LMFDB - Embedded newform 403.2.v.a.36.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(36,403)]

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([5, 4]))

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

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

chi := DirichletCharacter("403.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.v (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			36.11
Character	$\chi$	$=$	403.36
Dual form			403.2.v.a.56.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01226 + 0.584427i) q^{2} -1.01318 q^{3} +(-0.316890 + 0.548870i) q^{4} +(-2.14676 + 1.23943i) q^{5} +(1.02560 - 0.592128i) q^{6} +(-3.71079 + 2.14243i) q^{7} -3.07850i q^{8} -1.97347 q^{9} +O(q^{10})$	\(q+(-1.01226 + 0.584427i) q^{2} -1.01318 q^{3} +(-0.316890 + 0.548870i) q^{4} +(-2.14676 + 1.23943i) q^{5} +(1.02560 - 0.592128i) q^{6} +(-3.71079 + 2.14243i) q^{7} -3.07850i q^{8} -1.97347 q^{9} +(1.44872 - 2.50925i) q^{10} +(3.04472 + 1.75787i) q^{11} +(0.321066 - 0.556102i) q^{12} +(3.38197 - 1.24991i) q^{13} +(2.50419 - 4.33738i) q^{14} +(2.17505 - 1.25577i) q^{15} +(1.16538 + 2.01850i) q^{16} +(-1.70938 - 2.96072i) q^{17} +(1.99766 - 1.15335i) q^{18} +(1.13065 - 0.652784i) q^{19} -1.57106i q^{20} +(3.75969 - 2.17066i) q^{21} -4.10939 q^{22} +(1.09562 + 1.89767i) q^{23} +3.11907i q^{24} +(0.572396 - 0.991420i) q^{25} +(-2.69294 + 3.24175i) q^{26} +5.03901 q^{27} -2.71566i 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} +(0.625374 - 1.08318i) q^{36} -0.773685i q^{37} +(-0.763009 + 1.32157i) q^{38} +(-3.42653 + 1.26638i) q^{39} +(3.81561 + 6.60882i) q^{40} +(5.86934 + 3.38867i) q^{41} +(-2.53718 + 4.39453i) q^{42} +(-5.44144 - 9.42485i) q^{43} +(-1.92968 + 1.11410i) q^{44} +(4.23658 - 2.44599i) q^{45} +(-2.21810 - 1.28062i) q^{46} -6.24759i q^{47} +(-1.18074 - 2.04510i) q^{48} +(5.67999 - 9.83804i) q^{49} +1.33810i q^{50} +(1.73190 + 2.99974i) q^{51} +(-0.385673 + 2.25234i) q^{52} +(-4.77562 - 8.27161i) q^{53} +(-5.10077 + 2.94493i) q^{54} -8.71506 q^{55} +(6.59547 + 11.4237i) q^{56} +(-1.14555 + 0.661385i) q^{57} +(5.50815 + 3.18013i) q^{58} +(8.91085 - 5.14468i) q^{59} +1.59176i q^{60} +(-7.29296 + 12.6318i) q^{61} +(2.71314 - 5.91538i) q^{62} +(7.32315 - 4.22802i) q^{63} -8.67384 q^{64} +(-5.71110 + 6.87500i) q^{65} +4.16354 q^{66} +(4.68263 + 2.70352i) q^{67} +2.16674 q^{68} +(-1.11006 - 1.92268i) q^{69} +12.4151i q^{70} +0.805389i q^{71} +6.07534i q^{72} +(-13.1489 + 7.59150i) q^{73} +(0.452163 + 0.783168i) q^{74} +(-0.579939 + 1.00448i) q^{75} +0.827442i q^{76} -15.0644 q^{77} +(2.72843 - 3.28446i) q^{78} +(1.10947 - 1.92166i) q^{79} +(-5.00360 - 2.88883i) q^{80} +0.815011 q^{81} -7.92172 q^{82} +(5.12515 - 2.95901i) q^{83} +2.75144i q^{84} +(7.33925 + 4.23732i) q^{85} +(11.0163 + 6.36025i) q^{86} +(2.75658 + 4.77453i) q^{87} +(5.41161 - 9.37319i) q^{88} +(-1.16803 + 0.674360i) q^{89} +(-2.85901 + 4.95194i) q^{90} +(-9.87194 + 11.8838i) q^{91} -1.38877 q^{92} +(4.60046 - 3.26467i) 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} +13.2782i q^{98} +(-6.00867 - 3.46911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 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 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * 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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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	−0.813195	−	0.581991i	$-0.802274\pi$
$2$	−1.01226	+	0.584427i	−0.715774	+	0.413252i	0.0974212	+	0.995243i	$0.468941\pi$
$3$	−1.01318			−0.584958			−0.292479	−	0.956272i	$-0.594480\pi$
$3$	−1.01318			−0.584958			−0.292479	+	0.956272i	$0.594480\pi$
$4$	−0.316890	+	0.548870i	−0.158445	+	0.274435i
$5$	−2.14676	+	1.23943i	−0.960062	+	0.554292i	−0.896192	−	0.443666i	$-0.853678\pi$
$5$	−2.14676	+	1.23943i	−0.960062	+	0.554292i	−0.0638698	+	0.997958i	$0.520344\pi$
$6$	1.02560	−	0.592128i	0.418698	−	0.241735i
$7$	−3.71079	+	2.14243i	−1.40255	+	0.809762i	−0.994654	−	0.103267i	$-0.967070\pi$
$7$	−3.71079	+	2.14243i	−1.40255	+	0.809762i	−0.407895	+	0.913029i	$0.633737\pi$
$8$		−	3.07850i		−	1.08842i
$9$	−1.97347			−0.657824
$10$	1.44872	−	2.50925i	0.458125	−	0.793496i
$11$	3.04472	+	1.75787i	0.918018	+	0.530018i	0.883002	−	0.469369i	$-0.155519\pi$
$11$	3.04472	+	1.75787i	0.918018	+	0.530018i	0.0350158	+	0.999387i	$0.488852\pi$
$12$	0.321066	−	0.556102i	0.0926837	−	0.160533i
$13$	3.38197	−	1.24991i	0.937990	−	0.346663i
$13$	3.38197	−	1.24991i	0.937990	−	0.346663i
$14$	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
$17$	−1.70938	−	2.96072i	−0.414584	−	0.718081i	0.580800	−	0.814046i	$-0.302740\pi$
$17$	−1.70938	−	2.96072i	−0.414584	−	0.718081i	−0.995385	+	0.0959648i	$0.969406\pi$
$18$	1.99766	−	1.15335i	0.470853	−	0.271847i
$19$	1.13065	−	0.652784i	0.259390	−	0.149759i	−0.364666	−	0.931138i	$-0.618817\pi$
$19$	1.13065	−	0.652784i	0.259390	−	0.149759i	0.624056	+	0.781379i	$0.285484\pi$
$20$		−	1.57106i		−	0.351299i
$21$	3.75969	−	2.17066i	0.820432	−	0.473677i
$22$	−4.10939			−0.876125
$23$	1.09562	+	1.89767i	0.228453	+	0.395692i	0.957350	−	0.288932i	$-0.0933000\pi$
$23$	1.09562	+	1.89767i	0.228453	+	0.395692i	−0.728897	+	0.684623i	$0.759967\pi$
$24$			3.11907i			0.636678i
$25$	0.572396	−	0.991420i	0.114479	−	0.198284i
$26$	−2.69294	+	3.24175i	−0.528129	+	0.635759i
$27$	5.03901			0.969757
$28$		−	2.71566i		−	0.513211i
$29$	−2.72073	−	4.71244i	−0.505226	−	0.875077i	−0.999982	−	0.00604524i	$-0.998076\pi$
$29$	−2.72073	−	4.71244i	−0.505226	−	0.875077i	0.494756	−	0.869032i	$-0.335258\pi$
$30$	−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
$36$	0.625374	−	1.08318i	0.104229	−	0.180530i
$37$		−	0.773685i		−	0.127193i	−0.997976	−	0.0635965i	$-0.979743\pi$
$37$		−	0.773685i		−	0.127193i	0.997976	−	0.0635965i	$-0.0202571\pi$
$38$	−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
$41$	5.86934	+	3.38867i	0.916637	+	0.529221i	0.882561	−	0.470198i	$-0.155818\pi$
$41$	5.86934	+	3.38867i	0.916637	+	0.529221i	0.0340767	+	0.999419i	$0.489151\pi$
$42$	−2.53718	+	4.39453i	−0.391496	+	0.678091i
$43$	−5.44144	−	9.42485i	−0.829811	−	1.43728i	−0.898186	−	0.439616i	$-0.855115\pi$
$43$	−5.44144	−	9.42485i	−0.829811	−	1.43728i	0.0683746	−	0.997660i	$-0.478219\pi$
$44$	−1.92968	+	1.11410i	−0.290911	+	0.167957i
$45$	4.23658	−	2.44599i	0.631552	−	0.364627i
$46$	−2.21810	−	1.28062i	−0.327041	−	0.188817i
$47$		−	6.24759i		−	0.911304i	−0.890158	−	0.455652i	$-0.849406\pi$
$47$		−	6.24759i		−	0.911304i	0.890158	−	0.455652i	$-0.150594\pi$
$48$	−1.18074	−	2.04510i	−0.170425	−	0.295184i
$49$	5.67999	−	9.83804i	0.811428	−	1.40543i
$50$			1.33810i			0.189235i
$51$	1.73190	+	2.99974i	0.242514	+	0.420047i
$52$	−0.385673	+	2.25234i	−0.0534832	+	0.312344i
$53$	−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
$55$	−8.71506			−1.17514
$56$	6.59547	+	11.4237i	0.881357	+	1.52656i
$57$	−1.14555	+	0.661385i	−0.151732	+	0.0876026i
$58$	5.50815	+	3.18013i	0.723256	+	0.417572i
$59$	8.91085	−	5.14468i	1.16009	−	0.669781i	0.208768	−	0.977965i	$-0.433055\pi$
$59$	8.91085	−	5.14468i	1.16009	−	0.669781i	0.951327	+	0.308184i	$0.0997214\pi$
$60$			1.59176i			0.205495i
$61$	−7.29296	+	12.6318i	−0.933768	+	1.61733i	−0.156952	+	0.987606i	$0.550167\pi$
$61$	−7.29296	+	12.6318i	−0.933768	+	1.61733i	−0.776816	+	0.629727i	$0.783167\pi$
$62$	2.71314	−	5.91538i	0.344569	−	0.751254i
$63$	7.32315	−	4.22802i	0.922630	−	0.532681i
$64$	−8.67384			−1.08423
$65$	−5.71110	+	6.87500i	−0.708375	+	0.852738i
$66$	4.16354			0.512496
$67$	4.68263	+	2.70352i	0.572074	+	0.330287i	0.757977	−	0.652281i	$-0.226188\pi$
$67$	4.68263	+	2.70352i	0.572074	+	0.330287i	−0.185903	+	0.982568i	$0.559521\pi$
$68$	2.16674			0.262755
$69$	−1.11006	−	1.92268i	−0.133635	−	0.231463i
$70$			12.4151i			1.48389i
$71$			0.805389i			0.0955821i	0.998857	+	0.0477911i	$0.0152182\pi$
$71$			0.805389i			0.0955821i	−0.998857	+	0.0477911i	$0.984782\pi$
$72$			6.07534i			0.715986i
$73$	−13.1489	+	7.59150i	−1.53896	+	0.888518i	−0.540058	+	0.841628i	$0.681598\pi$
$73$	−13.1489	+	7.59150i	−1.53896	+	0.888518i	−0.998900	+	0.0468899i	$0.985069\pi$
$74$	0.452163	+	0.783168i	0.0525628	+	0.0910415i
$75$	−0.579939	+	1.00448i	−0.0669656	+	0.115988i
$76$			0.827442i			0.0949141i
$77$	−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	$0.126830\pi$
$80$	−5.00360	−	2.88883i	−0.559419	−	0.322981i
$81$	0.815011			0.0905567
$82$	−7.92172			−0.874807
$83$	5.12515	−	2.95901i	0.562559	−	0.324793i	−0.191613	−	0.981471i	$-0.561372\pi$
$83$	5.12515	−	2.95901i	0.562559	−	0.324793i	0.754172	+	0.656677i	$0.228039\pi$
$84$			2.75144i			0.300207i
$85$	7.33925	+	4.23732i	0.796053	+	0.459602i
$86$	11.0163	+	6.36025i	1.18791	+	0.685843i
$87$	2.75658	+	4.77453i	0.295536	+	0.511884i
$88$	5.41161	−	9.37319i	0.576880	−	0.999185i
$89$	−1.16803	+	0.674360i	−0.123810	+	0.0714820i	−0.560626	−	0.828069i	$-0.689440\pi$
$89$	−1.16803	+	0.674360i	−0.123810	+	0.0714820i	0.436816	+	0.899551i	$0.356106\pi$
$90$	−2.85901	+	4.95194i	−0.301366	+	0.521981i
$91$	−9.87194	+	11.8838i	−1.03486	+	1.24576i
$92$	−1.38877			−0.144789
$93$	4.60046	−	3.26467i	0.477046	−	0.338531i
$94$	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	−0.474677	−	0.880160i	$-0.657435\pi$
$97$	−14.5197	−	8.38298i	−1.47426	−	0.851163i	−0.999579	+	0.0289974i	$0.990769\pi$
$98$			13.2782i			1.34130i
$99$	−6.00867	−	3.46911i	−0.603894	−	0.348659i
$100$	0.362773	+	0.628342i	0.0362773	+	0.0628342i
$101$	−8.71992	−	15.1034i	−0.867665	−	1.50284i	−0.864376	−	0.502845i	$-0.832287\pi$
$101$	−8.71992	−	15.1034i	−0.867665	−	1.50284i	−0.00328846	−	0.999995i	$-0.501047\pi$
$102$	−3.50626	−	2.02434i	−0.347171	−	0.200439i
$103$	−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	$-0.359982\pi$
$104$	−3.84786	−	10.4114i	−0.377314	−	1.02092i
$105$	−5.38078	+	9.31978i	−0.525110	+	0.909518i
$106$	9.66830	+	5.58200i	0.939069	+	0.542172i
$107$	10.6807			1.03254			0.516271	−	0.856425i	$-0.327320\pi$
$107$	10.6807			1.03254			0.516271	+	0.856425i	$0.327320\pi$
$108$	−1.59681	+	2.76576i	−0.153653	+	0.266135i
$109$			16.8763i			1.61646i	0.588869	+	0.808229i	$0.299573\pi$
$109$			16.8763i			1.61646i	−0.588869	+	0.808229i	$0.700427\pi$
$110$	8.82189	−	5.09332i	0.841134	−	0.485629i
$111$			0.783880i			0.0744026i
$112$	−8.64898	−	4.99349i	−0.817252	−	0.471841i
$113$	5.90347			0.555352			0.277676	−	0.960675i	$-0.410436\pi$
$113$	5.90347			0.555352			0.277676	+	0.960675i	$0.410436\pi$
$114$	0.773063	−	1.33898i	0.0724040	−	0.125407i
$115$	−4.70408	−	2.71590i	−0.438658	−	0.253259i
$116$	3.44868			0.320202
$117$	−6.67422	+	2.46667i	−0.617032	+	0.228044i
$118$	−6.01339	+	10.4155i	−0.553577	+	0.958823i
$119$	12.6863	+	7.32443i	1.16295	+	0.671429i
$120$	−3.86588	−	6.69591i	−0.352905	−	0.611250i
$121$	0.680219	+	1.17817i	0.0618381	+	0.107107i
$122$		−	17.0488i		−	1.54353i
$123$	−5.94668	−	3.43332i	−0.536194	−	0.309572i
$124$	−0.329693	−	3.51330i	−0.0296073	−	0.315504i
$125$		−	9.55655i		−	0.854764i
$126$	−4.94194	+	8.55969i	−0.440263	+	0.762558i
$127$	3.42664			0.304065			0.152033	−	0.988375i	$-0.451418\pi$
$127$	3.42664			0.304065			0.152033	+	0.988375i	$0.451418\pi$
$128$	2.83457	−	1.63654i	0.250543	−	0.144651i
$129$	5.51314	+	9.54904i	0.485405	+	0.840746i
$130$	1.76317	−	10.2970i	0.154640	−	0.903106i
$131$	−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
$133$	−2.79708	+	4.84469i	−0.242538	+	0.420088i
$134$	−6.32004			−0.545968
$135$	−10.8176	+	6.24552i	−0.931027	+	0.537529i
$136$	−9.11461	+	5.26232i	−0.781571	+	0.451240i
$137$		−	4.63964i		−	0.396392i	−0.980162	−	0.198196i	$-0.936492\pi$
$137$		−	4.63964i		−	0.396392i	0.980162	−	0.198196i	$-0.0635082\pi$
$138$	2.24733	+	1.29750i	0.191305	+	0.110450i
$139$	6.25380	−	10.8319i	0.530441	−	0.918750i	−0.468929	−	0.883236i	$-0.655360\pi$
$139$	6.25380	−	10.8319i	0.530441	−	0.918750i	0.999369	−	0.0355140i	$-0.0113068\pi$
$140$	3.36588	+	5.82987i	0.284469	+	0.492714i
$141$			6.32991i			0.533075i
$142$	−0.470691	−	0.815261i	−0.0394995	−	0.0684152i
$143$	12.4943	+	2.13943i	1.04483	+	0.178908i
$144$	−2.29985	−	3.98345i	−0.191654	−	0.331955i
$145$	11.6815	+	6.74432i	0.970097	+	0.560086i
$146$	8.87336	−	15.3691i	0.734364	−	1.27196i
$147$	−5.75484	+	9.96767i	−0.474651	+	0.822120i
$148$	0.424652	+	0.245173i	0.0349062	+	0.0201531i
$149$	6.55646	−	3.78537i	0.537126	−	0.310110i	−0.206787	−	0.978386i	$-0.566301\pi$
$149$	6.55646	−	3.78537i	0.537126	−	0.310110i	0.743913	+	0.668276i	$0.232968\pi$
$150$		−	1.35573i		−	0.110695i
$151$			3.83153i			0.311806i	0.987772	+	0.155903i	$0.0498287\pi$
$151$			3.83153i			0.311806i	−0.987772	+	0.155903i	$0.950171\pi$
$152$	−2.00960	−	3.48073i	−0.163000	−	0.282324i
$153$	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	$0.345515\pi$
$158$			2.59362i			0.206338i
$159$	4.83854	+	8.38060i	0.383721	+	0.664625i
$160$	−8.50918			−0.672710
$161$	−8.13125	−	4.69458i	−0.640832	−	0.369985i
$162$	−0.825000	+	0.476314i	−0.0648182	+	0.0374228i
$163$	1.78776	+	1.03216i	0.140028	+	0.0808454i	0.568377	−	0.822768i	$-0.307571\pi$
$163$	1.78776	+	1.03216i	0.140028	+	0.0808454i	−0.428349	+	0.903613i	$0.640905\pi$
$164$	−3.71987	+	2.14767i	−0.290473	+	0.167705i
$165$	8.82990			0.687407
$166$	−3.45865	+	5.99056i	−0.268443	+	0.464957i
$167$		−	14.0188i		−	1.08481i	−0.840119	−	0.542403i	$-0.817515\pi$
$167$		−	14.0188i		−	1.08481i	0.840119	−	0.542403i	$-0.182485\pi$
$168$	−6.68238	−	11.5742i	−0.515557	−	0.892971i
$169$	9.87544	−	8.45433i	0.759649	−	0.650333i
$170$	−9.90561			−0.759726
$171$	−2.23132	+	1.28825i	−0.170633	+	0.0985150i
$172$	6.89735			0.525918
$173$	−14.6826			−1.11630			−0.558150	−	0.829740i	$-0.688489\pi$
$173$	−14.6826			−1.11630			−0.558150	+	0.829740i	$0.688489\pi$
$174$	−5.58073	−	3.22204i	−0.423074	−	0.244262i
$175$			4.90527i			0.370804i
$176$			8.19436i			0.617673i
$177$	−9.02827	+	5.21248i	−0.678607	+	0.391794i
$178$	0.788228	−	1.36525i	0.0590802	−	0.102330i
$179$	−2.81043			−0.210061			−0.105031	−	0.994469i	$-0.533494\pi$
$179$	−2.81043			−0.210061			−0.105031	+	0.994469i	$0.533494\pi$
$180$			3.10044i			0.231093i
$181$	−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
$186$	−2.74889	+	5.99332i	−0.201559	+	0.439452i
$187$		−	12.0194i		−	0.878949i
$188$	3.42911	+	1.97980i	0.250094	+	0.144392i
$189$	−18.6987	+	10.7957i	−1.36013	+	0.785272i
$190$		−	3.78280i		−	0.274433i
$191$	12.0580			0.872485			0.436242	−	0.899829i	$-0.356309\pi$
$191$	12.0580			0.872485			0.436242	+	0.899829i	$0.356309\pi$
$192$	8.78813			0.634229
$193$		−	17.7432i		−	1.27719i	−0.769545	−	0.638593i	$-0.779517\pi$
$193$		−	17.7432i		−	1.27719i	0.769545	−	0.638593i	$-0.220483\pi$
$194$	19.5970			1.40698
$195$	5.78636	−	6.96559i	0.414370	−	0.498816i
$196$	3.59987	+	6.23515i	0.257133	+	0.445368i
$197$	7.12081	+	4.11120i	0.507337	+	0.292911i	0.731738	−	0.681586i	$-0.238709\pi$
$197$	7.12081	+	4.11120i	0.507337	+	0.292911i	−0.224402	+	0.974497i	$0.572043\pi$
$198$	8.10977			0.576336
$199$	−3.65433			−0.259049			−0.129524	−	0.991576i	$-0.541345\pi$
$199$	−3.65433			−0.259049			−0.129524	+	0.991576i	$0.541345\pi$
$200$	−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
$204$	−2.19529			−0.153701
$205$	−16.8001			−1.17337
$206$	11.7252	+	6.76957i	0.816936	+	0.471658i
$207$	−2.16218	−	3.74500i	−0.150282	−	0.260296i
$208$	6.46423	+	5.36988i	0.448214	+	0.372334i
$209$	4.59004			0.317500
$210$		−	12.5787i		−	0.868012i
$211$	4.86764			0.335102			0.167551	−	0.985863i	$-0.446414\pi$
$211$	4.86764			0.335102			0.167551	+	0.985863i	$0.446414\pi$
$212$	6.05338			0.415748
$213$		−	0.816002i		−	0.0559115i
$214$	−10.8116	+	6.24209i	−0.739067	+	0.426701i
$215$	23.3630	+	13.4886i	1.59334	+	0.919916i
$216$		−	15.5126i		−	1.05550i
$217$	9.94600	−	21.6849i	0.675178	−	1.47207i
$218$	−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
$223$			10.1507i			0.679740i	0.940472	+	0.339870i	$0.110383\pi$
$223$			10.1507i			0.679740i	−0.940472	+	0.339870i	$0.889617\pi$
$224$	−14.7086			−0.982758
$225$	−1.12961	+	1.95654i	−0.0753072	+	0.130436i
$226$	−5.97583	+	3.45015i	−0.397506	+	0.229500i
$227$		−	3.60396i		−	0.239203i	−0.992822	−	0.119602i	$-0.961838\pi$
$227$		−	3.60396i		−	0.239203i	0.992822	−	0.119602i	$-0.0381617\pi$
$228$		−	0.838346i		−	0.0555208i
$229$	0.685131	+	0.395560i	0.0452747	+	0.0261394i	0.522467	−	0.852660i	$-0.325012\pi$
$229$	0.685131	+	0.395560i	0.0452747	+	0.0261394i	−0.477192	+	0.878799i	$0.658345\pi$
$230$	6.34899			0.418640
$231$	15.2629			1.00423
$232$	−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	$0.595308\pi$
$234$	5.31444	−	6.39750i	0.347416	−	0.418218i
$235$	7.74348	+	13.4121i	0.505129	+	0.874909i
$236$			6.52119i			0.424494i
$237$	−1.12409	+	1.94698i	−0.0730176	+	0.126470i
$238$	−17.1224			−1.10988
$239$	−8.36079	+	4.82711i	−0.540815	+	0.312240i	−0.745409	−	0.666607i	$-0.767746\pi$
$239$	−8.36079	+	4.82711i	−0.540815	+	0.312240i	0.204594	+	0.978847i	$0.434412\pi$
$240$	5.06953	+	2.92689i	0.327237	+	0.188930i
$241$	3.28910	−	1.89896i	0.211870	−	0.122323i	−0.390310	−	0.920683i	$-0.627632\pi$
$241$	3.28910	−	1.89896i	0.211870	−	0.122323i	0.602180	+	0.798360i	$0.294299\pi$
$242$	−1.37711	−	0.795077i	−0.0885243	−	0.0511095i
$243$	−15.9428			−1.02273
$244$	−4.62213	−	8.00577i	−0.295902	−	0.512517i
$245$			28.1599i			1.79907i
$246$	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
$251$	−7.87245	−	13.6355i	−0.496904	−	0.860664i	0.503089	−	0.864234i	$-0.332197\pi$
$251$	−7.87245	−	13.6355i	−0.496904	−	0.860664i	−0.999994	+	0.00357078i	$0.998863\pi$
$252$			5.35927i			0.337602i
$253$			7.70384i			0.484336i
$254$	−3.46864	+	2.00262i	−0.217642	+	0.125656i
$255$	−7.43596	−	4.29315i	−0.465658	−	0.268848i
$256$	6.76096	−	11.7103i	0.422560	−	0.731896i
$257$	−0.232805	+	0.403230i	−0.0145220	+	0.0251528i	−0.873195	−	0.487371i	$-0.837956\pi$
$257$	−0.232805	+	0.403230i	−0.0145220	+	0.0251528i	0.858673	+	0.512524i	$0.171289\pi$
$258$	−11.1614	−	6.44406i	−0.694880	−	0.401189i
$259$	1.65756	+	2.87099i	0.102996	+	0.178394i
$260$	−1.96368	−	5.31327i	−0.121783	−	0.329515i
$261$	5.36928	+	9.29986i	0.332350	+	0.575647i
$262$		−	19.7311i		−	1.21899i
$263$	−11.0160	−	19.0802i	−0.679274	−	1.17654i	−0.975200	−	0.221326i	$-0.928962\pi$
$263$	−11.0160	−	19.0802i	−0.679274	−	1.17654i	0.295926	−	0.955211i	$-0.404372\pi$
$264$	−5.48292	+	9.49670i	−0.337451	+	0.584481i
$265$	20.5042	+	11.8381i	1.25957	+	0.727210i
$266$		−	6.53877i		−	0.400917i
$267$	1.18342	−	0.683246i	0.0724239	−	0.0418140i
$268$	−2.96776	+	1.71344i	−0.181285	+	0.104665i
$269$	−24.9132			−1.51898			−0.759492	−	0.650517i	$-0.774552\pi$
$269$	−24.9132			−1.51898			−0.759492	+	0.650517i	$0.774552\pi$
$270$	7.30010	−	12.6441i	0.444270	−	0.769498i
$271$	0.126715	−	0.0731590i	0.00769739	−	0.00444409i	−0.496146	−	0.868239i	$-0.665252\pi$
$271$	0.126715	−	0.0731590i	0.00769739	−	0.00444409i	0.503844	+	0.863795i	$0.331919\pi$
$272$	3.98415	−	6.90075i	0.241575	−	0.418419i
$273$	10.0020	−	12.0404i	0.605350	−	0.728717i
$274$	2.71153	+	4.69651i	0.163810	+	0.283727i
$275$	3.48558	−	2.01240i	0.210188	−	0.121352i
$276$	1.40707			0.0846954
$277$	−4.68408	+	8.11307i	−0.281439	+	0.487467i	−0.971739	−	0.236056i	$-0.924145\pi$
$277$	−4.68408	+	8.11307i	−0.281439	+	0.487467i	0.690300	+	0.723523i	$0.257478\pi$
$278$			14.6196i			0.876823i
$279$	8.96081	−	6.35895i	0.536470	−	0.380700i
$280$	−28.3178	−	16.3493i	−1.69232	−	0.977059i
$281$			11.7302i			0.699767i	0.936793	+	0.349884i	$0.113779\pi$
$281$			11.7302i			0.699767i	−0.936793	+	0.349884i	$0.886221\pi$
$282$	−3.69937	−	6.40750i	−0.220294	−	0.381561i
$283$	−4.17114	−	7.22463i	−0.247949	−	0.429459i	0.715008	−	0.699116i	$-0.246423\pi$
$283$	−4.17114	−	7.22463i	−0.247949	−	0.429459i	−0.962956	+	0.269657i	$0.913090\pi$
$284$	−0.442054	−	0.255220i	−0.0262311	−	0.0151445i
$285$	1.63949	−	2.83968i	0.0971149	−	0.168208i
$286$	−13.8978	+	5.13638i	−0.821796	+	0.303720i
$287$	−29.0399			−1.71417
$288$	−5.86673	−	3.38716i	−0.345700	−	0.199590i
$289$	2.65607	−	4.60045i	0.156240	−	0.270615i
$290$	−15.7663			−0.925827
$291$	14.7111	+	8.49344i	0.862378	+	0.497894i
$292$		−	9.62268i		−	0.563125i
$293$	−19.7758	+	11.4175i	−1.15531	+	0.667020i	−0.950176	−	0.311713i	$-0.899097\pi$
$293$	−19.7758	+	11.4175i	−1.15531	+	0.667020i	−0.205137	+	0.978733i	$0.565764\pi$
$294$		−	13.4531i		−	0.784603i
$295$	−12.7530	+	22.0888i	−0.742508	+	1.28606i
$296$	−2.38179			−0.138439
$297$	15.3424	+	8.85792i	0.890255	+	0.513989i
$298$	−4.42455	+	7.66354i	−0.256307	+	0.443937i
$299$	6.07728	+	5.04844i	0.351458	+	0.291959i
$300$	−0.367554	−	0.636621i	−0.0212207	−	0.0367554i
$301$	40.3841	+	23.3158i	2.32770	+	1.34390i
$302$	−2.23925	−	3.87850i	−0.128855	−	0.223183i
$303$	8.83483	+	15.3024i	0.507548	+	0.879098i
$304$	2.63529	+	1.52148i	0.151144	+	0.0872631i
$305$		−	36.1566i		−	2.07032i
$306$	−6.82951	−	3.94302i	−0.390417	−	0.225407i
$307$	14.5589	+	8.40557i	0.830919	+	0.479731i	0.854167	−	0.519999i	$-0.174068\pi$
$307$	14.5589	+	8.40557i	0.830919	+	0.479731i	−0.0232484	+	0.999730i	$0.507401\pi$
$308$	4.77377	−	8.26841i	0.272011	−	0.471137i
$309$	5.86795	+	10.1636i	0.333816	+	0.578186i
$310$	1.50725	+	16.0617i	0.0856061	+	0.912242i
$311$	−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
$315$	−10.4807	+	18.1531i	−0.590521	+	1.02281i
$316$	0.703161	+	1.21791i	0.0395559	+	0.0685128i
$317$	−12.9118	−	7.45464i	−0.725200	−	0.418694i	0.0914636	−	0.995808i	$-0.470845\pi$
$317$	−12.9118	−	7.45464i	−0.725200	−	0.418694i	−0.816664	+	0.577114i	$0.804179\pi$
$318$	−9.79570	−	5.65555i	−0.549316	−	0.317148i
$319$		−	19.1307i		−	1.07112i
$320$	18.6207	−	10.7507i	1.04093	−	0.600980i
$321$	−10.8214			−0.603994
$322$	10.9746			0.611588
$323$	−3.86543	−	2.23170i	−0.215078	−	0.124175i
$324$	−0.258269	+	0.447334i	−0.0143483	+	0.0248519i
$325$	0.696639	−	4.06840i	0.0386426	−	0.225674i
$326$	−2.41290			−0.133638
$327$		−	17.0987i		−	0.945560i
$328$	10.4320	−	18.0688i	0.576012	−	0.997683i
$329$	13.3850	+	23.1835i	0.737939	+	1.27815i
$330$	−8.93813	+	5.16043i	−0.492028	+	0.284073i
$331$			24.2859i			1.33487i	0.744667	+	0.667436i	$0.232608\pi$
$331$			24.2859i			1.33487i	−0.744667	+	0.667436i	$0.767392\pi$
$332$			3.75072i			0.205848i
$333$			1.52685i			0.0836707i
$334$	8.19295	+	14.1906i	0.448298	+	0.776476i
$335$	−13.4033			−0.732302
$336$	8.76295	+	5.05929i	0.478058	+	0.276007i
$337$	−11.4686			−0.624737			−0.312368	−	0.949961i	$-0.601122\pi$
$337$	−11.4686			−0.624737			−0.312368	+	0.949961i	$0.601122\pi$
$338$	−5.05554	+	14.3294i	−0.274985	+	0.779418i
$339$	−5.98126			−0.324858
$340$	−4.65147	+	2.68553i	−0.252261	+	0.145643i
$341$	−19.4892	+	1.82889i	−1.05540	+	0.0990402i
$342$	1.50578	−	2.60808i	0.0814231	−	0.141029i
$343$			18.6819i			1.00873i
$344$	−29.0144	+	16.7515i	−1.56435	+	0.903180i
$345$	4.76606	+	2.75169i	0.256596	+	0.148146i
$346$	14.8626	−	8.58093i	0.799019	−	0.461314i
$347$	1.53331	+	2.65577i	0.0823124	+	0.142569i	0.904243	−	0.427019i	$-0.140436\pi$
$347$	1.53331	+	2.65577i	0.0823124	+	0.142569i	−0.821930	+	0.569588i	$0.807103\pi$
$348$	−3.49413			−0.187305
$349$	−17.8393	+	10.2995i	−0.954915	+	0.551320i	−0.894604	−	0.446859i	$-0.852542\pi$
$349$	−17.8393	+	10.2995i	−0.954915	+	0.551320i	−0.0603106	+	0.998180i	$0.519209\pi$
$350$	−2.86677	−	4.96540i	−0.153235	−	0.265412i
$351$	17.0418	−	6.29832i	0.909622	−	0.336179i
$352$	6.03422	+	10.4516i	0.321625	+	0.557071i
$353$		−	34.1839i		−	1.81943i	−0.415238	−	0.909713i	$-0.636302\pi$
$353$		−	34.1839i		−	1.81943i	0.415238	−	0.909713i	$-0.363698\pi$
$354$	6.09262	−	10.5527i	0.323819	−	0.560871i
$355$	−0.998227	−	1.72898i	−0.0529804	−	0.0917648i
$356$		−	0.854791i		−	0.0453038i
$357$	−12.8534	−	7.42094i	−0.680276	−	0.392758i
$358$	2.84488	−	1.64249i	0.150357	−	0.0868084i
$359$	5.37225	−	3.10167i	0.283537	−	0.163700i	−0.351487	−	0.936193i	$-0.614324\pi$
$359$	5.37225	−	3.10167i	0.283537	−	0.163700i	0.635023	+	0.772493i	$0.280990\pi$
$360$	−7.52999	−	13.0423i	−0.396865	−	0.687391i
$361$	−8.64775	+	14.9783i	−0.455145	+	0.788334i
$362$	19.7815	+	11.4209i	1.03969	+	0.600267i
$363$	−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
$366$			17.2735i			0.902899i
$367$	−11.8035	+	20.4442i	−0.616135	+	1.06718i	0.374049	+	0.927409i	$0.377969\pi$
$367$	−11.8035	+	20.4442i	−0.616135	+	1.06718i	−0.990184	+	0.139769i	$0.955364\pi$
$368$	−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	−0.272437	+	0.962174i	$0.587830\pi$
$373$	−18.7239	+	32.4307i	−0.969485	+	1.67920i	−0.697048	+	0.717024i	$0.745504\pi$
$374$	7.02449	+	12.1668i	0.363228	+	0.629129i
$375$			9.68248i			0.500001i
$376$	−19.2332			−0.991878
$377$	−15.0915	−	12.5366i	−0.777254	−	0.645670i
$378$	12.6186	−	21.8561i	0.649031	−	1.12416i
$379$		−	1.49487i		−	0.0767861i	−0.999263	−	0.0383930i	$-0.987776\pi$
$379$		−	1.49487i		−	0.0767861i	0.999263	−	0.0383930i	$-0.0122239\pi$
$380$	−1.02556	−	1.77632i	−0.0526102	−	0.0911235i
$381$	−3.47179			−0.177865
$382$	−12.2058	+	7.04701i	−0.624502	+	0.360556i
$383$			18.6352i			0.952213i	0.879388	+	0.476107i	$0.157952\pi$
$383$			18.6352i			0.952213i	−0.879388	+	0.476107i	$0.842048\pi$
$384$	−2.87192	+	1.65810i	−0.146557	+	0.0846147i
$385$	32.3398	−	18.6714i	1.64819	−	0.951582i
$386$	10.3696	+	17.9607i	0.527800	+	0.914177i
$387$	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	$0.100571\pi$
$390$	−1.78641	+	10.4327i	−0.0904582	+	0.528279i
$391$	3.74566	−	6.48767i	0.189426	−	0.328095i
$392$	−30.2864	−	17.4859i	−1.52970	−	0.883171i
$393$	8.55159	−	14.8118i	0.431371	−	0.747156i
$394$	−9.61079			−0.484185
$395$			5.50047i			0.276759i
$396$	3.80818	−	2.19865i	0.191368	−	0.110486i
$397$	−9.21992	+	5.32312i	−0.462734	+	0.267160i	−0.713193	−	0.700967i	$-0.752752\pi$
$397$	−9.21992	+	5.32312i	−0.462734	+	0.267160i	0.250459	+	0.968127i	$0.419418\pi$
$398$	3.69912	−	2.13569i	0.185420	−	0.107052i
$399$	2.83394	−	4.90853i	0.141875	−	0.245734i
$400$	2.66824			0.133412
$401$	−9.93735	+	5.73733i	−0.496247	+	0.286509i	−0.727163	−	0.686465i	$-0.759161\pi$
$401$	−9.93735	+	5.73733i	−0.496247	+	0.286509i	0.230915	+	0.972974i	$0.425828\pi$
$402$	6.40332			0.319368
$403$	−11.3288	+	16.5728i	−0.564328	+	0.825551i
$404$	11.0530			0.549909
$405$	−1.74964	+	1.01015i	−0.0869401	+	0.0501949i
$406$	−27.2528			−1.35253
$407$	1.36004	−	2.35566i	0.0674146	−	0.116766i
$408$	9.23471	−	5.33166i	0.457186	−	0.263957i
$409$	−4.45110	+	2.56985i	−0.220093	+	0.127071i	−0.605993	−	0.795470i	$-0.707224\pi$
$409$	−4.45110	+	2.56985i	−0.220093	+	0.127071i	0.385900	+	0.922540i	$0.373891\pi$
$410$	17.0061	−	9.81845i	0.839869	−	0.484899i
$411$			4.70078i			0.231872i
$412$	7.34124			0.361677
$413$	−22.0442	+	38.1817i	−1.08473	+	1.87880i
$414$	4.37736	+	2.52727i	0.215136	+	0.124209i
$415$	−7.33500	+	12.7046i	−0.360061	+	0.623644i
$416$	12.1992	+	2.08889i	0.598114	+	0.102416i
$417$	−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	0.997346	+	0.0728075i	$0.0231959\pi$
$419$	11.4982	+	19.9155i	0.561726	+	0.972938i	−0.435620	+	0.900131i	$0.643471\pi$
$420$	−3.41023	−	5.90669i	−0.166402	−	0.288217i
$421$	20.8178	−	12.0192i	1.01460	−	0.585779i	0.102064	−	0.994778i	$-0.467455\pi$
$421$	20.8178	−	12.0192i	1.01460	−	0.585779i	0.912535	+	0.408999i	$0.134122\pi$
$422$	−4.92730	+	2.84478i	−0.239857	+	0.138482i
$423$			12.3294i			0.599478i
$424$	−25.4642	+	14.7018i	−1.23665	+	0.713980i
$425$	−3.91376			−0.189845
$426$	0.476894	+	0.826004i	0.0231056	+	0.0400200i
$427$		−	62.4986i		−	3.02452i
$428$	−3.38461	+	5.86231i	−0.163601	+	0.283366i
$429$	−12.6590	−	2.16762i	−0.611181	−	0.104654i
$430$	−31.5324			−1.52063
$431$		−	12.3053i		−	0.592724i	−0.955076	−	0.296362i	$-0.904227\pi$
$431$		−	12.3053i		−	0.592724i	0.955076	−	0.296362i	$-0.0957735\pi$
$432$	5.87237	+	10.1712i	0.282534	+	0.489364i
$433$	−2.69026	+	4.65967i	−0.129286	+	0.223930i	−0.923400	−	0.383839i	$-0.874602\pi$
$433$	−2.69026	+	4.65967i	−0.129286	+	0.223930i	0.794114	+	0.607769i	$0.207935\pi$
$434$	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
$439$	16.8924	−	29.2585i	0.806230	−	1.39643i	−0.109228	−	0.994017i	$-0.534838\pi$
$439$	16.8924	−	29.2585i	0.806230	−	1.39643i	0.915458	−	0.402414i	$-0.131829\pi$
$440$			26.8294i			1.27904i
$441$	−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	$0.720174\pi$
$444$	−0.430248	−	0.248404i	−0.0204187	−	0.0117887i
$445$	1.67165	−	2.89538i	0.0792438	−	0.137254i
$446$	−5.93233	−	10.2751i	−0.280904	−	0.486540i
$447$	−6.64285	+	3.83525i	−0.314196	+	0.181401i
$448$	32.1868	−	18.5831i	1.52068	−	0.877968i
$449$	−3.20288	−	1.84918i	−0.151153	−	0.0872684i	0.422516	−	0.906356i	$-0.361147\pi$
$449$	−3.20288	−	1.84918i	−0.151153	−	0.0872684i	−0.573669	+	0.819087i	$0.694480\pi$
$450$		−	2.64070i		−	0.124484i
$451$	11.9137	+	20.6351i	0.560993	+	0.971669i
$452$	−1.87075	+	3.24024i	−0.0879927	+	0.152408i
$453$		−	3.88202i		−	0.182393i
$454$	2.10625	+	3.64813i	0.0988513	+	0.171215i
$455$	6.46355	−	37.7473i	0.303016	−	1.76962i
$456$	2.03608	+	3.52659i	0.0953481	+	0.165148i
$457$	1.87042	−	1.07989i	0.0874944	−	0.0505149i	−0.455614	−	0.890177i	$-0.650580\pi$
$457$	1.87042	−	1.07989i	0.0874944	−	0.0505149i	0.543109	+	0.839662i	$0.317247\pi$
$458$	−0.924705			−0.0432086
$459$	−8.61356	−	14.9191i	−0.402046	−	0.696365i
$460$	2.98135	−	1.72128i	0.139006	−	0.0802553i
$461$	−0.0377362	−	0.0217870i	−0.00175755	−	0.00101472i	0.499121	−	0.866532i	$-0.333656\pi$
$461$	−0.0377362	−	0.0217870i	−0.00175755	−	0.00101472i	−0.500879	+	0.865518i	$0.666990\pi$
$462$	−15.4500	+	8.92008i	−0.718801	+	0.415000i
$463$			4.48424i			0.208400i	0.994556	+	0.104200i	$0.0332282\pi$
$463$			4.48424i			0.208400i	−0.994556	+	0.104200i	$0.966772\pi$
$464$	6.34137	−	10.9836i	0.294391	−	0.509900i
$465$	−5.82976	+	12.7105i	−0.270349	+	0.589433i
$466$	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	$0.440667\pi$
$468$	0.761115	−	4.44494i	0.0351826	−	0.205467i
$469$	−23.1684			−1.06982
$470$	−15.6768	−	9.05100i	−0.723116	−	0.417491i
$471$	−11.8445			−0.545764
$472$	−15.8379	−	27.4321i	−0.729000	−	1.26267i
$473$		−	38.2614i		−	1.75926i
$474$		−	2.62780i		−	0.120699i
$475$		−	1.49460i		−	0.0685771i
$476$	−8.04031	+	4.64207i	−0.368527	+	0.212769i
$477$	9.42454	+	16.3238i	0.431520	+	0.747415i
$478$	5.64218	−	9.77255i	0.258067	−	0.446986i
$479$			21.1019i			0.964172i	0.876124	+	0.482086i	$0.160121\pi$
$479$			21.1019i			0.964172i	−0.876124	+	0.482086i	$0.839879\pi$
$480$	8.62131			0.393507
$481$	−0.967039	−	2.61658i	−0.0440932	−	0.119306i
$482$	−2.21961	+	3.84448i	−0.101101	+	0.175111i
$483$	8.23839	+	4.75644i	0.374860	+	0.216425i
$484$	−0.862219			−0.0391918
$485$	41.5606			1.88717
$486$	16.1382	−	9.31739i	0.732043	−	0.422645i
$487$		−	5.94762i		−	0.269512i	−0.990879	−	0.134756i	$-0.956975\pi$
$487$		−	5.94762i		−	0.269512i	0.990879	−	0.134756i	$-0.0430251\pi$
$488$	38.8870	+	22.4514i	1.76033	+	1.01633i
$489$	−1.81132	−	1.04577i	−0.0819107	−	0.0472912i
$490$	−16.4574	−	28.5051i	−0.743471	−	1.28773i
$491$	14.4600	−	25.0454i	0.652569	−	1.13028i	−0.329928	−	0.944006i	$-0.607024\pi$
$491$	14.4600	−	25.0454i	0.652569	−	1.13028i	0.982497	−	0.186277i	$-0.0596422\pi$
$492$	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
$496$	−11.7956	−	5.41016i	−0.529638	−	0.242923i
$497$	−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	0.0162742	−	0.999868i	$-0.494820\pi$
$499$	−18.7977	−	10.8528i	−0.841499	−	0.485840i	−0.857774	+	0.514028i	$0.828153\pi$
$500$	5.24530	+	3.02838i	0.234577	+	0.135433i
$501$			14.2035i			0.634566i
$502$	15.9379	+	9.20174i	0.711343	+	0.410694i
$503$	−4.42500	−	7.66432i	−0.197301	−	0.341735i	0.750351	−	0.661039i	$-0.229884\pi$
$503$	−4.42500	−	7.66432i	−0.197301	−	0.341735i	−0.947652	+	0.319304i	$0.896551\pi$
$504$	−13.0160	−	22.5443i	−0.579778	−	1.00421i
$505$	37.4392	+	21.6156i	1.66602	+	0.961880i
$506$	−4.50233	−	7.79827i	−0.200153	−	0.346675i
$507$	−10.0056	+	8.56574i	−0.444363	+	0.380418i
$508$	−1.08587	+	1.88078i	−0.0481776	+	0.0834461i
$509$	−18.0788	−	10.4378i	−0.801329	−	0.462647i	0.0426068	−	0.999092i	$-0.486434\pi$
$509$	−18.0788	−	10.4378i	−0.801329	−	0.462647i	−0.843936	+	0.536444i	$0.819767\pi$
$510$	10.0361			0.444408
$511$	32.5285	−	56.3410i	1.43898	−	2.49238i
$512$			22.3513i			0.987798i
$513$	5.69738	−	3.28938i	0.251545	−	0.145230i
$514$		−	0.544230i		−	0.0240050i
$515$	24.8665	+	14.3567i	1.09575	+	0.632631i
$516$	−6.98823			−0.307640
$517$	10.9825	−	19.0222i	0.483008	−	0.836594i
$518$	−3.35576	−	1.93745i	−0.147444	−	0.0851267i
$519$	14.8761			0.652989
$520$	21.1647	+	17.5817i	0.928134	+	0.771007i
$521$	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	$0.0733986\pi$
$522$	−10.8702	−	6.27590i	−0.475775	−	0.274689i
$523$	−3.50825	−	6.07647i	−0.153405	−	0.265706i	0.779072	−	0.626934i	$-0.215691\pi$
$523$	−3.50825	−	6.07647i	−0.153405	−	0.265706i	−0.932477	+	0.361229i	$0.882357\pi$
$524$	−5.34934	−	9.26532i	−0.233687	−	0.404757i
$525$		−	4.96991i		−	0.216905i
$526$	22.3020	+	12.8761i	0.972413	+	0.561423i
$527$	17.3017	+	7.93559i	0.753675	+	0.345680i
$528$		−	8.30234i		−	0.361313i
$529$	9.09923	−	15.7603i	0.395619	−	0.685232i
$530$	−27.6741			−1.20209
$531$	−17.5853	+	10.1529i	−0.763138	+	0.440598i
$532$	−1.77274	−	3.07047i	−0.0768578	−	0.133122i
$533$	24.0855	+	4.12420i	1.04326	+	0.178639i
$534$	−0.798614	+	1.38324i	−0.0345594	+	0.0598587i
$535$	−22.9289	+	13.2380i	−0.991305	+	0.572330i
$536$	8.32279	−	14.4155i	0.359490	−	0.622655i
$537$	2.84746			0.122877
$538$	25.2186	−	14.5599i	1.08725	−	0.627724i
$539$	34.5880	−	19.9694i	1.48981	−	0.860143i
$540$		−	7.91657i		−	0.340675i
$541$	3.20842	+	1.85238i	0.137941	+	0.0796402i	0.567382	−	0.823455i	$-0.307956\pi$
$541$	3.20842	+	1.85238i	0.137941	+	0.0796402i	−0.429441	+	0.903095i	$0.641290\pi$
$542$	−0.0855122	+	0.148111i	−0.00367306	+	0.00636193i
$543$	9.89973	+	17.1468i	0.424838	+	0.735841i
$544$		−	11.7355i		−	0.503155i
$545$	−20.9171	−	36.2294i	−0.895989	−	1.55190i
$546$	−3.08790	+	18.0334i	−0.132150	+	0.771759i
$547$	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	$0.540019\pi$
$548$	2.54656	+	1.47026i	0.108784	+	0.0628063i
$549$	14.3925	−	24.9285i	0.614255	−	1.06392i
$550$	−2.35220	+	4.07413i	−0.100298	+	0.173721i
$551$	−6.15240	−	3.55209i	−0.262101	−	0.151324i
$552$	−5.91897	+	3.41732i	−0.251928	+	0.145451i
$553$			9.50786i			0.404315i
$554$		−	10.9500i		−	0.465222i
$555$	−0.971568	−	1.68281i	−0.0412408	−	0.0714311i
$556$	3.96353	+	6.86504i	0.168091	+	0.291143i
$557$	−29.9953	+	17.3178i	−1.27094	+	0.733780i	−0.975166	−	0.221477i	$-0.928912\pi$
$557$	−29.9953	+	17.3178i	−1.27094	+	0.733780i	−0.295778	+	0.955257i	$0.595579\pi$
$558$	−5.35431	+	11.6738i	−0.226666	+	0.494193i
$559$	−30.1830	−	25.0732i	−1.27661	−	1.06048i
$560$	24.7564			1.04615
$561$			12.1778i			0.514148i
$562$	−6.85547	−	11.8740i	−0.289180	−	0.500875i
$563$	−35.3597			−1.49024			−0.745118	−	0.666933i	$-0.767607\pi$
$563$	−35.3597			−1.49024			−0.745118	+	0.666933i	$0.767607\pi$
$564$	−3.47430	−	2.00589i	−0.146294	−	0.0844630i
$565$	−12.6734	+	7.31697i	−0.533172	+	0.307827i
$566$	8.44453	+	4.87545i	0.354950	+	0.204931i
$567$	−3.02434	+	1.74610i	−0.127010	+	0.0733294i
$568$	2.47939			0.104033
$569$	−21.2017	+	36.7225i	−0.888823	+	1.53949i	−0.0475545	+	0.998869i	$0.515143\pi$
$569$	−21.2017	+	36.7225i	−0.888823	+	1.53949i	−0.841268	+	0.540618i	$0.818191\pi$
$570$			3.83264i			0.160532i
$571$	−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	$0.960488\pi$
$572$	−5.13360	+	6.17980i	−0.214647	+	0.258390i
$573$	−12.2169			−0.510367
$574$	29.3959	−	16.9717i	1.22696	−	0.708385i
$575$	2.50852			0.104612
$576$	17.1176			0.713232
$577$	−18.7381	−	10.8185i	−0.780078	−	0.450378i	0.0563798	−	0.998409i	$-0.482044\pi$
$577$	−18.7381	−	10.8185i	−0.780078	−	0.450378i	−0.836458	+	0.548031i	$0.815378\pi$
$578$			6.20912i			0.258265i
$579$			17.9770i			0.747100i
$580$	−7.40351	+	4.27442i	−0.307414	+	0.177486i
$581$	−12.6789	+	21.9605i	−0.526011	+	0.911077i
$582$	−19.8552			−0.823024
$583$		−	33.5797i		−	1.39073i
$584$	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	−0.955044	−	0.296463i	$-0.904193\pi$
$587$	−28.4879	+	16.4475i	−1.17582	+	0.678861i	−0.220778	+	0.975324i	$0.570860\pi$
$588$	−3.64730	−	6.31731i	−0.150412	−	0.260522i
$589$	−3.03048	+	6.60726i	−0.124869	+	0.272247i
$590$		−	29.8128i		−	1.22737i
$591$	−7.21464	−	4.16537i	−0.296771	−	0.171341i
$592$	1.56168	−	0.901638i	0.0641848	−	0.0370571i
$593$		−	34.6753i		−	1.42394i	−0.702208	−	0.711971i	$-0.747803\pi$
$593$		−	34.6753i		−	1.42394i	0.702208	−	0.711971i	$-0.252197\pi$
$594$	−20.7072			−0.849629
$595$	−36.3126			−1.48867
$596$			4.79819i			0.196541i
$597$	3.70248			0.151533
$598$	−9.10222	−	1.55859i	−0.372217	−	0.0637355i
$599$	−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	$0.833494\pi$
$600$	3.09231	+	1.78534i	0.126243	+	0.0728864i
$601$	13.1476			0.536300			0.268150	−	0.963377i	$-0.413588\pi$
$601$	13.1476			0.536300			0.268150	+	0.963377i	$0.413588\pi$
$602$	−54.5055			−2.22148
$603$	−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
$607$	−1.77389			−0.0719999			−0.0360000	−	0.999352i	$-0.511462\pi$
$607$	−1.77389			−0.0719999			−0.0360000	+	0.999352i	$0.511462\pi$
$608$	4.48160			0.181753
$609$	−20.4582	−	11.8115i	−0.829007	−	0.478628i
$610$	21.1309	+	36.5998i	0.855565	+	1.48188i
$611$	−7.80894	−	21.1292i	−0.315916	−	0.854794i
$612$	−4.27599			−0.172847
$613$			13.9621i			0.563925i	0.959425	+	0.281962i	$0.0909853\pi$
$613$			13.9621i			0.563925i	−0.959425	+	0.281962i	$0.909015\pi$
$614$	−19.6498			−0.793000
$615$	17.0215			0.686373
$616$			46.3760i			1.86854i
$617$	11.3258	−	6.53897i	0.455960	−	0.263249i	−0.254384	−	0.967103i	$-0.581873\pi$
$617$	11.3258	−	6.53897i	0.455960	−	0.263249i	0.710344	+	0.703854i	$0.248539\pi$
$618$	−11.8797	−	6.85877i	−0.477873	−	0.275900i
$619$			10.8427i			0.435804i	0.975971	+	0.217902i	$0.0699213\pi$
$619$			10.8427i			0.435804i	−0.975971	+	0.217902i	$0.930079\pi$
$620$	5.06228	+	7.13360i	0.203306	+	0.286492i
$621$	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
$626$			36.4942i			1.45860i
$627$	−4.65052			−0.185724
$628$	−3.70458	+	6.41652i	−0.147829	+	0.256047i
$629$	−2.29067	+	1.32252i	−0.0913349	+	0.0527323i
$630$		−	24.5009i		−	0.976137i
$631$			46.1760i			1.83824i	0.393980	+	0.919119i	$0.371098\pi$
$631$			46.1760i			1.83824i	−0.393980	+	0.919119i	$0.628902\pi$
$632$	−5.91585	−	3.41552i	−0.235320	−	0.135862i
$633$	−4.93178			−0.196021
$634$	17.4268			0.692106
$635$	−7.35619	+	4.24710i	−0.291922	+	0.168541i
$636$	−6.13314			−0.243195
$637$	6.91288	−	40.3714i	0.273898	−	1.59957i
$638$	11.1805	+	19.3652i	0.442641	+	0.766677i
$639$		−	1.58941i		−	0.0628762i
$640$	−4.05676	+	7.02652i	−0.160358	+	0.277748i
$641$	24.0310			0.949167			0.474583	−	0.880211i	$-0.342599\pi$
$641$	24.0310			0.949167			0.474583	+	0.880211i	$0.342599\pi$
$642$	10.9541	−	6.32434i	0.432323	−	0.249602i
$643$	−9.87327	−	5.70034i	−0.389364	−	0.224799i	0.292521	−	0.956259i	$-0.405506\pi$
$643$	−9.87327	−	5.70034i	−0.389364	−	0.224799i	−0.681884	+	0.731460i	$0.738839\pi$
$644$	5.15342	−	2.97533i	0.203073	−	0.117244i
$645$	−23.6708	−	13.6664i	−0.932037	−	0.538112i
$646$	5.21707			0.205263
$647$	0.779003	+	1.34927i	0.0306258	+	0.0530454i	0.880932	−	0.473243i	$-0.156917\pi$
$647$	0.779003	+	1.34927i	0.0306258	+	0.0530454i	−0.850306	+	0.526288i	$0.823583\pi$
$648$		−	2.50901i		−	0.0985634i
$649$	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	0.989318	−	0.145775i	$-0.0465675\pi$
$653$	9.41441	+	16.3062i	0.368414	+	0.638112i	−0.620904	+	0.783887i	$0.713234\pi$
$654$	9.99294	+	17.3083i	0.390755	+	0.676807i
$655$		−	41.8451i		−	1.63502i
$656$			15.7964i			0.616744i
$657$	25.9489	−	14.9816i	1.01236	−	0.584488i
$658$	−27.0981	−	15.6451i	−1.05640	−	0.609910i
$659$	16.2447	−	28.1366i	0.632804	−	1.09605i	−0.354172	−	0.935180i	$-0.615237\pi$
$659$	16.2447	−	28.1366i	0.632804	−	1.09605i	0.986976	−	0.160868i	$-0.0514293\pi$
$660$	−2.79811	+	4.84646i	−0.108916	+	0.188648i
$661$	−20.2696	−	11.7026i	−0.788395	−	0.455180i	0.0510022	−	0.998699i	$-0.483758\pi$
$661$	−20.2696	−	11.7026i	−0.788395	−	0.455180i	−0.839397	+	0.543518i	$0.817092\pi$
$662$	−14.1933	−	24.5835i	−0.551639	−	0.955467i
$663$	9.60664	+	7.98030i	0.373091	+	0.309929i
$664$	−9.10932	−	15.7778i	−0.353510	−	0.612298i
$665$		−	13.8672i		−	0.537747i
$666$	−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
$669$		−	10.2844i		−	0.397619i
$670$	13.5676	−	7.83327i	0.524163	−	0.302626i
$671$	−44.4101	+	25.6402i	−1.71443	+	0.989828i
$672$	14.9024			0.574872
$673$	1.42451	−	2.46732i	0.0549108	−	0.0951083i	−0.837263	−	0.546800i	$-0.815846\pi$
$673$	1.42451	−	2.46732i	0.0549108	−	0.0951083i	0.892174	+	0.451691i	$0.149179\pi$
$674$	11.6092	−	6.70258i	0.447170	−	0.258174i
$675$	2.88431	−	4.99577i	0.111017	−	0.192287i
$676$	1.51090	+	8.09942i	0.0581115	+	0.311516i
$677$	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
$679$	71.8397			2.75696
$680$	13.0446	−	22.5939i	0.500238	−	0.866437i
$681$			3.65145i			0.139924i
$682$	18.6592	−	13.2413i	0.714499	−	0.507037i
$683$	−37.2648	−	21.5148i	−1.42590	−	0.823242i	−0.429103	−	0.903256i	$-0.641170\pi$
$683$	−37.2648	−	21.5148i	−1.42590	−	0.823242i	−0.996794	+	0.0800140i	$0.974504\pi$
$684$		−	1.63293i		−	0.0624368i
$685$	5.75054	+	9.96022i	0.219717	+	0.380560i
$686$	−10.9182	−	18.9109i	−0.416860	−	0.722022i
$687$	−0.694159	−	0.400773i	−0.0264838	−	0.0152904i
$688$	12.6827	−	21.9671i	0.483523	−	0.837487i
$689$	−26.4898	−	22.0052i	−1.00918	−	0.838332i
$690$	−6.43265			−0.244887
$691$	4.43752	+	2.56200i	0.168811	+	0.0974631i	0.582025	−	0.813171i	$-0.302261\pi$
$691$	4.43752	+	2.56200i	0.168811	+	0.0974631i	−0.413214	+	0.910634i	$0.635594\pi$
$692$	4.65278	−	8.05885i	0.176872	−	0.306352i
$693$	29.7293			1.12932
$694$	−3.10421	−	1.79222i	−0.117834	−	0.0680316i
$695$			31.0047i			1.17608i
$696$	14.6984	−	8.48614i	0.557142	−	0.321666i
$697$		−	23.1700i		−	0.877627i
$698$	12.0386	−	20.8515i	0.455669	−	0.789242i
$699$	9.12354			0.345084
$700$	−2.69235	−	1.55443i	−0.101761	−	0.0587520i
$701$	−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	$0.872940\pi$
$702$	−13.5697	+	16.3352i	−0.512157	+	0.616532i
$703$	−0.505049	−	0.874771i	−0.0190483	−	0.0329926i
$704$	−26.4094	−	15.2475i	−0.995342	−	0.574661i
$705$	−7.84551	−	13.5888i	−0.295479	−	0.511785i
$706$	19.9780	+	34.6029i	0.751882	+	1.30230i
$707$	64.7157	+	37.3636i	2.43388	+	1.40520i
$708$		−	6.60712i		−	0.248311i
$709$	−5.64475	−	3.25900i	−0.211993	−	0.122394i	0.390244	−	0.920711i	$-0.372391\pi$
$709$	−5.64475	−	3.25900i	−0.211993	−	0.122394i	−0.602237	+	0.798317i	$0.705724\pi$
$710$	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
$713$	−11.0895	−	5.08631i	−0.415306	−	0.190484i
$714$	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
$718$	−3.62540	+	6.27938i	−0.135299	+	0.234344i
$719$	−4.18015	−	7.24023i	−0.155893	−	0.270015i	0.777491	−	0.628894i	$-0.216492\pi$
$719$	−4.18015	−	7.24023i	−0.155893	−	0.270015i	−0.933384	+	0.358879i	$0.883159\pi$
$720$	9.87446	+	5.70102i	0.367999	+	0.212465i
$721$	42.9831	+	24.8163i	1.60077	+	0.924207i
$722$		−	20.2159i		−	0.752358i
$723$	−3.33244	+	1.92399i	−0.123935	+	0.0715539i
$724$	12.3853			0.460296
$725$	−6.22934			−0.231352
$726$	1.39526	+	0.805554i	0.0517830	+	0.0298969i
$727$	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
$730$			43.9918i			1.62821i
$731$	−18.6029	+	32.2212i	−0.688054	+	1.19174i
$732$	4.68304	+	8.11126i	0.173090	+	0.299801i
$733$	26.8709	−	15.5139i	0.992499	−	0.573020i	0.0864787	−	0.996254i	$-0.472439\pi$
$733$	26.8709	−	15.5139i	0.992499	−	0.573020i	0.906020	+	0.423234i	$0.139105\pi$
$734$		−	27.5930i		−	1.01848i
$735$		−	28.5310i		−	1.05238i
$736$			7.52185i			0.277259i
$737$	9.50487	+	16.4629i	0.350116	+	0.606419i
$738$	15.6333			0.575469
$739$	−0.976612	−	0.563847i	−0.0359252	−	0.0207414i	0.481930	−	0.876210i	$-0.339936\pi$
$739$	−0.976612	−	0.563847i	−0.0359252	−	0.0207414i	−0.517855	+	0.855468i	$0.673269\pi$
$740$	−1.21550			−0.0446828
$741$	−3.04755	+	3.66863i	−0.111955	+	0.134770i
$742$	−47.8361			−1.75612
$743$	9.48013	−	5.47336i	0.347792	−	0.200798i	−0.315920	−	0.948786i	$-0.602313\pi$
$743$	9.48013	−	5.47336i	0.347792	−	0.200798i	0.663712	+	0.747988i	$0.268980\pi$
$744$	−10.0503	−	14.1626i	−0.368462	−	0.519224i
$745$	−9.38344	+	16.2526i	−0.343783	+	0.595449i
$746$		−	43.7709i		−	1.60257i
$747$	−10.1143	+	5.83952i	−0.370065	+	0.213657i
$748$	6.59711	+	3.80884i	0.241214	+	0.139265i
$749$	−39.6339	+	22.8826i	−1.44819	+	0.836113i
$750$	−5.65870	−	9.80116i	−0.206627	−	0.357888i
$751$	49.4399			1.80409			0.902044	−	0.431645i	$-0.142067\pi$
$751$	49.4399			1.80409			0.902044	+	0.431645i	$0.142067\pi$
$752$	12.6108	−	7.28082i	0.459867	−	0.265504i
$753$	7.97618	+	13.8152i	0.290668	+	0.503452i
$754$	22.6033	+	3.87040i	0.823163	+	0.140952i
$755$	−4.74894	−	8.22540i	−0.172831	−	0.299353i
$756$		−	13.6842i		−	0.497690i
$757$	5.65061	−	9.78714i	0.205375	−	0.355720i	−0.744877	−	0.667201i	$-0.767492\pi$
$757$	5.65061	−	9.78714i	0.205375	−	0.355720i	0.950252	+	0.311482i	$0.100825\pi$
$758$	0.873640	+	1.51319i	0.0317320	+	0.0549615i
$759$		−	7.80535i		−	0.283316i
$760$	8.62826	+	4.98153i	0.312980	+	0.180699i
$761$	−4.68908	+	2.70724i	−0.169979	+	0.0981375i	−0.582576	−	0.812776i	$-0.697955\pi$
$761$	−4.68908	+	2.70724i	−0.169979	+	0.0981375i	0.412597	+	0.910914i	$0.364622\pi$
$762$	3.51435	−	2.02901i	0.127311	−	0.0735033i
$763$	−36.1563	−	62.6245i	−1.30894	−	2.26716i
$764$	−3.82105	+	6.61826i	−0.138241	+	0.239440i
$765$	−14.4838	−	8.36223i	−0.523663	−	0.302337i
$766$	−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
$769$		−	4.01136i		−	0.144653i	−0.997381	−	0.0723266i	$-0.976958\pi$
$769$		−	4.01136i		−	0.144653i	0.997381	−	0.0723266i	$-0.0230424\pi$
$770$	−21.8241	+	37.8005i	−0.786487	+	1.36224i
$771$	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	0.583528	−	0.812093i	$-0.301672\pi$
$773$	4.78205	+	2.76092i	0.171998	+	0.0993033i	−0.411529	+	0.911396i	$0.635005\pi$
$774$	−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
$778$			9.50516i			0.340777i
$779$	8.84827			0.317022
$780$	1.98956	+	5.38328i	0.0712377	+	0.192752i
$781$	−1.41577	+	2.45219i	−0.0506602	+	0.0877461i
$782$			8.75625i			0.313123i
$783$	−13.7098	−	23.7460i	−0.489947	−	0.848613i
$784$	26.4774			0.945623
$785$	−25.0966	+	14.4895i	−0.895735	+	0.517153i
$786$			19.9911i			0.713060i
$787$	−48.1692	+	27.8105i	−1.71705	+	0.991338i	−0.792858	+	0.609407i	$0.791408\pi$
$787$	−48.1692	+	27.8105i	−1.71705	+	0.991338i	−0.924191	+	0.381931i	$0.875259\pi$
$788$	−4.51303	+	2.60560i	−0.160770	+	0.0928205i
$789$	11.1611	+	19.3316i	0.397347	+	0.688225i
$790$	−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
$793$	−8.87595	+	51.8359i	−0.315194	+	1.84075i
$794$	6.22195	−	10.7767i	0.220809	−	0.382452i
$795$	−20.7744	−	11.9941i	−0.736793	−	0.425387i
$796$	1.15802	−	2.00575i	0.0410450	−	0.0710920i
$797$	34.5184			1.22270			0.611352	−	0.791359i	$-0.290626\pi$
$797$	34.5184			1.22270			0.611352	+	0.791359i	$0.290626\pi$
$798$			6.62493i			0.234520i
$799$	−18.4974	+	10.6795i	−0.654391	+	0.377813i
$800$	3.40323	−	1.96486i	0.120322	−	0.0694682i
$801$	2.30507	−	1.33083i	0.0814455	−	0.0470226i
$802$	6.70610	−	11.6153i	0.236801	−	0.410151i
$803$	−53.3795			−1.88372
$804$	3.00686	−	1.73601i	0.106044	−	0.0612245i
$805$	23.2745			0.820318
$806$	1.78205	−	23.3968i	0.0627702	−	0.824118i
$807$	25.2415			0.888542
$808$	−46.4957	+	26.8443i	−1.63571	+	0.944380i
$809$	−17.2520			−0.606548			−0.303274	−	0.952903i	$-0.598080\pi$
$809$	−17.2520			−0.606548			−0.303274	+	0.952903i	$0.598080\pi$
$810$	1.18072	−	2.04507i	0.0414863	−	0.0718564i
$811$	17.0153	−	9.82381i	0.597489	−	0.344961i	−0.170564	−	0.985347i	$-0.554559\pi$
$811$	17.0153	−	9.82381i	0.597489	−	0.344961i	0.768053	+	0.640386i	$0.221226\pi$
$812$	−12.7974	+	7.38856i	−0.449099	+	0.259287i
$813$	−0.128385	+	0.0741230i	−0.00450265	+	0.00259961i
$814$			3.17937i			0.111437i
$815$	−5.11720			−0.179248
$816$	−4.03665	+	6.99168i	−0.141311	+	0.244758i
$817$	−12.3048	−	7.10416i	−0.430489	−	0.248543i
$818$	3.00378	−	5.20269i	0.105025	−	0.181908i
$819$	19.4820	−	23.4523i	0.680756	−	0.819491i
$820$	5.32379	−	9.22108i	0.185915	−	0.322014i
$821$	−4.11030	+	2.37308i	−0.143450	+	0.0828211i	−0.570007	−	0.821640i	$-0.693060\pi$
$821$	−4.11030	+	2.37308i	−0.143450	+	0.0828211i	0.426557	+	0.904461i	$0.359726\pi$
$822$	−2.74726	−	4.75840i	−0.0958218	−	0.165968i
$823$	5.35725	+	9.27903i	0.186742	+	0.323447i	0.944162	−	0.329481i	$-0.106874\pi$
$823$	5.35725	+	9.27903i	0.186742	+	0.323447i	−0.757420	+	0.652928i	$0.773540\pi$
$824$	−30.8817	+	17.8296i	−1.07581	+	0.621122i
$825$	−3.53150	+	2.03892i	−0.122951	+	0.0709859i
$826$		−	51.5330i		−	1.79306i
$827$	−33.7029	+	19.4584i	−1.17197	+	0.676635i	−0.954142	−	0.299354i	$-0.903229\pi$
$827$	−33.7029	+	19.4584i	−1.17197	+	0.676635i	−0.217823	+	0.975988i	$0.569896\pi$
$828$	2.74069			0.0952456
$829$	−1.91361	−	3.31446i	−0.0664623	−	0.115116i	0.830879	−	0.556453i	$-0.187838\pi$
$829$	−1.91361	−	3.31446i	−0.0664623	−	0.115116i	−0.897342	+	0.441336i	$0.854505\pi$
$830$		−	17.1471i		−	0.595184i
$831$	4.74580	−	8.21997i	0.164630	−	0.285148i
$832$	−29.3347	+	10.8415i	−1.01700	+	0.375863i
$833$	−38.8370			−1.34562
$834$		−	14.8122i		−	0.512905i
$835$	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	−0.479788	−	0.877384i	$-0.659287\pi$
$839$	−42.8550	−	24.7424i	−1.47952	−	0.854201i	−0.999731	+	0.0231832i	$0.992620\pi$
$840$	28.6910	+	16.5648i	0.989933	+	0.571538i
$841$	−0.304703	+	0.527762i	−0.0105070	+	0.0181987i
$842$	−14.0487	+	24.3330i	−0.484149	+	0.838570i
$843$		−	11.8848i		−	0.409334i
$844$	−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
$847$	−5.04831	−	2.91464i	−0.173462	−	0.100148i
$848$	11.1308	−	19.2792i	0.382234	−	0.662049i
$849$	4.22610	+	7.31983i	0.145039	+	0.251216i
$850$	3.96173	−	2.28731i	0.135886	−	0.0784540i
$851$	1.46820	−	0.847666i	0.0503293	−	0.0290576i
$852$	0.447879	+	0.258583i	0.0153441	+	0.00885890i
$853$		−	42.1435i		−	1.44296i	−0.692433	−	0.721482i	$-0.743461\pi$
$853$		−	42.1435i		−	1.44296i	0.692433	−	0.721482i	$-0.256539\pi$
$854$	36.5259	+	63.2646i	1.24989	+	2.16487i
$855$	3.19340	−	5.53114i	0.109212	−	0.189161i
$856$		−	32.8806i		−	1.12384i
$857$	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	$0.588470\pi$
$858$	14.0810	−	5.20406i	0.480716	−	0.177664i
$859$	−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
$861$	29.4226			1.00272
$862$	7.19153	+	12.4561i	0.244945	+	0.424257i
$863$	22.1471	−	12.7866i	0.753896	−	0.435262i	−0.0732040	−	0.997317i	$-0.523322\pi$
$863$	22.1471	−	12.7866i	0.753896	−	0.435262i	0.827100	+	0.562055i	$0.189989\pi$
$864$	14.9799	+	8.64867i	0.509628	+	0.294234i
$865$	31.5202	−	18.1982i	1.07172	−	0.618756i
$866$		−	6.28905i		−	0.213711i
$867$	−2.69107	+	4.66107i	−0.0913936	+	0.158298i
$868$	8.75042	+	12.3308i	0.297009	+	0.418534i
$869$	6.75607	−	3.90062i	0.229184	−	0.132319i
$870$	15.9740			0.541570
$871$	19.2157	+	3.29034i	0.651098	+	0.111489i
$872$	51.9538			1.75938
$873$	28.6543	+	16.5436i	0.969802	+	0.559915i
$874$	−3.34387			−0.113108
$875$	20.4742	+	35.4624i	0.692155	+	1.19885i
$876$			9.74948i			0.329404i
$877$		−	3.60752i		−	0.121817i	−0.998143	−	0.0609086i	$-0.980600\pi$
$877$		−	3.60752i		−	0.121817i	0.998143	−	0.0609086i	$-0.0193998\pi$
$878$			39.4895i			1.33271i
$879$	20.0364	−	11.5680i	0.675809	−	0.390179i
$880$	−10.1564	−	17.5914i	−0.342371	−	0.593005i
$881$	5.30936	−	9.19608i	0.178877	−	0.309824i	−0.762619	−	0.646848i	$-0.776087\pi$
$881$	5.30936	−	9.19608i	0.178877	−	0.309824i	0.941496	+	0.337024i	$0.109420\pi$
$882$		−	26.2041i		−	0.882338i
$883$	−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
$886$	−14.8312	−	8.56278i	−0.498263	−	0.287672i
$887$	−17.1667			−0.576403			−0.288201	−	0.957570i	$-0.593057\pi$
$887$	−17.1667			−0.576403			−0.288201	+	0.957570i	$0.593057\pi$
$888$	2.41318			0.0809810
$889$	−12.7156	+	7.34133i	−0.426466	+	0.246220i
$890$			3.90783i			0.130991i
$891$	2.48148	+	1.43268i	0.0831327	+	0.0479967i
$892$	−5.57140	−	3.21665i	−0.186544	−	0.107701i
$893$	−4.07832	−	7.06386i	−0.136476	−	0.236383i
$894$	4.48285	−	7.76452i	0.149929	−	0.259685i
$895$	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
$899$	27.5383	+	12.6307i	0.918453	+	0.421257i
$900$	−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
$904$		−	18.1739i		−	0.604454i
$905$	41.9520	+	24.2210i	1.39453	+	0.805133i
$906$	2.26876	+	3.92961i	0.0753745	+	0.130552i
$907$	14.4523	+	25.0321i	0.479881	+	0.831178i	0.999734	−	0.0230780i	$-0.00734660\pi$
$907$	14.4523	+	25.0321i	0.479881	+	0.831178i	−0.519853	+	0.854256i	$0.674013\pi$
$908$	1.97810	+	1.14206i	0.0656457	+	0.0379005i
$909$	17.2085	+	29.8060i	0.570771	+	0.988604i
$910$	15.5178	+	41.9875i	0.514410	+	1.39187i
$911$	−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	$0.827836\pi$
$912$	−2.67001	−	1.54153i	−0.0884130	−	0.0510452i
$913$	20.8062			0.688585
$914$	−1.26223	+	2.18624i	−0.0417508	+	0.0723145i
$915$			36.6330i			1.21105i
$916$	−0.434222	+	0.250698i	−0.0143471	+	0.00828330i
$917$		−	72.3315i		−	2.38860i
$918$	17.4383	+	10.0680i	0.575549	+	0.332293i
$919$	−18.9244			−0.624259			−0.312130	−	0.950039i	$-0.601042\pi$
$919$	−18.9244			−0.624259			−0.312130	+	0.950039i	$0.601042\pi$
$920$	−8.36092	+	14.4815i	−0.275651	+	0.477442i
$921$	−14.7507	−	8.51633i	−0.486053	−	0.280623i
$922$	0.0509317			0.00167735
$923$	1.00667	+	2.72380i	0.0331348	+	0.0896550i
$924$	−4.83668	+	8.37737i	−0.159115	+	0.275595i
$925$	−0.767047	−	0.442855i	−0.0252203	−	0.0145610i
$926$	−2.62071	−	4.53920i	−0.0861218	−	0.149167i
$927$	11.4296	+	19.7967i	0.375398	+	0.650208i
$928$		−	18.6788i		−	0.613162i
$929$	−40.1110	−	23.1581i	−1.31600	−	0.759792i	−0.332917	−	0.942956i	$-0.608033\pi$
$929$	−40.1110	−	23.1581i	−1.31600	−	0.759792i	−0.983082	+	0.183164i	$0.941366\pi$
$930$	−1.52711	−	16.2733i	−0.0500760	−	0.533623i
$931$		−	14.8312i		−	0.486074i
$932$	2.85356	−	4.94251i	0.0934714	−	0.161897i
$933$	1.01822			0.0333352
$934$	−8.10786	+	4.68107i	−0.265297	+	0.153169i
$935$	14.8973	+	25.8029i	0.487194	+	0.843845i
$936$	7.59365	+	20.5466i	0.248206	+	0.671588i
$937$	−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
$939$	−15.8168	+	27.3955i	−0.516161	+	0.894018i
$940$	−9.81532			−0.320140
$941$	33.6119	−	19.4058i	1.09572	−	0.632611i	0.160623	−	0.987016i	$-0.448650\pi$
$941$	33.6119	−	19.4058i	1.09572	−	0.632611i	0.935092	+	0.354404i	$0.115316\pi$
$942$	11.9897	−	6.92223i	0.390644	−	0.225538i
$943$			14.8508i			0.483608i
$944$	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
$947$			16.4423i			0.534303i	0.963655	+	0.267151i	$0.0860824\pi$
$947$			16.4423i			0.534303i	−0.963655	+	0.267151i	$0.913918\pi$
$948$	−0.712427	−	1.23396i	−0.0231385	−	0.0400771i
$949$	−34.9803	+	42.1092i	−1.13551	+	1.36692i
$950$	0.873487	+	1.51292i	0.0283397	+	0.0490857i
$951$	13.0820	+	7.55287i	0.424211	+	0.244919i
$952$	22.5483	−	39.0548i	0.730794	−	1.26577i
$953$	11.1814	−	19.3667i	0.362201	−	0.627351i	−0.626122	−	0.779725i	$-0.715359\pi$
$953$	11.1814	−	19.3667i	0.362201	−	0.627351i	0.988323	+	0.152375i	$0.0486921\pi$
$954$	−19.0801	−	11.0159i	−0.617742	−	0.356654i
$955$	−25.8856	+	14.9451i	−0.837639	+	0.483611i
$956$		−	6.11865i		−	0.197891i
$957$			19.3828i			0.626558i
$958$	−12.3325	−	21.3606i	−0.398446	−	0.690129i
$959$	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
$964$			2.40705i			0.0775259i
$965$	21.9916	+	38.0905i	0.707934	+	1.22618i
$966$	−11.1192			−0.357753
$967$	−7.14558	−	4.12550i	−0.229786	−	0.132667i	0.380687	−	0.924704i	$-0.375687\pi$
$967$	−7.14558	−	4.12550i	−0.229786	−	0.132667i	−0.610474	+	0.792037i	$0.709021\pi$
$968$	3.62702	−	2.09406i	0.116577	−	0.0673056i
$969$	3.91636	+	2.26111i	0.125812	+	0.0726374i
$970$	−42.0700	+	24.2891i	−1.35079	+	0.779878i
$971$	21.2094			0.680642			0.340321	−	0.940309i	$-0.389464\pi$
$971$	21.2094			0.680642			0.340321	+	0.940309i	$0.389464\pi$
$972$	5.05210	−	8.75050i	0.162046	−	0.280672i
$973$			53.5933i			1.71812i
$974$	3.47595	+	6.02052i	0.111377	+	0.192910i
$975$	−0.705819	+	4.12201i	−0.0226043	+	0.132010i
$976$	−33.9963			−1.08820
$977$	32.7463	−	18.9061i	1.04765	−	0.604859i	0.125658	−	0.992074i	$-0.459896\pi$
$977$	32.7463	−	18.9061i	1.04765	−	0.604859i	0.921990	+	0.387214i	$0.126563\pi$
$978$	2.44469			0.0781727
$979$	−4.74175			−0.151547
$980$	−15.4561	−	8.92360i	−0.493728	−	0.285054i
$981$		−	33.3049i		−	1.06334i
$982$			33.8032i			1.07870i
$983$	9.24576	−	5.33804i	0.294894	−	0.170257i	−0.345253	−	0.938510i	$-0.612207\pi$
$983$	9.24576	−	5.33804i	0.294894	−	0.170257i	0.640147	+	0.768253i	$0.278874\pi$
$984$	−10.5695	+	18.3069i	−0.336943	+	0.583602i
$985$	−20.3823			−0.649433
$986$		−	21.7442i		−	0.692475i
$987$	−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	−0.983417	−	0.181357i	$-0.941951\pi$
$991$	−20.4233	−	35.3742i	−0.648769	−	1.12370i	0.334649	−	0.942343i	$-0.391382\pi$
$992$	−19.0288	+	1.78569i	−0.604165	+	0.0566957i
$993$		−	24.6059i		−	0.780844i
$994$	3.49328	+	2.01684i	0.110800	+	0.0639704i
$995$	7.84499	−	4.52931i	0.248703	−	0.143589i
$996$		−	3.80014i		−	0.120412i
$997$	−45.7741			−1.44968			−0.724840	−	0.688917i	$-0.758086\pi$
$997$	−45.7741			−1.44968			−0.724840	+	0.688917i	$0.758086\pi$
$998$	25.3708			0.803098
$999$		−	3.89861i		−	0.123346i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.11	✓	70	13.4	even	6
403.2.s.a.335.11	yes	70	31.25	even	3
403.2.v.a.36.11	yes	70	1.1	even	1	trivial
403.2.v.a.56.11	yes	70	403.56	even	6	inner

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.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01226 + 0.584427i) q^{2} -1.01318 q^{3} +(-0.316890 + 0.548870i) q^{4} +(-2.14676 + 1.23943i) q^{5} +(1.02560 - 0.592128i) q^{6} +(-3.71079 + 2.14243i) q^{7} -3.07850i q^{8} -1.97347 q^{9} +O(q^{10})\)	\(q+(-1.01226 + 0.584427i) q^{2} -1.01318 q^{3} +(-0.316890 + 0.548870i) q^{4} +(-2.14676 + 1.23943i) q^{5} +(1.02560 - 0.592128i) q^{6} +(-3.71079 + 2.14243i) q^{7} -3.07850i q^{8} -1.97347 q^{9} +(1.44872 - 2.50925i) q^{10} +(3.04472 + 1.75787i) q^{11} +(0.321066 - 0.556102i) q^{12} +(3.38197 - 1.24991i) q^{13} +(2.50419 - 4.33738i) q^{14} +(2.17505 - 1.25577i) q^{15} +(1.16538 + 2.01850i) q^{16} +(-1.70938 - 2.96072i) q^{17} +(1.99766 - 1.15335i) q^{18} +(1.13065 - 0.652784i) q^{19} -1.57106i q^{20} +(3.75969 - 2.17066i) q^{21} -4.10939 q^{22} +(1.09562 + 1.89767i) q^{23} +3.11907i q^{24} +(0.572396 - 0.991420i) q^{25} +(-2.69294 + 3.24175i) q^{26} +5.03901 q^{27} -2.71566i 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} +(0.625374 - 1.08318i) q^{36} -0.773685i q^{37} +(-0.763009 + 1.32157i) q^{38} +(-3.42653 + 1.26638i) q^{39} +(3.81561 + 6.60882i) q^{40} +(5.86934 + 3.38867i) q^{41} +(-2.53718 + 4.39453i) q^{42} +(-5.44144 - 9.42485i) q^{43} +(-1.92968 + 1.11410i) q^{44} +(4.23658 - 2.44599i) q^{45} +(-2.21810 - 1.28062i) q^{46} -6.24759i q^{47} +(-1.18074 - 2.04510i) q^{48} +(5.67999 - 9.83804i) q^{49} +1.33810i q^{50} +(1.73190 + 2.99974i) q^{51} +(-0.385673 + 2.25234i) q^{52} +(-4.77562 - 8.27161i) q^{53} +(-5.10077 + 2.94493i) q^{54} -8.71506 q^{55} +(6.59547 + 11.4237i) q^{56} +(-1.14555 + 0.661385i) q^{57} +(5.50815 + 3.18013i) q^{58} +(8.91085 - 5.14468i) q^{59} +1.59176i q^{60} +(-7.29296 + 12.6318i) q^{61} +(2.71314 - 5.91538i) q^{62} +(7.32315 - 4.22802i) q^{63} -8.67384 q^{64} +(-5.71110 + 6.87500i) q^{65} +4.16354 q^{66} +(4.68263 + 2.70352i) q^{67} +2.16674 q^{68} +(-1.11006 - 1.92268i) q^{69} +12.4151i q^{70} +0.805389i q^{71} +6.07534i q^{72} +(-13.1489 + 7.59150i) q^{73} +(0.452163 + 0.783168i) q^{74} +(-0.579939 + 1.00448i) q^{75} +0.827442i q^{76} -15.0644 q^{77} +(2.72843 - 3.28446i) q^{78} +(1.10947 - 1.92166i) q^{79} +(-5.00360 - 2.88883i) q^{80} +0.815011 q^{81} -7.92172 q^{82} +(5.12515 - 2.95901i) q^{83} +2.75144i q^{84} +(7.33925 + 4.23732i) q^{85} +(11.0163 + 6.36025i) q^{86} +(2.75658 + 4.77453i) q^{87} +(5.41161 - 9.37319i) q^{88} +(-1.16803 + 0.674360i) q^{89} +(-2.85901 + 4.95194i) q^{90} +(-9.87194 + 11.8838i) q^{91} -1.38877 q^{92} +(4.60046 - 3.26467i) 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} +13.2782i q^{98} +(-6.00867 - 3.46911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Introduction

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