LMFDB - Embedded newform 441.4.p.d.80.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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([3, 1]))

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

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

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (of order $6$, 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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.17
Character	$\chi$	$=$	441.80
Dual form			441.4.p.d.215.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.10847 - 1.79468i) q^{2} +(2.44173 - 4.22919i) q^{4} +(0.428649 + 0.742442i) q^{5} +11.1864i q^{8} +O(q^{10})$	\(q+(3.10847 - 1.79468i) q^{2} +(2.44173 - 4.22919i) q^{4} +(0.428649 + 0.742442i) q^{5} +11.1864i q^{8} +(2.66489 + 1.53857i) q^{10} +(-0.321369 - 0.185543i) q^{11} +62.0038i q^{13} +(39.6098 + 68.6061i) q^{16} +(-51.9931 + 90.0547i) q^{17} +(-61.9469 + 35.7650i) q^{19} +4.18657 q^{20} -1.33196 q^{22} +(118.248 - 68.2704i) q^{23} +(62.1325 - 107.617i) q^{25} +(111.277 + 192.737i) q^{26} +17.8708i q^{29} +(-93.2782 - 53.8542i) q^{31} +(168.750 + 97.4278i) q^{32} +373.243i q^{34} +(190.857 + 330.575i) q^{37} +(-128.373 + 222.349i) q^{38} +(-8.30525 + 4.79504i) q^{40} +101.733 q^{41} -326.400 q^{43} +(-1.56939 + 0.906088i) q^{44} +(245.047 - 424.433i) q^{46} +(261.065 + 452.178i) q^{47} -446.031i q^{50} +(262.226 + 151.396i) q^{52} +(268.049 + 154.758i) q^{53} -0.318131i q^{55} +(32.0724 + 55.5510i) q^{58} +(-174.386 + 302.045i) q^{59} +(580.478 - 335.139i) q^{61} -386.604 q^{62} +65.6495 q^{64} +(-46.0342 + 26.5779i) q^{65} +(119.685 - 207.301i) q^{67} +(253.906 + 439.778i) q^{68} +178.563i q^{71} +(117.414 + 67.7891i) q^{73} +(1186.55 + 685.054i) q^{74} +349.314i q^{76} +(-428.404 - 742.018i) q^{79} +(-33.9574 + 58.8159i) q^{80} +(316.233 - 182.577i) q^{82} -1241.10 q^{83} -89.1472 q^{85} +(-1014.60 + 585.782i) q^{86} +(2.07555 - 3.59496i) q^{88} +(-282.464 - 489.242i) q^{89} -666.790i q^{92} +(1623.03 + 937.055i) q^{94} +(-53.1069 - 30.6613i) q^{95} -1730.44i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4}+O(q^{10}) $ 48 * q + 96 * q^4	$ 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) $ 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	3.10847	−	1.79468i	1.09901	−	0.634514i	0.163049	−	0.986618i	$-0.447867\pi$
$2$	3.10847	−	1.79468i	1.09901	−	0.634514i	0.935961	+	0.352104i	$0.114534\pi$
$3$		0			0
$3$		0			0
$4$	2.44173	−	4.22919i	0.305216	−	0.528649i
$5$	0.428649	+	0.742442i	0.0383395	+	0.0664060i	0.884558	−	0.466429i	$-0.154460\pi$
$5$	0.428649	+	0.742442i	0.0383395	+	0.0664060i	−0.846219	+	0.532835i	$0.821126\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			11.1864i			0.494373i
$9$		0			0
$10$	2.66489	+	1.53857i	0.0842711	+	0.0486539i
$11$	−0.321369	−	0.185543i	−0.00880877	−	0.00508574i	0.495589	−	0.868557i	$-0.334952\pi$
$11$	−0.321369	−	0.185543i	−0.00880877	−	0.00508574i	−0.504398	+	0.863471i	$0.668286\pi$
$12$		0			0
$13$			62.0038i			1.32283i	0.750021	+	0.661414i	$0.230043\pi$
$13$			62.0038i			1.32283i	−0.750021	+	0.661414i	$0.769957\pi$
$14$		0			0
$15$		0			0
$16$	39.6098	+	68.6061i	0.618902	+	1.07197i
$17$	−51.9931	+	90.0547i	−0.741775	+	1.28479i	0.209911	+	0.977720i	$0.432682\pi$
$17$	−51.9931	+	90.0547i	−0.741775	+	1.28479i	−0.951686	+	0.307072i	$0.900651\pi$
$18$		0			0
$19$	−61.9469	+	35.7650i	−0.747978	+	0.431845i	−0.824963	−	0.565187i	$-0.808804\pi$
$19$	−61.9469	+	35.7650i	−0.747978	+	0.431845i	0.0769848	+	0.997032i	$0.475471\pi$
$20$	4.18657			0.0468073
$21$		0			0
$22$	−1.33196			−0.0129079
$23$	118.248	−	68.2704i	1.07202	−	0.618929i	0.143284	−	0.989682i	$-0.454234\pi$
$23$	118.248	−	68.2704i	1.07202	−	0.618929i	0.928732	+	0.370753i	$0.120900\pi$
$24$		0			0
$25$	62.1325	−	107.617i	0.497060	−	0.860933i
$26$	111.277	+	192.737i	0.839353	+	1.45380i
$27$		0			0
$28$		0			0
$29$			17.8708i			0.114432i	0.998362	+	0.0572161i	$0.0182224\pi$
$29$			17.8708i			0.114432i	−0.998362	+	0.0572161i	$0.981778\pi$
$30$		0			0
$31$	−93.2782	−	53.8542i	−0.540428	−	0.312016i	0.204824	−	0.978799i	$-0.434338\pi$
$31$	−93.2782	−	53.8542i	−0.540428	−	0.312016i	−0.745252	+	0.666783i	$0.767671\pi$
$32$	168.750	+	97.4278i	0.932221	+	0.538218i
$33$		0			0
$34$			373.243i			1.88267i
$35$		0			0
$36$		0			0
$37$	190.857	+	330.575i	0.848020	+	1.46881i	0.882972	+	0.469425i	$0.155539\pi$
$37$	190.857	+	330.575i	0.848020	+	1.46881i	−0.0349518	+	0.999389i	$0.511128\pi$
$38$	−128.373	+	222.349i	−0.548024	+	0.949205i
$39$		0			0
$40$	−8.30525	+	4.79504i	−0.0328294	+	0.0189540i
$41$	101.733			0.387511			0.193756	−	0.981050i	$-0.437933\pi$
$41$	101.733			0.387511			0.193756	+	0.981050i	$0.437933\pi$
$42$		0			0
$43$	−326.400			−1.15757			−0.578785	−	0.815480i	$-0.696473\pi$
$43$	−326.400			−1.15757			−0.578785	+	0.815480i	$0.696473\pi$
$44$	−1.56939	+	0.906088i	−0.00537715	+	0.00310450i
$45$		0			0
$46$	245.047	−	424.433i	0.785438	−	1.36042i
$47$	261.065	+	452.178i	0.810218	+	1.40334i	0.912711	+	0.408606i	$0.133985\pi$
$47$	261.065	+	452.178i	0.810218	+	1.40334i	−0.102493	+	0.994734i	$0.532682\pi$
$48$		0			0
$49$		0			0
$50$		−	446.031i		−	1.26157i
$51$		0			0
$52$	262.226	+	151.396i	0.699312	+	0.403748i
$53$	268.049	+	154.758i	0.694704	+	0.401088i	0.805372	−	0.592770i	$-0.201966\pi$
$53$	268.049	+	154.758i	0.694704	+	0.401088i	−0.110668	+	0.993857i	$0.535299\pi$
$54$		0			0
$55$		−	0.318131i		−	0.000779940i
$56$		0			0
$57$		0			0
$58$	32.0724	+	55.5510i	0.0726088	+	0.125762i
$59$	−174.386	+	302.045i	−0.384799	+	0.666491i	−0.991741	−	0.128255i	$-0.959062\pi$
$59$	−174.386	+	302.045i	−0.384799	+	0.666491i	0.606943	+	0.794746i	$0.292396\pi$
$60$		0			0
$61$	580.478	−	335.139i	1.21840	−	0.703445i	0.253826	−	0.967250i	$-0.418311\pi$
$61$	580.478	−	335.139i	1.21840	−	0.703445i	0.964576	+	0.263805i	$0.0849775\pi$
$62$	−386.604			−0.791914
$63$		0			0
$64$	65.6495			0.128222
$65$	−46.0342	+	26.5779i	−0.0878437	+	0.0507166i
$66$		0			0
$67$	119.685	−	207.301i	0.218237	−	0.377997i	−0.736032	−	0.676947i	$-0.763303\pi$
$67$	119.685	−	207.301i	0.218237	−	0.377997i	0.954269	+	0.298949i	$0.0966362\pi$
$68$	253.906	+	439.778i	0.452803	+	0.784278i
$69$		0			0
$70$		0			0
$71$			178.563i			0.298472i	0.988802	+	0.149236i	$0.0476814\pi$
$71$			178.563i			0.298472i	−0.988802	+	0.149236i	$0.952319\pi$
$72$		0			0
$73$	117.414	+	67.7891i	0.188251	+	0.108687i	0.591163	−	0.806552i	$-0.298669\pi$
$73$	117.414	+	67.7891i	0.188251	+	0.108687i	−0.402913	+	0.915238i	$0.632002\pi$
$74$	1186.55	+	685.054i	1.86397	+	1.07616i
$75$		0			0
$76$			349.314i			0.527224i
$77$		0			0
$78$		0			0
$79$	−428.404	−	742.018i	−0.610117	−	1.05675i	−0.991220	−	0.132221i	$-0.957789\pi$
$79$	−428.404	−	742.018i	−0.610117	−	1.05675i	0.381103	−	0.924532i	$-0.375544\pi$
$80$	−33.9574	+	58.8159i	−0.0474569	+	0.0821977i
$81$		0			0
$82$	316.233	−	182.577i	0.425879	−	0.245881i
$83$	−1241.10			−1.64130			−0.820651	−	0.571430i	$-0.806389\pi$
$83$	−1241.10			−1.64130			−0.820651	+	0.571430i	$0.806389\pi$
$84$		0			0
$85$	−89.1472			−0.113757
$86$	−1014.60	+	585.782i	−1.27218	+	0.734494i
$87$		0			0
$88$	2.07555	−	3.59496i	0.00251426	−	0.00435482i
$89$	−282.464	−	489.242i	−0.336417	−	0.582691i	0.647339	−	0.762202i	$-0.275882\pi$
$89$	−282.464	−	489.242i	−0.336417	−	0.582691i	−0.983756	+	0.179511i	$0.942548\pi$
$90$		0			0
$91$		0			0
$92$		−	666.790i		−	0.755627i
$93$		0			0
$94$	1623.03	+	937.055i	1.78088	+	1.02819i
$95$	−53.1069	−	30.6613i	−0.0573543	−	0.0331135i
$96$		0			0
$97$		−	1730.44i		−	1.81134i	−0.423985	−	0.905669i	$-0.639369\pi$
$97$		−	1730.44i		−	1.81134i	0.423985	−	0.905669i	$-0.360631\pi$
$98$		0			0
$99$		0			0
$100$	−303.421	−	525.541i	−0.303421	−	0.525541i
$101$	−627.920	+	1087.59i	−0.618617	+	1.07148i	0.371121	+	0.928585i	$0.378974\pi$
$101$	−627.920	+	1087.59i	−0.618617	+	1.07148i	−0.989738	+	0.142892i	$0.954360\pi$
$102$		0			0
$103$	1351.32	−	780.186i	1.29272	−	0.746350i	0.313581	−	0.949561i	$-0.398471\pi$
$103$	1351.32	−	780.186i	1.29272	−	0.746350i	0.979135	+	0.203211i	$0.0651378\pi$
$104$	−693.599			−0.653971
$105$		0			0
$106$	1110.96			1.01798
$107$	145.139	−	83.7959i	0.131132	−	0.0757089i	−0.432999	−	0.901394i	$-0.642545\pi$
$107$	145.139	−	83.7959i	0.131132	−	0.0757089i	0.564131	+	0.825685i	$0.309211\pi$
$108$		0			0
$109$	−10.5542	+	18.2803i	−0.00927435	+	0.0160636i	−0.870625	−	0.491947i	$-0.836285\pi$
$109$	−10.5542	+	18.2803i	−0.00927435	+	0.0160636i	0.861351	+	0.508010i	$0.169619\pi$
$110$	−0.570941	−	0.988899i	−0.000494883	−	0.000857162i
$111$		0			0
$112$		0			0
$113$			1111.80i			0.925573i	0.886470	+	0.462787i	$0.153150\pi$
$113$			1111.80i			0.925573i	−0.886470	+	0.462787i	$0.846850\pi$
$114$		0			0
$115$	101.374	+	58.5281i	0.0822012	+	0.0474589i
$116$	75.5793	+	43.6357i	0.0604945	+	0.0349265i
$117$		0			0
$118$			1251.87i			0.976640i
$119$		0			0
$120$		0			0
$121$	−665.431	−	1152.56i	−0.499948	−	0.865936i
$122$	1202.93	−	2083.54i	0.892691	−	1.54619i
$123$		0			0
$124$	−455.520	+	262.994i	−0.329894	+	0.190465i
$125$	213.694			0.152907
$126$		0			0
$127$	−1725.08			−1.20532			−0.602662	−	0.797997i	$-0.705893\pi$
$127$	−1725.08			−1.20532			−0.602662	+	0.797997i	$0.705893\pi$
$128$	−1145.93	+	661.603i	−0.791304	+	0.456859i
$129$		0			0
$130$	−95.3974	+	165.233i	−0.0643608	+	0.111476i
$131$	−426.358	−	738.474i	−0.284359	−	0.492525i	0.688094	−	0.725621i	$-0.258448\pi$
$131$	−426.358	−	738.474i	−0.284359	−	0.492525i	−0.972454	+	0.233097i	$0.925114\pi$
$132$		0			0
$133$		0			0
$134$		−	859.184i		−	0.553897i
$135$		0			0
$136$	−1007.39	−	581.615i	−0.635167	−	0.366714i
$137$	264.199	+	152.536i	0.164760	+	0.0951241i	0.580113	−	0.814536i	$-0.303009\pi$
$137$	264.199	+	152.536i	0.164760	+	0.0951241i	−0.415353	+	0.909660i	$0.636342\pi$
$138$		0			0
$139$		−	1689.85i		−	1.03116i	−0.856841	−	0.515581i	$-0.827576\pi$
$139$		−	1689.85i		−	1.03116i	0.856841	−	0.515581i	$-0.172424\pi$
$140$		0			0
$141$		0			0
$142$	320.462	+	555.057i	0.189384	+	0.328024i
$143$	11.5043	−	19.9261i	0.00672756	−	0.0116525i
$144$		0			0
$145$	−13.2681	+	7.66032i	−0.00759899	+	0.00438728i
$146$	486.638			0.275852
$147$		0			0
$148$	1864.09			1.03532
$149$	1927.91	−	1113.08i	1.06000	−	0.611993i	0.134570	−	0.990904i	$-0.457035\pi$
$149$	1927.91	−	1113.08i	1.06000	−	0.611993i	0.925433	+	0.378911i	$0.123701\pi$
$150$		0			0
$151$	−410.604	+	711.188i	−0.221288	+	0.383282i	−0.955199	−	0.295963i	$-0.904359\pi$
$151$	−410.604	+	711.188i	−0.221288	+	0.383282i	0.733911	+	0.679245i	$0.237693\pi$
$152$	−400.082	−	692.962i	−0.213493	−	0.369780i
$153$		0			0
$154$		0			0
$155$		−	92.3382i		−	0.0478502i
$156$		0			0
$157$	−1384.34	−	799.250i	−0.703710	−	0.406287i	0.105018	−	0.994470i	$-0.466510\pi$
$157$	−1384.34	−	799.250i	−0.703710	−	0.406287i	−0.808728	+	0.588183i	$0.799843\pi$
$158$	−2663.36	−	1537.69i	−1.34105	−	0.774255i
$159$		0			0
$160$			167.049i			0.0825401i
$161$		0			0
$162$		0			0
$163$	1296.33	+	2245.31i	0.622923	+	1.07893i	0.988939	+	0.148326i	$0.0473883\pi$
$163$	1296.33	+	2245.31i	0.622923	+	1.07893i	−0.366016	+	0.930609i	$0.619278\pi$
$164$	248.403	−	430.247i	0.118275	−	0.204857i
$165$		0			0
$166$	−3857.91	+	2227.37i	−1.80381	+	1.04143i
$167$	4136.77			1.91685			0.958423	−	0.285352i	$-0.0921106\pi$
$167$	4136.77			1.91685			0.958423	+	0.285352i	$0.0921106\pi$
$168$		0			0
$169$	−1647.47			−0.749873
$170$	−277.111	+	159.990i	−0.125020	+	0.0721806i
$171$		0			0
$172$	−796.979	+	1380.41i	−0.353309	+	0.611948i
$173$	1583.86	+	2743.33i	0.696063	+	1.20562i	0.969821	+	0.243818i	$0.0784001\pi$
$173$	1583.86	+	2743.33i	0.696063	+	1.20562i	−0.273757	+	0.961799i	$0.588267\pi$
$174$		0			0
$175$		0			0
$176$		−	29.3972i		−	0.0125903i
$177$		0			0
$178$	−1756.06	−	1013.86i	−0.739451	−	0.426922i
$179$	−3110.97	−	1796.12i	−1.29902	−	0.749991i	−0.318787	−	0.947827i	$-0.603275\pi$
$179$	−3110.97	−	1796.12i	−1.29902	−	0.749991i	−0.980235	+	0.197836i	$0.936609\pi$
$180$		0			0
$181$			314.936i			0.129332i	0.997907	+	0.0646658i	$0.0205981\pi$
$181$			314.936i			0.129332i	−0.997907	+	0.0646658i	$0.979402\pi$
$182$		0			0
$183$		0			0
$184$	763.699	+	1322.77i	0.305982	+	0.529976i
$185$	−163.622	+	283.401i	−0.0650254	+	0.112627i
$186$		0			0
$187$	33.4179	−	19.2939i	0.0130682	−	0.00754495i
$188$	2549.80			0.989166
$189$		0			0
$190$	−220.108			−0.0840439
$191$	3051.20	−	1761.61i	1.15590	−	0.667359i	0.205582	−	0.978640i	$-0.434091\pi$
$191$	3051.20	−	1761.61i	1.15590	−	0.667359i	0.950318	+	0.311281i	$0.100758\pi$
$192$		0			0
$193$	−360.020	+	623.573i	−0.134274	+	0.232569i	−0.925320	−	0.379188i	$-0.876203\pi$
$193$	−360.020	+	623.573i	−0.134274	+	0.232569i	0.791046	+	0.611757i	$0.209537\pi$
$194$	−3105.58	−	5379.03i	−1.14932	−	1.99068i
$195$		0			0
$196$		0			0
$197$			3479.92i			1.25855i	0.777184	+	0.629274i	$0.216647\pi$
$197$			3479.92i			1.25855i	−0.777184	+	0.629274i	$0.783353\pi$
$198$		0			0
$199$	−3381.21	−	1952.14i	−1.20446	−	0.695395i	−0.242916	−	0.970047i	$-0.578104\pi$
$199$	−3381.21	−	1952.14i	−1.20446	−	0.695395i	−0.961544	+	0.274652i	$0.911437\pi$
$200$	1203.84	+	695.039i	0.425622	+	0.245733i
$201$		0			0
$202$			4507.65i			1.57009i
$203$		0			0
$204$		0			0
$205$	43.6076	+	75.5305i	0.0148570	+	0.0257331i
$206$	2800.36	−	4850.37i	0.947139	−	1.64049i
$207$		0			0
$208$	−4253.84	+	2455.96i	−1.41803	+	0.818701i
$209$	26.5437			0.00878502
$210$		0			0
$211$	2913.22			0.950494			0.475247	−	0.879852i	$-0.342359\pi$
$211$	2913.22			0.950494			0.475247	+	0.879852i	$0.342359\pi$
$212$	1309.00	−	755.753i	0.424069	−	0.244837i
$213$		0			0
$214$	300.773	−	520.954i	0.0960767	−	0.166410i
$215$	−139.911	−	242.333i	−0.0443807	−	0.0768696i
$216$		0			0
$217$		0			0
$218$			75.7651i			0.0235388i
$219$		0			0
$220$	−1.34544	−	0.776788i	−0.000412315	−	0.000238050i
$221$	−5583.73	−	3223.77i	−1.69956	−	0.981241i
$222$		0			0
$223$		−	1202.30i		−	0.361040i	−0.983571	−	0.180520i	$-0.942222\pi$
$223$		−	1202.30i		−	0.361040i	0.983571	−	0.180520i	$-0.0577780\pi$
$224$		0			0
$225$		0			0
$226$	1995.33	+	3456.01i	0.587289	+	1.01721i
$227$	−2567.71	+	4447.40i	−0.750770	+	1.30037i	0.196681	+	0.980468i	$0.436984\pi$
$227$	−2567.71	+	4447.40i	−0.750770	+	1.30037i	−0.947450	+	0.319903i	$0.896350\pi$
$228$		0			0
$229$	−1625.94	+	938.735i	−0.469192	+	0.270888i	−0.715901	−	0.698202i	$-0.753984\pi$
$229$	−1625.94	+	938.735i	−0.469192	+	0.270888i	0.246710	+	0.969089i	$0.420651\pi$
$230$	420.156			0.120453
$231$		0			0
$232$	−199.910			−0.0565722
$233$	3016.28	−	1741.45i	0.848081	−	0.489640i	−0.0119216	−	0.999929i	$-0.503795\pi$
$233$	3016.28	−	1741.45i	0.848081	−	0.489640i	0.860003	+	0.510289i	$0.170462\pi$
$234$		0			0
$235$	−223.811	+	387.651i	−0.0621268	+	0.107607i
$236$	851.605	+	1475.02i	0.234893	+	0.406847i
$237$		0			0
$238$		0			0
$239$			2466.36i			0.667514i	0.942659	+	0.333757i	$0.108316\pi$
$239$			2466.36i			0.667514i	−0.942659	+	0.333757i	$0.891684\pi$
$240$		0			0
$241$	2112.76	+	1219.80i	0.564709	+	0.326035i	0.755033	−	0.655686i	$-0.227621\pi$
$241$	2112.76	+	1219.80i	0.564709	+	0.326035i	−0.190324	+	0.981721i	$0.560954\pi$
$242$	−4136.95	−	2388.47i	−1.09890	−	0.634448i
$243$		0			0
$244$		−	3273.27i		−	0.858810i
$245$		0			0
$246$		0			0
$247$	−2217.57	−	3840.94i	−0.571257	−	0.989446i
$248$	602.434	−	1043.45i	0.154252	−	0.267173i
$249$		0			0
$250$	664.263	−	383.512i	0.168047	−	0.0970218i
$251$	4329.06			1.08864			0.544319	−	0.838878i	$-0.316788\pi$
$251$	4329.06			1.08864			0.544319	+	0.838878i	$0.316788\pi$
$252$		0			0
$253$	−50.6682			−0.0125909
$254$	−5362.36	+	3095.96i	−1.32466	+	0.764795i
$255$		0			0
$256$	−2637.32	+	4567.98i	−0.643878	+	1.11523i
$257$	−1570.68	−	2720.50i	−0.381231	−	0.660312i	0.610007	−	0.792396i	$-0.291166\pi$
$257$	−1570.68	−	2720.50i	−0.381231	−	0.660312i	−0.991239	+	0.132084i	$0.957833\pi$
$258$		0			0
$259$		0			0
$260$			259.584i			0.0619180i
$261$		0			0
$262$	−2650.64	−	1530.35i	−0.625028	−	0.360860i
$263$	6663.55	+	3847.20i	1.56233	+	0.902010i	0.997021	+	0.0771283i	$0.0245751\pi$
$263$	6663.55	+	3847.20i	1.56233	+	0.902010i	0.565306	+	0.824882i	$0.308758\pi$
$264$		0			0
$265$			265.348i			0.0615101i
$266$		0			0
$267$		0			0
$268$	−584.477	−	1012.34i	−0.133219	−	0.230741i
$269$	698.723	−	1210.22i	0.158371	−	0.274307i	−0.775910	−	0.630843i	$-0.782709\pi$
$269$	698.723	−	1210.22i	0.158371	−	0.274307i	0.934281	+	0.356536i	$0.116042\pi$
$270$		0			0
$271$	2135.91	−	1233.17i	0.478772	−	0.276419i	−0.241133	−	0.970492i	$-0.577519\pi$
$271$	2135.91	−	1233.17i	0.478772	−	0.276419i	0.719905	+	0.694073i	$0.244186\pi$
$272$	−8237.73			−1.83635
$273$		0			0
$274$	1095.01			0.241430
$275$	−39.9349	+	23.0564i	−0.00875697	+	0.00505584i
$276$		0			0
$277$	−1086.42	+	1881.73i	−0.235655	+	0.408167i	−0.959463	−	0.281835i	$-0.909057\pi$
$277$	−1086.42	+	1881.73i	−0.235655	+	0.408167i	0.723808	+	0.690002i	$0.242390\pi$
$278$	−3032.74	−	5252.86i	−0.654287	−	1.13326i
$279$		0			0
$280$		0			0
$281$		−	4631.24i		−	0.983191i	−0.870824	−	0.491596i	$-0.836414\pi$
$281$		−	4631.24i		−	0.983191i	0.870824	−	0.491596i	$-0.163586\pi$
$282$		0			0
$283$	5999.60	+	3463.87i	1.26021	+	0.727582i	0.973115	−	0.230320i	$-0.0739772\pi$
$283$	5999.60	+	3463.87i	1.26021	+	0.727582i	0.287095	+	0.957902i	$0.407311\pi$
$284$	755.176	+	436.001i	0.157787	+	0.0910983i
$285$		0			0
$286$		−	82.5863i		−	0.0170749i
$287$		0			0
$288$		0			0
$289$	−2950.06	−	5109.66i	−0.600460	−	1.04003i
$290$	−27.4956	+	47.6238i	−0.00556758	+	0.00964332i
$291$		0			0
$292$	573.387	−	331.045i	0.114914	−	0.0663457i
$293$	667.366			0.133065			0.0665323	−	0.997784i	$-0.478806\pi$
$293$	667.366			0.133065			0.0665323	+	0.997784i	$0.478806\pi$
$294$		0			0
$295$	−299.002			−0.0590120
$296$	−3697.94	+	2135.00i	−0.726143	+	0.419239i
$297$		0			0
$298$	3995.23	−	6919.94i	0.776636	−	1.34517i
$299$	4233.02	+	7331.81i	0.818736	+	1.41809i
$300$		0			0
$301$		0			0
$302$			2947.61i			0.561642i
$303$		0			0
$304$	−4907.40	−	2833.29i	−0.925851	−	0.534540i
$305$	497.642	+	287.314i	0.0934260	+	0.0539395i
$306$		0			0
$307$		−	10190.1i		−	1.89439i	−0.320658	−	0.947195i	$-0.603904\pi$
$307$		−	10190.1i		−	1.89439i	0.320658	−	0.947195i	$-0.396096\pi$
$308$		0			0
$309$		0			0
$310$	−165.717	−	287.031i	−0.0303616	−	0.0525879i
$311$	4800.99	−	8315.56i	0.875367	−	1.51618i	0.0189952	−	0.999820i	$-0.493953\pi$
$311$	4800.99	−	8315.56i	0.875367	−	1.51618i	0.856372	−	0.516360i	$-0.172713\pi$
$312$		0			0
$313$	5683.70	−	3281.48i	1.02639	−	0.592589i	0.110445	−	0.993882i	$-0.464772\pi$
$313$	5683.70	−	3281.48i	1.02639	−	0.592589i	0.915950	+	0.401293i	$0.131439\pi$
$314$	−5737.58			−1.03118
$315$		0			0
$316$	−4184.18			−0.744869
$317$	−115.552	+	66.7137i	−0.0204732	+	0.0118202i	−0.510202	−	0.860055i	$-0.670429\pi$
$317$	−115.552	+	66.7137i	−0.0204732	+	0.0118202i	0.489728	+	0.871875i	$0.337096\pi$
$318$		0			0
$319$	3.31580	−	5.74314i	0.000581973	−	0.00100801i
$320$	28.1406	+	48.7410i	0.00491596	+	0.00851470i
$321$		0			0
$322$		0			0
$323$		−	7438.14i		−	1.28133i
$324$		0			0
$325$	6672.64	+	3852.45i	1.13887	+	0.657525i
$326$	8059.21	+	4652.99i	1.36920	+	0.790507i
$327$		0			0
$328$			1138.02i			0.191575i
$329$		0			0
$330$		0			0
$331$	−2393.76	−	4146.11i	−0.397501	−	0.688492i	0.595916	−	0.803047i	$-0.296789\pi$
$331$	−2393.76	−	4146.11i	−0.397501	−	0.688492i	−0.993417	+	0.114555i	$0.963456\pi$
$332$	−3030.42	+	5248.84i	−0.500951	+	0.867673i
$333$		0			0
$334$	12859.0	−	7424.17i	2.10663	−	1.21627i
$335$	205.212			0.0334684
$336$		0			0
$337$	8273.70			1.33738			0.668690	−	0.743541i	$-0.266855\pi$
$337$	8273.70			1.33738			0.668690	+	0.743541i	$0.266855\pi$
$338$	−5121.12	+	2956.68i	−0.824118	+	0.475805i
$339$		0			0
$340$	−217.673	+	377.021i	−0.0347205	+	0.0601377i
$341$	19.9845	+	34.6142i	0.00317367	+	0.00549696i
$342$		0			0
$343$		0			0
$344$		−	3651.24i		−	0.572272i
$345$		0			0
$346$	9846.79	+	5685.05i	1.52996	+	0.883324i
$347$	−3203.79	−	1849.71i	−0.495644	−	0.286160i	0.231269	−	0.972890i	$-0.425712\pi$
$347$	−3203.79	−	1849.71i	−0.495644	−	0.286160i	−0.726913	+	0.686730i	$0.759046\pi$
$348$		0			0
$349$			903.273i			0.138542i	0.997598	+	0.0692709i	$0.0220673\pi$
$349$			903.273i			0.138542i	−0.997598	+	0.0692709i	$0.977933\pi$
$350$		0			0
$351$		0			0
$352$	−36.1540	−	62.6206i	−0.00547447	−	0.00948207i
$353$	−5080.80	+	8800.20i	−0.766073	+	1.32688i	0.173605	+	0.984815i	$0.444458\pi$
$353$	−5080.80	+	8800.20i	−0.766073	+	1.32688i	−0.939678	+	0.342061i	$0.888875\pi$
$354$		0			0
$355$	−132.572	+	76.5408i	−0.0198203	+	0.0114433i
$356$	−2758.80			−0.410719
$357$		0			0
$358$	−12893.8			−1.90352
$359$	−3651.25	+	2108.05i	−0.536784	+	0.309912i	−0.743775	−	0.668431i	$-0.766966\pi$
$359$	−3651.25	+	2108.05i	−0.536784	+	0.309912i	0.206991	+	0.978343i	$0.433633\pi$
$360$		0			0
$361$	−871.225	+	1509.01i	−0.127019	+	0.220004i
$362$	565.209	+	978.970i	0.0820627	+	0.142137i
$363$		0			0
$364$		0			0
$365$			116.231i			0.0166680i
$366$		0			0
$367$	−468.678	−	270.591i	−0.0666615	−	0.0384871i	0.466299	−	0.884627i	$-0.345587\pi$
$367$	−468.678	−	270.591i	−0.0666615	−	0.0384871i	−0.532960	+	0.846140i	$0.678921\pi$
$368$	9367.53	+	5408.35i	1.32695	+	0.766113i
$369$		0			0
$370$			1174.59i			0.165038i
$371$		0			0
$372$		0			0
$373$	−1120.17	−	1940.19i	−0.155496	−	0.269328i	0.777743	−	0.628582i	$-0.216364\pi$
$373$	−1120.17	−	1940.19i	−0.155496	−	0.269328i	−0.933240	+	0.359254i	$0.883031\pi$
$374$	69.2525	−	119.949i	0.00957476	−	0.0165840i
$375$		0			0
$376$	−5058.24	+	2920.38i	−0.693773	+	0.400550i
$377$	−1108.06			−0.151374
$378$		0			0
$379$	−2922.72			−0.396121			−0.198060	−	0.980190i	$-0.563464\pi$
$379$	−2922.72			−0.396121			−0.198060	+	0.980190i	$0.563464\pi$
$380$	−259.345	+	149.733i	−0.0350109	+	0.0202135i
$381$		0			0
$382$	6323.04	−	10951.8i	0.846897	−	1.46687i
$383$	3526.59	+	6108.23i	0.470497	+	0.814924i	0.999431	−	0.0337386i	$-0.0107414\pi$
$383$	3526.59	+	6108.23i	0.470497	+	0.814924i	−0.528934	+	0.848663i	$0.677408\pi$
$384$		0			0
$385$		0			0
$386$			2584.48i			0.340794i
$387$		0			0
$388$	−7318.38	−	4225.27i	−0.957562	−	0.552849i
$389$	8598.98	+	4964.62i	1.12079	+	0.647086i	0.941601	−	0.336730i	$-0.109321\pi$
$389$	8598.98	+	4964.62i	1.12079	+	0.647086i	0.179184	+	0.983816i	$0.442654\pi$
$390$		0			0
$391$			14198.4i			1.83642i
$392$		0			0
$393$		0			0
$394$	6245.32	+	10817.2i	0.798566	+	1.38316i
$395$	367.270	−	636.131i	0.0467832	−	0.0810309i
$396$		0			0
$397$	2207.29	−	1274.38i	0.279044	−	0.161106i	−0.353946	−	0.935266i	$-0.615160\pi$
$397$	2207.29	−	1274.38i	0.279044	−	0.161106i	0.632991	+	0.774159i	$0.281827\pi$
$398$	−14013.9			−1.76495
$399$		0			0
$400$	9844.22			1.23053
$401$	4468.23	−	2579.74i	0.556441	−	0.321261i	−0.195275	−	0.980749i	$-0.562560\pi$
$401$	4468.23	−	2579.74i	0.556441	−	0.321261i	0.751716	+	0.659487i	$0.229226\pi$
$402$		0			0
$403$	3339.17	−	5783.61i	0.412744	−	0.714893i
$404$	3066.42	+	5311.19i	0.377624	+	0.654063i
$405$		0			0
$406$		0			0
$407$		−	141.649i		−	0.0172513i
$408$		0			0
$409$	6922.74	+	3996.85i	0.836938	+	0.483206i	0.856222	−	0.516608i	$-0.172805\pi$
$409$	6922.74	+	3996.85i	0.836938	+	0.483206i	−0.0192844	+	0.999814i	$0.506139\pi$
$410$	271.106	+	156.523i	0.0326560	+	0.0188539i
$411$		0			0
$412$		−	7620.01i		−	0.911191i
$413$		0			0
$414$		0			0
$415$	−531.995	−	921.443i	−0.0629268	−	0.108992i
$416$	−6040.90	+	10463.1i	−0.711969	+	1.23317i
$417$		0			0
$418$	82.5104	−	47.6374i	0.00965483	−	0.00557422i
$419$	5972.30			0.696338			0.348169	−	0.937432i	$-0.386803\pi$
$419$	5972.30			0.696338			0.348169	+	0.937432i	$0.386803\pi$
$420$		0			0
$421$	12647.3			1.46412			0.732058	−	0.681242i	$-0.238560\pi$
$421$	12647.3			1.46412			0.732058	+	0.681242i	$0.238560\pi$
$422$	9055.66	−	5228.29i	1.04460	−	0.603102i
$423$		0			0
$424$	−1731.18	+	2998.50i	−0.198287	+	0.343443i
$425$	6460.92	+	11190.6i	0.737414	+	1.27724i
$426$		0			0
$427$		0			0
$428$		−	818.426i		−	0.0924302i
$429$		0			0
$430$	−869.818	−	502.190i	−0.0975497	−	0.0563203i
$431$	−2947.84	−	1701.94i	−0.329449	−	0.190207i	0.326148	−	0.945319i	$-0.394249\pi$
$431$	−2947.84	−	1701.94i	−0.329449	−	0.190207i	−0.655596	+	0.755111i	$0.727583\pi$
$432$		0			0
$433$			7413.29i			0.822772i	0.911461	+	0.411386i	$0.134955\pi$
$433$			7413.29i			0.822772i	−0.911461	+	0.411386i	$0.865045\pi$
$434$		0			0
$435$		0			0
$436$	51.5407	+	89.2711i	0.00566136	+	0.00980576i
$437$	−4883.39	+	8458.27i	−0.534563	+	0.925890i
$438$		0			0
$439$	−4020.87	+	2321.45i	−0.437142	+	0.252384i	−0.702385	−	0.711797i	$-0.747881\pi$
$439$	−4020.87	+	2321.45i	−0.437142	+	0.252384i	0.265242	+	0.964182i	$0.414548\pi$
$440$	3.55873			0.000385582
$441$		0			0
$442$	−23142.5			−2.49044
$443$	2570.90	−	1484.31i	0.275727	−	0.159191i	−0.355761	−	0.934577i	$-0.615778\pi$
$443$	2570.90	−	1484.31i	0.275727	−	0.159191i	0.631487	+	0.775386i	$0.282445\pi$
$444$		0			0
$445$	242.156	−	419.426i	0.0257961	−	0.0446802i
$446$	−2157.74	−	3737.31i	−0.229085	−	0.396786i
$447$		0			0
$448$		0			0
$449$			8732.52i			0.917847i	0.888476	+	0.458923i	$0.151765\pi$
$449$			8732.52i			0.917847i	−0.888476	+	0.458923i	$0.848235\pi$
$450$		0			0
$451$	−32.6937	−	18.8757i	−0.00341350	−	0.00197078i
$452$	4702.04	+	2714.72i	0.489304	+	0.282500i
$453$		0			0
$454$			18432.8i			1.90549i
$455$		0			0
$456$		0			0
$457$	6049.30	+	10477.7i	0.619200	+	1.07249i	0.989632	+	0.143626i	$0.0458762\pi$
$457$	6049.30	+	10477.7i	0.619200	+	1.07249i	−0.370432	+	0.928859i	$0.620790\pi$
$458$	−3369.45	+	5836.06i	−0.343764	+	0.595417i
$459$		0			0
$460$	495.053	−	285.819i	0.0501782	−	0.0289704i
$461$	7746.32			0.782608			0.391304	−	0.920261i	$-0.372024\pi$
$461$	7746.32			0.782608			0.391304	+	0.920261i	$0.372024\pi$
$462$		0			0
$463$	2573.36			0.258303			0.129152	−	0.991625i	$-0.458775\pi$
$463$	2573.36			0.258303			0.129152	+	0.991625i	$0.458775\pi$
$464$	−1226.05	+	707.860i	−0.122668	+	0.0708223i
$465$		0			0
$466$	6250.68	−	10826.5i	0.621367	−	1.07624i
$467$	1193.94	+	2067.96i	0.118306	+	0.204911i	0.919096	−	0.394033i	$-0.128920\pi$
$467$	1193.94	+	2067.96i	0.118306	+	0.204911i	−0.800791	+	0.598944i	$0.795587\pi$
$468$		0			0
$469$		0			0
$470$			1606.67i			0.157681i
$471$		0			0
$472$	−3378.80	−	1950.75i	−0.329495	−	0.190234i
$473$	104.895	+	60.5610i	0.0101968	+	0.00588710i
$474$		0			0
$475$			8888.69i			0.858612i
$476$		0			0
$477$		0			0
$478$	4426.32	+	7666.62i	0.423547	+	0.733605i
$479$	1453.00	−	2516.67i	0.138600	−	0.240062i	−0.788367	−	0.615205i	$-0.789073\pi$
$479$	1453.00	−	2516.67i	0.138600	−	0.240062i	0.926967	+	0.375143i	$0.122407\pi$
$480$		0			0
$481$	−20496.9	+	11833.9i	−1.94299	+	1.12178i
$482$	8756.60			0.827495
$483$		0			0
$484$	−6499.20			−0.610368
$485$	1284.75	−	741.753i	0.120284	−	0.0694459i
$486$		0			0
$487$	−132.268	+	229.095i	−0.0123072	+	0.0213168i	−0.872113	−	0.489304i	$-0.837251\pi$
$487$	−132.268	+	229.095i	−0.0123072	+	0.0213168i	0.859806	+	0.510621i	$0.170584\pi$
$488$	3748.99	+	6493.45i	0.347764	+	0.602346i
$489$		0			0
$490$		0			0
$491$		−	19788.0i		−	1.81878i	−0.415943	−	0.909391i	$-0.636548\pi$
$491$		−	19788.0i		−	1.81878i	0.415943	−	0.909391i	$-0.363452\pi$
$492$		0			0
$493$	−1609.35	−	929.160i	−0.147022	−	0.0848829i
$494$	−13786.5	−	7959.63i	−1.25563	−	0.724941i
$495$		0			0
$496$		−	8532.61i		−	0.772430i
$497$		0			0
$498$		0			0
$499$	5735.87	+	9934.82i	0.514575	+	0.891270i	0.999857	+	0.0169124i	$0.00538363\pi$
$499$	5735.87	+	9934.82i	0.514575	+	0.891270i	−0.485282	+	0.874358i	$0.661283\pi$
$500$	521.783	−	903.755i	0.0466697	−	0.0808343i
$501$		0			0
$502$	13456.8	−	7769.27i	1.19642	−	0.690756i
$503$	1261.66			0.111839			0.0559193	−	0.998435i	$-0.482191\pi$
$503$	1261.66			0.111839			0.0559193	+	0.998435i	$0.482191\pi$
$504$		0			0
$505$	−1076.63			−0.0948700
$506$	−157.501	+	90.9331i	−0.0138375	+	0.00798907i
$507$		0			0
$508$	−4212.17	+	7295.70i	−0.367884	+	0.637194i
$509$	−4261.39	−	7380.94i	−0.371086	−	0.642740i	0.618647	−	0.785669i	$-0.287681\pi$
$509$	−4261.39	−	7380.94i	−0.371086	−	0.642740i	−0.989733	+	0.142929i	$0.954348\pi$
$510$		0			0
$511$		0			0
$512$			8346.93i			0.720480i
$513$		0			0
$514$	−9764.83	−	5637.73i	−0.837954	−	0.483793i
$515$	1158.49	+	668.853i	0.0991243	+	0.0572294i
$516$		0			0
$517$		−	193.755i		−	0.0164823i
$518$		0			0
$519$		0			0
$520$	−297.310	−	514.957i	−0.0250729	−	0.0434276i
$521$	6608.58	−	11446.4i	0.555714	−	0.962525i	−0.442133	−	0.896949i	$-0.645778\pi$
$521$	6608.58	−	11446.4i	0.555714	−	0.962525i	0.997848	−	0.0655760i	$-0.0208885\pi$
$522$		0			0
$523$	7783.83	−	4493.99i	0.650790	−	0.375734i	−0.137969	−	0.990437i	$-0.544057\pi$
$523$	7783.83	−	4493.99i	0.650790	−	0.375734i	0.788759	+	0.614703i	$0.210724\pi$
$524$	−4164.20			−0.347164
$525$		0			0
$526$	27617.9			2.28935
$527$	9699.65	−	5600.09i	0.801752	−	0.462892i
$528$		0			0
$529$	3238.19	−	5608.72i	0.266146	−	0.460978i
$530$	476.213	+	824.825i	0.0390290	+	0.0676002i
$531$		0			0
$532$		0			0
$533$			6307.81i			0.512611i
$534$		0			0
$535$	124.427	+	71.8381i	0.0100551	+	0.00580529i
$536$	2318.95	+	1338.84i	0.186872	+	0.107890i
$537$		0			0
$538$		−	5015.92i		−	0.401955i
$539$		0			0
$540$		0			0
$541$	−5815.74	−	10073.2i	−0.462178	−	0.800516i	0.536891	−	0.843652i	$-0.319599\pi$
$541$	−5815.74	−	10073.2i	−0.462178	−	0.800516i	−0.999069	+	0.0431356i	$0.986265\pi$
$542$	4426.27	−	7666.53i	0.350784	−	0.607575i
$543$		0			0
$544$	−17547.7	+	10131.1i	−1.38300	+	0.798473i
$545$	−18.0961			−0.00142230
$546$		0			0
$547$	−23271.9			−1.81908			−0.909538	−	0.415622i	$-0.863564\pi$
$547$	−23271.9			−1.81908			−0.909538	+	0.415622i	$0.863564\pi$
$548$	1290.21	−	744.900i	0.100575	−	0.0580667i
$549$		0			0
$550$	−82.7577	+	143.341i	−0.00641600	+	0.0111128i
$551$	−639.151	−	1107.04i	−0.0494170	−	0.0855927i
$552$		0			0
$553$		0			0
$554$			7799.07i			0.598106i
$555$		0			0
$556$	−7146.72	−	4126.16i	−0.545123	−	0.314727i
$557$	−211.015	−	121.830i	−0.0160521	−	0.00926767i	0.491952	−	0.870622i	$-0.336283\pi$
$557$	−211.015	−	121.830i	−0.0160521	−	0.00926767i	−0.508005	+	0.861354i	$0.669617\pi$
$558$		0			0
$559$		−	20238.0i		−	1.53127i
$560$		0			0
$561$		0			0
$562$	−8311.58	−	14396.1i	−0.623848	−	1.08054i
$563$	4606.13	−	7978.05i	0.344805	−	0.597220i	−0.640513	−	0.767947i	$-0.721278\pi$
$563$	4606.13	−	7978.05i	0.344805	−	0.597220i	0.985318	+	0.170727i	$0.0546117\pi$
$564$		0			0
$565$	−825.450	+	476.574i	−0.0614637	+	0.0354861i
$566$	24866.1			1.84664
$567$		0			0
$568$	−1997.47			−0.147556
$569$	−6941.28	+	4007.55i	−0.511413	+	0.295264i	−0.733414	−	0.679782i	$-0.762074\pi$
$569$	−6941.28	+	4007.55i	−0.511413	+	0.295264i	0.222001	+	0.975046i	$0.428741\pi$
$570$		0			0
$571$	−10058.3	+	17421.5i	−0.737173	+	1.27682i	0.216590	+	0.976263i	$0.430507\pi$
$571$	−10058.3	+	17421.5i	−0.737173	+	1.27682i	−0.953763	+	0.300559i	$0.902827\pi$
$572$	−56.1809	−	97.3082i	−0.00410672	−	0.00711304i
$573$		0			0
$574$		0			0
$575$		−	16967.2i		−	1.23058i
$576$		0			0
$577$	−10355.4	−	5978.68i	−0.747141	−	0.431362i	0.0775191	−	0.996991i	$-0.475300\pi$
$577$	−10355.4	−	5978.68i	−0.747141	−	0.431362i	−0.824660	+	0.565629i	$0.808633\pi$
$578$	−18340.4	−	10588.8i	−1.31982	−	0.762001i
$579$		0			0
$580$			74.8176i			0.00535626i
$581$		0			0
$582$		0			0
$583$	−57.4284	−	99.4689i	−0.00407966	−	0.00706617i
$584$	−758.316	+	1313.44i	−0.0537317	+	0.0930661i
$585$		0			0
$586$	2074.49	−	1197.71i	0.146239	−	0.0844314i
$587$	5400.12			0.379705			0.189852	−	0.981813i	$-0.439199\pi$
$587$	5400.12			0.379705			0.189852	+	0.981813i	$0.439199\pi$
$588$		0			0
$589$	7704.39			0.538971
$590$	−929.437	+	536.611i	−0.0648548	+	0.0374439i
$591$		0			0
$592$	−15119.6	+	26188.0i	−1.04968	+	1.81811i
$593$	−11877.2	−	20571.9i	−0.822491	−	1.42460i	−0.903822	−	0.427909i	$-0.859250\pi$
$593$	−11877.2	−	20571.9i	−0.822491	−	1.42460i	0.0813305	−	0.996687i	$-0.474083\pi$
$594$		0			0
$595$		0			0
$596$		−	10871.3i		−	0.747160i
$597$		0			0
$598$	26316.5	+	15193.8i	1.79960	+	1.03900i
$599$	−1263.64	−	729.564i	−0.0861953	−	0.0497649i	0.456283	−	0.889835i	$-0.349181\pi$
$599$	−1263.64	−	729.564i	−0.0861953	−	0.0497649i	−0.542478	+	0.840070i	$0.682514\pi$
$600$		0			0
$601$			5357.92i			0.363651i	0.983331	+	0.181825i	$0.0582006\pi$
$601$			5357.92i			0.363651i	−0.983331	+	0.181825i	$0.941799\pi$
$602$		0			0
$603$		0			0
$604$	2005.17	+	3473.05i	0.135081	+	0.233968i
$605$	570.473	−	988.088i	0.0383356	−	0.0663992i
$606$		0			0
$607$	8773.63	−	5065.46i	0.586673	−	0.338716i	−0.177108	−	0.984191i	$-0.556674\pi$
$607$	8773.63	−	5065.46i	0.586673	−	0.338716i	0.763781	+	0.645475i	$0.223341\pi$
$608$	−13938.0			−0.929707
$609$		0			0
$610$	2062.54			0.136901
$611$	−28036.8	+	16187.0i	−1.85638	+	1.07178i
$612$		0			0
$613$	1217.62	−	2108.99i	0.0802274	−	0.138958i	−0.823120	−	0.567867i	$-0.807769\pi$
$613$	1217.62	−	2108.99i	0.0802274	−	0.138958i	0.903348	+	0.428909i	$0.141102\pi$
$614$	−18287.9	−	31675.5i	−1.20202	−	2.08195i
$615$		0			0
$616$		0			0
$617$			28047.4i			1.83006i	0.403389	+	0.915029i	$0.367832\pi$
$617$			28047.4i			1.83006i	−0.403389	+	0.915029i	$0.632168\pi$
$618$		0			0
$619$	−14086.2	−	8132.66i	−0.914655	−	0.528076i	−0.0327292	−	0.999464i	$-0.510420\pi$
$619$	−14086.2	−	8132.66i	−0.914655	−	0.528076i	−0.881926	+	0.471388i	$0.843753\pi$
$620$	−390.516	−	225.465i	−0.0252960	−	0.0146046i
$621$		0			0
$622$		−	34464.9i		−	2.22173i
$623$		0			0
$624$		0			0
$625$	−7674.97	−	13293.4i	−0.491198	−	0.850779i
$626$	11778.4	−	20400.8i	0.752012	−	1.30252i
$627$		0			0
$628$	−6760.36	+	3903.10i	−0.429567	+	0.248010i
$629$	−39693.0			−2.51616
$630$		0			0
$631$	13662.1			0.861931			0.430966	−	0.902368i	$-0.358173\pi$
$631$	13662.1			0.861931			0.430966	+	0.902368i	$0.358173\pi$
$632$	8300.50	−	4792.30i	0.522431	−	0.301625i
$633$		0			0
$634$	−239.459	+	414.755i	−0.0150002	+	0.0259811i
$635$	−739.454	−	1280.77i	−0.0462116	−	0.0800408i
$636$		0			0
$637$		0			0
$638$		−	23.8032i		−	0.00147708i
$639$		0			0
$640$	−982.404	−	567.191i	−0.0606764	−	0.0350316i
$641$	−23643.1	−	13650.3i	−1.45686	−	0.841117i	−0.458002	−	0.888951i	$-0.651435\pi$
$641$	−23643.1	−	13650.3i	−1.45686	−	0.841117i	−0.998855	+	0.0478346i	$0.984768\pi$
$642$		0			0
$643$		−	6857.85i		−	0.420602i	−0.977637	−	0.210301i	$-0.932556\pi$
$643$		−	6857.85i		−	0.420602i	0.977637	−	0.210301i	$-0.0674445\pi$
$644$		0			0
$645$		0			0
$646$	−13349.1	−	23121.2i	−0.813021	−	1.40819i
$647$	4134.32	−	7160.85i	0.251216	−	0.435119i	−0.712645	−	0.701525i	$-0.752503\pi$
$647$	4134.32	−	7160.85i	0.251216	−	0.435119i	0.963861	+	0.266406i	$0.0858362\pi$
$648$		0			0
$649$	112.084	−	64.7120i	0.00677920	−	0.00391397i
$650$	27655.6			1.66883
$651$		0			0
$652$	12661.1			0.760504
$653$	−10492.9	+	6058.07i	−0.628818	+	0.363048i	−0.780294	−	0.625413i	$-0.784931\pi$
$653$	−10492.9	+	6058.07i	−0.628818	+	0.363048i	0.151476	+	0.988461i	$0.451597\pi$
$654$		0			0
$655$	365.516	−	633.092i	0.0218044	−	0.0377663i
$656$	4029.60	+	6979.48i	0.239832	+	0.415401i
$657$		0			0
$658$		0			0
$659$			11814.0i			0.698343i	0.937059	+	0.349171i	$0.113537\pi$
$659$			11814.0i			0.698343i	−0.937059	+	0.349171i	$0.886463\pi$
$660$		0			0
$661$	23198.2	+	13393.5i	1.36506	+	0.788119i	0.990292	−	0.138999i	$-0.0443886\pi$
$661$	23198.2	+	13393.5i	1.36506	+	0.788119i	0.374769	+	0.927118i	$0.377722\pi$
$662$	−14881.9	−	8592.05i	−0.873716	−	0.504440i
$663$		0			0
$664$		−	13883.4i		−	0.811416i
$665$		0			0
$666$		0			0
$667$	1220.05	+	2113.19i	0.0708253	+	0.122673i
$668$	10100.9	−	17495.2i	0.585051	−	1.01334i
$669$		0			0
$670$	637.895	−	368.289i	0.0367821	−	0.0212362i
$671$	−248.730			−0.0143102
$672$		0			0
$673$	3317.25			0.190001			0.0950004	−	0.995477i	$-0.469715\pi$
$673$	3317.25			0.190001			0.0950004	+	0.995477i	$0.469715\pi$
$674$	25718.6	−	14848.6i	1.46980	−	0.848587i
$675$		0			0
$676$	−4022.67	+	6967.48i	−0.228873	+	0.396420i
$677$	−14873.9	−	25762.4i	−0.844388	−	1.46252i	−0.886152	−	0.463395i	$-0.846631\pi$
$677$	−14873.9	−	25762.4i	−0.844388	−	1.46252i	0.0417637	−	0.999128i	$-0.486702\pi$
$678$		0			0
$679$		0			0
$680$		−	997.235i		−	0.0562385i
$681$		0			0
$682$	124.242	+	71.7314i	0.00697579	+	0.00402747i
$683$	16830.2	+	9716.94i	0.942886	+	0.544375i	0.890864	−	0.454270i	$-0.150100\pi$
$683$	16830.2	+	9716.94i	0.942886	+	0.544375i	0.0520221	+	0.998646i	$0.483433\pi$
$684$		0			0
$685$			261.537i			0.0145881i
$686$		0			0
$687$		0			0
$688$	−12928.6	−	22393.0i	−0.716423	−	1.24088i
$689$	−9595.58	+	16620.0i	−0.530570	+	0.918974i
$690$		0			0
$691$	2798.73	−	1615.85i	0.154079	−	0.0889578i	−0.420978	−	0.907071i	$-0.638313\pi$
$691$	2798.73	−	1615.85i	0.154079	−	0.0889578i	0.575057	+	0.818113i	$0.304980\pi$
$692$	15469.5			0.849798
$693$		0			0
$694$	−13278.5			−0.726290
$695$	1254.62	−	724.354i	0.0684754	−	0.0395343i
$696$		0			0
$697$	−5289.39	+	9161.49i	−0.287446	+	0.497871i
$698$	1621.08	+	2807.80i	0.0879067	+	0.152259i
$699$		0			0
$700$		0			0
$701$			6802.40i			0.366509i	0.983065	+	0.183255i	$0.0586633\pi$
$701$			6802.40i			0.366509i	−0.983065	+	0.183255i	$0.941337\pi$
$702$		0			0
$703$	−23646.0	−	13652.0i	−1.26860	−	0.732427i
$704$	−21.0977	−	12.1808i	−0.00112948	−	0.000652103i
$705$		0			0
$706$			36473.6i			1.94433i
$707$		0			0
$708$		0			0
$709$	3508.04	+	6076.11i	0.185821	+	0.321852i	0.943853	−	0.330366i	$-0.107172\pi$
$709$	3508.04	+	6076.11i	0.185821	+	0.321852i	−0.758032	+	0.652218i	$0.773839\pi$
$710$	−274.732	+	475.849i	−0.0145218	+	0.0251525i
$711$		0			0
$712$	5472.85	−	3159.75i	0.288067	−	0.166316i
$713$	−14706.6			−0.772463
$714$		0			0
$715$	19.7253			0.00103173
$716$	−15192.3	+	8771.27i	−0.792964	+	0.457818i
$717$		0			0
$718$	−7566.53	+	13105.6i	−0.393287	+	0.681194i
$719$	−9045.55	−	15667.3i	−0.469182	−	0.812647i	0.530197	−	0.847874i	$-0.322118\pi$
$719$	−9045.55	−	15667.3i	−0.469182	−	0.812647i	−0.999379	+	0.0352269i	$0.988785\pi$
$720$		0			0
$721$		0			0
$722$			6254.26i			0.322382i
$723$		0			0
$724$	1331.93	+	768.988i	0.0683711	+	0.0394741i
$725$	1923.20	+	1110.36i	0.0985185	+	0.0568797i
$726$		0			0
$727$		−	35637.5i		−	1.81805i	−0.416745	−	0.909024i	$-0.636829\pi$
$727$		−	35637.5i		−	1.81805i	0.416745	−	0.909024i	$-0.363171\pi$
$728$		0			0
$729$		0			0
$730$	208.597	+	361.301i	0.0105761	+	0.0183183i
$731$	16970.5	−	29393.8i	0.858656	−	1.48724i
$732$		0			0
$733$	−10723.2	+	6191.06i	−0.540343	+	0.311967i	−0.745218	−	0.666821i	$-0.767655\pi$
$733$	−10723.2	+	6191.06i	−0.540343	+	0.311967i	0.204875	+	0.978788i	$0.434321\pi$
$734$	−1942.50			−0.0976823
$735$		0			0
$736$	26605.7			1.33247
$737$	−76.9262	+	44.4134i	−0.00384479	+	0.00221979i
$738$		0			0
$739$	5933.76	−	10277.6i	0.295368	−	0.511592i	−0.679703	−	0.733488i	$-0.737891\pi$
$739$	5933.76	−	10277.6i	0.295368	−	0.511592i	0.975070	+	0.221896i	$0.0712245\pi$
$740$	799.039	+	1383.98i	0.0396936	+	0.0687513i
$741$		0			0
$742$		0			0
$743$		−	6713.61i		−	0.331492i	−0.986168	−	0.165746i	$-0.946997\pi$
$743$		−	6713.61i		−	0.331492i	0.986168	−	0.165746i	$-0.0530032\pi$
$744$		0			0
$745$	1652.79	+	954.240i	0.0812801	+	0.0469271i
$746$	−6964.03	−	4020.68i	−0.341784	−	0.197329i
$747$		0			0
$748$		−	188.441i		−	0.00921136i
$749$		0			0
$750$		0			0
$751$	13144.8	+	22767.5i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538592\pi$
$751$	13144.8	+	22767.5i	0.638696	+	1.10625i	−0.347023	+	0.937857i	$0.612807\pi$
$752$	−20681.5	+	35821.3i	−1.00289	+	1.73706i
$753$		0			0
$754$	−3444.37	+	1988.61i	−0.166362	+	0.0960489i
$755$	−704.021			−0.0339363
$756$		0			0
$757$	−37236.6			−1.78783			−0.893915	−	0.448237i	$-0.852052\pi$
$757$	−37236.6			−1.78783			−0.893915	+	0.448237i	$0.852052\pi$
$758$	−9085.18	+	5245.33i	−0.435341	+	0.251344i
$759$		0			0
$760$	342.989	−	594.075i	0.0163704	−	0.0283544i
$761$	6028.60	+	10441.8i	0.287170	+	0.497393i	0.973133	−	0.230243i	$-0.0739522\pi$
$761$	6028.60	+	10441.8i	0.287170	+	0.497393i	−0.685963	+	0.727636i	$0.740619\pi$
$762$		0			0
$763$		0			0
$764$		−	17205.5i		−	0.814754i
$765$		0			0
$766$	21924.6	+	12658.2i	1.03416	+	0.597074i
$767$	−18728.0	−	10812.6i	−0.881652	−	0.509022i
$768$		0			0
$769$			17232.1i			0.808070i	0.914744	+	0.404035i	$0.132393\pi$
$769$			17232.1i			0.808070i	−0.914744	+	0.404035i	$0.867607\pi$
$770$		0			0
$771$		0			0
$772$	1758.14	+	3045.19i	0.0819649	+	0.141967i
$773$	−5556.40	+	9623.98i	−0.258538	+	0.447801i	−0.965851	−	0.259100i	$-0.916574\pi$
$773$	−5556.40	+	9623.98i	−0.258538	+	0.447801i	0.707312	+	0.706901i	$0.249907\pi$
$774$		0			0
$775$	−11591.2	+	6692.20i	−0.537250	+	0.310182i
$776$	19357.4			0.895477
$777$		0			0
$778$	35639.6			1.64234
$779$	−6302.01	+	3638.47i	−0.289850	+	0.167345i
$780$		0			0
$781$	33.1310	−	57.3845i	0.00151795	−	0.00262917i
$782$	25481.5	+	44135.2i	1.16524	+	2.01825i
$783$		0			0
$784$		0			0
$785$		−	1370.39i		−	0.0623074i
$786$		0			0
$787$	−28578.1	−	16499.6i	−1.29441	−	0.747328i	−0.314978	−	0.949099i	$-0.601997\pi$
$787$	−28578.1	−	16499.6i	−1.29441	−	0.747328i	−0.979433	+	0.201771i	$0.935330\pi$
$788$	14717.2	+	8497.00i	0.665330	+	0.384128i
$789$		0			0
$790$		−	2636.52i		−	0.118738i
$791$		0			0
$792$		0			0
$793$	20779.9	+	35991.8i	0.930537	+	1.61174i
$794$	4574.19	−	7922.73i	0.204448	−	0.354115i
$795$		0			0
$796$	−16512.0	+	9533.19i	−0.735240	+	0.424491i
$797$	−17247.7			−0.766554			−0.383277	−	0.923634i	$-0.625204\pi$
$797$	−17247.7			−0.766554			−0.383277	+	0.923634i	$0.625204\pi$
$798$		0			0
$799$	−54294.3			−2.40400
$800$	20969.7	−	12106.9i	0.926739	−	0.535053i
$801$		0			0
$802$	9259.58	−	16038.1i	0.407690	−	0.706139i
$803$	−25.1555	−	43.5707i	−0.00110550	−	0.00191479i
$804$		0			0
$805$		0			0
$806$		−	23970.9i		−	1.04757i
$807$		0			0
$808$	−12166.2	−	7024.15i	−0.529709	−	0.305828i
$809$	19029.1	+	10986.5i	0.826981	+	0.477458i	0.852818	−	0.522209i	$-0.174892\pi$
$809$	19029.1	+	10986.5i	0.826981	+	0.477458i	−0.0258371	+	0.999666i	$0.508225\pi$
$810$		0			0
$811$			30078.0i			1.30232i	0.758941	+	0.651159i	$0.225717\pi$
$811$			30078.0i			1.30232i	−0.758941	+	0.651159i	$0.774283\pi$
$812$		0			0
$813$		0			0
$814$	−254.213	−	440.311i	−0.0109462	−	0.0189593i
$815$	−1111.34	+	1924.90i	−0.0477652	+	0.0827317i
$816$		0			0
$817$	20219.4	−	11673.7i	0.865837	−	0.499891i
$818$	28692.2			1.22640
$819$		0			0
$820$	425.911			0.0181384
$821$	33411.0	−	19289.9i	1.42028	−	0.820001i	0.423961	−	0.905680i	$-0.360639\pi$
$821$	33411.0	−	19289.9i	1.42028	−	0.820001i	0.996323	+	0.0856788i	$0.0273059\pi$
$822$		0			0
$823$	14026.1	−	24293.9i	0.594068	−	1.02896i	−0.399610	−	0.916685i	$-0.630854\pi$
$823$	14026.1	−	24293.9i	0.594068	−	1.02896i	0.993678	−	0.112271i	$-0.0358124\pi$
$824$	8727.47	+	15116.4i	0.368976	+	0.639084i
$825$		0			0
$826$		0			0
$827$			2038.04i			0.0856948i	0.999082	+	0.0428474i	$0.0136429\pi$
$827$			2038.04i			0.0856948i	−0.999082	+	0.0428474i	$0.986357\pi$
$828$		0			0
$829$	−34603.1	−	19978.1i	−1.44972	−	0.836995i	−0.451254	−	0.892396i	$-0.649023\pi$
$829$	−34603.1	−	19978.1i	−1.44972	−	0.836995i	−0.998464	+	0.0554004i	$0.982356\pi$
$830$	−3307.38	−	1909.52i	−0.138314	−	0.0798558i
$831$		0			0
$832$			4070.52i			0.169615i
$833$		0			0
$834$		0			0
$835$	1773.22	+	3071.31i	0.0734910	+	0.127290i
$836$	64.8125	−	112.259i	0.00268133	−	0.00464419i
$837$		0			0
$838$	18564.7	−	10718.3i	0.765283	−	0.441836i
$839$	24277.8			0.999004			0.499502	−	0.866313i	$-0.333516\pi$
$839$	24277.8			0.999004			0.499502	+	0.866313i	$0.333516\pi$
$840$		0			0
$841$	24069.6			0.986905
$842$	39313.9	−	22697.9i	1.60908	−	0.929002i
$843$		0			0
$844$	7113.28	−	12320.6i	0.290106	−	0.502478i
$845$	−706.187	−	1223.15i	−0.0287498	−	0.0497961i
$846$		0			0
$847$		0			0
$848$			24519.7i			0.992937i
$849$		0			0
$850$	40167.2	+	23190.5i	1.62085	+	0.935798i
$851$	45136.9	+	26059.8i	1.81818	+	1.04973i
$852$		0			0
$853$			28395.8i			1.13981i	0.821712	+	0.569903i	$0.193019\pi$
$853$			28395.8i			1.13981i	−0.821712	+	0.569903i	$0.806981\pi$
$854$		0			0
$855$		0			0
$856$	937.373	+	1623.58i	0.0374285	+	0.0648280i
$857$	−17496.3	+	30304.5i	−0.697388	+	1.20791i	0.271981	+	0.962303i	$0.412321\pi$
$857$	−17496.3	+	30304.5i	−0.697388	+	1.20791i	−0.969369	+	0.245609i	$0.921012\pi$
$858$		0			0
$859$	−8360.94	+	4827.19i	−0.332097	+	0.191737i	−0.656772	−	0.754089i	$-0.728079\pi$
$859$	−8360.94	+	4827.19i	−0.332097	+	0.191737i	0.324675	+	0.945826i	$0.394745\pi$
$860$	−1366.50			−0.0541828
$861$		0			0
$862$	−12217.7			−0.482757
$863$	−36502.8	+	21074.9i	−1.43983	+	0.831284i	−0.997837	−	0.0657370i	$-0.979060\pi$
$863$	−36502.8	+	21074.9i	−1.43983	+	0.831284i	−0.441989	+	0.897021i	$0.645727\pi$
$864$		0			0
$865$	−1357.84	+	2351.85i	−0.0533735	+	0.0924456i
$866$	13304.5	+	23044.0i	0.522060	+	0.904235i
$867$		0			0
$868$		0			0
$869$			317.949i			0.0124116i
$870$		0			0
$871$	12853.4	+	7420.93i	0.500025	+	0.288690i
$872$	−204.491	−	118.063i	−0.00794144	−	0.00458499i
$873$		0			0
$874$			35056.4i			1.35675i
$875$		0			0
$876$		0			0
$877$	365.254	+	632.639i	0.0140636	+	0.0243588i	0.872972	−	0.487771i	$-0.162190\pi$
$877$	365.254	+	632.639i	0.0140636	+	0.0243588i	−0.858908	+	0.512130i	$0.828857\pi$
$878$	−8332.50	+	14432.3i	−0.320283	+	0.554746i
$879$		0			0
$880$	21.8257	−	12.6011i	0.000836073	−	0.000482707i
$881$	−36187.9			−1.38388			−0.691942	−	0.721953i	$-0.743245\pi$
$881$	−36187.9			−1.38388			−0.691942	+	0.721953i	$0.743245\pi$
$882$		0			0
$883$	−38996.6			−1.48623			−0.743115	−	0.669164i	$-0.766652\pi$
$883$	−38996.6			−1.48623			−0.743115	+	0.669164i	$0.766652\pi$
$884$	−27267.9	+	15743.1i	−1.03746	+	0.598980i
$885$		0			0
$886$	5327.70	−	9227.85i	0.202018	−	0.349905i
$887$	15147.0	+	26235.4i	0.573380	+	0.993123i	0.996216	+	0.0869165i	$0.0277013\pi$
$887$	15147.0	+	26235.4i	0.573380	+	0.993123i	−0.422836	+	0.906206i	$0.638965\pi$
$888$		0			0
$889$		0			0
$890$		−	1738.36i		−	0.0654720i
$891$		0			0
$892$	−5084.75	−	2935.68i	−0.190863	−	0.110195i
$893$	−32344.3	−	18674.0i	−1.21205	−	0.699778i
$894$		0			0
$895$		−	3079.62i		−	0.115017i
$896$		0			0
$897$		0			0
$898$	15672.1	+	27144.8i	0.582387	+	1.00872i
$899$	962.420	−	1666.96i	0.0357047	−	0.0618423i
$900$		0			0
$901$	−27873.4	+	16092.7i	−1.03063	+	0.595034i
$902$	−135.503			−0.00500196
$903$		0			0
$904$	−12437.1			−0.457579
$905$	−233.822	+	134.997i	−0.00858840	+	0.00495852i
$906$		0			0
$907$	26811.7	−	46439.3i	0.981554	−	1.70010i	0.325205	−	0.945644i	$-0.394567\pi$
$907$	26811.7	−	46439.3i	0.981554	−	1.70010i	0.656349	−	0.754458i	$-0.272100\pi$
$908$	12539.3	+	21718.7i	0.458293	+	0.793787i
$909$		0			0
$910$		0			0
$911$		−	29609.2i		−	1.07683i	−0.842678	−	0.538417i	$-0.819023\pi$
$911$		−	29609.2i		−	1.07683i	0.842678	−	0.538417i	$-0.180977\pi$
$912$		0			0
$913$	398.850	+	230.276i	0.0144578	+	0.00834724i
$914$	37608.1	+	21713.1i	1.36101	+	0.785782i
$915$		0			0
$916$			9168.53i			0.330717i
$917$		0			0
$918$		0			0
$919$	22783.3	+	39461.8i	0.817792	+	1.41646i	0.907306	+	0.420472i	$0.138135\pi$
$919$	22783.3	+	39461.8i	0.817792	+	1.41646i	−0.0895134	+	0.995986i	$0.528531\pi$
$920$	−654.718	+	1134.00i	−0.0234624	+	0.0406381i
$921$		0			0
$922$	24079.2	−	13902.1i	0.860094	−	0.496576i
$923$	−11071.6			−0.394827
$924$		0			0
$925$	47433.8			1.68607
$926$	7999.23	−	4618.35i	0.283878	−	0.163897i
$927$		0			0
$928$	−1741.12	+	3015.70i	−0.0615894	+	0.106676i
$929$	−19829.7	−	34346.0i	−0.700313	−	1.21298i	−0.968357	−	0.249571i	$-0.919711\pi$
$929$	−19829.7	−	34346.0i	−0.700313	−	1.21298i	0.268044	−	0.963407i	$-0.413623\pi$
$930$		0			0
$931$		0			0
$932$		−	17008.6i		−	0.597783i
$933$		0			0
$934$	7422.62	+	4285.45i	0.260038	+	0.150133i
$935$	28.6491	+	16.5406i	0.00100206	+	0.000578540i
$936$		0			0
$937$		−	1645.64i		−	0.0573753i	−0.999588	−	0.0286877i	$-0.990867\pi$
$937$		−	1645.64i		−	0.0573753i	0.999588	−	0.0286877i	$-0.00913282\pi$
$938$		0			0
$939$		0			0
$940$	1092.97	+	1893.08i	0.0379242	+	0.0656866i
$941$	−16471.6	+	28529.6i	−0.570626	+	0.988352i	0.425876	+	0.904781i	$0.359966\pi$
$941$	−16471.6	+	28529.6i	−0.570626	+	0.988352i	−0.996502	+	0.0835710i	$0.973367\pi$
$942$		0			0
$943$	12029.7	−	6945.32i	0.415418	−	0.239842i
$944$	−27629.5			−0.952611
$945$		0			0
$946$	434.750			0.0149418
$947$	19826.4	−	11446.8i	0.680328	−	0.392788i	−0.119650	−	0.992816i	$-0.538177\pi$
$947$	19826.4	−	11446.8i	0.680328	−	0.392788i	0.799979	+	0.600028i	$0.204844\pi$
$948$		0			0
$949$	−4203.18	+	7280.13i	−0.143774	+	0.249023i
$950$	15952.3	+	27630.2i	0.544802	+	0.943624i
$951$		0			0
$952$		0			0
$953$			31350.3i			1.06562i	0.846234	+	0.532811i	$0.178864\pi$
$953$			31350.3i			1.06562i	−0.846234	+	0.532811i	$0.821136\pi$
$954$		0			0
$955$	2615.79	+	1510.22i	0.0886333	+	0.0511725i
$956$	10430.7	+	6022.18i	0.352881	+	0.203736i
$957$		0			0
$958$		−	10430.6i		−	0.351773i
$959$		0			0
$960$		0			0
$961$	−9094.95	−	15752.9i	−0.305292	−	0.528781i
$962$	−42476.0	+	73570.5i	−1.42358	+	2.46571i
$963$		0			0
$964$	10317.6	−	5956.85i	0.344716	−	0.199022i
$965$	−617.289			−0.0205920
$966$		0			0
$967$	−1272.04			−0.0423021			−0.0211511	−	0.999776i	$-0.506733\pi$
$967$	−1272.04			−0.0423021			−0.0211511	+	0.999776i	$0.506733\pi$
$968$	12893.0	−	7443.77i	0.428095	−	0.247161i
$969$		0			0
$970$	2662.41	−	4611.43i	0.0881287	−	0.152643i
$971$	11659.6	+	20195.0i	0.385350	+	0.667445i	0.991818	−	0.127663i	$-0.0407475\pi$
$971$	11659.6	+	20195.0i	0.385350	+	0.667445i	−0.606468	+	0.795108i	$0.707414\pi$
$972$		0			0
$973$		0			0
$974$			949.512i			0.0312365i
$975$		0			0
$976$	45985.2	+	26549.5i	1.50814	+	0.870728i
$977$	25918.0	+	14963.7i	0.848710	+	0.490003i	0.860215	−	0.509931i	$-0.170329\pi$
$977$	25918.0	+	14963.7i	0.848710	+	0.490003i	−0.0115056	+	0.999934i	$0.503662\pi$
$978$		0			0
$979$			209.636i			0.00684372i
$980$		0			0
$981$		0			0
$982$	−35513.1	−	61510.5i	−1.15404	−	1.99886i
$983$	17281.3	−	29932.1i	0.560720	−	0.971195i	−0.436714	−	0.899600i	$-0.643858\pi$
$983$	17281.3	−	29932.1i	0.560720	−	0.971195i	0.997434	−	0.0715947i	$-0.0228088\pi$
$984$		0			0
$985$	−2583.64	+	1491.66i	−0.0835751	+	0.0482521i
$986$	−6670.17			−0.215438
$987$		0			0
$988$	−21658.8			−0.697427
$989$	−38596.1	+	22283.4i	−1.24093	+	0.716453i
$990$		0			0
$991$	−11458.6	+	19846.9i	−0.367300	+	0.636183i	−0.989142	−	0.146960i	$-0.953051\pi$
$991$	−11458.6	+	19846.9i	−0.367300	+	0.636183i	0.621842	+	0.783143i	$0.286385\pi$
$992$	−10493.8	−	18175.8i	−0.335865	−	0.581736i
$993$		0			0
$994$		0			0
$995$		−	3347.14i		−	0.106645i
$996$		0			0
$997$	28270.4	+	16321.9i	0.898027	+	0.518476i	0.876560	−	0.481294i	$-0.159833\pi$
$997$	28270.4	+	16321.9i	0.898027	+	0.518476i	0.0214673	+	0.999770i	$0.493166\pi$
$998$	35659.6	+	20588.1i	1.13105	+	0.653010i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.d.80.17		48
3.2	odd	2	inner	441.4.p.d.80.8		48
7.2	even	3	inner	441.4.p.d.215.8		48
7.3	odd	6		441.4.c.b.440.14	yes	24
7.4	even	3		441.4.c.b.440.12	yes	24
7.5	odd	6	inner	441.4.p.d.215.7		48
7.6	odd	2	inner	441.4.p.d.80.18		48
21.2	odd	6	inner	441.4.p.d.215.17		48
21.5	even	6	inner	441.4.p.d.215.18		48
21.11	odd	6		441.4.c.b.440.13	yes	24
21.17	even	6		441.4.c.b.440.11	✓	24
21.20	even	2	inner	441.4.p.d.80.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.c.b.440.11	✓	24	21.17	even	6
441.4.c.b.440.12	yes	24	7.4	even	3
441.4.c.b.440.13	yes	24	21.11	odd	6
441.4.c.b.440.14	yes	24	7.3	odd	6
441.4.p.d.80.7		48	21.20	even	2	inner
441.4.p.d.80.8		48	3.2	odd	2	inner
441.4.p.d.80.17		48	1.1	even	1	trivial
441.4.p.d.80.18		48	7.6	odd	2	inner
441.4.p.d.215.7		48	7.5	odd	6	inner
441.4.p.d.215.8		48	7.2	even	3	inner
441.4.p.d.215.17		48	21.2	odd	6	inner
441.4.p.d.215.18		48	21.5	even	6	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.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.10847 - 1.79468i) q^{2} +(2.44173 - 4.22919i) q^{4} +(0.428649 + 0.742442i) q^{5} +11.1864i q^{8} +O(q^{10})\)	\(q+(3.10847 - 1.79468i) q^{2} +(2.44173 - 4.22919i) q^{4} +(0.428649 + 0.742442i) q^{5} +11.1864i q^{8} +(2.66489 + 1.53857i) q^{10} +(-0.321369 - 0.185543i) q^{11} +62.0038i q^{13} +(39.6098 + 68.6061i) q^{16} +(-51.9931 + 90.0547i) q^{17} +(-61.9469 + 35.7650i) q^{19} +4.18657 q^{20} -1.33196 q^{22} +(118.248 - 68.2704i) q^{23} +(62.1325 - 107.617i) q^{25} +(111.277 + 192.737i) q^{26} +17.8708i q^{29} +(-93.2782 - 53.8542i) q^{31} +(168.750 + 97.4278i) q^{32} +373.243i q^{34} +(190.857 + 330.575i) q^{37} +(-128.373 + 222.349i) q^{38} +(-8.30525 + 4.79504i) q^{40} +101.733 q^{41} -326.400 q^{43} +(-1.56939 + 0.906088i) q^{44} +(245.047 - 424.433i) q^{46} +(261.065 + 452.178i) q^{47} -446.031i q^{50} +(262.226 + 151.396i) q^{52} +(268.049 + 154.758i) q^{53} -0.318131i q^{55} +(32.0724 + 55.5510i) q^{58} +(-174.386 + 302.045i) q^{59} +(580.478 - 335.139i) q^{61} -386.604 q^{62} +65.6495 q^{64} +(-46.0342 + 26.5779i) q^{65} +(119.685 - 207.301i) q^{67} +(253.906 + 439.778i) q^{68} +178.563i q^{71} +(117.414 + 67.7891i) q^{73} +(1186.55 + 685.054i) q^{74} +349.314i q^{76} +(-428.404 - 742.018i) q^{79} +(-33.9574 + 58.8159i) q^{80} +(316.233 - 182.577i) q^{82} -1241.10 q^{83} -89.1472 q^{85} +(-1014.60 + 585.782i) q^{86} +(2.07555 - 3.59496i) q^{88} +(-282.464 - 489.242i) q^{89} -666.790i q^{92} +(1623.03 + 937.055i) q^{94} +(-53.1069 - 30.6613i) q^{95} -1730.44i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4}+O(q^{10}) \) 48 * q + 96 * q^4	\( 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) \) 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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