LMFDB - Embedded newform 195.2.s.b.77.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(38,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("195.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.1
Character	$\chi$	$=$	195.77
Dual form			195.2.s.b.38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57280 - 1.57280i) q^{2} +(-1.73164 - 0.0375613i) q^{3} +2.94741i q^{4} +(2.12590 - 0.693215i) q^{5} +(2.66446 + 2.78261i) q^{6} +(3.19872 - 3.19872i) q^{7} +(1.49009 - 1.49009i) q^{8} +(2.99718 + 0.130086i) q^{9} +(-4.43391 - 2.25333i) q^{10} -2.81912 q^{11} +(0.110709 - 5.10387i) q^{12} +(-3.47350 - 0.966841i) q^{13} -10.0619 q^{14} +(-3.70734 + 1.12055i) q^{15} +1.20758 q^{16} +(2.03377 - 2.03377i) q^{17} +(-4.50937 - 4.91857i) q^{18} -1.12487 q^{19} +(2.04319 + 6.26591i) q^{20} +(-5.65918 + 5.41889i) q^{21} +(4.43391 + 4.43391i) q^{22} +(-2.81355 - 2.81355i) q^{23} +(-2.63628 + 2.52434i) q^{24} +(4.03891 - 2.94741i) q^{25} +(3.94248 + 6.98378i) q^{26} +(-5.18516 - 0.337840i) q^{27} +(9.42794 + 9.42794i) q^{28} -0.367259 q^{29} +(7.59331 + 4.06851i) q^{30} -6.89322i q^{31} +(-4.87948 - 4.87948i) q^{32} +(4.88170 + 0.105890i) q^{33} -6.39743 q^{34} +(4.58275 - 9.01755i) q^{35} +(-0.383416 + 8.83392i) q^{36} +(-2.07384 + 2.07384i) q^{37} +(1.76920 + 1.76920i) q^{38} +(5.97855 + 1.80469i) q^{39} +(2.13483 - 4.20074i) q^{40} +3.73081 q^{41} +(17.4236 + 0.377938i) q^{42} +(-3.25333 + 3.25333i) q^{43} -8.30910i q^{44} +(6.46188 - 1.80114i) q^{45} +8.85031i q^{46} +(1.65930 + 1.65930i) q^{47} +(-2.09110 - 0.0453585i) q^{48} -13.4636i q^{49} +(-10.9881 - 1.71670i) q^{50} +(-3.59815 + 3.44537i) q^{51} +(2.84968 - 10.2378i) q^{52} +(9.01755 + 9.01755i) q^{53} +(7.62387 + 8.68658i) q^{54} +(-5.99316 + 1.95425i) q^{55} -9.53277i q^{56} +(1.94788 + 0.0422518i) q^{57} +(0.577625 + 0.577625i) q^{58} -0.0290860i q^{59} +(-3.30272 - 10.9271i) q^{60} +9.93373 q^{61} +(-10.8417 + 10.8417i) q^{62} +(10.0032 - 9.17102i) q^{63} +12.9337i q^{64} +(-8.05455 + 0.352476i) q^{65} +(-7.51141 - 7.84450i) q^{66} +(-3.03050 + 3.03050i) q^{67} +(5.99436 + 5.99436i) q^{68} +(4.76638 + 4.97774i) q^{69} +(-21.3906 + 6.97506i) q^{70} +1.59810 q^{71} +(4.65991 - 4.27223i) q^{72} +(1.40984 + 1.40984i) q^{73} +6.52349 q^{74} +(-7.10465 + 4.95216i) q^{75} -3.31547i q^{76} +(-9.01755 + 9.01755i) q^{77} +(-6.56465 - 12.2415i) q^{78} -5.41757i q^{79} +(2.56720 - 0.837115i) q^{80} +(8.96616 + 0.779780i) q^{81} +(-5.86782 - 5.86782i) q^{82} +(4.58566 - 4.58566i) q^{83} +(-15.9717 - 16.6800i) q^{84} +(2.91375 - 5.73343i) q^{85} +10.2337 q^{86} +(0.635961 + 0.0137947i) q^{87} +(-4.20074 + 4.20074i) q^{88} +14.1084i q^{89} +(-12.9961 - 7.33042i) q^{90} +(-14.2034 + 8.01810i) q^{91} +(8.29269 - 8.29269i) q^{92} +(-0.258919 + 11.9366i) q^{93} -5.21949i q^{94} +(-2.39137 + 0.779780i) q^{95} +(8.26623 + 8.63279i) q^{96} +(-11.2986 + 11.2986i) q^{97} +(-21.1755 + 21.1755i) q^{98} +(-8.44939 - 0.366727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 24 q^{10} - 24 q^{12} + 24 q^{16} + 24 q^{22} - 8 q^{25} - 16 q^{27} + 36 q^{30} - 8 q^{36} + 16 q^{40} + 12 q^{42} - 64 q^{43} - 20 q^{48} + 16 q^{51} - 72 q^{52} - 80 q^{55} + 8 q^{61}+ \cdots - 40 q^{91}+O(q^{100}) $ 32 * q - 4 * q^3 - 24 * q^10 - 24 * q^12 + 24 * q^16 + 24 * q^22 - 8 * q^25 - 16 * q^27 + 36 * q^30 - 8 * q^36 + 16 * q^40 + 12 * q^42 - 64 * q^43 - 20 * q^48 + 16 * q^51 - 72 * q^52 - 80 * q^55 + 8 * q^61 - 72 * q^66 + 44 * q^75 + 84 * q^78 + 112 * q^81 + 48 * q^82 + 20 * q^87 - 8 * q^88 + 44 * q^90 - 40 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.57280	−	1.57280i	−1.11214	−	1.11214i	−0.992861	−	0.119278i	$-0.961942\pi$
$2$	−1.57280	−	1.57280i	−1.11214	−	1.11214i	−0.119278	−	0.992861i	$-0.538058\pi$
$3$	−1.73164	−	0.0375613i	−0.999765	−	0.0216860i
$3$	−1.73164	−	0.0375613i	−0.999765	−	0.0216860i
$4$			2.94741i			1.47371i
$5$	2.12590	−	0.693215i	0.950732	−	0.310015i
$5$	2.12590	−	0.693215i	0.950732	−	0.310015i
$6$	2.66446	+	2.78261i	1.08776	+	1.13600i
$7$	3.19872	−	3.19872i	1.20900	−	1.20900i	0.237650	−	0.971351i	$-0.423623\pi$
$7$	3.19872	−	3.19872i	1.20900	−	1.20900i	0.971351	−	0.237650i	$-0.0763772\pi$
$8$	1.49009	−	1.49009i	0.526827	−	0.526827i
$9$	2.99718	+	0.130086i	0.999059	+	0.0433619i
$10$	−4.43391	−	2.25333i	−1.40213	−	0.712566i
$11$	−2.81912			−0.849995			−0.424998	−	0.905194i	$-0.639725\pi$
$11$	−2.81912			−0.849995			−0.424998	+	0.905194i	$0.639725\pi$
$12$	0.110709	−	5.10387i	0.0319589	−	1.47336i
$13$	−3.47350	−	0.966841i	−0.963376	−	0.268154i
$13$	−3.47350	−	0.966841i	−0.963376	−	0.268154i
$14$	−10.0619			−2.68915
$15$	−3.70734	+	1.12055i	−0.957231	+	0.289325i
$16$	1.20758			0.301896
$17$	2.03377	−	2.03377i	0.493261	−	0.493261i	−0.416071	−	0.909332i	$-0.636593\pi$
$17$	2.03377	−	2.03377i	0.493261	−	0.493261i	0.909332	+	0.416071i	$0.136593\pi$
$18$	−4.50937	−	4.91857i	−1.06287	−	1.15932i
$19$	−1.12487			−0.258064			−0.129032	−	0.991640i	$-0.541187\pi$
$19$	−1.12487			−0.258064			−0.129032	+	0.991640i	$0.541187\pi$
$20$	2.04319	+	6.26591i	0.456871	+	1.40110i
$21$	−5.65918	+	5.41889i	−1.23494	+	1.18250i
$22$	4.43391	+	4.43391i	0.945313	+	0.945313i
$23$	−2.81355	−	2.81355i	−0.586666	−	0.586666i	0.350061	−	0.936727i	$-0.386161\pi$
$23$	−2.81355	−	2.81355i	−0.586666	−	0.586666i	−0.936727	+	0.350061i	$0.886161\pi$
$24$	−2.63628	+	2.52434i	−0.538128	+	0.515279i
$25$	4.03891	−	2.94741i	0.807781	−	0.589483i
$26$	3.94248	+	6.98378i	0.773184	+	1.36963i
$27$	−5.18516	−	0.337840i	−0.997884	−	0.0650173i
$28$	9.42794	+	9.42794i	1.78171	+	1.78171i
$29$	−0.367259			−0.0681982			−0.0340991	−	0.999418i	$-0.510856\pi$
$29$	−0.367259			−0.0681982			−0.0340991	+	0.999418i	$0.510856\pi$
$30$	7.59331	+	4.06851i	1.38634	+	0.742805i
$31$		−	6.89322i		−	1.23806i	−0.785368	−	0.619030i	$-0.787526\pi$
$31$		−	6.89322i		−	1.23806i	0.785368	−	0.619030i	$-0.212474\pi$
$32$	−4.87948	−	4.87948i	−0.862578	−	0.862578i
$33$	4.88170	+	0.105890i	0.849795	+	0.0184330i
$34$	−6.39743			−1.09715
$35$	4.58275	−	9.01755i	0.774627	−	1.52424i
$36$	−0.383416	+	8.83392i	−0.0639027	+	1.47232i
$37$	−2.07384	+	2.07384i	−0.340937	+	0.340937i	−0.856720	−	0.515782i	$-0.827501\pi$
$37$	−2.07384	+	2.07384i	−0.340937	+	0.340937i	0.515782	+	0.856720i	$0.327501\pi$
$38$	1.76920	+	1.76920i	0.287003	+	0.287003i
$39$	5.97855	+	1.80469i	0.957334	+	0.288982i
$40$	2.13483	−	4.20074i	0.337547	−	0.664196i
$41$	3.73081			0.582654			0.291327	−	0.956623i	$-0.405903\pi$
$41$	3.73081			0.582654			0.291327	+	0.956623i	$0.405903\pi$
$42$	17.4236	+	0.377938i	2.68852	+	0.0583171i
$43$	−3.25333	+	3.25333i	−0.496128	+	0.496128i	−0.910230	−	0.414102i	$-0.864096\pi$
$43$	−3.25333	+	3.25333i	−0.496128	+	0.496128i	0.414102	+	0.910230i	$0.364096\pi$
$44$		−	8.30910i		−	1.25264i
$45$	6.46188	−	1.80114i	0.963280	−	0.268498i
$46$			8.85031i			1.30491i
$47$	1.65930	+	1.65930i	0.242033	+	0.242033i	0.817691	−	0.575658i	$-0.195254\pi$
$47$	1.65930	+	1.65930i	0.242033	+	0.242033i	−0.575658	+	0.817691i	$0.695254\pi$
$48$	−2.09110	−	0.0453585i	−0.301825	−	0.00654693i
$49$		−	13.4636i		−	1.92337i
$50$	−10.9881	−	1.71670i	−1.55395	−	0.242778i
$51$	−3.59815	+	3.44537i	−0.503842	+	0.482449i
$52$	2.84968	−	10.2378i	0.395180	−	1.41973i
$53$	9.01755	+	9.01755i	1.23866	+	1.23866i	0.960551	+	0.278105i	$0.0897064\pi$
$53$	9.01755	+	9.01755i	1.23866	+	1.23866i	0.278105	+	0.960551i	$0.410294\pi$
$54$	7.62387	+	8.68658i	1.03748	+	1.18209i
$55$	−5.99316	+	1.95425i	−0.808117	+	0.263511i
$56$		−	9.53277i		−	1.27387i
$57$	1.94788	+	0.0422518i	0.258003	+	0.00559639i
$58$	0.577625	+	0.577625i	0.0758459	+	0.0758459i
$59$		−	0.0290860i		−	0.00378667i	−0.999998	−	0.00189334i	$-0.999397\pi$
$59$		−	0.0290860i		−	0.00378667i	0.999998	−	0.00189334i	$-0.000602668\pi$
$60$	−3.30272	−	10.9271i	−0.426380	−	1.41068i
$61$	9.93373			1.27188			0.635942	−	0.771737i	$-0.280612\pi$
$61$	9.93373			1.27188			0.635942	+	0.771737i	$0.280612\pi$
$62$	−10.8417	+	10.8417i	−1.37689	+	1.37689i
$63$	10.0032	−	9.17102i	1.26029	−	1.15544i
$64$			12.9337i			1.61672i
$65$	−8.05455	+	0.352476i	−0.999044	+	0.0437193i
$66$	−7.51141	−	7.84450i	−0.924591	−	0.965591i
$67$	−3.03050	+	3.03050i	−0.370235	+	0.370235i	−0.867563	−	0.497328i	$-0.834315\pi$
$67$	−3.03050	+	3.03050i	−0.370235	+	0.370235i	0.497328	+	0.867563i	$0.334315\pi$
$68$	5.99436	+	5.99436i	0.726923	+	0.726923i
$69$	4.76638	+	4.97774i	0.573805	+	0.599250i
$70$	−21.3906	+	6.97506i	−2.55666	+	0.833679i
$71$	1.59810			0.189660			0.0948300	−	0.995493i	$-0.469769\pi$
$71$	1.59810			0.189660			0.0948300	+	0.995493i	$0.469769\pi$
$72$	4.65991	−	4.27223i	0.549176	−	0.503488i
$73$	1.40984	+	1.40984i	0.165009	+	0.165009i	0.784782	−	0.619772i	$-0.212775\pi$
$73$	1.40984	+	1.40984i	0.165009	+	0.165009i	−0.619772	+	0.784782i	$0.712775\pi$
$74$	6.52349			0.758340
$75$	−7.10465	+	4.95216i	−0.820375	+	0.571826i
$76$		−	3.31547i		−	0.380310i
$77$	−9.01755	+	9.01755i	−1.02765	+	1.02765i
$78$	−6.56465	−	12.2415i	−0.743301	−	1.38608i
$79$		−	5.41757i		−	0.609525i	−0.952428	−	0.304762i	$-0.901423\pi$
$79$		−	5.41757i		−	0.609525i	0.952428	−	0.304762i	$-0.0985770\pi$
$80$	2.56720	−	0.837115i	0.287022	−	0.0935924i
$81$	8.96616	+	0.779780i	0.996239	+	0.0866422i
$82$	−5.86782	−	5.86782i	−0.647992	−	0.647992i
$83$	4.58566	−	4.58566i	0.503341	−	0.503341i	−0.409133	−	0.912475i	$-0.634169\pi$
$83$	4.58566	−	4.58566i	0.503341	−	0.503341i	0.912475	+	0.409133i	$0.134169\pi$
$84$	−15.9717	−	16.6800i	−1.74266	−	1.81993i
$85$	2.91375	−	5.73343i	0.316041	−	0.621878i
$86$	10.2337			1.10353
$87$	0.635961	+	0.0137947i	0.0681822	+	0.00147895i
$88$	−4.20074	+	4.20074i	−0.447801	+	0.447801i
$89$			14.1084i			1.49549i	0.663988	+	0.747744i	$0.268863\pi$
$89$			14.1084i			1.49549i	−0.663988	+	0.747744i	$0.731137\pi$
$90$	−12.9961	−	7.33042i	−1.36991	−	0.772694i
$91$	−14.2034	+	8.01810i	−1.48892	+	0.840525i
$92$	8.29269	−	8.29269i	0.864573	−	0.864573i
$93$	−0.258919	+	11.9366i	−0.0268486	+	1.23777i
$94$		−	5.21949i		−	0.538349i
$95$	−2.39137	+	0.779780i	−0.245349	+	0.0800037i
$96$	8.26623	+	8.63279i	0.843669	+	0.881081i
$97$	−11.2986	+	11.2986i	−1.14720	+	1.14720i	−0.160104	+	0.987100i	$0.551183\pi$
$97$	−11.2986	+	11.2986i	−1.14720	+	1.14720i	−0.987100	+	0.160104i	$0.948817\pi$
$98$	−21.1755	+	21.1755i	−2.13905	+	2.13905i
$99$	−8.44939	−	0.366727i	−0.849196	−	0.0368574i
$100$	8.68724	+	11.9043i	0.868724	+	1.19043i
$101$		−	12.5178i		−	1.24557i	−0.782392	−	0.622786i	$-0.786001\pi$
$101$		−	12.5178i		−	1.24557i	0.782392	−	0.622786i	$-0.213999\pi$
$102$	11.0781	+	0.240296i	1.09689	+	0.0237929i
$103$	2.86517	−	2.86517i	0.282313	−	0.282313i	−0.551718	−	0.834031i	$-0.686027\pi$
$103$	2.86517	−	2.86517i	0.282313	−	0.282313i	0.834031	+	0.551718i	$0.186027\pi$
$104$	−6.61652	+	3.73516i	−0.648803	+	0.366262i
$105$	−8.27441	+	15.4430i	−0.807499	+	1.50709i
$106$		−	28.3656i		−	2.75511i
$107$	9.17516	−	9.17516i	0.886997	−	0.886997i	−0.107237	−	0.994233i	$-0.534200\pi$
$107$	9.17516	−	9.17516i	0.886997	−	0.886997i	0.994233	+	0.107237i	$0.0342003\pi$
$108$	0.995754	−	15.2828i	0.0958165	−	1.47059i
$109$	6.92360			0.663160			0.331580	−	0.943427i	$-0.392418\pi$
$109$	6.92360			0.663160			0.331580	+	0.943427i	$0.392418\pi$
$110$	12.4997	+	6.35240i	1.19180	+	0.605677i
$111$	3.66905	−	3.51326i	0.348251	−	0.333464i
$112$	3.86272	−	3.86272i	0.364993	−	0.364993i
$113$	−3.53841	−	3.53841i	−0.332866	−	0.332866i	0.520808	−	0.853674i	$-0.325631\pi$
$113$	−3.53841	−	3.53841i	−0.332866	−	0.332866i	−0.853674	+	0.520808i	$0.825631\pi$
$114$	−2.99718	−	3.13009i	−0.280711	−	0.293159i
$115$	−7.93172	−	4.03093i	−0.739637	−	0.375886i
$116$		−	1.08246i		−	0.100504i
$117$	−10.2849	−	3.34965i	−0.950842	−	0.309675i
$118$	−0.0457465	+	0.0457465i	−0.00421131	+	0.00421131i
$119$		−	13.0109i		−	1.19271i
$120$	−3.85456	+	7.19400i	−0.351871	+	0.656720i
$121$	−3.05259			−0.277508
$122$	−15.6238	−	15.6238i	−1.41451	−	1.41451i
$123$	−6.46043	−	0.140134i	−0.582517	−	0.0126355i
$124$	20.3172			1.82454
$125$	6.54312	−	9.06574i	0.585234	−	0.810864i
$126$	−30.1573	−	1.30891i	−2.68663	−	0.116607i
$127$	7.34242	+	7.34242i	0.651534	+	0.651534i	0.953362	−	0.301828i	$-0.0975969\pi$
$127$	7.34242	+	7.34242i	0.651534	+	0.651534i	−0.301828	+	0.953362i	$0.597597\pi$
$128$	10.5832	−	10.5832i	0.935436	−	0.935436i
$129$	5.75581	−	5.51141i	0.506771	−	0.485253i
$130$	13.2226	+	12.1138i	1.15970	+	1.06245i
$131$			2.08869i			0.182490i	0.995828	+	0.0912448i	$0.0290846\pi$
$131$			2.08869i			0.182490i	−0.995828	+	0.0912448i	$0.970915\pi$
$132$	−0.312101	+	14.3884i	−0.0271649	+	1.25235i
$133$	−3.59815	+	3.59815i	−0.312000	+	0.312000i
$134$	9.53277			0.823506
$135$	−11.2573	+	2.87622i	−0.968876	+	0.247545i
$136$		−	6.06101i		−	0.519727i
$137$	3.91340	+	3.91340i	0.334344	+	0.334344i	0.854233	−	0.519890i	$-0.174027\pi$
$137$	3.91340	+	3.91340i	0.334344	+	0.334344i	−0.519890	+	0.854233i	$0.674027\pi$
$138$	0.332429	−	15.3256i	0.0282983	−	1.30460i
$139$			17.1532i			1.45492i	0.686152	+	0.727458i	$0.259299\pi$
$139$			17.1532i			1.45492i	−0.686152	+	0.727458i	$0.740701\pi$
$140$	26.5784	+	13.5073i	2.24629	+	1.14157i
$141$	−2.81098	−	2.93563i	−0.236727	−	0.247225i
$142$	−2.51350	−	2.51350i	−0.210928	−	0.210928i
$143$	9.79220	+	2.72564i	0.818865	+	0.227929i
$144$	3.61934	+	0.157089i	0.301612	+	0.0130908i
$145$	−0.780755	+	0.254589i	−0.0648382	+	0.0211425i
$146$		−	4.43480i		−	0.367026i
$147$	−0.505710	+	23.3141i	−0.0417102	+	1.92291i
$148$	−6.11247	−	6.11247i	−0.502442	−	0.502442i
$149$		−	2.94675i		−	0.241407i	−0.992689	−	0.120704i	$-0.961485\pi$
$149$		−	2.94675i		−	0.241407i	0.992689	−	0.120704i	$-0.0385151\pi$
$150$	18.9630	+	3.38544i	1.54832	+	0.276420i
$151$			1.12487i			0.0915410i	0.998952	+	0.0457705i	$0.0145743\pi$
$151$			1.12487i			0.0915410i	−0.998952	+	0.0457705i	$0.985426\pi$
$152$	−1.67617	+	1.67617i	−0.135955	+	0.135955i
$153$	6.36013	−	5.83100i	0.514186	−	0.471409i
$154$	28.3656			2.28577
$155$	−4.77849	−	14.6543i	−0.383817	−	1.17706i
$156$	−5.31918	+	17.6213i	−0.425875	+	1.41083i
$157$	12.5551	+	12.5551i	1.00200	+	1.00200i	0.999998	+	0.00200511i	$0.000638247\pi$
$157$	12.5551	+	12.5551i	1.00200	+	1.00200i	0.00200511	+	0.999998i	$0.499362\pi$
$158$	−8.52077	+	8.52077i	−0.677876	+	0.677876i
$159$	−15.2765	−	15.9539i	−1.21150	−	1.26523i
$160$	−13.7558	−	6.99075i	−1.08749	−	0.552668i
$161$	−17.9995			−1.41856
$162$	−12.8755	−	15.3284i	−1.01160	−	1.20431i
$163$	4.81938	+	4.81938i	0.377483	+	0.377483i	0.870193	−	0.492710i	$-0.163994\pi$
$163$	4.81938	+	4.81938i	0.377483	+	0.377483i	−0.492710	+	0.870193i	$0.663994\pi$
$164$			10.9962i			0.858661i
$165$	10.4514	−	3.15896i	0.813642	−	0.245925i
$166$	−14.4247			−1.11957
$167$	11.8176	+	11.8176i	0.914477	+	0.914477i	0.996620	−	0.0821438i	$-0.0261767\pi$
$167$	11.8176	+	11.8176i	0.914477	+	0.914477i	−0.0821438	+	0.996620i	$0.526177\pi$
$168$	−0.358063	+	16.5074i	−0.0276252	+	1.27357i
$169$	11.1304	+	6.71665i	0.856187	+	0.516665i
$170$	−13.6003	+	4.43480i	−1.04310	+	0.340133i
$171$	−3.37145	−	0.146330i	−0.257821	−	0.0111901i
$172$	−9.58891	−	9.58891i	−0.731147	−	0.731147i
$173$	4.16058	+	4.16058i	0.316323	+	0.316323i	0.847353	−	0.531030i	$-0.178195\pi$
$173$	4.16058	+	4.16058i	0.316323	+	0.316323i	−0.531030	+	0.847353i	$0.678195\pi$
$174$	−0.978544	−	1.02194i	−0.0741833	−	0.0774729i
$175$	3.49138	−	22.3472i	0.263923	−	1.68929i
$176$	−3.40432			−0.256610
$177$	−0.00109251	+	0.0503666i	−8.21180e−5	+	0.00378578i
$178$	22.1897	−	22.1897i	1.66319	−	1.66319i
$179$	−5.51726			−0.412379			−0.206190	−	0.978512i	$-0.566106\pi$
$179$	−5.51726			−0.412379			−0.206190	+	0.978512i	$0.566106\pi$
$180$	5.30870	+	19.0458i	0.395687	+	1.41959i
$181$	15.5001			1.15211			0.576056	−	0.817411i	$-0.304591\pi$
$181$	15.5001			1.15211			0.576056	+	0.817411i	$0.304591\pi$
$182$	34.9500	+	9.72826i	2.59067	+	0.721106i
$183$	−17.2017	−	0.373124i	−1.27158	−	0.0275821i
$184$	−8.38490			−0.618143
$185$	−2.97116	+	5.84640i	−0.218444	+	0.429836i
$186$	19.1811	−	18.3667i	1.40643	−	1.34671i
$187$	−5.73343	+	5.73343i	−0.419270	+	0.419270i
$188$	−4.89063	+	4.89063i	−0.356686	+	0.356686i
$189$	−17.6665	+	15.5052i	−1.28505	+	1.12784i
$190$	4.98759	+	2.53471i	0.361838	+	0.183887i
$191$			18.2212i			1.31844i	0.751951	+	0.659219i	$0.229113\pi$
$191$			18.2212i			1.31844i	−0.751951	+	0.659219i	$0.770887\pi$
$192$	0.485808	−	22.3966i	0.0350602	−	1.61634i
$193$	−6.02609	−	6.02609i	−0.433767	−	0.433767i	0.456140	−	0.889908i	$-0.349231\pi$
$193$	−6.02609	−	6.02609i	−0.433767	−	0.433767i	−0.889908	+	0.456140i	$0.849231\pi$
$194$	35.5411			2.55170
$195$	13.9608	−	0.307823i	0.999757	−	0.0220437i
$196$	39.6827			2.83448
$197$	−6.72726	−	6.72726i	−0.479297	−	0.479297i	0.425610	−	0.904907i	$-0.360060\pi$
$197$	−6.72726	−	6.72726i	−0.479297	−	0.479297i	−0.904907	+	0.425610i	$0.860060\pi$
$198$	12.7124	+	13.8660i	0.903433	+	0.985414i
$199$		−	5.43933i		−	0.385584i	−0.981240	−	0.192792i	$-0.938246\pi$
$199$		−	5.43933i		−	0.385584i	0.981240	−	0.192792i	$-0.0617543\pi$
$200$	1.62643	−	10.4103i	0.115006	−	0.736117i
$201$	5.36158	−	5.13392i	0.378177	−	0.362119i
$202$	−19.6881	+	19.6881i	−1.38525	+	1.38525i
$203$	−1.17476	+	1.17476i	−0.0824517	+	0.0824517i
$204$	−10.1549	−	10.6052i	−0.710987	−	0.742516i
$205$	7.93133	−	2.58625i	0.553948	−	0.180632i
$206$	−9.01268			−0.627943
$207$	−8.06671	−	8.79871i	−0.560675	−	0.611553i
$208$	−4.19455	−	1.16754i	−0.290839	−	0.0809545i
$209$	3.17115			0.219353
$210$	37.3029	−	11.2749i	2.57414	−	0.778039i
$211$	1.26400			0.0870171			0.0435086	−	0.999053i	$-0.486146\pi$
$211$	1.26400			0.0870171			0.0435086	+	0.999053i	$0.486146\pi$
$212$	−26.5784	+	26.5784i	−1.82541	+	1.82541i
$213$	−2.76735	−	0.0600269i	−0.189615	−	0.00411298i
$214$	−28.8614			−1.97293
$215$	−4.66100	+	9.17151i	−0.317877	+	0.625492i
$216$	−8.22978	+	7.22295i	−0.559965	+	0.491460i
$217$	−22.0495	−	22.0495i	−1.49682	−	1.49682i
$218$	−10.8894	−	10.8894i	−0.737527	−	0.737527i
$219$	−2.38838	−	2.49429i	−0.161392	−	0.168549i
$220$	−5.75999	−	17.6643i	−0.388339	−	1.19093i
$221$	−9.03063	+	5.09797i	−0.607466	+	0.342927i
$222$	−11.2964	−	0.245031i	−0.758161	−	0.0164454i
$223$	13.6651	+	13.6651i	0.915086	+	0.915086i	0.996667	−	0.0815806i	$-0.0259968\pi$
$223$	13.6651	+	13.6651i	0.915086	+	0.915086i	−0.0815806	+	0.996667i	$0.525997\pi$
$224$	−31.2161			−2.08571
$225$	12.4887	−	8.30852i	0.832582	−	0.553901i
$226$			11.1304i			0.740386i
$227$	0.319120	+	0.319120i	0.0211808	+	0.0211808i	0.717618	−	0.696437i	$-0.245232\pi$
$227$	0.319120	+	0.319120i	0.0211808	+	0.0211808i	−0.696437	+	0.717618i	$0.745232\pi$
$228$	−0.124533	+	5.74121i	−0.00824743	+	0.380221i
$229$	−9.97519			−0.659179			−0.329589	−	0.944124i	$-0.606910\pi$
$229$	−9.97519			−0.659179			−0.329589	+	0.944124i	$0.606910\pi$
$230$	6.13517	+	18.8149i	0.404541	+	1.24062i
$231$	15.9539	−	15.2765i	1.04969	−	1.00512i
$232$	−0.547249	+	0.547249i	−0.0359287	+	0.0359287i
$233$	−6.00827	−	6.00827i	−0.393615	−	0.393615i	0.482359	−	0.875974i	$-0.339780\pi$
$233$	−6.00827	−	6.00827i	−0.393615	−	0.393615i	−0.875974	+	0.482359i	$0.839780\pi$
$234$	10.9078	+	21.4445i	0.713067	+	1.40187i
$235$	4.67775	+	2.37725i	0.305142	+	0.155075i
$236$	0.0857284			0.00558044
$237$	−0.203491	+	9.38131i	−0.0132182	+	0.609381i
$238$	−20.4636	+	20.4636i	−1.32646	+	1.32646i
$239$			6.04966i			0.391320i	0.980672	+	0.195660i	$0.0626849\pi$
$239$			6.04966i			0.391320i	−0.980672	+	0.195660i	$0.937315\pi$
$240$	−4.47692	+	1.35316i	−0.288984	+	0.0873460i
$241$		−	25.5460i		−	1.64556i	−0.568360	−	0.822780i	$-0.692422\pi$
$241$		−	25.5460i		−	1.64556i	0.568360	−	0.822780i	$-0.307578\pi$
$242$	4.80112	+	4.80112i	0.308627	+	0.308627i
$243$	−15.4969	−	1.68708i	−0.994126	−	0.108226i
$244$			29.2788i			1.87438i
$245$	−9.33315	−	28.6222i	−0.596273	−	1.82861i
$246$	9.94057	+	10.3814i	0.633788	+	0.661892i
$247$	3.90725	+	1.08758i	0.248613	+	0.0692007i
$248$	−10.2715	−	10.2715i	−0.652243	−	0.652243i
$249$	−8.11297	+	7.76848i	−0.514138	+	0.492307i
$250$	−24.5496	+	3.96758i	−1.55266	+	0.250932i
$251$			7.41987i			0.468338i	0.972196	+	0.234169i	$0.0752369\pi$
$251$			7.41987i			0.468338i	−0.972196	+	0.234169i	$0.924763\pi$
$252$	27.0308	+	29.4836i	1.70278	+	1.85730i
$253$	7.93172	+	7.93172i	0.498663	+	0.498663i
$254$		−	23.0963i		−	1.44919i
$255$	−5.26093	+	9.81881i	−0.329452	+	0.614878i
$256$	−7.42324			−0.463953
$257$	9.78767	−	9.78767i	0.610538	−	0.610538i	−0.332548	−	0.943086i	$-0.607908\pi$
$257$	9.78767	−	9.78767i	0.610538	−	0.610538i	0.943086	+	0.332548i	$0.107908\pi$
$258$	−17.7211	−	0.384391i	−1.10327	−	0.0239311i
$259$			13.2673i			0.824388i
$260$	−1.03889	−	23.7401i	−0.0644293	−	1.47230i
$261$	−1.10074	−	0.0477751i	−0.0681341	−	0.00295720i
$262$	3.28509	−	3.28509i	0.202954	−	0.202954i
$263$	−7.39630	−	7.39630i	−0.456076	−	0.456076i	0.441289	−	0.897365i	$-0.354521\pi$
$263$	−7.39630	−	7.39630i	−0.456076	−	0.456076i	−0.897365	+	0.441289i	$0.854521\pi$
$264$	7.43197	−	7.11640i	0.457406	−	0.437984i
$265$	25.4215	+	12.9193i	1.56163	+	0.793627i
$266$	11.3184			0.693974
$267$	0.529930	−	24.4307i	0.0324312	−	1.49514i
$268$	−8.93215	−	8.93215i	−0.545618	−	0.545618i
$269$	−18.8601			−1.14992			−0.574962	−	0.818180i	$-0.694983\pi$
$269$	−18.8601			−1.14992			−0.574962	+	0.818180i	$0.694983\pi$
$270$	22.2293	+	13.1818i	1.35283	+	0.802220i
$271$			25.2837i			1.53587i	0.640525	+	0.767937i	$0.278717\pi$
$271$			25.2837i			1.53587i	−0.640525	+	0.767937i	$0.721283\pi$
$272$	2.45595	−	2.45595i	0.148914	−	0.148914i
$273$	24.8964	−	13.3510i	1.50680	−	0.808038i
$274$		−	12.3100i		−	0.743674i
$275$	−11.3861	+	8.30910i	−0.686610	+	0.501057i
$276$	−14.6715	+	14.0485i	−0.883119	+	0.845620i
$277$	−23.1897	−	23.1897i	−1.39334	−	1.39334i	−0.817723	−	0.575612i	$-0.804764\pi$
$277$	−23.1897	−	23.1897i	−1.39334	−	1.39334i	−0.575612	−	0.817723i	$-0.695236\pi$
$278$	26.9786	−	26.9786i	1.61807	−	1.61807i
$279$	0.896710	−	20.6602i	0.0536846	−	1.23689i
$280$	−6.60826	−	20.2657i	−0.394919	−	1.21111i
$281$	−10.5921			−0.631871			−0.315935	−	0.948781i	$-0.602318\pi$
$281$	−10.5921			−0.631871			−0.315935	+	0.948781i	$0.602318\pi$
$282$	−0.196051	+	9.03829i	−0.0116747	+	0.538222i
$283$	10.2884	−	10.2884i	0.611583	−	0.611583i	−0.331776	−	0.943358i	$-0.607648\pi$
$283$	10.2884	−	10.2884i	0.611583	−	0.611583i	0.943358	+	0.331776i	$0.107648\pi$
$284$			4.71027i			0.279503i
$285$	4.17029	−	1.26048i	0.247027	−	0.0746643i
$286$	−11.1143	−	19.6881i	−0.657203	−	1.16418i
$287$	11.9338	−	11.9338i	0.704430	−	0.704430i
$288$	−13.9899	−	15.2594i	−0.824363	−	0.899169i
$289$			8.72757i			0.513386i
$290$	1.62839	+	0.827555i	0.0956225	+	0.0485957i
$291$	19.9896	−	19.1408i	1.17181	−	1.12206i
$292$	−4.15538	+	4.15538i	−0.243175	+	0.243175i
$293$	17.5225	−	17.5225i	1.02368	−	1.02368i	0.0239636	−	0.999713i	$-0.492371\pi$
$293$	17.5225	−	17.5225i	1.02368	−	1.02368i	0.999713	−	0.0239636i	$-0.00762857\pi$
$294$	37.4639	−	35.8731i	2.18494	−	2.09216i
$295$	−0.0201628	−	0.0618339i	−0.00117393	−	0.00360011i
$296$			6.18043i			0.359230i
$297$	14.6176	+	0.952410i	0.848197	+	0.0552644i
$298$	−4.63465	+	4.63465i	−0.268478	+	0.268478i
$299$	7.05261	+	12.4931i	0.407863	+	0.722496i
$300$	−14.5961	−	20.9403i	−0.842704	−	1.20899i
$301$			20.8130i			1.19964i
$302$	1.76920	−	1.76920i	0.101806	−	0.101806i
$303$	−0.470187	+	21.6764i	−0.0270115	+	1.24528i
$304$	−1.35838			−0.0779085
$305$	21.1181	−	6.88621i	1.20922	−	0.394303i
$306$	−19.1742	−	0.832214i	−1.09612	−	0.0475745i
$307$	−3.40185	+	3.40185i	−0.194154	+	0.194154i	−0.797488	−	0.603335i	$-0.793838\pi$
$307$	−3.40185	+	3.40185i	−0.194154	+	0.194154i	0.603335	+	0.797488i	$0.293838\pi$
$308$	−26.5784	−	26.5784i	−1.51445	−	1.51445i
$309$	−5.06907	+	4.85383i	−0.288369	+	0.276125i
$310$	−15.5327	+	30.5639i	−0.882199	+	1.73591i
$311$		−	16.9575i		−	0.961573i	−0.876838	−	0.480787i	$-0.840351\pi$
$311$		−	16.9575i		−	0.961573i	0.876838	−	0.480787i	$-0.159649\pi$
$312$	11.5978	−	6.21943i	0.656594	−	0.352106i
$313$	−15.7739	+	15.7739i	−0.891595	+	0.891595i	−0.994673	−	0.103078i	$-0.967131\pi$
$313$	−15.7739	+	15.7739i	−0.891595	+	0.891595i	0.103078	+	0.994673i	$0.467131\pi$
$314$		−	39.4933i		−	2.22873i
$315$	14.9084	−	26.4311i	0.839992	−	1.48922i
$316$	15.9678			0.898260
$317$	9.13373	+	9.13373i	0.513001	+	0.513001i	0.915445	−	0.402443i	$-0.131839\pi$
$317$	9.13373	+	9.13373i	0.513001	+	0.513001i	−0.402443	+	0.915445i	$0.631839\pi$
$318$	−1.06545	+	49.1192i	−0.0597475	+	2.75447i
$319$	1.03534			0.0579682
$320$	8.96586	+	27.4958i	0.501207	+	1.53706i
$321$	−16.2327	+	15.5435i	−0.906023	+	0.867553i
$322$	28.3096	+	28.3096i	1.57763	+	1.57763i
$323$	−2.28773	+	2.28773i	−0.127293	+	0.127293i
$324$	−2.29833	+	26.4270i	−0.127685	+	1.46816i
$325$	−16.8788	+	6.33286i	−0.936269	+	0.351284i
$326$		−	15.1599i		−	0.839627i
$327$	−11.9892	−	0.260060i	−0.663004	−	0.0143813i
$328$	5.55925	−	5.55925i	0.306958	−	0.306958i
$329$	10.6152			0.585237
$330$	−21.4064	−	11.4696i	−1.17839	−	0.631380i
$331$		−	10.6346i		−	0.584533i	−0.956337	−	0.292266i	$-0.905591\pi$
$331$		−	10.6346i		−	0.584533i	0.956337	−	0.292266i	$-0.0944094\pi$
$332$	13.5158	+	13.5158i	0.741777	+	0.741777i
$333$	−6.48545	+	5.94590i	−0.355400	+	0.325833i
$334$		−	37.1736i		−	2.03405i
$335$	−4.34176	+	8.54334i	−0.237216	+	0.466773i
$336$	−6.83394	+	6.54376i	−0.372822	+	0.356992i
$337$	2.87201	+	2.87201i	0.156448	+	0.156448i	0.780991	−	0.624543i	$-0.214715\pi$
$337$	2.87201	+	2.87201i	0.156448	+	0.156448i	−0.624543	+	0.780991i	$0.714715\pi$
$338$	−6.94201	−	28.0699i	−0.377596	−	1.52680i
$339$	5.99436	+	6.26017i	0.325569	+	0.340006i
$340$	16.8988	+	8.58803i	0.916465	+	0.465751i
$341$			19.4328i			1.05234i
$342$	5.07247	+	5.53277i	0.274288	+	0.299178i
$343$	−20.6751	−	20.6751i	−1.11635	−	1.11635i
$344$			9.69553i			0.522748i
$345$	13.5835	+	7.27806i	0.731311	+	0.391838i
$346$		−	13.0875i		−	0.703590i
$347$	−12.2533	+	12.2533i	−0.657790	+	0.657790i	−0.954857	−	0.297066i	$-0.903992\pi$
$347$	−12.2533	+	12.2533i	−0.657790	+	0.657790i	0.297066	+	0.954857i	$0.403992\pi$
$348$	−0.0406587	+	1.87444i	−0.00217954	+	0.100481i
$349$	14.7082			0.787311			0.393656	−	0.919258i	$-0.371210\pi$
$349$	14.7082			0.787311			0.393656	+	0.919258i	$0.371210\pi$
$350$	−40.6390	+	29.6566i	−2.17225	+	1.58521i
$351$	17.6840	+	6.18671i	0.943903	+	0.330222i
$352$	13.7558	+	13.7558i	0.733187	+	0.733187i
$353$	−20.3803	+	20.3803i	−1.08474	+	1.08474i	−0.0886743	+	0.996061i	$0.528263\pi$
$353$	−20.3803	+	20.3803i	−1.08474	+	1.08474i	−0.996061	+	0.0886743i	$0.971737\pi$
$354$	0.0809349	−	0.0774983i	0.00430164	−	0.00411899i
$355$	3.39741	−	1.10783i	0.180316	−	0.0587975i
$356$	−41.5833			−2.20391
$357$	−0.488707	+	22.5302i	−0.0258651	+	1.19243i
$358$	8.67756	+	8.67756i	0.458623	+	0.458623i
$359$			11.3546i			0.599274i	0.954053	+	0.299637i	$0.0968656\pi$
$359$			11.3546i			0.599274i	−0.954053	+	0.299637i	$0.903134\pi$
$360$	6.94493	−	12.3127i	0.366030	−	0.648934i
$361$	−17.7347			−0.933403
$362$	−24.3785	−	24.3785i	−1.28131	−	1.28131i
$363$	5.28599	+	0.114659i	0.277443	+	0.00601805i
$364$	−23.6326	−	41.8633i	−1.23869	−	2.19423i
$365$	3.97450	+	2.01986i	0.208035	+	0.105724i
$366$	26.4680	+	27.6417i	1.38350	+	1.44485i
$367$	−7.61351	−	7.61351i	−0.397422	−	0.397422i	0.479901	−	0.877323i	$-0.340673\pi$
$367$	−7.61351	−	7.61351i	−0.397422	−	0.397422i	−0.877323	+	0.479901i	$0.840673\pi$
$368$	−3.39760	−	3.39760i	−0.177112	−	0.177112i
$369$	11.1819	+	0.485325i	0.582106	+	0.0252650i
$370$	13.8683	−	4.52218i	0.720978	−	0.235097i
$371$	57.6892			2.99507
$372$	−35.1821	−	0.763140i	−1.82411	−	0.0395670i
$373$	3.82793	−	3.82793i	0.198203	−	0.198203i	−0.601026	−	0.799229i	$-0.705241\pi$
$373$	3.82793	−	3.82793i	0.198203	−	0.198203i	0.799229	+	0.601026i	$0.205241\pi$
$374$	18.0351			0.932573
$375$	−11.6709	+	15.4529i	−0.602681	+	0.797982i
$376$	4.94501			0.255019
$377$	1.27567	+	0.355081i	0.0657005	+	0.0182876i
$378$	52.1725	+	3.39931i	2.68346	+	0.174842i
$379$	−34.1628			−1.75482			−0.877412	−	0.479738i	$-0.840732\pi$
$379$	−34.1628			−1.75482			−0.877412	+	0.479738i	$0.840732\pi$
$380$	−2.29833	−	7.04836i	−0.117902	−	0.361573i
$381$	−12.4387	−	12.9902i	−0.637252	−	0.665510i
$382$	28.6583	−	28.6583i	1.46629	−	1.46629i
$383$	−14.2931	+	14.2931i	−0.730343	+	0.730343i	−0.970688	−	0.240344i	$-0.922740\pi$
$383$	−14.2931	+	14.2931i	−0.730343	+	0.730343i	0.240344	+	0.970688i	$0.422740\pi$
$384$	−18.7239	+	17.9289i	−0.955502	+	0.914930i
$385$	−12.9193	+	25.4215i	−0.658429	+	1.29560i
$386$			18.9557i			0.964819i
$387$	−10.1740	+	9.32760i	−0.517175	+	0.474149i
$388$	−33.3018	−	33.3018i	−1.69064	−	1.69064i
$389$	−33.9053			−1.71907			−0.859533	−	0.511080i	$-0.829245\pi$
$389$	−33.9053			−1.71907			−0.859533	+	0.511080i	$0.829245\pi$
$390$	−22.4418	−	21.4735i	−1.13638	−	1.08735i
$391$	−11.4442			−0.578759
$392$	−20.0620	−	20.0620i	−1.01328	−	1.01328i
$393$	0.0784539	−	3.61686i	0.00395748	−	0.182447i
$394$			21.1613i			1.06609i
$395$	−3.75554	−	11.5172i	−0.188962	−	0.579494i
$396$	1.08089	−	24.9038i	0.0543170	−	1.25147i
$397$	−3.85818	+	3.85818i	−0.193636	+	0.193636i	−0.797265	−	0.603629i	$-0.793721\pi$
$397$	−3.85818	+	3.85818i	−0.193636	+	0.193636i	0.603629	+	0.797265i	$0.293721\pi$
$398$	−8.55499	+	8.55499i	−0.428823	+	0.428823i
$399$	6.36587	−	6.09557i	0.318692	−	0.305160i
$400$	4.87732	−	3.55925i	0.243866	−	0.177962i
$401$	11.0143			0.550028			0.275014	−	0.961440i	$-0.411318\pi$
$401$	11.0143			0.550028			0.275014	+	0.961440i	$0.411318\pi$
$402$	−16.5074	−	0.358063i	−0.823312	−	0.0178586i
$403$	−6.66465	+	23.9436i	−0.331990	+	1.19272i
$404$	36.8952			1.83561
$405$	19.6017	−	4.55774i	0.974017	−	0.226476i
$406$	3.69532			0.183396
$407$	5.84640	−	5.84640i	0.289795	−	0.289795i
$408$	−0.227660	+	10.4955i	−0.0112708	+	0.519605i
$409$	32.6861			1.61622			0.808111	−	0.589030i	$-0.200490\pi$
$409$	32.6861			1.61622			0.808111	+	0.589030i	$0.200490\pi$
$410$	−16.5421	−	8.40674i	−0.816954	−	0.415179i
$411$	−6.62961	−	6.92360i	−0.327015	−	0.341516i
$412$	8.44483	+	8.44483i	0.416047	+	0.416047i
$413$	−0.0930378	−	0.0930378i	−0.00457809	−	0.00457809i
$414$	−1.15130	+	26.5260i	−0.0565832	+	1.30368i
$415$	6.56980	−	12.9275i	0.322499	−	0.634586i
$416$	12.2312	+	21.6665i	0.599683	+	1.06229i
$417$	0.644298	−	29.7033i	0.0315514	−	1.45457i
$418$	−4.98759	−	4.98759i	−0.243951	−	0.243951i
$419$	25.4271			1.24220			0.621099	−	0.783732i	$-0.286687\pi$
$419$	25.4271			1.24220			0.621099	+	0.783732i	$0.286687\pi$
$420$	−45.5170	−	24.3881i	−2.22100	−	1.19002i
$421$			4.27667i			0.208432i	0.994555	+	0.104216i	$0.0332334\pi$
$421$			4.27667i			0.208432i	−0.994555	+	0.104216i	$0.966767\pi$
$422$	−1.98802	−	1.98802i	−0.0967752	−	0.0967752i
$423$	4.75735	+	5.18905i	0.231310	+	0.252300i
$424$	26.8740			1.30512
$425$	2.21984	−	14.2086i	0.107678	−	0.689216i
$426$	4.25808	+	4.44690i	0.206305	+	0.215453i
$427$	31.7752	−	31.7752i	1.53771	−	1.53771i
$428$	27.0430	+	27.0430i	1.30717	+	1.30717i
$429$	−16.8542	−	5.08764i	−0.813730	−	0.245634i
$430$	21.7558	−	7.09415i	1.04916	−	0.342110i
$431$	−17.6300			−0.849205			−0.424603	−	0.905380i	$-0.639586\pi$
$431$	−17.6300			−0.849205			−0.424603	+	0.905380i	$0.639586\pi$
$432$	−6.26151	−	0.407970i	−0.301257	−	0.0196285i
$433$	21.8405	−	21.8405i	1.04959	−	1.04959i	0.0508807	−	0.998705i	$-0.483797\pi$
$433$	21.8405	−	21.8405i	1.04959	−	1.04959i	0.998705	−	0.0508807i	$-0.0162028\pi$
$434$			69.3589i			3.32933i
$435$	1.36155	−	0.411532i	0.0652814	−	0.0197314i
$436$			20.4067i			0.977304i
$437$	3.16489	+	3.16489i	0.151397	+	0.151397i
$438$	−0.166577	+	7.67949i	−0.00795935	+	0.366940i
$439$		−	23.4447i		−	1.11896i	−0.828845	−	0.559478i	$-0.811002\pi$
$439$		−	23.4447i		−	1.11896i	0.828845	−	0.559478i	$-0.188998\pi$
$440$	−6.01834	+	11.8424i	−0.286913	+	0.564563i
$441$	1.75142	−	40.3527i	0.0834008	−	1.92156i
$442$	22.2215	+	6.18530i	1.05697	+	0.294205i
$443$	11.4089	+	11.4089i	0.542054	+	0.542054i	0.924131	−	0.382076i	$-0.124791\pi$
$443$	11.4089	+	11.4089i	0.542054	+	0.542054i	−0.382076	+	0.924131i	$0.624791\pi$
$444$	10.3550	+	10.8142i	0.491428	+	0.513220i
$445$	9.78015	+	29.9930i	0.463624	+	1.42181i
$446$		−	42.9852i		−	2.03541i
$447$	−0.110684	+	5.10272i	−0.00523517	+	0.241350i
$448$	41.3713	+	41.3713i	1.95461	+	1.95461i
$449$		−	20.1684i		−	0.951808i	−0.879497	−	0.475904i	$-0.842121\pi$
$449$		−	20.1684i		−	0.951808i	0.879497	−	0.475904i	$-0.157879\pi$
$450$	−32.7100	−	6.57466i	−1.54196	−	0.309932i
$451$	−10.5176			−0.495253
$452$	10.4292	−	10.4292i	0.490546	−	0.490546i
$453$	0.0422518	−	1.94788i	0.00198516	−	0.0915195i
$454$		−	1.00383i		−	0.0471119i
$455$	−24.6367	+	26.8917i	−1.15499	+	1.26070i
$456$	2.96548	−	2.83956i	0.138871	−	0.132975i
$457$	9.04890	−	9.04890i	0.423290	−	0.423290i	−0.463045	−	0.886335i	$-0.653243\pi$
$457$	9.04890	−	9.04890i	0.423290	−	0.423290i	0.886335	+	0.463045i	$0.153243\pi$
$458$	15.6890	+	15.6890i	0.733098	+	0.733098i
$459$	−11.2325	+	9.85833i	−0.524288	+	0.460147i
$460$	11.8808	−	23.3781i	0.553946	−	1.09001i
$461$	−17.6354			−0.821365			−0.410682	−	0.911779i	$-0.634709\pi$
$461$	−17.6354			−0.821365			−0.410682	+	0.911779i	$0.634709\pi$
$462$	−49.1192	−	1.06545i	−2.28523	−	0.0495693i
$463$	21.8211	+	21.8211i	1.01411	+	1.01411i	0.999899	+	0.0142127i	$0.00452421\pi$
$463$	21.8211	+	21.8211i	1.01411	+	1.01411i	0.0142127	+	0.999899i	$0.495476\pi$
$464$	−0.443496			−0.0205888
$465$	7.72420	+	25.5555i	0.358201	+	1.18511i
$466$			18.8996i			0.875509i
$467$	21.6520	−	21.6520i	1.00194	−	1.00194i	0.00193691	−	0.999998i	$-0.499383\pi$
$467$	21.6520	−	21.6520i	1.00194	−	1.00194i	0.999998	−	0.00193691i	$-0.000616538\pi$
$468$	9.87280	−	30.3139i	0.456370	−	1.40126i
$469$			19.3874i			0.895229i
$470$	−3.61823	−	11.0961i	−0.166896	−	0.511825i
$471$	−21.2693	−	22.2125i	−0.980038	−	1.02350i
$472$	−0.0433408	−	0.0433408i	−0.00199492	−	0.00199492i
$473$	9.17151	−	9.17151i	0.421707	−	0.421707i
$474$	15.0750	−	14.4349i	0.692417	−	0.663016i
$475$	−4.54326	+	3.31547i	−0.208459	+	0.152124i
$476$	38.3485			1.75770
$477$	25.8542	+	28.2003i	1.18378	+	1.29120i
$478$	9.51492	−	9.51492i	0.435202	−	0.435202i
$479$		−	32.2569i		−	1.47386i	−0.675971	−	0.736928i	$-0.736276\pi$
$479$		−	32.2569i		−	1.47386i	0.675971	−	0.736928i	$-0.263724\pi$
$480$	23.5576	+	12.6222i	1.07525	+	0.576121i
$481$	9.20857	−	5.19842i	0.419875	−	0.237027i
$482$	−40.1787	+	40.1787i	−1.83009	+	1.83009i
$483$	31.1687	+	0.676085i	1.41822	+	0.0307629i
$484$		−	8.99723i		−	0.408965i
$485$	−16.1874	+	31.8522i	−0.735032	+	1.44633i
$486$	21.7201	+	27.0270i	0.985244	+	1.22597i
$487$	−5.05289	+	5.05289i	−0.228968	+	0.228968i	−0.812262	−	0.583293i	$-0.801764\pi$
$487$	−5.05289	+	5.05289i	−0.228968	+	0.228968i	0.583293	+	0.812262i	$0.301764\pi$
$488$	14.8022	−	14.8022i	0.670063	−	0.670063i
$489$	−8.16443	−	8.52647i	−0.369208	−	0.385580i
$490$	−30.3379	+	59.6963i	−1.37053	+	2.69680i
$491$			26.1702i			1.18104i	0.807022	+	0.590522i	$0.201078\pi$
$491$			26.1702i			1.18104i	−0.807022	+	0.590522i	$0.798922\pi$
$492$	0.413033	−	19.0415i	0.0186210	−	0.858459i
$493$	−0.746919	+	0.746919i	−0.0336395	+	0.0336395i
$494$	−4.43480	−	7.85588i	−0.199531	−	0.353453i
$495$	−18.2168	+	5.07762i	−0.818784	+	0.228222i
$496$		−	8.32415i		−	0.373765i
$497$	5.11188	−	5.11188i	0.229299	−	0.229299i
$498$	24.9784	+	0.541810i	1.11931	+	0.0242791i
$499$	−19.6289			−0.878712			−0.439356	−	0.898313i	$-0.644793\pi$
$499$	−19.6289			−0.878712			−0.439356	+	0.898313i	$0.644793\pi$
$500$	26.7205	+	19.2853i	1.19498	+	0.862464i
$501$	−20.0201	−	20.9078i	−0.894430	−	0.934093i
$502$	11.6700	−	11.6700i	0.520857	−	0.520857i
$503$	30.7794	+	30.7794i	1.37239	+	1.37239i	0.856896	+	0.515489i	$0.172390\pi$
$503$	30.7794	+	30.7794i	1.37239	+	1.37239i	0.515489	+	0.856896i	$0.327610\pi$
$504$	1.24008	−	28.5714i	0.0552374	−	1.27267i
$505$	−8.67756	−	26.6117i	−0.386146	−	1.18420i
$506$		−	24.9501i		−	1.10917i
$507$	−19.0217	−	12.0489i	−0.844782	−	0.535111i
$508$	−21.6411	+	21.6411i	−0.960170	+	0.960170i
$509$		−	7.50375i		−	0.332598i	−0.986075	−	0.166299i	$-0.946818\pi$
$509$		−	7.50375i		−	0.332598i	0.986075	−	0.166299i	$-0.0531817\pi$
$510$	23.7175	−	7.16864i	1.05023	−	0.317433i
$511$	9.01935			0.398993
$512$	−9.49120	−	9.49120i	−0.419456	−	0.419456i
$513$	5.83265	+	0.380028i	0.257518	+	0.0167786i
$514$	−30.7881			−1.35801
$515$	4.10488	−	8.07723i	0.180883	−	0.355925i
$516$	16.2444	+	16.9647i	0.715120	+	0.746831i
$517$	−4.67775	−	4.67775i	−0.205727	−	0.205727i
$518$	20.8668	−	20.8668i	0.916834	−	0.916834i
$519$	−7.04836	−	7.36091i	−0.309389	−	0.323108i
$520$	−11.4768	+	12.5272i	−0.503291	+	0.549356i
$521$		−	3.88636i		−	0.170264i	−0.996370	−	0.0851322i	$-0.972869\pi$
$521$		−	3.88636i		−	0.170264i	0.996370	−	0.0851322i	$-0.0271312\pi$
$522$	1.65610	+	1.80639i	0.0724857	+	0.0790634i
$523$	26.2758	−	26.2758i	1.14896	−	1.14896i	0.162203	−	0.986757i	$-0.448140\pi$
$523$	26.2758	−	26.2758i	1.14896	−	1.14896i	0.986757	−	0.162203i	$-0.0518598\pi$
$524$	−6.15623			−0.268936
$525$	−6.88521	+	38.5663i	−0.300495	+	1.68317i
$526$			23.2658i			1.01444i
$527$	−14.0192	−	14.0192i	−0.610687	−	0.610687i
$528$	5.89507	+	0.127871i	0.256550	+	0.00556486i
$529$		−	7.16788i		−	0.311647i
$530$	−19.6635	−	60.3025i	−0.854128	−	2.61937i
$531$	0.00378367	−	0.0871759i	0.000164197	−	0.00378311i
$532$	−10.6052	−	10.6052i	−0.459796	−	0.459796i
$533$	−12.9590	−	3.60710i	−0.561315	−	0.156241i
$534$	−39.2582	+	37.5912i	−1.69887	+	1.62673i
$535$	13.1451	−	25.8658i	0.568313	−	1.11828i
$536$			9.03146i			0.390100i
$537$	9.55393	+	0.207236i	0.412282	+	0.00894288i
$538$	29.6633	+	29.6633i	1.27887	+	1.27887i
$539$			37.9554i			1.63485i
$540$	−8.47739	−	33.1800i	−0.364809	−	1.42784i
$541$		−	15.7873i		−	0.678749i	−0.940651	−	0.339374i	$-0.889785\pi$
$541$		−	15.7873i		−	0.678749i	0.940651	−	0.339374i	$-0.110215\pi$
$542$	39.7662	−	39.7662i	1.70811	−	1.70811i
$543$	−26.8406	−	0.582203i	−1.15184	−	0.0249847i
$544$	−19.8475			−0.850953
$545$	14.7189	−	4.79954i	0.630488	−	0.205590i
$546$	−60.1556	−	18.1586i	−2.57442	−	0.777118i
$547$	−12.4325	−	12.4325i	−0.531575	−	0.531575i	0.389466	−	0.921041i	$-0.372660\pi$
$547$	−12.4325	−	12.4325i	−0.531575	−	0.531575i	−0.921041	+	0.389466i	$0.872660\pi$
$548$	−11.5344	+	11.5344i	−0.492725	+	0.492725i
$549$	29.7732	+	1.29224i	1.27069	+	0.0551513i
$550$	30.9767	+	4.83958i	1.32085	+	0.206360i
$551$	0.413120			0.0175995
$552$	14.5197	+	0.314948i	0.617997	+	0.0134051i
$553$	−17.3293	−	17.3293i	−0.736916	−	0.736916i
$554$			72.9457i			3.09916i
$555$	5.36459	−	10.0123i	0.227714	−	0.424998i
$556$	−50.5576			−2.14412
$557$	27.1000	+	27.1000i	1.14826	+	1.14826i	0.986894	+	0.161370i	$0.0515914\pi$
$557$	27.1000	+	27.1000i	1.14826	+	1.14826i	0.161370	+	0.986894i	$0.448409\pi$
$558$	−33.9048	+	31.0841i	−1.43530	+	1.31589i
$559$	14.4459	−	8.15500i	0.610997	−	0.344920i
$560$	5.53406	−	10.8894i	0.233857	−	0.460163i
$561$	10.1436	−	9.71290i	0.428264	−	0.410079i
$562$	16.6593	+	16.6593i	0.702728	+	0.702728i
$563$	−11.3159	−	11.3159i	−0.476908	−	0.476908i	0.427234	−	0.904141i	$-0.359488\pi$
$563$	−11.3159	−	11.3159i	−0.476908	−	0.476908i	−0.904141	+	0.427234i	$0.859488\pi$
$564$	8.65252	−	8.28513i	0.364337	−	0.348867i
$565$	−9.97519	−	5.06943i	−0.419659	−	0.213272i
$566$	−32.3633			−1.36033
$567$	31.1745	−	26.1859i	1.30921	−	1.09970i
$568$	2.38132	−	2.38132i	0.0999181	−	0.0999181i
$569$	−24.5114			−1.02757			−0.513787	−	0.857918i	$-0.671758\pi$
$569$	−24.5114			−1.02757			−0.513787	+	0.857918i	$0.671758\pi$
$570$	−8.54153	−	4.57656i	−0.357765	−	0.191691i
$571$	−5.75974			−0.241038			−0.120519	−	0.992711i	$-0.538456\pi$
$571$	−5.75974			−0.241038			−0.120519	+	0.992711i	$0.538456\pi$
$572$	−8.03358	+	28.8617i	−0.335901	+	1.20677i
$573$	0.684412	−	31.5526i	0.0285917	−	1.31813i
$574$	−37.5390			−1.56685
$575$	−19.6563	−	3.07097i	−0.819726	−	0.128068i
$576$	−1.68249	+	38.7647i	−0.0701039	+	1.61520i
$577$	−12.2388	+	12.2388i	−0.509507	+	0.509507i	−0.914375	−	0.404868i	$-0.867317\pi$
$577$	−12.2388	+	12.2388i	−0.509507	+	0.509507i	0.404868	+	0.914375i	$0.367317\pi$
$578$	13.7267	−	13.7267i	0.570957	−	0.570957i
$579$	10.2087	+	10.6614i	0.424259	+	0.443072i
$580$	−0.750379	−	2.30121i	−0.0311578	−	0.0955525i
$581$		−	29.3364i		−	1.21708i
$582$	−61.5445	−	1.33497i	−2.55110	−	0.0553363i
$583$	−25.4215	−	25.4215i	−1.05285	−	1.05285i
$584$	4.20158			0.173863
$585$	−24.1868	+	0.00865171i	−1.00000	+	0.000357704i
$586$	−55.1189			−2.27694
$587$	−4.62321	−	4.62321i	−0.190820	−	0.190820i	0.605230	−	0.796051i	$-0.293081\pi$
$587$	−4.62321	−	4.62321i	−0.190820	−	0.190820i	−0.796051	+	0.605230i	$0.793081\pi$
$588$	−68.7163	−	1.49054i	−2.83381	−	0.0614686i
$589$			7.75401i			0.319498i
$590$	−0.0655403	+	0.128965i	−0.00269825	+	0.00530939i
$591$	11.3965	+	11.9019i	0.468791	+	0.489579i
$592$	−2.50434	+	2.50434i	−0.102928	+	0.102928i
$593$	1.14398	−	1.14398i	0.0469777	−	0.0469777i	−0.683228	−	0.730205i	$-0.739424\pi$
$593$	1.14398	−	1.14398i	0.0469777	−	0.0469777i	0.730205	+	0.683228i	$0.239424\pi$
$594$	−21.4926	−	24.4885i	−0.881851	−	1.00477i
$595$	−9.01935	−	27.6599i	−0.369757	−	1.13394i
$596$	8.68529			0.355763
$597$	−0.204309	+	9.41898i	−0.00836179	+	0.385493i
$598$	8.55685	−	30.7416i	0.349915	−	1.25712i
$599$	−20.1045			−0.821447			−0.410723	−	0.911760i	$-0.634724\pi$
$599$	−20.1045			−0.821447			−0.410723	+	0.911760i	$0.634724\pi$
$600$	−3.20741	+	17.9658i	−0.130942	+	0.733449i
$601$	−2.94840			−0.120268			−0.0601338	−	0.998190i	$-0.519153\pi$
$601$	−2.94840			−0.120268			−0.0601338	+	0.998190i	$0.519153\pi$
$602$	32.7347	−	32.7347i	1.33417	−	1.33417i
$603$	−9.47719	+	8.68874i	−0.385941	+	0.353833i
$604$	−3.31547			−0.134905
$605$	−6.48950	+	2.11610i	−0.263836	+	0.0860317i
$606$	34.8323	−	33.3532i	1.41496	−	1.35488i
$607$	13.2165	+	13.2165i	0.536440	+	0.536440i	0.922481	−	0.386041i	$-0.126158\pi$
$607$	13.2165	+	13.2165i	0.536440	+	0.536440i	−0.386041	+	0.922481i	$0.626158\pi$
$608$	5.48880	+	5.48880i	0.222600	+	0.222600i
$609$	2.07838	−	1.99013i	0.0842204	−	0.0806443i
$610$	−44.0453	−	22.3840i	−1.78334	−	0.906301i
$611$	−4.15929	−	7.36784i	−0.168267	−	0.298071i
$612$	17.1864	+	18.7459i	0.694718	+	0.757760i
$613$	−14.8172	−	14.8172i	−0.598463	−	0.598463i	0.341440	−	0.939903i	$-0.389085\pi$
$613$	−14.8172	−	14.8172i	−0.598463	−	0.598463i	−0.939903	+	0.341440i	$0.889085\pi$
$614$	10.7009			0.431852
$615$	−13.8314	+	4.18056i	−0.557735	+	0.168576i
$616$			26.8740i			1.08278i
$617$	−17.5429	−	17.5429i	−0.706252	−	0.706252i	0.259493	−	0.965745i	$-0.416445\pi$
$617$	−17.5429	−	17.5429i	−0.706252	−	0.706252i	−0.965745	+	0.259493i	$0.916445\pi$
$618$	15.6067	+	0.338528i	0.627795	+	0.0136176i
$619$	13.6862			0.550096			0.275048	−	0.961430i	$-0.411306\pi$
$619$	13.6862			0.550096			0.275048	+	0.961430i	$0.411306\pi$
$620$	43.1923	−	14.0842i	1.73464	−	0.565634i
$621$	13.6382	+	15.5392i	0.547281	+	0.623568i
$622$	−26.6708	+	26.6708i	−1.06940	+	1.06940i
$623$	45.1288	+	45.1288i	1.80805	+	1.80805i
$624$	7.21960	+	2.17932i	0.289015	+	0.0872426i
$625$	7.62552	−	23.8086i	0.305021	−	0.952346i
$626$	49.6185			1.98315
$627$	−5.49130	−	0.119113i	−0.219302	−	0.00475690i
$628$	−37.0050	+	37.0050i	−1.47666	+	1.47666i
$629$			8.43543i			0.336343i
$630$	−65.0188	+	18.1229i	−2.59041	+	0.722033i
$631$			23.8965i			0.951306i	0.879633	+	0.475653i	$0.157788\pi$
$631$			23.8965i			0.951306i	−0.879633	+	0.475653i	$0.842212\pi$
$632$	−8.07269	−	8.07269i	−0.321114	−	0.321114i
$633$	−2.18879	−	0.0474774i	−0.0869967	−	0.00188706i
$634$		−	28.7311i		−	1.14106i
$635$	20.6991	+	10.5194i	0.821420	+	0.417449i
$636$	47.0227	−	45.0261i	1.86457	−	1.78540i
$637$	−13.0171	+	46.7657i	−0.515758	+	1.85293i
$638$	−1.62839	−	1.62839i	−0.0644687	−	0.0644687i
$639$	4.78980	+	0.207890i	0.189482	+	0.00822402i
$640$	15.1625	−	29.8354i	0.599349	−	1.17935i
$641$		−	21.5542i		−	0.851340i	−0.904879	−	0.425670i	$-0.860039\pi$
$641$		−	21.5542i		−	0.851340i	0.904879	−	0.425670i	$-0.139961\pi$
$642$	49.9777	+	1.08407i	1.97246	+	0.0427850i
$643$	−12.9420	−	12.9420i	−0.510382	−	0.510382i	0.404261	−	0.914644i	$-0.367529\pi$
$643$	−12.9420	−	12.9420i	−0.510382	−	0.510382i	−0.914644	+	0.404261i	$0.867529\pi$
$644$		−	53.0519i		−	2.09054i
$645$	8.41568	−	15.7067i	0.331367	−	0.618452i
$646$	7.19631			0.283135
$647$	4.00836	−	4.00836i	0.157585	−	0.157585i	−0.623911	−	0.781496i	$-0.714457\pi$
$647$	4.00836	−	4.00836i	0.157585	−	0.157585i	0.781496	+	0.623911i	$0.214457\pi$
$648$	14.5223	−	12.1985i	0.570492	−	0.479201i
$649$			0.0819968i			0.00321865i
$650$	36.5074	+	16.5867i	1.43194	+	0.650584i
$651$	37.3536	+	39.0100i	1.46400	+	1.52892i
$652$	−14.2047	+	14.2047i	−0.556299	+	0.556299i
$653$	−30.3911	−	30.3911i	−1.18929	−	1.18929i	−0.977263	−	0.212032i	$-0.931992\pi$
$653$	−30.3911	−	30.3911i	−1.18929	−	1.18929i	−0.212032	−	0.977263i	$-0.568008\pi$
$654$	18.4476	+	19.2657i	0.721359	+	0.753347i
$655$	1.44791	+	4.44034i	0.0565745	+	0.173499i
$656$	4.50526			0.175901
$657$	4.04214	+	4.40894i	0.157699	+	0.172009i
$658$	−16.6957	−	16.6957i	−0.650864	−	0.650864i
$659$	0.825043			0.0321391			0.0160695	−	0.999871i	$-0.494885\pi$
$659$	0.825043			0.0321391			0.0160695	+	0.999871i	$0.494885\pi$
$660$	9.31076	+	30.8046i	0.362421	+	1.19907i
$661$		−	7.76920i		−	0.302187i	−0.988519	−	0.151093i	$-0.951721\pi$
$661$		−	7.76920i		−	0.302187i	0.988519	−	0.151093i	$-0.0482794\pi$
$662$	−16.7262	+	16.7262i	−0.650082	+	0.650082i
$663$	15.8293	−	8.48866i	0.614760	−	0.329672i
$664$		−	13.6661i		−	0.530348i
$665$	−5.15502	+	10.1436i	−0.199903	+	0.393352i
$666$	19.5520	+	0.848612i	0.757626	+	0.0328830i
$667$	1.03330	+	1.03330i	0.0400095	+	0.0400095i
$668$	−34.8315	+	34.8315i	−1.34767	+	1.34767i
$669$	−23.1499	−	24.1764i	−0.895026	−	0.934716i
$670$	20.2657	−	6.60826i	0.782933	−	0.255299i
$671$	−28.0043			−1.08110
$672$	54.0552	+	1.17252i	2.08522	+	0.0452309i
$673$	−0.296312	+	0.296312i	−0.0114220	+	0.0114220i	−0.712795	−	0.701373i	$-0.752571\pi$
$673$	−0.296312	+	0.296312i	−0.0114220	+	0.0114220i	0.701373	+	0.712795i	$0.252571\pi$
$674$		−	9.03420i		−	0.347984i
$675$	−21.9381	+	13.9183i	−0.844399	+	0.535715i
$676$	−19.7967	+	32.8060i	−0.761413	+	1.26177i
$677$	−33.5761	+	33.5761i	−1.29044	+	1.29044i	−0.355919	+	0.934517i	$0.615832\pi$
$677$	−33.5761	+	33.5761i	−1.29044	+	1.29044i	−0.934517	+	0.355919i	$0.884168\pi$
$678$	0.418074	−	19.2739i	0.0160560	−	0.740211i
$679$			72.2823i			2.77394i
$680$	−4.20158	−	12.8851i	−0.161123	−	0.494121i
$681$	−0.540616	−	0.564589i	−0.0207164	−	0.0216351i
$682$	30.5639	−	30.5639i	1.17035	−	1.17035i
$683$	−18.3743	+	18.3743i	−0.703075	+	0.703075i	−0.965069	−	0.261994i	$-0.915620\pi$
$683$	−18.3743	+	18.3743i	−0.703075	+	0.703075i	0.261994	+	0.965069i	$0.415620\pi$
$684$	0.431295	−	9.93705i	0.0164910	−	0.379953i
$685$	11.0323	+	5.60666i	0.421523	+	0.214220i
$686$			65.0358i			2.48308i
$687$	17.2735	+	0.374681i	0.659024	+	0.0142950i
$688$	−3.92867	+	3.92867i	−0.149779	+	0.149779i
$689$	−22.6039	−	40.0410i	−0.861142	−	1.52544i
$690$	−9.91721	−	32.8111i	−0.377542	−	1.24910i
$691$			50.1745i			1.90873i	0.298647	+	0.954364i	$0.403465\pi$
$691$			50.1745i			1.90873i	−0.298647	+	0.954364i	$0.596535\pi$
$692$	−12.2629	+	12.2629i	−0.466167	+	0.466167i
$693$	−28.2003	+	25.8542i	−1.07124	+	0.982118i
$694$	38.5440			1.46311
$695$	11.8909	+	36.4660i	0.451046	+	1.38324i
$696$	0.968196	−	0.927085i	0.0366994	−	0.0351411i
$697$	7.58760	−	7.58760i	0.287401	−	0.287401i
$698$	−23.1331	−	23.1331i	−0.875600	−	0.875600i
$699$	10.1785	+	10.6299i	0.384986	+	0.402058i
$700$	65.8666	+	10.2905i	2.48952	+	0.388945i
$701$			25.0442i			0.945906i	0.881088	+	0.472953i	$0.156812\pi$
$701$			25.0442i			0.945906i	−0.881088	+	0.472953i	$0.843188\pi$
$702$	−18.0830	−	37.5439i	−0.682498	−	1.41700i
$703$	2.33281	−	2.33281i	0.0879837	−	0.0879837i
$704$		−	36.4617i		−	1.37420i
$705$	−8.01089	−	4.29225i	−0.301708	−	0.161655i
$706$	64.1084			2.41275
$707$	−40.0410	−	40.0410i	−1.50590	−	1.50590i
$708$	−0.148451	−	0.00322007i	−0.00557913	−	0.000121018i
$709$	−34.4704			−1.29456			−0.647282	−	0.762251i	$-0.724094\pi$
$709$	−34.4704			−1.29456			−0.647282	+	0.762251i	$0.724094\pi$
$710$	−7.08585	−	3.60106i	−0.265927	−	0.135145i
$711$	0.704749	−	16.2374i	0.0264301	−	0.608951i
$712$	21.0228	+	21.0228i	0.787863	+	0.787863i
$713$	−19.3944	+	19.3944i	−0.726327	+	0.726327i
$714$	36.2042	−	34.6670i	1.35491	−	1.29738i
$715$	22.7067	−	0.993670i	0.849183	−	0.0371612i
$716$		−	16.2616i		−	0.607726i
$717$	0.227233	−	10.4759i	0.00848619	−	0.391228i
$718$	17.8586	−	17.8586i	0.666476	−	0.666476i
$719$	32.5125			1.21251			0.606255	−	0.795270i	$-0.292671\pi$
$719$	32.5125			1.21251			0.606255	+	0.795270i	$0.292671\pi$
$720$	7.80326	−	2.17503i	0.290810	−	0.0810585i
$721$		−	18.3297i		−	0.682634i
$722$	27.8931	+	27.8931i	1.03807	+	1.03807i
$723$	−0.959541	+	44.2365i	−0.0356857	+	1.64517i
$724$			45.6851i			1.69787i
$725$	−1.48332	+	1.08246i	−0.0550892	+	0.0402017i
$726$	−8.13348	−	8.49416i	−0.301862	−	0.315248i
$727$	24.3971	+	24.3971i	0.904837	+	0.904837i	0.995850	−	0.0910132i	$-0.0290105\pi$
$727$	24.3971	+	24.3971i	0.904837	+	0.904837i	−0.0910132	+	0.995850i	$0.529011\pi$
$728$	−9.21667	+	33.1121i	−0.341593	+	1.22722i
$729$	26.7717	+	3.50351i	0.991545	+	0.129760i
$730$	−3.07427	−	9.42794i	−0.113784	−	0.348944i
$731$			13.2330i			0.489442i
$732$	1.09975	−	50.7005i	0.0406480	−	1.87394i
$733$	3.61267	+	3.61267i	0.133437	+	0.133437i	0.770671	−	0.637234i	$-0.219921\pi$
$733$	3.61267	+	3.61267i	0.133437	+	0.133437i	−0.637234	+	0.770671i	$0.719921\pi$
$734$			23.9491i			0.883976i
$735$	15.0866	+	49.9140i	0.556478	+	1.84111i
$736$			27.4573i			1.01209i
$737$	8.54334	−	8.54334i	0.314698	−	0.314698i
$738$	−16.8236	−	18.3502i	−0.619285	−	0.675481i
$739$	8.45473			0.311012			0.155506	−	0.987835i	$-0.450299\pi$
$739$	8.45473			0.311012			0.155506	+	0.987835i	$0.450299\pi$
$740$	−17.2318	−	8.75724i	−0.633452	−	0.321923i
$741$	−6.72512	−	2.03005i	−0.247053	−	0.0745759i
$742$	−90.7336	−	90.7336i	−3.33094	−	3.33094i
$743$	21.2620	−	21.2620i	0.780028	−	0.780028i	−0.199807	−	0.979835i	$-0.564032\pi$
$743$	21.2620	−	21.2620i	0.780028	−	0.780028i	0.979835	+	0.199807i	$0.0640316\pi$
$744$	17.4008	+	18.1725i	0.637945	+	0.666235i
$745$	−2.04273	−	6.26450i	−0.0748399	−	0.229513i
$746$	−12.0412			−0.440858
$747$	14.3406	−	13.1475i	0.524694	−	0.481042i
$748$	−16.8988	−	16.8988i	−0.617881	−	0.617881i
$749$		−	58.6975i		−	2.14476i
$750$	42.6603	−	5.94831i	1.55773	−	0.217202i
$751$	−2.03706			−0.0743334			−0.0371667	−	0.999309i	$-0.511833\pi$
$751$	−2.03706			−0.0743334			−0.0371667	+	0.999309i	$0.511833\pi$
$752$	2.00374	+	2.00374i	0.0730688	+	0.0730688i
$753$	0.278700	−	12.8486i	0.0101564	−	0.468228i
$754$	−1.44791	−	2.56485i	−0.0527298	−	0.0934065i
$755$	0.779780	+	2.39137i	0.0283791	+	0.0870309i
$756$	−45.7002	−	52.0705i	−1.66210	−	1.89378i
$757$	−9.91296	−	9.91296i	−0.360293	−	0.360293i	0.503628	−	0.863921i	$-0.331998\pi$
$757$	−9.91296	−	9.91296i	−0.360293	−	0.360293i	−0.863921	+	0.503628i	$0.831998\pi$
$758$	53.7313	+	53.7313i	1.95161	+	1.95161i
$759$	−13.4370	−	14.0328i	−0.487732	−	0.509360i
$760$	−2.40142	+	4.72531i	−0.0871087	+	0.171405i
$761$	25.0081			0.906543			0.453272	−	0.891372i	$-0.350257\pi$
$761$	25.0081			0.906543			0.453272	+	0.891372i	$0.350257\pi$
$762$	−0.867529	+	39.9946i	−0.0314273	+	1.44885i
$763$	22.1466	−	22.1466i	0.801762	−	0.801762i
$764$	−53.7053			−1.94299
$765$	9.47887	−	16.8051i	0.342709	−	0.607589i
$766$	44.9604			1.62449
$767$	−0.0281215	+	0.101030i	−0.00101541	+	0.00364799i
$768$	12.8544	+	0.278827i	0.463844	+	0.0100613i
$769$	37.0720			1.33685			0.668425	−	0.743780i	$-0.266969\pi$
$769$	37.0720			1.33685			0.668425	+	0.743780i	$0.266969\pi$
$770$	60.3025	−	19.6635i	2.17315	−	0.708623i
$771$	−17.3164	+	16.5811i	−0.623635	+	0.597155i
$772$	17.7614	−	17.7614i	0.639246	−	0.639246i
$773$	−3.40655	+	3.40655i	−0.122525	+	0.122525i	−0.765711	−	0.643185i	$-0.777612\pi$
$773$	−3.40655	+	3.40655i	−0.122525	+	0.122525i	0.643185	+	0.765711i	$0.277612\pi$
$774$	30.6722	+	1.33126i	1.10249	+	0.0478510i
$775$	−20.3172	−	27.8411i	−0.729814	−	1.00008i
$776$			33.6721i			1.20876i
$777$	0.498336	−	22.9742i	0.0178777	−	0.824194i
$778$	53.3263	+	53.3263i	1.91184	+	1.91184i
$779$	−4.19669			−0.150362
$780$	0.907281	+	41.1484i	0.0324859	+	1.47335i
$781$	−4.50524			−0.161210
$782$	17.9995	+	17.9995i	0.643660	+	0.643660i
$783$	1.90429	+	0.124075i	0.0680539	+	0.00443407i
$784$		−	16.2584i		−	0.580657i
$785$	35.3942	+	17.9875i	1.26327	+	0.642000i
$786$	−5.81200	+	5.56522i	−0.207307	+	0.198505i
$787$	15.5327	−	15.5327i	0.553681	−	0.553681i	−0.373820	−	0.927501i	$-0.621952\pi$
$787$	15.5327	−	15.5327i	0.553681	−	0.553681i	0.927501	+	0.373820i	$0.121952\pi$
$788$	19.8280	−	19.8280i	0.706344	−	0.706344i
$789$	12.5299	+	13.0856i	0.446078	+	0.465859i
$790$	−12.2076	+	24.0210i	−0.434326	+	0.854630i
$791$	−22.6367			−0.804870
$792$	−13.1368	+	12.0439i	−0.466797	+	0.427962i
$793$	−34.5048	−	9.60434i	−1.22530	−	0.341060i
$794$	12.1363			0.430701
$795$	−43.5357	−	23.3265i	−1.54405	−	0.827306i
$796$	16.0320			0.568238
$797$	−25.0570	+	25.0570i	−0.887565	+	0.887565i	−0.994289	−	0.106724i	$-0.965964\pi$
$797$	−25.0570	+	25.0570i	−0.887565	+	0.887565i	0.106724	+	0.994289i	$0.465964\pi$
$798$	−19.5994	−	0.425133i	−0.693810	−	0.0150495i
$799$	6.74925			0.238771
$800$	−34.0896	−	5.32591i	−1.20525	−	0.188299i
$801$	−1.83530	+	42.2854i	−0.0648472	+	1.49408i
$802$	−17.3233	−	17.3233i	−0.611708	−	0.611708i
$803$	−3.97450	−	3.97450i	−0.140257	−	0.140257i
$804$	15.1318	+	15.8028i	0.533657	+	0.557322i
$805$	−38.2651	+	12.4775i	−1.34867	+	0.439775i
$806$	48.1408	−	27.1764i	1.69569	−	0.957248i
$807$	32.6590	+	0.708412i	1.14965	+	0.0249373i
$808$	−18.6527	−	18.6527i	−0.656201	−	0.656201i
$809$	46.4473			1.63300			0.816500	−	0.577345i	$-0.195911\pi$
$809$	46.4473			1.63300			0.816500	+	0.577345i	$0.195911\pi$
$810$	−37.9980	−	23.6612i	−1.33511	−	0.831369i
$811$			10.6193i			0.372892i	0.982465	+	0.186446i	$0.0596970\pi$
$811$			10.6193i			0.372892i	−0.982465	+	0.186446i	$0.940303\pi$
$812$	−3.46249	−	3.46249i	−0.121510	−	0.121510i
$813$	0.949689	−	43.7823i	0.0333070	−	1.53551i
$814$	−18.3905			−0.644585
$815$	13.5864	+	6.90466i	0.475911	+	0.241860i
$816$	−4.34507	+	4.16058i	−0.152108	+	0.145649i
$817$	3.65959	−	3.65959i	0.128033	−	0.128033i
$818$	−51.4087	−	51.4087i	−1.79746	−	1.79746i
$819$	−43.6132	+	22.1840i	−1.52397	+	0.775172i
$820$	7.62275	+	23.3769i	0.266198	+	0.816356i
$821$	−33.7003			−1.17615			−0.588075	−	0.808806i	$-0.700114\pi$
$821$	−33.7003			−1.17615			−0.588075	+	0.808806i	$0.700114\pi$
$822$	−0.462380	+	21.3165i	−0.0161273	+	0.743499i
$823$	21.0331	−	21.0331i	0.733169	−	0.733169i	−0.238078	−	0.971246i	$-0.576517\pi$
$823$	21.0331	−	21.0331i	0.733169	−	0.733169i	0.971246	+	0.238078i	$0.0765172\pi$
$824$		−	8.53873i		−	0.297461i
$825$	20.0288	−	13.9607i	0.697315	−	0.486050i
$826$			0.292660i			0.0101829i
$827$	29.1434	+	29.1434i	1.01342	+	1.01342i	0.999909	+	0.0135073i	$0.00429965\pi$
$827$	29.1434	+	29.1434i	1.01342	+	1.01342i	0.0135073	+	0.999909i	$0.495700\pi$
$828$	25.9334	−	23.7759i	0.901249	−	0.826270i
$829$			33.6661i			1.16927i	0.811296	+	0.584636i	$0.198763\pi$
$829$			33.6661i			1.16927i	−0.811296	+	0.584636i	$0.801237\pi$
$830$	−30.6654	+	9.99940i	−1.06441	+	0.347084i
$831$	39.2853	+	41.0274i	1.36279	+	1.42322i
$832$	12.5049	−	44.9253i	0.433528	−	1.55751i
$833$	−27.3818	−	27.3818i	−0.948723	−	0.948723i
$834$	−47.7307	+	45.7040i	−1.65278	+	1.58260i
$835$	33.3153	+	16.9310i	1.15292	+	0.585920i
$836$			9.34669i			0.323262i
$837$	−2.32881	+	35.7424i	−0.0804953	+	1.23544i
$838$	−39.9919	−	39.9919i	−1.38150	−	1.38150i
$839$			1.04638i			0.0361250i	0.999837	+	0.0180625i	$0.00574978\pi$
$839$			1.04638i			0.0361250i	−0.999837	+	0.0180625i	$0.994250\pi$
$840$	10.6819	+	35.3412i	0.368562	+	1.21939i
$841$	−28.8651			−0.995349
$842$	6.72636	−	6.72636i	0.231806	−	0.231806i
$843$	18.3417	+	0.397853i	0.631722	+	0.0137028i
$844$			3.72552i			0.128238i
$845$	28.3183	+	6.56314i	0.974179	+	0.225779i
$846$	0.678980	−	15.6437i	0.0233438	−	0.537843i
$847$	−9.76436	+	9.76436i	−0.335507	+	0.335507i
$848$	10.8894	+	10.8894i	0.373945	+	0.373945i
$849$	−18.2023	+	17.4294i	−0.624701	+	0.598176i
$850$	−25.8386	+	18.8559i	−0.886258	+	0.646751i
$851$	11.6697			0.400033
$852$	0.176924	−	8.15651i	0.00606132	−	0.279438i
$853$	1.27200	+	1.27200i	0.0435526	+	0.0435526i	0.728548	−	0.684995i	$-0.240196\pi$
$853$	1.27200	+	1.27200i	0.0435526	+	0.0435526i	−0.684995	+	0.728548i	$0.740196\pi$
$854$	−99.9522			−3.42029
$855$	−7.26880	+	2.02606i	−0.248588	+	0.0692897i
$856$		−	27.3437i		−	0.934588i
$857$	−32.9950	+	32.9950i	−1.12709	+	1.12709i	−0.136438	+	0.990649i	$0.543566\pi$
$857$	−32.9950	+	32.9950i	−1.12709	+	1.12709i	−0.990649	+	0.136438i	$0.956434\pi$
$858$	18.5065	+	34.5102i	0.631802	+	1.17816i
$859$		−	48.5229i		−	1.65558i	−0.561038	−	0.827790i	$-0.689598\pi$
$859$		−	48.5229i		−	1.65558i	0.561038	−	0.827790i	$-0.310402\pi$
$860$	−27.0322	−	13.7379i	−0.921792	−	0.468458i
$861$	−21.1133	+	20.2168i	−0.719540	+	0.688988i
$862$	27.7284	+	27.7284i	0.944435	+	0.944435i
$863$	19.3034	−	19.3034i	0.657097	−	0.657097i	−0.297595	−	0.954692i	$-0.596185\pi$
$863$	19.3034	−	19.3034i	0.657097	−	0.657097i	0.954692	+	0.297595i	$0.0961846\pi$
$864$	23.6524	+	26.9493i	0.804670	+	0.916835i
$865$	11.7291	+	5.96080i	0.398803	+	0.202673i
$866$	−68.7014			−2.33457
$867$	0.327819	−	15.1130i	0.0111333	−	0.513266i
$868$	64.9889	−	64.9889i	2.20587	−	2.20587i
$869$			15.2728i			0.518093i
$870$	−2.78871	−	1.49419i	−0.0945461	−	0.0506579i
$871$	13.4565	−	7.59645i	0.455955	−	0.257396i
$872$	10.3168	−	10.3168i	0.349371	−	0.349371i
$873$	−35.3339	+	32.3943i	−1.19587	+	1.09638i
$874$		−	9.95549i		−	0.336749i
$875$	−8.06913	−	49.9283i	−0.272786	−	1.68788i
$876$	7.35172	−	7.03955i	0.248391	−	0.237844i
$877$	−20.3172	+	20.3172i	−0.686062	+	0.686062i	−0.961359	−	0.275297i	$-0.911224\pi$
$877$	−20.3172	+	20.3172i	−0.686062	+	0.686062i	0.275297	+	0.961359i	$0.411224\pi$
$878$	−36.8739	+	36.8739i	−1.24443	+	1.24443i
$879$	−31.0009	+	29.6846i	−1.04564	+	1.00124i
$880$	−7.23724	+	2.35993i	−0.243967	+	0.0795531i
$881$			14.2114i			0.478796i	0.970922	+	0.239398i	$0.0769500\pi$
$881$			14.2114i			0.478796i	−0.970922	+	0.239398i	$0.923050\pi$
$882$	−66.2215	+	60.7122i	−2.22979	+	2.04429i
$883$	−40.2650	+	40.2650i	−1.35503	+	1.35503i	−0.475086	+	0.879939i	$0.657583\pi$
$883$	−40.2650	+	40.2650i	−1.35503	+	1.35503i	−0.879939	+	0.475086i	$0.842417\pi$
$884$	−15.0258	−	26.6170i	−0.505373	−	0.895227i
$885$	0.0325923	+	0.107832i	0.00109558	+	0.00362472i
$886$		−	35.8880i		−	1.20568i
$887$	−29.2301	+	29.2301i	−0.981451	+	0.981451i	−0.999831	−	0.0183797i	$-0.994149\pi$
$887$	−29.2301	+	29.2301i	−0.981451	+	0.981451i	0.0183797	+	0.999831i	$0.494149\pi$
$888$	0.232145	−	10.7023i	0.00779029	−	0.359146i
$889$	46.9726			1.57541
$890$	31.7909	−	62.5554i	1.06563	−	2.09686i
$891$	−25.2766	−	2.19829i	−0.846799	−	0.0736455i
$892$	−40.2768	+	40.2768i	−1.34857	+	1.34857i
$893$	−1.86650	−	1.86650i	−0.0624600	−	0.0624600i
$894$	8.19965	−	7.85148i	0.274237	−	0.262593i
$895$	−11.7291	+	3.82465i	−0.392062	+	0.127844i
$896$		−	67.7056i		−	2.26189i
$897$	−11.7434	−	21.8985i	−0.392099	−	0.731171i
$898$	−31.7210	+	31.7210i	−1.05854	+	1.05854i
$899$			2.53160i			0.0844334i
$900$	24.4886	+	36.8095i	0.816288	+	1.22698i
$901$	36.6792			1.22196
$902$	16.5421	+	16.5421i	0.550791	+	0.550791i
$903$	0.781763	−	36.0406i	0.0260154	−	1.19936i
$904$	−10.5451			−0.350725
$905$	32.9516	−	10.7449i	1.09535	−	0.357172i
$906$	−3.13009	+	2.99718i	−0.103990	+	0.0995746i
$907$	9.52059	+	9.52059i	0.316126	+	0.316126i	0.847277	−	0.531151i	$-0.178240\pi$
$907$	9.52059	+	9.52059i	0.316126	+	0.316126i	−0.531151	+	0.847277i	$0.678240\pi$
$908$	−0.940579	+	0.940579i	−0.0312142	+	0.0312142i
$909$	1.62839	−	37.5182i	0.0540104	−	1.24440i
$910$	81.0440	−	3.54658i	2.68658	−	0.117568i
$911$		−	1.77346i		−	0.0587574i	−0.999568	−	0.0293787i	$-0.990647\pi$
$911$		−	1.77346i		−	0.0587574i	0.999568	−	0.0293787i	$-0.00935287\pi$
$912$	2.35223	+	0.0510226i	0.0778901	+	0.00168953i
$913$	−12.9275	+	12.9275i	−0.427838	+	0.427838i
$914$	−28.4643			−0.941514
$915$	−36.8277	+	11.1312i	−1.21749	+	0.367987i
$916$		−	29.4010i		−	0.971436i
$917$	6.68112	+	6.68112i	0.220630	+	0.220630i
$918$	33.1717	+	2.16131i	1.09483	+	0.0713338i
$919$		−	30.1726i		−	0.995301i	−0.867378	−	0.497651i	$-0.834196\pi$
$919$		−	30.1726i		−	0.995301i	0.867378	−	0.497651i	$-0.165804\pi$
$920$	−17.8255	+	5.81254i	−0.587688	+	0.191634i
$921$	6.01856	−	5.76301i	0.198318	−	0.189898i
$922$	27.7371	+	27.7371i	0.913472	+	0.913472i
$923$	−5.55102	−	1.54511i	−0.182714	−	0.0508580i
$924$	45.0261	+	47.0227i	1.48125	+	1.54693i
$925$	−2.26358	+	14.4885i	−0.0744262	+	0.476380i
$926$		−	68.6405i		−	2.25567i
$927$	8.96013	−	8.21470i	0.294289	−	0.269806i
$928$	1.79203	+	1.79203i	0.0588262	+	0.0588262i
$929$			21.8725i			0.717614i	0.933412	+	0.358807i	$0.116816\pi$
$929$			21.8725i			0.717614i	−0.933412	+	0.358807i	$0.883184\pi$
$930$	28.0451	−	52.3424i	0.919636	−	1.71638i
$931$			15.1448i			0.496352i
$932$	17.7088	−	17.7088i	0.580073	−	0.580073i
$933$	−0.636947	+	29.3644i	−0.0208527	+	0.961347i
$934$	−68.1086			−2.22858
$935$	−8.21420	+	16.1632i	−0.268633	+	0.528593i
$936$	−20.3168	+	10.3342i	−0.664075	+	0.337784i
$937$	8.75074	+	8.75074i	0.285874	+	0.285874i	0.835446	−	0.549572i	$-0.185209\pi$
$937$	8.75074	+	8.75074i	0.285874	+	0.285874i	−0.549572	+	0.835446i	$0.685209\pi$
$938$	30.4926	−	30.4926i	0.995619	−	0.995619i
$939$	27.9073	−	26.7223i	0.910720	−	0.872050i
$940$	−7.00673	+	13.7872i	−0.228534	+	0.449690i
$941$	20.4642			0.667114			0.333557	−	0.942730i	$-0.391751\pi$
$941$	20.4642			0.667114			0.333557	+	0.942730i	$0.391751\pi$
$942$	−1.48342	+	68.3882i	−0.0483324	+	2.22821i
$943$	−10.4968	−	10.4968i	−0.341823	−	0.341823i
$944$		−	0.0351238i		−	0.00114318i
$945$	−26.8088	+	45.2092i	−0.872090	+	1.47065i
$946$	−28.8500			−0.937993
$947$	−38.3259	−	38.3259i	−1.24542	−	1.24542i	−0.957719	−	0.287704i	$-0.907108\pi$
$947$	−38.3259	−	38.3259i	−1.24542	−	1.24542i	−0.287704	−	0.957719i	$-0.592892\pi$
$948$	−27.6506	−	0.599773i	−0.898049	−	0.0194797i
$949$	−3.53399	−	6.26017i	−0.114718	−	0.203214i
$950$	12.3602	+	1.93107i	0.401019	+	0.0626523i
$951$	−15.4733	−	16.1594i	−0.501756	−	0.524006i
$952$	−19.3874	−	19.3874i	−0.628351	−	0.628351i
$953$	−6.53740	−	6.53740i	−0.211767	−	0.211767i	0.593251	−	0.805018i	$-0.297844\pi$
$953$	−6.53740	−	6.53740i	−0.211767	−	0.211767i	−0.805018	+	0.593251i	$0.797844\pi$
$954$	3.68996	−	85.0169i	0.119467	−	2.75252i
$955$	12.6312	+	38.7364i	0.408736	+	1.25348i
$956$	−17.8309			−0.576691
$957$	−1.79285	−	0.0388889i	−0.0579545	−	0.00125710i
$958$	−50.7338	+	50.7338i	−1.63913	+	1.63913i
$959$	25.0357			0.808444
$960$	−14.4929	−	47.9497i	−0.467756	−	1.54757i
$961$	−16.5165			−0.532791
$962$	−22.6593	−	6.30717i	−0.730566	−	0.203351i
$963$	28.6932	−	26.3060i	0.924624	−	0.847700i
$964$	75.2945			2.42507
$965$	−16.9882	−	8.63349i	−0.546871	−	0.277922i
$966$	−47.9588	−	50.0855i	−1.54305	−	1.61148i
$967$	−13.4620	+	13.4620i	−0.432909	+	0.432909i	−0.889617	−	0.456708i	$-0.849029\pi$
$967$	−13.4620	+	13.4620i	−0.432909	+	0.432909i	0.456708	+	0.889617i	$0.349029\pi$
$968$	−4.54864	+	4.54864i	−0.146199	+	0.146199i
$969$	4.04747	−	3.87561i	0.130024	−	0.124503i
$970$	75.5568	−	24.6376i	2.42598	−	0.791066i
$971$		−	22.3416i		−	0.716977i	−0.933534	−	0.358489i	$-0.883292\pi$
$971$		−	22.3416i		−	0.716977i	0.933534	−	0.358489i	$-0.116708\pi$
$972$	4.97253	−	45.6757i	0.159494	−	1.46505i
$973$	54.8683	+	54.8683i	1.75900	+	1.75900i
$974$	15.8944			0.509289
$975$	29.4660	−	10.3323i	0.943667	−	0.330897i
$976$	11.9958			0.383977
$977$	26.2653	+	26.2653i	0.840303	+	0.840303i	0.988898	−	0.148595i	$-0.0474751\pi$
$977$	26.2653	+	26.2653i	0.840303	+	0.840303i	−0.148595	+	0.988898i	$0.547475\pi$
$978$	−0.569425	+	26.2515i	−0.0182082	+	0.839430i
$979$		−	39.7732i		−	1.27116i
$980$	84.3615	−	27.5086i	2.69483	−	0.878731i
$981$	20.7513	+	0.900661i	0.662537	+	0.0287559i
$982$	41.1605	−	41.1605i	1.31348	−	1.31348i
$983$	17.4667	−	17.4667i	0.557100	−	0.557100i	−0.371381	−	0.928481i	$-0.621116\pi$
$983$	17.4667	−	17.4667i	0.557100	−	0.557100i	0.928481	+	0.371381i	$0.121116\pi$
$984$	−9.83545	+	9.41782i	−0.313543	+	0.300229i
$985$	−18.9649	−	9.63805i	−0.604273	−	0.307094i
$986$	2.34951			0.0748237
$987$	−18.3818	−	0.398722i	−0.585099	−	0.0126915i
$988$	−3.20553	+	11.5163i	−0.101982	+	0.366382i
$989$	18.3068			0.582123
$990$	36.6375	+	20.6653i	1.16442	+	0.656787i
$991$	−24.4390			−0.776332			−0.388166	−	0.921589i	$-0.626891\pi$
$991$	−24.4390			−0.776332			−0.388166	+	0.921589i	$0.626891\pi$
$992$	−33.6353	+	33.6353i	−1.06792	+	1.06792i
$993$	−0.399451	+	18.4154i	−0.0126762	+	0.584396i
$994$	−16.0800			−0.510025
$995$	−3.77063	−	11.5635i	−0.119537	−	0.366587i
$996$	−22.8969	−	23.9123i	−0.725517	−	0.757689i
$997$	−17.4390	−	17.4390i	−0.552298	−	0.552298i	0.374806	−	0.927103i	$-0.377709\pi$
$997$	−17.4390	−	17.4390i	−0.552298	−	0.552298i	−0.927103	+	0.374806i	$0.877709\pi$
$998$	30.8724	+	30.8724i	0.977250	+	0.977250i
$999$	11.4538	−	10.0526i	0.362383	−	0.318049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.s.b.77.1	yes	32
3.2	odd	2	inner	195.2.s.b.77.16	yes	32
5.2	odd	4		975.2.s.e.818.15		32
5.3	odd	4	inner	195.2.s.b.38.2	yes	32
5.4	even	2		975.2.s.e.857.16		32
13.12	even	2	inner	195.2.s.b.77.15	yes	32
15.2	even	4		975.2.s.e.818.2		32
15.8	even	4	inner	195.2.s.b.38.15	yes	32
15.14	odd	2		975.2.s.e.857.1		32
39.38	odd	2	inner	195.2.s.b.77.2	yes	32
65.12	odd	4		975.2.s.e.818.1		32
65.38	odd	4	inner	195.2.s.b.38.16	yes	32
65.64	even	2		975.2.s.e.857.2		32
195.38	even	4	inner	195.2.s.b.38.1	✓	32
195.77	even	4		975.2.s.e.818.16		32
195.194	odd	2		975.2.s.e.857.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.s.b.38.1	✓	32	195.38	even	4	inner
195.2.s.b.38.2	yes	32	5.3	odd	4	inner
195.2.s.b.38.15	yes	32	15.8	even	4	inner
195.2.s.b.38.16	yes	32	65.38	odd	4	inner
195.2.s.b.77.1	yes	32	1.1	even	1	trivial
195.2.s.b.77.2	yes	32	39.38	odd	2	inner
195.2.s.b.77.15	yes	32	13.12	even	2	inner
195.2.s.b.77.16	yes	32	3.2	odd	2	inner
975.2.s.e.818.1		32	65.12	odd	4
975.2.s.e.818.2		32	15.2	even	4
975.2.s.e.818.15		32	5.2	odd	4
975.2.s.e.818.16		32	195.77	even	4
975.2.s.e.857.1		32	15.14	odd	2
975.2.s.e.857.2		32	65.64	even	2
975.2.s.e.857.15		32	195.194	odd	2
975.2.s.e.857.16		32	5.4	even	2

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57280 - 1.57280i) q^{2} +(-1.73164 - 0.0375613i) q^{3} +2.94741i q^{4} +(2.12590 - 0.693215i) q^{5} +(2.66446 + 2.78261i) q^{6} +(3.19872 - 3.19872i) q^{7} +(1.49009 - 1.49009i) q^{8} +(2.99718 + 0.130086i) q^{9} +(-4.43391 - 2.25333i) q^{10} -2.81912 q^{11} +(0.110709 - 5.10387i) q^{12} +(-3.47350 - 0.966841i) q^{13} -10.0619 q^{14} +(-3.70734 + 1.12055i) q^{15} +1.20758 q^{16} +(2.03377 - 2.03377i) q^{17} +(-4.50937 - 4.91857i) q^{18} -1.12487 q^{19} +(2.04319 + 6.26591i) q^{20} +(-5.65918 + 5.41889i) q^{21} +(4.43391 + 4.43391i) q^{22} +(-2.81355 - 2.81355i) q^{23} +(-2.63628 + 2.52434i) q^{24} +(4.03891 - 2.94741i) q^{25} +(3.94248 + 6.98378i) q^{26} +(-5.18516 - 0.337840i) q^{27} +(9.42794 + 9.42794i) q^{28} -0.367259 q^{29} +(7.59331 + 4.06851i) q^{30} -6.89322i q^{31} +(-4.87948 - 4.87948i) q^{32} +(4.88170 + 0.105890i) q^{33} -6.39743 q^{34} +(4.58275 - 9.01755i) q^{35} +(-0.383416 + 8.83392i) q^{36} +(-2.07384 + 2.07384i) q^{37} +(1.76920 + 1.76920i) q^{38} +(5.97855 + 1.80469i) q^{39} +(2.13483 - 4.20074i) q^{40} +3.73081 q^{41} +(17.4236 + 0.377938i) q^{42} +(-3.25333 + 3.25333i) q^{43} -8.30910i q^{44} +(6.46188 - 1.80114i) q^{45} +8.85031i q^{46} +(1.65930 + 1.65930i) q^{47} +(-2.09110 - 0.0453585i) q^{48} -13.4636i q^{49} +(-10.9881 - 1.71670i) q^{50} +(-3.59815 + 3.44537i) q^{51} +(2.84968 - 10.2378i) q^{52} +(9.01755 + 9.01755i) q^{53} +(7.62387 + 8.68658i) q^{54} +(-5.99316 + 1.95425i) q^{55} -9.53277i q^{56} +(1.94788 + 0.0422518i) q^{57} +(0.577625 + 0.577625i) q^{58} -0.0290860i q^{59} +(-3.30272 - 10.9271i) q^{60} +9.93373 q^{61} +(-10.8417 + 10.8417i) q^{62} +(10.0032 - 9.17102i) q^{63} +12.9337i q^{64} +(-8.05455 + 0.352476i) q^{65} +(-7.51141 - 7.84450i) q^{66} +(-3.03050 + 3.03050i) q^{67} +(5.99436 + 5.99436i) q^{68} +(4.76638 + 4.97774i) q^{69} +(-21.3906 + 6.97506i) q^{70} +1.59810 q^{71} +(4.65991 - 4.27223i) q^{72} +(1.40984 + 1.40984i) q^{73} +6.52349 q^{74} +(-7.10465 + 4.95216i) q^{75} -3.31547i q^{76} +(-9.01755 + 9.01755i) q^{77} +(-6.56465 - 12.2415i) q^{78} -5.41757i q^{79} +(2.56720 - 0.837115i) q^{80} +(8.96616 + 0.779780i) q^{81} +(-5.86782 - 5.86782i) q^{82} +(4.58566 - 4.58566i) q^{83} +(-15.9717 - 16.6800i) q^{84} +(2.91375 - 5.73343i) q^{85} +10.2337 q^{86} +(0.635961 + 0.0137947i) q^{87} +(-4.20074 + 4.20074i) q^{88} +14.1084i q^{89} +(-12.9961 - 7.33042i) q^{90} +(-14.2034 + 8.01810i) q^{91} +(8.29269 - 8.29269i) q^{92} +(-0.258919 + 11.9366i) q^{93} -5.21949i q^{94} +(-2.39137 + 0.779780i) q^{95} +(8.26623 + 8.63279i) q^{96} +(-11.2986 + 11.2986i) q^{97} +(-21.1755 + 21.1755i) q^{98} +(-8.44939 - 0.366727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 24 q^{10} - 24 q^{12} + 24 q^{16} + 24 q^{22} - 8 q^{25} - 16 q^{27} + 36 q^{30} - 8 q^{36} + 16 q^{40} + 12 q^{42} - 64 q^{43} - 20 q^{48} + 16 q^{51} - 72 q^{52} - 80 q^{55} + 8 q^{61}+ \cdots - 40 q^{91}+O(q^{100}) \) 32 * q - 4 * q^3 - 24 * q^10 - 24 * q^12 + 24 * q^16 + 24 * q^22 - 8 * q^25 - 16 * q^27 + 36 * q^30 - 8 * q^36 + 16 * q^40 + 12 * q^42 - 64 * q^43 - 20 * q^48 + 16 * q^51 - 72 * q^52 - 80 * q^55 + 8 * q^61 - 72 * q^66 + 44 * q^75 + 84 * q^78 + 112 * q^81 + 48 * q^82 + 20 * q^87 - 8 * q^88 + 44 * q^90 - 40 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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