LMFDB - Embedded newform 441.4.e.z.361.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 74 x^{14} + 4007 x^{12} + 91050 x^{10} + 1502189 x^{8} + 12598332 x^{6} + 74261084 x^{4} + \cdots + 6250000 $ x^16 + 74x^14 + 4007x^12 + 91050x^10 + 1502189x^8 + 12598332x^6 + 74261084x^4 + 22070000*x^2 + 6250000
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.4
Root			$-1.68703 - 2.92202i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.4.e.z.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.979925 - 1.69728i) q^{2} +(2.07949 - 3.60179i) q^{4} +(5.94483 + 10.2967i) q^{5} -23.8298 q^{8} +O(q^{10})$	\(q+(-0.979925 - 1.69728i) q^{2} +(2.07949 - 3.60179i) q^{4} +(5.94483 + 10.2967i) q^{5} -23.8298 q^{8} +(11.6510 - 20.1801i) q^{10} +(-18.2065 + 31.5346i) q^{11} -0.964525 q^{13} +(6.71545 + 11.6315i) q^{16} +(49.1257 - 85.0882i) q^{17} +(-53.0004 - 91.7994i) q^{19} +49.4490 q^{20} +71.3640 q^{22} +(-27.1816 - 47.0800i) q^{23} +(-8.18202 + 14.1717i) q^{25} +(0.945162 + 1.63707i) q^{26} +229.725 q^{29} +(63.8645 - 110.616i) q^{31} +(-82.1579 + 142.302i) q^{32} -192.558 q^{34} +(-155.908 - 270.040i) q^{37} +(-103.873 + 179.913i) q^{38} +(-141.664 - 245.369i) q^{40} +419.919 q^{41} +523.180 q^{43} +(75.7207 + 131.152i) q^{44} +(-53.2719 + 92.2697i) q^{46} +(135.164 + 234.111i) q^{47} +32.0711 q^{50} +(-2.00572 + 3.47402i) q^{52} +(125.541 - 217.443i) q^{53} -432.938 q^{55} +(-225.113 - 389.907i) q^{58} +(204.015 - 353.364i) q^{59} +(-430.273 - 745.255i) q^{61} -250.329 q^{62} +429.481 q^{64} +(-5.73394 - 9.93147i) q^{65} +(-253.180 + 438.520i) q^{67} +(-204.313 - 353.881i) q^{68} -523.702 q^{71} +(314.982 - 545.565i) q^{73} +(-305.556 + 529.239i) q^{74} -440.856 q^{76} +(-159.774 - 276.737i) q^{79} +(-79.8444 + 138.295i) q^{80} +(-411.489 - 712.720i) q^{82} -1309.16 q^{83} +1168.18 q^{85} +(-512.677 - 887.982i) q^{86} +(433.857 - 751.463i) q^{88} +(-174.290 - 301.880i) q^{89} -226.096 q^{92} +(264.901 - 458.822i) q^{94} +(630.157 - 1091.46i) q^{95} +161.996 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 68 q^{4}+O(q^{10}) $ 16 * q - 68 * q^4	$ 16 q - 68 q^{4} - 804 q^{16} + 1952 q^{22} - 536 q^{25} - 64 q^{37} + 4320 q^{43} + 768 q^{46} - 2184 q^{58} + 15176 q^{64} - 5392 q^{79} + 5728 q^{85} - 5616 q^{88}+O(q^{100}) $ 16 * q - 68 * q^4 - 804 * q^16 + 1952 * q^22 - 536 * q^25 - 64 * q^37 + 4320 * q^43 + 768 * q^46 - 2184 * q^58 + 15176 * q^64 - 5392 * q^79 + 5728 * q^85 - 5616 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.979925	−	1.69728i	−0.346456	−	0.600079i	0.639161	−	0.769073i	$-0.279282\pi$
$2$	−0.979925	−	1.69728i	−0.346456	−	0.600079i	−0.985617	+	0.168994i	$0.945948\pi$
$3$		0			0
$3$		0			0
$4$	2.07949	−	3.60179i	0.259937	−	0.450224i
$5$	5.94483	+	10.2967i	0.531722	+	0.920969i	0.999314	+	0.0370251i	$0.0117881\pi$
$5$	5.94483	+	10.2967i	0.531722	+	0.920969i	−0.467593	+	0.883944i	$0.654879\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−23.8298			−1.05314
$9$		0			0
$10$	11.6510	−	20.1801i	0.368436	−	0.638150i
$11$	−18.2065	+	31.5346i	−0.499043	+	0.864367i	−0.999999	−	0.00110512i	$-0.999648\pi$
$11$	−18.2065	+	31.5346i	−0.499043	+	0.864367i	0.500957	+	0.865472i	$0.332982\pi$
$12$		0			0
$13$	−0.964525			−0.0205778			−0.0102889	−	0.999947i	$-0.503275\pi$
$13$	−0.964525			−0.0205778			−0.0102889	+	0.999947i	$0.503275\pi$
$14$		0			0
$15$		0			0
$16$	6.71545	+	11.6315i	0.104929	+	0.181742i
$17$	49.1257	−	85.0882i	0.700866	−	1.21394i	−0.267296	−	0.963614i	$-0.586130\pi$
$17$	49.1257	−	85.0882i	0.700866	−	1.21394i	0.968163	−	0.250322i	$-0.0805364\pi$
$18$		0			0
$19$	−53.0004	−	91.7994i	−0.639954	−	1.10843i	−0.985442	−	0.170010i	$-0.945620\pi$
$19$	−53.0004	−	91.7994i	−0.639954	−	1.10843i	0.345488	−	0.938423i	$-0.387713\pi$
$20$	49.4490			0.552856
$21$		0			0
$22$	71.3640			0.691585
$23$	−27.1816	−	47.0800i	−0.246424	−	0.426820i	0.716107	−	0.697991i	$-0.245922\pi$
$23$	−27.1816	−	47.0800i	−0.246424	−	0.426820i	−0.962531	+	0.271171i	$0.912589\pi$
$24$		0			0
$25$	−8.18202	+	14.1717i	−0.0654562	+	0.113373i
$26$	0.945162	+	1.63707i	0.00712929	+	0.0123483i
$27$		0			0
$28$		0			0
$29$	229.725			1.47099			0.735497	−	0.677528i	$-0.236949\pi$
$29$	229.725			1.47099			0.735497	+	0.677528i	$0.236949\pi$
$30$		0			0
$31$	63.8645	−	110.616i	0.370013	−	0.640881i	−0.619554	−	0.784954i	$-0.712687\pi$
$31$	63.8645	−	110.616i	0.370013	−	0.640881i	0.989567	+	0.144073i	$0.0460200\pi$
$32$	−82.1579	+	142.302i	−0.453863	+	0.786113i
$33$		0			0
$34$	−192.558			−0.971277
$35$		0			0
$36$		0			0
$37$	−155.908	−	270.040i	−0.692732	−	1.19985i	−0.970939	−	0.239326i	$-0.923073\pi$
$37$	−155.908	−	270.040i	−0.692732	−	1.19985i	0.278207	−	0.960521i	$-0.410260\pi$
$38$	−103.873	+	179.913i	−0.443432	+	0.768046i
$39$		0			0
$40$	−141.664	−	245.369i	−0.559976	−	0.969908i
$41$	419.919			1.59952			0.799760	−	0.600320i	$-0.204960\pi$
$41$	419.919			1.59952			0.799760	+	0.600320i	$0.204960\pi$
$42$		0			0
$43$	523.180			1.85545			0.927723	−	0.373270i	$-0.121763\pi$
$43$	523.180			1.85545			0.927723	+	0.373270i	$0.121763\pi$
$44$	75.7207	+	131.152i	0.259439	+	0.449362i
$45$		0			0
$46$	−53.2719	+	92.2697i	−0.170750	+	0.295748i
$47$	135.164	+	234.111i	0.419483	+	0.726566i	0.995887	−	0.0905985i	$-0.0288780\pi$
$47$	135.164	+	234.111i	0.419483	+	0.726566i	−0.576404	+	0.817165i	$0.695545\pi$
$48$		0			0
$49$		0			0
$50$	32.0711			0.0907107
$51$		0			0
$52$	−2.00572	+	3.47402i	−0.00534892	+	0.00926460i
$53$	125.541	−	217.443i	0.325366	−	0.563550i	−0.656221	−	0.754569i	$-0.727846\pi$
$53$	125.541	−	217.443i	0.325366	−	0.563550i	0.981586	+	0.191019i	$0.0611792\pi$
$54$		0			0
$55$	−432.938			−1.06141
$56$		0			0
$57$		0			0
$58$	−225.113	−	389.907i	−0.509634	−	0.882712i
$59$	204.015	−	353.364i	0.450177	−	0.779729i	−0.548220	−	0.836334i	$-0.684694\pi$
$59$	204.015	−	353.364i	0.450177	−	0.779729i	0.998397	+	0.0566051i	$0.0180276\pi$
$60$		0			0
$61$	−430.273	−	745.255i	−0.903128	−	1.56426i	−0.823411	−	0.567446i	$-0.807932\pi$
$61$	−430.273	−	745.255i	−0.903128	−	1.56426i	−0.0797171	−	0.996818i	$-0.525402\pi$
$62$	−250.329			−0.512772
$63$		0			0
$64$	429.481			0.838831
$65$	−5.73394	−	9.93147i	−0.0109417	−	0.0189515i
$66$		0			0
$67$	−253.180	+	438.520i	−0.461654	+	0.799609i	−0.999044	−	0.0437257i	$-0.986077\pi$
$67$	−253.180	+	438.520i	−0.461654	+	0.799609i	0.537389	+	0.843334i	$0.319411\pi$
$68$	−204.313	−	353.881i	−0.364362	−	0.631093i
$69$		0			0
$70$		0			0
$71$	−523.702			−0.875380			−0.437690	−	0.899126i	$-0.644203\pi$
$71$	−523.702			−0.875380			−0.437690	+	0.899126i	$0.644203\pi$
$72$		0			0
$73$	314.982	−	545.565i	0.505012	−	0.874706i	−0.494972	−	0.868909i	$-0.664822\pi$
$73$	314.982	−	545.565i	0.505012	−	0.874706i	0.999983	−	0.00579655i	$-0.00184511\pi$
$74$	−305.556	+	529.239i	−0.480002	+	0.831388i
$75$		0			0
$76$	−440.856			−0.665391
$77$		0			0
$78$		0			0
$79$	−159.774	−	276.737i	−0.227544	−	0.394118i	0.729535	−	0.683943i	$-0.239736\pi$
$79$	−159.774	−	276.737i	−0.227544	−	0.394118i	−0.957080	+	0.289825i	$0.906403\pi$
$80$	−79.8444	+	138.295i	−0.111586	+	0.193273i
$81$		0			0
$82$	−411.489	−	712.720i	−0.554163	−	0.959838i
$83$	−1309.16			−1.73131			−0.865654	−	0.500643i	$-0.833097\pi$
$83$	−1309.16			−1.73131			−0.865654	+	0.500643i	$0.833097\pi$
$84$		0			0
$85$	1168.18			1.49066
$86$	−512.677	−	887.982i	−0.642830	−	1.11341i
$87$		0			0
$88$	433.857	−	751.463i	0.525561	−	0.910298i
$89$	−174.290	−	301.880i	−0.207581	−	0.359542i	0.743371	−	0.668880i	$-0.233226\pi$
$89$	−174.290	−	301.880i	−0.207581	−	0.359542i	−0.950952	+	0.309338i	$0.899893\pi$
$90$		0			0
$91$		0			0
$92$	−226.096			−0.256219
$93$		0			0
$94$	264.901	−	458.822i	0.290665	−	0.503446i
$95$	630.157	−	1091.46i	0.680555	−	1.17876i
$96$		0			0
$97$	161.996			0.169569			0.0847844	−	0.996399i	$-0.472980\pi$
$97$	161.996			0.169569			0.0847844	+	0.996399i	$0.472980\pi$
$98$		0			0
$99$		0			0
$100$	34.0289	+	58.9399i	0.0340289	+	0.0589399i
$101$	−109.171	+	189.090i	−0.107554	+	0.186289i	−0.914779	−	0.403955i	$-0.867635\pi$
$101$	−109.171	+	189.090i	−0.107554	+	0.186289i	0.807225	+	0.590244i	$0.200968\pi$
$102$		0			0
$103$	−115.545	−	200.130i	−0.110534	−	0.191451i	0.805452	−	0.592661i	$-0.201923\pi$
$103$	−115.545	−	200.130i	−0.110534	−	0.191451i	−0.915986	+	0.401211i	$0.868589\pi$
$104$	22.9844			0.0216712
$105$		0			0
$106$	−492.083			−0.450899
$107$	932.562	+	1615.25i	0.842563	+	1.45936i	0.887721	+	0.460381i	$0.152287\pi$
$107$	932.562	+	1615.25i	0.842563	+	1.45936i	−0.0451586	+	0.998980i	$0.514379\pi$
$108$		0			0
$109$	−300.502	+	520.485i	−0.264063	+	0.457371i	−0.967318	−	0.253567i	$-0.918396\pi$
$109$	−300.502	+	520.485i	−0.264063	+	0.457371i	0.703255	+	0.710938i	$0.251729\pi$
$110$	424.247	+	734.818i	0.367731	+	0.636928i
$111$		0			0
$112$		0			0
$113$	−475.349			−0.395727			−0.197863	−	0.980230i	$-0.563400\pi$
$113$	−475.349			−0.395727			−0.197863	+	0.980230i	$0.563400\pi$
$114$		0			0
$115$	323.180	−	559.765i	0.262058	−	0.453899i
$116$	477.711	−	827.420i	0.382365	−	0.662276i
$117$		0			0
$118$	−799.676			−0.623865
$119$		0			0
$120$		0			0
$121$	2.54607	+	4.40992i	0.00191290	+	0.00331324i
$122$	−843.270	+	1460.59i	−0.625788	+	1.08390i
$123$		0			0
$124$	−265.612	−	460.053i	−0.192360	−	0.333177i
$125$	1291.64			0.924226
$126$		0			0
$127$	−29.0876			−0.0203237			−0.0101619	−	0.999948i	$-0.503235\pi$
$127$	−29.0876			−0.0203237			−0.0101619	+	0.999948i	$0.503235\pi$
$128$	236.404	+	409.463i	0.163245	+	0.282748i
$129$		0			0
$130$	−11.2377	+	19.4642i	−0.00758160	+	0.0131317i
$131$	−1057.63	−	1831.87i	−0.705387	−	1.22177i	−0.966552	−	0.256472i	$-0.917440\pi$
$131$	−1057.63	−	1831.87i	−0.705387	−	1.22177i	0.261164	−	0.965294i	$-0.415894\pi$
$132$		0			0
$133$		0			0
$134$	992.389			0.639771
$135$		0			0
$136$	−1170.65	+	2027.63i	−0.738109	+	1.27844i
$137$	−88.6708	+	153.582i	−0.0552968	+	0.0957768i	−0.892349	−	0.451347i	$-0.850944\pi$
$137$	−88.6708	+	153.582i	−0.0552968	+	0.0957768i	0.837052	+	0.547123i	$0.184277\pi$
$138$		0			0
$139$	2369.18			1.44569			0.722846	−	0.691009i	$-0.242834\pi$
$139$	2369.18			1.44569			0.722846	+	0.691009i	$0.242834\pi$
$140$		0			0
$141$		0			0
$142$	513.189	+	888.869i	0.303281	+	0.525297i
$143$	17.5606	−	30.4159i	0.0102692	−	0.0177868i
$144$		0			0
$145$	1365.67	+	2365.42i	0.782159	+	1.35474i
$146$	−1234.63			−0.699857
$147$		0			0
$148$	−1296.84			−0.720266
$149$	−745.517	−	1291.27i	−0.409900	−	0.709968i	0.584978	−	0.811049i	$-0.301103\pi$
$149$	−745.517	−	1291.27i	−0.409900	−	0.709968i	−0.994878	+	0.101081i	$0.967770\pi$
$150$		0			0
$151$	−205.230	+	355.469i	−0.110605	+	0.191574i	−0.916014	−	0.401145i	$-0.868612\pi$
$151$	−205.230	+	355.469i	−0.110605	+	0.191574i	0.805409	+	0.592719i	$0.201946\pi$
$152$	1262.99	+	2187.56i	0.673960	+	1.16733i
$153$		0			0
$154$		0			0
$155$	1518.65			0.786975
$156$		0			0
$157$	−226.750	+	392.743i	−0.115265	+	0.199645i	−0.917886	−	0.396845i	$-0.870105\pi$
$157$	−226.750	+	392.743i	−0.115265	+	0.199645i	0.802621	+	0.596490i	$0.203438\pi$
$158$	−313.133	+	542.363i	−0.157668	+	0.273089i
$159$		0			0
$160$	−1953.66			−0.965314
$161$		0			0
$162$		0			0
$163$	−374.083	−	647.931i	−0.179757	−	0.311349i	0.762040	−	0.647530i	$-0.224198\pi$
$163$	−374.083	−	647.931i	−0.179757	−	0.311349i	−0.941797	+	0.336181i	$0.890865\pi$
$164$	873.219	−	1512.46i	0.415774	−	0.720142i
$165$		0			0
$166$	1282.87	+	2222.00i	0.599821	+	1.03892i
$167$	518.269			0.240149			0.120074	−	0.992765i	$-0.461687\pi$
$167$	518.269			0.240149			0.120074	+	0.992765i	$0.461687\pi$
$168$		0			0
$169$	−2196.07			−0.999577
$170$	−1144.72	−	1982.72i	−0.516449	−	0.894516i
$171$		0			0
$172$	1087.95	−	1884.38i	0.482299	−	0.835366i
$173$	−656.742	−	1137.51i	−0.288620	−	0.499904i	0.684861	−	0.728674i	$-0.259863\pi$
$173$	−656.742	−	1137.51i	−0.288620	−	0.499904i	−0.973480	+	0.228770i	$0.926530\pi$
$174$		0			0
$175$		0			0
$176$	−489.060			−0.209456
$177$		0			0
$178$	−341.583	+	591.639i	−0.143836	+	0.249131i
$179$	−2066.57	+	3579.41i	−0.862921	+	1.49462i	0.00617538	+	0.999981i	$0.498034\pi$
$179$	−2066.57	+	3579.41i	−0.862921	+	1.49462i	−0.869097	+	0.494642i	$0.835299\pi$
$180$		0			0
$181$	3714.04			1.52521			0.762603	−	0.646867i	$-0.223921\pi$
$181$	3714.04			1.52521			0.762603	+	0.646867i	$0.223921\pi$
$182$		0			0
$183$		0			0
$184$	647.733	+	1121.91i	0.259519	+	0.449500i
$185$	1853.69	−	3210.69i	0.736682	−	1.27597i
$186$		0			0
$187$	1788.81	+	3098.32i	0.699524	+	1.21161i
$188$	1124.29			0.436156
$189$		0			0
$190$	−2470.03			−0.943129
$191$	1534.19	+	2657.29i	0.581203	+	1.00667i	0.995337	+	0.0964578i	$0.0307513\pi$
$191$	1534.19	+	2657.29i	0.581203	+	1.00667i	−0.414134	+	0.910216i	$0.635915\pi$
$192$		0			0
$193$	−1044.77	+	1809.59i	−0.389657	+	0.674906i	−0.992403	−	0.123027i	$-0.960740\pi$
$193$	−1044.77	+	1809.59i	−0.389657	+	0.674906i	0.602746	+	0.797933i	$0.294073\pi$
$194$	−158.744	−	274.952i	−0.0587481	−	0.101755i
$195$		0			0
$196$		0			0
$197$	−3729.89			−1.34895			−0.674476	−	0.738297i	$-0.735630\pi$
$197$	−3729.89			−1.34895			−0.674476	+	0.738297i	$0.735630\pi$
$198$		0			0
$199$	−1054.42	+	1826.31i	−0.375608	+	0.650573i	−0.990418	−	0.138103i	$-0.955900\pi$
$199$	−1054.42	+	1826.31i	−0.375608	+	0.650573i	0.614809	+	0.788676i	$0.289233\pi$
$200$	194.976	−	337.708i	0.0689344	−	0.119398i
$201$		0			0
$202$	427.918			0.149051
$203$		0			0
$204$		0			0
$205$	2496.35	+	4323.80i	0.850499	+	1.47311i
$206$	−226.451	+	392.225i	−0.0765903	+	0.132658i
$207$		0			0
$208$	−6.47722	−	11.2189i	−0.00215920	−	0.00373985i
$209$	3859.81			1.27746
$210$		0			0
$211$	−1546.53			−0.504584			−0.252292	−	0.967651i	$-0.581184\pi$
$211$	−1546.53			−0.504584			−0.252292	+	0.967651i	$0.581184\pi$
$212$	−522.124	−	904.345i	−0.169149	−	0.292975i
$213$		0			0
$214$	1827.68	−	3165.64i	0.583821	−	1.01121i
$215$	3110.22	+	5387.05i	0.986581	+	1.70881i
$216$		0			0
$217$		0			0
$218$	1177.88			0.365945
$219$		0			0
$220$	−900.293	+	1559.35i	−0.275899	+	0.477871i
$221$	−47.3829	+	82.0697i	−0.0144223	+	0.0249801i
$222$		0			0
$223$	4860.40			1.45954			0.729768	−	0.683695i	$-0.239628\pi$
$223$	4860.40			1.45954			0.729768	+	0.683695i	$0.239628\pi$
$224$		0			0
$225$		0			0
$226$	465.807	+	806.801i	0.137102	+	0.237467i
$227$	−350.471	+	607.034i	−0.102474	+	0.177490i	−0.912703	−	0.408623i	$-0.866009\pi$
$227$	−350.471	+	607.034i	−0.102474	+	0.177490i	0.810229	+	0.586113i	$0.199342\pi$
$228$		0			0
$229$	1847.12	+	3199.30i	0.533018	+	0.923214i	0.999256	+	0.0385550i	$0.0122755\pi$
$229$	1847.12	+	3199.30i	0.533018	+	0.923214i	−0.466239	+	0.884659i	$0.654391\pi$
$230$	−1266.77			−0.363167
$231$		0			0
$232$	−5474.29			−1.54916
$233$	−172.161	−	298.192i	−0.0484062	−	0.0838420i	0.840807	−	0.541335i	$-0.182081\pi$
$233$	−172.161	−	298.192i	−0.0484062	−	0.0838420i	−0.889213	+	0.457493i	$0.848748\pi$
$234$		0			0
$235$	−1607.06	+	2783.50i	−0.446097	+	0.772662i
$236$	−848.494	−	1469.64i	−0.234035	−	0.405361i
$237$		0			0
$238$		0			0
$239$	6144.21			1.66291			0.831456	−	0.555590i	$-0.187508\pi$
$239$	6144.21			1.66291			0.831456	+	0.555590i	$0.187508\pi$
$240$		0			0
$241$	2813.06	−	4872.36i	0.751888	−	1.30231i	−0.195019	−	0.980799i	$-0.562477\pi$
$241$	2813.06	−	4872.36i	0.751888	−	1.30231i	0.946907	−	0.321508i	$-0.104190\pi$
$242$	4.98991	−	8.64277i	0.00132547	−	0.00229578i
$243$		0			0
$244$	−3579.00			−0.939025
$245$		0			0
$246$		0			0
$247$	51.1202	+	88.5429i	0.0131688	+	0.0228091i
$248$	−1521.88	+	2635.97i	−0.389674	+	0.674936i
$249$		0			0
$250$	−1265.71	−	2192.28i	−0.320203	−	0.554608i
$251$	−520.460			−0.130881			−0.0654405	−	0.997856i	$-0.520845\pi$
$251$	−520.460			−0.130881			−0.0654405	+	0.997856i	$0.520845\pi$
$252$		0			0
$253$	1979.53			0.491905
$254$	28.5037	+	49.3699i	0.00704127	+	0.0121958i
$255$		0			0
$256$	2181.24	−	3778.02i	0.532530	−	0.922368i
$257$	−2004.75	−	3472.33i	−0.486587	−	0.842794i	0.513294	−	0.858213i	$-0.328425\pi$
$257$	−2004.75	−	3472.33i	−0.486587	−	0.842794i	−0.999881	+	0.0154192i	$0.995092\pi$
$258$		0			0
$259$		0			0
$260$	−47.6948			−0.0113766
$261$		0			0
$262$	−2072.80	+	3590.20i	−0.488771	+	0.846576i
$263$	1792.60	−	3104.87i	0.420290	−	0.727963i	−0.575678	−	0.817677i	$-0.695262\pi$
$263$	1792.60	−	3104.87i	0.420290	−	0.727963i	0.995968	+	0.0897135i	$0.0285951\pi$
$264$		0			0
$265$	2985.28			0.692016
$266$		0			0
$267$		0			0
$268$	1052.97	+	1823.80i	0.240002	+	0.415695i
$269$	−2754.59	+	4771.10i	−0.624352	+	1.08141i	0.364314	+	0.931276i	$0.381303\pi$
$269$	−2754.59	+	4771.10i	−0.624352	+	1.08141i	−0.988666	+	0.150133i	$0.952030\pi$
$270$		0			0
$271$	2909.95	+	5040.18i	0.652276	+	1.12977i	0.982569	+	0.185896i	$0.0595189\pi$
$271$	2909.95	+	5040.18i	0.652276	+	1.12977i	−0.330294	+	0.943878i	$0.607148\pi$
$272$	1319.60			0.294165
$273$		0			0
$274$	347.563			0.0766316
$275$	−297.932	−	516.034i	−0.0653308	−	0.113156i
$276$		0			0
$277$	575.226	−	996.320i	0.124772	−	0.216112i	−0.796872	−	0.604149i	$-0.793513\pi$
$277$	575.226	−	996.320i	0.124772	−	0.216112i	0.921644	+	0.388037i	$0.126847\pi$
$278$	−2321.62	−	4021.16i	−0.500868	−	0.867529i
$279$		0			0
$280$		0			0
$281$	−895.631			−0.190138			−0.0950692	−	0.995471i	$-0.530307\pi$
$281$	−895.631			−0.190138			−0.0950692	+	0.995471i	$0.530307\pi$
$282$		0			0
$283$	−61.2251	+	106.045i	−0.0128603	+	0.0222746i	−0.872384	−	0.488821i	$-0.837427\pi$
$283$	−61.2251	+	106.045i	−0.0128603	+	0.0222746i	0.859524	+	0.511096i	$0.170760\pi$
$284$	−1089.04	+	1886.27i	−0.227544	+	0.394117i
$285$		0			0
$286$	−68.8324			−0.0142313
$287$		0			0
$288$		0			0
$289$	−2370.16	−	4105.24i	−0.482427	−	0.835588i
$290$	2676.52	−	4635.86i	0.541967	−	0.938715i
$291$		0			0
$292$	−1310.01	−	2269.00i	−0.262542	−	0.454736i
$293$	−7601.77			−1.51570			−0.757850	−	0.652429i	$-0.773750\pi$
$293$	−7601.77			−1.51570			−0.757850	+	0.652429i	$0.773750\pi$
$294$		0			0
$295$	4851.33			0.957475
$296$	3715.25	+	6435.01i	0.729543	+	1.26360i
$297$		0			0
$298$	−1461.10	+	2530.70i	−0.284025	+	0.491945i
$299$	26.2174	+	45.4098i	0.00507087	+	0.00878300i
$300$		0			0
$301$		0			0
$302$	804.441			0.153279
$303$		0			0
$304$	711.844	−	1232.95i	0.134299	−	0.232613i
$305$	5115.80	−	8860.82i	0.960426	−	1.66351i
$306$		0			0
$307$	−3539.05			−0.657929			−0.328964	−	0.944342i	$-0.606700\pi$
$307$	−3539.05			−0.657929			−0.328964	+	0.944342i	$0.606700\pi$
$308$		0			0
$309$		0			0
$310$	−1488.17	−	2577.58i	−0.272652	−	0.472247i
$311$	1947.47	−	3373.11i	0.355083	−	0.615021i	−0.632049	−	0.774928i	$-0.717786\pi$
$311$	1947.47	−	3373.11i	0.355083	−	0.615021i	0.987132	+	0.159907i	$0.0511194\pi$
$312$		0			0
$313$	−4341.29	−	7519.33i	−0.783975	−	1.35788i	−0.929610	−	0.368546i	$-0.879856\pi$
$313$	−4341.29	−	7519.33i	−0.783975	−	1.35788i	0.145635	−	0.989338i	$-0.453478\pi$
$314$	888.792			0.159737
$315$		0			0
$316$	−1329.00			−0.236589
$317$	−4247.76	−	7357.34i	−0.752612	−	1.30356i	−0.946553	−	0.322549i	$-0.895460\pi$
$317$	−4247.76	−	7357.34i	−0.752612	−	1.30356i	0.193941	−	0.981013i	$-0.437873\pi$
$318$		0			0
$319$	−4182.48	+	7244.28i	−0.734088	+	1.27148i
$320$	2553.19	+	4422.26i	0.446025	+	0.772537i
$321$		0			0
$322$		0			0
$323$	−10414.7			−1.79409
$324$		0			0
$325$	7.89177	−	13.6689i	0.00134694	−	0.00233297i
$326$	−733.147	+	1269.85i	−0.124556	+	0.215737i
$327$		0			0
$328$	−10006.6			−1.68451
$329$		0			0
$330$		0			0
$331$	−635.355	−	1100.47i	−0.105505	−	0.182741i	0.808439	−	0.588580i	$-0.200313\pi$
$331$	−635.355	−	1100.47i	−0.105505	−	0.182741i	−0.913945	+	0.405839i	$0.866979\pi$
$332$	−2722.38	+	4715.30i	−0.450031	+	0.779476i
$333$		0			0
$334$	−507.865	−	879.647i	−0.0832010	−	0.144108i
$335$	−6020.44			−0.981886
$336$		0			0
$337$	4695.47			0.758986			0.379493	−	0.925195i	$-0.376098\pi$
$337$	4695.47			0.758986			0.379493	+	0.925195i	$0.376098\pi$
$338$	2151.98	+	3727.34i	0.346309	+	0.599825i
$339$		0			0
$340$	2429.21	−	4207.52i	0.387478	−	0.671132i
$341$	2325.50	+	4027.88i	0.369304	+	0.639654i
$342$		0			0
$343$		0			0
$344$	−12467.3			−1.95404
$345$		0			0
$346$	−1287.12	+	2229.35i	−0.199988	+	0.346389i
$347$	−3256.98	+	5641.26i	−0.503874	+	0.872735i	0.496116	+	0.868256i	$0.334759\pi$
$347$	−3256.98	+	5641.26i	−0.503874	+	0.872735i	−0.999990	+	0.00447854i	$0.998574\pi$
$348$		0			0
$349$	7184.75			1.10198			0.550990	−	0.834512i	$-0.314250\pi$
$349$	7184.75			1.10198			0.550990	+	0.834512i	$0.314250\pi$
$350$		0			0
$351$		0			0
$352$	−2991.62	−	5181.63i	−0.452994	−	0.784608i
$353$	−3034.27	+	5255.52i	−0.457502	+	0.792416i	−0.998828	−	0.0483961i	$-0.984589\pi$
$353$	−3034.27	+	5255.52i	−0.457502	+	0.792416i	0.541326	+	0.840813i	$0.317922\pi$
$354$		0			0
$355$	−3113.32	−	5392.43i	−0.465459	−	0.806198i
$356$	−1449.74			−0.215832
$357$		0			0
$358$	8100.34			1.19586
$359$	−871.857	−	1510.10i	−0.128175	−	0.222006i	0.794795	−	0.606879i	$-0.207579\pi$
$359$	−871.857	−	1510.10i	−0.128175	−	0.222006i	−0.922970	+	0.384873i	$0.874245\pi$
$360$		0			0
$361$	−2188.59	+	3790.75i	−0.319083	+	0.552668i
$362$	−3639.48	−	6303.76i	−0.528416	−	0.915244i
$363$		0			0
$364$		0			0
$365$	7490.06			1.07410
$366$		0			0
$367$	4500.06	−	7794.33i	0.640058	−	1.10861i	−0.345361	−	0.938470i	$-0.612244\pi$
$367$	4500.06	−	7794.33i	0.640058	−	1.10861i	0.985419	−	0.170143i	$-0.0544230\pi$
$368$	365.074	−	632.326i	0.0517141	−	0.0895714i
$369$		0			0
$370$	−7265.91			−1.02091
$371$		0			0
$372$		0			0
$373$	−2635.88	−	4565.47i	−0.365899	−	0.633757i	0.623021	−	0.782205i	$-0.285905\pi$
$373$	−2635.88	−	4565.47i	−0.365899	−	0.633757i	−0.988920	+	0.148449i	$0.952572\pi$
$374$	3505.81	−	6072.24i	0.484708	−	0.839540i
$375$		0			0
$376$	−3220.93	−	5578.82i	−0.441774	−	0.765174i
$377$	−221.575			−0.0302698
$378$		0			0
$379$	10480.0			1.42037			0.710185	−	0.704015i	$-0.248611\pi$
$379$	10480.0			1.42037			0.710185	+	0.704015i	$0.248611\pi$
$380$	−2620.82	−	4539.39i	−0.353803	−	0.612804i
$381$		0			0
$382$	3006.78	−	5207.89i	0.402723	−	0.697536i
$383$	−687.014	−	1189.94i	−0.0916574	−	0.158755i	0.816551	−	0.577273i	$-0.195883\pi$
$383$	−687.014	−	1189.94i	−0.0916574	−	0.158755i	−0.908209	+	0.418518i	$0.862550\pi$
$384$		0			0
$385$		0			0
$386$	4095.17			0.539996
$387$		0			0
$388$	336.869	−	583.475i	0.0440772	−	0.0763439i
$389$	−949.135	+	1643.95i	−0.123710	+	0.214271i	−0.921228	−	0.389024i	$-0.872812\pi$
$389$	−949.135	+	1643.95i	−0.123710	+	0.214271i	0.797518	+	0.603295i	$0.206146\pi$
$390$		0			0
$391$	−5341.26			−0.690842
$392$		0			0
$393$		0			0
$394$	3655.01	+	6330.66i	0.467352	+	0.809478i
$395$	1899.66	−	3290.31i	0.241980	−	0.419123i
$396$		0			0
$397$	−2786.15	−	4825.75i	−0.352224	−	0.610070i	0.634415	−	0.772993i	$-0.281241\pi$
$397$	−2786.15	−	4825.75i	−0.352224	−	0.610070i	−0.986639	+	0.162923i	$0.947908\pi$
$398$	4133.02			0.520527
$399$		0			0
$400$	−219.784			−0.0274730
$401$	2858.19	+	4950.53i	0.355938	+	0.616503i	0.987278	−	0.159003i	$-0.0508280\pi$
$401$	2858.19	+	4950.53i	0.355938	+	0.616503i	−0.631340	+	0.775506i	$0.717495\pi$
$402$		0			0
$403$	−61.5989	+	106.692i	−0.00761404	+	0.0131879i
$404$	454.042	+	786.423i	0.0559144	+	0.0968466i
$405$		0			0
$406$		0			0
$407$	11354.2			1.38281
$408$		0			0
$409$	5174.27	−	8962.09i	0.625553	−	1.08349i	−0.362881	−	0.931835i	$-0.618207\pi$
$409$	5174.27	−	8962.09i	0.625553	−	1.08349i	0.988434	−	0.151653i	$-0.0484597\pi$
$410$	4892.46	−	8474.00i	0.589321	−	1.02073i
$411$		0			0
$412$	−961.103			−0.114927
$413$		0			0
$414$		0			0
$415$	−7782.71	−	13480.0i	−0.920574	−	1.59448i
$416$	79.2433	−	137.253i	0.00933948	−	0.0161765i
$417$		0			0
$418$	−3782.33	−	6551.18i	−0.442583	−	0.766576i
$419$	3251.80			0.379142			0.189571	−	0.981867i	$-0.439290\pi$
$419$	3251.80			0.379142			0.189571	+	0.981867i	$0.439290\pi$
$420$		0			0
$421$	3708.63			0.429329			0.214664	−	0.976688i	$-0.431134\pi$
$421$	3708.63			0.429329			0.214664	+	0.976688i	$0.431134\pi$
$422$	1515.48	+	2624.89i	0.174816	+	0.302790i
$423$		0			0
$424$	−2991.62	+	5181.63i	−0.342655	+	0.593496i
$425$	803.895	+	1392.39i	0.0917521	+	0.158919i
$426$		0			0
$427$		0			0
$428$	7757.03			0.876052
$429$		0			0
$430$	6095.55	−	10557.8i	0.683613	−	1.18405i
$431$	−2074.37	+	3592.92i	−0.231831	+	0.401542i	−0.958347	−	0.285607i	$-0.907805\pi$
$431$	−2074.37	+	3592.92i	−0.231831	+	0.401542i	0.726516	+	0.687149i	$0.241138\pi$
$432$		0			0
$433$	−1985.64			−0.220378			−0.110189	−	0.993911i	$-0.535146\pi$
$433$	−1985.64			−0.220378			−0.110189	+	0.993911i	$0.535146\pi$
$434$		0			0
$435$		0			0
$436$	1249.79	+	2164.69i	0.137280	+	0.237775i
$437$	−2881.28	+	4990.52i	−0.315401	+	0.546290i
$438$		0			0
$439$	−3457.21	−	5988.07i	−0.375863	−	0.651013i	0.614593	−	0.788844i	$-0.289320\pi$
$439$	−3457.21	−	5988.07i	−0.375863	−	0.651013i	−0.990456	+	0.137831i	$0.955987\pi$
$440$	10316.8			1.11781
$441$		0			0
$442$	185.727			0.0199867
$443$	−2118.73	−	3669.76i	−0.227233	−	0.393579i	0.729754	−	0.683710i	$-0.239634\pi$
$443$	−2118.73	−	3669.76i	−0.227233	−	0.393579i	−0.956987	+	0.290131i	$0.906301\pi$
$444$		0			0
$445$	2072.25	−	3589.25i	0.220751	−	0.382352i
$446$	−4762.82	−	8249.45i	−0.505664	−	0.875836i
$447$		0			0
$448$		0			0
$449$	−2097.02			−0.220411			−0.110206	−	0.993909i	$-0.535151\pi$
$449$	−2097.02			−0.220411			−0.110206	+	0.993909i	$0.535151\pi$
$450$		0			0
$451$	−7645.26	+	13242.0i	−0.798228	+	1.38257i
$452$	−988.487	+	1712.11i	−0.102864	+	0.178166i
$453$		0			0
$454$	1373.74			0.142011
$455$		0			0
$456$		0			0
$457$	9338.14	+	16174.1i	0.955842	+	1.65557i	0.732429	+	0.680844i	$0.238387\pi$
$457$	9338.14	+	16174.1i	0.955842	+	1.65557i	0.223414	+	0.974724i	$0.428280\pi$
$458$	3620.08	−	6270.16i	0.369334	−	0.639706i
$459$		0			0
$460$	−1344.10	−	2328.06i	−0.136237	−	0.235970i
$461$	13879.5			1.40224			0.701121	−	0.713043i	$-0.252683\pi$
$461$	13879.5			1.40224			0.701121	+	0.713043i	$0.252683\pi$
$462$		0			0
$463$	4780.89			0.479885			0.239942	−	0.970787i	$-0.422871\pi$
$463$	4780.89			0.479885			0.239942	+	0.970787i	$0.422871\pi$
$464$	1542.70	+	2672.04i	0.154350	+	0.267342i
$465$		0			0
$466$	−337.410	+	584.411i	−0.0335412	+	0.0580951i
$467$	4188.09	+	7253.99i	0.414993	+	0.718789i	0.995428	−	0.0955176i	$-0.0304506\pi$
$467$	4188.09	+	7253.99i	0.414993	+	0.718789i	−0.580435	+	0.814307i	$0.697117\pi$
$468$		0			0
$469$		0			0
$470$	6299.17			0.618211
$471$		0			0
$472$	−4861.62	+	8420.58i	−0.474098	+	0.821162i
$473$	−9525.28	+	16498.3i	−0.925947	+	1.60379i
$474$		0			0
$475$	1734.60			0.167556
$476$		0			0
$477$		0			0
$478$	−6020.87	−	10428.4i	−0.576126	−	0.997879i
$479$	−8505.68	+	14732.3i	−0.811346	+	1.40529i	0.100577	+	0.994929i	$0.467931\pi$
$479$	−8505.68	+	14732.3i	−0.811346	+	1.40529i	−0.911922	+	0.410363i	$0.865402\pi$
$480$		0			0
$481$	150.377	+	260.461i	0.0142549	+	0.0246902i
$482$	−11026.3			−1.04198
$483$		0			0
$484$	21.1781			0.00198893
$485$	963.037	+	1668.03i	0.0901635	+	0.156168i
$486$		0			0
$487$	−3008.83	+	5211.44i	−0.279965	+	0.484913i	−0.971376	−	0.237548i	$-0.923656\pi$
$487$	−3008.83	+	5211.44i	−0.279965	+	0.484913i	0.691411	+	0.722462i	$0.256990\pi$
$488$	10253.3	+	17759.3i	0.951118	+	1.64739i
$489$		0			0
$490$		0			0
$491$	−12306.6			−1.13113			−0.565567	−	0.824702i	$-0.691343\pi$
$491$	−12306.6			−1.13113			−0.565567	+	0.824702i	$0.691343\pi$
$492$		0			0
$493$	11285.4	−	19546.9i	1.03097	−	1.78569i
$494$	100.188	−	173.531i	0.00912484	−	0.0158047i
$495$		0			0
$496$	1715.51			0.155300
$497$		0			0
$498$		0			0
$499$	−4282.96	−	7418.31i	−0.384232	−	0.665509i	0.607430	−	0.794373i	$-0.292200\pi$
$499$	−4282.96	−	7418.31i	−0.384232	−	0.665509i	−0.991662	+	0.128864i	$0.958867\pi$
$500$	2685.97	−	4652.23i	0.240240	−	0.416108i
$501$		0			0
$502$	510.012	+	883.366i	0.0453445	+	0.0785390i
$503$	10520.4			0.932568			0.466284	−	0.884635i	$-0.345592\pi$
$503$	10520.4			0.932568			0.466284	+	0.884635i	$0.345592\pi$
$504$		0			0
$505$	−2596.02			−0.228755
$506$	−1939.79	−	3359.82i	−0.170423	−	0.295182i
$507$		0			0
$508$	−60.4876	+	104.768i	−0.00528288	+	0.00915022i
$509$	2722.71	+	4715.86i	0.237096	+	0.410662i	0.959880	−	0.280412i	$-0.0904711\pi$
$509$	2722.71	+	4715.86i	0.237096	+	0.410662i	−0.722784	+	0.691074i	$0.757138\pi$
$510$		0			0
$511$		0			0
$512$	−4767.35			−0.411502
$513$		0			0
$514$	−3929.01	+	6805.24i	−0.337162	+	0.583981i
$515$	1373.79	−	2379.48i	0.117547	−	0.203597i
$516$		0			0
$517$	−9843.46			−0.837360
$518$		0			0
$519$		0			0
$520$	136.639	+	236.665i	0.0115231	+	0.0199585i
$521$	11108.9	−	19241.3i	0.934149	−	1.61799i	0.158005	−	0.987438i	$-0.449494\pi$
$521$	11108.9	−	19241.3i	0.934149	−	1.61799i	0.776144	−	0.630555i	$-0.217173\pi$
$522$		0			0
$523$	11054.9	+	19147.7i	0.924281	+	1.60090i	0.792713	+	0.609595i	$0.208668\pi$
$523$	11054.9	+	19147.7i	0.924281	+	1.60090i	0.131568	+	0.991307i	$0.457999\pi$
$524$	−8797.36			−0.733425
$525$		0			0
$526$	−7026.44			−0.582447
$527$	−6274.77	−	10868.2i	−0.518659	−	0.898344i
$528$		0			0
$529$	4605.82	−	7977.51i	0.378550	−	0.655668i
$530$	−2925.35	−	5066.86i	−0.239753	−	0.415265i
$531$		0			0
$532$		0			0
$533$	−405.022			−0.0329146
$534$		0			0
$535$	−11087.8	+	19204.7i	−0.896018	+	1.55195i
$536$	6033.22	−	10449.8i	0.486186	−	0.842098i
$537$		0			0
$538$	10797.2			0.865241
$539$		0			0
$540$		0			0
$541$	4315.67	+	7474.96i	0.342967	+	0.594036i	0.984982	−	0.172656i	$-0.0552348\pi$
$541$	4315.67	+	7474.96i	0.342967	+	0.594036i	−0.642015	+	0.766692i	$0.721901\pi$
$542$	5703.06	−	9877.99i	0.451969	−	0.782834i
$543$		0			0
$544$	8072.12	+	13981.3i	0.636194	+	1.10192i
$545$	−7145.74			−0.561633
$546$		0			0
$547$	−17846.7			−1.39501			−0.697505	−	0.716580i	$-0.745707\pi$
$547$	−17846.7			−1.39501			−0.697505	+	0.716580i	$0.745707\pi$
$548$	368.781	+	638.747i	0.0287473	+	0.0497918i
$549$		0			0
$550$	−583.902	+	1011.35i	−0.0452685	+	0.0784073i
$551$	−12175.5	−	21088.6i	−0.941369	−	1.63050i
$552$		0			0
$553$		0			0
$554$	−2254.71			−0.172913
$555$		0			0
$556$	4926.70	−	8533.29i	0.375789	−	0.650885i
$557$	−7851.64	+	13599.4i	−0.597279	+	1.03452i	0.395942	+	0.918276i	$0.370418\pi$
$557$	−7851.64	+	13599.4i	−0.597279	+	1.03452i	−0.993221	+	0.116242i	$0.962915\pi$
$558$		0			0
$559$	−504.620			−0.0381810
$560$		0			0
$561$		0			0
$562$	877.651	+	1520.14i	0.0658745	+	0.114098i
$563$	−336.839	+	583.423i	−0.0252151	+	0.0436738i	−0.878358	−	0.478004i	$-0.841360\pi$
$563$	−336.839	+	583.423i	−0.0252151	+	0.0436738i	0.853143	+	0.521678i	$0.174694\pi$
$564$		0			0
$565$	−2825.87	−	4894.55i	−0.210417	−	0.364452i
$566$	239.984			0.0178221
$567$		0			0
$568$	12479.7			0.921896
$569$	7593.10	+	13151.6i	0.559436	+	0.968972i	0.997544	+	0.0700496i	$0.0223158\pi$
$569$	7593.10	+	13151.6i	0.559436	+	0.968972i	−0.438107	+	0.898923i	$0.644351\pi$
$570$		0			0
$571$	−1263.33	+	2188.15i	−0.0925898	+	0.160370i	−0.908600	−	0.417667i	$-0.862848\pi$
$571$	−1263.33	+	2188.15i	−0.0925898	+	0.160370i	0.816010	+	0.578037i	$0.196181\pi$
$572$	−73.0345	−	126.499i	−0.00533868	−	0.00924687i
$573$		0			0
$574$		0			0
$575$	889.603			0.0645200
$576$		0			0
$577$	−10840.2	+	18775.8i	−0.782119	+	1.35467i	0.148586	+	0.988900i	$0.452528\pi$
$577$	−10840.2	+	18775.8i	−0.782119	+	1.35467i	−0.930705	+	0.365771i	$0.880805\pi$
$578$	−4645.17	+	8045.66i	−0.334279	+	0.578989i
$579$		0			0
$580$	11359.6			0.813248
$581$		0			0
$582$		0			0
$583$	4571.33	+	7917.77i	0.324743	+	0.562471i
$584$	−7505.95	+	13000.7i	−0.531847	+	0.921186i
$585$		0			0
$586$	7449.16	+	12902.3i	0.525123	+	0.909540i
$587$	−17458.1			−1.22755			−0.613776	−	0.789481i	$-0.710350\pi$
$587$	−17458.1			−1.22755			−0.613776	+	0.789481i	$0.710350\pi$
$588$		0			0
$589$	−13539.4			−0.947165
$590$	−4753.94	−	8234.06i	−0.331723	−	0.574561i
$591$		0			0
$592$	2093.98	−	3626.88i	0.145375	−	0.251797i
$593$	−2743.50	−	4751.88i	−0.189987	−	0.329066i	0.755259	−	0.655427i	$-0.227511\pi$
$593$	−2743.50	−	4751.88i	−0.189987	−	0.329066i	−0.945245	+	0.326360i	$0.894178\pi$
$594$		0			0
$595$		0			0
$596$	−6201.20			−0.426193
$597$		0			0
$598$	51.3821	−	88.9964i	0.00351366	−	0.00608584i
$599$	11498.6	−	19916.2i	0.784343	−	1.35852i	−0.145048	−	0.989425i	$-0.546334\pi$
$599$	11498.6	−	19916.2i	0.784343	−	1.35852i	0.929391	−	0.369097i	$-0.120333\pi$
$600$		0			0
$601$	18027.1			1.22353			0.611764	−	0.791040i	$-0.290460\pi$
$601$	18027.1			1.22353			0.611764	+	0.791040i	$0.290460\pi$
$602$		0			0
$603$		0			0
$604$	853.551	+	1478.39i	0.0575008	+	0.0995943i
$605$	−30.2719	+	52.4324i	−0.00203426	+	0.00352344i
$606$		0			0
$607$	5142.56	+	8907.18i	0.343872	+	0.595604i	0.985148	−	0.171707i	$-0.0549281\pi$
$607$	5142.56	+	8907.18i	0.343872	+	0.595604i	−0.641276	+	0.767310i	$0.721595\pi$
$608$	17417.6			1.16181
$609$		0			0
$610$	−20052.4			−1.33098
$611$	−130.369	−	225.806i	−0.00863203	−	0.0149511i
$612$		0			0
$613$	798.464	−	1382.98i	0.0526096	−	0.0911224i	−0.838521	−	0.544869i	$-0.816579\pi$
$613$	798.464	−	1382.98i	0.0526096	−	0.0911224i	0.891131	+	0.453746i	$0.149913\pi$
$614$	3468.00	+	6006.75i	0.227943	+	0.394809i
$615$		0			0
$616$		0			0
$617$	5850.74			0.381753			0.190877	−	0.981614i	$-0.438867\pi$
$617$	5850.74			0.381753			0.190877	+	0.981614i	$0.438867\pi$
$618$		0			0
$619$	860.808	−	1490.96i	0.0558947	−	0.0968124i	−0.836724	−	0.547625i	$-0.815532\pi$
$619$	860.808	−	1490.96i	0.0558947	−	0.0968124i	0.892619	+	0.450812i	$0.148866\pi$
$620$	3158.03	−	5469.87i	0.204564	−	0.354315i
$621$		0			0
$622$	−7633.48			−0.492082
$623$		0			0
$624$		0			0
$625$	8701.36	+	15071.2i	0.556887	+	0.964557i
$626$	−8508.27	+	14736.8i	−0.543225	+	0.940894i
$627$		0			0
$628$	943.051	+	1633.41i	0.0599233	+	0.103790i
$629$	−30636.3			−1.94205
$630$		0			0
$631$	−19533.5			−1.23235			−0.616177	−	0.787608i	$-0.711319\pi$
$631$	−19533.5			−1.23235			−0.616177	+	0.787608i	$0.711319\pi$
$632$	3807.38	+	6594.58i	0.239636	+	0.415061i
$633$		0			0
$634$	−8324.97	+	14419.3i	−0.521493	+	0.903253i
$635$	−172.921	−	299.508i	−0.0108066	−	0.0187175i
$636$		0			0
$637$		0			0
$638$	16394.1			1.01732
$639$		0			0
$640$	−2810.76	+	4868.38i	−0.173602	+	0.300687i
$641$	11748.1	−	20348.3i	0.723903	−	1.25384i	−0.235521	−	0.971869i	$-0.575680\pi$
$641$	11748.1	−	20348.3i	0.723903	−	1.25384i	0.959424	−	0.281967i	$-0.0909870\pi$
$642$		0			0
$643$	−1537.40			−0.0942913			−0.0471456	−	0.998888i	$-0.515012\pi$
$643$	−1537.40			−0.0942913			−0.0471456	+	0.998888i	$0.515012\pi$
$644$		0			0
$645$		0			0
$646$	10205.7	+	17676.7i	0.621573	+	1.07660i
$647$	−14136.5	+	24485.1i	−0.858985	+	1.48781i	0.0139128	+	0.999903i	$0.495571\pi$
$647$	−14136.5	+	24485.1i	−0.858985	+	1.48781i	−0.872898	+	0.487903i	$0.837762\pi$
$648$		0			0
$649$	7428.79	+	12867.0i	0.449315	+	0.778236i
$650$	−30.9333			−0.00186662
$651$		0			0
$652$	−3111.62			−0.186902
$653$	1334.48	+	2311.39i	0.0799730	+	0.138517i	0.903238	−	0.429140i	$-0.141183\pi$
$653$	1334.48	+	2311.39i	0.0799730	+	0.138517i	−0.823265	+	0.567657i	$0.807850\pi$
$654$		0			0
$655$	12574.9	−	21780.3i	0.750140	−	1.29928i
$656$	2819.94	+	4884.29i	0.167836	+	0.290700i
$657$		0			0
$658$		0			0
$659$	−6343.74			−0.374988			−0.187494	−	0.982266i	$-0.560036\pi$
$659$	−6343.74			−0.374988			−0.187494	+	0.982266i	$0.560036\pi$
$660$		0			0
$661$	4204.58	−	7282.54i	0.247412	−	0.428529i	−0.715395	−	0.698720i	$-0.753753\pi$
$661$	4204.58	−	7282.54i	0.247412	−	0.428529i	0.962807	+	0.270191i	$0.0870867\pi$
$662$	−1245.20	+	2156.75i	−0.0731059	+	0.126623i
$663$		0			0
$664$	31196.9			1.82331
$665$		0			0
$666$		0			0
$667$	−6244.29	−	10815.4i	−0.362489	−	0.627849i
$668$	1077.74	−	1866.70i	0.0624235	−	0.108121i
$669$		0			0
$670$	5899.58	+	10218.4i	0.340180	+	0.589209i
$671$	31335.1			1.80280
$672$		0			0
$673$	−15326.7			−0.877862			−0.438931	−	0.898521i	$-0.644643\pi$
$673$	−15326.7			−0.877862			−0.438931	+	0.898521i	$0.644643\pi$
$674$	−4601.20	−	7969.52i	−0.262955	−	0.455452i
$675$		0			0
$676$	−4566.71	+	7909.78i	−0.259827	+	0.450033i
$677$	6505.81	+	11268.4i	0.369333	+	0.639704i	0.989461	−	0.144797i	$-0.0462528\pi$
$677$	6505.81	+	11268.4i	0.369333	+	0.639704i	−0.620128	+	0.784500i	$0.712919\pi$
$678$		0			0
$679$		0			0
$680$	−27837.4			−1.56987
$681$		0			0
$682$	4557.63	−	7894.04i	0.255895	−	0.443223i
$683$	8736.00	−	15131.2i	0.489420	−	0.847700i	−0.510506	−	0.859874i	$-0.670542\pi$
$683$	8736.00	−	15131.2i	0.489420	−	0.847700i	0.999926	+	0.0121740i	$0.00387519\pi$
$684$		0			0
$685$	−2108.53			−0.117610
$686$		0			0
$687$		0			0
$688$	3513.39	+	6085.37i	0.194690	+	0.337213i
$689$	−121.087	+	209.730i	−0.00669531	+	0.0115966i
$690$		0			0
$691$	3658.55	+	6336.80i	0.201415	+	0.348861i	0.948985	−	0.315322i	$-0.102113\pi$
$691$	3658.55	+	6336.80i	0.201415	+	0.348861i	−0.747569	+	0.664184i	$0.768779\pi$
$692$	−5462.77			−0.300091
$693$		0			0
$694$	12766.4			0.698280
$695$	14084.4	+	24394.8i	0.768706	+	1.33144i
$696$		0			0
$697$	20628.8	−	35730.1i	1.12105	−	1.94171i
$698$	−7040.52	−	12194.5i	−0.381787	−	0.661275i
$699$		0			0
$700$		0			0
$701$	7874.65			0.424282			0.212141	−	0.977239i	$-0.431956\pi$
$701$	7874.65			0.424282			0.212141	+	0.977239i	$0.431956\pi$
$702$		0			0
$703$	−16526.4	+	28624.5i	−0.886634	+	1.53570i
$704$	−7819.36	+	13543.5i	−0.418612	+	0.725058i
$705$		0			0
$706$	11893.4			0.634017
$707$		0			0
$708$		0			0
$709$	12618.4	+	21855.7i	0.668398	+	1.15770i	0.978352	+	0.206948i	$0.0663531\pi$
$709$	12618.4	+	21855.7i	0.668398	+	1.15770i	−0.309954	+	0.950752i	$0.600314\pi$
$710$	−6101.64	+	10568.4i	−0.322522	+	0.558624i
$711$		0			0
$712$	4153.30	+	7193.73i	0.218612	+	0.378647i
$713$	−6943.76			−0.364721
$714$		0			0
$715$	417.580			0.0218414
$716$	8594.85	+	14886.7i	0.448610	+	0.777015i
$717$		0			0
$718$	−1708.71	+	2959.57i	−0.0888139	+	0.153830i
$719$	−9836.48	−	17037.3i	−0.510207	−	0.883704i	−0.999930	−	0.0118262i	$-0.996236\pi$
$719$	−9836.48	−	17037.3i	−0.510207	−	0.883704i	0.489723	−	0.871878i	$-0.337098\pi$
$720$		0			0
$721$		0			0
$722$	8578.62			0.442193
$723$		0			0
$724$	7723.32	−	13377.2i	0.396457	−	0.686684i
$725$	−1879.61	+	3255.58i	−0.0962856	+	0.166772i
$726$		0			0
$727$	−31921.7			−1.62849			−0.814243	−	0.580525i	$-0.802848\pi$
$727$	−31921.7			−1.62849			−0.814243	+	0.580525i	$0.802848\pi$
$728$		0			0
$729$		0			0
$730$	−7339.69	−	12712.7i	−0.372129	−	0.644546i
$731$	25701.6	−	44516.4i	1.30042	−	2.25239i
$732$		0			0
$733$	−6772.65	−	11730.6i	−0.341274	−	0.591103i	0.643396	−	0.765534i	$-0.277525\pi$
$733$	−6772.65	−	11730.6i	−0.341274	−	0.591103i	−0.984669	+	0.174430i	$0.944192\pi$
$734$	−17638.9			−0.887007
$735$		0			0
$736$	8932.74			0.447371
$737$	−9219.04	−	15967.8i	−0.460770	−	0.798078i
$738$		0			0
$739$	−12748.8	+	22081.6i	−0.634604	+	1.09917i	0.351995	+	0.936002i	$0.385503\pi$
$739$	−12748.8	+	22081.6i	−0.634604	+	1.09917i	−0.986599	+	0.163164i	$0.947830\pi$
$740$	−7709.48	−	13353.2i	−0.382981	−	0.663343i
$741$		0			0
$742$		0			0
$743$	−11146.9			−0.550390			−0.275195	−	0.961388i	$-0.588742\pi$
$743$	−11146.9			−0.550390			−0.275195	+	0.961388i	$0.588742\pi$
$744$		0			0
$745$	8863.95	−	15352.8i	0.435906	−	0.755011i
$746$	−5165.92	+	8947.64i	−0.253536	+	0.439137i
$747$		0			0
$748$	14879.3			0.727328
$749$		0			0
$750$		0			0
$751$	−10706.2	−	18543.8i	−0.520208	−	0.901027i	−0.999724	−	0.0234936i	$-0.992521\pi$
$751$	−10706.2	−	18543.8i	−0.520208	−	0.901027i	0.479516	−	0.877533i	$-0.340812\pi$
$752$	−1815.38	+	3144.32i	−0.0880318	+	0.152476i
$753$		0			0
$754$	217.127	+	376.075i	0.0104871	+	0.0181643i
$755$	−4880.24			−0.235245
$756$		0			0
$757$	−33963.9			−1.63070			−0.815350	−	0.578968i	$-0.803456\pi$
$757$	−33963.9			−1.63070			−0.815350	+	0.578968i	$0.803456\pi$
$758$	−10269.6	−	17787.5i	−0.492096	−	0.852335i
$759$		0			0
$760$	−15016.5	+	26009.4i	−0.716719	+	1.24139i
$761$	9959.98	+	17251.2i	0.474440	+	0.821754i	0.999572	−	0.0292668i	$-0.00931725\pi$
$761$	9959.98	+	17251.2i	0.474440	+	0.821754i	−0.525132	+	0.851021i	$0.675984\pi$
$762$		0			0
$763$		0			0
$764$	12761.3			0.604305
$765$		0			0
$766$	−1346.44	+	2332.11i	−0.0635105	+	0.110003i
$767$	−196.777	+	340.828i	−0.00926364	+	0.0160451i
$768$		0			0
$769$	10039.2			0.470769			0.235385	−	0.971902i	$-0.424365\pi$
$769$	10039.2			0.470769			0.235385	+	0.971902i	$0.424365\pi$
$770$		0			0
$771$		0			0
$772$	4345.17	+	7526.05i	0.202573	+	0.350866i
$773$	10692.7	−	18520.2i	0.497527	−	0.861742i	−0.502469	−	0.864595i	$-0.667575\pi$
$773$	10692.7	−	18520.2i	0.497527	−	0.861742i	0.999996	+	0.00285350i	$0.000908298\pi$
$774$		0			0
$775$	1045.08	+	1810.13i	0.0484392	+	0.0838992i
$776$	−3860.33			−0.178579
$777$		0			0
$778$	3720.32			0.171440
$779$	−22255.9	−	38548.3i	−1.02362	−	1.77296i
$780$		0			0
$781$	9534.79	−	16514.7i	0.436852	−	0.756650i
$782$	5234.04	+	9065.62i	0.239346	+	0.414560i
$783$		0			0
$784$		0			0
$785$	−5391.96			−0.245156
$786$		0			0
$787$	−18710.7	+	32407.8i	−0.847475	+	1.46787i	0.0359790	+	0.999353i	$0.488545\pi$
$787$	−18710.7	+	32407.8i	−0.847475	+	1.46787i	−0.883454	+	0.468518i	$0.844788\pi$
$788$	−7756.28	+	13434.3i	−0.350642	+	0.607330i
$789$		0			0
$790$	−7446.10			−0.335342
$791$		0			0
$792$		0			0
$793$	415.009	+	718.817i	0.0185844	+	0.0321891i
$794$	−5460.44	+	9457.75i	−0.244060	+	0.422724i
$795$		0			0
$796$	4385.33	+	7595.62i	0.195269	+	0.338216i
$797$	30888.7			1.37281			0.686407	−	0.727217i	$-0.259187\pi$
$797$	30888.7			1.37281			0.686407	+	0.727217i	$0.259187\pi$
$798$		0			0
$799$	26560.1			1.17601
$800$	−1344.44	−	2328.63i	−0.0594162	−	0.102912i
$801$		0			0
$802$	5601.63	−	9702.30i	0.246634	−	0.427182i
$803$	11469.4	+	19865.7i	0.504045	+	0.873031i
$804$		0			0
$805$		0			0
$806$	241.449			0.0105517
$807$		0			0
$808$	2601.53	−	4505.97i	0.113269	−	0.196188i
$809$	−3619.25	+	6268.73i	−0.157288	+	0.272431i	−0.933890	−	0.357561i	$-0.883608\pi$
$809$	−3619.25	+	6268.73i	−0.157288	+	0.272431i	0.776602	+	0.629992i	$0.216942\pi$
$810$		0			0
$811$	−35466.4			−1.53563			−0.767814	−	0.640673i	$-0.778656\pi$
$811$	−35466.4			−1.53563			−0.767814	+	0.640673i	$0.778656\pi$
$812$		0			0
$813$		0			0
$814$	−11126.2	−	19271.2i	−0.479083	−	0.829796i
$815$	4447.72	−	7703.68i	0.191162	−	0.331102i
$816$		0			0
$817$	−27728.8	−	48027.6i	−1.18740	−	2.05664i
$818$	−20281.6			−0.866905
$819$		0			0
$820$	20764.6			0.884304
$821$	18973.6	+	32863.3i	0.806558	+	1.39700i	0.915234	+	0.402923i	$0.132006\pi$
$821$	18973.6	+	32863.3i	0.806558	+	1.39700i	−0.108676	+	0.994077i	$0.534661\pi$
$822$		0			0
$823$	−13466.1	+	23324.0i	−0.570351	+	0.987876i	0.426179	+	0.904639i	$0.359859\pi$
$823$	−13466.1	+	23324.0i	−0.570351	+	0.987876i	−0.996530	+	0.0832376i	$0.973474\pi$
$824$	2753.42	+	4769.06i	0.116408	+	0.201624i
$825$		0			0
$826$		0			0
$827$	−1913.98			−0.0804783			−0.0402391	−	0.999190i	$-0.512812\pi$
$827$	−1913.98			−0.0804783			−0.0402391	+	0.999190i	$0.512812\pi$
$828$		0			0
$829$	7640.96	−	13234.5i	0.320122	−	0.554468i	−0.660391	−	0.750922i	$-0.729609\pi$
$829$	7640.96	−	13234.5i	0.320122	−	0.554468i	0.980513	+	0.196454i	$0.0629427\pi$
$830$	−15252.9	+	26418.9i	−0.637876	+	1.10483i
$831$		0			0
$832$	−414.246			−0.0172613
$833$		0			0
$834$		0			0
$835$	3081.02	+	5336.49i	0.127692	+	0.221170i
$836$	8026.46	−	13902.2i	0.332058	−	0.575142i
$837$		0			0
$838$	−3186.52	−	5519.21i	−0.131356	−	0.227515i
$839$	25779.5			1.06079			0.530397	−	0.847749i	$-0.322043\pi$
$839$	25779.5			1.06079			0.530397	+	0.847749i	$0.322043\pi$
$840$		0			0
$841$	28384.4			1.16382
$842$	−3634.18	−	6294.58i	−0.148743	−	0.257631i
$843$		0			0
$844$	−3215.99	+	5570.26i	−0.131160	+	0.227176i
$845$	−13055.3	−	22612.4i	−0.531497	−	0.920579i
$846$		0			0
$847$		0			0
$848$	3372.26			0.136561
$849$		0			0
$850$	1575.51	−	2728.87i	0.0635761	−	0.110117i
$851$	−8475.66	+	14680.3i	−0.341412	+	0.591343i
$852$		0			0
$853$	−6452.21			−0.258991			−0.129496	−	0.991580i	$-0.541336\pi$
$853$	−6452.21			−0.258991			−0.129496	+	0.991580i	$0.541336\pi$
$854$		0			0
$855$		0			0
$856$	−22222.8	−	38491.0i	−0.887335	−	1.53691i
$857$	−16030.9	+	27766.4i	−0.638980	+	1.10675i	0.346677	+	0.937984i	$0.387310\pi$
$857$	−16030.9	+	27766.4i	−0.638980	+	1.10675i	−0.985657	+	0.168761i	$0.946023\pi$
$858$		0			0
$859$	1967.32	+	3407.50i	0.0781421	+	0.135346i	0.902448	−	0.430798i	$-0.141768\pi$
$859$	1967.32	+	3407.50i	0.0781421	+	0.135346i	−0.824306	+	0.566144i	$0.808435\pi$
$860$	25870.7			1.02579
$861$		0			0
$862$	8130.91			0.321276
$863$	7021.57	+	12161.7i	0.276961	+	0.479710i	0.970628	−	0.240586i	$-0.0773395\pi$
$863$	7021.57	+	12161.7i	0.276961	+	0.479710i	−0.693667	+	0.720296i	$0.744006\pi$
$864$		0			0
$865$	7808.44	−	13524.6i	0.306931	−	0.531619i
$866$	1945.78	+	3370.19i	0.0763514	+	0.132244i
$867$		0			0
$868$		0			0
$869$	11635.7			0.454217
$870$		0			0
$871$	244.198	−	422.964i	0.00949982	−	0.0164542i
$872$	7160.91	−	12403.1i	0.278095	−	0.481675i
$873$		0			0
$874$	11293.7			0.437090
$875$		0			0
$876$		0			0
$877$	−1045.66	−	1811.13i	−0.0402614	−	0.0697348i	0.845193	−	0.534462i	$-0.179486\pi$
$877$	−1045.66	−	1811.13i	−0.0402614	−	0.0697348i	−0.885454	+	0.464727i	$0.846152\pi$
$878$	−6775.62	+	11735.7i	−0.260440	+	0.451095i
$879$		0			0
$880$	−2907.38	−	5035.72i	−0.111372	−	0.192903i
$881$	11548.6			0.441639			0.220819	−	0.975315i	$-0.429127\pi$
$881$	11548.6			0.441639			0.220819	+	0.975315i	$0.429127\pi$
$882$		0			0
$883$	7531.24			0.287029			0.143514	−	0.989648i	$-0.454160\pi$
$883$	7531.24			0.287029			0.143514	+	0.989648i	$0.454160\pi$
$884$	197.065	+	341.327i	0.00749776	+	0.0129865i
$885$		0			0
$886$	−4152.40	+	7192.17i	−0.157452	+	0.272715i
$887$	19251.3	+	33344.3i	0.728745	+	1.26222i	0.957414	+	0.288719i	$0.0932294\pi$
$887$	19251.3	+	33344.3i	0.728745	+	1.26222i	−0.228669	+	0.973504i	$0.573437\pi$
$888$		0			0
$889$		0			0
$890$	−8122.61			−0.305922
$891$		0			0
$892$	10107.2	−	17506.1i	0.379387	−	0.657117i
$893$	14327.5	−	24816.0i	0.536900	−	0.929938i
$894$		0			0
$895$	−49141.7			−1.83534
$896$		0			0
$897$		0			0
$898$	2054.92	+	3559.23i	0.0763627	+	0.132264i
$899$	14671.2	−	25411.3i	0.544286	−	0.942731i
$900$		0			0
$901$	−12334.6	−	21364.1i	−0.456076	−	0.789947i
$902$	29967.1			1.10620
$903$		0			0
$904$	11327.5			0.416755
$905$	22079.3	+	38242.5i	0.810985	+	1.40467i
$906$		0			0
$907$	15653.3	−	27112.4i	0.573054	−	0.992559i	−0.423196	−	0.906038i	$-0.639092\pi$
$907$	15653.3	−	27112.4i	0.573054	−	0.992559i	0.996250	−	0.0865211i	$-0.0275750\pi$
$908$	1457.61	+	2524.65i	0.0532735	+	0.0922724i
$909$		0			0
$910$		0			0
$911$	34154.3			1.24213			0.621067	−	0.783758i	$-0.286700\pi$
$911$	34154.3			1.24213			0.621067	+	0.783758i	$0.286700\pi$
$912$		0			0
$913$	23835.2	−	41283.7i	0.863996	−	1.49649i
$914$	18301.4	−	31698.9i	0.662314	−	1.14716i
$915$		0			0
$916$	15364.3			0.554204
$917$		0			0
$918$		0			0
$919$	−17994.4	−	31167.3i	−0.645899	−	1.11873i	−0.984093	−	0.177654i	$-0.943149\pi$
$919$	−17994.4	−	31167.3i	−0.645899	−	1.11873i	0.338194	−	0.941077i	$-0.390184\pi$
$920$	−7701.32	+	13339.1i	−0.275984	+	0.478018i
$921$		0			0
$922$	−13600.9	−	23557.4i	−0.485815	−	0.841456i
$923$	505.124			0.0180134
$924$		0			0
$925$	5102.57			0.181374
$926$	−4684.91	−	8114.50i	−0.166259	−	0.287969i
$927$		0			0
$928$	−18873.7	+	32690.2i	−0.667629	+	1.15637i
$929$	−6952.99	−	12042.9i	−0.245554	−	0.425313i	0.716733	−	0.697348i	$-0.245637\pi$
$929$	−6952.99	−	12042.9i	−0.245554	−	0.425313i	−0.962287	+	0.272035i	$0.912303\pi$
$930$		0			0
$931$		0			0
$932$	−1432.03			−0.0503302
$933$		0			0
$934$	8208.03	−	14216.7i	0.287554	−	0.498057i
$935$	−21268.4	+	36837.9i	−0.743905	+	1.28848i
$936$		0			0
$937$	−40905.3			−1.42617			−0.713083	−	0.701079i	$-0.752702\pi$
$937$	−40905.3			−1.42617			−0.713083	+	0.701079i	$0.752702\pi$
$938$		0			0
$939$		0			0
$940$	6683.72	+	11576.5i	0.231914	+	0.401687i
$941$	4033.75	−	6986.66i	0.139741	−	0.242039i	−0.787657	−	0.616113i	$-0.788706\pi$
$941$	4033.75	−	6986.66i	0.139741	−	0.242039i	0.927399	+	0.374075i	$0.122040\pi$
$942$		0			0
$943$	−11414.1	−	19769.8i	−0.394161	−	0.682706i
$944$	5480.20			0.188946
$945$		0			0
$946$	37336.2			1.28320
$947$	−19890.6	−	34451.5i	−0.682531	−	1.18218i	−0.974206	−	0.225661i	$-0.927546\pi$
$947$	−19890.6	−	34451.5i	−0.682531	−	1.18218i	0.291675	−	0.956518i	$-0.405788\pi$
$948$		0			0
$949$	−303.808	+	526.211i	−0.0103920	+	0.0179995i
$950$	−1699.78	−	2944.11i	−0.0580507	−	0.100547i
$951$		0			0
$952$		0			0
$953$	32354.0			1.09974			0.549868	−	0.835252i	$-0.314678\pi$
$953$	32354.0			1.09974			0.549868	+	0.835252i	$0.314678\pi$
$954$		0			0
$955$	−18241.0	+	31594.3i	−0.618077	+	1.07054i
$956$	12776.9	−	22130.2i	0.432252	−	0.748683i
$957$		0			0
$958$	33339.7			1.12438
$959$		0			0
$960$		0			0
$961$	6738.16	+	11670.8i	0.226181	+	0.391757i
$962$	294.716	−	510.464i	0.00987738	−	0.0171081i
$963$		0			0
$964$	−11699.5	−	20264.1i	−0.390887	−	0.677035i
$965$	−24843.8			−0.828757
$966$		0			0
$967$	17389.2			0.578282			0.289141	−	0.957287i	$-0.406630\pi$
$967$	17389.2			0.578282			0.289141	+	0.957287i	$0.406630\pi$
$968$	−60.6722	−	105.087i	−0.00201454	−	0.00348929i
$969$		0			0
$970$	1887.41	−	3269.09i	0.0624753	−	0.108210i
$971$	−26203.1	−	45385.1i	−0.866012	−	1.49998i	−0.866038	−	0.499977i	$-0.833342\pi$
$971$	−26203.1	−	45385.1i	−0.866012	−	1.49998i	2.60137e−5	−	1.00000i	$-0.499992\pi$
$972$		0			0
$973$		0			0
$974$	11793.7			0.387982
$975$		0			0
$976$	5778.95	−	10009.4i	0.189528	−	0.328273i
$977$	−3423.35	+	5929.42i	−0.112101	+	0.194165i	−0.916617	−	0.399766i	$-0.869091\pi$
$977$	−3423.35	+	5929.42i	−0.112101	+	0.194165i	0.804516	+	0.593931i	$0.202425\pi$
$978$		0			0
$979$	12692.9			0.414368
$980$		0			0
$981$		0			0
$982$	12059.5	+	20887.7i	0.391888	+	0.678770i
$983$	−18824.0	+	32604.1i	−0.610774	+	1.05789i	0.380336	+	0.924848i	$0.375808\pi$
$983$	−18824.0	+	32604.1i	−0.610774	+	1.05789i	−0.991110	+	0.133044i	$0.957525\pi$
$984$		0			0
$985$	−22173.6	−	38405.7i	−0.717267	−	1.24234i
$986$	−44235.3			−1.42874
$987$		0			0
$988$	425.217			0.0136923
$989$	−14220.9	−	24631.3i	−0.457227	−	0.791941i
$990$		0			0
$991$	−1018.09	+	1763.38i	−0.0326343	+	0.0565242i	−0.881881	−	0.471472i	$-0.843723\pi$
$991$	−1018.09	+	1763.38i	−0.0326343	+	0.0565242i	0.849247	+	0.527996i	$0.177056\pi$
$992$	10493.9	+	18176.0i	0.335870	+	0.581744i
$993$		0			0
$994$		0			0
$995$	−25073.5			−0.798877
$996$		0			0
$997$	6770.32	−	11726.5i	0.215064	−	0.372501i	−0.738229	−	0.674550i	$-0.764337\pi$
$997$	6770.32	−	11726.5i	0.215064	−	0.372501i	0.953292	+	0.302050i	$0.0976708\pi$
$998$	−8393.96	+	14538.8i	−0.266239	+	0.461139i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.z.361.4		16
3.2	odd	2	inner	441.4.e.z.361.5		16
7.2	even	3	inner	441.4.e.z.226.4		16
7.3	odd	6		441.4.a.x.1.6	yes	8
7.4	even	3		441.4.a.x.1.5	yes	8
7.5	odd	6	inner	441.4.e.z.226.3		16
7.6	odd	2	inner	441.4.e.z.361.3		16
21.2	odd	6	inner	441.4.e.z.226.5		16
21.5	even	6	inner	441.4.e.z.226.6		16
21.11	odd	6		441.4.a.x.1.4	yes	8
21.17	even	6		441.4.a.x.1.3	✓	8
21.20	even	2	inner	441.4.e.z.361.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.a.x.1.3	✓	8	21.17	even	6
441.4.a.x.1.4	yes	8	21.11	odd	6
441.4.a.x.1.5	yes	8	7.4	even	3
441.4.a.x.1.6	yes	8	7.3	odd	6
441.4.e.z.226.3		16	7.5	odd	6	inner
441.4.e.z.226.4		16	7.2	even	3	inner
441.4.e.z.226.5		16	21.2	odd	6	inner
441.4.e.z.226.6		16	21.5	even	6	inner
441.4.e.z.361.3		16	7.6	odd	2	inner
441.4.e.z.361.4		16	1.1	even	1	trivial
441.4.e.z.361.5		16	3.2	odd	2	inner
441.4.e.z.361.6		16	21.20	even	2	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.979925 - 1.69728i) q^{2} +(2.07949 - 3.60179i) q^{4} +(5.94483 + 10.2967i) q^{5} -23.8298 q^{8} +O(q^{10})\)	\(q+(-0.979925 - 1.69728i) q^{2} +(2.07949 - 3.60179i) q^{4} +(5.94483 + 10.2967i) q^{5} -23.8298 q^{8} +(11.6510 - 20.1801i) q^{10} +(-18.2065 + 31.5346i) q^{11} -0.964525 q^{13} +(6.71545 + 11.6315i) q^{16} +(49.1257 - 85.0882i) q^{17} +(-53.0004 - 91.7994i) q^{19} +49.4490 q^{20} +71.3640 q^{22} +(-27.1816 - 47.0800i) q^{23} +(-8.18202 + 14.1717i) q^{25} +(0.945162 + 1.63707i) q^{26} +229.725 q^{29} +(63.8645 - 110.616i) q^{31} +(-82.1579 + 142.302i) q^{32} -192.558 q^{34} +(-155.908 - 270.040i) q^{37} +(-103.873 + 179.913i) q^{38} +(-141.664 - 245.369i) q^{40} +419.919 q^{41} +523.180 q^{43} +(75.7207 + 131.152i) q^{44} +(-53.2719 + 92.2697i) q^{46} +(135.164 + 234.111i) q^{47} +32.0711 q^{50} +(-2.00572 + 3.47402i) q^{52} +(125.541 - 217.443i) q^{53} -432.938 q^{55} +(-225.113 - 389.907i) q^{58} +(204.015 - 353.364i) q^{59} +(-430.273 - 745.255i) q^{61} -250.329 q^{62} +429.481 q^{64} +(-5.73394 - 9.93147i) q^{65} +(-253.180 + 438.520i) q^{67} +(-204.313 - 353.881i) q^{68} -523.702 q^{71} +(314.982 - 545.565i) q^{73} +(-305.556 + 529.239i) q^{74} -440.856 q^{76} +(-159.774 - 276.737i) q^{79} +(-79.8444 + 138.295i) q^{80} +(-411.489 - 712.720i) q^{82} -1309.16 q^{83} +1168.18 q^{85} +(-512.677 - 887.982i) q^{86} +(433.857 - 751.463i) q^{88} +(-174.290 - 301.880i) q^{89} -226.096 q^{92} +(264.901 - 458.822i) q^{94} +(630.157 - 1091.46i) q^{95} +161.996 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 68 q^{4}+O(q^{10}) \) 16 * q - 68 * q^4	\( 16 q - 68 q^{4} - 804 q^{16} + 1952 q^{22} - 536 q^{25} - 64 q^{37} + 4320 q^{43} + 768 q^{46} - 2184 q^{58} + 15176 q^{64} - 5392 q^{79} + 5728 q^{85} - 5616 q^{88}+O(q^{100}) \) 16 * q - 68 * q^4 - 804 * q^16 + 1952 * q^22 - 536 * q^25 - 64 * q^37 + 4320 * q^43 + 768 * q^46 - 2184 * q^58 + 15176 * q^64 - 5392 * q^79 + 5728 * q^85 - 5616 * q^88

Introduction

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