LMFDB - Embedded newform 156.2.w.c.19.4

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			19.4
Character	$\chi$	$=$	156.19
Dual form			156.2.w.c.115.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0144886 - 1.41414i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.99958 - 0.0409778i) q^{4} +(-2.26006 + 2.26006i) q^{5} +(-0.719617 + 1.21744i) q^{6} +(-3.65215 - 0.978592i) q^{7} +(-0.0869195 + 2.82709i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.0144886 - 1.41414i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.99958 - 0.0409778i) q^{4} +(-2.26006 + 2.26006i) q^{5} +(-0.719617 + 1.21744i) q^{6} +(-3.65215 - 0.978592i) q^{7} +(-0.0869195 + 2.82709i) q^{8} +(0.500000 + 0.866025i) q^{9} +(3.16330 + 3.22879i) q^{10} +(-0.708226 - 2.64313i) q^{11} +(1.71120 + 1.03528i) q^{12} +(0.762837 - 3.52393i) q^{13} +(-1.43678 + 5.15048i) q^{14} +(3.08730 - 0.827240i) q^{15} +(3.99664 + 0.163877i) q^{16} +(-2.92423 + 1.68830i) q^{17} +(1.23192 - 0.694522i) q^{18} +(1.22193 - 4.56031i) q^{19} +(4.61179 - 4.42656i) q^{20} +(2.67356 + 2.67356i) q^{21} +(-3.74802 + 0.963235i) q^{22} +(-4.49580 + 7.78695i) q^{23} +(1.48882 - 2.40487i) q^{24} -5.21575i q^{25} +(-4.97227 - 1.12981i) q^{26} -1.00000i q^{27} +(7.26267 + 2.10643i) q^{28} +(0.750596 - 1.30007i) q^{29} +(-1.12510 - 4.37786i) q^{30} +(-1.32852 - 1.32852i) q^{31} +(0.289651 - 5.64943i) q^{32} +(-0.708226 + 2.64313i) q^{33} +(2.34513 + 4.15973i) q^{34} +(10.4658 - 6.04241i) q^{35} +(-0.964302 - 1.75218i) q^{36} +(-5.00911 + 1.34219i) q^{37} +(-6.43121 - 1.79405i) q^{38} +(-2.42260 + 2.67039i) q^{39} +(-6.19295 - 6.58584i) q^{40} +(-1.87044 - 6.98059i) q^{41} +(3.81953 - 3.74205i) q^{42} +(2.23980 + 3.87944i) q^{43} +(1.30784 + 5.31418i) q^{44} +(-3.08730 - 0.827240i) q^{45} +(10.9467 + 6.47050i) q^{46} +(-2.47884 + 2.47884i) q^{47} +(-3.37925 - 2.14024i) q^{48} +(6.31841 + 3.64793i) q^{49} +(-7.37580 - 0.0755690i) q^{50} +3.37661 q^{51} +(-1.66976 + 7.01512i) q^{52} +7.10124 q^{53} +(-1.41414 - 0.0144886i) q^{54} +(7.57428 + 4.37301i) q^{55} +(3.08401 - 10.2399i) q^{56} +(-3.33838 + 3.33838i) q^{57} +(-1.82761 - 1.08028i) q^{58} +(-1.32192 - 0.354208i) q^{59} +(-6.20720 + 1.52762i) q^{60} +(-5.16975 - 8.95428i) q^{61} +(-1.89796 + 1.85947i) q^{62} +(-0.978592 - 3.65215i) q^{63} +(-7.98489 - 0.491459i) q^{64} +(6.24024 + 9.68835i) q^{65} +(3.72750 + 1.03983i) q^{66} +(-3.12556 + 0.837493i) q^{67} +(5.91641 - 3.25607i) q^{68} +(7.78695 - 4.49580i) q^{69} +(-8.39318 - 14.8876i) q^{70} +(0.132920 - 0.496064i) q^{71} +(-2.49179 + 1.33827i) q^{72} +(4.08433 + 4.08433i) q^{73} +(1.82546 + 7.10303i) q^{74} +(-2.60788 + 4.51697i) q^{75} +(-2.63022 + 9.06863i) q^{76} +10.3462i q^{77} +(3.74121 + 3.46459i) q^{78} +12.8676i q^{79} +(-9.40302 + 8.66228i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.89862 + 2.54393i) q^{82} +(-2.30938 - 2.30938i) q^{83} +(-5.23645 - 5.45556i) q^{84} +(2.79326 - 10.4246i) q^{85} +(5.51853 - 3.11118i) q^{86} +(-1.30007 + 0.750596i) q^{87} +(7.53394 - 1.77248i) q^{88} +(1.63329 - 0.437637i) q^{89} +(-1.21456 + 4.35389i) q^{90} +(-6.23449 + 12.1234i) q^{91} +(9.30880 - 15.3864i) q^{92} +(0.486273 + 1.81479i) q^{93} +(3.46951 + 3.54134i) q^{94} +(7.54493 + 13.0682i) q^{95} +(-3.07556 + 4.74773i) q^{96} +(-6.08266 - 1.62984i) q^{97} +(5.25023 - 8.88226i) q^{98} +(1.93491 - 1.93491i) 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 $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.0144886	−	1.41414i	0.0102450	−	0.999948i
$2$	0.0144886	−	1.41414i	0.0102450	−	0.999948i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.99958	−	0.0409778i	−0.999790	−	0.0204889i
$5$	−2.26006	+	2.26006i	−1.01073	+	1.01073i	−0.0107881	+	0.999942i	$0.503434\pi$
$5$	−2.26006	+	2.26006i	−1.01073	+	1.01073i	−0.999942	+	0.0107881i	$0.996566\pi$
$6$	−0.719617	+	1.21744i	−0.293782	+	0.497016i
$7$	−3.65215	−	0.978592i	−1.38038	−	0.369873i	−0.509124	−	0.860693i	$-0.670030\pi$
$7$	−3.65215	−	0.978592i	−1.38038	−	0.369873i	−0.871261	+	0.490820i	$0.836697\pi$
$8$	−0.0869195	+	2.82709i	−0.0307307	+	0.999528i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	3.16330	+	3.22879i	1.00032	+	1.02103i
$11$	−0.708226	−	2.64313i	−0.213538	−	0.796935i	−0.986676	−	0.162697i	$-0.947981\pi$
$11$	−0.708226	−	2.64313i	−0.213538	−	0.796935i	0.773138	−	0.634238i	$-0.218686\pi$
$12$	1.71120	+	1.03528i	0.493980	+	0.298859i
$13$	0.762837	−	3.52393i	0.211573	−	0.977362i
$13$	0.762837	−	3.52393i	0.211573	−	0.977362i
$14$	−1.43678	+	5.15048i	−0.383995	+	1.37652i
$15$	3.08730	−	0.827240i	0.797138	−	0.213592i
$16$	3.99664	+	0.163877i	0.999160	+	0.0409692i
$17$	−2.92423	+	1.68830i	−0.709230	+	0.409474i	−0.810776	−	0.585357i	$-0.800954\pi$
$17$	−2.92423	+	1.68830i	−0.709230	+	0.409474i	0.101546	+	0.994831i	$0.467621\pi$
$18$	1.23192	−	0.694522i	0.290367	−	0.163700i
$19$	1.22193	−	4.56031i	0.280330	−	1.04621i	−0.671855	−	0.740683i	$-0.734502\pi$
$19$	1.22193	−	4.56031i	0.280330	−	1.04621i	0.952185	−	0.305523i	$-0.0988313\pi$
$20$	4.61179	−	4.42656i	1.03123	−	0.989809i
$21$	2.67356	+	2.67356i	0.583419	+	0.583419i
$22$	−3.74802	+	0.963235i	−0.799081	+	0.205362i
$23$	−4.49580	+	7.78695i	−0.937438	+	1.62369i	−0.167211	+	0.985921i	$0.553476\pi$
$23$	−4.49580	+	7.78695i	−0.937438	+	1.62369i	−0.770227	+	0.637769i	$0.779857\pi$
$24$	1.48882	−	2.40487i	0.303904	−	0.490893i
$25$		−	5.21575i		−	1.04315i
$26$	−4.97227	−	1.12981i	−0.975143	−	0.221575i
$27$		−	1.00000i		−	0.192450i
$28$	7.26267	+	2.10643i	1.37252	+	0.398078i
$29$	0.750596	−	1.30007i	0.139382	−	0.241417i	−0.787881	−	0.615828i	$-0.788822\pi$
$29$	0.750596	−	1.30007i	0.139382	−	0.241417i	0.927263	+	0.374411i	$0.122155\pi$
$30$	−1.12510	−	4.37786i	−0.205414	−	0.799284i
$31$	−1.32852	−	1.32852i	−0.238610	−	0.238610i	0.577665	−	0.816274i	$-0.303964\pi$
$31$	−1.32852	−	1.32852i	−0.238610	−	0.238610i	−0.816274	+	0.577665i	$0.803964\pi$
$32$	0.289651	−	5.64943i	0.0512035	−	0.998688i
$33$	−0.708226	+	2.64313i	−0.123286	+	0.460111i
$34$	2.34513	+	4.15973i	0.402186	+	0.713387i
$35$	10.4658	−	6.04241i	1.76904	−	1.02135i
$36$	−0.964302	−	1.75218i	−0.160717	−	0.292029i
$37$	−5.00911	+	1.34219i	−0.823493	+	0.220654i	−0.645873	−	0.763445i	$-0.723506\pi$
$37$	−5.00911	+	1.34219i	−0.823493	+	0.220654i	−0.177620	+	0.984099i	$0.556840\pi$
$38$	−6.43121	−	1.79405i	−1.04328	−	0.291034i
$39$	−2.42260	+	2.67039i	−0.387927	+	0.427605i
$40$	−6.19295	−	6.58584i	−0.979192	−	1.04131i
$41$	−1.87044	−	6.98059i	−0.292114	−	1.09018i	−0.943482	−	0.331423i	$-0.892471\pi$
$41$	−1.87044	−	6.98059i	−0.292114	−	1.09018i	0.651368	−	0.758762i	$-0.274195\pi$
$42$	3.81953	−	3.74205i	0.589366	−	0.577411i
$43$	2.23980	+	3.87944i	0.341566	+	0.591610i	0.984724	−	0.174124i	$-0.0557094\pi$
$43$	2.23980	+	3.87944i	0.341566	+	0.591610i	−0.643158	+	0.765734i	$0.722376\pi$
$44$	1.30784	+	5.31418i	0.197165	+	0.801143i
$45$	−3.08730	−	0.827240i	−0.460228	−	0.123318i
$46$	10.9467	+	6.47050i	1.61400	+	0.954024i
$47$	−2.47884	+	2.47884i	−0.361576	+	0.361576i	−0.864393	−	0.502817i	$-0.832297\pi$
$47$	−2.47884	+	2.47884i	−0.361576	+	0.361576i	0.502817	+	0.864393i	$0.332297\pi$
$48$	−3.37925	−	2.14024i	−0.487753	−	0.308917i
$49$	6.31841	+	3.64793i	0.902630	+	0.521134i
$50$	−7.37580	−	0.0755690i	−1.04310	−	0.0106871i
$51$	3.37661			0.472820
$52$	−1.66976	+	7.01512i	−0.231554	+	0.972822i
$53$	7.10124			0.975431			0.487715	−	0.873003i	$-0.337830\pi$
$53$	7.10124			0.975431			0.487715	+	0.873003i	$0.337830\pi$
$54$	−1.41414	−	0.0144886i	−0.192440	−	0.00197165i
$55$	7.57428	+	4.37301i	1.02132	+	0.589657i
$56$	3.08401	−	10.2399i	0.412118	−	1.36837i
$57$	−3.33838	+	3.33838i	−0.442179	+	0.442179i
$58$	−1.82761	−	1.08028i	−0.239976	−	0.141848i
$59$	−1.32192	−	0.354208i	−0.172100	−	0.0461140i	0.171740	−	0.985142i	$-0.445061\pi$
$59$	−1.32192	−	0.354208i	−0.172100	−	0.0461140i	−0.343840	+	0.939028i	$0.611728\pi$
$60$	−6.20720	+	1.52762i	−0.801347	+	0.197215i
$61$	−5.16975	−	8.95428i	−0.661919	−	1.14648i	−0.980111	−	0.198451i	$-0.936409\pi$
$61$	−5.16975	−	8.95428i	−0.661919	−	1.14648i	0.318192	−	0.948026i	$-0.396924\pi$
$62$	−1.89796	+	1.85947i	−0.241042	+	0.236152i
$63$	−0.978592	−	3.65215i	−0.123291	−	0.460128i
$64$	−7.98489	−	0.491459i	−0.998111	−	0.0614323i
$65$	6.24024	+	9.68835i	0.774006	+	1.20169i
$66$	3.72750	+	1.03983i	0.458823	+	0.127994i
$67$	−3.12556	+	0.837493i	−0.381849	+	0.102316i	−0.444637	−	0.895711i	$-0.646667\pi$
$67$	−3.12556	+	0.837493i	−0.381849	+	0.102316i	0.0627885	+	0.998027i	$0.480001\pi$
$68$	5.91641	−	3.25607i	0.717470	−	0.394857i
$69$	7.78695	−	4.49580i	0.937438	−	0.541230i
$70$	−8.39318	−	14.8876i	−1.00318	−	1.77941i
$71$	0.132920	−	0.496064i	0.0157747	−	0.0588719i	−0.957590	−	0.288135i	$-0.906965\pi$
$71$	0.132920	−	0.496064i	0.0157747	−	0.0588719i	0.973365	+	0.229263i	$0.0736315\pi$
$72$	−2.49179	+	1.33827i	−0.293661	+	0.157717i
$73$	4.08433	+	4.08433i	0.478035	+	0.478035i	0.904503	−	0.426468i	$-0.140242\pi$
$73$	4.08433	+	4.08433i	0.478035	+	0.478035i	−0.426468	+	0.904503i	$0.640242\pi$
$74$	1.82546	+	7.10303i	0.212206	+	0.825710i
$75$	−2.60788	+	4.51697i	−0.301131	+	0.521575i
$76$	−2.63022	+	9.06863i	−0.301707	+	1.04024i
$77$			10.3462i			1.17906i
$78$	3.74121	+	3.46459i	0.423609	+	0.392287i
$79$			12.8676i			1.44771i	0.689950	+	0.723857i	$0.257633\pi$
$79$			12.8676i			1.44771i	−0.689950	+	0.723857i	$0.742367\pi$
$80$	−9.40302	+	8.66228i	−1.05129	+	0.968473i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−9.89862	+	2.54393i	−1.09312	+	0.280930i
$83$	−2.30938	−	2.30938i	−0.253487	−	0.253487i	0.568912	−	0.822399i	$-0.307365\pi$
$83$	−2.30938	−	2.30938i	−0.253487	−	0.253487i	−0.822399	+	0.568912i	$0.807365\pi$
$84$	−5.23645	−	5.45556i	−0.571343	−	0.595250i
$85$	2.79326	−	10.4246i	0.302972	−	1.13071i
$86$	5.51853	−	3.11118i	0.595078	−	0.335487i
$87$	−1.30007	+	0.750596i	−0.139382	+	0.0804724i
$88$	7.53394	−	1.77248i	0.803121	−	0.188947i
$89$	1.63329	−	0.437637i	0.173128	−	0.0463895i	−0.171214	−	0.985234i	$-0.554769\pi$
$89$	1.63329	−	0.437637i	0.173128	−	0.0463895i	0.344342	+	0.938844i	$0.388102\pi$
$90$	−1.21456	+	4.35389i	−0.128026	+	0.458940i
$91$	−6.23449	+	12.1234i	−0.653552	+	1.27088i
$92$	9.30880	−	15.3864i	0.970509	−	1.60414i
$93$	0.486273	+	1.81479i	0.0504241	+	0.188185i
$94$	3.46951	+	3.54134i	0.357852	+	0.365261i
$95$	7.54493	+	13.0682i	0.774094	+	1.34077i
$96$	−3.07556	+	4.74773i	−0.313898	+	0.484563i
$97$	−6.08266	−	1.62984i	−0.617600	−	0.165485i	−0.0635635	−	0.997978i	$-0.520247\pi$
$97$	−6.08266	−	1.62984i	−0.617600	−	0.165485i	−0.554037	+	0.832492i	$0.686913\pi$
$98$	5.25023	−	8.88226i	0.530354	−	0.897243i
$99$	1.93491	−	1.93491i	0.194466	−	0.194466i
$100$	−0.213730	+	10.4293i	−0.0213730	+	1.04293i
$101$	−8.43259	−	4.86856i	−0.839075	−	0.484440i	0.0178750	−	0.999840i	$-0.494310\pi$
$101$	−8.43259	−	4.86856i	−0.839075	−	0.484440i	−0.856950	+	0.515400i	$0.827643\pi$
$102$	0.0489223	−	4.77499i	0.00484403	−	0.472795i
$103$	−7.83145			−0.771656			−0.385828	−	0.922571i	$-0.626084\pi$
$103$	−7.83145			−0.771656			−0.385828	+	0.922571i	$0.626084\pi$
$104$	9.89617	+	2.46291i	0.970399	+	0.241508i
$105$	−12.0848			−1.17936
$106$	0.102887	−	10.0421i	0.00999328	−	0.975379i
$107$	−7.51998	−	4.34166i	−0.726984	−	0.419725i	0.0903336	−	0.995912i	$-0.471207\pi$
$107$	−7.51998	−	4.34166i	−0.726984	−	0.419725i	−0.817318	+	0.576187i	$0.804540\pi$
$108$	−0.0409778	+	1.99958i	−0.00394309	+	0.192410i
$109$	−0.211691	+	0.211691i	−0.0202763	+	0.0202763i	−0.717172	−	0.696896i	$-0.754564\pi$
$109$	−0.211691	+	0.211691i	−0.0202763	+	0.0202763i	0.696896	+	0.717172i	$0.254564\pi$
$110$	6.29379	−	10.6477i	0.600089	−	1.01522i
$111$	5.00911	+	1.34219i	0.475444	+	0.127395i
$112$	−14.4360	−	4.50958i	−1.36407	−	0.426116i
$113$	−0.118135	−	0.204616i	−0.0111132	−	0.0192486i	0.860415	−	0.509593i	$-0.170204\pi$
$113$	−0.118135	−	0.204616i	−0.0111132	−	0.0192486i	−0.871529	+	0.490345i	$0.836871\pi$
$114$	4.67256	+	4.76930i	0.437625	+	0.446686i
$115$	−7.43820	−	27.7597i	−0.693616	−	2.58861i
$116$	−1.55415	+	2.56884i	−0.144299	+	0.238511i
$117$	3.43323	−	1.10133i	0.317402	−	0.101818i
$118$	−0.520052	+	1.86425i	−0.0478747	+	0.171618i
$119$	12.3319	−	3.30432i	1.13046	−	0.302907i
$120$	2.07034	+	8.79998i	0.188995	+	0.803325i
$121$	3.04170	−	1.75613i	0.276518	−	0.159648i
$122$	−12.7375	+	7.18102i	−1.15320	+	0.650139i
$123$	−1.87044	+	6.98059i	−0.168652	+	0.629418i
$124$	2.60205	+	2.71093i	0.233671	+	0.243448i
$125$	0.487608	+	0.487608i	0.0436130	+	0.0436130i
$126$	−5.17883	+	1.33095i	−0.461367	+	0.118570i
$127$	9.93912	−	17.2151i	0.881954	−	1.52759i	0.0327882	−	0.999462i	$-0.489561\pi$
$127$	9.93912	−	17.2151i	0.881954	−	1.52759i	0.849166	−	0.528127i	$-0.177105\pi$
$128$	−0.810681	+	11.2846i	−0.0716547	+	0.997429i
$129$		−	4.47960i		−	0.394407i
$130$	13.7911	−	8.68419i	1.20956	−	0.761654i
$131$		−	6.70196i		−	0.585553i	−0.956181	−	0.292776i	$-0.905421\pi$
$131$		−	6.70196i		−	0.585553i	0.956181	−	0.292776i	$-0.0945791\pi$
$132$	1.52446	−	5.25614i	0.132688	−	0.457488i
$133$	−8.92536	+	15.4592i	−0.773927	+	1.34048i
$134$	1.13905	+	4.43212i	0.0983986	+	0.382877i
$135$	2.26006	+	2.26006i	0.194515	+	0.194515i
$136$	−4.51882	−	8.41381i	−0.387485	−	0.721478i
$137$	−0.653281	+	2.43808i	−0.0558135	+	0.208299i	−0.988201	−	0.153161i	$-0.951055\pi$
$137$	−0.653281	+	2.43808i	−0.0558135	+	0.208299i	0.932388	+	0.361460i	$0.117721\pi$
$138$	−6.24486	−	11.0770i	−0.531598	−	0.942934i
$139$	16.5644	−	9.56345i	1.40497	−	0.811161i	0.410074	−	0.912052i	$-0.365503\pi$
$139$	16.5644	−	9.56345i	1.40497	−	0.811161i	0.994897	+	0.100891i	$0.0321694\pi$
$140$	−21.1747	+	11.6534i	−1.78959	+	0.984894i
$141$	3.38615	−	0.907317i	0.285166	−	0.0764099i
$142$	−0.699577	−	0.195154i	−0.0587072	−	0.0163770i
$143$	−9.85448	+	0.479457i	−0.824073	+	0.0400942i
$144$	1.85640	+	3.54313i	0.154700	+	0.295261i
$145$	1.24185	+	4.63463i	0.103130	+	0.384885i
$146$	5.83499	−	5.71664i	0.482907	−	0.473112i
$147$	−3.64793	−	6.31841i	−0.300877	−	0.521134i
$148$	10.0711	−	2.47855i	0.827841	−	0.203735i
$149$	1.64654	+	0.441189i	0.134890	+	0.0361436i	0.325632	−	0.945497i	$-0.394423\pi$
$149$	1.64654	+	0.441189i	0.134890	+	0.0361436i	−0.190742	+	0.981640i	$0.561090\pi$
$150$	6.34984	+	3.75334i	0.518463	+	0.306459i
$151$	−8.61808	+	8.61808i	−0.701329	+	0.701329i	−0.964696	−	0.263367i	$-0.915167\pi$
$151$	−8.61808	+	8.61808i	−0.701329	+	0.701329i	0.263367	+	0.964696i	$0.415167\pi$
$152$	12.7862	+	3.85089i	1.03710	+	0.312348i
$153$	−2.92423	−	1.68830i	−0.236410	−	0.136491i
$154$	14.6310	+	0.149902i	1.17900	+	0.0120794i
$155$	6.00508			0.482340
$156$	4.95361	−	5.24039i	0.396606	−	0.419567i
$157$	11.0155			0.879132			0.439566	−	0.898210i	$-0.355132\pi$
$157$	11.0155			0.879132			0.439566	+	0.898210i	$0.355132\pi$
$158$	18.1965	+	0.186433i	1.44764	+	0.0148318i
$159$	−6.14986	−	3.55062i	−0.487715	−	0.281583i
$160$	12.1134	+	13.4227i	0.957651	+	1.06116i
$161$	24.0396	−	24.0396i	1.89458	−	1.89458i
$162$	1.21744	+	0.719617i	0.0956508	+	0.0565385i
$163$	−0.267335	−	0.0716323i	−0.0209393	−	0.00561067i	0.248334	−	0.968674i	$-0.420117\pi$
$163$	−0.267335	−	0.0716323i	−0.0209393	−	0.00561067i	−0.269273	+	0.963064i	$0.586784\pi$
$164$	3.45405	+	14.0349i	0.269716	+	1.09594i
$165$	−4.37301	−	7.57428i	−0.340439	−	0.589657i
$166$	−3.29924	+	3.23232i	−0.256071	+	0.250877i
$167$	−6.14675	−	22.9400i	−0.475650	−	1.77515i	−0.618908	−	0.785464i	$-0.712424\pi$
$167$	−6.14675	−	22.9400i	−0.475650	−	1.77515i	0.143258	−	0.989685i	$-0.454242\pi$
$168$	−7.79079	+	7.32602i	−0.601072	+	0.565215i
$169$	−11.8362	−	5.37637i	−0.910474	−	0.413567i
$170$	−14.7014	−	4.10110i	−1.12754	−	0.314540i
$171$	4.56031	−	1.22193i	0.348735	−	0.0934434i
$172$	−4.31969	−	7.84904i	−0.329373	−	0.598484i
$173$	−17.6700	+	10.2018i	−1.34343	+	0.775629i	−0.987309	−	0.158812i	$-0.949234\pi$
$173$	−17.6700	+	10.2018i	−1.34343	+	0.775629i	−0.356119	+	0.934440i	$0.615900\pi$
$174$	1.04261	+	1.84936i	0.0790402	+	0.140199i
$175$	−5.10409	+	19.0487i	−0.385833	+	1.43995i
$176$	−2.39738	−	10.6797i	−0.180709	−	0.805015i
$177$	0.967714	+	0.967714i	0.0727379	+	0.0727379i
$178$	−0.595216	−	2.31603i	−0.0446133	−	0.173594i
$179$	−0.440840	+	0.763557i	−0.0329499	+	0.0570709i	−0.882030	−	0.471193i	$-0.843824\pi$
$179$	−0.440840	+	0.763557i	−0.0329499	+	0.0570709i	0.849080	+	0.528264i	$0.177157\pi$
$180$	6.13941	+	1.78064i	0.457604	+	0.132721i
$181$			24.4653i			1.81849i	0.416259	+	0.909246i	$0.363341\pi$
$181$			24.4653i			1.81849i	−0.416259	+	0.909246i	$0.636659\pi$
$182$	17.0539	+	8.99208i	1.26412	+	0.666538i
$183$			10.3395i			0.764318i
$184$	−21.6236	−	13.3869i	−1.59412	−	0.986893i
$185$	8.28747	−	14.3543i	0.609307	−	1.05535i
$186$	2.57342	−	0.661364i	0.188692	−	0.0484935i
$187$	6.53343	+	6.53343i	0.477772	+	0.477772i
$188$	5.05821	−	4.85506i	0.368908	−	0.354091i
$189$	−0.978592	+	3.65215i	−0.0711821	+	0.265655i
$190$	18.5896	−	10.4802i	1.34863	−	0.760317i
$191$	−5.43928	+	3.14037i	−0.393572	+	0.227229i	−0.683707	−	0.729757i	$-0.739633\pi$
$191$	−5.43928	+	3.14037i	−0.393572	+	0.227229i	0.290135	+	0.956986i	$0.406300\pi$
$192$	6.66939	+	4.41806i	0.481322	+	0.318846i
$193$	−13.3745	+	3.58368i	−0.962716	+	0.257959i	−0.705750	−	0.708461i	$-0.749390\pi$
$193$	−13.3745	+	3.58368i	−0.962716	+	0.257959i	−0.256966	+	0.966420i	$0.582723\pi$
$194$	−2.39295	+	8.57811i	−0.171804	+	0.615872i
$195$	−0.560027	−	11.5105i	−0.0401044	−	0.824283i
$196$	−12.4847	−	7.55325i	−0.891763	−	0.539518i
$197$	−1.77896	−	6.63917i	−0.126746	−	0.473021i	0.873150	−	0.487451i	$-0.162073\pi$
$197$	−1.77896	−	6.63917i	−0.126746	−	0.473021i	−0.999896	+	0.0144301i	$0.995407\pi$
$198$	−2.70820	−	2.76426i	−0.192463	−	0.196448i
$199$	2.16220	+	3.74505i	0.153275	+	0.265479i	0.932429	−	0.361352i	$-0.117685\pi$
$199$	2.16220	+	3.74505i	0.153275	+	0.265479i	−0.779155	+	0.626832i	$0.784351\pi$
$200$	14.7454	+	0.453350i	1.04266	+	0.0320567i
$201$	3.12556	+	0.837493i	0.220460	+	0.0590722i
$202$	−7.00700	+	11.8543i	−0.493011	+	0.834067i
$203$	−4.01353	+	4.01353i	−0.281695	+	0.281695i
$204$	−6.75180	−	0.138366i	−0.472720	−	0.00968756i
$205$	20.0039	+	11.5492i	1.39713	+	0.806634i
$206$	−0.113467	+	11.0748i	−0.00790561	+	0.771615i
$207$	−8.99159			−0.624959
$208$	3.62628	−	13.9589i	0.251437	−	0.967874i
$209$	−12.9189			−0.893620
$210$	−0.175092	+	17.0896i	−0.0120825	+	1.17930i
$211$	−5.63537	−	3.25358i	−0.387955	−	0.223986i	0.293319	−	0.956015i	$-0.405240\pi$
$211$	−5.63537	−	3.25358i	−0.387955	−	0.223986i	−0.681274	+	0.732029i	$0.738574\pi$
$212$	−14.1995	−	0.290993i	−0.975226	−	0.0199855i
$213$	−0.363144	+	0.363144i	−0.0248822	+	0.0248822i
$214$	−6.24867	+	10.5714i	−0.427151	+	0.722646i
$215$	−13.8299	−	3.70570i	−0.943189	−	0.252727i
$216$	2.82709	+	0.0869195i	0.192359	+	0.00591412i
$217$	3.55189	+	6.15205i	0.241118	+	0.417628i
$218$	0.296294	+	0.302428i	0.0200675	+	0.0204830i
$219$	−1.49497	−	5.57930i	−0.101021	−	0.377014i
$220$	−14.9662	−	9.05457i	−1.00902	−	0.610459i
$221$	3.71875	+	11.5927i	0.250150	+	0.779808i
$222$	1.97061	−	7.06413i	0.132259	−	0.474114i
$223$	13.6809	−	3.66579i	0.916141	−	0.245479i	0.230206	−	0.973142i	$-0.426060\pi$
$223$	13.6809	−	3.66579i	0.916141	−	0.245479i	0.685935	+	0.727663i	$0.259393\pi$
$224$	−6.58634	+	20.3492i	−0.440068	+	1.35963i
$225$	4.51697	−	2.60788i	0.301131	−	0.173858i
$226$	−0.291067	+	0.164095i	−0.0193615	+	0.0109154i
$227$	−2.51759	+	9.39578i	−0.167098	+	0.623620i	0.830665	+	0.556773i	$0.187961\pi$
$227$	−2.51759	+	9.39578i	−0.167098	+	0.623620i	−0.997763	+	0.0668470i	$0.978706\pi$
$228$	6.81215	−	6.53855i	0.451146	−	0.433026i
$229$	−13.9677	−	13.9677i	−0.923014	−	0.923014i	0.0742271	−	0.997241i	$-0.476351\pi$
$229$	−13.9677	−	13.9677i	−0.923014	−	0.923014i	−0.997241	+	0.0742271i	$0.976351\pi$
$230$	−39.3639	+	10.1165i	−2.59558	+	0.667059i
$231$	5.17310	−	8.96007i	0.340365	−	0.589529i
$232$	3.61018	+	2.23501i	0.237020	+	0.146735i
$233$		−	11.9025i		−	0.779756i	−0.920867	−	0.389878i	$-0.872517\pi$
$233$		−	11.9025i		−	0.779756i	0.920867	−	0.389878i	$-0.127483\pi$
$234$	−1.50769	−	4.87102i	−0.0985607	−	0.318429i
$235$		−	11.2046i		−	0.730910i
$236$	2.62877	+	0.762437i	0.171119	+	0.0496304i
$237$	6.43378	−	11.1436i	0.417919	−	0.723857i
$238$	−4.49410	−	17.4869i	−0.291309	−	1.13351i
$239$	13.6307	+	13.6307i	0.881697	+	0.881697i	0.993707	−	0.112010i	$-0.0357289\pi$
$239$	13.6307	+	13.6307i	0.881697	+	0.881697i	−0.112010	+	0.993707i	$0.535729\pi$
$240$	12.4744	−	2.80024i	0.805219	−	0.180755i
$241$	−5.00843	+	18.6917i	−0.322621	+	1.20404i	0.594061	+	0.804420i	$0.297524\pi$
$241$	−5.00843	+	18.6917i	−0.322621	+	1.20404i	−0.916682	+	0.399618i	$0.869143\pi$
$242$	−2.43934	−	4.32683i	−0.156807	−	0.278139i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	9.97041	+	18.1166i	0.638290	+	1.15980i
$245$	−22.5245	+	6.03543i	−1.43904	+	0.385590i
$246$	9.84442	+	2.74621i	0.627657	+	0.175092i
$247$	−15.1381	−	7.78477i	−0.963212	−	0.495333i
$248$	3.87133	−	3.64038i	0.245829	−	0.231164i
$249$	0.845291	+	3.15467i	0.0535681	+	0.199919i
$250$	0.696611	−	0.682481i	0.0440575	−	0.0431639i
$251$	0.188732	+	0.326893i	0.0119126	+	0.0206333i	0.871920	−	0.489648i	$-0.162875\pi$
$251$	0.188732	+	0.326893i	0.0119126	+	0.0206333i	−0.860008	+	0.510281i	$0.829541\pi$
$252$	1.80712	+	7.34287i	0.113838	+	0.462558i
$253$	23.7660	+	6.36808i	1.49415	+	0.400358i
$254$	−24.2005	−	14.3047i	−1.51847	−	0.897558i
$255$	−7.63134	+	7.63134i	−0.477893	+	0.477893i
$256$	15.9463	+	1.30991i	0.996643	+	0.0818696i
$257$	−24.2185	−	13.9826i	−1.51071	−	0.872210i	−0.999922	−	0.0125039i	$-0.996020\pi$
$257$	−24.2185	−	13.9826i	−1.51071	−	0.872210i	−0.510790	−	0.859706i	$-0.670647\pi$
$258$	−6.33477	−	0.0649031i	−0.394386	−	0.00404069i
$259$	19.6075			1.21835
$260$	−12.0808	−	19.6284i	−0.749222	−	1.21730i
$261$	1.50119			0.0929215
$262$	−9.47750	−	0.0971020i	−0.585522	−	0.00599898i
$263$	−7.97912	−	4.60675i	−0.492014	−	0.284064i	0.233396	−	0.972382i	$-0.425016\pi$
$263$	−7.97912	−	4.60675i	−0.492014	−	0.284064i	−0.725409	+	0.688318i	$0.758350\pi$
$264$	−7.41082	−	2.23196i	−0.456105	−	0.137368i
$265$	−16.0492	+	16.0492i	−0.985897	+	0.985897i
$266$	21.7321	+	12.8457i	1.33248	+	0.787619i
$267$	−1.63329	−	0.437637i	−0.0999554	−	0.0267830i
$268$	6.28414	−	1.54655i	0.383865	−	0.0944709i
$269$	3.91905	+	6.78800i	0.238949	+	0.413872i	0.960413	−	0.278580i	$-0.0898638\pi$
$269$	3.91905	+	6.78800i	0.238949	+	0.413872i	−0.721464	+	0.692452i	$0.756530\pi$
$270$	3.22879	−	3.16330i	0.196498	−	0.192512i
$271$	4.44713	+	16.5969i	0.270144	+	1.00819i	0.959026	+	0.283318i	$0.0914352\pi$
$271$	4.44713	+	16.5969i	0.270144	+	1.00819i	−0.688882	+	0.724874i	$0.741898\pi$
$272$	−11.9638	+	6.26833i	−0.725410	+	0.380073i
$273$	11.4609	−	7.38195i	0.693647	−	0.446776i
$274$	3.43831	+	0.959154i	0.207716	+	0.0579446i
$275$	−13.7859	+	3.69393i	−0.831323	+	0.222752i
$276$	−15.7549	+	8.67061i	−0.948331	+	0.521910i
$277$	26.3907	−	15.2367i	1.58566	−	0.915482i	0.591652	−	0.806194i	$-0.298476\pi$
$277$	26.3907	−	15.2367i	1.58566	−	0.915482i	0.994010	−	0.109289i	$-0.0348573\pi$
$278$	−13.2841	−	23.5629i	−0.796724	−	1.41321i
$279$	0.486273	−	1.81479i	0.0291124	−	0.108649i
$280$	16.1728	+	30.1129i	0.966508	+	1.79959i
$281$	2.55333	+	2.55333i	0.152319	+	0.152319i	0.779153	−	0.626834i	$-0.215650\pi$
$281$	2.55333	+	2.55333i	0.152319	+	0.152319i	−0.626834	+	0.779153i	$0.715650\pi$
$282$	−1.23401	−	4.80164i	−0.0734844	−	0.285933i
$283$	−3.71939	+	6.44217i	−0.221095	+	0.382947i	−0.955141	−	0.296152i	$-0.904296\pi$
$283$	−3.71939	+	6.44217i	−0.221095	+	0.382947i	0.734046	+	0.679100i	$0.237630\pi$
$284$	−0.286111	+	0.986472i	−0.0169776	+	0.0585364i
$285$		−	15.0899i		−	0.893847i
$286$	0.535241	+	13.9426i	0.0316494	+	0.824441i
$287$			27.3246i			1.61292i
$288$	5.03738	−	2.57387i	0.296830	−	0.151667i
$289$	−2.79926	+	4.84846i	−0.164662	+	0.285203i
$290$	6.57201	−	1.68899i	0.385922	−	0.0991811i
$291$	4.45281	+	4.45281i	0.261028	+	0.261028i
$292$	−7.99958	−	8.33432i	−0.468140	−	0.487729i
$293$	3.46994	−	12.9500i	0.202716	−	0.756547i	−0.787418	−	0.616420i	$-0.788582\pi$
$293$	3.46994	−	12.9500i	0.202716	−	0.756547i	0.990134	−	0.140127i	$-0.0447510\pi$
$294$	−8.98796	+	5.06714i	−0.524189	+	0.295522i
$295$	3.78816	−	2.18709i	0.220555	−	0.127337i
$296$	−3.35910	−	14.2779i	−0.195243	−	0.829884i
$297$	−2.64313	+	0.708226i	−0.153370	+	0.0410954i
$298$	0.647759	−	2.32204i	0.0375236	−	0.134512i
$299$	24.0111	+	21.7830i	1.38860	+	1.25975i
$300$	5.39975	−	8.92518i	0.311755	−	0.515296i
$301$	−4.38370	−	16.3602i	−0.252672	−	0.942985i
$302$	12.0623	+	12.3120i	0.694107	+	0.708477i
$303$	4.86856	+	8.43259i	0.279692	+	0.484440i
$304$	5.63095	−	18.0257i	0.322957	−	1.03384i
$305$	31.9212	+	8.55325i	1.82780	+	0.489758i
$306$	−2.42987	+	4.11081i	−0.138906	+	0.234999i
$307$	10.7142	−	10.7142i	0.611494	−	0.611494i	−0.331841	−	0.943335i	$-0.607670\pi$
$307$	10.7142	−	10.7142i	0.611494	−	0.611494i	0.943335	+	0.331841i	$0.107670\pi$
$308$	0.423965	−	20.6881i	0.0241576	−	1.17881i
$309$	6.78223	+	3.91572i	0.385828	+	0.222758i
$310$	0.0870052	−	8.49202i	0.00494157	−	0.482314i
$311$	6.72178			0.381157			0.190578	−	0.981672i	$-0.438964\pi$
$311$	6.72178			0.381157			0.190578	+	0.981672i	$0.438964\pi$
$312$	−7.33888	−	7.08102i	−0.415482	−	0.400884i
$313$	25.7571			1.45588			0.727939	−	0.685642i	$-0.240479\pi$
$313$	25.7571			1.45588			0.727939	+	0.685642i	$0.240479\pi$
$314$	0.159599	−	15.5774i	0.00900670	−	0.879085i
$315$	10.4658	+	6.04241i	0.589679	+	0.340451i
$316$	0.527285	−	25.7297i	0.0296621	−	1.44741i
$317$	−14.3805	+	14.3805i	−0.807688	+	0.807688i	−0.984283	−	0.176596i	$-0.943491\pi$
$317$	−14.3805	+	14.3805i	−0.807688	+	0.807688i	0.176596	+	0.984283i	$0.443491\pi$
$318$	−5.11018	+	8.64531i	−0.286564	+	0.484805i
$319$	−3.96785	−	1.06318i	−0.222157	−	0.0595268i
$320$	19.1571	−	16.9356i	1.07091	−	0.946729i
$321$	4.34166	+	7.51998i	0.242328	+	0.419725i
$322$	−33.6470	−	34.3436i	−1.87507	−	1.91389i
$323$	4.12598	+	15.3984i	0.229576	+	0.856788i
$324$	1.03528	−	1.71120i	0.0575154	−	0.0950666i
$325$	−18.3799	−	3.97877i	−1.01954	−	0.220702i
$326$	−0.105171	+	0.377011i	−0.00582490	+	0.0208807i
$327$	0.289176	−	0.0774844i	0.0159914	−	0.00428490i
$328$	19.8973	−	4.68116i	1.09865	−	0.258474i
$329$	11.4789	−	6.62732i	0.632850	−	0.365376i
$330$	−10.7744	+	6.07431i	−0.593114	+	0.334380i
$331$	−5.38366	+	20.0921i	−0.295913	+	1.10436i	0.644577	+	0.764540i	$0.277034\pi$
$331$	−5.38366	+	20.0921i	−0.295913	+	1.10436i	−0.940490	+	0.339822i	$0.889633\pi$
$332$	4.52315	+	4.71242i	0.248240	+	0.258628i
$333$	−3.66692	−	3.66692i	−0.200946	−	0.200946i
$334$	−32.5294	+	8.35999i	−1.77993	+	0.457438i
$335$	5.17118	−	8.95675i	0.282532	−	0.489360i
$336$	10.2471	+	11.1234i	0.559027	+	0.606831i
$337$		−	10.9352i		−	0.595678i	−0.954616	−	0.297839i	$-0.903734\pi$
$337$		−	10.9352i		−	0.595678i	0.954616	−	0.297839i	$-0.0962659\pi$
$338$	−7.77442	+	16.6601i	−0.422873	+	0.906189i
$339$			0.236270i			0.0128324i
$340$	−6.01253	+	20.7304i	−0.326075	+	1.12426i
$341$	−2.57057	+	4.45236i	−0.139204	+	0.241109i
$342$	−1.66191	−	6.46661i	−0.0898657	−	0.349674i
$343$	−0.791024	−	0.791024i	−0.0427113	−	0.0427113i
$344$	−11.1622	+	5.99492i	−0.601827	+	0.323224i
$345$	−7.43820	+	27.7597i	−0.400459	+	1.49453i
$346$	14.1708	+	25.1357i	0.761825	+	1.35130i
$347$	29.0843	−	16.7919i	1.56133	−	0.901434i	0.564206	−	0.825634i	$-0.309182\pi$
$347$	29.0843	−	16.7919i	1.56133	−	0.901434i	0.997123	−	0.0758000i	$-0.0241510\pi$
$348$	2.63035	−	1.44760i	0.141002	−	0.0775997i
$349$	11.6004	−	3.10832i	0.620956	−	0.166385i	0.0653936	−	0.997860i	$-0.479170\pi$
$349$	11.6004	−	3.10832i	0.620956	−	0.166385i	0.555562	+	0.831475i	$0.312503\pi$
$350$	26.8636	+	7.49388i	1.43592	+	0.400565i
$351$	−3.52393	−	0.762837i	−0.188093	−	0.0407172i
$352$	−15.1374	+	3.23549i	−0.806824	+	0.172452i
$353$	4.02574	+	15.0243i	0.214269	+	0.799661i	0.986423	+	0.164226i	$0.0525127\pi$
$353$	4.02574	+	15.0243i	0.214269	+	0.799661i	−0.772154	+	0.635435i	$0.780821\pi$
$354$	1.38250	−	1.35446i	0.0734792	−	0.0719888i
$355$	0.820727	+	1.42154i	0.0435597	+	0.0754476i
$356$	−3.28382	+	0.808163i	−0.174042	+	0.0428325i
$357$	−12.3319	−	3.30432i	−0.652673	−	0.174883i
$358$	1.07339	+	0.634472i	0.0567303	+	0.0335329i
$359$	23.6459	−	23.6459i	1.24798	−	1.24798i	0.291373	−	0.956609i	$-0.405888\pi$
$359$	23.6459	−	23.6459i	1.24798	−	1.24798i	0.956609	−	0.291373i	$-0.0941121\pi$
$360$	2.60703	−	8.65618i	0.137402	−	0.456221i
$361$	−2.84880	−	1.64476i	−0.149937	−	0.0865662i
$362$	34.5974	+	0.354468i	1.81840	+	0.0186304i
$363$	−3.51225			−0.184346
$364$	12.9631	−	23.9863i	0.679454	−	1.25722i
$365$	−18.4617			−0.966328
$366$	14.6215	+	0.149805i	0.764278	+	0.00783044i
$367$	−9.74715	−	5.62752i	−0.508797	−	0.293754i	0.223542	−	0.974694i	$-0.428238\pi$
$367$	−9.74715	−	5.62752i	−0.508797	−	0.293754i	−0.732339	+	0.680940i	$0.761571\pi$
$368$	−19.2442	+	30.3849i	−1.00317	+	1.58392i
$369$	5.11014	−	5.11014i	0.266023	−	0.266023i
$370$	−20.1789	−	11.9276i	−1.04905	−	0.620087i
$371$	−25.9348	−	6.94922i	−1.34647	−	0.360785i
$372$	−0.897975	−	3.64875i	−0.0465578	−	0.189179i
$373$	−4.18386	−	7.24666i	−0.216632	−	0.375218i	0.737144	−	0.675736i	$-0.236174\pi$
$373$	−4.18386	−	7.24666i	−0.216632	−	0.375218i	−0.953776	+	0.300518i	$0.902841\pi$
$374$	9.33384	−	9.14452i	0.482641	−	0.472852i
$375$	−0.178477	−	0.666085i	−0.00921651	−	0.0343965i
$376$	−6.79244	−	7.22336i	−0.350293	−	0.372516i
$377$	−4.00878	−	3.63679i	−0.206462	−	0.187304i
$378$	5.15048	+	1.43678i	0.264912	+	0.0739000i
$379$	−15.9643	+	4.27762i	−0.820031	+	0.219727i	−0.644360	−	0.764722i	$-0.722876\pi$
$379$	−15.9643	+	4.27762i	−0.820031	+	0.219727i	−0.175671	+	0.984449i	$0.556209\pi$
$380$	−14.5512	−	26.4401i	−0.746460	−	1.35635i
$381$	−17.2151	+	9.93912i	−0.881954	+	0.509196i
$382$	4.36211	+	7.73740i	0.223185	+	0.395880i
$383$	3.17094	−	11.8341i	0.162027	−	0.604694i	−0.836373	−	0.548160i	$-0.815328\pi$
$383$	3.17094	−	11.8341i	0.162027	−	0.604694i	0.998401	−	0.0565339i	$-0.0180049\pi$
$384$	6.34438	−	9.36743i	0.323760	−	0.478030i
$385$	−23.3830	−	23.3830i	−1.19171	−	1.19171i
$386$	4.87405	+	18.9653i	0.248082	+	0.965308i
$387$	−2.23980	+	3.87944i	−0.113855	+	0.197203i
$388$	12.0960	+	3.50825i	0.614080	+	0.178105i
$389$		−	21.3616i		−	1.08308i	−0.840676	−	0.541539i	$-0.817842\pi$
$389$		−	21.3616i		−	1.08308i	0.840676	−	0.541539i	$-0.182158\pi$
$390$	−16.2855	+	0.625185i	−0.824650	+	0.0316575i
$391$		−	30.3611i		−	1.53543i
$392$	−10.8622	+	17.5456i	−0.548626	+	0.886189i
$393$	−3.35098	+	5.80406i	−0.169034	+	0.292776i
$394$	−9.41448	+	2.41950i	−0.474295	+	0.121893i
$395$	−29.0815	−	29.0815i	−1.46325	−	1.46325i
$396$	−3.94829	+	3.78972i	−0.198409	+	0.190440i
$397$	7.52801	−	28.0949i	0.377820	−	1.41004i	−0.471360	−	0.881941i	$-0.656237\pi$
$397$	7.52801	−	28.0949i	0.377820	−	1.41004i	0.849180	−	0.528103i	$-0.177097\pi$
$398$	5.32735	−	3.00340i	0.267036	−	0.150547i
$399$	15.4592	−	8.92536i	0.773927	−	0.446827i
$400$	0.854741	−	20.8455i	0.0427370	−	1.04227i
$401$	24.7767	−	6.63890i	1.23729	−	0.331531i	0.419876	−	0.907581i	$-0.362074\pi$
$401$	24.7767	−	6.63890i	1.23729	−	0.331531i	0.817414	+	0.576051i	$0.195407\pi$
$402$	1.22962	−	4.40785i	0.0613277	−	0.219844i
$403$	−5.69506	+	3.66817i	−0.283691	+	0.182725i
$404$	16.6621	+	10.0806i	0.828973	+	0.501530i
$405$	−0.827240	−	3.08730i	−0.0411059	−	0.153409i
$406$	5.61754	+	5.73384i	0.278794	+	0.284566i
$407$	7.09516	+	12.2892i	0.351694	+	0.609152i
$408$	−0.293493	+	9.54598i	−0.0145301	+	0.472596i
$409$	−21.7250	−	5.82120i	−1.07423	−	0.287840i	−0.322002	−	0.946739i	$-0.604356\pi$
$409$	−21.7250	−	5.82120i	−1.07423	−	0.287840i	−0.752231	+	0.658899i	$0.771022\pi$
$410$	16.6221	−	28.1209i	0.820905	−	1.38879i
$411$	1.78480	−	1.78480i	0.0880375	−	0.0880375i
$412$	15.6596	+	0.320916i	0.771494	+	0.0158104i
$413$	4.48124	+	2.58724i	0.220507	+	0.127310i
$414$	−0.130276	+	12.7154i	−0.00640270	+	0.624926i
$415$	10.4387			0.512414
$416$	−19.6873	−	5.33031i	−0.965247	−	0.261340i
$417$	−19.1269			−0.936648
$418$	−0.187177	+	18.2691i	−0.00915513	+	0.893573i
$419$	−13.3082	−	7.68351i	−0.650149	−	0.375364i	0.138364	−	0.990381i	$-0.455816\pi$
$419$	−13.3082	−	7.68351i	−0.650149	−	0.375364i	−0.788513	+	0.615017i	$0.789149\pi$
$420$	24.1646	+	0.495210i	1.17911	+	0.0241638i
$421$	−2.47227	+	2.47227i	−0.120491	+	0.120491i	−0.764781	−	0.644290i	$-0.777153\pi$
$421$	−2.47227	+	2.47227i	−0.120491	+	0.120491i	0.644290	+	0.764781i	$0.277153\pi$
$422$	−4.68267	+	7.92206i	−0.227949	+	0.385640i
$423$	−3.38615	−	0.907317i	−0.164640	−	0.0441153i
$424$	−0.617236	+	20.0759i	−0.0299756	+	0.974970i
$425$	8.80577	+	15.2520i	0.427143	+	0.739833i
$426$	0.508274	+	0.518797i	0.0246260	+	0.0251358i
$427$	10.1182	+	37.7615i	0.489652	+	1.82741i
$428$	14.8589	+	8.98966i	0.718232	+	0.434532i
$429$	8.77396	+	4.51202i	0.423611	+	0.217842i
$430$	−5.44075	+	19.5037i	−0.262376	+	0.940550i
$431$	−8.93302	+	2.39360i	−0.430289	+	0.115295i	−0.467462	−	0.884013i	$-0.654831\pi$
$431$	−8.93302	+	2.39360i	−0.430289	+	0.115295i	0.0371731	+	0.999309i	$0.488165\pi$
$432$	0.163877	−	3.99664i	0.00788453	−	0.192289i
$433$	−17.9719	+	10.3761i	−0.863674	+	0.498642i	−0.865241	−	0.501356i	$-0.832835\pi$
$433$	−17.9719	+	10.3761i	−0.863674	+	0.498642i	0.00156701	+	0.999999i	$0.499501\pi$
$434$	8.75131	−	4.93373i	0.420076	−	0.236826i
$435$	1.24185	−	4.63463i	0.0595420	−	0.222214i
$436$	0.431968	−	0.414619i	0.0206875	−	0.0198566i
$437$	30.0173	+	30.0173i	1.43592	+	1.43592i
$438$	−7.91157	+	2.03326i	−0.378029	+	0.0971528i
$439$	5.54214	−	9.59926i	0.264512	−	0.458148i	−0.702924	−	0.711265i	$-0.748123\pi$
$439$	5.54214	−	9.59926i	0.264512	−	0.458148i	0.967436	+	0.253117i	$0.0814559\pi$
$440$	−13.0213	+	21.0331i	−0.620764	+	1.00271i
$441$			7.29587i			0.347422i
$442$	16.4475	−	5.09088i	0.782330	−	0.242148i
$443$			30.2963i			1.43942i	0.694273	+	0.719711i	$0.255726\pi$
$443$			30.2963i			1.43942i	−0.694273	+	0.719711i	$0.744274\pi$
$444$	−9.96112	−	2.88907i	−0.472734	−	0.137109i
$445$	−2.70224	+	4.68041i	−0.128098	+	0.221873i
$446$	−4.98572	−	19.3998i	−0.236080	−	0.918608i
$447$	−1.20535	−	1.20535i	−0.0570111	−	0.0570111i
$448$	28.6811	+	9.60883i	1.35506	+	0.453975i
$449$	−2.17285	+	8.10918i	−0.102543	+	0.382696i	−0.998055	−	0.0623419i	$-0.980143\pi$
$449$	−2.17285	+	8.10918i	−0.102543	+	0.382696i	0.895512	+	0.445038i	$0.146810\pi$
$450$	−3.62245	−	6.42541i	−0.170764	−	0.302897i
$451$	−17.1259	+	9.88766i	−0.806429	+	0.465592i
$452$	0.227836	+	0.413986i	0.0107165	+	0.0194723i
$453$	11.7725	−	3.15443i	0.553121	−	0.148208i
$454$	13.2505	+	3.69636i	0.621875	+	0.173479i
$455$	−13.3094	−	41.4900i	−0.623953	−	1.94508i
$456$	−9.14773	−	9.72807i	−0.428381	−	0.455558i
$457$	7.08160	+	26.4289i	0.331263	+	1.23629i	0.907864	+	0.419265i	$0.137712\pi$
$457$	7.08160	+	26.4289i	0.331263	+	1.23629i	−0.576600	+	0.817026i	$0.695621\pi$
$458$	−19.9547	+	19.5500i	−0.932422	+	0.913510i
$459$	1.68830	+	2.92423i	0.0788033	+	0.136491i
$460$	13.7357	+	55.8126i	0.640432	+	2.60228i
$461$	−29.1493	−	7.81054i	−1.35762	−	0.363773i	−0.494677	−	0.869077i	$-0.664714\pi$
$461$	−29.1493	−	7.81054i	−1.35762	−	0.363773i	−0.862942	+	0.505304i	$0.831380\pi$
$462$	−12.5958	−	7.44530i	−0.586011	−	0.346387i
$463$	−15.7462	+	15.7462i	−0.731788	+	0.731788i	−0.970974	−	0.239186i	$-0.923119\pi$
$463$	−15.7462	+	15.7462i	−0.731788	+	0.731788i	0.239186	+	0.970974i	$0.423119\pi$
$464$	3.21292	−	5.07291i	0.149156	−	0.235504i
$465$	−5.20055	−	3.00254i	−0.241170	−	0.139239i
$466$	−16.8317	−	0.172450i	−0.779715	−	0.00798859i
$467$	5.70186			0.263851			0.131925	−	0.991260i	$-0.457884\pi$
$467$	5.70186			0.263851			0.131925	+	0.991260i	$0.457884\pi$
$468$	−6.91015	+	2.06151i	−0.319422	+	0.0952933i
$469$	12.2346			0.564942
$470$	−15.8449	−	0.162340i	−0.730872	−	0.00748817i
$471$	−9.53969	−	5.50774i	−0.439566	−	0.253783i
$472$	1.11628	−	3.70641i	0.0513809	−	0.170601i
$473$	8.66761	−	8.66761i	0.398537	−	0.398537i
$474$	−15.6654	−	9.25972i	−0.719538	−	0.425313i
$475$	−23.7854	−	6.37328i	−1.09135	−	0.292426i
$476$	−24.7940	+	6.10192i	−1.13643	+	0.279681i
$477$	3.55062	+	6.14986i	0.162572	+	0.281583i
$478$	19.4732	−	19.0782i	0.890684	−	0.872618i
$479$	0.105190	+	0.392575i	0.00480626	+	0.0179372i	0.968287	−	0.249839i	$-0.0803778\pi$
$479$	0.105190	+	0.392575i	0.00480626	+	0.0179372i	−0.963481	+	0.267776i	$0.913711\pi$
$480$	−3.77920	−	17.6811i	−0.172496	−	0.807029i
$481$	0.908637	+	18.6756i	0.0414303	+	0.851535i
$482$	26.3601	+	7.35343i	1.20067	+	0.334940i
$483$	−32.8387	+	8.79910i	−1.49421	+	0.400373i
$484$	−6.15409	+	3.38688i	−0.279731	+	0.153949i
$485$	17.4307	−	10.0636i	0.791488	−	0.456966i
$486$	−0.694522	−	1.23192i	−0.0315042	−	0.0558812i
$487$	9.61574	−	35.8864i	0.435731	−	1.62617i	−0.303580	−	0.952806i	$-0.598182\pi$
$487$	9.61574	−	35.8864i	0.435731	−	1.62617i	0.739311	−	0.673364i	$-0.235151\pi$
$488$	25.7639	−	13.8371i	1.16628	−	0.626374i
$489$	0.195703	+	0.195703i	0.00884999	+	0.00884999i
$490$	8.20859	+	31.9403i	0.370826	+	1.44291i
$491$	−14.5641	+	25.2258i	−0.657271	+	1.13843i	0.324049	+	0.946040i	$0.394956\pi$
$491$	−14.5641	+	25.2258i	−0.657271	+	1.13843i	−0.981319	+	0.192386i	$0.938378\pi$
$492$	4.02615	−	13.8816i	0.181513	−	0.625831i
$493$			5.06894i			0.228294i
$494$	−11.2281	+	21.2945i	−0.505175	+	0.958087i
$495$			8.74602i			0.393105i
$496$	−5.09191	−	5.52734i	−0.228634	−	0.248185i
$497$	−0.970887	+	1.68163i	−0.0435503	+	0.0754312i
$498$	4.47339	−	1.14965i	0.200457	−	0.0515172i
$499$	−0.958202	−	0.958202i	−0.0428950	−	0.0428950i	0.685334	−	0.728229i	$-0.259656\pi$
$499$	−0.958202	−	0.958202i	−0.0428950	−	0.0428950i	−0.728229	+	0.685334i	$0.759656\pi$
$500$	−0.955031	−	0.994993i	−0.0427103	−	0.0444974i
$501$	−6.14675	+	22.9400i	−0.274617	+	1.02488i
$502$	0.465006	−	0.262157i	0.0207542	−	0.0117006i
$503$	−14.4180	+	8.32421i	−0.642865	+	0.371158i	−0.785717	−	0.618586i	$-0.787706\pi$
$503$	−14.4180	+	8.32421i	−0.642865	+	0.371158i	0.142853	+	0.989744i	$0.454373\pi$
$504$	10.4100	−	2.44912i	0.463700	−	0.109093i
$505$	30.0614	−	8.05493i	1.33772	−	0.358440i
$506$	9.34968	−	33.5162i	0.415644	−	1.48997i
$507$	7.56223	+	10.5742i	0.335850	+	0.469615i
$508$	−20.5795	+	34.0156i	−0.913067	+	1.50920i
$509$	10.0685	+	37.5760i	0.446277	+	1.66553i	0.712543	+	0.701628i	$0.247543\pi$
$509$	10.0685	+	37.5760i	0.446277	+	1.66553i	−0.266266	+	0.963900i	$0.585790\pi$
$510$	10.6812	+	10.9023i	0.472972	+	0.482764i
$511$	−10.9197	−	18.9135i	−0.483060	−	0.836684i
$512$	2.08344	−	22.5313i	0.0920759	−	0.995752i
$513$	−4.56031	−	1.22193i	−0.201342	−	0.0539496i
$514$	−20.1242	+	34.0458i	−0.887641	+	1.50170i
$515$	17.6996	−	17.6996i	0.779935	−	0.779935i
$516$	−0.183564	+	8.95731i	−0.00808096	+	0.394324i
$517$	8.30748	+	4.79632i	0.365362	+	0.210942i
$518$	0.284085	−	27.7277i	0.0124820	−	1.21829i
$519$	20.4036			0.895619
$520$	−27.9323	+	16.7996i	−1.22491	+	0.736712i
$521$	9.12032			0.399568			0.199784	−	0.979840i	$-0.435976\pi$
$521$	9.12032			0.399568			0.199784	+	0.979840i	$0.435976\pi$
$522$	0.0217502	−	2.12290i	0.000951980	−	0.0929166i
$523$	−19.1104	−	11.0334i	−0.835639	−	0.482456i	0.0201407	−	0.999797i	$-0.493589\pi$
$523$	−19.1104	−	11.0334i	−0.835639	−	0.482456i	−0.855779	+	0.517341i	$0.826922\pi$
$524$	−0.274632	+	13.4011i	−0.0119973	+	0.585430i
$525$	13.9446	−	13.9446i	0.608594	−	0.608594i
$526$	−6.63019	+	11.2168i	−0.289090	+	0.489078i
$527$	6.12785	+	1.64195i	0.266933	+	0.0715246i
$528$	−3.26367	+	10.4476i	−0.142033	+	0.454673i
$529$	−28.9244	−	50.0985i	−1.25758	−	2.17819i
$530$	22.4633	+	22.9284i	0.975745	+	0.995946i
$531$	−0.354208	−	1.32192i	−0.0153713	−	0.0573665i
$532$	18.4805	−	30.5461i	0.801229	−	1.32434i
$533$	−26.0259	+	1.26626i	−1.12731	+	0.0548477i
$534$	−0.642544	+	2.30335i	−0.0278056	+	0.0996758i
$535$	26.8080	−	7.18320i	1.15901	−	0.310557i
$536$	−2.09600	−	8.90905i	−0.0905332	−	0.384812i
$537$	0.763557	−	0.440840i	0.0329499	−	0.0190236i
$538$	9.65596	−	5.44374i	0.416298	−	0.234696i
$539$	5.16712	−	19.2840i	0.222564	−	0.830619i
$540$	−4.42656	−	4.61179i	−0.190489	−	0.198460i
$541$	−22.2379	−	22.2379i	−0.956082	−	0.956082i	0.0429932	−	0.999075i	$-0.486311\pi$
$541$	−22.2379	−	22.2379i	−0.956082	−	0.956082i	−0.999075	+	0.0429932i	$0.986311\pi$
$542$	23.5348	−	6.04840i	1.01091	−	0.259801i
$543$	12.2327	−	21.1876i	0.524954	−	0.909246i
$544$	8.69096	+	17.0093i	0.372622	+	0.729266i
$545$		−	0.956870i		−	0.0409878i
$546$	−10.2731	−	16.3143i	−0.439646	−	0.698188i
$547$			3.81844i			0.163265i	0.996663	+	0.0816325i	$0.0260134\pi$
$547$			3.81844i			0.163265i	−0.996663	+	0.0816325i	$0.973987\pi$
$548$	1.40619	−	4.84836i	0.0600696	−	0.207112i
$549$	5.16975	−	8.95428i	0.220640	−	0.382159i
$550$	5.02399	+	19.5487i	0.214224	+	0.833561i
$551$	−5.01155	−	5.01155i	−0.213499	−	0.213499i
$552$	12.0332	+	22.4052i	0.512166	+	0.953628i
$553$	12.5921	−	46.9943i	0.535470	−	1.99840i
$554$	−21.1644	−	37.5408i	−0.899189	−	1.59496i
$555$	−14.3543	+	8.28747i	−0.609307	+	0.351783i
$556$	−33.5137	+	18.4441i	−1.42130	+	0.782204i
$557$	−34.5379	+	9.25442i	−1.46342	+	0.392122i	−0.900670	−	0.434505i	$-0.856923\pi$
$557$	−34.5379	+	9.25442i	−1.46342	+	0.392122i	−0.562750	+	0.826627i	$0.690257\pi$
$558$	−2.55933	−	0.713951i	−0.108345	−	0.0302240i
$559$	15.3795	−	4.93351i	0.650483	−	0.208665i
$560$	42.8181	−	22.4343i	1.80940	−	0.948021i
$561$	−2.39140	−	8.92483i	−0.100965	−	0.376807i
$562$	3.64776	−	3.57378i	0.153872	−	0.150751i
$563$	−7.18338	−	12.4420i	−0.302743	−	0.524367i	0.674013	−	0.738720i	$-0.264569\pi$
$563$	−7.18338	−	12.4420i	−0.302743	−	0.524367i	−0.976756	+	0.214352i	$0.931236\pi$
$564$	−6.80807	+	1.67550i	−0.286671	+	0.0705511i
$565$	0.729436	+	0.195452i	0.0306876	+	0.00822272i
$566$	9.05624	+	5.35307i	0.380662	+	0.225007i
$567$	2.67356	−	2.67356i	0.112279	−	0.112279i
$568$	1.39086	+	0.418894i	0.0583593	+	0.0175764i
$569$	−10.6934	−	6.17387i	−0.448293	−	0.258822i	0.258816	−	0.965927i	$-0.416668\pi$
$569$	−10.6934	−	6.17387i	−0.448293	−	0.258822i	−0.707109	+	0.707105i	$0.750001\pi$
$570$	−21.3392	−	0.218631i	−0.893800	−	0.00915745i
$571$	36.2097			1.51533			0.757665	−	0.652643i	$-0.226340\pi$
$571$	36.2097			1.51533			0.757665	+	0.652643i	$0.226340\pi$
$572$	19.7245	−	0.554897i	0.824722	−	0.0232014i
$573$	6.28074			0.262382
$574$	38.6408	+	0.395895i	1.61283	+	0.0165243i
$575$	40.6148	+	23.4489i	1.69375	+	0.977889i
$576$	−3.56683	−	7.16085i	−0.148618	−	0.298369i
$577$	−9.88739	+	9.88739i	−0.411618	+	0.411618i	−0.882302	−	0.470684i	$-0.844007\pi$
$577$	−9.88739	+	9.88739i	−0.411618	+	0.411618i	0.470684	+	0.882302i	$0.344007\pi$
$578$	6.81584	+	4.02879i	0.283502	+	0.167576i
$579$	13.3745	+	3.58368i	0.555824	+	0.148933i
$580$	−2.29325	−	9.31821i	−0.0952222	−	0.386918i
$581$	6.17426	+	10.6941i	0.256152	+	0.443668i
$582$	6.36141	−	6.23238i	0.263689	−	0.258341i
$583$	−5.02928	−	18.7695i	−0.208292	−	0.777355i
$584$	−11.9018	+	11.1918i	−0.492499	+	0.463119i
$585$	−5.27024	+	10.2484i	−0.217898	+	0.423718i
$586$	−18.2628	−	5.09461i	−0.754430	−	0.210456i
$587$	9.32533	−	2.49871i	0.384897	−	0.103133i	−0.0611813	−	0.998127i	$-0.519487\pi$
$587$	9.32533	−	2.49871i	0.384897	−	0.103133i	0.446079	+	0.894994i	$0.352820\pi$
$588$	7.03542	+	12.7836i	0.290136	+	0.527189i
$589$	−7.68183	+	4.43511i	−0.316524	+	0.182745i
$590$	−3.03797	−	5.38867i	−0.125071	−	0.221848i
$591$	−1.77896	+	6.63917i	−0.0731766	+	0.273099i
$592$	−20.2396	+	4.54336i	−0.831841	+	0.186731i
$593$	14.6686	+	14.6686i	0.602367	+	0.602367i	0.940940	−	0.338573i	$-0.109944\pi$
$593$	14.6686	+	14.6686i	0.602367	+	0.602367i	−0.338573	+	0.940940i	$0.609944\pi$
$594$	0.963235	+	3.74802i	0.0395220	+	0.153783i
$595$	−20.4029	+	35.3388i	−0.836436	+	1.44875i
$596$	−3.27431	−	0.949664i	−0.134121	−	0.0388998i
$597$		−	4.32441i		−	0.176986i
$598$	31.1521	−	33.6394i	1.27391	−	1.37562i
$599$		−	31.6259i		−	1.29220i	−0.763253	−	0.646099i	$-0.776399\pi$
$599$		−	31.6259i		−	1.29220i	0.763253	−	0.646099i	$-0.223601\pi$
$600$	−12.5432	−	7.76531i	−0.512075	−	0.317018i
$601$	−8.25858	+	14.3043i	−0.336874	+	0.583484i	−0.983843	−	0.179033i	$-0.942703\pi$
$601$	−8.25858	+	14.3043i	−0.336874	+	0.583484i	0.646969	+	0.762517i	$0.276036\pi$
$602$	−23.1991	+	5.96212i	−0.945524	+	0.242998i
$603$	−2.28807	−	2.28807i	−0.0931775	−	0.0931775i
$604$	17.5857	−	16.8794i	0.715551	−	0.686812i
$605$	−2.90548	+	10.8434i	−0.118124	+	0.440846i
$606$	11.9954	−	6.76265i	0.487280	−	0.274714i
$607$	−42.1831	+	24.3544i	−1.71216	+	0.988516i	−0.780523	+	0.625127i	$0.785047\pi$
$607$	−42.1831	+	24.3544i	−1.71216	+	0.988516i	−0.931637	+	0.363389i	$0.881620\pi$
$608$	−25.4092	−	8.22411i	−1.03048	−	0.333532i
$609$	5.48259	−	1.46905i	0.222166	−	0.0595291i
$610$	12.5580	−	45.0171i	0.508458	−	1.82269i
$611$	6.84430	+	10.6262i	0.276891	+	0.429890i
$612$	5.77805	+	3.49573i	0.233564	+	0.141306i
$613$	0.145840	+	0.544281i	0.00589041	+	0.0219833i	0.968808	−	0.247811i	$-0.0797111\pi$
$613$	0.145840	+	0.544281i	0.00589041	+	0.0219833i	−0.962918	+	0.269794i	$0.913044\pi$
$614$	−14.9962	−	15.3067i	−0.605197	−	0.617727i
$615$	−11.5492	−	20.0039i	−0.465710	−	0.806634i
$616$	−29.2496	−	0.899286i	−1.17850	−	0.0362333i
$617$	−8.47217	−	2.27011i	−0.341077	−	0.0913912i	0.0842149	−	0.996448i	$-0.473162\pi$
$617$	−8.47217	−	2.27011i	−0.341077	−	0.0913912i	−0.425292	+	0.905056i	$0.639828\pi$
$618$	5.63565	−	9.53429i	0.226699	−	0.383525i
$619$	−2.54356	+	2.54356i	−0.102235	+	0.102235i	−0.756374	−	0.654139i	$-0.773031\pi$
$619$	−2.54356	+	2.54356i	−0.102235	+	0.102235i	0.654139	+	0.756374i	$0.273031\pi$
$620$	−12.0076	−	0.246075i	−0.482238	−	0.00988261i
$621$	7.78695	+	4.49580i	0.312479	+	0.180410i
$622$	0.0973892	−	9.50553i	0.00390495	−	0.381137i
$623$	−6.39328			−0.256141
$624$	−10.1199	+	10.2756i	−0.405120	+	0.411353i
$625$	23.8747			0.954988
$626$	0.373185	−	36.4241i	0.0149155	−	1.45580i
$627$	11.1881	+	6.45945i	0.446810	+	0.257966i
$628$	−22.0264	−	0.451391i	−0.878947	−	0.0180124i
$629$	12.3818	−	12.3818i	0.493693	−	0.493693i
$630$	8.69645	−	14.7125i	0.346475	−	0.586160i
$631$	35.2361	+	9.44150i	1.40273	+	0.375860i	0.879324	−	0.476224i	$-0.157995\pi$
$631$	35.2361	+	9.44150i	1.40273	+	0.375860i	0.523405	+	0.852084i	$0.324662\pi$
$632$	−36.3778	−	1.11844i	−1.44703	−	0.0444892i
$633$	3.25358	+	5.63537i	0.129318	+	0.223986i
$634$	20.1276	+	20.5443i	0.799370	+	0.815920i
$635$	16.4441	+	61.3701i	0.652563	+	2.43540i
$636$	12.1516	+	7.35176i	0.481844	+	0.291516i
$637$	17.6750	−	19.4828i	0.700308	−	0.771938i
$638$	−1.56098	+	5.59570i	−0.0617997	+	0.221536i
$639$	0.496064	−	0.132920i	0.0196240	−	0.00525823i
$640$	−23.6718	−	27.3361i	−0.935708	−	1.08056i
$641$	−24.1007	+	13.9145i	−0.951919	+	0.549591i	−0.893677	−	0.448712i	$-0.851883\pi$
$641$	−24.1007	+	13.9145i	−0.951919	+	0.549591i	−0.0582425	+	0.998302i	$0.518550\pi$
$642$	10.6972	−	6.03077i	0.422185	−	0.238015i
$643$	0.964826	−	3.60078i	0.0380490	−	0.142001i	−0.944288	−	0.329119i	$-0.893248\pi$
$643$	0.964826	−	3.60078i	0.0380490	−	0.142001i	0.982337	+	0.187118i	$0.0599148\pi$
$644$	−49.0542	+	47.0840i	−1.93300	+	1.85537i
$645$	10.1242	+	10.1242i	0.398638	+	0.398638i
$646$	21.8352	−	5.61161i	0.859095	−	0.220786i
$647$	8.90223	−	15.4191i	0.349983	−	0.606188i	−0.636263	−	0.771472i	$-0.719521\pi$
$647$	8.90223	−	15.4191i	0.349983	−	0.606188i	0.986246	+	0.165284i	$0.0528541\pi$
$648$	−2.40487	−	1.48882i	−0.0944723	−	0.0584864i
$649$			3.74488i			0.146999i
$650$	−5.89283	+	25.9341i	−0.231136	+	1.01722i
$651$		−	7.10377i		−	0.278419i
$652$	0.531623	+	0.154189i	0.0208200	+	0.00603852i
$653$	4.33824	−	7.51406i	0.169769	−	0.294048i	−0.768570	−	0.639766i	$-0.779031\pi$
$653$	4.33824	−	7.51406i	0.169769	−	0.294048i	0.938338	+	0.345718i	$0.112365\pi$
$654$	−0.105384	−	0.410057i	−0.00412084	−	0.0160345i
$655$	15.1468	+	15.1468i	0.591836	+	0.591836i
$656$	−6.33153	−	28.2054i	−0.247205	−	1.10124i
$657$	−1.49497	+	5.57930i	−0.0583243	+	0.217669i
$658$	−9.20565	−	16.3287i	−0.358873	−	0.636560i
$659$	−13.7704	+	7.95034i	−0.536419	+	0.309701i	−0.743626	−	0.668596i	$-0.766896\pi$
$659$	−13.7704	+	7.95034i	−0.536419	+	0.309701i	0.207208	+	0.978297i	$0.433562\pi$
$660$	8.43381	+	15.3246i	0.328286	+	0.596508i
$661$	−0.688415	+	0.184460i	−0.0267762	+	0.00717467i	−0.272182	−	0.962246i	$-0.587745\pi$
$661$	−0.688415	+	0.184460i	−0.0267762	+	0.00717467i	0.245406	+	0.969420i	$0.421079\pi$
$662$	28.3350	+	7.90436i	1.10127	+	0.307211i
$663$	2.57580	−	11.8989i	0.100036	−	0.462116i
$664$	6.72955	−	6.32809i	0.261157	−	0.245578i
$665$	−14.7668	−	55.1105i	−0.572633	−	2.13709i
$666$	−5.23867	+	5.13241i	−0.202994	+	0.198877i
$667$	6.74906	+	11.6897i	0.261324	+	0.452627i
$668$	11.3509	+	46.1222i	0.439179	+	1.78452i
$669$	−13.6809	−	3.66579i	−0.528934	−	0.141727i
$670$	−12.5912	−	7.44254i	−0.486439	−	0.287531i
$671$	−20.0060	+	20.0060i	−0.772323	+	0.772323i
$672$	15.8785	−	14.3297i	0.612527	−	0.552781i
$673$	19.9608	+	11.5244i	0.769431	+	0.444231i	0.832672	−	0.553767i	$-0.186810\pi$
$673$	19.9608	+	11.5244i	0.769431	+	0.444231i	−0.0632403	+	0.997998i	$0.520143\pi$
$674$	−15.4639	−	0.158436i	−0.595647	−	0.00610272i
$675$	−5.21575			−0.200754
$676$	23.4470	+	11.2355i	0.901809	+	0.432135i
$677$	−14.2183			−0.546455			−0.273227	−	0.961949i	$-0.588091\pi$
$677$	−14.2183			−0.546455			−0.273227	+	0.961949i	$0.588091\pi$
$678$	0.334118	+	0.00342322i	0.0128317	+	0.000131468i
$679$	20.6198	+	11.9049i	0.791317	+	0.456867i
$680$	29.2285	+	8.80291i	1.12086	+	0.337576i
$681$	6.87819	−	6.87819i	0.263573	−	0.263573i
$682$	6.25901	+	3.69965i	0.239670	+	0.141667i
$683$	37.6381	+	10.0851i	1.44018	+	0.385895i	0.892597	−	0.450856i	$-0.148881\pi$
$683$	37.6381	+	10.0851i	1.44018	+	0.385895i	0.547584	+	0.836751i	$0.315548\pi$
$684$	−9.16877	+	2.25648i	−0.350577	+	0.0862785i
$685$	−4.03375	−	6.98665i	−0.154122	−	0.266946i
$686$	−1.13008	+	1.10716i	−0.0431466	+	0.0422715i
$687$	5.11255	+	19.0803i	0.195056	+	0.727958i
$688$	8.31592	+	15.8718i	0.317041	+	0.605107i
$689$	5.41709	−	25.0243i	0.206375	−	0.953349i
$690$	39.1484	+	10.9209i	1.49035	+	0.415750i
$691$	−5.31063	+	1.42298i	−0.202026	+	0.0541326i	−0.358413	−	0.933563i	$-0.616682\pi$
$691$	−5.31063	+	1.42298i	−0.202026	+	0.0541326i	0.156387	+	0.987696i	$0.450015\pi$
$692$	35.7507	−	19.6752i	1.35904	−	0.747941i
$693$	−8.96007	+	5.17310i	−0.340365	+	0.196510i
$694$	−23.3246	−	41.3726i	−0.885391	−	1.57048i
$695$	−15.8225	+	59.0505i	−0.600183	+	2.23991i
$696$	−2.00900	−	3.74066i	−0.0761511	−	0.141789i
$697$	17.2550	+	17.2550i	0.653578	+	0.653578i
$698$	−4.22753	−	16.4496i	−0.160014	−	0.622628i
$699$	−5.95123	+	10.3078i	−0.225096	+	0.389878i
$700$	10.9866	−	37.8803i	0.415255	−	1.43174i
$701$		−	35.5205i		−	1.34159i	−0.741642	−	0.670796i	$-0.765953\pi$
$701$		−	35.5205i		−	1.34159i	0.741642	−	0.670796i	$-0.234047\pi$
$702$	−1.12981	+	4.97227i	−0.0426421	+	0.187666i
$703$			24.4831i			0.923399i
$704$	4.35611	+	21.4532i	0.164177	+	0.808548i
$705$	−5.60232	+	9.70351i	−0.210996	+	0.365455i
$706$	21.3047	−	5.47528i	0.801815	−	0.206065i
$707$	26.0328	+	26.0328i	0.979064	+	0.979064i
$708$	−1.89537	−	1.97468i	−0.0712323	−	0.0742129i
$709$	−6.38711	+	23.8370i	−0.239873	+	0.895217i	0.736019	+	0.676961i	$0.236704\pi$
$709$	−6.38711	+	23.8370i	−0.239873	+	0.895217i	−0.975892	+	0.218256i	$0.929963\pi$
$710$	2.02215	−	1.14003i	0.0758899	−	0.0427844i
$711$	−11.1436	+	6.43378i	−0.417919	+	0.241286i
$712$	1.09528	+	4.65549i	0.0410472	+	0.174472i
$713$	16.3179	−	4.37237i	0.611110	−	0.163746i
$714$	−4.85144	+	17.3911i	−0.181561	+	0.650847i
$715$	21.1881	−	23.3553i	0.792391	−	0.873440i
$716$	0.912783	−	1.50873i	0.0341123	−	0.0563838i
$717$	−4.98919	−	18.6199i	−0.186325	−	0.695373i
$718$	−33.0960	−	33.7812i	−1.23513	−	1.26070i
$719$	−23.4652	−	40.6430i	−0.875105	−	1.51573i	−0.856651	−	0.515897i	$-0.827459\pi$
$719$	−23.4652	−	40.6430i	−0.875105	−	1.51573i	−0.0184542	−	0.999830i	$-0.505874\pi$
$720$	−12.2033	−	3.81212i	−0.454789	−	0.142069i
$721$	28.6017	+	7.66379i	1.06518	+	0.285415i
$722$	−2.36719	+	4.00478i	−0.0880978	+	0.149042i
$723$	13.6833	−	13.6833i	0.508886	−	0.508886i
$724$	1.00254	−	48.9204i	0.0372589	−	1.81811i
$725$	−6.78085	−	3.91492i	−0.251834	−	0.145397i
$726$	−0.0508877	+	4.96682i	−0.00188862	+	0.184336i
$727$	−35.7566			−1.32614			−0.663070	−	0.748558i	$-0.730747\pi$
$727$	−35.7566			−1.32614			−0.663070	+	0.748558i	$0.730747\pi$
$728$	−33.7321	−	18.6792i	−1.25020	−	0.692298i
$729$	−1.00000			−0.0370370
$730$	−0.267484	+	26.1074i	−0.00990003	+	0.966278i
$731$	−13.0994	−	7.56292i	−0.484497	−	0.279725i
$732$	0.423690	−	20.6747i	0.0156601	−	0.764158i
$733$	2.79942	−	2.79942i	0.103399	−	0.103399i	−0.653515	−	0.756914i	$-0.726706\pi$
$733$	2.79942	−	2.79942i	0.103399	−	0.103399i	0.756914	+	0.653515i	$0.226706\pi$
$734$	−8.09932	+	13.7023i	−0.298951	+	0.505761i
$735$	22.5245	+	6.03543i	0.830830	+	0.222620i
$736$	42.6896	+	27.6542i	1.57356	+	1.01935i
$737$	4.42721	+	7.66816i	0.163078	+	0.282460i
$738$	−7.15242	−	7.30049i	−0.263284	−	0.268735i
$739$	−6.37587	−	23.7951i	−0.234540	−	0.875316i	−0.978356	−	0.206931i	$-0.933653\pi$
$739$	−6.37587	−	23.7951i	−0.234540	−	0.875316i	0.743815	−	0.668385i	$-0.233014\pi$
$740$	−17.1597	+	28.3630i	−0.630802	+	1.04264i
$741$	9.21757	+	14.3108i	0.338616	+	0.525722i
$742$	−10.2029	+	36.5748i	−0.374561	+	1.34270i
$743$	−29.6562	+	7.94635i	−1.08798	+	0.291523i	−0.757861	−	0.652416i	$-0.773756\pi$
$743$	−29.6562	+	7.94635i	−1.08798	+	0.291523i	−0.330119	+	0.943939i	$0.607089\pi$
$744$	−5.17286	+	1.21700i	−0.189646	+	0.0446172i
$745$	−4.71839	+	2.72417i	−0.172869	+	0.0998057i
$746$	−10.3084	+	5.81157i	−0.377417	+	0.212777i
$747$	0.845291	−	3.15467i	0.0309276	−	0.115423i
$748$	−12.7964	−	13.3318i	−0.467882	−	0.487460i
$749$	23.2154	+	23.2154i	0.848273	+	0.848273i
$750$	−0.944523	+	0.242741i	−0.0344891	+	0.00886364i
$751$	18.1720	−	31.4749i	0.663107	−	1.14853i	−0.316688	−	0.948530i	$-0.602571\pi$
$751$	18.1720	−	31.4749i	0.663107	−	1.14853i	0.979795	−	0.200005i	$-0.0640959\pi$
$752$	−10.3132	+	9.50080i	−0.376085	+	0.346458i
$753$		−	0.377463i		−	0.0137555i
$754$	−5.20101	+	5.61628i	−0.189410	+	0.204533i
$755$		−	38.9548i		−	1.41771i
$756$	2.10643	−	7.26267i	0.0766101	−	0.264141i
$757$	8.44519	−	14.6275i	0.306946	−	0.531645i	−0.670747	−	0.741686i	$-0.734026\pi$
$757$	8.44519	−	14.6275i	0.306946	−	0.531645i	0.977693	+	0.210041i	$0.0673597\pi$
$758$	5.81785	+	22.6377i	0.211314	+	0.822239i
$759$	−17.3979	−	17.3979i	−0.631504	−	0.631504i
$760$	−37.6008	+	20.1943i	−1.36393	+	0.732526i
$761$	−0.236137	+	0.881276i	−0.00855997	+	0.0319462i	−0.970074	−	0.242811i	$-0.921931\pi$
$761$	−0.236137	+	0.881276i	−0.00855997	+	0.0319462i	0.961514	+	0.274757i	$0.0885973\pi$
$762$	13.8059	+	24.4885i	0.500134	+	0.887124i
$763$	0.980288	−	0.565970i	0.0354888	−	0.0204895i
$764$	11.0050	−	6.05653i	0.398145	−	0.219118i
$765$	10.4246	−	2.79326i	0.376902	−	0.100991i
$766$	−16.6891	−	4.65561i	−0.603002	−	0.168214i
$767$	−2.25662	+	4.38816i	−0.0814817	+	0.158447i
$768$	−13.1549	−	9.10756i	−0.474688	−	0.328641i
$769$	5.90914	+	22.0532i	0.213089	+	0.795260i	0.986830	+	0.161758i	$0.0517164\pi$
$769$	5.90914	+	22.0532i	0.213089	+	0.795260i	−0.773741	+	0.633502i	$0.781617\pi$
$770$	−33.4057	+	32.7281i	−1.20386	+	1.17944i
$771$	13.9826	+	24.2185i	0.503570	+	0.872210i
$772$	26.8902	−	6.61780i	0.967799	−	0.238180i
$773$	11.7329	+	3.14381i	0.422001	+	0.113075i	0.463569	−	0.886061i	$-0.346569\pi$
$773$	11.7329	+	3.14381i	0.422001	+	0.113075i	−0.0415678	+	0.999136i	$0.513235\pi$
$774$	5.45362	+	3.22359i	0.196026	+	0.115870i
$775$	−6.92924	+	6.92924i	−0.248906	+	0.248906i
$776$	5.13641	−	17.0546i	0.184387	−	0.612223i
$777$	−16.9806	−	9.80375i	−0.609175	−	0.351707i
$778$	−30.2083	−	0.309500i	−1.08302	−	0.0110961i
$779$	−34.1192			−1.22245
$780$	0.648144	+	23.0391i	0.0232073	+	0.824931i
$781$	−1.40530			−0.0502856
$782$	−42.9348	−	0.439890i	−1.53535	−	0.0157304i
$783$	−1.30007	−	0.750596i	−0.0464607	−	0.0268241i
$784$	24.6546	+	15.6149i	0.880521	+	0.557676i
$785$	−24.8957	+	24.8957i	−0.888565	+	0.888565i
$786$	8.15920	+	4.82284i	0.291029	+	0.172025i
$787$	−37.3775	−	10.0153i	−1.33236	−	0.357006i	−0.478768	−	0.877942i	$-0.658916\pi$
$787$	−37.3775	−	10.0153i	−1.33236	−	0.357006i	−0.853596	+	0.520936i	$0.825583\pi$
$788$	3.28511	+	13.3484i	0.117027	+	0.475519i
$789$	4.60675	+	7.97912i	0.164005	+	0.284064i
$790$	−41.5466	+	40.7039i	−1.47816	+	1.44818i
$791$	0.231212	+	0.862894i	0.00822094	+	0.0306810i
$792$	5.30198	+	5.63835i	0.188398	+	0.200350i
$793$	−35.4979	+	11.3872i	−1.26057	+	0.404371i
$794$	−39.6211	−	11.0527i	−1.40610	−	0.392246i
$795$	21.9237	−	5.87443i	0.777552	−	0.208345i
$796$	−4.17004	−	7.57712i	−0.147803	−	0.268564i
$797$	−5.24767	+	3.02975i	−0.185882	+	0.107319i	−0.590053	−	0.807364i	$-0.700893\pi$
$797$	−5.24767	+	3.02975i	−0.185882	+	0.107319i	0.404171	+	0.914683i	$0.367560\pi$
$798$	−12.3977	−	21.9907i	−0.438874	−	0.778464i
$799$	3.06365	−	11.4337i	0.108384	−	0.404496i
$800$	−29.4660	−	1.51074i	−1.04178	−	0.0534129i
$801$	1.19565	+	1.19565i	0.0422461	+	0.0422461i
$802$	−9.02935	−	35.1339i	−0.318837	−	1.24062i
$803$	7.90281	−	13.6881i	0.278884	−	0.483041i
$804$	−6.21550	−	1.80271i	−0.219204	−	0.0635768i
$805$			108.662i			3.82983i
$806$	5.10479	+	8.10676i	0.179809	+	0.285548i
$807$		−	7.83811i		−	0.275914i
$808$	14.4968	−	23.4165i	0.509996	−	0.823791i
$809$	−11.4722	+	19.8704i	−0.403341	+	0.698607i	−0.994127	−	0.108221i	$-0.965485\pi$
$809$	−11.4722	+	19.8704i	−0.403341	+	0.698607i	0.590786	+	0.806829i	$0.298818\pi$
$810$	−4.37786	+	1.12510i	−0.153822	+	0.0395320i
$811$	4.97593	+	4.97593i	0.174729	+	0.174729i	0.789053	−	0.614325i	$-0.210571\pi$
$811$	4.97593	+	4.97593i	0.174729	+	0.174729i	−0.614325	+	0.789053i	$0.710571\pi$
$812$	8.18984	−	7.86091i	0.287407	−	0.275864i
$813$	4.44713	−	16.5969i	0.155968	−	0.582080i
$814$	17.4814	−	9.85549i	0.612723	−	0.345435i
$815$	0.766087	−	0.442301i	0.0268349	−	0.0154931i
$816$	13.4951	+	0.553348i	0.472423	+	0.0193711i
$817$	20.4283	−	5.47376i	0.714697	−	0.191502i
$818$	−8.54676	+	30.6379i	−0.298830	+	1.07123i
$819$	−13.6164	+	0.662490i	−0.475797	+	0.0231493i
$820$	−39.5261	−	23.9133i	−1.38031	−	0.835090i
$821$	−9.29628	−	34.6942i	−0.324442	−	1.21083i	−0.914871	−	0.403745i	$-0.867708\pi$
$821$	−9.29628	−	34.6942i	−0.324442	−	1.21083i	0.590429	−	0.807089i	$-0.298959\pi$
$822$	−2.49809	−	2.54981i	−0.0871309	−	0.0889348i
$823$	−17.6629	−	30.5931i	−0.615691	−	1.06641i	−0.990263	−	0.139210i	$-0.955544\pi$
$823$	−17.6629	−	30.5931i	−0.615691	−	1.06641i	0.374572	−	0.927198i	$-0.377790\pi$
$824$	0.680706	−	22.1402i	0.0237135	−	0.771291i
$825$	13.7859	+	3.69393i	0.479964	+	0.128606i
$826$	3.72365	−	6.29961i	0.129562	−	0.219191i
$827$	−34.5740	+	34.5740i	−1.20226	+	1.20226i	−0.228777	+	0.973479i	$0.573473\pi$
$827$	−34.5740	+	34.5740i	−1.20226	+	1.20226i	−0.973479	+	0.228777i	$0.926527\pi$
$828$	17.9794	+	0.368456i	0.624828	+	0.0128047i
$829$	−49.0371	−	28.3116i	−1.70313	−	0.983301i	−0.942556	−	0.334048i	$-0.891585\pi$
$829$	−49.0371	−	28.3116i	−1.70313	−	0.983301i	−0.760572	−	0.649254i	$-0.775081\pi$
$830$	0.151242	−	14.7617i	0.00524968	−	0.512387i
$831$	−30.4733			−1.05711
$832$	−7.82304	+	27.7633i	−0.271215	+	0.962519i
$833$	−24.6353			−0.853562
$834$	−0.277122	+	27.0481i	−0.00959595	+	0.936599i
$835$	65.7378	+	37.9537i	2.27495	+	1.31344i
$836$	25.8324	+	0.529389i	0.893432	+	0.0183093i
$837$	−1.32852	+	1.32852i	−0.0459204	+	0.0459204i
$838$	−11.0584	+	18.7084i	−0.382005	+	0.646270i
$839$	48.9778	+	13.1236i	1.69090	+	0.453076i	0.970622	−	0.240609i	$-0.0773471\pi$
$839$	48.9778	+	13.1236i	1.69090	+	0.453076i	0.720279	+	0.693685i	$0.244014\pi$
$840$	1.05041	−	34.1649i	0.0362425	−	1.17880i
$841$	13.3732	+	23.1631i	0.461145	+	0.798727i
$842$	3.46032	+	3.53196i	0.119250	+	0.121719i
$843$	−0.934585	−	3.48792i	−0.0321888	−	0.120130i
$844$	11.1351	+	6.73673i	0.383284	+	0.231888i
$845$	38.9014	−	14.5995i	1.33825	−	0.502239i
$846$	−1.33213	+	4.77535i	−0.0457997	+	0.164180i
$847$	−12.8273	+	3.43706i	−0.440751	+	0.118099i
$848$	28.3811	+	1.16373i	0.974612	+	0.0399626i
$849$	6.44217	−	3.71939i	0.221095	−	0.127649i
$850$	21.6961	−	12.2316i	0.744170	−	0.419541i
$851$	12.0684	−	45.0399i	0.413699	−	1.54395i
$852$	0.741016	−	0.711254i	0.0253868	−	0.0243672i
$853$	−30.6522	−	30.6522i	−1.04951	−	1.04951i	−0.998709	−	0.0508029i	$-0.983822\pi$
$853$	−30.6522	−	30.6522i	−1.04951	−	1.04951i	−0.0508029	−	0.998709i	$-0.516178\pi$
$854$	53.5466	−	13.7614i	1.83233	−	0.470904i
$855$	−7.54493	+	13.0682i	−0.258031	+	0.446923i
$856$	12.9279	−	20.8823i	0.441867	−	0.713743i
$857$			1.04493i			0.0356942i	0.999841	+	0.0178471i	$0.00568120\pi$
$857$			1.04493i			0.0356942i	−0.999841	+	0.0178471i	$0.994319\pi$
$858$	6.50775	−	12.3422i	0.222171	−	0.421357i
$859$		−	7.93583i		−	0.270767i	−0.990793	−	0.135384i	$-0.956773\pi$
$859$		−	7.93583i		−	0.270767i	0.990793	−	0.135384i	$-0.0432267\pi$
$860$	27.5021	+	7.97656i	0.937813	+	0.271999i
$861$	13.6623	−	23.6638i	0.465609	−	0.806459i
$862$	3.25545	+	12.6672i	0.110881	+	0.431447i
$863$	−5.48968	−	5.48968i	−0.186871	−	0.186871i	0.607471	−	0.794342i	$-0.292184\pi$
$863$	−5.48968	−	5.48968i	−0.186871	−	0.186871i	−0.794342	+	0.607471i	$0.792184\pi$
$864$	−5.64943	−	0.289651i	−0.192198	−	0.00985411i
$865$	16.8787	−	62.9921i	0.573892	−	2.14179i
$866$	14.4128	+	25.5651i	0.489768	+	0.868737i
$867$	4.84846	−	2.79926i	0.164662	−	0.0950678i
$868$	−6.85018	−	12.4471i	−0.232510	−	0.422481i
$869$	34.0107	−	9.11314i	1.15373	−	0.309142i
$870$	−6.53602	−	1.82329i	−0.221592	−	0.0618154i
$871$	0.566968	+	11.6531i	0.0192110	+	0.394852i
$872$	−0.580070	−	0.616871i	−0.0196437	−	0.0208899i
$873$	−1.62984	−	6.08266i	−0.0551618	−	0.205867i
$874$	42.8836	−	42.0138i	1.45056	−	1.42114i
$875$	−1.30365	−	2.25799i	−0.0440715	−	0.0763340i
$876$	2.76068	+	11.2175i	0.0932748	+	0.379005i
$877$	22.5771	+	6.04953i	0.762376	+	0.204278i	0.619001	−	0.785390i	$-0.287538\pi$
$877$	22.5771	+	6.04953i	0.762376	+	0.204278i	0.143375	+	0.989668i	$0.454204\pi$
$878$	−13.4944	−	7.97643i	−0.455414	−	0.269192i
$879$	−9.48005	+	9.48005i	−0.319754	+	0.319754i
$880$	29.5550	+	18.7186i	0.996300	+	0.631004i
$881$	14.0257	+	8.09772i	0.472537	+	0.272819i	0.717301	−	0.696763i	$-0.245377\pi$
$881$	14.0257	+	8.09772i	0.472537	+	0.272819i	−0.244764	+	0.969583i	$0.578711\pi$
$882$	10.3174	+	0.105707i	0.347404	+	0.00355934i
$883$	−40.7988			−1.37299			−0.686494	−	0.727136i	$-0.740851\pi$
$883$	−40.7988			−1.37299			−0.686494	+	0.727136i	$0.740851\pi$
$884$	−6.96091	−	23.3329i	−0.234121	−	0.784769i
$885$	−4.37419			−0.147037
$886$	42.8433	+	0.438952i	1.43935	+	0.0147469i
$887$	24.3982	+	14.0863i	0.819213	+	0.472973i	0.850145	−	0.526549i	$-0.176514\pi$
$887$	24.3982	+	14.0863i	0.819213	+	0.472973i	−0.0309322	+	0.999521i	$0.509848\pi$
$888$	−4.22987	+	14.0445i	−0.141945	+	0.471304i
$889$	−53.1457	+	53.1457i	−1.78245	+	1.78245i
$890$	6.57960	+	3.88915i	0.220549	+	0.130365i
$891$	2.64313	+	0.708226i	0.0885483	+	0.0237265i
$892$	−27.5063	+	6.76942i	−0.920978	+	0.226657i
$893$	8.27529	+	14.3332i	0.276922	+	0.479643i
$894$	−1.72200	+	1.68707i	−0.0575922	+	0.0564240i
$895$	−0.729360	−	2.72201i	−0.0243798	−	0.0909867i
$896$	14.0038	−	40.4199i	0.467833	−	1.35033i
$897$	−9.90270	−	30.8702i	−0.330641	−	1.03073i
$898$	11.4360	+	3.19020i	0.381625	+	0.106458i
$899$	−2.72436	+	0.729989i	−0.0908624	+	0.0243465i
$900$	−9.13891	+	5.02956i	−0.304630	+	0.167652i
$901$	−20.7657	+	11.9891i	−0.691804	+	0.399413i
$902$	13.7344	+	24.3617i	0.457306	+	0.811156i
$903$	−4.38370	+	16.3602i	−0.145880	+	0.544433i
$904$	0.588735	−	0.316193i	0.0195810	−	0.0105164i
$905$	−55.2931	−	55.2931i	−1.83800	−	1.83800i
$906$	−4.29024	−	16.6937i	−0.142534	−	0.554610i
$907$	6.80614	−	11.7886i	0.225994	−	0.391433i	−0.730623	−	0.682781i	$-0.760770\pi$
$907$	6.80614	−	11.7886i	0.225994	−	0.391433i	0.956617	+	0.291348i	$0.0941037\pi$
$908$	5.41914	−	18.6844i	0.179841	−	0.620065i
$909$		−	9.73712i		−	0.322960i
$910$	−58.8655	+	18.2202i	−1.95137	+	0.603992i
$911$		−	38.5002i		−	1.27557i	−0.770215	−	0.637784i	$-0.779851\pi$
$911$		−	38.5002i		−	1.27557i	0.770215	−	0.637784i	$-0.220149\pi$
$912$	−13.8894	+	12.7952i	−0.459923	+	0.423692i
$913$	−4.46844	+	7.73956i	−0.147884	+	0.256142i
$914$	37.4767	−	9.63145i	1.23962	−	0.318580i
$915$	−23.3679	−	23.3679i	−0.772519	−	0.772519i
$916$	27.3573	+	28.5020i	0.903909	+	0.941732i
$917$	−6.55848	+	24.4766i	−0.216580	+	0.808288i
$918$	4.15973	−	2.34513i	0.137291	−	0.0774008i
$919$	−30.6766	+	17.7111i	−1.01193	+	0.584237i	−0.911756	−	0.410733i	$-0.865273\pi$
$919$	−30.6766	+	17.7111i	−1.01193	+	0.584237i	−0.100172	+	0.994970i	$0.531939\pi$
$920$	79.1259	−	18.6156i	2.60870	−	0.613739i
$921$	−14.6359	+	3.92169i	−0.482270	+	0.129224i
$922$	−11.4675	+	41.1080i	−0.377663	+	1.35382i
$923$	−1.64670	−	0.846816i	−0.0542017	−	0.0278733i
$924$	−10.7112	+	17.7044i	−0.352372	+	0.582432i
$925$	7.00051	+	26.1263i	0.230175	+	0.859026i
$926$	22.0392	+	22.4955i	0.724252	+	0.739247i
$927$	−3.91572	−	6.78223i	−0.128609	−	0.222758i
$928$	−7.12725	−	4.61701i	−0.233964	−	0.151561i
$929$	−6.58363	−	1.76408i	−0.216002	−	0.0578776i	0.149195	−	0.988808i	$-0.452332\pi$
$929$	−6.58363	−	1.76408i	−0.216002	−	0.0578776i	−0.365197	+	0.930930i	$0.618998\pi$
$930$	−4.32136	+	7.31080i	−0.141703	+	0.239731i
$931$	24.3564	−	24.3564i	0.798247	−	0.798247i
$932$	−0.487737	+	23.7999i	−0.0159763	+	0.779592i
$933$	−5.82123	−	3.36089i	−0.190578	−	0.110031i
$934$	0.0826120	−	8.06323i	0.00270315	−	0.263837i
$935$	−29.5319			−0.965796
$936$	2.81514	+	9.80178i	0.0920158	+	0.320381i
$937$	42.2849			1.38139			0.690693	−	0.723148i	$-0.257306\pi$
$937$	42.2849			1.38139			0.690693	+	0.723148i	$0.257306\pi$
$938$	0.177262	−	17.3014i	0.00578782	−	0.564912i
$939$	−22.3063	−	12.8786i	−0.727939	−	0.420276i
$940$	−0.459142	+	22.4046i	−0.0149756	+	0.730757i
$941$	−8.08226	+	8.08226i	−0.263474	+	0.263474i	−0.826464	−	0.562990i	$-0.809651\pi$
$941$	−8.08226	+	8.08226i	−0.263474	+	0.263474i	0.562990	+	0.826464i	$0.309651\pi$
$942$	−7.92693	+	13.4107i	−0.258273	+	0.436943i
$943$	62.7666	+	16.8183i	2.04396	+	0.547678i
$944$	−5.22520	−	1.63227i	−0.170066	−	0.0531260i
$945$	−6.04241	−	10.4658i	−0.196560	−	0.340451i
$946$	−12.1316	−	12.3828i	−0.394433	−	0.402599i
$947$	−6.68864	−	24.9623i	−0.217351	−	0.811167i	−0.985326	−	0.170686i	$-0.945402\pi$
$947$	−6.68864	−	24.9623i	−0.217351	−	0.811167i	0.767974	−	0.640481i	$-0.221265\pi$
$948$	−13.3215	+	22.0190i	−0.432662	+	0.715142i
$949$	17.5086	−	11.2772i	0.568352	−	0.366074i
$950$	−9.35733	+	33.5436i	−0.303592	+	1.08830i
$951$	19.6441	−	5.26362i	0.637003	−	0.170684i
$952$	8.26973	+	35.1506i	0.268024	+	1.13924i
$953$	18.0436	−	10.4175i	0.584491	−	0.337456i	−0.178425	−	0.983953i	$-0.557100\pi$
$953$	18.0436	−	10.4175i	0.584491	−	0.337456i	0.762916	+	0.646498i	$0.223767\pi$
$954$	8.74820	−	4.93197i	0.283233	−	0.159678i
$955$	5.19567	−	19.3905i	0.168128	−	0.627463i
$956$	−26.6971	−	27.8142i	−0.863447	−	0.899577i
$957$	2.90467	+	2.90467i	0.0938947	+	0.0938947i
$958$	0.556679	−	0.143066i	0.0179855	−	0.00462224i
$959$	4.77176	−	8.26493i	0.154088	−	0.266889i
$960$	−25.0583	+	5.08814i	−0.808753	+	0.164219i
$961$		−	27.4701i		−	0.886131i
$962$	26.4231	−	1.01436i	0.851915	−	0.0327041i
$963$		−	8.68333i		−	0.279816i
$964$	10.7807	−	37.1703i	0.347223	−	1.19718i
$965$	22.1278	−	38.3265i	0.712319	−	1.23377i
$966$	11.9674	+	46.5659i	0.385044	+	1.49823i
$967$	8.87448	+	8.87448i	0.285384	+	0.285384i	0.835252	−	0.549868i	$-0.185322\pi$
$967$	8.87448	+	8.87448i	0.285384	+	0.285384i	−0.549868	+	0.835252i	$0.685322\pi$
$968$	4.70035	+	8.75181i	0.151075	+	0.281294i
$969$	4.12598	−	15.3984i	0.132546	−	0.494667i
$970$	−13.9788	−	24.7953i	−0.448833	−	0.796128i
$971$	−17.7417	+	10.2432i	−0.569358	+	0.328719i	−0.756893	−	0.653539i	$-0.773284\pi$
$971$	−17.7417	+	10.2432i	−0.569358	+	0.328719i	0.187535	+	0.982258i	$0.439950\pi$
$972$	−1.75218	+	0.964302i	−0.0562011	+	0.0309300i
$973$	−69.8544	+	18.7174i	−2.23943	+	0.600053i
$974$	−50.6091	−	14.1179i	−1.62162	−	0.452368i
$975$	13.9281	+	12.6357i	0.446056	+	0.404666i
$976$	−19.1943	−	36.6342i	−0.614393	−	1.17263i
$977$	5.26065	+	19.6330i	0.168303	+	0.628116i	0.997596	+	0.0693013i	$0.0220770\pi$
$977$	5.26065	+	19.6330i	0.168303	+	0.628116i	−0.829293	+	0.558815i	$0.811256\pi$
$978$	0.279587	−	0.273916i	0.00894020	−	0.00875886i
$979$	−2.31347	−	4.00705i	−0.0739388	−	0.128066i
$980$	45.2869	−	11.1453i	1.44664	−	0.356024i
$981$	−0.289176	−	0.0774844i	−0.00923267	−	0.00247389i
$982$	35.4618	+	20.9612i	1.13163	+	0.668899i
$983$	35.4506	−	35.4506i	1.13070	−	1.13070i	0.140639	−	0.990061i	$-0.455084\pi$
$983$	35.4506	−	35.4506i	1.13070	−	1.13070i	0.990061	−	0.140639i	$-0.0449156\pi$
$984$	−19.5722	−	5.89466i	−0.623938	−	0.187915i
$985$	19.0255	+	10.9844i	0.606202	+	0.349991i
$986$	7.16819	+	0.0734419i	0.228282	+	0.00233887i
$987$	−13.2546			−0.421900
$988$	29.9508	+	16.1866i	0.952861	+	0.514964i
$989$	−40.2787			−1.28079
$990$	12.3681	+	0.126718i	0.393084	+	0.00402735i
$991$	−33.2950	−	19.2229i	−1.05765	−	0.610636i	−0.132870	−	0.991133i	$-0.542419\pi$
$991$	−33.2950	−	19.2229i	−1.05765	−	0.610636i	−0.924782	+	0.380498i	$0.875753\pi$
$992$	−7.89020	+	7.12059i	−0.250514	+	0.226079i
$993$	14.7084	−	14.7084i	0.466758	−	0.466758i
$994$	2.36399	+	1.39733i	0.0749811	+	0.0443208i
$995$	−13.3507	−	3.57732i	−0.423247	−	0.113409i
$996$	−1.56096	−	6.34265i	−0.0494608	−	0.200975i
$997$	20.4782	+	35.4693i	0.648552	+	1.12332i	0.983469	+	0.181077i	$0.0579582\pi$
$997$	20.4782	+	35.4693i	0.648552	+	1.12332i	−0.334917	+	0.942247i	$0.608708\pi$
$998$	−1.36891	+	1.34115i	−0.0433322	+	0.0424533i
$999$	1.34219	+	5.00911i	0.0424649	+	0.158481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.19.4	✓	24
3.2	odd	2		468.2.cb.h.19.3		24
4.3	odd	2		156.2.w.d.19.2	yes	24
12.11	even	2		468.2.cb.g.19.5		24
13.11	odd	12		156.2.w.d.115.2	yes	24
39.11	even	12		468.2.cb.g.271.5		24
52.11	even	12	inner	156.2.w.c.115.4	yes	24
156.11	odd	12		468.2.cb.h.271.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.19.4	✓	24	1.1	even	1	trivial
156.2.w.c.115.4	yes	24	52.11	even	12	inner
156.2.w.d.19.2	yes	24	4.3	odd	2
156.2.w.d.115.2	yes	24	13.11	odd	12
468.2.cb.g.19.5		24	12.11	even	2
468.2.cb.g.271.5		24	39.11	even	12
468.2.cb.h.19.3		24	3.2	odd	2
468.2.cb.h.271.3		24	156.11	odd	12

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)

\(f(q)\)	\(=\)	\(q+(0.0144886 - 1.41414i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.99958 - 0.0409778i) q^{4} +(-2.26006 + 2.26006i) q^{5} +(-0.719617 + 1.21744i) q^{6} +(-3.65215 - 0.978592i) q^{7} +(-0.0869195 + 2.82709i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.0144886 - 1.41414i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.99958 - 0.0409778i) q^{4} +(-2.26006 + 2.26006i) q^{5} +(-0.719617 + 1.21744i) q^{6} +(-3.65215 - 0.978592i) q^{7} +(-0.0869195 + 2.82709i) q^{8} +(0.500000 + 0.866025i) q^{9} +(3.16330 + 3.22879i) q^{10} +(-0.708226 - 2.64313i) q^{11} +(1.71120 + 1.03528i) q^{12} +(0.762837 - 3.52393i) q^{13} +(-1.43678 + 5.15048i) q^{14} +(3.08730 - 0.827240i) q^{15} +(3.99664 + 0.163877i) q^{16} +(-2.92423 + 1.68830i) q^{17} +(1.23192 - 0.694522i) q^{18} +(1.22193 - 4.56031i) q^{19} +(4.61179 - 4.42656i) q^{20} +(2.67356 + 2.67356i) q^{21} +(-3.74802 + 0.963235i) q^{22} +(-4.49580 + 7.78695i) q^{23} +(1.48882 - 2.40487i) q^{24} -5.21575i q^{25} +(-4.97227 - 1.12981i) q^{26} -1.00000i q^{27} +(7.26267 + 2.10643i) q^{28} +(0.750596 - 1.30007i) q^{29} +(-1.12510 - 4.37786i) q^{30} +(-1.32852 - 1.32852i) q^{31} +(0.289651 - 5.64943i) q^{32} +(-0.708226 + 2.64313i) q^{33} +(2.34513 + 4.15973i) q^{34} +(10.4658 - 6.04241i) q^{35} +(-0.964302 - 1.75218i) q^{36} +(-5.00911 + 1.34219i) q^{37} +(-6.43121 - 1.79405i) q^{38} +(-2.42260 + 2.67039i) q^{39} +(-6.19295 - 6.58584i) q^{40} +(-1.87044 - 6.98059i) q^{41} +(3.81953 - 3.74205i) q^{42} +(2.23980 + 3.87944i) q^{43} +(1.30784 + 5.31418i) q^{44} +(-3.08730 - 0.827240i) q^{45} +(10.9467 + 6.47050i) q^{46} +(-2.47884 + 2.47884i) q^{47} +(-3.37925 - 2.14024i) q^{48} +(6.31841 + 3.64793i) q^{49} +(-7.37580 - 0.0755690i) q^{50} +3.37661 q^{51} +(-1.66976 + 7.01512i) q^{52} +7.10124 q^{53} +(-1.41414 - 0.0144886i) q^{54} +(7.57428 + 4.37301i) q^{55} +(3.08401 - 10.2399i) q^{56} +(-3.33838 + 3.33838i) q^{57} +(-1.82761 - 1.08028i) q^{58} +(-1.32192 - 0.354208i) q^{59} +(-6.20720 + 1.52762i) q^{60} +(-5.16975 - 8.95428i) q^{61} +(-1.89796 + 1.85947i) q^{62} +(-0.978592 - 3.65215i) q^{63} +(-7.98489 - 0.491459i) q^{64} +(6.24024 + 9.68835i) q^{65} +(3.72750 + 1.03983i) q^{66} +(-3.12556 + 0.837493i) q^{67} +(5.91641 - 3.25607i) q^{68} +(7.78695 - 4.49580i) q^{69} +(-8.39318 - 14.8876i) q^{70} +(0.132920 - 0.496064i) q^{71} +(-2.49179 + 1.33827i) q^{72} +(4.08433 + 4.08433i) q^{73} +(1.82546 + 7.10303i) q^{74} +(-2.60788 + 4.51697i) q^{75} +(-2.63022 + 9.06863i) q^{76} +10.3462i q^{77} +(3.74121 + 3.46459i) q^{78} +12.8676i q^{79} +(-9.40302 + 8.66228i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-9.89862 + 2.54393i) q^{82} +(-2.30938 - 2.30938i) q^{83} +(-5.23645 - 5.45556i) q^{84} +(2.79326 - 10.4246i) q^{85} +(5.51853 - 3.11118i) q^{86} +(-1.30007 + 0.750596i) q^{87} +(7.53394 - 1.77248i) q^{88} +(1.63329 - 0.437637i) q^{89} +(-1.21456 + 4.35389i) q^{90} +(-6.23449 + 12.1234i) q^{91} +(9.30880 - 15.3864i) q^{92} +(0.486273 + 1.81479i) q^{93} +(3.46951 + 3.54134i) q^{94} +(7.54493 + 13.0682i) q^{95} +(-3.07556 + 4.74773i) q^{96} +(-6.08266 - 1.62984i) q^{97} +(5.25023 - 8.88226i) q^{98} +(1.93491 - 1.93491i) 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

Varieties

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Representations

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Database

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