LMFDB - Embedded newform 234.2.z.a.227.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(41,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("234.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			227.12
Character	$\chi$	$=$	234.227
Dual form			234.2.z.a.167.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.612305 - 1.62021i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.266463 - 0.994452i) q^{5} +(-1.40653 - 1.01078i) q^{6} +(-0.248284 - 0.248284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.25016 - 1.98413i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.612305 - 1.62021i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.266463 - 0.994452i) q^{5} +(-1.40653 - 1.01078i) q^{6} +(-0.248284 - 0.248284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.25016 - 1.98413i) q^{9} +(-0.891601 - 0.514766i) q^{10} +(3.50922 + 0.940292i) q^{11} +(-1.34038 + 1.09699i) q^{12} +(-3.13452 - 1.78180i) q^{13} +(-0.304085 + 0.175564i) q^{14} +(-1.44807 - 1.04063i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.67236 + 2.89660i) q^{17} +(-2.49890 + 1.65996i) q^{18} +(-0.969723 - 0.259837i) q^{19} +(-0.727989 + 0.727989i) q^{20} +(-0.554299 + 0.250247i) q^{21} +(1.81650 - 3.14628i) q^{22} +1.47052 q^{23} +(0.712697 + 1.57863i) q^{24} +(3.41219 + 1.97003i) q^{25} +(-2.53236 + 2.56655i) q^{26} +(-4.59249 + 2.43085i) q^{27} +(0.0908784 + 0.339163i) q^{28} +(5.04092 - 2.91038i) q^{29} +(-1.37996 + 1.12939i) q^{30} +(-5.54424 - 1.48558i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.67218 - 5.10993i) q^{33} +(3.23074 - 0.865675i) q^{34} +(-0.313065 + 0.180748i) q^{35} +(0.956637 + 2.84339i) q^{36} +(4.96682 - 1.33085i) q^{37} +(-0.501966 + 0.869430i) q^{38} +(-4.80617 + 3.98757i) q^{39} +(0.514766 + 0.891601i) q^{40} +(6.60980 + 6.60980i) q^{41} +(0.0982571 + 0.600180i) q^{42} -2.73886i q^{43} +(-2.56893 - 2.56893i) q^{44} +(-2.57270 + 1.70899i) q^{45} +(0.380599 - 1.42041i) q^{46} +(2.19251 + 8.18256i) q^{47} +(1.70930 - 0.279834i) q^{48} -6.87671i q^{49} +(2.78605 - 2.78605i) q^{50} +(5.71710 - 0.935962i) q^{51} +(1.82367 + 3.11034i) q^{52} -2.67501i q^{53} +(1.15940 + 5.06516i) q^{54} +(1.87015 - 3.23920i) q^{55} +0.351127 q^{56} +(-1.01476 + 1.41206i) q^{57} +(-1.50652 - 5.62241i) q^{58} +(1.25408 + 4.68030i) q^{59} +(0.733745 + 1.62525i) q^{60} +5.72649 q^{61} +(-2.86991 + 4.97083i) q^{62} +(0.0660532 + 1.05131i) q^{63} -1.00000i q^{64} +(-2.60715 + 2.64234i) q^{65} +(-3.98538 - 4.86960i) q^{66} +(-10.6589 + 10.6589i) q^{67} -3.34471i q^{68} +(0.900407 - 2.38255i) q^{69} +(0.0935622 + 0.349179i) q^{70} +(1.53985 - 5.74681i) q^{71} +(2.99410 - 0.188118i) q^{72} +(2.47165 + 2.47165i) q^{73} -5.14203i q^{74} +(5.28117 - 4.32221i) q^{75} +(0.709887 + 0.709887i) q^{76} +(-0.637824 - 1.10474i) q^{77} +(2.60777 + 5.67446i) q^{78} +(-1.76544 + 3.05783i) q^{79} +(0.994452 - 0.266463i) q^{80} +(1.12648 + 8.92922i) q^{81} +(8.09532 - 4.67384i) q^{82} +(-8.34680 + 2.23652i) q^{83} +(0.605160 + 0.0604289i) q^{84} +(3.32615 - 0.891240i) q^{85} +(-2.64553 - 0.708868i) q^{86} +(-1.62884 - 9.94939i) q^{87} +(-3.14628 + 1.81650i) q^{88} +(2.68520 + 10.0213i) q^{89} +(0.984889 + 2.92736i) q^{90} +(0.335858 + 1.22064i) q^{91} +(-1.27351 - 0.735260i) q^{92} +(-5.80171 + 8.07321i) q^{93} +8.47121 q^{94} +(-0.516790 + 0.895107i) q^{95} +(0.172100 - 1.72348i) q^{96} +(-10.4441 + 10.4441i) q^{97} +(-6.64239 - 1.77982i) q^{98} +(-6.03066 - 9.07854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7}+O(q^{10}) $ 56 * q - 8 * q^7	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	0.612305	−	1.62021i	0.353515	−	0.935429i
$3$	0.612305	−	1.62021i	0.353515	−	0.935429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.266463	−	0.994452i	0.119166	−	0.444732i	−0.880399	−	0.474234i	$-0.842725\pi$
$5$	0.266463	−	0.994452i	0.119166	−	0.444732i	0.999565	+	0.0295011i	$0.00939187\pi$
$6$	−1.40653	−	1.01078i	−0.574212	−	0.412650i
$7$	−0.248284	−	0.248284i	−0.0938426	−	0.0938426i	0.658627	−	0.752470i	$-0.271138\pi$
$7$	−0.248284	−	0.248284i	−0.0938426	−	0.0938426i	−0.752470	+	0.658627i	$0.771138\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.25016	−	1.98413i	−0.750055	−	0.661375i
$10$	−0.891601	−	0.514766i	−0.281949	−	0.162783i
$11$	3.50922	+	0.940292i	1.05807	+	0.283509i	0.745582	−	0.666413i	$-0.232171\pi$
$11$	3.50922	+	0.940292i	1.05807	+	0.283509i	0.312487	+	0.949922i	$0.398838\pi$
$12$	−1.34038	+	1.09699i	−0.386934	+	0.316674i
$13$	−3.13452	−	1.78180i	−0.869358	−	0.494182i
$13$	−3.13452	−	1.78180i	−0.869358	−	0.494182i
$14$	−0.304085	+	0.175564i	−0.0812701	+	0.0469213i
$15$	−1.44807	−	1.04063i	−0.373889	−	0.268690i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.67236	+	2.89660i	0.405606	+	0.702530i	0.994392	−	0.105759i	$-0.0337273\pi$
$17$	1.67236	+	2.89660i	0.405606	+	0.702530i	−0.588786	+	0.808289i	$0.700394\pi$
$18$	−2.49890	+	1.65996i	−0.588997	+	0.391257i
$19$	−0.969723	−	0.259837i	−0.222470	−	0.0596106i	0.145862	−	0.989305i	$-0.453404\pi$
$19$	−0.969723	−	0.259837i	−0.222470	−	0.0596106i	−0.368332	+	0.929694i	$0.620071\pi$
$20$	−0.727989	+	0.727989i	−0.162783	+	0.162783i
$21$	−0.554299	+	0.250247i	−0.120958	+	0.0546084i
$22$	1.81650	−	3.14628i	0.387280	−	0.670789i
$23$	1.47052			0.306625			0.153312	−	0.988178i	$-0.451006\pi$
$23$	1.47052			0.306625			0.153312	+	0.988178i	$0.451006\pi$
$24$	0.712697	+	1.57863i	0.145479	+	0.322236i
$25$	3.41219	+	1.97003i	0.682439	+	0.394006i
$26$	−2.53236	+	2.56655i	−0.496636	+	0.503341i
$27$	−4.59249	+	2.43085i	−0.883825	+	0.467817i
$28$	0.0908784	+	0.339163i	0.0171744	+	0.0640957i
$29$	5.04092	−	2.91038i	0.936075	−	0.540443i	0.0473474	−	0.998878i	$-0.484923\pi$
$29$	5.04092	−	2.91038i	0.936075	−	0.540443i	0.888728	+	0.458435i	$0.151590\pi$
$30$	−1.37996	+	1.12939i	−0.251945	+	0.206197i
$31$	−5.54424	−	1.48558i	−0.995775	−	0.266817i	−0.276101	−	0.961129i	$-0.589042\pi$
$31$	−5.54424	−	1.48558i	−0.995775	−	0.266817i	−0.719675	+	0.694312i	$0.755709\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	3.67218	−	5.10993i	0.639245	−	0.889524i
$34$	3.23074	−	0.865675i	0.554068	−	0.148462i
$35$	−0.313065	+	0.180748i	−0.0529177	+	0.0305520i
$36$	0.956637	+	2.84339i	0.159439	+	0.473898i
$37$	4.96682	−	1.33085i	0.816540	−	0.218791i	0.173707	−	0.984797i	$-0.444426\pi$
$37$	4.96682	−	1.33085i	0.816540	−	0.218791i	0.642833	+	0.766006i	$0.277759\pi$
$38$	−0.501966	+	0.869430i	−0.0814296	+	0.141040i
$39$	−4.80617	+	3.98757i	−0.769603	+	0.638522i
$40$	0.514766	+	0.891601i	0.0813917	+	0.140975i
$41$	6.60980	+	6.60980i	1.03228	+	1.03228i	0.999461	+	0.0328164i	$0.0104476\pi$
$41$	6.60980	+	6.60980i	1.03228	+	1.03228i	0.0328164	+	0.999461i	$0.489552\pi$
$42$	0.0982571	+	0.600180i	0.0151614	+	0.0926098i
$43$		−	2.73886i		−	0.417672i	−0.977951	−	0.208836i	$-0.933033\pi$
$43$		−	2.73886i		−	0.417672i	0.977951	−	0.208836i	$-0.0669674\pi$
$44$	−2.56893	−	2.56893i	−0.387280	−	0.387280i
$45$	−2.57270	+	1.70899i	−0.383516	+	0.254761i
$46$	0.380599	−	1.42041i	0.0561162	−	0.209429i
$47$	2.19251	+	8.18256i	0.319811	+	1.19355i	0.919427	+	0.393262i	$0.128653\pi$
$47$	2.19251	+	8.18256i	0.319811	+	1.19355i	−0.599616	+	0.800288i	$0.704680\pi$
$48$	1.70930	−	0.279834i	0.246716	−	0.0403905i
$49$		−	6.87671i		−	0.982387i
$50$	2.78605	−	2.78605i	0.394006	−	0.394006i
$51$	5.71710	−	0.935962i	0.800554	−	0.131061i
$52$	1.82367	+	3.11034i	0.252898	+	0.431327i
$53$		−	2.67501i		−	0.367442i	−0.982978	−	0.183721i	$-0.941186\pi$
$53$		−	2.67501i		−	0.367442i	0.982978	−	0.183721i	$-0.0588142\pi$
$54$	1.15940	+	5.06516i	0.157774	+	0.689280i
$55$	1.87015	−	3.23920i	0.252171	−	0.436773i
$56$	0.351127			0.0469213
$57$	−1.01476	+	1.41206i	−0.134408	+	0.187031i
$58$	−1.50652	−	5.62241i	−0.197816	−	0.738259i
$59$	1.25408	+	4.68030i	0.163268	+	0.609323i	0.998255	+	0.0590536i	$0.0188083\pi$
$59$	1.25408	+	4.68030i	0.163268	+	0.609323i	−0.834987	+	0.550269i	$0.814525\pi$
$60$	0.733745	+	1.62525i	0.0947260	+	0.209819i
$61$	5.72649			0.733202			0.366601	−	0.930378i	$-0.380521\pi$
$61$	5.72649			0.733202			0.366601	+	0.930378i	$0.380521\pi$
$62$	−2.86991	+	4.97083i	−0.364479	+	0.631296i
$63$	0.0660532	+	1.05131i	0.00832192	+	0.132452i
$64$		−	1.00000i		−	0.125000i
$65$	−2.60715	+	2.64234i	−0.323377	+	0.327742i
$66$	−3.98538	−	4.86960i	−0.490566	−	0.599407i
$67$	−10.6589	+	10.6589i	−1.30219	+	1.30219i	−0.375282	+	0.926911i	$0.622454\pi$
$67$	−10.6589	+	10.6589i	−1.30219	+	1.30219i	−0.926911	+	0.375282i	$0.877546\pi$
$68$		−	3.34471i		−	0.405606i
$69$	0.900407	−	2.38255i	0.108396	−	0.286826i
$70$	0.0935622	+	0.349179i	0.0111828	+	0.0417349i
$71$	1.53985	−	5.74681i	0.182747	−	0.682021i	−0.812355	−	0.583164i	$-0.801815\pi$
$71$	1.53985	−	5.74681i	0.182747	−	0.682021i	0.995102	−	0.0988571i	$-0.0315187\pi$
$72$	2.99410	−	0.188118i	0.352858	−	0.0221699i
$73$	2.47165	+	2.47165i	0.289285	+	0.289285i	0.836797	−	0.547513i	$-0.184425\pi$
$73$	2.47165	+	2.47165i	0.289285	+	0.289285i	−0.547513	+	0.836797i	$0.684425\pi$
$74$		−	5.14203i		−	0.597749i
$75$	5.28117	−	4.32221i	0.609817	−	0.499086i
$76$	0.709887	+	0.709887i	0.0814296	+	0.0814296i
$77$	−0.637824	−	1.10474i	−0.0726868	−	0.125897i
$78$	2.60777	+	5.67446i	0.295272	+	0.642506i
$79$	−1.76544	+	3.05783i	−0.198627	+	0.344033i	−0.948084	−	0.318021i	$-0.896982\pi$
$79$	−1.76544	+	3.05783i	−0.198627	+	0.344033i	0.749456	+	0.662054i	$0.230315\pi$
$80$	0.994452	−	0.266463i	0.111183	−	0.0297914i
$81$	1.12648	+	8.92922i	0.125165	+	0.992136i
$82$	8.09532	−	4.67384i	0.893979	−	0.516139i
$83$	−8.34680	+	2.23652i	−0.916181	+	0.245490i	−0.685952	−	0.727647i	$-0.740614\pi$
$83$	−8.34680	+	2.23652i	−0.916181	+	0.245490i	−0.230228	+	0.973137i	$0.573947\pi$
$84$	0.605160	+	0.0604289i	0.0660284	+	0.00659334i
$85$	3.32615	−	0.891240i	0.360772	−	0.0966686i
$86$	−2.64553	−	0.708868i	−0.285275	−	0.0764392i
$87$	−1.62884	−	9.94939i	−0.174630	−	1.06669i
$88$	−3.14628	+	1.81650i	−0.335394	+	0.193640i
$89$	2.68520	+	10.0213i	0.284630	+	1.06225i	0.949109	+	0.314947i	$0.101987\pi$
$89$	2.68520	+	10.0213i	0.284630	+	1.06225i	−0.664479	+	0.747307i	$0.731347\pi$
$90$	0.984889	+	2.92736i	0.103816	+	0.308571i
$91$	0.335858	+	1.22064i	0.0352075	+	0.127958i
$92$	−1.27351	−	0.735260i	−0.132772	−	0.0766562i
$93$	−5.80171	+	8.07321i	−0.601610	+	0.837153i
$94$	8.47121			0.873739
$95$	−0.516790	+	0.895107i	−0.0530215	+	0.0918360i
$96$	0.172100	−	1.72348i	0.0175649	−	0.175902i
$97$	−10.4441	+	10.4441i	−1.06044	+	1.06044i	−0.0623848	+	0.998052i	$0.519871\pi$
$97$	−10.4441	+	10.4441i	−1.06044	+	1.06044i	−0.998052	+	0.0623848i	$0.980129\pi$
$98$	−6.64239	−	1.77982i	−0.670983	−	0.179789i
$99$	−6.03066	−	9.07854i	−0.606104	−	0.912428i
$100$	−1.97003	−	3.41219i	−0.197003	−	0.341219i
$101$	−8.67108	−	15.0187i	−0.862804	−	1.49442i	−0.869211	−	0.494442i	$-0.835373\pi$
$101$	−8.67108	−	15.0187i	−0.862804	−	1.49442i	0.00640634	−	0.999979i	$-0.497961\pi$
$102$	0.575624	−	5.76454i	0.0569953	−	0.570774i
$103$	−9.22402	+	5.32549i	−0.908870	+	0.524736i	−0.880067	−	0.474849i	$-0.842503\pi$
$103$	−9.22402	+	5.32549i	−0.908870	+	0.524736i	−0.0288023	+	0.999585i	$0.509169\pi$
$104$	3.47636	−	0.956515i	0.340885	−	0.0937940i
$105$	0.101159	+	0.617905i	0.00987210	+	0.0603013i
$106$	−2.58387	−	0.692345i	−0.250967	−	0.0672465i
$107$	−0.693025	−	0.400118i	−0.0669973	−	0.0386809i	0.466127	−	0.884718i	$-0.345649\pi$
$107$	−0.693025	−	0.400118i	−0.0669973	−	0.0386809i	−0.533124	+	0.846037i	$0.678982\pi$
$108$	5.19264	+	0.191067i	0.499662	+	0.0183854i
$109$	5.83921	−	5.83921i	0.559294	−	0.559294i	−0.369812	−	0.929107i	$-0.620578\pi$
$109$	5.83921	−	5.83921i	0.559294	−	0.559294i	0.929107	+	0.369812i	$0.120578\pi$
$110$	−2.64479	−	2.64479i	−0.252171	−	0.252171i
$111$	0.884943	−	8.86218i	0.0839950	−	0.841161i
$112$	0.0908784	−	0.339163i	0.00858720	−	0.0320479i
$113$	−11.6846	−	6.74613i	−1.09920	−	0.634623i	−0.163188	−	0.986595i	$-0.552178\pi$
$113$	−11.6846	−	6.74613i	−1.09920	−	0.634623i	−0.936010	+	0.351972i	$0.885511\pi$
$114$	1.10130	+	1.34565i	0.103147	+	0.126031i
$115$	0.391839	−	1.46236i	0.0365391	−	0.136366i
$116$	−5.82075			−0.540443
$117$	3.51786	+	10.2286i	0.325227	+	0.945636i
$118$	4.84540			0.446055
$119$	0.303962	−	1.13440i	0.0278641	−	0.103990i
$120$	1.75978	−	0.288098i	0.160645	−	0.0262996i
$121$	1.90418	+	1.09938i	0.173107	+	0.0999436i
$122$	1.48213	−	5.53137i	0.134185	−	0.500787i
$123$	14.7565	−	6.66206i	1.33055	−	0.600697i
$124$	4.05867	+	4.05867i	0.364479	+	0.364479i
$125$	6.50827	−	6.50827i	0.582117	−	0.582117i
$126$	1.03258	+	0.208296i	0.0919897	+	0.0185565i
$127$	−16.2637	−	9.38987i	−1.44317	−	0.833216i	−0.445112	−	0.895475i	$-0.646836\pi$
$127$	−16.2637	−	9.38987i	−1.44317	−	0.833216i	−0.998060	+	0.0622590i	$0.980170\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	−4.43753	−	1.67702i	−0.390702	−	0.147653i
$130$	1.87753	+	3.20220i	0.164670	+	0.280851i
$131$	−2.91497	+	1.68296i	−0.254682	+	0.147041i	−0.621906	−	0.783092i	$-0.713642\pi$
$131$	−2.91497	+	1.68296i	−0.254682	+	0.147041i	0.367224	+	0.930133i	$0.380308\pi$
$132$	−5.73517	+	2.58923i	−0.499182	+	0.225364i
$133$	0.176254	+	0.305280i	0.0152831	+	0.0264712i
$134$	7.53699	+	13.0544i	0.651096	+	1.12773i
$135$	1.19364	+	5.21474i	0.102732	+	0.448814i
$136$	−3.23074	−	0.865675i	−0.277034	−	0.0742310i
$137$	2.75305	−	2.75305i	0.235209	−	0.235209i	−0.579654	−	0.814863i	$-0.696812\pi$
$137$	2.75305	−	2.75305i	0.235209	−	0.235209i	0.814863	+	0.579654i	$0.196812\pi$
$138$	−2.06833	−	1.48638i	−0.176068	−	0.126529i
$139$	−0.276245	+	0.478471i	−0.0234308	+	0.0405833i	−0.877503	−	0.479571i	$-0.840792\pi$
$139$	−0.276245	+	0.478471i	−0.0234308	+	0.0405833i	0.854072	+	0.520154i	$0.174126\pi$
$140$	0.361497			0.0305520
$141$	14.6000	+	1.45790i	1.22954	+	0.122777i
$142$	−5.15245	−	2.97477i	−0.432384	−	0.249637i
$143$	−9.32429	−	9.20008i	−0.779736	−	0.769350i
$144$	0.593221	−	2.94076i	0.0494351	−	0.245064i
$145$	−1.55101	−	5.78846i	−0.128805	−	0.480705i
$146$	3.02714	−	1.74772i	0.250528	−	0.144642i
$147$	−11.1417	−	4.21064i	−0.918953	−	0.347288i
$148$	−4.96682	−	1.33085i	−0.408270	−	0.109396i
$149$	−12.5052	+	3.35075i	−1.02446	+	0.274504i	−0.731661	−	0.681669i	$-0.761255\pi$
$149$	−12.5052	+	3.35075i	−1.02446	+	0.274504i	−0.292803	+	0.956173i	$0.594588\pi$
$150$	−2.80807	−	6.21989i	−0.229278	−	0.507852i
$151$	−8.72875	+	2.33886i	−0.710336	+	0.190334i	−0.595856	−	0.803092i	$-0.703187\pi$
$151$	−8.72875	+	2.33886i	−0.710336	+	0.190334i	−0.114480	+	0.993426i	$0.536520\pi$
$152$	0.869430	−	0.501966i	0.0705201	−	0.0407148i
$153$	1.98415	−	9.83600i	0.160409	−	0.795194i
$154$	−1.23218	+	0.330162i	−0.0992920	+	0.0266052i
$155$	−2.95467	+	5.11763i	−0.237325	+	0.411058i
$156$	6.15605	−	1.05025i	0.492879	−	0.0840876i
$157$	5.60064	+	9.70059i	0.446980	+	0.774191i	0.998188	−	0.0601763i	$-0.0191663\pi$
$157$	5.60064	+	9.70059i	0.446980	+	0.774191i	−0.551208	+	0.834368i	$0.685833\pi$
$158$	2.49671	+	2.49671i	0.198627	+	0.198627i
$159$	−4.33409	−	1.63793i	−0.343715	−	0.129896i
$160$		−	1.02953i		−	0.0813917i
$161$	−0.365107	−	0.365107i	−0.0287745	−	0.0287745i
$162$	8.91652	+	1.22295i	0.700548	+	0.0960842i
$163$	−2.29883	+	8.57937i	−0.180059	+	0.671988i	0.815576	+	0.578650i	$0.196420\pi$
$163$	−2.29883	+	8.57937i	−0.180059	+	0.671988i	−0.995635	+	0.0933377i	$0.970246\pi$
$164$	−2.41936	−	9.02916i	−0.188920	−	0.705059i
$165$	−4.10308	−	5.01341i	−0.319424	−	0.390294i
$166$			8.64124i			0.670691i
$167$	−6.56988	+	6.56988i	−0.508392	+	0.508392i	−0.914033	−	0.405640i	$-0.867049\pi$
$167$	−6.56988	+	6.56988i	−0.508392	+	0.508392i	0.405640	+	0.914033i	$0.367049\pi$
$168$	0.214997	−	0.568900i	0.0165874	−	0.0438916i
$169$	6.65038	+	11.1702i	0.511568	+	0.859243i
$170$		−	3.44349i		−	0.264103i
$171$	1.66649	+	2.50873i	0.127440	+	0.191847i
$172$	−1.36943	+	2.37192i	−0.104418	+	0.180857i
$173$	10.5884			0.805023			0.402512	−	0.915415i	$-0.368137\pi$
$173$	10.5884			0.805023			0.402512	+	0.915415i	$0.368137\pi$
$174$	−10.0319	−	1.00175i	−0.760520	−	0.0759425i
$175$	−0.358066	−	1.33632i	−0.0270673	−	0.101016i
$176$	0.940292	+	3.50922i	0.0708772	+	0.264517i
$177$	8.35095	+	0.833893i	0.627696	+	0.0626792i
$178$	10.3748			0.777624
$179$	12.5097	−	21.6674i	0.935018	−	1.61950i	0.160417	−	0.987049i	$-0.448716\pi$
$179$	12.5097	−	21.6674i	0.935018	−	1.61950i	0.774601	−	0.632450i	$-0.217951\pi$
$180$	3.08252	−	0.193673i	0.229757	−	0.0144356i
$181$			23.3875i			1.73838i	0.494482	+	0.869188i	$0.335358\pi$
$181$			23.3875i			1.73838i	−0.494482	+	0.869188i	$0.664642\pi$
$182$	1.26598	−	0.00848836i	0.0938405	−	0.000629199i
$183$	3.50636	−	9.27813i	0.259198	−	0.685859i
$184$	−1.03981	+	1.03981i	−0.0766562	+	0.0766562i
$185$		−	5.29389i		−	0.389214i
$186$	6.29653	+	7.69353i	0.461684	+	0.564117i
$187$	3.14500	+	11.7373i	0.229986	+	0.858318i
$188$	2.19251	−	8.18256i	0.159905	−	0.596775i
$189$	1.74379	+	0.536701i	0.126842	+	0.0390393i
$190$	0.730852	+	0.730852i	0.0530215	+	0.0530215i
$191$			12.3120i			0.890865i	0.895316	+	0.445432i	$0.146950\pi$
$191$			12.3120i			0.890865i	−0.895316	+	0.445432i	$0.853050\pi$
$192$	−1.62021	−	0.612305i	−0.116929	−	0.0441893i
$193$	−9.14996	−	9.14996i	−0.658629	−	0.658629i	0.296427	−	0.955056i	$-0.404205\pi$
$193$	−9.14996	−	9.14996i	−0.658629	−	0.658629i	−0.955056	+	0.296427i	$0.904205\pi$
$194$	7.38509	+	12.7913i	0.530218	+	0.918365i
$195$	2.68478	+	5.84204i	0.192261	+	0.418358i
$196$	−3.43835	+	5.95541i	−0.245597	+	0.425386i
$197$	20.6372	−	5.52972i	1.47034	−	0.393976i	0.567292	−	0.823517i	$-0.307991\pi$
$197$	20.6372	−	5.52972i	1.47034	−	0.393976i	0.903048	+	0.429540i	$0.141324\pi$
$198$	−10.3300	+	3.47547i	−0.734125	+	0.246991i
$199$	19.2376	−	11.1069i	1.36372	−	0.787344i	0.373603	−	0.927589i	$-0.378122\pi$
$199$	19.2376	−	11.1069i	1.36372	−	0.787344i	0.990117	+	0.140245i	$0.0447889\pi$
$200$	−3.80581	+	1.01976i	−0.269111	+	0.0721082i
$201$	10.7432	+	23.7962i	0.757765	+	1.67845i
$202$	−16.7512	+	4.48848i	−1.17861	+	0.315808i
$203$	−1.97418	−	0.528980i	−0.138560	−	0.0371271i
$204$	−5.41914	−	2.04798i	−0.379415	−	0.143387i
$205$	8.33440	−	4.81187i	0.582100	−	0.336075i
$206$	2.75668	+	10.2881i	0.192067	+	0.716803i
$207$	−3.30891	−	2.91770i	−0.229985	−	0.202794i
$208$	−0.0241746	−	3.60547i	−0.00167621	−	0.249994i
$209$	−3.15865	−	1.82365i	−0.218488	−	0.126144i
$210$	0.623032	+	0.0622135i	0.0429933	+	0.00429314i
$211$	18.3511			1.26334			0.631670	−	0.775237i	$-0.282370\pi$
$211$	18.3511			1.26334			0.631670	+	0.775237i	$0.282370\pi$
$212$	−1.33751	+	2.31663i	−0.0918604	+	0.159107i
$213$	−8.36818	−	6.01369i	−0.573378	−	0.412051i
$214$	−0.565853	+	0.565853i	−0.0386809	+	0.0386809i
$215$	−2.72366	−	0.729803i	−0.185752	−	0.0497722i
$216$	1.52851	−	4.96625i	0.104002	−	0.337911i
$217$	1.00770	+	1.74539i	0.0684073	+	0.118485i
$218$	−4.12894	−	7.15154i	−0.279647	−	0.484363i
$219$	5.51800	−	2.49119i	0.372872	−	0.168339i
$220$	−3.23920	+	1.87015i	−0.218387	+	0.126086i
$221$	−0.0808571	−	12.0593i	−0.00543904	−	0.811193i
$222$	−8.33117	−	3.14849i	−0.559151	−	0.211313i
$223$	−24.4901	−	6.56211i	−1.63998	−	0.439432i	−0.683198	−	0.730233i	$-0.739411\pi$
$223$	−24.4901	−	6.56211i	−1.63998	−	0.439432i	−0.956783	+	0.290802i	$0.906078\pi$
$224$	−0.304085	−	0.175564i	−0.0203175	−	0.0117303i
$225$	−3.76921	−	11.2031i	−0.251281	−	0.746875i
$226$	−9.54047	+	9.54047i	−0.634623	+	0.634623i
$227$	17.6248	+	17.6248i	1.16980	+	1.16980i	0.982257	+	0.187539i	$0.0600511\pi$
$227$	17.6248	+	17.6248i	1.16980	+	1.16980i	0.187539	+	0.982257i	$0.439949\pi$
$228$	1.58483	−	0.715499i	0.104958	−	0.0473851i
$229$	0.401688	−	1.49912i	0.0265443	−	0.0990647i	−0.951383	−	0.308011i	$-0.900337\pi$
$229$	0.401688	−	1.49912i	0.0265443	−	0.0990647i	0.977927	+	0.208946i	$0.0670033\pi$
$230$	−1.31112	−	0.756974i	−0.0864525	−	0.0499134i
$231$	−2.18046	+	0.356969i	−0.143464	+	0.0234868i
$232$	−1.50652	+	5.62241i	−0.0989080	+	0.369130i
$233$	−9.96467			−0.652807			−0.326403	−	0.945231i	$-0.605837\pi$
$233$	−9.96467			−0.652807			−0.326403	+	0.945231i	$0.605837\pi$
$234$	10.7906	−	0.750634i	0.705402	−	0.0490705i
$235$	8.72139			0.568921
$236$	1.25408	−	4.68030i	0.0816338	−	0.304661i
$237$	3.87334	+	4.73271i	0.251600	+	0.307422i
$238$	−1.01708	−	0.587209i	−0.0659272	−	0.0380631i
$239$	−0.0186887	+	0.0697473i	−0.00120887	+	0.00451158i	−0.966528	−	0.256563i	$-0.917410\pi$
$239$	−0.0186887	+	0.0697473i	−0.00120887	+	0.00451158i	0.965319	+	0.261074i	$0.0840767\pi$
$240$	0.177182	−	1.77438i	0.0114371	−	0.114536i
$241$	13.2296	+	13.2296i	0.852192	+	0.852192i	0.990403	−	0.138211i	$-0.0441351\pi$
$241$	13.2296	+	13.2296i	0.852192	+	0.852192i	−0.138211	+	0.990403i	$0.544135\pi$
$242$	1.55476	−	1.55476i	0.0999436	−	0.0999436i
$243$	15.1570	+	3.64227i	0.972320	+	0.233651i
$244$	−4.95929	−	2.86325i	−0.317486	−	0.183301i
$245$	−6.83856	−	1.83239i	−0.436899	−	0.117067i
$246$	−2.61579	−	15.9779i	−0.166777	−	1.01872i
$247$	2.57664	+	2.54231i	0.163947	+	0.161764i
$248$	4.97083	−	2.86991i	0.315648	−	0.182240i
$249$	−1.48716	+	14.8930i	−0.0942448	+	0.943806i
$250$	−4.60204	−	7.97097i	−0.291059	−	0.504129i
$251$	10.5789	+	18.3232i	0.667735	+	1.15655i	0.978536	+	0.206075i	$0.0660692\pi$
$251$	10.5789	+	18.3232i	0.667735	+	1.15655i	−0.310802	+	0.950475i	$0.600597\pi$
$252$	0.468450	−	0.943486i	0.0295096	−	0.0594340i
$253$	5.16037	+	1.38272i	0.324430	+	0.0869308i
$254$	−13.2793	+	13.2793i	−0.833216	+	0.833216i
$255$	0.592624	−	5.93478i	0.0371116	−	0.371650i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.6439			−0.913460			−0.456730	−	0.889605i	$-0.650979\pi$
$257$	−14.6439			−0.913460			−0.456730	+	0.889605i	$0.650979\pi$
$258$	−2.76839	+	3.85228i	−0.172352	+	0.239832i
$259$	−1.56361	−	0.902752i	−0.0971582	−	0.0560943i
$260$	3.57903	−	0.984764i	0.221962	−	0.0610724i
$261$	−17.1175	−	3.45299i	−1.05954	−	0.213735i
$262$	0.871165	+	3.25123i	0.0538207	+	0.200862i
$263$	9.98128	−	5.76269i	0.615472	−	0.355343i	−0.159632	−	0.987177i	$-0.551031\pi$
$263$	9.98128	−	5.76269i	0.615472	−	0.355343i	0.775104	+	0.631834i	$0.217697\pi$
$264$	1.01664	+	6.20989i	0.0625697	+	0.382192i
$265$	−2.66017	−	0.712791i	−0.163413	−	0.0437864i
$266$	0.340496	−	0.0912356i	0.0208772	−	0.00559402i
$267$	17.8808	+	1.78550i	1.09428	+	0.109271i
$268$	14.5603	−	3.90143i	0.889414	−	0.238318i
$269$	−17.7279	+	10.2352i	−1.08089	+	0.624052i	−0.931136	−	0.364671i	$-0.881182\pi$
$269$	−17.7279	+	10.2352i	−1.08089	+	0.624052i	−0.149754	+	0.988723i	$0.547848\pi$
$270$	5.34599	+	0.196709i	0.325347	+	0.0119714i
$271$	0.537040	−	0.143899i	0.0326229	−	0.00874127i	−0.242471	−	0.970159i	$-0.577958\pi$
$271$	0.537040	−	0.143899i	0.0326229	−	0.00874127i	0.275094	+	0.961417i	$0.411291\pi$
$272$	−1.67236	+	2.89660i	−0.101401	+	0.175632i
$273$	2.18335	+	0.203245i	0.132142	+	0.0123010i
$274$	−1.94670	−	3.37178i	−0.117604	−	0.203697i
$275$	10.1217	+	10.1217i	0.610363	+	0.610363i
$276$	−1.97105	+	1.61315i	−0.118643	+	0.0971001i
$277$		−	12.0749i		−	0.725509i	−0.931885	−	0.362754i	$-0.881836\pi$
$277$		−	12.0749i		−	0.725509i	0.931885	−	0.362754i	$-0.118164\pi$
$278$	0.390670	+	0.390670i	0.0234308	+	0.0234308i
$279$	9.52789	+	14.3433i	0.570420	+	0.858709i
$280$	0.0935622	−	0.349179i	0.00559141	−	0.0208674i
$281$	3.77024	+	14.0707i	0.224913	+	0.839388i	0.982439	+	0.186583i	$0.0597414\pi$
$281$	3.77024	+	14.0707i	0.224913	+	0.839388i	−0.757526	+	0.652805i	$0.773592\pi$
$282$	5.18697	−	13.7251i	0.308879	−	0.817321i
$283$		−	13.3436i		−	0.793192i	−0.917993	−	0.396596i	$-0.870191\pi$
$283$		−	13.3436i		−	0.793192i	0.917993	−	0.396596i	$-0.129809\pi$
$284$	−4.20696	+	4.20696i	−0.249637	+	0.249637i
$285$	1.13383	+	1.38539i	0.0671622	+	0.0820632i
$286$	−11.2999	+	6.62541i	−0.668177	+	0.391769i
$287$		−	3.28222i		−	0.193743i
$288$	−2.68702	−	1.33413i	−0.158334	−	0.0786146i
$289$	2.90646	−	5.03413i	0.170968	−	0.296125i
$290$	−5.99265			−0.351901
$291$	10.5267	+	23.3166i	0.617084	+	1.36684i
$292$	−0.904687	−	3.37634i	−0.0529428	−	0.197585i
$293$	−5.46383	−	20.3913i	−0.319200	−	1.19127i	−0.920015	−	0.391883i	$-0.871824\pi$
$293$	−5.46383	−	20.3913i	−0.319200	−	1.19127i	0.600815	−	0.799388i	$-0.294843\pi$
$294$	−6.95086	+	9.67228i	−0.405382	+	0.564099i
$295$	4.98850			0.290442
$296$	−2.57101	+	4.45313i	−0.149437	+	0.258833i
$297$	−18.4018	+	4.21210i	−1.06778	+	0.244411i
$298$			12.9463i			0.749960i
$299$	−4.60937	−	2.62017i	−0.266567	−	0.151528i
$300$	−6.73473	+	1.10256i	−0.388830	+	0.0636564i
$301$	−0.680015	+	0.680015i	−0.0391954	+	0.0391954i
$302$			9.03667i			0.520002i
$303$	−29.6429	+	4.85292i	−1.70294	+	0.278793i
$304$	−0.259837	−	0.969723i	−0.0149027	−	0.0556174i
$305$	1.52590	−	5.69472i	0.0873726	−	0.326079i
$306$	−8.98731	−	4.46229i	−0.513770	−	0.255092i
$307$	−10.9437	−	10.9437i	−0.624590	−	0.624590i	0.322111	−	0.946702i	$-0.395607\pi$
$307$	−10.9437	−	10.9437i	−0.624590	−	0.624590i	−0.946702	+	0.322111i	$0.895607\pi$
$308$			1.27565i			0.0726868i
$309$	2.98050	+	18.2057i	0.169555	+	1.03568i
$310$	4.17853	+	4.17853i	0.237325	+	0.237325i
$311$	−12.9553	−	22.4392i	−0.734626	−	1.27241i	−0.954887	−	0.296968i	$-0.904024\pi$
$311$	−12.9553	−	22.4392i	−0.734626	−	1.27241i	0.220262	−	0.975441i	$-0.429309\pi$
$312$	0.578837	−	6.21811i	0.0327702	−	0.352031i
$313$	17.6482	−	30.5676i	0.997537	−	1.72779i	0.438028	−	0.898961i	$-0.355677\pi$
$313$	17.6482	−	30.5676i	0.997537	−	1.72779i	0.559509	−	0.828824i	$-0.310990\pi$
$314$	10.8196	−	2.89910i	0.610586	−	0.163606i
$315$	1.06308	+	0.214448i	0.0598976	+	0.0120828i
$316$	3.05783	−	1.76544i	0.172016	−	0.0993137i
$317$	−12.2048	+	3.27025i	−0.685487	+	0.183676i	−0.584721	−	0.811234i	$-0.698796\pi$
$317$	−12.2048	+	3.27025i	−0.685487	+	0.183676i	−0.100766	+	0.994910i	$0.532129\pi$
$318$	−2.70386	+	3.76248i	−0.151625	+	0.210989i
$319$	20.4263	−	5.47321i	1.14365	−	0.306441i
$320$	−0.994452	−	0.266463i	−0.0555916	−	0.0148957i
$321$	−1.07262	+	0.877852i	−0.0598677	+	0.0489969i
$322$	−0.447163	+	0.258170i	−0.0249194	+	0.0143872i
$323$	−0.869078	−	3.24344i	−0.0483568	−	0.180470i
$324$	3.48905	−	8.29618i	0.193836	−	0.460899i
$325$	−7.18538	−	12.2549i	−0.398573	−	0.679782i
$326$	7.69205	+	4.44101i	0.426023	+	0.245965i
$327$	−5.88537	−	13.0361i	−0.325462	−	0.720899i
$328$	−9.34767			−0.516139
$329$	1.48724	−	2.57597i	0.0819940	−	0.142018i
$330$	−5.90454	+	2.66570i	−0.325034	+	0.146742i
$331$	−7.04833	+	7.04833i	−0.387411	+	0.387411i	−0.873763	−	0.486352i	$-0.838327\pi$
$331$	−7.04833	+	7.04833i	−0.387411	+	0.387411i	0.486352	+	0.873763i	$0.338327\pi$
$332$	8.34680	+	2.23652i	0.458090	+	0.122745i
$333$	−13.8167	−	6.86015i	−0.757153	−	0.375934i
$334$	4.64560	+	8.04642i	0.254196	+	0.440281i
$335$	7.75957	+	13.4400i	0.423951	+	0.734304i
$336$	−0.493870	−	0.354913i	−0.0269428	−	0.0193621i
$337$	25.2475	−	14.5766i	1.37532	−	0.794040i	0.383727	−	0.923447i	$-0.374640\pi$
$337$	25.2475	−	14.5766i	1.37532	−	0.794040i	0.991592	+	0.129406i	$0.0413072\pi$
$338$	12.5108	−	3.53273i	0.680497	−	0.192155i
$339$	−18.0847	+	14.8009i	−0.982227	+	0.803874i
$340$	−3.32615	−	0.891240i	−0.180386	−	0.0483343i
$341$	−18.0591	−	10.4264i	−0.977954	−	0.564622i
$342$	2.85457	−	0.960398i	0.154357	−	0.0519324i
$343$	−3.44537	+	3.44537i	−0.186032	+	0.186032i
$344$	1.93666	+	1.93666i	0.104418	+	0.104418i
$345$	−2.12941	−	1.53027i	−0.114644	−	0.0823871i
$346$	2.74049	−	10.2276i	0.147329	−	0.549841i
$347$	12.4232	+	7.17253i	0.666912	+	0.385042i	0.794906	−	0.606733i	$-0.207520\pi$
$347$	12.4232	+	7.17253i	0.666912	+	0.385042i	−0.127994	+	0.991775i	$0.540854\pi$
$348$	−3.56408	+	9.43084i	−0.191055	+	0.505546i
$349$	6.84815	−	25.5577i	0.366573	−	1.36807i	−0.498702	−	0.866773i	$-0.666190\pi$
$349$	6.84815	−	25.5577i	0.366573	−	1.36807i	0.865276	−	0.501296i	$-0.167143\pi$
$350$	−1.38346			−0.0739492
$351$	18.7265	+	0.563355i	0.999548	+	0.0300697i
$352$	3.63301			0.193640
$353$	3.08503	−	11.5135i	0.164200	−	0.612801i	−0.833941	−	0.551853i	$-0.813921\pi$
$353$	3.08503	−	11.5135i	0.164200	−	0.612801i	0.998141	−	0.0609479i	$-0.0194124\pi$
$354$	2.96686	−	7.85057i	0.157687	−	0.417253i
$355$	−5.30461	−	3.06262i	−0.281540	−	0.162547i
$356$	2.68520	−	10.0213i	0.142315	−	0.531127i
$357$	−1.65185	−	1.18708i	−0.0874252	−	0.0628270i
$358$	−17.6914	−	17.6914i	−0.935018	−	0.935018i
$359$	−13.9898	+	13.9898i	−0.738351	+	0.738351i	−0.972259	−	0.233907i	$-0.924849\pi$
$359$	−13.9898	+	13.9898i	−0.738351	+	0.738351i	0.233907	+	0.972259i	$0.424849\pi$
$360$	0.610741	−	3.02761i	0.0321889	−	0.159569i
$361$	−15.5816	−	8.99606i	−0.820086	−	0.473477i
$362$	22.5905	+	6.05312i	1.18733	+	0.318145i
$363$	2.94717	−	2.41202i	0.154686	−	0.126598i
$364$	0.319460	−	1.22504i	0.0167443	−	0.0642094i
$365$	3.11654	−	1.79934i	0.163127	−	0.0941815i
$366$	−8.05447	−	5.78824i	−0.421014	−	0.302556i
$367$	−8.33971	−	14.4448i	−0.435329	−	0.754012i	0.561993	−	0.827142i	$-0.310035\pi$
$367$	−8.33971	−	14.4448i	−0.435329	−	0.754012i	−0.997322	+	0.0731295i	$0.976701\pi$
$368$	0.735260	+	1.27351i	0.0383281	+	0.0663862i
$369$	−1.75846	−	27.9878i	−0.0915419	−	1.45699i
$370$	−5.11350	−	1.37016i	−0.265838	−	0.0712311i
$371$	−0.664164	+	0.664164i	−0.0344817	+	0.0344817i
$372$	9.06104	−	4.09075i	0.469793	−	0.212096i
$373$	0.266680	−	0.461903i	0.0138082	−	0.0239164i	−0.859039	−	0.511911i	$-0.828938\pi$
$373$	0.266680	−	0.461903i	0.0138082	−	0.0239164i	0.872847	+	0.487994i	$0.162271\pi$
$374$	12.1514			0.628332
$375$	−6.55972	−	14.5298i	−0.338743	−	0.750317i
$376$	−7.33629	−	4.23561i	−0.378340	−	0.218435i
$377$	−20.9865	+	0.140715i	−1.08086	+	0.00724717i
$378$	0.969738	−	1.54546i	0.0498780	−	0.0794898i
$379$	−8.93403	−	33.3422i	−0.458910	−	1.71268i	−0.676331	−	0.736598i	$-0.736431\pi$
$379$	−8.93403	−	33.3422i	−0.458910	−	1.71268i	0.217421	−	0.976078i	$-0.430236\pi$
$380$	0.895107	−	0.516790i	0.0459180	−	0.0265108i
$381$	−25.1719	+	20.6012i	−1.28960	+	1.05543i
$382$	11.8925	+	3.18658i	0.608472	+	0.163040i
$383$	1.95166	−	0.522945i	0.0997250	−	0.0267212i	−0.208611	−	0.977999i	$-0.566894\pi$
$383$	1.95166	−	0.522945i	0.0997250	−	0.0267212i	0.308336	+	0.951277i	$0.400228\pi$
$384$	−1.01078	+	1.40653i	−0.0515813	+	0.0717765i
$385$	−1.26857	+	0.339912i	−0.0646523	+	0.0173235i
$386$	−11.2064	+	6.47000i	−0.570389	+	0.329314i
$387$	−5.43424	+	6.16288i	−0.276238	+	0.313277i
$388$	14.2669	−	3.82280i	0.724292	−	0.194073i
$389$	−0.968658	+	1.67777i	−0.0491129	+	0.0850661i	−0.889537	−	0.456864i	$-0.848973\pi$
$389$	−0.968658	+	1.67777i	−0.0491129	+	0.0850661i	0.840424	+	0.541930i	$0.182306\pi$
$390$	6.33786	−	1.08127i	0.320930	−	0.0547522i
$391$	2.45923	+	4.25951i	0.124369	+	0.215413i
$392$	4.86257	+	4.86257i	0.245597	+	0.245597i
$393$	0.941898	+	5.75336i	0.0475125	+	0.290218i
$394$		−	21.3652i		−	1.07636i
$395$	2.57044	+	2.57044i	0.129333	+	0.129333i
$396$	0.683433	+	10.8776i	0.0343438	+	0.546619i
$397$	−8.86089	+	33.0693i	−0.444716	+	1.65970i	0.271971	+	0.962305i	$0.412324\pi$
$397$	−8.86089	+	33.0693i	−0.444716	+	1.65970i	−0.716687	+	0.697395i	$0.754342\pi$
$398$	−5.74933	−	21.4568i	−0.288188	−	1.07553i
$399$	0.602540	−	0.0986434i	0.0301647	−	0.00493835i
$400$			3.94006i			0.197003i
$401$	6.35686	−	6.35686i	0.317446	−	0.317446i	−0.530339	−	0.847786i	$-0.677935\pi$
$401$	6.35686	−	6.35686i	0.317446	−	0.317446i	0.847786	+	0.530339i	$0.177935\pi$
$402$	25.7659	−	4.21820i	1.28509	−	0.210385i
$403$	14.7315	+	14.5353i	0.733829	+	0.724054i
$404$			17.3422i			0.862804i
$405$	9.17985	+	1.25907i	0.456150	+	0.0625636i
$406$	−1.02191	+	1.77000i	−0.0507166	+	0.0878438i
$407$	18.6810			0.925985
$408$	−3.38078	+	4.70443i	−0.167373	+	0.232904i
$409$	−3.81796	−	14.2488i	−0.188786	−	0.704558i	−0.993788	−	0.111287i	$-0.964503\pi$
$409$	−3.81796	−	14.2488i	−0.188786	−	0.704558i	0.805003	−	0.593271i	$-0.202164\pi$
$410$	−2.49081	−	9.29581i	−0.123012	−	0.459087i
$411$	−2.77481	−	6.14622i	−0.136871	−	0.303171i
$412$	10.6510			0.524736
$413$	0.850676	−	1.47341i	0.0418590	−	0.0725019i
$414$	−3.67469	+	2.44101i	−0.180601	+	0.119969i
$415$			8.89644i			0.436709i
$416$	−3.48887	−	0.909813i	−0.171056	−	0.0446073i
$417$	0.606077	+	0.740545i	0.0296797	+	0.0362647i
$418$	−2.57903	+	2.57903i	−0.126144	+	0.126144i
$419$			34.9519i			1.70751i	0.520675	+	0.853755i	$0.325680\pi$
$419$			34.9519i			1.70751i	−0.520675	+	0.853755i	$0.674320\pi$
$420$	0.221346	−	0.585701i	0.0108006	−	0.0285793i
$421$	−0.685052	−	2.55665i	−0.0333874	−	0.124603i	0.947221	−	0.320582i	$-0.103878\pi$
$421$	−0.685052	−	2.55665i	−0.0333874	−	0.124603i	−0.980608	+	0.195978i	$0.937212\pi$
$422$	4.74961	−	17.7258i	0.231207	−	0.862878i
$423$	11.3017	−	22.7623i	0.549509	−	1.10674i
$424$	1.89152	+	1.89152i	0.0918604	+	0.0918604i
$425$			13.1784i			0.639245i
$426$	−7.97462	+	6.52659i	−0.386372	+	0.316214i
$427$	−1.42180	−	1.42180i	−0.0688057	−	0.0688057i
$428$	0.400118	+	0.693025i	0.0193404	+	0.0334986i
$429$	−20.6154	+	9.47405i	−0.995320	+	0.457412i
$430$	−1.40987	+	2.44197i	−0.0679900	+	0.117762i
$431$	14.1857	−	3.80104i	0.683301	−	0.183090i	0.0995618	−	0.995031i	$-0.468256\pi$
$431$	14.1857	−	3.80104i	0.683301	−	0.183090i	0.583739	+	0.811942i	$0.301589\pi$
$432$	−4.40142	−	2.76179i	−0.211764	−	0.132877i
$433$	−13.2828	+	7.66884i	−0.638332	+	0.368541i	−0.783972	−	0.620797i	$-0.786809\pi$
$433$	−13.2828	+	7.66884i	−0.638332	+	0.368541i	0.145640	+	0.989338i	$0.453476\pi$
$434$	1.94673	−	0.521626i	0.0934462	−	0.0250388i
$435$	−10.3282	−	1.03134i	−0.495200	−	0.0494487i
$436$	−7.97650	+	2.13730i	−0.382005	+	0.102358i
$437$	−1.42600	−	0.382095i	−0.0682147	−	0.0182781i
$438$	−0.978142	−	5.97474i	−0.0467374	−	0.285484i
$439$	9.39837	−	5.42615i	0.448560	−	0.258976i	−0.258662	−	0.965968i	$-0.583282\pi$
$439$	9.39837	−	5.42615i	0.448560	−	0.258976i	0.707222	+	0.706992i	$0.249948\pi$
$440$	0.968061	+	3.61285i	0.0461505	+	0.172236i
$441$	−13.6443	+	15.4737i	−0.649727	+	0.736844i
$442$	−11.6693	−	3.04306i	−0.555051	−	0.144744i
$443$	28.8694	+	16.6678i	1.37163	+	0.791909i	0.991133	−	0.132874i	$-0.0424205\pi$
$443$	28.8694	+	16.6678i	1.37163	+	0.791909i	0.380494	+	0.924783i	$0.375754\pi$
$444$	−5.19747	+	7.23240i	−0.246661	+	0.343235i
$445$	10.6812			0.506337
$446$	−12.6770	+	21.9573i	−0.600275	+	1.03971i
$447$	−2.22806	+	22.3127i	−0.105384	+	1.05535i
$448$	−0.248284	+	0.248284i	−0.0117303	+	0.0117303i
$449$	17.6413	+	4.72697i	0.832543	+	0.223079i	0.649823	−	0.760086i	$-0.274843\pi$
$449$	17.6413	+	4.72697i	0.832543	+	0.223079i	0.182720	+	0.983165i	$0.441510\pi$
$450$	−11.7969	+	0.741196i	−0.556112	+	0.0349403i
$451$	16.9801	+	29.4104i	0.799561	+	1.38488i
$452$	6.74613	+	11.6846i	0.317311	+	0.549599i
$453$	−1.55521	+	15.5745i	−0.0730701	+	0.731755i
$454$	21.5858	−	12.4626i	1.01307	−	0.584898i
$455$	1.30337	−	0.00873905i	0.0611027	−	0.000409693i
$456$	−0.280934	−	1.71602i	−0.0131559	−	0.0803598i
$457$	−6.16260	−	1.65126i	−0.288274	−	0.0772428i	0.111784	−	0.993733i	$-0.464343\pi$
$457$	−6.16260	−	1.65126i	−0.288274	−	0.0772428i	−0.400058	+	0.916490i	$0.631010\pi$
$458$	−1.34408	−	0.776002i	−0.0628045	−	0.0362602i
$459$	−14.7215	−	9.23738i	−0.687140	−	0.431164i
$460$	−1.07052	+	1.07052i	−0.0499134	+	0.0499134i
$461$	−25.4639	−	25.4639i	−1.18597	−	1.18597i	−0.978171	−	0.207804i	$-0.933368\pi$
$461$	−25.4639	−	25.4639i	−1.18597	−	1.18597i	−0.207804	−	0.978171i	$-0.566632\pi$
$462$	−0.219539	+	2.19855i	−0.0102139	+	0.102286i
$463$	−5.81062	+	21.6855i	−0.270042	+	1.00781i	0.689049	+	0.724715i	$0.258028\pi$
$463$	−5.81062	+	21.6855i	−0.270042	+	1.00781i	−0.959091	+	0.283097i	$0.908638\pi$
$464$	5.04092	+	2.91038i	0.234019	+	0.135111i
$465$	6.48249	+	7.92073i	0.300618	+	0.367315i
$466$	−2.57905	+	9.62513i	−0.119472	+	0.445875i
$467$	−14.0000			−0.647843			−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000			−0.647843			−0.323921	+	0.946084i	$0.605001\pi$
$468$	2.06775	−	10.6172i	0.0955818	−	0.490779i
$469$	5.29288			0.244402
$470$	2.25726	−	8.42422i	0.104120	−	0.388580i
$471$	19.1463	−	3.13449i	0.882215	−	0.144430i
$472$	−4.19624	−	2.42270i	−0.193148	−	0.111514i
$473$	2.57533	−	9.61125i	0.118414	−	0.441926i
$474$	5.57394	−	2.51644i	0.256019	−	0.115584i
$475$	−2.79700	−	2.79700i	−0.128335	−	0.128335i
$476$	−0.830439	+	0.830439i	−0.0380631	+	0.0380631i
$477$	−5.30757	+	6.01922i	−0.243017	+	0.275601i
$478$	0.0625337	+	0.0361039i	0.00286023	+	0.00165135i
$479$	−25.7135	−	6.88992i	−1.17488	−	0.314809i	−0.381987	−	0.924168i	$-0.624760\pi$
$479$	−25.7135	−	6.88992i	−1.17488	−	0.314809i	−0.792894	+	0.609359i	$0.791427\pi$
$480$	−1.66806	−	0.630388i	−0.0761362	−	0.0287731i
$481$	−17.9399	−	4.67829i	−0.817988	−	0.213311i
$482$	16.2029	−	9.35472i	0.738020	−	0.426096i
$483$	−0.815107	+	0.367993i	−0.0370887	+	0.0167443i
$484$	−1.09938	−	1.90418i	−0.0499718	−	0.0865537i
$485$	7.60319	+	13.1691i	0.345243	+	0.597978i
$486$	7.44107	−	13.6978i	0.337534	−	0.621346i
$487$	−14.7534	−	3.95317i	−0.668542	−	0.179135i	−0.0914441	−	0.995810i	$-0.529148\pi$
$487$	−14.7534	−	3.95317i	−0.668542	−	0.179135i	−0.577098	+	0.816675i	$0.695815\pi$
$488$	−4.04924	+	4.04924i	−0.183301	+	0.183301i
$489$	12.4928	+	8.97778i	0.564944	+	0.405989i
$490$	−3.53990	+	6.13128i	−0.159916	+	0.276983i
$491$	−1.87163			−0.0844656			−0.0422328	−	0.999108i	$-0.513447\pi$
$491$	−1.87163			−0.0844656			−0.0422328	+	0.999108i	$0.513447\pi$
$492$	−16.1105	−	1.60873i	−0.726318	−	0.0725273i
$493$	16.8604	+	9.73437i	0.759355	+	0.438414i
$494$	3.12257	−	1.83084i	0.140491	−	0.0823734i
$495$	−10.6351	+	3.57811i	−0.478013	+	0.160824i
$496$	−1.48558	−	5.54424i	−0.0667043	−	0.248944i
$497$	−1.80916	+	1.04452i	−0.0811521	+	0.0468532i
$498$	14.0006	+	5.29108i	0.627384	+	0.237099i
$499$	10.9455	+	2.93283i	0.489986	+	0.131291i	0.495349	−	0.868694i	$-0.335040\pi$
$499$	10.9455	+	2.93283i	0.489986	+	0.131291i	−0.00536247	+	0.999986i	$0.501707\pi$
$500$	−8.89046	+	2.38219i	−0.397594	+	0.106535i
$501$	6.62181	+	14.6674i	0.295841	+	0.655289i
$502$	20.4369	−	5.47604i	0.912142	−	0.244408i
$503$	−0.311572	+	0.179886i	−0.0138923	+	0.00802072i	−0.506930	−	0.861987i	$-0.669220\pi$
$503$	−0.311572	+	0.179886i	−0.0138923	+	0.00802072i	0.493038	+	0.870008i	$0.335886\pi$
$504$	−0.790094	−	0.696680i	−0.0351936	−	0.0310326i
$505$	−17.2459	+	4.62104i	−0.767434	+	0.205633i
$506$	2.67121	−	4.62667i	0.118750	−	0.205680i
$507$	22.1701	−	3.93548i	0.984607	−	0.174781i
$508$	9.38987	+	16.2637i	0.416608	+	0.721586i
$509$	30.5184	+	30.5184i	1.35270	+	1.35270i	0.882623	+	0.470082i	$0.155776\pi$
$509$	30.5184	+	30.5184i	1.35270	+	1.35270i	0.470082	+	0.882623i	$0.344224\pi$
$510$	−5.57918	−	2.10847i	−0.247050	−	0.0933644i
$511$		−	1.22734i		−	0.0542945i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	5.08507	−	1.16396i	0.224511	−	0.0513899i
$514$	−3.79011	+	14.1449i	−0.167175	+	0.623905i
$515$	2.83809	+	10.5919i	0.125061	+	0.466734i
$516$	3.00450	+	3.67110i	0.132266	+	0.161611i
$517$			30.7760i			1.35353i
$518$	−1.27668	+	1.27668i	−0.0560943	+	0.0560943i
$519$	6.48335	−	17.1555i	0.284587	−	0.753042i
$520$	−0.0248886	−	3.71195i	−0.00109144	−	0.162780i
$521$			39.0644i			1.71144i	0.517436	+	0.855722i	$0.326887\pi$
$521$			39.0644i			1.71144i	−0.517436	+	0.855722i	$0.673113\pi$
$522$	−7.76566	+	15.6405i	−0.339894	+	0.684566i
$523$	−22.3670	+	38.7408i	−0.978041	+	1.69402i	−0.308529	+	0.951215i	$0.599837\pi$
$523$	−22.3670	+	38.7408i	−0.978041	+	1.69402i	−0.669512	+	0.742801i	$0.733497\pi$
$524$	3.36592			0.147041
$525$	−2.38437	−	0.238094i	−0.104062	−	0.0103913i
$526$	−2.98299	−	11.1327i	−0.130065	−	0.485407i
$527$	−4.96882	−	18.5439i	−0.216445	−	0.807784i
$528$	6.26142	+	0.625241i	0.272493	+	0.0272101i
$529$	−20.8376			−0.905981
$530$	−1.37701	+	2.38505i	−0.0598134	+	0.103600i
$531$	6.46441	−	13.0197i	0.280532	−	0.565007i
$532$		−	0.352507i		−	0.0152831i
$533$	−8.94119	−	32.4959i	−0.387286	−	1.40755i
$534$	6.35254	−	16.8094i	0.274901	−	0.727412i
$535$	−0.582564	+	0.582564i	−0.0251864	+	0.0251864i
$536$		−	15.0740i		−	0.651096i
$537$	−27.4460	−	33.5354i	−1.18438	−	1.44716i
$538$	5.29814	+	19.7729i	0.228419	+	0.852471i
$539$	6.46612	−	24.1319i	0.278515	−	1.03943i
$540$	1.57365	−	5.11292i	0.0677191	−	0.220025i
$541$	20.3887	+	20.3887i	0.876580	+	0.876580i	0.993179	−	0.116599i	$-0.0371993\pi$
$541$	20.3887	+	20.3887i	0.876580	+	0.876580i	−0.116599	+	0.993179i	$0.537199\pi$
$542$		−	0.555985i		−	0.0238816i
$543$	37.8926	+	14.3203i	1.62613	+	0.614541i
$544$	2.36507	+	2.36507i	0.101401	+	0.101401i
$545$	−4.25088	−	7.36274i	−0.182088	−	0.315385i
$546$	0.761412	−	2.05635i	0.0325854	−	0.0880036i
$547$	9.46079	−	16.3866i	0.404514	−	0.700639i	−0.589751	−	0.807585i	$-0.700774\pi$
$547$	9.46079	−	16.3866i	0.404514	−	0.700639i	0.994265	+	0.106947i	$0.0341074\pi$
$548$	−3.76073	+	1.00768i	−0.160650	+	0.0430462i
$549$	−12.8856	−	11.3621i	−0.549942	−	0.484922i
$550$	12.3965	−	7.15714i	0.528590	−	0.305182i
$551$	−5.64452	+	1.51244i	−0.240465	+	0.0644323i
$552$	1.04803	+	2.32140i	0.0446073	+	0.0988055i
$553$	1.19754	−	0.320880i	0.0509246	−	0.0136452i
$554$	−11.6634	−	3.12521i	−0.495532	−	0.132777i
$555$	−8.57721	−	3.24147i	−0.364082	−	0.137593i
$556$	0.478471	−	0.276245i	0.0202917	−	0.0117154i
$557$	−0.839623	−	3.13351i	−0.0355760	−	0.132771i	0.945854	−	0.324593i	$-0.105227\pi$
$557$	−0.839623	−	3.13351i	−0.0355760	−	0.132771i	−0.981430	+	0.191821i	$0.938561\pi$
$558$	16.3205	−	5.49092i	0.690903	−	0.232449i
$559$	−4.88009	+	8.58499i	−0.206406	+	0.363106i
$560$	−0.313065	−	0.180748i	−0.0132294	−	0.00763801i
$561$	20.9426	+	2.09125i	0.884198	+	0.0882926i
$562$	14.5671			0.614475
$563$	1.15338	−	1.99771i	0.0486090	−	0.0841933i	−0.840697	−	0.541506i	$-0.817855\pi$
$563$	1.15338	−	1.99771i	0.0486090	−	0.0841933i	0.889306	+	0.457312i	$0.151188\pi$
$564$	−11.9150	−	8.56256i	−0.501712	−	0.360549i
$565$	−9.82222	+	9.82222i	−0.413224	+	0.413224i
$566$	−12.8889	−	3.45357i	−0.541761	−	0.145164i
$567$	1.93730	−	2.49667i	0.0813588	−	0.104850i
$568$	2.97477	+	5.15245i	0.124818	+	0.216192i
$569$	4.75114	+	8.22922i	0.199178	+	0.344987i	0.948262	−	0.317488i	$-0.102839\pi$
$569$	4.75114	+	8.22922i	0.199178	+	0.344987i	−0.749084	+	0.662475i	$0.769506\pi$
$570$	1.63164	−	0.736629i	0.0683418	−	0.0308540i
$571$	22.0695	−	12.7418i	0.923578	−	0.533228i	0.0388033	−	0.999247i	$-0.487645\pi$
$571$	22.0695	−	12.7418i	0.923578	−	0.533228i	0.884775	+	0.466019i	$0.154312\pi$
$572$	3.47503	+	12.6296i	0.145298	+	0.528072i
$573$	19.9480	+	7.53870i	0.833341	+	0.314934i
$574$	−3.17038	−	0.849501i	−0.132329	−	0.0354575i
$575$	5.01770	+	2.89697i	0.209253	+	0.120812i
$576$	−1.98413	+	2.25016i	−0.0826719	+	0.0937569i
$577$	17.9008	−	17.9008i	0.745221	−	0.745221i	−0.228357	−	0.973577i	$-0.573335\pi$
$577$	17.9008	−	17.9008i	0.745221	−	0.745221i	0.973577	+	0.228357i	$0.0733353\pi$
$578$	−4.11035	−	4.11035i	−0.170968	−	0.170968i
$579$	−20.4274	+	9.22230i	−0.848935	+	0.383266i
$580$	−1.55101	+	5.78846i	−0.0644023	+	0.240353i
$581$	2.62767	+	1.51709i	0.109014	+	0.0629394i
$582$	25.2466	−	4.13319i	1.04651	−	0.171326i
$583$	2.51529	−	9.38721i	0.104173	−	0.388778i
$584$	−3.49544			−0.144642
$585$	11.1093	−	0.772802i	0.459311	−	0.0319514i
$586$	−21.1106			−0.872071
$587$	7.99701	−	29.8452i	0.330072	−	1.23185i	−0.579042	−	0.815298i	$-0.696573\pi$
$587$	7.99701	−	29.8452i	0.330072	−	1.23185i	0.909114	−	0.416547i	$-0.136760\pi$
$588$	7.54369	+	9.21738i	0.311096	+	0.380119i
$589$	4.99037	+	2.88119i	0.205625	+	0.118718i
$590$	1.29112	−	4.81852i	0.0531545	−	0.198375i
$591$	3.67695	−	36.8225i	0.151250	−	1.51468i
$592$	3.63596	+	3.63596i	0.149437	+	0.149437i
$593$	−1.91150	+	1.91150i	−0.0784959	+	0.0784959i	−0.745265	−	0.666769i	$-0.767677\pi$
$593$	−1.91150	+	1.91150i	−0.0784959	+	0.0784959i	0.666769	+	0.745265i	$0.267677\pi$
$594$	−0.694147	+	18.8649i	−0.0284812	+	0.774036i
$595$	−1.04711	−	0.604551i	−0.0429274	−	0.0247842i
$596$	12.5052	+	3.35075i	0.512232	+	0.137252i
$597$	−6.21614	−	37.9698i	−0.254410	−	1.55400i
$598$	−3.72388	+	3.77416i	−0.152281	+	0.154337i
$599$	−24.8798	+	14.3643i	−1.01656	+	0.586911i	−0.913105	−	0.407723i	$-0.866323\pi$
$599$	−24.8798	+	14.3643i	−1.01656	+	0.586911i	−0.103454	+	0.994634i	$0.532989\pi$
$600$	−0.678084	+	6.79062i	−0.0276827	+	0.277226i
$601$	−15.4935	−	26.8355i	−0.631993	−	1.09464i	−0.987144	−	0.159835i	$-0.948904\pi$
$601$	−15.4935	−	26.8355i	−0.631993	−	1.09464i	0.355151	−	0.934809i	$-0.384430\pi$
$602$	0.480843	+	0.832845i	0.0195977	+	0.0339442i
$603$	45.1329	−	2.83568i	1.83795	−	0.115478i
$604$	8.72875	+	2.33886i	0.355168	+	0.0951670i
$605$	1.60067	−	1.60067i	0.0650766	−	0.0650766i
$606$	−2.98458	+	29.8888i	−0.121240	+	1.21415i
$607$	−5.03399	+	8.71913i	−0.204323	+	0.353899i	−0.949917	−	0.312502i	$-0.898833\pi$
$607$	−5.03399	+	8.71913i	−0.204323	+	0.353899i	0.745594	+	0.666401i	$0.232166\pi$
$608$	−1.00393			−0.0407148
$609$	−2.06586	+	2.87469i	−0.0837129	+	0.116488i
$610$	−5.10575	−	2.94781i	−0.206726	−	0.119353i
$611$	7.70722	−	29.5550i	0.311801	−	1.19567i
$612$	−6.63633	+	7.52615i	−0.268258	+	0.304227i
$613$	−5.97413	−	22.2957i	−0.241293	−	0.900516i	−0.975211	−	0.221278i	$-0.928977\pi$
$613$	−5.97413	−	22.2957i	−0.241293	−	0.900516i	0.733918	−	0.679238i	$-0.237690\pi$
$614$	−13.4032	+	7.73837i	−0.540911	+	0.312295i
$615$	−2.69304	−	16.4498i	−0.108594	−	0.663320i
$616$	1.23218	+	0.330162i	0.0496460	+	0.0133026i
$617$	25.3370	−	6.78904i	1.02003	−	0.273316i	0.290216	−	0.956961i	$-0.406273\pi$
$617$	25.3370	−	6.78904i	1.02003	−	0.273316i	0.729815	+	0.683645i	$0.239606\pi$
$618$	18.3567	+	1.83303i	0.738417	+	0.0737354i
$619$	−20.5005	+	5.49310i	−0.823985	+	0.220786i	−0.646088	−	0.763263i	$-0.723596\pi$
$619$	−20.5005	+	5.49310i	−0.823985	+	0.220786i	−0.177897	+	0.984049i	$0.556929\pi$
$620$	5.11763	−	2.95467i	0.205529	−	0.118662i
$621$	−6.75335	+	3.57461i	−0.271003	+	0.143444i
$622$	−25.0277	+	6.70614i	−1.00352	+	0.268892i
$623$	1.82144	−	3.15482i	0.0729743	−	0.126395i
$624$	−5.85642	−	2.16848i	−0.234445	−	0.0868087i
$625$	5.11220	+	8.85460i	0.204488	+	0.354184i
$626$	−24.9584	−	24.9584i	−0.997537	−	0.997537i
$627$	−4.88875	+	4.00105i	−0.195238	+	0.159786i
$628$		−	11.2013i		−	0.446980i
$629$	12.1612	+	12.1612i	0.484900	+	0.484900i
$630$	0.482285	−	0.971350i	0.0192147	−	0.0386995i
$631$	2.60255	−	9.71284i	0.103606	−	0.386662i	−0.894578	−	0.446913i	$-0.852523\pi$
$631$	2.60255	−	9.71284i	0.103606	−	0.386662i	0.998183	+	0.0602509i	$0.0191901\pi$
$632$	−0.913858	−	3.41056i	−0.0363513	−	0.135665i
$633$	11.2365	−	29.7326i	0.446609	−	1.18177i
$634$			12.6353i			0.501811i
$635$	−13.6714	+	13.6714i	−0.542535	+	0.542535i
$636$	2.93447	+	3.58553i	0.116359	+	0.142175i
$637$	−12.2529	+	21.5552i	−0.485478	+	0.854046i
$638$		−	21.1468i		−	0.837212i
$639$	−14.8673	+	9.87601i	−0.588142	+	0.390689i
$640$	−0.514766	+	0.891601i	−0.0203479	+	0.0352436i
$641$	−6.47708			−0.255829			−0.127915	−	0.991785i	$-0.540828\pi$
$641$	−6.47708			−0.255829			−0.127915	+	0.991785i	$0.540828\pi$
$642$	0.570326	+	1.26328i	0.0225090	+	0.0498575i
$643$	−1.88381	−	7.03049i	−0.0742904	−	0.277255i	0.918781	−	0.394767i	$-0.129175\pi$
$643$	−1.88381	−	7.03049i	−0.0742904	−	0.277255i	−0.993071	+	0.117512i	$0.962508\pi$
$644$	0.133638	+	0.498745i	0.00526609	+	0.0196533i
$645$	−2.85015	+	3.96604i	−0.112224	+	0.156163i
$646$	−3.35786			−0.132113
$647$	2.67717	−	4.63699i	0.105250	−	0.182299i	−0.808590	−	0.588372i	$-0.799769\pi$
$647$	2.67717	−	4.63699i	0.105250	−	0.182299i	0.913840	+	0.406073i	$0.133102\pi$
$648$	−7.11046	−	5.51737i	−0.279325	−	0.216743i
$649$			17.6034i			0.690993i
$650$	−13.6971	+	3.76873i	−0.537244	+	0.147822i
$651$	3.44493	−	0.563978i	0.135017	−	0.0221041i
$652$	6.28053	−	6.28053i	0.245965	−	0.245965i
$653$			13.5198i			0.529072i	0.964376	+	0.264536i	$0.0852189\pi$
$653$			13.5198i			0.529072i	−0.964376	+	0.264536i	$0.914781\pi$
$654$	−14.1152	+	2.31083i	−0.551947	+	0.0903607i
$655$	0.896892	+	3.34725i	0.0350445	+	0.130788i
$656$	−2.41936	+	9.02916i	−0.0944600	+	0.352529i
$657$	−0.657554	−	10.4657i	−0.0256536	−	0.408305i
$658$	−2.10327	−	2.10327i	−0.0819940	−	0.0819940i
$659$		−	25.9719i		−	1.01172i	−0.862615	−	0.505861i	$-0.831175\pi$
$659$		−	25.9719i		−	1.01172i	0.862615	−	0.505861i	$-0.168825\pi$
$660$	1.04666	+	6.39328i	0.0407413	+	0.248858i
$661$	9.76168	+	9.76168i	0.379685	+	0.379685i	0.870989	−	0.491303i	$-0.163479\pi$
$661$	9.76168	+	9.76168i	0.379685	+	0.379685i	−0.491303	+	0.870989i	$0.663479\pi$
$662$	4.98392	+	8.63240i	0.193706	+	0.335508i
$663$	−19.5880	−	7.25294i	−0.760736	−	0.281681i
$664$	4.32062	−	7.48354i	0.167673	−	0.290418i
$665$	0.350552	−	0.0939301i	0.0135938	−	0.00364245i
$666$	−10.2024	+	11.5704i	−0.395336	+	0.448344i
$667$	7.41277	−	4.27977i	0.287024	−	0.165713i
$668$	8.97462	−	2.40474i	0.347238	−	0.0930422i
$669$	−25.6274	+	35.6612i	−0.990814	+	1.37874i
$670$	14.9903	−	4.01665i	0.579127	−	0.155177i
$671$	20.0955	+	5.38458i	0.775779	+	0.207869i
$672$	−0.470643	+	0.385183i	−0.0181554	+	0.0148588i
$673$	−24.4924	+	14.1407i	−0.944112	+	0.545083i	−0.891247	−	0.453518i	$-0.850169\pi$
$673$	−24.4924	+	14.1407i	−0.944112	+	0.545083i	−0.0528649	+	0.998602i	$0.516835\pi$
$674$	−7.54543	−	28.1599i	−0.290639	−	1.08468i
$675$	−20.4593	−	0.752815i	−0.787480	−	0.0289759i
$676$	−0.174322	−	12.9988i	−0.00670468	−	0.499955i
$677$	−34.1714	−	19.7289i	−1.31331	−	0.758242i	−0.330671	−	0.943746i	$-0.607275\pi$
$677$	−34.1714	−	19.7289i	−1.31331	−	0.758242i	−0.982644	+	0.185504i	$0.940608\pi$
$678$	9.61589	+	21.2992i	0.369296	+	0.817993i
$679$	5.18621			0.199028
$680$	−1.72174	+	2.98215i	−0.0660259	+	0.114360i
$681$	39.3475	−	17.7641i	1.50780	−	0.680721i
$682$	−14.7452	+	14.7452i	−0.564622	+	0.564622i
$683$	−25.3130	−	6.78259i	−0.968574	−	0.259529i	−0.260348	−	0.965515i	$-0.583837\pi$
$683$	−25.3130	−	6.78259i	−0.968574	−	0.259529i	−0.708226	+	0.705986i	$0.750504\pi$
$684$	−0.188857	−	3.00587i	−0.00722114	−	0.114932i
$685$	−2.00419	−	3.47136i	−0.0765761	−	0.132634i
$686$	2.43624	+	4.21970i	0.0930162	+	0.161109i
$687$	−2.18294	−	1.56874i	−0.0832842	−	0.0598511i
$688$	2.37192	−	1.36943i	0.0904286	−	0.0522090i
$689$	−4.76634	+	8.38488i	−0.181583	+	0.319438i
$690$	−2.02926	+	1.66079i	−0.0772527	+	0.0632251i
$691$	−11.3975	−	3.05395i	−0.433581	−	0.116178i	0.0354255	−	0.999372i	$-0.488721\pi$
$691$	−11.3975	−	3.05395i	−0.433581	−	0.116178i	−0.469007	+	0.883195i	$0.655388\pi$
$692$	−9.16985	−	5.29421i	−0.348585	−	0.201256i
$693$	−0.756742	+	3.75138i	−0.0287462	+	0.142503i
$694$	10.1435	−	10.1435i	0.385042	−	0.385042i
$695$	0.402207	+	0.402207i	0.0152566	+	0.0152566i
$696$	8.18705	+	5.88352i	0.310329	+	0.223014i
$697$	−8.09204	+	30.1999i	−0.306508	+	1.14390i
$698$	−22.9144	−	13.2296i	−0.867321	−	0.500748i
$699$	−6.10142	+	16.1449i	−0.230777	+	0.610655i
$700$	−0.358066	+	1.33632i	−0.0135336	+	0.0505082i
$701$	32.2520			1.21814			0.609071	−	0.793115i	$-0.291542\pi$
$701$	32.2520			1.21814			0.609071	+	0.793115i	$0.291542\pi$
$702$	5.39094	−	17.9426i	0.203468	−	0.677201i
$703$	−5.16224			−0.194698
$704$	0.940292	−	3.50922i	0.0354386	−	0.132259i
$705$	5.34015	−	14.1305i	0.201122	−	0.532185i
$706$	−10.3227	−	5.95982i	−0.388500	−	0.224301i
$707$	−1.57603	+	5.88181i	−0.0592726	+	0.221208i
$708$	−6.81519	−	4.89765i	−0.256130	−	0.184065i
$709$	9.57038	+	9.57038i	0.359423	+	0.359423i	0.863600	−	0.504177i	$-0.168204\pi$
$709$	9.57038	+	9.57038i	0.359423	+	0.359423i	−0.504177	+	0.863600i	$0.668204\pi$
$710$	−4.33120	+	4.33120i	−0.162547	+	0.162547i
$711$	10.0396	−	3.37777i	0.376516	−	0.126676i
$712$	−8.98484	−	5.18740i	−0.336721	−	0.194406i
$713$	−8.15292	−	2.18457i	−0.305329	−	0.0818127i
$714$	−1.57416	+	1.28833i	−0.0589116	+	0.0482144i
$715$	−11.6336	+	6.82108i	−0.435073	+	0.255094i
$716$	−21.6674	+	12.5097i	−0.809750	+	0.467509i
$717$	0.101562	+	0.0729863i	0.00379291	+	0.00272572i
$718$	9.89226	+	17.1339i	0.369176	+	0.639431i
$719$	−5.20762	−	9.01985i	−0.194211	−	0.336384i	0.752430	−	0.658672i	$-0.228881\pi$
$719$	−5.20762	−	9.01985i	−0.194211	−	0.336384i	−0.946642	+	0.322288i	$0.895548\pi$
$720$	−2.76638	−	1.37353i	−0.103097	−	0.0511886i
$721$	3.61241	+	0.967944i	0.134533	+	0.0360481i
$722$	−12.7224	+	12.7224i	−0.473477	+	0.473477i
$723$	29.5352	−	13.3342i	1.09843	−	0.495903i
$724$	11.6937	−	20.2541i	0.434594	−	0.752739i
$725$	22.9341			0.851752
$726$	−1.56705	−	3.47102i	−0.0581586	−	0.128822i
$727$	−20.0010	−	11.5476i	−0.741796	−	0.428276i	0.0809260	−	0.996720i	$-0.474212\pi$
$727$	−20.0010	−	11.5476i	−0.741796	−	0.428276i	−0.822722	+	0.568444i	$0.807546\pi$
$728$	−1.10061	−	0.625638i	−0.0407914	−	0.0231877i
$729$	15.1819	−	22.3273i	0.562294	−	0.826938i
$730$	−0.931405	−	3.47605i	−0.0344728	−	0.128654i
$731$	7.93338	−	4.58034i	0.293427	−	0.169410i
$732$	−7.67566	+	6.28191i	−0.283701	+	0.232186i
$733$	−24.5643	−	6.58200i	−0.907305	−	0.243112i	−0.225154	−	0.974323i	$-0.572289\pi$
$733$	−24.5643	−	6.58200i	−0.907305	−	0.243112i	−0.682151	+	0.731212i	$0.738955\pi$
$734$	−16.1111	+	4.31695i	−0.594671	+	0.159342i
$735$	−7.15614	+	9.95793i	−0.263958	+	0.367304i
$736$	1.42041	−	0.380599i	0.0523571	−	0.0140290i
$737$	−47.4269	+	27.3819i	−1.74699	+	1.00863i
$738$	−27.4893	−	5.54524i	−1.01189	−	0.204123i
$739$	23.9997	−	6.43070i	0.882843	−	0.236557i	0.211209	−	0.977441i	$-0.432260\pi$
$739$	23.9997	−	6.43070i	0.882843	−	0.236557i	0.671633	+	0.740884i	$0.265593\pi$
$740$	−2.64694	+	4.58464i	−0.0973035	+	0.168535i
$741$	5.69677	−	2.61802i	0.209276	−	0.0961755i
$742$	0.469635	+	0.813432i	0.0172408	+	0.0298620i
$743$	−15.1274	−	15.1274i	−0.554971	−	0.554971i	0.372901	−	0.927871i	$-0.378363\pi$
$743$	−15.1274	−	15.1274i	−0.554971	−	0.554971i	−0.927871	+	0.372901i	$0.878363\pi$
$744$	−1.60619	−	9.81105i	−0.0588860	−	0.359691i
$745$			13.3286i			0.488324i
$746$	−0.377142	−	0.377142i	−0.0138082	−	0.0138082i
$747$	23.2192	+	11.5286i	0.849547	+	0.421808i
$748$	3.14500	−	11.7373i	0.114993	−	0.429159i
$749$	0.0727242	+	0.271410i	0.00265728	+	0.00991712i
$750$	−15.7325	+	2.57561i	−0.574470	+	0.0940481i
$751$			42.6857i			1.55762i	0.627258	+	0.778812i	$0.284177\pi$
$751$			42.6857i			1.55762i	−0.627258	+	0.778812i	$0.715823\pi$
$752$	−5.99005	+	5.99005i	−0.218435	+	0.218435i
$753$	36.1650	−	5.92066i	1.31792	−	0.215761i
$754$	−5.29580	+	20.3079i	−0.192862	+	0.739569i
$755$			9.30355i			0.338591i
$756$	−1.24181	−	1.33669i	−0.0451643	−	0.0486149i
$757$	8.17298	−	14.1560i	0.297052	−	0.514509i	−0.678408	−	0.734685i	$-0.737330\pi$
$757$	8.17298	−	14.1560i	0.297052	−	0.514509i	0.975460	+	0.220176i	$0.0706632\pi$
$758$	−34.5184			−1.25377
$759$	5.40002	−	7.51425i	0.196008	−	0.272750i
$760$	−0.267510	−	0.998362i	−0.00970362	−	0.0362144i
$761$	1.60666	+	5.99615i	0.0582415	+	0.217360i	0.988913	−	0.148496i	$-0.0474431\pi$
$761$	1.60666	+	5.99615i	0.0582415	+	0.217360i	−0.930672	+	0.365856i	$0.880776\pi$
$762$	13.3843	+	29.6462i	0.484860	+	1.07397i
$763$	−2.89957			−0.104971
$764$	6.15600	−	10.6625i	0.222716	−	0.385756i
$765$	−9.25273	−	4.59407i	−0.334533	−	0.166099i
$766$		−	2.02050i		−	0.0730038i
$767$	4.40841	−	16.9050i	0.159179	−	0.610404i
$768$	1.09699	+	1.34038i	0.0395843	+	0.0483667i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.612305 - 1.62021i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.266463 - 0.994452i) q^{5} +(-1.40653 - 1.01078i) q^{6} +(-0.248284 - 0.248284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.25016 - 1.98413i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.612305 - 1.62021i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.266463 - 0.994452i) q^{5} +(-1.40653 - 1.01078i) q^{6} +(-0.248284 - 0.248284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.25016 - 1.98413i) q^{9} +(-0.891601 - 0.514766i) q^{10} +(3.50922 + 0.940292i) q^{11} +(-1.34038 + 1.09699i) q^{12} +(-3.13452 - 1.78180i) q^{13} +(-0.304085 + 0.175564i) q^{14} +(-1.44807 - 1.04063i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.67236 + 2.89660i) q^{17} +(-2.49890 + 1.65996i) q^{18} +(-0.969723 - 0.259837i) q^{19} +(-0.727989 + 0.727989i) q^{20} +(-0.554299 + 0.250247i) q^{21} +(1.81650 - 3.14628i) q^{22} +1.47052 q^{23} +(0.712697 + 1.57863i) q^{24} +(3.41219 + 1.97003i) q^{25} +(-2.53236 + 2.56655i) q^{26} +(-4.59249 + 2.43085i) q^{27} +(0.0908784 + 0.339163i) q^{28} +(5.04092 - 2.91038i) q^{29} +(-1.37996 + 1.12939i) q^{30} +(-5.54424 - 1.48558i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.67218 - 5.10993i) q^{33} +(3.23074 - 0.865675i) q^{34} +(-0.313065 + 0.180748i) q^{35} +(0.956637 + 2.84339i) q^{36} +(4.96682 - 1.33085i) q^{37} +(-0.501966 + 0.869430i) q^{38} +(-4.80617 + 3.98757i) q^{39} +(0.514766 + 0.891601i) q^{40} +(6.60980 + 6.60980i) q^{41} +(0.0982571 + 0.600180i) q^{42} -2.73886i q^{43} +(-2.56893 - 2.56893i) q^{44} +(-2.57270 + 1.70899i) q^{45} +(0.380599 - 1.42041i) q^{46} +(2.19251 + 8.18256i) q^{47} +(1.70930 - 0.279834i) q^{48} -6.87671i q^{49} +(2.78605 - 2.78605i) q^{50} +(5.71710 - 0.935962i) q^{51} +(1.82367 + 3.11034i) q^{52} -2.67501i q^{53} +(1.15940 + 5.06516i) q^{54} +(1.87015 - 3.23920i) q^{55} +0.351127 q^{56} +(-1.01476 + 1.41206i) q^{57} +(-1.50652 - 5.62241i) q^{58} +(1.25408 + 4.68030i) q^{59} +(0.733745 + 1.62525i) q^{60} +5.72649 q^{61} +(-2.86991 + 4.97083i) q^{62} +(0.0660532 + 1.05131i) q^{63} -1.00000i q^{64} +(-2.60715 + 2.64234i) q^{65} +(-3.98538 - 4.86960i) q^{66} +(-10.6589 + 10.6589i) q^{67} -3.34471i q^{68} +(0.900407 - 2.38255i) q^{69} +(0.0935622 + 0.349179i) q^{70} +(1.53985 - 5.74681i) q^{71} +(2.99410 - 0.188118i) q^{72} +(2.47165 + 2.47165i) q^{73} -5.14203i q^{74} +(5.28117 - 4.32221i) q^{75} +(0.709887 + 0.709887i) q^{76} +(-0.637824 - 1.10474i) q^{77} +(2.60777 + 5.67446i) q^{78} +(-1.76544 + 3.05783i) q^{79} +(0.994452 - 0.266463i) q^{80} +(1.12648 + 8.92922i) q^{81} +(8.09532 - 4.67384i) q^{82} +(-8.34680 + 2.23652i) q^{83} +(0.605160 + 0.0604289i) q^{84} +(3.32615 - 0.891240i) q^{85} +(-2.64553 - 0.708868i) q^{86} +(-1.62884 - 9.94939i) q^{87} +(-3.14628 + 1.81650i) q^{88} +(2.68520 + 10.0213i) q^{89} +(0.984889 + 2.92736i) q^{90} +(0.335858 + 1.22064i) q^{91} +(-1.27351 - 0.735260i) q^{92} +(-5.80171 + 8.07321i) q^{93} +8.47121 q^{94} +(-0.516790 + 0.895107i) q^{95} +(0.172100 - 1.72348i) q^{96} +(-10.4441 + 10.4441i) q^{97} +(-6.64239 - 1.77982i) q^{98} +(-6.03066 - 9.07854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7}+O(q^{10}) \) 56 * q - 8 * q^7	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47} - 24 q^{50} + 8 q^{52} - 36 q^{54} + 36 q^{57} + 24 q^{60} - 48 q^{63} - 36 q^{65} + 28 q^{67} + 84 q^{69} - 24 q^{71} - 24 q^{72} + 28 q^{73} + 4 q^{76} + 24 q^{77} - 60 q^{78} - 24 q^{79} + 24 q^{81} - 96 q^{83} - 72 q^{85} + 4 q^{91} - 24 q^{92} - 36 q^{93} - 52 q^{97} + 48 q^{98} + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more