LMFDB - Embedded newform 135.2.q.a.122.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.13
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23715 + 0.866263i) q^{2} +(1.45553 + 0.938839i) q^{3} +(0.0960923 + 0.264011i) q^{4} +(-2.23168 - 0.140023i) q^{5} +(0.987435 + 2.42236i) q^{6} +(0.677826 + 1.45360i) q^{7} +(0.671958 - 2.50778i) q^{8} +(1.23716 + 2.73303i) q^{9} +O(q^{10})$	\(q+(1.23715 + 0.866263i) q^{2} +(1.45553 + 0.938839i) q^{3} +(0.0960923 + 0.264011i) q^{4} +(-2.23168 - 0.140023i) q^{5} +(0.987435 + 2.42236i) q^{6} +(0.677826 + 1.45360i) q^{7} +(0.671958 - 2.50778i) q^{8} +(1.23716 + 2.73303i) q^{9} +(-2.63963 - 2.10645i) q^{10} +(-1.78545 - 2.12782i) q^{11} +(-0.107999 + 0.474493i) q^{12} +(0.176418 + 0.251952i) q^{13} +(-0.420628 + 2.38550i) q^{14} +(-3.11683 - 2.29900i) q^{15} +(3.43416 - 2.88160i) q^{16} +(-1.88139 - 7.02145i) q^{17} +(-0.836964 + 4.45287i) q^{18} +(-5.07203 + 2.92834i) q^{19} +(-0.177479 - 0.602644i) q^{20} +(-0.378100 + 2.75214i) q^{21} +(-0.365624 - 4.17910i) q^{22} +(0.116642 + 0.0543910i) q^{23} +(3.33246 - 3.01930i) q^{24} +(4.96079 + 0.624975i) q^{25} +0.464527i q^{26} +(-0.765143 + 5.13951i) q^{27} +(-0.318634 + 0.318634i) q^{28} +(1.51659 + 8.60103i) q^{29} +(-1.86445 - 5.54420i) q^{30} +(4.22026 - 1.53605i) q^{31} +(1.57207 - 0.137538i) q^{32} +(-0.601106 - 4.77337i) q^{33} +(3.75485 - 10.3164i) q^{34} +(-1.30915 - 3.33889i) q^{35} +(-0.602668 + 0.589247i) q^{36} +(2.08386 - 0.558369i) q^{37} +(-8.81158 - 0.770913i) q^{38} +(0.0202409 + 0.532353i) q^{39} +(-1.85074 + 5.50247i) q^{40} +(-4.62442 - 0.815410i) q^{41} +(-2.85184 + 3.07728i) q^{42} +(-0.429127 + 4.90494i) q^{43} +(0.390200 - 0.675847i) q^{44} +(-2.37826 - 6.27247i) q^{45} +(0.0971868 + 0.168333i) q^{46} +(-7.69135 + 3.58654i) q^{47} +(7.70389 - 0.970146i) q^{48} +(2.84600 - 3.39173i) q^{49} +(5.59585 + 5.07053i) q^{50} +(3.85358 - 11.9863i) q^{51} +(-0.0495656 + 0.0707870i) q^{52} +(0.483003 + 0.483003i) q^{53} +(-5.39876 + 5.69554i) q^{54} +(3.68661 + 4.99861i) q^{55} +(4.10079 - 0.723079i) q^{56} +(-10.1318 - 0.499526i) q^{57} +(-5.57450 + 11.9546i) q^{58} +(7.43127 + 6.23558i) q^{59} +(0.307459 - 1.04379i) q^{60} +(2.50049 + 0.910105i) q^{61} +(6.55173 + 1.75553i) q^{62} +(-3.13415 + 3.65086i) q^{63} +(-5.70071 - 3.29131i) q^{64} +(-0.358430 - 0.586978i) q^{65} +(3.39133 - 6.42609i) q^{66} +(-0.884390 + 0.619257i) q^{67} +(1.67295 - 1.17142i) q^{68} +(0.118712 + 0.188676i) q^{69} +(1.27273 - 5.26478i) q^{70} +(9.03942 + 5.21891i) q^{71} +(7.68515 - 1.26605i) q^{72} +(-6.65047 - 1.78199i) q^{73} +(3.06175 + 1.11439i) q^{74} +(6.63384 + 5.56706i) q^{75} +(-1.26050 - 1.05768i) q^{76} +(1.88278 - 4.03763i) q^{77} +(-0.436116 + 0.676135i) q^{78} +(2.04188 - 0.360038i) q^{79} +(-8.06743 + 5.94995i) q^{80} +(-5.93887 + 6.76239i) q^{81} +(-5.01475 - 5.01475i) q^{82} +(7.55956 - 10.7962i) q^{83} +(-0.762929 + 0.164636i) q^{84} +(3.21549 + 15.9331i) q^{85} +(-4.77986 + 5.69642i) q^{86} +(-5.86754 + 13.9429i) q^{87} +(-6.53585 + 3.04772i) q^{88} +(-5.58181 - 9.66798i) q^{89} +(2.49134 - 9.82019i) q^{90} +(-0.246656 + 0.427222i) q^{91} +(-0.00315146 + 0.0360214i) q^{92} +(7.58484 + 1.72638i) q^{93} +(-12.6222 - 2.22564i) q^{94} +(11.7292 - 5.82491i) q^{95} +(2.41732 + 1.27573i) q^{96} +(-11.8062 - 1.03291i) q^{97} +(6.45906 - 1.73070i) q^{98} +(3.60649 - 7.51214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.23715	+	0.866263i	0.874798	+	0.612540i	0.922361	−	0.386328i	$-0.126257\pi$
$2$	1.23715	+	0.866263i	0.874798	+	0.612540i	−0.0475633	+	0.998868i	$0.515146\pi$
$3$	1.45553	+	0.938839i	0.840353	+	0.542039i
$3$	1.45553	+	0.938839i	0.840353	+	0.542039i
$4$	0.0960923	+	0.264011i	0.0480461	+	0.132006i
$5$	−2.23168	−	0.140023i	−0.998037	−	0.0626204i
$5$	−2.23168	−	0.140023i	−0.998037	−	0.0626204i
$6$	0.987435	+	2.42236i	0.403119	+	0.988925i
$7$	0.677826	+	1.45360i	0.256194	+	0.549410i	0.991770	−	0.128032i	$-0.0408661\pi$
$7$	0.677826	+	1.45360i	0.256194	+	0.549410i	−0.735576	+	0.677442i	$0.763088\pi$
$8$	0.671958	−	2.50778i	0.237573	−	0.886634i
$9$	1.23716	+	2.73303i	0.412387	+	0.911009i
$10$	−2.63963	−	2.10645i	−0.834724	−	0.666118i
$11$	−1.78545	−	2.12782i	−0.538334	−	0.641561i	0.426479	−	0.904497i	$-0.359754\pi$
$11$	−1.78545	−	2.12782i	−0.538334	−	0.641561i	−0.964813	+	0.262936i	$0.915309\pi$
$12$	−0.107999	+	0.474493i	−0.0311765	+	0.136974i
$13$	0.176418	+	0.251952i	0.0489296	+	0.0698788i	0.842871	−	0.538115i	$-0.180863\pi$
$13$	0.176418	+	0.251952i	0.0489296	+	0.0698788i	−0.793942	+	0.607994i	$0.791975\pi$
$14$	−0.420628	+	2.38550i	−0.112418	+	0.637552i
$15$	−3.11683	−	2.29900i	−0.804761	−	0.593599i
$16$	3.43416	−	2.88160i	0.858539	−	0.720400i
$17$	−1.88139	−	7.02145i	−0.456304	−	1.70295i	−0.684225	−	0.729271i	$-0.739859\pi$
$17$	−1.88139	−	7.02145i	−0.456304	−	1.70295i	0.227921	−	0.973680i	$-0.426807\pi$
$18$	−0.836964	+	4.45287i	−0.197274	+	1.04955i
$19$	−5.07203	+	2.92834i	−1.16360	+	0.671807i	−0.952165	−	0.305584i	$-0.901148\pi$
$19$	−5.07203	+	2.92834i	−1.16360	+	0.671807i	−0.211439	+	0.977391i	$0.567815\pi$
$20$	−0.177479	−	0.602644i	−0.0396856	−	0.134755i
$21$	−0.378100	+	2.75214i	−0.0825083	+	0.600566i
$22$	−0.365624	−	4.17910i	−0.0779514	−	0.890988i
$23$	0.116642	+	0.0543910i	0.0243215	+	0.0113413i	0.434741	−	0.900556i	$-0.356840\pi$
$23$	0.116642	+	0.0543910i	0.0243215	+	0.0113413i	−0.410419	+	0.911897i	$0.634618\pi$
$24$	3.33246	−	3.01930i	0.680236	−	0.616312i
$25$	4.96079	+	0.624975i	0.992157	+	0.124995i
$26$			0.464527i			0.0911012i
$27$	−0.765143	+	5.13951i	−0.147252	+	0.989099i
$28$	−0.318634	+	0.318634i	−0.0602161	+	0.0602161i
$29$	1.51659	+	8.60103i	0.281625	+	1.59717i	0.717099	+	0.696971i	$0.245469\pi$
$29$	1.51659	+	8.60103i	0.281625	+	1.59717i	−0.435475	+	0.900201i	$0.643419\pi$
$30$	−1.86445	−	5.54420i	−0.340401	−	1.01223i
$31$	4.22026	−	1.53605i	0.757981	−	0.275883i	0.0660211	−	0.997818i	$-0.478970\pi$
$31$	4.22026	−	1.53605i	0.757981	−	0.275883i	0.691960	+	0.721936i	$0.256747\pi$
$32$	1.57207	−	0.137538i	0.277905	−	0.0243135i
$33$	−0.601106	−	4.77337i	−0.104639	−	0.830936i
$34$	3.75485	−	10.3164i	0.643952	−	1.76924i
$35$	−1.30915	−	3.33889i	−0.221287	−	0.564375i
$36$	−0.602668	+	0.589247i	−0.100445	+	0.0982079i
$37$	2.08386	−	0.558369i	0.342585	−	0.0917953i	−0.0834245	−	0.996514i	$-0.526586\pi$
$37$	2.08386	−	0.558369i	0.342585	−	0.0917953i	0.426009	+	0.904719i	$0.359919\pi$
$38$	−8.81158	−	0.770913i	−1.42943	−	0.125059i
$39$	0.0202409	+	0.532353i	0.00324114	+	0.0852446i
$40$	−1.85074	+	5.50247i	−0.292628	+	0.870017i
$41$	−4.62442	−	0.815410i	−0.722213	−	0.127346i	−0.199553	−	0.979887i	$-0.563949\pi$
$41$	−4.62442	−	0.815410i	−0.722213	−	0.127346i	−0.522660	+	0.852541i	$0.675060\pi$
$42$	−2.85184	+	3.07728i	−0.440049	+	0.474834i
$43$	−0.429127	+	4.90494i	−0.0654412	+	0.747997i	0.890604	+	0.454779i	$0.150282\pi$
$43$	−0.429127	+	4.90494i	−0.0654412	+	0.747997i	−0.956046	+	0.293218i	$0.905274\pi$
$44$	0.390200	−	0.675847i	0.0588249	−	0.101888i
$45$	−2.37826	−	6.27247i	−0.354530	−	0.935045i
$46$	0.0971868	+	0.168333i	0.0143294	+	0.0248193i
$47$	−7.69135	+	3.58654i	−1.12190	+	0.523150i	−0.892890	−	0.450274i	$-0.851326\pi$
$47$	−7.69135	+	3.58654i	−1.12190	+	0.523150i	−0.229009	+	0.973424i	$0.573548\pi$
$48$	7.70389	−	0.970146i	1.11196	−	0.140028i
$49$	2.84600	−	3.39173i	0.406571	−	0.484533i
$50$	5.59585	+	5.07053i	0.791373	+	0.717082i
$51$	3.85358	−	11.9863i	0.539609	−	1.67841i
$52$	−0.0495656	+	0.0707870i	−0.00687352	+	0.00981640i
$53$	0.483003	+	0.483003i	0.0663456	+	0.0663456i	0.739501	−	0.673155i	$-0.235062\pi$
$53$	0.483003	+	0.483003i	0.0663456	+	0.0663456i	−0.673155	+	0.739501i	$0.735062\pi$
$54$	−5.39876	+	5.69554i	−0.734679	+	0.775064i
$55$	3.68661	+	4.99861i	0.497103	+	0.674013i
$56$	4.10079	−	0.723079i	0.547991	−	0.0966255i
$57$	−10.1318	−	0.499526i	−1.34198	−	0.0661638i
$58$	−5.57450	+	11.9546i	−0.731968	+	1.56971i
$59$	7.43127	+	6.23558i	0.967469	+	0.811803i	0.982152	−	0.188089i	$-0.0602295\pi$
$59$	7.43127	+	6.23558i	0.967469	+	0.811803i	−0.0146830	+	0.999892i	$0.504674\pi$
$60$	0.307459	−	1.04379i	0.0396927	−	0.134753i
$61$	2.50049	+	0.910105i	0.320155	+	0.116527i	0.497099	−	0.867694i	$-0.334399\pi$
$61$	2.50049	+	0.910105i	0.320155	+	0.116527i	−0.176943	+	0.984221i	$0.556621\pi$
$62$	6.55173	+	1.75553i	0.832070	+	0.222952i
$63$	−3.13415	+	3.65086i	−0.394866	+	0.459965i
$64$	−5.70071	−	3.29131i	−0.712589	−	0.411413i
$65$	−0.358430	−	0.586978i	−0.0444578	−	0.0728056i
$66$	3.39133	−	6.42609i	0.417444	−	0.790997i
$67$	−0.884390	+	0.619257i	−0.108045	+	0.0756543i	−0.626350	−	0.779542i	$-0.715452\pi$
$67$	−0.884390	+	0.619257i	−0.108045	+	0.0756543i	0.518305	+	0.855196i	$0.326563\pi$
$68$	1.67295	−	1.17142i	0.202876	−	0.142055i
$69$	0.118712	+	0.188676i	0.0142912	+	0.0227139i
$70$	1.27273	−	5.26478i	0.152121	−	0.629261i
$71$	9.03942	+	5.21891i	1.07278	+	0.619371i	0.928940	−	0.370230i	$-0.120721\pi$
$71$	9.03942	+	5.21891i	1.07278	+	0.619371i	0.143842	+	0.989601i	$0.454054\pi$
$72$	7.68515	−	1.26605i	0.905703	−	0.149205i
$73$	−6.65047	−	1.78199i	−0.778378	−	0.208566i	−0.152309	−	0.988333i	$-0.548671\pi$
$73$	−6.65047	−	1.78199i	−0.778378	−	0.208566i	−0.626070	+	0.779767i	$0.715337\pi$
$74$	3.06175	+	1.11439i	0.355921	+	0.129545i
$75$	6.63384	+	5.56706i	0.766010	+	0.642828i
$76$	−1.26050	−	1.05768i	−0.144589	−	0.121325i
$77$	1.88278	−	4.03763i	0.214562	−	0.460130i
$78$	−0.436116	+	0.676135i	−0.0493804	+	0.0765572i
$79$	2.04188	−	0.360038i	0.229729	−	0.0405074i	−0.0575985	−	0.998340i	$-0.518344\pi$
$79$	2.04188	−	0.360038i	0.229729	−	0.0405074i	0.287327	+	0.957832i	$0.407233\pi$
$80$	−8.06743	+	5.94995i	−0.901966	+	0.665224i
$81$	−5.93887	+	6.76239i	−0.659874	+	0.751376i
$82$	−5.01475	−	5.01475i	−0.553787	−	0.553787i
$83$	7.55956	−	10.7962i	0.829770	−	1.18503i	−0.150742	−	0.988573i	$-0.548166\pi$
$83$	7.55956	−	10.7962i	0.829770	−	1.18503i	0.980512	−	0.196461i	$-0.0629449\pi$
$84$	−0.762929	+	0.164636i	−0.0832423	+	0.0179633i
$85$	3.21549	+	15.9331i	0.348769	+	1.72818i
$86$	−4.77986	+	5.69642i	−0.515426	+	0.614261i
$87$	−5.86754	+	13.9429i	−0.629066	+	1.49484i
$88$	−6.53585	+	3.04772i	−0.696724	+	0.324888i
$89$	−5.58181	−	9.66798i	−0.591671	−	1.02480i	−0.994007	−	0.109312i	$-0.965135\pi$
$89$	−5.58181	−	9.66798i	−0.591671	−	1.02480i	0.402337	−	0.915492i	$-0.368198\pi$
$90$	2.49134	−	9.82019i	0.262610	−	1.03514i
$91$	−0.246656	+	0.427222i	−0.0258566	+	0.0447850i
$92$	−0.00315146	+	0.0360214i	−0.000328562	+	0.00375549i
$93$	7.58484	+	1.72638i	0.786511	+	0.179017i
$94$	−12.6222	−	2.22564i	−1.30189	−	0.229558i
$95$	11.7292	−	5.82491i	1.20339	−	0.597623i
$96$	2.41732	+	1.27573i	0.246717	+	0.130203i
$97$	−11.8062	−	1.03291i	−1.19874	−	0.104876i	−0.529754	−	0.848151i	$-0.677716\pi$
$97$	−11.8062	−	1.03291i	−1.19874	−	0.104876i	−0.668986	+	0.743275i	$0.733271\pi$
$98$	6.45906	−	1.73070i	0.652464	−	0.174827i
$99$	3.60649	−	7.51214i	0.362466	−	0.754999i
$100$	0.311693	+	1.36976i	0.0311693	+	0.136976i
$101$	−4.61138	+	12.6697i	−0.458850	+	1.26068i	0.467493	+	0.883997i	$0.345157\pi$
$101$	−4.61138	+	12.6697i	−0.458850	+	1.26068i	−0.926343	+	0.376682i	$0.877065\pi$
$102$	15.1507	−	11.4906i	1.50015	−	1.13774i
$103$	2.96335	−	0.259260i	0.291988	−	0.0255456i	0.0597791	−	0.998212i	$-0.480960\pi$
$103$	2.96335	−	0.259260i	0.291988	−	0.0255456i	0.232209	+	0.972666i	$0.425405\pi$
$104$	0.750384	−	0.273118i	0.0735813	−	0.0267814i
$105$	1.22916	−	6.08895i	0.119954	−	0.594221i
$106$	0.179140	+	1.01596i	0.0173997	+	0.0986783i
$107$	7.80800	−	7.80800i	0.754828	−	0.754828i	−0.220548	−	0.975376i	$-0.570785\pi$
$107$	7.80800	−	7.80800i	0.754828	−	0.754828i	0.975376	+	0.220548i	$0.0707846\pi$
$108$	−1.43041	+	0.291861i	−0.137642	+	0.0280843i
$109$		−	0.464359i		−	0.0444775i	−0.999753	−	0.0222388i	$-0.992921\pi$
$109$		−	0.464359i		−	0.0444775i	0.999753	−	0.0222388i	$-0.00707940\pi$
$110$	0.230783	+	9.37762i	0.0220043	+	0.894121i
$111$	3.55735	+	1.14369i	0.337649	+	0.108554i
$112$	6.51646	+	3.03868i	0.615748	+	0.287128i
$113$	0.0417367	+	0.477053i	0.00392626	+	0.0448774i	0.997905	−	0.0646950i	$-0.0206074\pi$
$113$	0.0417367	+	0.477053i	0.00392626	+	0.0448774i	−0.993979	+	0.109572i	$0.965052\pi$
$114$	−12.1018	−	9.39475i	−1.13344	−	0.879899i
$115$	−0.252691	−	0.137716i	−0.0235636	−	0.0128421i
$116$	−2.12504	+	1.22689i	−0.197305	+	0.113914i
$117$	−0.470332	+	0.793861i	−0.0434822	+	0.0733924i
$118$	3.79196	+	14.1518i	0.349078	+	1.30278i
$119$	8.93114	−	7.49411i	0.818716	−	0.686984i
$120$	−7.85976	+	6.27149i	−0.717494	+	0.572506i
$121$	0.570356	−	3.23465i	0.0518506	−	0.294059i
$122$	2.30510	+	3.29202i	0.208694	+	0.298046i
$123$	−5.96547	−	5.52845i	−0.537888	−	0.498483i
$124$	0.811069	+	0.966595i	0.0728362	+	0.0868028i
$125$	−10.9834	−	2.08937i	−0.982383	−	0.186879i
$126$	−7.04003	+	1.80166i	−0.627175	+	0.160505i
$127$	3.48210	−	12.9954i	0.308987	−	1.15315i	−0.620473	−	0.784228i	$-0.713059\pi$
$127$	3.48210	−	12.9954i	0.308987	−	1.15315i	0.929459	−	0.368925i	$-0.120274\pi$
$128$	−5.53535	−	11.8706i	−0.489260	−	1.04922i
$129$	−5.22956	+	6.73643i	−0.460437	+	0.593110i
$130$	0.0650447	−	1.03667i	0.00570479	−	0.0909224i
$131$	−2.11500	−	5.81092i	−0.184788	−	0.507702i	0.812361	−	0.583155i	$-0.198182\pi$
$131$	−2.11500	−	5.81092i	−0.184788	−	0.507702i	−0.997149	+	0.0754528i	$0.975960\pi$
$132$	1.20246	−	0.617383i	0.104661	−	0.0537363i
$133$	−7.69460	−	5.38781i	−0.667206	−	0.467183i
$134$	−1.63056			−0.140859
$135$	2.42721	−	11.3626i	0.208901	−	0.977937i
$136$	−18.8725			−1.61830
$137$	−6.04873	−	4.23537i	−0.516778	−	0.361852i	0.285905	−	0.958258i	$-0.407706\pi$
$137$	−6.04873	−	4.23537i	−0.516778	−	0.361852i	−0.802683	+	0.596406i	$0.796595\pi$
$138$	−0.0165784	+	0.336257i	−0.00141125	+	0.0286241i
$139$	3.50715	+	9.63582i	0.297473	+	0.817299i	0.994921	+	0.100664i	$0.0320966\pi$
$139$	3.50715	+	9.63582i	0.297473	+	0.817299i	−0.697448	+	0.716635i	$0.745681\pi$
$140$	0.755705	−	0.666472i	0.0638687	−	0.0563272i
$141$	−14.5622	−	2.00062i	−1.22636	−	0.168482i
$142$	6.66218	+	14.2871i	0.559078	+	1.19895i
$143$	0.221121	−	0.825233i	0.0184910	−	0.0690095i
$144$	12.1241	+	5.82064i	1.01034	+	0.485053i
$145$	−2.18021	−	19.4071i	−0.181056	−	1.61167i
$146$	−6.68396	−	7.96564i	−0.553169	−	0.659241i
$147$	7.32674	−	2.26484i	0.604300	−	0.186801i
$148$	0.347659	+	0.496508i	0.0285774	+	0.0408127i
$149$	−0.210055	+	1.19128i	−0.0172084	+	0.0975937i	−0.992202	−	0.124638i	$-0.960223\pi$
$149$	−0.210055	+	1.19128i	−0.0172084	+	0.0975937i	0.974994	+	0.222232i	$0.0713341\pi$
$150$	3.38454	+	12.6339i	0.276346	+	1.03156i
$151$	−12.3858	+	10.3930i	−1.00795	+	0.845766i	−0.988065	−	0.154036i	$-0.950773\pi$
$151$	−12.3858	+	10.3930i	−1.00795	+	0.845766i	−0.0198800	+	0.999802i	$0.506328\pi$
$152$	3.93544	+	14.6873i	0.319206	+	1.19129i
$153$	16.8622	−	13.8285i	1.36323	−	1.11797i
$154$	5.82693	−	3.36418i	0.469547	−	0.271093i
$155$	−9.63335	+	2.83703i	−0.773770	+	0.227876i
$156$	−0.138602	+	0.0564988i	−0.0110971	+	0.00452353i
$157$	−1.80822	−	20.6680i	−0.144311	−	1.64949i	−0.630907	−	0.775858i	$-0.717317\pi$
$157$	−1.80822	−	20.6680i	−0.144311	−	1.64949i	0.486596	−	0.873627i	$-0.338238\pi$
$158$	2.83800	+	1.32338i	0.225779	+	0.105282i
$159$	0.249565	+	1.15649i	0.0197918	+	0.0917156i
$160$	−3.52761	+	0.0868145i	−0.278882	+	0.00686329i
$161$			0.206419i			0.0162681i
$162$	−13.2053	+	3.22148i	−1.03750	+	0.253103i
$163$	9.24417	−	9.24417i	0.724060	−	0.724060i	−0.245370	−	0.969430i	$-0.578909\pi$
$163$	9.24417	−	9.24417i	0.724060	−	0.724060i	0.969430	+	0.245370i	$0.0789094\pi$
$164$	−0.229094	−	1.29925i	−0.0178892	−	0.101455i
$165$	0.673094	+	10.7368i	0.0524003	+	0.835858i
$166$	18.7046	−	6.80794i	1.45176	−	0.528398i
$167$	16.0301	−	1.40245i	1.24044	−	0.108525i	0.552018	−	0.833832i	$-0.313858\pi$
$167$	16.0301	−	1.40245i	1.24044	−	0.108525i	0.688425	+	0.725307i	$0.258302\pi$
$168$	6.64769	+	2.79751i	0.512880	+	0.215833i
$169$	4.41391	−	12.1271i	0.339531	−	0.932854i
$170$	−9.82416	+	22.4971i	−0.753479	+	1.72545i
$171$	−14.2781	−	10.2392i	−1.09188	−	0.783009i
$172$	−1.33620	+	0.358033i	−0.101884	+	0.0272997i
$173$	−2.64260	−	0.231197i	−0.200913	−	0.0175776i	−0.0137449	−	0.999906i	$-0.504375\pi$
$173$	−2.64260	−	0.231197i	−0.200913	−	0.0175776i	−0.187168	+	0.982328i	$0.559931\pi$
$174$	−19.3373	+	12.1667i	−1.46596	+	0.922355i
$175$	2.45409	+	7.63464i	0.185511	+	0.577124i
$176$	−12.2630	−	2.16231i	−0.924362	−	0.162990i
$177$	4.96226	+	16.0529i	0.372987	+	1.20661i
$178$	1.46947	−	16.7961i	0.110141	−	1.25892i
$179$	−3.43088	+	5.94245i	−0.256436	+	0.444160i	−0.965284	−	0.261201i	$-0.915882\pi$
$179$	−3.43088	+	5.94245i	−0.256436	+	0.444160i	0.708849	+	0.705360i	$0.249215\pi$
$180$	1.42747	−	1.23062i	0.106397	−	0.0917253i
$181$	10.0120	+	17.3412i	0.744183	+	1.28896i	0.950575	+	0.310494i	$0.100494\pi$
$181$	10.0120	+	17.3412i	0.744183	+	1.28896i	−0.206392	+	0.978469i	$0.566172\pi$
$182$	−0.675238	+	0.314868i	−0.0500519	+	0.0233396i
$183$	2.78511	+	3.67225i	0.205881	+	0.271460i
$184$	0.214779	−	0.255964i	0.0158337	−	0.0188699i
$185$	−4.72870	+	0.954312i	−0.347661	+	0.0701624i
$186$	7.88810	+	8.70625i	0.578384	+	0.638373i
$187$	−11.5812	+	16.5397i	−0.846903	+	1.20950i
$188$	−1.68597	−	1.68597i	−0.122962	−	0.122962i
$189$	−7.98944	+	2.37148i	−0.581146	+	0.172500i
$190$	19.5567	+	2.95426i	1.41879	+	0.214325i
$191$	9.22577	−	1.62675i	0.667553	−	0.117708i	0.170406	−	0.985374i	$-0.445492\pi$
$191$	9.22577	−	1.62675i	0.667553	−	0.117708i	0.497147	+	0.867666i	$0.334381\pi$
$192$	−5.20757	−	10.1427i	−0.375824	−	0.731984i
$193$	8.90711	−	19.1014i	0.641148	−	1.37495i	−0.269998	−	0.962861i	$-0.587023\pi$
$193$	8.90711	−	19.1014i	0.641148	−	1.37495i	0.911146	−	0.412085i	$-0.135199\pi$
$194$	−13.7113	−	11.5052i	−0.984414	−	0.826022i
$195$	0.0293706	−	1.19087i	0.00210327	−	0.0852803i
$196$	1.16893	+	0.425457i	0.0834953	+	0.0303898i
$197$	7.09801	+	1.90191i	0.505712	+	0.135505i	0.502650	−	0.864490i	$-0.332358\pi$
$197$	7.09801	+	1.90191i	0.505712	+	0.135505i	0.00306257	+	0.999995i	$0.499025\pi$
$198$	10.9693	−	6.16948i	0.779552	−	0.438446i
$199$	22.3449	+	12.9008i	1.58399	+	0.914516i	0.994269	+	0.106906i	$0.0340945\pi$
$199$	22.3449	+	12.9008i	1.58399	+	0.914516i	0.589718	+	0.807609i	$0.299239\pi$
$200$	4.90074	−	12.0206i	0.346534	−	0.849985i
$201$	−1.86864	+	0.0710490i	−0.131804	+	0.00501141i
$202$	−16.6802	+	11.6796i	−1.17362	+	0.821776i
$203$	−11.4745	+	8.03453i	−0.805352	+	0.563914i
$204$	3.53481	−	0.134400i	0.247486	−	0.00940985i
$205$	10.2061	+	2.46726i	0.712821	+	0.172321i
$206$	3.89070	+	2.24630i	0.271078	+	0.156507i
$207$	−0.00434728	+	0.386076i	−0.000302157	+	0.0268341i
$208$	1.33187	+	0.356874i	0.0923487	+	0.0247448i
$209$	15.2868	+	5.56395i	1.05741	+	0.384867i
$210$	6.79529	−	6.46817i	0.468920	−	0.446346i
$211$	−0.268205	−	0.225051i	−0.0184640	−	0.0154932i	0.633509	−	0.773735i	$-0.281614\pi$
$211$	−0.268205	−	0.225051i	−0.0184640	−	0.0154932i	−0.651973	+	0.758242i	$0.726058\pi$
$212$	−0.0811054	+	0.173931i	−0.00557035	+	0.0119456i
$213$	8.25747	+	16.0829i	0.565792	+	1.10198i
$214$	16.4235	−	2.89590i	1.12268	−	0.197960i
$215$	1.64448	−	10.8862i	0.112153	−	0.742431i
$216$	12.3746	+	5.37234i	0.841986	+	0.365542i
$217$	5.09341	+	5.09341i	0.345763	+	0.345763i
$218$	0.402257	−	0.574483i	0.0272443	−	0.0389089i
$219$	−8.00698	−	8.83746i	−0.541062	−	0.597180i
$220$	−0.965436	+	1.45364i	−0.0650897	+	0.0980041i
$221$	1.43715	−	1.71273i	0.0966733	−	0.115211i
$222$	3.41025	+	4.49652i	0.228881	+	0.301786i
$223$	−14.2401	+	6.64028i	−0.953590	+	0.444666i	−0.836203	−	0.548420i	$-0.815230\pi$
$223$	−14.2401	+	6.64028i	−0.953590	+	0.444666i	−0.117387	+	0.993086i	$0.537452\pi$
$224$	1.26551	+	2.19193i	0.0845557	+	0.146455i
$225$	4.42922	+	14.3312i	0.295281	+	0.955410i
$226$	−0.361618	+	0.626342i	−0.0240545	+	0.0416636i
$227$	−2.05222	+	23.4570i	−0.136211	+	1.55690i	0.553522	+	0.832834i	$0.313283\pi$
$227$	−2.05222	+	23.4570i	−0.136211	+	1.55690i	−0.689733	+	0.724064i	$0.742272\pi$
$228$	−0.841703	−	2.72290i	−0.0557431	−	0.180328i
$229$	−22.8004	−	4.02032i	−1.50669	−	0.265671i	−0.641505	−	0.767119i	$-0.721690\pi$
$229$	−22.8004	−	4.02032i	−1.50669	−	0.265671i	−0.865188	+	0.501448i	$0.832801\pi$
$230$	−0.193319	−	0.389273i	−0.0127471	−	0.0256679i
$231$	6.53113	−	4.10928i	0.429717	−	0.270371i
$232$	22.5886	+	1.97625i	1.48301	+	0.129747i
$233$	−20.8931	+	5.59828i	−1.36875	+	0.366755i	−0.867022	−	0.498270i	$-0.833969\pi$
$233$	−20.8931	+	5.59828i	−1.36875	+	0.366755i	−0.501728	+	0.865026i	$0.667302\pi$
$234$	−1.26956	+	0.574694i	−0.0829940	+	0.0375689i
$235$	17.6668	−	6.92703i	1.15246	−	0.451870i
$236$	−0.932175	+	2.56113i	−0.0606794	+	0.166715i
$237$	3.31004	+	1.39295i	0.215010	+	0.0904816i
$238$	17.5410	−	1.53464i	1.13702	−	0.0994761i
$239$	−13.3597	+	4.86252i	−0.864165	+	0.314530i	−0.735802	−	0.677197i	$-0.763195\pi$
$239$	−13.3597	+	4.86252i	−0.864165	+	0.314530i	−0.128363	+	0.991727i	$0.540972\pi$
$240$	−17.3285	+	1.08633i	−1.11855	+	0.0701222i
$241$	−1.44826	−	8.21348i	−0.0932905	−	0.529077i	−0.995258	−	0.0972724i	$-0.968988\pi$
$241$	−1.44826	−	8.21348i	−0.0932905	−	0.529077i	0.901967	−	0.431804i	$-0.142123\pi$
$242$	3.50767	−	3.50767i	0.225482	−	0.225482i
$243$	−14.9930	+	4.26724i	−0.961803	+	0.273744i
$244$			0.747612i			0.0478610i
$245$	−6.82628	+	7.17075i	−0.436115	+	0.458122i
$246$	−2.59110	−	12.0072i	−0.165202	−	0.765550i
$247$	−1.63260	−	0.761293i	−0.103880	−	0.0484399i
$248$	−1.01624	−	11.6156i	−0.0645311	−	0.737594i
$249$	21.1391	−	8.61699i	1.33963	−	0.546079i
$250$	−11.7782	−	12.0994i	−0.744916	−	0.765231i
$251$	4.13040	−	2.38469i	0.260708	−	0.150520i	−0.363949	−	0.931419i	$-0.618572\pi$
$251$	4.13040	−	2.38469i	0.260708	−	0.150520i	0.624658	+	0.780899i	$0.285239\pi$
$252$	−1.26504	−	0.476633i	−0.0796898	−	0.0300251i
$253$	−0.0925243	−	0.345305i	−0.00581695	−	0.0217092i
$254$	15.5653	−	13.0608i	0.976654	−	0.819510i
$255$	−10.2783	+	26.2099i	−0.643653	+	1.64133i
$256$	1.14887	−	6.51557i	0.0718045	−	0.407223i
$257$	−2.70759	−	3.86684i	−0.168895	−	0.241207i	0.725778	−	0.687929i	$-0.241480\pi$
$257$	−2.70759	−	3.86684i	−0.168895	−	0.241207i	−0.894673	+	0.446722i	$0.852591\pi$
$258$	−12.3053	+	3.80381i	−0.766093	+	0.236815i
$259$	2.22414	+	2.65063i	0.138202	+	0.164702i
$260$	0.120526	−	0.151034i	0.00747473	−	0.00936671i
$261$	−21.6306	+	14.7858i	−1.33890	+	0.915215i
$262$	2.41720	−	9.02113i	0.149335	−	0.557327i
$263$	1.40761	+	3.01862i	0.0867967	+	0.186136i	0.944915	−	0.327316i	$-0.106144\pi$
$263$	1.40761	+	3.01862i	0.0867967	+	0.186136i	−0.858118	+	0.513452i	$0.828366\pi$
$264$	−12.3745	−	1.70006i	−0.761596	−	0.104631i
$265$	−1.01028	−	1.14554i	−0.0620608	−	0.0703700i
$266$	−4.85212	−	13.3311i	−0.297502	−	0.817381i
$267$	0.952164	−	19.3125i	0.0582715	−	1.18191i
$268$	−0.248474	−	0.173983i	−0.0151780	−	0.0106277i
$269$	−8.37429			−0.510589			−0.255295	−	0.966863i	$-0.582172\pi$
$269$	−8.37429			−0.510589			−0.255295	+	0.966863i	$0.582172\pi$
$270$	12.8458	−	11.9547i	0.781772	−	0.727537i
$271$	−13.7893			−0.837641			−0.418821	−	0.908069i	$-0.637556\pi$
$271$	−13.7893			−0.837641			−0.418821	+	0.908069i	$0.637556\pi$
$272$	−26.6940	−	18.6913i	−1.61856	−	1.13333i
$273$	−0.760109	+	0.390265i	−0.0460039	+	0.0236199i
$274$	−3.81425	−	10.4796i	−0.230428	−	0.633094i
$275$	−7.52741	−	11.6715i	−0.453920	−	0.703819i
$276$	−0.0384053	+	0.0494716i	−0.00231173	+	0.00297784i
$277$	0.0519757	+	0.111462i	0.00312292	+	0.00669711i	0.907863	−	0.419267i	$-0.137713\pi$
$277$	0.0519757	+	0.111462i	0.00312292	+	0.00669711i	−0.904740	+	0.425964i	$0.859935\pi$
$278$	−4.00827	+	14.9591i	−0.240400	+	0.897186i
$279$	9.41921	+	9.63375i	0.563913	+	0.576757i
$280$	−9.25289	+	1.03947i	−0.552966	+	0.0621205i
$281$	15.4444	+	18.4059i	0.921334	+	1.09800i	0.994915	+	0.100714i	$0.0321127\pi$
$281$	15.4444	+	18.4059i	0.921334	+	1.09800i	−0.0735813	+	0.997289i	$0.523443\pi$
$282$	−16.2826	−	15.0898i	−0.969614	−	0.898582i
$283$	−9.14396	−	13.0589i	−0.543552	−	0.776273i	0.449584	−	0.893238i	$-0.351572\pi$
$283$	−9.14396	−	13.0589i	−0.543552	−	0.776273i	−0.993136	+	0.116965i	$0.962683\pi$
$284$	−0.509233	+	2.88801i	−0.0302174	+	0.171372i
$285$	22.5409	+	2.53346i	1.33521	+	0.150069i
$286$	0.988429	−	0.829390i	0.0584470	−	0.0490429i
$287$	−1.94927	−	7.27478i	−0.115062	−	0.429417i
$288$	2.32079	+	4.12634i	0.136754	+	0.243147i
$289$	−31.0386	+	17.9202i	−1.82580	+	1.05413i
$290$	14.1144	−	25.8982i	0.828827	−	1.52079i
$291$	−16.2146	−	12.5876i	−0.950518	−	0.737897i
$292$	−0.168594	−	1.92703i	−0.00986619	−	0.112771i
$293$	−4.77657	−	2.22735i	−0.279050	−	0.130123i	0.278055	−	0.960565i	$-0.410310\pi$
$293$	−4.77657	−	2.22735i	−0.279050	−	0.130123i	−0.557105	+	0.830442i	$0.688088\pi$
$294$	11.0262	+	3.54493i	0.643063	+	0.206744i
$295$	−15.7111	−	14.9564i	−0.914735	−	0.870793i
$296$		−	5.60107i		−	0.325555i
$297$	12.3021	−	7.54826i	0.713838	−	0.437994i
$298$	−1.29183	+	1.29183i	−0.0748340	+	0.0748340i
$299$	0.00687388	+	0.0389837i	0.000397526	+	0.00225448i
$300$	−0.832305	+	2.28636i	−0.0480531	+	0.132003i
$301$	−7.42071	+	2.70092i	−0.427723	+	0.155678i
$302$	−24.3262	+	2.12827i	−1.39981	+	0.122468i
$303$	−18.6068	+	14.1118i	−1.06893	+	0.810701i
$304$	−8.97985	+	24.6719i	−0.515030	+	1.41503i
$305$	−5.45286	−	2.38119i	−0.312230	−	0.136347i
$306$	32.8403	−	2.50090i	1.87735	−	0.142967i
$307$	−21.3785	+	5.72834i	−1.22013	+	0.326934i	−0.810730	−	0.585420i	$-0.800930\pi$
$307$	−21.3785	+	5.72834i	−1.22013	+	0.326934i	−0.409403	+	0.912353i	$0.634263\pi$
$308$	1.24690	+	0.109090i	0.0710487	+	0.00621596i
$309$	4.55666	+	2.40475i	0.259220	+	0.136801i
$310$	−14.3755	−	4.83517i	−0.816476	−	0.274619i
$311$	14.1711	+	2.49874i	0.803567	+	0.141691i	0.560322	−	0.828275i	$-0.310677\pi$
$311$	14.1711	+	2.49874i	0.803567	+	0.141691i	0.243244	+	0.969965i	$0.421788\pi$
$312$	1.34862	+	0.306959i	0.0763508	+	0.0173781i
$313$	−1.85245	+	21.1736i	−0.104707	+	1.19680i	0.744088	+	0.668081i	$0.232884\pi$
$313$	−1.85245	+	21.1736i	−0.104707	+	1.19680i	−0.848795	+	0.528722i	$0.822671\pi$
$314$	15.6669	−	27.1358i	0.884133	−	1.53136i
$315$	7.50564	−	7.70869i	0.422895	−	0.434335i
$316$	0.291263	+	0.504482i	0.0163848	+	0.0283793i
$317$	20.8348	−	9.71542i	1.17020	−	0.545672i	0.262350	−	0.964973i	$-0.415502\pi$
$317$	20.8348	−	9.71542i	1.17020	−	0.545672i	0.907848	+	0.419300i	$0.137725\pi$
$318$	−0.693074	+	1.64694i	−0.0388657	+	0.0923559i
$319$	15.5936	−	18.5838i	0.873076	−	1.04049i
$320$	12.2613	+	8.14338i	0.685428	+	0.455229i
$321$	18.6953	−	4.03435i	1.04347	−	0.225176i
$322$	−0.178813	+	0.255371i	−0.00996485	+	0.0142313i
$323$	30.1036	+	30.1036i	1.67501	+	1.67501i
$324$	−2.35603	−	0.918115i	−0.130890	−	0.0510064i
$325$	0.717710	+	1.36013i	0.0398114	+	0.0754467i
$326$	19.4443	−	3.42856i	1.07692	−	0.189890i
$327$	0.435959	−	0.675891i	0.0241086	−	0.0373768i
$328$	−5.15228	+	11.0491i	−0.284487	+	0.610085i
$329$	−10.4268	−	8.74912i	−0.574848	−	0.482355i
$330$	−8.46816	+	13.8661i	−0.466157	+	0.763304i
$331$	13.1133	+	4.77285i	0.720772	+	0.262340i	0.676253	−	0.736669i	$-0.263602\pi$
$331$	13.1133	+	4.77285i	0.720772	+	0.262340i	0.0445184	+	0.999009i	$0.485825\pi$
$332$	3.57673	+	0.958382i	0.196298	+	0.0525980i
$333$	4.10411	+	5.00446i	0.224904	+	0.274243i
$334$	21.0465	+	12.1512i	1.15161	+	0.664884i
$335$	2.06039	−	1.25815i	0.112571	−	0.0687399i
$336$	6.63211	+	10.5408i	0.361811	+	0.575049i
$337$	11.8702	−	8.31162i	0.646612	−	0.452763i	−0.203705	−	0.979032i	$-0.565299\pi$
$337$	11.8702	−	8.31162i	0.646612	−	0.452763i	0.850318	+	0.526269i	$0.176410\pi$
$338$	15.9659	−	11.1795i	0.868432	−	0.608083i
$339$	−0.387127	+	0.733551i	−0.0210258	+	0.0398410i
$340$	−3.89752	+	2.37997i	−0.211373	+	0.129072i
$341$	−10.8035	−	6.23741i	−0.585043	−	0.337775i
$342$	−8.79441	−	25.0360i	−0.475547	−	1.35379i
$343$	17.7039	+	4.74374i	0.955920	+	0.256138i
$344$	12.0122	+	4.37207i	0.647652	+	0.235726i
$345$	−0.238508	−	0.437687i	−0.0128408	−	0.0235643i
$346$	−3.06901	−	2.57521i	−0.164991	−	0.138444i
$347$	−3.83685	+	8.22815i	−0.205973	+	0.441710i	−0.981973	−	0.189023i	$-0.939468\pi$
$347$	−3.83685	+	8.22815i	−0.205973	+	0.441710i	0.776000	+	0.630733i	$0.217246\pi$
$348$	−4.24492	−	0.209287i	−0.227552	−	0.0112190i
$349$	8.20842	−	1.44737i	0.439387	−	0.0774757i	0.0504212	−	0.998728i	$-0.483944\pi$
$349$	8.20842	−	1.44737i	0.439387	−	0.0774757i	0.388966	+	0.921252i	$0.372833\pi$
$350$	−3.57753	+	11.5711i	−0.191227	+	0.618501i
$351$	−1.42989	+	0.713925i	−0.0763220	+	0.0381065i
$352$	−3.09950	−	3.09950i	−0.165204	−	0.165204i
$353$	−1.51501	+	2.16366i	−0.0806358	+	0.115160i	−0.857444	−	0.514578i	$-0.827949\pi$
$353$	−1.51501	+	2.16366i	−0.0806358	+	0.115160i	0.776808	+	0.629738i	$0.216838\pi$
$354$	−7.76693	+	24.1585i	−0.412808	+	1.28401i
$355$	−19.4423	−	12.9127i	−1.03189	−	0.685333i
$356$	2.01609	−	2.40268i	0.106852	−	0.127342i
$357$	20.0353	−	2.52304i	1.06038	−	0.133533i
$358$	−9.39224	+	4.37967i	−0.496395	+	0.231473i
$359$	−7.06131	−	12.2306i	−0.372682	−	0.645504i	0.617295	−	0.786732i	$-0.288228\pi$
$359$	−7.06131	−	12.2306i	−0.372682	−	0.645504i	−0.989977	+	0.141228i	$0.954895\pi$
$360$	−17.3281	+	1.74931i	−0.913269	+	0.0921970i
$361$	7.65033	−	13.2508i	0.402649	−	0.697408i
$362$	−2.63575	+	30.1267i	−0.138532	+	1.58342i
$363$	3.86699	−	4.17267i	0.202964	−	0.219009i
$364$	−0.136493	−	0.0240674i	−0.00715418	−	0.00126148i
$365$	14.5922	+	4.90804i	0.763790	+	0.256899i
$366$	0.264470	+	6.95577i	0.0138241	+	0.363584i
$367$	−13.7173	−	1.20011i	−0.716037	−	0.0626451i	−0.276686	−	0.960961i	$-0.589236\pi$
$367$	−13.7173	−	1.20011i	−0.716037	−	0.0626451i	−0.439351	+	0.898315i	$0.644792\pi$
$368$	0.557300	−	0.149328i	0.0290513	−	0.00778426i
$369$	−3.49262	−	13.6475i	−0.181818	−	0.710458i
$370$	−6.67680	−	2.91567i	−0.347110	−	0.151578i
$371$	−0.374703	+	1.02949i	−0.0194536	+	0.0534483i
$372$	0.273062	+	2.16838i	0.0141576	+	0.112425i
$373$	−20.2366	+	1.77048i	−1.04781	+	0.0916718i	−0.598036	−	0.801469i	$-0.704052\pi$
$373$	−20.2366	+	1.77048i	−1.04781	+	0.0916718i	−0.449777	+	0.893141i	$0.648497\pi$
$374$	−28.6555	+	10.4297i	−1.48174	+	0.539309i
$375$	−14.0251	−	13.3528i	−0.724253	−	0.689534i
$376$	3.82598	+	21.6982i	0.197310	+	1.11900i
$377$	−1.89949	+	1.89949i	−0.0978286	+	0.0978286i
$378$	−11.9385	−	3.98707i	−0.614049	−	0.205073i
$379$			20.8542i			1.07121i	0.844469	+	0.535605i	$0.179916\pi$
$379$			20.8542i			1.07121i	−0.844469	+	0.535605i	$0.820084\pi$
$380$	2.66493	+	2.53691i	0.136708	+	0.130141i
$381$	17.2689	−	15.6461i	0.884712	−	0.801573i
$382$	12.8229	+	5.97940i	0.656075	+	0.305933i
$383$	1.27835	+	14.6116i	0.0653206	+	0.746618i	0.956264	+	0.292504i	$0.0944885\pi$
$383$	1.27835	+	14.6116i	0.0653206	+	0.746618i	−0.890944	+	0.454114i	$0.849956\pi$
$384$	3.08769	−	22.4749i	0.157568	−	1.14692i
$385$	−4.76712	+	8.74706i	−0.242955	+	0.445791i
$386$	27.5662	−	15.9154i	1.40308	−	0.810071i
$387$	−13.9362	+	4.89539i	−0.708419	+	0.248847i
$388$	−0.861786	−	3.21623i	−0.0437506	−	0.163279i
$389$	−4.79561	+	4.02400i	−0.243147	+	0.204025i	−0.756215	−	0.654323i	$-0.772953\pi$
$389$	−4.79561	+	4.02400i	−0.243147	+	0.204025i	0.513067	+	0.858348i	$0.328509\pi$
$390$	1.06795	−	1.44785i	0.0540776	−	0.0733147i
$391$	0.162455	−	0.921326i	0.00821568	−	0.0465934i
$392$	−6.59332	−	9.41624i	−0.333013	−	0.475592i
$393$	2.37706	−	10.4436i	0.119907	−	0.526812i
$394$	7.13377	+	8.50169i	0.359394	+	0.428309i
$395$	−4.60723	+	0.517578i	−0.231815	+	0.0260422i
$396$	2.32985	+	0.230297i	0.117079	+	0.0115728i
$397$	0.120732	−	0.450577i	0.00605935	−	0.0226138i	−0.962830	−	0.270108i	$-0.912941\pi$
$397$	0.120732	−	0.450577i	0.00605935	−	0.0226138i	0.968889	+	0.247494i	$0.0796072\pi$
$398$	16.4685	+	35.3168i	0.825492	+	1.77027i
$399$	−6.14146	−	15.0661i	−0.307457	−	0.754250i
$400$	18.8371	−	12.1487i	0.941853	−	0.607437i
$401$	3.19304	+	8.77280i	0.159453	+	0.438093i	0.993532	−	0.113552i	$-0.0362228\pi$
$401$	3.19304	+	8.77280i	0.159453	+	0.438093i	−0.834079	+	0.551644i	$0.814001\pi$
$402$	−2.37334	−	1.53084i	−0.118372	−	0.0763513i
$403$	1.13154	+	0.792314i	0.0563661	+	0.0394680i
$404$	−3.78805			−0.188463
$405$	14.2005	−	14.2599i	0.705630	−	0.708580i
$406$	−21.1557			−1.04994
$407$	−4.90874	−	3.43714i	−0.243317	−	0.170373i
$408$	−27.4695	−	17.7182i	−1.35994	−	0.877182i
$409$	−0.240362	−	0.660389i	−0.0118851	−	0.0326541i	0.933608	−	0.358296i	$-0.116642\pi$
$409$	−0.240362	−	0.660389i	−0.0118851	−	0.0326541i	−0.945493	+	0.325641i	$0.894420\pi$
$410$	10.4891	+	11.8935i	0.518021	+	0.587378i
$411$	−4.82780	−	11.8435i	−0.238138	−	0.584197i
$412$	0.353203	+	0.757446i	0.0174010	+	0.0373167i
$413$	−4.02694	+	15.0288i	−0.198153	+	0.739517i
$414$	−0.339821	+	0.473869i	−0.0167013	+	0.0232894i
$415$	−18.3822	+	23.0351i	−0.902349	+	1.13075i
$416$	0.311994	+	0.371820i	0.0152968	+	0.0182300i
$417$	−3.94171	+	17.3179i	−0.193026	+	0.848062i
$418$	14.0923	+	20.1259i	0.689276	+	0.984389i
$419$	−3.72329	+	21.1158i	−0.181894	+	1.03157i	0.747986	+	0.663714i	$0.231021\pi$
$419$	−3.72329	+	21.1158i	−0.181894	+	1.03157i	−0.929881	+	0.367861i	$0.880090\pi$
$420$	1.72566	−	0.260588i	0.0842038	−	0.0127154i
$421$	13.6486	−	11.4526i	0.665194	−	0.558164i	−0.246445	−	0.969157i	$-0.579262\pi$
$421$	13.6486	−	11.4526i	0.665194	−	0.558164i	0.911638	+	0.410993i	$0.134818\pi$
$422$	−0.136857	−	0.510759i	−0.00666211	−	0.0248633i
$423$	−19.3175	−	16.5835i	−0.939251	−	0.806319i
$424$	1.53582	−	0.886708i	0.0745862	−	0.0430623i
$425$	−4.94495	−	36.0077i	−0.239865	−	1.74663i
$426$	−3.71625	+	27.0501i	−0.180053	+	1.31058i
$427$	0.371968	+	4.25162i	0.0180008	+	0.205750i
$428$	2.81169	+	1.31111i	0.135908	+	0.0633750i
$429$	1.09661	−	0.993559i	0.0529449	−	0.0479695i
$430$	11.4648	−	12.0433i	0.552880	−	0.580779i
$431$			13.6942i			0.659624i	0.944047	+	0.329812i	$0.106985\pi$
$431$			13.6942i			0.659624i	−0.944047	+	0.329812i	$0.893015\pi$
$432$	12.1824	+	19.8547i	0.586126	+	0.955261i
$433$	22.8337	−	22.8337i	1.09732	−	1.09732i	0.102594	−	0.994723i	$-0.467286\pi$
$433$	22.8337	−	22.8337i	1.09732	−	1.09732i	0.994723	−	0.102594i	$-0.0327142\pi$
$434$	1.88909	+	10.7136i	0.0906791	+	0.514267i
$435$	15.0468	−	30.2946i	0.721439	−	1.45251i
$436$	0.122596	−	0.0446213i	0.00587129	−	0.00213697i
$437$	−0.750887	+	0.0656941i	−0.0359198	+	0.00314257i
$438$	−2.25028	−	17.8694i	−0.107523	−	0.853834i
$439$	3.85214	−	10.5837i	0.183852	−	0.505130i	−0.813189	−	0.582000i	$-0.802270\pi$
$439$	3.85214	−	10.5837i	0.183852	−	0.505130i	0.997041	+	0.0768697i	$0.0244925\pi$
$440$	15.0127	−	5.88635i	0.715701	−	0.280621i
$441$	12.7907	+	3.58208i	0.609079	+	0.170575i
$442$	3.26165	−	0.873956i	0.155141	−	0.0415699i
$443$	6.73147	+	0.588927i	0.319822	+	0.0279808i	0.245936	−	0.969286i	$-0.420905\pi$
$443$	6.73147	+	0.588927i	0.319822	+	0.0279808i	0.0738853	+	0.997267i	$0.476460\pi$
$444$	0.0398878	+	1.04908i	0.00189299	+	0.0497872i
$445$	11.1031	+	22.3574i	0.526336	+	1.05984i
$446$	−23.3694	−	4.12066i	−1.10657	−	0.195119i
$447$	−1.42417	+	1.53674i	−0.0673607	+	0.0726855i
$448$	0.920162	−	10.5175i	0.0434736	−	0.496905i
$449$	−5.70190	+	9.87598i	−0.269089	+	0.466076i	−0.968627	−	0.248519i	$-0.920056\pi$
$449$	−5.70190	+	9.87598i	−0.269089	+	0.466076i	0.699538	+	0.714596i	$0.253389\pi$
$450$	−6.93493	+	21.5667i	−0.326916	+	1.01666i
$451$	6.52164	+	11.2958i	0.307092	+	0.531899i
$452$	−0.121937	+	0.0568601i	−0.00573542	+	0.00267447i
$453$	−27.7853	+	3.49899i	−1.30547	+	0.164397i
$454$	−22.8589	+	27.2421i	−1.07282	+	1.27854i
$455$	0.610279	−	0.918884i	0.0286103	−	0.0430779i
$456$	−8.06081	+	25.0725i	−0.377482	+	1.17413i
$457$	−4.25450	+	6.07605i	−0.199017	+	0.284226i	−0.906239	−	0.422766i	$-0.861059\pi$
$457$	−4.25450	+	6.07605i	−0.199017	+	0.284226i	0.707222	+	0.706992i	$0.249948\pi$
$458$	−24.7249	−	24.7249i	−1.15532	−	1.15532i
$459$	37.5263	−	4.29701i	1.75158	−	0.200567i
$460$	0.0120769	−	0.0799468i	0.000563088	−	0.00372754i
$461$	−41.0458	+	7.23749i	−1.91170	+	0.337083i	−0.997649	−	0.0685275i	$-0.978170\pi$
$461$	−41.0458	+	7.23749i	−1.91170	+	0.337083i	−0.914046	+	0.405611i	$0.867059\pi$
$462$	11.6397	+	0.573873i	0.541529	+	0.0266990i
$463$	1.40671	−	3.01669i	0.0653752	−	0.140198i	−0.870905	−	0.491451i	$-0.836467\pi$
$463$	1.40671	−	3.01669i	0.0653752	−	0.140198i	0.936280	+	0.351253i	$0.114244\pi$
$464$	29.9930	+	25.1671i	1.39239	+	1.16835i
$465$	−16.6852	−	4.91477i	−0.773758	−	0.227917i
$466$	−30.6975	−	11.1730i	−1.42203	−	0.517577i
$467$	−4.32129	−	1.15789i	−0.199966	−	0.0535806i	0.157446	−	0.987528i	$-0.449674\pi$
$467$	−4.32129	−	1.15789i	−0.199966	−	0.0535806i	−0.357412	+	0.933947i	$0.616341\pi$
$468$	−0.254784	−	0.0478892i	−0.0117774	−	0.00221368i
$469$	−1.49962	−	0.865804i	−0.0692458	−	0.0399791i
$470$	27.8572	+	6.73433i	1.28496	+	0.310632i
$471$	16.7720	−	31.7806i	0.772813	−	1.46437i
$472$	20.6309	−	14.4459i	0.949616	−	0.664929i
$473$	11.2030	−	7.84443i	0.515115	−	0.360687i
$474$	2.88836	+	4.59065i	0.132667	+	0.210855i
$475$	−26.9914	+	11.3570i	−1.23845	+	0.521093i
$476$	2.83674	+	1.63780i	0.130022	+	0.0750682i
$477$	−0.722508	+	1.91761i	−0.0330814	+	0.0878015i
$478$	−20.7402	−	5.55731i	−0.948632	−	0.254185i
$479$	−34.5314	−	12.5684i	−1.57778	−	0.574264i	−0.603059	−	0.797697i	$-0.706052\pi$
$479$	−34.5314	−	12.5684i	−1.57778	−	0.574264i	−0.974719	+	0.223432i	$0.928274\pi$
$480$	−5.21606	−	3.18549i	−0.238079	−	0.145397i
$481$	0.508314	+	0.426526i	0.0231771	+	0.0194479i
$482$	5.32332	−	11.4159i	0.242470	−	0.519980i
$483$	−0.193794	+	0.300450i	−0.00881793	+	0.0136709i
$484$	0.908792	−	0.160244i	0.0413087	−	0.00728384i
$485$	26.2031	+	3.95827i	1.18982	+	0.179736i
$486$	−22.2452	−	7.70867i	−1.00906	−	0.349672i
$487$	9.05628	+	9.05628i	0.410379	+	0.410379i	0.881871	−	0.471492i	$-0.156284\pi$
$487$	9.05628	+	9.05628i	0.410379	+	0.410379i	−0.471492	+	0.881871i	$0.656284\pi$
$488$	3.96257	−	5.65913i	0.179377	−	0.256177i
$489$	22.1340	−	4.77642i	1.00093	−	0.215997i
$490$	−14.6569	+	2.95795i	−0.662131	+	0.133627i
$491$	14.7648	−	17.5960i	0.666326	−	0.794096i	−0.321953	−	0.946756i	$-0.604339\pi$
$491$	14.7648	−	17.5960i	0.666326	−	0.794096i	0.988279	+	0.152660i	$0.0487838\pi$
$492$	0.886338	−	2.10619i	0.0399592	−	0.0949545i
$493$	57.5384	−	26.8306i	2.59140	−	1.20839i
$494$	−1.36029	−	2.35609i	−0.0612024	−	0.106006i
$495$	−9.10041	+	16.2597i	−0.409033	+	0.730819i
$496$	10.0668	−	17.4361i	0.452011	−	0.782906i
$497$	−1.45907	+	16.6772i	−0.0654482	+	0.748076i
$498$	33.6168	+	7.65148i	1.50641	+	0.342871i
$499$	−9.11992	−	1.60809i	−0.408264	−	0.0719879i	−0.0342550	−	0.999413i	$-0.510906\pi$
$499$	−9.11992	−	1.60809i	−0.408264	−	0.0719879i	−0.374009	+	0.927425i	$0.622017\pi$
$500$	−0.503800	−	3.10051i	−0.0225306	−	0.138659i
$501$	24.6490	+	13.0083i	1.10124	+	0.581170i
$502$	7.17569	+	0.627792i	0.320267	+	0.0280197i
$503$	8.31780	−	2.22875i	0.370873	−	0.0993750i	−0.0685686	−	0.997646i	$-0.521843\pi$
$503$	8.31780	−	2.22875i	0.370873	−	0.0993750i	0.439441	+	0.898271i	$0.355177\pi$
$504$	7.04953	+	10.3130i	0.314011	+	0.459377i
$505$	12.0652	−	27.6289i	0.536893	−	1.22947i
$506$	0.184659	−	0.507345i	0.00820908	−	0.0225543i
$507$	17.8100	−	13.5075i	0.790970	−	0.599888i
$508$	3.76553	−	0.329441i	0.167068	−	0.0146166i
$509$	20.6614	−	7.52013i	0.915799	−	0.333324i	0.159233	−	0.987241i	$-0.449098\pi$
$509$	20.6614	−	7.52013i	0.915799	−	0.333324i	0.756566	+	0.653917i	$0.226876\pi$
$510$	−35.4205	+	23.5219i	−1.56845	+	1.04157i
$511$	−1.91756	−	10.8750i	−0.0848278	−	0.481082i
$512$	−11.4575	+	11.4575i	−0.506354	+	0.506354i
$513$	−11.1694	−	28.3083i	−0.493141	−	1.24984i
$514$		−	7.12936i		−	0.314463i
$515$	−6.64955	+	0.163646i	−0.293014	+	0.00721109i
$516$	−2.28102	−	0.733345i	−0.100416	−	0.0322837i
$517$	21.3640	+	9.96221i	0.939589	+	0.438138i
$518$	0.455459	+	5.20593i	0.0200117	+	0.228735i
$519$	−3.62933	−	2.81749i	−0.159310	−	0.123674i
$520$	−1.71286	+	0.504440i	−0.0751139	+	0.0221211i
$521$	−4.43677	+	2.56157i	−0.194378	+	0.112224i	−0.594031	−	0.804442i	$-0.702464\pi$
$521$	−4.43677	+	2.56157i	−0.194378	+	0.112224i	0.399652	+	0.916667i	$0.369131\pi$
$522$	−39.5687	−	0.445550i	−1.73187	−	0.0195012i
$523$	2.02890	+	7.57196i	0.0887177	+	0.331099i	0.995992	−	0.0894400i	$-0.0285077\pi$
$523$	2.02890	+	7.57196i	0.0887177	+	0.331099i	−0.907275	+	0.420539i	$0.861841\pi$
$524$	1.33091	−	1.11677i	0.0581412	−	0.0487863i
$525$	−3.59569	+	13.4165i	−0.156929	+	0.585543i
$526$	−0.873497	+	4.95385i	−0.0380863	+	0.215998i
$527$	−18.7252	−	26.7424i	−0.815685	−	1.16492i
$528$	−15.8192	−	14.6603i	−0.688443	−	0.638009i
$529$	−14.7735	−	17.6063i	−0.642325	−	0.765493i
$530$	−0.257526	−	2.29237i	−0.0111862	−	0.0995742i
$531$	−7.84832	+	28.0243i	−0.340588	+	1.21615i
$532$	0.683053	−	2.54919i	0.0296141	−	0.110521i
$533$	−0.610389	−	1.30898i	−0.0264389	−	0.0566984i
$534$	17.9077	−	23.0677i	0.774941	−	0.998236i
$535$	−18.5183	+	16.3317i	−0.800614	+	0.706079i
$536$	0.958687	+	2.63397i	0.0414090	+	0.113770i
$537$	−10.5728	+	5.42840i	−0.456248	+	0.234253i
$538$	−10.3603	−	7.25433i	−0.446663	−	0.312757i
$539$	−12.2984			−0.529729
$540$	3.23309	−	0.451048i	0.139130	−	0.0194100i
$541$	−12.2903			−0.528401			−0.264200	−	0.964468i	$-0.585108\pi$
$541$	−12.2903			−0.528401			−0.264200	+	0.964468i	$0.585108\pi$
$542$	−17.0595	−	11.9452i	−0.732767	−	0.513089i
$543$	−1.70787	+	34.6404i	−0.0732919	+	1.48656i
$544$	−3.92339	−	10.7794i	−0.168214	−	0.462164i
$545$	−0.0650212	+	1.03630i	−0.00278520	+	0.0443903i
$546$	−1.27844	−	0.175638i	−0.0547123	−	0.00751660i
$547$	−0.220177	−	0.472172i	−0.00941410	−	0.0201886i	0.901545	−	0.432686i	$-0.142434\pi$
$547$	−0.220177	−	0.472172i	−0.00941410	−	0.0201886i	−0.910959	+	0.412498i	$0.864656\pi$
$548$	0.536948	−	2.00392i	0.0229373	−	0.0856032i
$549$	0.606171	+	7.95986i	0.0258707	+	0.339718i
$550$	0.798052	−	20.9602i	0.0340290	−	0.893744i
$551$	−32.8789	−	39.1836i	−1.40069	−	1.66928i
$552$	0.552927	−	0.170921i	0.0235342	−	0.00727488i
$553$	1.90739	+	2.72403i	0.0811104	+	0.115838i
$554$	−0.0322538	+	0.182920i	−0.00137033	+	0.00777153i
$555$	−7.77873	−	3.05046i	−0.330189	−	0.129485i
$556$	−2.20695	+	1.85185i	−0.0935957	+	0.0785361i
$557$	6.03527	+	22.5239i	0.255723	+	0.954370i	0.967687	+	0.252155i	$0.0811391\pi$
$557$	6.03527	+	22.5239i	0.255723	+	0.954370i	−0.711964	+	0.702216i	$0.752194\pi$
$558$	3.30763	+	20.0779i	0.140023	+	0.849966i
$559$	−1.31151	+	0.757203i	−0.0554711	+	0.0320263i
$560$	−14.1172	−	7.69381i	−0.596559	−	0.325123i
$561$	−32.3850	+	13.2012i	−1.36730	+	0.557355i
$562$	3.16269	+	36.1498i	0.133410	+	1.52489i
$563$	31.1449	+	14.5231i	1.31260	+	0.612076i	0.947757	−	0.318993i	$-0.103344\pi$
$563$	31.1449	+	14.5231i	1.31260	+	0.612076i	0.364844	+	0.931069i	$0.381122\pi$
$564$	−0.871130	−	4.03683i	−0.0366812	−	0.169981i
$565$	−0.0263444	−	1.07047i	−0.00110832	−	0.0450351i
$566$		−	24.0770i		−	1.01203i
$567$	−13.8553	−	4.04903i	−0.581870	−	0.170043i
$568$	19.1620	−	19.1620i	0.804019	−	0.804019i
$569$	0.227444	+	1.28990i	0.00953495	+	0.0540754i	0.989204	−	0.146545i	$-0.0468153\pi$
$569$	0.227444	+	1.28990i	0.00953495	+	0.0540754i	−0.979669	+	0.200620i	$0.935704\pi$
$570$	25.6918	+	22.6606i	1.07611	+	0.949148i
$571$	−17.9969	+	6.55033i	−0.753146	+	0.274123i	−0.689929	−	0.723877i	$-0.742358\pi$
$571$	−17.9969	+	6.55033i	−0.753146	+	0.274123i	−0.0632171	+	0.998000i	$0.520136\pi$
$572$	0.239119	−	0.0209202i	0.00999807	−	0.000874718i
$573$	14.9557	+	6.29372i	0.624782	+	0.262924i
$574$	3.89033	−	10.6886i	0.162379	−	0.446133i
$575$	0.544643	+	0.342721i	0.0227132	+	0.0142924i
$576$	1.94253	−	19.6521i	0.0809389	−	0.818836i
$577$	−12.6473	+	3.38883i	−0.526514	+	0.141079i	−0.512278	−	0.858820i	$-0.671198\pi$
$577$	−12.6473	+	3.38883i	−0.526514	+	0.141079i	−0.0142358	+	0.999899i	$0.504532\pi$
$578$	−53.9231	−	4.71766i	−2.24290	−	0.196229i
$579$	30.8977	−	19.4403i	1.28406	−	0.807913i
$580$	4.91420	−	2.44047i	0.204051	−	0.101335i
$581$	20.8174	+	3.67067i	0.863652	+	0.152285i
$582$	−9.15579	−	29.6189i	−0.379520	−	1.22774i
$583$	0.165364	−	1.89012i	0.00684869	−	0.0782808i
$584$	−8.93766	+	15.4805i	−0.369843	+	0.640587i
$585$	1.16079	−	1.70578i	0.0479928	−	0.0705255i
$586$	−3.97987	−	6.89333i	−0.164407	−	0.284761i
$587$	26.3137	−	12.2703i	1.08608	−	0.506449i	0.204687	−	0.978827i	$-0.434382\pi$
$587$	26.3137	−	12.2703i	1.08608	−	0.506449i	0.881396	+	0.472379i	$0.156605\pi$
$588$	1.30199	+	1.71671i	0.0536931	+	0.0707959i
$589$	−16.9072	+	20.1492i	−0.696650	+	0.830235i
$590$	−6.48086	−	32.1132i	−0.266813	−	1.32208i
$591$	8.54582	+	9.43219i	0.351528	+	0.387988i
$592$	5.54732	−	7.92239i	0.227993	−	0.325608i
$593$	−18.8092	−	18.8092i	−0.772402	−	0.772402i	0.206124	−	0.978526i	$-0.433915\pi$
$593$	−18.8092	−	18.8092i	−0.772402	−	0.772402i	−0.978526	+	0.206124i	$0.933915\pi$
$594$	21.7583	+	1.31848i	0.892754	+	0.0540980i
$595$	−20.9808	+	15.4739i	−0.860128	+	0.634368i
$596$	−0.334697	+	0.0590161i	−0.0137097	+	0.00241739i
$597$	20.4120	+	39.7559i	0.835406	+	1.62710i
$598$	−0.0252661	+	0.0541833i	−0.00103321	+	0.00221572i
$599$	3.51169	+	2.94665i	0.143484	+	0.120397i	0.711704	−	0.702479i	$-0.247924\pi$
$599$	3.51169	+	2.94665i	0.143484	+	0.120397i	−0.568221	+	0.822876i	$0.692368\pi$
$600$	18.4186	−	12.8954i	0.751937	−	0.526452i
$601$	25.1131	+	9.14041i	1.02438	+	0.372845i	0.798940	−	0.601411i	$-0.205395\pi$
$601$	25.1131	+	9.14041i	1.02438	+	0.372845i	0.225443	+	0.974256i	$0.427617\pi$
$602$	−11.5202	−	3.08684i	−0.469530	−	0.125810i
$603$	−2.78658	−	1.65094i	−0.113478	−	0.0672316i
$604$	−3.93404	−	2.27132i	−0.160074	−	0.0924187i
$605$	−1.72578	+	7.13884i	−0.0701629	+	0.290235i
$606$	−35.2440	+	1.34003i	−1.43169	+	0.0544352i
$607$	29.2803	−	20.5023i	1.18845	−	0.832163i	0.199428	−	0.979913i	$-0.436092\pi$
$607$	29.2803	−	20.5023i	1.18845	−	0.832163i	0.989025	+	0.147749i	$0.0472028\pi$
$608$	−7.57081	+	5.30114i	−0.307037	+	0.214990i
$609$	−24.2447	+	0.921823i	−0.982443	+	0.0373542i
$610$	−4.68328	−	7.66950i	−0.189620	−	0.310529i
$611$	−2.26053	−	1.30512i	−0.0914512	−	0.0527994i
$612$	5.27122	+	3.12300i	0.213077	+	0.126240i
$613$	−35.8682	−	9.61085i	−1.44870	−	0.388179i	−0.553130	−	0.833095i	$-0.686567\pi$
$613$	−35.8682	−	9.61085i	−1.44870	−	0.388179i	−0.895572	+	0.444916i	$0.853233\pi$
$614$	−31.4107	−	11.4325i	−1.26763	−	0.461380i
$615$	12.5389	+	13.1730i	0.505617	+	0.531188i
$616$	−8.86034	−	7.43471i	−0.356993	−	0.299553i
$617$	19.6545	−	42.1491i	0.791258	−	1.69686i	0.0769428	−	0.997036i	$-0.475484\pi$
$617$	19.6545	−	42.1491i	0.791258	−	1.69686i	0.714316	−	0.699824i	$-0.246738\pi$
$618$	3.55414	+	6.92231i	0.142968	+	0.278456i
$619$	−13.9352	+	2.45716i	−0.560104	+	0.0987615i	−0.446531	−	0.894768i	$-0.647341\pi$
$619$	−13.9352	+	2.45716i	−0.560104	+	0.0987615i	−0.113573	+	0.993530i	$0.536230\pi$
$620$	−1.67470	−	2.27070i	−0.0672576	−	0.0911934i
$621$	−0.368791	+	0.557865i	−0.0147991	+	0.0223864i
$622$	15.3672	+	15.3672i	0.616168	+	0.616168i
$623$	10.2699	−	14.6669i	0.411455	−	0.587619i
$624$	1.60354	+	1.76986i	0.0641929	+	0.0708510i
$625$	24.2188	+	6.20074i	0.968752	+	0.248029i
$626$	−20.6337	+	24.5903i	−0.824687	+	0.982824i
$627$	17.0269	+	22.4504i	0.679987	+	0.896583i
$628$	5.28283	−	2.46342i	0.210808	−	0.0983013i
$629$	−7.84112	−	13.5812i	−0.312646	−	0.541519i
$630$	15.9634	−	3.03496i	0.635995	−	0.120916i
$631$	16.2979	−	28.2288i	0.648810	−	1.12377i	−0.334597	−	0.942361i	$-0.608600\pi$
$631$	16.2979	−	28.2288i	0.648810	−	1.12377i	0.983407	−	0.181411i	$-0.0580664\pi$
$632$	0.469158	−	5.36250i	0.0186621	−	0.213309i
$633$	−0.179095	−	0.579371i	−0.00711840	−	0.0230279i
$634$	34.1919	+	6.02895i	1.35793	+	0.239440i
$635$	−9.59059	+	28.5139i	−0.380591	+	1.13154i
$636$	−0.281345	+	0.177018i	−0.0111561	+	0.00701921i
$637$	1.35664	+	0.118690i	0.0537520	+	0.00470269i
$638$	35.3901	−	9.48275i	1.40111	−	0.375426i
$639$	−3.08021	+	31.1616i	−0.121851	+	1.23273i
$640$	10.6910	+	27.2664i	0.422597	+	1.07780i
$641$	−11.8689	+	32.6096i	−0.468794	+	1.28800i	0.449916	+	0.893071i	$0.351454\pi$
$641$	−11.8689	+	32.6096i	−0.468794	+	1.28800i	−0.918711	+	0.394931i	$0.870768\pi$
$642$	26.6237	+	11.2039i	1.05075	+	0.442183i
$643$	8.82626	−	0.772198i	0.348074	−	0.0304525i	0.0882215	−	0.996101i	$-0.471882\pi$
$643$	8.82626	−	0.772198i	0.348074	−	0.0304525i	0.259852	+	0.965648i	$0.416326\pi$
$644$	−0.0544969	+	0.0198352i	−0.00214748	+	0.000781618i
$645$	12.6140	−	14.3013i	0.496674	−	0.563113i
$646$	11.1651	+	63.3204i	0.439285	+	2.49131i
$647$	−14.1426	+	14.1426i	−0.556003	+	0.556003i	−0.928167	−	0.372164i	$-0.878616\pi$
$647$	−14.1426	+	14.1426i	−0.556003	+	0.556003i	0.372164	+	0.928167i	$0.378616\pi$
$648$	12.9679	+	19.4374i	0.509428	+	0.763573i
$649$		−	26.9457i		−	1.05771i
$650$	−0.290318	+	2.30442i	−0.0113872	+	0.0903867i
$651$	2.63174	+	12.1955i	0.103146	+	0.477980i
$652$	3.32886	+	1.55227i	0.130368	+	0.0607917i
$653$	−0.173231	−	1.98004i	−0.00677904	−	0.0774848i	0.992052	−	0.125832i	$-0.0401601\pi$
$653$	−0.173231	−	1.98004i	−0.00677904	−	0.0774848i	−0.998831	+	0.0483474i	$0.984605\pi$
$654$	1.12485	−	0.458524i	0.0439850	−	0.0179297i
$655$	3.90634	+	13.2643i	0.152633	+	0.518277i
$656$	−18.2307	+	10.5255i	−0.711788	+	0.410951i
$657$	−3.35748	−	20.3805i	−0.130988	−	0.795119i
$658$	−5.32049	−	19.8563i	−0.207414	−	0.774081i
$659$	−9.93910	+	8.33989i	−0.387172	+	0.324876i	−0.815510	−	0.578742i	$-0.803544\pi$
$659$	−9.93910	+	8.33989i	−0.387172	+	0.324876i	0.428338	+	0.903619i	$0.359099\pi$
$660$	−2.76996	+	1.20943i	−0.107820	+	0.0470769i
$661$	2.91716	−	16.5440i	0.113464	−	0.643489i	−0.874035	−	0.485864i	$-0.838505\pi$
$661$	2.91716	−	16.5440i	0.113464	−	0.643489i	0.987499	−	0.157625i	$-0.0503837\pi$
$662$	12.0886	+	17.2643i	0.469836	+	0.670996i
$663$	3.69980	−	1.14368i	0.143688	−	0.0444170i
$664$	−21.9947	−	26.2123i	−0.853561	−	1.01723i
$665$	16.4174	+	13.1013i	0.636641	+	0.508047i
$666$	0.742231	+	9.74651i	0.0287609	+	0.377670i
$667$	−0.290921	+	1.08573i	−0.0112645	+	0.0420396i
$668$	1.91063	+	4.09735i	0.0739244	+	0.158531i
$669$	−26.9612	−	3.70404i	−1.04238	−	0.143206i
$670$	3.63890	+	0.228317i	0.140583	+	0.00882066i
$671$	−2.52797	−	6.94554i	−0.0975912	−	0.268130i
$672$	−0.215875	+	4.37855i	−0.00832758	+	0.168906i
$673$	7.48390	+	5.24028i	0.288483	+	0.201998i	0.708856	−	0.705353i	$-0.249212\pi$
$673$	7.48390	+	5.24028i	0.288483	+	0.201998i	−0.420373	+	0.907352i	$0.638101\pi$
$674$	21.8853			0.842991
$675$	−7.00778	+	25.0178i	−0.269729	+	0.962936i
$676$	3.62584			0.139455
$677$	−0.0991212	−	0.0694054i	−0.00380954	−	0.00266747i	0.571670	−	0.820484i	$-0.306296\pi$
$677$	−0.0991212	−	0.0694054i	−0.00380954	−	0.00266747i	−0.575480	+	0.817816i	$0.695185\pi$
$678$	−1.11438	+	0.572160i	−0.0427976	+	0.0219737i
$679$	−6.50112	−	17.8617i	−0.249490	−	0.685468i
$680$	42.1173	+	2.64259i	1.61512	+	0.101339i
$681$	−25.0095	+	32.2158i	−0.958365	+	1.23451i
$682$	−7.96234	−	17.0753i	−0.304894	−	0.653847i
$683$	3.58403	−	13.3758i	0.137139	−	0.511810i	−0.862841	−	0.505476i	$-0.831317\pi$
$683$	3.58403	−	13.3758i	0.137139	−	0.511810i	0.999980	−	0.00633429i	$-0.00201628\pi$
$684$	1.33124	−	4.75350i	0.0509011	−	0.181755i
$685$	12.9058	+	10.2989i	0.493104	+	0.393502i
$686$	17.7931	+	21.2049i	0.679342	+	0.809608i
$687$	−29.4123	−	27.2576i	−1.12215	−	1.03994i
$688$	12.6604	+	18.0809i	0.482673	+	0.689329i
$689$	−0.0364828	+	0.206904i	−0.00138988	+	0.00788241i
$690$	0.0840816	−	0.748096i	0.00320093	−	0.0284795i
$691$	17.4891	−	14.6751i	0.665315	−	0.558266i	−0.246359	−	0.969179i	$-0.579234\pi$
$691$	17.4891	−	14.6751i	0.665315	−	0.558266i	0.911675	+	0.410913i	$0.134790\pi$
$692$	−0.192894	−	0.719892i	−0.00733274	−	0.0273662i
$693$	13.3642	+	0.150484i	0.507666	+	0.00571640i
$694$	−11.8745	+	6.85575i	−0.450750	+	0.260241i
$695$	−6.47759	−	21.9951i	−0.245709	−	0.834323i
$696$	31.0231	+	24.0835i	1.17593	+	0.912885i
$697$	2.97498	+	34.0042i	0.112686	+	1.28800i
$698$	11.4089	+	5.32004i	0.431832	+	0.201366i
$699$	−35.6664	−	11.4667i	−1.34903	−	0.433712i
$700$	−1.77981	+	1.38154i	−0.0672706	+	0.0522172i
$701$		−	15.6693i		−	0.591821i	−0.955216	−	0.295910i	$-0.904377\pi$
$701$		−	15.6693i		−	0.591821i	0.955216	−	0.295910i	$-0.0956230\pi$
$702$	−2.38744	−	0.355429i	−0.0901081	−	0.0134148i
$703$	−8.93432	+	8.93432i	−0.336964	+	0.336964i
$704$	3.17504	+	18.0065i	0.119664	+	0.678647i
$705$	32.2180	+	6.50379i	1.21340	+	0.244947i
$706$	−3.74859	+	1.36438i	−0.141080	+	0.0513490i
$707$	−21.5424	+	1.88471i	−0.810184	+	0.0708820i
$708$	−3.76130	+	2.85265i	−0.141358	+	0.107209i
$709$	−2.91839	+	8.01821i	−0.109602	+	0.301130i	−0.982353	−	0.187036i	$-0.940112\pi$
$709$	−2.91839	+	8.01821i	−0.109602	+	0.301130i	0.872751	+	0.488166i	$0.162334\pi$
$710$	−12.8673	−	32.8171i	−0.482902	−	1.23160i
$711$	3.51012	+	5.13508i	0.131640	+	0.192580i
$712$	−27.9959	+	7.50148i	−1.04919	+	0.281130i
$713$	0.575807	+	0.0503766i	0.0215641	+	0.00188662i
$714$	26.9724	+	14.2345i	1.00942	+	0.532713i
$715$	−0.609022	+	1.81069i	−0.0227761	+	0.0677161i
$716$	−1.89856	−	0.334767i	−0.0709523	−	0.0125108i
$717$	−24.0106	−	5.46502i	−0.896692	−	0.204095i
$718$	1.85896	−	21.2480i	0.0693758	−	0.792968i
$719$	19.9277	−	34.5157i	0.743176	−	1.28722i	−0.207866	−	0.978157i	$-0.566652\pi$
$719$	19.9277	−	34.5157i	0.743176	−	1.28722i	0.951042	−	0.309062i	$-0.100015\pi$
$720$	−26.2421	−	14.6875i	−0.977984	−	0.547369i
$721$	2.38550	+	4.13180i	0.0888406	+	0.153876i
$722$	20.9433	−	9.76600i	0.779427	−	0.363453i
$723$	5.60315	−	13.3147i	0.208383	−	0.495178i
$724$	−3.61621	+	4.30963i	−0.134395	+	0.160166i
$725$	2.14807	+	43.6157i	0.0797773	+	1.61985i
$726$	8.39869	−	1.81240i	0.311704	−	0.0672644i
$727$	26.2725	−	37.5210i	0.974393	−	1.39158i	0.0548911	−	0.998492i	$-0.482519\pi$
$727$	26.2725	−	37.5210i	0.974393	−	1.39158i	0.919502	−	0.393085i	$-0.128592\pi$
$728$	0.905635	+	0.905635i	0.0335651	+	0.0335651i
$729$	−25.8291	−	7.86492i	−0.956634	−	0.291293i
$730$	13.8011	+	18.7127i	0.510801	+	0.692587i
$731$	35.2471	−	6.21502i	1.30366	−	0.229871i
$732$	−0.701888	+	1.08818i	−0.0259425	+	0.0402201i
$733$	−15.6365	+	33.5325i	−0.577546	+	1.23855i	0.372961	+	0.927847i	$0.378343\pi$
$733$	−15.6365	+	33.5325i	−0.577546	+	1.23855i	−0.950507	+	0.310704i	$0.899435\pi$
$734$	−15.9308	−	13.3675i	−0.588015	−	0.493403i
$735$	−16.6681	+	4.02849i	−0.614811	+	0.148593i
$736$	0.190850	+	0.0694636i	0.00703481	+	0.00256046i
$737$	2.89670	+	0.776169i	0.106701	+	0.0285906i
$738$	7.50139	−	19.9095i	0.276130	−	0.732879i
$739$	−9.45965	−	5.46153i	−0.347979	−	0.200906i	0.315816	−	0.948820i	$-0.397722\pi$
$739$	−9.45965	−	5.46153i	−0.347979	−	0.200906i	−0.663795	+	0.747915i	$0.731055\pi$
$740$	−0.706341	−	1.15673i	−0.0259656	−	0.0425222i
$741$	−1.66157	−	2.64084i	−0.0610393	−	0.0970135i
$742$	−1.35537	+	0.949040i	−0.0497572	+	0.0348404i
$743$	−6.78635	+	4.75185i	−0.248967	+	0.174329i	−0.691398	−	0.722474i	$-0.743005\pi$
$743$	−6.78635	+	4.75185i	−0.248967	+	0.174329i	0.442431	+	0.896802i	$0.354116\pi$
$744$	9.42606	−	17.8611i	0.345576	−	0.654818i
$745$	0.635584	−	2.62915i	0.0232860	−	0.0963246i
$746$	−26.5695	−	15.3399i	−0.972778	−	0.561633i
$747$	38.8586	+	7.30388i	1.42176	+	0.267235i
$748$	−5.47954	−	1.46824i	−0.200352	−	0.0536841i
$749$	16.6422	+	6.05726i	0.608093	+	0.221328i
$750$	−5.78416	−	28.6688i	−0.211207	−	1.04684i
$751$	1.01418	+	0.851000i	0.0370080	+	0.0310534i	0.661104	−	0.750294i	$-0.270088\pi$
$751$	1.01418	+	0.851000i	0.0370080	+	0.0310534i	−0.624096	+	0.781348i	$0.714533\pi$
$752$	−16.0783	+	34.4801i	−0.586317	+	1.25736i
$753$	8.25077	+	0.406788i	0.300675	+	0.0148242i
$754$	−3.99541	+	0.704499i	−0.145504	+	0.0256563i
$755$	29.0965	−	21.4594i	1.05893	−	0.780989i
$756$	−1.39382	−	1.88142i	−0.0506928	−	0.0684267i
$757$	−26.5719	−	26.5719i	−0.965772	−	0.965772i	0.0336615	−	0.999433i	$-0.489283\pi$
$757$	−26.5719	−	26.5719i	−0.965772	−	0.965772i	−0.999433	+	0.0336615i	$0.989283\pi$
$758$	−18.0652	+	25.7998i	−0.656159	+	0.937092i
$759$	0.189514	−	0.589469i	0.00687892	−	0.0213964i
$760$	−6.72608	−	33.3283i	−0.243980	−	1.20894i
$761$	6.97127	−	8.30804i	0.252708	−	0.301166i	−0.624744	−	0.780829i	$-0.714797\pi$
$761$	6.97127	−	8.30804i	0.252708	−	0.301166i	0.877453	+	0.479663i	$0.159241\pi$
$762$	34.9179	−	4.39718i	1.26494	−	0.159293i
$763$	0.674994	−	0.314755i	0.0244364	−	0.0113949i
$764$	1.31601	+	2.27939i	0.0476114	+	0.0824654i
$765$	−39.5674	+	28.4998i	−1.43056	+	1.03041i
$766$	−11.0760	+	19.1841i	−0.400191	+	0.693151i
$767$	−0.260050	+	2.97239i	−0.00938988	+	0.107327i
$768$	7.78930	−	8.40504i	0.281072	−	0.303291i
$769$	44.1842	+	7.79087i	1.59332	+	0.280946i	0.898745	−	0.438471i	$-0.144480\pi$
$769$	44.1842	+	7.79087i	1.59332	+	0.280946i	0.694579	+	0.719417i	$0.255591\pi$
$770$	−13.4749	+	6.69186i	−0.485602	+	0.241158i
$771$	−0.310649	−	8.17032i	−0.0111878	−	0.294247i
$772$	5.89888	+	0.516085i	0.212305	+	0.0185743i
$773$	−30.3757	+	8.13915i	−1.09254	+	0.292745i	−0.759723	−	0.650247i	$-0.774666\pi$
$773$	−30.3757	+	8.13915i	−1.09254	+	0.292745i	−0.332816	+	0.942992i	$0.607999\pi$
$774$	−21.4819	−	6.01611i	−0.772152	−	0.216244i
$775$	21.8958	−	4.98246i	0.786521	−	0.178975i
$776$	−10.5236	+	28.9133i	−0.377775	+	1.03793i
$777$	0.748800	+	5.94620i	0.0268631	+	0.213319i
$778$	−9.41874	+	0.824033i	−0.337678	+	0.0295430i
$779$	25.8430	−	9.40608i	0.925922	−	0.337008i
$780$	0.317227	−	0.106680i	0.0113585	−	0.00381975i
$781$	−5.03455	−	28.5524i	−0.180150	−	1.02168i
$782$	0.999091	−	0.999091i	0.0357274	−	0.0357274i
$783$	−45.3655	+	1.21353i	−1.62123	+	0.0433680i
$784$		−	19.8488i		−	0.708885i
$785$	1.14135	+	46.3775i	0.0407366	+	1.65529i
$786$	11.9877	−	10.8612i	0.427588	−	0.387406i
$787$	−28.5680	−	13.3215i	−1.01834	−	0.474860i	−0.159552	−	0.987190i	$-0.551005\pi$
$787$	−28.5680	−	13.3215i	−1.01834	−	0.474860i	−0.858789	+	0.512330i	$0.828783\pi$
$788$	0.179939	+	2.05671i	0.00641007	+	0.0732674i
$789$	−0.785181	+	5.71522i	−0.0279532	+	0.203467i
$790$	−6.14820	−	3.35075i	−0.218743	−	0.119214i
$791$	−0.665155	+	0.384027i	−0.0236502	+	0.0136544i
$792$	−16.4154	−	14.0921i	−0.583295	−	0.500742i
$793$	0.211830	+	0.790562i	0.00752232	+	0.0280737i
$794$	0.539681	−	0.452846i	0.0191526	−	0.0160709i
$795$	−0.395014	−	2.61586i	−0.0140097	−	0.0927750i
$796$	−1.25879	+	7.13898i	−0.0446168	+	0.253034i
$797$	−3.73721	−	5.33729i	−0.132379	−	0.189057i	0.747490	−	0.664273i	$-0.231259\pi$
$797$	−3.73721	−	5.33729i	−0.132379	−	0.189057i	−0.879869	+	0.475216i	$0.842370\pi$
$798$	5.45332	−	23.9592i	0.193046	−	0.848147i
$799$	39.6531	+	47.2567i	1.40283	+	1.67182i
$800$	7.88464	+	0.300206i	0.278764	+	0.0106139i
$801$	19.5173	−	27.2161i	0.689608	−	0.961633i
$802$	−3.64928	+	13.6193i	−0.128860	+	0.480914i
$803$	8.08234	+	17.3326i	0.285220	+	0.611655i
$804$	−0.198320	−	0.486516i	−0.00699421	−	0.0171581i
$805$	0.0289035	−	0.460660i	0.00101871	−	0.0162361i
$806$	0.713536	+	1.96042i	0.0251332	+	0.0690530i
$807$	−12.1891	−	7.86211i	−0.429075	−	0.276759i
$808$	28.6741	+	20.0778i	1.00875	+	0.706335i
$809$	−21.5117			−0.756312			−0.378156	−	0.925742i	$-0.623442\pi$
$809$	−21.5117			−0.756312			−0.378156	+	0.925742i	$0.623442\pi$
$810$	29.9210	−	5.34026i	1.05132	−	0.187637i
$811$	15.2216			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$811$	15.2216			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$812$	−3.22382	−	2.25734i	−0.113134	−	0.0792172i
$813$	−20.0708	−	12.9460i	−0.703914	−	0.454034i
$814$	−3.09539	−	8.50453i	−0.108494	−	0.298083i
$815$	−21.9244	+	19.3356i	−0.767979	+	0.677298i
$816$	−21.3059	−	52.2673i	−0.745854	−	1.82972i
$817$	−12.1868	−	26.1346i	−0.426362	−	0.914335i
$818$	0.274706	−	1.02522i	0.00960488	−	0.0358459i
$819$	−1.47276	−	0.145577i	−0.0514624	−	0.00508687i
$820$	0.329337	+	2.93160i	0.0115010	+	0.102376i
$821$	−32.2494	−	38.4334i	−1.12551	−	1.34133i	−0.932932	−	0.360053i	$-0.882758\pi$
$821$	−32.2494	−	38.4334i	−1.12551	−	1.34133i	−0.192581	−	0.981281i	$-0.561686\pi$
$822$	4.28686	−	18.8344i	0.149522	−	0.656924i
$823$	2.01204	+	2.87349i	0.0701354	+	0.100164i	0.852687	−	0.522422i	$-0.174971\pi$
$823$	2.01204	+	2.87349i	0.0701354	+	0.100164i	−0.782552	+	0.622585i	$0.786082\pi$
$824$	1.34108	−	7.60564i	0.0467187	−	0.264955i
$825$	0.00127373	−	24.0553i	4.43458e−5	−	0.837499i
$826$	−18.0008	+	15.1045i	−0.626327	+	0.525551i
$827$	0.686704	+	2.56281i	0.0238790	+	0.0891178i	0.976837	−	0.213985i	$-0.0686442\pi$
$827$	0.686704	+	2.56281i	0.0238790	+	0.0891178i	−0.952958	+	0.303102i	$0.901978\pi$
$828$	−0.102346	+	0.0359512i	−0.00355678	+	0.00124939i
$829$	13.2911	−	7.67359i	0.461617	−	0.266515i	−0.251107	−	0.967959i	$-0.580794\pi$
$829$	13.2911	−	7.67359i	0.461617	−	0.266515i	0.712724	+	0.701444i	$0.247461\pi$
$830$	−42.6960	+	12.5740i	−1.48200	+	0.436451i
$831$	−0.0289927	+	0.211034i	−0.00100575	+	0.00732068i
$832$	−0.176460	−	2.01695i	−0.00611766	−	0.0699251i
$833$	−29.1693	−	13.6019i	−1.01066	−	0.471277i
$834$	−19.8784	+	18.0103i	−0.688331	+	0.623647i
$835$	−35.9703	+	0.885231i	−1.24480	+	0.0306347i
$836$			4.57055i			0.158076i
$837$	4.66544	+	22.8654i	0.161261	+	0.790343i
$838$	−22.8981	+	22.8981i	−0.791002	+	0.791002i
$839$	−2.05282	−	11.6421i	−0.0708712	−	0.401931i	−0.999520	−	0.0309713i	$-0.990140\pi$
$839$	−2.05282	−	11.6421i	−0.0708712	−	0.401931i	0.928649	−	0.370960i	$-0.120971\pi$
$840$	−14.4438	−	7.17399i	−0.498358	−	0.247526i
$841$	−44.4266	+	16.1700i	−1.53195	+	0.557585i
$842$	26.8064	−	2.34525i	0.923808	−	0.0808227i
$843$	5.19964	+	41.2902i	0.179085	+	1.42211i
$844$	0.0336436	−	0.0924350i	0.00115806	−	0.00318174i
$845$	−11.5485	+	26.4458i	−0.397281	+	0.909762i
$846$	−9.53301	−	37.2504i	−0.327752	−	1.28070i
$847$	5.08850	−	1.36346i	0.174843	−	0.0468490i
$848$	3.05053	+	0.266887i	0.104756	+	0.00916493i
$849$	−1.04911	−	27.5924i	−0.0360054	−	0.946970i
$850$	25.0745	−	48.8306i	0.860048	−	1.67488i
$851$	0.273436	+	0.0482142i	0.00937327	+	0.00165276i
$852$	−3.45258	+	3.72550i	−0.118283	+	0.127634i
$853$	−2.93357	+	33.5308i	−0.100443	+	1.14807i	0.763956	+	0.645268i	$0.223254\pi$
$853$	−2.93357	+	33.5308i	−0.100443	+	1.14807i	−0.864400	+	0.502805i	$0.832301\pi$
$854$	−3.22284	+	5.58211i	−0.110283	+	0.191016i
$855$	30.4305	+	24.8498i	1.04070	+	0.849846i
$856$	−14.3341	−	24.8274i	−0.489929	−	0.848583i
$857$	33.6303	−	15.6821i	1.14879	−	0.535689i	0.247491	−	0.968890i	$-0.420394\pi$
$857$	33.6303	−	15.6821i	1.14879	−	0.535689i	0.901297	+	0.433201i	$0.142616\pi$
$858$	2.21736	−	0.279230i	0.0756993	−	0.00953276i
$859$	18.6876	−	22.2710i	0.637613	−	0.759878i	−0.346378	−	0.938095i	$-0.612588\pi$
$859$	18.6876	−	22.2710i	0.637613	−	0.759878i	0.983991	+	0.178217i	$0.0570329\pi$
$860$	3.03210	−	0.611915i	0.103394	−	0.0208661i
$861$	3.99262	−	12.4187i	0.136068	−	0.423230i
$862$	−11.8627	+	16.9417i	−0.404046	+	0.577038i
$863$	9.57951	+	9.57951i	0.326090	+	0.326090i	0.851098	−	0.525007i	$-0.175937\pi$
$863$	9.57951	+	9.57951i	0.326090	+	0.326090i	−0.525007	+	0.851098i	$0.675937\pi$
$864$	−0.495978	+	8.18489i	−0.0168735	+	0.278455i
$865$	5.86505	+	0.885983i	0.199418	+	0.0301243i
$866$	48.0287	−	8.46876i	1.63208	−	0.287780i
$867$	−62.0020	−	3.05688i	−2.10570	−	0.103817i
$868$	−0.855281	+	1.83416i	−0.0290301	+	0.0622553i
$869$	−4.41177	−	3.70191i	−0.149659	−	0.125579i
$870$	44.8582	−	24.4445i	1.52084	−	0.828746i
$871$	−0.312045	−	0.113575i	−0.0105733	−	0.00384835i
$872$	−1.16451	−	0.312030i	−0.0394353	−	0.0105667i
$873$	−11.7832	−	33.5446i	−0.398801	−	1.13531i
$874$	−0.985869	−	0.569192i	−0.0333475	−	0.0192532i
$875$	−4.40770	−	17.3817i	−0.149008	−	0.587609i
$876$	1.56378	−	2.96315i	0.0528353	−	0.100115i
$877$	−18.1337	+	12.6973i	−0.612331	+	0.428759i	−0.838172	−	0.545405i	$-0.816376\pi$
$877$	−18.1337	+	12.6973i	−0.612331	+	0.428759i	0.225842	+	0.974164i	$0.427487\pi$
$878$	13.9339	−	9.75663i	0.470247	−	0.329270i
$879$	−4.86133	−	7.72641i	−0.163969	−	0.260605i
$880$	27.0644	+	6.54269i	0.912341	+	0.220554i
$881$	38.5171	+	22.2379i	1.29768	+	0.749213i	0.980002	−	0.198987i	$-0.0637651\pi$
$881$	38.5171	+	22.2379i	1.29768	+	0.749213i	0.317673	+	0.948200i	$0.397098\pi$
$882$	12.7210	+	15.5116i	0.428337	+	0.522304i
$883$	−15.2412	−	4.08387i	−0.512907	−	0.137433i	−0.00692327	−	0.999976i	$-0.502204\pi$
$883$	−15.2412	−	4.08387i	−0.512907	−	0.137433i	−0.505984	+	0.862543i	$0.668870\pi$
$884$	0.590280	+	0.214844i	0.0198533	+	0.00722599i
$885$	−8.82641	−	36.5197i	−0.296696	−	1.22760i
$886$	7.81768	+	6.55981i	0.262640	+	0.220381i
$887$	−11.6632	+	25.0117i	−0.391610	+	0.839811i	0.607359	+	0.794427i	$0.292229\pi$
$887$	−11.6632	+	25.0117i	−0.391610	+	0.839811i	−0.998970	+	0.0453839i	$0.985549\pi$
$888$	5.25850	−	8.15255i	0.176464	−	0.273582i
$889$	21.2504	−	3.74702i	0.712715	−	0.125671i
$890$	−5.63122	+	37.2777i	−0.188759	+	1.24955i
$891$	24.9927	+	0.562915i	0.837287	+	0.0188584i
$892$	−3.12148	−	3.12148i	−0.104515	−	0.104515i
$893$	28.5082	−	40.7139i	0.953990	−	1.36244i
$894$	−3.09313	+	0.667484i	−0.103450	+	0.0223240i
$895$	8.48870	−	12.7812i	0.283746	−	0.427230i
$896$	13.5031	−	16.0924i	0.451108	−	0.537609i
$897$	−0.0265943	+	0.0631956i	−0.000887957	+	0.00211004i
$898$	−15.6093	+	7.27874i	−0.520890	+	0.242895i
$899$	19.6120	+	33.9690i	0.654098	+	1.13293i
$900$	−3.35797	+	2.54648i	−0.111932	+	0.0848826i
$901$	2.48266	−	4.30010i	0.0827095	−	0.143257i
$902$	−1.71688	+	19.6241i	−0.0571660	+	0.653410i
$903$	−13.3368	−	3.03558i	−0.443822	−	0.101018i
$904$	1.22439	+	0.215893i	0.0407226	+	0.00718049i
$905$	−19.9153	−	40.1020i	−0.662007	−	1.33303i
$906$	−37.4057	−	19.7406i	−1.24272	−	0.655838i
$907$	−3.71818	−	0.325298i	−0.123460	−	0.0108014i	0.0252582	−	0.999681i	$-0.491959\pi$
$907$	−3.71818	−	0.325298i	−0.123460	−	0.0108014i	−0.148718	+	0.988880i	$0.547515\pi$
$908$	−6.39013	+	1.71223i	−0.212064	+	0.0568223i
$909$	−40.3316	+	3.07139i	−1.33771	+	0.101871i
$910$	1.55100	−	0.608136i	0.0514152	−	0.0201595i
$911$	−8.20345	+	22.5388i	−0.271792	+	0.746743i	0.726435	+	0.687235i	$0.241176\pi$
$911$	−8.20345	+	22.5388i	−0.271792	+	0.746743i	−0.998228	+	0.0595086i	$0.981047\pi$
$912$	−36.2335	+	27.4802i	−1.19981	+	0.909961i
$913$	−36.4695	+	3.19067i	−1.20697	+	0.105596i
$914$	−10.5269	+	3.83148i	−0.348199	+	0.126734i
$915$	−5.70127	−	8.58526i	−0.188478	−	0.283820i
$916$	−1.12953	−	6.40589i	−0.0373207	−	0.211656i
$917$	7.01316	−	7.01316i	0.231595	−	0.231595i
$918$	50.1481	+	27.1916i	1.65513	+	0.897456i
$919$			55.8452i			1.84216i	0.389370	+	0.921081i	$0.372693\pi$
$919$			55.8452i			1.84216i	−0.389370	+	0.921081i	$0.627307\pi$
$920$	−0.515159	+	0.541155i	−0.0169843	+	0.0178414i
$921$	−36.4951	−	11.7332i	−1.20255	−	0.386620i
$922$	−57.0495	−	26.6026i	−1.87882	−	0.876110i
$923$	0.279807	+	3.19821i	0.00920995	+	0.105270i
$924$	1.71249	+	1.32942i	0.0563367	+	0.0437348i
$925$	10.6866	−	1.46759i	0.351372	−	0.0482540i
$926$	4.35356	−	2.51353i	0.143067	−	0.0825997i
$927$	4.37471	+	7.77817i	0.143684	+	0.255469i
$928$	3.56716	+	13.3128i	0.117098	+	0.437014i
$929$	43.9037	−	36.8395i	1.44043	−	1.20867i	0.501224	−	0.865317i	$-0.332883\pi$
$929$	43.9037	−	36.8395i	1.44043	−	1.20867i	0.939208	−	0.343349i	$-0.111561\pi$
$930$	−16.3846	−	20.5341i	−0.537273	−	0.673339i
$931$	−4.50286	+	25.5370i	−0.147575	+	0.836942i
$932$	−3.48567	−	4.97805i	−0.114177	−	0.163062i
$933$	18.2805	+	16.9413i	0.598478	+	0.554635i
$934$	−4.34306	−	5.17586i	−0.142109	−	0.169359i
$935$	28.1615	−	35.2897i	0.920981	−	1.15410i
$936$	1.67478	+	1.71293i	0.0547420	+	0.0559889i
$937$	−14.6753	+	54.7688i	−0.479420	+	1.78922i	0.124551	+	0.992213i	$0.460251\pi$
$937$	−14.6753	+	54.7688i	−0.479420	+	1.78922i	−0.603971	+	0.797006i	$0.706416\pi$
$938$	−1.10524	−	2.37019i	−0.0360873	−	0.0773895i
$939$	−22.5749	+	29.0798i	−0.736705	+	0.948982i
$940$	3.52646	+	3.99861i	0.115020	+	0.130420i
$941$	13.7044	+	37.6526i	0.446751	+	1.22744i	0.934973	+	0.354719i	$0.115423\pi$
$941$	13.7044	+	37.6526i	0.446751	+	1.22744i	−0.488222	+	0.872719i	$0.662354\pi$
$942$	48.2799	−	24.7885i	1.57304	−	0.807651i
$943$	−0.495050	−	0.346638i	−0.0161211	−	0.0112881i
$944$	43.4886			1.41543
$945$	18.1619	−	4.17367i	0.590808	−	0.135770i
$946$	20.6552			0.671557
$947$	38.0843	+	26.6669i	1.23757	+	0.866557i	0.994631	−	0.103484i	$-0.0329990\pi$
$947$	38.0843	+	26.6669i	1.23757	+	0.866557i	0.242941	+	0.970041i	$0.421888\pi$
$948$	−0.0496845	+	1.00774i	−0.00161368	+	0.0327298i
$949$	−0.724290	−	1.98997i	−0.0235114	−	0.0645972i
$950$	−43.2306	−	9.33135i	−1.40258	−	0.302749i
$951$	39.4470	+	5.41939i	1.27916	+	0.175736i
$952$	−12.7922	−	27.4331i	−0.414599	−	0.889110i
$953$	14.9234	−	55.6950i	0.483417	−	1.80414i	−0.103668	−	0.994612i	$-0.533058\pi$
$953$	14.9234	−	55.6950i	0.483417	−	1.80414i	0.587085	−	0.809526i	$-0.300276\pi$
$954$	−2.55501	+	1.74650i	−0.0827214	+	0.0565449i
$955$	−20.8167	+	2.33856i	−0.673614	+	0.0756742i
$956$	−2.56752	−	3.05985i	−0.0830396	−	0.0989627i
$957$	40.1442	−	12.4094i	1.29768	−	0.401139i
$958$	−31.8330	−	45.4622i	−1.02848	−	1.46882i
$959$	2.05655	−	11.6633i	0.0664095	−	0.376627i
$960$	10.2014	+	23.3644i	0.329249	+	0.754081i
$961$	−8.29622	+	6.96135i	−0.267620	+	0.224560i
$962$	0.259378	+	0.968010i	0.00836267	+	0.0312099i
$963$	30.9992	+	11.6797i	0.998936	+	0.376374i
$964$	2.02929	−	1.17161i	0.0653589	−	0.0377350i
$965$	−22.5524	+	41.3809i	−0.725989	+	1.33210i
$966$	−0.500021	+	0.203825i	−0.0160879	+	0.00655796i
$967$	2.27121	+	25.9600i	0.0730371	+	0.834818i	0.941048	+	0.338273i	$0.109843\pi$
$967$	2.27121	+	25.9600i	0.0730371	+	0.834818i	−0.868011	+	0.496545i	$0.834602\pi$
$968$	−7.72854	−	3.60388i	−0.248405	−	0.115833i
$969$	15.5544	+	72.0794i	0.499679	+	2.31552i
$970$	28.9882	+	27.5957i	0.930757	+	0.886045i
$971$			24.3222i			0.780536i	0.920701	+	0.390268i	$0.127618\pi$
$971$			24.3222i			0.780536i	−0.920701	+	0.390268i	$0.872382\pi$
$972$	−2.56731	−	3.54828i	−0.0823466	−	0.113811i
$973$	−11.6294	+	11.6294i	−0.372822	+	0.372822i
$974$	3.35887	+	19.0491i	0.107625	+	0.610372i
$975$	−0.232296	+	2.65354i	−0.00743943	+	0.0849812i
$976$	11.2096	−	4.07998i	0.358812	−	0.130597i
$977$	−4.39652	+	0.384646i	−0.140657	+	0.0123059i	−0.157267	−	0.987556i	$-0.550268\pi$
$977$	−4.39652	+	0.384646i	−0.140657	+	0.0123059i	0.0166097	+	0.999862i	$0.494713\pi$
$978$	31.5208	+	13.2647i	1.00792	+	0.424159i
$979$	−10.6057	+	29.1388i	−0.338958	+	0.931280i
$980$	−2.54911	−	1.11316i	−0.0814284	−	0.0355587i
$981$	1.26911	−	0.574487i	0.0405194	−	0.0183420i
$982$	33.5090	−	8.97872i	1.06932	−	0.286522i
$983$	6.29396	+	0.550651i	0.200746	+	0.0175630i	0.187085	−	0.982344i	$-0.440096\pi$
$983$	6.29396	+	0.550651i	0.200746	+	0.0175630i	0.0136609	+	0.999907i	$0.495651\pi$
$984$	−17.8727	+	11.2452i	−0.569760	+	0.358484i
$985$	−15.5742	−	5.23833i	−0.496235	−	0.166907i
$986$	94.4260	+	16.6499i	3.00714	+	0.530240i
$987$	−6.96254	−	22.5237i	−0.221620	−	0.716938i
$988$	0.0441099	−	0.504179i	0.00140332	−	0.0160401i
$989$	−0.316839	+	0.548781i	−0.0100749	+	0.0174502i
$990$	−25.3438	+	12.2324i	−0.805478	+	0.388770i
$991$	3.28793	+	5.69486i	0.104445	+	0.180903i	0.913511	−	0.406814i	$-0.133360\pi$
$991$	3.28793	+	5.69486i	0.104445	+	0.180903i	−0.809067	+	0.587717i	$0.800027\pi$
$992$	6.42327	−	2.99522i	0.203939	−	0.0950983i
$993$	14.6059	+	19.2583i	0.463505	+	0.611144i
$994$	−16.2520	+	19.3683i	−0.515481	+	0.614326i
$995$	−48.0602	−	31.9193i	−1.52361	−	1.01191i
$996$	4.30628	+	4.75293i	0.136450	+	0.150602i
$997$	11.4987	−	16.4219i	0.364168	−	0.520086i	−0.594696	−	0.803951i	$-0.702728\pi$
$997$	11.4987	−	16.4219i	0.364168	−	0.520086i	0.958864	+	0.283864i	$0.0916165\pi$
$998$	−9.88969	−	9.88969i	−0.313053	−	0.313053i
$999$	1.27529	+	11.1373i	0.0403484	+	0.352367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.13	yes	192
3.2	odd	2		405.2.r.a.152.4		192
5.2	odd	4		675.2.ba.b.68.4		192
5.3	odd	4	inner	135.2.q.a.68.13	yes	192
5.4	even	2		675.2.ba.b.257.4		192
15.8	even	4		405.2.r.a.233.4		192
27.2	odd	18	inner	135.2.q.a.2.13	✓	192
27.25	even	9		405.2.r.a.332.4		192
135.2	even	36		675.2.ba.b.218.4		192
135.29	odd	18		675.2.ba.b.407.4		192
135.83	even	36	inner	135.2.q.a.83.13	yes	192
135.133	odd	36		405.2.r.a.8.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.13	✓	192	27.2	odd	18	inner
135.2.q.a.68.13	yes	192	5.3	odd	4	inner
135.2.q.a.83.13	yes	192	135.83	even	36	inner
135.2.q.a.122.13	yes	192	1.1	even	1	trivial
405.2.r.a.8.4		192	135.133	odd	36
405.2.r.a.152.4		192	3.2	odd	2
405.2.r.a.233.4		192	15.8	even	4
405.2.r.a.332.4		192	27.25	even	9
675.2.ba.b.68.4		192	5.2	odd	4
675.2.ba.b.218.4		192	135.2	even	36
675.2.ba.b.257.4		192	5.4	even	2
675.2.ba.b.407.4		192	135.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23715 + 0.866263i) q^{2} +(1.45553 + 0.938839i) q^{3} +(0.0960923 + 0.264011i) q^{4} +(-2.23168 - 0.140023i) q^{5} +(0.987435 + 2.42236i) q^{6} +(0.677826 + 1.45360i) q^{7} +(0.671958 - 2.50778i) q^{8} +(1.23716 + 2.73303i) q^{9} +O(q^{10})\)	\(q+(1.23715 + 0.866263i) q^{2} +(1.45553 + 0.938839i) q^{3} +(0.0960923 + 0.264011i) q^{4} +(-2.23168 - 0.140023i) q^{5} +(0.987435 + 2.42236i) q^{6} +(0.677826 + 1.45360i) q^{7} +(0.671958 - 2.50778i) q^{8} +(1.23716 + 2.73303i) q^{9} +(-2.63963 - 2.10645i) q^{10} +(-1.78545 - 2.12782i) q^{11} +(-0.107999 + 0.474493i) q^{12} +(0.176418 + 0.251952i) q^{13} +(-0.420628 + 2.38550i) q^{14} +(-3.11683 - 2.29900i) q^{15} +(3.43416 - 2.88160i) q^{16} +(-1.88139 - 7.02145i) q^{17} +(-0.836964 + 4.45287i) q^{18} +(-5.07203 + 2.92834i) q^{19} +(-0.177479 - 0.602644i) q^{20} +(-0.378100 + 2.75214i) q^{21} +(-0.365624 - 4.17910i) q^{22} +(0.116642 + 0.0543910i) q^{23} +(3.33246 - 3.01930i) q^{24} +(4.96079 + 0.624975i) q^{25} +0.464527i q^{26} +(-0.765143 + 5.13951i) q^{27} +(-0.318634 + 0.318634i) q^{28} +(1.51659 + 8.60103i) q^{29} +(-1.86445 - 5.54420i) q^{30} +(4.22026 - 1.53605i) q^{31} +(1.57207 - 0.137538i) q^{32} +(-0.601106 - 4.77337i) q^{33} +(3.75485 - 10.3164i) q^{34} +(-1.30915 - 3.33889i) q^{35} +(-0.602668 + 0.589247i) q^{36} +(2.08386 - 0.558369i) q^{37} +(-8.81158 - 0.770913i) q^{38} +(0.0202409 + 0.532353i) q^{39} +(-1.85074 + 5.50247i) q^{40} +(-4.62442 - 0.815410i) q^{41} +(-2.85184 + 3.07728i) q^{42} +(-0.429127 + 4.90494i) q^{43} +(0.390200 - 0.675847i) q^{44} +(-2.37826 - 6.27247i) q^{45} +(0.0971868 + 0.168333i) q^{46} +(-7.69135 + 3.58654i) q^{47} +(7.70389 - 0.970146i) q^{48} +(2.84600 - 3.39173i) q^{49} +(5.59585 + 5.07053i) q^{50} +(3.85358 - 11.9863i) q^{51} +(-0.0495656 + 0.0707870i) q^{52} +(0.483003 + 0.483003i) q^{53} +(-5.39876 + 5.69554i) q^{54} +(3.68661 + 4.99861i) q^{55} +(4.10079 - 0.723079i) q^{56} +(-10.1318 - 0.499526i) q^{57} +(-5.57450 + 11.9546i) q^{58} +(7.43127 + 6.23558i) q^{59} +(0.307459 - 1.04379i) q^{60} +(2.50049 + 0.910105i) q^{61} +(6.55173 + 1.75553i) q^{62} +(-3.13415 + 3.65086i) q^{63} +(-5.70071 - 3.29131i) q^{64} +(-0.358430 - 0.586978i) q^{65} +(3.39133 - 6.42609i) q^{66} +(-0.884390 + 0.619257i) q^{67} +(1.67295 - 1.17142i) q^{68} +(0.118712 + 0.188676i) q^{69} +(1.27273 - 5.26478i) q^{70} +(9.03942 + 5.21891i) q^{71} +(7.68515 - 1.26605i) q^{72} +(-6.65047 - 1.78199i) q^{73} +(3.06175 + 1.11439i) q^{74} +(6.63384 + 5.56706i) q^{75} +(-1.26050 - 1.05768i) q^{76} +(1.88278 - 4.03763i) q^{77} +(-0.436116 + 0.676135i) q^{78} +(2.04188 - 0.360038i) q^{79} +(-8.06743 + 5.94995i) q^{80} +(-5.93887 + 6.76239i) q^{81} +(-5.01475 - 5.01475i) q^{82} +(7.55956 - 10.7962i) q^{83} +(-0.762929 + 0.164636i) q^{84} +(3.21549 + 15.9331i) q^{85} +(-4.77986 + 5.69642i) q^{86} +(-5.86754 + 13.9429i) q^{87} +(-6.53585 + 3.04772i) q^{88} +(-5.58181 - 9.66798i) q^{89} +(2.49134 - 9.82019i) q^{90} +(-0.246656 + 0.427222i) q^{91} +(-0.00315146 + 0.0360214i) q^{92} +(7.58484 + 1.72638i) q^{93} +(-12.6222 - 2.22564i) q^{94} +(11.7292 - 5.82491i) q^{95} +(2.41732 + 1.27573i) q^{96} +(-11.8062 - 1.03291i) q^{97} +(6.45906 - 1.73070i) q^{98} +(3.60649 - 7.51214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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