LMFDB - Embedded newform 336.2.bo.a.5.6

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			5.6
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35186 + 0.415301i) q^{2} +(1.14217 + 1.30209i) q^{3} +(1.65505 - 1.12286i) q^{4} +(0.248314 - 0.0665356i) q^{5} +(-2.08481 - 1.28590i) q^{6} +(0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-0.390898 + 2.97442i) q^{9} +O(q^{10})$	\(q+(-1.35186 + 0.415301i) q^{2} +(1.14217 + 1.30209i) q^{3} +(1.65505 - 1.12286i) q^{4} +(0.248314 - 0.0665356i) q^{5} +(-2.08481 - 1.28590i) q^{6} +(0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-0.390898 + 2.97442i) q^{9} +(-0.308054 + 0.193072i) q^{10} +(-5.69873 - 1.52697i) q^{11} +(3.35241 + 0.872539i) q^{12} +(1.65400 + 1.65400i) q^{13} +(-1.30591 - 3.50636i) q^{14} +(0.370253 + 0.247334i) q^{15} +(1.47839 - 3.71677i) q^{16} +(3.31337 + 5.73893i) q^{17} +(-0.706842 - 4.18334i) q^{18} +(4.20068 - 1.12557i) q^{19} +(0.336263 - 0.388941i) q^{20} +(-3.26254 + 3.21805i) q^{21} +(8.33804 - 0.302437i) q^{22} +(2.18135 - 3.77821i) q^{23} +(-4.89436 + 0.212710i) q^{24} +(-4.27289 + 2.46696i) q^{25} +(-2.92289 - 1.54907i) q^{26} +(-4.31945 + 2.88831i) q^{27} +(3.22161 + 4.19777i) q^{28} +(0.853732 + 0.853732i) q^{29} +(-0.603247 - 0.180594i) q^{30} +(-3.82842 + 2.21034i) q^{31} +(-0.454993 + 5.63853i) q^{32} +(-4.52066 - 9.16434i) q^{33} +(-6.86260 - 6.38218i) q^{34} +(0.214127 + 0.645568i) q^{35} +(2.69290 + 5.36174i) q^{36} +(3.93158 - 1.05346i) q^{37} +(-5.21129 + 3.26616i) q^{38} +(-0.264516 + 4.04282i) q^{39} +(-0.293052 + 0.665444i) q^{40} -2.05452i q^{41} +(3.07404 - 5.70529i) q^{42} +(-2.94440 - 2.94440i) q^{43} +(-11.1463 + 3.87165i) q^{44} +(0.100840 + 0.764600i) q^{45} +(-1.37979 + 6.01352i) 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} +(-3.68819 + 10.8692i) q^{51} +(4.59467 + 0.880250i) q^{52} +(11.8996 + 3.18848i) q^{53} +(4.63978 - 5.69846i) q^{54} -1.51667 q^{55} +(-6.09850 - 4.33686i) q^{56} +(6.26349 + 4.18409i) q^{57} +(-1.50868 - 0.799570i) q^{58} +(-0.338459 + 1.26315i) q^{59} +(0.890507 - 0.00639107i) q^{60} +(14.1926 - 3.80291i) q^{61} +(4.25753 - 4.57801i) q^{62} +(-7.91657 - 0.572578i) q^{63} +(-1.72660 - 7.81146i) q^{64} +(0.520763 + 0.300662i) q^{65} +(9.91726 + 10.5115i) q^{66} +(-6.87409 - 1.84191i) q^{67} +(11.9278 + 5.77778i) q^{68} +(7.41105 - 1.47503i) q^{69} +(-0.557575 - 0.783790i) q^{70} +9.22268 q^{71} +(-5.86716 - 6.12997i) q^{72} +(-2.87170 - 4.97393i) q^{73} +(-4.87744 + 3.05692i) q^{74} +(-8.09258 - 2.74603i) q^{75} +(5.68849 - 6.57964i) q^{76} +(3.15201 - 15.2877i) q^{77} +(-1.32140 - 5.57518i) q^{78} +(2.19461 - 3.80118i) q^{79} +(0.119807 - 1.02129i) q^{80} +(-8.69440 - 2.32539i) q^{81} +(0.853245 + 2.77743i) q^{82} +(6.70882 - 6.70882i) q^{83} +(-1.78626 + 8.98940i) q^{84} +(1.20460 + 1.20460i) q^{85} +(5.20322 + 2.75760i) q^{86} +(-0.136533 + 2.08674i) q^{87} +(13.4603 - 9.86297i) q^{88} +(-0.982700 - 0.567362i) q^{89} +(-0.453860 - 0.991754i) q^{90} +(-4.11288 + 4.62433i) q^{91} +(-0.632143 - 8.70246i) q^{92} +(-7.25077 - 2.46038i) q^{93} +(0.225800 - 0.984104i) q^{94} +(0.968199 - 0.558990i) q^{95} +(-7.86157 + 5.84771i) q^{96} -11.1323i q^{97} +(9.05921 - 3.99133i) 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 $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.35186	+	0.415301i	−0.955909	+	0.293662i
$2$	−1.35186	+	0.415301i	−0.955909	+	0.293662i
$3$	1.14217	+	1.30209i	0.659432	+	0.751764i
$3$	1.14217	+	1.30209i	0.659432	+	0.751764i
$4$	1.65505	−	1.12286i	0.827525	−	0.561428i
$5$	0.248314	−	0.0665356i	0.111049	−	0.0297556i	−0.202866	−	0.979206i	$-0.565026\pi$
$5$	0.248314	−	0.0665356i	0.111049	−	0.0297556i	0.313916	+	0.949451i	$0.398359\pi$
$6$	−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
$9$	−0.390898	+	2.97442i	−0.130299	+	0.991475i
$10$	−0.308054	+	0.193072i	−0.0974152	+	0.0610547i
$11$	−5.69873	−	1.52697i	−1.71823	−	0.460399i	−0.740813	−	0.671711i	$-0.765560\pi$
$11$	−5.69873	−	1.52697i	−1.71823	−	0.460399i	−0.977419	+	0.211312i	$0.932226\pi$
$12$	3.35241	+	0.872539i	0.967758	+	0.251880i
$13$	1.65400	+	1.65400i	0.458738	+	0.458738i	0.898241	−	0.439503i	$-0.144845\pi$
$13$	1.65400	+	1.65400i	0.458738	+	0.458738i	−0.439503	+	0.898241i	$0.644845\pi$
$14$	−1.30591	−	3.50636i	−0.349020	−	0.937115i
$15$	0.370253	+	0.247334i	0.0955988	+	0.0638612i
$16$	1.47839	−	3.71677i	0.369596	−	0.929192i
$17$	3.31337	+	5.73893i	0.803611	+	1.39190i	0.917225	+	0.398370i	$0.130424\pi$
$17$	3.31337	+	5.73893i	0.803611	+	1.39190i	−0.113614	+	0.993525i	$0.536243\pi$
$18$	−0.706842	−	4.18334i	−0.166604	−	0.986024i
$19$	4.20068	−	1.12557i	0.963703	−	0.258223i	0.257536	−	0.966269i	$-0.417089\pi$
$19$	4.20068	−	1.12557i	0.963703	−	0.258223i	0.706167	+	0.708045i	$0.250423\pi$
$20$	0.336263	−	0.388941i	0.0751906	−	0.0869699i
$21$	−3.26254	+	3.21805i	−0.711945	+	0.702236i
$22$	8.33804	−	0.302437i	1.77768	−	0.0644798i
$23$	2.18135	−	3.77821i	0.454843	−	0.787810i	−0.543837	−	0.839191i	$-0.683029\pi$
$23$	2.18135	−	3.77821i	0.454843	−	0.787810i	0.998679	+	0.0513807i	$0.0163622\pi$
$24$	−4.89436	+	0.212710i	−0.999057	+	0.0434192i
$25$	−4.27289	+	2.46696i	−0.854579	+	0.493391i
$26$	−2.92289	−	1.54907i	−0.573226	−	0.303798i
$27$	−4.31945	+	2.88831i	−0.831279	+	0.555856i
$28$	3.22161	+	4.19777i	0.608827	+	0.793303i
$29$	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	$0.714242\pi$
$30$	−0.603247	−	0.180594i	−0.110137	−	0.0329718i
$31$	−3.82842	+	2.21034i	−0.687604	+	0.396988i	−0.802714	−	0.596365i	$-0.796611\pi$
$31$	−3.82842	+	2.21034i	−0.687604	+	0.396988i	0.115110	+	0.993353i	$0.463278\pi$
$32$	−0.454993	+	5.63853i	−0.0804321	+	0.996760i
$33$	−4.52066	−	9.16434i	−0.786946	−	1.59531i
$34$	−6.86260	−	6.38218i	−1.17693	−	1.09454i
$35$	0.214127	+	0.645568i	0.0361941	+	0.109121i
$36$	2.69290	+	5.36174i	0.448816	+	0.893624i
$37$	3.93158	−	1.05346i	0.646348	−	0.173188i	0.0792707	−	0.996853i	$-0.474741\pi$
$37$	3.93158	−	1.05346i	0.646348	−	0.173188i	0.567077	+	0.823665i	$0.308074\pi$
$38$	−5.21129	+	3.26616i	−0.845382	+	0.529841i
$39$	−0.264516	+	4.04282i	−0.0423564	+	0.647369i
$40$	−0.293052	+	0.665444i	−0.0463357	+	0.105216i
$41$		−	2.05452i		−	0.320863i	−0.987047	−	0.160431i	$-0.948711\pi$
$41$		−	2.05452i		−	0.320863i	0.987047	−	0.160431i	$-0.0512885\pi$
$42$	3.07404	−	5.70529i	0.474335	−	0.880345i
$43$	−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	$0.852844\pi$
$44$	−11.1463	+	3.87165i	−1.68036	+	0.583673i
$45$	0.100840	+	0.764600i	0.0150323	+	0.113980i
$46$	−1.37979	+	6.01352i	−0.203438	+	0.886645i
$47$	−0.356974	+	0.618298i	−0.0520701	+	0.0901880i	−0.890886	−	0.454228i	$-0.849915\pi$
$47$	−0.356974	+	0.618298i	−0.0520701	+	0.0901880i	0.838816	+	0.544416i	$0.183249\pi$
$48$	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
$51$	−3.68819	+	10.8692i	−0.516450	+	1.52199i
$52$	4.59467	+	0.880250i	0.637166	+	0.122069i
$53$	11.8996	+	3.18848i	1.63453	+	0.437971i	0.955224	−	0.295882i	$-0.0956136\pi$
$53$	11.8996	+	3.18848i	1.63453	+	0.437971i	0.679307	+	0.733854i	$0.262280\pi$
$54$	4.63978	−	5.69846i	0.631393	−	0.775463i
$55$	−1.51667			−0.204508
$56$	−6.09850	−	4.33686i	−0.814946	−	0.579537i
$57$	6.26349	+	4.18409i	0.829620	+	0.554197i
$58$	−1.50868	−	0.799570i	−0.198099	−	0.104989i
$59$	−0.338459	+	1.26315i	−0.0440636	+	0.164448i	−0.984452	−	0.175656i	$-0.943795\pi$
$59$	−0.338459	+	1.26315i	−0.0440636	+	0.164448i	0.940388	+	0.340103i	$0.110462\pi$
$60$	0.890507	−	0.00639107i	0.114964	−	0.000825084i
$61$	14.1926	−	3.80291i	1.81718	−	0.486913i	0.820748	−	0.571290i	$-0.193557\pi$
$61$	14.1926	−	3.80291i	1.81718	−	0.486913i	0.996434	+	0.0843772i	$0.0268901\pi$
$62$	4.25753	−	4.57801i	0.540707	−	0.581408i
$63$	−7.91657	−	0.572578i	−0.997395	−	0.0721380i
$64$	−1.72660	−	7.81146i	−0.215825	−	0.976432i
$65$	0.520763	+	0.300662i	0.0645927	+	0.0372926i
$66$	9.91726	+	10.5115i	1.22073	+	1.29387i
$67$	−6.87409	−	1.84191i	−0.839804	−	0.225025i	−0.186818	−	0.982395i	$-0.559817\pi$
$67$	−6.87409	−	1.84191i	−0.839804	−	0.225025i	−0.652986	+	0.757370i	$0.726484\pi$
$68$	11.9278	+	5.77778i	1.44646	+	0.700658i
$69$	7.41105	−	1.47503i	0.892185	−	0.177573i
$70$	−0.557575	−	0.783790i	−0.0666430	−	0.0936808i
$71$	9.22268			1.09453			0.547265	−	0.836959i	$-0.315669\pi$
$71$	9.22268			1.09453			0.547265	+	0.836959i	$0.315669\pi$
$72$	−5.86716	−	6.12997i	−0.691451	−	0.722423i
$73$	−2.87170	−	4.97393i	−0.336107	−	0.582155i	0.647590	−	0.761989i	$-0.275777\pi$
$73$	−2.87170	−	4.97393i	−0.336107	−	0.582155i	−0.983697	+	0.179834i	$0.942444\pi$
$74$	−4.87744	+	3.05692i	−0.566991	+	0.355360i
$75$	−8.09258	−	2.74603i	−0.934450	−	0.317084i
$76$	5.68849	−	6.57964i	0.652515	−	0.754737i
$77$	3.15201	−	15.2877i	0.359204	−	1.74220i
$78$	−1.32140	−	5.57518i	−0.149619	−	0.631265i
$79$	2.19461	−	3.80118i	0.246913	−	0.427666i	−0.715755	−	0.698352i	$-0.753917\pi$
$79$	2.19461	−	3.80118i	0.246913	−	0.427666i	0.962668	+	0.270686i	$0.0872504\pi$
$80$	0.119807	−	1.02129i	0.0133948	−	0.114184i
$81$	−8.69440	−	2.32539i	−0.966044	−	0.258377i
$82$	0.853245	+	2.77743i	0.0942252	+	0.306716i
$83$	6.70882	−	6.70882i	0.736389	−	0.736389i	−0.235488	−	0.971877i	$-0.575669\pi$
$83$	6.70882	−	6.70882i	0.736389	−	0.736389i	0.971877	+	0.235488i	$0.0756689\pi$
$84$	−1.78626	+	8.98940i	−0.194897	+	0.980824i
$85$	1.20460	+	1.20460i	0.130657	+	0.130657i
$86$	5.20322	+	2.75760i	0.561078	+	0.297360i
$87$	−0.136533	+	2.08674i	−0.0146378	+	0.223723i
$88$	13.4603	−	9.86297i	1.43487	−	1.05140i
$89$	−0.982700	−	0.567362i	−0.104166	−	0.0601402i	0.447012	−	0.894528i	$-0.352488\pi$
$89$	−0.982700	−	0.567362i	−0.104166	−	0.0601402i	−0.551178	+	0.834388i	$0.685821\pi$
$90$	−0.453860	−	0.991754i	−0.0478411	−	0.104540i
$91$	−4.11288	+	4.62433i	−0.431147	+	0.484761i
$92$	−0.632143	−	8.70246i	−0.0659054	−	0.907295i
$93$	−7.25077	−	2.46038i	−0.751869	−	0.255129i
$94$	0.225800	−	0.984104i	0.0232895	−	0.101503i
$95$	0.968199	−	0.558990i	0.0993351	−	0.0573512i
$96$	−7.86157	+	5.84771i	−0.802368	+	0.596829i
$97$		−	11.1323i		−	1.13031i	−0.824985	−	0.565155i	$-0.808816\pi$
$97$		−	11.1323i		−	1.13031i	0.824985	−	0.565155i	$-0.191184\pi$
$98$	9.05921	−	3.99133i	0.915118	−	0.403186i
$99$	6.76948	−	16.3536i	0.680358	−	1.64359i
$100$	−4.30182	+	8.88079i	−0.430182	+	0.888079i
$101$	3.25569	−	12.1504i	0.323953	−	1.20901i	−0.591407	−	0.806373i	$-0.701427\pi$
$101$	3.25569	−	12.1504i	0.323953	−	1.20901i	0.915360	−	0.402636i	$-0.131906\pi$
$102$	0.471953	−	16.2253i	0.0467303	−	1.60654i
$103$	−2.11657	+	3.66601i	−0.208552	+	0.361222i	−0.951259	−	0.308394i	$-0.900208\pi$
$103$	−2.11657	+	3.66601i	−0.208552	+	0.361222i	0.742707	+	0.669617i	$0.233542\pi$
$104$	−6.57692	+	0.718194i	−0.644920	+	0.0704247i
$105$	−0.596020	+	1.01616i	−0.0581656	+	0.0991673i
$106$	−17.4107	+	0.631521i	−1.69108	+	0.0613388i
$107$	−1.84865	−	6.89925i	−0.178715	−	0.666975i	−0.995889	−	0.0905833i	$-0.971127\pi$
$107$	−1.84865	−	6.89925i	−0.178715	−	0.666975i	0.817173	−	0.576392i	$-0.195540\pi$
$108$	−3.90575	+	9.63043i	−0.375831	+	0.926688i
$109$	5.24379	+	1.40507i	0.502264	+	0.134581i	0.501050	−	0.865418i	$-0.332947\pi$
$109$	5.24379	+	1.40507i	0.502264	+	0.134581i	0.00121322	+	0.999999i	$0.499614\pi$
$110$	2.05033	−	0.629876i	0.195491	−	0.0600563i
$111$	5.86224	+	3.91605i	0.556419	+	0.371695i
$112$	10.0454	+	3.33011i	0.949203	+	0.314666i
$113$			11.2533i			1.05862i	0.848429	+	0.529309i	$0.177549\pi$
$113$			11.2533i			1.05862i	−0.848429	+	0.529309i	$0.822451\pi$
$114$	−10.2050	−	3.05508i	−0.955788	−	0.286134i
$115$	0.290275	−	1.08332i	0.0270682	−	0.101020i
$116$	2.37159	+	0.454351i	0.220196	+	0.0421854i
$117$	−5.56625	+	4.27316i	−0.514600	+	0.395054i
$118$	−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
$122$	−17.6071	+	11.0352i	−1.59407	+	0.999082i
$123$	2.67518	−	2.34661i	0.241213	−	0.211587i
$124$	−3.85433	+	7.95698i	−0.346129	+	0.714558i
$125$	−1.80577	+	1.80577i	−0.161513	+	0.161513i
$126$	10.9399	−	2.51371i	0.974603	−	0.223939i
$127$	13.0977			1.16223			0.581115	−	0.813822i	$-0.302617\pi$
$127$	13.0977			1.16223			0.581115	+	0.813822i	$0.302617\pi$
$128$	5.57822	+	9.84294i	0.493050	+	0.870001i
$129$	0.470881	−	7.19688i	0.0414588	−	0.633650i
$130$	−0.828864	−	0.190180i	−0.0726961	−	0.0166799i
$131$	3.26791	+	12.1960i	0.285518	+	1.06557i	0.948460	+	0.316898i	$0.102641\pi$
$131$	3.26791	+	12.1960i	0.285518	+	1.06557i	−0.662941	+	0.748671i	$0.730692\pi$
$132$	−17.7722	−	10.0914i	−1.54687	−	0.878344i
$133$	3.62235	+	10.9209i	0.314098	+	0.946966i
$134$	10.0578	−	0.364815i	0.868858	−	0.0315152i
$135$	−0.880406	+	1.00461i	−0.0757732	+	0.0864627i
$136$	−18.5242	−	2.85712i	−1.58844	−	0.244996i
$137$	3.08371	+	5.34114i	0.263459	+	0.456324i	0.967159	−	0.254173i	$-0.0818033\pi$
$137$	3.08371	+	5.34114i	0.263459	+	0.456324i	−0.703700	+	0.710498i	$0.748470\pi$
$138$	−9.40612	+	5.07185i	−0.800702	+	0.431745i
$139$	6.01159	−	6.01159i	0.509896	−	0.509896i	−0.404598	−	0.914495i	$-0.632589\pi$
$139$	6.01159	−	6.01159i	0.509896	−	0.509896i	0.914495	+	0.404598i	$0.132589\pi$
$140$	1.07927	+	0.828013i	0.0912151	+	0.0699799i
$141$	−1.21281	+	0.241387i	−0.102137	+	0.0203284i
$142$	−12.4678	+	3.83019i	−1.04627	+	0.321422i
$143$	−6.90011	−	11.9513i	−0.577016	−	0.999421i
$144$	10.4774	+	5.85022i	0.873113	+	0.487518i
$145$	0.268797	+	0.155190i	0.0223224	+	0.0128878i
$146$	5.94782	+	5.53144i	0.492245	+	0.457785i
$147$	−9.00402	−	8.11958i	−0.742639	−	0.669692i
$148$	5.32407	−	6.15814i	0.437636	−	0.506196i
$149$	−2.70047	−	10.0783i	−0.221231	−	0.825646i	−0.983880	−	0.178832i	$-0.942768\pi$
$149$	−2.70047	−	10.0783i	−0.221231	−	0.825646i	0.762648	−	0.646813i	$-0.223899\pi$
$150$	12.0805	+	0.351390i	0.986365	+	0.0286909i
$151$	−20.1655	+	11.6426i	−1.64104	+	0.947458i	−0.660582	+	0.750754i	$0.729690\pi$
$151$	−20.1655	+	11.6426i	−1.64104	+	0.947458i	−0.980463	+	0.196703i	$0.936976\pi$
$152$	−4.95751	+	11.2572i	−0.402107	+	0.913078i
$153$	−18.3652	+	7.61204i	−1.48474	+	0.615397i
$154$	2.08794	+	21.9759i	0.168251	+	1.77087i
$155$	−0.803584	+	0.803584i	−0.0645454	+	0.0645454i
$156$	4.10172	+	6.98809i	0.328401	+	0.559495i
$157$	3.30303	−	12.3271i	0.263611	−	0.983808i	−0.699485	−	0.714648i	$-0.746587\pi$
$157$	3.30303	−	12.3271i	0.263611	−	0.983808i	0.963095	−	0.269161i	$-0.0867463\pi$
$158$	−1.38818	+	6.05009i	−0.110437	+	0.481319i
$159$	9.43963	+	19.1361i	0.748611	+	1.51760i
$160$	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
$163$	−0.548548	−	2.04721i	−0.0429656	−	0.160350i	0.941110	−	0.338101i	$-0.109785\pi$
$163$	−0.548548	−	2.04721i	−0.0429656	−	0.160350i	−0.984076	+	0.177751i	$0.943118\pi$
$164$	−2.30694	−	3.40034i	−0.180141	−	0.265522i
$165$	−1.73230	−	1.97485i	−0.134859	−	0.153742i
$166$	−6.28321	+	11.8556i	−0.487672	+	0.920171i
$167$		−	7.69272i		−	0.595280i	−0.954678	−	0.297640i	$-0.903800\pi$
$167$		−	7.69272i		−	0.595280i	0.954678	−	0.297640i	$-0.0961996\pi$
$168$	−1.31853	−	12.8942i	−0.101727	−	0.994812i
$169$		−	7.52854i		−	0.579119i
$170$	−2.12872	−	1.12818i	−0.163266	−	0.0865274i
$171$	1.70589	+	12.9346i	0.130452	+	0.989133i
$172$	−8.17926	−	1.56699i	−0.623663	−	0.119482i
$173$	−3.57219	−	13.3316i	−0.271589	−	1.01358i	−0.958093	−	0.286457i	$-0.907522\pi$
$173$	−3.57219	−	13.3316i	−0.271589	−	1.01358i	0.686505	−	0.727126i	$-0.259144\pi$
$174$	−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
$177$	−2.03131	+	1.00202i	−0.152683	+	0.0753166i
$178$	1.56410	+	0.358878i	0.117234	+	0.0268990i
$179$	0.735152	−	2.74363i	0.0549479	−	0.205068i	−0.932994	−	0.359891i	$-0.882814\pi$
$179$	0.735152	−	2.74363i	0.0549479	−	0.205068i	0.987942	+	0.154823i	$0.0494806\pi$
$180$	1.02543	+	1.15222i	0.0764312	+	0.0858817i
$181$	−12.8523	+	12.8523i	−0.955307	+	0.955307i	−0.999043	−	0.0437364i	$-0.986074\pi$
$181$	−12.8523	+	12.8523i	−0.955307	+	0.955307i	0.0437364	+	0.999043i	$0.486074\pi$
$182$	3.63955	−	7.95953i	0.269782	−	0.589999i
$183$	21.1622	+	14.1366i	1.56435	+	1.04501i
$184$	4.46871	+	11.5020i	0.329438	+	0.847937i
$185$	0.906174	−	0.523180i	0.0666233	−	0.0384650i
$186$	10.8238	+	0.314838i	0.793641	+	0.0230850i
$187$	−10.1188	−	37.7640i	−0.739963	−	2.76158i
$188$	0.103449	+	1.42415i	0.00754481	+	0.103866i
$189$	−8.29652	−	10.9621i	−0.603483	−	0.797376i
$190$	−1.07672	+	1.15777i	−0.0781135	+	0.0839935i
$191$	8.47464	+	4.89284i	0.613204	+	0.354033i	0.774218	−	0.632919i	$-0.218143\pi$
$191$	8.47464	+	4.89284i	0.613204	+	0.354033i	−0.161015	+	0.986952i	$0.551477\pi$
$192$	8.19918	−	11.1702i	0.591725	−	0.806140i
$193$	9.39914	+	16.2798i	0.676565	+	1.17185i	0.976009	+	0.217731i	$0.0698656\pi$
$193$	9.39914	+	16.2798i	0.676565	+	1.17185i	−0.299444	+	0.954114i	$0.596801\pi$
$194$	4.62324	+	15.0493i	0.331929	+	1.08047i
$195$	0.203308	+	1.02149i	0.0145592	+	0.0731504i
$196$	−10.5892	+	9.15802i	−0.756370	+	0.654144i
$197$	−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	$0.327692\pi$
$198$	−2.35974	+	24.9191i	−0.167700	+	1.77092i
$199$	2.87699	+	4.98310i	0.203945	+	0.353242i	0.949796	−	0.312870i	$-0.101290\pi$
$199$	2.87699	+	4.98310i	0.203945	+	0.353242i	−0.745851	+	0.666112i	$0.767957\pi$
$200$	2.12726	−	13.7921i	0.150420	−	0.975251i
$201$	−5.45304	−	11.0545i	−0.384628	−	0.779723i
$202$	0.644833	+	17.7777i	0.0453703	+	1.25084i
$203$	−2.12291	+	2.38690i	−0.148999	+	0.167527i
$204$	6.10036	+	22.1303i	0.427110	+	1.54943i
$205$	−0.136699	−	0.510168i	−0.00954747	−	0.0356316i
$206$	1.33881	−	5.83494i	0.0932794	−	0.406540i
$207$	10.3853	+	7.96515i	0.721828	+	0.553616i
$208$	8.59281	−	3.70230i	0.595804	−	0.256708i
$209$	−25.6573			−1.77475
$210$	0.383723	−	1.62124i	0.0264794	−	0.111876i
$211$	−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	$0.326575\pi$
$212$	23.2746	−	8.08442i	1.59851	−	0.555240i
$213$	10.5339	+	12.0088i	0.721768	+	0.822829i
$214$	5.36437	+	8.55907i	0.366701	+	0.585086i
$215$	−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
$219$	3.19656	−	9.42030i	0.216003	−	0.636565i
$220$	−2.51017	+	1.70301i	−0.169236	+	0.114817i
$221$	−4.01188	+	14.9725i	−0.269868	+	1.00716i
$222$	−9.55126	−	2.85936i	−0.641039	−	0.191908i
$223$			2.31556i			0.155062i	0.996990	+	0.0775308i	$0.0247036\pi$
$223$			2.31556i			0.155062i	−0.996990	+	0.0775308i	$0.975296\pi$
$224$	−14.9630	−	0.329974i	−0.999757	−	0.0220473i
$225$	−5.66751	−	13.6737i	−0.377834	−	0.911582i
$226$	−4.67349	−	15.2128i	−0.310876	−	1.01194i
$227$	−8.41776	−	2.25553i	−0.558706	−	0.149705i	−0.0315943	−	0.999501i	$-0.510058\pi$
$227$	−8.41776	−	2.25553i	−0.558706	−	0.149705i	−0.527112	+	0.849796i	$0.676725\pi$
$228$	15.0645	−	0.108117i	0.997673	−	0.00716020i
$229$	−3.76254	−	14.0420i	−0.248635	−	0.927920i	−0.971521	−	0.236953i	$-0.923851\pi$
$229$	−3.76254	−	14.0420i	−0.248635	−	0.927920i	0.722886	−	0.690968i	$-0.242815\pi$
$230$	0.0574928	+	1.58505i	0.00379096	+	0.104515i
$231$	23.5062	−	13.3570i	1.54659	−	0.878825i
$232$	−3.39475	+	0.370703i	−0.222876	+	0.0243379i
$233$	1.97360	−	3.41838i	0.129295	−	0.223946i	−0.794109	−	0.607776i	$-0.792062\pi$
$233$	1.97360	−	3.41838i	0.129295	−	0.223946i	0.923404	+	0.383830i	$0.125395\pi$
$234$	5.75015	−	8.08839i	0.375899	−	0.528754i
$235$	−0.0475030	+	0.177284i	−0.00309875	+	0.0115647i
$236$	0.858166	+	2.47061i	0.0558618	+	0.160823i
$237$	7.45612	−	1.48400i	0.484327	−	0.0963962i
$238$	15.7958	−	19.1124i	1.02389	−	1.23888i
$239$		−	9.42859i		−	0.609885i	−0.952371	−	0.304942i	$-0.901363\pi$
$239$		−	9.42859i		−	0.609885i	0.952371	−	0.304942i	$-0.0986372\pi$
$240$	1.46666	−	1.01049i	0.0946723	−	0.0652268i
$241$	−4.21351	+	2.43267i	−0.271416	+	0.156702i	−0.629531	−	0.776975i	$-0.716753\pi$
$241$	−4.21351	+	2.43267i	−0.271416	+	0.156702i	0.358115	+	0.933678i	$0.383420\pi$
$242$	−32.8157	−	7.52947i	−2.10947	−	0.484013i
$243$	−6.90260	−	13.9769i	−0.442802	−	0.896619i
$244$	19.2194	−	22.2303i	1.23040	−	1.42315i
$245$	−1.67199	+	0.665370i	−0.106819	+	0.0425089i
$246$	−2.64192	+	4.28330i	−0.168443	+	0.273093i
$247$	8.80964	+	5.08625i	0.560544	+	0.323630i
$248$	1.90597	−	12.3574i	0.121029	−	0.784698i
$249$	16.3981	+	1.07291i	1.03919	+	0.0679926i
$250$	1.69121	−	3.19109i	0.106962	−	0.201822i
$251$	6.18550	+	6.18550i	0.390425	+	0.390425i	0.874839	−	0.484414i	$-0.160967\pi$
$251$	6.18550	+	6.18550i	0.390425	+	0.390425i	−0.484414	+	0.874839i	$0.660967\pi$
$252$	−13.7453	+	7.94153i	−0.865870	+	0.500270i
$253$	−18.2001	+	18.2001i	−1.14423	+	1.14423i
$254$	−17.7062	+	5.43947i	−1.11099	+	0.341302i
$255$	−0.192645	+	2.94436i	−0.0120639	+	0.184383i
$256$	−11.6288	−	10.9896i	−0.726797	−	0.686852i
$257$	−5.99043	+	10.3757i	−0.373673	+	0.647221i	−0.990127	−	0.140170i	$-0.955235\pi$
$257$	−5.99043	+	10.3757i	−0.373673	+	0.647221i	0.616455	+	0.787391i	$0.288568\pi$
$258$	2.35230	+	9.92473i	0.146448	+	0.617887i
$259$	3.39030	+	10.2213i	0.210663	+	0.635123i
$260$	1.19949	−	0.0871303i	0.0743892	−	0.00540359i
$261$	−2.87308	+	2.20564i	−0.177839	+	0.136526i
$262$	−9.48276	−	15.1301i	−0.585847	−	0.934742i
$263$	−2.37212	−	4.10863i	−0.146271	−	0.253349i	0.783575	−	0.621297i	$-0.213394\pi$
$263$	−2.37212	−	4.10863i	−0.146271	−	0.253349i	−0.929846	+	0.367948i	$0.880061\pi$
$264$	28.2164	+	6.26137i	1.73660	+	0.385360i
$265$	3.16698			0.194546
$266$	−9.43239	−	13.2592i	−0.578337	−	0.812975i
$267$	−0.383651	−	1.92759i	−0.0234791	−	0.117967i
$268$	−13.4452	+	4.67017i	−0.821295	+	0.285276i
$269$	−3.99085	−	1.06934i	−0.243326	−	0.0651991i	0.135095	−	0.990833i	$-0.456866\pi$
$269$	−3.99085	−	1.06934i	−0.243326	−	0.0651991i	−0.378421	+	0.925634i	$0.623533\pi$
$270$	0.772971	−	1.72372i	0.0470415	−	0.104902i
$271$	−10.7958	−	6.23296i	−0.655799	−	0.378626i	0.134876	−	0.990863i	$-0.456937\pi$
$271$	−10.7958	−	6.23296i	−0.655799	−	0.378626i	−0.790674	+	0.612237i	$0.790270\pi$
$272$	26.2287	−	3.83069i	1.59035	−	0.232270i
$273$	−10.7189	−	0.0735907i	−0.648738	−	0.00445391i
$274$	−6.38692	−	5.93981i	−0.385848	−	0.358837i
$275$	28.1170	−	7.53394i	1.69552	−	0.454314i
$276$	10.6094	−	10.7628i	0.638612	−	0.647844i
$277$	−3.25036	+	12.1305i	−0.195295	+	0.728851i	0.796895	+	0.604118i	$0.206474\pi$
$277$	−3.25036	+	12.1305i	−0.195295	+	0.728851i	−0.992190	+	0.124734i	$0.960192\pi$
$278$	−5.63021	+	10.6234i	−0.337677	+	0.637152i
$279$	−5.07796	−	12.2513i	−0.304010	−	0.733469i
$280$	−1.80290	−	0.671136i	−0.107744	−	0.0401080i
$281$	−13.1985			−0.787359			−0.393679	−	0.919248i	$-0.628798\pi$
$281$	−13.1985			−0.787359			−0.393679	+	0.919248i	$0.628798\pi$
$282$	1.53930	−	0.830000i	0.0916638	−	0.0494258i
$283$	22.0207	+	5.90043i	1.30899	+	0.350744i	0.844844	−	0.535012i	$-0.179693\pi$
$283$	22.0207	+	5.90043i	1.30899	+	0.350744i	0.464150	+	0.885756i	$0.346360\pi$
$284$	15.2640	−	10.3557i	0.905752	−	0.614501i
$285$	1.83370	+	0.622225i	0.108619	+	0.0368574i
$286$	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
$290$	−0.427827	−	0.0981637i	−0.0251229	−	0.00576437i
$291$	14.4953	−	12.7149i	0.849727	−	0.745363i
$292$	−10.3378	−	5.00760i	−0.604976	−	0.293048i
$293$	−2.13884	−	2.13884i	−0.124952	−	0.124952i	0.641865	−	0.766818i	$-0.278161\pi$
$293$	−2.13884	−	2.13884i	−0.124952	−	0.124952i	−0.766818	+	0.641865i	$0.778161\pi$
$294$	15.5442	+	7.23716i	0.906559	+	0.422080i
$295$			0.336177i			0.0195730i
$296$	−4.63992	+	10.5360i	−0.269690	+	0.612394i
$297$	29.0258	−	9.86404i	1.68425	−	0.572369i
$298$	7.83618	+	12.5029i	0.453938	+	0.724275i
$299$	9.85712	−	2.64121i	0.570052	−	0.152745i
$300$	−16.4770	+	4.54199i	−0.951301	+	0.262232i
$301$	7.32160	−	8.23206i	0.422010	−	0.474488i
$302$	22.4258	−	24.1138i	1.29046	−	1.38760i
$303$	19.5395	−	9.63860i	1.12252	−	0.553723i
$304$	2.02674	−	17.2770i	0.116242	−	0.990904i
$305$	3.27121	−	1.88863i	0.187309	−	0.108143i
$306$	21.6659	−	17.9175i	1.23856	−	1.02428i
$307$	−17.3994	−	17.3994i	−0.993038	−	0.993038i	0.00693770	−	0.999976i	$-0.497792\pi$
$307$	−17.3994	−	17.3994i	−0.993038	−	0.993038i	−0.999976	+	0.00693770i	$0.997792\pi$
$308$	−11.9492	−	28.8412i	−0.680870	−	1.64338i
$309$	−7.19097	+	1.43123i	−0.409080	+	0.0814197i
$310$	0.752604	−	1.42006i	0.0427450	−	0.0806541i
$311$	−16.1458	+	9.32176i	−0.915542	+	0.528589i	−0.882210	−	0.470856i	$-0.843945\pi$
$311$	−16.1458	+	9.32176i	−0.915542	+	0.528589i	−0.0333321	+	0.999444i	$0.510612\pi$
$312$	−8.44711	−	7.74347i	−0.478223	−	0.438387i
$313$	−13.7259	+	23.7740i	−0.775836	+	1.34379i	0.158488	+	0.987361i	$0.449338\pi$
$313$	−13.7259	+	23.7740i	−0.775836	+	1.34379i	−0.934323	+	0.356426i	$0.883995\pi$
$314$	0.654210	+	18.0362i	0.0369192	+	1.01784i
$315$	−2.00389	+	0.384555i	−0.112907	+	0.0216672i
$316$	−0.635987	−	8.75538i	−0.0357770	−	0.492529i
$317$	−5.65181	+	1.51440i	−0.317437	+	0.0850571i	−0.414020	−	0.910268i	$-0.635876\pi$
$317$	−5.65181	+	1.51440i	−0.317437	+	0.0850571i	0.0965823	+	0.995325i	$0.469209\pi$
$318$	−20.7083	−	21.9491i	−1.16126	−	1.23084i
$319$	−3.56156	−	6.16881i	−0.199409	−	0.345387i
$320$	−0.948479	−	1.82482i	−0.0530216	−	0.102010i
$321$	6.87200	−	10.2872i	0.383558	−	0.574177i
$322$	−16.0964	−	2.71459i	−0.897018	−	0.151278i
$323$	20.3780	+	20.3780i	1.13386	+	1.13386i
$324$	−17.0007	+	5.91393i	−0.944486	+	0.328551i
$325$	−11.1477	−	2.98703i	−0.618365	−	0.165690i
$326$	1.59177	+	2.53973i	0.0881599	+	0.140663i
$327$	4.15976	+	8.43273i	0.230035	+	0.466331i
$328$	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
$331$	−0.842477	+	0.225741i	−0.0463067	+	0.0124079i	−0.281898	−	0.959444i	$-0.590964\pi$
$331$	−0.842477	+	0.225741i	−0.0463067	+	0.0124079i	0.235591	+	0.971852i	$0.424297\pi$
$332$	3.57039	−	18.6365i	0.195951	−	1.02281i
$333$	1.59660	+	12.1060i	0.0874933	+	0.663404i
$334$	3.19479	+	10.3995i	0.174811	+	0.569034i
$335$	−1.82949			−0.0999556
$336$	7.13745	+	16.8836i	0.389380	+	0.921077i
$337$	9.71606			0.529268			0.264634	−	0.964349i	$-0.414749\pi$
$337$	9.71606			0.529268			0.264634	+	0.964349i	$0.414749\pi$
$338$	3.12661	+	10.1775i	0.170065	+	0.553585i
$339$	−14.6528	+	12.8531i	−0.795831	+	0.698086i
$340$	3.34627	+	0.641081i	0.181477	+	0.0347675i
$341$	25.1922	−	6.75024i	1.36424	−	0.365546i
$342$	−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
$345$	1.74213	−	0.859370i	0.0937929	−	0.0462669i
$346$	10.3657	+	16.5389i	0.557265	+	0.889138i
$347$	24.5245	+	6.57133i	1.31655	+	0.352768i	0.847683	−	0.530503i	$-0.177997\pi$
$347$	24.5245	+	6.57133i	1.31655	+	0.352768i	0.468863	+	0.883271i	$0.344664\pi$
$348$	2.11715	+	3.60697i	0.113491	+	0.193354i
$349$	21.4932	+	21.4932i	1.15051	+	1.15051i	0.986451	+	0.164054i	$0.0524573\pi$
$349$	21.4932	+	21.4932i	1.15051	+	1.15051i	0.164054	+	0.986451i	$0.447543\pi$
$350$	14.2301	+	11.7607i	0.760630	+	0.628635i
$351$	−11.9217	−	2.36711i	−0.636331	−	0.126347i
$352$	11.2027	−	31.4377i	0.597108	−	1.67563i
$353$	6.41440	+	11.1101i	0.341404	+	0.591329i	0.984694	−	0.174294i	$-0.0557642\pi$
$353$	6.41440	+	11.1101i	0.341404	+	0.591329i	−0.643290	+	0.765623i	$0.722431\pi$
$354$	2.32991	−	2.19820i	0.123833	−	0.116833i
$355$	2.29012	−	0.613636i	0.121547	−	0.0325684i
$356$	−2.26348	+	0.164418i	−0.119964	+	0.00871415i
$357$	−29.2782	−	8.06090i	−1.54956	−	0.426628i
$358$	0.145607	+	4.01431i	0.00769556	+	0.212163i
$359$	−11.6168	+	20.1209i	−0.613110	+	1.06194i	0.377603	+	0.925968i	$0.376748\pi$
$359$	−11.6168	+	20.1209i	−0.613110	+	1.06194i	−0.990713	+	0.135970i	$0.956585\pi$
$360$	−1.86476	−	1.13178i	−0.0982814	−	0.0596502i
$361$	−0.0756479	+	0.0436753i	−0.00398147	+	0.00229870i
$362$	12.0370	−	22.7121i	0.632649	−	1.19372i
$363$	8.04923	+	40.4420i	0.422475	+	2.12265i
$364$	−1.61457	+	12.2717i	−0.0846263	+	0.643210i
$365$	−1.04403	−	1.04403i	−0.0546469	−	0.0546469i
$366$	−34.4792	−	10.3220i	−1.80226	−	0.539542i
$367$	−21.4355	+	12.3758i	−1.11892	+	0.646011i	−0.941126	−	0.338056i	$-0.890231\pi$
$367$	−21.4355	+	12.3758i	−1.11892	+	0.646011i	−0.177798	+	0.984067i	$0.556897\pi$
$368$	−10.8178	−	13.6932i	−0.563919	−	0.713808i
$369$	6.11103	+	0.803108i	0.318127	+	0.0418082i
$370$	−1.00774	+	1.08360i	−0.0523901	+	0.0563337i
$371$	−6.58173	+	31.9225i	−0.341706	+	1.65733i
$372$	−14.7630	+	4.06952i	−0.765428	+	0.210995i
$373$	16.9933	−	4.55333i	0.879877	−	0.235762i	0.209523	−	0.977804i	$-0.432809\pi$
$373$	16.9933	−	4.55333i	0.879877	−	0.235762i	0.670354	+	0.742041i	$0.266142\pi$
$374$	29.3627	+	46.8493i	1.51831	+	2.42252i
$375$	−4.41379	−	0.288787i	−0.227927	−	0.0149129i
$376$	−0.731297	−	1.88228i	−0.0377138	−	0.0970713i
$377$			2.82415i			0.145451i
$378$	15.7683	+	11.3737i	0.811034	+	0.584999i
$379$	−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	$0.842552\pi$
$380$	0.974753	−	2.01231i	0.0500038	−	0.103229i
$381$	14.9597	+	17.0544i	0.766411	+	0.873722i
$382$	−13.4885	−	3.09491i	−0.690133	−	0.158349i
$383$	−1.49970	+	2.59756i	−0.0766311	+	0.132729i	−0.901794	−	0.432165i	$-0.857750\pi$
$383$	−1.49970	+	2.59756i	−0.0766311	+	0.132729i	0.825163	+	0.564894i	$0.191083\pi$
$384$	−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
$387$	9.90884	−	7.60692i	0.503695	−	0.386682i
$388$	−12.4999	−	18.4245i	−0.634588	−	0.935360i
$389$	−20.1967	−	5.41170i	−1.02402	−	0.274384i	−0.292541	−	0.956253i	$-0.594501\pi$
$389$	−20.1967	−	5.41170i	−1.02402	−	0.274384i	−0.731474	+	0.681869i	$0.761167\pi$
$390$	−0.699070	−	1.29648i	−0.0353988	−	0.0656496i
$391$	28.9105			1.46207
$392$	10.5117	−	16.7781i	0.530924	−	0.847420i
$393$	−12.1478	+	18.1850i	−0.612777	+	0.917313i
$394$	4.49249	−	8.47673i	0.226329	−	0.427051i
$395$	0.292040	−	1.08991i	0.0146941	−	0.0548392i
$396$	−7.15887	−	34.6671i	−0.359747	−	1.74209i
$397$	−5.09248	+	1.36453i	−0.255584	+	0.0684836i	−0.384336	−	0.923193i	$-0.625570\pi$
$397$	−5.09248	+	1.36453i	−0.255584	+	0.0684836i	0.128752	+	0.991677i	$0.458903\pi$
$398$	−5.95877	−	5.54163i	−0.298686	−	0.277777i
$399$	−10.0828	+	17.1902i	−0.504769	+	0.860587i
$400$	2.85213	+	19.5285i	0.142606	+	0.976424i
$401$	−5.79531	−	3.34592i	−0.289404	−	0.167087i	0.348269	−	0.937395i	$-0.386770\pi$
$401$	−5.79531	−	3.34592i	−0.289404	−	0.167087i	−0.637673	+	0.770307i	$0.720103\pi$
$402$	11.9627	+	12.6795i	0.596645	+	0.632394i
$403$	−9.98812	−	2.67631i	−0.497544	−	0.133316i
$404$	−8.25483	−	23.7652i	−0.410693	−	1.18236i
$405$	−2.31366	+	0.00105953i	−0.114967	+	5.26484e-5i
$406$	1.87859	−	4.10839i	0.0932330	−	0.203896i
$407$	−24.0136			−1.19031
$408$	−17.4376	−	27.3836i	−0.863288	−	1.35569i
$409$	−16.2052	−	28.0683i	−0.801298	−	1.38789i	−0.918762	−	0.394811i	$-0.870810\pi$
$409$	−16.2052	−	28.0683i	−0.801298	−	1.38789i	0.117464	−	0.993077i	$-0.462523\pi$
$410$	0.396671	+	0.632904i	0.0195902	+	0.0312569i
$411$	−3.43255	+	10.1158i	−0.169315	+	0.498974i
$412$	0.613370	+	8.44403i	0.0302186	+	0.416008i
$413$	−3.38859	−	0.698655i	−0.166742	−	0.0343785i
$414$	−17.3474	−	6.45474i	−0.852579	−	0.317233i
$415$	1.21952	−	2.11227i	0.0598639	−	0.103687i
$416$	−10.0787	+	8.57358i	−0.494149	+	0.420355i
$417$	14.6939	+	0.961400i	0.719564	+	0.0470800i
$418$	34.6850	−	10.6555i	1.69650	−	0.521177i
$419$	−15.7548	+	15.7548i	−0.769673	+	0.769673i	−0.978049	−	0.208376i	$-0.933182\pi$
$419$	−15.7548	+	15.7548i	−0.769673	+	0.769673i	0.208376	+	0.978049i	$0.433182\pi$
$420$	0.154561	+	2.35105i	0.00754178	+	0.114719i
$421$	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	$0.648182\pi$
$422$	4.58386	−	8.64913i	0.223139	−	0.421033i
$423$	−1.69954	−	1.30348i	−0.0826344	−	0.0633776i
$424$	−28.1065	+	20.5950i	−1.36497	+	1.00018i
$425$	−28.3154	−	16.3479i	−1.37350	−	0.792989i
$426$	−19.2276	−	11.8595i	−0.931579	−	0.574594i
$427$	12.2387	+	36.8981i	0.592271	+	1.78562i
$428$	−10.8065	−	9.34283i	−0.522350	−	0.451603i
$429$	7.68067	−	22.6350i	0.370826	−	1.09283i
$430$	1.47551	+	0.338552i	0.0711555	+	0.0163264i
$431$	22.6516	−	13.0779i	1.09109	−	0.629940i	0.157223	−	0.987563i	$-0.449746\pi$
$431$	22.6516	−	13.0779i	1.09109	−	0.629940i	0.933866	+	0.357623i	$0.116413\pi$
$432$	4.34938	+	20.3244i	0.209259	+	0.977860i
$433$		−	7.93525i		−	0.381344i	−0.981654	−	0.190672i	$-0.938933\pi$
$433$		−	7.93525i		−	0.381344i	0.981654	−	0.190672i	$-0.0610667\pi$
$434$	12.7498	+	10.5373i	0.612011	+	0.505807i
$435$	0.104940	+	0.527253i	0.00503148	+	0.0252798i
$436$	10.2564	−	3.56256i	0.491193	−	0.170616i
$437$	4.91052	−	18.3263i	0.234902	−	0.876666i
$438$	−0.409042	+	14.0625i	−0.0195448	+	0.671930i
$439$	14.5020	−	25.1183i	0.692145	−	1.19883i	−0.278989	−	0.960294i	$-0.589999\pi$
$439$	14.5020	−	25.1183i	0.692145	−	1.19883i	0.971134	−	0.238535i	$-0.0766673\pi$
$440$	2.68614	−	3.34470i	0.128057	−	0.159453i
$441$	0.288337	−	20.9980i	0.0137303	−	0.999906i
$442$	−0.794607	−	21.9069i	−0.0377956	−	1.04201i
$443$	−6.88323	−	25.6886i	−0.327032	−	1.22050i	−0.912253	−	0.409627i	$-0.865659\pi$
$443$	−6.88323	−	25.6886i	−0.327032	−	1.22050i	0.585221	−	0.810874i	$-0.301008\pi$
$444$	14.0995	−	0.101190i	0.669131	−	0.00480228i
$445$	−0.281768	−	0.0754995i	−0.0133571	−	0.00357902i
$446$	−0.961656	−	3.13032i	−0.0455357	−	0.148225i
$447$	10.0385	−	15.0274i	0.474804	−	0.710771i
$448$	20.3649	−	5.76806i	0.962151	−	0.272515i
$449$		−	15.4797i		−	0.730532i	−0.930903	−	0.365266i	$-0.880978\pi$
$449$		−	15.4797i		−	0.730532i	0.930903	−	0.365266i	$-0.119022\pi$
$450$	13.3404	+	16.1312i	0.628872	+	0.760434i
$451$	−3.13720	+	11.7082i	−0.147725	+	0.551317i
$452$	12.6358	+	18.6247i	0.594338	+	0.876033i
$453$	−38.1921	−	12.9596i	−1.79442	−	0.608895i
$454$	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	$-0.244872\pi$
$457$	10.1582	+	5.86483i	0.475180	+	0.274345i	−0.243226	+	0.969970i	$0.578206\pi$
$458$	10.9181	+	17.4202i	0.510168	+	0.813993i
$459$	−30.8878	−	15.2190i	−1.44172	−	0.710361i
$460$	−0.735994	−	2.11889i	−0.0343159	−	0.0987935i
$461$	−0.758145	+	0.758145i	−0.0353103	+	0.0353103i	−0.724542	−	0.689231i	$-0.757948\pi$
$461$	−0.758145	+	0.758145i	−0.0353103	+	0.0353103i	0.689231	+	0.724542i	$0.257948\pi$
$462$	−26.2299	+	27.8189i	−1.22033	+	1.29425i
$463$	−1.73370			−0.0805719			−0.0402859	−	0.999188i	$-0.512827\pi$
$463$	−1.73370			−0.0805719			−0.0402859	+	0.999188i	$0.512827\pi$
$464$	4.43527	−	1.91098i	0.205902	−	0.0887150i
$465$	−1.96417	−	0.128513i	−0.0910863	−	0.00595964i
$466$	−1.24838	+	5.44081i	−0.0578300	+	0.252041i
$467$	−7.44883	−	27.7994i	−0.344691	−	1.28640i	−0.892973	−	0.450110i	$-0.851385\pi$
$467$	−7.44883	−	27.7994i	−0.344691	−	1.28640i	0.548282	−	0.836293i	$-0.315282\pi$
$468$	−4.41428	+	13.3224i	−0.204050	+	0.615828i
$469$	3.80211	−	18.4408i	0.175565	−	0.851519i
$470$	−0.00940861	−	0.259391i	−0.000433987	−	0.0119648i
$471$	19.8236	−	9.77876i	0.913425	−	0.450581i
$472$	−2.18617	−	2.98353i	−0.100627	−	0.137328i
$473$	12.2833	+	21.2753i	0.564787	+	0.978241i
$474$	−9.46332	+	5.10269i	−0.434665	+	0.234374i
$475$	−15.1723	+	15.1723i	−0.696155	+	0.696155i
$476$	−13.4163	+	32.3974i	−0.614935	+	1.48493i
$477$	−14.1354	+	34.1480i	−0.647216	+	1.56353i
$478$	3.91570	+	12.7461i	0.179100	+	0.582994i
$479$	5.25251	+	9.09761i	0.239993	+	0.415681i	0.960712	−	0.277547i	$-0.0895214\pi$
$479$	5.25251	+	9.09761i	0.239993	+	0.415681i	−0.720719	+	0.693228i	$0.756188\pi$
$480$	−1.56306	+	1.97514i	−0.0713435	+	0.0901526i
$481$	8.24528	+	4.76041i	0.375952	+	0.217056i
$482$	4.68579	−	5.03851i	0.213432	−	0.229498i
$483$	5.04171	+	19.3462i	0.229406	+	0.880284i
$484$	47.4892	−	3.44959i	2.15860	−	0.156800i
$485$	−0.740692	−	2.76430i	−0.0336331	−	0.125520i
$486$	15.1360	+	16.0282i	0.686582	+	0.727053i
$487$	−1.31361	+	0.758412i	−0.0595252	+	0.0343669i	−0.529467	−	0.848330i	$-0.677608\pi$
$487$	−1.31361	+	0.758412i	−0.0595252	+	0.0343669i	0.469942	+	0.882697i	$0.344275\pi$
$488$	−16.7497	+	38.0341i	−0.758224	+	1.72172i
$489$	2.03913	−	3.05252i	0.0922124	−	0.138040i
$490$	1.98396	−	1.59386i	0.0896264	−	0.0720035i
$491$	−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	$0.497273\pi$
$492$	1.79265	−	6.88761i	0.0808190	−	0.310518i
$493$	−2.07077	+	7.72824i	−0.0932630	+	0.348062i
$494$	−14.0217	−	3.21725i	−0.630867	−	0.144751i
$495$	0.592864	−	4.51123i	0.0266473	−	0.202765i
$496$	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
$499$	2.39167	+	8.92584i	0.107066	+	0.399575i	0.998571	−	0.0534345i	$-0.0170168\pi$
$499$	2.39167	+	8.92584i	0.107066	+	0.399575i	−0.891505	+	0.453010i	$0.850350\pi$
$500$	−0.961021	+	5.01627i	−0.0429782	+	0.224334i
$501$	10.0166	−	8.78639i	0.447511	−	0.392547i
$502$	−10.9308	−	5.79309i	−0.487864	−	0.258558i
$503$			2.20977i			0.0985286i	0.998786	+	0.0492643i	$0.0156877\pi$
$503$			2.20977i			0.0985286i	−0.998786	+	0.0492643i	$0.984312\pi$
$504$	15.2835	−	16.4443i	0.680783	−	0.732485i
$505$		−	3.23374i		−	0.143899i
$506$	17.0455	−	32.1625i	0.757765	−	1.42980i
$507$	9.80287	−	8.59887i	0.435361	−	0.381889i
$508$	21.6773	−	14.7068i	0.961774	−	0.652508i
$509$	5.53502	+	20.6570i	0.245336	+	0.915605i	0.973214	+	0.229899i	$0.0738396\pi$
$509$	5.53502	+	20.6570i	0.245336	+	0.915605i	−0.727879	+	0.685706i	$0.759494\pi$
$510$	−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
$513$	−14.8937	+	16.9947i	−0.657571	+	0.750335i
$514$	3.78918	−	16.5144i	0.167133	−	0.728418i
$515$	−0.281655	+	1.05115i	−0.0124112	+	0.0463192i
$516$	−7.30173	−	12.4399i	−0.321441	−	0.547637i
$517$	2.97842	−	2.97842i	0.130991	−	0.130991i
$518$	−8.82813	−	12.4098i	−0.387886	−	0.545256i
$519$	13.2789	−	19.8783i	0.582881	−	0.872559i
$520$	−1.58536	+	0.615937i	−0.0695225	+	0.0270106i
$521$	17.1413	−	9.89655i	0.750975	−	0.433576i	−0.0750709	−	0.997178i	$-0.523918\pi$
$521$	17.1413	−	9.89655i	0.750975	−	0.433576i	0.826046	+	0.563602i	$0.190585\pi$
$522$	2.96800	−	4.17491i	0.129906	−	0.182731i
$523$	8.49076	+	31.6880i	0.371275	+	1.38562i	0.858711	+	0.512459i	$0.171265\pi$
$523$	8.49076	+	31.6880i	0.371275	+	1.38562i	−0.487436	+	0.873159i	$0.662068\pi$
$524$	19.1029	+	16.5156i	0.834515	+	0.721487i
$525$	6.00170	−	21.7989i	0.261936	−	0.951383i
$526$	4.91309	+	4.56915i	0.214221	+	0.199224i
$527$	−25.3699	−	14.6473i	−1.10513	−	0.638048i
$528$	−40.7450	+	3.25382i	−1.77320	+	0.141604i
$529$	1.98344	+	3.43542i	0.0862365	+	0.149366i
$530$	−4.28131	+	1.31525i	−0.185968	+	0.0571308i
$531$	−3.62483	−	1.50048i	−0.157304	−	0.0651154i
$532$	18.2578	+	14.0073i	0.791578	+	0.607295i
$533$	3.39819	−	3.39819i	0.147192	−	0.147192i
$534$	1.31917	+	2.44650i	0.0570862	+	0.105870i
$535$	−0.918091	−	1.59018i	−0.0396925	−	0.0687495i
$536$	16.2365	−	11.8972i	0.701308	−	0.513881i
$537$	4.41213	−	2.17645i	0.190397	−	0.0939207i
$538$	5.83917	−	0.211798i	0.251744	−	0.00913126i
$539$	40.8658	+	5.96155i	1.76021	+	0.256782i
$540$	−0.329087	+	2.65124i	−0.0141617	+	0.114091i
$541$	−10.2102	−	38.1048i	−0.438969	−	1.63825i	−0.731386	−	0.681963i	$-0.761126\pi$
$541$	−10.2102	−	38.1048i	−0.438969	−	1.63825i	0.292418	−	0.956291i	$-0.405540\pi$
$542$	17.1830	+	3.94259i	0.738072	+	0.169349i
$543$	−31.4145	−	2.05540i	−1.34813	−	0.0882058i
$544$	−33.8667	+	16.0714i	−1.45202	+	0.689054i
$545$	1.39559			0.0597807
$546$	14.5210	−	4.35209i	0.621443	−	0.186252i
$547$	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	$-0.00504485\pi$
$548$	11.1010	+	5.37729i	0.474213	+	0.229707i
$549$	5.76359	+	43.7015i	0.245984	+	1.86513i
$550$	−34.8815	+	21.8619i	−1.48735	+	0.932193i
$551$	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
$555$	1.71623	+	0.582364i	0.0728501	+	0.0247200i
$556$	3.19933	−	16.6996i	0.135682	−	0.708222i
$557$	−6.20580	+	23.1604i	−0.262948	+	0.981336i	0.700546	+	0.713607i	$0.252940\pi$
$557$	−6.20580	+	23.1604i	−0.262948	+	0.981336i	−0.963494	+	0.267729i	$0.913727\pi$
$558$	11.9527	+	14.4532i	0.505998	+	0.611854i
$559$		−	9.74008i		−	0.411962i
$560$	2.71599	+	0.158536i	0.114772	+	0.00669936i
$561$	37.6149	−	56.3086i	1.58810	−	2.37735i
$562$	17.8426	−	5.48136i	0.752644	−	0.231217i
$563$	−14.9452	−	4.00455i	−0.629865	−	0.168772i	−0.0702563	−	0.997529i	$-0.522382\pi$
$563$	−14.9452	−	4.00455i	−0.629865	−	0.168772i	−0.559608	+	0.828757i	$0.689048\pi$
$564$	−1.73621	+	1.76132i	−0.0731078	+	0.0741648i
$565$	0.748742	+	2.79434i	0.0314998	+	0.117559i
$566$	−32.2194	+	1.16866i	−1.35428	+	0.0491224i
$567$	4.79766	−	23.3234i	0.201483	−	0.979492i
$568$	−16.3340	+	20.3387i	−0.685361	+	0.853392i
$569$	−8.95775	+	15.5153i	−0.375528	+	0.650434i	−0.990406	−	0.138188i	$-0.955872\pi$
$569$	−8.95775	+	15.5153i	−0.375528	+	0.650434i	0.614878	+	0.788622i	$0.289205\pi$
$570$	−2.73732	−	0.0796218i	−0.114654	−	0.00333499i
$571$	−2.25312	+	8.40874i	−0.0942900	+	0.351895i	−0.996911	−	0.0785415i	$-0.974974\pi$
$571$	−2.25312	+	8.40874i	−0.0942900	+	0.351895i	0.902621	+	0.430436i	$0.141640\pi$
$572$	−24.8397	−	12.0322i	−1.03860	−	0.503093i
$573$	3.30854	+	16.6232i	0.138216	+	0.694445i
$574$	−7.20391	+	2.68303i	−0.300685	+	0.111988i
$575$			21.5252i			0.897661i
$576$	23.9095	−	2.08216i	0.996230	−	0.0867565i
$577$	23.5254	−	13.5824i	0.979374	−	0.565442i	0.0772926	−	0.997008i	$-0.475372\pi$
$577$	23.5254	−	13.5824i	0.979374	−	0.565442i	0.902081	+	0.431567i	$0.142039\pi$
$578$	8.51199	−	37.0978i	0.354052	−	1.54307i
$579$	−10.4624	+	30.8329i	−0.434803	+	1.28137i
$580$	0.619129	−	0.0449732i	0.0257079	−	0.00186741i
$581$	18.7568	+	16.6823i	0.778163	+	0.692099i
$582$	−14.3150	+	23.2087i	−0.593377	+	0.962032i
$583$	−62.9437	−	36.3406i	−2.60686	−	1.50507i
$584$	16.0550	+	2.47627i	0.664359	+	0.102469i
$585$	−1.09786	+	1.43144i	−0.0453910	+	0.0591828i
$586$	3.77967	+	2.00315i	0.156137	+	0.0827494i
$587$	−21.5392	−	21.5392i	−0.889018	−	0.889018i	0.105411	−	0.994429i	$-0.466384\pi$
$587$	−21.5392	−	21.5392i	−0.889018	−	0.889018i	−0.994429	+	0.105411i	$0.966384\pi$
$588$	−24.0192	−	3.32809i	−0.990537	−	0.137248i
$589$	−13.5941	+	13.5941i	−0.560134	+	0.560134i
$590$	−0.139614	−	0.454464i	−0.00574784	−	0.0187100i
$591$	−11.7247	−	0.767127i	−0.482288	−	0.0315554i
$592$	1.89691	−	16.1702i	0.0779624	−	0.664591i
$593$	17.4428	−	30.2118i	0.716290	−	1.24065i	−0.246170	−	0.969227i	$-0.579172\pi$
$593$	17.4428	−	30.2118i	0.716290	−	1.24065i	0.962460	−	0.271424i	$-0.0874947\pi$
$594$	−35.1422	+	25.3892i	−1.44190	+	1.04173i
$595$	−2.99539	+	3.36787i	−0.122799	+	0.138069i
$596$	−15.7859	−	13.6478i	−0.646615	−	0.559037i
$597$	−3.20245	+	9.43766i	−0.131067	+	0.386258i
$598$	−12.2286	+	7.66421i	−0.500063	+	0.313413i
$599$	−20.2847	−	35.1341i	−0.828810	−	1.43554i	−0.898972	−	0.438006i	$-0.855685\pi$
$599$	−20.2847	−	35.1341i	−0.828810	−	1.43554i	0.0701622	−	0.997536i	$-0.477648\pi$
$600$	20.3883	−	12.9831i	0.832350	−	0.530031i
$601$	−4.61131			−0.188099			−0.0940496	−	0.995568i	$-0.529981\pi$
$601$	−4.61131			−0.188099			−0.0940496	+	0.995568i	$0.529981\pi$
$602$	−6.47899	+	14.1693i	−0.264064	+	0.577496i
$603$	8.16568	−	19.7265i	0.332532	−	0.803324i
$604$	−20.3020	+	41.9120i	−0.826076	+	1.70537i
$605$	5.91166	+	1.58402i	0.240343	+	0.0643998i
$606$	−22.4118	+	21.1448i	−0.910416	+	0.858949i
$607$	30.6074	+	17.6712i	1.24232	+	0.717252i	0.969565	−	0.244832i	$-0.0787330\pi$
$607$	30.6074	+	17.6712i	1.24232	+	0.717252i	0.272752	+	0.962084i	$0.412066\pi$
$608$	4.43528	+	24.1978i	0.179874	+	0.981350i
$609$	−5.53268	−	0.0379846i	−0.224196	−	0.00153921i
$610$	−3.63786	+	3.91170i	−0.147293	+	0.158380i
$611$	−1.61310	+	0.432230i	−0.0652592	+	0.0174861i
$612$	−21.8481	+	33.2198i	−0.883157	+	1.34283i
$613$	5.54306	−	20.6870i	0.223882	−	0.835539i	−0.758967	−	0.651129i	$-0.774296\pi$
$613$	5.54306	−	20.6870i	0.223882	−	0.835539i	0.982849	−	0.184410i	$-0.0590376\pi$
$614$	30.7476	+	16.2956i	1.24087	+	0.657637i
$615$	0.508153	−	0.760693i	0.0204907	−	0.0306741i
$616$	28.1315	+	34.0268i	1.13345	+	1.37098i
$617$	−46.9110			−1.88856			−0.944282	−	0.329137i	$-0.893242\pi$
$617$	−46.9110			−1.88856			−0.944282	+	0.329137i	$0.893242\pi$
$618$	9.12679	−	4.92123i	0.367133	−	0.197961i
$619$	8.61843	+	2.30930i	0.346404	+	0.0928186i	0.427826	−	0.903861i	$-0.359280\pi$
$619$	8.61843	+	2.30930i	0.346404	+	0.0928186i	−0.0814223	+	0.996680i	$0.525946\pi$
$620$	−0.427662	+	2.23228i	−0.0171753	+	0.0896506i
$621$	1.49041	+	22.6202i	0.0598080	+	0.907717i
$622$	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
$626$	8.68218	−	37.8395i	0.347010	−	1.51237i
$627$	−29.3050	−	33.4082i	−1.17033	−	1.33419i
$628$	−8.37486	−	24.1108i	−0.334193	−	0.962125i
$629$	19.0725	+	19.0725i	0.760472	+	0.760472i
$630$	2.54928	−	1.35208i	0.101566	−	0.0538683i
$631$			31.7177i			1.26266i	0.775514	+	0.631330i	$0.217491\pi$
$631$			31.7177i			1.26266i	−0.775514	+	0.631330i	$0.782509\pi$
$632$	4.49588	+	11.5719i	0.178837	+	0.460307i
$633$	−11.9631	−	0.782729i	−0.475491	−	0.0311107i
$634$	7.01153	−	4.39446i	0.278463	−	0.174526i
$635$	3.25233	−	0.871460i	0.129065	−	0.0345829i
$636$	37.1102	+	21.0719i	1.47152	+	0.835557i
$637$	−12.8498	−	10.1481i	−0.509128	−	0.402082i
$638$	7.37665	+	6.86025i	0.292044	+	0.271600i
$639$	−3.60512	+	27.4322i	−0.142616	+	1.08520i
$640$	2.04006	+	2.07299i	0.0806404	+	0.0819422i
$641$	6.80777	−	3.93047i	0.268891	−	0.155244i	−0.359493	−	0.933148i	$-0.617050\pi$
$641$	6.80777	−	3.93047i	0.268891	−	0.155244i	0.628383	+	0.777904i	$0.283717\pi$
$642$	−5.01769	+	16.7608i	−0.198032	+	0.661497i
$643$	9.14146	+	9.14146i	0.360504	+	0.360504i	0.863998	−	0.503495i	$-0.167953\pi$
$643$	9.14146	+	9.14146i	0.360504	+	0.360504i	−0.503495	+	0.863998i	$0.667953\pi$
$644$	22.8875	−	3.01511i	0.901893	−	0.118812i
$645$	−0.361922	−	1.81842i	−0.0142507	−	0.0716001i
$646$	−36.0112	−	19.0852i	−1.41684	−	0.750897i
$647$	−10.2346	+	5.90896i	−0.402364	+	0.232305i	−0.687504	−	0.726181i	$-0.741293\pi$
$647$	−10.2346	+	5.90896i	−0.402364	+	0.232305i	0.285139	+	0.958486i	$0.407960\pi$
$648$	20.5266	−	15.0552i	0.806360	−	0.591425i
$649$	3.85758	−	6.68152i	0.151423	−	0.262272i
$650$	16.3107	−	0.591621i	0.639758	−	0.0232053i
$651$	5.37739	−	19.5313i	0.210757	−	0.765494i
$652$	−3.20660	−	2.77230i	−0.125580	−	0.108571i
$653$	−18.2397	+	4.88732i	−0.713776	+	0.191256i	−0.597393	−	0.801949i	$-0.703797\pi$
$653$	−18.2397	+	4.88732i	−0.713776	+	0.191256i	−0.116383	+	0.993204i	$0.537130\pi$
$654$	−9.12553	−	9.67231i	−0.356837	−	0.378217i
$655$	1.62294	+	2.81101i	0.0634134	+	0.109835i
$656$	−7.63619	−	3.03738i	−0.298143	−	0.118590i
$657$	15.9171	−	6.59736i	0.620986	−	0.257388i
$658$	2.63415	+	0.444238i	0.102690	+	0.0173182i
$659$	−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	$0.754141\pi$
$660$	−5.08452	−	1.32336i	−0.197915	−	0.0515116i
$661$	−22.7033	−	6.08332i	−0.883055	−	0.236614i	−0.211330	−	0.977415i	$-0.567780\pi$
$661$	−22.7033	−	6.08332i	−0.883055	−	0.236614i	−0.671725	+	0.740801i	$0.734446\pi$
$662$	1.04516	−	0.655052i	0.0406213	−	0.0254593i
$663$	−24.0779	+	11.8773i	−0.935108	+	0.461277i
$664$	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
$667$	5.08786	−	1.36329i	0.197003	−	0.0527867i
$668$	−8.63782	−	12.7318i	−0.334207	−	0.492610i
$669$	−3.01508	+	2.64477i	−0.116570	+	0.102253i
$670$	2.47321	−	0.759787i	0.0955485	−	0.0293532i
$671$	−86.6870			−3.34652
$672$	−16.6606	−	19.8601i	−0.642697	−	0.766120i
$673$	35.4810			1.36769			0.683845	−	0.729627i	$-0.260306\pi$
$673$	35.4810			1.36769			0.683845	+	0.729627i	$0.260306\pi$
$674$	−13.1348	+	4.03509i	−0.505932	+	0.155426i
$675$	11.3312	−	22.9973i	0.436139	−	0.885168i
$676$	−8.45348	−	12.4601i	−0.325134	−	0.479235i
$677$	4.83474	−	1.29546i	0.185814	−	0.0497887i	−0.164712	−	0.986342i	$-0.552669\pi$
$677$	4.83474	−	1.29546i	0.185814	−	0.0497887i	0.350526	+	0.936553i	$0.386003\pi$
$678$	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
$681$	−6.67759	−	13.5369i	−0.255886	−	0.518735i
$682$	−31.2530	+	19.5877i	−1.19674	+	0.750053i
$683$	−8.84813	−	2.37085i	−0.338564	−	0.0907181i	0.0855312	−	0.996335i	$-0.472741\pi$
$683$	−8.84813	−	2.37085i	−0.338564	−	0.0907181i	−0.424096	+	0.905617i	$0.639408\pi$
$684$	17.3470	+	19.4919i	0.663280	+	0.745293i
$685$	1.12110	+	1.12110i	0.0428352	+	0.0428352i
$686$	11.9427	+	23.3104i	0.455973	+	0.889994i
$687$	13.9865	−	20.9375i	0.533619	−	0.798815i
$688$	−15.2966	+	6.59069i	−0.583177	+	0.251268i
$689$	14.4082	+	24.9557i	0.548908	+	0.950736i
$690$	−1.99821	+	1.88525i	−0.0760707	+	0.0717704i
$691$	16.3324	−	4.37626i	0.621315	−	0.166481i	0.0655894	−	0.997847i	$-0.479107\pi$
$691$	16.3324	−	4.37626i	0.621315	−	0.166481i	0.555725	+	0.831366i	$0.312441\pi$
$692$	−20.8816	−	18.0534i	−0.793800	−	0.686288i
$693$	44.2401	+	15.3513i	1.68054	+	0.583149i
$694$	−35.8828	+	1.30154i	−1.36209	+	0.0494058i
$695$	1.09278	−	1.89275i	0.0414514	−	0.0717960i
$696$	−4.36007	−	3.99687i	−0.165268	−	0.151501i
$697$	11.7908	−	6.80740i	0.446607	−	0.257849i
$698$	−37.9820	−	20.1297i	−1.43764	−	0.761919i
$699$	6.70524	−	1.33455i	0.253616	−	0.0504775i
$700$	−24.1213	−	9.98904i	−0.911699	−	0.377550i
$701$	−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	$-0.518284\pi$
$702$	17.0995	−	1.75107i	0.645378	−	0.0660900i
$703$	15.3296	−	8.85053i	0.578166	−	0.333804i
$704$	−2.08845	+	47.1519i	−0.0787113	+	1.77710i
$705$	−0.285096	+	0.140635i	−0.0107374	+	0.00529660i
$706$	−13.2854	−	12.3554i	−0.500002	−	0.465000i
$707$	32.5954	+	6.72047i	1.22587	+	0.252749i
$708$	−2.23680	+	3.93927i	−0.0840641	+	0.148047i
$709$	14.8418	−	3.97685i	0.557395	−	0.149354i	0.0308858	−	0.999523i	$-0.490167\pi$
$709$	14.8418	−	3.97685i	0.557395	−	0.149354i	0.526509	+	0.850169i	$0.323501\pi$
$710$	−2.84108	+	1.78064i	−0.106624	+	0.0668262i
$711$	10.4485	+	8.01358i	0.391848	+	0.300533i
$712$	2.99163	−	1.16230i	0.112116	−	0.0435589i
$713$			19.2861i			0.722269i
$714$	42.9277	−	1.26204i	1.60653	−	0.0472305i
$715$	−2.50858	−	2.50858i	−0.0938157	−	0.0938157i
$716$	−1.86399	−	5.36631i	−0.0696604	−	0.200548i
$717$	12.2769	−	10.7690i	0.458489	−	0.402177i
$718$	7.34805	−	32.0250i	0.274227	−	1.19516i
$719$	15.1260	−	26.1990i	0.564105	−	0.977058i	−0.433028	−	0.901381i	$-0.642555\pi$
$719$	15.1260	−	26.1990i	0.564105	−	0.977058i	0.997132	−	0.0756772i	$-0.0241119\pi$
$720$	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
$723$	−7.98011	−	2.70787i	−0.296784	−	0.100707i
$724$	−6.83993	+	35.7026i	−0.254204	+	1.32688i
$725$	−5.75402	−	1.54179i	−0.213699	−	0.0572605i
$726$	−27.6770	−	51.3291i	−1.02719	−	1.90500i
$727$	47.7498			1.77094			0.885470	−	0.464696i	$-0.153836\pi$
$727$	47.7498			1.77094			0.885470	+	0.464696i	$0.153836\pi$
$728$	−2.91377	−	17.2601i	−0.107991	−	0.639702i
$729$	10.3153	−	24.9518i	0.382049	−	0.924142i
$730$	1.84497	+	0.977794i	0.0682852	+	0.0361898i
$731$	7.14180	−	26.6536i	0.264149	−	0.985818i
$732$	50.8978	−	0.365288i	1.88124	−	0.0135014i
$733$	−44.8500	+	12.0175i	−1.65657	+	0.443877i	−0.961442	−	0.275006i	$-0.911320\pi$
$733$	−44.8500	+	12.0175i	−1.65657	+	0.443877i	−0.695130	+	0.718884i	$0.744653\pi$
$734$	23.8381	−	25.6325i	0.879881	−	0.946113i
$735$	−2.77607	−	1.41712i	−0.102397	−	0.0522712i
$736$	20.3110	+	14.0186i	0.748674	+	0.516734i
$737$	36.3611	+	20.9931i	1.33938	+	0.773290i
$738$	−8.59478	+	1.45222i	−0.316378	+	0.0534571i
$739$	8.76344	+	2.34816i	0.322368	+	0.0863783i	0.416374	−	0.909193i	$-0.363301\pi$
$739$	8.76344	+	2.34816i	0.322368	+	0.0863783i	−0.0940060	+	0.995572i	$0.529967\pi$
$740$	0.912308	−	1.88339i	0.0335371	−	0.0692349i
$741$	3.43933	+	17.2803i	0.126347	+	0.634809i
$742$	−4.35985	−	45.8881i	−0.160055	−	1.68461i
$743$	46.3396			1.70003			0.850017	−	0.526756i	$-0.176592\pi$
$743$	46.3396			1.70003			0.850017	+	0.526756i	$0.176592\pi$
$744$	18.2675	−	11.6325i	0.669718	−	0.426469i
$745$	−1.34113	−	2.32291i	−0.0491352	−	0.0851047i
$746$	−21.0815	+	13.2128i	−0.771848	+	0.483754i
$747$	17.3324	+	22.5774i	0.634160	+	0.826062i
$748$	−59.1508	−	51.1394i	−2.16277	−	1.86984i
$749$	17.9367	−	5.94939i	0.655392	−	0.217386i
$750$	6.08675	−	1.44265i	0.222257	−	0.0526781i
$751$	−2.89758	+	5.01876i	−0.105734	+	0.183137i	−0.914038	−	0.405629i	$-0.867053\pi$
$751$	−2.89758	+	5.01876i	−0.105734	+	0.183137i	0.808304	+	0.588766i	$0.200386\pi$
$752$	1.77032	+	2.24087i	0.0645571	+	0.0817162i
$753$	−0.989213	+	15.1190i	−0.0360489	+	0.550967i
$754$	−1.17287	−	3.81786i	−0.0427135	−	0.139038i
$755$	−4.23273	+	4.23273i	−0.154045	+	0.154045i
$756$	−26.0400	−	8.82704i	−0.947067	−	0.321036i
$757$	−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	$-0.731483\pi$
$758$	13.9480	+	7.39213i	0.506612	+	0.268494i
$759$	−44.4859	−	2.91065i	−1.61474	−	0.105650i
$760$	−0.482017	+	3.12517i	−0.0174846	+	0.113362i
$761$	18.6665	+	10.7771i	0.676661	+	0.390670i	0.798596	−	0.601868i	$-0.205577\pi$
$761$	18.6665	+	10.7771i	0.676661	+	0.390670i	−0.121935	+	0.992538i	$0.538910\pi$
$762$	−27.3062	−	16.8423i	−0.989198	−	0.610134i
$763$	−2.90037	+	14.0673i	−0.105001	+	0.509270i
$764$	19.5199	−	1.41792i	0.706206	−	0.0512984i
$765$	−4.05387	+	3.11212i	−0.146568	+	0.112519i
$766$	0.948617	−	4.13436i	0.0342749	−	0.149380i
$767$	−2.64906	+	1.52944i	−0.0956521	+	0.0552247i
$768$	1.02753	−	27.6938i	0.0370777	−	0.999312i
$769$		−	8.51995i		−	0.307237i	−0.988130	−	0.153619i	$-0.950907\pi$
$769$		−	8.51995i		−	0.307237i	0.988130	−	0.153619i	$-0.0490927\pi$
$770$	1.98065	+	5.31801i	0.0713775	+	0.191648i
$771$	−20.3523	+	4.05074i	−0.732969	+	0.145884i
$772$	33.8359	+	16.3900i	1.21778	+	0.589889i
$773$	9.67007	−	36.0892i	0.347808	−	1.29804i	−0.541489	−	0.840708i	$-0.682139\pi$
$773$	9.67007	−	36.0892i	0.347808	−	1.29804i	0.889297	−	0.457330i	$-0.151194\pi$
$774$	−10.2362	+	14.3986i	−0.367933	+	0.517549i
$775$	10.9056	−	18.8891i	0.391741	−	0.678515i
$776$	24.5499	+	19.7161i	0.881289	+	0.707765i
$777$	−9.43684	+	16.0890i	−0.338545	+	0.577189i
$778$	29.5506	−	1.07186i	1.05944	−	0.0384280i
$779$	−2.31251	−	8.63041i	−0.0828543	−	0.309216i
$780$	1.48347	+	1.46233i	0.0531168	+	0.0523598i
$781$	−52.5576	−	14.0828i	−1.88066	−	0.503921i
$782$	−39.0829	+	12.0065i	−1.39760	+	0.429353i
$783$	−6.15349	−	1.22181i	−0.219908	−	0.0436639i
$784$	−7.24248	+	27.0471i	−0.258660	+	0.965968i
$785$		−	3.28076i		−	0.117095i
$786$	8.86991	−	29.6286i	0.316379	−	1.05682i
$787$	−6.30906	+	23.5457i	−0.224894	+	0.839315i	0.757553	+	0.652773i	$0.226395\pi$
$787$	−6.30906	+	23.5457i	−0.224894	+	0.839315i	−0.982447	+	0.186542i	$0.940272\pi$
$788$	−2.55283	+	13.3251i	−0.0909408	+	0.474686i
$789$	2.64046	−	7.78148i	0.0940029	−	0.277028i
$790$	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
$794$	6.31763	−	3.95956i	0.224204	−	0.140519i
$795$	3.61723	+	4.12371i	0.128290	+	0.146253i
$796$	10.3569	+	5.01683i	0.367090	+	0.177817i
$797$	35.2425	−	35.2425i	1.24835	−	1.24835i	0.291905	−	0.956447i	$-0.405711\pi$
$797$	35.2425	−	35.2425i	1.24835	−	1.24835i	0.956447	−	0.291905i	$-0.0942891\pi$
$798$	6.49137	−	27.4261i	0.229792	−	0.970875i
$799$	−4.73116			−0.167376
$800$	−11.9659	−	25.2153i	−0.423057	−	0.891495i
$801$	2.07171	−	2.70118i	0.0732003	−	0.0954417i
$802$	9.22401	+	2.11642i	0.325711	+	0.0747335i
$803$	8.77001	+	32.7301i	0.309487	+	1.15502i
$804$	−21.4377	−	12.1727i	−0.756048	−	0.429300i
$805$	2.90618	+	0.599191i	0.102429	+	0.0211187i
$806$	14.6140	−	0.530079i	0.514757	−	0.0186712i
$807$	−3.16584	−	6.41783i	−0.111443	−	0.225918i
$808$	21.0291	+	28.6990i	0.739800	+	1.00963i
$809$	−9.59893	−	16.6258i	−0.337480	−	0.584533i	0.646478	−	0.762933i	$-0.276241\pi$
$809$	−9.59893	−	16.6258i	−0.337480	−	0.584533i	−0.983958	+	0.178400i	$0.942908\pi$
$810$	3.12731	−	0.962299i	0.109882	−	0.0338117i
$811$	−13.4386	+	13.4386i	−0.471894	+	0.471894i	−0.902527	−	0.430633i	$-0.858290\pi$
$811$	−13.4386	+	13.4386i	−0.471894	+	0.471894i	0.430633	+	0.902527i	$0.358290\pi$
$812$	−0.833376	+	6.33415i	−0.0292458	+	0.222285i
$813$	−4.21474	−	21.1763i	−0.147817	−	0.742684i
$814$	32.4631	−	9.97287i	1.13783	−	0.349549i
$815$	−0.272425	−	0.471854i	−0.00954262	−	0.0165283i
$816$	34.9456	+	29.7770i	1.22334	+	1.04240i
$817$	−15.6826	−	9.05435i	−0.548665	−	0.316772i
$818$	33.5640	+	31.2144i	1.17354	+	1.09138i
$819$	−12.1470	−	14.0411i	−0.424450	−	0.490635i
$820$	−0.799089	−	0.690860i	−0.0279054	−	0.0241259i
$821$	1.58937	+	5.93160i	0.0554693	+	0.207014i	0.988099	−	0.153822i	$-0.0491581\pi$
$821$	1.58937	+	5.93160i	0.0554693	+	0.207014i	−0.932629	+	0.360836i	$0.882491\pi$
$822$	0.439240	−	15.1006i	0.0153202	−	0.526695i
$823$	−11.1673	+	6.44742i	−0.389266	+	0.224743i	−0.681842	−	0.731499i	$-0.738821\pi$
$823$	−11.1673	+	6.44742i	−0.389266	+	0.224743i	0.292576	+	0.956242i	$0.405488\pi$
$824$	−4.33600	−	11.1604i	−0.151052	−	0.388792i
$825$	41.9243	+	28.0060i	1.45962	+	0.975044i
$826$	4.87105	−	0.462800i	0.169486	−	0.0161029i
$827$	−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	$0.253781\pi$
$828$	26.1319	+	1.52151i	0.908147	+	0.0528762i
$829$	10.4688	−	39.0702i	0.363597	−	1.35696i	−0.505715	−	0.862700i	$-0.668771\pi$
$829$	10.4688	−	39.0702i	0.363597	−	1.35696i	0.869313	−	0.494263i	$-0.164562\pi$
$830$	−0.771393	+	3.36196i	−0.0267754	+	0.116695i
$831$	−19.5075	+	9.62282i	−0.676708	+	0.333812i
$832$	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
$835$	−0.511840	−	1.91021i	−0.0177129	−	0.0661056i
$836$	−42.4641	+	28.8095i	−1.46865	+	0.996396i
$837$	10.1525	−	20.6051i	0.350922	−	0.712216i
$838$	14.7553	−	27.8413i	0.509714	−	0.961762i
$839$		−	34.3619i		−	1.18631i	−0.805090	−	0.593153i	$-0.797883\pi$
$839$		−	34.3619i		−	1.18631i	0.805090	−	0.593153i	$-0.202117\pi$
$840$	−1.18533	−	3.11409i	−0.0408979	−	0.107446i
$841$		−	27.5423i		−	0.949734i
$842$	−16.1241	−	8.54547i	−0.555675	−	0.294496i
$843$	−15.0750	−	17.1857i	−0.519209	−	0.591908i
$844$	−2.60475	+	13.5961i	−0.0896592	+	0.467997i
$845$	−0.500916	−	1.86944i	−0.0172320	−	0.0643108i
$846$	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
$849$	17.4685	+	35.4123i	0.599516	+	1.21535i
$850$	45.0677	+	10.3407i	1.54581	+	0.354682i
$851$	4.59594	−	17.1523i	0.157547	−	0.587973i
$852$	30.9182	+	8.04714i	1.05924	+	0.275691i
$853$	11.0188	−	11.0188i	0.377277	−	0.377277i	−0.492842	−	0.870119i	$-0.664042\pi$
$853$	11.0188	−	11.0188i	0.377277	−	0.377277i	0.870119	+	0.492842i	$0.164042\pi$
$854$	−31.8688	−	44.7983i	−1.09053	−	1.53297i
$855$	1.28421	+	3.09834i	0.0439189	+	0.105961i
$856$	18.4889	+	8.14227i	0.631938	+	0.278297i
$857$	21.8476	−	12.6137i	0.746299	−	0.430876i	−0.0780562	−	0.996949i	$-0.524871\pi$
$857$	21.8476	−	12.6137i	0.746299	−	0.430876i	0.824355	+	0.566073i	$0.191538\pi$
$858$	−0.982843	+	33.7892i	−0.0335537	+	1.15354i
$859$	−9.19576	−	34.3191i	−0.313755	−	1.17095i	−0.925143	−	0.379619i	$-0.876055\pi$
$859$	−9.19576	−	34.3191i	−0.313755	−	1.17095i	0.611387	−	0.791331i	$-0.290612\pi$
$860$	−2.13529	+	0.155106i	−0.0728127	+	0.00528908i
$861$	6.61156	+	6.70297i	0.225321	+	0.228437i
$862$	−25.1905	+	27.0867i	−0.857992	+	0.922577i
$863$	43.1016	+	24.8847i	1.46720	+	0.847086i	0.999326	−	0.0367120i	$-0.0116884\pi$
$863$	43.1016	+	24.8847i	1.46720	+	0.847086i	0.467869	+	0.883798i	$0.345022\pi$
$864$	−14.3205	−	25.6695i	−0.487193	−	0.873294i
$865$	−1.77405	−	3.07275i	−0.0603195	−	0.104477i
$866$	3.29552	+	10.7274i	0.111986	+	0.364530i
$867$	−45.7192	+	9.09956i	−1.55271	+	0.309037i
$868$	−21.6121	−	8.94995i	−0.733564	−	0.303781i
$869$	−18.3108	+	18.3108i	−0.621151	+	0.621151i
$870$	−0.360832	−	0.669190i	−0.0122334	−	0.0226877i
$871$	−8.32325	−	14.4163i	−0.282023	−	0.488478i
$872$	−12.3857	+	9.07558i	−0.419433	+	0.307338i
$873$	33.1121	+	4.35157i	1.12067	+	0.147278i
$874$	0.972594	+	26.8139i	0.0328985	+	0.906995i
$875$	−5.04865	−	4.49027i	−0.170676	−	0.151799i
$876$	−5.28718	−	19.1804i	−0.178637	−	0.648044i
$877$	10.9931	+	41.0267i	0.371210	+	1.38537i	0.858804	+	0.512304i	$0.171208\pi$
$877$	10.9931	+	41.0267i	0.371210	+	1.38537i	−0.487595	+	0.873070i	$0.662126\pi$
$878$	−9.17309	+	39.9791i	−0.309577	+	1.34923i
$879$	0.342053	−	5.22789i	0.0115372	−	0.176332i
$880$	−2.24223	+	5.63713i	−0.0755855	+	0.190028i
$881$	−36.3081			−1.22325			−0.611625	−	0.791148i	$-0.709484\pi$
$881$	−36.3081			−1.22325			−0.611625	+	0.791148i	$0.709484\pi$
$882$	8.33070	+	28.5061i	0.280509	+	0.959851i
$883$	−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	$0.282825\pi$
$884$	10.1722	+	29.2851i	0.342127	+	0.984964i
$885$	−0.437734	+	0.383971i	−0.0147143	+	0.0129070i
$886$	19.9736	+	31.8687i	0.671028	+	1.07065i
$887$	−7.96269	−	4.59726i	−0.267361	−	0.154361i	0.360327	−	0.932826i	$-0.382665\pi$
$887$	−7.96269	−	4.59726i	−0.267361	−	0.154361i	−0.627688	+	0.778465i	$0.715999\pi$
$888$	−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
$891$	45.9962	+	26.5279i	1.54093	+	0.888717i
$892$	2.60005	+	3.83238i	0.0870560	+	0.128317i
$893$	−0.803599	+	2.99907i	−0.0268914	+	0.100360i
$894$	−7.32975	+	24.4839i	−0.245143	+	0.818864i
$895$		−	0.730195i		−	0.0244077i
$896$	−25.1350	+	16.2552i	−0.839702	+	0.543047i
$897$	14.6976	+	9.81819i	0.490739	+	0.327820i
$898$	6.42873	+	20.9264i	0.214530	+	0.698323i
$899$	−5.15547	−	1.38141i	−0.171945	−	0.0460724i
$900$	−24.7337	−	16.2669i	−0.824455	−	0.542230i
$901$	21.1293	+	78.8554i	0.703917	+	2.62706i
$902$	−0.621364	−	17.1307i	−0.0206892	−	0.570390i
$903$	19.0814	+	0.131003i	0.634990	+	0.00435952i
$904$	−24.8167	−	19.9303i	−0.825391	−	0.662873i
$905$	−2.33628	+	4.04656i	−0.0776606	+	0.134512i
$906$	57.0125	+	1.65835i	1.89411	+	0.0550950i
$907$	1.99039	−	7.42823i	0.0660898	−	0.246650i	−0.924976	−	0.380026i	$-0.875915\pi$
$907$	1.99039	−	7.42823i	0.0660898	−	0.246650i	0.991066	+	0.133376i	$0.0425817\pi$
$908$	−16.4645	+	5.71892i	−0.546392	+	0.189789i
$909$	34.8678	+	14.4334i	1.15649	+	0.478724i
$910$	0.374161	−	2.21862i	0.0124033	−	0.0735466i
$911$			33.8700i			1.12216i	0.827761	+	0.561081i	$0.189615\pi$
$911$			33.8700i			1.12216i	−0.827761	+	0.561081i	$0.810385\pi$
$912$	24.8112	−	17.0942i	0.821580	−	0.566047i
$913$	−48.4760	+	27.9876i	−1.60432	+	0.926255i
$914$	−16.1681	−	3.70973i	−0.534794	−	0.122707i
$915$	6.19545	+	2.10228i	0.204815	+	0.0694993i
$916$	−21.9943	−	19.0154i	−0.726713	−	0.628286i
$917$	−31.7072	+	10.5169i	−1.04706	+	0.347299i
$918$	48.0764	+	7.74621i	1.58676	+	0.255663i
$919$	−39.7129	−	22.9283i	−1.31001	−	0.756334i	−0.327911	−	0.944708i	$-0.606345\pi$
$919$	−39.7129	−	22.9283i	−1.31001	−	0.756334i	−0.982097	+	0.188375i	$0.939678\pi$
$920$	1.87493	+	2.55878i	0.0618148	+	0.0843604i
$921$	2.78260	−	42.5288i	0.0916896	−	1.40137i
$922$	0.710048	−	1.33976i	0.0233842	−	0.0441228i
$923$	15.2543	+	15.2543i	0.502103	+	0.502103i
$924$	23.9060	−	48.5006i	0.786449	−	1.59555i
$925$	−14.2004	+	14.2004i	−0.466905	+	0.466905i
$926$	2.34372	−	0.720007i	0.0770194	−	0.0236609i
$927$	−10.0769	−	7.72861i	−0.330969	−	0.253841i
$928$	−5.20223	+	4.42535i	−0.170772	+	0.145269i
$929$	−3.28103	+	5.68291i	−0.107647	+	0.186450i	−0.914817	−	0.403869i	$-0.867665\pi$
$929$	−3.28103	+	5.68291i	−0.107647	+	0.186450i	0.807170	+	0.590320i	$0.200998\pi$
$930$	2.70866	−	0.641990i	0.0888203	−	0.0210517i
$931$	−28.2847	+	11.2559i	−0.926993	+	0.368899i
$932$	−0.571939	−	7.87367i	−0.0187345	−	0.257911i
$933$	−30.5790	−	10.3763i	−1.00111	−	0.339704i
$934$	21.6149	+	34.4874i	0.707261	+	1.12846i
$935$	−5.02531	−	8.70409i	−0.164345	−	0.284654i
$936$	0.434687	−	19.8433i	0.0142082	−	0.648598i
$937$	−43.7826			−1.43032			−0.715158	−	0.698963i	$-0.753645\pi$
$937$	−43.7826			−1.43032			−0.715158	+	0.698963i	$0.753645\pi$
$938$	2.51858	+	26.5084i	0.0822345	+	0.865531i
$939$	−46.6334	+	9.28150i	−1.52182	+	0.302890i
$940$	0.120444	+	0.346752i	0.00392846	+	0.0113098i
$941$	10.6433	+	2.85186i	0.346961	+	0.0929680i	0.428091	−	0.903736i	$-0.359186\pi$
$941$	10.6433	+	2.85186i	0.346961	+	0.0929680i	−0.0811299	+	0.996704i	$0.525853\pi$
$942$	−22.7377	+	21.4523i	−0.740833	+	0.698953i
$943$	−7.76242	−	4.48163i	−0.252779	−	0.145942i
$944$	4.19445	+	3.12539i	0.136518	+	0.101723i
$945$	−2.78951	−	2.17003i	−0.0907429	−	0.0705912i
$946$	−25.4410	−	23.6600i	−0.827158	−	0.769253i
$947$	−28.3926	+	7.60778i	−0.922637	+	0.247220i	−0.688712	−	0.725035i	$-0.741824\pi$
$947$	−28.3926	+	7.60778i	−0.922637	+	0.247220i	−0.233925	+	0.972255i	$0.575157\pi$
$948$	10.6739	−	10.8282i	0.346673	−	0.351685i
$949$	3.47710	−	12.9767i	0.112871	−	0.421242i
$950$	14.2098	−	26.8120i	0.461027	−	0.869895i
$951$	−8.42722	−	5.62949i	−0.273271	−	0.182549i
$952$	4.68231	−	49.3685i	0.151754	−	1.60004i
$953$	2.94243			0.0953146			0.0476573	−	0.998864i	$-0.484824\pi$
$953$	2.94243			0.0953146			0.0476573	+	0.998864i	$0.484824\pi$
$954$	4.92740	−	52.0338i	0.159530	−	1.68466i
$955$	2.42992	+	0.651096i	0.0786304	+	0.0210690i
$956$	−10.5870	−	15.6048i	−0.342406	−	0.504695i
$957$	3.96446	−	11.6833i	0.128153	−	0.377668i
$958$	−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
$962$	−13.1235	−	3.01114i	−0.423118	−	0.0970831i
$963$	21.2439	−	2.80176i	0.684576	−	0.0902856i
$964$	−4.24203	+	8.75737i	−0.136627	+	0.282056i
$965$	3.41713	+	3.41713i	0.110001	+	0.110001i
$966$	−14.8502	−	24.0596i	−0.477797	−	0.774104i
$967$			25.0313i			0.804953i	0.915430	+	0.402476i	$0.131850\pi$
$967$			25.0313i			0.804953i	−0.915430	+	0.402476i	$0.868150\pi$
$968$	−62.7662	+	24.3857i	−2.01738	+	0.783785i
$969$	−3.25894	+	49.8092i	−0.104692	+	1.60010i
$970$	2.14933	+	3.42934i	0.0690107	+	0.110109i
$971$	28.3734	−	7.60263i	0.910545	−	0.243980i	0.227006	−	0.973893i	$-0.427106\pi$
$971$	28.3734	−	7.60263i	0.910545	−	0.243980i	0.683540	+	0.729914i	$0.260440\pi$
$972$	−27.1182	−	15.3819i	−0.869817	−	0.493374i
$973$	16.8074	+	14.9485i	0.538822	+	0.479228i
$974$	1.46084	−	1.57081i	0.0468085	−	0.0503320i
$975$	−8.84322	−	17.9271i	−0.283210	−	0.574126i
$976$	6.84766	−	58.3730i	0.219188	−	1.86847i
$977$	20.0661	−	11.5852i	0.641971	−	0.370642i	−0.143402	−	0.989664i	$-0.545804\pi$
$977$	20.0661	−	11.5852i	0.641971	−	0.370642i	0.785373	+	0.619022i	$0.212471\pi$
$978$	−1.48890	+	4.97343i	−0.0476097	+	0.159033i
$979$	4.73380	+	4.73380i	0.151293	+	0.151293i
$980$	−2.02011	+	2.97862i	−0.0645300	+	0.0951487i
$981$	−6.22905	+	15.0480i	−0.198878	+	0.480446i
$982$	20.5742	−	38.8208i	0.656550	−	1.23882i
$983$	23.3046	−	13.4549i	0.743303	−	0.429146i	−0.0799662	−	0.996798i	$-0.525481\pi$
$983$	23.3046	−	13.4549i	0.743303	−	0.429146i	0.823269	+	0.567652i	$0.192148\pi$
$984$	0.437017	+	10.0556i	0.0139316	+	0.320560i
$985$	−0.871957	+	1.51027i	−0.0277829	+	0.0481213i
$986$	−0.410145	−	11.3075i	−0.0130617	−	0.360104i
$987$	−0.825068	−	3.16598i	−0.0262622	−	0.100774i
$988$	20.2915	−	1.47397i	0.645560	−	0.0468931i
$989$	−17.5473	+	4.70178i	−0.557971	+	0.149508i
$990$	1.07205	+	6.34477i	0.0340719	+	0.201650i
$991$	17.8951	+	30.9953i	0.568458	+	0.984598i	0.996719	+	0.0809428i	$0.0257931\pi$
$991$	17.8951	+	30.9953i	0.568458	+	0.984598i	−0.428261	+	0.903655i	$0.640874\pi$
$992$	−10.7211	−	22.5923i	−0.340397	−	0.717307i
$993$	−1.25619	−	0.839150i	−0.0398639	−	0.0266296i
$994$	−12.0440	−	32.3381i	−0.382013	−	1.02570i
$995$	1.04595	+	1.04595i	0.0331589	+	0.0331589i
$996$	28.3445	−	16.6370i	0.898129	−	0.527165i
$997$	7.39932	+	1.98264i	0.234339	+	0.0627909i	0.374077	−	0.927398i	$-0.377960\pi$
$997$	7.39932	+	1.98264i	0.234339	+	0.0627909i	−0.139738	+	0.990188i	$0.544626\pi$
$998$	−6.94011	−	11.0732i	−0.219685	−	0.350517i
$999$	−13.9395	+	15.9060i	−0.441027	+	0.503244i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.6	✓	240	1.1	even	1	trivial
336.2.bo.a.5.55	yes	240	3.2	odd	2	inner
336.2.bo.a.101.27	yes	240	21.17	even	6	inner
336.2.bo.a.101.34	yes	240	7.3	odd	6	inner
336.2.bo.a.173.27	yes	240	16.13	even	4	inner
336.2.bo.a.173.34	yes	240	48.29	odd	4	inner
336.2.bo.a.269.6	yes	240	336.269	even	12	inner
336.2.bo.a.269.55	yes	240	112.45	odd	12	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)

\(f(q)\)	\(=\)	\(q+(-1.35186 + 0.415301i) q^{2} +(1.14217 + 1.30209i) q^{3} +(1.65505 - 1.12286i) q^{4} +(0.248314 - 0.0665356i) q^{5} +(-2.08481 - 1.28590i) q^{6} +(0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-0.390898 + 2.97442i) q^{9} +O(q^{10})\)	\(q+(-1.35186 + 0.415301i) q^{2} +(1.14217 + 1.30209i) q^{3} +(1.65505 - 1.12286i) q^{4} +(0.248314 - 0.0665356i) q^{5} +(-2.08481 - 1.28590i) q^{6} +(0.154609 + 2.64123i) q^{7} +(-1.77107 + 2.20529i) q^{8} +(-0.390898 + 2.97442i) q^{9} +(-0.308054 + 0.193072i) q^{10} +(-5.69873 - 1.52697i) q^{11} +(3.35241 + 0.872539i) q^{12} +(1.65400 + 1.65400i) q^{13} +(-1.30591 - 3.50636i) q^{14} +(0.370253 + 0.247334i) q^{15} +(1.47839 - 3.71677i) q^{16} +(3.31337 + 5.73893i) q^{17} +(-0.706842 - 4.18334i) q^{18} +(4.20068 - 1.12557i) q^{19} +(0.336263 - 0.388941i) q^{20} +(-3.26254 + 3.21805i) q^{21} +(8.33804 - 0.302437i) q^{22} +(2.18135 - 3.77821i) q^{23} +(-4.89436 + 0.212710i) q^{24} +(-4.27289 + 2.46696i) q^{25} +(-2.92289 - 1.54907i) q^{26} +(-4.31945 + 2.88831i) q^{27} +(3.22161 + 4.19777i) q^{28} +(0.853732 + 0.853732i) q^{29} +(-0.603247 - 0.180594i) q^{30} +(-3.82842 + 2.21034i) q^{31} +(-0.454993 + 5.63853i) q^{32} +(-4.52066 - 9.16434i) q^{33} +(-6.86260 - 6.38218i) q^{34} +(0.214127 + 0.645568i) q^{35} +(2.69290 + 5.36174i) q^{36} +(3.93158 - 1.05346i) q^{37} +(-5.21129 + 3.26616i) q^{38} +(-0.264516 + 4.04282i) q^{39} +(-0.293052 + 0.665444i) q^{40} -2.05452i q^{41} +(3.07404 - 5.70529i) q^{42} +(-2.94440 - 2.94440i) q^{43} +(-11.1463 + 3.87165i) q^{44} +(0.100840 + 0.764600i) q^{45} +(-1.37979 + 6.01352i) 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} +(-3.68819 + 10.8692i) q^{51} +(4.59467 + 0.880250i) q^{52} +(11.8996 + 3.18848i) q^{53} +(4.63978 - 5.69846i) q^{54} -1.51667 q^{55} +(-6.09850 - 4.33686i) q^{56} +(6.26349 + 4.18409i) q^{57} +(-1.50868 - 0.799570i) q^{58} +(-0.338459 + 1.26315i) q^{59} +(0.890507 - 0.00639107i) q^{60} +(14.1926 - 3.80291i) q^{61} +(4.25753 - 4.57801i) q^{62} +(-7.91657 - 0.572578i) q^{63} +(-1.72660 - 7.81146i) q^{64} +(0.520763 + 0.300662i) q^{65} +(9.91726 + 10.5115i) q^{66} +(-6.87409 - 1.84191i) q^{67} +(11.9278 + 5.77778i) q^{68} +(7.41105 - 1.47503i) q^{69} +(-0.557575 - 0.783790i) q^{70} +9.22268 q^{71} +(-5.86716 - 6.12997i) q^{72} +(-2.87170 - 4.97393i) q^{73} +(-4.87744 + 3.05692i) q^{74} +(-8.09258 - 2.74603i) q^{75} +(5.68849 - 6.57964i) q^{76} +(3.15201 - 15.2877i) q^{77} +(-1.32140 - 5.57518i) q^{78} +(2.19461 - 3.80118i) q^{79} +(0.119807 - 1.02129i) q^{80} +(-8.69440 - 2.32539i) q^{81} +(0.853245 + 2.77743i) q^{82} +(6.70882 - 6.70882i) q^{83} +(-1.78626 + 8.98940i) q^{84} +(1.20460 + 1.20460i) q^{85} +(5.20322 + 2.75760i) q^{86} +(-0.136533 + 2.08674i) q^{87} +(13.4603 - 9.86297i) q^{88} +(-0.982700 - 0.567362i) q^{89} +(-0.453860 - 0.991754i) q^{90} +(-4.11288 + 4.62433i) q^{91} +(-0.632143 - 8.70246i) q^{92} +(-7.25077 - 2.46038i) q^{93} +(0.225800 - 0.984104i) q^{94} +(0.968199 - 0.558990i) q^{95} +(-7.86157 + 5.84771i) q^{96} -11.1323i q^{97} +(9.05921 - 3.99133i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more