LMFDB - Embedded newform 441.4.e.z.226.2

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			226.2
Root			$-1.99285 + 3.45171i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.4.e.z.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.69995 + 4.67646i) q^{2} +(-10.5795 - 18.3242i) q^{4} +(7.78839 - 13.4899i) q^{5} +71.0573 q^{8} +O(q^{10})$	\(q+(-2.69995 + 4.67646i) q^{2} +(-10.5795 - 18.3242i) q^{4} +(7.78839 - 13.4899i) q^{5} +71.0573 q^{8} +(42.0566 + 72.8441i) q^{10} +(-15.9851 - 27.6870i) q^{11} +72.5746 q^{13} +(-107.215 + 185.703i) q^{16} +(-14.5144 - 25.1397i) q^{17} +(-54.4146 + 94.2489i) q^{19} -329.589 q^{20} +172.636 q^{22} +(27.6434 - 47.8798i) q^{23} +(-58.8180 - 101.876i) q^{25} +(-195.948 + 339.392i) q^{26} +17.7363 q^{29} +(-28.0594 - 48.6004i) q^{31} +(-294.724 - 510.477i) q^{32} +156.753 q^{34} +(147.908 - 256.184i) q^{37} +(-293.834 - 508.935i) q^{38} +(553.422 - 958.555i) q^{40} -238.605 q^{41} +16.8202 q^{43} +(-338.228 + 585.829i) q^{44} +(149.272 + 258.547i) q^{46} +(255.954 - 443.326i) q^{47} +635.223 q^{50} +(-767.802 - 1329.87i) q^{52} +(-132.603 - 229.674i) q^{53} -497.992 q^{55} +(-47.8871 + 82.9429i) q^{58} +(-127.091 - 220.128i) q^{59} +(36.4176 - 63.0771i) q^{61} +303.037 q^{62} +1467.52 q^{64} +(565.239 - 979.023i) q^{65} +(253.180 + 438.520i) q^{67} +(-307.110 + 531.930i) q^{68} -827.722 q^{71} +(186.288 + 322.661i) q^{73} +(798.689 + 1383.37i) q^{74} +2302.72 q^{76} +(-514.226 + 890.665i) q^{79} +(1670.07 + 2892.65i) q^{80} +(644.222 - 1115.82i) q^{82} -453.148 q^{83} -452.175 q^{85} +(-45.4138 + 78.6590i) q^{86} +(-1135.86 - 1967.36i) q^{88} +(166.033 - 287.577i) q^{89} -1169.81 q^{92} +(1382.13 + 2393.92i) q^{94} +(847.605 + 1468.09i) q^{95} -1164.54 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.69995	+	4.67646i	−0.954578	+	1.65338i	−0.219246	+	0.975670i	$0.570360\pi$
$2$	−2.69995	+	4.67646i	−0.954578	+	1.65338i	−0.735332	+	0.677707i	$0.762974\pi$
$3$		0			0
$3$		0			0
$4$	−10.5795	−	18.3242i	−1.32244	−	2.29053i
$5$	7.78839	−	13.4899i	0.696615	−	1.20657i	−0.273019	−	0.962009i	$-0.588022\pi$
$5$	7.78839	−	13.4899i	0.696615	−	1.20657i	0.969633	−	0.244563i	$-0.0786446\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	71.0573			3.14032
$9$		0			0
$10$	42.0566	+	72.8441i	1.32995	+	2.30353i
$11$	−15.9851	−	27.6870i	−0.438153	−	0.758904i	0.559394	−	0.828902i	$-0.311034\pi$
$11$	−15.9851	−	27.6870i	−0.438153	−	0.758904i	−0.997547	+	0.0699983i	$0.977701\pi$
$12$		0			0
$13$	72.5746			1.54835			0.774176	−	0.632971i	$-0.218165\pi$
$13$	72.5746			1.54835			0.774176	+	0.632971i	$0.218165\pi$
$14$		0			0
$15$		0			0
$16$	−107.215	+	185.703i	−1.67524	+	2.90160i
$17$	−14.5144	−	25.1397i	−0.207074	−	0.358663i	0.743717	−	0.668494i	$-0.233061\pi$
$17$	−14.5144	−	25.1397i	−0.207074	−	0.358663i	−0.950792	+	0.309831i	$0.899727\pi$
$18$		0			0
$19$	−54.4146	+	94.2489i	−0.657030	+	1.13801i	0.324350	+	0.945937i	$0.394854\pi$
$19$	−54.4146	+	94.2489i	−0.657030	+	1.13801i	−0.981381	+	0.192073i	$0.938479\pi$
$20$	−329.589			−3.68492
$21$		0			0
$22$	172.636			1.67300
$23$	27.6434	−	47.8798i	0.250611	−	0.434071i	−0.713083	−	0.701079i	$-0.752702\pi$
$23$	27.6434	−	47.8798i	0.250611	−	0.434071i	0.963694	+	0.267008i	$0.0860352\pi$
$24$		0			0
$25$	−58.8180	−	101.876i	−0.470544	−	0.815006i
$26$	−195.948	+	339.392i	−1.47802	+	2.56001i
$27$		0			0
$28$		0			0
$29$	17.7363			0.113570			0.0567852	−	0.998386i	$-0.481915\pi$
$29$	17.7363			0.113570			0.0567852	+	0.998386i	$0.481915\pi$
$30$		0			0
$31$	−28.0594	−	48.6004i	−0.162568	−	0.281577i	0.773221	−	0.634137i	$-0.218644\pi$
$31$	−28.0594	−	48.6004i	−0.162568	−	0.281577i	−0.935789	+	0.352560i	$0.885311\pi$
$32$	−294.724	−	510.477i	−1.62814	−	2.82001i
$33$		0			0
$34$	156.753			0.790673
$35$		0			0
$36$		0			0
$37$	147.908	−	256.184i	0.657187	−	1.13828i	−0.324154	−	0.946004i	$-0.605080\pi$
$37$	147.908	−	256.184i	0.657187	−	1.13828i	0.981341	−	0.192276i	$-0.0615870\pi$
$38$	−293.834	−	508.935i	−1.25437	−	2.17264i
$39$		0			0
$40$	553.422	−	958.555i	2.18759	−	3.78902i
$41$	−238.605			−0.908873			−0.454437	−	0.890779i	$-0.650159\pi$
$41$	−238.605			−0.908873			−0.454437	+	0.890779i	$0.650159\pi$
$42$		0			0
$43$	16.8202			0.0596526			0.0298263	−	0.999555i	$-0.490505\pi$
$43$	16.8202			0.0596526			0.0298263	+	0.999555i	$0.490505\pi$
$44$	−338.228	+	585.829i	−1.15886	+	2.00720i
$45$		0			0
$46$	149.272	+	258.547i	0.478455	+	0.828709i
$47$	255.954	−	443.326i	0.794357	−	1.37587i	−0.128889	−	0.991659i	$-0.541141\pi$
$47$	255.954	−	443.326i	0.794357	−	1.37587i	0.923246	−	0.384208i	$-0.125526\pi$
$48$		0			0
$49$		0			0
$50$	635.223			1.79668
$51$		0			0
$52$	−767.802	−	1329.87i	−2.04760	−	3.54654i
$53$	−132.603	−	229.674i	−0.343667	−	0.595249i	0.641443	−	0.767170i	$-0.278336\pi$
$53$	−132.603	−	229.674i	−0.343667	−	0.595249i	−0.985111	+	0.171921i	$0.945003\pi$
$54$		0			0
$55$	−497.992			−1.22090
$56$		0			0
$57$		0			0
$58$	−47.8871	+	82.9429i	−0.108412	+	0.187775i
$59$	−127.091	−	220.128i	−0.280437	−	0.485732i	0.691055	−	0.722802i	$-0.257146\pi$
$59$	−127.091	−	220.128i	−0.280437	−	0.485732i	−0.971493	+	0.237070i	$0.923813\pi$
$60$		0			0
$61$	36.4176	−	63.0771i	0.0764392	−	0.132397i	−0.825272	−	0.564735i	$-0.808978\pi$
$61$	36.4176	−	63.0771i	0.0764392	−	0.132397i	0.901711	+	0.432339i	$0.142312\pi$
$62$	303.037			0.620737
$63$		0			0
$64$	1467.52			2.86625
$65$	565.239	−	979.023i	1.07860	−	1.86820i
$66$		0			0
$67$	253.180	+	438.520i	0.461654	+	0.799609i	0.999044	−	0.0437257i	$-0.0139228\pi$
$67$	253.180	+	438.520i	0.461654	+	0.799609i	−0.537389	+	0.843334i	$0.680589\pi$
$68$	−307.110	+	531.930i	−0.547685	+	0.948618i
$69$		0			0
$70$		0			0
$71$	−827.722			−1.38356			−0.691779	−	0.722110i	$-0.743173\pi$
$71$	−827.722			−1.38356			−0.691779	+	0.722110i	$0.743173\pi$
$72$		0			0
$73$	186.288	+	322.661i	0.298677	+	0.517324i	0.975834	−	0.218515i	$-0.0701214\pi$
$73$	186.288	+	322.661i	0.298677	+	0.517324i	−0.677157	+	0.735839i	$0.736788\pi$
$74$	798.689	+	1383.37i	1.25467	+	2.17315i
$75$		0			0
$76$	2302.72			3.47552
$77$		0			0
$78$		0			0
$79$	−514.226	+	890.665i	−0.732341	+	1.26845i	0.223539	+	0.974695i	$0.428239\pi$
$79$	−514.226	+	890.665i	−0.732341	+	1.26845i	−0.955880	+	0.293757i	$0.905094\pi$
$80$	1670.07	+	2892.65i	2.33400	+	4.04260i
$81$		0			0
$82$	644.222	−	1115.82i	0.867590	−	1.50271i
$83$	−453.148			−0.599270			−0.299635	−	0.954054i	$-0.596865\pi$
$83$	−453.148			−0.599270			−0.299635	+	0.954054i	$0.596865\pi$
$84$		0			0
$85$	−452.175			−0.577003
$86$	−45.4138	+	78.6590i	−0.0569430	+	0.0986282i
$87$		0			0
$88$	−1135.86	−	1967.36i	−1.37594	−	2.38320i
$89$	166.033	−	287.577i	0.197746	−	0.342507i	−0.750051	−	0.661380i	$-0.769971\pi$
$89$	166.033	−	287.577i	0.197746	−	0.342507i	0.947797	+	0.318873i	$0.103304\pi$
$90$		0			0
$91$		0			0
$92$	−1169.81			−1.32567
$93$		0			0
$94$	1382.13	+	2393.92i	1.51655	+	2.62674i
$95$	847.605	+	1468.09i	0.915394	+	1.58551i
$96$		0			0
$97$	−1164.54			−1.21898			−0.609489	−	0.792795i	$-0.708625\pi$
$97$	−1164.54			−1.21898			−0.609489	+	0.792795i	$0.708625\pi$
$98$		0			0
$99$		0			0
$100$	−1244.53	+	2155.59i	−1.24453	+	2.15559i
$101$	−931.771	−	1613.88i	−0.917967	−	1.58997i	−0.802498	−	0.596655i	$-0.796496\pi$
$101$	−931.771	−	1613.88i	−0.917967	−	1.58997i	−0.115470	−	0.993311i	$-0.536837\pi$
$102$		0			0
$103$	−493.140	+	854.144i	−0.471753	+	0.817100i	−0.999478	−	0.0323154i	$-0.989712\pi$
$103$	−493.140	+	854.144i	−0.471753	+	0.817100i	0.527725	+	0.849415i	$0.323045\pi$
$104$	5156.95			4.86232
$105$		0			0
$106$	1432.08			1.31223
$107$	347.843	−	602.481i	0.314273	−	0.544337i	−0.665010	−	0.746835i	$-0.731573\pi$
$107$	347.843	−	602.481i	0.314273	−	0.544337i	0.979283	+	0.202498i	$0.0649059\pi$
$108$		0			0
$109$	−857.498	−	1485.23i	−0.753517	−	1.30513i	−0.946108	−	0.323851i	$-0.895022\pi$
$109$	−857.498	−	1485.23i	−0.753517	−	1.30513i	0.192591	−	0.981279i	$-0.438311\pi$
$110$	1344.56	−	2328.84i	1.16544	−	2.01860i
$111$		0			0
$112$		0			0
$113$	877.721			0.730700			0.365350	−	0.930870i	$-0.380949\pi$
$113$	877.721			0.730700			0.365350	+	0.930870i	$0.380949\pi$
$114$		0			0
$115$	−430.595	−	745.813i	−0.349159	−	0.604760i
$116$	−187.641	−	325.003i	−0.150190	−	0.260136i
$117$		0			0
$118$	1372.56			1.07080
$119$		0			0
$120$		0			0
$121$	154.454	−	267.522i	0.116044	−	0.200993i
$122$	196.652	+	340.610i	0.145934	+	0.252766i
$123$		0			0
$124$	−593.709	+	1028.33i	−0.429973	+	0.744735i
$125$	114.708			0.0820784
$126$		0			0
$127$	781.088			0.545751			0.272875	−	0.962049i	$-0.412025\pi$
$127$	781.088			0.545751			0.272875	+	0.962049i	$0.412025\pi$
$128$	−1604.44	+	2778.97i	−1.10792	+	1.91897i
$129$		0			0
$130$	3052.24	+	5286.63i	2.05922	+	3.56668i
$131$	980.619	−	1698.48i	0.654024	−	1.13280i	−0.328114	−	0.944638i	$-0.606413\pi$
$131$	980.619	−	1698.48i	0.654024	−	1.13280i	0.982138	−	0.188164i	$-0.0602537\pi$
$132$		0			0
$133$		0			0
$134$	−2734.29			−1.76274
$135$		0			0
$136$	−1031.35	−	1786.36i	−0.650279	−	1.12632i
$137$	610.155	+	1056.82i	0.380504	+	0.659053i	0.991134	−	0.132863i	$-0.0424171\pi$
$137$	610.155	+	1056.82i	0.380504	+	0.659053i	−0.610630	+	0.791916i	$0.709084\pi$
$138$		0			0
$139$	1068.10			0.651765			0.325882	−	0.945410i	$-0.394339\pi$
$139$	1068.10			0.651765			0.325882	+	0.945410i	$0.394339\pi$
$140$		0			0
$141$		0			0
$142$	2234.81	−	3870.81i	1.32071	−	2.28754i
$143$	−1160.11	−	2009.37i	−0.678415	−	1.17505i
$144$		0			0
$145$	138.137	−	239.260i	0.0791148	−	0.137031i
$146$	−2011.88			−1.14044
$147$		0			0
$148$	−6259.16			−3.47635
$149$	1295.41	−	2243.72i	0.712243	−	1.23364i	−0.251770	−	0.967787i	$-0.581013\pi$
$149$	1295.41	−	2243.72i	0.712243	−	1.23364i	0.964013	−	0.265855i	$-0.0856541\pi$
$150$		0			0
$151$	−964.770	−	1671.03i	−0.519946	−	0.900573i	−0.999731	−	0.0231868i	$-0.992619\pi$
$151$	−964.770	−	1671.03i	−0.519946	−	0.900573i	0.479785	−	0.877386i	$-0.340715\pi$
$152$	−3866.56	+	6697.08i	−2.06328	+	3.57371i
$153$		0			0
$154$		0			0
$155$	−874.151			−0.452990
$156$		0			0
$157$	−1312.87	−	2273.95i	−0.667377	−	1.15593i	−0.978635	−	0.205605i	$-0.934084\pi$
$157$	−1312.87	−	2273.95i	−0.667377	−	1.15593i	0.311259	−	0.950325i	$-0.399249\pi$
$158$	−2776.77	−	4809.51i	−1.39815	−	2.42167i
$159$		0			0
$160$	−9181.70			−4.53673
$161$		0			0
$162$		0			0
$163$	1550.08	−	2684.82i	0.744858	−	1.29013i	−0.205403	−	0.978678i	$-0.565850\pi$
$163$	1550.08	−	2684.82i	0.744858	−	1.29013i	0.950261	−	0.311455i	$-0.100816\pi$
$164$	2524.32	+	4372.25i	1.20193	+	2.08180i
$165$		0			0
$166$	1223.48	−	2119.13i	0.572050	−	0.990819i
$167$	−3264.73			−1.51277			−0.756386	−	0.654126i	$-0.773037\pi$
$167$	−3264.73			−1.51277			−0.756386	+	0.654126i	$0.773037\pi$
$168$		0			0
$169$	3070.07			1.39739
$170$	1220.85	−	2114.58i	0.550795	−	0.954004i
$171$		0			0
$172$	−177.949	−	308.217i	−0.0788867	−	0.136636i
$173$	−1018.15	+	1763.49i	−0.447450	+	0.775006i	−0.998219	−	0.0596516i	$-0.981001\pi$
$173$	−1018.15	+	1763.49i	−0.447450	+	0.775006i	0.550769	+	0.834657i	$0.314334\pi$
$174$		0			0
$175$		0			0
$176$	6855.39			2.93605
$177$		0			0
$178$	896.561	+	1552.89i	0.377529	+	0.653899i
$179$	1791.17	+	3102.40i	0.747925	+	1.29544i	0.948816	+	0.315831i	$0.102283\pi$
$179$	1791.17	+	3102.40i	0.747925	+	1.29544i	−0.200890	+	0.979614i	$0.564383\pi$
$180$		0			0
$181$	−1637.35			−0.672392			−0.336196	−	0.941792i	$-0.609140\pi$
$181$	−1637.35			−0.672392			−0.336196	+	0.941792i	$0.609140\pi$
$182$		0			0
$183$		0			0
$184$	1964.27	−	3402.21i	0.786998	−	1.36312i
$185$	−2303.93	−	3990.52i	−0.915612	−	1.58589i
$186$		0			0
$187$	−464.028	+	803.720i	−0.181460	+	0.314299i
$188$	−10831.5			−4.20195
$189$		0			0
$190$	−9153.97			−3.49526
$191$	−1412.39	+	2446.33i	−0.535063	+	0.926756i	0.464098	+	0.885784i	$0.346379\pi$
$191$	−1412.39	+	2446.33i	−0.535063	+	0.926756i	−0.999160	+	0.0409717i	$0.986955\pi$
$192$		0			0
$193$	828.765	+	1435.46i	0.309098	+	0.535373i	0.978165	−	0.207829i	$-0.0666397\pi$
$193$	828.765	+	1435.46i	0.309098	+	0.535373i	−0.669068	+	0.743201i	$0.733306\pi$
$194$	3144.19	−	5445.90i	1.16361	−	2.01543i
$195$		0			0
$196$		0			0
$197$	1890.78			0.683819			0.341909	−	0.939733i	$-0.388926\pi$
$197$	1890.78			0.683819			0.341909	+	0.939733i	$0.388926\pi$
$198$		0			0
$199$	696.373	+	1206.15i	0.248063	+	0.429658i	0.962988	−	0.269543i	$-0.0868726\pi$
$199$	696.373	+	1206.15i	0.248063	+	0.429658i	−0.714925	+	0.699201i	$0.753539\pi$
$200$	−4179.45	−	7239.01i	−1.47766	−	2.55938i
$201$		0			0
$202$	10063.0			3.50508
$203$		0			0
$204$		0			0
$205$	−1858.35	+	3218.75i	−0.633134	+	1.09662i
$206$	−2662.91	−	4612.30i	−0.900650	−	1.55997i
$207$		0			0
$208$	−7781.12	+	13477.3i	−2.59386	+	4.49270i
$209$	3479.29			1.15152
$210$		0			0
$211$	3314.53			1.08143			0.540714	−	0.841206i	$-0.318154\pi$
$211$	3314.53			1.08143			0.540714	+	0.841206i	$0.318154\pi$
$212$	−2805.74	+	4859.68i	−0.908957	+	1.57436i
$213$		0			0
$214$	1878.32	+	3253.34i	0.599996	+	1.03922i
$215$	131.002	−	226.903i	0.0415548	−	0.0719751i
$216$		0			0
$217$		0			0
$218$	9260.82			2.87716
$219$		0			0
$220$	5268.51	+	9125.32i	1.61456	+	2.79650i
$221$	−1053.38	−	1824.50i	−0.320624	−	0.555336i
$222$		0			0
$223$	−5576.50			−1.67457			−0.837287	−	0.546764i	$-0.815860\pi$
$223$	−5576.50			−1.67457			−0.837287	+	0.546764i	$0.815860\pi$
$224$		0			0
$225$		0			0
$226$	−2369.81	+	4104.63i	−0.697510	+	1.20812i
$227$	723.961	+	1253.94i	0.211678	+	0.366638i	0.952240	−	0.305351i	$-0.0987737\pi$
$227$	723.961	+	1253.94i	0.211678	+	0.366638i	−0.740562	+	0.671989i	$0.765440\pi$
$228$		0			0
$229$	−808.774	+	1400.84i	−0.233385	+	0.404235i	−0.958802	−	0.284074i	$-0.908314\pi$
$229$	−808.774	+	1400.84i	−0.233385	+	0.404235i	0.725417	+	0.688310i	$0.241647\pi$
$230$	4650.35			1.33320
$231$		0			0
$232$	1260.29			0.356647
$233$	3046.05	−	5275.92i	0.856454	−	1.48342i	−0.0188365	−	0.999823i	$-0.505996\pi$
$233$	3046.05	−	5275.92i	0.856454	−	1.48342i	0.875290	−	0.483598i	$-0.160670\pi$
$234$		0			0
$235$	−3986.94	−	6905.59i	−1.10672	−	1.91690i
$236$	−2689.11	+	4657.68i	−0.741721	+	1.28470i
$237$		0			0
$238$		0			0
$239$	−1595.90			−0.431927			−0.215963	−	0.976401i	$-0.569289\pi$
$239$	−1595.90			−0.431927			−0.215963	+	0.976401i	$0.569289\pi$
$240$		0			0
$241$	−1094.42	−	1895.58i	−0.292521	−	0.506661i	0.681884	−	0.731460i	$-0.261161\pi$
$241$	−1094.42	−	1895.58i	−0.292521	−	0.506661i	−0.974405	+	0.224799i	$0.927827\pi$
$242$	834.037	+	1444.59i	0.221545	+	0.383727i
$243$		0			0
$244$	−1541.12			−0.404344
$245$		0			0
$246$		0			0
$247$	−3949.12	+	6840.08i	−1.01731	+	1.76204i
$248$	−1993.83	−	3453.41i	−0.510517	−	0.884241i
$249$		0			0
$250$	−309.706	+	536.427i	−0.0783502	+	0.135707i
$251$	−6203.07			−1.55990			−0.779949	−	0.625843i	$-0.784755\pi$
$251$	−6203.07			−1.55990			−0.779949	+	0.625843i	$0.784755\pi$
$252$		0			0
$253$	−1767.53			−0.439224
$254$	−2108.90	+	3652.72i	−0.520961	+	0.902331i
$255$		0			0
$256$	−2793.74	−	4838.90i	−0.682066	−	1.18137i
$257$	134.162	−	232.375i	0.0325633	−	0.0564013i	−0.849284	−	0.527935i	$-0.822966\pi$
$257$	134.162	−	232.375i	0.0325633	−	0.0564013i	0.881848	+	0.471534i	$0.156300\pi$
$258$		0			0
$259$		0			0
$260$	−23919.8			−5.70554
$261$		0			0
$262$	5295.25	+	9171.65i	1.24863	+	2.16270i
$263$	−1862.48	−	3225.91i	−0.436675	−	0.756343i	0.560756	−	0.827981i	$-0.310511\pi$
$263$	−1862.48	−	3225.91i	−0.436675	−	0.756343i	−0.997431	+	0.0716384i	$0.977177\pi$
$264$		0			0
$265$	−4131.04			−0.957615
$266$		0			0
$267$		0			0
$268$	5357.03	−	9278.64i	1.22102	−	2.11486i
$269$	4278.63	+	7410.80i	0.969786	+	1.67972i	0.696167	+	0.717880i	$0.254888\pi$
$269$	4278.63	+	7410.80i	0.969786	+	1.67972i	0.273619	+	0.961838i	$0.411779\pi$
$270$		0			0
$271$	2639.83	−	4572.32i	0.591728	−	1.02490i	−0.402271	−	0.915521i	$-0.631779\pi$
$271$	2639.83	−	4572.32i	0.591728	−	1.02490i	0.994000	−	0.109383i	$-0.0348875\pi$
$272$	6224.67			1.38760
$273$		0			0
$274$	−6589.56			−1.45288
$275$	−1880.42	+	3256.98i	−0.412341	+	0.714195i
$276$		0			0
$277$	220.774	+	382.392i	0.0478882	+	0.0829448i	0.888976	−	0.457954i	$-0.151418\pi$
$277$	220.774	+	382.392i	0.0478882	+	0.0829448i	−0.841088	+	0.540899i	$0.818084\pi$
$278$	−2883.83	+	4994.94i	−0.622160	+	1.07761i
$279$		0			0
$280$		0			0
$281$	−3766.49			−0.799609			−0.399804	−	0.916601i	$-0.630922\pi$
$281$	−3766.49			−0.799609			−0.399804	+	0.916601i	$0.630922\pi$
$282$		0			0
$283$	−905.511	−	1568.39i	−0.190201	−	0.329439i	0.755115	−	0.655592i	$-0.227581\pi$
$283$	−905.511	−	1568.39i	−0.190201	−	0.329439i	−0.945317	+	0.326153i	$0.894247\pi$
$284$	8756.88	+	15167.4i	1.82967	+	3.16908i
$285$		0			0
$286$	12529.0			2.59040
$287$		0			0
$288$		0			0
$289$	2035.16	−	3525.01i	0.414241	−	0.717486i
$290$	745.926	+	1291.98i	0.151042	+	0.261613i
$291$		0			0
$292$	3941.68	−	6827.18i	0.789963	−	1.36826i
$293$	5815.74			1.15959			0.579794	−	0.814763i	$-0.303133\pi$
$293$	5815.74			1.15959			0.579794	+	0.814763i	$0.303133\pi$
$294$		0			0
$295$	−3959.33			−0.781427
$296$	10509.9	−	18203.7i	2.06378	−	3.57456i
$297$		0			0
$298$	6995.10	+	12115.9i	1.35978	+	2.35521i
$299$	2006.21	−	3474.86i	0.388034	−	0.672094i
$300$		0			0
$301$		0			0
$302$	10419.3			1.98532
$303$		0			0
$304$	−11668.2	−	20209.9i	−2.20137	−	3.81288i
$305$	−567.269	−	982.538i	−0.106497	−	0.184459i
$306$		0			0
$307$	−1974.93			−0.367150			−0.183575	−	0.983006i	$-0.558767\pi$
$307$	−1974.93			−0.367150			−0.183575	+	0.983006i	$0.558767\pi$
$308$		0			0
$309$		0			0
$310$	2360.17	−	4087.93i	0.432414	−	0.748964i
$311$	579.535	+	1003.78i	0.105667	+	0.183020i	0.914010	−	0.405691i	$-0.132969\pi$
$311$	579.535	+	1003.78i	0.105667	+	0.183020i	−0.808344	+	0.588711i	$0.799636\pi$
$312$		0			0
$313$	−2246.84	+	3891.64i	−0.405747	+	0.702774i	−0.994408	−	0.105606i	$-0.966322\pi$
$313$	−2246.84	+	3891.64i	−0.405747	+	0.702774i	0.588661	+	0.808380i	$0.299655\pi$
$314$	14178.7			2.54825
$315$		0			0
$316$	21761.0			3.87390
$317$	−2338.75	+	4050.83i	−0.414376	+	0.717721i	−0.995363	−	0.0961925i	$-0.969334\pi$
$317$	−2338.75	+	4050.83i	−0.414376	+	0.717721i	0.580987	+	0.813913i	$0.302667\pi$
$318$		0			0
$319$	−283.516	−	491.064i	−0.0497612	−	0.0861890i
$320$	11429.6	−	19796.7i	1.99667	−	3.45833i
$321$		0			0
$322$		0			0
$323$	3159.19			0.544216
$324$		0			0
$325$	−4268.69	−	7393.59i	−0.728567	−	1.26192i
$326$	8370.30	+	14497.8i	1.42205	+	2.46306i
$327$		0			0
$328$	−16954.6			−2.85415
$329$		0			0
$330$		0			0
$331$	1491.36	−	2583.10i	0.247650	−	0.428943i	−0.715223	−	0.698896i	$-0.753675\pi$
$331$	1491.36	−	2583.10i	0.247650	−	0.428943i	0.962873	+	0.269953i	$0.0870082\pi$
$332$	4794.07	+	8303.58i	0.792497	+	1.37264i
$333$		0			0
$334$	8814.63	−	15267.4i	1.44406	−	2.50118i
$335$	7887.45			1.28638
$336$		0			0
$337$	7328.53			1.18460			0.592301	−	0.805717i	$-0.298220\pi$
$337$	7328.53			1.18460			0.592301	+	0.805717i	$0.298220\pi$
$338$	−8289.04	+	14357.0i	−1.33392	+	2.31042i
$339$		0			0
$340$	4783.79	+	8285.76i	0.763051	+	1.32164i
$341$	−897.065	+	1553.76i	−0.142460	+	0.246748i
$342$		0			0
$343$		0			0
$344$	1195.20			0.187328
$345$		0			0
$346$	−5497.94	−	9522.71i	−0.854251	−	1.47961i
$347$	−4154.66	−	7196.09i	−0.642749	−	1.11327i	−0.984816	−	0.173599i	$-0.944460\pi$
$347$	−4154.66	−	7196.09i	−0.642749	−	1.11327i	0.342067	−	0.939676i	$-0.388873\pi$
$348$		0			0
$349$	334.303			0.0512745			0.0256373	−	0.999671i	$-0.491839\pi$
$349$	334.303			0.0512745			0.0256373	+	0.999671i	$0.491839\pi$
$350$		0			0
$351$		0			0
$352$	−9422.38	+	16320.0i	−1.42675	+	2.47120i
$353$	2729.09	+	4726.93i	0.411487	+	0.712717i	0.995053	−	0.0993491i	$-0.0316761\pi$
$353$	2729.09	+	4726.93i	0.411487	+	0.712717i	−0.583565	+	0.812066i	$0.698343\pi$
$354$		0			0
$355$	−6446.62	+	11165.9i	−0.963806	+	1.66936i
$356$	−7026.17			−1.04603
$357$		0			0
$358$	−19344.3			−2.85581
$359$	−3598.45	+	6232.70i	−0.529022	+	0.916293i	0.470405	+	0.882451i	$0.344108\pi$
$359$	−3598.45	+	6232.70i	−0.529022	+	0.916293i	−0.999427	+	0.0338425i	$0.989226\pi$
$360$		0			0
$361$	−2492.41	−	4316.98i	−0.363378	−	0.629389i
$362$	4420.76	−	7656.98i	0.641851	−	1.11172i
$363$		0			0
$364$		0			0
$365$	5803.55			0.832251
$366$		0			0
$367$	3162.21	+	5477.12i	0.449772	+	0.779028i	0.998371	−	0.0570579i	$-0.0181720\pi$
$367$	3162.21	+	5477.12i	0.449772	+	0.779028i	−0.548599	+	0.836086i	$0.684839\pi$
$368$	5927.60	+	10266.9i	0.839668	+	1.45435i
$369$		0			0
$370$	24882.0			3.49609
$371$		0			0
$372$		0			0
$373$	5465.88	−	9467.18i	0.758746	−	1.31419i	−0.184744	−	0.982787i	$-0.559146\pi$
$373$	5465.88	−	9467.18i	0.758746	−	1.31419i	0.943490	−	0.331400i	$-0.107521\pi$
$374$	−2505.71	−	4340.01i	−0.346436	−	0.600045i
$375$		0			0
$376$	18187.4	−	31501.6i	2.49454	−	4.32066i
$377$	1287.20			0.175847
$378$		0			0
$379$	6024.02			0.816446			0.408223	−	0.912882i	$-0.366149\pi$
$379$	6024.02			0.816446			0.408223	+	0.912882i	$0.366149\pi$
$380$	17934.5	−	31063.4i	2.42110	−	4.19347i
$381$		0			0
$382$	−7626.78	−	13210.0i	−1.02152	−	1.76932i
$383$	−3424.05	+	5930.63i	−0.456816	+	0.791229i	−0.998791	−	0.0491658i	$-0.984344\pi$
$383$	−3424.05	+	5930.63i	−0.456816	+	0.791229i	0.541974	+	0.840395i	$0.317677\pi$
$384$		0			0
$385$		0			0
$386$	−8950.51			−1.18023
$387$		0			0
$388$	12320.2	+	21339.2i	1.61202	+	2.79210i
$389$	−2580.94	−	4470.32i	−0.336398	−	0.582659i	0.647354	−	0.762189i	$-0.275875\pi$
$389$	−2580.94	−	4470.32i	−0.336398	−	0.582659i	−0.983752	+	0.179531i	$0.942542\pi$
$390$		0			0
$391$	−1604.91			−0.207580
$392$		0			0
$393$		0			0
$394$	−5105.01	+	8842.14i	−0.652758	+	1.13061i
$395$	8009.98	+	13873.7i	1.02032	+	1.76724i
$396$		0			0
$397$	172.384	−	298.578i	0.0217927	−	0.0377461i	−0.854923	−	0.518754i	$-0.826396\pi$
$397$	172.384	−	298.578i	0.0217927	−	0.0377461i	0.876716	+	0.481008i	$0.159729\pi$
$398$	−7520.70			−0.947182
$399$		0			0
$400$	25224.8			3.15310
$401$	−2549.42	+	4415.72i	−0.317486	+	0.549902i	−0.979963	−	0.199180i	$-0.936172\pi$
$401$	−2549.42	+	4415.72i	−0.317486	+	0.549902i	0.662477	+	0.749083i	$0.269505\pi$
$402$		0			0
$403$	−2036.40	−	3527.15i	−0.251713	−	0.435980i
$404$	−19715.3	+	34148.0i	−2.42791	+	4.20526i
$405$		0			0
$406$		0			0
$407$	−9457.28			−1.15179
$408$		0			0
$409$	−161.562	−	279.834i	−0.0195323	−	0.0338310i	0.856094	−	0.516820i	$-0.172884\pi$
$409$	−161.562	−	279.834i	−0.0195323	−	0.0338310i	−0.875626	+	0.482989i	$0.839551\pi$
$410$	−10034.9	−	17380.9i	−1.20875	−	2.09362i
$411$		0			0
$412$	20868.7			2.49545
$413$		0			0
$414$		0			0
$415$	−3529.29	+	6112.91i	−0.417460	+	0.723062i
$416$	−21389.5	−	37047.7i	−2.52093	−	4.36637i
$417$		0			0
$418$	−9393.92	+	16270.8i	−1.09922	+	1.90390i
$419$	−4415.98			−0.514880			−0.257440	−	0.966294i	$-0.582879\pi$
$419$	−4415.98			−0.514880			−0.257440	+	0.966294i	$0.582879\pi$
$420$		0			0
$421$	1379.37			0.159683			0.0798415	−	0.996808i	$-0.474559\pi$
$421$	1379.37			0.159683			0.0798415	+	0.996808i	$0.474559\pi$
$422$	−8949.06	+	15500.2i	−1.03231	+	1.78801i
$423$		0			0
$424$	−9422.38	−	16320.0i	−1.07922	−	1.86927i
$425$	−1707.42	+	2957.33i	−0.194875	+	0.337533i
$426$		0			0
$427$		0			0
$428$	−14720.0			−1.66243
$429$		0			0
$430$	707.401	+	1225.25i	0.0793346	+	0.137412i
$431$	−827.893	−	1433.95i	−0.0925248	−	0.160258i	0.816048	−	0.577984i	$-0.196160\pi$
$431$	−827.893	−	1433.95i	−0.0925248	−	0.160258i	−0.908573	+	0.417726i	$0.862827\pi$
$432$		0			0
$433$	−8612.65			−0.955883			−0.477942	−	0.878392i	$-0.658617\pi$
$433$	−8612.65			−0.955883			−0.477942	+	0.878392i	$0.658617\pi$
$434$		0			0
$435$		0			0
$436$	−18143.8	+	31426.0i	−1.99296	+	3.45190i
$437$	3008.41	+	5210.73i	0.329318	+	0.570396i
$438$		0			0
$439$	−2987.69	+	5174.84i	−0.324817	+	0.562600i	−0.981475	−	0.191588i	$-0.938636\pi$
$439$	−2987.69	+	5174.84i	−0.324817	+	0.562600i	0.656658	+	0.754188i	$0.271969\pi$
$440$	−35386.0			−3.83400
$441$		0			0
$442$	11376.3			1.22424
$443$	−403.266	+	698.477i	−0.0432500	+	0.0749112i	−0.886840	−	0.462077i	$-0.847105\pi$
$443$	−403.266	+	698.477i	−0.0432500	+	0.0749112i	0.843590	+	0.536988i	$0.180438\pi$
$444$		0			0
$445$	−2586.25	−	4479.52i	−0.275506	−	0.477190i
$446$	15056.3	−	26078.2i	1.59851	−	2.76870i
$447$		0			0
$448$		0			0
$449$	6253.04			0.657237			0.328618	−	0.944463i	$-0.393417\pi$
$449$	6253.04			0.657237			0.328618	+	0.944463i	$0.393417\pi$
$450$		0			0
$451$	3814.12	+	6606.24i	0.398226	+	0.689747i
$452$	−9285.85	−	16083.6i	−0.966304	−	1.67369i
$453$		0			0
$454$	−7818.65			−0.808254
$455$		0			0
$456$		0			0
$457$	−80.1439	+	138.813i	−0.00820344	+	0.0142088i	−0.870098	−	0.492879i	$-0.835945\pi$
$457$	−80.1439	+	138.813i	−0.00820344	+	0.0142088i	0.861895	+	0.507088i	$0.169278\pi$
$458$	−4367.30	−	7564.39i	−0.445569	−	0.771748i
$459$		0			0
$460$	−9110.96	+	15780.7i	−0.923480	+	1.59951i
$461$	2408.80			0.243360			0.121680	−	0.992569i	$-0.461172\pi$
$461$	2408.80			0.243360			0.121680	+	0.992569i	$0.461172\pi$
$462$		0			0
$463$	−1092.89			−0.109699			−0.0548496	−	0.998495i	$-0.517468\pi$
$463$	−1092.89			−0.109699			−0.0548496	+	0.998495i	$0.517468\pi$
$464$	−1901.60	+	3293.67i	−0.190258	+	0.329536i
$465$		0			0
$466$	16448.4	+	28489.5i	1.63510	+	2.83208i
$467$	−7527.42	+	13037.9i	−0.745884	+	1.29191i	0.203897	+	0.978992i	$0.434639\pi$
$467$	−7527.42	+	13037.9i	−0.745884	+	1.29191i	−0.949781	+	0.312916i	$0.898694\pi$
$468$		0			0
$469$		0			0
$470$	43058.3			4.22581
$471$		0			0
$472$	−9030.73	−	15641.7i	−0.880663	−	1.52535i
$473$	−268.873	−	465.701i	−0.0261370	−	0.0452705i
$474$		0			0
$475$	12802.2			1.23665
$476$		0			0
$477$		0			0
$478$	4308.87	−	7463.18i	0.412308	−	0.714138i
$479$	−5227.80	−	9054.82i	−0.498673	−	0.863727i	0.501326	−	0.865259i	$-0.332846\pi$
$479$	−5227.80	−	9054.82i	−0.498673	−	0.863727i	−0.999999	+	0.00153157i	$0.999512\pi$
$480$		0			0
$481$	10734.4	−	18592.4i	1.01756	−	1.76246i
$482$	11819.5			1.11693
$483$		0			0
$484$	−6536.18			−0.613841
$485$	−9069.86	+	15709.5i	−0.849157	+	1.47078i
$486$		0			0
$487$	6358.83	+	11013.8i	0.591675	+	1.02481i	0.994007	+	0.109318i	$0.0348666\pi$
$487$	6358.83	+	11013.8i	0.591675	+	1.02481i	−0.402331	+	0.915494i	$0.631800\pi$
$488$	2587.74	−	4482.09i	0.240044	−	0.415768i
$489$		0			0
$490$		0			0
$491$	20983.1			1.92863			0.964313	−	0.264763i	$-0.0852937\pi$
$491$	20983.1			1.92863			0.964313	+	0.264763i	$0.0852937\pi$
$492$		0			0
$493$	−257.431	−	445.884i	−0.0235175	−	0.0407335i
$494$	−21324.9	−	36935.8i	−1.94221	−	3.36401i
$495$		0			0
$496$	12033.6			1.08937
$497$		0			0
$498$		0			0
$499$	−6359.04	+	11014.2i	−0.570480	+	0.988101i	0.426036	+	0.904706i	$0.359910\pi$
$499$	−6359.04	+	11014.2i	−0.570480	+	0.988101i	−0.996517	+	0.0833946i	$0.973424\pi$
$500$	−1213.55	−	2101.94i	−0.108544	−	0.188003i
$501$		0			0
$502$	16748.0	−	29008.4i	1.48904	−	2.57910i
$503$	15675.9			1.38957			0.694785	−	0.719218i	$-0.255500\pi$
$503$	15675.9			1.38957			0.694785	+	0.719218i	$0.255500\pi$
$504$		0			0
$505$	−29028.0			−2.55788
$506$	4772.25	−	8265.78i	0.419273	−	0.726203i
$507$		0			0
$508$	−8263.51	−	14312.8i	−0.721721	−	1.25006i
$509$	−5109.15	+	8849.30i	−0.444910	+	0.770606i	−0.998046	−	0.0624847i	$-0.980098\pi$
$509$	−5109.15	+	8849.30i	−0.444910	+	0.770606i	0.553136	+	0.833091i	$0.313431\pi$
$510$		0			0
$511$		0			0
$512$	4500.87			0.388501
$513$		0			0
$514$	724.460	+	1254.80i	0.0621684	+	0.107679i
$515$	7681.54	+	13304.8i	0.657260	+	1.13841i
$516$		0			0
$517$	−16365.8			−1.39220
$518$		0			0
$519$		0			0
$520$	40164.4	−	69566.7i	3.38716	−	5.86674i
$521$	−2404.07	−	4163.96i	−0.202157	−	0.350147i	0.747066	−	0.664750i	$-0.231462\pi$
$521$	−2404.07	−	4163.96i	−0.202157	−	0.350147i	−0.949223	+	0.314603i	$0.898129\pi$
$522$		0			0
$523$	−4968.09	+	8604.99i	−0.415372	+	0.719445i	−0.995467	−	0.0951032i	$-0.969682\pi$
$523$	−4968.09	+	8604.99i	−0.415372	+	0.719445i	0.580095	+	0.814548i	$0.303015\pi$
$524$	−41497.8			−3.45962
$525$		0			0
$526$	20114.4			1.66736
$527$	−814.532	+	1410.81i	−0.0673274	+	0.116615i
$528$		0			0
$529$	4555.18	+	7889.81i	0.374388	+	0.648459i
$530$	11153.6	−	19318.6i	0.914117	−	1.58330i
$531$		0			0
$532$		0			0
$533$	−17316.6			−1.40725
$534$		0			0
$535$	−5418.27	−	9384.72i	−0.437854	−	0.758386i
$536$	17990.3	+	31160.1i	1.44974	+	2.51103i
$537$		0			0
$538$	−46208.4			−3.70294
$539$		0			0
$540$		0			0
$541$	1024.33	−	1774.19i	0.0814038	−	0.140995i	−0.822449	−	0.568838i	$-0.807393\pi$
$541$	1024.33	−	1774.19i	0.0814038	−	0.140995i	0.903853	+	0.427843i	$0.140726\pi$
$542$	14254.8	+	24690.1i	1.12970	+	1.95670i
$543$		0			0
$544$	−8555.49	+	14818.5i	−0.674290	+	1.16790i
$545$	−26714.1			−2.09964
$546$		0			0
$547$	6154.72			0.481091			0.240546	−	0.970638i	$-0.422674\pi$
$547$	6154.72			0.481091			0.240546	+	0.970638i	$0.422674\pi$
$548$	12910.3	−	22361.2i	1.00639	−	1.74311i
$549$		0			0
$550$	−10154.1	−	17587.4i	−0.787222	−	1.36351i
$551$	−965.112	+	1671.62i	−0.0746192	+	0.129244i
$552$		0			0
$553$		0			0
$554$	−2384.32			−0.182852
$555$		0			0
$556$	−11300.0	−	19572.2i	−0.861918	−	1.49289i
$557$	2223.38	+	3851.00i	0.169134	+	0.292948i	0.938116	−	0.346322i	$-0.112570\pi$
$557$	2223.38	+	3851.00i	0.169134	+	0.292948i	−0.768982	+	0.639271i	$0.779236\pi$
$558$		0			0
$559$	1220.72			0.0923631
$560$		0			0
$561$		0			0
$562$	10169.3	−	17613.8i	0.763288	−	1.32205i
$563$	4843.29	+	8388.83i	0.362559	+	0.627970i	0.988381	−	0.151996i	$-0.0485699\pi$
$563$	4843.29	+	8388.83i	0.362559	+	0.627970i	−0.625823	+	0.779965i	$0.715237\pi$
$564$		0			0
$565$	6836.04	−	11840.4i	0.509016	−	0.881642i
$566$	9779.35			0.726248
$567$		0			0
$568$	−58815.7			−4.34481
$569$	−3653.46	+	6327.98i	−0.269176	+	0.466226i	−0.968649	−	0.248433i	$-0.920085\pi$
$569$	−3653.46	+	6327.98i	−0.269176	+	0.466226i	0.699473	+	0.714659i	$0.253418\pi$
$570$		0			0
$571$	−4554.67	−	7888.92i	−0.333813	−	0.578180i	0.649443	−	0.760410i	$-0.275002\pi$
$571$	−4554.67	−	7888.92i	−0.333813	−	0.578180i	−0.983256	+	0.182230i	$0.941669\pi$
$572$	−24546.8	+	42516.3i	−1.79432	+	3.10786i
$573$		0			0
$574$		0			0
$575$	−6503.72			−0.471694
$576$		0			0
$577$	−9353.85	−	16201.3i	−0.674880	−	1.16893i	−0.976504	−	0.215500i	$-0.930862\pi$
$577$	−9353.85	−	16201.3i	−0.674880	−	1.16893i	0.301624	−	0.953427i	$-0.402471\pi$
$578$	10989.7	+	19034.7i	0.790850	+	1.36979i
$579$		0			0
$580$	−5845.67			−0.418497
$581$		0			0
$582$		0			0
$583$	−4239.33	+	7342.73i	−0.301158	+	0.521621i
$584$	13237.2	+	22927.4i	0.937941	+	1.62456i
$585$		0			0
$586$	−15702.2	+	27197.0i	−1.10692	+	1.91723i
$587$	24610.4			1.73046			0.865230	−	0.501375i	$-0.167172\pi$
$587$	24610.4			1.73046			0.865230	+	0.501375i	$0.167172\pi$
$588$		0			0
$589$	6107.38			0.427250
$590$	10690.0	−	18515.6i	0.745933	−	1.29199i
$591$		0			0
$592$	31716.0	+	54933.8i	2.20189	+	3.81379i
$593$	9420.00	−	16315.9i	0.652332	−	1.12987i	−0.330223	−	0.943903i	$-0.607124\pi$
$593$	9420.00	−	16315.9i	0.652332	−	1.12987i	0.982555	−	0.185970i	$-0.0595427\pi$
$594$		0			0
$595$		0			0
$596$	−54819.2			−3.76759
$597$		0			0
$598$	10833.3	+	18763.9i	0.740817	+	1.28313i
$599$	−10323.8	−	17881.4i	−0.704206	−	1.21972i	−0.966977	−	0.254862i	$-0.917970\pi$
$599$	−10323.8	−	17881.4i	−0.704206	−	1.21972i	0.262771	−	0.964858i	$-0.415363\pi$
$600$		0			0
$601$	15772.8			1.07053			0.535264	−	0.844685i	$-0.320212\pi$
$601$	15772.8			1.07053			0.535264	+	0.844685i	$0.320212\pi$
$602$		0			0
$603$		0			0
$604$	−20413.6	+	35357.3i	−1.37519	+	2.38190i
$605$	−2405.89	−	4167.13i	−0.161675	−	0.280030i
$606$		0			0
$607$	2591.32	−	4488.30i	0.173276	−	0.300123i	−0.766287	−	0.642498i	$-0.777898\pi$
$607$	2591.32	−	4488.30i	0.173276	−	0.300123i	0.939563	+	0.342375i	$0.111231\pi$
$608$	64149.2			4.27894
$609$		0			0
$610$	6126.39			0.406640
$611$	18575.8	−	32174.2i	1.22994	−	2.13033i
$612$		0			0
$613$	14419.5	+	24975.4i	0.950081	+	1.64559i	0.745244	+	0.666792i	$0.232333\pi$
$613$	14419.5	+	24975.4i	0.950081	+	1.64559i	0.204837	+	0.978796i	$0.434333\pi$
$614$	5332.21	−	9235.66i	0.350473	−	0.607037i
$615$		0			0
$616$		0			0
$617$	5114.80			0.333734			0.166867	−	0.985979i	$-0.446635\pi$
$617$	5114.80			0.333734			0.166867	+	0.985979i	$0.446635\pi$
$618$		0			0
$619$	14607.0	+	25300.0i	0.948471	+	1.64280i	0.748648	+	0.662968i	$0.230703\pi$
$619$	14607.0	+	25300.0i	0.948471	+	1.64280i	0.199823	+	0.979832i	$0.435963\pi$
$620$	9248.07	+	16018.1i	0.599051	+	1.03759i
$621$		0			0
$622$	−6258.87			−0.403469
$623$		0			0
$624$		0			0
$625$	8245.64	−	14281.9i	0.527721	−	0.914039i
$626$	−12132.7	−	21014.5i	−0.774634	−	1.34170i
$627$		0			0
$628$	−27778.9	+	48114.5i	−1.76513	+	3.05729i
$629$	−8587.18			−0.544345
$630$		0			0
$631$	19557.5			1.23387			0.616934	−	0.787015i	$-0.288374\pi$
$631$	19557.5			1.23387			0.616934	+	0.787015i	$0.288374\pi$
$632$	−36539.5	+	63288.3i	−2.29978	+	3.98334i
$633$		0			0
$634$	−12629.0	−	21874.1i	−0.791108	−	1.37024i
$635$	6083.41	−	10536.8i	0.380178	−	0.658487i
$636$		0			0
$637$		0			0
$638$	3061.92			0.190004
$639$		0			0
$640$	24992.0	+	43287.4i	1.54359	+	2.67357i
$641$	7316.15	+	12671.9i	0.450812	+	0.780829i	0.998437	−	0.0558950i	$-0.0178012\pi$
$641$	7316.15	+	12671.9i	0.450812	+	0.780829i	−0.547625	+	0.836724i	$0.684468\pi$
$642$		0			0
$643$	23808.1			1.46019			0.730094	−	0.683347i	$-0.239476\pi$
$643$	23808.1			1.46019			0.730094	+	0.683347i	$0.239476\pi$
$644$		0			0
$645$		0			0
$646$	−8529.65	+	14773.8i	−0.519496	+	0.899794i
$647$	−8661.08	−	15001.4i	−0.526279	−	0.911541i	−0.999531	−	0.0306145i	$-0.990254\pi$
$647$	−8661.08	−	15001.4i	−0.526279	−	0.911541i	0.473253	−	0.880927i	$-0.343080\pi$
$648$		0			0
$649$	−4063.11	+	7037.52i	−0.245749	+	0.425650i
$650$	46101.1			2.78190
$651$		0			0
$652$	−65596.4			−3.94011
$653$	−1620.84	+	2807.38i	−0.0971338	+	0.168241i	−0.910497	−	0.413515i	$-0.864301\pi$
$653$	−1620.84	+	2807.38i	−0.0971338	+	0.168241i	0.813363	+	0.581756i	$0.197634\pi$
$654$		0			0
$655$	−15274.9	−	26456.9i	−0.911205	−	1.57825i
$656$	25582.1	−	44309.5i	1.52258	−	2.63719i
$657$		0			0
$658$		0			0
$659$	16358.2			0.966958			0.483479	−	0.875356i	$-0.339373\pi$
$659$	16358.2			0.966958			0.483479	+	0.875356i	$0.339373\pi$
$660$		0			0
$661$	6286.30	+	10888.2i	0.369907	+	0.640698i	0.989551	−	0.144185i	$-0.0460562\pi$
$661$	6286.30	+	10888.2i	0.369907	+	0.640698i	−0.619644	+	0.784883i	$0.712723\pi$
$662$	8053.18	+	13948.5i	0.472803	+	0.818919i
$663$		0			0
$664$	−32199.5			−1.88190
$665$		0			0
$666$		0			0
$667$	490.291	−	849.209i	0.0284620	−	0.0492976i
$668$	34539.2	+	59823.7i	2.00054	+	3.46504i
$669$		0			0
$670$	−21295.7	+	36885.3i	−1.22795	+	2.12687i
$671$	−2328.55			−0.133968
$672$		0			0
$673$	13130.7			0.752082			0.376041	−	0.926603i	$-0.377285\pi$
$673$	13130.7			0.752082			0.376041	+	0.926603i	$0.377285\pi$
$674$	−19786.7	+	34271.6i	−1.13079	+	1.95859i
$675$		0			0
$676$	−32479.8	−	56256.6i	−1.84796	−	3.20076i
$677$	9312.08	−	16129.0i	0.528644	−	0.915639i	−0.470798	−	0.882241i	$-0.656034\pi$
$677$	9312.08	−	16129.0i	0.528644	−	0.915639i	0.999442	−	0.0333977i	$-0.0106328\pi$
$678$		0			0
$679$		0			0
$680$	−32130.4			−1.81198
$681$		0			0
$682$	−4844.07	−	8390.17i	−0.271978	−	0.471079i
$683$	12688.5	+	21977.1i	0.710852	+	1.23123i	0.964538	+	0.263946i	$0.0850240\pi$
$683$	12688.5	+	21977.1i	0.710852	+	1.23123i	−0.253685	+	0.967287i	$0.581643\pi$
$684$		0			0
$685$	19008.5			1.06026
$686$		0			0
$687$		0			0
$688$	−1803.39	+	3123.56i	−0.0999324	+	0.173088i
$689$	−9623.58	−	16668.5i	−0.532118	−	0.921655i
$690$		0			0
$691$	1067.71	−	1849.33i	0.0587810	−	0.101812i	−0.835137	−	0.550041i	$-0.814612\pi$
$691$	1067.71	−	1849.33i	0.0587810	−	0.101812i	0.893918	+	0.448230i	$0.147945\pi$
$692$	43086.2			2.36690
$693$		0			0
$694$	44869.6			2.45422
$695$	8318.80	−	14408.6i	0.454029	−	0.786401i
$696$		0			0
$697$	3463.21	+	5998.45i	0.188204	+	0.325979i
$698$	−902.602	+	1563.35i	−0.0489455	+	0.0847761i
$699$		0			0
$700$		0			0
$701$	−9679.27			−0.521513			−0.260757	−	0.965405i	$-0.583972\pi$
$701$	−9679.27			−0.521513			−0.260757	+	0.965405i	$0.583972\pi$
$702$		0			0
$703$	16096.7	+	27880.3i	0.863583	+	1.49577i
$704$	−23458.4	−	40631.2i	−1.25586	−	2.17521i
$705$		0			0
$706$	−29473.7			−1.57119
$707$		0			0
$708$		0			0
$709$	12871.6	−	22294.2i	0.681809	−	1.18093i	−0.292619	−	0.956229i	$-0.594527\pi$
$709$	12871.6	−	22294.2i	0.681809	−	1.18093i	0.974428	−	0.224699i	$-0.0721399\pi$
$710$	−34811.2	−	60294.7i	−1.84006	−	3.18707i
$711$		0			0
$712$	11797.8	−	20434.5i	0.620987	−	1.07558i
$713$	−3102.63			−0.162966
$714$		0			0
$715$	−36141.6			−1.89038
$716$	37899.4	−	65643.7i	1.97817	−	3.42629i
$717$		0			0
$718$	−19431.3	−	33656.0i	−1.00999	−	1.74935i
$719$	5254.26	−	9100.64i	0.272532	−	0.472040i	−0.696977	−	0.717093i	$-0.745472\pi$
$719$	5254.26	−	9100.64i	0.272532	−	0.472040i	0.969510	+	0.245053i	$0.0788055\pi$
$720$		0			0
$721$		0			0
$722$	26917.5			1.38749
$723$		0			0
$724$	17322.3	+	30003.1i	0.889196	+	1.54013i
$725$	−1043.21	−	1806.89i	−0.0534398	−	0.0925605i
$726$		0			0
$727$	24259.4			1.23759			0.618797	−	0.785551i	$-0.287620\pi$
$727$	24259.4			1.23759			0.618797	+	0.785551i	$0.287620\pi$
$728$		0			0
$729$		0			0
$730$	−15669.3	+	27140.0i	−0.794448	+	1.37602i
$731$	−244.136	−	422.855i	−0.0123525	−	0.0213952i
$732$		0			0
$733$	9816.08	−	17001.9i	0.494632	−	0.856727i	−0.505349	−	0.862915i	$-0.668636\pi$
$733$	9816.08	−	17001.9i	0.494632	−	0.856727i	0.999981	+	0.00618771i	$0.00196962\pi$
$734$	−34151.3			−1.71737
$735$		0			0
$736$	−32588.7			−1.63212
$737$	8094.20	−	14019.6i	0.404551	−	0.700702i
$738$		0			0
$739$	13176.8	+	22822.9i	0.655909	+	1.13607i	0.981665	+	0.190614i	$0.0610478\pi$
$739$	13176.8	+	22822.9i	0.655909	+	1.13607i	−0.325756	+	0.945454i	$0.605619\pi$
$740$	−48748.8	+	84435.4i	−2.42168	+	4.19447i
$741$		0			0
$742$		0			0
$743$	−31464.6			−1.55360			−0.776799	−	0.629749i	$-0.783158\pi$
$743$	−31464.6			−1.55360			−0.776799	+	0.629749i	$0.783158\pi$
$744$		0			0
$745$	−20178.3	−	34949.9i	−0.992318	−	1.71875i
$746$	29515.2	+	51121.9i	1.44856	+	2.50899i
$747$		0			0
$748$	19636.7			0.959880
$749$		0			0
$750$		0			0
$751$	−2705.76	+	4686.51i	−0.131471	+	0.227714i	−0.924244	−	0.381803i	$-0.875303\pi$
$751$	−2705.76	+	4686.51i	−0.131471	+	0.227714i	0.792773	+	0.609517i	$0.208637\pi$
$752$	54884.5	+	95062.8i	2.66148	+	4.60982i
$753$		0			0
$754$	−3475.38	+	6019.54i	−0.167859	+	0.290741i
$755$	−30056.0			−1.44881
$756$		0			0
$757$	3607.94			0.173227			0.0866135	−	0.996242i	$-0.472395\pi$
$757$	3607.94			0.173227			0.0866135	+	0.996242i	$0.472395\pi$
$758$	−16264.6	+	28171.1i	−0.779361	+	1.34989i
$759$		0			0
$760$	60228.5	+	104319.i	2.87463	+	4.97900i
$761$	−2331.85	+	4038.89i	−0.111077	+	0.192391i	−0.916205	−	0.400710i	$-0.868763\pi$
$761$	−2331.85	+	4038.89i	−0.111077	+	0.192391i	0.805128	+	0.593101i	$0.202097\pi$
$762$		0			0
$763$		0			0
$764$	59769.5			2.83035
$765$		0			0
$766$	−18489.5	−	32024.8i	−0.872134	−	1.51058i
$767$	−9223.56	−	15975.7i	−0.434216	−	0.752083i
$768$		0			0
$769$	9725.21			0.456047			0.228023	−	0.973656i	$-0.426774\pi$
$769$	9725.21			0.456047			0.228023	+	0.973656i	$0.426774\pi$
$770$		0			0
$771$		0			0
$772$	17535.8	−	30373.0i	0.817524	−	1.41599i
$773$	1546.40	+	2678.44i	0.0719536	+	0.124627i	0.899757	−	0.436390i	$-0.143743\pi$
$773$	1546.40	+	2678.44i	0.0719536	+	0.124627i	−0.827804	+	0.561018i	$0.810410\pi$
$774$		0			0
$775$	−3300.80	+	5717.15i	−0.152991	+	0.264988i
$776$	−82748.8			−3.82798
$777$		0			0
$778$	27873.7			1.28447
$779$	12983.6	−	22488.2i	0.597157	−	1.03431i
$780$		0			0
$781$	13231.2	+	22917.1i	0.606210	+	1.04999i
$782$	4333.19	−	7505.30i	0.198151	−	0.343208i
$783$		0			0
$784$		0			0
$785$	−40900.4			−1.85962
$786$		0			0
$787$	11406.4	+	19756.5i	0.516640	+	0.894846i	0.999813	+	0.0193216i	$0.00615065\pi$
$787$	11406.4	+	19756.5i	0.516640	+	0.894846i	−0.483174	+	0.875525i	$0.660516\pi$
$788$	−20003.5	−	34647.0i	−0.904307	−	1.56631i
$789$		0			0
$790$	−86506.3			−3.89589
$791$		0			0
$792$		0			0
$793$	2642.99	−	4577.79i	0.118355	−	0.204997i
$794$	930.857	+	1612.29i	0.0416056	+	0.0720631i
$795$		0			0
$796$	14734.5	−	25521.0i	0.656096	−	1.13639i
$797$	−34305.4			−1.52467			−0.762334	−	0.647184i	$-0.775947\pi$
$797$	−34305.4			−1.52467			−0.762334	+	0.647184i	$0.775947\pi$
$798$		0			0
$799$	−14860.1			−0.657963
$800$	−34670.2	+	60050.5i	−1.53222	+	2.65388i
$801$		0			0
$802$	−13766.6	−	23844.5i	−0.606130	−	1.04985i
$803$	5955.68	−	10315.5i	0.261733	−	0.453334i
$804$		0			0
$805$		0			0
$806$	21992.8			0.961119
$807$		0			0
$808$	−66209.2	−	114678.i	−2.88271	−	4.99300i
$809$	−1632.40	−	2827.40i	−0.0709421	−	0.122875i	0.828372	−	0.560178i	$-0.189267\pi$
$809$	−1632.40	−	2827.40i	−0.0709421	−	0.122875i	−0.899314	+	0.437303i	$0.855934\pi$
$810$		0			0
$811$	−27264.0			−1.18048			−0.590239	−	0.807228i	$-0.700967\pi$
$811$	−27264.0			−1.18048			−0.590239	+	0.807228i	$0.700967\pi$
$812$		0			0
$813$		0			0
$814$	25534.2	−	44226.6i	1.09948	−	1.90435i
$815$	−24145.3	−	41820.9i	−1.03776	−	1.79745i
$816$		0			0
$817$	−915.266	+	1585.29i	−0.0391935	+	0.0678852i
$818$	1744.84			0.0745805
$819$		0			0
$820$	78641.4			3.34912
$821$	18167.1	−	31466.3i	0.772272	−	1.33761i	−0.164043	−	0.986453i	$-0.552454\pi$
$821$	18167.1	−	31466.3i	0.772272	−	1.33761i	0.936315	−	0.351161i	$-0.114213\pi$
$822$		0			0
$823$	−3895.90	−	6747.90i	−0.165009	−	0.285804i	0.771649	−	0.636048i	$-0.219432\pi$
$823$	−3895.90	−	6747.90i	−0.165009	−	0.285804i	−0.936659	+	0.350244i	$0.886099\pi$
$824$	−35041.2	+	60693.2i	−1.48145	+	2.56595i
$825$		0			0
$826$		0			0
$827$	36082.7			1.51719			0.758596	−	0.651561i	$-0.225886\pi$
$827$	36082.7			1.51719			0.758596	+	0.651561i	$0.225886\pi$
$828$		0			0
$829$	−21497.5	−	37234.8i	−0.900650	−	1.55997i	−0.826652	−	0.562714i	$-0.809757\pi$
$829$	−21497.5	−	37234.8i	−0.900650	−	1.55997i	−0.0739984	−	0.997258i	$-0.523576\pi$
$830$	−19057.8	−	33009.1i	−0.796997	−	1.38044i
$831$		0			0
$832$	106505.			4.43796
$833$		0			0
$834$		0			0
$835$	−25427.0	+	44040.9i	−1.05382	+	1.82527i
$836$	−36809.1	−	63755.3i	−1.52281	−	2.63759i
$837$		0			0
$838$	11922.9	−	20651.1i	0.491493	−	0.851291i
$839$	28252.8			1.16257			0.581283	−	0.813701i	$-0.302551\pi$
$839$	28252.8			1.16257			0.581283	+	0.813701i	$0.302551\pi$
$840$		0			0
$841$	−24074.4			−0.987102
$842$	−3724.24	+	6450.58i	−0.152430	+	0.264016i
$843$		0			0
$844$	−35066.0	−	60736.1i	−1.43012	−	2.47704i
$845$	23910.9	−	41414.9i	0.973444	−	1.68605i
$846$		0			0
$847$		0			0
$848$	56868.2			2.30290
$849$		0			0
$850$	−9219.89	−	15969.3i	−0.372046	−	0.644403i
$851$	−8177.36	−	14163.6i	−0.329396	−	0.570531i
$852$		0			0
$853$	−28994.8			−1.16385			−0.581924	−	0.813243i	$-0.697700\pi$
$853$	−28994.8			−1.16385			−0.581924	+	0.813243i	$0.697700\pi$
$854$		0			0
$855$		0			0
$856$	24716.8	−	42810.7i	0.986918	−	1.70939i
$857$	4316.44	+	7476.28i	0.172050	+	0.297999i	0.939136	−	0.343545i	$-0.111628\pi$
$857$	4316.44	+	7476.28i	0.172050	+	0.297999i	−0.767087	+	0.641544i	$0.778294\pi$
$858$		0			0
$859$	16973.5	−	29399.0i	0.674191	−	1.16773i	−0.302514	−	0.953145i	$-0.597826\pi$
$859$	16973.5	−	29399.0i	0.674191	−	1.16773i	0.976705	−	0.214587i	$-0.0688407\pi$
$860$	−5543.76			−0.219815
$861$		0			0
$862$	8941.09			0.353288
$863$	35.3306	−	61.1944i	0.00139359	−	0.00241377i	−0.865328	−	0.501206i	$-0.832890\pi$
$863$	35.3306	−	61.1944i	0.00139359	−	0.00241377i	0.866721	+	0.498793i	$0.166223\pi$
$864$		0			0
$865$	15859.6	+	27469.6i	0.623400	+	1.07976i
$866$	23253.7	−	40276.7i	0.912465	−	1.58044i
$867$		0			0
$868$		0			0
$869$	32879.8			1.28351
$870$		0			0
$871$	18374.4	+	31825.4i	0.714803	+	1.23807i
$872$	−60931.5	−	105536.i	−2.36628	−	4.09853i
$873$		0			0
$874$	−32490.3			−1.25744
$875$		0			0
$876$		0			0
$877$	5587.66	−	9678.10i	0.215144	−	0.372641i	−0.738173	−	0.674612i	$-0.764311\pi$
$877$	5587.66	−	9678.10i	0.215144	−	0.372641i	0.953317	+	0.301971i	$0.0976444\pi$
$878$	−16133.3	−	27943.6i	−0.620127	−	1.07409i
$879$		0			0
$880$	53392.5	−	92478.5i	2.04530	−	3.54255i
$881$	14341.3			0.548433			0.274216	−	0.961668i	$-0.411582\pi$
$881$	14341.3			0.548433			0.274216	+	0.961668i	$0.411582\pi$
$882$		0			0
$883$	−23559.2			−0.897884			−0.448942	−	0.893561i	$-0.648199\pi$
$883$	−23559.2			−0.897884			−0.448942	+	0.893561i	$0.648199\pi$
$884$	−22288.4	+	38604.6i	−0.848009	+	1.46879i
$885$		0			0
$886$	−2177.60	−	3771.71i	−0.0825710	−	0.143017i
$887$	−15872.2	+	27491.5i	−0.600831	+	1.04067i	0.391865	+	0.920023i	$0.371830\pi$
$887$	−15872.2	+	27491.5i	−0.600831	+	1.04067i	−0.992696	+	0.120647i	$0.961503\pi$
$888$		0			0
$889$		0			0
$890$	27931.1			1.05197
$891$		0			0
$892$	58996.5	+	102185.i	2.21452	+	3.83566i
$893$	27855.3	+	48246.9i	1.04383	+	1.80797i
$894$		0			0
$895$	55801.4			2.08406
$896$		0			0
$897$		0			0
$898$	−16882.9	+	29242.1i	−0.627384	+	1.08666i
$899$	−497.669	−	861.989i	−0.0184630	−	0.0319788i
$900$		0			0
$901$	−3849.30	+	6667.18i	−0.142329	+	0.246521i
$902$	−41191.8			−1.52055
$903$		0			0
$904$	62368.5			2.29463
$905$	−12752.3	+	22087.6i	−0.468398	+	0.811290i
$906$		0			0
$907$	−3031.33	−	5250.42i	−0.110974	−	0.192213i	0.805189	−	0.593018i	$-0.202064\pi$
$907$	−3031.33	−	5250.42i	−0.110974	−	0.192213i	−0.916163	+	0.400805i	$0.868730\pi$
$908$	15318.3	−	26532.1i	0.559863	−	0.969711i
$909$		0			0
$910$		0			0
$911$	−25862.9			−0.940589			−0.470295	−	0.882509i	$-0.655852\pi$
$911$	−25862.9			−0.940589			−0.470295	+	0.882509i	$0.655852\pi$
$912$		0			0
$913$	7243.61	+	12546.3i	0.262572	+	0.454788i
$914$	−432.769	−	749.579i	−0.0156616	−	0.0271268i
$915$		0			0
$916$	34225.7			1.23455
$917$		0			0
$918$		0			0
$919$	−727.570	+	1260.19i	−0.0261157	+	0.0452337i	−0.878788	−	0.477213i	$-0.841647\pi$
$919$	−727.570	+	1260.19i	−0.0261157	+	0.0452337i	0.852672	+	0.522446i	$0.174980\pi$
$920$	−30597.0	−	52995.5i	−1.09647	−	1.89914i
$921$		0			0
$922$	−6503.65	+	11264.6i	−0.232306	+	0.402366i
$923$	−60071.6			−2.14223
$924$		0			0
$925$	−34798.6			−1.23694
$926$	2950.74	−	5110.83i	0.104716	−	0.181374i
$927$		0			0
$928$	−5227.30	−	9053.96i	−0.184908	−	0.320270i
$929$	1538.87	−	2665.40i	0.0543474	−	0.0941325i	−0.837572	−	0.546327i	$-0.816025\pi$
$929$	1538.87	−	2665.40i	0.0543474	−	0.0941325i	0.891919	+	0.452195i	$0.149359\pi$
$930$		0			0
$931$		0			0
$932$	−128903.			−4.53042
$933$		0			0
$934$	−40647.4	−	70403.3i	−1.42401	−	2.46645i
$935$	7228.06	+	12519.4i	0.252816	+	0.437890i
$936$		0			0
$937$	−5354.80			−0.186695			−0.0933477	−	0.995634i	$-0.529757\pi$
$937$	−5354.80			−0.186695			−0.0933477	+	0.995634i	$0.529757\pi$
$938$		0			0
$939$		0			0
$940$	−84359.7	+	146115.i	−2.92714	+	5.06995i
$941$	−23898.9	−	41394.1i	−0.827930	−	1.43402i	−0.899659	−	0.436593i	$-0.856185\pi$
$941$	−23898.9	−	41394.1i	−0.827930	−	1.43402i	0.0717294	−	0.997424i	$-0.477148\pi$
$942$		0			0
$943$	−6595.85	+	11424.4i	−0.227774	+	0.394515i
$944$	54504.4			1.87920
$945$		0			0
$946$	2903.78			0.0997990
$947$	−1245.85	+	2157.87i	−0.0427503	+	0.0740457i	−0.886609	−	0.462520i	$-0.846945\pi$
$947$	−1245.85	+	2157.87i	−0.0427503	+	0.0740457i	0.843859	+	0.536566i	$0.180279\pi$
$948$		0			0
$949$	13519.8	+	23417.0i	0.462457	+	0.800999i
$950$	−34565.4	+	59869.1i	−1.18047	+	2.04464i
$951$		0			0
$952$		0			0
$953$	13130.4			0.446313			0.223156	−	0.974783i	$-0.428364\pi$
$953$	13130.4			0.446313			0.223156	+	0.974783i	$0.428364\pi$
$954$		0			0
$955$	22000.5	+	38106.0i	0.745465	+	1.29118i
$956$	16883.9	+	29243.7i	0.571196	+	0.989340i
$957$		0			0
$958$	56459.3			1.90409
$959$		0			0
$960$		0			0
$961$	13320.8	−	23072.4i	0.447143	−	0.774474i
$962$	57964.5	+	100397.i	1.94267	+	3.36481i
$963$		0			0
$964$	−23156.7	+	40108.6i	−0.773680	+	1.34005i
$965$	25819.0			0.861287
$966$		0			0
$967$	43314.8			1.44044			0.720222	−	0.693743i	$-0.244040\pi$
$967$	43314.8			1.44044			0.720222	+	0.693743i	$0.244040\pi$
$968$	10975.1	−	19009.4i	0.364414	−	0.631183i
$969$		0			0
$970$	−48976.4	−	84829.6i	−1.62117	−	2.80795i
$971$	−9877.90	+	17109.0i	−0.326464	+	0.565453i	−0.981808	−	0.189878i	$-0.939191\pi$
$971$	−9877.90	+	17109.0i	−0.326464	+	0.565453i	0.655343	+	0.755331i	$0.272524\pi$
$972$		0			0
$973$		0			0
$974$	−68674.1			−2.25920
$975$		0			0
$976$	7809.06	+	13525.7i	0.256108	+	0.443593i
$977$	−5570.05	−	9647.61i	−0.182397	−	0.315921i	0.760299	−	0.649573i	$-0.225052\pi$
$977$	−5570.05	−	9647.61i	−0.182397	−	0.315921i	−0.942696	+	0.333652i	$0.891719\pi$
$978$		0			0
$979$	−10616.2			−0.346573
$980$		0			0
$981$		0			0
$982$	−56653.5	+	98126.7i	−1.84102	+	3.18875i
$983$	−1787.88	−	3096.70i	−0.0580107	−	0.100478i	0.835562	−	0.549397i	$-0.185142\pi$
$983$	−1787.88	−	3096.70i	−0.0580107	−	0.100478i	−0.893572	+	0.448919i	$0.851809\pi$
$984$		0			0
$985$	14726.1	−	25506.4i	0.476358	−	0.825077i
$986$	2780.21			0.0897971
$987$		0			0
$988$	167119.			5.38133
$989$	464.969	−	805.349i	0.0149496	−	0.0258934i
$990$		0			0
$991$	−11195.9	−	19391.9i	−0.358880	−	0.621598i	0.628894	−	0.777491i	$-0.283508\pi$
$991$	−11195.9	−	19391.9i	−0.358880	−	0.621598i	−0.987774	+	0.155893i	$0.950175\pi$
$992$	−16539.6	+	28647.4i	−0.529367	+	0.916891i
$993$		0			0
$994$		0			0
$995$	21694.5			0.691218
$996$		0			0
$997$	8733.25	+	15126.4i	0.277417	+	0.480501i	0.970742	−	0.240124i	$-0.0771883\pi$
$997$	8733.25	+	15126.4i	0.277417	+	0.480501i	−0.693325	+	0.720625i	$0.743855\pi$
$998$	−34338.2	−	59475.5i	−1.08914	−	1.88644i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.e.z.226.2		16
3.2	odd	2	inner	441.4.e.z.226.7		16
7.2	even	3		441.4.a.x.1.7	yes	8
7.3	odd	6	inner	441.4.e.z.361.1		16
7.4	even	3	inner	441.4.e.z.361.2		16
7.5	odd	6		441.4.a.x.1.8	yes	8
7.6	odd	2	inner	441.4.e.z.226.1		16
21.2	odd	6		441.4.a.x.1.2	yes	8
21.5	even	6		441.4.a.x.1.1	✓	8
21.11	odd	6	inner	441.4.e.z.361.7		16
21.17	even	6	inner	441.4.e.z.361.8		16
21.20	even	2	inner	441.4.e.z.226.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.a.x.1.1	✓	8	21.5	even	6
441.4.a.x.1.2	yes	8	21.2	odd	6
441.4.a.x.1.7	yes	8	7.2	even	3
441.4.a.x.1.8	yes	8	7.5	odd	6
441.4.e.z.226.1		16	7.6	odd	2	inner
441.4.e.z.226.2		16	1.1	even	1	trivial
441.4.e.z.226.7		16	3.2	odd	2	inner
441.4.e.z.226.8		16	21.20	even	2	inner
441.4.e.z.361.1		16	7.3	odd	6	inner
441.4.e.z.361.2		16	7.4	even	3	inner
441.4.e.z.361.7		16	21.11	odd	6	inner
441.4.e.z.361.8		16	21.17	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.69995 + 4.67646i) q^{2} +(-10.5795 - 18.3242i) q^{4} +(7.78839 - 13.4899i) q^{5} +71.0573 q^{8} +O(q^{10})\)	\(q+(-2.69995 + 4.67646i) q^{2} +(-10.5795 - 18.3242i) q^{4} +(7.78839 - 13.4899i) q^{5} +71.0573 q^{8} +(42.0566 + 72.8441i) q^{10} +(-15.9851 - 27.6870i) q^{11} +72.5746 q^{13} +(-107.215 + 185.703i) q^{16} +(-14.5144 - 25.1397i) q^{17} +(-54.4146 + 94.2489i) q^{19} -329.589 q^{20} +172.636 q^{22} +(27.6434 - 47.8798i) q^{23} +(-58.8180 - 101.876i) q^{25} +(-195.948 + 339.392i) q^{26} +17.7363 q^{29} +(-28.0594 - 48.6004i) q^{31} +(-294.724 - 510.477i) q^{32} +156.753 q^{34} +(147.908 - 256.184i) q^{37} +(-293.834 - 508.935i) q^{38} +(553.422 - 958.555i) q^{40} -238.605 q^{41} +16.8202 q^{43} +(-338.228 + 585.829i) q^{44} +(149.272 + 258.547i) q^{46} +(255.954 - 443.326i) q^{47} +635.223 q^{50} +(-767.802 - 1329.87i) q^{52} +(-132.603 - 229.674i) q^{53} -497.992 q^{55} +(-47.8871 + 82.9429i) q^{58} +(-127.091 - 220.128i) q^{59} +(36.4176 - 63.0771i) q^{61} +303.037 q^{62} +1467.52 q^{64} +(565.239 - 979.023i) q^{65} +(253.180 + 438.520i) q^{67} +(-307.110 + 531.930i) q^{68} -827.722 q^{71} +(186.288 + 322.661i) q^{73} +(798.689 + 1383.37i) q^{74} +2302.72 q^{76} +(-514.226 + 890.665i) q^{79} +(1670.07 + 2892.65i) q^{80} +(644.222 - 1115.82i) q^{82} -453.148 q^{83} -452.175 q^{85} +(-45.4138 + 78.6590i) q^{86} +(-1135.86 - 1967.36i) q^{88} +(166.033 - 287.577i) q^{89} -1169.81 q^{92} +(1382.13 + 2393.92i) q^{94} +(847.605 + 1468.09i) q^{95} -1164.54 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 68 q^{4}+O(q^{10}) \) 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

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