LMFDB - Embedded newform 144.2.u.a.131.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,2,Mod(11,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			131.16
Character	$\chi$	$=$	144.131
Dual form			144.2.u.a.11.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.717593 - 1.21863i) q^{2} +(1.11494 + 1.32549i) q^{3} +(-0.970121 - 1.74896i) q^{4} +(1.20583 - 0.323102i) q^{5} +(2.41535 - 0.407536i) q^{6} +(0.140266 + 0.242948i) q^{7} +(-2.82749 - 0.0728225i) q^{8} +(-0.513832 + 2.95567i) q^{9} +(0.471556 - 1.70132i) q^{10} +(-3.07444 - 0.823794i) q^{11} +(1.23660 - 3.23586i) q^{12} +(2.76539 - 0.740984i) q^{13} +(0.396717 + 0.00340517i) q^{14} +(1.77270 + 1.23808i) q^{15} +(-2.11773 + 3.39341i) q^{16} -3.72031i q^{17} +(3.23315 + 2.74714i) q^{18} +(-4.10860 + 4.10860i) q^{19} +(-1.73490 - 1.79551i) q^{20} +(-0.165636 + 0.456792i) q^{21} +(-3.21010 + 3.15546i) q^{22} +(-1.57595 - 0.909876i) q^{23} +(-3.05595 - 3.82899i) q^{24} +(-2.98049 + 1.72078i) q^{25} +(1.08144 - 3.90172i) q^{26} +(-4.49059 + 2.61431i) q^{27} +(0.288831 - 0.481009i) q^{28} +(-3.83006 - 1.02626i) q^{29} +(2.78084 - 1.27183i) q^{30} +(8.81101 + 5.08704i) q^{31} +(2.61564 + 5.01582i) q^{32} +(-2.33588 - 4.99361i) q^{33} +(-4.53369 - 2.66967i) q^{34} +(0.247635 + 0.247635i) q^{35} +(5.66783 - 1.96868i) q^{36} +(1.76964 - 1.76964i) q^{37} +(2.05856 + 7.95516i) q^{38} +(4.06540 + 2.83934i) q^{39} +(-3.43301 + 0.825757i) q^{40} +(2.66819 - 4.62144i) q^{41} +(0.437801 + 0.529640i) q^{42} +(-1.84748 + 6.89490i) q^{43} +(1.54180 + 6.17626i) q^{44} +(0.335387 + 3.73007i) q^{45} +(-2.23969 + 1.26758i) q^{46} +(-5.48486 - 9.50006i) q^{47} +(-6.85905 + 0.976412i) q^{48} +(3.46065 - 5.99402i) q^{49} +(-0.0417747 + 4.86693i) q^{50} +(4.93123 - 4.14791i) q^{51} +(-3.97872 - 4.11772i) q^{52} +(8.58403 + 8.58403i) q^{53} +(-0.0365433 + 7.34838i) q^{54} -3.97344 q^{55} +(-0.378909 - 0.697147i) q^{56} +(-10.0267 - 0.865067i) q^{57} +(-3.99906 + 3.93099i) q^{58} +(1.44299 + 5.38532i) q^{59} +(0.445622 - 4.30146i) q^{60} +(1.66977 - 6.23168i) q^{61} +(12.5219 - 7.08695i) q^{62} +(-0.790146 + 0.289745i) q^{63} +(7.98939 + 0.411810i) q^{64} +(3.09519 - 1.78701i) q^{65} +(-7.76158 - 0.736806i) q^{66} +(-1.00652 - 3.75640i) q^{67} +(-6.50668 + 3.60915i) q^{68} +(-0.551057 - 3.10336i) q^{69} +(0.479476 - 0.124074i) q^{70} -10.6808i q^{71} +(1.66809 - 8.31970i) q^{72} -9.30419i q^{73} +(-0.886658 - 3.42643i) q^{74} +(-5.60393 - 2.03203i) q^{75} +(11.1716 + 3.19994i) q^{76} +(-0.231101 - 0.862479i) q^{77} +(6.37741 - 2.91673i) q^{78} +(8.70990 - 5.02866i) q^{79} +(-1.45721 + 4.77613i) q^{80} +(-8.47195 - 3.03744i) q^{81} +(-3.71715 - 6.56784i) q^{82} +(0.588691 - 2.19703i) q^{83} +(0.959599 - 0.153452i) q^{84} +(-1.20204 - 4.48608i) q^{85} +(7.07659 + 7.19913i) q^{86} +(-2.90998 - 6.22091i) q^{87} +(8.63296 + 2.55316i) q^{88} -1.87637 q^{89} +(4.78625 + 2.26796i) q^{90} +(0.567911 + 0.567911i) q^{91} +(-0.0624738 + 3.63897i) q^{92} +(3.08091 + 17.3506i) q^{93} +(-15.5130 - 0.133153i) q^{94} +(-3.62679 + 6.28179i) q^{95} +(-3.73212 + 9.05932i) q^{96} +(9.19070 + 15.9188i) q^{97} +(-4.82116 - 8.51852i) q^{98} +(4.01461 - 8.66374i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100}) $ 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.717593	−	1.21863i	0.507415	−	0.861702i
$2$	0.717593	−	1.21863i	0.507415	−	0.861702i
$3$	1.11494	+	1.32549i	0.643709	+	0.765270i
$3$	1.11494	+	1.32549i	0.643709	+	0.765270i
$4$	−0.970121	−	1.74896i	−0.485061	−	0.874481i
$5$	1.20583	−	0.323102i	0.539266	−	0.144496i	0.0211020	−	0.999777i	$-0.493283\pi$
$5$	1.20583	−	0.323102i	0.539266	−	0.144496i	0.518164	+	0.855282i	$0.326616\pi$
$6$	2.41535	−	0.407536i	0.986062	−	0.166376i
$7$	0.140266	+	0.242948i	0.0530156	+	0.0918256i	0.891315	−	0.453384i	$-0.149783\pi$
$7$	0.140266	+	0.242948i	0.0530156	+	0.0918256i	−0.838300	+	0.545210i	$0.816450\pi$
$8$	−2.82749	−	0.0728225i	−0.999669	−	0.0257466i
$9$	−0.513832	+	2.95567i	−0.171277	+	0.985223i
$10$	0.471556	−	1.70132i	0.149119	−	0.538005i
$11$	−3.07444	−	0.823794i	−0.926979	−	0.248383i	−0.236413	−	0.971653i	$-0.575972\pi$
$11$	−3.07444	−	0.823794i	−0.926979	−	0.248383i	−0.690566	+	0.723269i	$0.742639\pi$
$12$	1.23660	−	3.23586i	0.356976	−	0.934113i
$13$	2.76539	−	0.740984i	0.766982	−	0.205512i	0.145944	−	0.989293i	$-0.453378\pi$
$13$	2.76539	−	0.740984i	0.766982	−	0.205512i	0.621038	+	0.783781i	$0.286711\pi$
$14$	0.396717	+	0.00340517i	0.106027	+	0.000910071i
$15$	1.77270	+	1.23808i	0.457708	+	0.319671i
$16$	−2.11773	+	3.39341i	−0.529432	+	0.848352i
$17$		−	3.72031i		−	0.902309i	−0.892446	−	0.451154i	$-0.851012\pi$
$17$		−	3.72031i		−	0.902309i	0.892446	−	0.451154i	$-0.148988\pi$
$18$	3.23315	+	2.74714i	0.762060	+	0.647507i
$19$	−4.10860	+	4.10860i	−0.942577	+	0.942577i	−0.998439	−	0.0558614i	$-0.982209\pi$
$19$	−4.10860	+	4.10860i	−0.942577	+	0.942577i	0.0558614	+	0.998439i	$0.482209\pi$
$20$	−1.73490	−	1.79551i	−0.387935	−	0.401488i
$21$	−0.165636	+	0.456792i	−0.0361448	+	0.0996802i
$22$	−3.21010	+	3.15546i	−0.684395	+	0.672747i
$23$	−1.57595	−	0.909876i	−0.328609	−	0.189722i	0.326615	−	0.945158i	$-0.394092\pi$
$23$	−1.57595	−	0.909876i	−0.328609	−	0.189722i	−0.655223	+	0.755435i	$0.727425\pi$
$24$	−3.05595	−	3.82899i	−0.623792	−	0.781590i
$25$	−2.98049	+	1.72078i	−0.596097	+	0.344157i
$26$	1.08144	−	3.90172i	0.212088	−	0.765189i
$27$	−4.49059	+	2.61431i	−0.864215	+	0.503123i
$28$	0.288831	−	0.481009i	0.0545840	−	0.0909021i
$29$	−3.83006	−	1.02626i	−0.711224	−	0.190572i	−0.114972	−	0.993369i	$-0.536678\pi$
$29$	−3.83006	−	1.02626i	−0.711224	−	0.190572i	−0.596253	+	0.802797i	$0.703344\pi$
$30$	2.78084	−	1.27183i	0.507709	−	0.232203i
$31$	8.81101	+	5.08704i	1.58250	+	0.913659i	0.994493	+	0.104807i	$0.0334225\pi$
$31$	8.81101	+	5.08704i	1.58250	+	0.913659i	0.588012	+	0.808852i	$0.299911\pi$
$32$	2.61564	+	5.01582i	0.462385	+	0.886679i
$33$	−2.33588	−	4.99361i	−0.406625	−	0.869276i
$34$	−4.53369	−	2.66967i	−0.777521	−	0.457845i
$35$	0.247635	+	0.247635i	0.0418579	+	0.0418579i
$36$	5.66783	−	1.96868i	0.944638	−	0.328114i
$37$	1.76964	−	1.76964i	0.290928	−	0.290928i	−0.546519	−	0.837447i	$-0.684047\pi$
$37$	1.76964	−	1.76964i	0.290928	−	0.290928i	0.837447	+	0.546519i	$0.184047\pi$
$38$	2.05856	+	7.95516i	0.333943	+	1.29050i
$39$	4.06540	+	2.83934i	0.650985	+	0.454658i
$40$	−3.43301	+	0.825757i	−0.542807	+	0.130564i
$41$	2.66819	−	4.62144i	0.416701	−	0.721747i	−0.578904	−	0.815395i	$-0.696520\pi$
$41$	2.66819	−	4.62144i	0.416701	−	0.721747i	0.995605	+	0.0936482i	$0.0298529\pi$
$42$	0.437801	+	0.529640i	0.0675542	+	0.0817253i
$43$	−1.84748	+	6.89490i	−0.281738	+	1.05146i	0.669452	+	0.742856i	$0.266529\pi$
$43$	−1.84748	+	6.89490i	−0.281738	+	1.05146i	−0.951190	+	0.308606i	$0.900138\pi$
$44$	1.54180	+	6.17626i	0.232435	+	0.931106i
$45$	0.335387	+	3.73007i	0.0499965	+	0.556046i
$46$	−2.23969	+	1.26758i	−0.330225	+	0.186895i
$47$	−5.48486	−	9.50006i	−0.800049	−	1.38573i	−0.919583	−	0.392896i	$-0.871473\pi$
$47$	−5.48486	−	9.50006i	−0.800049	−	1.38573i	0.119534	−	0.992830i	$-0.461860\pi$
$48$	−6.85905	+	0.976412i	−0.990019	+	0.140933i
$49$	3.46065	−	5.99402i	0.494379	−	0.856289i
$50$	−0.0417747	+	4.86693i	−0.00590783	+	0.688288i
$51$	4.93123	−	4.14791i	0.690510	−	0.580824i
$52$	−3.97872	−	4.11772i	−0.551749	−	0.571025i
$53$	8.58403	+	8.58403i	1.17911	+	1.17911i	0.979972	+	0.199135i	$0.0638133\pi$
$53$	8.58403	+	8.58403i	1.17911	+	1.17911i	0.199135	+	0.979972i	$0.436187\pi$
$54$	−0.0365433	+	7.34838i	−0.00497291	+	0.999988i
$55$	−3.97344			−0.535778
$56$	−0.378909	−	0.697147i	−0.0506338	−	0.0931602i
$57$	−10.0267	−	0.865067i	−1.32807	−	0.114581i
$58$	−3.99906	+	3.93099i	−0.525102	+	0.516164i
$59$	1.44299	+	5.38532i	0.187862	+	0.701109i	0.994000	+	0.109382i	$0.0348871\pi$
$59$	1.44299	+	5.38532i	0.187862	+	0.701109i	−0.806138	+	0.591727i	$0.798446\pi$
$60$	0.445622	−	4.30146i	0.0575295	−	0.555317i
$61$	1.66977	−	6.23168i	0.213793	−	0.797885i	−0.772796	−	0.634655i	$-0.781142\pi$
$61$	1.66977	−	6.23168i	0.213793	−	0.797885i	0.986588	−	0.163230i	$-0.0521911\pi$
$62$	12.5219	−	7.08695i	1.59029	−	0.900043i
$63$	−0.790146	+	0.289745i	−0.0995491	+	0.0365045i
$64$	7.98939	+	0.411810i	0.998674	+	0.0514762i
$65$	3.09519	−	1.78701i	0.383911	−	0.221651i
$66$	−7.76158	−	0.736806i	−0.955384	−	0.0906945i
$67$	−1.00652	−	3.75640i	−0.122967	−	0.458918i	0.876792	−	0.480869i	$-0.159679\pi$
$67$	−1.00652	−	3.75640i	−0.122967	−	0.458918i	−0.999759	+	0.0219514i	$0.993012\pi$
$68$	−6.50668	+	3.60915i	−0.789051	+	0.437674i
$69$	−0.551057	−	3.10336i	−0.0663395	−	0.373600i
$70$	0.479476	−	0.124074i	0.0573083	−	0.0148297i
$71$		−	10.6808i		−	1.26758i	−0.773506	−	0.633789i	$-0.781499\pi$
$71$		−	10.6808i		−	1.26758i	0.773506	−	0.633789i	$-0.218501\pi$
$72$	1.66809	−	8.31970i	0.196587	−	0.980486i
$73$		−	9.30419i		−	1.08897i	−0.838770	−	0.544487i	$-0.816725\pi$
$73$		−	9.30419i		−	1.08897i	0.838770	−	0.544487i	$-0.183275\pi$
$74$	−0.886658	−	3.42643i	−0.103072	−	0.398314i
$75$	−5.60393	−	2.03203i	−0.647086	−	0.234639i
$76$	11.1716	+	3.19994i	1.28147	+	0.367058i
$77$	−0.231101	−	0.862479i	−0.0263364	−	0.0982886i
$78$	6.37741	−	2.91673i	0.722099	−	0.330255i
$79$	8.70990	−	5.02866i	0.979940	−	0.565769i	0.0776882	−	0.996978i	$-0.475246\pi$
$79$	8.70990	−	5.02866i	0.979940	−	0.565769i	0.902252	+	0.431209i	$0.141913\pi$
$80$	−1.45721	+	4.77613i	−0.162921	+	0.533988i
$81$	−8.47195	−	3.03744i	−0.941328	−	0.337493i
$82$	−3.71715	−	6.56784i	−0.410491	−	0.725297i
$83$	0.588691	−	2.19703i	0.0646173	−	0.241155i	−0.926062	−	0.377372i	$-0.876828\pi$
$83$	0.588691	−	2.19703i	0.0646173	−	0.241155i	0.990679	+	0.136217i	$0.0434945\pi$
$84$	0.959599	−	0.153452i	0.104701	−	0.0167430i
$85$	−1.20204	−	4.48608i	−0.130380	−	0.486584i
$86$	7.07659	+	7.19913i	0.763089	+	0.776302i
$87$	−2.90998	−	6.22091i	−0.311982	−	0.666952i
$88$	8.63296	+	2.55316i	0.920277	+	0.272168i
$89$	−1.87637			−0.198895			−0.0994475	−	0.995043i	$-0.531708\pi$
$89$	−1.87637			−0.198895			−0.0994475	+	0.995043i	$0.531708\pi$
$90$	4.78625	+	2.26796i	0.504515	+	0.239064i
$91$	0.567911	+	0.567911i	0.0595332	+	0.0595332i
$92$	−0.0624738	+	3.63897i	−0.00651335	+	0.379389i
$93$	3.08091	+	17.3506i	0.319476	+	1.79917i
$94$	−15.5130	−	0.133153i	−1.60004	−	0.0137337i
$95$	−3.62679	+	6.28179i	−0.372101	+	0.644498i
$96$	−3.73212	+	9.05932i	−0.380908	+	0.924613i
$97$	9.19070	+	15.9188i	0.933175	+	1.61631i	0.777857	+	0.628441i	$0.216307\pi$
$97$	9.19070	+	15.9188i	0.933175	+	1.61631i	0.155317	+	0.987865i	$0.450360\pi$
$98$	−4.82116	−	8.51852i	−0.487011	−	0.860501i
$99$	4.01461	−	8.66374i	0.403484	−	0.870739i
$100$	5.90102	+	3.54338i	0.590102	+	0.354338i
$101$	−4.18566	+	15.6211i	−0.416488	+	1.55436i	0.365347	+	0.930871i	$0.380950\pi$
$101$	−4.18566	+	15.6211i	−0.416488	+	1.55436i	−0.781836	+	0.623485i	$0.785716\pi$
$102$	−1.51616	−	8.98586i	−0.150122	−	0.889733i
$103$	0.0611378	−	0.105894i	0.00602409	−	0.0104340i	−0.862998	−	0.505208i	$-0.831416\pi$
$103$	0.0611378	−	0.105894i	0.00602409	−	0.0104340i	0.869022	+	0.494774i	$0.164749\pi$
$104$	−7.87308	+	1.89374i	−0.772019	+	0.185697i
$105$	−0.0521396	+	0.604333i	−0.00508830	+	0.0589769i
$106$	16.6206	−	4.30092i	1.61434	−	0.417743i
$107$	5.97359	−	5.97359i	0.577489	−	0.577489i	−0.356722	−	0.934211i	$-0.616106\pi$
$107$	5.97359	−	5.97359i	0.577489	−	0.577489i	0.934211	+	0.356722i	$0.116106\pi$
$108$	8.92874	+	5.31768i	0.859168	+	0.511694i
$109$	−3.40913	−	3.40913i	−0.326536	−	0.326536i	0.524732	−	0.851268i	$-0.324166\pi$
$109$	−3.40913	−	3.40913i	−0.326536	−	0.326536i	−0.851268	+	0.524732i	$0.824166\pi$
$110$	−2.85131	+	4.84215i	−0.271862	+	0.461681i
$111$	4.31868	+	0.372599i	0.409911	+	0.0353655i
$112$	−1.12147	−	0.0385180i	−0.105969	−	0.00363961i
$113$	1.91330	+	1.10464i	0.179988	+	0.103916i	0.587287	−	0.809379i	$-0.300196\pi$
$113$	1.91330	+	1.10464i	0.179988	+	0.103916i	−0.407299	+	0.913295i	$0.633529\pi$
$114$	−8.24930	+	11.5981i	−0.772618	+	1.08626i
$115$	−2.19432	−	0.587966i	−0.204621	−	0.0548281i
$116$	1.92073	+	7.69422i	0.178335	+	0.714391i
$117$	0.769157	+	8.55432i	0.0711086	+	0.790847i
$118$	7.59820	+	2.10599i	0.699471	+	0.193872i
$119$	0.903842	−	0.521833i	0.0828551	−	0.0478364i
$120$	−4.92212	−	3.62975i	−0.449326	−	0.331349i
$121$	−0.752719	−	0.434583i	−0.0684290	−	0.0395075i
$122$	−6.39590	−	6.50664i	−0.579057	−	0.589084i
$123$	9.10052	−	1.61596i	0.820566	−	0.145706i
$124$	0.349286	−	20.3452i	0.0313668	−	1.82705i
$125$	−7.45164	+	7.45164i	−0.666495	+	0.666495i
$126$	−0.213911	+	1.17082i	−0.0190567	+	0.104305i
$127$		−	3.63934i		−	0.322939i	−0.986878	−	0.161470i	$-0.948377\pi$
$127$		−	3.63934i		−	0.322939i	0.986878	−	0.161470i	$-0.0516234\pi$
$128$	6.23498	−	9.44061i	0.551099	−	0.834440i
$129$	−11.1989	+	5.23856i	−0.986010	+	0.461229i
$130$	0.0433824	−	5.05424i	0.00380489	−	0.443286i
$131$	−14.9890	+	4.01630i	−1.30960	+	0.350906i	−0.845072	−	0.534653i	$-0.820442\pi$
$131$	−14.9890	+	4.01630i	−1.30960	+	0.350906i	−0.464527	+	0.885559i	$0.653776\pi$
$132$	−6.46755	+	8.92977i	−0.562928	+	0.777237i
$133$	−1.57447	−	0.421878i	−0.136524	−	0.0365815i
$134$	−5.29994	−	1.46899i	−0.457845	−	0.126901i
$135$	−4.57022	+	4.60334i	−0.393342	+	0.396192i
$136$	−0.270922	+	10.5191i	−0.0232314	+	0.902009i
$137$	10.4065	+	18.0245i	0.889085	+	1.53994i	0.840959	+	0.541099i	$0.181992\pi$
$137$	10.4065	+	18.0245i	0.889085	+	1.53994i	0.0481263	+	0.998841i	$0.484675\pi$
$138$	−4.17728	−	1.55541i	−0.355594	−	0.132405i
$139$	0.802043	−	0.214907i	0.0680284	−	0.0182282i	−0.224644	−	0.974441i	$-0.572122\pi$
$139$	0.802043	−	0.214907i	0.0680284	−	0.0182282i	0.292673	+	0.956213i	$0.405455\pi$
$140$	0.192868	−	0.673339i	0.0163003	−	0.0569075i
$141$	6.47693	−	17.8621i	0.545456	−	1.50426i
$142$	−13.0159	−	7.66446i	−1.09227	−	0.643187i
$143$	−9.11246			−0.762022
$144$	−8.94163	−	8.00295i	−0.745136	−	0.666913i
$145$	−4.95000			−0.411076
$146$	−11.3384	−	6.67662i	−0.938370	−	0.552561i
$147$	11.8034	−	2.09591i	0.973529	−	0.172868i
$148$	−4.81181	−	1.37827i	−0.395528	−	0.113293i
$149$	5.13681	−	1.37640i	0.420824	−	0.112759i	−0.0421919	−	0.999110i	$-0.513434\pi$
$149$	5.13681	−	1.37640i	0.420824	−	0.112759i	0.463015	+	0.886350i	$0.346767\pi$
$150$	−6.49763	+	5.37095i	−0.530530	+	0.438536i
$151$	−1.53487	−	2.65847i	−0.124906	−	0.216343i	0.796790	−	0.604256i	$-0.206529\pi$
$151$	−1.53487	−	2.65847i	−0.124906	−	0.216343i	−0.921696	+	0.387913i	$0.873196\pi$
$152$	11.9162	−	11.3178i	0.966533	−	0.917996i
$153$	10.9960	+	1.91162i	0.888975	+	0.154545i
$154$	−1.21688	−	0.337283i	−0.0980590	−	0.0271790i
$155$	12.2683	+	3.28727i	0.985410	+	0.264040i
$156$	1.02196	−	9.86473i	0.0818225	−	0.789811i
$157$	−5.63885	+	1.51093i	−0.450029	+	0.120585i	−0.476713	−	0.879059i	$-0.658172\pi$
$157$	−5.63885	+	1.51093i	−0.450029	+	0.120585i	0.0266838	+	0.999644i	$0.491505\pi$
$158$	0.122079	−	14.2227i	0.00971205	−	1.13150i
$159$	−1.80737	+	20.9487i	−0.143334	+	1.66134i
$160$	4.77465	+	5.20312i	0.377470	+	0.411343i
$161$		−	0.510499i		−	0.0402329i
$162$	−9.78092	+	8.14454i	−0.768462	+	0.639895i
$163$	−12.5565	+	12.5565i	−0.983500	+	0.983500i	−0.999866	−	0.0163656i	$-0.994790\pi$
$163$	−12.5565	+	12.5565i	−0.983500	+	0.983500i	0.0163656	+	0.999866i	$0.494790\pi$
$164$	−10.6712	−	0.183203i	−0.833279	−	0.0143057i
$165$	−4.43013	−	5.26674i	−0.344885	−	0.410015i
$166$	−2.25492	−	2.29397i	−0.175016	−	0.178046i
$167$	12.0834	+	6.97635i	0.935041	+	0.539846i	0.888402	−	0.459066i	$-0.151816\pi$
$167$	12.0834	+	6.97635i	0.935041	+	0.539846i	0.0466388	+	0.998912i	$0.485149\pi$
$168$	0.501600	−	1.27951i	0.0386993	−	0.0987166i
$169$	−4.16000	+	2.40178i	−0.320000	+	0.184752i
$170$	−6.32945	−	1.75433i	−0.485447	−	0.134551i
$171$	−10.0325	−	14.2548i	−0.767206	−	1.09009i
$172$	13.8512	−	3.45771i	1.05614	−	0.263648i
$173$	−2.38993	−	0.640380i	−0.181703	−	0.0486872i	0.166820	−	0.985987i	$-0.446650\pi$
$173$	−2.38993	−	0.640380i	−0.181703	−	0.0486872i	−0.348523	+	0.937300i	$0.613317\pi$
$174$	−9.66917	−	0.917893i	−0.733018	−	0.0695853i
$175$	−0.836121	−	0.482735i	−0.0632048	−	0.0364913i
$176$	9.30631	−	8.68827i	0.701489	−	0.654903i
$177$	−5.52933	+	7.91696i	−0.415610	+	0.595075i
$178$	−1.34647	+	2.28661i	−0.100922	+	0.171388i
$179$	9.53870	+	9.53870i	0.712956	+	0.712956i	0.967153	−	0.254197i	$-0.0818111\pi$
$179$	9.53870	+	9.53870i	0.712956	+	0.712956i	−0.254197	+	0.967153i	$0.581811\pi$
$180$	6.19838	−	4.20520i	0.462000	−	0.313437i
$181$	−6.83874	+	6.83874i	−0.508320	+	0.508320i	−0.914010	−	0.405691i	$-0.867031\pi$
$181$	−6.83874	+	6.83874i	−0.508320	+	0.508320i	0.405691	+	0.914010i	$0.367031\pi$
$182$	1.09960	−	0.284545i	0.0815079	−	0.0210919i
$183$	10.1217	−	4.73466i	0.748218	−	0.349996i
$184$	4.38973	+	2.68743i	0.323615	+	0.198120i
$185$	1.56212	−	2.70567i	0.114849	−	0.198925i
$186$	23.3548	+	8.69618i	1.71246	+	0.637635i
$187$	−3.06477	+	11.4379i	−0.224118	+	0.836421i
$188$	−11.2943	+	18.8090i	−0.823718	+	1.37179i
$189$	−1.26502	−	0.724281i	−0.0920164	−	0.0526837i
$190$	5.05262	+	8.92748i	0.366555	+	0.647668i
$191$	−7.08629	−	12.2738i	−0.512746	−	0.888102i	−0.999891	−	0.0147810i	$-0.995295\pi$
$191$	−7.08629	−	12.2738i	−0.512746	−	0.888102i	0.487145	−	0.873321i	$-0.338038\pi$
$192$	8.36182	+	11.0490i	0.603462	+	0.797391i
$193$	−6.47017	+	11.2067i	−0.465733	+	0.806673i	−0.999234	−	0.0391263i	$-0.987543\pi$
$193$	−6.47017	+	11.2067i	−0.465733	+	0.806673i	0.533501	+	0.845799i	$0.320876\pi$
$194$	25.9943	+	0.223119i	1.86628	+	0.0160190i
$195$	5.81960	+	2.11023i	0.416750	+	0.151117i
$196$	−13.8406	−	0.237615i	−0.988612	−	0.0169725i
$197$	−8.02294	−	8.02294i	−0.571611	−	0.571611i	0.360968	−	0.932578i	$-0.382447\pi$
$197$	−8.02294	−	8.02294i	−0.571611	−	0.571611i	−0.932578	+	0.360968i	$0.882447\pi$
$198$	−7.67704	−	11.1094i	−0.545584	−	0.789508i
$199$	10.9199			0.774093			0.387046	−	0.922060i	$-0.373495\pi$
$199$	10.9199			0.774093			0.387046	+	0.922060i	$0.373495\pi$
$200$	8.55260	−	4.64845i	0.604760	−	0.328695i
$201$	3.85685	−	5.52229i	0.272041	−	0.389512i
$202$	16.0327	+	16.3103i	1.12806	+	1.14759i
$203$	−0.287899	−	1.07445i	−0.0202066	−	0.0754119i
$204$	−12.0384	−	4.60055i	−0.842859	−	0.322103i
$205$	1.72420	−	6.43478i	0.120423	−	0.449425i
$206$	−0.0851733	−	0.150493i	−0.00593431	−	0.0104853i
$207$	3.49907	−	4.19047i	0.243202	−	0.291258i
$208$	−3.34189	+	10.9533i	−0.231718	+	0.759475i
$209$	16.0163	−	9.24701i	1.10787	−	0.639629i
$210$	0.699044	+	0.497204i	0.0482386	+	0.0343103i
$211$	−4.37047	−	16.3108i	−0.300875	−	1.12288i	−0.936438	−	0.350833i	$-0.885899\pi$
$211$	−4.37047	−	16.3108i	−0.300875	−	1.12288i	0.635563	−	0.772049i	$-0.280768\pi$
$212$	6.68559	−	23.3407i	0.459168	−	1.60304i
$213$	14.1573	−	11.9084i	0.970039	−	0.815951i
$214$	−2.99300	−	11.5662i	−0.204597	−	0.790650i
$215$			8.91103i			0.607727i
$216$	12.8875	−	7.06490i	0.876882	−	0.480706i
$217$			2.85415i			0.193753i
$218$	−6.60085	+	1.70811i	−0.447066	+	0.115688i
$219$	12.3326	−	10.3736i	0.833359	−	0.700982i
$220$	3.85472	+	6.94939i	0.259885	+	0.468528i
$221$	−2.75669	−	10.2881i	−0.185435	−	0.692054i
$222$	3.55311	−	4.99550i	0.238469	−	0.335276i
$223$	−12.3586	+	7.13522i	−0.827591	+	0.477810i	−0.853027	−	0.521867i	$-0.825236\pi$
$223$	−12.3586	+	7.13522i	−0.827591	+	0.477810i	0.0254364	+	0.999676i	$0.491902\pi$
$224$	−0.851696	+	1.33901i	−0.0569063	+	0.0894666i
$225$	−3.55460	−	9.69352i	−0.236973	−	0.646235i
$226$	2.71912	−	1.53892i	0.180873	−	0.102367i
$227$	−2.27906	+	8.50557i	−0.151267	+	0.564535i	0.848130	+	0.529789i	$0.177729\pi$
$227$	−2.27906	+	8.50557i	−0.151267	+	0.564535i	−0.999396	+	0.0347459i	$0.988938\pi$
$228$	8.21417	+	18.3756i	0.543996	+	1.21695i
$229$	−6.45185	−	24.0786i	−0.426350	−	1.59116i	−0.760957	−	0.648803i	$-0.775270\pi$
$229$	−6.45185	−	24.0786i	−0.426350	−	1.59116i	0.334606	−	0.942358i	$-0.391397\pi$
$230$	−2.29114	+	2.25214i	−0.151073	+	0.148502i
$231$	0.885543	−	1.26793i	0.0582644	−	0.0834237i
$232$	10.7547	+	3.18066i	0.706082	+	0.208820i
$233$	−6.51295			−0.426678			−0.213339	−	0.976978i	$-0.568434\pi$
$233$	−6.51295			−0.426678			−0.213339	+	0.976978i	$0.568434\pi$
$234$	10.9765	+	5.20120i	0.717556	+	0.340013i
$235$	−9.68332	−	9.68332i	−0.631670	−	0.631670i
$236$	8.01884	−	7.74815i	0.521982	−	0.504362i
$237$	16.3764	+	5.93822i	1.06376	+	0.385729i
$238$	0.0126683	−	1.47591i	0.000821165	−	0.0956693i
$239$	−2.36907	+	4.10336i	−0.153243	+	0.265424i	−0.932418	−	0.361382i	$-0.882305\pi$
$239$	−2.36907	+	4.10336i	−0.153243	+	0.265424i	0.779175	+	0.626806i	$0.215638\pi$
$240$	−7.95540	+	3.39357i	−0.513519	+	0.219054i
$241$	7.43805	+	12.8831i	0.479127	+	0.829872i	0.999713	−	0.0239367i	$-0.00762000\pi$
$241$	7.43805	+	12.8831i	0.479127	+	0.829872i	−0.520586	+	0.853809i	$0.674287\pi$
$242$	−1.06974	+	0.605434i	−0.0687656	+	0.0389187i
$243$	−5.41961	−	14.6160i	−0.347668	−	0.937618i
$244$	−12.5188	+	3.12512i	−0.801437	+	0.200065i
$245$	2.23629	−	8.34594i	0.142871	−	0.533203i
$246$	4.56120	−	12.2498i	0.290812	−	0.781017i
$247$	−8.31748	+	14.4063i	−0.529228	+	0.916650i
$248$	−24.5426	−	15.0252i	−1.55846	−	0.954101i
$249$	3.56848	−	1.66924i	0.226143	−	0.105784i
$250$	3.73355	+	14.4280i	0.236131	+	0.912510i
$251$	6.89508	−	6.89508i	0.435213	−	0.435213i	−0.455184	−	0.890397i	$-0.650427\pi$
$251$	6.89508	−	6.89508i	0.435213	−	0.435213i	0.890397	+	0.455184i	$0.150427\pi$
$252$	1.27329	+	1.10085i	0.0802098	+	0.0693469i
$253$	4.09562	+	4.09562i	0.257489	+	0.257489i
$254$	−4.43501	−	2.61156i	−0.278277	−	0.163864i
$255$	4.60604	−	6.59499i	0.288442	−	0.412994i
$256$	−7.03044	−	14.3726i	−0.439403	−	0.898290i
$257$	2.17437	+	1.25537i	0.135633	+	0.0783080i	0.566281	−	0.824212i	$-0.308382\pi$
$257$	2.17437	+	1.25537i	0.135633	+	0.0783080i	−0.430648	+	0.902520i	$0.641715\pi$
$258$	−1.65240	+	17.4065i	−0.102874	+	1.08368i
$259$	0.678152	+	0.181710i	0.0421383	+	0.0112909i
$260$	−6.12812	−	3.67975i	−0.380050	−	0.228209i
$261$	5.00130	−	10.7931i	0.309572	−	0.668074i
$262$	−5.86164	+	21.1482i	−0.362133	+	1.30654i
$263$	−3.14718	+	1.81703i	−0.194064	+	0.112043i	−0.593884	−	0.804551i	$-0.702406\pi$
$263$	−3.14718	+	1.81703i	−0.194064	+	0.112043i	0.399820	+	0.916594i	$0.369073\pi$
$264$	6.24103	+	14.2895i	0.384109	+	0.879457i
$265$	13.1244	+	7.57740i	0.806228	+	0.465476i
$266$	−1.64394	+	1.61596i	−0.100797	+	0.0990810i
$267$	−2.09204	−	2.48711i	−0.128031	−	0.152209i
$268$	−5.59335	+	5.40454i	−0.341668	+	0.330135i
$269$	−12.3633	+	12.3633i	−0.753802	+	0.753802i	−0.975187	−	0.221384i	$-0.928942\pi$
$269$	−12.3633	+	12.3633i	−0.753802	+	0.753802i	0.221384	+	0.975187i	$0.428942\pi$
$270$	2.33021	+	8.87273i	0.141812	+	0.539977i
$271$		−	27.2658i		−	1.65628i	−0.560523	−	0.828139i	$-0.689400\pi$
$271$		−	27.2658i		−	1.65628i	0.560523	−	0.828139i	$-0.310600\pi$
$272$	12.6245	+	7.87862i	0.765475	+	0.477711i
$273$	−0.119574	+	1.38594i	−0.00723694	+	0.0838811i
$274$	29.4329	+	0.252633i	1.77810	+	0.0152621i
$275$	10.5809	−	2.83514i	0.638053	−	0.170966i
$276$	−4.89306	+	3.97441i	−0.294528	+	0.239231i
$277$	−16.7042	−	4.47587i	−1.00366	−	0.268929i	−0.280680	−	0.959801i	$-0.590560\pi$
$277$	−16.7042	−	4.47587i	−1.00366	−	0.268929i	−0.722977	+	0.690872i	$0.757227\pi$
$278$	0.313648	−	1.13161i	0.0188114	−	0.0678694i
$279$	−19.5630	+	23.4285i	−1.17121	+	1.40263i
$280$	−0.682151	−	0.718217i	−0.0407663	−	0.0429217i
$281$	−7.04702	−	12.2058i	−0.420390	−	0.728137i	0.575588	−	0.817740i	$-0.304773\pi$
$281$	−7.04702	−	12.2058i	−0.420390	−	0.728137i	−0.995978	+	0.0896034i	$0.971440\pi$
$282$	−17.1195	−	20.7107i	−1.01945	−	1.23330i
$283$	0.628767	−	0.168478i	0.0373763	−	0.0100149i	−0.240082	−	0.970753i	$-0.577174\pi$
$283$	0.628767	−	0.168478i	0.0373763	−	0.0100149i	0.277459	+	0.960738i	$0.410508\pi$
$284$	−18.6803	+	10.3617i	−1.10847	+	0.614852i
$285$	−12.3701	+	2.19653i	−0.732740	+	0.130111i
$286$	−6.53903	+	11.1047i	−0.386661	+	0.656636i
$287$	1.49702			0.0883665
$288$	−16.1691	+	5.15369i	−0.952773	+	0.303684i
$289$	3.15927			0.185839
$290$	−3.55209	+	6.03223i	−0.208586	+	0.354225i
$291$	−10.8531	+	29.9306i	−0.636218	+	1.75456i
$292$	−16.2727	+	9.02619i	−0.952286	+	0.528218i
$293$	−8.09169	+	2.16816i	−0.472722	+	0.126665i	−0.487312	−	0.873228i	$-0.662022\pi$
$293$	−8.09169	+	2.16816i	−0.472722	+	0.126665i	0.0145900	+	0.999894i	$0.495356\pi$
$294$	5.91590	−	15.8880i	0.345022	−	0.926607i
$295$	3.48002	+	6.02757i	0.202615	+	0.350939i
$296$	−5.13252	+	4.87478i	−0.298322	+	0.283341i
$297$	15.9597	−	4.33821i	0.926077	−	0.251728i
$298$	2.00881	−	7.24757i	0.116367	−	0.419840i
$299$	−5.03233	−	1.34841i	−0.291027	−	0.0779804i
$300$	1.88255	+	11.7724i	0.108689	+	0.679678i
$301$	−1.93424	+	0.518278i	−0.111488	+	0.0298730i
$302$	−4.34110	−	0.0372612i	−0.249802	−	0.00214414i
$303$	−25.3723	+	11.8685i	−1.45760	+	0.681827i
$304$	−5.24125	−	22.6431i	−0.300606	−	1.29867i
$305$		−	8.05388i		−	0.461164i
$306$	10.2202	−	12.0283i	0.584251	−	0.687613i
$307$	10.1250	−	10.1250i	0.577865	−	0.577865i	−0.356449	−	0.934315i	$-0.616013\pi$
$307$	10.1250	−	10.1250i	0.577865	−	0.577865i	0.934315	+	0.356449i	$0.116013\pi$
$308$	−1.28425	+	1.24090i	−0.0731768	+	0.0707066i
$309$	0.208526	−	0.0370275i	0.0118626	−	0.00210642i
$310$	12.8096	−	12.5916i	0.727535	−	0.715152i
$311$	−13.7848	−	7.95868i	−0.781667	−	0.451295i	0.0553539	−	0.998467i	$-0.482371\pi$
$311$	−13.7848	−	7.95868i	−0.781667	−	0.451295i	−0.837021	+	0.547171i	$0.815705\pi$
$312$	−11.2881	−	8.32426i	−0.639064	−	0.471268i
$313$	−9.90266	+	5.71730i	−0.559732	+	0.323161i	−0.753038	−	0.657977i	$-0.771412\pi$
$313$	−9.90266	+	5.71730i	−0.559732	+	0.323161i	0.193306	+	0.981138i	$0.438079\pi$
$314$	−2.20514	+	7.95591i	−0.124443	+	0.448978i
$315$	−0.859168	+	0.604683i	−0.0484086	+	0.0340700i
$316$	−17.2446	−	10.3549i	−0.970084	−	0.582507i
$317$	26.3682	+	7.06533i	1.48098	+	0.396828i	0.906682	−	0.421815i	$-0.138607\pi$
$317$	26.3682	+	7.06533i	1.48098	+	0.396828i	0.574302	+	0.818644i	$0.305274\pi$
$318$	24.2317	+	17.2351i	1.35885	+	0.966498i
$319$	10.9299	+	6.31036i	0.611955	+	0.353313i
$320$	9.76694	−	2.08482i	0.545989	−	0.116545i
$321$	14.5781	+	1.25774i	0.813670	+	0.0702004i
$322$	−0.622109	−	0.366330i	−0.0346688	−	0.0204148i
$323$	15.2853	+	15.2853i	0.850495	+	0.850495i
$324$	2.90646	+	17.7638i	0.161470	+	0.986878i
$325$	−6.96714	+	6.96714i	−0.386467	+	0.386467i
$326$	6.29128	+	24.3122i	0.348442	+	1.34653i
$327$	0.717795	−	8.31973i	0.0396941	−	0.460082i
$328$	−7.88082	+	12.8728i	−0.435145	+	0.710779i
$329$	1.53868	−	2.66507i	0.0848301	−	0.146930i
$330$	−9.59724	+	1.61932i	−0.528311	+	0.0891406i
$331$	2.97493	−	11.1026i	0.163517	−	0.610254i	−0.834708	−	0.550693i	$-0.814363\pi$
$331$	2.97493	−	11.1026i	0.163517	−	0.610254i	0.998225	−	0.0595605i	$-0.0189699\pi$
$332$	−4.41362	+	1.10178i	−0.242229	+	0.0604682i
$333$	4.32118	+	6.13978i	0.236799	+	0.336458i
$334$	17.1726	−	9.71902i	0.939640	−	0.531801i
$335$	−2.42740	−	4.20439i	−0.132623	−	0.229710i
$336$	−1.19931	−	1.52943i	−0.0654277	−	0.0834375i
$337$	4.37194	−	7.57242i	0.238155	−	0.412496i	−0.722030	−	0.691862i	$-0.756791\pi$
$337$	4.37194	−	7.57242i	0.238155	−	0.412496i	0.960185	+	0.279366i	$0.0901242\pi$
$338$	−0.0583068	+	6.79300i	−0.00317147	+	0.369490i
$339$	0.669016	+	3.76766i	0.0363360	+	0.204631i
$340$	−6.67986	+	6.45437i	−0.362266	+	0.350037i
$341$	−22.8983	−	22.8983i	−1.24001	−	1.24001i
$342$	−24.5706	+	1.99681i	−1.32863	+	0.107975i
$343$	3.90537			0.210870
$344$	5.72584	−	19.3607i	0.308717	−	1.04386i
$345$	−1.66719	−	3.56409i	−0.0897583	−	0.191884i
$346$	−2.49538	+	2.45291i	−0.134153	+	0.131869i
$347$	0.832493	+	3.10690i	0.0446905	+	0.166787i	0.984664	−	0.174459i	$-0.0558176\pi$
$347$	0.832493	+	3.10690i	0.0446905	+	0.166787i	−0.939974	+	0.341246i	$0.889151\pi$
$348$	−8.05710	+	11.1245i	−0.431906	+	0.596334i
$349$	8.57705	−	32.0100i	0.459119	−	1.71346i	−0.216568	−	0.976268i	$-0.569486\pi$
$349$	8.57705	−	32.0100i	0.459119	−	1.71346i	0.675687	−	0.737188i	$-0.263847\pi$
$350$	−1.18827	+	0.672516i	−0.0635157	+	0.0359475i
$351$	−10.4811	+	10.5570i	−0.559439	+	0.563493i
$352$	−3.90965	−	17.5756i	−0.208385	−	0.936782i
$353$	−7.18886	+	4.15049i	−0.382624	+	0.220908i	−0.678959	−	0.734176i	$-0.737569\pi$
$353$	−7.18886	+	4.15049i	−0.382624	+	0.220908i	0.296335	+	0.955084i	$0.404235\pi$
$354$	5.68004	+	12.4194i	0.301891	+	0.660082i
$355$	−3.45099	−	12.8793i	−0.183160	−	0.683561i
$356$	1.82031	+	3.28170i	0.0964762	+	0.173930i
$357$	1.69941	+	0.616220i	0.0899423	+	0.0326138i
$358$	18.4691	−	4.77925i	0.976120	−	0.252591i
$359$			17.1616i			0.905754i	0.891573	+	0.452877i	$0.149602\pi$
$359$			17.1616i			0.905754i	−0.891573	+	0.452877i	$0.850398\pi$
$360$	−0.676670	−	10.5711i	−0.0356636	−	0.557148i
$361$		−	14.7612i		−	0.776903i
$362$	3.42647	+	13.2413i	0.180091	+	0.695949i
$363$	−0.263201	−	1.48225i	−0.0138145	−	0.0777981i
$364$	0.442312	−	1.54420i	0.0231834	−	0.0809379i
$365$	−3.00621	−	11.2193i	−0.157352	−	0.587246i
$366$	1.49345	−	15.7322i	0.0780640	−	0.822334i
$367$	−1.27977	+	0.738875i	−0.0668034	+	0.0385690i	−0.533030	−	0.846097i	$-0.678947\pi$
$367$	−1.27977	+	0.738875i	−0.0668034	+	0.0385690i	0.466226	+	0.884666i	$0.345613\pi$
$368$	6.42502	−	3.42097i	0.334927	−	0.178331i
$369$	12.2884	+	10.2609i	0.639710	+	0.534162i
$370$	−2.17625	−	3.84522i	−0.113138	−	0.199903i
$371$	−0.881424	+	3.28952i	−0.0457612	+	0.170783i
$372$	27.3567	−	22.2206i	1.41838	−	1.15208i
$373$	8.48049	+	31.6496i	0.439103	+	1.63876i	0.731052	+	0.682322i	$0.239030\pi$
$373$	8.48049	+	31.6496i	0.439103	+	1.63876i	−0.291948	+	0.956434i	$0.594304\pi$
$374$	11.7393	+	11.9426i	0.607025	+	0.617536i
$375$	−18.1852	−	1.56895i	−0.939078	−	0.0810200i
$376$	14.8166	+	27.2607i	0.764106	+	1.40587i
$377$	−11.3521			−0.584661
$378$	−1.79040	+	1.02185i	−0.0920881	+	0.0525583i
$379$	19.2548	+	19.2548i	0.989053	+	0.989053i	0.999941	−	0.0108880i	$-0.00346583\pi$
$379$	19.2548	+	19.2548i	0.989053	+	0.989053i	−0.0108880	+	0.999941i	$0.503466\pi$
$380$	14.5050	+	0.249022i	0.744092	+	0.0127746i
$381$	4.82390	−	4.05763i	0.247136	−	0.207879i
$382$	−20.0423	−	0.172031i	−1.02545	−	0.00880186i
$383$	−3.99635	+	6.92189i	−0.204204	+	0.353692i	−0.949879	−	0.312618i	$-0.898794\pi$
$383$	−3.99635	+	6.92189i	−0.204204	+	0.353692i	0.745675	+	0.666310i	$0.232127\pi$
$384$	19.4650	−	2.26130i	0.993320	−	0.115397i
$385$	−0.557338	−	0.965338i	−0.0284046	−	0.0491982i
$386$	9.01383	+	15.9266i	0.458792	+	0.810641i
$387$	−19.4297	−	9.00336i	−0.987669	−	0.457667i
$388$	18.9252	−	31.5173i	0.960782	−	1.60005i
$389$	−2.21212	+	8.25574i	−0.112159	+	0.418583i	−0.999059	−	0.0433793i	$-0.986188\pi$
$389$	−2.21212	+	8.25574i	−0.112159	+	0.418583i	0.886900	+	0.461962i	$0.152854\pi$
$390$	6.74770	−	5.57765i	0.341683	−	0.282435i
$391$	−3.38502	+	5.86303i	−0.171188	+	0.296506i
$392$	−10.2215	+	16.6960i	−0.516261	+	0.843277i
$393$	−22.0354	−	15.3899i	−1.11154	−	0.776316i
$394$	−15.5342	+	4.01980i	−0.782602	+	0.202514i
$395$	8.87792	−	8.87792i	0.446697	−	0.446697i
$396$	−19.0472	+	1.38348i	−0.957158	+	0.0695225i
$397$	21.9949	+	21.9949i	1.10389	+	1.10389i	0.993936	+	0.109957i	$0.0350713\pi$
$397$	21.9949	+	21.9949i	1.10389	+	1.10389i	0.109957	+	0.993936i	$0.464929\pi$
$398$	7.83606	−	13.3073i	0.392786	−	0.667037i
$399$	−1.19624	−	2.55731i	−0.0598870	−	0.128026i
$400$	0.472540	−	13.7582i	0.0236270	−	0.687908i
$401$	−15.4215	−	8.90359i	−0.770111	−	0.444624i	0.0628030	−	0.998026i	$-0.479996\pi$
$401$	−15.4215	−	8.90359i	−0.770111	−	0.444624i	−0.832914	+	0.553402i	$0.813329\pi$
$402$	−3.96198	−	8.66283i	−0.197606	−	0.432063i
$403$	28.1353	+	7.53883i	1.40152	+	0.375536i
$404$	31.3813	−	7.83379i	1.56128	−	0.389746i
$405$	−11.1972	−	0.925337i	−0.556392	−	0.0459803i
$406$	−1.51596	−	0.420178i	−0.0752357	−	0.0208531i
$407$	−6.89849	+	3.98284i	−0.341945	+	0.197422i
$408$	−14.2451	+	11.3691i	−0.705235	+	0.562853i
$409$	21.0100	+	12.1301i	1.03888	+	0.599797i	0.919515	−	0.393054i	$-0.128581\pi$
$409$	21.0100	+	12.1301i	1.03888	+	0.599797i	0.119363	+	0.992851i	$0.461915\pi$
$410$	−6.60436	−	6.71871i	−0.326166	−	0.331814i
$411$	−12.2887	+	33.8899i	−0.606159	+	1.67166i
$412$	−0.244515	−	0.00419784i	−0.0120464	−	0.000206813i
$413$	−1.10595	+	1.10595i	−0.0544202	+	0.0544202i
$414$	−2.59573	−	7.27112i	−0.127573	−	0.357356i
$415$		−	2.83946i		−	0.139383i
$416$	10.9499	+	11.9325i	0.536864	+	0.585041i
$417$	1.17908	+	0.823490i	0.0577399	+	0.0403265i
$418$	0.224485	−	26.1535i	0.0109799	−	1.27921i
$419$	11.0392	−	2.95796i	0.539302	−	0.144506i	0.0211217	−	0.999777i	$-0.493276\pi$
$419$	11.0392	−	2.95796i	0.539302	−	0.144506i	0.518180	+	0.855271i	$0.326610\pi$
$420$	1.10754	−	0.495086i	0.0540423	−	0.0241577i
$421$	16.7104	+	4.47753i	0.814413	+	0.218221i	0.641903	−	0.766786i	$-0.278145\pi$
$421$	16.7104	+	4.47753i	0.814413	+	0.218221i	0.172511	+	0.985008i	$0.444812\pi$
$422$	−23.0131	−	6.37853i	−1.12026	−	0.310502i
$423$	30.8973	−	11.3300i	1.50228	−	0.550883i
$424$	−23.6461	−	24.8964i	−1.14836	−	1.20907i
$425$	6.40186	+	11.0883i	0.310536	+	0.537864i
$426$	−4.35281	−	25.7979i	−0.210894	−	1.24991i
$427$	1.74819	−	0.468425i	0.0846006	−	0.0226687i
$428$	−16.2427	−	4.65247i	−0.785120	−	0.224886i
$429$	−10.1598	−	12.0784i	−0.490520	−	0.583153i
$430$	10.8593	+	6.39449i	0.523680	+	0.308370i
$431$	33.7821			1.62723			0.813613	−	0.581407i	$-0.197498\pi$
$431$	33.7821			1.62723			0.813613	+	0.581407i	$0.197498\pi$
$432$	0.638453	−	20.7748i	0.0307176	−	0.999528i
$433$	−32.7436			−1.57356			−0.786779	−	0.617235i	$-0.788253\pi$
$433$	−32.7436			−1.57356			−0.786779	+	0.617235i	$0.788253\pi$
$434$	3.47816	+	2.04812i	0.166957	+	0.0983129i
$435$	−5.51894	−	6.56117i	−0.264613	−	0.314584i
$436$	−2.65517	+	9.26972i	−0.127160	+	0.443939i
$437$	10.2133	−	2.73664i	0.488567	−	0.130911i
$438$	−3.79179	−	22.4729i	−0.181179	−	1.07380i
$439$	−14.7258	−	25.5058i	−0.702824	−	1.21733i	−0.967471	−	0.252982i	$-0.918589\pi$
$439$	−14.7258	−	25.5058i	−0.702824	−	1.21733i	0.264647	−	0.964345i	$-0.414745\pi$
$440$	11.2349	+	0.289356i	0.535601	+	0.0137945i
$441$	15.9382	+	13.3085i	0.758960	+	0.633736i
$442$	−14.5156	−	4.02329i	−0.690437	−	0.191368i
$443$	−8.80422	−	2.35908i	−0.418301	−	0.112083i	0.0435282	−	0.999052i	$-0.486140\pi$
$443$	−8.80422	−	2.35908i	−0.418301	−	0.112083i	−0.461830	+	0.886969i	$0.652807\pi$
$444$	−3.53798	−	7.91467i	−0.167905	−	0.375614i
$445$	−2.26259	+	0.606260i	−0.107257	+	0.0287395i
$446$	−0.173218	+	20.1807i	−0.00820213	+	0.955584i
$447$	7.55162	+	5.27417i	0.357179	+	0.249460i
$448$	1.02059	+	1.99877i	0.0482184	+	0.0944329i
$449$			2.79179i			0.131753i	0.997828	+	0.0658765i	$0.0209843\pi$
$449$			2.79179i			0.131753i	−0.997828	+	0.0658765i	$0.979016\pi$
$450$	−14.3636	−	2.62426i	−0.677105	−	0.123709i
$451$	−12.0103	+	12.0103i	−0.565543	+	0.565543i
$452$	0.0758469	−	4.41792i	0.00356754	−	0.207802i
$453$	1.81248	−	4.99847i	0.0851579	−	0.234848i
$454$	8.72971	+	8.88087i	0.409706	+	0.416800i
$455$	0.868300	+	0.501313i	0.0407065	+	0.0235019i
$456$	28.2875	+	3.17614i	1.32468	+	0.148736i
$457$	1.90950	−	1.10245i	0.0893226	−	0.0515704i	−0.454673	−	0.890658i	$-0.650244\pi$
$457$	1.90950	−	1.10245i	0.0893226	−	0.0515704i	0.543996	+	0.839088i	$0.316911\pi$
$458$	−33.9728	−	9.41623i	−1.58744	−	0.439992i
$459$	9.72604	+	16.7064i	0.453972	+	0.779788i
$460$	1.10043	+	4.40818i	0.0513076	+	0.205532i
$461$	−19.1849	−	5.14058i	−0.893531	−	0.239421i	−0.217295	−	0.976106i	$-0.569723\pi$
$461$	−19.1849	−	5.14058i	−0.893531	−	0.239421i	−0.676236	+	0.736685i	$0.736390\pi$
$462$	−0.909680	−	1.98901i	−0.0423222	−	0.0925370i
$463$	−1.39347	−	0.804523i	−0.0647602	−	0.0373893i	0.467270	−	0.884115i	$-0.345238\pi$
$463$	−1.39347	−	0.804523i	−0.0647602	−	0.0373893i	−0.532031	+	0.846725i	$0.678571\pi$
$464$	11.5936	−	10.8236i	0.538217	−	0.502474i
$465$	9.32109	+	19.9265i	0.432255	+	0.924070i
$466$	−4.67365	+	7.93688i	−0.216503	+	0.367669i
$467$	−9.94383	−	9.94383i	−0.460145	−	0.460145i	0.438558	−	0.898703i	$-0.355489\pi$
$467$	−9.94383	−	9.94383i	−0.460145	−	0.460145i	−0.898703	+	0.438558i	$0.855489\pi$
$468$	14.2150	−	9.64395i	0.657089	−	0.445792i
$469$	0.771428	−	0.771428i	0.0356213	−	0.0356213i
$470$	−18.7491	+	4.85171i	−0.864831	+	0.223793i
$471$	−8.28968	−	5.78964i	−0.381968	−	0.266772i
$472$	−3.68787	−	15.3320i	−0.169748	−	0.705713i
$473$	11.3600	−	19.6760i	0.522331	−	0.904704i
$474$	18.9881	−	15.6956i	0.872152	−	0.720922i
$475$	5.17561	−	19.3156i	0.237473	−	0.886262i
$476$	−1.78950	−	1.07454i	−0.0820217	−	0.0492516i
$477$	−29.7823	+	20.9608i	−1.36364	+	0.959729i
$478$	3.30045	+	5.83157i	0.150959	+	0.266730i
$479$	14.3867	+	24.9185i	0.657346	+	1.13856i	0.981300	+	0.192483i	$0.0616542\pi$
$479$	14.3867	+	24.9185i	0.657346	+	1.13856i	−0.323955	+	0.946073i	$0.605013\pi$
$480$	−1.57323	+	12.1299i	−0.0718080	+	0.553651i
$481$	3.58248	−	6.20504i	0.163347	−	0.282925i
$482$	21.0372	+	0.180570i	0.958219	+	0.00822475i
$483$	0.676659	−	0.569174i	0.0307891	−	0.0258983i
$484$	−0.0298393	+	1.73808i	−0.00135633	+	0.0790034i
$485$	16.2259	+	16.2259i	0.736778	+	0.736778i
$486$	−21.7006	−	3.88384i	−0.984359	−	0.176175i
$487$	43.0194			1.94939			0.974697	−	0.223530i	$-0.0717581\pi$
$487$	43.0194			1.94939			0.974697	+	0.223530i	$0.0717581\pi$
$488$	−5.17507	+	17.4984i	−0.234265	+	0.792116i
$489$	−30.6432	−	2.64377i	−1.38573	−	0.119556i
$490$	−8.56588	−	8.71420i	−0.386967	−	0.393667i
$491$	1.40962	+	5.26076i	0.0636152	+	0.237415i	0.990411	−	0.138150i	$-0.0441155\pi$
$491$	1.40962	+	5.26076i	0.0636152	+	0.237415i	−0.926796	+	0.375565i	$0.877449\pi$
$492$	−11.6549	−	14.3488i	−0.525441	−	0.646892i
$493$	−3.81801	+	14.2490i	−0.171955	+	0.641744i
$494$	11.5874	+	20.4738i	0.521341	+	0.921159i
$495$	2.04168	−	11.7442i	0.0917667	−	0.527861i
$496$	−35.9217	+	19.1264i	−1.61293	+	0.858800i
$497$	2.59488	−	1.49815i	0.116396	−	0.0672013i
$498$	0.526528	−	5.54650i	0.0235943	−	0.248545i
$499$	−4.61454	−	17.2217i	−0.206575	−	0.770950i	−0.988964	−	0.148159i	$-0.952665\pi$
$499$	−4.61454	−	17.2217i	−0.206575	−	0.770950i	0.782388	−	0.622791i	$-0.214001\pi$
$500$	20.2616	+	5.80364i	0.906128	+	0.259547i
$501$	4.22516	+	23.7946i	0.188766	+	1.06306i
$502$	−3.45469	−	13.3504i	−0.154191	−	0.595858i
$503$		−	0.254767i		−	0.0113595i	−0.999984	−	0.00567974i	$-0.998192\pi$
$503$		−	0.254767i		−	0.0113595i	0.999984	−	0.00567974i	$-0.00180793\pi$
$504$	2.25523	−	0.761711i	0.100456	−	0.0339293i
$505$			20.1888i			0.898391i
$506$	7.93004	−	2.05206i	0.352533	−	0.0912252i
$507$	−7.82166	−	2.83620i	−0.347372	−	0.125960i
$508$	−6.36506	+	3.53060i	−0.282404	+	0.156645i
$509$	2.84712	+	10.6256i	0.126196	+	0.470971i	0.999879	−	0.0155245i	$-0.00494181\pi$
$509$	2.84712	+	10.6256i	0.126196	+	0.470971i	−0.873683	+	0.486495i	$0.838275\pi$
$510$	−4.73159	−	10.3456i	−0.209518	−	0.458110i
$511$	2.26043	−	1.30506i	0.0999956	−	0.0577325i
$512$	−22.5599	−	1.74619i	−0.997018	−	0.0771716i
$513$	7.70890	−	29.1912i	0.340356	−	1.28882i
$514$	3.09015	−	1.74891i	0.136301	−	0.0771410i
$515$	0.0395075	−	0.147444i	0.00174091	−	0.00649716i
$516$	20.0263	+	14.5044i	0.881611	+	0.638522i
$517$	9.03680	+	33.7258i	0.397438	+	1.48326i
$518$	0.708074	−	0.696023i	0.0311110	−	0.0305815i
$519$	−1.81581	−	3.88180i	−0.0797050	−	0.170392i
$520$	−8.88175	+	4.82735i	−0.389491	+	0.211693i
$521$	−8.17552			−0.358176			−0.179088	−	0.983833i	$-0.557315\pi$
$521$	−8.17552			−0.358176			−0.179088	+	0.983833i	$0.557315\pi$
$522$	−9.56386	−	13.8398i	−0.418599	−	0.605750i
$523$	−11.4305	−	11.4305i	−0.499820	−	0.499820i	0.411562	−	0.911382i	$-0.364983\pi$
$523$	−11.4305	−	11.4305i	−0.499820	−	0.499820i	−0.911382	+	0.411562i	$0.864983\pi$
$524$	21.5655	+	22.3189i	0.942095	+	0.975008i
$525$	−0.292364	−	1.64649i	−0.0127598	−	0.0718586i
$526$	−0.0441112	+	5.13914i	−0.00192334	+	0.224077i
$527$	18.9254	−	32.7797i	0.824403	−	1.42791i
$528$	21.8921	+	2.64853i	0.952733	+	0.115262i
$529$	−9.84425	−	17.0507i	−0.428011	−	0.741337i
$530$	18.6521	−	10.5564i	0.810193	−	0.458539i
$531$	−16.6587	+	1.49786i	−0.722925	+	0.0650014i
$532$	0.789579	+	3.16296i	0.0342326	+	0.137132i
$533$	3.95417	−	14.7572i	0.171274	−	0.639204i
$534$	−4.53210	+	0.764689i	−0.196123	+	0.0330913i
$535$	5.27308	−	9.13325i	0.227975	−	0.394865i
$536$	2.57239	+	10.6945i	0.111110	+	0.461931i
$537$	−2.00838	+	23.2785i	−0.0866679	+	1.00454i
$538$	6.19447	+	23.9381i	0.267063	+	1.03204i
$539$	−15.5774	+	15.5774i	−0.670967	+	0.670967i
$540$	12.4847	+	3.52734i	0.537257	+	0.151793i
$541$	9.93863	+	9.93863i	0.427295	+	0.427295i	0.887706	−	0.460411i	$-0.152298\pi$
$541$	9.93863	+	9.93863i	0.427295	+	0.427295i	−0.460411	+	0.887706i	$0.652298\pi$
$542$	−33.2269	−	19.5657i	−1.42722	−	0.840420i
$543$	−16.6894	−	1.43990i	−0.716212	−	0.0617920i
$544$	18.6604	−	9.73101i	0.800058	−	0.417214i
$545$	−5.21235	−	3.00935i	−0.223273	−	0.128906i
$546$	1.60315	+	1.14026i	0.0686084	+	0.0487986i
$547$	2.81747	+	0.754938i	0.120466	+	0.0322788i	0.318548	−	0.947907i	$-0.396805\pi$
$547$	2.81747	+	0.754938i	0.120466	+	0.0322788i	−0.198082	+	0.980185i	$0.563471\pi$
$548$	21.4287	−	35.6865i	0.915388	−	1.52445i
$549$	17.5608	+	8.13733i	0.749476	+	0.347293i
$550$	4.13779	−	14.9287i	0.176436	−	0.636562i
$551$	19.9527	−	11.5197i	0.850012	−	0.490755i
$552$	1.33211	+	8.81484i	0.0566985	+	0.375184i
$553$	2.44341	+	1.41070i	0.103904	+	0.0599891i
$554$	−17.4412	+	17.1444i	−0.741007	+	0.728395i
$555$	5.32800	−	0.946083i	0.226161	−	0.0401590i
$556$	−1.15394	−	1.19426i	−0.0489380	−	0.0506477i
$557$	11.5964	−	11.5964i	0.491356	−	0.491356i	−0.417377	−	0.908733i	$-0.637051\pi$
$557$	11.5964	−	11.5964i	0.491356	−	0.491356i	0.908733	+	0.417377i	$0.137051\pi$
$558$	14.5125	+	40.6522i	0.614362	+	1.72095i
$559$			20.4360i			0.864352i
$560$	−1.36475	+	0.315902i	−0.0576711	+	0.0133493i
$561$	−18.5778	+	8.69021i	−0.784356	+	0.366901i
$562$	−19.9312	−	0.171077i	−0.840749	−	0.00721646i
$563$	−7.42718	+	1.99011i	−0.313018	+	0.0838730i	−0.411908	−	0.911225i	$-0.635138\pi$
$563$	−7.42718	+	1.99011i	−0.313018	+	0.0838730i	0.0988898	+	0.995098i	$0.468471\pi$
$564$	−37.5235	+	6.00048i	−1.58002	+	0.252666i
$565$	2.66403	+	0.713826i	0.112077	+	0.0300309i
$566$	0.245887	−	0.887133i	0.0103354	−	0.0372890i
$567$	−0.450388	−	2.48429i	−0.0189145	−	0.104330i
$568$	−0.777802	+	30.1998i	−0.0326359	+	1.26716i
$569$	−11.7897	−	20.4204i	−0.494250	−	0.856066i	0.505728	−	0.862693i	$-0.331224\pi$
$569$	−11.7897	−	20.4204i	−0.494250	−	0.856066i	−0.999978	+	0.00662697i	$0.997891\pi$
$570$	−6.19992	+	16.6508i	−0.259686	+	0.697424i
$571$	−7.46185	+	1.99940i	−0.312269	+	0.0836722i	−0.411550	−	0.911387i	$-0.635012\pi$
$571$	−7.46185	+	1.99940i	−0.312269	+	0.0836722i	0.0992811	+	0.995059i	$0.468346\pi$
$572$	8.84019	+	15.9373i	0.369627	+	0.666373i
$573$	8.36802	−	23.0773i	0.349579	−	0.964069i
$574$	1.07425	−	1.82432i	0.0448385	−	0.0761456i
$575$	6.26280			0.261177
$576$	−5.32238	+	23.4024i	−0.221766	+	0.975100i
$577$	16.4238			0.683733			0.341866	−	0.939749i	$-0.388941\pi$
$577$	16.4238			0.683733			0.341866	+	0.939749i	$0.388941\pi$
$578$	2.26707	−	3.84998i	0.0942976	−	0.160138i
$579$	−22.0681	+	3.91859i	−0.917119	+	0.162851i
$580$	4.80210	+	8.65737i	0.199397	+	0.359478i
$581$	0.616336	−	0.165147i	0.0255699	−	0.00685144i
$582$	28.6862	+	34.7038i	1.18908	+	1.43852i
$583$	−19.3196	−	33.4626i	−0.800137	−	1.38588i
$584$	−0.677554	+	26.3075i	−0.0280374	+	1.08861i
$585$	3.69140	+	10.0666i	0.152621	+	0.416202i
$586$	−3.16435	+	11.4166i	−0.130718	+	0.471617i
$587$	−44.0249	−	11.7964i	−1.81710	−	0.486891i	−0.820680	−	0.571388i	$-0.806405\pi$
$587$	−44.0249	−	11.7964i	−1.81710	−	0.486891i	−0.996424	+	0.0844969i	$0.973072\pi$
$588$	−15.1164	−	18.6104i	−0.623390	−	0.767481i
$589$	−57.1015	+	15.3003i	−2.35283	+	0.630438i
$590$	9.84262	+	0.0844828i	0.405214	+	0.00347810i
$591$	1.68923	−	19.5794i	0.0694858	−	0.805388i
$592$	2.25750	+	9.75275i	0.0927825	+	0.400836i
$593$			9.66931i			0.397071i	0.980094	+	0.198535i	$0.0636185\pi$
$593$			9.66931i			0.397071i	−0.980094	+	0.198535i	$0.936382\pi$
$594$	6.16590	−	22.5621i	0.252990	−	0.925733i
$595$	0.921278	−	0.921278i	0.0377687	−	0.0377687i
$596$	−7.39060	−	7.64880i	−0.302731	−	0.313307i
$597$	12.1750	+	14.4742i	0.498290	+	0.592390i
$598$	−5.25437	+	5.16494i	−0.214867	+	0.211210i
$599$	−8.99479	−	5.19314i	−0.367517	−	0.212186i	0.304856	−	0.952398i	$-0.401392\pi$
$599$	−8.99479	−	5.19314i	−0.367517	−	0.212186i	−0.672373	+	0.740212i	$0.734725\pi$
$600$	15.6971	+	6.15364i	0.640830	+	0.251221i
$601$	−16.6353	+	9.60440i	−0.678569	+	0.391772i	−0.799316	−	0.600912i	$-0.794804\pi$
$601$	−16.6353	+	9.60440i	−0.678569	+	0.391772i	0.120747	+	0.992683i	$0.461471\pi$
$602$	−0.756407	+	2.72903i	−0.0308288	+	0.111227i
$603$	11.6199	−	1.04479i	0.473197	−	0.0425473i
$604$	−3.16055	+	5.26345i	−0.128601	+	0.214167i
$605$	−1.04807	−	0.280829i	−0.0426101	−	0.0114173i
$606$	−3.74367	+	39.4362i	−0.152076	+	1.60199i
$607$	−12.1261	−	7.00100i	−0.492183	−	0.284162i	0.233297	−	0.972406i	$-0.425049\pi$
$607$	−12.1261	−	7.00100i	−0.492183	−	0.284162i	−0.725480	+	0.688244i	$0.758382\pi$
$608$	−31.3546	−	9.86134i	−1.27160	−	0.399930i
$609$	1.10319	−	1.57955i	0.0447033	−	0.0640068i
$610$	−9.81470	−	5.77941i	−0.397386	−	0.234001i
$611$	−22.2072	−	22.2072i	−0.898406	−	0.898406i
$612$	−7.32412	−	21.0861i	−0.296060	−	0.852355i
$613$	17.8303	−	17.8303i	0.720159	−	0.720159i	−0.248478	−	0.968637i	$-0.579930\pi$
$613$	17.8303	−	17.8303i	0.720159	−	0.720159i	0.968637	+	0.248478i	$0.0799304\pi$
$614$	−5.07302	−	19.6043i	−0.204730	−	0.791165i
$615$	10.4516	−	4.88898i	0.421449	−	0.197143i
$616$	0.590627	+	2.45548i	0.0237970	+	0.0989341i
$617$	−24.3668	+	42.2045i	−0.980970	+	1.69909i	−0.322340	+	0.946624i	$0.604469\pi$
$617$	−24.3668	+	42.2045i	−0.980970	+	1.69909i	−0.658630	+	0.752467i	$0.728864\pi$
$618$	0.104514	−	0.280686i	0.00420415	−	0.0112909i
$619$	−2.99775	+	11.1877i	−0.120490	+	0.449673i	−0.999639	−	0.0268731i	$-0.991445\pi$
$619$	−2.99775	+	11.1877i	−0.120490	+	0.449673i	0.879149	+	0.476547i	$0.158112\pi$
$620$	−6.15239	−	24.6457i	−0.247086	−	0.989797i
$621$	9.45565	−	0.0341372i	0.379442	−	0.00136988i
$622$	−19.5906	+	11.0875i	−0.785511	+	0.444570i
$623$	−0.263191	−	0.455861i	−0.0105445	−	0.0182637i
$624$	−18.2445	+	7.78261i	−0.730363	+	0.311554i
$625$	2.02612	−	3.50934i	0.0810447	−	0.140374i
$626$	−0.138796	+	16.1704i	−0.00554742	+	0.646299i
$627$	30.1139	+	10.9196i	1.20264	+	0.436085i
$628$	8.11292	+	8.39635i	0.323741	+	0.335051i
$629$	−6.58363	−	6.58363i	−0.262506	−	0.262506i
$630$	0.120352	+	1.48092i	0.00479495	+	0.0590015i
$631$	1.63509			0.0650918			0.0325459	−	0.999470i	$-0.489638\pi$
$631$	1.63509			0.0650918			0.0325459	+	0.999470i	$0.489638\pi$
$632$	−24.9934	+	13.5842i	−0.994182	+	0.540351i
$633$	16.7470	−	23.9785i	0.665632	−	0.953060i
$634$	27.5316	−	27.0630i	1.09342	−	1.07481i
$635$	−1.17588	−	4.38844i	−0.0466633	−	0.174150i
$636$	38.3918	−	17.1617i	1.52233	−	0.680507i
$637$	5.12858	−	19.1401i	0.203202	−	0.758359i
$638$	15.5332	−	8.79120i	0.614965	−	0.348047i
$639$	31.5689	+	5.48814i	1.24885	+	0.217107i
$640$	4.46806	−	13.3983i	0.176616	−	0.529616i
$641$	−33.5608	+	19.3763i	−1.32557	+	0.765319i	−0.984611	−	0.174759i	$-0.944085\pi$
$641$	−33.5608	+	19.3763i	−1.32557	+	0.765319i	−0.340960	+	0.940078i	$0.610752\pi$
$642$	11.9939	−	16.8628i	0.473360	−	0.665521i
$643$	5.22528	+	19.5010i	0.206065	+	0.769044i	0.989122	+	0.147095i	$0.0469924\pi$
$643$	5.22528	+	19.5010i	0.206065	+	0.769044i	−0.783058	+	0.621949i	$0.786341\pi$
$644$	−0.892842	+	0.495245i	−0.0351829	+	0.0195154i
$645$	−11.8115	+	9.93523i	−0.465076	+	0.391199i
$646$	29.5957	−	7.65850i	1.16443	−	0.301320i
$647$		−	28.2882i		−	1.11212i	−0.831141	−	0.556062i	$-0.812312\pi$
$647$		−	28.2882i		−	1.11212i	0.831141	−	0.556062i	$-0.187688\pi$
$648$	23.7332	+	9.20527i	0.932327	+	0.361617i
$649$		−	17.7456i		−	0.696575i
$650$	3.49080	+	13.4899i	0.136920	+	0.529119i
$651$	−3.78315	+	3.18220i	−0.148273	+	0.124720i
$652$	34.1421	+	9.77950i	1.33711	+	0.382995i
$653$	0.228971	+	0.854532i	0.00896033	+	0.0334404i	0.970261	−	0.242060i	$-0.0778231\pi$
$653$	0.228971	+	0.854532i	0.00896033	+	0.0334404i	−0.961301	+	0.275500i	$0.911156\pi$
$654$	−9.62360	−	6.84491i	−0.376312	−	0.267657i
$655$	−16.7766	+	9.68599i	−0.655517	+	0.378463i
$656$	10.0319	+	18.8412i	0.391681	+	0.735625i
$657$	27.5001	+	4.78079i	1.07288	+	0.186517i
$658$	−2.14359	−	3.78752i	−0.0835659	−	0.147653i
$659$	13.0375	−	48.6567i	0.507869	−	1.89539i	0.0671656	−	0.997742i	$-0.478604\pi$
$659$	13.0375	−	48.6567i	0.507869	−	1.89539i	0.440704	−	0.897653i	$-0.354729\pi$
$660$	−4.91356	+	12.8575i	−0.191260	+	0.500478i
$661$	−7.17239	−	26.7677i	−0.278974	−	1.04114i	−0.953131	−	0.302557i	$-0.902160\pi$
$661$	−7.17239	−	26.7677i	−0.278974	−	1.04114i	0.674158	−	0.738587i	$-0.264507\pi$
$662$	−11.3952	−	11.5925i	−0.442886	−	0.450555i
$663$	10.5632	−	15.1246i	0.410242	−	0.587390i
$664$	−1.82451	+	6.16920i	−0.0708048	+	0.239411i
$665$	−2.03486			−0.0789086
$666$	10.5830	−	0.860060i	0.410082	−	0.0333267i
$667$	5.10222	+	5.10222i	0.197559	+	0.197559i
$668$	0.479010	−	27.9013i	0.0185334	−	1.07953i
$669$	−23.2367	−	8.42580i	−0.898381	−	0.325760i
$670$	−6.86548	−	0.0589290i	−0.265237	−	0.00227663i
$671$	−10.2672	+	17.7834i	−0.396363	+	0.686520i
$672$	−2.72443	+	0.364003i	−0.105097	+	0.0140417i
$673$	−16.5237	−	28.6198i	−0.636941	−	1.10321i	−0.986100	−	0.166150i	$-0.946866\pi$
$673$	−16.5237	−	28.6198i	−0.636941	−	1.10321i	0.349160	−	0.937063i	$-0.386467\pi$
$674$	−6.09071	−	10.7617i	−0.234605	−	0.414525i
$675$	8.88549	−	15.5192i	0.342003	−	0.597336i
$676$	8.23631	+	4.94566i	0.316781	+	0.190218i
$677$	2.69118	−	10.0436i	0.103430	−	0.386007i	−0.894732	−	0.446603i	$-0.852633\pi$
$677$	2.69118	−	10.0436i	0.103430	−	0.386007i	0.998162	+	0.0605961i	$0.0193002\pi$
$678$	5.07147	+	1.88836i	0.194768	+	0.0725221i
$679$	−2.57829	+	4.46572i	−0.0989455	+	0.171379i
$680$	3.07207	+	12.7719i	0.117809	+	0.489779i
$681$	−13.8150	+	6.46231i	−0.529393	+	0.247636i
$682$	−44.3362	+	11.4729i	−1.69772	+	0.439320i
$683$	−9.18142	+	9.18142i	−0.351317	+	0.351317i	−0.860600	−	0.509282i	$-0.829911\pi$
$683$	−9.18142	+	9.18142i	−0.351317	+	0.351317i	0.509282	+	0.860600i	$0.329911\pi$
$684$	−15.1983	+	31.3754i	−0.581122	+	1.19967i
$685$	18.3723	+	18.3723i	0.701968	+	0.701968i
$686$	2.80247	−	4.75920i	0.106999	−	0.181707i
$687$	24.7225	−	35.3980i	0.943223	−	1.35052i
$688$	−19.4847	−	20.8708i	−0.742848	−	0.795691i
$689$	30.0988	+	17.3776i	1.14667	+	0.662033i
$690$	−5.53967	−	0.525880i	−0.210891	−	0.0200199i
$691$	24.3744	+	6.53111i	0.927247	+	0.248455i	0.690680	−	0.723160i	$-0.257311\pi$
$691$	24.3744	+	6.53111i	0.927247	+	0.248455i	0.236567	+	0.971615i	$0.423978\pi$
$692$	1.19852	+	4.80114i	0.0455610	+	0.182512i
$693$	2.66795	−	0.239887i	0.101347	−	0.00911256i
$694$	4.38356	+	1.21499i	0.166398	+	0.0461204i
$695$	0.897694	−	0.518284i	0.0340515	−	0.0196596i
$696$	7.77491	+	17.8015i	0.294707	+	0.674763i
$697$	−17.1932	−	9.92649i	−0.651239	−	0.375993i
$698$	−32.8535	−	33.4224i	−1.24352	−	1.26506i
$699$	−7.26153	−	8.63283i	−0.274656	−	0.326524i
$700$	−0.0331455	+	1.93066i	−0.00125278	+	0.0729719i
$701$	32.8695	−	32.8695i	1.24146	−	1.24146i	0.282069	−	0.959394i	$-0.408979\pi$
$701$	32.8695	−	32.8695i	1.24146	−	1.24146i	0.959394	−	0.282069i	$-0.0910207\pi$
$702$	5.34398	+	20.3482i	0.201695	+	0.767994i
$703$			14.5415i			0.548443i
$704$	−24.2237	−	7.84770i	−0.912965	−	0.295771i
$705$	2.03883	−	23.6314i	0.0767867	−	0.890011i
$706$	−0.100760	+	11.7389i	−0.00379213	+	0.441800i
$707$	−4.38221	+	1.17421i	−0.164810	+	0.0441607i
$708$	19.2106	+	1.99017i	0.721977	+	0.0747951i
$709$	41.1714	+	11.0318i	1.54622	+	0.414310i	0.928271	−	0.371905i	$-0.121295\pi$
$709$	41.1714	+	11.0318i	1.54622	+	0.414310i	0.617953	+	0.786215i	$0.287962\pi$
$710$	−18.1715	−	5.03659i	−0.681964	−	0.189020i
$711$	10.3876	+	28.3275i	0.389567	+	1.06236i
$712$	5.30542	+	0.136642i	0.198829	+	0.00512088i
$713$	−9.25715	−	16.0339i	−0.346683	−	0.600473i
$714$	1.97043	−	1.62876i	0.0737414	−	0.0609548i
$715$	−10.9881	+	2.94426i	−0.410932	+	0.110109i
$716$	7.42912	−	25.9365i	0.277639	−	0.969293i
$717$	−8.08031	+	1.43481i	−0.301765	+	0.0535838i
$718$	20.9136	+	12.3150i	0.780490	+	0.459593i
$719$	−8.84226			−0.329761			−0.164880	−	0.986314i	$-0.552724\pi$
$719$	−8.84226			−0.329761			−0.164880	+	0.986314i	$0.552724\pi$
$720$	−13.3679	−	6.76117i	−0.498192	−	0.251974i
$721$	0.0343022			0.00127748
$722$	−17.9884	−	10.5925i	−0.669459	−	0.394212i
$723$	−8.78340	+	24.2229i	−0.326658	+	0.900858i
$724$	18.5951	+	5.32629i	0.691082	+	0.197950i
$725$	13.1814	−	3.53195i	0.489545	−	0.131173i
$726$	−1.99519	−	0.742909i	−0.0740484	−	0.0275719i
$727$	11.4146	+	19.7707i	0.423344	+	0.733254i	0.996264	−	0.0863576i	$-0.0275228\pi$
$727$	11.4146	+	19.7707i	0.423344	+	0.733254i	−0.572920	+	0.819611i	$0.694189\pi$
$728$	−1.56441	−	1.64712i	−0.0579807	−	0.0610463i
$729$	13.3308	−	23.4796i	0.493734	−	0.869613i
$730$	−15.8294	−	4.38744i	−0.585873	−	0.162387i
$731$	25.6512	+	6.87321i	0.948743	+	0.254215i
$732$	−18.1000	−	13.1093i	−0.668996	−	0.484532i
$733$	−28.8645	+	7.73423i	−1.06614	+	0.285670i	−0.748905	−	0.662678i	$-0.769420\pi$
$733$	−28.8645	+	7.73423i	−1.06614	+	0.285670i	−0.317232	+	0.948348i	$0.602753\pi$
$734$	−0.0179373	+	2.08978i	−0.000662079	+	0.0771351i
$735$	13.5558	−	6.34103i	0.500012	−	0.233892i
$736$	0.441643	−	10.2846i	0.0162792	−	0.379095i
$737$			12.3780i			0.455950i
$738$	21.3224	−	7.61190i	0.784887	−	0.280198i
$739$	6.92568	−	6.92568i	0.254765	−	0.254765i	−0.568156	−	0.822921i	$-0.692343\pi$
$739$	6.92568	−	6.92568i	0.254765	−	0.254765i	0.822921	+	0.568156i	$0.192343\pi$
$740$	−6.24756	−	0.107258i	−0.229665	−	0.00394289i
$741$	−28.3688	+	5.03740i	−1.04215	+	0.185053i
$742$	3.37620	+	3.43467i	0.123944	+	0.126091i
$743$	27.7583	+	16.0262i	1.01835	+	0.587946i	0.913626	−	0.406555i	$-0.133270\pi$
$743$	27.7583	+	16.0262i	1.01835	+	0.587946i	0.104726	+	0.994501i	$0.466603\pi$
$744$	−7.44774	−	49.2830i	−0.273047	−	1.80680i
$745$	5.74942	−	3.31943i	0.210642	−	0.121614i
$746$	44.6548	+	12.3770i	1.63493	+	0.453153i
$747$	6.19119	+	2.86888i	0.226524	+	0.104967i
$748$	22.9776	−	5.73597i	0.840145	−	0.209728i
$749$	2.28916	+	0.613380i	0.0836442	+	0.0224124i
$750$	−14.9615	+	21.0351i	−0.546317	+	0.768095i
$751$	−7.35037	−	4.24374i	−0.268219	−	0.154856i	0.359859	−	0.933007i	$-0.382825\pi$
$751$	−7.35037	−	4.24374i	−0.268219	−	0.154856i	−0.628078	+	0.778151i	$0.716158\pi$
$752$	43.8530	+	1.50618i	1.59916	+	0.0549248i
$753$	16.8269	+	1.45176i	0.613207	+	0.0529051i
$754$	−8.14615	+	13.8340i	−0.296665	+	0.503803i
$755$	−2.70975	−	2.70975i	−0.0986179	−	0.0986179i
$756$	−0.0395199	+	2.91511i	−0.00143732	+	0.106021i
$757$	−15.2511	+	15.2511i	−0.554309	+	0.554309i	−0.927682	−	0.373372i	$-0.878201\pi$
$757$	−15.2511	+	15.2511i	−0.554309	+	0.554309i	0.373372	+	0.927682i	$0.378201\pi$
$758$	37.2816	−	9.64738i	1.35413	−	0.350409i
$759$	−0.862335	+	9.99505i	−0.0313008	+	0.362797i
$760$	10.7122	−	17.4976i	0.388571	−	0.634704i
$761$	1.63439	−	2.83084i	0.0592465	−	0.102618i	−0.834881	−	0.550431i	$-0.814464\pi$
$761$	1.63439	−	2.83084i	0.0592465	−	0.102618i	0.894127	+	0.447813i	$0.147797\pi$
$762$	−1.48316	−	8.79028i	−0.0537293	−	0.318438i
$763$	0.350056	−	1.30643i	0.0126729	−	0.0472959i
$764$	−14.5919	+	24.3007i	−0.527915	+	0.879170i
$765$	13.8770	−	1.24774i	0.501725	−	0.0451123i
$766$	5.56747	+	9.83718i	0.201161	+	0.355432i
$767$	7.98088	+	13.8233i	0.288173	+	0.499130i
$768$	11.2123	−	25.3433i	0.404588	−	0.914499i
$769$	19.1814	−	33.2232i	0.691701	−	1.19806i	−0.279580	−	0.960123i	$-0.590195\pi$
$769$	19.1814	−	33.2232i	0.691701	−	1.19806i	0.971280	−	0.237938i	$-0.0764716\pi$
$770$	−1.57633	−	0.0135302i	−0.0568071	−	0.000487596i
$771$	0.760304	+	4.28176i	0.0273817	+	0.154204i
$772$	25.8769	+	0.444254i	0.931328	+	0.0159891i
$773$	20.0548	+	20.0548i	0.721320	+	0.721320i	0.968874	−	0.247554i	$-0.0796267\pi$
$773$	20.0548	+	20.0548i	0.721320	+	0.721320i	−0.247554	+	0.968874i	$0.579627\pi$
$774$	−24.9144	+	17.2169i	−0.895530	+	0.618849i
$775$	−35.0148			−1.25777
$776$	−24.8274	−	45.6794i	−0.891251	−	1.63980i
$777$	0.515242	+	1.10148i	0.0184842	+	0.0395153i
$778$	8.47329	+	8.62001i	0.303782	+	0.309042i
$779$	8.02512	+	29.9501i	0.287530	+	1.07308i
$780$	−1.95500	−	12.2254i	−0.0700002	−	0.437741i
$781$	−8.79878	+	32.8375i	−0.314845	+	1.17502i
$782$	4.71580	+	8.33236i	0.168637	+	0.297965i
$783$	19.8822	−	5.40442i	0.710532	−	0.193138i
$784$	13.0114	+	24.4371i	0.464694	+	0.872754i
$785$	−6.31134	+	3.64385i	−0.225261	+	0.130055i
$786$	−34.5670	+	15.8093i	−1.23296	+	0.563901i
$787$	2.45116	+	9.14785i	0.0873744	+	0.326086i	0.995753	−	0.0920625i	$-0.0293460\pi$
$787$	2.45116	+	9.14785i	0.0873744	+	0.326086i	−0.908379	+	0.418148i	$0.862679\pi$
$788$	−6.24859	+	21.8150i	−0.222597	+	0.777128i
$789$	−5.91736	−	2.14568i	−0.210664	−	0.0763883i
$790$	−4.44818	−	17.1896i	−0.158259	−	0.611580i
$791$			0.619775i			0.0220367i
$792$	−11.9822	+	24.2043i	−0.425768	+	0.860062i
$793$		−	18.4703i		−	0.655900i
$794$	42.5871	−	11.0203i	1.51136	−	0.391095i
$795$	4.58917	+	25.8446i	0.162761	+	0.916613i
$796$	−10.5936	−	19.0985i	−0.375482	−	0.676929i
$797$	7.19855	+	26.8654i	0.254986	+	0.951620i	0.968098	+	0.250571i	$0.0806182\pi$
$797$	7.19855	+	26.8654i	0.254986	+	0.951620i	−0.713112	+	0.701050i	$0.752715\pi$
$798$	−3.97483	−	0.377330i	−0.140707	−	0.0133573i
$799$	−35.3432	+	20.4054i	−1.25035	+	0.721891i
$800$	−16.4270	−	10.4486i	−0.580783	−	0.369414i
$801$	0.964141	−	5.54594i	0.0340662	−	0.195956i
$802$	−21.9165	+	12.4039i	−0.773899	+	0.437998i
$803$	−7.66474	+	28.6052i	−0.270483	+	1.00946i
$804$	−13.3999	−	1.38820i	−0.472577	−	0.0489579i
$805$	−0.164943	−	0.615577i	−0.00581349	−	0.0216962i
$806$	29.3768	−	28.8767i	1.03475	−	1.01714i
$807$	−30.1716	−	2.60309i	−1.06209	−	0.0916332i
$808$	12.9725	−	43.8636i	0.456370	−	1.54312i
$809$	48.8492			1.71745			0.858724	−	0.512439i	$-0.171258\pi$
$809$	48.8492			1.71745			0.858724	+	0.512439i	$0.171258\pi$
$810$	−9.16266	+	12.9812i	−0.321943	+	0.456113i
$811$	−5.86383	−	5.86383i	−0.205907	−	0.205907i	0.596618	−	0.802525i	$-0.296511\pi$
$811$	−5.86383	−	5.86383i	−0.205907	−	0.205907i	−0.802525	+	0.596618i	$0.796511\pi$
$812$	−1.59988	+	1.54587i	−0.0561448	+	0.0542496i
$813$	36.1404	−	30.3996i	1.26750	−	1.06616i
$814$	−0.0966897	+	11.2648i	−0.00338897	+	0.394830i
$815$	−11.0840	+	19.1981i	−0.388256	+	0.672480i
$816$	3.63256	+	25.5178i	0.127165	+	0.893303i
$817$	−20.7378	−	35.9189i	−0.725524	−	1.25664i
$818$	29.8588	−	16.8990i	1.04399	−	0.590858i
$819$	−1.97037	+	1.38675i	−0.0688502	+	0.0484568i
$820$	−12.9269	+	3.22697i	−0.451426	+	0.112691i
$821$	−0.828375	+	3.09154i	−0.0289105	+	0.107895i	−0.978873	−	0.204467i	$-0.934454\pi$
$821$	−0.828375	+	3.09154i	−0.0289105	+	0.107895i	0.949963	+	0.312363i	$0.101120\pi$
$822$	32.4809	+	39.2946i	1.13290	+	1.37056i
$823$	−20.9908	+	36.3572i	−0.731695	+	1.26733i	0.224464	+	0.974482i	$0.427937\pi$
$823$	−20.9908	+	36.3572i	−0.731695	+	1.26733i	−0.956158	+	0.292850i	$0.905396\pi$
$824$	−0.180578	+	0.294961i	−0.00629073	+	0.0102755i
$825$	15.5550	+	10.8638i	0.541555	+	0.378231i
$826$	0.554122	+	2.14136i	0.0192804	+	0.0745076i
$827$	−12.7209	+	12.7209i	−0.442348	+	0.442348i	−0.892800	−	0.450453i	$-0.851263\pi$
$827$	−12.7209	+	12.7209i	−0.442348	+	0.442348i	0.450453	+	0.892800i	$0.351263\pi$
$828$	−10.7235	−	2.05447i	−0.372667	−	0.0713978i
$829$	−10.4132	−	10.4132i	−0.361665	−	0.361665i	0.502761	−	0.864425i	$-0.332318\pi$
$829$	−10.4132	−	10.4132i	−0.361665	−	0.361665i	−0.864425	+	0.502761i	$0.832318\pi$
$830$	−3.46025	−	2.03757i	−0.120107	−	0.0707252i
$831$	−12.6914	−	27.1315i	−0.440260	−	0.941181i
$832$	22.3989	−	4.78120i	0.776544	−	0.165758i
$833$	−22.2996	−	12.8747i	−0.772637	−	0.446082i
$834$	1.84963	−	0.845936i	0.0640475	−	0.0292924i
$835$	16.8246	+	4.50815i	0.582241	+	0.156011i
$836$	−31.7104	−	19.0411i	−1.09673	−	0.658552i
$837$	−52.8657	+	0.190858i	−1.82731	+	0.00659702i
$838$	4.31702	−	15.5754i	0.149129	−	0.538042i
$839$	−25.7863	+	14.8877i	−0.890241	+	0.513981i	−0.874021	−	0.485888i	$-0.838496\pi$
$839$	−25.7863	+	14.8877i	−0.890241	+	0.513981i	−0.0162196	+	0.999868i	$0.505163\pi$
$840$	0.191433	−	1.70495i	0.00660507	−	0.0588263i
$841$	−11.4986	−	6.63872i	−0.396503	−	0.228921i
$842$	17.4477	−	17.1507i	0.601287	−	0.591053i
$843$	8.32164	−	22.9494i	0.286613	−	0.790420i
$844$	−24.2871	+	23.4672i	−0.835996	+	0.807775i
$845$	−4.24025	+	4.24025i	−0.145869	+	0.145869i
$846$	8.36462	−	45.7827i	0.287581	−	1.57404i
$847$		−	0.243829i		−	0.00837805i
$848$	−47.3078	+	10.9505i	−1.62456	+	0.376040i
$849$	0.924350	+	0.645580i	0.0317236	+	0.0221563i
$850$	18.1065	+	0.155415i	0.621048	+	0.00533069i
$851$	−4.39903	+	1.17872i	−0.150797	+	0.0404059i
$852$	−34.5616	−	13.2079i	−1.18406	−	0.452495i
$853$	−28.4092	−	7.61221i	−0.972711	−	0.260637i	−0.262739	−	0.964867i	$-0.584626\pi$
$853$	−28.4092	−	7.61221i	−0.972711	−	0.260637i	−0.709972	+	0.704230i	$0.751292\pi$
$854$	0.683648	−	2.46653i	0.0233940	−	0.0844029i
$855$	−16.7033	−	13.9474i	−0.571241	−	0.476990i
$856$	−17.3253	+	16.4553i	−0.592166	+	0.562429i
$857$	14.3783	+	24.9039i	0.491152	+	0.850700i	0.999948	−	0.0101867i	$-0.00324259\pi$
$857$	14.3783	+	24.9039i	0.491152	+	0.850700i	−0.508796	+	0.860887i	$0.669909\pi$
$858$	−22.0098	+	3.71365i	−0.751401	+	0.126782i
$859$	9.26004	−	2.48122i	0.315949	−	0.0846582i	−0.0973599	−	0.995249i	$-0.531040\pi$
$859$	9.26004	−	2.48122i	0.315949	−	0.0846582i	0.413308	+	0.910591i	$0.364373\pi$
$860$	15.5850	−	8.64478i	0.531446	−	0.294784i
$861$	1.66909	+	1.98429i	0.0568823	+	0.0676243i
$862$	24.2418	−	41.1679i	0.825678	−	1.40218i
$863$	38.6895			1.31700			0.658502	−	0.752579i	$-0.271190\pi$
$863$	38.6895			1.31700			0.658502	+	0.752579i	$0.271190\pi$
$864$	−24.8587	−	15.6859i	−0.845709	−	0.533645i
$865$	−3.08877			−0.105021
$866$	−23.4966	+	39.9024i	−0.798446	+	1.35594i
$867$	3.52238	+	4.18757i	0.119626	+	0.142217i
$868$	4.99181	−	2.76888i	0.169433	−	0.0939818i
$869$	−30.9207	+	8.28517i	−1.04891	+	0.281055i
$870$	−11.9560	+	2.01731i	−0.405346	+	0.0683931i
$871$	−5.56687	−	9.64210i	−0.188626	−	0.326710i
$872$	9.39103	+	9.88755i	0.318020	+	0.334835i
$873$	−51.7731	+	18.9851i	−1.75225	+	0.642548i
$874$	3.99402	−	14.4100i	0.135100	−	0.487425i
$875$	−2.85557	−	0.765148i	−0.0965360	−	0.0258667i
$876$	−30.1071	−	11.5056i	−1.01722	−	0.388737i
$877$	33.8645	−	9.07397i	1.14352	−	0.306406i	0.363157	−	0.931728i	$-0.381699\pi$
$877$	33.8645	−	9.07397i	1.14352	−	0.306406i	0.780367	+	0.625322i	$0.215032\pi$
$878$	−41.6493	−	0.357492i	−1.40560	−	0.0120648i
$879$	−11.8956	−	8.30807i	−0.401228	−	0.280224i
$880$	8.41467	−	13.4835i	0.283658	−	0.454529i
$881$			15.5358i			0.523415i	0.965147	+	0.261708i	$0.0842856\pi$
$881$			15.5358i			0.523415i	−0.965147	+	0.261708i	$0.915714\pi$
$882$	27.6552	−	9.87267i	0.931199	−	0.332430i
$883$	−35.3696	+	35.3696i	−1.19028	+	1.19028i	−0.213292	+	0.976988i	$0.568419\pi$
$883$	−35.3696	+	35.3696i	−1.19028	+	1.19028i	−0.976988	+	0.213292i	$0.931581\pi$
$884$	−15.3192	+	14.8021i	−0.515240	+	0.497848i
$885$	−4.10946	+	11.3331i	−0.138138	+	0.380957i
$886$	−9.19270	+	9.03623i	−0.308835	+	0.303578i
$887$	−22.5037	−	12.9925i	−0.755599	−	0.436246i	0.0721141	−	0.997396i	$-0.477025\pi$
$887$	−22.5037	−	12.9925i	−0.755599	−	0.436246i	−0.827714	+	0.561151i	$0.810359\pi$
$888$	−12.1839	−	1.36802i	−0.408865	−	0.0459077i
$889$	0.884169	−	0.510475i	0.0296541	−	0.0171208i
$890$	−0.884814	+	3.19231i	−0.0296590	+	0.107007i
$891$	23.5443	+	16.3176i	0.788764	+	0.546659i
$892$	24.4685	+	14.6926i	0.819267	+	0.491945i
$893$	61.5670	+	16.4968i	2.06026	+	0.552045i
$894$	11.8462	−	5.41793i	0.396198	−	0.181203i
$895$	14.5841	+	8.42011i	0.487492	+	0.281453i
$896$	3.16813	+	0.190577i	0.105840	+	0.00636674i
$897$	−3.82343	−	8.17367i	−0.127661	−	0.272911i
$898$	3.40217	+	2.00337i	0.113532	+	0.0668534i
$899$	−28.5261	−	28.5261i	−0.951398	−	0.951398i
$900$	−13.5052	+	15.6207i	−0.450173	+	0.520691i
$901$	31.9353	−	31.9353i	1.06392	−	1.06392i
$902$	6.01762	+	23.2546i	0.200365	+	0.774295i
$903$	−2.84352	−	1.98596i	−0.0946266	−	0.0660887i
$904$	−5.32939	−	3.26270i	−0.177253	−	0.108516i
$905$	−6.03678	+	10.4560i	−0.200669	+	0.347569i
$906$	−4.79066	−	5.79561i	−0.159159	−	0.192546i
$907$	7.10188	−	26.5046i	0.235814	−	0.880070i	−0.741966	−	0.670437i	$-0.766106\pi$
$907$	7.10188	−	26.5046i	0.235814	−	0.880070i	0.977780	−	0.209633i	$-0.0672268\pi$
$908$	17.0869	−	4.26545i	0.567048	−	0.141554i
$909$	−44.0200	−	20.3980i	−1.46005	−	0.676560i
$910$	1.23400	−	0.698398i	0.0409067	−	0.0231517i
$911$	23.4177	+	40.5606i	0.775863	+	1.34383i	0.934308	+	0.356466i	$0.116018\pi$
$911$	23.4177	+	40.5606i	0.775863	+	1.34383i	−0.158445	+	0.987368i	$0.550648\pi$
$912$	24.1694	−	32.1928i	0.800329	−	1.06601i
$913$	−3.61980	+	6.26967i	−0.119798	+	0.207496i
$914$	0.0267637	−	3.11809i	0.000885264	−	0.103137i
$915$	10.6753	−	8.97957i	0.352915	−	0.296855i
$916$	−35.8535	+	34.6432i	−1.18463	+	1.14464i
$917$	−3.07820	−	3.07820i	−0.101651	−	0.101651i
$918$	27.3383	+	0.135952i	0.902297	+	0.00448710i
$919$	−0.421071			−0.0138899			−0.00694493	−	0.999976i	$-0.502211\pi$
$919$	−0.421071			−0.0138899			−0.00694493	+	0.999976i	$0.502211\pi$
$920$	6.16160	+	1.82226i	0.203142	+	0.0600783i
$921$	24.7093	+	2.13183i	0.814200	+	0.0702461i
$922$	−20.0314	+	19.6905i	−0.659700	+	0.648472i
$923$	−7.91430	−	29.5366i	−0.260503	−	0.972209i
$924$	−3.07665	−	0.318733i	−0.101214	−	0.0104856i
$925$	−2.22922	+	8.31957i	−0.0732964	+	0.273546i
$926$	−1.98036	+	1.12081i	−0.0650788	+	0.0368321i
$927$	0.281572	+	0.235115i	0.00924805	+	0.00772218i
$928$	−4.87053	−	21.8952i	−0.159883	−	0.718745i
$929$	−5.41100	+	3.12404i	−0.177529	+	0.102496i	−0.586131	−	0.810216i	$-0.699350\pi$
$929$	−5.41100	+	3.12404i	−0.177529	+	0.102496i	0.408602	+	0.912713i	$0.366016\pi$
$930$	30.9718	+	2.94015i	1.01561	+	0.0964113i
$931$	10.4086	+	38.8455i	0.341128	+	1.27311i
$932$	6.31835	+	11.3909i	0.206965	+	0.373121i
$933$	−4.82010	−	27.1451i	−0.157803	−	0.888689i
$934$	−19.2535	+	4.98223i	−0.629993	+	0.163024i
$935$			14.7824i			0.483437i
$936$	−1.55184	−	24.2433i	−0.0507234	−	0.792416i
$937$		−	41.2133i		−	1.34638i	−0.739470	−	0.673189i	$-0.764924\pi$
$937$		−	41.2133i		−	1.34638i	0.739470	−	0.673189i	$-0.235076\pi$
$938$	−0.386515	−	1.49366i	−0.0126202	−	0.0487697i
$939$	−18.6191	−	6.75142i	−0.607610	−	0.220324i
$940$	−7.54176	+	26.3298i	−0.245985	+	0.858782i
$941$	3.22526	+	12.0368i	0.105141	+	0.392390i	0.998361	−	0.0572290i	$-0.0182265\pi$
$941$	3.22526	+	12.0368i	0.105141	+	0.392390i	−0.893221	+	0.449619i	$0.851560\pi$
$942$	−13.0040	+	5.94745i	−0.423695	+	0.193778i
$943$	−8.40987	+	4.85544i	−0.273863	+	0.158115i
$944$	−21.3305	−	6.50799i	−0.694247	−	0.211817i
$945$	−1.75942	−	0.464633i	−0.0572339	−	0.0151145i
$946$	−15.8260	−	27.9630i	−0.514547	−	0.909154i
$947$	3.96886	−	14.8120i	0.128971	−	0.481325i	−0.870979	−	0.491320i	$-0.836515\pi$
$947$	3.96886	−	14.8120i	0.128971	−	0.481325i	0.999950	+	0.00999447i	$0.00318139\pi$
$948$	−5.50139	−	34.4025i	−0.178677	−	1.11734i
$949$	−6.89426	−	25.7297i	−0.223797	−	0.835222i
$950$	−19.8246	−	20.1679i	−0.643196	−	0.654333i
$951$	20.0338	+	42.8281i	0.649642	+	1.38879i
$952$	−2.59360	+	1.40966i	−0.0840592	+	0.0456873i
$953$	20.0192			0.648486			0.324243	−	0.945974i	$-0.394890\pi$
$953$	20.0192			0.648486			0.324243	+	0.945974i	$0.394890\pi$
$954$	4.17190	+	51.3349i	0.135070	+	1.66203i
$955$	−12.5106	−	12.5106i	−0.404833	−	0.404833i
$956$	9.47490	+	0.162665i	0.306440	+	0.00526097i
$957$	3.82181	+	21.5231i	0.123541	+	0.695742i
$958$	40.6903	+	0.349260i	1.31464	+	0.0112841i
$959$	−2.91935	+	5.05646i	−0.0942707	+	0.163282i
$960$	13.6529	+	10.6215i	0.440646	+	0.342808i
$961$	36.2559	+	62.7971i	1.16955	+	2.02571i
$962$	−4.99088	−	8.81841i	−0.160913	−	0.284317i
$963$	14.5865	+	20.7254i	0.470045	+	0.667866i
$964$	15.3162	−	25.5070i	0.493302	−	0.821526i
$965$	−4.18105	+	15.6039i	−0.134593	+	0.502307i
$966$	−0.208047	−	1.23303i	−0.00669379	−	0.0396722i
$967$	−16.3485	+	28.3164i	−0.525732	+	0.910594i	0.473819	+	0.880622i	$0.342875\pi$
$967$	−16.3485	+	28.3164i	−0.525732	+	0.910594i	−0.999551	+	0.0299719i	$0.990458\pi$
$968$	2.09666	+	1.28359i	0.0673892	+	0.0412562i
$969$	−3.21832	+	37.3025i	−0.103387	+	1.19833i
$970$	31.4169	−	8.12977i	1.00874	−	0.261031i
$971$	−12.2406	+	12.2406i	−0.392820	+	0.392820i	−0.875691	−	0.482871i	$-0.839594\pi$
$971$	−12.2406	+	12.2406i	−0.392820	+	0.392820i	0.482871	+	0.875691i	$0.339594\pi$
$972$	−20.3052	+	23.6580i	−0.651288	+	0.758830i
$973$	0.164710	+	0.164710i	0.00528037	+	0.00528037i
$974$	30.8704	−	52.4247i	0.989151	−	1.67980i
$975$	−17.0028	−	1.46693i	−0.544524	−	0.0469795i
$976$	17.6105	+	18.8632i	0.563698	+	0.603797i
$977$	34.1771	+	19.7322i	1.09342	+	0.631288i	0.934486	−	0.356000i	$-0.115860\pi$
$977$	34.1771	+	19.7322i	1.09342	+	0.631288i	0.158938	+	0.987289i	$0.449193\pi$
$978$	−25.2111	+	35.4455i	−0.806162	+	1.13342i
$979$	5.76880	+	1.54575i	0.184372	+	0.0494022i
$980$	−16.7662	+	4.18539i	−0.535577	+	0.133698i
$981$	11.8280	−	8.32455i	0.377639	−	0.265782i
$982$	7.42246	+	2.05728i	0.236860	+	0.0656506i
$983$	3.78032	−	2.18257i	0.120574	−	0.0696132i	−0.438500	−	0.898731i	$-0.644490\pi$
$983$	3.78032	−	2.18257i	0.120574	−	0.0696132i	0.559074	+	0.829118i	$0.311157\pi$
$984$	−25.8493	+	3.90639i	−0.824045	+	0.124531i
$985$	−12.2666	−	7.08211i	−0.390845	−	0.225655i
$986$	14.6245	+	14.8777i	0.465739	+	0.473804i
$987$	5.24804	−	0.931885i	0.167047	−	0.0296622i
$988$	33.2650	+	0.571094i	1.05830	+	0.0181689i
$989$	9.18504	−	9.18504i	0.292067	−	0.292067i
$990$	−12.8467	−	10.9156i	−0.408295	−	0.346920i
$991$		−	21.1610i		−	0.672200i	−0.941826	−	0.336100i	$-0.890892\pi$
$991$		−	21.1610i		−	0.672200i	0.941826	−	0.336100i	$-0.109108\pi$
$992$	−2.46919	+	57.5003i	−0.0783968	+	1.82564i
$993$	18.0332	−	8.43546i	0.572266	−	0.267691i
$994$	0.0363700	−	4.23726i	0.00115359	−	0.134398i
$995$	13.1676	−	3.52825i	0.417441	−	0.111853i
$996$	−6.38130	−	4.62177i	−0.202199	−	0.146446i
$997$	12.7473	+	3.41563i	0.403712	+	0.108174i	0.454960	−	0.890512i	$-0.349653\pi$
$997$	12.7473	+	3.41563i	0.403712	+	0.108174i	−0.0512486	+	0.998686i	$0.516320\pi$
$998$	−24.2983	−	6.73475i	−0.769148	−	0.213185i
$999$	−3.32036	+	12.5731i	−0.105051	+	0.397796i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.u.a.131.16	yes	88
3.2	odd	2		432.2.v.a.179.7		88
4.3	odd	2		576.2.y.a.239.6		88
9.2	odd	6	inner	144.2.u.a.83.22	yes	88
9.7	even	3		432.2.v.a.35.1		88
12.11	even	2		1728.2.z.a.1583.7		88
16.5	even	4		576.2.y.a.527.17		88
16.11	odd	4	inner	144.2.u.a.59.22	yes	88
36.7	odd	6		1728.2.z.a.1007.7		88
36.11	even	6		576.2.y.a.47.17		88
48.5	odd	4		1728.2.z.a.719.7		88
48.11	even	4		432.2.v.a.395.1		88
144.11	even	12	inner	144.2.u.a.11.16	✓	88
144.43	odd	12		432.2.v.a.251.7		88
144.101	odd	12		576.2.y.a.335.6		88
144.133	even	12		1728.2.z.a.143.7		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.16	✓	88	144.11	even	12	inner
144.2.u.a.59.22	yes	88	16.11	odd	4	inner
144.2.u.a.83.22	yes	88	9.2	odd	6	inner
144.2.u.a.131.16	yes	88	1.1	even	1	trivial
432.2.v.a.35.1		88	9.7	even	3
432.2.v.a.179.7		88	3.2	odd	2
432.2.v.a.251.7		88	144.43	odd	12
432.2.v.a.395.1		88	48.11	even	4
576.2.y.a.47.17		88	36.11	even	6
576.2.y.a.239.6		88	4.3	odd	2
576.2.y.a.335.6		88	144.101	odd	12
576.2.y.a.527.17		88	16.5	even	4
1728.2.z.a.143.7		88	144.133	even	12
1728.2.z.a.719.7		88	48.5	odd	4
1728.2.z.a.1007.7		88	36.7	odd	6
1728.2.z.a.1583.7		88	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.717593 - 1.21863i) q^{2} +(1.11494 + 1.32549i) q^{3} +(-0.970121 - 1.74896i) q^{4} +(1.20583 - 0.323102i) q^{5} +(2.41535 - 0.407536i) q^{6} +(0.140266 + 0.242948i) q^{7} +(-2.82749 - 0.0728225i) q^{8} +(-0.513832 + 2.95567i) q^{9} +(0.471556 - 1.70132i) q^{10} +(-3.07444 - 0.823794i) q^{11} +(1.23660 - 3.23586i) q^{12} +(2.76539 - 0.740984i) q^{13} +(0.396717 + 0.00340517i) q^{14} +(1.77270 + 1.23808i) q^{15} +(-2.11773 + 3.39341i) q^{16} -3.72031i q^{17} +(3.23315 + 2.74714i) q^{18} +(-4.10860 + 4.10860i) q^{19} +(-1.73490 - 1.79551i) q^{20} +(-0.165636 + 0.456792i) q^{21} +(-3.21010 + 3.15546i) q^{22} +(-1.57595 - 0.909876i) q^{23} +(-3.05595 - 3.82899i) q^{24} +(-2.98049 + 1.72078i) q^{25} +(1.08144 - 3.90172i) q^{26} +(-4.49059 + 2.61431i) q^{27} +(0.288831 - 0.481009i) q^{28} +(-3.83006 - 1.02626i) q^{29} +(2.78084 - 1.27183i) q^{30} +(8.81101 + 5.08704i) q^{31} +(2.61564 + 5.01582i) q^{32} +(-2.33588 - 4.99361i) q^{33} +(-4.53369 - 2.66967i) q^{34} +(0.247635 + 0.247635i) q^{35} +(5.66783 - 1.96868i) q^{36} +(1.76964 - 1.76964i) q^{37} +(2.05856 + 7.95516i) q^{38} +(4.06540 + 2.83934i) q^{39} +(-3.43301 + 0.825757i) q^{40} +(2.66819 - 4.62144i) q^{41} +(0.437801 + 0.529640i) q^{42} +(-1.84748 + 6.89490i) q^{43} +(1.54180 + 6.17626i) q^{44} +(0.335387 + 3.73007i) q^{45} +(-2.23969 + 1.26758i) q^{46} +(-5.48486 - 9.50006i) q^{47} +(-6.85905 + 0.976412i) q^{48} +(3.46065 - 5.99402i) q^{49} +(-0.0417747 + 4.86693i) q^{50} +(4.93123 - 4.14791i) q^{51} +(-3.97872 - 4.11772i) q^{52} +(8.58403 + 8.58403i) q^{53} +(-0.0365433 + 7.34838i) q^{54} -3.97344 q^{55} +(-0.378909 - 0.697147i) q^{56} +(-10.0267 - 0.865067i) q^{57} +(-3.99906 + 3.93099i) q^{58} +(1.44299 + 5.38532i) q^{59} +(0.445622 - 4.30146i) q^{60} +(1.66977 - 6.23168i) q^{61} +(12.5219 - 7.08695i) q^{62} +(-0.790146 + 0.289745i) q^{63} +(7.98939 + 0.411810i) q^{64} +(3.09519 - 1.78701i) q^{65} +(-7.76158 - 0.736806i) q^{66} +(-1.00652 - 3.75640i) q^{67} +(-6.50668 + 3.60915i) q^{68} +(-0.551057 - 3.10336i) q^{69} +(0.479476 - 0.124074i) q^{70} -10.6808i q^{71} +(1.66809 - 8.31970i) q^{72} -9.30419i q^{73} +(-0.886658 - 3.42643i) q^{74} +(-5.60393 - 2.03203i) q^{75} +(11.1716 + 3.19994i) q^{76} +(-0.231101 - 0.862479i) q^{77} +(6.37741 - 2.91673i) q^{78} +(8.70990 - 5.02866i) q^{79} +(-1.45721 + 4.77613i) q^{80} +(-8.47195 - 3.03744i) q^{81} +(-3.71715 - 6.56784i) q^{82} +(0.588691 - 2.19703i) q^{83} +(0.959599 - 0.153452i) q^{84} +(-1.20204 - 4.48608i) q^{85} +(7.07659 + 7.19913i) q^{86} +(-2.90998 - 6.22091i) q^{87} +(8.63296 + 2.55316i) q^{88} -1.87637 q^{89} +(4.78625 + 2.26796i) q^{90} +(0.567911 + 0.567911i) q^{91} +(-0.0624738 + 3.63897i) q^{92} +(3.08091 + 17.3506i) q^{93} +(-15.5130 - 0.133153i) q^{94} +(-3.62679 + 6.28179i) q^{95} +(-3.73212 + 9.05932i) q^{96} +(9.19070 + 15.9188i) q^{97} +(-4.82116 - 8.51852i) q^{98} +(4.01461 - 8.66374i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27}+ \cdots + 46 q^{99}+O(q^{100}) \) 88 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^10 - 6 * q^11 - 16 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^18 - 8 * q^19 - 48 * q^20 + 2 * q^21 - 2 * q^22 - 12 * q^23 - 16 * q^27 + 8 * q^28 - 6 * q^29 - 34 * q^30 - 6 * q^32 - 8 * q^33 + 2 * q^34 - 26 * q^36 - 8 * q^37 - 6 * q^38 - 32 * q^39 - 2 * q^40 + 48 * q^42 - 2 * q^43 + 6 * q^45 - 40 * q^46 + 42 * q^48 - 24 * q^49 + 72 * q^50 - 12 * q^51 - 2 * q^52 - 38 * q^54 - 16 * q^55 + 36 * q^56 + 16 * q^58 - 42 * q^59 + 70 * q^60 - 2 * q^61 - 44 * q^64 - 12 * q^65 + 104 * q^66 - 2 * q^67 + 96 * q^68 - 10 * q^69 - 16 * q^70 - 10 * q^72 + 78 * q^74 - 56 * q^75 - 14 * q^76 - 6 * q^77 + 12 * q^78 - 8 * q^81 - 36 * q^82 + 54 * q^83 + 158 * q^84 + 8 * q^85 + 54 * q^86 + 48 * q^87 + 22 * q^88 + 64 * q^90 + 20 * q^91 + 108 * q^92 - 34 * q^93 + 6 * q^94 - 58 * q^96 - 4 * q^97 + 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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