0			0
$271$	−61.1957	−	188.341i	−0.225814	−	0.694985i	−0.998208	−	0.0598408i	$-0.980941\pi$
$271$	−61.1957	−	188.341i	−0.225814	−	0.694985i	0.772394	−	0.635144i	$-0.219059\pi$
$272$		0			0
$273$	203.029	−	32.1566i	0.743696	−	0.117790i
$274$		0			0
$275$	−86.1879	−	261.145i	−0.313411	−	0.949618i
$276$		0			0
$277$	82.5757	+	521.363i	0.298107	+	1.88218i	0.448857	+	0.893604i	$0.351831\pi$
$277$	82.5757	+	521.363i	0.298107	+	1.88218i	−0.150750	+	0.988572i	$0.548169\pi$
$278$		0			0
$279$	−8.57783	+	2.78711i	−0.0307449	+	0.00998963i
$280$		0			0
$281$	−44.9696	+	32.6723i	−0.160034	+	0.116272i	−0.664920	−	0.746914i	$-0.731534\pi$
$281$	−44.9696	+	32.6723i	−0.160034	+	0.116272i	0.504886	+	0.863186i	$0.331534\pi$
$282$		0			0
$283$	146.864	+	288.238i	0.518955	+	1.01851i	0.990609	+	0.136724i	$0.0436572\pi$
$283$	146.864	+	288.238i	0.518955	+	1.01851i	−0.471654	+	0.881784i	$0.656343\pi$
$284$		0			0
$285$	−289.409	−	176.986i	−1.01547	−	0.621003i
$286$		0			0
$287$	39.3076	+	39.3076i	0.136960	+	0.136960i
$288$		0			0
$289$	469.545	+	152.565i	1.62472	+	0.527905i
$290$		0			0
$291$	−348.291	+	253.048i	−1.19688	+	0.869581i
$292$		0			0
$293$	−164.116	−	83.6214i	−0.560124	−	0.285397i	0.150919	−	0.988546i	$-0.451777\pi$
$293$	−164.116	−	83.6214i	−0.560124	−	0.285397i	−0.711043	+	0.703149i	$0.751777\pi$
$294$		0			0
$295$	4.80824	−	11.6382i	0.0162991	−	0.0394516i
$296$		0			0
$297$	−40.6106	+	0.113446i	−0.136736	+	0.000381973i
$298$		0			0
$299$	2.35786	−	3.24531i	0.00788582	−	0.0108539i
$300$		0			0
$301$	−68.0313	−	209.379i	−0.226017	−	0.695610i
$302$		0			0
$303$	−37.8208	+	238.791i	−0.124821	+	0.788090i
$304$		0			0
$305$	−24.2919	+	312.310i	−0.0796454	+	1.02397i
$306$		0			0
$307$	164.082	+	164.082i	0.534470	+	0.534470i	0.921899	−	0.387429i	$-0.126637\pi$
$307$	164.082	+	164.082i	0.534470	+	0.534470i	−0.387429	+	0.921899i	$0.626637\pi$
$308$		0			0
$309$			64.7246i			0.209465i
$310$		0			0
$311$	−74.5979	+	229.589i	−0.239865	+	0.738228i	0.756574	+	0.653908i	$0.226872\pi$
$311$	−74.5979	+	229.589i	−0.239865	+	0.738228i	−0.996439	+	0.0843197i	$0.973128\pi$
$312$		0			0
$313$	−8.73869	+	55.1739i	−0.0279191	+	0.176274i	−0.997708	−	0.0676731i	$-0.978442\pi$
$313$	−8.73869	+	55.1739i	−0.0279191	+	0.176274i	0.969788	+	0.243948i	$0.0784425\pi$
$314$		0			0
$315$	219.328	+	52.4439i	0.696280	+	0.166489i
$316$		0			0
$317$	−85.6712	−	540.907i	−0.270256	−	1.70633i	−0.632760	−	0.774348i	$-0.718078\pi$
$317$	−85.6712	−	540.907i	−0.270256	−	1.70633i	0.362504	−	0.931982i	$-0.381922\pi$
$318$		0			0
$319$	−104.363	+	53.5433i	−0.327156	+	0.167847i
$320$		0			0
$321$	−237.131	−	172.285i	−0.738724	−	0.536715i
$322$		0			0
$323$	−408.904	−	208.347i	−1.26596	−	0.645037i
$324$		0			0
$325$	69.4049	+	212.284i	0.213553	+	0.653181i
$326$		0			0
$327$	−342.010	+	174.263i	−1.04590	+	0.532914i
$328$		0			0
$329$		−	315.389i		−	0.958629i
$330$		0			0
$331$	−25.0559			−0.0756975			−0.0378487	−	0.999283i	$-0.512051\pi$
$331$	−25.0559			−0.0756975			−0.0378487	+	0.999283i	$0.512051\pi$
$332$		0			0
$333$	−105.064	−	206.199i	−0.315507	−	0.619218i
$334$		0			0
$335$	−418.929	+	33.3561i	−1.25054	+	0.0995704i
$336$		0			0
$337$	−62.1436	+	121.964i	−0.184402	+	0.361910i	−0.964639	−	0.263574i	$-0.915099\pi$
$337$	−62.1436	+	121.964i	−0.184402	+	0.361910i	0.780237	+	0.625484i	$0.215099\pi$
$338$		0			0
$339$	−64.7664	+	89.1433i	−0.191051	+	0.262960i
$340$		0			0
$341$	10.9189	+	5.52509i	0.0320202	+	0.0162026i
$342$		0			0
$343$	368.424	−	58.3526i	1.07412	−	0.170124i
$344$		0			0
$345$	7.91323	−	4.85919i	0.0229369	−	0.0140846i
$346$		0			0
$347$	237.598	+	37.6318i	0.684719	+	0.108449i	0.489096	−	0.872230i	$-0.337327\pi$
$347$	237.598	+	37.6318i	0.684719	+	0.108449i	0.195624	+	0.980679i	$0.437327\pi$
$348$		0			0
$349$	−430.260	−	139.800i	−1.23284	−	0.400573i	−0.381095	−	0.924536i	$-0.624453\pi$
$349$	−430.260	−	139.800i	−1.23284	−	0.400573i	−0.851741	+	0.523963i	$0.824453\pi$
$350$		0			0
$351$	32.9821			0.0939661
$352$		0			0
$353$	76.2189	−	76.2189i	0.215918	−	0.215918i	−0.590858	−	0.806776i	$-0.701211\pi$
$353$	76.2189	−	76.2189i	0.215918	−	0.215918i	0.806776	+	0.590858i	$0.201211\pi$
$354$		0			0
$355$	52.8705	−	679.732i	0.148931	−	1.91474i
$356$		0			0
$357$	635.812	+	100.703i	1.78098	+	0.282080i
$358$		0			0
$359$	−248.655	+	80.7928i	−0.692631	+	0.225050i	−0.634117	−	0.773237i	$-0.718636\pi$
$359$	−248.655	+	80.7928i	−0.692631	+	0.225050i	−0.0585141	+	0.998287i	$0.518636\pi$
$360$		0			0
$361$	−74.3651	−	54.0294i	−0.205997	−	0.149666i
$362$		0			0
$363$	−355.857	−	351.903i	−0.980322	−	0.969428i
$364$		0			0
$365$	505.304	−	209.845i	1.38439	−	0.574919i
$366$		0			0
$367$	−38.7468	+	76.0448i	−0.105577	+	0.207207i	−0.937751	−	0.347308i	$-0.887096\pi$
$367$	−38.7468	+	76.0448i	−0.105577	+	0.207207i	0.832174	+	0.554514i	$0.187096\pi$
$368$		0			0
$369$	−47.6185	−	65.5413i	−0.129048	−	0.177619i
$370$		0			0
$371$	157.598	−	485.037i	0.424793	−	1.30738i
$372$		0			0
$373$	−478.171	+	478.171i	−1.28196	+	1.28196i	−0.342408	+	0.939551i	$0.611243\pi$
$373$	−478.171	+	478.171i	−1.28196	+	1.28196i	−0.939551	+	0.342408i	$0.888757\pi$
$374$		0			0
$375$	−39.1497	+	515.529i	−0.104399	+	1.37474i
$376$		0			0
$377$	84.8796	−	43.2483i	0.225145	−	0.114717i
$378$		0			0
$379$	−380.805	−	524.134i	−1.00476	−	1.38294i	−0.922357	−	0.386340i	$-0.873739\pi$
$379$	−380.805	−	524.134i	−1.00476	−	1.38294i	−0.0824071	−	0.996599i	$-0.526261\pi$
$380$		0			0
$381$	5.32820	+	16.3985i	0.0139848	+	0.0430407i
$382$		0			0
$383$	−181.455	+	28.7396i	−0.473772	+	0.0750381i	−0.388755	−	0.921341i	$-0.627095\pi$
$383$	−181.455	+	28.7396i	−0.473772	+	0.0750381i	−0.0850175	+	0.996379i	$0.527095\pi$
$384$		0			0
$385$	−160.835	−	260.288i	−0.417754	−	0.676072i
$386$		0			0
$387$	50.1908	+	316.892i	0.129692	+	0.818843i
$388$		0			0
$389$	175.343	−	56.9723i	0.450752	−	0.146458i	−0.0748387	−	0.997196i	$-0.523844\pi$
$389$	175.343	−	56.9723i	0.450752	−	0.146458i	0.525591	+	0.850737i	$0.323844\pi$
$390$		0			0
$391$	10.1631	−	7.38394i	0.0259926	−	0.0188848i
$392$		0			0
$393$	−359.779	−	706.105i	−0.915467	−	1.79671i
$394$		0			0
$395$	46.4017	+	192.501i	0.117473	+	0.487345i
$396$		0			0
$397$	−200.989	−	200.989i	−0.506268	−	0.506268i	0.407111	−	0.913379i	$-0.366536\pi$
$397$	−200.989	−	200.989i	−0.506268	−	0.506268i	−0.913379	+	0.407111i	$0.866536\pi$
$398$		0			0
$399$	−358.967	−	116.636i	−0.899668	−	0.292320i
$400$		0			0
$401$	468.980	−	340.734i	1.16953	−	0.849710i	0.178573	−	0.983927i	$-0.442852\pi$
$401$	468.980	−	340.734i	1.16953	−	0.849710i	0.990952	+	0.134217i	$0.0428519\pi$
$402$		0			0
$403$	−8.85523	−	4.51197i	−0.0219733	−	0.0111959i
$404$		0			0
$405$	407.754	+	168.461i	1.00680	+	0.415952i
$406$		0			0
$407$	−96.1941	+	298.893i	−0.236349	+	0.734382i
$408$		0			0
$409$	15.4076	−	21.2067i	0.0376714	−	0.0518502i	−0.789766	−	0.613408i	$-0.789798\pi$
$409$	15.4076	−	21.2067i	0.0376714	−	0.0518502i	0.827437	+	0.561558i	$0.189798\pi$
$410$		0			0
$411$	−221.822	−	682.697i	−0.539713	−	1.66106i
$412$		0			0
$413$	2.19172	−	13.8380i	0.00530683	−	0.0335060i
$414$		0			0
$415$	446.473	+	521.786i	1.07584	+	1.25731i
$416$		0			0
$417$	627.732	+	627.732i	1.50535	+	1.50535i
$418$		0			0
$419$		−	440.962i		−	1.05242i	−0.850356	−	0.526208i	$-0.823613\pi$
$419$		−	440.962i		−	1.05242i	0.850356	−	0.526208i	$-0.176387\pi$
$420$		0			0
$421$	102.669	−	315.981i	0.243868	−	0.750549i	−0.751952	−	0.659217i	$-0.770888\pi$
$421$	102.669	−	315.981i	0.243868	−	0.750549i	0.995821	−	0.0913316i	$-0.0291123\pi$
$422$		0			0
$423$	−71.9026	+	453.975i	−0.169982	+	1.07323i
$424$		0			0
$425$	1.27967	+	699.422i	0.00301099	+	1.64570i
$426$		0			0
$427$	54.5223	+	344.240i	0.127687	+	0.806183i
$428$		0			0
$429$	288.210	+	286.604i	0.671818	+	0.668075i
$430$		0			0
$431$	−581.221	−	422.282i	−1.34854	−	0.979772i	−0.999083	−	0.0428194i	$-0.986366\pi$
$431$	−581.221	−	422.282i	−1.34854	−	0.979772i	−0.349457	−	0.936952i	$-0.613634\pi$
$432$		0			0
$433$	200.916	+	102.372i	0.464010	+	0.236425i	0.670335	−	0.742059i	$-0.266150\pi$
$433$	200.916	+	102.372i	0.464010	+	0.236425i	−0.206325	+	0.978483i	$0.566150\pi$
$434$		0			0
$435$	219.828	−	17.5032i	0.505351	−	0.0402372i
$436$		0			0
$437$	−6.56283	+	3.34393i	−0.0150179	+	0.00765201i
$438$		0			0
$439$		−	782.369i		−	1.78216i	−0.453845	−	0.891081i	$-0.649948\pi$
$439$		−	782.369i		−	1.78216i	0.453845	−	0.891081i	$-0.350052\pi$
$440$		0			0
$441$	−146.355			−0.331870
$442$		0			0
$443$	159.764	+	313.555i	0.360642	+	0.707800i	0.998030	−	0.0627435i	$-0.0199850\pi$
$443$	159.764	+	313.555i	0.360642	+	0.707800i	−0.637388	+	0.770543i	$0.719985\pi$
$444$		0			0
$445$	−490.343	−	418.017i	−1.10189	−	0.939364i
$446$		0			0
$447$	408.439	−	801.606i	0.913734	−	1.79330i
$448$		0			0
$449$	−371.767	+	511.693i	−0.827988	+	1.13963i	0.160306	+	0.987067i	$0.448752\pi$
$449$	−371.767	+	511.693i	−0.827988	+	1.13963i	−0.988294	+	0.152561i	$0.951248\pi$
$450$		0			0
$451$	−16.8916	+	108.612i	−0.0374537	+	0.240825i
$452$		0			0
$453$	−915.343	+	144.976i	−2.02062	+	0.320035i
$454$		0			0
$455$	130.032	+	211.757i	0.285784	+	0.465400i
$456$		0			0
$457$	−302.823	−	47.9625i	−0.662632	−	0.104951i	−0.183946	−	0.982936i	$-0.558887\pi$
$457$	−302.823	−	47.9625i	−0.662632	−	0.104951i	−0.478687	+	0.877986i	$0.658887\pi$
$458$		0			0
$459$	98.2325	+	31.9177i	0.214014	+	0.0695374i
$460$		0			0
$461$	−144.086			−0.312552			−0.156276	−	0.987713i	$-0.549949\pi$
$461$	−144.086			−0.312552			−0.156276	+	0.987713i	$0.549949\pi$
$462$		0			0
$463$	158.018	−	158.018i	0.341291	−	0.341291i	−0.515562	−	0.856852i	$-0.672417\pi$
$463$	158.018	−	158.018i	0.341291	−	0.341291i	0.856852	+	0.515562i	$0.172417\pi$
$464$		0			0
$465$	−14.9576	−	17.4806i	−0.0321668	−	0.0375928i
$466$		0			0
$467$	35.2784	+	5.58755i	0.0755427	+	0.0119648i	0.194091	−	0.980983i	$-0.437824\pi$
$467$	35.2784	+	5.58755i	0.0755427	+	0.0119648i	−0.118549	+	0.992948i	$0.537824\pi$
$468$		0			0
$469$	−444.698	+	144.491i	−0.948184	+	0.308084i
$470$		0			0
$471$	125.284	+	91.0242i	0.265996	+	0.193257i
$472$		0			0
$473$	254.886	−	352.890i	0.538872	−	0.746067i
$474$		0			0
$475$	63.4112	−	405.159i	0.133497	−	0.852966i
$476$		0			0
$477$	−337.428	+	662.239i	−0.707395	+	1.38834i
$478$		0			0
$479$	−336.947	−	463.768i	−0.703438	−	0.968200i	−0.999913	−	0.0131593i	$-0.995811\pi$
$479$	−336.947	−	463.768i	−0.703438	−	0.968200i	0.296475	−	0.955041i	$-0.404189\pi$
$480$		0			0
$481$	78.8020	−	242.528i	0.163829	−	0.504215i
$482$		0			0
$483$	7.30572	−	7.30572i	0.0151257	−	0.0151257i
$484$		0			0
$485$	−443.988	−	271.518i	−0.915440	−	0.559831i
$486$		0			0
$487$	−341.752	+	174.131i	−0.701749	+	0.357559i	−0.768182	−	0.640232i	$-0.778838\pi$
$487$	−341.752	+	174.131i	−0.701749	+	0.357559i	0.0664324	+	0.997791i	$0.478838\pi$
$488$		0			0
$489$	303.050	+	417.113i	0.619734	+	0.852991i
$490$		0			0
$491$	139.926	+	430.648i	0.284981	+	0.877083i	0.986404	+	0.164337i	$0.0525485\pi$
$491$	139.926	+	430.648i	0.284981	+	0.877083i	−0.701423	+	0.712746i	$0.747451\pi$
$492$		0			0
$493$	294.654	−	46.6687i	0.597676	−	0.0946626i
$494$		0			0
$495$	172.168	+	411.329i	0.347814	+	0.830967i
$496$		0			0
$497$	−118.666	−	749.228i	−0.238765	−	1.50750i
$498$		0			0
$499$	833.197	−	270.722i	1.66973	−	0.542530i	0.686857	−	0.726792i	$-0.258990\pi$
$499$	833.197	−	270.722i	1.66973	−	0.542530i	0.982877	+	0.184263i	$0.0589897\pi$
$500$		0			0
$501$	−547.193	+	397.559i	−1.09220	+	0.793531i
$502$		0			0
$503$	209.126	+	410.432i	0.415757	+	0.815968i	0.999990	+	0.00438284i	$0.00139511\pi$
$503$	209.126	+	410.432i	0.415757	+	0.815968i	−0.584234	+	0.811585i	$0.698605\pi$
$504$		0			0
$505$	−284.127	+	68.4879i	−0.562628	+	0.135620i
$506$		0			0
$507$	260.850	+	260.850i	0.514498	+	0.514498i
$508$		0			0
$509$	20.1931	+	6.56113i	0.0396721	+	0.0128902i	0.328786	−	0.944405i	$-0.393361\pi$
$509$	20.1931	+	6.56113i	0.0396721	+	0.0128902i	−0.289114	+	0.957295i	$0.593361\pi$
$510$		0			0
$511$	492.499	−	357.822i	0.963795	−	0.700238i
$512$		0			0
$513$	−53.9597	−	27.4939i	−0.105185	−	0.0535943i
$514$		0			0
$515$	−72.2600	+	30.0085i	−0.140311	+	0.0582690i
$516$		0			0
$517$	503.497	−	367.965i	0.973881	−	0.711731i
$518$		0			0
$519$	−400.858	+	551.733i	−0.772365	+	1.06307i
$520$		0			0
$521$	318.668	+	980.759i	0.611646	+	1.88245i	0.442205	+	0.896914i	$0.354196\pi$
$521$	318.668	+	980.759i	0.611646	+	1.88245i	0.169442	+	0.985540i	$0.445804\pi$
$522$		0			0
$523$	−43.7964	+	276.520i	−0.0837407	+	0.528718i	0.909782	+	0.415086i	$0.136249\pi$
$523$	−43.7964	+	276.520i	−0.0837407	+	0.528718i	−0.993523	+	0.113632i	$0.963751\pi$
$524$		0			0
$525$	91.0266	+	567.991i	0.173384	+	1.08189i
$526$		0			0
$527$	−22.0077	−	22.0077i	−0.0417603	−	0.0417603i
$528$		0			0
$529$			528.798i			0.999619i
$530$		0			0
$531$	−6.30958	+	19.4189i	−0.0118825	+	0.0365704i
$532$		0			0
$533$	13.9649	−	88.1709i	0.0262006	−	0.165424i
$534$		0			0
$535$	82.4015	−	344.615i	0.154021	−	0.644141i
$536$		0			0
$537$	−203.232	−	1283.15i	−0.378458	−	2.38949i
$538$		0			0
$539$	140.803	+	140.019i	0.261231	+	0.259775i
$540$		0			0
$541$	−417.605	−	303.408i	−0.771913	−	0.560828i	0.130628	−	0.991431i	$-0.458301\pi$
$541$	−417.605	−	303.408i	−0.771913	−	0.560828i	−0.902541	+	0.430604i	$0.858301\pi$
$542$		0			0
$543$	1057.78	+	538.964i	1.94802	+	0.992568i
$544$		0			0
$545$	−353.119	−	301.033i	−0.647924	−	0.552355i
$546$		0			0
$547$	−176.799	+	90.0835i	−0.323216	+	0.164687i	−0.608068	−	0.793885i	$-0.708055\pi$
$547$	−176.799	+	90.0835i	−0.323216	+	0.164687i	0.284853	+	0.958571i	$0.408055\pi$
$548$		0			0
$549$		−	507.934i		−	0.925198i
$550$		0			0
$551$	−174.918			−0.317455
$552$		0			0
$553$	100.021	+	196.302i	0.180869	+	0.354976i
$554$		0			0
$555$	382.971	−	449.233i	0.690038	−	0.809429i
$556$		0			0
$557$	−401.407	+	787.805i	−0.720658	+	1.41437i	0.181687	+	0.983356i	$0.441844\pi$
$557$	−401.407	+	787.805i	−0.720658	+	1.41437i	−0.902345	+	0.431015i	$0.858156\pi$
$558$		0			0
$559$	−207.806	+	286.021i	−0.371746	+	0.511665i
$560$		0			0
$561$	581.038	+	1132.52i	1.03572	+	2.01875i
$562$		0			0
$563$	−390.052	+	61.7782i	−0.692811	+	0.109730i	−0.492903	−	0.870084i	$-0.664064\pi$
$563$	−390.052	+	61.7782i	−0.692811	+	0.109730i	−0.199908	+	0.979815i	$0.564064\pi$
$564$		0			0
$565$	−129.550	−	30.9768i	−0.229291	−	0.0548262i
$566$		0			0
$567$	484.825	+	76.7888i	0.855071	+	0.135430i
$568$		0			0
$569$	104.189	+	33.8529i	0.183108	+	0.0594955i	0.399136	−	0.916892i	$-0.369310\pi$
$569$	104.189	+	33.8529i	0.183108	+	0.0594955i	−0.216028	+	0.976387i	$0.569310\pi$
$570$		0			0
$571$	385.565			0.675245			0.337622	−	0.941282i	$-0.390377\pi$
$571$	385.565			0.675245			0.337622	+	0.941282i	$0.390377\pi$
$572$		0			0
$573$	−293.962	+	293.962i	−0.513022	+	0.513022i
$574$		0			0
$575$	9.09376	+	6.58161i	0.0158152	+	0.0114463i
$576$		0			0
$577$	390.122	+	61.7893i	0.676122	+	0.107087i	0.485047	−	0.874488i	$-0.338803\pi$
$577$	390.122	+	61.7893i	0.676122	+	0.107087i	0.191075	+	0.981575i	$0.438803\pi$
$578$		0			0
$579$	894.742	−	290.719i	1.54532	−	0.502106i
$580$		0			0
$581$	618.145	+	449.108i	1.06393	+	0.772992i
$582$		0			0
$583$	958.198	−	314.299i	1.64356	−	0.539107i
$584$		0			0
$585$	−138.893	−	334.451i	−0.237423	−	0.571710i
$586$		0			0
$587$	−457.106	+	897.122i	−0.778716	+	1.52832i	0.0688501	+	0.997627i	$0.478067\pi$
$587$	−457.106	+	897.122i	−0.778716	+	1.52832i	−0.847566	+	0.530690i	$0.821933\pi$
$588$		0			0
$589$	10.7263	+	14.7634i	0.0182110	+	0.0250653i
$590$		0			0
$591$	224.688	−	691.518i	0.380182	−	1.17008i
$592$		0			0
$593$	246.661	−	246.661i	0.415955	−	0.415955i	−0.467852	−	0.883807i	$-0.654972\pi$
$593$	246.661	−	246.661i	0.415955	−	0.415955i	0.883807	+	0.467852i	$0.154972\pi$
$594$		0			0
$595$	182.357	+	756.523i	0.306483	+	1.27147i
$596$		0			0
$597$	411.788	−	209.816i	0.689762	−	0.351451i
$598$		0			0
$599$	−109.173	−	150.263i	−0.182258	−	0.250857i	0.708106	−	0.706106i	$-0.249550\pi$
$599$	−109.173	−	150.263i	−0.182258	−	0.250857i	−0.890364	+	0.455250i	$0.849550\pi$
$600$		0			0
$601$	−97.6385	−	300.500i	−0.162460	−	0.500001i	0.836380	−	0.548150i	$-0.184668\pi$
$601$	−97.6385	−	300.500i	−0.162460	−	0.500001i	−0.998840	+	0.0481492i	$0.984668\pi$
$602$		0			0
$603$	673.046	−	106.600i	1.11616	−	0.176783i
$604$		0			0
$605$	227.884	−	560.441i	0.376669	−	0.926348i
$606$		0			0
$607$	67.7731	+	427.903i	0.111653	+	0.704947i	0.978480	+	0.206339i	$0.0661551\pi$
$607$	67.7731	+	427.903i	0.111653	+	0.704947i	−0.866828	+	0.498608i	$0.833845\pi$
$608$		0			0
$609$	233.350	−	75.8199i	0.383169	−	0.124499i
$610$		0			0
$611$	−409.749	+	297.700i	−0.670620	+	0.487234i
$612$		0			0
$613$	92.7555	+	182.043i	0.151314	+	0.296970i	0.954204	−	0.299157i	$-0.0967054\pi$
$613$	92.7555	+	182.043i	0.151314	+	0.296970i	−0.802890	+	0.596127i	$0.796705\pi$
$614$		0			0
$615$	107.814	−	176.298i	0.175307	−	0.286663i
$616$		0			0
$617$	−628.117	−	628.117i	−1.01802	−	1.01802i	−0.999835	−	0.0181832i	$-0.994212\pi$
$617$	−628.117	−	628.117i	−1.01802	−	1.01802i	−0.0181832	−	0.999835i	$-0.505788\pi$
$618$		0			0
$619$	856.567	+	278.315i	1.38379	+	0.449621i	0.903914	−	0.427714i	$-0.140681\pi$
$619$	856.567	+	278.315i	1.38379	+	0.449621i	0.479877	+	0.877336i	$0.340681\pi$
$620$		0			0
$621$	1.34114	−	0.974399i	0.00215965	−	0.00156908i
$622$		0			0
$623$	−638.767	−	325.468i	−1.02531	−	0.522420i
$624$		0			0
$625$	−593.700	+	195.309i	−0.949919	+	0.312495i
$626$		0			0
$627$	−232.608	−	709.146i	−0.370985	−	1.13101i
$628$		0			0
$629$	469.401	−	646.075i	0.746265	−	1.02715i
$630$		0			0
$631$	95.6576	+	294.404i	0.151597	+	0.466567i	0.997800	−	0.0662931i	$-0.0211172\pi$
$631$	95.6576	+	294.404i	0.151597	+	0.466567i	−0.846203	+	0.532860i	$0.821117\pi$
$632$		0			0
$633$	136.495	−	861.798i	0.215633	−	1.36145i
$634$		0			0
$635$	−15.8373	+	13.5514i	−0.0249407	+	0.0213409i
$636$		0			0
$637$	−114.036	−	114.036i	−0.179020	−	0.179020i
$638$		0			0
$639$			1105.50i			1.73005i
$640$		0			0
$641$	0.345660	−	1.06383i	0.000539251	−	0.00165964i	−0.950787	−	0.309847i	$-0.899722\pi$
$641$	0.345660	−	1.06383i	0.000539251	−	0.00165964i	0.951326	+	0.308187i	$0.0997223\pi$
$642$		0			0
$643$	−42.4197	+	267.827i	−0.0659715	+	0.416528i	0.932496	+	0.361181i	$0.117626\pi$
$643$	−42.4197	+	267.827i	−0.0659715	+	0.416528i	−0.998467	+	0.0553467i	$0.982374\pi$
$644$		0			0
$645$	−697.419	+	428.257i	−1.08127	+	0.663965i
$646$		0			0
$647$	−161.868	−	1021.99i	−0.250183	−	1.57959i	−0.718178	−	0.695859i	$-0.755024\pi$
$647$	−161.868	−	1021.99i	−0.250183	−	1.57959i	0.467996	−	0.883731i	$-0.344976\pi$
$648$		0			0
$649$	24.6485	−	12.6459i	0.0379792	−	0.0194852i
$650$		0			0
$651$	−20.7088	−	15.0458i	−0.0318108	−	0.0231119i
$652$		0			0
$653$	−131.438	−	66.9709i	−0.201283	−	0.102559i	0.350444	−	0.936584i	$-0.386031\pi$
$653$	−131.438	−	66.9709i	−0.201283	−	0.102559i	−0.551727	+	0.834025i	$0.686031\pi$
$654$		0			0
$655$	621.506	−	729.040i	0.948865	−	1.11304i
$656$		0			0
$657$	−790.486	+	402.773i	−1.20318	+	0.613048i
$658$		0			0
$659$			1208.66i			1.83408i	0.398795	+	0.917040i	$0.369428\pi$
$659$			1208.66i			1.83408i	−0.398795	+	0.917040i	$0.630572\pi$
$660$		0			0
$661$	−548.913			−0.830429			−0.415214	−	0.909724i	$-0.636293\pi$
$661$	−548.913			−0.830429			−0.415214	+	0.909724i	$0.636293\pi$
$662$		0			0
$663$	−469.320	−	921.091i	−0.707873	−	1.38928i
$664$		0			0
$665$	−36.2150	−	454.836i	−0.0544587	−	0.683963i
$666$		0			0
$667$	2.17375	−	4.26622i	0.00325899	−	0.00639613i
$668$		0			0
$669$	148.905	−	204.950i	0.222579	−	0.306354i
$670$		0			0
$671$	−485.944	+	488.667i	−0.724209	+	0.728266i
$672$		0			0
$673$	−304.761	+	48.2694i	−0.452839	+	0.0717227i	−0.378688	−	0.925524i	$-0.623625\pi$
$673$	−304.761	+	48.2694i	−0.452839	+	0.0717227i	−0.0741511	+	0.997247i	$0.523625\pi$
$674$		0			0
$675$	0.168868	+	92.2970i	0.000250175	+	0.136736i
$676$		0			0
$677$	−163.784	−	25.9409i	−0.241927	−	0.0383174i	0.0342936	−	0.999412i	$-0.489082\pi$
$677$	−163.784	−	25.9409i	−0.241927	−	0.0383174i	−0.276220	+	0.961094i	$0.589082\pi$
$678$		0			0
$679$	−550.700	−	178.933i	−0.811046	−	0.263525i
$680$		0			0
$681$	82.3849			0.120976
$682$		0			0
$683$	−184.023	+	184.023i	−0.269434	+	0.269434i	−0.828872	−	0.559438i	$-0.811017\pi$
$683$	−184.023	+	184.023i	−0.269434	+	0.269434i	0.559438	+	0.828872i	$0.311017\pi$
$684$		0			0
$685$	659.335	−	564.169i	0.962532	−	0.823604i
$686$		0			0
$687$	1004.16	+	159.044i	1.46166	+	0.231504i
$688$		0			0
$689$	−778.912	+	253.084i	−1.13050	+	0.367320i
$690$		0			0
$691$	414.275	+	300.988i	0.599529	+	0.435584i	0.845712	−	0.533640i	$-0.179176\pi$
$691$	414.275	+	300.988i	0.599529	+	0.435584i	−0.246182	+	0.969224i	$0.579176\pi$
$692$		0			0
$693$	292.735	+	400.557i	0.422417	+	0.578004i
$694$		0			0
$695$	−409.776	+	991.853i	−0.589606	+	1.42713i
$696$		0			0
$697$	126.918	−	249.090i	0.182092	−	0.357375i
$698$		0			0
$699$	−454.389	−	625.412i	−0.650055	−	0.894724i
$700$		0			0
$701$	−202.798	+	624.148i	−0.289298	+	0.890368i	0.695779	+	0.718256i	$0.255059\pi$
$701$	−202.798	+	624.148i	−0.289298	+	0.890368i	−0.985077	+	0.172112i	$0.944941\pi$
$702$		0			0
$703$	−331.093	+	331.093i	−0.470972	+	0.470972i
$704$		0			0
$705$	−1139.80	+	274.745i	−1.61674	+	0.389709i
$706$		0			0
$707$	−289.737	+	147.628i	−0.409812	+	0.208810i
$708$		0			0
$709$	−182.881	−	251.714i	−0.257942	−	0.355027i	0.660331	−	0.750975i	$-0.270416\pi$
$709$	−182.881	−	251.714i	−0.257942	−	0.355027i	−0.918273	+	0.395948i	$0.870416\pi$
$710$		0			0
$711$	−99.2182	−	305.362i	−0.139547	−	0.429483i
$712$		0			0
$713$	−0.493377	+	0.0781432i	−0.000691973	+	0.000109598i
$714$		0			0
$715$	−186.347	+	454.644i	−0.260626	+	0.635866i
$716$		0			0
$717$	−117.119	−	739.461i	−0.163346	−	1.03133i
$718$		0			0
$719$	694.526	−	225.665i	0.965960	−	0.313860i	0.216776	−	0.976221i	$-0.430446\pi$
$719$	694.526	−	225.665i	0.965960	−	0.313860i	0.749184	+	0.662362i	$0.230446\pi$
$720$		0			0
$721$	−70.4290	+	51.1696i	−0.0976823	+	0.0709704i
$722$		0			0
$723$	−522.952	−	1026.35i	−0.723308	−	1.41957i
$724$		0			0
$725$	121.461	+	237.306i	0.167532	+	0.327318i
$726$		0			0
$727$	−449.679	−	449.679i	−0.618540	−	0.618540i	0.326617	−	0.945157i	$-0.394091\pi$
$727$	−449.679	−	449.679i	−0.618540	−	0.618540i	−0.945157	+	0.326617i	$0.894091\pi$
$728$		0			0
$729$	−549.653	−	178.593i	−0.753982	−	0.244984i
$730$		0			0
$731$	−895.711	+	650.772i	−1.22532	+	0.890249i
$732$		0			0
$733$	1020.27	+	519.854i	1.39191	+	0.709215i	0.979436	−	0.201754i	$-0.0646640\pi$
$733$	1020.27	+	519.854i	1.39191	+	0.709215i	0.412476	+	0.910968i	$0.364664\pi$
$734$		0			0
$735$	−143.181	−	344.777i	−0.194804	−	0.469084i
$736$		0			0
$737$	−749.501	−	541.352i	−1.01696	−	0.734534i
$738$		0			0
$739$	−650.090	+	894.772i	−0.879689	+	1.21079i	0.0968179	+	0.995302i	$0.469134\pi$
$739$	−650.090	+	894.772i	−0.879689	+	1.21079i	−0.976507	+	0.215486i	$0.930866\pi$
$740$		0			0
$741$	187.303	+	576.459i	0.252770	+	0.777948i
$742$		0			0
$743$	45.6572	−	288.268i	0.0614498	−	0.387979i	−0.937726	−	0.347377i	$-0.887072\pi$
$743$	45.6572	−	288.268i	0.0614498	−	0.387979i	0.999175	−	0.0406019i	$-0.0129275\pi$
$744$		0			0
$745$	1084.30	+	84.3381i	1.45543	+	0.113205i
$746$		0			0
$747$	−787.377	−	787.377i	−1.05405	−	1.05405i
$748$		0			0
$749$		−	394.234i		−	0.526347i
$750$		0			0
$751$	46.4459	−	142.946i	0.0618454	−	0.190340i	−0.915360	−	0.402636i	$-0.868094\pi$
$751$	46.4459	−	142.946i	0.0618454	−	0.190340i	0.977205	+	0.212296i	$0.0680940\pi$
$752$		0			0
$753$	−76.2873	+	481.659i	−0.101311	+	0.639653i
$754$		0			0
$755$	−586.239	−	954.693i	−0.776475	−	1.26449i
$756$		0			0
$757$	157.621	+	995.182i	0.208218	+	1.31464i	0.841306	+	0.540559i	$0.181787\pi$
$757$	157.621	+	995.182i	0.208218	+	1.31464i	−0.633087	+	0.774080i	$0.718213\pi$
$758$		0			0
$759$	20.1867	+	3.13947i	0.0265964	+	0.00413633i
$760$		0			0
$761$	−380.309	−	276.311i	−0.499750	−	0.363089i	0.309172	−	0.951006i	$-0.399948\pi$
$761$	−380.309	−	276.311i	−0.499750	−	0.363089i	−0.808921	+	0.587917i	$0.799948\pi$
$762$		0			0
$763$	−460.006	−	234.385i	−0.602891	−	0.307188i
$764$		0			0
$765$	−90.0148	−	1130.52i	−0.117666	−	1.47781i
$766$		0			0
$767$	−20.0469	+	10.2144i	−0.0261368	+	0.0133173i
$768$		0			0
$769$			825.962i			1.07407i	0.843559	+	0.537036i	$0.180456\pi$
$769$			825.962i			1.07407i	−0.843559	+	0.537036i	$0.819544\pi$
$770$		0			0
$771$	881.912			1.14385
$772$		0			0
$773$	−447.129	−	877.540i	−0.578433	−	1.13524i	−0.976021	−	0.217675i	$-0.930153\pi$
$773$	−447.129	−	877.540i	−0.578433	−	1.13524i	0.397588	−	0.917564i	$-0.369847\pi$
$774$		0			0
$775$	12.5809	−	24.8036i	0.0162335	−	0.0320046i
$776$		0			0
$777$	298.181	−	585.213i	0.383759	−	0.753170i
$778$		0			0
$779$	−96.3463	+	132.609i	−0.123679	+	0.170230i
$780$		0			0
$781$	1057.64	−	1063.57i	1.35422	−	1.36180i
$782$		0			0
$783$	38.8831	−	6.15848i	0.0496592	−	0.00786524i
$784$		0			0
$785$	−43.5355	+	182.072i	−0.0554592	+	0.231939i
$786$		0			0
$787$	1165.82	+	184.647i	1.48134	+	0.234622i	0.844160	−	0.536091i	$-0.180100\pi$
$787$	1165.82	+	184.647i	1.48134	+	0.234622i	0.637183	+	0.770713i	$0.280100\pi$
$788$		0			0
$789$	1235.81	+	401.538i	1.56629	+	0.508920i
$790$		0			0
$791$	−148.202			−0.187361
$792$		0			0
$793$	395.767	−	395.767i	0.499076	−	0.499076i
$794$		0			0
$795$	−1890.19	−	147.021i	−2.37759	−	0.184932i
$796$		0			0
$797$	396.600	+	62.8153i	0.497616	+	0.0788147i	0.400198	−	0.916429i	$-0.368941\pi$
$797$	396.600	+	62.8153i	0.497616	+	0.0788147i	0.0974186	+	0.995243i	$0.468941\pi$
$798$		0			0
$799$	−1508.47	+	490.132i	−1.88795	+	0.613431i
$800$		0			0
$801$	845.249	+	614.109i	1.05524	+	0.766678i
$802$		0			0
$803$	1145.84	+	368.770i	1.42695	+	0.459240i
$804$		0			0
$805$	11.5434	+	4.76908i	0.0143397	+	0.00592433i
$806$		0			0
$807$	484.467	−	950.820i	0.600331	−	1.17822i
$808$		0			0
$809$	−210.983	−	290.393i	−0.260794	−	0.358953i	0.658461	−	0.752615i	$-0.271208\pi$
$809$	−210.983	−	290.393i	−0.260794	−	0.358953i	−0.919255	+	0.393662i	$0.871208\pi$
$810$		0			0
$811$	40.8440	−	125.705i	0.0503625	−	0.155000i	−0.922712	−	0.385489i	$-0.874033\pi$
$811$	40.8440	−	125.705i	0.0503625	−	0.155000i	0.973075	+	0.230489i	$0.0740327\pi$
$812$		0			0
$813$	−579.182	+	579.182i	−0.712401	+	0.712401i
$814$		0			0
$815$	−325.169	+	531.720i	−0.398981	+	0.652417i
$816$		0			0
$817$	578.404	−	294.712i	0.707961	−	0.360724i
$818$		0			0
$819$	−236.835	−	325.976i	−0.289176	−	0.398017i
$820$		0			0
$821$	−319.821	−	984.308i	−0.389551	−	1.19891i	−0.933125	−	0.359553i	$-0.882929\pi$
$821$	−319.821	−	984.308i	−0.389551	−	1.19891i	0.543574	−	0.839361i	$-0.317071\pi$
$822$		0			0
$823$	1014.87	−	160.739i	1.23313	−	0.195309i	0.494356	−	0.869259i	$-0.335404\pi$
$823$	1014.87	−	160.739i	1.23313	−	0.195309i	0.738777	+	0.673950i	$0.235404\pi$
$824$		0			0
$825$	−800.558	+	807.994i	−0.970373	+	0.979387i
$826$		0			0
$827$	242.787	+	1532.90i	0.293576	+	1.85357i	0.488259	+	0.872699i	$0.337632\pi$
$827$	242.787	+	1532.90i	0.293576	+	1.85357i	−0.194683	+	0.980866i	$0.562368\pi$
$828$		0			0
$829$	−646.186	+	209.959i	−0.779476	+	0.253267i	−0.671617	−	0.740899i	$-0.734400\pi$
$829$	−646.186	+	209.959i	−0.779476	+	0.253267i	−0.107860	+	0.994166i	$0.534400\pi$
$830$		0			0
$831$	1766.32	−	1283.31i	2.12554	−	1.54429i
$832$		0			0
$833$	−229.283	−	449.994i	−0.275250	−	0.540209i
$834$		0			0
$835$	−697.541	−	426.577i	−0.835379	−	0.510870i
$836$		0			0
$837$	−2.90418	−	2.90418i	−0.00346974	−	0.00346974i
$838$		0			0
$839$	−590.414	−	191.837i	−0.703711	−	0.228650i	−0.0647644	−	0.997901i	$-0.520630\pi$
$839$	−590.414	−	191.837i	−0.703711	−	0.228650i	−0.638947	+	0.769251i	$0.720630\pi$
$840$		0			0
$841$	−588.393	+	427.492i	−0.699635	+	0.508314i
$842$		0			0
$843$	204.849	+	104.376i	0.243000	+	0.123815i
$844$		0			0
$845$	−170.280	+	412.158i	−0.201515	+	0.487761i
$846$		0			0
$847$	101.585	−	665.425i	0.119935	−	0.785625i
$848$		0			0
$849$	786.467	−	1082.48i	0.926345	−	1.27500i
$850$		0			0
$851$	−3.96074	−	12.1899i	−0.00465422	−	0.0143242i
$852$		0			0
$853$	186.393	−	1176.84i	0.218514	−	1.37964i	−0.597619	−	0.801781i	$-0.703886\pi$
$853$	186.393	−	1176.84i	0.218514	−	1.37964i	0.816133	−	0.577864i	$-0.196114\pi$
$854$		0			0
$855$	−51.5653	+	662.952i	−0.0603103	+	0.775383i
$856$		0			0
$857$	763.933	+	763.933i	0.891404	+	0.891404i	0.994655	−	0.103252i	$-0.0329247\pi$
$857$	763.933	+	763.933i	0.891404	+	0.891404i	−0.103252	+	0.994655i	$0.532925\pi$
$858$		0			0
$859$			36.1166i			0.0420449i	0.999779	+	0.0210225i	$0.00669215\pi$
$859$			36.1166i			0.0420449i	−0.999779	+	0.0210225i	$0.993308\pi$
$860$		0			0
$861$	71.0504	−	218.671i	0.0825207	−	0.253973i
$862$		0			0
$863$	−7.74352	+	48.8907i	−0.00897279	+	0.0566520i	−0.991768	−	0.128044i	$-0.959130\pi$
$863$	−7.74352	+	48.8907i	−0.00897279	+	0.0566520i	0.982796	+	0.184696i	$0.0591301\pi$
$864$		0			0
$865$	−801.819	−	191.724i	−0.926958	−	0.221646i
$866$		0			0
$867$	−319.445	−	2016.89i	−0.368448	−	2.32629i
$868$		0			0
$869$	−196.688	+	388.702i	−0.226338	+	0.447298i
$870$		0			0
$871$	607.478	+	441.358i	0.697449	+	0.506726i
$872$		0			0
$873$	751.891	+	383.108i	0.861273	+	0.438841i
$874$		0			0
$875$	−591.915	+	364.964i	−0.676474	+	0.417102i
$876$		0			0
$877$	−617.514	+	314.639i	−0.704121	+	0.358768i	−0.769108	−	0.639118i	$-0.779299\pi$
$877$	−617.514	+	314.639i	−0.704121	+	0.358768i	0.0649870	+	0.997886i	$0.479299\pi$
$878$		0			0
$879$			761.838i			0.866710i
$880$		0			0
$881$	1360.50			1.54427			0.772135	−	0.635458i	$-0.219189\pi$
$881$	1360.50			1.54427			0.772135	+	0.635458i	$0.219189\pi$
$882$		0			0
$883$	711.863	+	1397.11i	0.806187	+	1.58223i	0.813006	+	0.582255i	$0.197829\pi$
$883$	711.863	+	1397.11i	0.806187	+	1.58223i	−0.00681890	+	0.999977i	$0.502171\pi$
$884$		0			0
$885$	−51.9190	+	4.13391i	−0.0586655	+	0.00467108i
$886$		0			0
$887$	312.581	−	613.475i	0.352403	−	0.691629i	−0.644959	−	0.764217i	$-0.723126\pi$
$887$	312.581	−	613.475i	0.352403	−	0.691629i	0.997362	+	0.0725877i	$0.0231257\pi$
$888$		0			0
$889$	−13.6314	+	18.7620i	−0.0153334	+	0.0211047i
$890$		0			0
$891$	443.059	+	863.580i	0.497260	+	0.969225i
$892$		0			0
$893$	918.524	−	145.480i	1.02858	−	0.162911i
$894$		0			0
$895$	1338.32	−	821.807i	1.49533	−	0.918220i
$896$		0			0
$897$	−16.3874	−	2.59552i	−0.0182692	−	0.00289355i
$898$		0			0
$899$	−11.2821	−	3.66576i	−0.0125496	−	0.00407760i
$900$		0			0
$901$	−2564.79			−2.84661
$902$		0			0
$903$	−643.877	+	643.877i	−0.713043	+	0.713043i
$904$		0			0
$905$	−111.290	+	1430.81i	−0.122973	+	1.58100i
$906$		0			0
$907$	−880.279	−	139.422i	−0.970539	−	0.153718i	−0.349018	−	0.937116i	$-0.613485\pi$
$907$	−880.279	−	139.422i	−0.970539	−	0.153718i	−0.621521	+	0.783398i	$0.713485\pi$
$908$		0			0
$909$	450.707	−	146.444i	0.495828	−	0.161104i
$910$		0			0
$911$	1003.91	+	729.382i	1.10198	+	0.800639i	0.981383	−	0.192062i	$-0.0615175\pi$
$911$	1003.91	+	729.382i	1.10198	+	0.800639i	0.120602	+	0.992701i	$0.461517\pi$
$912$		0			0
$913$	4.22043	+	1510.80i	0.00462260	+	1.65477i
$914$		0			0
$915$	1196.57	−	496.918i	1.30773	−	0.543080i
$916$		0			0
$917$	483.905	−	949.716i	0.527704	−	1.03568i
$918$		0			0
$919$	−230.134	−	316.753i	−0.250418	−	0.344671i	0.665239	−	0.746630i	$-0.268329\pi$
$919$	−230.134	−	316.753i	−0.250418	−	0.344671i	−0.915658	+	0.401959i	$0.868329\pi$
$920$		0			0
$921$	296.586	−	912.799i	0.322026	−	0.991096i
$922$		0			0
$923$	−861.375	+	861.375i	−0.933234	+	0.933234i
$924$		0			0
$925$	679.092	+	219.278i	0.734154	+	0.237057i
$926$		0			0
$927$	113.042	−	57.5978i	0.121944	−	0.0621335i
$928$		0			0
$929$	−340.328	−	468.421i	−0.366338	−	0.504221i	0.585563	−	0.810627i	$-0.300873\pi$
$929$	−340.328	−	468.421i	−0.366338	−	0.504221i	−0.951901	+	0.306406i	$0.900873\pi$
$930$		0			0
$931$	91.5057	+	281.626i	0.0982876	+	0.302498i
$932$		0			0
$933$	986.180	−	156.196i	1.05700	−	0.167412i
$934$		0			0
$935$	−994.980	+	1173.76i	−1.06415	+	1.25536i
$936$		0			0
$937$	102.959	+	650.056i	0.109881	+	0.693763i	0.979712	+	0.200412i	$0.0642281\pi$
$937$	102.959	+	650.056i	0.109881	+	0.693763i	−0.869830	+	0.493351i	$0.835772\pi$
$938$		0			0
$939$	219.742	−	71.3984i	0.234017	−	0.0760366i
$940$		0			0
$941$	−399.074	+	289.944i	−0.424096	+	0.308124i	−0.779284	−	0.626671i	$-0.784417\pi$
$941$	−399.074	+	289.944i	−0.424096	+	0.308124i	0.355188	+	0.934795i	$0.384417\pi$
$942$		0			0
$943$	−2.03700	−	3.99785i	−0.00216013	−	0.00423950i
$944$		0			0
$945$	24.0642	+	99.8322i	0.0254648	+	0.105643i
$946$		0			0
$947$	−177.734	−	177.734i	−0.187681	−	0.187681i	0.607012	−	0.794693i	$-0.292368\pi$
$947$	−177.734	−	177.734i	−0.187681	−	0.187681i	−0.794693	+	0.607012i	$0.792368\pi$
$948$		0			0
$949$	−929.753	−	302.095i	−0.979719	−	0.318330i
$950$		0			0
$951$	−1832.53	+	1331.41i	−1.92695	+	1.40001i
$952$		0			0
$953$	−497.529	−	253.504i	−0.522067	−	0.266006i	0.173038	−	0.984915i	$-0.444642\pi$
$953$	−497.529	−	253.504i	−0.522067	−	0.266006i	−0.695104	+	0.718909i	$0.744642\pi$
$954$		0			0
$955$	−464.476	−	191.895i	−0.486363	−	0.200937i
$956$		0			0
$957$	393.291	+	284.067i	0.410962	+	0.296831i
$958$		0			0
$959$	567.499	−	781.095i	0.591761	−	0.814489i
$960$		0			0
$961$	−296.583	−	912.788i	−0.308619	−	0.949832i
$962$		0			0
$963$	−89.8777	+	567.465i	−0.0933309	+	0.589268i
$964$		0			0
$965$	739.399	+	864.123i	0.766217	+	0.895464i
$966$		0			0
$967$	−372.624	−	372.624i	−0.385341	−	0.385341i	0.487681	−	0.873022i	$-0.337843\pi$
$967$	−372.624	−	372.624i	−0.385341	−	0.385341i	−0.873022	+	0.487681i	$0.837843\pi$
$968$		0			0
$969$			1898.16i			1.95888i
$970$		0			0
$971$	−36.7825	+	113.205i	−0.0378811	+	0.116586i	−0.968209	−	0.250143i	$-0.919522\pi$
$971$	−36.7825	+	113.205i	−0.0378811	+	0.116586i	0.930328	+	0.366729i	$0.119522\pi$
$972$		0			0
$973$	−186.787	+	1179.33i	−0.191970	+	1.21205i
$974$		0			0
$975$	652.005	−	654.395i	0.668723	−	0.671174i
$976$		0			0
$977$	−9.01848	−	56.9404i	−0.00923078	−	0.0582809i	0.982643	−	0.185507i	$-0.0593927\pi$
$977$	−9.01848	−	56.9404i	−0.00923078	−	0.0582809i	−0.991874	+	0.127226i	$0.959393\pi$
$978$		0			0
$979$	−225.664	−	1399.47i	−0.230504	−	1.42949i
$980$		0			0
$981$	608.703	+	442.248i	0.620492	+	0.450814i
$982$		0			0
$983$	−743.194	−	378.676i	−0.756047	−	0.385225i	0.0330819	−	0.999453i	$-0.489468\pi$
$983$	−743.194	−	378.676i	−0.756047	−	0.385225i	−0.789129	+	0.614227i	$0.789468\pi$
$984$		0			0
$985$	876.199	−	69.7649i	0.889542	−	0.0708273i
$986$		0			0
$987$	−1162.30	+	592.223i	−1.17761	+	0.600023i
$988$		0			0
$989$			17.7697i			0.0179673i
$990$		0			0
$991$	−410.257			−0.413983			−0.206991	−	0.978343i	$-0.566367\pi$
$991$	−410.257			−0.413983			−0.206991	+	0.978343i	$0.566367\pi$
$992$		0			0
$993$	47.0488	+	92.3384i	0.0473804	+	0.0929893i
$994$		0			0
$995$	425.163	+	362.451i	0.427299	+	0.364272i
$996$		0			0
$997$	−607.975	+	1193.22i	−0.609804	+	1.19681i	0.355254	+	0.934770i	$0.384394\pi$
$997$	−607.975	+	1193.22i	−0.609804	+	1.19681i	−0.965058	+	0.262038i	$0.915606\pi$
$998$		0			0
$999$	61.9430	−	85.2572i	0.0620050	−	0.0853426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.37.2	✓	96
5.3	odd	4	inner	220.3.x.a.213.11	yes	96
11.3	even	5	inner	220.3.x.a.157.11	yes	96
55.3	odd	20	inner	220.3.x.a.113.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.2	✓	96	1.1	even	1	trivial
220.3.x.a.113.2	yes	96	55.3	odd	20	inner
220.3.x.a.157.11	yes	96	11.3	even	5	inner
220.3.x.a.213.11	yes	96	5.3	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87775 - 3.68530i) q^{3} +(3.24376 - 3.80500i) q^{5} +(2.52559 - 4.95675i) q^{7} +(-4.76541 + 6.55902i) q^{9} +(10.8597 - 1.75112i) q^{11} +(-8.82368 + 1.39753i) q^{13} +(-20.1135 - 4.80938i) q^{15} +(-27.6325 - 4.37656i) q^{17} +(15.6008 + 5.06901i) q^{19} -23.0096 q^{21} +(-0.317508 + 0.317508i) q^{23} +(-3.95603 - 24.6850i) q^{25} +(-3.64643 - 0.577539i) q^{27} +(-10.1414 + 3.29515i) q^{29} +(0.900009 + 0.653895i) q^{31} +(-26.8453 - 36.7332i) q^{33} +(-10.6680 - 25.6884i) q^{35} +(-12.9590 + 25.4335i) q^{37} +(21.7190 + 29.8937i) q^{39} +(-3.08786 + 9.50347i) q^{41} +(27.9830 - 27.9830i) q^{43} +(9.49923 + 39.4083i) q^{45} +(50.5139 - 25.7381i) q^{47} +(10.6107 + 14.6044i) q^{49} +(35.7581 + 110.052i) q^{51} +(90.5466 - 14.3412i) q^{53} +(28.5633 - 47.0015i) q^{55} +(-10.6137 - 67.0120i) q^{57} +(2.39521 - 0.778250i) q^{59} +(-50.6854 + 36.8251i) q^{61} +(20.4760 + 40.1864i) q^{63} +(-23.3043 + 38.1073i) q^{65} +(-59.4330 - 59.4330i) q^{67} +(1.76631 + 0.573910i) q^{69} +(110.315 - 80.1487i) q^{71} +(97.5018 + 49.6796i) q^{73} +(-83.5432 + 60.9316i) q^{75} +(18.7473 - 58.2516i) q^{77} +(-23.2780 + 32.0394i) q^{79} +(27.2666 + 83.9181i) q^{81} +(-21.4857 + 135.655i) q^{83} +(-106.286 + 90.9451i) q^{85} +(31.1867 + 31.1867i) q^{87} -128.868i q^{89} +(-15.3578 + 47.2664i) q^{91} +(0.719803 - 4.54466i) q^{93} +(69.8928 - 42.9184i) q^{95} +(-16.2826 - 102.805i) q^{97} +(-40.2654 + 79.5740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 + 4 * q^5 - 2 * q^7 - 20 * q^11 - 8 * q^13 + 88 * q^15 + 42 * q^17 + 56 * q^21 - 104 * q^23 - 126 * q^25 - 14 * q^27 - 32 * q^31 + 52 * q^33 + 56 * q^35 - 134 * q^37 + 24 * q^41 + 332 * q^43 + 344 * q^45 + 258 * q^47 - 320 * q^51 + 222 * q^53 - 46 * q^55 + 504 * q^57 - 168 * q^61 - 298 * q^63 - 416 * q^65 - 632 * q^67 - 252 * q^71 + 56 * q^73 - 352 * q^75 - 820 * q^77 + 336 * q^81 + 236 * q^83 + 88 * q^85 - 176 * q^87 - 756 * q^91 - 770 * q^93 - 334 * q^95 - 310 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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