LMFDB - Embedded newform 731.2.e.a.307.9

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			307.9
Character	$\chi$	$=$	731.307
Dual form			731.2.e.a.681.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.65452 q^{2} +(-0.422449 + 0.731703i) q^{3} +0.737422 q^{4} +(0.952877 - 1.65043i) q^{5} +(0.698949 - 1.21061i) q^{6} +(2.62410 + 4.54507i) q^{7} +2.08895 q^{8} +(1.14307 + 1.97986i) q^{9} +O(q^{10})$	\(q-1.65452 q^{2} +(-0.422449 + 0.731703i) q^{3} +0.737422 q^{4} +(0.952877 - 1.65043i) q^{5} +(0.698949 - 1.21061i) q^{6} +(2.62410 + 4.54507i) q^{7} +2.08895 q^{8} +(1.14307 + 1.97986i) q^{9} +(-1.57655 + 2.73067i) q^{10} +5.81812 q^{11} +(-0.311523 + 0.539574i) q^{12} +(-2.92272 - 5.06230i) q^{13} +(-4.34161 - 7.51989i) q^{14} +(0.805084 + 1.39445i) q^{15} -4.93105 q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.89123 - 3.27571i) q^{18} +(1.56761 - 2.71518i) q^{19} +(0.702673 - 1.21706i) q^{20} -4.43419 q^{21} -9.62617 q^{22} +(-2.16761 + 3.75442i) q^{23} +(-0.882477 + 1.52850i) q^{24} +(0.684050 + 1.18481i) q^{25} +(4.83569 + 8.37566i) q^{26} -4.46626 q^{27} +(1.93507 + 3.35163i) q^{28} +(-1.31320 - 2.27452i) q^{29} +(-1.33202 - 2.30713i) q^{30} +(3.13386 - 5.42801i) q^{31} +3.98059 q^{32} +(-2.45786 + 4.25714i) q^{33} +(-0.827258 - 1.43285i) q^{34} +10.0018 q^{35} +(0.842928 + 1.45999i) q^{36} +(-0.267266 + 0.462917i) q^{37} +(-2.59364 + 4.49231i) q^{38} +4.93880 q^{39} +(1.99052 - 3.44768i) q^{40} +3.24274 q^{41} +7.33644 q^{42} +(5.74674 - 3.15832i) q^{43} +4.29041 q^{44} +4.35683 q^{45} +(3.58635 - 6.21174i) q^{46} +1.95647 q^{47} +(2.08312 - 3.60807i) q^{48} +(-10.2718 + 17.7912i) q^{49} +(-1.13177 - 1.96029i) q^{50} -0.844898 q^{51} +(-2.15528 - 3.73305i) q^{52} +(0.175590 - 0.304130i) q^{53} +7.38949 q^{54} +(5.54395 - 9.60241i) q^{55} +(5.48162 + 9.49444i) q^{56} +(1.32447 + 2.29405i) q^{57} +(2.17270 + 3.76323i) q^{58} -0.189298 q^{59} +(0.593687 + 1.02830i) q^{60} +(4.52767 + 7.84215i) q^{61} +(-5.18502 + 8.98072i) q^{62} +(-5.99907 + 10.3907i) q^{63} +3.27615 q^{64} -11.1400 q^{65} +(4.06657 - 7.04350i) q^{66} +(-0.944186 + 1.63538i) q^{67} +(0.368711 + 0.638626i) q^{68} +(-1.83141 - 3.17210i) q^{69} -16.5481 q^{70} +(4.26051 + 7.37941i) q^{71} +(2.38783 + 4.13584i) q^{72} +(-6.92192 - 11.9891i) q^{73} +(0.442195 - 0.765904i) q^{74} -1.15591 q^{75} +(1.15599 - 2.00224i) q^{76} +(15.2673 + 26.4437i) q^{77} -8.17133 q^{78} +(-3.84853 - 6.66585i) q^{79} +(-4.69869 + 8.13837i) q^{80} +(-1.54245 + 2.67161i) q^{81} -5.36517 q^{82} +(-2.39376 + 4.14611i) q^{83} -3.26987 q^{84} +1.90575 q^{85} +(-9.50807 + 5.22548i) q^{86} +2.21903 q^{87} +12.1538 q^{88} +(1.35676 - 2.34997i) q^{89} -7.20845 q^{90} +(15.3390 - 26.5679i) q^{91} +(-1.59845 + 2.76859i) q^{92} +(2.64779 + 4.58611i) q^{93} -3.23701 q^{94} +(-2.98748 - 5.17447i) q^{95} +(-1.68160 + 2.91261i) q^{96} -13.2705 q^{97} +(16.9948 - 29.4359i) q^{98} +(6.65054 + 11.5191i) 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 $

$2$	−1.65452			−1.16992			−0.584960	−	0.811062i	$-0.698890\pi$
$2$	−1.65452			−1.16992			−0.584960	+	0.811062i	$0.698890\pi$
$3$	−0.422449	+	0.731703i	−0.243901	+	0.422449i	−0.961822	−	0.273675i	$-0.911761\pi$
$3$	−0.422449	+	0.731703i	−0.243901	+	0.422449i	0.717921	+	0.696125i	$0.245094\pi$
$4$	0.737422			0.368711
$5$	0.952877	−	1.65043i	0.426140	−	0.738096i	−0.570386	−	0.821376i	$-0.693207\pi$
$5$	0.952877	−	1.65043i	0.426140	−	0.738096i	0.996526	+	0.0832809i	$0.0265399\pi$
$6$	0.698949	−	1.21061i	0.285345	−	0.494231i
$7$	2.62410	+	4.54507i	0.991815	+	1.71787i	0.606482	+	0.795097i	$0.292580\pi$
$7$	2.62410	+	4.54507i	0.991815	+	1.71787i	0.385333	+	0.922778i	$0.374087\pi$
$8$	2.08895			0.738557
$9$	1.14307	+	1.97986i	0.381024	+	0.659954i
$10$	−1.57655	+	2.73067i	−0.498549	+	0.863512i
$11$	5.81812			1.75423			0.877114	−	0.480282i	$-0.159466\pi$
$11$	5.81812			1.75423			0.877114	+	0.480282i	$0.159466\pi$
$12$	−0.311523	+	0.539574i	−0.0899290	+	0.155762i
$13$	−2.92272	−	5.06230i	−0.810617	−	1.40403i	−0.912433	−	0.409227i	$-0.865799\pi$
$13$	−2.92272	−	5.06230i	−0.810617	−	1.40403i	0.101816	−	0.994803i	$-0.467535\pi$
$14$	−4.34161	−	7.51989i	−1.16034	−	2.00977i
$15$	0.805084	+	1.39445i	0.207872	+	0.360045i
$16$	−4.93105			−1.23276
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	−1.89123	−	3.27571i	−0.445768	−	0.772093i
$19$	1.56761	−	2.71518i	0.359635	−	0.622906i	−0.628265	−	0.778000i	$-0.716235\pi$
$19$	1.56761	−	2.71518i	0.359635	−	0.622906i	0.987900	+	0.155094i	$0.0495679\pi$
$20$	0.702673	−	1.21706i	0.157122	−	0.272144i
$21$	−4.43419			−0.967620
$22$	−9.62617			−2.05231
$23$	−2.16761	+	3.75442i	−0.451979	+	0.782850i	−0.998509	−	0.0545895i	$-0.982615\pi$
$23$	−2.16761	+	3.75442i	−0.451979	+	0.782850i	0.546530	+	0.837439i	$0.315948\pi$
$24$	−0.882477	+	1.52850i	−0.180135	+	0.312003i
$25$	0.684050	+	1.18481i	0.136810	+	0.236962i
$26$	4.83569	+	8.37566i	0.948357	+	1.64260i
$27$	−4.46626			−0.859531
$28$	1.93507	+	3.35163i	0.365693	+	0.633399i
$29$	−1.31320	−	2.27452i	−0.243854	−	0.422368i	0.717954	−	0.696090i	$-0.245079\pi$
$29$	−1.31320	−	2.27452i	−0.243854	−	0.422368i	−0.961809	+	0.273722i	$0.911745\pi$
$30$	−1.33202	−	2.30713i	−0.243193	−	0.421223i
$31$	3.13386	−	5.42801i	0.562858	−	0.974899i	−0.434387	−	0.900726i	$-0.643035\pi$
$31$	3.13386	−	5.42801i	0.562858	−	0.974899i	0.997245	−	0.0741725i	$-0.0236316\pi$
$32$	3.98059			0.703676
$33$	−2.45786	+	4.25714i	−0.427858	+	0.741072i
$34$	−0.827258	−	1.43285i	−0.141874	−	0.245732i
$35$	10.0018			1.69061
$36$	0.842928	+	1.45999i	0.140488	+	0.243332i
$37$	−0.267266	+	0.462917i	−0.0439382	+	0.0761032i	−0.887158	−	0.461466i	$-0.847324\pi$
$37$	−0.267266	+	0.462917i	−0.0439382	+	0.0761032i	0.843220	+	0.537569i	$0.180657\pi$
$38$	−2.59364	+	4.49231i	−0.420744	+	0.728750i
$39$	4.93880			0.790842
$40$	1.99052	−	3.44768i	0.314728	−	0.545126i
$41$	3.24274			0.506431			0.253216	−	0.967410i	$-0.418512\pi$
$41$	3.24274			0.506431			0.253216	+	0.967410i	$0.418512\pi$
$42$	7.33644			1.13204
$43$	5.74674	−	3.15832i	0.876370	−	0.481639i
$43$	5.74674	−	3.15832i	0.876370	−	0.481639i
$44$	4.29041			0.646803
$45$	4.35683			0.649479
$46$	3.58635	−	6.21174i	0.528778	−	0.915871i
$47$	1.95647			0.285381			0.142690	−	0.989767i	$-0.454425\pi$
$47$	1.95647			0.285381			0.142690	+	0.989767i	$0.454425\pi$
$48$	2.08312	−	3.60807i	0.300672	−	0.520780i
$49$	−10.2718	+	17.7912i	−1.46740	+	2.54160i
$50$	−1.13177	−	1.96029i	−0.160057	−	0.277226i
$51$	−0.844898			−0.118309
$52$	−2.15528	−	3.73305i	−0.298883	−	0.517681i
$53$	0.175590	−	0.304130i	0.0241191	−	0.0417755i	−0.853714	−	0.520742i	$-0.825655\pi$
$53$	0.175590	−	0.304130i	0.0241191	−	0.0417755i	0.877833	+	0.478967i	$0.158989\pi$
$54$	7.38949			1.00558
$55$	5.54395	−	9.60241i	0.747546	−	1.29479i
$56$	5.48162	+	9.49444i	0.732512	+	1.26875i
$57$	1.32447	+	2.29405i	0.175431	+	0.303855i
$58$	2.17270	+	3.76323i	0.285290	+	0.494137i
$59$	−0.189298			−0.0246445			−0.0123222	−	0.999924i	$-0.503922\pi$
$59$	−0.189298			−0.0246445			−0.0123222	+	0.999924i	$0.503922\pi$
$60$	0.593687	+	1.02830i	0.0766447	+	0.132752i
$61$	4.52767	+	7.84215i	0.579709	+	1.00408i	0.995512	+	0.0946304i	$0.0301669\pi$
$61$	4.52767	+	7.84215i	0.579709	+	1.00408i	−0.415804	+	0.909454i	$0.636500\pi$
$62$	−5.18502	+	8.98072i	−0.658498	+	1.14055i
$63$	−5.99907	+	10.3907i	−0.755812	+	1.30910i
$64$	3.27615			0.409519
$65$	−11.1400			−1.38174
$66$	4.06657	−	7.04350i	0.500560	−	0.866995i
$67$	−0.944186	+	1.63538i	−0.115351	+	0.199793i	−0.917920	−	0.396766i	$-0.870133\pi$
$67$	−0.944186	+	1.63538i	−0.115351	+	0.199793i	0.802569	+	0.596559i	$0.203466\pi$
$68$	0.368711	+	0.638626i	0.0447128	+	0.0774448i
$69$	−1.83141	−	3.17210i	−0.220476	−	0.381876i
$70$	−16.5481			−1.97787
$71$	4.26051	+	7.37941i	0.505629	+	0.875775i	0.999979	+	0.00651210i	$0.00207288\pi$
$71$	4.26051	+	7.37941i	0.505629	+	0.875775i	−0.494350	+	0.869263i	$0.664594\pi$
$72$	2.38783	+	4.13584i	0.281408	+	0.487414i
$73$	−6.92192	−	11.9891i	−0.810150	−	1.40322i	−0.912759	−	0.408499i	$-0.866052\pi$
$73$	−6.92192	−	11.9891i	−0.810150	−	1.40322i	0.102609	−	0.994722i	$-0.467281\pi$
$74$	0.442195	−	0.765904i	0.0514041	−	0.0890346i
$75$	−1.15591			−0.133472
$76$	1.15599	−	2.00224i	0.132601	−	0.229672i
$77$	15.2673	+	26.4437i	1.73987	+	3.01354i
$78$	−8.17133			−0.925221
$79$	−3.84853	−	6.66585i	−0.432994	−	0.749967i	0.564136	−	0.825682i	$-0.309209\pi$
$79$	−3.84853	−	6.66585i	−0.432994	−	0.749967i	−0.997129	+	0.0757150i	$0.975876\pi$
$80$	−4.69869	+	8.13837i	−0.525329	+	0.909897i
$81$	−1.54245	+	2.67161i	−0.171384	+	0.296845i
$82$	−5.36517			−0.592484
$83$	−2.39376	+	4.14611i	−0.262749	+	0.455095i	−0.966971	−	0.254885i	$-0.917963\pi$
$83$	−2.39376	+	4.14611i	−0.262749	+	0.455095i	0.704222	+	0.709980i	$0.251296\pi$
$84$	−3.26987			−0.356772
$85$	1.90575			0.206708
$86$	−9.50807	+	5.22548i	−1.02528	+	0.563478i
$87$	2.21903			0.237906
$88$	12.1538			1.29560
$89$	1.35676	−	2.34997i	0.143816	−	0.249096i	−0.785115	−	0.619350i	$-0.787396\pi$
$89$	1.35676	−	2.34997i	0.143816	−	0.249096i	0.928930	+	0.370254i	$0.120729\pi$
$90$	−7.20845			−0.759837
$91$	15.3390	−	26.5679i	1.60796	−	2.78508i
$92$	−1.59845	+	2.76859i	−0.166649	+	0.288645i
$93$	2.64779	+	4.58611i	0.274563	+	0.475558i
$94$	−3.23701			−0.333872
$95$	−2.98748	−	5.17447i	−0.306509	−	0.530890i
$96$	−1.68160	+	2.91261i	−0.171627	+	0.297267i
$97$	−13.2705			−1.34742			−0.673708	−	0.738998i	$-0.735299\pi$
$97$	−13.2705			−1.34742			−0.673708	+	0.738998i	$0.735299\pi$
$98$	16.9948	−	29.4359i	1.71673	−	2.97347i
$99$	6.65054	+	11.5191i	0.668404	+	1.15771i
$100$	0.504433	+	0.873704i	0.0504433	+	0.0873704i
$101$	5.34568	+	9.25898i	0.531915	+	0.921303i	0.999306	+	0.0372526i	$0.0118606\pi$
$101$	5.34568	+	9.25898i	0.531915	+	0.921303i	−0.467391	+	0.884051i	$0.654806\pi$
$102$	1.39790			0.138412
$103$	8.40336	+	14.5550i	0.828007	+	1.43415i	0.899599	+	0.436717i	$0.143859\pi$
$103$	8.40336	+	14.5550i	0.828007	+	1.43415i	−0.0715915	+	0.997434i	$0.522808\pi$
$104$	−6.10543	−	10.5749i	−0.598687	−	1.03696i
$105$	−4.22524	+	7.31833i	−0.412341	+	0.714196i
$106$	−0.290516	+	0.503188i	−0.0282174	+	0.0488740i
$107$	−8.08584			−0.781687			−0.390844	−	0.920457i	$-0.627817\pi$
$107$	−8.08584			−0.781687			−0.390844	+	0.920457i	$0.627817\pi$
$108$	−3.29352			−0.316919
$109$	4.63758	−	8.03253i	0.444200	−	0.769377i	−0.553796	−	0.832652i	$-0.686821\pi$
$109$	4.63758	−	8.03253i	0.444200	−	0.769377i	0.997996	+	0.0632756i	$0.0201547\pi$
$110$	−9.17256	+	15.8873i	−0.874569	+	1.51480i
$111$	−0.225812	−	0.391118i	−0.0214331	−	0.0371233i
$112$	−12.9396	−	22.4120i	−1.22267	−	2.11773i
$113$	−4.72384			−0.444382			−0.222191	−	0.975003i	$-0.571321\pi$
$113$	−4.72384			−0.444382			−0.222191	+	0.975003i	$0.571321\pi$
$114$	−2.19136	−	3.79555i	−0.205240	−	0.355486i
$115$	4.13094	+	7.15499i	0.385212	+	0.667207i
$116$	−0.968380	−	1.67728i	−0.0899118	−	0.155732i
$117$	6.68177	−	11.5732i	0.617730	−	1.06994i
$118$	0.313196			0.0288321
$119$	−2.62410	+	4.54507i	−0.240551	+	0.416646i
$120$	1.68178	+	2.91294i	0.153525	+	0.265914i
$121$	22.8505			2.07732
$122$	−7.49110	−	12.9750i	−0.678212	−	1.17470i
$123$	−1.36989	+	2.37273i	−0.123519	+	0.213941i
$124$	2.31098	−	4.00273i	0.207532	−	0.359456i
$125$	12.1360			1.08548
$126$	9.92556	−	17.1916i	0.884239	−	1.53155i
$127$	7.17014			0.636247			0.318123	−	0.948049i	$-0.396947\pi$
$127$	7.17014			0.636247			0.318123	+	0.948049i	$0.396947\pi$
$128$	−13.3816			−1.18278
$129$	−0.116756	+	5.53914i	−0.0102798	+	0.487694i
$130$	18.4313			1.61653
$131$	−2.05816			−0.179822			−0.0899111	−	0.995950i	$-0.528658\pi$
$131$	−2.05816			−0.179822			−0.0899111	+	0.995950i	$0.528658\pi$
$132$	−1.81248	+	3.13931i	−0.157756	+	0.273242i
$133$	16.4543			1.42677
$134$	1.56217	−	2.70576i	0.134951	−	0.233742i
$135$	−4.25579	+	7.37125i	−0.366280	+	0.634416i
$136$	1.04448	+	1.80909i	0.0895632	+	0.155128i
$137$	−22.2663			−1.90234			−0.951168	−	0.308675i	$-0.900114\pi$
$137$	−22.2663			−1.90234			−0.951168	+	0.308675i	$0.900114\pi$
$138$	3.03010	+	5.24829i	0.257939	+	0.446764i
$139$	4.09862	−	7.09901i	0.347640	−	0.602130i	−0.638190	−	0.769879i	$-0.720316\pi$
$139$	4.09862	−	7.09901i	0.347640	−	0.602130i	0.985830	+	0.167749i	$0.0536498\pi$
$140$	7.37553			0.623346
$141$	−0.826510	+	1.43156i	−0.0696047	+	0.120559i
$142$	−7.04907	−	12.2094i	−0.591545	−	1.02459i
$143$	−17.0047	−	29.4531i	−1.42201	−	2.46299i
$144$	−5.63656	−	9.76280i	−0.469713	−	0.813567i
$145$	−5.00526			−0.415664
$146$	11.4524	+	19.8362i	0.947810	+	1.64166i
$147$	−8.67860	−	15.0318i	−0.715799	−	1.23980i
$148$	−0.197088	+	0.341366i	−0.0162005	+	0.0280601i
$149$	−0.0840199	+	0.145527i	−0.00688318	+	0.0119220i	−0.869446	−	0.494027i	$-0.835524\pi$
$149$	−0.0840199	+	0.145527i	−0.00688318	+	0.0119220i	0.862563	+	0.505949i	$0.168858\pi$
$150$	1.91246			0.156152
$151$	−2.74388			−0.223293			−0.111647	−	0.993748i	$-0.535612\pi$
$151$	−2.74388			−0.223293			−0.111647	+	0.993748i	$0.535612\pi$
$152$	3.27467	−	5.67190i	0.265611	−	0.460052i
$153$	−1.14307	+	1.97986i	−0.0924120	+	0.160062i
$154$	−25.2600	−	43.7516i	−2.03551	−	3.52560i
$155$	−5.97237	−	10.3444i	−0.479712	−	0.830886i
$156$	3.64198			0.291592
$157$	−2.93011	−	5.07510i	−0.233848	−	0.405037i	0.725089	−	0.688655i	$-0.241799\pi$
$157$	−2.93011	−	5.07510i	−0.233848	−	0.405037i	−0.958937	+	0.283618i	$0.908465\pi$
$158$	6.36746	+	11.0288i	0.506568	+	0.877401i
$159$	0.148355	+	0.256959i	0.0117654	+	0.0203782i
$160$	3.79302	−	6.56970i	0.299864	−	0.519380i
$161$	−22.7521			−1.79312
$162$	2.55201	−	4.42022i	0.200505	−	0.347285i
$163$	−5.53310	−	9.58362i	−0.433386	−	0.750647i	0.563776	−	0.825928i	$-0.309348\pi$
$163$	−5.53310	−	9.58362i	−0.433386	−	0.750647i	−0.997162	+	0.0752807i	$0.976015\pi$
$164$	2.39127			0.186727
$165$	4.68408	+	8.11306i	0.364655	+	0.631601i
$166$	3.96051	−	6.85981i	0.307395	−	0.532424i
$167$	−9.15907	+	15.8640i	−0.708750	+	1.22759i	0.256571	+	0.966525i	$0.417407\pi$
$167$	−9.15907	+	15.8640i	−0.708750	+	1.22759i	−0.965321	+	0.261066i	$0.915926\pi$
$168$	−9.26282			−0.714642
$169$	−10.5846	+	18.3331i	−0.814200	+	1.41024i
$170$	−3.15310			−0.241832
$171$	7.16758			0.548119
$172$	4.23777	−	2.32901i	0.323127	−	0.177585i
$173$	20.7498			1.57758			0.788789	−	0.614665i	$-0.210709\pi$
$173$	20.7498			1.57758			0.788789	+	0.614665i	$0.210709\pi$
$174$	−3.67143			−0.278330
$175$	−3.59003	+	6.21811i	−0.271380	+	0.470045i
$176$	−28.6894			−2.16255
$177$	0.0799688	−	0.138510i	0.00601082	−	0.0104110i
$178$	−2.24477	+	3.88806i	−0.168253	+	0.291422i
$179$	2.33117	+	4.03770i	0.174240	+	0.301792i	0.939898	−	0.341456i	$-0.110920\pi$
$179$	2.33117	+	4.03770i	0.174240	+	0.301792i	−0.765658	+	0.643248i	$0.777587\pi$
$180$	3.21283			0.239470
$181$	−5.74188	−	9.94522i	−0.426790	−	0.739222i	0.569796	−	0.821786i	$-0.307022\pi$
$181$	−5.74188	−	9.94522i	−0.426790	−	0.739222i	−0.996586	+	0.0825642i	$0.973689\pi$
$182$	−25.3786	+	43.9571i	−1.88119	+	3.25832i
$183$	−7.65084			−0.565566
$184$	−4.52805	+	7.84281i	−0.333812	+	0.578179i
$185$	0.509342	+	0.882207i	0.0374476	+	0.0648612i
$186$	−4.38082	−	7.58780i	−0.321217	−	0.556364i
$187$	2.90906	+	5.03864i	0.212731	+	0.368462i
$188$	1.44275			0.105223
$189$	−11.7199	−	20.2994i	−0.852496	−	1.47657i
$190$	4.94284	+	8.56125i	0.358591	+	0.621098i
$191$	0.839179	−	1.45350i	0.0607208	−	0.105172i	−0.834067	−	0.551663i	$-0.813993\pi$
$191$	0.839179	−	1.45350i	0.0607208	−	0.105172i	0.894788	+	0.446492i	$0.147327\pi$
$192$	−1.38401	+	2.39717i	−0.0998821	+	0.173001i
$193$	1.02661			0.0738971			0.0369486	−	0.999317i	$-0.488236\pi$
$193$	1.02661			0.0738971			0.0369486	+	0.999317i	$0.488236\pi$
$194$	21.9563			1.57637
$195$	4.70607	−	8.15116i	0.337009	−	0.583717i
$196$	−7.57463	+	13.1196i	−0.541045	+	0.937117i
$197$	9.74662	+	16.8816i	0.694418	+	1.20277i	0.970376	+	0.241598i	$0.0776715\pi$
$197$	9.74662	+	16.8816i	0.694418	+	1.20277i	−0.275958	+	0.961170i	$0.588995\pi$
$198$	−11.0034	−	19.0585i	−0.781979	−	1.35443i
$199$	14.7304			1.04421			0.522104	−	0.852882i	$-0.325147\pi$
$199$	14.7304			1.04421			0.522104	+	0.852882i	$0.325147\pi$
$200$	1.42895	+	2.47501i	0.101042	+	0.175010i
$201$	−0.797741	−	1.38173i	−0.0562683	−	0.0974596i
$202$	−8.84451	−	15.3191i	−0.622297	−	1.07785i
$203$	6.89191	−	11.9371i	0.483717	−	0.837823i
$204$	−0.623047			−0.0436220
$205$	3.08994	−	5.35193i	0.215810	−	0.373795i
$206$	−13.9035	−	24.0815i	−0.968702	−	1.67784i
$207$	−9.91096			−0.688860
$208$	14.4121	+	24.9625i	0.999299	+	1.73084i
$209$	9.12055	−	15.7973i	0.630882	−	1.09272i
$210$	6.99072	−	12.1083i	0.482406	−	0.835551i
$211$	−23.0570			−1.58731			−0.793654	−	0.608370i	$-0.791824\pi$
$211$	−23.0570			−1.58731			−0.793654	+	0.608370i	$0.791824\pi$
$212$	0.129484	−	0.224272i	0.00889298	−	0.0154031i
$213$	−7.19939			−0.493294
$214$	13.3781			0.914511
$215$	0.263354	−	12.4941i	0.0179606	−	0.852090i
$216$	−9.32981			−0.634813
$217$	32.8942			2.23300
$218$	−7.67295	+	13.2899i	−0.519678	+	0.900108i
$219$	11.6966			0.790386
$220$	4.08823	−	7.08103i	0.275629	−	0.477403i
$221$	2.92272	−	5.06230i	0.196604	−	0.340527i
$222$	0.373610	+	0.647111i	0.0250750	+	0.0434313i
$223$	−0.0533378			−0.00357176			−0.00178588	−	0.999998i	$-0.500568\pi$
$223$	−0.0533378			−0.00357176			−0.00178588	+	0.999998i	$0.500568\pi$
$224$	10.4455	+	18.0921i	0.697917	+	1.20883i
$225$	−1.56384	+	2.70865i	−0.104256	+	0.180577i
$226$	7.81567			0.519891
$227$	−7.36994	+	12.7651i	−0.489160	+	0.847250i	−0.999922	−	0.0124720i	$-0.996030\pi$
$227$	−7.36994	+	12.7651i	−0.489160	+	0.847250i	0.510762	+	0.859722i	$0.329363\pi$
$228$	0.976696	+	1.69169i	0.0646832	+	0.112035i
$229$	1.21118	+	2.09782i	0.0800370	+	0.138628i	0.903266	−	0.429082i	$-0.141163\pi$
$229$	1.21118	+	2.09782i	0.0800370	+	0.138628i	−0.823229	+	0.567710i	$0.807829\pi$
$230$	−6.83470	−	11.8381i	−0.450667	−	0.780578i
$231$	−25.7986			−1.69743
$232$	−2.74321	−	4.75138i	−0.180100	−	0.311943i
$233$	8.62642	+	14.9414i	0.565135	+	0.978843i	0.997037	+	0.0769226i	$0.0245094\pi$
$233$	8.62642	+	14.9414i	0.565135	+	0.978843i	−0.431902	+	0.901921i	$0.642157\pi$
$234$	−11.0551	+	19.1480i	−0.722694	+	1.25174i
$235$	1.86428	−	3.22902i	0.121612	−	0.210638i
$236$	−0.139593			−0.00908670
$237$	6.50324			0.422431
$238$	4.34161	−	7.51989i	0.281425	−	0.487442i
$239$	−0.102695	+	0.177873i	−0.00664278	+	0.0115056i	−0.869328	−	0.494236i	$-0.835448\pi$
$239$	−0.102695	+	0.177873i	−0.00664278	+	0.0115056i	0.862685	+	0.505742i	$0.168781\pi$
$240$	−3.96991	−	6.87609i	−0.256257	−	0.443850i
$241$	−7.23459	−	12.5307i	−0.466021	−	0.807172i	0.533226	−	0.845973i	$-0.320979\pi$
$241$	−7.23459	−	12.5307i	−0.466021	−	0.807172i	−0.999247	+	0.0388011i	$0.987646\pi$
$242$	−37.8065			−2.43029
$243$	−8.00260	−	13.8609i	−0.513367	−	0.889178i
$244$	3.33880	+	5.78298i	0.213745	+	0.370217i
$245$	19.5755	+	33.9057i	1.25063	+	2.16616i
$246$	2.26651	−	3.92571i	0.144507	−	0.250294i
$247$	−18.3268			−1.16610
$248$	6.54649	−	11.3389i	0.415703	−	0.720018i
$249$	−2.02248	−	3.50304i	−0.128170	−	0.221996i
$250$	−20.0793			−1.26992
$251$	−13.2266	−	22.9091i	−0.834855	−	1.44601i	−0.894148	−	0.447771i	$-0.852218\pi$
$251$	−13.2266	−	22.9091i	−0.834855	−	1.44601i	0.0592934	−	0.998241i	$-0.481115\pi$
$252$	−4.42385	+	7.66233i	−0.278676	+	0.482681i
$253$	−12.6114	+	21.8436i	−0.792874	+	1.37330i
$254$	−11.8631			−0.744357
$255$	−0.805084	+	1.39445i	−0.0504163	+	0.0873237i
$256$	15.5878			0.974239
$257$	17.2369			1.07521			0.537604	−	0.843197i	$-0.319329\pi$
$257$	17.2369			1.07521			0.537604	+	0.843197i	$0.319329\pi$
$258$	0.193174	−	9.16459i	0.0120265	−	0.570563i
$259$	−2.80532			−0.174314
$260$	−8.21487			−0.509464
$261$	3.00216	−	5.19989i	0.185829	−	0.321865i
$262$	3.40526			0.210378
$263$	4.84903	−	8.39877i	0.299004	−	0.517890i	−0.676904	−	0.736071i	$-0.736679\pi$
$263$	4.84903	−	8.39877i	0.299004	−	0.517890i	0.975908	+	0.218181i	$0.0700122\pi$
$264$	−5.13436	+	8.89297i	−0.315998	+	0.547324i
$265$	−0.334631	−	0.579598i	−0.0205562	−	0.0356044i
$266$	−27.2238			−1.66920
$267$	1.14632	+	1.98548i	0.0701536	+	0.121510i
$268$	−0.696264	+	1.20596i	−0.0425311	+	0.0736660i
$269$	−10.3908			−0.633536			−0.316768	−	0.948503i	$-0.602598\pi$
$269$	−10.3908			−0.633536			−0.316768	+	0.948503i	$0.602598\pi$
$270$	7.04128	−	12.1959i	0.428519	−	0.742216i
$271$	−9.35674	−	16.2064i	−0.568382	−	0.984466i	−0.996726	−	0.0808504i	$-0.974236\pi$
$271$	−9.35674	−	16.2064i	−0.568382	−	0.984466i	0.428345	−	0.903615i	$-0.359097\pi$
$272$	−2.46553	−	4.27042i	−0.149494	−	0.258932i
$273$	12.9599	+	22.4472i	0.784369	+	1.35857i
$274$	36.8399			2.22558
$275$	3.97988	+	6.89336i	0.239996	+	0.415685i
$276$	−1.35052	−	2.33918i	−0.0812920	−	0.140802i
$277$	−9.60160	+	16.6305i	−0.576904	+	0.999228i	0.418927	+	0.908020i	$0.362406\pi$
$277$	−9.60160	+	16.6305i	−0.576904	+	0.999228i	−0.995832	+	0.0912080i	$0.970927\pi$
$278$	−6.78122	+	11.7454i	−0.406711	+	0.704444i
$279$	14.3289			0.857851
$280$	20.8932			1.24861
$281$	1.84118	−	3.18901i	0.109835	−	0.190240i	−0.805868	−	0.592095i	$-0.798301\pi$
$281$	1.84118	−	3.18901i	0.109835	−	0.190240i	0.915703	+	0.401855i	$0.131634\pi$
$282$	1.36747	−	2.36853i	0.0814319	−	0.141044i
$283$	−9.45384	−	16.3745i	−0.561973	−	0.973365i	−0.997324	−	0.0731046i	$-0.976709\pi$
$283$	−9.45384	−	16.3745i	−0.561973	−	0.973365i	0.435352	−	0.900260i	$-0.356624\pi$
$284$	3.14179	+	5.44174i	0.186431	+	0.322908i
$285$	5.04824			0.299032
$286$	28.1346	+	48.7306i	1.66363	+	2.88150i
$287$	8.50927	+	14.7385i	0.502286	+	0.869986i
$288$	4.55011	+	7.88102i	0.268118	+	0.464394i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	8.28128			0.486294
$291$	5.60612	−	9.71008i	0.328636	−	0.569215i
$292$	−5.10438	−	8.84105i	−0.298711	−	0.517383i
$293$	−3.31501			−0.193665			−0.0968324	−	0.995301i	$-0.530871\pi$
$293$	−3.31501			−0.193665			−0.0968324	+	0.995301i	$0.530871\pi$
$294$	14.3589	+	24.8703i	0.837427	+	1.45047i
$295$	−0.180378	+	0.312423i	−0.0105020	+	0.0181900i
$296$	−0.558306	+	0.967014i	−0.0324509	+	0.0562065i
$297$	−25.9852			−1.50781
$298$	0.139012	−	0.240776i	0.00805276	−	0.0139478i
$299$	25.3413			1.46553
$300$	−0.852390			−0.0492128
$301$	29.4348	+	17.8316i	1.69659	+	1.02780i
$302$	4.53978			0.261235
$303$	−9.03311			−0.518938
$304$	−7.72998	+	13.3887i	−0.443345	+	0.767896i
$305$	17.2573			0.988147
$306$	1.89123	−	3.27571i	0.108115	−	0.187260i
$307$	1.28281	−	2.22189i	0.0732138	−	0.126810i	−0.827094	−	0.562063i	$-0.810008\pi$
$307$	1.28281	−	2.22189i	0.0732138	−	0.126810i	0.900308	+	0.435253i	$0.143341\pi$
$308$	11.2584	+	19.5002i	0.641510	+	1.11113i
$309$	−14.2000			−0.807808
$310$	9.88138	+	17.1150i	0.561225	+	0.972070i
$311$	14.5361	−	25.1772i	0.824266	−	1.42767i	−0.0782137	−	0.996937i	$-0.524922\pi$
$311$	14.5361	−	25.1772i	0.824266	−	1.42767i	0.902479	−	0.430733i	$-0.141745\pi$
$312$	10.3169			0.584082
$313$	9.34096	−	16.1790i	0.527982	−	0.914492i	−0.471486	−	0.881874i	$-0.656282\pi$
$313$	9.34096	−	16.1790i	0.527982	−	0.914492i	0.999468	−	0.0326183i	$-0.0103846\pi$
$314$	4.84792	+	8.39684i	0.273584	+	0.473861i
$315$	11.4328	+	19.8021i	0.644163	+	1.11572i
$316$	−2.83799	−	4.91555i	−0.159650	−	0.276521i
$317$	6.70481			0.376579			0.188290	−	0.982114i	$-0.439706\pi$
$317$	6.70481			0.376579			0.188290	+	0.982114i	$0.439706\pi$
$318$	−0.245456	−	0.425143i	−0.0137645	−	0.0238408i
$319$	−7.64033	−	13.2334i	−0.427776	−	0.740931i
$320$	3.12177	−	5.40706i	0.174512	−	0.302264i
$321$	3.41585	−	5.91643i	0.190654	−	0.330223i
$322$	37.6437			2.09780
$323$	3.13522			0.174449
$324$	−1.13744	+	1.97010i	−0.0631911	+	0.109450i
$325$	3.99857	−	6.92573i	0.221801	−	0.384171i
$326$	9.15461	+	15.8562i	0.507027	+	0.878196i
$327$	3.91828	+	6.78667i	0.216682	+	0.375304i
$328$	6.77394			0.374028
$329$	5.13397	+	8.89230i	0.283045	+	0.490248i
$330$	−7.74988	−	13.4232i	−0.426617	−	0.738922i
$331$	−9.88908	−	17.1284i	−0.543553	−	0.941461i	−0.998696	−	0.0510430i	$-0.983745\pi$
$331$	−9.88908	−	17.1284i	−0.543553	−	0.941461i	0.455144	−	0.890418i	$-0.349588\pi$
$332$	−1.76521	+	3.05743i	−0.0968785	+	0.167799i
$333$	−1.22202			−0.0669661
$334$	15.1538	−	26.2472i	0.829180	−	1.43618i
$335$	1.79939	+	3.11663i	0.0983110	+	0.170280i
$336$	21.8652			1.19285
$337$	−5.90572	−	10.2290i	−0.321705	−	0.557209i	0.659135	−	0.752025i	$-0.270923\pi$
$337$	−5.90572	−	10.2290i	−0.321705	−	0.557209i	−0.980840	+	0.194815i	$0.937589\pi$
$338$	17.5124	−	30.3323i	0.952548	−	1.64986i
$339$	1.99558	−	3.45645i	0.108385	−	0.187729i
$340$	1.40535			0.0762156
$341$	18.2332	−	31.5808i	0.987381	−	1.71019i
$342$	−11.8589			−0.641255
$343$	−71.0791			−3.83791
$344$	12.0047	−	6.59758i	0.647249	−	0.355718i
$345$	−6.98045			−0.375815
$346$	−34.3309			−1.84564
$347$	−16.9084	+	29.2862i	−0.907691	+	1.57217i	−0.0904269	+	0.995903i	$0.528823\pi$
$347$	−16.9084	+	29.2862i	−0.907691	+	1.57217i	−0.817264	+	0.576264i	$0.804510\pi$
$348$	1.63637			0.0877184
$349$	−9.65322	+	16.7199i	−0.516725	+	0.894994i	0.483086	+	0.875573i	$0.339516\pi$
$349$	−9.65322	+	16.7199i	−0.516725	+	0.894994i	−0.999811	+	0.0194212i	$0.993818\pi$
$350$	5.93975	−	10.2880i	0.317493	−	0.549914i
$351$	13.0536	+	22.6095i	0.696751	+	1.20681i
$352$	23.1596			1.23441
$353$	−1.02607	−	1.77721i	−0.0546125	−	0.0945916i	0.837427	−	0.546550i	$-0.184059\pi$
$353$	−1.02607	−	1.77721i	−0.0546125	−	0.0945916i	−0.892039	+	0.451958i	$0.850726\pi$
$354$	−0.132310	+	0.229167i	−0.00703218	+	0.0121801i
$355$	16.2390			0.861874
$356$	1.00050	−	1.73292i	0.0530265	−	0.0918445i
$357$	−2.21709	−	3.84012i	−0.117341	−	0.203241i
$358$	−3.85695	−	6.68044i	−0.203846	−	0.353072i
$359$	10.8615	+	18.8127i	0.573248	+	0.992894i	0.996230	+	0.0867559i	$0.0276500\pi$
$359$	10.8615	+	18.8127i	0.573248	+	0.992894i	−0.422982	+	0.906138i	$0.639017\pi$
$360$	9.10123			0.479677
$361$	4.58518	+	7.94177i	0.241325	+	0.417988i
$362$	9.50002	+	16.4545i	0.499310	+	0.864830i
$363$	−9.65317	+	16.7198i	−0.506660	+	0.877561i
$364$	11.3113	−	19.5918i	0.592874	−	1.02689i
$365$	−26.3830			−1.38095
$366$	12.6584			0.661667
$367$	−2.02142	+	3.50121i	−0.105517	+	0.182762i	−0.913949	−	0.405828i	$-0.866983\pi$
$367$	−2.02142	+	3.50121i	−0.105517	+	0.182762i	0.808432	+	0.588590i	$0.200317\pi$
$368$	10.6886	−	18.5132i	0.557183	−	0.965068i
$369$	3.70669	+	6.42018i	0.192963	+	0.334221i
$370$	−0.842715	−	1.45963i	−0.0438107	−	0.0758823i
$371$	1.84306			0.0956868
$372$	1.95254	+	3.38190i	0.101235	+	0.175343i
$373$	2.50829	+	4.34448i	0.129874	+	0.224949i	0.923628	−	0.383291i	$-0.125209\pi$
$373$	2.50829	+	4.34448i	0.129874	+	0.224949i	−0.793753	+	0.608240i	$0.791876\pi$
$374$	−4.81308	−	8.33650i	−0.248879	−	0.431070i
$375$	−5.12686	+	8.87998i	−0.264750	+	0.458560i
$376$	4.08698			0.210770
$377$	−7.67622	+	13.2956i	−0.395345	+	0.684758i
$378$	19.3907	+	33.5857i	0.997352	+	1.72746i
$379$	−17.2726			−0.887234			−0.443617	−	0.896217i	$-0.646305\pi$
$379$	−17.2726			−0.887234			−0.443617	+	0.896217i	$0.646305\pi$
$380$	−2.20304	−	3.81577i	−0.113013	−	0.195745i
$381$	−3.02902	+	5.24641i	−0.155181	+	0.268782i
$382$	−1.38843	+	2.40484i	−0.0710385	+	0.123042i
$383$	−7.71229			−0.394080			−0.197040	−	0.980395i	$-0.563133\pi$
$383$	−7.71229			−0.394080			−0.197040	+	0.980395i	$0.563133\pi$
$384$	5.65306	−	9.79138i	0.288481	−	0.499664i
$385$	58.1915			2.96571
$386$	−1.69855			−0.0864537
$387$	12.8220	+	7.76756i	0.651778	+	0.394847i
$388$	−9.78597			−0.496807
$389$	−14.4313			−0.731698			−0.365849	−	0.930674i	$-0.619221\pi$
$389$	−14.4313			−0.731698			−0.365849	+	0.930674i	$0.619221\pi$
$390$	−7.78627	+	13.4862i	−0.394273	+	0.682901i
$391$	−4.33523			−0.219242
$392$	−21.4573	+	37.1651i	−1.08376	+	1.87712i
$393$	0.869468	−	1.50596i	0.0438589	−	0.0759658i
$394$	−16.1259	−	27.9310i	−0.812413	−	1.40714i
$395$	−14.6687			−0.738063
$396$	4.90425	+	8.49441i	0.246448	+	0.426860i
$397$	12.6086	−	21.8388i	0.632809	−	1.09606i	−0.354166	−	0.935183i	$-0.615235\pi$
$397$	12.6086	−	21.8388i	0.632809	−	1.09606i	0.986975	−	0.160875i	$-0.0514315\pi$
$398$	−24.3716			−1.22164
$399$	−6.95109	+	12.0396i	−0.347990	+	0.602736i
$400$	−3.37309	−	5.84236i	−0.168654	−	0.292118i
$401$	−13.8287	−	23.9521i	−0.690574	−	1.19611i	−0.971650	−	0.236424i	$-0.924025\pi$
$401$	−13.8287	−	23.9521i	−0.690574	−	1.19611i	0.281076	−	0.959685i	$-0.409309\pi$
$402$	1.31988	+	2.28609i	0.0658294	+	0.114020i
$403$	−36.6376			−1.82505
$404$	3.94202	+	6.82778i	0.196123	+	0.339695i
$405$	2.93954	+	5.09143i	0.146067	+	0.252995i
$406$	−11.4028	+	19.7502i	−0.565910	+	0.980185i
$407$	−1.55498	+	2.69331i	−0.0770776	+	0.133502i
$408$	−1.76495			−0.0873783
$409$	12.9351			0.639598			0.319799	−	0.947485i	$-0.396385\pi$
$409$	12.9351			0.639598			0.319799	+	0.947485i	$0.396385\pi$
$410$	−5.11235	+	8.85485i	−0.252481	+	0.437310i
$411$	9.40636	−	16.2923i	0.463982	−	0.803640i
$412$	6.19682	+	10.7332i	0.305296	+	0.528787i
$413$	−0.496736	−	0.860372i	−0.0244428	−	0.0423362i
$414$	16.3978			0.805910
$415$	4.56192	+	7.90147i	0.223936	+	0.387868i
$416$	−11.6342	−	20.1510i	−0.570412	−	0.987983i
$417$	3.46291	+	5.99794i	0.169580	+	0.293721i
$418$	−15.0901	+	26.1368i	−0.738081	+	1.27839i
$419$	11.1168			0.543090			0.271545	−	0.962426i	$-0.412465\pi$
$419$	11.1168			0.543090			0.271545	+	0.962426i	$0.412465\pi$
$420$	−3.11578	+	5.39670i	−0.152035	+	0.263332i
$421$	−17.5508	−	30.3989i	−0.855373	−	1.48155i	−0.876298	−	0.481769i	$-0.839994\pi$
$421$	−17.5508	−	30.3989i	−0.855373	−	1.48155i	0.0209247	−	0.999781i	$-0.493339\pi$
$422$	38.1481			1.85702
$423$	2.23639	+	3.87354i	0.108737	+	0.188338i
$424$	0.366799	−	0.635315i	0.0178133	−	0.0308536i
$425$	−0.684050	+	1.18481i	−0.0331813	+	0.0574717i
$426$	11.9115			0.577114
$427$	−23.7621	+	41.1571i	−1.14993	+	1.99173i
$428$	−5.96267			−0.288217
$429$	28.7345			1.38732
$430$	−0.435724	+	20.6717i	−0.0210125	+	0.996877i
$431$	−3.31824			−0.159834			−0.0799171	−	0.996802i	$-0.525466\pi$
$431$	−3.31824			−0.159834			−0.0799171	+	0.996802i	$0.525466\pi$
$432$	22.0233			1.05960
$433$	−12.7897	+	22.1524i	−0.614634	+	1.06458i	0.375814	+	0.926695i	$0.377363\pi$
$433$	−12.7897	+	22.1524i	−0.614634	+	1.06458i	−0.990449	+	0.137883i	$0.955970\pi$
$434$	−54.4240			−2.61244
$435$	2.11447	−	3.66237i	0.101381	−	0.175597i
$436$	3.41986	−	5.92336i	0.163781	−	0.283678i
$437$	6.79595	+	11.7709i	0.325095	+	0.563080i
$438$	−19.3523			−0.924688
$439$	9.95279	+	17.2387i	0.475021	+	0.822760i	0.999591	−	0.0286071i	$-0.00910716\pi$
$439$	9.95279	+	17.2387i	0.475021	+	0.822760i	−0.524570	+	0.851367i	$0.675774\pi$
$440$	11.5811	−	20.0590i	0.552106	−	0.956275i
$441$	−46.9655			−2.23645
$442$	−4.83569	+	8.37566i	−0.230010	+	0.398389i
$443$	9.79515	+	16.9657i	0.465382	+	0.806065i	0.999219	−	0.0395228i	$-0.0125838\pi$
$443$	9.79515	+	16.9657i	0.465382	+	0.806065i	−0.533837	+	0.845587i	$0.679250\pi$
$444$	−0.166519	−	0.288419i	−0.00790264	−	0.0136878i
$445$	−2.58564	−	4.47846i	−0.122571	−	0.212300i
$446$	0.0882483			0.00417868
$447$	−0.0709883	−	0.122955i	−0.00335763	−	0.00581559i
$448$	8.59693	+	14.8903i	0.406167	+	0.703502i
$449$	−10.4108	+	18.0319i	−0.491314	+	0.850980i	−0.999950	−	0.0100012i	$-0.996816\pi$
$449$	−10.4108	+	18.0319i	−0.491314	+	0.850980i	0.508636	+	0.860982i	$0.330150\pi$
$450$	2.58740	−	4.48150i	0.121971	−	0.211260i
$451$	18.8667			0.888396
$452$	−3.48347			−0.163849
$453$	1.15915	−	2.00770i	0.0544615	−	0.0943301i
$454$	12.1937	−	21.1201i	0.572278	−	0.991214i
$455$	−29.2324	−	50.6320i	−1.37044	−	2.37366i
$456$	2.76676	+	4.79218i	0.129566	+	0.224414i
$457$	−27.5750			−1.28990			−0.644951	−	0.764224i	$-0.723122\pi$
$457$	−27.5750			−1.28990			−0.644951	+	0.764224i	$0.723122\pi$
$458$	−2.00391	−	3.47088i	−0.0936368	−	0.162184i
$459$	−2.23313	−	3.86789i	−0.104233	−	0.180538i
$460$	3.04625	+	5.27625i	0.142032	+	0.246006i
$461$	19.9190	−	34.5007i	0.927720	−	1.60686i	0.140592	−	0.990068i	$-0.455099\pi$
$461$	19.9190	−	34.5007i	0.927720	−	1.60686i	0.787128	−	0.616790i	$-0.211567\pi$
$462$	42.6842			1.98585
$463$	−6.23597	+	10.8010i	−0.289810	+	0.501966i	−0.973764	−	0.227559i	$-0.926926\pi$
$463$	−6.23597	+	10.8010i	−0.289810	+	0.501966i	0.683954	+	0.729525i	$0.260259\pi$
$464$	6.47544	+	11.2158i	0.300615	+	0.520680i
$465$	10.0921			0.468009
$466$	−14.2725	−	24.7208i	−0.661163	−	1.14517i
$467$	9.35949	−	16.2111i	0.433106	−	0.750161i	−0.564033	−	0.825752i	$-0.690751\pi$
$467$	9.35949	−	16.2111i	0.433106	−	0.750161i	0.997139	+	0.0755912i	$0.0240844\pi$
$468$	4.92729	−	8.53431i	0.227764	−	0.394499i
$469$	−9.91055			−0.457626
$470$	−3.08448	+	5.34247i	−0.142276	+	0.246430i
$471$	4.95129			0.228144
$472$	−0.395435			−0.0182014
$473$	33.4352	−	18.3755i	1.53735	−	0.844904i
$474$	−10.7597			−0.494210
$475$	4.28930			0.196807
$476$	−1.93507	+	3.35163i	−0.0886936	+	0.153622i
$477$	0.802848			0.0367599
$478$	0.169910	−	0.294293i	0.00777152	−	0.0134607i
$479$	18.5289	−	32.0930i	0.846607	−	1.46637i	−0.0376105	−	0.999292i	$-0.511975\pi$
$479$	18.5289	−	32.0930i	0.846607	−	1.46637i	0.884218	−	0.467075i	$-0.154692\pi$
$480$	3.20471	+	5.55073i	0.146275	+	0.253355i
$481$	3.12457			0.142468
$482$	11.9697	+	20.7322i	0.545207	+	0.944326i
$483$	9.61161	−	16.6478i	0.437343	−	0.757501i
$484$	16.8505			0.765930
$485$	−12.6452	+	21.9021i	−0.574187	+	0.994522i
$486$	13.2404	+	22.9331i	0.600598	+	1.04027i
$487$	−12.1520	−	21.0478i	−0.550657	−	0.953767i	−0.998227	−	0.0595177i	$-0.981044\pi$
$487$	−12.1520	−	21.0478i	−0.550657	−	0.953767i	0.447570	−	0.894249i	$-0.352290\pi$
$488$	9.45810	+	16.3819i	0.428148	+	0.741574i
$489$	9.34982			0.422814
$490$	−32.3879	−	56.0975i	−1.46314	−	2.53423i
$491$	−1.34606	−	2.33144i	−0.0607468	−	0.105217i	0.834053	−	0.551685i	$-0.186015\pi$
$491$	−1.34606	−	2.33144i	−0.0607468	−	0.105217i	−0.894799	+	0.446468i	$0.852682\pi$
$492$	−1.01019	+	1.74970i	−0.0455429	+	0.0788826i
$493$	1.31320	−	2.27452i	0.0591434	−	0.102439i
$494$	30.3219			1.36425
$495$	25.3486			1.13933
$496$	−15.4532	+	26.7658i	−0.693871	+	1.20182i
$497$	−22.3600	+	38.7286i	−1.00298	+	1.73721i
$498$	3.34623	+	5.79584i	0.149948	+	0.259718i
$499$	0.0477932	+	0.0827802i	0.00213952	+	0.00370575i	0.867093	−	0.498146i	$-0.165986\pi$
$499$	0.0477932	+	0.0827802i	0.00213952	+	0.00370575i	−0.864954	+	0.501852i	$0.832652\pi$
$500$	8.94938			0.400228
$501$	−7.73848	−	13.4034i	−0.345730	−	0.598822i
$502$	21.8836	+	37.9035i	0.976713	+	1.69172i
$503$	5.21658	+	9.03538i	0.232596	+	0.402868i	0.958571	−	0.284853i	$-0.0919448\pi$
$503$	5.21658	+	9.03538i	0.232596	+	0.402868i	−0.725976	+	0.687721i	$0.758611\pi$
$504$	−12.5318	+	21.7057i	−0.558210	+	0.966848i
$505$	20.3751			0.906680
$506$	20.8658	−	36.1406i	0.927598	−	1.60665i
$507$	−8.94291	−	15.4896i	−0.397169	−	0.687916i
$508$	5.28742			0.234591
$509$	−6.81444	−	11.8029i	−0.302045	−	0.523157i	0.674554	−	0.738225i	$-0.264336\pi$
$509$	−6.81444	−	11.8029i	−0.302045	−	0.523157i	−0.976599	+	0.215069i	$0.931002\pi$
$510$	1.33202	−	2.30713i	0.0589830	−	0.102162i
$511$	36.3276	−	62.9212i	1.60704	−	2.78347i
$512$	0.972972			0.0429997
$513$	−7.00136	+	12.1267i	−0.309118	+	0.535407i
$514$	−28.5187			−1.25791
$515$	32.0295			1.41139
$516$	−0.0860982	+	4.08468i	−0.00379026	+	0.179818i
$517$	11.3830			0.500623
$518$	4.64145			0.203934
$519$	−8.76573	+	15.1827i	−0.384773	+	0.666446i
$520$	−23.2709			−1.02050
$521$	−15.3439	+	26.5765i	−0.672230	+	1.16434i	0.305041	+	0.952339i	$0.401330\pi$
$521$	−15.3439	+	26.5765i	−0.672230	+	1.16434i	−0.977270	+	0.211997i	$0.932003\pi$
$522$	−4.96712	+	8.60331i	−0.217405	+	0.376556i
$523$	−12.4883	−	21.6303i	−0.546074	−	0.945828i	−0.998538	−	0.0540454i	$-0.982788\pi$
$523$	−12.4883	−	21.6303i	−0.546074	−	0.945828i	0.452465	−	0.891782i	$-0.350545\pi$
$524$	−1.51773			−0.0663025
$525$	−3.03321	−	5.25367i	−0.132380	−	0.229289i
$526$	−8.02280	+	13.8959i	−0.349811	+	0.605890i
$527$	6.26772			0.273026
$528$	12.1198	−	20.9922i	0.527448	−	0.913567i
$529$	2.10291	+	3.64234i	0.0914308	+	0.158363i
$530$	0.553652	+	0.958954i	0.0240491	+	0.0416543i
$531$	−0.216381	−	0.374784i	−0.00939016	−	0.0162642i
$532$	12.1337			0.526064
$533$	−9.47763	−	16.4157i	−0.410522	−	0.711045i
$534$	−1.89660	−	3.28502i	−0.0820741	−	0.142157i
$535$	−7.70481	+	13.3451i	−0.333108	+	0.576960i
$536$	−1.97236	+	3.41623i	−0.0851931	+	0.147559i
$537$	−3.93920			−0.169989
$538$	17.1917			0.741186
$539$	−59.7623	+	103.511i	−2.57415	+	4.45855i
$540$	−3.13832	+	5.43572i	−0.135052	+	0.233916i
$541$	−19.9237	−	34.5088i	−0.856586	−	1.48365i	−0.875166	−	0.483823i	$-0.839248\pi$
$541$	−19.9237	−	34.5088i	−0.856586	−	1.48365i	0.0185803	−	0.999827i	$-0.494085\pi$
$542$	15.4809	+	26.8137i	0.664961	+	1.15175i
$543$	9.70260			0.416378
$544$	1.99030	+	3.44730i	0.0853333	+	0.147802i
$545$	−8.83809	−	15.3080i	−0.378582	−	0.655724i
$546$	−21.4424	−	37.1393i	−0.917648	−	1.58941i
$547$	13.0349	−	22.5772i	0.557334	−	0.965330i	−0.440384	−	0.897809i	$-0.645158\pi$
$547$	13.0349	−	22.5772i	0.557334	−	0.965330i	0.997718	−	0.0675209i	$-0.0215089\pi$
$548$	−16.4196			−0.701412
$549$	−10.3509	+	17.9283i	−0.441766	+	0.765162i
$550$	−6.58478	−	11.4052i	−0.280776	−	0.486318i
$551$	−8.23433			−0.350794
$552$	−3.82574	−	6.62637i	−0.162834	−	0.282037i
$553$	20.1978	−	34.9837i	0.858899	−	1.48766i
$554$	15.8860	−	27.5154i	0.674932	−	1.16902i
$555$	−0.860685			−0.0365341
$556$	3.02241	−	5.23497i	0.128179	−	0.222012i
$557$	25.1303			1.06481			0.532403	−	0.846491i	$-0.321289\pi$
$557$	25.1303			1.06481			0.532403	+	0.846491i	$0.321289\pi$
$558$	−23.7074			−1.00362
$559$	−32.7845	−	19.8609i	−1.38664	−	0.840025i
$560$	−49.3192			−2.08412
$561$	−4.91572			−0.207542
$562$	−3.04625	+	5.27627i	−0.128498	+	0.222566i
$563$	38.5358			1.62409			0.812045	−	0.583595i	$-0.198354\pi$
$563$	38.5358			1.62409			0.812045	+	0.583595i	$0.198354\pi$
$564$	−0.609487	+	1.05566i	−0.0256640	+	0.0444514i
$565$	−4.50124	+	7.79638i	−0.189369	+	0.327996i
$566$	15.6415	+	27.0919i	0.657463	+	1.13876i
$567$	−16.1902			−0.679924
$568$	8.90000	+	15.4153i	0.373436	+	0.646810i
$569$	2.97761	−	5.15737i	0.124828	−	0.216208i	−0.796838	−	0.604193i	$-0.793495\pi$
$569$	2.97761	−	5.15737i	0.124828	−	0.216208i	0.921666	+	0.387985i	$0.126829\pi$
$570$	−8.35239			−0.349843
$571$	6.59609	−	11.4248i	0.276038	−	0.478112i	−0.694359	−	0.719629i	$-0.744312\pi$
$571$	6.59609	−	11.4248i	0.276038	−	0.478112i	0.970396	+	0.241518i	$0.0776451\pi$
$572$	−12.5397	−	21.7193i	−0.524310	−	0.908131i
$573$	0.709021	+	1.22806i	0.0296198	+	0.0513029i
$574$	−14.0787	−	24.3851i	−0.587634	−	1.01781i
$575$	−5.93102			−0.247341
$576$	3.74488	+	6.48632i	0.156037	+	0.270263i
$577$	−3.47084	−	6.01167i	−0.144493	−	0.250269i	0.784691	−	0.619888i	$-0.212822\pi$
$577$	−3.47084	−	6.01167i	−0.144493	−	0.250269i	−0.929184	+	0.369618i	$0.879488\pi$
$578$	0.827258	−	1.43285i	0.0344094	−	0.0595988i
$579$	−0.433691	+	0.751175i	−0.0180236	+	0.0312178i
$580$	−3.69099			−0.153260
$581$	−25.1258			−1.04239
$582$	−9.27541	+	16.0655i	−0.384478	+	0.665935i
$583$	1.02160	−	1.76947i	0.0423104	−	0.0732838i
$584$	−14.4596	−	25.0447i	−0.598342	−	1.03636i
$585$	−12.7338	−	22.0556i	−0.526478	−	0.911887i
$586$	5.48473			0.226572
$587$	−9.04655	−	15.6691i	−0.373391	−	0.646732i	0.616694	−	0.787203i	$-0.288472\pi$
$587$	−9.04655	−	15.6691i	−0.373391	−	0.646732i	−0.990085	+	0.140471i	$0.955138\pi$
$588$	−6.39979	−	11.0848i	−0.263923	−	0.457128i
$589$	−9.82536	−	17.0180i	−0.404847	−	0.701215i
$590$	0.298438	−	0.516909i	0.0122865	−	0.0212808i
$591$	−16.4698			−0.677478
$592$	1.31790	−	2.28267i	0.0541654	−	0.0938172i
$593$	−9.22782	−	15.9831i	−0.378941	−	0.656345i	0.611967	−	0.790883i	$-0.290378\pi$
$593$	−9.22782	−	15.9831i	−0.378941	−	0.656345i	−0.990908	+	0.134538i	$0.957045\pi$
$594$	42.9929			1.76402
$595$	5.00088	+	8.66179i	0.205016	+	0.355099i
$596$	−0.0619581	+	0.107315i	−0.00253790	+	0.00439578i
$597$	−6.22283	+	10.7783i	−0.254684	+	0.441125i
$598$	−41.9276			−1.71455
$599$	15.9226	−	27.5787i	0.650579	−	1.12684i	−0.332404	−	0.943137i	$-0.607860\pi$
$599$	15.9226	−	27.5787i	0.650579	−	1.12684i	0.982983	−	0.183699i	$-0.0588071\pi$
$600$	−2.41463			−0.0985770
$601$	−39.4036			−1.60731			−0.803653	−	0.595098i	$-0.797113\pi$
$601$	−39.4036			−1.60731			−0.803653	+	0.595098i	$0.797113\pi$
$602$	−48.7003	−	29.5027i	−1.98488	−	1.20244i
$603$	−4.31710			−0.175806
$604$	−2.02339			−0.0823307
$605$	21.7737	−	37.7132i	0.885227	−	1.53326i
$606$	14.9454			0.607116
$607$	0.841251	−	1.45709i	0.0341453	−	0.0591414i	−0.848448	−	0.529279i	$-0.822462\pi$
$607$	0.841251	−	1.45709i	0.0341453	−	0.0591414i	0.882593	+	0.470138i	$0.155796\pi$
$608$	6.24003	−	10.8080i	0.253067	−	0.438324i
$609$	5.82296	+	10.0857i	0.235958	+	0.408692i
$610$	−28.5524			−1.15605
$611$	−5.71822	−	9.90425i	−0.231335	−	0.400683i
$612$	−0.842928	+	1.45999i	−0.0340733	+	0.0590167i
$613$	18.0083			0.727348			0.363674	−	0.931526i	$-0.381522\pi$
$613$	18.0083			0.727348			0.363674	+	0.931526i	$0.381522\pi$
$614$	−2.12243	+	3.67616i	−0.0856543	+	0.148358i
$615$	2.61068	+	4.52183i	0.105273	+	0.182338i
$616$	31.8927	+	55.2398i	1.28499	+	2.22567i
$617$	−14.6771	−	25.4216i	−0.590880	−	1.02343i	−0.994114	−	0.108337i	$-0.965447\pi$
$617$	−14.6771	−	25.4216i	−0.590880	−	1.02343i	0.403235	−	0.915097i	$-0.367886\pi$
$618$	23.4941			0.945070
$619$	3.08521	+	5.34375i	0.124005	+	0.214783i	0.921344	−	0.388749i	$-0.127093\pi$
$619$	3.08521	+	5.34375i	0.124005	+	0.214783i	−0.797338	+	0.603532i	$0.793759\pi$
$620$	−4.40416	−	7.62822i	−0.176875	−	0.306357i
$621$	9.68112	−	16.7682i	0.388490	−	0.672884i
$622$	−24.0502	+	41.6561i	−0.964324	+	1.67026i
$623$	14.2410			0.570555
$624$	−24.3535			−0.974921
$625$	8.14390	−	14.1057i	0.325756	−	0.564226i
$626$	−15.4548	+	26.7684i	−0.617697	+	1.06988i
$627$	7.70594	+	13.3471i	0.307746	+	0.533031i
$628$	−2.16073	−	3.74249i	−0.0862225	−	0.149342i
$629$	−0.534531			−0.0213131
$630$	−18.9157	−	32.7629i	−0.753618	−	1.30531i
$631$	−14.4572	−	25.0406i	−0.575532	−	0.996851i	−0.995984	−	0.0895357i	$-0.971462\pi$
$631$	−14.4572	−	25.0406i	−0.575532	−	0.996851i	0.420452	−	0.907315i	$-0.361872\pi$
$632$	−8.03941	−	13.9247i	−0.319790	−	0.553893i
$633$	9.74040	−	16.8709i	0.387146	−	0.670557i
$634$	−11.0932			−0.440568
$635$	6.83226	−	11.8338i	0.271130	−	0.469611i
$636$	0.109401	+	0.189487i	0.00433802	+	0.00751366i
$637$	120.086			4.75798
$638$	12.6410	+	21.8949i	0.500464	+	0.866829i
$639$	−9.74014	+	16.8704i	−0.385314	+	0.667384i
$640$	−12.7511	+	22.0855i	−0.504030	+	0.873005i
$641$	−11.0036			−0.434614			−0.217307	−	0.976103i	$-0.569727\pi$
$641$	−11.0036			−0.434614			−0.217307	+	0.976103i	$0.569727\pi$
$642$	−5.65159	+	9.78883i	−0.223050	+	0.386334i
$643$	−40.7776			−1.60811			−0.804055	−	0.594554i	$-0.797328\pi$
$643$	−40.7776			−1.60811			−0.804055	+	0.594554i	$0.797328\pi$
$644$	−16.7779			−0.661142
$645$	9.03072	+	5.47082i	0.355584	+	0.215413i
$646$	−5.18728			−0.204091
$647$	19.2904			0.758382			0.379191	−	0.925318i	$-0.376202\pi$
$647$	19.2904			0.758382			0.379191	+	0.925318i	$0.376202\pi$
$648$	−3.22212	+	5.58087i	−0.126577	+	0.219237i
$649$	−1.10136			−0.0432321
$650$	−6.61570	+	11.4587i	−0.259489	+	0.449449i
$651$	−13.8961	+	24.0688i	−0.544632	+	0.943331i
$652$	−4.08023	−	7.06717i	−0.159794	−	0.276772i
$653$	18.5022			0.724046			0.362023	−	0.932169i	$-0.382086\pi$
$653$	18.5022			0.724046			0.362023	+	0.932169i	$0.382086\pi$
$654$	−6.48286	−	11.2286i	−0.253500	−	0.439075i
$655$	−1.96117	+	3.39685i	−0.0766294	+	0.132726i
$656$	−15.9901			−0.624310
$657$	15.8245	−	27.4089i	0.617374	−	1.06932i
$658$	−8.49424	−	14.7124i	−0.331140	−	0.573551i
$659$	−5.06189	−	8.76746i	−0.197183	−	0.341532i	0.750431	−	0.660949i	$-0.229846\pi$
$659$	−5.06189	−	8.76746i	−0.197183	−	0.341532i	−0.947614	+	0.319418i	$0.896513\pi$
$660$	3.45414	+	5.98275i	0.134452	+	0.232878i
$661$	27.8467			1.08311			0.541556	−	0.840665i	$-0.317836\pi$
$661$	27.8467			1.08311			0.541556	+	0.840665i	$0.317836\pi$
$662$	16.3616	+	28.3392i	0.635913	+	1.10143i
$663$	2.46940	+	4.27713i	0.0959036	+	0.166110i
$664$	−5.00045	+	8.66104i	−0.194055	+	0.336114i
$665$	15.6789	−	27.1566i	0.608001	−	1.05309i
$666$	2.02185			0.0783449
$667$	11.3860			0.440868
$668$	−6.75410	+	11.6984i	−0.261324	+	0.452626i
$669$	0.0225325	−	0.0390275i	0.000871157	−	0.00150889i
$670$	−2.97711	−	5.15651i	−0.115016	−	0.199214i
$671$	26.3425	+	45.6266i	1.01694	+	1.76139i
$672$	−17.6507			−0.680891
$673$	11.0234	+	19.0931i	0.424922	+	0.735986i	0.996413	−	0.0846221i	$-0.0269683\pi$
$673$	11.0234	+	19.0931i	0.424922	+	0.735986i	−0.571491	+	0.820608i	$0.693635\pi$
$674$	9.77110	+	16.9240i	0.376369	+	0.651890i
$675$	−3.05514	−	5.29166i	−0.117592	−	0.203676i
$676$	−7.80532	+	13.5192i	−0.300205	+	0.519970i
$677$	−25.2367			−0.969926			−0.484963	−	0.874535i	$-0.661167\pi$
$677$	−25.2367			−0.969926			−0.484963	+	0.874535i	$0.661167\pi$
$678$	−3.30173	+	5.71876i	−0.126802	+	0.219627i
$679$	−34.8231	−	60.3154i	−1.33639	−	2.31469i
$680$	3.98104			0.152666
$681$	−6.22685	−	10.7852i	−0.238613	−	0.413291i
$682$	−30.1671	+	52.2509i	−1.15516	+	2.00079i
$683$	−8.50876	+	14.7376i	−0.325579	+	0.563919i	−0.981629	−	0.190798i	$-0.938892\pi$
$683$	−8.50876	+	14.7376i	−0.325579	+	0.563919i	0.656051	+	0.754717i	$0.272226\pi$
$684$	5.28553			0.202097
$685$	−21.2170	+	36.7489i	−0.810660	+	1.40411i
$686$	117.601			4.49004
$687$	−2.04665			−0.0780844
$688$	−28.3375	+	15.5738i	−1.08036	+	0.593746i
$689$	−2.05280			−0.0782054
$690$	11.5493			0.439673
$691$	14.4396	−	25.0101i	0.549308	−	0.951430i	−0.449014	−	0.893525i	$-0.648225\pi$
$691$	14.4396	−	25.0101i	0.549308	−	0.951430i	0.998322	−	0.0579052i	$-0.0184421\pi$
$692$	15.3014			0.581670
$693$	−34.9033	+	60.4543i	−1.32587	+	2.29647i
$694$	27.9752	−	48.4545i	1.06192	−	1.83931i
$695$	−7.81096	−	13.5290i	−0.296286	−	0.513183i
$696$	4.63546			0.175707
$697$	1.62137	+	2.80830i	0.0614138	+	0.106372i
$698$	15.9714	−	27.6633i	0.604526	−	1.04707i
$699$	−14.5769			−0.551349
$700$	−2.64736	+	4.58537i	−0.100061	+	0.173311i
$701$	1.11547	+	1.93206i	0.0421309	+	0.0729728i	0.886322	−	0.463070i	$-0.153252\pi$
$701$	1.11547	+	1.93206i	0.0421309	+	0.0729728i	−0.844191	+	0.536042i	$0.819919\pi$
$702$	−21.5974	−	37.4078i	−0.815142	−	1.41187i
$703$	0.837937	+	1.45135i	0.0316034	+	0.0547387i
$704$	19.0610			0.718389
$705$	1.57513	+	2.72820i	0.0593226	+	0.102750i
$706$	1.69766	+	2.94043i	0.0638922	+	0.110664i
$707$	−28.0551	+	48.5929i	−1.05512	+	1.82753i
$708$	0.0589707	−	0.102140i	0.00221626	−	0.00383867i
$709$	51.6630			1.94025			0.970123	−	0.242613i	$-0.0780044\pi$
$709$	51.6630			1.94025			0.970123	+	0.242613i	$0.0780044\pi$
$710$	−26.8676			−1.00832
$711$	8.79831	−	15.2391i	0.329962	−	0.571512i
$712$	2.83420	−	4.90898i	0.106216	−	0.183972i
$713$	13.5860	+	23.5316i	0.508799	+	0.881267i
$714$	3.66822	+	6.35354i	0.137280	+	0.237775i
$715$	−64.8137			−2.42390
$716$	1.71906	+	2.97749i	0.0642441	+	0.111274i
$717$	−0.0867668	−	0.150284i	−0.00324036	−	0.00561248i
$718$	−17.9705	−	31.1258i	−0.670653	−	1.16161i
$719$	6.50590	−	11.2685i	0.242629	−	0.420246i	−0.718833	−	0.695182i	$-0.755324\pi$
$719$	6.50590	−	11.2685i	0.242629	−	0.420246i	0.961462	+	0.274937i	$0.0886569\pi$
$720$	−21.4838			−0.800653
$721$	−44.1024	+	76.3877i	−1.64246	+	2.84483i
$722$	−7.58626	−	13.1398i	−0.282331	−	0.489012i
$723$	12.2250			0.454652
$724$	−4.23419	−	7.33382i	−0.157362	−	0.272559i
$725$	1.79658	−	3.11177i	0.0667234	−	0.115568i
$726$	15.9713	−	27.6631i	0.592751	−	1.02668i
$727$	13.2381			0.490974			0.245487	−	0.969400i	$-0.421052\pi$
$727$	13.2381			0.490974			0.245487	+	0.969400i	$0.421052\pi$
$728$	32.0425	−	55.4992i	1.18757	−	2.05694i
$729$	4.26804			0.158076
$730$	43.6510			1.61560
$731$	5.60855	+	3.39767i	0.207440	+	0.125667i
$732$	−5.64190			−0.208531
$733$	−53.0608			−1.95985			−0.979923	−	0.199375i	$-0.936109\pi$
$733$	−53.0608			−1.95985			−0.979923	+	0.199375i	$0.936109\pi$
$734$	3.34448	−	5.79280i	0.123447	−	0.213816i
$735$	−33.0786			−1.22012
$736$	−8.62839	+	14.9448i	−0.318047	+	0.550873i
$737$	−5.49339	+	9.51483i	−0.202352	+	0.350483i
$738$	−6.13278	−	10.6223i	−0.225751	−	0.391012i
$739$	13.6787			0.503181			0.251590	−	0.967834i	$-0.419046\pi$
$739$	13.6787			0.503181			0.251590	+	0.967834i	$0.419046\pi$
$740$	0.375600	+	0.650559i	0.0138073	+	0.0239150i
$741$	7.74213	−	13.4098i	0.284414	−	0.492620i
$742$	−3.04937			−0.111946
$743$	7.22385	−	12.5121i	0.265017	−	0.459023i	−0.702551	−	0.711634i	$-0.747956\pi$
$743$	7.22385	−	12.5121i	0.265017	−	0.459023i	0.967568	+	0.252610i	$0.0812890\pi$
$744$	5.53112	+	9.58018i	0.202781	+	0.351227i
$745$	0.160121	+	0.277338i	0.00586639	+	0.0101609i
$746$	−4.15000	−	7.18802i	−0.151942	−	0.263172i
$747$	−10.9450			−0.400455
$748$	2.14520	+	3.71560i	0.0784364	+	0.135856i
$749$	−21.2180	−	36.7507i	−0.775289	−	1.34284i
$750$	8.48247	−	14.6921i	0.309736	−	0.536478i
$751$	−17.5914	+	30.4692i	−0.641920	+	1.11184i	0.343084	+	0.939305i	$0.388529\pi$
$751$	−17.5914	+	30.4692i	−0.641920	+	1.11184i	−0.985004	+	0.172533i	$0.944805\pi$
$752$	−9.64747			−0.351807
$753$	22.3502			0.814488
$754$	12.7004	−	21.9978i	0.462522	−	0.801112i
$755$	−2.61458	+	4.52858i	−0.0951542	+	0.164812i
$756$	−8.64251	−	14.9693i	−0.314325	−	0.544427i
$757$	−14.8539	−	25.7277i	−0.539874	−	0.935089i	−0.998910	−	0.0466718i	$-0.985139\pi$
$757$	−14.8539	−	25.7277i	−0.539874	−	0.935089i	0.459036	−	0.888418i	$-0.348195\pi$
$758$	28.5778			1.03799
$759$	−10.6554	−	18.4556i	−0.386766	−	0.669898i
$760$	−6.24072	−	10.8092i	−0.226375	−	0.392092i
$761$	21.3523	+	36.9832i	0.774019	+	1.34064i	0.935344	+	0.353739i	$0.115090\pi$
$761$	21.3523	+	36.9832i	0.774019	+	1.34064i	−0.161326	+	0.986901i	$0.551577\pi$
$762$	5.01156	−	8.68027i	0.181550	−	0.314453i
$763$	48.6779			1.76226
$764$	0.618829	−	1.07184i	0.0223884	−	0.0387779i
$765$	2.17842	+	3.77313i	0.0787608	+	0.136418i
$766$	12.7601			0.461041
$767$	0.553265	+	0.958284i	0.0199773	+	0.0346016i
$768$	−6.58506	+	11.4057i	−0.237618	+	0.411566i
$769$	6.40905	−	11.1008i	0.231116	−	0.400305i	−0.727021	−	0.686616i	$-0.759096\pi$
$769$	6.40905	−	11.1008i	0.231116	−	0.400305i	0.958137	+	0.286311i	$0.0924289\pi$
$770$	−96.2787			−3.46964
$771$	−7.28172	+	12.6123i	−0.262245	+	0.454221i
$772$	0.757046			0.0272467
$773$	−21.1123			−0.759358			−0.379679	−	0.925118i	$-0.623966\pi$
$773$	−21.1123			−0.759358			−0.379679	+	0.925118i	$0.623966\pi$
$774$	−21.2142	−	12.8516i	−0.762527	−	0.461940i
$775$	8.57487			0.308018
$776$	−27.7215			−0.995144
$777$	1.18511	−	2.05266i	0.0425154	−	0.0736389i
$778$	23.8769			0.856027
$779$	5.08336	−	8.80464i	0.182130	−	0.315459i
$780$	3.47036	−	6.01085i	0.124259	−	0.215223i
$781$	24.7881	+	42.9343i	0.886989	+	1.53631i
$782$	7.17270			0.256495
$783$	5.86507	+	10.1586i	0.209601	+	0.363039i
$784$	50.6506	−	87.7295i	1.80895	−	3.13319i
$785$	−11.1682			−0.398608
$786$	−1.43855	+	2.49164i	−0.0513113	+	0.0888738i
$787$	−9.75977	−	16.9044i	−0.347898	−	0.602577i	0.637978	−	0.770055i	$-0.279771\pi$
$787$	−9.75977	−	16.9044i	−0.347898	−	0.602577i	−0.985876	+	0.167478i	$0.946438\pi$
$788$	7.18738	+	12.4489i	0.256040	+	0.443474i
$789$	4.09694	+	7.09611i	0.145855	+	0.252628i
$790$	24.2696			0.863474
$791$	−12.3958	−	21.4702i	−0.440745	−	0.763392i
$792$	13.8927	+	24.0628i	0.493654	+	0.855035i
$793$	26.4662	−	45.8409i	0.939843	−	1.62786i
$794$	−20.8612	+	36.1326i	−0.740335	+	1.28230i
$795$	0.565458			0.0200547
$796$	10.8625			0.385011
$797$	−2.60322	+	4.50891i	−0.0922107	+	0.159714i	−0.908441	−	0.418013i	$-0.862727\pi$
$797$	−2.60322	+	4.50891i	−0.0922107	+	0.159714i	0.816230	+	0.577727i	$0.196060\pi$
$798$	11.5007	−	19.9198i	0.407120	−	0.705152i
$799$	0.978236	+	1.69435i	0.0346075	+	0.0599420i
$800$	2.72293	+	4.71624i	0.0962699	+	0.166744i
$801$	6.20348			0.219189
$802$	22.8799	+	39.6291i	0.807916	+	1.39935i
$803$	−40.2726	−	69.7541i	−1.42119	−	2.46157i
$804$	−0.588272	−	1.01892i	−0.0207468	−	0.0359344i
$805$	−21.6800	+	37.5508i	−0.764118	+	1.32349i
$806$	60.6175			2.13516
$807$	4.38957	−	7.60295i	0.154520	−	0.267637i
$808$	11.1669	+	19.3416i	0.392849	+	0.680435i
$809$	47.3044			1.66313			0.831567	−	0.555424i	$-0.187444\pi$
$809$	47.3044			1.66313			0.831567	+	0.555424i	$0.187444\pi$
$810$	−4.86351	−	8.42385i	−0.170886	−	0.295984i
$811$	3.34883	−	5.80034i	0.117593	−	0.203677i	−0.801220	−	0.598370i	$-0.795815\pi$
$811$	3.34883	−	5.80034i	0.117593	−	0.203677i	0.918813	+	0.394692i	$0.129149\pi$
$812$	5.08225	−	8.80271i	0.178352	−	0.308915i
$813$	15.8110			0.554516
$814$	2.57274	−	4.45612i	0.0901746	−	0.156187i
$815$	−21.0895			−0.738732
$816$	4.16624			0.145848
$817$	0.433254	−	20.5545i	0.0151576	−	0.719110i
$818$	−21.4013			−0.748278
$819$	70.1344			2.45070
$820$	2.27859	−	3.94663i	0.0795717	−	0.137822i
$821$	−34.5117			−1.20447			−0.602233	−	0.798320i	$-0.705722\pi$
$821$	−34.5117			−1.20447			−0.602233	+	0.798320i	$0.705722\pi$
$822$	−15.5630	+	26.9559i	−0.542821	+	0.940194i
$823$	−9.65619	+	16.7250i	−0.336594	+	0.582997i	−0.983790	−	0.179326i	$-0.942608\pi$
$823$	−9.65619	+	16.7250i	−0.336594	+	0.582997i	0.647196	+	0.762324i	$0.275942\pi$
$824$	17.5542	+	30.4048i	0.611531	+	1.05920i
$825$	−6.72519			−0.234141
$826$	0.821858	+	1.42350i	0.0285961	+	0.0495299i
$827$	2.87298	−	4.97614i	0.0999032	−	0.173037i	−0.811741	−	0.584017i	$-0.801480\pi$
$827$	2.87298	−	4.97614i	0.0999032	−	0.173037i	0.911644	+	0.410980i	$0.134813\pi$
$828$	−7.30856			−0.253990
$829$	−17.6410	+	30.5551i	−0.612697	+	1.06122i	0.378087	+	0.925770i	$0.376582\pi$
$829$	−17.6410	+	30.5551i	−0.612697	+	1.06122i	−0.990784	+	0.135452i	$0.956751\pi$
$830$	−7.54776	−	13.0731i	−0.261987	−	0.453774i
$831$	−8.11238	−	14.0511i	−0.281415	−	0.487426i
$832$	−9.57527	−	16.5849i	−0.331963	−	0.574977i
$833$	−20.5435			−0.711791
$834$	−5.72945	−	9.92369i	−0.198394	−	0.343629i
$835$	17.4549	+	30.2328i	0.604053	+	1.04625i
$836$	6.72570	−	11.6492i	0.232613	−	0.402898i
$837$	−13.9966	+	24.2429i	−0.483794	+	0.837956i
$838$	−18.3929			−0.635371
$839$	−12.1554			−0.419652			−0.209826	−	0.977739i	$-0.567290\pi$
$839$	−12.1554			−0.419652			−0.209826	+	0.977739i	$0.567290\pi$
$840$	−8.82633	+	15.2877i	−0.304537	+	0.527474i
$841$	11.0510	−	19.1409i	0.381070	−	0.660033i
$842$	29.0381	+	50.2954i	1.00072	+	1.73329i
$843$	1.55561	+	2.69439i	0.0535779	+	0.0927997i
$844$	−17.0027			−0.585258
$845$	20.1717	+	34.9383i	0.693926	+	1.20192i
$846$	−3.70014	−	6.40884i	−0.127214	−	0.220340i
$847$	59.9619	+	103.857i	2.06032	+	3.56857i
$848$	−0.865842	+	1.49968i	−0.0297331	+	0.0514993i
$849$	15.9751			0.548263
$850$	1.13177	−	1.96029i	0.0388194	−	0.0672372i
$851$	−1.15866	−	2.00685i	−0.0397182	−	0.0687940i
$852$	−5.30899			−0.181883
$853$	2.34145	+	4.05551i	0.0801697	+	0.138858i	0.903323	−	0.428962i	$-0.141120\pi$
$853$	2.34145	+	4.05551i	0.0801697	+	0.138858i	−0.823153	+	0.567820i	$0.807787\pi$
$854$	39.3147	−	68.0951i	1.34532	−	2.33017i
$855$	6.82983	−	11.8296i	0.233575	−	0.404564i
$856$	−16.8909			−0.577321
$857$	−11.2199	+	19.4335i	−0.383265	+	0.663834i	−0.991527	−	0.129902i	$-0.958534\pi$
$857$	−11.2199	+	19.4335i	−0.383265	+	0.663834i	0.608262	+	0.793736i	$0.291867\pi$
$858$	−47.5418			−1.62305
$859$	−28.2315			−0.963248			−0.481624	−	0.876378i	$-0.659953\pi$
$859$	−28.2315			−0.963248			−0.481624	+	0.876378i	$0.659953\pi$
$860$	0.194203	−	9.21342i	0.00662228	−	0.314175i
$861$	−14.3789			−0.490033
$862$	5.49009			0.186993
$863$	23.1171	−	40.0400i	0.786916	−	1.36298i	−0.140932	−	0.990019i	$-0.545010\pi$
$863$	23.1171	−	40.0400i	0.786916	−	1.36298i	0.927848	−	0.372959i	$-0.121657\pi$
$864$	−17.7784			−0.604832
$865$	19.7720	−	34.2461i	0.672268	−	1.16440i
$866$	21.1608	−	36.6515i	0.719073	−	1.24547i
$867$	−0.422449	−	0.731703i	−0.0143471	−	0.0248499i
$868$	24.2569			0.823334
$869$	−22.3912	−	38.7827i	−0.759570	−	1.31561i
$870$	−3.49842	+	6.05944i	−0.118608	+	0.205434i
$871$	11.0384			0.374021
$872$	9.68770	−	16.7796i	0.328067	−	0.568229i
$873$	−15.1692	−	26.2738i	−0.513399	−	0.889232i
$874$	−11.2440	−	19.4752i	−0.380334	−	0.658758i
$875$	31.8461	+	55.1591i	1.07660	+	1.86472i
$876$	8.62536			0.291424
$877$	11.2685	+	19.5177i	0.380512	+	0.659066i	0.991135	−	0.132855i	$-0.0424145\pi$
$877$	11.2685	+	19.5177i	0.380512	+	0.659066i	−0.610624	+	0.791921i	$0.709081\pi$
$878$	−16.4671	−	28.5218i	−0.555736	−	0.962563i
$879$	1.40042	−	2.42560i	0.0472350	−	0.0818135i
$880$	−27.3375	+	47.3500i	−0.921548	+	1.59617i
$881$	4.86818			0.164013			0.0820065	−	0.996632i	$-0.473867\pi$
$881$	4.86818			0.164013			0.0820065	+	0.996632i	$0.473867\pi$
$882$	77.7052			2.61647
$883$	−13.4102	+	23.2271i	−0.451289	+	0.781655i	−0.998466	−	0.0553615i	$-0.982369\pi$
$883$	−13.4102	+	23.2271i	−0.451289	+	0.781655i	0.547178	+	0.837016i	$0.315702\pi$
$884$	2.15528	−	3.73305i	0.0724899	−	0.125556i
$885$	−0.152401	−	0.263966i	−0.00512290	−	0.00887312i
$886$	−16.2062	−	28.0700i	−0.544459	−	0.943030i
$887$	37.6624			1.26458			0.632290	−	0.774732i	$-0.282115\pi$
$887$	37.6624			1.26458			0.632290	+	0.774732i	$0.282115\pi$
$888$	−0.471711	−	0.817028i	−0.0158296	−	0.0274177i
$889$	18.8151	+	32.5888i	0.631039	+	1.09299i
$890$	4.27799	+	7.40969i	0.143398	+	0.248373i
$891$	−8.97418	+	15.5437i	−0.300646	+	0.520735i
$892$	−0.0393325			−0.00131695
$893$	3.06699	−	5.31218i	0.102633	−	0.177765i
$894$	0.117451	+	0.203431i	0.00392816	+	0.00680377i
$895$	8.88527			0.297002
$896$	−35.1147	−	60.8204i	−1.17310	−	2.03187i
$897$	−10.7054	+	18.5423i	−0.357443	+	0.619110i
$898$	17.2248	−	29.8341i	0.574797	−	0.995578i
$899$	−16.4615			−0.549022
$900$	−1.15321	+	1.99742i	−0.0384403	+	0.0665806i
$901$	0.351179			0.0116995
$902$	−31.2152			−1.03935
$903$	−25.4821	+	14.0046i	−0.847993	+	0.466043i
$904$	−9.86790			−0.328201
$905$	−21.8852			−0.727489
$906$	−1.91783	+	3.32178i	−0.0637156	+	0.110359i
$907$	44.2722			1.47003			0.735017	−	0.678049i	$-0.237174\pi$
$907$	44.2722			1.47003			0.735017	+	0.678049i	$0.237174\pi$
$908$	−5.43476	+	9.41327i	−0.180359	+	0.312390i
$909$	−12.2210	+	21.1674i	−0.405345	+	0.702078i
$910$	48.3654	+	83.7714i	1.60330	+	2.77699i
$911$	−6.19110			−0.205120			−0.102560	−	0.994727i	$-0.532703\pi$
$911$	−6.19110			−0.205120			−0.102560	+	0.994727i	$0.532703\pi$
$912$	−6.53105	−	11.3121i	−0.216265	−	0.374581i
$913$	−13.9272	+	24.1226i	−0.460922	+	0.798340i
$914$	45.6232			1.50908
$915$	−7.29031	+	12.6272i	−0.241010	+	0.417442i
$916$	0.893150	+	1.54698i	0.0295105	+	0.0511137i
$917$	−5.40081	−	9.35448i	−0.178351	−	0.308912i
$918$	3.69475	+	6.39949i	0.121945	+	0.211215i
$919$	6.38792			0.210718			0.105359	−	0.994434i	$-0.466401\pi$
$919$	6.38792			0.210718			0.105359	+	0.994434i	$0.466401\pi$
$920$	8.62934	+	14.9465i	0.284501	+	0.492770i
$921$	1.08384	+	1.87727i	0.0357139	+	0.0618583i
$922$	−32.9563	+	57.0819i	−1.08536	+	1.87989i
$923$	24.9045	−	43.1359i	0.819743	−	1.41984i
$924$	−19.0245			−0.625860
$925$	−0.731292			−0.0240447
$926$	10.3175	−	17.8705i	0.339055	−	0.587260i
$927$	−19.2113	+	33.2750i	−0.630982	+	1.09289i
$928$	−5.22730	−	9.05395i	−0.171595	−	0.297211i
$929$	13.7841	+	23.8747i	0.452240	+	0.783303i	0.998525	−	0.0542965i	$-0.0172916\pi$
$929$	13.7841	+	23.8747i	0.452240	+	0.783303i	−0.546285	+	0.837600i	$0.683958\pi$
$930$	−16.6975			−0.547533
$931$	32.2043	+	55.7795i	1.05545	+	1.82810i
$932$	6.36131	+	11.0181i	0.208372	+	0.360910i
$933$	12.2815	+	21.2722i	0.402079	+	0.696421i
$934$	−15.4854	+	26.8215i	−0.506699	+	0.877628i
$935$	11.0879			0.362613
$936$	13.9579	−	24.1758i	0.456229	−	0.790211i
$937$	5.25655	+	9.10460i	0.171724	+	0.297434i	0.939023	−	0.343855i	$-0.111733\pi$
$937$	5.25655	+	9.10460i	0.171724	+	0.297434i	−0.767299	+	0.641290i	$0.778400\pi$
$938$	16.3972			0.535386
$939$	7.89216	+	13.6696i	0.257551	+	0.446091i
$940$	1.37476	−	2.38115i	0.0448397	−	0.0776647i
$941$	−26.1429	+	45.2809i	−0.852235	+	1.47611i	0.0269515	+	0.999637i	$0.491420\pi$
$941$	−26.1429	+	45.2809i	−0.852235	+	1.47611i	−0.879187	+	0.476478i	$0.841913\pi$
$942$	−8.19199			−0.266910
$943$	−7.02901	+	12.1746i	−0.228896	+	0.396460i
$944$	0.933438			0.0303808
$945$	−44.6705			−1.45313
$946$	−55.3191	+	30.4025i	−1.79858	+	0.988470i
$947$	−50.9471			−1.65556			−0.827779	−	0.561055i	$-0.810396\pi$
$947$	−50.9471			−1.65556			−0.827779	+	0.561055i	$0.810396\pi$
$948$	4.79563			0.155755
$949$	−40.4617	+	70.0817i	−1.31344	+	2.27495i
$950$	−7.09671			−0.230248
$951$	−2.83244	+	4.90593i	−0.0918481	+	0.159086i
$952$	−5.48162	+	9.49444i	−0.177660	+	0.307717i
$953$	−17.7767	−	30.7902i	−0.575845	−	0.997392i	−0.995949	−	0.0899164i	$-0.971340\pi$
$953$	−17.7767	−	30.7902i	−0.575845	−	0.997392i	0.420105	−	0.907476i	$-0.361993\pi$
$954$	−1.32832			−0.0430061
$955$	−1.59927	−	2.77001i	−0.0517511	−	0.0896356i
$956$	−0.0757295	+	0.131167i	−0.00244927	+	0.00424226i
$957$	12.9106			0.417341
$958$	−30.6564	+	53.0984i	−0.990462	+	1.71553i
$959$	−58.4288	−	101.202i	−1.88677	−	3.26797i
$960$	2.63758	+	4.56842i	0.0851274	+	0.147445i
$961$	−4.14217	−	7.17444i	−0.133618	−	0.231434i
$962$	−5.16965			−0.166676
$963$	−9.24270	−	16.0088i	−0.297842	−	0.515877i
$964$	−5.33495	−	9.24040i	−0.171827	−	0.297613i
$965$	0.978235	−	1.69435i	0.0314905	−	0.0545431i
$966$	−15.9026	+	27.5440i	−0.511656	+	0.886215i
$967$	−54.3483			−1.74772			−0.873861	−	0.486175i	$-0.838392\pi$
$967$	−54.3483			−1.74772			−0.873861	+	0.486175i	$0.838392\pi$
$968$	47.7336			1.53422
$969$	−1.32447	+	2.29405i	−0.0425482	+	0.0736956i
$970$	20.9216	−	36.2373i	0.671753	−	1.16351i
$971$	10.4944	+	18.1769i	0.336783	+	0.583324i	0.983826	−	0.179129i	$-0.0573280\pi$
$971$	10.4944	+	18.1769i	0.336783	+	0.583324i	−0.647043	+	0.762453i	$0.723995\pi$
$972$	−5.90130	−	10.2213i	−0.189284	−	0.327850i
$973$	43.0207			1.37918
$974$	20.1056	+	34.8239i	0.644225	+	1.11583i
$975$	3.37839	+	5.85154i	0.108195	+	0.187399i
$976$	−22.3262	−	38.6701i	−0.714643	−	1.23780i
$977$	7.45540	−	12.9131i	0.238519	−	0.413128i	−0.721770	−	0.692133i	$-0.756671\pi$
$977$	7.45540	−	12.9131i	0.238519	−	0.413128i	0.960290	+	0.279005i	$0.0900046\pi$
$978$	−15.4694			−0.494658
$979$	7.89376	−	13.6724i	0.252286	−	0.436972i
$980$	14.4354	+	25.0028i	0.461121	+	0.798686i
$981$	21.2044			0.677004
$982$	2.22708	+	3.85741i	0.0710689	+	0.123095i
$983$	13.9181	−	24.1069i	0.443920	−	0.768891i	−0.554057	−	0.832479i	$-0.686921\pi$
$983$	13.9181	−	24.1069i	0.443920	−	0.768891i	0.997976	+	0.0635878i	$0.0202543\pi$
$984$	−2.86165	+	4.95652i	−0.0912260	+	0.158008i
$985$	37.1493			1.18368
$986$	−2.17270	+	3.76323i	−0.0691930	+	0.119846i
$987$	−8.67537			−0.276140
$988$	−13.5146			−0.429956
$989$	−0.599081	+	28.4217i	−0.0190497	+	0.903756i
$990$	−41.9396			−1.33293
$991$	30.9330			0.982619			0.491310	−	0.870985i	$-0.336518\pi$
$991$	30.9330			0.982619			0.491310	+	0.870985i	$0.336518\pi$
$992$	12.4746	−	21.6067i	0.396070	−	0.686013i
$993$	16.7105			0.530293
$994$	36.9949	−	64.0771i	1.17341	−	2.03240i
$995$	14.0362	−	24.3115i	0.444979	−	0.770726i
$996$	−1.49142	−	2.58322i	−0.0472576	−	0.0818525i
$997$	−6.48292			−0.205316			−0.102658	−	0.994717i	$-0.532735\pi$
$997$	−6.48292			−0.205316			−0.102658	+	0.994717i	$0.532735\pi$
$998$	−0.0790745	−	0.136961i	−0.00250306	−	0.00433543i
$999$	1.19368	−	2.06751i	0.0377662	−	0.0654131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.307.9	✓	58
43.36	even	3	inner	731.2.e.a.681.9	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.9	✓	58	1.1	even	1	trivial
731.2.e.a.681.9	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)

\(f(q)\)	\(=\)	\(q-1.65452 q^{2} +(-0.422449 + 0.731703i) q^{3} +0.737422 q^{4} +(0.952877 - 1.65043i) q^{5} +(0.698949 - 1.21061i) q^{6} +(2.62410 + 4.54507i) q^{7} +2.08895 q^{8} +(1.14307 + 1.97986i) q^{9} +O(q^{10})\)	\(q-1.65452 q^{2} +(-0.422449 + 0.731703i) q^{3} +0.737422 q^{4} +(0.952877 - 1.65043i) q^{5} +(0.698949 - 1.21061i) q^{6} +(2.62410 + 4.54507i) q^{7} +2.08895 q^{8} +(1.14307 + 1.97986i) q^{9} +(-1.57655 + 2.73067i) q^{10} +5.81812 q^{11} +(-0.311523 + 0.539574i) q^{12} +(-2.92272 - 5.06230i) q^{13} +(-4.34161 - 7.51989i) q^{14} +(0.805084 + 1.39445i) q^{15} -4.93105 q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.89123 - 3.27571i) q^{18} +(1.56761 - 2.71518i) q^{19} +(0.702673 - 1.21706i) q^{20} -4.43419 q^{21} -9.62617 q^{22} +(-2.16761 + 3.75442i) q^{23} +(-0.882477 + 1.52850i) q^{24} +(0.684050 + 1.18481i) q^{25} +(4.83569 + 8.37566i) q^{26} -4.46626 q^{27} +(1.93507 + 3.35163i) q^{28} +(-1.31320 - 2.27452i) q^{29} +(-1.33202 - 2.30713i) q^{30} +(3.13386 - 5.42801i) q^{31} +3.98059 q^{32} +(-2.45786 + 4.25714i) q^{33} +(-0.827258 - 1.43285i) q^{34} +10.0018 q^{35} +(0.842928 + 1.45999i) q^{36} +(-0.267266 + 0.462917i) q^{37} +(-2.59364 + 4.49231i) q^{38} +4.93880 q^{39} +(1.99052 - 3.44768i) q^{40} +3.24274 q^{41} +7.33644 q^{42} +(5.74674 - 3.15832i) q^{43} +4.29041 q^{44} +4.35683 q^{45} +(3.58635 - 6.21174i) q^{46} +1.95647 q^{47} +(2.08312 - 3.60807i) q^{48} +(-10.2718 + 17.7912i) q^{49} +(-1.13177 - 1.96029i) q^{50} -0.844898 q^{51} +(-2.15528 - 3.73305i) q^{52} +(0.175590 - 0.304130i) q^{53} +7.38949 q^{54} +(5.54395 - 9.60241i) q^{55} +(5.48162 + 9.49444i) q^{56} +(1.32447 + 2.29405i) q^{57} +(2.17270 + 3.76323i) q^{58} -0.189298 q^{59} +(0.593687 + 1.02830i) q^{60} +(4.52767 + 7.84215i) q^{61} +(-5.18502 + 8.98072i) q^{62} +(-5.99907 + 10.3907i) q^{63} +3.27615 q^{64} -11.1400 q^{65} +(4.06657 - 7.04350i) q^{66} +(-0.944186 + 1.63538i) q^{67} +(0.368711 + 0.638626i) q^{68} +(-1.83141 - 3.17210i) q^{69} -16.5481 q^{70} +(4.26051 + 7.37941i) q^{71} +(2.38783 + 4.13584i) q^{72} +(-6.92192 - 11.9891i) q^{73} +(0.442195 - 0.765904i) q^{74} -1.15591 q^{75} +(1.15599 - 2.00224i) q^{76} +(15.2673 + 26.4437i) q^{77} -8.17133 q^{78} +(-3.84853 - 6.66585i) q^{79} +(-4.69869 + 8.13837i) q^{80} +(-1.54245 + 2.67161i) q^{81} -5.36517 q^{82} +(-2.39376 + 4.14611i) q^{83} -3.26987 q^{84} +1.90575 q^{85} +(-9.50807 + 5.22548i) q^{86} +2.21903 q^{87} +12.1538 q^{88} +(1.35676 - 2.34997i) q^{89} -7.20845 q^{90} +(15.3390 - 26.5679i) q^{91} +(-1.59845 + 2.76859i) q^{92} +(2.64779 + 4.58611i) q^{93} -3.23701 q^{94} +(-2.98748 - 5.17447i) q^{95} +(-1.68160 + 2.91261i) q^{96} -13.2705 q^{97} +(16.9948 - 29.4359i) q^{98} +(6.65054 + 11.5191i) 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

Properties

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