LMFDB - Embedded newform 357.2.bh.a.100.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(25,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 16, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bh (of order $24$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$24$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			100.9
Character	$\chi$	$=$	357.100
Dual form			357.2.bh.a.25.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.840803 + 0.225292i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(-1.07586 + 0.621147i) q^{4} +(0.0284677 - 0.216234i) q^{5} +(0.333112 - 0.804203i) q^{6} +(0.929728 - 2.47702i) q^{7} +(1.99567 - 1.99567i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.0247801 + 0.188224i) q^{10} +(-1.06830 + 0.140644i) q^{11} +(0.162152 - 1.23167i) q^{12} -1.49163i q^{13} +(-0.223665 + 2.29214i) q^{14} +(0.154220 + 0.154220i) q^{15} +(0.0139413 - 0.0241470i) q^{16} +(1.95621 + 3.62949i) q^{17} +(0.435232 + 0.753843i) q^{18} +(5.13340 - 1.37549i) q^{19} +(0.103686 + 0.250320i) q^{20} +(1.39917 + 2.24551i) q^{21} +(0.866542 - 0.358933i) q^{22} +(0.849331 + 1.10687i) q^{23} +(0.368384 + 2.79815i) q^{24} +(4.78368 + 1.28178i) q^{25} +(0.336053 + 1.25417i) q^{26} +(0.923880 + 0.382683i) q^{27} +(0.538336 + 3.24242i) q^{28} +(2.90262 - 1.20230i) q^{29} +(-0.164413 - 0.0949240i) q^{30} +(4.37359 - 5.69977i) q^{31} +(-1.46721 + 5.47570i) q^{32} +(0.538758 - 0.933156i) q^{33} +(-2.46249 - 2.61097i) q^{34} +(-0.509148 - 0.271554i) q^{35} +(0.878435 + 0.878435i) q^{36} +(1.96876 + 0.259192i) q^{37} +(-4.00629 + 2.31303i) q^{38} +(1.18339 + 0.908047i) q^{39} +(-0.374719 - 0.488343i) q^{40} +(-8.81025 - 3.64932i) q^{41} +(-1.68232 - 1.57281i) q^{42} +(3.75109 - 3.75109i) q^{43} +(1.06198 - 0.814883i) q^{44} +(-0.216234 + 0.0284677i) q^{45} +(-0.963489 - 0.739311i) q^{46} +(-0.912015 - 0.526552i) q^{47} +(0.0106702 + 0.0257601i) q^{48} +(-5.27121 - 4.60590i) q^{49} -4.31091 q^{50} +(-4.07034 - 0.657528i) q^{51} +(0.926522 + 1.60478i) q^{52} +(-0.403336 + 1.50527i) q^{53} +(-0.863016 - 0.113618i) q^{54} +0.235006i q^{55} +(-3.08787 - 6.79872i) q^{56} +(-2.03376 + 4.90994i) q^{57} +(-2.16966 + 1.66484i) q^{58} +(10.4648 + 2.80403i) q^{59} +(-0.261712 - 0.0701255i) q^{60} +(3.70374 - 2.84198i) q^{61} +(-2.39321 + 5.77772i) q^{62} +(-2.63324 - 0.256949i) q^{63} -4.87877i q^{64} +(-0.322541 - 0.0424634i) q^{65} +(-0.242756 + 0.905978i) q^{66} +(-4.99373 - 8.64940i) q^{67} +(-4.35906 - 2.68973i) q^{68} -1.39518 q^{69} +(0.489272 + 0.113616i) q^{70} +(2.61157 + 6.30489i) q^{71} +(-2.44418 - 1.41115i) q^{72} +(-1.92764 - 1.47913i) q^{73} +(-1.71373 + 0.225617i) q^{74} +(-3.92903 + 3.01485i) q^{75} +(-4.66842 + 4.66842i) q^{76} +(-0.644849 + 2.77695i) q^{77} +(-1.19957 - 0.496880i) q^{78} +(5.26746 + 6.86469i) q^{79} +(-0.00482453 - 0.00370199i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(8.22984 + 1.08348i) q^{82} +(-7.10788 - 7.10788i) q^{83} +(-2.90010 - 1.54677i) q^{84} +(0.840509 - 0.319676i) q^{85} +(-2.30883 + 3.99902i) q^{86} +(-0.813151 + 3.03472i) q^{87} +(-1.85129 + 2.41264i) q^{88} +(1.70711 + 0.985601i) q^{89} +(0.175397 - 0.0726516i) q^{90} +(-3.69479 - 1.38681i) q^{91} +(-1.60129 - 0.663276i) q^{92} +(1.85946 + 6.93960i) q^{93} +(0.885453 + 0.237256i) q^{94} +(-0.151291 - 1.14917i) q^{95} +(-3.45099 - 4.49741i) q^{96} +(-11.0570 + 4.57996i) q^{97} +(5.46972 + 2.68509i) q^{98} +(0.412348 + 0.995495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) $ 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.840803	+	0.225292i	−0.594537	+	0.159306i	−0.543526	−	0.839392i	$-0.682911\pi$
$2$	−0.840803	+	0.225292i	−0.594537	+	0.159306i	−0.0510113	+	0.998698i	$0.516244\pi$
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$3$	−0.608761	+	0.793353i	−0.351469	+	0.458043i
$4$	−1.07586	+	0.621147i	−0.537929	+	0.310574i
$5$	0.0284677	−	0.216234i	0.0127312	−	0.0967028i	−0.983900	−	0.178722i	$-0.942804\pi$
$5$	0.0284677	−	0.216234i	0.0127312	−	0.0967028i	0.996631	+	0.0820195i	$0.0261370\pi$
$6$	0.333112	−	0.804203i	0.135992	−	0.328315i
$7$	0.929728	−	2.47702i	0.351404	−	0.936224i
$7$	0.929728	−	2.47702i	0.351404	−	0.936224i
$8$	1.99567	−	1.99567i	0.705574	−	0.705574i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	0.0247801	+	0.188224i	0.00783616	+	0.0595216i
$11$	−1.06830	+	0.140644i	−0.322104	+	0.0424058i	−0.289845	−	0.957074i	$-0.593604\pi$
$11$	−1.06830	+	0.140644i	−0.322104	+	0.0424058i	−0.0322594	+	0.999480i	$0.510270\pi$
$12$	0.162152	−	1.23167i	0.0468092	−	0.355551i
$13$		−	1.49163i		−	0.413704i	−0.978372	−	0.206852i	$-0.933678\pi$
$13$		−	1.49163i		−	0.413704i	0.978372	−	0.206852i	$-0.0663218\pi$
$14$	−0.223665	+	2.29214i	−0.0597769	+	0.612601i
$15$	0.154220	+	0.154220i	0.0398194	+	0.0398194i
$16$	0.0139413	−	0.0241470i	0.00348532	−	0.00603675i
$17$	1.95621	+	3.62949i	0.474451	+	0.880282i
$17$	1.95621	+	3.62949i	0.474451	+	0.880282i
$18$	0.435232	+	0.753843i	0.102585	+	0.177683i
$19$	5.13340	−	1.37549i	1.17768	−	0.315559i	0.383675	−	0.923468i	$-0.374658\pi$
$19$	5.13340	−	1.37549i	1.17768	−	0.315559i	0.794006	+	0.607909i	$0.207992\pi$
$20$	0.103686	+	0.250320i	0.0231849	+	0.0559732i
$21$	1.39917	+	2.24551i	0.305323	+	0.490011i
$22$	0.866542	−	0.358933i	0.184747	−	0.0765248i
$23$	0.849331	+	1.10687i	0.177098	+	0.230798i	0.873465	−	0.486888i	$-0.161868\pi$
$23$	0.849331	+	1.10687i	0.177098	+	0.230798i	−0.696367	+	0.717686i	$0.745201\pi$
$24$	0.368384	+	2.79815i	0.0751960	+	0.571170i
$25$	4.78368	+	1.28178i	0.956736	+	0.256357i
$26$	0.336053	+	1.25417i	0.0659054	+	0.245962i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	0.538336	+	3.24242i	0.101736	+	0.612759i
$29$	2.90262	−	1.20230i	0.539003	−	0.223262i	−0.0965382	−	0.995329i	$-0.530777\pi$
$29$	2.90262	−	1.20230i	0.539003	−	0.223262i	0.635541	+	0.772067i	$0.280777\pi$
$30$	−0.164413	−	0.0949240i	−0.0300176	−	0.0173307i
$31$	4.37359	−	5.69977i	0.785519	−	1.02371i	−0.213388	−	0.976968i	$-0.568450\pi$
$31$	4.37359	−	5.69977i	0.785519	−	1.02371i	0.998907	−	0.0467409i	$-0.0148835\pi$
$32$	−1.46721	+	5.47570i	−0.259369	+	0.967977i
$33$	0.538758	−	0.933156i	0.0937857	−	0.162442i
$34$	−2.46249	−	2.61097i	−0.422313	−	0.447777i
$35$	−0.509148	−	0.271554i	−0.0860617	−	0.0459010i
$36$	0.878435	+	0.878435i	0.146406	+	0.146406i
$37$	1.96876	+	0.259192i	0.323662	+	0.0426109i	0.290607	−	0.956843i	$-0.406143\pi$
$37$	1.96876	+	0.259192i	0.323662	+	0.0426109i	0.0330555	+	0.999454i	$0.489476\pi$
$38$	−4.00629	+	2.31303i	−0.649905	+	0.375223i
$39$	1.18339	+	0.908047i	0.189494	+	0.145404i
$40$	−0.374719	−	0.488343i	−0.0592482	−	0.0772138i
$41$	−8.81025	−	3.64932i	−1.37593	−	0.569929i	−0.432540	−	0.901615i	$-0.642382\pi$
$41$	−8.81025	−	3.64932i	−1.37593	−	0.569929i	−0.943390	+	0.331686i	$0.892382\pi$
$42$	−1.68232	−	1.57281i	−0.259588	−	0.242690i
$43$	3.75109	−	3.75109i	0.572036	−	0.572036i	−0.360661	−	0.932697i	$-0.617449\pi$
$43$	3.75109	−	3.75109i	0.572036	−	0.572036i	0.932697	+	0.360661i	$0.117449\pi$
$44$	1.06198	−	0.814883i	0.160099	−	0.122848i
$45$	−0.216234	+	0.0284677i	−0.0322343	+	0.00424372i
$46$	−0.963489	−	0.739311i	−0.142059	−	0.109006i
$47$	−0.912015	−	0.526552i	−0.133031	−	0.0768055i	0.432007	−	0.901870i	$-0.357805\pi$
$47$	−0.912015	−	0.526552i	−0.133031	−	0.0768055i	−0.565039	+	0.825064i	$0.691139\pi$
$48$	0.0106702	+	0.0257601i	0.00154011	+	0.00371815i
$49$	−5.27121	−	4.60590i	−0.753030	−	0.657986i
$50$	−4.31091			−0.609655
$51$	−4.07034	−	0.657528i	−0.569961	−	0.0920723i
$52$	0.926522	+	1.60478i	0.128485	+	0.222543i
$53$	−0.403336	+	1.50527i	−0.0554025	+	0.206765i	−0.988079	−	0.153950i	$-0.950801\pi$
$53$	−0.403336	+	1.50527i	−0.0554025	+	0.206765i	0.932676	+	0.360715i	$0.117467\pi$
$54$	−0.863016	−	0.113618i	−0.117442	−	0.0154615i
$55$			0.235006i			0.0316882i
$56$	−3.08787	−	6.79872i	−0.412634	−	0.908517i
$57$	−2.03376	+	4.90994i	−0.269379	+	0.650338i
$58$	−2.16966	+	1.66484i	−0.284890	+	0.218604i
$59$	10.4648	+	2.80403i	1.36240	+	0.365054i	0.864697	−	0.502294i	$-0.167510\pi$
$59$	10.4648	+	2.80403i	1.36240	+	0.365054i	0.497703	+	0.867348i	$0.334177\pi$
$60$	−0.261712	−	0.0701255i	−0.0337869	−	0.00905317i
$61$	3.70374	−	2.84198i	0.474216	−	0.363879i	−0.343830	−	0.939032i	$-0.611724\pi$
$61$	3.70374	−	2.84198i	0.474216	−	0.363879i	0.818046	+	0.575153i	$0.195058\pi$
$62$	−2.39321	+	5.77772i	−0.303938	+	0.733771i
$63$	−2.63324	−	0.256949i	−0.331758	−	0.0323726i
$64$		−	4.87877i		−	0.609847i
$65$	−0.322541	−	0.0424634i	−0.0400063	−	0.00526693i
$66$	−0.242756	+	0.905978i	−0.0298812	+	0.111518i
$67$	−4.99373	−	8.64940i	−0.610081	−	1.05669i	−0.991226	−	0.132177i	$-0.957803\pi$
$67$	−4.99373	−	8.64940i	−0.610081	−	1.05669i	0.381145	−	0.924515i	$-0.375530\pi$
$68$	−4.35906	−	2.68973i	−0.528613	−	0.326177i
$69$	−1.39518			−0.167960
$70$	0.489272	+	0.113616i	0.0584792	+	0.0135797i
$71$	2.61157	+	6.30489i	0.309936	+	0.748253i	0.999707	+	0.0242244i	$0.00771161\pi$
$71$	2.61157	+	6.30489i	0.309936	+	0.748253i	−0.689770	+	0.724028i	$0.742288\pi$
$72$	−2.44418	−	1.41115i	−0.288050	−	0.166305i
$73$	−1.92764	−	1.47913i	−0.225613	−	0.173119i	0.489769	−	0.871852i	$-0.337081\pi$
$73$	−1.92764	−	1.47913i	−0.225613	−	0.173119i	−0.715383	+	0.698733i	$0.753748\pi$
$74$	−1.71373	+	0.225617i	−0.199217	+	0.0262275i
$75$	−3.92903	+	3.01485i	−0.453685	+	0.348125i
$76$	−4.66842	+	4.66842i	−0.535505	+	0.535505i
$77$	−0.644849	+	2.77695i	−0.0734873	+	0.316463i
$78$	−1.19957	−	0.496880i	−0.135825	−	0.0562605i
$79$	5.26746	+	6.86469i	0.592636	+	0.772338i	0.989342	−	0.145607i	$-0.0465136\pi$
$79$	5.26746	+	6.86469i	0.592636	+	0.772338i	−0.396707	+	0.917945i	$0.629847\pi$
$80$	−0.00482453	−	0.00370199i	−0.000539398	−	0.000413895i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	8.22984	+	1.08348i	0.908834	+	0.119650i
$83$	−7.10788	−	7.10788i	−0.780191	−	0.780191i	0.199672	−	0.979863i	$-0.436012\pi$
$83$	−7.10788	−	7.10788i	−0.780191	−	0.780191i	−0.979863	+	0.199672i	$0.936012\pi$
$84$	−2.90010	−	1.54677i	−0.316427	−	0.168766i
$85$	0.840509	−	0.319676i	0.0911660	−	0.0346738i
$86$	−2.30883	+	3.99902i	−0.248968	+	0.431225i
$87$	−0.813151	+	3.03472i	−0.0871789	+	0.325356i
$88$	−1.85129	+	2.41264i	−0.197348	+	0.257189i
$89$	1.70711	+	0.985601i	0.180953	+	0.104474i	0.587741	−	0.809049i	$-0.300018\pi$
$89$	1.70711	+	0.985601i	0.180953	+	0.104474i	−0.406787	+	0.913523i	$0.633351\pi$
$90$	0.175397	−	0.0726516i	0.0184884	−	0.00765816i
$91$	−3.69479	−	1.38681i	−0.387319	−	0.145377i
$92$	−1.60129	−	0.663276i	−0.166946	−	0.0691513i
$93$	1.85946	+	6.93960i	0.192817	+	0.719603i
$94$	0.885453	+	0.237256i	0.0913275	+	0.0244711i
$95$	−0.151291	−	1.14917i	−0.0155222	−	0.117903i
$96$	−3.45099	−	4.49741i	−0.352215	−	0.459015i
$97$	−11.0570	+	4.57996i	−1.12267	+	0.465025i	−0.865283	−	0.501284i	$-0.832861\pi$
$97$	−11.0570	+	4.57996i	−1.12267	+	0.465025i	−0.257386	+	0.966309i	$0.582861\pi$
$98$	5.46972	+	2.68509i	0.552526	+	0.271235i
$99$	0.412348	+	0.995495i	0.0414425	+	0.100051i
$100$	−5.94274	+	1.59235i	−0.594274	+	0.159235i
$101$	−6.66428	−	11.5429i	−0.663121	−	1.14856i	−0.979791	−	0.200023i	$-0.935898\pi$
$101$	−6.66428	−	11.5429i	−0.663121	−	1.14856i	0.316670	−	0.948536i	$-0.397435\pi$
$102$	3.57049	−	0.364165i	0.353531	−	0.0360577i
$103$	7.42358	−	12.8580i	0.731467	−	1.26694i	−0.224789	−	0.974407i	$-0.572169\pi$
$103$	7.42358	−	12.8580i	0.731467	−	1.26694i	0.956256	−	0.292530i	$-0.0944973\pi$
$104$	−2.97680	−	2.97680i	−0.291899	−	0.291899i
$105$	0.525388	−	0.238623i	0.0512726	−	0.0232872i
$106$		−	1.35650i		−	0.131755i
$107$	1.53042	−	11.6247i	0.147951	−	1.12380i	−0.742866	−	0.669440i	$-0.766534\pi$
$107$	1.53042	−	11.6247i	0.147951	−	1.12380i	0.890818	−	0.454361i	$-0.150132\pi$
$108$	−1.23167	+	0.162152i	−0.118517	+	0.0156031i
$109$	1.46530	+	11.1301i	0.140351	+	1.06607i	0.906140	+	0.422977i	$0.139015\pi$
$109$	1.46530	+	11.1301i	0.140351	+	1.06607i	−0.765790	+	0.643091i	$0.777652\pi$
$110$	−0.0529451	−	0.197594i	−0.00504812	−	0.0188398i
$111$	−1.40414	+	1.40414i	−0.133275	+	0.133275i
$112$	−0.0468509	−	0.0569829i	−0.00442699	−	0.00538438i
$113$	−2.43989	+	5.89041i	−0.229525	+	0.554123i	−0.996120	−	0.0880084i	$-0.971950\pi$
$113$	−2.43989	+	5.89041i	−0.229525	+	0.554123i	0.766594	+	0.642132i	$0.221950\pi$
$114$	0.603822	−	4.58648i	0.0565531	−	0.429564i
$115$	0.263522	−	0.152144i	0.0245735	−	0.0141875i
$116$	−2.37600	+	3.09646i	−0.220606	+	0.287499i
$117$	−1.44080	+	0.386062i	−0.133202	+	0.0356915i
$118$	−9.43055			−0.868153
$119$	10.8091	−	1.47113i	0.990865	−	0.134858i
$120$	0.615543			0.0561911
$121$	−9.50370	+	2.54651i	−0.863973	+	0.231501i
$122$	−2.47384	+	3.22397i	−0.223971	+	0.291885i
$123$	8.25854	−	4.76807i	0.744648	−	0.429922i
$124$	−1.16496	+	8.84878i	−0.104617	+	0.794644i
$125$	0.830662	−	2.00540i	0.0742967	−	0.179368i
$126$	2.27193	−	0.377206i	0.202399	−	0.0336042i
$127$	−0.377480	+	0.377480i	−0.0334959	+	0.0334959i	−0.723656	−	0.690160i	$-0.757540\pi$
$127$	−0.377480	+	0.377480i	−0.0334959	+	0.0334959i	0.690160	+	0.723656i	$0.257540\pi$
$128$	−1.83527	−	6.84932i	−0.162216	−	0.605400i
$129$	0.692421	+	5.25946i	0.0609642	+	0.463069i
$130$	0.280760	−	0.0369628i	0.0246243	−	0.00324185i
$131$	0.271922	−	2.06545i	0.0237579	−	0.180459i	−0.975452	−	0.220214i	$-0.929324\pi$
$131$	0.271922	−	2.06545i	0.0237579	−	0.180459i	0.999209	+	0.0397549i	$0.0126577\pi$
$132$			1.33859i			0.116509i
$133$	1.36555	−	13.9943i	0.118408	−	1.21346i
$134$	6.14739	+	6.14739i	0.531053	+	0.531053i
$135$	0.109050	−	0.188880i	0.00938553	−	0.0162562i
$136$	11.1472	+	3.33931i	0.955865	+	0.286343i
$137$	9.73326	+	16.8585i	0.831569	+	1.44032i	0.896794	+	0.442449i	$0.145890\pi$
$137$	9.73326	+	16.8585i	0.831569	+	1.44032i	−0.0652251	+	0.997871i	$0.520777\pi$
$138$	1.17307	−	0.314323i	0.0998584	−	0.0267570i
$139$	0.0370575	+	0.0894647i	0.00314317	+	0.00758829i	0.925443	−	0.378886i	$-0.123693\pi$
$139$	0.0370575	+	0.0894647i	0.00314317	+	0.00758829i	−0.922300	+	0.386474i	$0.873693\pi$
$140$	0.716446	−	0.0241022i	0.0605507	−	0.00203701i
$141$	0.972942	−	0.403006i	0.0819365	−	0.0339392i
$142$	−3.61626	−	4.71280i	−0.303470	−	0.395490i
$143$	0.209789	+	1.59351i	0.0175434	+	0.133256i
$144$	−0.0269325	−	0.00721654i	−0.00224437	−	0.000601378i
$145$	−0.177348	−	0.661872i	−0.0147280	−	0.0549655i
$146$	1.95400	+	0.809374i	0.161714	+	0.0669843i
$147$	6.86302	−	1.37804i	0.566052	−	0.113659i
$148$	−2.27910	+	0.944035i	−0.187341	+	0.0775992i
$149$	11.3521	+	6.55412i	0.929998	+	0.536935i	0.886811	−	0.462132i	$-0.152916\pi$
$149$	11.3521	+	6.55412i	0.929998	+	0.536935i	0.0431870	+	0.999067i	$0.486249\pi$
$150$	2.62432	−	3.42007i	0.214274	−	0.279248i
$151$	−5.31587	+	19.8391i	−0.432599	+	1.61448i	0.314148	+	0.949374i	$0.398281\pi$
$151$	−5.31587	+	19.8391i	−0.432599	+	1.61448i	−0.746747	+	0.665108i	$0.768386\pi$
$152$	7.49952	−	12.9896i	0.608292	−	1.05359i
$153$	2.99952	−	2.82894i	0.242497	−	0.228706i
$154$	−0.0834355	−	2.48015i	−0.00672343	−	0.199856i
$155$	−1.10798	−	1.10798i	−0.0889949	−	0.0889949i
$156$	−1.83719	−	0.241871i	−0.147093	−	0.0193652i
$157$	−5.47198	+	3.15925i	−0.436711	+	0.252135i	−0.702202	−	0.711978i	$-0.747800\pi$
$157$	−5.47198	+	3.15925i	−0.436711	+	0.252135i	0.265490	+	0.964114i	$0.414466\pi$
$158$	−5.97546	−	4.58513i	−0.475382	−	0.364773i
$159$	−0.948676	−	1.23634i	−0.0752349	−	0.0980480i
$160$	1.14227	+	0.473142i	0.0903040	+	0.0374051i
$161$	3.53138	−	1.07472i	0.278312	−	0.0846997i
$162$	0.615510	−	0.615510i	0.0483591	−	0.0483591i
$163$	−3.60960	+	2.76975i	−0.282726	+	0.216943i	−0.740382	−	0.672186i	$-0.765356\pi$
$163$	−3.60960	+	2.76975i	−0.282726	+	0.216943i	0.457657	+	0.889129i	$0.348689\pi$
$164$	11.7453	−	1.54630i	0.917157	−	0.120746i
$165$	−0.186443	−	0.143063i	−0.0145146	−	0.0111374i
$166$	7.57767	+	4.37497i	0.588142	+	0.339564i
$167$	−6.85435	−	16.5479i	−0.530406	−	1.28051i	−0.931255	−	0.364369i	$-0.881285\pi$
$167$	−6.85435	−	16.5479i	−0.530406	−	1.28051i	0.400849	−	0.916144i	$-0.368715\pi$
$168$	7.27356	+	1.68903i	0.561168	+	0.130311i
$169$	10.7750			0.828849
$170$	−0.634682	+	0.458145i	−0.0486779	+	0.0351381i
$171$	−2.65724	−	4.60248i	−0.203204	−	0.351960i
$172$	−1.70566	+	6.36562i	−0.130055	+	0.485374i
$173$	−8.70119	−	1.14553i	−0.661539	−	0.0870933i	−0.207722	−	0.978188i	$-0.566605\pi$
$173$	−8.70119	−	1.14553i	−0.661539	−	0.0870933i	−0.453818	+	0.891095i	$0.649938\pi$
$174$		−	2.73480i		−	0.207324i
$175$	7.62252	−	10.6575i	0.576208	−	0.805635i
$176$	−0.0114973	+	0.0277569i	−0.000866642	+	0.00209226i
$177$	−8.59515	+	6.59529i	−0.646051	+	0.495732i
$178$	−1.65739	−	0.444097i	−0.124227	−	0.0332865i
$179$	23.3378	+	6.25334i	1.74435	+	0.467397i	0.983405	−	0.181421i	$-0.0580697\pi$
$179$	23.3378	+	6.25334i	1.74435	+	0.467397i	0.760944	+	0.648818i	$0.224736\pi$
$180$	0.214954	−	0.164940i	0.0160218	−	0.0122939i
$181$	1.67474	−	4.04318i	0.124483	−	0.300528i	−0.849337	−	0.527852i	$-0.822998\pi$
$181$	1.67474	−	4.04318i	0.124483	−	0.300528i	0.973819	+	0.227324i	$0.0729977\pi$
$182$	3.41903	+	0.333625i	0.253435	+	0.0247300i
$183$			4.66847i			0.345103i
$184$	3.90392	+	0.513961i	0.287801	+	0.0378897i
$185$	0.112092	−	0.418334i	0.00824119	−	0.0307565i
$186$	−3.12688	−	5.41591i	−0.229274	−	0.397114i
$187$	−2.60028	−	3.60225i	−0.190152	−	0.263423i
$188$	1.30827			0.0954151
$189$	1.80687	−	1.93267i	0.131430	−	0.140581i
$190$	0.386106	+	0.932142i	0.0280111	+	0.0676247i
$191$	1.40634	+	0.811953i	0.101759	+	0.0587508i	0.550016	−	0.835154i	$-0.314622\pi$
$191$	1.40634	+	0.811953i	0.101759	+	0.0587508i	−0.448257	+	0.893905i	$0.647955\pi$
$192$	3.87059	+	2.97001i	0.279336	+	0.214342i
$193$	−26.5863	+	3.50015i	−1.91372	+	0.251947i	−0.991036	−	0.133598i	$-0.957347\pi$
$193$	−26.5863	+	3.50015i	−1.91372	+	0.251947i	−0.922689	+	0.385545i	$0.874014\pi$
$194$	8.26494	−	6.34191i	0.593388	−	0.455322i
$195$	0.230039	−	0.230039i	0.0164734	−	0.0164734i
$196$	8.53202	+	1.68110i	0.609430	+	0.120078i
$197$	8.69335	+	3.60090i	0.619376	+	0.256554i	0.670231	−	0.742152i	$-0.266195\pi$
$197$	8.69335	+	3.60090i	0.619376	+	0.256554i	−0.0508557	+	0.998706i	$0.516195\pi$
$198$	−0.570980	−	0.744116i	−0.0405778	−	0.0528820i
$199$	−0.364258	−	0.279505i	−0.0258216	−	0.0198136i	0.595770	−	0.803155i	$-0.296847\pi$
$199$	−0.364258	−	0.279505i	−0.0258216	−	0.0198136i	−0.621592	+	0.783341i	$0.713514\pi$
$200$	12.1046	−	6.98862i	0.855927	−	0.494170i
$201$	9.90202	+	1.30363i	0.698435	+	0.0919507i
$202$	8.20387	+	8.20387i	0.577222	+	0.577222i
$203$	−0.279481	−	8.30765i	−0.0196157	−	0.583083i
$204$	4.78753	−	1.82087i	0.335194	−	0.127487i
$205$	−1.03992	+	1.80119i	−0.0726309	+	0.125800i
$206$	−3.34495	+	12.4835i	−0.233054	+	0.869769i
$207$	0.849331	−	1.10687i	0.0590326	−	0.0769328i
$208$	−0.0360184	−	0.0207952i	−0.00249743	−	0.00144189i
$209$	−5.29054	+	2.19141i	−0.365954	+	0.151583i
$210$	−0.387988	+	0.319000i	−0.0267737	+	0.0220131i
$211$	13.0532	+	5.40683i	0.898623	+	0.372222i	0.783690	−	0.621152i	$-0.213335\pi$
$211$	13.0532	+	5.40683i	0.898623	+	0.372222i	0.114932	+	0.993373i	$0.463335\pi$
$212$	−0.501062	−	1.86999i	−0.0344131	−	0.128431i
$213$	−6.59183	−	1.76628i	−0.451665	−	0.121023i
$214$	1.33217	+	10.1189i	0.0910655	+	0.691711i
$215$	−0.704328	−	0.917898i	−0.0480348	−	0.0626001i
$216$	2.60746	−	1.08005i	0.177415	−	0.0734878i
$217$	−10.0522	−	16.1327i	−0.682386	−	1.09516i
$218$	−3.73955	−	9.02808i	−0.253274	−	0.611459i
$219$	2.34695	−	0.628862i	0.158592	−	0.0424946i
$220$	−0.145973	−	0.252833i	−0.00984152	−	0.0170460i
$221$	5.41386	−	2.91795i	0.364176	−	0.196282i
$222$	0.864260	−	1.49694i	0.0580054	−	0.100468i
$223$	15.6591	+	15.6591i	1.04861	+	1.04861i	0.998757	+	0.0498533i	$0.0158754\pi$
$223$	15.6591	+	15.6591i	1.04861	+	1.04861i	0.0498533	+	0.998757i	$0.484125\pi$
$224$	12.1993	+	8.72522i	0.815100	+	0.582978i
$225$		−	4.95243i		−	0.330162i
$226$	0.724400	−	5.50236i	0.0481864	−	0.366012i
$227$	−15.8467	+	2.08626i	−1.05178	+	0.138470i	−0.636543	−	0.771241i	$-0.719636\pi$
$227$	−15.8467	+	2.08626i	−1.05178	+	0.138470i	−0.415242	+	0.909711i	$0.636303\pi$
$228$	−0.861753	−	6.54567i	−0.0570710	−	0.433497i
$229$	6.42568	+	23.9810i	0.424621	+	1.58471i	0.764749	+	0.644328i	$0.222863\pi$
$229$	6.42568	+	23.9810i	0.424621	+	1.58471i	−0.340128	+	0.940379i	$0.610471\pi$
$230$	−0.187293	+	0.187293i	−0.0123497	+	0.0123497i
$231$	−1.81054	−	2.20209i	−0.119125	−	0.144887i
$232$	3.39326	−	8.19206i	0.222779	−	0.537835i
$233$	−0.559100	+	4.24679i	−0.0366279	+	0.278216i	0.963323	+	0.268343i	$0.0864761\pi$
$233$	−0.559100	+	4.24679i	−0.0366279	+	0.278216i	−0.999951	+	0.00987313i	$0.996857\pi$
$234$	1.12446	−	0.649205i	0.0735079	−	0.0424398i
$235$	−0.139822	+	0.182219i	−0.00912095	+	0.0118867i
$236$	−13.0003	+	3.48343i	−0.846251	+	0.226752i
$237$	−8.65275			−0.562057
$238$	−8.75685	+	3.67213i	−0.567622	+	0.238029i
$239$	−15.3236			−0.991204			−0.495602	−	0.868550i	$-0.665052\pi$
$239$	−15.3236			−0.991204			−0.495602	+	0.868550i	$0.665052\pi$
$240$	0.00587397	−	0.00157393i	0.000379163	−	0.000101596i
$241$	−3.90019	+	5.08283i	−0.251234	+	0.327414i	−0.901896	−	0.431953i	$-0.857825\pi$
$241$	−3.90019	+	5.08283i	−0.251234	+	0.327414i	0.650662	+	0.759367i	$0.274491\pi$
$242$	7.41703	−	4.28223i	0.476785	−	0.275272i
$243$	0.130526	−	0.991445i	0.00837326	−	0.0636012i
$244$	−2.21941	+	5.35814i	−0.142083	+	0.343020i
$245$	−1.14601	+	1.00870i	−0.0732160	+	0.0644432i
$246$	−5.86959	+	5.86959i	−0.374232	+	0.374232i
$247$	−2.05172	−	7.65713i	−0.130548	−	0.487211i
$248$	−2.64662	−	20.1030i	−0.168060	−	1.27654i
$249$	9.96606	−	1.31206i	0.631573	−	0.0831482i
$250$	−0.246623	+	1.87328i	−0.0155978	+	0.118477i
$251$		−	2.03781i		−	0.128626i	−0.997930	−	0.0643128i	$-0.979514\pi$
$251$		−	2.03781i		−	0.128626i	0.997930	−	0.0643128i	$-0.0204855\pi$
$252$	2.99260	−	1.35919i	0.188516	−	0.0856210i
$253$	−1.06301	−	1.06301i	−0.0668311	−	0.0668311i
$254$	0.232343	−	0.402429i	0.0145785	−	0.0252507i
$255$	−0.258053	+	0.861427i	−0.0161599	+	0.0539447i
$256$	7.96497	+	13.7957i	0.497811	+	0.862234i
$257$	−17.3196	+	4.64077i	−1.08037	+	0.289483i	−0.754746	−	0.656017i	$-0.772240\pi$
$257$	−17.3196	+	4.64077i	−1.08037	+	0.289483i	−0.325621	+	0.945500i	$0.605573\pi$
$258$	−1.76710	−	4.26617i	−0.110015	−	0.265600i
$259$	2.47243	−	4.63567i	0.153630	−	0.288047i
$260$	0.373385	−	0.154661i	0.0231563	−	0.00959167i
$261$	−1.91259	−	2.49254i	−0.118386	−	0.154284i
$262$	0.236698	+	1.79790i	0.0146232	+	0.111075i
$263$	4.87012	+	1.30494i	0.300304	+	0.0804663i	0.405825	−	0.913951i	$-0.366984\pi$
$263$	4.87012	+	1.30494i	0.300304	+	0.0804663i	−0.105521	+	0.994417i	$0.533651\pi$
$264$	−0.787087	−	2.93745i	−0.0484419	−	0.180787i
$265$	0.314009	+	0.130067i	0.0192894	+	0.00798993i
$266$	2.00466	+	12.0741i	0.122913	+	0.740312i
$267$	−1.82115	+	0.754346i	−0.111453	+	0.0461652i
$268$	10.7451	+	6.20368i	0.656361	+	0.378950i
$269$	0.572877	−	0.746588i	0.0349289	−	0.0455203i	−0.775562	−	0.631271i	$-0.782534\pi$
$269$	0.572877	−	0.746588i	0.0349289	−	0.0455203i	0.810491	+	0.585751i	$0.199200\pi$
$270$	−0.0491363	+	0.183379i	−0.00299034	+	0.0111601i
$271$	11.3324	−	19.6283i	0.688396	−	1.19234i	−0.283961	−	0.958836i	$-0.591649\pi$
$271$	11.3324	−	19.6283i	0.688396	−	1.19234i	0.972357	−	0.233500i	$-0.0750180\pi$
$272$	0.114914	+	0.00336311i	0.00696765	+	0.000203918i
$273$	3.34948	−	2.08704i	0.202720	−	0.126313i
$274$	−11.9818	−	11.9818i	−0.723850	−	0.723850i
$275$	−5.29067	−	0.696530i	−0.319040	−	0.0420024i
$276$	1.50101	−	0.866611i	0.0903505	−	0.0521639i
$277$	−13.5713	−	10.4136i	−0.815419	−	0.625693i	0.114514	−	0.993422i	$-0.463469\pi$
$277$	−13.5713	−	10.4136i	−0.815419	−	0.625693i	−0.929933	+	0.367729i	$0.880136\pi$
$278$	−0.0513137	−	0.0668734i	−0.00307759	−	0.00401080i
$279$	−6.63752	−	2.74935i	−0.397378	−	0.164599i
$280$	−1.55802	+	0.474158i	−0.0931095	+	0.0283364i
$281$	−22.3561	+	22.3561i	−1.33366	+	1.33366i	−0.431581	+	0.902074i	$0.642044\pi$
$281$	−22.3561	+	22.3561i	−1.33366	+	1.33366i	−0.902074	+	0.431581i	$0.857956\pi$
$282$	−0.727258	+	0.558045i	−0.0433076	+	0.0332311i
$283$	−22.4390	+	2.95415i	−1.33386	+	0.175606i	−0.763510	−	0.645796i	$-0.776526\pi$
$283$	−22.4390	+	2.95415i	−1.33386	+	0.175606i	−0.570350	+	0.821402i	$0.693192\pi$
$284$	−6.72594	−	5.16100i	−0.399111	−	0.306249i
$285$	1.00380	+	0.579544i	0.0594600	+	0.0343292i
$286$	−0.535396	−	1.29256i	−0.0316586	−	0.0764307i
$287$	−17.2306	+	18.4302i	−1.01709	+	1.08790i
$288$	5.66887			0.334041
$289$	−9.34646	+	14.2001i	−0.549792	+	0.835302i
$290$	0.298230	+	0.516549i	0.0175126	+	0.0303328i
$291$	3.09755	−	11.5602i	0.181582	−	0.677672i
$292$	2.99263	+	0.393987i	0.175130	+	0.0230563i
$293$			1.31519i			0.0768345i	0.999262	+	0.0384172i	$0.0122316\pi$
$293$			1.31519i			0.0768345i	−0.999262	+	0.0384172i	$0.987768\pi$
$294$	−5.45998	+	2.70485i	−0.318433	+	0.157750i
$295$	0.904236	−	2.18302i	0.0526467	−	0.127100i
$296$	4.44625	−	3.41173i	0.258433	−	0.198303i
$297$	−1.04080	−	0.278882i	−0.0603934	−	0.0161824i
$298$	−11.0214	−	2.95319i	−0.638455	−	0.171074i
$299$	1.65104	−	1.26689i	0.0954822	−	0.0732660i
$300$	2.35441	−	5.68406i	0.135932	−	0.328169i
$301$	−5.80401	−	12.7790i	−0.334538	−	0.736569i
$302$		−	17.8784i		−	1.02879i
$303$	13.2145	+	1.73973i	0.759155	+	0.0999447i
$304$	0.0383521	−	0.143132i	0.00219965	−	0.00820919i
$305$	−0.509096	−	0.881780i	−0.0291508	−	0.0504906i
$306$	−1.88466	+	3.05435i	−0.107739	+	0.174605i
$307$	21.7836			1.24325			0.621627	−	0.783314i	$-0.286472\pi$
$307$	21.7836			1.24325			0.621627	+	0.783314i	$0.286472\pi$
$308$	−1.03113	−	3.38815i	−0.0587540	−	0.193058i
$309$	5.68176	+	13.7170i	0.323224	+	0.780332i
$310$	1.18121	+	0.681972i	0.0670882	+	0.0387334i
$311$	−24.6581	−	18.9208i	−1.39823	−	1.07290i	−0.986885	−	0.161423i	$-0.948392\pi$
$311$	−24.6581	−	18.9208i	−1.39823	−	1.07290i	−0.411348	−	0.911479i	$-0.634942\pi$
$312$	4.17381	−	0.549492i	0.236295	−	0.0311089i
$313$	−17.5304	+	13.4516i	−0.990878	+	0.760328i	−0.970903	−	0.239473i	$-0.923025\pi$
$313$	−17.5304	+	13.4516i	−0.990878	+	0.760328i	−0.0199751	+	0.999800i	$0.506359\pi$
$314$	3.88910	−	3.88910i	0.219475	−	0.219475i
$315$	−0.130524	+	0.562082i	−0.00735418	+	0.0316697i
$316$	−9.93102	−	4.11357i	−0.558664	−	0.231406i
$317$	8.45492	+	11.0187i	0.474875	+	0.618870i	0.967958	−	0.251113i	$-0.0807966\pi$
$317$	8.45492	+	11.0187i	0.474875	+	0.618870i	−0.493082	+	0.869983i	$0.664130\pi$
$318$	1.07619	+	0.825788i	0.0603496	+	0.0463079i
$319$	−2.93177	+	1.69266i	−0.164147	+	0.0947705i
$320$	−1.05496	−	0.138888i	−0.0589739	−	0.00776406i
$321$	8.29082	+	8.29082i	0.462749	+	0.462749i
$322$	−2.72707	+	1.69922i	−0.151974	+	0.0946938i
$323$	15.0343	+	15.9409i	0.836533	+	0.886974i
$324$	0.621147	−	1.07586i	0.0345082	−	0.0597699i
$325$	1.91195	−	7.13549i	0.106056	−	0.395806i
$326$	2.41096	−	3.14203i	0.133531	−	0.174021i
$327$	−9.72210	−	5.61306i	−0.537633	−	0.310403i
$328$	−24.8651	+	10.2995i	−1.37295	+	0.568693i
$329$	−2.15220	+	1.76953i	−0.118655	+	0.0975571i
$330$	0.188993	+	0.0782833i	0.0104037	+	0.00430935i
$331$	2.97714	+	11.1108i	0.163638	+	0.610707i	0.998210	+	0.0598073i	$0.0190486\pi$
$331$	2.97714	+	11.1108i	0.163638	+	0.610707i	−0.834572	+	0.550900i	$0.814285\pi$
$332$	12.0621	+	3.23203i	0.661994	+	0.177381i
$333$	−0.259192	−	1.96876i	−0.0142036	−	0.107887i
$334$	9.49127	+	12.3693i	0.519339	+	0.676816i
$335$	−2.01245	+	0.833586i	−0.109952	+	0.0455437i
$336$	0.0737286	−	0.00248033i	0.00402222	−	0.000135313i
$337$	−6.12673	−	14.7912i	−0.333744	−	0.805730i	−0.998289	−	0.0584813i	$-0.981374\pi$
$337$	−6.12673	−	14.7912i	−0.333744	−	0.805730i	0.664544	−	0.747249i	$-0.268626\pi$
$338$	−9.05968	+	2.42753i	−0.492782	+	0.132040i
$339$	−3.18787	−	5.52155i	−0.173141	−	0.299889i
$340$	−0.705703	+	0.866006i	−0.0382721	+	0.0469658i
$341$	−3.87065	+	6.70417i	−0.209608	+	0.363051i
$342$	3.27112	+	3.27112i	0.176882	+	0.176882i
$343$	−16.3097	+	8.77464i	−0.880640	+	0.473786i
$344$		−	14.9718i		−	0.807227i
$345$	−0.0397176	+	0.301685i	−0.00213832	+	0.0162422i
$346$	7.57407	−	0.997145i	0.407184	−	0.0536068i
$347$	−3.00855	−	22.8522i	−0.161508	−	1.22677i	−0.859676	−	0.510839i	$-0.829335\pi$
$347$	−3.00855	−	22.8522i	−0.161508	−	1.22677i	0.698169	−	0.715933i	$-0.253999\pi$
$348$	−1.01017	−	3.77001i	−0.0541509	−	0.202094i
$349$	13.3148	−	13.3148i	0.712726	−	0.712726i	−0.254379	−	0.967105i	$-0.581871\pi$
$349$	13.3148	−	13.3148i	0.712726	−	0.712726i	0.967105	+	0.254379i	$0.0818710\pi$
$350$	−4.00797	+	10.6782i	−0.214235	+	0.570773i
$351$	0.570822	−	1.37809i	0.0304682	−	0.0735568i
$352$	0.797292	−	6.05604i	0.0424958	−	0.322788i
$353$	−3.48667	+	2.01303i	−0.185577	+	0.107143i	−0.589910	−	0.807469i	$-0.700837\pi$
$353$	−3.48667	+	2.01303i	−0.185577	+	0.107143i	0.404333	+	0.914612i	$0.367504\pi$
$354$	5.74096	−	7.48176i	0.305128	−	0.397651i
$355$	1.43768	−	0.385224i	0.0763040	−	0.0204456i
$356$	−2.44881			−0.129787
$357$	−5.41301	+	9.47097i	−0.286487	+	0.501257i
$358$	−21.0313			−1.11154
$359$	11.4782	−	3.07558i	0.605798	−	0.162323i	0.0571346	−	0.998366i	$-0.481804\pi$
$359$	11.4782	−	3.07558i	0.605798	−	0.162323i	0.548663	+	0.836043i	$0.315137\pi$
$360$	−0.374719	+	0.488343i	−0.0197494	+	0.0257379i
$361$	8.00529	−	4.62186i	0.421331	−	0.243256i
$362$	−0.497229	+	3.77683i	−0.0261338	+	0.198506i
$363$	3.76521	−	9.09001i	0.197622	−	0.477102i
$364$	4.83649	−	0.802998i	0.253501	−	0.0420885i
$365$	−0.374714	+	0.374714i	−0.0196134	+	0.0196134i
$366$	−1.05177	−	3.92526i	−0.0549769	−	0.205177i
$367$	0.0262663	+	0.199512i	0.00137109	+	0.0104145i	0.992117	−	0.125317i	$-0.0399948\pi$
$367$	0.0262663	+	0.199512i	0.00137109	+	0.0104145i	−0.990746	+	0.135732i	$0.956662\pi$
$368$	0.0385684	−	0.00507762i	0.00201051	−	0.000264689i
$369$	−1.24472	+	9.45456i	−0.0647973	+	0.492185i
$370$			0.376990i			0.0195988i
$371$	3.35359	+	2.39856i	0.174110	+	0.124527i
$372$	−6.31103	−	6.31103i	−0.327211	−	0.327211i
$373$	1.59561	−	2.76368i	0.0826175	−	0.143098i	−0.821756	−	0.569840i	$-0.807005\pi$
$373$	1.59561	−	2.76368i	0.0826175	−	0.143098i	0.904373	+	0.426742i	$0.140339\pi$
$374$	2.99789	+	2.44296i	0.155017	+	0.126322i
$375$	1.08531	+	1.87982i	0.0560453	+	0.0970733i
$376$	−2.87090	+	0.769255i	−0.148055	+	0.0396713i
$377$	−1.79339	−	4.32964i	−0.0923645	−	0.222988i
$378$	−1.08380	+	2.03207i	−0.0557449	+	0.104518i
$379$	−21.2202	+	8.78971i	−1.09001	+	0.451497i	−0.854010	−	0.520256i	$-0.825837\pi$
$379$	−21.2202	+	8.78971i	−1.09001	+	0.451497i	−0.236000	+	0.971753i	$0.575837\pi$
$380$	0.876573	+	1.14237i	0.0449672	+	0.0586024i
$381$	−0.0696797	−	0.529270i	−0.00356980	−	0.0271153i
$382$	−1.36538	−	0.365854i	−0.0698591	−	0.0187187i
$383$	4.71493	+	17.5964i	0.240922	+	0.899132i	0.975390	+	0.220488i	$0.0707651\pi$
$383$	4.71493	+	17.5964i	0.240922	+	0.899132i	−0.734468	+	0.678643i	$0.762568\pi$
$384$	6.55117	+	2.71358i	0.334313	+	0.138477i
$385$	0.582114	+	0.218492i	0.0296673	+	0.0111354i
$386$	21.5653	−	8.93263i	1.09764	−	0.454659i
$387$	−4.59413	−	2.65242i	−0.233533	−	0.134830i
$388$	9.05095	−	11.7954i	0.459492	−	0.598822i
$389$	0.684367	−	2.55409i	0.0346988	−	0.129498i	−0.946404	−	0.322986i	$-0.895313\pi$
$389$	0.684367	−	2.55409i	0.0346988	−	0.129498i	0.981103	+	0.193488i	$0.0619801\pi$
$390$	−0.141591	+	0.245244i	−0.00716976	+	0.0124184i
$391$	−2.35591	+	5.24792i	−0.119143	+	0.265399i
$392$	−19.7114	+	1.32774i	−0.995577	+	0.0670610i
$393$	1.47310	+	1.47310i	0.0743079	+	0.0743079i
$394$	−8.12065	−	1.06910i	−0.409112	−	0.0538607i
$395$	1.63433	−	0.943582i	0.0822322	−	0.0474768i
$396$	−1.06198	−	0.814883i	−0.0533663	−	0.0409494i
$397$	11.3689	+	14.8163i	0.570591	+	0.743609i	0.986131	−	0.165966i	$-0.0530742\pi$
$397$	11.3689	+	14.8163i	0.570591	+	0.743609i	−0.415540	+	0.909575i	$0.636408\pi$
$398$	0.369240	+	0.152944i	0.0185083	+	0.00766639i
$399$	10.2712	+	9.60257i	0.514201	+	0.480730i
$400$	0.0976419	−	0.0976419i	0.00488209	−	0.00488209i
$401$	−6.00857	+	4.61054i	−0.300054	+	0.230239i	−0.747804	−	0.663919i	$-0.768892\pi$
$401$	−6.00857	+	4.61054i	−0.300054	+	0.230239i	0.447751	+	0.894158i	$0.352225\pi$
$402$	−8.61934	+	1.13476i	−0.429894	+	0.0565966i
$403$	−8.50195	−	6.52377i	−0.423512	−	0.324972i
$404$	14.3396	+	8.27900i	0.713424	+	0.411896i
$405$	0.0834632	+	0.201498i	0.00414732	+	0.0100125i
$406$	2.10664	+	6.92213i	0.104551	+	0.343540i
$407$	−2.13968			−0.106060
$408$	−9.43524	+	6.81083i	−0.467114	+	0.337186i
$409$	3.32817	+	5.76456i	0.164567	+	0.285039i	0.936502	−	0.350663i	$-0.114044\pi$
$409$	3.32817	+	5.76456i	0.164567	+	0.285039i	−0.771934	+	0.635702i	$0.780711\pi$
$410$	0.468570	−	1.74873i	0.0231410	−	0.0863635i
$411$	−19.3000	−	2.54089i	−0.951998	−	0.125333i
$412$			18.4445i			0.908697i
$413$	16.6750	−	23.3145i	0.820525	−	1.14723i
$414$	−0.464751	+	1.12201i	−0.0228412	+	0.0551436i
$415$	−1.73931	+	1.33462i	−0.0853794	+	0.0655139i
$416$	8.16773	+	2.18854i	0.400456	+	0.107302i
$417$	−0.0935363	−	0.0250630i	−0.00458049	−	0.00122734i
$418$	3.95459	−	3.03446i	0.193425	−	0.148421i
$419$	10.4581	−	25.2480i	0.510911	−	1.23345i	−0.432444	−	0.901661i	$-0.642349\pi$
$419$	10.4581	−	25.2480i	0.510911	−	1.23345i	0.943355	−	0.331786i	$-0.107651\pi$
$420$	−0.417023	+	0.583067i	−0.0203486	+	0.0284508i
$421$		−	21.2726i		−	1.03676i	−0.855149	−	0.518382i	$-0.826535\pi$
$421$		−	21.2726i		−	1.03676i	0.855149	−	0.518382i	$-0.173465\pi$
$422$	−12.1933	−	1.60528i	−0.593562	−	0.0781439i
$423$	−0.272564	+	1.01722i	−0.0132525	+	0.0494590i
$424$	2.19909	+	3.80894i	0.106797	+	0.184979i
$425$	4.70568	+	19.8698i	0.228259	+	0.963826i
$426$	5.94036			0.287811
$427$	−3.59616	−	11.8165i	−0.174030	−	0.571841i
$428$	5.57412	+	13.4571i	0.269435	+	0.650475i
$429$	−1.39192	−	0.803628i	−0.0672027	−	0.0387995i
$430$	0.798996	+	0.613091i	0.0385310	+	0.0295659i
$431$	−28.4406	+	3.74427i	−1.36993	+	0.180355i	−0.779334	−	0.626609i	$-0.784442\pi$
$431$	−28.4406	+	3.74427i	−1.36993	+	0.180355i	−0.590600	+	0.806964i	$0.701109\pi$
$432$	0.0221207	−	0.0169738i	0.00106428	−	0.000816653i
$433$	10.9944	−	10.9944i	0.528355	−	0.528355i	−0.391726	−	0.920082i	$-0.628122\pi$
$433$	10.9944	−	10.9944i	0.528355	−	0.528355i	0.920082	+	0.391726i	$0.128122\pi$
$434$	12.0865	+	11.2997i	0.580169	+	0.542404i
$435$	0.633061	+	0.262223i	0.0303530	+	0.0125726i
$436$	−8.48987	−	11.0642i	−0.406591	−	0.529880i
$437$	5.88244	+	4.51376i	0.281395	+	0.215922i
$438$	−1.83164	+	1.05750i	−0.0875192	+	0.0505292i
$439$	22.9274	+	3.01845i	1.09427	+	0.144063i	0.655984	−	0.754775i	$-0.272254\pi$
$439$	22.9274	+	3.01845i	1.09427	+	0.144063i	0.438282	+	0.898838i	$0.355587\pi$
$440$	0.468994	+	0.468994i	0.0223584	+	0.0223584i
$441$	−3.08467	+	6.28369i	−0.146889	+	0.299224i
$442$	−3.89460	+	3.67312i	−0.185247	+	0.174713i
$443$	−3.28348	+	5.68716i	−0.156003	+	0.270205i	−0.933424	−	0.358776i	$-0.883194\pi$
$443$	−3.28348	+	5.68716i	−0.156003	+	0.270205i	0.777421	+	0.628981i	$0.216528\pi$
$444$	0.638476	−	2.38283i	0.0303008	−	0.113084i
$445$	0.261718	−	0.341078i	0.0124066	−	0.0161686i
$446$	−16.6941	−	9.63833i	−0.790487	−	0.456388i
$447$	−12.1104	+	5.01631i	−0.572804	+	0.237263i
$448$	−12.0848	−	4.53593i	−0.570953	−	0.214303i
$449$	14.3056	+	5.92557i	0.675123	+	0.279645i	0.693786	−	0.720181i	$-0.255941\pi$
$449$	14.3056	+	5.92557i	0.675123	+	0.279645i	−0.0186636	+	0.999826i	$0.505941\pi$
$450$	1.11575	+	4.16402i	0.0525967	+	0.196294i
$451$	9.92522	+	2.65945i	0.467360	+	0.125229i
$452$	−1.03384	−	7.85278i	−0.0486276	−	0.369364i
$453$	−12.5033	−	16.2946i	−0.587457	−	0.765588i
$454$	12.8540	−	5.32428i	0.603266	−	0.249881i
$455$	−0.405058	+	0.759460i	−0.0189894	+	0.0356040i
$456$	5.73989	+	13.8573i	0.268795	+	0.648928i
$457$	37.1558	−	9.95588i	1.73808	−	0.465716i	0.756059	−	0.654504i	$-0.227122\pi$
$457$	37.1558	−	9.95588i	1.73808	−	0.465716i	0.982018	+	0.188788i	$0.0604558\pi$
$458$	−10.8055	−	18.7156i	−0.504906	−	0.874523i
$459$	0.418358	+	4.10183i	0.0195273	+	0.191457i
$460$	−0.189008	+	0.327371i	−0.00881254	+	0.0152638i
$461$	16.3804	+	16.3804i	0.762911	+	0.762911i	0.976848	−	0.213937i	$-0.0686286\pi$
$461$	16.3804	+	16.3804i	0.762911	+	0.762911i	−0.213937	+	0.976848i	$0.568629\pi$
$462$	2.01843	+	1.44362i	0.0939057	+	0.0671635i
$463$			23.4659i			1.09055i	0.838256	+	0.545277i	$0.183576\pi$
$463$			23.4659i			1.09055i	−0.838256	+	0.545277i	$0.816424\pi$
$464$	0.0114342	−	0.0868512i	0.000530819	−	0.00403197i
$465$	1.55351	−	0.204524i	0.0720424	−	0.00948456i
$466$	−0.486676	−	3.69667i	−0.0225448	−	0.171245i
$467$	−10.8707	−	40.5700i	−0.503036	−	1.87736i	−0.479326	−	0.877637i	$-0.659119\pi$
$467$	−10.8707	−	40.5700i	−0.503036	−	1.87736i	−0.0237103	−	0.999719i	$-0.507548\pi$
$468$	1.31030	−	1.31030i	0.0605686	−	0.0605686i
$469$	−26.0675	+	4.32797i	−1.20369	+	0.199847i
$470$	0.0765098	−	0.184711i	0.00352913	−	0.00852008i
$471$	0.824729	−	6.26444i	0.0380015	−	0.288650i
$472$	26.4801	−	15.2883i	1.21885	−	0.703702i
$473$	−3.47971	+	4.53485i	−0.159997	+	0.208513i
$474$	7.27526	−	1.94940i	0.334164	−	0.0895389i
$475$	26.3196			1.20763
$476$	−10.7152	+	8.29674i	−0.491132	+	0.380281i
$477$	1.55837			0.0713529
$478$	12.8842	−	3.45230i	0.589308	−	0.157905i
$479$	−12.2124	+	15.9156i	−0.558001	+	0.727200i	−0.984127	−	0.177463i	$-0.943211\pi$
$479$	−12.2124	+	15.9156i	−0.558001	+	0.727200i	0.426127	+	0.904663i	$0.359878\pi$
$480$	−1.07074	+	0.618189i	−0.0488722	+	0.0282164i
$481$	0.386619	−	2.93666i	0.0176283	−	0.133900i
$482$	2.13417	−	5.15234i	0.0972088	−	0.234683i
$483$	−1.29714	+	3.45588i	−0.0590218	+	0.157248i
$484$	8.64288	−	8.64288i	0.392858	−	0.392858i
$485$	0.675576	+	2.52128i	0.0306763	+	0.114486i
$486$	0.113618	+	0.863016i	0.00515383	+	0.0391472i
$487$	−24.6307	+	3.24269i	−1.11612	+	0.146940i	−0.665947	−	0.745999i	$-0.731972\pi$
$487$	−24.6307	+	3.24269i	−1.11612	+	0.146940i	−0.450176	+	0.892940i	$0.648639\pi$
$488$	1.71979	−	13.0631i	0.0778511	−	0.591338i
$489$		−	4.54980i		−	0.205749i
$490$	0.736318	−	1.10630i	0.0332635	−	0.0499776i
$491$	−14.2099	−	14.2099i	−0.641285	−	0.641285i	0.309586	−	0.950871i	$-0.399809\pi$
$491$	−14.2099	−	14.2099i	−0.641285	−	0.641285i	−0.950871	+	0.309586i	$0.899809\pi$
$492$	−5.92335	+	10.2595i	−0.267045	+	0.462536i
$493$	10.0419	+	8.18308i	0.452265	+	0.368547i
$494$	3.45019	+	5.97590i	0.155231	+	0.268868i
$495$	0.226998	−	0.0608241i	0.0102028	−	0.00273384i
$496$	−0.0766589	−	0.185071i	−0.00344209	−	0.00830993i
$497$	18.0454	−	0.607070i	0.809445	−	0.0272308i
$498$	−8.08389	+	3.34846i	−0.362248	+	0.150048i
$499$	4.09338	+	5.33460i	0.183245	+	0.238809i	0.875939	−	0.482422i	$-0.160243\pi$
$499$	4.09338	+	5.33460i	0.183245	+	0.238809i	−0.692694	+	0.721232i	$0.743576\pi$
$500$	0.351971	+	2.67348i	0.0157406	+	0.119562i
$501$	17.3010	+	4.63578i	0.772951	+	0.207111i
$502$	0.459104	+	1.71340i	0.0204908	+	0.0764727i
$503$	37.9034	+	15.7001i	1.69003	+	0.700032i	0.999724	−	0.0234872i	$-0.00747689\pi$
$503$	37.9034	+	15.7001i	1.69003	+	0.700032i	0.690304	+	0.723520i	$0.257477\pi$
$504$	−5.76786	+	4.74229i	−0.256921	+	0.211238i
$505$	−2.68568	+	1.11244i	−0.119511	+	0.0495031i
$506$	1.13327	+	0.654296i	0.0503801	+	0.0290870i
$507$	−6.55943	+	8.54841i	−0.291314	+	0.379648i
$508$	0.171644	−	0.640585i	0.00761548	−	0.0284214i
$509$	−10.5680	+	18.3044i	−0.468421	+	0.811328i	−0.999349	−	0.0360888i	$-0.988510\pi$
$509$	−10.5680	+	18.3044i	−0.468421	+	0.811328i	0.530928	+	0.847417i	$0.321843\pi$
$510$	0.0228989	−	0.782428i	0.00101398	−	0.0346465i
$511$	−5.45601	+	3.39961i	−0.241360	+	0.150390i
$512$	0.223056	+	0.223056i	0.00985775	+	0.00985775i
$513$	5.26902	+	0.693679i	0.232633	+	0.0306267i
$514$	13.5168	−	7.80395i	0.596202	−	0.344217i
$515$	−2.56901	−	1.97127i	−0.113204	−	0.0868645i
$516$	−4.01184	−	5.22833i	−0.176611	−	0.230165i
$517$	1.04836	+	0.434245i	0.0461068	+	0.0190981i
$518$	−1.03445	+	4.45471i	−0.0454510	+	0.195729i
$519$	6.20576	−	6.20576i	0.272403	−	0.272403i
$520$	−0.728427	+	0.558942i	−0.0319436	+	0.0245112i
$521$	18.6503	−	2.45536i	0.817084	−	0.107571i	0.289612	−	0.957144i	$-0.406474\pi$
$521$	18.6503	−	2.45536i	0.817084	−	0.107571i	0.527471	+	0.849573i	$0.323140\pi$
$522$	2.16966	+	1.66484i	0.0949635	+	0.0728680i
$523$	−11.8654	−	6.85050i	−0.518838	−	0.299551i	0.217621	−	0.976033i	$-0.430170\pi$
$523$	−11.8654	−	6.85050i	−0.518838	−	0.299551i	−0.736459	+	0.676482i	$0.763504\pi$
$524$	0.990400	+	2.39104i	0.0432658	+	0.104453i
$525$	3.81490	+	12.5353i	0.166496	+	0.547083i
$526$	−4.38880			−0.191361
$527$	29.2429	+	4.72394i	1.27384	+	0.205778i
$528$	−0.0150219	−	0.0260188i	−0.000653746	−	0.00113232i
$529$	5.44904	−	20.3361i	0.236915	−	0.884178i
$530$	−0.293322	−	0.0386166i	−0.0127411	−	0.00167740i
$531$		−	10.8339i		−	0.470153i
$532$	7.22340	+	15.9041i	0.313174	+	0.689531i
$533$	−5.44344	+	13.1416i	−0.235782	+	0.569227i
$534$	1.36128	−	1.04455i	0.0589084	−	0.0452020i
$535$	−2.47008	−	0.661857i	−0.106791	−	0.0286146i
$536$	−27.2271	−	7.29549i	−1.17603	−	0.315117i
$537$	−19.1683	+	14.7083i	−0.827172	+	0.634711i
$538$	−0.313476	+	0.756798i	−0.0135149	+	0.0326279i
$539$	6.27902	+	4.17911i	0.270456	+	0.180007i
$540$			0.270944i			0.0116596i
$541$	22.7951	+	3.00103i	0.980036	+	0.129024i	0.603487	−	0.797373i	$-0.293777\pi$
$541$	22.7951	+	3.00103i	0.980036	+	0.129024i	0.376549	+	0.926397i	$0.377111\pi$
$542$	−5.10622	+	19.0567i	−0.219331	+	0.818554i
$543$	2.18816	+	3.79000i	0.0939028	+	0.162644i
$544$	−22.7442	+	5.38641i	−0.975150	+	0.230941i
$545$	2.44841			0.104879
$546$	−2.34606	+	2.50940i	−0.100402	+	0.107392i
$547$	−8.74839	−	21.1205i	−0.374054	−	0.903046i	−0.993054	−	0.117656i	$-0.962462\pi$
$547$	−8.74839	−	21.1205i	−0.374054	−	0.903046i	0.619000	−	0.785391i	$-0.287538\pi$
$548$	−20.9432	−	12.0916i	−0.894650	−	0.516526i
$549$	−3.70374	−	2.84198i	−0.158072	−	0.121293i
$550$	4.60533	−	0.606304i	0.196372	−	0.0258529i
$551$	13.2465	−	10.1644i	0.564322	−	0.433019i
$552$	−2.78431	+	2.78431i	−0.118508	+	0.118508i
$553$	21.9013	−	6.66529i	0.931336	−	0.283437i
$554$	13.7569	+	5.69828i	0.584473	+	0.242097i
$555$	0.263649	+	0.343595i	0.0111913	+	0.0145848i
$556$	−0.0954393	−	0.0732332i	−0.00404753	−	0.00310578i
$557$	−12.0437	+	6.95345i	−0.510309	+	0.294627i	−0.732961	−	0.680271i	$-0.761862\pi$
$557$	−12.0437	+	6.95345i	−0.510309	+	0.294627i	0.222652	+	0.974898i	$0.428529\pi$
$558$	6.20025	+	0.816279i	0.262478	+	0.0345558i
$559$	−5.59524	−	5.59524i	−0.236653	−	0.236653i
$560$	−0.0136554	+	0.00850858i	−0.000577045	+	0.000359553i
$561$	4.44081	+	0.129967i	0.187491	+	0.00548719i
$562$	13.7604	−	23.8338i	0.580449	−	1.00537i
$563$	−3.22296	+	12.0282i	−0.135831	+	0.506930i	0.864162	+	0.503214i	$0.167849\pi$
$563$	−3.22296	+	12.0282i	−0.135831	+	0.506930i	−0.999993	+	0.00371545i	$0.998817\pi$
$564$	−0.796422	+	1.03792i	−0.0335354	+	0.0437042i
$565$	1.20425	+	0.695274i	0.0506631	+	0.0292504i
$566$	18.2012	−	7.53919i	0.765054	−	0.316896i
$567$	0.433340	+	2.61002i	0.0181986	+	0.109611i
$568$	17.7943	+	7.37063i	0.746631	+	0.309265i
$569$	−12.2394	−	45.6779i	−0.513100	−	1.91492i	−0.384167	−	0.923264i	$-0.625511\pi$
$569$	−12.2394	−	45.6779i	−0.513100	−	1.91492i	−0.128934	−	0.991653i	$-0.541155\pi$
$570$	−0.974564	−	0.261134i	−0.0408200	−	0.0109377i
$571$	−0.939543	−	7.13654i	−0.0393187	−	0.298655i	−0.999794	−	0.0202903i	$-0.993541\pi$
$571$	−0.939543	−	7.13654i	−0.0393187	−	0.298655i	0.960475	−	0.278365i	$-0.0897924\pi$
$572$	−1.21550	−	1.58408i	−0.0508228	−	0.0662335i
$573$	−1.50029	+	0.621442i	−0.0626756	+	0.0259611i
$574$	10.3353	−	19.3781i	0.431388	−	0.808827i
$575$	2.64416	+	6.38357i	0.110269	+	0.266213i
$576$	−4.71253	+	1.26272i	−0.196356	+	0.0526133i
$577$	−7.37617	−	12.7759i	−0.307074	−	0.531868i	0.670647	−	0.741777i	$-0.266017\pi$
$577$	−7.37617	−	12.7759i	−0.307074	−	0.531868i	−0.977721	+	0.209909i	$0.932683\pi$
$578$	4.65935	−	14.0452i	0.193803	−	0.584203i
$579$	13.4079	−	23.2231i	0.557212	−	0.965119i
$580$	0.601921	+	0.601921i	0.0249934	+	0.0249934i
$581$	−24.2147	+	10.9979i	−1.00460	+	0.456271i
$582$			10.4177i			0.431829i
$583$	0.219176	−	1.66480i	0.00907733	−	0.0689491i
$584$	−6.79878	+	0.895076i	−0.281335	+	0.0370385i
$585$	0.0424634	+	0.322541i	0.00175564	+	0.0133354i
$586$	−0.296303	−	1.10582i	−0.0122402	−	0.0456810i
$587$	−16.8557	+	16.8557i	−0.695710	+	0.695710i	−0.963482	−	0.267772i	$-0.913713\pi$
$587$	−16.8557	+	16.8557i	−0.695710	+	0.695710i	0.267772	+	0.963482i	$0.413713\pi$
$588$	−6.52767	+	5.74552i	−0.269197	+	0.236941i
$589$	14.6114	−	35.2750i	0.602051	−	1.45348i
$590$	−0.268467	+	2.03921i	−0.0110526	+	0.0839528i
$591$	−8.14897	+	4.70481i	−0.335204	+	0.193530i
$592$	0.0337057	−	0.0439262i	0.00138530	−	0.00180535i
$593$	−5.59128	+	1.49818i	−0.229606	+	0.0615228i	−0.371788	−	0.928318i	$-0.621255\pi$
$593$	−5.59128	+	1.49818i	−0.229606	+	0.0615228i	0.142181	+	0.989841i	$0.454588\pi$
$594$	0.937938			0.0384841
$595$	−0.0103985	−	2.37917i	−0.000426297	−	0.0975363i
$596$	−16.2843			−0.667031
$597$	0.443492	−	0.118833i	0.0181509	−	0.00486353i
$598$	−1.10278	+	1.43717i	−0.0450960	+	0.0587703i
$599$	35.8128	−	20.6765i	1.46327	−	0.844821i	0.464112	−	0.885777i	$-0.346374\pi$
$599$	35.8128	−	20.6765i	1.46327	−	0.844821i	0.999161	+	0.0409560i	$0.0130404\pi$
$600$	−1.82440	+	13.8577i	−0.0744806	+	0.565737i
$601$	−4.24262	+	10.2426i	−0.173060	+	0.417804i	−0.986482	−	0.163870i	$-0.947602\pi$
$601$	−4.24262	+	10.2426i	−0.173060	+	0.417804i	0.813422	+	0.581674i	$0.197602\pi$
$602$	7.75904	+	9.43701i	0.316235	+	0.384624i
$603$	−7.06220	+	7.06220i	−0.287595	+	0.287595i
$604$	−6.60387	−	24.6460i	−0.268708	−	1.00283i
$605$	0.280093	+	2.12752i	0.0113874	+	0.0864959i
$606$	−11.5028	+	1.51437i	−0.467268	+	0.0615170i
$607$	−2.13178	+	16.1925i	−0.0865265	+	0.657234i	0.892137	+	0.451765i	$0.149205\pi$
$607$	−2.13178	+	16.1925i	−0.0865265	+	0.657234i	−0.978664	+	0.205469i	$0.934128\pi$
$608$			30.1271i			1.22181i
$609$	6.76104	+	4.83565i	0.273971	+	0.195950i
$610$	0.626708	+	0.626708i	0.0253747	+	0.0253747i
$611$	−0.785421	+	1.36039i	−0.0317748	+	0.0550355i
$612$	−1.46987	+	4.90668i	−0.0594159	+	0.198341i
$613$	6.87929	+	11.9153i	0.277852	+	0.481254i	0.970851	−	0.239685i	$-0.0770442\pi$
$613$	6.87929	+	11.9153i	0.277852	+	0.481254i	−0.692999	+	0.720939i	$0.743711\pi$
$614$	−18.3157	+	4.90767i	−0.739161	+	0.198057i
$615$	−0.795917	−	1.92151i	−0.0320945	−	0.0774829i
$616$	4.25496	+	6.82877i	0.171437	+	0.275139i
$617$	12.1219	−	5.02105i	0.488009	−	0.202140i	−0.125091	−	0.992145i	$-0.539922\pi$
$617$	12.1219	−	5.02105i	0.488009	−	0.202140i	0.613100	+	0.790005i	$0.289922\pi$
$618$	−7.86757	−	10.2532i	−0.316480	−	0.412445i
$619$	1.11152	+	8.44282i	0.0446757	+	0.339345i	0.999156	+	0.0410721i	$0.0130773\pi$
$619$	1.11152	+	8.44282i	0.0446757	+	0.339345i	−0.954481	+	0.298273i	$0.903589\pi$
$620$	1.88024	+	0.503810i	0.0755124	+	0.0202335i
$621$	0.361099	+	1.34764i	0.0144904	+	0.0540789i
$622$	24.9953	+	10.3534i	1.00222	+	0.415134i
$623$	4.02850	−	3.31220i	0.161398	−	0.132700i
$624$	0.0384246	−	0.0159160i	0.00153821	−	0.000637149i
$625$	21.0347	+	12.1444i	0.841387	+	0.485775i
$626$	11.7091	−	15.2596i	0.467989	−	0.609896i
$627$	1.48211	−	5.53132i	0.0591898	−	0.220899i
$628$	3.92472	−	6.79781i	0.156613	−	0.271262i
$629$	2.91058	+	7.65264i	0.116052	+	0.305131i
$630$	−0.0168882	−	0.502006i	−0.000672841	−	0.0200004i
$631$	8.03130	+	8.03130i	0.319721	+	0.319721i	0.848660	−	0.528939i	$-0.177410\pi$
$631$	8.03130	+	8.03130i	0.319721	+	0.319721i	−0.528939	+	0.848660i	$0.677410\pi$
$632$	24.2117	+	3.18753i	0.963091	+	0.126793i
$633$	−12.2358	+	7.06437i	−0.486331	+	0.280783i
$634$	−9.59134	−	7.35969i	−0.380921	−	0.292291i
$635$	0.0708779	+	0.0923699i	0.00281271	+	0.00366559i
$636$	1.78859	+	0.740858i	0.0709222	+	0.0293769i
$637$	−6.87030	+	7.86270i	−0.272211	+	0.311532i
$638$	2.08369	−	2.08369i	0.0824942	−	0.0824942i
$639$	5.41413	−	4.15441i	0.214180	−	0.164346i
$640$	−1.53330	+	0.201863i	−0.0606091	+	0.00797934i
$641$	−16.2504	−	12.4693i	−0.641851	−	0.492509i	0.235805	−	0.971800i	$-0.424227\pi$
$641$	−16.2504	−	12.4693i	−0.641851	−	0.492509i	−0.877656	+	0.479291i	$0.840894\pi$
$642$	−8.83881	−	5.10309i	−0.348840	−	0.201403i
$643$	−6.47266	−	15.6264i	−0.255257	−	0.616245i	0.743356	−	0.668896i	$-0.233233\pi$
$643$	−6.47266	−	15.6264i	−0.255257	−	0.616245i	−0.998613	+	0.0526512i	$0.983233\pi$
$644$	−3.13171	+	3.34975i	−0.123407	+	0.131999i
$645$	1.15699			0.0455562
$646$	−16.2323	−	10.0160i	−0.638650	−	0.394075i
$647$	7.46210	+	12.9247i	0.293365	+	0.508124i	0.974603	−	0.223938i	$-0.0718914\pi$
$647$	7.46210	+	12.9247i	0.293365	+	0.508124i	−0.681238	+	0.732062i	$0.738558\pi$
$648$	−0.730464	+	2.72613i	−0.0286953	+	0.107092i
$649$	−11.5739	−	1.52373i	−0.454315	−	0.0598117i
$650$			6.43028i			0.252216i
$651$	18.9183	+	1.84603i	0.741466	+	0.0723515i
$652$	2.16300	−	5.22195i	0.0847097	−	0.204507i
$653$	−4.13475	+	3.17270i	−0.161805	+	0.124157i	−0.686490	−	0.727139i	$-0.740850\pi$
$653$	−4.13475	+	3.17270i	−0.161805	+	0.124157i	0.524685	+	0.851296i	$0.324183\pi$
$654$	9.43895	+	2.52916i	0.369092	+	0.0988979i
$655$	−0.438880	−	0.117598i	−0.0171485	−	0.00459492i
$656$	−0.210946	+	0.161865i	−0.00823607	+	0.00631976i
$657$	−0.929820	+	2.24479i	−0.0362758	+	0.0875774i
$658$	1.41092	−	1.97270i	0.0550033	−	0.0769038i
$659$		−	35.9750i		−	1.40139i	−0.713463	−	0.700693i	$-0.752874\pi$
$659$		−	35.9750i		−	1.40139i	0.713463	−	0.700693i	$-0.247126\pi$
$660$	0.289449	+	0.0381067i	0.0112668	+	0.00148330i
$661$	6.67450	−	24.9096i	0.259608	−	0.968870i	−0.705861	−	0.708351i	$-0.749440\pi$
$661$	6.67450	−	24.9096i	0.259608	−	0.968870i	0.965469	−	0.260519i	$-0.0838938\pi$
$662$	−5.00638	−	8.67130i	−0.194578	−	0.337019i
$663$	−0.980789	+	6.07144i	−0.0380907	+	0.235795i
$664$	−28.3699			−1.10097
$665$	−2.98718	−	0.693666i	−0.115838	−	0.0268992i
$666$	0.661476	+	1.59694i	0.0256317	+	0.0618804i
$667$	3.79608	+	2.19167i	0.146985	+	0.0848617i
$668$	17.6530	+	13.5456i	0.683014	+	0.524095i
$669$	−21.9558	+	2.89054i	−0.848862	+	0.111755i
$670$	1.50428	−	1.15427i	0.0581153	−	0.0445934i
$671$	−3.55699	+	3.55699i	−0.137316	+	0.137316i
$672$	−14.3486	+	4.36678i	−0.553511	+	0.168452i
$673$	−30.2034	−	12.5107i	−1.16426	−	0.482250i	−0.284966	−	0.958538i	$-0.591982\pi$
$673$	−30.2034	−	12.5107i	−1.16426	−	0.482250i	−0.879290	+	0.476287i	$0.841982\pi$
$674$	8.48373	+	11.0562i	0.326781	+	0.425869i
$675$	3.92903	+	3.01485i	0.151228	+	0.116042i
$676$	−11.5924	+	6.69288i	−0.445862	+	0.257419i
$677$	−27.7828	−	3.65768i	−1.06778	−	0.140576i	−0.423906	−	0.905706i	$-0.639341\pi$
$677$	−27.7828	−	3.65768i	−1.06778	−	0.140576i	−0.643876	+	0.765130i	$0.722675\pi$
$678$	3.92433	+	3.92433i	0.150713	+	0.150713i
$679$	1.06463	+	31.6465i	0.0408568	+	1.21448i
$680$	1.03941	−	2.31534i	0.0398595	−	0.0887893i
$681$	7.99174	−	13.8421i	0.306244	−	0.530430i
$682$	1.74406	−	6.50891i	0.0667834	−	0.249239i
$683$	24.1136	−	31.4254i	0.922681	−	1.20246i	−0.0562808	−	0.998415i	$-0.517924\pi$
$683$	24.1136	−	31.4254i	0.922681	−	1.20246i	0.978961	−	0.204046i	$-0.0654091\pi$
$684$	5.71763	+	3.30107i	0.218619	+	0.126220i
$685$	3.92247	−	1.62474i	0.149870	−	0.0620781i
$686$	11.7364	−	11.0522i	0.448096	−	0.421975i
$687$	−22.9371	−	9.50085i	−0.875105	−	0.362480i
$688$	−0.0382826	−	0.142872i	−0.00145951	−	0.00544696i
$689$	2.24531	+	0.601628i	0.0855394	+	0.0229202i
$690$	−0.0345727	−	0.262606i	−0.00131616	−	0.00999723i
$691$	6.81346	+	8.87948i	0.259196	+	0.337791i	0.904765	−	0.425911i	$-0.140046\pi$
$691$	6.81346	+	8.87948i	0.259196	+	0.337791i	−0.645569	+	0.763702i	$0.723380\pi$
$692$	10.0728	−	4.17229i	0.382910	−	0.158607i
$693$	2.84923	−	0.0958519i	0.108233	−	0.00364111i
$694$	7.67804	+	18.5364i	0.291454	+	0.703633i
$695$	0.0204002	−	0.00546623i	0.000773826	−	0.000207346i
$696$	4.43351	+	7.67906i	0.168052	+	0.291074i
$697$	−3.98952	−	39.1156i	−0.151114	−	1.48161i
$698$	−8.19541	+	14.1949i	−0.310201	+	0.537284i
$699$	−3.02884	−	3.02884i	−0.114561	−	0.114561i
$700$	−1.58085	+	16.2007i	−0.0597505	+	0.612329i
$701$			32.2435i			1.21782i	0.793240	+	0.608909i	$0.208393\pi$
$701$			32.2435i			1.21782i	−0.793240	+	0.608909i	$0.791607\pi$
$702$	−0.169476	+	1.28730i	−0.00639647	+	0.0485861i
$703$	10.4629	−	1.37747i	0.394617	−	0.0519523i
$704$	0.686170	+	5.21198i	0.0258610	+	0.196434i
$705$	−0.0594461	−	0.221856i	−0.00223887	−	0.00835557i
$706$	2.47808	−	2.47808i	0.0932639	−	0.0932639i
$707$	−34.7879	+	5.77580i	−1.30833	+	0.217221i
$708$	5.15052	−	12.4344i	0.193568	−	0.467315i
$709$	−4.43143	+	33.6600i	−0.166426	+	1.26413i	0.680631	+	0.732627i	$0.261706\pi$
$709$	−4.43143	+	33.6600i	−0.166426	+	1.26413i	−0.847056	+	0.531503i	$0.821627\pi$
$710$	−1.12201	+	0.647796i	−0.0421085	+	0.0243113i
$711$	5.26746	−	6.86469i	0.197545	−	0.257446i
$712$	5.37375	−	1.43989i	0.201390	−	0.0539623i
$713$	10.0235			0.375384
$714$	2.41754	−	9.18273i	0.0904741	−	0.343655i
$715$	0.350542			0.0131095
$716$	−28.9924	+	7.76849i	−1.08350	+	0.290322i
$717$	9.32844	−	12.1571i	0.348377	−	0.454014i
$718$	−8.95802	+	5.17192i	−0.334310	+	0.193014i
$719$	−2.25309	+	17.1139i	−0.0840260	+	0.638241i	0.896670	+	0.442700i	$0.145979\pi$
$719$	−2.25309	+	17.1139i	−0.0840260	+	0.638241i	−0.980696	+	0.195540i	$0.937354\pi$
$720$	−0.00232717	+	0.00561828i	−8.67284e−5	+	0.000209381i
$721$	−24.9476	−	30.3428i	−0.929097	−	1.13002i
$722$	−5.68960	+	5.68960i	−0.211745	+	0.211745i
$723$	−1.65819	−	6.18847i	−0.0616689	−	0.230152i
$724$	0.709627	+	5.39015i	0.0263731	+	0.200324i
$725$	15.4263	−	2.03091i	0.572919	−	0.0754262i
$726$	−1.11789	+	8.49118i	−0.0414886	+	0.315137i
$727$			22.9334i			0.850554i	0.905063	+	0.425277i	$0.139823\pi$
$727$			22.9334i			0.850554i	−0.905063	+	0.425277i	$0.860177\pi$
$728$	−10.1412	+	4.60596i	−0.375857	+	0.170708i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	0.230640	−	0.399481i	0.00853638	−	0.0147854i
$731$	20.9525	+	6.27663i	0.774956	+	0.232149i
$732$	−2.89980	−	5.02261i	−0.107180	−	0.185641i
$733$	−23.1803	+	6.21114i	−0.856184	+	0.229414i	−0.660104	−	0.751174i	$-0.729488\pi$
$733$	−23.1803	+	6.21114i	−0.856184	+	0.229414i	−0.196080	+	0.980588i	$0.562821\pi$
$734$	−0.0670334	−	0.161833i	−0.00247425	−	0.00597337i
$735$	−0.102604	−	1.52325i	−0.00378462	−	0.0561858i
$736$	−7.30704	+	3.02667i	−0.269341	+	0.111565i
$737$	6.55128	+	8.53779i	0.241319	+	0.314494i
$738$	−1.08348	−	8.22984i	−0.0398834	−	0.302945i
$739$	30.9774	+	8.30038i	1.13952	+	0.305334i	0.778759	−	0.627323i	$-0.215849\pi$
$739$	30.9774	+	8.30038i	1.13952	+	0.305334i	0.360764	+	0.932657i	$0.382516\pi$
$740$	0.139252	+	0.519694i	0.00511899	+	0.0191043i
$741$	7.32382	+	3.03362i	0.269047	+	0.111443i
$742$	−3.36008	−	1.26118i	−0.123353	−	0.0462994i
$743$	−47.7801	+	19.7912i	−1.75288	+	0.726067i	−0.755389	+	0.655276i	$0.772552\pi$
$743$	−47.7801	+	19.7912i	−1.75288	+	0.726067i	−0.997491	+	0.0707906i	$0.977448\pi$
$744$	17.5600	+	10.1383i	0.643780	+	0.371686i
$745$	1.74039	−	2.26812i	0.0637630	−	0.0830976i
$746$	−0.718957	+	2.68318i	−0.0263229	+	0.0982384i
$747$	−5.02603	+	8.70534i	−0.183893	+	0.318512i
$748$	5.03507	+	2.26035i	0.184100	+	0.0826466i
$749$	−27.3717	−	14.5987i	−1.00014	−	0.533424i
$750$	−1.33604	−	1.33604i	−0.0487853	−	0.0487853i
$751$	−7.33092	−	0.965134i	−0.267509	−	0.0352182i	−0.00442166	−	0.999990i	$-0.501407\pi$
$751$	−7.33092	−	0.965134i	−0.267509	−	0.0352182i	−0.263088	+	0.964772i	$0.584741\pi$
$752$	−0.0254293	+	0.0146816i	−0.000927312	+	0.000535384i
$753$	1.61671	+	1.24054i	0.0589160	+	0.0452079i
$754$	2.48333	+	3.23633i	0.0904374	+	0.117860i
$755$	4.13855	+	1.71425i	0.150617	+	0.0623878i
$756$	−0.743461	+	3.20161i	−0.0270394	+	0.116442i
$757$	1.99870	−	1.99870i	0.0726441	−	0.0726441i	−0.669851	−	0.742495i	$-0.733642\pi$
$757$	1.99870	−	1.99870i	0.0726441	−	0.0726441i	0.742495	+	0.669851i	$0.233642\pi$
$758$	15.8618	−	12.1712i	0.576126	−	0.442077i
$759$	1.49047	−	0.196224i	0.0541005	−	0.00712247i
$760$	−2.59529	−	1.99144i	−0.0941410	−	0.0722370i
$761$	32.4209	+	18.7182i	1.17525	+	0.678534i	0.954912	−	0.296889i	$-0.0959491\pi$
$761$	32.4209	+	18.7182i	1.17525	+	0.678534i	0.220343	+	0.975422i	$0.429282\pi$
$762$	0.177827	+	0.429313i	0.00644201	+	0.0155524i
$763$	28.9317	+	6.71836i	1.04740	+	0.243221i
$764$	−2.01737			−0.0729858
$765$	−0.526323	−	0.729131i	−0.0190293	−	0.0263618i
$766$	−7.92865	−	13.7328i	−0.286474	−	0.496187i
$767$	4.18258	−	15.6096i	0.151024	−	0.563630i
$768$	−15.7937	−	2.07928i	−0.569905	−	0.0750294i
$769$			20.5694i			0.741751i	0.928683	+	0.370876i	$0.120942\pi$
$769$			20.5694i			0.741751i	−0.928683	+	0.370876i	$0.879058\pi$
$770$	−0.538667	−	0.0525626i	−0.0194122	−	0.00189423i
$771$	6.86173	−	16.5657i	0.247119	−	0.596599i
$772$	26.4290	−	20.2797i	0.951200	−	0.729882i
$773$	−42.8270	−	11.4755i	−1.54038	−	0.412744i	−0.613992	−	0.789313i	$-0.710437\pi$
$773$	−42.8270	−	11.4755i	−1.54038	−	0.412744i	−0.926389	+	0.376569i	$0.877104\pi$
$774$	4.46032	+	1.19514i	0.160323	+	0.0429584i
$775$	28.2277	−	21.6599i	1.01397	−	0.778046i
$776$	−12.9260	+	31.2062i	−0.464017	+	1.12024i
$777$	2.17260	+	4.78353i	0.0779417	+	0.171608i
$778$			2.30167i			0.0825189i
$779$	−50.2461	−	6.61502i	−1.80025	−	0.237008i
$780$	−0.104601	+	0.390378i	−0.00374533	+	0.0139778i
$781$	−3.67668	−	6.36820i	−0.131562	−	0.227872i
$782$	0.798536	−	4.94323i	0.0285556	−	0.176770i
$783$	3.14177			0.112278
$784$	−0.184706	+	0.0630718i	−0.00659665	+	0.00225257i
$785$	0.527362	+	1.27316i	0.0188224	+	0.0454412i
$786$	−1.57046	−	0.906707i	−0.0560165	−	0.0323412i
$787$	22.6104	+	17.3496i	0.805974	+	0.618446i	0.927365	−	0.374159i	$-0.122069\pi$
$787$	22.6104	+	17.3496i	0.805974	+	0.618446i	−0.121390	+	0.992605i	$0.538735\pi$
$788$	−11.5895	+	1.52579i	−0.412859	+	0.0543539i
$789$	−4.00002	+	3.06932i	−0.142405	+	0.109271i
$790$	−1.16157	+	1.16157i	−0.0413268	+	0.0413268i
$791$	12.3222	+	11.5201i	0.438127	+	0.409608i
$792$	2.80958	+	1.16377i	0.0998342	+	0.0413527i
$793$	−4.23919	−	5.52462i	−0.150538	−	0.196185i
$794$	−12.8970	−	9.89625i	−0.457699	−	0.351205i
$795$	−0.294345	+	0.169940i	−0.0104393	+	0.00602716i
$796$	0.565504	+	0.0744500i	0.0200437	+	0.00263881i
$797$	−12.4444	−	12.4444i	−0.440802	−	0.440802i	0.451479	−	0.892282i	$-0.350896\pi$
$797$	−12.4444	−	12.4444i	−0.440802	−	0.440802i	−0.892282	+	0.451479i	$0.850896\pi$
$798$	−10.7994	−	5.75986i	−0.382295	−	0.203897i
$799$	0.127022	−	4.34020i	0.00449372	−	0.153545i
$800$	−14.0373	+	24.3134i	−0.496295	+	0.859608i
$801$	0.510185	−	1.90403i	0.0180265	−	0.0672758i
$802$	4.01330	−	5.23024i	0.141715	−	0.184686i
$803$	2.26733	+	1.30904i	0.0800122	+	0.0461950i
$804$	−11.4629	+	4.74809i	−0.404266	+	0.167452i
$805$	−0.131860	−	0.794200i	−0.00464747	−	0.0279919i
$806$	8.61822	+	3.56978i	0.303564	+	0.125740i
$807$	0.243563	+	0.908988i	0.00857381	+	0.0319979i
$808$	−36.3354	−	9.73604i	−1.27827	−	0.342513i
$809$	2.95415	+	22.4390i	0.103862	+	0.788914i	0.961528	+	0.274706i	$0.0885806\pi$
$809$	2.95415	+	22.4390i	0.103862	+	0.788914i	−0.857666	+	0.514208i	$0.828086\pi$
$810$	−0.115572	−	0.150616i	−0.00406079	−	0.00529212i
$811$	−34.7562	+	14.3965i	−1.22046	+	0.505529i	−0.897555	−	0.440903i	$-0.854658\pi$
$811$	−34.7562	+	14.3965i	−1.22046	+	0.505529i	−0.322901	+	0.946433i	$0.604658\pi$
$812$	5.46095	+	8.76426i	0.191642	+	0.307565i
$813$	8.67346	+	20.9396i	0.304192	+	0.734383i
$814$	1.79905	−	0.482053i	0.0630565	−	0.0168959i
$815$	0.496156	+	0.859367i	0.0173796	+	0.0301023i
$816$	−0.0726230	+	0.0891197i	−0.00254232	+	0.00311981i
$817$	14.0962	−	24.4154i	0.493165	−	0.854187i
$818$	−4.09705	−	4.09705i	−0.143250	−	0.143250i
$819$	−0.383273	+	3.92783i	−0.0133927	+	0.137249i
$820$		−	2.58376i		−	0.0902289i
$821$	6.92636	−	52.6109i	0.241732	−	1.83613i	−0.253454	−	0.967347i	$-0.581567\pi$
$821$	6.92636	−	52.6109i	0.241732	−	1.83613i	0.495186	−	0.868787i	$-0.335100\pi$
$822$	16.7999	−	2.21175i	0.585965	−	0.0771437i
$823$	2.12473	+	16.1389i	0.0740635	+	0.562568i	0.987738	+	0.156121i	$0.0498990\pi$
$823$	2.12473	+	16.1389i	0.0740635	+	0.562568i	−0.913674	+	0.406447i	$0.866768\pi$
$824$	−10.8453	−	40.4753i	−0.377815	−	1.41002i
$825$	3.77335	−	3.77335i	0.131371	−	0.131371i
$826$	−8.76785	+	23.3596i	−0.305072	+	0.812785i
$827$	3.35156	−	8.09138i	0.116545	−	0.281365i	−0.854833	−	0.518903i	$-0.826341\pi$
$827$	3.35156	−	8.09138i	0.116545	−	0.281365i	0.971378	+	0.237538i	$0.0763405\pi$
$828$	−0.226231	+	1.71839i	−0.00786207	+	0.0597183i
$829$	−22.8359	+	13.1843i	−0.793124	+	0.457910i	−0.841061	−	0.540940i	$-0.818069\pi$
$829$	−22.8359	+	13.1843i	−0.793124	+	0.457910i	0.0479371	+	0.998850i	$0.484735\pi$
$830$	1.16174	−	1.51401i	0.0403245	−	0.0525519i
$831$	16.5233	−	4.42741i	0.573188	−	0.153585i
$832$	−7.27733			−0.252296
$833$	6.40547	−	28.1420i	0.221937	−	0.975061i
$834$	0.0842920			0.00291879
$835$	−3.77334	+	1.01106i	−0.130582	+	0.0349893i
$836$	4.33068	−	5.64385i	0.149780	−	0.195197i
$837$	6.22187	−	3.59220i	0.215059	−	0.124165i
$838$	−3.10499	+	23.5847i	−0.107260	+	0.814721i
$839$	3.73445	−	9.01576i	0.128927	−	0.311258i	−0.846213	−	0.532844i	$-0.821123\pi$
$839$	3.73445	−	9.01576i	0.128927	−	0.311258i	0.975141	+	0.221586i	$0.0711232\pi$
$840$	0.572287	−	1.52471i	0.0197458	−	0.0526075i
$841$	−13.5264	+	13.5264i	−0.466429	+	0.466429i
$842$	4.79256	+	17.8861i	0.165162	+	0.616394i
$843$	−4.12676	−	31.3459i	−0.142133	−	1.07961i
$844$	−17.4019	+	2.29100i	−0.598998	+	0.0788595i
$845$	0.306741	−	2.32993i	0.0105522	−	0.0801520i
$846$		−	0.916689i		−	0.0315164i
$847$	−2.52811	+	25.9084i	−0.0868670	+	0.890223i
$848$	0.0307248	+	0.0307248i	0.00105509	+	0.00105509i
$849$	11.3163	−	19.6004i	0.388375	−	0.672685i
$850$	−8.43306	−	15.6464i	−0.289252	−	0.536668i
$851$	1.38524	+	2.39930i	0.0474853	+	0.0822470i
$852$	8.18899	−	2.19423i	0.280550	−	0.0751732i
$853$	−14.2568	−	34.4190i	−0.488144	−	1.17848i	−0.955653	−	0.294496i	$-0.904848\pi$
$853$	−14.2568	−	34.4190i	−0.488144	−	1.17848i	0.467509	−	0.883988i	$-0.345152\pi$
$854$	5.68583	+	9.12516i	0.194565	+	0.312257i
$855$	−1.07086	+	0.443564i	−0.0366226	+	0.0151696i
$856$	−20.1448	−	26.2532i	−0.688534	−	0.897315i
$857$	2.30319	+	17.4945i	0.0786756	+	0.597601i	0.984685	+	0.174343i	$0.0557802\pi$
$857$	2.30319	+	17.4945i	0.0786756	+	0.597601i	−0.906009	+	0.423258i	$0.860887\pi$
$858$	1.35138	+	0.362103i	0.0461355	+	0.0123620i
$859$	11.5196	+	42.9916i	0.393042	+	1.46685i	0.825089	+	0.565003i	$0.191125\pi$
$859$	11.5196	+	42.9916i	0.393042	+	1.46685i	−0.432046	+	0.901851i	$0.642208\pi$
$860$	1.32791	+	0.550037i	0.0452812	+	0.0187561i
$861$	−4.13239	−	24.8895i	−0.140831	−	0.848233i
$862$	23.0693	−	9.55564i	0.785745	−	0.325466i
$863$	−17.5436	−	10.1288i	−0.597192	−	0.344789i	0.170744	−	0.985315i	$-0.445383\pi$
$863$	−17.5436	−	10.1288i	−0.597192	−	0.344789i	−0.767936	+	0.640527i	$0.778716\pi$
$864$	−3.45099	+	4.49741i	−0.117405	+	0.153005i
$865$	−0.495407	+	1.84888i	−0.0168443	+	0.0628639i
$866$	−6.76714	+	11.7210i	−0.229957	+	0.398297i
$867$	−5.57596	−	16.0595i	−0.189369	−	0.545410i
$868$	20.8355	+	11.1126i	0.707202	+	0.377186i
$869$	−6.59270	−	6.59270i	−0.223642	−	0.223642i
$870$	−0.591356	−	0.0778535i	−0.0200489	−	0.00263948i
$871$	−12.9017	+	7.44880i	−0.437158	+	0.252393i
$872$	25.1362	+	19.2877i	0.851218	+	0.653162i
$873$	7.28567	+	9.49487i	0.246583	+	0.321353i
$874$	−5.96289	−	2.46991i	−0.201698	−	0.0835459i
$875$	−4.19511	−	3.92203i	−0.141820	−	0.132589i
$876$	−2.13437	+	2.13437i	−0.0721135	+	0.0721135i
$877$	−26.9902	+	20.7103i	−0.911394	+	0.699337i	−0.954016	−	0.299754i	$-0.903095\pi$
$877$	−26.9902	+	20.7103i	−0.911394	+	0.699337i	0.0426228	+	0.999091i	$0.486429\pi$
$878$	−19.9575	+	2.62745i	−0.673532	+	0.0886722i
$879$	−1.04341	−	0.800640i	−0.0351935	−	0.0270049i
$880$	0.00567469	+	0.00327629i	0.000191294	+	0.000110444i
$881$	−8.08150	−	19.5105i	−0.272273	−	0.657324i	0.727307	−	0.686312i	$-0.240772\pi$
$881$	−8.08150	−	19.5105i	−0.272273	−	0.657324i	−0.999580	+	0.0289880i	$0.990772\pi$
$882$	1.17793	−	5.97830i	0.0396629	−	0.201300i
$883$	−33.2848			−1.12012			−0.560061	−	0.828452i	$-0.689222\pi$
$883$	−33.2848			−1.12012			−0.560061	+	0.828452i	$0.689222\pi$
$884$	−4.01208	+	6.50210i	−0.134941	+	0.218689i
$885$	1.18144	+	2.04632i	0.0397137	+	0.0687862i
$886$	1.47949	−	5.52152i	0.0497044	−	0.185499i
$887$	−1.85366	−	0.244039i	−0.0622399	−	0.00819404i	0.0993419	−	0.995053i	$-0.468326\pi$
$887$	−1.85366	−	0.244039i	−0.0622399	−	0.00819404i	−0.161582	+	0.986859i	$0.551660\pi$
$888$			5.60437i			0.188070i
$889$	0.584070	+	1.28598i	0.0195891	+	0.0431303i
$890$	−0.143211	+	0.345742i	−0.00480045	+	0.0115893i
$891$	0.854851	−	0.655950i	0.0286386	−	0.0219752i
$892$	−26.5735	−	7.12036i	−0.889748	−	0.238407i
$893$	−5.40600	−	1.44853i	−0.180905	−	0.0484733i
$894$	9.05235	−	6.94611i	0.302756	−	0.232313i
$895$	2.01656	−	4.86841i	0.0674062	−	0.162733i
$896$	−18.6722	−	1.82201i	−0.623794	−	0.0608691i
$897$			2.08109i			0.0694856i
$898$	−13.3632	−	1.75930i	−0.445935	−	0.0587084i
$899$	5.84200	−	21.8026i	0.194842	−	0.727159i
$900$	3.07619	+	5.32812i	0.102540	+	0.177604i
$901$	−6.25238	+	1.48072i	−0.208297	+	0.0493301i
$902$	−8.94431			−0.297813
$903$	13.6715	+	3.17473i	0.454960	+	0.105648i
$904$	6.88609	+	16.6245i	0.229028	+	0.552922i
$905$	−0.826598	−	0.477237i	−0.0274770	−	0.0158639i
$906$	14.1839	+	10.8837i	0.471228	+	0.361586i
$907$	−14.0966	+	1.85585i	−0.468070	+	0.0616226i	−0.360873	−	0.932615i	$-0.617521\pi$
$907$	−14.0966	+	1.85585i	−0.468070	+	0.0616226i	−0.107198	+	0.994238i	$0.534188\pi$
$908$	15.7530	−	12.0877i	0.522780	−	0.401144i
$909$	−9.42472	+	9.42472i	−0.312598	+	0.312598i
$910$	0.169473	−	0.729813i	0.00561798	−	0.0241931i
$911$	−33.5613	−	13.9015i	−1.11194	−	0.460579i	−0.250332	−	0.968160i	$-0.580540\pi$
$911$	−33.5613	−	13.9015i	−1.11194	−	0.460579i	−0.861604	+	0.507581i	$0.830540\pi$
$912$	0.0902071	+	0.117560i	0.00298705	+	0.00389281i
$913$	8.59301	+	6.59365i	0.284387	+	0.218218i
$914$	−28.9977	+	16.7419i	−0.959160	+	0.553771i
$915$	1.00948	+	0.132901i	0.0333724	+	0.00439356i
$916$	−21.8088	−	21.8088i	−0.720584	−	0.720584i
$917$	−4.86334	−	2.59386i	−0.160602	−	0.0856569i
$918$	−1.27587	−	3.35457i	−0.0421099	−	0.110717i
$919$	−2.80953	+	4.86625i	−0.0926779	+	0.160523i	−0.908637	−	0.417587i	$-0.862876\pi$
$919$	−2.80953	+	4.86625i	−0.0926779	+	0.160523i	0.815959	+	0.578109i	$0.196209\pi$
$920$	0.222272	−	0.829530i	0.00732808	−	0.0273488i
$921$	−13.2610	+	17.2821i	−0.436965	+	0.569463i
$922$	−17.4631	−	10.0823i	−0.575115	−	0.332043i
$923$	9.40457	−	3.89550i	0.309555	−	0.128222i
$924$	3.31571	+	1.24453i	0.109079	+	0.0409419i
$925$	9.08570	+	3.76342i	0.298736	+	0.123740i
$926$	−5.28670	−	19.7302i	−0.173732	−	0.648375i
$927$	−14.3413	−	3.84273i	−0.471028	−	0.126212i
$928$	2.32471	+	17.6579i	0.0763123	+	0.579650i
$929$	5.77932	+	7.53176i	0.189613	+	0.247109i	0.878480	−	0.477779i	$-0.158558\pi$
$929$	5.77932	+	7.53176i	0.189613	+	0.247109i	−0.688867	+	0.724888i	$0.741891\pi$
$930$	−1.26012	+	0.521958i	−0.0413209	+	0.0171157i
$931$	−33.3946	−	16.3934i	−1.09446	−	0.537272i
$932$	−2.03637	−	4.91622i	−0.0667034	−	0.161036i
$933$	30.0218	−	8.04432i	0.982870	−	0.263359i
$934$	18.2802	+	31.6623i	0.598147	+	1.03602i
$935$	−0.852953	+	0.459722i	−0.0278946	+	0.0150345i
$936$	−2.10491	+	3.64581i	−0.0688012	+	0.119167i
$937$	13.7900	+	13.7900i	0.450499	+	0.450499i	0.895520	−	0.445021i	$-0.146804\pi$
$937$	13.7900	+	13.7900i	0.450499	+	0.450499i	−0.445021	+	0.895520i	$0.646804\pi$
$938$	20.9426	−	9.51178i	0.683799	−	0.310571i
$939$		−	22.0966i		−	0.721096i
$940$	0.0372434	−	0.282892i	0.00121474	−	0.00922690i
$941$	49.5007	−	6.51689i	1.61368	−	0.212445i	0.730984	−	0.682395i	$-0.239061\pi$
$941$	49.5007	−	6.51689i	1.61368	−	0.212445i	0.882693	+	0.469950i	$0.155728\pi$
$942$	0.717896	+	5.45296i	0.0233903	+	0.177667i
$943$	−3.44349	−	12.8513i	−0.112135	−	0.418495i
$944$	0.213602	−	0.213602i	0.00695214	−	0.00695214i
$945$	−0.366472	−	0.445725i	−0.0119213	−	0.0144994i
$946$	1.90408	−	4.59686i	0.0619071	−	0.149457i
$947$	0.320355	−	2.43334i	0.0104101	−	0.0790729i	−0.985451	−	0.169959i	$-0.945637\pi$
$947$	0.320355	−	2.43334i	0.0104101	−	0.0790729i	0.995861	+	0.0908859i	$0.0289699\pi$
$948$	9.30914	−	5.37463i	0.302347	−	0.174560i
$949$	−2.20632	+	2.87533i	−0.0716201	+	0.0933371i
$950$	−22.1296	+	5.92961i	−0.717979	+	0.192382i
$951$	−13.8887			−0.450373
$952$	18.6354	−	24.5071i	0.603976	−	0.794281i
$953$	33.7181			1.09224			0.546119	−	0.837708i	$-0.316105\pi$
$953$	33.7181			1.09224			0.546119	+	0.837708i	$0.316105\pi$
$954$	−1.31028	+	0.351089i	−0.0424220	+	0.0113669i
$955$	0.215607	−	0.280985i	0.00697688	−	0.00909245i
$956$	16.4861	−	9.51823i	0.533197	−	0.307842i
$957$	0.441872	−	3.35635i	0.0142837	−	0.108495i
$958$	6.68260	−	16.1332i	0.215905	−	0.521241i
$959$	50.8081	−	8.43562i	1.64068	−	0.272400i
$960$	0.752404	−	0.752404i	0.0242837	−	0.0242837i
$961$	−5.33571	−	19.9131i	−0.172120	−	0.642359i
$962$	0.336538	+	2.55626i	0.0108504	+	0.0824170i
$963$	−11.6247	+	1.53042i	−0.374600	+	0.0493171i
$964$	1.03887	−	7.89100i	0.0334598	−	0.254152i
$965$			5.84851i			0.188270i
$966$	0.312053	−	3.19795i	0.0100401	−	0.102892i
$967$	26.9308	+	26.9308i	0.866036	+	0.866036i	0.992031	−	0.125995i	$-0.0402124\pi$
$967$	26.9308	+	26.9308i	0.866036	+	0.866036i	−0.125995	+	0.992031i	$0.540212\pi$
$968$	−13.8842	+	24.0482i	−0.446256	+	0.772938i
$969$	−21.7991	+	2.22336i	−0.700287	+	0.0714245i
$970$	−1.13605	−	1.96770i	−0.0364764	−	0.0631790i
$971$	24.4149	−	6.54195i	0.783512	−	0.209941i	0.155179	−	0.987886i	$-0.450404\pi$
$971$	24.4149	−	6.54195i	0.783512	−	0.209941i	0.628332	+	0.777945i	$0.283738\pi$
$972$	0.475405	+	1.14773i	0.0152486	+	0.0368135i
$973$	0.256059	−	0.00861416i	0.00820887	−	0.000276157i
$974$	19.9790	−	8.27557i	0.640168	−	0.265166i
$975$	4.49704	+	5.86066i	0.144021	+	0.187691i
$976$	−0.0169904	−	0.129055i	−0.000543851	−	0.00413096i
$977$	21.1215	+	5.65949i	0.675737	+	0.181063i	0.580338	−	0.814376i	$-0.302921\pi$
$977$	21.1215	+	5.65949i	0.675737	+	0.181063i	0.0953994	+	0.995439i	$0.469587\pi$
$978$	1.02504	+	3.82549i	0.0327771	+	0.122326i
$979$	−1.96232	−	0.812820i	−0.0627161	−	0.0259778i
$980$	0.606398	−	1.79706i	0.0193707	−	0.0574048i
$981$	10.3716	−	4.29605i	0.331139	−	0.137162i
$982$	15.1491	+	8.74636i	0.483428	+	0.279107i
$983$	−29.2852	+	38.1652i	−0.934052	+	1.21728i	0.0418613	+	0.999123i	$0.486671\pi$
$983$	−29.2852	+	38.1652i	−0.934052	+	1.21728i	−0.975914	+	0.218157i	$0.929995\pi$
$984$	6.96581	−	25.9968i	0.222062	−	0.828746i
$985$	1.02612	−	1.77729i	0.0326948	−	0.0566291i
$986$	−10.2868	−	4.61799i	−0.327600	−	0.147067i
$987$	−0.0936803	−	2.78468i	−0.00298188	−	0.0886373i
$988$	6.96356	+	6.96356i	0.221540	+	0.221540i
$989$	7.33788	+	0.966051i	0.233331	+	0.0307186i
$990$	−0.177158	+	0.102282i	−0.00563044	+	0.00325074i
$991$	23.0378	+	17.6775i	0.731821	+	0.561546i	0.906056	−	0.423158i	$-0.139079\pi$
$991$	23.0378	+	17.6775i	0.731821	+	0.561546i	−0.174235	+	0.984704i	$0.555745\pi$
$992$	24.7933	+	32.3112i	0.787187	+	1.02588i
$993$	−10.6272	−	4.40193i	−0.337244	−	0.139691i
$994$	−15.0358	+	4.57591i	−0.476907	+	0.145139i
$995$	−0.0708081	+	0.0708081i	−0.00224477	+	0.00224477i
$996$	−9.90709	+	7.60197i	−0.313918	+	0.240878i
$997$	−10.8843	+	1.43294i	−0.344708	+	0.0453817i	−0.300893	−	0.953658i	$-0.597285\pi$
$997$	−10.8843	+	1.43294i	−0.344708	+	0.0453817i	−0.0438155	+	0.999040i	$0.513951\pi$
$998$	−4.64357	−	3.56314i	−0.146990	−	0.112789i
$999$	1.71971	+	0.992874i	0.0544092	+	0.0314132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bh.a.100.9	yes	192
7.4	even	3	inner	357.2.bh.a.151.16	yes	192
17.8	even	8	inner	357.2.bh.a.331.16	yes	192
119.25	even	24	inner	357.2.bh.a.25.9	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bh.a.25.9	✓	192	119.25	even	24	inner
357.2.bh.a.100.9	yes	192	1.1	even	1	trivial
357.2.bh.a.151.16	yes	192	7.4	even	3	inner
357.2.bh.a.331.16	yes	192	17.8	even	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.840803 + 0.225292i) q^{2} +(-0.608761 + 0.793353i) q^{3} +(-1.07586 + 0.621147i) q^{4} +(0.0284677 - 0.216234i) q^{5} +(0.333112 - 0.804203i) q^{6} +(0.929728 - 2.47702i) q^{7} +(1.99567 - 1.99567i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(0.0247801 + 0.188224i) q^{10} +(-1.06830 + 0.140644i) q^{11} +(0.162152 - 1.23167i) q^{12} -1.49163i q^{13} +(-0.223665 + 2.29214i) q^{14} +(0.154220 + 0.154220i) q^{15} +(0.0139413 - 0.0241470i) q^{16} +(1.95621 + 3.62949i) q^{17} +(0.435232 + 0.753843i) q^{18} +(5.13340 - 1.37549i) q^{19} +(0.103686 + 0.250320i) q^{20} +(1.39917 + 2.24551i) q^{21} +(0.866542 - 0.358933i) q^{22} +(0.849331 + 1.10687i) q^{23} +(0.368384 + 2.79815i) q^{24} +(4.78368 + 1.28178i) q^{25} +(0.336053 + 1.25417i) q^{26} +(0.923880 + 0.382683i) q^{27} +(0.538336 + 3.24242i) q^{28} +(2.90262 - 1.20230i) q^{29} +(-0.164413 - 0.0949240i) q^{30} +(4.37359 - 5.69977i) q^{31} +(-1.46721 + 5.47570i) q^{32} +(0.538758 - 0.933156i) q^{33} +(-2.46249 - 2.61097i) q^{34} +(-0.509148 - 0.271554i) q^{35} +(0.878435 + 0.878435i) q^{36} +(1.96876 + 0.259192i) q^{37} +(-4.00629 + 2.31303i) q^{38} +(1.18339 + 0.908047i) q^{39} +(-0.374719 - 0.488343i) q^{40} +(-8.81025 - 3.64932i) q^{41} +(-1.68232 - 1.57281i) q^{42} +(3.75109 - 3.75109i) q^{43} +(1.06198 - 0.814883i) q^{44} +(-0.216234 + 0.0284677i) q^{45} +(-0.963489 - 0.739311i) q^{46} +(-0.912015 - 0.526552i) q^{47} +(0.0106702 + 0.0257601i) q^{48} +(-5.27121 - 4.60590i) q^{49} -4.31091 q^{50} +(-4.07034 - 0.657528i) q^{51} +(0.926522 + 1.60478i) q^{52} +(-0.403336 + 1.50527i) q^{53} +(-0.863016 - 0.113618i) q^{54} +0.235006i q^{55} +(-3.08787 - 6.79872i) q^{56} +(-2.03376 + 4.90994i) q^{57} +(-2.16966 + 1.66484i) q^{58} +(10.4648 + 2.80403i) q^{59} +(-0.261712 - 0.0701255i) q^{60} +(3.70374 - 2.84198i) q^{61} +(-2.39321 + 5.77772i) q^{62} +(-2.63324 - 0.256949i) q^{63} -4.87877i q^{64} +(-0.322541 - 0.0424634i) q^{65} +(-0.242756 + 0.905978i) q^{66} +(-4.99373 - 8.64940i) q^{67} +(-4.35906 - 2.68973i) q^{68} -1.39518 q^{69} +(0.489272 + 0.113616i) q^{70} +(2.61157 + 6.30489i) q^{71} +(-2.44418 - 1.41115i) q^{72} +(-1.92764 - 1.47913i) q^{73} +(-1.71373 + 0.225617i) q^{74} +(-3.92903 + 3.01485i) q^{75} +(-4.66842 + 4.66842i) q^{76} +(-0.644849 + 2.77695i) q^{77} +(-1.19957 - 0.496880i) q^{78} +(5.26746 + 6.86469i) q^{79} +(-0.00482453 - 0.00370199i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(8.22984 + 1.08348i) q^{82} +(-7.10788 - 7.10788i) q^{83} +(-2.90010 - 1.54677i) q^{84} +(0.840509 - 0.319676i) q^{85} +(-2.30883 + 3.99902i) q^{86} +(-0.813151 + 3.03472i) q^{87} +(-1.85129 + 2.41264i) q^{88} +(1.70711 + 0.985601i) q^{89} +(0.175397 - 0.0726516i) q^{90} +(-3.69479 - 1.38681i) q^{91} +(-1.60129 - 0.663276i) q^{92} +(1.85946 + 6.93960i) q^{93} +(0.885453 + 0.237256i) q^{94} +(-0.151291 - 1.14917i) q^{95} +(-3.45099 - 4.49741i) q^{96} +(-11.0570 + 4.57996i) q^{97} +(5.46972 + 2.68509i) q^{98} +(0.412348 + 0.995495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 8 q^{5} + 8 q^{11} - 80 q^{14} + 96 q^{16} - 16 q^{17} + 16 q^{22} + 8 q^{25} - 64 q^{26} - 88 q^{28} - 40 q^{32} - 32 q^{33} - 32 q^{35} + 32 q^{37} - 64 q^{40} - 64 q^{41} - 56 q^{42} - 32 q^{43}+ \cdots - 16 q^{99}+O(q^{100}) \) 192 * q - 8 * q^5 + 8 * q^11 - 80 * q^14 + 96 * q^16 - 16 * q^17 + 16 * q^22 + 8 * q^25 - 64 * q^26 - 88 * q^28 - 40 * q^32 - 32 * q^33 - 32 * q^35 + 32 * q^37 - 64 * q^40 - 64 * q^41 - 56 * q^42 - 32 * q^43 + 32 * q^44 + 56 * q^49 + 64 * q^50 + 96 * q^52 + 64 * q^53 - 152 * q^56 - 32 * q^58 - 16 * q^59 + 40 * q^61 - 112 * q^62 + 32 * q^65 - 16 * q^67 + 48 * q^68 - 128 * q^69 - 120 * q^70 + 96 * q^71 + 8 * q^73 - 64 * q^74 - 112 * q^76 + 32 * q^77 - 16 * q^78 + 16 * q^79 + 192 * q^80 - 8 * q^82 - 16 * q^83 + 48 * q^84 - 64 * q^86 + 24 * q^87 - 136 * q^88 - 160 * q^92 + 48 * q^93 - 64 * q^94 - 104 * q^95 - 48 * q^96 - 96 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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