LMFDB - Embedded newform 216.2.v.b.11.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 13]))

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.27
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16920 - 0.795599i) q^{2} +(-1.63375 + 0.575207i) q^{3} +(0.734044 - 1.86042i) q^{4} +(-3.21529 - 1.17027i) q^{5} +(-1.45254 + 1.97234i) q^{6} +(-2.85909 - 0.504135i) q^{7} +(-0.621910 - 2.75921i) q^{8} +(2.33827 - 1.87949i) q^{9} +(-4.69037 + 1.18981i) q^{10} +(-0.927560 - 2.54845i) q^{11} +(-0.129115 + 3.46169i) q^{12} +(1.60411 + 1.91170i) q^{13} +(-3.74393 + 1.68526i) q^{14} +(5.92612 + 0.0624707i) q^{15} +(-2.92236 - 2.73127i) q^{16} +(4.30856 - 2.48755i) q^{17} +(1.23858 - 4.05782i) q^{18} +(-1.31569 + 2.27884i) q^{19} +(-4.53736 + 5.12277i) q^{20} +(4.96102 - 0.820939i) q^{21} +(-3.11204 - 2.24167i) q^{22} +(0.157970 + 0.895893i) q^{23} +(2.60316 + 4.15013i) q^{24} +(5.13833 + 4.31157i) q^{25} +(3.39646 + 0.958928i) q^{26} +(-2.73906 + 4.41560i) q^{27} +(-3.03660 + 4.94907i) q^{28} +(-7.00248 - 5.87578i) q^{29} +(6.97851 - 4.64178i) q^{30} +(2.90502 - 0.512234i) q^{31} +(-5.58981 - 0.868362i) q^{32} +(2.98129 + 3.62999i) q^{33} +(3.05847 - 6.33633i) q^{34} +(8.60284 + 4.96685i) q^{35} +(-1.78025 - 5.72981i) q^{36} +(9.78021 - 5.64661i) q^{37} +(0.274743 + 3.71117i) q^{38} +(-3.72033 - 2.20055i) q^{39} +(-1.22939 + 9.59946i) q^{40} +(-3.04161 - 3.62485i) q^{41} +(5.14728 - 4.90683i) q^{42} +(-6.12779 + 2.23033i) q^{43} +(-5.42207 - 0.145018i) q^{44} +(-9.71774 + 3.30669i) q^{45} +(0.897470 + 0.921795i) q^{46} +(-0.225833 + 1.28076i) q^{47} +(6.34545 + 2.78124i) q^{48} +(1.34241 + 0.488598i) q^{49} +(9.43801 + 0.953026i) q^{50} +(-5.60826 + 6.54235i) q^{51} +(4.73406 - 1.58105i) q^{52} +10.3399 q^{53} +(0.310550 + 7.34190i) q^{54} +9.27950i q^{55} +(0.387086 + 8.20236i) q^{56} +(0.838700 - 4.47984i) q^{57} +(-12.8621 - 1.29878i) q^{58} +(2.96267 - 8.13988i) q^{59} +(4.46626 - 10.9793i) q^{60} +(0.720351 + 0.127017i) q^{61} +(2.98901 - 2.91014i) q^{62} +(-7.63286 + 4.19482i) q^{63} +(-7.22645 + 3.43196i) q^{64} +(-2.92046 - 8.02391i) q^{65} +(6.37373 + 1.87226i) q^{66} +(5.00144 - 4.19671i) q^{67} +(-1.46523 - 9.84173i) q^{68} +(-0.773408 - 1.37280i) q^{69} +(14.0100 - 1.03718i) q^{70} +(-5.18176 - 8.97507i) q^{71} +(-6.64009 - 5.28291i) q^{72} +(-7.34034 + 12.7138i) q^{73} +(6.94256 - 14.3831i) q^{74} +(-10.8748 - 4.08843i) q^{75} +(3.27383 + 4.12050i) q^{76} +(1.36722 + 7.75387i) q^{77} +(-6.10055 + 0.387021i) q^{78} +(5.64811 - 6.73115i) q^{79} +(6.19991 + 12.2018i) q^{80} +(1.93505 - 8.78952i) q^{81} +(-6.44017 - 1.81826i) q^{82} +(3.15228 - 3.75674i) q^{83} +(2.11431 - 9.83222i) q^{84} +(-16.7644 + 2.95601i) q^{85} +(-5.39014 + 7.48296i) q^{86} +(14.8201 + 5.57168i) q^{87} +(-6.45484 + 4.14424i) q^{88} +(-4.90094 - 2.82956i) q^{89} +(-8.73115 + 11.5976i) q^{90} +(-3.62253 - 6.27441i) q^{91} +(1.78270 + 0.363733i) q^{92} +(-4.45144 + 2.50785i) q^{93} +(0.754930 + 1.67714i) q^{94} +(6.89717 - 5.78741i) q^{95} +(9.63183 - 1.79661i) q^{96} +(-0.126739 + 0.0461291i) q^{97} +(1.95827 - 0.496754i) q^{98} +(-6.95867 - 4.21564i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	1.16920	−	0.795599i	0.826747	−	0.562574i
$2$	1.16920	−	0.795599i	0.826747	−	0.562574i
$3$	−1.63375	+	0.575207i	−0.943246	+	0.332096i
$3$	−1.63375	+	0.575207i	−0.943246	+	0.332096i
$4$	0.734044	−	1.86042i	0.367022	−	0.930212i
$5$	−3.21529	−	1.17027i	−1.43792	−	0.523361i	−0.498731	−	0.866757i	$-0.666200\pi$
$5$	−3.21529	−	1.17027i	−1.43792	−	0.523361i	−0.939191	+	0.343396i	$0.888423\pi$
$6$	−1.45254	+	1.97234i	−0.592997	+	0.805204i
$7$	−2.85909	−	0.504135i	−1.08064	−	0.190545i	−0.395139	−	0.918621i	$-0.629304\pi$
$7$	−2.85909	−	0.504135i	−1.08064	−	0.190545i	−0.685496	+	0.728076i	$0.740415\pi$
$8$	−0.621910	−	2.75921i	−0.219879	−	0.975527i
$9$	2.33827	−	1.87949i	0.779425	−	0.626496i
$10$	−4.69037	+	1.18981i	−1.48323	+	0.376250i
$11$	−0.927560	−	2.54845i	−0.279670	−	0.768386i	−0.997400	−	0.0720650i	$-0.977041\pi$
$11$	−0.927560	−	2.54845i	−0.279670	−	0.768386i	0.717730	−	0.696321i	$-0.245181\pi$
$12$	−0.129115	+	3.46169i	−0.0372722	+	0.999305i
$13$	1.60411	+	1.91170i	0.444899	+	0.530210i	0.941159	−	0.337964i	$-0.109738\pi$
$13$	1.60411	+	1.91170i	0.444899	+	0.530210i	−0.496260	+	0.868174i	$0.665294\pi$
$14$	−3.74393	+	1.68526i	−1.00061	+	0.450404i
$15$	5.92612	+	0.0624707i	1.53012	+	0.0161299i
$16$	−2.92236	−	2.73127i	−0.730590	−	0.682817i
$17$	4.30856	−	2.48755i	1.04498	−	0.603319i	0.123740	−	0.992315i	$-0.460511\pi$
$17$	4.30856	−	2.48755i	1.04498	−	0.603319i	0.921240	+	0.388995i	$0.127178\pi$
$18$	1.23858	−	4.05782i	0.291937	−	0.956438i
$19$	−1.31569	+	2.27884i	−0.301839	+	0.522801i	−0.976553	−	0.215279i	$-0.930934\pi$
$19$	−1.31569	+	2.27884i	−0.301839	+	0.522801i	0.674713	+	0.738080i	$0.264267\pi$
$20$	−4.53736	+	5.12277i	−1.01458	+	1.14549i
$21$	4.96102	−	0.820939i	1.08258	−	0.179144i
$22$	−3.11204	−	2.24167i	−0.663490	−	0.477926i
$23$	0.157970	+	0.895893i	0.0329391	+	0.186807i	0.996838	−	0.0794621i	$-0.0253203\pi$
$23$	0.157970	+	0.895893i	0.0329391	+	0.186807i	−0.963899	+	0.266269i	$0.914209\pi$
$24$	2.60316	+	4.15013i	0.531368	+	0.847141i
$25$	5.13833	+	4.31157i	1.02767	+	0.862315i
$26$	3.39646	+	0.958928i	0.666101	+	0.188061i
$27$	−2.73906	+	4.41560i	−0.527132	+	0.849783i
$28$	−3.03660	+	4.94907i	−0.573864	+	0.935286i
$29$	−7.00248	−	5.87578i	−1.30033	−	1.09111i	−0.990088	−	0.140447i	$-0.955146\pi$
$29$	−7.00248	−	5.87578i	−1.30033	−	1.09111i	−0.310241	−	0.950658i	$-0.600410\pi$
$30$	6.97851	−	4.64178i	1.27410	−	0.847469i
$31$	2.90502	−	0.512234i	0.521758	−	0.0920000i	0.0934343	−	0.995625i	$-0.470215\pi$
$31$	2.90502	−	0.512234i	0.521758	−	0.0920000i	0.428324	+	0.903625i	$0.359104\pi$
$32$	−5.58981	−	0.868362i	−0.988148	−	0.153506i
$33$	2.98129	+	3.62999i	0.518975	+	0.631900i
$34$	3.05847	−	6.33633i	0.524523	−	1.08667i
$35$	8.60284	+	4.96685i	1.45414	+	0.839551i
$36$	−1.78025	−	5.72981i	−0.296708	−	0.954968i
$37$	9.78021	−	5.64661i	1.60786	−	0.928296i	0.618008	−	0.786172i	$-0.287940\pi$
$37$	9.78021	−	5.64661i	1.60786	−	0.928296i	0.989849	−	0.142124i	$-0.0453932\pi$
$38$	0.274743	+	3.71117i	0.0445692	+	0.602031i
$39$	−3.72033	−	2.20055i	−0.595730	−	0.352369i
$40$	−1.22939	+	9.59946i	−0.194384	+	1.51781i
$41$	−3.04161	−	3.62485i	−0.475020	−	0.566106i	0.474322	−	0.880351i	$-0.342693\pi$
$41$	−3.04161	−	3.62485i	−0.475020	−	0.566106i	−0.949342	+	0.314245i	$0.898249\pi$
$42$	5.14728	−	4.90683i	0.794242	−	0.757140i
$43$	−6.12779	+	2.23033i	−0.934479	+	0.340123i	−0.763983	−	0.645236i	$-0.776759\pi$
$43$	−6.12779	+	2.23033i	−0.934479	+	0.340123i	−0.170496	+	0.985358i	$0.554537\pi$
$44$	−5.42207	−	0.145018i	−0.817407	−	0.0218624i
$45$	−9.71774	+	3.30669i	−1.44863	+	0.492932i
$46$	0.897470	+	0.921795i	0.132325	+	0.135911i
$47$	−0.225833	+	1.28076i	−0.0329411	+	0.186818i	−0.996838	−	0.0794561i	$-0.974682\pi$
$47$	−0.225833	+	1.28076i	−0.0329411	+	0.186818i	0.963897	+	0.266275i	$0.0857928\pi$
$48$	6.34545	+	2.78124i	0.915886	+	0.401438i
$49$	1.34241	+	0.488598i	0.191773	+	0.0697997i
$50$	9.43801	+	0.953026i	1.33474	+	0.134778i
$51$	−5.60826	+	6.54235i	−0.785313	+	0.916112i
$52$	4.73406	−	1.58105i	0.656496	−	0.219252i
$53$	10.3399			1.42029			0.710146	−	0.704054i	$-0.248629\pi$
$53$	10.3399			1.42029			0.710146	+	0.704054i	$0.248629\pi$
$54$	0.310550	+	7.34190i	0.0422605	+	0.999107i
$55$			9.27950i			1.25125i
$56$	0.387086	+	8.20236i	0.0517266	+	1.09609i
$57$	0.838700	−	4.47984i	0.111089	−	0.593369i
$58$	−12.8621	−	1.29878i	−1.68887	−	0.170538i
$59$	2.96267	−	8.13988i	0.385707	−	1.05972i	−0.583207	−	0.812324i	$-0.698202\pi$
$59$	2.96267	−	8.13988i	0.385707	−	1.05972i	0.968914	−	0.247398i	$-0.0795755\pi$
$60$	4.46626	−	10.9793i	0.576591	−	1.41742i
$61$	0.720351	+	0.127017i	0.0922315	+	0.0162629i	0.219573	−	0.975596i	$-0.429533\pi$
$61$	0.720351	+	0.127017i	0.0922315	+	0.0162629i	−0.127342	+	0.991859i	$0.540645\pi$
$62$	2.98901	−	2.91014i	0.379605	−	0.369588i
$63$	−7.63286	+	4.19482i	−0.961650	+	0.528498i
$64$	−7.22645	+	3.43196i	−0.903307	+	0.428995i
$65$	−2.92046	−	8.02391i	−0.362239	−	0.995243i
$66$	6.37373	+	1.87226i	0.784551	+	0.230460i
$67$	5.00144	−	4.19671i	0.611023	−	0.512709i	−0.283944	−	0.958841i	$-0.591643\pi$
$67$	5.00144	−	4.19671i	0.611023	−	0.512709i	0.894968	+	0.446131i	$0.147199\pi$
$68$	−1.46523	−	9.84173i	−0.177685	−	1.19348i
$69$	−0.773408	−	1.37280i	−0.0931073	−	0.165266i
$70$	14.0100	−	1.03718i	1.67452	−	0.123967i
$71$	−5.18176	−	8.97507i	−0.614961	−	1.06514i	−0.990391	−	0.138294i	$-0.955838\pi$
$71$	−5.18176	−	8.97507i	−0.614961	−	1.06514i	0.375430	−	0.926851i	$-0.377495\pi$
$72$	−6.64009	−	5.28291i	−0.782543	−	0.622597i
$73$	−7.34034	+	12.7138i	−0.859122	+	1.48804i	0.0136452	+	0.999907i	$0.495656\pi$
$73$	−7.34034	+	12.7138i	−0.859122	+	1.48804i	−0.872767	+	0.488136i	$0.837677\pi$
$74$	6.94256	−	14.3831i	0.807056	−	1.67200i
$75$	−10.8748	−	4.08843i	−1.25571	−	0.472091i
$76$	3.27383	+	4.12050i	0.375534	+	0.472654i
$77$	1.36722	+	7.75387i	0.155809	+	0.883635i
$78$	−6.10055	+	0.387021i	−0.690752	+	0.0438215i
$79$	5.64811	−	6.73115i	0.635462	−	0.757314i	−0.348184	−	0.937426i	$-0.613202\pi$
$79$	5.64811	−	6.73115i	0.635462	−	0.757314i	0.983646	+	0.180112i	$0.0576461\pi$
$80$	6.19991	+	12.2018i	0.693171	+	1.36420i
$81$	1.93505	−	8.78952i	0.215006	−	0.976613i
$82$	−6.44017	−	1.81826i	−0.711197	−	0.200793i
$83$	3.15228	−	3.75674i	0.346007	−	0.412356i	−0.564773	−	0.825246i	$-0.691036\pi$
$83$	3.15228	−	3.75674i	0.346007	−	0.412356i	0.910781	+	0.412891i	$0.135481\pi$
$84$	2.11431	−	9.83222i	0.230690	−	1.07278i
$85$	−16.7644	+	2.95601i	−1.81835	+	0.320625i
$86$	−5.39014	+	7.48296i	−0.581234	+	0.806909i
$87$	14.8201	+	5.57168i	1.58888	+	0.597347i
$88$	−6.45484	+	4.14424i	−0.688088	+	0.441777i
$89$	−4.90094	−	2.82956i	−0.519499	−	0.299933i	0.217231	−	0.976120i	$-0.430298\pi$
$89$	−4.90094	−	2.82956i	−0.519499	−	0.299933i	−0.736730	+	0.676187i	$0.763631\pi$
$90$	−8.73115	+	11.5976i	−0.920344	+	1.22249i
$91$	−3.62253	−	6.27441i	−0.379745	−	0.657737i
$92$	1.78270	+	0.363733i	0.185859	+	0.0379218i
$93$	−4.45144	+	2.50785i	−0.461593	+	0.260052i
$94$	0.754930	+	1.67714i	0.0778651	+	0.172983i
$95$	6.89717	−	5.78741i	0.707635	−	0.593776i
$96$	9.63183	−	1.79661i	0.983045	−	0.183366i
$97$	−0.126739	+	0.0461291i	−0.0128684	+	0.00468370i	−0.348446	−	0.937329i	$-0.613291\pi$
$97$	−0.126739	+	0.0461291i	−0.0128684	+	0.00468370i	0.335578	+	0.942012i	$0.391068\pi$
$98$	1.95827	−	0.496754i	0.197815	−	0.0501798i
$99$	−6.95867	−	4.21564i	−0.699372	−	0.423687i
$100$	11.7931	−	6.39460i	1.17931	−	0.639460i
$101$	−2.26461	+	12.8432i	−0.225337	+	1.27795i	0.636704	+	0.771109i	$0.280298\pi$
$101$	−2.26461	+	12.8432i	−0.225337	+	1.27795i	−0.862040	+	0.506840i	$0.830814\pi$
$102$	−1.35207	+	12.1112i	−0.133875	+	1.19919i
$103$	0.422665	−	1.16126i	0.0416464	−	0.114423i	−0.917126	−	0.398597i	$-0.869497\pi$
$103$	0.422665	−	1.16126i	0.0416464	−	0.114423i	0.958773	+	0.284174i	$0.0917195\pi$
$104$	4.27717	−	5.61497i	0.419411	−	0.550593i
$105$	−16.9118	−	3.16618i	−1.65043	−	0.308987i
$106$	12.0894	−	8.22641i	1.17422	−	0.799019i
$107$			15.9792i			1.54476i	0.635159	+	0.772382i	$0.280935\pi$
$107$			15.9792i			1.54476i	−0.635159	+	0.772382i	$0.719065\pi$
$108$	6.20431	+	8.33706i	0.597010	+	0.802234i
$109$			2.38211i			0.228165i	0.993471	+	0.114082i	$0.0363927\pi$
$109$			2.38211i			0.228165i	−0.993471	+	0.114082i	$0.963607\pi$
$110$	7.38276	+	10.8496i	0.703919	+	1.03446i
$111$	−12.7304	+	14.8508i	−1.20832	+	1.40957i
$112$	6.97837	+	9.28221i	0.659394	+	0.877086i
$113$	−3.24570	+	8.91748i	−0.305330	+	0.838886i	0.688221	+	0.725501i	$0.258392\pi$
$113$	−3.24570	+	8.91748i	−0.305330	+	0.838886i	−0.993551	+	0.113386i	$0.963830\pi$
$114$	−2.58355	−	5.90509i	−0.241972	−	0.553062i
$115$	0.540517	−	3.06542i	0.0504035	−	0.285852i
$116$	−16.0716	+	8.71451i	−1.49221	+	0.809122i
$117$	7.34386	+	1.45518i	0.678940	+	0.134531i
$118$	−3.01213	−	11.8742i	−0.277289	−	1.09311i
$119$	−13.5726	+	4.94004i	−1.24420	+	0.452853i
$120$	−3.51315	−	16.3903i	−0.320705	−	1.49622i
$121$	2.79226	−	2.34299i	0.253842	−	0.212999i
$122$	0.943287	−	0.424602i	0.0854012	−	0.0384417i
$123$	7.05426	+	4.17254i	0.636062	+	0.376225i
$124$	1.17944	−	5.78058i	0.105917	−	0.519112i
$125$	−2.92143	−	5.06006i	−0.261300	−	0.452586i
$126$	−5.58692	+	10.9773i	−0.497722	+	0.977933i
$127$	−3.94090	−	2.27528i	−0.349698	−	0.201898i	0.314854	−	0.949140i	$-0.398044\pi$
$127$	−3.94090	−	2.27528i	−0.349698	−	0.201898i	−0.664552	+	0.747242i	$0.731378\pi$
$128$	−5.71868	+	9.76200i	−0.505465	+	0.862847i
$129$	8.72837	−	7.16855i	0.768490	−	0.631156i
$130$	−9.79841	−	7.05801i	−0.859378	−	0.619028i
$131$	1.53208	−	0.270147i	0.133858	−	0.0236028i	−0.106318	−	0.994332i	$-0.533906\pi$
$131$	1.53208	−	0.270147i	0.133858	−	0.0236028i	0.240176	+	0.970729i	$0.422795\pi$
$132$	8.94171	−	2.88189i	0.778276	−	0.250836i
$133$	4.91051	−	5.85212i	0.425796	−	0.507443i
$134$	2.50877	−	8.88592i	0.216725	−	0.767627i
$135$	13.9743	−	10.9920i	1.20272	−	0.946041i
$136$	−9.54321	−	10.3412i	−0.818323	−	0.886749i
$137$	−0.557261	+	0.664118i	−0.0476101	+	0.0567394i	−0.789324	−	0.613977i	$-0.789569\pi$
$137$	−0.557261	+	0.664118i	−0.0476101	+	0.0567394i	0.741714	+	0.670716i	$0.234013\pi$
$138$	−1.99646	−	0.989751i	−0.169950	−	0.0842532i
$139$	−2.63752	−	14.9581i	−0.223711	−	1.26873i	−0.865133	−	0.501542i	$-0.832766\pi$
$139$	−2.63752	−	14.9581i	−0.223711	−	1.26873i	0.641422	−	0.767188i	$-0.278345\pi$
$140$	15.5553	−	12.3590i	1.31466	−	1.04453i
$141$	−0.367749	−	2.22235i	−0.0309700	−	0.187155i
$142$	−13.1991	−	6.37102i	−1.10764	−	0.534644i
$143$	3.38397	−	5.86120i	0.282981	−	0.490138i
$144$	−11.9667	−	0.893910i	−0.997222	−	0.0744925i
$145$	15.6388	+	27.0871i	1.29873	+	2.24946i
$146$	1.53282	+	20.7050i	0.126857	+	1.71356i
$147$	−2.47421	−	0.0260821i	−0.204069	−	0.00215121i
$148$	−3.32598	−	22.3402i	−0.273394	−	1.83635i
$149$	−6.54605	+	5.49279i	−0.536273	+	0.449987i	−0.870261	−	0.492591i	$-0.836050\pi$
$149$	−6.54605	+	5.49279i	−0.536273	+	0.449987i	0.333988	+	0.942577i	$0.391606\pi$
$150$	−15.9675	+	3.87180i	−1.30374	+	0.316131i
$151$	3.59322	+	9.87229i	0.292412	+	0.803396i	0.995712	+	0.0925028i	$0.0294867\pi$
$151$	3.59322	+	9.87229i	0.292412	+	0.803396i	−0.703300	+	0.710893i	$0.748291\pi$
$152$	7.10602	+	2.21302i	0.576375	+	0.179500i
$153$	5.39928	−	13.9145i	0.436506	−	1.12492i
$154$	7.76752	+	7.97804i	0.625924	+	0.642889i
$155$	−9.93995	−	1.75268i	−0.798396	−	0.140779i
$156$	−6.82483	+	5.30610i	−0.546424	+	0.424828i
$157$	3.29479	−	9.05237i	0.262953	−	0.722458i	−0.736012	−	0.676969i	$-0.763293\pi$
$157$	3.29479	−	9.05237i	0.262953	−	0.722458i	0.998965	−	0.0454891i	$-0.0144846\pi$
$158$	1.24845	−	12.3637i	0.0993215	−	0.983601i
$159$	−16.8928	+	5.94757i	−1.33968	+	0.471673i
$160$	16.9566	+	9.33362i	1.34054	+	0.737887i
$161$		−	2.64108i		−	0.208146i
$162$	−4.73047	−	11.8162i	−0.371661	−	0.928368i
$163$	19.6202			1.53678			0.768388	−	0.639984i	$-0.221059\pi$
$163$	19.6202			1.53678			0.768388	+	0.639984i	$0.221059\pi$
$164$	−8.97643	+	2.99789i	−0.700942	+	0.234096i
$165$	−5.33763	−	15.1604i	−0.415534	−	1.18023i
$166$	0.696776	−	6.90032i	0.0540803	−	0.535568i
$167$	−10.7043	−	3.89606i	−0.828327	−	0.301486i	−0.107155	−	0.994242i	$-0.534174\pi$
$167$	−10.7043	−	3.89606i	−0.828327	−	0.301486i	−0.721172	+	0.692756i	$0.756396\pi$
$168$	−5.35045	−	13.1779i	−0.412797	−	1.01670i
$169$	1.17599	−	6.66936i	0.0904606	−	0.513028i
$170$	−17.2491	+	16.7939i	−1.32294	+	1.28803i
$171$	1.20661	+	7.80136i	0.0922717	+	0.596585i
$172$	−0.348699	+	13.0375i	−0.0265881	+	0.994096i
$173$	14.8832	−	5.41704i	1.13155	−	0.411850i	0.292694	−	0.956206i	$-0.405448\pi$
$173$	14.8832	−	5.41704i	1.13155	−	0.411850i	0.838854	+	0.544356i	$0.183226\pi$
$174$	21.7604	−	5.27647i	1.64965	−	0.400008i
$175$	−12.5174	−	14.9176i	−0.946223	−	1.12767i
$176$	−4.24983	+	9.98090i	−0.320343	+	0.752338i
$177$	−0.158152	+	15.0027i	−0.0118874	+	1.12767i
$178$	−7.98136	+	0.590872i	−0.598229	+	0.0442877i
$179$	13.6572	−	7.88498i	1.02079	−	0.589351i	0.106454	−	0.994318i	$-0.466050\pi$
$179$	13.6572	−	7.88498i	1.02079	−	0.589351i	0.914331	+	0.404967i	$0.132717\pi$
$180$	−0.981403	+	20.5064i	−0.0731495	+	1.52845i
$181$	4.39147	+	2.53542i	0.326416	+	0.188456i	0.654249	−	0.756280i	$-0.272985\pi$
$181$	4.39147	+	2.53542i	0.326416	+	0.188456i	−0.327833	+	0.944736i	$0.606318\pi$
$182$	−9.22738	−	4.45394i	−0.683979	−	0.330148i
$183$	−1.24993	+	0.206836i	−0.0923978	+	0.0152898i
$184$	2.37371	−	0.993038i	0.174992	−	0.0732077i
$185$	−38.0543	+	6.70999i	−2.79780	+	0.493328i
$186$	−3.20937	+	6.47374i	−0.235322	+	0.474677i
$187$	−10.3358	−	8.67280i	−0.755832	−	0.634218i
$188$	2.21699	+	1.36028i	0.161691	+	0.0992087i
$189$	10.0573	−	11.2438i	0.731560	−	0.817863i
$190$	3.45969	−	12.2540i	0.250992	−	0.888999i
$191$	19.1259	+	16.0486i	1.38390	+	1.16123i	0.967742	+	0.251944i	$0.0810697\pi$
$191$	19.1259	+	16.0486i	1.38390	+	1.16123i	0.416163	+	0.909290i	$0.363375\pi$
$192$	9.83213	−	9.76367i	0.709573	−	0.704632i
$193$	−1.63585	−	9.27734i	−0.117751	−	0.667798i	−0.985351	−	0.170536i	$-0.945450\pi$
$193$	−1.63585	−	9.27734i	−0.117751	−	0.667798i	0.867601	−	0.497262i	$-0.165661\pi$
$194$	−0.111482	+	0.154767i	−0.00800396	+	0.0111116i
$195$	9.38671	+	11.4292i	0.672196	+	0.818461i
$196$	1.89439	−	2.13880i	0.135313	−	0.152772i
$197$	0.195281	−	0.338236i	0.0139132	−	0.0240983i	−0.858985	−	0.512001i	$-0.828904\pi$
$197$	0.195281	−	0.338236i	0.0139132	−	0.0240983i	0.872898	+	0.487902i	$0.162238\pi$
$198$	−11.4900	+	0.607402i	−0.816559	+	0.0431661i
$199$	6.27422	−	3.62242i	0.444768	−	0.256787i	−0.260850	−	0.965379i	$-0.584003\pi$
$199$	6.27422	−	3.62242i	0.444768	−	0.256787i	0.705618	+	0.708592i	$0.250670\pi$
$200$	8.70095	−	16.8591i	0.615250	−	1.19212i
$201$	−5.75713	+	9.73323i	−0.406076	+	0.686529i
$202$	7.57029	+	16.8180i	0.532643	+	1.18331i
$203$	17.0586	+	20.3296i	1.19728	+	1.42686i
$204$	8.05484	+	15.2361i	0.563952	+	1.06674i
$205$	5.53760	+	15.2144i	0.386763	+	1.06262i
$206$	−0.429721	−	1.69402i	−0.0299401	−	0.118028i
$207$	2.05320	+	1.79794i	0.142707	+	0.124966i
$208$	0.533585	−	9.96792i	0.0369975	−	0.691151i
$209$	7.02788	+	1.23920i	0.486128	+	0.0857176i
$210$	−22.2923	+	9.75317i	−1.53831	+	0.673032i
$211$	20.9809	+	7.63642i	1.44438	+	0.525713i	0.941017	−	0.338359i	$-0.109872\pi$
$211$	20.9809	+	7.63642i	1.44438	+	0.525713i	0.503368	+	0.864072i	$0.332094\pi$
$212$	7.58993	−	19.2366i	0.521279	−	1.32117i
$213$	13.6282	+	11.6824i	0.933790	+	0.800467i
$214$	12.7130	+	18.6828i	0.869043	+	1.27713i
$215$	22.3127			1.52171
$216$	13.8870	+	4.81152i	0.944892	+	0.327383i
$217$	−8.56397			−0.581360
$218$	1.89520	+	2.78515i	0.128359	+	0.188634i
$219$	4.67919	−	24.9935i	0.316190	−	1.68890i
$220$	17.2638	+	6.81156i	1.16393	+	0.459235i
$221$	11.6668	+	4.24638i	0.784797	+	0.285643i
$222$	−3.06913	+	27.4918i	−0.205986	+	1.84513i
$223$	−7.83765	−	1.38199i	−0.524848	−	0.0925448i	−0.0950544	−	0.995472i	$-0.530303\pi$
$223$	−7.83765	−	1.38199i	−0.524848	−	0.0925448i	−0.429793	+	0.902927i	$0.641414\pi$
$224$	15.5440	+	5.30075i	1.03858	+	0.354171i
$225$	20.1184	+	0.424206i	1.34123	+	0.0282804i
$226$	3.29988	+	13.0086i	0.219505	+	0.865317i
$227$	−2.95471	−	8.11801i	−0.196111	−	0.538811i	0.802190	−	0.597068i	$-0.203668\pi$
$227$	−2.95471	−	8.11801i	−0.196111	−	0.538811i	−0.998302	+	0.0582571i	$0.981446\pi$
$228$	−7.71876	−	4.84874i	−0.511188	−	0.321116i
$229$	−4.90565	−	5.84633i	−0.324175	−	0.386336i	0.579202	−	0.815184i	$-0.303364\pi$
$229$	−4.90565	−	5.84633i	−0.324175	−	0.386336i	−0.903377	+	0.428848i	$0.858920\pi$
$230$	−1.80688	−	4.01412i	−0.119142	−	0.264683i
$231$	−6.69377	−	11.8814i	−0.440417	−	0.781742i
$232$	−11.8576	+	22.9755i	−0.778489	+	1.50842i
$233$	−6.15633	+	3.55436i	−0.403315	+	0.232854i	−0.687913	−	0.725793i	$-0.741473\pi$
$233$	−6.15633	+	3.55436i	−0.403315	+	0.232854i	0.284599	+	0.958647i	$0.408140\pi$
$234$	9.74416	−	4.14138i	0.636995	−	0.270730i
$235$	2.22496	−	3.85374i	0.145140	−	0.251390i
$236$	−12.9689	−	11.4869i	−0.844203	−	0.747731i
$237$	−5.35579	+	14.2459i	−0.347896	+	0.925367i
$238$	−11.9388	+	16.5743i	−0.773878	+	1.07435i
$239$	0.386367	+	2.19120i	0.0249920	+	0.141737i	0.994751	−	0.102330i	$-0.0326297\pi$
$239$	0.386367	+	2.19120i	0.0249920	+	0.141737i	−0.969759	+	0.244066i	$0.921519\pi$
$240$	−17.1476	−	16.3684i	−1.10688	−	1.05657i
$241$	0.156407	+	0.131241i	0.0100750	+	0.00845397i	0.647811	−	0.761801i	$-0.275685\pi$
$241$	0.156407	+	0.131241i	0.0100750	+	0.00845397i	−0.637736	+	0.770255i	$0.720129\pi$
$242$	1.40063	−	4.96094i	0.0900358	−	0.318901i
$243$	1.89440	+	15.4729i	0.121526	+	0.992588i
$244$	0.765075	−	1.24692i	0.0489789	−	0.0798260i
$245$	−3.74445	−	3.14197i	−0.239224	−	0.200733i
$246$	11.5675	−	0.733846i	0.737517	−	0.0467883i
$247$	−6.46696	+	1.14030i	−0.411483	+	0.0725555i
$248$	−3.22003	−	7.69700i	−0.204472	−	0.488760i
$249$	−2.98913	+	7.95078i	−0.189428	+	0.503860i
$250$	−7.44151	−	3.59192i	−0.470642	−	0.227173i
$251$	11.4836	+	6.63004i	0.724837	+	0.418485i	0.816530	−	0.577303i	$-0.195895\pi$
$251$	11.4836	+	6.63004i	0.724837	+	0.418485i	−0.0916936	+	0.995787i	$0.529228\pi$
$252$	2.20130	+	17.2795i	0.138669	+	1.08851i
$253$	2.13661	−	1.23357i	0.134328	−	0.0775541i
$254$	−6.41790	+	0.475126i	−0.402695	+	0.0298121i
$255$	25.6885	−	14.4724i	1.60868	−	0.906295i
$256$	1.08037	+	15.9635i	0.0675231	+	0.997718i
$257$	14.5879	+	17.3851i	0.909966	+	1.08446i	0.996105	+	0.0881721i	$0.0281025\pi$
$257$	14.5879	+	17.3851i	0.909966	+	1.08446i	−0.0861393	+	0.996283i	$0.527453\pi$
$258$	4.50189	−	15.3257i	0.280275	−	0.954138i
$259$	−30.8092	+	11.2136i	−1.91439	+	0.696781i
$260$	−17.0716	−	0.456597i	−1.05874	−	0.0283170i
$261$	−27.4172	−	0.578105i	−1.69708	−	0.0357838i
$262$	1.57637	−	1.53478i	0.0973887	−	0.0948188i
$263$	3.05022	−	17.2987i	0.188085	−	1.06668i	−0.733843	−	0.679319i	$-0.762275\pi$
$263$	3.05022	−	17.2987i	0.188085	−	1.06668i	0.921927	−	0.387363i	$-0.126614\pi$
$264$	8.16180	−	10.4835i	0.502324	−	0.645216i
$265$	−33.2457	−	12.1005i	−2.04227	−	0.743325i
$266$	1.08541	−	10.7491i	0.0665510	−	0.659069i
$267$	9.63450	+	1.80374i	0.589622	+	0.110387i
$268$	−4.13638	−	12.3854i	−0.252670	−	0.756557i
$269$	−25.2404			−1.53894			−0.769468	−	0.638686i	$-0.779478\pi$
$269$	−25.2404			−1.53894			−0.769468	+	0.638686i	$0.779478\pi$
$270$	7.59350	−	23.9698i	0.462126	−	1.45875i
$271$		−	28.2779i		−	1.71776i	−0.512175	−	0.858881i	$-0.671160\pi$
$271$		−	28.2779i		−	1.71776i	0.512175	−	0.858881i	$-0.328840\pi$
$272$	−19.3853	−	4.49832i	−1.17541	−	0.272751i
$273$	9.52740	+	8.16711i	0.576625	+	0.494296i
$274$	−0.123176	+	1.21984i	−0.00744136	+	0.0736933i
$275$	6.22172	−	17.0940i	0.375184	−	1.03081i
$276$	−3.12171	+	0.431172i	−0.187905	+	0.0259535i
$277$	−10.7115	−	1.88873i	−0.643592	−	0.113483i	−0.157680	−	0.987490i	$-0.550401\pi$
$277$	−10.7115	−	1.88873i	−0.643592	−	0.113483i	−0.485912	+	0.874008i	$0.661512\pi$
$278$	−14.9844	−	15.3906i	−0.898707	−	0.923065i
$279$	5.83001	−	6.65770i	0.349033	−	0.398586i
$280$	8.35438	−	26.8260i	0.499270	−	1.60316i
$281$	1.98862	+	5.46370i	0.118631	+	0.325937i	0.984769	−	0.173869i	$-0.0556269\pi$
$281$	1.98862	+	5.46370i	0.118631	+	0.325937i	−0.866137	+	0.499806i	$0.833405\pi$
$282$	−2.19807	−	2.30578i	−0.130893	−	0.137307i
$283$	6.97262	−	5.85072i	0.414479	−	0.347789i	−0.411579	−	0.911374i	$-0.635023\pi$
$283$	6.97262	−	5.85072i	0.414479	−	0.347789i	0.826058	+	0.563585i	$0.190578\pi$
$284$	−20.5011	+	3.05218i	−1.21651	+	0.181113i
$285$	−7.93929	+	13.4225i	−0.470283	+	0.795079i
$286$	−0.706643	−	9.54518i	−0.0417847	−	0.564418i
$287$	6.86883	+	11.8972i	0.405454	+	0.702267i
$288$	−14.7026	+	8.47551i	−0.866358	+	0.499424i
$289$	3.87581	−	6.71310i	0.227989	−	0.394888i
$290$	39.8353	+	19.2280i	2.33921	+	1.12911i
$291$	0.180526	−	0.148264i	0.0105826	−	0.00869141i
$292$	18.2650	+	22.9887i	1.06888	+	1.34531i
$293$	0.704403	+	3.99487i	0.0411517	+	0.233383i	0.998446	−	0.0557335i	$-0.0177497\pi$
$293$	0.704403	+	3.99487i	0.0411517	+	0.233383i	−0.957294	+	0.289116i	$0.906639\pi$
$294$	−2.91359	+	1.93798i	−0.169924	+	0.113025i
$295$	−19.0517	+	22.7049i	−1.10923	+	1.32193i
$296$	−21.6626	−	23.4739i	−1.25911	−	1.36440i
$297$	13.7936	+	2.88462i	0.800385	+	0.167383i
$298$	−3.28357	+	11.6302i	−0.190212	+	0.673719i
$299$	−1.45928	+	1.73910i	−0.0843922	+	0.100575i
$300$	−15.5888	+	17.2307i	−0.900019	+	0.994812i
$301$	18.6443	−	3.28749i	1.07464	−	0.189488i
$302$	12.0556	+	8.68389i	0.693720	+	0.499702i
$303$	−3.68771	−	22.2852i	−0.211853	−	1.28025i
$304$	10.0690	−	3.06609i	0.577498	−	0.175852i
$305$	−2.16749	−	1.25140i	−0.124110	−	0.0716551i
$306$	−4.75751	−	20.5644i	−0.271969	−	1.17559i
$307$	−16.8379	−	29.1641i	−0.960989	−	1.66448i	−0.720025	−	0.693948i	$-0.755870\pi$
$307$	−16.8379	−	29.1641i	−0.960989	−	1.66448i	−0.240964	−	0.970534i	$-0.577464\pi$
$308$	15.4291	+	3.14808i	0.879154	+	0.179378i
$309$	−0.0225625	+	2.14033i	−0.00128353	+	0.121759i
$310$	−13.0162	+	5.85899i	−0.739270	+	0.332768i
$311$	−9.39589	+	7.88409i	−0.532792	+	0.447066i	−0.869064	−	0.494699i	$-0.835278\pi$
$311$	−9.39589	+	7.88409i	−0.532792	+	0.447066i	0.336272	+	0.941765i	$0.390834\pi$
$312$	−3.75805	+	11.6337i	−0.212758	+	0.658629i
$313$	−5.01611	+	1.82572i	−0.283528	+	0.103196i	−0.479869	−	0.877340i	$-0.659316\pi$
$313$	−5.01611	+	1.82572i	−0.283528	+	0.103196i	0.196342	+	0.980535i	$0.437094\pi$
$314$	−3.34980	−	13.2053i	−0.189040	−	0.745221i
$315$	29.4509	−	4.55507i	1.65937	−	0.256649i
$316$	−8.37685	−	15.4488i	−0.471234	−	0.869065i
$317$	0.00253246	−	0.0143623i	0.000142237	−	0.000806666i	−0.984737	−	0.174051i	$-0.944314\pi$
$317$	0.00253246	−	0.0143623i	0.000142237	−	0.000806666i	0.984879	+	0.173245i	$0.0554252\pi$
$318$	−15.0191	+	20.3938i	−0.842230	+	1.14363i
$319$	−8.47891	+	23.2956i	−0.474728	+	1.30430i
$320$	27.2515	−	2.57785i	1.52340	−	0.144106i
$321$	−9.19132	−	26.1059i	−0.513010	−	1.45709i
$322$	−2.10124	−	3.08794i	−0.117098	−	0.172084i
$323$			13.0914i			0.728422i
$324$	−14.9318	−	10.0519i	−0.829545	−	0.558439i
$325$			16.7392i			0.928523i
$326$	22.9399	−	15.6099i	1.27053	−	0.864550i
$327$	−1.37020	−	3.89177i	−0.0757725	−	0.215215i
$328$	−8.11010	+	10.6468i	−0.447805	+	0.587869i
$329$	1.29136	−	3.54797i	0.0711947	−	0.195606i
$330$	−18.3023	−	13.4788i	−1.00751	−	0.741986i
$331$	0.663118	−	3.76073i	0.0364482	−	0.206708i	−0.961145	−	0.276043i	$-0.910977\pi$
$331$	0.663118	−	3.76073i	0.0364482	−	0.206708i	0.997593	+	0.0693351i	$0.0220878\pi$
$332$	−4.67522	−	8.62219i	−0.256586	−	0.473204i
$333$	12.2561	−	31.5851i	0.671629	−	1.73085i
$334$	−15.6152	+	3.96110i	−0.854425	+	0.216742i
$335$	−20.9924	+	7.64060i	−1.14694	+	0.417450i
$336$	−16.7401	−	11.1508i	−0.913247	−	0.608326i
$337$	6.62429	−	5.55844i	0.360848	−	0.302787i	−0.444281	−	0.895888i	$-0.646541\pi$
$337$	6.62429	−	5.55844i	0.360848	−	0.302787i	0.805129	+	0.593100i	$0.202096\pi$
$338$	−3.93118	−	8.73341i	−0.213828	−	0.475035i
$339$	0.173260	−	16.4359i	0.00941020	−	0.892674i
$340$	−6.80635	+	33.3587i	−0.369126	+	1.80913i
$341$	−3.99999	−	6.92818i	−0.216611	−	0.375182i
$342$	7.61752	+	8.16135i	0.411908	+	0.441315i
$343$	14.0079	+	8.08749i	0.756358	+	0.436684i
$344$	9.96489	+	15.5208i	0.537271	+	0.836824i
$345$	0.880184	+	5.31904i	0.0473875	+	0.286368i
$346$	13.0916	−	18.1746i	0.703809	−	0.977075i
$347$	−24.1858	+	4.26461i	−1.29836	+	0.228936i	−0.779759	−	0.626079i	$-0.784659\pi$
$347$	−24.1858	+	4.26461i	−1.29836	+	0.228936i	−0.518602	+	0.855016i	$0.673547\pi$
$348$	21.2443	−	23.4818i	1.13881	−	1.25876i
$349$	−4.36508	+	5.20210i	−0.233658	+	0.278462i	−0.870114	−	0.492850i	$-0.835955\pi$
$349$	−4.36508	+	5.20210i	−0.233658	+	0.278462i	0.636457	+	0.771313i	$0.280399\pi$
$350$	−26.5037	−	7.48282i	−1.41668	−	0.399974i
$351$	−12.8351	+	1.84684i	−0.685084	+	0.0985770i
$352$	2.97190	+	15.0508i	0.158403	+	0.802210i
$353$	9.32471	−	11.1128i	0.496304	−	0.591472i	−0.458505	−	0.888692i	$-0.651615\pi$
$353$	9.32471	−	11.1128i	0.496304	−	0.591472i	0.954809	+	0.297220i	$0.0960594\pi$
$354$	11.7512	+	17.6669i	0.624569	+	0.938985i
$355$	6.15760	+	34.9215i	0.326812	+	1.85344i
$356$	−8.86169	+	7.04081i	−0.469669	+	0.373162i
$357$	19.3328	−	15.8779i	1.02320	−	0.840346i
$358$	9.69466	−	20.0847i	0.512379	−	1.06151i
$359$	−1.61294	+	2.79370i	−0.0851279	+	0.147446i	−0.905446	−	0.424462i	$-0.860463\pi$
$359$	−1.61294	+	2.79370i	−0.0851279	+	0.147446i	0.820318	+	0.571908i	$0.193797\pi$
$360$	15.1674	+	24.7568i	0.799392	+	1.30480i
$361$	6.03793	+	10.4580i	0.317786	+	0.550422i
$362$	7.15167	−	0.529449i	0.375884	−	0.0278272i
$363$	−3.21416	+	5.43398i	−0.168699	+	0.285210i
$364$	−14.3322	+	2.13376i	−0.751210	+	0.111839i
$365$	38.4800	−	32.2885i	2.01413	−	1.69006i
$366$	−1.29686	+	1.23628i	−0.0677880	+	0.0646213i
$367$	10.2734	+	28.2260i	0.536268	+	1.47338i	0.851492	+	0.524367i	$0.175698\pi$
$367$	10.2734	+	28.2260i	0.536268	+	1.47338i	−0.315224	+	0.949017i	$0.602080\pi$
$368$	1.98528	−	3.04958i	0.103490	−	0.158970i
$369$	−13.9250	−	2.75922i	−0.724905	−	0.143639i
$370$	−39.1545	+	38.1212i	−2.03554	+	1.98183i
$371$	−29.5627	−	5.21270i	−1.53482	−	0.270630i
$372$	1.39812	+	10.1224i	0.0724890	+	0.524824i
$373$	−5.31103	+	14.5919i	−0.274995	+	0.755542i	0.722916	+	0.690936i	$0.242801\pi$
$373$	−5.31103	+	14.5919i	−0.274995	+	0.755542i	−0.997911	+	0.0646062i	$0.979421\pi$
$374$	−18.9847	−	1.91703i	−0.981676	−	0.0991271i
$375$	7.68346	+	6.58645i	0.396772	+	0.340123i
$376$	3.67434	−	0.173400i	0.189490	−	0.00894240i
$377$		−	22.8120i		−	1.17488i
$378$	2.81342	−	21.1477i	0.144707	−	1.08772i
$379$	−6.68763			−0.343521			−0.171760	−	0.985139i	$-0.554945\pi$
$379$	−6.68763			−0.343521			−0.171760	+	0.985139i	$0.554945\pi$
$380$	−5.70422	−	17.0799i	−0.292620	−	0.876179i
$381$	7.74719	+	1.45040i	0.396901	+	0.0743064i
$382$	35.1302	+	3.54736i	1.79742	+	0.181499i
$383$	6.52420	+	2.37461i	0.333371	+	0.121337i	0.503282	−	0.864122i	$-0.332126\pi$
$383$	6.52420	+	2.37461i	0.333371	+	0.121337i	−0.169911	+	0.985459i	$0.554348\pi$
$384$	3.72773	−	19.2381i	0.190230	−	0.981740i
$385$	4.67812	−	26.5309i	0.238419	−	1.35214i
$386$	−9.29367	−	9.54556i	−0.473035	−	0.485856i
$387$	−10.1366	+	16.7322i	−0.515271	+	0.850547i
$388$	−0.00721202	+	0.269649i	−0.000366135	+	0.0136893i
$389$	−1.33770	+	0.486883i	−0.0678241	+	0.0246860i	−0.375709	−	0.926738i	$-0.622601\pi$
$389$	−1.33770	+	0.486883i	−0.0678241	+	0.0246860i	0.307885	+	0.951423i	$0.400379\pi$
$390$	20.0680	+	5.89491i	1.01618	+	0.298500i
$391$	2.90920	+	3.46705i	0.147125	+	0.175336i
$392$	0.513283	−	4.00786i	0.0259247	−	0.202427i
$393$	−2.34764	+	1.32261i	−0.118423	+	0.0667171i
$394$	−0.0407787	−	0.550830i	−0.00205440	−	0.0277504i
$395$	−26.0376	+	15.0328i	−1.31009	+	0.756382i
$396$	−12.9508	+	9.85161i	−0.650804	+	0.495062i
$397$	−16.5544	−	9.55769i	−0.830842	−	0.479687i	0.0232990	−	0.999729i	$-0.492583\pi$
$397$	−16.5544	−	9.55769i	−0.830842	−	0.479687i	−0.854141	+	0.520042i	$0.825916\pi$
$398$	4.45381	−	9.22709i	0.223249	−	0.462512i
$399$	−4.65637	+	12.3855i	−0.233110	+	0.620049i
$400$	−3.24000	−	26.6341i	−0.162000	−	1.33171i
$401$	−18.4212	+	3.24815i	−0.919909	+	0.162205i	−0.613500	−	0.789695i	$-0.710239\pi$
$401$	−18.4212	+	3.24815i	−0.919909	+	0.162205i	−0.306409	+	0.951900i	$0.599128\pi$
$402$	1.01254	+	15.9604i	0.0505007	+	0.796034i
$403$	5.63921	+	4.73186i	0.280909	+	0.235711i
$404$	22.2315	+	13.6406i	1.10606	+	0.678646i
$405$	−16.5079	+	25.9963i	−0.820282	+	1.29177i
$406$	36.1190	+	10.1975i	1.79256	+	0.506095i
$407$	−23.4618	−	19.6868i	−1.16296	−	0.975838i
$408$	21.5395	+	11.4056i	1.06637	+	0.564661i
$409$	−3.21877	−	18.2546i	−0.159158	−	0.902630i	−0.954885	−	0.296975i	$-0.904022\pi$
$409$	−3.21877	−	18.2546i	−0.159158	−	0.902630i	0.795727	−	0.605655i	$-0.207089\pi$
$410$	18.5791	+	13.3830i	0.917559	+	0.660938i
$411$	0.528420	−	1.40554i	0.0260650	−	0.0693303i
$412$	−1.85019	−	1.63875i	−0.0911521	−	0.0807356i
$413$	−12.5742	+	21.7791i	−0.618734	+	1.07168i
$414$	3.83103	+	0.468625i	0.188285	+	0.0230317i
$415$	−14.5319	+	8.38999i	−0.713342	+	0.411848i
$416$	−7.30660	−	12.0790i	−0.358236	−	0.592221i
$417$	12.9130	+	22.9207i	0.632355	+	1.12243i
$418$	9.20288	−	4.14250i	0.450128	−	0.202616i
$419$	−14.4375	−	17.2059i	−0.705317	−	0.840564i	0.287800	−	0.957691i	$-0.407076\pi$
$419$	−14.4375	−	17.2059i	−0.705317	−	0.840564i	−0.993117	+	0.117126i	$0.962632\pi$
$420$	−18.3045	+	29.1391i	−0.893167	+	1.42184i
$421$	−5.98056	−	16.4314i	−0.291475	−	0.800820i	−0.995851	−	0.0909935i	$-0.970996\pi$
$421$	−5.98056	−	16.4314i	−0.291475	−	0.800820i	0.704377	−	0.709826i	$-0.251226\pi$
$422$	30.6063	−	7.76390i	1.48989	−	0.377941i
$423$	1.87912	+	3.41922i	0.0913659	+	0.166248i
$424$	−6.43048	−	28.5299i	−0.312292	−	1.38553i
$425$	32.8641	+	5.79483i	1.59414	+	0.281090i
$426$	25.2286	+	2.81646i	1.22233	+	0.136458i
$427$	−1.99552	−	0.726309i	−0.0965698	−	0.0351485i
$428$	29.7280	+	11.7294i	1.43696	+	0.566962i
$429$	−2.15715	+	11.5222i	−0.104148	+	0.556298i
$430$	26.0880	−	17.7520i	1.25807	−	0.856076i
$431$	−13.1374			−0.632807			−0.316403	−	0.948625i	$-0.602475\pi$
$431$	−13.1374			−0.632807			−0.316403	+	0.948625i	$0.602475\pi$
$432$	20.0647	−	5.42288i	0.965364	−	0.260908i
$433$	−22.6607			−1.08900			−0.544502	−	0.838759i	$-0.683281\pi$
$433$	−22.6607			−1.08900			−0.544502	+	0.838759i	$0.683281\pi$
$434$	−10.0130	+	6.81349i	−0.480638	+	0.327058i
$435$	−41.1305	−	35.2581i	−1.97206	−	1.69049i
$436$	4.43173	+	1.74857i	0.212241	+	0.0837414i
$437$	−2.24943	−	0.818727i	−0.107605	−	0.0391650i
$438$	−14.4139	−	32.9450i	−0.688722	−	1.57417i
$439$	14.8982	+	2.62696i	0.711053	+	0.125378i	0.517464	−	0.855705i	$-0.326876\pi$
$439$	14.8982	+	2.62696i	0.711053	+	0.125378i	0.193589	+	0.981083i	$0.437987\pi$
$440$	25.6041	−	5.77102i	1.22063	−	0.275122i
$441$	4.05724	−	1.38057i	0.193202	−	0.0657414i
$442$	17.0193	−	4.31727i	0.809524	−	0.205352i
$443$	1.36146	+	3.74057i	0.0646848	+	0.177720i	0.967824	−	0.251628i	$-0.0809658\pi$
$443$	1.36146	+	3.74057i	0.0646848	+	0.177720i	−0.903139	+	0.429347i	$0.858744\pi$
$444$	18.2841	+	34.5852i	0.867723	+	1.64134i
$445$	12.4466	+	14.8333i	0.590026	+	0.703165i
$446$	−10.2633	+	4.61981i	−0.485980	+	0.218754i
$447$	7.53512	−	12.7392i	0.356399	−	0.602542i
$448$	22.3913	−	6.16918i	1.05789	−	0.291467i
$449$	22.3682	−	12.9143i	1.05562	−	0.609464i	0.131404	−	0.991329i	$-0.458052\pi$
$449$	22.3682	−	12.9143i	1.05562	−	0.609464i	0.924218	+	0.381865i	$0.124718\pi$
$450$	23.8599	−	15.5102i	1.12476	−	0.731157i
$451$	−6.41647	+	11.1136i	−0.302140	+	0.523321i
$452$	14.2078	+	12.5842i	0.668280	+	0.591911i
$453$	−11.5490	−	14.0620i	−0.542621	−	0.660691i
$454$	−9.91333	−	7.14079i	−0.465255	−	0.335134i
$455$	4.30474	+	24.4134i	0.201809	+	1.14452i
$456$	−12.8824	+	0.471912i	−0.603274	+	0.0220993i
$457$	2.14884	+	1.80309i	0.100518	+	0.0843449i	0.691662	−	0.722221i	$-0.256879\pi$
$457$	2.14884	+	1.80309i	0.100518	+	0.0843449i	−0.591143	+	0.806566i	$0.701323\pi$
$458$	−10.3870	−	2.93258i	−0.485353	−	0.137030i
$459$	−0.817376	+	25.8385i	−0.0381519	+	1.20604i
$460$	−5.30623	−	3.25575i	−0.247404	−	0.151800i
$461$	−11.5119	−	9.65964i	−0.536163	−	0.449894i	0.334060	−	0.942552i	$-0.391581\pi$
$461$	−11.5119	−	9.65964i	−0.536163	−	0.449894i	−0.870223	+	0.492657i	$0.836026\pi$
$462$	−17.2792	−	8.56619i	−0.803901	−	0.398535i
$463$	21.5380	−	3.79772i	1.00095	−	0.176495i	0.350924	−	0.936404i	$-0.385868\pi$
$463$	21.5380	−	3.79772i	1.00095	−	0.176495i	0.650030	+	0.759909i	$0.274756\pi$
$464$	4.41545	+	36.2968i	0.204982	+	1.68504i
$465$	17.2475	−	2.85409i	0.799835	−	0.132355i
$466$	−4.37012	+	9.05372i	−0.202442	+	0.419405i
$467$	−16.2109	−	9.35938i	−0.750152	−	0.433100i	0.0755968	−	0.997138i	$-0.475914\pi$
$467$	−16.2109	−	9.35938i	−0.750152	−	0.433100i	−0.825749	+	0.564038i	$0.809247\pi$
$468$	8.09796	−	12.5945i	0.374329	−	0.582182i
$469$	−16.4153	+	9.47738i	−0.757988	+	0.437625i
$470$	−0.464618	−	6.27595i	−0.0214312	−	0.289488i
$471$	−0.175881	+	16.6845i	−0.00810416	+	0.768781i
$472$	−24.3021	−	3.11235i	−1.11860	−	0.143258i
$473$	11.3678	+	13.5476i	0.522691	+	0.622919i
$474$	5.07202	+	20.9173i	0.232965	+	0.960762i
$475$	−16.5858	+	6.03674i	−0.761009	+	0.276985i
$476$	−0.772346	+	28.8771i	−0.0354004	+	1.32358i
$477$	24.1775	−	19.4337i	1.10701	−	0.889808i
$478$	2.19505	+	2.25455i	0.100399	+	0.103121i
$479$	3.48398	−	19.7587i	0.159187	−	0.902796i	−0.795670	−	0.605731i	$-0.792881\pi$
$479$	3.48398	−	19.7587i	0.159187	−	0.902796i	0.954857	−	0.297065i	$-0.0960080\pi$
$480$	−33.0716	−	5.49522i	−1.50951	−	0.250821i
$481$	26.4831	+	9.63907i	1.20753	+	0.439504i
$482$	0.287286	+	0.0290093i	0.0130855	+	0.00132134i
$483$	1.51917	+	4.31486i	0.0691245	+	0.196333i
$484$	−2.30931	−	6.91465i	−0.104969	−	0.314302i
$485$	0.461485			0.0209550
$486$	14.5252	+	16.5837i	0.658875	+	0.752252i
$487$		−	14.0996i		−	0.638916i	−0.947600	−	0.319458i	$-0.896499\pi$
$487$		−	14.0996i		−	0.638916i	0.947600	−	0.319458i	$-0.103501\pi$
$488$	−0.0975267	−	2.06659i	−0.00441482	−	0.0935502i
$489$	−32.0546	+	11.2857i	−1.44956	+	0.510357i
$490$	−6.87775	−	0.694497i	−0.310705	−	0.0313742i
$491$	0.766879	−	2.10698i	0.0346088	−	0.0950868i	−0.921185	−	0.389125i	$-0.872777\pi$
$491$	0.766879	−	2.10698i	0.0346088	−	0.0950868i	0.955794	+	0.294039i	$0.0949995\pi$
$492$	12.9408	−	10.0611i	0.583418	−	0.453589i
$493$	−44.7869	−	7.89715i	−2.01710	−	0.355670i
$494$	−6.65392	+	6.47834i	−0.299374	+	0.291474i
$495$	17.4407	+	21.6980i	0.783901	+	0.975253i
$496$	−9.88858	−	6.43746i	−0.444010	−	0.289051i
$497$	10.2905	+	28.2729i	0.461591	+	1.26821i
$498$	2.83075	+	11.6742i	0.126849	+	0.523132i
$499$	−7.09602	+	5.95427i	−0.317661	+	0.266550i	−0.787650	−	0.616123i	$-0.788702\pi$
$499$	−7.09602	+	5.95427i	−0.317661	+	0.266550i	0.469989	+	0.882672i	$0.344258\pi$
$500$	−11.5583	+	1.72079i	−0.516904	+	0.0769561i
$501$	19.7293	+	0.207977i	0.881438	+	0.00929175i
$502$	18.7014	−	1.38449i	0.834685	−	0.0617930i
$503$	7.08381	+	12.2695i	0.315852	+	0.547071i	0.979618	−	0.200869i	$-0.0643765\pi$
$503$	7.08381	+	12.2695i	0.315852	+	0.547071i	−0.663767	+	0.747940i	$0.731043\pi$
$504$	16.3213	+	18.4518i	0.727011	+	0.821910i
$505$	22.3114	−	38.6445i	0.992844	−	1.71966i
$506$	1.51669	−	3.14218i	0.0674251	−	0.139687i
$507$	1.91499	+	11.5725i	0.0850478	+	0.513953i
$508$	−7.12577	+	5.66159i	−0.316155	+	0.251192i
$509$	7.28735	+	41.3286i	0.323006	+	1.83186i	0.523333	+	0.852129i	$0.324689\pi$
$509$	7.28735	+	41.3286i	0.323006	+	1.83186i	−0.200327	+	0.979729i	$0.564200\pi$
$510$	18.5207	−	37.3588i	0.820110	−	1.65428i
$511$	27.3962	−	32.6495i	1.21194	−	1.44433i
$512$	13.9637	+	17.8049i	0.617114	+	0.786874i
$513$	−6.45869	−	12.0514i	−0.285158	−	0.532083i
$514$	30.8877	+	8.72056i	1.36240	+	0.384647i
$515$	−2.71798	+	3.23916i	−0.119769	+	0.142735i
$516$	−6.92954	−	21.5005i	−0.305056	−	0.946507i
$517$	3.47343	−	0.612460i	0.152761	−	0.0269359i
$518$	−27.1005	+	37.6227i	−1.19073	+	1.65305i
$519$	−21.1995	+	17.4110i	−0.930555	+	0.764258i
$520$	−20.3234	+	13.0483i	−0.891238	+	0.572207i
$521$	4.99532	+	2.88405i	0.218849	+	0.126353i	0.605417	−	0.795908i	$-0.293006\pi$
$521$	4.99532	+	2.88405i	0.218849	+	0.126353i	−0.386568	+	0.922261i	$0.626340\pi$
$522$	−32.5160	+	21.1372i	−1.42319	+	0.925149i
$523$	−3.83688	−	6.64566i	−0.167775	−	0.290595i	0.769862	−	0.638210i	$-0.220325\pi$
$523$	−3.83688	−	6.64566i	−0.167775	−	0.290595i	−0.937637	+	0.347615i	$0.886991\pi$
$524$	0.622025	−	3.04862i	0.0271733	−	0.133179i
$525$	29.0309	+	17.1716i	1.26701	+	0.749428i
$526$	−10.1965	−	22.6523i	−0.444589	−	0.987688i
$527$	11.2423	−	9.43339i	0.489721	−	0.410925i
$528$	1.20208	−	18.7508i	0.0523137	−	0.816024i
$529$	20.8353	−	7.58341i	0.905881	−	0.329714i
$530$	−48.4979	+	12.3025i	−2.10662	+	0.534385i
$531$	−8.37126	−	24.6016i	−0.363282	−	1.06762i
$532$	−7.28290	−	13.4314i	−0.315754	−	0.582323i
$533$	2.05056	−	11.6293i	0.0888195	−	0.503720i
$534$	12.6997	−	5.55627i	0.549569	−	0.240443i
$535$	18.6999	−	51.3776i	0.808468	−	2.22125i
$536$	−14.6900	−	11.1900i	−0.634513	−	0.483336i
$537$	−17.7769	+	20.7378i	−0.767131	+	0.894902i
$538$	−29.5110	+	20.0813i	−1.27231	+	0.865764i
$539$		−	3.87427i		−	0.166877i
$540$	−10.1920	−	34.0668i	−0.438595	−	1.46600i
$541$		−	34.8844i		−	1.49980i	−0.661552	−	0.749899i	$-0.730102\pi$
$541$		−	34.8844i		−	1.49980i	0.661552	−	0.749899i	$-0.269898\pi$
$542$	−22.4979	−	33.0625i	−0.966367	−	1.42015i
$543$	−8.63295	−	1.61623i	−0.370475	−	0.0693591i
$544$	−26.2441	+	10.1635i	−1.12521	+	0.435758i
$545$	2.78771	−	7.65917i	0.119412	−	0.328083i
$546$	17.6372	+	1.96897i	0.754801	+	0.0842643i
$547$	−5.15974	+	29.2623i	−0.220614	+	1.25117i	0.650279	+	0.759695i	$0.274652\pi$
$547$	−5.15974	+	29.2623i	−0.220614	+	1.25117i	−0.870894	+	0.491471i	$0.836459\pi$
$548$	0.826488	+	1.52423i	0.0353058	+	0.0651121i
$549$	1.92311	−	1.05689i	0.0820761	−	0.0451069i
$550$	−6.32558	−	24.9363i	−0.269724	−	1.06329i
$551$	22.6030	−	8.22683i	0.962921	−	0.350475i
$552$	−3.30685	+	2.98775i	−0.140749	+	0.127167i
$553$	−19.5419	+	16.3976i	−0.831005	+	0.697296i
$554$	−14.0265	+	6.31377i	−0.595930	+	0.268246i
$555$	58.3115	−	32.8515i	2.47518	−	1.39447i
$556$	−29.7645	−	6.07300i	−1.26229	−	0.257553i
$557$	8.65814	+	14.9963i	0.366857	+	0.635415i	0.989072	−	0.147431i	$-0.0471004\pi$
$557$	8.65814	+	14.9963i	0.366857	+	0.635415i	−0.622215	+	0.782846i	$0.713767\pi$
$558$	1.51956	−	12.4225i	0.0643282	−	0.525887i
$559$	−14.0934	−	8.13680i	−0.596085	−	0.344150i
$560$	−11.5748	−	38.0116i	−0.489124	−	1.60628i
$561$	21.8748	+	8.22394i	0.923556	+	0.347215i
$562$	6.67201	+	4.80600i	0.281442	+	0.202729i
$563$	19.0265	−	3.35488i	0.801870	−	0.141391i	0.242329	−	0.970194i	$-0.422089\pi$
$563$	19.0265	−	3.35488i	0.801870	−	0.141391i	0.559541	+	0.828803i	$0.310978\pi$
$564$	−4.40445	−	0.947130i	−0.185461	−	0.0398814i
$565$	20.8717	−	24.8739i	0.878080	−	1.04645i
$566$	3.49753	−	12.3881i	0.147012	−	0.520709i
$567$	−9.96360	+	24.1545i	−0.418432	+	1.01439i
$568$	−21.5415	+	19.8792i	−0.903861	+	0.834114i
$569$	14.3568	−	17.1097i	0.601867	−	0.717277i	−0.375973	−	0.926631i	$-0.622691\pi$
$569$	14.3568	−	17.1097i	0.601867	−	0.717277i	0.977840	+	0.209353i	$0.0671359\pi$
$570$	1.39632	+	22.0100i	0.0584856	+	0.921898i
$571$	6.51955	+	36.9742i	0.272835	+	1.54732i	0.745757	+	0.666218i	$0.232088\pi$
$571$	6.51955	+	36.9742i	0.272835	+	1.54732i	−0.472922	+	0.881104i	$0.656801\pi$
$572$	−8.42034	−	10.5980i	−0.352072	−	0.443124i
$573$	−40.4782	−	15.2180i	−1.69100	−	0.635740i
$574$	17.4964	+	8.44529i	0.730285	+	0.352500i
$575$	−3.05101	+	5.28450i	−0.127236	+	0.220379i
$576$	−10.4471	+	21.6069i	−0.435296	+	0.900287i
$577$	11.0922	+	19.2123i	0.461775	+	0.799817i	0.999050	−	0.0435901i	$-0.0138796\pi$
$577$	11.0922	+	19.2123i	0.461775	+	0.799817i	−0.537275	+	0.843407i	$0.680546\pi$
$578$	−0.809351	−	10.9325i	−0.0336646	−	0.454733i
$579$	8.00895	+	14.2159i	0.332841	+	0.590793i
$580$	61.8731	−	9.21160i	2.56914	−	0.382491i
$581$	−10.9066	+	9.15169i	−0.452480	+	0.379676i
$582$	0.0931109	−	0.316976i	0.00385957	−	0.0131391i
$583$	−9.59086	−	26.3507i	−0.397213	−	1.09133i
$584$	39.6452	+	12.3467i	1.64053	+	0.510908i
$585$	−21.9097	−	13.2731i	−0.905854	−	0.548776i
$586$	4.00190	+	4.11037i	0.165317	+	0.169798i
$587$	−8.52654	−	1.50346i	−0.351928	−	0.0620544i	−0.00511024	−	0.999987i	$-0.501627\pi$
$587$	−8.52654	−	1.50346i	−0.351928	−	0.0620544i	−0.346818	+	0.937933i	$0.612738\pi$
$588$	−1.86470	+	4.58393i	−0.0768990	+	0.189038i
$589$	−2.65481	+	7.29402i	−0.109389	+	0.300545i
$590$	−4.21117	+	41.7041i	−0.173371	+	1.71693i
$591$	−0.124484	+	0.664920i	−0.00512059	+	0.0273511i
$592$	−44.0037	−	10.2109i	−1.80854	−	0.419667i
$593$		−	19.4361i		−	0.798144i	−0.916920	−	0.399072i	$-0.869332\pi$
$593$		−	19.4361i		−	0.798144i	0.916920	−	0.399072i	$-0.130668\pi$
$594$	18.4224	−	7.60147i	0.755881	−	0.311892i
$595$	49.4212			2.02607
$596$	5.41383	+	16.2104i	0.221759	+	0.664003i
$597$	−8.16686	+	9.52711i	−0.334248	+	0.389919i
$598$	−0.322557	+	3.19435i	−0.0131903	+	0.130627i
$599$	−6.17877	−	2.24889i	−0.252458	−	0.0918871i	0.212691	−	0.977119i	$-0.431777\pi$
$599$	−6.17877	−	2.24889i	−0.252458	−	0.0918871i	−0.465149	+	0.885232i	$0.653999\pi$
$600$	−4.51767	+	32.5485i	−0.184433	+	1.32879i
$601$	−0.821185	+	4.65717i	−0.0334968	+	0.189970i	−0.996965	−	0.0778536i	$-0.975193\pi$
$601$	−0.821185	+	4.65717i	−0.0334968	+	0.189970i	0.963468	+	0.267824i	$0.0863044\pi$
$602$	19.1833	−	18.6771i	0.781855	−	0.761223i
$603$	3.80708	−	19.2132i	0.155036	−	0.782422i
$604$	21.0042	+	0.561779i	0.854650	+	0.0228585i
$605$	−11.7199	+	4.26568i	−0.476480	+	0.173425i
$606$	−22.0418	−	23.1219i	−0.895386	−	0.939262i
$607$	22.8132	+	27.1877i	0.925960	+	1.10352i	0.994381	+	0.105859i	$0.0337594\pi$
$607$	22.8132	+	27.1877i	0.925960	+	1.10352i	−0.0684212	+	0.997657i	$0.521796\pi$
$608$	9.33329	−	11.5958i	0.378515	−	0.470270i
$609$	−39.5631	−	23.4013i	−1.60318	−	0.948268i
$610$	−3.52984	+	0.261319i	−0.142919	+	0.0105805i
$611$	−2.81069	+	1.62275i	−0.113709	+	0.0656496i
$612$	−21.9235	−	20.2588i	−0.886205	−	0.818913i
$613$	35.0635	+	20.2439i	1.41620	+	0.817644i	0.995963	−	0.0897701i	$-0.0286132\pi$
$613$	35.0635	+	20.2439i	1.41620	+	0.817644i	0.420238	+	0.907414i	$0.361947\pi$
$614$	−42.8897	−	20.7023i	−1.73089	−	0.835479i
$615$	−17.7985	−	21.6713i	−0.717705	−	0.873872i
$616$	20.5442	−	8.59464i	0.827751	−	0.346288i
$617$	10.1725	−	1.79368i	0.409528	−	0.0722109i	0.0349111	−	0.999390i	$-0.488885\pi$
$617$	10.1725	−	1.79368i	0.409528	−	0.0722109i	0.374617	+	0.927179i	$0.377774\pi$
$618$	1.67647	+	2.52042i	0.0674374	+	0.101386i
$619$	10.0980	+	8.47326i	0.405874	+	0.340569i	0.822759	−	0.568390i	$-0.192434\pi$
$619$	10.0980	+	8.47326i	0.405874	+	0.340569i	−0.416885	+	0.908959i	$0.636878\pi$
$620$	−10.5571	+	17.2060i	−0.423983	+	0.691009i
$621$	−4.38860	−	1.75637i	−0.176108	−	0.0704808i
$622$	−4.71307	+	16.6934i	−0.188977	+	0.669345i
$623$	12.5858	+	10.5607i	0.504238	+	0.423106i
$624$	4.86187	+	16.5920i	0.194631	+	0.664212i
$625$	−2.35223	−	13.3402i	−0.0940891	−	0.533606i
$626$	−4.41229	+	6.12544i	−0.176350	+	0.244822i
$627$	−12.1946	+	2.01793i	−0.487005	+	0.0805885i
$628$	−14.4227	−	12.7746i	−0.575530	−	0.509760i
$629$	28.0924	−	48.6575i	1.12012	−	1.94010i
$630$	30.8099	−	28.7569i	1.22750	−	1.14570i
$631$	−30.9490	+	17.8684i	−1.23206	+	0.711329i	−0.967459	−	0.253029i	$-0.918573\pi$
$631$	−30.9490	+	17.8684i	−1.23206	+	0.711329i	−0.264600	+	0.964358i	$0.585240\pi$
$632$	−22.0853	−	11.3981i	−0.878505	−	0.453393i
$633$	−38.6701	−	0.407643i	−1.53700	−	0.0162024i
$634$	−0.00846568	−	0.0188072i	−0.000336215	−	0.000746928i
$635$	10.0084	+	11.9276i	0.397173	+	0.473332i
$636$	−1.33503	+	35.7935i	−0.0529374	+	1.41931i
$637$	1.21932	+	3.35005i	0.0483112	+	0.132734i
$638$	8.62045	+	33.9830i	0.341287	+	1.34540i
$639$	−28.9849	−	11.2471i	−1.14662	−	0.444929i
$640$	29.8114	−	24.6953i	1.17840	−	0.976166i
$641$	23.8743	+	4.20968i	0.942977	+	0.166272i	0.623942	−	0.781471i	$-0.285530\pi$
$641$	23.8743	+	4.20968i	0.942977	+	0.166272i	0.319035	+	0.947743i	$0.396641\pi$
$642$	−31.5163	−	23.2104i	−1.24385	−	0.916041i
$643$	24.2825	+	8.83811i	0.957609	+	0.348541i	0.773096	−	0.634289i	$-0.218707\pi$
$643$	24.2825	+	8.83811i	0.957609	+	0.348541i	0.184513	+	0.982830i	$0.440929\pi$
$644$	−4.91353	−	1.93867i	−0.193620	−	0.0763943i
$645$	−36.4534	+	12.8344i	−1.43535	+	0.505355i
$646$	10.4155	+	15.3064i	0.409791	+	0.602221i
$647$	−19.0593			−0.749298			−0.374649	−	0.927167i	$-0.622237\pi$
$647$	−19.0593			−0.749298			−0.374649	+	0.927167i	$0.622237\pi$
$648$	−25.4555	+	0.127083i	−0.999988	+	0.00499229i
$649$	−23.4921			−0.922146
$650$	13.3177	+	19.5714i	0.522362	+	0.767653i
$651$	13.9914	−	4.92606i	0.548366	−	0.193067i
$652$	14.4021	−	36.5020i	0.564031	−	1.42953i
$653$	−37.3455	−	13.5927i	−1.46144	−	0.531922i	−0.515680	−	0.856781i	$-0.672461\pi$
$653$	−37.3455	−	13.5927i	−1.46144	−	0.531922i	−0.945762	+	0.324860i	$0.894683\pi$
$654$	−4.69833	−	3.46011i	−0.183719	−	0.135301i
$655$	−5.24222	−	0.924345i	−0.204831	−	0.0361172i
$656$	−1.01175	+	18.9006i	−0.0395023	+	0.737943i
$657$	6.73179	+	43.5245i	0.262632	+	1.69805i
$658$	−1.31291	−	5.17568i	−0.0511827	−	0.201769i
$659$	−8.73494	−	23.9990i	−0.340265	−	0.934870i	−0.985318	−	0.170732i	$-0.945387\pi$
$659$	−8.73494	−	23.9990i	−0.340265	−	0.934870i	0.645053	−	0.764138i	$-0.276835\pi$
$660$	−32.1228	−	1.19812i	−1.25038	−	0.0466367i
$661$	−4.94246	−	5.89019i	−0.192239	−	0.229102i	0.661312	−	0.750111i	$-0.270000\pi$
$661$	−4.94246	−	5.89019i	−0.192239	−	0.229102i	−0.853551	+	0.521009i	$0.825556\pi$
$662$	−2.21672	−	4.92461i	−0.0861551	−	0.191400i
$663$	−21.5032	−	0.226678i	−0.835117	−	0.00880345i
$664$	−12.3261	−	6.36143i	−0.478344	−	0.246872i
$665$	−22.6373	+	13.0696i	−0.877836	+	0.506819i
$666$	−10.7993	−	46.6801i	−0.418464	−	1.80882i
$667$	4.15789	−	7.20168i	0.160994	−	0.278850i
$668$	−15.1058	+	17.0547i	−0.584460	+	0.659868i
$669$	13.5997	−	2.25045i	0.525794	−	0.0870073i
$670$	−18.4654	+	25.6349i	−0.713379	+	0.990362i
$671$	−0.344471	−	1.95359i	−0.0132982	−	0.0754176i
$672$	−28.4440	+	0.280930i	−1.09725	+	0.0108371i
$673$	8.06476	+	6.76714i	0.310874	+	0.260854i	0.784853	−	0.619682i	$-0.212738\pi$
$673$	8.06476	+	6.76714i	0.310874	+	0.260854i	−0.473979	+	0.880536i	$0.657183\pi$
$674$	3.32281	−	11.7692i	0.127990	−	0.453332i
$675$	−33.1124	+	10.8792i	−1.27450	+	0.418740i
$676$	−11.5446	−	7.08344i	−0.444024	−	0.272440i
$677$	27.3660	+	22.9628i	1.05176	+	0.882533i	0.993278	−	0.115756i	$-0.0369290\pi$
$677$	27.3660	+	22.9628i	1.05176	+	0.882533i	0.0584838	+	0.998288i	$0.481373\pi$
$678$	−12.8738	−	19.3546i	−0.494415	−	0.743310i
$679$	0.385613	−	0.0679940i	0.0147985	−	0.00260937i
$680$	18.5822	+	44.4180i	0.712595	+	1.70335i
$681$	9.49680	+	11.5632i	0.363918	+	0.443104i
$682$	−10.1888	−	4.91802i	−0.390150	−	0.188321i
$683$	11.6024	+	6.69864i	0.443953	+	0.256316i	0.705273	−	0.708936i	$-0.250824\pi$
$683$	11.6024	+	6.69864i	0.443953	+	0.256316i	−0.261320	+	0.965252i	$0.584158\pi$
$684$	15.3996	+	3.48174i	0.588817	+	0.133128i
$685$	2.56895	−	1.48319i	0.0981547	−	0.0566696i
$686$	22.8125	−	1.68884i	0.870984	−	0.0644802i
$687$	11.3775	+	6.72967i	0.434077	+	0.256753i
$688$	23.9992	+	10.2188i	0.914962	+	0.389588i
$689$	16.5863	+	19.7668i	0.631887	+	0.753054i
$690$	5.26094	+	5.51874i	0.200280	+	0.210095i
$691$	32.2794	−	11.7487i	1.22797	−	0.446943i	0.355066	−	0.934841i	$-0.384458\pi$
$691$	32.2794	−	11.7487i	1.22797	−	0.446943i	0.872901	+	0.487898i	$0.162236\pi$
$692$	0.846922	−	31.6654i	0.0321952	−	1.20374i
$693$	17.7702	+	15.5610i	0.675035	+	0.591114i
$694$	−24.8850	+	24.2284i	−0.944623	+	0.919696i
$695$	−9.02463	+	51.1812i	−0.342324	+	1.94142i
$696$	6.15664	−	44.3568i	0.233367	−	1.68134i
$697$	−22.1220	−	8.05173i	−0.837929	−	0.304981i
$698$	−0.964853	+	9.55514i	−0.0365202	+	0.361667i
$699$	8.01341	−	9.34810i	0.303095	−	0.353577i
$700$	−36.9414	+	12.3374i	−1.39625	+	0.466311i
$701$	5.81942			0.219796			0.109898	−	0.993943i	$-0.464948\pi$
$701$	5.81942			0.219796			0.109898	+	0.993943i	$0.464948\pi$
$702$	−13.5374	+	12.3709i	−0.510935	+	0.466909i
$703$			29.7167i			1.12079i
$704$	15.4491	+	15.2329i	0.582261	+	0.574112i
$705$	−1.41832	+	7.57585i	−0.0534172	+	0.285323i
$706$	2.06112	−	20.4117i	0.0775714	−	0.768205i
$707$	12.9494	−	35.5783i	0.487014	−	1.33806i
$708$	27.7952	+	11.3068i	1.04461	+	0.424937i
$709$	43.2874	+	7.63273i	1.62569	+	0.286653i	0.910882	−	0.412666i	$-0.135402\pi$
$709$	43.2874	+	7.63273i	1.62569	+	0.286653i	0.714809	+	0.699320i	$0.246514\pi$
$710$	34.9830	+	35.9311i	1.31289	+	1.34847i
$711$	0.555705	−	26.3548i	0.0208406	−	0.988384i
$712$	−4.75940	+	15.2825i	−0.178366	+	0.572734i
$713$	0.917815	+	2.52167i	0.0343724	+	0.0944375i
$714$	9.97139	−	33.9455i	0.373170	−	1.27038i
$715$	−17.7396	+	14.8853i	−0.663424	+	0.556679i
$716$	−4.64444	−	31.1961i	−0.173571	−	1.16585i
$717$	−1.89162	−	3.35762i	−0.0706438	−	0.125393i
$718$	0.336817	+	4.54965i	0.0125699	+	0.169791i
$719$	−13.4590	−	23.3117i	−0.501938	−	0.869381i	−0.999997	−	0.00223877i	$-0.999287\pi$
$719$	−13.4590	−	23.3117i	−0.501938	−	0.869381i	0.498060	−	0.867143i	$-0.334046\pi$
$720$	37.4302	+	16.8784i	1.39494	+	0.629021i
$721$	−1.79387	+	3.10708i	−0.0668073	+	0.115714i
$722$	15.3799	+	7.42370i	0.572381	+	0.276281i
$723$	−0.331020	−	0.124448i	−0.0123108	−	0.00462829i
$724$	7.94048	−	6.30889i	0.295106	−	0.234468i
$725$	−10.6472	−	60.3835i	−0.395428	−	2.24259i
$726$	0.565291	+	8.91058i	0.0209799	+	0.330703i
$727$	−7.10391	+	8.46611i	−0.263470	+	0.313991i	−0.881519	−	0.472148i	$-0.843479\pi$
$727$	−7.10391	+	8.46611i	−0.263470	+	0.313991i	0.618050	+	0.786139i	$0.287923\pi$
$728$	−15.0595	+	13.8975i	−0.558143	+	0.515074i
$729$	−11.9951	−	24.1892i	−0.444263	−	0.895896i
$730$	19.3019	−	68.3663i	0.714397	−	2.53035i
$731$	−20.8539	+	24.8527i	−0.771309	+	0.919211i
$732$	−0.532703	+	2.47724i	−0.0196893	+	0.0915612i
$733$	5.25607	−	0.926787i	0.194137	−	0.0342316i	−0.0757339	−	0.997128i	$-0.524130\pi$
$733$	5.25607	−	0.926787i	0.194137	−	0.0342316i	0.269871	+	0.962896i	$0.413019\pi$
$734$	34.4682	+	24.8282i	1.27225	+	0.916426i
$735$	7.92477	+	2.97935i	0.292310	+	0.109895i
$736$	−0.105063	−	5.14505i	−0.00387269	−	0.189649i
$737$	−15.3342	−	8.85322i	−0.564844	−	0.326113i
$738$	−18.4763	+	7.85262i	−0.680121	+	0.289059i
$739$	7.72474	+	13.3796i	0.284159	+	0.492178i	0.972405	−	0.233299i	$-0.0749522\pi$
$739$	7.72474	+	13.3796i	0.284159	+	0.492178i	−0.688246	+	0.725478i	$0.741619\pi$
$740$	−15.4501	+	75.7225i	−0.567955	+	2.78361i
$741$	9.90948	−	5.58280i	0.364034	−	0.205089i
$742$	−38.7118	+	17.4254i	−1.42116	+	0.639706i
$743$	21.9616	−	18.4280i	0.805692	−	0.676056i	−0.143883	−	0.989595i	$-0.545959\pi$
$743$	21.9616	−	18.4280i	0.805692	−	0.676056i	0.949575	+	0.313539i	$0.101515\pi$
$744$	9.68809	+	10.7228i	0.355182	+	0.393117i
$745$	27.4755	−	10.0003i	1.00662	−	0.366381i
$746$	5.39969	+	21.2863i	0.197697	+	0.779347i
$747$	0.310146	−	14.7090i	0.0113476	−	0.538172i
$748$	−23.7221	+	12.8628i	−0.867364	+	0.470312i
$749$	8.05566	−	45.6859i	0.294347	−	1.66933i
$750$	14.2237	+	1.58790i	0.519375	+	0.0579818i
$751$	8.91474	−	24.4930i	0.325303	−	0.893764i	−0.663979	−	0.747751i	$-0.731134\pi$
$751$	8.91474	−	24.4930i	0.325303	−	0.893764i	0.989283	−	0.146013i	$-0.0466440\pi$
$752$	4.15807	−	3.12604i	0.151629	−	0.113995i
$753$	−22.5749	−	4.22640i	−0.822676	−	0.154019i
$754$	−18.1492	−	26.6718i	−0.660956	−	0.971328i
$755$		−	35.9473i		−	1.30826i
$756$	−13.5357	−	26.9642i	−0.492288	−	0.980680i
$757$			6.07158i			0.220675i	0.993894	+	0.110338i	$0.0351932\pi$
$757$			6.07158i			0.220675i	−0.993894	+	0.110338i	$0.964807\pi$
$758$	−7.81916	+	5.32068i	−0.284005	+	0.193256i
$759$	−2.78113	+	3.24434i	−0.100949	+	0.117762i
$760$	−20.2581	−	15.4315i	−0.734838	−	0.559758i
$761$	7.74422	−	21.2771i	0.280728	−	0.771293i	−0.716549	−	0.697537i	$-0.754279\pi$
$761$	7.74422	−	21.2771i	0.280728	−	0.771293i	0.997276	−	0.0737560i	$-0.0234986\pi$
$762$	10.2119	−	4.46785i	0.369939	−	0.161853i
$763$	1.20090	−	6.81067i	0.0434757	−	0.246563i
$764$	43.8964	−	23.8020i	1.58812	−	0.861127i
$765$	−33.6439	+	38.4204i	−1.21640	+	1.38909i
$766$	9.51731	−	2.41425i	0.343874	−	0.0872306i
$767$	20.3134	−	7.39349i	0.733476	−	0.266963i
$768$	−10.9474	−	25.4589i	−0.395029	−	0.918669i
$769$	−11.2565	+	9.44536i	−0.405921	+	0.340608i	−0.822777	−	0.568364i	$-0.807576\pi$
$769$	−11.2565	+	9.44536i	−0.405921	+	0.340608i	0.416856	+	0.908973i	$0.363132\pi$
$770$	−15.6384	−	34.7418i	−0.563567	−	1.25201i
$771$	−33.8330	−	20.0119i	−1.21846	−	0.720712i
$772$	−18.4606	−	3.76661i	−0.664411	−	0.135563i
$773$	9.84699	+	17.0555i	0.354172	+	0.613443i	0.986976	−	0.160869i	$-0.0514296\pi$
$773$	9.84699	+	17.0555i	0.354172	+	0.613443i	−0.632804	+	0.774312i	$0.718096\pi$
$774$	1.46051	+	27.6279i	0.0524969	+	0.993065i
$775$	17.1355	+	9.89320i	0.615526	+	0.355374i
$776$	0.206100	+	0.321010i	0.00739856	+	0.0115236i
$777$	43.8843	−	36.0419i	1.57434	−	1.29300i
$778$	−1.17667	+	1.63354i	−0.0421857	+	0.0585651i
$779$	12.2622	−	2.16216i	0.439341	−	0.0774676i
$780$	28.1534	−	9.07375i	1.00805	−	0.324892i
$781$	−18.0661	+	21.5304i	−0.646456	+	0.770417i
$782$	6.15982	+	1.73911i	0.220275	+	0.0621904i
$783$	45.1253	−	14.8261i	1.61265	−	0.529841i
$784$	−2.58852	−	5.09434i	−0.0924471	−	0.181941i
$785$	−21.1874	+	25.2502i	−0.756212	+	0.901218i
$786$	−1.69259	+	3.41418i	−0.0603725	+	0.121780i
$787$	−2.49296	−	14.1383i	−0.0888646	−	0.503976i	−0.996456	−	0.0841207i	$-0.973192\pi$
$787$	−2.49296	−	14.1383i	−0.0888646	−	0.503976i	0.907591	−	0.419855i	$-0.137919\pi$
$788$	−0.485918	−	0.611585i	−0.0173101	−	0.0217868i
$789$	4.96702	+	30.0162i	0.176830	+	1.06861i
$790$	−18.4830	+	38.2918i	−0.657595	+	1.36236i
$791$	13.7754	−	23.8596i	0.489796	−	0.848351i
$792$	−7.30415	+	21.8222i	−0.259541	+	0.775417i
$793$	0.912701	+	1.58084i	0.0324110	+	0.0561374i
$794$	−26.9595	+	1.99585i	−0.956755	+	0.0708300i
$795$	61.2755	+	0.645940i	2.17322	+	0.0229091i
$796$	−2.13369	−	14.3317i	−0.0756267	−	0.507975i
$797$	−16.5677	+	13.9019i	−0.586857	+	0.492431i	−0.887191	−	0.461403i	$-0.847346\pi$
$797$	−16.5677	+	13.9019i	−0.586857	+	0.492431i	0.300334	+	0.953834i	$0.402902\pi$
$798$	4.40965	+	18.1856i	0.156100	+	0.643765i
$799$	2.21295	+	6.08002i	0.0782884	+	0.215096i
$800$	−24.9783	−	28.5628i	−0.883116	−	1.00985i
$801$	−16.7779	+	2.59497i	−0.592817	+	0.0916889i
$802$	−18.9537	+	18.4536i	−0.669280	+	0.651619i
$803$	39.2092	+	6.91364i	1.38366	+	0.243977i
$804$	13.8820	+	17.8553i	0.489579	+	0.629709i
$805$	−3.09078	+	8.49184i	−0.108936	+	0.299298i
$806$	10.3580	+	1.04592i	0.364845	+	0.0368411i
$807$	41.2365	−	14.5185i	1.45159	−	0.511074i
$808$	36.8455	−	1.73881i	1.29622	−	0.0611713i
$809$			27.7706i			0.976363i	0.872742	+	0.488182i	$0.162340\pi$
$809$			27.7706i			0.976363i	−0.872742	+	0.488182i	$0.837660\pi$
$810$	1.38170	+	43.5284i	0.0485482	+	1.52943i
$811$	−6.91746			−0.242905			−0.121452	−	0.992597i	$-0.538755\pi$
$811$	−6.91746			−0.242905			−0.121452	+	0.992597i	$0.538755\pi$
$812$	50.3434	−	16.8134i	1.76671	−	0.590033i
$813$	16.2657	+	46.1990i	0.570462	+	1.62027i
$814$	−43.0943	−	4.35155i	−1.51045	−	0.152522i
$815$	−63.0848	−	22.9610i	−2.20976	−	0.804288i
$816$	34.2582	−	3.80145i	1.19928	−	0.133077i
$817$	2.97969	−	16.8987i	0.104246	−	0.591209i
$818$	−18.2867	−	18.7823i	−0.639380	−	0.656709i
$819$	−20.2632	−	7.86279i	−0.708052	−	0.274748i
$820$	32.3702	+	0.865772i	1.13042	+	0.0302341i
$821$	6.71754	−	2.44498i	0.234444	−	0.0853305i	−0.222127	−	0.975018i	$-0.571300\pi$
$821$	6.71754	−	2.44498i	0.234444	−	0.0853305i	0.456570	+	0.889687i	$0.349078\pi$
$822$	−0.500422	−	2.06377i	−0.0174542	−	0.0719822i
$823$	1.29022	+	1.53762i	0.0449742	+	0.0535981i	0.788063	−	0.615595i	$-0.211084\pi$
$823$	1.29022	+	1.53762i	0.0449742	+	0.0535981i	−0.743088	+	0.669193i	$0.766640\pi$
$824$	−3.46702	−	0.444019i	−0.120779	−	0.0154681i
$825$	−0.332124	+	31.5061i	−0.0115631	+	1.09690i
$826$	2.62575	+	35.4680i	0.0913615	+	1.23409i
$827$	−22.7464	+	13.1326i	−0.790969	+	0.456666i	−0.840303	−	0.542116i	$-0.817623\pi$
$827$	−22.7464	+	13.1326i	−0.790969	+	0.456666i	0.0493347	+	0.998782i	$0.484290\pi$
$828$	4.85207	−	2.50005i	0.168621	−	0.0868828i
$829$	−36.0689	−	20.8244i	−1.25272	−	0.723260i	−0.281074	−	0.959686i	$-0.590691\pi$
$829$	−36.0689	−	20.8244i	−1.25272	−	0.723260i	−0.971649	+	0.236426i	$0.924024\pi$
$830$	−10.3156	+	21.3711i	−0.358059	+	0.741802i
$831$	18.5863	−	3.07562i	0.644752	−	0.106692i
$832$	−18.1529	−	8.30958i	−0.629338	−	0.288083i
$833$	6.99928	−	1.23416i	0.242511	−	0.0427611i
$834$	33.3336	+	16.5252i	1.15425	+	0.572220i
$835$	29.8581	+	25.0539i	1.03328	+	0.867027i
$836$	7.46422	−	12.1652i	0.258155	−	0.420742i
$837$	−5.69521	+	14.2305i	−0.196855	+	0.491877i
$838$	−30.5693	−	8.63066i	−1.05600	−	0.298141i
$839$	17.8040	+	14.9393i	0.614662	+	0.515762i	0.896120	−	0.443811i	$-0.146374\pi$
$839$	17.8040	+	14.9393i	0.614662	+	0.515762i	−0.281459	+	0.959573i	$0.590818\pi$
$840$	1.78151	+	48.6324i	0.0614680	+	1.67798i
$841$	9.47417	+	53.7307i	0.326696	+	1.85278i
$842$	−20.0653	−	14.4535i	−0.691496	−	0.498100i
$843$	−6.39167	−	7.78245i	−0.220141	−	0.268042i
$844$	29.6079	−	33.4279i	1.01915	−	1.15064i
$845$	−11.5861	+	20.0677i	−0.398574	+	0.690350i
$846$	4.91739	+	2.50272i	0.169063	+	0.0860454i
$847$	−9.16452	+	5.29114i	−0.314897	+	0.181806i
$848$	−30.2169	−	28.2410i	−1.03765	−	0.969799i
$849$	−8.02613	+	13.5693i	−0.275456	+	0.465697i
$850$	43.0350	−	19.3714i	1.47609	−	0.664432i
$851$	6.60374	+	7.87003i	0.226373	+	0.269781i
$852$	31.7380	−	16.7788i	1.08733	−	0.574834i
$853$	0.546744	+	1.50217i	0.0187202	+	0.0514332i	0.948701	−	0.316175i	$-0.102399\pi$
$853$	0.546744	+	1.50217i	0.0187202	+	0.0514332i	−0.929981	+	0.367609i	$0.880177\pi$
$854$	−2.91100	+	0.738433i	−0.0996125	+	0.0252687i
$855$	5.25010	−	26.4957i	0.179550	−	0.906134i
$856$	44.0898	−	9.93761i	1.50696	−	0.339660i
$857$	−21.3303	−	3.76110i	−0.728629	−	0.128477i	−0.202985	−	0.979182i	$-0.565064\pi$
$857$	−21.3303	−	3.76110i	−0.728629	−	0.128477i	−0.525644	+	0.850705i	$0.676175\pi$
$858$	6.64493	+	15.1880i	0.226854	+	0.518508i
$859$	−13.9293	−	5.06987i	−0.475263	−	0.172982i	0.0932719	−	0.995641i	$-0.470267\pi$
$859$	−13.9293	−	5.06987i	−0.475263	−	0.172982i	−0.568535	+	0.822659i	$0.692490\pi$
$860$	16.3785	−	41.5111i	0.558502	−	1.41552i
$861$	−18.0653	−	15.4860i	−0.615663	−	0.527761i
$862$	−15.3602	+	10.4521i	−0.523171	+	0.356000i
$863$	−37.5749			−1.27907			−0.639533	−	0.768764i	$-0.720872\pi$
$863$	−37.5749			−1.27907			−0.639533	+	0.768764i	$0.720872\pi$
$864$	19.1452	−	22.3039i	0.651331	−	0.758793i
$865$	−54.1932			−1.84262
$866$	−26.4949	+	18.0289i	−0.900332	+	0.612645i
$867$	−2.47068	+	13.1969i	−0.0839087	+	0.448191i
$868$	−6.28633	+	15.9326i	−0.213372	+	0.540788i
$869$	−22.3930	−	8.15037i	−0.759629	−	0.276482i
$870$	−76.1410	−	8.50021i	−2.58142	−	0.288184i
$871$	16.0457	+	2.82929i	0.543688	+	0.0958668i
$872$	6.57273	−	1.48146i	0.222581	−	0.0501685i
$873$	−0.209651	+	0.346066i	−0.00709560	+	0.0117126i
$874$	−3.28141	+	0.832395i	−0.110995	+	0.0281562i
$875$	5.80168	+	15.9400i	0.196133	+	0.538870i
$876$	−43.0637	−	27.0516i	−1.45499	−	0.913988i
$877$	−25.3049	−	30.1572i	−0.854484	−	1.01833i	−0.999582	−	0.0289176i	$-0.990794\pi$
$877$	−25.3049	−	30.1572i	−0.854484	−	1.01833i	0.145097	−	0.989417i	$-0.453650\pi$
$878$	19.5090	−	8.78158i	0.658396	−	0.296364i
$879$	−3.44869	−	6.12144i	−0.116322	−	0.206471i
$880$	25.3448	−	27.1180i	0.854372	−	0.914148i
$881$	22.6325	−	13.0669i	0.762509	−	0.440235i	−0.0676867	−	0.997707i	$-0.521562\pi$
$881$	22.6325	−	13.0669i	0.762509	−	0.440235i	0.830196	+	0.557472i	$0.188228\pi$
$882$	3.64533	−	4.84210i	0.122745	−	0.163042i
$883$	−24.4508	+	42.3501i	−0.822837	+	1.42519i	0.0807251	+	0.996736i	$0.474276\pi$
$883$	−24.4508	+	42.3501i	−0.822837	+	1.42519i	−0.903562	+	0.428458i	$0.859057\pi$
$884$	16.4641	−	18.5883i	0.553746	−	0.625191i
$885$	18.0657	−	48.0528i	0.607271	−	1.61528i
$886$	4.56781	+	3.29029i	0.153459	+	0.110540i
$887$	−2.89846	−	16.4380i	−0.0973207	−	0.551933i	−0.994011	−	0.109276i	$-0.965147\pi$
$887$	−2.89846	−	16.4380i	−0.0973207	−	0.551933i	0.896691	−	0.442658i	$-0.145964\pi$
$888$	48.8936	+	25.8901i	1.64076	+	0.868814i
$889$	10.1203	+	8.49198i	0.339425	+	0.284812i
$890$	26.3539	+	7.44052i	0.883384	+	0.249407i
$891$	−24.1945	+	3.22142i	−0.810546	+	0.107922i
$892$	−8.32427	+	13.5669i	−0.278717	+	0.454254i
$893$	−2.62152	−	2.19972i	−0.0877259	−	0.0736108i
$894$	−1.32524	−	20.8895i	−0.0443227	−	0.698651i
$895$	−53.1394	+	9.36990i	−1.77625	+	0.313201i
$896$	21.2716	−	25.0275i	0.710635	−	0.836109i
$897$	1.38375	−	3.68064i	0.0462022	−	0.122893i
$898$	15.8783	−	32.8955i	0.529864	−	1.09774i
$899$	−23.3522	−	13.4824i	−0.778838	−	0.449663i
$900$	15.5570	−	37.1174i	0.518566	−	1.23725i
$901$	44.5501	−	25.7210i	1.48418	−	0.856890i
$902$	1.33989	+	18.0990i	0.0446136	+	0.602630i
$903$	−28.5691	+	16.0953i	−0.950721	+	0.535617i
$904$	26.6237	+	3.40968i	0.885492	+	0.113404i
$905$	−11.1527	−	13.2913i	−0.370729	−	0.441818i
$906$	−24.6908	−	7.25286i	−0.820297	−	0.240960i
$907$	9.94085	−	3.61817i	0.330081	−	0.120140i	−0.171663	−	0.985156i	$-0.554914\pi$
$907$	9.94085	−	3.61817i	0.330081	−	0.120140i	0.501744	+	0.865016i	$0.332692\pi$
$908$	−17.2718	−	0.461952i	−0.573186	−	0.0153304i
$909$	18.8434	+	34.2873i	0.624996	+	1.13724i
$910$	24.4564	+	25.1192i	0.810721	+	0.832694i
$911$	−10.2298	+	58.0158i	−0.338927	+	1.92215i	0.0454332	+	0.998967i	$0.485533\pi$
$911$	−10.2298	+	58.0158i	−0.338927	+	1.92215i	−0.384360	+	0.923183i	$0.625578\pi$
$912$	−14.6866	+	10.8010i	−0.486323	+	0.357657i
$913$	−12.4978	−	4.54882i	−0.413616	−	0.150544i
$914$	3.94695	+	0.398553i	0.130554	+	0.0131830i
$915$	4.26095	+	0.797721i	0.140863	+	0.0263719i
$916$	−14.4776	+	4.83513i	−0.478354	+	0.159757i
$917$	−4.51655			−0.149150
$918$	19.6014	+	30.8605i	0.646942	+	1.01855i
$919$		−	25.4259i		−	0.838724i	−0.907819	−	0.419362i	$-0.862254\pi$
$919$		−	25.4259i		−	0.838724i	0.907819	−	0.419362i	$-0.137746\pi$
$920$	−8.79430	+	0.415021i	−0.289939	+	0.0136828i
$921$	44.2843	+	37.9615i	1.45922	+	1.25087i
$922$	−21.1449	−	2.13516i	−0.696370	−	0.0703176i
$923$	8.84554	−	24.3029i	0.291155	−	0.799941i
$924$	−27.0180	+	3.73175i	−0.888829	+	0.122765i
$925$	74.5997	+	13.1539i	2.45282	+	0.432499i
$926$	22.1607	−	21.5759i	0.728244	−	0.709027i
$927$	−1.19427	−	3.50974i	−0.0392250	−	0.115275i
$928$	34.0402	+	38.9252i	1.11743	+	1.27778i
$929$	−1.65289	−	4.54128i	−0.0542296	−	0.148995i	0.909620	−	0.415441i	$-0.136373\pi$
$929$	−1.65289	−	4.54128i	−0.0542296	−	0.148995i	−0.963850	+	0.266446i	$0.914151\pi$
$930$	17.8951	−	17.0591i	0.586802	−	0.559390i
$931$	−2.87963	+	2.41630i	−0.0943760	+	0.0791909i
$932$	2.09360	+	14.0624i	0.0685782	+	0.460631i
$933$	10.8156	−	18.2852i	0.354085	−	0.598631i
$934$	−26.4001	+	1.95444i	−0.863837	+	0.0639511i
$935$	23.0832	+	39.9813i	0.754902	+	1.30753i
$936$	−0.552080	−	21.1682i	−0.0180453	−	0.691905i
$937$	25.7048	−	44.5220i	0.839738	−	1.45447i	−0.0503753	−	0.998730i	$-0.516042\pi$
$937$	25.7048	−	44.5220i	0.839738	−	1.45447i	0.890114	−	0.455739i	$-0.150625\pi$
$938$	−11.6525	+	24.1409i	−0.380468	+	0.788229i
$939$	7.14491	−	5.86807i	0.233165	−	0.191497i
$940$	−5.53637	−	6.96817i	−0.180577	−	0.227277i
$941$	6.83831	+	38.7820i	0.222922	+	1.26426i	0.866617	+	0.498973i	$0.166289\pi$
$941$	6.83831	+	38.7820i	0.222922	+	1.26426i	−0.643695	+	0.765282i	$0.722599\pi$
$942$	13.0685	+	19.6474i	0.425796	+	0.640147i
$943$	2.76699	−	3.29758i	0.0901057	−	0.107384i
$944$	−30.8902	+	15.6958i	−1.00539	+	0.510855i
$945$	−45.4953	+	24.3822i	−1.47996	+	0.793154i
$946$	24.0696	+	6.79561i	0.782571	+	0.220944i
$947$	18.2848	−	21.7910i	0.594178	−	0.708113i	−0.382226	−	0.924069i	$-0.624842\pi$
$947$	18.2848	−	21.7910i	0.594178	−	0.708113i	0.976403	+	0.215956i	$0.0692867\pi$
$948$	22.5719	+	20.4211i	0.733103	+	0.663247i
$949$	−36.0798	+	6.36183i	−1.17120	+	0.206514i
$950$	−14.5893	+	20.2538i	−0.473338	+	0.657120i
$951$	0.00412388	+	0.0249211i	0.000133726	+	0.000808121i
$952$	22.0716	+	34.3775i	0.715343	+	1.11418i
$953$	−24.5811	−	14.1919i	−0.796261	−	0.459722i	0.0459008	−	0.998946i	$-0.485384\pi$
$953$	−24.5811	−	14.1919i	−0.796261	−	0.459722i	−0.842162	+	0.539224i	$0.818718\pi$
$954$	12.8068	−	41.9574i	0.414636	−	1.35842i
$955$	−42.7143	−	73.9833i	−1.38220	−	2.39404i
$956$	4.36017	+	0.889627i	0.141018	+	0.0287726i
$957$	0.452616	−	42.9363i	0.0146310	−	1.38793i
$958$	−11.6465	−	25.8736i	−0.376282	−	0.835939i
$959$	1.92807	−	1.61784i	0.0622605	−	0.0522428i
$960$	−43.0393	+	19.8868i	−1.38909	+	0.641843i
$961$	−20.9537	+	7.62652i	−0.675925	+	0.246017i
$962$	38.6328	−	9.79998i	1.24557	−	0.315964i
$963$	30.0326	+	37.3636i	0.967788	+	1.20403i
$964$	0.358973	−	0.194647i	0.0115618	−	0.00626914i
$965$	−5.59727	+	31.7437i	−0.180183	+	1.02187i
$966$	5.20911	+	3.83628i	0.167600	+	0.123430i
$967$	−14.1101	+	38.7671i	−0.453749	+	1.24667i	0.476317	+	0.879274i	$0.341972\pi$
$967$	−14.1101	+	38.7671i	−0.453749	+	1.24667i	−0.930066	+	0.367392i	$0.880251\pi$
$968$	−8.20133	−	6.24731i	−0.263601	−	0.200796i
$969$	−7.53023	−	21.3880i	−0.241906	−	0.687081i
$970$	0.539567	−	0.367157i	0.0173245	−	0.0117887i
$971$			5.59715i			0.179621i	0.995959	+	0.0898105i	$0.0286261\pi$
$971$			5.59715i			0.179621i	−0.995959	+	0.0898105i	$0.971374\pi$
$972$	30.1768	+	7.83341i	0.967920	+	0.251257i
$973$			44.0963i			1.41366i
$974$	−11.2177	−	16.4853i	−0.359437	−	0.528222i
$975$	−9.62849	−	27.3476i	−0.308358	−	0.875825i
$976$	−1.75821	−	2.33866i	−0.0562788	−	0.0748587i
$977$	7.61083	−	20.9106i	0.243492	−	0.668989i	−0.756397	−	0.654112i	$-0.773042\pi$
$977$	7.61083	−	20.9106i	0.243492	−	0.668989i	0.999889	−	0.0148763i	$-0.00473544\pi$
$978$	−28.4992	+	38.6978i	−0.911304	+	1.23742i
$979$	−2.66507	+	15.1144i	−0.0851762	+	0.483058i
$980$	−8.59398	+	4.65993i	−0.274525	+	0.148856i
$981$	4.47714	+	5.57002i	0.142944	+	0.177837i
$982$	−0.779681	−	3.07361i	−0.0248806	−	0.0980827i
$983$	43.7402	−	15.9201i	1.39510	−	0.507774i	0.468378	−	0.883528i	$-0.344839\pi$
$983$	43.7402	−	15.9201i	1.39510	−	0.507774i	0.926719	+	0.375755i	$0.122617\pi$
$984$	7.12578	−	22.0591i	0.227162	−	0.703219i
$985$	−1.02371	+	0.858996i	−0.0326182	+	0.0273699i
$986$	−58.6477	+	26.3991i	−1.86772	+	0.840720i
$987$	−0.0689344	+	6.53929i	−0.00219421	+	0.208148i
$988$	−2.62559	+	12.8683i	−0.0835311	+	0.409396i
$989$	−2.96615	−	5.13752i	−0.0943180	−	0.163364i
$990$	37.6545	+	11.4934i	1.19674	+	0.365285i
$991$	38.1847	+	22.0460i	1.21298	+	0.700313i	0.963407	−	0.268044i	$-0.0863772\pi$
$991$	38.1847	+	22.0460i	1.21298	+	0.700313i	0.249571	+	0.968357i	$0.419711\pi$
$992$	−16.6833	+	0.340679i	−0.529696	+	0.0108166i
$993$	1.07983	+	6.52552i	0.0342673	+	0.207081i
$994$	34.5255	+	24.8694i	1.09508	+	0.788811i
$995$	−24.4127	+	4.30461i	−0.773933	+	0.136465i
$996$	12.5977	+	11.3973i	0.399173	+	0.361136i
$997$	−13.4946	+	16.0822i	−0.427378	+	0.509330i	−0.936164	−	0.351563i	$-0.885650\pi$
$997$	−13.4946	+	16.0822i	−0.427378	+	0.509330i	0.508786	+	0.860893i	$0.330095\pi$
$998$	−3.55943	+	12.6073i	−0.112672	+	0.399077i
$999$	−1.85540	+	58.6519i	−0.0587023	+	1.85566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.27	yes	192
3.2	odd	2		648.2.v.b.35.6		192
4.3	odd	2		864.2.bh.b.335.27		192
8.3	odd	2	inner	216.2.v.b.11.21	✓	192
8.5	even	2		864.2.bh.b.335.28		192
24.11	even	2		648.2.v.b.35.12		192
27.5	odd	18	inner	216.2.v.b.59.21	yes	192
27.22	even	9		648.2.v.b.611.12		192
108.59	even	18		864.2.bh.b.815.28		192
216.5	odd	18		864.2.bh.b.815.27		192
216.59	even	18	inner	216.2.v.b.59.27	yes	192
216.211	odd	18		648.2.v.b.611.6		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.21	✓	192	8.3	odd	2	inner
216.2.v.b.11.27	yes	192	1.1	even	1	trivial
216.2.v.b.59.21	yes	192	27.5	odd	18	inner
216.2.v.b.59.27	yes	192	216.59	even	18	inner
648.2.v.b.35.6		192	3.2	odd	2
648.2.v.b.35.12		192	24.11	even	2
648.2.v.b.611.6		192	216.211	odd	18
648.2.v.b.611.12		192	27.22	even	9
864.2.bh.b.335.27		192	4.3	odd	2
864.2.bh.b.335.28		192	8.5	even	2
864.2.bh.b.815.27		192	216.5	odd	18
864.2.bh.b.815.28		192	108.59	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16920 - 0.795599i) q^{2} +(-1.63375 + 0.575207i) q^{3} +(0.734044 - 1.86042i) q^{4} +(-3.21529 - 1.17027i) q^{5} +(-1.45254 + 1.97234i) q^{6} +(-2.85909 - 0.504135i) q^{7} +(-0.621910 - 2.75921i) q^{8} +(2.33827 - 1.87949i) q^{9} +(-4.69037 + 1.18981i) q^{10} +(-0.927560 - 2.54845i) q^{11} +(-0.129115 + 3.46169i) q^{12} +(1.60411 + 1.91170i) q^{13} +(-3.74393 + 1.68526i) q^{14} +(5.92612 + 0.0624707i) q^{15} +(-2.92236 - 2.73127i) q^{16} +(4.30856 - 2.48755i) q^{17} +(1.23858 - 4.05782i) q^{18} +(-1.31569 + 2.27884i) q^{19} +(-4.53736 + 5.12277i) q^{20} +(4.96102 - 0.820939i) q^{21} +(-3.11204 - 2.24167i) q^{22} +(0.157970 + 0.895893i) q^{23} +(2.60316 + 4.15013i) q^{24} +(5.13833 + 4.31157i) q^{25} +(3.39646 + 0.958928i) q^{26} +(-2.73906 + 4.41560i) q^{27} +(-3.03660 + 4.94907i) q^{28} +(-7.00248 - 5.87578i) q^{29} +(6.97851 - 4.64178i) q^{30} +(2.90502 - 0.512234i) q^{31} +(-5.58981 - 0.868362i) q^{32} +(2.98129 + 3.62999i) q^{33} +(3.05847 - 6.33633i) q^{34} +(8.60284 + 4.96685i) q^{35} +(-1.78025 - 5.72981i) q^{36} +(9.78021 - 5.64661i) q^{37} +(0.274743 + 3.71117i) q^{38} +(-3.72033 - 2.20055i) q^{39} +(-1.22939 + 9.59946i) q^{40} +(-3.04161 - 3.62485i) q^{41} +(5.14728 - 4.90683i) q^{42} +(-6.12779 + 2.23033i) q^{43} +(-5.42207 - 0.145018i) q^{44} +(-9.71774 + 3.30669i) q^{45} +(0.897470 + 0.921795i) q^{46} +(-0.225833 + 1.28076i) q^{47} +(6.34545 + 2.78124i) q^{48} +(1.34241 + 0.488598i) q^{49} +(9.43801 + 0.953026i) q^{50} +(-5.60826 + 6.54235i) q^{51} +(4.73406 - 1.58105i) q^{52} +10.3399 q^{53} +(0.310550 + 7.34190i) q^{54} +9.27950i q^{55} +(0.387086 + 8.20236i) q^{56} +(0.838700 - 4.47984i) q^{57} +(-12.8621 - 1.29878i) q^{58} +(2.96267 - 8.13988i) q^{59} +(4.46626 - 10.9793i) q^{60} +(0.720351 + 0.127017i) q^{61} +(2.98901 - 2.91014i) q^{62} +(-7.63286 + 4.19482i) q^{63} +(-7.22645 + 3.43196i) q^{64} +(-2.92046 - 8.02391i) q^{65} +(6.37373 + 1.87226i) q^{66} +(5.00144 - 4.19671i) q^{67} +(-1.46523 - 9.84173i) q^{68} +(-0.773408 - 1.37280i) q^{69} +(14.0100 - 1.03718i) q^{70} +(-5.18176 - 8.97507i) q^{71} +(-6.64009 - 5.28291i) q^{72} +(-7.34034 + 12.7138i) q^{73} +(6.94256 - 14.3831i) q^{74} +(-10.8748 - 4.08843i) q^{75} +(3.27383 + 4.12050i) q^{76} +(1.36722 + 7.75387i) q^{77} +(-6.10055 + 0.387021i) q^{78} +(5.64811 - 6.73115i) q^{79} +(6.19991 + 12.2018i) q^{80} +(1.93505 - 8.78952i) q^{81} +(-6.44017 - 1.81826i) q^{82} +(3.15228 - 3.75674i) q^{83} +(2.11431 - 9.83222i) q^{84} +(-16.7644 + 2.95601i) q^{85} +(-5.39014 + 7.48296i) q^{86} +(14.8201 + 5.57168i) q^{87} +(-6.45484 + 4.14424i) q^{88} +(-4.90094 - 2.82956i) q^{89} +(-8.73115 + 11.5976i) q^{90} +(-3.62253 - 6.27441i) q^{91} +(1.78270 + 0.363733i) q^{92} +(-4.45144 + 2.50785i) q^{93} +(0.754930 + 1.67714i) q^{94} +(6.89717 - 5.78741i) q^{95} +(9.63183 - 1.79661i) q^{96} +(-0.126739 + 0.0461291i) q^{97} +(1.95827 - 0.496754i) q^{98} +(-6.95867 - 4.21564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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