LMFDB - Embedded newform 135.3.l.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,3,Mod(37,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("135.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.l (of order $12$, degree $4$, 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:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	135.37
Dual form			135.3.l.a.73.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930497 - 3.47266i) q^{2} +(-7.72947 - 4.46261i) q^{4} +(-4.99913 + 0.0933744i) q^{5} +(1.28323 - 4.78910i) q^{7} +(-12.5207 + 12.5207i) q^{8} +(-4.32742 + 17.4472i) q^{10} +(-1.37764 - 2.38615i) q^{11} +(2.45318 + 9.15539i) q^{13} +(-15.4369 - 8.91249i) q^{14} +(13.9793 + 24.2129i) q^{16} +(-9.17504 - 9.17504i) q^{17} -32.1912i q^{19} +(39.0573 + 21.5874i) q^{20} +(-9.56819 + 2.56379i) q^{22} +(-0.179412 - 0.669573i) q^{23} +(24.9826 - 0.933581i) q^{25} +34.0763 q^{26} +(-31.2906 + 31.2906i) q^{28} +(30.1349 - 17.3984i) q^{29} +(12.8482 - 22.2537i) q^{31} +(28.6765 - 7.68384i) q^{32} +(-40.3992 + 23.3245i) q^{34} +(-5.96788 + 24.0611i) q^{35} +(-13.0331 - 13.0331i) q^{37} +(-111.789 - 29.9538i) q^{38} +(61.4236 - 63.7618i) q^{40} +(-20.2139 + 35.0116i) q^{41} +(3.68527 + 0.987466i) q^{43} +24.5915i q^{44} -2.49214 q^{46} +(-0.993231 + 3.70679i) q^{47} +(21.1465 + 12.2089i) q^{49} +(20.0042 - 87.6247i) q^{50} +(21.8952 - 81.7139i) q^{52} +(31.2240 - 31.2240i) q^{53} +(7.10982 + 11.8000i) q^{55} +(43.8959 + 76.0300i) q^{56} +(-32.3783 - 120.837i) q^{58} +(36.8611 + 21.2818i) q^{59} +(-6.56994 - 11.3795i) q^{61} +(-65.3243 - 65.3243i) q^{62} +5.10100i q^{64} +(-13.1186 - 45.5399i) q^{65} +(-44.9977 + 12.0571i) q^{67} +(29.9735 + 111.863i) q^{68} +(78.0031 + 43.1133i) q^{70} +114.062 q^{71} +(-18.7982 + 18.7982i) q^{73} +(-57.3867 + 33.1322i) q^{74} +(-143.657 + 248.821i) q^{76} +(-13.1953 + 3.53568i) q^{77} +(-18.3057 + 10.5688i) q^{79} +(-72.1453 - 119.738i) q^{80} +(102.774 + 102.774i) q^{82} +(14.7688 + 3.95730i) q^{83} +(46.7239 + 45.0105i) q^{85} +(6.85828 - 11.8789i) q^{86} +(47.1254 + 12.6272i) q^{88} +92.4405i q^{89} +46.9941 q^{91} +(-1.60129 + 5.97609i) q^{92} +(11.9482 + 6.89832i) q^{94} +(3.00583 + 160.928i) q^{95} +(-40.7091 + 151.928i) q^{97} +(62.0742 - 62.0742i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) $ 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.930497	−	3.47266i	0.465249	−	1.73633i	−0.190815	−	0.981626i	$-0.561113\pi$
$2$	0.930497	−	3.47266i	0.465249	−	1.73633i	0.656063	−	0.754706i	$-0.272220\pi$
$3$		0			0
$3$		0			0
$4$	−7.72947	−	4.46261i	−1.93237	−	1.11565i
$5$	−4.99913	+	0.0933744i	−0.999826	+	0.0186749i
$5$	−4.99913	+	0.0933744i	−0.999826	+	0.0186749i
$6$		0			0
$7$	1.28323	−	4.78910i	0.183319	−	0.684157i	−0.811665	−	0.584123i	$-0.801438\pi$
$7$	1.28323	−	4.78910i	0.183319	−	0.684157i	0.994984	−	0.100033i	$-0.0318950\pi$
$8$	−12.5207	+	12.5207i	−1.56509	+	1.56509i
$9$		0			0
$10$	−4.32742	+	17.4472i	−0.432742	+	1.74472i
$11$	−1.37764	−	2.38615i	−0.125240	−	0.216923i	0.796587	−	0.604525i	$-0.206637\pi$
$11$	−1.37764	−	2.38615i	−0.125240	−	0.216923i	−0.921827	+	0.387602i	$0.873304\pi$
$12$		0			0
$13$	2.45318	+	9.15539i	0.188706	+	0.704261i	0.993807	+	0.111123i	$0.0354446\pi$
$13$	2.45318	+	9.15539i	0.188706	+	0.704261i	−0.805101	+	0.593138i	$0.797889\pi$
$14$	−15.4369	−	8.91249i	−1.10263	−	0.636606i
$15$		0			0
$16$	13.9793	+	24.2129i	0.873708	+	1.51331i
$17$	−9.17504	−	9.17504i	−0.539708	−	0.539708i	0.383735	−	0.923443i	$-0.374638\pi$
$17$	−9.17504	−	9.17504i	−0.539708	−	0.539708i	−0.923443	+	0.383735i	$0.874638\pi$
$18$		0			0
$19$		−	32.1912i		−	1.69427i	−0.531375	−	0.847137i	$-0.678324\pi$
$19$		−	32.1912i		−	1.69427i	0.531375	−	0.847137i	$-0.321676\pi$
$20$	39.0573	+	21.5874i	1.95286	+	1.07937i
$21$		0			0
$22$	−9.56819	+	2.56379i	−0.434918	+	0.116536i
$23$	−0.179412	−	0.669573i	−0.00780050	−	0.0291119i	0.961916	−	0.273346i	$-0.0881303\pi$
$23$	−0.179412	−	0.669573i	−0.00780050	−	0.0291119i	−0.969716	+	0.244234i	$0.921464\pi$
$24$		0			0
$25$	24.9826	−	0.933581i	0.999302	−	0.0373432i
$26$	34.0763			1.31063
$27$		0			0
$28$	−31.2906	+	31.2906i	−1.11752	+	1.11752i
$29$	30.1349	−	17.3984i	1.03913	−	0.599944i	0.119546	−	0.992829i	$-0.461856\pi$
$29$	30.1349	−	17.3984i	1.03913	−	0.599944i	0.919588	+	0.392884i	$0.128523\pi$
$30$		0			0
$31$	12.8482	−	22.2537i	0.414457	−	0.717860i	−0.580914	−	0.813965i	$-0.697305\pi$
$31$	12.8482	−	22.2537i	0.414457	−	0.717860i	0.995371	+	0.0961042i	$0.0306382\pi$
$32$	28.6765	−	7.68384i	0.896140	−	0.240120i
$33$		0			0
$34$	−40.3992	+	23.3245i	−1.18821	+	0.686014i
$35$	−5.96788	+	24.0611i	−0.170511	+	0.687461i
$36$		0			0
$37$	−13.0331	−	13.0331i	−0.352245	−	0.352245i	0.508699	−	0.860944i	$-0.330127\pi$
$37$	−13.0331	−	13.0331i	−0.352245	−	0.352245i	−0.860944	+	0.508699i	$0.830127\pi$
$38$	−111.789	−	29.9538i	−2.94182	−	0.788259i
$39$		0			0
$40$	61.4236	−	63.7618i	1.53559	−	1.59405i
$41$	−20.2139	+	35.0116i	−0.493023	+	0.853941i	−0.999968	−	0.00803768i	$-0.997442\pi$
$41$	−20.2139	+	35.0116i	−0.493023	+	0.853941i	0.506945	+	0.861979i	$0.330775\pi$
$42$		0			0
$43$	3.68527	+	0.987466i	0.0857040	+	0.0229643i	0.301416	−	0.953493i	$-0.402541\pi$
$43$	3.68527	+	0.987466i	0.0857040	+	0.0229643i	−0.215712	+	0.976457i	$0.569207\pi$
$44$			24.5915i			0.558899i
$45$		0			0
$46$	−2.49214			−0.0541770
$47$	−0.993231	+	3.70679i	−0.0211326	+	0.0788679i	−0.975687	−	0.219169i	$-0.929665\pi$
$47$	−0.993231	+	3.70679i	−0.0211326	+	0.0788679i	0.954554	+	0.298037i	$0.0963320\pi$
$48$		0			0
$49$	21.1465	+	12.2089i	0.431561	+	0.249162i
$50$	20.0042	−	87.6247i	0.400084	−	1.75249i
$51$		0			0
$52$	21.8952	−	81.7139i	0.421061	−	1.57142i
$53$	31.2240	−	31.2240i	0.589132	−	0.589132i	−0.348265	−	0.937396i	$-0.613229\pi$
$53$	31.2240	−	31.2240i	0.589132	−	0.589132i	0.937396	+	0.348265i	$0.113229\pi$
$54$		0			0
$55$	7.10982	+	11.8000i	0.129269	+	0.214546i
$56$	43.8959	+	76.0300i	0.783856	+	1.35768i
$57$		0			0
$58$	−32.3783	−	120.837i	−0.558247	−	2.08340i
$59$	36.8611	+	21.2818i	0.624765	+	0.360708i	0.778722	−	0.627369i	$-0.215868\pi$
$59$	36.8611	+	21.2818i	0.624765	+	0.360708i	−0.153957	+	0.988078i	$0.549202\pi$
$60$		0			0
$61$	−6.56994	−	11.3795i	−0.107704	−	0.186549i	0.807136	−	0.590366i	$-0.201017\pi$
$61$	−6.56994	−	11.3795i	−0.107704	−	0.186549i	−0.914840	+	0.403817i	$0.867683\pi$
$62$	−65.3243	−	65.3243i	−1.05362	−	1.05362i
$63$		0			0
$64$			5.10100i			0.0797032i
$65$	−13.1186	−	45.5399i	−0.201825	−	0.700614i
$66$		0			0
$67$	−44.9977	+	12.0571i	−0.671607	+	0.179957i	−0.578479	−	0.815697i	$-0.696353\pi$
$67$	−44.9977	+	12.0571i	−0.671607	+	0.179957i	−0.0931285	+	0.995654i	$0.529687\pi$
$68$	29.9735	+	111.863i	0.440787	+	1.64504i
$69$		0			0
$70$	78.0031	+	43.1133i	1.11433	+	0.615904i
$71$	114.062			1.60651			0.803254	−	0.595637i	$-0.203100\pi$
$71$	114.062			1.60651			0.803254	+	0.595637i	$0.203100\pi$
$72$		0			0
$73$	−18.7982	+	18.7982i	−0.257510	+	0.257510i	−0.824041	−	0.566531i	$-0.808285\pi$
$73$	−18.7982	+	18.7982i	−0.257510	+	0.257510i	0.566531	+	0.824041i	$0.308285\pi$
$74$	−57.3867	+	33.1322i	−0.775496	+	0.447733i
$75$		0			0
$76$	−143.657	+	248.821i	−1.89022	+	3.27396i
$77$	−13.1953	+	3.53568i	−0.171368	+	0.0459179i
$78$		0			0
$79$	−18.3057	+	10.5688i	−0.231717	+	0.133782i	−0.611364	−	0.791350i	$-0.709379\pi$
$79$	−18.3057	+	10.5688i	−0.231717	+	0.133782i	0.379647	+	0.925132i	$0.376046\pi$
$80$	−72.1453	−	119.738i	−0.901816	−	1.49673i
$81$		0			0
$82$	102.774	+	102.774i	1.25335	+	1.25335i
$83$	14.7688	+	3.95730i	0.177938	+	0.0476783i	0.346688	−	0.937981i	$-0.387306\pi$
$83$	14.7688	+	3.95730i	0.177938	+	0.0476783i	−0.168750	+	0.985659i	$0.553973\pi$
$84$		0			0
$85$	46.7239	+	45.0105i	0.549693	+	0.529535i
$86$	6.85828	−	11.8789i	0.0797474	−	0.138127i
$87$		0			0
$88$	47.1254	+	12.6272i	0.535516	+	0.143491i
$89$			92.4405i			1.03866i	0.854575	+	0.519329i	$0.173818\pi$
$89$			92.4405i			1.03866i	−0.854575	+	0.519329i	$0.826182\pi$
$90$		0			0
$91$	46.9941			0.516418
$92$	−1.60129	+	5.97609i	−0.0174053	+	0.0649574i
$93$		0			0
$94$	11.9482	+	6.89832i	0.127109	+	0.0733864i
$95$	3.00583	+	160.928i	0.0316404	+	1.69398i
$96$		0			0
$97$	−40.7091	+	151.928i	−0.419681	+	1.56627i	0.355590	+	0.934642i	$0.384280\pi$
$97$	−40.7091	+	151.928i	−0.419681	+	1.56627i	−0.775271	+	0.631629i	$0.782387\pi$
$98$	62.0742	−	62.0742i	0.633411	−	0.633411i
$99$		0			0
$100$	−197.268	−	104.271i	−1.97268	−	1.04271i
$101$	−41.2983	−	71.5307i	−0.408894	−	0.708225i	0.585872	−	0.810404i	$-0.300752\pi$
$101$	−41.2983	−	71.5307i	−0.408894	−	0.708225i	−0.994766	+	0.102178i	$0.967419\pi$
$102$		0			0
$103$	−12.9609	−	48.3706i	−0.125834	−	0.469617i	0.874034	−	0.485864i	$-0.161495\pi$
$103$	−12.9609	−	48.3706i	−0.125834	−	0.469617i	−0.999868	+	0.0162466i	$0.994828\pi$
$104$	−145.348	−	83.9166i	−1.39757	−	0.806890i
$105$		0			0
$106$	−79.3765	−	137.484i	−0.748835	−	1.29702i
$107$	57.4669	+	57.4669i	0.537074	+	0.537074i	0.922668	−	0.385595i	$-0.126004\pi$
$107$	57.4669	+	57.4669i	0.537074	+	0.537074i	−0.385595	+	0.922668i	$0.626004\pi$
$108$		0			0
$109$		−	145.852i		−	1.33809i	−0.743220	−	0.669047i	$-0.766702\pi$
$109$		−	145.852i		−	1.33809i	0.743220	−	0.669047i	$-0.233298\pi$
$110$	47.5932	−	13.7101i	0.432665	−	0.124638i
$111$		0			0
$112$	133.897	−	35.8775i	1.19551	−	0.320335i
$113$	−14.0319	−	52.3679i	−0.124176	−	0.463432i	0.875633	−	0.482978i	$-0.160445\pi$
$113$	−14.0319	−	52.3679i	−0.124176	−	0.463432i	−0.999809	+	0.0195453i	$0.993778\pi$
$114$		0			0
$115$	0.959422	+	3.33053i	0.00834280	+	0.0289611i
$116$	−310.569			−2.67732
$117$		0			0
$118$	108.204	−	108.204i	0.916980	−	0.916980i
$119$	−55.7139	+	32.1664i	−0.468184	+	0.270306i
$120$		0			0
$121$	56.7042	−	98.2145i	0.468630	−	0.811690i
$122$	−45.6304	+	12.2266i	−0.374019	+	0.100218i
$123$		0			0
$124$	−198.619	+	114.673i	−1.60177	+	0.924780i
$125$	−124.804	+	6.99982i	−0.998431	+	0.0559986i
$126$		0			0
$127$	50.4054	+	50.4054i	0.396893	+	0.396893i	0.877136	−	0.480243i	$-0.159451\pi$
$127$	50.4054	+	50.4054i	0.396893	+	0.396893i	−0.480243	+	0.877136i	$0.659451\pi$
$128$	132.420	+	35.4818i	1.03453	+	0.277202i
$129$		0			0
$130$	−170.352	+	3.18185i	−1.31040	+	0.0244758i
$131$	89.6936	−	155.354i	0.684684	−	1.18591i	−0.288852	−	0.957374i	$-0.593274\pi$
$131$	89.6936	−	155.354i	0.684684	−	1.18591i	0.973536	−	0.228534i	$-0.0733931\pi$
$132$		0			0
$133$	−154.167	−	41.3089i	−1.15915	−	0.310593i
$134$			167.481i			1.24986i
$135$		0			0
$136$	229.756			1.68938
$137$	36.5154	−	136.277i	0.266536	−	0.994725i	−0.694768	−	0.719234i	$-0.744493\pi$
$137$	36.5154	−	136.277i	0.266536	−	0.994725i	0.961304	−	0.275491i	$-0.0888404\pi$
$138$		0			0
$139$	236.063	+	136.291i	1.69829	+	0.980510i	0.947381	+	0.320108i	$0.103719\pi$
$139$	236.063	+	136.291i	1.69829	+	0.980510i	0.750912	+	0.660402i	$0.229614\pi$
$140$	153.504	−	159.347i	1.09646	−	1.13820i
$141$		0			0
$142$	106.134	−	396.099i	0.747426	−	2.78943i
$143$	18.4665	−	18.4665i	0.129137	−	0.129137i
$144$		0			0
$145$	−149.024	+	89.7906i	−1.02775	+	0.619245i
$146$	47.7882	+	82.7716i	0.327317	+	0.566929i
$147$		0			0
$148$	42.5772	+	158.900i	0.287684	+	1.07365i
$149$	−174.004	−	100.461i	−1.16781	−	0.674235i	−0.214646	−	0.976692i	$-0.568860\pi$
$149$	−174.004	−	100.461i	−1.16781	−	0.674235i	−0.953163	+	0.302457i	$0.902193\pi$
$150$		0			0
$151$	58.6560	+	101.595i	0.388450	+	0.672816i	0.992241	−	0.124327i	$-0.0396771\pi$
$151$	58.6560	+	101.595i	0.388450	+	0.672816i	−0.603791	+	0.797143i	$0.706344\pi$
$152$	403.057	+	403.057i	2.65169	+	2.65169i
$153$		0			0
$154$			49.1129i			0.318915i
$155$	−62.1517	+	112.449i	−0.400979	+	0.725475i
$156$		0			0
$157$	−205.058	+	54.9450i	−1.30610	+	0.349968i	−0.843753	−	0.536731i	$-0.819659\pi$
$157$	−205.058	+	54.9450i	−1.30610	+	0.349968i	−0.462346	+	0.886700i	$0.652992\pi$
$158$	19.6684	+	73.4036i	0.124484	+	0.464580i
$159$		0			0
$160$	−142.640	+	41.0902i	−0.891500	+	0.256814i
$161$	−3.43688			−0.0213471
$162$		0			0
$163$	61.1545	−	61.1545i	0.375181	−	0.375181i	−0.494179	−	0.869360i	$-0.664531\pi$
$163$	61.1545	−	61.1545i	0.375181	−	0.375181i	0.869360	+	0.494179i	$0.164531\pi$
$164$	312.486	−	180.414i	1.90540	−	1.10008i
$165$		0			0
$166$	27.4847	−	47.6049i	0.165571	−	0.286777i
$167$	−234.945	+	62.9533i	−1.40686	+	0.376966i	−0.880802	−	0.473486i	$-0.842996\pi$
$167$	−234.945	+	62.9533i	−1.40686	+	0.376966i	−0.526054	+	0.850451i	$0.676329\pi$
$168$		0			0
$169$	68.5552	−	39.5803i	0.405652	−	0.234203i
$170$	199.783	−	120.374i	1.17519	−	0.708084i
$171$		0			0
$172$	−24.0785	−	24.0785i	−0.139991	−	0.139991i
$173$	16.3284	+	4.37517i	0.0943835	+	0.0252900i	0.305702	−	0.952127i	$-0.401109\pi$
$173$	16.3284	+	4.37517i	0.0943835	+	0.0252900i	−0.211318	+	0.977417i	$0.567776\pi$
$174$		0			0
$175$	27.5875	−	120.842i	0.157643	−	0.690525i
$176$	38.5171	−	66.7135i	0.218847	−	0.379054i
$177$		0			0
$178$	321.015	+	86.0157i	1.80345	+	0.483234i
$179$		−	274.512i		−	1.53359i	−0.641895	−	0.766793i	$-0.721851\pi$
$179$		−	274.512i		−	1.53359i	0.641895	−	0.766793i	$-0.278149\pi$
$180$		0			0
$181$	−261.649			−1.44557			−0.722787	−	0.691070i	$-0.757139\pi$
$181$	−261.649			−1.44557			−0.722787	+	0.691070i	$0.757139\pi$
$182$	43.7279	−	163.195i	0.240263	−	0.896674i
$183$		0			0
$184$	10.6299	+	6.13718i	0.0577712	+	0.0333542i
$185$	66.3709	+	63.9370i	0.358762	+	0.345606i
$186$		0			0
$187$	−9.25307	+	34.5329i	−0.0494817	+	0.184668i
$188$	24.2191	−	24.2191i	0.128825	−	0.128825i
$189$		0			0
$190$	561.646	+	139.305i	2.95603	+	0.733183i
$191$	89.7939	+	155.528i	0.470125	+	0.814280i	0.999416	−	0.0341597i	$-0.0108755\pi$
$191$	89.7939	+	155.528i	0.470125	+	0.814280i	−0.529291	+	0.848440i	$0.677542\pi$
$192$		0			0
$193$	6.95596	+	25.9600i	0.0360412	+	0.134508i	0.981602	−	0.190937i	$-0.0611526\pi$
$193$	6.95596	+	25.9600i	0.0360412	+	0.134508i	−0.945561	+	0.325445i	$0.894486\pi$
$194$	489.716	+	282.738i	2.52431	+	1.45741i
$195$		0			0
$196$	−108.967	−	188.737i	−0.555956	−	0.962944i
$197$	−118.588	−	118.588i	−0.601967	−	0.601967i	0.338867	−	0.940834i	$-0.389956\pi$
$197$	−118.588	−	118.588i	−0.601967	−	0.601967i	−0.940834	+	0.338867i	$0.889956\pi$
$198$		0			0
$199$		−	23.9129i		−	0.120166i	−0.998193	−	0.0600828i	$-0.980864\pi$
$199$		−	23.9129i		−	0.120166i	0.998193	−	0.0600828i	$-0.0191365\pi$
$200$	−301.111	+	324.489i	−1.50555	+	1.62244i
$201$		0			0
$202$	−286.830	+	76.8559i	−1.41995	+	0.380475i
$203$	−44.6524	−	166.645i	−0.219963	−	0.820912i
$204$		0			0
$205$	97.7829	−	176.915i	0.476990	−	0.862999i
$206$	−180.035			−0.873956
$207$		0			0
$208$	−187.385	+	187.385i	−0.900889	+	0.900889i
$209$	−76.8130	+	44.3480i	−0.367526	+	0.212191i
$210$		0			0
$211$	68.1081	−	117.967i	0.322787	−	0.559084i	−0.658275	−	0.752778i	$-0.728713\pi$
$211$	68.1081	−	117.967i	0.322787	−	0.559084i	0.981062	+	0.193694i	$0.0620468\pi$
$212$	−380.685	+	102.004i	−1.79568	+	0.481152i
$213$		0			0
$214$	253.036	−	146.090i	1.18241	−	0.682665i
$215$	−18.5154	−	4.59236i	−0.0861180	−	0.0213598i
$216$		0			0
$217$	−90.0878	−	90.0878i	−0.415151	−	0.415151i
$218$	−506.496	−	135.715i	−2.32338	−	0.622547i
$219$		0			0
$220$	−2.29622	−	122.936i	−0.0104374	−	0.558801i
$221$	61.4931	−	106.509i	0.278249	−	0.481942i
$222$		0			0
$223$	−387.566	−	103.848i	−1.73796	−	0.465686i	−0.755970	−	0.654606i	$-0.772834\pi$
$223$	−387.566	−	103.848i	−1.73796	−	0.465686i	−0.981992	+	0.188921i	$0.939501\pi$
$224$		−	147.195i		−	0.657119i
$225$		0			0
$226$	−194.913			−0.862445
$227$	−48.9929	+	182.844i	−0.215828	+	0.805480i	0.770046	+	0.637988i	$0.220233\pi$
$227$	−48.9929	+	182.844i	−0.215828	+	0.805480i	−0.985874	+	0.167491i	$0.946433\pi$
$228$		0			0
$229$	−128.197	−	74.0143i	−0.559810	−	0.323207i	0.193259	−	0.981148i	$-0.438094\pi$
$229$	−128.197	−	74.0143i	−0.559810	−	0.323207i	−0.753069	+	0.657941i	$0.771428\pi$
$230$	12.4585	−	0.232702i	0.0541676	−	0.00101175i
$231$		0			0
$232$	−159.470	+	595.151i	−0.687372	+	2.56531i
$233$	−191.869	+	191.869i	−0.823473	+	0.823473i	−0.986604	−	0.163131i	$-0.947841\pi$
$233$	−191.869	+	191.869i	−0.823473	+	0.823473i	0.163131	+	0.986604i	$0.447841\pi$
$234$		0			0
$235$	4.61917	−	18.6235i	0.0196561	−	0.0792488i
$236$	−189.945	−	328.994i	−0.804850	−	1.39404i
$237$		0			0
$238$	59.8616	+	223.406i	0.251519	+	0.938682i
$239$	113.709	+	65.6499i	0.475770	+	0.274686i	0.718652	−	0.695370i	$-0.244760\pi$
$239$	113.709	+	65.6499i	0.475770	+	0.274686i	−0.242882	+	0.970056i	$0.578093\pi$
$240$		0			0
$241$	106.787	+	184.961i	0.443101	+	0.767473i	0.997918	−	0.0644993i	$-0.0205450\pi$
$241$	106.787	+	184.961i	0.443101	+	0.767473i	−0.554817	+	0.831972i	$0.687212\pi$
$242$	−288.303	−	288.303i	−1.19133	−	1.19133i
$243$		0			0
$244$			117.276i			0.480640i
$245$	−106.854	−	59.0594i	−0.436139	−	0.241059i
$246$		0			0
$247$	294.723	−	78.9708i	1.19321	−	0.319720i
$248$	117.764	+	439.501i	0.474854	+	1.77218i
$249$		0			0
$250$	−91.8216	+	439.915i	−0.367287	+	1.75966i
$251$	−48.4611			−0.193072			−0.0965360	−	0.995329i	$-0.530776\pi$
$251$	−48.4611			−0.193072			−0.0965360	+	0.995329i	$0.530776\pi$
$252$		0			0
$253$	−1.35054	+	1.35054i	−0.00533809	+	0.00533809i
$254$	221.943	−	128.139i	0.873792	−	0.504484i
$255$		0			0
$256$	236.231	−	409.164i	0.922777	−	1.59830i
$257$	450.204	−	120.632i	1.75177	−	0.469385i	0.766766	−	0.641927i	$-0.221865\pi$
$257$	450.204	−	120.632i	1.75177	−	0.469385i	0.985002	+	0.172542i	$0.0551979\pi$
$258$		0			0
$259$	−79.1411	+	45.6921i	−0.305564	+	0.176418i
$260$	−101.827	+	410.543i	−0.391641	+	1.57901i
$261$		0			0
$262$	−456.032	−	456.032i	−1.74058	−	1.74058i
$263$	104.698	+	28.0536i	0.398090	+	0.106668i	0.452309	−	0.891861i	$-0.350600\pi$
$263$	104.698	+	28.0536i	0.398090	+	0.106668i	−0.0542194	+	0.998529i	$0.517267\pi$
$264$		0			0
$265$	−153.177	+	159.008i	−0.578027	+	0.600031i
$266$	−286.904	+	496.932i	−1.07859	+	1.86816i
$267$		0			0
$268$	401.614	+	107.612i	1.49856	+	0.401538i
$269$		−	271.965i		−	1.01102i	−0.862821	−	0.505510i	$-0.831304\pi$
$269$		−	271.965i		−	1.01102i	0.862821	−	0.505510i	$-0.168696\pi$
$270$		0			0
$271$	283.330			1.04550			0.522749	−	0.852487i	$-0.324907\pi$
$271$	283.330			1.04550			0.522749	+	0.852487i	$0.324907\pi$
$272$	93.8935	−	350.415i	0.345197	−	1.28829i
$273$		0			0
$274$	−439.268	−	253.611i	−1.60317	−	0.925589i
$275$	−36.6447	−	58.3260i	−0.133254	−	0.212094i
$276$		0			0
$277$	−38.5154	+	143.741i	−0.139045	+	0.518922i	0.860904	+	0.508768i	$0.169899\pi$
$277$	−38.5154	+	143.741i	−0.139045	+	0.518922i	−0.999948	+	0.0101539i	$0.996768\pi$
$278$	692.948	−	692.948i	2.49262	−	2.49262i
$279$		0			0
$280$	−226.541	−	375.985i	−0.809074	−	1.34280i
$281$	126.241	+	218.657i	0.449258	+	0.778137i	0.998338	−	0.0576326i	$-0.0183552\pi$
$281$	126.241	+	218.657i	0.449258	+	0.778137i	−0.549080	+	0.835770i	$0.685022\pi$
$282$		0			0
$283$	124.137	+	463.286i	0.438647	+	1.63705i	0.732184	+	0.681107i	$0.238501\pi$
$283$	124.137	+	463.286i	0.438647	+	1.63705i	−0.293537	+	0.955948i	$0.594832\pi$
$284$	−881.639	−	509.015i	−3.10436	−	1.79230i
$285$		0			0
$286$	−46.9450	−	81.3111i	−0.164143	−	0.284304i
$287$	141.735	+	141.735i	0.493849	+	0.493849i
$288$		0			0
$289$		−	120.637i		−	0.417430i
$290$	173.146	+	601.059i	0.597056	+	2.07262i
$291$		0			0
$292$	229.189	−	61.4111i	0.784895	−	0.210312i
$293$	52.5299	+	196.044i	0.179283	+	0.669093i	0.995782	+	0.0917468i	$0.0292450\pi$
$293$	52.5299	+	196.044i	0.179283	+	0.669093i	−0.816499	+	0.577346i	$0.804088\pi$
$294$		0			0
$295$	−186.261	−	102.948i	−0.631392	−	0.348978i
$296$	326.367			1.10259
$297$		0			0
$298$	−510.777	+	510.777i	−1.71402	+	1.71402i
$299$	5.69008	−	3.28517i	0.0190304	−	0.0109872i
$300$		0			0
$301$	9.45814	−	16.3820i	0.0314224	−	0.0544252i
$302$	407.385	−	109.159i	1.34896	−	0.361452i
$303$		0			0
$304$	779.443	−	450.011i	2.56396	−	1.48030i
$305$	33.9065	+	56.2739i	0.111169	+	0.184505i
$306$		0			0
$307$	364.680	+	364.680i	1.18788	+	1.18788i	0.977652	+	0.210232i	$0.0674220\pi$
$307$	364.680	+	364.680i	1.18788	+	1.18788i	0.210232	+	0.977652i	$0.432578\pi$
$308$	117.771	+	31.5567i	0.382374	+	0.102457i
$309$		0			0
$310$	332.664	+	320.465i	1.07311	+	1.03376i
$311$	102.480	−	177.501i	0.329518	−	0.570743i	−0.652898	−	0.757446i	$-0.726447\pi$
$311$	102.480	−	177.501i	0.329518	−	0.570743i	0.982416	+	0.186703i	$0.0597803\pi$
$312$		0			0
$313$	343.429	+	92.0214i	1.09722	+	0.293998i	0.761631	−	0.648011i	$-0.224399\pi$
$313$	343.429	+	92.0214i	1.09722	+	0.293998i	0.335586	+	0.942010i	$0.391066\pi$
$314$			763.222i			2.43064i
$315$		0			0
$316$	188.657			0.597017
$317$	6.68768	−	24.9588i	0.0210968	−	0.0787343i	−0.954575	−	0.297971i	$-0.903690\pi$
$317$	6.68768	−	24.9588i	0.0210968	−	0.0787343i	0.975672	+	0.219237i	$0.0703567\pi$
$318$		0			0
$319$	−83.0303	−	47.9375i	−0.260283	−	0.150274i
$320$	−0.476303	−	25.5006i	−0.00148845	−	0.0796893i
$321$		0			0
$322$	−3.19801	+	11.9351i	−0.00993169	+	0.0370656i
$323$	−295.356	+	295.356i	−0.914414	+	0.914414i
$324$		0			0
$325$	69.8340	+	226.435i	0.214874	+	0.696723i
$326$	−155.465	−	269.273i	−0.476886	−	0.825992i
$327$		0			0
$328$	−185.277	−	691.464i	−0.564869	−	2.10812i
$329$	16.4776	+	9.51337i	0.0500840	+	0.0289160i
$330$		0			0
$331$	96.8582	+	167.763i	0.292623	+	0.506838i	0.974429	−	0.224695i	$-0.0721386\pi$
$331$	96.8582	+	167.763i	0.292623	+	0.506838i	−0.681806	+	0.731533i	$0.738805\pi$
$332$	−96.4953	−	96.4953i	−0.290649	−	0.290649i
$333$		0			0
$334$			874.462i			2.61815i
$335$	223.823	−	64.4766i	0.668129	−	0.192467i
$336$		0			0
$337$	88.6729	−	23.7598i	0.263124	−	0.0705039i	−0.124845	−	0.992176i	$-0.539843\pi$
$337$	88.6729	−	23.7598i	0.263124	−	0.0705039i	0.387969	+	0.921672i	$0.373177\pi$
$338$	−73.6588	−	274.898i	−0.217925	−	0.813309i
$339$		0			0
$340$	−160.287	−	556.418i	−0.471431	−	1.63652i
$341$	−70.8008			−0.207627
$342$		0			0
$343$	257.393	−	257.393i	0.750417	−	0.750417i
$344$	−58.5061	+	33.7785i	−0.170076	+	0.0981933i
$345$		0			0
$346$	30.3870	−	52.6318i	0.0878236	−	0.152115i
$347$	−5.84253	+	1.56550i	−0.0168372	+	0.00451153i	−0.267228	−	0.963633i	$-0.586108\pi$
$347$	−5.84253	+	1.56550i	−0.0168372	+	0.00451153i	0.250391	+	0.968145i	$0.419441\pi$
$348$		0			0
$349$	67.8704	−	39.1850i	0.194471	−	0.112278i	−0.399603	−	0.916688i	$-0.630852\pi$
$349$	67.8704	−	39.1850i	0.194471	−	0.112278i	0.594074	+	0.804410i	$0.297519\pi$
$350$	−393.973	−	208.245i	−1.12564	−	0.594986i
$351$		0			0
$352$	−57.8408	−	57.8408i	−0.164320	−	0.164320i
$353$	−38.2322	−	10.2443i	−0.108307	−	0.0290207i	0.204259	−	0.978917i	$-0.434522\pi$
$353$	−38.2322	−	10.2443i	−0.108307	−	0.0290207i	−0.312565	+	0.949896i	$0.601188\pi$
$354$		0			0
$355$	−570.211	+	10.6505i	−1.60623	+	0.0300013i
$356$	412.526	−	714.516i	1.15878	−	2.00707i
$357$		0			0
$358$	−953.287	−	255.433i	−2.66281	−	0.713499i
$359$			116.601i			0.324795i	0.986725	+	0.162398i	$0.0519227\pi$
$359$			116.601i			0.324795i	−0.986725	+	0.162398i	$0.948077\pi$
$360$		0			0
$361$	−675.274			−1.87056
$362$	−243.464	+	908.619i	−0.672552	+	2.51000i
$363$		0			0
$364$	−363.239	−	209.716i	−0.997910	−	0.576144i
$365$	92.2195	−	95.7300i	0.252656	−	0.262274i
$366$		0			0
$367$	112.479	−	419.779i	0.306483	−	1.14381i	−0.625177	−	0.780483i	$-0.714973\pi$
$367$	112.479	−	419.779i	0.306483	−	1.14381i	0.931661	−	0.363329i	$-0.118360\pi$
$368$	13.7043	−	13.7043i	0.0372398	−	0.0372398i
$369$		0			0
$370$	283.790	−	170.991i	0.766999	−	0.462137i
$371$	−109.467	−	189.602i	−0.295059	−	0.511058i
$372$		0			0
$373$	−167.428	−	624.849i	−0.448868	−	1.67520i	−0.705516	−	0.708694i	$-0.749285\pi$
$373$	−167.428	−	624.849i	−0.448868	−	1.67520i	0.256647	−	0.966505i	$-0.417382\pi$
$374$	111.311	+	64.2656i	0.297624	+	0.171833i
$375$		0			0
$376$	−33.9757	−	58.8477i	−0.0903610	−	0.156510i
$377$	233.215	+	233.215i	0.618608	+	0.618608i
$378$		0			0
$379$		−	297.836i		−	0.785846i	−0.919571	−	0.392923i	$-0.871464\pi$
$379$		−	297.836i		−	0.785846i	0.919571	−	0.392923i	$-0.128536\pi$
$380$	694.925	−	1257.30i	1.82875	−	3.30869i
$381$		0			0
$382$	623.648	−	167.106i	1.63259	−	0.437450i
$383$	111.047	+	414.434i	0.289941	+	1.08207i	0.945153	+	0.326629i	$0.105913\pi$
$383$	111.047	+	414.434i	0.289941	+	1.08207i	−0.655212	+	0.755445i	$0.727421\pi$
$384$		0			0
$385$	65.6351	−	18.9074i	0.170481	−	0.0491102i
$386$	96.6228			0.250318
$387$		0			0
$388$	992.656	−	992.656i	2.55839	−	2.55839i
$389$	197.682	−	114.132i	0.508181	−	0.293398i	−0.223905	−	0.974611i	$-0.571880\pi$
$389$	197.682	−	114.132i	0.508181	−	0.293398i	0.732086	+	0.681213i	$0.238547\pi$
$390$		0			0
$391$	−4.49725	+	7.78947i	−0.0115019	+	0.0199219i
$392$	−417.634	+	111.905i	−1.06539	+	0.285471i
$393$		0			0
$394$	−522.160	+	301.469i	−1.32528	+	0.765151i
$395$	90.5255	−	54.5440i	0.229178	−	0.138086i
$396$		0			0
$397$	120.533	+	120.533i	0.303609	+	0.303609i	0.842424	−	0.538815i	$-0.181128\pi$
$397$	120.533	+	120.533i	0.303609	+	0.303609i	−0.538815	+	0.842424i	$0.681128\pi$
$398$	−83.0416	−	22.2509i	−0.208647	−	0.0559069i
$399$		0			0
$400$	371.844	+	591.850i	0.929610	+	1.47962i
$401$	−226.669	+	392.602i	−0.565259	+	0.979057i	0.431766	+	0.901985i	$0.357890\pi$
$401$	−226.669	+	392.602i	−0.565259	+	0.979057i	−0.997026	+	0.0770720i	$0.975443\pi$
$402$		0			0
$403$	235.260	+	63.0377i	0.583772	+	0.156421i
$404$			737.193i			1.82473i
$405$		0			0
$406$	−620.251			−1.52771
$407$	−13.1439	+	49.0538i	−0.0322946	+	0.120525i
$408$		0			0
$409$	427.158	+	246.620i	1.04440	+	0.602982i	0.921075	−	0.389385i	$-0.127312\pi$
$409$	427.158	+	246.620i	1.04440	+	0.602982i	0.123320	+	0.992367i	$0.460646\pi$
$410$	−523.379	−	504.186i	−1.27653	−	1.22972i
$411$		0			0
$412$	−115.679	+	431.718i	−0.280773	+	1.04786i
$413$	149.222	−	149.222i	0.361312	−	0.361312i
$414$		0			0
$415$	−74.2008	−	18.4040i	−0.178797	−	0.0443470i
$416$	140.697	+	243.695i	0.338214	+	0.585805i
$417$		0			0
$418$	82.5314	+	308.011i	0.197444	+	0.736870i
$419$	22.7963	+	13.1615i	0.0544066	+	0.0314116i	0.526957	−	0.849892i	$-0.323333\pi$
$419$	22.7963	+	13.1615i	0.0544066	+	0.0314116i	−0.472550	+	0.881304i	$0.656666\pi$
$420$		0			0
$421$	243.419	+	421.613i	0.578192	+	1.00146i	0.995687	+	0.0927780i	$0.0295747\pi$
$421$	243.419	+	421.613i	0.578192	+	1.00146i	−0.417495	+	0.908679i	$0.637092\pi$
$422$	−346.284	−	346.284i	−0.820579	−	0.820579i
$423$		0			0
$424$			781.894i			1.84409i
$425$	−237.782	−	220.650i	−0.559486	−	0.519177i
$426$		0			0
$427$	−62.9281	+	16.8615i	−0.147373	+	0.0394884i
$428$	−187.736	−	700.641i	−0.438636	−	1.63701i
$429$		0			0
$430$	−33.1762	+	60.0244i	−0.0771540	+	0.139592i
$431$	−73.2818			−0.170027			−0.0850137	−	0.996380i	$-0.527093\pi$
$431$	−73.2818			−0.170027			−0.0850137	+	0.996380i	$0.527093\pi$
$432$		0			0
$433$	79.7731	−	79.7731i	0.184234	−	0.184234i	−0.608964	−	0.793198i	$-0.708415\pi$
$433$	79.7731	−	79.7731i	0.184234	−	0.184234i	0.793198	+	0.608964i	$0.208415\pi$
$434$	−396.671	+	229.018i	−0.913989	+	0.527692i
$435$		0			0
$436$	−650.882	+	1127.36i	−1.49285	+	2.58569i
$437$	−21.5544	+	5.77547i	−0.0493235	+	0.0132162i
$438$		0			0
$439$	−97.4363	+	56.2549i	−0.221951	+	0.128143i	−0.606853	−	0.794814i	$-0.707568\pi$
$439$	−97.4363	+	56.2549i	−0.221951	+	0.128143i	0.384903	+	0.922957i	$0.374235\pi$
$440$	−236.765	−	58.7248i	−0.538102	−	0.133465i
$441$		0			0
$442$	−312.651	−	312.651i	−0.707356	−	0.707356i
$443$	154.045	+	41.2762i	0.347731	+	0.0931742i	0.428457	−	0.903562i	$-0.359057\pi$
$443$	154.045	+	41.2762i	0.347731	+	0.0931742i	−0.0807263	+	0.996736i	$0.525724\pi$
$444$		0			0
$445$	−8.63158	−	462.122i	−0.0193968	−	1.03848i
$446$	−721.258	+	1249.25i	−1.61717	+	2.80102i
$447$		0			0
$448$	24.4292	+	6.54578i	0.0545295	+	0.0146111i
$449$		−	291.806i		−	0.649901i	−0.945731	−	0.324951i	$-0.894652\pi$
$449$		−	291.806i		−	0.649901i	0.945731	−	0.324951i	$-0.105348\pi$
$450$		0			0
$451$	111.390			0.246985
$452$	−125.238	+	467.395i	−0.277075	+	1.03406i
$453$		0			0
$454$	589.367	+	340.271i	1.29817	+	0.749497i
$455$	−234.929	+	4.38804i	−0.516328	+	0.00964405i
$456$		0			0
$457$	121.316	−	452.757i	0.265462	−	0.990716i	−0.696506	−	0.717551i	$-0.745263\pi$
$457$	121.316	−	452.757i	0.265462	−	0.990716i	0.961967	−	0.273165i	$-0.0880705\pi$
$458$	−376.313	+	376.313i	−0.821645	+	0.821645i
$459$		0			0
$460$	7.44703	−	30.0247i	0.0161892	−	0.0652712i
$461$	248.770	+	430.882i	0.539631	+	0.934668i	0.998924	+	0.0463832i	$0.0147695\pi$
$461$	248.770	+	430.882i	0.539631	+	0.934668i	−0.459293	+	0.888285i	$0.651897\pi$
$462$		0			0
$463$	235.850	+	880.204i	0.509395	+	1.90109i	0.426391	+	0.904539i	$0.359785\pi$
$463$	235.850	+	880.204i	0.509395	+	1.90109i	0.0830044	+	0.996549i	$0.473548\pi$
$464$	842.531	+	486.435i	1.81580	+	1.04835i
$465$		0			0
$466$	487.764	+	844.831i	1.04670	+	1.81294i
$467$	204.884	+	204.884i	0.438724	+	0.438724i	0.891582	−	0.452859i	$-0.149596\pi$
$467$	204.884	+	204.884i	0.438724	+	0.438724i	−0.452859	+	0.891582i	$0.649596\pi$
$468$		0			0
$469$			230.970i			0.492474i
$470$	−60.3749	−	33.3699i	−0.128457	−	0.0709998i
$471$		0			0
$472$	−727.991	+	195.065i	−1.54235	+	0.413273i
$473$	−2.72075	−	10.1540i	−0.00575212	−	0.0214672i
$474$		0			0
$475$	−30.0531	−	804.219i	−0.0632697	−	1.69309i
$476$	574.185			1.20627
$477$		0			0
$478$	333.786	−	333.786i	0.698297	−	0.698297i
$479$	177.082	−	102.238i	0.369691	−	0.213441i	−0.303632	−	0.952789i	$-0.598199\pi$
$479$	177.082	−	102.238i	0.369691	−	0.213441i	0.673324	+	0.739348i	$0.264866\pi$
$480$		0			0
$481$	87.3504	−	151.295i	0.181602	−	0.314543i
$482$	741.673	−	198.731i	1.53874	−	0.412304i
$483$		0			0
$484$	−876.586	+	506.097i	−1.81113	+	1.04566i
$485$	189.324	−	763.310i	0.390358	−	1.57384i
$486$		0			0
$487$	−506.650	−	506.650i	−1.04035	−	1.04035i	−0.999151	−	0.0411985i	$-0.986882\pi$
$487$	−506.650	−	506.650i	−1.04035	−	1.04035i	−0.0411985	−	0.999151i	$-0.513118\pi$
$488$	224.740	+	60.2188i	0.460532	+	0.123399i
$489$		0			0
$490$	−304.521	+	316.113i	−0.621471	+	0.645129i
$491$	104.633	−	181.229i	0.213101	−	0.369102i	−0.739582	−	0.673066i	$-0.764977\pi$
$491$	104.633	−	181.229i	0.213101	−	0.369102i	0.952684	+	0.303964i	$0.0983102\pi$
$492$		0			0
$493$	−436.120	−	116.858i	−0.884624	−	0.237034i
$494$		−	1096.96i		−	2.22056i
$495$		0			0
$496$	718.435			1.44846
$497$	146.368	−	546.254i	0.294504	−	1.09910i
$498$		0			0
$499$	−287.007	−	165.704i	−0.575165	−	0.332072i	0.184044	−	0.982918i	$-0.441081\pi$
$499$	−287.007	−	165.704i	−0.575165	−	0.332072i	−0.759210	+	0.650846i	$0.774414\pi$
$500$	995.905	+	502.846i	1.99181	+	1.00569i
$501$		0			0
$502$	−45.0929	+	168.289i	−0.0898265	+	0.335237i
$503$	278.209	−	278.209i	0.553100	−	0.553100i	−0.374234	−	0.927334i	$-0.622094\pi$
$503$	278.209	−	278.209i	0.553100	−	0.553100i	0.927334	+	0.374234i	$0.122094\pi$
$504$		0			0
$505$	213.135	+	353.735i	0.422049	+	0.700466i
$506$	3.43329	+	5.94663i	0.00678515	+	0.0117522i
$507$		0			0
$508$	−164.667	−	614.546i	−0.324148	−	1.20974i
$509$	−679.279	−	392.182i	−1.33454	−	0.770495i	−0.348546	−	0.937292i	$-0.613324\pi$
$509$	−679.279	−	392.182i	−1.33454	−	0.770495i	−0.985991	+	0.166797i	$0.946658\pi$
$510$		0			0
$511$	65.9040	+	114.149i	0.128971	+	0.223384i
$512$	−813.324	−	813.324i	−1.58852	−	1.58852i
$513$		0			0
$514$		−	1675.66i		−	3.26003i
$515$	69.3096	+	240.601i	0.134582	+	0.467186i
$516$		0			0
$517$	10.2133	−	2.73664i	0.0197549	−	0.00529330i
$518$	85.0329	+	317.347i	0.164156	+	0.612639i
$519$		0			0
$520$	734.448	+	405.938i	1.41240	+	0.780650i
$521$	−763.749			−1.46593			−0.732964	−	0.680267i	$-0.761864\pi$
$521$	−763.749			−1.46593			−0.732964	+	0.680267i	$0.761864\pi$
$522$		0			0
$523$	−284.699	+	284.699i	−0.544358	+	0.544358i	−0.924803	−	0.380445i	$-0.875771\pi$
$523$	−284.699	+	284.699i	−0.544358	+	0.544358i	0.380445	+	0.924803i	$0.375771\pi$
$524$	−1386.57	+	800.535i	−2.64612	+	1.52774i
$525$		0			0
$526$	194.842	−	337.476i	0.370421	−	0.641589i
$527$	−322.061	+	86.2959i	−0.611121	+	0.163749i
$528$		0			0
$529$	457.711	−	264.260i	0.865239	−	0.499546i
$530$	409.651	+	679.889i	0.772926	+	1.28281i
$531$		0			0
$532$	1007.28	+	1007.28i	1.89339	+	1.89339i
$533$	−370.133	−	99.1769i	−0.694434	−	0.186073i
$534$		0			0
$535$	−292.650	−	281.918i	−0.547010	−	0.526950i
$536$	412.440	−	714.367i	0.769478	−	1.33277i
$537$		0			0
$538$	−944.442	−	253.062i	−1.75547	−	0.470376i
$539$		−	67.2782i		−	0.124820i
$540$		0			0
$541$	120.576			0.222876			0.111438	−	0.993771i	$-0.464454\pi$
$541$	120.576			0.222876			0.111438	+	0.993771i	$0.464454\pi$
$542$	263.638	−	983.909i	0.486416	−	1.81533i
$543$		0			0
$544$	−333.608	−	192.608i	−0.613249	−	0.354060i
$545$	13.6189	+	729.134i	0.0249887	+	1.33786i
$546$		0			0
$547$	59.6213	−	222.510i	0.108997	−	0.406782i	−0.889771	−	0.456407i	$-0.849136\pi$
$547$	59.6213	−	222.510i	0.108997	−	0.406782i	0.998768	+	0.0496252i	$0.0158027\pi$
$548$	−890.397	+	890.397i	−1.62481	+	1.62481i
$549$		0			0
$550$	−236.644	+	72.9827i	−0.430262	+	0.132696i
$551$	−560.075	−	970.078i	−1.01647	−	1.76058i
$552$		0			0
$553$	27.1244	+	101.230i	0.0490496	+	0.183056i
$554$	463.327	+	267.502i	0.836330	+	0.482855i
$555$		0			0
$556$	−1216.43	−	2106.91i	−2.18782	−	3.78941i
$557$	664.417	+	664.417i	1.19285	+	1.19285i	0.976264	+	0.216586i	$0.0694922\pi$
$557$	664.417	+	664.417i	1.19285	+	1.19285i	0.216586	+	0.976264i	$0.430508\pi$
$558$		0			0
$559$			36.1626i			0.0646915i
$560$	−666.017	+	191.859i	−1.18932	+	0.342605i
$561$		0			0
$562$	876.788	−	234.935i	1.56012	−	0.418033i
$563$	−71.6752	−	267.496i	−0.127309	−	0.475125i	0.872602	−	0.488432i	$-0.162431\pi$
$563$	−71.6752	−	267.496i	−0.127309	−	0.475125i	−0.999911	+	0.0133066i	$0.995764\pi$
$564$		0			0
$565$	75.0372	+	260.483i	0.132809	+	0.461033i
$566$	1724.35			3.04655
$567$		0			0
$568$	−1428.14	+	1428.14i	−2.51433	+	2.51433i
$569$	−830.591	+	479.542i	−1.45974	+	0.842780i	−0.998998	−	0.0447548i	$-0.985749\pi$
$569$	−830.591	+	479.542i	−1.45974	+	0.842780i	−0.460740	+	0.887535i	$0.652416\pi$
$570$		0			0
$571$	−222.371	+	385.158i	−0.389442	+	0.674533i	−0.992375	−	0.123259i	$-0.960665\pi$
$571$	−222.371	+	385.158i	−0.389442	+	0.674533i	0.602933	+	0.797792i	$0.293999\pi$
$572$	−225.145	+	60.3275i	−0.393611	+	0.105468i
$573$		0			0
$574$	624.080	−	360.313i	1.08725	−	0.627723i
$575$	−5.10726	−	16.5602i	−0.00888219	−	0.0288003i
$576$		0			0
$577$	670.378	+	670.378i	1.16183	+	1.16183i	0.984074	+	0.177761i	$0.0568852\pi$
$577$	670.378	+	670.378i	1.16183	+	1.16183i	0.177761	+	0.984074i	$0.443115\pi$
$578$	−418.933	−	112.253i	−0.724797	−	0.194209i
$579$		0			0
$580$	1552.57	−	28.9992i	2.67685	−	0.0499986i
$581$	37.9038	−	65.6513i	0.0652388	−	0.112997i
$582$		0			0
$583$	−117.521	−	31.4895i	−0.201579	−	0.0540129i
$584$		−	470.735i		−	0.806053i
$585$		0			0
$586$	729.675			1.24518
$587$	116.613	−	435.207i	0.198660	−	0.741410i	−0.792629	−	0.609704i	$-0.791288\pi$
$587$	116.613	−	435.207i	0.198660	−	0.741410i	0.991289	−	0.131705i	$-0.0420452\pi$
$588$		0			0
$589$	−716.373	−	413.598i	−1.21625	−	0.702204i
$590$	−530.820	+	551.027i	−0.899696	+	0.933945i
$591$		0			0
$592$	133.375	−	497.762i	0.225295	−	0.840814i
$593$	−292.884	+	292.884i	−0.493902	+	0.493902i	−0.909533	−	0.415631i	$-0.863561\pi$
$593$	−292.884	+	292.884i	−0.493902	+	0.493902i	0.415631	+	0.909533i	$0.363561\pi$
$594$		0			0
$595$	275.517	−	166.006i	0.463054	−	0.279002i
$596$	896.636	+	1553.02i	1.50442	+	2.60574i
$597$		0			0
$598$	−6.11368	−	22.8166i	−0.0102235	−	0.0381548i
$599$	434.899	+	251.089i	0.726042	+	0.419180i	0.816972	−	0.576677i	$-0.195651\pi$
$599$	434.899	+	251.089i	0.726042	+	0.419180i	−0.0909308	+	0.995857i	$0.528984\pi$
$600$		0			0
$601$	−99.8075	−	172.872i	−0.166069	−	0.287640i	0.770965	−	0.636877i	$-0.219774\pi$
$601$	−99.8075	−	172.872i	−0.166069	−	0.287640i	−0.937034	+	0.349237i	$0.886441\pi$
$602$	−48.0883	−	48.0883i	−0.0798810	−	0.0798810i
$603$		0			0
$604$		−	1047.04i		−	1.73350i
$605$	−274.301	+	496.282i	−0.453390	+	0.820301i
$606$		0			0
$607$	−837.927	+	224.522i	−1.38044	+	0.369888i	−0.871281	−	0.490785i	$-0.836710\pi$
$607$	−837.927	+	224.522i	−1.38044	+	0.369888i	−0.509159	+	0.860672i	$0.670043\pi$
$608$	−247.352	−	923.131i	−0.406829	−	1.51831i
$609$		0			0
$610$	226.970	−	65.3831i	0.372083	−	0.107185i
$611$	−36.3737			−0.0595314
$612$		0			0
$613$	−31.6781	+	31.6781i	−0.0516771	+	0.0516771i	−0.732473	−	0.680796i	$-0.761634\pi$
$613$	−31.6781	+	31.6781i	−0.0516771	+	0.0516771i	0.680796	+	0.732473i	$0.261634\pi$
$614$	1605.75	−	927.078i	2.61522	−	1.50990i
$615$		0			0
$616$	120.946	−	209.485i	0.196341	−	0.340072i
$617$	−253.302	+	67.8722i	−0.410539	+	0.110004i	−0.458177	−	0.888861i	$-0.651497\pi$
$617$	−253.302	+	67.8722i	−0.410539	+	0.110004i	0.0476380	+	0.998865i	$0.484831\pi$
$618$		0			0
$619$	−422.528	+	243.947i	−0.682598	+	0.394098i	−0.800833	−	0.598887i	$-0.795610\pi$
$619$	−422.528	+	243.947i	−0.682598	+	0.394098i	0.118235	+	0.992986i	$0.462276\pi$
$620$	982.214	−	591.809i	1.58422	−	0.954531i
$621$		0			0
$622$	−521.044	−	521.044i	−0.837691	−	0.837691i
$623$	442.707	+	118.623i	0.710605	+	0.190406i
$624$		0			0
$625$	623.257	−	46.6465i	0.997211	−	0.0746344i
$626$	639.119	−	1106.99i	1.02096	−	1.76835i
$627$		0			0
$628$	1830.18	+	490.396i	2.91431	+	0.780886i
$629$			239.158i			0.380219i
$630$		0			0
$631$	263.490			0.417576			0.208788	−	0.977961i	$-0.433048\pi$
$631$	263.490			0.417576			0.208788	+	0.977961i	$0.433048\pi$
$632$	96.8714	−	361.529i	0.153277	−	0.572039i
$633$		0			0
$634$	−80.4505	−	46.4481i	−0.126894	−	0.0732620i
$635$	−256.690	−	247.276i	−0.404236	−	0.389412i
$636$		0			0
$637$	−59.9014	+	223.555i	−0.0940367	+	0.350950i
$638$	−243.730	+	243.730i	−0.382023	+	0.382023i
$639$		0			0
$640$	−665.298	−	165.014i	−1.03953	−	0.257834i
$641$	459.262	+	795.464i	0.716477	+	1.24097i	0.962387	+	0.271682i	$0.0875797\pi$
$641$	459.262	+	795.464i	0.716477	+	1.24097i	−0.245911	+	0.969293i	$0.579087\pi$
$642$		0			0
$643$	10.9456	+	40.8497i	0.0170228	+	0.0635298i	0.973915	−	0.226914i	$-0.0728637\pi$
$643$	10.9456	+	40.8497i	0.0170228	+	0.0635298i	−0.956892	+	0.290444i	$0.906197\pi$
$644$	26.5652	+	15.3374i	0.0412504	+	0.0238159i
$645$		0			0
$646$	750.843	+	1300.50i	1.16230	+	2.01316i
$647$	12.5734	+	12.5734i	0.0194334	+	0.0194334i	0.716757	−	0.697323i	$-0.245626\pi$
$647$	12.5734	+	12.5734i	0.0194334	+	0.0194334i	−0.697323	+	0.716757i	$0.745626\pi$
$648$		0			0
$649$		−	117.275i		−	0.180701i
$650$	851.313	−	31.8130i	1.30971	−	0.0489430i
$651$		0			0
$652$	−745.601	+	199.783i	−1.14356	+	0.306416i
$653$	−137.591	−	513.495i	−0.210705	−	0.786363i	−0.987634	−	0.156775i	$-0.949890\pi$
$653$	−137.591	−	513.495i	−0.210705	−	0.786363i	0.776929	−	0.629588i	$-0.216776\pi$
$654$		0			0
$655$	−433.884	+	785.009i	−0.662418	+	1.19849i
$656$	−1130.31			−1.72303
$657$		0			0
$658$	48.3691	−	48.3691i	0.0735093	−	0.0735093i
$659$	64.8393	−	37.4350i	0.0983905	−	0.0568058i	−0.449997	−	0.893030i	$-0.648575\pi$
$659$	64.8393	−	37.4350i	0.0983905	−	0.0568058i	0.548388	+	0.836224i	$0.315242\pi$
$660$		0			0
$661$	11.3687	−	19.6912i	0.0171993	−	0.0297900i	−0.857298	−	0.514821i	$-0.827858\pi$
$661$	11.3687	−	19.6912i	0.0171993	−	0.0297900i	0.874497	+	0.485031i	$0.161192\pi$
$662$	672.712	−	180.253i	1.01618	−	0.272285i
$663$		0			0
$664$	−234.465	+	135.368i	−0.353110	+	0.203868i
$665$	774.557	+	192.113i	1.16475	+	0.288892i
$666$		0			0
$667$	−17.0560	−	17.0560i	−0.0255713	−	0.0255713i
$668$	2096.93	+	561.872i	3.13912	+	0.841125i
$669$		0			0
$670$	−15.6384	−	837.259i	−0.0233409	−	1.24964i
$671$	−18.1021	+	31.3537i	−0.0269777	+	0.0467268i
$672$		0			0
$673$	619.582	+	166.017i	0.920628	+	0.246681i	0.687854	−	0.725849i	$-0.258553\pi$
$673$	619.582	+	166.017i	0.920628	+	0.246681i	0.232774	+	0.972531i	$0.425220\pi$
$674$		−	330.040i		−	0.489673i
$675$		0			0
$676$	−706.526			−1.04516
$677$	150.613	−	562.095i	0.222471	−	0.830273i	−0.760931	−	0.648833i	$-0.775258\pi$
$677$	150.613	−	562.095i	0.222471	−	0.830273i	0.983402	−	0.181440i	$-0.0580758\pi$
$678$		0			0
$679$	675.360	+	389.919i	0.994639	+	0.574255i
$680$	−1148.58	+	21.4534i	−1.68909	+	0.0315490i
$681$		0			0
$682$	−65.8799	+	245.867i	−0.0965982	+	0.360509i
$683$	−599.384	+	599.384i	−0.877576	+	0.877576i	−0.993283	−	0.115708i	$-0.963086\pi$
$683$	−599.384	+	599.384i	−0.877576	+	0.877576i	0.115708	+	0.993283i	$0.463086\pi$
$684$		0			0
$685$	−169.820	+	684.677i	−0.247913	+	0.999529i
$686$	−654.336	−	1133.34i	−0.953842	−	1.65210i
$687$		0			0
$688$	27.6082	+	103.035i	0.0401282	+	0.149761i
$689$	362.466	+	209.270i	0.526075	+	0.303730i
$690$		0			0
$691$	−348.543	−	603.695i	−0.504404	−	0.873654i	−0.999987	−	0.00509303i	$-0.998379\pi$
$691$	−348.543	−	603.695i	−0.504404	−	0.873654i	0.495583	−	0.868561i	$-0.334955\pi$
$692$	−106.685	−	106.685i	−0.154169	−	0.154169i
$693$		0			0
$694$			21.7458i			0.0313340i
$695$	−1192.83	−	659.293i	−1.71631	−	0.948624i
$696$		0			0
$697$	506.696	−	135.769i	0.726967	−	0.194790i
$698$	−72.9231	−	272.153i	−0.104474	−	0.389904i
$699$		0			0
$700$	−752.507	+	810.932i	−1.07501	+	1.15847i
$701$	643.602			0.918119			0.459060	−	0.888405i	$-0.348186\pi$
$701$	643.602			0.918119			0.459060	+	0.888405i	$0.348186\pi$
$702$		0			0
$703$	−419.550	+	419.550i	−0.596800	+	0.596800i
$704$	12.1718	−	7.02736i	0.0172894	−	0.00998205i
$705$		0			0
$706$	−71.1500	+	123.235i	−0.100779	+	0.174554i
$707$	−395.563	+	105.991i	−0.559495	+	0.149916i
$708$		0			0
$709$	−1069.69	+	617.583i	−1.50872	+	0.871062i	−0.508775	+	0.860899i	$0.669902\pi$
$709$	−1069.69	+	617.583i	−1.50872	+	0.871062i	−0.999948	+	0.0101629i	$0.996765\pi$
$710$	−493.594	+	1990.06i	−0.695203	+	2.80290i
$711$		0			0
$712$	−1157.42	−	1157.42i	−1.62559	−	1.62559i
$713$	−17.2056	−	4.61022i	−0.0241312	−	0.00646594i
$714$		0			0
$715$	−90.5922	+	94.0408i	−0.126702	+	0.131526i
$716$	−1225.04	+	2121.83i	−1.71095	+	2.96345i
$717$		0			0
$718$	404.918	+	108.497i	0.563952	+	0.151110i
$719$			219.618i			0.305449i	0.988269	+	0.152724i	$0.0488047\pi$
$719$			219.618i			0.305449i	−0.988269	+	0.152724i	$0.951195\pi$
$720$		0			0
$721$	−248.283			−0.344360
$722$	−628.340	+	2345.00i	−0.870278	+	3.24792i
$723$		0			0
$724$	2022.41	+	1167.64i	2.79338	+	1.61276i
$725$	736.604	−	462.789i	1.01601	−	0.638330i
$726$		0			0
$727$	73.8261	−	275.523i	0.101549	−	0.378986i	−0.896382	−	0.443283i	$-0.853814\pi$
$727$	73.8261	−	275.523i	0.101549	−	0.378986i	0.997931	+	0.0642969i	$0.0204805\pi$
$728$	−588.400	+	588.400i	−0.808242	+	0.808242i
$729$		0			0
$730$	−246.628	−	409.324i	−0.337847	−	0.560718i
$731$	−24.7525	−	42.8726i	−0.0338611	−	0.0586492i
$732$		0			0
$733$	−181.709	−	678.149i	−0.247898	−	0.925169i	−0.971905	−	0.235375i	$-0.924368\pi$
$733$	−181.709	−	678.149i	−0.247898	−	0.925169i	0.724006	−	0.689793i	$-0.242299\pi$
$734$	−1353.09	−	781.206i	−1.84345	−	1.06431i
$735$		0			0
$736$	−10.2898	−	17.8224i	−0.0139807	−	0.0242153i
$737$	90.7608	+	90.7608i	0.123149	+	0.123149i
$738$		0			0
$739$			1147.21i			1.55238i	0.630497	+	0.776192i	$0.282851\pi$
$739$			1147.21i			1.55238i	−0.630497	+	0.776192i	$0.717149\pi$
$740$	−227.686	−	790.387i	−0.307684	−	1.06809i
$741$		0			0
$742$	−760.284	+	203.717i	−1.02464	+	0.274552i
$743$	−226.953	−	847.001i	−0.305455	−	1.13997i	−0.932553	−	0.361034i	$-0.882424\pi$
$743$	−226.953	−	847.001i	−0.305455	−	1.13997i	0.627098	−	0.778941i	$-0.284243\pi$
$744$		0			0
$745$	879.246	+	485.970i	1.18020	+	0.652308i
$746$	−2325.68			−3.11754
$747$		0			0
$748$	225.628	−	225.628i	0.301642	−	0.301642i
$749$	348.958	−	201.471i	0.465899	−	0.268987i
$750$		0			0
$751$	147.537	−	255.542i	0.196455	−	0.340269i	−0.750922	−	0.660391i	$-0.770391\pi$
$751$	147.537	−	255.542i	0.196455	−	0.340269i	0.947376	+	0.320122i	$0.103724\pi$
$752$	−103.637	+	27.7694i	−0.137815	+	0.0369274i
$753$		0			0
$754$	1026.88	−	592.872i	1.36192	−	0.786303i
$755$	−302.715	−	502.410i	−0.400947	−	0.665444i
$756$		0			0
$757$	89.6510	+	89.6510i	0.118429	+	0.118429i	0.763838	−	0.645408i	$-0.223313\pi$
$757$	89.6510	+	89.6510i	0.118429	+	0.118429i	−0.645408	+	0.763838i	$0.723313\pi$
$758$	−1034.28	−	277.135i	−1.36449	−	0.365614i
$759$		0			0
$760$	−2052.57	−	1977.30i	−2.70075	−	2.60171i
$761$	−80.6635	+	139.713i	−0.105997	+	0.183592i	−0.914145	−	0.405387i	$-0.867137\pi$
$761$	−80.6635	+	139.713i	−0.105997	+	0.183592i	0.808148	+	0.588979i	$0.200470\pi$
$762$		0			0
$763$	−698.501	−	187.163i	−0.915466	−	0.245298i
$764$		−	1602.86i		−	2.09798i
$765$		0			0
$766$	1542.52			2.01373
$767$	−104.416	+	389.686i	−0.136136	+	0.508065i
$768$		0			0
$769$	−129.486	−	74.7588i	−0.168382	−	0.0972156i	0.413440	−	0.910531i	$-0.364327\pi$
$769$	−129.486	−	74.7588i	−0.168382	−	0.0972156i	−0.581823	+	0.813316i	$0.697660\pi$
$770$	−4.58589	−	245.522i	−0.00595570	−	0.318859i
$771$		0			0
$772$	62.0835	−	231.699i	0.0804190	−	0.300128i
$773$	994.453	−	994.453i	1.28649	−	1.28649i	0.349578	−	0.936907i	$-0.386325\pi$
$773$	994.453	−	994.453i	1.28649	−	1.28649i	0.936907	−	0.349578i	$-0.113675\pi$
$774$		0			0
$775$	300.204	−	567.949i	0.387361	−	0.732837i
$776$	−1392.55	−	2411.96i	−1.79452	−	3.10819i
$777$		0			0
$778$	−212.399	−	792.684i	−0.273006	−	1.01887i
$779$	1127.06	+	650.711i	1.44681	+	0.835316i
$780$		0			0
$781$	−157.137	−	272.169i	−0.201200	−	0.348488i
$782$	22.8655	+	22.8655i	0.0292398	+	0.0292398i
$783$		0			0
$784$			682.690i			0.870778i
$785$	1019.98	−	293.824i	1.29934	−	0.374298i
$786$		0			0
$787$	−887.757	+	237.874i	−1.12803	+	0.302254i	−0.774128	−	0.633030i	$-0.781811\pi$
$787$	−887.757	+	237.874i	−1.12803	+	0.302254i	−0.353899	+	0.935284i	$0.615144\pi$
$788$	387.409	+	1445.83i	0.491635	+	1.83481i
$789$		0			0
$790$	−105.179	−	365.118i	−0.133138	−	0.462174i
$791$	−268.801			−0.339824
$792$		0			0
$793$	88.0662	−	88.0662i	0.111055	−	0.111055i
$794$	530.725	−	306.414i	0.668420	−	0.385912i
$795$		0			0
$796$	−106.714	+	184.834i	−0.134063	+	0.232204i
$797$	−860.450	+	230.557i	−1.07961	+	0.289281i	−0.754437	−	0.656373i	$-0.772090\pi$
$797$	−860.450	+	230.557i	−1.07961	+	0.289281i	−0.325175	+	0.945654i	$0.605423\pi$
$798$		0			0
$799$	43.1229	−	24.8970i	0.0539711	−	0.0311602i
$800$	709.239	−	218.734i	0.886549	−	0.273417i
$801$		0			0
$802$	1152.46	+	1152.46i	1.43698	+	1.43698i
$803$	70.7526	+	18.9581i	0.0881104	+	0.0236091i
$804$		0			0
$805$	17.1814	−	0.320916i	0.0213433	−	0.000398654i
$806$	437.818	−	758.323i	0.543198	−	0.940847i
$807$		0			0
$808$	1412.70	+	378.532i	1.74839	+	0.468480i
$809$			1398.60i			1.72880i	0.502802	+	0.864402i	$0.332302\pi$
$809$			1398.60i			1.72880i	−0.502802	+	0.864402i	$0.667698\pi$
$810$		0			0
$811$	−347.451			−0.428423			−0.214211	−	0.976787i	$-0.568718\pi$
$811$	−347.451			−0.428423			−0.214211	+	0.976787i	$0.568718\pi$
$812$	−398.533	+	1487.34i	−0.490804	+	1.83170i
$813$		0			0
$814$	158.117	+	91.2888i	0.194247	+	0.112148i
$815$	−300.009	+	311.430i	−0.368109	+	0.382122i
$816$		0			0
$817$	31.7877	−	118.633i	0.0389079	−	0.145206i
$818$	1253.90	−	1253.90i	1.53288	−	1.53288i
$819$		0			0
$820$	−1545.31	+	931.090i	−1.88453	+	1.13548i
$821$	493.294	+	854.410i	0.600845	+	1.04069i	0.992693	+	0.120665i	$0.0385026\pi$
$821$	493.294	+	854.410i	0.600845	+	1.04069i	−0.391848	+	0.920030i	$0.628164\pi$
$822$		0			0
$823$	65.3381	+	243.845i	0.0793902	+	0.296288i	0.994193	−	0.107613i	$-0.0343207\pi$
$823$	65.3381	+	243.845i	0.0793902	+	0.296288i	−0.914803	+	0.403901i	$0.867654\pi$
$824$	767.914	+	443.356i	0.931935	+	0.538053i
$825$		0			0
$826$	−379.347	−	657.049i	−0.459258	−	0.795458i
$827$	−1054.44	−	1054.44i	−1.27502	−	1.27502i	−0.943419	−	0.331604i	$-0.892410\pi$
$827$	−1054.44	−	1054.44i	−1.27502	−	1.27502i	−0.331604	−	0.943419i	$-0.607590\pi$
$828$		0			0
$829$		−	819.644i		−	0.988714i	−0.869259	−	0.494357i	$-0.835404\pi$
$829$		−	819.644i		−	0.988714i	0.869259	−	0.494357i	$-0.164596\pi$
$830$	−132.955	+	240.550i	−0.160186	+	0.289819i
$831$		0			0
$832$	−46.7017	+	12.5137i	−0.0561318	+	0.0150405i
$833$	−82.0024	−	306.037i	−0.0984423	−	0.367392i
$834$		0			0
$835$	1168.64	−	336.649i	1.39957	−	0.403173i
$836$	791.631			0.946928
$837$		0			0
$838$	66.9173	−	66.9173i	0.0798536	−	0.0798536i
$839$	−425.345	+	245.573i	−0.506966	+	0.292697i	−0.731586	−	0.681749i	$-0.761219\pi$
$839$	−425.345	+	245.573i	−0.506966	+	0.292697i	0.224619	+	0.974447i	$0.427886\pi$
$840$		0			0
$841$	184.907	−	320.269i	0.219866	−	0.380819i
$842$	1690.62	−	453.001i	2.00786	−	0.538006i
$843$		0			0
$844$	−1052.88	+	607.880i	−1.24749	+	0.720237i
$845$	−339.020	+	204.268i	−0.401207	+	0.241738i
$846$		0			0
$847$	−397.594	−	397.594i	−0.469415	−	0.469415i
$848$	1192.51	+	319.533i	1.40627	+	0.376808i
$849$		0			0
$850$	−987.500	+	620.421i	−1.16176	+	0.729907i
$851$	−6.38831	+	11.0649i	−0.00750682	+	0.0130022i
$852$		0			0
$853$	336.484	+	90.1607i	0.394472	+	0.105698i	0.450602	−	0.892725i	$-0.351209\pi$
$853$	336.484	+	90.1607i	0.394472	+	0.105698i	−0.0561301	+	0.998423i	$0.517876\pi$
$854$			234.218i			0.274260i
$855$		0			0
$856$	−1439.05			−1.68114
$857$	−210.885	+	787.034i	−0.246074	+	0.918359i	0.726767	+	0.686884i	$0.241022\pi$
$857$	−210.885	+	787.034i	−0.246074	+	0.918359i	−0.972841	+	0.231475i	$0.925645\pi$
$858$		0			0
$859$	101.706	+	58.7201i	0.118401	+	0.0683587i	0.558031	−	0.829820i	$-0.311557\pi$
$859$	101.706	+	58.7201i	0.118401	+	0.0683587i	−0.439630	+	0.898179i	$0.644890\pi$
$860$	122.620	+	118.123i	0.142581	+	0.137353i
$861$		0			0
$862$	−68.1886	+	254.483i	−0.0791051	+	0.295224i
$863$	148.570	−	148.570i	0.172155	−	0.172155i	−0.615770	−	0.787926i	$-0.711155\pi$
$863$	148.570	−	148.570i	0.172155	−	0.172155i	0.787926	+	0.615770i	$0.211155\pi$
$864$		0			0
$865$	−82.0360	−	20.3474i	−0.0948394	−	0.0235230i
$866$	−202.797	−	351.254i	−0.234176	−	0.405605i
$867$		0			0
$868$	294.304	+	1098.36i	0.339060	+	1.26539i
$869$	50.4374	+	29.1200i	0.0580407	+	0.0335098i
$870$		0			0
$871$	−220.775	−	382.393i	−0.253473	−	0.439028i
$872$	1826.18	+	1826.18i	2.09424	+	2.09424i
$873$		0			0
$874$			80.2251i			0.0917907i
$875$	−126.630	+	606.680i	−0.144720	+	0.693349i
$876$		0			0
$877$	480.790	−	128.827i	0.548221	−	0.146895i	0.0259318	−	0.999664i	$-0.491745\pi$
$877$	480.790	−	128.827i	0.548221	−	0.146895i	0.522289	+	0.852768i	$0.325078\pi$
$878$	104.690	+	390.709i	0.119237	+	0.444998i
$879$		0			0
$880$	−186.322	+	337.106i	−0.211730	+	0.383075i
$881$	−306.447			−0.347840			−0.173920	−	0.984760i	$-0.555643\pi$
$881$	−306.447			−0.347840			−0.173920	+	0.984760i	$0.555643\pi$
$882$		0			0
$883$	930.058	−	930.058i	1.05329	−	1.05329i	0.0547963	−	0.998498i	$-0.482549\pi$
$883$	930.058	−	930.058i	1.05329	−	1.05329i	0.998498	−	0.0547963i	$-0.0174509\pi$
$884$	−950.617	+	548.839i	−1.07536	+	0.620859i
$885$		0			0
$886$	286.676	−	496.538i	0.323563	−	0.560427i
$887$	130.986	−	35.0975i	0.147673	−	0.0395688i	−0.184225	−	0.982884i	$-0.558978\pi$
$887$	130.986	−	35.0975i	0.147673	−	0.0395688i	0.331898	+	0.943315i	$0.392311\pi$
$888$		0			0
$889$	306.078	−	176.714i	0.344295	−	0.198779i
$890$	−1612.83	−	400.029i	−1.81216	−	0.449471i
$891$		0			0
$892$	2532.24	+	2532.24i	2.83884	+	2.83884i
$893$	119.326	+	31.9733i	0.133624	+	0.0358044i
$894$		0			0
$895$	25.6324	+	1372.32i	0.0286395	+	1.53332i
$896$	339.852	−	588.641i	0.379299	−	0.656965i
$897$		0			0
$898$	−1013.34	−	271.524i	−1.12844	−	0.302366i
$899$		−	894.149i		−	0.994604i
$900$		0			0
$901$	−572.962			−0.635918
$902$	103.649	−	386.822i	0.114910	−	0.428849i
$903$		0			0
$904$	831.374	+	479.994i	0.919661	+	0.530967i
$905$	1308.02	−	24.4313i	1.44532	−	0.0269959i
$906$		0			0
$907$	35.1572	−	131.208i	0.0387621	−	0.144662i	−0.943833	−	0.330423i	$-0.892808\pi$
$907$	35.1572	−	131.208i	0.0387621	−	0.144662i	0.982595	+	0.185761i	$0.0594751\pi$
$908$	1194.65	−	1194.65i	1.31569	−	1.31569i
$909$		0			0
$910$	−203.363	+	819.914i	−0.223476	+	0.901004i
$911$	−545.263	−	944.423i	−0.598532	−	1.03669i	−0.993038	−	0.117795i	$-0.962417\pi$
$911$	−545.263	−	944.423i	−0.598532	−	1.03669i	0.394506	−	0.918894i	$-0.370916\pi$
$912$		0			0
$913$	−10.9035	−	40.6924i	−0.0119425	−	0.0445700i
$914$	−1459.39	−	842.579i	−1.59671	−	0.921859i
$915$		0			0
$916$	660.594	+	1144.18i	0.721173	+	1.24911i
$917$	−628.907	−	628.907i	−0.685831	−	0.685831i
$918$		0			0
$919$		−	367.996i		−	0.400431i	−0.979752	−	0.200215i	$-0.935836\pi$
$919$		−	367.996i		−	0.400431i	0.979752	−	0.200215i	$-0.0641642\pi$
$920$	−53.7133	−	29.6880i	−0.0583840	−	0.0322695i
$921$		0			0
$922$	1727.79	−	462.959i	1.87396	−	0.502125i
$923$	279.815	+	1044.28i	0.303158	+	1.13140i
$924$		0			0
$925$	−337.767	−	313.432i	−0.365153	−	0.338845i
$926$	3276.11			3.53792
$927$		0			0
$928$	730.476	−	730.476i	0.787151	−	0.787151i
$929$	−62.7337	+	36.2193i	−0.0675282	+	0.0389874i	−0.533384	−	0.845873i	$-0.679080\pi$
$929$	−62.7337	+	36.2193i	−0.0675282	+	0.0389874i	0.465856	+	0.884861i	$0.345747\pi$
$930$		0			0
$931$	393.020	−	680.731i	0.422148	−	0.731182i
$932$	2339.28	−	626.810i	2.50996	−	0.672542i
$933$		0			0
$934$	902.137	−	520.849i	0.965886	−	0.557655i
$935$	43.0328	−	173.499i	0.0460244	−	0.185560i
$936$		0			0
$937$	−887.903	−	887.903i	−0.947602	−	0.947602i	0.0510921	−	0.998694i	$-0.483730\pi$
$937$	−887.903	−	887.903i	−0.947602	−	0.947602i	−0.998694	+	0.0510921i	$0.983730\pi$
$938$	802.082	+	214.917i	0.855099	+	0.229123i
$939$		0			0
$940$	−118.813	+	123.336i	−0.126397	+	0.131208i
$941$	−190.349	+	329.694i	−0.202284	+	0.350366i	−0.949264	−	0.314480i	$-0.898170\pi$
$941$	−190.349	+	329.694i	−0.202284	+	0.350366i	0.746980	+	0.664846i	$0.231503\pi$
$942$		0			0
$943$	27.0694	+	7.25323i	0.0287056	+	0.00769165i
$944$			1190.02i			1.26061i
$945$		0			0
$946$	−37.7930			−0.0399504
$947$	139.605	−	521.012i	0.147418	−	0.550172i	−0.852218	−	0.523187i	$-0.824743\pi$
$947$	139.605	−	521.012i	0.147418	−	0.550172i	0.999636	−	0.0269844i	$-0.00859046\pi$
$948$		0			0
$949$	−218.221	−	125.990i	−0.229948	−	0.132761i
$950$	−2820.75	−	643.959i	−2.96921	−	0.677852i
$951$		0			0
$952$	294.831	−	1100.33i	0.309697	−	1.15580i
$953$	52.0743	−	52.0743i	0.0546425	−	0.0546425i	−0.679258	−	0.733900i	$-0.737698\pi$
$953$	52.0743	−	52.0743i	0.0546425	−	0.0546425i	0.733900	+	0.679258i	$0.237698\pi$
$954$		0			0
$955$	−463.413	−	769.118i	−0.485250	−	0.805359i
$956$	−585.940	−	1014.88i	−0.612908	−	1.06159i
$957$		0			0
$958$	−190.265	−	710.080i	−0.198607	−	0.741210i
$959$	−605.788	−	349.752i	−0.631687	−	0.364705i
$960$		0			0
$961$	150.349	+	260.413i	0.156451	+	0.270981i
$962$	−444.118	−	444.118i	−0.461662	−	0.461662i
$963$		0			0
$964$		−	1906.20i		−	1.97739i
$965$	−37.1977	−	129.128i	−0.0385469	−	0.133811i
$966$		0			0
$967$	278.265	−	74.5608i	0.287761	−	0.0771053i	−0.112051	−	0.993702i	$-0.535742\pi$
$967$	278.265	−	74.5608i	0.287761	−	0.0771053i	0.399812	+	0.916597i	$0.369075\pi$
$968$	519.740	+	1939.70i	0.536921	+	2.00382i
$969$		0			0
$970$	−2474.55	−	1367.72i	−2.55109	−	1.41002i
$971$	227.938			0.234745			0.117373	−	0.993088i	$-0.462553\pi$
$971$	227.938			0.234745			0.117373	+	0.993088i	$0.462553\pi$
$972$		0			0
$973$	955.634	−	955.634i	0.982152	−	0.982152i
$974$	−2230.86	+	1287.99i	−2.29041	+	1.32237i
$975$		0			0
$976$	183.687	−	318.155i	0.188203	−	0.325978i
$977$	−613.083	+	164.275i	−0.627516	+	0.168142i	−0.558542	−	0.829476i	$-0.688639\pi$
$977$	−613.083	+	164.275i	−0.627516	+	0.168142i	−0.0689735	+	0.997618i	$0.521972\pi$
$978$		0			0
$979$	220.577	−	127.350i	0.225308	−	0.130082i
$980$	562.365	+	933.345i	0.573842	+	0.952393i
$981$		0			0
$982$	−531.988	−	531.988i	−0.541739	−	0.541739i
$983$	1316.59	+	352.779i	1.33936	+	0.358880i	0.856196	−	0.516651i	$-0.172821\pi$
$983$	1316.59	+	352.779i	1.33936	+	0.358880i	0.483163	+	0.875531i	$0.339488\pi$
$984$		0			0
$985$	603.908	+	581.761i	0.613104	+	0.590621i
$986$	−811.616	+	1405.76i	−0.823140	+	1.42572i
$987$		0			0
$988$	−2630.47	−	704.832i	−2.66242	−	0.713393i
$989$		−	2.64472i		−	0.00267414i
$990$		0			0
$991$	1111.32			1.12141			0.560705	−	0.828016i	$-0.310530\pi$
$991$	1111.32			1.12141			0.560705	+	0.828016i	$0.310530\pi$
$992$	197.447	−	736.881i	0.199039	−	0.742823i
$993$		0			0
$994$	−1760.76	−	1016.58i	−1.77139	−	1.02271i
$995$	2.23286	+	119.544i	0.00224408	+	0.120145i
$996$		0			0
$997$	−164.802	+	615.048i	−0.165297	+	0.616898i	0.832705	+	0.553717i	$0.186791\pi$
$997$	−164.802	+	615.048i	−0.165297	+	0.616898i	−0.998002	+	0.0631810i	$0.979875\pi$
$998$	−842.493	+	842.493i	−0.844182	+	0.844182i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.l.a.37.10		40
3.2	odd	2		45.3.k.a.22.1	yes	40
5.3	odd	4	inner	135.3.l.a.118.1		40
9.2	odd	6		45.3.k.a.7.10	✓	40
9.4	even	3		405.3.g.g.82.10		20
9.5	odd	6		405.3.g.h.82.1		20
9.7	even	3	inner	135.3.l.a.127.1		40
15.2	even	4		225.3.o.b.193.1		40
15.8	even	4		45.3.k.a.13.10	yes	40
15.14	odd	2		225.3.o.b.157.10		40
45.2	even	12		225.3.o.b.43.10		40
45.13	odd	12		405.3.g.g.163.10		20
45.23	even	12		405.3.g.h.163.1		20
45.29	odd	6		225.3.o.b.7.1		40
45.38	even	12		45.3.k.a.43.1	yes	40
45.43	odd	12	inner	135.3.l.a.73.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.10	✓	40	9.2	odd	6
45.3.k.a.13.10	yes	40	15.8	even	4
45.3.k.a.22.1	yes	40	3.2	odd	2
45.3.k.a.43.1	yes	40	45.38	even	12
135.3.l.a.37.10		40	1.1	even	1	trivial
135.3.l.a.73.10		40	45.43	odd	12	inner
135.3.l.a.118.1		40	5.3	odd	4	inner
135.3.l.a.127.1		40	9.7	even	3	inner
225.3.o.b.7.1		40	45.29	odd	6
225.3.o.b.43.10		40	45.2	even	12
225.3.o.b.157.10		40	15.14	odd	2
225.3.o.b.193.1		40	15.2	even	4
405.3.g.g.82.10		20	9.4	even	3
405.3.g.g.163.10		20	45.13	odd	12
405.3.g.h.82.1		20	9.5	odd	6
405.3.g.h.163.1		20	45.23	even	12

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.930497 - 3.47266i) q^{2} +(-7.72947 - 4.46261i) q^{4} +(-4.99913 + 0.0933744i) q^{5} +(1.28323 - 4.78910i) q^{7} +(-12.5207 + 12.5207i) q^{8} +(-4.32742 + 17.4472i) q^{10} +(-1.37764 - 2.38615i) q^{11} +(2.45318 + 9.15539i) q^{13} +(-15.4369 - 8.91249i) q^{14} +(13.9793 + 24.2129i) q^{16} +(-9.17504 - 9.17504i) q^{17} -32.1912i q^{19} +(39.0573 + 21.5874i) q^{20} +(-9.56819 + 2.56379i) q^{22} +(-0.179412 - 0.669573i) q^{23} +(24.9826 - 0.933581i) q^{25} +34.0763 q^{26} +(-31.2906 + 31.2906i) q^{28} +(30.1349 - 17.3984i) q^{29} +(12.8482 - 22.2537i) q^{31} +(28.6765 - 7.68384i) q^{32} +(-40.3992 + 23.3245i) q^{34} +(-5.96788 + 24.0611i) q^{35} +(-13.0331 - 13.0331i) q^{37} +(-111.789 - 29.9538i) q^{38} +(61.4236 - 63.7618i) q^{40} +(-20.2139 + 35.0116i) q^{41} +(3.68527 + 0.987466i) q^{43} +24.5915i q^{44} -2.49214 q^{46} +(-0.993231 + 3.70679i) q^{47} +(21.1465 + 12.2089i) q^{49} +(20.0042 - 87.6247i) q^{50} +(21.8952 - 81.7139i) q^{52} +(31.2240 - 31.2240i) q^{53} +(7.10982 + 11.8000i) q^{55} +(43.8959 + 76.0300i) q^{56} +(-32.3783 - 120.837i) q^{58} +(36.8611 + 21.2818i) q^{59} +(-6.56994 - 11.3795i) q^{61} +(-65.3243 - 65.3243i) q^{62} +5.10100i q^{64} +(-13.1186 - 45.5399i) q^{65} +(-44.9977 + 12.0571i) q^{67} +(29.9735 + 111.863i) q^{68} +(78.0031 + 43.1133i) q^{70} +114.062 q^{71} +(-18.7982 + 18.7982i) q^{73} +(-57.3867 + 33.1322i) q^{74} +(-143.657 + 248.821i) q^{76} +(-13.1953 + 3.53568i) q^{77} +(-18.3057 + 10.5688i) q^{79} +(-72.1453 - 119.738i) q^{80} +(102.774 + 102.774i) q^{82} +(14.7688 + 3.95730i) q^{83} +(46.7239 + 45.0105i) q^{85} +(6.85828 - 11.8789i) q^{86} +(47.1254 + 12.6272i) q^{88} +92.4405i q^{89} +46.9941 q^{91} +(-1.60129 + 5.97609i) q^{92} +(11.9482 + 6.89832i) q^{94} +(3.00583 + 160.928i) q^{95} +(-40.7091 + 151.928i) q^{97} +(62.0742 - 62.0742i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) \) 40 * q + 2 * q^2 + 2 * q^5 - 2 * q^7 + 24 * q^8 - 8 * q^10 - 8 * q^11 - 2 * q^13 + 28 * q^16 - 28 * q^17 + 114 * q^20 + 14 * q^22 - 82 * q^23 - 8 * q^25 + 112 * q^26 - 88 * q^28 - 4 * q^31 + 14 * q^32 - 352 * q^35 - 92 * q^37 - 330 * q^38 + 30 * q^40 + 28 * q^41 - 2 * q^43 - 136 * q^46 - 64 * q^47 + 458 * q^50 - 74 * q^52 + 608 * q^53 + 224 * q^55 + 192 * q^56 + 30 * q^58 + 92 * q^61 + 100 * q^62 + 326 * q^65 - 80 * q^67 - 626 * q^68 - 102 * q^70 - 248 * q^71 - 8 * q^73 - 96 * q^76 - 338 * q^77 - 1444 * q^80 + 104 * q^82 - 370 * q^83 - 98 * q^85 + 328 * q^86 - 210 * q^88 + 152 * q^91 - 388 * q^92 + 360 * q^95 + 292 * q^97 + 1876 * q^98

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