LMFDB - Embedded newform 370.2.q.e.273.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			273.4
Root			$0.339278 + 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	370.273
Dual form			370.2.q.e.267.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.465926 + 0.124844i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0994727 + 2.23385i) q^{5} +(-0.341081 + 0.341081i) q^{6} +(-4.54399 - 1.21756i) q^{7} +1.00000 q^{8} +(-2.39658 - 1.38366i) q^{9} +(-1.88484 - 1.20307i) q^{10} +1.91095i q^{11} +(-0.124844 - 0.465926i) q^{12} +(-2.72701 - 4.72333i) q^{13} +(3.32643 - 3.32643i) q^{14} +(-0.325231 + 1.02839i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.281601 - 0.162582i) q^{17} +(2.39658 - 1.38366i) q^{18} +(-1.07793 + 4.02290i) q^{19} +(1.98431 - 1.03078i) q^{20} +(-1.96515 - 1.13458i) q^{21} +(-1.65493 - 0.955475i) q^{22} +2.87357 q^{23} +(0.465926 + 0.124844i) q^{24} +(-4.98021 - 0.444415i) q^{25} +5.45403 q^{26} +(-1.96713 - 1.96713i) q^{27} +(1.21756 + 4.54399i) q^{28} +(-1.73064 + 1.73064i) q^{29} +(-0.727998 - 0.795854i) q^{30} +(2.83892 + 2.83892i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.238572 + 0.890361i) q^{33} +(0.281601 - 0.162582i) q^{34} +(3.17185 - 10.0295i) q^{35} +2.76733i q^{36} +(-6.05437 - 0.586988i) q^{37} +(-2.94497 - 2.94497i) q^{38} +(-0.680905 - 2.54117i) q^{39} +(-0.0994727 + 2.23385i) q^{40} +(-10.4672 + 6.04322i) q^{41} +(1.96515 - 1.13458i) q^{42} +2.45934 q^{43} +(1.65493 - 0.955475i) q^{44} +(3.32930 - 5.21596i) q^{45} +(-1.43679 + 2.48858i) q^{46} +(8.46521 - 8.46521i) q^{47} +(-0.341081 + 0.341081i) q^{48} +(13.1032 + 7.56512i) q^{49} +(2.87498 - 4.09078i) q^{50} +(-0.110908 - 0.110908i) q^{51} +(-2.72701 + 4.72333i) q^{52} +(-8.97931 + 2.40600i) q^{53} +(2.68715 - 0.720019i) q^{54} +(-4.26879 - 0.190087i) q^{55} +(-4.54399 - 1.21756i) q^{56} +(-1.00447 + 1.73980i) q^{57} +(-0.633459 - 2.36410i) q^{58} +(-4.67260 + 1.25202i) q^{59} +(1.05323 - 0.232537i) q^{60} +(2.59133 - 9.67096i) q^{61} +(-3.87804 + 1.03912i) q^{62} +(9.20531 + 9.20531i) q^{63} +1.00000 q^{64} +(10.8225 - 5.62191i) q^{65} +(-0.651790 - 0.651790i) q^{66} +(-2.17645 + 8.12261i) q^{67} +0.325164i q^{68} +(1.33887 + 0.358749i) q^{69} +(7.09987 + 7.76164i) q^{70} +(6.64478 + 11.5091i) q^{71} +(-2.39658 - 1.38366i) q^{72} +(-5.52677 + 5.52677i) q^{73} +(3.53553 - 4.94975i) q^{74} +(-2.26493 - 0.828816i) q^{75} +(4.02290 - 1.07793i) q^{76} +(2.32669 - 8.68333i) q^{77} +(2.54117 + 0.680905i) q^{78} +(2.31420 - 8.63670i) q^{79} +(-1.88484 - 1.20307i) q^{80} +(3.48004 + 6.02761i) q^{81} -12.0864i q^{82} +(1.07135 - 0.287067i) q^{83} +2.26917i q^{84} +(0.391197 - 0.612882i) q^{85} +(-1.22967 + 2.12985i) q^{86} +(-1.02241 + 0.590290i) q^{87} +1.91095i q^{88} +(0.363814 + 1.35777i) q^{89} +(2.85251 + 5.49124i) q^{90} +(6.64059 + 24.7830i) q^{91} +(-1.43679 - 2.48858i) q^{92} +(0.968304 + 1.67715i) q^{93} +(3.09848 + 11.5637i) q^{94} +(-8.87935 - 2.80812i) q^{95} +(-0.124844 - 0.465926i) q^{96} +7.73607i q^{97} +(-13.1032 + 7.56512i) q^{98} +(2.64411 - 4.57974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9} - 4 q^{10} + 16 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 24 q^{18} - 24 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{23} - 8 q^{24}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9 - 4 * q^10 + 16 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 24 * q^18 - 24 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^23 - 8 * q^24 + 32 * q^25 + 8 * q^26 + 16 * q^27 + 16 * q^29 - 4 * q^30 + 24 * q^31 - 8 * q^32 + 12 * q^33 - 20 * q^35 - 4 * q^40 - 36 * q^41 + 12 * q^42 - 16 * q^43 + 4 * q^45 + 4 * q^46 + 32 * q^47 - 8 * q^48 + 24 * q^49 - 16 * q^50 - 16 * q^51 - 4 * q^52 - 48 * q^53 - 8 * q^54 - 24 * q^55 + 20 * q^57 - 8 * q^58 - 8 * q^59 - 4 * q^60 + 8 * q^61 - 12 * q^62 + 16 * q^63 + 16 * q^64 + 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^69 + 28 * q^70 + 4 * q^71 - 24 * q^72 + 48 * q^73 - 36 * q^75 + 24 * q^76 - 60 * q^77 + 20 * q^79 - 4 * q^80 + 16 * q^81 + 24 * q^83 + 8 * q^85 + 8 * q^86 + 12 * q^87 - 8 * q^89 - 8 * q^90 - 8 * q^91 + 4 * q^92 + 36 * q^93 - 28 * q^94 + 28 * q^95 + 16 * q^96 - 24 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.465926	+	0.124844i	0.269002	+	0.0720790i	0.390799	−	0.920476i	$-0.372199\pi$
$3$	0.465926	+	0.124844i	0.269002	+	0.0720790i	−0.121796	+	0.992555i	$0.538865\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.0994727	+	2.23385i	−0.0444856	+	0.999010i
$5$	−0.0994727	+	2.23385i	−0.0444856	+	0.999010i
$6$	−0.341081	+	0.341081i	−0.139246	+	0.139246i
$7$	−4.54399	−	1.21756i	−1.71747	−	0.460193i	−0.740230	−	0.672354i	$-0.765283\pi$
$7$	−4.54399	−	1.21756i	−1.71747	−	0.460193i	−0.977235	+	0.212160i	$0.931950\pi$
$8$	1.00000			0.353553
$9$	−2.39658	−	1.38366i	−0.798858	−	0.461221i
$10$	−1.88484	−	1.20307i	−0.596038	−	0.380445i
$11$			1.91095i			0.576173i	0.957604	+	0.288087i	$0.0930191\pi$
$11$			1.91095i			0.576173i	−0.957604	+	0.288087i	$0.906981\pi$
$12$	−0.124844	−	0.465926i	−0.0360395	−	0.134501i
$13$	−2.72701	−	4.72333i	−0.756338	−	1.31002i	−0.944707	−	0.327917i	$-0.893653\pi$
$13$	−2.72701	−	4.72333i	−0.756338	−	1.31002i	0.188369	−	0.982098i	$-0.439680\pi$
$14$	3.32643	−	3.32643i	0.889025	−	0.889025i
$15$	−0.325231	+	1.02839i	−0.0839743	+	0.265530i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.281601	−	0.162582i	−0.0682982	−	0.0394320i	0.465462	−	0.885068i	$-0.345888\pi$
$17$	−0.281601	−	0.162582i	−0.0682982	−	0.0394320i	−0.533760	+	0.845636i	$0.679222\pi$
$18$	2.39658	−	1.38366i	0.564878	−	0.326133i
$19$	−1.07793	+	4.02290i	−0.247295	+	0.922917i	0.724921	+	0.688832i	$0.241876\pi$
$19$	−1.07793	+	4.02290i	−0.247295	+	0.922917i	−0.972216	+	0.234085i	$0.924790\pi$
$20$	1.98431	−	1.03078i	0.443705	−	0.230490i
$21$	−1.96515	−	1.13458i	−0.428832	−	0.247586i
$22$	−1.65493	−	0.955475i	−0.352833	−	0.203708i
$23$	2.87357			0.599181			0.299590	−	0.954068i	$-0.403150\pi$
$23$	2.87357			0.599181			0.299590	+	0.954068i	$0.403150\pi$
$24$	0.465926	+	0.124844i	0.0951067	+	0.0254838i
$25$	−4.98021	−	0.444415i	−0.996042	−	0.0888830i
$26$	5.45403			1.06962
$27$	−1.96713	−	1.96713i	−0.378574	−	0.378574i
$28$	1.21756	+	4.54399i	0.230097	+	0.858733i
$29$	−1.73064	+	1.73064i	−0.321372	+	0.321372i	−0.849293	−	0.527921i	$-0.822972\pi$
$29$	−1.73064	+	1.73064i	−0.321372	+	0.321372i	0.527921	+	0.849293i	$0.322972\pi$
$30$	−0.727998	−	0.795854i	−0.132914	−	0.145302i
$31$	2.83892	+	2.83892i	0.509886	+	0.509886i	0.914491	−	0.404606i	$-0.132591\pi$
$31$	2.83892	+	2.83892i	0.509886	+	0.509886i	−0.404606	+	0.914491i	$0.632591\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.238572	+	0.890361i	−0.0415300	+	0.154992i
$34$	0.281601	−	0.162582i	0.0482941	−	0.0278826i
$35$	3.17185	−	10.0295i	0.536140	−	1.69529i
$36$			2.76733i			0.461221i
$37$	−6.05437	−	0.586988i	−0.995333	−	0.0965003i
$37$	−6.05437	−	0.586988i	−0.995333	−	0.0965003i
$38$	−2.94497	−	2.94497i	−0.477737	−	0.477737i
$39$	−0.680905	−	2.54117i	−0.109032	−	0.406913i
$40$	−0.0994727	+	2.23385i	−0.0157280	+	0.353203i
$41$	−10.4672	+	6.04322i	−1.63470	+	0.943792i	−0.652078	+	0.758152i	$0.726103\pi$
$41$	−10.4672	+	6.04322i	−1.63470	+	0.943792i	−0.982618	+	0.185640i	$0.940564\pi$
$42$	1.96515	−	1.13458i	0.303230	−	0.175070i
$43$	2.45934			0.375045			0.187523	−	0.982260i	$-0.439954\pi$
$43$	2.45934			0.375045			0.187523	+	0.982260i	$0.439954\pi$
$44$	1.65493	−	0.955475i	0.249490	−	0.144043i
$45$	3.32930	−	5.21596i	0.496302	−	0.777550i
$46$	−1.43679	+	2.48858i	−0.211842	+	0.366922i
$47$	8.46521	−	8.46521i	1.23478	−	1.23478i	0.272670	−	0.962108i	$-0.412093\pi$
$47$	8.46521	−	8.46521i	1.23478	−	1.23478i	0.962108	−	0.272670i	$-0.0879068\pi$
$48$	−0.341081	+	0.341081i	−0.0492309	+	0.0492309i
$49$	13.1032	+	7.56512i	1.87188	+	1.08073i
$50$	2.87498	−	4.09078i	0.406584	−	0.578524i
$51$	−0.110908	−	0.110908i	−0.0155302	−	0.0155302i
$52$	−2.72701	+	4.72333i	−0.378169	+	0.655008i
$53$	−8.97931	+	2.40600i	−1.23340	+	0.330489i	−0.815904	−	0.578188i	$-0.803760\pi$
$53$	−8.97931	+	2.40600i	−1.23340	+	0.330489i	−0.417499	+	0.908677i	$0.637093\pi$
$54$	2.68715	−	0.720019i	0.365674	−	0.0979821i
$55$	−4.26879	−	0.190087i	−0.575603	−	0.0256314i
$56$	−4.54399	−	1.21756i	−0.607216	−	0.162703i
$57$	−1.00447	+	1.73980i	−0.133046	+	0.230442i
$58$	−0.633459	−	2.36410i	−0.0831772	−	0.310422i
$59$	−4.67260	+	1.25202i	−0.608320	+	0.162999i	−0.549813	−	0.835288i	$-0.685301\pi$
$59$	−4.67260	+	1.25202i	−0.608320	+	0.162999i	−0.0585077	+	0.998287i	$0.518634\pi$
$60$	1.05323	−	0.232537i	0.135971	−	0.0300204i
$61$	2.59133	−	9.67096i	0.331785	−	1.23824i	−0.575527	−	0.817783i	$-0.695203\pi$
$61$	2.59133	−	9.67096i	0.331785	−	1.23824i	0.907312	−	0.420457i	$-0.138130\pi$
$62$	−3.87804	+	1.03912i	−0.492512	+	0.131968i
$63$	9.20531	+	9.20531i	1.15976	+	1.15976i
$64$	1.00000			0.125000
$65$	10.8225	−	5.62191i	1.34236	−	0.697312i
$66$	−0.651790	−	0.651790i	−0.0802298	−	0.0802298i
$67$	−2.17645	+	8.12261i	−0.265895	+	0.992335i	0.695805	+	0.718231i	$0.255048\pi$
$67$	−2.17645	+	8.12261i	−0.265895	+	0.992335i	−0.961700	+	0.274104i	$0.911619\pi$
$68$			0.325164i			0.0394320i
$69$	1.33887	+	0.358749i	0.161181	+	0.0431883i
$70$	7.09987	+	7.76164i	0.848596	+	0.927694i
$71$	6.64478	+	11.5091i	0.788591	+	1.36588i	0.926830	+	0.375480i	$0.122522\pi$
$71$	6.64478	+	11.5091i	0.788591	+	1.36588i	−0.138240	+	0.990399i	$0.544145\pi$
$72$	−2.39658	−	1.38366i	−0.282439	−	0.163066i
$73$	−5.52677	+	5.52677i	−0.646860	+	0.646860i	−0.952233	−	0.305373i	$-0.901219\pi$
$73$	−5.52677	+	5.52677i	−0.646860	+	0.646860i	0.305373	+	0.952233i	$0.401219\pi$
$74$	3.53553	−	4.94975i	0.410997	−	0.575396i
$75$	−2.26493	−	0.828816i	−0.261531	−	0.0957034i
$76$	4.02290	−	1.07793i	0.461459	−	0.123647i
$77$	2.32669	−	8.68333i	0.265151	−	0.989558i
$78$	2.54117	+	0.680905i	0.287731	+	0.0770973i
$79$	2.31420	−	8.63670i	0.260367	−	0.971704i	−0.704658	−	0.709547i	$-0.748899\pi$
$79$	2.31420	−	8.63670i	0.260367	−	0.971704i	0.965025	−	0.262157i	$-0.0844339\pi$
$80$	−1.88484	−	1.20307i	−0.210731	−	0.134508i
$81$	3.48004	+	6.02761i	0.386671	+	0.669734i
$82$		−	12.0864i		−	1.33472i
$83$	1.07135	−	0.287067i	0.117596	−	0.0315097i	−0.199541	−	0.979889i	$-0.563945\pi$
$83$	1.07135	−	0.287067i	0.117596	−	0.0315097i	0.317137	+	0.948380i	$0.397278\pi$
$84$			2.26917i			0.247586i
$85$	0.391197	−	0.612882i	0.0424312	−	0.0664764i
$86$	−1.22967	+	2.12985i	−0.132598	+	0.229667i
$87$	−1.02241	+	0.590290i	−0.109614	+	0.0632857i
$88$			1.91095i			0.203708i
$89$	0.363814	+	1.35777i	0.0385642	+	0.143924i	0.982524	−	0.186138i	$-0.0595972\pi$
$89$	0.363814	+	1.35777i	0.0385642	+	0.143924i	−0.943959	+	0.330062i	$0.892930\pi$
$90$	2.85251	+	5.49124i	0.300681	+	0.578827i
$91$	6.64059	+	24.7830i	0.696123	+	2.59797i
$92$	−1.43679	−	2.48858i	−0.149795	−	0.259453i
$93$	0.968304	+	1.67715i	0.100408	+	0.173913i
$94$	3.09848	+	11.5637i	0.319584	+	1.19270i
$95$	−8.87935	−	2.80812i	−0.911003	−	0.288107i
$96$	−0.124844	−	0.465926i	−0.0127419	−	0.0475534i
$97$			7.73607i			0.785479i	0.919650	+	0.392739i	$0.128473\pi$
$97$			7.73607i			0.785479i	−0.919650	+	0.392739i	$0.871527\pi$
$98$	−13.1032	+	7.56512i	−1.32362	+	0.764193i
$99$	2.64411	−	4.57974i	0.265743	−	0.460281i
$100$	2.10523	+	4.53520i	0.210523	+	0.453520i
$101$			2.99759i			0.298272i	0.988817	+	0.149136i	$0.0476492\pi$
$101$			2.99759i			0.298272i	−0.988817	+	0.149136i	$0.952351\pi$
$102$	0.151502	−	0.0405950i	0.0150010	−	0.00401950i
$103$			12.2297i			1.20503i	0.798109	+	0.602513i	$0.205834\pi$
$103$			12.2297i			1.20503i	−0.798109	+	0.602513i	$0.794166\pi$
$104$	−2.72701	−	4.72333i	−0.267406	−	0.463160i
$105$	2.72997	−	4.27701i	0.266418	−	0.417393i
$106$	2.40600	−	8.97931i	0.233691	−	0.872148i
$107$	−9.02595	−	2.41850i	−0.872571	−	0.233805i	−0.205372	−	0.978684i	$-0.565840\pi$
$107$	−9.02595	−	2.41850i	−0.872571	−	0.233805i	−0.667199	+	0.744879i	$0.732507\pi$
$108$	−0.720019	+	2.68715i	−0.0692838	+	0.258571i
$109$	−3.19987	+	0.857402i	−0.306492	+	0.0821242i	−0.408787	−	0.912630i	$-0.634048\pi$
$109$	−3.19987	+	0.857402i	−0.306492	+	0.0821242i	0.102295	+	0.994754i	$0.467381\pi$
$110$	2.29901	−	3.60183i	0.219202	−	0.343421i
$111$	−2.74761	−	1.02935i	−0.260791	−	0.0977014i
$112$	3.32643	−	3.32643i	0.314318	−	0.314318i
$113$	−6.56880	−	3.79250i	−0.617940	−	0.356768i	0.158126	−	0.987419i	$-0.449455\pi$
$113$	−6.56880	−	3.79250i	−0.617940	−	0.356768i	−0.776067	+	0.630651i	$0.782788\pi$
$114$	−1.00447	−	1.73980i	−0.0940776	−	0.162947i
$115$	−0.285842	+	6.41914i	−0.0266549	+	0.598588i
$116$	2.36410	+	0.633459i	0.219501	+	0.0588152i
$117$			15.0931i			1.39536i
$118$	1.25202	−	4.67260i	0.115258	−	0.430147i
$119$	1.08164	+	1.08164i	0.0991534	+	0.0991534i
$120$	−0.325231	+	1.02839i	−0.0296894	+	0.0938789i
$121$	7.34827			0.668024
$122$	7.07964	+	7.07964i	0.640960	+	0.640960i
$123$	−5.63138	+	1.50892i	−0.507765	+	0.136055i
$124$	1.03912	−	3.87804i	0.0933156	−	0.348258i
$125$	1.48815	−	11.0809i	0.133105	−	0.991102i
$126$	−12.5747	+	3.36938i	−1.12024	+	0.300168i
$127$	−1.51178	−	5.64206i	−0.134149	−	0.500652i	−1.00000		0.000349241i	$-0.999889\pi$
$127$	−1.51178	−	5.64206i	−0.134149	−	0.500652i	0.865851	−	0.500302i	$-0.166778\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.14587	+	0.307034i	0.100888	+	0.0270329i
$130$	−0.542527	+	12.1835i	−0.0475828	+	1.06856i
$131$	6.23376	−	1.67033i	0.544646	−	0.145938i	0.0240031	−	0.999712i	$-0.492359\pi$
$131$	6.23376	−	1.67033i	0.544646	−	0.145938i	0.520643	+	0.853774i	$0.325692\pi$
$132$	0.890361	−	0.238572i	0.0774960	−	0.0207650i
$133$	9.79623	−	16.9676i	0.849441	−	1.47127i
$134$	−5.94617	−	5.94617i	−0.513671	−	0.513671i
$135$	4.58995	−	4.19860i	0.395040	−	0.361358i
$136$	−0.281601	−	0.162582i	−0.0241471	−	0.0139413i
$137$	10.8117	−	10.8117i	0.923708	−	0.923708i	−0.0735809	−	0.997289i	$-0.523443\pi$
$137$	10.8117	−	10.8117i	0.923708	−	0.923708i	0.997289	+	0.0735809i	$0.0234427\pi$
$138$	−0.980121	+	0.980121i	−0.0834335	+	0.0834335i
$139$	−1.53525	+	2.65913i	−0.130218	+	0.225544i	−0.923761	−	0.382971i	$-0.874901\pi$
$139$	−1.53525	+	2.65913i	−0.130218	+	0.225544i	0.793543	+	0.608515i	$0.208234\pi$
$140$	−10.2717	+	2.26784i	−0.868118	+	0.191668i
$141$	5.00099	−	2.88733i	0.421160	−	0.243157i
$142$	−13.2896			−1.11524
$143$	9.02605	−	5.21119i	0.754796	−	0.435782i
$144$	2.39658	−	1.38366i	0.199715	−	0.115305i
$145$	−3.69385	−	4.03815i	−0.306757	−	0.335350i
$146$	−2.02294	−	7.54971i	−0.167420	−	0.624819i
$147$	5.16065	+	5.16065i	0.425643	+	0.425643i
$148$	2.51884	+	5.53674i	0.207047	+	0.455117i
$149$		−	23.7300i		−	1.94404i	−0.234897	−	0.972020i	$-0.575475\pi$
$149$		−	23.7300i		−	1.94404i	0.234897	−	0.972020i	$-0.424525\pi$
$150$	1.85024	−	1.54708i	0.151071	−	0.126318i
$151$	11.9781	−	6.91554i	0.974761	−	0.562779i	0.0740769	−	0.997253i	$-0.476399\pi$
$151$	11.9781	−	6.91554i	0.974761	−	0.562779i	0.900684	+	0.434474i	$0.143066\pi$
$152$	−1.07793	+	4.02290i	−0.0874320	+	0.326301i
$153$	0.449918	+	0.779281i	0.0363737	+	0.0630011i
$154$	6.35664	+	6.35664i	0.512233	+	0.512233i
$155$	−6.62414	+	6.05935i	−0.532064	+	0.486698i
$156$	−1.86027	+	1.86027i	−0.148941	+	0.148941i
$157$	−1.71166	−	6.38801i	−0.136606	−	0.509819i	−0.999986	−	0.00526573i	$-0.998324\pi$
$157$	−1.71166	−	6.38801i	−0.136606	−	0.509819i	0.863381	−	0.504553i	$-0.168343\pi$
$158$	6.32250	+	6.32250i	0.502991	+	0.502991i
$159$	−4.48407			−0.355610
$160$	1.98431	−	1.03078i	0.156874	−	0.0814904i
$161$	−13.0575	−	3.49874i	−1.02907	−	0.275739i
$162$	−6.96008			−0.546835
$163$	−17.5264	−	10.1189i	−1.37277	−	0.792571i	−0.381496	−	0.924370i	$-0.624591\pi$
$163$	−17.5264	−	10.1189i	−1.37277	−	0.792571i	−0.991276	+	0.131800i	$0.957924\pi$
$164$	10.4672	+	6.04322i	0.817348	+	0.471896i
$165$	−1.96521	−	0.621501i	−0.152991	−	0.0483838i
$166$	−0.287067	+	1.07135i	−0.0222807	+	0.0831528i
$167$	−0.225059	+	0.129938i	−0.0174156	+	0.0100549i	−0.508683	−	0.860954i	$-0.669867\pi$
$167$	−0.225059	+	0.129938i	−0.0174156	+	0.0100549i	0.491267	+	0.871009i	$0.336534\pi$
$168$	−1.96515	−	1.13458i	−0.151615	−	0.0875350i
$169$	−8.37321	+	14.5028i	−0.644093	+	1.11560i
$170$	0.335173	+	0.645227i	0.0257066	+	0.0494867i
$171$	8.14969	−	8.14969i	0.623223	−	0.623223i
$172$	−1.22967	−	2.12985i	−0.0937613	−	0.162399i
$173$	−0.240624	−	0.898022i	−0.0182943	−	0.0682754i	0.956175	−	0.292795i	$-0.0945854\pi$
$173$	−0.240624	−	0.898022i	−0.0182943	−	0.0682754i	−0.974470	+	0.224520i	$0.927919\pi$
$174$		−	1.18058i		−	0.0894995i
$175$	22.0889	+	8.08311i	1.66976	+	0.611025i
$176$	−1.65493	−	0.955475i	−0.124745	−	0.0720217i
$177$	−2.33339			−0.175388
$178$	−1.35777	−	0.363814i	−0.101769	−	0.0272690i
$179$	2.22094	−	2.22094i	0.166001	−	0.166001i	−0.619218	−	0.785219i	$-0.712550\pi$
$179$	2.22094	−	2.22094i	0.166001	−	0.166001i	0.785219	+	0.619218i	$0.212550\pi$
$180$	−6.18181	−	0.275274i	−0.460765	−	0.0205177i
$181$	−5.70435	−	9.88022i	−0.424001	−	0.734391i	0.572326	−	0.820026i	$-0.306041\pi$
$181$	−5.70435	−	9.88022i	−0.424001	−	0.734391i	−0.996327	+	0.0856353i	$0.972708\pi$
$182$	−24.7830	−	6.64059i	−1.83704	−	0.492233i
$183$	2.41473	−	4.18244i	0.178502	−	0.309175i
$184$	2.87357			0.211842
$185$	1.91349	−	13.4662i	0.140683	−	0.990055i
$186$	−1.93661			−0.141999
$187$	0.310687	−	0.538125i	0.0227197	−	0.0393516i
$188$	−11.5637	−	3.09848i	−0.843369	−	0.225980i
$189$	6.54351	+	11.3337i	0.475970	+	0.824405i
$190$	6.87158	−	6.28569i	0.498517	−	0.456012i
$191$	8.98072	−	8.98072i	0.649822	−	0.649822i	−0.303128	−	0.952950i	$-0.598031\pi$
$191$	8.98072	−	8.98072i	0.649822	−	0.649822i	0.952950	+	0.303128i	$0.0980309\pi$
$192$	0.465926	+	0.124844i	0.0336253	+	0.00900987i
$193$	−21.5361			−1.55020			−0.775102	−	0.631837i	$-0.782301\pi$
$193$	−21.5361			−1.55020			−0.775102	+	0.631837i	$0.782301\pi$
$194$	−6.69963	−	3.86803i	−0.481005	−	0.277709i
$195$	5.74434	−	1.26827i	0.411361	−	0.0908224i
$196$		−	15.1302i		−	1.08073i
$197$	4.62766	+	17.2707i	0.329707	+	1.23048i	0.909494	+	0.415717i	$0.136469\pi$
$197$	4.62766	+	17.2707i	0.329707	+	1.23048i	−0.579787	+	0.814768i	$0.696864\pi$
$198$	2.64411	+	4.57974i	0.187909	+	0.325468i
$199$	−11.0205	+	11.0205i	−0.781222	+	0.781222i	−0.980037	−	0.198815i	$-0.936291\pi$
$199$	−11.0205	+	11.0205i	−0.781222	+	0.781222i	0.198815	+	0.980037i	$0.436291\pi$
$200$	−4.98021	−	0.444415i	−0.352154	−	0.0314249i
$201$	−2.02813	+	3.51282i	−0.143053	+	0.247775i
$202$	−2.59599	−	1.49880i	−0.182653	−	0.105455i
$203$	9.97116	−	5.75685i	0.699839	−	0.404052i
$204$	−0.0405950	+	0.151502i	−0.00284222	+	0.0106073i
$205$	−12.4585	−	23.9832i	−0.870137	−	1.67506i
$206$	−10.5912	−	6.11483i	−0.737924	−	0.426041i
$207$	−6.88673	−	3.97605i	−0.478661	−	0.276355i
$208$	5.45403			0.378169
$209$	−7.68757	−	2.05988i	−0.531760	−	0.142485i
$210$	2.33901	+	4.50273i	0.161407	+	0.310718i
$211$	−18.9690			−1.30588			−0.652940	−	0.757410i	$-0.726465\pi$
$211$	−18.9690			−1.30588			−0.652940	+	0.757410i	$0.726465\pi$
$212$	6.57331	+	6.57331i	0.451457	+	0.451457i
$213$	1.65913	+	6.19195i	0.113682	+	0.424265i
$214$	6.60745	−	6.60745i	0.451676	−	0.451676i
$215$	−0.244637	+	5.49380i	−0.0166841	+	0.374674i
$216$	−1.96713	−	1.96713i	−0.133846	−	0.133846i
$217$	−9.44348	−	16.3566i	−0.641065	−	1.11036i
$218$	0.857402	−	3.19987i	0.0580706	−	0.216722i
$219$	−3.26505	+	1.88508i	−0.220632	+	0.127382i
$220$	1.96977	+	3.79192i	0.132802	+	0.255651i
$221$			1.77346i			0.119296i
$222$	2.26525	−	1.86482i	0.152033	−	0.125159i
$223$	2.14486	+	2.14486i	0.143631	+	0.143631i	0.775266	−	0.631635i	$-0.217616\pi$
$223$	2.14486	+	2.14486i	0.143631	+	0.143631i	−0.631635	+	0.775266i	$0.717616\pi$
$224$	1.21756	+	4.54399i	0.0813515	+	0.303608i
$225$	11.3205	+	7.95601i	0.754702	+	0.530401i
$226$	6.56880	−	3.79250i	0.436950	−	0.252273i
$227$	−10.1843	+	5.87992i	−0.675957	+	0.390264i	−0.798330	−	0.602220i	$-0.794283\pi$
$227$	−10.1843	+	5.87992i	−0.675957	+	0.390264i	0.122373	+	0.992484i	$0.460950\pi$
$228$	2.00895			0.133046
$229$	−11.9595	+	6.90484i	−0.790308	+	0.456285i	−0.840071	−	0.542476i	$-0.817487\pi$
$229$	−11.9595	+	6.90484i	−0.790308	+	0.456285i	0.0497627	+	0.998761i	$0.484154\pi$
$230$	−5.41622	−	3.45712i	−0.357135	−	0.227955i
$231$	2.16813	−	3.75531i	0.142653	−	0.247082i
$232$	−1.73064	+	1.73064i	−0.113622	+	0.113622i
$233$	6.84816	−	6.84816i	0.448638	−	0.448638i	−0.446264	−	0.894901i	$-0.647246\pi$
$233$	6.84816	−	6.84816i	0.448638	−	0.448638i	0.894901	+	0.446264i	$0.147246\pi$
$234$	−13.0710	−	7.54654i	−0.854477	−	0.493333i
$235$	18.0680	+	19.7521i	1.17863	+	1.28849i
$236$	3.42058	+	3.42058i	0.222661	+	0.222661i
$237$	2.15649	−	3.73515i	0.140079	−	0.242624i
$238$	−1.47754	+	0.395906i	−0.0957748	+	0.0256628i
$239$	−9.81663	+	2.63036i	−0.634985	+	0.170144i	−0.561931	−	0.827184i	$-0.689941\pi$
$239$	−9.81663	+	2.63036i	−0.634985	+	0.170144i	−0.0730543	+	0.997328i	$0.523275\pi$
$240$	−0.727998	−	0.795854i	−0.0469921	−	0.0513722i
$241$	−23.3607	−	6.25949i	−1.50480	−	0.403209i	−0.590094	−	0.807335i	$-0.700909\pi$
$241$	−23.3607	−	6.25949i	−1.50480	−	0.403209i	−0.914704	+	0.404126i	$0.867576\pi$
$242$	−3.67413	+	6.36379i	−0.236182	+	0.409080i
$243$	3.02898	+	11.3043i	0.194309	+	0.725173i
$244$	−9.67096	+	2.59133i	−0.619120	+	0.165893i
$245$	−18.2028	+	28.5181i	−1.16293	+	1.82195i
$246$	1.50892	−	5.63138i	0.0962055	−	0.359044i
$247$	21.9410	−	5.87908i	1.39607	−	0.374077i
$248$	2.83892	+	2.83892i	0.180272	+	0.180272i
$249$	0.535008			0.0339048
$250$	8.85223	+	6.82921i	0.559864	+	0.431917i
$251$	−3.97203	−	3.97203i	−0.250712	−	0.250712i	0.570551	−	0.821263i	$-0.306730\pi$
$251$	−3.97203	−	3.97203i	−0.250712	−	0.250712i	−0.821263	+	0.570551i	$0.806730\pi$
$252$	3.36938	−	12.5747i	0.212251	−	0.792131i
$253$			5.49125i			0.345232i
$254$	5.64206	+	1.51178i	0.354014	+	0.0948578i
$255$	0.258784	−	0.236719i	0.0162057	−	0.0148239i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.30715	+	2.48674i	0.268673	+	0.155118i	0.628284	−	0.777984i	$-0.283757\pi$
$257$	4.30715	+	2.48674i	0.268673	+	0.155118i	−0.359612	+	0.933102i	$0.617091\pi$
$258$	−0.838834	+	0.838834i	−0.0522235	+	0.0522235i
$259$	26.7963	+	10.0388i	1.66504	+	0.623782i
$260$	−10.2800	−	6.56159i	−0.637536	−	0.406933i
$261$	6.54224	−	1.75299i	0.404954	−	0.108507i
$262$	−1.67033	+	6.23376i	−0.103193	+	0.385123i
$263$	2.62382	+	0.703051i	0.161792	+	0.0433520i	0.338806	−	0.940856i	$-0.389977\pi$
$263$	2.62382	+	0.703051i	0.161792	+	0.0433520i	−0.177014	+	0.984208i	$0.556644\pi$
$264$	−0.238572	+	0.890361i	−0.0146831	+	0.0547980i
$265$	−4.48145	−	20.2978i	−0.275294	−	1.24688i
$266$	9.79623	+	16.9676i	0.600645	+	1.04035i
$267$			0.678041i			0.0414955i
$268$	8.12261	−	2.17645i	0.496168	−	0.132948i
$269$		−	0.875890i		−	0.0534040i	−0.999643	−	0.0267020i	$-0.991499\pi$
$269$		−	0.875890i		−	0.0534040i	0.999643	−	0.0267020i	$-0.00850052\pi$
$270$	1.34112	+	6.07432i	0.0816179	+	0.369671i
$271$	1.36060	−	2.35662i	0.0826503	−	0.143155i	−0.821737	−	0.569867i	$-0.806995\pi$
$271$	1.36060	−	2.35662i	0.0826503	−	0.143155i	0.904388	+	0.426712i	$0.140328\pi$
$272$	0.281601	−	0.162582i	0.0170745	−	0.00985799i
$273$			12.3761i			0.749035i
$274$	3.95737	+	14.7691i	0.239073	+	0.892234i
$275$	0.849255	−	9.51694i	0.0512120	−	0.573893i
$276$	−0.358749	−	1.33887i	−0.0215942	−	0.0805905i
$277$	10.6283	+	18.4088i	0.638595	+	1.10608i	0.985741	+	0.168268i	$0.0538175\pi$
$277$	10.6283	+	18.4088i	0.638595	+	1.10608i	−0.347146	+	0.937811i	$0.612849\pi$
$278$	−1.53525	−	2.65913i	−0.0920780	−	0.159484i
$279$	−2.87558	−	10.7318i	−0.172156	−	0.642497i
$280$	3.17185	−	10.0295i	0.189554	−	0.599377i
$281$	0.709898	+	2.64937i	0.0423490	+	0.158048i	0.983862	−	0.178927i	$-0.0572627\pi$
$281$	0.709898	+	2.64937i	0.0423490	+	0.158048i	−0.941513	+	0.336976i	$0.890596\pi$
$282$			5.77465i			0.343875i
$283$	1.59801	−	0.922612i	0.0949919	−	0.0548436i	−0.451752	−	0.892144i	$-0.649201\pi$
$283$	1.59801	−	0.922612i	0.0949919	−	0.0548436i	0.546743	+	0.837300i	$0.315867\pi$
$284$	6.64478	−	11.5091i	0.394295	−	0.682939i
$285$	−3.78654	−	2.41691i	−0.224295	−	0.143165i
$286$			10.4224i			0.616288i
$287$	54.9206	−	14.7159i	3.24186	−	0.868654i
$288$			2.76733i			0.163066i
$289$	−8.44713	−	14.6309i	−0.496890	−	0.860639i
$290$	5.34407	−	1.17989i	0.313814	−	0.0692856i
$291$	−0.965805	+	3.60443i	−0.0566165	+	0.211296i
$292$	7.54971	+	2.02294i	0.441813	+	0.118384i
$293$	−0.856934	+	3.19812i	−0.0500626	+	0.186836i	−0.986429	−	0.164188i	$-0.947500\pi$
$293$	−0.856934	+	3.19812i	−0.0500626	+	0.186836i	0.936366	+	0.351024i	$0.114166\pi$
$294$	−7.04957	+	1.88893i	−0.411139	+	0.110164i
$295$	−2.33203	−	10.5624i	−0.135776	−	0.614969i
$296$	−6.05437	−	0.586988i	−0.351903	−	0.0341180i
$297$	3.75908	−	3.75908i	0.218124	−	0.218124i
$298$	20.5508	+	11.8650i	1.19048	+	0.687322i
$299$	−7.83627	−	13.5728i	−0.453183	−	0.784936i
$300$	0.414687	+	2.37589i	0.0239420	+	0.137172i
$301$	−11.1752	−	2.99438i	−0.644127	−	0.172593i
$302$			13.8311i			0.795889i
$303$	−0.374233	+	1.39666i	−0.0214991	+	0.0802358i
$304$	−2.94497	−	2.94497i	−0.168906	−	0.168906i
$305$	21.3458	+	6.75064i	1.22225	+	0.386541i
$306$	−0.899836			−0.0514402
$307$	22.9767	+	22.9767i	1.31135	+	1.31135i	0.920419	+	0.390933i	$0.127848\pi$
$307$	22.9767	+	22.9767i	1.31135	+	1.31135i	0.390933	+	0.920419i	$0.372152\pi$
$308$	−8.68333	+	2.32669i	−0.494779	+	0.132576i
$309$	−1.52681	+	5.69812i	−0.0868570	+	0.324155i
$310$	−1.93548	−	8.76635i	−0.109928	−	0.497895i
$311$	−7.89651	+	2.11586i	−0.447770	+	0.119980i	−0.475656	−	0.879632i	$-0.657789\pi$
$311$	−7.89651	+	2.11586i	−0.447770	+	0.119980i	0.0278858	+	0.999611i	$0.491123\pi$
$312$	−0.680905	−	2.54117i	−0.0385487	−	0.143866i
$313$	16.6518	−	28.8417i	0.941214	−	1.63023i	0.178054	−	0.984021i	$-0.443020\pi$
$313$	16.6518	−	28.8417i	0.941214	−	1.63023i	0.763160	−	0.646209i	$-0.223647\pi$
$314$	6.38801	+	1.71166i	0.360497	+	0.0965948i
$315$	−21.4790	+	19.6477i	−1.21021	+	1.10702i
$316$	−8.63670	+	2.31420i	−0.485852	+	0.130184i
$317$	2.80328	−	0.751135i	0.157448	−	0.0421880i	−0.179234	−	0.983806i	$-0.557362\pi$
$317$	2.80328	−	0.751135i	0.157448	−	0.0421880i	0.336682	+	0.941618i	$0.390695\pi$
$318$	2.24203	−	3.88332i	0.125727	−	0.217766i
$319$	−3.30717	−	3.30717i	−0.185166	−	0.185166i
$320$	−0.0994727	+	2.23385i	−0.00556069	+	0.124876i
$321$	−3.90349	−	2.25368i	−0.217871	−	0.125788i
$322$	9.55873	−	9.55873i	0.532687	−	0.532687i
$323$	0.957599	−	0.957599i	0.0532822	−	0.0532822i
$324$	3.48004	−	6.02761i	0.193336	−	0.334867i
$325$	11.4820	+	24.7351i	0.636906	+	1.37206i
$326$	17.5264	−	10.1189i	0.970697	−	0.560432i
$327$	−1.59794			−0.0883664
$328$	−10.4672	+	6.04322i	−0.577952	+	0.333681i
$329$	−48.7727	+	28.1589i	−2.68892	+	1.55245i
$330$	1.52084	−	1.39117i	0.0837194	−	0.0765813i
$331$	7.63989	+	28.5124i	0.419926	+	1.56719i	0.774760	+	0.632256i	$0.217871\pi$
$331$	7.63989	+	28.5124i	0.419926	+	1.56719i	−0.354833	+	0.934930i	$0.615462\pi$
$332$	−0.784282	−	0.784282i	−0.0430431	−	0.0430431i
$333$	13.6976	+	9.78398i	0.750622	+	0.536159i
$334$		−	0.259876i		−	0.0142198i
$335$	−17.9282	−	5.66985i	−0.979524	−	0.309777i
$336$	1.96515	−	1.13458i	0.107208	−	0.0618966i
$337$	1.88042	−	7.01784i	0.102433	−	0.382286i	−0.895608	−	0.444844i	$-0.853259\pi$
$337$	1.88042	−	7.01784i	0.102433	−	0.382286i	0.998041	+	0.0625579i	$0.0199258\pi$
$338$	−8.37321	−	14.5028i	−0.455443	−	0.788850i
$339$	−2.58710	−	2.58710i	−0.140512	−	0.140512i
$340$	−0.726370	−	0.0323450i	−0.0393929	−	0.00175415i
$341$	−5.42504	+	5.42504i	−0.293783	+	0.293783i
$342$	2.98299	+	11.1327i	0.161302	+	0.601987i
$343$	−27.0447	−	27.0447i	−1.46028	−	1.46028i
$344$	2.45934			0.132598
$345$	−0.934575	+	2.95516i	−0.0503158	+	0.159100i
$346$	0.898022	+	0.240624i	0.0482780	+	0.0129360i
$347$	−32.3909			−1.73884			−0.869418	−	0.494077i	$-0.835506\pi$
$347$	−32.3909			−1.73884			−0.869418	+	0.494077i	$0.835506\pi$
$348$	1.02241	+	0.590290i	0.0548070	+	0.0316428i
$349$	−12.2807	−	7.09028i	−0.657372	−	0.379534i	0.133903	−	0.990994i	$-0.457249\pi$
$349$	−12.2807	−	7.09028i	−0.657372	−	0.379534i	−0.791275	+	0.611461i	$0.790582\pi$
$350$	−18.0446	+	15.0880i	−0.964526	+	0.806487i
$351$	−3.92700	+	14.6558i	−0.209608	+	0.782267i
$352$	1.65493	−	0.955475i	0.0882082	−	0.0509270i
$353$	23.7720	+	13.7248i	1.26526	+	0.730497i	0.974087	−	0.226174i	$-0.0726217\pi$
$353$	23.7720	+	13.7248i	1.26526	+	0.730497i	0.291171	+	0.956671i	$0.405955\pi$
$354$	1.16670	−	2.02078i	0.0620092	−	0.107403i
$355$	−26.3706	+	13.6986i	−1.39961	+	0.727048i
$356$	0.993958	−	0.993958i	0.0526797	−	0.0526797i
$357$	0.368926	+	0.638998i	0.0195256	+	0.0338194i
$358$	0.812920	+	3.03386i	0.0429641	+	0.160344i
$359$			5.73798i			0.302839i	0.988470	+	0.151420i	$0.0483844\pi$
$359$			5.73798i			0.302839i	−0.988470	+	0.151420i	$0.951616\pi$
$360$	3.32930	−	5.21596i	0.175469	−	0.274905i
$361$	1.43267	+	0.827155i	0.0754039	+	0.0435345i
$362$	11.4087			0.599628
$363$	3.42375	+	0.917390i	0.179700	+	0.0481505i
$364$	18.1424	−	18.1424i	0.950922	−	0.950922i
$365$	−11.7962	−	12.8958i	−0.617443	−	0.674995i
$366$	2.41473	+	4.18244i	0.126220	+	0.218620i
$367$	−34.6305	−	9.27922i	−1.80770	−	0.484371i	−0.812562	−	0.582875i	$-0.801928\pi$
$367$	−34.6305	−	9.27922i	−1.80770	−	0.484371i	−0.995137	+	0.0985034i	$0.968594\pi$
$368$	−1.43679	+	2.48858i	−0.0748976	+	0.129726i
$369$	33.4471			1.74119
$370$	10.7053	+	8.39023i	0.556543	+	0.436187i
$371$	43.7313			2.27042
$372$	0.968304	−	1.67715i	0.0502042	−	0.0869563i
$373$	−10.4103	−	2.78944i	−0.539027	−	0.144432i	−0.0209735	−	0.999780i	$-0.506677\pi$
$373$	−10.4103	−	2.78944i	−0.539027	−	0.144432i	−0.518054	+	0.855348i	$0.673343\pi$
$374$	0.310687	+	0.538125i	0.0160652	+	0.0278258i
$375$	2.07675	−	4.97707i	0.107243	−	0.257015i
$376$	8.46521	−	8.46521i	0.436560	−	0.436560i
$377$	12.8939	+	3.45490i	0.664068	+	0.177937i
$378$	−13.0870			−0.673124
$379$	−3.24154	−	1.87150i	−0.166507	−	0.0961326i	0.414431	−	0.910081i	$-0.363981\pi$
$379$	−3.24154	−	1.87150i	−0.166507	−	0.0961326i	−0.580938	+	0.813948i	$0.697314\pi$
$380$	2.00778	+	9.09380i	0.102997	+	0.466502i
$381$		−	2.81752i		−	0.144346i
$382$	3.28717	+	12.2679i	0.168186	+	0.627680i
$383$	−15.0051	−	25.9896i	−0.766726	−	1.32801i	−0.939329	−	0.343017i	$-0.888551\pi$
$383$	−15.0051	−	25.9896i	−0.766726	−	1.32801i	0.172603	−	0.984992i	$-0.444782\pi$
$384$	−0.341081	+	0.341081i	−0.0174057	+	0.0174057i
$385$	19.1659	+	6.06125i	0.976783	+	0.308910i
$386$	10.7681	−	18.6508i	0.548080	−	0.949302i
$387$	−5.89398	−	3.40289i	−0.299608	−	0.172979i
$388$	6.69963	−	3.86803i	0.340122	−	0.196370i
$389$	−3.39248	+	12.6609i	−0.172005	+	0.641933i	0.825037	+	0.565079i	$0.191154\pi$
$389$	−3.39248	+	12.6609i	−0.172005	+	0.641933i	−0.997042	+	0.0768540i	$0.975512\pi$
$390$	−1.77382	+	5.60888i	−0.0898209	+	0.284017i
$391$	−0.809199	−	0.467191i	−0.0409230	−	0.0236269i
$392$	13.1032	+	7.56512i	0.661810	+	0.382096i
$393$	3.11300			0.157030
$394$	−17.2707	−	4.62766i	−0.870084	−	0.233138i
$395$	19.0629	+	6.02869i	0.959160	+	0.303336i
$396$	−5.28823			−0.265743
$397$	20.7980	+	20.7980i	1.04382	+	1.04382i	0.998995	+	0.0448253i	$0.0142731\pi$
$397$	20.7980	+	20.7980i	1.04382	+	1.04382i	0.0448253	+	0.998995i	$0.485727\pi$
$398$	−4.03378	−	15.0543i	−0.202195	−	0.754602i
$399$	6.68262	−	6.68262i	0.334550	−	0.334550i
$400$	2.87498	−	4.09078i	0.143749	−	0.204539i
$401$	16.1162	+	16.1162i	0.804805	+	0.804805i	0.983842	−	0.179038i	$-0.0572984\pi$
$401$	16.1162	+	16.1162i	0.804805	+	0.804805i	−0.179038	+	0.983842i	$0.557298\pi$
$402$	−2.02813	−	3.51282i	−0.101154	−	0.175203i
$403$	5.66738	−	21.1510i	0.282312	−	1.05360i
$404$	2.59599	−	1.49880i	0.129155	−	0.0745679i
$405$	−13.8110	+	7.17432i	−0.686272	+	0.356495i
$406$			11.5137i			0.571416i
$407$	1.12171	−	11.5696i	0.0556009	−	0.573484i
$408$	−0.110908	−	0.110908i	−0.00549074	−	0.00549074i
$409$	4.05950	+	15.1503i	0.200730	+	0.749133i	0.990709	+	0.136000i	$0.0434246\pi$
$409$	4.05950	+	15.1503i	0.200730	+	0.749133i	−0.789979	+	0.613134i	$0.789909\pi$
$410$	26.9993	+	1.20227i	1.33340	+	0.0593759i
$411$	6.38725	−	3.68768i	0.315060	−	0.181900i
$412$	10.5912	−	6.11483i	0.521791	−	0.301256i
$413$	22.7566			1.11978
$414$	6.88673	−	3.97605i	0.338464	−	0.195412i
$415$	0.534696	+	2.42179i	0.0262472	+	0.118881i
$416$	−2.72701	+	4.72333i	−0.133703	+	0.231580i
$417$	−1.04729	+	1.04729i	−0.0512859	+	0.0512859i
$418$	5.62769	−	5.62769i	0.275259	−	0.275259i
$419$	27.4386	+	15.8417i	1.34046	+	0.773916i	0.986875	−	0.161485i	$-0.0516283\pi$
$419$	27.4386	+	15.8417i	1.34046	+	0.773916i	0.353588	+	0.935401i	$0.384962\pi$
$420$	−5.06898	−	0.225720i	−0.247341	−	0.0110140i
$421$	−11.4598	−	11.4598i	−0.558516	−	0.558516i	0.370369	−	0.928885i	$-0.379231\pi$
$421$	−11.4598	−	11.4598i	−0.558516	−	0.558516i	−0.928885	+	0.370369i	$0.879231\pi$
$422$	9.48450	−	16.4276i	0.461698	−	0.799685i
$423$	−32.0005	+	8.57451i	−1.55592	+	0.416907i
$424$	−8.97931	+	2.40600i	−0.436074	+	0.116846i
$425$	1.33018	+	0.934841i	0.0645230	+	0.0453465i
$426$	−6.19195	−	1.65913i	−0.300001	−	0.0803850i
$427$	−23.5499	+	40.7896i	−1.13966	+	1.97395i
$428$	2.41850	+	9.02595i	0.116902	+	0.436286i
$429$	4.85606	−	1.30118i	0.234453	−	0.0628214i
$430$	−4.63545	−	2.95876i	−0.223541	−	0.142684i
$431$	5.09414	−	19.0116i	0.245376	−	0.915756i	−0.727818	−	0.685771i	$-0.759465\pi$
$431$	5.09414	−	19.0116i	0.245376	−	0.915756i	0.973194	−	0.229986i	$-0.0738680\pi$
$432$	2.68715	−	0.720019i	0.129285	−	0.0346419i
$433$	4.81336	+	4.81336i	0.231315	+	0.231315i	0.813242	−	0.581926i	$-0.197701\pi$
$433$	4.81336	+	4.81336i	0.231315	+	0.231315i	−0.581926	+	0.813242i	$0.697701\pi$
$434$	18.8870			0.906603
$435$	−1.21692	−	2.34264i	−0.0583468	−	0.112321i
$436$	2.34246	+	2.34246i	0.112184	+	0.112184i
$437$	−3.09752	+	11.5601i	−0.148174	+	0.552994i
$438$		−	3.77016i		−	0.180145i
$439$	−17.1646	−	4.59924i	−0.819221	−	0.219510i	−0.175215	−	0.984530i	$-0.556062\pi$
$439$	−17.1646	−	4.59924i	−0.819221	−	0.219510i	−0.644006	+	0.765020i	$0.722729\pi$
$440$	−4.26879	−	0.190087i	−0.203506	−	0.00906206i
$441$	−20.9352	−	36.2608i	−0.996913	−	1.72670i
$442$	−1.53586	−	0.886728i	−0.0730533	−	0.0421773i
$443$	4.32917	−	4.32917i	0.205685	−	0.205685i	−0.596745	−	0.802431i	$-0.703540\pi$
$443$	4.32917	−	4.32917i	0.205685	−	0.205685i	0.802431	+	0.596745i	$0.203540\pi$
$444$	0.482362	+	2.89417i	0.0228919	+	0.137351i
$445$	−3.06925	+	0.677646i	−0.145497	+	0.0321235i
$446$	−2.92994	+	0.785075i	−0.138737	+	0.0371744i
$447$	2.96256	−	11.0564i	0.140124	−	0.522952i
$448$	−4.54399	−	1.21756i	−0.214683	−	0.0575242i
$449$	2.31024	−	8.62193i	0.109027	−	0.406894i	−0.889744	−	0.456460i	$-0.849117\pi$
$449$	2.31024	−	8.62193i	0.109027	−	0.406894i	0.998771	+	0.0495659i	$0.0157838\pi$
$450$	−12.5504	+	5.82586i	−0.591630	+	0.274634i
$451$	−11.5483	−	20.0022i	−0.543788	−	0.941868i
$452$			7.58499i			0.356768i
$453$	6.44426	−	1.72673i	0.302778	−	0.0811290i
$454$		−	11.7598i		−	0.551917i
$455$	−56.0222	+	12.3689i	−2.62636	+	0.579862i
$456$	−1.00447	+	1.73980i	−0.0470388	+	0.0814736i
$457$	−8.25284	+	4.76478i	−0.386052	+	0.222887i	−0.680448	−	0.732796i	$-0.738215\pi$
$457$	−8.25284	+	4.76478i	−0.386052	+	0.222887i	0.294396	+	0.955683i	$0.404881\pi$
$458$		−	13.8097i		−	0.645284i
$459$	0.234124	+	0.873764i	0.0109280	+	0.0407838i
$460$	5.70206	−	2.96202i	0.265860	−	0.138105i
$461$	−2.78931	−	10.4099i	−0.129911	−	0.484836i	0.870056	−	0.492953i	$-0.164083\pi$
$461$	−2.78931	−	10.4099i	−0.129911	−	0.484836i	−0.999967	+	0.00811777i	$0.997416\pi$
$462$	2.16813	+	3.75531i	0.100871	+	0.174713i
$463$	−7.44658	−	12.8979i	−0.346072	−	0.599414i	0.639476	−	0.768811i	$-0.279151\pi$
$463$	−7.44658	−	12.8979i	−0.346072	−	0.599414i	−0.985548	+	0.169397i	$0.945818\pi$
$464$	−0.633459	−	2.36410i	−0.0294076	−	0.109751i
$465$	−3.84283	+	1.99622i	−0.178207	+	0.0925725i
$466$	2.50660	+	9.35476i	0.116116	+	0.433351i
$467$			14.9484i			0.691729i	0.938284	+	0.345864i	$0.112414\pi$
$467$			14.9484i			0.691729i	−0.938284	+	0.345864i	$0.887586\pi$
$468$	13.0710	−	7.54654i	0.604207	−	0.348839i
$469$	19.7795	−	34.2591i	0.913332	−	1.58194i
$470$	−26.1398	+	5.77128i	−1.20574	+	0.266210i
$471$		−	3.19003i		−	0.146989i
$472$	−4.67260	+	1.25202i	−0.215074	+	0.0576288i
$473$			4.69967i			0.216091i
$474$	2.15649	+	3.73515i	0.0990508	+	0.171561i
$475$	7.15618	−	19.5559i	0.328348	−	0.897284i
$476$	0.395906	−	1.47754i	0.0181463	−	0.0677230i
$477$	24.8487	+	6.65819i	1.13774	+	0.304857i
$478$	2.63036	−	9.81663i	0.120310	−	0.449002i
$479$	11.7479	−	3.14783i	0.536774	−	0.143828i	0.0197595	−	0.999805i	$-0.493710\pi$
$479$	11.7479	−	3.14783i	0.536774	−	0.143828i	0.517015	+	0.855977i	$0.327043\pi$
$480$	1.05323	−	0.232537i	0.0480731	−	0.0106138i
$481$	13.7378	+	30.1975i	0.626391	+	1.37689i
$482$	17.1012	−	17.1012i	0.778940	−	0.778940i
$483$	−5.64701	−	3.26030i	−0.256948	−	0.148349i
$484$	−3.67413	−	6.36379i	−0.167006	−	0.289263i
$485$	−17.2812	−	0.769528i	−0.784701	−	0.0349425i
$486$	−11.3043	−	3.02898i	−0.512774	−	0.137397i
$487$			21.2624i			0.963492i	0.876311	+	0.481746i	$0.159997\pi$
$487$			21.2624i			0.963492i	−0.876311	+	0.481746i	$0.840003\pi$
$488$	2.59133	−	9.67096i	0.117304	−	0.437784i
$489$	−6.90271	−	6.90271i	−0.312151	−	0.312151i
$490$	−15.5960	−	30.0231i	−0.704554	−	1.35631i
$491$	−23.6185			−1.06589			−0.532945	−	0.846150i	$-0.678915\pi$
$491$	−23.6185			−1.06589			−0.532945	+	0.846150i	$0.678915\pi$
$492$	4.12246	+	4.12246i	0.185855	+	0.185855i
$493$	0.768721	−	0.205978i	0.0346215	−	0.00927679i
$494$	−5.87908	+	21.9410i	−0.264512	+	0.987174i
$495$	9.96745	+	6.36212i	0.448004	+	0.285956i
$496$	−3.87804	+	1.03912i	−0.174129	+	0.0466578i
$497$	−16.1808	−	60.3876i	−0.725808	−	2.70875i
$498$	−0.267504	+	0.463331i	−0.0119871	+	0.0207623i
$499$	29.3919	+	7.87554i	1.31576	+	0.352558i	0.847389	−	0.530973i	$-0.178173\pi$
$499$	29.3919	+	7.87554i	1.31576	+	0.352558i	0.468374	+	0.883530i	$0.344840\pi$
$500$	−10.3404	+	4.25165i	−0.462436	+	0.190140i
$501$	−0.121083	+	0.0324441i	−0.00540959	+	0.00144949i
$502$	5.42589	−	1.45386i	0.242169	−	0.0648890i
$503$	−14.4145	+	24.9667i	−0.642711	+	1.11321i	0.342114	+	0.939659i	$0.388857\pi$
$503$	−14.4145	+	24.9667i	−0.642711	+	1.11321i	−0.984825	+	0.173550i	$0.944476\pi$
$504$	9.20531	+	9.20531i	0.410037	+	0.410037i
$505$	−6.69618	−	0.298179i	−0.297976	−	0.0132688i
$506$	−4.75556	−	2.74563i	−0.211411	−	0.122058i
$507$	−5.71189	+	5.71189i	−0.253674	+	0.253674i
$508$	−4.13027	+	4.13027i	−0.183251	+	0.183251i
$509$	−9.59508	+	16.6192i	−0.425294	+	0.736632i	−0.996448	−	0.0842118i	$-0.973163\pi$
$509$	−9.59508	+	16.6192i	−0.425294	+	0.736632i	0.571153	+	0.820843i	$0.306496\pi$
$510$	0.0756129	+	0.342473i	0.00334819	+	0.0151649i
$511$	31.8427	−	18.3844i	1.40864	−	0.813278i
$512$	1.00000			0.0441942
$513$	10.0340	−	5.79313i	0.443012	−	0.255773i
$514$	−4.30715	+	2.48674i	−0.189980	+	0.109685i
$515$	−27.3193	−	1.21652i	−1.20383	−	0.0536062i
$516$	−0.307034	−	1.14587i	−0.0135164	−	0.0504440i
$517$	16.1766	+	16.1766i	0.711446	+	0.711446i
$518$	−22.0920	+	18.1869i	−0.970667	+	0.799085i
$519$		−	0.448452i		−	0.0196849i
$520$	10.8225	−	5.62191i	0.474598	−	0.246537i
$521$	−18.0440	+	10.4177i	−0.790523	+	0.456409i	−0.840147	−	0.542359i	$-0.817531\pi$
$521$	−18.0440	+	10.4177i	−0.790523	+	0.456409i	0.0496237	+	0.998768i	$0.484198\pi$
$522$	−1.75299	+	6.54224i	−0.0767262	+	0.286346i
$523$	1.03668	+	1.79558i	0.0453307	+	0.0785150i	0.887800	−	0.460229i	$-0.152233\pi$
$523$	1.03668	+	1.79558i	0.0453307	+	0.0785150i	−0.842470	+	0.538744i	$0.818899\pi$
$524$	−4.56343	−	4.56343i	−0.199354	−	0.199354i
$525$	9.28266	+	6.52381i	0.405128	+	0.284722i
$526$	−1.92077	+	1.92077i	−0.0837496	+	0.0837496i
$527$	−0.337884	−	1.26100i	−0.0147185	−	0.0549301i
$528$	−0.651790	−	0.651790i	−0.0283655	−	0.0283655i
$529$	−14.7426			−0.640982
$530$	19.8191	+	6.26785i	0.860888	+	0.272258i
$531$	12.9306	+	3.46475i	0.561140	+	0.150357i
$532$	−19.5925			−0.849441
$533$	57.0882	+	32.9599i	2.47276	+	1.42765i
$534$	−0.587201	−	0.339021i	−0.0254107	−	0.0146709i
$535$	6.30040	−	19.9221i	0.272390	−	0.861307i
$536$	−2.17645	+	8.12261i	−0.0940082	+	0.350844i
$537$	1.31206	−	0.757521i	0.0566198	−	0.0326894i
$538$	0.758543	+	0.437945i	0.0327031	+	0.0188812i
$539$	−14.4566	+	25.0395i	−0.622689	+	1.07853i
$540$	−5.93107	−	1.87571i	−0.255233	−	0.0807179i
$541$	1.38201	−	1.38201i	0.0594171	−	0.0594171i	−0.676774	−	0.736191i	$-0.736623\pi$
$541$	1.38201	−	1.38201i	0.0594171	−	0.0594171i	0.736191	+	0.676774i	$0.236623\pi$
$542$	1.36060	+	2.35662i	0.0584426	+	0.101226i
$543$	−1.42431	−	5.31561i	−0.0611231	−	0.228115i
$544$			0.325164i			0.0139413i
$545$	−1.59701	−	7.23332i	−0.0684084	−	0.309842i
$546$	−10.7180	−	6.18805i	−0.458689	−	0.264824i
$547$	−27.3892			−1.17108			−0.585540	−	0.810644i	$-0.699117\pi$
$547$	−27.3892			−1.17108			−0.585540	+	0.810644i	$0.699117\pi$
$548$	−14.7691	−	3.95737i	−0.630905	−	0.169050i
$549$	−19.5917	+	19.5917i	−0.836152	+	0.836152i
$550$	7.81728	+	5.49395i	0.333330	+	0.234263i
$551$	−5.09669	−	8.82772i	−0.217126	−	0.376073i
$552$	1.33887	+	0.358749i	0.0569861	+	0.0152694i
$553$	−21.0313	+	36.4274i	−0.894344	+	1.54905i
$554$	−21.2567			−0.903110
$555$	2.57273	−	6.03536i	0.109206	−	0.256187i
$556$	3.07049			0.130218
$557$	10.4061	−	18.0238i	0.440919	−	0.763694i	−0.556839	−	0.830621i	$-0.687986\pi$
$557$	10.4061	−	18.0238i	0.440919	−	0.763694i	0.997758	+	0.0669264i	$0.0213193\pi$
$558$	10.7318	+	2.87558i	0.454314	+	0.121733i
$559$	−6.70664	−	11.6162i	−0.283661	−	0.491315i
$560$	7.09987	+	7.76164i	0.300024	+	0.327989i
$561$	0.211939	−	0.211939i	0.00894806	−	0.00894806i
$562$	−2.64937	−	0.709898i	−0.111757	−	0.0299452i
$563$	24.4930			1.03226			0.516129	−	0.856511i	$-0.327373\pi$
$563$	24.4930			1.03226			0.516129	+	0.856511i	$0.327373\pi$
$564$	−5.00099	−	2.88733i	−0.210580	−	0.121578i
$565$	9.12530	−	14.2965i	0.383904	−	0.601458i
$566$			1.84522i			0.0775605i
$567$	−8.47430	−	31.6265i	−0.355887	−	1.32819i
$568$	6.64478	+	11.5091i	0.278809	+	0.482911i
$569$	20.9645	−	20.9645i	0.878879	−	0.878879i	−0.114540	−	0.993419i	$-0.536539\pi$
$569$	20.9645	−	20.9645i	0.878879	−	0.878879i	0.993419	+	0.114540i	$0.0365393\pi$
$570$	3.98638	−	2.07079i	0.166971	−	0.0867357i
$571$	1.88090	−	3.25781i	0.0787132	−	0.136335i	−0.823982	−	0.566616i	$-0.808252\pi$
$571$	1.88090	−	3.25781i	0.0787132	−	0.136335i	0.902695	+	0.430281i	$0.141586\pi$
$572$	−9.02605	−	5.21119i	−0.377398	−	0.217891i
$573$	5.30554	−	3.06316i	0.221642	−	0.127965i
$574$	−14.7159	+	54.9206i	−0.614231	+	2.29234i
$575$	−14.3110	−	1.27706i	−0.596809	−	0.0532570i
$576$	−2.39658	−	1.38366i	−0.0998573	−	0.0576526i
$577$	1.48355	+	0.856526i	0.0617609	+	0.0356576i	0.530562	−	0.847646i	$-0.321981\pi$
$577$	1.48355	+	0.856526i	0.0617609	+	0.0356576i	−0.468802	+	0.883303i	$0.655314\pi$
$578$	16.8943			0.702709
$579$	−10.0342	−	2.68866i	−0.417008	−	0.111737i
$580$	−1.65022	+	5.21804i	−0.0685216	+	0.216667i
$581$	−5.21772			−0.216467
$582$	−2.63863	−	2.63863i	−0.109375	−	0.109375i
$583$	−4.59775	−	17.1590i	−0.190419	−	0.710654i
$584$	−5.52677	+	5.52677i	−0.228699	+	0.228699i
$585$	−33.7157	−	1.50135i	−1.39397	−	0.0620732i
$586$	−2.34119	−	2.34119i	−0.0967136	−	0.0967136i
$587$	6.73328	+	11.6624i	0.277912	+	0.481358i	0.970866	−	0.239624i	$-0.0770243\pi$
$587$	6.73328	+	11.6624i	0.277912	+	0.481358i	−0.692954	+	0.720982i	$0.743691\pi$
$588$	1.88893	−	7.04957i	0.0778981	−	0.290720i
$589$	−14.4809	+	8.36054i	−0.596675	+	0.344490i
$590$	10.3134	+	3.26162i	0.424594	+	0.134279i
$591$			8.62459i			0.354768i
$592$	3.53553	−	4.94975i	0.145310	−	0.203433i
$593$	−7.08621	−	7.08621i	−0.290996	−	0.290996i	0.546478	−	0.837474i	$-0.315968\pi$
$593$	−7.08621	−	7.08621i	−0.290996	−	0.290996i	−0.837474	+	0.546478i	$0.815968\pi$
$594$	1.37592	+	5.13500i	0.0564547	+	0.210692i
$595$	−2.52381	+	2.30862i	−0.103466	+	0.0946444i
$596$	−20.5508	+	11.8650i	−0.841794	+	0.486010i
$597$	−6.51058	+	3.75888i	−0.266460	+	0.153841i
$598$	15.6725			0.640898
$599$	26.4564	−	15.2746i	1.08098	−	0.624104i	0.149819	−	0.988713i	$-0.452131\pi$
$599$	26.4564	−	15.2746i	1.08098	−	0.624104i	0.931160	+	0.364610i	$0.118798\pi$
$600$	−2.26493	−	0.828816i	−0.0924652	−	0.0338363i
$601$	2.28313	−	3.95450i	0.0931308	−	0.161307i	−0.815696	−	0.578481i	$-0.803646\pi$
$601$	2.28313	−	3.95450i	0.0931308	−	0.161307i	0.908827	+	0.417173i	$0.136979\pi$
$602$	8.18080	−	8.18080i	0.333425	−	0.333425i
$603$	16.4550	−	16.4550i	0.670099	−	0.670099i
$604$	−11.9781	−	6.91554i	−0.487381	−	0.281389i
$605$	−0.730952	+	16.4150i	−0.0297174	+	0.667363i
$606$	−1.02242	−	1.02242i	−0.0415331	−	0.0415331i
$607$	−18.9717	+	32.8600i	−0.770040	+	1.33375i	0.167501	+	0.985872i	$0.446430\pi$
$607$	−18.9717	+	32.8600i	−0.770040	+	1.33375i	−0.937541	+	0.347876i	$0.886903\pi$
$608$	4.02290	−	1.07793i	0.163150	−	0.0437160i
$609$	5.36453	−	1.43742i	0.217382	−	0.0582473i
$610$	−16.5191	+	15.1106i	−0.668839	+	0.611812i
$611$	−63.0687	−	16.8992i	−2.55149	−	0.683669i
$612$	0.449918	−	0.779281i	0.0181869	−	0.0315006i
$613$	−7.04706	−	26.3000i	−0.284628	−	1.06225i	−0.949111	−	0.314943i	$-0.898015\pi$
$613$	−7.04706	−	26.3000i	−0.284628	−	1.06225i	0.664483	−	0.747304i	$-0.268652\pi$
$614$	−31.3868	+	8.41007i	−1.26667	+	0.339403i
$615$	−2.81055	−	12.7298i	−0.113332	−	0.513314i
$616$	2.32669	−	8.68333i	0.0937451	−	0.349861i
$617$	−8.21970	+	2.20246i	−0.330913	+	0.0886678i	−0.420450	−	0.907316i	$-0.638128\pi$
$617$	−8.21970	+	2.20246i	−0.330913	+	0.0886678i	0.0895375	+	0.995983i	$0.471461\pi$
$618$	−4.17131	−	4.17131i	−0.167795	−	0.167795i
$619$	9.02320			0.362673			0.181336	−	0.983421i	$-0.441958\pi$
$619$	9.02320			0.362673			0.181336	+	0.983421i	$0.441958\pi$
$620$	8.55962	+	2.70700i	0.343763	+	0.108716i
$621$	−5.65268	−	5.65268i	−0.226834	−	0.226834i
$622$	2.11586	−	7.89651i	0.0848384	−	0.316621i
$623$		−	6.61266i		−	0.264931i
$624$	2.54117	+	0.680905i	0.101728	+	0.0272580i
$625$	24.6050	+	4.42656i	0.984200	+	0.177062i
$626$	16.6518	+	28.8417i	0.665539	+	1.15275i
$627$	−3.32467	−	1.91950i	−0.132775	−	0.0766575i
$628$	−4.67635	+	4.67635i	−0.186607	+	0.186607i
$629$	1.60948	+	1.14963i	0.0641742	+	0.0458387i
$630$	−6.27586	−	28.4252i	−0.250036	−	1.13249i
$631$	−4.27383	+	1.14517i	−0.170138	+	0.0455884i	−0.342883	−	0.939378i	$-0.611403\pi$
$631$	−4.27383	+	1.14517i	−0.170138	+	0.0455884i	0.172744	+	0.984967i	$0.444737\pi$
$632$	2.31420	−	8.63670i	0.0920538	−	0.343549i
$633$	−8.83814	−	2.36817i	−0.351285	−	0.0941265i
$634$	−0.751135	+	2.80328i	−0.0298314	+	0.111332i
$635$	12.7539	−	2.81588i	0.506124	−	0.111745i
$636$	2.24203	+	3.88332i	0.0889024	+	0.153984i
$637$		−	82.5208i		−	3.26959i
$638$	4.51768	−	1.21051i	0.178857	−	0.0479245i
$639$		−	36.7766i		−	1.45486i
$640$	−1.88484	−	1.20307i	−0.0745048	−	0.0475556i
$641$	−5.39495	+	9.34433i	−0.213088	+	0.369079i	−0.952679	−	0.303977i	$-0.901685\pi$
$641$	−5.39495	+	9.34433i	−0.213088	+	0.369079i	0.739592	+	0.673056i	$0.235019\pi$
$642$	3.90349	−	2.25368i	0.154058	−	0.0889456i
$643$		−	15.9654i		−	0.629614i	−0.949156	−	0.314807i	$-0.898060\pi$
$643$		−	15.9654i		−	0.629614i	0.949156	−	0.314807i	$-0.101940\pi$
$644$	3.49874	+	13.0575i	0.137870	+	0.514536i
$645$	−0.799853	+	2.52916i	−0.0314942	+	0.0995856i
$646$	0.350506	+	1.30810i	0.0137905	+	0.0514667i
$647$	21.2204	+	36.7549i	0.834261	+	1.44498i	0.894630	+	0.446807i	$0.147439\pi$
$647$	21.2204	+	36.7549i	0.834261	+	1.44498i	−0.0603689	+	0.998176i	$0.519228\pi$
$648$	3.48004	+	6.02761i	0.136709	+	0.236787i
$649$	−2.39255	−	8.92910i	−0.0939157	−	0.350498i
$650$	−27.1622	−	2.42385i	−1.06539	−	0.0950713i
$651$	−2.35793	−	8.79992i	−0.0924146	−	0.344896i
$652$			20.2377i			0.792571i
$653$	−25.8783	+	14.9408i	−1.01269	+	0.584679i	−0.911979	−	0.410236i	$-0.865446\pi$
$653$	−25.8783	+	14.9408i	−1.01269	+	0.584679i	−0.100715	+	0.994915i	$0.532113\pi$
$654$	0.798971	−	1.38386i	0.0312422	−	0.0541132i
$655$	3.11119	+	14.0915i	0.121564	+	0.550599i
$656$		−	12.0864i		−	0.471896i
$657$	20.8925	−	5.59813i	0.815095	−	0.218404i
$658$		−	56.3178i		−	2.19550i
$659$	9.79067	+	16.9579i	0.381390	+	0.660587i	0.991261	−	0.131913i	$-0.0421121\pi$
$659$	9.79067	+	16.9579i	0.381390	+	0.660587i	−0.609871	+	0.792501i	$0.708779\pi$
$660$	0.444368	+	2.01267i	0.0172970	+	0.0783430i
$661$	2.39638	−	8.94340i	0.0932082	−	0.347858i	−0.903533	−	0.428517i	$-0.859036\pi$
$661$	2.39638	−	8.94340i	0.0932082	−	0.347858i	0.996742	+	0.0806597i	$0.0257027\pi$
$662$	−28.5124	−	7.63989i	−1.10817	−	0.296933i
$663$	−0.221406	+	0.826299i	−0.00859870	+	0.0320908i
$664$	1.07135	−	0.287067i	0.0415764	−	0.0111404i
$665$	36.9286	+	23.5712i	1.43203	+	0.914050i
$666$	−15.3220	+	6.97045i	−0.593714	+	0.270100i
$667$	−4.97312	+	4.97312i	−0.192560	+	0.192560i
$668$	0.225059	+	0.129938i	0.00870780	+	0.00502745i
$669$	0.731573	+	1.26712i	0.0282843	+	0.0489898i
$670$	13.8744	−	12.6914i	0.536013	−	0.490311i
$671$	18.4807	+	4.95190i	0.713441	+	0.191166i
$672$			2.26917i			0.0875350i
$673$	−2.06660	+	7.71264i	−0.0796614	+	0.297300i	−0.994250	−	0.107086i	$-0.965848\pi$
$673$	−2.06660	+	7.71264i	−0.0796614	+	0.297300i	0.914588	+	0.404386i	$0.132515\pi$
$674$	5.13742	+	5.13742i	0.197886	+	0.197886i
$675$	8.92249	+	10.6709i	0.343427	+	0.410724i
$676$	16.7464			0.644093
$677$	6.77376	+	6.77376i	0.260337	+	0.260337i	0.825191	−	0.564854i	$-0.191068\pi$
$677$	6.77376	+	6.77376i	0.260337	+	0.260337i	−0.564854	+	0.825191i	$0.691068\pi$
$678$	3.53404	−	0.946944i	0.135724	−	0.0363672i
$679$	9.41910	−	35.1526i	0.361472	−	1.34903i
$680$	0.391197	−	0.612882i	0.0150017	−	0.0235030i
$681$	−5.47921	+	1.46815i	−0.209964	+	0.0562597i
$682$	−1.98570	−	7.41075i	−0.0760365	−	0.283772i
$683$	−17.5198	+	30.3452i	−0.670377	+	1.16113i	0.307420	+	0.951574i	$0.400534\pi$
$683$	−17.5198	+	30.3452i	−0.670377	+	1.16113i	−0.977797	+	0.209554i	$0.932799\pi$
$684$	−11.1327	−	2.98299i	−0.425669	−	0.114058i
$685$	23.0764	+	25.2273i	0.881702	+	0.963886i
$686$	36.9437	−	9.89904i	1.41052	−	0.377947i
$687$	−6.43429	+	1.72406i	−0.245483	+	0.0657771i
$688$	−1.22967	+	2.12985i	−0.0468806	+	0.0811997i
$689$	35.8510	+	35.8510i	1.36582	+	1.36582i
$690$	−2.09195	−	2.28694i	−0.0796393	−	0.0870625i
$691$	21.8014	+	12.5870i	0.829363	+	0.478833i	0.853635	−	0.520872i	$-0.174393\pi$
$691$	21.8014	+	12.5870i	0.829363	+	0.478833i	−0.0242713	+	0.999705i	$0.507727\pi$
$692$	−0.657398	+	0.657398i	−0.0249905	+	0.0249905i
$693$	−17.5909	+	17.5909i	−0.668223	+	0.668223i
$694$	16.1955	−	28.0514i	0.614771	−	1.06482i
$695$	−5.78739	−	3.69403i	−0.219528	−	0.140123i
$696$	−1.02241	+	0.590290i	−0.0387544	+	0.0223749i
$697$	3.93008			0.148862
$698$	12.2807	−	7.09028i	0.464832	−	0.268371i
$699$	4.04569	−	2.33578i	0.153022	−	0.0883473i
$700$	−4.04428	−	23.1711i	−0.152859	−	0.875785i
$701$	−3.09394	−	11.5467i	−0.116856	−	0.436114i	0.882563	−	0.470195i	$-0.155816\pi$
$701$	−3.09394	−	11.5467i	−0.116856	−	0.436114i	−0.999419	+	0.0340806i	$0.989150\pi$
$702$	−10.7288	−	10.7288i	−0.404931	−	0.404931i
$703$	8.88761	−	23.7234i	0.335203	−	0.894746i
$704$			1.91095i			0.0720217i
$705$	5.95240	+	11.4587i	0.224180	+	0.431560i
$706$	−23.7720	+	13.7248i	−0.894673	+	0.516540i
$707$	3.64974	−	13.6210i	0.137263	−	0.512271i
$708$	1.16670	+	2.02078i	0.0438471	+	0.0759454i
$709$	−32.8380	−	32.8380i	−1.23326	−	1.23326i	−0.962706	−	0.270551i	$-0.912794\pi$
$709$	−32.8380	−	32.8380i	−1.23326	−	1.23326i	−0.270551	−	0.962706i	$-0.587206\pi$
$710$	1.32195	−	29.6869i	0.0496119	−	1.11413i
$711$	−17.4964	+	17.4964i	−0.656167	+	0.656167i
$712$	0.363814	+	1.35777i	0.0136345	+	0.0508847i
$713$	8.15785	+	8.15785i	0.305514	+	0.305514i
$714$	−0.737852			−0.0276134
$715$	10.7432	+	20.6812i	0.401773	+	0.773435i
$716$	−3.03386	−	0.812920i	−0.113381	−	0.0303802i
$717$	−4.90221			−0.183076
$718$	−4.96924	−	2.86899i	−0.185450	−	0.107070i
$719$	37.1722	+	21.4614i	1.38629	+	0.800375i	0.992895	−	0.118995i	$-0.0379673\pi$
$719$	37.1722	+	21.4614i	1.38629	+	0.800375i	0.393395	+	0.919370i	$0.371301\pi$
$720$	2.85251	+	5.49124i	0.106307	+	0.204646i
$721$	14.8903	−	55.5714i	0.554545	−	2.06959i
$722$	−1.43267	+	0.827155i	−0.0533186	+	0.0307835i
$723$	−10.1029	−	5.83292i	−0.375731	−	0.216928i
$724$	−5.70435	+	9.88022i	−0.212000	+	0.367196i
$725$	9.38808	−	7.84984i	0.348665	−	0.291536i
$726$	−2.50636	+	2.50636i	−0.0930196	+	0.0930196i
$727$	−19.0390	−	32.9764i	−0.706116	−	1.22303i	−0.966287	−	0.257466i	$-0.917112\pi$
$727$	−19.0390	−	32.9764i	−0.706116	−	1.22303i	0.260172	−	0.965562i	$-0.416221\pi$
$728$	6.64059	+	24.7830i	0.246117	+	0.918520i
$729$		−	15.2351i		−	0.564263i
$730$	17.0662	−	3.76796i	0.631648	−	0.139458i
$731$	−0.692550	−	0.399844i	−0.0256149	−	0.0147888i
$732$	−4.82946			−0.178502
$733$	24.2354	+	6.49385i	0.895154	+	0.239856i	0.676934	−	0.736044i	$-0.263308\pi$
$733$	24.2354	+	6.49385i	0.895154	+	0.239856i	0.218220	+	0.975900i	$0.429975\pi$
$734$	25.3513	−	25.3513i	0.935734	−	0.935734i
$735$	−12.0415	+	11.0148i	−0.444156	+	0.406287i
$736$	−1.43679	−	2.48858i	−0.0529606	−	0.0917305i
$737$	−15.5219	−	4.15909i	−0.571757	−	0.153202i
$738$	−16.7236	+	28.9661i	−0.615603	+	1.06626i
$739$	0.687987			0.0253080			0.0126540	−	0.999920i	$-0.495972\pi$
$739$	0.687987			0.0253080			0.0126540	+	0.999920i	$0.495972\pi$
$740$	−12.6188	+	5.07597i	−0.463877	+	0.186596i
$741$	10.9569			0.402510
$742$	−21.8656	+	37.8724i	−0.802713	+	1.39034i
$743$	0.204732	+	0.0548577i	0.00751088	+	0.00201254i	0.262573	−	0.964912i	$-0.415429\pi$
$743$	0.204732	+	0.0548577i	0.00751088	+	0.00201254i	−0.255062	+	0.966925i	$0.582096\pi$
$744$	0.968304	+	1.67715i	0.0354998	+	0.0614874i
$745$	53.0094	+	2.36049i	1.94212	+	0.0864817i
$746$	7.62090	−	7.62090i	0.279021	−	0.279021i
$747$	−2.96477	−	0.794409i	−0.108475	−	0.0290659i
$748$	−0.621373			−0.0227197
$749$	38.0691	+	21.9792i	1.39102	+	0.803103i
$750$	3.27189	+	4.28706i	0.119473	+	0.156541i
$751$			44.1323i			1.61041i	0.592997	+	0.805204i	$0.297944\pi$
$751$			44.1323i			1.61041i	−0.592997	+	0.805204i	$0.702056\pi$
$752$	3.09848	+	11.5637i	0.112990	+	0.421684i
$753$	−1.35478	−	2.34655i	−0.0493711	−	0.0855132i
$754$	−9.43897	+	9.43897i	−0.343747	+	0.343747i
$755$	14.2568	+	27.4452i	0.518859	+	0.998832i
$756$	6.54351	−	11.3337i	0.237985	−	0.412202i
$757$	8.61975	+	4.97661i	0.313290	+	0.180878i	0.648398	−	0.761302i	$-0.275439\pi$
$757$	8.61975	+	4.97661i	0.313290	+	0.180878i	−0.335108	+	0.942180i	$0.608773\pi$
$758$	3.24154	−	1.87150i	0.117738	−	0.0679760i
$759$	−0.685552	+	2.55852i	−0.0248840	+	0.0928682i
$760$	−8.87935	−	2.80812i	−0.322088	−	0.101861i
$761$	37.8033	+	21.8257i	1.37037	+	0.791182i	0.990974	−	0.134054i	$-0.0427994\pi$
$761$	37.8033	+	21.8257i	1.37037	+	0.791182i	0.379393	+	0.925236i	$0.376133\pi$
$762$	2.44004	+	1.40876i	0.0883934	+	0.0510340i
$763$	15.5841			0.564182
$764$	−12.2679	−	3.28717i	−0.443837	−	0.118926i
$765$	−1.78555	+	0.927534i	−0.0645569	+	0.0335351i
$766$	30.0103			1.08431
$767$	18.6559	+	18.6559i	0.673627	+	0.673627i
$768$	−0.124844	−	0.465926i	−0.00450494	−	0.0168127i
$769$	1.12417	−	1.12417i	0.0405388	−	0.0405388i	−0.686547	−	0.727086i	$-0.740874\pi$
$769$	1.12417	−	1.12417i	0.0405388	−	0.0405388i	0.727086	+	0.686547i	$0.240874\pi$
$770$	−14.8321	+	13.5675i	−0.534513	+	0.488939i
$771$	1.69636	+	1.69636i	0.0610929	+	0.0610929i
$772$	10.7681	+	18.6508i	0.387551	+	0.671258i
$773$	−13.5600	+	50.6065i	−0.487718	+	1.82019i	0.0797772	+	0.996813i	$0.474579\pi$
$773$	−13.5600	+	50.6065i	−0.487718	+	1.82019i	−0.567495	+	0.823377i	$0.692088\pi$
$774$	5.89398	−	3.40289i	0.211855	−	0.122314i
$775$	−12.8768	−	15.4001i	−0.462548	−	0.553188i
$776$			7.73607i			0.277709i
$777$	11.2318	+	8.02271i	0.402938	+	0.287813i
$778$	−9.26841	−	9.26841i	−0.332289	−	0.332289i
$779$	−13.0284	−	48.6226i	−0.466790	−	1.74208i
$780$	−3.97052	−	4.34061i	−0.142167	−	0.155419i
$781$	−21.9933	+	12.6979i	−0.786983	+	0.454365i
$782$	0.809199	−	0.467191i	0.0289369	−	0.0167067i
$783$	6.80879			0.243326
$784$	−13.1032	+	7.56512i	−0.467971	+	0.270183i
$785$	14.4402	−	3.18817i	0.515391	−	0.113791i
$786$	−1.55650	+	2.69594i	−0.0555186	+	0.0961610i
$787$	6.36141	−	6.36141i	0.226760	−	0.226760i	−0.584578	−	0.811338i	$-0.698740\pi$
$787$	6.36141	−	6.36141i	0.226760	−	0.226760i	0.811338	+	0.584578i	$0.198740\pi$
$788$	12.6430	−	12.6430i	0.450389	−	0.450389i
$789$	1.13473	+	0.655139i	0.0403976	+	0.0233236i
$790$	−14.7525	+	13.4946i	−0.524869	+	0.480117i
$791$	25.2309	+	25.2309i	0.897109	+	0.897109i
$792$	2.64411	−	4.57974i	0.0939545	−	0.162734i
$793$	−52.7457	+	14.1332i	−1.87306	+	0.501884i
$794$	−28.4106	+	7.61259i	−1.00825	+	0.270161i
$795$	0.446042	−	10.0168i	0.0158195	−	0.355258i
$796$	15.0543	+	4.03378i	0.533584	+	0.142974i
$797$	2.06615	−	3.57868i	0.0731869	−	0.126763i	−0.827109	−	0.562041i	$-0.810016\pi$
$797$	2.06615	−	3.57868i	0.0731869	−	0.126763i	0.900296	+	0.435277i	$0.143350\pi$
$798$	2.44601	+	9.12863i	0.0865878	+	0.323150i
$799$	−3.76010	+	1.00752i	−0.133023	+	0.0356433i
$800$	2.10523	+	4.53520i	0.0744311	+	0.160343i
$801$	1.00679	−	3.75740i	0.0355733	−	0.132761i
$802$	−22.0151	+	5.89894i	−0.777382	+	0.208299i
$803$	−10.5614	−	10.5614i	−0.372703	−	0.372703i
$804$	4.05625			0.143053
$805$	9.11453	−	28.8204i	0.321245	−	1.01579i
$806$	15.4836	+	15.4836i	0.545386	+	0.545386i
$807$	0.109350	−	0.408100i	0.00384930	−	0.0143658i
$808$			2.99759i			0.105455i
$809$	−24.6333	−	6.60047i	−0.866060	−	0.232060i	−0.201677	−	0.979452i	$-0.564639\pi$
$809$	−24.6333	−	6.60047i	−0.866060	−	0.232060i	−0.664383	+	0.747392i	$0.731306\pi$
$810$	0.692338	−	15.5478i	0.0243263	−	0.546294i
$811$	10.4650	+	18.1260i	0.367477	+	0.636489i	0.989170	−	0.146772i	$-0.0468883\pi$
$811$	10.4650	+	18.1260i	0.367477	+	0.636489i	−0.621693	+	0.783261i	$0.713555\pi$
$812$	−9.97116	−	5.75685i	−0.349919	−	0.202026i
$813$	0.928148	−	0.928148i	0.0325516	−	0.0325516i
$814$	9.45872	+	6.75623i	0.331528	+	0.236806i
$815$	24.3475	−	38.1448i	0.852855	−	1.33616i
$816$	0.151502	−	0.0405950i	0.00530365	−	0.00142111i
$817$	−2.65100	+	9.89367i	−0.0927468	+	0.346136i
$818$	−15.1503	−	4.05950i	−0.529717	−	0.141937i
$819$	18.3767	−	68.5827i	0.642133	−	2.39647i
$820$	−14.5409	+	22.7810i	−0.507789	+	0.795546i
$821$	−23.3330	−	40.4139i	−0.814326	−	1.41045i	−0.909811	−	0.415024i	$-0.863773\pi$
$821$	−23.3330	−	40.4139i	−0.814326	−	1.41045i	0.0954843	−	0.995431i	$-0.469560\pi$
$822$			7.37536i			0.257245i
$823$	7.38766	−	1.97952i	0.257517	−	0.0690016i	−0.127750	−	0.991806i	$-0.540776\pi$
$823$	7.38766	−	1.97952i	0.257517	−	0.0690016i	0.385268	+	0.922805i	$0.374109\pi$
$824$			12.2297i			0.426041i
$825$	1.58383	−	4.32816i	0.0551418	−	0.150687i
$826$	−11.3783	+	19.7078i	−0.395902	+	0.685722i
$827$	20.3522	−	11.7504i	0.707716	−	0.408600i	−0.102499	−	0.994733i	$-0.532684\pi$
$827$	20.3522	−	11.7504i	0.707716	−	0.408600i	0.810215	+	0.586133i	$0.199350\pi$
$828$			7.95211i			0.276355i
$829$	8.07674	+	30.1428i	0.280517	+	1.04690i	0.952054	+	0.305931i	$0.0989678\pi$
$829$	8.07674	+	30.1428i	0.280517	+	1.04690i	−0.671537	+	0.740971i	$0.734366\pi$
$830$	−2.36468	−	0.747836i	−0.0820793	−	0.0259578i
$831$	2.65378	+	9.90404i	0.0920586	+	0.343567i
$832$	−2.72701	−	4.72333i	−0.0945422	−	0.163752i
$833$	−2.45991	−	4.26069i	−0.0852308	−	0.147624i
$834$	−0.383334	−	1.43062i	−0.0132738	−	0.0495384i
$835$	−0.267875	−	0.515675i	−0.00927021	−	0.0178457i
$836$	2.05988	+	7.68757i	0.0712424	+	0.265880i
$837$		−	11.1691i		−	0.386059i
$838$	−27.4386	+	15.8417i	−0.947850	+	0.547242i
$839$	−4.31759	+	7.47828i	−0.149060	+	0.258179i	−0.930880	−	0.365325i	$-0.880958\pi$
$839$	−4.31759	+	7.47828i	−0.149060	+	0.258179i	0.781820	+	0.623504i	$0.214291\pi$
$840$	2.72997	−	4.27701i	0.0941930	−	0.147571i
$841$			23.0098i			0.793440i
$842$	15.6544	−	4.19458i	0.539485	−	0.144555i
$843$			1.32304i			0.0455679i
$844$	9.48450	+	16.4276i	0.326470	+	0.565462i
$845$	−31.5643	−	20.1472i	−1.08585	−	0.693084i
$846$	8.57451	−	32.0005i	0.294798	−	1.10020i
$847$	−33.3904	−	8.94694i	−1.14731	−	0.307420i
$848$	2.40600	−	8.97931i	0.0826223	−	0.308351i
$849$	0.859737	−	0.230366i	0.0295061	−	0.00790614i
$850$	−1.47468	+	0.684546i	−0.0505813	+	0.0234797i
$851$	−17.3977	−	1.68675i	−0.596384	−	0.0578211i
$852$	4.53282	−	4.53282i	0.155292	−	0.155292i
$853$	−13.9856	−	8.07457i	−0.478857	−	0.276468i	0.241083	−	0.970504i	$-0.422497\pi$
$853$	−13.9856	−	8.07457i	−0.478857	−	0.276468i	−0.719940	+	0.694036i	$0.755831\pi$
$854$	−23.5499	−	40.7896i	−0.805861	−	1.39579i
$855$	17.3946	+	19.0159i	0.594881	+	0.650330i
$856$	−9.02595	−	2.41850i	−0.308501	−	0.0826625i
$857$			58.0749i			1.98380i	0.127017	+	0.991901i	$0.459460\pi$
$857$			58.0749i			1.98380i	−0.127017	+	0.991901i	$0.540540\pi$
$858$	−1.30118	+	4.85606i	−0.0444214	+	0.165783i
$859$	−14.5696	−	14.5696i	−0.497109	−	0.497109i	0.413428	−	0.910537i	$-0.364331\pi$
$859$	−14.5696	−	14.5696i	−0.497109	−	0.497109i	−0.910537	+	0.413428i	$0.864331\pi$
$860$	4.88009	−	2.53504i	0.166410	−	0.0864440i
$861$	27.4261			0.934680
$862$	13.9175	+	13.9175i	0.474030	+	0.474030i
$863$	−25.8546	+	6.92772i	−0.880101	+	0.235822i	−0.670451	−	0.741954i	$-0.733899\pi$
$863$	−25.8546	+	6.92772i	−0.880101	+	0.235822i	−0.209650	+	0.977776i	$0.567233\pi$
$864$	−0.720019	+	2.68715i	−0.0244955	+	0.0914186i
$865$	2.02999	−	0.448191i	0.0690216	−	0.0152389i
$866$	−6.57517	+	1.76181i	−0.223433	+	0.0598688i
$867$	−2.10916	−	7.87148i	−0.0716307	−	0.267329i
$868$	−9.44348	+	16.3566i	−0.320532	+	0.555179i
$869$	16.5043	+	4.42232i	0.559870	+	0.150017i
$870$	2.63724	+	0.117435i	0.0894109	+	0.00398143i
$871$	44.3010	−	11.8704i	1.50108	−	0.402213i
$872$	−3.19987	+	0.857402i	−0.108361	+	0.0290353i
$873$	10.7041	−	18.5401i	0.362279	−	0.627486i
$874$	−8.46258	−	8.46258i	−0.286251	−	0.286251i
$875$	−20.2537	+	48.5393i	−0.684701	+	1.64093i
$876$	3.26505	+	1.88508i	0.110316	+	0.0636909i
$877$	−25.0150	+	25.0150i	−0.844697	+	0.844697i	−0.989465	−	0.144769i	$-0.953756\pi$
$877$	−25.0150	+	25.0150i	−0.844697	+	0.844697i	0.144769	+	0.989465i	$0.453756\pi$
$878$	12.5654	−	12.5654i	0.424060	−	0.424060i
$879$	−0.798536	+	1.38310i	−0.0269339	+	0.0466510i
$880$	2.29901	−	3.60183i	0.0774997	−	0.121418i
$881$	−10.7234	+	6.19117i	−0.361281	+	0.208586i	−0.669643	−	0.742684i	$-0.733553\pi$
$881$	−10.7234	+	6.19117i	−0.361281	+	0.208586i	0.308362	+	0.951269i	$0.400219\pi$
$882$	41.8703			1.40985
$883$	−45.1461	+	26.0651i	−1.51929	+	0.877161i	−0.519545	+	0.854443i	$0.673899\pi$
$883$	−45.1461	+	26.0651i	−1.51929	+	0.877161i	−0.999742	+	0.0227176i	$0.992768\pi$
$884$	1.53586	−	0.886728i	0.0516565	−	0.0298239i
$885$	0.232109	−	5.21246i	0.00780225	−	0.175215i
$886$	1.58459	+	5.91376i	0.0532352	+	0.198677i
$887$	−3.12493	−	3.12493i	−0.104925	−	0.104925i	0.652696	−	0.757620i	$-0.273638\pi$
$887$	−3.12493	−	3.12493i	−0.104925	−	0.104925i	−0.757620	+	0.652696i	$0.773638\pi$
$888$	−2.74761	−	1.02935i	−0.0922037	−	0.0345427i
$889$			27.4781i			0.921586i
$890$	0.947769	−	2.99688i	0.0317693	−	0.100456i
$891$	−11.5185	+	6.65018i	−0.385883	+	0.222790i
$892$	0.785075	−	2.92994i	0.0262862	−	0.0981016i
$893$	24.9298	+	43.1797i	0.834243	+	1.44495i
$894$	8.09387	+	8.09387i	0.270700	+	0.270700i
$895$	4.74033	+	5.18218i	0.158452	+	0.173221i
$896$	3.32643	−	3.32643i	0.111128	−	0.111128i
$897$	−1.95663	−	7.30224i	−0.0653299	−	0.243815i
$898$	6.31169	+	6.31169i	0.210624	+	0.210624i
$899$	−9.82632			−0.327726
$900$	1.22984	−	13.7819i	0.0409947	−	0.459396i
$901$	2.91975	+	0.782345i	0.0972710	+	0.0260637i
$902$	23.0966			0.769032
$903$	−4.83298	−	2.79032i	−0.160831	−	0.0928560i
$904$	−6.56880	−	3.79250i	−0.218475	−	0.126137i
$905$	22.6384	−	11.7599i	0.752526	−	0.390911i
$906$	−1.72673	+	6.44426i	−0.0573669	+	0.214096i
$907$	17.3281	−	10.0044i	0.575370	−	0.332190i	−0.183922	−	0.982941i	$-0.558879\pi$
$907$	17.3281	−	10.0044i	0.575370	−	0.332190i	0.759291	+	0.650751i	$0.225546\pi$
$908$	10.1843	+	5.87992i	0.337979	+	0.195132i
$909$	4.14766	−	7.18396i	0.137569	−	0.238277i
$910$	17.2993	−	54.7011i	0.573468	−	1.81332i
$911$	30.9529	−	30.9529i	1.02551	−	1.02551i	0.0258481	−	0.999666i	$-0.491771\pi$
$911$	30.9529	−	30.9529i	1.02551	−	1.02551i	0.999666	−	0.0258481i	$-0.00822863\pi$
$912$	−1.00447	−	1.73980i	−0.0332615	−	0.0576105i
$913$	0.548571	+	2.04730i	0.0181551	+	0.0677556i
$914$		−	9.52956i		−	0.315210i
$915$	9.10276	+	5.81020i	0.300928	+	0.192079i
$916$	11.9595	+	6.90484i	0.395154	+	0.228142i
$917$	−30.3598			−1.00257
$918$	−0.873764	−	0.234124i	−0.0288385	−	0.00772726i
$919$	−0.705891	+	0.705891i	−0.0232852	+	0.0232852i	−0.718654	−	0.695368i	$-0.755241\pi$
$919$	−0.705891	+	0.705891i	−0.0232852	+	0.0232852i	0.695368	+	0.718654i	$0.255241\pi$
$920$	−0.285842	+	6.41914i	−0.00942393	+	0.211633i
$921$	7.83694	+	13.5740i	0.258236	+	0.447278i
$922$	10.4099	+	2.78931i	0.342831	+	0.0918612i
$923$	36.2408	−	62.7710i	1.19288	−	2.06613i
$924$	−4.33626			−0.142653
$925$	29.8912	+	5.61398i	0.982816	+	0.184587i
$926$	14.8932			0.489420
$927$	16.9217	−	29.3093i	0.555783	−	0.962644i
$928$	2.36410	+	0.633459i	0.0776054	+	0.0207943i
$929$	27.7665	+	48.0930i	0.910989	+	1.57788i	0.812669	+	0.582725i	$0.198014\pi$
$929$	27.7665	+	48.0930i	0.910989	+	1.57788i	0.0983200	+	0.995155i	$0.468653\pi$
$930$	0.192640	−	4.32610i	0.00631690	−	0.141858i
$931$	−44.5581	+	44.5581i	−1.46033	+	1.46033i
$932$	−9.35476	−	2.50660i	−0.306425	−	0.0821064i
$933$	−3.94334			−0.129099
$934$	−12.9457	−	7.47419i	−0.423596	−	0.244563i
$935$	1.17119	+	0.747557i	0.0383019	+	0.0244477i
$936$			15.0931i			0.493333i
$937$	1.90979	+	7.12742i	0.0623900	+	0.232843i	0.990079	−	0.140511i	$-0.0448745\pi$
$937$	1.90979	+	7.12742i	0.0623900	+	0.232843i	−0.927689	+	0.373354i	$0.878208\pi$
$938$	19.7795	+	34.2591i	0.645823	+	1.11860i
$939$	11.3592	−	11.3592i	0.370694	−	0.370694i
$940$	8.07183	−	25.5234i	0.263274	−	0.832481i
$941$	−5.21250	+	9.02832i	−0.169923	+	0.294315i	−0.938393	−	0.345571i	$-0.887685\pi$
$941$	−5.21250	+	9.02832i	−0.169923	+	0.294315i	0.768470	+	0.639886i	$0.221019\pi$
$942$	2.76265	+	1.59502i	0.0900120	+	0.0519684i
$943$	−30.0781	+	17.3656i	−0.979478	+	0.565502i
$944$	1.25202	−	4.67260i	0.0407497	−	0.152080i
$945$	−25.9687	+	13.4899i	−0.844762	+	0.438825i
$946$	−4.07003	−	2.34983i	−0.132328	−	0.0763997i
$947$	−26.6694	−	15.3976i	−0.866637	−	0.500353i	−0.000408080	−	1.00000i	$-0.500130\pi$
$947$	−26.6694	−	15.3976i	−0.866637	−	0.500353i	−0.866229	+	0.499647i	$0.833463\pi$
$948$	−4.31298			−0.140079
$949$	41.1763	+	11.0332i	1.33664	+	0.358152i
$950$	13.3578	+	15.9754i	0.433384	+	0.518309i
$951$	1.39989			0.0453947
$952$	1.08164	+	1.08164i	0.0350560	+	0.0350560i
$953$	−3.13576	−	11.7028i	−0.101577	−	0.379091i	0.896357	−	0.443333i	$-0.146204\pi$
$953$	−3.13576	−	11.7028i	−0.101577	−	0.379091i	−0.997934	+	0.0642413i	$0.979537\pi$
$954$	−18.1905	+	18.1905i	−0.588939	+	0.588939i
$955$	19.1683	+	20.9550i	0.620271	+	0.678086i
$956$	7.18627	+	7.18627i	0.232421	+	0.232421i
$957$	−1.12801	−	1.95378i	−0.0364635	−	0.0631567i
$958$	−3.14783	+	11.7479i	−0.101702	+	0.379557i
$959$	−62.2922	+	35.9644i	−2.01152	+	1.16135i
$960$	−0.325231	+	1.02839i	−0.0104968	+	0.0331912i
$961$		−	14.8810i		−	0.480033i
$962$	−33.0207	−	3.20145i	−1.06463	−	0.103219i
$963$	18.2850	+	18.2850i	0.589225	+	0.589225i
$964$	6.25949	+	23.3607i	0.201605	+	0.752399i
$965$	2.14226	−	48.1085i	0.0689617	−	1.54867i
$966$	5.64701	−	3.26030i	0.181690	−	0.104899i
$967$	28.0117	−	16.1726i	0.900795	−	0.520074i	0.0233370	−	0.999728i	$-0.492571\pi$
$967$	28.0117	−	16.1726i	0.900795	−	0.520074i	0.877458	+	0.479653i	$0.159238\pi$
$968$	7.34827			0.236182
$969$	0.565721	−	0.326619i	0.0181736	−	0.0104925i
$970$	9.30705	−	14.5812i	0.298832	−	0.468175i
$971$	9.25347	−	16.0275i	0.296958	−	0.514346i	−0.678481	−	0.734618i	$-0.737361\pi$
$971$	9.25347	−	16.0275i	0.296958	−	0.514346i	0.975438	+	0.220272i	$0.0706946\pi$
$972$	8.27534	−	8.27534i	0.265432	−	0.265432i
$973$	10.2138	−	10.2138i	0.327439	−	0.327439i
$974$	−18.4138	−	10.6312i	−0.590016	−	0.340646i
$975$	2.26172	+	12.9582i	0.0724329	+	0.414994i
$976$	7.07964	+	7.07964i	0.226614	+	0.226614i
$977$	1.28381	−	2.22362i	0.0410726	−	0.0711399i	−0.844758	−	0.535148i	$-0.820256\pi$
$977$	1.28381	−	2.22362i	0.0410726	−	0.0711399i	0.885831	+	0.464008i	$0.153589\pi$
$978$	9.42928	−	2.52657i	0.301515	−	0.0807907i
$979$	−2.59464	+	0.695231i	−0.0829249	+	0.0222197i
$980$	33.7988	+	1.50505i	1.07966	+	0.0480770i
$981$	8.85508	+	2.37271i	0.282721	+	0.0757548i
$982$	11.8093	−	20.4542i	0.376849	−	0.652721i
$983$	−3.31406	−	12.3683i	−0.105702	−	0.394486i	0.892722	−	0.450608i	$-0.148793\pi$
$983$	−3.31406	−	12.3683i	−0.105702	−	0.394486i	−0.998424	+	0.0561225i	$0.982126\pi$
$984$	−5.63138	+	1.50892i	−0.179522	+	0.0481028i
$985$	−39.0405	+	8.61957i	−1.24393	+	0.274642i
$986$	−0.205978	+	0.768721i	−0.00655968	+	0.0244811i
$987$	−26.2399	+	7.03097i	−0.835226	+	0.223798i
$988$	−16.0619	−	16.0619i	−0.510999	−	0.510999i
$989$	7.06707			0.224720
$990$	−10.4935	+	5.45100i	−0.333505	+	0.173244i
$991$	−39.6203	−	39.6203i	−1.25858	−	1.25858i	−0.951771	−	0.306808i	$-0.900739\pi$
$991$	−39.6203	−	39.6203i	−1.25858	−	1.25858i	−0.306808	−	0.951771i	$-0.599261\pi$
$992$	1.03912	−	3.87804i	0.0329920	−	0.123128i
$993$			14.2385i			0.451845i
$994$	60.3876	+	16.1808i	1.91538	+	0.513224i
$995$	−23.5219	−	25.7144i	−0.745695	−	0.815202i
$996$	−0.267504	−	0.463331i	−0.00847619	−	0.0146812i
$997$	−44.4320	−	25.6529i	−1.40718	−	0.812434i	−0.412062	−	0.911156i	$-0.635191\pi$
$997$	−44.4320	−	25.6529i	−1.40718	−	0.812434i	−0.995115	+	0.0987219i	$0.968525\pi$
$998$	−21.5164	+	21.5164i	−0.681089	+	0.681089i
$999$	10.7550	+	13.0644i	0.340275	+	0.413340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.e.273.4	yes	16
5.2	odd	4		370.2.r.e.347.4	yes	16
37.8	odd	12		370.2.r.e.193.4	yes	16
185.82	even	12	inner	370.2.q.e.267.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.e.267.4	✓	16	185.82	even	12	inner
370.2.q.e.273.4	yes	16	1.1	even	1	trivial
370.2.r.e.193.4	yes	16	37.8	odd	12
370.2.r.e.347.4	yes	16	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.465926 + 0.124844i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.0994727 + 2.23385i) q^{5} +(-0.341081 + 0.341081i) q^{6} +(-4.54399 - 1.21756i) q^{7} +1.00000 q^{8} +(-2.39658 - 1.38366i) q^{9} +(-1.88484 - 1.20307i) q^{10} +1.91095i q^{11} +(-0.124844 - 0.465926i) q^{12} +(-2.72701 - 4.72333i) q^{13} +(3.32643 - 3.32643i) q^{14} +(-0.325231 + 1.02839i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.281601 - 0.162582i) q^{17} +(2.39658 - 1.38366i) q^{18} +(-1.07793 + 4.02290i) q^{19} +(1.98431 - 1.03078i) q^{20} +(-1.96515 - 1.13458i) q^{21} +(-1.65493 - 0.955475i) q^{22} +2.87357 q^{23} +(0.465926 + 0.124844i) q^{24} +(-4.98021 - 0.444415i) q^{25} +5.45403 q^{26} +(-1.96713 - 1.96713i) q^{27} +(1.21756 + 4.54399i) q^{28} +(-1.73064 + 1.73064i) q^{29} +(-0.727998 - 0.795854i) q^{30} +(2.83892 + 2.83892i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.238572 + 0.890361i) q^{33} +(0.281601 - 0.162582i) q^{34} +(3.17185 - 10.0295i) q^{35} +2.76733i q^{36} +(-6.05437 - 0.586988i) q^{37} +(-2.94497 - 2.94497i) q^{38} +(-0.680905 - 2.54117i) q^{39} +(-0.0994727 + 2.23385i) q^{40} +(-10.4672 + 6.04322i) q^{41} +(1.96515 - 1.13458i) q^{42} +2.45934 q^{43} +(1.65493 - 0.955475i) q^{44} +(3.32930 - 5.21596i) q^{45} +(-1.43679 + 2.48858i) q^{46} +(8.46521 - 8.46521i) q^{47} +(-0.341081 + 0.341081i) q^{48} +(13.1032 + 7.56512i) q^{49} +(2.87498 - 4.09078i) q^{50} +(-0.110908 - 0.110908i) q^{51} +(-2.72701 + 4.72333i) q^{52} +(-8.97931 + 2.40600i) q^{53} +(2.68715 - 0.720019i) q^{54} +(-4.26879 - 0.190087i) q^{55} +(-4.54399 - 1.21756i) q^{56} +(-1.00447 + 1.73980i) q^{57} +(-0.633459 - 2.36410i) q^{58} +(-4.67260 + 1.25202i) q^{59} +(1.05323 - 0.232537i) q^{60} +(2.59133 - 9.67096i) q^{61} +(-3.87804 + 1.03912i) q^{62} +(9.20531 + 9.20531i) q^{63} +1.00000 q^{64} +(10.8225 - 5.62191i) q^{65} +(-0.651790 - 0.651790i) q^{66} +(-2.17645 + 8.12261i) q^{67} +0.325164i q^{68} +(1.33887 + 0.358749i) q^{69} +(7.09987 + 7.76164i) q^{70} +(6.64478 + 11.5091i) q^{71} +(-2.39658 - 1.38366i) q^{72} +(-5.52677 + 5.52677i) q^{73} +(3.53553 - 4.94975i) q^{74} +(-2.26493 - 0.828816i) q^{75} +(4.02290 - 1.07793i) q^{76} +(2.32669 - 8.68333i) q^{77} +(2.54117 + 0.680905i) q^{78} +(2.31420 - 8.63670i) q^{79} +(-1.88484 - 1.20307i) q^{80} +(3.48004 + 6.02761i) q^{81} -12.0864i q^{82} +(1.07135 - 0.287067i) q^{83} +2.26917i q^{84} +(0.391197 - 0.612882i) q^{85} +(-1.22967 + 2.12985i) q^{86} +(-1.02241 + 0.590290i) q^{87} +1.91095i q^{88} +(0.363814 + 1.35777i) q^{89} +(2.85251 + 5.49124i) q^{90} +(6.64059 + 24.7830i) q^{91} +(-1.43679 - 2.48858i) q^{92} +(0.968304 + 1.67715i) q^{93} +(3.09848 + 11.5637i) q^{94} +(-8.87935 - 2.80812i) q^{95} +(-0.124844 - 0.465926i) q^{96} +7.73607i q^{97} +(-13.1032 + 7.56512i) q^{98} +(2.64411 - 4.57974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9} - 4 q^{10} + 16 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 24 q^{18} - 24 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{23} - 8 q^{24}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9 - 4 * q^10 + 16 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 24 * q^18 - 24 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^23 - 8 * q^24 + 32 * q^25 + 8 * q^26 + 16 * q^27 + 16 * q^29 - 4 * q^30 + 24 * q^31 - 8 * q^32 + 12 * q^33 - 20 * q^35 - 4 * q^40 - 36 * q^41 + 12 * q^42 - 16 * q^43 + 4 * q^45 + 4 * q^46 + 32 * q^47 - 8 * q^48 + 24 * q^49 - 16 * q^50 - 16 * q^51 - 4 * q^52 - 48 * q^53 - 8 * q^54 - 24 * q^55 + 20 * q^57 - 8 * q^58 - 8 * q^59 - 4 * q^60 + 8 * q^61 - 12 * q^62 + 16 * q^63 + 16 * q^64 + 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^69 + 28 * q^70 + 4 * q^71 - 24 * q^72 + 48 * q^73 - 36 * q^75 + 24 * q^76 - 60 * q^77 + 20 * q^79 - 4 * q^80 + 16 * q^81 + 24 * q^83 + 8 * q^85 + 8 * q^86 + 12 * q^87 - 8 * q^89 - 8 * q^90 - 8 * q^91 + 4 * q^92 + 36 * q^93 - 28 * q^94 + 28 * q^95 + 16 * q^96 - 24 * q^98 + 8 * q^99

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