LMFDB - Embedded newform 575.2.k.g.26.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.8
Character	$\chi$	$=$	575.26
Dual form			575.2.k.g.376.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.179828 + 1.25073i) q^{2} +(0.104253 - 0.228282i) q^{3} +(0.387001 - 0.113634i) q^{4} +(0.304267 + 0.0893407i) q^{6} +(-0.933848 + 0.600148i) q^{7} +(1.26155 + 2.76240i) q^{8} +(1.92334 + 2.21965i) q^{9} +O(q^{10})$	\(q+(0.179828 + 1.25073i) q^{2} +(0.104253 - 0.228282i) q^{3} +(0.387001 - 0.113634i) q^{4} +(0.304267 + 0.0893407i) q^{6} +(-0.933848 + 0.600148i) q^{7} +(1.26155 + 2.76240i) q^{8} +(1.92334 + 2.21965i) q^{9} +(0.315580 - 2.19491i) q^{11} +(0.0144054 - 0.100192i) q^{12} +(1.22342 + 0.786244i) q^{13} +(-0.918554 - 1.06007i) q^{14} +(-2.54954 + 1.63849i) q^{16} +(-1.45125 - 0.426125i) q^{17} +(-2.43031 + 2.80473i) q^{18} +(4.41642 - 1.29678i) q^{19} +(0.0396466 + 0.275748i) q^{21} +2.80198 q^{22} +(-1.62947 + 4.51052i) q^{23} +0.762127 q^{24} +(-0.763374 + 1.67156i) q^{26} +(1.42961 - 0.419770i) q^{27} +(-0.293203 + 0.338374i) q^{28} +(-2.74520 - 0.806064i) q^{29} +(2.13071 + 4.66561i) q^{31} +(1.46963 + 1.69604i) q^{32} +(-0.468158 - 0.300867i) q^{33} +(0.271992 - 1.89175i) q^{34} +(0.996560 + 0.640450i) q^{36} +(3.05761 + 3.52867i) q^{37} +(2.41611 + 5.29054i) q^{38} +(0.307031 - 0.197317i) q^{39} +(6.27418 - 7.24079i) q^{41} +(-0.337757 + 0.0991743i) q^{42} +(-1.45618 + 3.18859i) q^{43} +(-0.127286 - 0.885290i) q^{44} +(-5.93447 - 1.22691i) q^{46} -6.68542 q^{47} +(0.108241 + 0.752831i) q^{48} +(-2.39601 + 5.24653i) q^{49} +(-0.248574 + 0.286869i) q^{51} +(0.562808 + 0.165255i) q^{52} +(10.0208 - 6.43995i) q^{53} +(0.782101 + 1.71256i) q^{54} +(-2.83594 - 1.82255i) q^{56} +(0.164393 - 1.14338i) q^{57} +(0.514505 - 3.57846i) q^{58} +(-10.6462 - 6.84187i) q^{59} +(-1.55135 - 3.39697i) q^{61} +(-5.45225 + 3.50395i) q^{62} +(-3.12822 - 0.918530i) q^{63} +(-5.82630 + 6.72391i) q^{64} +(0.292115 - 0.639643i) q^{66} +(-2.02315 - 14.0713i) q^{67} -0.610056 q^{68} +(0.859794 + 0.842215i) q^{69} +(0.307965 + 2.14194i) q^{71} +(-3.70519 + 8.11323i) q^{72} +(-4.25266 + 1.24869i) q^{73} +(-3.86356 + 4.45879i) q^{74} +(1.56180 - 1.00371i) q^{76} +(1.02256 + 2.23910i) q^{77} +(0.302002 + 0.348529i) q^{78} +(-0.581406 - 0.373647i) q^{79} +(-1.20073 + 8.35126i) q^{81} +(10.1845 + 6.54520i) q^{82} +(-7.60116 - 8.77221i) q^{83} +(0.0466775 + 0.102209i) q^{84} +(-4.24992 - 1.24789i) q^{86} +(-0.470206 + 0.542646i) q^{87} +(6.46134 - 1.89722i) q^{88} +(2.67790 - 5.86378i) q^{89} -1.61435 q^{91} +(-0.118060 + 1.93074i) q^{92} +1.28721 q^{93} +(-1.20222 - 8.36165i) q^{94} +(0.540389 - 0.158672i) q^{96} +(8.78742 - 10.1412i) q^{97} +(-6.99286 - 2.05329i) q^{98} +(5.47889 - 3.52107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$

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 $

$2$	0.179828	+	1.25073i	0.127157	+	0.884399i	0.949133	+	0.314876i	$0.101963\pi$
$2$	0.179828	+	1.25073i	0.127157	+	0.884399i	−0.821975	+	0.569523i	$0.807128\pi$
$3$	0.104253	−	0.228282i	0.0601905	−	0.131799i	−0.877147	−	0.480223i	$-0.840556\pi$
$3$	0.104253	−	0.228282i	0.0601905	−	0.131799i	0.937337	+	0.348424i	$0.113283\pi$
$4$	0.387001	−	0.113634i	0.193500	−	0.0568168i
$5$		0			0
$5$		0			0
$6$	0.304267	+	0.0893407i	0.124216	+	0.0364732i
$7$	−0.933848	+	0.600148i	−0.352961	+	0.226835i	−0.705091	−	0.709117i	$-0.749094\pi$
$7$	−0.933848	+	0.600148i	−0.352961	+	0.226835i	0.352130	+	0.935951i	$0.385458\pi$
$8$	1.26155	+	2.76240i	0.446024	+	0.976657i
$9$	1.92334	+	2.21965i	0.641113	+	0.739884i
$10$		0			0
$11$	0.315580	−	2.19491i	0.0951509	−	0.661789i	−0.885299	−	0.465022i	$-0.846047\pi$
$11$	0.315580	−	2.19491i	0.0951509	−	0.661789i	0.980450	−	0.196767i	$-0.0630444\pi$
$12$	0.0144054	−	0.100192i	0.00415849	−	0.0289229i
$13$	1.22342	+	0.786244i	0.339316	+	0.218065i	0.699190	−	0.714936i	$-0.253544\pi$
$13$	1.22342	+	0.786244i	0.339316	+	0.218065i	−0.359874	+	0.933001i	$0.617180\pi$
$14$	−0.918554	−	1.06007i	−0.245494	−	0.283315i
$15$		0			0
$16$	−2.54954	+	1.63849i	−0.637384	+	0.409622i
$17$	−1.45125	−	0.426125i	−0.351979	−	0.103350i	0.100963	−	0.994890i	$-0.467808\pi$
$17$	−1.45125	−	0.426125i	−0.351979	−	0.103350i	−0.452943	+	0.891540i	$0.649626\pi$
$18$	−2.43031	+	2.80473i	−0.572830	+	0.661081i
$19$	4.41642	−	1.29678i	1.01320	−	0.297501i	0.267335	−	0.963604i	$-0.413857\pi$
$19$	4.41642	−	1.29678i	1.01320	−	0.297501i	0.745860	+	0.666103i	$0.232039\pi$
$20$		0			0
$21$	0.0396466	+	0.275748i	0.00865159	+	0.0601731i
$22$	2.80198			0.597385
$23$	−1.62947	+	4.51052i	−0.339769	+	0.940509i
$23$	−1.62947	+	4.51052i	−0.339769	+	0.940509i
$24$	0.762127			0.155569
$25$		0			0
$26$	−0.763374	+	1.67156i	−0.149710	+	0.327819i
$27$	1.42961	−	0.419770i	0.275128	−	0.0807848i
$28$	−0.293203	+	0.338374i	−0.0554101	+	0.0639467i
$29$	−2.74520	−	0.806064i	−0.509771	−	0.149682i	0.0167243	−	0.999860i	$-0.494676\pi$
$29$	−2.74520	−	0.806064i	−0.509771	−	0.149682i	−0.526496	+	0.850178i	$0.676494\pi$
$30$		0			0
$31$	2.13071	+	4.66561i	0.382687	+	0.837968i	0.998736	+	0.0502603i	$0.0160051\pi$
$31$	2.13071	+	4.66561i	0.382687	+	0.837968i	−0.616049	+	0.787708i	$0.711268\pi$
$32$	1.46963	+	1.69604i	0.259796	+	0.299820i
$33$	−0.468158	−	0.300867i	−0.0814958	−	0.0523742i
$34$	0.271992	−	1.89175i	0.0466463	−	0.324432i
$35$		0			0
$36$	0.996560	+	0.640450i	0.166093	+	0.106742i
$37$	3.05761	+	3.52867i	0.502668	+	0.580109i	0.949206	−	0.314655i	$-0.101889\pi$
$37$	3.05761	+	3.52867i	0.502668	+	0.580109i	−0.446539	+	0.894764i	$0.647343\pi$
$38$	2.41611	+	5.29054i	0.391945	+	0.858239i
$39$	0.307031	−	0.197317i	0.0491642	−	0.0315959i
$40$		0			0
$41$	6.27418	−	7.24079i	0.979862	−	1.13082i	−0.0115349	−	0.999933i	$-0.503672\pi$
$41$	6.27418	−	7.24079i	0.979862	−	1.13082i	0.991397	−	0.130888i	$-0.0417828\pi$
$42$	−0.337757	+	0.0991743i	−0.0521170	+	0.0153029i
$43$	−1.45618	+	3.18859i	−0.222065	+	0.486255i	−0.987571	−	0.157174i	$-0.949762\pi$
$43$	−1.45618	+	3.18859i	−0.222065	+	0.486255i	0.765506	+	0.643429i	$0.222489\pi$
$44$	−0.127286	−	0.885290i	−0.0191890	−	0.133463i
$45$		0			0
$46$	−5.93447	−	1.22691i	−0.874989	−	0.180899i
$47$	−6.68542			−0.975169			−0.487584	−	0.873076i	$-0.662122\pi$
$47$	−6.68542			−0.975169			−0.487584	+	0.873076i	$0.662122\pi$
$48$	0.108241	+	0.752831i	0.0156232	+	0.108662i
$49$	−2.39601	+	5.24653i	−0.342287	+	0.749504i
$50$		0			0
$51$	−0.248574	+	0.286869i	−0.0348073	+	0.0401697i
$52$	0.562808	+	0.165255i	0.0780474	+	0.0229168i
$53$	10.0208	−	6.43995i	1.37646	−	0.884595i	0.377317	−	0.926084i	$-0.376847\pi$
$53$	10.0208	−	6.43995i	1.37646	−	0.884595i	0.999139	+	0.0414895i	$0.0132103\pi$
$54$	0.782101	+	1.71256i	0.106431	+	0.233050i
$55$		0			0
$56$	−2.83594	−	1.82255i	−0.378969	−	0.243549i
$57$	0.164393	−	1.14338i	0.0217744	−	0.151445i
$58$	0.514505	−	3.57846i	0.0675578	−	0.469875i
$59$	−10.6462	−	6.84187i	−1.38601	−	0.890735i	−0.386509	−	0.922286i	$-0.626319\pi$
$59$	−10.6462	−	6.84187i	−1.38601	−	0.890735i	−0.999502	+	0.0315502i	$0.989956\pi$
$60$		0			0
$61$	−1.55135	−	3.39697i	−0.198629	−	0.434938i	0.783939	−	0.620837i	$-0.213207\pi$
$61$	−1.55135	−	3.39697i	−0.198629	−	0.434938i	−0.982569	+	0.185900i	$0.940480\pi$
$62$	−5.45225	+	3.50395i	−0.692437	+	0.445002i
$63$	−3.12822	−	0.918530i	−0.394119	−	0.115724i
$64$	−5.82630	+	6.72391i	−0.728288	+	0.840489i
$65$		0			0
$66$	0.292115	−	0.639643i	0.0359569	−	0.0787346i
$67$	−2.02315	−	14.0713i	−0.247167	−	1.71908i	−0.614434	−	0.788968i	$-0.710616\pi$
$67$	−2.02315	−	14.0713i	−0.247167	−	1.71908i	0.367268	−	0.930115i	$-0.380293\pi$
$68$	−0.610056			−0.0739801
$69$	0.859794	+	0.842215i	0.103507	+	0.101391i
$70$		0			0
$71$	0.307965	+	2.14194i	0.0365487	+	0.254202i	0.999901	−	0.0140357i	$-0.00446785\pi$
$71$	0.307965	+	2.14194i	0.0365487	+	0.254202i	−0.963353	+	0.268238i	$0.913559\pi$
$72$	−3.70519	+	8.11323i	−0.436661	+	0.956153i
$73$	−4.25266	+	1.24869i	−0.497736	+	0.146148i	−0.520959	−	0.853582i	$-0.674425\pi$
$73$	−4.25266	+	1.24869i	−0.497736	+	0.146148i	0.0232229	+	0.999730i	$0.492607\pi$
$74$	−3.86356	+	4.45879i	−0.449130	+	0.518324i
$75$		0			0
$76$	1.56180	−	1.00371i	0.179151	−	0.115133i
$77$	1.02256	+	2.23910i	0.116532	+	0.255170i
$78$	0.302002	+	0.348529i	0.0341950	+	0.0394632i
$79$	−0.581406	−	0.373647i	−0.0654133	−	0.0420386i	0.507525	−	0.861637i	$-0.330560\pi$
$79$	−0.581406	−	0.373647i	−0.0654133	−	0.0420386i	−0.572939	+	0.819598i	$0.694197\pi$
$80$		0			0
$81$	−1.20073	+	8.35126i	−0.133414	+	0.927917i
$82$	10.1845	+	6.54520i	1.12469	+	0.722797i
$83$	−7.60116	−	8.77221i	−0.834336	−	0.962875i	0.165391	−	0.986228i	$-0.447111\pi$
$83$	−7.60116	−	8.77221i	−0.834336	−	0.962875i	−0.999727	+	0.0233527i	$0.992566\pi$
$84$	0.0466775	+	0.102209i	0.00509293	+	0.0111520i
$85$		0			0
$86$	−4.24992	−	1.24789i	−0.458281	−	0.134563i
$87$	−0.470206	+	0.542646i	−0.0504113	+	0.0581778i
$88$	6.46134	−	1.89722i	0.688781	−	0.202244i
$89$	2.67790	−	5.86378i	0.283857	−	0.621559i	−0.712967	−	0.701197i	$-0.752649\pi$
$89$	2.67790	−	5.86378i	0.283857	−	0.621559i	0.996824	+	0.0796380i	$0.0253764\pi$
$90$		0			0
$91$	−1.61435			−0.169230
$92$	−0.118060	+	1.93074i	−0.0123086	+	0.201293i
$93$	1.28721			0.133477
$94$	−1.20222	−	8.36165i	−0.124000	−	0.862438i
$95$		0			0
$96$	0.540389	−	0.158672i	0.0551532	−	0.0161944i
$97$	8.78742	−	10.1412i	0.892227	−	1.02968i	−0.107145	−	0.994243i	$-0.534171\pi$
$97$	8.78742	−	10.1412i	0.892227	−	1.02968i	0.999372	−	0.0354415i	$-0.0112837\pi$
$98$	−6.99286	−	2.05329i	−0.706385	−	0.207413i
$99$	5.47889	−	3.52107i	0.550649	−	0.353881i
$100$		0			0
$101$	−4.50029	−	5.19361i	−0.447795	−	0.516783i	0.486308	−	0.873788i	$-0.338343\pi$
$101$	−4.50029	−	5.19361i	−0.447795	−	0.516783i	−0.934103	+	0.357005i	$0.883798\pi$
$102$	−0.403496	−	0.259311i	−0.0399521	−	0.0256756i
$103$	0.564925	−	3.92914i	0.0556638	−	0.387150i	−0.942877	−	0.333142i	$-0.891891\pi$
$103$	0.564925	−	3.92914i	0.0556638	−	0.387150i	0.998540	−	0.0540081i	$-0.0171997\pi$
$104$	−0.628522	+	4.37146i	−0.0616316	+	0.428657i
$105$		0			0
$106$	9.85664	+	11.3752i	0.957361	+	1.10485i
$107$	−4.52054	−	9.89861i	−0.437017	−	0.956935i	−0.992136	−	0.125164i	$-0.960054\pi$
$107$	−4.52054	−	9.89861i	−0.437017	−	0.956935i	0.555119	−	0.831771i	$-0.312673\pi$
$108$	0.505558	−	0.324903i	0.0486474	−	0.0312638i
$109$	8.34058	+	2.44902i	0.798883	+	0.234573i	0.655600	−	0.755109i	$-0.272416\pi$
$109$	8.34058	+	2.44902i	0.798883	+	0.234573i	0.143283	+	0.989682i	$0.454234\pi$
$110$		0			0
$111$	1.12430	−	0.330123i	0.106713	−	0.0313339i
$112$	1.39755	−	3.06020i	0.132056	−	0.289162i
$113$	0.422516	+	2.93866i	0.0397469	+	0.276446i	0.999996	−	0.00269741i	$-0.000858613\pi$
$113$	0.422516	+	2.93866i	0.0397469	+	0.276446i	−0.960249	+	0.279143i	$0.909950\pi$
$114$	1.45962			0.136706
$115$		0			0
$116$	−1.15399			−0.107145
$117$	0.607863	+	4.22778i	0.0561969	+	0.390858i
$118$	6.64285	−	14.5458i	0.611524	−	1.33905i
$119$	1.61098	−	0.473027i	0.147679	−	0.0433624i
$120$		0			0
$121$	5.83640	+	1.71372i	0.530582	+	0.155793i
$122$	3.96972	−	2.55118i	0.359401	−	0.230973i
$123$	−0.998841	−	2.18716i	−0.0900624	−	0.197209i
$124$	1.35476	+	1.56347i	0.121661	+	0.140404i
$125$		0			0
$126$	0.586290	−	4.07774i	0.0522309	−	0.363274i
$127$	2.65502	−	18.4661i	0.235595	−	1.63860i	−0.437625	−	0.899157i	$-0.644180\pi$
$127$	2.65502	−	18.4661i	0.235595	−	1.63860i	0.673220	−	0.739442i	$-0.264911\pi$
$128$	−5.68167	−	3.65139i	−0.502193	−	0.322740i
$129$	0.576086	+	0.664839i	0.0507216	+	0.0585358i
$130$		0			0
$131$	−7.40597	+	4.75952i	−0.647062	+	0.415842i	−0.822592	−	0.568633i	$-0.807473\pi$
$131$	−7.40597	+	4.75952i	−0.647062	+	0.415842i	0.175529	+	0.984474i	$0.443836\pi$
$132$	−0.215366	−	0.0632371i	−0.0187452	−	0.00550408i
$133$	−3.34600	+	3.86150i	−0.290135	+	0.334834i
$134$	17.2356	−	5.06082i	1.48893	−	0.437188i
$135$		0			0
$136$	−0.653689	−	4.54651i	−0.0560534	−	0.389860i
$137$	−22.5463			−1.92626			−0.963130	−	0.269036i	$-0.913295\pi$
$137$	−22.5463			−1.92626			−0.963130	+	0.269036i	$0.913295\pi$
$138$	−0.898768	+	1.22682i	−0.0765082	+	0.104434i
$139$	8.55468			0.725598			0.362799	−	0.931867i	$-0.381821\pi$
$139$	8.55468			0.725598			0.362799	+	0.931867i	$0.381821\pi$
$140$		0			0
$141$	−0.696975	+	1.52616i	−0.0586959	+	0.128526i
$142$	−2.62361	+	0.770362i	−0.220168	+	0.0646473i
$143$	2.11182	−	2.43717i	0.176599	−	0.203806i
$144$	−8.54049	−	2.50772i	−0.711708	−	0.208976i
$145$		0			0
$146$	−2.32652	−	5.09437i	−0.192544	−	0.421613i
$147$	0.947898	+	1.09393i	0.0781813	+	0.0902260i
$148$	1.58427	+	1.01815i	0.130226	+	0.0836913i
$149$	−2.40317	+	16.7144i	−0.196875	+	1.36930i	0.616407	+	0.787428i	$0.288588\pi$
$149$	−2.40317	+	16.7144i	−0.196875	+	1.36930i	−0.813282	+	0.581870i	$0.802321\pi$
$150$		0			0
$151$	0.635989	+	0.408725i	0.0517561	+	0.0332616i	0.566263	−	0.824225i	$-0.308389\pi$
$151$	0.635989	+	0.408725i	0.0517561	+	0.0332616i	−0.514507	+	0.857486i	$0.672025\pi$
$152$	9.15374	+	10.5640i	0.742466	+	0.856852i
$153$	−1.84539	−	4.04085i	−0.149191	−	0.326683i
$154$	−2.61663	+	1.68160i	−0.210854	+	0.135508i
$155$		0			0
$156$	0.0963992	−	0.111251i	0.00771811	−	0.00890718i
$157$	−0.597407	+	0.175414i	−0.0476783	+	0.0139996i	−0.305485	−	0.952197i	$-0.598818\pi$
$157$	−0.597407	+	0.175414i	−0.0476783	+	0.0139996i	0.257806	+	0.966197i	$0.417000\pi$
$158$	0.362778	−	0.794374i	0.0288611	−	0.0631970i
$159$	−0.425432	−	2.95894i	−0.0337389	−	0.234659i
$160$		0			0
$161$	−1.18530	−	5.19007i	−0.0934147	−	0.409035i
$162$	−10.6611			−0.837614
$163$	−2.59937	−	18.0790i	−0.203599	−	1.41606i	−0.793493	−	0.608579i	$-0.791740\pi$
$163$	−2.59937	−	18.0790i	−0.203599	−	1.41606i	0.589894	−	0.807480i	$-0.299169\pi$
$164$	1.60531	−	3.51515i	0.125354	−	0.274487i
$165$		0			0
$166$	9.60476	−	11.0845i	0.745474	−	0.860323i
$167$	13.6068	+	3.99532i	1.05293	+	0.309167i	0.762000	−	0.647577i	$-0.224218\pi$
$167$	13.6068	+	3.99532i	1.05293	+	0.309167i	0.290928	+	0.956745i	$0.406036\pi$
$168$	−0.711711	+	0.457389i	−0.0549097	+	0.0352883i
$169$	−4.52182	−	9.90140i	−0.347832	−	0.761646i
$170$		0			0
$171$	11.3727	+	7.30876i	0.869688	+	0.558915i
$172$	−0.201211	+	1.39946i	−0.0153422	+	0.106707i
$173$	2.00301	−	13.9312i	0.152286	−	1.05917i	−0.760090	−	0.649818i	$-0.774845\pi$
$173$	2.00301	−	13.9312i	0.152286	−	1.05917i	0.912376	−	0.409354i	$-0.134246\pi$
$174$	−0.763259	−	0.490517i	−0.0578625	−	0.0371860i
$175$		0			0
$176$	2.79175	+	6.11307i	0.210436	+	0.460790i
$177$	−2.67177	+	1.71704i	−0.200822	+	0.129061i
$178$	7.81556	+	2.29486i	0.585801	+	0.172007i
$179$	−2.53928	+	2.93049i	−0.189795	+	0.219035i	−0.842670	−	0.538431i	$-0.819017\pi$
$179$	−2.53928	+	2.93049i	−0.189795	+	0.219035i	0.652875	+	0.757466i	$0.273563\pi$
$180$		0			0
$181$	4.34617	−	9.51678i	0.323048	−	0.707377i	−0.676530	−	0.736415i	$-0.736517\pi$
$181$	4.34617	−	9.51678i	0.323048	−	0.707377i	0.999578	+	0.0290380i	$0.00924439\pi$
$182$	−0.290305	−	2.01912i	−0.0215188	−	0.149667i
$183$	−0.937200			−0.0692798
$184$	−14.5155	+	1.18897i	−1.07010	+	0.0876523i
$185$		0			0
$186$	0.231476	+	1.60995i	0.0169726	+	0.118047i
$187$	−1.39329	+	3.05088i	−0.101887	+	0.223102i
$188$	−2.58726	+	0.759688i	−0.188695	+	0.0554060i
$189$	−1.08311	+	1.24998i	−0.0787847	+	0.0909224i
$190$		0			0
$191$	−7.23267	+	4.64816i	−0.523338	+	0.336329i	−0.775491	−	0.631358i	$-0.782498\pi$
$191$	−7.23267	+	4.64816i	−0.523338	+	0.336329i	0.252153	+	0.967687i	$0.418861\pi$
$192$	0.927539	+	2.03103i	0.0669394	+	0.146577i
$193$	6.83042	+	7.88273i	0.491665	+	0.567411i	0.946310	−	0.323261i	$-0.104779\pi$
$193$	6.83042	+	7.88273i	0.491665	+	0.567411i	−0.454645	+	0.890673i	$0.650234\pi$
$194$	14.2641	+	9.16701i	1.02411	+	0.658153i
$195$		0			0
$196$	−0.331075	+	2.30268i	−0.0236482	+	0.164477i
$197$	9.25535	+	5.94805i	0.659416	+	0.423781i	0.827096	−	0.562060i	$-0.189991\pi$
$197$	9.25535	+	5.94805i	0.659416	+	0.423781i	−0.167680	+	0.985841i	$0.553628\pi$
$198$	5.38916	+	6.21942i	0.382991	+	0.441995i
$199$	8.29502	+	18.1636i	0.588018	+	1.28758i	0.936632	+	0.350314i	$0.113925\pi$
$199$	8.29502	+	18.1636i	0.588018	+	1.28758i	−0.348614	+	0.937266i	$0.613347\pi$
$200$		0			0
$201$	−3.42315	−	1.00513i	−0.241450	−	0.0708961i
$202$	5.68652	−	6.56259i	0.400102	−	0.461742i
$203$	3.04736	−	0.894786i	0.213883	−	0.0628017i
$204$	−0.0636001	+	0.139265i	−0.00445290	+	0.00975049i
$205$		0			0
$206$	5.01588			0.349473
$207$	−13.1458	+	5.05840i	−0.913697	+	0.351583i
$208$	−4.40741			−0.305599
$209$	−1.45257	−	10.1029i	−0.100476	−	0.698829i
$210$		0			0
$211$	−1.37678	+	0.404258i	−0.0947813	+	0.0278303i	−0.328779	−	0.944407i	$-0.606637\pi$
$211$	−1.37678	+	0.404258i	−0.0947813	+	0.0278303i	0.233998	+	0.972237i	$0.424819\pi$
$212$	3.14624	−	3.63096i	0.216085	−	0.249375i
$213$	0.521074	+	0.153001i	0.0357034	+	0.0104835i
$214$	11.5676	−	7.43402i	0.790742	−	0.508179i
$215$		0			0
$216$	2.96309	+	3.41959i	0.201613	+	0.232673i
$217$	−4.78982	−	3.07823i	−0.325154	−	0.208964i
$218$	−1.56319	+	10.8722i	−0.105872	+	0.736359i
$219$	−0.158298	+	1.10098i	−0.0106968	+	0.0743977i
$220$		0			0
$221$	−1.44045	−	1.66237i	−0.0968950	−	0.111823i
$222$	0.615074	+	1.34682i	0.0412811	+	0.0903929i
$223$	−1.14534	+	0.736063i	−0.0766974	+	0.0492904i	−0.578427	−	0.815734i	$-0.696333\pi$
$223$	−1.14534	+	0.736063i	−0.0766974	+	0.0492904i	0.501730	+	0.865024i	$0.332697\pi$
$224$	−2.39028	−	0.701851i	−0.159708	−	0.0468944i
$225$		0			0
$226$	−3.59949	+	1.05691i	−0.239434	+	0.0703043i
$227$	−0.775903	+	1.69899i	−0.0514985	+	0.112766i	−0.933632	−	0.358233i	$-0.883379\pi$
$227$	−0.775903	+	1.69899i	−0.0514985	+	0.112766i	0.882134	+	0.470999i	$0.156107\pi$
$228$	−0.0663062	−	0.461170i	−0.00439124	−	0.0305417i
$229$	−4.57722			−0.302471			−0.151235	−	0.988498i	$-0.548325\pi$
$229$	−4.57722			−0.302471			−0.151235	+	0.988498i	$0.548325\pi$
$230$		0			0
$231$	0.617753			0.0406451
$232$	−1.23653	−	8.60025i	−0.0811821	−	0.564634i
$233$	−12.2777	+	26.8845i	−0.804342	+	1.76126i	−0.174316	+	0.984690i	$0.555771\pi$
$233$	−12.2777	+	26.8845i	−0.804342	+	1.76126i	−0.630026	+	0.776574i	$0.716956\pi$
$234$	−5.17850	+	1.52054i	−0.338529	+	0.0994010i
$235$		0			0
$236$	−4.89753	−	1.43805i	−0.318802	−	0.0936088i
$237$	−0.145910	+	0.0937708i	−0.00947789	+	0.00609107i
$238$	0.881329	+	1.92984i	0.0571281	+	0.125093i
$239$	−15.3346	−	17.6970i	−0.991911	−	1.14473i	−0.989471	−	0.144729i	$-0.953769\pi$
$239$	−15.3346	−	17.6970i	−0.991911	−	1.14473i	−0.00243982	−	0.999997i	$-0.500777\pi$
$240$		0			0
$241$	−2.54571	+	17.7058i	−0.163983	+	1.14053i	0.727048	+	0.686587i	$0.240892\pi$
$241$	−2.54571	+	17.7058i	−0.163983	+	1.14053i	−0.891031	+	0.453942i	$0.850017\pi$
$242$	−1.09386	+	7.60793i	−0.0703157	+	0.489056i
$243$	5.54156	+	3.56135i	0.355491	+	0.228461i
$244$	−0.986382	−	1.13835i	−0.0631466	−	0.0728751i
$245$		0			0
$246$	2.55592	−	1.64259i	0.162960	−	0.104728i
$247$	6.42271	+	1.88588i	0.408668	+	0.119996i
$248$	−10.2003	+	11.7718i	−0.647720	+	0.747509i
$249$	−2.79498	+	0.820681i	−0.177125	+	0.0520085i
$250$		0			0
$251$	−3.63146	−	25.2573i	−0.229215	−	1.59423i	−0.701426	−	0.712742i	$-0.747453\pi$
$251$	−3.63146	−	25.2573i	−0.229215	−	1.59423i	0.472210	−	0.881486i	$-0.343456\pi$
$252$	−1.31500			−0.0828372
$253$	9.38595	+	4.99997i	0.590089	+	0.314346i
$254$	23.5735			1.47913
$255$		0			0
$256$	−3.84673	+	8.42316i	−0.240421	+	0.526448i
$257$	1.56251	−	0.458793i	0.0974664	−	0.0286187i	−0.232636	−	0.972564i	$-0.574735\pi$
$257$	1.56251	−	0.458793i	0.0974664	−	0.0286187i	0.330102	+	0.943945i	$0.392917\pi$
$258$	−0.727937	+	0.840084i	−0.0453194	+	0.0523014i
$259$	−4.97306	−	1.46022i	−0.309011	−	0.0907338i
$260$		0			0
$261$	−3.49077	−	7.64373i	−0.216073	−	0.473135i
$262$	−7.28467	−	8.40696i	−0.450049	−	0.519384i
$263$	−9.47079	−	6.08651i	−0.583994	−	0.375310i	0.215032	−	0.976607i	$-0.431015\pi$
$263$	−9.47079	−	6.08651i	−0.583994	−	0.375310i	−0.799026	+	0.601297i	$0.794651\pi$
$264$	0.240512	−	1.67280i	0.0148025	−	0.102954i
$265$		0			0
$266$	−5.43139	−	3.49054i	−0.333020	−	0.214019i
$267$	−1.05942	−	1.22263i	−0.0648353	−	0.0748239i
$268$	−2.38193	−	5.21570i	−0.145500	−	0.318600i
$269$	−15.3317	+	9.85307i	−0.934789	+	0.600752i	−0.916913	−	0.399088i	$-0.869327\pi$
$269$	−15.3317	+	9.85307i	−0.934789	+	0.600752i	−0.0178759	+	0.999840i	$0.505690\pi$
$270$		0			0
$271$	−9.05504	+	10.4501i	−0.550054	+	0.634797i	−0.960896	−	0.276910i	$-0.910690\pi$
$271$	−9.05504	+	10.4501i	−0.550054	+	0.634797i	0.410841	+	0.911707i	$0.365235\pi$
$272$	4.39821	−	1.29143i	0.266681	−	0.0783045i
$273$	−0.168301	+	0.368528i	−0.0101860	+	0.0223043i
$274$	−4.05445	−	28.1993i	−0.244938	−	1.70358i
$275$		0			0
$276$	0.428445	+	0.228236i	0.0257893	+	0.0137382i
$277$	18.4357			1.10769			0.553846	−	0.832619i	$-0.313160\pi$
$277$	18.4357			1.10769			0.553846	+	0.832619i	$0.313160\pi$
$278$	1.53837	+	10.6996i	0.0922652	+	0.641718i
$279$	−6.25794	+	13.7030i	−0.374653	+	0.820376i
$280$		0			0
$281$	−16.9041	+	19.5084i	−1.00841	+	1.16377i	−0.0219559	+	0.999759i	$0.506989\pi$
$281$	−16.9041	+	19.5084i	−1.00841	+	1.16377i	−0.986458	+	0.164013i	$0.947556\pi$
$282$	−2.03415	−	0.597280i	−0.121132	−	0.0355675i
$283$	−2.34825	+	1.50913i	−0.139589	+	0.0897085i	−0.608572	−	0.793499i	$-0.708257\pi$
$283$	−2.34825	+	1.50913i	−0.139589	+	0.0897085i	0.468982	+	0.883208i	$0.344621\pi$
$284$	0.362579	+	0.793938i	0.0215151	+	0.0471116i
$285$		0			0
$286$	3.42800	+	2.20304i	0.202702	+	0.130269i
$287$	−1.51359	+	10.5272i	−0.0893443	+	0.621403i
$288$	−0.938027	+	6.52412i	−0.0552737	+	0.384437i
$289$	−12.3768	−	7.95407i	−0.728045	−	0.467886i
$290$		0			0
$291$	−1.39894	−	3.06326i	−0.0820076	−	0.179572i
$292$	−1.50389	+	0.966489i	−0.0880083	+	0.0565595i
$293$	19.2647	+	5.65664i	1.12546	+	0.330464i	0.790921	−	0.611918i	$-0.209602\pi$
$293$	19.2647	+	5.65664i	1.12546	+	0.330464i	0.334537	+	0.942383i	$0.391420\pi$
$294$	−1.19775	+	1.38228i	−0.0698545	+	0.0806164i
$295$		0			0
$296$	−5.89028	+	12.8979i	−0.342366	+	0.749677i
$297$	−0.470201	−	3.27032i	−0.0272838	−	0.189763i
$298$	−21.3374			−1.23604
$299$	−5.53990	+	4.23710i	−0.320381	+	0.245038i
$300$		0			0
$301$	−0.553773	−	3.85158i	−0.0319190	−	0.222001i
$302$	−0.396836	+	0.868950i	−0.0228354	+	0.0500025i
$303$	−1.65477	+	0.485886i	−0.0950643	+	0.0279134i
$304$	−9.13506	+	10.5424i	−0.523932	+	0.604650i
$305$		0			0
$306$	4.72215	−	3.03474i	0.269947	−	0.173485i
$307$	13.0144	+	28.4976i	0.742772	+	1.62644i	0.778941	+	0.627098i	$0.215757\pi$
$307$	13.0144	+	28.4976i	0.742772	+	1.62644i	−0.0361690	+	0.999346i	$0.511515\pi$
$308$	0.650171	+	0.750337i	0.0370469	+	0.0427544i
$309$	−0.838058	−	0.538587i	−0.0476754	−	0.0306391i
$310$		0			0
$311$	2.80088	−	19.4806i	0.158824	−	1.10464i	−0.741982	−	0.670420i	$-0.766114\pi$
$311$	2.80088	−	19.4806i	0.158824	−	1.10464i	0.900806	−	0.434222i	$-0.142977\pi$
$312$	0.932402	+	0.599218i	0.0527869	+	0.0339240i
$313$	15.2935	+	17.6497i	0.864440	+	0.997617i	0.999977	+	0.00684507i	$0.00217887\pi$
$313$	15.2935	+	17.6497i	0.864440	+	0.997617i	−0.135536	+	0.990772i	$0.543276\pi$
$314$	−0.326826	−	0.715650i	−0.0184439	−	0.0403864i
$315$		0			0
$316$	−0.267463	−	0.0785343i	−0.0150460	−	0.00441790i
$317$	−17.0432	+	19.6689i	−0.957242	+	1.10472i	0.0371867	+	0.999308i	$0.488160\pi$
$317$	−17.0432	+	19.6689i	−0.957242	+	1.10472i	−0.994429	+	0.105408i	$0.966385\pi$
$318$	3.62433	−	1.06420i	0.203242	−	0.0596773i
$319$	−2.63557	+	5.77109i	−0.147563	+	0.323119i
$320$		0			0
$321$	−2.73095			−0.152427
$322$	6.27822	−	2.41581i	0.349872	−	0.134628i
$323$	−6.96190			−0.387371
$324$	0.484301	+	3.36838i	0.0269056	+	0.187132i
$325$		0			0
$326$	22.1445	−	6.50222i	1.22647	−	0.360125i
$327$	1.42860	−	1.64869i	0.0790016	−	0.0911727i
$328$	27.9172	+	8.19722i	1.54147	+	0.452616i
$329$	6.24317	−	4.01224i	0.344197	−	0.221202i
$330$		0			0
$331$	0.0756102	+	0.0872588i	0.00415591	+	0.00479618i	0.757824	−	0.652459i	$-0.226263\pi$
$331$	0.0756102	+	0.0872588i	0.00415591	+	0.00479618i	−0.753668	+	0.657256i	$0.771717\pi$
$332$	−3.93847	−	2.53110i	−0.216152	−	0.138912i
$333$	−1.95159	+	13.5736i	−0.106947	+	0.743831i
$334$	−2.55018	+	17.7369i	−0.139540	+	0.970521i
$335$		0			0
$336$	−0.552890	−	0.638069i	−0.0301626	−	0.0348095i
$337$	−4.27822	−	9.36799i	−0.233049	−	0.510307i	0.756589	−	0.653891i	$-0.226865\pi$
$337$	−4.27822	−	9.36799i	−0.233049	−	0.510307i	−0.989638	+	0.143584i	$0.954137\pi$
$338$	11.5708	−	7.43612i	0.629370	−	0.404471i
$339$	0.714892	+	0.209911i	0.0388276	+	0.0114008i
$340$		0			0
$341$	10.9130	−	3.20434i	0.590971	−	0.173525i
$342$	−7.09616	+	15.5384i	−0.383716	+	0.840222i
$343$	−2.01704	−	14.0288i	−0.108910	−	0.757484i
$344$	−10.6452			−0.573951
$345$		0			0
$346$	17.7844			0.956095
$347$	−2.41200	−	16.7759i	−0.129483	−	0.900575i	−0.946211	−	0.323551i	$-0.895123\pi$
$347$	−2.41200	−	16.7759i	−0.129483	−	0.900575i	0.816727	−	0.577024i	$-0.195786\pi$
$348$	−0.120307	+	0.263436i	−0.00644913	+	0.0141216i
$349$	18.6503	−	5.47622i	0.998327	−	0.293135i	0.258558	−	0.965996i	$-0.416753\pi$
$349$	18.6503	−	5.47622i	0.998327	−	0.293135i	0.739770	+	0.672860i	$0.234935\pi$
$350$		0			0
$351$	2.07905	+	0.610464i	0.110971	+	0.0325842i
$352$	4.18643	−	2.69046i	0.223138	−	0.143402i
$353$	6.39768	+	14.0090i	0.340514	+	0.745622i	0.999981	−	0.00611166i	$-0.00194542\pi$
$353$	6.39768	+	14.0090i	0.340514	+	0.745622i	−0.659467	+	0.751733i	$0.729218\pi$
$354$	−2.62801	−	3.03289i	−0.139677	−	0.161196i
$355$		0			0
$356$	0.370026	−	2.57359i	0.0196113	−	0.136400i
$357$	0.0599661	−	0.417073i	0.00317374	−	0.0220739i
$358$	−4.12188	−	2.64897i	−0.217848	−	0.140002i
$359$	10.7911	+	12.4536i	0.569531	+	0.657274i	0.965321	−	0.261067i	$-0.0840745\pi$
$359$	10.7911	+	12.4536i	0.569531	+	0.657274i	−0.395790	+	0.918341i	$0.629529\pi$
$360$		0			0
$361$	1.83928	−	1.18203i	0.0968042	−	0.0622123i
$362$	12.6845	+	3.72450i	0.666682	+	0.195755i
$363$	0.999674	−	1.15368i	0.0524693	−	0.0605527i
$364$	−0.624755	+	0.183445i	−0.0327461	+	0.00961511i
$365$		0			0
$366$	−0.168535	−	1.17218i	−0.00880944	−	0.0612710i
$367$	−20.2777			−1.05849			−0.529244	−	0.848470i	$-0.677524\pi$
$367$	−20.2777			−1.05849			−0.529244	+	0.848470i	$0.677524\pi$
$368$	−3.23603	−	14.1696i	−0.168690	−	0.738642i
$369$	28.1394			1.46488
$370$		0			0
$371$	−5.49294	+	12.0279i	−0.285179	+	0.624456i
$372$	0.498150	−	0.146270i	0.0258279	−	0.00758375i
$373$	−6.65556	+	7.68093i	−0.344612	+	0.397703i	−0.901426	−	0.432934i	$-0.857478\pi$
$373$	−6.65556	+	7.68093i	−0.344612	+	0.397703i	0.556814	+	0.830637i	$0.312024\pi$
$374$	−4.06637	−	1.19399i	−0.210267	−	0.0617400i
$375$		0			0
$376$	−8.43397	−	18.4678i	−0.434949	−	0.952405i
$377$	−2.72477	−	3.14456i	−0.140333	−	0.161953i
$378$	−1.75816	−	1.12990i	−0.0904298	−	0.0581157i
$379$	−3.27043	+	22.7463i	−0.167991	+	1.16840i	0.715040	+	0.699084i	$0.246409\pi$
$379$	−3.27043	+	22.7463i	−0.167991	+	1.16840i	−0.883030	+	0.469316i	$0.844500\pi$
$380$		0			0
$381$	−3.93868	−	2.53124i	−0.201785	−	0.129679i
$382$	−7.11422	−	8.21025i	−0.363995	−	0.420073i
$383$	−5.74275	−	12.5749i	−0.293441	−	0.642546i	0.704287	−	0.709915i	$-0.251267\pi$
$383$	−5.74275	−	12.5749i	−0.293441	−	0.642546i	−0.997728	+	0.0673691i	$0.978539\pi$
$384$	−1.42588	+	0.916355i	−0.0727640	+	0.0467626i
$385$		0			0
$386$	−8.63086	+	9.96054i	−0.439299	+	0.506978i
$387$	−9.87827	+	2.90052i	−0.502141	+	0.147442i
$388$	2.24835	−	4.92320i	0.114143	−	0.249938i
$389$	−4.16592	−	28.9746i	−0.211221	−	1.46907i	−0.769088	−	0.639142i	$-0.779289\pi$
$389$	−4.16592	−	28.9746i	−0.211221	−	1.46907i	0.557868	−	0.829930i	$-0.311620\pi$
$390$		0			0
$391$	4.28682	−	5.85153i	0.216794	−	0.295924i
$392$	−17.5157			−0.884677
$393$	0.314421	+	2.18684i	0.0158604	+	0.110312i
$394$	−5.77503	+	12.6456i	−0.290942	+	0.637074i
$395$		0			0
$396$	1.72022	−	1.98524i	0.0864444	−	0.0997622i
$397$	30.0067	+	8.81078i	1.50600	+	0.442200i	0.927606	−	0.373560i	$-0.121863\pi$
$397$	30.0067	+	8.81078i	1.50600	+	0.442200i	0.578390	+	0.815761i	$0.303681\pi$
$398$	−21.2260	+	13.6411i	−1.06396	+	0.683768i
$399$	0.532679	+	1.16641i	0.0266673	+	0.0583933i
$400$		0			0
$401$	13.0975	+	8.41724i	0.654057	+	0.420337i	0.825147	−	0.564919i	$-0.191092\pi$
$401$	13.0975	+	8.41724i	0.654057	+	0.420337i	−0.171090	+	0.985255i	$0.554729\pi$
$402$	0.641564	−	4.46218i	0.0319983	−	0.222553i
$403$	−1.06155	+	7.38326i	−0.0528797	+	0.367786i
$404$	−2.33178	−	1.49854i	−0.116010	−	0.0745554i
$405$		0			0
$406$	1.66714	+	3.65052i	0.0827385	+	0.181172i
$407$	8.71001	−	5.59759i	0.431739	−	0.277462i
$408$	−1.10604	−	0.324761i	−0.0547569	−	0.0160781i
$409$	21.9729	−	25.3581i	1.08649	−	1.25388i	0.121218	−	0.992626i	$-0.461320\pi$
$409$	21.9729	−	25.3581i	1.08649	−	1.25388i	0.965271	−	0.261250i	$-0.0841347\pi$
$410$		0			0
$411$	−2.35052	+	5.14692i	−0.115942	+	0.253879i
$412$	−0.227856	−	1.58477i	−0.0112257	−	0.0780763i
$413$	14.0480			0.691258
$414$	−8.69067	−	15.5322i	−0.427123	−	0.763367i
$415$		0			0
$416$	0.464469	+	3.23046i	0.0227725	+	0.158386i
$417$	0.891850	−	1.95288i	0.0436741	−	0.0956329i
$418$	12.3747	−	3.63355i	0.605268	−	0.177723i
$419$	7.40743	−	8.54863i	0.361877	−	0.417628i	−0.545391	−	0.838182i	$-0.683619\pi$
$419$	7.40743	−	8.54863i	0.361877	−	0.417628i	0.907268	+	0.420554i	$0.138164\pi$
$420$		0			0
$421$	−5.13915	+	3.30273i	−0.250467	+	0.160965i	−0.659850	−	0.751397i	$-0.729380\pi$
$421$	−5.13915	+	3.30273i	−0.250467	+	0.160965i	0.409383	+	0.912363i	$0.365744\pi$
$422$	−0.753200	−	1.64928i	−0.0366652	−	0.0802856i
$423$	−12.8583	−	14.8393i	−0.625193	−	0.721511i
$424$	30.4314	+	19.5571i	1.47788	+	0.949775i
$425$		0			0
$426$	−0.0976593	+	0.679236i	−0.00473161	+	0.0329091i
$427$	3.48741	+	2.24122i	0.168767	+	0.108460i
$428$	−2.87427	−	3.31708i	−0.138933	−	0.160337i
$429$	−0.336199	−	0.736173i	−0.0162318	−	0.0355427i
$430$		0			0
$431$	23.6924	+	6.95671i	1.14122	+	0.335093i	0.797109	−	0.603835i	$-0.206361\pi$
$431$	23.6924	+	6.95671i	1.14122	+	0.335093i	0.344113	+	0.938928i	$0.388180\pi$
$432$	−2.95704	+	3.41261i	−0.142271	+	0.164189i
$433$	−23.0996	+	6.78265i	−1.11010	+	0.325953i	−0.784856	−	0.619678i	$-0.787263\pi$
$433$	−23.0996	+	6.78265i	−1.11010	+	0.325953i	−0.325239	+	0.945632i	$0.605445\pi$
$434$	2.98869	−	6.54432i	0.143462	−	0.314137i
$435$		0			0
$436$	3.50610			0.167912
$437$	−1.34729	+	22.0334i	−0.0644498	+	1.05400i
$438$	−1.40550			−0.0671574
$439$	−3.45082	−	24.0010i	−0.164699	−	1.14551i	−0.889629	−	0.456683i	$-0.849037\pi$
$439$	−3.45082	−	24.0010i	−0.164699	−	1.14551i	0.724930	−	0.688822i	$-0.241872\pi$
$440$		0			0
$441$	−16.2538	+	4.77255i	−0.773990	+	0.227264i
$442$	1.82014	−	2.10055i	0.0865751	−	0.0999129i
$443$	−3.09964	−	0.910135i	−0.147268	−	0.0432418i	0.207268	−	0.978284i	$-0.433543\pi$
$443$	−3.09964	−	0.910135i	−0.147268	−	0.0432418i	−0.354536	+	0.935042i	$0.615361\pi$
$444$	0.397590	−	0.255516i	0.0188688	−	0.0121262i
$445$		0			0
$446$	−1.12658	−	1.30014i	−0.0533450	−	0.0615635i
$447$	3.56506	+	2.29113i	0.168622	+	0.108367i
$448$	1.40554	−	9.77576i	0.0664056	−	0.461861i
$449$	−1.95771	+	13.6162i	−0.0923900	+	0.642587i	0.890030	+	0.455902i	$0.150683\pi$
$449$	−1.95771	+	13.6162i	−0.0923900	+	0.642587i	−0.982420	+	0.186685i	$0.940226\pi$
$450$		0			0
$451$	−13.9129	−	16.0563i	−0.655131	−	0.756061i
$452$	0.497444	+	1.08925i	0.0233978	+	0.0512341i
$453$	0.159608	−	0.102574i	0.00749906	−	0.00481935i
$454$	−2.26451	−	0.664919i	−0.106279	−	0.0312062i
$455$		0			0
$456$	3.36587	−	0.988309i	0.157621	−	0.0462818i
$457$	10.5636	−	23.1311i	0.494145	−	1.08203i	−0.484183	−	0.874967i	$-0.660883\pi$
$457$	10.5636	−	23.1311i	0.494145	−	1.08203i	0.978328	−	0.207061i	$-0.0663898\pi$
$458$	−0.823110	−	5.72486i	−0.0384614	−	0.267505i
$459$	−2.25359			−0.105188
$460$		0			0
$461$	18.3213			0.853307			0.426653	−	0.904415i	$-0.359692\pi$
$461$	18.3213			0.853307			0.426653	+	0.904415i	$0.359692\pi$
$462$	0.111089	+	0.772641i	0.00516833	+	0.0359465i
$463$	−5.45895	+	11.9534i	−0.253699	+	0.555523i	−0.993036	−	0.117813i	$-0.962412\pi$
$463$	−5.45895	+	11.9534i	−0.253699	+	0.555523i	0.739337	+	0.673336i	$0.235139\pi$
$464$	8.31973	−	2.44289i	0.386234	−	0.113408i
$465$		0			0
$466$	−35.8331	−	10.5216i	−1.65994	−	0.487402i
$467$	7.38279	−	4.74463i	0.341635	−	0.219555i	−0.358561	−	0.933506i	$-0.616732\pi$
$467$	7.38279	−	4.74463i	0.341635	−	0.219555i	0.700196	+	0.713951i	$0.253096\pi$
$468$	0.715661	+	1.56708i	0.0330814	+	0.0724383i
$469$	10.3342	+	11.9263i	0.477188	+	0.550704i
$470$		0			0
$471$	−0.0222374	+	0.154665i	−0.00102465	+	0.00712657i
$472$	5.46937	−	38.0403i	0.251748	−	1.75095i
$473$	6.53911	+	4.20243i	0.300669	+	0.193228i
$474$	−0.143521	−	0.165632i	−0.00659212	−	0.00760771i
$475$		0			0
$476$	0.569700	−	0.366124i	0.0261121	−	0.0167813i
$477$	33.5677	+	9.85637i	1.53696	+	0.451292i
$478$	19.3766	−	22.3618i	0.886266	−	1.02281i
$479$	31.8308	−	9.34638i	1.45439	−	0.427047i	0.543398	−	0.839475i	$-0.317138\pi$
$479$	31.8308	−	9.34638i	1.45439	−	0.427047i	0.910990	+	0.412429i	$0.135319\pi$
$480$		0			0
$481$	0.966344	+	6.72107i	0.0440615	+	0.306454i
$482$	−22.6029			−1.02953
$483$	−1.30837	−	0.270497i	−0.0595329	−	0.0123081i
$484$	2.45343			0.111519
$485$		0			0
$486$	−3.45775	+	7.57142i	−0.156847	+	0.343447i
$487$	−19.0378	+	5.58999i	−0.862683	+	0.253307i	−0.683000	−	0.730418i	$-0.739325\pi$
$487$	−19.0378	+	5.58999i	−0.862683	+	0.253307i	−0.179683	+	0.983725i	$0.557507\pi$
$488$	7.42671	−	8.57088i	0.336191	−	0.387986i
$489$	−4.39811	−	1.29140i	−0.198890	−	0.0583992i
$490$		0			0
$491$	14.1226	+	30.9241i	0.637343	+	1.39559i	0.902208	+	0.431300i	$0.141945\pi$
$491$	14.1226	+	30.9241i	0.637343	+	1.39559i	−0.264866	+	0.964285i	$0.585328\pi$
$492$	−0.635086	−	0.732929i	−0.0286319	−	0.0330430i
$493$	3.64049	+	2.33960i	0.163959	+	0.105370i
$494$	−1.20374	+	8.37221i	−0.0541589	+	0.376684i
$495$		0			0
$496$	−13.0769	−	8.40400i	−0.587169	−	0.377351i
$497$	−1.57308	−	1.81543i	−0.0705621	−	0.0814330i
$498$	−1.52906	−	3.34818i	−0.0685190	−	0.150036i
$499$	−14.0206	+	9.01052i	−0.627650	+	0.403366i	−0.815439	−	0.578843i	$-0.803504\pi$
$499$	−14.0206	+	9.01052i	−0.627650	+	0.403366i	0.187789	+	0.982209i	$0.439868\pi$
$500$		0			0
$501$	2.33061	−	2.68967i	0.104124	−	0.120166i
$502$	30.9370	−	9.08393i	1.38079	−	0.405436i
$503$	7.23818	−	15.8494i	0.322735	−	0.706690i	−0.676832	−	0.736138i	$-0.736648\pi$
$503$	7.23818	−	15.8494i	0.322735	−	0.706690i	0.999566	+	0.0294475i	$0.00937480\pi$
$504$	−1.40905	−	9.80019i	−0.0627643	−	0.436535i
$505$		0			0
$506$	−4.56576	+	12.6384i	−0.202973	+	0.561846i
$507$	−2.73173			−0.121320
$508$	−1.07087	−	7.44808i	−0.0475123	−	0.330455i
$509$	−16.4990	+	36.1278i	−0.731305	+	1.60133i	0.0660446	+	0.997817i	$0.478962\pi$
$509$	−16.4990	+	36.1278i	−0.731305	+	1.60133i	−0.797350	+	0.603518i	$0.793765\pi$
$510$		0			0
$511$	3.22194	−	3.71831i	0.142530	−	0.164488i
$512$	−24.1873	−	7.10204i	−1.06894	−	0.313869i
$513$	5.76939	−	3.70776i	0.254725	−	0.163702i
$514$	0.854807	+	1.87177i	0.0377039	+	0.0825601i
$515$		0			0
$516$	0.298494	+	0.191830i	0.0131405	+	0.00844486i
$517$	−2.10978	+	14.6739i	−0.0927882	+	0.645356i
$518$	0.932049	−	6.48254i	0.0409519	−	0.284827i
$519$	−2.97143	−	1.90962i	−0.130431	−	0.0838231i
$520$		0			0
$521$	5.85707	+	12.8252i	0.256603	+	0.561882i	0.993462	−	0.114164i	$-0.0364190\pi$
$521$	5.85707	+	12.8252i	0.256603	+	0.561882i	−0.736859	+	0.676047i	$0.763692\pi$
$522$	8.93249	−	5.74057i	0.390965	−	0.251258i
$523$	−17.3202	−	5.08568i	−0.757361	−	0.222381i	−0.119818	−	0.992796i	$-0.538231\pi$
$523$	−17.3202	−	5.08568i	−0.757361	−	0.222381i	−0.637543	+	0.770415i	$0.720049\pi$
$524$	−2.32527	+	2.68351i	−0.101580	+	0.117229i
$525$		0			0
$526$	5.90946	−	12.9399i	0.257665	−	0.564207i
$527$	−1.10406	−	7.67891i	−0.0480936	−	0.334498i
$528$	1.68655			0.0733977
$529$	−17.6896	−	14.6996i	−0.769114	−	0.639111i
$530$		0			0
$531$	−5.28960	−	36.7900i	−0.229549	−	1.59655i
$532$	−0.856110	+	1.87462i	−0.0371171	+	0.0812751i
$533$	13.3690	−	3.92549i	0.579075	−	0.170032i
$534$	1.33867	−	1.54491i	0.0579299	−	0.0668547i
$535$		0			0
$536$	36.3183	−	23.3404i	1.56871	−	1.00815i
$537$	0.404250	+	0.885184i	0.0174447	+	0.0381985i
$538$	−15.0806	−	17.4039i	−0.650170	−	0.750336i
$539$	10.7595	+	6.91472i	0.463445	+	0.297838i
$540$		0			0
$541$	−2.48235	+	17.2651i	−0.106725	+	0.742287i	0.864243	+	0.503075i	$0.167798\pi$
$541$	−2.48235	+	17.2651i	−0.106725	+	0.742287i	−0.970967	+	0.239212i	$0.923111\pi$
$542$	−14.6986	−	9.44619i	−0.631357	−	0.405749i
$543$	−1.71941	−	1.98431i	−0.0737870	−	0.0851547i
$544$	−1.41007	−	3.08762i	−0.0604562	−	0.132381i
$545$		0			0
$546$	−0.491193	−	0.144227i	−0.0210211	−	0.00617236i
$547$	−22.7152	+	26.2148i	−0.971233	+	1.12086i	0.0214078	+	0.999771i	$0.493185\pi$
$547$	−22.7152	+	26.2148i	−0.971233	+	1.12086i	−0.992641	+	0.121092i	$0.961360\pi$
$548$	−8.72543	+	2.56202i	−0.372732	+	0.109444i
$549$	4.55633	−	9.97697i	0.194459	−	0.425807i
$550$		0			0
$551$	−13.1692			−0.561029
$552$	−1.24187	+	3.43759i	−0.0528573	+	0.146314i
$553$	0.767189			0.0326242
$554$	3.31524	+	23.0580i	0.140851	+	0.979642i
$555$		0			0
$556$	3.31066	−	0.972099i	0.140403	−	0.0412262i
$557$	3.20499	−	3.69876i	0.135800	−	0.156721i	−0.683776	−	0.729692i	$-0.739664\pi$
$557$	3.20499	−	3.69876i	0.135800	−	0.156721i	0.819576	+	0.572970i	$0.194209\pi$
$558$	−18.2641	−	5.36282i	−0.773180	−	0.227026i
$559$	−4.28853	+	2.75607i	−0.181385	+	0.116569i
$560$		0			0
$561$	0.551206	+	0.636126i	0.0232719	+	0.0268573i
$562$	−27.4395	−	17.6343i	−1.15747	−	0.743858i
$563$	1.69779	−	11.8084i	0.0715534	−	0.497665i	−0.922257	−	0.386577i	$-0.873657\pi$
$563$	1.69779	−	11.8084i	0.0715534	−	0.497665i	0.993811	−	0.111088i	$-0.0354336\pi$
$564$	−0.0963063	+	0.669825i	−0.00405523	+	0.0282047i
$565$		0			0
$566$	−2.30979	−	2.66564i	−0.0970879	−	0.112045i
$567$	−3.89069	−	8.51942i	−0.163394	−	0.357782i
$568$	−5.52840	+	3.55289i	−0.231966	+	0.149076i
$569$	−34.4238	−	10.1077i	−1.44312	−	0.423738i	−0.535859	−	0.844307i	$-0.680012\pi$
$569$	−34.4238	−	10.1077i	−1.44312	−	0.423738i	−0.907260	+	0.420569i	$0.861830\pi$
$570$		0			0
$571$	20.5988	−	6.04837i	0.862035	−	0.253116i	0.179311	−	0.983793i	$-0.442613\pi$
$571$	20.5988	−	6.04837i	0.862035	−	0.253116i	0.682724	+	0.730676i	$0.260795\pi$
$572$	0.540331	−	1.18316i	0.0225924	−	0.0494704i
$573$	0.307064	+	2.13567i	0.0128278	+	0.0892190i
$574$	−13.4389			−0.560929
$575$		0			0
$576$	−26.1307			−1.08878
$577$	−0.468540	−	3.25877i	−0.0195056	−	0.135664i	0.977742	−	0.209812i	$-0.0672853\pi$
$577$	−0.468540	−	3.25877i	−0.0195056	−	0.135664i	−0.997247	+	0.0741481i	$0.976376\pi$
$578$	7.72270	−	16.9104i	0.321222	−	0.703378i
$579$	2.51158	−	0.737466i	0.104378	−	0.0306480i
$580$		0			0
$581$	12.3630	+	3.63009i	0.512902	+	0.150602i
$582$	3.57974	−	2.30056i	0.148385	−	0.0953613i
$583$	−10.9727	−	24.0269i	−0.454444	−	0.995094i
$584$	−8.81432	−	10.1723i	−0.364739	−	0.420931i
$585$		0			0
$586$	−3.61059	+	25.1122i	−0.149152	+	1.03738i
$587$	−0.531824	+	3.69891i	−0.0219507	+	0.152671i	−0.997849	−	0.0655557i	$-0.979118\pi$
$587$	−0.531824	+	3.69891i	−0.0219507	+	0.152671i	0.975898	+	0.218226i	$0.0700271\pi$
$588$	0.491144	+	0.315639i	0.0202545	+	0.0130167i
$589$	15.4604	+	17.8422i	0.637033	+	0.735176i
$590$		0			0
$591$	2.32273	−	1.49273i	0.0955444	−	0.0614026i
$592$	−13.5772	−	3.98661i	−0.558018	−	0.163849i
$593$	17.8592	−	20.6106i	0.733390	−	0.846378i	−0.259459	−	0.965754i	$-0.583544\pi$
$593$	17.8592	−	20.6106i	0.733390	−	0.846378i	0.992849	+	0.119377i	$0.0380896\pi$
$594$	4.00573	−	1.17619i	0.164357	−	0.0482596i
$595$		0			0
$596$	0.969291	+	6.74157i	0.0397037	+	0.276145i
$597$	5.01120			0.205095
$598$	−6.29569	−	6.16697i	−0.257450	−	0.252186i
$599$	−8.45633			−0.345516			−0.172758	−	0.984964i	$-0.555268\pi$
$599$	−8.45633			−0.345516			−0.172758	+	0.984964i	$0.555268\pi$
$600$		0			0
$601$	12.5674	−	27.5187i	0.512634	−	1.12251i	−0.459520	−	0.888167i	$-0.651979\pi$
$601$	12.5674	−	27.5187i	0.512634	−	1.12251i	0.972154	−	0.234344i	$-0.0752941\pi$
$602$	4.71770	−	1.38524i	0.192279	−	0.0564582i
$603$	27.3422	−	31.5546i	1.11346	−	1.28500i
$604$	0.292573	+	0.0859072i	0.0119046	+	0.00349552i
$605$		0			0
$606$	−0.905286	−	1.98230i	−0.0367747	−	0.0805254i
$607$	19.1983	+	22.1560i	0.779235	+	0.899286i	0.997054	−	0.0767037i	$-0.0244395\pi$
$607$	19.1983	+	22.1560i	0.779235	+	0.899286i	−0.217819	+	0.975989i	$0.569894\pi$
$608$	8.68987	+	5.58464i	0.352421	+	0.226487i
$609$	0.113433	−	0.788942i	0.00459653	−	0.0319695i
$610$		0			0
$611$	−8.17908	−	5.25637i	−0.330890	−	0.212650i
$612$	−1.17334	−	1.35411i	−0.0474296	−	0.0547367i
$613$	3.03888	+	6.65422i	0.122739	+	0.268761i	0.961021	−	0.276476i	$-0.0891667\pi$
$613$	3.03888	+	6.65422i	0.122739	+	0.268761i	−0.838282	+	0.545238i	$0.816439\pi$
$614$	−33.3024	+	21.4022i	−1.34398	+	0.863721i
$615$		0			0
$616$	−4.89530	+	5.64947i	−0.197237	+	0.227624i
$617$	12.9847	−	3.81264i	0.522743	−	0.153491i	−0.00970688	−	0.999953i	$-0.503090\pi$
$617$	12.9847	−	3.81264i	0.522743	−	0.153491i	0.532449	+	0.846462i	$0.321272\pi$
$618$	0.522920	−	1.14504i	0.0210349	−	0.0460601i
$619$	−6.62810	−	46.0994i	−0.266406	−	1.85289i	−0.481691	−	0.876341i	$-0.659977\pi$
$619$	−6.62810	−	46.0994i	−0.266406	−	1.85289i	0.215285	−	0.976551i	$-0.430932\pi$
$620$		0			0
$621$	−0.436122	+	7.13227i	−0.0175010	+	0.286208i
$622$	24.8686			0.997140
$623$	1.01838	+	7.08302i	0.0408007	+	0.283775i
$624$	−0.459485	+	1.00613i	−0.0183941	+	0.0402775i
$625$		0			0
$626$	−19.3247	+	22.3019i	−0.772372	+	0.891365i
$627$	−2.45774	−	0.721656i	−0.0981525	−	0.0288202i
$628$	−0.211264	+	0.135771i	−0.00843034	+	0.00541785i
$629$	−2.93369	−	6.42389i	−0.116974	−	0.256137i
$630$		0			0
$631$	−15.3687	−	9.87684i	−0.611817	−	0.393191i	0.197721	−	0.980258i	$-0.436646\pi$
$631$	−15.3687	−	9.87684i	−0.611817	−	0.393191i	−0.809538	+	0.587068i	$0.800282\pi$
$632$	0.298693	−	2.07745i	0.0118814	−	0.0826366i
$633$	−0.0512482	+	0.356439i	−0.00203693	+	0.0141672i
$634$	−27.6653	−	17.7794i	−1.09873	−	0.706111i
$635$		0			0
$636$	−0.500877	−	1.09677i	−0.0198611	−	0.0434897i
$637$	−7.05638	+	4.53486i	−0.279584	+	0.179678i
$638$	−7.69201	−	2.25858i	−0.304530	−	0.0894180i
$639$	−4.16205	+	4.80326i	−0.164648	+	0.190014i
$640$		0			0
$641$	5.65791	−	12.3891i	0.223474	−	0.489339i	−0.764372	−	0.644775i	$-0.776951\pi$
$641$	5.65791	−	12.3891i	0.223474	−	0.489339i	0.987846	+	0.155436i	$0.0496782\pi$
$642$	−0.491101	−	3.41568i	−0.0193822	−	0.134806i
$643$	−14.5439			−0.573556			−0.286778	−	0.957997i	$-0.592584\pi$
$643$	−14.5439			−0.573556			−0.286778	+	0.957997i	$0.592584\pi$
$644$	−1.04848	−	1.87387i	−0.0413158	−	0.0738408i
$645$		0			0
$646$	−1.25194	−	8.70746i	−0.0492570	−	0.342590i
$647$	0.306918	−	0.672056i	0.0120662	−	0.0264212i	−0.903503	−	0.428582i	$-0.859013\pi$
$647$	0.306918	−	0.672056i	0.0120662	−	0.0264212i	0.915569	+	0.402161i	$0.131741\pi$
$648$	−24.5843	+	7.21861i	−0.965763	+	0.283574i
$649$	−18.3770	+	21.2082i	−0.721359	+	0.832493i
$650$		0			0
$651$	−1.20206	+	0.772515i	−0.0471123	+	0.0302773i
$652$	−3.06035	−	6.70122i	−0.119852	−	0.262440i
$653$	12.4101	+	14.3220i	0.485645	+	0.560464i	0.944697	−	0.327945i	$-0.106356\pi$
$653$	12.4101	+	14.3220i	0.485645	+	0.560464i	−0.459052	+	0.888410i	$0.651811\pi$
$654$	2.31896	+	1.49031i	0.0906786	+	0.0582756i
$655$		0			0
$656$	−4.13231	+	28.7408i	−0.161340	+	1.12214i
$657$	−10.9510	−	7.03775i	−0.427237	−	0.274569i
$658$	6.14092	+	7.08700i	0.239398	+	0.276280i
$659$	7.45644	+	16.3273i	0.290462	+	0.636023i	0.997463	−	0.0711899i	$-0.0226796\pi$
$659$	7.45644	+	16.3273i	0.290462	+	0.636023i	−0.707001	+	0.707213i	$0.749952\pi$
$660$		0			0
$661$	−38.9698	−	11.4426i	−1.51575	−	0.445064i	−0.585096	−	0.810964i	$-0.698943\pi$
$661$	−38.9698	−	11.4426i	−1.51575	−	0.445064i	−0.930654	+	0.365900i	$0.880761\pi$
$662$	−0.0955403	+	0.110259i	−0.00371328	+	0.00428535i
$663$	−0.529659	+	0.155522i	−0.0205703	+	0.00603997i
$664$	14.6432	−	32.0640i	0.568265	−	1.24433i
$665$		0			0
$666$	−17.3279			−0.671442
$667$	8.10901	−	11.0688i	0.313982	−	0.428587i
$668$	5.71985			0.221308
$669$	0.0486253	+	0.338196i	0.00187996	+	0.0130754i
$670$		0			0
$671$	−7.94561	+	2.33304i	−0.306737	+	0.0900661i
$672$	−0.409414	+	0.472489i	−0.0157935	+	0.0182267i
$673$	24.7557	+	7.26894i	0.954264	+	0.280197i	0.721561	−	0.692351i	$-0.243425\pi$
$673$	24.7557	+	7.26894i	0.954264	+	0.280197i	0.232703	+	0.972548i	$0.425243\pi$
$674$	10.9475	−	7.03552i	0.421681	−	0.270998i
$675$		0			0
$676$	−2.87508	−	3.31802i	−0.110580	−	0.127616i
$677$	23.5192	+	15.1149i	0.903916	+	0.580911i	0.907949	−	0.419081i	$-0.137648\pi$
$677$	23.5192	+	15.1149i	0.903916	+	0.580911i	−0.00403344	+	0.999992i	$0.501284\pi$
$678$	−0.133985	+	0.931884i	−0.00514565	+	0.0357888i
$679$	−2.11988	+	14.7441i	−0.0813537	+	0.565827i
$680$		0			0
$681$	0.306959	+	0.354250i	0.0117627	+	0.0135749i
$682$	5.97022	+	13.0730i	0.228612	+	0.500590i
$683$	−27.6000	+	17.7375i	−1.05609	+	0.678705i	−0.948914	−	0.315535i	$-0.897816\pi$
$683$	−27.6000	+	17.7375i	−1.05609	+	0.678705i	−0.107172	+	0.994240i	$0.534180\pi$
$684$	5.23174	+	1.53618i	0.200041	+	0.0587372i
$685$		0			0
$686$	17.1835	−	5.04554i	0.656070	−	0.192639i
$687$	−0.477188	+	1.04490i	−0.0182059	+	0.0398653i
$688$	−1.51188	−	10.5154i	−0.0576399	−	0.400894i
$689$	17.3230			0.659952
$690$		0			0
$691$	41.5822			1.58186			0.790931	−	0.611905i	$-0.209597\pi$
$691$	41.5822			1.58186			0.790931	+	0.611905i	$0.209597\pi$
$692$	−0.807891	−	5.61900i	−0.0307114	−	0.213602i
$693$	−3.00329	+	6.57629i	−0.114086	+	0.249813i
$694$	20.5483	−	6.03353i	0.780003	−	0.229030i
$695$		0			0
$696$	−2.09219	−	0.614324i	−0.0793044	−	0.0232859i
$697$	−12.1909	+	7.83460i	−0.461762	+	0.296757i
$698$	10.2031	+	22.3417i	0.386193	+	0.845646i
$699$	4.85726	+	5.60558i	0.183719	+	0.212023i
$700$		0			0
$701$	1.19274	−	8.29572i	0.0450493	−	0.313325i	−0.954820	−	0.297183i	$-0.903953\pi$
$701$	1.19274	−	8.29572i	0.0450493	−	0.313325i	0.999870	−	0.0161415i	$-0.00513821\pi$
$702$	−0.389655	+	2.71011i	−0.0147066	+	0.102286i
$703$	18.0796	+	11.6190i	0.681883	+	0.438220i
$704$	12.9197	+	14.9101i	0.486929	+	0.561946i
$705$		0			0
$706$	−16.3709	+	10.5210i	−0.616128	+	0.395961i
$707$	7.31952	+	2.14920i	0.275279	+	0.0808291i
$708$	−0.838862	+	0.968099i	−0.0315264	+	0.0363834i
$709$	13.8754	−	4.07419i	0.521102	−	0.153009i	−0.0105950	−	0.999944i	$-0.503373\pi$
$709$	13.8754	−	4.07419i	0.521102	−	0.153009i	0.531697	+	0.846934i	$0.321554\pi$
$710$		0			0
$711$	−0.288875	−	2.00917i	−0.0108337	−	0.0753497i
$712$	19.5764			0.733657
$713$	−24.5163	+	2.00814i	−0.918142	+	0.0752054i
$714$	0.532429			0.0199257
$715$		0			0
$716$	−0.649701	+	1.42265i	−0.0242805	+	0.0531668i
$717$	−5.63859	+	1.65564i	−0.210577	+	0.0618310i
$718$	−13.6355	+	15.7362i	−0.508872	+	0.587270i
$719$	−17.9551	−	5.27210i	−0.669613	−	0.196616i	−0.0707825	−	0.997492i	$-0.522550\pi$
$719$	−17.9551	−	5.27210i	−0.669613	−	0.196616i	−0.598831	+	0.800876i	$0.704368\pi$
$720$		0			0
$721$	1.83051	+	4.00826i	0.0681718	+	0.149275i
$722$	1.80916	+	2.08788i	0.0673299	+	0.0777028i
$723$	3.77651	+	2.42702i	0.140450	+	0.0902617i
$724$	0.600543	−	4.17687i	0.0223190	−	0.155232i
$725$		0			0
$726$	1.62272	+	1.04286i	0.0602246	+	0.0387040i
$727$	−8.27804	−	9.55337i	−0.307016	−	0.354315i	0.581184	−	0.813772i	$-0.302590\pi$
$727$	−8.27804	−	9.55337i	−0.307016	−	0.354315i	−0.888200	+	0.459457i	$0.848044\pi$
$728$	−2.03658	−	4.45949i	−0.0754807	−	0.165280i
$729$	−19.9026	+	12.7906i	−0.737133	+	0.473727i
$730$		0			0
$731$	3.47201	−	4.00692i	0.128417	−	0.148201i
$732$	−0.362697	+	0.106497i	−0.0134057	+	0.00393626i
$733$	−11.2480	+	24.6297i	−0.415455	+	0.909720i	0.580011	+	0.814608i	$0.303048\pi$
$733$	−11.2480	+	24.6297i	−0.415455	+	0.909720i	−0.995467	+	0.0951119i	$0.969679\pi$
$734$	−3.64649	−	25.3619i	−0.134594	−	0.936125i
$735$		0			0
$736$	−10.0447	+	3.86513i	−0.370254	+	0.142471i
$737$	−31.5237			−1.16119
$738$	5.06024	+	35.1948i	0.186270	+	1.29554i
$739$	−7.81374	+	17.1097i	−0.287433	+	0.629391i	−0.997178	−	0.0750677i	$-0.976083\pi$
$739$	−7.81374	+	17.1097i	−0.287433	+	0.629391i	0.709745	+	0.704458i	$0.248810\pi$
$740$		0			0
$741$	1.10010	−	1.26958i	0.0404132	−	0.0466393i
$742$	−16.0314	−	4.70724i	−0.588531	−	0.172808i
$743$	15.8615	−	10.1936i	0.581903	−	0.373966i	−0.216325	−	0.976321i	$-0.569407\pi$
$743$	15.8615	−	10.1936i	0.581903	−	0.373966i	0.798228	+	0.602355i	$0.205771\pi$
$744$	1.62387	+	3.55579i	0.0595341	+	0.130362i
$745$		0			0
$746$	−10.8036	−	6.94306i	−0.395549	−	0.254204i
$747$	4.85163	−	33.7439i	0.177512	−	1.23462i
$748$	−0.192521	+	1.33902i	−0.00703928	+	0.0489593i
$749$	10.1621	+	6.53081i	0.371316	+	0.238630i
$750$		0			0
$751$	14.5630	+	31.8886i	0.531412	+	1.16363i	0.964935	+	0.262488i	$0.0845430\pi$
$751$	14.5630	+	31.8886i	0.531412	+	1.16363i	−0.433523	+	0.901142i	$0.642730\pi$
$752$	17.0447	−	10.9540i	0.621557	−	0.399451i
$753$	−6.14438	−	1.80415i	−0.223914	−	0.0657470i
$754$	3.44300	−	3.97343i	0.125387	−	0.144704i
$755$		0			0
$756$	−0.277125	+	0.606819i	−0.0100789	+	0.0220698i
$757$	2.65301	+	18.4521i	0.0964252	+	0.670652i	0.979504	+	0.201426i	$0.0645577\pi$
$757$	2.65301	+	18.4521i	0.0964252	+	0.670652i	−0.883078	+	0.469225i	$0.844533\pi$
$758$	−29.0376			−1.05469
$759$	2.11992	−	1.62138i	0.0769481	−	0.0588524i
$760$		0			0
$761$	0.566333	+	3.93893i	0.0205295	+	0.142786i	0.997508	−	0.0705511i	$-0.0224758\pi$
$761$	0.566333	+	3.93893i	0.0205295	+	0.142786i	−0.976979	+	0.213337i	$0.931567\pi$
$762$	2.45761	−	5.38141i	0.0890297	−	0.194948i
$763$	−9.25861	+	2.71857i	−0.335184	+	0.0984189i
$764$	−2.27086	+	2.62071i	−0.0821569	+	0.0948141i
$765$		0			0
$766$	14.6951	−	9.44394i	0.530954	−	0.341223i
$767$	−7.64534	−	16.7410i	−0.276057	−	0.604481i
$768$	1.52182	+	1.75628i	0.0549141	+	0.0633742i
$769$	13.4271	+	8.62904i	0.484192	+	0.311171i	0.759866	−	0.650080i	$-0.225265\pi$
$769$	13.4271	+	8.62904i	0.484192	+	0.311171i	−0.275674	+	0.961251i	$0.588901\pi$
$770$		0			0
$771$	0.0581615	−	0.404522i	0.00209464	−	0.0145685i
$772$	3.53912	+	2.27445i	0.127376	+	0.0818594i
$773$	−12.1253	−	13.9933i	−0.436116	−	0.503305i	0.494563	−	0.869142i	$-0.335328\pi$
$773$	−12.1253	−	13.9933i	−0.436116	−	0.503305i	−0.930679	+	0.365837i	$0.880783\pi$
$774$	−5.40415	−	11.8334i	−0.194248	−	0.425345i
$775$		0			0
$776$	39.0999	+	11.4808i	1.40360	+	0.412135i
$777$	−0.851799	+	0.983029i	−0.0305581	+	0.0352660i
$778$	35.4903	−	10.4209i	1.27239	−	0.373607i
$779$	18.3197	−	40.1145i	0.656371	−	1.43725i
$780$		0			0
$781$	4.79855			0.171706
$782$	8.08956	+	4.30938i	0.289282	+	0.154103i
$783$	−4.26292			−0.152344
$784$	−2.48766	−	17.3021i	−0.0888450	−	0.617931i
$785$		0			0
$786$	−2.67861	+	0.786510i	−0.0955428	+	0.0280539i
$787$	−31.8728	+	36.7832i	−1.13614	+	1.31118i	−0.192093	+	0.981377i	$0.561528\pi$
$787$	−31.8728	+	36.7832i	−1.13614	+	1.31118i	−0.944050	+	0.329802i	$0.893018\pi$
$788$	4.25772	+	1.25018i	0.151675	+	0.0445358i
$789$	−2.37680	+	1.52748i	−0.0846163	+	0.0543796i
$790$		0			0
$791$	−2.15820	−	2.49069i	−0.0767366	−	0.0885588i
$792$	16.6385	+	10.6929i	0.591223	+	0.379956i
$793$	0.772903	−	5.37566i	0.0274466	−	0.190895i
$794$	−5.62385	+	39.1147i	−0.199583	+	1.38813i
$795$		0			0
$796$	5.27417	+	6.08672i	0.186938	+	0.215738i
$797$	5.46377	+	11.9640i	0.193537	+	0.423786i	0.981377	−	0.192094i	$-0.0615278\pi$
$797$	5.46377	+	11.9640i	0.193537	+	0.423786i	−0.787840	+	0.615880i	$0.788801\pi$
$798$	−1.36307	+	0.875990i	−0.0482520	+	0.0310097i
$799$	9.70220	+	2.84882i	0.343239	+	0.100784i
$800$		0			0
$801$	18.1660	−	5.33403i	0.641866	−	0.188469i
$802$	−8.17240	+	17.8951i	−0.288577	+	0.631896i
$803$	1.39871	+	9.72824i	0.0493594	+	0.343302i
$804$	−1.43898			−0.0507487
$805$		0			0
$806$	−9.42536			−0.331994
$807$	0.650907	+	4.52716i	0.0229130	+	0.159363i
$808$	8.66951	−	18.9836i	0.304992	−	0.667840i
$809$	12.9550	−	3.80394i	0.455475	−	0.133739i	−0.0459443	−	0.998944i	$-0.514630\pi$
$809$	12.9550	−	3.80394i	0.455475	−	0.133739i	0.501419	+	0.865205i	$0.332812\pi$
$810$		0			0
$811$	−1.85713	−	0.545304i	−0.0652128	−	0.0191482i	0.248963	−	0.968513i	$-0.419910\pi$
$811$	−1.85713	−	0.545304i	−0.0652128	−	0.0191482i	−0.314176	+	0.949365i	$0.601728\pi$
$812$	1.07765	−	0.692565i	0.0378182	−	0.0243043i
$813$	1.44155	+	3.15655i	0.0505574	+	0.110705i
$814$	8.56736	+	9.88727i	0.300286	+	0.346548i
$815$		0			0
$816$	0.163716	−	1.13867i	0.00573120	−	0.0398614i
$817$	−2.29621	+	15.9705i	−0.0803341	+	0.558736i
$818$	35.6674	+	22.9221i	1.24708	+	0.801451i
$819$	−3.10494	−	3.58330i	−0.108496	−	0.125211i
$820$		0			0
$821$	2.30770	−	1.48307i	0.0805394	−	0.0517595i	−0.499751	−	0.866169i	$-0.666575\pi$
$821$	2.30770	−	1.48307i	0.0805394	−	0.0517595i	0.580291	+	0.814409i	$0.302939\pi$
$822$	−6.86008	−	2.01430i	−0.239273	−	0.0702569i
$823$	−11.1113	+	12.8231i	−0.387316	+	0.446987i	−0.915606	−	0.402078i	$-0.868288\pi$
$823$	−11.1113	+	12.8231i	−0.387316	+	0.446987i	0.528289	+	0.849064i	$0.322834\pi$
$824$	11.5666	−	3.39625i	0.402940	−	0.118314i
$825$		0			0
$826$	2.52622	+	17.5703i	0.0878986	+	0.611348i
$827$	46.7763			1.62657			0.813286	−	0.581864i	$-0.197676\pi$
$827$	46.7763			1.62657			0.813286	+	0.581864i	$0.197676\pi$
$828$	−4.51263	+	3.45141i	−0.156825	+	0.119945i
$829$	14.1933			0.492955			0.246478	−	0.969148i	$-0.420727\pi$
$829$	14.1933			0.492955			0.246478	+	0.969148i	$0.420727\pi$
$830$		0			0
$831$	1.92197	−	4.20853i	0.0666725	−	0.145992i
$832$	−12.4147	+	3.64527i	−0.430401	+	0.126377i
$833$	5.71288	−	6.59302i	0.197940	−	0.228434i
$834$	2.60290	+	0.764281i	0.0901311	+	0.0264649i
$835$		0			0
$836$	−1.71017	−	3.74475i	−0.0591475	−	0.129515i
$837$	5.00456	+	5.77557i	0.172983	+	0.199633i
$838$	12.0241	+	7.72741i	0.415365	+	0.266939i
$839$	−3.36859	+	23.4291i	−0.116297	+	0.808861i	0.845280	+	0.534324i	$0.179434\pi$
$839$	−3.36859	+	23.4291i	−0.116297	+	0.808861i	−0.961577	+	0.274537i	$0.911475\pi$
$840$		0			0
$841$	−17.5100	−	11.2530i	−0.603791	−	0.388033i
$842$	−5.05499	−	5.83376i	−0.174206	−	0.201045i
$843$	2.69111	+	5.89271i	0.0926867	+	0.202956i
$844$	−0.486876	+	0.312896i	−0.0167590	+	0.0107703i
$845$		0			0
$846$	16.2477	−	18.7508i	0.558606	−	0.644666i
$847$	−6.47880	+	1.90235i	−0.222614	+	0.0653654i
$848$	−14.9965	+	32.8378i	−0.514982	+	1.12765i
$849$	0.0996952	+	0.693395i	0.00342153	+	0.0237973i
$850$		0			0
$851$	−20.8984	+	8.04154i	−0.716389	+	0.275660i
$852$	0.219042			0.00750425
$853$	−3.01690	−	20.9830i	−0.103297	−	0.718444i	−0.973986	−	0.226610i	$-0.927236\pi$
$853$	−3.01690	−	20.9830i	−0.103297	−	0.718444i	0.870689	−	0.491834i	$-0.163673\pi$
$854$	−2.17603	+	4.76483i	−0.0744621	+	0.163049i
$855$		0			0
$856$	21.6411	−	24.9751i	0.739677	−	0.853632i
$857$	−8.26379	−	2.42647i	−0.282286	−	0.0828866i	0.137525	−	0.990498i	$-0.456085\pi$
$857$	−8.26379	−	2.42647i	−0.282286	−	0.0828866i	−0.419811	+	0.907612i	$0.637903\pi$
$858$	0.860295	−	0.552878i	0.0293700	−	0.0188749i
$859$	−4.11134	−	9.00257i	−0.140277	−	0.307164i	0.826434	−	0.563033i	$-0.190366\pi$
$859$	−4.11134	−	9.00257i	−0.140277	−	0.307164i	−0.966711	+	0.255869i	$0.917638\pi$
$860$		0			0
$861$	2.24538	+	1.44302i	0.0765224	+	0.0491780i
$862$	−4.44042	+	30.8838i	−0.151241	+	1.05191i
$863$	−2.21923	+	15.4351i	−0.0755435	+	0.525417i	0.916550	+	0.399919i	$0.130962\pi$
$863$	−2.21923	+	15.4351i	−0.0755435	+	0.525417i	−0.992094	+	0.125498i	$0.959947\pi$
$864$	2.81293	+	1.80776i	0.0956980	+	0.0615014i
$865$		0			0
$866$	−12.6372	−	27.6716i	−0.429430	−	0.940320i
$867$	−3.10609	+	1.99616i	−0.105488	+	0.0677932i
$868$	−2.20345	−	0.646992i	−0.0747901	−	0.0219603i
$869$	−1.00360	+	1.15822i	−0.0340448	+	0.0392898i
$870$		0			0
$871$	8.58832	−	18.8058i	0.291004	−	0.637210i
$872$	3.75687	+	26.1296i	0.127224	+	0.884860i
$873$	39.4111			1.33387
$874$	−27.8001	+	2.27712i	−0.940353	+	0.0770247i
$875$		0			0
$876$	0.0638476	+	0.444070i	0.00215721	+	0.0150037i
$877$	1.81472	−	3.97367i	0.0612786	−	0.134181i	−0.876515	−	0.481374i	$-0.840138\pi$
$877$	1.81472	−	3.97367i	0.0612786	−	0.134181i	0.937794	+	0.347193i	$0.112865\pi$
$878$	29.3982	−	8.63209i	0.992141	−	0.291319i
$879$	3.29971	−	3.80807i	0.111297	−	0.128443i
$880$		0			0
$881$	−5.55749	+	3.57158i	−0.187236	+	0.120330i	−0.630901	−	0.775863i	$-0.717315\pi$
$881$	−5.55749	+	3.57158i	−0.187236	+	0.120330i	0.443664	+	0.896193i	$0.353678\pi$
$882$	−8.89205	−	19.4709i	−0.299411	−	0.655618i
$883$	22.6003	+	26.0821i	0.760559	+	0.877732i	0.995547	−	0.0942662i	$-0.0300505\pi$
$883$	22.6003	+	26.0821i	0.760559	+	0.877732i	−0.234988	+	0.971998i	$0.575505\pi$
$884$	−0.746355	−	0.479653i	−0.0251026	−	0.0161325i
$885$		0			0
$886$	0.580932	−	4.04047i	0.0195168	−	0.135742i
$887$	3.39108	+	2.17932i	0.113861	+	0.0731743i	0.596332	−	0.802738i	$-0.296624\pi$
$887$	3.39108	+	2.17932i	0.113861	+	0.0731743i	−0.482471	+	0.875912i	$0.660260\pi$
$888$	2.33029	+	2.68929i	0.0781993	+	0.0902468i
$889$	8.60299	+	18.8379i	0.288535	+	0.631804i
$890$		0			0
$891$	17.9513	+	5.27098i	0.601391	+	0.176584i
$892$	−0.359604	+	0.415005i	−0.0120404	+	0.0138954i
$893$	−29.5256	+	8.66950i	−0.988036	+	0.290114i
$894$	−2.22448	+	4.87094i	−0.0743978	+	0.162908i
$895$		0			0
$896$	7.49719			0.250464
$897$	0.389703	+	1.70639i	0.0130118	+	0.0569747i
$898$	−17.3822			−0.580051
$899$	−2.08846	−	14.5255i	−0.0696540	−	0.484454i
$900$		0			0
$901$	−17.2868	+	5.07587i	−0.575907	+	0.169102i
$902$	17.5801	−	20.2886i	0.585355	−	0.675536i
$903$	−0.936979	−	0.275122i	−0.0311807	−	0.00915548i
$904$	−7.58474	+	4.87442i	−0.252265	+	0.162121i
$905$		0			0
$906$	0.156994	+	0.181181i	0.00521579	+	0.00601934i
$907$	−24.6750	−	15.8577i	−0.819322	−	0.526546i	0.0625466	−	0.998042i	$-0.480078\pi$
$907$	−24.6750	−	15.8577i	−0.819322	−	0.526546i	−0.881868	+	0.471496i	$0.843714\pi$
$908$	−0.107212	+	0.745679i	−0.00355797	+	0.0247462i
$909$	2.87242	−	19.9781i	0.0952722	−	0.662632i
$910$		0			0
$911$	0.0171162	+	0.0197532i	0.000567086	+	0.000654452i	0.756033	−	0.654533i	$-0.227135\pi$
$911$	0.0171162	+	0.0197532i	0.000567086	+	0.000654452i	−0.755466	+	0.655188i	$0.772589\pi$
$912$	1.45429	+	3.18445i	0.0481563	+	0.105448i
$913$	−21.6530	+	13.9155i	−0.716608	+	0.460536i
$914$	30.8304	+	9.05262i	1.01978	+	0.299434i
$915$		0			0
$916$	−1.77139	+	0.520126i	−0.0585282	+	0.0171854i
$917$	4.05963	−	8.88935i	0.134061	−	0.293552i
$918$	−0.405257	−	2.81863i	−0.0133755	−	0.0930286i
$919$	0.764083			0.0252048			0.0126024	−	0.999921i	$-0.495988\pi$
$919$	0.764083			0.0252048			0.0126024	+	0.999921i	$0.495988\pi$
$920$		0			0
$921$	7.86228			0.259071
$922$	3.29467	+	22.9149i	0.108504	+	0.754663i
$923$	−1.30732	+	2.86263i	−0.0430310	+	0.0942247i
$924$	0.239071	−	0.0701975i	0.00786485	−	0.00230933i
$925$		0			0
$926$	−15.9322	−	4.67811i	−0.523564	−	0.153732i
$927$	9.80787	−	6.30313i	0.322133	−	0.207022i
$928$	−2.66731	−	5.84059i	−0.0875587	−	0.191727i
$929$	−9.07791	−	10.4765i	−0.297837	−	0.343722i	0.587031	−	0.809564i	$-0.300297\pi$
$929$	−9.07791	−	10.4765i	−0.297837	−	0.343722i	−0.884867	+	0.465843i	$0.845751\pi$
$930$		0			0
$931$	−3.77820	+	26.2779i	−0.123825	+	0.861225i
$932$	−1.69651	+	11.7995i	−0.0555711	+	0.386505i
$933$	−4.15507	−	2.67030i	−0.136031	−	0.0874216i
$934$	7.26188	+	8.38065i	0.237616	+	0.274223i
$935$		0			0
$936$	−10.9120	+	7.01271i	−0.356669	+	0.229217i
$937$	−51.7354	−	15.1909i	−1.69012	−	0.496264i	−0.711631	−	0.702554i	$-0.752043\pi$
$937$	−51.7354	−	15.1909i	−1.69012	−	0.496264i	−0.978491	+	0.206289i	$0.933861\pi$
$938$	−13.0582	+	15.0699i	−0.426364	+	0.492051i
$939$	5.62349	−	1.65121i	0.183516	−	0.0538851i
$940$		0			0
$941$	−4.99056	−	34.7101i	−0.162687	−	1.13152i	−0.893541	−	0.448982i	$-0.851787\pi$
$941$	−4.99056	−	34.7101i	−0.162687	−	1.13152i	0.730853	−	0.682534i	$-0.239122\pi$
$942$	−0.197443			−0.00643303
$943$	22.4361	+	40.0985i	0.730621	+	1.30579i
$944$	38.3531			1.24829
$945$		0			0
$946$	−4.08019	+	8.93437i	−0.132658	+	0.290481i
$947$	24.1188	−	7.08193i	0.783757	−	0.230132i	0.134715	−	0.990884i	$-0.456988\pi$
$947$	24.1188	−	7.08193i	0.783757	−	0.230132i	0.649042	+	0.760752i	$0.275170\pi$
$948$	−0.0458118	+	0.0528697i	−0.00148790	+	0.00171713i
$949$	−6.18456	−	1.81595i	−0.200759	−	0.0589483i
$950$		0			0
$951$	2.71326	+	5.94120i	0.0879834	+	0.192657i
$952$	3.33902	+	3.85344i	0.108218	+	0.124891i
$953$	−14.3975	−	9.25271i	−0.466381	−	0.299725i	0.286265	−	0.958151i	$-0.407586\pi$
$953$	−14.3975	−	9.25271i	−0.466381	−	0.299725i	−0.752646	+	0.658426i	$0.771223\pi$
$954$	−6.29125	+	43.7566i	−0.203687	+	1.41667i
$955$		0			0
$956$	−7.94547	−	5.10624i	−0.256975	−	0.165148i
$957$	1.04267	+	1.20331i	0.0337047	+	0.0388973i
$958$	17.4138	+	38.1310i	0.562616	+	1.23196i
$959$	21.0548	−	13.5311i	0.679896	−	0.436942i
$960$		0			0
$961$	3.07270	−	3.54609i	0.0991194	−	0.114390i
$962$	−8.23246	+	2.41727i	−0.265425	+	0.0779359i
$963$	13.2769	−	29.0724i	0.427843	−	0.936845i
$964$	1.02678	+	7.14142i	0.0330704	+	0.230010i
$965$		0			0
$966$	0.103038	−	1.68506i	0.00331518	−	0.0542159i
$967$	48.0304			1.54455			0.772277	−	0.635286i	$-0.219118\pi$
$967$	48.0304			1.54455			0.772277	+	0.635286i	$0.219118\pi$
$968$	2.62890	+	18.2844i	0.0844962	+	0.587684i
$969$	−0.725799	+	1.58928i	−0.0233160	+	0.0510550i
$970$		0			0
$971$	−24.1951	+	27.9226i	−0.776457	+	0.896079i	−0.996848	−	0.0793324i	$-0.974721\pi$
$971$	−24.1951	+	27.9226i	−0.776457	+	0.896079i	0.220391	+	0.975412i	$0.429267\pi$
$972$	2.54928	+	0.748535i	0.0817681	+	0.0240093i
$973$	−7.98877	+	5.13407i	−0.256108	+	0.164591i
$974$	−10.4151	−	22.8058i	−0.333721	−	0.730746i
$975$		0			0
$976$	9.52111	+	6.11885i	0.304763	+	0.195859i
$977$	1.59927	−	11.1232i	0.0511652	−	0.355862i	−0.948115	−	0.317927i	$-0.897013\pi$
$977$	1.59927	−	11.1232i	0.0511652	−	0.355862i	0.999280	−	0.0379343i	$-0.0120778\pi$
$978$	0.824292	−	5.73308i	0.0263580	−	0.183324i
$979$	−12.0254	−	7.72823i	−0.384332	−	0.246995i
$980$		0			0
$981$	10.6058	+	23.2235i	0.338617	+	0.741468i
$982$	−36.1381	+	23.2245i	−1.15321	+	0.741124i
$983$	−41.2206	−	12.1035i	−1.31473	−	0.386041i	−0.452144	−	0.891945i	$-0.649341\pi$
$983$	−41.2206	−	12.1035i	−1.31473	−	0.386041i	−0.862590	+	0.505904i	$0.831159\pi$
$984$	4.78172	−	5.51840i	0.152436	−	0.175920i
$985$		0			0
$986$	−2.27154	+	4.97399i	−0.0723407	+	0.158404i
$987$	−0.265054	−	1.84349i	−0.00843676	−	0.0586790i
$988$	2.69989			0.0858951
$989$	−12.0094	−	11.7638i	−0.381876	−	0.374069i
$990$		0			0
$991$	2.28497	+	15.8923i	0.0725845	+	0.504836i	0.993388	+	0.114809i	$0.0366255\pi$
$991$	2.28497	+	15.8923i	0.0725845	+	0.504836i	−0.920803	+	0.390028i	$0.872465\pi$
$992$	−4.78171	+	10.4705i	−0.151819	+	0.332438i
$993$	0.0278022	−	0.00816346i	0.000882276	−	0.000259060i
$994$	1.98772	−	2.29396i	0.0630468	−	0.0727598i
$995$		0			0
$996$	−0.988403	+	0.635208i	−0.0313187	+	0.0201273i
$997$	−3.81954	−	8.36364i	−0.120966	−	0.264879i	0.839456	−	0.543428i	$-0.182874\pi$
$997$	−3.81954	−	8.36364i	−0.120966	−	0.264879i	−0.960422	+	0.278549i	$0.910147\pi$
$998$	−13.7910	−	15.9157i	−0.436547	−	0.503802i
$999$	5.85240	+	3.76111i	0.185162	+	0.118996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.26.8		100
5.2	odd	4		115.2.j.a.49.3	✓	100
5.3	odd	4		115.2.j.a.49.8	yes	100
5.4	even	2	inner	575.2.k.g.26.3		100
23.8	even	11	inner	575.2.k.g.376.8		100
115.8	odd	44		115.2.j.a.54.3	yes	100
115.54	even	22	inner	575.2.k.g.376.3		100
115.77	odd	44		115.2.j.a.54.8	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.49.3	✓	100	5.2	odd	4
115.2.j.a.49.8	yes	100	5.3	odd	4
115.2.j.a.54.3	yes	100	115.8	odd	44
115.2.j.a.54.8	yes	100	115.77	odd	44
575.2.k.g.26.3		100	5.4	even	2	inner
575.2.k.g.26.8		100	1.1	even	1	trivial
575.2.k.g.376.3		100	115.54	even	22	inner
575.2.k.g.376.8		100	23.8	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.179828 + 1.25073i) q^{2} +(0.104253 - 0.228282i) q^{3} +(0.387001 - 0.113634i) q^{4} +(0.304267 + 0.0893407i) q^{6} +(-0.933848 + 0.600148i) q^{7} +(1.26155 + 2.76240i) q^{8} +(1.92334 + 2.21965i) q^{9} +O(q^{10})\)	\(q+(0.179828 + 1.25073i) q^{2} +(0.104253 - 0.228282i) q^{3} +(0.387001 - 0.113634i) q^{4} +(0.304267 + 0.0893407i) q^{6} +(-0.933848 + 0.600148i) q^{7} +(1.26155 + 2.76240i) q^{8} +(1.92334 + 2.21965i) q^{9} +(0.315580 - 2.19491i) q^{11} +(0.0144054 - 0.100192i) q^{12} +(1.22342 + 0.786244i) q^{13} +(-0.918554 - 1.06007i) q^{14} +(-2.54954 + 1.63849i) q^{16} +(-1.45125 - 0.426125i) q^{17} +(-2.43031 + 2.80473i) q^{18} +(4.41642 - 1.29678i) q^{19} +(0.0396466 + 0.275748i) q^{21} +2.80198 q^{22} +(-1.62947 + 4.51052i) q^{23} +0.762127 q^{24} +(-0.763374 + 1.67156i) q^{26} +(1.42961 - 0.419770i) q^{27} +(-0.293203 + 0.338374i) q^{28} +(-2.74520 - 0.806064i) q^{29} +(2.13071 + 4.66561i) q^{31} +(1.46963 + 1.69604i) q^{32} +(-0.468158 - 0.300867i) q^{33} +(0.271992 - 1.89175i) q^{34} +(0.996560 + 0.640450i) q^{36} +(3.05761 + 3.52867i) q^{37} +(2.41611 + 5.29054i) q^{38} +(0.307031 - 0.197317i) q^{39} +(6.27418 - 7.24079i) q^{41} +(-0.337757 + 0.0991743i) q^{42} +(-1.45618 + 3.18859i) q^{43} +(-0.127286 - 0.885290i) q^{44} +(-5.93447 - 1.22691i) q^{46} -6.68542 q^{47} +(0.108241 + 0.752831i) q^{48} +(-2.39601 + 5.24653i) q^{49} +(-0.248574 + 0.286869i) q^{51} +(0.562808 + 0.165255i) q^{52} +(10.0208 - 6.43995i) q^{53} +(0.782101 + 1.71256i) q^{54} +(-2.83594 - 1.82255i) q^{56} +(0.164393 - 1.14338i) q^{57} +(0.514505 - 3.57846i) q^{58} +(-10.6462 - 6.84187i) q^{59} +(-1.55135 - 3.39697i) q^{61} +(-5.45225 + 3.50395i) q^{62} +(-3.12822 - 0.918530i) q^{63} +(-5.82630 + 6.72391i) q^{64} +(0.292115 - 0.639643i) q^{66} +(-2.02315 - 14.0713i) q^{67} -0.610056 q^{68} +(0.859794 + 0.842215i) q^{69} +(0.307965 + 2.14194i) q^{71} +(-3.70519 + 8.11323i) q^{72} +(-4.25266 + 1.24869i) q^{73} +(-3.86356 + 4.45879i) q^{74} +(1.56180 - 1.00371i) q^{76} +(1.02256 + 2.23910i) q^{77} +(0.302002 + 0.348529i) q^{78} +(-0.581406 - 0.373647i) q^{79} +(-1.20073 + 8.35126i) q^{81} +(10.1845 + 6.54520i) q^{82} +(-7.60116 - 8.77221i) q^{83} +(0.0466775 + 0.102209i) q^{84} +(-4.24992 - 1.24789i) q^{86} +(-0.470206 + 0.542646i) q^{87} +(6.46134 - 1.89722i) q^{88} +(2.67790 - 5.86378i) q^{89} -1.61435 q^{91} +(-0.118060 + 1.93074i) q^{92} +1.28721 q^{93} +(-1.20222 - 8.36165i) q^{94} +(0.540389 - 0.158672i) q^{96} +(8.78742 - 10.1412i) q^{97} +(-6.99286 - 2.05329i) q^{98} +(5.47889 - 3.52107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more