LMFDB - Embedded newform 195.2.ba.a.94.5

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			94.5
Character	$\chi$	$=$	195.94
Dual form			195.2.ba.a.139.5

$q$-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} +(-1.60827 + 0.981632i) q^{10} +(2.45354 + 4.24965i) q^{11} +1.28998i q^{12} +(-3.55974 - 0.572960i) q^{13} -0.338199 q^{14} +(1.90863 - 1.16496i) q^{15} +(-0.121995 - 0.211302i) q^{16} +(6.13203 + 3.54033i) q^{17} +0.842629i q^{18} +(1.12724 - 1.95244i) q^{19} +(-1.38084 + 2.53248i) 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} +(-0.901983 + 1.65425i) q^{30} -6.30120 q^{31} +(4.97969 + 2.87503i) q^{32} +(4.24965 + 2.45354i) q^{33} -5.96637 q^{34} +(0.787953 + 0.429632i) 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} +(1.07044 - 1.96320i) q^{45} +(0.419208 - 0.726090i) q^{46} -4.62317i q^{47} +(-0.211302 - 0.121995i) q^{48} +(-3.41945 - 5.92267i) q^{49} +(-3.54155 + 2.28211i) q^{50} +7.08066 q^{51} +(2.93607 - 3.60721i) q^{52} -10.8496i q^{53} +(0.421315 + 0.729738i) q^{54} +(5.71656 + 9.36577i) 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} +(-7.98871 - 1.08653i) 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} +(4.20297 - 2.70832i) q^{75} +(1.45411 + 2.51860i) q^{76} +1.96951i q^{77} +(1.91788 - 2.35628i) q^{78} +10.2755 q^{79} +(-0.284240 - 0.465687i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.88212 + 2.24134i) q^{82} +10.5337i q^{83} +(-0.258873 + 0.448381i) q^{84} +(13.9008 + 7.57941i) 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} +(2.41329 - 4.42601i) 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	−0.735298	−	0.677744i	$-0.762958\pi$
$2$	−0.729738	+	0.421315i	−0.516003	+	0.297914i	0.219295	+	0.975659i	$0.429624\pi$
$3$	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	0.564248	−	0.825606i	$-0.309166\pi$
$7$	0.347589	+	0.200681i	0.131376	+	0.0758501i	−0.432871	+	0.901456i	$0.642500\pi$
$8$		−	2.77223i		−	0.980131i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.60827	+	0.981632i	−0.508578	+	0.310419i
$11$	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
$15$	1.90863	−	1.16496i	0.492806	−	0.300792i
$16$	−0.121995	−	0.211302i	−0.0304988	−	0.0528254i
$17$	6.13203	+	3.54033i	1.48724	+	0.858656i	0.999894	−	0.0145544i	$-0.00463296\pi$
$17$	6.13203	+	3.54033i	1.48724	+	0.858656i	0.487343	+	0.873211i	$0.337966\pi$
$18$			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	$0.0834032\pi$
$20$	−1.38084	+	2.53248i	−0.308765	+	0.566281i
$21$	0.401361			0.0875842
$22$	−3.58088	−	2.06742i	−0.763446	−	0.440776i
$23$	−0.861695	+	0.497500i	−0.179676	+	0.103736i	−0.587140	−	0.809485i	$-0.699746\pi$
$23$	−0.861695	+	0.497500i	−0.179676	+	0.103736i	0.407465	+	0.913221i	$0.366413\pi$
$24$	−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	$-0.428027\pi$
$30$	−0.901983	+	1.65425i	−0.164679	+	0.302024i
$31$	−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
$35$	0.787953	+	0.429632i	0.133188	+	0.0726211i
$36$	0.644988	+	1.11715i	0.107498	+	0.186192i
$37$	−7.62688	+	4.40338i	−1.25385	+	0.723912i	−0.971872	−	0.235509i	$-0.924324\pi$
$37$	−7.62688	+	4.40338i	−1.25385	+	0.723912i	−0.281980	+	0.959420i	$0.590991\pi$
$38$			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	0.361078	−	0.932536i	$-0.382409\pi$
$43$	−1.74416	−	1.00699i	−0.265982	−	0.153565i	−0.627060	+	0.778971i	$0.715742\pi$
$44$	−6.33001			−0.954284
$45$	1.07044	−	1.96320i	0.159572	−	0.292657i
$46$	0.419208	−	0.726090i	0.0618088	−	0.107056i
$47$		−	4.62317i		−	0.674359i	−0.941440	−	0.337180i	$-0.890527\pi$
$47$		−	4.62317i		−	0.674359i	0.941440	−	0.337180i	$-0.109473\pi$
$48$	−0.211302	−	0.121995i	−0.0304988	−	0.0176085i
$49$	−3.41945	−	5.92267i	−0.488494	−	0.846096i
$50$	−3.54155	+	2.28211i	−0.500851	+	0.322739i
$51$	7.08066			0.991491
$52$	2.93607	−	3.60721i	0.407160	−	0.500230i
$53$		−	10.8496i		−	1.49031i	−0.666890	−	0.745156i	$-0.732375\pi$
$53$		−	10.8496i		−	1.49031i	0.666890	−	0.745156i	$-0.267625\pi$
$54$	0.421315	+	0.729738i	0.0573337	+	0.0993048i
$55$	5.71656	+	9.36577i	0.770821	+	1.26288i
$56$	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
$65$	−7.98871	−	1.08653i	−0.990877	−	0.134767i
$66$	−4.13484			−0.508964
$67$	−5.32891	+	3.07665i	−0.651030	+	0.375873i	−0.788851	−	0.614585i	$-0.789324\pi$
$67$	−5.32891	+	3.07665i	−0.651030	+	0.375873i	0.137821	+	0.990457i	$0.455990\pi$
$68$	−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	$0.0188759\pi$
$73$			1.01273i			0.118531i	−0.998242	+	0.0592655i	$0.981124\pi$
$74$	3.71042	−	6.42663i	0.431327	−	0.747081i
$75$	4.20297	−	2.70832i	0.485318	−	0.312730i
$76$	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	$0.303817\pi$
$80$	−0.284240	−	0.465687i	−0.0317790	−	0.0520653i
$81$	−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	$0.196211\pi$
$83$			10.5337i			1.15623i	−0.815956	+	0.578114i	$0.803789\pi$
$84$	−0.258873	+	0.448381i	−0.0282454	+	0.0489224i
$85$	13.9008	+	7.57941i	1.50775	+	0.822103i
$86$	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
$95$	2.41329	−	4.42601i	0.247598	−	0.454099i
$96$	5.75005			0.586862
$97$	−8.15979	−	4.71106i	−0.828502	−	0.478336i	0.0248378	−	0.999691i	$-0.492093\pi$
$97$	−8.15979	−	4.71106i	−0.828502	−	0.478336i	−0.853339	+	0.521356i	$0.825426\pi$
$98$	4.99061	+	2.88133i	0.504128	+	0.291059i
$99$	4.90707			0.493179
$100$	−2.94852	+	5.73648i	−0.294852	+	0.573648i
$101$	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	$0.274148\pi$
$103$			15.3992i			1.51733i	−0.651481	+	0.758665i	$0.725852\pi$
$104$	−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	0.276746	−	0.960943i	$-0.410744\pi$
$107$	12.9024	−	7.44919i	1.24732	−	0.720141i	0.970574	+	0.240802i	$0.0774106\pi$
$108$	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	$0.474092\pi$
$110$	−8.11753	−	4.42609i	−0.773976	−	0.422011i
$111$	−4.40338	+	7.62688i	−0.417951	+	0.723912i
$112$		−	0.0979282i		−	0.00925335i
$113$	−1.94685	−	1.12402i	−0.183145	−	0.105739i	0.405625	−	0.914040i	$-0.367054\pi$
$113$	−1.94685	−	1.12402i	−0.183145	−	0.105739i	−0.588769	+	0.808301i	$0.700387\pi$
$114$	0.949847	+	1.64518i	0.0889613	+	0.154086i
$115$	−1.89908	+	1.15914i	−0.177091	+	0.108090i
$116$	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
$120$	−3.22955	−	5.29115i	−0.294816	−	0.483014i
$121$	−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	0.341871	−	0.939747i	$-0.388939\pi$
$127$	14.9506	−	8.63173i	1.32665	−	0.765942i	0.984780	+	0.173804i	$0.0556060\pi$
$128$	−6.77978	+	3.91431i	−0.599254	+	0.345979i
$129$	−2.01398			−0.177321
$130$	6.28744	−	2.57288i	0.551445	−	0.225656i
$131$	−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	0.671834	−	0.740702i	$-0.265507\pi$
$137$	4.28724	+	2.47524i	0.366284	+	0.211474i	−0.305550	+	0.952176i	$0.598840\pi$
$138$		−	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	$0.976495\pi$
$140$	−0.988185	+	0.603155i	−0.0835169	+	0.0509759i
$141$	−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
$145$	−9.18301	−	15.0451i	−0.762607	−	1.24942i
$146$	−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	$0.207954\pi$
$150$	−1.92601	+	3.74714i	−0.157258	+	0.305953i
$151$	−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	$-0.858452\pi$
$157$		−	10.7802i		−	0.860351i	0.902745	−	0.430175i	$-0.141548\pi$
$158$	−7.49843	+	4.32922i	−0.596543	+	0.344414i
$159$	−5.42482	−	9.39606i	−0.430216	−	0.745156i
$160$	11.2885	+	6.15508i	0.892435	+	0.486602i
$161$	−0.399354			−0.0314735
$162$	0.729738	+	0.421315i	0.0573337	+	0.0331016i
$163$	1.36302	+	0.786941i	0.106760	+	0.0616380i	0.552429	−	0.833560i	$-0.313701\pi$
$163$	1.36302	+	0.786941i	0.106760	+	0.0616380i	−0.445669	+	0.895198i	$0.647034\pi$
$164$	6.86252			0.535873
$165$	9.63357	+	5.25272i	0.749973	+	0.408924i
$166$	−4.43802	−	7.68687i	−0.344457	−	0.596617i
$167$	−13.0492	+	7.53397i	−1.00978	+	0.582996i	−0.911127	−	0.412126i	$-0.864786\pi$
$167$	−13.0492	+	7.53397i	−1.00978	+	0.582996i	−0.0986516	+	0.995122i	$0.531453\pi$
$168$		−	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	0.607926	−	0.793994i	$-0.292002\pi$
$173$	2.94981	+	1.70307i	0.224270	+	0.129482i	−0.383656	+	0.923476i	$0.625335\pi$
$174$	6.64216			0.503541
$175$	1.78484	+	0.917399i	0.134921	+	0.0693488i
$176$	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	$0.840484\pi$
$180$	1.50278	+	2.46208i	0.112010	+	0.183513i
$181$	−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
$185$	−16.8088	+	10.2596i	−1.23581	+	0.754298i
$186$	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	−0.187366	−	0.982290i	$-0.559995\pi$
$193$	7.91367	−	4.56896i	0.569639	−	0.328881i	0.757005	+	0.653409i	$0.226662\pi$
$194$	7.93935			0.570012
$195$	−7.46169	+	3.05339i	−0.534343	+	0.218658i
$196$	8.82203			0.630145
$197$	18.7148	−	10.8050i	1.33337	−	0.769823i	0.347557	−	0.937659i	$-0.387011\pi$
$197$	18.7148	−	10.8050i	1.33337	−	0.769823i	0.985815	+	0.167836i	$0.0536780\pi$
$198$	−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
$205$	−6.19747	−	10.1537i	−0.432850	−	0.709164i
$206$	−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
$210$	−0.645495	+	0.393989i	−0.0445434	+	0.0271878i
$211$	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
$215$	−3.95386	−	2.15585i	−0.269651	−	0.147027i
$216$	−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	−0.515334	−	0.856989i	$-0.672332\pi$
$223$	−0.460340	+	0.265778i	−0.0308267	+	0.0177978i	0.484507	+	0.874787i	$0.338999\pi$
$224$	1.15392	+	1.99865i	0.0770998	+	0.133541i
$225$	2.28572	−	4.44696i	0.152381	−	0.296464i
$226$	1.89426			0.126004
$227$	18.5220	+	10.6937i	1.22935	+	0.709764i	0.966894	−	0.255180i	$-0.0821348\pi$
$227$	18.5220	+	10.6937i	1.22935	+	0.709764i	0.262454	+	0.964944i	$0.415468\pi$
$228$	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	$0.495725\pi$
$230$	0.897473	−	1.64598i	0.0591776	−	0.108533i
$231$	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	$-0.972190\pi$
$233$		−	2.66379i		−	0.174510i	0.996186	−	0.0872552i	$-0.0278096\pi$
$234$	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	$0.328892\pi$
$240$	−0.479002	−	0.261177i	−0.0309195	−	0.0168589i
$241$	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
$245$	−7.96708	−	13.0529i	−0.508998	−	0.833921i
$246$	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
$250$	−7.79224	+	5.29472i	−0.492824	+	0.334867i
$251$	−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	−0.742399	−	0.669958i	$-0.766312\pi$
$257$	−8.55103	+	4.93694i	−0.533399	+	0.307958i	0.209001	+	0.977915i	$0.432979\pi$
$258$	1.46968	−	0.848521i	0.0914983	−	0.0528266i
$259$	−3.53469			−0.219635
$260$	6.36644	−	8.22380i	0.394830	−	0.510019i
$261$	−7.88266			−0.487924
$262$	3.35001	−	1.93413i	0.206965	−	0.119491i
$263$	−0.462121	+	0.266805i	−0.0284956	+	0.0164519i	−0.514180	−	0.857682i	$-0.671904\pi$
$263$	−0.462121	+	0.266805i	−0.0284956	+	0.0164519i	0.485685	+	0.874134i	$0.338570\pi$
$264$	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	$0.302789\pi$
$270$	0.981632	+	1.60827i	0.0597402	+	0.0978759i
$271$	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
$275$	13.2899	+	20.6243i	0.801413	+	1.24369i
$276$	−0.641763	−	1.11157i	−0.0386296	−	0.0669084i
$277$	−16.6388	−	9.60639i	−0.999726	−	0.577192i	−0.0915586	−	0.995800i	$-0.529185\pi$
$277$	−16.6388	−	9.60639i	−0.999726	−	0.577192i	−0.908167	+	0.418608i	$0.862518\pi$
$278$		−	11.1769i		−	0.670344i
$279$	−3.15060	+	5.45700i	−0.188621	+	0.326702i
$280$	1.19104	−	2.18439i	0.0711782	−	0.130542i
$281$	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	$0.688143\pi$
$283$	−26.1587	+	15.1027i	−1.55497	+	0.897765i	−0.997725	+	0.0674193i	$0.978523\pi$
$284$	−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
$290$	13.0399	+	7.11002i	0.765729	+	0.417515i
$291$	−9.42212			−0.552334
$292$	−1.13137	−	0.653199i	−0.0662086	−	0.0382256i
$293$	6.18072	+	3.56844i	0.361081	+	0.208470i	0.669555	−	0.742762i	$-0.266485\pi$
$293$	6.18072	+	3.56844i	0.361081	+	0.208470i	−0.308474	+	0.951233i	$0.599818\pi$
$294$	5.76266			0.336085
$295$	−3.25892	+	5.97692i	−0.189742	+	0.347990i
$296$	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
$305$	7.60200	−	13.9422i	0.435289	−	0.798328i
$306$	−2.98319	+	5.16703i	−0.170537	+	0.295379i
$307$		−	9.91349i		−	0.565793i	−0.959150	−	0.282897i	$-0.908705\pi$
$307$		−	9.91349i		−	0.565793i	0.959150	−	0.282897i	$-0.0912953\pi$
$308$	−2.20024	−	1.27031i	−0.125370	−	0.0723826i
$309$	7.69961	+	13.3361i	0.438015	+	0.758665i
$310$	10.1340	−	6.18546i	0.575572	−	0.351310i
$311$	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	$0.0416820\pi$
$313$			4.62017i			0.261148i	−0.991439	+	0.130574i	$0.958318\pi$
$314$	4.54184	+	7.86670i	0.256311	+	0.443944i
$315$	0.766049	−	0.467571i	0.0431620	−	0.0263446i
$316$	−6.62758	+	11.4793i	−0.372830	+	0.645761i
$317$			25.0793i			1.40860i	0.709905	+	0.704298i	$0.248738\pi$
$317$			25.0793i			1.40860i	−0.709905	+	0.704298i	$0.751262\pi$
$318$	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
$325$	−17.9173	−	1.99285i	−0.993871	−	0.110543i
$326$	−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
$335$	−11.7444	+	7.16837i	−0.641663	+	0.391650i
$336$	−0.0489641	−	0.0848083i	−0.00267121	−	0.00462667i
$337$		−	9.01512i		−	0.491085i	−0.969386	−	0.245543i	$-0.921034\pi$
$337$		−	9.01512i		−	0.491085i	0.969386	−	0.245543i	$-0.0789661\pi$
$338$	−10.7261	+	2.22374i	−0.583422	+	0.120955i
$339$	−2.24803			−0.122096
$340$	−17.4332	+	10.6406i	−0.945447	+	0.577070i
$341$	−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
$345$	−1.06509	+	1.95339i	−0.0573423	+	0.105167i
$346$	−2.87012			−0.154299
$347$	−9.40767	−	5.43152i	−0.505030	−	0.291579i	0.225758	−	0.974183i	$-0.427514\pi$
$347$	−9.40767	−	5.43152i	−0.505030	−	0.291579i	−0.730788	+	0.682604i	$0.760847\pi$
$348$	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	−0.00588009	−	0.999983i	$-0.501872\pi$
$353$	16.1051	−	9.29831i	0.857190	−	0.494899i	0.863070	+	0.505084i	$0.168538\pi$
$354$	−1.28268	−	2.22167i	−0.0681738	−	0.118080i
$355$	−6.77473	+	12.4250i	−0.359565	+	0.659448i
$356$	−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	$0.603847\pi$
$360$	−5.44245	−	2.96750i	−0.286842	−	0.156401i
$361$	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	0.408220	−	0.912884i	$-0.366150\pi$
$367$	26.8759	−	15.5168i	1.40291	−	0.809971i	0.994690	+	0.102913i	$0.0328163\pi$
$368$	0.210245	+	0.121385i	0.0109598	+	0.00632764i
$369$	−5.31988			−0.276942
$370$	7.94355	−	14.5686i	0.412965	−	0.757386i
$371$	2.17731	−	3.77121i	0.113040	−	0.195792i
$372$		−	8.12839i		−	0.421437i
$373$	9.03380	+	5.21567i	0.467752	+	0.270057i	0.715298	−	0.698819i	$-0.246291\pi$
$373$	9.03380	+	5.21567i	0.467752	+	0.270057i	−0.247546	+	0.968876i	$0.579624\pi$
$374$	−14.6387	−	25.3550i	−0.756950	−	1.31108i
$375$	9.24753	−	6.28357i	0.477540	−	0.324482i
$376$	−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	$-0.456119\pi$
$380$	3.38798	+	5.55073i	0.173800	+	0.284746i
$381$	8.63173	−	14.9506i	0.442217	−	0.765942i
$382$		−	5.22569i		−	0.267370i
$383$	−7.37251	−	4.25652i	−0.376718	−	0.217498i	0.299672	−	0.954042i	$-0.403123\pi$
$383$	−7.37251	−	4.25652i	−0.376718	−	0.217498i	−0.676389	+	0.736544i	$0.736456\pi$
$384$	−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	$0.314745\pi$
$390$	4.15864	−	5.37190i	0.210581	−	0.272017i
$391$	−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	−0.0250477	−	0.999686i	$-0.507974\pi$
$397$	−17.9986	−	10.3915i	−0.903325	−	0.521535i	−0.878278	+	0.478151i	$0.841307\pi$
$398$			2.14404i			0.107471i
$399$	0.452431	−	0.783633i	0.0226499	−	0.0392307i
$400$	−0.660805	−	1.02548i	−0.0330402	−	0.0512742i
$401$	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
$405$	−1.16496	−	1.90863i	−0.0578875	−	0.0948405i
$406$	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	$0.191963\pi$
$410$	8.80042	+	4.79844i	0.434622	+	0.236978i
$411$	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	$0.954852\pi$
$420$	−0.554215	+	1.01644i	−0.0270429	+	0.0495972i
$421$	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
$425$	31.4874	+	16.1844i	1.52737	+	0.785059i
$426$	−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	0.139854	−	0.990172i	$-0.455337\pi$
$433$	−13.4785	−	7.78179i	−0.647733	−	0.373969i	−0.787587	+	0.616203i	$0.788670\pi$
$434$	2.13106			0.102294
$435$	−15.4752	−	8.43790i	−0.741981	−	0.404566i
$436$	−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	$0.893115\pi$
$440$	25.9641	−	15.8476i	1.23779	−	0.755506i
$441$	−6.83891			−0.325662
$442$	21.2387	+	3.41850i	1.01022	+	0.162601i
$443$		−	24.8136i		−	1.17893i	−0.807794	−	0.589465i	$-0.799338\pi$
$443$		−	24.8136i		−	1.17893i	0.807794	−	0.589465i	$-0.200662\pi$
$444$	−5.68026	−	9.83850i	−0.269573	−	0.466914i
$445$	0.611046	+	1.00111i	0.0289664	+	0.0474573i
$446$	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
$455$	−2.55874	−	1.98084i	−0.119956	−	0.0928634i
$456$	−6.24995			−0.292681
$457$	15.9839	−	9.22831i	0.747696	−	0.431682i	−0.0771651	−	0.997018i	$-0.524587\pi$
$457$	15.9839	−	9.22831i	0.747696	−	0.431682i	0.824861	+	0.565336i	$0.191254\pi$
$458$	−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	$0.407897\pi$
$463$			41.2459i			1.91686i	−0.285329	+	0.958430i	$0.592103\pi$
$464$	−0.961646	+	1.66562i	−0.0446433	+	0.0773245i
$465$	−12.0266	+	7.34066i	−0.557722	+	0.340415i
$466$	1.12229	+	1.94387i	0.0519892	+	0.0900479i
$467$		−	29.7045i		−	1.37456i	−0.726393	−	0.687280i	$-0.758805\pi$
$467$		−	29.7045i		−	1.37456i	0.726393	−	0.687280i	$-0.241195\pi$
$468$	−1.65590	−	4.34632i	−0.0765441	−	0.200909i
$469$	−2.46969			−0.114040
$470$	4.53826	+	7.43529i	0.209334	+	0.342964i
$471$	−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
$475$	5.15312	−	10.0256i	0.236441	−	0.460006i
$476$	−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
$485$	−18.4975	−	10.0858i	−0.839929	−	0.457972i
$486$	0.842629			0.0382224
$487$	21.0473	+	12.1517i	0.953745	+	0.550645i	0.894242	−	0.447583i	$-0.147715\pi$
$487$	21.0473	+	12.1517i	0.953745	+	0.550645i	0.0595026	+	0.998228i	$0.481049\pi$
$488$	−17.0501	−	9.84386i	−0.771820	−	0.445610i
$489$	1.57388			0.0711734
$490$	11.3133	+	6.16858i	0.511082	+	0.278668i
$491$	−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	$0.515755\pi$
$500$	−6.27807	+	12.9842i	−0.280764	+	0.580673i
$501$	−7.53397	+	13.0492i	−0.336593	+	0.582996i
$502$		−	1.09679i		−	0.0489521i
$503$	25.3122	+	14.6140i	1.12862	+	0.651607i	0.943587	−	0.331126i	$-0.107428\pi$
$503$	25.3122	+	14.6140i	1.12862	+	0.651607i	0.185030	+	0.982733i	$0.440762\pi$
$504$	−0.556333	−	0.963596i	−0.0247810	−	0.0429220i
$505$	6.70337	+	10.9825i	0.298296	+	0.488716i
$506$	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	$0.884450\pi$
$510$	−11.3876	+	6.95061i	−0.504251	+	0.307778i
$511$	−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
$520$	−3.01210	+	22.1465i	−0.132089	+	0.971190i
$521$	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	−0.501503	−	0.865156i	$-0.667219\pi$
$523$	−0.0687721	+	0.0397056i	−0.00300719	+	0.00173620i	0.498496	+	0.866892i	$0.333886\pi$
$524$	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
$530$	10.6504	+	17.4491i	0.462622	+	0.757940i
$531$	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
$535$	28.4355	−	17.3561i	1.22937	−	0.750369i
$536$	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
$540$	2.53248	+	1.38084i	0.108981	+	0.0594219i
$541$	−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	$0.0893988\pi$
$547$			12.9652i			0.554354i	−0.960819	+	0.277177i	$0.910601\pi$
$548$	−5.53043	+	3.19300i	−0.236248	+	0.136398i
$549$	−3.55088	−	6.15031i	−0.151548	−	0.262489i
$550$	−18.3875	−	9.45109i	−0.784045	−	0.402996i
$551$	−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
$555$	−9.42710	+	17.2895i	−0.400158	+	0.733897i
$556$	−8.55530	−	14.8182i	−0.362825	−	0.628432i
$557$	−27.7896	+	16.0443i	−1.17748	+	0.679820i	−0.955431	−	0.295215i	$-0.904609\pi$
$557$	−27.7896	+	16.0443i	−1.17748	+	0.679820i	−0.222051	+	0.975035i	$0.571275\pi$
$558$		−	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	0.527474	−	0.849571i	$-0.323139\pi$
$563$	1.31596	+	0.759773i	0.0554613	+	0.0320206i	−0.472013	+	0.881592i	$0.656472\pi$
$564$	5.96378			0.251121
$565$	−4.41334	−	2.40638i	−0.185671	−	0.101237i
$566$	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	$0.696964\pi$
$570$	2.21307	+	3.62581i	0.0926955	+	0.151868i
$571$	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
$575$	−4.18196	+	2.69478i	−0.174400	+	0.112380i
$576$	−2.17859	+	3.77343i	−0.0907746	+	0.157226i
$577$			11.7411i			0.488787i	0.969676	+	0.244393i	$0.0785888\pi$
$577$			11.7411i			0.488787i	−0.969676	+	0.244393i	$0.921411\pi$
$578$	−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
$585$	−4.93531	+	6.37516i	−0.204050	+	0.263580i
$586$	−6.01374			−0.248425
$587$	−22.3360	+	12.8957i	−0.921907	+	0.532263i	−0.884243	−	0.467027i	$-0.845325\pi$
$587$	−22.3360	+	12.8957i	−0.921907	+	0.532263i	−0.0376643	+	0.999290i	$0.511992\pi$
$588$	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	$0.0691792\pi$
$593$			10.5017i			0.431252i	−0.976476	+	0.215626i	$0.930821\pi$
$594$	−2.06742	+	3.58088i	−0.0848273	+	0.146925i
$595$	3.31071	+	5.42413i	0.135726	+	0.222368i
$596$	−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	$0.781079\pi$
$600$	−7.50810	−	11.6516i	−0.306517	−	0.475675i
$601$	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
$605$	−14.0006	+	25.6774i	−0.569207	+	1.04394i
$606$	−4.84861			−0.196961
$607$	14.0175	+	8.09298i	0.568951	+	0.328484i	0.756730	−	0.653727i	$-0.226796\pi$
$607$	14.0175	+	8.09298i	0.568951	+	0.328484i	−0.187779	+	0.982211i	$0.560129\pi$
$608$	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	0.0174640	−	0.999847i	$-0.494441\pi$
$613$	22.0871	−	12.7520i	0.892089	−	0.515048i	0.874625	+	0.484799i	$0.161107\pi$
$614$	4.17670	+	7.23426i	0.168558	+	0.291951i
$615$	−10.4440	−	5.69461i	−0.421143	−	0.229629i
$616$	5.45993			0.219987
$617$	−10.1748	−	5.87440i	−0.409620	−	0.236494i	0.281006	−	0.959706i	$-0.409332\pi$
$617$	−10.1748	−	5.87440i	−0.409620	−	0.236494i	−0.690626	+	0.723212i	$0.742665\pi$
$618$	−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	$0.438917\pi$
$620$	8.70094	−	15.9577i	0.349438	−	0.640876i
$621$	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
$630$	−0.362021	+	0.663952i	−0.0144233	+	0.0264525i
$631$	−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
$635$	32.9495	−	20.1113i	1.30756	−	0.798093i
$636$	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
$640$	−14.9419	+	9.12005i	−0.590631	+	0.360502i
$641$	−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	−0.490500	−	0.871441i	$-0.663186\pi$
$643$	−37.7938	−	21.8202i	−1.49044	−	0.860506i	−0.999940	+	0.0109350i	$0.996519\pi$
$644$	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	−0.555289	−	0.831657i	$-0.687392\pi$
$647$	−2.86660	+	1.65503i	−0.112698	+	0.0650661i	0.442592	+	0.896723i	$0.354059\pi$
$648$	−2.40082	+	1.38611i	−0.0943132	+	0.0544517i
$649$	−14.9395			−0.586425
$650$	13.9145	−	6.09455i	0.545773	−	0.239048i
$651$	−2.52905			−0.0991215
$652$	−1.75827	+	1.01514i	−0.0688590	+	0.0397558i
$653$	3.12790	−	1.80589i	0.122404	−	0.0706701i	−0.437548	−	0.899195i	$-0.644153\pi$
$653$	3.12790	−	1.80589i	0.122404	−	0.0706701i	0.559952	+	0.828525i	$0.310820\pi$
$654$	−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	$-0.149695\pi$
$660$	−12.0816	+	7.37423i	−0.470277	+	0.287041i
$661$	−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
$665$	1.72704	−	1.05413i	0.0669719	−	0.0408775i
$666$	−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
$670$	5.55017	−	10.1791i	0.214422	−	0.393253i
$671$	34.8489			1.34532
$672$	1.99865	+	1.15392i	0.0770998	+	0.0445136i
$673$	−38.7794	+	22.3893i	−1.49484	+	0.863045i	−0.999982	−	0.00593030i	$-0.998112\pi$
$673$	−38.7794	+	22.3893i	−1.49484	+	0.863045i	−0.494855	+	0.868975i	$0.664779\pi$
$674$	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	$0.288845\pi$
$677$			41.0024i			1.57585i	−0.615770	+	0.787926i	$0.711155\pi$
$678$	1.64048	−	0.947129i	0.0630021	−	0.0363743i
$679$	−1.89084	−	3.27502i	−0.0725636	−	0.125684i
$680$	21.0119	−	38.5361i	0.805769	−	1.47779i
$681$	21.3874			0.819565
$682$	22.5638	+	13.0272i	0.864013	+	0.498838i
$683$	17.7354	+	10.2395i	0.678627	+	0.391805i	0.799338	−	0.600882i	$-0.205184\pi$
$683$	17.7354	+	10.2395i	0.678627	+	0.391805i	−0.120711	+	0.992688i	$0.538517\pi$
$684$	2.90823			0.111199
$685$	9.71879	+	5.29918i	0.371336	+	0.202471i
$686$	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
$695$	−14.1986	+	26.0404i	−0.538583	+	0.987770i
$696$	−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
$700$	−2.17607	+	1.40222i	−0.0822478	+	0.0529991i
$701$	−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
$705$	−5.38583	−	8.82392i	−0.202842	−	0.332328i
$706$	−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
$715$	−14.9832	−	36.6150i	−0.560341	−	1.36932i
$716$	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
$725$	−21.3488	−	33.1306i	−0.792874	−	1.23044i
$726$	−5.51052	−	9.54451i	−0.204515	−	0.354230i
$727$			1.91130i			0.0708862i	0.999372	+	0.0354431i	$0.0112842\pi$
$727$			1.91130i			0.0708862i	−0.999372	+	0.0354431i	$0.988716\pi$
$728$	−2.53250	+	3.11139i	−0.0938607	+	0.115316i
$729$	−1.00000			−0.0370370
$730$	−0.994129	−	1.62874i	−0.0367944	−	0.0602823i
$731$	−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	$0.110411\pi$
$733$			18.4077i			0.679904i	−0.940443	+	0.339952i	$0.889589\pi$
$734$	−13.0749	+	22.6464i	−0.482604	+	0.835894i
$735$	−13.4262	−	7.32063i	−0.495231	−	0.270026i
$736$	−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	−0.353693	−	0.935361i	$-0.615074\pi$
$743$	7.61880	−	4.39871i	0.279507	−	0.161373i	0.633200	+	0.773988i	$0.281741\pi$
$744$	8.73418	+	15.1280i	0.320211	+	0.554621i
$745$	−3.38015	+	6.19925i	−0.123839	+	0.227123i
$746$	−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
$750$	−4.10092	+	8.48148i	−0.149744	+	0.309700i
$751$	−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	0.0334996	−	0.999439i	$-0.489335\pi$
$757$	25.1967	−	14.5473i	0.915789	−	0.528731i	0.882289	+	0.470708i	$0.156001\pi$
$758$	22.4207	+	12.9446i	0.814355	+	0.470168i
$759$	−4.88254			−0.177225
$760$	−12.2699	−	6.69018i	−0.445076	−	0.242678i
$761$	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
$765$	13.5143	−	8.24871i	0.488612	−	0.298233i
$766$	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	$0.685584\pi$
$770$	−1.93333	−	3.16749i	−0.0696725	−	0.114148i
$771$	−4.93694	+	8.55103i	−0.177800	+	0.307958i
$772$			11.7877i			0.424249i
$773$	15.4061	+	8.89469i	0.554117	+	0.319920i	0.750781	−	0.660551i	$-0.229677\pi$
$773$	15.4061	+	8.89469i	0.554117	+	0.319920i	−0.196664	+	0.980471i	$0.563011\pi$
$774$	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
$780$	1.40159	−	10.3052i	0.0501851	−	0.368987i
$781$	−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	0.105742	−	0.994394i	$-0.466278\pi$
$787$	−19.7092	−	11.3791i	−0.702557	−	0.405622i	−0.808299	+	0.588772i	$0.799612\pi$
$788$			27.8763i			0.993053i
$789$	−0.266805	+	0.462121i	−0.00949852	+	0.0164519i
$790$	−16.5257	+	10.0868i	−0.587959	+	0.358871i
$791$	−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
$795$	−12.6394	−	20.7079i	−0.448274	−	0.734434i
$796$	1.64115	+	2.84255i	0.0581689	+	0.100751i
$797$	−20.7232	−	11.9646i	−0.734055	−	0.423807i	0.0858488	−	0.996308i	$-0.472640\pi$
$797$	−20.7232	−	11.9646i	−0.734055	−	0.423807i	−0.819904	+	0.572501i	$0.805973\pi$
$798$			0.762463i			0.0269909i
$799$	16.3676	−	28.3495i	0.579043	−	1.00293i
$800$	25.5703	+	13.1430i	0.904046	+	0.464676i
$801$	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	$0.737966\pi$
$810$	1.65425	+	0.901983i	0.0581245	+	0.0316924i
$811$	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
$815$	3.08985	+	1.68474i	0.108233	+	0.0590140i
$816$	−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	0.323255	−	0.946312i	$-0.395223\pi$
$823$	−9.60038	−	5.54278i	−0.334648	−	0.193209i	−0.657903	+	0.753103i	$0.728556\pi$
$824$	42.6902			1.48718
$825$	21.8216	+	11.2162i	0.759730	+	0.390498i
$826$	0.514819	−	0.891692i	0.0179128	−	0.0310259i
$827$			41.0529i			1.42755i	0.700375	+	0.713775i	$0.253016\pi$
$827$			41.0529i			1.42755i	−0.700375	+	0.713775i	$0.746984\pi$
$828$	−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	$0.714629\pi$
$830$	−10.3403	−	16.9410i	−0.358916	−	0.588032i
$831$	−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
$835$	−28.7591	+	17.5536i	−0.995249	+	0.607467i
$836$	−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
$845$	27.8152	+	8.44496i	0.956870	+	0.290516i
$846$	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	$-0.813199\pi$
$853$		−	32.3455i		−	1.10749i	0.832687	−	0.553744i	$-0.186801\pi$
$854$	−1.20090	+	2.08002i	−0.0410940	+	0.0711770i
$855$	−2.62639	−	4.30297i	−0.0898207	−	0.147158i
$856$	−20.6509	−	35.7684i	−0.705832	−	1.22254i
$857$			23.8618i			0.815103i	0.913182	+	0.407551i	$0.133617\pi$
$857$			23.8618i			0.815103i	−0.913182	+	0.407551i	$0.866383\pi$
$858$	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	$0.614656\pi$
$860$	4.95860	−	3.02656i	0.169087	−	0.103205i
$861$	−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	$0.00250119\pi$
$863$			0.461666i			0.0157153i	−0.999969	+	0.00785765i	$0.997499\pi$
$864$	2.87503	−	4.97969i	0.0978104	−	0.169413i
$865$	6.68695	+	3.64607i	0.227363	+	0.123970i
$866$	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
$875$	4.03990	+	1.95335i	0.136573	+	0.0660353i
$876$	−1.30640			−0.0441391
$877$	17.6624	+	10.1974i	0.596417	+	0.344342i	0.767631	−	0.640892i	$-0.221435\pi$
$877$	17.6624	+	10.1974i	0.596417	+	0.344342i	−0.171214	+	0.985234i	$0.554769\pi$
$878$	5.70941	+	3.29633i	0.192683	+	0.111246i
$879$	7.13688			0.240721
$880$	1.28161	−	2.35050i	0.0432031	−	0.0792353i
$881$	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	$0.0453647\pi$
$883$			8.44125i			0.284071i	−0.989862	+	0.142035i	$0.954635\pi$
$884$	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	0.154157	−	0.988046i	$-0.450734\pi$
$887$	32.3709	−	18.6894i	1.08691	−	0.627527i	0.932752	+	0.360519i	$0.117400\pi$
$888$	21.1435	+	12.2072i	0.709528	+	0.409646i
$889$	6.92888			0.232387
$890$	−0.867687	−	0.473108i	−0.0290849	−	0.0158586i
$891$	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
$895$	−0.700179	−	1.14714i	−0.0234044	−	0.0383448i
$896$	−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
$900$	3.49367	+	5.42173i	0.116456	+	0.180724i
$901$	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	−0.995631	−	0.0933771i	$-0.970234\pi$
$907$	−42.5419	+	24.5616i	−1.41258	+	0.815553i	−0.416948	+	0.908930i	$0.636900\pi$
$908$	−23.8929	+	13.7946i	−0.792915	+	0.457789i
$909$	5.75415			0.190853
$910$	2.70177	+	0.367462i	0.0895628	+	0.0121812i
$911$	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	$0.328165\pi$
$920$	3.21340	+	5.26470i	0.105943	+	0.173572i
$921$	−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
$925$	−37.0146	+	23.8516i	−1.21703	+	0.784235i
$926$	−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	$0.0447230\pi$
$930$	5.68357	−	10.4238i	0.186372	−	0.341809i
$931$	−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	$-0.816335\pi$
$937$		−	33.3968i		−	1.09103i	0.838102	−	0.545513i	$-0.183665\pi$
$938$	1.80223	−	1.04052i	0.0588449	−	0.0339741i
$939$	2.31009	+	4.00119i	0.0753869	+	0.130574i
$940$	11.7081	+	6.38386i	0.381877	+	0.208219i
$941$	−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
$945$	0.429632	−	0.787953i	0.0139759	−	0.0256321i
$946$	4.16375	+	7.21183i	0.135375	+	0.234477i
$947$	8.35815	−	4.82558i	0.271603	−	0.156810i	−0.358013	−	0.933717i	$-0.616546\pi$
$947$	8.35815	−	4.82558i	0.271603	−	0.156810i	0.629616	+	0.776906i	$0.283212\pi$
$948$			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	−0.0576363	−	0.998338i	$-0.518356\pi$
$953$	−29.3593	−	16.9506i	−0.951040	−	0.549083i	−0.893404	+	0.449254i	$0.851690\pi$
$954$	9.14222			0.295990
$955$	−6.63849	+	12.1751i	−0.214816	+	0.393977i
$956$	−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
$960$	−8.31624	+	5.07596i	−0.268405	+	0.163826i
$961$	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
$965$	17.4409	−	10.6453i	0.561442	−	0.342686i
$966$	0.168254	−	0.291424i	0.00541348	−	0.00937642i
$967$			20.9057i			0.672283i	0.941812	+	0.336141i	$0.109122\pi$
$967$			20.9057i			0.672283i	−0.941812	+	0.336141i	$0.890878\pi$
$968$	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
$975$	−16.5132	+	7.23278i	−0.528847	+	0.231634i
$976$	−1.73276			−0.0554643
$977$	28.5119	−	16.4614i	0.912177	−	0.526646i	0.0310460	−	0.999518i	$-0.490116\pi$
$977$	28.5119	−	16.4614i	0.912177	−	0.526646i	0.881131	+	0.472872i	$0.156783\pi$
$978$	−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	$0.0563663\pi$
$983$			11.0460i			0.352312i	−0.984362	+	0.176156i	$0.943634\pi$
$984$	−7.37397	+	12.7721i	−0.235074	+	0.407159i
$985$	41.2454	−	25.1748i	1.31419	−	0.802136i
$986$	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
$990$	−7.89187	+	4.81694i	−0.250820	+	0.153092i
$991$	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
$995$	2.72369	−	4.99529i	0.0863467	−	0.158361i
$996$	−13.5883			−0.430561
$997$	−43.6735	−	25.2149i	−1.38315	−	0.798565i	−0.390623	−	0.920551i	$-0.627740\pi$
$997$	−43.6735	−	25.2149i	−1.38315	−	0.798565i	−0.992532	+	0.121986i	$0.961074\pi$
$998$	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.94.5	✓	24
3.2	odd	2		585.2.bs.b.289.8		24
5.2	odd	4		975.2.i.o.601.3		12
5.3	odd	4		975.2.i.q.601.4		12
5.4	even	2	inner	195.2.ba.a.94.8	yes	24
13.9	even	3	inner	195.2.ba.a.139.8	yes	24
15.14	odd	2		585.2.bs.b.289.5		24
39.35	odd	6		585.2.bs.b.334.5		24
65.9	even	6	inner	195.2.ba.a.139.5	yes	24
65.22	odd	12		975.2.i.o.451.3		12
65.48	odd	12		975.2.i.q.451.4		12
195.74	odd	6		585.2.bs.b.334.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.ba.a.94.5	✓	24	1.1	even	1	trivial
195.2.ba.a.94.8	yes	24	5.4	even	2	inner
195.2.ba.a.139.5	yes	24	65.9	even	6	inner
195.2.ba.a.139.8	yes	24	13.9	even	3	inner
585.2.bs.b.289.5		24	15.14	odd	2
585.2.bs.b.289.8		24	3.2	odd	2
585.2.bs.b.334.5		24	39.35	odd	6
585.2.bs.b.334.8		24	195.74	odd	6
975.2.i.o.451.3		12	65.22	odd	12
975.2.i.o.601.3		12	5.2	odd	4
975.2.i.q.451.4		12	65.48	odd	12
975.2.i.q.601.4		12	5.3	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} +(-1.60827 + 0.981632i) q^{10} +(2.45354 + 4.24965i) q^{11} +1.28998i q^{12} +(-3.55974 - 0.572960i) q^{13} -0.338199 q^{14} +(1.90863 - 1.16496i) q^{15} +(-0.121995 - 0.211302i) q^{16} +(6.13203 + 3.54033i) q^{17} +0.842629i q^{18} +(1.12724 - 1.95244i) q^{19} +(-1.38084 + 2.53248i) 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} +(-0.901983 + 1.65425i) q^{30} -6.30120 q^{31} +(4.97969 + 2.87503i) q^{32} +(4.24965 + 2.45354i) q^{33} -5.96637 q^{34} +(0.787953 + 0.429632i) 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} +(1.07044 - 1.96320i) q^{45} +(0.419208 - 0.726090i) q^{46} -4.62317i q^{47} +(-0.211302 - 0.121995i) q^{48} +(-3.41945 - 5.92267i) q^{49} +(-3.54155 + 2.28211i) q^{50} +7.08066 q^{51} +(2.93607 - 3.60721i) q^{52} -10.8496i q^{53} +(0.421315 + 0.729738i) q^{54} +(5.71656 + 9.36577i) 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} +(-7.98871 - 1.08653i) 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} +(4.20297 - 2.70832i) q^{75} +(1.45411 + 2.51860i) q^{76} +1.96951i q^{77} +(1.91788 - 2.35628i) q^{78} +10.2755 q^{79} +(-0.284240 - 0.465687i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.88212 + 2.24134i) q^{82} +10.5337i q^{83} +(-0.258873 + 0.448381i) q^{84} +(13.9008 + 7.57941i) 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} +(2.41329 - 4.42601i) 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

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