LMFDB - Embedded newform 460.2.w.a.3.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13266 - 0.846813i) q^{2} +(-0.616030 - 1.65164i) q^{3} +(0.565816 + 1.91829i) q^{4} +(-1.87330 - 1.22097i) q^{5} +(-0.700881 + 2.39240i) q^{6} +(2.66779 + 0.580342i) q^{7} +(0.983562 - 2.65191i) q^{8} +(-0.0811762 + 0.0703396i) q^{9} +O(q^{10})$	\(q+(-1.13266 - 0.846813i) q^{2} +(-0.616030 - 1.65164i) q^{3} +(0.565816 + 1.91829i) q^{4} +(-1.87330 - 1.22097i) q^{5} +(-0.700881 + 2.39240i) q^{6} +(2.66779 + 0.580342i) q^{7} +(0.983562 - 2.65191i) q^{8} +(-0.0811762 + 0.0703396i) q^{9} +(1.08787 + 2.96927i) q^{10} +(-4.98028 - 0.716056i) q^{11} +(2.81977 - 2.11625i) q^{12} +(-0.949890 - 4.36657i) q^{13} +(-2.53024 - 2.91644i) q^{14} +(-0.862596 + 3.84617i) q^{15} +(-3.35971 + 2.17080i) q^{16} +(1.21696 - 0.664508i) q^{17} +(0.151509 - 0.0109294i) q^{18} +(-1.47083 + 0.431875i) q^{19} +(1.28224 - 4.28437i) q^{20} +(-0.684922 - 4.76374i) q^{21} +(5.03457 + 5.02841i) q^{22} +(-4.37785 + 1.95817i) q^{23} +(-4.98590 + 0.00916246i) q^{24} +(2.01847 + 4.57447i) q^{25} +(-2.62177 + 5.75020i) q^{26} +(-4.47530 - 2.44370i) q^{27} +(0.396210 + 5.44597i) q^{28} +(-0.708856 + 2.41414i) q^{29} +(4.23401 - 3.62592i) q^{30} +(-3.84805 + 1.75734i) q^{31} +(5.64365 + 0.386272i) q^{32} +(1.88534 + 8.66675i) q^{33} +(-1.94111 - 0.277875i) q^{34} +(-4.28898 - 4.34444i) q^{35} +(-0.180863 - 0.115921i) q^{36} +(5.75468 + 0.411583i) q^{37} +(2.03166 + 0.756353i) q^{38} +(-6.62685 + 4.25882i) q^{39} +(-5.08040 + 3.76690i) q^{40} +(1.10383 - 1.27388i) q^{41} +(-3.25821 + 5.97567i) q^{42} +(3.07313 + 8.23937i) q^{43} +(-1.44431 - 9.95880i) q^{44} +(0.237949 - 0.0326532i) q^{45} +(6.61680 + 1.48929i) q^{46} +(-0.464816 - 0.464816i) q^{47} +(5.65507 + 4.21175i) q^{48} +(0.412873 + 0.188553i) q^{49} +(1.58749 - 6.89056i) q^{50} +(-1.84721 - 1.60062i) q^{51} +(7.83891 - 4.29284i) q^{52} +(-4.56415 - 0.992870i) q^{53} +(2.99961 + 6.55760i) q^{54} +(8.45525 + 7.42215i) q^{55} +(4.16295 - 6.50392i) q^{56} +(1.61938 + 2.16323i) q^{57} +(2.84721 - 2.13412i) q^{58} +(-3.65707 - 2.35026i) q^{59} +(-7.86615 + 0.521507i) q^{60} +(-5.60696 - 12.2775i) q^{61} +(5.84665 + 1.26811i) q^{62} +(-0.257382 + 0.140541i) q^{63} +(-6.06521 - 5.21663i) q^{64} +(-3.55203 + 9.33966i) q^{65} +(5.20368 - 11.4130i) q^{66} +(-1.82635 + 2.43972i) q^{67} +(1.96329 + 1.95849i) q^{68} +(5.93108 + 6.02435i) q^{69} +(1.17900 + 8.55271i) q^{70} +(-11.6846 + 1.68000i) q^{71} +(0.106692 + 0.284455i) q^{72} +(-8.57648 - 4.68311i) q^{73} +(-6.16954 - 5.33932i) q^{74} +(6.31195 - 6.15180i) q^{75} +(-1.66068 - 2.57712i) q^{76} +(-12.8708 - 4.80055i) q^{77} +(11.1124 + 0.787930i) q^{78} +(4.42399 + 2.84313i) q^{79} +(8.94420 + 0.0355436i) q^{80} +(-1.32505 + 9.21593i) q^{81} +(-2.32899 + 0.508136i) q^{82} +(9.58439 + 0.685489i) q^{83} +(8.75071 - 4.00928i) q^{84} +(-3.09106 - 0.241045i) q^{85} +(3.49641 - 11.9347i) q^{86} +(4.42397 - 0.316409i) q^{87} +(-6.79733 + 12.5029i) q^{88} +(2.59743 + 1.18621i) q^{89} +(-0.297166 - 0.164514i) q^{90} -12.2003i q^{91} +(-6.23340 - 7.29005i) q^{92} +(5.27302 + 5.27302i) q^{93} +(0.132864 + 0.920088i) q^{94} +(3.28260 + 0.986809i) q^{95} +(-2.83868 - 9.55924i) q^{96} +(-1.02300 - 14.3034i) q^{97} +(-0.307974 - 0.563191i) q^{98} +(0.454647 - 0.292184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−1.13266	−	0.846813i	−0.800908	−	0.598787i
$2$	−1.13266	−	0.846813i	−0.800908	−	0.598787i
$3$	−0.616030	−	1.65164i	−0.355665	−	0.953575i	−0.984398	−	0.175954i	$-0.943699\pi$
$3$	−0.616030	−	1.65164i	−0.355665	−	0.953575i	0.628733	−	0.777621i	$-0.283574\pi$
$4$	0.565816	+	1.91829i	0.282908	+	0.959147i
$5$	−1.87330	−	1.22097i	−0.837763	−	0.546034i
$5$	−1.87330	−	1.22097i	−0.837763	−	0.546034i
$6$	−0.700881	+	2.39240i	−0.286134	+	0.976694i
$7$	2.66779	+	0.580342i	1.00833	+	0.219349i	0.686251	−	0.727365i	$-0.259255\pi$
$7$	2.66779	+	0.580342i	1.00833	+	0.219349i	0.322078	+	0.946713i	$0.395619\pi$
$8$	0.983562	−	2.65191i	0.347742	−	0.937590i
$9$	−0.0811762	+	0.0703396i	−0.0270587	+	0.0234465i
$10$	1.08787	+	2.96927i	0.344013	+	0.938965i
$11$	−4.98028	−	0.716056i	−1.50161	−	0.215899i	−0.658067	−	0.752959i	$-0.728626\pi$
$11$	−4.98028	−	0.716056i	−1.50161	−	0.215899i	−0.843544	+	0.537060i	$0.819535\pi$
$12$	2.81977	−	2.11625i	0.813999	−	0.610909i
$13$	−0.949890	−	4.36657i	−0.263452	−	1.21107i	−0.898631	−	0.438704i	$-0.855437\pi$
$13$	−0.949890	−	4.36657i	−0.263452	−	1.21107i	0.635179	−	0.772365i	$-0.280926\pi$
$14$	−2.53024	−	2.91644i	−0.676236	−	0.779453i
$15$	−0.862596	+	3.84617i	−0.222721	+	0.993076i
$16$	−3.35971	+	2.17080i	−0.839926	+	0.542700i
$17$	1.21696	−	0.664508i	0.295155	−	0.161167i	−0.324848	−	0.945766i	$-0.605313\pi$
$17$	1.21696	−	0.664508i	0.295155	−	0.161167i	0.620003	+	0.784599i	$0.287131\pi$
$18$	0.151509	−	0.0109294i	0.0357110	−	0.00257609i
$19$	−1.47083	+	0.431875i	−0.337431	+	0.0990788i	−0.446059	−	0.895004i	$-0.647173\pi$
$19$	−1.47083	+	0.431875i	−0.337431	+	0.0990788i	0.108627	+	0.994083i	$0.465355\pi$
$20$	1.28224	−	4.28437i	0.286717	−	0.958015i
$21$	−0.684922	−	4.76374i	−0.149462	−	1.03953i
$22$	5.03457	+	5.02841i	1.07337	+	1.07206i
$23$	−4.37785	+	1.95817i	−0.912845	+	0.408306i
$23$	−4.37785	+	1.95817i	−0.912845	+	0.408306i
$24$	−4.98590	+	0.00916246i	−1.01774	+	0.00187028i
$25$	2.01847	+	4.57447i	0.403694	+	0.914894i
$26$	−2.62177	+	5.75020i	−0.514172	+	1.12771i
$27$	−4.47530	−	2.44370i	−0.861271	−	0.470290i
$28$	0.396210	+	5.44597i	0.0748767	+	1.02919i
$29$	−0.708856	+	2.41414i	−0.131631	+	0.448295i	−0.998760	−	0.0497898i	$-0.984145\pi$
$29$	−0.708856	+	2.41414i	−0.131631	+	0.448295i	0.867129	+	0.498084i	$0.165963\pi$
$30$	4.23401	−	3.62592i	0.773020	−	0.662000i
$31$	−3.84805	+	1.75734i	−0.691130	+	0.315628i	−0.729836	−	0.683622i	$-0.760404\pi$
$31$	−3.84805	+	1.75734i	−0.691130	+	0.315628i	0.0387063	+	0.999251i	$0.487676\pi$
$32$	5.64365	+	0.386272i	0.997666	+	0.0682839i
$33$	1.88534	+	8.66675i	0.328195	+	1.50869i
$34$	−1.94111	−	0.277875i	−0.332897	−	0.0476552i
$35$	−4.28898	−	4.34444i	−0.724969	−	0.734344i
$36$	−0.180863	−	0.115921i	−0.0301438	−	0.0193201i
$37$	5.75468	+	0.411583i	0.946064	+	0.0676639i	0.535839	−	0.844320i	$-0.319995\pi$
$37$	5.75468	+	0.411583i	0.946064	+	0.0676639i	0.410225	+	0.911984i	$0.365450\pi$
$38$	2.03166	+	0.756353i	0.329579	+	0.122697i
$39$	−6.62685	+	4.25882i	−1.06115	+	0.681956i
$40$	−5.08040	+	3.76690i	−0.803281	+	0.595600i
$41$	1.10383	−	1.27388i	0.172389	−	0.198947i	−0.662980	−	0.748637i	$-0.730709\pi$
$41$	1.10383	−	1.27388i	0.172389	−	0.198947i	0.835369	+	0.549690i	$0.185254\pi$
$42$	−3.25821	+	5.97567i	−0.502753	+	0.922066i
$43$	3.07313	+	8.23937i	0.468647	+	1.25649i	0.929436	+	0.368982i	$0.120294\pi$
$43$	3.07313	+	8.23937i	0.468647	+	1.25649i	−0.460789	+	0.887510i	$0.652434\pi$
$44$	−1.44431	−	9.95880i	−0.217739	−	1.50135i
$45$	0.237949	−	0.0326532i	0.0354714	−	0.00486765i
$46$	6.61680	+	1.48929i	0.975594	+	0.219584i
$47$	−0.464816	−	0.464816i	−0.0678003	−	0.0678003i	0.672394	−	0.740194i	$-0.265266\pi$
$47$	−0.464816	−	0.464816i	−0.0678003	−	0.0678003i	−0.740194	+	0.672394i	$0.765266\pi$
$48$	5.65507	+	4.21175i	0.816238	+	0.607913i
$49$	0.412873	+	0.188553i	0.0589819	+	0.0269361i
$50$	1.58749	−	6.89056i	0.224505	−	0.974473i
$51$	−1.84721	−	1.60062i	−0.258661	−	0.224131i
$52$	7.83891	−	4.29284i	1.08706	−	0.595310i
$53$	−4.56415	−	0.992870i	−0.626934	−	0.136381i	−0.112136	−	0.993693i	$-0.535769\pi$
$53$	−4.56415	−	0.992870i	−0.626934	−	0.136381i	−0.514798	+	0.857312i	$0.672133\pi$
$54$	2.99961	+	6.55760i	0.408196	+	0.892377i
$55$	8.45525	+	7.42215i	1.14011	+	1.00080i
$56$	4.16295	−	6.50392i	0.556297	−	0.869123i
$57$	1.61938	+	2.16323i	0.214492	+	0.286527i
$58$	2.84721	−	2.13412i	0.373858	−	0.280224i
$59$	−3.65707	−	2.35026i	−0.476110	−	0.305977i	0.280488	−	0.959857i	$-0.409504\pi$
$59$	−3.65707	−	2.35026i	−0.476110	−	0.305977i	−0.756598	+	0.653880i	$0.773140\pi$
$60$	−7.86615	+	0.521507i	−1.01552	+	0.0673263i
$61$	−5.60696	−	12.2775i	−0.717898	−	1.57198i	−0.816827	−	0.576883i	$-0.804269\pi$
$61$	−5.60696	−	12.2775i	−0.717898	−	1.57198i	0.0989282	−	0.995095i	$-0.468459\pi$
$62$	5.84665	+	1.26811i	0.742526	+	0.161050i
$63$	−0.257382	+	0.140541i	−0.0324271	+	0.0177065i
$64$	−6.06521	−	5.21663i	−0.758151	−	0.652079i
$65$	−3.55203	+	9.33966i	−0.440575	+	1.15844i
$66$	5.20368	−	11.4130i	0.640529	−	1.40484i
$67$	−1.82635	+	2.43972i	−0.223124	+	0.298059i	−0.898109	−	0.439772i	$-0.855059\pi$
$67$	−1.82635	+	2.43972i	−0.223124	+	0.298059i	0.674985	+	0.737831i	$0.264150\pi$
$68$	1.96329	+	1.95849i	0.238084	+	0.237502i
$69$	5.93108	+	6.02435i	0.714018	+	0.725246i
$70$	1.17900	+	8.55271i	0.140918	+	1.02224i
$71$	−11.6846	+	1.68000i	−1.38671	+	0.199379i	−0.794921	−	0.606713i	$-0.792488\pi$
$71$	−11.6846	+	1.68000i	−1.38671	+	0.199379i	−0.591790	+	0.806092i	$0.701578\pi$
$72$	0.106692	+	0.284455i	0.0125738	+	0.0335233i
$73$	−8.57648	−	4.68311i	−1.00380	−	0.548117i	−0.108744	−	0.994070i	$-0.534683\pi$
$73$	−8.57648	−	4.68311i	−1.00380	−	0.548117i	−0.895056	+	0.445953i	$0.852865\pi$
$74$	−6.16954	−	5.33932i	−0.717194	−	0.620684i
$75$	6.31195	−	6.15180i	0.728841	−	0.710349i
$76$	−1.66068	−	2.57712i	−0.190493	−	0.295616i
$77$	−12.8708	−	4.80055i	−1.46676	−	0.547074i
$78$	11.1124	+	0.787930i	1.25823	+	0.0892155i
$79$	4.42399	+	2.84313i	0.497738	+	0.319877i	0.765311	−	0.643661i	$-0.222585\pi$
$79$	4.42399	+	2.84313i	0.497738	+	0.319877i	−0.267573	+	0.963538i	$0.586222\pi$
$80$	8.94420	+	0.0355436i	0.999992	+	0.00397390i
$81$	−1.32505	+	9.21593i	−0.147228	+	1.02399i
$82$	−2.32899	+	0.508136i	−0.257194	+	0.0561142i
$83$	9.58439	+	0.685489i	1.05202	+	0.0752422i	0.586625	−	0.809859i	$-0.300456\pi$
$83$	9.58439	+	0.685489i	1.05202	+	0.0752422i	0.465399	+	0.885101i	$0.345911\pi$
$84$	8.75071	−	4.00928i	0.954781	−	0.437448i
$85$	−3.09106	−	0.241045i	−0.335273	−	0.0261450i
$86$	3.49641	−	11.9347i	0.377028	−	1.28695i
$87$	4.42397	−	0.316409i	0.474299	−	0.0339226i
$88$	−6.79733	+	12.5029i	−0.724598	+	1.33282i
$89$	2.59743	+	1.18621i	0.275327	+	0.125738i	0.548294	−	0.836286i	$-0.315278\pi$
$89$	2.59743	+	1.18621i	0.275327	+	0.125738i	−0.272966	+	0.962024i	$0.588005\pi$
$90$	−0.297166	−	0.164514i	−0.0313240	−	0.0173413i
$91$		−	12.2003i		−	1.27894i
$92$	−6.23340	−	7.29005i	−0.649877	−	0.760040i
$93$	5.27302	+	5.27302i	0.546786	+	0.546786i
$94$	0.132864	+	0.920088i	0.0137039	+	0.0948998i
$95$	3.28260	+	0.986809i	0.336788	+	0.101244i
$96$	−2.83868	−	9.55924i	−0.289721	−	0.975636i
$97$	−1.02300	−	14.3034i	−0.103870	−	1.45229i	−0.735763	−	0.677239i	$-0.763176\pi$
$97$	−1.02300	−	14.3034i	−0.103870	−	1.45229i	0.631893	−	0.775056i	$-0.282278\pi$
$98$	−0.307974	−	0.563191i	−0.0311101	−	0.0568909i
$99$	0.454647	−	0.292184i	0.0456938	−	0.0293656i
$100$	−7.63310	+	6.46032i	−0.763310	+	0.646032i
$101$	6.89975	+	7.96273i	0.686550	+	0.792321i	0.986870	−	0.161517i	$-0.0516387\pi$
$101$	6.89975	+	7.96273i	0.686550	+	0.792321i	−0.300319	+	0.953839i	$0.597093\pi$
$102$	0.736829	+	3.37719i	0.0729570	+	0.334391i
$103$	−10.0525	−	13.4286i	−0.990504	−	1.32316i	−0.946006	−	0.324149i	$-0.894922\pi$
$103$	−10.0525	−	13.4286i	−0.990504	−	1.32316i	−0.0444977	−	0.999009i	$-0.514169\pi$
$104$	−12.5140	−	1.77578i	−1.22710	−	0.174129i
$105$	−4.53331	+	9.76015i	−0.442406	+	0.952493i
$106$	4.32883	+	4.98956i	0.420453	+	0.484629i
$107$	6.56141	−	17.5918i	0.634316	−	1.70067i	−0.0762989	−	0.997085i	$-0.524310\pi$
$107$	6.56141	−	17.5918i	0.634316	−	1.70067i	0.710615	−	0.703581i	$-0.248417\pi$
$108$	2.15554	−	9.96762i	0.207417	−	0.959134i
$109$	−0.839937	+	2.86056i	−0.0804514	+	0.273992i	−0.989888	−	0.141850i	$-0.954695\pi$
$109$	−0.839937	+	2.86056i	−0.0804514	+	0.273992i	0.909437	+	0.415842i	$0.136513\pi$
$110$	−3.29171	−	15.5668i	−0.313852	−	1.48423i
$111$	−2.86527	−	9.75822i	−0.271960	−	0.926209i
$112$	−10.2228	+	3.84146i	−0.965963	+	0.362984i
$113$	6.75569	−	9.02455i	0.635522	−	0.848958i	−0.360976	−	0.932575i	$-0.617556\pi$
$113$	6.75569	−	9.02455i	0.635522	−	0.848958i	0.996498	+	0.0836171i	$0.0266473\pi$
$114$	−0.00234089	−	3.82151i	−0.000219245	−	0.357917i
$115$	10.5919	+	1.67700i	0.987697	+	0.156381i
$116$	−5.03211	+	0.00616492i	−0.467220	+	0.000572398i
$117$	0.384251	+	0.287647i	0.0355240	+	0.0265930i
$118$	2.15197	+	5.75888i	0.198105	+	0.530148i
$119$	3.63222	−	1.06652i	0.332965	−	0.0977674i
$120$	9.35125	+	6.07047i	0.853649	+	0.554155i
$121$	13.7360	+	4.03326i	1.24873	+	0.366660i
$122$	−4.04602	+	18.6543i	−0.366310	+	1.68888i
$123$	−2.78399	−	1.03837i	−0.251024	−	0.0936270i
$124$	−5.54839	−	6.38735i	−0.498260	−	0.573601i
$125$	1.80410	−	11.0338i	0.161363	−	0.986895i
$126$	0.410537	+	0.0587697i	0.0365735	+	0.00523562i
$127$	15.4844	−	11.5915i	1.37402	−	1.02858i	0.379376	−	0.925242i	$-0.376139\pi$
$127$	15.4844	−	11.5915i	1.37402	−	1.02858i	0.994646	−	0.103338i	$-0.0329523\pi$
$128$	2.45228	+	11.0447i	0.216753	+	0.976226i
$129$	11.7153	−	10.1514i	1.03148	−	0.893781i
$130$	11.9322	−	7.57072i	1.04652	−	0.663996i
$131$	−1.10039	−	1.71225i	−0.0961419	−	0.149600i	0.789851	−	0.613299i	$-0.210158\pi$
$131$	−1.10039	−	1.71225i	−0.0961419	−	0.149600i	−0.885992	+	0.463700i	$0.846522\pi$
$132$	−15.5586	+	8.52041i	−1.35420	+	0.741607i
$133$	−4.17450	+	0.298566i	−0.361975	+	0.0258889i
$134$	4.13461	−	1.21678i	0.357176	−	0.105114i
$135$	5.39987	+	10.0420i	0.464747	+	0.864274i
$136$	−0.565261	−	3.88084i	−0.0484707	−	0.332779i
$137$	10.7555	−	10.7555i	0.918901	−	0.918901i	−0.0780484	−	0.996950i	$-0.524869\pi$
$137$	10.7555	−	10.7555i	0.918901	−	0.918901i	0.996950	+	0.0780484i	$0.0248689\pi$
$138$	−1.61637	−	11.8460i	−0.137594	−	1.00840i
$139$	8.79712			0.746162			0.373081	−	0.927799i	$-0.378301\pi$
$139$	8.79712			0.746162			0.373081	+	0.927799i	$0.378301\pi$
$140$	5.90714	−	10.6857i	0.499245	−	0.903104i
$141$	−0.481368	+	1.05405i	−0.0405385	+	0.0887670i
$142$	14.6573	+	7.99184i	1.23001	+	0.670660i
$143$	1.60401	+	22.4269i	0.134134	+	1.87543i
$144$	0.120035	−	0.412538i	0.0100029	−	0.0343781i
$145$	4.27549	−	3.65691i	0.355060	−	0.303690i
$146$	5.74847	+	12.5670i	0.475747	+	1.04005i
$147$	0.0570793	−	0.798072i	0.00470782	−	0.0658239i
$148$	2.46655	+	11.2721i	0.202749	+	0.926557i
$149$	2.61603	+	0.376128i	0.214313	+	0.0308136i	0.248635	−	0.968597i	$-0.420018\pi$
$149$	2.61603	+	0.376128i	0.214313	+	0.0308136i	−0.0343218	+	0.999411i	$0.510927\pi$
$150$	−12.3587	+	1.62283i	−1.00908	+	0.132504i
$151$	1.41272	−	2.19824i	0.114966	−	0.178890i	−0.779002	−	0.627021i	$-0.784274\pi$
$151$	1.41272	−	2.19824i	0.114966	−	0.178890i	0.893968	+	0.448131i	$0.147910\pi$
$152$	−0.301362	+	4.32528i	−0.0244437	+	0.350826i
$153$	−0.0520466	+	0.139542i	−0.00420772	+	0.0112813i
$154$	10.5130	+	16.3365i	0.847160	+	1.31643i
$155$	9.35419	+	1.40632i	0.751347	+	0.112959i
$156$	−11.9192	−	10.3025i	−0.954303	−	0.824863i
$157$	−10.8348	+	19.8424i	−0.864710	+	1.58360i	−0.0537062	+	0.998557i	$0.517103\pi$
$157$	−10.8348	+	19.8424i	−0.864710	+	1.58360i	−0.811004	+	0.585041i	$0.801078\pi$
$158$	−2.60326	−	6.96658i	−0.207104	−	0.554231i
$159$	1.17179	+	8.14997i	0.0929289	+	0.646335i
$160$	−10.1006	−	7.61432i	−0.798522	−	0.601965i
$161$	−12.8156	+	2.68332i	−1.01001	+	0.211476i
$162$	9.30499	−	9.31640i	0.731069	−	0.731965i
$163$	−17.1502	−	12.8385i	−1.34331	−	1.00559i	−0.997740	−	0.0671975i	$-0.978594\pi$
$163$	−17.1502	−	12.8385i	−1.34331	−	1.00559i	−0.345571	−	0.938393i	$-0.612315\pi$
$164$	3.06824	+	1.39668i	0.239590	+	0.109062i
$165$	7.05004	−	18.5373i	0.548845	−	1.44313i
$166$	−10.2753	−	8.89261i	−0.797520	−	0.690200i
$167$	−6.29813	−	11.5342i	−0.487364	−	0.892540i	−0.999435	−	0.0335975i	$-0.989304\pi$
$167$	−6.29813	−	11.5342i	−0.487364	−	0.892540i	0.512072	−	0.858943i	$-0.328878\pi$
$168$	−13.3066	−	2.86908i	−1.02663	−	0.221355i
$169$	−6.33944	+	2.89513i	−0.487649	+	0.222702i
$170$	3.29699	+	2.89057i	0.252867	+	0.221697i
$171$	0.0890185	−	0.138515i	0.00680741	−	0.0105925i
$172$	−14.0667	+	10.5571i	−1.07258	+	0.804973i
$173$	−10.1483	+	7.59693i	−0.771561	+	0.577584i	−0.910884	−	0.412664i	$-0.864599\pi$
$173$	−10.1483	+	7.59693i	−0.771561	+	0.577584i	0.139322	+	0.990247i	$0.455508\pi$
$174$	−5.27877	−	3.38789i	−0.400183	−	0.256836i
$175$	2.73009	+	13.3751i	0.206376	+	1.01106i
$176$	18.2867	−	8.40546i	1.37841	−	0.633586i
$177$	−1.62891	+	7.48799i	−0.122437	+	0.562832i
$178$	−1.93750	−	3.54310i	−0.145222	−	0.265567i
$179$	−2.30222	+	2.65690i	−0.172076	+	0.198586i	−0.835236	−	0.549891i	$-0.814669\pi$
$179$	−2.30222	+	2.65690i	−0.172076	+	0.198586i	0.663161	+	0.748477i	$0.269215\pi$
$180$	0.197274	+	0.437981i	0.0147039	+	0.0326452i
$181$	0.195921	−	0.429008i	0.0145627	−	0.0318879i	−0.902211	−	0.431295i	$-0.858057\pi$
$181$	0.195921	−	0.429008i	0.0145627	−	0.0318879i	0.916774	+	0.399407i	$0.130784\pi$
$182$	−10.3314	+	13.8188i	−0.765815	+	1.02432i
$183$	−16.8240	+	16.8240i	−1.24367	+	1.24367i
$184$	0.886984	+	13.5356i	0.0653894	+	0.997860i
$185$	−10.2777	−	7.79731i	−0.755631	−	0.573269i
$186$	−1.50725	−	10.4378i	−0.110517	−	0.765334i
$187$	−6.53661	+	2.43803i	−0.478004	+	0.178286i
$188$	0.628653	−	1.15465i	0.0458493	−	0.0842117i
$189$	−10.5210	−	9.11647i	−0.765287	−	0.663125i
$190$	−2.88242	−	3.89747i	−0.209112	−	0.282752i
$191$	14.6356	+	22.7735i	1.05900	+	1.64783i	0.699411	+	0.714720i	$0.253446\pi$
$191$	14.6356	+	22.7735i	1.05900	+	1.64783i	0.359586	+	0.933112i	$0.382918\pi$
$192$	−4.87965	+	13.2312i	−0.352158	+	0.954876i
$193$	0.428306	−	5.98850i	0.0308302	−	0.431062i	−0.958473	−	0.285185i	$-0.907945\pi$
$193$	0.428306	−	5.98850i	0.0308302	−	0.431062i	0.989303	−	0.145877i	$-0.0466004\pi$
$194$	−10.9536	+	17.0672i	−0.786425	+	1.22535i
$195$	17.6139	+	0.113156i	1.26136	+	0.00810326i
$196$	−0.128090	+	0.898698i	−0.00914926	+	0.0641927i
$197$	−0.332553	+	0.0723424i	−0.0236934	+	0.00515418i	−0.224396	−	0.974498i	$-0.572041\pi$
$197$	−0.332553	+	0.0723424i	−0.0236934	+	0.00515418i	0.200703	+	0.979652i	$0.435677\pi$
$198$	−0.762384	−	0.0540574i	−0.0541803	−	0.00384169i
$199$	3.21815	+	7.04676i	0.228128	+	0.499532i	0.988734	−	0.149682i	$-0.0478251\pi$
$199$	3.21815	+	7.04676i	0.228128	+	0.499532i	−0.760606	+	0.649214i	$0.775098\pi$
$200$	14.1164	−	0.853514i	0.998177	−	0.0603525i
$201$	5.15463	+	1.51354i	0.363579	+	0.106757i
$202$	−1.07209	−	14.8618i	−0.0754319	−	1.04567i
$203$	−3.29210	+	6.02904i	−0.231060	+	0.423155i
$204$	2.02527	−	4.44915i	0.141797	−	0.311503i
$205$	−3.62316	+	1.03862i	−0.253053	+	0.0725405i
$206$	0.0145314	+	23.7226i	0.00101245	+	1.65283i
$207$	0.217641	−	0.466893i	0.0151271	−	0.0324513i
$208$	12.6703	+	12.6084i	0.878528	+	0.874233i
$209$	7.63439	−	1.09766i	0.528082	−	0.0759267i
$210$	13.3997	−	7.21602i	0.924668	−	0.497953i
$211$	−1.58747	−	5.40641i	−0.109286	−	0.372193i	0.886630	−	0.462479i	$-0.153040\pi$
$211$	−1.58747	−	5.40641i	−0.109286	−	0.372193i	−0.995916	+	0.0902864i	$0.971222\pi$
$212$	−0.677851	−	9.31716i	−0.0465550	−	0.639905i
$213$	9.97284	+	18.2639i	0.683327	+	1.25142i
$214$	−22.3288	+	14.3692i	−1.52637	+	0.982258i
$215$	4.30314	−	19.1870i	0.293472	−	1.30854i
$216$	−10.8822	+	9.46454i	−0.740439	+	0.643980i
$217$	−11.2856	+	2.45504i	−0.766119	+	0.166659i
$218$	3.37372	−	2.52876i	0.228497	−	0.171269i
$219$	−2.45145	+	17.0502i	−0.165654	+	1.15215i
$220$	−9.45376	+	20.4192i	−0.637372	+	1.37666i
$221$	−4.05760	−	4.68271i	−0.272943	−	0.314993i
$222$	−5.01802	+	13.4790i	−0.336788	+	0.904655i
$223$	1.73045	−	7.95475i	0.115880	−	0.532690i	−0.882207	−	0.470861i	$-0.843943\pi$
$223$	1.73045	−	7.95475i	0.115880	−	0.532690i	0.998087	−	0.0618283i	$-0.0196931\pi$
$224$	14.8319	+	4.30574i	0.990998	+	0.287689i
$225$	−0.485618	−	0.229360i	−0.0323745	−	0.0152907i
$226$	−15.2940	+	4.50089i	−1.01734	+	0.299395i
$227$	23.0513	−	8.59769i	1.52997	−	0.570649i	0.563204	−	0.826318i	$-0.309568\pi$
$227$	23.0513	−	8.59769i	1.52997	−	0.570649i	0.966764	+	0.255669i	$0.0822957\pi$
$228$	−3.23345	+	4.33043i	−0.214141	+	0.286790i
$229$			7.30626i			0.482811i	0.970424	+	0.241406i	$0.0776084\pi$
$229$			7.30626i			0.482811i	−0.970424	+	0.241406i	$0.922392\pi$
$230$	−10.5768	−	10.8688i	−0.697416	−	0.716667i
$231$			24.2152i			1.59324i
$232$	5.70487	+	4.25428i	0.374543	+	0.279307i
$233$	18.6864	−	6.96968i	1.22419	−	0.456599i	0.347511	−	0.937676i	$-0.387027\pi$
$233$	18.6864	−	6.96968i	1.22419	−	0.456599i	0.876678	+	0.481077i	$0.159754\pi$
$234$	−0.191641	−	0.651194i	−0.0125280	−	0.0425699i
$235$	0.303211	+	1.43826i	0.0197793	+	0.0938219i
$236$	2.43925	−	8.34515i	0.158782	−	0.543223i
$237$	1.97051	−	9.05830i	0.127999	−	0.588400i
$238$	−5.01719	−	1.86782i	−0.325216	−	0.121073i
$239$	−18.4214	−	21.2594i	−1.19158	−	1.37516i	−0.909467	−	0.415775i	$-0.863510\pi$
$239$	−18.4214	−	21.2594i	−1.19158	−	1.37516i	−0.282112	−	0.959381i	$-0.591035\pi$
$240$	−5.45119	−	14.7945i	−0.351873	−	0.954981i
$241$	−0.446131	+	3.10291i	−0.0287378	+	0.199876i	−0.999132	−	0.0416495i	$-0.986739\pi$
$241$	−0.446131	+	3.10291i	−0.0287378	+	0.199876i	0.970394	+	0.241526i	$0.0776478\pi$
$242$	−12.1428	−	16.2001i	−0.780567	−	1.04138i
$243$	1.09022	−	0.237164i	0.0699380	−	0.0152141i
$244$	20.3794	−	17.7026i	1.30466	−	1.13329i
$245$	−0.543216	−	0.857320i	−0.0347048	−	0.0547722i
$246$	2.27399	+	3.53364i	0.144984	+	0.225296i
$247$	3.28294	+	6.01225i	0.208888	+	0.382550i
$248$	0.875518	+	11.9331i	0.0555954	+	0.757754i
$249$	−4.77209	−	16.2522i	−0.302419	−	1.02994i
$250$	−11.3870	+	10.9698i	−0.720177	+	0.693790i
$251$	−2.99860	+	0.431133i	−0.189270	+	0.0272129i	−0.236298	−	0.971681i	$-0.575934\pi$
$251$	−2.99860	+	0.431133i	−0.189270	+	0.0272129i	0.0470281	+	0.998894i	$0.485025\pi$
$252$	−0.415230	−	0.414214i	−0.0261570	−	0.0260930i
$253$	23.2051	−	6.61743i	1.45889	−	0.416034i
$254$	−27.3544	+	0.0167561i	−1.71637	+	0.00105137i
$255$	1.50607	+	5.25381i	0.0943135	+	0.329007i
$256$	6.57524	−	14.5865i	0.410952	−	0.911657i
$257$	3.04891	−	5.58367i	0.190186	−	0.348300i	−0.765135	−	0.643870i	$-0.777328\pi$
$257$	3.04891	−	5.58367i	0.190186	−	0.348300i	0.955321	+	0.295570i	$0.0955096\pi$
$258$	−21.8658	+	1.57733i	−1.36130	+	0.0982005i
$259$	15.1134	+	4.43770i	0.939102	+	0.275745i
$260$	−19.9260	−	1.52930i	−1.23576	−	0.0948433i
$261$	−0.112267	−	0.245831i	−0.00694918	−	0.0152166i
$262$	−0.203585	+	2.87121i	−0.0125776	+	0.177384i
$263$	−22.6652	+	4.93052i	−1.39760	+	0.304029i	−0.847378	−	0.530990i	$-0.821820\pi$
$263$	−22.6652	+	4.93052i	−1.39760	+	0.304029i	−0.550221	+	0.835019i	$0.685456\pi$
$264$	24.8377	+	3.52455i	1.52866	+	0.216921i
$265$	7.33774	+	7.43262i	0.450754	+	0.456582i
$266$	4.98109	+	3.19685i	0.305411	+	0.196011i
$267$	0.359092	−	5.02077i	0.0219761	−	0.307266i
$268$	−5.71348	−	2.12305i	−0.349006	−	0.129686i
$269$	−3.11937	−	4.85384i	−0.190192	−	0.295944i	0.733042	−	0.680184i	$-0.238100\pi$
$269$	−3.11937	−	4.85384i	−0.190192	−	0.295944i	−0.923233	+	0.384240i	$0.874464\pi$
$270$	2.38747	−	15.9468i	0.145297	−	0.970489i
$271$	2.74122	+	2.37528i	0.166517	+	0.144288i	0.734133	−	0.679005i	$-0.237589\pi$
$271$	2.74122	+	2.37528i	0.166517	+	0.144288i	−0.567616	+	0.823293i	$0.692134\pi$
$272$	−2.64610	+	4.87432i	−0.160443	+	0.295549i
$273$	−20.1506	+	7.51578i	−1.21957	+	0.454876i
$274$	−21.2901	+	3.07437i	−1.28618	+	0.185729i
$275$	−6.77696	−	24.2275i	−0.408666	−	1.46097i
$276$	−8.20058	+	14.7862i	−0.493617	+	0.890026i
$277$	−16.6232	+	16.6232i	−0.998793	+	0.998793i	−0.999999	−	0.00120577i	$-0.999616\pi$
$277$	−16.6232	+	16.6232i	−0.998793	+	0.998793i	0.00120577	+	0.999999i	$0.499616\pi$
$278$	−9.96411	−	7.44952i	−0.597607	−	0.446792i
$279$	0.188759	−	0.413325i	0.0113007	−	0.0247451i
$280$	−15.7395	+	7.10093i	−0.940616	+	0.424362i
$281$	13.4202	−	15.4877i	0.800581	−	0.923920i	−0.197832	−	0.980236i	$-0.563390\pi$
$281$	13.4202	−	15.4877i	0.800581	−	0.923920i	0.998413	+	0.0563158i	$0.0179354\pi$
$282$	1.43781	−	0.786246i	0.0856201	−	0.0468202i
$283$	3.73991	−	17.1921i	0.222315	−	1.02196i	−0.721737	−	0.692167i	$-0.756656\pi$
$283$	3.73991	−	17.1921i	0.222315	−	1.02196i	0.944052	−	0.329797i	$-0.106980\pi$
$284$	−9.83407	−	21.4640i	−0.583545	−	1.27365i
$285$	−0.392329	−	6.02959i	−0.0232396	−	0.357162i
$286$	17.1746	−	26.7603i	1.01556	−	1.58237i
$287$	3.68406	−	2.75785i	0.217463	−	0.162791i
$288$	−0.485300	+	0.365616i	−0.0285966	+	0.0215441i
$289$	−8.15148	+	12.6840i	−0.479499	+	0.746115i
$290$	−7.93937	+	0.521477i	−0.466216	+	0.0306222i
$291$	−22.9940	+	10.5010i	−1.34793	+	0.615579i
$292$	4.13088	−	19.1020i	0.241741	−	1.11786i
$293$	−0.488998	−	0.895534i	−0.0285676	−	0.0523176i	0.863005	−	0.505195i	$-0.168579\pi$
$293$	−0.488998	−	0.895534i	−0.0285676	−	0.0523176i	−0.891573	+	0.452877i	$0.850398\pi$
$294$	−0.740469	+	0.855605i	−0.0431850	+	0.0498999i
$295$	3.98118	+	8.86789i	0.231793	+	0.516309i
$296$	6.75157	−	14.8561i	0.392427	−	0.863491i
$297$	20.5384	+	15.3749i	1.19176	+	0.892140i
$298$	−2.64455	−	2.64131i	−0.153194	−	0.153007i
$299$	12.7090	+	17.2562i	0.734978	+	0.997950i
$300$	15.3724	+	8.62738i	0.887524	+	0.498102i
$301$	3.41680	+	23.7643i	0.196941	+	1.36975i
$302$	−3.46162	+	1.29353i	−0.199194	+	0.0744345i
$303$	8.90112	−	16.3012i	0.511356	−	0.936479i
$304$	4.00404	−	4.64385i	0.229647	−	0.266343i
$305$	−4.48700	+	29.8454i	−0.256925	+	1.70894i
$306$	0.177117	−	0.113980i	0.0101251	−	0.00651578i
$307$	−0.732721	+	1.96450i	−0.0418186	+	0.112120i	−0.956180	−	0.292778i	$-0.905420\pi$
$307$	−0.732721	+	1.96450i	−0.0418186	+	0.112120i	0.914362	+	0.404898i	$0.132693\pi$
$308$	1.92638	−	27.4062i	0.109766	−	1.56161i
$309$	−15.9866	+	24.8756i	−0.909443	+	1.41512i
$310$	−9.40418	−	9.51413i	−0.534122	−	0.540366i
$311$	10.2807	+	1.47814i	0.582964	+	0.0838176i	0.427486	−	0.904022i	$-0.359399\pi$
$311$	10.2807	+	1.47814i	0.582964	+	0.0838176i	0.155478	+	0.987839i	$0.450308\pi$
$312$	4.77606	+	21.7626i	0.270391	+	1.23206i
$313$	2.03257	−	28.4191i	0.114888	−	1.60634i	−0.534018	−	0.845473i	$-0.679319\pi$
$313$	2.03257	−	28.4191i	0.114888	−	1.60634i	0.648906	−	0.760869i	$-0.275227\pi$
$314$	29.0749	−	13.2996i	1.64079	−	0.750539i
$315$	0.653749	+	0.0509803i	0.0368346	+	0.00287241i
$316$	−2.95079	+	10.0952i	−0.165995	+	0.567900i
$317$	0.873531	+	12.2136i	0.0490624	+	0.685982i	0.961157	+	0.276002i	$0.0890097\pi$
$317$	0.873531	+	12.2136i	0.0490624	+	0.685982i	−0.912095	+	0.409980i	$0.865536\pi$
$318$	5.57427	−	10.2234i	0.312590	−	0.573300i
$319$	5.25896	−	11.5155i	0.294445	−	0.644745i
$320$	4.99259	+	17.1777i	0.279094	+	0.960264i
$321$	−33.0974			−1.84732
$322$	16.7879	+	7.81312i	0.935554	+	0.435408i
$323$	−1.50295	+	1.50295i	−0.0836264	+	0.0836264i
$324$	−18.4286	+	2.67268i	−1.02381	+	0.148482i
$325$	18.0574	−	13.1590i	1.00165	−	0.729932i
$326$	8.55350	+	29.0647i	0.473734	+	1.60974i
$327$	5.24205	−	0.374919i	0.289886	−	0.0207331i
$328$	−2.29254	−	4.18019i	−0.126584	−	0.230812i
$329$	−0.970278	−	1.50978i	−0.0534931	−	0.0832370i
$330$	−23.6829	+	15.0263i	−1.30370	+	0.827172i
$331$	21.6854	−	18.7905i	1.19194	−	1.03282i	0.193276	−	0.981145i	$-0.438089\pi$
$331$	21.6854	−	18.7905i	1.19194	−	1.03282i	0.998664	−	0.0516769i	$-0.0164566\pi$
$332$	4.10803	+	18.7735i	0.225457	+	1.03033i
$333$	−0.496094	+	0.371371i	−0.0271858	+	0.0203510i
$334$	−2.63367	+	18.3976i	−0.144108	+	1.00667i
$335$	6.40012	−	2.34040i	0.349676	−	0.127869i
$336$	12.6423	+	14.5179i	0.689692	+	0.792018i
$337$	19.2653	+	7.18557i	1.04945	+	0.391423i	0.814243	−	0.580524i	$-0.197152\pi$
$337$	19.2653	+	7.18557i	1.04945	+	0.391423i	0.235202	+	0.971947i	$0.424425\pi$
$338$	9.63203	+	2.08914i	0.523914	+	0.113634i
$339$	−19.0670	−	5.59858i	−1.03558	−	0.304073i
$340$	−1.28657	−	6.06595i	−0.0697743	−	0.328972i
$341$	20.4227	−	5.99665i	1.10595	−	0.324737i
$342$	−0.218124	+	0.0815083i	−0.0117948	+	0.00440746i
$343$	−14.3073	−	10.7103i	−0.772523	−	0.578303i
$344$	24.8726	−	0.0457078i	1.34104	−	0.00246440i
$345$	−3.75511	−	18.5270i	−0.202169	−	0.997463i
$346$	17.9277	−	0.0109817i	0.963799	−	0.000590382i
$347$	−14.6208	+	19.5312i	−0.784888	+	1.04849i	0.212564	+	0.977147i	$0.431819\pi$
$347$	−14.6208	+	19.5312i	−0.784888	+	1.04849i	−0.997452	+	0.0713407i	$0.977272\pi$
$348$	3.11012	+	8.30745i	0.166720	+	0.445326i
$349$	−8.49909	−	28.9452i	−0.454946	−	1.54940i	−0.793569	−	0.608481i	$-0.791779\pi$
$349$	−8.49909	−	28.9452i	−0.454946	−	1.54940i	0.338623	−	0.940922i	$-0.390039\pi$
$350$	8.23397	−	17.4613i	0.440124	−	0.933345i
$351$	−6.41954	+	21.8629i	−0.342650	+	1.16696i
$352$	−27.8304	−	5.96491i	−1.48336	−	0.317931i
$353$	−11.5113	+	30.8631i	−0.612687	+	1.64268i	0.144520	+	0.989502i	$0.453836\pi$
$353$	−11.5113	+	30.8631i	−0.612687	+	1.64268i	−0.757207	+	0.653175i	$0.773436\pi$
$354$	8.18593	−	7.10193i	0.435077	−	0.377463i
$355$	23.9400	+	11.1194i	1.27060	+	0.590159i
$356$	−0.805827	+	5.65382i	−0.0427088	+	0.299652i
$357$	−3.99906	−	5.34212i	−0.211653	−	0.282735i
$358$	4.85752	−	1.05980i	0.256728	−	0.0560124i
$359$	−10.4356	−	12.0433i	−0.550771	−	0.635623i	0.410292	−	0.911954i	$-0.365427\pi$
$359$	−10.4356	−	12.0433i	−0.550771	−	0.635623i	−0.961063	+	0.276331i	$0.910881\pi$
$360$	0.147445	−	0.663136i	0.00777103	−	0.0349503i
$361$	−14.0070	+	9.00175i	−0.737210	+	0.473776i
$362$	−0.585201	+	0.320009i	−0.0307575	+	0.0168193i
$363$	−1.80031	−	25.1716i	−0.0944917	−	1.32117i
$364$	23.4039	−	6.90315i	1.22670	−	0.361823i
$365$	10.3483	+	19.2445i	0.541657	+	1.00730i
$366$	33.3026	−	4.80902i	1.74076	−	0.251371i
$367$	8.07631	+	8.07631i	0.421580	+	0.421580i	0.885747	−	0.464168i	$-0.153646\pi$
$367$	8.07631	+	8.07631i	0.421580	+	0.421580i	−0.464168	+	0.885747i	$0.653646\pi$
$368$	10.4575	−	16.0823i	0.545135	−	0.838348i
$369$			0.181052i			0.00942517i
$370$	5.03822	+	17.5349i	0.261925	+	0.911598i
$371$	−11.6000	−	5.29753i	−0.602241	−	0.275034i
$372$	−7.13164	+	13.0988i	−0.369758	+	0.679139i
$373$	−21.3344	+	1.52587i	−1.10466	+	0.0790065i	−0.611731	−	0.791066i	$-0.709527\pi$
$373$	−21.3344	+	1.52587i	−1.10466	+	0.0790065i	−0.492924	+	0.870072i	$0.664072\pi$
$374$	9.46827	+	2.77384i	0.489593	+	0.143432i
$375$	−19.3353	+	3.81745i	−0.998470	+	0.197132i
$376$	−1.68982	+	0.775472i	−0.0871460	+	0.0399919i
$377$	11.2149	+	0.802102i	0.577594	+	0.0413104i
$378$	4.19668	+	19.2351i	0.215854	+	0.989347i
$379$	−2.21019	+	15.3722i	−0.113530	+	0.789616i	0.850910	+	0.525312i	$0.176051\pi$
$379$	−2.21019	+	15.3722i	−0.113530	+	0.789616i	−0.964439	+	0.264304i	$0.914858\pi$
$380$	−0.0356415	+	6.85535i	−0.00182837	+	0.351672i
$381$	−28.6839	−	18.4340i	−1.46952	−	0.944404i
$382$	2.70776	−	38.1881i	0.138541	−	1.95388i
$383$	19.9752	+	7.45036i	1.02068	+	0.380696i	0.803417	−	0.595417i	$-0.203013\pi$
$383$	19.9752	+	7.45036i	1.02068	+	0.380696i	0.217267	+	0.976112i	$0.430286\pi$
$384$	16.7313	−	10.8542i	0.853814	−	0.553900i
$385$	18.2494	+	24.7077i	0.930077	+	1.25922i
$386$	−5.55626	+	6.42021i	−0.282806	+	0.326780i
$387$	−0.829018	−	0.452678i	−0.0421414	−	0.0230109i
$388$	26.8594	−	10.0555i	1.36358	−	0.510492i
$389$	−0.386519	+	0.0555730i	−0.0195973	+	0.00281766i	−0.152107	−	0.988364i	$-0.548606\pi$
$389$	−0.386519	+	0.0555730i	−0.0195973	+	0.00281766i	0.132509	+	0.991182i	$0.457697\pi$
$390$	−19.8547	−	15.0439i	−1.00538	−	0.761776i
$391$	−4.02643	+	5.29212i	−0.203625	+	0.267634i
$392$	0.906111	−	0.909447i	0.0457655	−	0.0459340i
$393$	−2.15014	+	2.87225i	−0.108460	+	0.144886i
$394$	0.437928	+	0.199671i	0.0220625	+	0.0100593i
$395$	−4.81607	−	10.7276i	−0.242323	−	0.539763i
$396$	0.817742	+	0.706825i	0.0410931	+	0.0355193i
$397$	21.5666	−	11.7763i	1.08240	−	0.591034i	0.163907	−	0.986476i	$-0.447590\pi$
$397$	21.5666	−	11.7763i	1.08240	−	0.591034i	0.918491	+	0.395442i	$0.129408\pi$
$398$	2.32224	−	10.7067i	0.116403	−	0.536679i
$399$	3.06474	+	6.71084i	0.153429	+	0.335962i
$400$	−16.7117	−	10.9872i	−0.835587	−	0.549359i
$401$	−3.09466	−	1.98882i	−0.154540	−	0.0993168i	0.461085	−	0.887356i	$-0.347460\pi$
$401$	−3.09466	−	1.98882i	−0.154540	−	0.0993168i	−0.615625	+	0.788039i	$0.711097\pi$
$402$	−4.55673	−	6.07932i	−0.227269	−	0.303209i
$403$	11.3288	+	15.1335i	0.564327	+	0.753853i
$404$	−11.3709	+	17.7412i	−0.565722	+	0.882657i
$405$	13.7346	−	15.6463i	0.682476	−	0.777471i
$406$	8.83428	−	4.04102i	0.438438	−	0.200553i
$407$	−28.3652	−	6.17048i	−1.40601	−	0.305859i
$408$	−6.06153	+	3.32432i	−0.300091	+	0.164578i
$409$	−12.4954	−	10.8273i	−0.617857	−	0.535376i	0.288722	−	0.957413i	$-0.406770\pi$
$409$	−12.4954	−	10.8273i	−0.617857	−	0.535376i	−0.906579	+	0.422037i	$0.861315\pi$
$410$	4.98331	+	1.89174i	0.246108	+	0.0934264i
$411$	−24.3899	−	11.1385i	−1.20306	−	0.549420i
$412$	20.0721	−	26.8818i	0.988882	−	1.32437i
$413$	−8.39233	−	8.39233i	−0.412960	−	0.412960i
$414$	−0.641883	+	0.344528i	−0.0315468	+	0.0169326i
$415$	−17.1174	−	12.9864i	−0.840261	−	0.637475i
$416$	−3.67416	−	25.0103i	−0.180141	−	1.22623i
$417$	−5.41929	−	14.5297i	−0.265384	−	0.711522i
$418$	−9.57664	−	5.22163i	−0.468409	−	0.255398i
$419$	16.4944	−	19.0356i	0.805805	−	0.929949i	−0.192879	−	0.981223i	$-0.561783\pi$
$419$	16.4944	−	19.0356i	0.805805	−	0.929949i	0.998685	+	0.0512735i	$0.0163280\pi$
$420$	−21.2879	−	3.17378i	−1.03874	−	0.154865i
$421$	13.2784	−	8.53349i	0.647148	−	0.415897i	−0.175475	−	0.984484i	$-0.556146\pi$
$421$	13.2784	−	8.53349i	0.647148	−	0.415897i	0.822623	+	0.568587i	$0.192510\pi$
$422$	−2.78017	+	7.46788i	−0.135336	+	0.363531i
$423$	0.0704269	+	0.00503703i	0.00342427	+	0.000244909i
$424$	−7.12212	+	11.1271i	−0.345881	+	0.540382i
$425$	5.49616	+	4.22564i	0.266603	+	0.204974i
$426$	4.17031	−	29.1318i	0.202052	−	1.41144i
$427$	−7.83302	−	36.0078i	−0.379067	−	1.74254i
$428$	37.4589	+	2.63299i	1.81064	+	0.127270i
$429$	36.0531	−	16.4649i	1.74066	−	0.794933i
$430$	−21.1217	+	18.0883i	−1.01858	+	0.872293i
$431$	−3.41556	+	11.6323i	−0.164522	+	0.560310i	0.835421	+	0.549611i	$0.185224\pi$
$431$	−3.41556	+	11.6323i	−0.164522	+	0.560310i	−0.999943	+	0.0106991i	$0.996594\pi$
$432$	20.3405	−	1.50488i	0.978631	−	0.0724036i
$433$	23.5769	+	12.8740i	1.13303	+	0.618684i	0.932560	−	0.361015i	$-0.117570\pi$
$433$	23.5769	+	12.8740i	1.13303	+	0.618684i	0.200475	+	0.979699i	$0.435752\pi$
$434$	14.8617	+	6.77611i	0.713384	+	0.325264i
$435$	−8.67373	−	4.80880i	−0.415873	−	0.230565i
$436$	−5.96265	+	0.00730493i	−0.285559	+	0.000349843i
$437$	5.59339	−	4.77081i	0.267568	−	0.228219i
$438$	17.2150	−	17.2361i	0.822563	−	0.823572i
$439$	4.82069	+	33.5287i	0.230079	+	1.60024i	0.697756	+	0.716336i	$0.254182\pi$
$439$	4.82069	+	33.5287i	0.230079	+	1.60024i	−0.467677	+	0.883900i	$0.654909\pi$
$440$	27.9991	−	15.1224i	1.33481	−	0.720931i
$441$	−0.0467782	+	0.0137353i	−0.00222753	+	0.000654063i
$442$	0.630473	+	8.73993i	0.0299885	+	0.415716i
$443$	11.8828	−	6.48851i	0.564570	−	0.308279i	−0.171500	−	0.985184i	$-0.554861\pi$
$443$	11.8828	−	6.48851i	0.564570	−	0.308279i	0.736070	+	0.676906i	$0.236679\pi$
$444$	17.0979	−	11.0178i	0.811431	−	0.522881i
$445$	−3.41744	−	5.39350i	−0.162002	−	0.255677i
$446$	−8.69619	+	7.54462i	−0.411777	+	0.357248i
$447$	−0.990323	−	4.55244i	−0.0468407	−	0.215323i
$448$	−13.1533	−	17.4368i	−0.621434	−	0.823809i
$449$	−39.8422	−	5.72844i	−1.88027	−	0.270342i	−0.895610	−	0.444840i	$-0.853261\pi$
$449$	−39.8422	−	5.72844i	−1.88027	−	0.270342i	−0.984658	+	0.174498i	$0.944170\pi$
$450$	0.355813	+	0.671013i	0.0167732	+	0.0316319i
$451$	−6.40953	+	5.55389i	−0.301813	+	0.261523i
$452$	21.1342	+	7.85317i	0.994070	+	0.369382i
$453$	−4.50097	−	0.979127i	−0.211474	−	0.0460034i
$454$	−33.3898	−	9.78192i	−1.56706	−	0.459088i
$455$	−14.8962	+	22.8549i	−0.698347	+	1.07145i
$456$	7.32945	−	2.16676i	0.343233	−	0.101468i
$457$	−2.01052	−	5.39041i	−0.0940481	−	0.252153i	0.881405	−	0.472362i	$-0.156599\pi$
$457$	−2.01052	−	5.39041i	−0.0940481	−	0.252153i	−0.975453	+	0.220210i	$0.929326\pi$
$458$	6.18703	−	8.27547i	0.289101	−	0.386687i
$459$	−7.07009			−0.330004
$460$	2.77607	+	21.2672i	0.129435	+	0.991588i
$461$	22.0662			1.02773			0.513864	−	0.857872i	$-0.328214\pi$
$461$	22.0662			1.02773			0.513864	+	0.857872i	$0.328214\pi$
$462$	20.5057	−	27.4275i	0.954013	−	1.27604i
$463$	−11.3435	−	30.4132i	−0.527179	−	1.41342i	−0.878760	−	0.477263i	$-0.841629\pi$
$463$	−11.3435	−	30.4132i	−0.527179	−	1.41342i	0.351582	−	0.936157i	$-0.385644\pi$
$464$	−2.85907	−	9.64959i	−0.132729	−	0.447971i
$465$	−3.43973	−	16.3161i	−0.159513	−	0.756641i
$466$	−27.0673	−	7.92967i	−1.25387	−	0.367335i
$467$	−13.1971	−	2.87086i	−0.610690	−	0.132847i	−0.103424	−	0.994637i	$-0.532980\pi$
$467$	−13.1971	−	2.87086i	−0.610690	−	0.132847i	−0.507265	+	0.861790i	$0.669344\pi$
$468$	−0.334376	+	0.899862i	−0.0154565	+	0.0415961i
$469$	−6.28819	+	5.44875i	−0.290362	+	0.251600i
$470$	0.874505	−	1.88582i	0.0403379	−	0.0869863i
$471$	39.4471	+	5.67164i	1.81763	+	0.261335i
$472$	−9.82961	+	7.38658i	−0.452445	+	0.339995i
$473$	−9.40517	−	43.2349i	−0.432450	−	1.98794i
$474$	−9.90259	+	8.59127i	−0.454841	+	0.394610i
$475$	−4.94442	−	5.85654i	−0.226866	−	0.268717i
$476$	4.10106	+	6.36422i	0.187972	+	0.291703i
$477$	0.440338	−	0.240443i	0.0201617	−	0.0110091i
$478$	2.86233	+	39.6790i	0.130920	+	1.81488i
$479$	11.1424	−	3.27169i	0.509107	−	0.149487i	−0.0170834	−	0.999854i	$-0.505438\pi$
$479$	11.1424	−	3.27169i	0.509107	−	0.149487i	0.526190	+	0.850367i	$0.323620\pi$
$480$	−6.35386	+	21.3732i	−0.290013	+	0.975549i
$481$	−3.66911	−	25.5192i	−0.167297	−	1.16358i
$482$	3.13290	−	3.13674i	0.142700	−	0.142875i
$483$	12.3267	+	19.5137i	0.560883	+	0.887906i
$484$	0.0350773	+	28.6318i	0.00159442	+	1.30145i
$485$	−15.5477	+	28.0436i	−0.705984	+	1.27340i
$486$	−1.43568	−	0.654592i	−0.0651239	−	0.0296929i
$487$	−37.5072	−	20.4805i	−1.69961	−	0.928058i	−0.969625	−	0.244598i	$-0.921344\pi$
$487$	−37.5072	−	20.4805i	−1.69961	−	0.928058i	−0.729987	−	0.683461i	$-0.760474\pi$
$488$	−38.0737	+	2.79342i	−1.72351	+	0.126452i
$489$	−10.6395	+	36.2350i	−0.481137	+	1.63860i
$490$	−0.110714	+	1.43105i	−0.00500153	+	0.0646483i
$491$	0.248186	−	0.113343i	0.0112005	−	0.00511509i	−0.409807	−	0.912172i	$-0.634404\pi$
$491$	0.248186	−	0.113343i	0.0112005	−	0.00511509i	0.421007	+	0.907057i	$0.361677\pi$
$492$	0.416682	−	5.92803i	0.0187855	−	0.267256i
$493$	0.741570	+	3.40894i	0.0333986	+	0.153531i
$494$	1.37282	−	9.58984i	0.0617659	−	0.431467i
$495$	−1.20844	−	0.00776327i	−0.0543152	−	0.000348933i
$496$	9.11346	−	14.2575i	0.409206	−	0.640181i
$497$	−32.1471	−	2.29921i	−1.44199	−	0.103133i
$498$	−8.35748	+	22.4493i	−0.374508	+	1.00598i
$499$	21.2459	−	13.6539i	0.951097	−	0.611233i	0.0295768	−	0.999563i	$-0.490584\pi$
$499$	21.2459	−	13.6539i	0.951097	−	0.611233i	0.921521	+	0.388329i	$0.126948\pi$
$500$	22.1869	−	2.78232i	0.992229	−	0.124429i
$501$	−15.1705	+	17.5076i	−0.677766	+	0.782184i
$502$	3.76146	+	2.05092i	0.167882	+	0.0915373i
$503$	−0.115642	−	0.310049i	−0.00515624	−	0.0138244i	0.934346	−	0.356367i	$-0.115985\pi$
$503$	−0.115642	−	0.310049i	−0.00515624	−	0.0138244i	−0.939502	+	0.342542i	$0.888712\pi$
$504$	0.119551	+	0.820784i	0.00532521	+	0.0365606i
$505$	−3.20301	−	23.3409i	−0.142532	−	1.03866i
$506$	−31.8871	−	12.1551i	−1.41755	−	0.540360i
$507$	8.68700	+	8.68700i	0.385803	+	0.385803i
$508$	30.9973	+	23.1451i	1.37528	+	1.02690i
$509$	27.0648	+	12.3601i	1.19963	+	0.547851i	0.912119	−	0.409927i	$-0.134446\pi$
$509$	27.0648	+	12.3601i	1.19963	+	0.547851i	0.287509	+	0.957778i	$0.407173\pi$
$510$	2.74314	−	7.22612i	0.121468	−	0.319978i
$511$	−20.1624	−	17.4708i	−0.891933	−	0.772864i
$512$	−19.7995	+	10.9535i	−0.875024	+	0.484080i
$513$	7.63777	+	1.66149i	0.337216	+	0.0733568i
$514$	−8.18169	+	3.74251i	−0.360879	+	0.165075i
$515$	2.43544	+	37.4295i	0.107318	+	1.64934i
$516$	26.1021	+	16.7296i	1.14908	+	0.736482i
$517$	1.98208	+	2.64775i	0.0871717	+	0.116448i
$518$	−13.3604	−	17.8246i	−0.587022	−	0.783169i
$519$	18.7991	+	12.0814i	0.825187	+	0.530315i
$520$	21.2743	+	18.6058i	0.932938	+	0.815917i
$521$	−4.65779	−	10.1991i	−0.204061	−	0.446832i	0.779738	−	0.626106i	$-0.215352\pi$
$521$	−4.65779	−	10.1991i	−0.204061	−	0.446832i	−0.983799	+	0.179274i	$0.942625\pi$
$522$	−0.0810129	+	0.373512i	−0.00354584	+	0.0163482i
$523$	−2.08909	+	1.14073i	−0.0913495	+	0.0498806i	−0.524274	−	0.851549i	$-0.675663\pi$
$523$	−2.08909	+	1.14073i	−0.0913495	+	0.0498806i	0.432925	+	0.901430i	$0.357482\pi$
$524$	2.66197	−	3.07969i	0.116289	−	0.134537i
$525$	20.4091	−	12.7486i	0.890725	−	0.556395i
$526$	29.8471	+	13.6086i	1.30140	+	0.593365i
$527$	−3.51513	+	4.69567i	−0.153122	+	0.204547i
$528$	−25.1480	−	25.0250i	−1.09442	−	1.08907i
$529$	15.3312	−	17.1451i	0.666572	−	0.745440i
$530$	−2.01708	−	14.6323i	−0.0876165	−	0.635586i
$531$	0.462183	−	0.0664519i	0.0200570	−	0.00288377i
$532$	−2.93473	−	7.83898i	−0.127237	−	0.339863i
$533$	−6.61101	−	3.60989i	−0.286355	−	0.156362i
$534$	−4.65838	+	5.38271i	−0.201588	+	0.232933i
$535$	−33.7705	+	24.9434i	−1.46003	+	1.07840i
$536$	4.67358	+	7.24293i	0.201868	+	0.312847i
$537$	5.80648	+	2.16571i	0.250568	+	0.0934571i
$538$	−0.577120	+	8.13926i	−0.0248814	+	0.350908i
$539$	−1.92121	−	1.23469i	−0.0827523	−	0.0531817i
$540$	−16.2081	+	16.0404i	−0.697486	+	0.690271i
$541$	−5.11186	+	35.5538i	−0.219776	+	1.52858i	0.519088	+	0.854721i	$0.326272\pi$
$541$	−5.11186	+	35.5538i	−0.219776	+	1.52858i	−0.738864	+	0.673854i	$0.764637\pi$
$542$	−1.09344	−	5.01167i	−0.0469672	−	0.215270i
$543$	−0.829261	−	0.0593099i	−0.0355870	−	0.00254523i
$544$	7.12475	−	3.28018i	0.305471	−	0.140636i
$545$	5.06611	−	4.33314i	0.217008	−	0.185611i
$546$	29.1881	+	8.55099i	1.24914	+	0.365949i
$547$	16.4367	−	1.17558i	0.702783	−	0.0502641i	0.284626	−	0.958639i	$-0.408131\pi$
$547$	16.4367	−	1.17558i	0.702783	−	0.0502641i	0.418157	+	0.908375i	$0.362676\pi$
$548$	26.7178	+	14.5465i	1.14133	+	0.621397i
$549$	1.31875	+	0.602252i	0.0562828	+	0.0257035i
$550$	−12.8402	+	33.1802i	−0.547507	+	1.41481i
$551$		−	3.85693i		−	0.164311i
$552$	21.8096	−	9.80334i	0.928278	−	0.417258i
$553$	10.1523	+	10.1523i	0.431719	+	0.431719i
$554$	32.9052	−	4.75162i	1.39801	−	0.201877i
$555$	−6.54699	+	21.7784i	−0.277904	+	0.924443i
$556$	4.97755	+	16.8755i	0.211095	+	0.715679i
$557$	1.63440	+	22.8519i	0.0692518	+	0.968267i	0.906707	+	0.421761i	$0.138588\pi$
$557$	1.63440	+	22.8519i	0.0692518	+	0.968267i	−0.837455	+	0.546506i	$0.815958\pi$
$558$	−0.563807	+	0.308311i	−0.0238679	+	0.0130518i
$559$	33.0587	−	21.2455i	1.39823	−	0.898589i
$560$	23.8406	+	5.28552i	1.00745	+	0.223354i
$561$	8.05349	+	9.29423i	0.340019	+	0.392403i
$562$	−28.3157	+	6.17786i	−1.19442	+	0.260597i
$563$	−1.02818	−	1.37349i	−0.0433326	−	0.0578855i	0.778352	−	0.627829i	$-0.216056\pi$
$563$	−1.02818	−	1.37349i	−0.0433326	−	0.0578855i	−0.821684	+	0.569943i	$0.806965\pi$
$564$	−2.29434	−	0.327008i	−0.0966092	−	0.0137695i
$565$	−23.6741	+	8.65715i	−0.995977	+	0.364209i
$566$	−18.7945	+	16.3057i	−0.789993	+	0.685381i
$567$	−8.88334	+	23.8172i	−0.373065	+	1.00023i
$568$	−7.03737	+	32.6389i	−0.295281	+	1.36950i
$569$	−2.07939	+	7.08174i	−0.0871724	+	0.296882i	−0.991527	−	0.129900i	$-0.958534\pi$
$569$	−2.07939	+	7.08174i	−0.0871724	+	0.296882i	0.904355	+	0.426782i	$0.140353\pi$
$570$	−4.66156	+	7.16167i	−0.195251	+	0.299969i
$571$	−9.41234	−	32.0555i	−0.393894	−	1.34148i	−0.883048	−	0.469283i	$-0.844513\pi$
$571$	−9.41234	−	32.0555i	−0.393894	−	1.34148i	0.489154	−	0.872198i	$-0.337306\pi$
$572$	−42.1139	+	15.7665i	−1.76087	+	0.659229i
$573$	28.5976	−	38.2020i	1.19468	−	1.59591i
$574$	−6.50816	+	0.00398662i	−0.271645	+	0.000166398i
$575$	−17.7941	−	16.0739i	−0.742067	−	0.670326i
$576$	0.859286	−	0.00315819i	0.0358036	−	0.000131591i
$577$	−10.5394	−	7.88971i	−0.438762	−	0.328453i	0.356955	−	0.934122i	$-0.383815\pi$
$577$	−10.5394	−	7.88971i	−0.438762	−	0.328453i	−0.795717	+	0.605668i	$0.792906\pi$
$578$	19.9738	−	7.46377i	0.830799	−	0.310452i
$579$	−10.1547	+	2.98169i	−0.422015	+	0.123915i
$580$	9.43416	+	6.13251i	0.391732	+	0.254638i
$581$	25.1713	+	7.39096i	1.04428	+	0.306629i
$582$	34.9366	+	7.57758i	1.44817	+	0.314101i
$583$	22.0198	+	8.21296i	0.911967	+	0.340146i
$584$	−20.8547	+	18.1379i	−0.862972	+	0.750551i
$585$	−0.368608	−	1.00801i	−0.0152401	−	0.0416759i
$586$	−0.204483	+	1.42842i	−0.00844711	+	0.0590075i
$587$	−8.64930	+	6.47479i	−0.356995	+	0.267243i	−0.762688	−	0.646766i	$-0.776121\pi$
$587$	−8.64930	+	6.47479i	−0.356995	+	0.267243i	0.405693	+	0.914009i	$0.367030\pi$
$588$	1.56323	−	0.342067i	0.0644667	−	0.0141066i
$589$	4.90087	−	4.24663i	0.201937	−	0.174979i
$590$	3.00014	−	13.4156i	0.123514	−	0.552311i
$591$	0.324346	+	0.504692i	0.0133418	+	0.0207603i
$592$	−20.2275	+	11.1095i	−0.831345	+	0.456597i
$593$	10.3989	−	0.743743i	0.427031	−	0.0305419i	0.143830	−	0.989602i	$-0.454058\pi$
$593$	10.3989	−	0.743743i	0.427031	−	0.0305419i	0.283201	+	0.959061i	$0.408604\pi$
$594$	−10.2433	−	34.8066i	−0.420288	−	1.42813i
$595$	−8.10641	−	2.43693i	−0.332330	−	0.0999044i
$596$	0.758665	+	5.23113i	0.0310761	+	0.214275i
$597$	9.65624	−	9.65624i	0.395204	−	0.395204i
$598$	0.217881	−	30.3074i	0.00890980	−	1.23936i
$599$	−16.4094			−0.670471			−0.335236	−	0.942134i	$-0.608816\pi$
$599$	−16.4094			−0.670471			−0.335236	+	0.942134i	$0.608816\pi$
$600$	−10.1058	−	22.7894i	−0.412568	−	0.930372i
$601$	−4.31560	+	9.44985i	−0.176037	+	0.385467i	−0.976998	−	0.213250i	$-0.931595\pi$
$601$	−4.31560	+	9.44985i	−0.176037	+	0.385467i	0.800961	+	0.598717i	$0.204323\pi$
$602$	16.2539	−	29.8102i	0.662460	−	1.21497i
$603$	−0.0233526	−	0.326512i	−0.000950991	−	0.0132966i
$604$	5.01620	+	1.46622i	0.204106	+	0.0596595i
$605$	−20.8072	−	24.3268i	−0.845931	−	0.989024i
$606$	−23.8860	+	10.9260i	−0.970301	+	0.443840i
$607$	−1.31389	+	18.3705i	−0.0533290	+	0.745636i	0.898494	+	0.438987i	$0.144663\pi$
$607$	−1.31389	+	18.3705i	−0.0533290	+	0.745636i	−0.951822	+	0.306650i	$0.900792\pi$
$608$	−8.46767	+	1.86921i	−0.343409	+	0.0758064i
$609$	11.9858	+	1.72330i	0.485691	+	0.0698318i
$610$	30.3557	−	30.0049i	1.22907	−	1.21486i
$611$	−1.58813	+	2.47117i	−0.0642488	+	0.0999730i
$612$	−0.297132	−	0.0208855i	−0.0120109	−	0.000844245i
$613$	−5.06999	+	13.5932i	−0.204775	+	0.549022i	−0.998221	−	0.0596175i	$-0.981012\pi$
$613$	−5.06999	+	13.5932i	−0.204775	+	0.549022i	0.793447	+	0.608640i	$0.208285\pi$
$614$	2.49349	−	1.60463i	0.100629	−	0.0647574i
$615$	3.94741	+	5.34434i	0.159175	+	0.215505i
$616$	−25.3898	+	29.4104i	−1.02298	+	1.18498i
$617$	−1.72821	+	3.16498i	−0.0695752	+	0.127417i	−0.910151	−	0.414276i	$-0.864035\pi$
$617$	−1.72821	+	3.16498i	−0.0695752	+	0.127417i	0.840576	+	0.541693i	$0.182217\pi$
$618$	39.1722	−	14.6378i	1.57574	−	0.588819i
$619$	0.0878256	+	0.610841i	0.00353001	+	0.0245518i	0.991510	−	0.130028i	$-0.0415067\pi$
$619$	0.0878256	+	0.610841i	0.00353001	+	0.0245518i	−0.987980	+	0.154580i	$0.950598\pi$
$620$	2.59501	+	18.7398i	0.104218	+	0.752609i
$621$	24.3773	+	1.93476i	0.978229	+	0.0776394i
$622$	−10.3928	−	10.3800i	−0.416712	−	0.416202i
$623$	6.24099	+	4.67195i	0.250040	+	0.187178i
$624$	13.0192	−	28.6939i	0.521186	−	1.14868i
$625$	−16.8516	+	18.4669i	−0.674063	+	0.738674i
$626$	−26.3679	+	30.4678i	−1.05387	+	1.21774i
$627$	−6.51596	−	11.9331i	−0.260222	−	0.476561i
$628$	−44.1941	−	9.55715i	−1.76354	−	0.381372i
$629$	7.27670	−	3.32316i	0.290141	−	0.132503i
$630$	−0.697301	−	0.611346i	−0.0277811	−	0.0243566i
$631$	−11.7006	+	18.2065i	−0.465794	+	0.724789i	−0.992092	−	0.125511i	$-0.959943\pi$
$631$	−11.7006	+	18.2065i	−0.465794	+	0.724789i	0.526299	+	0.850300i	$0.323579\pi$
$632$	11.8910	−	8.93562i	0.472998	−	0.355440i
$633$	−7.95152	+	5.95243i	−0.316045	+	0.236588i
$634$	9.35319	−	14.5735i	0.371463	−	0.578786i
$635$	−43.1598	+	2.80829i	−1.71275	+	0.111444i
$636$	−14.9710	+	6.85922i	−0.593640	+	0.271986i
$637$	0.431145	−	1.98194i	0.0170826	−	0.0785275i
$638$	−15.7081	+	8.58975i	−0.621889	+	0.340072i
$639$	0.830344	−	0.958268i	0.0328479	−	0.0379085i
$640$	8.89144	−	23.6842i	0.351465	−	0.936201i
$641$	−17.9025	+	39.2010i	−0.707105	+	1.54834i	0.124032	+	0.992278i	$0.460417\pi$
$641$	−17.9025	+	39.2010i	−0.707105	+	1.54834i	−0.831138	+	0.556067i	$0.812310\pi$
$642$	37.4880	+	28.0273i	1.47953	+	1.10615i
$643$	24.5624	−	24.5624i	0.968648	−	0.968648i	−0.0308753	−	0.999523i	$-0.509829\pi$
$643$	24.5624	−	24.5624i	0.968648	−	0.968648i	0.999523	+	0.0308753i	$0.00982948\pi$
$644$	−12.3987	−	23.0658i	−0.488576	−	0.908920i
$645$	−34.3408	+	4.71250i	−1.35217	+	0.185555i
$646$	2.97504	−	0.429607i	0.117051	−	0.0169026i
$647$	5.02050	−	1.87255i	0.197376	−	0.0736175i	−0.248832	−	0.968547i	$-0.580047\pi$
$647$	5.02050	−	1.87255i	0.197376	−	0.0736175i	0.446208	+	0.894929i	$0.352774\pi$
$648$	23.1365	+	12.5783i	0.908888	+	0.494124i
$649$	16.5303	+	14.3236i	0.648872	+	0.562250i
$650$	−31.5961	−	0.386620i	−1.23930	−	0.0151645i
$651$	11.0071	+	17.1274i	0.431404	+	0.671277i
$652$	14.9242	−	40.1635i	0.584476	−	1.57292i
$653$	−2.91403	+	40.7435i	−0.114035	+	1.59442i	0.542458	+	0.840083i	$0.317494\pi$
$653$	−2.91403	+	40.7435i	−0.114035	+	1.59442i	−0.656493	+	0.754332i	$0.727961\pi$
$654$	−6.25492	−	4.01438i	−0.244587	−	0.156975i
$655$	−0.0292372	+	4.55109i	−0.00114239	+	0.177826i
$656$	−0.943182	+	6.67606i	−0.0368251	+	0.260656i
$657$	1.02561	−	0.223109i	0.0400130	−	0.00870430i
$658$	−0.179513	+	2.53171i	−0.00699813	+	0.0986962i
$659$	−5.78258	−	12.6621i	−0.225257	−	0.493244i	0.762933	−	0.646478i	$-0.223759\pi$
$659$	−5.78258	−	12.6621i	−0.225257	−	0.493244i	−0.988190	+	0.153233i	$0.951031\pi$
$660$	39.5490	+	3.03535i	1.53944	+	0.118151i
$661$	23.5279	+	6.90841i	0.915129	+	0.268706i	0.705198	−	0.709010i	$-0.250858\pi$
$661$	23.5279	+	6.90841i	0.915129	+	0.268706i	0.209931	+	0.977716i	$0.432676\pi$
$662$	−40.4742	+	2.91969i	−1.57307	+	0.113477i
$663$	−5.23456	+	9.58638i	−0.203294	+	0.372304i
$664$	11.2447	−	24.7427i	0.436379	−	0.960202i
$665$	8.18460	+	4.53763i	0.317385	+	0.175962i
$666$	0.876385		0.000536836i	0.0339592		2.08020e-5i
$667$	−1.62403	−	11.9568i	−0.0628825	−	0.462969i
$668$	18.5623	−	18.6079i	0.718198	−	0.719960i
$669$	−14.2044	+	2.04229i	−0.549174	+	0.0789593i
$670$	−9.23100	−	2.76884i	−0.356625	−	0.106970i
$671$	19.1328	+	65.1605i	0.738615	+	2.51549i
$672$	−2.02536	−	27.1494i	−0.0781301	−	1.04731i
$673$	6.45771	+	11.8264i	0.248927	+	0.455875i	0.972027	−	0.234868i	$-0.0754656\pi$
$673$	6.45771	+	11.8264i	0.248927	+	0.455875i	−0.723101	+	0.690743i	$0.757284\pi$
$674$	−15.7361	−	24.4528i	−0.606130	−	0.941888i
$675$	2.14537	−	25.4046i	0.0825754	−	0.977825i
$676$	−9.14066	−	10.5228i	−0.351564	−	0.404723i
$677$	−30.8434	+	6.70958i	−1.18541	+	0.257870i	−0.761701	−	0.647929i	$-0.775635\pi$
$677$	−30.8434	+	6.70958i	−1.18541	+	0.257870i	−0.423708	+	0.905799i	$0.639272\pi$
$678$	16.8554	+	22.4875i	0.647328	+	0.863626i
$679$	5.57173	−	38.7523i	0.213823	−	1.48718i
$680$	−3.67948	+	7.96012i	−0.141102	+	0.305257i
$681$	−28.4006	−	32.7760i	−1.08831	−	1.25598i
$682$	−28.2099	−	10.5021i	−1.08021	−	0.402145i
$683$	−4.34198	+	19.9598i	−0.166141	+	0.763739i	0.816369	+	0.577531i	$0.195984\pi$
$683$	−4.34198	+	19.9598i	−0.166141	+	0.763739i	−0.982510	+	0.186208i	$0.940380\pi$
$684$	0.316081	+	0.0923894i	0.0120857	+	0.00353260i
$685$	−33.2802	+	7.01607i	−1.27157	+	0.268070i
$686$	7.13562	+	24.2467i	0.272439	+	0.925745i
$687$	12.0673	−	4.50088i	0.460397	−	0.171719i
$688$	−28.2108	−	21.0107i	−1.07553	−	0.801025i
$689$			20.8728i			0.795190i
$690$	−11.4357	+	24.1646i	−0.435349	+	0.919932i
$691$		−	12.7152i		−	0.483709i	−0.970312	−	0.241855i	$-0.922244\pi$
$691$		−	12.7152i		−	0.483709i	0.970312	−	0.241855i	$-0.0777557\pi$
$692$	−20.3152	−	15.1690i	−0.772268	−	0.576638i
$693$	1.38247	−	0.515634i	0.0525157	−	0.0195873i
$694$	33.0996	−	9.74095i	1.25644	−	0.369762i
$695$	−16.4796	−	10.7410i	−0.625107	−	0.407430i
$696$	3.51216	−	12.0432i	0.133128	−	0.456495i
$697$	0.496802	−	2.28376i	0.0188177	−	0.0865036i
$698$	−14.8847	+	39.9821i	−0.563393	+	1.51334i
$699$	−23.0228	−	26.5697i	−0.870803	−	1.00496i
$700$	−24.1127	+	12.8050i	−0.911374	+	0.483982i
$701$	−1.41988	+	9.87551i	−0.0536283	+	0.372993i	0.945279	+	0.326262i	$0.105789\pi$
$701$	−1.41988	+	9.87551i	−0.0536283	+	0.372993i	−0.998908	+	0.0467304i	$0.985120\pi$
$702$	25.7849	−	19.3270i	0.973190	−	0.729452i
$703$	−8.64191	+	1.87993i	−0.325936	+	0.0709030i
$704$	26.4710	+	30.3233i	0.997665	+	1.14285i
$705$	2.18871	−	1.38681i	0.0824314	−	0.0522303i
$706$	39.1737	−	25.2093i	1.47432	−	0.948765i
$707$	13.7860	+	25.2471i	0.518474	+	0.949515i
$708$	−15.2858	+	1.11209i	−0.574477	+	0.0417949i
$709$	−9.34904	−	31.8399i	−0.351111	−	1.19577i	−0.925994	−	0.377538i	$-0.876771\pi$
$709$	−9.34904	−	31.8399i	−0.351111	−	1.19577i	0.574883	−	0.818235i	$-0.305047\pi$
$710$	−17.6997	−	32.8672i	−0.664256	−	1.23348i
$711$	−0.559107	+	0.0803875i	−0.0209682	+	0.00301477i
$712$	5.70045	−	5.72144i	0.213633	−	0.214420i
$713$	13.4050	−	15.2285i	0.502021	−	0.570312i
$714$	0.00578085	+	9.43724i	0.000216343	+	0.353180i
$715$	24.3778	−	43.9707i	0.911678	−	1.64441i
$716$	−6.39935	−	2.91301i	−0.239155	−	0.108864i
$717$	−23.7648	+	43.5219i	−0.887512	+	1.62536i
$718$	1.62150	+	22.4780i	0.0605137	+	0.838870i
$719$	−22.7986	−	6.69427i	−0.850244	−	0.249654i	−0.172552	−	0.985000i	$-0.555201\pi$
$719$	−22.7986	−	6.69427i	−0.850244	−	0.249654i	−0.677692	+	0.735346i	$0.737020\pi$
$720$	−0.728556	+	0.626246i	−0.0271517	+	0.0233388i
$721$	−19.0248	−	41.6585i	−0.708521	−	1.55144i
$722$	23.4879	+	1.66543i	0.874129	+	0.0619808i
$723$	5.39973	−	1.17464i	0.200818	−	0.0436853i
$724$	0.933819	+	0.133095i	0.0347051	+	0.00494645i
$725$	−12.4742	+	1.63023i	−0.463281	+	0.0605452i
$726$	−19.2765	+	30.0353i	−0.715419	+	1.11471i
$727$	−1.36743	+	19.1192i	−0.0507153	+	0.709092i	0.906955	+	0.421226i	$0.138400\pi$
$727$	−1.36743	+	19.1192i	−0.0507153	+	0.709092i	−0.957671	+	0.287866i	$0.907054\pi$
$728$	−32.3542	−	11.9998i	−1.19913	−	0.444742i
$729$	14.0379	+	21.8434i	0.519923	+	0.809015i
$730$	4.57536	−	30.5605i	0.169342	−	1.13109i
$731$	9.21498	+	7.98483i	0.340828	+	0.295330i
$732$	−41.7927	−	22.7541i	−1.54470	−	0.841017i
$733$	3.43781	−	1.28224i	0.126978	−	0.0473605i	−0.285172	−	0.958476i	$-0.592051\pi$
$733$	3.43781	−	1.28224i	0.126978	−	0.0473605i	0.412150	+	0.911116i	$0.364778\pi$
$734$	−2.30855	−	15.9868i	−0.0852102	−	0.590083i
$735$	−1.08135	+	1.42533i	−0.0398861	+	0.0525742i
$736$	−25.4634	+	9.36017i	−0.938595	+	0.345020i
$737$	10.8427	−	10.8427i	0.399397	−	0.399397i
$738$	0.153317	−	0.205069i	0.00564367	−	0.00754870i
$739$	−6.22250	+	13.6254i	−0.228898	+	0.501217i	−0.988878	−	0.148730i	$-0.952482\pi$
$739$	−6.22250	+	13.6254i	−0.228898	+	0.501217i	0.759980	+	0.649947i	$0.225209\pi$
$740$	9.14225	−	24.1275i	0.336076	−	0.886944i
$741$	7.90769	−	9.12596i	0.290496	−	0.335251i
$742$	8.65276	+	15.8233i	0.317653	+	0.580891i
$743$	−0.420876	+	1.93474i	−0.0154404	+	0.0709786i	−0.984222	−	0.176936i	$-0.943382\pi$
$743$	−0.420876	+	1.93474i	−0.0154404	+	0.0709786i	0.968782	+	0.247914i	$0.0797451\pi$
$744$	19.1699	−	8.79720i	0.702802	−	0.322521i
$745$	−4.44135	−	3.89869i	−0.162718	−	0.142837i
$746$	25.4567	+	16.3380i	0.932035	+	0.598176i
$747$	−0.826241	+	0.618516i	−0.0302306	+	0.0226303i
$748$	−8.37537	−	11.1597i	−0.306234	−	0.408037i
$749$	27.7137	−	43.1234i	1.01264	−	1.57570i
$750$	25.1329	+	12.0495i	0.917723	+	0.439987i
$751$	22.0110	−	10.0521i	0.803192	−	0.366805i	0.0288586	−	0.999584i	$-0.490813\pi$
$751$	22.0110	−	10.0521i	0.803192	−	0.366805i	0.774333	+	0.632778i	$0.218085\pi$
$752$	2.57067	+	0.552621i	0.0937426	+	0.0201520i
$753$	2.55930	+	4.68701i	0.0932662	+	0.170804i
$754$	−12.0233	−	10.4054i	−0.437864	−	0.378942i
$755$	−5.33042	+	2.39306i	−0.193994	+	0.0870922i
$756$	11.5351	−	25.3405i	0.419529	−	0.921626i
$757$	−27.4270	−	20.5316i	−0.996852	−	0.746234i	−0.0294727	−	0.999566i	$-0.509383\pi$
$757$	−27.4270	−	20.5316i	−0.996852	−	0.746234i	−0.967380	+	0.253331i	$0.918474\pi$
$758$	15.5207	−	15.5398i	0.563739	−	0.564430i
$759$	−25.2247	−	34.2499i	−0.915597	−	1.24319i
$760$	5.84557	−	7.73457i	0.212041	−	0.280562i
$761$	−5.53659	−	38.5078i	−0.200701	−	1.39591i	−0.802210	−	0.597042i	$-0.796343\pi$
$761$	−5.53659	−	38.5078i	−0.200701	−	1.39591i	0.601509	−	0.798866i	$-0.294566\pi$
$762$	16.8788	+	45.1693i	0.611455	+	1.63631i
$763$	−3.90088	+	7.14392i	−0.141221	+	0.258627i
$764$	−35.4052	+	40.9610i	−1.28091	+	1.48192i
$765$	0.267876	−	0.197857i	0.00968506	−	0.00715353i
$766$	−16.3159	−	25.3539i	−0.589519	−	0.916075i
$767$	−6.78875	+	18.2013i	−0.245127	+	0.657212i
$768$	−28.1422	−	1.87420i	−1.01549	−	0.0676295i
$769$	4.58972	−	7.14174i	0.165509	−	0.257538i	−0.748585	−	0.663039i	$-0.769267\pi$
$769$	4.58972	−	7.14174i	0.165509	−	0.257538i	0.914095	+	0.405501i	$0.132903\pi$
$770$	0.252453	−	43.4391i	0.00909777	−	1.56544i
$771$	−11.1004	−	1.59600i	−0.399773	−	0.0574786i
$772$	11.7301	−	2.56677i	0.422174	−	0.0923801i
$773$	0.308170	−	4.30879i	0.0110841	−	0.154976i	−0.988896	−	0.148612i	$-0.952520\pi$
$773$	0.308170	−	4.30879i	0.0110841	−	0.154976i	0.999980	−	0.00636455i	$-0.00202591\pi$
$774$	0.555658	+	1.21475i	0.0199727	+	0.0436633i
$775$	−15.8061	−	14.0556i	−0.567771	−	0.504893i
$776$	−38.9376	−	11.3554i	−1.39778	−	0.407636i
$777$	−1.98084	−	27.6957i	−0.0710621	−	0.993578i
$778$	0.484852	+	0.264364i	0.0173828	+	0.00947791i
$779$	−1.07338	+	2.35038i	−0.0384579	+	0.0842111i
$780$	9.74917	+	33.8527i	0.349076	+	1.21212i
$781$	59.3957			2.12535
$782$	9.04200	−	2.58451i	0.323341	−	0.0924219i
$783$	9.07177	−	9.07177i	0.324198	−	0.324198i
$784$	−1.79644	+	0.262784i	−0.0641587	+	0.00938513i
$785$	44.5237	−	23.9418i	1.58912	−	0.854519i
$786$	4.86763	−	1.43250i	0.173622	−	0.0510957i
$787$	23.3077	−	1.66700i	0.830831	−	0.0594222i	0.350558	−	0.936541i	$-0.385992\pi$
$787$	23.3077	−	1.66700i	0.830831	−	0.0594222i	0.480273	+	0.877119i	$0.340538\pi$
$788$	−0.326937	−	0.597001i	−0.0116467	−	0.0212673i
$789$	22.1059	+	34.3975i	0.786992	+	1.22458i
$790$	−3.62930	+	16.2290i	−0.129125	+	0.577400i
$791$	23.2601	−	20.1550i	0.827033	−	0.716628i
$792$	−0.327671	−	1.49306i	−0.0116433	−	0.0530537i
$793$	−48.2848	+	36.1455i	−1.71464	+	1.28357i
$794$	−34.3999	−	4.92445i	−1.22081	−	0.174762i
$795$	7.75576	−	16.6980i	0.275068	−	0.592218i
$796$	−11.6969	+	10.1605i	−0.414585	+	0.360130i
$797$	−9.21823	−	3.43822i	−0.326527	−	0.121788i	0.180855	−	0.983510i	$-0.442114\pi$
$797$	−9.21823	−	3.43822i	−0.326527	−	0.121788i	−0.507381	+	0.861722i	$0.669386\pi$
$798$	2.21154	−	10.1963i	0.0782875	−	0.360946i
$799$	−0.874534	−	0.256786i	−0.0309388	−	0.00908445i
$800$	9.62455	+	26.5964i	0.340279	+	0.940324i
$801$	−0.294287	+	0.0864105i	−0.0103981	+	0.00305316i
$802$	1.82103	+	4.87324i	0.0643027	+	0.172080i
$803$	39.3599	+	29.4644i	1.38898	+	1.03978i
$804$	0.0131632	+	10.7445i	0.000464231	+	0.378928i
$805$	27.2836	+	10.6208i	0.961622	+	0.374333i
$806$	−0.0163764	−	26.7344i	−0.000576832	−	0.941679i
$807$	−6.09517	+	8.14220i	−0.214560	+	0.286619i
$808$	27.9027	−	10.4656i	0.981615	−	0.368180i
$809$	6.76421	+	23.0368i	0.237817	+	0.809930i	0.988753	+	0.149555i	$0.0477842\pi$
$809$	6.76421	+	23.0368i	0.237817	+	0.809930i	−0.750936	+	0.660374i	$0.770398\pi$
$810$	−28.8060	+	6.09126i	−1.01214	+	0.214025i
$811$	−2.86181	+	9.74642i	−0.100492	+	0.342243i	−0.994356	−	0.106094i	$-0.966165\pi$
$811$	−2.86181	+	9.74642i	−0.100492	+	0.342243i	0.893864	+	0.448337i	$0.147984\pi$
$812$	−13.4282	−	2.90390i	−0.471237	−	0.101907i
$813$	2.23444	−	5.99075i	0.0783651	−	0.210105i
$814$	26.9028	+	31.0091i	0.942942	+	1.08687i
$815$	16.4520	+	44.9902i	0.576290	+	1.57594i
$816$	9.68070	+	1.36767i	0.338892	+	0.0478781i
$817$	−8.07842	−	10.7915i	−0.282628	−	0.377547i
$818$	4.98426	+	22.8449i	0.174270	+	0.798752i
$819$	0.858167	+	0.990378i	0.0299868	+	0.0346066i
$820$	−4.04242	−	6.36262i	−0.141168	−	0.222192i
$821$	−12.8784	+	8.27645i	−0.449460	+	0.288850i	−0.745723	−	0.666256i	$-0.767896\pi$
$821$	−12.8784	+	8.27645i	−0.449460	+	0.288850i	0.296263	+	0.955106i	$0.404259\pi$
$822$	18.1931	+	33.2697i	0.634557	+	1.16041i
$823$	−0.387257	−	5.41456i	−0.0134989	−	0.188740i	−0.999727	−	0.0233507i	$-0.992567\pi$
$823$	−0.387257	−	5.41456i	−0.0134989	−	0.188740i	0.986228	−	0.165389i	$-0.0528880\pi$
$824$	−45.4986	+	13.4505i	−1.58502	+	0.468569i
$825$	−35.8403	+	26.1180i	−1.24780	+	0.909311i
$826$	2.39888	+	16.6124i	0.0834678	+	0.578018i
$827$	5.92455	+	5.92455i	0.206017	+	0.206017i	0.802572	−	0.596555i	$-0.203464\pi$
$827$	5.92455	+	5.92455i	0.206017	+	0.206017i	−0.596555	+	0.802572i	$0.703464\pi$
$828$	1.01878	+	0.153324i	0.0354051	+	0.00532837i
$829$		−	17.2775i		−	0.600071i	−0.953928	−	0.300036i	$-0.903001\pi$
$829$		−	17.2775i		−	0.600071i	0.953928	−	0.300036i	$-0.0969986\pi$
$830$	8.39112	+	29.2043i	0.291260	+	1.01370i
$831$	37.6960	+	17.2152i	1.30766	+	0.597189i
$832$	−17.0175	+	31.4394i	−0.589976	+	1.08997i
$833$	0.627743	−	0.0448971i	0.0217500	−	0.00155559i
$834$	−6.16574	+	21.0463i	−0.213502	+	0.728772i
$835$	−2.28460	+	29.2967i	−0.0790619	+	1.01385i
$836$	6.42529	+	14.0239i	0.222223	+	0.485028i
$837$	21.5156	+	1.53882i	0.743687	+	0.0531895i
$838$	−34.8021	+	7.59306i	−1.20222	+	0.262298i
$839$	−3.62974	+	25.2454i	−0.125313	+	0.871568i	0.826072	+	0.563564i	$0.190570\pi$
$839$	−3.62974	+	25.2454i	−0.125313	+	0.871568i	−0.951385	+	0.308004i	$0.900339\pi$
$840$	21.4242	+	21.6216i	0.739206	+	0.746017i
$841$	19.0708	+	12.2560i	0.657612	+	0.422622i
$842$	−22.2661	−	1.57879i	−0.767340	−	0.0544088i
$843$	−33.8474	−	12.6244i	−1.16577	−	0.434808i
$844$	9.47287	−	6.10426i	0.326070	−	0.210117i
$845$	15.4105	+	2.31684i	0.530138	+	0.0797016i
$846$	−0.0755040	−	0.0653436i	−0.00259588	−	0.00224656i
$847$	34.3042	+	18.7315i	1.17870	+	0.643621i
$848$	17.4895	−	6.57211i	0.600593	−	0.225687i
$849$	−30.6991	+	4.41386i	−1.05359	+	0.151483i
$850$	−2.64693	−	9.44041i	−0.0907889	−	0.323803i
$851$	−25.9991	+	9.46678i	−0.891238	+	0.324517i
$852$	−29.3927	+	29.4648i	−1.00698	+	1.00945i
$853$	−19.3857	+	25.8963i	−0.663754	+	0.886671i	−0.998450	−	0.0556548i	$-0.982275\pi$
$853$	−19.3857	+	25.8963i	−0.663754	+	0.886671i	0.334696	+	0.942326i	$0.391366\pi$
$854$	−21.6198	+	47.4176i	−0.739814	+	1.62260i
$855$	−0.335881	+	0.150792i	−0.0114869	+	0.00515696i
$856$	−40.1983	−	34.7029i	−1.37395	−	1.18612i
$857$	40.1463	−	21.9216i	1.37137	−	0.748826i	0.386531	−	0.922277i	$-0.373673\pi$
$857$	40.1463	−	21.9216i	1.37137	−	0.748826i	0.984843	+	0.173450i	$0.0554916\pi$
$858$	−54.7784	−	11.8812i	−1.87011	−	0.405617i
$859$	17.2691	+	37.8141i	0.589214	+	1.29020i	0.935916	+	0.352224i	$0.114574\pi$
$859$	17.2691	+	37.8141i	0.589214	+	1.29020i	−0.346702	+	0.937975i	$0.612698\pi$
$860$	39.2410	−	2.60159i	1.33811	−	0.0887134i
$861$	−6.82448	−	4.38583i	−0.232578	−	0.149469i
$862$	13.7191	−	10.2831i	0.467273	−	0.350243i
$863$	4.76422	+	6.36426i	0.162176	+	0.216642i	0.874267	−	0.485445i	$-0.161343\pi$
$863$	4.76422	+	6.36426i	0.162176	+	0.216642i	−0.712091	+	0.702087i	$0.752252\pi$
$864$	−24.3131	−	15.5200i	−0.827148	−	0.528003i
$865$	28.2864	−	1.84052i	0.961766	−	0.0625795i
$866$	−15.8027	−	34.5470i	−0.536997	−	1.17396i
$867$	25.9709	+	5.64962i	0.882018	+	0.191871i
$868$	−11.0951	−	20.2601i	−0.376592	−	0.687672i
$869$	−19.9969	−	17.3274i	−0.678348	−	0.587792i
$870$	5.75218	+	12.7917i	0.195017	+	0.433681i
$871$	12.3880	+	5.65743i	0.419753	+	0.191695i
$872$	6.75981	+	5.04097i	0.228916	+	0.170709i
$873$	1.08914	+	1.08914i	0.0368619	+	0.0368619i
$874$	−10.3754	+	0.667129i	−0.350952	+	0.0225660i
$875$	11.2163	−	28.3889i	0.379182	−	0.959720i
$876$	−34.0944	+	4.94467i	−1.15194	+	0.167065i
$877$	−1.94829	−	5.22358i	−0.0657892	−	0.176388i	0.899895	−	0.436106i	$-0.143643\pi$
$877$	−1.94829	−	5.22358i	−0.0657892	−	0.176388i	−0.965684	+	0.259719i	$0.916370\pi$
$878$	22.9323	−	42.0586i	0.773928	−	1.41941i
$879$	−1.17786	+	1.35933i	−0.0397283	+	0.0458489i
$880$	−44.5192	−	6.58157i	−1.50074	−	0.221865i
$881$	5.32748	−	3.42376i	0.179487	−	0.115350i	−0.447812	−	0.894128i	$-0.647797\pi$
$881$	5.32748	−	3.42376i	0.179487	−	0.115350i	0.627299	+	0.778778i	$0.284160\pi$
$882$	0.0646148	+	0.0240550i	0.00217569	+	0.000809974i
$883$	−14.6073	−	1.04473i	−0.491574	−	0.0351581i	−0.176648	−	0.984274i	$-0.556525\pi$
$883$	−14.6073	−	1.04473i	−0.491574	−	0.0351581i	−0.314926	+	0.949116i	$0.601980\pi$
$884$	6.68697	−	10.4332i	0.224907	−	0.350907i
$885$	12.1940	−	12.0384i	0.409898	−	0.404665i
$886$	−18.9537	−	2.71328i	−0.636762	−	0.0911545i
$887$	5.67457	+	26.0856i	0.190534	+	0.875869i	0.968782	+	0.247913i	$0.0797446\pi$
$887$	5.67457	+	26.0856i	0.190534	+	0.875869i	−0.778249	+	0.627956i	$0.783892\pi$
$888$	−28.6961	−	1.99939i	−0.962977	−	0.0670950i
$889$	48.0363	−	21.9374i	1.61108	−	0.735758i
$890$	−0.696512	+	9.00291i	−0.0233471	+	0.301778i
$891$	13.1982	−	44.9491i	0.442158	−	1.50585i
$892$	16.2387	−	1.18141i	0.543711	−	0.0395565i
$893$	0.884407	+	0.482923i	0.0295955	+	0.0161604i
$894$	−2.73337	+	5.99497i	−0.0914176	+	0.200502i
$895$	7.55673	−	2.16622i	0.252593	−	0.0724088i
$896$	0.132446	+	30.8882i	0.00442472	+	1.03190i
$897$	20.6719	−	31.6209i	0.690214	−	1.05579i
$898$	40.2765	+	40.2272i	1.34404	+	1.34240i
$899$	−1.51477	−	10.5354i	−0.0505203	−	0.351376i
$900$	0.165209	−	1.06133i	0.00550698	−	0.0353778i
$901$	−6.21414	+	1.82464i	−0.207023	+	0.0607874i
$902$	11.9629	−	0.862969i	0.398321	−	0.0287337i
$903$	37.1453	−	20.2829i	1.23612	−	0.674972i
$904$	−17.2876	−	26.7917i	−0.574977	−	0.891077i
$905$	−0.890824	+	0.564445i	−0.0296120	+	0.0187628i
$906$	4.26891	+	4.92050i	0.141825	+	0.163473i
$907$	−6.64426	−	30.5432i	−0.220619	−	1.01417i	−0.945583	−	0.325382i	$-0.894507\pi$
$907$	−6.64426	−	30.5432i	−0.220619	−	1.01417i	0.724964	−	0.688787i	$-0.241856\pi$
$908$	29.5357	+	39.3545i	0.980176	+	1.30602i
$909$	−1.12019	−	0.161059i	−0.0371544	−	0.00534199i
$910$	36.2261	−	13.2723i	1.20088	−	0.439974i
$911$	40.0420	−	34.6966i	1.32665	−	1.14955i	0.349514	−	0.936931i	$-0.386347\pi$
$911$	40.0420	−	34.6966i	1.32665	−	1.14955i	0.977136	−	0.212617i	$-0.0681988\pi$
$912$	−10.1366	−	3.75248i	−0.335656	−	0.124257i
$913$	−47.2421	−	10.2769i	−1.56348	−	0.340115i
$914$	−2.28744	+	7.80801i	−0.0756619	+	0.258266i
$915$	52.0580	−	10.9748i	1.72098	−	0.362814i
$916$	−14.0156	+	4.13400i	−0.463087	+	0.136591i
$917$	−1.94193	−	5.20651i	−0.0641282	−	0.171934i
$918$	8.00798	+	5.98705i	0.264303	+	0.197602i
$919$	14.6011			0.481644			0.240822	−	0.970569i	$-0.422583\pi$
$919$	14.6011			0.481644			0.240822	+	0.970569i	$0.422583\pi$
$920$	14.8650	−	26.4392i	0.490085	−	0.871675i
$921$	3.69603			0.121788
$922$	−24.9935	−	18.6860i	−0.823116	−	0.615390i
$923$	18.4349	+	49.4260i	0.606793	+	1.62688i
$924$	−46.4519	+	13.7013i	−1.52815	+	0.450741i
$925$	9.73288	+	27.1554i	0.320015	+	0.892864i
$926$	−12.9060	+	44.0535i	−0.424116	+	1.44769i
$927$	1.76059	+	0.382992i	0.0578252	+	0.0125791i
$928$	−4.93305	+	13.3508i	−0.161935	+	0.438260i
$929$	−12.9820	+	11.2489i	−0.425925	+	0.369066i	−0.841286	−	0.540591i	$-0.818201\pi$
$929$	−12.9820	+	11.2489i	−0.425925	+	0.369066i	0.415361	+	0.909657i	$0.363655\pi$
$930$	−9.92067	+	21.3933i	−0.325311	+	0.701515i
$931$	−0.688697	−	0.0990197i	−0.0225711	−	0.00324524i
$932$	23.9430	+	31.9025i	0.784278	+	1.04500i
$933$	−3.89186	−	17.8906i	−0.127414	−	0.585711i
$934$	12.5167	+	14.4272i	0.409559	+	0.472072i
$935$	15.2217	+	3.41385i	0.497804	+	0.111645i
$936$	1.14075	−	0.736079i	0.0372865	−	0.0240595i
$937$	−3.41308	+	1.86368i	−0.111501	+	0.0608839i	−0.534031	−	0.845465i	$-0.679324\pi$
$937$	−3.41308	+	1.86368i	−0.111501	+	0.0608839i	0.422531	+	0.906349i	$0.361142\pi$
$938$	11.7364	−	0.846631i	0.383208	−	0.0276435i
$939$	−48.1903	+	14.1499i	−1.57263	+	0.461766i
$940$	−2.58745	+	1.39544i	−0.0843933	+	0.0455142i
$941$	−5.18688	−	36.0755i	−0.169087	−	1.17603i	−0.880776	−	0.473533i	$-0.842978\pi$
$941$	−5.18688	−	36.0755i	−0.169087	−	1.17603i	0.711689	−	0.702495i	$-0.247931\pi$
$942$	−39.8772	−	39.8283i	−1.29927	−	1.29768i
$943$	−2.33791	+	7.73834i	−0.0761328	+	0.251995i
$944$	17.3886	−	0.0426062i	0.565951	−	0.00138671i
$945$	8.57794	+	29.9236i	0.279041	+	0.973415i
$946$	−25.9590	+	56.9346i	−0.844001	+	1.85110i
$947$	11.5085	+	6.28411i	0.373976	+	0.204206i	0.655234	−	0.755426i	$-0.272570\pi$
$947$	11.5085	+	6.28411i	0.373976	+	0.204206i	−0.281258	+	0.959632i	$0.590752\pi$
$948$	18.4914	−	1.34530i	0.600574	−	0.0436935i
$949$	−12.3024	+	41.8982i	−0.399354	+	1.36007i
$950$	0.640930	+	10.8204i	0.0207945	+	0.351062i
$951$	19.6343	−	8.96668i	0.636685	−	0.290765i
$952$	0.744215	−	10.6813i	0.0241201	−	0.346183i
$953$	−7.27103	−	33.4244i	−0.235532	−	1.08272i	−0.931243	−	0.364400i	$-0.881274\pi$
$953$	−7.27103	−	33.4244i	−0.235532	−	1.08272i	0.695711	−	0.718322i	$-0.255090\pi$
$954$	−0.702362	−	0.100545i	−0.0227398	−	0.00325527i
$955$	0.388866	−	60.5311i	0.0125834	−	1.95874i
$956$	30.3587	−	47.3665i	0.981870	−	1.53194i
$957$	−22.2592	−	1.59201i	−0.719537	−	0.0514623i
$958$	−15.3910	−	5.72979i	−0.497259	−	0.185121i
$959$	34.9351	−	22.4515i	1.12811	−	0.724995i
$960$	25.2958	−	18.8280i	0.816420	−	0.607670i
$961$	−8.58147	+	9.90355i	−0.276822	+	0.319469i
$962$	−17.4542	+	32.0115i	−0.562745	+	1.03209i
$963$	0.704771	+	1.88956i	0.0227109	+	0.0608904i
$964$	−6.20473	+	0.899865i	−0.199841	+	0.0289827i
$965$	−8.11412	+	10.6953i	−0.261203	+	0.344293i
$966$	2.56261	−	32.5407i	0.0824507	−	1.04698i
$967$	−18.0577	−	18.0577i	−0.580696	−	0.580696i	0.354398	−	0.935095i	$-0.384686\pi$
$967$	−18.0577	−	18.0577i	−0.580696	−	0.580696i	−0.935095	+	0.354398i	$0.884686\pi$
$968$	24.2061	−	32.4597i	0.778013	−	1.04329i
$969$	3.40820	+	1.55647i	0.109487	+	0.0500011i
$970$	41.3579	−	18.5978i	1.32792	−	0.597139i
$971$	−20.3473	−	17.6310i	−0.652975	−	0.565806i	0.264113	−	0.964492i	$-0.414921\pi$
$971$	−20.3473	−	17.6310i	−0.652975	−	0.565806i	−0.917087	+	0.398686i	$0.869466\pi$
$972$	1.07182	+	1.95718i	0.0343785	+	0.0627766i
$973$	23.4689	+	5.10534i	0.752377	+	0.163670i
$974$	25.1396	+	54.9589i	0.805524	+	1.76100i
$975$	−32.8579	−	21.7180i	−1.05230	−	0.695534i
$976$	45.4899	+	29.0773i	1.45609	+	0.930742i
$977$	13.5823	+	18.1438i	0.434535	+	0.580471i	0.963344	−	0.268270i	$-0.0864520\pi$
$977$	13.5823	+	18.1438i	0.434535	+	0.580471i	−0.528809	+	0.848741i	$0.677361\pi$
$978$	42.7352	−	32.0320i	1.36652	−	1.02427i
$979$	−12.0866	−	7.76756i	−0.386288	−	0.248252i
$980$	1.33723	−	1.52713i	0.0427163	−	0.0487825i
$981$	−0.133028	−	0.291290i	−0.00424725	−	0.00930019i
$982$	−0.377089	−	0.0817889i	−0.0120334	−	0.00260999i
$983$	28.6049	−	15.6194i	0.912353	−	0.498183i	0.0467463	−	0.998907i	$-0.485115\pi$
$983$	28.6049	−	15.6194i	0.912353	−	0.498183i	0.865607	+	0.500724i	$0.166933\pi$
$984$	−5.49189	+	6.36157i	−0.175075	+	0.202799i
$985$	0.711297	+	0.270518i	0.0226638	+	0.00861941i
$986$	2.04679	−	4.48913i	0.0651832	−	0.142963i
$987$	−1.89590	+	2.53262i	−0.0603471	+	0.0806142i
$988$	−9.67573	+	9.69946i	−0.307826	+	0.308581i
$989$	−29.5877	−	30.0530i	−0.940835	−	0.955631i
$990$	1.36217	+	1.03211i	0.0432925	+	0.0328027i
$991$	41.1447	−	5.91571i	1.30700	−	0.187919i	0.546613	−	0.837385i	$-0.315917\pi$
$991$	41.1447	−	5.91571i	1.30700	−	0.187919i	0.760390	+	0.649467i	$0.225008\pi$
$992$	−22.3958	+	8.43145i	−0.711069	+	0.267699i
$993$	−44.3941	−	24.2410i	−1.40880	−	0.769265i
$994$	34.4646	+	29.8268i	1.09315	+	0.946048i
$995$	2.57534	−	17.1299i	0.0816437	−	0.543055i
$996$	28.4765	−	18.3501i	0.902311	−	0.581444i
$997$	22.1273	+	8.25307i	0.700780	+	0.261377i	0.674498	−	0.738277i	$-0.264360\pi$
$997$	22.1273	+	8.25307i	0.700780	+	0.261377i	0.0262825	+	0.999655i	$0.491633\pi$
$998$	−35.6266	−	2.52613i	−1.12774	−	0.0799633i
$999$	−24.7481	−	15.9047i	−0.782996	−	0.503201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.3.13	✓	1360
4.3	odd	2	inner	460.2.w.a.3.14	yes	1360
5.2	odd	4	inner	460.2.w.a.187.48	yes	1360
20.7	even	4	inner	460.2.w.a.187.49	yes	1360
23.8	even	11	inner	460.2.w.a.123.49	yes	1360
92.31	odd	22	inner	460.2.w.a.123.48	yes	1360
115.77	odd	44	inner	460.2.w.a.307.14	yes	1360
460.307	even	44	inner	460.2.w.a.307.13	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.13	✓	1360	1.1	even	1	trivial
460.2.w.a.3.14	yes	1360	4.3	odd	2	inner
460.2.w.a.123.48	yes	1360	92.31	odd	22	inner
460.2.w.a.123.49	yes	1360	23.8	even	11	inner
460.2.w.a.187.48	yes	1360	5.2	odd	4	inner
460.2.w.a.187.49	yes	1360	20.7	even	4	inner
460.2.w.a.307.13	yes	1360	460.307	even	44	inner
460.2.w.a.307.14	yes	1360	115.77	odd	44	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13266 - 0.846813i) q^{2} +(-0.616030 - 1.65164i) q^{3} +(0.565816 + 1.91829i) q^{4} +(-1.87330 - 1.22097i) q^{5} +(-0.700881 + 2.39240i) q^{6} +(2.66779 + 0.580342i) q^{7} +(0.983562 - 2.65191i) q^{8} +(-0.0811762 + 0.0703396i) q^{9} +O(q^{10})\)	\(q+(-1.13266 - 0.846813i) q^{2} +(-0.616030 - 1.65164i) q^{3} +(0.565816 + 1.91829i) q^{4} +(-1.87330 - 1.22097i) q^{5} +(-0.700881 + 2.39240i) q^{6} +(2.66779 + 0.580342i) q^{7} +(0.983562 - 2.65191i) q^{8} +(-0.0811762 + 0.0703396i) q^{9} +(1.08787 + 2.96927i) q^{10} +(-4.98028 - 0.716056i) q^{11} +(2.81977 - 2.11625i) q^{12} +(-0.949890 - 4.36657i) q^{13} +(-2.53024 - 2.91644i) q^{14} +(-0.862596 + 3.84617i) q^{15} +(-3.35971 + 2.17080i) q^{16} +(1.21696 - 0.664508i) q^{17} +(0.151509 - 0.0109294i) q^{18} +(-1.47083 + 0.431875i) q^{19} +(1.28224 - 4.28437i) q^{20} +(-0.684922 - 4.76374i) q^{21} +(5.03457 + 5.02841i) q^{22} +(-4.37785 + 1.95817i) q^{23} +(-4.98590 + 0.00916246i) q^{24} +(2.01847 + 4.57447i) q^{25} +(-2.62177 + 5.75020i) q^{26} +(-4.47530 - 2.44370i) q^{27} +(0.396210 + 5.44597i) q^{28} +(-0.708856 + 2.41414i) q^{29} +(4.23401 - 3.62592i) q^{30} +(-3.84805 + 1.75734i) q^{31} +(5.64365 + 0.386272i) q^{32} +(1.88534 + 8.66675i) q^{33} +(-1.94111 - 0.277875i) q^{34} +(-4.28898 - 4.34444i) q^{35} +(-0.180863 - 0.115921i) q^{36} +(5.75468 + 0.411583i) q^{37} +(2.03166 + 0.756353i) q^{38} +(-6.62685 + 4.25882i) q^{39} +(-5.08040 + 3.76690i) q^{40} +(1.10383 - 1.27388i) q^{41} +(-3.25821 + 5.97567i) q^{42} +(3.07313 + 8.23937i) q^{43} +(-1.44431 - 9.95880i) q^{44} +(0.237949 - 0.0326532i) q^{45} +(6.61680 + 1.48929i) q^{46} +(-0.464816 - 0.464816i) q^{47} +(5.65507 + 4.21175i) q^{48} +(0.412873 + 0.188553i) q^{49} +(1.58749 - 6.89056i) q^{50} +(-1.84721 - 1.60062i) q^{51} +(7.83891 - 4.29284i) q^{52} +(-4.56415 - 0.992870i) q^{53} +(2.99961 + 6.55760i) q^{54} +(8.45525 + 7.42215i) q^{55} +(4.16295 - 6.50392i) q^{56} +(1.61938 + 2.16323i) q^{57} +(2.84721 - 2.13412i) q^{58} +(-3.65707 - 2.35026i) q^{59} +(-7.86615 + 0.521507i) q^{60} +(-5.60696 - 12.2775i) q^{61} +(5.84665 + 1.26811i) q^{62} +(-0.257382 + 0.140541i) q^{63} +(-6.06521 - 5.21663i) q^{64} +(-3.55203 + 9.33966i) q^{65} +(5.20368 - 11.4130i) q^{66} +(-1.82635 + 2.43972i) q^{67} +(1.96329 + 1.95849i) q^{68} +(5.93108 + 6.02435i) q^{69} +(1.17900 + 8.55271i) q^{70} +(-11.6846 + 1.68000i) q^{71} +(0.106692 + 0.284455i) q^{72} +(-8.57648 - 4.68311i) q^{73} +(-6.16954 - 5.33932i) q^{74} +(6.31195 - 6.15180i) q^{75} +(-1.66068 - 2.57712i) q^{76} +(-12.8708 - 4.80055i) q^{77} +(11.1124 + 0.787930i) q^{78} +(4.42399 + 2.84313i) q^{79} +(8.94420 + 0.0355436i) q^{80} +(-1.32505 + 9.21593i) q^{81} +(-2.32899 + 0.508136i) q^{82} +(9.58439 + 0.685489i) q^{83} +(8.75071 - 4.00928i) q^{84} +(-3.09106 - 0.241045i) q^{85} +(3.49641 - 11.9347i) q^{86} +(4.42397 - 0.316409i) q^{87} +(-6.79733 + 12.5029i) q^{88} +(2.59743 + 1.18621i) q^{89} +(-0.297166 - 0.164514i) q^{90} -12.2003i q^{91} +(-6.23340 - 7.29005i) q^{92} +(5.27302 + 5.27302i) q^{93} +(0.132864 + 0.920088i) q^{94} +(3.28260 + 0.986809i) q^{95} +(-2.83868 - 9.55924i) q^{96} +(-1.02300 - 14.3034i) q^{97} +(-0.307974 - 0.563191i) q^{98} +(0.454647 - 0.292184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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