LMFDB - Embedded newform 220.3.x.a.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(37,220)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

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

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	220.157
Dual form			220.3.x.a.213.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.64938 - 1.34992i) q^{3} +(-4.68210 - 1.75440i) q^{5} +(7.03139 - 3.58267i) q^{7} +(-0.0931732 - 0.128242i) q^{9} +(-6.18826 + 9.09425i) q^{11} +(-2.37948 + 15.0235i) q^{13} +(10.0363 + 10.9686i) q^{15} +(0.343110 + 2.16631i) q^{17} +(-19.4291 + 6.31290i) q^{19} -23.4651 q^{21} +(-26.5643 + 26.5643i) q^{23} +(18.8441 + 16.4286i) q^{25} +(4.26010 + 26.8972i) q^{27} +(-7.54043 - 2.45004i) q^{29} +(19.0407 - 13.8339i) q^{31} +(28.6716 - 15.7404i) q^{33} +(-39.2071 + 4.43853i) q^{35} +(45.3507 - 23.1073i) q^{37} +(26.5847 - 36.5906i) q^{39} +(-16.8469 - 51.8496i) q^{41} +(-37.5264 + 37.5264i) q^{43} +(0.211258 + 0.763905i) q^{45} +(-32.7034 + 64.1840i) q^{47} +(7.80344 - 10.7405i) q^{49} +(2.01533 - 6.20255i) q^{51} +(5.18513 - 32.7376i) q^{53} +(44.9291 - 31.7235i) q^{55} +(59.9970 + 9.50259i) q^{57} +(-68.0751 - 22.1189i) q^{59} +(-43.1118 - 31.3225i) q^{61} +(-1.11459 - 0.567910i) q^{63} +(37.4982 - 66.1667i) q^{65} +(2.89959 + 2.89959i) q^{67} +(106.238 - 34.5190i) q^{69} +(44.2385 + 32.1412i) q^{71} +(-1.06243 - 2.08514i) q^{73} +(-27.7478 - 68.9637i) q^{75} +(-10.9304 + 86.1158i) q^{77} +(-52.5752 - 72.3635i) q^{79} +(24.5818 - 75.6549i) q^{81} +(61.9680 - 9.81477i) q^{83} +(2.19411 - 10.7449i) q^{85} +(16.6701 + 16.6701i) q^{87} -36.0140i q^{89} +(37.0931 + 114.161i) q^{91} +(-69.1207 + 10.9476i) q^{93} +(102.044 + 4.52889i) q^{95} +(7.88225 + 1.24843i) q^{97} +(1.74284 - 0.0537454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.64938	−	1.34992i	−0.883125	−	0.449975i	−0.0472428	−	0.998883i	$-0.515043\pi$
$3$	−2.64938	−	1.34992i	−0.883125	−	0.449975i	−0.835882	+	0.548909i	$0.815043\pi$
$4$		0			0
$5$	−4.68210	−	1.75440i	−0.936420	−	0.350881i
$5$	−4.68210	−	1.75440i	−0.936420	−	0.350881i
$6$		0			0
$7$	7.03139	−	3.58267i	1.00448	−	0.511810i	0.127249	−	0.991871i	$-0.459385\pi$
$7$	7.03139	−	3.58267i	1.00448	−	0.511810i	0.877235	+	0.480060i	$0.159385\pi$
$8$		0			0
$9$	−0.0931732	−	0.128242i	−0.0103526	−	0.0142491i
$10$		0			0
$11$	−6.18826	+	9.09425i	−0.562570	+	0.826750i
$11$	−6.18826	+	9.09425i	−0.562570	+	0.826750i
$12$		0			0
$13$	−2.37948	+	15.0235i	−0.183037	+	1.15565i	0.709510	+	0.704696i	$0.248916\pi$
$13$	−2.37948	+	15.0235i	−0.183037	+	1.15565i	−0.892547	+	0.450955i	$0.851084\pi$
$14$		0			0
$15$	10.0363	+	10.9686i	0.669089	+	0.731237i
$16$		0			0
$17$	0.343110	+	2.16631i	0.0201830	+	0.127430i	0.995723	−	0.0923935i	$-0.0294518\pi$
$17$	0.343110	+	2.16631i	0.0201830	+	0.127430i	−0.975540	+	0.219824i	$0.929452\pi$
$18$		0			0
$19$	−19.4291	+	6.31290i	−1.02259	+	0.332258i	−0.771855	−	0.635799i	$-0.780671\pi$
$19$	−19.4291	+	6.31290i	−1.02259	+	0.332258i	−0.250730	+	0.968057i	$0.580671\pi$
$20$		0			0
$21$	−23.4651			−1.11739
$22$		0			0
$23$	−26.5643	+	26.5643i	−1.15497	+	1.15497i	−0.169425	+	0.985543i	$0.554191\pi$
$23$	−26.5643	+	26.5643i	−1.15497	+	1.15497i	−0.985543	+	0.169425i	$0.945809\pi$
$24$		0			0
$25$	18.8441	+	16.4286i	0.753765	+	0.657144i
$26$		0			0
$27$	4.26010	+	26.8972i	0.157782	+	0.996194i
$28$		0			0
$29$	−7.54043	−	2.45004i	−0.260015	−	0.0844840i	0.176109	−	0.984371i	$-0.443649\pi$
$29$	−7.54043	−	2.45004i	−0.260015	−	0.0844840i	−0.436124	+	0.899887i	$0.643649\pi$
$30$		0			0
$31$	19.0407	−	13.8339i	0.614217	−	0.446255i	−0.236680	−	0.971588i	$-0.576059\pi$
$31$	19.0407	−	13.8339i	0.614217	−	0.446255i	0.850897	+	0.525333i	$0.176059\pi$
$32$		0			0
$33$	28.6716	−	15.7404i	0.868836	−	0.476982i
$34$		0			0
$35$	−39.2071	+	4.43853i	−1.12020	+	0.126815i
$36$		0			0
$37$	45.3507	−	23.1073i	1.22569	−	0.624522i	0.283301	−	0.959031i	$-0.408570\pi$
$37$	45.3507	−	23.1073i	1.22569	−	0.624522i	0.942393	+	0.334509i	$0.108570\pi$
$38$		0			0
$39$	26.5847	−	36.5906i	0.681658	−	0.938222i
$40$		0			0
$41$	−16.8469	−	51.8496i	−0.410901	−	1.26462i	−0.915866	−	0.401484i	$-0.868495\pi$
$41$	−16.8469	−	51.8496i	−0.410901	−	1.26462i	0.504965	−	0.863140i	$-0.331505\pi$
$42$		0			0
$43$	−37.5264	+	37.5264i	−0.872707	+	0.872707i	−0.992767	−	0.120060i	$-0.961691\pi$
$43$	−37.5264	+	37.5264i	−0.872707	+	0.872707i	0.120060	+	0.992767i	$0.461691\pi$
$44$		0			0
$45$	0.211258	+	0.763905i	0.00469462	+	0.0169757i
$46$		0			0
$47$	−32.7034	+	64.1840i	−0.695816	+	1.36562i	0.224513	+	0.974471i	$0.427921\pi$
$47$	−32.7034	+	64.1840i	−0.695816	+	1.36562i	−0.920329	+	0.391145i	$0.872079\pi$
$48$		0			0
$49$	7.80344	−	10.7405i	0.159254	−	0.219194i
$50$		0			0
$51$	2.01533	−	6.20255i	0.0395163	−	0.121619i
$52$		0			0
$53$	5.18513	−	32.7376i	0.0978326	−	0.617690i	−0.889243	−	0.457435i	$-0.848768\pi$
$53$	5.18513	−	32.7376i	0.0978326	−	0.617690i	0.987076	−	0.160255i	$-0.0512318\pi$
$54$		0			0
$55$	44.9291	−	31.7235i	0.816892	−	0.576790i
$56$		0			0
$57$	59.9970	+	9.50259i	1.05258	+	0.166712i
$58$		0			0
$59$	−68.0751	−	22.1189i	−1.15382	−	0.374897i	−0.331236	−	0.943548i	$-0.607466\pi$
$59$	−68.0751	−	22.1189i	−1.15382	−	0.374897i	−0.822579	+	0.568651i	$0.807466\pi$
$60$		0			0
$61$	−43.1118	−	31.3225i	−0.706750	−	0.513484i	0.175374	−	0.984502i	$-0.443887\pi$
$61$	−43.1118	−	31.3225i	−0.706750	−	0.513484i	−0.882124	+	0.471018i	$0.843887\pi$
$62$		0			0
$63$	−1.11459	−	0.567910i	−0.0176918	−	0.00901444i
$64$		0			0
$65$	37.4982	−	66.1667i	0.576895	−	1.01795i
$66$		0			0
$67$	2.89959	+	2.89959i	0.0432774	+	0.0432774i	0.728414	−	0.685137i	$-0.240258\pi$
$67$	2.89959	+	2.89959i	0.0432774	+	0.0432774i	−0.685137	+	0.728414i	$0.740258\pi$
$68$		0			0
$69$	106.238	−	34.5190i	1.53969	−	0.500275i
$70$		0			0
$71$	44.2385	+	32.1412i	0.623078	+	0.452693i	0.853995	−	0.520281i	$-0.174173\pi$
$71$	44.2385	+	32.1412i	0.623078	+	0.452693i	−0.230917	+	0.972973i	$0.574173\pi$
$72$		0			0
$73$	−1.06243	−	2.08514i	−0.0145539	−	0.0285636i	0.883615	−	0.468214i	$-0.155102\pi$
$73$	−1.06243	−	2.08514i	−0.0145539	−	0.0285636i	−0.898169	+	0.439650i	$0.855102\pi$
$74$		0			0
$75$	−27.7478	−	68.9637i	−0.369971	−	0.919516i
$76$		0			0
$77$	−10.9304	+	86.1158i	−0.141953	+	1.11839i
$78$		0			0
$79$	−52.5752	−	72.3635i	−0.665508	−	0.915994i	0.334140	−	0.942524i	$-0.391554\pi$
$79$	−52.5752	−	72.3635i	−0.665508	−	0.915994i	−0.999648	+	0.0265298i	$0.991554\pi$
$80$		0			0
$81$	24.5818	−	75.6549i	0.303478	−	0.934011i
$82$		0			0
$83$	61.9680	−	9.81477i	0.746602	−	0.118250i	0.228470	−	0.973551i	$-0.426628\pi$
$83$	61.9680	−	9.81477i	0.746602	−	0.118250i	0.518132	+	0.855301i	$0.326628\pi$
$84$		0			0
$85$	2.19411	−	10.7449i	0.0258131	−	0.126410i
$86$		0			0
$87$	16.6701	+	16.6701i	0.191610	+	0.191610i
$88$		0			0
$89$		−	36.0140i		−	0.404652i	−0.979318	−	0.202326i	$-0.935150\pi$
$89$		−	36.0140i		−	0.404652i	0.979318	−	0.202326i	$-0.0648501\pi$
$90$		0			0
$91$	37.0931	+	114.161i	0.407616	+	1.25451i
$92$		0			0
$93$	−69.1207	+	10.9476i	−0.743234	+	0.117717i
$94$		0			0
$95$	102.044	+	4.52889i	1.07415	+	0.0476725i
$96$		0			0
$97$	7.88225	+	1.24843i	0.0812603	+	0.0128704i	0.196932	−	0.980417i	$-0.436902\pi$
$97$	7.88225	+	1.24843i	0.0812603	+	0.0128704i	−0.115672	+	0.993287i	$0.536902\pi$
$98$		0			0
$99$	1.74284	−	0.0537454i	0.0176045	−	0.000542883i
$100$		0			0
$101$	−149.483	+	108.606i	−1.48003	+	1.07531i	−0.502487	+	0.864585i	$0.667581\pi$
$101$	−149.483	+	108.606i	−1.48003	+	1.07531i	−0.977546	+	0.210722i	$0.932419\pi$
$102$		0			0
$103$	−76.8415	−	150.810i	−0.746034	−	1.46417i	−0.880896	−	0.473310i	$-0.843059\pi$
$103$	−76.8415	−	150.810i	−0.746034	−	1.46417i	0.134862	−	0.990864i	$-0.456941\pi$
$104$		0			0
$105$	109.866	+	41.1673i	1.04634	+	0.392070i
$106$		0			0
$107$	−20.7782	+	40.7795i	−0.194189	+	0.381117i	−0.967485	−	0.252928i	$-0.918606\pi$
$107$	−20.7782	+	40.7795i	−0.194189	+	0.381117i	0.773296	+	0.634045i	$0.218606\pi$
$108$		0			0
$109$			208.005i			1.90830i	0.299322	+	0.954152i	$0.403240\pi$
$109$			208.005i			1.90830i	−0.299322	+	0.954152i	$0.596760\pi$
$110$		0			0
$111$	−151.344			−1.36346
$112$		0			0
$113$	−37.7122	−	19.2153i	−0.333736	−	0.170047i	0.279090	−	0.960265i	$-0.409967\pi$
$113$	−37.7122	−	19.2153i	−0.333736	−	0.170047i	−0.612826	+	0.790218i	$0.709967\pi$
$114$		0			0
$115$	170.981	−	77.7721i	1.48679	−	0.676279i
$116$		0			0
$117$	2.14834	−	1.09463i	0.0183619	−	0.00935584i
$118$		0			0
$119$	10.1737	+	14.0029i	0.0854936	+	0.117672i
$120$		0			0
$121$	−44.4108	−	112.555i	−0.367031	−	0.930209i
$122$		0			0
$123$	−25.3591	+	160.111i	−0.206172	+	1.30172i
$124$		0			0
$125$	−59.4077	−	109.981i	−0.475262	−	0.879845i
$126$		0			0
$127$	14.2156	+	89.7535i	0.111934	+	0.706721i	0.978282	+	0.207280i	$0.0664611\pi$
$127$	14.2156	+	89.7535i	0.111934	+	0.706721i	−0.866348	+	0.499441i	$0.833539\pi$
$128$		0			0
$129$	150.079	−	48.7637i	1.16341	−	0.378013i
$130$		0			0
$131$	−177.199			−1.35267			−0.676333	−	0.736596i	$-0.736432\pi$
$131$	−177.199			−1.35267			−0.676333	+	0.736596i	$0.736432\pi$
$132$		0			0
$133$	−113.997	+	113.997i	−0.857118	+	0.857118i
$134$		0			0
$135$	27.2424	−	133.409i	0.201796	−	0.988218i
$136$		0			0
$137$	14.9198	+	94.2000i	0.108904	+	0.687592i	0.980375	+	0.197144i	$0.0631667\pi$
$137$	14.9198	+	94.2000i	0.108904	+	0.687592i	−0.871471	+	0.490448i	$0.836833\pi$
$138$		0			0
$139$	65.8473	+	21.3951i	0.473722	+	0.153922i	0.536141	−	0.844128i	$-0.319882\pi$
$139$	65.8473	+	21.3951i	0.473722	+	0.153922i	−0.0624192	+	0.998050i	$0.519882\pi$
$140$		0			0
$141$	173.287	−	125.900i	1.22899	−	0.892910i
$142$		0			0
$143$	−121.902	−	114.609i	−0.852463	−	0.801459i
$144$		0			0
$145$	31.0067	+	24.7003i	0.213839	+	0.170347i
$146$		0			0
$147$	−35.1731	+	17.9216i	−0.239273	+	0.121916i
$148$		0			0
$149$	91.5925	−	126.066i	0.614715	−	0.846083i	−0.382240	−	0.924063i	$-0.624847\pi$
$149$	91.5925	−	126.066i	0.614715	−	0.846083i	0.996955	+	0.0779806i	$0.0248472\pi$
$150$		0			0
$151$	7.29942	+	22.4653i	0.0483405	+	0.148777i	0.972313	−	0.233682i	$-0.0750774\pi$
$151$	7.29942	+	22.4653i	0.0483405	+	0.148777i	−0.923973	+	0.382459i	$0.875077\pi$
$152$		0			0
$153$	0.245843	−	0.245843i	0.00160682	−	0.00160682i
$154$		0			0
$155$	−113.421	+	31.3665i	−0.731747	+	0.202365i
$156$		0			0
$157$	14.3514	−	28.1663i	0.0914104	−	0.179403i	−0.840774	−	0.541385i	$-0.817900\pi$
$157$	14.3514	−	28.1663i	0.0914104	−	0.179403i	0.932185	+	0.361982i	$0.117900\pi$
$158$		0			0
$159$	−57.9306	+	79.7346i	−0.364343	+	0.501476i
$160$		0			0
$161$	−91.6127	+	281.955i	−0.569023	+	1.75127i
$162$		0			0
$163$	−36.0420	+	227.560i	−0.221116	+	1.39607i	0.588207	+	0.808710i	$0.299834\pi$
$163$	−36.0420	+	227.560i	−0.221116	+	1.39607i	−0.809323	+	0.587363i	$0.800166\pi$
$164$		0			0
$165$	−161.858	+	23.3965i	−0.980959	+	0.141797i
$166$		0			0
$167$	−79.6950	−	12.6224i	−0.477216	−	0.0755835i	−0.0868069	−	0.996225i	$-0.527666\pi$
$167$	−79.6950	−	12.6224i	−0.477216	−	0.0755835i	−0.390409	+	0.920642i	$0.627666\pi$
$168$		0			0
$169$	−59.3137	−	19.2722i	−0.350969	−	0.114037i
$170$		0			0
$171$	2.61985	+	1.90343i	0.0153208	+	0.0111312i
$172$		0			0
$173$	81.4089	+	41.4799i	0.470572	+	0.239768i	0.673162	−	0.739495i	$-0.264936\pi$
$173$	81.4089	+	41.4799i	0.470572	+	0.239768i	−0.202590	+	0.979264i	$0.564936\pi$
$174$		0			0
$175$	191.359	+	48.0035i	1.09348	+	0.274306i
$176$		0			0
$177$	150.498	+	150.498i	0.850269	+	0.850269i
$178$		0			0
$179$	−56.9862	+	18.5159i	−0.318359	+	0.103441i	−0.463837	−	0.885920i	$-0.653528\pi$
$179$	−56.9862	+	18.5159i	−0.318359	+	0.103441i	0.145479	+	0.989361i	$0.453528\pi$
$180$		0			0
$181$	−168.899	−	122.712i	−0.933143	−	0.677968i	0.0136175	−	0.999907i	$-0.495665\pi$
$181$	−168.899	−	122.712i	−0.933143	−	0.677968i	−0.946760	+	0.321939i	$0.895665\pi$
$182$		0			0
$183$	71.9362	+	141.183i	0.393094	+	0.771490i
$184$		0			0
$185$	−252.876	+	28.6274i	−1.36690	+	0.154743i
$186$		0			0
$187$	−21.8243	−	10.2854i	−0.116707	−	0.0550021i
$188$		0			0
$189$	126.318	+	173.862i	0.668351	+	0.919907i
$190$		0			0
$191$	−19.9880	+	61.5168i	−0.104649	+	0.322078i	−0.989648	−	0.143516i	$-0.954159\pi$
$191$	−19.9880	+	61.5168i	−0.104649	+	0.322078i	0.884999	+	0.465594i	$0.154159\pi$
$192$		0			0
$193$	268.577	−	42.5384i	1.39159	−	0.220406i	0.584769	−	0.811200i	$-0.301185\pi$
$193$	268.577	−	42.5384i	1.39159	−	0.220406i	0.806823	+	0.590794i	$0.201185\pi$
$194$		0			0
$195$	−188.667	+	124.681i	−0.967522	+	0.639389i
$196$		0			0
$197$	−152.219	−	152.219i	−0.772686	−	0.772686i	0.205890	−	0.978575i	$-0.433991\pi$
$197$	−152.219	−	152.219i	−0.772686	−	0.772686i	−0.978575	+	0.205890i	$0.933991\pi$
$198$		0			0
$199$			150.100i			0.754269i	0.926159	+	0.377135i	$0.123091\pi$
$199$			150.100i			0.754269i	−0.926159	+	0.377135i	$0.876909\pi$
$200$		0			0
$201$	−3.76787	−	11.5963i	−0.0187456	−	0.0576931i
$202$		0			0
$203$	−61.7974	+	9.78775i	−0.304421	+	0.0482155i
$204$		0			0
$205$	−12.0860	+	272.321i	−0.0589562	+	1.32840i
$206$		0			0
$207$	5.88173	+	0.931574i	0.0284141	+	0.00450036i
$208$		0			0
$209$	62.8214	−	215.759i	0.300581	−	1.03234i
$210$		0			0
$211$	249.829	−	181.511i	1.18402	−	0.860244i	0.191404	−	0.981511i	$-0.438696\pi$
$211$	249.829	−	181.511i	1.18402	−	0.860244i	0.992620	+	0.121267i	$0.0386958\pi$
$212$		0			0
$213$	−73.8163	−	144.873i	−0.346556	−	0.680154i
$214$		0			0
$215$	241.539	−	109.866i	1.12344	−	0.511004i
$216$		0			0
$217$	84.3204	−	165.488i	0.388573	−	0.762618i
$218$		0			0
$219$			6.95853i			0.0317741i
$220$		0			0
$221$	−33.3619			−0.150959
$222$		0			0
$223$	106.362	+	54.1939i	0.476958	+	0.243022i	0.675906	−	0.736988i	$-0.263753\pi$
$223$	106.362	+	54.1939i	0.476958	+	0.243022i	−0.198948	+	0.980010i	$0.563753\pi$
$224$		0			0
$225$	0.351067	−	3.94731i	0.00156030	−	0.0175436i
$226$		0			0
$227$	188.221	−	95.9036i	0.829169	−	0.422483i	0.0127332	−	0.999919i	$-0.495947\pi$
$227$	188.221	−	95.9036i	0.829169	−	0.422483i	0.816436	+	0.577436i	$0.195947\pi$
$228$		0			0
$229$	−251.849	−	346.641i	−1.09978	−	1.51371i	−0.835678	−	0.549219i	$-0.814925\pi$
$229$	−251.849	−	346.641i	−1.09978	−	1.51371i	−0.264100	−	0.964495i	$-0.585075\pi$
$230$		0			0
$231$	145.208	−	213.398i	0.628608	−	0.923800i
$232$		0			0
$233$	16.0897	−	101.586i	0.0690546	−	0.435994i	−0.928803	−	0.370573i	$-0.879161\pi$
$233$	16.0897	−	101.586i	0.0690546	−	0.435994i	0.997858	−	0.0654202i	$-0.0208388\pi$
$234$		0			0
$235$	265.725	−	243.141i	1.13075	−	1.03464i
$236$		0			0
$237$	41.6061	+	262.691i	0.175553	+	1.10840i
$238$		0			0
$239$	−407.279	+	132.333i	−1.70410	+	0.553695i	−0.989333	−	0.145672i	$-0.953466\pi$
$239$	−407.279	+	132.333i	−1.70410	+	0.553695i	−0.714764	+	0.699366i	$0.753466\pi$
$240$		0			0
$241$	60.3944			0.250599			0.125300	−	0.992119i	$-0.460011\pi$
$241$	60.3944			0.250599			0.125300	+	0.992119i	$0.460011\pi$
$242$		0			0
$243$	6.05202	−	6.05202i	0.0249054	−	0.0249054i
$244$		0			0
$245$	−55.3797	+	36.5978i	−0.226040	+	0.149379i
$246$		0			0
$247$	−48.6104	−	306.914i	−0.196803	−	1.24257i
$248$		0			0
$249$	−177.426	−	57.6491i	−0.712553	−	0.231522i
$250$		0			0
$251$	368.024	−	267.385i	1.46623	−	1.06528i	0.484545	−	0.874766i	$-0.338985\pi$
$251$	368.024	−	267.385i	1.46623	−	1.06528i	0.981685	−	0.190513i	$-0.0610150\pi$
$252$		0			0
$253$	−77.1954	−	405.969i	−0.305120	−	1.60462i
$254$		0			0
$255$	−20.3178	+	25.5053i	−0.0796775	+	0.100021i
$256$		0			0
$257$	−67.4972	+	34.3916i	−0.262635	+	0.133819i	−0.580350	−	0.814367i	$-0.697084\pi$
$257$	−67.4972	+	34.3916i	−0.262635	+	0.133819i	0.317715	+	0.948186i	$0.397084\pi$
$258$		0			0
$259$	236.092	−	324.953i	0.911553	−	1.25465i
$260$		0			0
$261$	0.388369	+	1.19528i	0.00148800	+	0.00457960i
$262$		0			0
$263$	−101.777	+	101.777i	−0.386984	+	0.386984i	−0.873610	−	0.486626i	$-0.838227\pi$
$263$	−101.777	+	101.777i	−0.386984	+	0.386984i	0.486626	+	0.873610i	$0.338227\pi$
$264$		0			0
$265$	−81.7123	+	144.184i	−0.308348	+	0.544090i
$266$		0			0
$267$	−48.6162	+	95.4147i	−0.182083	+	0.357358i
$268$		0			0
$269$	−83.8954	+	115.472i	−0.311879	+	0.429265i	−0.935966	−	0.352090i	$-0.885471\pi$
$269$	−83.8954	+	115.472i	−0.311879	+	0.429265i	0.624087	+	0.781355i	$0.285471\pi$
$270$		0			0
$271$	−20.0339	+	61.6580i	−0.0739258	+	0.227520i	−0.981191	−	0.193038i	$-0.938166\pi$
$271$	−20.0339	+	61.6580i	−0.0739258	+	0.227520i	0.907265	+	0.420559i	$0.138166\pi$
$272$		0			0
$273$	55.8348	−	352.527i	0.204523	−	1.29131i
$274$		0			0
$275$	−266.018	+	69.7087i	−0.967339	+	0.253486i
$276$		0			0
$277$	502.673	+	79.6156i	1.81470	+	0.287421i	0.969150	−	0.246470i	$-0.0792706\pi$
$277$	502.673	+	79.6156i	1.81470	+	0.287421i	0.845553	+	0.533891i	$0.179271\pi$
$278$		0			0
$279$	−3.54817	−	1.15287i	−0.0127174	−	0.00413215i
$280$		0			0
$281$	427.771	+	310.794i	1.52232	+	1.10603i	0.960324	+	0.278885i	$0.0899649\pi$
$281$	427.771	+	310.794i	1.52232	+	1.10603i	0.561992	+	0.827143i	$0.310035\pi$
$282$		0			0
$283$	116.313	+	59.2646i	0.411001	+	0.209415i	0.647251	−	0.762277i	$-0.275919\pi$
$283$	116.313	+	59.2646i	0.411001	+	0.209415i	−0.236250	+	0.971692i	$0.575919\pi$
$284$		0			0
$285$	−264.240	−	149.751i	−0.927160	−	0.525442i
$286$		0			0
$287$	−304.217	−	304.217i	−1.05999	−	1.05999i
$288$		0			0
$289$	270.280	−	87.8193i	0.935225	−	0.303873i
$290$		0			0
$291$	−19.1977	−	13.9480i	−0.0659716	−	0.0479312i
$292$		0			0
$293$	59.1428	+	116.074i	0.201853	+	0.396158i	0.969636	−	0.244551i	$-0.0786406\pi$
$293$	59.1428	+	116.074i	0.201853	+	0.396158i	−0.767784	+	0.640709i	$0.778641\pi$
$294$		0			0
$295$	279.929	+	222.994i	0.948911	+	0.755913i
$296$		0			0
$297$	−270.973	−	127.705i	−0.912366	−	0.429982i
$298$		0			0
$299$	−335.878	−	462.296i	−1.12334	−	1.54614i
$300$		0			0
$301$	−129.418	+	398.308i	−0.429960	+	1.32328i
$302$		0			0
$303$	542.647	−	85.9469i	1.79091	−	0.283653i
$304$		0			0
$305$	146.901	+	222.291i	0.481643	+	0.728822i
$306$		0			0
$307$	−53.8112	−	53.8112i	−0.175281	−	0.175281i	0.614014	−	0.789295i	$-0.289554\pi$
$307$	−53.8112	−	53.8112i	−0.175281	−	0.175281i	−0.789295	+	0.614014i	$0.789554\pi$
$308$		0			0
$309$			503.282i			1.62875i
$310$		0			0
$311$	55.3408	+	170.321i	0.177945	+	0.547657i	0.999756	−	0.0221029i	$-0.00703613\pi$
$311$	55.3408	+	170.321i	0.177945	+	0.547657i	−0.821811	+	0.569760i	$0.807036\pi$
$312$		0			0
$313$	−128.259	+	20.3142i	−0.409772	+	0.0649016i	−0.357918	−	0.933753i	$-0.616513\pi$
$313$	−128.259	+	20.3142i	−0.409772	+	0.0649016i	−0.0518545	+	0.998655i	$0.516513\pi$
$314$		0			0
$315$	4.22226	+	4.61444i	0.0134040	+	0.0146490i
$316$		0			0
$317$	−107.830	−	17.0787i	−0.340159	−	0.0538759i	−0.0159819	−	0.999872i	$-0.505087\pi$
$317$	−107.830	−	17.0787i	−0.340159	−	0.0538759i	−0.324177	+	0.945996i	$0.605087\pi$
$318$		0			0
$319$	68.9434	−	53.4131i	0.216124	−	0.167439i
$320$		0			0
$321$	110.098	−	79.9912i	0.342986	−	0.249194i
$322$		0			0
$323$	−20.3421	−	39.9235i	−0.0629785	−	0.123602i
$324$		0			0
$325$	−291.654	+	244.012i	−0.897395	+	0.750807i
$326$		0			0
$327$	280.791	−	551.084i	0.858689	−	1.68527i
$328$		0			0
$329$			568.468i			1.72787i
$330$		0			0
$331$	292.474			0.883607			0.441804	−	0.897112i	$-0.354339\pi$
$331$	292.474			0.883607			0.441804	+	0.897112i	$0.354339\pi$
$332$		0			0
$333$	−7.18879	−	3.66287i	−0.0215880	−	0.0109996i
$334$		0			0
$335$	−8.48911	−	18.6632i	−0.0253406	−	0.0557111i
$336$		0			0
$337$	−199.701	+	101.753i	−0.592584	+	0.301937i	−0.724446	−	0.689331i	$-0.757904\pi$
$337$	−199.701	+	101.753i	−0.592584	+	0.301937i	0.131862	+	0.991268i	$0.457904\pi$
$338$		0			0
$339$	73.9745	+	101.817i	0.218214	+	0.300346i
$340$		0			0
$341$	7.97986	+	258.769i	0.0234013	+	0.758853i
$342$		0			0
$343$	−44.1014	+	278.446i	−0.128576	+	0.811795i
$344$		0			0
$345$	−557.979	−	24.7640i	−1.61733	−	0.0717796i
$346$		0			0
$347$	−24.8851	−	157.118i	−0.0717150	−	0.452791i	−0.997249	−	0.0741260i	$-0.976383\pi$
$347$	−24.8851	−	157.118i	−0.0717150	−	0.452791i	0.925534	−	0.378665i	$-0.123617\pi$
$348$		0			0
$349$	−623.519	+	202.593i	−1.78659	+	0.580497i	−0.999346	−	0.0361497i	$-0.988491\pi$
$349$	−623.519	+	202.593i	−1.78659	+	0.580497i	−0.787240	+	0.616647i	$0.788491\pi$
$350$		0			0
$351$	−414.226			−1.18013
$352$		0			0
$353$	240.681	−	240.681i	0.681817	−	0.681817i	−0.278593	−	0.960409i	$-0.589868\pi$
$353$	240.681	−	240.681i	0.681817	−	0.681817i	0.960409	+	0.278593i	$0.0898679\pi$
$354$		0			0
$355$	−150.741	−	228.101i	−0.424622	−	0.642537i
$356$		0			0
$357$	−8.05113	−	50.8328i	−0.0225522	−	0.142389i
$358$		0			0
$359$	332.050	+	107.889i	0.924930	+	0.300528i	0.732487	−	0.680780i	$-0.238359\pi$
$359$	332.050	+	107.889i	0.924930	+	0.300528i	0.192442	+	0.981308i	$0.438359\pi$
$360$		0			0
$361$	45.5828	−	33.1179i	0.126268	−	0.0917392i
$362$		0			0
$363$	−34.2803	+	358.152i	−0.0944361	+	0.986645i
$364$		0			0
$365$	1.31624	+	11.6268i	0.00360613	+	0.0318542i
$366$		0			0
$367$	−156.066	+	79.5195i	−0.425247	+	0.216674i	−0.653498	−	0.756928i	$-0.726699\pi$
$367$	−156.066	+	79.5195i	−0.425247	+	0.216674i	0.228251	+	0.973602i	$0.426699\pi$
$368$		0			0
$369$	−5.07960	+	6.99147i	−0.0137659	+	0.0189471i
$370$		0			0
$371$	−80.8294	−	248.767i	−0.217869	−	0.670532i
$372$		0			0
$373$	−207.975	+	207.975i	−0.557573	+	0.557573i	−0.928616	−	0.371042i	$-0.879000\pi$
$373$	−207.975	+	207.975i	−0.557573	+	0.557573i	0.371042	+	0.928616i	$0.379000\pi$
$374$		0			0
$375$	8.92785	+	371.576i	0.0238076	+	0.990868i
$376$		0			0
$377$	54.7503	−	107.454i	0.145226	−	0.285023i
$378$		0			0
$379$	−66.0392	+	90.8951i	−0.174246	+	0.239829i	−0.887204	−	0.461378i	$-0.847355\pi$
$379$	−66.0392	+	90.8951i	−0.174246	+	0.239829i	0.712958	+	0.701207i	$0.247355\pi$
$380$		0			0
$381$	83.4981	−	256.981i	0.219155	−	0.674490i
$382$		0			0
$383$	77.4342	−	488.900i	0.202178	−	1.27650i	−0.652678	−	0.757636i	$-0.726354\pi$
$383$	77.4342	−	488.900i	0.202178	−	1.27650i	0.854856	−	0.518866i	$-0.173646\pi$
$384$		0			0
$385$	202.259	−	384.026i	0.525348	−	0.997471i
$386$		0			0
$387$	8.30891	+	1.31600i	0.0214700	+	0.00340052i
$388$		0			0
$389$	426.589	+	138.607i	1.09663	+	0.356316i	0.800804	−	0.598926i	$-0.204406\pi$
$389$	426.589	+	138.607i	1.09663	+	0.356316i	0.295824	+	0.955242i	$0.404406\pi$
$390$		0			0
$391$	−66.6610	−	48.4321i	−0.170489	−	0.123867i
$392$		0			0
$393$	469.467	+	239.205i	1.19457	+	0.608665i
$394$		0			0
$395$	119.207	+	431.051i	0.301791	+	1.09127i
$396$		0			0
$397$	−510.808	−	510.808i	−1.28667	−	1.28667i	−0.936798	−	0.349872i	$-0.886225\pi$
$397$	−510.808	−	510.808i	−1.28667	−	1.28667i	−0.349872	−	0.936798i	$-0.613775\pi$
$398$		0			0
$399$	455.907	−	148.133i	1.14262	−	0.371261i
$400$		0			0
$401$	−117.926	−	85.6783i	−0.294080	−	0.213662i	0.430955	−	0.902373i	$-0.358177\pi$
$401$	−117.926	−	85.6783i	−0.294080	−	0.213662i	−0.725035	+	0.688712i	$0.758177\pi$
$402$		0			0
$403$	162.526	+	318.975i	0.403290	+	0.791501i
$404$		0			0
$405$	−247.823	+	311.097i	−0.611910	+	0.768142i
$406$		0			0
$407$	−70.4982	+	555.425i	−0.173214	+	1.36468i
$408$		0			0
$409$	107.001	+	147.274i	0.261615	+	0.360083i	0.919537	−	0.393004i	$-0.128564\pi$
$409$	107.001	+	147.274i	0.261615	+	0.360083i	−0.657921	+	0.753087i	$0.728564\pi$
$410$		0			0
$411$	87.6347	−	269.712i	0.213223	−	0.656233i
$412$		0			0
$413$	−557.907	+	88.3639i	−1.35087	+	0.213956i
$414$		0			0
$415$	−307.359	−	62.7632i	−0.740625	−	0.151237i
$416$		0			0
$417$	−145.573	−	145.573i	−0.349095	−	0.349095i
$418$		0			0
$419$			33.8672i			0.0808286i	0.999183	+	0.0404143i	$0.0128678\pi$
$419$			33.8672i			0.0808286i	−0.999183	+	0.0404143i	$0.987132\pi$
$420$		0			0
$421$	92.2752	+	283.994i	0.219181	+	0.674570i	0.998830	+	0.0483532i	$0.0153973\pi$
$421$	92.2752	+	283.994i	0.219181	+	0.674570i	−0.779649	+	0.626216i	$0.784603\pi$
$422$		0			0
$423$	11.2781	−	1.78628i	0.0266623	−	0.00422289i
$424$		0			0
$425$	−29.1239	+	46.4591i	−0.0685268	+	0.109316i
$426$		0			0
$427$	−415.354	−	65.7856i	−0.972726	−	0.154065i
$428$		0			0
$429$	168.252	+	468.200i	0.392195	+	1.09138i
$430$		0			0
$431$	−470.349	+	341.729i	−1.09130	+	0.792874i	−0.979618	−	0.200871i	$-0.935623\pi$
$431$	−470.349	+	341.729i	−1.09130	+	0.792874i	−0.111679	+	0.993744i	$0.535623\pi$
$432$		0			0
$433$	−89.2385	−	175.140i	−0.206093	−	0.404481i	0.764704	−	0.644382i	$-0.222885\pi$
$433$	−89.2385	−	175.140i	−0.206093	−	0.404481i	−0.970797	+	0.239901i	$0.922885\pi$
$434$		0			0
$435$	−48.8049	−	107.297i	−0.112195	−	0.246660i
$436$		0			0
$437$	348.423	−	683.818i	0.797306	−	1.56480i
$438$		0			0
$439$			116.632i			0.265676i	0.991138	+	0.132838i	$0.0424091\pi$
$439$			116.632i			0.265676i	−0.991138	+	0.132838i	$0.957591\pi$
$440$		0			0
$441$	−2.10445			−0.00477200
$442$		0			0
$443$	31.3026	+	15.9495i	0.0706605	+	0.0360033i	0.488964	−	0.872304i	$-0.337375\pi$
$443$	31.3026	+	15.9495i	0.0706605	+	0.0360033i	−0.418303	+	0.908307i	$0.637375\pi$
$444$		0			0
$445$	−63.1832	+	168.621i	−0.141985	+	0.378924i
$446$		0			0
$447$	−412.843	+	210.354i	−0.923586	+	0.470591i
$448$		0			0
$449$	248.055	+	341.418i	0.552460	+	0.760396i	0.990343	−	0.138635i	$-0.0442716\pi$
$449$	248.055	+	341.418i	0.552460	+	0.760396i	−0.437883	+	0.899032i	$0.644272\pi$
$450$		0			0
$451$	575.786	+	167.649i	1.27669	+	0.371726i
$452$		0			0
$453$	10.9875	−	69.3727i	0.0242551	−	0.153141i
$454$		0			0
$455$	26.6106	−	599.588i	0.0584849	−	1.31778i
$456$		0			0
$457$	8.18788	+	51.6963i	0.0179166	+	0.113121i	0.995026	−	0.0996173i	$-0.0317618\pi$
$457$	8.18788	+	51.6963i	0.0179166	+	0.113121i	−0.977109	+	0.212738i	$0.931762\pi$
$458$		0			0
$459$	−56.8062	+	18.4574i	−0.123761	+	0.0402123i
$460$		0			0
$461$	−360.723			−0.782479			−0.391240	−	0.920289i	$-0.627954\pi$
$461$	−360.723			−0.782479			−0.391240	+	0.920289i	$0.627954\pi$
$462$		0			0
$463$	−221.558	+	221.558i	−0.478526	+	0.478526i	−0.904660	−	0.426134i	$-0.859875\pi$
$463$	−221.558	+	221.558i	−0.478526	+	0.478526i	0.426134	+	0.904660i	$0.359875\pi$
$464$		0			0
$465$	342.837	+	70.0077i	0.737283	+	0.150554i
$466$		0			0
$467$	46.2371	+	291.930i	0.0990089	+	0.625117i	0.986433	+	0.164164i	$0.0524925\pi$
$467$	46.2371	+	291.930i	0.0990089	+	0.625117i	−0.887424	+	0.460954i	$0.847507\pi$
$468$		0			0
$469$	30.7764	+	9.99986i	0.0656213	+	0.0213217i
$470$		0			0
$471$	−76.0447	+	55.2497i	−0.161454	+	0.117303i
$472$		0			0
$473$	−109.051	−	573.498i	−0.230552	−	1.21247i
$474$		0			0
$475$	−469.837	−	200.232i	−0.989131	−	0.421541i
$476$		0			0
$477$	−4.68144	+	2.38532i	−0.00981435	+	0.00500066i
$478$		0			0
$479$	−150.645	+	207.345i	−0.314499	+	0.432871i	−0.936778	−	0.349925i	$-0.886207\pi$
$479$	−150.645	+	207.345i	−0.314499	+	0.432871i	0.622279	+	0.782796i	$0.286207\pi$
$480$		0			0
$481$	239.241	+	736.307i	0.497382	+	1.53078i
$482$		0			0
$483$	623.334	−	623.334i	1.29055	−	1.29055i
$484$		0			0
$485$	−34.7152	−	19.6739i	−0.0715778	−	0.0405647i
$486$		0			0
$487$	−307.333	+	603.175i	−0.631074	+	1.23855i	0.325080	+	0.945686i	$0.394609\pi$
$487$	−307.333	+	603.175i	−0.631074	+	1.23855i	−0.956154	+	0.292865i	$0.905391\pi$
$488$		0			0
$489$	402.678	−	554.238i	0.823471	−	1.13341i
$490$		0			0
$491$	133.739	−	411.608i	0.272382	−	0.838305i	−0.717518	−	0.696540i	$-0.754722\pi$
$491$	133.739	−	411.608i	0.272382	−	0.838305i	0.989900	−	0.141766i	$-0.0452779\pi$
$492$		0			0
$493$	2.72034	−	17.1756i	0.00551794	−	0.0348389i
$494$		0			0
$495$	−8.25446	−	2.80601i	−0.0166757	−	0.00566871i
$496$		0			0
$497$	426.210	+	67.5050i	0.857565	+	0.135825i
$498$		0			0
$499$	−230.428	−	74.8705i	−0.461779	−	0.150041i	0.0688828	−	0.997625i	$-0.478057\pi$
$499$	−230.428	−	74.8705i	−0.461779	−	0.150041i	−0.530662	+	0.847584i	$0.678057\pi$
$500$		0			0
$501$	194.103	+	141.024i	0.387430	+	0.281485i
$502$		0			0
$503$	362.339	+	184.621i	0.720356	+	0.367039i	0.775422	−	0.631443i	$-0.217537\pi$
$503$	362.339	+	184.621i	0.720356	+	0.367039i	−0.0550666	+	0.998483i	$0.517537\pi$
$504$		0			0
$505$	890.435	−	246.250i	1.76324	−	0.487624i
$506$		0			0
$507$	131.128	+	131.128i	0.258636	+	0.258636i
$508$		0			0
$509$	−297.341	+	96.6120i	−0.584168	+	0.189808i	−0.586167	−	0.810190i	$-0.699364\pi$
$509$	−297.341	+	96.6120i	−0.584168	+	0.189808i	0.00199918	+	0.999998i	$0.499364\pi$
$510$		0			0
$511$	−14.9408	−	10.8551i	−0.0292383	−	0.0212429i
$512$		0			0
$513$	−252.570	−	495.696i	−0.492339	−	0.966269i
$514$		0			0
$515$	95.1979	+	840.918i	0.184850	+	1.63285i
$516$		0			0
$517$	−381.328	−	694.600i	−0.737578	−	1.34352i
$518$		0			0
$519$	−159.688	−	219.792i	−0.307684	−	0.423491i
$520$		0			0
$521$	−33.9003	+	104.335i	−0.0650678	+	0.200258i	−0.978305	−	0.207171i	$-0.933575\pi$
$521$	−33.9003	+	104.335i	−0.0650678	+	0.200258i	0.913237	+	0.407429i	$0.133575\pi$
$522$		0			0
$523$	−793.754	+	125.718i	−1.51769	+	0.240379i	−0.858978	−	0.512012i	$-0.828900\pi$
$523$	−793.754	+	125.718i	−1.51769	+	0.240379i	−0.658716	+	0.752391i	$0.728900\pi$
$524$		0			0
$525$	−442.180	−	385.499i	−0.842247	−	0.734284i
$526$		0			0
$527$	36.5016	+	36.5016i	0.0692630	+	0.0692630i
$528$		0			0
$529$		−	882.321i		−	1.66790i
$530$		0			0
$531$	3.50620	+	10.7910i	0.00660301	+	0.0203220i
$532$		0			0
$533$	819.046	−	129.724i	1.53667	−	0.243385i
$534$		0			0
$535$	168.829	−	154.480i	0.315569	−	0.288748i
$536$		0			0
$537$	175.973	+	27.8714i	0.327696	+	0.0519020i
$538$		0			0
$539$	49.3871	+	137.432i	0.0916274	+	0.254975i
$540$		0			0
$541$	−79.5754	+	57.8149i	−0.147089	+	0.106867i	−0.658896	−	0.752234i	$-0.728976\pi$
$541$	−79.5754	+	57.8149i	−0.147089	+	0.106867i	0.511807	+	0.859101i	$0.328976\pi$
$542$		0			0
$543$	281.824	+	553.111i	0.519013	+	1.01862i
$544$		0			0
$545$	364.925	−	973.901i	0.669588	−	1.78697i
$546$		0			0
$547$	−21.3834	+	41.9672i	−0.0390921	+	0.0767225i	−0.909726	−	0.415208i	$-0.863709\pi$
$547$	−21.3834	+	41.9672i	−0.0390921	+	0.0767225i	0.870634	+	0.491931i	$0.163709\pi$
$548$		0			0
$549$			8.44715i			0.0153864i
$550$		0			0
$551$	161.971			0.293958
$552$		0			0
$553$	−628.931	−	320.457i	−1.13731	−	0.579487i
$554$		0			0
$555$	708.608	+	265.519i	1.27677	+	0.478412i
$556$		0			0
$557$	724.062	−	368.928i	1.29993	−	0.662348i	0.339433	−	0.940630i	$-0.389765\pi$
$557$	724.062	−	368.928i	1.29993	−	0.662348i	0.960499	+	0.278282i	$0.0897650\pi$
$558$		0			0
$559$	−474.483	−	653.069i	−0.848806	−	1.16828i
$560$		0			0
$561$	43.9361	+	56.7110i	0.0783176	+	0.101089i
$562$		0			0
$563$	−43.4505	+	274.336i	−0.0771767	+	0.487275i	0.918579	+	0.395238i	$0.129338\pi$
$563$	−43.4505	+	274.336i	−0.0771767	+	0.487275i	−0.995756	+	0.0920370i	$0.970662\pi$
$564$		0			0
$565$	142.861	+	156.130i	0.252851	+	0.276337i
$566$		0			0
$567$	−98.2027	−	620.027i	−0.173197	−	1.09352i
$568$		0			0
$569$	−151.476	+	49.2175i	−0.266214	+	0.0864983i	−0.439083	−	0.898447i	$-0.644696\pi$
$569$	−151.476	+	49.2175i	−0.266214	+	0.0864983i	0.172868	+	0.984945i	$0.444696\pi$
$570$		0			0
$571$	514.236			0.900588			0.450294	−	0.892880i	$-0.351319\pi$
$571$	514.236			0.900588			0.450294	+	0.892880i	$0.351319\pi$
$572$		0			0
$573$	135.999	−	135.999i	0.237345	−	0.237345i
$574$		0			0
$575$	−936.994	+	64.1668i	−1.62956	+	0.111594i
$576$		0			0
$577$	150.204	+	948.349i	0.260319	+	1.64359i	0.678050	+	0.735016i	$0.262825\pi$
$577$	150.204	+	948.349i	0.260319	+	1.64359i	−0.417731	+	0.908571i	$0.637175\pi$
$578$		0			0
$579$	−768.985	−	249.858i	−1.32813	−	0.431534i
$580$		0			0
$581$	400.558	−	291.023i	0.689429	−	0.500899i
$582$		0			0
$583$	265.637	+	249.744i	0.455638	+	0.428377i
$584$		0			0
$585$	−11.9792	+	1.35613i	−0.0204772	+	0.00231817i
$586$		0			0
$587$	771.894	−	393.300i	1.31498	−	0.670016i	0.351097	−	0.936339i	$-0.385809\pi$
$587$	771.894	−	393.300i	1.31498	−	0.670016i	0.963884	+	0.266323i	$0.0858087\pi$
$588$		0			0
$589$	−282.612	+	388.983i	−0.479817	+	0.660412i
$590$		0			0
$591$	197.801	+	608.770i	0.334689	+	1.03007i
$592$		0			0
$593$	649.577	−	649.577i	1.09541	−	1.09541i	0.100468	−	0.994940i	$-0.467966\pi$
$593$	649.577	−	649.577i	1.09541	−	1.09541i	0.994940	−	0.100468i	$-0.0320341\pi$
$594$		0			0
$595$	−23.0676	−	83.4121i	−0.0387691	−	0.140188i
$596$		0			0
$597$	202.623	−	397.670i	0.339402	−	0.666114i
$598$		0			0
$599$	−356.047	+	490.056i	−0.594402	+	0.818124i	−0.995181	−	0.0980508i	$-0.968739\pi$
$599$	−356.047	+	490.056i	−0.594402	+	0.818124i	0.400780	+	0.916174i	$0.368739\pi$
$600$		0			0
$601$	142.502	−	438.575i	0.237108	−	0.729742i	−0.759727	−	0.650242i	$-0.774668\pi$
$601$	142.502	−	438.575i	0.237108	−	0.729742i	0.996835	−	0.0795001i	$-0.0253324\pi$
$602$		0			0
$603$	0.101685	−	0.642012i	0.000168631	−	0.00106470i
$604$		0			0
$605$	10.4682	+	604.909i	0.0173027	+	0.999850i
$606$		0			0
$607$	−690.800	−	109.412i	−1.13806	−	0.180250i	−0.441164	−	0.897426i	$-0.645434\pi$
$607$	−690.800	−	109.412i	−1.13806	−	0.180250i	−0.696892	+	0.717176i	$0.745434\pi$
$608$		0			0
$609$	176.937	+	57.4904i	0.290537	+	0.0944013i
$610$		0			0
$611$	−886.448	−	644.042i	−1.45081	−	1.05408i
$612$		0			0
$613$	−367.019	−	187.006i	−0.598726	−	0.305066i	0.128236	−	0.991744i	$-0.459068\pi$
$613$	−367.019	−	187.006i	−0.598726	−	0.305066i	−0.726962	+	0.686677i	$0.759068\pi$
$614$		0			0
$615$	399.633	−	705.166i	0.649810	−	1.14661i
$616$		0			0
$617$	418.073	+	418.073i	0.677590	+	0.677590i	0.959454	−	0.281864i	$-0.0909527\pi$
$617$	418.073	+	418.073i	0.677590	+	0.677590i	−0.281864	+	0.959454i	$0.590953\pi$
$618$		0			0
$619$	523.296	−	170.029i	0.845390	−	0.274684i	0.145876	−	0.989303i	$-0.453400\pi$
$619$	523.296	−	170.029i	0.845390	−	0.274684i	0.699514	+	0.714619i	$0.253400\pi$
$620$		0			0
$621$	−827.672	−	601.339i	−1.33280	−	0.968339i
$622$		0			0
$623$	−129.026	−	253.229i	−0.207105	−	0.406467i
$624$		0			0
$625$	85.2024	+	619.165i	0.136324	+	0.990664i
$626$		0			0
$627$	−457.696	+	486.823i	−0.729978	+	0.776432i
$628$		0			0
$629$	65.6180	+	90.3154i	0.104321	+	0.143586i
$630$		0			0
$631$	254.599	−	783.575i	0.403485	−	1.24180i	−0.518669	−	0.854975i	$-0.673572\pi$
$631$	254.599	−	783.575i	0.403485	−	1.24180i	0.922154	−	0.386823i	$-0.126428\pi$
$632$		0			0
$633$	−906.918	+	143.642i	−1.43273	+	0.226922i
$634$		0			0
$635$	90.9053	−	445.175i	0.143158	−	0.701063i
$636$		0			0
$637$	142.791	+	142.791i	0.224162	+	0.224162i
$638$		0			0
$639$		−	8.66793i		−	0.0135648i
$640$		0			0
$641$	−199.661	−	614.494i	−0.311484	−	0.958649i	−0.977178	−	0.212424i	$-0.931864\pi$
$641$	−199.661	−	614.494i	−0.311484	−	0.958649i	0.665694	−	0.746225i	$-0.268136\pi$
$642$		0			0
$643$	−204.293	+	32.3568i	−0.317719	+	0.0503217i	−0.313257	−	0.949668i	$-0.601420\pi$
$643$	−204.293	+	32.3568i	−0.317719	+	0.0503217i	−0.00446153	+	0.999990i	$0.501420\pi$
$644$		0			0
$645$	−788.238	−	34.9832i	−1.22207	−	0.0542375i
$646$		0			0
$647$	359.495	+	56.9385i	0.555634	+	0.0880038i	0.427936	−	0.903809i	$-0.359241\pi$
$647$	359.495	+	56.9385i	0.555634	+	0.0880038i	0.127699	+	0.991813i	$0.459241\pi$
$648$		0			0
$649$	622.422	−	482.214i	0.959048	−	0.743011i
$650$		0			0
$651$	−446.793	+	324.614i	−0.686318	+	0.498639i
$652$		0			0
$653$	177.649	+	348.656i	0.272050	+	0.533929i	0.986097	−	0.166169i	$-0.0531397\pi$
$653$	177.649	+	348.656i	0.272050	+	0.533929i	−0.714047	+	0.700098i	$0.753140\pi$
$654$		0			0
$655$	829.664	+	310.879i	1.26666	+	0.474625i
$656$		0			0
$657$	−0.168412	+	0.330528i	−0.000256335	+	0.000503087i
$658$		0			0
$659$		−	1045.08i		−	1.58586i	−0.609312	−	0.792931i	$-0.708554\pi$
$659$		−	1045.08i		−	1.58586i	0.609312	−	0.792931i	$-0.291446\pi$
$660$		0			0
$661$	908.162			1.37392			0.686960	−	0.726695i	$-0.258945\pi$
$661$	908.162			1.37392			0.686960	+	0.726695i	$0.258945\pi$
$662$		0			0
$663$	88.3883	+	45.0361i	0.133316	+	0.0679277i
$664$		0			0
$665$	733.740	−	333.748i	1.10337	−	0.501876i
$666$		0			0
$667$	265.389	−	135.223i	0.397885	−	0.202733i
$668$		0			0
$669$	−208.634	−	287.160i	−0.311860	−	0.429238i
$670$		0			0
$671$	551.642	−	198.237i	0.822119	−	0.295435i
$672$		0			0
$673$	−198.155	+	1251.10i	−0.294435	+	1.85899i	0.186798	+	0.982398i	$0.440189\pi$
$673$	−198.155	+	1251.10i	−0.294435	+	1.85899i	−0.481233	+	0.876593i	$0.659811\pi$
$674$		0			0
$675$	−361.606	+	576.842i	−0.535712	+	0.854581i
$676$		0			0
$677$	197.985	+	1250.03i	0.292444	+	1.84642i	0.497235	+	0.867616i	$0.334349\pi$
$677$	197.985	+	1250.03i	0.292444	+	1.84642i	−0.204791	+	0.978806i	$0.565651\pi$
$678$		0			0
$679$	59.8959	−	19.4613i	0.0882119	−	0.0286618i
$680$		0			0
$681$	−628.132			−0.922367
$682$		0			0
$683$	295.545	−	295.545i	0.432715	−	0.432715i	−0.456836	−	0.889551i	$-0.651017\pi$
$683$	295.545	−	295.545i	0.432715	−	0.432715i	0.889551	+	0.456836i	$0.151017\pi$
$684$		0			0
$685$	95.4089	−	467.229i	0.139283	−	0.682087i
$686$		0			0
$687$	199.304	+	1258.36i	0.290108	+	1.83167i
$688$		0			0
$689$	479.494	+	155.797i	0.695927	+	0.226120i
$690$		0			0
$691$	−1042.47	+	757.400i	−1.50864	+	1.09609i	−0.541867	+	0.840464i	$0.682282\pi$
$691$	−1042.47	+	757.400i	−1.50864	+	1.09609i	−0.966775	+	0.255628i	$0.917718\pi$
$692$		0			0
$693$	12.0621	−	6.62194i	0.0174056	−	0.00955547i
$694$		0			0
$695$	−270.768	−	215.697i	−0.389594	−	0.310355i
$696$		0			0
$697$	106.542	−	54.2859i	0.152858	−	0.0778851i
$698$		0			0
$699$	−179.762	+	247.421i	−0.257170	+	0.353964i
$700$		0			0
$701$	169.091	+	520.409i	0.241214	+	0.742382i	0.996236	+	0.0866817i	$0.0276263\pi$
$701$	169.091	+	520.409i	0.241214	+	0.742382i	−0.755022	+	0.655700i	$0.772374\pi$
$702$		0			0
$703$	−735.249	+	735.249i	−1.04587	+	1.04587i
$704$		0			0
$705$	−1032.23	+	285.463i	−1.46415	+	0.404912i
$706$		0			0
$707$	−661.976	+	1299.20i	−0.936317	+	1.83762i
$708$		0			0
$709$	698.138	−	960.905i	0.984680	−	1.35530i	0.0504104	−	0.998729i	$-0.483947\pi$
$709$	698.138	−	960.905i	0.984680	−	1.35530i	0.934270	−	0.356567i	$-0.116053\pi$
$710$		0			0
$711$	−4.38144	+	13.4847i	−0.00616236	+	0.0189658i
$712$		0			0
$713$	−138.316	+	873.290i	−0.193991	+	1.22481i
$714$		0			0
$715$	369.688	+	750.475i	0.517046	+	1.04962i
$716$		0			0
$717$	1257.67	+	199.196i	1.75408	+	0.277819i
$718$		0			0
$719$	760.081	+	246.965i	1.05714	+	0.343485i	0.785466	−	0.618905i	$-0.212424\pi$
$719$	760.081	+	246.965i	1.05714	+	0.343485i	0.271671	+	0.962390i	$0.412424\pi$
$720$		0			0
$721$	−1080.61	−	785.106i	−1.49876	−	1.08891i
$722$		0			0
$723$	−160.007	−	81.5278i	−0.221310	−	0.112763i
$724$		0			0
$725$	−101.842	−	170.048i	−0.140472	−	0.234548i
$726$		0			0
$727$	−365.797	−	365.797i	−0.503160	−	0.503160i	0.409258	−	0.912419i	$-0.365787\pi$
$727$	−365.797	−	365.797i	−0.503160	−	0.503160i	−0.912419	+	0.409258i	$0.865787\pi$
$728$		0			0
$729$	−705.098	+	229.100i	−0.967212	+	0.314266i
$730$		0			0
$731$	−94.1696	−	68.4183i	−0.128823	−	0.0935954i
$732$		0			0
$733$	211.249	+	414.599i	0.288198	+	0.565620i	0.989032	−	0.147705i	$-0.0471885\pi$
$733$	211.249	+	414.599i	0.288198	+	0.565620i	−0.700834	+	0.713325i	$0.747189\pi$
$734$		0			0
$735$	196.126	−	22.2028i	0.266838	−	0.0302079i
$736$		0			0
$737$	−44.3130	+	8.42616i	−0.0601262	+	0.0114331i
$738$		0			0
$739$	−803.504	−	1105.93i	−1.08729	−	1.49652i	−0.851239	−	0.524778i	$-0.824148\pi$
$739$	−803.504	−	1105.93i	−1.08729	−	1.49652i	−0.236046	−	0.971742i	$-0.575852\pi$
$740$		0			0
$741$	−285.523	+	878.750i	−0.385322	+	1.18590i
$742$		0			0
$743$	−797.167	+	126.259i	−1.07290	+	0.169931i	−0.667800	−	0.744340i	$-0.732764\pi$
$743$	−797.167	+	126.259i	−1.07290	+	0.169931i	−0.405102	+	0.914271i	$0.632764\pi$
$744$		0			0
$745$	−650.017	+	429.565i	−0.872506	+	0.576597i
$746$		0			0
$747$	−7.03242	−	7.03242i	−0.00941422	−	0.00941422i
$748$		0			0
$749$			361.178i			0.482214i
$750$		0			0
$751$	−162.000	−	498.585i	−0.215712	−	0.663894i	−0.999102	−	0.0423638i	$-0.986511\pi$
$751$	−162.000	−	498.585i	−0.215712	−	0.663894i	0.783390	−	0.621531i	$-0.213489\pi$
$752$		0			0
$753$	−1335.98	+	211.599i	−1.77421	+	0.281008i
$754$		0			0
$755$	5.23662	−	117.991i	0.00693591	−	0.156279i
$756$		0			0
$757$	−406.489	−	64.3815i	−0.536973	−	0.0850482i	−0.117943	−	0.993020i	$-0.537630\pi$
$757$	−406.489	−	64.3815i	−0.536973	−	0.0850482i	−0.419030	+	0.907972i	$0.637630\pi$
$758$		0			0
$759$	−343.508	+	1179.77i	−0.452579	+	1.55438i
$760$		0			0
$761$	442.423	−	321.439i	0.581371	−	0.422391i	−0.257847	−	0.966186i	$-0.583013\pi$
$761$	442.423	−	321.439i	0.581371	−	0.422391i	0.839218	+	0.543795i	$0.183013\pi$
$762$		0			0
$763$	745.214	+	1462.57i	0.976690	+	1.91686i
$764$		0			0
$765$	−1.58237	+	0.719755i	−0.00206846	+	0.000940856i
$766$		0			0
$767$	494.286	−	970.091i	0.644441	−	1.26479i
$768$		0			0
$769$			662.450i			0.861443i	0.902485	+	0.430722i	$0.141741\pi$
$769$			662.450i			0.861443i	−0.902485	+	0.430722i	$0.858259\pi$
$770$		0			0
$771$	225.251			0.292155
$772$		0			0
$773$	340.487	+	173.487i	0.440475	+	0.224433i	0.660141	−	0.751142i	$-0.270497\pi$
$773$	340.487	+	173.487i	0.440475	+	0.224433i	−0.219666	+	0.975575i	$0.570497\pi$
$774$		0			0
$775$	586.077	+	52.1247i	0.756229	+	0.0672576i
$776$		0			0
$777$	−1064.16	+	542.216i	−1.36957	+	0.697833i
$778$		0			0
$779$	654.643	+	901.038i	0.840363	+	1.15666i
$780$		0			0
$781$	−566.060	+	203.418i	−0.724788	+	0.260459i
$782$		0			0
$783$	33.7761	−	213.254i	0.0431368	−	0.272355i
$784$		0			0
$785$	−116.610	+	106.699i	−0.148548	+	0.135922i
$786$		0			0
$787$	56.2423	+	355.100i	0.0714641	+	0.451207i	0.997310	+	0.0733045i	$0.0233545\pi$
$787$	56.2423	+	355.100i	0.0714641	+	0.451207i	−0.925845	+	0.377902i	$0.876646\pi$
$788$		0			0
$789$	407.036	−	132.254i	0.515889	−	0.167622i
$790$		0			0
$791$	−334.011			−0.422265
$792$		0			0
$793$	573.156	−	573.156i	0.722769	−	0.722769i
$794$		0			0
$795$	411.124	−	271.692i	0.517137	−	0.341751i
$796$		0			0
$797$	−147.695	−	932.508i	−0.185313	−	1.17002i	−0.888452	−	0.458970i	$-0.848219\pi$
$797$	−147.695	−	932.508i	−0.185313	−	1.17002i	0.703138	−	0.711053i	$-0.251781\pi$
$798$		0			0
$799$	−150.263	−	48.8236i	−0.188064	−	0.0611058i
$800$		0			0
$801$	−4.61851	+	3.35554i	−0.00576592	+	0.00418919i
$802$		0			0
$803$	25.5374	+	3.24138i	0.0318025	+	0.00403659i
$804$		0			0
$805$	923.603	−	1159.42i	1.14733	−	1.44027i
$806$		0			0
$807$	378.149	−	192.677i	0.468586	−	0.238757i
$808$		0			0
$809$	−148.538	+	204.445i	−0.183607	+	0.252713i	−0.890892	−	0.454215i	$-0.849920\pi$
$809$	−148.538	+	204.445i	−0.183607	+	0.252713i	0.707285	+	0.706929i	$0.249920\pi$
$810$		0			0
$811$	16.5757	+	51.0148i	0.0204386	+	0.0629035i	0.960756	−	0.277396i	$-0.0894715\pi$
$811$	16.5757	+	51.0148i	0.0204386	+	0.0629035i	−0.940317	+	0.340300i	$0.889471\pi$
$812$		0			0
$813$	136.311	−	136.311i	0.167664	−	0.167664i
$814$		0			0
$815$	567.985	−	1002.23i	0.696914	−	1.22973i
$816$		0			0
$817$	492.204	−	966.005i	0.602453	−	1.18238i
$818$		0			0
$819$	11.1841	−	15.3936i	0.0136558	−	0.0187956i
$820$		0			0
$821$	269.289	−	828.788i	0.328002	−	1.00949i	−0.642066	−	0.766650i	$-0.721922\pi$
$821$	269.289	−	828.788i	0.328002	−	1.00949i	0.970067	−	0.242836i	$-0.0780777\pi$
$822$		0			0
$823$	91.9788	−	580.731i	0.111760	−	0.705628i	−0.866644	−	0.498927i	$-0.833727\pi$
$823$	91.9788	−	580.731i	0.111760	−	0.705628i	0.978404	−	0.206700i	$-0.0662725\pi$
$824$		0			0
$825$	798.884	+	174.420i	0.968344	+	0.211418i
$826$		0			0
$827$	1425.68	+	225.805i	1.72392	+	0.273042i	0.938338	−	0.345719i	$-0.112365\pi$
$827$	1425.68	+	225.805i	1.72392	+	0.273042i	0.785579	+	0.618761i	$0.212365\pi$
$828$		0			0
$829$	−1263.48	−	410.531i	−1.52411	−	0.495212i	−0.577167	−	0.816626i	$-0.695842\pi$
$829$	−1263.48	−	410.531i	−1.52411	−	0.495212i	−0.946939	+	0.321414i	$0.895842\pi$
$830$		0			0
$831$	−1224.29	−	889.502i	−1.47328	−	1.07040i
$832$		0			0
$833$	25.9448	+	13.2195i	0.0311462	+	0.0158698i
$834$		0			0
$835$	350.995	+	198.917i	0.420353	+	0.238224i
$836$		0			0
$837$	453.209	+	453.209i	0.541468	+	0.541468i
$838$		0			0
$839$	216.137	−	70.2272i	0.257613	−	0.0837035i	−0.177363	−	0.984145i	$-0.556757\pi$
$839$	216.137	−	70.2272i	0.257613	−	0.0837035i	0.434976	+	0.900442i	$0.356757\pi$
$840$		0			0
$841$	−629.528	−	457.379i	−0.748547	−	0.543851i
$842$		0			0
$843$	−713.778	−	1400.87i	−0.846711	−	1.66176i
$844$		0			0
$845$	243.901	+	194.294i	0.288641	+	0.229934i
$846$		0			0
$847$	−715.518	−	632.311i	−0.844767	−	0.746530i
$848$		0			0
$849$	−228.155	−	314.028i	−0.268734	−	0.369880i
$850$		0			0
$851$	−590.878	+	1818.54i	−0.694334	+	2.13694i
$852$		0			0
$853$	−587.796	+	93.0977i	−0.689093	+	0.109142i	−0.491154	−	0.871073i	$-0.663425\pi$
$853$	−587.796	+	93.0977i	−0.689093	+	0.109142i	−0.197939	+	0.980214i	$0.563425\pi$
$854$		0			0
$855$	−8.92701	−	13.5083i	−0.0104410	−	0.0157992i
$856$		0			0
$857$	1137.02	+	1137.02i	1.32674	+	1.32674i	0.908196	+	0.418544i	$0.137460\pi$
$857$	1137.02	+	1137.02i	1.32674	+	1.32674i	0.418544	+	0.908196i	$0.362540\pi$
$858$		0			0
$859$		−	678.461i		−	0.789827i	−0.918718	−	0.394914i	$-0.870775\pi$
$859$		−	678.461i		−	0.789827i	0.918718	−	0.394914i	$-0.129225\pi$
$860$		0			0
$861$	395.316	+	1216.66i	0.459136	+	1.41307i
$862$		0			0
$863$	−1377.20	+	218.128i	−1.59583	+	0.252755i	−0.890114	−	0.455737i	$-0.849376\pi$
$863$	−1377.20	+	218.128i	−1.59583	+	0.252755i	−0.705718	+	0.708492i	$0.749376\pi$
$864$		0			0
$865$	−308.392	−	337.037i	−0.356523	−	0.389638i
$866$		0			0
$867$	−834.623	−	132.191i	−0.962656	−	0.152470i
$868$		0			0
$869$	983.441	−	30.3271i	1.13169	−	0.0348989i
$870$		0			0
$871$	−50.4613	+	36.6623i	−0.0579349	+	0.0420922i
$872$		0			0
$873$	−0.574313	−	1.12715i	−0.000657862	−	0.00129113i
$874$		0			0
$875$	−811.743	−	560.478i	−0.927706	−	0.640546i
$876$		0			0
$877$	59.3387	−	116.459i	0.0676610	−	0.132792i	−0.854699	−	0.519124i	$-0.826258\pi$
$877$	59.3387	−	116.459i	0.0676610	−	0.132792i	0.922360	+	0.386332i	$0.126258\pi$
$878$		0			0
$879$		−	387.363i		−	0.440685i
$880$		0			0
$881$	−211.392			−0.239946			−0.119973	−	0.992777i	$-0.538281\pi$
$881$	−211.392			−0.239946			−0.119973	+	0.992777i	$0.538281\pi$
$882$		0			0
$883$	−483.894	−	246.556i	−0.548011	−	0.279226i	0.157985	−	0.987442i	$-0.449500\pi$
$883$	−483.894	−	246.556i	−0.548011	−	0.279226i	−0.705996	+	0.708216i	$0.749500\pi$
$884$		0			0
$885$	−440.611	−	968.678i	−0.497866	−	1.09455i
$886$		0			0
$887$	279.069	−	142.193i	0.314621	−	0.160307i	−0.289548	−	0.957163i	$-0.593505\pi$
$887$	279.069	−	142.193i	0.314621	−	0.160307i	0.604169	+	0.796856i	$0.293505\pi$
$888$		0			0
$889$	421.513	+	580.162i	0.474142	+	0.652601i
$890$		0			0
$891$	535.906	+	691.725i	0.601466	+	0.776347i
$892$		0			0
$893$	230.210	−	1453.49i	0.257794	−	1.62765i
$894$		0			0
$895$	299.299	+	13.2834i	0.334413	+	0.0148417i
$896$		0			0
$897$	265.802	+	1678.21i	0.296323	+	1.87091i
$898$		0			0
$899$	−177.469	+	57.6631i	−0.197407	+	0.0641414i
$900$		0			0
$901$	72.6990			0.0806870
$902$		0			0
$903$	880.562	−	880.562i	0.975151	−	0.975151i
$904$		0			0
$905$	575.515	+	870.868i	0.635928	+	0.962285i
$906$		0			0
$907$	238.592	+	1506.41i	0.263056	+	1.66087i	0.666229	+	0.745747i	$0.267907\pi$
$907$	238.592	+	1506.41i	0.263056	+	1.66087i	−0.403173	+	0.915124i	$0.632093\pi$
$908$		0			0
$909$	27.8557	+	9.05085i	0.0306443	+	0.00995694i
$910$		0			0
$911$	771.138	−	560.264i	0.846474	−	0.614999i	−0.0776975	−	0.996977i	$-0.524757\pi$
$911$	771.138	−	560.264i	0.846474	−	0.614999i	0.924172	+	0.381978i	$0.124757\pi$
$912$		0			0
$913$	−294.216	+	624.289i	−0.322252	+	0.683777i
$914$		0			0
$915$	−89.1208	−	787.237i	−0.0973998	−	0.860368i
$916$		0			0
$917$	−1245.96	+	634.847i	−1.35873	+	0.692308i
$918$		0			0
$919$	258.510	−	355.809i	0.281295	−	0.387170i	−0.644867	−	0.764295i	$-0.723087\pi$
$919$	258.510	−	355.809i	0.281295	−	0.387170i	0.926162	+	0.377125i	$0.123087\pi$
$920$		0			0
$921$	69.9250	+	215.207i	0.0759229	+	0.233667i
$922$		0			0
$923$	−588.136	+	588.136i	−0.637201	+	0.637201i
$924$		0			0
$925$	1234.21	+	309.611i	1.33429	+	0.334714i
$926$		0			0
$927$	−12.1806	+	23.9057i	−0.0131398	+	0.0257883i
$928$		0			0
$929$	585.018	−	805.208i	0.629729	−	0.866747i	−0.368287	−	0.929712i	$-0.620056\pi$
$929$	585.018	−	805.208i	0.629729	−	0.866747i	0.998016	+	0.0629648i	$0.0200556\pi$
$930$		0			0
$931$	−83.8101	+	257.941i	−0.0900216	+	0.277058i
$932$		0			0
$933$	83.3025	−	525.951i	0.0892845	−	0.563720i
$934$		0			0
$935$	84.1386	+	86.4458i	0.0899878	+	0.0924554i
$936$		0			0
$937$	−1068.38	−	169.215i	−1.14022	−	0.180593i	−0.442365	−	0.896835i	$-0.645860\pi$
$937$	−1068.38	−	169.215i	−1.14022	−	0.180593i	−0.697851	+	0.716243i	$0.745860\pi$
$938$		0			0
$939$	367.228	+	119.320i	0.391084	+	0.127071i
$940$		0			0
$941$	871.044	+	632.850i	0.925657	+	0.672529i	0.944926	−	0.327285i	$-0.106134\pi$
$941$	871.044	+	632.850i	0.925657	+	0.672529i	−0.0192683	+	0.999814i	$0.506134\pi$
$942$		0			0
$943$	1824.87	+	929.819i	1.93518	+	0.986022i
$944$		0			0
$945$	−286.411	−	1035.65i	−0.303080	−	1.09593i
$946$		0			0
$947$	−1103.75	−	1103.75i	−1.16552	−	1.16552i	−0.983248	−	0.182275i	$-0.941654\pi$
$947$	−1103.75	−	1103.75i	−1.16552	−	1.16552i	−0.182275	−	0.983248i	$-0.558346\pi$
$948$		0			0
$949$	33.8541	−	10.9999i	0.0356734	−	0.0115910i
$950$		0			0
$951$	262.628	+	190.811i	0.276160	+	0.200642i
$952$		0			0
$953$	330.603	+	648.844i	0.346907	+	0.680844i	0.996865	−	0.0791267i	$-0.0252132\pi$
$953$	330.603	+	648.844i	0.346907	+	0.680844i	−0.649957	+	0.759971i	$0.725213\pi$
$954$		0			0
$955$	201.511	−	252.961i	0.211007	−	0.264881i
$956$		0			0
$957$	−254.761	+	48.4430i	−0.266208	+	0.0506196i
$958$		0			0
$959$	442.395	+	608.904i	0.461309	+	0.634937i
$960$		0			0
$961$	−125.793	+	387.151i	−0.130898	+	0.402862i
$962$		0			0
$963$	7.16561	−	1.13492i	0.00744093	−	0.00117853i
$964$		0			0
$965$	−1332.13	−	272.024i	−1.38045	−	0.281890i
$966$		0			0
$967$	485.778	+	485.778i	0.502355	+	0.502355i	0.912169	−	0.409814i	$-0.134406\pi$
$967$	485.778	+	485.778i	0.502355	+	0.502355i	−0.409814	+	0.912169i	$0.634406\pi$
$968$		0			0
$969$			133.233i			0.137495i
$970$		0			0
$971$	−501.435	−	1543.26i	−0.516411	−	1.58935i	−0.780700	−	0.624906i	$-0.785137\pi$
$971$	−501.435	−	1543.26i	−0.516411	−	1.58935i	0.264289	−	0.964444i	$-0.414863\pi$
$972$		0			0
$973$	539.650	−	85.4721i	0.554625	−	0.0878439i
$974$		0			0
$975$	1102.10	−	252.770i	1.13036	−	0.259251i
$976$		0			0
$977$	−1802.47	−	285.484i	−1.84491	−	0.292205i	−0.866544	−	0.499101i	$-0.833664\pi$
$977$	−1802.47	−	285.484i	−1.84491	−	0.292205i	−0.978363	+	0.206897i	$0.933664\pi$
$978$		0			0
$979$	327.521	+	222.864i	0.334546	+	0.227645i
$980$		0			0
$981$	26.6750	−	19.3805i	0.0271916	−	0.0197559i
$982$		0			0
$983$	−257.091	−	504.570i	−0.261537	−	0.513296i	0.722475	−	0.691397i	$-0.243005\pi$
$983$	−257.091	−	504.570i	−0.261537	−	0.513296i	−0.984012	+	0.178101i	$0.943005\pi$
$984$		0			0
$985$	445.651	+	979.759i	0.452438	+	0.994679i
$986$		0			0
$987$	767.389	−	1506.09i	0.777496	−	1.52592i
$988$		0			0
$989$		−	1993.72i		−	2.01590i
$990$		0			0
$991$	765.723			0.772677			0.386339	−	0.922357i	$-0.373740\pi$
$991$	765.723			0.772677			0.386339	+	0.922357i	$0.373740\pi$
$992$		0			0
$993$	−774.873	−	394.818i	−0.780336	−	0.397601i
$994$		0			0
$995$	263.335	−	702.781i	0.264659	−	0.706313i
$996$		0			0
$997$	−1027.27	+	523.420i	−1.03036	+	0.524995i	−0.885589	−	0.464471i	$-0.846245\pi$
$997$	−1027.27	+	523.420i	−1.03036	+	0.524995i	−0.144771	+	0.989465i	$0.546245\pi$
$998$		0			0
$999$	814.722	+	1121.37i	0.815537	+	1.12249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.x.a.157.4	yes	96
5.3	odd	4	inner	220.3.x.a.113.9	yes	96
11.4	even	5	inner	220.3.x.a.37.9	✓	96
55.48	odd	20	inner	220.3.x.a.213.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.x.a.37.9	✓	96	11.4	even	5	inner
220.3.x.a.113.9	yes	96	5.3	odd	4	inner
220.3.x.a.157.4	yes	96	1.1	even	1	trivial
220.3.x.a.213.4	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.64938 - 1.34992i) q^{3} +(-4.68210 - 1.75440i) q^{5} +(7.03139 - 3.58267i) q^{7} +(-0.0931732 - 0.128242i) q^{9} +(-6.18826 + 9.09425i) q^{11} +(-2.37948 + 15.0235i) q^{13} +(10.0363 + 10.9686i) q^{15} +(0.343110 + 2.16631i) q^{17} +(-19.4291 + 6.31290i) q^{19} -23.4651 q^{21} +(-26.5643 + 26.5643i) q^{23} +(18.8441 + 16.4286i) q^{25} +(4.26010 + 26.8972i) q^{27} +(-7.54043 - 2.45004i) q^{29} +(19.0407 - 13.8339i) q^{31} +(28.6716 - 15.7404i) q^{33} +(-39.2071 + 4.43853i) q^{35} +(45.3507 - 23.1073i) q^{37} +(26.5847 - 36.5906i) q^{39} +(-16.8469 - 51.8496i) q^{41} +(-37.5264 + 37.5264i) q^{43} +(0.211258 + 0.763905i) q^{45} +(-32.7034 + 64.1840i) q^{47} +(7.80344 - 10.7405i) q^{49} +(2.01533 - 6.20255i) q^{51} +(5.18513 - 32.7376i) q^{53} +(44.9291 - 31.7235i) q^{55} +(59.9970 + 9.50259i) q^{57} +(-68.0751 - 22.1189i) q^{59} +(-43.1118 - 31.3225i) q^{61} +(-1.11459 - 0.567910i) q^{63} +(37.4982 - 66.1667i) q^{65} +(2.89959 + 2.89959i) q^{67} +(106.238 - 34.5190i) q^{69} +(44.2385 + 32.1412i) q^{71} +(-1.06243 - 2.08514i) q^{73} +(-27.7478 - 68.9637i) q^{75} +(-10.9304 + 86.1158i) q^{77} +(-52.5752 - 72.3635i) q^{79} +(24.5818 - 75.6549i) q^{81} +(61.9680 - 9.81477i) q^{83} +(2.19411 - 10.7449i) q^{85} +(16.6701 + 16.6701i) q^{87} -36.0140i q^{89} +(37.0931 + 114.161i) q^{91} +(-69.1207 + 10.9476i) q^{93} +(102.044 + 4.52889i) q^{95} +(7.88225 + 1.24843i) q^{97} +(1.74284 - 0.0537454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} + 4 q^{5} - 2 q^{7} - 20 q^{11} - 8 q^{13} + 88 q^{15} + 42 q^{17} + 56 q^{21} - 104 q^{23} - 126 q^{25} - 14 q^{27} - 32 q^{31} + 52 q^{33} + 56 q^{35} - 134 q^{37} + 24 q^{41} + 332 q^{43}+ \cdots - 310 q^{97}+O(q^{100}) \) 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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