LMFDB - Embedded newform 224.3.n.a.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(17,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("224.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.10355792167$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	224.17
Dual form			224.3.n.a.145.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94818 - 3.37434i) q^{3} +(-4.42985 - 7.67272i) q^{5} +(6.92329 + 1.03347i) q^{7} +(-3.09078 - 5.35338i) q^{9} +O(q^{10})$	\(q+(1.94818 - 3.37434i) q^{3} +(-4.42985 - 7.67272i) q^{5} +(6.92329 + 1.03347i) q^{7} +(-3.09078 - 5.35338i) q^{9} +(3.15749 + 1.82298i) q^{11} -7.79378 q^{13} -34.5205 q^{15} +(-9.07152 - 5.23744i) q^{17} +(-5.39264 - 9.34032i) q^{19} +(16.9751 - 21.3482i) q^{21} +(-6.45553 - 11.1813i) q^{23} +(-26.7471 + 46.3273i) q^{25} +10.9817 q^{27} +17.2327i q^{29} +(26.1797 + 15.1148i) q^{31} +(12.3027 - 7.10296i) q^{33} +(-22.7396 - 57.6986i) q^{35} +(34.2810 - 19.7922i) q^{37} +(-15.1837 + 26.2989i) q^{39} -73.6801i q^{41} +40.8501i q^{43} +(-27.3833 + 47.4293i) q^{45} +(36.2025 - 20.9015i) q^{47} +(46.8639 + 14.3100i) q^{49} +(-35.3458 + 20.4069i) q^{51} +(-5.55272 - 3.20586i) q^{53} -32.3020i q^{55} -42.0232 q^{57} +(7.95742 - 13.7827i) q^{59} +(-6.07848 - 10.5282i) q^{61} +(-15.8658 - 40.2572i) q^{63} +(34.5253 + 59.7995i) q^{65} +(-6.75274 - 3.89870i) q^{67} -50.3060 q^{69} +41.3627 q^{71} +(77.6038 + 44.8046i) q^{73} +(104.216 + 180.507i) q^{75} +(19.9762 + 15.8842i) q^{77} +(35.3975 + 61.3103i) q^{79} +(49.2112 - 85.2363i) q^{81} +60.8673 q^{83} +92.8043i q^{85} +(58.1489 + 33.5723i) q^{87} +(-23.4004 + 13.5102i) q^{89} +(-53.9586 - 8.05463i) q^{91} +(102.005 - 58.8927i) q^{93} +(-47.7771 + 82.7524i) q^{95} +3.26608i q^{97} -22.5377i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) $ 28 * q + 4 * q^7 - 32 * q^9	$ 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) $ 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.94818	−	3.37434i	0.649392	−	1.12478i	−0.333876	−	0.942617i	$-0.608357\pi$
$3$	1.94818	−	3.37434i	0.649392	−	1.12478i	0.983268	−	0.182163i	$-0.0583098\pi$
$4$		0			0
$5$	−4.42985	−	7.67272i	−0.885969	−	1.53454i	−0.844599	−	0.535400i	$-0.820161\pi$
$5$	−4.42985	−	7.67272i	−0.885969	−	1.53454i	−0.0413705	−	0.999144i	$-0.513172\pi$
$6$		0			0
$7$	6.92329	+	1.03347i	0.989041	+	0.147638i
$7$	6.92329	+	1.03347i	0.989041	+	0.147638i
$8$		0			0
$9$	−3.09078	−	5.35338i	−0.343420	−	0.594820i
$10$		0			0
$11$	3.15749	+	1.82298i	0.287045	+	0.165725i	0.636608	−	0.771187i	$-0.280337\pi$
$11$	3.15749	+	1.82298i	0.287045	+	0.165725i	−0.349564	+	0.936913i	$0.613670\pi$
$12$		0			0
$13$	−7.79378			−0.599522			−0.299761	−	0.954014i	$-0.596907\pi$
$13$	−7.79378			−0.599522			−0.299761	+	0.954014i	$0.596907\pi$
$14$		0			0
$15$	−34.5205			−2.30136
$16$		0			0
$17$	−9.07152	−	5.23744i	−0.533619	−	0.308085i	0.208870	−	0.977943i	$-0.433021\pi$
$17$	−9.07152	−	5.23744i	−0.533619	−	0.308085i	−0.742489	+	0.669858i	$0.766355\pi$
$18$		0			0
$19$	−5.39264	−	9.34032i	−0.283823	−	0.491596i	0.688500	−	0.725236i	$-0.258269\pi$
$19$	−5.39264	−	9.34032i	−0.283823	−	0.491596i	−0.972323	+	0.233640i	$0.924936\pi$
$20$		0			0
$21$	16.9751	−	21.3482i	0.808336	−	1.01658i
$22$		0			0
$23$	−6.45553	−	11.1813i	−0.280675	−	0.486144i	0.690876	−	0.722973i	$-0.257225\pi$
$23$	−6.45553	−	11.1813i	−0.280675	−	0.486144i	−0.971551	+	0.236829i	$0.923892\pi$
$24$		0			0
$25$	−26.7471	+	46.3273i	−1.06988	+	1.85309i
$26$		0			0
$27$	10.9817			0.406728
$28$		0			0
$29$			17.2327i			0.594231i	0.954842	+	0.297115i	$0.0960246\pi$
$29$			17.2327i			0.594231i	−0.954842	+	0.297115i	$0.903975\pi$
$30$		0			0
$31$	26.1797	+	15.1148i	0.844505	+	0.487575i	0.858793	−	0.512323i	$-0.171215\pi$
$31$	26.1797	+	15.1148i	0.844505	+	0.487575i	−0.0142878	+	0.999898i	$0.504548\pi$
$32$		0			0
$33$	12.3027	−	7.10296i	0.372809	−	0.215241i
$34$		0			0
$35$	−22.7396	−	57.6986i	−0.649703	−	1.64853i
$36$		0			0
$37$	34.2810	−	19.7922i	0.926515	−	0.534924i	0.0408071	−	0.999167i	$-0.487007\pi$
$37$	34.2810	−	19.7922i	0.926515	−	0.534924i	0.885708	+	0.464244i	$0.153674\pi$
$38$		0			0
$39$	−15.1837	+	26.2989i	−0.389324	+	0.674330i
$40$		0			0
$41$		−	73.6801i		−	1.79707i	−0.438897	−	0.898537i	$-0.644631\pi$
$41$		−	73.6801i		−	1.79707i	0.438897	−	0.898537i	$-0.355369\pi$
$42$		0			0
$43$			40.8501i			0.950002i	0.879985	+	0.475001i	$0.157552\pi$
$43$			40.8501i			0.950002i	−0.879985	+	0.475001i	$0.842448\pi$
$44$		0			0
$45$	−27.3833	+	47.4293i	−0.608518	+	1.05398i
$46$		0			0
$47$	36.2025	−	20.9015i	0.770266	−	0.444713i	−0.0627038	−	0.998032i	$-0.519972\pi$
$47$	36.2025	−	20.9015i	0.770266	−	0.444713i	0.832969	+	0.553319i	$0.186639\pi$
$48$		0			0
$49$	46.8639	+	14.3100i	0.956406	+	0.292041i
$50$		0			0
$51$	−35.3458	+	20.4069i	−0.693055	+	0.400136i
$52$		0			0
$53$	−5.55272	−	3.20586i	−0.104768	−	0.0604880i	0.446700	−	0.894684i	$-0.352599\pi$
$53$	−5.55272	−	3.20586i	−0.104768	−	0.0604880i	−0.551469	+	0.834196i	$0.685932\pi$
$54$		0			0
$55$		−	32.3020i		−	0.587310i
$56$		0			0
$57$	−42.0232			−0.737249
$58$		0			0
$59$	7.95742	−	13.7827i	0.134871	−	0.233604i	−0.790677	−	0.612234i	$-0.790271\pi$
$59$	7.95742	−	13.7827i	0.134871	−	0.233604i	0.925548	+	0.378629i	$0.123605\pi$
$60$		0			0
$61$	−6.07848	−	10.5282i	−0.0996472	−	0.172594i	0.811891	−	0.583808i	$-0.198438\pi$
$61$	−6.07848	−	10.5282i	−0.0996472	−	0.172594i	−0.911539	+	0.411214i	$0.865105\pi$
$62$		0			0
$63$	−15.8658	−	40.2572i	−0.251838	−	0.639004i
$64$		0			0
$65$	34.5253	+	59.7995i	0.531158	+	0.919992i
$66$		0			0
$67$	−6.75274	−	3.89870i	−0.100787	−	0.0581895i	0.448759	−	0.893653i	$-0.351866\pi$
$67$	−6.75274	−	3.89870i	−0.100787	−	0.0581895i	−0.549546	+	0.835463i	$0.685199\pi$
$68$		0			0
$69$	−50.3060			−0.729073
$70$		0			0
$71$	41.3627			0.582574			0.291287	−	0.956636i	$-0.405917\pi$
$71$	41.3627			0.582574			0.291287	+	0.956636i	$0.405917\pi$
$72$		0			0
$73$	77.6038	+	44.8046i	1.06307	+	0.613761i	0.926279	−	0.376839i	$-0.122989\pi$
$73$	77.6038	+	44.8046i	1.06307	+	0.613761i	0.136787	+	0.990601i	$0.456322\pi$
$74$		0			0
$75$	104.216	+	180.507i	1.38955	+	2.40677i
$76$		0			0
$77$	19.9762	+	15.8842i	0.259432	+	0.206288i
$78$		0			0
$79$	35.3975	+	61.3103i	0.448070	+	0.776080i	0.998260	−	0.0589594i	$-0.0187783\pi$
$79$	35.3975	+	61.3103i	0.448070	+	0.776080i	−0.550191	+	0.835039i	$0.685445\pi$
$80$		0			0
$81$	49.2112	−	85.2363i	0.607546	−	1.05230i
$82$		0			0
$83$	60.8673			0.733341			0.366671	−	0.930351i	$-0.380498\pi$
$83$	60.8673			0.733341			0.366671	+	0.930351i	$0.380498\pi$
$84$		0			0
$85$			92.8043i			1.09182i
$86$		0			0
$87$	58.1489	+	33.5723i	0.668379	+	0.385889i
$88$		0			0
$89$	−23.4004	+	13.5102i	−0.262926	+	0.151800i	−0.625668	−	0.780089i	$-0.715174\pi$
$89$	−23.4004	+	13.5102i	−0.262926	+	0.151800i	0.362743	+	0.931889i	$0.381840\pi$
$90$		0			0
$91$	−53.9586	−	8.05463i	−0.592952	−	0.0885124i
$92$		0			0
$93$	102.005	−	58.8927i	1.09683	−	0.633255i
$94$		0			0
$95$	−47.7771	+	82.7524i	−0.502917	+	0.871078i
$96$		0			0
$97$			3.26608i			0.0336710i	0.999858	+	0.0168355i	$0.00535916\pi$
$97$			3.26608i			0.0336710i	−0.999858	+	0.0168355i	$0.994641\pi$
$98$		0			0
$99$		−	22.5377i		−	0.227653i
$100$		0			0
$101$	−68.8571	+	119.264i	−0.681754	+	1.18083i	0.292691	+	0.956207i	$0.405449\pi$
$101$	−68.8571	+	119.264i	−0.681754	+	1.18083i	−0.974445	+	0.224625i	$0.927884\pi$
$102$		0			0
$103$	−86.3243	+	49.8393i	−0.838100	+	0.483877i	−0.856618	−	0.515952i	$-0.827438\pi$
$103$	−86.3243	+	49.8393i	−0.838100	+	0.483877i	0.0185182	+	0.999829i	$0.494105\pi$
$104$		0			0
$105$	−238.995	−	35.6758i	−2.27615	−	0.339770i
$106$		0			0
$107$	81.4157	−	47.0054i	0.760894	−	0.439302i	−0.0687226	−	0.997636i	$-0.521892\pi$
$107$	81.4157	−	47.0054i	0.760894	−	0.439302i	0.829617	+	0.558333i	$0.188559\pi$
$108$		0			0
$109$	−169.697	−	97.9745i	−1.55685	−	0.898849i	−0.997555	−	0.0698815i	$-0.977738\pi$
$109$	−169.697	−	97.9745i	−1.55685	−	0.898849i	−0.559297	−	0.828967i	$-0.688929\pi$
$110$		0			0
$111$		−	154.234i		−	1.38950i
$112$		0			0
$113$	101.873			0.901527			0.450763	−	0.892643i	$-0.351152\pi$
$113$	101.873			0.901527			0.450763	+	0.892643i	$0.351152\pi$
$114$		0			0
$115$	−57.1940	+	99.0629i	−0.497339	+	0.861417i
$116$		0			0
$117$	24.0888	+	41.7231i	0.205887	+	0.356608i
$118$		0			0
$119$	−57.3920	−	45.6355i	−0.482286	−	0.383491i
$120$		0			0
$121$	−53.8535	−	93.2770i	−0.445070	−	0.770884i
$122$		0			0
$123$	−248.622	−	143.542i	−2.02131	−	1.16701i
$124$		0			0
$125$	252.449			2.01960
$126$		0			0
$127$	139.079			1.09511			0.547554	−	0.836770i	$-0.315559\pi$
$127$	139.079			1.09511			0.547554	+	0.836770i	$0.315559\pi$
$128$		0			0
$129$	137.842	+	79.5831i	1.06854	+	0.616924i
$130$		0			0
$131$	−45.8526	−	79.4190i	−0.350020	−	0.606252i	0.636233	−	0.771497i	$-0.280492\pi$
$131$	−45.8526	−	79.4190i	−0.350020	−	0.606252i	−0.986252	+	0.165245i	$0.947158\pi$
$132$		0			0
$133$	−27.6819	−	70.2389i	−0.208134	−	0.528112i
$134$		0			0
$135$	−48.6471	−	84.2592i	−0.360349	−	0.624142i
$136$		0			0
$137$	−99.7904	+	172.842i	−0.728397	+	1.26162i	0.229163	+	0.973388i	$0.426401\pi$
$137$	−99.7904	+	172.842i	−0.728397	+	1.26162i	−0.957560	+	0.288233i	$0.906932\pi$
$138$		0			0
$139$	39.4768			0.284006			0.142003	−	0.989866i	$-0.454646\pi$
$139$	39.4768			0.284006			0.142003	+	0.989866i	$0.454646\pi$
$140$		0			0
$141$		−	162.879i		−	1.15517i
$142$		0			0
$143$	−24.6088	−	14.2079i	−0.172089	−	0.0993559i
$144$		0			0
$145$	132.222	−	76.3382i	0.911873	−	0.526470i
$146$		0			0
$147$	139.586	−	130.256i	0.949564	−	0.886097i
$148$		0			0
$149$	82.0846	−	47.3916i	0.550903	−	0.318064i	−0.198583	−	0.980084i	$-0.563634\pi$
$149$	82.0846	−	47.3916i	0.550903	−	0.318064i	0.749486	+	0.662020i	$0.230301\pi$
$150$		0			0
$151$	33.2843	−	57.6501i	0.220426	−	0.381789i	−0.734511	−	0.678596i	$-0.762589\pi$
$151$	33.2843	−	57.6501i	0.220426	−	0.381789i	0.954937	+	0.296807i	$0.0959220\pi$
$152$		0			0
$153$			64.7511i			0.423210i
$154$		0			0
$155$		−	267.826i		−	1.72791i
$156$		0			0
$157$	−12.7597	+	22.1004i	−0.0812720	+	0.140767i	−0.903797	−	0.427962i	$-0.859232\pi$
$157$	−12.7597	+	22.1004i	−0.0812720	+	0.140767i	0.822525	+	0.568730i	$0.192565\pi$
$158$		0			0
$159$	−21.6353	+	12.4912i	−0.136071	+	0.0785608i
$160$		0			0
$161$	−33.1380	−	84.0830i	−0.205826	−	0.522255i
$162$		0			0
$163$	−166.364	+	96.0504i	−1.02064	+	0.589267i	−0.914289	−	0.405062i	$-0.867250\pi$
$163$	−166.364	+	96.0504i	−1.02064	+	0.589267i	−0.106350	+	0.994329i	$0.533917\pi$
$164$		0			0
$165$	−108.998	−	62.9301i	−0.660594	−	0.381394i
$166$		0			0
$167$			184.150i			1.10269i	0.834276	+	0.551346i	$0.185886\pi$
$167$			184.150i			1.10269i	−0.834276	+	0.551346i	$0.814114\pi$
$168$		0			0
$169$	−108.257			−0.640574
$170$		0			0
$171$	−33.3349	+	57.7377i	−0.194941	+	0.337647i
$172$		0			0
$173$	−34.9519	−	60.5384i	−0.202034	−	0.349933i	0.747150	−	0.664656i	$-0.231422\pi$
$173$	−34.9519	−	60.5384i	−0.202034	−	0.349933i	−0.949184	+	0.314723i	$0.898088\pi$
$174$		0			0
$175$	−233.056	+	293.095i	−1.33175	+	1.67483i
$176$		0			0
$177$	−31.0049	−	53.7021i	−0.175169	−	0.303401i
$178$		0			0
$179$	207.251	+	119.657i	1.15783	+	0.668473i	0.950783	−	0.309858i	$-0.100281\pi$
$179$	207.251	+	119.657i	1.15783	+	0.668473i	0.207047	+	0.978331i	$0.433615\pi$
$180$		0			0
$181$	36.2834			0.200461			0.100230	−	0.994964i	$-0.468042\pi$
$181$	36.2834			0.200461			0.100230	+	0.994964i	$0.468042\pi$
$182$		0			0
$183$	−47.3678			−0.258840
$184$		0			0
$185$	−303.720	−	175.353i	−1.64173	−	0.947852i
$186$		0			0
$187$	−19.0955	−	33.0744i	−0.102115	−	0.176868i
$188$		0			0
$189$	76.0292	+	11.3492i	0.402271	+	0.0600487i
$190$		0			0
$191$	−162.622	−	281.669i	−0.851422	−	1.47471i	−0.879925	−	0.475113i	$-0.842407\pi$
$191$	−162.622	−	281.669i	−0.851422	−	1.47471i	0.0285024	−	0.999594i	$-0.490926\pi$
$192$		0			0
$193$	−99.8198	+	172.893i	−0.517201	+	0.895818i	0.482599	+	0.875841i	$0.339693\pi$
$193$	−99.8198	+	172.893i	−0.517201	+	0.895818i	−0.999800	+	0.0199772i	$0.993641\pi$
$194$		0			0
$195$	269.045			1.37972
$196$		0			0
$197$			15.5053i			0.0787071i	0.999225	+	0.0393536i	$0.0125299\pi$
$197$			15.5053i			0.0787071i	−0.999225	+	0.0393536i	$0.987470\pi$
$198$		0			0
$199$	48.6375	+	28.0809i	0.244409	+	0.141110i	0.617202	−	0.786805i	$-0.288266\pi$
$199$	48.6375	+	28.0809i	0.244409	+	0.141110i	−0.372792	+	0.927915i	$0.621600\pi$
$200$		0			0
$201$	−26.3110	+	15.1907i	−0.130901	+	0.0755756i
$202$		0			0
$203$	−17.8094	+	119.307i	−0.0877312	+	0.587719i
$204$		0			0
$205$	−565.326	+	326.391i	−2.75769	+	1.59215i
$206$		0			0
$207$	−39.9052	+	69.1178i	−0.192779	+	0.333903i
$208$		0			0
$209$		−	39.3226i		−	0.188147i
$210$		0			0
$211$			370.470i			1.75578i	0.478859	+	0.877892i	$0.341051\pi$
$211$			370.470i			1.75578i	−0.478859	+	0.877892i	$0.658949\pi$
$212$		0			0
$213$	80.5819	−	139.572i	0.378319	−	0.655267i
$214$		0			0
$215$	313.431	−	180.960i	1.45782	−	0.841673i
$216$		0			0
$217$	165.629	+	131.700i	0.763266	+	0.606914i
$218$		0			0
$219$	302.372	−	174.574i	1.38069	−	0.797143i
$220$		0			0
$221$	70.7014	+	40.8195i	0.319916	+	0.184704i
$222$		0			0
$223$			6.78533i			0.0304275i	0.999884	+	0.0152137i	$0.00484287\pi$
$223$			6.78533i			0.0304275i	−0.999884	+	0.0152137i	$0.995157\pi$
$224$		0			0
$225$	330.677			1.46968
$226$		0			0
$227$	−148.309	+	256.879i	−0.653344	+	1.13163i	0.328962	+	0.944343i	$0.393301\pi$
$227$	−148.309	+	256.879i	−0.653344	+	1.13163i	−0.982306	+	0.187282i	$0.940032\pi$
$228$		0			0
$229$	89.0964	+	154.320i	0.389067	+	0.673885i	0.992324	−	0.123662i	$-0.0394640\pi$
$229$	89.0964	+	154.320i	0.389067	+	0.673885i	−0.603257	+	0.797547i	$0.706131\pi$
$230$		0			0
$231$	92.5158	−	36.4614i	0.400501	−	0.157842i
$232$		0			0
$233$	−58.9011	−	102.020i	−0.252795	−	0.437853i	0.711500	−	0.702687i	$-0.248016\pi$
$233$	−58.9011	−	102.020i	−0.252795	−	0.437853i	−0.964294	+	0.264833i	$0.914683\pi$
$234$		0			0
$235$	−320.743	−	185.181i	−1.36486	−	0.788004i
$236$		0			0
$237$	275.842			1.16389
$238$		0			0
$239$	−46.3543			−0.193951			−0.0969755	−	0.995287i	$-0.530917\pi$
$239$	−46.3543			−0.193951			−0.0969755	+	0.995287i	$0.530917\pi$
$240$		0			0
$241$	317.501	+	183.309i	1.31743	+	0.760619i	0.983315	−	0.181914i	$-0.0582291\pi$
$241$	317.501	+	183.309i	1.31743	+	0.760619i	0.334115	+	0.942532i	$0.391562\pi$
$242$		0			0
$243$	−142.327	−	246.517i	−0.585706	−	1.01447i
$244$		0			0
$245$	−97.8032	−	422.965i	−0.399197	−	1.72639i
$246$		0			0
$247$	42.0290	+	72.7964i	0.170158	+	0.294722i
$248$		0			0
$249$	118.580	−	205.387i	0.476226	−	0.824847i
$250$		0			0
$251$	−129.896			−0.517513			−0.258756	−	0.965943i	$-0.583313\pi$
$251$	−129.896			−0.517513			−0.258756	+	0.965943i	$0.583313\pi$
$252$		0			0
$253$		−	47.0732i		−	0.186060i
$254$		0			0
$255$	313.153	+	180.799i	1.22805	+	0.709016i
$256$		0			0
$257$	232.394	−	134.173i	0.904256	−	0.522073i	0.0256776	−	0.999670i	$-0.491826\pi$
$257$	232.394	−	134.173i	0.904256	−	0.522073i	0.878579	+	0.477598i	$0.158492\pi$
$258$		0			0
$259$	257.792	−	101.599i	0.995337	−	0.392272i
$260$		0			0
$261$	92.2532	−	53.2624i	0.353460	−	0.204070i
$262$		0			0
$263$	−117.691	+	203.847i	−0.447495	+	0.775085i	−0.998222	−	0.0596008i	$-0.981017\pi$
$263$	−117.691	+	203.847i	−0.447495	+	0.775085i	0.550727	+	0.834685i	$0.314351\pi$
$264$		0			0
$265$			56.8059i			0.214362i
$266$		0			0
$267$			105.281i			0.394311i
$268$		0			0
$269$	−177.348	+	307.175i	−0.659285	+	1.14192i	0.321516	+	0.946904i	$0.395808\pi$
$269$	−177.348	+	307.175i	−0.659285	+	1.14192i	−0.980801	+	0.195011i	$0.937526\pi$
$270$		0			0
$271$	365.350	−	210.935i	1.34816	−	0.778358i	0.360168	−	0.932888i	$-0.382719\pi$
$271$	365.350	−	210.935i	1.34816	−	0.778358i	0.987988	+	0.154529i	$0.0493861\pi$
$272$		0			0
$273$	−132.300	+	166.383i	−0.484615	+	0.609461i
$274$		0			0
$275$	−168.907	+	97.5186i	−0.614208	+	0.354613i
$276$		0			0
$277$	319.155	+	184.264i	1.15218	+	0.665214i	0.949419	−	0.314013i	$-0.101674\pi$
$277$	319.155	+	184.264i	1.15218	+	0.665214i	0.202766	+	0.979227i	$0.435007\pi$
$278$		0			0
$279$		−	186.866i		−	0.669772i
$280$		0			0
$281$	−35.2868			−0.125576			−0.0627879	−	0.998027i	$-0.519999\pi$
$281$	−35.2868			−0.125576			−0.0627879	+	0.998027i	$0.519999\pi$
$282$		0			0
$283$	−98.3087	+	170.276i	−0.347380	+	0.601681i	−0.985783	−	0.168022i	$-0.946262\pi$
$283$	−98.3087	+	170.276i	−0.347380	+	0.601681i	0.638403	+	0.769702i	$0.279595\pi$
$284$		0			0
$285$	186.156	+	322.432i	0.653180	+	1.13134i
$286$		0			0
$287$	76.1460	−	510.108i	0.265317	−	1.77738i
$288$		0			0
$289$	−89.6384	−	155.258i	−0.310167	−	0.537226i
$290$		0			0
$291$	11.0209	+	6.36291i	0.0378724	+	0.0218657i
$292$		0			0
$293$	−317.573			−1.08387			−0.541933	−	0.840421i	$-0.682307\pi$
$293$	−317.573			−1.08387			−0.541933	+	0.840421i	$0.682307\pi$
$294$		0			0
$295$	−141.001			−0.477968
$296$		0			0
$297$	34.6745	+	20.0193i	0.116749	+	0.0674051i
$298$		0			0
$299$	50.3130	+	87.1447i	0.168271	+	0.291454i
$300$		0			0
$301$	−42.2173	+	282.817i	−0.140257	+	0.939591i
$302$		0			0
$303$	268.292	+	464.695i	0.885451	+	1.53365i
$304$		0			0
$305$	−53.8535	+	93.2769i	−0.176569	+	0.305826i
$306$		0			0
$307$	−132.193			−0.430596			−0.215298	−	0.976548i	$-0.569072\pi$
$307$	−132.193			−0.430596			−0.215298	+	0.976548i	$0.569072\pi$
$308$		0			0
$309$			388.383i			1.25690i
$310$		0			0
$311$	−400.453	−	231.202i	−1.28763	−	0.743414i	−0.309400	−	0.950932i	$-0.600128\pi$
$311$	−400.453	−	231.202i	−1.28763	−	0.743414i	−0.978231	+	0.207518i	$0.933462\pi$
$312$		0			0
$313$	−490.206	+	283.021i	−1.56615	+	0.904220i	−0.569544	+	0.821961i	$0.692880\pi$
$313$	−490.206	+	283.021i	−1.56615	+	0.904220i	−0.996611	+	0.0822589i	$0.973787\pi$
$314$		0			0
$315$	−238.599	+	300.067i	−0.757458	+	0.952594i
$316$		0			0
$317$	153.315	−	88.5163i	0.483643	−	0.279231i	−0.238291	−	0.971194i	$-0.576587\pi$
$317$	153.315	−	88.5163i	0.483643	−	0.279231i	0.721933	+	0.691963i	$0.243254\pi$
$318$		0			0
$319$	−31.4148	+	54.4120i	−0.0984790	+	0.170571i
$320$		0			0
$321$		−	366.299i		−	1.14112i
$322$		0			0
$323$			112.975i			0.349766i
$324$		0			0
$325$	208.461	−	361.065i	0.641418	−	1.11097i
$326$		0			0
$327$	−661.199	+	381.743i	−2.02201	+	1.16741i
$328$		0			0
$329$	272.241	−	107.293i	0.827481	−	0.326119i
$330$		0			0
$331$	429.688	−	248.080i	1.29815	−	0.749487i	0.318065	−	0.948069i	$-0.396967\pi$
$331$	429.688	−	248.080i	1.29815	−	0.749487i	0.980084	+	0.198582i	$0.0636335\pi$
$332$		0			0
$333$	−211.910	−	122.346i	−0.636367	−	0.367406i
$334$		0			0
$335$			69.0825i			0.206216i
$336$		0			0
$337$	−206.191			−0.611843			−0.305922	−	0.952057i	$-0.598965\pi$
$337$	−206.191			−0.611843			−0.305922	+	0.952057i	$0.598965\pi$
$338$		0			0
$339$	198.466	−	343.752i	0.585444	−	1.01402i
$340$		0			0
$341$	55.1080	+	95.4499i	0.161607	+	0.279912i
$342$		0			0
$343$	309.663	+	147.505i	0.902809	+	0.430043i
$344$		0			0
$345$	222.848	+	385.984i	0.645936	+	1.11879i
$346$		0			0
$347$	524.976	+	303.095i	1.51290	+	0.873472i	0.999886	+	0.0150913i	$0.00480389\pi$
$347$	524.976	+	303.095i	1.51290	+	0.873472i	0.513013	+	0.858381i	$0.328529\pi$
$348$		0			0
$349$	−136.343			−0.390669			−0.195335	−	0.980737i	$-0.562579\pi$
$349$	−136.343			−0.390669			−0.195335	+	0.980737i	$0.562579\pi$
$350$		0			0
$351$	−85.5887			−0.243842
$352$		0			0
$353$	−8.72457	−	5.03713i	−0.0247155	−	0.0142695i	0.487591	−	0.873072i	$-0.337876\pi$
$353$	−8.72457	−	5.03713i	−0.0247155	−	0.0142695i	−0.512307	+	0.858802i	$0.671209\pi$
$354$		0			0
$355$	−183.231	−	317.365i	−0.516143	−	0.893985i
$356$		0			0
$357$	−265.799	+	104.754i	−0.744536	+	0.293429i
$358$		0			0
$359$	197.808	+	342.613i	0.550997	+	0.954354i	0.998203	+	0.0599236i	$0.0190857\pi$
$359$	197.808	+	342.613i	0.550997	+	0.954354i	−0.447206	+	0.894431i	$0.647581\pi$
$360$		0			0
$361$	122.339	−	211.897i	0.338889	−	0.586973i
$362$		0			0
$363$	−419.664			−1.15610
$364$		0			0
$365$		−	793.909i		−	2.17509i
$366$		0			0
$367$	−164.486	−	94.9661i	−0.448191	−	0.258763i	0.258875	−	0.965911i	$-0.416648\pi$
$367$	−164.486	−	94.9661i	−0.448191	−	0.258763i	−0.707066	+	0.707148i	$0.749982\pi$
$368$		0			0
$369$	−394.438	+	227.729i	−1.06894	+	0.617151i
$370$		0			0
$371$	−35.1299	−	27.9337i	−0.0946898	−	0.0752930i
$372$		0			0
$373$	311.859	−	180.052i	0.836083	−	0.482713i	−0.0198479	−	0.999803i	$-0.506318\pi$
$373$	311.859	−	180.052i	0.836083	−	0.482713i	0.855931	+	0.517090i	$0.172985\pi$
$374$		0			0
$375$	491.816	−	851.850i	1.31151	−	2.27160i
$376$		0			0
$377$		−	134.308i		−	0.356254i
$378$		0			0
$379$		−	11.2929i		−	0.0297966i	−0.999889	−	0.0148983i	$-0.995258\pi$
$379$		−	11.2929i		−	0.0297966i	0.999889	−	0.0148983i	$-0.00474246\pi$
$380$		0			0
$381$	270.950	−	469.299i	0.711154	−	1.23176i
$382$		0			0
$383$	−376.075	+	217.127i	−0.981918	+	0.566910i	−0.902849	−	0.429959i	$-0.858528\pi$
$383$	−376.075	+	217.127i	−0.981918	+	0.566910i	−0.0790692	+	0.996869i	$0.525195\pi$
$384$		0			0
$385$	33.3831	−	223.636i	0.0867095	−	0.580874i
$386$		0			0
$387$	218.686	−	126.258i	0.565080	−	0.326249i
$388$		0			0
$389$	−37.3803	−	21.5816i	−0.0960934	−	0.0554796i	0.451183	−	0.892431i	$-0.351002\pi$
$389$	−37.3803	−	21.5816i	−0.0960934	−	0.0554796i	−0.547277	+	0.836952i	$0.684335\pi$
$390$		0			0
$391$			135.242i			0.345887i
$392$		0			0
$393$	−357.315			−0.909199
$394$		0			0
$395$	313.611	−	543.190i	0.793952	−	1.37517i
$396$		0			0
$397$	−243.395	−	421.573i	−0.613086	−	1.06190i	−0.990717	−	0.135940i	$-0.956595\pi$
$397$	−243.395	−	421.573i	−0.613086	−	1.06190i	0.377631	−	0.925956i	$-0.376739\pi$
$398$		0			0
$399$	−290.939	−	43.4297i	−0.729170	−	0.108846i
$400$		0			0
$401$	273.457	+	473.641i	0.681938	+	1.18115i	0.974389	+	0.224870i	$0.0721958\pi$
$401$	273.457	+	473.641i	0.681938	+	1.18115i	−0.292451	+	0.956280i	$0.594471\pi$
$402$		0			0
$403$	−204.039	−	117.802i	−0.506299	−	0.292312i
$404$		0			0
$405$	−871.992			−2.15307
$406$		0			0
$407$	144.323			0.354601
$408$		0			0
$409$	57.8217	+	33.3834i	0.141373	+	0.0816220i	0.569018	−	0.822325i	$-0.307323\pi$
$409$	57.8217	+	33.3834i	0.141373	+	0.0816220i	−0.427645	+	0.903947i	$0.640657\pi$
$410$		0			0
$411$	388.819	+	673.453i	0.946030	+	1.63857i
$412$		0			0
$413$	69.3354	−	87.1976i	0.167882	−	0.211132i
$414$		0			0
$415$	−269.633	−	467.018i	−0.649718	−	1.12534i
$416$		0			0
$417$	76.9077	−	133.208i	0.184431	−	0.319444i
$418$		0			0
$419$	−550.169			−1.31305			−0.656527	−	0.754303i	$-0.727975\pi$
$419$	−550.169			−1.31305			−0.656527	+	0.754303i	$0.727975\pi$
$420$		0			0
$421$			579.599i			1.37672i	0.725369	+	0.688360i	$0.241669\pi$
$421$			579.599i			1.37672i	−0.725369	+	0.688360i	$0.758331\pi$
$422$		0			0
$423$	−223.788	−	129.204i	−0.529049	−	0.305446i
$424$		0			0
$425$	485.273	−	280.173i	1.14182	−	0.659230i
$426$		0			0
$427$	−31.2025	−	79.1719i	−0.0730737	−	0.185414i
$428$		0			0
$429$	−95.8845	+	55.3589i	−0.223507	+	0.129042i
$430$		0			0
$431$	−215.935	+	374.010i	−0.501009	+	0.867773i	0.498990	+	0.866607i	$0.333704\pi$
$431$	−215.935	+	374.010i	−0.501009	+	0.867773i	−0.999999	+	0.00116534i	$0.999629\pi$
$432$		0			0
$433$		−	0.143463i		−	0.000331322i	−1.00000		0.000165661i	$-0.999947\pi$
$433$		−	0.143463i		−	0.000331322i	1.00000		0.000165661i	$-5.27316e-5\pi$
$434$		0			0
$435$		−	594.881i		−	1.36754i
$436$		0			0
$437$	−69.6247	+	120.593i	−0.159324	+	0.275958i
$438$		0			0
$439$	165.713	−	95.6744i	0.377478	−	0.217937i	−0.299242	−	0.954177i	$-0.596734\pi$
$439$	165.713	−	95.6744i	0.377478	−	0.217937i	0.676721	+	0.736240i	$0.263401\pi$
$440$		0			0
$441$	−68.2389	−	295.109i	−0.154737	−	0.669182i
$442$		0			0
$443$	−340.782	+	196.751i	−0.769260	+	0.444133i	−0.832611	−	0.553859i	$-0.813155\pi$
$443$	−340.782	+	196.751i	−0.769260	+	0.444133i	0.0633505	+	0.997991i	$0.479821\pi$
$444$		0			0
$445$	207.320	+	119.696i	0.465888	+	0.268981i
$446$		0			0
$447$		−	369.308i		−	0.826193i
$448$		0			0
$449$	−725.831			−1.61655			−0.808275	−	0.588805i	$-0.799598\pi$
$449$	−725.831			−1.61655			−0.808275	+	0.588805i	$0.799598\pi$
$450$		0			0
$451$	134.317	−	232.644i	0.297821	−	0.515841i
$452$		0			0
$453$	−129.687	−	224.625i	−0.286286	−	0.495861i
$454$		0			0
$455$	177.227	+	449.690i	0.389511	+	0.988330i
$456$		0			0
$457$	34.6713	+	60.0525i	0.0758673	+	0.131406i	0.901463	−	0.432856i	$-0.142494\pi$
$457$	34.6713	+	60.0525i	0.0758673	+	0.131406i	−0.825596	+	0.564262i	$0.809161\pi$
$458$		0			0
$459$	−99.6203	−	57.5158i	−0.217038	−	0.125307i
$460$		0			0
$461$	768.006			1.66596			0.832978	−	0.553306i	$-0.186634\pi$
$461$	768.006			1.66596			0.832978	+	0.553306i	$0.186634\pi$
$462$		0			0
$463$	−215.717			−0.465911			−0.232956	−	0.972487i	$-0.574840\pi$
$463$	−215.717			−0.465911			−0.232956	+	0.972487i	$0.574840\pi$
$464$		0			0
$465$	−903.734	−	521.771i	−1.94351	−	1.12209i
$466$		0			0
$467$	−14.4688	−	25.0607i	−0.0309824	−	0.0536631i	0.850118	−	0.526592i	$-0.176530\pi$
$467$	−14.4688	−	25.0607i	−0.0309824	−	0.0536631i	−0.881101	+	0.472928i	$0.843197\pi$
$468$		0			0
$469$	−42.7220	−	33.9705i	−0.0910917	−	0.0724319i
$470$		0			0
$471$	49.7163	+	86.1111i	0.105555	+	0.182826i
$472$		0			0
$473$	−74.4688	+	128.984i	−0.157439	+	0.272693i
$474$		0			0
$475$	576.949			1.21463
$476$		0			0
$477$			39.6344i			0.0830911i
$478$		0			0
$479$	695.377	+	401.476i	1.45173	+	0.838154i	0.998580	−	0.0532818i	$-0.0169682\pi$
$479$	695.377	+	401.476i	1.45173	+	0.838154i	0.453146	+	0.891436i	$0.350302\pi$
$480$		0			0
$481$	−267.179	+	154.256i	−0.555466	+	0.320698i
$482$		0			0
$483$	−348.283	−	51.9897i	−0.721083	−	0.107639i
$484$		0			0
$485$	25.0598	−	14.4683i	0.0516696	−	0.0298315i
$486$		0			0
$487$	9.96197	−	17.2546i	0.0204558	−	0.0354305i	−0.855616	−	0.517611i	$-0.826822\pi$
$487$	9.96197	−	17.2546i	0.0204558	−	0.0354305i	0.876072	+	0.482180i	$0.160155\pi$
$488$		0			0
$489$			748.493i			1.53066i
$490$		0			0
$491$		−	76.2017i		−	0.155197i	−0.996985	−	0.0775985i	$-0.975275\pi$
$491$		−	76.2017i		−	0.155197i	0.996985	−	0.0775985i	$-0.0247252\pi$
$492$		0			0
$493$	90.2552	−	156.327i	0.183073	−	0.317093i
$494$		0			0
$495$	−172.925	+	99.8384i	−0.349344	+	0.201694i
$496$		0			0
$497$	286.366	+	42.7471i	0.576190	+	0.0860102i
$498$		0			0
$499$	−452.819	+	261.435i	−0.907454	+	0.523919i	−0.879611	−	0.475694i	$-0.842197\pi$
$499$	−452.819	+	261.435i	−0.907454	+	0.523919i	−0.0278428	+	0.999612i	$0.508864\pi$
$500$		0			0
$501$	621.384	+	358.756i	1.24029	+	0.716080i
$502$		0			0
$503$			132.060i			0.262545i	0.991346	+	0.131273i	$0.0419064\pi$
$503$			132.060i			0.262545i	−0.991346	+	0.131273i	$0.958094\pi$
$504$		0			0
$505$	1220.11			2.41605
$506$		0			0
$507$	−210.904	+	365.296i	−0.415983	+	0.720504i
$508$		0			0
$509$	−155.079	−	268.604i	−0.304673	−	0.527709i	0.672515	−	0.740083i	$-0.265214\pi$
$509$	−155.079	−	268.604i	−0.304673	−	0.527709i	−0.977189	+	0.212374i	$0.931881\pi$
$510$		0			0
$511$	490.969	+	390.396i	0.960801	+	0.763984i
$512$		0			0
$513$	−59.2201	−	102.572i	−0.115439	−	0.199946i
$514$		0			0
$515$	764.806	+	441.561i	1.48506	+	0.857400i
$516$		0			0
$517$	152.412			0.294801
$518$		0			0
$519$	−272.369			−0.524797
$520$		0			0
$521$	52.9121	+	30.5488i	0.101559	+	0.0586349i	0.549919	−	0.835218i	$-0.314659\pi$
$521$	52.9121	+	30.5488i	0.101559	+	0.0586349i	−0.448360	+	0.893853i	$0.647992\pi$
$522$		0			0
$523$	−256.923	−	445.004i	−0.491249	−	0.850868i	0.508701	−	0.860944i	$-0.330126\pi$
$523$	−256.923	−	445.004i	−0.491249	−	0.850868i	−0.999949	+	0.0100759i	$0.996793\pi$
$524$		0			0
$525$	534.969	+	1357.41i	1.01899	+	2.58554i
$526$		0			0
$527$	−158.326	−	274.229i	−0.300429	−	0.520359i
$528$		0			0
$529$	181.152	−	313.765i	0.342443	−	0.593128i
$530$		0			0
$531$	−98.3784			−0.185270
$532$		0			0
$533$			574.246i			1.07739i
$534$		0			0
$535$	−721.318	−	416.453i	−1.34826	−	0.778417i
$536$		0			0
$537$	807.525	−	466.225i	1.50377	−	0.868202i
$538$		0			0
$539$	121.885	+	130.616i	0.226133	+	0.242329i
$540$		0			0
$541$	−92.7322	+	53.5390i	−0.171409	+	0.0989630i	−0.583250	−	0.812293i	$-0.698219\pi$
$541$	−92.7322	+	53.5390i	−0.171409	+	0.0989630i	0.411841	+	0.911256i	$0.364886\pi$
$542$		0			0
$543$	70.6863	−	122.432i	0.130177	−	0.225474i
$544$		0			0
$545$			1736.05i			3.18541i
$546$		0			0
$547$			43.3240i			0.0792030i	0.999216	+	0.0396015i	$0.0126088\pi$
$547$			43.3240i			0.0792030i	−0.999216	+	0.0396015i	$0.987391\pi$
$548$		0			0
$549$	−37.5744	+	65.0808i	−0.0684416	+	0.118544i
$550$		0			0
$551$	160.959	−	92.9296i	0.292121	−	0.168656i
$552$		0			0
$553$	181.705	+	461.051i	0.328581	+	0.833727i
$554$		0			0
$555$	−1183.40	+	683.235i	−2.13225	+	1.23105i
$556$		0			0
$557$	−62.7878	−	36.2506i	−0.112725	−	0.0650818i	0.442577	−	0.896730i	$-0.354064\pi$
$557$	−62.7878	−	36.2506i	−0.112725	−	0.0650818i	−0.555302	+	0.831648i	$0.687397\pi$
$558$		0			0
$559$		−	318.377i		−	0.569547i
$560$		0			0
$561$	−148.805			−0.265250
$562$		0			0
$563$	292.471	−	506.575i	0.519487	−	0.899779i	−0.480256	−	0.877128i	$-0.659456\pi$
$563$	292.471	−	506.575i	0.519487	−	0.899779i	0.999743	−	0.0226503i	$-0.00721043\pi$
$564$		0			0
$565$	−451.280	−	781.639i	−0.798725	−	1.38343i
$566$		0			0
$567$	428.792	−	539.257i	0.756247	−	0.951071i
$568$		0			0
$569$	−371.765	−	643.915i	−0.653365	−	1.13166i	−0.982301	−	0.187309i	$-0.940023\pi$
$569$	−371.765	−	643.915i	−0.653365	−	1.13166i	0.328936	−	0.944352i	$-0.393310\pi$
$570$		0			0
$571$	893.793	+	516.031i	1.56531	+	0.903733i	0.996704	+	0.0811234i	$0.0258508\pi$
$571$	893.793	+	516.031i	1.56531	+	0.903733i	0.568607	+	0.822609i	$0.307483\pi$
$572$		0			0
$573$	−1267.26			−2.21163
$574$		0			0
$575$	690.666			1.20116
$576$		0			0
$577$	−825.404	−	476.547i	−1.43051	−	0.825905i	−0.433350	−	0.901226i	$-0.642668\pi$
$577$	−825.404	−	476.547i	−1.43051	−	0.825905i	−0.997159	+	0.0753213i	$0.976002\pi$
$578$		0			0
$579$	388.933	+	673.652i	0.671732	+	1.16347i
$580$		0			0
$581$	421.402	+	62.9044i	0.725305	+	0.108269i
$582$		0			0
$583$	−11.6884	−	20.2450i	−0.0200488	−	0.0347255i
$584$		0			0
$585$	213.420	−	369.654i	0.364820	−	0.631887i
$586$		0			0
$587$	−96.2876			−0.164033			−0.0820167	−	0.996631i	$-0.526136\pi$
$587$	−96.2876			−0.164033			−0.0820167	+	0.996631i	$0.526136\pi$
$588$		0			0
$589$		−	326.035i		−	0.553540i
$590$		0			0
$591$	52.3201	+	30.2071i	0.0885282	+	0.0511118i
$592$		0			0
$593$	44.1840	−	25.5096i	0.0745092	−	0.0430179i	−0.462283	−	0.886733i	$-0.652969\pi$
$593$	44.1840	−	25.5096i	0.0745092	−	0.0430179i	0.536792	+	0.843715i	$0.319636\pi$
$594$		0			0
$595$	−95.9103	+	642.511i	−0.161194	+	1.07985i
$596$		0			0
$597$	189.509	−	109.413i	0.317435	−	0.183271i
$598$		0			0
$599$	451.118	−	781.359i	0.753119	−	1.30444i	−0.193186	−	0.981162i	$-0.561882\pi$
$599$	451.118	−	781.359i	0.753119	−	1.30444i	0.946304	−	0.323277i	$-0.104785\pi$
$600$		0			0
$601$		−	903.595i		−	1.50349i	−0.659456	−	0.751743i	$-0.729213\pi$
$601$		−	903.595i		−	1.50349i	0.659456	−	0.751743i	$-0.270787\pi$
$602$		0			0
$603$			48.2000i			0.0799337i
$604$		0			0
$605$	−477.125	+	826.406i	−0.788637	+	1.36596i
$606$		0			0
$607$	306.928	−	177.205i	0.505648	−	0.291936i	−0.225395	−	0.974267i	$-0.572367\pi$
$607$	306.928	−	177.205i	0.505648	−	0.291936i	0.731043	+	0.682332i	$0.239034\pi$
$608$		0			0
$609$	367.886	+	292.526i	0.604082	+	0.480338i
$610$		0			0
$611$	−282.154	+	162.902i	−0.461791	+	0.266615i
$612$		0			0
$613$	290.984	+	168.000i	0.474688	+	0.274061i	0.718200	−	0.695837i	$-0.244966\pi$
$613$	290.984	+	168.000i	0.474688	+	0.274061i	−0.243512	+	0.969898i	$0.578300\pi$
$614$		0			0
$615$			2543.47i			4.13573i
$616$		0			0
$617$	223.359			0.362008			0.181004	−	0.983482i	$-0.442065\pi$
$617$	223.359			0.362008			0.181004	+	0.983482i	$0.442065\pi$
$618$		0			0
$619$	363.026	−	628.780i	0.586472	−	1.01580i	−0.408218	−	0.912885i	$-0.633850\pi$
$619$	363.026	−	628.780i	0.586472	−	1.01580i	0.994690	−	0.102915i	$-0.0328170\pi$
$620$		0			0
$621$	−70.8925	−	122.789i	−0.114159	−	0.197728i
$622$		0			0
$623$	−175.970	+	69.3516i	−0.282456	+	0.111319i
$624$		0			0
$625$	−449.635	−	778.791i	−0.719416	−	1.24607i
$626$		0			0
$627$	−132.688	−	76.6074i	−0.211623	−	0.122181i
$628$		0			0
$629$	−414.642			−0.659208
$630$		0			0
$631$	326.157			0.516888			0.258444	−	0.966026i	$-0.416790\pi$
$631$	326.157			0.516888			0.258444	+	0.966026i	$0.416790\pi$
$632$		0			0
$633$	1250.09	+	721.741i	1.97487	+	1.14019i
$634$		0			0
$635$	−616.097	−	1067.11i	−0.970232	−	1.68049i
$636$		0			0
$637$	−365.247	−	111.529i	−0.573386	−	0.175085i
$638$		0			0
$639$	−127.843	−	221.431i	−0.200067	−	0.346527i
$640$		0			0
$641$	299.187	−	518.208i	0.466751	−	0.808436i	−0.532528	−	0.846413i	$-0.678758\pi$
$641$	299.187	−	518.208i	0.466751	−	0.808436i	0.999279	+	0.0379764i	$0.0120912\pi$
$642$		0			0
$643$	1008.20			1.56796			0.783979	−	0.620787i	$-0.213187\pi$
$643$	1008.20			1.56796			0.783979	+	0.620787i	$0.213187\pi$
$644$		0			0
$645$		−	1410.16i		−	2.18630i
$646$		0			0
$647$	−574.378	−	331.617i	−0.887756	−	0.512546i	−0.0145481	−	0.999894i	$-0.504631\pi$
$647$	−574.378	−	331.617i	−0.887756	−	0.512546i	−0.873208	+	0.487348i	$0.837964\pi$
$648$		0			0
$649$	50.2509	−	29.0124i	0.0774283	−	0.0447032i
$650$		0			0
$651$	767.075	−	302.312i	1.17830	−	0.464381i
$652$		0			0
$653$	−857.892	+	495.304i	−1.31377	+	0.758506i	−0.982718	−	0.185107i	$-0.940737\pi$
$653$	−857.892	+	495.304i	−1.31377	+	0.758506i	−0.331052	+	0.943612i	$0.607404\pi$
$654$		0			0
$655$	−406.240	+	703.628i	−0.620213	+	1.07424i
$656$		0			0
$657$		−	553.924i		−	0.843110i
$658$		0			0
$659$		−	82.2318i		−	0.124783i	−0.998052	−	0.0623914i	$-0.980127\pi$
$659$		−	82.2318i		−	0.124783i	0.998052	−	0.0623914i	$-0.0198727\pi$
$660$		0			0
$661$	313.110	−	542.322i	0.473691	−	0.820457i	−0.525855	−	0.850574i	$-0.676255\pi$
$661$	313.110	−	542.322i	0.473691	−	0.820457i	0.999546	+	0.0301171i	$0.00958802\pi$
$662$		0			0
$663$	275.478	−	159.047i	0.415502	−	0.239890i
$664$		0			0
$665$	−416.297	+	523.543i	−0.626010	+	0.787282i
$666$		0			0
$667$	192.684	−	111.246i	0.288882	−	0.166786i
$668$		0			0
$669$	22.8960	+	13.2190i	0.0342242	+	0.0197594i
$670$		0			0
$671$		−	44.3237i		−	0.0660562i
$672$		0			0
$673$	−150.211			−0.223196			−0.111598	−	0.993753i	$-0.535597\pi$
$673$	−150.211			−0.223196			−0.111598	+	0.993753i	$0.535597\pi$
$674$		0			0
$675$	−293.727	+	508.751i	−0.435152	+	0.753705i
$676$		0			0
$677$	278.207	+	481.869i	0.410941	+	0.711771i	0.994993	−	0.0999455i	$-0.0318668\pi$
$677$	278.207	+	481.869i	0.410941	+	0.711771i	−0.584052	+	0.811716i	$0.698533\pi$
$678$		0			0
$679$	−3.37540	+	22.6121i	−0.00497113	+	0.0333020i
$680$		0			0
$681$	577.865	+	1000.89i	0.848553	+	1.46974i
$682$		0			0
$683$	−685.334	−	395.678i	−1.00342	−	0.579323i	−0.0941597	−	0.995557i	$-0.530016\pi$
$683$	−685.334	−	395.678i	−1.00342	−	0.579323i	−0.909258	+	0.416234i	$0.863350\pi$
$684$		0			0
$685$	1768.22			2.58135
$686$		0			0
$687$	694.302			1.01063
$688$		0			0
$689$	43.2767	+	24.9858i	0.0628109	+	0.0362639i
$690$		0			0
$691$	488.267	+	845.703i	0.706609	+	1.22388i	0.966108	+	0.258139i	$0.0831093\pi$
$691$	488.267	+	845.703i	0.706609	+	1.22388i	−0.259499	+	0.965743i	$0.583557\pi$
$692$		0			0
$693$	23.2920	−	156.035i	0.0336103	−	0.225158i
$694$		0			0
$695$	−174.876	−	302.894i	−0.251620	−	0.435819i
$696$		0			0
$697$	−385.895	+	668.390i	−0.553652	+	0.958953i
$698$		0			0
$699$	−458.999			−0.656651
$700$		0			0
$701$			855.098i			1.21983i	0.792468	+	0.609913i	$0.208796\pi$
$701$			855.098i			1.21983i	−0.792468	+	0.609913i	$0.791204\pi$
$702$		0			0
$703$	−369.730	−	213.464i	−0.525932	−	0.303647i
$704$		0			0
$705$	−1249.73	+	721.530i	−1.77266	+	1.02345i
$706$		0			0
$707$	−599.974	+	754.538i	−0.848619	+	1.06724i
$708$		0			0
$709$	288.794	−	166.735i	0.407326	−	0.235170i	−0.282314	−	0.959322i	$-0.591102\pi$
$709$	288.794	−	166.735i	0.407326	−	0.235170i	0.689640	+	0.724152i	$0.257769\pi$
$710$		0			0
$711$	218.812	−	378.993i	0.307752	−	0.533042i
$712$		0			0
$713$		−	390.297i		−	0.547401i
$714$		0			0
$715$			251.755i			0.352105i
$716$		0			0
$717$	−90.3063	+	156.415i	−0.125950	+	0.218152i
$718$		0			0
$719$	34.4877	−	19.9115i	0.0479662	−	0.0276933i	−0.475825	−	0.879540i	$-0.657850\pi$
$719$	34.4877	−	19.9115i	0.0479662	−	0.0276933i	0.523791	+	0.851847i	$0.324517\pi$
$720$		0			0
$721$	−649.155	+	255.839i	−0.900354	+	0.354839i
$722$		0			0
$723$	1237.09	−	714.237i	1.71106	−	0.987879i
$724$		0			0
$725$	−798.344	−	460.924i	−1.10116	−	0.635757i
$726$		0			0
$727$		−	489.402i		−	0.673180i	−0.941651	−	0.336590i	$-0.890726\pi$
$727$		−	489.402i		−	0.673180i	0.941651	−	0.336590i	$-0.109274\pi$
$728$		0			0
$729$	−223.307			−0.306320
$730$		0			0
$731$	213.950	−	370.572i	0.292681	−	0.506939i
$732$		0			0
$733$	−89.1592	−	154.428i	−0.121636	−	0.210680i	0.798777	−	0.601627i	$-0.205481\pi$
$733$	−89.1592	−	154.428i	−0.121636	−	0.210680i	−0.920413	+	0.390948i	$0.872147\pi$
$734$		0			0
$735$	−1617.76	−	493.988i	−2.20104	−	0.672093i
$736$		0			0
$737$	−14.2145	−	24.6202i	−0.0192869	−	0.0334060i
$738$		0			0
$739$	−764.182	−	441.200i	−1.03408	−	0.597024i	−0.115926	−	0.993258i	$-0.536983\pi$
$739$	−764.182	−	441.200i	−1.03408	−	0.597024i	−0.918149	+	0.396234i	$0.870317\pi$
$740$		0			0
$741$	327.520			0.441997
$742$		0			0
$743$	−1404.00			−1.88964			−0.944819	−	0.327591i	$-0.893763\pi$
$743$	−1404.00			−1.88964			−0.944819	+	0.327591i	$0.893763\pi$
$744$		0			0
$745$	−727.244	−	419.875i	−0.976167	−	0.563590i
$746$		0			0
$747$	−188.127	−	325.846i	−0.251844	−	0.436206i
$748$		0			0
$749$	612.243	−	241.291i	0.817414	−	0.322151i
$750$		0			0
$751$	102.840	+	178.124i	0.136938	+	0.237183i	0.926336	−	0.376698i	$-0.122941\pi$
$751$	102.840	+	178.124i	0.136938	+	0.237183i	−0.789398	+	0.613881i	$0.789607\pi$
$752$		0			0
$753$	−253.060	+	438.312i	−0.336069	+	0.582088i
$754$		0			0
$755$	−589.777			−0.781162
$756$		0			0
$757$			15.0345i			0.0198606i	0.999951	+	0.00993032i	$0.00316097\pi$
$757$			15.0345i			0.0198606i	−0.999951	+	0.00993032i	$0.996839\pi$
$758$		0			0
$759$	−158.841	−	91.7068i	−0.209276	−	0.120826i
$760$		0			0
$761$	−544.290	+	314.246i	−0.715229	+	0.412938i	−0.812994	−	0.582272i	$-0.802164\pi$
$761$	−544.290	+	314.246i	−0.715229	+	0.412938i	0.0977649	+	0.995210i	$0.468831\pi$
$762$		0			0
$763$	−1073.61	−	853.682i	−1.40709	−	1.11885i
$764$		0			0
$765$	496.817	−	286.837i	0.649434	−	0.374951i
$766$		0			0
$767$	−62.0184	+	107.419i	−0.0808584	+	0.140051i
$768$		0			0
$769$		−	442.918i		−	0.575967i	−0.957635	−	0.287983i	$-0.907015\pi$
$769$		−	442.918i		−	0.575967i	0.957635	−	0.287983i	$-0.0929848\pi$
$770$		0			0
$771$		−	1045.57i		−	1.35612i
$772$		0			0
$773$	84.5990	−	146.530i	0.109442	−	0.189560i	−0.806102	−	0.591777i	$-0.798427\pi$
$773$	84.5990	−	146.530i	0.109442	−	0.189560i	0.915545	+	0.402217i	$0.131760\pi$
$774$		0			0
$775$	−1400.46	+	808.555i	−1.80704	+	1.04330i
$776$		0			0
$777$	159.396	−	1067.81i	0.205143	−	1.37427i
$778$		0			0
$779$	−688.196	+	397.330i	−0.883435	+	0.510051i
$780$		0			0
$781$	130.602	+	75.4034i	0.167225	+	0.0965472i
$782$		0			0
$783$			189.244i			0.241690i
$784$		0			0
$785$	226.094			0.288018
$786$		0			0
$787$	−23.2437	+	40.2593i	−0.0295346	+	0.0511554i	−0.880415	−	0.474204i	$-0.842736\pi$
$787$	−23.2437	+	40.2593i	−0.0295346	+	0.0511554i	0.850880	+	0.525360i	$0.176069\pi$
$788$		0			0
$789$	458.567	+	794.261i	0.581200	+	1.00667i
$790$		0			0
$791$	705.293	+	105.282i	0.891647	+	0.133100i
$792$		0			0
$793$	47.3743	+	82.0548i	0.0597407	+	0.103474i
$794$		0			0
$795$	191.683	+	110.668i	0.241110	+	0.139205i
$796$		0			0
$797$	−1351.86			−1.69618			−0.848092	−	0.529850i	$-0.822248\pi$
$797$	−1351.86			−1.69618			−0.848092	+	0.529850i	$0.822248\pi$
$798$		0			0
$799$	−437.882			−0.548038
$800$		0			0
$801$	144.651	+	83.5141i	0.180588	+	0.104262i
$802$		0			0
$803$	163.355	+	282.940i	0.203431	+	0.352354i
$804$		0			0
$805$	−498.349	+	626.733i	−0.619067	+	0.778551i
$806$		0			0
$807$	691.009	+	1196.86i	0.856269	+	1.48310i
$808$		0			0
$809$	701.563	−	1215.14i	0.867198	−	1.50203i	0.00235012	−	0.999997i	$-0.499252\pi$
$809$	701.563	−	1215.14i	0.867198	−	1.50203i	0.864848	−	0.502034i	$-0.167415\pi$
$810$		0			0
$811$	689.037			0.849614			0.424807	−	0.905284i	$-0.360342\pi$
$811$	689.037			0.849614			0.424807	+	0.905284i	$0.360342\pi$
$812$		0			0
$813$		−	1643.75i		−	2.02184i
$814$		0			0
$815$	1473.94	+	850.977i	1.80851	+	1.04414i
$816$		0			0
$817$	381.553	−	220.290i	0.467017	−	0.269632i
$818$		0			0
$819$	123.655	+	313.756i	0.150982	+	0.383097i
$820$		0			0
$821$	19.3490	−	11.1711i	0.0235675	−	0.0136067i	−0.488170	−	0.872749i	$-0.662335\pi$
$821$	19.3490	−	11.1711i	0.0235675	−	0.0136067i	0.511737	+	0.859142i	$0.329002\pi$
$822$		0			0
$823$	512.111	−	887.003i	0.622249	−	1.07777i	−0.366816	−	0.930293i	$-0.619552\pi$
$823$	512.111	−	887.003i	0.622249	−	1.07777i	0.989066	−	0.147474i	$-0.0471144\pi$
$824$		0			0
$825$			759.934i			0.921132i
$826$		0			0
$827$		−	466.377i		−	0.563938i	−0.959424	−	0.281969i	$-0.909012\pi$
$827$		−	466.377i		−	0.563938i	0.959424	−	0.281969i	$-0.0909875\pi$
$828$		0			0
$829$	750.350	−	1299.64i	0.905126	−	1.56773i	0.0843791	−	0.996434i	$-0.473109\pi$
$829$	750.350	−	1299.64i	0.905126	−	1.56773i	0.820747	−	0.571291i	$-0.193557\pi$
$830$		0			0
$831$	1243.54	−	717.958i	1.49644	−	0.863969i
$832$		0			0
$833$	−350.179	−	375.260i	−0.420383	−	0.450493i
$834$		0			0
$835$	1412.93	−	815.755i	1.69213	−	0.976952i
$836$		0			0
$837$	287.496	+	165.986i	0.343484	+	0.198311i
$838$		0			0
$839$		−	1068.18i		−	1.27316i	−0.771212	−	0.636579i	$-0.780349\pi$
$839$		−	1068.18i		−	1.27316i	0.771212	−	0.636579i	$-0.219651\pi$
$840$		0			0
$841$	544.034			0.646890
$842$		0			0
$843$	−68.7449	+	119.070i	−0.0815479	+	0.141245i
$844$		0			0
$845$	479.562	+	830.625i	0.567529	+	0.982988i
$846$		0			0
$847$	−276.445	−	701.440i	−0.326381	−	0.828146i
$848$		0			0
$849$	383.045	+	663.453i	0.451172	+	0.781453i
$850$		0			0
$851$	−442.605	−	255.538i	−0.520100	−	0.300280i
$852$		0			0
$853$	−918.640			−1.07695			−0.538476	−	0.842641i	$-0.681000\pi$
$853$	−918.640			−1.07695			−0.538476	+	0.842641i	$0.681000\pi$
$854$		0			0
$855$	590.673			0.690846
$856$		0			0
$857$	−438.167	−	252.976i	−0.511280	−	0.295188i	0.222080	−	0.975029i	$-0.428716\pi$
$857$	−438.167	−	252.976i	−0.511280	−	0.295188i	−0.733360	+	0.679841i	$0.762049\pi$
$858$		0			0
$859$	−688.516	−	1192.54i	−0.801532	−	1.38829i	−0.918607	−	0.395171i	$-0.870685\pi$
$859$	−688.516	−	1192.54i	−0.801532	−	1.38829i	0.117075	−	0.993123i	$-0.462648\pi$
$860$		0			0
$861$	−1572.93	−	1250.72i	−1.82687	−	1.45264i
$862$		0			0
$863$	458.817	+	794.695i	0.531654	+	0.920852i	0.999317	+	0.0369450i	$0.0117626\pi$
$863$	458.817	+	794.695i	0.531654	+	0.920852i	−0.467663	+	0.883907i	$0.654904\pi$
$864$		0			0
$865$	−309.663	+	536.352i	−0.357992	+	0.620060i
$866$		0			0
$867$	−698.525			−0.805681
$868$		0			0
$869$			258.116i			0.297026i
$870$		0			0
$871$	52.6294	+	30.3856i	0.0604241	+	0.0348859i
$872$		0			0
$873$	17.4846	−	10.0947i	0.0200282	−	0.0115633i
$874$		0			0
$875$	1747.78	+	260.898i	1.99746	+	0.298170i
$876$		0			0
$877$	606.173	−	349.974i	0.691189	−	0.399058i	−0.112868	−	0.993610i	$-0.536004\pi$
$877$	606.173	−	349.974i	0.691189	−	0.399058i	0.804057	+	0.594552i	$0.202671\pi$
$878$		0			0
$879$	−618.688	+	1071.60i	−0.703854	+	1.21911i
$880$		0			0
$881$			6.37652i			0.00723783i	0.999993	+	0.00361891i	$0.00115194\pi$
$881$			6.37652i			0.00723783i	−0.999993	+	0.00361891i	$0.998848\pi$
$882$		0			0
$883$			1548.35i			1.75351i	0.480935	+	0.876756i	$0.340297\pi$
$883$			1548.35i			1.75351i	−0.480935	+	0.876756i	$0.659703\pi$
$884$		0			0
$885$	−274.694	+	475.784i	−0.310389	+	0.537609i
$886$		0			0
$887$	−634.250	+	366.185i	−0.715051	+	0.412835i	−0.812928	−	0.582364i	$-0.802128\pi$
$887$	−634.250	+	366.185i	−0.715051	+	0.412835i	0.0978774	+	0.995198i	$0.468795\pi$
$888$		0			0
$889$	962.882	+	143.733i	1.08311	+	0.161680i
$890$		0			0
$891$	310.768	−	179.422i	0.348785	−	0.201371i
$892$		0			0
$893$	−390.454	−	225.429i	−0.437238	−	0.252440i
$894$		0			0
$895$		−	2120.24i		−	2.36899i
$896$		0			0
$897$	392.074			0.437095
$898$		0			0
$899$	−260.469	+	451.146i	−0.289732	+	0.501831i
$900$		0			0
$901$	33.5811	+	58.1641i	0.0372709	+	0.0645551i
$902$		0			0
$903$	872.074	+	693.433i	0.965752	+	0.767921i
$904$		0			0
$905$	−160.730	−	278.392i	−0.177602	−	0.307615i
$906$		0			0
$907$	626.862	+	361.919i	0.691138	+	0.399029i	0.804038	−	0.594578i	$-0.202681\pi$
$907$	626.862	+	361.919i	0.691138	+	0.399029i	−0.112900	+	0.993606i	$0.536014\pi$
$908$		0			0
$909$	851.288			0.936511
$910$		0			0
$911$	−1600.04			−1.75636			−0.878179	−	0.478332i	$-0.841242\pi$
$911$	−1600.04			−1.75636			−0.878179	+	0.478332i	$0.841242\pi$
$912$		0			0
$913$	192.188	+	110.960i	0.210502	+	0.121533i
$914$		0			0
$915$	209.832	+	363.440i	0.229325	+	0.397202i
$916$		0			0
$917$	−235.374	−	597.228i	−0.256678	−	0.651284i
$918$		0			0
$919$	−262.042	−	453.871i	−0.285139	−	0.493875i	0.687504	−	0.726180i	$-0.258706\pi$
$919$	−262.042	−	453.871i	−0.285139	−	0.493875i	−0.972643	+	0.232306i	$0.925373\pi$
$920$		0			0
$921$	−257.535	+	446.064i	−0.279626	+	0.484326i
$922$		0			0
$923$	−322.372			−0.349266
$924$		0			0
$925$			2117.53i			2.28922i
$926$		0			0
$927$	533.618	+	308.084i	0.575640	+	0.332346i
$928$		0			0
$929$	551.791	−	318.577i	0.593962	−	0.342924i	−0.172700	−	0.984974i	$-0.555249\pi$
$929$	551.791	−	318.577i	0.593962	−	0.342924i	0.766663	+	0.642050i	$0.221916\pi$
$930$		0			0
$931$	−119.060	−	514.892i	−0.127884	−	0.553053i
$932$		0			0
$933$	−1560.31	+	900.844i	−1.67235	+	0.965534i
$934$		0			0
$935$	−169.180	+	293.029i	−0.180941	+	0.313400i
$936$		0			0
$937$			383.587i			0.409378i	0.978827	+	0.204689i	$0.0656182\pi$
$937$			383.587i			0.409378i	−0.978827	+	0.204689i	$0.934382\pi$
$938$		0			0
$939$			2205.50i			2.34877i
$940$		0			0
$941$	130.295	−	225.678i	0.138465	−	0.239828i	−0.788451	−	0.615098i	$-0.789117\pi$
$941$	130.295	−	225.678i	0.138465	−	0.239828i	0.926916	+	0.375270i	$0.122450\pi$
$942$		0			0
$943$	−823.840	+	475.644i	−0.873637	+	0.504394i
$944$		0			0
$945$	−249.719	−	633.626i	−0.264252	−	0.670504i
$946$		0			0
$947$	851.444	−	491.581i	0.899096	−	0.519093i	0.0221894	−	0.999754i	$-0.492936\pi$
$947$	851.444	−	491.581i	0.899096	−	0.519093i	0.876907	+	0.480660i	$0.159603\pi$
$948$		0			0
$949$	−604.827	−	349.197i	−0.637331	−	0.367963i
$950$		0			0
$951$		−	689.781i		−	0.725322i
$952$		0			0
$953$	−1137.60			−1.19370			−0.596851	−	0.802352i	$-0.703582\pi$
$953$	−1137.60			−1.19370			−0.596851	+	0.802352i	$0.703582\pi$
$954$		0			0
$955$	−1440.78	+	2495.50i	−1.50867	+	2.61309i
$956$		0			0
$957$	122.403	+	212.008i	0.127903	+	0.221534i
$958$		0			0
$959$	−869.505	+	1093.51i	−0.906679	+	1.14026i
$960$		0			0
$961$	−23.5835	−	40.8479i	−0.0245406	−	0.0425056i
$962$		0			0
$963$	−503.275	−	290.566i	−0.522612	−	0.301730i
$964$		0			0
$965$	1768.75			1.83290
$966$		0			0
$967$	1296.35			1.34059			0.670297	−	0.742093i	$-0.266167\pi$
$967$	1296.35			1.34059			0.670297	+	0.742093i	$0.266167\pi$
$968$		0			0
$969$	381.214	+	220.094i	0.393410	+	0.227135i
$970$		0			0
$971$	665.237	+	1152.22i	0.685105	+	1.18664i	0.973404	+	0.229096i	$0.0735768\pi$
$971$	665.237	+	1152.22i	0.685105	+	1.18664i	−0.288299	+	0.957540i	$0.593090\pi$
$972$		0			0
$973$	273.309	+	40.7980i	0.280893	+	0.0419301i
$974$		0			0
$975$	−812.237	−	1406.84i	−0.833063	−	1.44291i
$976$		0			0
$977$	−693.081	+	1200.45i	−0.709397	+	1.22871i	0.255684	+	0.966760i	$0.417699\pi$
$977$	−693.081	+	1200.45i	−0.709397	+	1.22871i	−0.965081	+	0.261952i	$0.915634\pi$
$978$		0			0
$979$	−98.5153			−0.100629
$980$		0			0
$981$			1211.27i			1.23473i
$982$		0			0
$983$	601.161	+	347.081i	0.611558	+	0.353083i	0.773575	−	0.633705i	$-0.218467\pi$
$983$	601.161	+	347.081i	0.611558	+	0.353083i	−0.162017	+	0.986788i	$0.551800\pi$
$984$		0			0
$985$	118.968	−	68.6861i	0.120780	−	0.0697321i
$986$		0			0
$987$	168.331	−	1127.66i	0.170548	−	1.14251i
$988$		0			0
$989$	456.757	−	263.709i	0.461838	−	0.266642i
$990$		0			0
$991$	−467.257	+	809.312i	−0.471500	+	0.816662i	−0.999468	−	0.0326018i	$-0.989621\pi$
$991$	−467.257	+	809.312i	−0.471500	+	0.816662i	0.527968	+	0.849264i	$0.322954\pi$
$992$		0			0
$993$		−	1933.22i		−	1.94684i
$994$		0			0
$995$		−	497.576i		−	0.500076i
$996$		0			0
$997$	−769.103	+	1332.12i	−0.771417	+	1.33613i	0.165370	+	0.986232i	$0.447118\pi$
$997$	−769.103	+	1332.12i	−0.771417	+	1.33613i	−0.936786	+	0.349902i	$0.886215\pi$
$998$		0			0
$999$	376.463	−	217.351i	0.376840	−	0.217568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.n.a.17.13		28
4.3	odd	2		56.3.j.a.45.1	yes	28
7.3	odd	6		1568.3.h.a.881.25		28
7.4	even	3		1568.3.h.a.881.3		28
7.5	odd	6	inner	224.3.n.a.145.2		28
8.3	odd	2		56.3.j.a.45.10	yes	28
8.5	even	2	inner	224.3.n.a.17.2		28
28.3	even	6		392.3.h.a.293.17		28
28.11	odd	6		392.3.h.a.293.18		28
28.19	even	6		56.3.j.a.5.10	yes	28
28.23	odd	6		392.3.j.e.117.10		28
28.27	even	2		392.3.j.e.325.1		28
56.3	even	6		392.3.h.a.293.20		28
56.5	odd	6	inner	224.3.n.a.145.13		28
56.11	odd	6		392.3.h.a.293.19		28
56.19	even	6		56.3.j.a.5.1	✓	28
56.27	even	2		392.3.j.e.325.10		28
56.45	odd	6		1568.3.h.a.881.4		28
56.51	odd	6		392.3.j.e.117.1		28
56.53	even	6		1568.3.h.a.881.26		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.1	✓	28	56.19	even	6
56.3.j.a.5.10	yes	28	28.19	even	6
56.3.j.a.45.1	yes	28	4.3	odd	2
56.3.j.a.45.10	yes	28	8.3	odd	2
224.3.n.a.17.2		28	8.5	even	2	inner
224.3.n.a.17.13		28	1.1	even	1	trivial
224.3.n.a.145.2		28	7.5	odd	6	inner
224.3.n.a.145.13		28	56.5	odd	6	inner
392.3.h.a.293.17		28	28.3	even	6
392.3.h.a.293.18		28	28.11	odd	6
392.3.h.a.293.19		28	56.11	odd	6
392.3.h.a.293.20		28	56.3	even	6
392.3.j.e.117.1		28	56.51	odd	6
392.3.j.e.117.10		28	28.23	odd	6
392.3.j.e.325.1		28	28.27	even	2
392.3.j.e.325.10		28	56.27	even	2
1568.3.h.a.881.3		28	7.4	even	3
1568.3.h.a.881.4		28	56.45	odd	6
1568.3.h.a.881.25		28	7.3	odd	6
1568.3.h.a.881.26		28	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.94818 - 3.37434i) q^{3} +(-4.42985 - 7.67272i) q^{5} +(6.92329 + 1.03347i) q^{7} +(-3.09078 - 5.35338i) q^{9} +O(q^{10})\)	\(q+(1.94818 - 3.37434i) q^{3} +(-4.42985 - 7.67272i) q^{5} +(6.92329 + 1.03347i) q^{7} +(-3.09078 - 5.35338i) q^{9} +(3.15749 + 1.82298i) q^{11} -7.79378 q^{13} -34.5205 q^{15} +(-9.07152 - 5.23744i) q^{17} +(-5.39264 - 9.34032i) q^{19} +(16.9751 - 21.3482i) q^{21} +(-6.45553 - 11.1813i) q^{23} +(-26.7471 + 46.3273i) q^{25} +10.9817 q^{27} +17.2327i q^{29} +(26.1797 + 15.1148i) q^{31} +(12.3027 - 7.10296i) q^{33} +(-22.7396 - 57.6986i) q^{35} +(34.2810 - 19.7922i) q^{37} +(-15.1837 + 26.2989i) q^{39} -73.6801i q^{41} +40.8501i q^{43} +(-27.3833 + 47.4293i) q^{45} +(36.2025 - 20.9015i) q^{47} +(46.8639 + 14.3100i) q^{49} +(-35.3458 + 20.4069i) q^{51} +(-5.55272 - 3.20586i) q^{53} -32.3020i q^{55} -42.0232 q^{57} +(7.95742 - 13.7827i) q^{59} +(-6.07848 - 10.5282i) q^{61} +(-15.8658 - 40.2572i) q^{63} +(34.5253 + 59.7995i) q^{65} +(-6.75274 - 3.89870i) q^{67} -50.3060 q^{69} +41.3627 q^{71} +(77.6038 + 44.8046i) q^{73} +(104.216 + 180.507i) q^{75} +(19.9762 + 15.8842i) q^{77} +(35.3975 + 61.3103i) q^{79} +(49.2112 - 85.2363i) q^{81} +60.8673 q^{83} +92.8043i q^{85} +(58.1489 + 33.5723i) q^{87} +(-23.4004 + 13.5102i) q^{89} +(-53.9586 - 8.05463i) q^{91} +(102.005 - 58.8927i) q^{93} +(-47.7771 + 82.7524i) q^{95} +3.26608i q^{97} -22.5377i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{7} - 32 q^{9}+O(q^{10}) \) 28 * q + 4 * q^7 - 32 * q^9	\( 28 q + 4 q^{7} - 32 q^{9} - 28 q^{15} - 6 q^{17} - 30 q^{23} - 32 q^{25} + 6 q^{31} - 6 q^{33} + 20 q^{39} + 294 q^{47} - 20 q^{49} + 124 q^{57} - 432 q^{63} - 52 q^{65} + 136 q^{71} + 234 q^{73} + 162 q^{79} - 18 q^{81} - 48 q^{87} - 150 q^{89} - 290 q^{95}+O(q^{100}) \) 28 * q + 4 * q^7 - 32 * q^9 - 28 * q^15 - 6 * q^17 - 30 * q^23 - 32 * q^25 + 6 * q^31 - 6 * q^33 + 20 * q^39 + 294 * q^47 - 20 * q^49 + 124 * q^57 - 432 * q^63 - 52 * q^65 + 136 * q^71 + 234 * q^73 + 162 * q^79 - 18 * q^81 - 48 * q^87 - 150 * q^89 - 290 * q^95

Introduction

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