LMFDB - Embedded newform 731.2.e.a.307.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.11
Character	$\chi$	$=$	731.307
Dual form			731.2.e.a.681.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.966012 q^{2} +(-0.835198 + 1.44661i) q^{3} -1.06682 q^{4} +(-0.811572 + 1.40568i) q^{5} +(0.806812 - 1.39744i) q^{6} +(-1.19805 - 2.07509i) q^{7} +2.96259 q^{8} +(0.104888 + 0.181671i) q^{9} +O(q^{10})$	\(q-0.966012 q^{2} +(-0.835198 + 1.44661i) q^{3} -1.06682 q^{4} +(-0.811572 + 1.40568i) q^{5} +(0.806812 - 1.39744i) q^{6} +(-1.19805 - 2.07509i) q^{7} +2.96259 q^{8} +(0.104888 + 0.181671i) q^{9} +(0.783988 - 1.35791i) q^{10} +5.63250 q^{11} +(0.891006 - 1.54327i) q^{12} +(1.57930 + 2.73543i) q^{13} +(1.15733 + 2.00456i) q^{14} +(-1.35565 - 2.34805i) q^{15} -0.728255 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.101323 - 0.175497i) q^{18} +(-0.504465 + 0.873759i) q^{19} +(0.865801 - 1.49961i) q^{20} +4.00245 q^{21} -5.44107 q^{22} +(1.36035 - 2.35619i) q^{23} +(-2.47435 + 4.28569i) q^{24} +(1.18270 + 2.04850i) q^{25} +(-1.52563 - 2.64246i) q^{26} -5.36160 q^{27} +(1.27811 + 2.21375i) q^{28} +(1.40740 + 2.43769i) q^{29} +(1.30957 + 2.26824i) q^{30} +(-1.44009 + 2.49432i) q^{31} -5.22167 q^{32} +(-4.70425 + 8.14801i) q^{33} +(-0.483006 - 0.836591i) q^{34} +3.88922 q^{35} +(-0.111897 - 0.193811i) q^{36} +(-1.99180 + 3.44990i) q^{37} +(0.487319 - 0.844062i) q^{38} -5.27612 q^{39} +(-2.40435 + 4.16446i) q^{40} -2.86909 q^{41} -3.86641 q^{42} +(-2.90632 - 5.87821i) q^{43} -6.00886 q^{44} -0.340496 q^{45} +(-1.31411 + 2.27611i) q^{46} -1.65710 q^{47} +(0.608237 - 1.05350i) q^{48} +(0.629337 - 1.09004i) q^{49} +(-1.14251 - 1.97888i) q^{50} -1.67040 q^{51} +(-1.68483 - 2.91821i) q^{52} +(0.0801212 - 0.138774i) q^{53} +5.17937 q^{54} +(-4.57118 + 7.91751i) q^{55} +(-3.54934 - 6.14763i) q^{56} +(-0.842657 - 1.45952i) q^{57} +(-1.35956 - 2.35484i) q^{58} -4.21511 q^{59} +(1.44623 + 2.50494i) q^{60} +(0.614954 + 1.06513i) q^{61} +(1.39115 - 2.40954i) q^{62} +(0.251323 - 0.435304i) q^{63} +6.50071 q^{64} -5.12687 q^{65} +(4.54437 - 7.87108i) q^{66} +(-1.94684 + 3.37202i) q^{67} +(-0.533410 - 0.923893i) q^{68} +(2.27232 + 3.93577i) q^{69} -3.75704 q^{70} +(5.92002 + 10.2538i) q^{71} +(0.310740 + 0.538217i) q^{72} +(3.47752 + 6.02323i) q^{73} +(1.92410 - 3.33264i) q^{74} -3.95117 q^{75} +(0.538173 - 0.932144i) q^{76} +(-6.74803 - 11.6879i) q^{77} +5.09680 q^{78} +(4.80987 + 8.33093i) q^{79} +(0.591031 - 1.02370i) q^{80} +(4.16333 - 7.21110i) q^{81} +2.77158 q^{82} +(1.76086 - 3.04990i) q^{83} -4.26989 q^{84} -1.62314 q^{85} +(2.80754 + 5.67842i) q^{86} -4.70183 q^{87} +16.6868 q^{88} +(-9.13771 + 15.8270i) q^{89} +0.328924 q^{90} +(3.78418 - 6.55438i) q^{91} +(-1.45125 + 2.51363i) q^{92} +(-2.40553 - 4.16650i) q^{93} +1.60078 q^{94} +(-0.818819 - 1.41824i) q^{95} +(4.36113 - 7.55370i) q^{96} -8.05023 q^{97} +(-0.607948 + 1.05300i) q^{98} +(0.590782 + 1.02326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.966012			−0.683074			−0.341537	−	0.939868i	$-0.610947\pi$
$2$	−0.966012			−0.683074			−0.341537	+	0.939868i	$0.610947\pi$
$3$	−0.835198	+	1.44661i	−0.482202	+	0.835198i	−0.999791	−	0.0204310i	$-0.993496\pi$
$3$	−0.835198	+	1.44661i	−0.482202	+	0.835198i	0.517589	+	0.855629i	$0.326830\pi$
$4$	−1.06682			−0.533410
$5$	−0.811572	+	1.40568i	−0.362946	+	0.628641i	−0.988444	−	0.151585i	$-0.951562\pi$
$5$	−0.811572	+	1.40568i	−0.362946	+	0.628641i	0.625498	+	0.780225i	$0.284896\pi$
$6$	0.806812	−	1.39744i	0.329380	−	0.570502i
$7$	−1.19805	−	2.07509i	−0.452822	−	0.784310i	0.545739	−	0.837956i	$-0.316249\pi$
$7$	−1.19805	−	2.07509i	−0.452822	−	0.784310i	−0.998560	+	0.0536456i	$0.982916\pi$
$8$	2.96259			1.04743
$9$	0.104888	+	0.181671i	0.0349627	+	0.0605571i
$10$	0.783988	−	1.35791i	0.247919	−	0.429408i
$11$	5.63250			1.69826			0.849131	−	0.528182i	$-0.177126\pi$
$11$	5.63250			1.69826			0.849131	+	0.528182i	$0.177126\pi$
$12$	0.891006	−	1.54327i	0.257211	−	0.445503i
$13$	1.57930	+	2.73543i	0.438020	+	0.758672i	0.997537	−	0.0701467i	$-0.0223467\pi$
$13$	1.57930	+	2.73543i	0.438020	+	0.758672i	−0.559517	+	0.828819i	$0.689013\pi$
$14$	1.15733	+	2.00456i	0.309311	+	0.535742i
$15$	−1.35565	−	2.34805i	−0.350026	−	0.606263i
$16$	−0.728255			−0.182064
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	−0.101323	−	0.175497i	−0.0238821	−	0.0413650i
$19$	−0.504465	+	0.873759i	−0.115732	+	0.200454i	−0.918072	−	0.396413i	$-0.870255\pi$
$19$	−0.504465	+	0.873759i	−0.115732	+	0.200454i	0.802340	+	0.596867i	$0.203588\pi$
$20$	0.865801	−	1.49961i	0.193599	−	0.335323i
$21$	4.00245			0.873406
$22$	−5.44107			−1.16004
$23$	1.36035	−	2.35619i	0.283652	−	0.491300i	−0.688629	−	0.725114i	$-0.741787\pi$
$23$	1.36035	−	2.35619i	0.283652	−	0.491300i	0.972281	+	0.233814i	$0.0751206\pi$
$24$	−2.47435	+	4.28569i	−0.505074	+	0.874814i
$25$	1.18270	+	2.04850i	0.236541	+	0.409700i
$26$	−1.52563	−	2.64246i	−0.299200	−	0.518229i
$27$	−5.36160			−1.03184
$28$	1.27811	+	2.21375i	0.241540	+	0.418359i
$29$	1.40740	+	2.43769i	0.261347	+	0.452667i	0.966600	−	0.256289i	$-0.0824998\pi$
$29$	1.40740	+	2.43769i	0.261347	+	0.452667i	−0.705253	+	0.708956i	$0.749167\pi$
$30$	1.30957	+	2.26824i	0.239094	+	0.414123i
$31$	−1.44009	+	2.49432i	−0.258649	+	0.447992i	−0.965880	−	0.258990i	$-0.916610\pi$
$31$	−1.44009	+	2.49432i	−0.258649	+	0.447992i	0.707232	+	0.706982i	$0.249944\pi$
$32$	−5.22167			−0.923069
$33$	−4.70425	+	8.14801i	−0.818905	+	1.41839i
$34$	−0.483006	−	0.836591i	−0.0828349	−	0.143474i
$35$	3.88922			0.657399
$36$	−0.111897	−	0.193811i	−0.0186494	−	0.0323018i
$37$	−1.99180	+	3.44990i	−0.327450	+	0.567160i	−0.982005	−	0.188854i	$-0.939523\pi$
$37$	−1.99180	+	3.44990i	−0.327450	+	0.567160i	0.654555	+	0.756014i	$0.272856\pi$
$38$	0.487319	−	0.844062i	0.0790537	−	0.136925i
$39$	−5.27612			−0.844855
$40$	−2.40435	+	4.16446i	−0.380161	+	0.658459i
$41$	−2.86909			−0.448077			−0.224039	−	0.974580i	$-0.571924\pi$
$41$	−2.86909			−0.448077			−0.224039	+	0.974580i	$0.571924\pi$
$42$	−3.86641			−0.596601
$43$	−2.90632	−	5.87821i	−0.443210	−	0.896418i
$43$	−2.90632	−	5.87821i	−0.443210	−	0.896418i
$44$	−6.00886			−0.905870
$45$	−0.340496			−0.0507582
$46$	−1.31411	+	2.27611i	−0.193755	+	0.335594i
$47$	−1.65710			−0.241713			−0.120857	−	0.992670i	$-0.538564\pi$
$47$	−1.65710			−0.241713			−0.120857	+	0.992670i	$0.538564\pi$
$48$	0.608237	−	1.05350i	0.0877915	−	0.152059i
$49$	0.629337	−	1.09004i	0.0899053	−	0.155721i
$50$	−1.14251	−	1.97888i	−0.161575	−	0.279856i
$51$	−1.67040			−0.233902
$52$	−1.68483	−	2.91821i	−0.233644	−	0.404683i
$53$	0.0801212	−	0.138774i	0.0110055	−	0.0190621i	−0.860470	−	0.509501i	$-0.829830\pi$
$53$	0.0801212	−	0.138774i	0.0110055	−	0.0190621i	0.871476	+	0.490439i	$0.163163\pi$
$54$	5.17937			0.704823
$55$	−4.57118	+	7.91751i	−0.616377	+	1.06760i
$56$	−3.54934	−	6.14763i	−0.474300	−	0.821512i
$57$	−0.842657	−	1.45952i	−0.111613	−	0.193319i
$58$	−1.35956	−	2.35484i	−0.178520	−	0.309205i
$59$	−4.21511			−0.548760			−0.274380	−	0.961621i	$-0.588473\pi$
$59$	−4.21511			−0.548760			−0.274380	+	0.961621i	$0.588473\pi$
$60$	1.44623	+	2.50494i	0.186708	+	0.323387i
$61$	0.614954	+	1.06513i	0.0787368	+	0.136376i	0.902705	−	0.430260i	$-0.141578\pi$
$61$	0.614954	+	1.06513i	0.0787368	+	0.136376i	−0.823968	+	0.566636i	$0.808245\pi$
$62$	1.39115	−	2.40954i	0.176676	−	0.306012i
$63$	0.251323	−	0.435304i	0.0316637	−	0.0548431i
$64$	6.50071			0.812588
$65$	−5.12687			−0.635909
$66$	4.54437	−	7.87108i	0.559373	−	0.968862i
$67$	−1.94684	+	3.37202i	−0.237844	+	0.411958i	−0.960095	−	0.279673i	$-0.909774\pi$
$67$	−1.94684	+	3.37202i	−0.237844	+	0.411958i	0.722251	+	0.691631i	$0.243107\pi$
$68$	−0.533410	−	0.923893i	−0.0646855	−	0.112039i
$69$	2.27232	+	3.93577i	0.273555	+	0.473811i
$70$	−3.75704			−0.449052
$71$	5.92002	+	10.2538i	0.702578	+	1.21690i	0.967559	+	0.252647i	$0.0813010\pi$
$71$	5.92002	+	10.2538i	0.702578	+	1.21690i	−0.264981	+	0.964254i	$0.585366\pi$
$72$	0.310740	+	0.538217i	0.0366210	+	0.0634295i
$73$	3.47752	+	6.02323i	0.407012	+	0.704966i	0.994553	−	0.104228i	$-0.0332373\pi$
$73$	3.47752	+	6.02323i	0.407012	+	0.704966i	−0.587541	+	0.809194i	$0.699904\pi$
$74$	1.92410	−	3.33264i	0.223672	−	0.387412i
$75$	−3.95117			−0.456241
$76$	0.538173	−	0.932144i	0.0617327	−	0.106924i
$77$	−6.74803	−	11.6879i	−0.769010	−	1.33196i
$78$	5.09680			0.577099
$79$	4.80987	+	8.33093i	0.541152	+	0.937303i	0.998838	+	0.0481893i	$0.0153451\pi$
$79$	4.80987	+	8.33093i	0.541152	+	0.937303i	−0.457686	+	0.889114i	$0.651322\pi$
$80$	0.591031	−	1.02370i	0.0660793	−	0.114453i
$81$	4.16333	−	7.21110i	0.462593	−	0.801234i
$82$	2.77158			0.306070
$83$	1.76086	−	3.04990i	0.193279	−	0.334770i	−0.753056	−	0.657957i	$-0.771421\pi$
$83$	1.76086	−	3.04990i	0.193279	−	0.334770i	0.946335	+	0.323187i	$0.104754\pi$
$84$	−4.26989			−0.465883
$85$	−1.62314			−0.176055
$86$	2.80754	+	5.67842i	0.302745	+	0.612320i
$87$	−4.70183			−0.504089
$88$	16.6868			1.77882
$89$	−9.13771	+	15.8270i	−0.968595	+	1.67766i	−0.268966	+	0.963150i	$0.586682\pi$
$89$	−9.13771	+	15.8270i	−0.968595	+	1.67766i	−0.699629	+	0.714506i	$0.746651\pi$
$90$	0.328924			0.0346716
$91$	3.78418	−	6.55438i	0.396689	−	0.687086i
$92$	−1.45125	+	2.51363i	−0.151303	+	0.262064i
$93$	−2.40553	−	4.16650i	−0.249442	−	0.432046i
$94$	1.60078			0.165108
$95$	−0.818819	−	1.41824i	−0.0840091	−	0.145508i
$96$	4.36113	−	7.55370i	0.445106	−	0.770946i
$97$	−8.05023			−0.817377			−0.408689	−	0.912674i	$-0.634014\pi$
$97$	−8.05023			−0.817377			−0.408689	+	0.912674i	$0.634014\pi$
$98$	−0.607948	+	1.05300i	−0.0614120	+	0.106369i
$99$	0.590782	+	1.02326i	0.0593758	+	0.102842i
$100$	−1.26173	−	2.18538i	−0.126173	−	0.218538i
$101$	−1.82223	−	3.15619i	−0.181319	−	0.314053i	0.761011	−	0.648739i	$-0.224703\pi$
$101$	−1.82223	−	3.15619i	−0.181319	−	0.314053i	−0.942330	+	0.334686i	$0.891370\pi$
$102$	1.61362			0.159773
$103$	8.39209	+	14.5355i	0.826897	+	1.43223i	0.900461	+	0.434937i	$0.143229\pi$
$103$	8.39209	+	14.5355i	0.826897	+	1.43223i	−0.0735636	+	0.997291i	$0.523437\pi$
$104$	4.67882	+	8.10395i	0.458796	+	0.794658i
$105$	−3.24827	+	5.62617i	−0.316999	+	0.549058i
$106$	−0.0773981	+	0.134057i	−0.00751756	+	0.0130208i
$107$	0.847248			0.0819065			0.0409533	−	0.999161i	$-0.486961\pi$
$107$	0.847248			0.0819065			0.0409533	+	0.999161i	$0.486961\pi$
$108$	5.71986			0.550394
$109$	−2.05952	+	3.56719i	−0.197266	+	0.341675i	−0.947641	−	0.319338i	$-0.896540\pi$
$109$	−2.05952	+	3.56719i	−0.197266	+	0.341675i	0.750375	+	0.661012i	$0.229873\pi$
$110$	4.41581	−	7.64841i	0.421031	−	0.729248i
$111$	−3.32709	−	5.76270i	−0.315794	−	0.546971i
$112$	0.872489	+	1.51119i	0.0824424	+	0.142794i
$113$	−8.31088			−0.781822			−0.390911	−	0.920429i	$-0.627840\pi$
$113$	−8.31088			−0.781822			−0.390911	+	0.920429i	$0.627840\pi$
$114$	0.814017	+	1.40992i	0.0762396	+	0.132051i
$115$	2.20804	+	3.82444i	0.205901	+	0.356631i
$116$	−1.50144	−	2.60057i	−0.139405	−	0.241457i
$117$	−0.331300	+	0.573828i	−0.0306287	+	0.0530504i
$118$	4.07184			0.374844
$119$	1.19805	−	2.07509i	0.109825	−	0.190223i
$120$	−4.01622	−	6.95630i	−0.366629	−	0.635020i
$121$	20.7251			1.88410
$122$	−0.594053	−	1.02893i	−0.0537830	−	0.0931550i
$123$	2.39626	−	4.15045i	0.216064	−	0.374233i
$124$	1.53632	−	2.66099i	0.137966	−	0.238964i
$125$	−11.9551			−1.06930
$126$	−0.242781	+	0.420509i	−0.0216286	+	0.0374619i
$127$	−2.43499			−0.216071			−0.108035	−	0.994147i	$-0.534456\pi$
$127$	−2.43499			−0.216071			−0.108035	+	0.994147i	$0.534456\pi$
$128$	4.16357			0.368011
$129$	10.9308	+	0.705169i	0.962403	+	0.0620867i
$130$	4.95262			0.434373
$131$	−11.0671			−0.966941			−0.483470	−	0.875361i	$-0.660624\pi$
$131$	−11.0671			−0.966941			−0.483470	+	0.875361i	$0.660624\pi$
$132$	5.01859	−	8.69246i	0.436812	−	0.756581i
$133$	2.41750			0.209624
$134$	1.88067	−	3.25741i	0.162465	−	0.281398i
$135$	4.35132	−	7.53671i	0.374502	−	0.648657i
$136$	1.48129	+	2.56567i	0.127020	+	0.220005i
$137$	6.83961			0.584347			0.292174	−	0.956365i	$-0.405622\pi$
$137$	6.83961			0.584347			0.292174	+	0.956365i	$0.405622\pi$
$138$	−2.19509	−	3.80201i	−0.186858	−	0.323648i
$139$	10.2779	−	17.8018i	0.871757	−	1.50993i	0.0115800	−	0.999933i	$-0.496314\pi$
$139$	10.2779	−	17.8018i	0.871757	−	1.50993i	0.860177	−	0.509995i	$-0.170353\pi$
$140$	−4.14910			−0.350663
$141$	1.38401	−	2.39717i	0.116555	−	0.201879i
$142$	−5.71882	−	9.90528i	−0.479913	−	0.831233i
$143$	8.89542	+	15.4073i	0.743872	+	1.28842i
$144$	−0.0763852	−	0.132303i	−0.00636544	−	0.0110253i
$145$	−4.56882			−0.379420
$146$	−3.35932	−	5.81852i	−0.278020	−	0.481544i
$147$	1.05124	+	1.82081i	0.0867050	+	0.150178i
$148$	2.12489	−	3.68042i	0.174665	−	0.302529i
$149$	−3.52700	+	6.10894i	−0.288943	+	0.500464i	−0.973558	−	0.228441i	$-0.926637\pi$
$149$	−3.52700	+	6.10894i	−0.288943	+	0.500464i	0.684615	+	0.728905i	$0.259971\pi$
$150$	3.81688			0.311647
$151$	8.93045			0.726750			0.363375	−	0.931643i	$-0.381624\pi$
$151$	8.93045			0.726750			0.363375	+	0.931643i	$0.381624\pi$
$152$	−1.49452	+	2.58859i	−0.121222	+	0.209962i
$153$	−0.104888	+	0.181671i	−0.00847969	+	0.0146873i
$154$	6.51869	+	11.2907i	0.525291	+	0.909830i
$155$	−2.33748	−	4.04863i	−0.187751	−	0.325194i
$156$	5.62867			0.450654
$157$	3.08965	+	5.35143i	0.246581	+	0.427091i	0.962575	−	0.271016i	$-0.0873596\pi$
$157$	3.08965	+	5.35143i	0.246581	+	0.427091i	−0.715994	+	0.698106i	$0.754026\pi$
$158$	−4.64639	−	8.04779i	−0.369647	−	0.640247i
$159$	0.133834	+	0.231808i	0.0106137	+	0.0183835i
$160$	4.23776	−	7.34001i	0.335024	−	0.580279i
$161$	−6.51908			−0.513775
$162$	−4.02183	+	6.96602i	−0.315985	+	0.547302i
$163$	−9.79193	−	16.9601i	−0.766963	−	1.32842i	−0.939203	−	0.343364i	$-0.888434\pi$
$163$	−9.79193	−	16.9601i	−0.766963	−	1.32842i	0.172240	−	0.985055i	$-0.444900\pi$
$164$	3.06081			0.239009
$165$	−7.63568	−	13.2254i	−0.594437	−	1.02959i
$166$	−1.70101	+	2.94624i	−0.132024	+	0.228673i
$167$	−1.25085	+	2.16653i	−0.0967935	+	0.167651i	−0.910356	−	0.413827i	$-0.864192\pi$
$167$	−1.25085	+	2.16653i	−0.0967935	+	0.167651i	0.813562	+	0.581478i	$0.197525\pi$
$168$	11.8576			0.914833
$169$	1.51161	−	2.61819i	0.116278	−	0.201399i
$170$	1.56798			0.120258
$171$	−0.211649			−0.0161852
$172$	3.10052	+	6.27099i	0.236412	+	0.478158i
$173$	−10.2228			−0.777227			−0.388614	−	0.921401i	$-0.627046\pi$
$173$	−10.2228			−0.777227			−0.388614	+	0.921401i	$0.627046\pi$
$174$	4.54202			0.344330
$175$	2.83388	−	4.90843i	0.214221	−	0.371042i
$176$	−4.10190			−0.309192
$177$	3.52045	−	6.09760i	0.264613	−	0.458323i
$178$	8.82714	−	15.2891i	0.661622	−	1.14596i
$179$	−3.05215	−	5.28647i	−0.228128	−	0.395129i	0.729125	−	0.684380i	$-0.239927\pi$
$179$	−3.05215	−	5.28647i	−0.228128	−	0.395129i	−0.957253	+	0.289251i	$0.906594\pi$
$180$	0.363248			0.0270749
$181$	5.76750	+	9.98961i	0.428695	+	0.742522i	0.996758	−	0.0804637i	$-0.0256401\pi$
$181$	5.76750	+	9.98961i	0.428695	+	0.742522i	−0.568062	+	0.822985i	$0.692307\pi$
$182$	−3.65556	+	6.33162i	−0.270968	+	0.469331i
$183$	−2.05443			−0.151868
$184$	4.03015	−	6.98042i	0.297106	−	0.514603i
$185$	−3.23298	−	5.59968i	−0.237693	−	0.411696i
$186$	2.32377	+	4.02489i	0.170387	+	0.295119i
$187$	2.81625	+	4.87789i	0.205945	+	0.356707i
$188$	1.76783			0.128932
$189$	6.42348	+	11.1258i	0.467239	+	0.809282i
$190$	0.790989	+	1.37003i	0.0573844	+	0.0993927i
$191$	−8.39356	+	14.5381i	−0.607337	+	1.05194i	0.384341	+	0.923191i	$0.374429\pi$
$191$	−8.39356	+	14.5381i	−0.607337	+	1.05194i	−0.991677	+	0.128747i	$0.958905\pi$
$192$	−5.42938	+	9.40396i	−0.391832	+	0.678672i
$193$	−1.18229			−0.0851030			−0.0425515	−	0.999094i	$-0.513549\pi$
$193$	−1.18229			−0.0851030			−0.0425515	+	0.999094i	$0.513549\pi$
$194$	7.77662			0.558329
$195$	4.28195	−	7.41655i	0.306637	−	0.531110i
$196$	−0.671390	+	1.16288i	−0.0479564	+	0.0830629i
$197$	−10.4025	−	18.0176i	−0.741144	−	1.28370i	−0.951975	−	0.306177i	$-0.900950\pi$
$197$	−10.4025	−	18.0176i	−0.741144	−	1.28370i	0.210830	−	0.977523i	$-0.432383\pi$
$198$	−0.570702	−	0.988485i	−0.0405581	−	0.0702486i
$199$	−22.1669			−1.57137			−0.785685	−	0.618626i	$-0.787690\pi$
$199$	−22.1669			−1.57137			−0.785685	+	0.618626i	$0.787690\pi$
$200$	3.50386	+	6.06886i	0.247760	+	0.429133i
$201$	−3.25199	−	5.63261i	−0.229378	−	0.397294i
$202$	1.76030	+	3.04892i	0.123854	+	0.214521i
$203$	3.37228	−	5.84096i	0.236687	−	0.409955i
$204$	1.78201			0.124766
$205$	2.32847	−	4.03304i	0.162628	−	0.281679i
$206$	−8.10686	−	14.0415i	−0.564832	−	0.978318i
$207$	0.570737			0.0396689
$208$	−1.15013	−	1.99209i	−0.0797475	−	0.138127i
$209$	−2.84140	+	4.92145i	−0.196544	+	0.340424i
$210$	3.13787	−	5.43495i	0.216534	−	0.375047i
$211$	5.53430			0.380997			0.190499	−	0.981687i	$-0.438990\pi$
$211$	5.53430			0.380997			0.190499	+	0.981687i	$0.438990\pi$
$212$	−0.0854749	+	0.148047i	−0.00587044	+	0.0101679i
$213$	−19.7776			−1.35514
$214$	−0.818452			−0.0559482
$215$	10.6216	+	0.685221i	0.724386	+	0.0467317i
$216$	−15.8842			−1.08078
$217$	6.90124			0.468486
$218$	1.98952	−	3.44595i	0.134747	−	0.233389i
$219$	−11.6177			−0.785049
$220$	4.87662	−	8.44656i	0.328782	−	0.569467i
$221$	−1.57930	+	2.73543i	−0.106235	+	0.184005i
$222$	3.21401	+	5.56684i	0.215711	+	0.373622i
$223$	21.2269			1.42146			0.710728	−	0.703467i	$-0.248366\pi$
$223$	21.2269			1.42146			0.710728	+	0.703467i	$0.248366\pi$
$224$	6.25584	+	10.8354i	0.417986	+	0.723972i
$225$	−0.248103	+	0.429726i	−0.0165402	+	0.0286484i
$226$	8.02841			0.534042
$227$	10.5173	−	18.2165i	0.698056	−	1.20907i	−0.271083	−	0.962556i	$-0.587382\pi$
$227$	10.5173	−	18.2165i	0.698056	−	1.20907i	0.969139	−	0.246513i	$-0.0792848\pi$
$228$	0.898963	+	1.55705i	0.0595353	+	0.103118i
$229$	11.7257	+	20.3095i	0.774854	+	1.34209i	0.934876	+	0.354973i	$0.115510\pi$
$229$	11.7257	+	20.3095i	0.774854	+	1.34209i	−0.160022	+	0.987113i	$0.551157\pi$
$230$	−2.13299	−	3.69445i	−0.140645	−	0.243605i
$231$	22.5438			1.48327
$232$	4.16954	+	7.22186i	0.273744	+	0.474138i
$233$	−4.16875	−	7.22049i	−0.273104	−	0.473030i	0.696551	−	0.717507i	$-0.254717\pi$
$233$	−4.16875	−	7.22049i	−0.273104	−	0.473030i	−0.969655	+	0.244477i	$0.921384\pi$
$234$	0.320040	−	0.554325i	0.0209216	−	0.0362373i
$235$	1.34486	−	2.32936i	0.0877289	−	0.151951i
$236$	4.49676			0.292714
$237$	−16.0688			−1.04378
$238$	−1.15733	+	2.00456i	−0.0750188	+	0.129936i
$239$	10.7921	−	18.6925i	0.698084	−	1.20912i	−0.271046	−	0.962566i	$-0.587369\pi$
$239$	10.7921	−	18.6925i	0.698084	−	1.20912i	0.969130	−	0.246551i	$-0.0792972\pi$
$240$	0.987257	+	1.70998i	0.0637271	+	0.110379i
$241$	−8.52187	−	14.7603i	−0.548942	−	0.950795i	−0.998347	−	0.0574673i	$-0.981697\pi$
$241$	−8.52187	−	14.7603i	−0.548942	−	0.950795i	0.449406	−	0.893328i	$-0.351636\pi$
$242$	−20.0207			−1.28698
$243$	−1.08798	−	1.88444i	−0.0697940	−	0.120887i
$244$	−0.656045	−	1.13630i	−0.0419990	−	0.0727444i
$245$	1.02150	+	1.76930i	0.0652615	+	0.113036i
$246$	−2.31482	+	4.00938i	−0.147587	+	0.255629i
$247$	−3.18681			−0.202772
$248$	−4.26640	+	7.38963i	−0.270917	+	0.469242i
$249$	2.94133	+	5.09454i	0.186399	+	0.322853i
$250$	11.5488			0.730409
$251$	5.03434	+	8.71972i	0.317764	+	0.550384i	0.980021	−	0.198893i	$-0.0637346\pi$
$251$	5.03434	+	8.71972i	0.317764	+	0.550384i	−0.662257	+	0.749277i	$0.730401\pi$
$252$	−0.268116	+	0.464391i	−0.0168897	+	0.0292539i
$253$	7.66216	−	13.2712i	0.481716	−	0.834356i
$254$	2.35223			0.147592
$255$	1.35565	−	2.34805i	0.0848939	−	0.147040i
$256$	−17.0235			−1.06397
$257$	4.86599			0.303532			0.151766	−	0.988416i	$-0.451504\pi$
$257$	4.86599			0.303532			0.151766	+	0.988416i	$0.451504\pi$
$258$	−10.5593	−	0.681202i	−0.657393	−	0.0424098i
$259$	9.54512			0.593105
$260$	5.46944			0.339200
$261$	−0.295238	+	0.511368i	−0.0182748	+	0.0316529i
$262$	10.6910			0.660492
$263$	−0.221067	+	0.382898i	−0.0136315	+	0.0236105i	−0.872761	−	0.488148i	$-0.837673\pi$
$263$	−0.221067	+	0.382898i	−0.0136315	+	0.0236105i	0.859129	+	0.511759i	$0.171006\pi$
$264$	−13.9368	+	24.1392i	−0.857748	+	1.48566i
$265$	0.130048	+	0.225250i	0.00798880	+	0.0138370i
$266$	−2.33534			−0.143189
$267$	−15.2636	−	26.4373i	−0.934117	−	1.61794i
$268$	2.07692	−	3.59734i	0.126868	−	0.219742i
$269$	−15.7482			−0.960187			−0.480094	−	0.877217i	$-0.659397\pi$
$269$	−15.7482			−0.960187			−0.480094	+	0.877217i	$0.659397\pi$
$270$	−4.20343	+	7.28055i	−0.255813	+	0.443080i
$271$	15.2225	+	26.3662i	0.924701	+	1.60163i	0.792041	+	0.610468i	$0.209019\pi$
$271$	15.2225	+	26.3662i	0.924701	+	1.60163i	0.132661	+	0.991162i	$0.457648\pi$
$272$	−0.364128	−	0.630688i	−0.0220785	−	0.0382411i
$273$	6.32107	+	10.9484i	0.382569	+	0.662628i
$274$	−6.60715			−0.399152
$275$	6.66157	+	11.5382i	0.401708	+	0.695779i
$276$	−2.42416	−	4.19876i	−0.145917	−	0.252736i
$277$	−3.35046	+	5.80317i	−0.201310	+	0.348679i	−0.948951	−	0.315425i	$-0.897853\pi$
$277$	−3.35046	+	5.80317i	−0.201310	+	0.348679i	0.747641	+	0.664103i	$0.231186\pi$
$278$	−9.92855	+	17.1967i	−0.595475	+	1.03139i
$279$	−0.604194			−0.0361722
$280$	11.5222			0.688581
$281$	−6.33798	+	10.9777i	−0.378092	+	0.654875i	−0.990785	−	0.135447i	$-0.956753\pi$
$281$	−6.33798	+	10.9777i	−0.378092	+	0.654875i	0.612692	+	0.790321i	$0.290086\pi$
$282$	−1.33697	+	2.31570i	−0.0796154	+	0.137898i
$283$	1.63412	+	2.83038i	0.0971383	+	0.168248i	0.910499	−	0.413511i	$-0.135698\pi$
$283$	1.63412	+	2.83038i	0.0971383	+	0.168248i	−0.813361	+	0.581760i	$0.802364\pi$
$284$	−6.31560	−	10.9389i	−0.374762	−	0.649107i
$285$	2.73550			0.162037
$286$	−8.59308	−	14.8837i	−0.508120	−	0.880089i
$287$	3.43733	+	5.95362i	0.202899	+	0.351431i
$288$	−0.547690	−	0.948627i	−0.0322730	−	0.0558984i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	4.41354			0.259172
$291$	6.72354	−	11.6455i	0.394141	−	0.682672i
$292$	−3.70988	−	6.42571i	−0.217104	−	0.376036i
$293$	2.47307			0.144478			0.0722391	−	0.997387i	$-0.476986\pi$
$293$	2.47307			0.144478			0.0722391	+	0.997387i	$0.476986\pi$
$294$	−1.01551	−	1.75892i	−0.0592260	−	0.102582i
$295$	3.42086	−	5.92510i	0.199170	−	0.344973i
$296$	−5.90088	+	10.2206i	−0.342981	+	0.594061i
$297$	−30.1992			−1.75234
$298$	3.40713	−	5.90132i	0.197370	−	0.341854i
$299$	8.59360			0.496981
$300$	4.21518			0.243364
$301$	−8.71588	+	13.0733i	−0.502375	+	0.753531i
$302$	−8.62693			−0.496424
$303$	6.08769			0.349729
$304$	0.367379	−	0.636320i	0.0210706	−	0.0364954i
$305$	−1.99632			−0.114309
$306$	0.101323	−	0.175497i	0.00579226	−	0.0100325i
$307$	1.47371	−	2.55254i	0.0841092	−	0.145681i	−0.820902	−	0.571069i	$-0.806529\pi$
$307$	1.47371	−	2.55254i	0.0841092	−	0.145681i	0.905011	+	0.425388i	$0.139862\pi$
$308$	7.19894	+	12.4689i	0.410198	+	0.710483i
$309$	−28.0362			−1.59493
$310$	2.25803	+	3.91103i	0.128248	+	0.222132i
$311$	12.8861	−	22.3194i	0.730703	−	1.26562i	−0.225880	−	0.974155i	$-0.572526\pi$
$311$	12.8861	−	22.3194i	0.730703	−	1.26562i	0.956583	−	0.291460i	$-0.0941410\pi$
$312$	−15.6310			−0.884929
$313$	3.15636	−	5.46697i	0.178408	−	0.309011i	−0.762928	−	0.646484i	$-0.776239\pi$
$313$	3.15636	−	5.46697i	0.178408	−	0.309011i	0.941335	+	0.337473i	$0.109572\pi$
$314$	−2.98464	−	5.16955i	−0.168433	−	0.291734i
$315$	0.407933	+	0.706560i	0.0229844	+	0.0398102i
$316$	−5.13126	−	8.88761i	−0.288656	−	0.499967i
$317$	−7.79584			−0.437858			−0.218929	−	0.975741i	$-0.570256\pi$
$317$	−7.79584			−0.437858			−0.218929	+	0.975741i	$0.570256\pi$
$318$	−0.129285	−	0.223929i	−0.00724997	−	0.0125573i
$319$	7.92717	+	13.7303i	0.443837	+	0.768747i
$320$	−5.27579	+	9.13794i	−0.294926	+	0.510826i
$321$	−0.707620	+	1.22563i	−0.0394955	+	0.0684082i
$322$	6.29751			0.350946
$323$	−1.00893			−0.0561384
$324$	−4.44153	+	7.69295i	−0.246751	+	0.427386i
$325$	−3.73569	+	6.47041i	−0.207219	+	0.358914i
$326$	9.45912	+	16.3837i	0.523892	+	0.907408i
$327$	−3.44021	−	5.95862i	−0.190244	−	0.329513i
$328$	−8.49994			−0.469330
$329$	1.98530	+	3.43864i	0.109453	+	0.189578i
$330$	7.37616	+	12.7759i	0.406044	+	0.703289i
$331$	8.78546	+	15.2169i	0.482892	+	0.836394i	0.999807	−	0.0196428i	$-0.00625289\pi$
$331$	8.78546	+	15.2169i	0.482892	+	0.836394i	−0.516915	+	0.856037i	$0.672920\pi$
$332$	−1.87852	+	3.25369i	−0.103097	+	0.178570i
$333$	−0.835663			−0.0457941
$334$	1.20833	−	2.09290i	0.0661171	−	0.114518i
$335$	−3.16000	−	5.47327i	−0.172649	−	0.299037i
$336$	−2.91480			−0.159016
$337$	−2.00377	−	3.47064i	−0.109152	−	0.189058i	0.806275	−	0.591541i	$-0.201480\pi$
$337$	−2.00377	−	3.47064i	−0.109152	−	0.189058i	−0.915427	+	0.402484i	$0.868147\pi$
$338$	−1.46024	+	2.52920i	−0.0794263	+	0.137570i
$339$	6.94123	−	12.0226i	0.376996	−	0.652976i
$340$	1.73160			0.0939093
$341$	−8.11133	+	14.0492i	−0.439253	+	0.760809i
$342$	0.204456			0.0110557
$343$	−19.7887			−1.06849
$344$	−8.61022	−	17.4147i	−0.464232	−	0.938937i
$345$	−7.37660			−0.397143
$346$	9.87538			0.530904
$347$	5.28346	−	9.15122i	0.283631	−	0.491263i	−0.688645	−	0.725098i	$-0.741794\pi$
$347$	5.28346	−	9.15122i	0.283631	−	0.491263i	0.972276	+	0.233835i	$0.0751276\pi$
$348$	5.01600			0.268886
$349$	1.12511	−	1.94875i	0.0602258	−	0.104314i	−0.834340	−	0.551249i	$-0.814151\pi$
$349$	1.12511	−	1.94875i	0.0602258	−	0.104314i	0.894566	+	0.446935i	$0.147485\pi$
$350$	−2.73757	+	4.74160i	−0.146329	+	0.253449i
$351$	−8.46758	−	14.6663i	−0.451966	−	0.782828i
$352$	−29.4111			−1.56761
$353$	−8.58495	−	14.8696i	−0.456931	−	0.791428i	0.541866	−	0.840465i	$-0.317718\pi$
$353$	−8.58495	−	14.8696i	−0.456931	−	0.791428i	−0.998797	+	0.0490372i	$0.984385\pi$
$354$	−3.40080	+	5.89035i	−0.180750	+	0.313069i
$355$	−19.2181			−1.01999
$356$	9.74829	−	16.8845i	0.516658	−	0.894878i
$357$	2.00122	+	3.46622i	0.105916	+	0.183452i
$358$	2.94841	+	5.10680i	0.155828	+	0.269903i
$359$	17.7554	+	30.7533i	0.937094	+	1.62309i	0.770856	+	0.637009i	$0.219829\pi$
$359$	17.7554	+	30.7533i	0.937094	+	1.62309i	0.166238	+	0.986086i	$0.446838\pi$
$360$	−1.00875			−0.0531658
$361$	8.99103	+	15.5729i	0.473212	+	0.819627i
$362$	−5.57148	−	9.65009i	−0.292830	−	0.507197i
$363$	−17.3095	+	29.9810i	−0.908515	+	1.57359i
$364$	−4.03703	+	6.99235i	−0.211598	+	0.366499i
$365$	−11.2890			−0.590894
$366$	1.98461			0.103737
$367$	−12.9865	+	22.4934i	−0.677892	+	1.17414i	0.297722	+	0.954653i	$0.403773\pi$
$367$	−12.9865	+	22.4934i	−0.677892	+	1.17414i	−0.975614	+	0.219491i	$0.929560\pi$
$368$	−0.990680	+	1.71591i	−0.0516428	+	0.0894479i
$369$	−0.300933	−	0.521232i	−0.0156660	−	0.0271342i
$370$	3.12309	+	5.40936i	0.162362	+	0.281219i
$371$	−0.383958			−0.0199341
$372$	2.56627	+	4.44490i	0.133055	+	0.230457i
$373$	1.00128	+	1.73427i	0.0518443	+	0.0897969i	0.890783	−	0.454429i	$-0.150157\pi$
$373$	1.00128	+	1.73427i	0.0518443	+	0.0897969i	−0.838939	+	0.544226i	$0.816823\pi$
$374$	−2.72053	−	4.71210i	−0.140675	−	0.243657i
$375$	9.98489	−	17.2943i	0.515617	−	0.893075i
$376$	−4.90931			−0.253178
$377$	−4.44542	+	7.69969i	−0.228951	+	0.396554i
$378$	−6.20516	−	10.7477i	−0.319159	−	0.552800i
$379$	26.9435			1.38400			0.691998	−	0.721900i	$-0.256731\pi$
$379$	26.9435			1.38400			0.691998	+	0.721900i	$0.256731\pi$
$380$	0.873532	+	1.51300i	0.0448113	+	0.0776154i
$381$	2.03370	−	3.52248i	0.104190	−	0.180462i
$382$	8.10828	−	14.0440i	0.414856	−	0.718552i
$383$	−27.4071			−1.40044			−0.700218	−	0.713930i	$-0.746914\pi$
$383$	−27.4071			−1.40044			−0.700218	+	0.713930i	$0.746914\pi$
$384$	−3.47741	+	6.02305i	−0.177456	+	0.307362i
$385$	21.9061			1.11644
$386$	1.14211			0.0581316
$387$	0.763063	−	1.14455i	0.0387887	−	0.0581806i
$388$	8.58815			0.435997
$389$	−5.58060			−0.282947			−0.141474	−	0.989942i	$-0.545184\pi$
$389$	−5.58060			−0.282947			−0.141474	+	0.989942i	$0.545184\pi$
$390$	−4.13642	+	7.16448i	−0.209456	+	0.362788i
$391$	2.72070			0.137591
$392$	1.86447	−	3.22935i	0.0941698	−	0.163107i
$393$	9.24326	−	16.0098i	0.466261	−	0.807587i
$394$	10.0489	+	17.4052i	0.506256	+	0.876862i
$395$	−15.6142			−0.785636
$396$	−0.630258	−	1.09164i	−0.0316716	−	0.0548569i
$397$	2.73742	−	4.74135i	0.137387	−	0.237961i	−0.789120	−	0.614239i	$-0.789463\pi$
$397$	2.73742	−	4.74135i	0.137387	−	0.237961i	0.926507	+	0.376278i	$0.122796\pi$
$398$	21.4135			1.07336
$399$	−2.01909	+	3.49717i	−0.101081	+	0.175078i
$400$	−0.861310	−	1.49183i	−0.0430655	−	0.0745916i
$401$	15.0892	+	26.1352i	0.753516	+	1.30513i	0.946108	+	0.323850i	$0.104977\pi$
$401$	15.0892	+	26.1352i	0.753516	+	1.30513i	−0.192592	+	0.981279i	$0.561689\pi$
$402$	3.14146	+	5.44117i	0.156682	+	0.271381i
$403$	−9.09737			−0.453172
$404$	1.94399	+	3.36709i	0.0967171	+	0.167519i
$405$	6.75769	+	11.7047i	0.335792	+	0.581609i
$406$	−3.25766	+	5.64244i	−0.161675	+	0.280029i
$407$	−11.2188	+	19.4315i	−0.556096	+	0.963186i
$408$	−4.94869			−0.244997
$409$	8.07919			0.399490			0.199745	−	0.979848i	$-0.435989\pi$
$409$	8.07919			0.399490			0.199745	+	0.979848i	$0.435989\pi$
$410$	−2.24934	+	3.89596i	−0.111087	+	0.192408i
$411$	−5.71243	+	9.89422i	−0.281773	+	0.488046i
$412$	−8.95285	−	15.5068i	−0.441075	−	0.763965i
$413$	5.04992	+	8.74672i	0.248490	+	0.430398i
$414$	−0.551339			−0.0270968
$415$	2.85813	+	4.95042i	0.140300	+	0.243007i
$416$	−8.24659	−	14.2835i	−0.404322	−	0.700307i
$417$	17.1681	+	29.7360i	0.840726	+	1.45618i
$418$	2.74483	−	4.75418i	0.134254	−	0.232535i
$419$	30.2812			1.47933			0.739667	−	0.672973i	$-0.234983\pi$
$419$	30.2812			1.47933			0.739667	+	0.672973i	$0.234983\pi$
$420$	3.46532	−	6.00211i	0.169090	−	0.292873i
$421$	4.05941	+	7.03110i	0.197843	+	0.342675i	0.947829	−	0.318779i	$-0.103273\pi$
$421$	4.05941	+	7.03110i	0.197843	+	0.342675i	−0.749985	+	0.661454i	$0.769940\pi$
$422$	−5.34621			−0.260249
$423$	−0.173810	−	0.301048i	−0.00845094	−	0.0146375i
$424$	0.237366	−	0.411130i	0.0115275	−	0.0199662i
$425$	−1.18270	+	2.04850i	−0.0573695	+	0.0993669i
$426$	19.1054			0.925659
$427$	1.47349	−	2.55217i	0.0713074	−	0.123508i
$428$	−0.903861			−0.0436898
$429$	−29.7177			−1.43479
$430$	−10.2606	−	0.661932i	−0.494809	−	0.0319212i
$431$	36.7615			1.77074			0.885370	−	0.464887i	$-0.153905\pi$
$431$	36.7615			1.77074			0.885370	+	0.464887i	$0.153905\pi$
$432$	3.90461			0.187861
$433$	−13.1778	+	22.8247i	−0.633286	+	1.09688i	0.353589	+	0.935401i	$0.384961\pi$
$433$	−13.1778	+	22.8247i	−0.633286	+	1.09688i	−0.986875	+	0.161483i	$0.948372\pi$
$434$	−6.66668			−0.320011
$435$	3.81587	−	6.60928i	0.182957	−	0.316891i
$436$	2.19714	−	3.80555i	0.105224	−	0.182253i
$437$	1.37250	+	2.37723i	0.0656554	+	0.113718i
$438$	11.2228			0.536246
$439$	12.5550	+	21.7459i	0.599217	+	1.03787i	0.992937	+	0.118643i	$0.0378545\pi$
$439$	12.5550	+	21.7459i	0.599217	+	1.03787i	−0.393720	+	0.919230i	$0.628812\pi$
$440$	−13.5425	+	23.4563i	−0.645614	+	1.11824i
$441$	0.264040			0.0125733
$442$	1.52563	−	2.64246i	0.0725666	−	0.125689i
$443$	11.4129	+	19.7677i	0.542244	+	0.939194i	0.998775	+	0.0494864i	$0.0157584\pi$
$443$	11.4129	+	19.7677i	0.542244	+	0.939194i	−0.456531	+	0.889708i	$0.650908\pi$
$444$	3.54941	+	6.14776i	0.168448	+	0.291760i
$445$	−14.8318	−	25.6894i	−0.703095	−	1.21780i
$446$	−20.5054			−0.970959
$447$	−5.89149	−	10.2044i	−0.278658	−	0.482650i
$448$	−7.78819	−	13.4895i	−0.367958	−	0.637321i
$449$	2.64182	−	4.57577i	0.124675	−	0.215944i	−0.796931	−	0.604071i	$-0.793544\pi$
$449$	2.64182	−	4.57577i	0.124675	−	0.215944i	0.921606	+	0.388127i	$0.126878\pi$
$450$	0.239670	−	0.415121i	0.0112982	−	0.0195690i
$451$	−16.1602			−0.760953
$452$	8.86621			0.417031
$453$	−7.45870	+	12.9188i	−0.350440	+	0.606980i
$454$	−10.1598	+	17.5973i	−0.476824	+	0.825884i
$455$	6.14226	+	10.6387i	0.287954	+	0.498750i
$456$	−2.49644	−	4.32397i	−0.116907	−	0.202488i
$457$	3.96331			0.185396			0.0926979	−	0.995694i	$-0.470451\pi$
$457$	3.96331			0.185396			0.0926979	+	0.995694i	$0.470451\pi$
$458$	−11.3271	−	19.6192i	−0.529283	−	0.916744i
$459$	−2.68080	−	4.64328i	−0.125129	−	0.216730i
$460$	−2.35558	−	4.07998i	−0.109829	−	0.190230i
$461$	−8.73731	+	15.1335i	−0.406937	+	0.704836i	−0.994545	−	0.104310i	$-0.966736\pi$
$461$	−8.73731	+	15.1335i	−0.406937	+	0.704836i	0.587608	+	0.809146i	$0.300070\pi$
$462$	−21.7776			−1.01318
$463$	4.26632	−	7.38948i	0.198273	−	0.343418i	−0.749696	−	0.661783i	$-0.769800\pi$
$463$	4.26632	−	7.38948i	0.198273	−	0.343418i	0.947968	+	0.318364i	$0.103134\pi$
$464$	−1.02495	−	1.77526i	−0.0475819	−	0.0824143i
$465$	7.80903			0.362135
$466$	4.02706	+	6.97508i	0.186550	+	0.323114i
$467$	1.89941	−	3.28987i	0.0878942	−	0.152237i	−0.818727	−	0.574184i	$-0.805320\pi$
$467$	1.89941	−	3.28987i	0.0878942	−	0.152237i	0.906621	+	0.421946i	$0.138653\pi$
$468$	0.353437	−	0.612171i	0.0163376	−	0.0282976i
$469$	9.32966			0.430804
$470$	−1.29915	+	2.25019i	−0.0599253	+	0.103794i
$471$	−10.3219			−0.475607
$472$	−12.4876			−0.574789
$473$	−16.3698	−	33.1090i	−0.752686	−	1.52235i
$474$	15.5226			0.712978
$475$	−2.38653			−0.109501
$476$	−1.27811	+	2.21375i	−0.0585819	+	0.101467i
$477$	0.0336150			0.00153913
$478$	−10.4253	+	18.0572i	−0.476843	+	0.825917i
$479$	14.0157	−	24.2759i	0.640393	−	1.10919i	−0.344953	−	0.938620i	$-0.612105\pi$
$479$	14.0157	−	24.2759i	0.640393	−	1.10919i	0.985345	−	0.170572i	$-0.0545617\pi$
$480$	7.07874	+	12.2607i	0.323099	+	0.559623i
$481$	−12.5826			−0.573718
$482$	8.23223	+	14.2586i	0.374968	+	0.649463i
$483$	5.44472	−	9.43053i	0.247743	−	0.429104i
$484$	−22.1099			−1.00500
$485$	6.53334	−	11.3161i	0.296664	−	0.513837i
$486$	1.05100	+	1.82039i	0.0476745	+	0.0825746i
$487$	−9.32066	−	16.1439i	−0.422359	−	0.731548i	0.573810	−	0.818988i	$-0.305465\pi$
$487$	−9.32066	−	16.1439i	−0.422359	−	0.731548i	−0.996170	+	0.0874402i	$0.972131\pi$
$488$	1.82185	+	3.15554i	0.0824714	+	0.142845i
$489$	32.7128			1.47932
$490$	−0.986786	−	1.70916i	−0.0445785	−	0.0772121i
$491$	−2.48589	−	4.30568i	−0.112187	−	0.194313i	0.804465	−	0.594000i	$-0.202452\pi$
$491$	−2.48589	−	4.30568i	−0.112187	−	0.194313i	−0.916652	+	0.399687i	$0.869119\pi$
$492$	−2.55638	+	4.42778i	−0.115250	+	0.199620i
$493$	−1.40740	+	2.43769i	−0.0633861	+	0.109788i
$494$	3.07850			0.138508
$495$	−1.91785			−0.0862008
$496$	1.04876	−	1.81650i	0.0470905	−	0.0815632i
$497$	14.1850	−	24.5692i	0.636285	−	1.10208i
$498$	−2.84136	−	4.92139i	−0.127325	−	0.220533i
$499$	−18.9904	−	32.8923i	−0.850126	−	1.47246i	−0.881094	−	0.472940i	$-0.843193\pi$
$499$	−18.9904	−	32.8923i	−0.850126	−	1.47246i	0.0309688	−	0.999520i	$-0.490141\pi$
$500$	12.7539			0.570374
$501$	−2.08941	−	3.61897i	−0.0933480	−	0.161684i
$502$	−4.86323	−	8.42336i	−0.217057	−	0.375953i
$503$	−4.58131	−	7.93506i	−0.204271	−	0.353807i	0.745630	−	0.666361i	$-0.232149\pi$
$503$	−4.58131	−	7.93506i	−0.204271	−	0.353807i	−0.949900	+	0.312554i	$0.898816\pi$
$504$	0.744565	−	1.28962i	0.0331656	−	0.0574445i
$505$	5.91548			0.263235
$506$	−7.40174	+	12.8202i	−0.329048	+	0.569927i
$507$	2.52499	+	4.37341i	0.112139	+	0.194230i
$508$	2.59770			0.115254
$509$	−16.3223	−	28.2710i	−0.723472	−	1.25309i	−0.959600	−	0.281369i	$-0.909212\pi$
$509$	−16.3223	−	28.2710i	−0.723472	−	1.25309i	0.236127	−	0.971722i	$-0.424122\pi$
$510$	−1.30957	+	2.26824i	−0.0579888	+	0.100440i
$511$	8.33250	−	14.4323i	0.368608	−	0.638448i
$512$	8.11775			0.358757
$513$	2.70474	−	4.68474i	0.119417	−	0.206837i
$514$	−4.70061			−0.207335
$515$	−27.2431			−1.20048
$516$	−11.6612	−	0.752288i	−0.513355	−	0.0331176i
$517$	−9.33363			−0.410493
$518$	−9.22071			−0.405135
$519$	8.53809	−	14.7884i	0.374780	−	0.649139i
$520$	−15.1888			−0.666072
$521$	17.7285	−	30.7066i	0.776699	−	1.34528i	−0.157135	−	0.987577i	$-0.550226\pi$
$521$	17.7285	−	30.7066i	0.776699	−	1.34528i	0.933834	−	0.357706i	$-0.116441\pi$
$522$	0.285204	−	0.493988i	0.0124830	−	0.0216213i
$523$	19.8182	+	34.3261i	0.866588	+	1.50097i	0.865462	+	0.500975i	$0.167025\pi$
$523$	19.8182	+	34.3261i	0.866588	+	1.50097i	0.00112600	+	0.999999i	$0.499642\pi$
$524$	11.8066			0.515776
$525$	4.73371	+	8.19902i	0.206596	+	0.357835i
$526$	0.213553	−	0.369885i	0.00931135	−	0.0161277i
$527$	−2.88019			−0.125463
$528$	3.42590	−	5.93383i	0.149093	−	0.258237i
$529$	7.79891	+	13.5081i	0.339083	+	0.587309i
$530$	−0.125628	−	0.217594i	−0.00545694	−	0.00945169i
$531$	−0.442114	−	0.765764i	−0.0191861	−	0.0332313i
$532$	−2.57904			−0.111816
$533$	−4.53116	−	7.84821i	−0.196266	−	0.339944i
$534$	14.7448	+	25.5388i	0.638071	+	1.10517i
$535$	−0.687602	+	1.19096i	−0.0297276	+	0.0514898i
$536$	−5.76767	+	9.98990i	−0.249126	+	0.431498i
$537$	10.1966			0.440015
$538$	15.2130			0.655879
$539$	3.54474	−	6.13967i	0.152683	−	0.264454i
$540$	−4.64208	+	8.04031i	−0.199763	+	0.346000i
$541$	14.3545	+	24.8627i	0.617149	+	1.06893i	0.990003	+	0.141043i	$0.0450456\pi$
$541$	14.3545	+	24.8627i	0.617149	+	1.06893i	−0.372855	+	0.927890i	$0.621621\pi$
$542$	−14.7051	−	25.4700i	−0.631639	−	1.09403i
$543$	−19.2680			−0.826870
$544$	−2.61083	−	4.52210i	−0.111939	−	0.193883i
$545$	−3.34289	−	5.79006i	−0.143194	−	0.248019i
$546$	−6.10623	−	10.5763i	−0.261323	−	0.452624i
$547$	4.10831	−	7.11581i	0.175659	−	0.304250i	−0.764730	−	0.644351i	$-0.777128\pi$
$547$	4.10831	−	7.11581i	0.175659	−	0.304250i	0.940389	+	0.340101i	$0.110461\pi$
$548$	−7.29663			−0.311697
$549$	−0.129003	+	0.223439i	−0.00550569	+	0.00953614i
$550$	−6.43516	−	11.1460i	−0.274396	−	0.475268i
$551$	−2.83993			−0.120985
$552$	6.73194	+	11.6601i	0.286531	+	0.496285i
$553$	11.5250	−	19.9618i	0.490091	−	0.848862i
$554$	3.23659	−	5.60593i	0.137509	−	0.238173i
$555$	10.8007			0.458464
$556$	−10.9646	+	18.9913i	−0.465004	+	0.805411i
$557$	27.0542			1.14632			0.573162	−	0.819442i	$-0.305717\pi$
$557$	27.0542			1.14632			0.573162	+	0.819442i	$0.305717\pi$
$558$	0.583659			0.0247083
$559$	11.4895	−	17.2335i	0.485953	−	0.728899i
$560$	−2.83235			−0.119689
$561$	−9.40851			−0.397228
$562$	6.12257	−	10.6046i	0.258265	−	0.447328i
$563$	−29.0459			−1.22414			−0.612070	−	0.790804i	$-0.709663\pi$
$563$	−29.0459			−1.22414			−0.612070	+	0.790804i	$0.709663\pi$
$564$	−1.47649	+	2.55735i	−0.0621714	+	0.107684i
$565$	6.74487	−	11.6825i	0.283759	−	0.491485i
$566$	−1.57858	−	2.73418i	−0.0663526	−	0.114926i
$567$	−19.9516			−0.837887
$568$	17.5386	+	30.3777i	0.735903	+	1.27462i
$569$	16.7964	−	29.0922i	0.704142	−	1.21961i	−0.262858	−	0.964835i	$-0.584665\pi$
$569$	16.7964	−	29.0922i	0.704142	−	1.21961i	0.967000	−	0.254776i	$-0.0820017\pi$
$570$	−2.64253			−0.110683
$571$	15.2367	−	26.3907i	0.637636	−	1.10442i	−0.348314	−	0.937378i	$-0.613246\pi$
$571$	15.2367	−	26.3907i	0.637636	−	1.10442i	0.985950	−	0.167040i	$-0.0534208\pi$
$572$	−9.48981	−	16.4368i	−0.396789	−	0.687258i
$573$	−14.0206	−	24.2843i	−0.585718	−	1.01449i
$574$	−3.32050	−	5.75127i	−0.138595	−	0.240054i
$575$	6.43555			0.268381
$576$	0.681846	+	1.18099i	0.0284103	+	0.0492080i
$577$	−15.8742	−	27.4950i	−0.660853	−	1.14463i	−0.980392	−	0.197058i	$-0.936861\pi$
$577$	−15.8742	−	27.4950i	−0.660853	−	1.14463i	0.319539	−	0.947573i	$-0.396472\pi$
$578$	0.483006	−	0.836591i	0.0200904	−	0.0347976i
$579$	0.987445	−	1.71030i	0.0410368	−	0.0710778i
$580$	4.87411			0.202386
$581$	−8.43841			−0.350084
$582$	−6.49502	+	11.2497i	−0.269227	+	0.466315i
$583$	0.451283	−	0.781644i	0.0186902	−	0.0323724i
$584$	10.3024	+	17.8443i	0.426318	+	0.738404i
$585$	−0.537747	−	0.931405i	−0.0222331	−	0.0385088i
$586$	−2.38901			−0.0986893
$587$	−2.14668	−	3.71816i	−0.0886030	−	0.153465i	0.818318	−	0.574766i	$-0.194907\pi$
$587$	−2.14668	−	3.71816i	−0.0886030	−	0.153465i	−0.906921	+	0.421301i	$0.861574\pi$
$588$	−1.12149	−	1.94247i	−0.0462493	−	0.0801062i
$589$	−1.45295	−	2.51659i	−0.0598679	−	0.103694i
$590$	−3.30459	+	5.72372i	−0.136048	+	0.235642i
$591$	34.7525			1.42953
$592$	1.45054	−	2.51241i	0.0596168	−	0.103259i
$593$	15.4625	+	26.7818i	0.634967	+	1.09980i	0.986522	+	0.163628i	$0.0523197\pi$
$593$	15.4625	+	26.7818i	0.634967	+	1.09980i	−0.351555	+	0.936167i	$0.614347\pi$
$594$	29.1728			1.19697
$595$	1.94461	+	3.36817i	0.0797213	+	0.138081i
$596$	3.76267	−	6.51714i	0.154125	−	0.266953i
$597$	18.5138	−	32.0668i	0.757718	−	1.31241i
$598$	−8.30152			−0.339475
$599$	10.8230	−	18.7460i	0.442216	−	0.765940i	−0.555638	−	0.831424i	$-0.687526\pi$
$599$	10.8230	−	18.7460i	0.442216	−	0.765940i	0.997854	+	0.0654844i	$0.0208592\pi$
$600$	−11.7057			−0.477882
$601$	18.1882			0.741911			0.370956	−	0.928651i	$-0.379030\pi$
$601$	18.1882			0.741911			0.370956	+	0.928651i	$0.379030\pi$
$602$	8.41964	−	12.6289i	0.343159	−	0.514717i
$603$	−0.816799			−0.0332626
$604$	−9.52718			−0.387656
$605$	−16.8199	+	29.1329i	−0.683825	+	1.18442i
$606$	−5.88078			−0.238890
$607$	−17.9365	+	31.0670i	−0.728021	+	1.26097i	0.229698	+	0.973262i	$0.426226\pi$
$607$	−17.9365	+	31.0670i	−0.728021	+	1.26097i	−0.957719	+	0.287707i	$0.907107\pi$
$608$	2.63415	−	4.56248i	0.106829	−	0.185033i
$609$	5.63304	+	9.75671i	0.228262	+	0.395362i
$610$	1.92847			0.0780813
$611$	−2.61707	−	4.53289i	−0.105875	−	0.183381i
$612$	0.111897	−	0.193811i	0.00452315	−	0.00783433i
$613$	37.7047			1.52288			0.761439	−	0.648237i	$-0.224493\pi$
$613$	37.7047			1.52288			0.761439	+	0.648237i	$0.224493\pi$
$614$	−1.42362	+	2.46579i	−0.0574528	+	0.0995112i
$615$	3.88948	+	6.73677i	0.156839	+	0.271653i
$616$	−19.9916	−	34.6265i	−0.805486	−	1.39514i
$617$	−10.0939	−	17.4832i	−0.406366	−	0.703847i	0.588113	−	0.808779i	$-0.299871\pi$
$617$	−10.0939	−	17.4832i	−0.406366	−	0.703847i	−0.994479	+	0.104932i	$0.966538\pi$
$618$	27.0833			1.08945
$619$	−9.66312	−	16.7370i	−0.388394	−	0.672718i	0.603840	−	0.797106i	$-0.293637\pi$
$619$	−9.66312	−	16.7370i	−0.388394	−	0.672718i	−0.992234	+	0.124388i	$0.960303\pi$
$620$	2.49367	+	4.31916i	0.100148	+	0.173462i
$621$	−7.29364	+	12.6330i	−0.292684	+	0.506943i
$622$	−12.4481	+	21.5608i	−0.499124	+	0.864509i
$623$	43.7898			1.75440
$624$	3.84236			0.153818
$625$	3.78891	−	6.56259i	0.151556	−	0.262504i
$626$	−3.04908	+	5.28116i	−0.121866	+	0.211078i
$627$	−4.74626	−	8.22077i	−0.189547	−	0.328306i
$628$	−3.29610	−	5.70901i	−0.131529	−	0.227814i
$629$	−3.98360			−0.158836
$630$	−0.394068	−	0.682546i	−0.0157001	−	0.0271933i
$631$	−15.3159	−	26.5280i	−0.609717	−	1.05606i	−0.991287	−	0.131721i	$-0.957950\pi$
$631$	−15.3159	−	26.5280i	−0.609717	−	1.05606i	0.381569	−	0.924340i	$-0.375384\pi$
$632$	14.2496	+	24.6811i	0.566820	+	0.981762i
$633$	−4.62224	+	8.00596i	−0.183718	+	0.318208i
$634$	7.53088			0.299090
$635$	1.97617	−	3.42283i	0.0784220	−	0.135831i
$636$	−0.142777	−	0.247297i	−0.00566147	−	0.00980596i
$637$	3.97565			0.157521
$638$	−7.65775	−	13.2636i	−0.303173	−	0.525111i
$639$	−1.24188	+	2.15100i	−0.0491280	+	0.0850921i
$640$	−3.37904	+	5.85267i	−0.133568	+	0.231347i
$641$	−10.9984			−0.434411			−0.217206	−	0.976126i	$-0.569694\pi$
$641$	−10.9984			−0.434411			−0.217206	+	0.976126i	$0.569694\pi$
$642$	0.683570	−	1.18398i	0.0269783	−	0.0467279i
$643$	32.7328			1.29086			0.645428	−	0.763821i	$-0.276679\pi$
$643$	32.7328			1.29086			0.645428	+	0.763821i	$0.276679\pi$
$644$	6.95468			0.274053
$645$	−9.86237	+	14.7929i	−0.388330	+	0.582472i
$646$	0.974639			0.0383467
$647$	1.55886			0.0612852			0.0306426	−	0.999530i	$-0.490245\pi$
$647$	1.55886			0.0612852			0.0306426	+	0.999530i	$0.490245\pi$
$648$	12.3342	−	21.3635i	0.484534	−	0.839238i
$649$	−23.7416			−0.931939
$650$	3.60872	−	6.25049i	0.141546	−	0.245164i
$651$	−5.76390	+	9.98337i	−0.225905	+	0.391279i
$652$	10.4462	+	18.0934i	0.409106	+	0.708592i
$653$	−45.9321			−1.79746			−0.898731	−	0.438500i	$-0.855510\pi$
$653$	−45.9321			−1.79746			−0.898731	+	0.438500i	$0.855510\pi$
$654$	3.32329	+	5.75610i	0.129951	+	0.225081i
$655$	8.98178	−	15.5569i	0.350947	−	0.607858i
$656$	2.08943			0.0815786
$657$	−0.729499	+	1.26353i	−0.0284605	+	0.0492950i
$658$	−1.91782	−	3.32177i	−0.0747645	−	0.129496i
$659$	−17.4295	−	30.1889i	−0.678959	−	1.17599i	−0.975295	−	0.220907i	$-0.929098\pi$
$659$	−17.4295	−	30.1889i	−0.678959	−	1.17599i	0.296336	−	0.955084i	$-0.404235\pi$
$660$	8.14589	+	14.1091i	0.317078	+	0.549196i
$661$	6.06816			0.236024			0.118012	−	0.993012i	$-0.462348\pi$
$661$	6.06816			0.236024			0.118012	+	0.993012i	$0.462348\pi$
$662$	−8.48686	−	14.6997i	−0.329851	−	0.571319i
$663$	−2.63806	−	4.56925i	−0.102454	−	0.177455i
$664$	5.21670	−	9.03559i	0.202447	−	0.350649i
$665$	−1.96198	+	3.39824i	−0.0760822	+	0.131778i
$666$	0.807261			0.0312807
$667$	7.65821			0.296527
$668$	1.33443	−	2.31130i	0.0516306	−	0.0894269i
$669$	−17.7286	+	30.7069i	−0.685429	+	1.18720i
$670$	3.05259	+	5.28725i	0.117932	+	0.204264i
$671$	3.46373	+	5.99935i	0.133716	+	0.231602i
$672$	−20.8995			−0.806214
$673$	4.15016	+	7.18829i	0.159977	+	0.277088i	0.934860	−	0.355016i	$-0.115525\pi$
$673$	4.15016	+	7.18829i	0.159977	+	0.277088i	−0.774883	+	0.632104i	$0.782191\pi$
$674$	1.93567	+	3.35268i	0.0745592	+	0.129140i
$675$	−6.34118	−	10.9832i	−0.244072	−	0.422745i
$676$	−1.61262	+	2.79313i	−0.0620237	+	0.107428i
$677$	4.29386			0.165027			0.0825133	−	0.996590i	$-0.473705\pi$
$677$	4.29386			0.165027			0.0825133	+	0.996590i	$0.473705\pi$
$678$	−6.70531	+	11.6139i	−0.257516	+	0.446031i
$679$	9.64461	+	16.7049i	0.370126	+	0.641077i
$680$	−4.80870			−0.184405
$681$	17.5680	+	30.4287i	0.673208	+	1.16603i
$682$	7.83565	−	13.5717i	0.300042	−	0.519689i
$683$	6.90684	−	11.9630i	0.264283	−	0.457752i	−0.703092	−	0.711098i	$-0.748198\pi$
$683$	6.90684	−	11.9630i	0.264283	−	0.457752i	0.967376	+	0.253347i	$0.0815313\pi$
$684$	0.225792			0.00863336
$685$	−5.55083	+	9.61432i	−0.212086	+	0.367344i
$686$	19.1161			0.729856
$687$	−39.1730			−1.49454
$688$	2.11654	+	4.28083i	0.0806924	+	0.163205i
$689$	0.506142			0.0192825
$690$	7.12589			0.271278
$691$	−9.79320	+	16.9623i	−0.372551	+	0.645277i	−0.989957	−	0.141368i	$-0.954850\pi$
$691$	−9.79320	+	16.9623i	−0.372551	+	0.645277i	0.617406	+	0.786644i	$0.288183\pi$
$692$	10.9059			0.414581
$693$	1.41558	−	2.45185i	0.0537733	−	0.0931380i
$694$	−5.10389	+	8.84019i	−0.193741	+	0.335569i
$695$	16.6825	+	28.8949i	0.632801	+	1.09604i
$696$	−13.9296			−0.527999
$697$	−1.43455	−	2.48471i	−0.0543373	−	0.0941150i
$698$	−1.08687	+	1.88252i	−0.0411387	+	0.0712543i
$699$	13.9269			0.526765
$700$	−3.02324	+	5.23641i	−0.114268	+	0.197918i
$701$	−9.47681	−	16.4143i	−0.357934	−	0.619960i	0.629681	−	0.776854i	$-0.283185\pi$
$701$	−9.47681	−	16.4143i	−0.357934	−	0.619960i	−0.987616	+	0.156893i	$0.949852\pi$
$702$	8.17979	+	14.1678i	0.308726	+	0.534730i
$703$	−2.00959	−	3.48070i	−0.0757930	−	0.131277i
$704$	36.6152			1.37999
$705$	2.24645	+	3.89096i	0.0846060	+	0.146542i
$706$	8.29317	+	14.3642i	0.312118	+	0.540604i
$707$	−4.36625	+	7.56257i	−0.164210	+	0.284420i
$708$	−3.75568	+	6.50504i	−0.141147	+	0.244474i
$709$	34.1097			1.28102			0.640508	−	0.767952i	$-0.278724\pi$
$709$	34.1097			1.28102			0.640508	+	0.767952i	$0.278724\pi$
$710$	18.5649			0.696729
$711$	−1.00899	+	1.74763i	−0.0378402	+	0.0655412i
$712$	−27.0712	+	46.8888i	−1.01454	+	1.75723i
$713$	3.91806	+	6.78627i	0.146732	+	0.254148i
$714$	−1.93321	−	3.34841i	−0.0723485	−	0.125311i
$715$	−28.8771			−1.07994
$716$	3.25609	+	5.63971i	0.121686	+	0.210766i
$717$	18.0271	+	31.2239i	0.673235	+	1.16608i
$718$	−17.1519	−	29.7080i	−0.640105	−	1.10869i
$719$	−5.85751	+	10.1455i	−0.218448	+	0.378364i	−0.954334	−	0.298742i	$-0.903433\pi$
$719$	−5.85751	+	10.1455i	−0.218448	+	0.378364i	0.735885	+	0.677106i	$0.236766\pi$
$720$	0.247968			0.00924123
$721$	20.1083	−	34.8287i	0.748874	−	1.29709i
$722$	−8.68545	−	15.0436i	−0.323239	−	0.559866i
$723$	28.4698			1.05880
$724$	−6.15289	−	10.6571i	−0.228670	−	0.396068i
$725$	−3.32907	+	5.76612i	−0.123639	+	0.214148i
$726$	16.7212	−	28.9620i	0.620583	−	1.07488i
$727$	28.0986			1.04212			0.521059	−	0.853521i	$-0.325537\pi$
$727$	28.0986			1.04212			0.521059	+	0.853521i	$0.325537\pi$
$728$	11.2109	−	19.4179i	0.415505	−	0.719676i
$729$	28.6147			1.05980
$730$	10.9053			0.403624
$731$	3.63752	−	5.45605i	0.134538	−	0.201799i
$732$	2.19171			0.0810079
$733$	−5.86421			−0.216600			−0.108300	−	0.994118i	$-0.534541\pi$
$733$	−5.86421			−0.216600			−0.108300	+	0.994118i	$0.534541\pi$
$734$	12.5452	−	21.7289i	0.463051	−	0.802027i
$735$	−3.41264			−0.125877
$736$	−7.10329	+	12.3033i	−0.261831	+	0.453504i
$737$	−10.9656	+	18.9929i	−0.403922	+	0.699613i
$738$	0.290705	+	0.503516i	0.0107010	+	0.0185347i
$739$	47.7460			1.75636			0.878182	−	0.478326i	$-0.158756\pi$
$739$	47.7460			1.75636			0.878182	+	0.478326i	$0.158756\pi$
$740$	3.44900	+	5.97385i	0.126788	+	0.219603i
$741$	2.66162	−	4.61006i	0.0977770	−	0.169355i
$742$	0.370908			0.0136165
$743$	25.2393	−	43.7157i	0.925940	−	1.60378i	0.135898	−	0.990723i	$-0.456608\pi$
$743$	25.2393	−	43.7157i	0.925940	−	1.60378i	0.790042	−	0.613052i	$-0.210059\pi$
$744$	−7.12658	−	12.3436i	−0.261273	−	0.452539i
$745$	−5.72483	−	9.91569i	−0.209741	−	0.363283i
$746$	−0.967248	−	1.67532i	−0.0354135	−	0.0613380i
$747$	0.738772			0.0270303
$748$	−3.00443	−	5.20383i	−0.109853	−	0.190271i
$749$	−1.01505	−	1.75811i	−0.0370890	−	0.0642401i
$750$	−9.64552	+	16.7065i	−0.352205	+	0.610036i
$751$	8.58116	−	14.8630i	0.313131	−	0.542359i	−0.665907	−	0.746034i	$-0.731955\pi$
$751$	8.58116	−	14.8630i	0.313131	−	0.542359i	0.979038	+	0.203675i	$0.0652887\pi$
$752$	1.20679			0.0440073
$753$	−16.8187			−0.612906
$754$	4.29433	−	7.43799i	0.156390	−	0.270876i
$755$	−7.24770	+	12.5534i	−0.263771	+	0.456864i
$756$	−6.85270	−	11.8692i	−0.249230	−	0.431679i
$757$	−2.47231	−	4.28218i	−0.0898578	−	0.155638i	0.817593	−	0.575796i	$-0.195308\pi$
$757$	−2.47231	−	4.28218i	−0.0898578	−	0.155638i	−0.907451	+	0.420158i	$0.861975\pi$
$758$	−26.0278			−0.945371
$759$	12.7988	+	22.1682i	0.464569	+	0.804656i
$760$	−2.42582	−	4.20165i	−0.0879938	−	0.152410i
$761$	−15.4746	−	26.8027i	−0.560952	−	0.971598i	−0.997414	−	0.0718749i	$-0.977102\pi$
$761$	−15.4746	−	26.8027i	−0.560952	−	0.971598i	0.436461	−	0.899723i	$-0.356232\pi$
$762$	−1.96458	+	3.40276i	−0.0711693	+	0.123269i
$763$	9.86965			0.357305
$764$	8.95442	−	15.5095i	0.323960	−	0.561114i
$765$	−0.170248	−	0.294879i	−0.00615534	−	0.0106614i
$766$	26.4756			0.956601
$767$	−6.65692	−	11.5301i	−0.240368	−	0.416329i
$768$	14.2180	−	24.6263i	0.513047	−	0.888624i
$769$	−6.60718	+	11.4440i	−0.238261	+	0.412680i	−0.960215	−	0.279260i	$-0.909911\pi$
$769$	−6.60718	+	11.4440i	−0.238261	+	0.412680i	0.721954	+	0.691941i	$0.243244\pi$
$770$	−21.1615			−0.762608
$771$	−4.06407	+	7.03917i	−0.146364	+	0.253510i
$772$	1.26129			0.0453948
$773$	32.3836			1.16476			0.582378	−	0.812918i	$-0.302122\pi$
$773$	32.3836			1.16476			0.582378	+	0.812918i	$0.302122\pi$
$774$	−0.737129	+	1.10565i	−0.0264955	+	0.0397417i
$775$	−6.81281			−0.244724
$776$	−23.8495			−0.856147
$777$	−7.97207	+	13.8080i	−0.285996	+	0.495360i
$778$	5.39093			0.193274
$779$	1.44736	−	2.50690i	0.0518569	−	0.0898189i
$780$	−4.56807	+	7.91213i	−0.163563	+	0.283300i
$781$	33.3445	+	57.7544i	1.19316	+	2.06662i
$782$	−2.62823			−0.0939852
$783$	−7.54591	−	13.0699i	−0.269669	−	0.467080i
$784$	−0.458318	+	0.793830i	−0.0163685	+	0.0283511i
$785$	−10.0299			−0.357982
$786$	−8.92910	+	15.4657i	−0.318490	+	0.551642i
$787$	−18.7345	−	32.4491i	−0.667813	−	1.15669i	−0.978515	−	0.206178i	$-0.933897\pi$
$787$	−18.7345	−	32.4491i	−0.667813	−	1.15669i	0.310702	−	0.950507i	$-0.399436\pi$
$788$	11.0976	+	19.2215i	0.395334	+	0.684738i
$789$	−0.369269	−	0.639592i	−0.0131463	−	0.0227701i
$790$	15.0835			0.536647
$791$	9.95687	+	17.2458i	0.354026	+	0.613190i
$792$	1.75024	+	3.03151i	0.0621921	+	0.107720i
$793$	−1.94240	+	3.36433i	−0.0689765	+	0.119471i
$794$	−2.64438	+	4.58020i	−0.0938455	+	0.162545i
$795$	−0.434464			−0.0154088
$796$	23.6481			0.838185
$797$	1.34597	−	2.33130i	0.0476769	−	0.0825788i	−0.841202	−	0.540721i	$-0.818152\pi$
$797$	1.34597	−	2.33130i	0.0476769	−	0.0825788i	0.888879	+	0.458142i	$0.151485\pi$
$798$	1.95047	−	3.37831i	0.0690459	−	0.119591i
$799$	−0.828552	−	1.43509i	−0.0293120	−	0.0507700i
$800$	−6.17568	−	10.6966i	−0.218343	−	0.378182i
$801$	−3.83374			−0.135459
$802$	−14.5763	−	25.2469i	−0.514707	−	0.891499i
$803$	19.5871	+	33.9259i	0.691214	+	1.19722i
$804$	3.46929	+	6.00898i	0.122352	+	0.211920i
$805$	5.29070	−	9.16376i	0.186473	−	0.322980i
$806$	8.78818			0.309550
$807$	13.1529	−	22.7815i	0.463004	−	0.801946i
$808$	−5.39851	−	9.35049i	−0.189919	−	0.328949i
$809$	−9.00804			−0.316706			−0.158353	−	0.987383i	$-0.550618\pi$
$809$	−9.00804			−0.316706			−0.158353	+	0.987383i	$0.550618\pi$
$810$	−6.52801	−	11.3068i	−0.229371	−	0.397282i
$811$	−20.7411	+	35.9247i	−0.728319	+	1.26149i	0.229274	+	0.973362i	$0.426365\pi$
$811$	−20.7411	+	35.9247i	−0.728319	+	1.26149i	−0.957593	+	0.288124i	$0.906968\pi$
$812$	−3.59761	+	6.23125i	−0.126251	+	0.218674i
$813$	−50.8552			−1.78357
$814$	10.8375	−	18.7711i	0.379854	−	0.657927i
$815$	31.7874			1.11346
$816$	1.21647			0.0425851
$817$	6.60227	+	0.425927i	0.230984	+	0.0149013i
$818$	−7.80460			−0.272881
$819$	1.58766			0.0554773
$820$	−2.48406	+	4.30252i	−0.0867472	+	0.150251i
$821$	19.9704			0.696971			0.348485	−	0.937314i	$-0.386696\pi$
$821$	19.9704			0.696971			0.348485	+	0.937314i	$0.386696\pi$
$822$	5.51828	−	9.55794i	0.192472	−	0.333371i
$823$	2.77764	−	4.81102i	0.0968226	−	0.167702i	−0.813545	−	0.581502i	$-0.802465\pi$
$823$	2.77764	−	4.81102i	0.0968226	−	0.167702i	0.910368	+	0.413800i	$0.135799\pi$
$824$	24.8623	+	43.0627i	0.866119	+	1.50016i
$825$	−22.2549			−0.774818
$826$	−4.87829	−	8.44944i	−0.169737	−	0.293994i
$827$	−14.0094	+	24.2650i	−0.487155	+	0.843777i	−0.999891	−	0.0147696i	$-0.995299\pi$
$827$	−14.0094	+	24.2650i	−0.487155	+	0.843777i	0.512736	+	0.858546i	$0.328632\pi$
$828$	−0.608873			−0.0211598
$829$	1.21451	−	2.10360i	0.0421817	−	0.0730609i	−0.844164	−	0.536085i	$-0.819902\pi$
$829$	1.21451	−	2.10360i	0.0421817	−	0.0730609i	0.886345	+	0.463025i	$0.153236\pi$
$830$	−2.76099	−	4.78217i	−0.0958352	−	0.165991i
$831$	−5.59660	−	9.69359i	−0.194144	−	0.336267i
$832$	10.2666	+	17.7822i	0.355930	+	0.616488i
$833$	1.25867			0.0436105
$834$	−16.5846	−	28.7254i	−0.574278	−	0.994679i
$835$	−2.03031	−	3.51659i	−0.0702616	−	0.121697i
$836$	3.03126	−	5.25030i	0.104838	−	0.181585i
$837$	7.72121	−	13.3735i	0.266884	−	0.462256i
$838$	−29.2520			−1.01049
$839$	3.94192			0.136090			0.0680452	−	0.997682i	$-0.478324\pi$
$839$	3.94192			0.136090			0.0680452	+	0.997682i	$0.478324\pi$
$840$	−9.62329	+	16.6680i	−0.332035	+	0.575101i
$841$	10.5385	−	18.2531i	0.363395	−	0.629419i
$842$	−3.92144	−	6.79213i	−0.135142	−	0.234072i
$843$	−10.5869	−	18.3371i	−0.364634	−	0.631564i
$844$	−5.90411			−0.203228
$845$	2.45356	+	4.24969i	0.0844051	+	0.146194i
$846$	0.167903	+	0.290816i	0.00577262	+	0.00999847i
$847$	−24.8297	−	43.0063i	−0.853159	−	1.47772i
$848$	−0.0583487	+	0.101063i	−0.00200370	+	0.00347051i
$849$	−5.45925			−0.187361
$850$	1.14251	−	1.97888i	0.0391876	−	0.0678750i
$851$	5.41908	+	9.38612i	0.185764	+	0.321752i
$852$	21.0991			0.722844
$853$	−1.57146	−	2.72185i	−0.0538058	−	0.0931944i	0.837868	−	0.545873i	$-0.183802\pi$
$853$	−1.57146	−	2.72185i	−0.0538058	−	0.0931944i	−0.891674	+	0.452679i	$0.850469\pi$
$854$	−1.42341	+	2.46543i	−0.0487082	+	0.0843651i
$855$	0.171769	−	0.297512i	0.00587436	−	0.0101747i
$856$	2.51004			0.0857916
$857$	17.4670	−	30.2537i	0.596661	−	1.03345i	−0.396649	−	0.917970i	$-0.629827\pi$
$857$	17.4670	−	30.2537i	0.596661	−	1.03345i	0.993310	−	0.115477i	$-0.0368397\pi$
$858$	28.7077			0.980065
$859$	−36.6879			−1.25177			−0.625887	−	0.779914i	$-0.715263\pi$
$859$	−36.6879			−1.25177			−0.625887	+	0.779914i	$0.715263\pi$
$860$	−11.3313	−	0.731007i	−0.386395	−	0.0249271i
$861$	−11.4834			−0.391353
$862$	−35.5121			−1.20955
$863$	4.57661	−	7.92692i	0.155790	−	0.269835i	−0.777557	−	0.628813i	$-0.783541\pi$
$863$	4.57661	−	7.92692i	0.155790	−	0.269835i	0.933346	+	0.358977i	$0.116874\pi$
$864$	27.9965			0.952460
$865$	8.29656	−	14.3701i	0.282091	−	0.488597i
$866$	12.7300	−	22.0489i	0.432581	−	0.749253i
$867$	−0.835198	−	1.44661i	−0.0283648	−	0.0491293i
$868$	−7.36238			−0.249895
$869$	27.0916	+	46.9240i	0.919019	+	1.59179i
$870$	−3.68618	+	6.38465i	−0.124973	+	0.216460i
$871$	−12.2986			−0.416721
$872$	−6.10150	+	10.5681i	−0.206623	+	0.357881i
$873$	−0.844373	−	1.46250i	−0.0285777	−	0.0494980i
$874$	−1.32585	−	2.29644i	−0.0448475	−	0.0776781i
$875$	14.3229	+	24.8079i	0.484201	+	0.838661i
$876$	12.3939			0.418753
$877$	−11.2284	−	19.4481i	−0.379156	−	0.656717i	0.611784	−	0.791025i	$-0.290452\pi$
$877$	−11.2284	−	19.4481i	−0.379156	−	0.656717i	−0.990940	+	0.134308i	$0.957119\pi$
$878$	−12.1283	−	21.0068i	−0.409309	−	0.708944i
$879$	−2.06550	+	3.57755i	−0.0696677	+	0.120668i
$880$	3.32898	−	5.76597i	0.112220	−	0.194371i
$881$	−29.1905			−0.983453			−0.491727	−	0.870750i	$-0.663634\pi$
$881$	−29.1905			−0.983453			−0.491727	+	0.870750i	$0.663634\pi$
$882$	−0.255066			−0.00858851
$883$	−16.7582	+	29.0261i	−0.563959	+	0.976806i	0.433186	+	0.901304i	$0.357389\pi$
$883$	−16.7582	+	29.0261i	−0.563959	+	0.976806i	−0.997146	+	0.0755019i	$0.975944\pi$
$884$	1.68483	−	2.91821i	0.0566670	−	0.0981501i
$885$	5.71419	+	9.89727i	0.192080	+	0.332693i
$886$	−11.0250	−	19.0959i	−0.370393	−	0.641539i
$887$	9.37310			0.314718			0.157359	−	0.987541i	$-0.449702\pi$
$887$	9.37310			0.314718			0.157359	+	0.987541i	$0.449702\pi$
$888$	−9.85680	−	17.0725i	−0.330773	−	0.572915i
$889$	2.91725	+	5.05283i	0.0978415	+	0.169466i
$890$	14.3277	+	24.8163i	0.480266	+	0.831845i
$891$	23.4500	−	40.6165i	0.785604	−	1.36071i
$892$	−22.6452			−0.758219
$893$	0.835951	−	1.44791i	0.0279740	−	0.0484524i
$894$	5.69125	+	9.85754i	0.190344	+	0.329685i
$895$	9.90814			0.331193
$896$	−4.98818	−	8.63978i	−0.166643	−	0.288635i
$897$	−7.17736	+	12.4315i	−0.239645	+	0.415077i
$898$	−2.55203	+	4.42025i	−0.0851624	+	0.147506i
$899$	−8.10715			−0.270388
$900$	0.264681	−	0.458441i	0.00882270	−	0.0152814i
$901$	0.160242			0.00533845
$902$	15.6109			0.519787
$903$	−11.6324	−	23.5272i	−0.387102	−	0.782937i
$904$	−24.6217			−0.818905
$905$	−18.7230			−0.622372
$906$	7.20519	−	12.4798i	0.239377	−	0.414612i
$907$	−59.0643			−1.96120			−0.980599	−	0.196022i	$-0.937197\pi$
$907$	−59.0643			−1.96120			−0.980599	+	0.196022i	$0.937197\pi$
$908$	−11.2200	+	19.4337i	−0.372350	+	0.644929i
$909$	0.382260	−	0.662093i	0.0126788	−	0.0219602i
$910$	−5.93350	−	10.2771i	−0.196694	−	0.340683i
$911$	−15.6852			−0.519674			−0.259837	−	0.965653i	$-0.583669\pi$
$911$	−15.6852			−0.519674			−0.259837	+	0.965653i	$0.583669\pi$
$912$	0.613669	+	1.06291i	0.0203206	+	0.0351963i
$913$	9.91804	−	17.1786i	0.328239	−	0.568527i
$914$	−3.82860			−0.126639
$915$	1.66732	−	2.88788i	0.0551199	−	0.0954705i
$916$	−12.5092	−	21.6665i	−0.413315	−	0.715882i
$917$	13.2590	+	22.9653i	0.437851	+	0.758381i
$918$	2.58969	+	4.48547i	0.0854723	+	0.148042i
$919$	−45.9687			−1.51637			−0.758183	−	0.652042i	$-0.773913\pi$
$919$	−45.9687			−1.51637			−0.758183	+	0.652042i	$0.773913\pi$
$920$	6.54151	+	11.3302i	0.215667	+	0.373546i
$921$	2.46168	+	4.26376i	0.0811152	+	0.140496i
$922$	8.44035	−	14.6191i	0.277968	−	0.481455i
$923$	−18.6990	+	32.3876i	−0.615485	+	1.06605i
$924$	−24.0502			−0.791192
$925$	−9.42283			−0.309821
$926$	−4.12132	+	7.13833i	−0.135435	+	0.234580i
$927$	−1.76046	+	3.04920i	−0.0578210	+	0.100149i
$928$	−7.34897	−	12.7288i	−0.241242	−	0.417843i
$929$	10.6209	+	18.3960i	0.348461	+	0.603553i	0.985976	−	0.166885i	$-0.0533709\pi$
$929$	10.6209	+	18.3960i	0.348461	+	0.603553i	−0.637515	+	0.770438i	$0.720038\pi$
$930$	−7.54362			−0.247365
$931$	0.634957	+	1.09978i	0.0208099	+	0.0360438i
$932$	4.44731	+	7.70296i	0.145676	+	0.252319i
$933$	21.5249	+	37.2822i	0.704693	+	1.22056i
$934$	−1.83485	+	3.17806i	−0.0600382	+	0.103989i
$935$	−9.14235			−0.298987
$936$	−0.981504	+	1.70001i	−0.0320814	+	0.0555667i
$937$	−2.20223	−	3.81437i	−0.0719436	−	0.124610i	0.827809	−	0.561009i	$-0.189587\pi$
$937$	−2.20223	−	3.81437i	−0.0719436	−	0.124610i	−0.899753	+	0.436399i	$0.856253\pi$
$938$	−9.01257			−0.294271
$939$	5.27237	+	9.13200i	0.172057	+	0.298012i
$940$	−1.43472	+	2.48501i	−0.0467954	+	0.0810521i
$941$	−30.2702	+	52.4295i	−0.986780	+	1.70915i	−0.353034	+	0.935610i	$0.614850\pi$
$941$	−30.2702	+	52.4295i	−0.986780	+	1.70915i	−0.633745	+	0.773542i	$0.718483\pi$
$942$	9.97106			0.324875
$943$	−3.90296	+	6.76013i	−0.127098	+	0.220140i
$944$	3.06967			0.0999094
$945$	−20.8525			−0.678330
$946$	15.8135	+	31.9837i	0.514140	+	1.03988i
$947$	−49.6343			−1.61290			−0.806449	−	0.591304i	$-0.798613\pi$
$947$	−49.6343			−1.61290			−0.806449	+	0.591304i	$0.798613\pi$
$948$	17.1425			0.556762
$949$	−10.9841	+	19.0250i	−0.356559	+	0.617578i
$950$	2.30542			0.0747976
$951$	6.51107	−	11.2775i	0.211136	−	0.365698i
$952$	3.54934	−	6.14763i	0.115035	−	0.199246i
$953$	29.1397	+	50.4715i	0.943928	+	1.63493i	0.757884	+	0.652390i	$0.226233\pi$
$953$	29.1397	+	50.4715i	0.943928	+	1.63493i	0.186044	+	0.982541i	$0.440433\pi$
$954$	−0.0324725			−0.00105134
$955$	−13.6240	−	23.5974i	−0.440861	−	0.763593i
$956$	−11.5132	+	19.9415i	−0.372365	+	0.644955i
$957$	−26.4830			−0.856075
$958$	−13.5393	+	23.4508i	−0.437435	+	0.757660i
$959$	−8.19421	−	14.1928i	−0.264605	−	0.458309i
$960$	−8.81266	−	15.2640i	−0.284427	−	0.492643i
$961$	11.3523	+	19.6627i	0.366202	+	0.634280i
$962$	12.1550			0.391892
$963$	0.0888661	+	0.153921i	0.00286367	+	0.00496002i
$964$	9.09130	+	15.7466i	0.292811	+	0.507164i
$965$	0.959512	−	1.66192i	0.0308878	−	0.0534992i
$966$	−5.25967	+	9.11001i	−0.169227	+	0.293110i
$967$	36.5266			1.17462			0.587308	−	0.809363i	$-0.300188\pi$
$967$	36.5266			1.17462			0.587308	+	0.809363i	$0.300188\pi$
$968$	61.3998			1.97346
$969$	0.842657	−	1.45952i	0.0270700	−	0.0468867i
$970$	−6.31129	+	10.9315i	−0.202643	+	0.350988i
$971$	−12.6873	−	21.9750i	−0.407154	−	0.705211i	0.587416	−	0.809285i	$-0.300145\pi$
$971$	−12.6873	−	21.9750i	−0.407154	−	0.705211i	−0.994570	+	0.104074i	$0.966812\pi$
$972$	1.16068	+	2.01036i	0.0372288	+	0.0644822i
$973$	−49.2537			−1.57900
$974$	9.00387	+	15.5952i	0.288503	+	0.499701i
$975$	−6.24008	−	10.8081i	−0.199843	−	0.346138i
$976$	−0.447843	−	0.775687i	−0.0143351	−	0.0248292i
$977$	−21.8796	+	37.8966i	−0.699990	+	1.21242i	0.268479	+	0.963285i	$0.413479\pi$
$977$	−21.8796	+	37.8966i	−0.699990	+	1.21242i	−0.968469	+	0.249133i	$0.919854\pi$
$978$	−31.6010			−1.01049
$979$	−51.4681	+	89.1454i	−1.64493	+	2.84910i
$980$	−1.08976	−	1.88752i	−0.0348112	−	0.0602947i
$981$	−0.864075			−0.0275878
$982$	2.40140	+	4.15934i	0.0766317	+	0.132730i
$983$	16.9201	−	29.3064i	0.539667	−	0.934730i	−0.459255	−	0.888304i	$-0.651884\pi$
$983$	16.9201	−	29.3064i	0.539667	−	0.934730i	0.998922	−	0.0464257i	$-0.0147831\pi$
$984$	7.09913	−	12.2961i	0.226312	−	0.391984i
$985$	33.7694			1.07598
$986$	1.35956	−	2.35484i	0.0432974	−	0.0749932i
$987$	−6.63247			−0.211114
$988$	3.39975			0.108161
$989$	−17.8038	−	1.14856i	−0.566127	−	0.0365221i
$990$	1.85266			0.0588815
$991$	53.5945			1.70249			0.851243	−	0.524771i	$-0.175849\pi$
$991$	53.5945			1.70249			0.851243	+	0.524771i	$0.175849\pi$
$992$	7.51969	−	13.0245i	0.238751	−	0.413528i
$993$	−29.3504			−0.931407
$994$	−13.7029	+	23.7341i	−0.434629	+	0.752800i
$995$	17.9900	−	31.1597i	0.570322	−	0.987828i
$996$	−3.13787	−	5.43496i	−0.0994273	−	0.172213i
$997$	−35.2366			−1.11595			−0.557977	−	0.829857i	$-0.688422\pi$
$997$	−35.2366			−1.11595			−0.557977	+	0.829857i	$0.688422\pi$
$998$	18.3449	+	31.7744i	0.580699	+	1.00580i
$999$	10.6792	−	18.4970i	0.337876	−	0.585218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.307.11	✓	58
43.36	even	3	inner	731.2.e.a.681.11	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.11	✓	58	1.1	even	1	trivial
731.2.e.a.681.11	yes	58	43.36	even	3	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.966012 q^{2} +(-0.835198 + 1.44661i) q^{3} -1.06682 q^{4} +(-0.811572 + 1.40568i) q^{5} +(0.806812 - 1.39744i) q^{6} +(-1.19805 - 2.07509i) q^{7} +2.96259 q^{8} +(0.104888 + 0.181671i) q^{9} +O(q^{10})\)	\(q-0.966012 q^{2} +(-0.835198 + 1.44661i) q^{3} -1.06682 q^{4} +(-0.811572 + 1.40568i) q^{5} +(0.806812 - 1.39744i) q^{6} +(-1.19805 - 2.07509i) q^{7} +2.96259 q^{8} +(0.104888 + 0.181671i) q^{9} +(0.783988 - 1.35791i) q^{10} +5.63250 q^{11} +(0.891006 - 1.54327i) q^{12} +(1.57930 + 2.73543i) q^{13} +(1.15733 + 2.00456i) q^{14} +(-1.35565 - 2.34805i) q^{15} -0.728255 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.101323 - 0.175497i) q^{18} +(-0.504465 + 0.873759i) q^{19} +(0.865801 - 1.49961i) q^{20} +4.00245 q^{21} -5.44107 q^{22} +(1.36035 - 2.35619i) q^{23} +(-2.47435 + 4.28569i) q^{24} +(1.18270 + 2.04850i) q^{25} +(-1.52563 - 2.64246i) q^{26} -5.36160 q^{27} +(1.27811 + 2.21375i) q^{28} +(1.40740 + 2.43769i) q^{29} +(1.30957 + 2.26824i) q^{30} +(-1.44009 + 2.49432i) q^{31} -5.22167 q^{32} +(-4.70425 + 8.14801i) q^{33} +(-0.483006 - 0.836591i) q^{34} +3.88922 q^{35} +(-0.111897 - 0.193811i) q^{36} +(-1.99180 + 3.44990i) q^{37} +(0.487319 - 0.844062i) q^{38} -5.27612 q^{39} +(-2.40435 + 4.16446i) q^{40} -2.86909 q^{41} -3.86641 q^{42} +(-2.90632 - 5.87821i) q^{43} -6.00886 q^{44} -0.340496 q^{45} +(-1.31411 + 2.27611i) q^{46} -1.65710 q^{47} +(0.608237 - 1.05350i) q^{48} +(0.629337 - 1.09004i) q^{49} +(-1.14251 - 1.97888i) q^{50} -1.67040 q^{51} +(-1.68483 - 2.91821i) q^{52} +(0.0801212 - 0.138774i) q^{53} +5.17937 q^{54} +(-4.57118 + 7.91751i) q^{55} +(-3.54934 - 6.14763i) q^{56} +(-0.842657 - 1.45952i) q^{57} +(-1.35956 - 2.35484i) q^{58} -4.21511 q^{59} +(1.44623 + 2.50494i) q^{60} +(0.614954 + 1.06513i) q^{61} +(1.39115 - 2.40954i) q^{62} +(0.251323 - 0.435304i) q^{63} +6.50071 q^{64} -5.12687 q^{65} +(4.54437 - 7.87108i) q^{66} +(-1.94684 + 3.37202i) q^{67} +(-0.533410 - 0.923893i) q^{68} +(2.27232 + 3.93577i) q^{69} -3.75704 q^{70} +(5.92002 + 10.2538i) q^{71} +(0.310740 + 0.538217i) q^{72} +(3.47752 + 6.02323i) q^{73} +(1.92410 - 3.33264i) q^{74} -3.95117 q^{75} +(0.538173 - 0.932144i) q^{76} +(-6.74803 - 11.6879i) q^{77} +5.09680 q^{78} +(4.80987 + 8.33093i) q^{79} +(0.591031 - 1.02370i) q^{80} +(4.16333 - 7.21110i) q^{81} +2.77158 q^{82} +(1.76086 - 3.04990i) q^{83} -4.26989 q^{84} -1.62314 q^{85} +(2.80754 + 5.67842i) q^{86} -4.70183 q^{87} +16.6868 q^{88} +(-9.13771 + 15.8270i) q^{89} +0.328924 q^{90} +(3.78418 - 6.55438i) q^{91} +(-1.45125 + 2.51363i) q^{92} +(-2.40553 - 4.16650i) q^{93} +1.60078 q^{94} +(-0.818819 - 1.41824i) q^{95} +(4.36113 - 7.55370i) q^{96} -8.05023 q^{97} +(-0.607948 + 1.05300i) q^{98} +(0.590782 + 1.02326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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