LMFDB - Embedded newform 360.4.m.c.179.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.10
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59365 - 1.12826i) q^{2} +(5.45407 + 5.85262i) q^{4} +(6.79264 + 8.88032i) q^{5} -14.0413 q^{7} +(-7.54271 - 21.3333i) q^{8} +O(q^{10})$	\(q+(-2.59365 - 1.12826i) q^{2} +(5.45407 + 5.85262i) q^{4} +(6.79264 + 8.88032i) q^{5} -14.0413 q^{7} +(-7.54271 - 21.3333i) q^{8} +(-7.59846 - 30.6963i) q^{10} +30.3917i q^{11} +63.3338 q^{13} +(36.4182 + 15.8422i) q^{14} +(-4.50624 + 63.8412i) q^{16} -111.898 q^{17} +151.363 q^{19} +(-14.9256 + 88.1886i) q^{20} +(34.2896 - 78.8254i) q^{22} +48.6086i q^{23} +(-32.7201 + 120.642i) q^{25} +(-164.266 - 71.4569i) q^{26} +(-76.5821 - 82.1782i) q^{28} -140.714 q^{29} -148.439i q^{31} +(83.7169 - 160.498i) q^{32} +(290.223 + 126.249i) q^{34} +(-95.3774 - 124.691i) q^{35} -313.282 q^{37} +(-392.583 - 170.776i) q^{38} +(138.211 - 211.891i) q^{40} +317.260i q^{41} -185.037i q^{43} +(-177.871 + 165.758i) q^{44} +(54.8431 - 126.074i) q^{46} -5.81902i q^{47} -145.842 q^{49} +(220.979 - 275.986i) q^{50} +(345.427 + 370.669i) q^{52} +11.0336i q^{53} +(-269.888 + 206.440i) q^{55} +(105.909 + 299.546i) q^{56} +(364.962 + 158.761i) q^{58} +487.075i q^{59} +615.070i q^{61} +(-167.478 + 385.000i) q^{62} +(-398.215 + 321.821i) q^{64} +(430.204 + 562.425i) q^{65} +1052.25i q^{67} +(-610.297 - 654.893i) q^{68} +(106.692 + 431.016i) q^{70} -731.511 q^{71} +712.466i q^{73} +(812.545 + 353.463i) q^{74} +(825.543 + 885.868i) q^{76} -426.738i q^{77} -1183.32i q^{79} +(-597.539 + 393.633i) q^{80} +(357.951 - 822.862i) q^{82} +571.286 q^{83} +(-760.079 - 993.685i) q^{85} +(-208.769 + 479.921i) q^{86} +(648.353 - 229.235i) q^{88} +210.625i q^{89} -889.288 q^{91} +(-284.488 + 265.115i) q^{92} +(-6.56536 + 15.0925i) q^{94} +(1028.15 + 1344.15i) q^{95} +796.429i q^{97} +(378.264 + 164.548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.59365	−	1.12826i	−0.916995	−	0.398899i
$2$	−2.59365	−	1.12826i	−0.916995	−	0.398899i
$3$		0			0
$3$		0			0
$4$	5.45407	+	5.85262i	0.681759	+	0.731577i
$5$	6.79264	+	8.88032i	0.607552	+	0.794280i
$5$	6.79264	+	8.88032i	0.607552	+	0.794280i
$6$		0			0
$7$	−14.0413			−0.758158			−0.379079	−	0.925364i	$-0.623759\pi$
$7$	−14.0413			−0.758158			−0.379079	+	0.925364i	$0.623759\pi$
$8$	−7.54271	−	21.3333i	−0.333344	−	0.942805i
$9$		0			0
$10$	−7.59846	−	30.6963i	−0.240285	−	0.970702i
$11$			30.3917i			0.833039i	0.909127	+	0.416520i	$0.136750\pi$
$11$			30.3917i			0.833039i	−0.909127	+	0.416520i	$0.863250\pi$
$12$		0			0
$13$	63.3338			1.35120			0.675602	−	0.737267i	$-0.263884\pi$
$13$	63.3338			1.35120			0.675602	+	0.737267i	$0.263884\pi$
$14$	36.4182	+	15.8422i	0.695227	+	0.302429i
$15$		0			0
$16$	−4.50624	+	63.8412i	−0.0704100	+	0.997518i
$17$	−111.898			−1.59642			−0.798210	−	0.602380i	$-0.794219\pi$
$17$	−111.898			−1.59642			−0.798210	+	0.602380i	$0.794219\pi$
$18$		0			0
$19$	151.363			1.82763			0.913816	−	0.406128i	$-0.133121\pi$
$19$	151.363			1.82763			0.913816	+	0.406128i	$0.133121\pi$
$20$	−14.9256	+	88.1886i	−0.166873	+	0.985978i
$21$		0			0
$22$	34.2896	−	78.8254i	0.332299	−	0.763893i
$23$			48.6086i			0.440678i	0.975423	+	0.220339i	$0.0707164\pi$
$23$			48.6086i			0.440678i	−0.975423	+	0.220339i	$0.929284\pi$
$24$		0			0
$25$	−32.7201	+	120.642i	−0.261761	+	0.965133i
$26$	−164.266	−	71.4569i	−1.23905	−	0.538994i
$27$		0			0
$28$	−76.5821	−	82.1782i	−0.516881	−	0.554651i
$29$	−140.714			−0.901029			−0.450515	−	0.892769i	$-0.648760\pi$
$29$	−140.714			−0.901029			−0.450515	+	0.892769i	$0.648760\pi$
$30$		0			0
$31$		−	148.439i		−	0.860016i	−0.902825	−	0.430008i	$-0.858511\pi$
$31$		−	148.439i		−	0.860016i	0.902825	−	0.430008i	$-0.141489\pi$
$32$	83.7169	−	160.498i	0.462475	−	0.886632i
$33$		0			0
$34$	290.223	+	126.249i	1.46391	+	0.636811i
$35$	−95.3774	−	124.691i	−0.460621	−	0.602190i
$36$		0			0
$37$	−313.282			−1.39198			−0.695990	−	0.718052i	$-0.745034\pi$
$37$	−313.282			−1.39198			−0.695990	+	0.718052i	$0.745034\pi$
$38$	−392.583	−	170.776i	−1.67593	−	0.729041i
$39$		0			0
$40$	138.211	−	211.891i	0.546328	−	0.837572i
$41$			317.260i			1.20848i	0.796803	+	0.604240i	$0.206523\pi$
$41$			317.260i			1.20848i	−0.796803	+	0.604240i	$0.793477\pi$
$42$		0			0
$43$		−	185.037i		−	0.656228i	−0.944638	−	0.328114i	$-0.893587\pi$
$43$		−	185.037i		−	0.656228i	0.944638	−	0.328114i	$-0.106413\pi$
$44$	−177.871	+	165.758i	−0.609432	+	0.567932i
$45$		0			0
$46$	54.8431	−	126.074i	0.175786	−	0.404100i
$47$		−	5.81902i		−	0.0180594i	−0.999959	−	0.00902970i	$-0.997126\pi$
$47$		−	5.81902i		−	0.0180594i	0.999959	−	0.00902970i	$-0.00287428\pi$
$48$		0			0
$49$	−145.842			−0.425196
$50$	220.979	−	275.986i	0.625024	−	0.780606i
$51$		0			0
$52$	345.427	+	370.669i	0.921195	+	0.988510i
$53$			11.0336i			0.0285959i	0.999898	+	0.0142979i	$0.00455133\pi$
$53$			11.0336i			0.0285959i	−0.999898	+	0.0142979i	$0.995449\pi$
$54$		0			0
$55$	−269.888	+	206.440i	−0.661666	+	0.506115i
$56$	105.909	+	299.546i	0.252727	+	0.714796i
$57$		0			0
$58$	364.962	+	158.761i	0.826239	+	0.359420i
$59$			487.075i			1.07478i	0.843335	+	0.537388i	$0.180589\pi$
$59$			487.075i			1.07478i	−0.843335	+	0.537388i	$0.819411\pi$
$60$		0			0
$61$			615.070i			1.29101i	0.763755	+	0.645506i	$0.223353\pi$
$61$			615.070i			1.29101i	−0.763755	+	0.645506i	$0.776647\pi$
$62$	−167.478	+	385.000i	−0.343060	+	0.788630i
$63$		0			0
$64$	−398.215	+	321.821i	−0.777764	+	0.628556i
$65$	430.204	+	562.425i	0.820927	+	1.07323i
$66$		0			0
$67$			1052.25i			1.91870i	0.282211	+	0.959352i	$0.408932\pi$
$67$			1052.25i			1.91870i	−0.282211	+	0.959352i	$0.591068\pi$
$68$	−610.297	−	654.893i	−1.08837	−	1.16790i
$69$		0			0
$70$	106.692	+	431.016i	0.182174	+	0.735946i
$71$	−731.511			−1.22274			−0.611369	−	0.791345i	$-0.709381\pi$
$71$	−731.511			−1.22274			−0.611369	+	0.791345i	$0.709381\pi$
$72$		0			0
$73$			712.466i			1.14230i	0.820846	+	0.571150i	$0.193503\pi$
$73$			712.466i			1.14230i	−0.820846	+	0.571150i	$0.806497\pi$
$74$	812.545	+	353.463i	1.27644	+	0.555260i
$75$		0			0
$76$	825.543	+	885.868i	1.24600	+	1.33705i
$77$		−	426.738i		−	0.631575i
$78$		0			0
$79$		−	1183.32i		−	1.68523i	−0.538513	−	0.842617i	$-0.681014\pi$
$79$		−	1183.32i		−	1.68523i	0.538513	−	0.842617i	$-0.318986\pi$
$80$	−597.539	+	393.633i	−0.835086	+	0.550119i
$81$		0			0
$82$	357.951	−	822.862i	0.482062	−	1.10817i
$83$	571.286			0.755504			0.377752	−	0.925907i	$-0.376697\pi$
$83$	571.286			0.755504			0.377752	+	0.925907i	$0.376697\pi$
$84$		0			0
$85$	−760.079	−	993.685i	−0.969908	−	1.26800i
$86$	−208.769	+	479.921i	−0.261769	+	0.601758i
$87$		0			0
$88$	648.353	−	229.235i	0.785394	−	0.277688i
$89$			210.625i			0.250856i	0.992103	+	0.125428i	$0.0400304\pi$
$89$			210.625i			0.250856i	−0.992103	+	0.125428i	$0.959970\pi$
$90$		0			0
$91$	−889.288			−1.02443
$92$	−284.488	+	265.115i	−0.322390	+	0.300436i
$93$		0			0
$94$	−6.56536	+	15.0925i	−0.00720388	+	0.0165604i
$95$	1028.15	+	1344.15i	1.11038	+	1.45165i
$96$		0			0
$97$			796.429i			0.833661i	0.908984	+	0.416831i	$0.136859\pi$
$97$			796.429i			0.833661i	−0.908984	+	0.416831i	$0.863141\pi$
$98$	378.264	+	164.548i	0.389903	+	0.169611i
$99$		0			0
$100$	−884.527	+	466.490i	−0.884527	+	0.466490i
$101$	−1735.89			−1.71018			−0.855089	−	0.518482i	$-0.826497\pi$
$101$	−1735.89			−1.71018			−0.855089	+	0.518482i	$0.826497\pi$
$102$		0			0
$103$	−314.830			−0.301175			−0.150588	−	0.988597i	$-0.548117\pi$
$103$	−314.830			−0.301175			−0.150588	+	0.988597i	$0.548117\pi$
$104$	−477.708	−	1351.12i	−0.450415	−	1.27392i
$105$		0			0
$106$	12.4487	−	28.6173i	0.0114069	−	0.0262223i
$107$	644.370			0.582183			0.291092	−	0.956695i	$-0.405982\pi$
$107$	644.370			0.582183			0.291092	+	0.956695i	$0.405982\pi$
$108$		0			0
$109$			119.444i			0.104960i	0.998622	+	0.0524800i	$0.0167126\pi$
$109$			119.444i			0.104960i	−0.998622	+	0.0524800i	$0.983287\pi$
$110$	932.912	−	230.930i	0.808633	−	0.200166i
$111$		0			0
$112$	63.2734	−	896.412i	0.0533819	−	0.756276i
$113$	−632.581			−0.526621			−0.263311	−	0.964711i	$-0.584814\pi$
$113$	−632.581			−0.526621			−0.263311	+	0.964711i	$0.584814\pi$
$114$		0			0
$115$	−431.660	+	330.181i	−0.350022	+	0.267735i
$116$	−767.462	−	823.543i	−0.614285	−	0.659172i
$117$		0			0
$118$	549.546	−	1263.30i	0.428728	−	0.985564i
$119$	1571.18			1.21034
$120$		0			0
$121$	407.347			0.306046
$122$	693.958	−	1595.28i	0.514984	−	1.18385i
$123$		0			0
$124$	868.758	−	809.598i	0.629168	−	0.586323i
$125$	−1293.59	+	528.910i	−0.925619	+	0.378457i
$126$		0			0
$127$	928.550			0.648784			0.324392	−	0.945923i	$-0.394840\pi$
$127$	928.550			0.648784			0.324392	+	0.945923i	$0.394840\pi$
$128$	1395.93	−	385.402i	0.963936	−	0.266133i
$129$		0			0
$130$	−481.240	−	1944.12i	−0.324673	−	1.31162i
$131$		−	154.216i		−	0.102854i	−0.998677	−	0.0514272i	$-0.983623\pi$
$131$		−	154.216i		−	0.102854i	0.998677	−	0.0514272i	$-0.0163770\pi$
$132$		0			0
$133$	−2125.33			−1.38563
$134$	1187.21	−	2729.18i	0.765370	−	1.75944i
$135$		0			0
$136$	844.010	+	2387.14i	0.532156	+	1.50511i
$137$	1307.59			0.815435			0.407717	−	0.913108i	$-0.366325\pi$
$137$	1307.59			0.815435			0.407717	+	0.913108i	$0.366325\pi$
$138$		0			0
$139$	−2549.37			−1.55565			−0.777823	−	0.628484i	$-0.783676\pi$
$139$	−2549.37			−1.55565			−0.777823	+	0.628484i	$0.783676\pi$
$140$	209.574	−	1238.28i	0.126516	−	0.747527i
$141$		0			0
$142$	1897.29	+	825.333i	1.12124	+	0.487750i
$143$			1924.82i			1.12561i
$144$		0			0
$145$	−955.817	−	1249.58i	−0.547422	−	0.715669i
$146$	803.846	−	1847.89i	0.455663	−	1.04748i
$147$		0			0
$148$	−1708.66	−	1833.52i	−0.948994	−	1.01834i
$149$	354.753			0.195050			0.0975251	−	0.995233i	$-0.468907\pi$
$149$	354.753			0.195050			0.0975251	+	0.995233i	$0.468907\pi$
$150$		0			0
$151$		−	436.218i		−	0.235092i	−0.993067	−	0.117546i	$-0.962497\pi$
$151$		−	436.218i		−	0.235092i	0.993067	−	0.117546i	$-0.0375028\pi$
$152$	−1141.69	−	3229.06i	−0.609230	−	1.72310i
$153$		0			0
$154$	−481.470	+	1106.81i	−0.251935	+	0.579151i
$155$	1318.19	−	1008.29i	0.683093	−	0.522504i
$156$		0			0
$157$	810.917			0.412218			0.206109	−	0.978529i	$-0.433920\pi$
$157$	810.917			0.412218			0.206109	+	0.978529i	$0.433920\pi$
$158$	−1335.09	+	3069.11i	−0.672239	+	1.54535i
$159$		0			0
$160$	1993.93	−	346.770i	0.985212	−	0.171341i
$161$		−	682.528i		−	0.334104i
$162$		0			0
$163$		−	119.040i		−	0.0572019i	−0.999591	−	0.0286010i	$-0.990895\pi$
$163$		−	119.040i		−	0.0572019i	0.999591	−	0.0286010i	$-0.00910521\pi$
$164$	−1856.80	+	1730.36i	−0.884096	+	0.823891i
$165$		0			0
$166$	−1481.72	−	644.558i	−0.692793	−	0.301370i
$167$			1454.55i			0.673992i	0.941506	+	0.336996i	$0.109411\pi$
$167$			1454.55i			0.673992i	−0.941506	+	0.336996i	$0.890589\pi$
$168$		0			0
$169$	1814.17			0.825751
$170$	850.249	+	3434.84i	0.383595	+	1.54965i
$171$		0			0
$172$	1082.95	−	1009.20i	0.480082	−	0.447389i
$173$		−	173.514i		−	0.0762545i	−0.999273	−	0.0381273i	$-0.987861\pi$
$173$		−	173.514i		−	0.0762545i	0.999273	−	0.0381273i	$-0.0121392\pi$
$174$		0			0
$175$	459.432	−	1693.96i	0.198456	−	0.731723i
$176$	−1940.24	−	136.952i	−0.830972	−	0.0586543i
$177$		0			0
$178$	237.639	−	546.288i	0.100066	−	0.230034i
$179$		−	1292.81i		−	0.539829i	−0.962884	−	0.269915i	$-0.913005\pi$
$179$		−	1292.81i		−	0.539829i	0.962884	−	0.269915i	$-0.0869955\pi$
$180$		0			0
$181$			1101.84i			0.452480i	0.974072	+	0.226240i	$0.0726434\pi$
$181$			1101.84i			0.452480i	−0.974072	+	0.226240i	$0.927357\pi$
$182$	2306.51	+	1003.35i	0.939393	+	0.408643i
$183$		0			0
$184$	1036.98	−	366.641i	0.415474	−	0.146897i
$185$	−2128.01	−	2782.04i	−0.845700	−	1.10562i
$186$		0			0
$187$		−	3400.75i		−	1.32988i
$188$	34.0565	−	31.7374i	0.0132118	−	0.0123122i
$189$		0			0
$190$	−1150.12	−	4646.28i	−0.439152	−	1.77409i
$191$	2525.60			0.956785			0.478392	−	0.878146i	$-0.341220\pi$
$191$	2525.60			0.956785			0.478392	+	0.878146i	$0.341220\pi$
$192$		0			0
$193$			714.880i			0.266623i	0.991074	+	0.133311i	$0.0425611\pi$
$193$			714.880i			0.266623i	−0.991074	+	0.133311i	$0.957439\pi$
$194$	898.577	−	2065.66i	0.332547	−	0.764463i
$195$		0			0
$196$	−795.434	−	853.559i	−0.289881	−	0.311064i
$197$		−	4074.92i		−	1.47374i	−0.676036	−	0.736869i	$-0.736304\pi$
$197$		−	4074.92i		−	1.47374i	0.676036	−	0.736869i	$-0.263696\pi$
$198$		0			0
$199$		−	4544.61i		−	1.61889i	−0.587197	−	0.809444i	$-0.699769\pi$
$199$		−	4544.61i		−	1.61889i	0.587197	−	0.809444i	$-0.300231\pi$
$200$	2820.48	−	211.938i	0.997189	−	0.0749315i
$201$		0			0
$202$	4502.31	+	1958.54i	1.56822	+	0.682189i
$203$	1975.80			0.683123
$204$		0			0
$205$	−2817.37	+	2155.03i	−0.959871	+	0.734214i
$206$	816.558	+	355.209i	0.276176	+	0.120139i
$207$		0			0
$208$	−285.397	+	4043.31i	−0.0951382	+	1.34785i
$209$			4600.17i			1.52249i
$210$		0			0
$211$	354.896			0.115792			0.0578959	−	0.998323i	$-0.481561\pi$
$211$	354.896			0.115792			0.0578959	+	0.998323i	$0.481561\pi$
$212$	−64.5754	+	60.1780i	−0.0209201	+	0.0194955i
$213$		0			0
$214$	−1671.27	−	727.016i	−0.533859	−	0.232233i
$215$	1643.18	−	1256.89i	0.521229	−	0.398693i
$216$		0			0
$217$			2084.28i			0.652028i
$218$	134.763	−	309.796i	0.0418685	−	0.0962478i
$219$		0			0
$220$	−2680.20	−	453.613i	−0.821359	−	0.139012i
$221$	−7086.90			−2.15709
$222$		0			0
$223$	−1709.19			−0.513255			−0.256627	−	0.966510i	$-0.582611\pi$
$223$	−1709.19			−0.513255			−0.256627	+	0.966510i	$0.582611\pi$
$224$	−1175.49	+	2253.59i	−0.350629	+	0.672207i
$225$		0			0
$226$	1640.70	+	713.714i	0.482909	+	0.210069i
$227$	2398.30			0.701236			0.350618	−	0.936519i	$-0.385972\pi$
$227$	2398.30			0.701236			0.350618	+	0.936519i	$0.385972\pi$
$228$		0			0
$229$			3355.07i			0.968161i	0.875023	+	0.484081i	$0.160846\pi$
$229$			3355.07i			0.968161i	−0.875023	+	0.484081i	$0.839154\pi$
$230$	1492.11	−	369.351i	0.427768	−	0.105888i
$231$		0			0
$232$	1061.36	+	3001.88i	0.300352	+	0.849495i
$233$	1851.67			0.520632			0.260316	−	0.965523i	$-0.416173\pi$
$233$	1851.67			0.520632			0.260316	+	0.965523i	$0.416173\pi$
$234$		0			0
$235$	51.6748	−	39.5265i	0.0143442	−	0.0109720i
$236$	−2850.67	+	2656.54i	−0.786282	+	0.732738i
$237$		0			0
$238$	−4075.11	−	1772.70i	−1.10987	−	0.482803i
$239$	2717.82			0.735570			0.367785	−	0.929911i	$-0.380116\pi$
$239$	2717.82			0.735570			0.367785	+	0.929911i	$0.380116\pi$
$240$		0			0
$241$	−4677.83			−1.25031			−0.625157	−	0.780499i	$-0.714965\pi$
$241$	−4677.83			−1.25031			−0.625157	+	0.780499i	$0.714965\pi$
$242$	−1056.52	−	459.592i	−0.280642	−	0.122081i
$243$		0			0
$244$	−3599.77	+	3354.64i	−0.944474	+	0.880158i
$245$	−990.655	−	1295.13i	−0.258329	−	0.337725i
$246$		0			0
$247$	9586.39			2.46950
$248$	−3166.69	+	1119.63i	−0.810827	+	0.286681i
$249$		0			0
$250$	3951.87	+	87.6950i	0.999754	+	0.0221853i
$251$		−	5063.30i		−	1.27328i	−0.771162	−	0.636639i	$-0.780324\pi$
$251$		−	5063.30i		−	1.27328i	0.771162	−	0.636639i	$-0.219676\pi$
$252$		0			0
$253$	−1477.30			−0.367102
$254$	−2408.34	−	1047.64i	−0.594931	−	0.258799i
$255$		0			0
$256$	−4055.39	−	575.367i	−0.990085	−	0.140471i
$257$	−2324.70			−0.564245			−0.282123	−	0.959378i	$-0.591038\pi$
$257$	−2324.70			−0.564245			−0.282123	+	0.959378i	$0.591038\pi$
$258$		0			0
$259$	4398.88			1.05534
$260$	−945.293	+	5585.32i	−0.225479	+	1.33226i
$261$		0			0
$262$	−173.996	+	399.983i	−0.0410285	+	0.0943169i
$263$			6005.08i			1.40794i	0.710229	+	0.703971i	$0.248592\pi$
$263$			6005.08i			1.40794i	−0.710229	+	0.703971i	$0.751408\pi$
$264$		0			0
$265$	−97.9819	+	74.9473i	−0.0227131	+	0.0173735i
$266$	5512.36	+	2397.92i	1.27062	+	0.552728i
$267$		0			0
$268$	−6158.44	+	5739.06i	−1.40368	+	1.30809i
$269$	3360.97			0.761791			0.380896	−	0.924618i	$-0.375616\pi$
$269$	3360.97			0.761791			0.380896	+	0.924618i	$0.375616\pi$
$270$		0			0
$271$			3737.81i			0.837844i	0.908022	+	0.418922i	$0.137592\pi$
$271$			3737.81i			0.837844i	−0.908022	+	0.418922i	$0.862408\pi$
$272$	504.237	−	7143.67i	0.112404	−	1.59246i
$273$		0			0
$274$	−3391.42	−	1475.29i	−0.747749	−	0.325276i
$275$	−3666.50	−	994.418i	−0.803994	−	0.218057i
$276$		0			0
$277$	5971.68			1.29532			0.647659	−	0.761930i	$-0.275748\pi$
$277$	5971.68			1.29532			0.647659	+	0.761930i	$0.275748\pi$
$278$	6612.18	+	2876.35i	1.42652	+	0.620546i
$279$		0			0
$280$	−1940.66	+	2975.22i	−0.414203	+	0.635012i
$281$			5259.86i			1.11664i	0.829624	+	0.558322i	$0.188555\pi$
$281$			5259.86i			1.11664i	−0.829624	+	0.558322i	$0.811445\pi$
$282$		0			0
$283$		−	5246.76i		−	1.10208i	−0.834480	−	0.551038i	$-0.814232\pi$
$283$		−	5246.76i		−	1.10208i	0.834480	−	0.551038i	$-0.185768\pi$
$284$	−3989.71	−	4281.26i	−0.833613	−	0.894527i
$285$		0			0
$286$	2171.69	−	4992.32i	0.449003	−	1.03217i
$287$		−	4454.73i		−	0.916218i
$288$		0			0
$289$	7608.05			1.54856
$290$	1069.21	+	4319.39i	0.216503	+	0.874632i
$291$		0			0
$292$	−4169.79	+	3885.84i	−0.835680	+	0.778773i
$293$		−	4962.29i		−	0.989419i	−0.869058	−	0.494710i	$-0.835274\pi$
$293$		−	4962.29i		−	0.989419i	0.869058	−	0.494710i	$-0.164726\pi$
$294$		0			0
$295$	−4325.38	+	3308.53i	−0.853673	+	0.652983i
$296$	2362.99	+	6683.32i	0.464008	+	1.31237i
$297$		0			0
$298$	−920.105	−	400.252i	−0.178860	−	0.0778053i
$299$			3078.57i			0.595446i
$300$		0			0
$301$			2598.15i			0.497525i
$302$	−492.166	+	1131.40i	−0.0937780	+	0.215578i
$303$		0			0
$304$	−682.077	+	9663.18i	−0.128684	+	1.82310i
$305$	−5462.02	+	4177.95i	−1.02542	+	0.784357i
$306$		0			0
$307$			9589.90i			1.78282i	0.453201	+	0.891408i	$0.350282\pi$
$307$			9589.90i			1.78282i	−0.453201	+	0.891408i	$0.649718\pi$
$308$	2497.53	−	2327.46i	0.462046	−	0.430582i
$309$		0			0
$310$	−4556.54	+	1127.91i	−0.834819	+	0.206648i
$311$	5604.82			1.02193			0.510965	−	0.859602i	$-0.329288\pi$
$311$	5604.82			1.02193			0.510965	+	0.859602i	$0.329288\pi$
$312$		0			0
$313$			353.882i			0.0639060i	0.999489	+	0.0319530i	$0.0101727\pi$
$313$			353.882i			0.0639060i	−0.999489	+	0.0319530i	$0.989827\pi$
$314$	−2103.24	−	914.923i	−0.378002	−	0.164433i
$315$		0			0
$316$	6925.50	−	6453.89i	1.23288	−	1.14892i
$317$		−	5733.38i		−	1.01583i	−0.861406	−	0.507916i	$-0.830416\pi$
$317$		−	5733.38i		−	1.01583i	0.861406	−	0.507916i	$-0.169584\pi$
$318$		0			0
$319$		−	4276.52i		−	0.750593i
$320$	−5562.80	−	1350.26i	−0.971782	−	0.235881i
$321$		0			0
$322$	−770.067	+	1770.24i	−0.133274	+	0.306371i
$323$	−16937.1			−2.91767
$324$		0			0
$325$	−2072.29	+	7640.70i	−0.353692	+	1.30409i
$326$	−134.308	+	308.748i	−0.0228178	+	0.0524539i
$327$		0			0
$328$	6768.18	−	2393.00i	1.13936	−	0.402839i
$329$			81.7066i			0.0136919i
$330$		0			0
$331$	1836.15			0.304907			0.152453	−	0.988311i	$-0.451283\pi$
$331$	1836.15			0.304907			0.152453	+	0.988311i	$0.451283\pi$
$332$	3115.84	+	3343.52i	0.515072	+	0.552709i
$333$		0			0
$334$	1641.11	−	3772.60i	0.268855	−	0.618047i
$335$	−9344.34	+	7147.58i	−1.52399	+	1.16571i
$336$		0			0
$337$		−	7168.05i		−	1.15866i	−0.815093	−	0.579330i	$-0.803314\pi$
$337$		−	7168.05i		−	1.15866i	0.815093	−	0.579330i	$-0.196686\pi$
$338$	−4705.34	−	2046.86i	−0.757209	−	0.329391i
$339$		0			0
$340$	1670.13	−	9868.08i	0.266399	−	1.57404i
$341$	4511.32			0.716427
$342$		0			0
$343$	6863.97			1.08052
$344$	−3947.43	+	1395.68i	−0.618696	+	0.218750i
$345$		0			0
$346$	−195.769	+	450.035i	−0.0304179	+	0.0699250i
$347$	2846.06			0.440301			0.220150	−	0.975466i	$-0.429345\pi$
$347$	2846.06			0.440301			0.220150	+	0.975466i	$0.429345\pi$
$348$		0			0
$349$		−	3078.32i		−	0.472145i	−0.971735	−	0.236072i	$-0.924140\pi$
$349$		−	3078.32i		−	0.472145i	0.971735	−	0.236072i	$-0.0758602\pi$
$350$	−3102.83	+	3875.19i	−0.473867	+	0.591822i
$351$		0			0
$352$	4877.79	+	2544.30i	0.738600	+	0.385260i
$353$	−1195.28			−0.180222			−0.0901111	−	0.995932i	$-0.528722\pi$
$353$	−1195.28			−0.180222			−0.0901111	+	0.995932i	$0.528722\pi$
$354$		0			0
$355$	−4968.89	−	6496.05i	−0.742877	−	0.971196i
$356$	−1232.71	+	1148.76i	−0.183520	+	0.171023i
$357$		0			0
$358$	−1458.63	+	3353.11i	−0.215338	+	0.495021i
$359$	11369.4			1.67146			0.835730	−	0.549140i	$-0.185045\pi$
$359$	11369.4			1.67146			0.835730	+	0.549140i	$0.185045\pi$
$360$		0			0
$361$	16051.7			2.34024
$362$	1243.16	−	2857.78i	0.180494	−	0.414922i
$363$		0			0
$364$	−4850.24	−	5204.66i	−0.698411	−	0.749446i
$365$	−6326.93	+	4839.53i	−0.907306	+	0.694007i
$366$		0			0
$367$	3778.32			0.537402			0.268701	−	0.963224i	$-0.413406\pi$
$367$	3778.32			0.537402			0.268701	+	0.963224i	$0.413406\pi$
$368$	−3103.23	−	219.042i	−0.439585	−	0.0310282i
$369$		0			0
$370$	2380.46	+	9616.60i	0.334471	+	1.35120i
$371$		−	154.926i		−	0.0216802i
$372$		0			0
$373$	2667.45			0.370282			0.185141	−	0.982712i	$-0.440726\pi$
$373$	2667.45			0.370282			0.185141	+	0.982712i	$0.440726\pi$
$374$	−3836.92	+	8820.37i	−0.530488	+	1.21949i
$375$		0			0
$376$	−124.139	+	43.8912i	−0.0170265	+	0.00601999i
$377$	−8911.93			−1.21747
$378$		0			0
$379$	10276.0			1.39272			0.696359	−	0.717694i	$-0.254802\pi$
$379$	10276.0			1.39272			0.696359	+	0.717694i	$0.254802\pi$
$380$	−2259.17	+	13348.5i	−0.304982	+	1.80201i
$381$		0			0
$382$	−6550.53	−	2849.53i	−0.877367	−	0.381661i
$383$		−	7183.82i		−	0.958423i	−0.877699	−	0.479212i	$-0.840923\pi$
$383$		−	7183.82i		−	0.958423i	0.877699	−	0.479212i	$-0.159077\pi$
$384$		0			0
$385$	3789.57	−	2898.68i	0.501648	−	0.383715i
$386$	806.569	−	1854.15i	0.106356	−	0.244492i
$387$		0			0
$388$	−4661.20	+	4343.78i	−0.609887	+	0.568356i
$389$	−6021.10			−0.784786			−0.392393	−	0.919798i	$-0.628353\pi$
$389$	−6021.10			−0.784786			−0.392393	+	0.919798i	$0.628353\pi$
$390$		0			0
$391$		−	5439.19i		−	0.703507i
$392$	1100.05	+	3111.29i	0.141737	+	0.400877i
$393$		0			0
$394$	−4597.56	+	10568.9i	−0.587873	+	1.35141i
$395$	10508.2	−	8037.85i	1.33855	−	1.02387i
$396$		0			0
$397$	−2203.60			−0.278578			−0.139289	−	0.990252i	$-0.544482\pi$
$397$	−2203.60			−0.278578			−0.139289	+	0.990252i	$0.544482\pi$
$398$	−5127.49	+	11787.1i	−0.645773	+	1.48451i
$399$		0			0
$400$	−7554.46	−	2632.53i	−0.944307	−	0.329066i
$401$		−	13798.8i		−	1.71841i	−0.511634	−	0.859203i	$-0.670960\pi$
$401$		−	13798.8i		−	1.71841i	0.511634	−	0.859203i	$-0.329040\pi$
$402$		0			0
$403$		−	9401.23i		−	1.16206i
$404$	−9467.69	−	10159.5i	−1.16593	−	1.25113i
$405$		0			0
$406$	−5124.54	−	2229.21i	−0.626420	−	0.272497i
$407$		−	9521.16i		−	1.15957i
$408$		0			0
$409$	−6090.24			−0.736290			−0.368145	−	0.929768i	$-0.620007\pi$
$409$	−6090.24			−0.736290			−0.368145	+	0.929768i	$0.620007\pi$
$410$	9738.70	−	2410.69i	1.17307	−	0.290379i
$411$		0			0
$412$	−1717.10	−	1842.58i	−0.205329	−	0.220333i
$413$		−	6839.16i		−	0.814850i
$414$		0			0
$415$	3880.54	+	5073.21i	0.459008	+	0.600082i
$416$	5302.11	−	10164.9i	0.624898	−	1.19802i
$417$		0			0
$418$	5190.17	−	11931.2i	0.607320	−	1.39611i
$419$			14952.8i			1.74341i	0.490029	+	0.871706i	$0.336986\pi$
$419$			14952.8i			1.74341i	−0.490029	+	0.871706i	$0.663014\pi$
$420$		0			0
$421$			101.209i			0.0117164i	0.999983	+	0.00585822i	$0.00186474\pi$
$421$			101.209i			0.0117164i	−0.999983	+	0.00585822i	$0.998135\pi$
$422$	−920.478	−	400.414i	−0.106180	−	0.0461893i
$423$		0			0
$424$	235.383	−	83.2232i	0.0269603	−	0.00953225i
$425$	3661.30	−	13499.5i	0.417880	−	1.54076i
$426$		0			0
$427$		−	8636.38i		−	0.978791i
$428$	3514.44	+	3771.25i	0.396909	+	0.425912i
$429$		0			0
$430$	−5679.94	+	1405.99i	−0.637002	+	0.157682i
$431$	−5279.77			−0.590064			−0.295032	−	0.955487i	$-0.595330\pi$
$431$	−5279.77			−0.590064			−0.295032	+	0.955487i	$0.595330\pi$
$432$		0			0
$433$			3777.19i			0.419215i	0.977786	+	0.209607i	$0.0672186\pi$
$433$			3777.19i			0.419215i	−0.977786	+	0.209607i	$0.932781\pi$
$434$	2351.60	−	5405.89i	0.260093	−	0.597906i
$435$		0			0
$436$	−699.059	+	651.455i	−0.0767864	+	0.0715574i
$437$			7357.54i			0.805398i
$438$		0			0
$439$			15445.6i			1.67922i	0.543189	+	0.839610i	$0.317217\pi$
$439$			15445.6i			1.67922i	−0.543189	+	0.839610i	$0.682783\pi$
$440$	6439.71	+	4200.47i	0.697730	+	0.455112i
$441$		0			0
$442$	18381.0	+	7995.85i	1.97804	+	0.860461i
$443$	8125.60			0.871465			0.435732	−	0.900076i	$-0.356489\pi$
$443$	8125.60			0.871465			0.435732	+	0.900076i	$0.356489\pi$
$444$		0			0
$445$	−1870.41	+	1430.70i	−0.199250	+	0.152408i
$446$	4433.05	+	1928.41i	0.470652	+	0.204737i
$447$		0			0
$448$	5591.45	−	4518.78i	0.589668	−	0.476545i
$449$			4045.56i			0.425216i	0.977138	+	0.212608i	$0.0681957\pi$
$449$			4045.56i			0.425216i	−0.977138	+	0.212608i	$0.931804\pi$
$450$		0			0
$451$	−9642.05			−1.00671
$452$	−3450.14	−	3702.25i	−0.359029	−	0.385264i
$453$		0			0
$454$	−6220.35	−	2705.90i	−0.643030	−	0.279722i
$455$	−6040.62	−	7897.16i	−0.622392	−	0.813681i
$456$		0			0
$457$			919.130i			0.0940811i	0.998893	+	0.0470406i	$0.0149790\pi$
$457$			919.130i			0.0940811i	−0.998893	+	0.0470406i	$0.985021\pi$
$458$	3785.38	−	8701.88i	0.386199	−	0.887799i
$459$		0			0
$460$	−4286.73	−	725.511i	−0.434499	−	0.0735372i
$461$	15971.7			1.61361			0.806807	−	0.590816i	$-0.201194\pi$
$461$	15971.7			1.61361			0.806807	+	0.590816i	$0.201194\pi$
$462$		0			0
$463$	−16002.9			−1.60630			−0.803149	−	0.595778i	$-0.796844\pi$
$463$	−16002.9			−1.60630			−0.803149	+	0.595778i	$0.796844\pi$
$464$	634.089	−	8983.32i	0.0634415	−	0.898793i
$465$		0			0
$466$	−4802.60	−	2089.17i	−0.477417	−	0.207680i
$467$	−1542.18			−0.152813			−0.0764065	−	0.997077i	$-0.524345\pi$
$467$	−1542.18			−0.152813			−0.0764065	+	0.997077i	$0.524345\pi$
$468$		0			0
$469$		−	14775.0i		−	1.45468i
$470$	−178.623	+	44.2156i	−0.0175303	+	0.00433939i
$471$		0			0
$472$	10390.9	−	3673.87i	1.01331	−	0.358270i
$473$	5623.57			0.546664
$474$		0			0
$475$	−4952.60	+	18260.7i	−0.478402	+	1.76391i
$476$	8569.35	+	9195.54i	0.825159	+	0.885456i
$477$		0			0
$478$	−7049.08	−	3066.40i	−0.674514	−	0.293418i
$479$	8896.60			0.848635			0.424318	−	0.905513i	$-0.360514\pi$
$479$	8896.60			0.848635			0.424318	+	0.905513i	$0.360514\pi$
$480$		0			0
$481$	−19841.4			−1.88085
$482$	12132.7	+	5277.80i	1.14653	+	0.498749i
$483$		0			0
$484$	2221.70	+	2384.04i	0.208649	+	0.223896i
$485$	−7072.54	+	5409.86i	−0.662160	+	0.506493i
$486$		0			0
$487$	−7971.71			−0.741751			−0.370876	−	0.928683i	$-0.620942\pi$
$487$	−7971.71			−0.741751			−0.370876	+	0.928683i	$0.620942\pi$
$488$	13121.5	−	4639.30i	1.21717	−	0.430350i
$489$		0			0
$490$	1108.18	+	4476.82i	0.102168	+	0.412739i
$491$		−	363.130i		−	0.0333764i	−0.999861	−	0.0166882i	$-0.994688\pi$
$491$		−	363.130i		−	0.0333764i	0.999861	−	0.0166882i	$-0.00531227\pi$
$492$		0			0
$493$	15745.5			1.43842
$494$	−24863.8	−	10815.9i	−2.26452	−	0.985083i
$495$		0			0
$496$	9476.54	+	668.903i	0.857881	+	0.0605537i
$497$	10271.4			0.927029
$498$		0			0
$499$	−1076.60			−0.0965840			−0.0482920	−	0.998833i	$-0.515378\pi$
$499$	−1076.60			−0.0965840			−0.0482920	+	0.998833i	$0.515378\pi$
$500$	−10150.8	−	4686.18i	−0.907919	−	0.419145i
$501$		0			0
$502$	−5712.71	+	13132.5i	−0.507910	+	1.16759i
$503$			7166.05i			0.635226i	0.948220	+	0.317613i	$0.102881\pi$
$503$			7166.05i			0.635226i	−0.948220	+	0.317613i	$0.897119\pi$
$504$		0			0
$505$	−11791.3	−	15415.3i	−1.03902	−	1.35836i
$506$	3831.60	+	1666.77i	0.336631	+	0.146437i
$507$		0			0
$508$	5064.38	+	5434.45i	0.442314	+	0.474635i
$509$	16936.2			1.47482			0.737409	−	0.675446i	$-0.236049\pi$
$509$	16936.2			1.47482			0.737409	+	0.675446i	$0.236049\pi$
$510$		0			0
$511$		−	10003.9i		−	0.866044i
$512$	9869.11	+	6067.82i	0.851869	+	0.523755i
$513$		0			0
$514$	6029.47	+	2622.86i	0.517410	+	0.225077i
$515$	−2138.52	−	2795.79i	−0.182980	−	0.239218i
$516$		0			0
$517$	176.850			0.0150442
$518$	−11409.2	−	4963.07i	−0.967742	−	0.420975i
$519$		0			0
$520$	8753.44	−	13419.9i	0.738200	−	1.13173i
$521$		−	3334.10i		−	0.280364i	−0.990126	−	0.140182i	$-0.955231\pi$
$521$		−	3334.10i		−	0.280364i	0.990126	−	0.140182i	$-0.0447687\pi$
$522$		0			0
$523$		−	3964.78i		−	0.331487i	−0.986169	−	0.165743i	$-0.946998\pi$
$523$		−	3964.78i		−	0.331487i	0.986169	−	0.165743i	$-0.0530023\pi$
$524$	902.568	−	841.106i	0.0752459	−	0.0701219i
$525$		0			0
$526$	6775.27	−	15575.1i	0.561627	−	1.29108i
$527$			16610.0i			1.37295i
$528$		0			0
$529$	9804.20			0.805803
$530$	338.691	−	83.8384i	0.0277581	−	0.00687115i
$531$		0			0
$532$	−11591.7	−	12438.7i	−0.944668	−	1.01370i
$533$			20093.3i			1.63290i
$534$		0			0
$535$	4376.97	+	5722.21i	0.353707	+	0.462416i
$536$	22448.0	−	7936.84i	1.80897	−	0.639588i
$537$		0			0
$538$	−8717.19	−	3792.04i	−0.698559	−	0.303878i
$539$		−	4432.39i		−	0.354205i
$540$		0			0
$541$		−	286.199i		−	0.0227443i	−0.999935	−	0.0113722i	$-0.996380\pi$
$541$		−	286.199i		−	0.0227443i	0.999935	−	0.0113722i	$-0.00361995\pi$
$542$	4217.21	−	9694.58i	0.334215	−	0.768299i
$543$		0			0
$544$	−9367.71	+	17959.3i	−0.738304	+	1.41544i
$545$	−1060.70	+	811.339i	−0.0833676	+	0.0637687i
$546$		0			0
$547$			19478.4i			1.52255i	0.648428	+	0.761276i	$0.275427\pi$
$547$			19478.4i			1.52255i	−0.648428	+	0.761276i	$0.724573\pi$
$548$	7131.66	+	7652.80i	0.555930	+	0.596553i
$549$		0			0
$550$	8387.67	+	6715.93i	0.650275	+	0.520670i
$551$	−21298.8			−1.64675
$552$		0			0
$553$			16615.3i			1.27767i
$554$	−15488.5	−	6737.59i	−1.18780	−	0.516702i
$555$		0			0
$556$	−13904.4	−	14920.5i	−1.06058	−	1.13807i
$557$		−	3805.21i		−	0.289465i	−0.989471	−	0.144733i	$-0.953768\pi$
$557$		−	3805.21i		−	0.289465i	0.989471	−	0.144733i	$-0.0462322\pi$
$558$		0			0
$559$		−	11719.1i		−	0.886698i
$560$	8390.22	−	5527.11i	0.633127	−	0.417077i
$561$		0			0
$562$	5934.47	−	13642.2i	0.445428	−	1.02396i
$563$	3093.37			0.231563			0.115781	−	0.993275i	$-0.463063\pi$
$563$	3093.37			0.231563			0.115781	+	0.993275i	$0.463063\pi$
$564$		0			0
$565$	−4296.89	−	5617.52i	−0.319950	−	0.418285i
$566$	−5919.70	+	13608.3i	−0.439618	+	1.01060i
$567$		0			0
$568$	5517.58	+	15605.5i	0.407592	+	1.15280i
$569$			24728.1i			1.82189i	0.412525	+	0.910946i	$0.364647\pi$
$569$			24728.1i			1.82189i	−0.412525	+	0.910946i	$0.635353\pi$
$570$		0			0
$571$	−9393.97			−0.688486			−0.344243	−	0.938881i	$-0.611864\pi$
$571$	−9393.97			−0.688486			−0.344243	+	0.938881i	$0.611864\pi$
$572$	−11265.2	+	10498.1i	−0.823467	+	0.767391i
$573$		0			0
$574$	−5026.09	+	11554.0i	−0.365479	+	0.840167i
$575$	−5864.22	−	1590.48i	−0.425313	−	0.115352i
$576$		0			0
$577$			10793.5i			0.778751i	0.921079	+	0.389376i	$0.127309\pi$
$577$			10793.5i			0.778751i	−0.921079	+	0.389376i	$0.872691\pi$
$578$	−19732.6	−	8583.84i	−1.42002	−	0.617718i
$579$		0			0
$580$	2100.23	−	12409.3i	0.150357	−	0.888396i
$581$	−8021.60			−0.572792
$582$		0			0
$583$	−335.329			−0.0238215
$584$	15199.2	−	5373.92i	1.07697	−	0.380778i
$585$		0			0
$586$	−5598.74	+	12870.4i	−0.394679	+	0.907292i
$587$	−10562.7			−0.742708			−0.371354	−	0.928491i	$-0.621106\pi$
$587$	−10562.7			−0.742708			−0.371354	+	0.928491i	$0.621106\pi$
$588$		0			0
$589$		−	22468.2i		−	1.57179i
$590$	14951.4	−	3701.02i	1.04329	−	0.258252i
$591$		0			0
$592$	1411.72	−	20000.3i	0.0980093	−	1.38852i
$593$	25688.7			1.77894			0.889469	−	0.456996i	$-0.151075\pi$
$593$	25688.7			1.77894			0.889469	+	0.456996i	$0.151075\pi$
$594$		0			0
$595$	10672.5	+	13952.6i	0.735344	+	0.961347i
$596$	1934.85	+	2076.23i	0.132977	+	0.142694i
$597$		0			0
$598$	3473.42	−	7984.75i	0.237523	−	0.546021i
$599$	−11053.0			−0.753947			−0.376973	−	0.926224i	$-0.623035\pi$
$599$	−11053.0			−0.753947			−0.376973	+	0.926224i	$0.623035\pi$
$600$		0			0
$601$	−10934.8			−0.742164			−0.371082	−	0.928600i	$-0.621013\pi$
$601$	−10934.8			−0.742164			−0.371082	+	0.928600i	$0.621013\pi$
$602$	2931.38	−	6738.70i	0.198462	−	0.456228i
$603$		0			0
$604$	2553.01	−	2379.16i	0.171988	−	0.160276i
$605$	2766.96	+	3617.37i	0.185939	+	0.243086i
$606$		0			0
$607$	−9715.02			−0.649622			−0.324811	−	0.945779i	$-0.605301\pi$
$607$	−9715.02			−0.649622			−0.324811	+	0.945779i	$0.605301\pi$
$608$	12671.6	−	24293.4i	0.845234	−	1.62044i
$609$		0			0
$610$	18880.4	−	4673.59i	1.25319	−	0.310210i
$611$		−	368.541i		−	0.0244019i
$612$		0			0
$613$	−3849.43			−0.253633			−0.126817	−	0.991926i	$-0.540476\pi$
$613$	−3849.43			−0.253633			−0.126817	+	0.991926i	$0.540476\pi$
$614$	10819.9	−	24872.9i	0.711164	−	1.63483i
$615$		0			0
$616$	−9103.71	+	3218.76i	−0.595453	+	0.210532i
$617$	16340.1			1.06617			0.533086	−	0.846061i	$-0.321032\pi$
$617$	16340.1			1.06617			0.533086	+	0.846061i	$0.321032\pi$
$618$		0			0
$619$	7719.88			0.501274			0.250637	−	0.968081i	$-0.419360\pi$
$619$	7719.88			0.501274			0.250637	+	0.968081i	$0.419360\pi$
$620$	13090.7	+	2215.54i	0.847957	+	0.143513i
$621$		0			0
$622$	−14536.9	−	6323.68i	−0.937104	−	0.407647i
$623$		−	2957.44i		−	0.190188i
$624$		0			0
$625$	−13483.8	−	7894.81i	−0.862963	−	0.505268i
$626$	399.270	−	917.846i	0.0254920	−	0.0586014i
$627$		0			0
$628$	4422.80	+	4745.99i	0.281033	+	0.301569i
$629$	35055.5			2.22218
$630$		0			0
$631$			21913.5i			1.38251i	0.722611	+	0.691254i	$0.242942\pi$
$631$			21913.5i			1.38251i	−0.722611	+	0.691254i	$0.757058\pi$
$632$	−25244.0	+	8925.41i	−1.58885	+	0.561762i
$633$		0			0
$634$	−6468.73	+	14870.4i	−0.405215	+	0.931513i
$635$	6307.31	+	8245.82i	0.394170	+	0.515316i
$636$		0			0
$637$	−9236.76			−0.574527
$638$	−4825.02	+	11091.8i	−0.299411	+	0.688290i
$639$		0			0
$640$	12904.5	+	9778.39i	0.797026	+	0.603945i
$641$		−	8731.46i		−	0.538022i	−0.963137	−	0.269011i	$-0.913303\pi$
$641$		−	8731.46i		−	0.538022i	0.963137	−	0.269011i	$-0.0866968\pi$
$642$		0			0
$643$		−	14460.4i		−	0.886878i	−0.896305	−	0.443439i	$-0.853758\pi$
$643$		−	14460.4i		−	0.886878i	0.896305	−	0.443439i	$-0.146242\pi$
$644$	3994.57	−	3722.55i	0.244423	−	0.227778i
$645$		0			0
$646$	43929.0	+	19109.4i	2.67549	+	1.16386i
$647$		−	26965.2i		−	1.63850i	−0.573434	−	0.819252i	$-0.694389\pi$
$647$		−	26965.2i		−	1.63850i	0.573434	−	0.819252i	$-0.305611\pi$
$648$		0			0
$649$	−14803.0			−0.895331
$650$	13995.5	−	17479.2i	0.844535	−	1.05476i
$651$		0			0
$652$	696.694	−	649.251i	0.0418476	−	0.0389979i
$653$			12180.8i			0.729972i	0.931013	+	0.364986i	$0.118926\pi$
$653$			12180.8i			0.729972i	−0.931013	+	0.364986i	$0.881074\pi$
$654$		0			0
$655$	1369.49	−	1047.53i	0.0816952	−	0.0624894i
$656$	−20254.2	−	1429.65i	−1.20548	−	0.0850890i
$657$		0			0
$658$	92.1860	−	211.918i	0.00546168	−	0.0125554i
$659$			3442.68i			0.203502i	0.994810	+	0.101751i	$0.0324445\pi$
$659$			3442.68i			0.203502i	−0.994810	+	0.101751i	$0.967556\pi$
$660$		0			0
$661$			1292.22i			0.0760387i	0.999277	+	0.0380193i	$0.0121048\pi$
$661$			1292.22i			0.0760387i	−0.999277	+	0.0380193i	$0.987895\pi$
$662$	−4762.35	−	2071.65i	−0.279598	−	0.121627i
$663$		0			0
$664$	−4309.05	−	12187.4i	−0.251842	−	0.712293i
$665$	−14436.6	−	18873.6i	−0.841845	−	1.10058i
$666$		0			0
$667$		−	6839.89i		−	0.397064i
$668$	−8512.93	+	7933.23i	−0.493077	+	0.459500i
$669$		0			0
$670$	32300.3	−	7995.51i	1.86249	−	0.461035i
$671$	−18693.0			−1.07546
$672$		0			0
$673$			27423.0i			1.57070i	0.619053	+	0.785350i	$0.287517\pi$
$673$			27423.0i			1.57070i	−0.619053	+	0.785350i	$0.712483\pi$
$674$	−8087.40	+	18591.4i	−0.462189	+	1.06249i
$675$		0			0
$676$	9894.64	+	10617.7i	0.562963	+	0.604101i
$677$			35099.8i			1.99261i	0.0859011	+	0.996304i	$0.472623\pi$
$677$			35099.8i			1.99261i	−0.0859011	+	0.996304i	$0.527377\pi$
$678$		0			0
$679$		−	11182.9i		−	0.632047i
$680$	−15465.5	+	23710.0i	−0.872168	+	1.33712i
$681$		0			0
$682$	−11700.8	−	5089.93i	−0.656960	−	0.285782i
$683$	−26455.9			−1.48215			−0.741074	−	0.671423i	$-0.765683\pi$
$683$	−26455.9			−1.48215			−0.741074	+	0.671423i	$0.765683\pi$
$684$		0			0
$685$	8881.96	+	11611.8i	0.495419	+	0.647683i
$686$	−17802.8	−	7744.33i	−0.990835	−	0.431020i
$687$		0			0
$688$	11813.0	+	833.819i	0.654600	+	0.0462050i
$689$			698.800i			0.0386388i
$690$		0			0
$691$	25601.3			1.40943			0.704716	−	0.709490i	$-0.251074\pi$
$691$	25601.3			1.40943			0.704716	+	0.709490i	$0.251074\pi$
$692$	1015.51	−	946.358i	0.0557861	−	0.0519872i
$693$		0			0
$694$	−7381.69	−	3211.09i	−0.403754	−	0.175636i
$695$	−17317.0	−	22639.2i	−0.945136	−	1.23562i
$696$		0			0
$697$		−	35500.6i		−	1.92924i
$698$	−3473.13	+	7984.08i	−0.188338	+	0.432954i
$699$		0			0
$700$	12419.9	−	6550.11i	0.670611	−	0.353673i
$701$	−8555.70			−0.460976			−0.230488	−	0.973075i	$-0.574032\pi$
$701$	−8555.70			−0.460976			−0.230488	+	0.973075i	$0.574032\pi$
$702$		0			0
$703$	−47419.2			−2.54403
$704$	−9780.67	−	12102.4i	−0.523612	−	0.647908i
$705$		0			0
$706$	3100.15	+	1348.59i	0.165263	+	0.0718905i
$707$	24374.2			1.29658
$708$		0			0
$709$		−	20124.0i		−	1.06597i	−0.846124	−	0.532986i	$-0.821070\pi$
$709$		−	20124.0i		−	1.06597i	0.846124	−	0.532986i	$-0.178930\pi$
$710$	5558.36	+	22454.7i	0.293805	+	1.18692i
$711$		0			0
$712$	4493.31	−	1588.68i	0.236508	−	0.0836212i
$713$	7215.43			0.378990
$714$		0			0
$715$	−17093.0	+	13074.6i	−0.894046	+	0.683864i
$716$	7566.34	−	7051.10i	0.394927	−	0.368033i
$717$		0			0
$718$	−29488.3	−	12827.6i	−1.53272	−	0.666744i
$719$	−13891.8			−0.720550			−0.360275	−	0.932846i	$-0.617317\pi$
$719$	−13891.8			−0.720550			−0.360275	+	0.932846i	$0.617317\pi$
$720$		0			0
$721$	4420.61			0.228339
$722$	−41632.5	−	18110.5i	−2.14599	−	0.933520i
$723$		0			0
$724$	−6448.63	+	6009.50i	−0.331024	+	0.308482i
$725$	4604.16	−	16975.9i	0.235854	−	0.869613i
$726$		0			0
$727$	−22036.5			−1.12419			−0.562097	−	0.827072i	$-0.690005\pi$
$727$	−22036.5			−1.12419			−0.562097	+	0.827072i	$0.690005\pi$
$728$	6707.64	+	18971.4i	0.341486	+	0.965834i
$729$		0			0
$730$	21870.1	−	5413.65i	1.10883	−	0.274477i
$731$			20705.1i			1.04762i
$732$		0			0
$733$	4002.94			0.201708			0.100854	−	0.994901i	$-0.467843\pi$
$733$	4002.94			0.201708			0.100854	+	0.994901i	$0.467843\pi$
$734$	−9799.64	−	4262.91i	−0.492795	−	0.214369i
$735$		0			0
$736$	7801.57	+	4069.36i	0.390720	+	0.203803i
$737$	−31979.7			−1.59836
$738$		0			0
$739$	6204.07			0.308823			0.154412	−	0.988007i	$-0.450652\pi$
$739$	6204.07			0.308823			0.154412	+	0.988007i	$0.450652\pi$
$740$	4675.91	−	27627.9i	0.232284	−	1.37246i
$741$		0			0
$742$	−174.796	+	401.824i	−0.00864821	+	0.0198806i
$743$			1520.13i			0.0750583i	0.999296	+	0.0375292i	$0.0119487\pi$
$743$			1520.13i			0.0750583i	−0.999296	+	0.0375292i	$0.988051\pi$
$744$		0			0
$745$	2409.71	+	3150.32i	0.118503	+	0.154924i
$746$	−6918.43	−	3009.57i	−0.339547	−	0.147705i
$747$		0			0
$748$	19903.3	−	18547.9i	0.972910	−	0.906657i
$749$	−9047.78			−0.441387
$750$		0			0
$751$			12993.9i			0.631362i	0.948865	+	0.315681i	$0.102233\pi$
$751$			12993.9i			0.631362i	−0.948865	+	0.315681i	$0.897767\pi$
$752$	371.493	+	26.2219i	0.0180146	+	0.00127156i
$753$		0			0
$754$	23114.5	+	10055.0i	1.11642	+	0.485650i
$755$	3873.75	−	2963.07i	0.186729	−	0.142831i
$756$		0			0
$757$	−8162.89			−0.391922			−0.195961	−	0.980612i	$-0.562783\pi$
$757$	−8162.89			−0.391922			−0.195961	+	0.980612i	$0.562783\pi$
$758$	−26652.3	−	11593.9i	−1.27712	−	0.555554i
$759$		0			0
$760$	20920.0	−	32072.4i	0.998486	−	1.53077i
$761$			22163.0i			1.05573i	0.849329	+	0.527864i	$0.177007\pi$
$761$			22163.0i			1.05573i	−0.849329	+	0.527864i	$0.822993\pi$
$762$		0			0
$763$		−	1677.14i		−	0.0795763i
$764$	13774.8	+	14781.4i	0.652297	+	0.699962i
$765$		0			0
$766$	−8105.20	+	18632.3i	−0.382314	+	0.878869i
$767$			30848.4i			1.45224i
$768$		0			0
$769$	37388.7			1.75328			0.876639	−	0.481149i	$-0.159780\pi$
$769$	37388.7			1.75328			0.876639	+	0.481149i	$0.159780\pi$
$770$	−13099.3	+	3242.55i	−0.613072	+	0.151758i
$771$		0			0
$772$	−4183.92	+	3899.01i	−0.195055	+	0.181772i
$773$		−	42163.6i		−	1.96186i	−0.194351	−	0.980932i	$-0.562260\pi$
$773$		−	42163.6i		−	1.96186i	0.194351	−	0.980932i	$-0.437740\pi$
$774$		0			0
$775$	17908.0	+	4856.95i	0.830029	+	0.225118i
$776$	16990.4	−	6007.23i	0.785980	−	0.277896i
$777$		0			0
$778$	15616.6	+	6793.35i	0.719645	+	0.313051i
$779$			48021.3i			2.20866i
$780$		0			0
$781$		−	22231.9i		−	1.01859i
$782$	−6136.80	+	14107.4i	−0.280629	+	0.645113i
$783$		0			0
$784$	657.201	−	9310.75i	0.0299381	−	0.424141i
$785$	5508.27	+	7201.20i	0.250444	+	0.327416i
$786$		0			0
$787$			28907.6i			1.30933i	0.755917	+	0.654667i	$0.227191\pi$
$787$			28907.6i			1.30933i	−0.755917	+	0.654667i	$0.772809\pi$
$788$	23849.0	−	22224.9i	1.07815	−	1.00473i
$789$		0			0
$790$	−36323.5	+	8991.39i	−1.63586	+	0.404936i
$791$	8882.25			0.399262
$792$		0			0
$793$			38954.8i			1.74442i
$794$	5715.38	+	2486.23i	0.255455	+	0.111125i
$795$		0			0
$796$	26597.8	−	24786.6i	1.18434	−	1.10369i
$797$			37052.8i			1.64677i	0.567483	+	0.823385i	$0.307917\pi$
$797$			37052.8i			1.64677i	−0.567483	+	0.823385i	$0.692083\pi$
$798$		0			0
$799$			651.134i			0.0288304i
$800$	16623.5	+	15351.2i	0.734660	+	0.678435i
$801$		0			0
$802$	−15568.6	+	35789.4i	−0.685471	+	1.57577i
$803$	−21653.0			−0.951581
$804$		0			0
$805$	6061.06	−	4636.16i	0.265372	−	0.202985i
$806$	−10607.0	+	24383.5i	−0.463543	+	1.06560i
$807$		0			0
$808$	13093.3	+	37032.3i	0.570077	+	1.61236i
$809$		−	8571.51i		−	0.372507i	−0.982502	−	0.186254i	$-0.940365\pi$
$809$		−	8571.51i		−	0.372507i	0.982502	−	0.186254i	$-0.0596346\pi$
$810$		0			0
$811$	−3327.82			−0.144088			−0.0720441	−	0.997401i	$-0.522952\pi$
$811$	−3327.82			−0.144088			−0.0720441	+	0.997401i	$0.522952\pi$
$812$	10776.1	+	11563.6i	0.465725	+	0.499757i
$813$		0			0
$814$	−10742.3	+	24694.6i	−0.462553	+	1.06332i
$815$	1057.11	−	808.594i	0.0454343	−	0.0347532i
$816$		0			0
$817$		−	28007.7i		−	1.19934i
$818$	15796.0	+	6871.35i	0.675174	+	0.293706i
$819$		0			0
$820$	−27978.7	−	4735.28i	−1.19153	−	0.201662i
$821$	−17328.1			−0.736607			−0.368304	−	0.929706i	$-0.620061\pi$
$821$	−17328.1			−0.736607			−0.368304	+	0.929706i	$0.620061\pi$
$822$		0			0
$823$	30676.2			1.29928			0.649638	−	0.760244i	$-0.274920\pi$
$823$	30676.2			1.29928			0.649638	+	0.760244i	$0.274920\pi$
$824$	2374.67	+	6716.34i	0.100395	+	0.283950i
$825$		0			0
$826$	−7716.34	+	17738.4i	−0.325043	+	0.747214i
$827$	−9379.82			−0.394399			−0.197200	−	0.980363i	$-0.563185\pi$
$827$	−9379.82			−0.394399			−0.197200	+	0.980363i	$0.563185\pi$
$828$		0			0
$829$			16891.6i			0.707682i	0.935305	+	0.353841i	$0.115125\pi$
$829$			16891.6i			0.707682i	−0.935305	+	0.353841i	$0.884875\pi$
$830$	−4340.90	−	17536.4i	−0.181536	−	0.733370i
$831$		0			0
$832$	−25220.5	+	20382.2i	−1.05092	+	0.849308i
$833$	16319.4			0.678792
$834$		0			0
$835$	−12916.9	+	9880.25i	−0.535338	+	0.409485i
$836$	−26923.0	+	25089.6i	−1.11382	+	1.03797i
$837$		0			0
$838$	16870.6	−	38782.3i	0.695446	−	1.59870i
$839$	30994.7			1.27539			0.637697	−	0.770287i	$-0.279887\pi$
$839$	30994.7			1.27539			0.637697	+	0.770287i	$0.279887\pi$
$840$		0			0
$841$	−4588.69			−0.188146
$842$	114.190	−	262.501i	0.00467368	−	0.0107439i
$843$		0			0
$844$	1935.63	+	2077.07i	0.0789421	+	0.0847106i
$845$	12323.0	+	16110.5i	0.501687	+	0.655877i
$846$		0			0
$847$	−5719.67			−0.232031
$848$	−704.398	−	49.7200i	−0.0285249	−	0.00201344i
$849$		0			0
$850$	−24727.0	+	30882.1i	−0.997801	+	1.24617i
$851$		−	15228.2i		−	0.613415i
$852$		0			0
$853$	47292.8			1.89833			0.949164	−	0.314781i	$-0.101931\pi$
$853$	47292.8			1.89833			0.949164	+	0.314781i	$0.101931\pi$
$854$	−9744.06	+	22399.8i	−0.390439	+	0.897546i
$855$		0			0
$856$	−4860.29	−	13746.5i	−0.194067	−	0.548886i
$857$	−21758.8			−0.867289			−0.433645	−	0.901084i	$-0.642773\pi$
$857$	−21758.8			−0.867289			−0.433645	+	0.901084i	$0.642773\pi$
$858$		0			0
$859$	5929.89			0.235536			0.117768	−	0.993041i	$-0.462426\pi$
$859$	5929.89			0.235536			0.117768	+	0.993041i	$0.462426\pi$
$860$	16318.1	+	2761.78i	0.647027	+	0.109507i
$861$		0			0
$862$	13693.9	+	5956.94i	0.541086	+	0.235376i
$863$		−	29287.0i		−	1.15520i	−0.816318	−	0.577602i	$-0.803989\pi$
$863$		−	29287.0i		−	1.15520i	0.816318	−	0.577602i	$-0.196011\pi$
$864$		0			0
$865$	1540.86	−	1178.62i	0.0605674	−	0.0463286i
$866$	4261.64	−	9796.72i	0.167225	−	0.384418i
$867$		0			0
$868$	−12198.5	+	11367.8i	−0.477009	+	0.444526i
$869$	35963.0			1.40387
$870$		0			0
$871$			66643.2i			2.59256i
$872$	2548.13	−	900.930i	0.0989569	−	0.0349878i
$873$		0			0
$874$	8301.20	−	19082.9i	0.321273	−	0.738546i
$875$	18163.7	−	7426.58i	0.701765	−	0.286930i
$876$		0			0
$877$	−44840.5			−1.72652			−0.863259	−	0.504761i	$-0.831581\pi$
$877$	−44840.5			−1.72652			−0.863259	+	0.504761i	$0.831581\pi$
$878$	17426.6	−	40060.5i	0.669840	−	1.53984i
$879$		0			0
$880$	−11963.2	−	18160.2i	−0.458271	−	0.695660i
$881$		−	16919.3i		−	0.647019i	−0.946225	−	0.323510i	$-0.895137\pi$
$881$		−	16919.3i		−	0.647019i	0.946225	−	0.323510i	$-0.104863\pi$
$882$		0			0
$883$		−	29836.2i		−	1.13711i	−0.822646	−	0.568554i	$-0.807503\pi$
$883$		−	29836.2i		−	1.13711i	0.822646	−	0.568554i	$-0.192497\pi$
$884$	−38652.4	−	41476.9i	−1.47061	−	1.57808i
$885$		0			0
$886$	−21075.0	−	9167.77i	−0.799129	−	0.347627i
$887$		−	9728.82i		−	0.368277i	−0.982900	−	0.184139i	$-0.941050\pi$
$887$		−	9728.82i		−	0.368277i	0.982900	−	0.184139i	$-0.0589495\pi$
$888$		0			0
$889$	−13038.0			−0.491881
$890$	6465.40	−	1600.42i	0.243507	−	0.0602768i
$891$		0			0
$892$	−9322.04	−	10003.2i	−0.349916	−	0.375485i
$893$		−	880.784i		−	0.0330059i
$894$		0			0
$895$	11480.6	−	8781.62i	0.428776	−	0.327975i
$896$	−19600.6	+	5411.54i	−0.730816	+	0.201771i
$897$		0			0
$898$	4564.44	−	10492.8i	0.169618	−	0.389921i
$899$			20887.4i			0.774900i
$900$		0			0
$901$		−	1234.63i		−	0.0456510i
$902$	25008.1	+	10878.7i	0.923149	+	0.401576i
$903$		0			0
$904$	4771.37	+	13495.0i	0.175546	+	0.496501i
$905$	−9784.66	+	7484.38i	−0.359396	+	0.274905i
$906$		0			0
$907$			13644.2i			0.499502i	0.968310	+	0.249751i	$0.0803488\pi$
$907$			13644.2i			0.499502i	−0.968310	+	0.249751i	$0.919651\pi$
$908$	13080.5	+	14036.3i	0.478074	+	0.513008i
$909$		0			0
$910$	6757.23	+	27297.9i	0.246154	+	0.994413i
$911$	−38984.1			−1.41778			−0.708891	−	0.705318i	$-0.750804\pi$
$911$	−38984.1			−1.41778			−0.708891	+	0.705318i	$0.750804\pi$
$912$		0			0
$913$			17362.3i			0.629365i
$914$	1037.01	−	2383.90i	0.0375289	−	0.0862719i
$915$		0			0
$916$	−19635.9	+	18298.8i	−0.708285	+	0.660053i
$917$			2165.39i			0.0779799i
$918$		0			0
$919$		−	28789.0i		−	1.03337i	−0.856177	−	0.516683i	$-0.827167\pi$
$919$		−	28789.0i		−	1.03337i	0.856177	−	0.516683i	$-0.172833\pi$
$920$	10299.7	+	6718.26i	0.369100	+	0.240755i
$921$		0			0
$922$	−41425.0	−	18020.2i	−1.47967	−	0.643669i
$923$	−46329.4			−1.65217
$924$		0			0
$925$	10250.6	−	37794.8i	0.364366	−	1.34345i
$926$	41505.9	+	18055.3i	1.47297	+	0.640751i
$927$		0			0
$928$	−11780.1	+	22584.2i	−0.416703	+	0.798882i
$929$		−	25965.9i		−	0.917020i	−0.888689	−	0.458510i	$-0.848383\pi$
$929$		−	25965.9i		−	0.917020i	0.888689	−	0.458510i	$-0.151617\pi$
$930$		0			0
$931$	−22075.1			−0.777103
$932$	10099.2	+	10837.1i	0.354945	+	0.380882i
$933$		0			0
$934$	3999.89	+	1739.98i	0.140129	+	0.0609570i
$935$	30199.8	−	23100.1i	1.05630	−	0.807972i
$936$		0			0
$937$		−	6807.93i		−	0.237359i	−0.992933	−	0.118680i	$-0.962134\pi$
$937$		−	6807.93i		−	0.237359i	0.992933	−	0.118680i	$-0.0378661\pi$
$938$	−16670.0	+	38321.2i	−0.580271	+	1.33394i
$939$		0			0
$940$	513.171	+	86.8522i	0.0178062	+	0.00301362i
$941$	−24816.3			−0.859711			−0.429856	−	0.902898i	$-0.641436\pi$
$941$	−24816.3			−0.859711			−0.429856	+	0.902898i	$0.641436\pi$
$942$		0			0
$943$	−15421.6			−0.532551
$944$	−31095.5	−	2194.88i	−1.07211	−	0.0756750i
$945$		0			0
$946$	−14585.6	−	6344.84i	−0.501288	−	0.218064i
$947$	28529.3			0.978964			0.489482	−	0.872013i	$-0.337186\pi$
$947$	28529.3			0.978964			0.489482	+	0.872013i	$0.337186\pi$
$948$		0			0
$949$			45123.2i			1.54348i
$950$	33448.1	−	41774.0i	1.14231	−	1.42666i
$951$		0			0
$952$	−11851.0	−	33518.5i	−0.403459	−	1.14111i
$953$	26691.5			0.907264			0.453632	−	0.891189i	$-0.350128\pi$
$953$	26691.5			0.907264			0.453632	+	0.891189i	$0.350128\pi$
$954$		0			0
$955$	17155.5	+	22428.1i	0.581297	+	0.759955i
$956$	14823.2	+	15906.4i	0.501481	+	0.538126i
$957$		0			0
$958$	−23074.7	−	10037.7i	−0.778194	−	0.338520i
$959$	−18360.2			−0.618228
$960$		0			0
$961$	7756.77			0.260373
$962$	51461.6	+	22386.2i	1.72473	+	0.750269i
$963$		0			0
$964$	−25513.2	−	27377.6i	−0.852413	−	0.914701i
$965$	−6348.36	+	4855.92i	−0.211773	+	0.161987i
$966$		0			0
$967$	38780.1			1.28964			0.644821	−	0.764334i	$-0.276932\pi$
$967$	38780.1			1.28964			0.644821	+	0.764334i	$0.276932\pi$
$968$	−3072.50	−	8690.03i	−0.102018	−	0.288541i
$969$		0			0
$970$	24447.4	−	6051.64i	0.809237	−	0.200316i
$971$		−	35691.4i		−	1.17960i	−0.807549	−	0.589801i	$-0.799206\pi$
$971$		−	35691.4i		−	1.17960i	0.807549	−	0.589801i	$-0.200794\pi$
$972$		0			0
$973$	35796.4			1.17943
$974$	20675.9	+	8994.14i	0.680182	+	0.295884i
$975$		0			0
$976$	−39266.8	−	2771.66i	−1.28781	−	0.0909001i
$977$	5592.27			0.183125			0.0915623	−	0.995799i	$-0.470814\pi$
$977$	5592.27			0.183125			0.0915623	+	0.995799i	$0.470814\pi$
$978$		0			0
$979$	−6401.24			−0.208973
$980$	2176.78	−	12861.6i	0.0709537	−	0.419234i
$981$		0			0
$982$	−409.704	+	941.834i	−0.0133138	+	0.0306060i
$983$			40885.1i			1.32658i	0.748361	+	0.663292i	$0.230841\pi$
$983$			40885.1i			1.32658i	−0.748361	+	0.663292i	$0.769159\pi$
$984$		0			0
$985$	36186.6	−	27679.5i	1.17056	−	0.895372i
$986$	−40838.4	−	17765.0i	−1.31902	−	0.573785i
$987$		0			0
$988$	52284.8	+	56105.4i	1.68361	+	1.80663i
$989$	8994.38			0.289186
$990$		0			0
$991$		−	42428.6i		−	1.36003i	−0.733198	−	0.680015i	$-0.761973\pi$
$991$		−	42428.6i		−	1.36003i	0.733198	−	0.680015i	$-0.238027\pi$
$992$	−23824.2	−	12426.9i	−0.762518	−	0.397736i
$993$		0			0
$994$	−26640.3	−	11588.7i	−0.850081	−	0.369791i
$995$	40357.6	−	30869.9i	1.28585	−	0.983559i
$996$		0			0
$997$	8673.44			0.275517			0.137759	−	0.990466i	$-0.456010\pi$
$997$	8673.44			0.275517			0.137759	+	0.990466i	$0.456010\pi$
$998$	2792.34	+	1214.69i	0.0885670	+	0.0385273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.10	yes	64
3.2	odd	2	inner	360.4.m.c.179.55	yes	64
4.3	odd	2		1440.4.m.c.719.48		64
5.4	even	2	inner	360.4.m.c.179.56	yes	64
8.3	odd	2	inner	360.4.m.c.179.11	yes	64
8.5	even	2		1440.4.m.c.719.17		64
12.11	even	2		1440.4.m.c.719.18		64
15.14	odd	2	inner	360.4.m.c.179.9	✓	64
20.19	odd	2		1440.4.m.c.719.45		64
24.5	odd	2		1440.4.m.c.719.47		64
24.11	even	2	inner	360.4.m.c.179.54	yes	64
40.19	odd	2	inner	360.4.m.c.179.53	yes	64
40.29	even	2		1440.4.m.c.719.20		64
60.59	even	2		1440.4.m.c.719.19		64
120.29	odd	2		1440.4.m.c.719.46		64
120.59	even	2	inner	360.4.m.c.179.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.9	✓	64	15.14	odd	2	inner
360.4.m.c.179.10	yes	64	1.1	even	1	trivial
360.4.m.c.179.11	yes	64	8.3	odd	2	inner
360.4.m.c.179.12	yes	64	120.59	even	2	inner
360.4.m.c.179.53	yes	64	40.19	odd	2	inner
360.4.m.c.179.54	yes	64	24.11	even	2	inner
360.4.m.c.179.55	yes	64	3.2	odd	2	inner
360.4.m.c.179.56	yes	64	5.4	even	2	inner
1440.4.m.c.719.17		64	8.5	even	2
1440.4.m.c.719.18		64	12.11	even	2
1440.4.m.c.719.19		64	60.59	even	2
1440.4.m.c.719.20		64	40.29	even	2
1440.4.m.c.719.45		64	20.19	odd	2
1440.4.m.c.719.46		64	120.29	odd	2
1440.4.m.c.719.47		64	24.5	odd	2
1440.4.m.c.719.48		64	4.3	odd	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.59365 - 1.12826i) q^{2} +(5.45407 + 5.85262i) q^{4} +(6.79264 + 8.88032i) q^{5} -14.0413 q^{7} +(-7.54271 - 21.3333i) q^{8} +O(q^{10})\)	\(q+(-2.59365 - 1.12826i) q^{2} +(5.45407 + 5.85262i) q^{4} +(6.79264 + 8.88032i) q^{5} -14.0413 q^{7} +(-7.54271 - 21.3333i) q^{8} +(-7.59846 - 30.6963i) q^{10} +30.3917i q^{11} +63.3338 q^{13} +(36.4182 + 15.8422i) q^{14} +(-4.50624 + 63.8412i) q^{16} -111.898 q^{17} +151.363 q^{19} +(-14.9256 + 88.1886i) q^{20} +(34.2896 - 78.8254i) q^{22} +48.6086i q^{23} +(-32.7201 + 120.642i) q^{25} +(-164.266 - 71.4569i) q^{26} +(-76.5821 - 82.1782i) q^{28} -140.714 q^{29} -148.439i q^{31} +(83.7169 - 160.498i) q^{32} +(290.223 + 126.249i) q^{34} +(-95.3774 - 124.691i) q^{35} -313.282 q^{37} +(-392.583 - 170.776i) q^{38} +(138.211 - 211.891i) q^{40} +317.260i q^{41} -185.037i q^{43} +(-177.871 + 165.758i) q^{44} +(54.8431 - 126.074i) q^{46} -5.81902i q^{47} -145.842 q^{49} +(220.979 - 275.986i) q^{50} +(345.427 + 370.669i) q^{52} +11.0336i q^{53} +(-269.888 + 206.440i) q^{55} +(105.909 + 299.546i) q^{56} +(364.962 + 158.761i) q^{58} +487.075i q^{59} +615.070i q^{61} +(-167.478 + 385.000i) q^{62} +(-398.215 + 321.821i) q^{64} +(430.204 + 562.425i) q^{65} +1052.25i q^{67} +(-610.297 - 654.893i) q^{68} +(106.692 + 431.016i) q^{70} -731.511 q^{71} +712.466i q^{73} +(812.545 + 353.463i) q^{74} +(825.543 + 885.868i) q^{76} -426.738i q^{77} -1183.32i q^{79} +(-597.539 + 393.633i) q^{80} +(357.951 - 822.862i) q^{82} +571.286 q^{83} +(-760.079 - 993.685i) q^{85} +(-208.769 + 479.921i) q^{86} +(648.353 - 229.235i) q^{88} +210.625i q^{89} -889.288 q^{91} +(-284.488 + 265.115i) q^{92} +(-6.56536 + 15.0925i) q^{94} +(1028.15 + 1344.15i) q^{95} +796.429i q^{97} +(378.264 + 164.548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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