LMFDB - Embedded newform 195.2.ba.a.94.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(94,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.94"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.ba (of order $6$, degree $2$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			94.8
Character	$\chi$	$=$	195.94
Dual form			195.2.ba.a.139.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.729738 - 0.421315i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.644988 + 1.11715i) q^{4} +(2.23540 + 0.0545741i) q^{5} +(-0.421315 + 0.729738i) q^{6} +(-0.347589 - 0.200681i) q^{7} +2.77223i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.65425 - 0.901983i) q^{10} +(2.45354 + 4.24965i) q^{11} -1.28998i q^{12} +(3.55974 + 0.572960i) q^{13} -0.338199 q^{14} +(-1.96320 + 1.07044i) q^{15} +(-0.121995 - 0.211302i) q^{16} +(-6.13203 - 3.54033i) q^{17} -0.842629i q^{18} +(1.12724 - 1.95244i) q^{19} +(-1.50278 + 2.46208i) q^{20} +0.401361 q^{21} +(3.58088 + 2.06742i) q^{22} +(0.861695 - 0.497500i) q^{23} +(-1.38611 - 2.40082i) q^{24} +(4.99404 + 0.243990i) q^{25} +(2.83907 - 1.08166i) q^{26} +1.00000i q^{27} +(0.448381 - 0.258873i) q^{28} +(-3.94133 - 6.82658i) q^{29} +(-0.981632 + 1.60827i) q^{30} -6.30120 q^{31} +(-4.97969 - 2.87503i) q^{32} +(-4.24965 - 2.45354i) q^{33} -5.96637 q^{34} +(-0.766049 - 0.467571i) q^{35} +(0.644988 + 1.11715i) q^{36} +(7.62688 - 4.40338i) q^{37} -1.89969i q^{38} +(-3.36930 + 1.28367i) q^{39} +(-0.151292 + 6.19705i) q^{40} +(-2.65994 - 4.60715i) q^{41} +(0.292889 - 0.169099i) q^{42} +(1.74416 + 1.00699i) q^{43} -6.33001 q^{44} +(1.16496 - 1.90863i) q^{45} +(0.419208 - 0.726090i) q^{46} +4.62317i q^{47} +(0.211302 + 0.121995i) q^{48} +(-3.41945 - 5.92267i) q^{49} +(3.74714 - 1.92601i) q^{50} +7.08066 q^{51} +(-2.93607 + 3.60721i) q^{52} +10.8496i q^{53} +(0.421315 + 0.729738i) q^{54} +(5.25272 + 9.63357i) q^{55} +(0.556333 - 0.963596i) q^{56} +2.25448i q^{57} +(-5.75228 - 3.32108i) q^{58} +(-1.52224 + 2.63659i) q^{59} +(0.0703993 - 2.88361i) q^{60} +(3.55088 - 6.15031i) q^{61} +(-4.59822 + 2.65479i) q^{62} +(-0.347589 + 0.200681i) q^{63} -4.35718 q^{64} +(7.92617 + 1.47507i) q^{65} -4.13484 q^{66} +(5.32891 - 3.07665i) q^{67} +(7.91018 - 4.56694i) q^{68} +(-0.497500 + 0.861695i) q^{69} +(-0.756010 - 0.0184569i) q^{70} +(-3.16446 + 5.48101i) q^{71} +(2.40082 + 1.38611i) q^{72} -1.01273i q^{73} +(3.71042 - 6.42663i) q^{74} +(-4.44696 + 2.28572i) q^{75} +(1.45411 + 2.51860i) q^{76} -1.96951i q^{77} +(-1.91788 + 2.35628i) q^{78} +10.2755 q^{79} +(-0.261177 - 0.479002i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.88212 - 2.24134i) q^{82} -10.5337i q^{83} +(-0.258873 + 0.448381i) q^{84} +(-13.5143 - 8.24871i) q^{85} +1.69704 q^{86} +(6.82658 + 3.94133i) q^{87} +(-11.7810 + 6.80177i) q^{88} +(0.262260 + 0.454247i) q^{89} +(0.0459858 - 1.88361i) q^{90} +(-1.12234 - 0.913524i) q^{91} +1.28353i q^{92} +(5.45700 - 3.15060i) q^{93} +(1.94781 + 3.37371i) q^{94} +(2.62639 - 4.30297i) q^{95} +5.75005 q^{96} +(8.15979 + 4.71106i) q^{97} +(-4.99061 - 2.88133i) q^{98} +4.90707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9} - 4 q^{10} + 4 q^{11} + 24 q^{14} - 2 q^{15} + 16 q^{16} - 16 q^{19} - 16 q^{20} - 8 q^{21} - 16 q^{25} - 48 q^{26} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 32 q^{34} + 10 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q + 8 * q^4 + 4 * q^5 + 12 * q^9 - 4 * q^10 + 4 * q^11 + 24 * q^14 - 2 * q^15 + 16 * q^16 - 16 * q^19 - 16 * q^20 - 8 * q^21 - 16 * q^25 - 48 * q^26 - 12 * q^29 - 4 * q^30 + 8 * q^31 - 32 * q^34 + 10 * q^35 - 8 * q^36 + 8 * q^39 - 48 * q^40 - 40 * q^41 + 40 * q^44 + 2 * q^45 - 24 * q^46 - 16 * q^49 + 20 * q^50 - 24 * q^51 + 20 * q^55 - 24 * q^56 + 12 * q^59 + 48 * q^60 + 20 * q^61 + 48 * q^64 + 14 * q^65 - 56 * q^66 - 8 * q^69 - 56 * q^70 + 4 * q^71 - 12 * q^74 + 16 * q^75 + 8 * q^76 + 136 * q^79 - 4 * q^80 - 12 * q^81 - 16 * q^84 - 4 * q^85 + 48 * q^86 - 64 * q^89 - 8 * q^90 + 60 * q^91 - 48 * q^94 - 28 * q^95 + 40 * q^96 + 8 * q^99

Character values

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

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$	0.729738	−	0.421315i	0.516003	−	0.297914i	−0.219295	−	0.975659i	$-0.570376\pi$
$2$	0.729738	−	0.421315i	0.516003	−	0.297914i	0.735298	+	0.677744i	$0.237042\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.644988	+	1.11715i	−0.322494	+	0.558576i
$5$	2.23540	+	0.0545741i	0.999702	+	0.0244063i
$5$	2.23540	+	0.0545741i	0.999702	+	0.0244063i
$6$	−0.421315	+	0.729738i	−0.172001	+	0.297914i
$7$	−0.347589	−	0.200681i	−0.131376	−	0.0758501i	0.432871	−	0.901456i	$-0.357500\pi$
$7$	−0.347589	−	0.200681i	−0.131376	−	0.0758501i	−0.564248	+	0.825606i	$0.690834\pi$
$8$			2.77223i			0.980131i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.65425	−	0.901983i	0.523120	−	0.285232i
$11$	2.45354	+	4.24965i	0.739769	+	1.28132i	0.952599	+	0.304228i	$0.0983985\pi$
$11$	2.45354	+	4.24965i	0.739769	+	1.28132i	−0.212830	+	0.977089i	$0.568268\pi$
$12$		−	1.28998i		−	0.372384i
$13$	3.55974	+	0.572960i	0.987293	+	0.158911i
$13$	3.55974	+	0.572960i	0.987293	+	0.158911i
$14$	−0.338199			−0.0903874
$15$	−1.96320	+	1.07044i	−0.506897	+	0.276386i
$16$	−0.121995	−	0.211302i	−0.0304988	−	0.0528254i
$17$	−6.13203	−	3.54033i	−1.48724	−	0.858656i	−0.487343	−	0.873211i	$-0.662034\pi$
$17$	−6.13203	−	3.54033i	−1.48724	−	0.858656i	−0.999894	+	0.0145544i	$0.995367\pi$
$18$		−	0.842629i		−	0.198610i
$19$	1.12724	−	1.95244i	0.258607	−	0.447920i	−0.707262	−	0.706952i	$-0.750070\pi$
$19$	1.12724	−	1.95244i	0.258607	−	0.447920i	0.965869	+	0.259031i	$0.0834032\pi$
$20$	−1.50278	+	2.46208i	−0.336031	+	0.550539i
$21$	0.401361			0.0875842
$22$	3.58088	+	2.06742i	0.763446	+	0.440776i
$23$	0.861695	−	0.497500i	0.179676	−	0.103736i	−0.407465	−	0.913221i	$-0.633587\pi$
$23$	0.861695	−	0.497500i	0.179676	−	0.103736i	0.587140	+	0.809485i	$0.300254\pi$
$24$	−1.38611	−	2.40082i	−0.282940	−	0.490066i
$25$	4.99404	+	0.243990i	0.998809	+	0.0487981i
$26$	2.83907	−	1.08166i	0.556788	−	0.212130i
$27$			1.00000i			0.192450i
$28$	0.448381	−	0.258873i	0.0847361	−	0.0489224i
$29$	−3.94133	−	6.82658i	−0.731886	−	1.26766i	−0.956076	−	0.293119i	$-0.905307\pi$
$29$	−3.94133	−	6.82658i	−0.731886	−	1.26766i	0.224190	−	0.974546i	$-0.428027\pi$
$30$	−0.981632	+	1.60827i	−0.179221	+	0.293628i
$31$	−6.30120			−1.13173			−0.565864	−	0.824499i	$-0.691457\pi$
$31$	−6.30120			−1.13173			−0.565864	+	0.824499i	$0.691457\pi$
$32$	−4.97969	−	2.87503i	−0.880293	−	0.508238i
$33$	−4.24965	−	2.45354i	−0.739769	−	0.427106i
$34$	−5.96637			−1.02322
$35$	−0.766049	−	0.467571i	−0.129486	−	0.0790339i
$36$	0.644988	+	1.11715i	0.107498	+	0.186192i
$37$	7.62688	−	4.40338i	1.25385	−	0.723912i	0.281980	−	0.959420i	$-0.409009\pi$
$37$	7.62688	−	4.40338i	1.25385	−	0.723912i	0.971872	+	0.235509i	$0.0756756\pi$
$38$		−	1.89969i		−	0.308171i
$39$	−3.36930	+	1.28367i	−0.539520	+	0.205552i
$40$	−0.151292	+	6.19705i	−0.0239214	+	0.979839i
$41$	−2.65994	−	4.60715i	−0.415413	−	0.719517i	0.580059	−	0.814575i	$-0.303030\pi$
$41$	−2.65994	−	4.60715i	−0.415413	−	0.719517i	−0.995472	+	0.0950582i	$0.969696\pi$
$42$	0.292889	−	0.169099i	0.0451937	−	0.0260926i
$43$	1.74416	+	1.00699i	0.265982	+	0.153565i	0.627060	−	0.778971i	$-0.284258\pi$
$43$	1.74416	+	1.00699i	0.265982	+	0.153565i	−0.361078	+	0.932536i	$0.617591\pi$
$44$	−6.33001			−0.954284
$45$	1.16496	−	1.90863i	0.173663	−	0.284521i
$46$	0.419208	−	0.726090i	0.0618088	−	0.107056i
$47$			4.62317i			0.674359i	0.941440	+	0.337180i	$0.109473\pi$
$47$			4.62317i			0.674359i	−0.941440	+	0.337180i	$0.890527\pi$
$48$	0.211302	+	0.121995i	0.0304988	+	0.0176085i
$49$	−3.41945	−	5.92267i	−0.488494	−	0.846096i
$50$	3.74714	−	1.92601i	0.529926	−	0.272380i
$51$	7.08066			0.991491
$52$	−2.93607	+	3.60721i	−0.407160	+	0.500230i
$53$			10.8496i			1.49031i	0.666890	+	0.745156i	$0.267625\pi$
$53$			10.8496i			1.49031i	−0.666890	+	0.745156i	$0.732375\pi$
$54$	0.421315	+	0.729738i	0.0573337	+	0.0993048i
$55$	5.25272	+	9.63357i	0.708276	+	1.29899i
$56$	0.556333	−	0.963596i	0.0743431	−	0.128766i
$57$			2.25448i			0.298614i
$58$	−5.75228	−	3.32108i	−0.755311	−	0.436079i
$59$	−1.52224	+	2.63659i	−0.198178	+	0.343255i	−0.947938	−	0.318455i	$-0.896836\pi$
$59$	−1.52224	+	2.63659i	−0.198178	+	0.343255i	0.749759	+	0.661711i	$0.230169\pi$
$60$	0.0703993	−	2.88361i	0.00908852	−	0.372273i
$61$	3.55088	−	6.15031i	0.454644	−	0.787466i	−0.544024	−	0.839070i	$-0.683100\pi$
$61$	3.55088	−	6.15031i	0.454644	−	0.787466i	0.998668	+	0.0516038i	$0.0164333\pi$
$62$	−4.59822	+	2.65479i	−0.583975	+	0.337158i
$63$	−0.347589	+	0.200681i	−0.0437921	+	0.0252834i
$64$	−4.35718			−0.544648
$65$	7.92617	+	1.47507i	0.983120	+	0.182959i
$66$	−4.13484			−0.508964
$67$	5.32891	−	3.07665i	0.651030	−	0.375873i	−0.137821	−	0.990457i	$-0.544010\pi$
$67$	5.32891	−	3.07665i	0.651030	−	0.375873i	0.788851	+	0.614585i	$0.210676\pi$
$68$	7.91018	−	4.56694i	0.959250	−	0.553823i
$69$	−0.497500	+	0.861695i	−0.0598920	+	0.103736i
$70$	−0.756010	−	0.0184569i	−0.0903604	−	0.00220602i
$71$	−3.16446	+	5.48101i	−0.375553	+	0.650476i	−0.990410	−	0.138162i	$-0.955880\pi$
$71$	−3.16446	+	5.48101i	−0.375553	+	0.650476i	0.614857	+	0.788639i	$0.289214\pi$
$72$	2.40082	+	1.38611i	0.282940	+	0.163355i
$73$		−	1.01273i		−	0.118531i	−0.998242	−	0.0592655i	$-0.981124\pi$
$73$		−	1.01273i		−	0.118531i	0.998242	−	0.0592655i	$-0.0188759\pi$
$74$	3.71042	−	6.42663i	0.431327	−	0.747081i
$75$	−4.44696	+	2.28572i	−0.513491	+	0.263932i
$76$	1.45411	+	2.51860i	0.166798	+	0.288903i
$77$		−	1.96951i		−	0.224446i
$78$	−1.91788	+	2.35628i	−0.217157	+	0.266796i
$79$	10.2755			1.15608			0.578042	−	0.816007i	$-0.303817\pi$
$79$	10.2755			1.15608			0.578042	+	0.816007i	$0.303817\pi$
$80$	−0.261177	−	0.479002i	−0.0292004	−	0.0535541i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.88212	−	2.24134i	−0.428709	−	0.247515i
$83$		−	10.5337i		−	1.15623i	−0.815956	−	0.578114i	$-0.803789\pi$
$83$		−	10.5337i		−	1.15623i	0.815956	−	0.578114i	$-0.196211\pi$
$84$	−0.258873	+	0.448381i	−0.0282454	+	0.0489224i
$85$	−13.5143	−	8.24871i	−1.46584	−	0.894699i
$86$	1.69704			0.182997
$87$	6.82658	+	3.94133i	0.731886	+	0.422555i
$88$	−11.7810	+	6.80177i	−1.25586	+	0.725071i
$89$	0.262260	+	0.454247i	0.0277995	+	0.0481501i	0.879590	−	0.475732i	$-0.157817\pi$
$89$	0.262260	+	0.454247i	0.0277995	+	0.0481501i	−0.851791	+	0.523882i	$0.824483\pi$
$90$	0.0459858	−	1.88361i	0.00484733	−	0.198550i
$91$	−1.12234	−	0.913524i	−0.117653	−	0.0957634i
$92$			1.28353i			0.133817i
$93$	5.45700	−	3.15060i	0.565864	−	0.326702i
$94$	1.94781	+	3.37371i	0.200901	+	0.347971i
$95$	2.62639	−	4.30297i	0.269462	−	0.441475i
$96$	5.75005			0.586862
$97$	8.15979	+	4.71106i	0.828502	+	0.478336i	0.853339	−	0.521356i	$-0.174574\pi$
$97$	8.15979	+	4.71106i	0.828502	+	0.478336i	−0.0248378	+	0.999691i	$0.507907\pi$
$98$	−4.99061	−	2.88133i	−0.504128	−	0.291059i
$99$	4.90707			0.493179
$100$	−3.49367	+	5.42173i	−0.349367	+	0.542173i
$101$	2.87707	+	4.98324i	0.286280	+	0.495851i	0.972919	−	0.231148i	$-0.0742481\pi$
$101$	2.87707	+	4.98324i	0.286280	+	0.495851i	−0.686639	+	0.726998i	$0.740915\pi$
$102$	5.16703	−	2.98319i	0.511612	−	0.295379i
$103$		−	15.3992i		−	1.51733i	−0.651481	−	0.758665i	$-0.725852\pi$
$103$		−	15.3992i		−	1.51733i	0.651481	−	0.758665i	$-0.274148\pi$
$104$	−1.58838	+	9.86840i	−0.155753	+	0.967677i
$105$	0.897203	+	0.0219039i	0.0875581	+	0.00213761i
$106$	4.57111	+	7.91739i	0.443985	+	0.769005i
$107$	−12.9024	+	7.44919i	−1.24732	+	0.720141i	−0.970574	−	0.240802i	$-0.922589\pi$
$107$	−12.9024	+	7.44919i	−1.24732	+	0.720141i	−0.276746	+	0.960943i	$0.589256\pi$
$108$	−1.11715	−	0.644988i	−0.107498	−	0.0620640i
$109$	1.69762			0.162602			0.0813011	−	0.996690i	$-0.474092\pi$
$109$	1.69762			0.162602			0.0813011	+	0.996690i	$0.474092\pi$
$110$	7.89187	+	4.81694i	0.752461	+	0.459277i
$111$	−4.40338	+	7.62688i	−0.417951	+	0.723912i
$112$			0.0979282i			0.00925335i
$113$	1.94685	+	1.12402i	0.183145	+	0.105739i	0.588769	−	0.808301i	$-0.299613\pi$
$113$	1.94685	+	1.12402i	0.183145	+	0.105739i	−0.405625	+	0.914040i	$0.632946\pi$
$114$	0.949847	+	1.64518i	0.0889613	+	0.154086i
$115$	1.95339	−	1.06509i	0.182154	−	0.0993198i
$116$	10.1684			0.944116
$117$	2.27607	−	2.79634i	0.210422	−	0.258522i
$118$			2.56536i			0.236161i
$119$	1.42095	+	2.46116i	0.130258	+	0.225614i
$120$	−2.96750	−	5.44245i	−0.270895	−	0.496825i
$121$	−6.53968	+	11.3271i	−0.594516	+	1.02973i
$122$		−	5.98415i		−	0.541780i
$123$	4.60715	+	2.65994i	0.415413	+	0.239839i
$124$	4.06420	−	7.03939i	0.364976	−	0.632156i
$125$	11.1504	+	0.817962i	0.997320	+	0.0731607i
$126$	−0.169099	+	0.292889i	−0.0150646	+	0.0260926i
$127$	−14.9506	+	8.63173i	−1.32665	+	0.765942i	−0.984780	−	0.173804i	$-0.944394\pi$
$127$	−14.9506	+	8.63173i	−1.32665	+	0.765942i	−0.341871	+	0.939747i	$0.611061\pi$
$128$	6.77978	−	3.91431i	0.599254	−	0.345979i
$129$	−2.01398			−0.177321
$130$	6.40550	−	2.26300i	0.561799	−	0.198478i
$131$	−4.59071			−0.401092			−0.200546	−	0.979684i	$-0.564272\pi$
$131$	−4.59071			−0.401092			−0.200546	+	0.979684i	$0.564272\pi$
$132$	5.48195	−	3.16500i	0.477142	−	0.275478i
$133$	−0.783633	+	0.452431i	−0.0679496	+	0.0392307i
$134$	2.59247	−	4.49030i	0.223956	−	0.387903i
$135$	−0.0545741	+	2.23540i	−0.00469699	+	0.192393i
$136$	9.81461	−	16.9994i	0.841596	−	1.45769i
$137$	−4.28724	−	2.47524i	−0.366284	−	0.211474i	0.305550	−	0.952176i	$-0.401160\pi$
$137$	−4.28724	−	2.47524i	−0.366284	−	0.211474i	−0.671834	+	0.740702i	$0.734493\pi$
$138$			0.838416i			0.0713707i
$139$	−6.63214	+	11.4872i	−0.562530	+	0.974331i	0.434744	+	0.900554i	$0.356839\pi$
$139$	−6.63214	+	11.4872i	−0.562530	+	0.974331i	−0.997275	+	0.0737774i	$0.976495\pi$
$140$	1.01644	−	0.554215i	0.0859049	−	0.0468397i
$141$	−2.31159	−	4.00379i	−0.194671	−	0.337180i
$142$			5.33294i			0.447530i
$143$	6.29906	+	16.5334i	0.526754	+	1.38259i
$144$	−0.243990			−0.0203325
$145$	−8.43790	−	15.4752i	−0.700729	−	1.28515i
$146$	−0.426678	−	0.739028i	−0.0353121	−	0.0611624i
$147$	5.92267	+	3.41945i	0.488494	+	0.282032i
$148$			11.3605i			0.933829i
$149$	−1.57886	+	2.73467i	−0.129345	+	0.224033i	−0.923423	−	0.383783i	$-0.874621\pi$
$149$	−1.57886	+	2.73467i	−0.129345	+	0.224033i	0.794078	+	0.607816i	$0.207954\pi$
$150$	−2.28211	+	3.54155i	−0.186334	+	0.289166i
$151$	−18.5878			−1.51266			−0.756328	−	0.654193i	$-0.773009\pi$
$151$	−18.5878			−1.51266			−0.756328	+	0.654193i	$0.773009\pi$
$152$	5.41261	+	3.12497i	0.439021	+	0.253469i
$153$	−6.13203	+	3.54033i	−0.495746	+	0.286219i
$154$	−0.829782	−	1.43723i	−0.0668658	−	0.115815i
$155$	−14.0857	−	0.343882i	−1.13139	−	0.0276213i
$156$	0.739105	−	4.59197i	0.0591758	−	0.367652i
$157$			10.7802i			0.860351i	0.902745	+	0.430175i	$0.141548\pi$
$157$			10.7802i			0.860351i	−0.902745	+	0.430175i	$0.858452\pi$
$158$	7.49843	−	4.32922i	0.596543	−	0.344414i
$159$	−5.42482	−	9.39606i	−0.430216	−	0.745156i
$160$	−10.9747	−	6.69860i	−0.867627	−	0.529571i
$161$	−0.399354			−0.0314735
$162$	−0.729738	−	0.421315i	−0.0573337	−	0.0331016i
$163$	−1.36302	−	0.786941i	−0.106760	−	0.0616380i	0.445669	−	0.895198i	$-0.352966\pi$
$163$	−1.36302	−	0.786941i	−0.106760	−	0.0616380i	−0.552429	+	0.833560i	$0.686299\pi$
$164$	6.86252			0.535873
$165$	−9.36577	−	5.71656i	−0.729124	−	0.445034i
$166$	−4.43802	−	7.68687i	−0.344457	−	0.596617i
$167$	13.0492	−	7.53397i	1.00978	−	0.582996i	0.0986516	−	0.995122i	$-0.468547\pi$
$167$	13.0492	−	7.53397i	1.00978	−	0.582996i	0.911127	+	0.412126i	$0.135214\pi$
$168$			1.11267i			0.0858440i
$169$	12.3434	+	4.07917i	0.949495	+	0.313783i
$170$	−13.3372	−	0.325610i	−1.02292	−	0.0249731i
$171$	−1.12724	−	1.95244i	−0.0862023	−	0.149307i
$172$	−2.24993	+	1.29900i	−0.171555	+	0.0990475i
$173$	−2.94981	−	1.70307i	−0.224270	−	0.129482i	0.383656	−	0.923476i	$-0.374665\pi$
$173$	−2.94981	−	1.70307i	−0.224270	−	0.129482i	−0.607926	+	0.793994i	$0.707998\pi$
$174$	6.64216			0.503541
$175$	−1.68691	−	1.08702i	−0.127518	−	0.0821707i
$176$	0.598639	−	1.03687i	0.0451241	−	0.0781572i
$177$		−	3.04448i		−	0.228837i
$178$	0.382762	+	0.220988i	0.0286892	+	0.0165637i
$179$	−0.300516	−	0.520508i	−0.0224616	−	0.0389046i	0.854576	−	0.519326i	$-0.173817\pi$
$179$	−0.300516	−	0.520508i	−0.0224616	−	0.0389046i	−0.877038	+	0.480422i	$0.840484\pi$
$180$	1.38084	+	2.53248i	0.102922	+	0.188760i
$181$	−17.0607			−1.26811			−0.634056	−	0.773287i	$-0.718611\pi$
$181$	−17.0607			−1.26811			−0.634056	+	0.773287i	$0.718611\pi$
$182$	−1.20390	−	0.193774i	−0.0892388	−	0.0143635i
$183$			7.10176i			0.524977i
$184$	1.37918	+	2.38882i	0.101675	+	0.176106i
$185$	17.2895	−	9.42710i	1.27115	−	0.693094i
$186$	2.65479	−	4.59822i	0.194658	−	0.337158i
$187$		−	34.7453i		−	2.54083i
$188$	−5.16479	−	2.98189i	−0.376681	−	0.217477i
$189$	0.200681	−	0.347589i	0.0145974	−	0.0252834i
$190$	0.103674	−	4.24658i	0.00752131	−	0.308079i
$191$	−3.10083	+	5.37079i	−0.224368	+	0.388617i	−0.956130	−	0.292944i	$-0.905365\pi$
$191$	−3.10083	+	5.37079i	−0.224368	+	0.388617i	0.731762	+	0.681561i	$0.238698\pi$
$192$	3.77343	−	2.17859i	0.272324	−	0.157226i
$193$	−7.91367	+	4.56896i	−0.569639	+	0.328881i	−0.757005	−	0.653409i	$-0.773338\pi$
$193$	−7.91367	+	4.56896i	−0.569639	+	0.328881i	0.187366	+	0.982290i	$0.440005\pi$
$194$	7.93935			0.570012
$195$	−7.60180	+	2.68564i	−0.544376	+	0.192323i
$196$	8.82203			0.630145
$197$	−18.7148	+	10.8050i	−1.33337	+	0.769823i	−0.985815	−	0.167836i	$-0.946322\pi$
$197$	−18.7148	+	10.8050i	−1.33337	+	0.769823i	−0.347557	+	0.937659i	$0.612989\pi$
$198$	3.58088	−	2.06742i	0.254482	−	0.146925i
$199$	1.27223	−	2.20357i	0.0901860	−	0.156207i	−0.817403	−	0.576066i	$-0.804587\pi$
$199$	1.27223	−	2.20357i	0.0901860	−	0.156207i	0.907589	+	0.419859i	$0.137921\pi$
$200$	−0.676397	+	13.8446i	−0.0478285	+	0.978964i
$201$	−3.07665	+	5.32891i	−0.217010	+	0.375873i
$202$	4.19902	+	2.42431i	0.295442	+	0.170574i
$203$			3.16379i			0.222055i
$204$	−4.56694	+	7.91018i	−0.319750	+	0.553823i
$205$	−5.69461	−	10.4440i	−0.397729	−	0.729441i
$206$	−6.48792	−	11.2374i	−0.452034	−	0.782947i
$207$		−	0.995000i		−	0.0691573i
$208$	−0.313203	−	0.822077i	−0.0217167	−	0.0570008i
$209$	11.0629			0.765238
$210$	0.663952	−	0.362021i	0.0458170	−	0.0249818i
$211$	5.54061	+	9.59663i	0.381432	+	0.660659i	0.991267	−	0.131869i	$-0.0420978\pi$
$211$	5.54061	+	9.59663i	0.381432	+	0.660659i	−0.609836	+	0.792528i	$0.708765\pi$
$212$	−12.1207	−	6.99789i	−0.832453	−	0.480617i
$213$		−	6.32893i		−	0.433651i
$214$	−6.27691	+	10.8719i	−0.429081	+	0.743189i
$215$	3.84394	+	2.34622i	0.262155	+	0.160011i
$216$	−2.77223			−0.188626
$217$	2.19023	+	1.26453i	0.148682	+	0.0858417i
$218$	1.23882	−	0.715231i	0.0839032	−	0.0484416i
$219$	0.506365	+	0.877050i	0.0342170	+	0.0592655i
$220$	−14.1501	−	0.345455i	−0.954000	−	0.0232905i
$221$	−19.7999	−	16.1161i	−1.33189	−	1.08408i
$222$			7.42084i			0.498054i
$223$	0.460340	−	0.265778i	0.0308267	−	0.0177978i	−0.484507	−	0.874787i	$-0.661001\pi$
$223$	0.460340	−	0.265778i	0.0308267	−	0.0177978i	0.515334	+	0.856989i	$0.327668\pi$
$224$	1.15392	+	1.99865i	0.0770998	+	0.133541i
$225$	2.70832	−	4.20297i	0.180555	−	0.280198i
$226$	1.89426			0.126004
$227$	−18.5220	−	10.6937i	−1.22935	−	0.709764i	−0.262454	−	0.964944i	$-0.584532\pi$
$227$	−18.5220	−	10.6937i	−1.22935	−	0.709764i	−0.966894	+	0.255180i	$0.917865\pi$
$228$	−2.51860	−	1.45411i	−0.166798	−	0.0963011i
$229$	0.406502			0.0268624			0.0134312	−	0.999910i	$-0.495725\pi$
$229$	0.406502			0.0268624			0.0134312	+	0.999910i	$0.495725\pi$
$230$	0.976724	−	1.60022i	0.0644033	−	0.105516i
$231$	0.984754	+	1.70564i	0.0647920	+	0.112223i
$232$	18.9249	−	10.9263i	1.24248	−	0.717345i
$233$			2.66379i			0.174510i	0.996186	+	0.0872552i	$0.0278096\pi$
$233$			2.66379i			0.174510i	−0.996186	+	0.0872552i	$0.972190\pi$
$234$	0.482793	−	2.99954i	0.0315612	−	0.196086i
$235$	−0.252306	+	10.3347i	−0.0164586	+	0.674158i
$236$	−1.96365	−	3.40114i	−0.127823	−	0.221395i
$237$	−8.89885	+	5.13775i	−0.578042	+	0.333733i
$238$	2.07385	+	1.19734i	0.134427	+	0.0776117i
$239$	15.8317			1.02407			0.512034	−	0.858965i	$-0.328892\pi$
$239$	15.8317			1.02407			0.512034	+	0.858965i	$0.328892\pi$
$240$	0.465687	+	0.284240i	0.0300599	+	0.0183476i
$241$	11.6570	−	20.1906i	0.750895	−	1.30059i	−0.196495	−	0.980505i	$-0.562956\pi$
$241$	11.6570	−	20.1906i	0.750895	−	1.30059i	0.947390	−	0.320083i	$-0.103711\pi$
$242$			11.0210i			0.708460i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.58055	+	7.93375i	0.293240	+	0.507906i
$245$	−7.32063	−	13.4262i	−0.467698	−	0.857766i
$246$	4.48269			0.285806
$247$	5.13135	−	6.30431i	0.326500	−	0.401133i
$248$		−	17.4684i		−	1.10924i
$249$	5.26687	+	9.12248i	0.333774	+	0.578114i
$250$	8.48148	−	4.10092i	0.536416	−	0.259365i
$251$	−0.650814	+	1.12724i	−0.0410790	+	0.0711509i	−0.885834	−	0.464002i	$-0.846413\pi$
$251$	−0.650814	+	1.12724i	−0.0410790	+	0.0711509i	0.844755	+	0.535153i	$0.179746\pi$
$252$		−	0.517746i		−	0.0326149i
$253$	4.22840	+	2.44127i	0.265837	+	0.153481i
$254$	−7.27335	+	12.5978i	−0.456371	+	0.790457i
$255$	15.8281	+	0.386421i	0.991196	+	0.0241986i
$256$	7.65549	−	13.2597i	0.478468	−	0.828731i
$257$	8.55103	−	4.93694i	0.533399	−	0.307958i	−0.209001	−	0.977915i	$-0.567021\pi$
$257$	8.55103	−	4.93694i	0.533399	−	0.307958i	0.742399	+	0.669958i	$0.233688\pi$
$258$	−1.46968	+	0.848521i	−0.0914983	+	0.0528266i
$259$	−3.53469			−0.219635
$260$	−6.76016	+	7.90334i	−0.419247	+	0.490144i
$261$	−7.88266			−0.487924
$262$	−3.35001	+	1.93413i	−0.206965	+	0.119491i
$263$	0.462121	−	0.266805i	0.0284956	−	0.0164519i	−0.485685	−	0.874134i	$-0.661430\pi$
$263$	0.462121	−	0.266805i	0.0284956	−	0.0164519i	0.514180	+	0.857682i	$0.328096\pi$
$264$	6.80177	−	11.7810i	0.418620	−	0.725071i
$265$	−0.592110	+	24.2533i	−0.0363730	+	1.48987i
$266$	−0.381232	+	0.660312i	−0.0233748	+	0.0404864i
$267$	−0.454247	−	0.262260i	−0.0277995	−	0.0160500i
$268$			7.93761i			0.484867i
$269$	−6.80199	+	11.7814i	−0.414725	+	0.718324i	−0.995400	−	0.0958112i	$-0.969455\pi$
$269$	−6.80199	+	11.7814i	−0.414725	+	0.718324i	0.580675	+	0.814136i	$0.302789\pi$
$270$	0.901983	+	1.65425i	0.0548929	+	0.100675i
$271$	11.9163	+	20.6396i	0.723862	+	1.25377i	0.959441	+	0.281911i	$0.0909681\pi$
$271$	11.9163	+	20.6396i	0.723862	+	1.25377i	−0.235579	+	0.971855i	$0.575699\pi$
$272$			1.72761i			0.104752i
$273$	1.42874	+	0.229964i	0.0864712	+	0.0139181i
$274$	−4.17142			−0.252004
$275$	11.2162	+	21.8216i	0.676362	+	1.31589i
$276$	−0.641763	−	1.11157i	−0.0386296	−	0.0669084i
$277$	16.6388	+	9.60639i	0.999726	+	0.577192i	0.908167	−	0.418608i	$-0.137482\pi$
$277$	16.6388	+	9.60639i	0.999726	+	0.577192i	0.0915586	+	0.995800i	$0.470815\pi$
$278$			11.1769i			0.670344i
$279$	−3.15060	+	5.45700i	−0.188621	+	0.326702i
$280$	1.29621	−	2.12366i	0.0774636	−	0.126913i
$281$	6.31792			0.376895			0.188448	−	0.982083i	$-0.439654\pi$
$281$	6.31792			0.376895			0.188448	+	0.982083i	$0.439654\pi$
$282$	−3.37371	−	1.94781i	−0.200901	−	0.115990i
$283$	26.1587	−	15.1027i	1.55497	−	0.897765i	0.557249	−	0.830345i	$-0.311857\pi$
$283$	26.1587	−	15.1027i	1.55497	−	0.897765i	0.997725	−	0.0674193i	$-0.0214765\pi$
$284$	−4.08208	−	7.07037i	−0.242227	−	0.419549i
$285$	−0.123037	+	5.03968i	−0.00728805	+	0.298525i
$286$	11.5624	+	9.41117i	0.683701	+	0.556494i
$287$			2.13519i			0.126037i
$288$	−4.97969	+	2.87503i	−0.293431	+	0.169413i
$289$	16.5679	+	28.6964i	0.974582	+	1.68803i
$290$	−12.6774	−	7.73787i	−0.744443	−	0.454383i
$291$	−9.42212			−0.552334
$292$	1.13137	+	0.653199i	0.0662086	+	0.0382256i
$293$	−6.18072	−	3.56844i	−0.361081	−	0.208470i	0.308474	−	0.951233i	$-0.400182\pi$
$293$	−6.18072	−	3.56844i	−0.361081	−	0.208470i	−0.669555	+	0.742762i	$0.733515\pi$
$294$	5.76266			0.336085
$295$	−3.54670	+	5.81077i	−0.206497	+	0.338316i
$296$	12.2072	+	21.1435i	0.709528	+	1.22894i
$297$	−4.24965	+	2.45354i	−0.246590	+	0.142369i
$298$			2.66079i			0.154135i
$299$	3.35245	−	1.27725i	0.193877	−	0.0738653i
$300$	0.314742	−	6.44220i	0.0181716	−	0.371940i
$301$	−0.404167	−	0.700038i	−0.0232958	−	0.0403495i
$302$	−13.5642	+	7.83132i	−0.780535	+	0.450642i
$303$	−4.98324	−	2.87707i	−0.286280	−	0.165284i
$304$	−0.550072			−0.0315488
$305$	8.27329	−	13.5546i	0.473727	−	0.776135i
$306$	−2.98319	+	5.16703i	−0.170537	+	0.295379i
$307$			9.91349i			0.565793i	0.959150	+	0.282897i	$0.0912953\pi$
$307$			9.91349i			0.565793i	−0.959150	+	0.282897i	$0.908705\pi$
$308$	2.20024	+	1.27031i	0.125370	+	0.0723826i
$309$	7.69961	+	13.3361i	0.438015	+	0.758665i
$310$	−10.4238	+	5.68357i	−0.592030	+	0.322805i
$311$	6.04584			0.342828			0.171414	−	0.985199i	$-0.445166\pi$
$311$	6.04584			0.342828			0.171414	+	0.985199i	$0.445166\pi$
$312$	−3.55863	−	9.34048i	−0.201468	−	0.528800i
$313$		−	4.62017i		−	0.261148i	−0.991439	−	0.130574i	$-0.958318\pi$
$313$		−	4.62017i		−	0.261148i	0.991439	−	0.130574i	$-0.0416820\pi$
$314$	4.54184	+	7.86670i	0.256311	+	0.443944i
$315$	−0.787953	+	0.429632i	−0.0443961	+	0.0242070i
$316$	−6.62758	+	11.4793i	−0.372830	+	0.645761i
$317$		−	25.0793i		−	1.40860i	−0.709905	−	0.704298i	$-0.751262\pi$
$317$		−	25.0793i		−	1.40860i	0.709905	−	0.704298i	$-0.248738\pi$
$318$	−7.91739	−	4.57111i	−0.443985	−	0.256335i
$319$	19.3404	−	33.4985i	1.08285	−	1.87556i
$320$	−9.74005	−	0.237789i	−0.544486	−	0.0132928i
$321$	7.44919	−	12.9024i	0.415773	−	0.720141i
$322$	−0.291424	+	0.168254i	−0.0162404	+	0.00937642i
$323$	−13.8246	+	7.98162i	−0.769220	+	0.444109i
$324$	1.28998			0.0716653
$325$	17.6377	+	3.72993i	0.978362	+	0.206899i
$326$	−1.32620			−0.0734514
$327$	−1.47018	+	0.848809i	−0.0813011	+	0.0469392i
$328$	12.7721	−	7.37397i	0.705221	−	0.407159i
$329$	0.927781	−	1.60696i	0.0511502	−	0.0885948i
$330$	−9.24303	−	0.225655i	−0.508812	−	0.0124219i
$331$	−6.84346	+	11.8532i	−0.376150	+	0.651512i	−0.990499	−	0.137524i	$-0.956086\pi$
$331$	−6.84346	+	11.8532i	−0.376150	+	0.651512i	0.614348	+	0.789035i	$0.289419\pi$
$332$	11.7678	+	6.79413i	0.645841	+	0.372877i
$333$		−	8.80677i		−	0.482608i
$334$	6.34834	−	10.9956i	0.347366	−	0.601655i
$335$	12.0802	−	6.58673i	0.660010	−	0.359871i
$336$	−0.0489641	−	0.0848083i	−0.00267121	−	0.00462667i
$337$			9.01512i			0.491085i	0.969386	+	0.245543i	$0.0789661\pi$
$337$			9.01512i			0.491085i	−0.969386	+	0.245543i	$0.921034\pi$
$338$	10.7261	−	2.22374i	0.583422	−	0.120955i
$339$	−2.24803			−0.122096
$340$	17.9317	−	9.77726i	0.972481	−	0.530246i
$341$	−15.4602	−	26.7779i	−0.837217	−	1.45010i
$342$	−1.64518	−	0.949847i	−0.0889613	−	0.0513618i
$343$			5.55440i			0.299909i
$344$	−2.79161	+	4.83521i	−0.150514	+	0.260697i
$345$	−1.15914	+	1.89908i	−0.0624059	+	0.102243i
$346$	−2.87012			−0.154299
$347$	9.40767	+	5.43152i	0.505030	+	0.291579i	0.730788	−	0.682604i	$-0.239153\pi$
$347$	9.40767	+	5.43152i	0.505030	+	0.291579i	−0.225758	+	0.974183i	$0.572486\pi$
$348$	−8.80613	+	5.08422i	−0.472058	+	0.272543i
$349$	−9.86492	−	17.0865i	−0.528057	−	0.914622i	−0.999465	−	0.0327066i	$-0.989587\pi$
$349$	−9.86492	−	17.0865i	−0.528057	−	0.914622i	0.471408	−	0.881915i	$-0.343746\pi$
$350$	−1.68898	−	0.0825172i	−0.0902797	−	0.00441073i
$351$	−0.572960	+	3.55974i	−0.0305824	+	0.190005i
$352$		−	28.2159i		−	1.50391i
$353$	−16.1051	+	9.29831i	−0.857190	+	0.494899i	−0.863070	−	0.505084i	$-0.831462\pi$
$353$	−16.1051	+	9.29831i	−0.857190	+	0.494899i	0.00588009	+	0.999983i	$0.498128\pi$
$354$	−1.28268	−	2.22167i	−0.0681738	−	0.118080i
$355$	−7.37297	+	12.0796i	−0.391317	+	0.641117i
$356$	−0.676618			−0.0358607
$357$	−2.46116	−	1.42095i	−0.130258	−	0.0752047i
$358$	−0.438595	−	0.253223i	−0.0231805	−	0.0133833i
$359$	−12.1448			−0.640976			−0.320488	−	0.947253i	$-0.603847\pi$
$359$	−12.1448			−0.640976			−0.320488	+	0.947253i	$0.603847\pi$
$360$	5.29115	+	3.22955i	0.278868	+	0.170212i
$361$	6.95865	+	12.0527i	0.366245	+	0.634355i
$362$	−12.4498	+	7.18792i	−0.654350	+	0.377789i
$363$		−	13.0794i		−	0.686488i
$364$	1.74444	−	0.664615i	0.0914337	−	0.0348353i
$365$	0.0552689	−	2.26386i	0.00289291	−	0.118496i
$366$	2.99208	+	5.18243i	0.156398	+	0.270890i
$367$	−26.8759	+	15.5168i	−1.40291	+	0.809971i	−0.994690	−	0.102913i	$-0.967184\pi$
$367$	−26.8759	+	15.5168i	−1.40291	+	0.809971i	−0.408220	+	0.912884i	$0.633850\pi$
$368$	−0.210245	−	0.121385i	−0.0109598	−	0.00632764i
$369$	−5.31988			−0.276942
$370$	8.64501	−	14.1636i	0.449432	−	0.736331i
$371$	2.17731	−	3.77121i	0.113040	−	0.195792i
$372$			8.12839i			0.421437i
$373$	−9.03380	−	5.21567i	−0.467752	−	0.270057i	0.247546	−	0.968876i	$-0.420376\pi$
$373$	−9.03380	−	5.21567i	−0.467752	−	0.270057i	−0.715298	+	0.698819i	$0.753709\pi$
$374$	−14.6387	−	25.3550i	−0.756950	−	1.31108i
$375$	−10.0655	+	4.86681i	−0.519780	+	0.251321i
$376$	−12.8165			−0.660961
$377$	−10.1187	−	26.5591i	−0.521141	−	1.36786i
$378$		−	0.338199i		−	0.0173951i
$379$	−15.3621	−	26.6080i	−0.789099	−	1.36676i	−0.926519	−	0.376247i	$-0.877214\pi$
$379$	−15.3621	−	26.6080i	−0.789099	−	1.36676i	0.137420	−	0.990513i	$-0.456119\pi$
$380$	3.11308	+	5.70944i	0.159698	+	0.292888i
$381$	8.63173	−	14.9506i	0.442217	−	0.765942i
$382$			5.22569i			0.267370i
$383$	7.37251	+	4.25652i	0.376718	+	0.217498i	0.676389	−	0.736544i	$-0.263544\pi$
$383$	7.37251	+	4.25652i	0.376718	+	0.217498i	−0.299672	+	0.954042i	$0.596877\pi$
$384$	−3.91431	+	6.77978i	−0.199751	+	0.345979i
$385$	0.107484	−	4.40264i	0.00547790	−	0.224379i
$386$	−3.84994	+	6.66829i	−0.195957	+	0.339407i
$387$	1.74416	−	1.00699i	0.0886607	−	0.0511883i
$388$	−10.5259	+	6.07715i	−0.534374	+	0.308521i
$389$	21.6832			1.09938			0.549691	−	0.835368i	$-0.314745\pi$
$389$	21.6832			1.09938			0.549691	+	0.835368i	$0.314745\pi$
$390$	−4.41582	+	5.16256i	−0.223604	+	0.261417i
$391$	−7.04526			−0.356294
$392$	16.4190	−	9.47951i	0.829285	−	0.478788i
$393$	3.97567	−	2.29535i	0.200546	−	0.115785i
$394$	−9.10459	+	15.7696i	−0.458683	+	0.794461i
$395$	22.9699	+	0.560777i	1.15574	+	0.0282157i
$396$	−3.16500	+	5.48195i	−0.159047	+	0.275478i
$397$	17.9986	+	10.3915i	0.903325	+	0.521535i	0.878278	−	0.478151i	$-0.158693\pi$
$397$	17.9986	+	10.3915i	0.903325	+	0.521535i	0.0250477	+	0.999686i	$0.492026\pi$
$398$		−	2.14404i		−	0.107471i
$399$	0.452431	−	0.783633i	0.0226499	−	0.0392307i
$400$	−0.557693	−	1.08502i	−0.0278847	−	0.0542508i
$401$	18.3709	+	31.8194i	0.917400	+	1.58898i	0.803350	+	0.595508i	$0.203049\pi$
$401$	18.3709	+	31.8194i	0.917400	+	1.58898i	0.114050	+	0.993475i	$0.463618\pi$
$402$			5.18495i			0.258602i
$403$	−22.4306	−	3.61034i	−1.11735	−	0.179844i
$404$	−7.42271			−0.369294
$405$	−1.07044	−	1.96320i	−0.0531905	−	0.0975523i
$406$	1.33295	+	2.30874i	0.0661533	+	0.114581i
$407$	37.4257	+	21.6077i	1.85512	+	1.07105i
$408$			19.6292i			0.971791i
$409$	−1.60553	+	2.78087i	−0.0793885	+	0.137505i	−0.902986	−	0.429669i	$-0.858630\pi$
$409$	−1.60553	+	2.78087i	−0.0793885	+	0.137505i	0.823598	+	0.567174i	$0.191963\pi$
$410$	−8.55578	−	5.22217i	−0.422540	−	0.257905i
$411$	4.95048			0.244189
$412$	17.2033	+	9.93231i	0.847544	+	0.489330i
$413$	1.05823	−	0.610967i	0.0520719	−	0.0300637i
$414$	−0.419208	−	0.726090i	−0.0206029	−	0.0356854i
$415$	0.574870	−	23.5471i	0.0282192	−	1.15588i
$416$	−16.0791	−	13.0875i	−0.788343	−	0.641667i
$417$		−	13.2643i		−	0.649554i
$418$	8.07303	−	4.66097i	0.394865	−	0.227975i
$419$	−7.62605	−	13.2087i	−0.372557	−	0.645288i	0.617401	−	0.786649i	$-0.288186\pi$
$419$	−7.62605	−	13.2087i	−0.372557	−	0.645288i	−0.989958	+	0.141361i	$0.954852\pi$
$420$	−0.603155	+	0.988185i	−0.0294310	+	0.0482185i
$421$	0.122664			0.00597828			0.00298914	−	0.999996i	$-0.499049\pi$
$421$	0.122664			0.00597828			0.00298914	+	0.999996i	$0.499049\pi$
$422$	8.08640	+	4.66868i	0.393640	+	0.227268i
$423$	4.00379	+	2.31159i	0.194671	+	0.112393i
$424$	−30.0777			−1.46070
$425$	−29.7598	−	19.1767i	−1.44356	−	0.930208i
$426$	−2.66647	−	4.61846i	−0.129191	−	0.223765i
$427$	−2.46849	+	1.42519i	−0.119459	+	0.0689695i
$428$		−	19.2186i		−	0.928964i
$429$	−13.7218	−	11.1688i	−0.662497	−	0.539236i
$430$	3.79357	+	0.0926146i	0.182942	+	0.00446627i
$431$	−0.809141	−	1.40147i	−0.0389750	−	0.0675066i	0.845880	−	0.533373i	$-0.179076\pi$
$431$	−0.809141	−	1.40147i	−0.0389750	−	0.0675066i	−0.884855	+	0.465867i	$0.845743\pi$
$432$	0.211302	−	0.121995i	0.0101663	−	0.00586949i
$433$	13.4785	+	7.78179i	0.647733	+	0.373969i	0.787587	−	0.616203i	$-0.211330\pi$
$433$	13.4785	+	7.78179i	0.647733	+	0.373969i	−0.139854	+	0.990172i	$0.544663\pi$
$434$	2.13106			0.102294
$435$	15.0451	+	9.18301i	0.721355	+	0.440292i
$436$	−1.09494	+	1.89650i	−0.0524383	+	0.0908257i
$437$		−	2.24321i		−	0.107307i
$438$	0.739028	+	0.426678i	0.0353121	+	0.0203875i
$439$	−3.91196	−	6.77571i	−0.186708	−	0.323387i	0.757443	−	0.652901i	$-0.226448\pi$
$439$	−3.91196	−	6.77571i	−0.186708	−	0.323387i	−0.944151	+	0.329514i	$0.893115\pi$
$440$	−26.7065	+	14.5617i	−1.27318	+	0.694204i
$441$	−6.83891			−0.325662
$442$	−21.2387	−	3.41850i	−1.01022	−	0.162601i
$443$			24.8136i			1.17893i	0.807794	+	0.589465i	$0.200662\pi$
$443$			24.8136i			1.17893i	−0.807794	+	0.589465i	$0.799338\pi$
$444$	−5.68026	−	9.83850i	−0.269573	−	0.466914i
$445$	0.561466	+	1.02974i	0.0266160	+	0.0488143i
$446$	0.223952	−	0.387896i	0.0106044	−	0.0183674i
$447$		−	3.15772i		−	0.149355i
$448$	1.51451	+	0.874402i	0.0715538	+	0.0413116i
$449$	−16.7743	+	29.0539i	−0.791626	+	1.37114i	0.133333	+	0.991071i	$0.457432\pi$
$449$	−16.7743	+	29.0539i	−0.791626	+	1.37114i	−0.924959	+	0.380066i	$0.875901\pi$
$450$	0.205593	−	4.20813i	0.00969176	−	0.198373i
$451$	13.0525	−	22.6076i	0.614619	−	1.06455i
$452$	−2.51140	+	1.44995i	−0.118126	+	0.0682001i
$453$	16.0975	−	9.29391i	0.756328	−	0.436666i
$454$	−18.0216			−0.845796
$455$	−2.45903	−	2.10334i	−0.115281	−	0.0986063i
$456$	−6.24995			−0.292681
$457$	−15.9839	+	9.22831i	−0.747696	+	0.431682i	−0.824861	−	0.565336i	$-0.808746\pi$
$457$	−15.9839	+	9.22831i	−0.747696	+	0.431682i	0.0771651	+	0.997018i	$0.475413\pi$
$458$	0.296640	−	0.171265i	0.0138611	−	0.00800271i
$459$	3.54033	−	6.13203i	0.165249	−	0.286219i
$460$	−0.0700473	+	2.86920i	−0.00326597	+	0.133777i
$461$	−3.47162	+	6.01302i	−0.161689	+	0.280054i	−0.935475	−	0.353394i	$-0.885028\pi$
$461$	−3.47162	+	6.01302i	−0.161689	+	0.280054i	0.773785	+	0.633448i	$0.218361\pi$
$462$	1.43723	+	0.829782i	0.0668658	+	0.0386050i
$463$		−	41.2459i		−	1.91686i	−0.285329	−	0.958430i	$-0.592103\pi$
$463$		−	41.2459i		−	1.91686i	0.285329	−	0.958430i	$-0.407897\pi$
$464$	−0.961646	+	1.66562i	−0.0446433	+	0.0773245i
$465$	12.3705	−	6.74504i	0.573669	−	0.312794i
$466$	1.12229	+	1.94387i	0.0519892	+	0.0900479i
$467$			29.7045i			1.37456i	0.726393	+	0.687280i	$0.241195\pi$
$467$			29.7045i			1.37456i	−0.726393	+	0.687280i	$0.758805\pi$
$468$	1.65590	+	4.34632i	0.0765441	+	0.200909i
$469$	−2.46969			−0.114040
$470$	4.17002	+	7.64789i	0.192349	+	0.352771i
$471$	−5.39008	−	9.33590i	−0.248362	−	0.430175i
$472$	−7.30924	−	4.21999i	−0.336435	−	0.194241i
$473$			9.88276i			0.454410i
$474$	−4.32922	+	7.49843i	−0.198848	+	0.344414i
$475$	6.10587	−	9.47553i	0.280157	−	0.434767i
$476$	−3.66599			−0.168030
$477$	9.39606	+	5.42482i	0.430216	+	0.248385i
$478$	11.5530	−	6.67013i	0.528422	−	0.305084i
$479$	−9.86981	−	17.0950i	−0.450963	−	0.781091i	0.547483	−	0.836817i	$-0.315586\pi$
$479$	−9.86981	−	17.0950i	−0.450963	−	0.781091i	−0.998446	+	0.0557257i	$0.982253\pi$
$480$	12.8537	+	0.313804i	0.586688	+	0.0143231i
$481$	29.6726	−	11.3050i	1.35296	−	0.515463i
$482$		−	19.6451i		−	0.894809i
$483$	0.345851	−	0.199677i	0.0157368	−	0.00908562i
$484$	−8.43603	−	14.6116i	−0.383456	−	0.664165i
$485$	17.9833	+	10.9764i	0.816580	+	0.498414i
$486$	0.842629			0.0382224
$487$	−21.0473	−	12.1517i	−0.953745	−	0.550645i	−0.0595026	−	0.998228i	$-0.518951\pi$
$487$	−21.0473	−	12.1517i	−0.953745	−	0.550645i	−0.894242	+	0.447583i	$0.852285\pi$
$488$	17.0501	+	9.84386i	0.771820	+	0.445610i
$489$	1.57388			0.0711734
$490$	−10.9988	−	6.71329i	−0.496874	−	0.303276i
$491$	−3.45543	−	5.98497i	−0.155941	−	0.270098i	0.777460	−	0.628932i	$-0.216508\pi$
$491$	−3.45543	−	5.98497i	−0.155941	−	0.270098i	−0.933401	+	0.358834i	$0.883174\pi$
$492$	−5.94312	+	3.43126i	−0.267936	+	0.154693i
$493$			55.8144i			2.51376i
$494$	1.08845	−	6.76241i	0.0489716	−	0.304255i
$495$	10.9693	+	0.267799i	0.493032	+	0.0120367i
$496$	0.768715	+	1.33145i	0.0345163	+	0.0597840i
$497$	2.19986	−	1.27009i	0.0986774	−	0.0569714i
$498$	7.68687	+	4.43802i	0.344457	+	0.198872i
$499$	−2.21036			−0.0989495			−0.0494747	−	0.998775i	$-0.515755\pi$
$499$	−2.21036			−0.0989495			−0.0494747	+	0.998775i	$0.515755\pi$
$500$	−8.10565	+	11.9291i	−0.362496	+	0.533485i
$501$	−7.53397	+	13.0492i	−0.336593	+	0.582996i
$502$			1.09679i			0.0489521i
$503$	−25.3122	−	14.6140i	−1.12862	−	0.651607i	−0.185030	−	0.982733i	$-0.559238\pi$
$503$	−25.3122	−	14.6140i	−1.12862	−	0.651607i	−0.943587	+	0.331126i	$0.892572\pi$
$504$	−0.556333	−	0.963596i	−0.0247810	−	0.0429220i
$505$	6.15946	+	11.2966i	0.274092	+	0.502690i
$506$	4.11417			0.182897
$507$	−12.7293	+	2.63905i	−0.565329	+	0.117204i
$508$		−	22.2695i		−	0.988047i
$509$	−3.60746	−	6.24830i	−0.159898	−	0.276951i	0.774934	−	0.632042i	$-0.217783\pi$
$509$	−3.60746	−	6.24830i	−0.159898	−	0.276951i	−0.934832	+	0.355091i	$0.884450\pi$
$510$	11.7132	−	6.38663i	0.518669	−	0.282805i
$511$	−0.203235	+	0.352014i	−0.00899060	+	0.0155722i
$512$			2.75575i			0.121788i
$513$	1.95244	+	1.12724i	0.0862023	+	0.0497689i
$514$	4.16001	−	7.20535i	0.183490	−	0.317814i
$515$	0.840399	−	34.4234i	0.0370324	−	1.51688i
$516$	1.29900	−	2.24993i	0.0571851	−	0.0990475i
$517$	−19.6469	+	11.3431i	−0.864068	+	0.498870i
$518$	−2.57940	+	1.48922i	−0.113332	+	0.0654325i
$519$	3.40615			0.149513
$520$	−4.08922	+	21.9732i	−0.179324	+	0.963587i
$521$	38.0923			1.66886			0.834428	−	0.551118i	$-0.185798\pi$
$521$	38.0923			1.66886			0.834428	+	0.551118i	$0.185798\pi$
$522$	−5.75228	+	3.32108i	−0.251770	+	0.145360i
$523$	0.0687721	−	0.0397056i	0.00300719	−	0.00173620i	−0.498496	−	0.866892i	$-0.666114\pi$
$523$	0.0687721	−	0.0397056i	0.00300719	−	0.00173620i	0.501503	+	0.865156i	$0.332781\pi$
$524$	2.96095	−	5.12852i	0.129350	−	0.224040i
$525$	2.00441	+	0.0979282i	0.0874798	+	0.00427394i
$526$	0.224818	−	0.389396i	0.00980253	−	0.0169785i
$527$	38.6391	+	22.3083i	1.68315	+	0.971766i
$528$			1.19728i			0.0521048i
$529$	−11.0050	+	19.0612i	−0.478478	+	0.828748i
$530$	9.78618	+	17.9480i	0.425085	+	0.779612i
$531$	1.52224	+	2.63659i	0.0660595	+	0.114418i
$532$		−	1.16725i		−	0.0506067i
$533$	−6.82897	−	17.9243i	−0.295796	−	0.776387i
$534$	−0.441976			−0.0191262
$535$	−29.2485	+	15.9478i	−1.26452	+	0.689484i
$536$	8.52918	+	14.7730i	0.368404	+	0.638095i
$537$	0.520508	+	0.300516i	0.0224616	+	0.0129682i
$538$			11.4631i			0.494210i
$539$	16.7795	−	29.0630i	0.722745	−	1.25183i
$540$	−2.46208	−	1.50278i	−0.105951	−	0.0646691i
$541$	−29.1429			−1.25295			−0.626476	−	0.779441i	$-0.715503\pi$
$541$	−29.1429			−1.25295			−0.626476	+	0.779441i	$0.715503\pi$
$542$	17.3915	+	10.0410i	0.747030	+	0.431298i
$543$	14.7750	−	8.53035i	0.634056	−	0.366072i
$544$	20.3571	+	35.2595i	0.872803	+	1.51174i
$545$	3.79486	+	0.0926460i	0.162554	+	0.00396852i
$546$	1.13949	−	0.434135i	0.0487658	−	0.0185793i
$547$		−	12.9652i		−	0.554354i	−0.960819	−	0.277177i	$-0.910601\pi$
$547$		−	12.9652i		−	0.554354i	0.960819	−	0.277177i	$-0.0893988\pi$
$548$	5.53043	−	3.19300i	0.236248	−	0.136398i
$549$	−3.55088	−	6.15031i	−0.151548	−	0.262489i
$550$	17.3786	+	11.1985i	0.741027	+	0.477505i
$551$	−17.7713			−0.757084
$552$	−2.38882	−	1.37918i	−0.101675	−	0.0587020i
$553$	−3.57165	−	2.06209i	−0.151882	−	0.0876891i
$554$	16.1892			0.687815
$555$	−10.2596	+	16.8088i	−0.435494	+	0.713495i
$556$	−8.55530	−	14.8182i	−0.362825	−	0.628432i
$557$	27.7896	−	16.0443i	1.17748	−	0.679820i	0.222051	−	0.975035i	$-0.428725\pi$
$557$	27.7896	−	16.0443i	1.17748	−	0.679820i	0.955431	+	0.295215i	$0.0953914\pi$
$558$			5.30957i			0.224772i
$559$	5.63178	+	4.58396i	0.238199	+	0.193881i
$560$	−0.00534435	+	0.218909i	−0.000225840	+	0.00925059i
$561$	17.3727	+	30.0903i	0.733474	+	1.27041i
$562$	4.61043	−	2.66183i	0.194479	−	0.112283i
$563$	−1.31596	−	0.759773i	−0.0554613	−	0.0320206i	0.472013	−	0.881592i	$-0.343528\pi$
$563$	−1.31596	−	0.759773i	−0.0554613	−	0.0320206i	−0.527474	+	0.849571i	$0.676861\pi$
$564$	5.96378			0.251121
$565$	4.29066	+	2.61888i	0.180509	+	0.110177i
$566$	12.7260	−	22.0421i	0.534914	−	0.926498i
$567$			0.401361i			0.0168556i
$568$	−15.1946	−	8.77262i	−0.637552	−	0.368091i
$569$	9.90956	+	17.1639i	0.415430	+	0.719546i	0.995474	−	0.0950394i	$-0.0302977\pi$
$569$	9.90956	+	17.1639i	0.415430	+	0.719546i	−0.580043	+	0.814586i	$0.696964\pi$
$570$	2.03351	+	3.72948i	0.0851742	+	0.156211i
$571$	43.8106			1.83342			0.916708	−	0.399558i	$-0.130836\pi$
$571$	43.8106			1.83342			0.916708	+	0.399558i	$0.130836\pi$
$572$	−22.5331	−	3.62684i	−0.942158	−	0.151646i
$573$		−	6.20165i		−	0.259078i
$574$	0.899588	+	1.55813i	0.0375481	+	0.0650352i
$575$	4.42473	−	2.27429i	0.184524	−	0.0948445i
$576$	−2.17859	+	3.77343i	−0.0907746	+	0.157226i
$577$		−	11.7411i		−	0.488787i	−0.969676	−	0.244393i	$-0.921411\pi$
$577$		−	11.7411i		−	0.488787i	0.969676	−	0.244393i	$-0.0785888\pi$
$578$	24.1805	+	13.9606i	1.00577	+	0.580684i
$579$	4.56896	−	7.91367i	0.189880	−	0.328881i
$580$	22.7306	+	0.554934i	0.943835	+	0.0230424i
$581$	−2.11392	+	3.66141i	−0.0877000	+	0.151901i
$582$	−6.87568	+	3.96968i	−0.285006	+	0.164548i
$583$	−46.1071	+	26.6200i	−1.90956	+	1.10249i
$584$	2.80752			0.116176
$585$	5.24053	−	6.12673i	0.216669	−	0.253309i
$586$	−6.01374			−0.248425
$587$	22.3360	−	12.8957i	0.921907	−	0.532263i	0.0376643	−	0.999290i	$-0.488008\pi$
$587$	22.3360	−	12.8957i	0.921907	−	0.532263i	0.884243	+	0.467027i	$0.154675\pi$
$588$	−7.64010	+	4.41101i	−0.315072	+	0.181907i
$589$	−7.10297	+	12.3027i	−0.292673	+	0.506924i
$590$	−0.140003	+	5.73462i	−0.00576381	+	0.236091i
$591$	10.8050	−	18.7148i	0.444457	−	0.769823i
$592$	−1.86089	−	1.07438i	−0.0764819	−	0.0441569i
$593$		−	10.5017i		−	0.431252i	−0.976476	−	0.215626i	$-0.930821\pi$
$593$		−	10.5017i		−	0.431252i	0.976476	−	0.215626i	$-0.0691792\pi$
$594$	−2.06742	+	3.58088i	−0.0848273	+	0.146925i
$595$	3.04208	+	5.57923i	0.124713	+	0.228726i
$596$	−2.03669	−	3.52766i	−0.0834262	−	0.144498i
$597$			2.54446i			0.104138i
$598$	1.90829	−	2.34450i	0.0780358	−	0.0958736i
$599$	−37.8214			−1.54534			−0.772669	−	0.634809i	$-0.781079\pi$
$599$	−37.8214			−1.54534			−0.772669	+	0.634809i	$0.781079\pi$
$600$	−6.33654	−	12.3280i	−0.258688	−	0.503289i
$601$	14.8477	+	25.7170i	0.605652	+	1.04902i	0.991948	+	0.126645i	$0.0404208\pi$
$601$	14.8477	+	25.7170i	0.605652	+	1.04902i	−0.386297	+	0.922375i	$0.626246\pi$
$602$	−0.589873	−	0.340563i	−0.0240414	−	0.0138803i
$603$		−	6.15330i		−	0.250582i
$604$	11.9889	−	20.7654i	0.487823	−	0.844933i
$605$	−15.2370	+	24.9636i	−0.619471	+	1.01492i
$606$	−4.84861			−0.196961
$607$	−14.0175	−	8.09298i	−0.568951	−	0.328484i	0.187779	−	0.982211i	$-0.439871\pi$
$607$	−14.0175	−	8.09298i	−0.568951	−	0.328484i	−0.756730	+	0.653727i	$0.773204\pi$
$608$	−11.2266	+	6.48170i	−0.455300	+	0.262868i
$609$	−1.58190	−	2.73992i	−0.0641017	−	0.111027i
$610$	0.326580	−	13.3770i	0.0132228	−	0.541618i
$611$	−2.64890	+	16.4573i	−0.107163	+	0.665790i
$612$		−	9.13389i		−	0.369215i
$613$	−22.0871	+	12.7520i	−0.892089	+	0.515048i	−0.874625	−	0.484799i	$-0.838893\pi$
$613$	−22.0871	+	12.7520i	−0.892089	+	0.515048i	−0.0174640	+	0.999847i	$0.505559\pi$
$614$	4.17670	+	7.23426i	0.168558	+	0.291951i
$615$	10.1537	+	6.19747i	0.409436	+	0.249906i
$616$	5.45993			0.219987
$617$	10.1748	+	5.87440i	0.409620	+	0.236494i	0.690626	−	0.723212i	$-0.257335\pi$
$617$	10.1748	+	5.87440i	0.409620	+	0.236494i	−0.281006	+	0.959706i	$0.590668\pi$
$618$	11.2374	+	6.48792i	0.452034	+	0.260982i
$619$	9.49031			0.381448			0.190724	−	0.981644i	$-0.438917\pi$
$619$	9.49031			0.381448			0.190724	+	0.981644i	$0.438917\pi$
$620$	9.46928	−	15.5141i	0.380295	−	0.623060i
$621$	0.497500	+	0.861695i	0.0199640	+	0.0345786i
$622$	4.41188	−	2.54720i	0.176900	−	0.102133i
$623$		−	0.210522i		−	0.00843438i
$624$	0.682280	+	0.555338i	0.0273131	+	0.0222313i
$625$	24.8809	+	2.43700i	0.995237	+	0.0974798i
$626$	−1.94655	−	3.37152i	−0.0777997	−	0.134753i
$627$	−9.58076	+	5.53146i	−0.382619	+	0.220905i
$628$	−12.0431	−	6.95308i	−0.480571	−	0.277458i
$629$	−62.3577			−2.48637
$630$	−0.393989	+	0.645495i	−0.0156969	+	0.0257171i
$631$	−11.7563	+	20.3625i	−0.468010	+	0.810617i	−0.999332	−	0.0365534i	$-0.988362\pi$
$631$	−11.7563	+	20.3625i	−0.468010	+	0.810617i	0.531322	+	0.847170i	$0.321695\pi$
$632$			28.4861i			1.13311i
$633$	−9.59663	−	5.54061i	−0.381432	−	0.220220i
$634$	−10.5663	−	18.3014i	−0.419641	−	0.726839i
$635$	−33.8917	+	18.4795i	−1.34495	+	0.733336i
$636$	13.9958			0.554968
$637$	−8.77890	−	23.0423i	−0.347833	−	0.912971i
$638$		−	32.5935i		−	1.29039i
$639$	3.16446	+	5.48101i	0.125184	+	0.216825i
$640$	15.3692	−	8.38005i	0.607519	−	0.331251i
$641$	−9.54940	+	16.5400i	−0.377179	+	0.653292i	−0.990651	−	0.136424i	$-0.956439\pi$
$641$	−9.54940	+	16.5400i	−0.377179	+	0.653292i	0.613472	+	0.789717i	$0.289772\pi$
$642$		−	12.5538i		−	0.495460i
$643$	37.7938	+	21.8202i	1.49044	+	0.860506i	0.999940	−	0.0109350i	$-0.00348080\pi$
$643$	37.7938	+	21.8202i	1.49044	+	0.860506i	0.490500	+	0.871441i	$0.336814\pi$
$644$	0.257579	−	0.446139i	0.0101500	−	0.0175804i
$645$	−4.50206	−	0.109911i	−0.177269	−	0.00432776i
$646$	−6.72555	+	11.6490i	−0.264613	+	0.458323i
$647$	2.86660	−	1.65503i	0.112698	−	0.0650661i	−0.442592	−	0.896723i	$-0.645941\pi$
$647$	2.86660	−	1.65503i	0.112698	−	0.0650661i	0.555289	+	0.831657i	$0.312608\pi$
$648$	2.40082	−	1.38611i	0.0943132	−	0.0544517i
$649$	−14.9395			−0.586425
$650$	14.4424	−	4.70914i	0.566476	−	0.184708i
$651$	−2.52905			−0.0991215
$652$	1.75827	−	1.01514i	0.0688590	−	0.0397558i
$653$	−3.12790	+	1.80589i	−0.122404	+	0.0706701i	−0.559952	−	0.828525i	$-0.689180\pi$
$653$	−3.12790	+	1.80589i	−0.122404	+	0.0706701i	0.437548	+	0.899195i	$0.355847\pi$
$654$	−0.715231	+	1.23882i	−0.0279677	+	0.0484416i
$655$	−10.2621	−	0.250534i	−0.400972	−	0.00978917i
$656$	−0.649000	+	1.12410i	−0.0253392	+	0.0438888i
$657$	−0.877050	−	0.506365i	−0.0342170	−	0.0197552i
$658$		−	1.56355i		−	0.0609536i
$659$	21.5161	−	37.2670i	0.838148	−	1.45172i	−0.0532932	−	0.998579i	$-0.516972\pi$
$659$	21.5161	−	37.2670i	0.838148	−	1.45172i	0.891441	−	0.453136i	$-0.149695\pi$
$660$	12.4271	−	6.77588i	0.483723	−	0.263751i
$661$	−18.8524	−	32.6533i	−0.733273	−	1.27007i	−0.955477	−	0.295066i	$-0.904658\pi$
$661$	−18.8524	−	32.6533i	−0.733273	−	1.27007i	0.222204	−	0.975000i	$-0.428675\pi$
$662$			11.5330i			0.448242i
$663$	25.2053	+	4.05694i	0.978892	+	0.157558i
$664$	29.2019			1.13325
$665$	−1.77643	+	0.968599i	−0.0688869	+	0.0375607i
$666$	−3.71042	−	6.42663i	−0.143776	−	0.249027i
$667$	−6.79245	−	3.92162i	−0.263005	−	0.151846i
$668$			19.4373i			0.752051i
$669$	−0.265778	+	0.460340i	−0.0102756	+	0.0177978i
$670$	6.04028	−	9.89614i	0.233356	−	0.382321i
$671$	34.8489			1.34532
$672$	−1.99865	−	1.15392i	−0.0770998	−	0.0445136i
$673$	38.7794	−	22.3893i	1.49484	−	0.863045i	0.494855	−	0.868975i	$-0.335221\pi$
$673$	38.7794	−	22.3893i	1.49484	−	0.863045i	0.999982	+	0.00593030i	$0.00188768\pi$
$674$	3.79820	+	6.57868i	0.146301	+	0.253401i
$675$	−0.243990	+	4.99404i	−0.00939119	+	0.192221i
$676$	−12.5184	+	11.1585i	−0.481478	+	0.429172i
$677$		−	41.0024i		−	1.57585i	−0.615770	−	0.787926i	$-0.711155\pi$
$677$		−	41.0024i		−	1.57585i	0.615770	−	0.787926i	$-0.288845\pi$
$678$	−1.64048	+	0.947129i	−0.0630021	+	0.0363743i
$679$	−1.89084	−	3.27502i	−0.0725636	−	0.125684i
$680$	22.8673	−	37.4649i	0.876922	−	1.43671i
$681$	21.3874			0.819565
$682$	−22.5638	−	13.0272i	−0.864013	−	0.498838i
$683$	−17.7354	−	10.2395i	−0.678627	−	0.391805i	0.120711	−	0.992688i	$-0.461483\pi$
$683$	−17.7354	−	10.2395i	−0.678627	−	0.391805i	−0.799338	+	0.600882i	$0.794816\pi$
$684$	2.90823			0.111199
$685$	−9.44862	−	5.76712i	−0.361013	−	0.220351i
$686$	2.34015	+	4.05326i	0.0893473	+	0.154754i
$687$	−0.352041	+	0.203251i	−0.0134312	+	0.00775452i
$688$		−	0.491392i		−	0.0187342i
$689$	−6.21641	+	38.6218i	−0.236826	+	1.47137i
$690$	−0.0457558	+	1.87420i	−0.00174189	+	0.0713494i
$691$	−13.8702	−	24.0240i	−0.527649	−	0.913915i	−0.999481	−	0.0322263i	$-0.989740\pi$
$691$	−13.8702	−	24.0240i	−0.527649	−	0.913915i	0.471832	−	0.881689i	$-0.343593\pi$
$692$	3.80518	−	2.19692i	0.144651	−	0.0835145i
$693$	−1.70564	−	0.984754i	−0.0647920	−	0.0374077i
$694$	9.15352			0.347463
$695$	−15.4524	+	25.3166i	−0.586143	+	0.960312i
$696$	−10.9263	+	18.9249i	−0.414159	+	0.717345i
$697$			37.6683i			1.42679i
$698$	−14.3976	−	8.31247i	−0.544958	−	0.314632i
$699$	−1.33189	−	2.30691i	−0.0503768	−	0.0872552i
$700$	2.30240	−	1.18342i	0.0870225	−	0.0447292i
$701$	−6.02633			−0.227611			−0.113806	−	0.993503i	$-0.536304\pi$
$701$	−6.02633			−0.227611			−0.113806	+	0.993503i	$0.536304\pi$
$702$	1.08166	+	2.83907i	0.0408245	+	0.107154i
$703$		−	19.8547i		−	0.748835i
$704$	−10.6905	−	18.5165i	−0.402913	−	0.697867i
$705$	−4.94882	−	9.07623i	−0.186383	−	0.341830i
$706$	−7.83503	+	13.5707i	−0.294875	+	0.510739i
$707$		−	2.30949i		−	0.0868573i
$708$	3.40114	+	1.96365i	0.127823	+	0.0737985i
$709$	−11.3864	+	19.7218i	−0.427625	+	0.740668i	−0.996662	−	0.0816444i	$-0.973983\pi$
$709$	−11.3864	+	19.7218i	−0.427625	+	0.740668i	0.569037	+	0.822312i	$0.307316\pi$
$710$	−0.291041	+	11.9213i	−0.0109226	+	0.447397i
$711$	5.13775	−	8.89885i	0.192681	−	0.333733i
$712$	−1.25928	+	0.727045i	−0.0471934	+	0.0272471i
$713$	−5.42971	+	3.13484i	−0.203344	+	0.117401i
$714$	−2.39467			−0.0896183
$715$	13.1786	+	37.3026i	0.492853	+	1.39504i
$716$	0.775316			0.0289749
$717$	−13.7107	+	7.91585i	−0.512034	+	0.295623i
$718$	−8.86250	+	5.11677i	−0.330746	+	0.190956i
$719$	13.1830	−	22.8336i	0.491643	−	0.851551i	−0.508310	−	0.861174i	$-0.669730\pi$
$719$	13.1830	−	22.8336i	0.491643	−	0.851551i	0.999954	+	0.00962269i	$0.00306304\pi$
$720$	−0.545416	−	0.0133156i	−0.0203265	−	0.000496242i
$721$	−3.09032	+	5.35260i	−0.115090	+	0.199341i
$722$	10.1560	+	5.86356i	0.377967	+	0.218219i
$723$			23.3140i			0.867058i
$724$	11.0039	−	19.0594i	0.408959	−	0.708337i
$725$	−18.0175	−	35.0539i	−0.669155	−	1.30187i
$726$	−5.51052	−	9.54451i	−0.204515	−	0.354230i
$727$		−	1.91130i		−	0.0708862i	−0.999372	−	0.0354431i	$-0.988716\pi$
$727$		−	1.91130i		−	0.0708862i	0.999372	−	0.0354431i	$-0.0112842\pi$
$728$	2.53250	−	3.11139i	0.0938607	−	0.115316i
$729$	−1.00000			−0.0370370
$730$	−0.913465	−	1.67531i	−0.0338089	−	0.0620060i
$731$	−7.13017	−	12.3498i	−0.263719	−	0.456774i
$732$	−7.93375	−	4.58055i	−0.293240	−	0.169302i
$733$		−	18.4077i		−	0.679904i	−0.940443	−	0.339952i	$-0.889589\pi$
$733$		−	18.4077i		−	0.679904i	0.940443	−	0.339952i	$-0.110411\pi$
$734$	−13.0749	+	22.6464i	−0.482604	+	0.835894i
$735$	13.0529	+	7.96708i	0.481465	+	0.293870i
$736$	−5.72130			−0.210890
$737$	26.1494	+	15.0973i	0.963224	+	0.556118i
$738$	−3.88212	+	2.24134i	−0.142903	+	0.0825050i
$739$	−0.909425	−	1.57517i	−0.0334538	−	0.0579436i	0.848814	−	0.528692i	$-0.177317\pi$
$739$	−0.909425	−	1.57517i	−0.0334538	−	0.0579436i	−0.882268	+	0.470748i	$0.843984\pi$
$740$	−0.619990	+	25.3953i	−0.0227913	+	0.933551i
$741$	−1.29173	+	8.02537i	−0.0474529	+	0.294819i
$742$		−	3.66933i		−	0.134705i
$743$	−7.61880	+	4.39871i	−0.279507	+	0.161373i	−0.633200	−	0.773988i	$-0.718259\pi$
$743$	−7.61880	+	4.39871i	−0.279507	+	0.161373i	0.353693	+	0.935361i	$0.384926\pi$
$744$	8.73418	+	15.1280i	0.320211	+	0.554621i
$745$	−3.67863	+	6.02692i	−0.134775	+	0.220809i
$746$	−8.78974			−0.321815
$747$	−9.12248	−	5.26687i	−0.333774	−	0.192705i
$748$	38.8158	+	22.4103i	1.41925	+	0.819402i
$749$	5.97963			0.218491
$750$	−5.29472	+	7.79224i	−0.193336	+	0.284532i
$751$	−18.0751	−	31.3070i	−0.659571	−	1.14241i	−0.980727	−	0.195384i	$-0.937405\pi$
$751$	−18.0751	−	31.3070i	−0.659571	−	1.14241i	0.321156	−	0.947026i	$-0.395929\pi$
$752$	0.976885	−	0.564005i	0.0356233	−	0.0205671i
$753$		−	1.30163i		−	0.0474339i
$754$	−18.5737	−	15.1180i	−0.676416	−	0.550565i
$755$	−41.5513	−	1.01441i	−1.51221	−	0.0369183i
$756$	0.258873	+	0.448381i	0.00941512	+	0.0163075i
$757$	−25.1967	+	14.5473i	−0.915789	+	0.528731i	−0.882289	−	0.470708i	$-0.843999\pi$
$757$	−25.1967	+	14.5473i	−0.915789	+	0.528731i	−0.0334996	+	0.999439i	$0.510665\pi$
$758$	−22.4207	−	12.9446i	−0.814355	−	0.470168i
$759$	−4.88254			−0.177225
$760$	11.9288	+	7.28096i	0.432704	+	0.264108i
$761$	13.2927	−	23.0236i	0.481859	−	0.834603i	−0.517925	−	0.855426i	$-0.673295\pi$
$761$	13.2927	−	23.0236i	0.481859	−	0.834603i	0.999783	+	0.0208228i	$0.00662858\pi$
$762$		−	14.5467i		−	0.526971i
$763$	−0.590073	−	0.340679i	−0.0213621	−	0.0123334i
$764$	−3.99999	−	6.92819i	−0.144715	−	0.250653i
$765$	−13.9008	+	7.57941i	−0.502583	+	0.274034i
$766$	7.17334			0.259183
$767$	−6.92943	+	8.51339i	−0.250207	+	0.307401i
$768$			15.3110i			0.552488i
$769$	12.4145	+	21.5026i	0.447679	+	0.775403i	0.998235	−	0.0593958i	$-0.0189174\pi$
$769$	12.4145	+	21.5026i	0.447679	+	0.775403i	−0.550556	+	0.834799i	$0.685584\pi$
$770$	−1.77646	−	3.25806i	−0.0640192	−	0.117412i
$771$	−4.93694	+	8.55103i	−0.177800	+	0.307958i
$772$		−	11.7877i		−	0.424249i
$773$	−15.4061	−	8.89469i	−0.554117	−	0.319920i	0.196664	−	0.980471i	$-0.436989\pi$
$773$	−15.4061	−	8.89469i	−0.554117	−	0.319920i	−0.750781	+	0.660551i	$0.770323\pi$
$774$	0.848521	−	1.46968i	0.0304994	−	0.0528266i
$775$	−31.4684	−	1.53743i	−1.13038	−	0.0552261i
$776$	−13.0601	+	22.6208i	−0.468832	+	0.812040i
$777$	3.06113	−	1.76735i	0.109818	−	0.0634032i
$778$	15.8231	−	9.13545i	0.567285	−	0.327522i
$779$	−11.9936			−0.429715
$780$	1.90280	−	10.2246i	0.0681312	−	0.366098i
$781$	−31.0565			−1.11129
$782$	−5.14120	+	2.96827i	−0.183849	+	0.106145i
$783$	6.82658	−	3.94133i	0.243962	−	0.140852i
$784$	−0.834314	+	1.44507i	−0.0297969	+	0.0516098i
$785$	−0.588318	+	24.0980i	−0.0209980	+	0.860095i
$786$	1.93413	−	3.35001i	0.0689882	−	0.119491i
$787$	19.7092	+	11.3791i	0.702557	+	0.405622i	0.808299	−	0.588772i	$-0.200388\pi$
$787$	19.7092	+	11.3791i	0.702557	+	0.405622i	−0.105742	+	0.994394i	$0.533722\pi$
$788$		−	27.8763i		−	0.993053i
$789$	−0.266805	+	0.462121i	−0.00949852	+	0.0164519i
$790$	16.9983	−	9.26832i	0.604771	−	0.329752i
$791$	−0.451137	−	0.781392i	−0.0160406	−	0.0277831i
$792$			13.6035i			0.483380i
$793$	16.1641	−	19.8589i	0.574003	−	0.705212i
$794$	17.5124			0.621491
$795$	−11.6139	−	21.3000i	−0.411901	−	0.755434i
$796$	1.64115	+	2.84255i	0.0581689	+	0.100751i
$797$	20.7232	+	11.9646i	0.734055	+	0.423807i	0.819904	−	0.572501i	$-0.194027\pi$
$797$	20.7232	+	11.9646i	0.734055	+	0.423807i	−0.0858488	+	0.996308i	$0.527360\pi$
$798$		−	0.762463i		−	0.0269909i
$799$	16.3676	−	28.3495i	0.579043	−	1.00293i
$800$	−24.1673	−	15.5730i	−0.854444	−	0.550589i
$801$	0.524520			0.0185330
$802$	26.8119	+	15.4799i	0.946762	+	0.546613i
$803$	4.30375	−	2.48477i	0.151876	−	0.0876856i
$804$	−3.96880	−	6.87417i	−0.139969	−	0.242433i
$805$	−0.892717	−	0.0217944i	−0.0314641	−	0.000768152i
$806$	−17.8895	+	6.81574i	−0.630132	+	0.240074i
$807$		−	13.6040i		−	0.478883i
$808$	−13.8147	+	7.97591i	−0.485999	+	0.280592i
$809$	8.39474	+	14.5401i	0.295143	+	0.511203i	0.975018	−	0.222125i	$-0.0712993\pi$
$809$	8.39474	+	14.5401i	0.295143	+	0.511203i	−0.679875	+	0.733328i	$0.737966\pi$
$810$	−1.60827	−	0.981632i	−0.0565087	−	0.0344910i
$811$	14.0218			0.492373			0.246186	−	0.969222i	$-0.420822\pi$
$811$	14.0218			0.492373			0.246186	+	0.969222i	$0.420822\pi$
$812$	−3.53444	−	2.04061i	−0.124034	−	0.0716113i
$813$	−20.6396	−	11.9163i	−0.723862	−	0.417922i
$814$	36.4146			1.27633
$815$	−3.00396	−	1.83352i	−0.105224	−	0.0642253i
$816$	−0.863806	−	1.49616i	−0.0302393	−	0.0523760i
$817$	3.93218	−	2.27025i	0.137570	−	0.0794259i
$818$			2.70574i			0.0946040i
$819$	−1.35231	+	0.515215i	−0.0472534	+	0.0180031i
$820$	15.3405	+	0.374516i	0.535713	+	0.0130787i
$821$	−19.4895	−	33.7568i	−0.680189	−	1.17812i	−0.974923	−	0.222542i	$-0.928564\pi$
$821$	−19.4895	−	33.7568i	−0.680189	−	1.17812i	0.294734	−	0.955579i	$-0.404769\pi$
$822$	3.61255	−	2.08571i	0.126002	−	0.0727474i
$823$	9.60038	+	5.54278i	0.334648	+	0.193209i	0.657903	−	0.753103i	$-0.271444\pi$
$823$	9.60038	+	5.54278i	0.334648	+	0.193209i	−0.323255	+	0.946312i	$0.604777\pi$
$824$	42.6902			1.48718
$825$	−20.6243	−	13.2899i	−0.718046	−	0.462696i
$826$	0.514819	−	0.891692i	0.0179128	−	0.0310259i
$827$		−	41.0529i		−	1.42755i	−0.700375	−	0.713775i	$-0.746984\pi$
$827$		−	41.0529i		−	1.42755i	0.700375	−	0.713775i	$-0.253016\pi$
$828$	1.11157	+	0.641763i	0.0386296	+	0.0223028i
$829$	10.4901	+	18.1694i	0.364337	+	0.631051i	0.988670	−	0.150108i	$-0.0479622\pi$
$829$	10.4901	+	18.1694i	0.364337	+	0.631051i	−0.624332	+	0.781159i	$0.714629\pi$
$830$	−9.50125	−	17.4254i	−0.329793	−	0.604846i
$831$	−19.2128			−0.666484
$832$	−15.5104	−	2.49649i	−0.537727	−	0.0865503i
$833$			48.4240i			1.67779i
$834$	−5.58843	−	9.67945i	−0.193512	−	0.335172i
$835$	29.5814	−	16.1293i	1.02371	−	0.558177i
$836$	−7.13545	+	12.3590i	−0.246785	+	0.427443i
$837$		−	6.30120i		−	0.217801i
$838$	−11.1300	−	6.42594i	−0.384481	−	0.221980i
$839$	−5.27731	+	9.14057i	−0.182193	+	0.315568i	−0.942627	−	0.333848i	$-0.891653\pi$
$839$	−5.27731	+	9.14057i	−0.182193	+	0.315568i	0.760434	+	0.649415i	$0.224986\pi$
$840$	−0.0607227	+	2.48725i	−0.00209513	+	0.0858184i
$841$	−16.5682	+	28.6969i	−0.571316	+	0.989548i
$842$	0.0895126	−	0.0516801i	0.00308481	−	0.00178101i
$843$	−5.47148	+	3.15896i	−0.188448	+	0.108800i
$844$	−14.2945			−0.492038
$845$	27.3699	+	9.79223i	0.941554	+	0.336863i
$846$	3.89562			0.133934
$847$	4.54624	−	2.62477i	0.156211	−	0.0901882i
$848$	2.29255	−	1.32360i	0.0787264	−	0.0454527i
$849$	−15.1027	+	26.1587i	−0.518325	+	0.897765i
$850$	−29.7963	−	1.45574i	−1.02201	−	0.0499314i
$851$	4.38137	−	7.58875i	0.150191	−	0.260139i
$852$	7.07037	+	4.08208i	0.242227	+	0.139850i
$853$			32.3455i			1.10749i	0.832687	+	0.553744i	$0.186801\pi$
$853$			32.3455i			1.10749i	−0.832687	+	0.553744i	$0.813199\pi$
$854$	−1.20090	+	2.08002i	−0.0410940	+	0.0711770i
$855$	−2.41329	−	4.42601i	−0.0825326	−	0.151366i
$856$	−20.6509	−	35.7684i	−0.705832	−	1.22254i
$857$		−	23.8618i		−	0.815103i	−0.913182	−	0.407551i	$-0.866383\pi$
$857$		−	23.8618i		−	0.815103i	0.913182	−	0.407551i	$-0.133617\pi$
$858$	−14.7189	−	2.36910i	−0.502496	−	0.0808798i
$859$	−20.6605			−0.704926			−0.352463	−	0.935826i	$-0.614656\pi$
$859$	−20.6605			−0.704926			−0.352463	+	0.935826i	$0.614656\pi$
$860$	−5.10038	+	2.78099i	−0.173921	+	0.0948309i
$861$	−1.06760	−	1.84913i	−0.0363836	−	0.0630183i
$862$	−1.18092	−	0.681806i	−0.0402224	−	0.0232224i
$863$		−	0.461666i		−	0.0157153i	−0.999969	−	0.00785765i	$-0.997499\pi$
$863$		−	0.461666i		−	0.0157153i	0.999969	−	0.00785765i	$-0.00250119\pi$
$864$	2.87503	−	4.97969i	0.0978104	−	0.169413i
$865$	−6.50107	−	3.96804i	−0.221043	−	0.134917i
$866$	13.1143			0.445643
$867$	−28.6964	−	16.5679i	−0.974582	−	0.562675i
$868$	−2.82534	+	1.63121i	−0.0958982	+	0.0553669i
$869$	25.2113	+	43.6673i	0.855235	+	1.48131i
$870$	14.8479	+	0.362490i	0.503391	+	0.0122896i
$871$	20.7323	−	7.89880i	0.702488	−	0.267641i
$872$			4.70619i			0.159372i
$873$	8.15979	−	4.71106i	0.276167	−	0.159445i
$874$	−0.945098	−	1.63696i	−0.0319684	−	0.0553709i
$875$	−3.71160	−	2.52198i	−0.125475	−	0.0852584i
$876$	−1.30640			−0.0441391
$877$	−17.6624	−	10.1974i	−0.596417	−	0.344342i	0.171214	−	0.985234i	$-0.445231\pi$
$877$	−17.6624	−	10.1974i	−0.596417	−	0.344342i	−0.767631	+	0.640892i	$0.778565\pi$
$878$	−5.70941	−	3.29633i	−0.192683	−	0.111246i
$879$	7.13688			0.240721
$880$	1.39479	−	2.28516i	0.0470182	−	0.0770327i
$881$	12.6173	+	21.8538i	0.425087	+	0.736272i	0.996429	−	0.0844405i	$-0.0269103\pi$
$881$	12.6173	+	21.8538i	0.425087	+	0.736272i	−0.571342	+	0.820712i	$0.693577\pi$
$882$	−4.99061	+	2.88133i	−0.168043	+	0.0970195i
$883$		−	8.44125i		−	0.284071i	−0.989862	−	0.142035i	$-0.954635\pi$
$883$		−	8.44125i		−	0.284071i	0.989862	−	0.142035i	$-0.0453647\pi$
$884$	30.7748	−	11.7249i	1.03507	−	0.394351i
$885$	0.166150	−	6.80563i	0.00558506	−	0.228769i
$886$	10.4543	+	18.1075i	0.351221	+	0.608332i
$887$	−32.3709	+	18.6894i	−1.08691	+	0.627527i	−0.932752	−	0.360519i	$-0.882600\pi$
$887$	−32.3709	+	18.6894i	−1.08691	+	0.627527i	−0.154157	+	0.988046i	$0.549266\pi$
$888$	−21.1435	−	12.2072i	−0.709528	−	0.409646i
$889$	6.92888			0.232387
$890$	0.843567	+	0.514885i	0.0282764	+	0.0172590i
$891$	2.45354	−	4.24965i	0.0821965	−	0.142369i
$892$			0.685693i			0.0229587i
$893$	9.02647	+	5.21144i	0.302059	+	0.174394i
$894$	−1.33039	−	2.30431i	−0.0444951	−	0.0770677i
$895$	−0.643367	−	1.17995i	−0.0215054	−	0.0394412i
$896$	−3.14210			−0.104970
$897$	−2.26469	+	2.78236i	−0.0756156	+	0.0929003i
$898$			28.2690i			0.943348i
$899$	24.8351	+	43.0156i	0.828297	+	1.43465i
$900$	2.94852	+	5.73648i	0.0982841	+	0.191216i
$901$	38.4113	−	66.5303i	1.27967	−	2.21645i
$902$		−	21.9969i		−	0.732416i
$903$	0.700038	+	0.404167i	0.0232958	+	0.0134498i
$904$	−3.11603	+	5.39713i	−0.103638	+	0.179506i
$905$	−38.1375	−	0.931073i	−1.26773	−	0.0309499i
$906$	7.83132	−	13.5642i	0.260178	−	0.450642i
$907$	42.5419	−	24.5616i	1.41258	−	0.815553i	0.416948	−	0.908930i	$-0.363100\pi$
$907$	42.5419	−	24.5616i	1.41258	−	0.815553i	0.995631	+	0.0933771i	$0.0297662\pi$
$908$	23.8929	−	13.7946i	0.792915	−	0.457789i
$909$	5.75415			0.190853
$910$	−2.68062	−	0.498865i	−0.0888617	−	0.0165372i
$911$	46.1927			1.53043			0.765217	−	0.643773i	$-0.222632\pi$
$911$	46.1927			1.53043			0.765217	+	0.643773i	$0.222632\pi$
$912$	0.476376	−	0.275036i	0.0157744	−	0.00910735i
$913$	44.7647	−	25.8449i	1.48149	−	0.855341i
$914$	−7.77604	+	13.4685i	−0.257209	+	0.445499i
$915$	−0.387573	+	15.8753i	−0.0128128	+	0.524821i
$916$	−0.262189	+	0.454125i	−0.00866297	+	0.0150047i
$917$	1.59568	+	0.921265i	0.0526939	+	0.0304229i
$918$		−	5.96637i		−	0.196920i
$919$	−14.7292	+	25.5118i	−0.485872	+	0.841556i	−0.999868	−	0.0162371i	$-0.994831\pi$
$919$	−14.7292	+	25.5118i	−0.485872	+	0.841556i	0.513996	+	0.857793i	$0.328165\pi$
$920$	2.95266	+	5.41523i	0.0973464	+	0.178535i
$921$	−4.95675	−	8.58534i	−0.163330	−	0.282897i
$922$			5.85057i			0.192678i
$923$	−14.4051	+	17.6978i	−0.474148	+	0.582531i
$924$	−2.54062			−0.0835802
$925$	39.1634	−	20.1298i	1.28768	−	0.661864i
$926$	−17.3775	−	30.0987i	−0.571060	−	0.989105i
$927$	−13.3361	−	7.69961i	−0.438015	−	0.252888i
$928$			45.3257i			1.48789i
$929$	11.3931	−	19.7334i	0.373795	−	0.647432i	−0.616351	−	0.787472i	$-0.711390\pi$
$929$	11.3931	−	19.7334i	0.373795	−	0.647432i	0.990146	+	0.140040i	$0.0447230\pi$
$930$	6.18546	−	10.1340i	0.202829	−	0.332307i
$931$	−15.4182			−0.505311
$932$	−2.97585	−	1.71811i	−0.0974773	−	0.0562786i
$933$	−5.23585	+	3.02292i	−0.171414	+	0.0989659i
$934$	12.5149	+	21.6765i	0.409501	+	0.709277i
$935$	1.89620	−	77.6698i	0.0620122	−	2.54007i
$936$	7.75210	+	6.30978i	0.253385	+	0.206242i
$937$			33.3968i			1.09103i	0.838102	+	0.545513i	$0.183665\pi$
$937$			33.3968i			1.09103i	−0.838102	+	0.545513i	$0.816335\pi$
$938$	−1.80223	+	1.04052i	−0.0588449	+	0.0339741i
$939$	2.31009	+	4.00119i	0.0753869	+	0.130574i
$940$	−11.3826	−	6.94759i	−0.371261	−	0.226605i
$941$	−4.59203			−0.149696			−0.0748480	−	0.997195i	$-0.523847\pi$
$941$	−4.59203			−0.149696			−0.0748480	+	0.997195i	$0.523847\pi$
$942$	−7.86670	−	4.54184i	−0.256311	−	0.147981i
$943$	−4.58412	−	2.64664i	−0.149279	−	0.0861865i
$944$	0.742822			0.0241768
$945$	0.467571	−	0.766049i	0.0152101	−	0.0249196i
$946$	4.16375	+	7.21183i	0.135375	+	0.234477i
$947$	−8.35815	+	4.82558i	−0.271603	+	0.156810i	−0.629616	−	0.776906i	$-0.716788\pi$
$947$	−8.35815	+	4.82558i	−0.271603	+	0.156810i	0.358013	+	0.933717i	$0.383454\pi$
$948$		−	13.2552i		−	0.430507i
$949$	0.580254	−	3.60505i	0.0188359	−	0.117025i
$950$	0.463507	−	9.48715i	0.0150381	−	0.307804i
$951$	12.5397	+	21.7193i	0.406627	+	0.704298i
$952$	−6.82290	+	3.93920i	−0.221131	+	0.127670i
$953$	29.3593	+	16.9506i	0.951040	+	0.549083i	0.893404	−	0.449254i	$-0.148310\pi$
$953$	29.3593	+	16.9506i	0.951040	+	0.549083i	0.0576363	+	0.998338i	$0.481644\pi$
$954$	9.14222			0.295990
$955$	−7.22470	+	11.8366i	−0.233786	+	0.383025i
$956$	−10.2113	+	17.6864i	−0.330256	+	0.572020i
$957$			38.6808i			1.25037i
$958$	−14.4048	−	8.31659i	−0.465397	−	0.268697i
$959$	0.993464	+	1.72073i	0.0320806	+	0.0555653i
$960$	8.55403	−	4.66409i	0.276080	−	0.150533i
$961$	8.70507			0.280809
$962$	16.8903	−	20.7512i	0.544566	−	0.669045i
$963$			14.8984i			0.480094i
$964$	15.0373	+	26.0453i	0.484318	+	0.838863i
$965$	−17.9396	+	9.78158i	−0.577496	+	0.314880i
$966$	0.168254	−	0.291424i	0.00541348	−	0.00937642i
$967$		−	20.9057i		−	0.672283i	−0.941812	−	0.336141i	$-0.890878\pi$
$967$		−	20.9057i		−	0.672283i	0.941812	−	0.336141i	$-0.109122\pi$
$968$	−31.4012	−	18.1295i	−1.00927	−	0.582704i
$969$	7.98162	−	13.8246i	0.256407	−	0.444109i
$970$	17.7476	+	0.433283i	0.569842	+	0.0139119i
$971$	−24.1043	+	41.7499i	−0.773545	+	1.33982i	0.162064	+	0.986780i	$0.448185\pi$
$971$	−24.1043	+	41.7499i	−0.773545	+	1.33982i	−0.935609	+	0.353038i	$0.885149\pi$
$972$	−1.11715	+	0.644988i	−0.0358327	+	0.0206880i
$973$	4.61051	−	2.66188i	0.147806	−	0.0853360i
$974$	−20.4787			−0.656180
$975$	−17.1396	+	5.58862i	−0.548908	+	0.178979i
$976$	−1.73276			−0.0554643
$977$	−28.5119	+	16.4614i	−0.912177	+	0.526646i	−0.881131	−	0.472872i	$-0.843217\pi$
$977$	−28.5119	+	16.4614i	−0.912177	+	0.526646i	−0.0310460	+	0.999518i	$0.509884\pi$
$978$	1.14852	−	0.663100i	0.0367257	−	0.0212036i
$979$	−1.28693	+	2.22902i	−0.0411304	+	0.0712399i
$980$	19.7208	+	0.481455i	0.629957	+	0.0153795i
$981$	0.848809	−	1.47018i	0.0271004	−	0.0469392i
$982$	−5.04311	−	2.91164i	−0.160932	−	0.0929143i
$983$		−	11.0460i		−	0.352312i	−0.984362	−	0.176156i	$-0.943634\pi$
$983$		−	11.0460i		−	0.352312i	0.984362	−	0.176156i	$-0.0563663\pi$
$984$	−7.37397	+	12.7721i	−0.235074	+	0.407159i
$985$	−42.4247	+	23.1321i	−1.35176	+	0.737051i
$986$	23.5154	+	40.7299i	0.748884	+	1.29711i
$987$			1.85556i			0.0590632i
$988$	3.73321	+	9.79870i	0.118769	+	0.311738i
$989$	2.00391			0.0637207
$990$	8.11753	−	4.42609i	0.257992	−	0.140670i
$991$	4.83587	+	8.37598i	0.153617	+	0.266072i	0.932554	−	0.361029i	$-0.117575\pi$
$991$	4.83587	+	8.37598i	0.153617	+	0.266072i	−0.778938	+	0.627101i	$0.784241\pi$
$992$	31.3780	+	18.1161i	0.996253	+	0.575187i
$993$		−	13.6869i		−	0.434341i
$994$	1.07022	−	1.85367i	0.0339452	−	0.0587948i
$995$	2.96420	−	4.85643i	0.0939715	−	0.153959i
$996$	−13.5883			−0.430561
$997$	43.6735	+	25.2149i	1.38315	+	0.798565i	0.992532	−	0.121986i	$-0.0389263\pi$
$997$	43.6735	+	25.2149i	1.38315	+	0.798565i	0.390623	+	0.920551i	$0.372260\pi$
$998$	−1.61299	+	0.931258i	−0.0510582	+	0.0294785i
$999$	4.40338	+	7.62688i	0.139317	+	0.241304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.ba.a.94.8	yes	24
3.2	odd	2		585.2.bs.b.289.5		24
5.2	odd	4		975.2.i.q.601.4		12
5.3	odd	4		975.2.i.o.601.3		12
5.4	even	2	inner	195.2.ba.a.94.5	✓	24
13.9	even	3	inner	195.2.ba.a.139.5	yes	24
15.14	odd	2		585.2.bs.b.289.8		24
39.35	odd	6		585.2.bs.b.334.8		24
65.9	even	6	inner	195.2.ba.a.139.8	yes	24
65.22	odd	12		975.2.i.q.451.4		12
65.48	odd	12		975.2.i.o.451.3		12
195.74	odd	6		585.2.bs.b.334.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.5	✓	24	5.4	even	2	inner
195.2.ba.a.94.8	yes	24	1.1	even	1	trivial
195.2.ba.a.139.5	yes	24	13.9	even	3	inner
195.2.ba.a.139.8	yes	24	65.9	even	6	inner
585.2.bs.b.289.5		24	3.2	odd	2
585.2.bs.b.289.8		24	15.14	odd	2
585.2.bs.b.334.5		24	195.74	odd	6
585.2.bs.b.334.8		24	39.35	odd	6
975.2.i.o.451.3		12	65.48	odd	12
975.2.i.o.601.3		12	5.3	odd	4
975.2.i.q.451.4		12	65.22	odd	12
975.2.i.q.601.4		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.729738 - 0.421315i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.644988 + 1.11715i) q^{4} +(2.23540 + 0.0545741i) q^{5} +(-0.421315 + 0.729738i) q^{6} +(-0.347589 - 0.200681i) q^{7} +2.77223i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.65425 - 0.901983i) q^{10} +(2.45354 + 4.24965i) q^{11} -1.28998i q^{12} +(3.55974 + 0.572960i) q^{13} -0.338199 q^{14} +(-1.96320 + 1.07044i) q^{15} +(-0.121995 - 0.211302i) q^{16} +(-6.13203 - 3.54033i) q^{17} -0.842629i q^{18} +(1.12724 - 1.95244i) q^{19} +(-1.50278 + 2.46208i) q^{20} +0.401361 q^{21} +(3.58088 + 2.06742i) q^{22} +(0.861695 - 0.497500i) q^{23} +(-1.38611 - 2.40082i) q^{24} +(4.99404 + 0.243990i) q^{25} +(2.83907 - 1.08166i) q^{26} +1.00000i q^{27} +(0.448381 - 0.258873i) q^{28} +(-3.94133 - 6.82658i) q^{29} +(-0.981632 + 1.60827i) q^{30} -6.30120 q^{31} +(-4.97969 - 2.87503i) q^{32} +(-4.24965 - 2.45354i) q^{33} -5.96637 q^{34} +(-0.766049 - 0.467571i) q^{35} +(0.644988 + 1.11715i) q^{36} +(7.62688 - 4.40338i) q^{37} -1.89969i q^{38} +(-3.36930 + 1.28367i) q^{39} +(-0.151292 + 6.19705i) q^{40} +(-2.65994 - 4.60715i) q^{41} +(0.292889 - 0.169099i) q^{42} +(1.74416 + 1.00699i) q^{43} -6.33001 q^{44} +(1.16496 - 1.90863i) q^{45} +(0.419208 - 0.726090i) q^{46} +4.62317i q^{47} +(0.211302 + 0.121995i) q^{48} +(-3.41945 - 5.92267i) q^{49} +(3.74714 - 1.92601i) q^{50} +7.08066 q^{51} +(-2.93607 + 3.60721i) q^{52} +10.8496i q^{53} +(0.421315 + 0.729738i) q^{54} +(5.25272 + 9.63357i) q^{55} +(0.556333 - 0.963596i) q^{56} +2.25448i q^{57} +(-5.75228 - 3.32108i) q^{58} +(-1.52224 + 2.63659i) q^{59} +(0.0703993 - 2.88361i) q^{60} +(3.55088 - 6.15031i) q^{61} +(-4.59822 + 2.65479i) q^{62} +(-0.347589 + 0.200681i) q^{63} -4.35718 q^{64} +(7.92617 + 1.47507i) q^{65} -4.13484 q^{66} +(5.32891 - 3.07665i) q^{67} +(7.91018 - 4.56694i) q^{68} +(-0.497500 + 0.861695i) q^{69} +(-0.756010 - 0.0184569i) q^{70} +(-3.16446 + 5.48101i) q^{71} +(2.40082 + 1.38611i) q^{72} -1.01273i q^{73} +(3.71042 - 6.42663i) q^{74} +(-4.44696 + 2.28572i) q^{75} +(1.45411 + 2.51860i) q^{76} -1.96951i q^{77} +(-1.91788 + 2.35628i) q^{78} +10.2755 q^{79} +(-0.261177 - 0.479002i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.88212 - 2.24134i) q^{82} -10.5337i q^{83} +(-0.258873 + 0.448381i) q^{84} +(-13.5143 - 8.24871i) q^{85} +1.69704 q^{86} +(6.82658 + 3.94133i) q^{87} +(-11.7810 + 6.80177i) q^{88} +(0.262260 + 0.454247i) q^{89} +(0.0459858 - 1.88361i) q^{90} +(-1.12234 - 0.913524i) q^{91} +1.28353i q^{92} +(5.45700 - 3.15060i) q^{93} +(1.94781 + 3.37371i) q^{94} +(2.62639 - 4.30297i) q^{95} +5.75005 q^{96} +(8.15979 + 4.71106i) q^{97} +(-4.99061 - 2.88133i) q^{98} +4.90707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{4} + 4 q^{5} + 12 q^{9} - 4 q^{10} + 4 q^{11} + 24 q^{14} - 2 q^{15} + 16 q^{16} - 16 q^{19} - 16 q^{20} - 8 q^{21} - 16 q^{25} - 48 q^{26} - 12 q^{29} - 4 q^{30} + 8 q^{31} - 32 q^{34} + 10 q^{35}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q + 8 * q^4 + 4 * q^5 + 12 * q^9 - 4 * q^10 + 4 * q^11 + 24 * q^14 - 2 * q^15 + 16 * q^16 - 16 * q^19 - 16 * q^20 - 8 * q^21 - 16 * q^25 - 48 * q^26 - 12 * q^29 - 4 * q^30 + 8 * q^31 - 32 * q^34 + 10 * q^35 - 8 * q^36 + 8 * q^39 - 48 * q^40 - 40 * q^41 + 40 * q^44 + 2 * q^45 - 24 * q^46 - 16 * q^49 + 20 * q^50 - 24 * q^51 + 20 * q^55 - 24 * q^56 + 12 * q^59 + 48 * q^60 + 20 * q^61 + 48 * q^64 + 14 * q^65 - 56 * q^66 - 8 * q^69 - 56 * q^70 + 4 * q^71 - 12 * q^74 + 16 * q^75 + 8 * q^76 + 136 * q^79 - 4 * q^80 - 12 * q^81 - 16 * q^84 - 4 * q^85 + 48 * q^86 - 64 * q^89 - 8 * q^90 + 60 * q^91 - 48 * q^94 - 28 * q^95 + 40 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more