LMFDB - Embedded newform 220.3.x.a.157.11

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			157.11
Character	$\chi$	$=$	220.157
Dual form			220.3.x.a.213.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.68530 + 1.87775i) q^{3} +(4.62115 + 1.90919i) q^{5} +(-4.95675 + 2.52559i) q^{7} +(4.76541 + 6.55902i) q^{9} +(10.8597 + 1.75112i) q^{11} +(-1.39753 + 8.82368i) q^{13} +(13.4453 + 15.7133i) q^{15} +(-4.37656 - 27.6325i) q^{17} +(-15.6008 + 5.06901i) q^{19} -23.0096 q^{21} +(-0.317508 + 0.317508i) q^{23} +(17.7100 + 17.6453i) q^{25} +(-0.577539 - 3.64643i) q^{27} +(10.1414 + 3.29515i) q^{29} +(0.900009 - 0.653895i) q^{31} +(36.7332 + 26.8453i) q^{33} +(-27.7277 + 2.20774i) q^{35} +(25.4335 - 12.9590i) q^{37} +(-21.7190 + 29.8937i) q^{39} +(-3.08786 - 9.50347i) q^{41} +(27.9830 - 27.9830i) q^{43} +(9.49923 + 39.4083i) q^{45} +(-25.7381 + 50.5139i) q^{47} +(-10.6107 + 14.6044i) q^{49} +(35.7581 - 110.052i) q^{51} +(14.3412 - 90.5466i) q^{53} +(46.8411 + 28.8255i) q^{55} +(-67.0120 - 10.6137i) q^{57} +(-2.39521 - 0.778250i) q^{59} +(-50.6854 - 36.8251i) q^{61} +(-40.1864 - 20.4760i) q^{63} +(-23.3043 + 38.1073i) q^{65} +(-59.4330 - 59.4330i) q^{67} +(-1.76631 + 0.573910i) q^{69} +(110.315 + 80.1487i) q^{71} +(-49.6796 - 97.5018i) q^{73} +(32.1331 + 98.2832i) q^{75} +(-58.2516 + 18.7473i) q^{77} +(23.2780 + 32.0394i) q^{79} +(27.2666 - 83.9181i) q^{81} +(-135.655 + 21.4857i) q^{83} +(32.5310 - 136.049i) q^{85} +(31.1867 + 31.1867i) q^{87} -128.868i q^{89} +(-15.3578 - 47.2664i) q^{91} +(4.54466 - 0.719803i) q^{93} +(-81.7713 - 6.36028i) q^{95} +(-102.805 - 16.2826i) q^{97} +(40.2654 + 79.5740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

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

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
$3$	3.68530	+	1.87775i	1.22843	+	0.625918i	0.943100	−	0.332510i	$-0.107896\pi$
$3$	3.68530	+	1.87775i	1.22843	+	0.625918i	0.285334	+	0.958428i	$0.407896\pi$
$4$		0			0
$5$	4.62115	+	1.90919i	0.924229	+	0.381838i
$5$	4.62115	+	1.90919i	0.924229	+	0.381838i
$6$		0			0
$7$	−4.95675	+	2.52559i	−0.708107	+	0.360799i	−0.770663	−	0.637243i	$-0.780075\pi$
$7$	−4.95675	+	2.52559i	−0.708107	+	0.360799i	0.0625558	+	0.998041i	$0.480075\pi$
$8$		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
$13$	−1.39753	+	8.82368i	−0.107503	+	0.678744i	0.873802	+	0.486282i	$0.161647\pi$
$13$	−1.39753	+	8.82368i	−0.107503	+	0.678744i	−0.981304	+	0.192462i	$0.938353\pi$
$14$		0			0
$15$	13.4453	+	15.7133i	0.896355	+	1.04755i
$16$		0			0
$17$	−4.37656	−	27.6325i	−0.257445	−	1.62544i	−0.689983	−	0.723826i	$-0.742382\pi$
$17$	−4.37656	−	27.6325i	−0.257445	−	1.62544i	0.432539	−	0.901615i	$-0.357618\pi$
$18$		0			0
$19$	−15.6008	+	5.06901i	−0.821095	+	0.266790i	−0.689290	−	0.724486i	$-0.742077\pi$
$19$	−15.6008	+	5.06901i	−0.821095	+	0.266790i	−0.131805	+	0.991276i	$0.542077\pi$
$20$		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
$25$	17.7100	+	17.6453i	0.708399	+	0.705812i
$26$		0			0
$27$	−0.577539	−	3.64643i	−0.0213903	−	0.135053i
$28$		0			0
$29$	10.1414	+	3.29515i	0.349704	+	0.113626i	0.478602	−	0.878032i	$-0.341144\pi$
$29$	10.1414	+	3.29515i	0.349704	+	0.113626i	−0.128897	+	0.991658i	$0.541144\pi$
$30$		0			0
$31$	0.900009	−	0.653895i	0.0290326	−	0.0210934i	−0.573174	−	0.819433i	$-0.694288\pi$
$31$	0.900009	−	0.653895i	0.0290326	−	0.0210934i	0.602207	+	0.798340i	$0.294288\pi$
$32$		0			0
$33$	36.7332	+	26.8453i	1.11313	+	0.813494i
$34$		0			0
$35$	−27.7277	+	2.20774i	−0.792220	+	0.0630784i
$36$		0			0
$37$	25.4335	−	12.9590i	0.687392	−	0.350244i	−0.0751595	−	0.997172i	$-0.523947\pi$
$37$	25.4335	−	12.9590i	0.687392	−	0.350244i	0.762551	+	0.646928i	$0.223947\pi$
$38$		0			0
$39$	−21.7190	+	29.8937i	−0.556898	+	0.766505i
$40$		0			0
$41$	−3.08786	−	9.50347i	−0.0753137	−	0.231792i	0.906312	−	0.422610i	$-0.138886\pi$
$41$	−3.08786	−	9.50347i	−0.0753137	−	0.231792i	−0.981625	+	0.190818i	$0.938886\pi$
$42$		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
$47$	−25.7381	+	50.5139i	−0.547620	+	1.07476i	0.436903	+	0.899509i	$0.356075\pi$
$47$	−25.7381	+	50.5139i	−0.547620	+	1.07476i	−0.984523	+	0.175256i	$0.943925\pi$
$48$		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
$53$	14.3412	−	90.5466i	0.270588	−	1.70843i	−0.360537	−	0.932745i	$-0.617407\pi$
$53$	14.3412	−	90.5466i	0.270588	−	1.70843i	0.631125	−	0.775681i	$-0.282593\pi$
$54$		0			0
$55$	46.8411	+	28.8255i	0.851657	+	0.524099i
$56$		0			0
$57$	−67.0120	−	10.6137i	−1.17565	−	0.186204i
$58$		0			0
$59$	−2.39521	−	0.778250i	−0.0405967	−	0.0131907i	0.288648	−	0.957435i	$-0.406794\pi$
$59$	−2.39521	−	0.778250i	−0.0405967	−	0.0131907i	−0.329245	+	0.944245i	$0.606794\pi$
$60$		0			0
$61$	−50.6854	−	36.8251i	−0.830908	−	0.603690i	0.0889078	−	0.996040i	$-0.471662\pi$
$61$	−50.6854	−	36.8251i	−0.830908	−	0.603690i	−0.919816	+	0.392350i	$0.871662\pi$
$62$		0			0
$63$	−40.1864	−	20.4760i	−0.637879	−	0.325016i
$64$		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	0.940920	+	0.338629i	$0.109963\pi$
$71$	110.315	+	80.1487i	1.55374	+	1.12885i	0.612815	+	0.790226i	$0.290037\pi$
$72$		0			0
$73$	−49.6796	−	97.5018i	−0.680543	−	1.33564i	−0.930109	−	0.367283i	$-0.880288\pi$
$73$	−49.6796	−	97.5018i	−0.680543	−	1.33564i	0.249566	−	0.968358i	$-0.419712\pi$
$74$		0			0
$75$	32.1331	+	98.2832i	0.428441	+	1.31044i
$76$		0			0
$77$	−58.2516	+	18.7473i	−0.756514	+	0.243472i
$78$		0			0
$79$	23.2780	+	32.0394i	0.294658	+	0.405562i	0.930520	−	0.366240i	$-0.119355\pi$
$79$	23.2780	+	32.0394i	0.294658	+	0.405562i	−0.635862	+	0.771803i	$0.719355\pi$
$80$		0			0
$81$	27.2666	−	83.9181i	0.336625	−	1.03603i
$82$		0			0
$83$	−135.655	+	21.4857i	−1.63440	+	0.258863i	−0.905058	−	0.425288i	$-0.860173\pi$
$83$	−135.655	+	21.4857i	−1.63440	+	0.258863i	−0.729341	+	0.684151i	$0.760173\pi$
$84$		0			0
$85$	32.5310	−	136.049i	0.382718	−	1.60058i
$86$		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
$93$	4.54466	−	0.719803i	0.0488673	−	0.00773982i
$94$		0			0
$95$	−81.7713	−	6.36028i	−0.860750	−	0.0669503i
$96$		0			0
$97$	−102.805	−	16.2826i	−1.05984	−	0.167862i	−0.397908	−	0.917425i	$-0.630264\pi$
$97$	−102.805	−	16.2826i	−1.05984	−	0.167862i	−0.661933	+	0.749563i	$0.730264\pi$
$98$		0			0
$99$	40.2654	+	79.5740i	0.406721	+	0.803778i
$100$		0			0
$101$	−47.2895	+	34.3578i	−0.468213	+	0.340176i	−0.796744	−	0.604317i	$-0.793446\pi$
$101$	−47.2895	+	34.3578i	−0.468213	+	0.340176i	0.328532	+	0.944493i	$0.393446\pi$
$102$		0			0
$103$	7.10435	+	13.9431i	0.0689742	+	0.135370i	0.922919	−	0.384994i	$-0.125796\pi$
$103$	7.10435	+	13.9431i	0.0689742	+	0.135370i	−0.853945	+	0.520363i	$0.825796\pi$
$104$		0			0
$105$	−106.331	−	43.9296i	−1.01267	−	0.418377i
$106$		0			0
$107$	−32.1725	+	63.1421i	−0.300677	+	0.590113i	−0.991073	−	0.133319i	$-0.957436\pi$
$107$	−32.1725	+	63.1421i	−0.300677	+	0.590113i	0.690396	+	0.723432i	$0.257436\pi$
$108$		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
$113$	23.7367	+	12.0944i	0.210059	+	0.107030i	0.555855	−	0.831279i	$-0.312391\pi$
$113$	23.7367	+	12.0944i	0.210059	+	0.107030i	−0.345796	+	0.938310i	$0.612391\pi$
$114$		0			0
$115$	−2.07343	+	0.861067i	−0.0180299	+	0.00748754i
$116$		0			0
$117$	−64.5345	+	32.8820i	−0.551577	+	0.281043i
$118$		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
$123$	6.46547	−	40.8214i	0.0525648	−	0.331881i
$124$		0			0
$125$	48.1522	+	115.353i	0.385217	+	0.922826i
$126$		0			0
$127$	−0.652137	−	4.11743i	−0.00513494	−	0.0324207i	0.984988	−	0.172624i	$-0.0552245\pi$
$127$	−0.652137	−	4.11743i	−0.00513494	−	0.0324207i	−0.990123	+	0.140203i	$0.955224\pi$
$128$		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
$135$	4.29285	−	17.9533i	0.0317989	−	0.132988i
$136$		0			0
$137$	27.1495	+	171.415i	0.198172	+	1.25121i	0.863382	+	0.504551i	$0.168342\pi$
$137$	27.1495	+	171.415i	0.198172	+	1.25121i	−0.665210	+	0.746656i	$0.731658\pi$
$138$		0			0
$139$	204.129	+	66.3254i	1.46855	+	0.477161i	0.930670	−	0.365860i	$-0.119225\pi$
$139$	204.129	+	66.3254i	1.46855	+	0.477161i	0.537881	+	0.843021i	$0.319225\pi$
$140$		0			0
$141$	−189.705	+	137.829i	−1.34543	+	0.977511i
$142$		0			0
$143$	−30.6282	+	93.3754i	−0.214183	+	0.652975i
$144$		0			0
$145$	40.5740	+	34.5893i	0.279820	+	0.238547i
$146$		0			0
$147$	−66.5271	+	33.8972i	−0.452565	+	0.230593i
$148$		0			0
$149$	−127.852	+	175.973i	−0.858066	+	1.18103i	0.123961	+	0.992287i	$0.460440\pi$
$149$	−127.852	+	175.973i	−0.858066	+	1.18103i	−0.982027	+	0.188740i	$0.939560\pi$
$150$		0			0
$151$	69.2395	+	213.097i	0.458540	+	1.41124i	0.866928	+	0.498433i	$0.166091\pi$
$151$	69.2395	+	213.097i	0.458540	+	1.41124i	−0.408388	+	0.912808i	$0.633909\pi$
$152$		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
$157$	16.9978	−	33.3601i	0.108266	−	0.212485i	−0.830517	−	0.556994i	$-0.811955\pi$
$157$	16.9978	−	33.3601i	0.108266	−	0.212485i	0.938783	+	0.344509i	$0.111955\pi$
$158$		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
$163$	−19.5001	+	123.119i	−0.119632	+	0.755329i	0.852816	+	0.522211i	$0.174893\pi$
$163$	−19.5001	+	123.119i	−0.119632	+	0.755329i	−0.972449	+	0.233118i	$0.925107\pi$
$164$		0			0
$165$	118.497	+	194.187i	0.718161	+	1.17689i
$166$		0			0
$167$	−161.514	−	25.5813i	−0.967151	−	0.153182i	−0.347173	−	0.937801i	$-0.612858\pi$
$167$	−161.514	−	25.5813i	−0.967151	−	0.153182i	−0.619978	+	0.784619i	$0.712858\pi$
$168$		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
$173$	146.913	+	74.8559i	0.849208	+	0.432693i	0.823730	−	0.566982i	$-0.191889\pi$
$173$	146.913	+	74.8559i	0.849208	+	0.432693i	0.0254781	+	0.999675i	$0.491889\pi$
$174$		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	$-0.940706\pi$
$179$	−298.726	+	97.0620i	−1.66886	+	0.542246i	−0.686161	+	0.727449i	$0.740706\pi$
$180$		0			0
$181$	−232.209	−	168.710i	−1.28292	−	0.932098i	−0.283285	−	0.959036i	$-0.591424\pi$
$181$	−232.209	−	168.710i	−1.28292	−	0.932098i	−0.999637	+	0.0269379i	$0.991424\pi$
$182$		0			0
$183$	−117.642	−	230.886i	−0.642855	−	1.26167i
$184$		0			0
$185$	142.273	−	11.3281i	0.769044	−	0.0612330i
$186$		0			0
$187$	0.859688	−	307.745i	0.00459726	−	1.64570i
$188$		0			0
$189$	12.0721	+	16.6158i	0.0638736	+	0.0879145i
$190$		0			0
$191$	−31.0596	+	95.5917i	−0.162616	+	0.500480i	−0.998853	−	0.0478882i	$-0.984751\pi$
$191$	−31.0596	+	95.5917i	−0.162616	+	0.500480i	0.836237	+	0.548368i	$0.184751\pi$
$192$		0			0
$193$	−224.657	+	35.5821i	−1.16402	+	0.184363i	−0.708402	−	0.705809i	$-0.750584\pi$
$193$	−224.657	+	35.5821i	−1.16402	+	0.184363i	−0.455623	+	0.890173i	$0.650584\pi$
$194$		0			0
$195$	−157.440	+	96.6773i	−0.807382	+	0.495781i
$196$		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
$203$	−58.5907	+	9.27986i	−0.288624	+	0.0457136i
$204$		0			0
$205$	3.87446	−	49.8122i	0.0188998	−	0.242986i
$206$		0			0
$207$	−3.59560	−	0.569487i	−0.0173700	−	0.00275114i
$208$		0			0
$209$	−178.297	+	27.7291i	−0.853095	+	0.132675i
$210$		0			0
$211$	170.668	−	123.997i	0.808851	−	0.587665i	−0.104646	−	0.994510i	$-0.533371\pi$
$211$	170.668	−	123.997i	0.808851	−	0.587665i	0.913497	+	0.406845i	$0.133371\pi$
$212$		0			0
$213$	256.045	+	502.517i	1.20209	+	2.35923i
$214$		0			0
$215$	182.739	−	75.8888i	0.849947	−	0.352971i
$216$		0			0
$217$	−2.80965	+	5.51425i	−0.0129477	+	0.0254113i
$218$		0			0
$219$		−	452.610i		−	2.06671i
$220$		0			0
$221$	249.937			1.13093
$222$		0			0
$223$	−54.5733	−	27.8065i	−0.244723	−	0.124693i	0.327327	−	0.944911i	$-0.393852\pi$
$223$	−54.5733	−	27.8065i	−0.244723	−	0.124693i	−0.572051	+	0.820218i	$0.693852\pi$
$224$		0			0
$225$	−31.3406	+	200.247i	−0.139292	+	0.889988i
$226$		0			0
$227$	17.7475	−	9.04279i	0.0781827	−	0.0398361i	−0.414462	−	0.910067i	$-0.636030\pi$
$227$	17.7475	−	9.04279i	0.0781827	−	0.0398361i	0.492645	+	0.870231i	$0.336030\pi$
$228$		0			0
$229$	144.481	+	198.861i	0.630921	+	0.868388i	0.998091	−	0.0617661i	$-0.0196733\pi$
$229$	144.481	+	198.861i	0.630921	+	0.868388i	−0.367170	+	0.930154i	$0.619673\pi$
$230$		0			0
$231$	−249.877	−	40.2926i	−1.08172	−	0.174427i
$232$		0			0
$233$	29.2381	−	184.602i	0.125485	−	0.792284i	−0.842022	−	0.539443i	$-0.818635\pi$
$233$	29.2381	−	184.602i	0.125485	−	0.792284i	0.967508	−	0.252841i	$-0.0813650\pi$
$234$		0			0
$235$	−215.380	+	184.293i	−0.916512	+	0.784227i
$236$		0			0
$237$	25.6243	+	161.785i	0.108119	+	0.682639i
$238$		0			0
$239$	−172.151	+	55.9353i	−0.720298	+	0.234039i	−0.646152	−	0.763209i	$-0.723623\pi$
$239$	−172.151	+	55.9353i	−0.720298	+	0.234039i	−0.0741454	+	0.997247i	$0.523623\pi$
$240$		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
$245$	−76.9161	+	47.2311i	−0.313943	+	0.192780i
$246$		0			0
$247$	−22.9246	−	144.741i	−0.0928123	−	0.585994i
$248$		0			0
$249$	−540.275	−	175.546i	−2.16978	−	0.705003i
$250$		0			0
$251$	−95.3862	+	69.3021i	−0.380025	+	0.276104i	−0.761356	−	0.648335i	$-0.775466\pi$
$251$	−95.3862	+	69.3021i	−0.380025	+	0.276104i	0.381331	+	0.924439i	$0.375466\pi$
$252$		0			0
$253$	−4.00404	+	2.89205i	−0.0158263	+	0.0114310i
$254$		0			0
$255$	375.354	−	440.298i	1.47198	−	1.72666i
$256$		0			0
$257$	189.983	−	96.8010i	0.739232	−	0.376658i	−0.0434692	−	0.999055i	$-0.513841\pi$
$257$	189.983	−	96.8010i	0.739232	−	0.376658i	0.782702	+	0.622397i	$0.213841\pi$
$258$		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
$267$	241.982	−	474.917i	0.906301	−	1.77872i
$268$		0			0
$269$	−151.651	+	208.729i	−0.563757	+	0.775945i	−0.991798	−	0.127814i	$-0.959204\pi$
$269$	−151.651	+	208.729i	−0.563757	+	0.775945i	0.428041	+	0.903759i	$0.359204\pi$
$270$		0			0
$271$	−61.1957	+	188.341i	−0.225814	+	0.694985i	0.772394	+	0.635144i	$0.219059\pi$
$271$	−61.1957	+	188.341i	−0.225814	+	0.694985i	−0.998208	+	0.0598408i	$0.980941\pi$
$272$		0			0
$273$	32.1566	−	203.029i	0.117790	−	0.743696i
$274$		0			0
$275$	161.426	+	222.635i	0.587005	+	0.809583i
$276$		0			0
$277$	521.363	+	82.5757i	1.88218	+	0.298107i	0.988572	−	0.150750i	$-0.0481688\pi$
$277$	521.363	+	82.5757i	1.88218	+	0.298107i	0.893604	+	0.448857i	$0.148169\pi$
$278$		0			0
$279$	8.57783	+	2.78711i	0.0307449	+	0.00998963i
$280$		0			0
$281$	−44.9696	−	32.6723i	−0.160034	−	0.116272i	0.504886	−	0.863186i	$-0.331534\pi$
$281$	−44.9696	−	32.6723i	−0.160034	−	0.116272i	−0.664920	+	0.746914i	$0.731534\pi$
$282$		0			0
$283$	−288.238	−	146.864i	−1.01851	−	0.518955i	−0.136724	−	0.990609i	$-0.543657\pi$
$283$	−288.238	−	146.864i	−1.01851	−	0.518955i	−0.881784	+	0.471654i	$0.843657\pi$
$284$		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
$293$	83.6214	+	164.116i	0.285397	+	0.560124i	0.988546	−	0.150919i	$-0.0482233\pi$
$293$	83.6214	+	164.116i	0.285397	+	0.560124i	−0.703149	+	0.711043i	$0.748223\pi$
$294$		0			0
$295$	−9.58277	−	8.16931i	−0.0324840	−	0.0276926i
$296$		0			0
$297$	0.113446	−	40.6106i	0.000381973	−	0.136736i
$298$		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
$303$	−238.791	+	37.8208i	−0.788090	+	0.124821i
$304$		0			0
$305$	−163.919	−	266.942i	−0.537438	−	0.875221i
$306$		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	−0.996439	−	0.0843197i	$-0.973128\pi$
$311$	−74.5979	−	229.589i	−0.239865	−	0.738228i	0.756574	−	0.653908i	$-0.226872\pi$
$312$		0			0
$313$	−55.1739	+	8.73869i	−0.176274	+	0.0279191i	−0.243948	−	0.969788i	$-0.578442\pi$
$313$	−55.1739	+	8.73869i	−0.176274	+	0.0279191i	0.0676731	+	0.997708i	$0.478442\pi$
$314$		0			0
$315$	−146.615	−	171.346i	−0.465443	−	0.543955i
$316$		0			0
$317$	−540.907	−	85.6712i	−1.70633	−	0.270256i	−0.774348	−	0.632760i	$-0.781922\pi$
$317$	−540.907	−	85.6712i	−1.70633	−	0.270256i	−0.931982	+	0.362504i	$0.881922\pi$
$318$		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
$323$	208.347	+	408.904i	0.645037	+	1.26596i
$324$		0			0
$325$	−180.447	+	131.607i	−0.555221	+	0.404945i
$326$		0			0
$327$	174.263	−	342.010i	0.532914	−	1.04590i
$328$		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
$333$	206.199	+	105.064i	0.619218	+	0.315507i
$334$		0			0
$335$	−161.180	−	388.118i	−0.481134	−	1.15856i
$336$		0			0
$337$	121.964	−	62.1436i	0.361910	−	0.184402i	−0.263574	−	0.964639i	$-0.584901\pi$
$337$	121.964	−	62.1436i	0.361910	−	0.184402i	0.625484	+	0.780237i	$0.284901\pi$
$338$		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
$343$	58.3526	−	368.424i	0.170124	−	1.07412i
$344$		0			0
$345$	−9.25810	−	0.720107i	−0.0268351	−	0.00208727i
$346$		0			0
$347$	37.6318	+	237.598i	0.108449	+	0.684719i	0.980679	+	0.195624i	$0.0626731\pi$
$347$	37.6318	+	237.598i	0.108449	+	0.684719i	−0.872230	+	0.489096i	$0.837327\pi$
$348$		0			0
$349$	430.260	−	139.800i	1.23284	−	0.400573i	0.381095	−	0.924536i	$-0.375547\pi$
$349$	430.260	−	139.800i	1.23284	−	0.400573i	0.851741	+	0.523963i	$0.175547\pi$
$350$		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
$355$	356.764	+	580.992i	1.00497	+	1.63660i
$356$		0			0
$357$	100.703	+	635.812i	0.282080	+	1.78098i
$358$		0			0
$359$	248.655	+	80.7928i	0.692631	+	0.225050i	0.634117	−	0.773237i	$-0.281364\pi$
$359$	248.655	+	80.7928i	0.692631	+	0.225050i	0.0585141	+	0.998287i	$0.481364\pi$
$360$		0			0
$361$	−74.3651	+	54.0294i	−0.205997	+	0.149666i
$362$		0			0
$363$	351.903	+	355.857i	0.969428	+	0.980322i
$364$		0			0
$365$	−43.4274	−	545.418i	−0.118979	−	1.49430i
$366$		0			0
$367$	76.0448	−	38.7468i	0.207207	−	0.105577i	−0.347308	−	0.937751i	$-0.612904\pi$
$367$	76.0448	−	38.7468i	0.207207	−	0.105577i	0.554514	+	0.832174i	$0.312904\pi$
$368$		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
$377$	−43.2483	+	84.8796i	−0.114717	+	0.225145i
$378$		0			0
$379$	380.805	−	524.134i	1.00476	−	1.38294i	0.0824071	−	0.996599i	$-0.473739\pi$
$379$	380.805	−	524.134i	1.00476	−	1.38294i	0.922357	−	0.386340i	$-0.126261\pi$
$380$		0			0
$381$	5.32820	−	16.3985i	0.0139848	−	0.0430407i
$382$		0			0
$383$	−28.7396	+	181.455i	−0.0750381	+	0.473772i	0.921341	+	0.388755i	$0.127095\pi$
$383$	−28.7396	+	181.455i	−0.0750381	+	0.473772i	−0.996379	+	0.0850175i	$0.972905\pi$
$384$		0			0
$385$	−304.981	−	24.5791i	−0.792159	−	0.0638419i
$386$		0			0
$387$	316.892	+	50.1908i	0.818843	+	0.129692i
$388$		0			0
$389$	−175.343	−	56.9723i	−0.450752	−	0.146458i	0.0748387	−	0.997196i	$-0.476156\pi$
$389$	−175.343	−	56.9723i	−0.450752	−	0.146458i	−0.525591	+	0.850737i	$0.676156\pi$
$390$		0			0
$391$	10.1631	+	7.38394i	0.0259926	+	0.0188848i
$392$		0			0
$393$	706.105	+	359.779i	1.79671	+	0.915467i
$394$		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	0.990952	−	0.134217i	$-0.0428519\pi$
$401$	468.980	+	340.734i	1.16953	+	0.849710i	0.178573	+	0.983927i	$0.442852\pi$
$402$		0			0
$403$	4.51197	+	8.85523i	0.0111959	+	0.0219733i
$404$		0			0
$405$	286.219	−	335.740i	0.706713	−	0.828989i
$406$		0			0
$407$	298.893	−	96.1941i	0.734382	−	0.236349i
$408$		0			0
$409$	−15.4076	−	21.2067i	−0.0376714	−	0.0518502i	0.789766	−	0.613408i	$-0.210202\pi$
$409$	−15.4076	−	21.2067i	−0.0376714	−	0.0518502i	−0.827437	+	0.561558i	$0.810202\pi$
$410$		0			0
$411$	−221.822	+	682.697i	−0.539713	+	1.66106i
$412$		0			0
$413$	13.8380	−	2.19172i	0.0335060	−	0.00530683i
$414$		0			0
$415$	−667.902	−	159.703i	−1.60940	−	0.384827i
$416$		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	0.995821	+	0.0913316i	$0.0291123\pi$
$421$	102.669	+	315.981i	0.243868	+	0.750549i	−0.751952	+	0.659217i	$0.770888\pi$
$422$		0			0
$423$	−453.975	+	71.9026i	−1.07323	+	0.169982i
$424$		0			0
$425$	410.075	−	566.597i	0.964882	−	1.33317i
$426$		0			0
$427$	344.240	+	54.5223i	0.806183	+	0.127687i
$428$		0			0
$429$	−288.210	+	286.604i	−0.671818	+	0.668075i
$430$		0			0
$431$	−581.221	+	422.282i	−1.34854	+	0.979772i	−0.349457	+	0.936952i	$0.613634\pi$
$431$	−581.221	+	422.282i	−1.34854	+	0.979772i	−0.999083	+	0.0428194i	$0.986366\pi$
$432$		0			0
$433$	−102.372	−	200.916i	−0.236425	−	0.464010i	0.742059	−	0.670335i	$-0.233850\pi$
$433$	−102.372	−	200.916i	−0.236425	−	0.464010i	−0.978483	+	0.206325i	$0.933850\pi$
$434$		0			0
$435$	84.5770	+	203.660i	0.194430	+	0.468184i
$436$		0			0
$437$	3.34393	−	6.56283i	0.00765201	−	0.0150179i
$438$		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
$443$	−313.555	−	159.764i	−0.707800	−	0.360642i	0.0627435	−	0.998030i	$-0.480015\pi$
$443$	−313.555	−	159.764i	−0.707800	−	0.360642i	−0.770543	+	0.637388i	$0.780015\pi$
$444$		0			0
$445$	246.034	−	595.518i	0.552884	−	1.33824i
$446$		0			0
$447$	−801.606	+	408.439i	−1.79330	+	0.913734i
$448$		0			0
$449$	371.767	+	511.693i	0.827988	+	1.13963i	0.988294	+	0.152561i	$0.0487519\pi$
$449$	371.767	+	511.693i	0.827988	+	1.13963i	−0.160306	+	0.987067i	$0.551248\pi$
$450$		0			0
$451$	−16.8916	−	108.612i	−0.0374537	−	0.240825i
$452$		0			0
$453$	−144.976	+	915.343i	−0.320035	+	2.02062i
$454$		0			0
$455$	19.2700	−	247.746i	0.0423516	−	0.544496i
$456$		0			0
$457$	−47.9625	−	302.823i	−0.104951	−	0.662632i	−0.982936	−	0.183946i	$-0.941113\pi$
$457$	−47.9625	−	302.823i	−0.104951	−	0.662632i	0.877986	−	0.478687i	$-0.158887\pi$
$458$		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
$465$	22.3758	+	5.35030i	0.0481200	+	0.0115060i
$466$		0			0
$467$	5.58755	+	35.2784i	0.0119648	+	0.0755427i	0.992948	−	0.118549i	$-0.0378242\pi$
$467$	5.58755	+	35.2784i	0.0119648	+	0.0755427i	−0.980983	+	0.194091i	$0.937824\pi$
$468$		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
$473$	352.890	−	254.886i	0.746067	−	0.538872i
$474$		0			0
$475$	−365.734	−	185.509i	−0.769966	−	0.390545i
$476$		0			0
$477$	662.239	−	337.428i	1.38834	−	0.707395i
$478$		0			0
$479$	336.947	−	463.768i	0.703438	−	0.968200i	−0.296475	−	0.955041i	$-0.595811\pi$
$479$	336.947	−	463.768i	0.703438	−	0.968200i	0.999913	−	0.0131593i	$-0.00418885\pi$
$480$		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
$487$	174.131	−	341.752i	0.357559	−	0.701749i	−0.640232	−	0.768182i	$-0.721162\pi$
$487$	174.131	−	341.752i	0.357559	−	0.701749i	0.997791	+	0.0664324i	$0.0211617\pi$
$488$		0			0
$489$	−303.050	+	417.113i	−0.619734	+	0.852991i
$490$		0			0
$491$	139.926	−	430.648i	0.284981	−	0.877083i	−0.701423	−	0.712746i	$-0.747451\pi$
$491$	139.926	−	430.648i	0.284981	−	0.877083i	0.986404	−	0.164337i	$-0.0525485\pi$
$492$		0			0
$493$	46.6687	−	294.654i	0.0946626	−	0.597676i
$494$		0			0
$495$	34.1503	+	444.597i	0.0689904	+	0.898177i
$496$		0			0
$497$	−749.228	−	118.666i	−1.50750	−	0.238765i
$498$		0			0
$499$	−833.197	−	270.722i	−1.66973	−	0.542530i	−0.686857	−	0.726792i	$-0.741010\pi$
$499$	−833.197	−	270.722i	−1.66973	−	0.542530i	−0.982877	+	0.184263i	$0.941010\pi$
$500$		0			0
$501$	−547.193	−	397.559i	−1.09220	−	0.793531i
$502$		0			0
$503$	−410.432	−	209.126i	−0.815968	−	0.415757i	−0.00438284	−	0.999990i	$-0.501395\pi$
$503$	−410.432	−	209.126i	−0.815968	−	0.415757i	−0.811585	+	0.584234i	$0.801395\pi$
$504$		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	$-0.606639\pi$
$509$	−20.1931	+	6.56113i	−0.0396721	+	0.0128902i	0.289114	+	0.957295i	$0.406639\pi$
$510$		0			0
$511$	492.499	+	357.822i	0.963795	+	0.700238i
$512$		0			0
$513$	27.4939	+	53.9597i	0.0535943	+	0.105185i
$514$		0			0
$515$	6.21026	+	77.9965i	0.0120588	+	0.151450i
$516$		0			0
$517$	−367.965	+	503.497i	−0.711731	+	0.973881i
$518$		0			0
$519$	400.858	+	551.733i	0.772365	+	1.06307i
$520$		0			0
$521$	318.668	−	980.759i	0.611646	−	1.88245i	0.169442	−	0.985540i	$-0.445804\pi$
$521$	318.668	−	980.759i	0.611646	−	1.88245i	0.442205	−	0.896914i	$-0.354196\pi$
$522$		0			0
$523$	−276.520	+	43.7964i	−0.528718	+	0.0837407i	−0.415086	−	0.909782i	$-0.636249\pi$
$523$	−276.520	+	43.7964i	−0.528718	+	0.0837407i	−0.113632	+	0.993523i	$0.536249\pi$
$524$		0			0
$525$	−407.499	−	406.010i	−0.776188	−	0.773353i
$526$		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
$533$	88.1709	−	13.9649i	0.165424	−	0.0262006i
$534$		0			0
$535$	−269.224	+	230.365i	−0.503222	+	0.430589i
$536$		0			0
$537$	−1283.15	−	203.232i	−2.38949	−	0.378458i
$538$		0			0
$539$	−140.803	+	140.019i	−0.261231	+	0.259775i
$540$		0			0
$541$	−417.605	+	303.408i	−0.771913	+	0.560828i	−0.902541	−	0.430604i	$-0.858301\pi$
$541$	−417.605	+	303.408i	−0.771913	+	0.560828i	0.130628	+	0.991431i	$0.458301\pi$
$542$		0			0
$543$	−538.964	−	1057.78i	−0.992568	−	1.94802i
$544$		0			0
$545$	177.180	−	428.860i	0.325101	−	0.786899i
$546$		0			0
$547$	90.0835	−	176.799i	0.164687	−	0.323216i	−0.793885	−	0.608068i	$-0.791945\pi$
$547$	90.0835	−	176.799i	0.164687	−	0.323216i	0.958571	+	0.284853i	$0.0919447\pi$
$548$		0			0
$549$		−	507.934i		−	0.925198i
$550$		0			0
$551$	−174.918			−0.317455
$552$		0			0
$553$	−196.302	−	100.021i	−0.354976	−	0.180869i
$554$		0			0
$555$	545.590	+	225.406i	0.983046	+	0.406138i
$556$		0			0
$557$	787.805	−	401.407i	1.41437	−	0.720658i	0.431015	−	0.902345i	$-0.358156\pi$
$557$	787.805	−	401.407i	1.41437	−	0.720658i	0.983356	+	0.181687i	$0.0581557\pi$
$558$		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
$563$	−61.7782	+	390.052i	−0.109730	+	0.692811i	0.870084	+	0.492903i	$0.164064\pi$
$563$	−61.7782	+	390.052i	−0.109730	+	0.692811i	−0.979815	+	0.199908i	$0.935936\pi$
$564$		0			0
$565$	86.6001	+	101.208i	0.153275	+	0.179129i
$566$		0			0
$567$	76.7888	+	484.825i	0.135430	+	0.855071i
$568$		0			0
$569$	−104.189	+	33.8529i	−0.183108	+	0.0594955i	−0.399136	−	0.916892i	$-0.630690\pi$
$569$	−104.189	+	33.8529i	−0.183108	+	0.0594955i	0.216028	+	0.976387i	$0.430690\pi$
$570$		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
$575$	−11.2256	+	0.0205385i	−0.0195227	+	3.57191e-5i
$576$		0			0
$577$	61.7893	+	390.122i	0.107087	+	0.676122i	0.981575	+	0.191075i	$0.0611974\pi$
$577$	61.7893	+	390.122i	0.107087	+	0.676122i	−0.874488	+	0.485047i	$0.838803\pi$
$578$		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
$583$	314.299	−	958.198i	0.539107	−	1.64356i
$584$		0			0
$585$	−361.002	+	28.7438i	−0.617097	+	0.0491346i
$586$		0			0
$587$	897.122	−	457.106i	1.52832	−	0.778716i	0.530690	−	0.847566i	$-0.321933\pi$
$587$	897.122	−	457.106i	1.52832	−	0.778716i	0.997627	+	0.0688501i	$0.0219330\pi$
$588$		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
$597$	−209.816	+	411.788i	−0.351451	+	0.689762i
$598$		0			0
$599$	109.173	−	150.263i	0.182258	−	0.250857i	−0.708106	−	0.706106i	$-0.750450\pi$
$599$	109.173	−	150.263i	0.182258	−	0.250857i	0.890364	+	0.455250i	$0.150450\pi$
$600$		0			0
$601$	−97.6385	+	300.500i	−0.162460	+	0.500001i	−0.998840	−	0.0481492i	$-0.984668\pi$
$601$	−97.6385	+	300.500i	−0.162460	+	0.500001i	0.836380	+	0.548150i	$0.184668\pi$
$602$		0			0
$603$	106.600	−	673.046i	0.176783	−	1.11616i
$604$		0			0
$605$	458.205	+	395.061i	0.757363	+	0.652994i
$606$		0			0
$607$	427.903	+	67.7731i	0.704947	+	0.111653i	0.498608	−	0.866828i	$-0.333845\pi$
$607$	427.903	+	67.7731i	0.704947	+	0.111653i	0.206339	+	0.978480i	$0.433845\pi$
$608$		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
$613$	−182.043	−	92.7555i	−0.296970	−	0.151314i	0.299157	−	0.954204i	$-0.403295\pi$
$613$	−182.043	−	92.7555i	−0.296970	−	0.151314i	−0.596127	+	0.802890i	$0.703295\pi$
$614$		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	$-0.859319\pi$
$619$	−856.567	+	278.315i	−1.38379	+	0.449621i	−0.479877	+	0.877336i	$0.659319\pi$
$620$		0			0
$621$	1.34114	+	0.974399i	0.00215965	+	0.00156908i
$622$		0			0
$623$	325.468	+	638.767i	0.522420	+	1.02531i
$624$		0			0
$625$	2.28701	+	624.996i	0.00365921	+	0.999993i
$626$		0			0
$627$	−709.146	−	232.608i	−1.13101	−	0.370985i
$628$		0			0
$629$	−469.401	−	646.075i	−0.746265	−	1.02715i
$630$		0			0
$631$	95.6576	−	294.404i	0.151597	−	0.466567i	−0.846203	−	0.532860i	$-0.821117\pi$
$631$	95.6576	−	294.404i	0.151597	−	0.466567i	0.997800	+	0.0662931i	$0.0211172\pi$
$632$		0			0
$633$	861.798	−	136.495i	1.36145	−	0.215633i
$634$		0			0
$635$	4.84734	−	20.2723i	0.00763360	−	0.0319249i
$636$		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	0.951326	−	0.308187i	$-0.0997223\pi$
$641$	0.345660	+	1.06383i	0.000539251	+	0.00165964i	−0.950787	+	0.309847i	$0.899722\pi$
$642$		0			0
$643$	−267.827	+	42.4197i	−0.416528	+	0.0659715i	−0.361181	−	0.932496i	$-0.617626\pi$
$643$	−267.827	+	42.4197i	−0.416528	+	0.0659715i	−0.0553467	+	0.998467i	$0.517626\pi$
$644$		0			0
$645$	815.947	+	63.4655i	1.26503	+	0.0983960i
$646$		0			0
$647$	−1021.99	−	161.868i	−1.57959	−	0.250183i	−0.695859	−	0.718178i	$-0.744976\pi$
$647$	−1021.99	−	161.868i	−1.57959	−	0.250183i	−0.883731	+	0.467996i	$0.844976\pi$
$648$		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
$653$	66.9709	+	131.438i	0.102559	+	0.201283i	0.936584	−	0.350444i	$-0.113969\pi$
$653$	66.9709	+	131.438i	0.102559	+	0.201283i	−0.834025	+	0.551727i	$0.813969\pi$
$654$		0			0
$655$	885.414	+	365.802i	1.35178	+	0.558476i
$656$		0			0
$657$	402.773	−	790.486i	0.613048	−	1.20318i
$658$		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
$663$	921.091	+	469.320i	1.38928	+	0.707873i
$664$		0			0
$665$	421.383	−	174.994i	0.633659	−	0.263150i
$666$		0			0
$667$	−4.26622	+	2.17375i	−0.00639613	+	0.00325899i
$668$		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
$673$	−48.2694	+	304.761i	−0.0717227	+	0.452839i	0.925524	+	0.378688i	$0.123625\pi$
$673$	−48.2694	+	304.761i	−0.0717227	+	0.452839i	−0.997247	+	0.0741511i	$0.976375\pi$
$674$		0			0
$675$	54.1142	−	74.7691i	0.0801692	−	0.110769i
$676$		0			0
$677$	−25.9409	−	163.784i	−0.0383174	−	0.241927i	0.961094	−	0.276220i	$-0.0890819\pi$
$677$	−25.9409	−	163.784i	−0.0383174	−	0.241927i	−0.999412	+	0.0342936i	$0.989082\pi$
$678$		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
$685$	−201.803	+	843.969i	−0.294603	+	1.23207i
$686$		0			0
$687$	159.044	+	1004.16i	0.231504	+	1.46166i
$688$		0			0
$689$	778.912	+	253.084i	1.13050	+	0.367320i
$690$		0			0
$691$	414.275	−	300.988i	0.599529	−	0.435584i	−0.246182	−	0.969224i	$-0.579176\pi$
$691$	414.275	−	300.988i	0.599529	−	0.435584i	0.845712	+	0.533640i	$0.179176\pi$
$692$		0			0
$693$	−400.557	−	292.735i	−0.578004	−	0.422417i
$694$		0			0
$695$	816.680	+	696.220i	1.17508	+	1.00175i
$696$		0			0
$697$	−249.090	+	126.918i	−0.357375	+	0.182092i
$698$		0			0
$699$	454.389	−	625.412i	0.650055	−	0.894724i
$700$		0			0
$701$	−202.798	−	624.148i	−0.289298	−	0.890368i	−0.985077	−	0.172112i	$-0.944941\pi$
$701$	−202.798	−	624.148i	−0.289298	−	0.890368i	0.695779	−	0.718256i	$-0.255059\pi$
$702$		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
$707$	147.628	−	289.737i	0.208810	−	0.409812i
$708$		0			0
$709$	182.881	−	251.714i	0.257942	−	0.355027i	−0.660331	−	0.750975i	$-0.729584\pi$
$709$	182.881	−	251.714i	0.257942	−	0.355027i	0.918273	+	0.395948i	$0.129584\pi$
$710$		0			0
$711$	−99.2182	+	305.362i	−0.139547	+	0.429483i
$712$		0			0
$713$	−0.0781432	+	0.493377i	−0.000109598	+	0.000691973i
$714$		0			0
$715$	−319.809	+	373.027i	−0.447285	+	0.521715i
$716$		0			0
$717$	−739.461	−	117.119i	−1.03133	−	0.163346i
$718$		0			0
$719$	−694.526	−	225.665i	−0.965960	−	0.313860i	−0.216776	−	0.976221i	$-0.569554\pi$
$719$	−694.526	−	225.665i	−0.965960	−	0.313860i	−0.749184	+	0.662362i	$0.769554\pi$
$720$		0			0
$721$	−70.4290	−	51.1696i	−0.0976823	−	0.0709704i
$722$		0			0
$723$	1026.35	+	522.952i	1.41957	+	0.723308i
$724$		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
$733$	−519.854	−	1020.27i	−0.709215	−	1.39191i	−0.910968	−	0.412476i	$-0.864664\pi$
$733$	−519.854	−	1020.27i	−0.709215	−	1.39191i	0.201754	−	0.979436i	$-0.435336\pi$
$734$		0			0
$735$	−372.148	+	29.6312i	−0.506323	+	0.0403146i
$736$		0			0
$737$	−541.352	−	749.501i	−0.734534	−	1.01696i
$738$		0			0
$739$	650.090	+	894.772i	0.879689	+	1.21079i	0.976507	+	0.215486i	$0.0691335\pi$
$739$	650.090	+	894.772i	0.879689	+	1.21079i	−0.0968179	+	0.995302i	$0.530866\pi$
$740$		0			0
$741$	187.303	−	576.459i	0.252770	−	0.777948i
$742$		0			0
$743$	288.268	−	45.6572i	0.387979	−	0.0614498i	0.0406019	−	0.999175i	$-0.487072\pi$
$743$	288.268	−	45.6572i	0.387979	−	0.0614498i	0.347377	+	0.937726i	$0.387072\pi$
$744$		0			0
$745$	−926.788	+	569.103i	−1.24401	+	0.763897i
$746$		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	0.977205	−	0.212296i	$-0.0680940\pi$
$751$	46.4459	+	142.946i	0.0618454	+	0.190340i	−0.915360	+	0.402636i	$0.868094\pi$
$752$		0			0
$753$	−481.659	+	76.2873i	−0.639653	+	0.101311i
$754$		0			0
$755$	−86.8775	+	1116.95i	−0.115070	+	1.47940i
$756$		0			0
$757$	995.182	+	157.621i	1.31464	+	0.208218i	0.774080	−	0.633087i	$-0.218213\pi$
$757$	995.182	+	157.621i	1.31464	+	0.208218i	0.540559	+	0.841306i	$0.318213\pi$
$758$		0			0
$759$	−20.1867	+	3.13947i	−0.0265964	+	0.00413633i
$760$		0			0
$761$	−380.309	+	276.311i	−0.499750	+	0.363089i	−0.808921	−	0.587917i	$-0.799948\pi$
$761$	−380.309	+	276.311i	−0.499750	+	0.363089i	0.309172	+	0.951006i	$0.399948\pi$
$762$		0			0
$763$	234.385	+	460.006i	0.307188	+	0.602891i
$764$		0			0
$765$	1047.38	−	434.960i	1.36912	−	0.568575i
$766$		0			0
$767$	10.2144	−	20.0469i	0.0133173	−	0.0261368i
$768$		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
$773$	877.540	+	447.129i	1.13524	+	0.578433i	0.917564	−	0.397588i	$-0.130153\pi$
$773$	877.540	+	447.129i	1.13524	+	0.578433i	0.217675	+	0.976021i	$0.430153\pi$
$774$		0			0
$775$	27.4773	+	4.30046i	0.0354546	+	0.00554898i
$776$		0			0
$777$	−585.213	+	298.181i	−0.753170	+	0.383759i
$778$		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
$783$	6.15848	−	38.8831i	0.00786524	−	0.0496592i
$784$		0			0
$785$	142.240	−	121.710i	0.181198	−	0.155044i
$786$		0			0
$787$	184.647	+	1165.82i	0.234622	+	1.48134i	0.770713	+	0.637183i	$0.219900\pi$
$787$	184.647	+	1165.82i	0.234622	+	1.48134i	−0.536091	+	0.844160i	$0.680100\pi$
$788$		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
$795$	1615.61	−	992.081i	2.03221	−	1.24790i
$796$		0			0
$797$	62.8153	+	396.600i	0.0788147	+	0.497616i	0.995243	+	0.0974186i	$0.0310586\pi$
$797$	62.8153	+	396.600i	0.0788147	+	0.497616i	−0.916429	+	0.400198i	$0.868941\pi$
$798$		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
$803$	−368.770	−	1145.84i	−0.459240	−	1.42695i
$804$		0			0
$805$	8.10279	−	9.50474i	0.0100656	−	0.0118071i
$806$		0			0
$807$	−950.820	+	484.467i	−1.17822	+	0.600331i
$808$		0			0
$809$	210.983	−	290.393i	0.260794	−	0.358953i	−0.658461	−	0.752615i	$-0.728792\pi$
$809$	210.983	−	290.393i	0.260794	−	0.358953i	0.919255	+	0.393662i	$0.128792\pi$
$810$		0			0
$811$	40.8440	+	125.705i	0.0503625	+	0.155000i	0.973075	−	0.230489i	$-0.0740327\pi$
$811$	40.8440	+	125.705i	0.0503625	+	0.155000i	−0.922712	+	0.385489i	$0.874033\pi$
$812$		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
$817$	−294.712	+	578.404i	−0.360724	+	0.707961i
$818$		0			0
$819$	236.835	−	325.976i	0.289176	−	0.398017i
$820$		0			0
$821$	−319.821	+	984.308i	−0.389551	+	1.19891i	0.543574	+	0.839361i	$0.317071\pi$
$821$	−319.821	+	984.308i	−0.389551	+	1.19891i	−0.933125	+	0.359553i	$0.882929\pi$
$822$		0			0
$823$	160.739	−	1014.87i	0.195309	−	1.23313i	−0.673950	−	0.738777i	$-0.735404\pi$
$823$	160.739	−	1014.87i	0.195309	−	1.23313i	0.869259	−	0.494356i	$-0.164596\pi$
$824$		0			0
$825$	176.850	+	1123.60i	0.214364	+	1.36194i
$826$		0			0
$827$	1532.90	+	242.787i	1.85357	+	0.293576i	0.980866	−	0.194683i	$-0.0623677\pi$
$827$	1532.90	+	242.787i	1.85357	+	0.293576i	0.872699	+	0.488259i	$0.162368\pi$
$828$		0			0
$829$	646.186	+	209.959i	0.779476	+	0.253267i	0.671617	−	0.740899i	$-0.265600\pi$
$829$	646.186	+	209.959i	0.779476	+	0.253267i	0.107860	+	0.994166i	$0.465600\pi$
$830$		0			0
$831$	1766.32	+	1283.31i	2.12554	+	1.54429i
$832$		0			0
$833$	449.994	+	229.283i	0.540209	+	0.275250i
$834$		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	$-0.479370\pi$
$839$	590.414	−	191.837i	0.703711	−	0.228650i	0.638947	+	0.769251i	$0.279370\pi$
$840$		0			0
$841$	−588.393	−	427.492i	−0.699635	−	0.508314i
$842$		0			0
$843$	−104.376	−	204.849i	−0.123815	−	0.243000i
$844$		0			0
$845$	339.366	+	289.310i	0.401617	+	0.342378i
$846$		0			0
$847$	−665.425	+	101.585i	−0.785625	+	0.119935i
$848$		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
$853$	1176.84	−	186.393i	1.37964	−	0.218514i	0.577864	−	0.816133i	$-0.303886\pi$
$853$	1176.84	−	186.393i	1.37964	−	0.218514i	0.801781	+	0.597619i	$0.203886\pi$
$854$		0			0
$855$	−347.956	−	566.649i	−0.406967	−	0.662747i
$856$		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
$863$	−48.8907	+	7.74352i	−0.0566520	+	0.00897279i	−0.184696	−	0.982796i	$-0.559130\pi$
$863$	−48.8907	+	7.74352i	−0.0566520	+	0.00897279i	0.128044	+	0.991768i	$0.459130\pi$
$864$		0			0
$865$	535.992	+	626.405i	0.619644	+	0.724168i
$866$		0			0
$867$	−2016.89	−	319.445i	−2.32629	−	0.368448i
$868$		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
$873$	−383.108	−	751.891i	−0.438841	−	0.861273i
$874$		0			0
$875$	−530.014	−	450.165i	−0.605730	−	0.514474i
$876$		0			0
$877$	314.639	−	617.514i	0.358768	−	0.704121i	−0.639118	−	0.769108i	$-0.720701\pi$
$877$	314.639	−	617.514i	0.358768	−	0.704121i	0.997886	+	0.0649870i	$0.0207006\pi$
$878$		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
$883$	−1397.11	−	711.863i	−1.58223	−	0.806187i	−0.582255	−	0.813006i	$-0.697829\pi$
$883$	−1397.11	−	711.863i	−1.58223	−	0.806187i	−0.999977	+	0.00681890i	$0.997829\pi$
$884$		0			0
$885$	−19.9754	−	48.1005i	−0.0225711	−	0.0543508i
$886$		0			0
$887$	−613.475	+	312.581i	−0.691629	+	0.352403i	−0.764217	−	0.644959i	$-0.776874\pi$
$887$	−613.475	+	312.581i	−0.691629	+	0.352403i	0.0725877	+	0.997362i	$0.476874\pi$
$888$		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
$893$	145.480	−	918.524i	0.162911	−	1.02858i
$894$		0			0
$895$	−1565.77	−	121.787i	−1.74946	−	0.136075i
$896$		0			0
$897$	−2.59552	−	16.3874i	−0.00289355	−	0.0182692i
$898$		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
$905$	−750.973	−	1222.96i	−0.829804	−	1.35134i
$906$		0			0
$907$	−139.422	−	880.279i	−0.153718	−	0.970539i	−0.937116	−	0.349018i	$-0.886515\pi$
$907$	−139.422	−	880.279i	−0.153718	−	0.970539i	0.783398	−	0.621521i	$-0.213485\pi$
$908$		0			0
$909$	−450.707	−	146.444i	−0.495828	−	0.161104i
$910$		0			0
$911$	1003.91	−	729.382i	1.10198	−	0.800639i	0.120602	−	0.992701i	$-0.461517\pi$
$911$	1003.91	−	729.382i	1.10198	−	0.800639i	0.981383	+	0.192062i	$0.0615175\pi$
$912$		0			0
$913$	−1510.80	−	4.22043i	−1.65477	−	0.00462260i
$914$		0			0
$915$	−102.837	−	1291.56i	−0.112390	−	1.41154i
$916$		0			0
$917$	−949.716	+	483.905i	−1.03568	+	0.527704i
$918$		0			0
$919$	230.134	−	316.753i	0.250418	−	0.344671i	−0.665239	−	0.746630i	$-0.731671\pi$
$919$	230.134	−	316.753i	0.250418	−	0.344671i	0.915658	+	0.401959i	$0.131671\pi$
$920$		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
$927$	−57.5978	+	113.042i	−0.0621335	+	0.121944i
$928$		0			0
$929$	340.328	−	468.421i	0.366338	−	0.504221i	−0.585563	−	0.810627i	$-0.699127\pi$
$929$	340.328	−	468.421i	0.366338	−	0.504221i	0.951901	+	0.306406i	$0.0991266\pi$
$930$		0			0
$931$	91.5057	−	281.626i	0.0982876	−	0.302498i
$932$		0			0
$933$	156.196	−	986.180i	0.167412	−	1.05700i
$934$		0			0
$935$	591.517	−	1420.49i	0.632638	−	1.51924i
$936$		0			0
$937$	650.056	+	102.959i	0.693763	+	0.109881i	0.493351	−	0.869830i	$-0.335772\pi$
$937$	650.056	+	102.959i	0.693763	+	0.109881i	0.200412	+	0.979712i	$0.435772\pi$
$938$		0			0
$939$	−219.742	−	71.3984i	−0.234017	−	0.0760366i
$940$		0			0
$941$	−399.074	−	289.944i	−0.424096	−	0.308124i	0.355188	−	0.934795i	$-0.384417\pi$
$941$	−399.074	−	289.944i	−0.424096	−	0.308124i	−0.779284	+	0.626671i	$0.784417\pi$
$942$		0			0
$943$	3.99785	+	2.03700i	0.00423950	+	0.00216013i
$944$		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
$953$	253.504	+	497.529i	0.266006	+	0.522067i	0.984915	−	0.173038i	$-0.0553582\pi$
$953$	253.504	+	497.529i	0.266006	+	0.522067i	−0.718909	+	0.695104i	$0.755358\pi$
$954$		0			0
$955$	−326.034	+	382.445i	−0.341397	+	0.400466i
$956$		0			0
$957$	284.067	+	393.291i	0.296831	+	0.410962i
$958$		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
$963$	−567.465	+	89.8777i	−0.589268	+	0.0933309i
$964$		0			0
$965$	−1106.11	−	264.482i	−1.14622	−	0.274075i
$966$		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	0.930328	−	0.366729i	$-0.119522\pi$
$971$	−36.7825	−	113.205i	−0.0378811	−	0.116586i	−0.968209	+	0.250143i	$0.919522\pi$
$972$		0			0
$973$	−1179.33	+	186.787i	−1.21205	+	0.191970i
$974$		0			0
$975$	−912.126	+	146.178i	−0.935514	+	0.149926i
$976$		0			0
$977$	−56.9404	−	9.01848i	−0.0582809	−	0.00923078i	0.127226	−	0.991874i	$-0.459393\pi$
$977$	−56.9404	−	9.01848i	−0.0582809	−	0.00923078i	−0.185507	+	0.982643i	$0.559393\pi$
$978$		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
$983$	378.676	+	743.194i	0.385225	+	0.756047i	0.999453	−	0.0330819i	$-0.0105322\pi$
$983$	378.676	+	743.194i	0.385225	+	0.756047i	−0.614227	+	0.789129i	$0.710532\pi$
$984$		0			0
$985$	337.111	+	811.756i	0.342244	+	0.824118i
$986$		0			0
$987$	592.223	−	1162.30i	0.600023	−	1.17761i
$988$		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
$993$	−92.3384	−	47.0488i	−0.0929893	−	0.0473804i
$994$		0			0
$995$	−213.329	+	516.357i	−0.214401	+	0.518952i
$996$		0			0
$997$	1193.22	−	607.975i	1.19681	−	0.609804i	0.262038	−	0.965058i	$-0.415606\pi$
$997$	1193.22	−	607.975i	1.19681	−	0.609804i	0.934770	+	0.355254i	$0.115606\pi$
$998$		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.157.11	yes	96
5.3	odd	4	inner	220.3.x.a.113.2	yes	96
11.4	even	5	inner	220.3.x.a.37.2	✓	96
55.48	odd	20	inner	220.3.x.a.213.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.2	✓	96	11.4	even	5	inner
220.3.x.a.113.2	yes	96	5.3	odd	4	inner
220.3.x.a.157.11	yes	96	1.1	even	1	trivial
220.3.x.a.213.11	yes	96	55.48	odd	20	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)

\(f(q)\)	\(=\)	\(q+(3.68530 + 1.87775i) q^{3} +(4.62115 + 1.90919i) q^{5} +(-4.95675 + 2.52559i) q^{7} +(4.76541 + 6.55902i) q^{9} +(10.8597 + 1.75112i) q^{11} +(-1.39753 + 8.82368i) q^{13} +(13.4453 + 15.7133i) q^{15} +(-4.37656 - 27.6325i) q^{17} +(-15.6008 + 5.06901i) q^{19} -23.0096 q^{21} +(-0.317508 + 0.317508i) q^{23} +(17.7100 + 17.6453i) q^{25} +(-0.577539 - 3.64643i) q^{27} +(10.1414 + 3.29515i) q^{29} +(0.900009 - 0.653895i) q^{31} +(36.7332 + 26.8453i) q^{33} +(-27.7277 + 2.20774i) q^{35} +(25.4335 - 12.9590i) q^{37} +(-21.7190 + 29.8937i) q^{39} +(-3.08786 - 9.50347i) q^{41} +(27.9830 - 27.9830i) q^{43} +(9.49923 + 39.4083i) q^{45} +(-25.7381 + 50.5139i) q^{47} +(-10.6107 + 14.6044i) q^{49} +(35.7581 - 110.052i) q^{51} +(14.3412 - 90.5466i) q^{53} +(46.8411 + 28.8255i) q^{55} +(-67.0120 - 10.6137i) q^{57} +(-2.39521 - 0.778250i) q^{59} +(-50.6854 - 36.8251i) q^{61} +(-40.1864 - 20.4760i) q^{63} +(-23.3043 + 38.1073i) q^{65} +(-59.4330 - 59.4330i) q^{67} +(-1.76631 + 0.573910i) q^{69} +(110.315 + 80.1487i) q^{71} +(-49.6796 - 97.5018i) q^{73} +(32.1331 + 98.2832i) q^{75} +(-58.2516 + 18.7473i) q^{77} +(23.2780 + 32.0394i) q^{79} +(27.2666 - 83.9181i) q^{81} +(-135.655 + 21.4857i) q^{83} +(32.5310 - 136.049i) q^{85} +(31.1867 + 31.1867i) q^{87} -128.868i q^{89} +(-15.3578 - 47.2664i) q^{91} +(4.54466 - 0.719803i) q^{93} +(-81.7713 - 6.36028i) q^{95} +(-102.805 - 16.2826i) q^{97} +(40.2654 + 79.5740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 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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