LMFDB - Embedded newform 135.2.q.a.2.13

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			2.13
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866263 + 1.23715i) q^{2} +(-0.938839 - 1.45553i) q^{3} +(-0.0960923 + 0.264011i) q^{4} +(0.525423 - 2.17346i) q^{5} +(0.987435 - 2.42236i) q^{6} +(1.45360 + 0.677826i) q^{7} +(2.50778 - 0.671958i) q^{8} +(-1.23716 + 2.73303i) q^{9} +O(q^{10})$	\(q+(0.866263 + 1.23715i) q^{2} +(-0.938839 - 1.45553i) q^{3} +(-0.0960923 + 0.264011i) q^{4} +(0.525423 - 2.17346i) q^{5} +(0.987435 - 2.42236i) q^{6} +(1.45360 + 0.677826i) q^{7} +(2.50778 - 0.671958i) q^{8} +(-1.23716 + 2.73303i) q^{9} +(3.14405 - 1.23276i) q^{10} +(-1.78545 + 2.12782i) q^{11} +(0.474493 - 0.107999i) q^{12} +(-0.251952 - 0.176418i) q^{13} +(0.420628 + 2.38550i) q^{14} +(-3.65683 + 1.27576i) q^{15} +(3.43416 + 2.88160i) q^{16} +(-7.02145 - 1.88139i) q^{17} +(-4.45287 + 0.836964i) q^{18} +(5.07203 + 2.92834i) q^{19} +(0.523329 + 0.347571i) q^{20} +(-0.378100 - 2.75214i) q^{21} +(-4.17910 - 0.365624i) q^{22} +(-0.0543910 - 0.116642i) q^{23} +(-3.33246 - 3.01930i) q^{24} +(-4.44786 - 2.28397i) q^{25} -0.464527i q^{26} +(5.13951 - 0.765143i) q^{27} +(-0.318634 + 0.318634i) q^{28} +(-1.51659 + 8.60103i) q^{29} +(-4.74609 - 3.41892i) q^{30} +(4.22026 + 1.53605i) q^{31} +(-0.137538 + 1.57207i) q^{32} +(4.77337 + 0.601106i) q^{33} +(-3.75485 - 10.3164i) q^{34} +(2.23699 - 2.80320i) q^{35} +(-0.602668 - 0.589247i) q^{36} +(-0.558369 + 2.08386i) q^{37} +(0.770913 + 8.81158i) q^{38} +(-0.0202409 + 0.532353i) q^{39} +(-0.142827 - 5.80362i) q^{40} +(-4.62442 + 0.815410i) q^{41} +(3.07728 - 2.85184i) q^{42} +(-4.90494 + 0.429127i) q^{43} +(-0.390200 - 0.675847i) q^{44} +(5.29009 + 4.12492i) q^{45} +(0.0971868 - 0.168333i) q^{46} +(3.58654 - 7.69135i) q^{47} +(0.970146 - 7.70389i) q^{48} +(-2.84600 - 3.39173i) q^{49} +(-1.02740 - 7.48120i) q^{50} +(3.85358 + 11.9863i) q^{51} +(0.0707870 - 0.0495656i) 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} +(-0.499526 - 10.1318i) q^{57} +(-11.9546 + 5.57450i) q^{58} +(-7.43127 + 6.23558i) q^{59} +(0.0145787 - 1.08804i) q^{60} +(2.50049 - 0.910105i) q^{61} +(1.75553 + 6.55173i) q^{62} +(-3.65086 + 3.13415i) q^{63} +(5.70071 - 3.29131i) q^{64} +(-0.515819 + 0.454912i) q^{65} +(3.39133 + 6.42609i) q^{66} +(0.619257 - 0.884390i) q^{67} +(1.17142 - 1.67295i) q^{68} +(-0.118712 + 0.188676i) q^{69} +(5.40580 + 0.339179i) q^{70} +(9.03942 - 5.21891i) q^{71} +(-1.26605 + 7.68515i) q^{72} +(1.78199 + 6.65047i) q^{73} +(-3.06175 + 1.11439i) q^{74} +(0.851425 + 8.61830i) q^{75} +(-1.26050 + 1.05768i) q^{76} +(-4.03763 + 1.88278i) q^{77} +(-0.676135 + 0.436116i) 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} +(10.7962 - 7.55956i) q^{83} +(0.762929 + 0.164636i) q^{84} +(-7.77836 + 14.2723i) q^{85} +(-4.77986 - 5.69642i) q^{86} +(13.9429 - 5.86754i) q^{87} +(-3.04772 + 6.53585i) q^{88} +(5.58181 - 9.66798i) q^{89} +(-0.520536 + 10.1179i) q^{90} +(-0.246656 - 0.427222i) q^{91} +(0.0360214 - 0.00315146i) q^{92} +(-1.72638 - 7.58484i) q^{93} +(12.6222 - 2.22564i) q^{94} +(9.02959 - 9.48524i) q^{95} +(2.41732 - 1.27573i) q^{96} +(-1.03291 - 11.8062i) q^{97} +(1.73070 - 6.45906i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.866263	+	1.23715i	0.612540	+	0.874798i	0.998868	−	0.0475633i	$-0.0151456\pi$
$2$	0.866263	+	1.23715i	0.612540	+	0.874798i	−0.386328	+	0.922361i	$0.626257\pi$
$3$	−0.938839	−	1.45553i	−0.542039	−	0.840353i
$3$	−0.938839	−	1.45553i	−0.542039	−	0.840353i
$4$	−0.0960923	+	0.264011i	−0.0480461	+	0.132006i
$5$	0.525423	−	2.17346i	0.234976	−	0.972001i
$5$	0.525423	−	2.17346i	0.234976	−	0.972001i
$6$	0.987435	−	2.42236i	0.403119	−	0.988925i
$7$	1.45360	+	0.677826i	0.549410	+	0.256194i	0.677442	−	0.735576i	$-0.263088\pi$
$7$	1.45360	+	0.677826i	0.549410	+	0.256194i	−0.128032	+	0.991770i	$0.540866\pi$
$8$	2.50778	−	0.671958i	0.886634	−	0.237573i
$9$	−1.23716	+	2.73303i	−0.412387	+	0.911009i
$10$	3.14405	−	1.23276i	0.994237	−	0.389833i
$11$	−1.78545	+	2.12782i	−0.538334	+	0.641561i	−0.964813	−	0.262936i	$-0.915309\pi$
$11$	−1.78545	+	2.12782i	−0.538334	+	0.641561i	0.426479	+	0.904497i	$0.359754\pi$
$12$	0.474493	−	0.107999i	0.136974	−	0.0311765i
$13$	−0.251952	−	0.176418i	−0.0698788	−	0.0489296i	0.538115	−	0.842871i	$-0.319137\pi$
$13$	−0.251952	−	0.176418i	−0.0698788	−	0.0489296i	−0.607994	+	0.793942i	$0.708025\pi$
$14$	0.420628	+	2.38550i	0.112418	+	0.637552i
$15$	−3.65683	+	1.27576i	−0.944191	+	0.329400i
$16$	3.43416	+	2.88160i	0.858539	+	0.720400i
$17$	−7.02145	−	1.88139i	−1.70295	−	0.456304i	−0.729271	−	0.684225i	$-0.760141\pi$
$17$	−7.02145	−	1.88139i	−1.70295	−	0.456304i	−0.973680	+	0.227921i	$0.926807\pi$
$18$	−4.45287	+	0.836964i	−1.04955	+	0.197274i
$19$	5.07203	+	2.92834i	1.16360	+	0.671807i	0.952165	−	0.305584i	$-0.0988518\pi$
$19$	5.07203	+	2.92834i	1.16360	+	0.671807i	0.211439	+	0.977391i	$0.432185\pi$
$20$	0.523329	+	0.347571i	0.117020	+	0.0777191i
$21$	−0.378100	−	2.75214i	−0.0825083	−	0.600566i
$22$	−4.17910	−	0.365624i	−0.890988	−	0.0779514i
$23$	−0.0543910	−	0.116642i	−0.0113413	−	0.0243215i	0.900556	−	0.434741i	$-0.143160\pi$
$23$	−0.0543910	−	0.116642i	−0.0113413	−	0.0243215i	−0.911897	+	0.410419i	$0.865382\pi$
$24$	−3.33246	−	3.01930i	−0.680236	−	0.616312i
$25$	−4.44786	−	2.28397i	−0.889572	−	0.456795i
$26$		−	0.464527i		−	0.0911012i
$27$	5.13951	−	0.765143i	0.989099	−	0.147252i
$28$	−0.318634	+	0.318634i	−0.0602161	+	0.0602161i
$29$	−1.51659	+	8.60103i	−0.281625	+	1.59717i	0.435475	+	0.900201i	$0.356581\pi$
$29$	−1.51659	+	8.60103i	−0.281625	+	1.59717i	−0.717099	+	0.696971i	$0.754531\pi$
$30$	−4.74609	−	3.41892i	−0.866513	−	0.624206i
$31$	4.22026	+	1.53605i	0.757981	+	0.275883i	0.691960	−	0.721936i	$-0.256747\pi$
$31$	4.22026	+	1.53605i	0.757981	+	0.275883i	0.0660211	+	0.997818i	$0.478970\pi$
$32$	−0.137538	+	1.57207i	−0.0243135	+	0.277905i
$33$	4.77337	+	0.601106i	0.830936	+	0.104639i
$34$	−3.75485	−	10.3164i	−0.643952	−	1.76924i
$35$	2.23699	−	2.80320i	0.378119	−	0.473828i
$36$	−0.602668	−	0.589247i	−0.100445	−	0.0982079i
$37$	−0.558369	+	2.08386i	−0.0917953	+	0.342585i	−0.996514	−	0.0834245i	$-0.973414\pi$
$37$	−0.558369	+	2.08386i	−0.0917953	+	0.342585i	0.904719	+	0.426009i	$0.140081\pi$
$38$	0.770913	+	8.81158i	0.125059	+	1.42943i
$39$	−0.0202409	+	0.532353i	−0.00324114	+	0.0852446i
$40$	−0.142827	−	5.80362i	−0.0225830	−	0.917633i
$41$	−4.62442	+	0.815410i	−0.722213	+	0.127346i	−0.522660	−	0.852541i	$-0.675060\pi$
$41$	−4.62442	+	0.815410i	−0.722213	+	0.127346i	−0.199553	+	0.979887i	$0.563949\pi$
$42$	3.07728	−	2.85184i	0.474834	−	0.440049i
$43$	−4.90494	+	0.429127i	−0.747997	+	0.0654412i	−0.454779	−	0.890604i	$-0.650282\pi$
$43$	−4.90494	+	0.429127i	−0.747997	+	0.0654412i	−0.293218	+	0.956046i	$0.594726\pi$
$44$	−0.390200	−	0.675847i	−0.0588249	−	0.101888i
$45$	5.29009	+	4.12492i	0.788600	+	0.614906i
$46$	0.0971868	−	0.168333i	0.0143294	−	0.0248193i
$47$	3.58654	−	7.69135i	0.523150	−	1.12190i	−0.450274	−	0.892890i	$-0.648674\pi$
$47$	3.58654	−	7.69135i	0.523150	−	1.12190i	0.973424	−	0.229009i	$-0.0735484\pi$
$48$	0.970146	−	7.70389i	0.140028	−	1.11196i
$49$	−2.84600	−	3.39173i	−0.406571	−	0.484533i
$50$	−1.02740	−	7.48120i	−0.145296	−	1.05800i
$51$	3.85358	+	11.9863i	0.539609	+	1.67841i
$52$	0.0707870	−	0.0495656i	0.00981640	−	0.00687352i
$53$	−0.483003	−	0.483003i	−0.0663456	−	0.0663456i	0.673155	−	0.739501i	$-0.264938\pi$
$53$	−0.483003	−	0.483003i	−0.0663456	−	0.0663456i	−0.739501	+	0.673155i	$0.764938\pi$
$54$	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
$57$	−0.499526	−	10.1318i	−0.0661638	−	1.34198i
$58$	−11.9546	+	5.57450i	−1.56971	+	0.731968i
$59$	−7.43127	+	6.23558i	−0.967469	+	0.811803i	−0.982152	−	0.188089i	$-0.939771\pi$
$59$	−7.43127	+	6.23558i	−0.967469	+	0.811803i	0.0146830	+	0.999892i	$0.495326\pi$
$60$	0.0145787	−	1.08804i	0.00188211	−	0.140465i
$61$	2.50049	−	0.910105i	0.320155	−	0.116527i	−0.176943	−	0.984221i	$-0.556621\pi$
$61$	2.50049	−	0.910105i	0.320155	−	0.116527i	0.497099	+	0.867694i	$0.334399\pi$
$62$	1.75553	+	6.55173i	0.222952	+	0.832070i
$63$	−3.65086	+	3.13415i	−0.459965	+	0.394866i
$64$	5.70071	−	3.29131i	0.712589	−	0.411413i
$65$	−0.515819	+	0.454912i	−0.0639795	+	0.0564249i
$66$	3.39133	+	6.42609i	0.417444	+	0.790997i
$67$	0.619257	−	0.884390i	0.0756543	−	0.108045i	−0.779542	−	0.626350i	$-0.784548\pi$
$67$	0.619257	−	0.884390i	0.0756543	−	0.108045i	0.855196	+	0.518305i	$0.173437\pi$
$68$	1.17142	−	1.67295i	0.142055	−	0.202876i
$69$	−0.118712	+	0.188676i	−0.0142912	+	0.0227139i
$70$	5.40580	+	0.339179i	0.646117	+	0.0405397i
$71$	9.03942	−	5.21891i	1.07278	−	0.619371i	0.143842	−	0.989601i	$-0.454054\pi$
$71$	9.03942	−	5.21891i	1.07278	−	0.619371i	0.928940	+	0.370230i	$0.120721\pi$
$72$	−1.26605	+	7.68515i	−0.149205	+	0.905703i
$73$	1.78199	+	6.65047i	0.208566	+	0.778378i	0.988333	+	0.152309i	$0.0486707\pi$
$73$	1.78199	+	6.65047i	0.208566	+	0.778378i	−0.779767	+	0.626070i	$0.784663\pi$
$74$	−3.06175	+	1.11439i	−0.355921	+	0.129545i
$75$	0.851425	+	8.61830i	0.0983141	+	0.995155i
$76$	−1.26050	+	1.05768i	−0.144589	+	0.121325i
$77$	−4.03763	+	1.88278i	−0.460130	+	0.214562i
$78$	−0.676135	+	0.436116i	−0.0765572	+	0.0493804i
$79$	−2.04188	−	0.360038i	−0.229729	−	0.0405074i	0.0575985	−	0.998340i	$-0.481656\pi$
$79$	−2.04188	−	0.360038i	−0.229729	−	0.0405074i	−0.287327	+	0.957832i	$0.592767\pi$
$80$	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
$83$	10.7962	−	7.55956i	1.18503	−	0.829770i	0.196461	−	0.980512i	$-0.437055\pi$
$83$	10.7962	−	7.55956i	1.18503	−	0.829770i	0.988573	+	0.150742i	$0.0481662\pi$
$84$	0.762929	+	0.164636i	0.0832423	+	0.0179633i
$85$	−7.77836	+	14.2723i	−0.843681	+	1.54805i
$86$	−4.77986	−	5.69642i	−0.515426	−	0.614261i
$87$	13.9429	−	5.86754i	1.49484	−	0.629066i
$88$	−3.04772	+	6.53585i	−0.324888	+	0.696724i
$89$	5.58181	−	9.66798i	0.591671	−	1.02480i	−0.402337	−	0.915492i	$-0.631802\pi$
$89$	5.58181	−	9.66798i	0.591671	−	1.02480i	0.994007	−	0.109312i	$-0.0348648\pi$
$90$	−0.520536	+	10.1179i	−0.0548693	+	1.06652i
$91$	−0.246656	−	0.427222i	−0.0258566	−	0.0447850i
$92$	0.0360214	−	0.00315146i	0.00375549	−	0.000328562i
$93$	−1.72638	−	7.58484i	−0.179017	−	0.786511i
$94$	12.6222	−	2.22564i	1.30189	−	0.229558i
$95$	9.02959	−	9.48524i	0.926416	−	0.973165i
$96$	2.41732	−	1.27573i	0.246717	−	0.130203i
$97$	−1.03291	−	11.8062i	−0.104876	−	1.19874i	−0.848151	−	0.529754i	$-0.822284\pi$
$97$	−1.03291	−	11.8062i	−0.104876	−	1.19874i	0.743275	−	0.668986i	$-0.233271\pi$
$98$	1.73070	−	6.45906i	0.174827	−	0.652464i
$99$	−3.60649	−	7.51214i	−0.362466	−	0.754999i
$100$	1.03040	−	0.954814i	0.103040	−	0.0954814i
$101$	−4.61138	−	12.6697i	−0.458850	−	1.26068i	−0.926343	−	0.376682i	$-0.877065\pi$
$101$	−4.61138	−	12.6697i	−0.458850	−	1.26068i	0.467493	−	0.883997i	$-0.345157\pi$
$102$	−11.4906	+	15.1507i	−1.13774	+	1.50015i
$103$	0.259260	−	2.96335i	0.0255456	−	0.291988i	−0.972666	−	0.232209i	$-0.925405\pi$
$103$	0.259260	−	2.96335i	0.0255456	−	0.291988i	0.998212	−	0.0597791i	$-0.0190396\pi$
$104$	−0.750384	−	0.273118i	−0.0735813	−	0.0267814i
$105$	−6.18033	−	0.624251i	−0.603138	−	0.0609207i
$106$	0.179140	−	1.01596i	0.0173997	−	0.0986783i
$107$	−7.80800	+	7.80800i	−0.754828	+	0.754828i	−0.975376	−	0.220548i	$-0.929215\pi$
$107$	−7.80800	+	7.80800i	−0.754828	+	0.754828i	0.220548	+	0.975376i	$0.429215\pi$
$108$	−0.291861	+	1.43041i	−0.0280843	+	0.137642i
$109$		−	0.464359i		−	0.0444775i	−0.999753	−	0.0222388i	$-0.992921\pi$
$109$		−	0.464359i		−	0.0444775i	0.999753	−	0.0222388i	$-0.00707940\pi$
$110$	−2.99047	+	8.89101i	−0.285130	+	0.847725i
$111$	3.55735	−	1.14369i	0.337649	−	0.108554i
$112$	3.03868	+	6.51646i	0.287128	+	0.615748i
$113$	−0.477053	−	0.0417367i	−0.0448774	−	0.00392626i	0.0646950	−	0.997905i	$-0.479393\pi$
$113$	−0.477053	−	0.0417367i	−0.0448774	−	0.00392626i	−0.109572	+	0.993979i	$0.534948\pi$
$114$	12.1018	−	9.39475i	1.13344	−	0.879899i
$115$	−0.282095	+	0.0569304i	−0.0263055	+	0.00530878i
$116$	−2.12504	−	1.22689i	−0.197305	−	0.113914i
$117$	0.793861	−	0.470332i	0.0733924	−	0.0434822i
$118$	−14.1518	−	3.79196i	−1.30278	−	0.349078i
$119$	−8.93114	−	7.49411i	−0.818716	−	0.686984i
$120$	−8.31328	+	5.65656i	−0.758895	+	0.516371i
$121$	0.570356	+	3.23465i	0.0518506	+	0.294059i
$122$	3.29202	+	2.30510i	0.298046	+	0.208694i
$123$	5.52845	+	5.96547i	0.498483	+	0.537888i
$124$	−0.811069	+	0.966595i	−0.0728362	+	0.0868028i
$125$	−7.30114	+	8.46720i	−0.653033	+	0.757329i
$126$	−7.04003	−	1.80166i	−0.627175	−	0.160505i
$127$	−12.9954	+	3.48210i	−1.15315	+	0.308987i	−0.784228	−	0.620473i	$-0.786941\pi$
$127$	−12.9954	+	3.48210i	−1.15315	+	0.308987i	−0.368925	+	0.929459i	$0.620274\pi$
$128$	11.8706	+	5.53535i	1.04922	+	0.489260i
$129$	5.22956	+	6.73643i	0.460437	+	0.593110i
$130$	−1.00963	−	0.244073i	−0.0885505	−	0.0214066i
$131$	−2.11500	+	5.81092i	−0.184788	+	0.507702i	−0.997149	−	0.0754528i	$-0.975960\pi$
$131$	−2.11500	+	5.81092i	−0.184788	+	0.507702i	0.812361	+	0.583155i	$0.198182\pi$
$132$	−0.617383	+	1.20246i	−0.0537363	+	0.104661i
$133$	5.38781	+	7.69460i	0.467183	+	0.667206i
$134$	1.63056			0.140859
$135$	1.03741	−	11.5725i	0.0892860	−	0.996006i
$136$	−18.8725			−1.61830
$137$	−4.23537	−	6.04873i	−0.361852	−	0.516778i	0.596406	−	0.802683i	$-0.296595\pi$
$137$	−4.23537	−	6.04873i	−0.361852	−	0.516778i	−0.958258	+	0.285905i	$0.907706\pi$
$138$	−0.336257	+	0.0165784i	−0.0286241	+	0.00141125i
$139$	−3.50715	+	9.63582i	−0.297473	+	0.817299i	0.697448	+	0.716635i	$0.254319\pi$
$139$	−3.50715	+	9.63582i	−0.297473	+	0.817299i	−0.994921	+	0.100664i	$0.967903\pi$
$140$	0.525120	+	0.859956i	0.0443808	+	0.0726795i
$141$	−14.5622	+	2.00062i	−1.22636	+	0.168482i
$142$	14.2871	+	6.66218i	1.19895	+	0.559078i
$143$	0.825233	−	0.221121i	0.0690095	−	0.0184910i
$144$	−12.1241	+	5.82064i	−1.01034	+	0.485053i
$145$	17.8972	+	7.81544i	1.48628	+	0.649037i
$146$	−6.68396	+	7.96564i	−0.553169	+	0.659241i
$147$	−2.26484	+	7.32674i	−0.186801	+	0.604300i
$148$	−0.496508	−	0.347659i	−0.0408127	−	0.0285774i
$149$	0.210055	+	1.19128i	0.0172084	+	0.0975937i	0.992202	−	0.124638i	$-0.0397770\pi$
$149$	0.210055	+	1.19128i	0.0172084	+	0.0975937i	−0.974994	+	0.222232i	$0.928666\pi$
$150$	−9.92458	+	8.51905i	−0.810339	+	0.695578i
$151$	−12.3858	−	10.3930i	−1.00795	−	0.845766i	−0.0198800	−	0.999802i	$-0.506328\pi$
$151$	−12.3858	−	10.3930i	−1.00795	−	0.845766i	−0.988065	+	0.154036i	$0.950773\pi$
$152$	14.6873	+	3.93544i	1.19129	+	0.319206i
$153$	13.8285	−	16.8622i	1.11797	−	1.36323i
$154$	−5.82693	−	3.36418i	−0.469547	−	0.271093i
$155$	5.55597	−	8.36550i	0.446266	−	0.671933i
$156$	−0.138602	−	0.0564988i	−0.0110971	−	0.00452353i
$157$	−20.6680	−	1.80822i	−1.64949	−	0.144311i	−0.775858	−	0.630907i	$-0.782683\pi$
$157$	−20.6680	−	1.80822i	−1.64949	−	0.144311i	−0.873627	+	0.486596i	$0.838238\pi$
$158$	−1.32338	−	2.83800i	−0.105282	−	0.225779i
$159$	−0.249565	+	1.15649i	−0.0197918	+	0.0917156i
$160$	3.34456	+	1.12493i	0.264411	+	0.0889338i
$161$		−	0.206419i		−	0.0162681i
$162$	3.22148	−	13.2053i	0.253103	−	1.03750i
$163$	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
$165$	3.81452	−	10.0589i	0.296960	−	0.783083i
$166$	18.7046	+	6.80794i	1.45176	+	0.528398i
$167$	−1.40245	+	16.0301i	−0.108525	+	1.24044i	0.725307	+	0.688425i	$0.241698\pi$
$167$	−1.40245	+	16.0301i	−0.108525	+	1.24044i	−0.833832	+	0.552018i	$0.813858\pi$
$168$	−2.79751	−	6.64769i	−0.215833	−	0.512880i
$169$	−4.41391	−	12.1271i	−0.339531	−	0.932854i
$170$	−24.3951	+	2.74056i	−1.87102	+	0.210191i
$171$	−14.2781	+	10.2392i	−1.09188	+	0.783009i
$172$	0.358033	−	1.33620i	0.0272997	−	0.101884i
$173$	0.231197	+	2.64260i	0.0175776	+	0.200913i	0.999906	+	0.0137449i	$0.00437529\pi$
$173$	0.231197	+	2.64260i	0.0175776	+	0.200913i	−0.982328	+	0.187168i	$0.940069\pi$
$174$	19.3373	+	12.1667i	1.46596	+	0.922355i
$175$	−4.91729	−	6.33487i	−0.371712	−	0.478871i
$176$	−12.2630	+	2.16231i	−0.924362	+	0.162990i
$177$	16.0529	+	4.96226i	1.20661	+	0.372987i
$178$	16.7961	−	1.46947i	1.25892	−	0.110141i
$179$	3.43088	+	5.94245i	0.256436	+	0.444160i	0.965284	−	0.261201i	$-0.0841185\pi$
$179$	3.43088	+	5.94245i	0.256436	+	0.444160i	−0.708849	+	0.705360i	$0.750785\pi$
$180$	−1.59736	+	1.00027i	−0.119060	+	0.0745559i
$181$	10.0120	−	17.3412i	0.744183	−	1.28896i	−0.206392	−	0.978469i	$-0.566172\pi$
$181$	10.0120	−	17.3412i	0.744183	−	1.28896i	0.950575	−	0.310494i	$-0.100494\pi$
$182$	0.314868	−	0.675238i	0.0233396	−	0.0500519i
$183$	−3.67225	−	2.78511i	−0.271460	−	0.205881i
$184$	−0.214779	−	0.255964i	−0.0158337	−	0.0188699i
$185$	4.23581	+	2.30850i	0.311423	+	0.169725i
$186$	7.88810	−	8.70625i	0.578384	−	0.638373i
$187$	16.5397	−	11.5812i	1.20950	−	0.846903i
$188$	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	0.497147	−	0.867666i	$-0.334381\pi$
$191$	9.22577	+	1.62675i	0.667553	+	0.117708i	0.170406	+	0.985374i	$0.445492\pi$
$192$	−10.1427	−	5.20757i	−0.731984	−	0.375824i
$193$	19.1014	−	8.90711i	1.37495	−	0.641148i	0.412085	−	0.911146i	$-0.364801\pi$
$193$	19.1014	−	8.90711i	1.37495	−	0.641148i	0.962861	+	0.269998i	$0.0870230\pi$
$194$	13.7113	−	11.5052i	0.984414	−	0.826022i
$195$	1.14641	+	0.323703i	0.0820963	+	0.0231809i
$196$	1.16893	−	0.425457i	0.0834953	−	0.0303898i
$197$	1.90191	+	7.09801i	0.135505	+	0.505712i	0.999995	+	0.00306257i	$0.000974847\pi$
$197$	1.90191	+	7.09801i	0.135505	+	0.505712i	−0.864490	+	0.502650i	$0.832358\pi$
$198$	6.16948	−	10.9693i	0.438446	−	0.779552i
$199$	−22.3449	+	12.9008i	−1.58399	+	0.914516i	−0.589718	+	0.807609i	$0.700761\pi$
$199$	−22.3449	+	12.9008i	−1.58399	+	0.914516i	−0.994269	+	0.106906i	$0.965905\pi$
$200$	−12.6890	−	2.73893i	−0.897247	−	0.193671i
$201$	−1.86864	−	0.0710490i	−0.131804	−	0.00501141i
$202$	11.6796	−	16.6802i	0.821776	−	1.17362i
$203$	−8.03453	+	11.4745i	−0.563914	+	0.805352i
$204$	−3.53481	−	0.134400i	−0.247486	−	0.00940985i
$205$	−0.657517	+	10.4794i	−0.0459230	+	0.731915i
$206$	3.89070	−	2.24630i	0.271078	−	0.156507i
$207$	0.386076	−	0.00434728i	0.0268341	−	0.000302157i
$208$	−0.356874	−	1.33187i	−0.0247448	−	0.0923487i
$209$	−15.2868	+	5.56395i	−1.05741	+	0.384867i
$210$	−4.58149	−	8.18677i	−0.316153	−	0.564941i
$211$	−0.268205	+	0.225051i	−0.0184640	+	0.0154932i	−0.651973	−	0.758242i	$-0.726058\pi$
$211$	−0.268205	+	0.225051i	−0.0184640	+	0.0154932i	0.633509	+	0.773735i	$0.281614\pi$
$212$	0.173931	−	0.0811054i	0.0119456	−	0.00557035i
$213$	−16.0829	−	8.25747i	−1.10198	−	0.565792i
$214$	−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
$218$	0.574483	−	0.402257i	0.0389089	−	0.0272443i
$219$	8.00698	−	8.83746i	0.541062	−	0.597180i
$220$	−1.67395	+	0.492979i	−0.112857	+	0.0332366i
$221$	1.43715	+	1.71273i	0.0966733	+	0.115211i
$222$	4.49652	+	3.41025i	0.301786	+	0.228881i
$223$	−6.64028	+	14.2401i	−0.444666	+	0.953590i	0.548420	+	0.836203i	$0.315230\pi$
$223$	−6.64028	+	14.2401i	−0.444666	+	0.953590i	−0.993086	+	0.117387i	$0.962548\pi$
$224$	−1.26551	+	2.19193i	−0.0845557	+	0.146455i
$225$	11.7449	−	9.33048i	0.782992	−	0.622032i
$226$	−0.361618	−	0.626342i	−0.0240545	−	0.0416636i
$227$	23.4570	−	2.05222i	1.55690	−	0.136211i	0.724064	−	0.689733i	$-0.242272\pi$
$227$	23.4570	−	2.05222i	1.55690	−	0.136211i	0.832834	+	0.553522i	$0.186717\pi$
$228$	2.72290	+	0.841703i	0.180328	+	0.0557431i
$229$	22.8004	−	4.02032i	1.50669	−	0.265671i	0.641505	−	0.767119i	$-0.278310\pi$
$229$	22.8004	−	4.02032i	1.50669	−	0.265671i	0.865188	+	0.501448i	$0.167199\pi$
$230$	−0.314800	−	0.299678i	−0.0207573	−	0.0197602i
$231$	6.53113	+	4.10928i	0.429717	+	0.270371i
$232$	1.97625	+	22.5886i	0.129747	+	1.48301i
$233$	−5.59828	+	20.8931i	−0.366755	+	1.36875i	0.498270	+	0.867022i	$0.333969\pi$
$233$	−5.59828	+	20.8931i	−0.366755	+	1.36875i	−0.865026	+	0.501728i	$0.832698\pi$
$234$	1.26956	+	0.574694i	0.0829940	+	0.0375689i
$235$	−14.8324	−	11.8364i	−0.967559	−	0.772122i
$236$	−0.932175	−	2.56113i	−0.0606794	−	0.166715i
$237$	1.39295	+	3.31004i	0.0904816	+	0.215010i
$238$	1.53464	−	17.5410i	0.0994761	−	1.13702i
$239$	13.3597	+	4.86252i	0.864165	+	0.314530i	0.735802	−	0.677197i	$-0.236805\pi$
$239$	13.3597	+	4.86252i	0.864165	+	0.314530i	0.128363	+	0.991727i	$0.459028\pi$
$240$	−16.2344	−	6.15638i	−1.04792	−	0.397393i
$241$	−1.44826	+	8.21348i	−0.0932905	+	0.529077i	0.901967	+	0.431804i	$0.142123\pi$
$241$	−1.44826	+	8.21348i	−0.0932905	+	0.529077i	−0.995258	+	0.0972724i	$0.968988\pi$
$242$	−3.50767	+	3.50767i	−0.225482	+	0.225482i
$243$	−4.26724	+	14.9930i	−0.273744	+	0.961803i
$244$			0.747612i			0.0478610i
$245$	−8.86715	+	4.40357i	−0.566501	+	0.281334i
$246$	−2.59110	+	12.0072i	−0.165202	+	0.765550i
$247$	−0.761293	−	1.63260i	−0.0484399	−	0.103880i
$248$	11.6156	+	1.01624i	0.737594	+	0.0645311i
$249$	−21.1391	−	8.61699i	−1.33963	−	0.546079i
$250$	−16.7999	−	1.69779i	−1.06252	−	0.107378i
$251$	4.13040	+	2.38469i	0.260708	+	0.150520i	0.624658	−	0.780899i	$-0.285239\pi$
$251$	4.13040	+	2.38469i	0.260708	+	0.150520i	−0.363949	+	0.931419i	$0.618572\pi$
$252$	−0.476633	−	1.26504i	−0.0300251	−	0.0796898i
$253$	0.345305	+	0.0925243i	0.0217092	+	0.00581695i
$254$	−15.5653	−	13.0608i	−0.976654	−	0.819510i
$255$	28.0765	−	2.07774i	1.75822	−	0.130113i
$256$	1.14887	+	6.51557i	0.0718045	+	0.407223i
$257$	−3.86684	−	2.70759i	−0.241207	−	0.168895i	0.446722	−	0.894673i	$-0.352591\pi$
$257$	−3.86684	−	2.70759i	−0.241207	−	0.168895i	−0.687929	+	0.725778i	$0.741480\pi$
$258$	−3.80381	+	12.3053i	−0.236815	+	0.766093i
$259$	−2.22414	+	2.65063i	−0.138202	+	0.164702i
$260$	−0.0705358	−	0.179896i	−0.00437444	−	0.0111567i
$261$	−21.6306	−	14.7858i	−1.33890	−	0.915215i
$262$	−9.02113	+	2.41720i	−0.557327	+	0.149335i
$263$	−3.01862	−	1.40761i	−0.186136	−	0.0867967i	0.327316	−	0.944915i	$-0.393856\pi$
$263$	−3.01862	−	1.40761i	−0.186136	−	0.0867967i	−0.513452	+	0.858118i	$0.671634\pi$
$264$	12.3745	−	1.70006i	0.761596	−	0.104631i
$265$	−1.30357	+	0.796007i	−0.0800776	+	0.0488983i
$266$	−4.85212	+	13.3311i	−0.297502	+	0.817381i
$267$	−19.3125	+	0.952164i	−1.18191	+	0.0582715i
$268$	0.173983	+	0.248474i	0.0106277	+	0.0151780i
$269$	8.37429			0.510589			0.255295	−	0.966863i	$-0.417828\pi$
$269$	8.37429			0.510589			0.255295	+	0.966863i	$0.417828\pi$
$270$	15.2157	−	8.74143i	0.925996	−	0.531987i
$271$	−13.7893			−0.837641			−0.418821	−	0.908069i	$-0.637556\pi$
$271$	−13.7893			−0.837641			−0.418821	+	0.908069i	$0.637556\pi$
$272$	−18.6913	−	26.6940i	−1.13333	−	1.61856i
$273$	−0.390265	+	0.760109i	−0.0236199	+	0.0460039i
$274$	3.81425	−	10.4796i	0.230428	−	0.633094i
$275$	12.8013	−	5.38632i	0.771949	−	0.324807i
$276$	−0.0384053	−	0.0494716i	−0.00231173	−	0.00297784i
$277$	0.111462	+	0.0519757i	0.00669711	+	0.00312292i	0.425964	−	0.904740i	$-0.359935\pi$
$277$	0.111462	+	0.0519757i	0.00669711	+	0.00312292i	−0.419267	+	0.907863i	$0.637713\pi$
$278$	−14.9591	+	4.00827i	−0.897186	+	0.240400i
$279$	−9.41921	+	9.63375i	−0.563913	+	0.576757i
$280$	3.72623	−	8.53297i	0.222685	−	0.509943i
$281$	15.4444	−	18.4059i	0.921334	−	1.09800i	−0.0735813	−	0.997289i	$-0.523443\pi$
$281$	15.4444	−	18.4059i	0.921334	−	1.09800i	0.994915	−	0.100714i	$-0.0321127\pi$
$282$	−15.0898	−	16.2826i	−0.898582	−	0.969614i
$283$	13.0589	+	9.14396i	0.776273	+	0.543552i	0.893238	−	0.449584i	$-0.148428\pi$
$283$	13.0589	+	9.14396i	0.776273	+	0.543552i	−0.116965	+	0.993136i	$0.537317\pi$
$284$	0.509233	+	2.88801i	0.0302174	+	0.171372i
$285$	−22.2834	−	4.23776i	−1.31996	−	0.251023i
$286$	0.988429	+	0.829390i	0.0584470	+	0.0490429i
$287$	−7.27478	−	1.94927i	−0.429417	−	0.115062i
$288$	−4.12634	−	2.32079i	−0.243147	−	0.136754i
$289$	31.0386	+	17.9202i	1.82580	+	1.05413i
$290$	5.83475	+	28.9117i	0.342629	+	1.69775i
$291$	−16.2146	+	12.5876i	−0.950518	+	0.737897i
$292$	−1.92703	−	0.168594i	−0.112771	−	0.00986619i
$293$	2.22735	+	4.77657i	0.130123	+	0.279050i	0.960565	−	0.278055i	$-0.0896898\pi$
$293$	2.22735	+	4.77657i	0.130123	+	0.279050i	−0.830442	+	0.557105i	$0.811912\pi$
$294$	−11.0262	+	3.54493i	−0.643063	+	0.206744i
$295$	9.64822	+	19.4279i	0.561741	+	1.13114i
$296$			5.60107i			0.325555i
$297$	−7.54826	+	12.3021i	−0.437994	+	0.713838i
$298$	−1.29183	+	1.29183i	−0.0748340	+	0.0748340i
$299$	−0.00687388	+	0.0389837i	−0.000397526	+	0.00225448i
$300$	−2.35714	−	0.603366i	−0.136090	−	0.0348354i
$301$	−7.42071	−	2.70092i	−0.427723	−	0.155678i
$302$	2.12827	−	24.3262i	0.122468	−	1.39981i
$303$	−14.1118	+	18.6068i	−0.810701	+	1.06893i
$304$	8.97985	+	24.6719i	0.515030	+	1.41503i
$305$	−0.664260	−	5.91291i	−0.0380354	−	0.338572i
$306$	32.8403	+	2.50090i	1.87735	+	0.142967i
$307$	5.72834	−	21.3785i	0.326934	−	1.22013i	−0.585420	−	0.810730i	$-0.699070\pi$
$307$	5.72834	−	21.3785i	0.326934	−	1.22013i	0.912353	−	0.409403i	$-0.134263\pi$
$308$	−0.109090	−	1.24690i	−0.00621596	−	0.0710487i
$309$	−4.55666	+	2.40475i	−0.259220	+	0.136801i
$310$	15.1623	−	0.373145i	0.861161	−	0.0211932i
$311$	14.1711	−	2.49874i	0.803567	−	0.141691i	0.243244	−	0.969965i	$-0.421788\pi$
$311$	14.1711	−	2.49874i	0.803567	−	0.141691i	0.560322	+	0.828275i	$0.310677\pi$
$312$	0.306959	+	1.34862i	0.0173781	+	0.0763508i
$313$	−21.1736	+	1.85245i	−1.19680	+	0.104707i	−0.668081	−	0.744088i	$-0.732884\pi$
$313$	−21.1736	+	1.85245i	−1.19680	+	0.104707i	−0.528722	+	0.848795i	$0.677329\pi$
$314$	−15.6669	−	27.1358i	−0.884133	−	1.53136i
$315$	4.89372	+	9.58175i	0.275730	+	0.539871i
$316$	0.291263	−	0.504482i	0.0163848	−	0.0283793i
$317$	−9.71542	+	20.8348i	−0.545672	+	1.17020i	0.419300	+	0.907848i	$0.362275\pi$
$317$	−9.71542	+	20.8348i	−0.545672	+	1.17020i	−0.964973	+	0.262350i	$0.915502\pi$
$318$	−1.64694	+	0.693074i	−0.0923559	+	0.0388657i
$319$	−15.5936	−	18.5838i	−0.873076	−	1.04049i
$320$	−4.15824	−	14.1196i	−0.232453	−	0.789310i
$321$	18.6953	+	4.03435i	1.04347	+	0.225176i
$322$	0.255371	−	0.178813i	0.0142313	−	0.00996485i
$323$	−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
$327$	−0.675891	+	0.435959i	−0.0373768	+	0.0241086i
$328$	−11.0491	+	5.15228i	−0.610085	+	0.284487i
$329$	10.4268	−	8.74912i	0.574848	−	0.482355i
$330$	15.7487	−	3.99450i	0.866940	−	0.219890i
$331$	13.1133	−	4.77285i	0.720772	−	0.262340i	0.0445184	−	0.999009i	$-0.485825\pi$
$331$	13.1133	−	4.77285i	0.720772	−	0.262340i	0.676253	+	0.736669i	$0.263602\pi$
$332$	0.958382	+	3.57673i	0.0525980	+	0.196298i
$333$	−5.00446	−	4.10411i	−0.274243	−	0.224904i
$334$	−21.0465	+	12.1512i	−1.15161	+	0.664884i
$335$	−1.59682	−	1.81061i	−0.0872434	−	0.0989242i
$336$	6.63211	−	10.5408i	0.361811	−	0.575049i
$337$	−8.31162	+	11.8702i	−0.452763	+	0.646612i	−0.979032	−	0.203705i	$-0.934701\pi$
$337$	−8.31162	+	11.8702i	−0.452763	+	0.646612i	0.526269	+	0.850318i	$0.323590\pi$
$338$	11.1795	−	15.9659i	0.608083	−	0.868432i
$339$	0.387127	+	0.733551i	0.0210258	+	0.0398410i
$340$	−3.02061	−	3.42503i	−0.163816	−	0.185749i
$341$	−10.8035	+	6.23741i	−0.585043	+	0.337775i
$342$	−25.0360	−	8.79441i	−1.35379	−	0.475547i
$343$	−4.74374	−	17.7039i	−0.256138	−	0.955920i
$344$	−12.0122	+	4.37207i	−0.647652	+	0.235726i
$345$	0.347706	+	0.357150i	0.0187199	+	0.0192283i
$346$	−3.06901	+	2.57521i	−0.164991	+	0.138444i
$347$	8.22815	−	3.83685i	0.441710	−	0.205973i	−0.189023	−	0.981973i	$-0.560532\pi$
$347$	8.22815	−	3.83685i	0.441710	−	0.205973i	0.630733	+	0.776000i	$0.282754\pi$
$348$	0.209287	+	4.24492i	0.0112190	+	0.227552i
$349$	−8.20842	−	1.44737i	−0.439387	−	0.0774757i	−0.0504212	−	0.998728i	$-0.516056\pi$
$349$	−8.20842	−	1.44737i	−0.439387	−	0.0774757i	−0.388966	+	0.921252i	$0.627167\pi$
$350$	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
$353$	−2.16366	+	1.51501i	−0.115160	+	0.0806358i	−0.629738	−	0.776808i	$-0.716838\pi$
$353$	−2.16366	+	1.51501i	−0.115160	+	0.0806358i	0.514578	+	0.857444i	$0.327949\pi$
$354$	7.76693	+	24.1585i	0.412808	+	1.28401i
$355$	−6.59358	−	22.3890i	−0.349951	−	1.18828i
$356$	2.01609	+	2.40268i	0.106852	+	0.127342i
$357$	−2.52304	+	20.0353i	−0.133533	+	1.06038i
$358$	−4.37967	+	9.39224i	−0.231473	+	0.496395i
$359$	7.06131	−	12.2306i	0.372682	−	0.645504i	−0.617295	−	0.786732i	$-0.711772\pi$
$359$	7.06131	−	12.2306i	0.372682	−	0.645504i	0.989977	+	0.141228i	$0.0451049\pi$
$360$	16.0382	+	6.78966i	0.845285	+	0.357847i
$361$	7.65033	+	13.2508i	0.402649	+	0.697408i
$362$	30.1267	−	2.63575i	1.58342	−	0.138532i
$363$	4.17267	−	3.86699i	0.219009	−	0.202964i
$364$	0.136493	−	0.0240674i	0.00715418	−	0.00126148i
$365$	15.3908	−	0.378769i	0.805592	−	0.0198257i
$366$	0.264470	−	6.95577i	0.0138241	−	0.363584i
$367$	−1.20011	−	13.7173i	−0.0626451	−	0.716037i	−0.960961	−	0.276686i	$-0.910764\pi$
$367$	−1.20011	−	13.7173i	−0.0626451	−	0.716037i	0.898315	−	0.439351i	$-0.144792\pi$
$368$	0.149328	−	0.557300i	0.00778426	−	0.0290513i
$369$	3.49262	−	13.6475i	0.181818	−	0.710458i
$370$	0.813358	+	7.24011i	0.0422845	+	0.376396i
$371$	−0.374703	−	1.02949i	−0.0194536	−	0.0534483i
$372$	2.16838	+	0.273062i	0.112425	+	0.0141576i
$373$	−1.77048	+	20.2366i	−0.0916718	+	1.04781i	0.801469	+	0.598036i	$0.204052\pi$
$373$	−1.77048	+	20.2366i	−0.0916718	+	1.04781i	−0.893141	+	0.449777i	$0.851503\pi$
$374$	28.6555	+	10.4297i	1.48174	+	0.539309i
$375$	19.1789	+	2.67772i	0.990394	+	0.138277i
$376$	3.82598	−	21.6982i	0.197310	−	1.11900i
$377$	1.89949	−	1.89949i	0.0978286	−	0.0978286i
$378$	3.98707	+	11.9385i	0.205073	+	0.614049i
$379$			20.8542i			1.07121i	0.844469	+	0.535605i	$0.179916\pi$
$379$			20.8542i			1.07121i	−0.844469	+	0.535605i	$0.820084\pi$
$380$	1.63654	+	3.29537i	0.0839526	+	0.169049i
$381$	17.2689	+	15.6461i	0.884712	+	0.801573i
$382$	5.97940	+	12.8229i	0.305933	+	0.656075i
$383$	−14.6116	−	1.27835i	−0.746618	−	0.0653206i	−0.292504	−	0.956264i	$-0.594488\pi$
$383$	−14.6116	−	1.27835i	−0.746618	−	0.0653206i	−0.454114	+	0.890944i	$0.650044\pi$
$384$	−3.08769	−	22.4749i	−0.157568	−	1.14692i
$385$	1.97068	+	9.76488i	0.100435	+	0.497664i
$386$	27.5662	+	15.9154i	1.40308	+	0.810071i
$387$	4.89539	−	13.9362i	0.248847	−	0.708419i
$388$	3.21623	+	0.861786i	0.163279	+	0.0437506i
$389$	4.79561	+	4.02400i	0.243147	+	0.204025i	0.756215	−	0.654323i	$-0.227047\pi$
$389$	4.79561	+	4.02400i	0.243147	+	0.204025i	−0.513067	+	0.858348i	$0.671491\pi$
$390$	0.592624	+	1.69870i	0.0300087	+	0.0860169i
$391$	0.162455	+	0.921326i	0.00821568	+	0.0465934i
$392$	−9.41624	−	6.59332i	−0.475592	−	0.333013i
$393$	10.4436	−	2.37706i	0.526812	−	0.119907i
$394$	−7.13377	+	8.50169i	−0.359394	+	0.428309i
$395$	−1.85538	+	4.24876i	−0.0933541	+	0.213779i
$396$	2.32985	−	0.230297i	0.117079	−	0.0115728i
$397$	−0.450577	+	0.120732i	−0.0226138	+	0.00605935i	−0.270108	−	0.962830i	$-0.587059\pi$
$397$	−0.450577	+	0.120732i	−0.0226138	+	0.00605935i	0.247494	+	0.968889i	$0.420393\pi$
$398$	−35.3168	−	16.4685i	−1.77027	−	0.825492i
$399$	6.14146	−	15.0661i	0.307457	−	0.754250i
$400$	−8.69316	−	20.6605i	−0.434658	−	1.03302i
$401$	3.19304	−	8.77280i	0.159453	−	0.438093i	−0.834079	−	0.551644i	$-0.814001\pi$
$401$	3.19304	−	8.77280i	0.159453	−	0.438093i	0.993532	+	0.113552i	$0.0362228\pi$
$402$	−1.53084	−	2.37334i	−0.0763513	−	0.118372i
$403$	−0.792314	−	1.13154i	−0.0394680	−	0.0563661i
$404$	3.78805			0.188463
$405$	−17.8182	+	9.35478i	−0.885393	+	0.464843i
$406$	−21.1557			−1.04994
$407$	−3.43714	−	4.90874i	−0.170373	−	0.243317i
$408$	17.7182	+	27.4695i	0.877182	+	1.35994i
$409$	0.240362	−	0.660389i	0.0118851	−	0.0326541i	−0.933608	−	0.358296i	$-0.883358\pi$
$409$	0.240362	−	0.660389i	0.0118851	−	0.0326541i	0.945493	+	0.325641i	$0.105580\pi$
$410$	−13.5342	+	8.26450i	−0.668408	+	0.408154i
$411$	−4.82780	+	11.8435i	−0.238138	+	0.584197i
$412$	0.757446	+	0.353203i	0.0373167	+	0.0174010i
$413$	−15.0288	+	4.02694i	−0.739517	+	0.198153i
$414$	0.339821	+	0.473869i	0.0167013	+	0.0232894i
$415$	−10.7578	−	27.4370i	−0.528082	−	1.34683i
$416$	0.311994	−	0.371820i	0.0152968	−	0.0182300i
$417$	17.3179	−	3.94171i	0.848062	−	0.193026i
$418$	−20.1259	−	14.0923i	−0.984389	−	0.689276i
$419$	3.72329	+	21.1158i	0.181894	+	1.03157i	0.929881	+	0.367861i	$0.119910\pi$
$419$	3.72329	+	21.1158i	0.181894	+	1.03157i	−0.747986	+	0.663714i	$0.768979\pi$
$420$	0.758691	−	1.57169i	0.0370203	−	0.0766907i
$421$	13.6486	+	11.4526i	0.665194	+	0.558164i	0.911638	−	0.410993i	$-0.134818\pi$
$421$	13.6486	+	11.4526i	0.665194	+	0.558164i	−0.246445	+	0.969157i	$0.579262\pi$
$422$	−0.510759	−	0.136857i	−0.0248633	−	0.00666211i
$423$	16.5835	+	19.3175i	0.806319	+	0.939251i
$424$	−1.53582	−	0.886708i	−0.0745862	−	0.0430623i
$425$	26.9334	+	24.4050i	1.30646	+	1.18381i
$426$	−3.71625	−	27.0501i	−0.180053	−	1.31058i
$427$	4.25162	+	0.371968i	0.205750	+	0.0180008i
$428$	−1.31111	−	2.81169i	−0.0633750	−	0.135908i
$429$	−1.09661	−	0.993559i	−0.0529449	−	0.0479695i
$430$	−14.8924	+	7.39581i	−0.718175	+	0.356658i
$431$		−	13.6942i		−	0.659624i	−0.944047	−	0.329812i	$-0.893015\pi$
$431$		−	13.6942i		−	0.659624i	0.944047	−	0.329812i	$-0.106985\pi$
$432$	19.8547	+	12.1824i	0.955261	+	0.586126i
$433$	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
$435$	−5.42691	−	33.3874i	−0.260200	−	1.60080i
$436$	0.122596	+	0.0446213i	0.00587129	+	0.00213697i
$437$	0.0656941	−	0.750887i	0.00314257	−	0.0359198i
$438$	17.8694	+	2.25028i	0.853834	+	0.107523i
$439$	−3.85214	−	10.5837i	−0.183852	−	0.505130i	0.813189	−	0.582000i	$-0.197730\pi$
$439$	−3.85214	−	10.5837i	−0.183852	−	0.505130i	−0.997041	+	0.0768697i	$0.975507\pi$
$440$	12.6041	+	10.0582i	0.600875	+	0.479505i
$441$	12.7907	−	3.58208i	0.609079	−	0.170575i
$442$	−0.873956	+	3.26165i	−0.0415699	+	0.155141i
$443$	−0.588927	−	6.73147i	−0.0279808	−	0.319822i	−0.997267	−	0.0738853i	$-0.976460\pi$
$443$	−0.588927	−	6.73147i	−0.0279808	−	0.319822i	0.969286	−	0.245936i	$-0.0790954\pi$
$444$	−0.0398878	+	1.04908i	−0.00189299	+	0.0497872i
$445$	−18.0802	−	17.2116i	−0.857082	−	0.815910i
$446$	−23.3694	+	4.12066i	−1.10657	+	0.195119i
$447$	1.53674	−	1.42417i	0.0726855	−	0.0673607i
$448$	10.5175	−	0.920162i	0.496905	−	0.0434736i
$449$	5.70190	+	9.87598i	0.269089	+	0.466076i	0.968627	−	0.248519i	$-0.0799440\pi$
$449$	5.70190	+	9.87598i	0.269089	+	0.466076i	−0.699538	+	0.714596i	$0.746611\pi$
$450$	21.7174	+	6.44755i	1.02377	+	0.303940i
$451$	6.52164	−	11.2958i	0.307092	−	0.531899i
$452$	0.0568601	−	0.121937i	0.00267447	−	0.00573542i
$453$	−3.49899	+	27.7853i	−0.164397	+	1.30547i
$454$	22.8589	+	27.2421i	1.07282	+	1.27854i
$455$	−1.05815	+	0.311626i	−0.0496067	+	0.0146092i
$456$	−8.06081	−	25.0725i	−0.377482	−	1.17413i
$457$	6.07605	−	4.25450i	0.284226	−	0.199017i	−0.422766	−	0.906239i	$-0.638941\pi$
$457$	6.07605	−	4.25450i	0.284226	−	0.199017i	0.706992	+	0.707222i	$0.250052\pi$
$458$	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	−0.914046	−	0.405611i	$-0.867059\pi$
$461$	−41.0458	−	7.23749i	−1.91170	−	0.337083i	−0.997649	+	0.0685275i	$0.978170\pi$
$462$	0.573873	+	11.6397i	0.0266990	+	0.541529i
$463$	3.01669	−	1.40671i	0.140198	−	0.0653752i	−0.351253	−	0.936280i	$-0.614244\pi$
$463$	3.01669	−	1.40671i	0.140198	−	0.0653752i	0.491451	+	0.870905i	$0.336467\pi$
$464$	−29.9930	+	25.1671i	−1.39239	+	1.16835i
$465$	−17.3924	−	0.233043i	−0.806555	−	0.0108071i
$466$	−30.6975	+	11.1730i	−1.42203	+	0.517577i
$467$	−1.15789	−	4.32129i	−0.0535806	−	0.199966i	0.933947	−	0.357412i	$-0.116341\pi$
$467$	−1.15789	−	4.32129i	−0.0535806	−	0.199966i	−0.987528	+	0.157446i	$0.949674\pi$
$468$	0.0478892	+	0.254784i	0.00221368	+	0.0117774i
$469$	1.49962	−	0.865804i	0.0692458	−	0.0399791i
$470$	1.79468	−	28.6034i	0.0827822	−	1.31937i
$471$	16.7720	+	31.7806i	0.772813	+	1.46437i
$472$	−14.4459	+	20.6309i	−0.664929	+	0.949616i
$473$	7.84443	−	11.2030i	0.360687	−	0.515115i
$474$	−2.88836	+	4.59065i	−0.132667	+	0.210855i
$475$	−15.8714	−	24.6092i	−0.728232	−	1.12915i
$476$	2.83674	−	1.63780i	0.130022	−	0.0750682i
$477$	1.91761	−	0.722508i	0.0878015	−	0.0330814i
$478$	5.55731	+	20.7402i	0.254185	+	0.948632i
$479$	34.5314	−	12.5684i	1.57778	−	0.574264i	0.603059	−	0.797697i	$-0.293948\pi$
$479$	34.5314	−	12.5684i	1.57778	−	0.574264i	0.974719	+	0.223432i	$0.0717262\pi$
$480$	−1.50262	−	5.92425i	−0.0685851	−	0.270404i
$481$	0.508314	−	0.426526i	0.0231771	−	0.0194479i
$482$	−11.4159	+	5.32332i	−0.519980	+	0.242470i
$483$	−0.300450	+	0.193794i	−0.0136709	+	0.00881793i
$484$	−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	$0.656284\pi$
$488$	5.65913	−	3.96257i	0.256177	−	0.179377i
$489$	−22.1340	−	4.77642i	−1.00093	−	0.215997i
$490$	−13.1292	−	7.15535i	−0.593115	−	0.323246i
$491$	14.7648	+	17.5960i	0.666326	+	0.794096i	0.988279	−	0.152660i	$-0.0487838\pi$
$491$	14.7648	+	17.5960i	0.666326	+	0.794096i	−0.321953	+	0.946756i	$0.604339\pi$
$492$	−2.10619	+	0.886338i	−0.0949545	+	0.0399592i
$493$	26.8306	−	57.5384i	1.20839	−	2.59140i
$494$	1.36029	−	2.35609i	0.0612024	−	0.106006i
$495$	−18.2223	+	3.89152i	−0.819030	+	0.174911i
$496$	10.0668	+	17.4361i	0.452011	+	0.782906i
$497$	16.6772	−	1.45907i	0.748076	−	0.0654482i
$498$	−7.65148	−	33.6168i	−0.342871	−	1.50641i
$499$	9.11992	−	1.60809i	0.408264	−	0.0719879i	0.0342550	−	0.999413i	$-0.489094\pi$
$499$	9.11992	−	1.60809i	0.408264	−	0.0719879i	0.374009	+	0.927425i	$0.377983\pi$
$500$	−1.53385	−	2.74122i	−0.0685960	−	0.122591i
$501$	24.6490	−	13.0083i	1.10124	−	0.581170i
$502$	0.627792	+	7.17569i	0.0280197	+	0.320267i
$503$	2.22875	−	8.31780i	0.0993750	−	0.370873i	−0.898271	−	0.439441i	$-0.855177\pi$
$503$	2.22875	−	8.31780i	0.0993750	−	0.370873i	0.997646	+	0.0685686i	$0.0218432\pi$
$504$	−7.04953	+	10.3130i	−0.314011	+	0.459377i
$505$	−29.9599	+	3.36572i	−1.33320	+	0.149772i
$506$	0.184659	+	0.507345i	0.00820908	+	0.0225543i
$507$	−13.5075	+	17.8100i	−0.599888	+	0.790970i
$508$	0.329441	−	3.76553i	0.0146166	−	0.167068i
$509$	−20.6614	−	7.52013i	−0.915799	−	0.333324i	−0.159233	−	0.987241i	$-0.550902\pi$
$509$	−20.6614	−	7.52013i	−0.915799	−	0.333324i	−0.756566	+	0.653917i	$0.773124\pi$
$510$	26.8921	+	32.9350i	1.19080	+	1.45839i
$511$	−1.91756	+	10.8750i	−0.0848278	+	0.481082i
$512$	11.4575	−	11.4575i	0.506354	−	0.506354i
$513$	28.3083	+	11.1694i	1.24984	+	0.493141i
$514$		−	7.12936i		−	0.314463i
$515$	−6.30451	−	2.12050i	−0.277810	−	0.0934406i
$516$	−2.28102	+	0.733345i	−0.100416	+	0.0322837i
$517$	9.96221	+	21.3640i	0.438138	+	0.939589i
$518$	−5.20593	−	0.455459i	−0.228735	−	0.0200117i
$519$	3.62933	−	2.81749i	0.159310	−	0.123674i
$520$	−0.987880	+	1.48743i	−0.0433214	+	0.0652281i
$521$	−4.43677	−	2.56157i	−0.194378	−	0.112224i	0.399652	−	0.916667i	$-0.369131\pi$
$521$	−4.43677	−	2.56157i	−0.194378	−	0.112224i	−0.594031	+	0.804442i	$0.702464\pi$
$522$	−0.445550	−	39.5687i	−0.0195012	−	1.73187i
$523$	−7.57196	−	2.02890i	−0.331099	−	0.0887177i	0.0894400	−	0.995992i	$-0.471492\pi$
$523$	−7.57196	−	2.02890i	−0.331099	−	0.0887177i	−0.420539	+	0.907275i	$0.638159\pi$
$524$	−1.33091	−	1.11677i	−0.0581412	−	0.0487863i
$525$	−4.60407	+	13.1047i	−0.200938	+	0.571936i
$526$	−0.873497	−	4.95385i	−0.0380863	−	0.215998i
$527$	−26.7424	−	18.7252i	−1.16492	−	0.815685i
$528$	14.6603	+	15.8192i	0.638009	+	0.688443i
$529$	14.7735	−	17.6063i	0.642325	−	0.765493i
$530$	−2.11401	−	0.923161i	−0.0918269	−	0.0400996i
$531$	−7.84832	−	28.0243i	−0.340588	−	1.21615i
$532$	−2.54919	+	0.683053i	−0.110521	+	0.0296141i
$533$	1.30898	+	0.610389i	0.0566984	+	0.0264389i
$534$	−17.9077	−	23.0677i	−0.774941	−	0.998236i
$535$	12.8679	+	21.0729i	0.556327	+	0.911060i
$536$	0.958687	−	2.63397i	0.0414090	−	0.113770i
$537$	5.42840	−	10.5728i	0.234253	−	0.456248i
$538$	7.25433	+	10.3603i	0.312757	+	0.446663i
$539$	12.2984			0.529729
$540$	2.95560	+	1.38592i	0.127189	+	0.0596405i
$541$	−12.2903			−0.528401			−0.264200	−	0.964468i	$-0.585108\pi$
$541$	−12.2903			−0.528401			−0.264200	+	0.964468i	$0.585108\pi$
$542$	−11.9452	−	17.0595i	−0.513089	−	0.732767i
$543$	−34.6404	+	1.70787i	−1.48656	+	0.0732919i
$544$	3.92339	−	10.7794i	0.168214	−	0.462164i
$545$	−1.00927	−	0.243985i	−0.0432322	−	0.0104512i
$546$	−1.27844	+	0.175638i	−0.0547123	+	0.00751660i
$547$	−0.472172	−	0.220177i	−0.0201886	−	0.00941410i	0.412498	−	0.910959i	$-0.364656\pi$
$547$	−0.472172	−	0.220177i	−0.0201886	−	0.00941410i	−0.432686	+	0.901545i	$0.642434\pi$
$548$	2.00392	−	0.536948i	0.0856032	−	0.0229373i
$549$	−0.606171	+	7.95986i	−0.0258707	+	0.339718i
$550$	17.7530	+	11.1712i	0.756990	+	0.476342i
$551$	−32.8789	+	39.1836i	−1.40069	+	1.66928i
$552$	−0.170921	+	0.552927i	−0.00727488	+	0.0235342i
$553$	−2.72403	−	1.90739i	−0.115838	−	0.0811104i
$554$	0.0322538	+	0.182920i	0.00137033	+	0.00777153i
$555$	−0.616642	−	8.33269i	−0.0261750	−	0.353703i
$556$	−2.20695	−	1.85185i	−0.0935957	−	0.0785361i
$557$	22.5239	+	6.03527i	0.954370	+	0.255723i	0.702216	−	0.711964i	$-0.252194\pi$
$557$	22.5239	+	6.03527i	0.954370	+	0.255723i	0.252155	+	0.967687i	$0.418861\pi$
$558$	−20.0779	−	3.30763i	−0.849966	−	0.140023i
$559$	1.31151	+	0.757203i	0.0554711	+	0.0320263i
$560$	15.7599	−	3.18054i	0.665976	−	0.134402i
$561$	−32.3850	−	13.2012i	−1.36730	−	0.557355i
$562$	36.1498	+	3.16269i	1.52489	+	0.133410i
$563$	−14.5231	−	31.1449i	−0.612076	−	1.31260i	−0.931069	−	0.364844i	$-0.881122\pi$
$563$	−14.5231	−	31.1449i	−0.612076	−	1.31260i	0.318993	−	0.947757i	$-0.396656\pi$
$564$	0.871130	−	4.03683i	0.0366812	−	0.169981i
$565$	−0.341368	+	1.01493i	−0.0143614	+	0.0426983i
$566$			24.0770i			1.01203i
$567$	−4.04903	−	13.8553i	−0.170043	−	0.581870i
$568$	19.1620	−	19.1620i	0.804019	−	0.804019i
$569$	−0.227444	+	1.28990i	−0.00953495	+	0.0540754i	−0.989204	−	0.146545i	$-0.953185\pi$
$569$	−0.227444	+	1.28990i	−0.00953495	+	0.0540754i	0.979669	+	0.200620i	$0.0642958\pi$
$570$	−14.0606	−	31.2390i	−0.588932	−	1.30846i
$571$	−17.9969	−	6.55033i	−0.753146	−	0.274123i	−0.0632171	−	0.998000i	$-0.520136\pi$
$571$	−17.9969	−	6.55033i	−0.753146	−	0.274123i	−0.689929	+	0.723877i	$0.742358\pi$
$572$	−0.0209202	+	0.239119i	−0.000874718	+	0.00999807i
$573$	−6.29372	−	14.9557i	−0.262924	−	0.624782i
$574$	−3.89033	−	10.6886i	−0.162379	−	0.446133i
$575$	−0.0244834	+	0.643035i	−0.00102103	+	0.0268164i
$576$	1.94253	+	19.6521i	0.0809389	+	0.818836i
$577$	3.38883	−	12.6473i	0.141079	−	0.526514i	−0.858820	−	0.512278i	$-0.828802\pi$
$577$	3.38883	−	12.6473i	0.141079	−	0.526514i	0.999899	−	0.0142358i	$-0.00453155\pi$
$578$	4.71766	+	53.9231i	0.196229	+	2.24290i
$579$	−30.8977	−	19.4403i	−1.28406	−	0.807913i
$580$	−3.78314	+	3.97405i	−0.157087	+	0.165013i
$581$	20.8174	−	3.67067i	0.863652	−	0.152285i
$582$	−29.6189	−	9.15579i	−1.22774	−	0.379520i
$583$	1.89012	−	0.165364i	0.0782808	−	0.00684869i
$584$	8.93766	+	15.4805i	0.369843	+	0.640587i
$585$	−0.605136	−	1.97255i	−0.0250193	−	0.0815548i
$586$	−3.97987	+	6.89333i	−0.164407	+	0.284761i
$587$	−12.2703	+	26.3137i	−0.506449	+	1.08608i	0.472379	+	0.881396i	$0.343395\pi$
$587$	−12.2703	+	26.3137i	−0.506449	+	1.08608i	−0.978827	+	0.204687i	$0.934382\pi$
$588$	−1.71671	−	1.30199i	−0.0707959	−	0.0536931i
$589$	16.9072	+	20.1492i	0.696650	+	0.830235i
$590$	−15.6774	+	28.7660i	−0.645426	+	1.18428i
$591$	8.54582	−	9.43219i	0.351528	−	0.387988i
$592$	−7.92239	+	5.54732i	−0.325608	+	0.227993i
$593$	18.8092	+	18.8092i	0.772402	+	0.772402i	0.978526	−	0.206124i	$-0.0660851\pi$
$593$	18.8092	+	18.8092i	0.772402	+	0.772402i	−0.206124	+	0.978526i	$0.566085\pi$
$594$	−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
$597$	39.7559	+	20.4120i	1.62710	+	0.835406i
$598$	−0.0541833	+	0.0252661i	−0.00221572	+	0.00103321i
$599$	−3.51169	+	2.94665i	−0.143484	+	0.120397i	−0.711704	−	0.702479i	$-0.752076\pi$
$599$	−3.51169	+	2.94665i	−0.143484	+	0.120397i	0.568221	+	0.822876i	$0.307632\pi$
$600$	7.92632	+	21.0407i	0.323591	+	0.858982i
$601$	25.1131	−	9.14041i	1.02438	−	0.372845i	0.225443	−	0.974256i	$-0.427617\pi$
$601$	25.1131	−	9.14041i	1.02438	−	0.372845i	0.798940	+	0.601411i	$0.205395\pi$
$602$	−3.08684	−	11.5202i	−0.125810	−	0.469530i
$603$	1.65094	+	2.78658i	0.0672316	+	0.113478i
$604$	3.93404	−	2.27132i	0.160074	−	0.0924187i
$605$	7.33006	+	0.459914i	0.298009	+	0.0186982i
$606$	−35.2440	−	1.34003i	−1.43169	−	0.0544352i
$607$	−20.5023	+	29.2803i	−0.832163	+	1.18845i	0.147749	+	0.989025i	$0.452797\pi$
$607$	−20.5023	+	29.2803i	−0.832163	+	1.18845i	−0.979913	+	0.199428i	$0.936092\pi$
$608$	−5.30114	+	7.57081i	−0.214990	+	0.307037i
$609$	24.2447	+	0.921823i	0.982443	+	0.0373542i
$610$	6.73974	−	5.94392i	0.272884	−	0.240662i
$611$	−2.26053	+	1.30512i	−0.0914512	+	0.0527994i
$612$	3.12300	+	5.27122i	0.126240	+	0.213077i
$613$	9.61085	+	35.8682i	0.388179	+	1.44870i	0.833095	+	0.553130i	$0.186567\pi$
$613$	9.61085	+	35.8682i	0.388179	+	1.44870i	−0.444916	+	0.895572i	$0.646767\pi$
$614$	31.4107	−	11.4325i	1.26763	−	0.461380i
$615$	15.8705	−	8.88147i	0.639959	−	0.358135i
$616$	−8.86034	+	7.43471i	−0.356993	+	0.299553i
$617$	−42.1491	+	19.6545i	−1.69686	+	0.791258i	−0.699824	+	0.714316i	$0.746738\pi$
$617$	−42.1491	+	19.6545i	−1.69686	+	0.791258i	−0.997036	+	0.0769428i	$0.975484\pi$
$618$	−6.92231	−	3.55414i	−0.278456	−	0.142968i
$619$	13.9352	+	2.45716i	0.560104	+	0.0987615i	0.446531	−	0.894768i	$-0.352659\pi$
$619$	13.9352	+	2.45716i	0.560104	+	0.0987615i	0.113573	+	0.993530i	$0.463770\pi$
$620$	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
$623$	14.6669	−	10.2699i	0.587619	−	0.411455i
$624$	−1.60354	+	1.76986i	−0.0641929	+	0.0708510i
$625$	14.5669	+	20.3176i	0.582677	+	0.812704i
$626$	−20.6337	−	24.5903i	−0.824687	−	0.982824i
$627$	22.4504	+	17.0269i	0.896583	+	0.679987i
$628$	2.46342	−	5.28283i	0.0983013	−	0.210808i
$629$	7.84112	−	13.5812i	0.312646	−	0.541519i
$630$	−7.61483	+	14.3546i	−0.303382	+	0.571900i
$631$	16.2979	+	28.2288i	0.648810	+	1.12377i	0.983407	+	0.181411i	$0.0580664\pi$
$631$	16.2979	+	28.2288i	0.648810	+	1.12377i	−0.334597	+	0.942361i	$0.608600\pi$
$632$	−5.36250	+	0.469158i	−0.213309	+	0.0186621i
$633$	0.579371	+	0.179095i	0.0230279	+	0.00711840i
$634$	−34.1919	+	6.02895i	−1.35793	+	0.239440i
$635$	0.740135	+	30.0745i	0.0293714	+	1.19347i
$636$	−0.281345	−	0.177018i	−0.0111561	−	0.00701921i
$637$	0.118690	+	1.35664i	0.00470269	+	0.0537520i
$638$	9.48275	−	35.3901i	0.375426	−	1.40111i
$639$	3.08021	+	31.1616i	0.121851	+	1.23273i
$640$	18.2680	−	22.8919i	0.722104	−	0.904881i
$641$	−11.8689	−	32.6096i	−0.468794	−	1.28800i	−0.918711	−	0.394931i	$-0.870768\pi$
$641$	−11.8689	−	32.6096i	−0.468794	−	1.28800i	0.449916	−	0.893071i	$-0.351454\pi$
$642$	11.2039	+	26.6237i	0.442183	+	1.05075i
$643$	0.772198	−	8.82626i	0.0304525	−	0.348074i	−0.965648	−	0.259852i	$-0.916326\pi$
$643$	0.772198	−	8.82626i	0.0304525	−	0.348074i	0.996101	−	0.0882215i	$-0.0281183\pi$
$644$	0.0544969	+	0.0198352i	0.00214748	+	0.000781618i
$645$	17.3891	−	7.82677i	0.684695	−	0.308179i
$646$	11.1651	−	63.3204i	0.439285	−	2.49131i
$647$	14.1426	−	14.1426i	0.556003	−	0.556003i	−0.372164	−	0.928167i	$-0.621384\pi$
$647$	14.1426	−	14.1426i	0.556003	−	0.556003i	0.928167	+	0.372164i	$0.121384\pi$
$648$	−19.4374	−	12.9679i	−0.763573	−	0.509428i
$649$		−	26.9457i		−	1.05771i
$650$	−1.06097	+	2.06615i	−0.0416145	+	0.0810411i
$651$	2.63174	−	12.1955i	0.103146	−	0.477980i
$652$	1.55227	+	3.32886i	0.0607917	+	0.130368i
$653$	1.98004	+	0.173231i	0.0774848	+	0.00677904i	0.125832	−	0.992052i	$-0.459840\pi$
$653$	1.98004	+	0.173231i	0.0774848	+	0.00677904i	−0.0483474	+	0.998831i	$0.515395\pi$
$654$	−1.12485	−	0.458524i	−0.0439850	−	0.0179297i
$655$	11.5185	+	7.65006i	0.450066	+	0.298913i
$656$	−18.2307	−	10.5255i	−0.711788	−	0.410951i
$657$	−20.3805	−	3.35748i	−0.795119	−	0.130988i
$658$	19.8563	+	5.32049i	0.774081	+	0.207414i
$659$	9.93910	+	8.33989i	0.387172	+	0.324876i	0.815510	−	0.578742i	$-0.196456\pi$
$659$	9.93910	+	8.33989i	0.387172	+	0.324876i	−0.428338	+	0.903619i	$0.640901\pi$
$660$	2.28911	+	1.97366i	0.0891037	+	0.0768245i
$661$	2.91716	+	16.5440i	0.113464	+	0.643489i	0.987499	+	0.157625i	$0.0503837\pi$
$661$	2.91716	+	16.5440i	0.113464	+	0.643489i	−0.874035	+	0.485864i	$0.838505\pi$
$662$	17.2643	+	12.0886i	0.670996	+	0.469836i
$663$	1.14368	−	3.69980i	0.0444170	−	0.143688i
$664$	21.9947	−	26.2123i	0.853561	−	1.01723i
$665$	19.5548	−	7.66728i	0.758302	−	0.297324i
$666$	0.742231	−	9.74651i	0.0287609	−	0.377670i
$667$	1.08573	−	0.290921i	0.0420396	−	0.0112645i
$668$	−4.09735	−	1.91063i	−0.158531	−	0.0739244i
$669$	26.9612	−	3.70404i	1.04238	−	0.143206i
$670$	0.856736	−	3.54397i	0.0330986	−	0.136915i
$671$	−2.52797	+	6.94554i	−0.0975912	+	0.268130i
$672$	4.37855	−	0.215875i	0.168906	−	0.00832758i
$673$	−5.24028	−	7.48390i	−0.201998	−	0.288483i	0.705353	−	0.708856i	$-0.250788\pi$
$673$	−5.24028	−	7.48390i	−0.201998	−	0.288483i	−0.907352	+	0.420373i	$0.861899\pi$
$674$	−21.8853			−0.842991
$675$	−24.6074	−	8.33525i	−0.947139	−	0.320824i
$676$	3.62584			0.139455
$677$	−0.0694054	−	0.0991212i	−0.00266747	−	0.00380954i	0.817816	−	0.575480i	$-0.195185\pi$
$677$	−0.0694054	−	0.0991212i	−0.00266747	−	0.00380954i	−0.820484	+	0.571670i	$0.806296\pi$
$678$	−0.572160	+	1.11438i	−0.0219737	+	0.0427976i
$679$	6.50112	−	17.8617i	0.249490	−	0.685468i
$680$	−9.91603	+	41.0185i	−0.380262	+	1.57299i
$681$	−25.0095	−	32.2158i	−0.958365	−	1.23451i
$682$	−17.0753	−	7.96234i	−0.653847	−	0.304894i
$683$	13.3758	−	3.58403i	0.511810	−	0.137139i	0.00633429	−	0.999980i	$-0.497984\pi$
$683$	13.3758	−	3.58403i	0.511810	−	0.137139i	0.505476	+	0.862841i	$0.331317\pi$
$684$	−1.33124	−	4.75350i	−0.0509011	−	0.181755i
$685$	−15.3720	+	6.02726i	−0.587335	+	0.230290i
$686$	17.7931	−	21.2049i	0.679342	−	0.809608i
$687$	−27.2576	−	29.4123i	−1.03994	−	1.12215i
$688$	−18.0809	−	12.6604i	−0.689329	−	0.482673i
$689$	0.0364828	+	0.206904i	0.00138988	+	0.00788241i
$690$	−0.140644	+	0.739551i	−0.00535424	+	0.0281542i
$691$	17.4891	+	14.6751i	0.665315	+	0.558266i	0.911675	−	0.410913i	$-0.134790\pi$
$691$	17.4891	+	14.6751i	0.665315	+	0.558266i	−0.246359	+	0.969179i	$0.579234\pi$
$692$	−0.719892	−	0.192894i	−0.0273662	−	0.00733274i
$693$	−0.150484	−	13.3642i	−0.00571640	−	0.507666i
$694$	11.8745	+	6.85575i	0.450750	+	0.260241i
$695$	19.1003	+	12.6855i	0.724517	+	0.481190i
$696$	31.0231	−	24.0835i	1.17593	−	0.912885i
$697$	34.0042	+	2.97498i	1.28800	+	0.112686i
$698$	−5.32004	−	11.4089i	−0.201366	−	0.431832i
$699$	35.6664	−	11.4667i	1.34903	−	0.433712i
$700$	2.14499	−	0.689488i	0.0810730	−	0.0260602i
$701$			15.6693i			0.591821i	0.955216	+	0.295910i	$0.0956230\pi$
$701$			15.6693i			0.591821i	−0.955216	+	0.295910i	$0.904377\pi$
$702$	−0.355429	−	2.38744i	−0.0134148	−	0.0901081i
$703$	−8.93432	+	8.93432i	−0.336964	+	0.336964i
$704$	−3.17504	+	18.0065i	−0.119664	+	0.678647i
$705$	−3.30306	+	32.7016i	−0.124400	+	1.23161i
$706$	−3.74859	−	1.36438i	−0.141080	−	0.0513490i
$707$	1.88471	−	21.5424i	0.0708820	−	0.810184i
$708$	−2.85265	+	3.76130i	−0.107209	+	0.141358i
$709$	2.91839	+	8.01821i	0.109602	+	0.301130i	0.982353	−	0.187036i	$-0.0598882\pi$
$709$	2.91839	+	8.01821i	0.109602	+	0.301130i	−0.872751	+	0.488166i	$0.837666\pi$
$710$	21.9868	−	27.5520i	0.825148	−	1.03401i
$711$	3.51012	−	5.13508i	0.131640	−	0.192580i
$712$	7.50148	−	27.9959i	0.281130	−	1.04919i
$713$	−0.0503766	−	0.575807i	−0.00188662	−	0.0215641i
$714$	−26.9724	+	14.2345i	−1.00942	+	0.532713i
$715$	−0.0470001	−	1.90979i	−0.00175770	−	0.0714223i
$716$	−1.89856	+	0.334767i	−0.0709523	+	0.0125108i
$717$	−5.46502	−	24.0106i	−0.204095	−	0.896692i
$718$	21.2480	−	1.85896i	0.792968	−	0.0693758i
$719$	−19.9277	−	34.5157i	−0.743176	−	1.28722i	−0.951042	−	0.309062i	$-0.899985\pi$
$719$	−19.9277	−	34.5157i	−0.743176	−	1.28722i	0.207866	−	0.978157i	$-0.433348\pi$
$720$	6.28065	+	29.4095i	0.234066	+	1.09603i
$721$	2.38550	−	4.13180i	0.0888406	−	0.153876i
$722$	−9.76600	+	20.9433i	−0.363453	+	0.779427i
$723$	13.3147	−	5.60315i	0.495178	−	0.208383i
$724$	3.61621	+	4.30963i	0.134395	+	0.160166i
$725$	26.3901	−	34.7923i	0.980105	−	1.29216i
$726$	8.39869	+	1.81240i	0.311704	+	0.0672644i
$727$	−37.5210	+	26.2725i	−1.39158	+	0.974393i	−0.393085	+	0.919502i	$0.628592\pi$
$727$	−37.5210	+	26.2725i	−1.39158	+	0.974393i	−0.998492	+	0.0548911i	$0.982519\pi$
$728$	−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
$732$	1.08818	−	0.701888i	0.0402201	−	0.0259425i
$733$	−33.5325	+	15.6365i	−1.23855	+	0.577546i	−0.927847	−	0.372961i	$-0.878343\pi$
$733$	−33.5325	+	15.6365i	−1.23855	+	0.577546i	−0.310704	+	0.950507i	$0.600565\pi$
$734$	15.9308	−	13.3675i	0.588015	−	0.493403i
$735$	14.7344	+	8.77219i	0.543486	+	0.323567i
$736$	0.190850	−	0.0694636i	0.00703481	−	0.00256046i
$737$	0.776169	+	2.89670i	0.0285906	+	0.106701i
$738$	19.9095	−	7.50139i	0.732879	−	0.276130i
$739$	9.45965	−	5.46153i	0.347979	−	0.200906i	−0.315816	−	0.948820i	$-0.602278\pi$
$739$	9.45965	−	5.46153i	0.347979	−	0.200906i	0.663795	+	0.747915i	$0.268945\pi$
$740$	−1.01650	+	0.896473i	−0.0373673	+	0.0329550i
$741$	−1.66157	+	2.64084i	−0.0610393	+	0.0970135i
$742$	0.949040	−	1.35537i	0.0348404	−	0.0497572i
$743$	−4.75185	+	6.78635i	−0.174329	+	0.248967i	−0.896802	−	0.442431i	$-0.854116\pi$
$743$	−4.75185	+	6.78635i	−0.174329	+	0.248967i	0.722474	+	0.691398i	$0.243005\pi$
$744$	−9.42606	−	17.8611i	−0.345576	−	0.654818i
$745$	2.69957	+	0.169381i	0.0989047	+	0.00620563i
$746$	−26.5695	+	15.3399i	−0.972778	+	0.561633i
$747$	7.30388	+	38.8586i	0.267235	+	1.42176i
$748$	1.46824	+	5.47954i	0.0536841	+	0.200352i
$749$	−16.6422	+	6.05726i	−0.608093	+	0.221328i
$750$	13.3012	+	26.0468i	0.485692	+	0.951095i
$751$	1.01418	−	0.851000i	0.0370080	−	0.0310534i	−0.624096	−	0.781348i	$-0.714533\pi$
$751$	1.01418	−	0.851000i	0.0370080	−	0.0310534i	0.661104	+	0.750294i	$0.270088\pi$
$752$	34.4801	−	16.0783i	1.25736	−	0.586317i
$753$	−0.406788	−	8.25077i	−0.0148242	−	0.300675i
$754$	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	$0.989283\pi$
$758$	−25.7998	+	18.0652i	−0.937092	+	0.656159i
$759$	−0.189514	−	0.589469i	−0.00687892	−	0.0213964i
$760$	16.2705	−	29.8544i	0.590195	−	1.08293i
$761$	6.97127	+	8.30804i	0.252708	+	0.301166i	0.877453	−	0.479663i	$-0.159241\pi$
$761$	6.97127	+	8.30804i	0.252708	+	0.301166i	−0.624744	+	0.780829i	$0.714797\pi$
$762$	−4.39718	+	34.9179i	−0.159293	+	1.26494i
$763$	0.314755	−	0.674994i	0.0113949	−	0.0244364i
$764$	−1.31601	+	2.27939i	−0.0476114	+	0.0824654i
$765$	−29.3835	−	38.9156i	−1.06236	−	1.40700i
$766$	−11.0760	−	19.1841i	−0.400191	−	0.693151i
$767$	2.97239	−	0.260050i	0.107327	−	0.00938988i
$768$	8.40504	−	7.78930i	0.303291	−	0.281072i
$769$	−44.1842	+	7.79087i	−1.59332	+	0.280946i	−0.898745	−	0.438471i	$-0.855520\pi$
$769$	−44.1842	+	7.79087i	−1.59332	+	0.280946i	−0.694579	+	0.719417i	$0.744409\pi$
$770$	−10.3735	+	10.8970i	−0.373835	+	0.392700i
$771$	−0.310649	+	8.17032i	−0.0111878	+	0.294247i
$772$	0.516085	+	5.89888i	0.0185743	+	0.212305i
$773$	−8.13915	+	30.3757i	−0.292745	+	1.09254i	0.650247	+	0.759723i	$0.274666\pi$
$773$	−8.13915	+	30.3757i	−0.292745	+	1.09254i	−0.942992	+	0.332816i	$0.892001\pi$
$774$	21.4819	−	6.01611i	0.772152	−	0.216244i
$775$	−15.2628	−	16.4711i	−0.548257	−	0.591659i
$776$	−10.5236	−	28.9133i	−0.377775	−	1.03793i
$777$	5.94620	+	0.748800i	0.213319	+	0.0268631i
$778$	−0.824033	+	9.41874i	−0.0295430	+	0.337678i
$779$	−25.8430	−	9.40608i	−0.925922	−	0.337008i
$780$	−0.195623	+	0.271560i	−0.00700442	+	0.00972343i
$781$	−5.03455	+	28.5524i	−0.180150	+	1.02168i
$782$	−0.999091	+	0.999091i	−0.0357274	+	0.0357274i
$783$	−1.21353	+	45.3655i	−0.0433680	+	1.62123i
$784$		−	19.8488i		−	0.708885i
$785$	−14.7895	+	43.9710i	−0.527861	+	1.56939i
$786$	11.9877	+	10.8612i	0.427588	+	0.387406i
$787$	−13.3215	−	28.5680i	−0.474860	−	1.01834i	−0.987190	−	0.159552i	$-0.948995\pi$
$787$	−13.3215	−	28.5680i	−0.474860	−	1.01834i	0.512330	−	0.858789i	$-0.328783\pi$
$788$	−2.05671	−	0.179939i	−0.0732674	−	0.00641007i
$789$	0.785181	+	5.71522i	0.0279532	+	0.203467i
$790$	−6.86361	+	1.38516i	−0.244196	+	0.0492819i
$791$	−0.665155	−	0.384027i	−0.0236502	−	0.0136544i
$792$	−14.0921	−	16.4154i	−0.500742	−	0.583295i
$793$	−0.790562	−	0.211830i	−0.0280737	−	0.00752232i
$794$	−0.539681	−	0.452846i	−0.0191526	−	0.0160709i
$795$	2.38246	+	1.15007i	0.0844971	+	0.0407887i
$796$	−1.25879	−	7.13898i	−0.0446168	−	0.253034i
$797$	−5.33729	−	3.73721i	−0.189057	−	0.132379i	0.475216	−	0.879869i	$-0.342370\pi$
$797$	−5.33729	−	3.73721i	−0.189057	−	0.132379i	−0.664273	+	0.747490i	$0.731259\pi$
$798$	23.9592	−	5.45332i	0.848147	−	0.193046i
$799$	−39.6531	+	47.2567i	−1.40283	+	1.67182i
$800$	4.20231	−	6.67820i	0.148574	−	0.236110i
$801$	19.5173	+	27.2161i	0.689608	+	0.961633i
$802$	13.6193	−	3.64928i	0.480914	−	0.128860i
$803$	−17.3326	−	8.08234i	−0.611655	−	0.285220i
$804$	0.198320	−	0.486516i	0.00699421	−	0.0171581i
$805$	−0.448643	−	0.108457i	−0.0158126	−	0.00382261i
$806$	0.713536	−	1.96042i	0.0251332	−	0.0690530i
$807$	−7.86211	−	12.1891i	−0.276759	−	0.429075i
$808$	−20.0778	−	28.6741i	−0.706335	−	1.00875i
$809$	21.5117			0.756312			0.378156	−	0.925742i	$-0.376558\pi$
$809$	21.5117			0.756312			0.378156	+	0.925742i	$0.376558\pi$
$810$	−27.0085	−	13.9401i	−0.948983	−	0.489806i
$811$	15.2216			0.534502			0.267251	−	0.963627i	$-0.413885\pi$
$811$	15.2216			0.534502			0.267251	+	0.963627i	$0.413885\pi$
$812$	−2.25734	−	3.22382i	−0.0792172	−	0.113134i
$813$	12.9460	+	20.0708i	0.454034	+	0.703914i
$814$	3.09539	−	8.50453i	0.108494	−	0.298083i
$815$	−15.2347	−	24.9489i	−0.533650	−	0.873924i
$816$	−21.3059	+	52.2673i	−0.745854	+	1.82972i
$817$	−26.1346	−	12.1868i	−0.914335	−	0.426362i
$818$	1.02522	−	0.274706i	0.0358459	−	0.00960488i
$819$	1.47276	−	0.145577i	0.0514624	−	0.00508687i
$820$	−2.70351	−	1.18058i	−0.0944106	−	0.0412278i
$821$	−32.2494	+	38.4334i	−1.12551	+	1.34133i	−0.192581	+	0.981281i	$0.561686\pi$
$821$	−32.2494	+	38.4334i	−1.12551	+	1.34133i	−0.932932	+	0.360053i	$0.882758\pi$
$822$	−18.8344	+	4.28686i	−0.656924	+	0.149522i
$823$	−2.87349	−	2.01204i	−0.100164	−	0.0701354i	0.522422	−	0.852687i	$-0.325029\pi$
$823$	−2.87349	−	2.01204i	−0.100164	−	0.0701354i	−0.622585	+	0.782552i	$0.713918\pi$
$824$	−1.34108	−	7.60564i	−0.0467187	−	0.264955i
$825$	−19.8584	−	13.5759i	−0.691379	−	0.472651i
$826$	−18.0008	−	15.1045i	−0.626327	−	0.525551i
$827$	2.56281	+	0.686704i	0.0891178	+	0.0238790i	0.303102	−	0.952958i	$-0.401978\pi$
$827$	2.56281	+	0.686704i	0.0891178	+	0.0238790i	−0.213985	+	0.976837i	$0.568644\pi$
$828$	−0.0359512	+	0.102346i	−0.00124939	+	0.00355678i
$829$	−13.2911	−	7.67359i	−0.461617	−	0.266515i	0.251107	−	0.967959i	$-0.419206\pi$
$829$	−13.2911	−	7.67359i	−0.461617	−	0.266515i	−0.712724	+	0.701444i	$0.752539\pi$
$830$	24.6246	−	37.0768i	0.854734	−	1.28695i
$831$	−0.0289927	−	0.211034i	−0.00100575	−	0.00732068i
$832$	−2.01695	−	0.176460i	−0.0699251	−	0.00611766i
$833$	13.6019	+	29.1693i	0.471277	+	1.01066i
$834$	19.8784	+	18.0103i	0.688331	+	0.623647i
$835$	34.1038	+	11.4707i	1.18021	+	0.396961i
$836$		−	4.57055i		−	0.158076i
$837$	22.8654	+	4.66544i	0.790343	+	0.161261i
$838$	−22.8981	+	22.8981i	−0.791002	+	0.791002i
$839$	2.05282	−	11.6421i	0.0708712	−	0.401931i	−0.928649	−	0.370960i	$-0.879029\pi$
$839$	2.05282	−	11.6421i	0.0708712	−	0.401931i	0.999520	−	0.0309713i	$-0.00986003\pi$
$840$	−15.9184	+	2.58743i	−0.549236	+	0.0892749i
$841$	−44.4266	−	16.1700i	−1.53195	−	0.557585i
$842$	−2.34525	+	26.8064i	−0.0808227	+	0.923808i
$843$	−41.2902	−	5.19964i	−1.42211	−	0.179085i
$844$	−0.0336436	−	0.0924350i	−0.00115806	−	0.00318174i
$845$	−28.6770	+	3.22159i	−0.986517	+	0.110826i
$846$	−9.53301	+	37.2504i	−0.327752	+	1.28070i
$847$	−1.36346	+	5.08850i	−0.0468490	+	0.174843i
$848$	−0.266887	−	3.05053i	−0.00916493	−	0.104756i
$849$	1.04911	−	27.5924i	0.0360054	−	0.946970i
$850$	−6.86126	+	54.4618i	−0.235339	+	1.86802i
$851$	0.273436	−	0.0482142i	0.00937327	−	0.00165276i
$852$	3.72550	−	3.45258i	0.127634	−	0.118283i
$853$	−33.5308	+	2.93357i	−1.14807	+	0.100443i	−0.645268	−	0.763956i	$-0.723254\pi$
$853$	−33.5308	+	2.93357i	−1.14807	+	0.100443i	−0.502805	+	0.864400i	$0.667699\pi$
$854$	3.22284	+	5.58211i	0.110283	+	0.191016i
$855$	14.7524	+	36.4129i	0.504520	+	1.24529i
$856$	−14.3341	+	24.8274i	−0.489929	+	0.848583i
$857$	−15.6821	+	33.6303i	−0.535689	+	1.14879i	0.433201	+	0.901297i	$0.357384\pi$
$857$	−15.6821	+	33.6303i	−0.535689	+	1.14879i	−0.968890	+	0.247491i	$0.920394\pi$
$858$	0.279230	−	2.21736i	0.00953276	−	0.0756993i
$859$	−18.6876	−	22.2710i	−0.637613	−	0.759878i	0.346378	−	0.938095i	$-0.387412\pi$
$859$	−18.6876	−	22.2710i	−0.637613	−	0.759878i	−0.983991	+	0.178217i	$0.942967\pi$
$860$	−2.71605	−	1.48024i	−0.0926166	−	0.0504757i
$861$	3.99262	+	12.4187i	0.136068	+	0.423230i
$862$	16.9417	−	11.8627i	0.577038	−	0.404046i
$863$	−9.57951	−	9.57951i	−0.326090	−	0.326090i	0.525007	−	0.851098i	$-0.324063\pi$
$863$	−9.57951	−	9.57951i	−0.326090	−	0.326090i	−0.851098	+	0.525007i	$0.824063\pi$
$864$	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
$867$	−3.05688	−	62.0020i	−0.103817	−	2.10570i
$868$	−1.83416	+	0.855281i	−0.0622553	+	0.0290301i
$869$	4.41177	−	3.70191i	0.149659	−	0.125579i
$870$	36.6041	−	35.6361i	1.24100	−	1.20818i
$871$	−0.312045	+	0.113575i	−0.0105733	+	0.00384835i
$872$	−0.312030	−	1.16451i	−0.0105667	−	0.0394353i
$873$	33.5446	+	11.7832i	1.13531	+	0.398801i
$874$	0.985869	−	0.569192i	0.0333475	−	0.0192532i
$875$	−16.3522	+	7.35904i	−0.552807	+	0.248781i
$876$	1.56378	+	2.96315i	0.0528353	+	0.100115i
$877$	12.6973	−	18.1337i	0.428759	−	0.612331i	−0.545405	−	0.838172i	$-0.683624\pi$
$877$	12.6973	−	18.1337i	0.428759	−	0.612331i	0.974164	+	0.225842i	$0.0725132\pi$
$878$	9.75663	−	13.9339i	0.329270	−	0.470247i
$879$	4.86133	−	7.72641i	0.163969	−	0.260605i
$880$	−1.74360	+	27.7894i	−0.0587769	+	0.936779i
$881$	38.5171	−	22.2379i	1.29768	−	0.749213i	0.317673	−	0.948200i	$-0.397098\pi$
$881$	38.5171	−	22.2379i	1.29768	−	0.749213i	0.980002	+	0.198987i	$0.0637651\pi$
$882$	15.5116	+	12.7210i	0.522304	+	0.428337i
$883$	4.08387	+	15.2412i	0.137433	+	0.512907i	0.999976	+	0.00692327i	$0.00220376\pi$
$883$	4.08387	+	15.2412i	0.137433	+	0.512907i	−0.862543	+	0.505984i	$0.831130\pi$
$884$	−0.590280	+	0.214844i	−0.0198533	+	0.00722599i
$885$	19.2198	−	32.2830i	0.646068	−	1.08518i
$886$	7.81768	−	6.55981i	0.262640	−	0.220381i
$887$	25.0117	−	11.6632i	0.839811	−	0.391610i	0.0453839	−	0.998970i	$-0.485549\pi$
$887$	25.0117	−	11.6632i	0.839811	−	0.391610i	0.794427	+	0.607359i	$0.207771\pi$
$888$	8.15255	−	5.25850i	0.273582	−	0.176464i
$889$	−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
$893$	40.7139	−	28.5082i	1.36244	−	0.953990i
$894$	3.09313	+	0.667484i	0.103450	+	0.0223240i
$895$	14.7183	−	4.33457i	0.491980	−	0.144889i
$896$	13.5031	+	16.0924i	0.451108	+	0.537609i
$897$	0.0631956	−	0.0265943i	0.00211004	−	0.000887957i
$898$	−7.27874	+	15.6093i	−0.242895	+	0.520890i
$899$	−19.6120	+	33.9690i	−0.654098	+	1.13293i
$900$	1.33476	+	3.99737i	0.0444920	+	0.133246i
$901$	2.48266	+	4.30010i	0.0827095	+	0.143257i
$902$	19.6241	−	1.71688i	0.653410	−	0.0571660i
$903$	3.03558	+	13.3368i	0.101018	+	0.443822i
$904$	−1.22439	+	0.215893i	−0.0407226	+	0.00718049i
$905$	−32.4299	−	30.8721i	−1.07801	−	1.02622i
$906$	−37.4057	+	19.7406i	−1.24272	+	0.655838i
$907$	−0.325298	−	3.71818i	−0.0108014	−	0.123460i	0.988880	−	0.148718i	$-0.0475148\pi$
$907$	−0.325298	−	3.71818i	−0.0108014	−	0.123460i	−0.999681	+	0.0252582i	$0.991959\pi$
$908$	−1.71223	+	6.39013i	−0.0568223	+	0.212064i
$909$	40.3316	+	3.07139i	1.33771	+	0.101871i
$910$	−1.30216	−	1.03914i	−0.0431663	−	0.0344471i
$911$	−8.20345	−	22.5388i	−0.271792	−	0.746743i	−0.998228	−	0.0595086i	$-0.981047\pi$
$911$	−8.20345	−	22.5388i	−0.271792	−	0.746743i	0.726435	−	0.687235i	$-0.241176\pi$
$912$	27.4802	−	36.2335i	0.909961	−	1.19981i
$913$	−3.19067	+	36.4695i	−0.105596	+	1.20697i
$914$	10.5269	+	3.83148i	0.348199	+	0.126734i
$915$	−7.98281	+	6.51813i	−0.263904	+	0.215483i
$916$	−1.12953	+	6.40589i	−0.0373207	+	0.211656i
$917$	−7.01316	+	7.01316i	−0.231595	+	0.231595i
$918$	−27.1916	−	50.1481i	−0.897456	−	1.65513i
$919$			55.8452i			1.84216i	0.389370	+	0.921081i	$0.372693\pi$
$919$			55.8452i			1.84216i	−0.389370	+	0.921081i	$0.627307\pi$
$920$	−0.669177	+	0.332325i	−0.0220621	+	0.0109564i
$921$	−36.4951	+	11.7332i	−1.20255	+	0.386620i
$922$	−26.6026	−	57.0495i	−0.876110	−	1.87882i
$923$	−3.19821	−	0.279807i	−0.105270	−	0.00920995i
$924$	−1.71249	+	1.32942i	−0.0563367	+	0.0437348i
$925$	7.24304	−	7.99343i	0.238150	−	0.262822i
$926$	4.35356	+	2.51353i	0.143067	+	0.0825997i
$927$	7.77817	+	4.37471i	0.255469	+	0.143684i
$928$	−13.3128	−	3.56716i	−0.437014	−	0.117098i
$929$	−43.9037	−	36.8395i	−1.44043	−	1.20867i	−0.939208	−	0.343349i	$-0.888439\pi$
$929$	−43.9037	−	36.8395i	−1.44043	−	1.20867i	−0.501224	−	0.865317i	$-0.667117\pi$
$930$	−14.7781	−	21.7189i	−0.484593	−	0.712192i
$931$	−4.50286	−	25.5370i	−0.147575	−	0.836942i
$932$	−4.97805	−	3.48567i	−0.163062	−	0.114177i
$933$	−16.9413	−	18.2805i	−0.554635	−	0.598478i
$934$	4.34306	−	5.17586i	0.142109	−	0.169359i
$935$	−16.4810	−	42.0335i	−0.538986	−	1.37464i
$936$	1.67478	−	1.71293i	0.0547420	−	0.0559889i
$937$	54.7688	−	14.6753i	1.78922	−	0.479420i	0.797006	−	0.603971i	$-0.206416\pi$
$937$	54.7688	−	14.6753i	1.78922	−	0.479420i	0.992213	+	0.124551i	$0.0397491\pi$
$938$	2.37019	+	1.10524i	0.0773895	+	0.0360873i
$939$	22.5749	+	29.0798i	0.736705	+	0.948982i
$940$	4.55023	−	2.77853i	0.148412	−	0.0906258i
$941$	13.7044	−	37.6526i	0.446751	−	1.22744i	−0.488222	−	0.872719i	$-0.662354\pi$
$941$	13.7044	−	37.6526i	0.446751	−	1.22744i	0.934973	−	0.354719i	$-0.115423\pi$
$942$	−24.7885	+	48.2799i	−0.807651	+	1.57304i
$943$	0.346638	+	0.495050i	0.0112881	+	0.0161211i
$944$	−43.4886			−1.41543
$945$	9.35215	−	16.1187i	0.304226	−	0.524341i
$946$	20.6552			0.671557
$947$	26.6669	+	38.0843i	0.866557	+	1.23757i	0.970041	+	0.242941i	$0.0781121\pi$
$947$	26.6669	+	38.0843i	0.866557	+	1.23757i	−0.103484	+	0.994631i	$0.532999\pi$
$948$	−1.00774	+	0.0496845i	−0.0327298	+	0.00161368i
$949$	0.724290	−	1.98997i	0.0235114	−	0.0645972i
$950$	16.6965	−	40.9534i	0.541706	−	1.32870i
$951$	39.4470	−	5.41939i	1.27916	−	0.175736i
$952$	−27.4331	−	12.7922i	−0.889110	−	0.414599i
$953$	55.6950	−	14.9234i	1.80414	−	0.483417i	0.809526	−	0.587085i	$-0.199724\pi$
$953$	55.6950	−	14.9234i	1.80414	−	0.483417i	0.994612	+	0.103668i	$0.0330578\pi$
$954$	2.55501	+	1.74650i	0.0827214	+	0.0565449i
$955$	8.38311	−	19.1971i	0.271271	−	0.621204i
$956$	−2.56752	+	3.05985i	−0.0830396	+	0.0989627i
$957$	−12.4094	+	40.1442i	−0.401139	+	1.29768i
$958$	45.4622	+	31.8330i	1.46882	+	1.02848i
$959$	−2.05655	−	11.6633i	−0.0664095	−	0.376627i
$960$	−16.6476	+	19.3085i	−0.537300	+	0.623179i
$961$	−8.29622	−	6.96135i	−0.267620	−	0.224560i
$962$	0.968010	+	0.259378i	0.0312099	+	0.00836267i
$963$	−11.6797	−	30.9992i	−0.376374	−	0.998936i
$964$	−2.02929	−	1.17161i	−0.0653589	−	0.0377350i
$965$	−9.32295	−	46.1960i	−0.300116	−	1.48710i
$966$	−0.500021	−	0.203825i	−0.0160879	−	0.00655796i
$967$	25.9600	+	2.27121i	0.834818	+	0.0730371i	0.496545	−	0.868011i	$-0.334602\pi$
$967$	25.9600	+	2.27121i	0.834818	+	0.0730371i	0.338273	+	0.941048i	$0.390157\pi$
$968$	3.60388	+	7.72854i	0.115833	+	0.248405i
$969$	−15.5544	+	72.0794i	−0.499679	+	2.31552i
$970$	−17.8018	−	35.8461i	−0.571580	−	1.15095i
$971$		−	24.3222i		−	0.780536i	−0.920701	−	0.390268i	$-0.872382\pi$
$971$		−	24.3222i		−	0.780536i	0.920701	−	0.390268i	$-0.127618\pi$
$972$	−3.54828	−	2.56731i	−0.113811	−	0.0823466i
$973$	−11.6294	+	11.6294i	−0.372822	+	0.372822i
$974$	−3.35887	+	19.0491i	−0.107625	+	0.610372i
$975$	1.30591	−	2.32160i	0.0418225	−	0.0743507i
$976$	11.2096	+	4.07998i	0.358812	+	0.130597i
$977$	0.384646	−	4.39652i	0.0123059	−	0.140657i	−0.987556	−	0.157267i	$-0.949732\pi$
$977$	0.384646	−	4.39652i	0.0123059	−	0.140657i	0.999862	+	0.0166097i	$0.00528728\pi$
$978$	−13.2647	−	31.5208i	−0.424159	−	1.00792i
$979$	10.6057	+	29.1388i	0.338958	+	0.931280i
$980$	−0.310529	−	2.76418i	−0.00991949	−	0.0882984i
$981$	1.26911	+	0.574487i	0.0405194	+	0.0183420i
$982$	−8.97872	+	33.5090i	−0.286522	+	1.06932i
$983$	−0.550651	−	6.29396i	−0.0175630	−	0.200746i	−0.999907	−	0.0136609i	$-0.995651\pi$
$983$	−0.550651	−	6.29396i	−0.0175630	−	0.200746i	0.982344	−	0.187085i	$-0.0599041\pi$
$984$	17.8727	+	11.2452i	0.569760	+	0.358484i
$985$	16.4266	−	0.404258i	0.523394	−	0.0128807i
$986$	94.4260	−	16.6499i	3.00714	−	0.530240i
$987$	−22.5237	−	6.96254i	−0.716938	−	0.221620i
$988$	0.504179	−	0.0441099i	0.0160401	−	0.00140332i
$989$	0.316839	+	0.548781i	0.0100749	+	0.0174502i
$990$	−20.5997	−	19.1726i	−0.654701	−	0.609346i
$991$	3.28793	−	5.69486i	0.104445	−	0.180903i	−0.809067	−	0.587717i	$-0.800027\pi$
$991$	3.28793	−	5.69486i	0.104445	−	0.180903i	0.913511	+	0.406814i	$0.133360\pi$
$992$	−2.99522	+	6.42327i	−0.0950983	+	0.203939i
$993$	−19.2583	−	14.6059i	−0.611144	−	0.463505i
$994$	16.2520	+	19.3683i	0.515481	+	0.614326i
$995$	16.2989	+	55.3441i	0.516710	+	1.75453i
$996$	4.30628	−	4.75293i	0.136450	−	0.150602i
$997$	−16.4219	+	11.4987i	−0.520086	+	0.364168i	−0.803951	−	0.594696i	$-0.797272\pi$
$997$	−16.4219	+	11.4987i	−0.520086	+	0.364168i	0.283864	+	0.958864i	$0.408383\pi$
$998$	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.2.13	✓	192
3.2	odd	2		405.2.r.a.332.4		192
5.2	odd	4		675.2.ba.b.218.4		192
5.3	odd	4	inner	135.2.q.a.83.13	yes	192
5.4	even	2		675.2.ba.b.407.4		192
15.8	even	4		405.2.r.a.8.4		192
27.13	even	9		405.2.r.a.152.4		192
27.14	odd	18	inner	135.2.q.a.122.13	yes	192
135.13	odd	36		405.2.r.a.233.4		192
135.14	odd	18		675.2.ba.b.257.4		192
135.68	even	36	inner	135.2.q.a.68.13	yes	192
135.122	even	36		675.2.ba.b.68.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.13	✓	192	1.1	even	1	trivial
135.2.q.a.68.13	yes	192	135.68	even	36	inner
135.2.q.a.83.13	yes	192	5.3	odd	4	inner
135.2.q.a.122.13	yes	192	27.14	odd	18	inner
405.2.r.a.8.4		192	15.8	even	4
405.2.r.a.152.4		192	27.13	even	9
405.2.r.a.233.4		192	135.13	odd	36
405.2.r.a.332.4		192	3.2	odd	2
675.2.ba.b.68.4		192	135.122	even	36
675.2.ba.b.218.4		192	5.2	odd	4
675.2.ba.b.257.4		192	135.14	odd	18
675.2.ba.b.407.4		192	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.866263 + 1.23715i) q^{2} +(-0.938839 - 1.45553i) q^{3} +(-0.0960923 + 0.264011i) q^{4} +(0.525423 - 2.17346i) q^{5} +(0.987435 - 2.42236i) q^{6} +(1.45360 + 0.677826i) q^{7} +(2.50778 - 0.671958i) q^{8} +(-1.23716 + 2.73303i) q^{9} +O(q^{10})\)	\(q+(0.866263 + 1.23715i) q^{2} +(-0.938839 - 1.45553i) q^{3} +(-0.0960923 + 0.264011i) q^{4} +(0.525423 - 2.17346i) q^{5} +(0.987435 - 2.42236i) q^{6} +(1.45360 + 0.677826i) q^{7} +(2.50778 - 0.671958i) q^{8} +(-1.23716 + 2.73303i) q^{9} +(3.14405 - 1.23276i) q^{10} +(-1.78545 + 2.12782i) q^{11} +(0.474493 - 0.107999i) q^{12} +(-0.251952 - 0.176418i) q^{13} +(0.420628 + 2.38550i) q^{14} +(-3.65683 + 1.27576i) q^{15} +(3.43416 + 2.88160i) q^{16} +(-7.02145 - 1.88139i) q^{17} +(-4.45287 + 0.836964i) q^{18} +(5.07203 + 2.92834i) q^{19} +(0.523329 + 0.347571i) q^{20} +(-0.378100 - 2.75214i) q^{21} +(-4.17910 - 0.365624i) q^{22} +(-0.0543910 - 0.116642i) q^{23} +(-3.33246 - 3.01930i) q^{24} +(-4.44786 - 2.28397i) q^{25} -0.464527i q^{26} +(5.13951 - 0.765143i) q^{27} +(-0.318634 + 0.318634i) q^{28} +(-1.51659 + 8.60103i) q^{29} +(-4.74609 - 3.41892i) q^{30} +(4.22026 + 1.53605i) q^{31} +(-0.137538 + 1.57207i) q^{32} +(4.77337 + 0.601106i) q^{33} +(-3.75485 - 10.3164i) q^{34} +(2.23699 - 2.80320i) q^{35} +(-0.602668 - 0.589247i) q^{36} +(-0.558369 + 2.08386i) q^{37} +(0.770913 + 8.81158i) q^{38} +(-0.0202409 + 0.532353i) q^{39} +(-0.142827 - 5.80362i) q^{40} +(-4.62442 + 0.815410i) q^{41} +(3.07728 - 2.85184i) q^{42} +(-4.90494 + 0.429127i) q^{43} +(-0.390200 - 0.675847i) q^{44} +(5.29009 + 4.12492i) q^{45} +(0.0971868 - 0.168333i) q^{46} +(3.58654 - 7.69135i) q^{47} +(0.970146 - 7.70389i) q^{48} +(-2.84600 - 3.39173i) q^{49} +(-1.02740 - 7.48120i) q^{50} +(3.85358 + 11.9863i) q^{51} +(0.0707870 - 0.0495656i) 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} +(-0.499526 - 10.1318i) q^{57} +(-11.9546 + 5.57450i) q^{58} +(-7.43127 + 6.23558i) q^{59} +(0.0145787 - 1.08804i) q^{60} +(2.50049 - 0.910105i) q^{61} +(1.75553 + 6.55173i) q^{62} +(-3.65086 + 3.13415i) q^{63} +(5.70071 - 3.29131i) q^{64} +(-0.515819 + 0.454912i) q^{65} +(3.39133 + 6.42609i) q^{66} +(0.619257 - 0.884390i) q^{67} +(1.17142 - 1.67295i) q^{68} +(-0.118712 + 0.188676i) q^{69} +(5.40580 + 0.339179i) q^{70} +(9.03942 - 5.21891i) q^{71} +(-1.26605 + 7.68515i) q^{72} +(1.78199 + 6.65047i) q^{73} +(-3.06175 + 1.11439i) q^{74} +(0.851425 + 8.61830i) q^{75} +(-1.26050 + 1.05768i) q^{76} +(-4.03763 + 1.88278i) q^{77} +(-0.676135 + 0.436116i) 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} +(10.7962 - 7.55956i) q^{83} +(0.762929 + 0.164636i) q^{84} +(-7.77836 + 14.2723i) q^{85} +(-4.77986 - 5.69642i) q^{86} +(13.9429 - 5.86754i) q^{87} +(-3.04772 + 6.53585i) q^{88} +(5.58181 - 9.66798i) q^{89} +(-0.520536 + 10.1179i) q^{90} +(-0.246656 - 0.427222i) q^{91} +(0.0360214 - 0.00315146i) q^{92} +(-1.72638 - 7.58484i) q^{93} +(12.6222 - 2.22564i) q^{94} +(9.02959 - 9.48524i) q^{95} +(2.41732 - 1.27573i) q^{96} +(-1.03291 - 11.8062i) q^{97} +(1.73070 - 6.45906i) 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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