LMFDB - Embedded newform 900.3.y.a.89.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(89,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.89");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.y (of order $10$, degree $4$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			89.10
Character	$\chi$	$=$	900.89
Dual form			900.3.y.a.809.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.657760 + 4.95655i) q^{5} +12.7771i q^{7} +O(q^{10})$	$q+(-0.657760 + 4.95655i) q^{5} +12.7771i q^{7} +(4.29417 + 5.91041i) q^{11} +(2.97637 - 4.09662i) q^{13} +(8.56614 + 26.3639i) q^{17} +(-2.51888 - 7.75232i) q^{19} +(12.9789 - 9.42969i) q^{23} +(-24.1347 - 6.52044i) q^{25} +(-21.4717 - 6.97658i) q^{29} +(11.7476 + 36.1553i) q^{31} +(-63.3303 - 8.40427i) q^{35} +(34.7699 - 47.8567i) q^{37} +(-40.9447 + 56.3555i) q^{41} -73.6021i q^{43} +(-6.05918 + 18.6483i) q^{47} -114.254 q^{49} +(-3.58951 + 11.0474i) q^{53} +(-32.1198 + 17.3966i) q^{55} +(34.3273 - 47.2475i) q^{59} +(21.2315 - 15.4256i) q^{61} +(18.3474 + 17.4471i) q^{65} +(-64.0210 + 20.8017i) q^{67} +(-36.7994 - 11.9569i) q^{71} +(-36.7044 - 50.5192i) q^{73} +(-75.5179 + 54.8670i) q^{77} +(-0.317695 + 0.977763i) q^{79} +(37.7327 + 116.129i) q^{83} +(-136.308 + 25.1174i) q^{85} +(95.1407 + 130.950i) q^{89} +(52.3430 + 38.0294i) q^{91} +(40.0816 - 7.38579i) q^{95} +(46.7870 + 15.2020i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q+O(q^{10}) $ 80 * q	$ 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) $ 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.657760	+	4.95655i	−0.131552	+	0.991309i
$5$	−0.657760	+	4.95655i	−0.131552	+	0.991309i
$6$		0			0
$7$			12.7771i			1.82530i	0.408743	+	0.912650i	$0.365967\pi$
$7$			12.7771i			1.82530i	−0.408743	+	0.912650i	$0.634033\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.29417	+	5.91041i	0.390379	+	0.537310i	0.958297	−	0.285775i	$-0.0922509\pi$
$11$	4.29417	+	5.91041i	0.390379	+	0.537310i	−0.567918	+	0.823085i	$0.692251\pi$
$12$		0			0
$13$	2.97637	−	4.09662i	0.228952	−	0.315125i	−0.679050	−	0.734092i	$-0.737608\pi$
$13$	2.97637	−	4.09662i	0.228952	−	0.315125i	0.908001	+	0.418968i	$0.137608\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	8.56614	+	26.3639i	0.503891	+	1.55082i	0.802628	+	0.596481i	$0.203435\pi$
$17$	8.56614	+	26.3639i	0.503891	+	1.55082i	−0.298737	+	0.954336i	$0.596565\pi$
$18$		0			0
$19$	−2.51888	−	7.75232i	−0.132573	−	0.408017i	0.862632	−	0.505832i	$-0.168815\pi$
$19$	−2.51888	−	7.75232i	−0.132573	−	0.408017i	−0.995205	+	0.0978154i	$0.968815\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	12.9789	−	9.42969i	0.564298	−	0.409986i	−0.268732	−	0.963215i	$-0.586604\pi$
$23$	12.9789	−	9.42969i	0.564298	−	0.409986i	0.833029	+	0.553229i	$0.186604\pi$
$24$		0			0
$25$	−24.1347	−	6.52044i	−0.965388	−	0.260818i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−21.4717	−	6.97658i	−0.740404	−	0.240572i	−0.0855569	−	0.996333i	$-0.527267\pi$
$29$	−21.4717	−	6.97658i	−0.740404	−	0.240572i	−0.654847	+	0.755761i	$0.727267\pi$
$30$		0			0
$31$	11.7476	+	36.1553i	0.378953	+	1.16630i	0.940773	+	0.339038i	$0.110102\pi$
$31$	11.7476	+	36.1553i	0.378953	+	1.16630i	−0.561819	+	0.827260i	$0.689898\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−63.3303	−	8.40427i	−1.80944	−	0.240122i
$36$		0			0
$37$	34.7699	−	47.8567i	0.939728	−	1.29342i	−0.0162144	−	0.999869i	$-0.505161\pi$
$37$	34.7699	−	47.8567i	0.939728	−	1.29342i	0.955942	−	0.293556i	$-0.0948386\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−40.9447	+	56.3555i	−0.998650	+	1.37452i	−0.0725000	+	0.997368i	$0.523098\pi$
$41$	−40.9447	+	56.3555i	−0.998650	+	1.37452i	−0.926150	+	0.377155i	$0.876902\pi$
$42$		0			0
$43$		−	73.6021i		−	1.71168i	−0.517243	−	0.855839i	$-0.673042\pi$
$43$		−	73.6021i		−	1.71168i	0.517243	−	0.855839i	$-0.326958\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.05918	+	18.6483i	−0.128919	+	0.396771i	−0.994595	−	0.103834i	$-0.966889\pi$
$47$	−6.05918	+	18.6483i	−0.128919	+	0.396771i	0.865676	+	0.500605i	$0.166889\pi$
$48$		0			0
$49$	−114.254			−2.33172
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.58951	+	11.0474i	−0.0677266	+	0.208441i	−0.979192	−	0.202935i	$-0.934952\pi$
$53$	−3.58951	+	11.0474i	−0.0677266	+	0.208441i	0.911466	+	0.411376i	$0.134952\pi$
$54$		0			0
$55$	−32.1198	+	17.3966i	−0.583996	+	0.316302i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	34.3273	−	47.2475i	0.581818	−	0.800804i	−0.412075	−	0.911150i	$-0.635196\pi$
$59$	34.3273	−	47.2475i	0.581818	−	0.800804i	0.993893	+	0.110346i	$0.0351958\pi$
$60$		0			0
$61$	21.2315	−	15.4256i	0.348058	−	0.252879i	−0.399996	−	0.916517i	$-0.630988\pi$
$61$	21.2315	−	15.4256i	0.348058	−	0.252879i	0.748054	+	0.663638i	$0.230988\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	18.3474	+	17.4471i	0.282267	+	0.268417i
$66$		0			0
$67$	−64.0210	+	20.8017i	−0.955537	+	0.310473i	−0.744963	−	0.667105i	$-0.767533\pi$
$67$	−64.0210	+	20.8017i	−0.955537	+	0.310473i	−0.210573	+	0.977578i	$0.567533\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−36.7994	−	11.9569i	−0.518302	−	0.168407i	0.0381725	−	0.999271i	$-0.487846\pi$
$71$	−36.7994	−	11.9569i	−0.518302	−	0.168407i	−0.556475	+	0.830865i	$0.687846\pi$
$72$		0			0
$73$	−36.7044	−	50.5192i	−0.502799	−	0.692044i	0.479885	−	0.877331i	$-0.340678\pi$
$73$	−36.7044	−	50.5192i	−0.502799	−	0.692044i	−0.982684	+	0.185287i	$0.940678\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−75.5179	+	54.8670i	−0.980752	+	0.712558i
$78$		0			0
$79$	−0.317695	+	0.977763i	−0.00402145	+	0.0123768i	−0.953047	−	0.302822i	$-0.902071\pi$
$79$	−0.317695	+	0.977763i	−0.00402145	+	0.0123768i	0.949026	+	0.315199i	$0.102071\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	37.7327	+	116.129i	0.454611	+	1.39915i	0.871591	+	0.490234i	$0.163089\pi$
$83$	37.7327	+	116.129i	0.454611	+	1.39915i	−0.416979	+	0.908916i	$0.636911\pi$
$84$		0			0
$85$	−136.308	+	25.1174i	−1.60363	+	0.295498i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	95.1407	+	130.950i	1.06900	+	1.47135i	0.871088	+	0.491126i	$0.163415\pi$
$89$	95.1407	+	130.950i	1.06900	+	1.47135i	0.197908	+	0.980221i	$0.436585\pi$
$90$		0			0
$91$	52.3430	+	38.0294i	0.575197	+	0.417905i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	40.0816	−	7.38579i	0.421911	−	0.0777451i
$96$		0			0
$97$	46.7870	+	15.2020i	0.482341	+	0.156722i	0.540087	−	0.841609i	$-0.318391\pi$
$97$	46.7870	+	15.2020i	0.482341	+	0.156722i	−0.0577462	+	0.998331i	$0.518391\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			84.1951i			0.833614i	0.908995	+	0.416807i	$0.136851\pi$
$101$			84.1951i			0.833614i	−0.908995	+	0.416807i	$0.863149\pi$
$102$		0			0
$103$	−82.1808	−	26.7022i	−0.797872	−	0.259244i	−0.118419	−	0.992964i	$-0.537783\pi$
$103$	−82.1808	−	26.7022i	−0.797872	−	0.259244i	−0.679453	+	0.733719i	$0.737783\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.7209			0.128233			0.0641165	−	0.997942i	$-0.479577\pi$
$107$	13.7209			0.128233			0.0641165	+	0.997942i	$0.479577\pi$
$108$		0			0
$109$	68.9690	+	50.1089i	0.632743	+	0.459715i	0.857350	−	0.514735i	$-0.172110\pi$
$109$	68.9690	+	50.1089i	0.632743	+	0.459715i	−0.224606	+	0.974450i	$0.572110\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	47.5706	+	34.5621i	0.420979	+	0.305859i	0.778032	−	0.628225i	$-0.216218\pi$
$113$	47.5706	+	34.5621i	0.420979	+	0.305859i	−0.357053	+	0.934084i	$0.616218\pi$
$114$		0			0
$115$	38.2017	+	70.5327i	0.332189	+	0.613328i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−336.854	+	109.450i	−2.83070	+	0.919751i
$120$		0			0
$121$	20.8979	−	64.3172i	0.172710	−	0.531547i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	48.1937	−	115.336i	0.385550	−	0.922687i
$126$		0			0
$127$	−127.185	−	175.055i	−1.00145	−	1.37838i	−0.924429	−	0.381355i	$-0.875457\pi$
$127$	−127.185	−	175.055i	−1.00145	−	1.37838i	−0.0770262	−	0.997029i	$-0.524543\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−87.6167	+	28.4684i	−0.668830	+	0.217316i	−0.623698	−	0.781665i	$-0.714371\pi$
$131$	−87.6167	+	28.4684i	−0.668830	+	0.217316i	−0.0451313	+	0.998981i	$0.514371\pi$
$132$		0			0
$133$	99.0522	−	32.1840i	0.744753	−	0.241985i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−29.5671	−	21.4818i	−0.215818	−	0.156801i	0.474624	−	0.880189i	$-0.342584\pi$
$137$	−29.5671	−	21.4818i	−0.215818	−	0.156801i	−0.690442	+	0.723387i	$0.742584\pi$
$138$		0			0
$139$	4.56654	−	3.31779i	0.0328528	−	0.0238690i	−0.571238	−	0.820785i	$-0.693537\pi$
$139$	4.56654	−	3.31779i	0.0328528	−	0.0238690i	0.604090	+	0.796916i	$0.293537\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	36.9938			0.258698
$144$		0			0
$145$	48.7030	−	101.837i	0.335883	−	0.702322i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	110.697i		−	0.742935i	−0.928446	−	0.371468i	$-0.878855\pi$
$149$		−	110.697i		−	0.742935i	0.928446	−	0.371468i	$-0.121145\pi$
$150$		0			0
$151$	−44.1496			−0.292381			−0.146191	−	0.989256i	$-0.546701\pi$
$151$	−44.1496			−0.292381			−0.146191	+	0.989256i	$0.546701\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−186.932	+	34.4458i	−1.20601	+	0.222231i
$156$		0			0
$157$			300.101i			1.91147i	0.294224	+	0.955736i	$0.404939\pi$
$157$			300.101i			1.91147i	−0.294224	+	0.955736i	$0.595061\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	120.484	+	165.832i	0.748348	+	1.03001i
$162$		0			0
$163$	106.741	−	146.917i	0.654854	−	0.901329i	−0.344443	−	0.938807i	$-0.611932\pi$
$163$	106.741	−	146.917i	0.654854	−	0.901329i	0.999297	+	0.0374777i	$0.0119323\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−68.2818	−	210.150i	−0.408873	−	1.25838i	−0.917618	−	0.397464i	$-0.869890\pi$
$167$	−68.2818	−	210.150i	−0.408873	−	1.25838i	0.508745	−	0.860917i	$-0.330110\pi$
$168$		0			0
$169$	44.3003	+	136.342i	0.262132	+	0.806760i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−109.677	+	79.6851i	−0.633972	+	0.460607i	−0.857774	−	0.514027i	$-0.828153\pi$
$173$	−109.677	+	79.6851i	−0.633972	+	0.460607i	0.223802	+	0.974635i	$0.428153\pi$
$174$		0			0
$175$	83.3123	−	308.371i	0.476070	−	1.76212i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−151.594	−	49.2558i	−0.846892	−	0.275172i	−0.146749	−	0.989174i	$-0.546881\pi$
$179$	−151.594	−	49.2558i	−0.846892	−	0.275172i	−0.700144	+	0.714002i	$0.746881\pi$
$180$		0			0
$181$	−35.0295	−	107.810i	−0.193533	−	0.595634i	−0.999991	−	0.00434201i	$-0.998618\pi$
$181$	−35.0295	−	107.810i	−0.193533	−	0.595634i	0.806457	−	0.591292i	$-0.201382\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	214.334	+	203.817i	1.15856	+	1.10171i
$186$		0			0
$187$	−119.037	+	163.840i	−0.636561	+	0.876151i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	101.257	−	139.368i	0.530140	−	0.729676i	−0.457011	−	0.889461i	$-0.651080\pi$
$191$	101.257	−	139.368i	0.530140	−	0.729676i	0.987152	+	0.159785i	$0.0510801\pi$
$192$		0			0
$193$			357.438i			1.85201i	0.377514	+	0.926004i	$0.376779\pi$
$193$			357.438i			1.85201i	−0.377514	+	0.926004i	$0.623221\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	91.9080	−	282.864i	0.466538	−	1.43586i	−0.390500	−	0.920603i	$-0.627698\pi$
$197$	91.9080	−	282.864i	0.466538	−	1.43586i	0.857038	−	0.515254i	$-0.172302\pi$
$198$		0			0
$199$	324.763			1.63198			0.815988	−	0.578069i	$-0.196194\pi$
$199$	324.763			1.63198			0.815988	+	0.578069i	$0.196194\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	89.1405	−	274.346i	0.439116	−	1.35146i
$204$		0			0
$205$	−252.397	−	240.012i	−1.23120	−	1.17079i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	35.0029	−	48.1774i	0.167478	−	0.230514i
$210$		0			0
$211$	82.8049	−	60.1613i	0.392440	−	0.285125i	−0.374014	−	0.927423i	$-0.622019\pi$
$211$	82.8049	−	60.1613i	0.392440	−	0.285125i	0.766455	+	0.642298i	$0.222019\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	364.812	+	48.4125i	1.69680	+	0.225175i
$216$		0			0
$217$	−461.959	+	150.100i	−2.12884	+	0.691703i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	133.499	+	43.3764i	0.604067	+	0.196273i
$222$		0			0
$223$	−89.0831	−	122.612i	−0.399476	−	0.549831i	0.561137	−	0.827723i	$-0.310364\pi$
$223$	−89.0831	−	122.612i	−0.399476	−	0.549831i	−0.960612	+	0.277892i	$0.910364\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.29164	−	6.75077i	0.0409323	−	0.0297391i	−0.567131	−	0.823628i	$-0.691947\pi$
$227$	9.29164	−	6.75077i	0.0409323	−	0.0297391i	0.608063	+	0.793889i	$0.291947\pi$
$228$		0			0
$229$	−60.1264	+	185.050i	−0.262561	+	0.808079i	0.729684	+	0.683784i	$0.239667\pi$
$229$	−60.1264	+	185.050i	−0.262561	+	0.808079i	−0.992245	+	0.124295i	$0.960333\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−37.7839	−	116.287i	−0.162163	−	0.499086i	0.836653	−	0.547733i	$-0.184509\pi$
$233$	−37.7839	−	116.287i	−0.162163	−	0.499086i	−0.998816	+	0.0486472i	$0.984509\pi$
$234$		0			0
$235$	−88.4454	−	42.2987i	−0.376364	−	0.179994i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	253.481	+	348.887i	1.06059	+	1.45978i	0.879251	+	0.476359i	$0.158044\pi$
$239$	253.481	+	348.887i	1.06059	+	1.45978i	0.181341	+	0.983420i	$0.441956\pi$
$240$		0			0
$241$	76.5435	+	55.6121i	0.317608	+	0.230756i	0.735154	−	0.677900i	$-0.237110\pi$
$241$	76.5435	+	55.6121i	0.317608	+	0.230756i	−0.417546	+	0.908656i	$0.637110\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	75.1519	−	566.306i	0.306742	−	2.31145i
$246$		0			0
$247$	−39.2555	−	12.7549i	−0.158929	−	0.0516392i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			56.9011i			0.226698i	0.993555	+	0.113349i	$0.0361577\pi$
$251$			56.9011i			0.226698i	−0.993555	+	0.113349i	$0.963842\pi$
$252$		0			0
$253$	111.467	+	36.2177i	0.440580	+	0.143153i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	61.4420			0.239074			0.119537	−	0.992830i	$-0.461859\pi$
$257$	61.4420			0.239074			0.119537	+	0.992830i	$0.461859\pi$
$258$		0			0
$259$	611.470	+	444.259i	2.36089	+	1.71528i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	171.296	+	124.453i	0.651314	+	0.473207i	0.863718	−	0.503975i	$-0.168129\pi$
$263$	171.296	+	124.453i	0.651314	+	0.473207i	−0.212405	+	0.977182i	$0.568129\pi$
$264$		0			0
$265$	−52.3958	−	25.0581i	−0.197720	−	0.0945588i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−267.257	+	86.8372i	−0.993522	+	0.322815i	−0.760274	−	0.649602i	$-0.774935\pi$
$269$	−267.257	+	86.8372i	−0.993522	+	0.322815i	−0.233248	+	0.972417i	$0.574935\pi$
$270$		0			0
$271$	78.8843	−	242.781i	0.291086	−	0.895871i	−0.693422	−	0.720532i	$-0.743898\pi$
$271$	78.8843	−	242.781i	0.291086	−	0.895871i	0.984508	−	0.175339i	$-0.0561022\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−65.0999	−	170.646i	−0.236727	−	0.620531i
$276$		0			0
$277$	36.2393	+	49.8791i	0.130828	+	0.180069i	0.869405	−	0.494099i	$-0.164502\pi$
$277$	36.2393	+	49.8791i	0.130828	+	0.180069i	−0.738578	+	0.674169i	$0.764502\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	300.034	−	97.4870i	1.06774	−	0.346929i	0.278131	−	0.960543i	$-0.410285\pi$
$281$	300.034	−	97.4870i	1.06774	−	0.346929i	0.789606	+	0.613615i	$0.210285\pi$
$282$		0			0
$283$	414.898	−	134.809i	1.46607	−	0.476355i	0.536152	−	0.844121i	$-0.319877\pi$
$283$	414.898	−	134.809i	1.46607	−	0.476355i	0.929918	+	0.367766i	$0.119877\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−720.059	−	523.154i	−2.50892	−	1.82284i
$288$		0			0
$289$	−387.869	+	281.803i	−1.34211	+	0.975098i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	152.683			0.521104			0.260552	−	0.965460i	$-0.416095\pi$
$293$	152.683			0.521104			0.260552	+	0.965460i	$0.416095\pi$
$294$		0			0
$295$	211.605	+	201.222i	0.717305	+	0.682110i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		−	81.2357i		−	0.271691i
$300$		0			0
$301$	940.421			3.12432
$302$		0			0
$303$		0			0
$304$		0			0
$305$	62.4925	+	115.381i	0.204893	+	0.378300i
$306$		0			0
$307$			95.4249i			0.310830i	0.987849	+	0.155415i	$0.0496715\pi$
$307$			95.4249i			0.310830i	−0.987849	+	0.155415i	$0.950328\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−176.864	−	243.433i	−0.568695	−	0.782742i	0.423704	−	0.905801i	$-0.360730\pi$
$311$	−176.864	−	243.433i	−0.568695	−	0.782742i	−0.992399	+	0.123059i	$0.960730\pi$
$312$		0			0
$313$	−2.10736	+	2.90054i	−0.00673280	+	0.00926690i	−0.812370	−	0.583142i	$-0.801823\pi$
$313$	−2.10736	+	2.90054i	−0.00673280	+	0.00926690i	0.805637	+	0.592409i	$0.201823\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	149.771	+	460.947i	0.472463	+	1.45409i	0.849349	+	0.527832i	$0.176995\pi$
$317$	149.771	+	460.947i	0.472463	+	1.45409i	−0.376886	+	0.926260i	$0.623005\pi$
$318$		0			0
$319$	−50.9686	−	156.865i	−0.159776	−	0.491741i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	182.804	−	132.815i	0.565957	−	0.411192i
$324$		0			0
$325$	−98.5456	+	79.4635i	−0.303217	+	0.244503i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−238.270	−	77.4188i	−0.724226	−	0.235315i
$330$		0			0
$331$	153.765	+	473.239i	0.464546	+	1.42973i	0.859553	+	0.511047i	$0.170742\pi$
$331$	153.765	+	473.239i	0.464546	+	1.42973i	−0.395007	+	0.918678i	$0.629258\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−60.9940	−	331.005i	−0.182072	−	0.988076i
$336$		0			0
$337$	−30.9154	+	42.5514i	−0.0917371	+	0.126265i	−0.852418	−	0.522860i	$-0.824865\pi$
$337$	−30.9154	+	42.5514i	−0.0917371	+	0.126265i	0.760681	+	0.649125i	$0.224865\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−163.247	+	224.690i	−0.478729	+	0.658914i
$342$		0			0
$343$		−	833.759i		−	2.43078i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	141.970	−	436.938i	0.409134	−	1.25919i	−0.508259	−	0.861204i	$-0.669711\pi$
$347$	141.970	−	436.938i	0.409134	−	1.25919i	0.917393	−	0.397982i	$-0.130289\pi$
$348$		0			0
$349$	2.78004			0.00796573			0.00398286	−	0.999992i	$-0.498732\pi$
$349$	2.78004			0.00796573			0.00398286	+	0.999992i	$0.498732\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−109.317	+	336.444i	−0.309680	+	0.953098i	0.668209	+	0.743974i	$0.267061\pi$
$353$	−109.317	+	336.444i	−0.309680	+	0.953098i	−0.977889	+	0.209124i	$0.932939\pi$
$354$		0			0
$355$	83.4700	−	174.533i	0.235127	−	0.491643i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	314.418	−	432.760i	0.875817	−	1.20546i	−0.101745	−	0.994811i	$-0.532442\pi$
$359$	314.418	−	432.760i	0.875817	−	1.20546i	0.977562	−	0.210648i	$-0.0675575\pi$
$360$		0			0
$361$	238.301	−	173.136i	0.660115	−	0.479601i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	274.543	−	148.697i	0.752174	−	0.407390i
$366$		0			0
$367$	−75.4502	+	24.5152i	−0.205586	+	0.0667990i	−0.410000	−	0.912086i	$-0.634471\pi$
$367$	−75.4502	+	24.5152i	−0.205586	+	0.0667990i	0.204414	+	0.978885i	$0.434471\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−141.153	−	45.8635i	−0.380467	−	0.123621i
$372$		0			0
$373$	−238.293	−	327.982i	−0.638855	−	0.879309i	0.359699	−	0.933069i	$-0.382880\pi$
$373$	−238.293	−	327.982i	−0.638855	−	0.879309i	−0.998554	+	0.0537596i	$0.982880\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−92.4882	+	67.1966i	−0.245327	+	0.178240i
$378$		0			0
$379$	−77.8055	+	239.461i	−0.205291	+	0.631822i	0.794410	+	0.607382i	$0.207780\pi$
$379$	−77.8055	+	239.461i	−0.205291	+	0.631822i	−0.999701	+	0.0244401i	$0.992220\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−65.2228	−	200.735i	−0.170295	−	0.524113i	0.829093	−	0.559111i	$-0.188857\pi$
$383$	−65.2228	−	200.735i	−0.170295	−	0.524113i	−0.999387	+	0.0349982i	$0.988857\pi$
$384$		0			0
$385$	−222.278	−	410.397i	−0.577346	−	1.06597i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−89.0196	−	122.525i	−0.228842	−	0.314974i	0.679119	−	0.734028i	$-0.262362\pi$
$389$	−89.0196	−	122.525i	−0.228842	−	0.314974i	−0.907961	+	0.419054i	$0.862362\pi$
$390$		0			0
$391$	359.782	+	261.397i	0.920158	+	0.668534i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.63736	−	2.21780i	−0.0117402	−	0.00561469i
$396$		0			0
$397$	−24.2688	−	7.88541i	−0.0611305	−	0.0198625i	0.278292	−	0.960496i	$-0.410232\pi$
$397$	−24.2688	−	7.88541i	−0.0611305	−	0.0198625i	−0.339423	+	0.940634i	$0.610232\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			472.621i			1.17861i	0.807912	+	0.589303i	$0.200598\pi$
$401$			472.621i			1.17861i	−0.807912	+	0.589303i	$0.799402\pi$
$402$		0			0
$403$	183.080	+	59.4861i	0.454292	+	0.147608i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	432.161			1.06182
$408$		0			0
$409$	622.158	+	452.024i	1.52117	+	1.10519i	0.960904	+	0.276880i	$0.0893006\pi$
$409$	622.158	+	452.024i	1.52117	+	1.10519i	0.560265	+	0.828314i	$0.310699\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	603.685	+	438.603i	1.46171	+	1.06199i
$414$		0			0
$415$	−600.420	+	110.639i	−1.44680	+	0.266599i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−279.968	+	90.9673i	−0.668183	+	0.217106i	−0.623414	−	0.781892i	$-0.714255\pi$
$419$	−279.968	+	90.9673i	−0.668183	+	0.217106i	−0.0447683	+	0.998997i	$0.514255\pi$
$420$		0			0
$421$	−193.702	+	596.154i	−0.460100	+	1.41604i	0.404941	+	0.914343i	$0.367292\pi$
$421$	−193.702	+	596.154i	−0.460100	+	1.41604i	−0.865041	+	0.501700i	$0.832708\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−34.8373	−	692.139i	−0.0819701	−	1.62856i
$426$		0			0
$427$	197.095	+	271.277i	0.461580	+	0.635310i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−203.227	+	66.0324i	−0.471524	+	0.153207i	−0.535134	−	0.844767i	$-0.679739\pi$
$431$	−203.227	+	66.0324i	−0.471524	+	0.153207i	0.0636096	+	0.997975i	$0.479739\pi$
$432$		0			0
$433$	110.306	−	35.8406i	0.254748	−	0.0827728i	−0.178859	−	0.983875i	$-0.557241\pi$
$433$	110.306	−	35.8406i	0.254748	−	0.0827728i	0.433607	+	0.901102i	$0.357241\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−105.794	−	76.8640i	−0.242092	−	0.175890i
$438$		0			0
$439$	−602.260	+	437.567i	−1.37189	+	0.996737i	−0.374304	+	0.927306i	$0.622118\pi$
$439$	−602.260	+	437.567i	−1.37189	+	0.996737i	−0.997587	+	0.0694308i	$0.977882\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	776.701			1.75328			0.876638	−	0.481151i	$-0.159781\pi$
$443$	776.701			1.75328			0.876638	+	0.481151i	$0.159781\pi$
$444$		0			0
$445$	−711.639	+	385.435i	−1.59919	+	0.866147i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			520.597i			1.15946i	0.814809	+	0.579730i	$0.196842\pi$
$449$			520.597i			1.15946i	−0.814809	+	0.579730i	$0.803158\pi$
$450$		0			0
$451$	−508.907			−1.12840
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−222.923	+	234.426i	−0.489942	+	0.515222i
$456$		0			0
$457$			110.772i			0.242390i	0.992629	+	0.121195i	$0.0386726\pi$
$457$			110.772i			0.242390i	−0.992629	+	0.121195i	$0.961327\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	376.826	+	518.657i	0.817410	+	1.12507i	0.990137	+	0.140099i	$0.0447421\pi$
$461$	376.826	+	518.657i	0.817410	+	1.12507i	−0.172727	+	0.984970i	$0.555258\pi$
$462$		0			0
$463$	352.654	−	485.387i	0.761672	−	1.04835i	−0.235402	−	0.971898i	$-0.575641\pi$
$463$	352.654	−	485.387i	0.761672	−	1.04835i	0.997073	−	0.0764529i	$-0.0243595\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	22.5179	+	69.3029i	0.0482181	+	0.148400i	0.972267	−	0.233875i	$-0.0751407\pi$
$467$	22.5179	+	69.3029i	0.0482181	+	0.148400i	−0.924049	+	0.382275i	$0.875141\pi$
$468$		0			0
$469$	−265.785	−	818.002i	−0.566706	−	1.74414i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	435.019	−	316.060i	0.919702	−	0.668202i
$474$		0			0
$475$	10.2439	+	203.524i	0.0215662	+	0.428472i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−777.952	−	252.772i	−1.62412	−	0.527707i	−0.651208	−	0.758899i	$-0.725738\pi$
$479$	−777.952	−	252.772i	−1.62412	−	0.527707i	−0.972908	+	0.231192i	$0.925738\pi$
$480$		0			0
$481$	−92.5627	−	284.879i	−0.192438	−	0.592263i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−106.124	+	221.903i	−0.218813	+	0.457532i
$486$		0			0
$487$	−92.0246	+	126.661i	−0.188962	+	0.260084i	−0.892978	−	0.450100i	$-0.851388\pi$
$487$	−92.0246	+	126.661i	−0.188962	+	0.260084i	0.704016	+	0.710184i	$0.251388\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−531.221	+	731.163i	−1.08192	+	1.48913i	−0.224523	+	0.974469i	$0.572083\pi$
$491$	−531.221	+	731.163i	−1.08192	+	1.48913i	−0.857393	+	0.514662i	$0.827917\pi$
$492$		0			0
$493$		−	625.840i		−	1.26945i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	152.774	−	470.190i	0.307392	−	0.946056i
$498$		0			0
$499$	−50.1137			−0.100428			−0.0502141	−	0.998738i	$-0.515990\pi$
$499$	−50.1137			−0.100428			−0.0502141	+	0.998738i	$0.515990\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	131.545	−	404.855i	0.261522	−	0.804880i	−0.730953	−	0.682428i	$-0.760924\pi$
$503$	131.545	−	404.855i	0.261522	−	0.804880i	0.992474	−	0.122452i	$-0.0390759\pi$
$504$		0			0
$505$	−417.317	−	55.3802i	−0.826370	−	0.109664i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	180.844	−	248.910i	0.355293	−	0.489018i	−0.593537	−	0.804807i	$-0.702269\pi$
$509$	180.844	−	248.910i	0.355293	−	0.489018i	0.948830	+	0.315788i	$0.102269\pi$
$510$		0			0
$511$	645.489	−	468.975i	1.26319	−	0.917759i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	186.406	−	389.769i	0.361953	−	0.756834i
$516$		0			0
$517$	−136.238	+	44.2664i	−0.263516	+	0.0856217i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	415.983	+	135.161i	0.798432	+	0.259426i	0.679690	−	0.733499i	$-0.262114\pi$
$521$	415.983	+	135.161i	0.798432	+	0.259426i	0.118741	+	0.992925i	$0.462114\pi$
$522$		0			0
$523$	−365.611	−	503.220i	−0.699065	−	0.962180i	−0.999964	−	0.00852392i	$-0.997287\pi$
$523$	−365.611	−	503.220i	−0.699065	−	0.962180i	0.300899	−	0.953656i	$-0.402713\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−852.561	+	619.422i	−1.61776	+	1.17537i
$528$		0			0
$529$	−83.9384	+	258.336i	−0.158674	+	0.488348i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	109.001	+	335.470i	0.204504	+	0.629399i
$534$		0			0
$535$	−9.02509	+	68.0085i	−0.0168693	+	0.127119i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−490.626	−	675.289i	−0.910253	−	1.25286i
$540$		0			0
$541$	453.228	+	329.290i	0.837760	+	0.608669i	0.921744	−	0.387799i	$-0.126764\pi$
$541$	453.228	+	329.290i	0.837760	+	0.608669i	−0.0839838	+	0.996467i	$0.526764\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−293.732	+	308.889i	−0.538958	+	0.566768i
$546$		0			0
$547$	69.6668	+	22.6361i	0.127362	+	0.0413823i	0.372004	−	0.928231i	$-0.378671\pi$
$547$	69.6668	+	22.6361i	0.127362	+	0.0413823i	−0.244643	+	0.969613i	$0.578671\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			184.029i			0.333991i
$552$		0			0
$553$	−12.4930	−	4.05921i	−0.0225913	−	0.00734035i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−286.981			−0.515227			−0.257613	−	0.966248i	$-0.582936\pi$
$557$	−286.981			−0.515227			−0.257613	+	0.966248i	$0.582936\pi$
$558$		0			0
$559$	−301.520	−	219.067i	−0.539392	−	0.391891i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	164.992	+	119.874i	0.293058	+	0.212919i	0.724593	−	0.689177i	$-0.242028\pi$
$563$	164.992	+	119.874i	0.293058	+	0.212919i	−0.431535	+	0.902096i	$0.642028\pi$
$564$		0			0
$565$	−202.599	+	213.052i	−0.358582	+	0.377084i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−685.961	+	222.882i	−1.20556	+	0.391709i	−0.841802	−	0.539786i	$-0.818505\pi$
$569$	−685.961	+	222.882i	−1.20556	+	0.391709i	−0.363754	+	0.931495i	$0.618505\pi$
$570$		0			0
$571$	87.1234	−	268.138i	0.152580	−	0.469594i	−0.845327	−	0.534249i	$-0.820595\pi$
$571$	87.1234	−	268.138i	0.152580	−	0.469594i	0.997908	+	0.0646547i	$0.0205946\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−374.726	+	142.955i	−0.651698	+	0.248617i
$576$		0			0
$577$	−416.538	−	573.315i	−0.721902	−	0.993613i	−0.999459	−	0.0329037i	$-0.989525\pi$
$577$	−416.538	−	573.315i	−0.721902	−	0.993613i	0.277556	−	0.960709i	$-0.410475\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1483.80	+	482.115i	−2.55387	+	0.829802i
$582$		0			0
$583$	−80.7085	+	26.2238i	−0.138436	+	0.0449807i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	360.037	+	261.582i	0.613351	+	0.445626i	0.850593	−	0.525825i	$-0.176243\pi$
$587$	360.037	+	261.582i	0.613351	+	0.445626i	−0.237241	+	0.971451i	$0.576243\pi$
$588$		0			0
$589$	250.696	−	182.142i	0.425631	−	0.309239i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−503.466			−0.849015			−0.424507	−	0.905424i	$-0.639553\pi$
$593$	−503.466			−0.849015			−0.424507	+	0.905424i	$0.639553\pi$
$594$		0			0
$595$	−320.927	−	1741.62i	−0.539373	−	2.92710i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			943.301i			1.57479i	0.616446	+	0.787397i	$0.288572\pi$
$599$			943.301i			1.57479i	−0.616446	+	0.787397i	$0.711428\pi$
$600$		0			0
$601$	983.348			1.63619			0.818093	−	0.575086i	$-0.195031\pi$
$601$	983.348			1.63619			0.818093	+	0.575086i	$0.195031\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	305.046	+	145.887i	0.504208	+	0.241135i
$606$		0			0
$607$			281.312i			0.463446i	0.972782	+	0.231723i	$0.0744363\pi$
$607$			281.312i			0.463446i	−0.972782	+	0.231723i	$0.925564\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	58.3605	+	80.3263i	0.0955163	+	0.131467i
$612$		0			0
$613$	−193.872	+	266.842i	−0.316267	+	0.435305i	−0.937323	−	0.348462i	$-0.886704\pi$
$613$	−193.872	+	266.842i	−0.316267	+	0.435305i	0.621056	+	0.783767i	$0.286704\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−228.565	−	703.451i	−0.370446	−	1.14012i	−0.946500	−	0.322704i	$-0.895408\pi$
$617$	−228.565	−	703.451i	−0.370446	−	1.14012i	0.576054	−	0.817412i	$-0.304592\pi$
$618$		0			0
$619$	297.345	+	915.134i	0.480364	+	1.47841i	0.838585	+	0.544770i	$0.183383\pi$
$619$	297.345	+	915.134i	0.480364	+	1.47841i	−0.358222	+	0.933637i	$0.616617\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1673.16	+	1215.62i	−2.68565	+	1.95124i
$624$		0			0
$625$	539.968	+	314.738i	0.863948	+	0.503580i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1559.53	+	506.723i	2.47938	+	0.805600i
$630$		0			0
$631$	−10.7261	−	33.0115i	−0.0169985	−	0.0523162i	0.942197	−	0.335058i	$-0.108756\pi$
$631$	−10.7261	−	33.0115i	−0.0169985	−	0.0523162i	−0.959196	+	0.282742i	$0.908756\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	951.324	−	515.253i	1.49815	−	0.811422i
$636$		0			0
$637$	−340.063	+	468.056i	−0.533851	+	0.734782i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	527.686	−	726.298i	0.823223	−	1.13307i	−0.165924	−	0.986139i	$-0.553060\pi$
$641$	527.686	−	726.298i	0.823223	−	1.13307i	0.989147	−	0.146931i	$-0.0469395\pi$
$642$		0			0
$643$			288.639i			0.448894i	0.974486	+	0.224447i	$0.0720575\pi$
$643$			288.639i			0.448894i	−0.974486	+	0.224447i	$0.927942\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−236.502	+	727.878i	−0.365536	+	1.12500i	0.584109	+	0.811676i	$0.301444\pi$
$647$	−236.502	+	727.878i	−0.365536	+	1.12500i	−0.949645	+	0.313329i	$0.898556\pi$
$648$		0			0
$649$	426.659			0.657410
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−83.5194	+	257.046i	−0.127901	+	0.393639i	−0.994418	−	0.105508i	$-0.966353\pi$
$653$	−83.5194	+	257.046i	−0.127901	+	0.393639i	0.866517	+	0.499147i	$0.166353\pi$
$654$		0			0
$655$	−83.4741	−	453.001i	−0.127441	−	0.691605i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−576.812	+	793.914i	−0.875284	+	1.20472i	0.102421	+	0.994741i	$0.467341\pi$
$659$	−576.812	+	793.914i	−0.875284	+	1.20472i	−0.977705	+	0.209983i	$0.932659\pi$
$660$		0			0
$661$	−823.163	+	598.063i	−1.24533	+	0.904785i	−0.997941	−	0.0641309i	$-0.979572\pi$
$661$	−823.163	+	598.063i	−1.24533	+	0.904785i	−0.247389	+	0.968916i	$0.579572\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	94.3689	+	512.126i	0.141908	+	0.770114i
$666$		0			0
$667$	−344.465	+	111.924i	−0.516439	+	0.167801i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	182.344	+	59.2470i	0.271749	+	0.0882966i
$672$		0			0
$673$	251.303	+	345.889i	0.373408	+	0.513952i	0.953823	−	0.300369i	$-0.0971098\pi$
$673$	251.303	+	345.889i	0.373408	+	0.513952i	−0.580415	+	0.814321i	$0.697110\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	442.719	−	321.654i	0.653942	−	0.475116i	−0.210670	−	0.977557i	$-0.567565\pi$
$677$	442.719	−	321.654i	0.653942	−	0.475116i	0.864612	+	0.502441i	$0.167565\pi$
$678$		0			0
$679$	−194.238	+	597.802i	−0.286064	+	0.880416i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	47.8903	+	147.391i	0.0701176	+	0.215800i	0.979975	−	0.199122i	$-0.0638090\pi$
$683$	47.8903	+	147.391i	0.0701176	+	0.215800i	−0.909857	+	0.414922i	$0.863809\pi$
$684$		0			0
$685$	125.923	−	132.421i	0.183830	−	0.193315i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	34.5732	+	47.5859i	0.0501788	+	0.0690652i
$690$		0			0
$691$	−625.773	−	454.651i	−0.905605	−	0.657960i	0.0342947	−	0.999412i	$-0.489082\pi$
$691$	−625.773	−	454.651i	−0.905605	−	0.657960i	−0.939899	+	0.341451i	$0.889082\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	13.4411	+	24.8166i	0.0193397	+	0.0357073i
$696$		0			0
$697$	−1836.49	−	596.711i	−2.63484	−	0.856113i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	240.650i		−	0.343295i	−0.985158	−	0.171648i	$-0.945091\pi$
$701$		−	240.650i		−	0.343295i	0.985158	−	0.171648i	$-0.0549090\pi$
$702$		0			0
$703$	−458.582	−	149.002i	−0.652321	−	0.211952i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1075.77			−1.52160
$708$		0			0
$709$	−191.499	−	139.132i	−0.270097	−	0.196237i	0.444489	−	0.895784i	$-0.353385\pi$
$709$	−191.499	−	139.132i	−0.270097	−	0.196237i	−0.714586	+	0.699547i	$0.753385\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	493.402	+	358.478i	0.692009	+	0.502774i
$714$		0			0
$715$	−24.3330	+	183.361i	−0.0340322	+	0.256449i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−460.001	+	149.463i	−0.639778	+	0.207877i	−0.610902	−	0.791706i	$-0.709193\pi$
$719$	−460.001	+	149.463i	−0.639778	+	0.207877i	−0.0288766	+	0.999583i	$0.509193\pi$
$720$		0			0
$721$	341.176	−	1050.03i	0.473199	−	1.45636i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	472.723	+	308.383i	0.652032	+	0.425355i
$726$		0			0
$727$	411.687	+	566.638i	0.566282	+	0.779420i	0.992108	−	0.125385i	$-0.0400166\pi$
$727$	411.687	+	566.638i	0.566282	+	0.779420i	−0.425827	+	0.904805i	$0.640017\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1940.44	−	630.486i	2.65450	−	0.862498i
$732$		0			0
$733$	469.743	−	152.629i	0.640850	−	0.208225i	0.0294745	−	0.999566i	$-0.490617\pi$
$733$	469.743	−	152.629i	0.640850	−	0.208225i	0.611375	+	0.791341i	$0.290617\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−397.863	−	289.064i	−0.539841	−	0.392218i
$738$		0			0
$739$	324.932	−	236.077i	0.439691	−	0.319454i	−0.345821	−	0.938300i	$-0.612400\pi$
$739$	324.932	−	236.077i	0.439691	−	0.319454i	0.785512	+	0.618846i	$0.212400\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	565.340			0.760889			0.380444	−	0.924804i	$-0.375771\pi$
$743$	565.340			0.760889			0.380444	+	0.924804i	$0.375771\pi$
$744$		0			0
$745$	548.676	+	72.8123i	0.736478	+	0.0977346i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			175.314i			0.234064i
$750$		0			0
$751$	−950.813			−1.26606			−0.633031	−	0.774126i	$-0.718189\pi$
$751$	−950.813			−1.26606			−0.633031	+	0.774126i	$0.718189\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	29.0398	−	218.830i	0.0384634	−	0.289840i
$756$		0			0
$757$		−	424.990i		−	0.561414i	−0.959794	−	0.280707i	$-0.909431\pi$
$757$		−	424.990i		−	0.561414i	0.959794	−	0.280707i	$-0.0905689\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	186.504	+	256.701i	0.245078	+	0.337321i	0.913780	−	0.406210i	$-0.133150\pi$
$761$	186.504	+	256.701i	0.245078	+	0.337321i	−0.668702	+	0.743531i	$0.733150\pi$
$762$		0			0
$763$	−640.247	+	881.224i	−0.839117	+	1.15495i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−91.3843	−	281.252i	−0.119145	−	0.366691i
$768$		0			0
$769$	395.553	+	1217.39i	0.514373	+	1.58308i	0.784420	+	0.620230i	$0.212961\pi$
$769$	395.553	+	1217.39i	0.514373	+	1.58308i	−0.270047	+	0.962847i	$0.587039\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−427.486	+	310.587i	−0.553022	+	0.401794i	−0.828899	−	0.559399i	$-0.811032\pi$
$773$	−427.486	+	310.587i	−0.553022	+	0.401794i	0.275876	+	0.961193i	$0.411032\pi$
$774$		0			0
$775$	−47.7756	−	949.195i	−0.0616460	−	1.22477i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	540.021	+	175.463i	0.693223	+	0.225242i
$780$		0			0
$781$	−87.3529	−	268.845i	−0.111848	−	0.344231i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1487.47	−	197.395i	−1.89486	−	0.251458i
$786$		0			0
$787$	−258.075	+	355.210i	−0.327923	+	0.451347i	−0.940865	−	0.338781i	$-0.889986\pi$
$787$	−258.075	+	355.210i	−0.327923	+	0.451347i	0.612943	+	0.790127i	$0.289986\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−441.603	+	607.814i	−0.558284	+	0.768413i
$792$		0			0
$793$		−	132.890i		−	0.167579i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−172.927	+	532.214i	−0.216972	+	0.667772i	0.782035	+	0.623234i	$0.214182\pi$
$797$	−172.927	+	532.214i	−0.216972	+	0.667772i	−0.999008	+	0.0445381i	$0.985818\pi$
$798$		0			0
$799$	−543.544			−0.680280
$800$		0			0
$801$		0			0
$802$		0			0
$803$	140.975	−	433.876i	0.175560	−	0.540319i
$804$		0			0
$805$	−901.204	+	488.107i	−1.11951	+	0.606344i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−354.362	+	487.737i	−0.438025	+	0.602889i	−0.969772	−	0.244014i	$-0.921536\pi$
$809$	−354.362	+	487.737i	−0.438025	+	0.602889i	0.531747	+	0.846903i	$0.321536\pi$
$810$		0			0
$811$	600.245	−	436.104i	0.740130	−	0.537736i	−0.152622	−	0.988285i	$-0.548772\pi$
$811$	600.245	−	436.104i	0.740130	−	0.537736i	0.892752	+	0.450549i	$0.148772\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	657.989	+	625.704i	0.807349	+	0.767735i
$816$		0			0
$817$	−570.587	+	185.395i	−0.698393	+	0.226922i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−530.396	−	172.336i	−0.646037	−	0.209910i	−0.0323711	−	0.999476i	$-0.510306\pi$
$821$	−530.396	−	172.336i	−0.646037	−	0.209910i	−0.613666	+	0.789566i	$0.710306\pi$
$822$		0			0
$823$	−515.184	−	709.090i	−0.625983	−	0.861592i	0.371788	−	0.928318i	$-0.378745\pi$
$823$	−515.184	−	709.090i	−0.625983	−	0.861592i	−0.997771	+	0.0667254i	$0.978745\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1179.77	−	857.155i	1.42657	−	1.03646i	0.435926	−	0.899983i	$-0.356421\pi$
$827$	1179.77	−	857.155i	1.42657	−	1.03646i	0.990643	−	0.136480i	$-0.0435791\pi$
$828$		0			0
$829$	208.980	−	643.173i	0.252086	−	0.775842i	−0.742303	−	0.670064i	$-0.766267\pi$
$829$	208.980	−	643.173i	0.252086	−	0.775842i	0.994390	−	0.105778i	$-0.0337333\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−978.717	−	3012.18i	−1.17493	−	3.61607i
$834$		0			0
$835$	1086.53	−	200.214i	1.30123	−	0.239777i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−578.852	−	796.722i	−0.689931	−	0.949609i	0.310068	−	0.950714i	$-0.399648\pi$
$839$	−578.852	−	796.722i	−0.689931	−	0.949609i	−0.999999	+	0.00110545i	$0.999648\pi$
$840$		0			0
$841$	−268.022	−	194.729i	−0.318694	−	0.231545i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−704.926	+	129.896i	−0.834232	+	0.153723i
$846$		0			0
$847$	821.788	+	267.015i	0.970233	+	0.315248i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	948.994i		−	1.11515i
$852$		0			0
$853$	1048.19	+	340.578i	1.22883	+	0.399271i	0.850290	−	0.526314i	$-0.176426\pi$
$853$	1048.19	+	340.578i	1.22883	+	0.399271i	0.378540	+	0.925585i	$0.376426\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−174.377			−0.203474			−0.101737	−	0.994811i	$-0.532440\pi$
$857$	−174.377			−0.203474			−0.101737	+	0.994811i	$0.532440\pi$
$858$		0			0
$859$	−123.237	−	89.5368i	−0.143465	−	0.104234i	0.513737	−	0.857947i	$-0.328261\pi$
$859$	−123.237	−	89.5368i	−0.143465	−	0.104234i	−0.657203	+	0.753714i	$0.728261\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38.8132	−	28.1994i	−0.0449747	−	0.0326760i	0.565071	−	0.825042i	$-0.308849\pi$
$863$	−38.8132	−	28.1994i	−0.0449747	−	0.0326760i	−0.610045	+	0.792366i	$0.708849\pi$
$864$		0			0
$865$	−322.822	−	596.033i	−0.373204	−	0.689056i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.14322	+	2.32097i	−0.00822004	+	0.00267085i
$870$		0			0
$871$	−105.334	+	324.183i	−0.120934	+	0.372197i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1473.66	+	615.776i	1.68418	+	0.703743i
$876$		0			0
$877$	−181.134	−	249.310i	−0.206538	−	0.284276i	0.693164	−	0.720780i	$-0.256216\pi$
$877$	−181.134	−	249.310i	−0.206538	−	0.284276i	−0.899702	+	0.436504i	$0.856216\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−553.295	+	179.777i	−0.628031	+	0.204060i	−0.605703	−	0.795691i	$-0.707108\pi$
$881$	−553.295	+	179.777i	−0.628031	+	0.204060i	−0.0223283	+	0.999751i	$0.507108\pi$
$882$		0			0
$883$	655.467	−	212.974i	0.742318	−	0.241194i	0.0866457	−	0.996239i	$-0.472385\pi$
$883$	655.467	−	212.974i	0.742318	−	0.241194i	0.655673	+	0.755045i	$0.272385\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	916.527	+	665.896i	1.03329	+	0.750728i	0.968964	−	0.247201i	$-0.0795107\pi$
$887$	916.527	+	665.896i	1.03329	+	0.750728i	0.0643246	+	0.997929i	$0.479511\pi$
$888$		0			0
$889$	2236.69	−	1625.05i	2.51596	−	1.82795i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	159.830			0.178981
$894$		0			0
$895$	343.851	−	718.983i	0.384191	−	0.803333i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	858.273i		−	0.954697i
$900$		0			0
$901$	−322.000			−0.357380
$902$		0			0
$903$		0			0
$904$		0			0
$905$	557.406	−	102.713i	0.615918	−	0.113494i
$906$		0			0
$907$			252.483i			0.278372i	0.990266	+	0.139186i	$0.0444485\pi$
$907$			252.483i			0.278372i	−0.990266	+	0.139186i	$0.955551\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−272.692	−	375.329i	−0.299333	−	0.411996i	0.632685	−	0.774409i	$-0.281953\pi$
$911$	−272.692	−	375.329i	−0.299333	−	0.411996i	−0.932018	+	0.362413i	$0.881953\pi$
$912$		0			0
$913$	−524.342	+	721.695i	−0.574307	+	0.790466i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−363.743	−	1119.49i	−0.396667	−	1.22081i
$918$		0			0
$919$	131.225	+	403.870i	0.142792	+	0.439467i	0.996720	−	0.0809226i	$-0.0257867\pi$
$919$	131.225	+	403.870i	0.142792	+	0.439467i	−0.853929	+	0.520390i	$0.825787\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−158.512	+	115.165i	−0.171735	+	0.124773i
$924$		0			0
$925$	−1151.21	+	928.292i	−1.24455	+	1.00356i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	395.351	+	128.457i	0.425566	+	0.138275i	0.513967	−	0.857810i	$-0.328176\pi$
$929$	395.351	+	128.457i	0.425566	+	0.138275i	−0.0884005	+	0.996085i	$0.528176\pi$
$930$		0			0
$931$	287.793	+	885.735i	0.309122	+	0.951380i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−733.784	−	697.780i	−0.784796	−	0.746288i
$936$		0			0
$937$	177.366	−	244.123i	0.189291	−	0.260537i	−0.703814	−	0.710384i	$-0.748521\pi$
$937$	177.366	−	244.123i	0.189291	−	0.260537i	0.893106	+	0.449847i	$0.148521\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−44.7067	+	61.5335i	−0.0475098	+	0.0653916i	−0.832111	−	0.554609i	$-0.812868\pi$
$941$	−44.7067	+	61.5335i	−0.0475098	+	0.0653916i	0.784601	+	0.620001i	$0.212868\pi$
$942$		0			0
$943$			1117.52i			1.18507i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−307.692	+	946.977i	−0.324912	+	0.999976i	0.646569	+	0.762856i	$0.276203\pi$
$947$	−307.692	+	946.977i	−0.324912	+	0.999976i	−0.971480	+	0.237120i	$0.923797\pi$
$948$		0			0
$949$	−316.204			−0.333197
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−265.581	+	817.375i	−0.278679	+	0.857686i	0.709543	+	0.704662i	$0.248901\pi$
$953$	−265.581	+	817.375i	−0.278679	+	0.857686i	−0.988222	+	0.153024i	$0.951099\pi$
$954$		0			0
$955$	624.182	+	593.555i	0.653593	+	0.621523i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	274.475	−	377.782i	0.286209	−	0.393933i
$960$		0			0
$961$	−391.732	+	284.610i	−0.407629	+	0.296160i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1771.66	−	235.108i	−1.83591	−	0.243635i
$966$		0			0
$967$	1415.23	−	459.836i	1.46353	−	0.475528i	0.534381	−	0.845244i	$-0.320545\pi$
$967$	1415.23	−	459.836i	1.46353	−	0.475528i	0.929145	+	0.369715i	$0.120545\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	589.833	+	191.648i	0.607449	+	0.197372i	0.596560	−	0.802568i	$-0.296534\pi$
$971$	589.833	+	191.648i	0.607449	+	0.197372i	0.0108893	+	0.999941i	$0.496534\pi$
$972$		0			0
$973$	42.3917	+	58.3471i	0.0435680	+	0.0599662i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1449.53	−	1053.15i	1.48366	−	1.07794i	0.507301	−	0.861769i	$-0.330643\pi$
$977$	1449.53	−	1053.15i	1.48366	−	1.07794i	0.976355	−	0.216171i	$-0.0693569\pi$
$978$		0			0
$979$	−365.418	+	1124.64i	−0.373256	+	1.14877i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.9581	+	61.4247i	0.0203032	+	0.0624870i	0.960695	−	0.277607i	$-0.0895412\pi$
$983$	19.9581	+	61.4247i	0.0203032	+	0.0624870i	−0.940392	+	0.340094i	$0.889541\pi$
$984$		0			0
$985$	1341.57	+	641.603i	1.36200	+	0.651373i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−694.045	−	955.271i	−0.701764	−	0.965896i
$990$		0			0
$991$	−800.035	−	581.260i	−0.807301	−	0.586538i	0.105746	−	0.994393i	$-0.466277\pi$
$991$	−800.035	−	581.260i	−0.807301	−	0.586538i	−0.913047	+	0.407855i	$0.866277\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−213.616	+	1609.70i	−0.214690	+	1.61779i
$996$		0			0
$997$	1093.77	+	355.386i	1.09706	+	0.356456i	0.800970	−	0.598705i	$-0.204318\pi$
$997$	1093.77	+	355.386i	1.09706	+	0.356456i	0.296088	+	0.955161i	$0.404318\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.y.a.89.10	✓	80
3.2	odd	2	inner	900.3.y.a.89.11	yes	80
25.9	even	10	inner	900.3.y.a.809.11	yes	80
75.59	odd	10	inner	900.3.y.a.809.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.y.a.89.10	✓	80	1.1	even	1	trivial
900.3.y.a.89.11	yes	80	3.2	odd	2	inner
900.3.y.a.809.10	yes	80	75.59	odd	10	inner
900.3.y.a.809.11	yes	80	25.9	even	10	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.657760 + 4.95655i) q^{5} +12.7771i q^{7} +O(q^{10})\)	\(q+(-0.657760 + 4.95655i) q^{5} +12.7771i q^{7} +(4.29417 + 5.91041i) q^{11} +(2.97637 - 4.09662i) q^{13} +(8.56614 + 26.3639i) q^{17} +(-2.51888 - 7.75232i) q^{19} +(12.9789 - 9.42969i) q^{23} +(-24.1347 - 6.52044i) q^{25} +(-21.4717 - 6.97658i) q^{29} +(11.7476 + 36.1553i) q^{31} +(-63.3303 - 8.40427i) q^{35} +(34.7699 - 47.8567i) q^{37} +(-40.9447 + 56.3555i) q^{41} -73.6021i q^{43} +(-6.05918 + 18.6483i) q^{47} -114.254 q^{49} +(-3.58951 + 11.0474i) q^{53} +(-32.1198 + 17.3966i) q^{55} +(34.3273 - 47.2475i) q^{59} +(21.2315 - 15.4256i) q^{61} +(18.3474 + 17.4471i) q^{65} +(-64.0210 + 20.8017i) q^{67} +(-36.7994 - 11.9569i) q^{71} +(-36.7044 - 50.5192i) q^{73} +(-75.5179 + 54.8670i) q^{77} +(-0.317695 + 0.977763i) q^{79} +(37.7327 + 116.129i) q^{83} +(-136.308 + 25.1174i) q^{85} +(95.1407 + 130.950i) q^{89} +(52.3430 + 38.0294i) q^{91} +(40.0816 - 7.38579i) q^{95} +(46.7870 + 15.2020i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q+O(q^{10}) \) 80 * q	\( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) 80 * q + 60 * q^19 + 56 * q^25 - 120 * q^31 + 20 * q^37 - 680 * q^49 - 56 * q^55 - 80 * q^61 - 280 * q^67 - 360 * q^73 + 40 * q^79 + 192 * q^85 + 140 * q^91 - 40 * q^97

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