LMFDB - Embedded newform 156.2.w.c.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	156.67
Dual form			156.2.w.c.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39918 - 0.205665i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.91540 + 0.575524i) q^{4} +(-1.90811 + 1.90811i) q^{5} +(-1.31456 + 0.521479i) q^{6} +(1.18978 + 4.44032i) q^{7} +(-2.56163 - 1.19919i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.39918 - 0.205665i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.91540 + 0.575524i) q^{4} +(-1.90811 + 1.90811i) q^{5} +(-1.31456 + 0.521479i) q^{6} +(1.18978 + 4.44032i) q^{7} +(-2.56163 - 1.19919i) q^{8} +(0.500000 - 0.866025i) q^{9} +(3.06221 - 2.27735i) q^{10} +(3.19083 + 0.854979i) q^{11} +(1.94655 - 0.459284i) q^{12} +(-3.28338 - 1.48977i) q^{13} +(-0.751497 - 6.45749i) q^{14} +(-0.698415 + 2.60652i) q^{15} +(3.33754 + 2.20472i) q^{16} +(1.84571 + 1.06562i) q^{17} +(-0.877700 + 1.10889i) q^{18} +(3.91483 - 1.04898i) q^{19} +(-4.75295 + 2.55663i) q^{20} +(3.25054 + 3.25054i) q^{21} +(-4.28870 - 1.85251i) q^{22} +(2.32540 + 4.02770i) q^{23} +(-2.81803 + 0.242283i) q^{24} -2.28173i q^{25} +(4.28765 + 2.75973i) q^{26} -1.00000i q^{27} +(-0.276600 + 9.18974i) q^{28} +(-3.13929 - 5.43742i) q^{29} +(1.51328 - 3.50335i) q^{30} +(-5.89497 - 5.89497i) q^{31} +(-4.21639 - 3.77122i) q^{32} +(3.19083 - 0.854979i) q^{33} +(-2.36332 - 1.87059i) q^{34} +(-10.7428 - 6.20237i) q^{35} +(1.45612 - 1.37103i) q^{36} +(-0.0344030 + 0.128394i) q^{37} +(-5.69328 + 0.662561i) q^{38} +(-3.58838 + 0.351516i) q^{39} +(7.17604 - 2.59967i) q^{40} +(1.31950 + 0.353560i) q^{41} +(-3.87956 - 5.21660i) q^{42} +(3.76848 - 6.52719i) q^{43} +(5.61966 + 3.47403i) q^{44} +(0.698415 + 2.60652i) q^{45} +(-2.42529 - 6.11373i) q^{46} +(-0.970719 + 0.970719i) q^{47} +(3.99276 + 0.240572i) q^{48} +(-12.2386 + 7.06599i) q^{49} +(-0.469273 + 3.19255i) q^{50} +2.13124 q^{51} +(-5.43161 - 4.74317i) q^{52} +2.42711 q^{53} +(-0.205665 + 1.39918i) q^{54} +(-7.71982 + 4.45704i) q^{55} +(2.27702 - 12.8012i) q^{56} +(2.86585 - 2.86585i) q^{57} +(3.27415 + 8.25356i) q^{58} +(-0.519814 - 1.93997i) q^{59} +(-2.83786 + 4.59059i) q^{60} +(2.30863 - 3.99867i) q^{61} +(7.03573 + 9.46050i) q^{62} +(4.44032 + 1.18978i) q^{63} +(5.12388 + 6.14377i) q^{64} +(9.10767 - 3.42241i) q^{65} +(-4.64038 + 0.540028i) q^{66} +(-2.14394 + 8.00130i) q^{67} +(2.92199 + 3.10335i) q^{68} +(4.02770 + 2.32540i) q^{69} +(13.7555 + 10.8876i) q^{70} +(14.4065 - 3.86021i) q^{71} +(-2.31934 + 1.61884i) q^{72} +(-5.48681 - 5.48681i) q^{73} +(0.0745421 - 0.172571i) q^{74} +(-1.14087 - 1.97604i) q^{75} +(8.10219 + 0.243866i) q^{76} +15.1855i q^{77} +(5.09307 + 0.246169i) q^{78} +1.92264i q^{79} +(-10.5752 + 2.16155i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.77351 - 0.766069i) q^{82} +(-4.23405 - 4.23405i) q^{83} +(4.35533 + 8.09685i) q^{84} +(-5.55513 + 1.48849i) q^{85} +(-6.61519 + 8.35767i) q^{86} +(-5.43742 - 3.13929i) q^{87} +(-7.14842 - 6.01655i) q^{88} +(-0.809823 + 3.02230i) q^{89} +(-0.441138 - 3.79063i) q^{90} +(2.70853 - 16.3517i) q^{91} +(2.13603 + 9.05300i) q^{92} +(-8.05268 - 2.15771i) q^{93} +(1.55785 - 1.15857i) q^{94} +(-5.46835 + 9.47146i) q^{95} +(-5.53711 - 1.15777i) q^{96} +(-1.15441 - 4.30832i) q^{97} +(18.5773 - 7.36952i) q^{98} +(2.33585 - 2.33585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.39918	−	0.205665i	−0.989369	−	0.145427i
$2$	−1.39918	−	0.205665i	−0.989369	−	0.145427i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	1.91540	+	0.575524i	0.957702	+	0.287762i
$5$	−1.90811	+	1.90811i	−0.853331	+	0.853331i	−0.990542	−	0.137211i	$-0.956186\pi$
$5$	−1.90811	+	1.90811i	−0.853331	+	0.853331i	0.137211	+	0.990542i	$0.456186\pi$
$6$	−1.31456	+	0.521479i	−0.536666	+	0.212893i
$7$	1.18978	+	4.44032i	0.449694	+	1.67828i	0.703236	+	0.710957i	$0.251738\pi$
$7$	1.18978	+	4.44032i	0.449694	+	1.67828i	−0.253541	+	0.967325i	$0.581595\pi$
$8$	−2.56163	−	1.19919i	−0.905672	−	0.423978i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	3.06221	−	2.27735i	0.968356	−	0.720162i
$11$	3.19083	+	0.854979i	0.962070	+	0.257786i	0.705476	−	0.708733i	$-0.250733\pi$
$11$	3.19083	+	0.854979i	0.962070	+	0.257786i	0.256594	+	0.966519i	$0.417400\pi$
$12$	1.94655	−	0.459284i	0.561921	−	0.132584i
$13$	−3.28338	−	1.48977i	−0.910646	−	0.413187i
$13$	−3.28338	−	1.48977i	−0.910646	−	0.413187i
$14$	−0.751497	−	6.45749i	−0.200846	−	1.72584i
$15$	−0.698415	+	2.60652i	−0.180330	+	0.673001i
$16$	3.33754	+	2.20472i	0.834386	+	0.551180i
$17$	1.84571	+	1.06562i	0.447651	+	0.258451i	0.706838	−	0.707376i	$-0.250121\pi$
$17$	1.84571	+	1.06562i	0.447651	+	0.258451i	−0.259187	+	0.965827i	$0.583455\pi$
$18$	−0.877700	+	1.10889i	−0.206876	+	0.261368i
$19$	3.91483	−	1.04898i	0.898123	−	0.240651i	0.219913	−	0.975519i	$-0.429423\pi$
$19$	3.91483	−	1.04898i	0.898123	−	0.240651i	0.678210	+	0.734868i	$0.262756\pi$
$20$	−4.75295	+	2.55663i	−1.06279	+	0.571680i
$21$	3.25054	+	3.25054i	0.709325	+	0.709325i
$22$	−4.28870	−	1.85251i	−0.914353	−	0.394956i
$23$	2.32540	+	4.02770i	0.484879	+	0.839834i	0.999849	−	0.0173736i	$-0.00553048\pi$
$23$	2.32540	+	4.02770i	0.484879	+	0.839834i	−0.514971	+	0.857208i	$0.672197\pi$
$24$	−2.81803	+	0.242283i	−0.575228	+	0.0494558i
$25$		−	2.28173i		−	0.456347i
$26$	4.28765	+	2.75973i	0.840877	+	0.541227i
$27$		−	1.00000i		−	0.192450i
$28$	−0.276600	+	9.18974i	−0.0522725	+	1.73670i
$29$	−3.13929	−	5.43742i	−0.582952	−	1.00970i	−0.995127	−	0.0985984i	$-0.968564\pi$
$29$	−3.13929	−	5.43742i	−0.582952	−	1.00970i	0.412175	−	0.911105i	$-0.364769\pi$
$30$	1.51328	−	3.50335i	0.276285	−	0.639621i
$31$	−5.89497	−	5.89497i	−1.05877	−	1.05877i	−0.998162	−	0.0606056i	$-0.980697\pi$
$31$	−5.89497	−	5.89497i	−1.05877	−	1.05877i	−0.0606056	−	0.998162i	$-0.519303\pi$
$32$	−4.21639	−	3.77122i	−0.745359	−	0.666663i
$33$	3.19083	−	0.854979i	0.555451	−	0.148833i
$34$	−2.36332	−	1.87059i	−0.405306	−	0.320804i
$35$	−10.7428	−	6.20237i	−1.81587	−	1.04839i
$36$	1.45612	−	1.37103i	0.242687	−	0.228504i
$37$	−0.0344030	+	0.128394i	−0.00565583	+	0.0211078i	−0.968696	−	0.248250i	$-0.920145\pi$
$37$	−0.0344030	+	0.128394i	−0.00565583	+	0.0211078i	0.963040	+	0.269358i	$0.0868113\pi$
$38$	−5.69328	+	0.662561i	−0.923572	+	0.107482i
$39$	−3.58838	+	0.351516i	−0.574600	+	0.0562875i
$40$	7.17604	−	2.59967i	1.13463	−	0.411044i
$41$	1.31950	+	0.353560i	0.206072	+	0.0552168i	0.360378	−	0.932806i	$-0.382648\pi$
$41$	1.31950	+	0.353560i	0.206072	+	0.0552168i	−0.154306	+	0.988023i	$0.549314\pi$
$42$	−3.87956	−	5.21660i	−0.598629	−	0.804939i
$43$	3.76848	−	6.52719i	0.574687	−	0.995388i	−0.421388	−	0.906880i	$-0.638457\pi$
$43$	3.76848	−	6.52719i	0.574687	−	0.995388i	0.996076	−	0.0885072i	$-0.0282096\pi$
$44$	5.61966	+	3.47403i	0.847195	+	0.523729i
$45$	0.698415	+	2.60652i	0.104114	+	0.388557i
$46$	−2.42529	−	6.11373i	−0.357589	−	0.901420i
$47$	−0.970719	+	0.970719i	−0.141594	+	0.141594i	−0.774351	−	0.632757i	$-0.781923\pi$
$47$	−0.970719	+	0.970719i	−0.141594	+	0.141594i	0.632757	+	0.774351i	$0.281923\pi$
$48$	3.99276	+	0.240572i	0.576305	+	0.0347236i
$49$	−12.2386	+	7.06599i	−1.74838	+	1.00943i
$50$	−0.469273	+	3.19255i	−0.0663652	+	0.451495i
$51$	2.13124			0.298434
$52$	−5.43161	−	4.74317i	−0.753228	−	0.657759i
$53$	2.42711			0.333389			0.166695	−	0.986009i	$-0.446691\pi$
$53$	2.42711			0.333389			0.166695	+	0.986009i	$0.446691\pi$
$54$	−0.205665	+	1.39918i	−0.0279874	+	0.190404i
$55$	−7.71982	+	4.45704i	−1.04094	+	0.600987i
$56$	2.27702	−	12.8012i	0.304280	−	1.71063i
$57$	2.86585	−	2.86585i	0.379592	−	0.379592i
$58$	3.27415	+	8.25356i	0.429917	+	1.08375i
$59$	−0.519814	−	1.93997i	−0.0676740	−	0.252563i	0.923798	−	0.382879i	$-0.125067\pi$
$59$	−0.519814	−	1.93997i	−0.0676740	−	0.252563i	−0.991472	+	0.130316i	$0.958401\pi$
$60$	−2.83786	+	4.59059i	−0.366366	+	0.592642i
$61$	2.30863	−	3.99867i	0.295590	−	0.511978i	−0.679532	−	0.733646i	$-0.737817\pi$
$61$	2.30863	−	3.99867i	0.295590	−	0.511978i	0.975122	+	0.221669i	$0.0711503\pi$
$62$	7.03573	+	9.46050i	0.893538	+	1.20149i
$63$	4.44032	+	1.18978i	0.559427	+	0.149898i
$64$	5.12388	+	6.14377i	0.640485	+	0.767971i
$65$	9.10767	−	3.42241i	1.12967	−	0.424497i
$66$	−4.64038	+	0.540028i	−0.571191	+	0.0664729i
$67$	−2.14394	+	8.00130i	−0.261924	+	0.977515i	0.702182	+	0.711998i	$0.252209\pi$
$67$	−2.14394	+	8.00130i	−0.261924	+	0.977515i	−0.964106	+	0.265517i	$0.914457\pi$
$68$	2.92199	+	3.10335i	0.354344	+	0.376336i
$69$	4.02770	+	2.32540i	0.484879	+	0.279945i
$70$	13.7555	+	10.8876i	1.64410	+	1.30132i
$71$	14.4065	−	3.86021i	1.70973	−	0.458122i	0.734375	−	0.678744i	$-0.237475\pi$
$71$	14.4065	−	3.86021i	1.70973	−	0.458122i	0.975360	+	0.220621i	$0.0708085\pi$
$72$	−2.31934	+	1.61884i	−0.273337	+	0.190782i
$73$	−5.48681	−	5.48681i	−0.642183	−	0.642183i	0.308909	−	0.951092i	$-0.400036\pi$
$73$	−5.48681	−	5.48681i	−0.642183	−	0.642183i	−0.951092	+	0.308909i	$0.900036\pi$
$74$	0.0745421	−	0.172571i	0.00866535	−	0.0200609i
$75$	−1.14087	−	1.97604i	−0.131736	−	0.228173i
$76$	8.10219	+	0.243866i	0.929385	+	0.0279734i
$77$			15.1855i			1.73055i
$78$	5.09307	+	0.246169i	0.576677	+	0.0278732i
$79$			1.92264i			0.216314i	0.994134	+	0.108157i	$0.0344949\pi$
$79$			1.92264i			0.216314i	−0.994134	+	0.108157i	$0.965505\pi$
$80$	−10.5752	+	2.16155i	−1.18235	+	0.241668i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.77351	−	0.766069i	−0.195851	−	0.0845982i
$83$	−4.23405	−	4.23405i	−0.464748	−	0.464748i	0.435460	−	0.900208i	$-0.356586\pi$
$83$	−4.23405	−	4.23405i	−0.464748	−	0.464748i	−0.900208	+	0.435460i	$0.856586\pi$
$84$	4.35533	+	8.09685i	0.475205	+	0.883439i
$85$	−5.55513	+	1.48849i	−0.602539	+	0.161450i
$86$	−6.61519	+	8.35767i	−0.713334	+	0.901230i
$87$	−5.43742	−	3.13929i	−0.582952	−	0.336568i
$88$	−7.14842	−	6.01655i	−0.762025	−	0.641367i
$89$	−0.809823	+	3.02230i	−0.0858410	+	0.320363i	−0.995472	−	0.0950539i	$-0.969698\pi$
$89$	−0.809823	+	3.02230i	−0.0858410	+	0.320363i	0.909631	+	0.415417i	$0.136364\pi$
$90$	−0.441138	−	3.79063i	−0.0465000	−	0.399567i
$91$	2.70853	−	16.3517i	0.283931	−	1.71413i
$92$	2.13603	+	9.05300i	0.222697	+	0.943840i
$93$	−8.05268	−	2.15771i	−0.835024	−	0.223744i
$94$	1.55785	−	1.15857i	0.160680	−	0.119497i
$95$	−5.46835	+	9.47146i	−0.561041	+	0.971751i
$96$	−5.53711	−	1.15777i	−0.565129	−	0.118165i
$97$	−1.15441	−	4.30832i	−0.117213	−	0.437443i	0.882230	−	0.470818i	$-0.156041\pi$
$97$	−1.15441	−	4.30832i	−0.117213	−	0.437443i	−0.999443	+	0.0333748i	$0.989374\pi$
$98$	18.5773	−	7.36952i	1.87659	−	0.744434i
$99$	2.33585	−	2.33585i	0.234761	−	0.234761i
$100$	1.31319	−	4.37044i	0.131319	−	0.437044i
$101$	14.9555	−	8.63457i	1.48813	−	0.859172i	0.488221	−	0.872720i	$-0.337646\pi$
$101$	14.9555	−	8.63457i	1.48813	−	0.859172i	0.999908	+	0.0135483i	$0.00431267\pi$
$102$	−2.98199	−	0.438322i	−0.295261	−	0.0434003i
$103$	13.0360			1.28448			0.642239	−	0.766504i	$-0.278006\pi$
$103$	13.0360			1.28448			0.642239	+	0.766504i	$0.278006\pi$
$104$	6.62429	+	7.75363i	0.649565	+	0.760306i
$105$	−12.4047			−1.21058
$106$	−3.39596	−	0.499171i	−0.329845	−	0.0484838i
$107$	−2.08525	+	1.20392i	−0.201589	+	0.116387i	−0.597396	−	0.801946i	$-0.703798\pi$
$107$	−2.08525	+	1.20392i	−0.201589	+	0.116387i	0.395807	+	0.918334i	$0.370465\pi$
$108$	0.575524	−	1.91540i	0.0553798	−	0.184310i
$109$	7.91560	−	7.91560i	0.758177	−	0.758177i	−0.217814	−	0.975990i	$-0.569893\pi$
$109$	7.91560	−	7.91560i	0.758177	−	0.758177i	0.975990	+	0.217814i	$0.0698925\pi$
$110$	11.7181	−	4.64850i	1.11727	−	0.443217i
$111$	0.0344030	+	0.128394i	0.00326539	+	0.0121866i
$112$	−5.81872	+	17.4429i	−0.549817	+	1.64820i
$113$	−2.53729	+	4.39471i	−0.238688	+	0.413420i	−0.960338	−	0.278838i	$-0.910051\pi$
$113$	−2.53729	+	4.39471i	−0.238688	+	0.413420i	0.721650	+	0.692258i	$0.243384\pi$
$114$	−4.59925	+	3.42044i	−0.430759	+	0.320353i
$115$	−12.1224	−	3.24818i	−1.13042	−	0.302895i
$116$	−2.88365	−	12.2216i	−0.267741	−	1.13475i
$117$	−2.93187	+	2.09861i	−0.271051	+	0.194016i
$118$	0.328329	+	2.82127i	0.0302251	+	0.259719i
$119$	−2.53571	+	9.46340i	−0.232448	+	0.867508i
$120$	4.91480	−	5.83940i	0.448658	−	0.533062i
$121$	−0.0759014	−	0.0438217i	−0.00690013	−	0.00398379i
$122$	−4.05258	+	5.12005i	−0.366903	+	0.463548i
$123$	1.31950	−	0.353560i	0.118976	−	0.0318794i
$124$	−7.89855	−	14.6839i	−0.709311	−	1.31866i
$125$	−5.18674	−	5.18674i	−0.463916	−	0.463916i
$126$	−5.96810	−	2.57793i	−0.531681	−	0.229660i
$127$	7.58605	+	13.1394i	0.673153	+	1.16594i	0.977005	+	0.213217i	$0.0683940\pi$
$127$	7.58605	+	13.1394i	0.673153	+	1.16594i	−0.303852	+	0.952719i	$0.598273\pi$
$128$	−5.90566	−	9.65003i	−0.521992	−	0.852950i
$129$		−	7.53695i		−	0.663592i
$130$	−13.4471	+	2.91543i	−1.17939	+	0.255700i
$131$			0.375409i			0.0327996i	0.999866	+	0.0163998i	$0.00522046\pi$
$131$			0.375409i			0.0327996i	−0.999866	+	0.0163998i	$0.994780\pi$
$132$	6.60378	+	0.198766i	0.574785	+	0.0173003i
$133$	9.31556	+	16.1350i	0.807761	+	1.39908i
$134$	4.64535	−	10.7543i	0.401297	−	0.929032i
$135$	1.90811	+	1.90811i	0.164224	+	0.164224i
$136$	−3.45014	−	4.94309i	−0.295847	−	0.423867i
$137$	4.74366	−	1.27106i	0.405278	−	0.108594i	−0.0504206	−	0.998728i	$-0.516056\pi$
$137$	4.74366	−	1.27106i	0.405278	−	0.108594i	0.455698	+	0.890134i	$0.349390\pi$
$138$	−5.15723	−	4.08200i	−0.439012	−	0.347483i
$139$	−4.31059	−	2.48872i	−0.365619	−	0.211090i	0.305924	−	0.952056i	$-0.401035\pi$
$139$	−4.31059	−	2.48872i	−0.365619	−	0.211090i	−0.671543	+	0.740966i	$0.734368\pi$
$140$	−17.0072	−	18.0628i	−1.43737	−	1.52658i
$141$	−0.355308	+	1.32603i	−0.0299223	+	0.111672i
$142$	−20.9512	+	2.43821i	−1.75818	+	0.204610i
$143$	−9.20298	−	7.56081i	−0.769592	−	0.632266i
$144$	3.57812	−	1.78804i	0.298176	−	0.149003i
$145$	16.3653	+	4.38506i	1.35906	+	0.364160i
$146$	6.54859	+	8.80547i	0.541965	+	0.728746i
$147$	−7.06599	+	12.2386i	−0.582793	+	1.00943i
$148$	−0.139789	+	0.226126i	−0.0114906	+	0.0185875i
$149$	−2.93823	−	10.9656i	−0.240709	−	0.898338i	−0.975492	−	0.220036i	$-0.929383\pi$
$149$	−2.93823	−	10.9656i	−0.240709	−	0.898338i	0.734783	−	0.678303i	$-0.237284\pi$
$150$	1.18988	+	2.99947i	0.0971529	+	0.244906i
$151$	−2.07767	+	2.07767i	−0.169079	+	0.169079i	−0.786574	−	0.617496i	$-0.788147\pi$
$151$	−2.07767	+	2.07767i	−0.169079	+	0.169079i	0.617496	+	0.786574i	$0.288147\pi$
$152$	−11.2863	−	2.00755i	−0.915436	−	0.162834i
$153$	1.84571	−	1.06562i	0.149217	−	0.0861504i
$154$	3.12312	−	21.2472i	0.251669	−	1.71215i
$155$	22.4964			1.80696
$156$	−7.07549	−	1.39190i	−0.566493	−	0.111441i
$157$	−3.38110			−0.269841			−0.134921	−	0.990856i	$-0.543078\pi$
$157$	−3.38110			−0.269841			−0.134921	+	0.990856i	$0.543078\pi$
$158$	0.395419	−	2.69012i	0.0314579	−	0.214014i
$159$	2.10194	−	1.21356i	0.166695	−	0.0962412i
$160$	15.2412	−	0.849438i	1.20492	−	0.0671540i
$161$	−15.1176	+	15.1176i	−1.19143	+	1.19143i
$162$	0.521479	+	1.31456i	0.0409712	+	0.103281i
$163$	1.57696	+	5.88530i	0.123517	+	0.460972i	0.999782	−	0.0208566i	$-0.00663934\pi$
$163$	1.57696	+	5.88530i	0.123517	+	0.460972i	−0.876265	+	0.481829i	$0.839973\pi$
$164$	2.32390	+	1.43662i	0.181466	+	0.112181i
$165$	−4.45704	+	7.71982i	−0.346980	+	0.600987i
$166$	5.05340	+	6.79499i	0.392220	+	0.527394i
$167$	−8.58784	−	2.30110i	−0.664547	−	0.178065i	−0.0892497	−	0.996009i	$-0.528447\pi$
$167$	−8.58784	−	2.30110i	−0.664547	−	0.178065i	−0.575297	+	0.817944i	$0.695114\pi$
$168$	−4.42865	−	12.2247i	−0.341678	−	0.943155i
$169$	8.56119	+	9.78294i	0.658553	+	0.752534i
$170$	8.07876	−	0.940173i	0.619612	−	0.0721080i
$171$	1.04898	−	3.91483i	0.0802171	−	0.299374i
$172$	10.9747	−	10.3334i	0.836814	−	0.787911i
$173$	−9.17800	−	5.29892i	−0.697791	−	0.402870i	0.108733	−	0.994071i	$-0.465321\pi$
$173$	−9.17800	−	5.29892i	−0.697791	−	0.402870i	−0.806524	+	0.591201i	$0.798654\pi$
$174$	6.96228	+	5.51072i	0.527809	+	0.417767i
$175$	10.1316	−	2.71476i	0.765878	−	0.205217i
$176$	8.76453	+	9.88841i	0.660651	+	0.745367i
$177$	−1.42016	−	1.42016i	−0.106746	−	0.106746i
$178$	1.75467	−	4.06219i	0.131518	−	0.304474i
$179$	4.72045	+	8.17605i	0.352823	+	0.611107i	0.986743	−	0.162292i	$-0.0518885\pi$
$179$	4.72045	+	8.17605i	0.352823	+	0.611107i	−0.633920	+	0.773399i	$0.718555\pi$
$180$	−0.162368	+	5.39449i	−0.0121022	+	0.402082i
$181$		−	9.56599i		−	0.711035i	−0.934670	−	0.355517i	$-0.884305\pi$
$181$		−	9.56599i		−	0.711035i	0.934670	−	0.355517i	$-0.115695\pi$
$182$	−7.15270	+	22.3220i	−0.530194	+	1.65461i
$183$		−	4.61727i		−	0.341318i
$184$	−1.12681	−	13.1061i	−0.0830694	−	0.966193i
$185$	−0.179344	−	0.310634i	−0.0131857	−	0.0228382i
$186$	10.8234	+	4.67517i	0.793608	+	0.342800i
$187$	4.97826	+	4.97826i	0.364046	+	0.364046i
$188$	−2.41799	+	1.30065i	−0.176350	+	0.0948595i
$189$	4.44032	−	1.18978i	0.322985	−	0.0865437i
$190$	9.59915	−	12.1276i	0.696395	−	0.879830i
$191$	3.86310	+	2.23036i	0.279524	+	0.161383i	0.633208	−	0.773982i	$-0.281738\pi$
$191$	3.86310	+	2.23036i	0.279524	+	0.161383i	−0.353684	+	0.935365i	$0.615071\pi$
$192$	7.50929	+	2.75872i	0.541936	+	0.199094i
$193$	−3.89124	+	14.5223i	−0.280097	+	1.04534i	0.672251	+	0.740324i	$0.265328\pi$
$193$	−3.89124	+	14.5223i	−0.280097	+	1.04534i	−0.952348	+	0.305014i	$0.901339\pi$
$194$	0.729157	+	6.26553i	0.0523504	+	0.449839i
$195$	6.17627	−	7.51773i	0.442292	−	0.538356i
$196$	−27.5086	+	6.49058i	−1.96490	+	0.463613i
$197$	−24.2708	−	6.50334i	−1.72922	−	0.463344i	−0.749219	−	0.662323i	$-0.769571\pi$
$197$	−24.2708	−	6.50334i	−1.72922	−	0.463344i	−0.980004	+	0.198979i	$0.936238\pi$
$198$	−3.74867	+	2.78787i	−0.266406	+	0.198125i
$199$	−11.6238	+	20.1330i	−0.823990	+	1.42719i	0.0786981	+	0.996898i	$0.474924\pi$
$199$	−11.6238	+	20.1330i	−0.823990	+	1.42719i	−0.902688	+	0.430295i	$0.858410\pi$
$200$	−2.73624	+	5.84495i	−0.193481	+	0.413301i
$201$	2.14394	+	8.00130i	0.151222	+	0.564368i
$202$	−22.7013	+	9.00549i	−1.59726	+	0.633624i
$203$	20.4088	−	20.4088i	1.43242	−	1.43242i
$204$	4.08219	+	1.22658i	0.285811	+	0.0858779i
$205$	−3.19238	+	1.84312i	−0.222966	+	0.128729i
$206$	−18.2397	−	2.68105i	−1.27082	−	0.186798i
$207$	4.65079			0.323252
$208$	−7.67391	−	12.2111i	−0.532090	−	0.846688i
$209$	13.3884			0.926094
$210$	17.3564	+	2.55122i	1.19771	+	0.176051i
$211$	−0.658163	+	0.379991i	−0.0453098	+	0.0261596i	−0.522484	−	0.852649i	$-0.674994\pi$
$211$	−0.658163	+	0.379991i	−0.0453098	+	0.0261596i	0.477174	+	0.878809i	$0.341661\pi$
$212$	4.64890	+	1.39686i	0.319288	+	0.0959368i
$213$	10.5463	−	10.5463i	0.722619	−	0.722619i
$214$	3.16525	−	1.25564i	0.216372	−	0.0858337i
$215$	5.26392	+	19.6452i	0.358996	+	1.33979i
$216$	−1.19919	+	2.56163i	−0.0815947	+	0.174297i
$217$	19.1618	−	33.1892i	1.30079	−	2.25303i
$218$	−12.7033	+	9.44738i	−0.860376	+	0.639857i
$219$	−7.49512	−	2.00831i	−0.506473	−	0.135709i
$220$	−17.3517	+	4.09409i	−1.16985	+	0.276024i
$221$	−4.47265	−	6.24852i	−0.300863	−	0.420321i
$222$	−0.0217299	−	0.186722i	−0.00145842	−	0.0125319i
$223$	2.51924	−	9.40191i	0.168700	−	0.629599i	−0.828839	−	0.559488i	$-0.810998\pi$
$223$	2.51924	−	9.40191i	0.168700	−	0.629599i	0.997539	−	0.0701111i	$-0.0223354\pi$
$224$	11.7288	−	23.2090i	0.783664	−	1.55072i
$225$	−1.97604	−	1.14087i	−0.131736	−	0.0760578i
$226$	4.45396	−	5.62716i	0.296273	−	0.374313i
$227$	−20.2028	+	5.41331i	−1.34090	+	0.359294i	−0.856769	−	0.515700i	$-0.827532\pi$
$227$	−20.2028	+	5.41331i	−1.34090	+	0.359294i	−0.484134	+	0.874994i	$0.660865\pi$
$228$	7.13863	−	3.83990i	0.472768	−	0.254304i
$229$	15.9940	+	15.9940i	1.05692	+	1.05692i	0.998279	+	0.0586364i	$0.0186753\pi$
$229$	15.9940	+	15.9940i	1.05692	+	1.05692i	0.0586364	+	0.998279i	$0.481325\pi$
$230$	16.2933	+	7.03794i	1.07435	+	0.464068i
$231$	7.59275	+	13.1510i	0.499567	+	0.865275i
$232$	1.52120	+	17.6933i	0.0998714	+	1.16162i
$233$			8.56900i			0.561374i	0.959799	+	0.280687i	$0.0905622\pi$
$233$			8.56900i			0.561374i	−0.959799	+	0.280687i	$0.909438\pi$
$234$	4.53382	−	2.33335i	0.296385	−	0.152536i
$235$		−	3.70447i		−	0.241653i
$236$	0.120846	−	4.01499i	0.00786643	−	0.261354i
$237$	0.961320	+	1.66505i	0.0624444	+	0.108157i
$238$	5.49420	−	12.7195i	0.356136	−	0.824481i
$239$	−12.2020	−	12.2020i	−0.789282	−	0.789282i	0.192094	−	0.981376i	$-0.438472\pi$
$239$	−12.2020	−	12.2020i	−0.789282	−	0.789282i	−0.981376	+	0.192094i	$0.938472\pi$
$240$	−8.07764	+	7.15957i	−0.521410	+	0.462148i
$241$	−13.4642	+	3.60772i	−0.867305	+	0.232394i	−0.664922	−	0.746913i	$-0.731535\pi$
$241$	−13.4642	+	3.60772i	−0.867305	+	0.232394i	−0.202383	+	0.979306i	$0.564869\pi$
$242$	0.0971870	+	0.0769246i	0.00624742	+	0.00494490i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	6.72330	−	6.33040i	0.430415	−	0.405262i
$245$	9.86998	−	36.8353i	0.630570	−	2.35332i
$246$	−1.91894	+	0.223318i	−0.122347	+	0.0142382i
$247$	−14.4166	−	2.38799i	−0.917307	−	0.151944i
$248$	8.03152	+	22.1699i	0.510002	+	1.40779i
$249$	−5.78382	−	1.54977i	−0.366535	−	0.0982127i
$250$	6.19045	+	8.32390i	0.391518	+	0.526450i
$251$	−0.381787	+	0.661274i	−0.0240982	+	0.0417393i	−0.877823	−	0.478985i	$-0.841005\pi$
$251$	−0.381787	+	0.661274i	−0.0240982	+	0.0417393i	0.853725	+	0.520724i	$0.174338\pi$
$252$	7.82025	+	4.83441i	0.492630	+	0.304539i
$253$	3.97633	+	14.8399i	0.249990	+	0.932974i
$254$	−7.91193	−	19.9446i	−0.496439	−	1.25144i
$255$	−4.06664	+	4.06664i	−0.254663	+	0.254663i
$256$	6.27841	+	14.7167i	0.392400	+	0.919794i
$257$	−16.1333	+	9.31459i	−1.00637	+	0.581028i	−0.910127	−	0.414329i	$-0.864016\pi$
$257$	−16.1333	+	9.31459i	−1.00637	+	0.581028i	−0.0962437	+	0.995358i	$0.530683\pi$
$258$	−1.55009	+	10.5455i	−0.0965041	+	0.656537i
$259$	−0.611041			−0.0379683
$260$	19.4145	−	1.31361i	1.20404	−	0.0814668i
$261$	−6.27859			−0.388635
$262$	0.0772084	−	0.525264i	0.00476995	−	0.0324509i
$263$	4.65297	−	2.68639i	0.286914	−	0.165650i	−0.349635	−	0.936886i	$-0.613694\pi$
$263$	4.65297	−	2.68639i	0.286914	−	0.165650i	0.636549	+	0.771236i	$0.280361\pi$
$264$	−9.19899	−	1.63627i	−0.566159	−	0.100706i
$265$	−4.63118	+	4.63118i	−0.284491	+	0.284491i
$266$	−9.71573	−	24.4917i	−0.595710	−	1.50168i
$267$	0.809823	+	3.02230i	0.0495603	+	0.184962i
$268$	−8.71146	+	14.0918i	−0.532137	+	0.860796i
$269$	−15.2311	+	26.3810i	−0.928656	+	1.60848i	−0.143084	+	0.989711i	$0.545702\pi$
$269$	−15.2311	+	26.3810i	−0.928656	+	1.60848i	−0.785573	+	0.618769i	$0.787632\pi$
$270$	−2.27735	−	3.06221i	−0.138595	−	0.186360i
$271$	13.4264	+	3.59758i	0.815593	+	0.218538i	0.642419	−	0.766354i	$-0.277931\pi$
$271$	13.4264	+	3.59758i	0.815593	+	0.218538i	0.173174	+	0.984891i	$0.444598\pi$
$272$	3.81075	+	7.62584i	0.231060	+	0.462385i
$273$	−5.83021	−	15.5153i	−0.352861	−	0.939028i
$274$	−6.89864	+	0.802835i	−0.416762	+	0.0485011i
$275$	1.95084	−	7.28062i	0.117640	−	0.439038i
$276$	6.37636	+	6.77211i	0.383812	+	0.407633i
$277$	−9.31107	−	5.37575i	−0.559448	−	0.322998i	0.193476	−	0.981105i	$-0.438024\pi$
$277$	−9.31107	−	5.37575i	−0.559448	−	0.322998i	−0.752924	+	0.658107i	$0.771357\pi$
$278$	5.51944	+	4.36870i	0.331034	+	0.262017i
$279$	−8.05268	+	2.15771i	−0.482101	+	0.129179i
$280$	20.0813	+	28.7709i	1.20009	+	1.71939i
$281$	12.8695	+	12.8695i	0.767729	+	0.767729i	0.977706	−	0.209977i	$-0.0673389\pi$
$281$	12.8695	+	12.8695i	0.767729	+	0.767729i	−0.209977	+	0.977706i	$0.567339\pi$
$282$	0.769856	−	1.78227i	0.0458443	−	0.106133i
$283$	−7.40659	−	12.8286i	−0.440276	−	0.762580i	0.557434	−	0.830221i	$-0.311786\pi$
$283$	−7.40659	−	12.8286i	−0.440276	−	0.762580i	−0.997710	+	0.0676412i	$0.978453\pi$
$284$	29.8159	+	0.897422i	1.76925	+	0.0532522i
$285$			10.9367i			0.647834i
$286$	11.3216	+	12.4717i	0.669462	+	0.737464i
$287$			6.27967i			0.370677i
$288$	−5.37416	+	1.76589i	−0.316676	+	0.104056i
$289$	−6.22890	−	10.7888i	−0.366406	−	0.634634i
$290$	−21.9961	−	9.50125i	−1.29166	−	0.557932i
$291$	−3.15391	−	3.15391i	−0.184885	−	0.184885i
$292$	−7.35167	−	13.6672i	−0.430224	−	0.799815i
$293$	−1.02830	+	0.275531i	−0.0600738	+	0.0160967i	−0.288731	−	0.957410i	$-0.593233\pi$
$293$	−1.02830	+	0.275531i	−0.0600738	+	0.0160967i	0.228657	+	0.973507i	$0.426567\pi$
$294$	12.4036	−	15.6708i	0.723395	−	0.913942i
$295$	4.69353	+	2.70981i	0.273268	+	0.157771i
$296$	0.242097	−	0.287642i	0.0140716	−	0.0167188i
$297$	0.854979	−	3.19083i	0.0496109	−	0.185150i
$298$	1.85587	+	15.9472i	0.107507	+	0.923794i
$299$	−1.63483	−	16.6888i	−0.0945444	−	0.965137i
$300$	−1.04796	−	4.44151i	−0.0605042	−	0.256431i
$301$	33.4664	+	8.96731i	1.92897	+	0.516867i
$302$	3.33434	−	2.47973i	0.191870	−	0.142692i
$303$	8.63457	−	14.9555i	0.496043	−	0.859172i
$304$	15.3786	+	5.13010i	0.882024	+	0.294232i
$305$	3.22477	+	12.0350i	0.184650	+	0.689123i
$306$	−2.80164	+	1.11140i	−0.160159	+	0.0635344i
$307$	21.5612	−	21.5612i	1.23056	−	1.23056i	0.266815	−	0.963748i	$-0.414029\pi$
$307$	21.5612	−	21.5612i	1.23056	−	1.23056i	0.963748	−	0.266815i	$-0.0859714\pi$
$308$	−8.73962	+	29.0864i	−0.497986	+	1.65735i
$309$	11.2895	−	6.51802i	0.642239	−	0.370797i
$310$	−31.4765	−	4.62673i	−1.78775	−	0.262780i
$311$	−28.5012			−1.61615			−0.808077	−	0.589076i	$-0.799492\pi$
$311$	−28.5012			−1.61615			−0.808077	+	0.589076i	$0.799492\pi$
$312$	9.61362	+	3.40270i	0.544264	+	0.192640i
$313$	17.1584			0.969849			0.484924	−	0.874556i	$-0.338847\pi$
$313$	17.1584			0.969849			0.484924	+	0.874556i	$0.338847\pi$
$314$	4.73077	+	0.695374i	0.266973	+	0.0392422i
$315$	−10.7428	+	6.20237i	−0.605289	+	0.349464i
$316$	−1.10652	+	3.68263i	−0.0622469	+	0.207164i
$317$	6.36886	−	6.36886i	0.357711	−	0.357711i	−0.505258	−	0.862969i	$-0.668603\pi$
$317$	6.36886	−	6.36886i	0.357711	−	0.357711i	0.862969	+	0.505258i	$0.168603\pi$
$318$	−3.19058	+	1.26569i	−0.178919	+	0.0709762i
$319$	−5.36806	−	20.0339i	−0.300554	−	1.12168i
$320$	−21.4999	−	1.94606i	−1.20188	−	0.108788i
$321$	−1.20392	+	2.08525i	−0.0671963	+	0.116387i
$322$	24.2613	−	18.0430i	1.35203	−	1.00550i
$323$	8.34346	+	2.23562i	0.464242	+	0.124393i
$324$	−0.459284	−	1.94655i	−0.0255158	−	0.108142i
$325$	−3.39925	+	7.49181i	−0.188557	+	0.415571i
$326$	−0.996052	−	8.55891i	−0.0551662	−	0.474034i
$327$	2.89731	−	10.8129i	0.160222	−	0.597955i
$328$	−2.95609	−	2.48803i	−0.163223	−	0.137378i
$329$	−5.46524	−	3.15536i	−0.301308	−	0.173961i
$330$	7.82390	−	9.88476i	0.430691	−	0.544138i
$331$	−12.6991	+	3.40272i	−0.698007	+	0.187030i	−0.590338	−	0.807156i	$-0.701005\pi$
$331$	−12.6991	+	3.40272i	−0.698007	+	0.187030i	−0.107669	+	0.994187i	$0.534339\pi$
$332$	−5.67312	−	10.5467i	−0.311353	−	0.578826i
$333$	0.0939909	+	0.0939909i	0.00515067	+	0.00515067i
$334$	11.5427	+	4.98587i	0.631587	+	0.272815i
$335$	−11.1765	−	19.3582i	−0.610635	−	1.05765i
$336$	3.68228	+	18.0153i	0.200885	+	0.982817i
$337$		−	36.2888i		−	1.97678i	−0.151945	−	0.988389i	$-0.548554\pi$
$337$		−	36.2888i		−	1.97678i	0.151945	−	0.988389i	$-0.451446\pi$
$338$	−9.96663	−	15.4488i	−0.542113	−	0.840305i
$339$			5.07458i			0.275613i
$340$	−11.4970	−	0.346045i	−0.623512	−	0.0187669i
$341$	−13.7697	−	23.8499i	−0.745673	−	1.29154i
$342$	−2.27285	+	5.26181i	−0.122901	+	0.284526i
$343$	−23.1827	−	23.1827i	−1.25175	−	1.25175i
$344$	−17.4808	+	12.2011i	−0.942501	+	0.657840i
$345$	−12.1224	+	3.24818i	−0.652647	+	0.174876i
$346$	11.7519	+	9.30174i	0.631784	+	0.500064i
$347$	2.62927	+	1.51801i	0.141147	+	0.0814912i	0.568910	−	0.822399i	$-0.307365\pi$
$347$	2.62927	+	1.51801i	0.141147	+	0.0814912i	−0.427764	+	0.903891i	$0.640698\pi$
$348$	−8.60811	−	9.14238i	−0.461443	−	0.490083i
$349$	−2.02796	+	7.56845i	−0.108554	+	0.405130i	−0.998724	−	0.0504988i	$-0.983919\pi$
$349$	−2.02796	+	7.56845i	−0.108554	+	0.405130i	0.890170	+	0.455629i	$0.150586\pi$
$350$	−14.7343	+	1.71472i	−0.787580	+	0.0916554i
$351$	−1.48977	+	3.28338i	−0.0795178	+	0.175254i
$352$	−10.2295	−	15.6382i	−0.545232	−	0.833520i
$353$	−3.54976	−	0.951156i	−0.188935	−	0.0506249i	0.163111	−	0.986608i	$-0.447847\pi$
$353$	−3.54976	−	0.951156i	−0.188935	−	0.0506249i	−0.352046	+	0.935983i	$0.614514\pi$
$354$	1.69498	+	2.27913i	0.0900871	+	0.121134i
$355$	−20.1234	+	34.8548i	−1.06804	+	1.84990i
$356$	−3.29054	+	5.32285i	−0.174398	+	0.282111i
$357$	2.53571	+	9.46340i	0.134204	+	0.500856i
$358$	−4.92322	−	12.4106i	−0.260200	−	0.655920i
$359$	−10.8400	+	10.8400i	−0.572113	+	0.572113i	−0.932719	−	0.360605i	$-0.882570\pi$
$359$	−10.8400	+	10.8400i	−0.572113	+	0.572113i	0.360605	+	0.932719i	$0.382570\pi$
$360$	1.33664	−	7.51447i	0.0704471	−	0.396047i
$361$	−2.22895	+	1.28689i	−0.117313	+	0.0677308i
$362$	−1.96739	+	13.3845i	−0.103404	+	0.703476i
$363$	−0.0876434			−0.00460008
$364$	14.5988	−	29.7614i	0.765183	−	1.55992i
$365$	20.9388			1.09599
$366$	−0.949610	+	6.46039i	−0.0496369	+	0.337690i
$367$	1.26374	−	0.729618i	0.0659665	−	0.0380858i	−0.466654	−	0.884440i	$-0.654541\pi$
$367$	1.26374	−	0.729618i	0.0659665	−	0.0380858i	0.532620	+	0.846354i	$0.321207\pi$
$368$	−1.11885	+	18.5695i	−0.0583242	+	0.968002i
$369$	0.965944	−	0.965944i	0.0502850	−	0.0502850i
$370$	0.187049	+	0.471517i	0.00972419	+	0.0245130i
$371$	2.88773	+	10.7771i	0.149923	+	0.559521i
$372$	−14.1823	−	8.76739i	−0.735319	−	0.454568i
$373$	−6.27262	+	10.8645i	−0.324784	+	0.562542i	−0.981469	−	0.191623i	$-0.938625\pi$
$373$	−6.27262	+	10.8645i	−0.324784	+	0.562542i	0.656685	+	0.754165i	$0.271958\pi$
$374$	−5.94162	−	7.98933i	−0.307234	−	0.413118i
$375$	−7.08522	−	1.89848i	−0.365879	−	0.0980370i
$376$	3.65070	−	1.32254i	0.188270	−	0.0682049i
$377$	2.20702	+	22.5299i	0.113667	+	1.16035i
$378$	−6.45749	+	0.751497i	−0.332138	+	0.0386528i
$379$	−2.95404	+	11.0246i	−0.151739	+	0.566298i	0.847624	+	0.530598i	$0.178033\pi$
$379$	−2.95404	+	11.0246i	−0.151739	+	0.566298i	−0.999363	+	0.0356997i	$0.988634\pi$
$380$	−15.9252	+	14.9945i	−0.816943	+	0.769202i
$381$	13.1394	+	7.58605i	0.673153	+	0.388645i
$382$	−4.94646	−	3.91518i	−0.253083	−	0.200318i
$383$	34.7750	−	9.31792i	1.77692	−	0.476124i	0.786902	−	0.617078i	$-0.211684\pi$
$383$	34.7750	−	9.31792i	1.77692	−	0.476124i	0.990016	+	0.140954i	$0.0450171\pi$
$384$	−9.93947	−	5.40434i	−0.507222	−	0.275789i
$385$	−28.9756	−	28.9756i	−1.47673	−	1.47673i
$386$	8.43126	−	19.5190i	0.429140	−	0.993490i
$387$	−3.76848	−	6.52719i	−0.191562	−	0.331796i
$388$	0.268378	−	8.91656i	0.0136248	−	0.452670i
$389$			4.45190i			0.225720i	0.993611	+	0.112860i	$0.0360012\pi$
$389$			4.45190i			0.225720i	−0.993611	+	0.112860i	$0.963999\pi$
$390$	−10.1878	+	9.24841i	−0.515881	+	0.468311i
$391$			9.91197i			0.501270i
$392$	39.8243	−	3.42394i	2.01143	−	0.172935i
$393$	0.187704	+	0.325114i	0.00946844	+	0.0163998i
$394$	32.6217	+	14.0910i	1.64346	+	0.709894i
$395$	−3.66860	−	3.66860i	−0.184587	−	0.184587i
$396$	5.81842	−	3.12975i	0.292387	−	0.157276i
$397$	0.610699	−	0.163636i	0.0306501	−	0.00821266i	−0.243461	−	0.969911i	$-0.578283\pi$
$397$	0.610699	−	0.163636i	0.0306501	−	0.00821266i	0.274112	+	0.961698i	$0.411616\pi$
$398$	20.4045	−	25.7791i	1.02278	−	1.29219i
$399$	16.1350	+	9.31556i	0.807761	+	0.466361i
$400$	5.03059	−	7.61539i	0.251529	−	0.380769i
$401$	4.20272	−	15.6848i	0.209874	−	0.783260i	−0.778034	−	0.628222i	$-0.783783\pi$
$401$	4.20272	−	15.6848i	0.209874	−	0.783260i	0.987908	−	0.155039i	$-0.0495502\pi$
$402$	−1.35417	−	11.6362i	−0.0675400	−	0.580360i
$403$	10.5733	+	28.1376i	0.526694	+	1.40163i
$404$	33.6153	−	7.93143i	1.67242	−	0.394604i
$405$	2.60652	+	0.698415i	0.129519	+	0.0347045i
$406$	−32.7529	+	24.3582i	−1.62550	+	1.20888i
$407$	−0.219548	+	0.380269i	−0.0108826	+	0.0188492i
$408$	−5.45945	−	2.55577i	−0.270283	−	0.126530i
$409$	−0.100203	−	0.373963i	−0.00495472	−	0.0184913i	0.963404	−	0.268053i	$-0.0863802\pi$
$409$	−0.100203	−	0.373963i	−0.00495472	−	0.0184913i	−0.968359	+	0.249562i	$0.919714\pi$
$410$	4.84578	−	1.92230i	0.239316	−	0.0949355i
$411$	3.47260	−	3.47260i	0.171291	−	0.171291i
$412$	24.9693	+	7.50255i	1.23015	+	0.369624i
$413$	7.99562	−	4.61627i	0.393439	−	0.227152i
$414$	−6.50729	−	0.956504i	−0.319816	−	0.0470096i
$415$	16.1580			0.793167
$416$	8.22579	+	18.6638i	0.403302	+	0.915067i
$417$	−4.97744			−0.243746
$418$	−18.7327	−	2.75352i	−0.916249	−	0.134679i
$419$	−29.6128	+	17.0970i	−1.44668	+	0.835242i	−0.998282	−	0.0585905i	$-0.981339\pi$
$419$	−29.6128	+	17.0970i	−1.44668	+	0.835242i	−0.448400	+	0.893833i	$0.648006\pi$
$420$	−23.7601	−	7.13922i	−1.15937	−	0.348358i
$421$	−25.7532	+	25.7532i	−1.25513	+	1.25513i	−0.301746	+	0.953388i	$0.597570\pi$
$421$	−25.7532	+	25.7532i	−1.25513	+	1.25513i	−0.953388	+	0.301746i	$0.902430\pi$
$422$	0.999039	−	0.396314i	0.0486324	−	0.0192923i
$423$	0.355308	+	1.32603i	0.0172757	+	0.0644736i
$424$	−6.21736	−	2.91057i	−0.301942	−	0.141350i
$425$	2.43147	−	4.21142i	0.117943	−	0.204284i
$426$	−16.9251	+	12.5871i	−0.820025	+	0.609849i
$427$	20.5021	+	5.49353i	0.992168	+	0.265851i
$428$	−4.68699	+	1.10588i	−0.226554	+	0.0534549i
$429$	−11.7504	−	1.94636i	−0.567316	−	0.0939712i
$430$	−3.32484	−	28.5698i	−0.160338	−	1.37776i
$431$	10.0650	−	37.5630i	0.484813	−	1.80935i	−0.0960868	−	0.995373i	$-0.530633\pi$
$431$	10.0650	−	37.5630i	0.484813	−	1.80935i	0.580900	−	0.813975i	$-0.302701\pi$
$432$	2.20472	−	3.33754i	0.106075	−	0.160578i
$433$	−5.61230	−	3.24027i	−0.269710	−	0.155717i	0.359046	−	0.933320i	$-0.383102\pi$
$433$	−5.61230	−	3.24027i	−0.269710	−	0.155717i	−0.628756	+	0.777603i	$0.716436\pi$
$434$	−33.6367	+	42.4968i	−1.61461	+	2.03991i
$435$	16.3653	−	4.38506i	0.784655	−	0.210248i
$436$	19.7172	−	10.6060i	0.944282	−	0.507933i
$437$	13.3285	+	13.3285i	0.637588	+	0.637588i
$438$	10.0740	+	4.35147i	0.481353	+	0.207921i
$439$	−3.31480	−	5.74140i	−0.158207	−	0.274022i	0.776015	−	0.630714i	$-0.217238\pi$
$439$	−3.31480	−	5.74140i	−0.158207	−	0.274022i	−0.934222	+	0.356692i	$0.883905\pi$
$440$	25.1202	−	2.15973i	1.19756	−	0.102961i
$441$			14.1320i			0.672951i
$442$	4.97293	+	9.66267i	0.236538	+	0.459606i
$443$			18.6747i			0.887260i	0.896210	+	0.443630i	$0.146310\pi$
$443$			18.6747i			0.887260i	−0.896210	+	0.443630i	$0.853690\pi$
$444$	−0.00799803	+	0.265726i	−0.000379570	+	0.0126108i
$445$	−4.22164	−	7.31209i	−0.200125	−	0.346626i
$446$	−5.45850	+	12.6368i	−0.258468	+	0.598372i
$447$	−8.02739	−	8.02739i	−0.379682	−	0.379682i
$448$	−21.1840	+	30.0614i	−1.00085	+	1.42027i
$449$	28.0101	−	7.50529i	1.32188	−	0.354197i	0.472198	−	0.881492i	$-0.343461\pi$
$449$	28.0101	−	7.50529i	1.32188	−	0.354197i	0.849682	+	0.527296i	$0.176794\pi$
$450$	2.53020	+	2.00268i	0.119275	+	0.0944072i
$451$	3.90802	+	2.25630i	0.184021	+	0.106245i
$452$	−7.38919	+	6.95738i	−0.347558	+	0.327248i
$453$	−0.760481	+	2.83815i	−0.0357305	+	0.133348i
$454$	29.3806	−	3.41920i	1.37890	−	0.160471i
$455$	26.0327	+	36.3690i	1.22043	+	1.70501i
$456$	−10.7780	+	3.90454i	−0.504724	+	0.182847i
$457$	−7.60244	−	2.03707i	−0.355627	−	0.0952901i	0.0765822	−	0.997063i	$-0.475599\pi$
$457$	−7.60244	−	2.03707i	−0.355627	−	0.0952901i	−0.432210	+	0.901773i	$0.642266\pi$
$458$	−19.0891	−	25.6679i	−0.891976	−	1.19938i
$459$	1.06562	−	1.84571i	0.0497390	−	0.0861504i
$460$	−21.3499	−	13.1983i	−0.995442	−	0.615374i
$461$	−7.40576	−	27.6387i	−0.344921	−	1.28726i	−0.892705	−	0.450642i	$-0.851195\pi$
$461$	−7.40576	−	27.6387i	−0.344921	−	1.28726i	0.547784	−	0.836620i	$-0.315471\pi$
$462$	−7.91892	−	19.9622i	−0.368421	−	0.928726i
$463$	12.0356	−	12.0356i	0.559342	−	0.559342i	−0.369778	−	0.929120i	$-0.620566\pi$
$463$	12.0356	−	12.0356i	0.559342	−	0.559342i	0.929120	+	0.369778i	$0.120566\pi$
$464$	1.51045	−	25.0689i	0.0701211	−	1.16379i
$465$	19.4825	−	11.2482i	0.903479	−	0.521624i
$466$	1.76234	−	11.9896i	0.0816389	−	0.555406i
$467$	9.24937			0.428010			0.214005	−	0.976833i	$-0.431349\pi$
$467$	9.24937			0.428010			0.214005	+	0.976833i	$0.431349\pi$
$468$	−6.82351	+	2.33232i	−0.315417	+	0.107812i
$469$	−38.0791			−1.75833
$470$	−0.761879	+	5.18322i	−0.0351429	+	0.239084i
$471$	−2.92812	+	1.69055i	−0.134921	+	0.0778965i
$472$	−0.994829	+	5.59284i	−0.0457907	+	0.257431i
$473$	17.6052	−	17.6052i	0.809486	−	0.809486i
$474$	−1.00262	−	2.52742i	−0.0460516	−	0.116088i
$475$	−2.39348	−	8.93260i	−0.109821	−	0.409856i
$476$	−10.3033	+	16.6669i	−0.472252	+	0.763925i
$477$	1.21356	−	2.10194i	0.0555649	−	0.0962412i
$478$	14.5633	+	19.5823i	0.666108	+	0.895674i
$479$	36.4674	+	9.77141i	1.66624	+	0.446467i	0.964093	−	0.265566i	$-0.0855589\pi$
$479$	36.4674	+	9.77141i	1.66624	+	0.446467i	0.702145	+	0.712034i	$0.252226\pi$
$480$	12.7745	−	8.35623i	0.583075	−	0.381408i
$481$	0.304235	−	0.370314i	0.0138719	−	0.0168849i
$482$	19.5808	−	2.27873i	0.891881	−	0.103793i
$483$	−5.53341	+	20.6510i	−0.251779	+	0.939652i
$484$	−0.120161	−	0.127619i	−0.00546188	−	0.00580088i
$485$	10.4235	+	6.01799i	0.473305	+	0.273263i
$486$	1.10889	+	0.877700i	0.0503004	+	0.0398133i
$487$	−1.47397	+	0.394950i	−0.0667922	+	0.0178969i	−0.292060	−	0.956400i	$-0.594341\pi$
$487$	−1.47397	+	0.394950i	−0.0667922	+	0.0178969i	0.225268	+	0.974297i	$0.427674\pi$
$488$	−10.7090	+	7.47462i	−0.484776	+	0.338360i
$489$	4.30834	+	4.30834i	0.194830	+	0.194830i
$490$	−21.3856	+	49.5092i	−0.966103	+	2.23660i
$491$	19.9303	+	34.5203i	0.899442	+	1.55788i	0.828209	+	0.560419i	$0.189360\pi$
$491$	19.9303	+	34.5203i	0.899442	+	1.55788i	0.0712327	+	0.997460i	$0.477307\pi$
$492$	2.73086	+	0.0821957i	0.123117	+	0.00370567i
$493$		−	13.3812i		−	0.602659i
$494$	19.6803	+	6.30622i	0.885458	+	0.283730i
$495$			8.91408i			0.400658i
$496$	−6.67796	−	32.6715i	−0.299849	−	1.46699i
$497$	34.2811	+	59.3765i	1.53772	+	2.66340i
$498$	7.77387	+	3.35793i	0.348355	+	0.150473i
$499$	20.8152	+	20.8152i	0.931817	+	0.931817i	0.997819	−	0.0660025i	$-0.0210245\pi$
$499$	20.8152	+	20.8152i	0.931817	+	0.931817i	−0.0660025	+	0.997819i	$0.521025\pi$
$500$	−6.94961	−	12.9198i	−0.310796	−	0.577791i
$501$	−8.58784	+	2.30110i	−0.383676	+	0.102806i
$502$	0.670189	−	0.846721i	0.0299120	−	0.0377910i
$503$	9.93234	+	5.73444i	0.442861	+	0.255686i	0.704811	−	0.709396i	$-0.251032\pi$
$503$	9.93234	+	5.73444i	0.442861	+	0.255686i	−0.261949	+	0.965082i	$0.584365\pi$
$504$	−9.94766	−	8.37256i	−0.443104	−	0.372944i
$505$	−12.0610	+	45.0124i	−0.536709	+	2.00302i
$506$	−2.51156	−	21.5814i	−0.111652	−	0.959411i
$507$	12.3057	+	4.19168i	0.546515	+	0.186159i
$508$	6.96830	+	29.5333i	0.309168	+	1.31033i
$509$	−12.9231	−	3.46273i	−0.572805	−	0.153483i	−0.0392225	−	0.999231i	$-0.512488\pi$
$509$	−12.9231	−	3.46273i	−0.572805	−	0.153483i	−0.533583	+	0.845748i	$0.679155\pi$
$510$	6.52632	−	4.85359i	0.288990	−	0.214921i
$511$	17.8351	−	30.8913i	0.788977	−	1.36655i
$512$	−5.75791	−	21.8826i	−0.254466	−	0.967082i
$513$	−1.04898	−	3.91483i	−0.0463134	−	0.172844i
$514$	24.4891	−	9.71472i	1.08017	−	0.428498i
$515$	−24.8741	+	24.8741i	−1.09608	+	1.09608i
$516$	4.33770	−	14.4363i	0.190956	−	0.635523i
$517$	−3.92734	+	2.26745i	−0.172724	+	0.0997224i
$518$	0.854956	+	0.125670i	0.0375646	+	0.00552161i
$519$	−10.5978			−0.465194
$520$	−27.4346	−	2.15491i	−1.20309	−	0.0944991i
$521$	−12.9431			−0.567049			−0.283524	−	0.958965i	$-0.591504\pi$
$521$	−12.9431			−0.567049			−0.283524	+	0.958965i	$0.591504\pi$
$522$	8.78487	+	1.29128i	0.384503	+	0.0565180i
$523$	−3.80032	+	2.19411i	−0.166176	+	0.0959419i	−0.580782	−	0.814059i	$-0.697253\pi$
$523$	−3.80032	+	2.19411i	−0.166176	+	0.0959419i	0.414605	+	0.910001i	$0.363920\pi$
$524$	−0.216057	+	0.719060i	−0.00943849	+	0.0314123i
$525$	7.41686	−	7.41686i	0.323698	−	0.323698i
$526$	−7.06283	+	2.80179i	−0.307954	+	0.122164i
$527$	−4.59860	−	17.1622i	−0.200318	−	0.747598i
$528$	12.5345	+	4.18135i	0.545495	+	0.181970i
$529$	0.685070	−	1.18658i	0.0297857	−	0.0515903i
$530$	7.43233	−	5.52739i	0.322840	−	0.240094i
$531$	−1.93997	−	0.519814i	−0.0841876	−	0.0225580i
$532$	8.55697	+	36.2664i	0.370992	+	1.57235i
$533$	−3.80571	−	3.12662i	−0.164844	−	0.135429i
$534$	−0.511506	−	4.39529i	−0.0221350	−	0.190203i
$535$	1.68167	−	6.27609i	0.0727051	−	0.271339i
$536$	15.0871	−	17.9254i	0.651663	−	0.774258i
$537$	8.17605	+	4.72045i	0.352823	+	0.203702i
$538$	26.7367	−	33.7793i	1.15270	−	1.45633i
$539$	−45.0927	+	12.0825i	−1.94228	+	0.520432i
$540$	2.55663	+	4.75295i	0.110020	+	0.204535i
$541$	−23.4566	−	23.4566i	−1.00848	−	1.00848i	−0.999964	−	0.00851321i	$-0.997290\pi$
$541$	−23.4566	−	23.4566i	−1.00848	−	1.00848i	−0.00851321	−	0.999964i	$-0.502710\pi$
$542$	−18.0460	−	7.79499i	−0.775141	−	0.334824i
$543$	−4.78300	−	8.28439i	−0.205258	−	0.355517i
$544$	−3.76355	−	11.4537i	−0.161361	−	0.491071i
$545$			30.2076i			1.29395i
$546$	4.96656	+	22.9077i	0.212549	+	0.980361i
$547$		−	19.0186i		−	0.813176i	−0.913612	−	0.406588i	$-0.866719\pi$
$547$		−	19.0186i		−	0.813176i	0.913612	−	0.406588i	$-0.133281\pi$
$548$	9.81754	+	0.295496i	0.419385	+	0.0126230i
$549$	−2.30863	−	3.99867i	−0.0985301	−	0.170659i
$550$	−4.22693	+	9.78567i	−0.180237	+	0.417262i
$551$	−17.9935	−	17.9935i	−0.766550	−	0.766550i
$552$	−7.52888	−	10.7868i	−0.320450	−	0.459116i
$553$	−8.53712	+	2.28752i	−0.363035	+	0.0972751i
$554$	11.9223	+	9.43660i	0.506528	+	0.400923i
$555$	−0.310634	−	0.179344i	−0.0131857	−	0.00761275i
$556$	−6.82420	−	7.24775i	−0.289411	−	0.307373i
$557$	−10.6711	+	39.8251i	−0.452149	+	1.68744i	0.244189	+	0.969728i	$0.421478\pi$
$557$	−10.6711	+	39.8251i	−0.452149	+	1.68744i	−0.696337	+	0.717715i	$0.745188\pi$
$558$	11.7109	−	1.36287i	0.495762	−	0.0576948i
$559$	−22.0973	+	15.8171i	−0.934618	+	0.668993i
$560$	−22.1801	−	44.3856i	−0.937282	−	1.87563i
$561$	6.80043	+	1.82217i	0.287114	+	0.0769320i
$562$	−15.3599	−	20.6535i	−0.647919	−	0.871216i
$563$	4.61815	−	7.99887i	0.194632	−	0.337112i	−0.752148	−	0.658994i	$-0.770982\pi$
$563$	4.61815	−	7.99887i	0.194632	−	0.337112i	0.946780	+	0.321882i	$0.104315\pi$
$564$	−1.44372	+	2.33539i	−0.0607915	+	0.0983376i
$565$	−3.54416	−	13.2270i	−0.149104	−	0.556464i
$566$	7.72475	+	19.4728i	0.324696	+	0.818501i
$567$	3.25054	−	3.25054i	0.136510	−	0.136510i
$568$	−41.5332	−	7.38773i	−1.74269	−	0.309982i
$569$	11.5312	−	6.65752i	0.483412	−	0.279098i	−0.238426	−	0.971161i	$-0.576631\pi$
$569$	11.5312	−	6.65752i	0.483412	−	0.279098i	0.721837	+	0.692063i	$0.243298\pi$
$570$	2.24929	−	15.3024i	0.0942126	−	0.640947i
$571$	−1.68720			−0.0706071			−0.0353036	−	0.999377i	$-0.511240\pi$
$571$	−1.68720			−0.0706071			−0.0353036	+	0.999377i	$0.511240\pi$
$572$	−13.2760	−	19.7785i	−0.555097	−	0.826982i
$573$	4.46072			0.186349
$574$	1.29151	−	8.78638i	0.0539065	−	0.366736i
$575$	9.19015	−	5.30594i	0.383256	−	0.221273i
$576$	7.88260	−	1.36552i	0.328442	−	0.0568968i
$577$	15.6720	−	15.6720i	0.652433	−	0.652433i	−0.301145	−	0.953578i	$-0.597369\pi$
$577$	15.6720	−	15.6720i	0.652433	−	0.652433i	0.953578	+	0.301145i	$0.0973689\pi$
$578$	6.49647	+	16.3765i	0.270218	+	0.681172i
$579$	3.89124	+	14.5223i	0.161714	+	0.603526i
$580$	28.8224	+	17.8178i	1.19679	+	0.739843i
$581$	13.7629	−	23.8381i	0.570983	−	0.988971i
$582$	3.76423	+	5.06153i	0.156032	+	0.209807i
$583$	7.74449	+	2.07513i	0.320744	+	0.0859431i
$584$	7.47543	+	20.6349i	0.309335	+	0.853878i
$585$	1.58994	−	9.59868i	0.0657361	−	0.396857i
$586$	1.49544	−	0.174033i	0.0617760	−	0.00718924i
$587$	2.98620	−	11.1447i	0.123254	−	0.459989i	−0.876518	−	0.481370i	$-0.840139\pi$
$587$	2.98620	−	11.1447i	0.123254	−	0.459989i	0.999771	+	0.0213805i	$0.00680616\pi$
$588$	−20.5779	+	19.3753i	−0.848616	+	0.799024i
$589$	−29.2615	−	16.8941i	−1.20570	−	0.696110i
$590$	−6.00978	−	4.75680i	−0.247419	−	0.195835i
$591$	−24.2708	+	6.50334i	−0.998367	+	0.267512i
$592$	−0.397894	+	0.352671i	−0.0163534	+	0.0144947i
$593$	−2.04369	−	2.04369i	−0.0839244	−	0.0839244i	0.663898	−	0.747823i	$-0.268901\pi$
$593$	−2.04369	−	2.04369i	−0.0839244	−	0.0839244i	−0.747823	+	0.663898i	$0.768901\pi$
$594$	−1.85251	+	4.28870i	−0.0760094	+	0.175967i
$595$	−13.2188	−	22.8956i	−0.541916	−	0.938626i
$596$	0.683080	−	22.6946i	0.0279801	−	0.929607i
$597$			23.2476i			0.951462i
$598$	−1.14488	+	23.6868i	−0.0468177	+	0.968626i
$599$		−	36.2508i		−	1.48117i	−0.671965	−	0.740583i	$-0.734549\pi$
$599$		−	36.2508i		−	1.48117i	0.671965	−	0.740583i	$-0.265451\pi$
$600$	0.552826	+	6.43000i	0.0225690	+	0.262504i
$601$	−17.9642	−	31.1148i	−0.732774	−	1.26920i	−0.955693	−	0.294364i	$-0.904892\pi$
$601$	−17.9642	−	31.1148i	−0.732774	−	1.26920i	0.222920	−	0.974837i	$-0.428441\pi$
$602$	−44.9813	−	19.4297i	−1.83330	−	0.791897i
$603$	5.85736	+	5.85736i	0.238530	+	0.238530i
$604$	−5.17533	+	2.78383i	−0.210581	+	0.113272i
$605$	0.228444	−	0.0612115i	0.00928758	−	0.00248860i
$606$	−15.1571	+	19.1496i	−0.615716	+	0.777900i
$607$	−24.2160	−	13.9811i	−0.982895	−	0.567475i	−0.0797524	−	0.996815i	$-0.525413\pi$
$607$	−24.2160	−	13.9811i	−0.982895	−	0.567475i	−0.903143	+	0.429340i	$0.858746\pi$
$608$	−20.4623	−	10.3408i	−0.829858	−	0.419374i
$609$	7.47013	−	27.8789i	0.302705	−	1.12971i
$610$	−2.03685	−	17.5024i	−0.0824698	−	0.708650i
$611$	4.63339	−	1.74110i	0.187447	−	0.0704372i
$612$	4.14857	−	0.978846i	0.167696	−	0.0395675i
$613$	37.7958	+	10.1274i	1.52656	+	0.409040i	0.921895	−	0.387440i	$-0.126641\pi$
$613$	37.7958	+	10.1274i	1.52656	+	0.409040i	0.604664	+	0.796480i	$0.293307\pi$
$614$	−34.6024	+	25.7336i	−1.39644	+	1.03852i
$615$	−1.84312	+	3.19238i	−0.0743219	+	0.128729i
$616$	18.2103	−	38.8996i	0.733716	−	1.56731i
$617$	−8.93592	−	33.3493i	−0.359747	−	1.34259i	−0.874405	−	0.485197i	$-0.838748\pi$
$617$	−8.93592	−	33.3493i	−0.359747	−	1.34259i	0.514658	−	0.857396i	$-0.327919\pi$
$618$	−17.1366	+	6.79801i	−0.689335	+	0.273456i
$619$	−22.4141	+	22.4141i	−0.900900	+	0.900900i	−0.995514	−	0.0946143i	$-0.969838\pi$
$619$	−22.4141	+	22.4141i	−0.900900	+	0.900900i	0.0946143	+	0.995514i	$0.469838\pi$
$620$	43.0898	+	12.9472i	1.73053	+	0.519974i
$621$	4.02770	−	2.32540i	0.161626	−	0.0933149i
$622$	39.8783	+	5.86170i	1.59897	+	0.235033i
$623$	−14.3835			−0.576262
$624$	−12.7514	−	6.73817i	−0.510463	−	0.269743i
$625$	31.2024			1.24809
$626$	−24.0076	−	3.52887i	−0.959538	−	0.141042i
$627$	11.5947	−	6.69419i	0.463047	−	0.267340i
$628$	−6.47618	−	1.94590i	−0.258428	−	0.0776501i
$629$	−0.200317	+	0.200317i	−0.00798718	+	0.00798718i
$630$	16.3067	−	6.46880i	0.649676	−	0.257723i
$631$	6.65069	+	24.8207i	0.264760	+	0.988097i	0.962397	+	0.271646i	$0.0875680\pi$
$631$	6.65069	+	24.8207i	0.264760	+	0.988097i	−0.697637	+	0.716451i	$0.745765\pi$
$632$	2.30561	−	4.92509i	0.0917124	−	0.195909i
$633$	−0.379991	+	0.658163i	−0.0151033	+	0.0261596i
$634$	−10.2210	+	7.60133i	−0.405929	+	0.301887i
$635$	−39.5464	−	10.5964i	−1.56935	−	0.420506i
$636$	4.72449	−	1.11473i	0.187338	−	0.0442020i
$637$	50.7108	−	4.96761i	2.00924	−	0.196824i
$638$	3.39062	+	29.1350i	0.134236	+	1.15347i
$639$	3.86021	−	14.4065i	0.152707	−	0.569912i
$640$	29.6819	+	7.14465i	1.17328	+	0.282417i
$641$	2.87676	+	1.66090i	0.113625	+	0.0656014i	0.555735	−	0.831359i	$-0.312437\pi$
$641$	2.87676	+	1.66090i	0.113625	+	0.0656014i	−0.442110	+	0.896961i	$0.645770\pi$
$642$	2.11336	−	2.67004i	0.0834078	−	0.105378i
$643$	−28.6298	+	7.67132i	−1.12905	+	0.302527i	−0.774540	−	0.632525i	$-0.782018\pi$
$643$	−28.6298	+	7.67132i	−1.12905	+	0.302527i	−0.354508	+	0.935053i	$0.615352\pi$
$644$	−37.6568	+	20.2557i	−1.48388	+	0.798187i
$645$	14.3813	+	14.3813i	0.566263	+	0.566263i
$646$	−11.2142	−	4.84399i	−0.441217	−	0.190584i
$647$	−22.6688	−	39.2634i	−0.891201	−	1.54361i	−0.838437	−	0.544998i	$-0.816530\pi$
$647$	−22.6688	−	39.2634i	−0.891201	−	1.54361i	−0.0527637	−	0.998607i	$-0.516803\pi$
$648$	0.242283	+	2.81803i	0.00951778	+	0.110703i
$649$		−	6.63454i		−	0.260428i
$650$	6.29696	−	9.78327i	0.246987	−	0.383731i
$651$		−	38.3236i		−	1.50202i
$652$	−0.366612	+	12.1803i	−0.0143577	+	0.477018i
$653$	2.96116	+	5.12887i	0.115879	+	0.200708i	0.918131	−	0.396277i	$-0.129698\pi$
$653$	2.96116	+	5.12887i	0.115879	+	0.200708i	−0.802252	+	0.596986i	$0.796365\pi$
$654$	−6.27769	+	14.5333i	−0.245477	+	0.568298i
$655$	−0.716320	−	0.716320i	−0.0279889	−	0.0279889i
$656$	3.62440	+	4.08916i	0.141509	+	0.159655i
$657$	−7.49512	+	2.00831i	−0.292413	+	0.0783517i
$658$	6.99790	+	5.53892i	0.272807	+	0.215930i
$659$	8.32965	+	4.80913i	0.324477	+	0.187337i	0.653386	−	0.757025i	$-0.273348\pi$
$659$	8.32965	+	4.80913i	0.324477	+	0.187337i	−0.328909	+	0.944362i	$0.606681\pi$
$660$	−12.9800	+	12.2214i	−0.505245	+	0.475719i
$661$	−5.79550	+	21.6291i	−0.225419	+	0.841275i	0.756817	+	0.653626i	$0.226753\pi$
$661$	−5.79550	+	21.6291i	−0.225419	+	0.841275i	−0.982236	+	0.187648i	$0.939913\pi$
$662$	18.4682	−	2.14925i	0.717786	−	0.0835330i
$663$	−6.99769	−	3.17506i	−0.271768	−	0.123309i
$664$	5.76862	+	15.9235i	0.223866	+	0.617952i
$665$	−48.5624	−	13.0123i	−1.88317	−	0.504594i
$666$	−0.112179	−	0.150841i	−0.00434686	−	0.00584496i
$667$	14.6002	−	25.2883i	0.565322	−	0.979167i
$668$	−15.1248	−	9.35005i	−0.585198	−	0.361764i
$669$	−2.51924	−	9.40191i	−0.0973993	−	0.363499i
$670$	11.6566	+	29.3842i	0.450333	+	1.13521i
$671$	10.7852	−	10.7852i	0.416359	−	0.416359i
$672$	−1.44705	−	25.9640i	−0.0558213	−	1.00158i
$673$	−32.5397	+	18.7868i	−1.25431	+	0.724178i	−0.971963	−	0.235134i	$-0.924447\pi$
$673$	−32.5397	+	18.7868i	−1.25431	+	0.724178i	−0.282350	+	0.959312i	$0.591114\pi$
$674$	−7.46333	+	50.7746i	−0.287477	+	1.95576i
$675$	−2.28173			−0.0878240
$676$	10.7678	+	23.6655i	0.414147	+	0.910210i
$677$	−32.2937			−1.24115			−0.620574	−	0.784148i	$-0.713100\pi$
$677$	−32.2937			−1.24115			−0.620574	+	0.784148i	$0.713100\pi$
$678$	1.04366	−	7.10024i	0.0400816	−	0.272683i
$679$	17.7568	−	10.2519i	0.681443	−	0.393431i
$680$	16.0152	+	2.84871i	0.614154	+	0.109243i
$681$	−14.7894	+	14.7894i	−0.566733	+	0.566733i
$682$	14.3612	+	36.2022i	0.549921	+	1.38625i
$683$	−8.98563	−	33.5348i	−0.343826	−	1.28318i	−0.893978	−	0.448111i	$-0.852097\pi$
$683$	−8.98563	−	33.5348i	−0.343826	−	1.28318i	0.550152	−	0.835064i	$-0.314570\pi$
$684$	4.26229	−	6.89477i	0.162973	−	0.263628i
$685$	−6.62608	+	11.4767i	−0.253170	+	0.438503i
$686$	27.6689	+	37.2047i	1.05640	+	1.42048i
$687$	21.8483	+	5.85422i	0.833563	+	0.223353i
$688$	26.9681	−	13.4764i	1.02815	−	0.513781i
$689$	−7.96913	−	3.61583i	−0.303600	−	0.137752i
$690$	17.6294	−	2.05164i	0.671141	−	0.0781047i
$691$	−0.469206	+	1.75110i	−0.0178494	+	0.0666150i	−0.974276	−	0.225358i	$-0.927645\pi$
$691$	−0.469206	+	1.75110i	−0.0178494	+	0.0666150i	0.956427	+	0.291973i	$0.0943116\pi$
$692$	−14.5299	−	15.4317i	−0.552345	−	0.586627i
$693$	13.1510	+	7.59275i	0.499567	+	0.288425i
$694$	−3.36662	−	2.66472i	−0.127795	−	0.101151i
$695$	12.9738	−	3.47632i	0.492124	−	0.131864i
$696$	10.1640	+	14.5622i	0.385266	+	0.551979i
$697$	2.05866	+	2.05866i	0.0779774	+	0.0779774i
$698$	4.39404	−	10.1725i	0.166317	−	0.385036i
$699$	4.28450	+	7.42097i	0.162055	+	0.280687i
$700$	20.9686	+	0.631128i	0.792537	+	0.0238544i
$701$		−	5.81258i		−	0.219538i	−0.993957	−	0.109769i	$-0.964989\pi$
$701$		−	5.81258i		−	0.219538i	0.993957	−	0.109769i	$-0.0350111\pi$
$702$	2.75973	−	4.28765i	0.104159	−	0.161827i
$703$			0.538728i			0.0203185i
$704$	11.0966	+	23.9845i	0.418219	+	0.903950i
$705$	−1.85223	−	3.20816i	−0.0697592	−	0.120826i
$706$	4.77114	+	2.06090i	0.179564	+	0.0775630i
$707$	56.1340	+	56.1340i	2.11114	+	2.11114i
$708$	−1.90284	−	3.53751i	−0.0715131	−	0.132948i
$709$	45.4274	−	12.1722i	1.70606	−	0.457138i	0.731608	−	0.681726i	$-0.238770\pi$
$709$	45.4274	−	12.1722i	1.70606	−	0.457138i	0.974454	+	0.224588i	$0.0721037\pi$
$710$	35.3247	−	44.6294i	1.32571	−	1.67491i
$711$	1.66505	+	0.961320i	0.0624444	+	0.0360523i
$712$	5.69878	−	6.77087i	0.213571	−	0.253749i
$713$	10.0350	−	37.4513i	0.375816	−	1.40256i
$714$	−1.60162	−	13.7625i	−0.0599393	−	0.515048i
$715$	31.9871	−	3.13344i	1.19625	−	0.117184i
$716$	4.33605	+	18.3772i	0.162046	+	0.686787i
$717$	−16.6683	−	4.46625i	−0.622487	−	0.166795i
$718$	17.3965	−	12.9377i	0.649232	−	0.482830i
$719$	−4.20608	+	7.28514i	−0.156860	+	0.271690i	−0.933735	−	0.357965i	$-0.883471\pi$
$719$	−4.20608	+	7.28514i	−0.156860	+	0.271690i	0.776875	+	0.629655i	$0.216804\pi$
$720$	−3.41566	+	10.2392i	−0.127294	+	0.381592i
$721$	15.5100	+	57.8841i	0.577622	+	2.15572i
$722$	3.38337	−	1.34217i	0.125916	−	0.0499503i
$723$	−9.85647	+	9.85647i	−0.366566	+	0.366566i
$724$	5.50546	−	18.3227i	0.204609	−	0.680959i
$725$	−12.4067	+	7.16304i	−0.460775	+	0.266028i
$726$	0.122629	+	0.0180252i	0.00455118	+	0.000668976i
$727$	−48.5181			−1.79944			−0.899718	−	0.436471i	$-0.856228\pi$
$727$	−48.5181			−1.79944			−0.899718	+	0.436471i	$0.856228\pi$
$728$	−26.5471	+	38.6390i	−0.983902	+	1.43206i
$729$	−1.00000			−0.0370370
$730$	−29.2972	−	4.30638i	−1.08434	−	0.159386i
$731$	13.9110	−	8.03154i	0.514518	−	0.297057i
$732$	2.65735	−	8.84394i	0.0982184	−	0.326881i
$733$	10.5305	−	10.5305i	0.388952	−	0.388952i	−0.485362	−	0.874313i	$-0.661312\pi$
$733$	10.5305	−	10.5305i	0.388952	−	0.388952i	0.874313	+	0.485362i	$0.161312\pi$
$734$	−1.91825	+	0.760961i	−0.0708039	+	0.0280876i
$735$	−9.86998	−	36.8353i	−0.364060	−	1.35869i
$736$	5.38456	−	25.7519i	0.198478	−	0.949229i
$737$	−13.6819	+	23.6977i	−0.503979	+	0.872917i
$738$	−1.55019	+	1.15287i	−0.0570632	+	0.0424376i
$739$	−47.0058	−	12.5952i	−1.72914	−	0.463320i	−0.749152	−	0.662399i	$-0.769539\pi$
$739$	−47.0058	−	12.5952i	−1.72914	−	0.463320i	−0.979984	+	0.199078i	$0.936205\pi$
$740$	−0.164740	−	0.698206i	−0.00605596	−	0.0256666i
$741$	−13.6791	+	5.14024i	−0.502516	+	0.188831i
$742$	−1.82397	−	15.6731i	−0.0669599	−	0.575376i
$743$	−10.7642	+	40.1726i	−0.394901	+	1.47379i	0.427048	+	0.904229i	$0.359554\pi$
$743$	−10.7642	+	40.1726i	−0.394901	+	1.47379i	−0.821949	+	0.569561i	$0.807113\pi$
$744$	18.0405	+	15.1840i	0.661395	+	0.556671i
$745$	26.5300	+	15.3171i	0.971984	+	0.561175i
$746$	11.0110	−	13.9113i	0.403140	−	0.509329i
$747$	−5.78382	+	1.54977i	−0.211619	+	0.0567031i
$748$	6.67027	+	12.4005i	0.243889	+	0.453407i
$749$	−7.82678	−	7.82678i	−0.285984	−	0.285984i
$750$	9.52304	+	4.11349i	0.347732	+	0.150203i
$751$	12.6380	+	21.8896i	0.461166	+	0.798764i	0.999019	−	0.0442751i	$-0.0140978\pi$
$751$	12.6380	+	21.8896i	0.461166	+	0.798764i	−0.537853	+	0.843039i	$0.680764\pi$
$752$	−5.37998	+	1.09965i	−0.196188	+	0.0401002i
$753$			0.763574i			0.0278262i
$754$	1.54560	−	31.9773i	0.0562873	−	1.16455i
$755$		−	7.92883i		−	0.288560i
$756$	9.18974	+	0.276600i	0.334228	+	0.0100598i
$757$	3.61599	+	6.26309i	0.131426	+	0.227636i	0.924226	−	0.381845i	$-0.124711\pi$
$757$	3.61599	+	6.26309i	0.131426	+	0.227636i	−0.792801	+	0.609481i	$0.791378\pi$
$758$	6.40062	−	14.8179i	0.232481	−	0.538211i
$759$	10.8635	+	10.8635i	0.394321	+	0.394321i
$760$	25.3660	−	17.7048i	0.920121	−	0.642219i
$761$	−34.5339	+	9.25332i	−1.25185	+	0.335433i	−0.823052	−	0.567967i	$-0.807730\pi$
$761$	−34.5339	+	9.25332i	−1.25185	+	0.335433i	−0.428800	+	0.903399i	$0.641064\pi$
$762$	−16.8242	−	13.3166i	−0.609478	−	0.482408i
$763$	44.5656	+	25.7299i	1.61338	+	0.931486i
$764$	6.11577	+	6.49535i	0.221261	+	0.234993i
$765$	−1.48849	+	5.55513i	−0.0538166	+	0.200846i
$766$	−50.5728	+	5.88546i	−1.82727	+	0.212650i
$767$	−1.18336	+	7.14407i	−0.0427285	+	0.257957i
$768$	12.7956	+	9.60584i	0.461722	+	0.346621i
$769$	11.9971	+	3.21462i	0.432628	+	0.115922i	0.468559	−	0.883432i	$-0.344773\pi$
$769$	11.9971	+	3.21462i	0.432628	+	0.115922i	−0.0359318	+	0.999354i	$0.511440\pi$
$770$	34.5827	+	46.5012i	1.24628	+	1.67579i
$771$	−9.31459	+	16.1333i	−0.335457	+	0.581028i
$772$	−15.8112	+	25.5765i	−0.569058	+	0.920520i
$773$	−3.86583	−	14.4275i	−0.139044	−	0.518920i	−0.999948	−	0.0101529i	$-0.996768\pi$
$773$	−3.86583	−	14.4275i	−0.139044	−	0.518920i	0.860904	−	0.508767i	$-0.169898\pi$
$774$	3.93036	+	9.90775i	0.141274	+	0.356127i
$775$	−13.4507	+	13.4507i	−0.483165	+	0.483165i
$776$	−2.20933	+	12.4207i	−0.0793103	+	0.445876i
$777$	−0.529177	+	0.305521i	−0.0189841	+	0.0109605i
$778$	0.915600	−	6.22901i	0.0328259	−	0.223321i
$779$	5.53650			0.198366
$780$	16.1567	−	10.8449i	0.578502	−	0.388310i
$781$	49.2690			1.76298
$782$	2.03854	−	13.8686i	0.0728982	−	0.495941i
$783$	−5.43742	+	3.13929i	−0.194317	+	0.112189i
$784$	−56.4256	−	3.39976i	−2.01520	−	0.121420i
$785$	6.45150	−	6.45150i	0.230264	−	0.230264i
$786$	−0.195768	−	0.493496i	−0.00698280	−	0.0176024i
$787$	0.747527	+	2.78981i	0.0266465	+	0.0994459i	0.977968	−	0.208753i	$-0.0669404\pi$
$787$	0.747527	+	2.78981i	0.0266465	+	0.0994459i	−0.951322	+	0.308199i	$0.900274\pi$
$788$	−42.7456	−	26.4249i	−1.52275	−	0.941350i
$789$	2.68639	−	4.65297i	0.0956381	−	0.165650i
$790$	4.37852	+	5.88753i	0.155781	+	0.209469i
$791$	−22.5327	−	6.03762i	−0.801171	−	0.214673i
$792$	−8.78470	+	3.18244i	−0.312151	+	0.113083i
$793$	−13.5372	+	9.68984i	−0.480721	+	0.344096i
$794$	−0.888131	+	0.103357i	−0.0315186	+	0.00366801i
$795$	−1.69513	+	6.32632i	−0.0601201	+	0.224371i
$796$	−33.8513	+	31.8731i	−1.19983	+	1.12971i
$797$	10.6005	+	6.12021i	0.375490	+	0.216789i	0.675854	−	0.737036i	$-0.263775\pi$
$797$	10.6005	+	6.12021i	0.375490	+	0.216789i	−0.300364	+	0.953825i	$0.597108\pi$
$798$	−20.6599	−	16.3525i	−0.731353	−	0.578874i
$799$	−2.82609	+	0.757248i	−0.0999798	+	0.0267895i
$800$	−8.60491	+	9.62068i	−0.304230	+	0.340142i
$801$	2.21248	+	2.21248i	0.0781740	+	0.0781740i
$802$	−9.10617	+	21.0815i	−0.321550	+	0.744412i
$803$	−12.8163	−	22.1986i	−0.452279	−	0.783370i
$804$	−0.498424	+	16.5596i	−0.0175781	+	0.584013i
$805$		−	57.6918i		−	2.03337i
$806$	−9.00704	−	41.5440i	−0.317260	−	1.46333i
$807$			30.4622i			1.07232i
$808$	−48.6650	+	4.18402i	−1.71203	+	0.147193i
$809$	1.39060	+	2.40859i	0.0488909	+	0.0846816i	0.889435	−	0.457061i	$-0.151098\pi$
$809$	1.39060	+	2.40859i	0.0488909	+	0.0846816i	−0.840544	+	0.541743i	$0.817765\pi$
$810$	−3.50335	−	1.51328i	−0.123095	−	0.0531712i
$811$	25.8726	+	25.8726i	0.908509	+	0.908509i	0.996152	−	0.0876429i	$-0.0279334\pi$
$811$	25.8726	+	25.8726i	0.908509	+	0.908509i	−0.0876429	+	0.996152i	$0.527933\pi$
$812$	50.8368	−	27.3453i	1.78402	−	0.959633i
$813$	13.4264	−	3.59758i	0.470883	−	0.126173i
$814$	0.385395	−	0.486911i	0.0135081	−	0.0170662i
$815$	−14.2388	−	8.22077i	−0.498763	−	0.287961i
$816$	7.11312	+	4.69880i	0.249009	+	0.164491i
$817$	7.90608	−	29.5059i	0.276599	−	1.03228i
$818$	0.0632910	+	0.543849i	0.00221292	+	0.0190152i
$819$	−12.8068	−	10.5215i	−0.447504	−	0.367652i
$820$	−7.17546	+	1.69303i	−0.250578	+	0.0591232i
$821$	47.7749	+	12.8012i	1.66735	+	0.446766i	0.964395	−	0.264464i	$-0.0851951\pi$
$821$	47.7749	+	12.8012i	1.66735	+	0.446766i	0.702959	+	0.711230i	$0.251862\pi$
$822$	−5.57298	+	4.14459i	−0.194380	+	0.144559i
$823$	20.6954	−	35.8456i	0.721398	−	1.24950i	−0.239041	−	0.971009i	$-0.576833\pi$
$823$	20.6954	−	35.8456i	0.721398	−	1.24950i	0.960440	−	0.278489i	$-0.0898335\pi$
$824$	−33.3935	−	15.6327i	−1.16332	−	0.544591i
$825$	−1.95084	−	7.28062i	−0.0679194	−	0.253479i
$826$	−12.1367	+	4.81458i	−0.422290	+	0.167520i
$827$	16.9307	−	16.9307i	0.588738	−	0.588738i	−0.348552	−	0.937289i	$-0.613326\pi$
$827$	16.9307	−	16.9307i	0.588738	−	0.588738i	0.937289	+	0.348552i	$0.113326\pi$
$828$	8.90814	+	2.67664i	0.309579	+	0.0930197i
$829$	−43.6187	+	25.1833i	−1.51494	+	0.874652i	−0.515095	+	0.857133i	$0.672243\pi$
$829$	−43.6187	+	25.1833i	−1.51494	+	0.874652i	−0.999847	+	0.0175184i	$0.994423\pi$
$830$	−22.6080	−	3.32314i	−0.784735	−	0.115348i
$831$	−10.7515			−0.372965
$832$	−7.67086	−	27.8057i	−0.265939	−	0.963990i
$833$	−30.1187			−1.04355
$834$	6.96433	+	1.02368i	0.241155	+	0.0354473i
$835$	20.7773	−	11.9958i	0.719026	−	0.415130i
$836$	25.6442	+	7.70534i	0.886922	+	0.266495i
$837$	−5.89497	+	5.89497i	−0.203760	+	0.203760i
$838$	44.9499	−	17.8314i	1.55277	−	0.615976i
$839$	3.44426	+	12.8542i	0.118909	+	0.443775i	0.999550	−	0.0300104i	$-0.00955404\pi$
$839$	3.44426	+	12.8542i	0.118909	+	0.443775i	−0.880641	+	0.473785i	$0.842887\pi$
$840$	31.7763	+	14.8757i	1.09639	+	0.513259i
$841$	−5.21034	+	9.02457i	−0.179667	+	0.311192i
$842$	41.3299	−	30.7368i	1.42432	−	1.05926i
$843$	17.5800	+	4.71056i	0.605489	+	0.162240i
$844$	−1.47934	+	0.349047i	−0.0509210	+	0.0120147i
$845$	−35.0025	−	2.33123i	−1.20412	−	0.0801967i
$846$	−0.224422	−	1.92842i	−0.00771579	−	0.0663006i
$847$	0.104276	−	0.389164i	0.00358297	−	0.0133718i
$848$	8.10059	+	5.35110i	0.278175	+	0.183758i
$849$	−12.8286	−	7.40659i	−0.440276	−	0.254193i
$850$	−4.26820	+	5.39247i	−0.146398	+	0.184960i
$851$	−0.597133	+	0.160001i	−0.0204695	+	0.00548478i
$852$	26.2700	−	14.1307i	0.899996	−	0.484111i
$853$	20.3124	+	20.3124i	0.695483	+	0.695483i	0.963433	−	0.267950i	$-0.0863463\pi$
$853$	20.3124	+	20.3124i	0.695483	+	0.695483i	−0.267950	+	0.963433i	$0.586346\pi$
$854$	−27.5563	−	11.9030i	−0.942958	−	0.407312i
$855$	5.46835	+	9.47146i	0.187014	+	0.323917i
$856$	6.78537	−	0.583380i	0.231919	−	0.0199395i
$857$		−	14.6923i		−	0.501878i	−0.968003	−	0.250939i	$-0.919261\pi$
$857$		−	14.6923i		−	0.501878i	0.968003	−	0.250939i	$-0.0807394\pi$
$858$	16.0406	+	5.13996i	0.547618	+	0.175475i
$859$		−	24.8694i		−	0.848535i	−0.905537	−	0.424267i	$-0.860532\pi$
$859$		−	24.8694i		−	0.848535i	0.905537	−	0.424267i	$-0.139468\pi$
$860$	−1.22376	+	40.6581i	−0.0417298	+	1.38643i
$861$	3.13983	+	5.43835i	0.107005	+	0.185339i
$862$	−21.8081	+	50.4874i	−0.742787	+	1.71961i
$863$	22.8645	+	22.8645i	0.778318	+	0.778318i	0.979545	−	0.201227i	$-0.0644928\pi$
$863$	22.8645	+	22.8645i	0.778318	+	0.778318i	−0.201227	+	0.979545i	$0.564493\pi$
$864$	−3.77122	+	4.21639i	−0.128299	+	0.143444i
$865$	27.6235	−	7.40170i	0.939227	−	0.251665i
$866$	7.18621	+	5.68796i	0.244197	+	0.193285i
$867$	−10.7888	−	6.22890i	−0.366406	−	0.211545i
$868$	55.8038	−	52.5427i	1.89410	−	1.78342i
$869$	−1.64382	+	6.13481i	−0.0557627	+	0.208109i
$870$	−23.7998	+	2.76973i	−0.806889	+	0.0939025i
$871$	18.9595	−	23.0774i	0.642417	−	0.781946i
$872$	−29.7691	+	10.7845i	−1.00811	+	0.365209i
$873$	−4.30832	−	1.15441i	−0.145814	−	0.0390708i
$874$	−15.9077	−	21.3901i	−0.538087	−	0.723532i
$875$	16.8597	−	29.2018i	0.569961	−	0.987202i
$876$	−13.2004	−	8.16035i	−0.445999	−	0.275713i
$877$	−7.99885	−	29.8521i	−0.270102	−	1.00803i	−0.959053	−	0.283227i	$-0.908595\pi$
$877$	−7.99885	−	29.8521i	−0.270102	−	1.00803i	0.688951	−	0.724808i	$-0.258071\pi$
$878$	3.45719	+	8.71498i	0.116675	+	0.294116i
$879$	−0.752766	+	0.752766i	−0.0253902	+	0.0253902i
$880$	−35.5918	−	2.14448i	−1.19980	−	0.0722905i
$881$	13.5896	−	7.84594i	0.457844	−	0.264337i	−0.253293	−	0.967390i	$-0.581514\pi$
$881$	13.5896	−	7.84594i	0.457844	−	0.264337i	0.711137	+	0.703053i	$0.248180\pi$
$882$	2.90645	−	19.7732i	0.0978653	−	0.665797i
$883$	2.24315			0.0754879			0.0377440	−	0.999287i	$-0.487983\pi$
$883$	2.24315			0.0754879			0.0377440	+	0.999287i	$0.487983\pi$
$884$	−4.97075	−	14.5426i	−0.167185	−	0.489119i
$885$	5.41962			0.182179
$886$	3.84072	−	26.1292i	0.129032	−	0.877827i
$887$	8.74988	−	5.05175i	0.293792	−	0.169621i	−0.345859	−	0.938287i	$-0.612412\pi$
$887$	8.74988	−	5.05175i	0.293792	−	0.169621i	0.639651	+	0.768666i	$0.279079\pi$
$888$	0.0658412	−	0.370153i	0.00220948	−	0.0124215i
$889$	−49.3175	+	49.3175i	−1.65406	+	1.65406i
$890$	4.40299	+	11.0992i	0.147589	+	0.372045i
$891$	−0.854979	−	3.19083i	−0.0286429	−	0.106897i
$892$	10.2364	−	16.5586i	0.342739	−	0.554422i
$893$	−2.78194	+	4.81846i	−0.0930940	+	0.161244i
$894$	9.58080	+	12.8827i	0.320430	+	0.430862i
$895$	−24.6079	−	6.59366i	−0.822551	−	0.220402i
$896$	35.8228	−	37.7044i	1.19675	−	1.25962i
$897$	−9.76019	−	13.6355i	−0.325883	−	0.455276i
$898$	−40.7348	+	4.74055i	−1.35934	+	0.158194i
$899$	−13.5474	+	50.5594i	−0.451830	+	1.68625i
$900$	−3.12832	−	3.32248i	−0.104277	−	0.110749i
$901$	4.47975	+	2.58638i	0.149242	+	0.0861649i
$902$	−5.00398	−	3.96070i	−0.166614	−	0.131877i
$903$	33.4664	−	8.96731i	1.11369	−	0.298413i
$904$	11.7697	−	8.21492i	0.391454	−	0.273224i
$905$	18.2529	+	18.2529i	0.606748	+	0.606748i
$906$	1.64776	−	3.81468i	0.0547431	−	0.126734i
$907$	2.57422	+	4.45867i	0.0854755	+	0.148048i	0.905594	−	0.424146i	$-0.139426\pi$
$907$	2.57422	+	4.45867i	0.0854755	+	0.148048i	−0.820118	+	0.572194i	$0.806092\pi$
$908$	−41.8119	−	1.25849i	−1.38758	−	0.0417644i
$909$		−	17.2691i		−	0.572781i
$910$	−28.9446	−	56.2408i	−0.959503	−	1.86436i
$911$			34.7211i			1.15036i	0.818027	+	0.575180i	$0.195068\pi$
$911$			34.7211i			1.15036i	−0.818027	+	0.575180i	$0.804932\pi$
$912$	15.8833	−	3.24651i	0.525949	−	0.107503i
$913$	−9.89009	−	17.1301i	−0.327314	−	0.566925i
$914$	10.2182	+	4.41378i	0.337989	+	0.145995i
$915$	8.81024	+	8.81024i	0.291258	+	0.291258i
$916$	21.4301	+	39.8400i	0.708070	+	1.31635i
$917$	−1.66693	+	0.446654i	−0.0550470	+	0.0147498i
$918$	−1.87059	+	2.36332i	−0.0617388	+	0.0780012i
$919$	22.7085	+	13.1108i	0.749084	+	0.432484i	0.825363	−	0.564603i	$-0.190971\pi$
$919$	22.7085	+	13.1108i	0.749084	+	0.432484i	−0.0762788	+	0.997087i	$0.524304\pi$
$920$	27.1578	+	22.8577i	0.895368	+	0.753596i
$921$	7.89195	−	29.4532i	0.260049	−	0.970514i
$922$	4.67768	+	40.1946i	0.154051	+	1.32374i
$923$	−53.0528	−	8.78776i	−1.74625	−	0.289253i
$924$	6.97446	+	29.5594i	0.229443	+	0.972431i
$925$	0.292961	+	0.0784986i	0.00963249	+	0.00258102i
$926$	−19.3153	+	14.3647i	−0.634740	+	0.472053i
$927$	6.51802	−	11.2895i	0.214080	−	0.370797i
$928$	−7.26919	+	34.7652i	−0.238623	+	1.14122i
$929$	10.0544	+	37.5235i	0.329874	+	1.23111i	0.909321	+	0.416096i	$0.136602\pi$
$929$	10.0544	+	37.5235i	0.329874	+	1.23111i	−0.579447	+	0.815010i	$0.696731\pi$
$930$	−29.5729	+	11.7314i	−0.969732	+	0.384688i
$931$	−40.5002	+	40.5002i	−1.32734	+	1.32734i
$932$	−4.93166	+	16.4131i	−0.161542	+	0.537629i
$933$	−24.6828	+	14.2506i	−0.808077	+	0.466544i
$934$	−12.9415	−	1.90227i	−0.423460	−	0.0622442i
$935$	−18.9981			−0.621304
$936$	10.0270	−	1.85998i	0.327742	−	0.0607955i
$937$	−23.3624			−0.763216			−0.381608	−	0.924324i	$-0.624630\pi$
$937$	−23.3624			−0.763216			−0.381608	+	0.924324i	$0.624630\pi$
$938$	53.2795	+	7.83154i	1.73964	+	0.255709i
$939$	14.8596	−	8.57919i	0.484924	−	0.279971i
$940$	2.13201	−	7.09556i	0.0695385	−	0.231431i
$941$	2.20682	−	2.20682i	0.0719401	−	0.0719401i	−0.670221	−	0.742161i	$-0.733801\pi$
$941$	2.20682	−	2.20682i	0.0719401	−	0.0719401i	0.742161	+	0.670221i	$0.233801\pi$
$942$	4.44465	−	1.76317i	0.144815	−	0.0574473i
$943$	1.64433	+	6.13673i	0.0535469	+	0.199840i
$944$	2.54219	−	7.62078i	0.0827414	−	0.248035i
$945$	−6.20237	+	10.7428i	−0.201763	+	0.349464i
$946$	−28.2535	+	21.0120i	−0.918602	+	0.683159i
$947$	38.8705	+	10.4153i	1.26312	+	0.338453i	0.827392	−	0.561625i	$-0.189823\pi$
$947$	38.8705	+	10.4153i	1.26312	+	0.338453i	0.435730	+	0.900077i	$0.356490\pi$
$948$	0.883037	+	3.74251i	0.0286797	+	0.121551i
$949$	9.84123	+	26.1894i	0.319460	+	0.850142i
$950$	1.51179	+	12.9906i	0.0490489	+	0.421469i
$951$	2.33117	−	8.70003i	0.0755932	−	0.282118i
$952$	17.8440	−	21.2009i	0.578327	−	0.687125i
$953$	40.6872	+	23.4908i	1.31799	+	0.760941i	0.983405	−	0.181425i	$-0.0580711\pi$
$953$	40.6872	+	23.4908i	1.31799	+	0.760941i	0.334583	+	0.942366i	$0.391404\pi$
$954$	−2.13028	+	2.69140i	−0.0689703	+	0.0871374i
$955$	−11.6270	+	3.11544i	−0.376240	+	0.100813i
$956$	−16.3492	−	30.3943i	−0.528772	−	0.983023i
$957$	−14.6658	−	14.6658i	−0.474079	−	0.474079i
$958$	−49.0148	−	21.1720i	−1.58360	−	0.684037i
$959$	11.2878	+	19.5510i	0.364502	+	0.631336i
$960$	−19.5925	+	9.06459i	−0.632344	+	0.292558i
$961$			38.5013i			1.24198i
$962$	−0.501840	+	0.455565i	−0.0161800	+	0.0146880i
$963$			2.40784i			0.0775916i
$964$	−27.8657	−	0.838723i	−0.897493	−	0.0270135i
$965$	−20.2852	−	35.1349i	−0.653003	−	1.13103i
$966$	11.9894	−	27.7564i	0.385753	−	0.893047i
$967$	9.86151	+	9.86151i	0.317125	+	0.317125i	0.847662	−	0.530537i	$-0.178010\pi$
$967$	9.86151	+	9.86151i	0.317125	+	0.317125i	−0.530537	+	0.847662i	$0.678010\pi$
$968$	0.141880	+	0.203275i	0.00456021	+	0.00653351i
$969$	8.34346	−	2.23562i	0.268030	−	0.0718185i
$970$	−13.3466	−	10.5640i	−0.428533	−	0.339189i
$971$	32.5447	+	18.7897i	1.04441	+	0.602990i	0.921079	−	0.389376i	$-0.127309\pi$
$971$	32.5447	+	18.7897i	1.04441	+	0.602990i	0.123330	+	0.992366i	$0.460643\pi$
$972$	−1.37103	−	1.45612i	−0.0439757	−	0.0467051i
$973$	5.92205	−	22.1014i	0.189852	−	0.708538i
$974$	2.14358	−	0.249462i	0.0686848	−	0.00799326i
$975$	0.802065	+	8.18772i	0.0256866	+	0.262217i
$976$	16.5211	−	8.25585i	0.528829	−	0.264263i
$977$	−14.7175	−	3.94355i	−0.470856	−	0.126165i	0.0155859	−	0.999879i	$-0.495039\pi$
$977$	−14.7175	−	3.94355i	−0.470856	−	0.126165i	−0.486441	+	0.873713i	$0.661705\pi$
$978$	−5.14206	−	6.91421i	−0.164425	−	0.221092i
$979$	−5.16801	+	8.95125i	−0.165170	+	0.286083i
$980$	40.1046	−	64.8740i	1.28109	−	2.07232i
$981$	−2.89731	−	10.8129i	−0.0925040	−	0.345230i
$982$	−20.7864	−	52.3990i	−0.663322	−	1.67212i
$983$	−26.2623	+	26.2623i	−0.837638	+	0.837638i	−0.988548	−	0.150910i	$-0.951780\pi$
$983$	−26.2623	+	26.2623i	−0.837638	+	0.837638i	0.150910	+	0.988548i	$0.451780\pi$
$984$	−3.80406	−	0.676649i	−0.121269	−	0.0215708i
$985$	58.7203	−	33.9022i	1.87098	−	1.08021i
$986$	−2.75204	+	18.7227i	−0.0876429	+	0.596252i
$987$	−6.31072			−0.200872
$988$	−26.2393	−	12.8711i	−0.834782	−	0.409483i
$989$	35.0528			1.11461
$990$	1.83331	−	12.4724i	0.0582665	−	0.396399i
$991$	6.11519	−	3.53061i	0.194255	−	0.112153i	−0.399718	−	0.916638i	$-0.630892\pi$
$991$	6.11519	−	3.53061i	0.194255	−	0.112153i	0.593973	+	0.804485i	$0.297559\pi$
$992$	2.62428	+	47.0867i	0.0833211	+	1.49500i
$993$	−9.29640	+	9.29640i	−0.295012	+	0.295012i
$994$	−35.7537	−	90.1288i	−1.13404	−	2.85871i
$995$	−16.2365	−	60.5954i	−0.514732	−	1.92100i
$996$	−10.1864	−	6.29716i	−0.322769	−	0.199533i
$997$	18.0519	−	31.2668i	0.571709	−	0.990230i	−0.424681	−	0.905343i	$-0.639614\pi$
$997$	18.0519	−	31.2668i	0.571709	−	0.990230i	0.996391	−	0.0848868i	$-0.0270529\pi$
$998$	−24.8433	−	33.4052i	−0.786399	−	1.05742i
$999$	0.128394	+	0.0344030i	0.00406220	+	0.00108846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.67.1	yes	24
3.2	odd	2		468.2.cb.h.379.6		24
4.3	odd	2		156.2.w.d.67.1	yes	24
12.11	even	2		468.2.cb.g.379.6		24
13.7	odd	12		156.2.w.d.7.1	yes	24
39.20	even	12		468.2.cb.g.163.6		24
52.7	even	12	inner	156.2.w.c.7.1	✓	24
156.59	odd	12		468.2.cb.h.163.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.7.1	✓	24	52.7	even	12	inner
156.2.w.c.67.1	yes	24	1.1	even	1	trivial
156.2.w.d.7.1	yes	24	13.7	odd	12
156.2.w.d.67.1	yes	24	4.3	odd	2
468.2.cb.g.163.6		24	39.20	even	12
468.2.cb.g.379.6		24	12.11	even	2
468.2.cb.h.163.6		24	156.59	odd	12
468.2.cb.h.379.6		24	3.2	odd	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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39918 - 0.205665i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.91540 + 0.575524i) q^{4} +(-1.90811 + 1.90811i) q^{5} +(-1.31456 + 0.521479i) q^{6} +(1.18978 + 4.44032i) q^{7} +(-2.56163 - 1.19919i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.39918 - 0.205665i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.91540 + 0.575524i) q^{4} +(-1.90811 + 1.90811i) q^{5} +(-1.31456 + 0.521479i) q^{6} +(1.18978 + 4.44032i) q^{7} +(-2.56163 - 1.19919i) q^{8} +(0.500000 - 0.866025i) q^{9} +(3.06221 - 2.27735i) q^{10} +(3.19083 + 0.854979i) q^{11} +(1.94655 - 0.459284i) q^{12} +(-3.28338 - 1.48977i) q^{13} +(-0.751497 - 6.45749i) q^{14} +(-0.698415 + 2.60652i) q^{15} +(3.33754 + 2.20472i) q^{16} +(1.84571 + 1.06562i) q^{17} +(-0.877700 + 1.10889i) q^{18} +(3.91483 - 1.04898i) q^{19} +(-4.75295 + 2.55663i) q^{20} +(3.25054 + 3.25054i) q^{21} +(-4.28870 - 1.85251i) q^{22} +(2.32540 + 4.02770i) q^{23} +(-2.81803 + 0.242283i) q^{24} -2.28173i q^{25} +(4.28765 + 2.75973i) q^{26} -1.00000i q^{27} +(-0.276600 + 9.18974i) q^{28} +(-3.13929 - 5.43742i) q^{29} +(1.51328 - 3.50335i) q^{30} +(-5.89497 - 5.89497i) q^{31} +(-4.21639 - 3.77122i) q^{32} +(3.19083 - 0.854979i) q^{33} +(-2.36332 - 1.87059i) q^{34} +(-10.7428 - 6.20237i) q^{35} +(1.45612 - 1.37103i) q^{36} +(-0.0344030 + 0.128394i) q^{37} +(-5.69328 + 0.662561i) q^{38} +(-3.58838 + 0.351516i) q^{39} +(7.17604 - 2.59967i) q^{40} +(1.31950 + 0.353560i) q^{41} +(-3.87956 - 5.21660i) q^{42} +(3.76848 - 6.52719i) q^{43} +(5.61966 + 3.47403i) q^{44} +(0.698415 + 2.60652i) q^{45} +(-2.42529 - 6.11373i) q^{46} +(-0.970719 + 0.970719i) q^{47} +(3.99276 + 0.240572i) q^{48} +(-12.2386 + 7.06599i) q^{49} +(-0.469273 + 3.19255i) q^{50} +2.13124 q^{51} +(-5.43161 - 4.74317i) q^{52} +2.42711 q^{53} +(-0.205665 + 1.39918i) q^{54} +(-7.71982 + 4.45704i) q^{55} +(2.27702 - 12.8012i) q^{56} +(2.86585 - 2.86585i) q^{57} +(3.27415 + 8.25356i) q^{58} +(-0.519814 - 1.93997i) q^{59} +(-2.83786 + 4.59059i) q^{60} +(2.30863 - 3.99867i) q^{61} +(7.03573 + 9.46050i) q^{62} +(4.44032 + 1.18978i) q^{63} +(5.12388 + 6.14377i) q^{64} +(9.10767 - 3.42241i) q^{65} +(-4.64038 + 0.540028i) q^{66} +(-2.14394 + 8.00130i) q^{67} +(2.92199 + 3.10335i) q^{68} +(4.02770 + 2.32540i) q^{69} +(13.7555 + 10.8876i) q^{70} +(14.4065 - 3.86021i) q^{71} +(-2.31934 + 1.61884i) q^{72} +(-5.48681 - 5.48681i) q^{73} +(0.0745421 - 0.172571i) q^{74} +(-1.14087 - 1.97604i) q^{75} +(8.10219 + 0.243866i) q^{76} +15.1855i q^{77} +(5.09307 + 0.246169i) q^{78} +1.92264i q^{79} +(-10.5752 + 2.16155i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.77351 - 0.766069i) q^{82} +(-4.23405 - 4.23405i) q^{83} +(4.35533 + 8.09685i) q^{84} +(-5.55513 + 1.48849i) q^{85} +(-6.61519 + 8.35767i) q^{86} +(-5.43742 - 3.13929i) q^{87} +(-7.14842 - 6.01655i) q^{88} +(-0.809823 + 3.02230i) q^{89} +(-0.441138 - 3.79063i) q^{90} +(2.70853 - 16.3517i) q^{91} +(2.13603 + 9.05300i) q^{92} +(-8.05268 - 2.15771i) q^{93} +(1.55785 - 1.15857i) q^{94} +(-5.46835 + 9.47146i) q^{95} +(-5.53711 - 1.15777i) q^{96} +(-1.15441 - 4.30832i) q^{97} +(18.5773 - 7.36952i) q^{98} +(2.33585 - 2.33585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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