LMFDB - Embedded newform 441.4.p.c.80.7

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 $ x^16 - 48x^14 + 1647x^12 - 27620x^10 + 336765x^8 - 1200006x^6 + 3242464x^4 - 1762200*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.7
Root			$3.91663 - 2.26127i$ of defining polynomial
Character	$\chi$	$=$	441.80
Dual form			441.4.p.c.215.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.91663 - 2.26127i) q^{2} +(6.22668 - 10.7849i) q^{4} +(-0.632851 - 1.09613i) q^{5} -20.1405i q^{8} +O(q^{10})$	\(q+(3.91663 - 2.26127i) q^{2} +(6.22668 - 10.7849i) q^{4} +(-0.632851 - 1.09613i) q^{5} -20.1405i q^{8} +(-4.95730 - 2.86210i) q^{10} +(-36.0248 - 20.7989i) q^{11} -85.7355i q^{13} +(4.27028 + 7.39634i) q^{16} +(38.8929 - 67.3645i) q^{17} +(-42.1638 + 24.3433i) q^{19} -15.7623 q^{20} -188.128 q^{22} +(-78.7639 + 45.4743i) q^{23} +(61.6990 - 106.866i) q^{25} +(-193.871 - 335.795i) q^{26} -151.196i q^{29} +(-76.3661 - 44.0900i) q^{31} +(172.988 + 99.8747i) q^{32} -351.790i q^{34} +(-45.2914 - 78.4470i) q^{37} +(-110.093 + 190.687i) q^{38} +(-22.0767 + 12.7460i) q^{40} +383.530 q^{41} -227.894 q^{43} +(-448.630 + 259.017i) q^{44} +(-205.660 + 356.213i) q^{46} +(69.5529 + 120.469i) q^{47} -558.072i q^{50} +(-924.652 - 533.848i) q^{52} +(289.749 + 167.287i) q^{53} +52.6505i q^{55} +(-341.895 - 592.179i) q^{58} +(-440.050 + 762.189i) q^{59} +(-11.3944 + 6.57854i) q^{61} -398.797 q^{62} +835.050 q^{64} +(-93.9774 + 54.2579i) q^{65} +(221.212 - 383.151i) q^{67} +(-484.348 - 838.915i) q^{68} +341.552i q^{71} +(798.218 + 460.851i) q^{73} +(-354.780 - 204.832i) q^{74} +606.311i q^{76} +(206.564 + 357.780i) q^{79} +(5.40490 - 9.36157i) q^{80} +(1502.15 - 867.265i) q^{82} -954.307 q^{83} -98.4538 q^{85} +(-892.579 + 515.331i) q^{86} +(-418.901 + 725.558i) q^{88} +(-14.8490 - 25.7193i) q^{89} +1132.62i q^{92} +(544.826 + 314.556i) q^{94} +(53.3668 + 30.8113i) q^{95} -1199.63i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4}+O(q^{10}) $ 16 * q + 32 * q^4	$ 16 q + 32 q^{4} + 72 q^{10} - 188 q^{16} + 612 q^{19} + 528 q^{22} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} + 3204 q^{40} + 328 q^{43} - 1392 q^{46} - 4452 q^{52} - 3372 q^{58} + 1632 q^{61} + 5432 q^{64} + 308 q^{67} - 4068 q^{73} - 2176 q^{79} + 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 2916 q^{94}+O(q^{100}) $ 16 * q + 32 * q^4 + 72 * q^10 - 188 * q^16 + 612 * q^19 + 528 * q^22 - 20 * q^25 - 1128 * q^31 - 1196 * q^37 + 3204 * q^40 + 328 * q^43 - 1392 * q^46 - 4452 * q^52 - 3372 * q^58 + 1632 * q^61 + 5432 * q^64 + 308 * q^67 - 4068 * q^73 - 2176 * q^79 + 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 2916 * q^94

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 $

$2$	3.91663	−	2.26127i	1.38474	−	0.799480i	0.392023	−	0.919955i	$-0.371775\pi$
$2$	3.91663	−	2.26127i	1.38474	−	0.799480i	0.992716	+	0.120476i	$0.0384420\pi$
$3$		0			0
$3$		0			0
$4$	6.22668	−	10.7849i	0.778336	−	1.34812i
$5$	−0.632851	−	1.09613i	−0.0566040	−	0.0980409i	0.836335	−	0.548219i	$-0.184694\pi$
$5$	−0.632851	−	1.09613i	−0.0566040	−	0.0980409i	−0.892939	+	0.450178i	$0.851361\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	20.1405i		−	0.890094i
$9$		0			0
$10$	−4.95730	−	2.86210i	−0.156763	−	0.0905074i
$11$	−36.0248	−	20.7989i	−0.987443	−	0.570101i	−0.0829344	−	0.996555i	$-0.526429\pi$
$11$	−36.0248	−	20.7989i	−0.987443	−	0.570101i	−0.904509	+	0.426454i	$0.859763\pi$
$12$		0			0
$13$		−	85.7355i		−	1.82914i	−0.404433	−	0.914568i	$-0.632531\pi$
$13$		−	85.7355i		−	1.82914i	0.404433	−	0.914568i	$-0.367469\pi$
$14$		0			0
$15$		0			0
$16$	4.27028	+	7.39634i	0.0667231	+	0.115568i
$17$	38.8929	−	67.3645i	0.554878	−	0.961076i	−0.443035	−	0.896504i	$-0.646098\pi$
$17$	38.8929	−	67.3645i	0.554878	−	0.961076i	0.997913	−	0.0645722i	$-0.0205683\pi$
$18$		0			0
$19$	−42.1638	+	24.3433i	−0.509107	+	0.293933i	−0.732466	−	0.680803i	$-0.761631\pi$
$19$	−42.1638	+	24.3433i	−0.509107	+	0.293933i	0.223360	+	0.974736i	$0.428298\pi$
$20$	−15.7623			−0.176227
$21$		0			0
$22$	−188.128			−1.82314
$23$	−78.7639	+	45.4743i	−0.714061	+	0.412263i	−0.812563	−	0.582874i	$-0.801928\pi$
$23$	−78.7639	+	45.4743i	−0.714061	+	0.412263i	0.0985019	+	0.995137i	$0.468595\pi$
$24$		0			0
$25$	61.6990	−	106.866i	0.493592	−	0.854926i
$26$	−193.871	−	335.795i	−1.46236	−	2.53288i
$27$		0			0
$28$		0			0
$29$		−	151.196i		−	0.968151i	−0.875026	−	0.484075i	$-0.839156\pi$
$29$		−	151.196i		−	0.968151i	0.875026	−	0.484075i	$-0.160844\pi$
$30$		0			0
$31$	−76.3661	−	44.0900i	−0.442444	−	0.255445i	0.262190	−	0.965016i	$-0.415555\pi$
$31$	−76.3661	−	44.0900i	−0.442444	−	0.255445i	−0.704634	+	0.709571i	$0.748889\pi$
$32$	172.988	+	99.8747i	0.955633	+	0.551735i
$33$		0			0
$34$		−	351.790i		−	1.77445i
$35$		0			0
$36$		0			0
$37$	−45.2914	−	78.4470i	−0.201239	−	0.348557i	0.747689	−	0.664050i	$-0.231164\pi$
$37$	−45.2914	−	78.4470i	−0.201239	−	0.348557i	−0.948928	+	0.315493i	$0.897830\pi$
$38$	−110.093	+	190.687i	−0.469987	+	0.814041i
$39$		0			0
$40$	−22.0767	+	12.7460i	−0.0872657	+	0.0503829i
$41$	383.530			1.46091			0.730455	−	0.682961i	$-0.239308\pi$
$41$	383.530			1.46091			0.730455	+	0.682961i	$0.239308\pi$
$42$		0			0
$43$	−227.894			−0.808222			−0.404111	−	0.914710i	$-0.632419\pi$
$43$	−227.894			−0.808222			−0.404111	+	0.914710i	$0.632419\pi$
$44$	−448.630	+	259.017i	−1.53712	+	0.887459i
$45$		0			0
$46$	−205.660	+	356.213i	−0.659192	+	1.14175i
$47$	69.5529	+	120.469i	0.215858	+	0.373877i	0.953538	−	0.301274i	$-0.0974118\pi$
$47$	69.5529	+	120.469i	0.215858	+	0.373877i	−0.737680	+	0.675151i	$0.764078\pi$
$48$		0			0
$49$		0			0
$50$		−	558.072i		−	1.57847i
$51$		0			0
$52$	−924.652	−	533.848i	−2.46589	−	1.42368i
$53$	289.749	+	167.287i	0.750945	+	0.433558i	0.826035	−	0.563619i	$-0.190591\pi$
$53$	289.749	+	167.287i	0.750945	+	0.433558i	−0.0750904	+	0.997177i	$0.523925\pi$
$54$		0			0
$55$			52.6505i			0.129080i
$56$		0			0
$57$		0			0
$58$	−341.895	−	592.179i	−0.774017	−	1.34064i
$59$	−440.050	+	762.189i	−0.971010	+	1.68184i	−0.278493	+	0.960438i	$0.589835\pi$
$59$	−440.050	+	762.189i	−0.971010	+	1.68184i	−0.692518	+	0.721401i	$0.743499\pi$
$60$		0			0
$61$	−11.3944	+	6.57854i	−0.0239164	+	0.0138081i	−0.511911	−	0.859039i	$-0.671062\pi$
$61$	−11.3944	+	6.57854i	−0.0239164	+	0.0138081i	0.487994	+	0.872847i	$0.337729\pi$
$62$	−398.797			−0.816892
$63$		0			0
$64$	835.050			1.63096
$65$	−93.9774	+	54.2579i	−0.179330	+	0.103536i
$66$		0			0
$67$	221.212	−	383.151i	0.403364	−	0.698647i	−0.590766	−	0.806843i	$-0.701174\pi$
$67$	221.212	−	383.151i	0.403364	−	0.698647i	0.994130	+	0.108197i	$0.0345076\pi$
$68$	−484.348	−	838.915i	−0.863762	−	1.49608i
$69$		0			0
$70$		0			0
$71$			341.552i			0.570912i	0.958392	+	0.285456i	$0.0921450\pi$
$71$			341.552i			0.570912i	−0.958392	+	0.285456i	$0.907855\pi$
$72$		0			0
$73$	798.218	+	460.851i	1.27979	+	0.738885i	0.976809	−	0.214113i	$-0.0686862\pi$
$73$	798.218	+	460.851i	1.27979	+	0.738885i	0.302977	+	0.952998i	$0.402019\pi$
$74$	−354.780	−	204.832i	−0.557328	−	0.321774i
$75$		0			0
$76$			606.311i			0.915114i
$77$		0			0
$78$		0			0
$79$	206.564	+	357.780i	0.294181	+	0.509537i	0.974794	−	0.223107i	$-0.0716198\pi$
$79$	206.564	+	357.780i	0.294181	+	0.509537i	−0.680613	+	0.732643i	$0.738286\pi$
$80$	5.40490	−	9.36157i	0.00755358	−	0.0130832i
$81$		0			0
$82$	1502.15	−	867.265i	2.02298	−	1.16797i
$83$	−954.307			−1.26203			−0.631017	−	0.775769i	$-0.717362\pi$
$83$	−954.307			−1.26203			−0.631017	+	0.775769i	$0.717362\pi$
$84$		0			0
$85$	−98.4538			−0.125633
$86$	−892.579	+	515.331i	−1.11918	+	0.646157i
$87$		0			0
$88$	−418.901	+	725.558i	−0.507444	+	0.878918i
$89$	−14.8490	−	25.7193i	−0.0176853	−	0.0306319i	0.857047	−	0.515238i	$-0.172296\pi$
$89$	−14.8490	−	25.7193i	−0.0176853	−	0.0306319i	−0.874733	+	0.484606i	$0.838963\pi$
$90$		0			0
$91$		0			0
$92$			1132.62i			1.28352i
$93$		0			0
$94$	544.826	+	314.556i	0.597814	+	0.345148i
$95$	53.3668	+	30.8113i	0.0576349	+	0.0332755i
$96$		0			0
$97$		−	1199.63i		−	1.25572i	−0.778328	−	0.627858i	$-0.783932\pi$
$97$		−	1199.63i		−	1.25572i	0.778328	−	0.627858i	$-0.216068\pi$
$98$		0			0
$99$		0			0
$100$	−768.360	−	1330.84i	−0.768360	−	1.33084i
$101$	327.422	−	567.111i	0.322571	−	0.558710i	−0.658447	−	0.752628i	$-0.728786\pi$
$101$	327.422	−	567.111i	0.322571	−	0.558710i	0.981018	+	0.193918i	$0.0621195\pi$
$102$		0			0
$103$	1186.01	−	684.744i	1.13457	−	0.655047i	0.189493	−	0.981882i	$-0.439316\pi$
$103$	1186.01	−	684.744i	1.13457	−	0.655047i	0.945081	+	0.326836i	$0.105982\pi$
$104$	−1726.76			−1.62810
$105$		0			0
$106$	1513.12			1.38648
$107$	371.311	−	214.377i	0.335477	−	0.193688i	−0.322793	−	0.946470i	$-0.604622\pi$
$107$	371.311	−	214.377i	0.335477	−	0.193688i	0.658270	+	0.752782i	$0.271289\pi$
$108$		0			0
$109$	334.261	−	578.957i	0.293728	−	0.508752i	−0.680960	−	0.732321i	$-0.738437\pi$
$109$	334.261	−	578.957i	0.293728	−	0.508752i	0.974688	+	0.223568i	$0.0717706\pi$
$110$	119.057	+	206.213i	0.103197	+	0.178742i
$111$		0			0
$112$		0			0
$113$			914.837i			0.761598i	0.924658	+	0.380799i	$0.124351\pi$
$113$			914.837i			0.761598i	−0.924658	+	0.380799i	$0.875649\pi$
$114$		0			0
$115$	99.6917	+	57.5570i	0.0808374	+	0.0466715i
$116$	−1630.64	−	941.449i	−1.30518	−	0.753546i
$117$		0			0
$118$			3980.29i			3.10521i
$119$		0			0
$120$		0			0
$121$	199.690	+	345.873i	0.150030	+	0.259859i
$122$	−29.7517	+	51.5314i	−0.0220786	+	0.0382413i
$123$		0			0
$124$	−951.015	+	549.069i	−0.688739	+	0.397644i
$125$	−314.398			−0.224965
$126$		0			0
$127$	1260.95			0.881034			0.440517	−	0.897744i	$-0.354795\pi$
$127$	1260.95			0.881034			0.440517	+	0.897744i	$0.354795\pi$
$128$	1886.68	−	1089.28i	1.30282	−	0.752182i
$129$		0			0
$130$	−245.383	+	425.016i	−0.165550	+	0.286742i
$131$	683.600	+	1184.03i	0.455926	+	0.789688i	0.998741	−	0.0501648i	$-0.0159747\pi$
$131$	683.600	+	1184.03i	0.455926	+	0.789688i	−0.542814	+	0.839853i	$0.682641\pi$
$132$		0			0
$133$		0			0
$134$		−	2000.88i		−	1.28992i
$135$		0			0
$136$	−1356.76	−	783.325i	−0.855449	−	0.493894i
$137$	953.631	+	550.579i	0.594702	+	0.343351i	0.766955	−	0.641701i	$-0.221771\pi$
$137$	953.631	+	550.579i	0.594702	+	0.343351i	−0.172252	+	0.985053i	$0.555104\pi$
$138$		0			0
$139$		−	2306.56i		−	1.40748i	−0.710458	−	0.703739i	$-0.751512\pi$
$139$		−	2306.56i		−	1.40748i	0.710458	−	0.703739i	$-0.248488\pi$
$140$		0			0
$141$		0			0
$142$	772.341	+	1337.73i	0.456432	+	0.790564i
$143$	−1783.21	+	3088.60i	−1.04279	+	1.80617i
$144$		0			0
$145$	−165.730	+	95.6845i	−0.0949184	+	0.0548012i
$146$	4168.44			2.36289
$147$		0			0
$148$	−1128.06			−0.626527
$149$	−1520.57	+	877.901i	−0.836040	+	0.482688i	−0.855916	−	0.517115i	$-0.827006\pi$
$149$	−1520.57	+	877.901i	−0.836040	+	0.482688i	0.0198764	+	0.999802i	$0.493673\pi$
$150$		0			0
$151$	262.491	−	454.647i	0.141465	−	0.245024i	−0.786584	−	0.617484i	$-0.788152\pi$
$151$	262.491	−	454.647i	0.141465	−	0.245024i	0.928048	+	0.372460i	$0.121485\pi$
$152$	490.286	+	849.201i	0.261628	+	0.453153i
$153$		0			0
$154$		0			0
$155$			111.610i			0.0578368i
$156$		0			0
$157$	1141.44	+	659.009i	0.580233	+	0.334998i	0.761226	−	0.648487i	$-0.224598\pi$
$157$	1141.44	+	659.009i	0.580233	+	0.334998i	−0.180993	+	0.983484i	$0.557931\pi$
$158$	1618.07	+	934.195i	0.814728	+	0.470384i
$159$		0			0
$160$		−	252.823i		−	0.124921i
$161$		0			0
$162$		0			0
$163$	223.916	+	387.834i	0.107598	+	0.186365i	0.914797	−	0.403915i	$-0.132351\pi$
$163$	223.916	+	387.834i	0.107598	+	0.186365i	−0.807199	+	0.590280i	$0.799017\pi$
$164$	2388.12	−	4136.35i	1.13708	−	1.96948i
$165$		0			0
$166$	−3737.67	+	2157.95i	−1.74759	+	1.00897i
$167$	811.124			0.375848			0.187924	−	0.982184i	$-0.439824\pi$
$167$	811.124			0.375848			0.187924	+	0.982184i	$0.439824\pi$
$168$		0			0
$169$	−5153.58			−2.34574
$170$	−385.608	+	222.631i	−0.173969	+	0.100441i
$171$		0			0
$172$	−1419.03	+	2457.82i	−0.629068	+	1.08958i
$173$	1121.24	+	1942.04i	0.492751	+	0.853470i	0.999965	−	0.00834994i	$-0.00265790\pi$
$173$	1121.24	+	1942.04i	0.492751	+	0.853470i	−0.507214	+	0.861820i	$0.669325\pi$
$174$		0			0
$175$		0			0
$176$		−	355.269i		−	0.152156i
$177$		0			0
$178$	−116.317	−	67.1554i	−0.0489792	−	0.0282781i
$179$	2531.77	+	1461.72i	1.05717	+	0.610357i	0.924648	−	0.380824i	$-0.124359\pi$
$179$	2531.77	+	1461.72i	1.05717	+	0.610357i	0.132521	+	0.991180i	$0.457693\pi$
$180$		0			0
$181$			282.859i			0.116159i	0.998312	+	0.0580794i	$0.0184977\pi$
$181$			282.859i			0.116159i	−0.998312	+	0.0580794i	$0.981502\pi$
$182$		0			0
$183$		0			0
$184$	915.878	+	1586.35i	0.366953	+	0.635582i
$185$	−57.3255	+	99.2906i	−0.0227819	+	0.0394594i
$186$		0			0
$187$	−2802.22	+	1617.86i	−1.09582	+	0.632672i
$188$	1732.34			0.672040
$189$		0			0
$190$	278.691			0.106412
$191$	3998.63	−	2308.61i	1.51482	−	0.874582i	0.514971	−	0.857208i	$-0.327803\pi$
$191$	3998.63	−	2308.61i	1.51482	−	0.874582i	0.999849	−	0.0173741i	$-0.00553064\pi$
$192$		0			0
$193$	2077.73	−	3598.73i	0.774912	−	1.34219i	−0.159933	−	0.987128i	$-0.551128\pi$
$193$	2077.73	−	3598.73i	0.774912	−	1.34219i	0.934844	−	0.355058i	$-0.115539\pi$
$194$	−2712.70	−	4698.53i	−1.00392	−	1.73884i
$195$		0			0
$196$		0			0
$197$			1626.36i			0.588190i	0.955776	+	0.294095i	$0.0950183\pi$
$197$			1626.36i			0.588190i	−0.955776	+	0.294095i	$0.904982\pi$
$198$		0			0
$199$	−150.861	−	87.0995i	−0.0537399	−	0.0310267i	0.472889	−	0.881122i	$-0.343211\pi$
$199$	−150.861	−	87.0995i	−0.0537399	−	0.0310267i	−0.526629	+	0.850095i	$0.676544\pi$
$200$	−2152.33	−	1242.65i	−0.760965	−	0.439344i
$201$		0			0
$202$		−	2961.56i		−	1.03156i
$203$		0			0
$204$		0			0
$205$	−242.718	−	420.399i	−0.0826933	−	0.143229i
$206$	3096.78	−	5363.78i	1.04739	−	1.81414i
$207$		0			0
$208$	634.129	−	366.115i	0.211389	−	0.122046i
$209$	2025.25			0.670286
$210$		0			0
$211$	−2942.35			−0.959999			−0.479999	−	0.877269i	$-0.659363\pi$
$211$	−2942.35			−0.959999			−0.479999	+	0.877269i	$0.659363\pi$
$212$	3608.35	−	2083.28i	1.16897	−	0.674907i
$213$		0			0
$214$	969.527	−	1679.27i	0.309699	−	0.536414i
$215$	144.223	+	249.802i	0.0457486	+	0.0792389i
$216$		0			0
$217$		0			0
$218$		−	3023.42i		−	0.939319i
$219$		0			0
$220$	567.832	+	327.838i	0.174015	+	0.100467i
$221$	−5775.53	−	3334.51i	−1.75794	−	1.01495i
$222$		0			0
$223$		−	3374.75i		−	1.01341i	−0.862120	−	0.506704i	$-0.830864\pi$
$223$		−	3374.75i		−	1.01341i	0.862120	−	0.506704i	$-0.169136\pi$
$224$		0			0
$225$		0			0
$226$	2068.69	+	3583.08i	0.608882	+	1.05461i
$227$	1515.43	−	2624.79i	0.443094	−	0.767461i	−0.554823	−	0.831968i	$-0.687214\pi$
$227$	1515.43	−	2624.79i	0.443094	−	0.767461i	0.997917	+	0.0645069i	$0.0205475\pi$
$228$		0			0
$229$	−960.030	+	554.274i	−0.277033	+	0.159945i	−0.632080	−	0.774904i	$-0.717798\pi$
$229$	−960.030	+	554.274i	−0.277033	+	0.159945i	0.355046	+	0.934849i	$0.384465\pi$
$230$	520.608			0.149252
$231$		0			0
$232$	−3045.17			−0.861746
$233$	−2684.57	+	1549.94i	−0.754815	+	0.435793i	−0.827431	−	0.561567i	$-0.810199\pi$
$233$	−2684.57	+	1549.94i	−0.754815	+	0.435793i	0.0726160	+	0.997360i	$0.476865\pi$
$234$		0			0
$235$	88.0333	−	152.478i	0.0244368	−	0.0423259i
$236$	5480.10	+	9491.82i	1.51154	+	2.61807i
$237$		0			0
$238$		0			0
$239$		−	1735.25i		−	0.469640i	−0.972039	−	0.234820i	$-0.924550\pi$
$239$		−	1735.25i		−	0.469640i	0.972039	−	0.234820i	$-0.0754501\pi$
$240$		0			0
$241$	1039.26	+	600.019i	0.277779	+	0.160376i	0.632418	−	0.774628i	$-0.282063\pi$
$241$	1039.26	+	600.019i	0.277779	+	0.160376i	−0.354638	+	0.935004i	$0.615396\pi$
$242$	1564.22	+	903.104i	0.415504	+	0.239892i
$243$		0			0
$244$			163.850i			0.0429894i
$245$		0			0
$246$		0			0
$247$	2087.08	+	3614.93i	0.537643	+	0.931225i
$248$	−887.996	+	1538.05i	−0.227370	+	0.393817i
$249$		0			0
$250$	−1231.38	+	710.939i	−0.311518	+	0.179855i
$251$	−3712.56			−0.933603			−0.466802	−	0.884362i	$-0.654594\pi$
$251$	−3712.56			−0.933603			−0.466802	+	0.884362i	$0.654594\pi$
$252$		0			0
$253$	3783.27			0.940126
$254$	4938.69	−	2851.35i	1.22000	−	0.704369i
$255$		0			0
$256$	1586.09	−	2747.20i	0.387230	−	0.670702i
$257$	−389.574	−	674.762i	−0.0945563	−	0.163776i	0.814867	−	0.579648i	$-0.196810\pi$
$257$	−389.574	−	674.762i	−0.0945563	−	0.163776i	−0.909423	+	0.415872i	$0.863477\pi$
$258$		0			0
$259$		0			0
$260$			1351.39i			0.322344i
$261$		0			0
$262$	5354.82	+	3091.61i	1.26268	+	0.729008i
$263$	−1702.07	−	982.690i	−0.399065	−	0.230400i	0.287015	−	0.957926i	$-0.407337\pi$
$263$	−1702.07	−	982.690i	−0.399065	−	0.230400i	−0.686080	+	0.727526i	$0.740670\pi$
$264$		0			0
$265$		−	423.470i		−	0.0981644i
$266$		0			0
$267$		0			0
$268$	−2754.84	−	4771.52i	−0.627905	−	1.08756i
$269$	−1236.41	+	2141.53i	−0.280243	+	0.485395i	−0.971444	−	0.237267i	$-0.923748\pi$
$269$	−1236.41	+	2141.53i	−0.280243	+	0.485395i	0.691201	+	0.722662i	$0.257082\pi$
$270$		0			0
$271$	−4095.79	+	2364.71i	−0.918088	+	0.530058i	−0.883025	−	0.469327i	$-0.844497\pi$
$271$	−4095.79	+	2364.71i	−0.918088	+	0.530058i	−0.0350633	+	0.999385i	$0.511163\pi$
$272$	664.334			0.148093
$273$		0			0
$274$	4980.03			1.09801
$275$	−4445.39	+	2566.54i	−0.974788	+	0.562794i
$276$		0			0
$277$	−586.579	+	1015.98i	−0.127235	+	0.220378i	−0.922604	−	0.385747i	$-0.873944\pi$
$277$	−586.579	+	1015.98i	−0.127235	+	0.220378i	0.795369	+	0.606125i	$0.207277\pi$
$278$	−5215.74	−	9033.93i	−1.12525	−	1.94899i
$279$		0			0
$280$		0			0
$281$			8195.18i			1.73980i	0.493229	+	0.869899i	$0.335816\pi$
$281$			8195.18i			1.73980i	−0.493229	+	0.869899i	$0.664184\pi$
$282$		0			0
$283$	−2242.44	−	1294.67i	−0.471021	−	0.271944i	0.245646	−	0.969360i	$-0.421000\pi$
$283$	−2242.44	−	1294.67i	−0.471021	−	0.271944i	−0.716667	+	0.697415i	$0.754333\pi$
$284$	3683.61	+	2126.74i	0.769656	+	0.444361i
$285$		0			0
$286$			16129.2i			3.33476i
$287$		0			0
$288$		0			0
$289$	−568.820	−	985.225i	−0.115779	−	0.200534i
$290$	−432.737	+	749.523i	−0.0876248	+	0.151771i
$291$		0			0
$292$	9940.50	−	5739.15i	1.99221	−	1.15020i
$293$	−8871.16			−1.76880			−0.884400	−	0.466729i	$-0.845432\pi$
$293$	−8871.16			−1.76880			−0.884400	+	0.466729i	$0.845432\pi$
$294$		0			0
$295$	1113.94			0.219852
$296$	−1579.96	+	912.193i	−0.310249	+	0.179122i
$297$		0			0
$298$	−3970.34	+	6876.84i	−0.771798	+	1.33679i
$299$	3898.77	+	6752.86i	0.754085	+	1.30611i
$300$		0			0
$301$		0			0
$302$		−	2374.25i		−	0.452393i
$303$		0			0
$304$	−360.102	−	207.905i	−0.0679383	−	0.0392242i
$305$	14.4219	+	8.32647i	0.00270752	+	0.00156319i
$306$		0			0
$307$			2707.52i			0.503344i	0.967813	+	0.251672i	$0.0809804\pi$
$307$			2707.52i			0.503344i	−0.967813	+	0.251672i	$0.919020\pi$
$308$		0			0
$309$		0			0
$310$	252.379	+	437.134i	0.0462393	+	0.0800889i
$311$	−1080.55	+	1871.56i	−0.197017	+	0.341243i	−0.947560	−	0.319579i	$-0.896459\pi$
$311$	−1080.55	+	1871.56i	−0.197017	+	0.341243i	0.750543	+	0.660822i	$0.229792\pi$
$312$		0			0
$313$	7300.25	−	4214.80i	1.31832	−	0.761133i	0.334863	−	0.942267i	$-0.391310\pi$
$313$	7300.25	−	4214.80i	1.31832	−	0.761133i	0.983459	+	0.181133i	$0.0579766\pi$
$314$	5960.79			1.07130
$315$		0			0
$316$	5144.84			0.915886
$317$	8310.07	−	4797.82i	1.47237	−	0.850071i	0.472848	−	0.881144i	$-0.343226\pi$
$317$	8310.07	−	4797.82i	1.47237	−	0.850071i	0.999517	+	0.0310734i	$0.00989256\pi$
$318$		0			0
$319$	−3144.71	+	5446.80i	−0.551943	+	0.955994i
$320$	−528.463	−	915.324i	−0.0923186	−	0.159901i
$321$		0			0
$322$		0			0
$323$			3787.12i			0.652387i
$324$		0			0
$325$	−9162.20	−	5289.80i	−1.56378	−	0.902847i
$326$	1753.99	+	1012.67i	0.297990	+	0.172045i
$327$		0			0
$328$		−	7724.50i		−	1.30035i
$329$		0			0
$330$		0			0
$331$	−4271.96	−	7399.25i	−0.709390	−	1.22870i	−0.965084	−	0.261941i	$-0.915637\pi$
$331$	−4271.96	−	7399.25i	−0.709390	−	1.22870i	0.255694	−	0.966758i	$-0.417696\pi$
$332$	−5942.17	+	10292.1i	−0.982286	+	1.70137i
$333$		0			0
$334$	3176.88	−	1834.17i	0.520452	−	0.300483i
$335$	−559.978			−0.0913280
$336$		0			0
$337$	598.875			0.0968036			0.0484018	−	0.998828i	$-0.484587\pi$
$337$	598.875			0.0968036			0.0484018	+	0.998828i	$0.484587\pi$
$338$	−20184.7	+	11653.6i	−3.24823	+	1.87537i
$339$		0			0
$340$	−613.041	+	1061.82i	−0.0977847	+	0.169368i
$341$	1834.05	+	3176.66i	0.291259	+	0.504475i
$342$		0			0
$343$		0			0
$344$			4589.91i			0.719394i
$345$		0			0
$346$	8782.94	+	5070.83i	1.36466	+	0.787889i
$347$	6149.62	+	3550.49i	0.951381	+	0.549280i	0.893510	−	0.449044i	$-0.148235\pi$
$347$	6149.62	+	3550.49i	0.951381	+	0.549280i	0.0578712	+	0.998324i	$0.481569\pi$
$348$		0			0
$349$			3620.71i			0.555336i	0.960677	+	0.277668i	$0.0895616\pi$
$349$			3620.71i			0.555336i	−0.960677	+	0.277668i	$0.910438\pi$
$350$		0			0
$351$		0			0
$352$	−4154.57	−	7195.92i	−0.629089	−	1.08961i
$353$	1164.89	−	2017.64i	0.175639	−	0.304216i	−0.764743	−	0.644335i	$-0.777134\pi$
$353$	1164.89	−	2017.64i	0.175639	−	0.304216i	0.940382	+	0.340119i	$0.110467\pi$
$354$		0			0
$355$	374.386	−	216.152i	0.0559727	−	0.0323159i
$356$	−369.841			−0.0550605
$357$		0			0
$358$	13221.3			1.95187
$359$	1522.43	−	878.975i	0.223818	−	0.129222i	−0.383899	−	0.923375i	$-0.625419\pi$
$359$	1522.43	−	878.975i	0.223818	−	0.129222i	0.607717	+	0.794154i	$0.292086\pi$
$360$		0			0
$361$	−2244.31	+	3887.26i	−0.327207	+	0.566739i
$362$	639.621	+	1107.86i	0.0928667	+	0.160850i
$363$		0			0
$364$		0			0
$365$		−	1166.60i		−	0.167295i
$366$		0			0
$367$	−1458.89	−	842.290i	−0.207503	−	0.119802i	0.392648	−	0.919689i	$-0.371559\pi$
$367$	−1458.89	−	842.290i	−0.207503	−	0.119802i	−0.600150	+	0.799887i	$0.704893\pi$
$368$	−672.687	−	388.376i	−0.0952887	−	0.0550150i
$369$		0			0
$370$			518.513i			0.0728547i
$371$		0			0
$372$		0			0
$373$	148.646	+	257.462i	0.0206343	+	0.0357397i	0.876158	−	0.482024i	$-0.160098\pi$
$373$	148.646	+	257.462i	0.0206343	+	0.0357397i	−0.855524	+	0.517763i	$0.826765\pi$
$374$	−7316.84	+	12673.1i	−1.01162	+	1.75217i
$375$		0			0
$376$	2426.31	−	1400.83i	0.332786	−	0.192134i
$377$	−12962.9			−1.77088
$378$		0			0
$379$	−7402.78			−1.00331			−0.501656	−	0.865067i	$-0.667276\pi$
$379$	−7402.78			−1.00331			−0.501656	+	0.865067i	$0.667276\pi$
$380$	664.596	−	383.705i	0.0897186	−	0.0517991i
$381$		0			0
$382$	10440.8	−	18084.0i	1.39842	−	2.42214i
$383$	−6263.77	−	10849.2i	−0.835676	−	1.44743i	−0.893479	−	0.449105i	$-0.851743\pi$
$383$	−6263.77	−	10849.2i	−0.835676	−	1.44743i	0.0578031	−	0.998328i	$-0.481590\pi$
$384$		0			0
$385$		0			0
$386$		−	18793.2i		−	2.47810i
$387$		0			0
$388$	−12938.0	−	7469.75i	−1.69285	−	0.977368i
$389$	−6904.14	−	3986.11i	−0.899881	−	0.519547i	−0.0227196	−	0.999742i	$-0.507233\pi$
$389$	−6904.14	−	3986.11i	−0.899881	−	0.519547i	−0.877162	+	0.480195i	$0.840566\pi$
$390$		0			0
$391$			7074.52i			0.915023i
$392$		0			0
$393$		0			0
$394$	3677.64	+	6369.87i	0.470246	+	0.814491i
$395$	261.449	−	452.843i	0.0333036	−	0.0576836i
$396$		0			0
$397$	−10832.5	+	6254.16i	−1.36944	+	0.790648i	−0.990857	−	0.134918i	$-0.956923\pi$
$397$	−10832.5	+	6254.16i	−1.36944	+	0.790648i	−0.378586	+	0.925566i	$0.623590\pi$
$398$	−787.822			−0.0992210
$399$		0			0
$400$	1053.89			0.131736
$401$	6943.55	−	4008.86i	0.864699	−	0.499234i	−0.000883860	−	1.00000i	$-0.500281\pi$
$401$	6943.55	−	4008.86i	0.864699	−	0.499234i	0.865583	+	0.500765i	$0.166948\pi$
$402$		0			0
$403$	−3780.08	+	6547.29i	−0.467243	+	0.809289i
$404$	−4077.51	−	7062.45i	−0.502137	−	0.869728i
$405$		0			0
$406$		0			0
$407$			3768.05i			0.458907i
$408$		0			0
$409$	7566.04	+	4368.26i	0.914711	+	0.528109i	0.881944	−	0.471354i	$-0.156235\pi$
$409$	7566.04	+	4368.26i	0.914711	+	0.528109i	0.0327670	+	0.999463i	$0.489568\pi$
$410$	−1901.27	−	1097.70i	−0.229017	−	0.132223i
$411$		0			0
$412$		−	17054.7i		−	2.03938i
$413$		0			0
$414$		0			0
$415$	603.935	+	1046.05i	0.0714361	+	0.123731i
$416$	8562.81	−	14831.2i	1.00920	−	1.74798i
$417$		0			0
$418$	7932.18	−	4579.64i	0.928171	−	0.535880i
$419$	3926.67			0.457829			0.228914	−	0.973447i	$-0.426482\pi$
$419$	3926.67			0.457829			0.228914	+	0.973447i	$0.426482\pi$
$420$		0			0
$421$	1443.44			0.167100			0.0835499	−	0.996504i	$-0.473374\pi$
$421$	1443.44			0.167100			0.0835499	+	0.996504i	$0.473374\pi$
$422$	−11524.1	+	6653.45i	−1.32935	+	0.767500i
$423$		0			0
$424$	3369.24	−	5835.70i	0.385908	−	0.668412i
$425$	−4799.31	−	8312.65i	−0.547766	−	0.948759i
$426$		0			0
$427$		0			0
$428$		−	5339.42i		−	0.603016i
$429$		0			0
$430$	1129.74	+	652.255i	0.126700	+	0.0731501i
$431$	−12820.5	−	7401.92i	−1.43281	−	0.827234i	−0.435477	−	0.900200i	$-0.643420\pi$
$431$	−12820.5	−	7401.92i	−1.43281	−	0.827234i	−0.997334	+	0.0729655i	$0.976754\pi$
$432$		0			0
$433$		−	15872.1i		−	1.76158i	−0.473508	−	0.880790i	$-0.657012\pi$
$433$		−	15872.1i		−	1.76158i	0.473508	−	0.880790i	$-0.342988\pi$
$434$		0			0
$435$		0			0
$436$	−4162.67	−	7209.96i	−0.457238	−	0.791960i
$437$	2213.99	−	3834.74i	0.242356	−	0.419772i
$438$		0			0
$439$	2626.58	−	1516.45i	0.285557	−	0.164867i	−0.350379	−	0.936608i	$-0.613947\pi$
$439$	2626.58	−	1516.45i	0.285557	−	0.164867i	0.635937	+	0.771741i	$0.280614\pi$
$440$	1060.41			0.114893
$441$		0			0
$442$	−30160.9			−3.24572
$443$	−11126.8	+	6424.08i	−1.19334	+	0.688978i	−0.959064	−	0.283191i	$-0.908607\pi$
$443$	−11126.8	+	6424.08i	−1.19334	+	0.688978i	−0.234281	+	0.972169i	$0.575274\pi$
$444$		0			0
$445$	−18.7945	+	32.5530i	−0.00200212	+	0.00346777i
$446$	−7631.22	−	13217.7i	−0.810199	−	1.40331i
$447$		0			0
$448$		0			0
$449$			107.668i			0.0113166i	0.999984	+	0.00565831i	$0.00180111\pi$
$449$			107.668i			0.0113166i	−0.999984	+	0.00565831i	$0.998199\pi$
$450$		0			0
$451$	−13816.6	−	7977.01i	−1.44257	−	0.832866i
$452$	9866.45	+	5696.40i	1.02672	+	0.592779i
$453$		0			0
$454$		−	13707.1i		−	1.41698i
$455$		0			0
$456$		0			0
$457$	4888.53	+	8467.18i	0.500385	+	0.866691i	1.00000		0.000444115i	$0.000141366\pi$
$457$	4888.53	+	8467.18i	0.500385	+	0.866691i	−0.499615	+	0.866247i	$0.666525\pi$
$458$	−2506.72	+	4341.77i	−0.255746	+	0.442965i
$459$		0			0
$460$	1241.50	−	716.779i	0.125837	−	0.0726521i
$461$	−638.874			−0.0645452			−0.0322726	−	0.999479i	$-0.510274\pi$
$461$	−638.874			−0.0645452			−0.0322726	+	0.999479i	$0.510274\pi$
$462$		0			0
$463$	−5602.26			−0.562331			−0.281165	−	0.959659i	$-0.590721\pi$
$463$	−5602.26			−0.562331			−0.281165	+	0.959659i	$0.590721\pi$
$464$	1118.30	−	645.648i	0.111887	−	0.0645980i
$465$		0			0
$466$	−7009.65	+	12141.1i	−0.696815	+	1.20692i
$467$	2759.44	+	4779.49i	0.273430	+	0.473594i	0.969738	−	0.244149i	$-0.0785086\pi$
$467$	2759.44	+	4779.49i	0.273430	+	0.473594i	−0.696308	+	0.717743i	$0.745175\pi$
$468$		0			0
$469$		0			0
$470$		−	796.268i		−	0.0781470i
$471$		0			0
$472$	15350.9	+	8862.84i	1.49700	+	0.864291i
$473$	8209.84	+	4739.95i	0.798074	+	0.460768i
$474$		0			0
$475$			6007.82i			0.580332i
$476$		0			0
$477$		0			0
$478$	−3923.87	−	6796.34i	−0.375468	−	0.650329i
$479$	2734.40	−	4736.11i	0.260830	−	0.451771i	−0.705632	−	0.708578i	$-0.749337\pi$
$479$	2734.40	−	4736.11i	0.260830	−	0.451771i	0.966463	+	0.256807i	$0.0826703\pi$
$480$		0			0
$481$	−6725.70	+	3883.08i	−0.637558	+	0.368094i
$482$	5427.22			0.512869
$483$		0			0
$484$	4973.62			0.467094
$485$	−1314.96	+	759.190i	−0.123112	+	0.0710785i
$486$		0			0
$487$	5866.72	−	10161.5i	0.545886	−	0.945502i	−0.452665	−	0.891681i	$-0.649527\pi$
$487$	5866.72	−	10161.5i	0.545886	−	0.945502i	0.998551	−	0.0538213i	$-0.0171401\pi$
$488$	132.495	+	229.489i	0.0122905	+	0.0212878i
$489$		0			0
$490$		0			0
$491$			3514.92i			0.323068i	0.986867	+	0.161534i	$0.0516441\pi$
$491$			3514.92i			0.323068i	−0.986867	+	0.161534i	$0.948356\pi$
$492$		0			0
$493$	−10185.2	−	5880.45i	−0.930467	−	0.537205i
$494$	16348.7	+	9438.91i	1.48899	+	0.859670i
$495$		0			0
$496$		−	753.106i		−	0.0681763i
$497$		0			0
$498$		0			0
$499$	−4944.49	−	8564.11i	−0.443579	−	0.768301i	0.554373	−	0.832268i	$-0.312958\pi$
$499$	−4944.49	−	8564.11i	−0.443579	−	0.768301i	−0.997952	+	0.0639672i	$0.979625\pi$
$500$	−1957.66	+	3390.76i	−0.175098	+	0.303279i
$501$		0			0
$502$	−14540.7	+	8395.09i	−1.29280	+	0.746397i
$503$	10172.2			0.901698			0.450849	−	0.892600i	$-0.351121\pi$
$503$	10172.2			0.901698			0.450849	+	0.892600i	$0.351121\pi$
$504$		0			0
$505$	−828.838			−0.0730353
$506$	14817.7	−	8554.99i	1.30183	−	0.751612i
$507$		0			0
$508$	7851.55	−	13599.3i	0.685740	−	1.18774i
$509$	2149.56	+	3723.15i	0.187186	+	0.324216i	0.944311	−	0.329054i	$-0.106730\pi$
$509$	2149.56	+	3723.15i	0.187186	+	0.324216i	−0.757125	+	0.653270i	$0.773397\pi$
$510$		0			0
$511$		0			0
$512$			3082.06i			0.266033i
$513$		0			0
$514$	−3051.64	−	1761.86i	−0.261872	−	0.151192i
$515$	−1501.14	−	866.682i	−0.128443	−	0.0741565i
$516$		0			0
$517$		−	5786.50i		−	0.492243i
$518$		0			0
$519$		0			0
$520$	1092.78	+	1892.76i	0.0921571	+	0.159621i
$521$	5496.48	−	9520.18i	0.462198	−	0.800550i	−0.536872	−	0.843664i	$-0.680394\pi$
$521$	5496.48	−	9520.18i	0.462198	−	0.800550i	0.999070	+	0.0431133i	$0.0137276\pi$
$522$		0			0
$523$	−7386.80	+	4264.77i	−0.617595	+	0.356569i	−0.775932	−	0.630817i	$-0.782720\pi$
$523$	−7386.80	+	4264.77i	−0.617595	+	0.356569i	0.158337	+	0.987385i	$0.449387\pi$
$524$	17026.2			1.41946
$525$		0			0
$526$	−8888.51			−0.736801
$527$	−5940.20	+	3429.58i	−0.491004	+	0.283481i
$528$		0			0
$529$	−1947.67	+	3373.46i	−0.160078	+	0.277263i
$530$	−957.581	−	1658.58i	−0.0784805	−	0.135932i
$531$		0			0
$532$		0			0
$533$		−	32882.2i		−	2.67220i
$534$		0			0
$535$	−469.970	−	271.337i	−0.0379786	−	0.0219270i
$536$	−7716.86	−	4455.33i	−0.621862	−	0.359032i
$537$		0			0
$538$			11183.4i			0.896195i
$539$		0			0
$540$		0			0
$541$	4352.93	+	7539.49i	0.345928	+	0.599165i	0.985522	−	0.169548i	$-0.0542308\pi$
$541$	4352.93	+	7539.49i	0.345928	+	0.599165i	−0.639594	+	0.768713i	$0.720897\pi$
$542$	−10694.5	+	18523.4i	−0.847542	+	1.46799i
$543$		0			0
$544$	13456.0	−	7768.84i	1.06052	−	0.612291i
$545$	−846.150			−0.0665047
$546$		0			0
$547$	17183.8			1.34319			0.671596	−	0.740917i	$-0.265609\pi$
$547$	17183.8			1.34319			0.671596	+	0.740917i	$0.265609\pi$
$548$	11875.9	−	6856.56i	0.925756	−	0.534485i
$549$		0			0
$550$	−11607.3	+	20104.4i	−0.899885	+	1.55865i
$551$	3680.60	+	6374.99i	0.284571	+	0.492892i
$552$		0			0
$553$		0			0
$554$			5305.66i			0.406888i
$555$		0			0
$556$	−24876.0	−	14362.2i	−1.89744	−	1.09549i
$557$	−8989.79	−	5190.26i	−0.683859	−	0.394826i	0.117448	−	0.993079i	$-0.462529\pi$
$557$	−8989.79	−	5190.26i	−0.683859	−	0.394826i	−0.801307	+	0.598253i	$0.795862\pi$
$558$		0			0
$559$			19538.6i			1.47835i
$560$		0			0
$561$		0			0
$562$	18531.5	+	32097.5i	1.39093	+	2.40917i
$563$	−9248.22	+	16018.4i	−0.692302	+	1.19910i	0.278780	+	0.960355i	$0.410070\pi$
$563$	−9248.22	+	16018.4i	−0.692302	+	1.19910i	−0.971082	+	0.238747i	$0.923263\pi$
$564$		0			0
$565$	1002.78	−	578.956i	0.0746678	−	0.0431095i
$566$	−11710.4			−0.869656
$567$		0			0
$568$	6879.04			0.508166
$569$	−3493.45	+	2016.94i	−0.257386	+	0.148602i	−0.623142	−	0.782109i	$-0.714144\pi$
$569$	−3493.45	+	2016.94i	−0.257386	+	0.148602i	0.365755	+	0.930711i	$0.380811\pi$
$570$		0			0
$571$	−6430.01	+	11137.1i	−0.471257	+	0.816241i	−0.999459	−	0.0328777i	$-0.989533\pi$
$571$	−6430.01	+	11137.1i	−0.471257	+	0.816241i	0.528203	+	0.849118i	$0.322866\pi$
$572$	22206.9	+	38463.5i	1.62328	+	2.81161i
$573$		0			0
$574$		0			0
$575$			11222.9i			0.813959i
$576$		0			0
$577$	17669.2	+	10201.3i	1.27483	+	0.736026i	0.975894	−	0.218246i	$-0.0700335\pi$
$577$	17669.2	+	10201.3i	1.27483	+	0.736026i	0.298940	+	0.954272i	$0.403367\pi$
$578$	−4455.72	−	2572.51i	−0.320646	−	0.185125i
$579$		0			0
$580$			2383.19i			0.170615i
$581$		0			0
$582$		0			0
$583$	−6958.76	−	12052.9i	−0.494344	−	0.856228i
$584$	9281.80	−	16076.5i	0.657677	−	1.13913i
$585$		0			0
$586$	−34745.1	+	20060.1i	−2.44933	+	1.41412i
$587$	16279.7			1.14470			0.572348	−	0.820011i	$-0.306033\pi$
$587$	16279.7			1.14470			0.572348	+	0.820011i	$0.306033\pi$
$588$		0			0
$589$	4293.17			0.300335
$590$	4362.91	−	2518.93i	0.304438	−	0.175767i
$591$		0			0
$592$	386.814	−	669.981i	0.0268546	−	0.0465136i
$593$	−1342.16	−	2324.68i	−0.0929440	−	0.160984i	0.815805	−	0.578328i	$-0.196294\pi$
$593$	−1342.16	−	2324.68i	−0.0929440	−	0.160984i	−0.908749	+	0.417344i	$0.862961\pi$
$594$		0			0
$595$		0			0
$596$			21865.7i			1.50277i
$597$		0			0
$598$	30540.1	+	17632.3i	2.08842	+	1.20575i
$599$	12224.6	+	7057.90i	0.833865	+	0.481432i	0.855174	−	0.518341i	$-0.173450\pi$
$599$	12224.6	+	7057.90i	0.833865	+	0.481432i	−0.0213091	+	0.999773i	$0.506783\pi$
$600$		0			0
$601$			11096.1i			0.753109i	0.926394	+	0.376555i	$0.122891\pi$
$601$			11096.1i			0.753109i	−0.926394	+	0.376555i	$0.877109\pi$
$602$		0			0
$603$		0			0
$604$	−3268.89	−	5661.89i	−0.220214	−	0.381422i
$605$	252.748	−	437.772i	0.0169846	−	0.0294181i
$606$		0			0
$607$	9592.70	−	5538.35i	0.641442	−	0.370337i	−0.143728	−	0.989617i	$-0.545909\pi$
$607$	9592.70	−	5538.35i	0.641442	−	0.370337i	0.785170	+	0.619280i	$0.212576\pi$
$608$	−9725.10			−0.648692
$609$		0			0
$610$	75.3136			0.00499895
$611$	10328.5	−	5963.15i	0.683872	−	0.394834i
$612$		0			0
$613$	3801.34	−	6584.11i	0.250464	−	0.433817i	−0.713189	−	0.700971i	$-0.752750\pi$
$613$	3801.34	−	6584.11i	0.250464	−	0.433817i	0.963654	+	0.267154i	$0.0860834\pi$
$614$	6122.44	+	10604.4i	0.402413	+	0.697000i
$615$		0			0
$616$		0			0
$617$			11325.9i			0.738998i	0.929231	+	0.369499i	$0.120471\pi$
$617$			11325.9i			0.738998i	−0.929231	+	0.369499i	$0.879529\pi$
$618$		0			0
$619$	16595.2	+	9581.22i	1.07757	+	0.622136i	0.930240	−	0.366952i	$-0.119599\pi$
$619$	16595.2	+	9581.22i	1.07757	+	0.622136i	0.147330	+	0.989087i	$0.452932\pi$
$620$	1203.70	+	694.958i	0.0779707	+	0.0450164i
$621$		0			0
$622$			9773.64i			0.630044i
$623$		0			0
$624$		0			0
$625$	−7513.41	−	13013.6i	−0.480858	−	0.832871i
$626$	19061.6	−	33015.7i	1.21702	−	2.10794i
$627$		0			0
$628$	14214.7	−	8206.88i	0.903232	−	0.521481i
$629$	−7046.06			−0.446653
$630$		0			0
$631$	10140.7			0.639768			0.319884	−	0.947457i	$-0.396356\pi$
$631$	10140.7			0.639768			0.319884	+	0.947457i	$0.396356\pi$
$632$	7205.88	−	4160.32i	0.453536	−	0.261849i
$633$		0			0
$634$	21698.3	−	37582.6i	1.35923	−	2.35425i
$635$	−797.995	−	1382.17i	−0.0498700	−	0.0863774i
$636$		0			0
$637$		0			0
$638$			28444.2i			1.76507i
$639$		0			0
$640$	−2387.98	−	1378.70i	−0.147489	−	0.0851530i
$641$	−2950.66	−	1703.56i	−0.181816	−	0.104972i	0.406330	−	0.913727i	$-0.366808\pi$
$641$	−2950.66	−	1703.56i	−0.181816	−	0.104972i	−0.588146	+	0.808755i	$0.700142\pi$
$642$		0			0
$643$			659.110i			0.0404242i	0.999796	+	0.0202121i	$0.00643415\pi$
$643$			659.110i			0.0404242i	−0.999796	+	0.0202121i	$0.993566\pi$
$644$		0			0
$645$		0			0
$646$	8563.71	+	14832.8i	0.521570	+	0.903386i
$647$	−3303.47	+	5721.78i	−0.200731	+	0.347676i	−0.948764	−	0.315985i	$-0.897665\pi$
$647$	−3303.47	+	5721.78i	−0.200731	+	0.347676i	0.748033	+	0.663661i	$0.230998\pi$
$648$		0			0
$649$	31705.4	−	18305.1i	1.91764	−	1.10715i
$650$	−47846.6			−2.88723
$651$		0			0
$652$	5577.01			0.334989
$653$	22417.1	−	12942.5i	1.34342	−	0.775622i	0.356109	−	0.934444i	$-0.384103\pi$
$653$	22417.1	−	12942.5i	1.34342	−	0.775622i	0.987307	+	0.158823i	$0.0507698\pi$
$654$		0			0
$655$	865.234	−	1498.63i	0.0516145	−	0.0893989i
$656$	1637.78	+	2836.72i	0.0974764	+	0.168834i
$657$		0			0
$658$		0			0
$659$		−	7468.86i		−	0.441495i	−0.975331	−	0.220748i	$-0.929150\pi$
$659$		−	7468.86i		−	0.441495i	0.975331	−	0.220748i	$-0.0708497\pi$
$660$		0			0
$661$	5501.96	+	3176.56i	0.323754	+	0.186919i	0.653065	−	0.757302i	$-0.273483\pi$
$661$	5501.96	+	3176.56i	0.323754	+	0.186919i	−0.329311	+	0.944222i	$0.606816\pi$
$662$	−33463.4	−	19320.1i	−1.96464	−	1.13429i
$663$		0			0
$664$			19220.3i			1.12333i
$665$		0			0
$666$		0			0
$667$	6875.53	+	11908.8i	0.399133	+	0.691319i
$668$	5050.61	−	8747.92i	0.292536	−	0.506687i
$669$		0			0
$670$	−2193.23	+	1266.26i	−0.126465	+	0.0730148i
$671$	547.306			0.0314881
$672$		0			0
$673$	−20238.2			−1.15918			−0.579589	−	0.814909i	$-0.696787\pi$
$673$	−20238.2			−1.15918			−0.579589	+	0.814909i	$0.696787\pi$
$674$	2345.58	−	1354.22i	0.134048	−	0.0773925i
$675$		0			0
$676$	−32089.7	+	55581.1i	−1.82577	+	3.16233i
$677$	−5658.37	−	9800.59i	−0.321224	−	0.556377i	0.659516	−	0.751690i	$-0.270761\pi$
$677$	−5658.37	−	9800.59i	−0.321224	−	0.556377i	−0.980741	+	0.195313i	$0.937428\pi$
$678$		0			0
$679$		0			0
$680$			1982.91i			0.111825i
$681$		0			0
$682$	14366.6	+	8294.55i	0.806635	+	0.465711i
$683$	14869.4	+	8584.87i	0.833035	+	0.480953i	0.854891	−	0.518808i	$-0.173624\pi$
$683$	14869.4	+	8584.87i	0.833035	+	0.480953i	−0.0218557	+	0.999761i	$0.506957\pi$
$684$		0			0
$685$		−	1393.74i		−	0.0777402i
$686$		0			0
$687$		0			0
$688$	−973.172	−	1685.58i	−0.0539271	−	0.0934044i
$689$	14342.4	−	24841.8i	0.793037	−	1.37358i
$690$		0			0
$691$	7238.59	−	4179.20i	0.398508	−	0.230079i	−0.287332	−	0.957831i	$-0.592768\pi$
$691$	7238.59	−	4179.20i	0.398508	−	0.230079i	0.685840	+	0.727752i	$0.259435\pi$
$692$	27926.3			1.53410
$693$		0			0
$694$	32114.4			1.75655
$695$	−2528.29	+	1459.71i	−0.137990	+	0.0796688i
$696$		0			0
$697$	14916.6	−	25836.3i	0.810627	−	1.40405i
$698$	8187.41	+	14181.0i	0.443980	+	0.768996i
$699$		0			0
$700$		0			0
$701$			19235.8i			1.03641i	0.855256	+	0.518206i	$0.173400\pi$
$701$			19235.8i			1.03641i	−0.855256	+	0.518206i	$0.826600\pi$
$702$		0			0
$703$	3819.31	+	2205.08i	0.204905	+	0.118302i
$704$	−30082.5	−	17368.1i	−1.61048	−	0.929810i
$705$		0			0
$706$		−	10536.5i		−	0.561680i
$707$		0			0
$708$		0			0
$709$	5160.17	+	8937.67i	0.273334	+	0.473429i	0.969714	−	0.244245i	$-0.0785401\pi$
$709$	5160.17	+	8937.67i	0.273334	+	0.473429i	−0.696379	+	0.717674i	$0.745207\pi$
$710$	977.554	−	1693.17i	0.0516718	−	0.0894981i
$711$		0			0
$712$	−518.001	+	299.068i	−0.0272653	+	0.0157416i
$713$	8019.85			0.421242
$714$		0			0
$715$	4514.02			0.236105
$716$	31529.0	−	18203.3i	1.64566	−	0.950124i
$717$		0			0
$718$	3975.20	−	6885.25i	0.206620	−	0.357876i
$719$	11679.8	+	20229.9i	0.605815	+	1.04930i	0.991922	+	0.126849i	$0.0404864\pi$
$719$	11679.8	+	20229.9i	0.605815	+	1.04930i	−0.386107	+	0.922454i	$0.626180\pi$
$720$		0			0
$721$		0			0
$722$			20300.0i			1.04638i
$723$		0			0
$724$	3050.62	+	1761.28i	0.156596	+	0.0904106i
$725$	−16157.7	−	9328.63i	−0.827698	−	0.477871i
$726$		0			0
$727$		−	22260.4i		−	1.13561i	−0.823162	−	0.567807i	$-0.807792\pi$
$727$		−	22260.4i		−	1.13561i	0.823162	−	0.567807i	$-0.192208\pi$
$728$		0			0
$729$		0			0
$730$	−2638.00	−	4569.15i	−0.133749	−	0.231660i
$731$	−8863.48	+	15352.0i	−0.448464	+	0.776763i
$732$		0			0
$733$	−9047.84	+	5223.77i	−0.455920	+	0.263226i	−0.710327	−	0.703872i	$-0.751453\pi$
$733$	−9047.84	+	5223.77i	−0.455920	+	0.263226i	0.254407	+	0.967097i	$0.418120\pi$
$734$	−7618.58			−0.383116
$735$		0			0
$736$	−18166.9			−0.909840
$737$	−15938.2	+	9201.95i	−0.796598	+	0.459916i
$738$		0			0
$739$	−6595.44	+	11423.6i	−0.328304	+	0.568640i	−0.982176	−	0.187966i	$-0.939811\pi$
$739$	−6595.44	+	11423.6i	−0.328304	+	0.568640i	0.653871	+	0.756606i	$0.273144\pi$
$740$	713.895	+	1236.50i	0.0354639	+	0.0614253i
$741$		0			0
$742$		0			0
$743$		−	35382.2i		−	1.74703i	−0.486795	−	0.873517i	$-0.661834\pi$
$743$		−	35382.2i		−	1.74703i	0.486795	−	0.873517i	$-0.338166\pi$
$744$		0			0
$745$	1924.59	+	1111.16i	0.0946463	+	0.0546441i
$746$	1164.38	+	672.258i	0.0571463	+	0.0329934i
$747$		0			0
$748$			40295.6i			1.96973i
$749$		0			0
$750$		0			0
$751$	14692.3	+	25447.8i	0.713888	+	1.23649i	0.963387	+	0.268116i	$0.0864010\pi$
$751$	14692.3	+	25447.8i	0.713888	+	1.23649i	−0.249498	+	0.968375i	$0.580266\pi$
$752$	−594.020	+	1028.87i	−0.0288054	+	0.0498925i
$753$		0			0
$754$	−50770.8	+	29312.5i	−2.45221	+	1.41578i
$755$	−664.470			−0.0320299
$756$		0			0
$757$	11329.1			0.543939			0.271969	−	0.962306i	$-0.412325\pi$
$757$	11329.1			0.543939			0.271969	+	0.962306i	$0.412325\pi$
$758$	−28994.0	+	16739.7i	−1.38932	+	0.802127i
$759$		0			0
$760$	620.557	−	1074.84i	0.0296184	−	0.0513005i
$761$	−12696.5	−	21990.9i	−0.604792	−	1.04753i	−0.992084	−	0.125574i	$-0.959923\pi$
$761$	−12696.5	−	21990.9i	−0.604792	−	1.04753i	0.387292	−	0.921957i	$-0.373411\pi$
$762$		0			0
$763$		0			0
$764$		−	57499.9i		−	2.72287i
$765$		0			0
$766$	−49065.8	−	28328.2i	−2.31439	−	1.33621i
$767$	65346.7	+	37727.9i	3.07631	+	1.77611i
$768$		0			0
$769$		−	18120.8i		−	0.849744i	−0.905253	−	0.424872i	$-0.860319\pi$
$769$		−	18120.8i		−	0.849744i	0.905253	−	0.424872i	$-0.139681\pi$
$770$		0			0
$771$		0			0
$772$	−25874.7	−	44816.3i	−1.20628	−	2.08934i
$773$	−8673.05	+	15022.2i	−0.403555	+	0.698978i	−0.994152	−	0.107989i	$-0.965559\pi$
$773$	−8673.05	+	15022.2i	−0.403555	+	0.698978i	0.590597	+	0.806967i	$0.298892\pi$
$774$		0			0
$775$	−9423.42	+	5440.61i	−0.436773	+	0.252171i
$776$	−24161.3			−1.11771
$777$		0			0
$778$	−36054.7			−1.66147
$779$	−16171.1	+	9336.37i	−0.743759	+	0.429410i
$780$		0			0
$781$	7103.91	−	12304.3i	0.325477	−	0.563743i
$782$	15997.4	+	27708.3i	0.731542	+	1.26707i
$783$		0			0
$784$		0			0
$785$		−	1668.22i		−	0.0758488i
$786$		0			0
$787$	−1801.52	−	1040.11i	−0.0815977	−	0.0471104i	0.458646	−	0.888619i	$-0.348335\pi$
$787$	−1801.52	−	1040.11i	−0.0815977	−	0.0471104i	−0.540244	+	0.841509i	$0.681668\pi$
$788$	17540.2	+	10126.8i	0.792949	+	0.457810i
$789$		0			0
$790$		−	2364.83i		−	0.106502i
$791$		0			0
$792$		0			0
$793$	564.014	+	976.901i	0.0252569	+	0.0437463i
$794$	−28284.7	+	48990.5i	−1.26421	+	2.18968i
$795$		0			0
$796$	−1878.73	+	1084.68i	−0.0836554	+	0.0482984i
$797$	39737.3			1.76608			0.883041	−	0.469297i	$-0.155493\pi$
$797$	39737.3			1.76608			0.883041	+	0.469297i	$0.155493\pi$
$798$		0			0
$799$	10820.5			0.479099
$800$	21346.4	−	12324.3i	0.943385	−	0.544664i
$801$		0			0
$802$	18130.2	−	31402.5i	0.798255	−	1.38262i
$803$	−19170.4	−	33204.1i	−0.842477	−	1.45921i
$804$		0			0
$805$		0			0
$806$			34191.1i			1.49421i
$807$		0			0
$808$	−11421.9	−	6594.45i	−0.497305	−	0.287119i
$809$	−9713.37	−	5608.02i	−0.422131	−	0.243717i	0.273858	−	0.961770i	$-0.411700\pi$
$809$	−9713.37	−	5608.02i	−0.422131	−	0.243717i	−0.695989	+	0.718053i	$0.745034\pi$
$810$		0			0
$811$			14792.0i			0.640465i	0.947339	+	0.320232i	$0.103761\pi$
$811$			14792.0i			0.640465i	−0.947339	+	0.320232i	$0.896239\pi$
$812$		0			0
$813$		0			0
$814$	8520.57	+	14758.1i	0.366887	+	0.635467i
$815$	283.411	−	490.882i	0.0121809	−	0.0210980i
$816$		0			0
$817$	9608.88	−	5547.69i	0.411471	−	0.237563i
$818$	39511.2			1.68885
$819$		0			0
$820$	−6045.30			−0.257453
$821$	−28632.7	+	16531.1i	−1.21716	+	0.702726i	−0.964309	−	0.264779i	$-0.914701\pi$
$821$	−28632.7	+	16531.1i	−1.21716	+	0.702726i	−0.252849	+	0.967506i	$0.581368\pi$
$822$		0			0
$823$	−10045.4	+	17399.1i	−0.425467	+	0.736930i	−0.996464	−	0.0840220i	$-0.973223\pi$
$823$	−10045.4	+	17399.1i	−0.425467	+	0.736930i	0.570997	+	0.820952i	$0.306557\pi$
$824$	−13791.1	−	23886.9i	−0.583053	−	1.00988i
$825$		0			0
$826$		0			0
$827$		−	36882.5i		−	1.55082i	−0.631458	−	0.775410i	$-0.717543\pi$
$827$		−	36882.5i		−	1.55082i	0.631458	−	0.775410i	$-0.282457\pi$
$828$		0			0
$829$	32697.0	+	18877.6i	1.36986	+	0.790888i	0.990910	−	0.134530i	$-0.0429524\pi$
$829$	32697.0	+	18877.6i	1.36986	+	0.790888i	0.378949	+	0.925418i	$0.376286\pi$
$830$	4730.78	+	2731.32i	0.197841	+	0.114223i
$831$		0			0
$832$		−	71593.5i		−	2.98324i
$833$		0			0
$834$		0			0
$835$	−513.321	−	889.098i	−0.0212745	−	0.0368485i
$836$	12610.6	−	21842.2i	0.521707	−	0.903623i
$837$		0			0
$838$	15379.3	−	8879.25i	0.633973	−	0.366025i
$839$	44250.4			1.82085			0.910426	−	0.413672i	$-0.135754\pi$
$839$	44250.4			1.82085			0.910426	+	0.413672i	$0.135754\pi$
$840$		0			0
$841$	1528.81			0.0626844
$842$	5653.43	−	3264.01i	0.231390	−	0.133593i
$843$		0			0
$844$	−18321.1	+	31733.1i	−0.747201	+	1.29419i
$845$	3261.45	+	5649.00i	0.132778	+	0.229978i
$846$		0			0
$847$		0			0
$848$			2857.44i			0.115713i
$849$		0			0
$850$	−37594.3	−	21705.1i	−1.51703	−	0.875856i
$851$	7134.65	+	4119.19i	0.287394	+	0.165927i
$852$		0			0
$853$		−	14952.2i		−	0.600179i	−0.953911	−	0.300089i	$-0.902983\pi$
$853$		−	14952.2i		−	0.600179i	0.953911	−	0.300089i	$-0.0970165\pi$
$854$		0			0
$855$		0			0
$856$	−4317.66	−	7478.41i	−0.172400	−	0.298606i
$857$	1224.76	−	2121.35i	0.0488181	−	0.0845555i	−0.840584	−	0.541682i	$-0.817788\pi$
$857$	1224.76	−	2121.35i	0.0488181	−	0.0845555i	0.889402	+	0.457126i	$0.151121\pi$
$858$		0			0
$859$	5751.97	−	3320.90i	0.228469	−	0.131906i	−0.381397	−	0.924411i	$-0.624557\pi$
$859$	5751.97	−	3320.90i	0.228469	−	0.131906i	0.609865	+	0.792505i	$0.291223\pi$
$860$	3592.13			0.142431
$861$		0			0
$862$	−66951.0			−2.64543
$863$	16339.2	−	9433.46i	0.644489	−	0.372096i	−0.141853	−	0.989888i	$-0.545306\pi$
$863$	16339.2	−	9433.46i	0.644489	−	0.372096i	0.786342	+	0.617792i	$0.211973\pi$
$864$		0			0
$865$	1419.15	−	2458.04i	0.0557833	−	0.0966196i
$866$	−35891.1	−	62165.2i	−1.40835	−	2.43933i
$867$		0			0
$868$		0			0
$869$		−	17185.3i		−	0.670851i
$870$		0			0
$871$	−32849.6	−	18965.8i	−1.27792	−	0.737807i
$872$	−11660.5	−	6732.19i	−0.452837	−	0.261446i
$873$		0			0
$874$		−	20025.7i		−	0.775033i
$875$		0			0
$876$		0			0
$877$	−5989.84	−	10374.7i	−0.230630	−	0.399463i	0.727364	−	0.686252i	$-0.240745\pi$
$877$	−5989.84	−	10374.7i	−0.230630	−	0.399463i	−0.957994	+	0.286789i	$0.907412\pi$
$878$	6858.23	−	11878.8i	0.263615	−	0.456594i
$879$		0			0
$880$	−389.421	+	224.832i	−0.0149175	+	0.00861261i
$881$	−34504.0			−1.31949			−0.659743	−	0.751491i	$-0.729335\pi$
$881$	−34504.0			−1.31949			−0.659743	+	0.751491i	$0.729335\pi$
$882$		0			0
$883$	−8148.85			−0.310567			−0.155283	−	0.987870i	$-0.549629\pi$
$883$	−8148.85			−0.310567			−0.155283	+	0.987870i	$0.549629\pi$
$884$	−71924.9	+	41525.8i	−2.73653	+	1.57994i
$885$		0			0
$886$	−29053.2	+	50321.6i	−1.10165	+	1.90811i
$887$	17477.6	+	30272.1i	0.661602	+	1.14593i	0.980195	+	0.198036i	$0.0634563\pi$
$887$	17477.6	+	30272.1i	0.661602	+	1.14593i	−0.318593	+	0.947892i	$0.603210\pi$
$888$		0			0
$889$		0			0
$890$			169.998i			0.00640262i
$891$		0			0
$892$	−36396.4	−	21013.5i	−1.36619	−	0.788771i
$893$	−5865.22	−	3386.29i	−0.219790	−	0.126896i
$894$		0			0
$895$		−	3700.20i		−	0.138194i
$896$		0			0
$897$		0			0
$898$	243.466	+	421.696i	0.00904741	+	0.0156706i
$899$	−6666.22	+	11546.2i	−0.247309	+	0.428352i
$900$		0			0
$901$	22538.4	−	13012.5i	0.833365	−	0.481144i
$902$	−72152.7			−2.66344
$903$		0			0
$904$	18425.3			0.677894
$905$	310.051	−	179.008i	0.0113883	−	0.00657505i
$906$		0			0
$907$	12494.5	−	21641.1i	0.457412	−	0.792261i	−0.541411	−	0.840758i	$-0.682110\pi$
$907$	12494.5	−	21641.1i	0.457412	−	0.792261i	0.998823	+	0.0484970i	$0.0154431\pi$
$908$	−18872.2	−	32687.5i	−0.689752	−	1.19468i
$909$		0			0
$910$		0			0
$911$		−	41609.1i		−	1.51325i	−0.653849	−	0.756625i	$-0.726847\pi$
$911$		−	41609.1i		−	1.51325i	0.653849	−	0.756625i	$-0.273153\pi$
$912$		0			0
$913$	34378.7	+	19848.5i	1.24619	+	0.719486i
$914$	38293.2	+	22108.6i	1.38580	+	0.800095i
$915$		0			0
$916$			13805.1i			0.497964i
$917$		0			0
$918$		0			0
$919$	−25496.0	−	44160.4i	−0.915164	−	1.58511i	−0.806661	−	0.591014i	$-0.798728\pi$
$919$	−25496.0	−	44160.4i	−0.915164	−	1.58511i	−0.108502	−	0.994096i	$-0.534605\pi$
$920$	1159.23	−	2007.84i	0.0415420	−	0.0719529i
$921$		0			0
$922$	−2502.24	+	1444.67i	−0.0893782	+	0.0516025i
$923$	29283.1			1.04428
$924$		0			0
$925$	−11177.7			−0.397321
$926$	−21942.0	+	12668.2i	−0.778682	+	0.449572i
$927$		0			0
$928$	15100.6	−	26155.1i	0.534162	−	0.925196i
$929$	−23746.5	−	41130.2i	−0.838642	−	1.45257i	−0.891031	−	0.453943i	$-0.850017\pi$
$929$	−23746.5	−	41130.2i	−0.838642	−	1.45257i	0.0523888	−	0.998627i	$-0.483316\pi$
$930$		0			0
$931$		0			0
$932$			38603.9i			1.35677i
$933$		0			0
$934$	21615.4	+	12479.7i	0.757258	+	0.437203i
$935$	3546.78	+	2047.73i	0.124056	+	0.0716235i
$936$		0			0
$937$			6811.98i			0.237500i	0.992924	+	0.118750i	$0.0378887\pi$
$937$			6811.98i			0.237500i	−0.992924	+	0.118750i	$0.962111\pi$
$938$		0			0
$939$		0			0
$940$	−1096.31	−	1898.87i	−0.0380401	−	0.0658874i
$941$	16271.0	−	28182.2i	0.563677	−	0.976318i	−0.433494	−	0.901156i	$-0.642720\pi$
$941$	16271.0	−	28182.2i	0.563677	−	0.976318i	0.997171	−	0.0751612i	$-0.0239471\pi$
$942$		0			0
$943$	−30208.3	+	17440.8i	−1.04318	+	0.602280i
$944$	−7516.54			−0.259155
$945$		0			0
$946$	42873.3			1.47350
$947$	10119.9	−	5842.70i	0.347256	−	0.200488i	−0.316220	−	0.948686i	$-0.602414\pi$
$947$	10119.9	−	5842.70i	0.347256	−	0.200488i	0.663476	+	0.748198i	$0.269080\pi$
$948$		0			0
$949$	39511.3	−	68435.7i	1.35152	−	2.34090i
$950$	13585.3	+	23530.4i	0.463963	+	0.803608i
$951$		0			0
$952$		0			0
$953$			46457.5i			1.57912i	0.613671	+	0.789562i	$0.289692\pi$
$953$			46457.5i			1.57912i	−0.613671	+	0.789562i	$0.710308\pi$
$954$		0			0
$955$	−5061.08	−	2922.01i	−0.171490	−	0.0990096i
$956$	−18714.6	−	10804.9i	−0.633130	−	0.365538i
$957$		0			0
$958$		−	24732.8i		−	0.834114i
$959$		0			0
$960$		0			0
$961$	−11007.6	−	19065.8i	−0.369496	−	0.639986i
$962$	−17561.4	+	30417.2i	−0.588568	+	1.01943i
$963$		0			0
$964$	12942.3	−	7472.25i	0.432411	−	0.249653i
$965$	−5259.57			−0.175452
$966$		0			0
$967$	−27949.1			−0.929455			−0.464728	−	0.885454i	$-0.653848\pi$
$967$	−27949.1			−0.929455			−0.464728	+	0.885454i	$0.653848\pi$
$968$	6966.06	−	4021.86i	0.231299	−	0.133541i
$969$		0			0
$970$	−3433.47	+	5946.94i	−0.113652	+	0.196850i
$971$	−1609.85	−	2788.33i	−0.0532053	−	0.0921544i	0.838196	−	0.545369i	$-0.183610\pi$
$971$	−1609.85	−	2788.33i	−0.0532053	−	0.0921544i	−0.891401	+	0.453215i	$0.850277\pi$
$972$		0			0
$973$		0			0
$974$		−	53064.9i		−	1.74570i
$975$		0			0
$976$	−97.3141	−	56.1843i	−0.00319155	−	0.00184264i
$977$	−33258.6	−	19201.9i	−1.08909	−	0.628785i	−0.155754	−	0.987796i	$-0.549781\pi$
$977$	−33258.6	−	19201.9i	−1.08909	−	0.628785i	−0.933333	+	0.359011i	$0.883114\pi$
$978$		0			0
$979$			1235.38i			0.0403297i
$980$		0			0
$981$		0			0
$982$	7948.19	+	13766.7i	0.258286	+	0.447364i
$983$	−13709.1	+	23744.8i	−0.444814	+	0.770440i	−0.998039	−	0.0625917i	$-0.980063\pi$
$983$	−13709.1	+	23744.8i	−0.444814	+	0.770440i	0.553226	+	0.833031i	$0.313397\pi$
$984$		0			0
$985$	1782.71	−	1029.25i	0.0576667	−	0.0332939i
$986$	−53189.1			−1.71794
$987$		0			0
$988$	51982.4			1.67387
$989$	17949.8	−	10363.3i	0.577120	−	0.333200i
$990$		0			0
$991$	−21857.9	+	37859.1i	−0.700646	+	1.21355i	0.267594	+	0.963532i	$0.413771\pi$
$991$	−21857.9	+	37859.1i	−0.700646	+	1.21355i	−0.968240	+	0.250023i	$0.919562\pi$
$992$	−8806.94	−	15254.1i	−0.281876	−	0.488223i
$993$		0			0
$994$		0			0
$995$			220.484i			0.00702495i
$996$		0			0
$997$	21930.8	+	12661.7i	0.696644	+	0.402208i	0.806096	−	0.591784i	$-0.201576\pi$
$997$	21930.8	+	12661.7i	0.696644	+	0.402208i	−0.109452	+	0.993992i	$0.534910\pi$
$998$	−38731.5	−	22361.7i	−1.22848	−	0.709264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.c.80.7		16
3.2	odd	2	inner	441.4.p.c.80.2		16
7.2	even	3		63.4.p.a.26.2	yes	16
7.3	odd	6		441.4.c.a.440.13		16
7.4	even	3		441.4.c.a.440.14		16
7.5	odd	6	inner	441.4.p.c.215.2		16
7.6	odd	2		63.4.p.a.17.7	yes	16
21.2	odd	6		63.4.p.a.26.7	yes	16
21.5	even	6	inner	441.4.p.c.215.7		16
21.11	odd	6		441.4.c.a.440.3		16
21.17	even	6		441.4.c.a.440.4		16
21.20	even	2		63.4.p.a.17.2	✓	16
28.23	odd	6		1008.4.bt.a.593.4		16
28.27	even	2		1008.4.bt.a.17.5		16
84.23	even	6		1008.4.bt.a.593.5		16
84.83	odd	2		1008.4.bt.a.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.p.a.17.2	✓	16	21.20	even	2
63.4.p.a.17.7	yes	16	7.6	odd	2
63.4.p.a.26.2	yes	16	7.2	even	3
63.4.p.a.26.7	yes	16	21.2	odd	6
441.4.c.a.440.3		16	21.11	odd	6
441.4.c.a.440.4		16	21.17	even	6
441.4.c.a.440.13		16	7.3	odd	6
441.4.c.a.440.14		16	7.4	even	3
441.4.p.c.80.2		16	3.2	odd	2	inner
441.4.p.c.80.7		16	1.1	even	1	trivial
441.4.p.c.215.2		16	7.5	odd	6	inner
441.4.p.c.215.7		16	21.5	even	6	inner
1008.4.bt.a.17.4		16	84.83	odd	2
1008.4.bt.a.17.5		16	28.27	even	2
1008.4.bt.a.593.4		16	28.23	odd	6
1008.4.bt.a.593.5		16	84.23	even	6

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)

\(f(q)\)	\(=\)	\(q+(3.91663 - 2.26127i) q^{2} +(6.22668 - 10.7849i) q^{4} +(-0.632851 - 1.09613i) q^{5} -20.1405i q^{8} +O(q^{10})\)	\(q+(3.91663 - 2.26127i) q^{2} +(6.22668 - 10.7849i) q^{4} +(-0.632851 - 1.09613i) q^{5} -20.1405i q^{8} +(-4.95730 - 2.86210i) q^{10} +(-36.0248 - 20.7989i) q^{11} -85.7355i q^{13} +(4.27028 + 7.39634i) q^{16} +(38.8929 - 67.3645i) q^{17} +(-42.1638 + 24.3433i) q^{19} -15.7623 q^{20} -188.128 q^{22} +(-78.7639 + 45.4743i) q^{23} +(61.6990 - 106.866i) q^{25} +(-193.871 - 335.795i) q^{26} -151.196i q^{29} +(-76.3661 - 44.0900i) q^{31} +(172.988 + 99.8747i) q^{32} -351.790i q^{34} +(-45.2914 - 78.4470i) q^{37} +(-110.093 + 190.687i) q^{38} +(-22.0767 + 12.7460i) q^{40} +383.530 q^{41} -227.894 q^{43} +(-448.630 + 259.017i) q^{44} +(-205.660 + 356.213i) q^{46} +(69.5529 + 120.469i) q^{47} -558.072i q^{50} +(-924.652 - 533.848i) q^{52} +(289.749 + 167.287i) q^{53} +52.6505i q^{55} +(-341.895 - 592.179i) q^{58} +(-440.050 + 762.189i) q^{59} +(-11.3944 + 6.57854i) q^{61} -398.797 q^{62} +835.050 q^{64} +(-93.9774 + 54.2579i) q^{65} +(221.212 - 383.151i) q^{67} +(-484.348 - 838.915i) q^{68} +341.552i q^{71} +(798.218 + 460.851i) q^{73} +(-354.780 - 204.832i) q^{74} +606.311i q^{76} +(206.564 + 357.780i) q^{79} +(5.40490 - 9.36157i) q^{80} +(1502.15 - 867.265i) q^{82} -954.307 q^{83} -98.4538 q^{85} +(-892.579 + 515.331i) q^{86} +(-418.901 + 725.558i) q^{88} +(-14.8490 - 25.7193i) q^{89} +1132.62i q^{92} +(544.826 + 314.556i) q^{94} +(53.3668 + 30.8113i) q^{95} -1199.63i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4}+O(q^{10}) \) 16 * q + 32 * q^4	\( 16 q + 32 q^{4} + 72 q^{10} - 188 q^{16} + 612 q^{19} + 528 q^{22} - 20 q^{25} - 1128 q^{31} - 1196 q^{37} + 3204 q^{40} + 328 q^{43} - 1392 q^{46} - 4452 q^{52} - 3372 q^{58} + 1632 q^{61} + 5432 q^{64} + 308 q^{67} - 4068 q^{73} - 2176 q^{79} + 10188 q^{82} - 4608 q^{85} + 708 q^{88} + 2916 q^{94}+O(q^{100}) \) 16 * q + 32 * q^4 + 72 * q^10 - 188 * q^16 + 612 * q^19 + 528 * q^22 - 20 * q^25 - 1128 * q^31 - 1196 * q^37 + 3204 * q^40 + 328 * q^43 - 1392 * q^46 - 4452 * q^52 - 3372 * q^58 + 1632 * q^61 + 5432 * q^64 + 308 * q^67 - 4068 * q^73 - 2176 * q^79 + 10188 * q^82 - 4608 * q^85 + 708 * q^88 + 2916 * q^94

Introduction

L-functions

Modular forms

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Database

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