LMFDB - Embedded newform 403.2.s.a.160.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(160,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 4]))

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

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

chi := DirichletCharacter("403.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			160.11
Character	$\chi$	$=$	403.160
Dual form			403.2.s.a.335.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01226 - 0.584427i) q^{2} +(0.506588 + 0.877437i) q^{3} +(-0.316890 - 0.548870i) q^{4} +(2.14676 - 1.23943i) q^{5} -1.18426i q^{6} +4.28486i q^{7} +3.07850i q^{8} +(0.986736 - 1.70908i) q^{9} +O(q^{10})$	\(q+(-1.01226 - 0.584427i) q^{2} +(0.506588 + 0.877437i) q^{3} +(-0.316890 - 0.548870i) q^{4} +(2.14676 - 1.23943i) q^{5} -1.18426i q^{6} +4.28486i q^{7} +3.07850i q^{8} +(0.986736 - 1.70908i) q^{9} -2.89744 q^{10} +3.51574i q^{11} +(0.321066 - 0.556102i) q^{12} +(-2.77344 + 2.30392i) q^{13} +(2.50419 - 4.33738i) q^{14} +(2.17505 + 1.25577i) q^{15} +(1.16538 - 2.01850i) q^{16} +3.41875 q^{17} +(-1.99766 + 1.15335i) q^{18} -1.30557i q^{19} +(-1.36058 - 0.785529i) q^{20} +(-3.75969 + 2.17066i) q^{21} +(2.05469 - 3.55884i) q^{22} +(1.09562 - 1.89767i) q^{23} +(-2.70119 + 1.55954i) q^{24} +(0.572396 - 0.991420i) q^{25} +(4.15391 - 0.711281i) q^{26} +5.03901 q^{27} +(2.35183 - 1.35783i) q^{28} +(-2.72073 + 4.71244i) q^{29} +(-1.46781 - 2.54232i) q^{30} +(4.54063 - 3.22221i) q^{31} +(2.97279 - 1.71634i) q^{32} +(-3.08484 + 1.78103i) q^{33} +(-3.46066 - 1.99801i) q^{34} +(5.31080 + 9.19857i) q^{35} -1.25075 q^{36} +(0.670031 - 0.386843i) q^{37} +(-0.763009 + 1.32157i) q^{38} +(-3.42653 - 1.26638i) q^{39} +(3.81561 + 6.60882i) q^{40} +6.77733i q^{41} +5.07437 q^{42} +10.8829 q^{43} +(1.92968 - 1.11410i) q^{44} -4.89198i q^{45} +(-2.21810 + 1.28062i) q^{46} +6.24759i q^{47} +2.36148 q^{48} -11.3600 q^{49} +(-1.15882 + 0.669048i) q^{50} +(1.73190 + 2.99974i) q^{51} +(2.14342 + 0.792170i) q^{52} +(-4.77562 - 8.27161i) q^{53} +(-5.10077 - 2.94493i) q^{54} +(4.35753 + 7.54747i) q^{55} -13.1909 q^{56} +(1.14555 - 0.661385i) q^{57} +(5.50815 - 3.18013i) q^{58} -10.2894i q^{59} -1.59176i q^{60} +(-7.29296 - 12.6318i) q^{61} +(-6.47944 + 0.608040i) q^{62} +(7.32315 + 4.22802i) q^{63} -8.67384 q^{64} +(-3.09837 + 8.38346i) q^{65} +4.16354 q^{66} +5.40704i q^{67} +(-1.08337 - 1.87645i) q^{68} +2.22012 q^{69} -12.4151i q^{70} +(0.697488 + 0.402695i) q^{71} +(5.26140 + 3.03767i) q^{72} +(13.1489 - 7.59150i) q^{73} -0.904325 q^{74} +1.15988 q^{75} +(-0.716586 + 0.413721i) q^{76} -15.0644 q^{77} +(2.72843 + 3.28446i) q^{78} +(1.10947 - 1.92166i) q^{79} -5.77766i q^{80} +(-0.407505 - 0.705820i) q^{81} +(3.96086 - 6.86041i) q^{82} +(-5.12515 + 2.95901i) q^{83} +(2.38282 + 1.37572i) q^{84} +(7.33925 - 4.23732i) q^{85} +(-11.0163 - 6.36025i) q^{86} -5.51315 q^{87} -10.8232 q^{88} +(-1.16803 - 0.674360i) q^{89} +(-2.85901 + 4.95194i) q^{90} +(-9.87194 - 11.8838i) q^{91} -1.38877 q^{92} +(5.12752 + 2.35178i) q^{93} +(3.65126 - 6.32417i) q^{94} +(-1.61817 - 2.80274i) q^{95} +(3.01197 + 1.73896i) q^{96} +(-14.5197 + 8.38298i) q^{97} +(11.4992 + 6.63909i) q^{98} +(6.00867 + 3.46911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9}+O(q^{10}) $ 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9	$ 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26} + 34 q^{27} - 33 q^{28} - 18 q^{29} - 31 q^{30} - 2 q^{31} + 36 q^{32} - 12 q^{33} + 9 q^{34} - 12 q^{35} - 16 q^{36} - 18 q^{37} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 98 q^{42} - 38 q^{43} + 42 q^{44} - 6 q^{46} + 54 q^{48} - 18 q^{49} - 51 q^{50} - 7 q^{51} + 41 q^{52} - 22 q^{53} + 18 q^{54} - 15 q^{55} - 50 q^{56} + 15 q^{57} - 12 q^{58} - 13 q^{61} - 23 q^{62} - 6 q^{63} - 38 q^{64} - 12 q^{65} - 52 q^{66} - 44 q^{68} + 32 q^{69} + 27 q^{71} - 15 q^{72} - 9 q^{73} + 38 q^{74} - 50 q^{75} + 126 q^{76} + 34 q^{77} + 14 q^{78} + 6 q^{79} - 11 q^{81} + 39 q^{82} - 54 q^{83} + 15 q^{84} - 33 q^{85} - 24 q^{86} + 28 q^{87} - 32 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 14 q^{93} - 43 q^{94} + 25 q^{95} + 36 q^{96} - 75 q^{97} + 93 q^{99}+O(q^{100}) $ 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9 + 2 * q^10 + 13 * q^12 + q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 - 12 * q^17 - 3 * q^20 - 9 * q^21 + 4 * q^22 + 10 * q^23 + 18 * q^24 + 19 * q^25 + 6 * q^26 + 34 * q^27 - 33 * q^28 - 18 * q^29 - 31 * q^30 - 2 * q^31 + 36 * q^32 - 12 * q^33 + 9 * q^34 - 12 * q^35 - 16 * q^36 - 18 * q^37 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 98 * q^42 - 38 * q^43 + 42 * q^44 - 6 * q^46 + 54 * q^48 - 18 * q^49 - 51 * q^50 - 7 * q^51 + 41 * q^52 - 22 * q^53 + 18 * q^54 - 15 * q^55 - 50 * q^56 + 15 * q^57 - 12 * q^58 - 13 * q^61 - 23 * q^62 - 6 * q^63 - 38 * q^64 - 12 * q^65 - 52 * q^66 - 44 * q^68 + 32 * q^69 + 27 * q^71 - 15 * q^72 - 9 * q^73 + 38 * q^74 - 50 * q^75 + 126 * q^76 + 34 * q^77 + 14 * q^78 + 6 * q^79 - 11 * q^81 + 39 * q^82 - 54 * q^83 + 15 * q^84 - 33 * q^85 - 24 * q^86 + 28 * q^87 - 32 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 14 * q^93 - 43 * q^94 + 25 * q^95 + 36 * q^96 - 75 * q^97 + 93 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.01226	−	0.584427i	−0.715774	−	0.413252i	0.0974212	−	0.995243i	$-0.468941\pi$
$2$	−1.01226	−	0.584427i	−0.715774	−	0.413252i	−0.813195	+	0.581991i	$0.802274\pi$
$3$	0.506588	+	0.877437i	0.292479	+	0.506588i	0.974395	−	0.224842i	$-0.0721865\pi$
$3$	0.506588	+	0.877437i	0.292479	+	0.506588i	−0.681916	+	0.731430i	$0.738853\pi$
$4$	−0.316890	−	0.548870i	−0.158445	−	0.274435i
$5$	2.14676	−	1.23943i	0.960062	−	0.554292i	0.0638698	−	0.997958i	$-0.479656\pi$
$5$	2.14676	−	1.23943i	0.960062	−	0.554292i	0.896192	+	0.443666i	$0.146322\pi$
$6$		−	1.18426i		−	0.483471i
$7$			4.28486i			1.61952i	0.586759	+	0.809762i	$0.300404\pi$
$7$			4.28486i			1.61952i	−0.586759	+	0.809762i	$0.699596\pi$
$8$			3.07850i			1.08842i
$9$	0.986736	−	1.70908i	0.328912	−	0.569692i
$10$	−2.89744			−0.916250
$11$			3.51574i			1.06004i	0.847986	+	0.530018i	$0.177815\pi$
$11$			3.51574i			1.06004i	−0.847986	+	0.530018i	$0.822185\pi$
$12$	0.321066	−	0.556102i	0.0926837	−	0.160533i
$13$	−2.77344	+	2.30392i	−0.769214	+	0.638991i
$13$	−2.77344	+	2.30392i	−0.769214	+	0.638991i
$14$	2.50419	−	4.33738i	0.669272	−	1.15921i
$15$	2.17505	+	1.25577i	0.561596	+	0.324238i
$16$	1.16538	−	2.01850i	0.291345	−	0.504625i
$17$	3.41875			0.829169			0.414584	−	0.910011i	$-0.363927\pi$
$17$	3.41875			0.829169			0.414584	+	0.910011i	$0.363927\pi$
$18$	−1.99766	+	1.15335i	−0.470853	+	0.271847i
$19$		−	1.30557i		−	0.299518i	−0.988723	−	0.149759i	$-0.952150\pi$
$19$		−	1.30557i		−	0.299518i	0.988723	−	0.149759i	$-0.0478497\pi$
$20$	−1.36058	−	0.785529i	−0.304234	−	0.175650i
$21$	−3.75969	+	2.17066i	−0.820432	+	0.473677i
$22$	2.05469	−	3.55884i	0.438062	−	0.758746i
$23$	1.09562	−	1.89767i	0.228453	−	0.395692i	−0.728897	−	0.684623i	$-0.759967\pi$
$23$	1.09562	−	1.89767i	0.228453	−	0.395692i	0.957350	+	0.288932i	$0.0933000\pi$
$24$	−2.70119	+	1.55954i	−0.551379	+	0.318339i
$25$	0.572396	−	0.991420i	0.114479	−	0.198284i
$26$	4.15391	−	0.711281i	0.814648	−	0.139494i
$27$	5.03901			0.969757
$28$	2.35183	−	1.35783i	0.444453	−	0.256605i
$29$	−2.72073	+	4.71244i	−0.505226	+	0.875077i	0.494756	+	0.869032i	$0.335258\pi$
$29$	−2.72073	+	4.71244i	−0.505226	+	0.875077i	−0.999982	+	0.00604524i	$0.998076\pi$
$30$	−1.46781	−	2.54232i	−0.267984	−	0.464162i
$31$	4.54063	−	3.22221i	0.815522	−	0.578726i
$31$	4.54063	−	3.22221i	0.815522	−	0.578726i
$32$	2.97279	−	1.71634i	0.525521	−	0.303410i
$33$	−3.08484	+	1.78103i	−0.537002	+	0.310038i
$34$	−3.46066	−	1.99801i	−0.593498	−	0.342656i
$35$	5.31080	+	9.19857i	0.897689	+	1.55484i
$36$	−1.25075			−0.208458
$37$	0.670031	−	0.386843i	0.110152	−	0.0635965i	−0.443912	−	0.896071i	$-0.646410\pi$
$37$	0.670031	−	0.386843i	0.110152	−	0.0635965i	0.554064	+	0.832474i	$0.313076\pi$
$38$	−0.763009	+	1.32157i	−0.123776	+	0.214387i
$39$	−3.42653	−	1.26638i	−0.548685	−	0.202784i
$40$	3.81561	+	6.60882i	0.603300	+	1.04495i
$41$			6.77733i			1.05844i	0.848484	+	0.529221i	$0.177516\pi$
$41$			6.77733i			1.05844i	−0.848484	+	0.529221i	$0.822484\pi$
$42$	5.07437			0.782992
$43$	10.8829			1.65962			0.829811	−	0.558044i	$-0.188448\pi$
$43$	10.8829			1.65962			0.829811	+	0.558044i	$0.188448\pi$
$44$	1.92968	−	1.11410i	0.290911	−	0.167957i
$45$		−	4.89198i		−	0.729253i
$46$	−2.21810	+	1.28062i	−0.327041	+	0.188817i
$47$			6.24759i			0.911304i	0.890158	+	0.455652i	$0.150594\pi$
$47$			6.24759i			0.911304i	−0.890158	+	0.455652i	$0.849406\pi$
$48$	2.36148			0.340850
$49$	−11.3600			−1.62286
$50$	−1.15882	+	0.669048i	−0.163883	+	0.0946177i
$51$	1.73190	+	2.99974i	0.242514	+	0.420047i
$52$	2.14342	+	0.792170i	0.297239	+	0.109854i
$53$	−4.77562	−	8.27161i	−0.655981	−	1.13619i	−0.981647	−	0.190708i	$-0.938922\pi$
$53$	−4.77562	−	8.27161i	−0.655981	−	1.13619i	0.325666	−	0.945485i	$-0.394412\pi$
$54$	−5.10077	−	2.94493i	−0.694127	−	0.400755i
$55$	4.35753	+	7.54747i	0.587569	+	1.01770i
$56$	−13.1909			−1.76271
$57$	1.14555	−	0.661385i	0.151732	−	0.0876026i
$58$	5.50815	−	3.18013i	0.723256	−	0.417572i
$59$		−	10.2894i		−	1.33956i	−0.742559	−	0.669781i	$-0.766388\pi$
$59$		−	10.2894i		−	1.33956i	0.742559	−	0.669781i	$-0.233612\pi$
$60$		−	1.59176i		−	0.205495i
$61$	−7.29296	−	12.6318i	−0.933768	−	1.61733i	−0.776816	−	0.629727i	$-0.783167\pi$
$61$	−7.29296	−	12.6318i	−0.933768	−	1.61733i	−0.156952	−	0.987606i	$-0.550167\pi$
$62$	−6.47944	+	0.608040i	−0.822889	+	0.0772211i
$63$	7.32315	+	4.22802i	0.922630	+	0.532681i
$64$	−8.67384			−1.08423
$65$	−3.09837	+	8.38346i	−0.384306	+	1.03984i
$66$	4.16354			0.512496
$67$			5.40704i			0.660575i	0.943880	+	0.330287i	$0.107146\pi$
$67$			5.40704i			0.660575i	−0.943880	+	0.330287i	$0.892854\pi$
$68$	−1.08337	−	1.87645i	−0.131378	−	0.227553i
$69$	2.22012			0.267271
$70$		−	12.4151i		−	1.48389i
$71$	0.697488	+	0.402695i	0.0827765	+	0.0477911i	0.540817	−	0.841140i	$-0.318115\pi$
$71$	0.697488	+	0.402695i	0.0827765	+	0.0477911i	−0.458040	+	0.888931i	$0.651449\pi$
$72$	5.26140	+	3.03767i	0.620062	+	0.357993i
$73$	13.1489	−	7.59150i	1.53896	−	0.888518i	0.540058	−	0.841628i	$-0.318402\pi$
$73$	13.1489	−	7.59150i	1.53896	−	0.888518i	0.998900	−	0.0468899i	$-0.0149310\pi$
$74$	−0.904325			−0.105126
$75$	1.15988			0.133931
$76$	−0.716586	+	0.413721i	−0.0821981	+	0.0474571i
$77$	−15.0644			−1.71675
$78$	2.72843	+	3.28446i	0.308933	+	0.371892i
$79$	1.10947	−	1.92166i	0.124825	−	0.216204i	−0.796839	−	0.604191i	$-0.793496\pi$
$79$	1.10947	−	1.92166i	0.124825	−	0.216204i	0.921665	+	0.387987i	$0.126830\pi$
$80$		−	5.77766i		−	0.645962i
$81$	−0.407505	−	0.705820i	−0.0452784	−	0.0784244i
$82$	3.96086	−	6.86041i	0.437404	−	0.757605i
$83$	−5.12515	+	2.95901i	−0.562559	+	0.324793i	−0.754172	−	0.656677i	$-0.771961\pi$
$83$	−5.12515	+	2.95901i	−0.562559	+	0.324793i	0.191613	+	0.981471i	$0.438628\pi$
$84$	2.38282	+	1.37572i	0.259987	+	0.150103i
$85$	7.33925	−	4.23732i	0.796053	−	0.459602i
$86$	−11.0163	−	6.36025i	−1.18791	−	0.685843i
$87$	−5.51315			−0.591072
$88$	−10.8232			−1.15376
$89$	−1.16803	−	0.674360i	−0.123810	−	0.0714820i	0.436816	−	0.899551i	$-0.356106\pi$
$89$	−1.16803	−	0.674360i	−0.123810	−	0.0714820i	−0.560626	+	0.828069i	$0.689440\pi$
$90$	−2.85901	+	4.95194i	−0.301366	+	0.521981i
$91$	−9.87194	−	11.8838i	−1.03486	−	1.24576i
$92$	−1.38877			−0.144789
$93$	5.12752	+	2.35178i	0.531699	+	0.243869i
$94$	3.65126	−	6.32417i	0.376599	−	0.652288i
$95$	−1.61817	−	2.80274i	−0.166020	−	0.287556i
$96$	3.01197	+	1.73896i	0.307408	+	0.177482i
$97$	−14.5197	+	8.38298i	−1.47426	+	0.851163i	−0.999579	−	0.0289974i	$-0.990769\pi$
$97$	−14.5197	+	8.38298i	−1.47426	+	0.851163i	−0.474677	+	0.880160i	$0.657435\pi$
$98$	11.4992	+	6.63909i	1.16160	+	0.670649i
$99$	6.00867	+	3.46911i	0.603894	+	0.348659i
$100$	−0.725547			−0.0725547
$101$	−8.71992	+	15.1034i	−0.867665	+	1.50284i	−0.00328846	+	0.999995i	$0.501047\pi$
$101$	−8.71992	+	15.1034i	−0.867665	+	1.50284i	−0.864376	+	0.502845i	$0.832287\pi$
$102$		−	4.04868i		−	0.400879i
$103$	−5.79163	−	10.0314i	−0.570666	−	0.988423i	−0.996498	−	0.0836203i	$-0.973352\pi$
$103$	−5.79163	−	10.0314i	−0.570666	−	0.988423i	0.425832	−	0.904802i	$-0.359982\pi$
$104$	−7.09261	−	8.53805i	−0.695488	−	0.837225i
$105$	−5.38078	+	9.31978i	−0.525110	+	0.909518i
$106$			11.1640i			1.08434i
$107$	−5.34035	−	9.24976i	−0.516271	−	0.894208i	−0.999822	−	0.0188915i	$-0.993986\pi$
$107$	−5.34035	−	9.24976i	−0.516271	−	0.894208i	0.483550	−	0.875317i	$-0.339347\pi$
$108$	−1.59681	−	2.76576i	−0.153653	−	0.266135i
$109$		−	16.8763i		−	1.61646i	−0.588869	−	0.808229i	$-0.700427\pi$
$109$		−	16.8763i		−	1.61646i	0.588869	−	0.808229i	$-0.299573\pi$
$110$		−	10.1866i		−	0.971258i
$111$	0.678860	+	0.391940i	0.0644345	+	0.0372013i
$112$	8.64898	+	4.99349i	0.817252	+	0.471841i
$113$	−2.95174	+	5.11256i	−0.277676	+	0.480949i	−0.970807	−	0.239863i	$-0.922897\pi$
$113$	−2.95174	+	5.11256i	−0.277676	+	0.480949i	0.693131	+	0.720812i	$0.256231\pi$
$114$	−1.54613			−0.144808
$115$		−	5.43180i		−	0.506518i
$116$	3.44868			0.320202
$117$	1.20091	+	7.01338i	0.111025	+	0.648387i
$118$	−6.01339	+	10.4155i	−0.553577	+	0.958823i
$119$			14.6489i			1.34286i
$120$	−3.86588	+	6.69591i	−0.352905	+	0.611250i
$121$	−1.36044			−0.123676
$122$			17.0488i			1.54353i
$123$	−5.94668	+	3.43332i	−0.536194	+	0.309572i
$124$	−3.20746	−	1.47113i	−0.288038	−	0.132111i
$125$			9.55655i			0.854764i
$126$	−4.94194	−	8.55969i	−0.440263	−	0.762558i
$127$	−1.71332	−	2.96756i	−0.152033	−	0.263328i	0.779942	−	0.625852i	$-0.215249\pi$
$127$	−1.71332	−	2.96756i	−0.152033	−	0.263328i	−0.931975	+	0.362524i	$0.881915\pi$
$128$	2.83457	+	1.63654i	0.250543	+	0.144651i
$129$	5.51314	+	9.54904i	0.485405	+	0.840746i
$130$	8.03587	−	6.67545i	0.704792	−	0.585476i
$131$	−8.44037	+	14.6191i	−0.737438	+	1.27728i	0.216207	+	0.976348i	$0.430631\pi$
$131$	−8.44037	+	14.6191i	−0.737438	+	1.27728i	−0.953645	+	0.300933i	$0.902702\pi$
$132$	1.95511	+	1.12878i	0.170171	+	0.0982480i
$133$	5.59417			0.485076
$134$	3.16002	−	5.47331i	0.272984	−	0.472822i
$135$	10.8176	−	6.24552i	0.931027	−	0.537529i
$136$			10.5246i			0.902480i
$137$	−4.01805	−	2.31982i	−0.343285	−	0.198196i	0.318439	−	0.947943i	$-0.396842\pi$
$137$	−4.01805	−	2.31982i	−0.343285	−	0.198196i	−0.661724	+	0.749748i	$0.730175\pi$
$138$	−2.24733	−	1.29750i	−0.191305	−	0.110450i
$139$	6.25380	+	10.8319i	0.530441	+	0.918750i	0.999369	+	0.0355140i	$0.0113068\pi$
$139$	6.25380	+	10.8319i	0.530441	+	0.918750i	−0.468929	+	0.883236i	$0.655360\pi$
$140$	3.36588	−	5.82987i	0.284469	−	0.492714i
$141$	−5.48187	+	3.16496i	−0.461656	+	0.266537i
$142$	−0.470691	−	0.815261i	−0.0394995	−	0.0684152i
$143$	−8.09997	−	9.75070i	−0.677354	−	0.815395i
$144$	−2.29985	−	3.98345i	−0.191654	−	0.331955i
$145$			13.4886i			1.12017i
$146$	−17.7467			−1.46873
$147$	−5.75484	−	9.96767i	−0.474651	−	0.822120i
$148$	−0.424652	−	0.245173i	−0.0349062	−	0.0201531i
$149$		−	7.57074i		−	0.620219i	−0.950701	−	0.310110i	$-0.899634\pi$
$149$		−	7.57074i		−	0.620219i	0.950701	−	0.310110i	$-0.100366\pi$
$150$	−1.17409	−	0.677864i	−0.0958644	−	0.0553474i
$151$		−	3.83153i		−	0.311806i	−0.987772	−	0.155903i	$-0.950171\pi$
$151$		−	3.83153i		−	0.311806i	0.987772	−	0.155903i	$-0.0498287\pi$
$152$	4.01920			0.326000
$153$	3.37340	−	5.84291i	0.272724	−	0.472371i
$154$	15.2491	+	8.80407i	1.22881	+	0.709452i
$155$	5.75394	−	12.5451i	0.462168	−	1.00765i
$156$	0.390755	+	2.28202i	0.0312855	+	0.182708i
$157$	11.6904			0.932998			0.466499	−	0.884522i	$-0.345515\pi$
$157$	11.6904			0.932998			0.466499	+	0.884522i	$0.345515\pi$
$158$	−2.24614	+	1.29681i	−0.178694	+	0.103169i
$159$	4.83854	−	8.38060i	0.383721	−	0.664625i
$160$	4.25459	−	7.36917i	0.336355	−	0.582584i
$161$	8.13125	+	4.69458i	0.640832	+	0.369985i
$162$			0.952628i			0.0748456i
$163$	1.78776	−	1.03216i	0.140028	−	0.0808454i	−0.428349	−	0.903613i	$-0.640905\pi$
$163$	1.78776	−	1.03216i	0.140028	−	0.0808454i	0.568377	+	0.822768i	$0.307571\pi$
$164$	3.71987	−	2.14767i	0.290473	−	0.167705i
$165$	−4.41495	+	7.64692i	−0.343703	+	0.595312i
$166$	6.91730			0.536887
$167$	12.1406	−	7.00939i	0.939469	−	0.542403i	0.0496752	−	0.998765i	$-0.484181\pi$
$167$	12.1406	−	7.00939i	0.939469	−	0.542403i	0.889794	+	0.456363i	$0.150848\pi$
$168$	−6.68238	−	11.5742i	−0.515557	−	0.892971i
$169$	2.38395	−	12.7795i	0.183381	−	0.983042i
$170$	−9.90561			−0.759726
$171$	−2.23132	−	1.28825i	−0.170633	−	0.0985150i
$172$	−3.44867	−	5.97328i	−0.262959	−	0.455458i
$173$	7.34132	−	12.7155i	0.558150	−	0.966744i	−0.439501	−	0.898242i	$-0.644845\pi$
$173$	7.34132	−	12.7155i	0.558150	−	0.966744i	0.997651	−	0.0685022i	$-0.0218220\pi$
$174$	5.58073	+	3.22204i	0.423074	+	0.244262i
$175$	4.24809	+	2.45264i	0.321125	+	0.185402i
$176$	7.09652	+	4.09718i	0.534921	+	0.308837i
$177$	9.02827	−	5.21248i	0.678607	−	0.391794i
$178$	0.788228	+	1.36525i	0.0590802	+	0.102330i
$179$	1.40522	+	2.43390i	0.105031	+	0.181919i	0.913751	−	0.406275i	$-0.133173\pi$
$179$	1.40522	+	2.43390i	0.105031	+	0.181919i	−0.808720	+	0.588194i	$0.799839\pi$
$180$	−2.68506	+	1.55022i	−0.200132	+	0.115547i
$181$	−9.77098	−	16.9238i	−0.726271	−	1.25794i	−0.958449	−	0.285265i	$-0.907918\pi$
$181$	−9.77098	−	16.9238i	−0.726271	−	1.25794i	0.232177	−	0.972673i	$-0.425415\pi$
$182$	3.04774	+	17.7989i	0.225913	+	1.31934i
$183$	7.38906	−	12.7982i	0.546215	−	0.946072i
$184$	5.84199	+	3.37287i	0.430677	+	0.248652i
$185$	0.958932	−	1.66092i	0.0705021	−	0.122113i
$186$	−3.81592	−	5.37727i	−0.279797	−	0.394281i
$187$			12.0194i			0.878949i
$188$	3.42911	−	1.97980i	0.250094	−	0.144392i
$189$			21.5914i			1.57054i
$190$			3.78280i			0.274433i
$191$	−6.02899	+	10.4425i	−0.436242	+	0.755594i	−0.997396	−	0.0721176i	$-0.977024\pi$
$191$	−6.02899	+	10.4425i	−0.436242	+	0.755594i	0.561154	+	0.827712i	$0.310358\pi$
$192$	−4.39407	−	7.61075i	−0.317114	−	0.549258i
$193$	15.3661	−	8.87162i	1.10608	−	0.638593i	0.168266	−	0.985742i	$-0.446183\pi$
$193$	15.3661	−	8.87162i	1.10608	−	0.638593i	0.937810	+	0.347149i	$0.112850\pi$
$194$	19.5970			1.40698
$195$	−8.92556	+	1.52834i	−0.639172	+	0.109447i
$196$	3.59987	+	6.23515i	0.257133	+	0.445368i
$197$			8.22240i			0.585822i	0.956140	+	0.292911i	$0.0946239\pi$
$197$			8.22240i			0.585822i	−0.956140	+	0.292911i	$0.905376\pi$
$198$	−4.05488	−	7.02326i	−0.288168	−	0.499122i
$199$	1.82717	−	3.16474i	0.129524	−	0.224343i	−0.793968	−	0.607959i	$-0.791988\pi$
$199$	1.82717	−	3.16474i	0.129524	−	0.224343i	0.923492	+	0.383617i	$0.125322\pi$
$200$	3.05209	+	1.76212i	0.215815	+	0.124601i
$201$	−4.74433	+	2.73914i	−0.334639	+	0.193204i
$202$	17.6536	−	10.1923i	1.24210	−	0.717129i
$203$	−20.1921	−	11.6579i	−1.41721	−	0.818226i
$204$	1.09764	−	1.90117i	0.0768504	−	0.133109i
$205$	8.40006	+	14.5493i	0.586686	+	1.01617i
$206$			13.5391i			0.943317i
$207$	−2.16218	−	3.74500i	−0.150282	−	0.260296i
$208$	1.41834	+	8.28313i	0.0983439	+	0.574332i
$209$	4.59004			0.317500
$210$	10.8935	−	6.28935i	0.751721	−	0.434006i
$211$	−2.43382	−	4.21550i	−0.167551	−	0.290207i	0.770007	−	0.638035i	$-0.220253\pi$
$211$	−2.43382	−	4.21550i	−0.167551	−	0.290207i	−0.937558	+	0.347828i	$0.886919\pi$
$212$	−3.02669	+	5.24238i	−0.207874	+	0.360048i
$213$			0.816002i			0.0559115i
$214$			12.4842i			0.853401i
$215$	23.3630	−	13.4886i	1.59334	−	0.919916i
$216$			15.5126i			1.05550i
$217$	13.8067	+	19.4560i	0.937261	+	1.32076i
$218$	−9.86297	+	17.0832i	−0.668005	+	1.15702i
$219$	13.3221	+	7.69153i	0.900226	+	0.519746i
$220$	2.76172	−	4.78343i	0.186195	−	0.322499i
$221$	−9.48170	+	7.87651i	−0.637808	+	0.529831i
$222$	−0.458121	−	0.793488i	−0.0307470	−	0.0532554i
$223$	−8.79075	+	5.07534i	−0.588672	+	0.339870i	−0.764572	−	0.644538i	$-0.777050\pi$
$223$	−8.79075	+	5.07534i	−0.588672	+	0.339870i	0.175900	+	0.984408i	$0.443716\pi$
$224$	7.35428	+	12.7380i	0.491379	+	0.851093i
$225$	−1.12961	−	1.95654i	−0.0753072	−	0.130436i
$226$	5.97583	−	3.45015i	0.397506	−	0.229500i
$227$	−3.12112	−	1.80198i	−0.207156	−	0.119602i	0.392833	−	0.919610i	$-0.371495\pi$
$227$	−3.12112	−	1.80198i	−0.207156	−	0.119602i	−0.599989	+	0.800008i	$0.704828\pi$
$228$	−0.726029	−	0.419173i	−0.0480824	−	0.0277604i
$229$	−0.685131	−	0.395560i	−0.0452747	−	0.0261394i	0.477192	−	0.878799i	$-0.341655\pi$
$229$	−0.685131	−	0.395560i	−0.0452747	−	0.0261394i	−0.522467	+	0.852660i	$0.674988\pi$
$230$	−3.17449	+	5.49838i	−0.209320	+	0.362553i
$231$	−7.63147	−	13.2181i	−0.502114	−	0.869687i
$232$	−14.5073	−	8.37577i	−0.952448	−	0.549896i
$233$	−9.00489			−0.589930			−0.294965	−	0.955508i	$-0.595308\pi$
$233$	−9.00489			−0.589930			−0.294965	+	0.955508i	$0.595308\pi$
$234$	2.88318	−	7.80119i	0.188479	−	0.509980i
$235$	7.74348	+	13.4121i	0.505129	+	0.874909i
$236$	−5.64752	+	3.26060i	−0.367622	+	0.212247i
$237$	2.24818			0.146035
$238$	8.56119	−	14.8284i	0.554939	−	0.961183i
$239$	8.36079	−	4.82711i	0.540815	−	0.312240i	−0.204594	−	0.978847i	$-0.565588\pi$
$239$	8.36079	−	4.82711i	0.540815	−	0.312240i	0.745409	+	0.666607i	$0.232254\pi$
$240$	5.06953	−	2.92689i	0.327237	−	0.188930i
$241$		−	3.79793i		−	0.244646i	−0.992490	−	0.122323i	$-0.960966\pi$
$241$		−	3.79793i		−	0.244646i	0.992490	−	0.122323i	$-0.0390344\pi$
$242$	1.37711	+	0.795077i	0.0885243	+	0.0511095i
$243$	7.97139	−	13.8068i	0.511365	−	0.885710i
$244$	−4.62213	+	8.00577i	−0.295902	+	0.512517i
$245$	−24.3872	+	14.0800i	−1.55804	+	0.899536i
$246$	8.02610			0.511725
$247$	3.00792	+	3.62091i	0.191389	+	0.230393i
$248$	9.91960	+	13.9784i	0.629895	+	0.887627i
$249$	−5.19269	−	2.99800i	−0.329073	−	0.189991i
$250$	5.58511	−	9.67369i	0.353233	−	0.611818i
$251$	15.7449			0.993809			0.496904	−	0.867805i	$-0.334470\pi$
$251$	15.7449			0.993809			0.496904	+	0.867805i	$0.334470\pi$
$252$		−	5.35927i		−	0.337602i
$253$	6.67172	+	3.85192i	0.419448	+	0.242168i
$254$			4.00524i			0.251311i
$255$	7.43596	+	4.29315i	0.465658	+	0.268848i
$256$	6.76096	+	11.7103i	0.422560	+	0.731896i
$257$	0.465610			0.0290439			0.0145220	−	0.999895i	$-0.495377\pi$
$257$	0.465610			0.0290439			0.0145220	+	0.999895i	$0.495377\pi$
$258$		−	12.8881i		−	0.802379i
$259$	1.65756	+	2.87099i	0.102996	+	0.178394i
$260$	5.58327	−	0.956033i	0.346260	−	0.0592907i
$261$	5.36928	+	9.29986i	0.332350	+	0.575647i
$262$	17.0877	−	9.86556i	1.05568	−	0.609496i
$263$	−11.0160	+	19.0802i	−0.679274	+	1.17654i	0.295926	+	0.955211i	$0.404372\pi$
$263$	−11.0160	+	19.0802i	−0.679274	+	1.17654i	−0.975200	+	0.221326i	$0.928962\pi$
$264$	−5.48292	−	9.49670i	−0.337451	−	0.584481i
$265$	−20.5042	−	11.8381i	−1.25957	−	0.727210i
$266$	−5.66274	−	3.26938i	−0.347205	−	0.200459i
$267$		−	1.36649i		−	0.0836279i
$268$	2.96776	−	1.71344i	0.181285	−	0.104665i
$269$	12.4566	−	21.5755i	0.759492	−	1.31548i	−0.183618	−	0.982998i	$-0.558781\pi$
$269$	12.4566	−	21.5755i	0.759492	−	1.31548i	0.943110	−	0.332481i	$-0.107886\pi$
$270$	−14.6002			−0.888540
$271$	0.126715	+	0.0731590i	0.00769739	+	0.00444409i	0.503844	−	0.863795i	$-0.331919\pi$
$271$	0.126715	+	0.0731590i	0.00769739	+	0.00444409i	−0.496146	+	0.868239i	$0.665252\pi$
$272$	3.98415	−	6.90075i	0.241575	−	0.418419i
$273$	5.42627	−	14.6822i	0.328413	−	0.888607i
$274$	2.71153	+	4.69651i	0.163810	+	0.283727i
$275$	3.48558	+	2.01240i	0.210188	+	0.121352i
$276$	−0.703533	−	1.21855i	−0.0423477	−	0.0733483i
$277$	−4.68408	−	8.11307i	−0.281439	−	0.487467i	0.690300	−	0.723523i	$-0.257478\pi$
$277$	−4.68408	−	8.11307i	−0.281439	−	0.487467i	−0.971739	+	0.236056i	$0.924145\pi$
$278$		−	14.6196i		−	0.876823i
$279$	−1.02660	−	10.9398i	−0.0614611	−	0.654947i
$280$	−28.3178	+	16.3493i	−1.69232	+	0.977059i
$281$		−	11.7302i		−	0.699767i	−0.936793	−	0.349884i	$-0.886221\pi$
$281$		−	11.7302i		−	0.699767i	0.936793	−	0.349884i	$-0.113779\pi$
$282$	7.39874			0.440589
$283$	−4.17114	+	7.22463i	−0.247949	+	0.429459i	−0.962956	−	0.269657i	$-0.913090\pi$
$283$	−4.17114	+	7.22463i	−0.247949	+	0.429459i	0.715008	+	0.699116i	$0.246423\pi$
$284$		−	0.510440i		−	0.0302890i
$285$	1.63949	−	2.83968i	0.0971149	−	0.168208i
$286$	2.50068	+	14.6041i	0.147868	+	0.863556i
$287$	−29.0399			−1.71417
$288$		−	6.77431i		−	0.399180i
$289$	−5.31214			−0.312479
$290$	7.88313	−	13.6540i	0.462913	−	0.801790i
$291$	−14.7111	−	8.49344i	−0.862378	−	0.497894i
$292$	−8.33349	−	4.81134i	−0.487680	−	0.281562i
$293$			22.8351i			1.33404i	0.745040	+	0.667020i	$0.232431\pi$
$293$			22.8351i			1.33404i	−0.745040	+	0.667020i	$0.767569\pi$
$294$			13.4531i			0.784603i
$295$	−12.7530	−	22.0888i	−0.742508	−	1.28606i
$296$	1.19090	+	2.06269i	0.0692195	+	0.119892i
$297$			17.7158i			1.02798i
$298$	−4.42455	+	7.66354i	−0.256307	+	0.443937i
$299$	1.33343	+	7.78730i	0.0771144	+	0.450351i
$300$	−0.367554	−	0.636621i	−0.0212207	−	0.0367554i
$301$			46.6315i			2.68780i
$302$	−2.23925	+	3.87850i	−0.128855	+	0.223183i
$303$	−17.6697			−1.01510
$304$	−2.63529	−	1.52148i	−0.151144	−	0.0872631i
$305$	−31.3125	−	18.0783i	−1.79295	−	1.03516i
$306$	−6.82951	+	3.94302i	−0.390417	+	0.225407i
$307$	−14.5589	−	8.40557i	−0.830919	−	0.479731i	0.0232484	−	0.999730i	$-0.492599\pi$
$307$	−14.5589	−	8.40557i	−0.830919	−	0.479731i	−0.854167	+	0.519999i	$0.825932\pi$
$308$	4.77377	+	8.26841i	0.272011	+	0.471137i
$309$	5.86795	−	10.1636i	0.333816	−	0.578186i
$310$	−13.1562	+	9.33616i	−0.747222	+	0.530258i
$311$	−1.00498			−0.0569873			−0.0284937	−	0.999594i	$-0.509071\pi$
$311$	−1.00498			−0.0569873			−0.0284937	+	0.999594i	$0.509071\pi$
$312$	3.89857	−	10.5486i	0.220713	−	0.597197i
$313$	15.6111	−	27.0392i	0.882390	−	1.52835i	0.0337148	−	0.999431i	$-0.489266\pi$
$313$	15.6111	−	27.0392i	0.882390	−	1.52835i	0.848676	−	0.528914i	$-0.177400\pi$
$314$	−11.8337	−	6.83220i	−0.667816	−	0.385563i
$315$	20.9614			1.18104
$316$	−1.40632			−0.0791118
$317$	12.9118	+	7.45464i	0.725200	+	0.418694i	0.816664	−	0.577114i	$-0.195821\pi$
$317$	12.9118	+	7.45464i	0.725200	+	0.418694i	−0.0914636	+	0.995808i	$0.529155\pi$
$318$	−9.79570	+	5.65555i	−0.549316	+	0.317148i
$319$	−16.5677	−	9.56537i	−0.927614	−	0.535558i
$320$	−18.6207	+	10.7507i	−1.04093	+	0.600980i
$321$	5.41072	−	9.37164i	0.301997	−	0.523074i
$322$	−5.48728	−	9.50424i	−0.305794	−	0.529651i
$323$		−	4.46341i		−	0.248351i
$324$	−0.258269	+	0.447334i	−0.0143483	+	0.0248519i
$325$	0.696639	+	4.06840i	0.0386426	+	0.225674i
$326$	−2.41290			−0.133638
$327$	14.8079	−	8.54934i	0.818879	−	0.472780i
$328$	−20.8641			−1.15202
$329$	−26.7700			−1.47588
$330$	8.93813	−	5.16043i	0.492028	−	0.284073i
$331$	21.0322	+	12.1429i	1.15603	+	0.667436i	0.950350	−	0.311183i	$-0.100725\pi$
$331$	21.0322	+	12.1429i	1.15603	+	0.667436i	0.205683	+	0.978619i	$0.434058\pi$
$332$	3.24822	+	1.87536i	0.178269	+	0.102924i
$333$		−	1.52685i		−	0.0836707i
$334$	−16.3859			−0.896597
$335$	6.70167	+	11.6076i	0.366151	+	0.634193i
$336$			10.1186i			0.552014i
$337$	−11.4686			−0.624737			−0.312368	−	0.949961i	$-0.601122\pi$
$337$	−11.4686			−0.624737			−0.312368	+	0.949961i	$0.601122\pi$
$338$	−9.88188	+	11.5429i	−0.537504	+	0.627853i
$339$	−5.98126			−0.324858
$340$	−4.65147	−	2.68553i	−0.252261	−	0.145643i
$341$	11.3285	+	15.9637i	0.613471	+	0.864482i
$342$	1.50578	+	2.60808i	0.0814231	+	0.141029i
$343$		−	18.6819i		−	1.00873i
$344$			33.5030i			1.80636i
$345$	4.76606	−	2.75169i	0.256596	−	0.148146i
$346$	−14.8626	+	8.58093i	−0.799019	+	0.461314i
$347$	−3.06662			−0.164625			−0.0823124	−	0.996607i	$-0.526231\pi$
$347$	−3.06662			−0.164625			−0.0823124	+	0.996607i	$0.526231\pi$
$348$	1.74706	+	3.02600i	0.0936524	+	0.162211i
$349$	−17.8393	−	10.2995i	−0.954915	−	0.551320i	−0.0603106	−	0.998180i	$-0.519209\pi$
$349$	−17.8393	−	10.2995i	−0.954915	−	0.551320i	−0.894604	+	0.446859i	$0.852542\pi$
$350$	−2.86677	−	4.96540i	−0.153235	−	0.265412i
$351$	−13.9754	+	11.6094i	−0.745951	+	0.619666i
$352$	6.03422	+	10.4516i	0.321625	+	0.557071i
$353$	29.6041	−	17.0920i	1.57567	−	0.909713i	0.580216	−	0.814463i	$-0.302968\pi$
$353$	29.6041	−	17.0920i	1.57567	−	0.909713i	0.995453	−	0.0952500i	$-0.0303651\pi$
$354$	−12.1852			−0.647639
$355$	1.99645			0.105961
$356$			0.854791i			0.0453038i
$357$	−12.8534	+	7.42094i	−0.680276	+	0.392758i
$358$		−	3.28498i		−	0.173617i
$359$	−5.37225	+	3.10167i	−0.283537	+	0.163700i	−0.635023	−	0.772493i	$-0.719010\pi$
$359$	−5.37225	+	3.10167i	−0.283537	+	0.163700i	0.351487	+	0.936193i	$0.385676\pi$
$360$	15.0600			0.793731
$361$	17.2955			0.910289
$362$			22.8417i			1.20053i
$363$	−0.689183	−	1.19370i	−0.0361727	−	0.0626530i
$364$	−3.39433	+	9.18426i	−0.177911	+	0.481386i
$365$	18.8183	−	32.5943i	0.984997	−	1.70606i
$366$	−14.9593	+	8.63673i	−0.781933	+	0.451449i
$367$	23.6069			1.23227			0.616135	−	0.787640i	$-0.288697\pi$
$367$	23.6069			1.23227			0.616135	+	0.787640i	$0.288697\pi$
$368$	−2.55363	−	4.42302i	−0.133117	−	0.230566i
$369$	11.5830	+	6.68744i	0.602986	+	0.348134i
$370$	−1.94137	+	1.12085i	−0.100927	+	0.0582703i
$371$	35.4426	−	20.4628i	1.84009	−	1.06238i
$372$	−0.334038	−	3.55960i	−0.0173190	−	0.184556i
$373$	−18.7239	−	32.4307i	−0.969485	−	1.67920i	−0.697048	−	0.717024i	$-0.745504\pi$
$373$	−18.7239	−	32.4307i	−0.969485	−	1.67920i	−0.272437	−	0.962174i	$-0.587830\pi$
$374$	7.02449	−	12.1668i	0.363228	−	0.629129i
$375$	−8.38527	+	4.84124i	−0.433014	+	0.250001i
$376$	−19.2332			−0.991878
$377$	−3.31128	−	19.3380i	−0.170540	−	0.995957i
$378$	12.6186	−	21.8561i	0.649031	−	1.12416i
$379$	1.29459	−	0.747433i	0.0664987	−	0.0383930i	−0.466382	−	0.884583i	$-0.654443\pi$
$379$	1.29459	−	0.747433i	0.0664987	−	0.0383930i	0.532881	+	0.846190i	$0.321109\pi$
$380$	−1.02556	+	1.77632i	−0.0526102	+	0.0911235i
$381$	1.73590	−	3.00666i	0.0889327	−	0.154036i
$382$	12.2058	−	7.04701i	0.624502	−	0.360556i
$383$	16.1385	+	9.31759i	0.824641	+	0.476107i	0.852014	−	0.523519i	$-0.175381\pi$
$383$	16.1385	+	9.31759i	0.824641	+	0.476107i	−0.0273734	+	0.999625i	$0.508714\pi$
$384$			3.31621i			0.169229i
$385$	−32.3398	+	18.6714i	−1.64819	+	0.951582i
$386$	−20.7393			−1.05560
$387$	10.7385	−	18.5997i	0.545870	−	0.945474i
$388$	9.20232	+	5.31296i	0.467177	+	0.269725i
$389$	4.06602	−	7.04255i	0.206155	−	0.357071i	−0.744345	−	0.667795i	$-0.767238\pi$
$389$	4.06602	−	7.04255i	0.206155	−	0.357071i	0.950500	+	0.310724i	$0.100571\pi$
$390$	9.92816	+	3.66926i	0.502732	+	0.185800i
$391$	3.74566	−	6.48767i	0.189426	−	0.328095i
$392$		−	34.9718i		−	1.76634i
$393$	−17.1032			−0.862741
$394$	4.80539	−	8.32319i	0.242092	−	0.419316i
$395$		−	5.50047i		−	0.276759i
$396$		−	4.39730i		−	0.220973i
$397$			10.6462i			0.534320i	0.963652	+	0.267160i	$0.0860852\pi$
$397$			10.6462i			0.534320i	−0.963652	+	0.267160i	$0.913915\pi$
$398$	−3.69912	+	2.13569i	−0.185420	+	0.107052i
$399$	2.83394	+	4.90853i	0.141875	+	0.245734i
$400$	−1.33412	−	2.31076i	−0.0667060	−	0.115538i
$401$	−9.93735	−	5.73733i	−0.496247	−	0.286509i	0.230915	−	0.972974i	$-0.425828\pi$
$401$	−9.93735	−	5.73733i	−0.496247	−	0.286509i	−0.727163	+	0.686465i	$0.759161\pi$
$402$	6.40332			0.319368
$403$	−5.16947	+	19.3978i	−0.257510	+	0.966276i
$404$	11.0530			0.549909
$405$	−1.74964	−	1.01015i	−0.0869401	−	0.0501949i
$406$	13.6264	+	23.6016i	0.676267	+	1.17133i
$407$	1.36004	+	2.35566i	0.0674146	+	0.116766i
$408$	−9.23471	+	5.33166i	−0.457186	+	0.263957i
$409$			5.13969i			0.254141i	0.991894	+	0.127071i	$0.0405575\pi$
$409$			5.13969i			0.254141i	−0.991894	+	0.127071i	$0.959442\pi$
$410$		−	19.6369i		−	0.969797i
$411$		−	4.70078i		−	0.231872i
$412$	−3.67062	+	6.35770i	−0.180838	+	0.313221i
$413$	44.0885			2.16945
$414$			5.05454i			0.248417i
$415$	−7.33500	+	12.7046i	−0.360061	+	0.623644i
$416$	−4.29056	+	11.6092i	−0.210362	+	0.569190i
$417$	−6.33621	+	10.9746i	−0.310285	+	0.537430i
$418$	−4.64630	−	2.68254i	−0.227258	−	0.131207i
$419$	11.4982	−	19.9155i	0.561726	−	0.972938i	−0.435620	−	0.900131i	$-0.643471\pi$
$419$	11.4982	−	19.9155i	0.561726	−	0.972938i	0.997346	−	0.0728075i	$-0.0231959\pi$
$420$	6.82046			0.332804
$421$	−20.8178	+	12.0192i	−1.01460	+	0.585779i	−0.912535	−	0.408999i	$-0.865878\pi$
$421$	−20.8178	+	12.0192i	−1.01460	+	0.585779i	−0.102064	+	0.994778i	$0.532545\pi$
$422$			5.68956i			0.276963i
$423$	10.6776	+	6.16472i	0.519163	+	0.299739i
$424$	25.4642	−	14.7018i	1.23665	−	0.713980i
$425$	1.95688	−	3.38942i	0.0949226	−	0.164411i
$426$	0.476894	−	0.826004i	0.0231056	−	0.0400200i
$427$	54.1254	−	31.2493i	2.61931	−	1.51226i
$428$	−3.38461	+	5.86231i	−0.163601	+	0.283366i
$429$	4.45227	−	12.0468i	0.214958	−	0.581625i
$430$	−31.5324			−1.52063
$431$	10.6567	−	6.15264i	0.513314	−	0.296362i	−0.220881	−	0.975301i	$-0.570893\pi$
$431$	10.6567	−	6.15264i	0.513314	−	0.296362i	0.734195	+	0.678939i	$0.237560\pi$
$432$	5.87237	−	10.1712i	0.282534	−	0.489364i
$433$	−2.69026	−	4.65967i	−0.129286	−	0.223930i	0.794114	−	0.607769i	$-0.207935\pi$
$433$	−2.69026	−	4.65967i	−0.129286	−	0.223930i	−0.923400	+	0.383839i	$0.874602\pi$
$434$	−2.60536	−	27.7635i	−0.125061	−	1.33269i
$435$	−11.8354	+	6.83319i	−0.567466	+	0.327627i
$436$	−9.26289	+	5.34793i	−0.443612	+	0.256120i
$437$	−2.47754	−	1.43041i	−0.118517	−	0.0684257i
$438$	−8.99028	−	15.5716i	−0.429572	−	0.744041i
$439$	−33.7848			−1.61246			−0.806230	−	0.591602i	$-0.798496\pi$
$439$	−33.7848			−1.61246			−0.806230	+	0.591602i	$0.798496\pi$
$440$	−23.2349	+	13.4147i	−1.10768	+	0.639520i
$441$	−11.2093	+	19.4151i	−0.533777	+	0.924528i
$442$	14.2012	−	2.43169i	0.675481	−	0.115664i
$443$	7.32579	+	12.6886i	0.348059	+	0.602856i	0.985905	−	0.167309i	$-0.0535076\pi$
$443$	7.32579	+	12.6886i	0.348059	+	0.602856i	−0.637846	+	0.770164i	$0.720174\pi$
$444$		−	0.496807i		−	0.0235774i
$445$	−3.34330			−0.158488
$446$	11.8647			0.561808
$447$	6.64285	−	3.83525i	0.314196	−	0.181401i
$448$		−	37.1661i		−	1.75594i
$449$	−3.20288	+	1.84918i	−0.151153	+	0.0872684i	−0.573669	−	0.819087i	$-0.694480\pi$
$449$	−3.20288	+	1.84918i	−0.151153	+	0.0872684i	0.422516	+	0.906356i	$0.361147\pi$
$450$			2.64070i			0.124484i
$451$	−23.8274			−1.12199
$452$	3.74150			0.175985
$453$	3.36193	−	1.94101i	0.157957	−	0.0911967i
$454$	2.10625	+	3.64813i	0.0988513	+	0.171215i
$455$	−35.9219	−	13.2761i	−1.68405	−	0.622392i
$456$	2.03608	+	3.52659i	0.0953481	+	0.165148i
$457$	1.87042	+	1.07989i	0.0874944	+	0.0505149i	0.543109	−	0.839662i	$-0.317247\pi$
$457$	1.87042	+	1.07989i	0.0874944	+	0.0505149i	−0.455614	+	0.890177i	$0.650580\pi$
$458$	0.462352	+	0.800818i	0.0216043	+	0.0374198i
$459$	17.2271			0.804093
$460$	−2.98135	+	1.72128i	−0.139006	+	0.0802553i
$461$	−0.0377362	+	0.0217870i	−0.00175755	+	0.00101472i	−0.500879	−	0.865518i	$-0.666990\pi$
$461$	−0.0377362	+	0.0217870i	−0.00175755	+	0.00101472i	0.499121	+	0.866532i	$0.333656\pi$
$462$			17.8402i			0.829999i
$463$		−	4.48424i		−	0.208400i	−0.994556	−	0.104200i	$-0.966772\pi$
$463$		−	4.48424i		−	0.208400i	0.994556	−	0.104200i	$-0.0332282\pi$
$464$	6.34137	+	10.9836i	0.294391	+	0.509900i
$465$	13.9225	−	1.30650i	0.645639	−	0.0605876i
$466$	9.11526	+	5.26270i	0.422256	+	0.243790i
$467$	8.00968			0.370644			0.185322	−	0.982678i	$-0.440667\pi$
$467$	8.00968			0.370644			0.185322	+	0.982678i	$0.440667\pi$
$468$	3.46887	−	2.88162i	0.160349	−	0.133203i
$469$	−23.1684			−1.06982
$470$		−	18.1020i		−	0.834983i
$471$	5.92224	+	10.2576i	0.272882	+	0.472646i
$472$	31.6759			1.45800
$473$			38.2614i			1.75926i
$474$	−2.27574	−	1.31390i	−0.104528	−	0.0603494i
$475$	−1.29437	−	0.747302i	−0.0593895	−	0.0342886i
$476$	8.04031	−	4.64207i	0.368527	−	0.212769i
$477$	−18.8491			−0.863040
$478$	−11.2844			−0.516135
$479$	−18.2748	+	10.5510i	−0.834997	+	0.482086i	−0.855561	−	0.517703i	$-0.826787\pi$
$479$	−18.2748	+	10.5510i	−0.834997	+	0.482086i	0.0205633	+	0.999789i	$0.493454\pi$
$480$	8.62131			0.393507
$481$	−0.967039	+	2.61658i	−0.0440932	+	0.119306i
$482$	−2.21961	+	3.84448i	−0.101101	+	0.175111i
$483$			9.51288i			0.432851i
$484$	0.431109	+	0.746703i	0.0195959	+	0.0339411i
$485$	−20.7803	+	35.9925i	−0.943585	+	1.63434i
$486$	−16.1382	+	9.31739i	−0.732043	+	0.422645i
$487$	−5.15079	−	2.97381i	−0.233405	−	0.134756i	0.378737	−	0.925504i	$-0.376358\pi$
$487$	−5.15079	−	2.97381i	−0.233405	−	0.134756i	−0.612142	+	0.790748i	$0.709692\pi$
$488$	38.8870	−	22.4514i	1.76033	−	1.01633i
$489$	1.81132	+	1.04577i	0.0819107	+	0.0472912i
$490$	32.9148			1.48694
$491$	−28.9199			−1.30514			−0.652569	−	0.757729i	$-0.726309\pi$
$491$	−28.9199			−1.30514			−0.652569	+	0.757729i	$0.726309\pi$
$492$	3.76889	+	2.17597i	0.169915	+	0.0981003i
$493$	−9.30148	+	16.1106i	−0.418918	+	0.725587i
$494$	−0.928625	−	5.42320i	−0.0417808	−	0.244002i
$495$	17.1989			0.773035
$496$	−1.21247	−	12.9204i	−0.0544413	−	0.580142i
$497$	−1.72549	+	2.98863i	−0.0773987	+	0.134059i
$498$	3.50422	+	6.06949i	0.157028	+	0.271981i
$499$	18.7977	+	10.8528i	0.841499	+	0.485840i	0.857774	−	0.514028i	$-0.171847\pi$
$499$	18.7977	+	10.8528i	0.841499	+	0.485840i	−0.0162742	+	0.999868i	$0.505180\pi$
$500$	5.24530	−	3.02838i	0.234577	−	0.135433i
$501$	12.3006	+	7.10175i	0.549550	+	0.317283i
$502$	−15.9379	−	9.20174i	−0.711343	−	0.410694i
$503$	8.85000			0.394602			0.197301	−	0.980343i	$-0.436782\pi$
$503$	8.85000			0.394602			0.197301	+	0.980343i	$0.436782\pi$
$504$	−13.0160	+	22.5443i	−0.579778	+	1.00421i
$505$			43.2311i			1.92376i
$506$	−4.50233	−	7.79827i	−0.200153	−	0.346675i
$507$	12.4209	−	4.38220i	0.551633	−	0.194621i
$508$	−1.08587	+	1.88078i	−0.0481776	+	0.0834461i
$509$		−	20.8756i		−	0.925295i	−0.886542	−	0.462647i	$-0.846900\pi$
$509$		−	20.8756i		−	0.925295i	0.886542	−	0.462647i	$-0.153100\pi$
$510$	−5.01807	−	8.69155i	−0.222204	−	0.384868i
$511$	32.5285	+	56.3410i	1.43898	+	2.49238i
$512$		−	22.3513i		−	0.987798i
$513$		−	6.57876i		−	0.290460i
$514$	−0.471317	−	0.272115i	−0.0207889	−	0.0120025i
$515$	−24.8665	−	14.3567i	−1.09575	−	0.632631i
$516$	3.49412	−	6.05199i	0.153820	−	0.266424i
$517$	−21.9649			−0.966015
$518$		−	3.87490i		−	0.170253i
$519$	14.8761			0.652989
$520$	−25.8085	−	9.53835i	−1.13178	−	0.418284i
$521$	6.59279	−	11.4191i	0.288836	−	0.500278i	−0.684697	−	0.728828i	$-0.740065\pi$
$521$	6.59279	−	11.4191i	0.288836	−	0.500278i	0.973532	+	0.228550i	$0.0733986\pi$
$522$		−	12.5518i		−	0.549378i
$523$	−3.50825	+	6.07647i	−0.153405	+	0.265706i	−0.932477	−	0.361229i	$-0.882357\pi$
$523$	−3.50825	+	6.07647i	−0.153405	+	0.265706i	0.779072	+	0.626934i	$0.215691\pi$
$524$	10.6987			0.467374
$525$			4.96991i			0.216905i
$526$	22.3020	−	12.8761i	0.972413	−	0.561423i
$527$	15.5233	−	11.0159i	0.676205	−	0.479862i
$528$			8.30234i			0.361313i
$529$	9.09923	+	15.7603i	0.395619	+	0.685232i
$530$	13.8370	+	23.9665i	0.601043	+	1.04104i
$531$	−17.5853	−	10.1529i	−0.763138	−	0.440598i
$532$	−1.77274	−	3.07047i	−0.0768578	−	0.133122i
$533$	−15.6144	−	18.7965i	−0.676335	−	0.814168i
$534$	−0.798614	+	1.38324i	−0.0345594	+	0.0598587i
$535$	−22.9289	−	13.2380i	−0.991305	−	0.572330i
$536$	−16.6456			−0.718980
$537$	−1.42373	+	2.46598i	−0.0614386	+	0.106415i
$538$	−25.2186	+	14.5599i	−1.08725	+	0.627724i
$539$		−	39.9388i		−	1.72029i
$540$	−6.85595	−	3.95829i	−0.295033	−	0.170337i
$541$	−3.20842	−	1.85238i	−0.137941	−	0.0796402i	0.429441	−	0.903095i	$-0.358710\pi$
$541$	−3.20842	−	1.85238i	−0.137941	−	0.0796402i	−0.567382	+	0.823455i	$0.692044\pi$
$542$	−0.0855122	−	0.148111i	−0.00367306	−	0.00636193i
$543$	9.89973	−	17.1468i	0.424838	−	0.735841i
$544$	10.1632	−	5.86775i	0.435745	−	0.251578i
$545$	−20.9171	−	36.2294i	−0.895989	−	1.55190i
$546$	−14.0735	+	11.6909i	−0.602288	+	0.500325i
$547$	18.6284	+	32.2653i	0.796493	+	1.37957i	0.921887	+	0.387459i	$0.126647\pi$
$547$	18.6284	+	32.2653i	0.796493	+	1.37957i	−0.125394	+	0.992107i	$0.540019\pi$
$548$			2.94051i			0.125613i
$549$	−28.7849			−1.22851
$550$	−2.35220	−	4.07413i	−0.100298	−	0.173721i
$551$	6.15240	+	3.55209i	0.262101	+	0.151324i
$552$			6.83464i			0.290902i
$553$	8.23405	+	4.75393i	0.350147	+	0.202158i
$554$			10.9500i			0.465222i
$555$	1.94314			0.0824815
$556$	3.96353	−	6.86504i	0.168091	−	0.291143i
$557$	−29.9953	−	17.3178i	−1.27094	−	0.733780i	−0.295778	−	0.955257i	$-0.595579\pi$
$557$	−29.9953	−	17.3178i	−1.27094	−	0.733780i	−0.975166	+	0.221477i	$0.928912\pi$
$558$	−5.35431	+	11.6738i	−0.226666	+	0.494193i
$559$	−30.1830	+	25.0732i	−1.27661	+	1.06048i
$560$	24.7564			1.04615
$561$	−10.5463	+	6.08891i	−0.445265	+	0.257074i
$562$	−6.85547	+	11.8740i	−0.289180	+	0.500875i
$563$	17.6799	−	30.6224i	0.745118	−	1.29058i	−0.205022	−	0.978757i	$-0.565727\pi$
$563$	17.6799	−	30.6224i	0.745118	−	1.29058i	0.950140	−	0.311824i	$-0.100940\pi$
$564$	3.47430	+	2.00589i	0.146294	+	0.0844630i
$565$			14.6339i			0.615654i
$566$	8.44453	−	4.87545i	0.354950	−	0.204931i
$567$	3.02434	−	1.74610i	0.127010	−	0.0733294i
$568$	−1.23970	+	2.14722i	−0.0520165	+	0.0900953i
$569$	42.4035			1.77765			0.888823	−	0.458251i	$-0.151524\pi$
$569$	42.4035			1.77765			0.888823	+	0.458251i	$0.151524\pi$
$570$	−3.31917	+	1.91632i	−0.139025	+	0.0802659i
$571$	−9.29369	−	16.0971i	−0.388929	−	0.673645i	0.603377	−	0.797456i	$-0.293822\pi$
$571$	−9.29369	−	16.0971i	−0.388929	−	0.673645i	−0.992306	+	0.123812i	$0.960488\pi$
$572$	−2.78506	+	7.53573i	−0.116449	+	0.315085i
$573$	−12.2169			−0.510367
$574$	29.3959	+	16.9717i	1.22696	+	0.708385i
$575$	−1.25426	−	2.17244i	−0.0523062	−	0.0905970i
$576$	−8.55879	+	14.8243i	−0.356616	+	0.617677i
$577$	18.7381	+	10.8185i	0.780078	+	0.450378i	0.836458	−	0.548031i	$-0.184622\pi$
$577$	18.7381	+	10.8185i	0.780078	+	0.450378i	−0.0563798	+	0.998409i	$0.517956\pi$
$578$	5.37726	+	3.10456i	0.223664	+	0.129133i
$579$	15.5686	+	8.98852i	0.647008	+	0.373550i
$580$	7.40351	−	4.27442i	0.307414	−	0.177486i
$581$	−12.6789	−	21.9605i	−0.526011	−	0.911077i
$582$	9.92759	+	17.1951i	0.411512	+	0.712760i
$583$	29.0808	−	16.7898i	1.20441	−	0.695364i
$584$	23.3705	+	40.4788i	0.967077	+	1.67503i
$585$	11.2707	+	13.5676i	0.465986	+	0.560952i
$586$	13.3454	−	23.1150i	0.551295	−	0.954871i
$587$	−28.4879	−	16.4475i	−1.17582	−	0.678861i	−0.220778	−	0.975324i	$-0.570860\pi$
$587$	−28.4879	−	16.4475i	−1.17582	−	0.678861i	−0.955044	+	0.296463i	$0.904193\pi$
$588$	−3.64730	+	6.31731i	−0.150412	+	0.260522i
$589$	−4.20682	−	5.92810i	−0.173339	−	0.244263i
$590$			29.8128i			1.22737i
$591$	−7.21464	+	4.16537i	−0.296771	+	0.171341i
$592$		−	1.80328i		−	0.0741142i
$593$			34.6753i			1.42394i	0.702208	+	0.711971i	$0.252197\pi$
$593$			34.6753i			1.42394i	−0.702208	+	0.711971i	$0.747803\pi$
$594$	10.3536	−	17.9330i	0.424814	−	0.735800i
$595$	18.1563	+	31.4476i	0.744336	+	1.28923i
$596$	−4.15535	+	2.39909i	−0.170210	+	0.0982707i
$597$	3.70248			0.151533
$598$	3.20133	−	8.66204i	0.130912	−	0.354217i
$599$	−0.0123804	−	0.0214435i	−0.000505850	−	0.000876157i	0.865772	−	0.500438i	$-0.166828\pi$
$599$	−0.0123804	−	0.0214435i	−0.000505850	−	0.000876157i	−0.866278	+	0.499562i	$0.833494\pi$
$600$			3.57069i			0.145773i
$601$	−6.57378	−	11.3861i	−0.268150	−	0.464449i	0.700234	−	0.713913i	$-0.253079\pi$
$601$	−6.57378	−	11.3861i	−0.268150	−	0.464449i	−0.968384	+	0.249464i	$0.919746\pi$
$602$	27.2527	−	47.2031i	1.11074	−	1.92386i
$603$	9.24104	+	5.33532i	0.376324	+	0.217271i
$604$	−2.10301	+	1.21417i	−0.0855704	+	0.0494041i
$605$	−2.92054	+	1.68617i	−0.118737	+	0.0685528i
$606$	17.8862	+	10.3266i	0.726579	+	0.419490i
$607$	0.886944	−	1.53623i	0.0360000	−	0.0623538i	−0.847464	−	0.530853i	$-0.821872\pi$
$607$	0.886944	−	1.53623i	0.0360000	−	0.0623538i	0.883464	+	0.468499i	$0.155205\pi$
$608$	−2.24080	−	3.88118i	−0.0908765	−	0.157403i
$609$		−	23.6231i		−	0.957255i
$610$	21.1309	+	36.5998i	0.855565	+	1.48188i
$611$	−14.3939	−	17.3273i	−0.582315	−	0.700988i
$612$	−4.27599			−0.172847
$613$	−12.0916	+	6.98106i	−0.488373	+	0.281962i	−0.723899	−	0.689906i	$-0.757652\pi$
$613$	−12.0916	+	6.98106i	−0.488373	+	0.281962i	0.235526	+	0.971868i	$0.424319\pi$
$614$	9.82489	+	17.0172i	0.396500	+	0.686758i
$615$	−8.51075	+	14.7411i	−0.343187	+	0.594417i
$616$		−	46.3760i		−	1.86854i
$617$		−	13.0779i		−	0.526498i	−0.964728	−	0.263249i	$-0.915206\pi$
$617$		−	13.0779i		−	0.526498i	0.964728	−	0.263249i	$-0.0847940\pi$
$618$	−11.8797	+	6.85877i	−0.477873	+	0.275900i
$619$		−	10.8427i		−	0.435804i	−0.975971	−	0.217902i	$-0.930079\pi$
$619$		−	10.8427i		−	0.435804i	0.975971	−	0.217902i	$-0.0699213\pi$
$620$	−8.70902	+	0.817266i	−0.349762	+	0.0328222i
$621$	5.52084	−	9.56238i	0.221544	−	0.383725i
$622$	1.01730	+	0.587339i	0.0407900	+	0.0235501i
$623$	2.88953	−	5.00482i	0.115767	−	0.200514i
$624$	−6.54941	+	5.44064i	−0.262186	+	0.217800i
$625$	14.7067	+	25.4728i	0.588268	+	1.01891i
$626$	−31.6049	+	18.2471i	−1.26318	+	0.729300i
$627$	2.32526	+	4.02747i	0.0928619	+	0.160842i
$628$	−3.70458	−	6.41652i	−0.147829	−	0.256047i
$629$	2.29067	−	1.32252i	0.0913349	−	0.0527323i
$630$	−21.2184	−	12.2504i	−0.845360	−	0.488069i
$631$	39.9896	+	23.0880i	1.59196	+	0.919119i	0.992970	+	0.118362i	$0.0377645\pi$
$631$	39.9896	+	23.0880i	1.59196	+	0.919119i	0.598990	+	0.800756i	$0.295569\pi$
$632$	5.91585	+	3.41552i	0.235320	+	0.135862i
$633$	2.46589	−	4.27104i	0.0980103	−	0.169759i
$634$	−8.71339	−	15.0920i	−0.346053	−	0.599381i
$635$	−7.35619	−	4.24710i	−0.291922	−	0.168541i
$636$	−6.13314			−0.243195
$637$	31.5063	−	26.1725i	1.24832	−	1.03699i
$638$	11.1805	+	19.3652i	0.442641	+	0.766677i
$639$	1.37647	−	0.794707i	0.0544524	−	0.0314381i
$640$	8.11353			0.320715
$641$	−12.0155	+	20.8114i	−0.474583	+	0.822002i	−0.999576	−	0.0291041i	$-0.990735\pi$
$641$	−12.0155	+	20.8114i	−0.474583	+	0.822002i	0.524993	+	0.851106i	$0.324068\pi$
$642$	−10.9541	+	6.32434i	−0.432323	+	0.249602i
$643$	−9.87327	+	5.70034i	−0.389364	+	0.224799i	−0.681884	−	0.731460i	$-0.738839\pi$
$643$	−9.87327	+	5.70034i	−0.389364	+	0.224799i	0.292521	+	0.956259i	$0.405506\pi$
$644$		−	5.95066i		−	0.234489i
$645$	23.6708	+	13.6664i	0.932037	+	0.538112i
$646$	−2.60854	+	4.51812i	−0.102632	+	0.177763i
$647$	0.779003	−	1.34927i	0.0306258	−	0.0530454i	−0.850306	−	0.526288i	$-0.823583\pi$
$647$	0.779003	−	1.34927i	0.0306258	−	0.0530454i	0.880932	+	0.473243i	$0.156917\pi$
$648$	2.17287	−	1.25451i	0.0853584	−	0.0492817i
$649$	36.1748			1.41998
$650$	1.67250	−	4.52540i	0.0656010	−	0.177501i
$651$	−10.0771	+	21.9707i	−0.394951	+	0.861099i
$652$	−1.13305	−	0.654165i	−0.0443736	−	0.0256191i
$653$	9.41441	−	16.3062i	0.368414	−	0.638112i	−0.620904	−	0.783887i	$-0.713234\pi$
$653$	9.41441	−	16.3062i	0.368414	−	0.638112i	0.989318	+	0.145775i	$0.0465675\pi$
$654$	−19.9859			−0.781509
$655$			41.8451i			1.63502i
$656$	13.6800	+	7.89818i	0.534116	+	0.308372i
$657$		−	29.9632i		−	1.16898i
$658$	27.0981	+	15.6451i	1.05640	+	0.609910i
$659$	16.2447	+	28.1366i	0.632804	+	1.09605i	0.986976	+	0.160868i	$0.0514293\pi$
$659$	16.2447	+	28.1366i	0.632804	+	1.09605i	−0.354172	+	0.935180i	$0.615237\pi$
$660$	5.59621			0.217832
$661$		−	23.4053i		−	0.910360i	−0.890399	−	0.455180i	$-0.849575\pi$
$661$		−	23.4053i		−	0.910360i	0.890399	−	0.455180i	$-0.150425\pi$
$662$	−14.1933	−	24.5835i	−0.551639	−	0.955467i
$663$	−11.7145	−	4.32945i	−0.454952	−	0.168142i
$664$	−9.10932	−	15.7778i	−0.353510	−	0.612298i
$665$	12.0094	−	6.93361i	0.465703	−	0.268874i
$666$	−0.892330	+	1.54556i	−0.0345771	+	0.0598893i
$667$	5.96177	+	10.3261i	0.230841	+	0.399828i
$668$	−7.69448	−	4.44241i	−0.297708	−	0.171882i
$669$	−8.90659	−	5.14222i	−0.344349	−	0.198810i
$670$		−	15.6665i		−	0.605251i
$671$	44.4101	−	25.6402i	1.71443	−	0.989828i
$672$	−7.45119	+	12.9058i	−0.287436	+	0.497854i
$673$	−2.84902			−0.109822			−0.0549108	−	0.998491i	$-0.517487\pi$
$673$	−2.84902			−0.109822			−0.0549108	+	0.998491i	$0.517487\pi$
$674$	11.6092	+	6.70258i	0.447170	+	0.258174i
$675$	2.88431	−	4.99577i	0.111017	−	0.192287i
$676$	−7.76975	+	2.74123i	−0.298837	+	0.105432i
$677$	7.00045	+	12.1251i	0.269049	+	0.466007i	0.968617	−	0.248560i	$-0.0799572\pi$
$677$	7.00045	+	12.1251i	0.269049	+	0.466007i	−0.699567	+	0.714567i	$0.746624\pi$
$678$	6.05458	+	3.49561i	0.232525	+	0.134248i
$679$	−35.9199	−	62.2150i	−1.37848	−	2.38759i
$680$	13.0446	+	22.5939i	0.500238	+	0.866437i
$681$		−	3.65145i		−	0.139924i
$682$	−2.13771	−	22.7800i	−0.0818572	−	0.872292i
$683$	−37.2648	+	21.5148i	−1.42590	+	0.823242i	−0.996794	−	0.0800140i	$-0.974504\pi$
$683$	−37.2648	+	21.5148i	−1.42590	+	0.823242i	−0.429103	+	0.903256i	$0.641170\pi$
$684$			1.63293i			0.0624368i
$685$	−11.5011			−0.439433
$686$	−10.9182	+	18.9109i	−0.416860	+	0.722022i
$687$		−	0.801545i		−	0.0305809i
$688$	12.6827	−	21.9671i	0.483523	−	0.837487i
$689$	32.3020	+	11.9382i	1.23061	+	0.454809i
$690$	−6.43265			−0.244887
$691$			5.12400i			0.194926i	0.995239	+	0.0974631i	$0.0310728\pi$
$691$			5.12400i			0.194926i	−0.995239	+	0.0974631i	$0.968927\pi$
$692$	−9.30556			−0.353744
$693$	−14.8646	+	25.7463i	−0.564661	+	0.978021i
$694$	3.10421	+	1.79222i	0.117834	+	0.0680316i
$695$	26.8509	+	15.5024i	1.01851	+	0.588038i
$696$		−	16.9723i		−	0.643332i
$697$			23.1700i			0.877627i
$698$	12.0386	+	20.8515i	0.455669	+	0.789242i
$699$	−4.56177	−	7.90122i	−0.172542	−	0.298852i
$700$		−	3.10886i		−	0.117504i
$701$	−21.1090	+	36.5619i	−0.797277	+	1.38092i	0.124107	+	0.992269i	$0.460394\pi$
$701$	−21.1090	+	36.5619i	−0.797277	+	1.38092i	−0.921383	+	0.388655i	$0.872940\pi$
$702$	20.9316	−	3.58415i	0.790011	−	0.135275i
$703$	−0.505049	−	0.874771i	−0.0190483	−	0.0329926i
$704$		−	30.4950i		−	1.14932i
$705$	−7.84551	+	13.5888i	−0.295479	+	0.511785i
$706$	−39.9560			−1.50376
$707$	−64.7157	−	37.3636i	−2.43388	−	1.40520i
$708$	−5.72194	−	3.30356i	−0.215044	−	0.124155i
$709$	−5.64475	+	3.25900i	−0.211993	+	0.122394i	−0.602237	−	0.798317i	$-0.705724\pi$
$709$	−5.64475	+	3.25900i	−0.211993	+	0.122394i	0.390244	+	0.920711i	$0.372391\pi$
$710$	−2.02093	−	1.16678i	−0.0758440	−	0.0437886i
$711$	−2.18951	−	3.79235i	−0.0821132	−	0.142224i
$712$	2.07602	−	3.59577i	0.0778021	−	0.134757i
$713$	−1.13989	−	12.1470i	−0.0426891	−	0.454907i
$714$	17.3480			0.649232
$715$	−29.4741	−	10.8931i	−1.10227	−	0.407378i
$716$	0.890597	−	1.54256i	0.0332832	−	0.0576482i
$717$	8.47096	+	4.89071i	0.316354	+	0.182647i
$718$	7.25080			0.270597
$719$	8.36030			0.311786			0.155893	−	0.987774i	$-0.450174\pi$
$719$	8.36030			0.311786			0.155893	+	0.987774i	$0.450174\pi$
$720$	−9.87446	−	5.70102i	−0.367999	−	0.212465i
$721$	42.9831	−	24.8163i	1.60077	−	0.924207i
$722$	−17.5075	−	10.1080i	−0.651561	−	0.376179i
$723$	3.33244	−	1.92399i	0.123935	−	0.0715539i
$724$	−6.19265	+	10.7260i	−0.230148	+	0.398628i
$725$	3.11467	+	5.39476i	0.115676	+	0.200356i
$726$			1.61111i			0.0597938i
$727$	17.7235	−	30.6980i	0.657328	−	1.13853i	−0.323977	−	0.946065i	$-0.605020\pi$
$727$	17.7235	−	30.6980i	0.657328	−	1.13853i	0.981305	−	0.192460i	$-0.0616467\pi$
$728$	36.5843	−	30.3908i	1.35591	−	1.12636i
$729$	13.7078			0.507697
$730$	−38.0980	+	21.9959i	−1.41007	+	0.814104i
$731$	37.2058			1.37611
$732$	−9.36608			−0.346180
$733$	−26.8709	+	15.5139i	−0.992499	+	0.573020i	−0.906020	−	0.423234i	$-0.860895\pi$
$733$	−26.8709	+	15.5139i	−0.992499	+	0.573020i	−0.0864787	+	0.996254i	$0.527561\pi$
$734$	−23.8963	−	13.7965i	−0.882028	−	0.509239i
$735$	−24.7086	−	14.2655i	−0.911389	−	0.526191i
$736$		−	7.52185i		−	0.277259i
$737$	−19.0097			−0.700233
$738$	−7.81664	−	13.5388i	−0.287735	−	0.498371i
$739$		−	1.12769i		−	0.0414829i	−0.999785	−	0.0207414i	$-0.993397\pi$
$739$		−	1.12769i		−	0.0414829i	0.999785	−	0.0207414i	$-0.00660268\pi$
$740$	−1.21550			−0.0446828
$741$	−1.65335	+	4.47357i	−0.0607373	+	0.164341i
$742$	−47.8361			−1.75612
$743$	9.48013	+	5.47336i	0.347792	+	0.200798i	0.663712	−	0.747988i	$-0.268980\pi$
$743$	9.48013	+	5.47336i	0.347792	+	0.200798i	−0.315920	+	0.948786i	$0.602313\pi$
$744$	−7.23998	+	15.7851i	−0.265430	+	0.578710i
$745$	−9.38344	−	16.2526i	−0.343783	−	0.595449i
$746$			43.7709i			1.60257i
$747$			11.6790i			0.427314i
$748$	6.59711	−	3.80884i	0.241214	−	0.139265i
$749$	39.6339	−	22.8826i	1.44819	−	0.836113i
$750$	11.3174			0.413253
$751$	−24.7199	−	42.8162i	−0.902044	−	1.56239i	−0.824837	−	0.565370i	$-0.808733\pi$
$751$	−24.7199	−	42.8162i	−0.902044	−	1.56239i	−0.0772065	−	0.997015i	$-0.524600\pi$
$752$	12.6108	+	7.28082i	0.459867	+	0.265504i
$753$	7.97618	+	13.8152i	0.290668	+	0.503452i
$754$	−7.94978	+	21.5102i	−0.289514	+	0.783356i
$755$	−4.74894	−	8.22540i	−0.172831	−	0.299353i
$756$	11.8509	−	6.84210i	0.431012	−	0.248845i
$757$	−11.3012			−0.410750			−0.205375	−	0.978683i	$-0.565841\pi$
$757$	−11.3012			−0.410750			−0.205375	+	0.978683i	$0.565841\pi$
$758$	−1.74728			−0.0634640
$759$			7.80535i			0.283316i
$760$	8.62826	−	4.98153i	0.312980	−	0.180699i
$761$			5.41449i			0.196275i	0.995173	+	0.0981375i	$0.0312885\pi$
$761$			5.41449i			0.196275i	−0.995173	+	0.0981375i	$0.968712\pi$
$762$	−3.51435	+	2.02901i	−0.127311	+	0.0735033i
$763$	72.3125			2.61789
$764$	7.64210			0.276482
$765$		−	16.7245i		−	0.604674i
$766$	−10.8909	−	18.8636i	−0.393504	−	0.681569i
$767$	23.7058	+	28.5370i	0.855968	+	1.03041i
$768$	−6.85005	+	11.8646i	−0.247180	+	0.428128i
$769$	3.47394	−	2.00568i	0.125273	−	0.0723266i	−0.436054	−	0.899921i	$-0.643624\pi$
$769$	3.47394	−	2.00568i	0.125273	−	0.0723266i	0.561327	+	0.827594i	$0.310291\pi$
$770$	43.6483			1.57297
$771$	0.235873	+	0.408543i	0.00849474	+	0.0147133i
$772$	−9.73872	−	5.62265i	−0.350504	−	0.202364i
$773$	4.78205	−	2.76092i	0.171998	−	0.0993033i	−0.411529	−	0.911396i	$-0.635005\pi$
$773$	4.78205	−	2.76092i	0.171998	−	0.0993033i	0.583528	+	0.812093i	$0.301672\pi$
$774$	−21.7403	+	12.5518i	−0.781439	+	0.451164i
$775$	−0.595523	−	6.34606i	−0.0213918	−	0.227957i
$776$	−25.8070	−	44.6991i	−0.926419	−	1.60460i
$777$	−1.67941	+	2.90882i	−0.0602484	+	0.104353i
$778$	−8.23171	+	4.75258i	−0.295121	+	0.170388i
$779$	8.84827			0.317022
$780$	3.66728	+	4.41465i	0.131310	+	0.158070i
$781$	−1.41577	+	2.45219i	−0.0506602	+	0.0877461i
$782$	−7.58313	+	4.37812i	−0.271172	+	0.156561i
$783$	−13.7098	+	23.7460i	−0.489947	+	0.848613i
$784$	−13.2387	+	22.9301i	−0.472811	+	0.818934i
$785$	25.0966	−	14.4895i	0.895735	−	0.517153i
$786$	17.3128	+	9.99556i	0.617528	+	0.356530i
$787$			55.6211i			1.98268i	0.131333	+	0.991338i	$0.458074\pi$
$787$			55.6211i			1.98268i	−0.131333	+	0.991338i	$0.541926\pi$
$788$	4.51303	−	2.60560i	0.160770	−	0.0928205i
$789$	−22.3223			−0.794693
$790$	−3.21463	+	5.56789i	−0.114371	+	0.198097i
$791$	−21.9066	−	12.6478i	−0.778908	−	0.449703i
$792$	−10.6797	+	18.4977i	−0.379486	+	0.657288i
$793$	49.3291	+	18.2311i	1.75173	+	0.647406i
$794$	6.22195	−	10.7767i	0.220809	−	0.382452i
$795$		−	23.9882i		−	0.850775i
$796$	−2.31604			−0.0820899
$797$	−17.2592	+	29.8938i	−0.611352	+	1.05889i	0.379661	+	0.925126i	$0.376041\pi$
$797$	−17.2592	+	29.8938i	−0.611352	+	1.05889i	−0.991013	+	0.133766i	$0.957293\pi$
$798$		−	6.62493i		−	0.234520i
$799$			21.3589i			0.755625i
$800$		−	3.92972i		−	0.138936i
$801$	−2.30507	+	1.33083i	−0.0814455	+	0.0470226i
$802$	6.70610	+	11.6153i	0.236801	+	0.410151i
$803$	26.6897	+	46.2280i	0.941861	+	1.63135i
$804$	3.00686	+	1.73601i	0.106044	+	0.0612245i
$805$	23.2745			0.820318
$806$	16.5695	−	16.6144i	0.583635	−	0.585219i
$807$	25.2415			0.888542
$808$	−46.4957	−	26.8443i	−1.63571	−	0.944380i
$809$	8.62600	+	14.9407i	0.303274	+	0.525286i	0.976876	−	0.213809i	$-0.0685869\pi$
$809$	8.62600	+	14.9407i	0.303274	+	0.525286i	−0.673601	+	0.739095i	$0.735254\pi$
$810$	1.18072	+	2.04507i	0.0414863	+	0.0718564i
$811$	−17.0153	+	9.82381i	−0.597489	+	0.344961i	−0.768053	−	0.640386i	$-0.778774\pi$
$811$	−17.0153	+	9.82381i	−0.597489	+	0.344961i	0.170564	+	0.985347i	$0.445441\pi$
$812$			14.7771i			0.518575i
$813$			0.148246i			0.00519922i
$814$		−	3.17937i		−	0.111437i
$815$	2.55860	−	4.43163i	0.0896239	−	0.155233i
$816$	8.07330			0.282622
$817$		−	14.2083i		−	0.497086i
$818$	3.00378	−	5.20269i	0.105025	−	0.181908i
$819$	−30.0513	+	5.14574i	−1.05008	+	0.179807i
$820$	5.32379	−	9.22108i	0.185915	−	0.322014i
$821$	−4.11030	−	2.37308i	−0.143450	−	0.0828211i	0.426557	−	0.904461i	$-0.359726\pi$
$821$	−4.11030	−	2.37308i	−0.143450	−	0.0828211i	−0.570007	+	0.821640i	$0.693060\pi$
$822$	−2.74726	+	4.75840i	−0.0958218	+	0.165968i
$823$	−10.7145			−0.373484			−0.186742	−	0.982409i	$-0.559793\pi$
$823$	−10.7145			−0.373484			−0.186742	+	0.982409i	$0.559793\pi$
$824$	30.8817	−	17.8296i	1.07581	−	0.621122i
$825$			4.07783i			0.141972i
$826$	−44.6289	−	25.7665i	−1.55284	−	0.896531i
$827$	33.7029	−	19.4584i	1.17197	−	0.676635i	0.217823	−	0.975988i	$-0.430104\pi$
$827$	33.7029	−	19.4584i	1.17197	−	0.676635i	0.954142	+	0.299354i	$0.0967710\pi$
$828$	−1.37035	+	2.37351i	−0.0476228	+	0.0824851i
$829$	−1.91361	+	3.31446i	−0.0664623	+	0.115116i	−0.897342	−	0.441336i	$-0.854505\pi$
$829$	−1.91361	+	3.31446i	−0.0664623	+	0.115116i	0.830879	+	0.556453i	$0.187838\pi$
$830$	14.8498	−	8.57354i	0.515444	−	0.297592i
$831$	4.74580	−	8.21997i	0.164630	−	0.285148i
$832$	24.0564	−	19.9838i	0.834005	−	0.692813i
$833$	−38.8370			−1.34562
$834$	12.8277	−	7.40610i	0.444189	−	0.256452i
$835$	17.3754	−	30.0950i	0.601299	−	1.04148i
$836$	−1.45454	−	2.51933i	−0.0503062	−	0.0871329i
$837$	22.8803	−	16.2368i	0.790858	−	0.561224i
$838$	−23.2784	+	13.4398i	−0.804138	+	0.464269i
$839$	−42.8550	+	24.7424i	−1.47952	+	0.854201i	−0.999731	−	0.0231832i	$-0.992620\pi$
$839$	−42.8550	+	24.7424i	−1.47952	+	0.854201i	−0.479788	+	0.877384i	$0.659287\pi$
$840$	−28.6910	−	16.5648i	−0.989933	−	0.571538i
$841$	−0.304703	−	0.527762i	−0.0105070	−	0.0181987i
$842$	28.0973			0.968298
$843$	10.2925	−	5.94240i	0.354494	−	0.204667i
$844$	−1.54250	+	2.67170i	−0.0530952	+	0.0919636i
$845$	−10.7216	−	30.3894i	−0.368835	−	1.04543i
$846$	−7.20566	−	12.4806i	−0.247736	−	0.429091i
$847$		−	5.82928i		−	0.200297i
$848$	−22.2617			−0.764468
$849$	−8.45221			−0.290079
$850$	−3.96173	+	2.28731i	−0.135886	+	0.0784540i
$851$		−	1.69533i		−	0.0581152i
$852$	0.447879	−	0.258583i	0.0153441	−	0.00885890i
$853$			42.1435i			1.44296i	0.692433	+	0.721482i	$0.256539\pi$
$853$			42.1435i			1.44296i	−0.692433	+	0.721482i	$0.743461\pi$
$854$	−73.0517			−2.49978
$855$	−6.38681			−0.218424
$856$	28.4754	−	16.4403i	0.973270	−	0.561918i
$857$	20.3635	+	35.2706i	0.695603	+	1.20482i	0.969977	+	0.243197i	$0.0781962\pi$
$857$	20.3635	+	35.2706i	0.695603	+	1.20482i	−0.274374	+	0.961623i	$0.588470\pi$
$858$	−11.5473	+	9.59244i	−0.394219	+	0.327480i
$859$	−15.3397	−	26.5692i	−0.523385	−	0.906530i	−0.999630	−	0.0272168i	$-0.991336\pi$
$859$	−15.3397	−	26.5692i	−0.523385	−	0.906530i	0.476244	−	0.879313i	$-0.341998\pi$
$860$	−14.8070	−	8.54881i	−0.504914	−	0.291512i
$861$	−14.7113	−	25.4807i	−0.501359	−	0.868379i
$862$	−14.3831			−0.489889
$863$	−22.1471	+	12.7866i	−0.753896	+	0.435262i	−0.827100	−	0.562055i	$-0.810011\pi$
$863$	−22.1471	+	12.7866i	−0.753896	+	0.435262i	0.0732040	+	0.997317i	$0.476678\pi$
$864$	14.9799	−	8.64867i	0.509628	−	0.294234i
$865$		−	36.3963i		−	1.23751i
$866$			6.28905i			0.213711i
$867$	−2.69107	−	4.66107i	−0.0913936	−	0.158298i
$868$	6.30357	−	13.7435i	0.213957	−	0.466484i
$869$	6.75607	+	3.90062i	0.229184	+	0.132319i
$870$	15.9740			0.541570
$871$	−12.4574	−	14.9961i	−0.422101	−	0.508123i
$872$	51.9538			1.75938
$873$			33.0872i			1.11983i
$874$	1.67194	+	2.89588i	0.0565541	+	0.0979546i
$875$	−40.9485			−1.38431
$876$		−	9.74948i		−	0.329404i
$877$	−3.12420	−	1.80376i	−0.105497	−	0.0609086i	0.446323	−	0.894872i	$-0.352733\pi$
$877$	−3.12420	−	1.80376i	−0.105497	−	0.0609086i	−0.551820	+	0.833963i	$0.686066\pi$
$878$	34.1989	+	19.7447i	1.15416	+	0.666353i
$879$	−20.0364	+	11.5680i	−0.675809	+	0.390179i
$880$	20.3127			0.684743
$881$	−10.6187			−0.357754			−0.178877	−	0.983871i	$-0.557246\pi$
$881$	−10.6187			−0.357754			−0.178877	+	0.983871i	$0.557246\pi$
$882$	22.6934	−	13.1021i	0.764127	−	0.441169i
$883$	−41.2462			−1.38804			−0.694022	−	0.719953i	$-0.744163\pi$
$883$	−41.2462			−1.38804			−0.694022	+	0.719953i	$0.744163\pi$
$884$	7.32783	+	2.70823i	0.246462	+	0.0910876i
$885$	12.9210	−	22.3799i	0.434336	−	0.752292i
$886$		−	17.1256i		−	0.575345i
$887$	8.58337	+	14.8668i	0.288201	+	0.499179i	0.973380	−	0.229195i	$-0.0736094\pi$
$887$	8.58337	+	14.8668i	0.288201	+	0.499179i	−0.685179	+	0.728375i	$0.740276\pi$
$888$	−1.20659	+	2.08987i	−0.0404905	+	0.0701316i
$889$	12.7156	−	7.34133i	0.426466	−	0.246220i
$890$	3.38428	+	1.95391i	0.113441	+	0.0654954i
$891$	2.48148	−	1.43268i	0.0831327	−	0.0479967i
$892$	5.57140	+	3.21665i	0.186544	+	0.107701i
$893$	8.15665			0.272952
$894$	−8.96570			−0.299858
$895$	6.03333	+	3.48334i	0.201672	+	0.116435i
$896$	−7.01233	+	12.1457i	−0.234266	+	0.405760i
$897$	−6.15736	+	5.11496i	−0.205588	+	0.170784i
$898$	4.32285			0.144255
$899$	2.83065	+	30.1642i	0.0944075	+	1.00603i
$900$	−0.715923	+	1.24002i	−0.0238641	+	0.0413338i
$901$	−16.3266	−	28.2786i	−0.543919	−	0.942096i
$902$	24.1194	+	13.9254i	0.803089	+	0.463664i
$903$	−40.9162	+	23.6230i	−1.36161	+	0.786124i
$904$	−15.7390	−	9.08693i	−0.523472	−	0.302227i
$905$	−41.9520	−	24.2210i	−1.39453	−	0.805133i
$906$	−4.53752			−0.150749
$907$	14.4523	−	25.0321i	0.479881	−	0.831178i	−0.519853	−	0.854256i	$-0.674013\pi$
$907$	14.4523	−	25.0321i	0.479881	−	0.831178i	0.999734	+	0.0230780i	$0.00734660\pi$
$908$			2.28412i			0.0758011i
$909$	17.2085	+	29.8060i	0.570771	+	0.988604i
$910$	28.6033	+	34.4325i	0.948191	+	1.14143i
$911$	−26.3958	+	45.7188i	−0.874531	+	1.51473i	−0.0172691	+	0.999851i	$0.505497\pi$
$911$	−26.3958	+	45.7188i	−0.874531	+	1.51473i	−0.857262	+	0.514881i	$0.827836\pi$
$912$		−	3.08307i		−	0.102090i
$913$	−10.4031	−	18.0187i	−0.344293	−	0.596332i
$914$	−1.26223	−	2.18624i	−0.0417508	−	0.0723145i
$915$		−	36.6330i		−	1.21105i
$916$			0.501396i			0.0165666i
$917$	−62.6409	−	36.1658i	−2.06859	−	1.19430i
$918$	−17.4383	−	10.0680i	−0.575549	−	0.332293i
$919$	9.46222	−	16.3890i	0.312130	−	0.540625i	−0.666693	−	0.745332i	$-0.732291\pi$
$919$	9.46222	−	16.3890i	0.312130	−	0.540625i	0.978823	+	0.204707i	$0.0656243\pi$
$920$	16.7218			0.551302
$921$		−	17.0327i		−	0.561245i
$922$	0.0509317			0.00167735
$923$	−2.86221	+	0.490102i	−0.0942110	+	0.0161319i
$924$	−4.83668	+	8.37737i	−0.159115	+	0.275595i
$925$		−	0.885709i		−	0.0291219i
$926$	−2.62071	+	4.53920i	−0.0861218	+	0.149167i
$927$	−22.8592			−0.750796
$928$			18.6788i			0.613162i
$929$	−40.1110	+	23.1581i	−1.31600	+	0.759792i	−0.983082	−	0.183164i	$-0.941366\pi$
$929$	−40.1110	+	23.1581i	−1.31600	+	0.759792i	−0.332917	+	0.942956i	$0.608033\pi$
$930$	−14.8567	−	6.81414i	−0.487169	−	0.223445i
$931$			14.8312i			0.486074i
$932$	2.85356	+	4.94251i	0.0934714	+	0.161897i
$933$	−0.509112	−	0.881808i	−0.0166676	−	0.0288691i
$934$	−8.10786	−	4.68107i	−0.265297	−	0.153169i
$935$	14.8973	+	25.8029i	0.487194	+	0.843845i
$936$	−21.5907	+	3.69702i	−0.705715	+	0.120841i
$937$	−9.41835	+	16.3131i	−0.307684	+	0.532925i	−0.977855	−	0.209282i	$-0.932887\pi$
$937$	−9.41835	+	16.3131i	−0.307684	+	0.532925i	0.670171	+	0.742207i	$0.266221\pi$
$938$	23.4524	+	13.5402i	0.765747	+	0.442104i
$939$	31.6336			1.03232
$940$	4.90766	−	8.50032i	0.160070	−	0.277250i
$941$	−33.6119	+	19.4058i	−1.09572	+	0.632611i	−0.935092	−	0.354404i	$-0.884684\pi$
$941$	−33.6119	+	19.4058i	−1.09572	+	0.632611i	−0.160623	+	0.987016i	$0.551350\pi$
$942$		−	13.8445i		−	0.451077i
$943$	12.8612	+	7.42539i	0.418817	+	0.241804i
$944$	−20.7691	−	11.9910i	−0.675976	−	0.390275i
$945$	26.7612	+	46.3517i	0.870540	+	1.50782i
$946$	22.3610	−	38.7304i	0.727018	−	1.25923i
$947$	−14.2394	+	8.22115i	−0.462720	+	0.267151i	−0.713187	−	0.700974i	$-0.752749\pi$
$947$	−14.2394	+	8.22115i	−0.462720	+	0.267151i	0.250467	+	0.968125i	$0.419416\pi$
$948$	−0.712427	−	1.23396i	−0.0231385	−	0.0400771i
$949$	−18.9774	+	51.3484i	−0.616033	+	1.66684i
$950$	0.873487	+	1.51292i	0.0283397	+	0.0490857i
$951$			15.1057i			0.489837i
$952$	−45.0966			−1.46159
$953$	11.1814	+	19.3667i	0.362201	+	0.627351i	0.988323	−	0.152375i	$-0.0486921\pi$
$953$	11.1814	+	19.3667i	0.362201	+	0.627351i	−0.626122	+	0.779725i	$0.715359\pi$
$954$	19.0801	+	11.0159i	0.617742	+	0.356654i
$955$			29.8902i			0.967223i
$956$	−5.29890	−	3.05932i	−0.171379	−	0.0989456i
$957$		−	19.3828i		−	0.626558i
$958$	24.6651			0.796893
$959$	9.94010	−	17.2168i	0.320983	−	0.555958i
$960$	−18.8660	−	10.8923i	−0.608899	−	0.351548i
$961$	10.2347	−	29.2618i	0.330151	−	0.943928i
$962$	2.50809	−	2.08349i	0.0808641	−	0.0671744i
$963$	−21.0781			−0.679231
$964$	−2.08457	+	1.20353i	−0.0671394	+	0.0387630i
$965$	21.9916	−	38.0905i	0.707934	−	1.22618i
$966$	5.55958	−	9.62948i	0.178877	−	0.309823i
$967$	7.14558	+	4.12550i	0.229786	+	0.132667i	0.610474	−	0.792037i	$-0.290979\pi$
$967$	7.14558	+	4.12550i	0.229786	+	0.132667i	−0.380687	+	0.924704i	$0.624313\pi$
$968$		−	4.18812i		−	0.134611i
$969$	3.91636	−	2.26111i	0.125812	−	0.0726374i
$970$	42.0700	−	24.2891i	1.35079	−	0.779878i
$971$	−10.6047	+	18.3679i	−0.340321	+	0.589453i	−0.984492	−	0.175428i	$-0.943869\pi$
$971$	−10.6047	+	18.3679i	−0.340321	+	0.589453i	0.644171	+	0.764881i	$0.277202\pi$
$972$	−10.1042			−0.324093
$973$	−46.4131	+	26.7966i	−1.48794	+	0.859061i
$974$	3.47595	+	6.02052i	0.111377	+	0.192910i
$975$	−3.21685	+	2.67226i	−0.103022	+	0.0855808i
$976$	−33.9963			−1.08820
$977$	32.7463	+	18.9061i	1.04765	+	0.604859i	0.921990	−	0.387214i	$-0.126563\pi$
$977$	32.7463	+	18.9061i	1.04765	+	0.604859i	0.125658	+	0.992074i	$0.459896\pi$
$978$	−1.22235	−	2.11717i	−0.0390864	−	0.0676996i
$979$	2.37087	−	4.10647i	0.0757735	−	0.131243i
$980$	15.4561	+	8.92360i	0.493728	+	0.285054i
$981$	−28.8429	−	16.6525i	−0.920883	−	0.531672i
$982$	29.2744	+	16.9016i	0.934184	+	0.539352i
$983$	−9.24576	+	5.33804i	−0.294894	+	0.170257i	−0.640147	−	0.768253i	$-0.721126\pi$
$983$	−9.24576	+	5.33804i	−0.294894	+	0.170257i	0.345253	+	0.938510i	$0.387793\pi$
$984$	−10.5695	−	18.3069i	−0.336943	−	0.583602i
$985$	10.1911	+	17.6516i	0.324716	+	0.562425i
$986$	18.8310	−	10.8721i	0.599701	−	0.346238i
$987$	−13.5614	−	23.4890i	−0.431664	−	0.747663i
$988$	1.03423	−	2.79838i	0.0329033	−	0.0890285i
$989$	11.9235	−	20.6521i	0.379145	−	0.656699i
$990$	−17.4098	−	10.0515i	−0.553318	−	0.319458i
$991$	−20.4233	+	35.3742i	−0.648769	+	1.12370i	0.334649	+	0.942343i	$0.391382\pi$
$991$	−20.4233	+	35.3742i	−0.648769	+	1.12370i	−0.983417	+	0.181357i	$0.941951\pi$
$992$	7.96794	−	17.3723i	0.252982	−	0.551570i
$993$			24.6059i			0.780844i
$994$	3.49328	−	2.01684i	0.110800	−	0.0639704i
$995$		−	9.05861i		−	0.287177i
$996$			3.80014i			0.120412i
$997$	22.8870	−	39.6415i	0.724840	−	1.25546i	−0.234200	−	0.972189i	$-0.575247\pi$
$997$	22.8870	−	39.6415i	0.724840	−	1.25546i	0.959040	−	0.283271i	$-0.0914197\pi$
$998$	−12.6854	−	21.9717i	−0.401549	−	0.695503i
$999$	3.37629	−	1.94930i	0.106821	−	0.0616732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.s.a.160.11	✓	70
13.10	even	6		403.2.v.a.36.11	yes	70
31.25	even	3		403.2.v.a.56.11	yes	70
403.335	even	6	inner	403.2.s.a.335.11	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.11	✓	70	1.1	even	1	trivial
403.2.s.a.335.11	yes	70	403.335	even	6	inner
403.2.v.a.36.11	yes	70	13.10	even	6
403.2.v.a.56.11	yes	70	31.25	even	3

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01226 - 0.584427i) q^{2} +(0.506588 + 0.877437i) q^{3} +(-0.316890 - 0.548870i) q^{4} +(2.14676 - 1.23943i) q^{5} -1.18426i q^{6} +4.28486i q^{7} +3.07850i q^{8} +(0.986736 - 1.70908i) q^{9} +O(q^{10})\)	\(q+(-1.01226 - 0.584427i) q^{2} +(0.506588 + 0.877437i) q^{3} +(-0.316890 - 0.548870i) q^{4} +(2.14676 - 1.23943i) q^{5} -1.18426i q^{6} +4.28486i q^{7} +3.07850i q^{8} +(0.986736 - 1.70908i) q^{9} -2.89744 q^{10} +3.51574i q^{11} +(0.321066 - 0.556102i) q^{12} +(-2.77344 + 2.30392i) q^{13} +(2.50419 - 4.33738i) q^{14} +(2.17505 + 1.25577i) q^{15} +(1.16538 - 2.01850i) q^{16} +3.41875 q^{17} +(-1.99766 + 1.15335i) q^{18} -1.30557i q^{19} +(-1.36058 - 0.785529i) q^{20} +(-3.75969 + 2.17066i) q^{21} +(2.05469 - 3.55884i) q^{22} +(1.09562 - 1.89767i) q^{23} +(-2.70119 + 1.55954i) q^{24} +(0.572396 - 0.991420i) q^{25} +(4.15391 - 0.711281i) q^{26} +5.03901 q^{27} +(2.35183 - 1.35783i) q^{28} +(-2.72073 + 4.71244i) q^{29} +(-1.46781 - 2.54232i) q^{30} +(4.54063 - 3.22221i) q^{31} +(2.97279 - 1.71634i) q^{32} +(-3.08484 + 1.78103i) q^{33} +(-3.46066 - 1.99801i) q^{34} +(5.31080 + 9.19857i) q^{35} -1.25075 q^{36} +(0.670031 - 0.386843i) q^{37} +(-0.763009 + 1.32157i) q^{38} +(-3.42653 - 1.26638i) q^{39} +(3.81561 + 6.60882i) q^{40} +6.77733i q^{41} +5.07437 q^{42} +10.8829 q^{43} +(1.92968 - 1.11410i) q^{44} -4.89198i q^{45} +(-2.21810 + 1.28062i) q^{46} +6.24759i q^{47} +2.36148 q^{48} -11.3600 q^{49} +(-1.15882 + 0.669048i) q^{50} +(1.73190 + 2.99974i) q^{51} +(2.14342 + 0.792170i) q^{52} +(-4.77562 - 8.27161i) q^{53} +(-5.10077 - 2.94493i) q^{54} +(4.35753 + 7.54747i) q^{55} -13.1909 q^{56} +(1.14555 - 0.661385i) q^{57} +(5.50815 - 3.18013i) q^{58} -10.2894i q^{59} -1.59176i q^{60} +(-7.29296 - 12.6318i) q^{61} +(-6.47944 + 0.608040i) q^{62} +(7.32315 + 4.22802i) q^{63} -8.67384 q^{64} +(-3.09837 + 8.38346i) q^{65} +4.16354 q^{66} +5.40704i q^{67} +(-1.08337 - 1.87645i) q^{68} +2.22012 q^{69} -12.4151i q^{70} +(0.697488 + 0.402695i) q^{71} +(5.26140 + 3.03767i) q^{72} +(13.1489 - 7.59150i) q^{73} -0.904325 q^{74} +1.15988 q^{75} +(-0.716586 + 0.413721i) q^{76} -15.0644 q^{77} +(2.72843 + 3.28446i) q^{78} +(1.10947 - 1.92166i) q^{79} -5.77766i q^{80} +(-0.407505 - 0.705820i) q^{81} +(3.96086 - 6.86041i) q^{82} +(-5.12515 + 2.95901i) q^{83} +(2.38282 + 1.37572i) q^{84} +(7.33925 - 4.23732i) q^{85} +(-11.0163 - 6.36025i) q^{86} -5.51315 q^{87} -10.8232 q^{88} +(-1.16803 - 0.674360i) q^{89} +(-2.85901 + 4.95194i) q^{90} +(-9.87194 - 11.8838i) q^{91} -1.38877 q^{92} +(5.12752 + 2.35178i) q^{93} +(3.65126 - 6.32417i) q^{94} +(-1.61817 - 2.80274i) q^{95} +(3.01197 + 1.73896i) q^{96} +(-14.5197 + 8.38298i) q^{97} +(11.4992 + 6.63909i) q^{98} +(6.00867 + 3.46911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9}+O(q^{10}) \) 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9	\( 70 q - 6 q^{2} - 2 q^{3} + 30 q^{4} - 29 q^{9} + 2 q^{10} + 13 q^{12} + q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} - 12 q^{17} - 3 q^{20} - 9 q^{21} + 4 q^{22} + 10 q^{23} + 18 q^{24} + 19 q^{25} + 6 q^{26} + 34 q^{27} - 33 q^{28} - 18 q^{29} - 31 q^{30} - 2 q^{31} + 36 q^{32} - 12 q^{33} + 9 q^{34} - 12 q^{35} - 16 q^{36} - 18 q^{37} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 98 q^{42} - 38 q^{43} + 42 q^{44} - 6 q^{46} + 54 q^{48} - 18 q^{49} - 51 q^{50} - 7 q^{51} + 41 q^{52} - 22 q^{53} + 18 q^{54} - 15 q^{55} - 50 q^{56} + 15 q^{57} - 12 q^{58} - 13 q^{61} - 23 q^{62} - 6 q^{63} - 38 q^{64} - 12 q^{65} - 52 q^{66} - 44 q^{68} + 32 q^{69} + 27 q^{71} - 15 q^{72} - 9 q^{73} + 38 q^{74} - 50 q^{75} + 126 q^{76} + 34 q^{77} + 14 q^{78} + 6 q^{79} - 11 q^{81} + 39 q^{82} - 54 q^{83} + 15 q^{84} - 33 q^{85} - 24 q^{86} + 28 q^{87} - 32 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 14 q^{93} - 43 q^{94} + 25 q^{95} + 36 q^{96} - 75 q^{97} + 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 - 2 * q^3 + 30 * q^4 - 29 * q^9 + 2 * q^10 + 13 * q^12 + q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 - 12 * q^17 - 3 * q^20 - 9 * q^21 + 4 * q^22 + 10 * q^23 + 18 * q^24 + 19 * q^25 + 6 * q^26 + 34 * q^27 - 33 * q^28 - 18 * q^29 - 31 * q^30 - 2 * q^31 + 36 * q^32 - 12 * q^33 + 9 * q^34 - 12 * q^35 - 16 * q^36 - 18 * q^37 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 98 * q^42 - 38 * q^43 + 42 * q^44 - 6 * q^46 + 54 * q^48 - 18 * q^49 - 51 * q^50 - 7 * q^51 + 41 * q^52 - 22 * q^53 + 18 * q^54 - 15 * q^55 - 50 * q^56 + 15 * q^57 - 12 * q^58 - 13 * q^61 - 23 * q^62 - 6 * q^63 - 38 * q^64 - 12 * q^65 - 52 * q^66 - 44 * q^68 + 32 * q^69 + 27 * q^71 - 15 * q^72 - 9 * q^73 + 38 * q^74 - 50 * q^75 + 126 * q^76 + 34 * q^77 + 14 * q^78 + 6 * q^79 - 11 * q^81 + 39 * q^82 - 54 * q^83 + 15 * q^84 - 33 * q^85 - 24 * q^86 + 28 * q^87 - 32 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 14 * q^93 - 43 * q^94 + 25 * q^95 + 36 * q^96 - 75 * q^97 + 93 * q^99

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