LMFDB - Embedded newform 336.2.bo.a.101.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			101.34
Character	$\chi$	$=$	336.101
Dual form			336.2.bo.a.173.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.316269 - 1.37840i) q^{2} +(-0.556562 + 1.64019i) q^{3} +(-1.79995 - 0.871887i) q^{4} +(0.0665356 - 0.248314i) q^{5} +(2.08481 + 1.28590i) q^{6} +(-0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-2.38048 - 1.82574i) q^{9} +O(q^{10})$	\(q+(0.316269 - 1.37840i) q^{2} +(-0.556562 + 1.64019i) q^{3} +(-1.79995 - 0.871887i) q^{4} +(0.0665356 - 0.248314i) q^{5} +(2.08481 + 1.28590i) q^{6} +(-0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-2.38048 - 1.82574i) q^{9} +(-0.321232 - 0.170246i) q^{10} +(1.52697 + 5.69873i) q^{11} +(2.43185 - 2.46701i) q^{12} +(-1.65400 - 1.65400i) q^{13} +(3.59176 + 1.04845i) q^{14} +(0.370253 + 0.247334i) q^{15} +(2.47962 + 3.13870i) q^{16} +(-3.31337 + 5.73893i) q^{17} +(-3.26946 + 2.70382i) q^{18} +(1.12557 - 4.20068i) q^{19} +(-0.336263 + 0.388941i) q^{20} +(-4.24608 - 1.72360i) q^{21} +(8.33804 - 0.302437i) q^{22} +(2.18135 + 3.77821i) q^{23} +(-2.63139 - 4.13228i) q^{24} +(4.27289 + 2.46696i) q^{25} +(-2.80298 + 1.75676i) q^{26} +(4.31945 - 2.88831i) q^{27} +(2.58114 - 4.61927i) q^{28} +(0.853732 + 0.853732i) q^{29} +(0.458023 - 0.432130i) q^{30} +(-3.82842 - 2.21034i) q^{31} +(5.11060 - 2.42523i) q^{32} +(-10.1969 - 0.667167i) q^{33} +(6.86260 + 6.38218i) q^{34} +(0.645568 + 0.214127i) q^{35} +(2.69290 + 5.36174i) q^{36} +(-1.05346 + 3.93158i) q^{37} +(-5.43422 - 2.88003i) q^{38} +(3.63344 - 1.79233i) q^{39} +(0.429765 + 0.586513i) q^{40} +2.05452i q^{41} +(-3.71870 + 5.30766i) q^{42} +(-2.94440 - 2.94440i) q^{43} +(2.22019 - 11.5888i) q^{44} +(-0.611744 + 0.469630i) q^{45} +(5.89775 - 1.81183i) q^{46} +(0.356974 + 0.618298i) q^{47} +(-6.52815 + 2.32018i) q^{48} +(-6.95219 - 0.816715i) q^{49} +(4.75183 - 5.10952i) q^{50} +(-7.56887 - 8.62865i) q^{51} +(1.53502 + 4.41923i) q^{52} +(-3.18848 - 11.8996i) q^{53} +(-2.61513 - 6.86739i) q^{54} +1.51667 q^{55} +(-5.55085 - 5.01877i) q^{56} +(6.26349 + 4.18409i) q^{57} +(1.44679 - 0.906771i) q^{58} +(-1.26315 + 0.338459i) q^{59} +(-0.450788 - 0.768006i) q^{60} +(3.80291 - 14.1926i) q^{61} +(-4.25753 + 4.57801i) q^{62} +(5.19024 - 6.00511i) q^{63} +(-1.72660 - 7.81146i) q^{64} +(-0.520763 + 0.300662i) q^{65} +(-4.14458 + 13.8443i) q^{66} +(1.84191 + 6.87409i) q^{67} +(10.9676 - 7.44089i) q^{68} +(-7.41105 + 1.47503i) q^{69} +(0.499325 - 0.822126i) q^{70} +9.22268 q^{71} +(8.24228 - 2.01612i) q^{72} +(2.87170 - 4.97393i) q^{73} +(5.08609 + 2.69553i) q^{74} +(-6.42442 + 5.63537i) q^{75} +(-5.68849 + 6.57964i) q^{76} +(-15.2877 + 3.15201i) q^{77} +(-1.32140 - 5.57518i) q^{78} +(2.19461 + 3.80118i) q^{79} +(0.944368 - 0.406890i) q^{80} +(2.33335 + 8.69226i) q^{81} +(2.83195 + 0.649782i) q^{82} +(-6.70882 + 6.70882i) q^{83} +(6.13995 + 6.80449i) q^{84} +(1.20460 + 1.20460i) q^{85} +(-4.98976 + 3.12732i) q^{86} +(-1.87544 + 0.925132i) q^{87} +(-15.2717 - 6.72546i) q^{88} +(-0.982700 + 0.567362i) q^{89} +(0.453860 + 0.991754i) q^{90} +(4.62433 - 4.11288i) q^{91} +(-0.632143 - 8.70246i) q^{92} +(5.75613 - 5.04916i) q^{93} +(0.965159 - 0.296503i) q^{94} +(-0.968199 - 0.558990i) q^{95} +(1.13348 + 9.73217i) q^{96} +11.1323i q^{97} +(-3.32452 + 9.32457i) q^{98} +(6.76948 - 16.3536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.316269	−	1.37840i	0.223636	−	0.974673i
$2$	0.316269	−	1.37840i	0.223636	−	0.974673i
$3$	−0.556562	+	1.64019i	−0.321331	+	0.946967i
$3$	−0.556562	+	1.64019i	−0.321331	+	0.946967i
$4$	−1.79995	−	0.871887i	−0.899974	−	0.435944i
$5$	0.0665356	−	0.248314i	0.0297556	−	0.111049i	−0.949451	−	0.313916i	$-0.898359\pi$
$5$	0.0665356	−	0.248314i	0.0297556	−	0.111049i	0.979206	+	0.202866i	$0.0650257\pi$
$6$	2.08481	+	1.28590i	0.851122	+	0.524968i
$7$	−0.154609	+	2.64123i	−0.0584367	+	0.998291i
$7$	−0.154609	+	2.64123i	−0.0584367	+	0.998291i
$8$	−1.77107	+	2.20529i	−0.626169	+	0.779687i
$9$	−2.38048	−	1.82574i	−0.793493	−	0.608580i
$10$	−0.321232	−	0.170246i	−0.101582	−	0.0538367i
$11$	1.52697	+	5.69873i	0.460399	+	1.71823i	0.671711	+	0.740813i	$0.265560\pi$
$11$	1.52697	+	5.69873i	0.460399	+	1.71823i	−0.211312	+	0.977419i	$0.567774\pi$
$12$	2.43185	−	2.46701i	0.702014	−	0.712163i
$13$	−1.65400	−	1.65400i	−0.458738	−	0.458738i	0.439503	−	0.898241i	$-0.355155\pi$
$13$	−1.65400	−	1.65400i	−0.458738	−	0.458738i	−0.898241	+	0.439503i	$0.855155\pi$
$14$	3.59176	+	1.04845i	0.959939	+	0.280210i
$15$	0.370253	+	0.247334i	0.0955988	+	0.0638612i
$16$	2.47962	+	3.13870i	0.619906	+	0.784676i
$17$	−3.31337	+	5.73893i	−0.803611	+	1.39190i	0.113614	+	0.993525i	$0.463757\pi$
$17$	−3.31337	+	5.73893i	−0.803611	+	1.39190i	−0.917225	+	0.398370i	$0.869576\pi$
$18$	−3.26946	+	2.70382i	−0.770620	+	0.637295i
$19$	1.12557	−	4.20068i	0.258223	−	0.963703i	−0.708045	−	0.706167i	$-0.750423\pi$
$19$	1.12557	−	4.20068i	0.258223	−	0.963703i	0.966269	−	0.257536i	$-0.0829106\pi$
$20$	−0.336263	+	0.388941i	−0.0751906	+	0.0869699i
$21$	−4.24608	−	1.72360i	−0.926571	−	0.376120i
$22$	8.33804	−	0.302437i	1.77768	−	0.0644798i
$23$	2.18135	+	3.77821i	0.454843	+	0.787810i	0.998679	−	0.0513807i	$-0.0163622\pi$
$23$	2.18135	+	3.77821i	0.454843	+	0.787810i	−0.543837	+	0.839191i	$0.683029\pi$
$24$	−2.63139	−	4.13228i	−0.537131	−	0.843499i
$25$	4.27289	+	2.46696i	0.854579	+	0.493391i
$26$	−2.80298	+	1.75676i	−0.549710	+	0.344529i
$27$	4.31945	−	2.88831i	0.831279	−	0.555856i
$28$	2.58114	−	4.61927i	0.487790	−	0.872961i
$29$	0.853732	+	0.853732i	0.158534	+	0.158534i	0.781917	−	0.623383i	$-0.214242\pi$
$29$	0.853732	+	0.853732i	0.158534	+	0.158534i	−0.623383	+	0.781917i	$0.714242\pi$
$30$	0.458023	−	0.432130i	0.0836231	−	0.0788959i
$31$	−3.82842	−	2.21034i	−0.687604	−	0.396988i	0.115110	−	0.993353i	$-0.463278\pi$
$31$	−3.82842	−	2.21034i	−0.687604	−	0.396988i	−0.802714	+	0.596365i	$0.796611\pi$
$32$	5.11060	−	2.42523i	0.903436	−	0.428724i
$33$	−10.1969	−	0.667167i	−1.77505	−	0.116139i
$34$	6.86260	+	6.38218i	1.17693	+	1.09454i
$35$	0.645568	+	0.214127i	0.109121	+	0.0361941i
$36$	2.69290	+	5.36174i	0.448816	+	0.893624i
$37$	−1.05346	+	3.93158i	−0.173188	+	0.646348i	0.823665	+	0.567077i	$0.191926\pi$
$37$	−1.05346	+	3.93158i	−0.173188	+	0.646348i	−0.996853	+	0.0792707i	$0.974741\pi$
$38$	−5.43422	−	2.88003i	−0.881547	−	0.467202i
$39$	3.63344	−	1.79233i	0.581817	−	0.287003i
$40$	0.429765	+	0.586513i	0.0679518	+	0.0927358i
$41$			2.05452i			0.320863i	0.987047	+	0.160431i	$0.0512885\pi$
$41$			2.05452i			0.320863i	−0.987047	+	0.160431i	$0.948711\pi$
$42$	−3.71870	+	5.30766i	−0.573808	+	0.818990i
$43$	−2.94440	−	2.94440i	−0.449016	−	0.449016i	0.446011	−	0.895027i	$-0.352844\pi$
$43$	−2.94440	−	2.94440i	−0.449016	−	0.449016i	−0.895027	+	0.446011i	$0.852844\pi$
$44$	2.22019	−	11.5888i	0.334706	−	1.74707i
$45$	−0.611744	+	0.469630i	−0.0911933	+	0.0700083i
$46$	5.89775	−	1.81183i	0.869576	−	0.267140i
$47$	0.356974	+	0.618298i	0.0520701	+	0.0901880i	0.890886	−	0.454228i	$-0.150085\pi$
$47$	0.356974	+	0.618298i	0.0520701	+	0.0901880i	−0.838816	+	0.544416i	$0.816751\pi$
$48$	−6.52815	+	2.32018i	−0.942257	+	0.334890i
$49$	−6.95219	−	0.816715i	−0.993170	−	0.116674i
$50$	4.75183	−	5.10952i	0.672010	−	0.722595i
$51$	−7.56887	−	8.62865i	−1.05985	−	1.20825i
$52$	1.53502	+	4.41923i	0.212868	+	0.612836i
$53$	−3.18848	−	11.8996i	−0.437971	−	1.63453i	−0.733854	−	0.679307i	$-0.762280\pi$
$53$	−3.18848	−	11.8996i	−0.437971	−	1.63453i	0.295882	−	0.955224i	$-0.404386\pi$
$54$	−2.61513	−	6.86739i	−0.355874	−	0.934534i
$55$	1.51667			0.204508
$56$	−5.55085	−	5.01877i	−0.741764	−	0.670661i
$57$	6.26349	+	4.18409i	0.829620	+	0.554197i
$58$	1.44679	−	0.906771i	0.189973	−	0.119065i
$59$	−1.26315	+	0.338459i	−0.164448	+	0.0440636i	−0.340103	−	0.940388i	$-0.610462\pi$
$59$	−1.26315	+	0.338459i	−0.164448	+	0.0440636i	0.175656	+	0.984452i	$0.443795\pi$
$60$	−0.450788	−	0.768006i	−0.0581965	−	0.0991491i
$61$	3.80291	−	14.1926i	0.486913	−	1.81718i	−0.0843772	−	0.996434i	$-0.526890\pi$
$61$	3.80291	−	14.1926i	0.486913	−	1.81718i	0.571290	−	0.820748i	$-0.306443\pi$
$62$	−4.25753	+	4.57801i	−0.540707	+	0.581408i
$63$	5.19024	−	6.00511i	0.653909	−	0.756573i
$64$	−1.72660	−	7.81146i	−0.215825	−	0.976432i
$65$	−0.520763	+	0.300662i	−0.0645927	+	0.0372926i
$66$	−4.14458	+	13.8443i	−0.510162	+	1.70412i
$67$	1.84191	+	6.87409i	0.225025	+	0.839804i	0.982395	+	0.186818i	$0.0598174\pi$
$67$	1.84191	+	6.87409i	0.225025	+	0.839804i	−0.757370	+	0.652986i	$0.773516\pi$
$68$	10.9676	−	7.44089i	1.33002	−	0.902340i
$69$	−7.41105	+	1.47503i	−0.892185	+	0.177573i
$70$	0.499325	−	0.822126i	0.0596808	−	0.0982629i
$71$	9.22268			1.09453			0.547265	−	0.836959i	$-0.315669\pi$
$71$	9.22268			1.09453			0.547265	+	0.836959i	$0.315669\pi$
$72$	8.24228	−	2.01612i	0.971362	−	0.237602i
$73$	2.87170	−	4.97393i	0.336107	−	0.582155i	−0.647590	−	0.761989i	$-0.724223\pi$
$73$	2.87170	−	4.97393i	0.336107	−	0.582155i	0.983697	+	0.179834i	$0.0575562\pi$
$74$	5.08609	+	2.69553i	0.591246	+	0.313349i
$75$	−6.42442	+	5.63537i	−0.741828	+	0.650716i
$76$	−5.68849	+	6.57964i	−0.652515	+	0.754737i
$77$	−15.2877	+	3.15201i	−1.74220	+	0.359204i
$78$	−1.32140	−	5.57518i	−0.149619	−	0.631265i
$79$	2.19461	+	3.80118i	0.246913	+	0.427666i	0.962668	−	0.270686i	$-0.0872504\pi$
$79$	2.19461	+	3.80118i	0.246913	+	0.427666i	−0.715755	+	0.698352i	$0.753917\pi$
$80$	0.944368	−	0.406890i	0.105584	−	0.0454917i
$81$	2.33335	+	8.69226i	0.259261	+	0.965807i
$82$	2.83195	+	0.649782i	0.312736	+	0.0717565i
$83$	−6.70882	+	6.70882i	−0.736389	+	0.736389i	−0.971877	−	0.235488i	$-0.924331\pi$
$83$	−6.70882	+	6.70882i	−0.736389	+	0.736389i	0.235488	+	0.971877i	$0.424331\pi$
$84$	6.13995	+	6.80449i	0.669923	+	0.742431i
$85$	1.20460	+	1.20460i	0.130657	+	0.130657i
$86$	−4.98976	+	3.12732i	−0.538060	+	0.337228i
$87$	−1.87544	+	0.925132i	−0.201068	+	0.0991845i
$88$	−15.2717	−	6.72546i	−1.62797	−	0.716937i
$89$	−0.982700	+	0.567362i	−0.104166	+	0.0601402i	−0.551178	−	0.834388i	$-0.685821\pi$
$89$	−0.982700	+	0.567362i	−0.104166	+	0.0601402i	0.447012	+	0.894528i	$0.352488\pi$
$90$	0.453860	+	0.991754i	0.0478411	+	0.104540i
$91$	4.62433	−	4.11288i	0.484761	−	0.431147i
$92$	−0.632143	−	8.70246i	−0.0659054	−	0.907295i
$93$	5.75613	−	5.04916i	0.596883	−	0.523573i
$94$	0.965159	−	0.296503i	0.0995485	−	0.0305820i
$95$	−0.968199	−	0.558990i	−0.0993351	−	0.0573512i
$96$	1.13348	+	9.73217i	0.115685	+	0.993286i
$97$			11.1323i			1.13031i	0.824985	+	0.565155i	$0.191184\pi$
$97$			11.1323i			1.13031i	−0.824985	+	0.565155i	$0.808816\pi$
$98$	−3.32452	+	9.32457i	−0.335827	+	0.941924i
$99$	6.76948	−	16.3536i	0.680358	−	1.64359i
$100$	−5.54008	−	8.16588i	−0.554008	−	0.816588i
$101$	12.1504	−	3.25569i	1.20901	−	0.323953i	0.402636	−	0.915360i	$-0.368094\pi$
$101$	12.1504	−	3.25569i	1.20901	−	0.323953i	0.806373	+	0.591407i	$0.201427\pi$
$102$	−14.2875	+	7.70392i	−1.41467	+	0.762802i
$103$	2.11657	+	3.66601i	0.208552	+	0.361222i	0.951259	−	0.308394i	$-0.0997917\pi$
$103$	2.11657	+	3.66601i	0.208552	+	0.361222i	−0.742707	+	0.669617i	$0.766458\pi$
$104$	6.57692	−	0.718194i	0.644920	−	0.0704247i
$105$	−0.710509	+	0.939682i	−0.0693386	+	0.0917036i
$106$	−17.4107	+	0.631521i	−1.69108	+	0.0613388i
$107$	6.89925	+	1.84865i	0.666975	+	0.178715i	0.576392	−	0.817173i	$-0.304460\pi$
$107$	6.89925	+	1.84865i	0.666975	+	0.178715i	0.0905833	+	0.995889i	$0.471127\pi$
$108$	−10.2931	+	1.43273i	−0.990451	+	0.137865i
$109$	−1.40507	−	5.24379i	−0.134581	−	0.502264i	−0.999999	−	0.00121322i	$-0.999614\pi$
$109$	−1.40507	−	5.24379i	−0.134581	−	0.502264i	0.865418	−	0.501050i	$-0.167053\pi$
$110$	0.479677	−	2.09058i	0.0457354	−	0.199329i
$111$	−5.86224	−	3.91605i	−0.556419	−	0.371695i
$112$	−8.67341	+	6.06399i	−0.819560	+	0.572993i
$113$			11.2533i			1.05862i	0.848429	+	0.529309i	$0.177549\pi$
$113$			11.2533i			1.05862i	−0.848429	+	0.529309i	$0.822451\pi$
$114$	7.74828	−	7.31027i	0.725693	−	0.684669i
$115$	1.08332	−	0.290275i	0.101020	−	0.0270682i
$116$	−0.792314	−	2.28103i	−0.0735645	−	0.211788i
$117$	0.917540	+	6.95710i	0.0848266	+	0.643184i
$118$	0.0670364	+	1.84816i	0.00617120	+	0.170137i
$119$	−14.6456	−	9.63867i	−1.34256	−	0.883575i
$120$	−1.20119	+	0.378468i	−0.109653	+	0.0345492i
$121$	−20.6176	+	11.9036i	−1.87433	+	1.08214i
$122$	−18.3603	−	9.73061i	−1.66227	−	0.880968i
$123$	−3.36982	−	1.14347i	−0.303846	−	0.103103i
$124$	4.96378	+	7.31644i	0.445761	+	0.657036i
$125$	1.80577	−	1.80577i	0.161513	−	0.161513i
$126$	−6.63591	−	9.05344i	−0.591174	−	0.806544i
$127$	13.0977			1.16223			0.581115	−	0.813822i	$-0.302617\pi$
$127$	13.0977			1.16223			0.581115	+	0.813822i	$0.302617\pi$
$128$	−11.3133	−	0.0905870i	−0.999968	−	0.00800683i
$129$	6.46812	−	3.19064i	0.569486	−	0.280921i
$130$	0.249731	+	0.812907i	0.0219028	+	0.0712967i
$131$	12.1960	+	3.26791i	1.06557	+	0.285518i	0.748671	−	0.662941i	$-0.230692\pi$
$131$	12.1960	+	3.26791i	1.06557	+	0.285518i	0.316898	+	0.948460i	$0.397359\pi$
$132$	17.7722	+	10.0914i	1.54687	+	0.878344i
$133$	10.9209	+	3.62235i	0.946966	+	0.314098i
$134$	10.0578	−	0.364815i	0.868858	−	0.0315152i
$135$	−0.429812	−	1.26476i	−0.0369923	−	0.108853i
$136$	−6.78777	−	17.4710i	−0.582047	−	1.49813i
$137$	3.08371	−	5.34114i	0.263459	−	0.456324i	−0.703700	−	0.710498i	$-0.748470\pi$
$137$	3.08371	−	5.34114i	0.263459	−	0.456324i	0.967159	+	0.254173i	$0.0818033\pi$
$138$	−0.310709	+	10.6819i	−0.0264493	+	0.909301i
$139$	−6.01159	+	6.01159i	−0.509896	+	0.509896i	−0.914495	−	0.404598i	$-0.867411\pi$
$139$	−6.01159	+	6.01159i	−0.509896	+	0.509896i	0.404598	+	0.914495i	$0.367411\pi$
$140$	−0.975294	−	0.948281i	−0.0824274	−	0.0801444i
$141$	−1.21281	+	0.241387i	−0.102137	+	0.0203284i
$142$	2.91685	−	12.7125i	0.244776	−	1.06681i
$143$	6.90011	−	11.9513i	0.577016	−	0.999421i
$144$	−0.172237	−	11.9988i	−0.0143531	−	0.999897i
$145$	0.268797	−	0.155190i	0.0223224	−	0.0128878i
$146$	−5.94782	−	5.53144i	−0.492245	−	0.457785i
$147$	5.20890	−	10.9484i	0.429623	−	0.903009i
$148$	5.32407	−	6.15814i	0.437636	−	0.506196i
$149$	10.0783	+	2.70047i	0.825646	+	0.221231i	0.646813	−	0.762648i	$-0.276101\pi$
$149$	10.0783	+	2.70047i	0.825646	+	0.221231i	0.178832	+	0.983880i	$0.442768\pi$
$150$	5.73592	+	10.6377i	0.468336	+	0.868563i
$151$	20.1655	+	11.6426i	1.64104	+	0.947458i	0.980463	+	0.196703i	$0.0630236\pi$
$151$	20.1655	+	11.6426i	1.64104	+	0.947458i	0.660582	+	0.750754i	$0.270310\pi$
$152$	7.27025	+	9.92193i	0.589695	+	0.804774i
$153$	18.3652	−	7.61204i	1.48474	−	0.615397i
$154$	−0.490329	+	22.0694i	−0.0395118	+	1.77841i
$155$	−0.803584	+	0.803584i	−0.0645454	+	0.0645454i
$156$	−8.10272	+	0.0581524i	−0.648737	+	0.00465592i
$157$	12.3271	−	3.30303i	0.983808	−	0.263611i	0.269161	−	0.963095i	$-0.413254\pi$
$157$	12.3271	−	3.30303i	0.983808	−	0.263611i	0.714648	+	0.699485i	$0.246587\pi$
$158$	5.93362	−	1.82285i	0.472053	−	0.145018i
$159$	21.2922	+	1.39312i	1.68858	+	0.110481i
$160$	−0.262182	−	1.43040i	−0.0207273	−	0.113083i
$161$	−10.3164	+	5.17730i	−0.813044	+	0.408028i
$162$	12.7193	−	0.467188i	0.999326	−	0.0367058i
$163$	2.04721	+	0.548548i	0.160350	+	0.0429656i	0.338101	−	0.941110i	$-0.390215\pi$
$163$	2.04721	+	0.548548i	0.160350	+	0.0429656i	−0.177751	+	0.984076i	$0.556882\pi$
$164$	1.79131	−	3.69804i	0.139878	−	0.288768i
$165$	−0.844123	+	2.48764i	−0.0657149	+	0.193663i
$166$	7.12562	+	11.3692i	0.553055	+	0.882421i
$167$			7.69272i			0.595280i	0.954678	+	0.297640i	$0.0961996\pi$
$167$			7.69272i			0.595280i	−0.954678	+	0.297640i	$0.903800\pi$
$168$	11.3212	−	6.31122i	0.873446	−	0.486921i
$169$		−	7.52854i		−	0.579119i
$170$	2.04139	−	1.27944i	0.156568	−	0.0981284i
$171$	−10.3487	+	7.94464i	−0.791388	+	0.607542i
$172$	2.73258	+	7.86694i	0.208357	+	0.599849i
$173$	−13.3316	−	3.57219i	−1.01358	−	0.271589i	−0.286457	−	0.958093i	$-0.592478\pi$
$173$	−13.3316	−	3.57219i	−1.01358	−	0.271589i	−0.727126	+	0.686505i	$0.759144\pi$
$174$	0.682054	+	2.87769i	0.0517064	+	0.218157i
$175$	−7.17643	+	10.9043i	−0.542487	+	0.824286i
$176$	−14.1003	+	18.9234i	−1.06285	+	1.42641i
$177$	0.147880	−	2.26018i	0.0111154	−	0.169886i
$178$	0.471252	+	1.53399i	0.0353218	+	0.114977i
$179$	−2.74363	+	0.735152i	−0.205068	+	0.0549479i	−0.359891	−	0.932994i	$-0.617186\pi$
$179$	−2.74363	+	0.735152i	−0.205068	+	0.0549479i	0.154823	+	0.987942i	$0.450519\pi$
$180$	1.51057	−	0.311938i	0.112591	−	0.0232505i
$181$	12.8523	−	12.8523i	0.955307	−	0.955307i	−0.0437364	−	0.999043i	$-0.513926\pi$
$181$	12.8523	−	12.8523i	0.955307	−	0.955307i	0.999043	+	0.0437364i	$0.0139262\pi$
$182$	−4.20664	−	7.67493i	−0.311817	−	0.568904i
$183$	21.1622	+	14.1366i	1.56435	+	1.04501i
$184$	−12.1954	−	1.88098i	−0.899054	−	0.138667i
$185$	0.906174	+	0.523180i	0.0666233	+	0.0384650i
$186$	−5.13925	−	9.53112i	−0.376828	−	0.698856i
$187$	−37.7640	−	10.1188i	−2.76158	−	0.739963i
$188$	−0.103449	−	1.42415i	−0.00754481	−	0.103866i
$189$	6.96087	+	11.8552i	0.506329	+	0.862341i
$190$	−1.07672	+	1.15777i	−0.0781135	+	0.0839935i
$191$	−8.47464	+	4.89284i	−0.613204	+	0.354033i	−0.774218	−	0.632919i	$-0.781857\pi$
$191$	−8.47464	+	4.89284i	−0.613204	+	0.354033i	0.161015	+	0.986952i	$0.448523\pi$
$192$	13.7733	+	1.51560i	0.994000	+	0.109379i
$193$	9.39914	−	16.2798i	0.676565	−	1.17185i	−0.299444	−	0.954114i	$-0.596801\pi$
$193$	9.39914	−	16.2798i	0.676565	−	1.17185i	0.976009	−	0.217731i	$-0.0698656\pi$
$194$	15.3447	+	3.52079i	1.10168	+	0.252778i
$195$	−0.203308	−	1.02149i	−0.0145592	−	0.0731504i
$196$	11.8015	+	7.53157i	0.842964	+	0.537970i
$197$	−4.79681	+	4.79681i	−0.341758	+	0.341758i	−0.857028	−	0.515270i	$-0.827692\pi$
$197$	−4.79681	+	4.79681i	−0.341758	+	0.341758i	0.515270	+	0.857028i	$0.327692\pi$
$198$	−20.4007	−	14.5031i	−1.44981	−	1.03069i
$199$	−2.87699	+	4.98310i	−0.203945	+	0.353242i	−0.949796	−	0.312870i	$-0.898710\pi$
$199$	−2.87699	+	4.98310i	−0.203945	+	0.353242i	0.745851	+	0.666112i	$0.232043\pi$
$200$	−13.0080	+	5.05380i	−0.919802	+	0.357358i
$201$	−12.3000	−	0.804770i	−0.867574	−	0.0567641i
$202$	−0.644833	−	17.7777i	−0.0453703	−	1.25084i
$203$	−2.38690	+	2.12291i	−0.167527	+	0.148999i
$204$	6.10036	+	22.1303i	0.427110	+	1.54943i
$205$	0.510168	+	0.136699i	0.0356316	+	0.00954747i
$206$	5.72261	−	1.75803i	0.398713	−	0.122487i
$207$	1.70537	−	12.9765i	0.118531	−	0.901930i
$208$	1.09012	−	9.29274i	0.0755862	−	0.644335i
$209$	25.6573			1.77475
$210$	1.07054	+	1.27655i	0.0738744	+	0.0880906i
$211$	−4.89437	+	4.89437i	−0.336942	+	0.336942i	−0.855215	−	0.518273i	$-0.826575\pi$
$211$	−4.89437	+	4.89437i	−0.336942	+	0.336942i	0.518273	+	0.855215i	$0.326575\pi$
$212$	−4.63599	+	24.1986i	−0.318401	+	1.66197i
$213$	−5.13299	+	15.1270i	−0.351707	+	1.03648i
$214$	4.73018	−	8.92522i	0.323349	−	0.610115i
$215$	−0.927042	+	0.535228i	−0.0632238	+	0.0365023i
$216$	−1.28050	+	14.6410i	−0.0871273	+	0.996197i
$217$	6.42992	−	9.76999i	0.436491	−	0.663230i
$218$	−7.67239	+	0.278293i	−0.519640	+	0.0188484i
$219$	6.55994	+	7.47845i	0.443280	+	0.505347i
$220$	−2.72993	−	1.32237i	−0.184052	−	0.0891541i
$221$	14.9725	−	4.01188i	1.00716	−	0.269868i
$222$	−7.25191	+	6.84196i	−0.486716	+	0.459202i
$223$		−	2.31556i		−	0.155062i	−0.996990	−	0.0775308i	$-0.975296\pi$
$223$		−	2.31556i		−	0.155062i	0.996990	−	0.0775308i	$-0.0247036\pi$
$224$	5.61544	+	13.8732i	0.375197	+	0.926945i
$225$	−5.66751	−	13.6737i	−0.377834	−	0.911582i
$226$	15.5114	+	3.55906i	1.03181	+	0.236745i
$227$	−2.25553	−	8.41776i	−0.149705	−	0.558706i	−0.999501	−	0.0315943i	$-0.989942\pi$
$227$	−2.25553	−	8.41776i	−0.149705	−	0.558706i	0.849796	−	0.527112i	$-0.176725\pi$
$228$	−7.62590	−	12.9922i	−0.505037	−	0.860430i
$229$	−14.0420	−	3.76254i	−0.927920	−	0.248635i	−0.236953	−	0.971521i	$-0.576149\pi$
$229$	−14.0420	−	3.76254i	−0.927920	−	0.248635i	−0.690968	+	0.722886i	$0.742815\pi$
$230$	−0.0574928	−	1.58505i	−0.00379096	−	0.104515i
$231$	3.33867	−	26.8292i	0.219668	−	1.76523i
$232$	−3.39475	+	0.370703i	−0.222876	+	0.0243379i
$233$	1.97360	+	3.41838i	0.129295	+	0.223946i	0.923404	−	0.383830i	$-0.125395\pi$
$233$	1.97360	+	3.41838i	0.129295	+	0.223946i	−0.794109	+	0.607776i	$0.792062\pi$
$234$	9.87982	+	0.935582i	0.645864	+	0.0611609i
$235$	0.177284	−	0.0475030i	0.0115647	−	0.00309875i
$236$	2.56870	+	0.492113i	0.167208	+	0.0320338i
$237$	−7.45612	+	1.48400i	−0.484327	+	0.0963962i
$238$	−17.9178	+	17.1390i	−1.16144	+	1.11095i
$239$		−	9.42859i		−	0.609885i	−0.952371	−	0.304942i	$-0.901363\pi$
$239$		−	9.42859i		−	0.609885i	0.952371	−	0.304942i	$-0.0986372\pi$
$240$	0.141781	+	1.77541i	0.00915189	+	0.114602i
$241$	−4.21351	−	2.43267i	−0.271416	−	0.156702i	0.358115	−	0.933678i	$-0.383420\pi$
$241$	−4.21351	−	2.43267i	−0.271416	−	0.156702i	−0.629531	+	0.776975i	$0.716753\pi$
$242$	9.88714	+	32.1840i	0.635569	+	2.06886i
$243$	−15.5557	−	1.01063i	−0.997896	−	0.0648319i
$244$	−19.2194	+	22.2303i	−1.23040	+	1.42315i
$245$	−0.665370	+	1.67199i	−0.0425089	+	0.106819i
$246$	−2.64192	+	4.28330i	−0.168443	+	0.273093i
$247$	−8.80964	+	5.08625i	−0.560544	+	0.323630i
$248$	11.6548	−	4.52809i	0.740083	−	0.287534i
$249$	−7.26990	−	14.7377i	−0.460711	−	0.933961i
$250$	−1.91796	−	3.06018i	−0.121302	−	0.193543i
$251$	−6.18550	−	6.18550i	−0.390425	−	0.390425i	0.484414	−	0.874839i	$-0.339033\pi$
$251$	−6.18550	−	6.18550i	−0.390425	−	0.390425i	−0.874839	+	0.484414i	$0.839033\pi$
$252$	−14.5779	+	6.28359i	−0.918324	+	0.395829i
$253$	−18.2001	+	18.2001i	−1.14423	+	1.14423i
$254$	4.14238	−	18.0538i	0.259916	−	1.13279i
$255$	−2.64621	+	1.30535i	−0.165712	+	0.0817439i
$256$	−3.70293	+	15.5656i	−0.231433	+	0.972851i
$257$	5.99043	+	10.3757i	0.373673	+	0.647221i	0.990127	−	0.140170i	$-0.0447649\pi$
$257$	5.99043	+	10.3757i	0.373673	+	0.647221i	−0.616455	+	0.787391i	$0.711432\pi$
$258$	−2.35230	−	9.92473i	−0.146448	−	0.617887i
$259$	−10.2213	−	3.39030i	−0.635123	−	0.210663i
$260$	1.19949	−	0.0871303i	0.0743892	−	0.00540359i
$261$	−0.473598	−	3.59098i	−0.0293150	−	0.222276i
$262$	8.36168	−	15.7774i	0.516587	−	0.974729i
$263$	−2.37212	+	4.10863i	−0.146271	+	0.253349i	−0.929846	−	0.367948i	$-0.880061\pi$
$263$	−2.37212	+	4.10863i	−0.146271	+	0.253349i	0.783575	+	0.621297i	$0.213394\pi$
$264$	19.5307	−	21.3055i	1.20203	−	1.31126i
$265$	−3.16698			−0.194546
$266$	8.44699	−	13.9077i	0.517918	−	0.852739i
$267$	−0.383651	−	1.92759i	−0.0234791	−	0.117967i
$268$	2.67810	−	13.9789i	0.163591	−	0.853900i
$269$	−1.06934	−	3.99085i	−0.0651991	−	0.243326i	0.925634	−	0.378421i	$-0.123533\pi$
$269$	−1.06934	−	3.99085i	−0.0651991	−	0.243326i	−0.990833	+	0.135095i	$0.956866\pi$
$270$	−1.87927	+	0.192447i	−0.114369	+	0.0117119i
$271$	−10.7958	+	6.23296i	−0.655799	+	0.378626i	−0.790674	−	0.612237i	$-0.790270\pi$
$271$	−10.7958	+	6.23296i	−0.655799	+	0.378626i	0.134876	+	0.990863i	$0.456937\pi$
$272$	−26.2287	+	3.83069i	−1.59035	+	0.232270i
$273$	4.17220	+	9.87387i	0.252513	+	0.597594i
$274$	−6.38692	−	5.93981i	−0.385848	−	0.358837i
$275$	−7.53394	+	28.1170i	−0.454314	+	1.69552i
$276$	14.6256	+	3.80662i	0.880355	+	0.229132i
$277$	12.1305	−	3.25036i	0.728851	−	0.195295i	0.124734	−	0.992190i	$-0.460192\pi$
$277$	12.1305	−	3.25036i	0.728851	−	0.195295i	0.604118	+	0.796895i	$0.293526\pi$
$278$	6.38507	+	10.1876i	0.382951	+	0.611013i
$279$	5.07796	+	12.2513i	0.304010	+	0.733469i
$280$	−1.61556	+	1.04443i	−0.0965482	+	0.0624165i
$281$	−13.1985			−0.787359			−0.393679	−	0.919248i	$-0.628798\pi$
$281$	−13.1985			−0.787359			−0.393679	+	0.919248i	$0.628798\pi$
$282$	−0.0508470	+	1.74807i	−0.00302789	+	0.104096i
$283$	5.90043	+	22.0207i	0.350744	+	1.30899i	0.885756	+	0.464150i	$0.153640\pi$
$283$	5.90043	+	22.0207i	0.350744	+	1.30899i	−0.535012	+	0.844844i	$0.679693\pi$
$284$	−16.6003	−	8.04114i	−0.985049	−	0.477154i
$285$	1.45571	−	1.27692i	0.0862291	−	0.0756384i
$286$	−14.2914	−	13.2909i	−0.845067	−	0.785908i
$287$	−5.42647	−	0.317648i	−0.320314	−	0.0187501i
$288$	−16.5935	−	3.55743i	−0.977782	−	0.209623i
$289$	−13.4569	−	23.3080i	−0.791581	−	1.37106i
$290$	−0.128901	−	0.419591i	−0.00756934	−	0.0246392i
$291$	−18.2591	−	6.19579i	−1.07037	−	0.363204i
$292$	−9.50562	+	6.44902i	−0.556275	+	0.377400i
$293$	2.13884	+	2.13884i	0.124952	+	0.124952i	0.766818	−	0.641865i	$-0.221839\pi$
$293$	2.13884	+	2.13884i	0.124952	+	0.124952i	−0.641865	+	0.766818i	$0.721839\pi$
$294$	−13.4438	−	10.6426i	−0.784059	−	0.620687i
$295$			0.336177i			0.0195730i
$296$	−6.80451	−	9.28631i	−0.395504	−	0.539756i
$297$	23.0554	+	20.2050i	1.33781	+	1.17241i
$298$	6.90977	−	13.0378i	0.400272	−	0.755259i
$299$	2.64121	−	9.85712i	0.152745	−	0.570052i
$300$	16.4770	−	4.54199i	0.951301	−	0.262232i
$301$	8.23206	−	7.32160i	0.474488	−	0.422010i
$302$	22.4258	−	24.1138i	1.29046	−	1.38760i
$303$	−1.42248	+	21.7410i	−0.0817194	+	1.24899i
$304$	15.9757	−	6.88329i	0.916269	−	0.394784i
$305$	−3.27121	−	1.88863i	−0.187309	−	0.108143i
$306$	−4.68406	−	27.7220i	−0.267770	−	1.58476i
$307$	17.3994	+	17.3994i	0.993038	+	0.993038i	0.999976	−	0.00693770i	$-0.00220836\pi$
$307$	17.3994	+	17.3994i	0.993038	+	0.993038i	−0.00693770	+	0.999976i	$0.502208\pi$
$308$	30.2653	+	7.65575i	1.72453	+	0.436227i
$309$	−7.19097	+	1.43123i	−0.409080	+	0.0814197i
$310$	0.853508	+	1.36181i	0.0484760	+	0.0773453i
$311$	−16.1458	−	9.32176i	−0.915542	−	0.528589i	−0.0333321	−	0.999444i	$-0.510612\pi$
$311$	−16.1458	−	9.32176i	−0.915542	−	0.528589i	−0.882210	+	0.470856i	$0.843945\pi$
$312$	−2.48248	+	11.1871i	−0.140543	+	0.633347i
$313$	13.7259	+	23.7740i	0.775836	+	1.34379i	0.934323	+	0.356426i	$0.116005\pi$
$313$	13.7259	+	23.7740i	0.775836	+	1.34379i	−0.158488	+	0.987361i	$0.550662\pi$
$314$	−0.654210	−	18.0362i	−0.0369192	−	1.01784i
$315$	−1.14582	−	1.68836i	−0.0645596	−	0.0951286i
$316$	−0.635987	−	8.75538i	−0.0357770	−	0.492529i
$317$	1.51440	−	5.65181i	0.0850571	−	0.317437i	−0.910268	−	0.414020i	$-0.864124\pi$
$317$	1.51440	−	5.65181i	0.0850571	−	0.317437i	0.995325	+	0.0965823i	$0.0307911\pi$
$318$	8.65433	−	28.9085i	0.485311	−	1.62111i
$319$	−3.56156	+	6.16881i	−0.199409	+	0.345387i
$320$	−2.05458	−	0.0910011i	−0.114854	−	0.00508712i
$321$	−6.87200	+	10.2872i	−0.383558	+	0.574177i
$322$	3.87362	+	15.8575i	0.215868	+	0.883701i
$323$	20.3780	+	20.3780i	1.13386	+	1.13386i
$324$	3.37876	−	17.6800i	0.187709	−	0.982225i
$325$	−2.98703	−	11.1477i	−0.165690	−	0.618365i
$326$	1.40359	−	2.64838i	0.0777374	−	0.146680i
$327$	9.38284	+	0.613905i	0.518872	+	0.0339490i
$328$	−4.53082	−	3.63871i	−0.250173	−	0.200914i
$329$	−1.68826	+	0.847257i	−0.0930767	+	0.0467108i
$330$	3.16198	+	1.95030i	0.174061	+	0.107360i
$331$	0.225741	−	0.842477i	0.0124079	−	0.0463067i	−0.959444	−	0.281898i	$-0.909036\pi$
$331$	0.225741	−	0.842477i	0.0124079	−	0.0463067i	0.971852	+	0.235591i	$0.0757027\pi$
$332$	17.9249	−	6.22619i	0.983755	−	0.341707i
$333$	9.68579	−	7.43569i	0.530778	−	0.407473i
$334$	10.6036	+	2.43297i	0.580204	+	0.133126i
$335$	1.82949			0.0999556
$336$	−5.11883	−	17.6011i	−0.279255	−	0.960217i
$337$	9.71606			0.529268			0.264634	−	0.964349i	$-0.414749\pi$
$337$	9.71606			0.529268			0.264634	+	0.964349i	$0.414749\pi$
$338$	−10.3773	−	2.38105i	−0.564451	−	0.129512i
$339$	−18.4575	−	6.26313i	−1.00248	−	0.340167i
$340$	−1.11794	−	3.21849i	−0.0606289	−	0.174547i
$341$	6.75024	−	25.1922i	0.365546	−	1.36424i
$342$	7.67787	+	16.7773i	0.415171	+	0.907213i
$343$	3.23200	−	18.2361i	0.174512	−	0.984655i
$344$	11.7080	−	1.27850i	0.631252	−	0.0689322i
$345$	−0.126827	+	1.93841i	−0.00682815	+	0.104361i
$346$	−9.14026	+	17.2464i	−0.491383	+	0.927174i
$347$	−6.57133	−	24.5245i	−0.352768	−	1.31655i	−0.883271	−	0.468863i	$-0.844664\pi$
$347$	−6.57133	−	24.5245i	−0.352768	−	1.31655i	0.530503	−	0.847683i	$-0.322003\pi$
$348$	4.18231	−	0.0300160i	0.224195	−	0.00160903i
$349$	−21.4932	−	21.4932i	−1.15051	−	1.15051i	−0.986451	−	0.164054i	$-0.947543\pi$
$349$	−21.4932	−	21.4932i	−1.15051	−	1.15051i	−0.164054	−	0.986451i	$-0.552457\pi$
$350$	12.7607	+	13.3406i	0.682090	+	0.713087i
$351$	−11.9217	−	2.36711i	−0.636331	−	0.126347i
$352$	21.6245	+	25.4207i	1.15259	+	1.35493i
$353$	−6.41440	+	11.1101i	−0.341404	+	0.591329i	−0.984694	−	0.174294i	$-0.944236\pi$
$353$	−6.41440	+	11.1101i	−0.341404	+	0.591329i	0.643290	+	0.765623i	$0.277569\pi$
$354$	−3.06865	−	0.918662i	−0.163097	−	0.0488263i
$355$	0.613636	−	2.29012i	0.0325684	−	0.121547i
$356$	2.26348	−	0.164418i	0.119964	−	0.00871415i
$357$	23.9605	−	18.6571i	1.26812	−	0.987436i
$358$	0.145607	+	4.01431i	0.00769556	+	0.212163i
$359$	−11.6168	−	20.1209i	−0.613110	−	1.06194i	−0.990713	−	0.135970i	$-0.956585\pi$
$359$	−11.6168	−	20.1209i	−0.613110	−	1.06194i	0.377603	−	0.925968i	$-0.376748\pi$
$360$	0.0477731	−	2.18082i	0.00251786	−	0.114939i
$361$	0.0756479	+	0.0436753i	0.00398147	+	0.00229870i
$362$	−13.6508	−	21.7804i	−0.717471	−	1.14475i
$363$	−8.04923	−	40.4420i	−0.422475	−	2.12265i
$364$	−11.9095	+	3.37108i	−0.624228	+	0.176692i
$365$	−1.04403	−	1.04403i	−0.0546469	−	0.0546469i
$366$	26.1788	−	24.6988i	1.36839	−	1.29103i
$367$	−21.4355	−	12.3758i	−1.11892	−	0.646011i	−0.177798	−	0.984067i	$-0.556897\pi$
$367$	−21.4355	−	12.3758i	−1.11892	−	0.646011i	−0.941126	+	0.338056i	$0.890231\pi$
$368$	−6.44975	+	16.2151i	−0.336216	+	0.845273i
$369$	3.75103	−	4.89075i	0.195271	−	0.254602i
$370$	1.00774	−	1.08360i	0.0523901	−	0.0563337i
$371$	31.9225	−	6.58173i	1.65733	−	0.341706i
$372$	−14.7630	+	4.06952i	−0.765428	+	0.210995i
$373$	−4.55333	+	16.9933i	−0.235762	+	0.879877i	0.742041	+	0.670354i	$0.233858\pi$
$373$	−4.55333	+	16.9933i	−0.235762	+	0.879877i	−0.977804	+	0.209523i	$0.932809\pi$
$374$	−25.8914	+	48.8535i	−1.33881	+	2.52615i
$375$	1.95680	+	3.96684i	0.101048	+	0.204847i
$376$	−1.99575	−	0.307819i	−0.102923	−	0.0158746i
$377$		−	2.82415i		−	0.145451i
$378$	18.5427	−	5.84539i	0.953733	−	0.300654i
$379$	−7.89286	−	7.89286i	−0.405429	−	0.405429i	0.474712	−	0.880141i	$-0.342552\pi$
$379$	−7.89286	−	7.89286i	−0.405429	−	0.405429i	−0.880141	+	0.474712i	$0.842552\pi$
$380$	1.25533	+	1.85031i	0.0643971	+	0.0949191i
$381$	−7.28965	+	21.4827i	−0.373460	+	1.10059i
$382$	4.06400	+	13.2289i	0.207932	+	0.676847i
$383$	1.49970	+	2.59756i	0.0766311	+	0.132729i	0.901794	−	0.432165i	$-0.142250\pi$
$383$	1.49970	+	2.59756i	0.0766311	+	0.132729i	−0.825163	+	0.564894i	$0.808917\pi$
$384$	6.44516	−	18.5057i	0.328903	−	0.944364i
$385$	−0.234491	+	4.00588i	−0.0119508	+	0.204159i
$386$	−19.4673	−	18.1045i	−0.990861	−	0.921496i
$387$	1.63337	+	12.3848i	0.0830289	+	0.629553i
$388$	9.70608	−	20.0375i	0.492752	−	1.01725i
$389$	5.41170	+	20.1967i	0.274384	+	1.02402i	0.956253	+	0.292541i	$0.0945008\pi$
$389$	5.41170	+	20.1967i	0.274384	+	1.02402i	−0.681869	+	0.731474i	$0.738833\pi$
$390$	−1.47232	−	0.0428260i	−0.0745537	−	0.00216858i
$391$	−28.9105			−1.46207
$392$	14.1139	−	13.8851i	0.712861	−	0.701305i
$393$	−12.1478	+	18.1850i	−0.612777	+	0.917313i
$394$	5.09481	+	8.12898i	0.256673	+	0.409532i
$395$	1.08991	−	0.292040i	0.0548392	−	0.0146941i
$396$	−26.4432	+	23.5333i	−1.32882	+	1.18259i
$397$	−1.36453	+	5.09248i	−0.0684836	+	0.255584i	−0.991677	−	0.128752i	$-0.958903\pi$
$397$	−1.36453	+	5.09248i	−0.0684836	+	0.255584i	0.923193	+	0.384336i	$0.125570\pi$
$398$	5.95877	+	5.54163i	0.298686	+	0.277777i
$399$	−12.0195	+	15.8964i	−0.601730	+	0.795816i
$400$	2.85213	+	19.5285i	0.142606	+	0.976424i
$401$	5.79531	−	3.34592i	0.289404	−	0.167087i	−0.348269	−	0.937395i	$-0.613230\pi$
$401$	5.79531	−	3.34592i	0.289404	−	0.167087i	0.637673	+	0.770307i	$0.279897\pi$
$402$	−4.99940	+	16.6997i	−0.249347	+	0.832906i
$403$	2.67631	+	9.98812i	0.133316	+	0.497544i
$404$	−24.7087	−	4.73371i	−1.22930	−	0.235511i
$405$	2.31366	−	0.00105953i	0.114967	−	5.26484e-5i
$406$	2.17130	+	3.96150i	0.107760	+	0.196606i
$407$	−24.0136			−1.19031
$408$	32.4337	−	1.40957i	1.60571	−	0.0697843i
$409$	16.2052	−	28.0683i	0.801298	−	1.38789i	−0.117464	−	0.993077i	$-0.537477\pi$
$409$	16.2052	−	28.0683i	0.801298	−	1.38789i	0.918762	−	0.394811i	$-0.129190\pi$
$410$	0.349775	−	0.659979i	0.0172742	−	0.0325940i
$411$	7.04424	+	8.03056i	0.347467	+	0.396118i
$412$	−0.613370	−	8.44403i	−0.0302186	−	0.416008i
$413$	−0.698655	−	3.38859i	−0.0343785	−	0.166742i
$414$	−17.3474	−	6.45474i	−0.852579	−	0.317233i
$415$	1.21952	+	2.11227i	0.0598639	+	0.103687i
$416$	−12.4643	−	4.44162i	−0.611112	−	0.217768i
$417$	−6.51436	−	13.2060i	−0.319009	−	0.646700i
$418$	8.11460	−	35.3659i	0.396898	−	1.72980i
$419$	15.7548	−	15.7548i	0.769673	−	0.769673i	−0.208376	−	0.978049i	$-0.566818\pi$
$419$	15.7548	−	15.7548i	0.769673	−	0.769673i	0.978049	+	0.208376i	$0.0668177\pi$
$420$	2.09818	−	1.07189i	0.102381	−	0.0523031i
$421$	9.12432	+	9.12432i	0.444692	+	0.444692i	0.893585	−	0.448893i	$-0.148182\pi$
$421$	9.12432	+	9.12432i	0.444692	+	0.444692i	−0.448893	+	0.893585i	$0.648182\pi$
$422$	5.19844	+	8.29431i	0.253056	+	0.403761i
$423$	0.279081	−	2.12359i	0.0135694	−	0.103252i
$424$	31.8890	+	14.0435i	1.54867	+	0.682012i
$425$	−28.3154	+	16.3479i	−1.37350	+	0.792989i
$426$	19.2276	+	11.8595i	0.931579	+	0.574594i
$427$	36.8981	+	12.2387i	1.78562	+	0.592271i
$428$	−10.8065	−	9.34283i	−0.522350	−	0.451603i
$429$	15.7622	+	17.9692i	0.761005	+	0.867560i
$430$	0.444561	+	1.44711i	0.0214386	+	0.0697857i
$431$	−22.6516	−	13.0779i	−1.09109	−	0.629940i	−0.157223	−	0.987563i	$-0.550254\pi$
$431$	−22.6516	−	13.0779i	−1.09109	−	0.629940i	−0.933866	+	0.357623i	$0.883587\pi$
$432$	19.7762	+	6.39555i	0.951481	+	0.307706i
$433$			7.93525i			0.381344i	0.981654	+	0.190672i	$0.0610667\pi$
$433$			7.93525i			0.381344i	−0.981654	+	0.190672i	$0.938933\pi$
$434$	−11.4333	−	11.9529i	−0.548817	−	0.573758i
$435$	0.104940	+	0.527253i	0.00503148	+	0.0252798i
$436$	−2.04294	+	10.6636i	−0.0978392	+	0.510694i
$437$	18.3263	−	4.91052i	0.876666	−	0.234902i
$438$	12.3830	−	6.67699i	0.591681	−	0.319039i
$439$	−14.5020	−	25.1183i	−0.692145	−	1.19883i	−0.971134	−	0.238535i	$-0.923333\pi$
$439$	−14.5020	−	25.1183i	−0.692145	−	1.19883i	0.278989	−	0.960294i	$-0.410001\pi$
$440$	−2.68614	+	3.34470i	−0.128057	+	0.159453i
$441$	15.0584	+	14.6371i	0.717068	+	0.697003i
$442$	−0.794607	−	21.9069i	−0.0377956	−	1.04201i
$443$	25.6886	+	6.88323i	1.22050	+	0.327032i	0.810874	−	0.585221i	$-0.198992\pi$
$443$	25.6886	+	6.88323i	1.22050	+	0.327032i	0.409627	+	0.912253i	$0.365659\pi$
$444$	7.13737	+	12.1599i	0.338724	+	0.577083i
$445$	0.0754995	+	0.281768i	0.00357902	+	0.0133571i
$446$	−3.19176	−	0.732341i	−0.151134	−	0.0346774i
$447$	−10.0385	+	15.0274i	−0.474804	+	0.710771i
$448$	20.8988	−	3.35262i	0.987376	−	0.158396i
$449$		−	15.4797i		−	0.730532i	−0.930903	−	0.365266i	$-0.880978\pi$
$449$		−	15.4797i		−	0.730532i	0.930903	−	0.365266i	$-0.119022\pi$
$450$	−20.6403	+	3.48750i	−0.972991	+	0.164402i
$451$	−11.7082	+	3.13720i	−0.551317	+	0.147725i
$452$	9.81158	−	20.2553i	0.461498	−	0.952728i
$453$	−30.3194	+	26.5955i	−1.42453	+	1.24957i
$454$	−12.3164	+	0.446738i	−0.578035	+	0.0209665i
$455$	−0.713604	−	1.42194i	−0.0334543	−	0.0666615i
$456$	−20.3202	+	6.40247i	−0.951582	+	0.299823i
$457$	−10.1582	+	5.86483i	−0.475180	+	0.274345i	−0.718406	−	0.695624i	$-0.755128\pi$
$457$	−10.1582	+	5.86483i	−0.475180	+	0.274345i	0.243226	+	0.969970i	$0.421794\pi$
$458$	−9.62731	+	18.1654i	−0.449855	+	0.848815i
$459$	2.26386	+	34.3591i	0.105668	+	1.60374i
$460$	−2.20301	−	0.422054i	−0.102716	−	0.0196784i
$461$	0.758145	−	0.758145i	0.0353103	−	0.0353103i	−0.689231	−	0.724542i	$-0.742052\pi$
$461$	0.758145	−	0.758145i	0.0353103	−	0.0353103i	0.724542	+	0.689231i	$0.242052\pi$
$462$	−35.9253	−	13.0872i	−1.67140	−	0.608873i
$463$	−1.73370			−0.0805719			−0.0402859	−	0.999188i	$-0.512827\pi$
$463$	−1.73370			−0.0805719			−0.0402859	+	0.999188i	$0.512827\pi$
$464$	−0.562677	+	4.79654i	−0.0261216	+	0.222674i
$465$	−0.870790	−	1.76528i	−0.0403819	−	0.0818628i
$466$	5.33607	−	1.63928i	0.247189	−	0.0759381i
$467$	−27.7994	−	7.44883i	−1.28640	−	0.344691i	−0.450110	−	0.892973i	$-0.648615\pi$
$467$	−27.7994	−	7.44883i	−1.28640	−	0.344691i	−0.836293	+	0.548282i	$0.815282\pi$
$468$	4.41428	−	13.3224i	0.204050	−	0.615828i
$469$	−18.4408	+	3.80211i	−0.851519	+	0.175565i
$470$	−0.00940861	−	0.259391i	−0.000433987	−	0.0119648i
$471$	−1.44317	+	22.0572i	−0.0664976	+	1.01634i
$472$	1.49073	−	3.38504i	0.0686162	−	0.155809i
$473$	12.2833	−	21.2753i	0.564787	−	0.978241i
$474$	−0.312598	+	10.7468i	−0.0143581	+	0.493618i
$475$	15.1723	−	15.1723i	0.696155	−	0.696155i
$476$	17.9574	+	30.1184i	0.823076	+	1.38047i
$477$	−14.1354	+	34.1480i	−0.647216	+	1.56353i
$478$	−12.9963	−	2.98197i	−0.594438	−	0.136392i
$479$	−5.25251	+	9.09761i	−0.239993	+	0.415681i	−0.960712	−	0.277547i	$-0.910479\pi$
$479$	−5.25251	+	9.09761i	−0.239993	+	0.415681i	0.720719	+	0.693228i	$0.243812\pi$
$480$	2.49205	+	0.366077i	0.113746	+	0.0167090i
$481$	8.24528	−	4.76041i	0.375952	−	0.217056i
$482$	−4.68579	+	5.03851i	−0.213432	+	0.229498i
$483$	−2.75008	−	19.8023i	−0.125133	−	0.901038i
$484$	47.4892	−	3.44959i	2.15860	−	0.156800i
$485$	2.76430	+	0.740692i	0.125520	+	0.0336331i
$486$	−6.31282	+	21.1222i	−0.286355	+	0.958123i
$487$	1.31361	+	0.758412i	0.0595252	+	0.0343669i	0.529467	−	0.848330i	$-0.322392\pi$
$487$	1.31361	+	0.758412i	0.0595252	+	0.0343669i	−0.469942	+	0.882697i	$0.655725\pi$
$488$	24.5637	+	33.5227i	1.11194	+	1.51750i
$489$	−2.03913	+	3.05252i	−0.0922124	+	0.138040i
$490$	2.09422	+	1.44594i	0.0946074	+	0.0653210i
$491$	−21.9679	+	21.9679i	−0.991397	+	0.991397i	−0.999963	−	0.00856657i	$-0.997273\pi$
$491$	−21.9679	+	21.9679i	−0.991397	+	0.991397i	0.00856657	+	0.999963i	$0.497273\pi$
$492$	5.06852	+	4.99629i	0.228507	+	0.225250i
$493$	−7.72824	+	2.07077i	−0.348062	+	0.0932630i
$494$	4.22465	+	13.7518i	0.190076	+	0.618722i
$495$	−3.61041	−	2.76905i	−0.162276	−	0.124460i
$496$	−2.55544	−	17.4971i	−0.114743	−	0.785642i
$497$	−1.42591	+	24.3592i	−0.0639607	+	1.09266i
$498$	−22.6136	+	5.35974i	−1.01334	+	0.240176i
$499$	−8.92584	−	2.39167i	−0.399575	−	0.107066i	0.0534345	−	0.998571i	$-0.482983\pi$
$499$	−8.92584	−	2.39167i	−0.399575	−	0.107066i	−0.453010	+	0.891505i	$0.649650\pi$
$500$	−4.82473	+	1.67587i	−0.215768	+	0.0749470i
$501$	−12.6176	−	4.28147i	−0.563711	−	0.191282i
$502$	−10.4823	+	6.56978i	−0.467850	+	0.293224i
$503$		−	2.20977i		−	0.0985286i	−0.998786	−	0.0492643i	$-0.984312\pi$
$503$		−	2.20977i		−	0.0985286i	0.998786	−	0.0492643i	$-0.0156877\pi$
$504$	4.05072	+	22.0815i	0.180433	+	0.983587i
$505$		−	3.23374i		−	0.143899i
$506$	19.3308	+	30.8431i	0.859360	+	1.37114i
$507$	12.3483	+	4.19010i	0.548406	+	0.186089i
$508$	−23.5751	−	11.4197i	−1.04598	−	0.506667i
$509$	20.6570	+	5.53502i	0.915605	+	0.245336i	0.685706	−	0.727879i	$-0.259494\pi$
$509$	20.6570	+	5.53502i	0.915605	+	0.245336i	0.229899	+	0.973214i	$0.426160\pi$
$510$	0.962366	+	4.06037i	0.0426143	+	0.179796i
$511$	12.6933	+	8.35384i	0.561519	+	0.369552i
$512$	20.2845	+	10.0270i	0.896455	+	0.443136i
$513$	−7.27104	−	21.3956i	−0.321024	−	0.944641i
$514$	16.1965	−	4.97566i	0.714395	−	0.219467i
$515$	1.05115	−	0.281655i	0.0463192	−	0.0124112i
$516$	−14.4242	+	0.103521i	−0.634988	+	0.00455725i
$517$	−2.97842	+	2.97842i	−0.130991	+	0.130991i
$518$	−7.90586	+	13.0168i	−0.347364	+	0.571925i
$519$	13.2789	−	19.8783i	0.582881	−	0.872559i
$520$	0.259261	−	1.68093i	0.0113694	−	0.0737136i
$521$	17.1413	+	9.89655i	0.750975	+	0.433576i	0.826046	−	0.563602i	$-0.190585\pi$
$521$	17.1413	+	9.89655i	0.750975	+	0.433576i	−0.0750709	+	0.997178i	$0.523918\pi$
$522$	−5.09958	−	0.482910i	−0.223202	−	0.0211364i
$523$	31.6880	+	8.49076i	1.38562	+	0.371275i	0.873159	−	0.487436i	$-0.162068\pi$
$523$	31.6880	+	8.49076i	1.38562	+	0.371275i	0.512459	+	0.858711i	$0.328735\pi$
$524$	−19.1029	−	16.5156i	−0.834515	−	0.721487i
$525$	−13.8910	−	17.8396i	−0.606254	−	0.778586i
$526$	4.91309	+	4.56915i	0.214221	+	0.199224i
$527$	25.3699	−	14.6473i	1.10513	−	0.638048i
$528$	−23.1904	−	33.6593i	−1.00923	−	1.46483i
$529$	1.98344	−	3.43542i	0.0862365	−	0.149366i
$530$	−1.00162	+	4.36535i	−0.0435075	+	0.189619i
$531$	3.62483	+	1.50048i	0.157304	+	0.0651154i
$532$	−16.4989	−	16.0419i	−0.715316	−	0.695504i
$533$	3.39819	−	3.39819i	0.147192	−	0.147192i
$534$	−2.77832	−	0.0808143i	−0.120230	−	0.00349718i
$535$	0.918091	−	1.59018i	0.0396925	−	0.0687495i
$536$	−18.4215	−	8.11259i	−0.795688	−	0.350410i
$537$	0.321204	−	4.90924i	0.0138610	−	0.211849i
$538$	−5.83917	+	0.211798i	−0.251744	+	0.00913126i
$539$	−5.96155	−	40.8658i	−0.256782	−	1.76021i
$540$	−0.329087	+	2.65124i	−0.0141617	+	0.114091i
$541$	38.1048	+	10.2102i	1.63825	+	0.438969i	0.956291	−	0.292418i	$-0.0944597\pi$
$541$	38.1048	+	10.2102i	1.63825	+	0.438969i	0.681963	+	0.731386i	$0.261126\pi$
$542$	5.17711	+	16.8522i	0.222376	+	0.723863i
$543$	13.9272	+	28.2335i	0.597674	+	1.21161i
$544$	−3.01512	+	37.3651i	−0.129272	+	1.60201i
$545$	−1.39559			−0.0597807
$546$	14.9296	−	2.62814i	0.638929	−	0.112474i
$547$	23.7558	−	23.7558i	1.01572	−	1.01572i	0.0158482	−	0.999874i	$-0.494955\pi$
$547$	23.7558	−	23.7558i	1.01572	−	1.01572i	0.999874	−	0.0158482i	$-0.00504485\pi$
$548$	−10.2074	+	6.92513i	−0.436038	+	0.295827i
$549$	−34.9648	+	26.8422i	−1.49226	+	1.14560i
$550$	36.3737	+	19.2773i	1.55098	+	0.821987i
$551$	4.54719	−	2.62532i	0.193717	−	0.111842i
$552$	9.87264	−	18.9559i	0.420208	−	0.806816i
$553$	−10.3791	+	5.20878i	−0.441364	+	0.221500i
$554$	−0.643777	−	17.7486i	−0.0273515	−	0.754066i
$555$	−1.36246	+	1.19512i	−0.0578332	+	0.0507300i
$556$	16.0620	−	5.57912i	0.681179	−	0.236607i
$557$	23.1604	−	6.20580i	0.981336	−	0.262948i	0.267729	−	0.963494i	$-0.413727\pi$
$557$	23.1604	−	6.20580i	0.981336	−	0.262948i	0.713607	+	0.700546i	$0.247060\pi$
$558$	18.4932	−	3.12472i	0.782880	−	0.132280i
$559$			9.74008i			0.411962i
$560$	0.928684	+	2.55720i	0.0392440	+	0.108062i
$561$	37.6149	−	56.3086i	1.58810	−	2.37735i
$562$	−4.17429	+	18.1928i	−0.176082	+	0.767417i
$563$	−4.00455	−	14.9452i	−0.168772	−	0.629865i	−0.997529	−	0.0702563i	$-0.977618\pi$
$563$	−4.00455	−	14.9452i	−0.168772	−	0.629865i	0.828757	−	0.559608i	$-0.189048\pi$
$564$	2.39345	+	0.622948i	0.100782	+	0.0262308i
$565$	2.79434	+	0.748742i	0.117559	+	0.0314998i
$566$	32.2194	−	1.16866i	1.35428	−	0.0491224i
$567$	−23.3190	+	4.81902i	−0.979307	+	0.202380i
$568$	−16.3340	+	20.3387i	−0.685361	+	0.853392i
$569$	−8.95775	−	15.5153i	−0.375528	−	0.650434i	0.614878	−	0.788622i	$-0.289205\pi$
$569$	−8.95775	−	15.5153i	−0.375528	−	0.650434i	−0.990406	+	0.138188i	$0.955872\pi$
$570$	−1.29971	−	2.41040i	−0.0544387	−	0.100961i
$571$	8.40874	−	2.25312i	0.351895	−	0.0942900i	−0.0785415	−	0.996911i	$-0.525026\pi$
$571$	8.40874	−	2.25312i	0.351895	−	0.0942900i	0.430436	+	0.902621i	$0.358360\pi$
$572$	−22.8401	+	15.4957i	−0.954991	+	0.647906i
$573$	−3.30854	−	16.6232i	−0.138216	−	0.694445i
$574$	−2.15407	+	7.37936i	−0.0899091	+	0.308009i
$575$			21.5252i			0.897661i
$576$	−10.1516	+	21.7473i	−0.422981	+	0.906138i
$577$	23.5254	+	13.5824i	0.979374	+	0.565442i	0.902081	−	0.431567i	$-0.142039\pi$
$577$	23.5254	+	13.5824i	0.979374	+	0.565442i	0.0772926	+	0.997008i	$0.475372\pi$
$578$	−36.3836	+	11.1773i	−1.51336	+	0.464915i
$579$	21.4708	+	24.4771i	0.892297	+	1.01724i
$580$	−0.619129	+	0.0449732i	−0.0257079	+	0.00186741i
$581$	−16.6823	−	18.7568i	−0.692099	−	0.778163i
$582$	−14.3150	+	23.2087i	−0.593377	+	0.962032i
$583$	62.9437	−	36.3406i	2.60686	−	1.50507i
$584$	5.88297	+	15.1421i	0.243439	+	0.626586i
$585$	1.78860	+	0.235056i	0.0739493	+	0.00971839i
$586$	3.62462	−	2.27172i	0.149732	−	0.0938438i
$587$	21.5392	+	21.5392i	0.889018	+	0.889018i	0.994429	−	0.105411i	$-0.0336158\pi$
$587$	21.5392	+	21.5392i	0.889018	+	0.889018i	−0.105411	+	0.994429i	$0.533616\pi$
$588$	−18.9215	+	15.1650i	−0.780310	+	0.625393i
$589$	−13.5941	+	13.5941i	−0.560134	+	0.560134i
$590$	0.463385	+	0.106322i	0.0190772	+	0.00437722i
$591$	−5.19798	−	10.5374i	−0.213816	−	0.433451i
$592$	−14.9523	+	6.44233i	−0.614534	+	0.264778i
$593$	−17.4428	−	30.2118i	−0.716290	−	1.24065i	−0.962460	−	0.271424i	$-0.912505\pi$
$593$	−17.4428	−	30.2118i	−0.716290	−	1.24065i	0.246170	−	0.969227i	$-0.420828\pi$
$594$	35.1422	−	25.3892i	1.44190	−	1.04173i
$595$	−3.36787	+	2.99539i	−0.138069	+	0.122799i
$596$	−15.7859	−	13.6478i	−0.646615	−	0.559037i
$597$	−6.57203	−	7.49223i	−0.268975	−	0.306637i
$598$	−12.7517	−	6.75813i	−0.521455	−	0.276361i
$599$	−20.2847	+	35.1341i	−0.828810	+	1.43554i	0.0701622	+	0.997536i	$0.477648\pi$
$599$	−20.2847	+	35.1341i	−0.828810	+	1.43554i	−0.898972	+	0.438006i	$0.855685\pi$
$600$	−1.04949	−	24.1483i	−0.0428453	−	0.985852i
$601$	4.61131			0.188099			0.0940496	−	0.995568i	$-0.470019\pi$
$601$	4.61131			0.188099			0.0940496	+	0.995568i	$0.470019\pi$
$602$	−7.48851	−	13.6626i	−0.305209	−	0.556847i
$603$	8.16568	−	19.7265i	0.332532	−	0.803324i
$604$	−26.1458	−	38.5380i	−1.06386	−	1.56809i
$605$	1.58402	+	5.91166i	0.0643998	+	0.240343i
$606$	29.5178	+	8.83675i	1.19908	+	0.358968i
$607$	30.6074	−	17.6712i	1.24232	−	0.717252i	0.272752	−	0.962084i	$-0.412066\pi$
$607$	30.6074	−	17.6712i	1.24232	−	0.717252i	0.969565	+	0.244832i	$0.0787330\pi$
$608$	−4.43528	−	24.1978i	−0.179874	−	0.981350i
$609$	−2.15353	−	5.09650i	−0.0872653	−	0.206521i
$610$	−3.63786	+	3.91170i	−0.147293	+	0.158380i
$611$	0.432230	−	1.61310i	0.0174861	−	0.0652592i
$612$	−39.6933	−	2.31111i	−1.60450	−	0.0934211i
$613$	−20.6870	+	5.54306i	−0.835539	+	0.223882i	−0.651129	−	0.758967i	$-0.725704\pi$
$613$	−20.6870	+	5.54306i	−0.835539	+	0.223882i	−0.184410	+	0.982849i	$0.559038\pi$
$614$	29.4862	−	18.4804i	1.18997	−	0.745808i
$615$	−0.508153	+	0.760693i	−0.0204907	+	0.0306741i
$616$	20.1246	−	39.2963i	0.810845	−	1.58329i
$617$	−46.9110			−1.88856			−0.944282	−	0.329137i	$-0.893242\pi$
$617$	−46.9110			−1.88856			−0.944282	+	0.329137i	$0.893242\pi$
$618$	−0.301482	+	10.3647i	−0.0121274	+	0.416927i
$619$	2.30930	+	8.61843i	0.0928186	+	0.346404i	0.996680	−	0.0814223i	$-0.0259462\pi$
$619$	2.30930	+	8.61843i	0.0928186	+	0.346404i	−0.903861	+	0.427826i	$0.859280\pi$
$620$	2.14704	−	0.745774i	0.0862274	−	0.0299510i
$621$	20.3349	+	10.0194i	0.816010	+	0.402063i
$622$	−17.9555	+	19.3071i	−0.719949	+	0.774143i
$623$	−1.34660	−	2.68325i	−0.0539504	−	0.107502i
$624$	14.6352	+	6.95999i	0.585876	+	0.278623i
$625$	12.0065	+	20.7959i	0.480261	+	0.831837i
$626$	37.1111	−	11.4008i	1.48326	−	0.455667i
$627$	−14.2799	+	42.0829i	−0.570283	+	1.68063i
$628$	−25.0680	−	4.80254i	−1.00032	−	0.191642i
$629$	−19.0725	−	19.0725i	−0.760472	−	0.760472i
$630$	−2.68962	+	1.04542i	−0.107157	+	0.0416503i
$631$			31.7177i			1.26266i	0.775514	+	0.631330i	$0.217491\pi$
$631$			31.7177i			1.26266i	−0.775514	+	0.631330i	$0.782509\pi$
$632$	−12.2695	−	1.89242i	−0.488055	−	0.0752762i
$633$	−5.30370	−	10.7517i	−0.210803	−	0.427343i
$634$	−7.31147	−	3.87493i	−0.290376	−	0.153893i
$635$	0.871460	−	3.25233i	0.0345829	−	0.129065i
$636$	−37.1102	−	21.0719i	−1.47152	−	0.835557i
$637$	10.1481	+	12.8498i	0.402082	+	0.509128i
$638$	7.37665	+	6.86025i	0.292044	+	0.271600i
$639$	−21.9544	−	16.8382i	−0.868502	−	0.666109i
$640$	−0.775234	+	2.80324i	−0.0306438	+	0.110808i
$641$	−6.80777	−	3.93047i	−0.268891	−	0.155244i	0.359493	−	0.933148i	$-0.382950\pi$
$641$	−6.80777	−	3.93047i	−0.268891	−	0.155244i	−0.628383	+	0.777904i	$0.716283\pi$
$642$	12.0065	+	12.7259i	0.473857	+	0.502250i
$643$	−9.14146	−	9.14146i	−0.360504	−	0.360504i	0.503495	−	0.863998i	$-0.332047\pi$
$643$	−9.14146	−	9.14146i	−0.360504	−	0.360504i	−0.863998	+	0.503495i	$0.832047\pi$
$644$	23.0829	−	0.324156i	0.909595	−	0.0127735i
$645$	−0.361922	−	1.81842i	−0.0142507	−	0.0716001i
$646$	34.5339	−	21.6440i	1.35872	−	0.851572i
$647$	−10.2346	−	5.90896i	−0.402364	−	0.232305i	0.285139	−	0.958486i	$-0.407960\pi$
$647$	−10.2346	−	5.90896i	−0.402364	−	0.232305i	−0.687504	+	0.726181i	$0.741293\pi$
$648$	−23.3015	−	10.2489i	−0.915369	−	0.402616i
$649$	−3.85758	−	6.68152i	−0.151423	−	0.262272i
$650$	−16.3107	+	0.591621i	−0.639758	+	0.0232053i
$651$	12.4460	+	15.9839i	0.487799	+	0.626459i
$652$	−3.20660	−	2.77230i	−0.125580	−	0.108571i
$653$	4.88732	−	18.2397i	0.191256	−	0.713776i	−0.801949	−	0.597393i	$-0.796203\pi$
$653$	4.88732	−	18.2397i	0.191256	−	0.713776i	0.993204	−	0.116383i	$-0.0371300\pi$
$654$	3.81370	−	12.7391i	0.149128	−	0.498138i
$655$	1.62294	−	2.81101i	0.0634134	−	0.109835i
$656$	−6.44854	+	5.09445i	−0.251773	+	0.198905i
$657$	−15.9171	+	6.59736i	−0.620986	+	0.257388i
$658$	0.633912	+	2.59505i	0.0247124	+	0.101166i
$659$	−0.472257	−	0.472257i	−0.0183965	−	0.0183965i	0.697849	−	0.716245i	$-0.254141\pi$
$659$	−0.472257	−	0.472257i	−0.0183965	−	0.0183965i	−0.716245	+	0.697849i	$0.754141\pi$
$660$	3.68832	−	3.74164i	0.143568	−	0.145643i
$661$	−6.08332	−	22.7033i	−0.236614	−	0.883055i	−0.977415	−	0.211330i	$-0.932220\pi$
$661$	−6.08332	−	22.7033i	−0.236614	−	0.883055i	0.740801	−	0.671725i	$-0.234446\pi$
$662$	−1.08987	−	0.577610i	−0.0423591	−	0.0224494i
$663$	−1.75288	+	26.7907i	−0.0680761	+	1.04047i
$664$	−2.91307	−	26.6767i	−0.113049	−	1.03526i
$665$	1.62611	−	2.47081i	0.0630580	−	0.0958140i
$666$	−7.18601	−	15.7025i	−0.278452	−	0.608460i
$667$	−1.36329	+	5.08786i	−0.0527867	+	0.197003i
$668$	6.70719	−	13.8465i	0.259509	−	0.535737i
$669$	3.79798	+	1.28875i	0.146838	+	0.0498261i
$670$	0.578610	−	2.52176i	0.0223537	−	0.0974240i
$671$	86.6870			3.34652
$672$	−25.8802	+	1.48910i	−0.998349	+	0.0574434i
$673$	35.4810			1.36769			0.683845	−	0.729627i	$-0.260306\pi$
$673$	35.4810			1.36769			0.683845	+	0.729627i	$0.260306\pi$
$674$	3.07289	−	13.3926i	0.118363	−	0.515863i
$675$	25.5819	−	1.68555i	0.984648	−	0.0648769i
$676$	−6.56404	+	13.5510i	−0.252463	+	0.521192i
$677$	1.29546	−	4.83474i	0.0497887	−	0.185814i	−0.936553	−	0.350526i	$-0.886003\pi$
$677$	1.29546	−	4.83474i	0.0497887	−	0.185814i	0.986342	+	0.164712i	$0.0526695\pi$
$678$	−14.4706	+	23.4609i	−0.555741	+	0.901012i
$679$	−29.4029	−	1.72115i	−1.12838	−	0.0660516i
$680$	−4.78993	+	0.523056i	−0.183685	+	0.0200583i
$681$	15.0621	+	0.985491i	0.577181	+	0.0377641i
$682$	−32.5900	−	17.2720i	−1.24793	−	0.661380i
$683$	2.37085	+	8.84813i	0.0907181	+	0.338564i	0.996335	−	0.0855312i	$-0.0272587\pi$
$683$	2.37085	+	8.84813i	0.0907181	+	0.338564i	−0.905617	+	0.424096i	$0.860592\pi$
$684$	25.5540	−	5.27699i	0.977083	−	0.201771i
$685$	−1.12110	−	1.12110i	−0.0428352	−	0.0428352i
$686$	−24.1143	−	10.2225i	−0.920689	−	0.390296i
$687$	13.9865	−	20.9375i	0.533619	−	0.798815i
$688$	1.94059	−	16.5426i	0.0739843	−	0.630680i
$689$	−14.4082	+	24.9557i	−0.548908	+	0.950736i
$690$	2.63179	+	0.787877i	0.100190	+	0.0299940i
$691$	4.37626	−	16.3324i	0.166481	−	0.621315i	−0.831366	−	0.555725i	$-0.812441\pi$
$691$	4.37626	−	16.3324i	0.166481	−	0.621315i	0.997847	−	0.0655894i	$-0.0208928\pi$
$692$	20.8816	+	18.0534i	0.793800	+	0.686288i
$693$	42.1469	+	20.4082i	1.60103	+	0.775242i
$694$	−35.8828	+	1.30154i	−1.36209	+	0.0494058i
$695$	1.09278	+	1.89275i	0.0414514	+	0.0717960i
$696$	1.28136	−	5.77436i	0.0485698	−	0.218877i
$697$	−11.7908	−	6.80740i	−0.446607	−	0.257849i
$698$	−36.4238	+	22.8285i	−1.37866	+	0.864072i
$699$	−6.70524	+	1.33455i	−0.253616	+	0.0504775i
$700$	22.4245	−	13.3701i	0.847567	−	0.505342i
$701$	−27.9528	−	27.9528i	−1.05576	−	1.05576i	−0.998351	−	0.0574104i	$-0.981716\pi$
$701$	−27.9528	−	27.9528i	−1.05576	−	1.05576i	−0.0574104	−	0.998351i	$-0.518284\pi$
$702$	−7.03327	+	15.6841i	−0.265454	+	0.591959i
$703$	15.3296	+	8.85053i	0.578166	+	0.333804i
$704$	41.8789	−	21.7673i	1.57837	−	0.820385i
$705$	−0.0207551	+	0.317218i	−0.000781682	+	0.0119471i
$706$	13.2854	+	12.3554i	0.500002	+	0.465000i
$707$	6.72047	+	32.5954i	0.252749	+	1.22587i
$708$	−2.23680	+	3.93927i	−0.0840641	+	0.148047i
$709$	−3.97685	+	14.8418i	−0.149354	+	0.557395i	0.850169	+	0.526509i	$0.176499\pi$
$709$	−3.97685	+	14.8418i	−0.149354	+	0.557395i	−0.999523	+	0.0308858i	$0.990167\pi$
$710$	−2.96262	−	1.57013i	−0.111185	−	0.0589259i
$711$	1.71574	−	13.0554i	0.0643452	−	0.489617i
$712$	0.489236	−	3.17198i	0.0183349	−	0.118875i
$713$		−	19.2861i		−	0.722269i
$714$	−18.1388	−	38.9276i	−0.678829	−	1.45683i
$715$	−2.50858	−	2.50858i	−0.0938157	−	0.0938157i
$716$	5.57935	+	1.06890i	0.208510	+	0.0399466i
$717$	15.4647	+	5.24759i	0.577540	+	0.195975i
$718$	−31.4085	+	9.64891i	−1.17216	+	0.360094i
$719$	−15.1260	−	26.1990i	−0.564105	−	0.977058i	−0.997132	−	0.0756772i	$-0.975888\pi$
$719$	−15.1260	−	26.1990i	−0.564105	−	0.977058i	0.433028	−	0.901381i	$-0.357445\pi$
$720$	−2.99092	−	0.755576i	−0.111465	−	0.0281587i
$721$	−10.0100	+	5.02355i	−0.372792	+	0.187087i
$722$	0.0841270	−	0.0904596i	0.00313088	−	0.00336656i
$723$	6.33514	−	5.55705i	0.235606	−	0.206669i
$724$	−34.3393	+	11.9277i	−1.27621	+	0.443291i
$725$	1.54179	+	5.75402i	0.0572605	+	0.213699i
$726$	−58.2908	−	1.69553i	−2.16337	−	0.0629271i
$727$	−47.7498			−1.77094			−0.885470	−	0.464696i	$-0.846164\pi$
$727$	−47.7498			−1.77094			−0.885470	+	0.464696i	$0.846164\pi$
$728$	0.880066	+	17.4822i	0.0326174	+	0.647933i
$729$	10.3153	−	24.9518i	0.382049	−	0.924142i
$730$	−1.76928	+	1.10889i	−0.0654839	+	0.0410419i
$731$	26.6536	−	7.14180i	0.985818	−	0.264149i
$732$	−25.7653	−	43.8962i	−0.952311	−	1.62245i
$733$	−12.0175	+	44.8500i	−0.443877	+	1.65657i	0.275006	+	0.961442i	$0.411320\pi$
$733$	−12.0175	+	44.8500i	−0.443877	+	1.65657i	−0.718884	+	0.695130i	$0.755347\pi$
$734$	−23.8381	+	25.6325i	−0.879881	+	0.946113i
$735$	−2.37207	−	2.02190i	−0.0874950	−	0.0745789i
$736$	20.3110	+	14.0186i	0.748674	+	0.516734i
$737$	−36.3611	+	20.9931i	−1.33938	+	0.773290i
$738$	−5.55505	−	6.71719i	−0.204484	−	0.247263i
$739$	−2.34816	−	8.76344i	−0.0863783	−	0.322368i	0.909193	−	0.416374i	$-0.136699\pi$
$739$	−2.34816	−	8.76344i	−0.0863783	−	0.322368i	−0.995572	+	0.0940060i	$0.970033\pi$
$740$	−1.17491	−	1.73178i	−0.0431906	−	0.0636614i
$741$	−3.43933	−	17.2803i	−0.126347	−	0.634809i
$742$	1.02386	−	46.0834i	0.0375871	−	1.69177i
$743$	46.3396			1.70003			0.850017	−	0.526756i	$-0.176592\pi$
$743$	46.3396			1.70003			0.850017	+	0.526756i	$0.176592\pi$
$744$	0.940320	+	21.6364i	0.0344738	+	0.793228i
$745$	1.34113	−	2.32291i	0.0491352	−	0.0851047i
$746$	21.9833	+	11.6507i	0.804867	+	0.426563i
$747$	28.2188	−	3.72165i	1.03247	−	0.136168i
$748$	59.1508	+	51.1394i	2.16277	+	1.86984i
$749$	−5.94939	+	17.9367i	−0.217386	+	0.655392i
$750$	6.08675	−	1.44265i	0.222257	−	0.0526781i
$751$	−2.89758	−	5.01876i	−0.105734	−	0.183137i	0.808304	−	0.588766i	$-0.200386\pi$
$751$	−2.89758	−	5.01876i	−0.105734	−	0.183137i	−0.914038	+	0.405629i	$0.867053\pi$
$752$	−1.05549	+	2.65358i	−0.0384898	+	0.0967662i
$753$	13.5880	−	6.70281i	0.495176	−	0.244264i
$754$	−3.89280	−	0.893191i	−0.141767	−	0.0325281i
$755$	4.23273	−	4.23273i	0.154045	−	0.154045i
$756$	−2.19278	−	27.4079i	−0.0797507	−	0.996815i
$757$	−38.8443	−	38.8443i	−1.41182	−	1.41182i	−0.747022	−	0.664800i	$-0.768517\pi$
$757$	−38.8443	−	38.8443i	−1.41182	−	1.41182i	−0.664800	−	0.747022i	$-0.731483\pi$
$758$	−13.3758	+	8.38322i	−0.485829	+	0.304492i
$759$	−19.7223	−	39.9812i	−0.715873	−	1.45123i
$760$	2.94749	−	1.14515i	0.106917	−	0.0415388i
$761$	18.6665	−	10.7771i	0.676661	−	0.390670i	−0.121935	−	0.992538i	$-0.538910\pi$
$761$	18.6665	−	10.7771i	0.676661	−	0.390670i	0.798596	+	0.601868i	$0.205577\pi$
$762$	27.3062	+	16.8423i	0.989198	+	0.610134i
$763$	14.0673	−	2.90037i	0.509270	−	0.105001i
$764$	19.5199	−	1.41792i	0.706206	−	0.0512984i
$765$	−0.668239	−	5.06681i	−0.0241602	−	0.183191i
$766$	4.05477	−	1.24565i	0.146505	−	0.0450073i
$767$	2.64906	+	1.52944i	0.0956521	+	0.0552247i
$768$	−23.4697	−	14.7367i	−0.846891	−	0.531766i
$769$			8.51995i			0.307237i	0.988130	+	0.153619i	$0.0490927\pi$
$769$			8.51995i			0.307237i	−0.988130	+	0.153619i	$0.950907\pi$
$770$	5.44753	+	1.59016i	0.196315	+	0.0573053i
$771$	−20.3523	+	4.05074i	−0.732969	+	0.145884i
$772$	−31.1121	+	21.1078i	−1.11975	+	0.759686i
$773$	36.0892	−	9.67007i	1.29804	−	0.347808i	0.457330	−	0.889297i	$-0.348806\pi$
$773$	36.0892	−	9.67007i	1.29804	−	0.347808i	0.840708	+	0.541489i	$0.182139\pi$
$774$	17.5877	+	1.66549i	0.632177	+	0.0598647i
$775$	−10.9056	−	18.8891i	−0.391741	−	0.678515i
$776$	−24.5499	−	19.7161i	−0.881289	−	0.707765i
$777$	11.2495	−	14.8781i	0.403575	−	0.533748i
$778$	29.5506	−	1.07186i	1.05944	−	0.0384280i
$779$	8.63041	+	2.31251i	0.309216	+	0.0828543i
$780$	−0.524679	+	2.01589i	−0.0187865	+	0.0721804i
$781$	14.0828	+	52.5576i	0.503921	+	1.88066i
$782$	−9.14349	+	39.8501i	−0.326970	+	1.42504i
$783$	6.15349	+	1.22181i	0.219908	+	0.0436639i
$784$	−14.6754	−	23.8460i	−0.524121	−	0.851644i
$785$		−	3.28076i		−	0.117095i
$786$	21.2242	+	22.4959i	0.757041	+	0.802401i
$787$	−23.5457	+	6.30906i	−0.839315	+	0.224894i	−0.652773	−	0.757553i	$-0.726395\pi$
$787$	−23.5457	+	6.30906i	−0.839315	+	0.224894i	−0.186542	+	0.982447i	$0.559728\pi$
$788$	12.8163	−	4.45173i	0.456561	−	0.158586i
$789$	−5.41873	−	6.17745i	−0.192912	−	0.219923i
$790$	−0.0578424	−	1.59469i	−0.00205794	−	0.0567364i
$791$	−29.7224	−	1.73985i	−1.05681	−	0.0618621i
$792$	24.0751	+	43.8920i	0.855470	+	1.55963i
$793$	−29.7647	+	17.1847i	−1.05698	+	0.610245i
$794$	6.58789	+	3.49145i	0.233796	+	0.123907i
$795$	1.76262	−	5.19446i	0.0625137	−	0.184229i
$796$	9.52314	−	6.46090i	0.337539	−	0.229001i
$797$	−35.2425	+	35.2425i	−1.24835	+	1.24835i	−0.291905	+	0.956447i	$0.594289\pi$
$797$	−35.2425	+	35.2425i	−1.24835	+	1.24835i	−0.956447	+	0.291905i	$0.905711\pi$
$798$	18.1101	+	21.5952i	0.641092	+	0.764463i
$799$	−4.73116			−0.167376
$800$	27.8200	+	2.24489i	0.983586	+	0.0793690i
$801$	3.37515	+	0.443561i	0.119255	+	0.0156724i
$802$	−2.77913	−	9.04644i	−0.0981344	−	0.319441i
$803$	32.7301	+	8.77001i	1.15502	+	0.309487i
$804$	21.4377	+	12.1727i	0.756048	+	0.429300i
$805$	0.599191	+	2.90618i	0.0211187	+	0.102429i
$806$	14.6140	−	0.530079i	0.514757	−	0.0186712i
$807$	7.14092	+	0.467220i	0.251372	+	0.0164469i
$808$	−14.3395	+	32.5612i	−0.504462	+	1.14550i
$809$	−9.59893	+	16.6258i	−0.337480	+	0.584533i	−0.983958	−	0.178400i	$-0.942908\pi$
$809$	−9.59893	+	16.6258i	−0.337480	+	0.584533i	0.646478	+	0.762933i	$0.276241\pi$
$810$	0.730280	−	3.18948i	0.0256594	−	0.112067i
$811$	13.4386	−	13.4386i	0.471894	−	0.471894i	−0.430633	−	0.902527i	$-0.641710\pi$
$811$	13.4386	−	13.4386i	0.471894	−	0.471894i	0.902527	+	0.430633i	$0.141710\pi$
$812$	6.14722	−	1.74002i	0.215725	−	0.0610626i
$813$	−4.21474	−	21.1763i	−0.147817	−	0.742684i
$814$	−7.59476	+	33.1003i	−0.266196	+	1.16016i
$815$	0.272425	−	0.471854i	0.00954262	−	0.0165283i
$816$	8.31482	−	45.1522i	0.291077	−	1.58064i
$817$	−15.6826	+	9.05435i	−0.548665	+	0.316772i
$818$	−33.5640	−	31.2144i	−1.17354	−	1.09138i
$819$	−18.5172	+	1.34781i	−0.647042	+	0.0470961i
$820$	−0.799089	−	0.690860i	−0.0279054	−	0.0241259i
$821$	−5.93160	−	1.58937i	−0.207014	−	0.0554693i	0.153822	−	0.988099i	$-0.450842\pi$
$821$	−5.93160	−	1.58937i	−0.207014	−	0.0554693i	−0.360836	+	0.932629i	$0.617509\pi$
$822$	13.2972	−	7.16993i	0.463792	−	0.250080i
$823$	11.1673	+	6.44742i	0.389266	+	0.224743i	0.681842	−	0.731499i	$-0.261179\pi$
$823$	11.1673	+	6.44742i	0.389266	+	0.224743i	−0.292576	+	0.956242i	$0.594512\pi$
$824$	−11.8332	−	1.82512i	−0.412229	−	0.0635810i
$825$	−41.9243	−	28.0060i	−1.45962	−	0.975044i
$826$	−4.89178	−	0.108683i	−0.170207	−	0.00378158i
$827$	−0.483112	+	0.483112i	−0.0167994	+	0.0167994i	−0.715457	−	0.698657i	$-0.753781\pi$
$827$	−0.483112	+	0.483112i	−0.0167994	+	0.0167994i	0.698657	+	0.715457i	$0.253781\pi$
$828$	−14.3836	+	21.8702i	−0.499866	+	0.760040i
$829$	39.0702	−	10.4688i	1.35696	−	0.363597i	0.494263	−	0.869313i	$-0.335438\pi$
$829$	39.0702	−	10.4688i	1.35696	−	0.363597i	0.862700	+	0.505715i	$0.168771\pi$
$830$	3.29724	−	1.01294i	0.114449	−	0.0351595i
$831$	−1.42015	+	21.7054i	−0.0492645	+	0.752952i
$832$	−10.0644	+	15.7760i	−0.348920	+	0.546934i
$833$	27.7223	−	37.1921i	0.960520	−	1.28863i
$834$	−20.2634	+	4.80271i	−0.701663	+	0.166304i
$835$	1.91021	+	0.511840i	0.0661056	+	0.0177129i
$836$	−46.1818	−	22.3703i	−1.59723	−	0.773692i
$837$	−22.9208	+	1.51021i	−0.792259	+	0.0522007i
$838$	−16.7336	−	26.6991i	−0.578053	−	0.922306i
$839$			34.3619i			1.18631i	0.805090	+	0.593153i	$0.202117\pi$
$839$			34.3619i			1.18631i	−0.805090	+	0.593153i	$0.797883\pi$
$840$	−0.813907	−	3.23112i	−0.0280825	−	0.111484i
$841$		−	27.5423i		−	0.949734i
$842$	15.4627	−	9.69118i	0.532878	−	0.333980i
$843$	7.34580	−	21.6482i	0.253003	−	0.745603i
$844$	13.0769	−	4.54227i	0.450127	−	0.156351i
$845$	−1.86944	−	0.500916i	−0.0643108	−	0.0172320i
$846$	−2.83888	−	1.05631i	−0.0976026	−	0.0363166i
$847$	−28.2525	−	56.2963i	−0.970766	−	1.93436i
$848$	29.4430	−	39.5142i	1.01108	−	1.35692i
$849$	−39.4022	−	2.57803i	−1.35228	−	0.0884776i
$850$	13.5786	+	44.2001i	0.465742	+	1.51605i
$851$	−17.1523	+	4.59594i	−0.587973	+	0.157547i
$852$	22.4281	−	22.7524i	0.768376	−	0.779484i
$853$	−11.0188	+	11.0188i	−0.377277	+	0.377277i	−0.870119	−	0.492842i	$-0.835958\pi$
$853$	−11.0188	+	11.0188i	−0.377277	+	0.377277i	0.492842	+	0.870119i	$0.335958\pi$
$854$	28.5394	−	46.9894i	0.976600	−	1.60795i
$855$	1.28421	+	3.09834i	0.0439189	+	0.105961i
$856$	−16.2959	+	11.9407i	−0.556981	+	0.408126i
$857$	21.8476	+	12.6137i	0.746299	+	0.430876i	0.824355	−	0.566073i	$-0.191538\pi$
$857$	21.8476	+	12.6137i	0.746299	+	0.430876i	−0.0780562	+	0.996949i	$0.524871\pi$
$858$	29.7537	−	16.0434i	1.01578	−	0.547714i
$859$	−34.3191	−	9.19576i	−1.17095	−	0.313755i	−0.379619	−	0.925143i	$-0.623945\pi$
$859$	−34.3191	−	9.19576i	−1.17095	−	0.313755i	−0.791331	+	0.611387i	$0.790612\pi$
$860$	2.13529	−	0.155106i	0.0728127	−	0.00528908i
$861$	3.54117	−	8.72368i	0.120683	−	0.297302i
$862$	−25.1905	+	27.0867i	−0.857992	+	0.922577i
$863$	−43.1016	+	24.8847i	−1.46720	+	0.847086i	−0.999326	−	0.0367120i	$-0.988312\pi$
$863$	−43.1016	+	24.8847i	−1.46720	+	0.847086i	−0.467869	+	0.883798i	$0.654978\pi$
$864$	15.0702	−	25.2367i	0.512698	−	0.858569i
$865$	−1.77405	+	3.07275i	−0.0603195	+	0.104477i
$866$	10.9379	+	2.50968i	0.371686	+	0.0852822i
$867$	45.7192	−	9.09956i	1.55271	−	0.309037i
$868$	−20.0918	+	11.9793i	−0.681962	+	0.406604i
$869$	−18.3108	+	18.3108i	−0.621151	+	0.621151i
$870$	0.759952	+	0.0221051i	0.0257648	+	0.000749433i
$871$	8.32325	−	14.4163i	0.282023	−	0.488478i
$872$	14.0525	+	6.18855i	0.475879	+	0.209571i
$873$	20.3246	−	26.5001i	0.687884	−	0.896893i
$874$	−0.972594	−	26.8139i	−0.0328985	−	0.906995i
$875$	4.49027	+	5.04865i	0.151799	+	0.170676i
$876$	−5.28718	−	19.1804i	−0.178637	−	0.648044i
$877$	−41.0267	−	10.9931i	−1.38537	−	0.371210i	−0.512304	−	0.858804i	$-0.671208\pi$
$877$	−41.0267	−	10.9931i	−1.38537	−	0.371210i	−0.873070	+	0.487595i	$0.837874\pi$
$878$	−39.2094	+	12.0454i	−1.32325	+	0.406513i
$879$	−4.69851	+	2.31772i	−0.158477	+	0.0781747i
$880$	3.76078	+	4.76039i	0.126776	+	0.160473i
$881$	36.3081			1.22325			0.611625	−	0.791148i	$-0.290516\pi$
$881$	36.3081			1.22325			0.611625	+	0.791148i	$0.290516\pi$
$882$	24.9382	−	16.1272i	0.839712	−	0.543032i
$883$	−4.32594	+	4.32594i	−0.145579	+	0.145579i	−0.776140	−	0.630561i	$-0.782825\pi$
$883$	−4.32594	+	4.32594i	−0.145579	+	0.145579i	0.630561	+	0.776140i	$0.282825\pi$
$884$	−30.4477	−	5.83320i	−1.02407	−	0.196192i
$885$	−0.551395	−	0.187103i	−0.0185350	−	0.00628940i
$886$	17.6123	−	33.2320i	0.591697	−	1.11645i
$887$	−7.96269	+	4.59726i	−0.267361	+	0.154361i	−0.627688	−	0.778465i	$-0.715999\pi$
$887$	−7.96269	+	4.59726i	−0.267361	+	0.154361i	0.360327	+	0.932826i	$0.382665\pi$
$888$	19.0185	−	5.99231i	0.638218	−	0.201089i
$889$	−2.02501	+	34.5939i	−0.0679168	+	1.16024i
$890$	0.412266	−	0.0149537i	0.0138192	−	0.000501249i
$891$	−45.9719	+	26.5700i	−1.54012	+	0.890128i
$892$	−2.01891	+	4.16790i	−0.0675982	+	0.139551i
$893$	2.99907	−	0.803599i	0.100360	−	0.0268914i
$894$	17.5388	+	18.5897i	0.586586	+	0.621733i
$895$			0.730195i			0.0244077i
$896$	1.98840	−	29.8671i	0.0664279	−	0.997791i
$897$	14.6976	+	9.81819i	0.490739	+	0.327820i
$898$	−21.3371	−	4.89575i	−0.712030	−	0.163373i
$899$	−1.38141	−	5.15547i	−0.0460724	−	0.171945i
$900$	−1.72073	+	29.5534i	−0.0573575	+	0.985114i
$901$	78.8554	+	21.1293i	2.62706	+	0.703917i
$902$	0.621364	+	17.1307i	0.0206892	+	0.570390i
$903$	7.42720	+	17.5771i	0.247162	+	0.584929i
$904$	−24.8167	−	19.9303i	−0.825391	−	0.662873i
$905$	−2.33628	−	4.04656i	−0.0776606	−	0.134512i
$906$	27.0701	+	50.2035i	0.899343	+	1.66790i
$907$	−7.42823	+	1.99039i	−0.246650	+	0.0660898i	−0.380026	−	0.924976i	$-0.624085\pi$
$907$	−7.42823	+	1.99039i	−0.246650	+	0.0660898i	0.133376	+	0.991066i	$0.457418\pi$
$908$	−3.27950	+	17.1181i	−0.108834	+	0.568084i
$909$	−34.8678	−	14.4334i	−1.15649	−	0.478724i
$910$	−2.18569	+	0.533914i	−0.0724548	+	0.0176991i
$911$			33.8700i			1.12216i	0.827761	+	0.561081i	$0.189615\pi$
$911$			33.8700i			1.12216i	−0.827761	+	0.561081i	$0.810385\pi$
$912$	2.39847	+	30.0342i	0.0794214	+	0.994532i
$913$	−48.4760	−	27.9876i	−1.60432	−	0.926255i
$914$	4.87134	+	15.8569i	0.161130	+	0.524499i
$915$	4.91835	−	4.31428i	0.162596	−	0.142626i
$916$	21.9943	+	19.0154i	0.726713	+	0.628286i
$917$	−10.5169	+	31.7072i	−0.347299	+	1.04706i
$918$	48.0764	+	7.74621i	1.58676	+	0.255663i
$919$	39.7129	−	22.9283i	1.31001	−	0.756334i	0.327911	−	0.944708i	$-0.393655\pi$
$919$	39.7129	−	22.9283i	1.31001	−	0.756334i	0.982097	+	0.188375i	$0.0603219\pi$
$920$	−1.27850	+	2.90313i	−0.0421509	+	0.0957134i
$921$	−38.2223	+	18.8546i	−1.25947	+	0.621280i
$922$	−0.805246	−	1.28480i	−0.0265194	−	0.0423127i
$923$	−15.2543	−	15.2543i	−0.502103	−	0.502103i
$924$	−29.4014	+	45.3802i	−0.967236	+	1.49290i
$925$	−14.2004	+	14.2004i	−0.466905	+	0.466905i
$926$	−0.548316	+	2.38972i	−0.0180188	+	0.0785312i
$927$	1.65472	−	12.5912i	0.0543483	−	0.413548i
$928$	6.43358	+	2.29259i	0.211193	+	0.0752579i
$929$	3.28103	+	5.68291i	0.107647	+	0.186450i	0.914817	−	0.403869i	$-0.132335\pi$
$929$	3.28103	+	5.68291i	0.107647	+	0.186450i	−0.807170	+	0.590320i	$0.799002\pi$
$930$	−2.70866	+	0.641990i	−0.0888203	+	0.0210517i
$931$	−11.2559	+	28.2847i	−0.368899	+	0.926993i
$932$	−0.571939	−	7.87367i	−0.0187345	−	0.257911i
$933$	24.2756	−	21.2941i	0.794748	−	0.697136i
$934$	−19.0595	+	35.9627i	−0.623647	+	1.17674i
$935$	−5.02531	+	8.70409i	−0.164345	+	0.284654i
$936$	−16.9674	−	10.2981i	−0.554598	−	0.336604i
$937$	43.7826			1.43032			0.715158	−	0.698963i	$-0.246355\pi$
$937$	43.7826			1.43032			0.715158	+	0.698963i	$0.246355\pi$
$938$	−0.591459	+	26.6213i	−0.0193118	+	0.869215i
$939$	−46.6334	+	9.28150i	−1.52182	+	0.302890i
$940$	−0.360518	−	0.0690684i	−0.0117588	−	0.00225276i
$941$	2.85186	+	10.6433i	0.0929680	+	0.346961i	0.996704	−	0.0811299i	$-0.0258529\pi$
$941$	2.85186	+	10.6433i	0.0929680	+	0.346961i	−0.903736	+	0.428091i	$0.859186\pi$
$942$	29.9471	+	8.96525i	0.975728	+	0.292104i
$943$	−7.76242	+	4.48163i	−0.252779	+	0.145942i
$944$	−4.19445	−	3.12539i	−0.136518	−	0.101723i
$945$	3.40697	−	0.939688i	0.110829	−	0.0305681i
$946$	−25.4410	−	23.6600i	−0.827158	−	0.769253i
$947$	7.60778	−	28.3926i	0.247220	−	0.922637i	−0.725035	−	0.688712i	$-0.758176\pi$
$947$	7.60778	−	28.3926i	0.247220	−	0.922637i	0.972255	−	0.233925i	$-0.0751569\pi$
$948$	14.7145	+	3.82977i	0.477905	+	0.124385i
$949$	−12.9767	+	3.47710i	−0.421242	+	0.112871i
$950$	−16.1149	−	25.7120i	−0.522838	−	0.834208i
$951$	8.42722	+	5.62949i	0.273271	+	0.182549i
$952$	47.1944	−	15.2269i	1.52958	−	0.493506i
$953$	2.94243			0.0953146			0.0476573	−	0.998864i	$-0.484824\pi$
$953$	2.94243			0.0953146			0.0476573	+	0.998864i	$0.484824\pi$
$954$	42.5989	+	30.2841i	1.37919	+	0.980485i
$955$	0.651096	+	2.42992i	0.0210690	+	0.0786304i
$956$	−8.22067	+	16.9710i	−0.265875	+	0.548880i
$957$	−8.13582	−	9.27498i	−0.262994	−	0.299818i
$958$	10.8789	+	10.1173i	0.351481	+	0.326876i
$959$	13.6304	+	8.97057i	0.440149	+	0.289675i
$960$	1.29276	−	3.31926i	0.0417236	−	0.107129i
$961$	−5.72882	−	9.92261i	−0.184801	−	0.320084i
$962$	−3.95401	−	12.8708i	−0.127482	−	0.414972i
$963$	−13.0484	−	16.9969i	−0.420477	−	0.547717i
$964$	5.46309	+	8.05239i	0.175954	+	0.259350i
$965$	−3.41713	−	3.41713i	−0.110001	−	0.110001i
$966$	−28.1652	−	2.47216i	−0.906201	−	0.0795406i
$967$			25.0313i			0.804953i	0.915430	+	0.402476i	$0.131850\pi$
$967$			25.0313i			0.804953i	−0.915430	+	0.402476i	$0.868150\pi$
$968$	10.2645	−	66.5499i	0.329913	−	2.13900i
$969$	−44.7655	+	22.0823i	−1.43807	+	0.709385i
$970$	1.89523	−	3.57604i	0.0608521	−	0.114820i
$971$	7.60263	−	28.3734i	0.243980	−	0.910545i	−0.729914	−	0.683540i	$-0.760440\pi$
$971$	7.60263	−	28.3734i	0.243980	−	0.910545i	0.973893	−	0.227006i	$-0.0728936\pi$
$972$	27.1182	+	15.3819i	0.869817	+	0.493374i
$973$	−14.9485	−	16.8074i	−0.479228	−	0.538822i
$974$	1.46084	−	1.57081i	0.0468085	−	0.0503320i
$975$	19.9469	+	1.30510i	0.638813	+	0.0417966i
$976$	53.9763	−	23.2562i	1.72774	−	0.744414i
$977$	−20.0661	−	11.5852i	−0.641971	−	0.370642i	0.143402	−	0.989664i	$-0.454196\pi$
$977$	−20.0661	−	11.5852i	−0.641971	−	0.370642i	−0.785373	+	0.619022i	$0.787529\pi$
$978$	3.56267	+	3.77614i	0.113922	+	0.120748i
$979$	−4.73380	−	4.73380i	−0.151293	−	0.151293i
$980$	2.65542	−	2.42936i	0.0848242	−	0.0776031i
$981$	−6.22905	+	15.0480i	−0.198878	+	0.480446i
$982$	23.3327	+	37.2282i	0.744575	+	1.18800i
$983$	23.3046	+	13.4549i	0.743303	+	0.429146i	0.823269	−	0.567652i	$-0.192148\pi$
$983$	23.3046	+	13.4549i	0.743303	+	0.429146i	−0.0799662	+	0.996798i	$0.525481\pi$
$984$	8.48988	−	5.40626i	0.270647	−	0.172345i
$985$	0.871957	+	1.51027i	0.0277829	+	0.0481213i
$986$	0.410145	+	11.3075i	0.0130617	+	0.360104i
$987$	−0.450047	−	3.24062i	−0.0143252	−	0.103150i
$988$	20.2915	−	1.47397i	0.645560	−	0.0468931i
$989$	4.70178	−	17.5473i	0.149508	−	0.557971i
$990$	−4.95871	+	4.10081i	−0.157598	+	0.130332i
$991$	17.8951	−	30.9953i	0.568458	−	0.984598i	−0.428261	−	0.903655i	$-0.640874\pi$
$991$	17.8951	−	30.9953i	0.568458	−	0.984598i	0.996719	−	0.0809428i	$-0.0257931\pi$
$992$	−24.9261	−	2.01137i	−0.791404	−	0.0638612i
$993$	1.25619	+	0.839150i	0.0398639	+	0.0266296i
$994$	33.1257	+	9.66953i	1.05068	+	0.306699i
$995$	1.04595	+	1.04595i	0.0331589	+	0.0331589i
$996$	0.235873	+	32.8655i	0.00747391	+	1.04138i
$997$	1.98264	+	7.39932i	0.0627909	+	0.234339i	0.990188	−	0.139738i	$-0.0446262\pi$
$997$	1.98264	+	7.39932i	0.0627909	+	0.234339i	−0.927398	+	0.374077i	$0.877960\pi$
$998$	−6.11964	+	11.5469i	−0.193714	+	0.365512i
$999$	6.80524	+	20.0250i	0.215308	+	0.633563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.101.34	yes	240
3.2	odd	2	inner	336.2.bo.a.101.27	yes	240
7.5	odd	6	inner	336.2.bo.a.5.6	✓	240
16.13	even	4	inner	336.2.bo.a.269.55	yes	240
21.5	even	6	inner	336.2.bo.a.5.55	yes	240
48.29	odd	4	inner	336.2.bo.a.269.6	yes	240
112.61	odd	12	inner	336.2.bo.a.173.27	yes	240
336.173	even	12	inner	336.2.bo.a.173.34	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.6	✓	240	7.5	odd	6	inner
336.2.bo.a.5.55	yes	240	21.5	even	6	inner
336.2.bo.a.101.27	yes	240	3.2	odd	2	inner
336.2.bo.a.101.34	yes	240	1.1	even	1	trivial
336.2.bo.a.173.27	yes	240	112.61	odd	12	inner
336.2.bo.a.173.34	yes	240	336.173	even	12	inner
336.2.bo.a.269.6	yes	240	48.29	odd	4	inner
336.2.bo.a.269.55	yes	240	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.316269 - 1.37840i) q^{2} +(-0.556562 + 1.64019i) q^{3} +(-1.79995 - 0.871887i) q^{4} +(0.0665356 - 0.248314i) q^{5} +(2.08481 + 1.28590i) q^{6} +(-0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-2.38048 - 1.82574i) q^{9} +O(q^{10})\)	\(q+(0.316269 - 1.37840i) q^{2} +(-0.556562 + 1.64019i) q^{3} +(-1.79995 - 0.871887i) q^{4} +(0.0665356 - 0.248314i) q^{5} +(2.08481 + 1.28590i) q^{6} +(-0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-2.38048 - 1.82574i) q^{9} +(-0.321232 - 0.170246i) q^{10} +(1.52697 + 5.69873i) q^{11} +(2.43185 - 2.46701i) q^{12} +(-1.65400 - 1.65400i) q^{13} +(3.59176 + 1.04845i) q^{14} +(0.370253 + 0.247334i) q^{15} +(2.47962 + 3.13870i) q^{16} +(-3.31337 + 5.73893i) q^{17} +(-3.26946 + 2.70382i) q^{18} +(1.12557 - 4.20068i) q^{19} +(-0.336263 + 0.388941i) q^{20} +(-4.24608 - 1.72360i) q^{21} +(8.33804 - 0.302437i) q^{22} +(2.18135 + 3.77821i) q^{23} +(-2.63139 - 4.13228i) q^{24} +(4.27289 + 2.46696i) q^{25} +(-2.80298 + 1.75676i) q^{26} +(4.31945 - 2.88831i) q^{27} +(2.58114 - 4.61927i) q^{28} +(0.853732 + 0.853732i) q^{29} +(0.458023 - 0.432130i) q^{30} +(-3.82842 - 2.21034i) q^{31} +(5.11060 - 2.42523i) q^{32} +(-10.1969 - 0.667167i) q^{33} +(6.86260 + 6.38218i) q^{34} +(0.645568 + 0.214127i) q^{35} +(2.69290 + 5.36174i) q^{36} +(-1.05346 + 3.93158i) q^{37} +(-5.43422 - 2.88003i) q^{38} +(3.63344 - 1.79233i) q^{39} +(0.429765 + 0.586513i) q^{40} +2.05452i q^{41} +(-3.71870 + 5.30766i) q^{42} +(-2.94440 - 2.94440i) q^{43} +(2.22019 - 11.5888i) q^{44} +(-0.611744 + 0.469630i) q^{45} +(5.89775 - 1.81183i) q^{46} +(0.356974 + 0.618298i) q^{47} +(-6.52815 + 2.32018i) q^{48} +(-6.95219 - 0.816715i) q^{49} +(4.75183 - 5.10952i) q^{50} +(-7.56887 - 8.62865i) q^{51} +(1.53502 + 4.41923i) q^{52} +(-3.18848 - 11.8996i) q^{53} +(-2.61513 - 6.86739i) q^{54} +1.51667 q^{55} +(-5.55085 - 5.01877i) q^{56} +(6.26349 + 4.18409i) q^{57} +(1.44679 - 0.906771i) q^{58} +(-1.26315 + 0.338459i) q^{59} +(-0.450788 - 0.768006i) q^{60} +(3.80291 - 14.1926i) q^{61} +(-4.25753 + 4.57801i) q^{62} +(5.19024 - 6.00511i) q^{63} +(-1.72660 - 7.81146i) q^{64} +(-0.520763 + 0.300662i) q^{65} +(-4.14458 + 13.8443i) q^{66} +(1.84191 + 6.87409i) q^{67} +(10.9676 - 7.44089i) q^{68} +(-7.41105 + 1.47503i) q^{69} +(0.499325 - 0.822126i) q^{70} +9.22268 q^{71} +(8.24228 - 2.01612i) q^{72} +(2.87170 - 4.97393i) q^{73} +(5.08609 + 2.69553i) q^{74} +(-6.42442 + 5.63537i) q^{75} +(-5.68849 + 6.57964i) q^{76} +(-15.2877 + 3.15201i) q^{77} +(-1.32140 - 5.57518i) q^{78} +(2.19461 + 3.80118i) q^{79} +(0.944368 - 0.406890i) q^{80} +(2.33335 + 8.69226i) q^{81} +(2.83195 + 0.649782i) q^{82} +(-6.70882 + 6.70882i) q^{83} +(6.13995 + 6.80449i) q^{84} +(1.20460 + 1.20460i) q^{85} +(-4.98976 + 3.12732i) q^{86} +(-1.87544 + 0.925132i) q^{87} +(-15.2717 - 6.72546i) q^{88} +(-0.982700 + 0.567362i) q^{89} +(0.453860 + 0.991754i) q^{90} +(4.62433 - 4.11288i) q^{91} +(-0.632143 - 8.70246i) q^{92} +(5.75613 - 5.04916i) q^{93} +(0.965159 - 0.296503i) q^{94} +(-0.968199 - 0.558990i) q^{95} +(1.13348 + 9.73217i) q^{96} +11.1323i q^{97} +(-3.32452 + 9.32457i) q^{98} +(6.76948 - 16.3536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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