LMFDB - Embedded newform 125.2.h.a.104.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			104.7
Character	$\chi$	$=$	125.104
Dual form			125.2.h.a.119.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0406317 + 0.158250i) q^{2} +(1.60542 - 0.306251i) q^{3} +(1.72922 - 0.950647i) q^{4} +(-2.21878 + 0.277488i) q^{5} +(0.113695 + 0.241615i) q^{6} +(0.875585 - 1.20514i) q^{7} +(0.444388 + 0.473226i) q^{8} +(-0.305740 + 0.121051i) q^{9} +O(q^{10})$	\(q+(0.0406317 + 0.158250i) q^{2} +(1.60542 - 0.306251i) q^{3} +(1.72922 - 0.950647i) q^{4} +(-2.21878 + 0.277488i) q^{5} +(0.113695 + 0.241615i) q^{6} +(0.875585 - 1.20514i) q^{7} +(0.444388 + 0.473226i) q^{8} +(-0.305740 + 0.121051i) q^{9} +(-0.134066 - 0.339848i) q^{10} +(-4.14806 + 1.06504i) q^{11} +(2.48499 - 2.05576i) q^{12} +(1.43255 + 3.61820i) q^{13} +(0.226290 + 0.0895946i) q^{14} +(-3.47710 + 1.12499i) q^{15} +(2.05787 - 3.24268i) q^{16} +(1.44547 - 2.62930i) q^{17} +(-0.0315791 - 0.0434649i) q^{18} +(-0.997848 + 5.23090i) q^{19} +(-3.57297 + 2.58912i) q^{20} +(1.03661 - 2.20291i) q^{21} +(-0.337085 - 0.613156i) q^{22} +(2.26254 + 0.142347i) q^{23} +(0.858356 + 0.623632i) q^{24} +(4.84600 - 1.23137i) q^{25} +(-0.514374 + 0.373715i) q^{26} +(-4.59360 + 2.91519i) q^{27} +(0.368418 - 2.91633i) q^{28} +(-4.03691 - 0.509980i) q^{29} +(-0.319310 - 0.504542i) q^{30} +(-7.84067 - 4.31044i) q^{31} +(1.83157 + 0.595112i) q^{32} +(-6.33321 + 2.98018i) q^{33} +(0.474819 + 0.121913i) q^{34} +(-1.60832 + 2.91691i) q^{35} +(-0.413616 + 0.499975i) q^{36} +(-5.64154 - 3.58023i) q^{37} +(-0.868336 + 0.0546310i) q^{38} +(3.40792 + 5.37002i) q^{39} +(-1.11732 - 0.926672i) q^{40} +(-0.106594 - 1.69427i) q^{41} +(0.390729 + 0.0745356i) q^{42} +(3.75815 - 1.22110i) q^{43} +(-6.16043 + 5.78503i) q^{44} +(0.644781 - 0.353425i) q^{45} +(0.0694046 + 0.363831i) q^{46} +(8.41038 - 8.95615i) q^{47} +(2.31067 - 5.83610i) q^{48} +(1.47741 + 4.54699i) q^{49} +(0.391766 + 0.716848i) q^{50} +(1.51536 - 4.66381i) q^{51} +(5.91683 + 4.89482i) q^{52} +(8.78940 + 4.13598i) q^{53} +(-0.647976 - 0.608490i) q^{54} +(8.90810 - 3.51413i) q^{55} +(0.959402 - 0.121201i) q^{56} +8.70340i q^{57} +(-0.0833222 - 0.659563i) q^{58} +(2.23942 + 2.70700i) q^{59} +(-4.94321 + 5.25085i) q^{60} +(0.0370600 - 0.589052i) q^{61} +(0.363548 - 1.41593i) q^{62} +(-0.121818 + 0.474450i) q^{63} +(0.462543 - 7.35191i) q^{64} +(-4.18252 - 7.63049i) q^{65} +(-0.728944 - 0.881141i) q^{66} +(-0.458471 - 3.62917i) q^{67} -5.92077i q^{68} +(3.67593 - 0.464378i) q^{69} +(-0.526950 - 0.135998i) q^{70} +(0.992574 + 0.932089i) q^{71} +(-0.193152 - 0.0908904i) q^{72} +(3.33869 + 2.76201i) q^{73} +(0.337346 - 1.03825i) q^{74} +(7.40277 - 3.46096i) q^{75} +(3.24724 + 9.99399i) q^{76} +(-2.34845 + 5.93152i) q^{77} +(-0.711337 + 0.757497i) q^{78} +(-2.80389 - 14.6985i) q^{79} +(-3.66616 + 7.76584i) q^{80} +(-5.76277 + 5.41160i) q^{81} +(0.263787 - 0.0857097i) q^{82} +(2.85082 + 0.543823i) q^{83} +(-0.301661 - 4.79476i) q^{84} +(-2.47758 + 6.23495i) q^{85} +(0.345939 + 0.545113i) q^{86} +(-6.63712 + 0.417572i) q^{87} +(-2.34735 - 1.48967i) q^{88} +(0.276132 - 0.333786i) q^{89} +(0.0821282 + 0.0876764i) q^{90} +(5.61476 + 1.44162i) q^{91} +(4.04776 - 1.90473i) q^{92} +(-13.9076 - 4.51887i) q^{93} +(1.75904 + 0.967041i) q^{94} +(0.762496 - 11.8831i) q^{95} +(3.12269 + 0.394488i) q^{96} +(-1.52301 + 12.0559i) q^{97} +(-0.659533 + 0.418552i) q^{98} +(1.13930 - 0.827752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	0.0406317	+	0.158250i	0.0287310	+	0.111900i	0.981331	−	0.192325i	$-0.0616027\pi$
$2$	0.0406317	+	0.158250i	0.0287310	+	0.111900i	−0.952600	+	0.304225i	$0.901603\pi$
$3$	1.60542	−	0.306251i	0.926891	−	0.176814i	0.298230	−	0.954494i	$-0.403604\pi$
$3$	1.60542	−	0.306251i	0.926891	−	0.176814i	0.628660	+	0.777680i	$0.283604\pi$
$4$	1.72922	−	0.950647i	0.864611	−	0.475324i
$5$	−2.21878	+	0.277488i	−0.992270	+	0.124096i
$5$	−2.21878	+	0.277488i	−0.992270	+	0.124096i
$6$	0.113695	+	0.241615i	0.0464159	+	0.0986388i
$7$	0.875585	−	1.20514i	0.330940	−	0.455500i	−0.610828	−	0.791763i	$-0.709163\pi$
$7$	0.875585	−	1.20514i	0.330940	−	0.455500i	0.941768	+	0.336264i	$0.109163\pi$
$8$	0.444388	+	0.473226i	0.157115	+	0.167310i
$9$	−0.305740	+	0.121051i	−0.101913	+	0.0403504i
$10$	−0.134066	−	0.339848i	−0.0423953	−	0.107469i
$11$	−4.14806	+	1.06504i	−1.25069	+	0.321122i	−0.815256	−	0.579101i	$-0.803404\pi$
$11$	−4.14806	+	1.06504i	−1.25069	+	0.321122i	−0.435430	+	0.900223i	$0.643404\pi$
$12$	2.48499	−	2.05576i	0.717356	−	0.593448i
$13$	1.43255	+	3.61820i	0.397317	+	1.00351i	0.981427	+	0.191834i	$0.0614436\pi$
$13$	1.43255	+	3.61820i	0.397317	+	1.00351i	−0.584110	+	0.811674i	$0.698556\pi$
$14$	0.226290	+	0.0895946i	0.0604786	+	0.0239452i
$15$	−3.47710	+	1.12499i	−0.897784	+	0.290471i
$16$	2.05787	−	3.24268i	0.514467	−	0.810671i
$17$	1.44547	−	2.62930i	0.350578	−	0.637699i	−0.640952	−	0.767581i	$-0.721460\pi$
$17$	1.44547	−	2.62930i	0.350578	−	0.637699i	0.991529	+	0.129883i	$0.0414601\pi$
$18$	−0.0315791	−	0.0434649i	−0.00744327	−	0.0102448i
$19$	−0.997848	+	5.23090i	−0.228922	+	1.20005i	0.663265	+	0.748385i	$0.269170\pi$
$19$	−0.997848	+	5.23090i	−0.228922	+	1.20005i	−0.892187	+	0.451667i	$0.850830\pi$
$20$	−3.57297	+	2.58912i	−0.798941	+	0.578945i
$21$	1.03661	−	2.20291i	0.226207	−	0.480713i
$22$	−0.337085	−	0.613156i	−0.0718668	−	0.130725i
$23$	2.26254	+	0.142347i	0.471773	+	0.0296814i	0.296898	−	0.954909i	$-0.404048\pi$
$23$	2.26254	+	0.142347i	0.471773	+	0.0296814i	0.174875	+	0.984591i	$0.444048\pi$
$24$	0.858356	+	0.623632i	0.175211	+	0.127298i
$25$	4.84600	−	1.23137i	0.969200	−	0.246274i
$26$	−0.514374	+	0.373715i	−0.100877	+	0.0732915i
$27$	−4.59360	+	2.91519i	−0.884040	+	0.561029i
$28$	0.368418	−	2.91633i	0.0696244	−	0.551134i
$29$	−4.03691	−	0.509980i	−0.749635	−	0.0947009i	−0.258773	−	0.965938i	$-0.583318\pi$
$29$	−4.03691	−	0.509980i	−0.749635	−	0.0947009i	−0.490862	+	0.871237i	$0.663318\pi$
$30$	−0.319310	−	0.504542i	−0.0582978	−	0.0921163i
$31$	−7.84067	−	4.31044i	−1.40823	−	0.774178i	−0.417322	−	0.908758i	$-0.637031\pi$
$31$	−7.84067	−	4.31044i	−1.40823	−	0.774178i	−0.990903	+	0.134580i	$0.957031\pi$
$32$	1.83157	+	0.595112i	0.323778	+	0.105202i
$33$	−6.33321	+	2.98018i	−1.10247	+	0.518783i
$34$	0.474819	+	0.121913i	0.0814308	+	0.0209079i
$35$	−1.60832	+	2.91691i	−0.271856	+	0.493047i
$36$	−0.413616	+	0.499975i	−0.0689359	+	0.0833292i
$37$	−5.64154	−	3.58023i	−0.927463	−	0.588586i	−0.0159571	−	0.999873i	$-0.505080\pi$
$37$	−5.64154	−	3.58023i	−0.927463	−	0.588586i	−0.911506	+	0.411287i	$0.865080\pi$
$38$	−0.868336	+	0.0546310i	−0.140863	+	0.00886233i
$39$	3.40792	+	5.37002i	0.545704	+	0.859892i
$40$	−1.11732	−	0.926672i	−0.176663	−	0.146520i
$41$	−0.106594	−	1.69427i	−0.0166473	−	0.264600i	−0.997543	−	0.0700639i	$-0.977680\pi$
$41$	−0.106594	−	1.69427i	−0.0166473	−	0.264600i	0.980895	−	0.194537i	$-0.0623203\pi$
$42$	0.390729	+	0.0745356i	0.0602908	+	0.0115011i
$43$	3.75815	−	1.22110i	0.573113	−	0.186216i	−0.00810001	−	0.999967i	$-0.502578\pi$
$43$	3.75815	−	1.22110i	0.573113	−	0.186216i	0.581213	+	0.813752i	$0.302578\pi$
$44$	−6.16043	+	5.78503i	−0.928719	+	0.872126i
$45$	0.644781	−	0.353425i	0.0961183	−	0.0526856i
$46$	0.0694046	+	0.363831i	0.0102331	+	0.0536440i
$47$	8.41038	−	8.95615i	1.22678	−	1.30639i	0.289766	−	0.957097i	$-0.406422\pi$
$47$	8.41038	−	8.95615i	1.22678	−	1.30639i	0.937014	−	0.349291i	$-0.113578\pi$
$48$	2.31067	−	5.83610i	0.333517	−	0.842368i
$49$	1.47741	+	4.54699i	0.211058	+	0.649570i
$50$	0.391766	+	0.716848i	0.0554041	+	0.101378i
$51$	1.51536	−	4.66381i	0.212193	−	0.653064i
$52$	5.91683	+	4.89482i	0.820516	+	0.678790i
$53$	8.78940	+	4.13598i	1.20732	+	0.568120i	0.920830	−	0.389964i	$-0.127513\pi$
$53$	8.78940	+	4.13598i	1.20732	+	0.568120i	0.286486	+	0.958084i	$0.407513\pi$
$54$	−0.647976	−	0.608490i	−0.0881783	−	0.0828049i
$55$	8.90810	−	3.51413i	1.20117	−	0.473845i
$56$	0.959402	−	0.121201i	0.128206	−	0.0161961i
$57$			8.70340i			1.15279i
$58$	−0.0833222	−	0.659563i	−0.0109407	−	0.0866048i
$59$	2.23942	+	2.70700i	0.291548	+	0.352421i	0.895868	−	0.444321i	$-0.146555\pi$
$59$	2.23942	+	2.70700i	0.291548	+	0.352421i	−0.604320	+	0.796742i	$0.706555\pi$
$60$	−4.94321	+	5.25085i	−0.638166	+	0.677882i
$61$	0.0370600	−	0.589052i	0.00474505	−	0.0754204i	−0.994942	−	0.100456i	$-0.967970\pi$
$61$	0.0370600	−	0.589052i	0.00474505	−	0.0754204i	0.999687	+	0.0250355i	$0.00796988\pi$
$62$	0.363548	−	1.41593i	0.0461707	−	0.179823i
$63$	−0.121818	+	0.474450i	−0.0153476	+	0.0597751i
$64$	0.462543	−	7.35191i	0.0578179	−	0.918989i
$65$	−4.18252	−	7.63049i	−0.518778	−	0.946446i
$66$	−0.728944	−	0.881141i	−0.0897268	−	0.108461i
$67$	−0.458471	−	3.62917i	−0.0560111	−	0.443374i	−0.995035	−	0.0995226i	$-0.968268\pi$
$67$	−0.458471	−	3.62917i	−0.0560111	−	0.443374i	0.939024	−	0.343851i	$-0.111732\pi$
$68$		−	5.92077i		−	0.717999i
$69$	3.67593	−	0.464378i	0.442530	−	0.0559045i
$70$	−0.526950	−	0.135998i	−0.0629826	−	0.0162549i
$71$	0.992574	+	0.932089i	0.117797	+	0.110619i	0.741207	−	0.671276i	$-0.234253\pi$
$71$	0.992574	+	0.932089i	0.117797	+	0.110619i	−0.623411	+	0.781895i	$0.714253\pi$
$72$	−0.193152	−	0.0908904i	−0.0227632	−	0.0107115i
$73$	3.33869	+	2.76201i	0.390765	+	0.323269i	0.811973	−	0.583695i	$-0.198394\pi$
$73$	3.33869	+	2.76201i	0.390765	+	0.323269i	−0.421208	+	0.906964i	$0.638394\pi$
$74$	0.337346	−	1.03825i	0.0392157	−	0.120694i
$75$	7.40277	−	3.46096i	0.854798	−	0.399637i
$76$	3.24724	+	9.99399i	0.372484	+	1.14639i
$77$	−2.34845	+	5.93152i	−0.267631	+	0.675959i
$78$	−0.711337	+	0.757497i	−0.0805431	+	0.0857697i
$79$	−2.80389	−	14.6985i	−0.315463	−	1.65371i	−0.688011	−	0.725701i	$-0.741516\pi$
$79$	−2.80389	−	14.6985i	−0.315463	−	1.65371i	0.372548	−	0.928013i	$-0.378484\pi$
$80$	−3.66616	+	7.76584i	−0.409889	+	0.868248i
$81$	−5.76277	+	5.41160i	−0.640308	+	0.601289i
$82$	0.263787	−	0.0857097i	0.0291304	−	0.00946505i
$83$	2.85082	+	0.543823i	0.312918	+	0.0596924i	0.341448	−	0.939901i	$-0.389083\pi$
$83$	2.85082	+	0.543823i	0.312918	+	0.0596924i	−0.0285299	+	0.999593i	$0.509083\pi$
$84$	−0.301661	−	4.79476i	−0.0329139	−	0.523151i
$85$	−2.47758	+	6.23495i	−0.268732	+	0.676275i
$86$	0.345939	+	0.545113i	0.0373036	+	0.0587810i
$87$	−6.63712	+	0.417572i	−0.711574	+	0.0447685i
$88$	−2.34735	−	1.48967i	−0.250228	−	0.158800i
$89$	0.276132	−	0.333786i	0.0292699	−	0.0353812i	−0.755675	−	0.654947i	$-0.772691\pi$
$89$	0.276132	−	0.333786i	0.0292699	−	0.0353812i	0.784945	+	0.619565i	$0.212691\pi$
$90$	0.0821282	+	0.0876764i	0.00865707	+	0.00924191i
$91$	5.61476	+	1.44162i	0.588586	+	0.151123i
$92$	4.04776	−	1.90473i	0.422008	−	0.198582i
$93$	−13.9076	−	4.51887i	−1.44216	−	0.468585i
$94$	1.75904	+	0.967041i	0.181431	+	0.0997426i
$95$	0.762496	−	11.8831i	0.0782304	−	1.21918i
$96$	3.12269	+	0.394488i	0.318708	+	0.0402622i
$97$	−1.52301	+	12.0559i	−0.154639	+	1.22409i	0.703509	+	0.710687i	$0.251616\pi$
$97$	−1.52301	+	12.0559i	−0.154639	+	1.22409i	−0.858147	+	0.513404i	$0.828384\pi$
$98$	−0.659533	+	0.418552i	−0.0666229	+	0.0422802i
$99$	1.13930	−	0.827752i	0.114504	−	0.0831922i
$100$	7.20921	−	6.73615i	0.720921	−	0.673615i
$101$	11.0928	+	8.05937i	1.10377	+	0.801937i	0.981672	−	0.190580i	$-0.0610370\pi$
$101$	11.0928	+	8.05937i	1.10377	+	0.801937i	0.122100	+	0.992518i	$0.461037\pi$
$102$	0.799621	+	0.0503079i	0.0791742	+	0.00498122i
$103$	−0.304120	−	0.553192i	−0.0299658	−	0.0545077i	0.860900	−	0.508774i	$-0.169901\pi$
$103$	−0.304120	−	0.553192i	−0.0299658	−	0.0545077i	−0.890866	+	0.454267i	$0.849901\pi$
$104$	−1.07562	+	2.28580i	−0.105473	+	0.224142i
$105$	−1.68873	+	5.17542i	−0.164803	+	0.505069i
$106$	−0.297390	+	1.55898i	−0.0288851	+	0.151421i
$107$	−6.29302	−	8.66160i	−0.608369	−	0.837348i	0.388073	−	0.921629i	$-0.373141\pi$
$107$	−6.29302	−	8.66160i	−0.608369	−	0.837348i	−0.996442	+	0.0842806i	$0.973141\pi$
$108$	−5.17204	+	9.40791i	−0.497680	+	0.905276i
$109$	4.27860	−	6.74200i	0.409816	−	0.645767i	−0.575243	−	0.817982i	$-0.695093\pi$
$109$	4.27860	−	6.74200i	0.409816	−	0.645767i	0.985059	+	0.172216i	$0.0550926\pi$
$110$	0.918063	+	1.26692i	0.0875339	+	0.120796i
$111$	−10.1535	−	4.02005i	−0.963727	−	0.381567i
$112$	−2.10604	−	5.31926i	−0.199003	−	0.502623i
$113$	−10.3271	+	8.54330i	−0.971489	+	0.803686i	−0.980549	−	0.196273i	$-0.937116\pi$
$113$	−10.3271	+	8.54330i	−0.971489	+	0.803686i	0.00905990	+	0.999959i	$0.497116\pi$
$114$	−1.37731	+	0.353634i	−0.128997	+	0.0331209i
$115$	−5.05959	+	0.311991i	−0.471809	+	0.0290933i
$116$	−7.46552	+	2.95581i	−0.693156	+	0.274440i
$117$	−0.875975	−	0.932818i	−0.0809839	−	0.0862391i
$118$	−0.337391	+	0.464379i	−0.0310594	+	0.0427496i
$119$	−1.90304	−	4.04417i	−0.174451	−	0.370728i
$120$	−2.07756	−	1.14552i	−0.189654	−	0.104571i
$121$	6.43268	−	3.53640i	0.584789	−	0.321490i
$122$	0.0947234	−	0.0180695i	0.00857585	−	0.00163593i
$123$	−0.690000	−	2.68737i	−0.0622152	−	0.242312i
$124$	−17.6560			−1.58555
$125$	−10.4105	+	4.07686i	−0.931147	+	0.364645i
$126$	−0.0800315			−0.00712977
$127$	−1.30444	−	5.08048i	−0.115751	−	0.450819i	0.884114	−	0.467271i	$-0.154763\pi$
$127$	−1.30444	−	5.08048i	−0.115751	−	0.450819i	−0.999865	+	0.0164521i	$0.994763\pi$
$128$	4.96566	−	0.947250i	0.438906	−	0.0837259i
$129$	5.65946	−	3.11131i	0.498287	−	0.273936i
$130$	1.03758	−	0.971925i	0.0910021	−	0.0852435i
$131$	6.02713	+	12.8083i	0.526593	+	1.11907i	0.974376	+	0.224925i	$0.0722137\pi$
$131$	6.02713	+	12.8083i	0.526593	+	1.11907i	−0.447783	+	0.894142i	$0.647786\pi$
$132$	−8.11842	+	11.1740i	−0.706617	+	0.972576i
$133$	5.43027	+	5.78265i	0.470864	+	0.501419i
$134$	0.555688	−	0.220013i	0.0480042	−	0.0190062i
$135$	9.38328	−	7.74285i	0.807585	−	0.666398i
$136$	1.88660	−	0.484397i	0.161775	−	0.0415367i
$137$	−9.22019	+	7.62761i	−0.787734	+	0.651670i	−0.941718	−	0.336403i	$-0.890790\pi$
$137$	−9.22019	+	7.62761i	−0.787734	+	0.651670i	0.153984	+	0.988073i	$0.450790\pi$
$138$	0.222847	+	0.562848i	0.0189700	+	0.0479128i
$139$	21.4738	+	8.50210i	1.82139	+	0.721138i	0.984893	+	0.173163i	$0.0553989\pi$
$139$	21.4738	+	8.50210i	1.82139	+	0.721138i	0.836495	+	0.547975i	$0.184601\pi$
$140$	−0.00819329	+	6.57293i	−0.000692459	+	0.555514i
$141$	10.7594	−	16.9541i	0.906104	−	1.42779i
$142$	−0.107173	+	0.194947i	−0.00899378	+	0.0163596i
$143$	−9.79582	−	13.4828i	−0.819167	−	1.12749i
$144$	−0.236643	+	1.24053i	−0.0197202	+	0.103377i
$145$	9.09854	+	0.0113415i	0.755593	+	0.000941862i
$146$	−0.301431	+	0.640574i	−0.0249466	+	0.0530143i
$147$	3.76438	+	6.84738i	0.310481	+	0.564763i
$148$	−13.1590	−	0.827894i	−1.08166	−	0.0680525i
$149$	−17.8909	−	12.9985i	−1.46568	−	1.06488i	−0.981838	−	0.189719i	$-0.939242\pi$
$149$	−17.8909	−	12.9985i	−1.46568	−	1.06488i	−0.483839	−	0.875157i	$-0.660758\pi$
$150$	0.848485	+	1.03086i	0.0692785	+	0.0841697i
$151$	−2.95732	+	2.14862i	−0.240663	+	0.174852i	−0.701579	−	0.712592i	$-0.747521\pi$
$151$	−2.95732	+	2.14862i	−0.240663	+	0.174852i	0.460915	+	0.887444i	$0.347521\pi$
$152$	−2.91883	+	1.85234i	−0.236748	+	0.150245i
$153$	−0.123659	+	0.978858i	−0.00999720	+	0.0791360i
$154$	−1.03409	−	0.130635i	−0.0833290	−	0.0105269i
$155$	18.5928	+	7.38825i	1.49341	+	0.593438i
$156$	10.9980	+	6.04623i	0.880548	+	0.484085i
$157$	−10.9673	−	3.56350i	−0.875288	−	0.284398i	−0.163289	−	0.986578i	$-0.552210\pi$
$157$	−10.9673	−	3.56350i	−0.875288	−	0.284398i	−0.712000	+	0.702180i	$0.752210\pi$
$158$	2.21212	−	1.04094i	0.175987	−	0.0828130i
$159$	15.3773	+	3.94823i	1.21950	+	0.313115i
$160$	−4.22899	−	0.812187i	−0.334331	−	0.0642090i
$161$	2.15260	−	2.60204i	0.169648	−	0.205070i
$162$	−1.09054	−	0.692077i	−0.0856808	−	0.0543747i
$163$	−17.4902	+	1.10039i	−1.36994	+	0.0861893i	−0.730637	−	0.682766i	$-0.760777\pi$
$163$	−17.4902	+	1.10039i	−1.36994	+	0.0861893i	−0.639302	+	0.768956i	$0.720777\pi$
$164$	−1.79498	−	2.82843i	−0.140164	−	0.220864i
$165$	13.2251	−	8.36977i	1.02957	−	0.651586i
$166$	0.0297737	+	0.473240i	0.00231089	+	0.0367305i
$167$	6.43823	+	1.22816i	0.498205	+	0.0950377i	0.430359	−	0.902658i	$-0.358387\pi$
$167$	6.43823	+	1.22816i	0.498205	+	0.0950377i	0.0678467	+	0.997696i	$0.478387\pi$
$168$	1.50313	−	0.488396i	0.115969	−	0.0376806i
$169$	−1.56260	+	1.46738i	−0.120200	+	0.112876i
$170$	−1.08735	−	0.138741i	−0.0833959	−	0.0106410i
$171$	−0.328124	−	1.72009i	−0.0250923	−	0.131538i
$172$	5.33784	−	5.68423i	0.407007	−	0.433418i
$173$	4.50909	−	11.3887i	0.342820	−	0.865863i	−0.651423	−	0.758714i	$-0.725828\pi$
$173$	4.50909	−	11.3887i	0.342820	−	0.865863i	0.994243	−	0.107149i	$-0.0341722\pi$
$174$	−0.335759	−	1.03336i	−0.0254538	−	0.0783387i
$175$	2.75911	−	6.91828i	0.208569	−	0.522973i
$176$	−5.08257	+	15.6425i	−0.383113	+	1.17910i
$177$	4.42424	+	3.66005i	0.332546	+	0.275106i
$178$	0.0640414	+	0.0301356i	0.00480010	+	0.00225876i
$179$	−1.50281	−	1.41123i	−0.112325	−	0.105481i	0.626350	−	0.779542i	$-0.284548\pi$
$179$	−1.50281	−	1.41123i	−0.112325	−	0.105481i	−0.738675	+	0.674062i	$0.764548\pi$
$180$	0.778986	−	1.22411i	0.0580622	−	0.0912398i
$181$	−10.6567	+	1.34626i	−0.792108	+	0.100067i	−0.510968	−	0.859600i	$-0.670713\pi$
$181$	−10.6567	+	1.34626i	−0.792108	+	0.100067i	−0.281141	+	0.959667i	$0.590713\pi$
$182$			0.947112i			0.0702046i
$183$	−0.120901	−	0.957026i	−0.00893723	−	0.0707454i
$184$	0.938085	+	1.13395i	0.0691565	+	0.0835959i
$185$	13.5108	+	6.37829i	0.993335	+	0.468941i
$186$	0.150020	−	2.38450i	0.0110000	−	0.174840i
$187$	−3.19558	+	12.4460i	−0.233684	+	0.910139i
$188$	6.02927	−	23.4825i	0.439730	−	1.71264i
$189$	−0.508881	+	8.08843i	−0.0370156	+	0.588347i
$190$	1.91149	−	0.362167i	0.138674	−	0.0262744i
$191$	−7.80278	−	9.43194i	−0.564589	−	0.682471i	0.408538	−	0.912742i	$-0.366039\pi$
$191$	−7.80278	−	9.43194i	−0.564589	−	0.682471i	−0.973127	+	0.230271i	$0.926039\pi$
$192$	−1.50895	−	11.9446i	−0.108899	−	0.862025i
$193$			19.8655i			1.42995i	0.699149	+	0.714976i	$0.253562\pi$
$193$			19.8655i			1.42995i	−0.699149	+	0.714976i	$0.746438\pi$
$194$	−1.96973	+	0.248835i	−0.141418	+	0.0178653i
$195$	−9.05155	−	10.9693i	−0.648195	−	0.785525i
$196$	6.87735	+	6.45826i	0.491239	+	0.461304i
$197$	23.8669	+	11.2309i	1.70044	+	0.800169i	0.995895	+	0.0905141i	$0.0288510\pi$
$197$	23.8669	+	11.2309i	1.70044	+	0.800169i	0.704550	+	0.709655i	$0.251149\pi$
$198$	0.177284	+	0.146662i	0.0125990	+	0.0104228i
$199$	−1.78603	+	5.49684i	−0.126609	+	0.389661i	−0.994191	−	0.107633i	$-0.965673\pi$
$199$	−1.78603	+	5.49684i	−0.126609	+	0.389661i	0.867582	+	0.497294i	$0.165673\pi$
$200$	2.73622	+	1.74604i	0.193480	+	0.123464i
$201$	−1.84747	−	5.68594i	−0.130311	−	0.401055i
$202$	−0.824678	+	2.08290i	−0.0580242	+	0.146552i
$203$	−4.14925	+	4.41851i	−0.291221	+	0.310118i
$204$	−1.81324	−	9.50533i	−0.126952	−	0.665507i
$205$	0.706650	+	3.72964i	0.0493545	+	0.260489i
$206$	0.0751859	−	0.0706042i	0.00523845	−	0.00491923i
$207$	−0.708981	+	0.230362i	−0.0492776	+	0.0160113i
$208$	14.6807	+	2.80049i	1.01792	+	0.194179i
$209$	−1.43199	−	22.7608i	−0.0990528	−	1.57440i
$210$	−0.887627	−	0.0569556i	−0.0612521	−	0.00393031i
$211$	−9.13143	−	14.3888i	−0.628633	−	0.990567i	−0.998118	−	0.0613305i	$-0.980466\pi$
$211$	−9.13143	−	14.3888i	−0.628633	−	0.990567i	0.369484	−	0.929237i	$-0.379534\pi$
$212$	19.1307	−	1.20360i	1.31390	−	0.0826635i
$213$	1.87895	+	1.19242i	0.128744	+	0.0817032i
$214$	1.11500	−	1.34781i	0.0762200	−	0.0921342i
$215$	−7.99969	+	3.75219i	−0.545574	+	0.255898i
$216$	−3.42089	−	0.878334i	−0.232762	−	0.0597631i
$217$	−12.0599	+	5.67494i	−0.818676	+	0.385240i
$218$	1.24077	+	0.403151i	0.0840355	+	0.0273048i
$219$	6.20588	+	3.41171i	0.419354	+	0.230542i
$220$	12.0634	−	14.5452i	0.813313	−	0.980635i
$221$	11.5840	+	1.46340i	0.779227	+	0.0984392i
$222$	0.223620	−	1.77013i	0.0150084	−	0.118804i
$223$	13.2626	−	8.41669i	0.888128	−	0.563623i	−0.0116690	−	0.999932i	$-0.503714\pi$
$223$	13.2626	−	8.41669i	0.888128	−	0.563623i	0.899797	+	0.436309i	$0.143714\pi$
$224$	2.32089	−	1.68622i	0.155071	−	0.112665i
$225$	−1.33256	+	0.963094i	−0.0888372	+	0.0642062i
$226$	−1.77159	−	1.28713i	−0.117844	−	0.0856188i
$227$	24.4170	+	1.53619i	1.62062	+	0.101961i	0.846964	−	0.531650i	$-0.178428\pi$
$227$	24.4170	+	1.53619i	1.62062	+	0.101961i	0.773652	+	0.633611i	$0.218428\pi$
$228$	8.27386	+	15.0501i	0.547950	+	0.996717i
$229$	−11.9652	+	25.4274i	−0.790685	+	1.68029i	−0.0593840	+	0.998235i	$0.518914\pi$
$229$	−11.9652	+	25.4274i	−0.790685	+	1.68029i	−0.731301	+	0.682055i	$0.761086\pi$
$230$	−0.254953	−	0.788004i	−0.0168111	−	0.0519595i
$231$	−1.95373	+	10.2418i	−0.128546	+	0.673861i
$232$	−1.55262	−	2.13700i	−0.101934	−	0.140301i
$233$	3.85827	−	7.01816i	0.252764	−	0.459775i	−0.719233	−	0.694768i	$-0.755507\pi$
$233$	3.85827	−	7.01816i	0.252764	−	0.459775i	0.971997	+	0.234993i	$0.0755068\pi$
$234$	0.112026	−	0.176525i	0.00732339	−	0.0115398i
$235$	−16.1756	+	22.2055i	−1.05518	+	1.44853i
$236$	6.44586	+	2.55210i	0.419590	+	0.166127i
$237$	−9.00286	−	22.7386i	−0.584799	−	1.47703i
$238$	0.562666	−	0.465478i	0.0364722	−	0.0301725i
$239$	−4.63146	+	1.18916i	−0.299584	+	0.0769202i	−0.395490	−	0.918470i	$-0.629425\pi$
$239$	−4.63146	+	1.18916i	−0.299584	+	0.0769202i	0.0959058	+	0.995390i	$0.469425\pi$
$240$	−3.50744	+	13.5902i	−0.226404	+	0.877245i
$241$	−12.0650	+	4.77686i	−0.777174	+	0.307705i	−0.723019	−	0.690828i	$-0.757246\pi$
$241$	−12.0650	+	4.77686i	−0.777174	+	0.307705i	−0.0541544	+	0.998533i	$0.517246\pi$
$242$	0.821006	+	0.874283i	0.0527763	+	0.0562010i
$243$	1.99925	−	2.75173i	0.128252	−	0.176524i
$244$	−0.495896	−	1.05383i	−0.0317465	−	0.0674647i
$245$	−4.53978	−	9.67883i	−0.290036	−	0.618358i
$246$	0.397241	−	0.218385i	0.0253272	−	0.0139237i
$247$	−20.3559	+	3.88310i	−1.29522	+	0.247076i
$248$	−1.44449	−	5.62591i	−0.0917251	−	0.357246i
$249$	4.74332			0.300596
$250$	−1.06816	−	1.48182i	−0.0675565	−	0.0937185i
$251$	−8.42741			−0.531934			−0.265967	−	0.963982i	$-0.585691\pi$
$251$	−8.42741			−0.531934			−0.265967	+	0.963982i	$0.585691\pi$
$252$	0.240384	+	0.936235i	0.0151428	+	0.0589773i
$253$	−9.53675	+	1.81923i	−0.599571	+	0.114374i
$254$	0.750984	−	0.412857i	0.0471210	−	0.0259050i
$255$	−2.06811	+	10.7685i	−0.129510	+	0.674348i
$256$	−5.92130	−	12.5834i	−0.370081	−	0.786462i
$257$	−13.4657	+	18.5339i	−0.839964	+	1.15611i	0.146021	+	0.989281i	$0.453353\pi$
$257$	−13.4657	+	18.5339i	−0.839964	+	1.15611i	−0.985986	+	0.166830i	$0.946647\pi$
$258$	0.722320	+	0.769192i	0.0449696	+	0.0478878i
$259$	−9.25432	+	3.66404i	−0.575036	+	0.227673i
$260$	−14.4864	−	9.21871i	−0.898409	−	0.571720i
$261$	1.29598	−	0.332751i	0.0802191	−	0.0205968i
$262$	−1.78202	+	1.47422i	−0.110094	+	0.0910776i
$263$	−2.61528	−	6.60545i	−0.161265	−	0.407309i	0.826566	−	0.562840i	$-0.190291\pi$
$263$	−2.61528	−	6.60545i	−0.161265	−	0.407309i	−0.987831	+	0.155531i	$0.950291\pi$
$264$	−4.22470	−	1.67268i	−0.260012	−	0.102946i
$265$	−20.6495	−	6.73788i	−1.26849	−	0.413905i
$266$	−0.694464	+	1.09430i	−0.0425803	+	0.0670958i
$267$	0.341086	−	0.620432i	0.0208741	−	0.0379699i
$268$	−4.24286	−	5.83979i	−0.259174	−	0.356722i
$269$	−0.533159	+	2.79492i	−0.0325073	+	0.170409i	−0.994839	−	0.101471i	$-0.967645\pi$
$269$	−0.533159	+	2.79492i	−0.0325073	+	0.170409i	0.962331	+	0.271880i	$0.0876452\pi$
$270$	1.60657	+	1.17030i	0.0977725	+	0.0712223i
$271$	−0.585443	+	1.24413i	−0.0355632	+	0.0755756i	−0.921819	−	0.387620i	$-0.873297\pi$
$271$	−0.585443	+	1.24413i	−0.0355632	+	0.0755756i	0.886256	+	0.463196i	$0.153297\pi$
$272$	−5.55140	−	10.0980i	−0.336603	−	0.612278i
$273$	9.45555	+	0.594893i	0.572276	+	0.0360045i
$274$	−1.58170	−	1.14917i	−0.0955541	−	0.0694241i
$275$	−18.7900	+	10.2690i	−1.13308	+	0.619243i
$276$	5.91503	−	4.29752i	0.356043	−	0.258680i
$277$	−5.21615	+	3.31027i	−0.313408	+	0.198895i	−0.683221	−	0.730211i	$-0.739422\pi$
$277$	−5.21615	+	3.31027i	−0.313408	+	0.198895i	0.369813	+	0.929106i	$0.379422\pi$
$278$	−0.472939	+	3.74369i	−0.0283650	+	0.224532i
$279$	2.91899	+	0.368754i	0.174755	+	0.0220767i
$280$	−2.09507	+	0.535141i	−0.125205	+	0.0319808i
$281$	5.60578	+	3.08180i	0.334413	+	0.183845i	0.640109	−	0.768284i	$-0.278889\pi$
$281$	5.60578	+	3.08180i	0.334413	+	0.183845i	−0.305696	+	0.952129i	$0.598889\pi$
$282$	3.12016	+	1.01380i	0.185803	+	0.0603710i
$283$	−13.4216	+	6.31571i	−0.797829	+	0.375430i	−0.781081	−	0.624430i	$-0.785331\pi$
$283$	−13.4216	+	6.31571i	−0.797829	+	0.375430i	−0.0167483	+	0.999860i	$0.505331\pi$
$284$	2.60247	+	0.668200i	0.154428	+	0.0396504i
$285$	−2.41509	−	19.3110i	−0.143058	−	1.14388i
$286$	1.73563	−	2.09802i	0.102630	−	0.124058i
$287$	−2.13516	−	1.35502i	−0.126035	−	0.0799841i
$288$	−0.632023	+	0.0397635i	−0.0372423	+	0.00234309i
$289$	4.28522	+	6.75243i	0.252072	+	0.397202i
$290$	0.367895	+	1.44031i	0.0216035	+	0.0845777i
$291$	1.24705	+	19.8212i	0.0731031	+	1.16194i
$292$	8.39904	+	1.60220i	0.491516	+	0.0937618i
$293$	0.717265	−	0.233053i	0.0419031	−	0.0136151i	−0.287990	−	0.957633i	$-0.592987\pi$
$293$	0.717265	−	0.233053i	0.0419031	−	0.0136151i	0.329894	+	0.944018i	$0.392987\pi$
$294$	−0.930646	+	0.873935i	−0.0542764	+	0.0509689i
$295$	−5.71996	−	5.38483i	−0.333029	−	0.313517i
$296$	−0.812778	−	4.26073i	−0.0472418	−	0.247650i
$297$	15.9497	−	16.9847i	0.925497	−	0.985555i
$298$	1.33007	−	3.35938i	0.0770491	−	0.194604i
$299$	2.72616	+	8.39025i	0.157658	+	0.485221i
$300$	9.51087	−	13.0222i	0.549110	−	0.751836i
$301$	1.81899	−	5.59827i	0.104845	−	0.322679i
$302$	−0.460180	−	0.380694i	−0.0264804	−	0.0219065i
$303$	20.2768	+	9.54152i	1.16487	+	0.548146i
$304$	14.9087	+	14.0002i	0.855073	+	0.802967i
$305$	0.0812268	+	1.31726i	0.00465103	+	0.0754262i
$306$	−0.159929	+	0.0202037i	−0.00914253	+	0.00115497i
$307$		−	24.1926i		−	1.38074i	−0.723455	−	0.690372i	$-0.757447\pi$
$307$		−	24.1926i		−	1.38074i	0.723455	−	0.690372i	$-0.242553\pi$
$308$	1.57779	+	12.4895i	0.0899027	+	0.711653i
$309$	−0.657656	−	0.794970i	−0.0374128	−	0.0452243i
$310$	−0.413732	+	3.24252i	−0.0234984	+	0.184163i
$311$	−0.656320	+	10.4319i	−0.0372165	+	0.591540i	0.934585	+	0.355740i	$0.115771\pi$
$311$	−0.656320	+	10.4319i	−0.0372165	+	0.591540i	−0.971802	+	0.235800i	$0.924229\pi$
$312$	−1.02679	+	3.99909i	−0.0581306	+	0.226404i
$313$	−5.89068	+	22.9427i	−0.332961	+	1.29680i	0.553055	+	0.833145i	$0.313462\pi$
$313$	−5.89068	+	22.9427i	−0.332961	+	1.29680i	−0.886017	+	0.463654i	$0.846538\pi$
$314$	0.118303	−	1.88037i	0.00667623	−	0.106116i
$315$	0.138634	−	1.08651i	0.00781112	−	0.0612176i
$316$	−18.8217	−	22.7515i	−1.05880	−	1.27987i
$317$	−3.74056	−	29.6096i	−0.210091	−	1.66304i	−0.646215	−	0.763155i	$-0.723649\pi$
$317$	−3.74056	−	29.6096i	−0.210091	−	1.66304i	0.436124	−	0.899887i	$-0.356351\pi$
$318$			2.59389i			0.145458i
$319$	17.2885	−	2.18404i	0.967968	−	0.122283i
$320$	1.01379	+	16.4407i	0.0566723	+	0.919061i
$321$	−12.7556	−	11.9783i	−0.711946	−	0.668562i
$322$	0.499237	+	0.234923i	0.0278214	+	0.0130918i
$323$	12.3112	+	10.1848i	0.685016	+	0.566695i
$324$	−4.82058	+	14.8362i	−0.267810	+	0.824234i
$325$	11.3975	+	15.7698i	0.632218	+	0.874752i
$326$	−0.884795	−	2.72312i	−0.0490043	−	0.150820i
$327$	4.80422	−	12.1341i	0.265674	−	0.671016i
$328$	0.754402	−	0.803357i	0.0416549	−	0.0443580i
$329$	−3.42940	−	17.9776i	−0.189069	−	0.991135i
$330$	1.86187	+	1.75279i	0.102493	+	0.0964879i
$331$	9.02161	−	8.47186i	0.495873	−	0.465655i	−0.395800	−	0.918337i	$-0.629533\pi$
$331$	9.02161	−	8.47186i	0.495873	−	0.465655i	0.891672	+	0.452682i	$0.149533\pi$
$332$	5.44669	−	1.76974i	0.298926	−	0.0971269i
$333$	2.15824	+	0.411705i	0.118271	+	0.0225613i
$334$	0.0672403	+	1.06875i	0.00367922	+	0.0584796i
$335$	2.02430	+	7.92512i	0.110599	+	0.432996i
$336$	−5.01012	−	7.89468i	−0.273324	−	0.430690i
$337$	25.7802	−	1.62195i	1.40434	−	0.0883534i	0.657547	−	0.753413i	$-0.271594\pi$
$337$	25.7802	−	1.62195i	1.40434	−	0.0883534i	0.746790	+	0.665060i	$0.231594\pi$
$338$	−0.295705	−	0.187660i	−0.0160842	−	0.0102074i
$339$	−13.9629	+	16.8783i	−0.758362	+	0.916702i
$340$	1.64294	+	13.1369i	0.0891011	+	0.712449i
$341$	37.1143	+	9.52933i	2.00985	+	0.516042i
$342$	0.258872	−	0.121816i	0.0139982	−	0.00658705i
$343$	16.6904	+	5.42305i	0.901199	+	0.292817i
$344$	2.24793	+	1.23581i	0.121200	+	0.0666305i
$345$	−8.02723	+	2.05038i	−0.432171	+	0.110389i
$346$	1.98547	+	0.250823i	0.106739	+	0.0134843i
$347$	−0.155697	+	1.23247i	−0.00835824	+	0.0661623i	−0.995742	−	0.0921824i	$-0.970616\pi$
$347$	−0.155697	+	1.23247i	−0.00835824	+	0.0661623i	0.987384	+	0.158345i	$0.0506157\pi$
$348$	−11.0801	+	7.03164i	−0.593955	+	0.376935i
$349$	4.49001	−	3.26218i	0.240344	−	0.174620i	−0.461092	−	0.887352i	$-0.652542\pi$
$349$	4.49001	−	3.26218i	0.240344	−	0.174620i	0.701437	+	0.712732i	$0.252542\pi$
$350$	1.20693	+	0.155528i	0.0645129	+	0.00831333i
$351$	−17.1283	−	12.4444i	−0.914241	−	0.664235i
$352$	−8.23126	−	0.517867i	−0.438728	−	0.0276024i
$353$	−13.1413	−	23.9040i	−0.699443	−	1.27228i	−0.952414	−	0.304808i	$-0.901408\pi$
$353$	−13.1413	−	23.9040i	−0.699443	−	1.27228i	0.252970	−	0.967474i	$-0.418592\pi$
$354$	−0.399439	+	0.848851i	−0.0212299	+	0.0451159i
$355$	−2.46095	−	1.79268i	−0.130614	−	0.0951454i
$356$	0.160180	−	0.839693i	0.00848953	−	0.0445037i
$357$	−4.29371	−	5.90979i	−0.227247	−	0.312779i
$358$	0.162266	−	0.295161i	0.00857604	−	0.0155998i
$359$	−9.41649	+	14.8380i	−0.496983	+	0.783120i	−0.996536	−	0.0831632i	$-0.973498\pi$
$359$	−9.41649	+	14.8380i	−0.496983	+	0.783120i	0.499553	+	0.866284i	$0.333498\pi$
$360$	0.453783	+	0.148069i	0.0239165	+	0.00780391i
$361$	−8.70089	−	3.44493i	−0.457942	−	0.181312i
$362$	−0.646047	−	1.63173i	−0.0339555	−	0.0857617i
$363$	9.24414	−	7.64742i	0.485192	−	0.401385i
$364$	11.0796	−	2.84477i	0.580730	−	0.149106i
$365$	−8.17426	−	5.20185i	−0.427861	−	0.272277i
$366$	0.146537	−	0.0580182i	0.00765962	−	0.00303266i
$367$	−2.29930	−	2.44850i	−0.120022	−	0.127811i	0.666151	−	0.745817i	$-0.267941\pi$
$367$	−2.29930	−	2.44850i	−0.120022	−	0.127811i	−0.786173	+	0.618006i	$0.787941\pi$
$368$	5.11760	−	7.04377i	0.266773	−	0.367182i
$369$	0.237683	+	0.505103i	0.0123733	+	0.0262946i
$370$	−0.460398	+	2.39725i	−0.0239349	+	0.124627i
$371$	12.6803	−	6.97105i	0.658328	−	0.361919i
$372$	−28.3453	+	5.40715i	−1.46963	+	0.280347i
$373$	2.27628	+	8.86553i	0.117861	+	0.459040i	0.999927	−	0.0120870i	$-0.00384751\pi$
$373$	2.27628	+	8.86553i	0.117861	+	0.459040i	−0.882066	+	0.471127i	$0.843848\pi$
$374$	−2.09942			−0.108558
$375$	−15.4648	+	9.73330i	−0.798597	+	0.502626i
$376$	7.97575			0.411318
$377$	−3.93785	−	15.3369i	−0.202810	−	0.789892i
$378$	−1.30067	+	0.248117i	−0.0668994	+	0.0127617i
$379$	−3.46106	+	1.90273i	−0.177783	+	0.0977369i	−0.568160	−	0.822918i	$-0.692345\pi$
$379$	−3.46106	+	1.90273i	−0.177783	+	0.0977369i	0.390377	+	0.920655i	$0.372345\pi$
$380$	−9.97814	−	21.2734i	−0.511868	−	1.09130i
$381$	−3.65008	−	7.75682i	−0.186999	−	0.397394i
$382$	1.17557	−	1.61803i	0.0601472	−	0.0827855i
$383$	−0.312583	−	0.332867i	−0.0159722	−	0.0170087i	0.720933	−	0.693005i	$-0.243714\pi$
$383$	−0.312583	−	0.332867i	−0.0159722	−	0.0170087i	−0.736905	+	0.675996i	$0.763714\pi$
$384$	7.68188	−	3.04147i	0.392014	−	0.155209i
$385$	3.56479	−	13.8124i	0.181678	−	0.703946i
$386$	−3.14372	+	0.807171i	−0.160011	+	0.0410839i
$387$	−1.00120	+	0.828267i	−0.0508940	+	0.0421032i
$388$	8.82728	+	22.2952i	0.448137	+	1.13186i
$389$	−4.37456	−	1.73201i	−0.221799	−	0.0878165i	0.254597	−	0.967047i	$-0.418057\pi$
$389$	−4.37456	−	1.73201i	−0.221799	−	0.0878165i	−0.476396	+	0.879231i	$0.658057\pi$
$390$	1.36811	−	1.87811i	0.0692768	−	0.0951018i
$391$	3.64471	−	5.74314i	0.184321	−	0.290443i
$392$	−1.49521	+	2.71978i	−0.0755195	+	0.137369i
$393$	13.5986	+	18.7169i	0.685961	+	0.944144i
$394$	−0.807539	+	4.23327i	−0.0406832	+	0.213269i
$395$	10.2999	+	31.8348i	0.518244	+	1.60178i
$396$	1.18321	−	2.51444i	0.0594584	−	0.126355i
$397$	12.3968	+	22.5497i	0.622177	+	1.13174i	0.980197	+	0.198022i	$0.0634519\pi$
$397$	12.3968	+	22.5497i	0.622177	+	1.13174i	−0.358020	+	0.933714i	$0.616548\pi$
$398$	−0.942446	−	0.0592937i	−0.0472406	−	0.00297212i
$399$	10.4888	+	7.62056i	0.525097	+	0.381505i
$400$	5.97948	−	18.2480i	0.298974	−	0.912402i
$401$	5.89068	−	4.27983i	0.294167	−	0.213725i	−0.430906	−	0.902397i	$-0.641806\pi$
$401$	5.89068	−	4.27983i	0.294167	−	0.213725i	0.725073	+	0.688672i	$0.241806\pi$
$402$	0.824735	−	0.523393i	0.0411340	−	0.0261045i
$403$	4.36393	−	34.5440i	0.217383	−	1.72076i
$404$	26.8435	+	3.39112i	1.33551	+	0.168715i
$405$	11.2847	−	13.6063i	0.560740	−	0.676101i
$406$	−0.867821	−	0.477089i	−0.0430692	−	0.0236775i
$407$	27.2145	+	8.84253i	1.34897	+	0.438308i
$408$	2.88044	−	1.35543i	0.142603	−	0.0671040i
$409$	−5.66370	−	1.45419i	−0.280052	−	0.0719051i	0.106051	−	0.994361i	$-0.466179\pi$
$409$	−5.66370	−	1.45419i	−0.280052	−	0.0719051i	−0.386103	+	0.922456i	$0.626179\pi$
$410$	−0.561504	+	0.263369i	−0.0277307	+	0.0130069i
$411$	−12.4663	+	15.0692i	−0.614919	+	0.743309i
$412$	−1.05178	−	0.667481i	−0.0518176	−	0.0328844i
$413$	5.22312	−	0.328611i	0.257013	−	0.0161699i
$414$	−0.0652620	−	0.102836i	−0.00320745	−	0.00505413i
$415$	−6.47626	−	0.415557i	−0.317907	−	0.0203989i
$416$	0.470571	+	7.47951i	0.0230716	+	0.366713i
$417$	37.0783	+	7.07307i	1.81573	+	0.346370i
$418$	3.54372	−	1.15142i	0.173329	−	0.0563180i
$419$	−11.2710	+	10.5841i	−0.550622	+	0.517069i	−0.909160	−	0.416446i	$-0.863275\pi$
$419$	−11.2710	+	10.5841i	−0.550622	+	0.517069i	0.358538	+	0.933515i	$0.383275\pi$
$420$	1.99981	+	10.5548i	0.0975807	+	0.515023i
$421$	2.56790	+	13.4614i	0.125152	+	0.656069i	0.988471	+	0.151411i	$0.0483816\pi$
$421$	2.56790	+	13.4614i	0.125152	+	0.656069i	−0.863319	+	0.504658i	$0.831618\pi$
$422$	1.90601	−	2.02969i	0.0927830	−	0.0988039i
$423$	−1.48724	+	3.75634i	−0.0723121	+	0.182640i
$424$	1.94866	+	5.99735i	0.0946351	+	0.291257i
$425$	3.76710	−	14.5215i	0.182731	−	0.704396i
$426$	−0.112355	+	0.345795i	−0.00544364	+	0.0167538i
$427$	−0.677441	−	0.560428i	−0.0327836	−	0.0271210i
$428$	−19.1161	−	8.99537i	−0.924014	−	0.434808i
$429$	−19.8555	−	18.6456i	−0.958634	−	0.900217i
$430$	−0.918827	−	1.11349i	−0.0443098	−	0.0536974i
$431$	−29.6109	+	3.74072i	−1.42631	+	0.180184i	−0.800284	−	0.599622i	$-0.795318\pi$
$431$	−29.6109	+	3.74072i	−1.42631	+	0.180184i	−0.626021	+	0.779806i	$0.715318\pi$
$432$			20.8947i			1.00530i
$433$	−3.05601	−	24.1908i	−0.146862	−	1.16254i	−0.877433	−	0.479698i	$-0.840746\pi$
$433$	−3.05601	−	24.1908i	−0.146862	−	1.16254i	0.730571	−	0.682837i	$-0.239254\pi$
$434$	−1.38807	−	1.67789i	−0.0666296	−	0.0805414i
$435$	14.6105	−	2.76822i	0.700518	−	0.132726i
$436$	0.989387	−	15.7259i	0.0473830	−	0.753132i
$437$	−3.00228	+	11.6931i	−0.143618	+	0.559357i
$438$	−0.287748	+	1.12071i	−0.0137491	+	0.0535494i
$439$	0.964622	−	15.3322i	0.0460389	−	0.731767i	−0.905521	−	0.424302i	$-0.860519\pi$
$439$	0.964622	−	15.3322i	0.0460389	−	0.731767i	0.951559	−	0.307465i	$-0.0994806\pi$
$440$	5.62163	+	2.65390i	0.268001	+	0.126520i
$441$	−1.00212	−	1.21136i	−0.0477201	−	0.0576836i
$442$	0.239096	+	1.89264i	0.0113726	+	0.0900236i
$443$		−	18.9603i		−	0.900830i	−0.892819	−	0.450415i	$-0.851276\pi$
$443$		−	18.9603i		−	0.900830i	0.892819	−	0.450415i	$-0.148724\pi$
$444$	−21.3793	+	2.70083i	−1.01462	+	0.128176i
$445$	−0.520055	+	0.817222i	−0.0246530	+	0.0387400i
$446$	1.87082	+	1.75682i	0.0885861	+	0.0831879i
$447$	−32.7032	−	15.3889i	−1.54681	−	0.727872i
$448$	−8.45508	−	6.99465i	−0.399465	−	0.330466i
$449$	8.44214	−	25.9822i	0.398409	−	1.22618i	−0.527866	−	0.849328i	$-0.677008\pi$
$449$	8.44214	−	25.9822i	0.398409	−	1.22618i	0.926275	−	0.376849i	$-0.122992\pi$
$450$	−0.206554	−	0.171745i	−0.00973704	−	0.00809616i
$451$	2.24662	+	6.91440i	0.105789	+	0.325586i
$452$	−9.73613	+	24.5907i	−0.457949	+	1.15665i
$453$	−4.08973	+	4.35512i	−0.192152	+	0.204621i
$454$	0.749005	+	3.92642i	0.0351525	+	0.184276i
$455$	−12.8580	−	1.64062i	−0.602790	−	0.0769136i
$456$	−4.11867	+	3.86769i	−0.192874	+	0.181121i
$457$	31.1582	−	10.1239i	1.45752	−	0.473576i	0.530206	−	0.847869i	$-0.322114\pi$
$457$	31.1582	−	10.1239i	1.45752	−	0.473576i	0.927311	+	0.374293i	$0.122114\pi$
$458$	−4.51006	−	0.860340i	−0.210741	−	0.0402010i
$459$	1.02499	+	16.2918i	0.0478425	+	0.760435i
$460$	−8.45256	+	5.34939i	−0.394102	+	0.249416i
$461$	21.7088	+	34.2076i	1.01108	+	1.59320i	0.785386	+	0.619006i	$0.212464\pi$
$461$	21.7088	+	34.2076i	1.01108	+	1.59320i	0.225692	+	0.974199i	$0.427536\pi$
$462$	−1.70015	+	0.106964i	−0.0790981	+	0.00497643i
$463$	10.7975	+	6.85233i	0.501805	+	0.318455i	0.762524	−	0.646960i	$-0.223960\pi$
$463$	10.7975	+	6.85233i	0.501805	+	0.318455i	−0.260720	+	0.965415i	$0.583960\pi$
$464$	−9.96113	+	12.0409i	−0.462434	+	0.558987i
$465$	32.1120	+	6.16719i	1.48916	+	0.285996i
$466$	1.26739	+	0.325411i	0.0587109	+	0.0150744i
$467$	−17.2207	+	8.10344i	−0.796878	+	0.374983i	−0.780715	−	0.624887i	$-0.785145\pi$
$467$	−17.2207	+	8.10344i	−0.796878	+	0.374983i	−0.0161631	+	0.999869i	$0.505145\pi$
$468$	−2.40154	−	0.780306i	−0.111011	−	0.0360697i
$469$	−4.77509	−	2.62513i	−0.220493	−	0.121217i
$470$	−4.17127	−	1.65754i	−0.192406	−	0.0764567i
$471$	−18.6985	−	2.36217i	−0.861582	−	0.108843i
$472$	−0.285847	+	2.26271i	−0.0131572	+	0.104150i
$473$	−14.2885	+	9.06776i	−0.656986	+	0.416936i
$474$	3.23259	−	2.34862i	0.148478	−	0.107875i
$475$	1.60561	+	26.5777i	0.0736707	+	1.21947i
$476$	−7.13535	−	5.18414i	−0.327048	−	0.237615i
$477$	−3.18794	−	0.200568i	−0.145966	−	0.00918337i
$478$	−0.376369	−	0.684612i	−0.0172147	−	0.0313134i
$479$	8.33691	−	17.7168i	0.380923	−	0.809503i	−0.618790	−	0.785556i	$-0.712377\pi$
$479$	8.33691	−	17.7168i	0.380923	−	0.809503i	0.999713	−	0.0239463i	$-0.00762307\pi$
$480$	−7.03804	−	0.00877306i	−0.321241	−	0.000400434i
$481$	4.87222	−	25.5411i	0.222154	−	1.16457i
$482$	−1.24616	−	1.71519i	−0.0567611	−	0.0781249i
$483$	2.65895	−	4.83661i	0.120986	−	0.220073i
$484$	7.76166	−	12.2304i	0.352803	−	0.555928i
$485$	0.0338705	−	27.1720i	0.00153798	−	1.23382i
$486$	0.516695	+	0.204574i	0.0234377	+	0.00927966i
$487$	−1.62012	−	4.09195i	−0.0734146	−	0.185424i	0.888435	−	0.459002i	$-0.151793\pi$
$487$	−1.62012	−	4.09195i	−0.0734146	−	0.185424i	−0.961850	+	0.273578i	$0.911793\pi$
$488$	0.295223	−	0.244230i	0.0133641	−	0.0110558i
$489$	−27.7422	+	7.12298i	−1.25454	+	0.322112i
$490$	1.34722	−	1.11169i	0.0608611	−	0.0502210i
$491$	−30.1074	+	11.9204i	−1.35873	+	0.537958i	−0.930692	−	0.365803i	$-0.880794\pi$
$491$	−30.1074	+	11.9204i	−1.35873	+	0.537958i	−0.428036	+	0.903762i	$0.640794\pi$
$492$	−3.74791	−	3.99112i	−0.168969	−	0.179933i
$493$	−7.17612	+	9.87708i	−0.323196	+	0.444841i
$494$	−1.44160	−	3.06355i	−0.0648606	−	0.137836i
$495$	−2.29818	+	2.15275i	−0.103295	+	0.0967587i
$496$	−30.1125	+	16.5545i	−1.35209	+	0.743317i
$497$	1.99238	−	0.380067i	0.0893704	−	0.0170483i
$498$	0.192729	+	0.750631i	0.00863641	+	0.0336366i
$499$	7.95945			0.356314			0.178157	−	0.984002i	$-0.442987\pi$
$499$	7.95945			0.356314			0.178157	+	0.984002i	$0.442987\pi$
$500$	−14.1265	+	16.9465i	−0.631755	+	0.757872i
$501$	10.7122			0.478586
$502$	−0.342421	−	1.33364i	−0.0152830	−	0.0595233i
$503$	18.1247	−	3.45746i	0.808139	−	0.154161i	0.233276	−	0.972411i	$-0.425055\pi$
$503$	18.1247	−	3.45746i	0.808139	−	0.154161i	0.574863	+	0.818250i	$0.305055\pi$
$504$	−0.278656	+	0.153193i	−0.0124123	+	0.00682374i
$505$	−26.8488	−	14.8039i	−1.19476	−	0.658764i
$506$	−0.675389	−	1.43527i	−0.0300247	−	0.0638057i
$507$	−2.05925	+	2.83431i	−0.0914545	+	0.125876i
$508$	−7.08541	−	7.54520i	−0.314364	−	0.334764i
$509$	−21.8248	+	8.64107i	−0.967369	+	0.383009i	−0.798076	−	0.602557i	$-0.794149\pi$
$509$	−21.8248	+	8.64107i	−0.967369	+	0.383009i	−0.169294	+	0.985566i	$0.554149\pi$
$510$	−1.78814	+	0.110263i	−0.0791804	+	0.00488252i
$511$	6.25192	−	1.60522i	0.276568	−	0.0710107i
$512$	9.54093	−	7.89294i	0.421654	−	0.348822i
$513$	−10.6654	−	26.9376i	−0.470887	−	1.18932i
$514$	−3.48012	−	1.37788i	−0.153502	−	0.0607756i
$515$	0.828281	+	1.14302i	0.0364984	+	0.0503677i
$516$	6.82869	−	10.7603i	0.300616	−	0.473696i
$517$	−25.3481	+	46.1080i	−1.11481	+	2.02783i
$518$	−0.955855	−	1.31562i	−0.0419979	−	0.0578051i
$519$	3.75120	−	19.6645i	0.164660	−	0.863176i
$520$	1.75228	−	5.37018i	0.0768426	−	0.235498i
$521$	6.85648	−	14.5708i	0.300388	−	0.638356i	−0.696469	−	0.717587i	$-0.745246\pi$
$521$	6.85648	−	14.5708i	0.300388	−	0.638356i	0.996856	+	0.0792310i	$0.0252465\pi$
$522$	0.105316	+	0.191569i	0.00460955	+	0.00838473i
$523$	12.7313	+	0.800988i	0.556703	+	0.0350248i	0.338650	−	0.940912i	$-0.390030\pi$
$523$	12.7313	+	0.800988i	0.556703	+	0.0350248i	0.218052	+	0.975937i	$0.430030\pi$
$524$	22.5984	+	16.4187i	0.987217	+	0.717255i
$525$	2.31081	−	11.9517i	0.100852	−	0.521616i
$526$	0.939050	−	0.682260i	0.0409445	−	0.0297479i
$527$	−22.6669	+	14.3848i	−0.987385	+	0.626614i
$528$	−3.36913	+	26.6694i	−0.146623	+	1.16064i
$529$	−17.7198	−	2.23853i	−0.770426	−	0.0973275i
$530$	0.227248	−	3.54155i	0.00987102	−	0.153835i
$531$	−1.01237	−	0.556554i	−0.0439330	−	0.0241524i
$532$	14.8874	+	4.83721i	0.645450	+	0.209719i
$533$	5.97751	−	2.81280i	0.258915	−	0.121836i
$534$	0.112042	+	0.0287676i	0.00484855	+	0.00124490i
$535$	16.3663	+	17.4720i	0.707578	+	0.755379i
$536$	1.51368	−	1.82972i	0.0653809	−	0.0790319i
$537$	−2.84484	−	1.80539i	−0.122764	−	0.0779083i
$538$	−0.463959	+	0.0291898i	−0.0200027	+	0.00125846i
$539$	−10.9711	−	17.2877i	−0.472558	−	0.744633i
$540$	8.86506	−	22.3093i	0.381491	−	0.960039i
$541$	2.53120	+	40.2323i	0.108825	+	1.72972i	0.552483	+	0.833524i	$0.313680\pi$
$541$	2.53120	+	40.2323i	0.108825	+	1.72972i	−0.443658	+	0.896196i	$0.646320\pi$
$542$	−0.220671	−	0.0420953i	−0.00947865	−	0.00180815i
$543$	−16.6962	+	5.42494i	−0.716505	+	0.232806i
$544$	4.21220	−	3.95552i	0.180597	−	0.169592i
$545$	−7.62247	+	16.1463i	−0.326511	+	0.691632i
$546$	0.290053	+	1.52051i	0.0124131	+	0.0650720i
$547$	19.1239	−	20.3649i	0.817679	−	0.870740i	−0.175838	−	0.984419i	$-0.556264\pi$
$547$	19.1239	−	20.3649i	0.817679	−	0.870740i	0.993518	+	0.113679i	$0.0362635\pi$
$548$	−8.69259	+	21.9550i	−0.371329	+	0.937870i
$549$	0.0599747	+	0.184583i	0.00255966	+	0.00787781i
$550$	−2.38854	−	2.55628i	−0.101848	−	0.109000i
$551$	6.69588	−	20.6078i	0.285254	−	0.877922i
$552$	1.85329	+	1.53318i	0.0788815	+	0.0652564i
$553$	−20.1688	−	9.49073i	−0.857666	−	0.403587i
$554$	−0.735792	−	0.690955i	−0.0312608	−	0.0293558i
$555$	23.6439	+	6.10215i	1.00363	+	0.259022i
$556$	45.2155	−	5.71205i	1.91757	−	0.242245i
$557$			7.51870i			0.318578i	0.987232	+	0.159289i	$0.0509201\pi$
$557$			7.51870i			0.318578i	−0.987232	+	0.159289i	$0.949080\pi$
$558$	0.0602482	+	0.476914i	0.00255051	+	0.0201894i
$559$	9.80191	+	11.8485i	0.414577	+	0.501137i
$560$	6.14889	+	11.2179i	0.259838	+	0.474042i
$561$	−1.31867	+	20.9597i	−0.0556743	+	0.884918i
$562$	−0.259923	+	1.01233i	−0.0109642	+	0.0427027i
$563$	−3.00396	+	11.6997i	−0.126602	+	0.493081i	0.873380	+	0.487039i	$0.161923\pi$
$563$	−3.00396	+	11.6997i	−0.126602	+	0.493081i	−0.999982	+	0.00604197i	$0.998077\pi$
$564$	2.48801	−	39.5457i	0.104764	−	1.66518i
$565$	20.5429	−	21.8214i	0.864245	−	0.918032i
$566$	−1.54480	−	1.86735i	−0.0649329	−	0.0784904i
$567$	1.47594	+	11.6833i	0.0619836	+	0.490651i
$568$			0.883921i			0.0370885i
$569$	17.6190	−	2.22580i	0.738628	−	0.0933104i	0.252988	−	0.967469i	$-0.418587\pi$
$569$	17.6190	−	2.22580i	0.738628	−	0.0933104i	0.485640	+	0.874159i	$0.338587\pi$
$570$	2.95783	−	1.16683i	0.123890	−	0.0488730i
$571$	18.2989	+	17.1838i	0.765783	+	0.719118i	0.965405	−	0.260755i	$-0.0839714\pi$
$571$	18.2989	+	17.1838i	0.765783	+	0.719118i	−0.199622	+	0.979873i	$0.563971\pi$
$572$	−29.7565	−	14.0023i	−1.24418	−	0.585468i
$573$	−15.4153	−	12.7526i	−0.643983	−	0.532749i
$574$	0.127676	−	0.392947i	0.00532910	−	0.0164013i
$575$	11.1396	−	2.09622i	0.464552	−	0.0874183i
$576$	0.748539	+	2.30377i	0.0311891	+	0.0959903i
$577$	10.7087	−	27.0470i	0.445807	−	1.12598i	−0.517047	−	0.855957i	$-0.672969\pi$
$577$	10.7087	−	27.0470i	0.445807	−	1.12598i	0.962854	−	0.270023i	$-0.0870313\pi$
$578$	−0.894457	+	0.952500i	−0.0372045	+	0.0396188i
$579$	6.08383	+	31.8925i	0.252835	+	1.32541i
$580$	15.7442	−	8.62989i	0.653741	−	0.358337i
$581$	3.15152	−	2.95947i	0.130747	−	0.122780i
$582$	−3.08604	+	1.00272i	−0.127921	+	0.0415639i
$583$	−40.8639	−	7.79520i	−1.69241	−	0.322844i
$584$	0.176624	+	2.80736i	0.00730876	+	0.116169i
$585$	2.20244	+	1.82665i	0.0910599	+	0.0755227i
$586$	0.0660245	+	0.104038i	0.00272745	+	0.00429777i
$587$	12.9475	−	0.814590i	0.534402	−	0.0336217i	0.206703	−	0.978404i	$-0.433727\pi$
$587$	12.9475	−	0.814590i	0.534402	−	0.0336217i	0.327699	+	0.944782i	$0.393727\pi$
$588$	13.0189	+	8.26204i	0.536890	+	0.340721i
$589$	30.3713	−	36.7126i	1.25143	−	1.51272i
$590$	0.619739	−	1.12398i	0.0255142	−	0.0462735i
$591$	41.7559	+	10.7211i	1.71761	+	0.441007i
$592$	−23.2191	+	10.9261i	−0.954299	+	0.449059i
$593$	0.398461	+	0.129468i	0.0163628	+	0.00531660i	0.317187	−	0.948363i	$-0.397262\pi$
$593$	0.398461	+	0.129468i	0.0163628	+	0.00531660i	−0.300824	+	0.953680i	$0.597262\pi$
$594$	3.33590	+	1.83393i	0.136874	+	0.0752470i
$595$	5.34464	+	8.44506i	0.219109	+	0.346214i
$596$	−43.2942	−	5.46933i	−1.77340	−	0.224033i
$597$	−1.18392	+	9.37173i	−0.0484548	+	0.383559i
$598$	−1.21699	+	0.772326i	−0.0497664	+	0.0315827i
$599$	23.1159	−	16.7947i	0.944491	−	0.686213i	−0.00500643	−	0.999987i	$-0.501594\pi$
$599$	23.1159	−	16.7947i	0.944491	−	0.686213i	0.949498	+	0.313775i	$0.101594\pi$
$600$	4.92752	+	1.96517i	0.201165	+	0.0802276i
$601$	14.3573	+	10.4312i	0.585646	+	0.425496i	0.840755	−	0.541416i	$-0.182111\pi$
$601$	14.3573	+	10.4312i	0.585646	+	0.425496i	−0.255109	+	0.966912i	$0.582111\pi$
$602$	0.959836	+	0.0603878i	0.0391200	+	0.00246122i
$603$	0.579488	+	1.05408i	0.0235986	+	0.0429257i
$604$	−3.07128	+	6.52681i	−0.124969	+	0.265572i
$605$	−13.2914	+	9.63149i	−0.540373	+	0.391576i
$606$	−0.686067	+	3.59649i	−0.0278696	+	0.146097i
$607$	−25.0852	−	34.5268i	−1.01817	−	1.40140i	−0.913476	−	0.406894i	$-0.866612\pi$
$607$	−25.0852	−	34.5268i	−1.01817	−	1.40140i	−0.104699	−	0.994504i	$-0.533388\pi$
$608$	−4.94060	+	8.98692i	−0.200368	+	0.364468i
$609$	−5.30813	+	8.36428i	−0.215096	+	0.338938i
$610$	−0.205157	+	0.0663768i	−0.00830655	+	0.00268752i
$611$	44.4534	+	17.6004i	1.79839	+	0.712034i
$612$	0.716716	+	1.81022i	0.0289715	+	0.0731737i
$613$	19.8887	−	16.4534i	0.803299	−	0.664546i	−0.142321	−	0.989821i	$-0.545457\pi$
$613$	19.8887	−	16.4534i	0.803299	−	0.664546i	0.945620	+	0.325274i	$0.105457\pi$
$614$	3.82848	−	0.982986i	0.154505	−	0.0396701i
$615$	2.27667	+	5.77123i	0.0918044	+	0.232719i
$616$	−3.85057	+	1.52455i	−0.155144	+	0.0614258i
$617$	25.2971	+	26.9387i	1.01842	+	1.08451i	0.996402	+	0.0847527i	$0.0270100\pi$
$617$	25.2971	+	26.9387i	1.01842	+	1.08451i	0.0220209	+	0.999758i	$0.492990\pi$
$618$	0.0990824	−	0.136375i	0.00398568	−	0.00548582i
$619$	−15.7832	−	33.5410i	−0.634379	−	1.34812i	−0.920805	−	0.390022i	$-0.872467\pi$
$619$	−15.7832	−	33.5410i	−0.634379	−	1.34812i	0.286426	−	0.958102i	$-0.407533\pi$
$620$	39.1747	−	4.89932i	1.57330	−	0.196761i
$621$	−10.8082	+	5.94185i	−0.433718	+	0.238438i
$622$	−1.67752	+	0.320004i	−0.0672624	+	0.0128310i
$623$	−0.160482	−	0.625035i	−0.00642956	−	0.0250415i
$624$	24.4263			0.977836
$625$	21.9674	−	11.9345i	0.878698	−	0.477378i
$626$	−3.87004			−0.154678
$627$	−9.26946	−	36.1022i	−0.370187	−	1.44178i
$628$	−22.3526	+	4.26398i	−0.891965	+	0.170151i
$629$	−17.5682	+	9.65818i	−0.700489	+	0.385097i
$630$	0.177573	−	0.0222078i	0.00707466	−	0.000884779i
$631$	−4.30633	−	9.15142i	−0.171432	−	0.364312i	0.800586	−	0.599218i	$-0.204522\pi$
$631$	−4.30633	−	9.15142i	−0.171432	−	0.364312i	−0.972018	+	0.234906i	$0.924522\pi$
$632$	5.70970	−	7.85873i	0.227120	−	0.312603i
$633$	−19.0664	−	20.3036i	−0.757820	−	0.806997i
$634$	4.53374	−	1.79504i	0.180058	−	0.0712900i
$635$	4.30405	+	10.9105i	0.170801	+	0.432970i
$636$	30.3442	−	7.79106i	1.20322	−	0.308936i
$637$	−14.3355	+	11.8593i	−0.567992	+	0.469884i
$638$	1.04809	+	2.64716i	0.0414941	+	0.104802i
$639$	−0.416300	−	0.164825i	−0.0164686	−	0.00652037i
$640$	−10.7549	+	3.47965i	−0.425124	+	0.137545i
$641$	10.9559	−	17.2638i	0.432734	−	0.681879i	−0.556064	−	0.831139i	$-0.687689\pi$
$641$	10.9559	−	17.2638i	0.432734	−	0.681879i	0.988798	+	0.149260i	$0.0476892\pi$
$642$	1.37728	−	2.50527i	0.0543570	−	0.0988751i
$643$	13.1357	+	18.0798i	0.518022	+	0.712997i	0.985246	−	0.171142i	$-0.0547458\pi$
$643$	13.1357	+	18.0798i	0.518022	+	0.712997i	−0.467224	+	0.884139i	$0.654746\pi$
$644$	1.24869	−	6.54586i	0.0492053	−	0.257943i
$645$	−11.6938	+	8.47376i	−0.460441	+	0.333654i
$646$	−1.11151	+	2.36208i	−0.0437318	+	0.0929349i
$647$	−0.328412	−	0.597379i	−0.0129112	−	0.0234854i	0.869772	−	0.493453i	$-0.164266\pi$
$647$	−0.328412	−	0.597379i	−0.0129112	−	0.0234854i	−0.882684	+	0.469968i	$0.844266\pi$
$648$	−5.12181	−	0.322237i	−0.201204	−	0.0126587i
$649$	−12.1723	−	8.84371i	−0.477805	−	0.347146i
$650$	−2.03248	+	2.44441i	−0.0797203	+	0.0958776i
$651$	−17.6232	+	12.8040i	−0.690708	+	0.501828i
$652$	−29.1984	+	18.5298i	−1.14350	+	0.725685i
$653$	−2.47685	+	19.6063i	−0.0969268	+	0.767254i	0.866480	+	0.499211i	$0.166377\pi$
$653$	−2.47685	+	19.6063i	−0.0969268	+	0.767254i	−0.963407	+	0.268043i	$0.913623\pi$
$654$	2.11542	+	0.267240i	0.0827196	+	0.0104499i
$655$	−16.9271	−	26.7464i	−0.661395	−	1.04507i
$656$	−5.71334	−	3.14093i	−0.223068	−	0.122633i
$657$	−1.35512	−	0.440304i	−0.0528682	−	0.0171779i
$658$	2.70561	−	1.27316i	0.105476	−	0.0496331i
$659$	−39.1292	−	10.0467i	−1.52426	−	0.391363i	−0.608651	−	0.793438i	$-0.708289\pi$
$659$	−39.1292	−	10.0467i	−1.52426	−	0.391363i	−0.915607	+	0.402075i	$0.868289\pi$
$660$	14.9123	−	27.0455i	0.580462	−	1.05275i
$661$	−2.47526	+	2.99208i	−0.0962765	+	0.116378i	−0.816451	−	0.577415i	$-0.804062\pi$
$661$	−2.47526	+	2.99208i	−0.0962765	+	0.116378i	0.720175	+	0.693793i	$0.244062\pi$
$662$	1.70724	+	1.08345i	0.0663536	+	0.0421093i
$663$	19.0454	−	1.19824i	0.739663	−	0.0465357i
$664$	1.00952	+	1.59075i	0.0391770	+	0.0617331i
$665$	−13.6532	−	11.3236i	−0.529448	−	0.439111i
$666$	0.0225404	+	0.358269i	0.000873423	+	0.0138827i
$667$	−9.06108	−	1.72849i	−0.350846	−	0.0669275i
$668$	12.3007	−	3.99673i	0.475927	−	0.154638i
$669$	18.7144	−	17.5740i	0.723541	−	0.679450i
$670$	−1.17190	+	0.642357i	−0.0452745	+	0.0248164i
$671$	0.473637	+	2.48289i	0.0182845	+	0.0958509i
$672$	3.20959	−	3.41787i	0.123813	−	0.131847i
$673$	−10.6297	+	26.8475i	−0.409744	+	1.03489i	0.567613	+	0.823296i	$0.307867\pi$
$673$	−10.6297	+	26.8475i	−0.409744	+	1.03489i	−0.977357	+	0.211599i	$0.932133\pi$
$674$	1.30417	+	4.01382i	0.0502347	+	0.154607i
$675$	−18.6709	+	19.7835i	−0.718644	+	0.761465i
$676$	−1.30712	+	4.02291i	−0.0502740	+	0.154727i
$677$	10.0730	+	8.33315i	0.387139	+	0.320269i	0.810551	−	0.585668i	$-0.199168\pi$
$677$	10.0730	+	8.33315i	0.387139	+	0.320269i	−0.423412	+	0.905937i	$0.639168\pi$
$678$	−3.23833	−	1.52384i	−0.124367	−	0.0585228i
$679$	13.1955	+	12.3914i	0.506397	+	0.475538i
$680$	−4.05155	+	1.59828i	−0.155370	+	0.0612913i
$681$	39.6701	−	5.01150i	1.52016	−	0.192041i
$682$			6.26054i			0.239728i
$683$	1.06316	+	8.41581i	0.0406809	+	0.322022i	0.999303	+	0.0373394i	$0.0118883\pi$
$683$	1.06316	+	8.41581i	0.0406809	+	0.322022i	−0.958622	+	0.284683i	$0.908112\pi$
$684$	−2.20260	−	2.66248i	−0.0842184	−	0.101803i
$685$	18.3410	−	19.4825i	0.700775	−	0.744388i
$686$	−0.180037	+	2.86161i	−0.00687386	+	0.109257i
$687$	−11.4221	+	44.4861i	−0.435780	+	1.69725i
$688$	3.77415	−	14.6994i	0.143888	−	0.560408i
$689$	−2.37357	+	37.7268i	−0.0904258	+	1.43728i
$690$	−0.650633	−	1.18700i	−0.0247692	−	0.0451883i
$691$	−2.26217	−	2.73449i	−0.0860570	−	0.104025i	0.725727	−	0.687983i	$-0.241503\pi$
$691$	−2.26217	−	2.73449i	−0.0860570	−	0.104025i	−0.811784	+	0.583958i	$0.801503\pi$
$692$	−3.02939	−	23.9801i	−0.115160	−	0.911585i
$693$		−	2.09779i		−	0.0796883i
$694$	−0.201364	+	0.0254382i	−0.00764369	+	0.000965622i
$695$	−50.0050	−	12.9056i	−1.89680	−	0.489536i
$696$	−3.14707	−	2.95529i	−0.119289	−	0.112020i
$697$	−4.60882	−	2.16875i	−0.174572	−	0.0821471i
$698$	0.698677	+	0.577996i	0.0264453	+	0.0218775i
$699$	4.04483	−	12.4487i	0.152990	−	0.470853i
$700$	−1.80573	−	14.5862i	−0.0682502	−	0.551305i
$701$	−6.48442	−	19.9570i	−0.244913	−	0.753765i	−0.995651	−	0.0931648i	$-0.970302\pi$
$701$	−6.48442	−	19.9570i	−0.244913	−	0.753765i	0.750737	−	0.660601i	$-0.229698\pi$
$702$	1.27338	−	3.21620i	0.0480607	−	0.121388i
$703$	24.3572	−	25.9378i	0.918650	−	0.978263i
$704$	5.91142	+	30.9888i	0.222795	+	1.16793i
$705$	−19.1682	+	40.6030i	−0.721916	+	1.52920i
$706$	3.24886	−	3.05088i	0.122272	−	0.114821i
$707$	19.4253	−	6.31167i	0.730565	−	0.237375i
$708$	11.1299	+	2.12314i	0.418288	+	0.0797926i
$709$	1.43737	+	22.8463i	0.0539815	+	0.858011i	0.928108	+	0.372312i	$0.121435\pi$
$709$	1.43737	+	22.8463i	0.0539815	+	0.858011i	−0.874126	+	0.485699i	$0.838565\pi$
$710$	0.183699	−	0.462285i	0.00689409	−	0.0173493i
$711$	2.63654	+	4.15452i	0.0988778	+	0.155807i
$712$	0.280666	−	0.0176580i	0.0105184	−	0.000661761i
$713$	−17.1263	−	10.8687i	−0.641383	−	0.407034i
$714$	0.760764	−	0.919605i	0.0284709	−	0.0344154i
$715$	25.4761	+	27.1972i	0.952752	+	1.01712i
$716$	−3.94028	−	1.01169i	−0.147255	−	0.0378087i
$717$	−7.07127	+	3.32749i	−0.264081	+	0.124267i
$718$	−2.73073	−	0.887267i	−0.101910	−	0.0331125i
$719$	−9.61148	−	5.28396i	−0.358448	−	0.197058i	0.292347	−	0.956312i	$-0.405564\pi$
$719$	−9.61148	−	5.28396i	−0.358448	−	0.197058i	−0.650794	+	0.759254i	$0.725564\pi$
$720$	0.180828	−	2.81812i	0.00673907	−	0.105025i
$721$	−0.932957	−	0.117860i	−0.0347451	−	0.00438933i
$722$	0.191628	−	1.51689i	0.00713165	−	0.0564528i
$723$	−17.9065	+	11.3638i	−0.665949	+	0.422624i
$724$	−17.1480	+	12.4588i	−0.637301	+	0.463026i
$725$	−20.1908	+	2.49957i	−0.749869	+	0.0928318i
$726$	1.58581	+	1.15216i	0.0588550	+	0.0427606i
$727$	48.7342	+	3.06610i	1.80745	+	0.113715i	0.930369	−	0.366624i	$-0.119487\pi$
$727$	48.7342	+	3.06610i	1.80745	+	0.113715i	0.877083	+	0.480340i	$0.159487\pi$
$728$	1.81292	+	3.29769i	0.0671912	+	0.122220i
$729$	12.4648	−	26.4889i	0.461657	−	0.981072i
$730$	0.491059	−	1.50494i	0.0181749	−	0.0557003i
$731$	2.22166	−	11.6464i	0.0821712	−	0.430756i
$732$	−1.11886	−	1.53998i	−0.0413542	−	0.0569192i
$733$	21.2187	−	38.5967i	0.783730	−	1.42560i	−0.117870	−	0.993029i	$-0.537607\pi$
$733$	21.2187	−	38.5967i	0.783730	−	1.42560i	0.901600	−	0.432571i	$-0.142393\pi$
$734$	0.294051	−	0.463351i	0.0108536	−	0.0171026i
$735$	−10.2524	−	14.1483i	−0.378166	−	0.521867i
$736$	4.05928	+	1.60718i	0.149627	+	0.0592416i
$737$	5.76697	+	14.5657i	0.212429	+	0.536535i
$738$	−0.0702751	+	0.0581367i	−0.00258686	+	0.00214004i
$739$	9.86167	−	2.53205i	0.362767	−	0.0931428i	−0.0629067	−	0.998019i	$-0.520037\pi$
$739$	9.86167	−	2.53205i	0.362767	−	0.0931428i	0.425674	+	0.904877i	$0.360037\pi$
$740$	29.4267	−	1.81455i	1.08175	−	0.0667041i
$741$	−31.4906	+	12.4680i	−1.15684	+	0.458025i
$742$	1.61839	+	1.72341i	0.0594130	+	0.0632685i
$743$	−5.10593	+	7.02771i	−0.187319	+	0.257822i	−0.892340	−	0.451364i	$-0.850937\pi$
$743$	−5.10593	+	7.02771i	−0.187319	+	0.257822i	0.705021	+	0.709186i	$0.250937\pi$
$744$	−4.04195	−	8.58959i	−0.148185	−	0.314910i
$745$	43.3029	+	23.8763i	1.58649	+	0.874760i
$746$	−1.31048	+	0.720443i	−0.0479801	+	0.0263773i
$747$	−0.937441	+	0.178827i	−0.0342992	+	0.00654292i
$748$	6.30586	+	24.5597i	0.230565	+	0.897991i
$749$	−15.9485			−0.582746
$750$	−2.16866	−	2.05182i	−0.0791882	−	0.0749219i
$751$	−24.8544			−0.906949			−0.453474	−	0.891269i	$-0.649816\pi$
$751$	−24.8544			−0.906949			−0.453474	+	0.891269i	$0.649816\pi$
$752$	−11.7345	−	45.7028i	−0.427912	−	1.66661i
$753$	−13.5296	+	2.58090i	−0.493044	+	0.0940532i
$754$	2.26707	−	1.24633i	0.0825618	−	0.0453887i
$755$	5.96544	−	5.58794i	0.217104	−	0.203366i
$756$	6.80928	+	14.4705i	0.247651	+	0.526285i
$757$	2.91770	−	4.01587i	0.106046	−	0.145959i	−0.752696	−	0.658368i	$-0.771247\pi$
$757$	2.91770	−	4.01587i	0.106046	−	0.145959i	0.858741	+	0.512409i	$0.171247\pi$
$758$	−0.441737	−	0.470402i	−0.0160446	−	0.0170858i
$759$	−14.7534	+	5.84127i	−0.535513	+	0.212025i
$760$	5.96225	−	4.91989i	0.216273	−	0.178463i
$761$	−35.1478	+	9.02441i	−1.27411	+	0.327135i	−0.824382	−	0.566033i	$-0.808477\pi$
$761$	−35.1478	+	9.02441i	−1.27411	+	0.327135i	−0.449723	+	0.893168i	$0.648477\pi$
$762$	1.07921	−	0.892799i	0.0390956	−	0.0323427i
$763$	−4.37877	−	11.0595i	−0.158522	−	0.400381i
$764$	−22.4592	−	8.89222i	−0.812544	−	0.321709i
$765$	0.00275006	−	2.20619i	9.94286e−5	−	0.0797649i
$766$	0.0399754	−	0.0629912i	0.00144437	−	0.00227597i
$767$	−6.58639	+	11.9806i	−0.237821	+	0.432594i
$768$	−13.3599	−	18.3883i	−0.482082	−	0.663529i
$769$	−0.712846	+	3.73687i	−0.0257059	+	0.134755i	−0.992827	−	0.119562i	$-0.961851\pi$
$769$	−0.712846	+	3.73687i	−0.0257059	+	0.134755i	0.967121	+	0.254318i	$0.0818508\pi$
$770$	2.33066	+	0.00290522i	0.0839912	+	0.000104697i
$771$	−15.9420	+	33.8786i	−0.574138	+	1.22011i
$772$	18.8851	+	34.3519i	0.679690	+	1.23635i
$773$	−40.1881	−	2.52842i	−1.44546	−	0.0909409i	−0.679430	−	0.733740i	$-0.737773\pi$
$773$	−40.1881	−	2.52842i	−1.44546	−	0.0909409i	−0.766034	+	0.642799i	$0.777773\pi$
$774$	−0.171754	−	0.124787i	−0.00617357	−	0.00448536i
$775$	−43.3036	−	11.2336i	−1.55551	−	0.403524i
$776$	−6.38197	+	4.63677i	−0.229099	+	0.166450i
$777$	−13.7350	+	8.71648i	−0.492739	+	0.312702i
$778$	0.0963451	−	0.762650i	0.00345414	−	0.0273423i
$779$	8.96893	+	1.13304i	0.321345	+	0.0405953i
$780$	−26.0800	−	10.3634i	−0.933815	−	0.371071i
$781$	−5.10996	−	2.80923i	−0.182849	−	0.100522i
$782$	1.05694	+	0.343422i	0.0377962	+	0.0122807i
$783$	20.0307	−	9.42571i	0.715837	−	0.336847i
$784$	17.7848	+	4.56635i	0.635170	+	0.163084i
$785$	25.3230	+	4.86334i	0.903815	+	0.173580i
$786$	−2.40942	+	2.91249i	−0.0859412	+	0.103885i
$787$	−15.4253	−	9.78921i	−0.549853	−	0.348948i	0.231699	−	0.972788i	$-0.425572\pi$
$787$	−15.4253	−	9.78921i	−0.549853	−	0.348948i	−0.781552	+	0.623840i	$0.785572\pi$
$788$	51.9477	−	3.26828i	1.85056	−	0.116427i
$789$	−6.22155	−	9.80360i	−0.221493	−	0.349017i
$790$	−4.61936	+	2.92346i	−0.164349	+	0.104012i
$791$	1.25363	+	19.9259i	0.0445741	+	0.708485i
$792$	0.898006	+	0.171304i	0.0319093	+	0.00608702i
$793$	2.18440	−	0.709754i	0.0775703	−	0.0252041i
$794$	−3.06479	+	2.87803i	−0.108765	+	0.102137i
$795$	−35.2146	−	4.49324i	−1.24893	−	0.159359i
$796$	2.13711	+	11.2031i	0.0757480	+	0.397085i
$797$	−17.3622	+	18.4888i	−0.615000	+	0.654908i	−0.958783	−	0.284141i	$-0.908292\pi$
$797$	−17.3622	+	18.4888i	−0.615000	+	0.654908i	0.343783	+	0.939049i	$0.388292\pi$
$798$	−0.779777	+	1.96949i	−0.0276038	+	0.0697193i
$799$	−11.3914	−	35.0593i	−0.403000	−	1.24031i
$800$	9.60858	+	0.628574i	0.339715	+	0.0222234i
$801$	−0.0440194	+	0.135478i	−0.00155535	+	0.00478687i
$802$	0.916633	+	0.758305i	0.0323674	+	0.0267767i
$803$	−16.7907	−	7.90112i	−0.592532	−	0.278825i
$804$	−8.60002	−	8.07595i	−0.303299	−	0.284817i
$805$	−4.05411	+	6.37069i	−0.142889	+	0.224537i
$806$	5.64391	−	0.712992i	0.198798	−	0.0251141i
$807$			4.65030i			0.163698i
$808$	1.11560	+	8.83087i	0.0392466	+	0.310669i
$809$	−0.815014	−	0.985183i	−0.0286544	−	0.0346372i	0.755991	−	0.654582i	$-0.227155\pi$
$809$	−0.815014	−	0.985183i	−0.0286544	−	0.0346372i	−0.784646	+	0.619944i	$0.787155\pi$
$810$	2.61171	+	1.23296i	0.0917662	+	0.0433217i
$811$	2.03363	−	32.3236i	0.0714104	−	1.13504i	−0.785258	−	0.619168i	$-0.787470\pi$
$811$	2.03363	−	32.3236i	0.0714104	−	1.13504i	0.856669	−	0.515867i	$-0.172530\pi$
$812$	−2.97454	+	11.5851i	−0.104386	+	0.406556i
$813$	−0.558868	+	2.17665i	−0.0196004	+	0.0763383i
$814$	−0.293559	+	4.66599i	−0.0102892	+	0.163543i
$815$	38.5017	−	7.29485i	1.34865	−	0.255528i
$816$	−12.0048	−	14.5114i	−0.420253	−	0.507999i
$817$	2.63738	+	20.8770i	0.0922702	+	0.730394i
$818$		−	0.955367i		−	0.0334036i
$819$	−1.89117	+	0.238910i	−0.0660827	+	0.00834819i
$820$	4.76753	+	5.77760i	0.166489	+	0.201762i
$821$	−29.3527	−	27.5640i	−1.02442	−	0.961991i	−0.0251272	−	0.999684i	$-0.507999\pi$
$821$	−29.3527	−	27.5640i	−1.02442	−	0.961991i	−0.999289	+	0.0376931i	$0.987999\pi$
$822$	−2.89123	−	1.36051i	−0.100843	−	0.0474533i
$823$	11.6096	+	9.60426i	0.404684	+	0.334783i	0.817394	−	0.576079i	$-0.195418\pi$
$823$	11.6096	+	9.60426i	0.404684	+	0.334783i	−0.412711	+	0.910862i	$0.635418\pi$
$824$	0.126637	−	0.389750i	0.00441162	−	0.0135776i
$825$	−27.0210	+	22.2405i	−0.940751	+	0.774315i
$826$	0.264227	+	0.813207i	0.00919364	+	0.0282951i
$827$	1.45717	−	3.68038i	0.0506707	−	0.127979i	−0.902237	−	0.431241i	$-0.858076\pi$
$827$	1.45717	−	3.68038i	0.0506707	−	0.127979i	0.952907	+	0.303262i	$0.0980757\pi$
$828$	−1.00699	+	1.07234i	−0.0349954	+	0.0372663i
$829$	8.22262	+	43.1045i	0.285583	+	1.49708i	0.778855	+	0.627205i	$0.215801\pi$
$829$	8.22262	+	43.1045i	0.285583	+	1.49708i	−0.493271	+	0.869876i	$0.664199\pi$
$830$	−0.197380	−	1.04175i	−0.00685115	−	0.0361598i
$831$	−7.36035	+	6.91183i	−0.255328	+	0.239769i
$832$	27.2633	−	8.85839i	0.945186	−	0.307109i
$833$	14.0909	+	2.68799i	0.488222	+	0.0931334i
$834$	0.387243	+	6.15505i	0.0134091	+	0.213132i
$835$	−14.6258	−	0.938485i	−0.506148	−	0.0324776i
$836$	−24.1137	−	37.9972i	−0.833991	−	1.31416i
$837$	48.5827	−	3.05656i	1.67926	−	0.105650i
$838$	−2.13290	−	1.35358i	−0.0736798	−	0.0467586i
$839$	4.22470	−	5.10678i	0.145853	−	0.176306i	−0.692528	−	0.721391i	$-0.743503\pi$
$839$	4.22470	−	5.10678i	0.145853	−	0.176306i	0.838380	+	0.545086i	$0.183503\pi$
$840$	−3.19959	+	1.50074i	−0.110396	+	0.0517806i
$841$	−12.0524	−	3.09452i	−0.415599	−	0.106708i
$842$	−2.02593	+	0.953331i	−0.0698182	+	0.0328540i
$843$	9.94344	+	3.23082i	0.342470	+	0.111275i
$844$	−29.4690	−	16.2007i	−1.01436	−	0.557651i
$845$	3.05990	−	3.68941i	0.105264	−	0.126919i
$846$	−0.654871	−	0.0827294i	−0.0225149	−	0.00284430i
$847$	1.37051	−	10.8487i	0.0470912	−	0.372765i
$848$	31.4991	−	19.9899i	1.08168	−	0.686457i
$849$	−19.6131	+	14.2497i	−0.673119	+	0.489050i
$850$	2.45109	+	0.00611069i	0.0840718	+	0.000209595i
$851$	−12.2546	−	8.90347i	−0.420082	−	0.305207i
$852$	4.38269	+	0.275736i	0.150149	+	0.00944655i
$853$	7.19883	+	13.0946i	0.246483	+	0.448352i	0.970389	−	0.241547i	$-0.0776549\pi$
$853$	7.19883	+	13.0946i	0.246483	+	0.448352i	−0.723906	+	0.689899i	$0.757655\pi$
$854$	0.0611622	−	0.129976i	0.00209293	−	0.00444770i
$855$	1.20534	+	3.72545i	0.0412218	+	0.127408i
$856$	1.30234	−	6.82713i	0.0445132	−	0.233346i
$857$	−24.9954	−	34.4032i	−0.853825	−	1.17519i	−0.983007	−	0.183568i	$-0.941235\pi$
$857$	−24.9954	−	34.4032i	−0.853825	−	1.17519i	0.129182	−	0.991621i	$-0.458765\pi$
$858$	2.14390	−	3.89974i	0.0731916	−	0.133135i
$859$	−14.5992	+	23.0047i	−0.498119	+	0.784910i	−0.996635	−	0.0819707i	$-0.973879\pi$
$859$	−14.5992	+	23.0047i	−0.498119	+	0.784910i	0.498516	+	0.866881i	$0.333879\pi$
$860$	−10.2662	+	14.0933i	−0.350075	+	0.480576i
$861$	−3.84281	−	1.52148i	−0.130963	−	0.0518518i
$862$	−1.79511	−	4.53393i	−0.0611417	−	0.154426i
$863$	9.90696	−	8.19575i	0.337237	−	0.278987i	−0.453355	−	0.891330i	$-0.649773\pi$
$863$	9.90696	−	8.19575i	0.337237	−	0.278987i	0.790592	+	0.612343i	$0.209773\pi$
$864$	−10.1484	+	2.60566i	−0.345254	+	0.0886462i
$865$	−6.84447	+	26.5202i	−0.232719	+	0.901713i
$866$	3.70403	−	1.46653i	0.125868	−	0.0498346i
$867$	8.94753	+	9.52815i	0.303874	+	0.323593i
$868$	−15.4593	+	21.2779i	−0.524722	+	0.722219i
$869$	27.2852	+	57.9840i	0.925588	+	1.96697i
$870$	1.03172	+	2.19963i	0.0349786	+	0.0745745i
$871$	12.4743	−	6.85780i	0.422675	−	0.232368i
$872$	5.09185	−	0.971322i	0.172432	−	0.0328931i
$873$	−0.993733	−	3.87033i	−0.0336328	−	0.130991i
$874$	−1.97242			−0.0667182
$875$	−4.20213	+	16.1158i	−0.142058	+	0.544813i
$876$	13.9747			0.472160
$877$	−8.87329	−	34.5592i	−0.299630	−	1.16698i	−0.922921	−	0.384990i	$-0.874205\pi$
$877$	−8.87329	−	34.5592i	−0.299630	−	1.16698i	0.623291	−	0.781990i	$-0.285795\pi$
$878$	2.46552	−	0.470323i	0.0832073	−	0.0158726i
$879$	1.08014	−	0.593812i	0.0364322	−	0.0200288i
$880$	6.93650	−	36.1178i	0.233829	−	1.21753i
$881$	8.21754	+	17.4632i	0.276856	+	0.588349i	0.994099	−	0.108474i	$-0.0345964\pi$
$881$	8.21754	+	17.4632i	0.276856	+	0.588349i	−0.717243	+	0.696823i	$0.754596\pi$
$882$	0.150979	−	0.207805i	0.00508374	−	0.00699717i
$883$	1.25668	+	1.33823i	0.0422908	+	0.0450351i	0.749766	−	0.661703i	$-0.230166\pi$
$883$	1.25668	+	1.33823i	0.0422908	+	0.0450351i	−0.707475	+	0.706738i	$0.750166\pi$
$884$	21.4225	−	8.48179i	0.720518	−	0.285273i
$885$	−10.8321	−	6.89319i	−0.364115	−	0.231712i
$886$	3.00047	−	0.770389i	0.100803	−	0.0258817i
$887$	14.4627	−	11.9646i	0.485611	−	0.401732i	−0.362142	−	0.932123i	$-0.617955\pi$
$887$	14.4627	−	11.9646i	0.485611	−	0.401732i	0.847754	+	0.530390i	$0.177955\pi$
$888$	−2.60970	−	6.59136i	−0.0875759	−	0.221191i
$889$	−7.26483	−	2.87635i	−0.243655	−	0.0964697i
$890$	−0.150456	−	0.0490936i	−0.00504330	−	0.00164562i
$891$	18.1407	−	28.5852i	0.607737	−	0.957640i
$892$	14.9326	−	27.1624i	0.499981	−	0.909463i
$893$	38.4565	+	52.9308i	1.28690	+	1.77126i
$894$	1.10652	−	5.80056i	0.0370075	−	0.194000i
$895$	3.72602	+	2.71421i	0.124547	+	0.0907261i
$896$	3.20629	−	6.81371i	0.107115	−	0.227630i
$897$	6.94615	+	12.6350i	0.231925	+	0.421871i
$898$	4.45471	+	0.280267i	0.148656	+	0.00935262i
$899$	29.4538	+	21.3994i	0.982340	+	0.713711i
$900$	−1.38873	+	2.93220i	−0.0462908	+	0.0977398i
$901$	23.5795	−	17.1315i	0.785548	−	0.570734i
$902$	−1.00292	+	0.636473i	−0.0333936	+	0.0211922i
$903$	1.20577	−	9.54465i	0.0401255	−	0.317626i
$904$	−8.63214	−	1.09049i	−0.287101	−	0.0362692i
$905$	23.2714	−	5.94417i	0.773568	−	0.197591i
$906$	−0.855371	−	0.470244i	−0.0284178	−	0.0156228i
$907$	−2.98485	−	0.969836i	−0.0991103	−	0.0322029i	0.259042	−	0.965866i	$-0.416593\pi$
$907$	−2.98485	−	0.969836i	−0.0991103	−	0.0322029i	−0.358152	+	0.933663i	$0.616593\pi$
$908$	43.6828	−	20.5556i	1.44967	−	0.682161i
$909$	−4.36710	−	1.12128i	−0.144848	−	0.0371906i
$910$	−0.262812	−	2.10144i	−0.00871214	−	0.0696619i
$911$	37.2809	−	45.0649i	1.23517	−	1.49307i	0.426851	−	0.904322i	$-0.359623\pi$
$911$	37.2809	−	45.0649i	1.23517	−	1.49307i	0.808320	−	0.588743i	$-0.200377\pi$
$912$	28.2223	+	17.9104i	0.934535	+	0.593074i
$913$	−12.4046	+	0.780429i	−0.410531	+	0.0258284i
$914$	2.86812	+	4.51943i	0.0948689	+	0.149490i
$915$	0.533816	+	2.08989i	0.0176474	+	0.0690895i
$916$	3.48197	+	55.3443i	0.115048	+	1.82863i
$917$	20.7131	+	3.95123i	0.684006	+	0.130481i
$918$	−2.53653	+	0.824169i	−0.0837180	+	0.0272016i
$919$	30.6984	−	28.8277i	1.01265	−	0.950939i	0.0138467	−	0.999904i	$-0.495592\pi$
$919$	30.6984	−	28.8277i	1.01265	−	0.950939i	0.998800	+	0.0489651i	$0.0155923\pi$
$920$	−2.39606	−	2.25568i	−0.0789959	−	0.0743676i
$921$	−7.40899	−	38.8393i	−0.244134	−	1.27980i
$922$	−4.53129	+	4.82533i	−0.149230	+	0.158914i
$923$	−1.95058	+	4.92659i	−0.0642040	+	0.162161i
$924$	6.35791	+	19.5676i	0.209160	+	0.643728i
$925$	−31.7475	−	10.4030i	−1.04385	−	0.342047i
$926$	−0.645660	+	1.98714i	−0.0212177	+	0.0653013i
$927$	0.159946	+	0.132319i	0.00525332	+	0.00434593i
$928$	−7.09037	−	3.33648i	−0.232753	−	0.109525i
$929$	10.3790	+	9.74654i	0.340524	+	0.319774i	0.835875	−	0.548919i	$-0.184961\pi$
$929$	10.3790	+	9.74654i	0.340524	+	0.319774i	−0.495351	+	0.868693i	$0.664961\pi$
$930$	0.328808	+	5.33231i	0.0107820	+	0.174853i
$931$	−25.2591	+	3.19097i	−0.827834	+	0.104580i
$932$		−	15.8038i		−	0.517671i
$933$	2.14111	+	16.9486i	0.0700967	+	0.554873i
$934$	−1.98208	−	2.39592i	−0.0648556	−	0.0783969i
$935$	3.63669	−	28.5016i	0.118933	−	0.932103i
$936$	0.0521605	−	0.829067i	0.00170492	−	0.0270989i
$937$	5.78396	−	22.5271i	0.188954	−	0.735927i	−0.801490	−	0.598009i	$-0.795959\pi$
$937$	5.78396	−	22.5271i	0.188954	−	0.735927i	0.990444	−	0.137918i	$-0.0440411\pi$
$938$	0.221407	−	0.862322i	0.00722918	−	0.0281558i
$939$	−2.43082	+	38.6367i	−0.0793267	+	1.26086i
$940$	−6.86155	+	53.7756i	−0.223799	+	1.75397i
$941$	−17.0057	−	20.5564i	−0.554370	−	0.670118i	0.416664	−	0.909061i	$-0.363199\pi$
$941$	−17.0057	−	20.5564i	−0.554370	−	0.670118i	−0.971034	+	0.238943i	$0.923199\pi$
$942$	−0.385939	−	3.05502i	−0.0125746	−	0.0995380i
$943$		−	3.84853i		−	0.125325i
$944$	13.3864	−	1.69109i	0.435690	−	0.0550404i
$945$	−1.11535	−	18.0877i	−0.0362822	−	0.588392i
$946$	−2.01554	−	1.89272i	−0.0655309	−	0.0615376i
$947$	−39.8945	−	18.7729i	−1.29640	−	0.610038i	−0.351127	−	0.936328i	$-0.614201\pi$
$947$	−39.8945	−	18.7729i	−1.29640	−	0.610038i	−0.945270	+	0.326290i	$0.894201\pi$
$948$	−37.1844	−	30.7616i	−1.20769	−	0.999090i
$949$	−5.21067	+	16.0368i	−0.169145	+	0.520576i
$950$	−4.14068	+	1.33399i	−0.134342	+	0.0432802i
$951$	−15.0731	−	46.3904i	−0.488780	−	1.50431i
$952$	1.06811	−	2.69775i	0.0346178	−	0.0874345i
$953$	−16.0892	+	17.1333i	−0.521180	+	0.555001i	−0.934674	−	0.355506i	$-0.884308\pi$
$953$	−16.0892	+	17.1333i	−0.521180	+	0.555001i	0.413494	+	0.910507i	$0.364308\pi$
$954$	−0.0977915	−	0.512641i	−0.00316612	−	0.0165974i
$955$	19.9299	+	18.7622i	0.644917	+	0.607132i
$956$	−6.87835	+	6.45920i	−0.222462	+	0.208905i
$957$	27.0864	−	8.80091i	0.875580	−	0.284493i
$958$	3.14243	+	0.599451i	0.101527	+	0.0193674i
$959$	1.11927	+	17.7902i	0.0361430	+	0.574477i
$960$	6.66251	+	26.0837i	0.215032	+	0.841848i
$961$	26.2855	+	41.4193i	0.847919	+	1.33611i
$962$	4.23985	−	0.266749i	0.136698	−	0.00860032i
$963$	2.97252	+	1.88642i	0.0957882	+	0.0607891i
$964$	−16.3219	+	19.7298i	−0.525693	+	0.635454i
$965$	−5.51245	−	44.0773i	−0.177452	−	1.41890i
$966$	0.873432	+	0.224259i	0.0281022	+	0.00721542i
$967$	−16.7480	+	7.88099i	−0.538578	+	0.253436i	−0.675775	−	0.737108i	$-0.736191\pi$
$967$	−16.7480	+	7.88099i	−0.538578	+	0.253436i	0.137197	+	0.990544i	$0.456191\pi$
$968$	4.53212	+	1.47258i	0.145668	+	0.0473304i
$969$	22.8838	+	12.5805i	0.735135	+	0.404144i
$970$	4.30136	−	1.09869i	0.138108	−	0.0352767i
$971$	45.5963	+	5.76015i	1.46326	+	0.184852i	0.816279	−	0.577658i	$-0.196033\pi$
$971$	45.5963	+	5.76015i	1.46326	+	0.184852i	0.646976	+	0.762510i	$0.276033\pi$
$972$	0.841219	−	6.65893i	0.0269821	−	0.213585i
$973$	29.0484	−	18.4347i	0.931249	−	0.590988i
$974$	0.581724	−	0.422647i	0.0186396	−	0.0135425i
$975$	23.1273	+	21.8267i	0.740666	+	0.699014i
$976$	−1.83384	−	1.33237i	−0.0586999	−	0.0426480i
$977$	−5.27063	−	0.331600i	−0.168623	−	0.0106088i	−0.0217452	−	0.999764i	$-0.506922\pi$
$977$	−5.27063	−	0.331600i	−0.168623	−	0.0106088i	−0.146877	+	0.989155i	$0.546922\pi$
$978$	−2.25443	−	4.10078i	−0.0720886	−	0.131129i
$979$	−0.789914	+	1.67865i	−0.0252458	+	0.0536500i
$980$	−17.0514	−	12.4211i	−0.544688	−	0.396778i
$981$	−0.492014	+	2.57923i	−0.0157088	+	0.0823485i
$982$	−3.10972	−	4.28016i	−0.0992350	−	0.136585i
$983$	−6.55866	+	11.9302i	−0.209189	+	0.380513i	−0.959998	−	0.280006i	$-0.909664\pi$
$983$	−6.55866	+	11.9302i	−0.209189	+	0.380513i	0.750810	+	0.660519i	$0.229664\pi$
$984$	0.965105	−	1.52076i	0.0307664	−	0.0484801i
$985$	−56.0719	−	18.2962i	−1.78660	−	0.582964i
$986$	−1.85463	−	0.734299i	−0.0590634	−	0.0233848i
$987$	−11.0113	−	27.8113i	−0.350493	−	0.885243i
$988$	−31.5084	+	26.0661i	−1.00242	+	0.829272i
$989$	8.67680	−	2.22782i	0.275906	−	0.0708406i
$990$	−0.434051	−	0.276217i	−0.0137951	−	0.00877875i
$991$	−51.2918	+	20.3078i	−1.62934	+	0.645100i	−0.992086	−	0.125557i	$-0.959928\pi$
$991$	−51.2918	+	20.3078i	−1.62934	+	0.645100i	−0.637250	+	0.770657i	$0.719928\pi$
$992$	−11.7955	−	12.5609i	−0.374508	−	0.398810i
$993$	11.8890	−	16.3638i	0.377285	−	0.519289i
$994$	0.141099	+	0.299852i	0.00447540	+	0.00951072i
$995$	2.43751	−	12.6919i	0.0772743	−	0.402361i
$996$	8.20225	−	4.50922i	0.259898	−	0.142880i
$997$	6.06499	−	1.15696i	0.192080	−	0.0366412i	−0.0904435	−	0.995902i	$-0.528828\pi$
$997$	6.06499	−	1.15696i	0.192080	−	0.0366412i	0.282524	+	0.959260i	$0.408828\pi$
$998$	0.323406	+	1.25958i	0.0102372	+	0.0398714i
$999$	36.3520			1.15013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.104.7	✓	240
5.2	odd	4		625.2.g.b.351.12		480
5.3	odd	4		625.2.g.b.351.13		480
5.4	even	2		625.2.h.a.274.6		240
125.6	even	25		625.2.h.a.349.6		240
125.33	odd	100		625.2.g.b.276.13		480
125.92	odd	100		625.2.g.b.276.12		480
125.119	even	50	inner	125.2.h.a.119.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.104.7	✓	240	1.1	even	1	trivial
125.2.h.a.119.7	yes	240	125.119	even	50	inner
625.2.g.b.276.12		480	125.92	odd	100
625.2.g.b.276.13		480	125.33	odd	100
625.2.g.b.351.12		480	5.2	odd	4
625.2.g.b.351.13		480	5.3	odd	4
625.2.h.a.274.6		240	5.4	even	2
625.2.h.a.349.6		240	125.6	even	25

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0406317 + 0.158250i) q^{2} +(1.60542 - 0.306251i) q^{3} +(1.72922 - 0.950647i) q^{4} +(-2.21878 + 0.277488i) q^{5} +(0.113695 + 0.241615i) q^{6} +(0.875585 - 1.20514i) q^{7} +(0.444388 + 0.473226i) q^{8} +(-0.305740 + 0.121051i) q^{9} +O(q^{10})\)	\(q+(0.0406317 + 0.158250i) q^{2} +(1.60542 - 0.306251i) q^{3} +(1.72922 - 0.950647i) q^{4} +(-2.21878 + 0.277488i) q^{5} +(0.113695 + 0.241615i) q^{6} +(0.875585 - 1.20514i) q^{7} +(0.444388 + 0.473226i) q^{8} +(-0.305740 + 0.121051i) q^{9} +(-0.134066 - 0.339848i) q^{10} +(-4.14806 + 1.06504i) q^{11} +(2.48499 - 2.05576i) q^{12} +(1.43255 + 3.61820i) q^{13} +(0.226290 + 0.0895946i) q^{14} +(-3.47710 + 1.12499i) q^{15} +(2.05787 - 3.24268i) q^{16} +(1.44547 - 2.62930i) q^{17} +(-0.0315791 - 0.0434649i) q^{18} +(-0.997848 + 5.23090i) q^{19} +(-3.57297 + 2.58912i) q^{20} +(1.03661 - 2.20291i) q^{21} +(-0.337085 - 0.613156i) q^{22} +(2.26254 + 0.142347i) q^{23} +(0.858356 + 0.623632i) q^{24} +(4.84600 - 1.23137i) q^{25} +(-0.514374 + 0.373715i) q^{26} +(-4.59360 + 2.91519i) q^{27} +(0.368418 - 2.91633i) q^{28} +(-4.03691 - 0.509980i) q^{29} +(-0.319310 - 0.504542i) q^{30} +(-7.84067 - 4.31044i) q^{31} +(1.83157 + 0.595112i) q^{32} +(-6.33321 + 2.98018i) q^{33} +(0.474819 + 0.121913i) q^{34} +(-1.60832 + 2.91691i) q^{35} +(-0.413616 + 0.499975i) q^{36} +(-5.64154 - 3.58023i) q^{37} +(-0.868336 + 0.0546310i) q^{38} +(3.40792 + 5.37002i) q^{39} +(-1.11732 - 0.926672i) q^{40} +(-0.106594 - 1.69427i) q^{41} +(0.390729 + 0.0745356i) q^{42} +(3.75815 - 1.22110i) q^{43} +(-6.16043 + 5.78503i) q^{44} +(0.644781 - 0.353425i) q^{45} +(0.0694046 + 0.363831i) q^{46} +(8.41038 - 8.95615i) q^{47} +(2.31067 - 5.83610i) q^{48} +(1.47741 + 4.54699i) q^{49} +(0.391766 + 0.716848i) q^{50} +(1.51536 - 4.66381i) q^{51} +(5.91683 + 4.89482i) q^{52} +(8.78940 + 4.13598i) q^{53} +(-0.647976 - 0.608490i) q^{54} +(8.90810 - 3.51413i) q^{55} +(0.959402 - 0.121201i) q^{56} +8.70340i q^{57} +(-0.0833222 - 0.659563i) q^{58} +(2.23942 + 2.70700i) q^{59} +(-4.94321 + 5.25085i) q^{60} +(0.0370600 - 0.589052i) q^{61} +(0.363548 - 1.41593i) q^{62} +(-0.121818 + 0.474450i) q^{63} +(0.462543 - 7.35191i) q^{64} +(-4.18252 - 7.63049i) q^{65} +(-0.728944 - 0.881141i) q^{66} +(-0.458471 - 3.62917i) q^{67} -5.92077i q^{68} +(3.67593 - 0.464378i) q^{69} +(-0.526950 - 0.135998i) q^{70} +(0.992574 + 0.932089i) q^{71} +(-0.193152 - 0.0908904i) q^{72} +(3.33869 + 2.76201i) q^{73} +(0.337346 - 1.03825i) q^{74} +(7.40277 - 3.46096i) q^{75} +(3.24724 + 9.99399i) q^{76} +(-2.34845 + 5.93152i) q^{77} +(-0.711337 + 0.757497i) q^{78} +(-2.80389 - 14.6985i) q^{79} +(-3.66616 + 7.76584i) q^{80} +(-5.76277 + 5.41160i) q^{81} +(0.263787 - 0.0857097i) q^{82} +(2.85082 + 0.543823i) q^{83} +(-0.301661 - 4.79476i) q^{84} +(-2.47758 + 6.23495i) q^{85} +(0.345939 + 0.545113i) q^{86} +(-6.63712 + 0.417572i) q^{87} +(-2.34735 - 1.48967i) q^{88} +(0.276132 - 0.333786i) q^{89} +(0.0821282 + 0.0876764i) q^{90} +(5.61476 + 1.44162i) q^{91} +(4.04776 - 1.90473i) q^{92} +(-13.9076 - 4.51887i) q^{93} +(1.75904 + 0.967041i) q^{94} +(0.762496 - 11.8831i) q^{95} +(3.12269 + 0.394488i) q^{96} +(-1.52301 + 12.0559i) q^{97} +(-0.659533 + 0.418552i) q^{98} +(1.13930 - 0.827752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

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