LMFDB - Embedded newform 99.2.e.e.34.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(34,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("99.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			34.3
Root			$0.947217 + 0.807294i$ of defining polynomial
Character	$\chi$	$=$	99.34
Dual form			99.2.e.e.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.447217 - 0.774602i) q^{2} +(1.22553 + 1.22396i) q^{3} +(0.599994 + 1.03922i) q^{4} +(-1.87447 - 3.24667i) q^{5} +(1.49616 - 0.401921i) q^{6} +(-0.725528 + 1.25665i) q^{7} +2.86218 q^{8} +(0.00384004 + 3.00000i) q^{9} +O(q^{10})$	\(q+(0.447217 - 0.774602i) q^{2} +(1.22553 + 1.22396i) q^{3} +(0.599994 + 1.03922i) q^{4} +(-1.87447 - 3.24667i) q^{5} +(1.49616 - 0.401921i) q^{6} +(-0.725528 + 1.25665i) q^{7} +2.86218 q^{8} +(0.00384004 + 3.00000i) q^{9} -3.35317 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.536655 + 2.00796i) q^{12} +(-2.87831 - 4.98537i) q^{13} +(0.648937 + 1.12399i) q^{14} +(1.67659 - 6.27316i) q^{15} +(0.0800260 - 0.138609i) q^{16} -4.79655 q^{17} +(2.32552 + 1.33868i) q^{18} +0.702126 q^{19} +(2.24934 - 3.89597i) q^{20} +(-2.42725 + 0.652045i) q^{21} +(0.447217 + 0.774602i) q^{22} +(0.825523 + 1.42985i) q^{23} +(3.50768 + 3.50319i) q^{24} +(-4.52724 + 7.84141i) q^{25} -5.14891 q^{26} +(-3.66717 + 3.68128i) q^{27} -1.74125 q^{28} +(2.15278 - 3.72872i) q^{29} +(-4.10941 - 4.10415i) q^{30} +(1.65278 + 2.86269i) q^{31} +(2.79060 + 4.83346i) q^{32} +(-1.67275 + 0.449358i) q^{33} +(-2.14510 + 3.71542i) q^{34} +5.43991 q^{35} +(-3.11535 + 1.80397i) q^{36} +9.73779 q^{37} +(0.314002 - 0.543868i) q^{38} +(2.57445 - 9.63265i) q^{39} +(-5.36505 - 9.29255i) q^{40} +(-2.12380 - 3.67853i) q^{41} +(-0.580431 + 2.17176i) q^{42} +(2.05278 - 3.55552i) q^{43} -1.19999 q^{44} +(9.73280 - 5.63586i) q^{45} +1.47675 q^{46} +(-0.898274 + 1.55586i) q^{47} +(0.267726 - 0.0719207i) q^{48} +(2.44722 + 4.23870i) q^{49} +(4.04932 + 7.01363i) q^{50} +(-5.87831 - 5.87079i) q^{51} +(3.45393 - 5.98239i) q^{52} -1.15318 q^{53} +(1.21151 + 4.48693i) q^{54} +3.74893 q^{55} +(-2.07659 + 3.59676i) q^{56} +(0.860475 + 0.859374i) q^{57} +(-1.92552 - 3.33509i) q^{58} +(2.32552 + 4.02792i) q^{59} +(7.52513 - 2.02152i) q^{60} +(-1.27447 + 2.20745i) q^{61} +2.95660 q^{62} +(-3.77274 - 2.17176i) q^{63} +5.31212 q^{64} +(-10.7906 + 18.6898i) q^{65} +(-0.400006 + 1.49667i) q^{66} +(-4.47062 - 7.74334i) q^{67} +(-2.87790 - 4.98467i) q^{68} +(-0.738375 + 2.76273i) q^{69} +(2.43282 - 4.21377i) q^{70} +5.14204 q^{71} +(0.0109909 + 8.58653i) q^{72} +10.5378 q^{73} +(4.35490 - 7.54291i) q^{74} +(-15.1458 + 4.06871i) q^{75} +(0.421271 + 0.729663i) q^{76} +(-0.725528 - 1.25665i) q^{77} +(-6.31013 - 6.30206i) q^{78} +(0.543371 - 0.941146i) q^{79} -0.600024 q^{80} +(-8.99997 + 0.0230402i) q^{81} -3.79920 q^{82} +(1.90171 - 3.29386i) q^{83} +(-2.13395 - 2.13122i) q^{84} +(8.99096 + 15.5728i) q^{85} +(-1.83608 - 3.18018i) q^{86} +(7.20210 - 1.93474i) q^{87} +(-1.43109 + 2.47872i) q^{88} -4.01536 q^{89} +(-0.0128763 - 10.0595i) q^{90} +8.35317 q^{91} +(-0.990617 + 1.71580i) q^{92} +(-1.47830 + 5.53125i) q^{93} +(0.803446 + 1.39161i) q^{94} +(-1.31611 - 2.27957i) q^{95} +(-2.49601 + 9.33913i) q^{96} +(-1.64550 + 2.85009i) q^{97} +4.37775 q^{98} +(-2.59999 - 1.49667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9	\( 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 7 q^{13} - q^{14} - q^{15} - 17 q^{16} - 10 q^{17} - 2 q^{18} + 18 q^{19} + 10 q^{20} - 13 q^{21} - q^{22} - 14 q^{23} + 18 q^{24} - 14 q^{25} + 44 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 37 q^{30} + 2 q^{31} + 34 q^{32} - 4 q^{33} - 16 q^{34} - 16 q^{35} + 11 q^{36} + 6 q^{37} - 3 q^{38} - 22 q^{39} - 12 q^{40} + 2 q^{41} - q^{42} + 21 q^{43} + 22 q^{44} + 49 q^{45} + 4 q^{46} + 7 q^{47} - 59 q^{48} + 15 q^{49} - 23 q^{50} - 31 q^{51} + 10 q^{52} - 12 q^{53} - 37 q^{54} + 8 q^{55} - 18 q^{56} + 33 q^{57} + 21 q^{58} - 2 q^{59} + 73 q^{60} - 15 q^{61} - 40 q^{62} - 5 q^{63} + 32 q^{64} - 19 q^{65} - 19 q^{66} - 14 q^{67} + 7 q^{68} - 2 q^{69} + 38 q^{70} - 6 q^{71} + 75 q^{72} + 44 q^{73} + 36 q^{74} + 10 q^{75} - 42 q^{76} - q^{77} + 29 q^{78} - 11 q^{79} - 68 q^{80} + 7 q^{81} - 34 q^{82} - 18 q^{83} + 34 q^{84} - 13 q^{85} + 24 q^{86} - 9 q^{87} - 12 q^{89} - 80 q^{90} + 38 q^{91} - 67 q^{92} + 20 q^{93} + 19 q^{94} + 30 q^{95} - 50 q^{96} - 26 q^{97} + 30 q^{98} - 5 q^{99}+O(q^{100}) \) 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 - 7 * q^13 - q^14 - q^15 - 17 * q^16 - 10 * q^17 - 2 * q^18 + 18 * q^19 + 10 * q^20 - 13 * q^21 - q^22 - 14 * q^23 + 18 * q^24 - 14 * q^25 + 44 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 37 * q^30 + 2 * q^31 + 34 * q^32 - 4 * q^33 - 16 * q^34 - 16 * q^35 + 11 * q^36 + 6 * q^37 - 3 * q^38 - 22 * q^39 - 12 * q^40 + 2 * q^41 - q^42 + 21 * q^43 + 22 * q^44 + 49 * q^45 + 4 * q^46 + 7 * q^47 - 59 * q^48 + 15 * q^49 - 23 * q^50 - 31 * q^51 + 10 * q^52 - 12 * q^53 - 37 * q^54 + 8 * q^55 - 18 * q^56 + 33 * q^57 + 21 * q^58 - 2 * q^59 + 73 * q^60 - 15 * q^61 - 40 * q^62 - 5 * q^63 + 32 * q^64 - 19 * q^65 - 19 * q^66 - 14 * q^67 + 7 * q^68 - 2 * q^69 + 38 * q^70 - 6 * q^71 + 75 * q^72 + 44 * q^73 + 36 * q^74 + 10 * q^75 - 42 * q^76 - q^77 + 29 * q^78 - 11 * q^79 - 68 * q^80 + 7 * q^81 - 34 * q^82 - 18 * q^83 + 34 * q^84 - 13 * q^85 + 24 * q^86 - 9 * q^87 - 12 * q^89 - 80 * q^90 + 38 * q^91 - 67 * q^92 + 20 * q^93 + 19 * q^94 + 30 * q^95 - 50 * q^96 - 26 * q^97 + 30 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.447217	−	0.774602i	0.316230	−	0.547727i	−0.663468	−	0.748205i	$-0.730916\pi$
$2$	0.447217	−	0.774602i	0.316230	−	0.547727i	0.979698	+	0.200478i	$0.0642495\pi$
$3$	1.22553	+	1.22396i	0.707559	+	0.706654i
$3$	1.22553	+	1.22396i	0.707559	+	0.706654i
$4$	0.599994	+	1.03922i	0.299997	+	0.519610i
$5$	−1.87447	−	3.24667i	−0.838287	−	1.45195i	−0.891326	−	0.453362i	$-0.850224\pi$
$5$	−1.87447	−	3.24667i	−0.838287	−	1.45195i	0.0530397	−	0.998592i	$-0.483109\pi$
$6$	1.49616	−	0.401921i	0.610805	−	0.164084i
$7$	−0.725528	+	1.25665i	−0.274224	+	0.474970i	−0.969939	−	0.243348i	$-0.921754\pi$
$7$	−0.725528	+	1.25665i	−0.274224	+	0.474970i	0.695715	+	0.718318i	$0.255088\pi$
$8$	2.86218			1.01193
$9$	0.00384004	+	3.00000i	0.00128001	+	0.999999i
$10$	−3.35317			−1.06037
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−0.536655	+	2.00796i	−0.154919	+	0.579649i
$13$	−2.87831	−	4.98537i	−0.798298	−	1.38269i	−0.920724	−	0.390216i	$-0.872400\pi$
$13$	−2.87831	−	4.98537i	−0.798298	−	1.38269i	0.122425	−	0.992478i	$-0.460933\pi$
$14$	0.648937	+	1.12399i	0.173436	+	0.300400i
$15$	1.67659	−	6.27316i	0.432892	−	1.61972i
$16$	0.0800260	−	0.138609i	0.0200065	−	0.0346523i
$17$	−4.79655			−1.16333			−0.581667	−	0.813427i	$-0.697599\pi$
$17$	−4.79655			−1.16333			−0.581667	+	0.813427i	$0.697599\pi$
$18$	2.32552	+	1.33868i	0.548131	+	0.315529i
$19$	0.702126			0.161079			0.0805393	−	0.996751i	$-0.474336\pi$
$19$	0.702126			0.161079			0.0805393	+	0.996751i	$0.474336\pi$
$20$	2.24934	−	3.89597i	0.502967	−	0.871164i
$21$	−2.42725	+	0.652045i	−0.529669	+	0.142288i
$22$	0.447217	+	0.774602i	0.0953470	+	0.165146i
$23$	0.825523	+	1.42985i	0.172133	+	0.298144i	0.939165	−	0.343465i	$-0.111601\pi$
$23$	0.825523	+	1.42985i	0.172133	+	0.298144i	−0.767032	+	0.641609i	$0.778267\pi$
$24$	3.50768	+	3.50319i	0.716002	+	0.715086i
$25$	−4.52724	+	7.84141i	−0.905449	+	1.56828i
$26$	−5.14891			−1.00978
$27$	−3.66717	+	3.68128i	−0.705748	+	0.708463i
$28$	−1.74125			−0.329066
$29$	2.15278	−	3.72872i	0.399761	−	0.692406i	−0.593935	−	0.804513i	$-0.702427\pi$
$29$	2.15278	−	3.72872i	0.399761	−	0.692406i	0.993696	+	0.112107i	$0.0357599\pi$
$30$	−4.10941	−	4.10415i	−0.750272	−	0.749312i
$31$	1.65278	+	2.86269i	0.296848	+	0.514155i	0.975413	−	0.220385i	$-0.0707313\pi$
$31$	1.65278	+	2.86269i	0.296848	+	0.514155i	−0.678565	+	0.734540i	$0.737398\pi$
$32$	2.79060	+	4.83346i	0.493313	+	0.854443i
$33$	−1.67275	+	0.449358i	−0.291188	+	0.0782233i
$34$	−2.14510	+	3.71542i	−0.367881	+	0.637189i
$35$	5.43991			0.919513
$36$	−3.11535	+	1.80397i	−0.519226	+	0.300662i
$37$	9.73779			1.60088			0.800441	−	0.599411i	$-0.204599\pi$
$37$	9.73779			1.60088			0.800441	+	0.599411i	$0.204599\pi$
$38$	0.314002	−	0.543868i	0.0509379	−	0.0882271i
$39$	2.57445	−	9.63265i	0.412243	−	1.54246i
$40$	−5.36505	−	9.29255i	−0.848289	−	1.46928i
$41$	−2.12380	−	3.67853i	−0.331682	−	0.574490i	0.651160	−	0.758941i	$-0.274283\pi$
$41$	−2.12380	−	3.67853i	−0.331682	−	0.574490i	−0.982842	+	0.184450i	$0.940949\pi$
$42$	−0.580431	+	2.17176i	−0.0895625	+	0.335110i
$43$	2.05278	−	3.55552i	0.313046	−	0.542212i	−0.665974	−	0.745975i	$-0.731984\pi$
$43$	2.05278	−	3.55552i	0.313046	−	0.542212i	0.979020	+	0.203763i	$0.0653171\pi$
$44$	−1.19999			−0.180905
$45$	9.73280	−	5.63586i	1.45088	−	0.840144i
$46$	1.47675			0.217735
$47$	−0.898274	+	1.55586i	−0.131027	+	0.226945i	−0.924073	−	0.382217i	$-0.875161\pi$
$47$	−0.898274	+	1.55586i	−0.131027	+	0.226945i	0.793046	+	0.609162i	$0.208494\pi$
$48$	0.267726	−	0.0719207i	0.0386429	−	0.0103809i
$49$	2.44722	+	4.23870i	0.349602	+	0.605529i
$50$	4.04932	+	7.01363i	0.572660	+	0.991877i
$51$	−5.87831	−	5.87079i	−0.823127	−	0.822074i
$52$	3.45393	−	5.98239i	0.478974	−	0.829608i
$53$	−1.15318			−0.158402			−0.0792009	−	0.996859i	$-0.525237\pi$
$53$	−1.15318			−0.158402			−0.0792009	+	0.996859i	$0.525237\pi$
$54$	1.21151	+	4.48693i	0.164865	+	0.610594i
$55$	3.74893			0.505506
$56$	−2.07659	+	3.59676i	−0.277496	+	0.480637i
$57$	0.860475	+	0.859374i	0.113973	+	0.113827i
$58$	−1.92552	−	3.33509i	−0.252833	−	0.437919i
$59$	2.32552	+	4.02792i	0.302757	+	0.524391i	0.976759	−	0.214338i	$-0.0687595\pi$
$59$	2.32552	+	4.02792i	0.302757	+	0.524391i	−0.674002	+	0.738729i	$0.735426\pi$
$60$	7.52513	−	2.02152i	0.971491	−	0.260977i
$61$	−1.27447	+	2.20745i	−0.163179	+	0.282635i	−0.936007	−	0.351981i	$-0.885508\pi$
$61$	−1.27447	+	2.20745i	−0.163179	+	0.282635i	0.772828	+	0.634616i	$0.218842\pi$
$62$	2.95660			0.375489
$63$	−3.77274	−	2.17176i	−0.475320	−	0.273616i
$64$	5.31212			0.664015
$65$	−10.7906	+	18.6898i	−1.33841	+	2.31819i
$66$	−0.400006	+	1.49667i	−0.0492373	+	0.184228i
$67$	−4.47062	−	7.74334i	−0.546173	−	0.946000i	−0.998532	−	0.0541636i	$-0.982751\pi$
$67$	−4.47062	−	7.74334i	−0.546173	−	0.946000i	0.452359	−	0.891836i	$-0.350583\pi$
$68$	−2.87790	−	4.98467i	−0.348997	−	0.604480i
$69$	−0.738375	+	2.76273i	−0.0888899	+	0.332593i
$70$	2.43282	−	4.21377i	0.290778	−	0.503642i
$71$	5.14204			0.610248			0.305124	−	0.952313i	$-0.401302\pi$
$71$	5.14204			0.610248			0.305124	+	0.952313i	$0.401302\pi$
$72$	0.0109909	+	8.58653i	0.00129529	+	1.01193i
$73$	10.5378			1.23336			0.616678	−	0.787215i	$-0.288478\pi$
$73$	10.5378			1.23336			0.616678	+	0.787215i	$0.288478\pi$
$74$	4.35490	−	7.54291i	0.506247	−	0.876846i
$75$	−15.1458	+	4.06871i	−1.74889	+	0.469814i
$76$	0.421271	+	0.729663i	0.0483231	+	0.0836981i
$77$	−0.725528	−	1.25665i	−0.0826816	−	0.143209i
$78$	−6.31013	−	6.30206i	−0.714482	−	0.713568i
$79$	0.543371	−	0.941146i	0.0611340	−	0.105887i	−0.833839	−	0.552008i	$-0.813862\pi$
$79$	0.543371	−	0.941146i	0.0611340	−	0.105887i	0.894973	+	0.446121i	$0.147195\pi$
$80$	−0.600024			−0.0670847
$81$	−8.99997	+	0.0230402i	−0.999997	+	0.00256002i
$82$	−3.79920			−0.419552
$83$	1.90171	−	3.29386i	0.208740	−	0.361548i	−0.742578	−	0.669759i	$-0.766397\pi$
$83$	1.90171	−	3.29386i	0.208740	−	0.361548i	0.951318	+	0.308212i	$0.0997305\pi$
$84$	−2.13395	−	2.13122i	−0.232833	−	0.232536i
$85$	8.99096	+	15.5728i	0.975207	+	1.68911i
$86$	−1.83608	−	3.18018i	−0.197989	−	0.342928i
$87$	7.20210	−	1.93474i	0.772146	−	0.207426i
$88$	−1.43109	+	2.47872i	−0.152555	+	0.264232i
$89$	−4.01536			−0.425627			−0.212814	−	0.977093i	$-0.568263\pi$
$89$	−4.01536			−0.425627			−0.212814	+	0.977093i	$0.568263\pi$
$90$	−0.0128763	−	10.0595i	−0.00135728	−	1.06036i
$91$	8.35317			0.875650
$92$	−0.990617	+	1.71580i	−0.103279	+	0.178884i
$93$	−1.47830	+	5.53125i	−0.153293	+	0.573564i
$94$	0.803446	+	1.39161i	0.0828692	+	0.143534i
$95$	−1.31611	−	2.27957i	−0.135030	−	0.233879i
$96$	−2.49601	+	9.33913i	−0.254748	+	0.953171i
$97$	−1.64550	+	2.85009i	−0.167075	+	0.289383i	−0.937390	−	0.348280i	$-0.886766\pi$
$97$	−1.64550	+	2.85009i	−0.167075	+	0.289383i	0.770315	+	0.637664i	$0.220099\pi$
$98$	4.37775			0.442219
$99$	−2.59999	−	1.49667i	−0.261309	−	0.150421i
$100$	−10.8653			−1.08653
$101$	−7.09653	+	12.2916i	−0.706131	+	1.22305i	0.260151	+	0.965568i	$0.416228\pi$
$101$	−7.09653	+	12.2916i	−0.706131	+	1.22305i	−0.966282	+	0.257487i	$0.917106\pi$
$102$	−7.17640	+	1.92783i	−0.710570	+	0.190884i
$103$	−9.58885	−	16.6084i	−0.944817	−	1.63647i	−0.756116	−	0.654437i	$-0.772906\pi$
$103$	−9.58885	−	16.6084i	−0.944817	−	1.63647i	−0.188701	−	0.982035i	$-0.560428\pi$
$104$	−8.23822	−	14.2690i	−0.807824	−	1.39919i
$105$	6.66677	+	6.65824i	0.650610	+	0.649778i
$106$	−0.515723	+	0.893258i	−0.0500914	+	0.0867609i
$107$	−10.0034			−0.967066			−0.483533	−	0.875326i	$-0.660647\pi$
$107$	−10.0034			−0.967066			−0.483533	+	0.875326i	$0.660647\pi$
$108$	−6.02595	−	1.60225i	−0.579847	−	0.154177i
$109$	−7.40766			−0.709525			−0.354762	−	0.934956i	$-0.615438\pi$
$109$	−7.40766			−0.709525			−0.354762	+	0.934956i	$0.615438\pi$
$110$	1.67659	−	2.90393i	0.159856	−	0.276879i
$111$	11.9339	+	11.9187i	1.13272	+	1.13127i
$112$	0.116122	+	0.201130i	0.0109725	+	0.0190050i
$113$	−0.821683	−	1.42320i	−0.0772974	−	0.133883i	0.824786	−	0.565446i	$-0.191296\pi$
$113$	−0.821683	−	1.42320i	−0.0772974	−	0.133883i	−0.902083	+	0.431563i	$0.857962\pi$
$114$	1.05049	−	0.282199i	0.0983876	−	0.0264304i
$115$	3.09483	−	5.36040i	0.288594	−	0.499860i
$116$	5.16661			0.479708
$117$	14.9450	−	8.65405i	1.38167	−	0.800068i
$118$	4.16005			0.382964
$119$	3.48003	−	6.02759i	0.319014	−	0.552548i
$120$	4.79869	−	17.9549i	0.438058	−	1.63905i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.13993	+	1.97442i	0.103204	+	0.178755i
$123$	1.89960	−	7.10760i	0.171281	−	0.640871i
$124$	−1.98331	+	3.43520i	−0.178107	+	0.308490i
$125$	15.2000			1.35953
$126$	−3.36948	+	1.95113i	−0.300177	+	0.173820i
$127$	−22.3309			−1.98155			−0.990773	−	0.135534i	$-0.956725\pi$
$127$	−22.3309			−1.98155			−0.990773	+	0.135534i	$0.956725\pi$
$128$	−3.20553	+	5.55214i	−0.283332	+	0.490745i
$129$	6.86757	−	1.84487i	0.604656	−	0.162432i
$130$	9.65145	+	16.7168i	0.846488	+	1.46616i
$131$	4.89443	+	8.47741i	0.427629	+	0.740675i	0.996662	−	0.0816400i	$-0.0260158\pi$
$131$	4.89443	+	8.47741i	0.427629	+	0.740675i	−0.569033	+	0.822315i	$0.692682\pi$
$132$	−1.47062	−	1.46874i	−0.128001	−	0.127837i
$133$	−0.509412	+	0.882328i	−0.0441716	+	0.0765075i
$134$	−7.99735			−0.690866
$135$	18.8259	+	5.00566i	1.62028	+	0.430819i
$136$	−13.7286			−1.17722
$137$	1.18811	−	2.05786i	0.101507	−	0.175815i	−0.810799	−	0.585325i	$-0.800967\pi$
$137$	1.18811	−	2.05786i	0.101507	−	0.175815i	0.912306	+	0.409510i	$0.134300\pi$
$138$	1.80980	+	1.80748i	0.154060	+	0.153863i
$139$	5.74336	+	9.94779i	0.487145	+	0.843761i	0.999891	−	0.0147802i	$-0.00470485\pi$
$139$	5.74336	+	9.94779i	0.487145	+	0.843761i	−0.512745	+	0.858541i	$0.671372\pi$
$140$	3.26392	+	5.65327i	0.275851	+	0.477788i
$141$	−3.00517	+	0.807294i	−0.253081	+	0.0679864i
$142$	2.29961	−	3.98304i	0.192979	−	0.334249i
$143$	5.75661			0.481392
$144$	0.416134	+	0.239545i	0.0346778	+	0.0199621i
$145$	−16.1412			−1.34046
$146$	4.71268	−	8.16260i	0.390024	−	0.675542i
$147$	−2.18887	+	8.18995i	−0.180535	+	0.675496i
$148$	5.84261	+	10.1197i	0.480260	+	0.831835i
$149$	0.350657	+	0.607357i	0.0287270	+	0.0497566i	0.880031	−	0.474915i	$-0.157521\pi$
$149$	0.350657	+	0.607357i	0.0287270	+	0.0497566i	−0.851305	+	0.524672i	$0.824188\pi$
$150$	−3.62185	+	13.5516i	−0.295723	+	1.10648i
$151$	1.25277	−	2.16986i	0.101949	−	0.176581i	−0.810539	−	0.585685i	$-0.800825\pi$
$151$	1.25277	−	2.16986i	0.101949	−	0.176581i	0.912488	+	0.409104i	$0.134159\pi$
$152$	2.00961			0.163001
$153$	−0.0184189	−	14.3896i	−0.00148908	−	1.16333i
$154$	−1.29787			−0.104586
$155$	6.19615	−	10.7320i	0.497687	−	0.862018i
$156$	11.5551	−	3.10411i	0.925148	−	0.248527i
$157$	−2.21785	−	3.84143i	−0.177004	−	0.306579i	0.763849	−	0.645395i	$-0.223307\pi$
$157$	−2.21785	−	3.84143i	−0.177004	−	0.306579i	−0.940853	+	0.338816i	$0.889974\pi$
$158$	−0.486009	−	0.841793i	−0.0386648	−	0.0669694i
$159$	−1.41326	−	1.41145i	−0.112079	−	0.111935i
$160$	10.4618	−	18.1203i	0.827075	−	1.43254i
$161$	−2.39576			−0.188812
$162$	−4.00709	+	6.98170i	−0.314827	+	0.548534i
$163$	17.6986			1.38626			0.693131	−	0.720812i	$-0.256231\pi$
$163$	17.6986			1.38626			0.693131	+	0.720812i	$0.256231\pi$
$164$	2.54854	−	4.41420i	0.199007	−	0.344691i
$165$	4.59442	+	4.58854i	0.357675	+	0.357218i
$166$	−1.70095	−	2.94614i	−0.132020	−	0.228664i
$167$	4.45065	+	7.70875i	0.344402	+	0.596521i	0.985245	−	0.171151i	$-0.0547484\pi$
$167$	4.45065	+	7.70875i	0.344402	+	0.596521i	−0.640843	+	0.767672i	$0.721415\pi$
$168$	−6.94722	+	1.86627i	−0.535989	+	0.143986i
$169$	−10.0693	+	17.4405i	−0.774561	+	1.34158i
$170$	16.0836			1.23356
$171$	0.00269619	+	2.10638i	0.000206183	+	0.161079i
$172$	4.92663			0.375652
$173$	12.3654	−	21.4176i	0.940126	−	1.62835i	0.174899	−	0.984586i	$-0.444040\pi$
$173$	12.3654	−	21.4176i	0.940126	−	1.62835i	0.765228	−	0.643760i	$-0.222626\pi$
$174$	1.72225	−	6.44401i	0.130563	−	0.488519i
$175$	−6.56929	−	11.3783i	−0.496591	−	0.860122i
$176$	0.0800260	+	0.138609i	0.00603218	+	0.0104480i
$177$	−2.08003	+	7.78268i	−0.156344	+	0.584982i
$178$	−1.79574	+	3.11031i	−0.134596	+	0.233127i
$179$	−11.8587			−0.886362			−0.443181	−	0.896432i	$-0.646150\pi$
$179$	−11.8587			−0.886362			−0.443181	+	0.896432i	$0.646150\pi$
$180$	11.6965	+	6.73304i	0.871807	+	0.501851i
$181$	−4.94546			−0.367593			−0.183796	−	0.982964i	$-0.558839\pi$
$181$	−4.94546			−0.367593			−0.183796	+	0.982964i	$0.558839\pi$
$182$	3.73568	−	6.47039i	0.276907	−	0.479617i
$183$	−4.26373	+	1.14539i	−0.315184	+	0.0846696i
$184$	2.36279	+	4.09248i	0.174187	+	0.301701i
$185$	−18.2531	−	31.6154i	−1.34200	−	2.32441i
$186$	3.62340	+	3.61876i	0.265680	+	0.265340i
$187$	2.39827	−	4.15393i	0.175379	−	0.303766i
$188$	−2.15584			−0.157230
$189$	−1.96545	−	7.27924i	−0.142966	−	0.529487i
$190$	−2.35435			−0.170802
$191$	−0.161784	+	0.280218i	−0.0117063	+	0.0202759i	−0.871819	−	0.489828i	$-0.837060\pi$
$191$	−0.161784	+	0.280218i	−0.0117063	+	0.0202759i	0.860113	+	0.510104i	$0.170393\pi$
$192$	6.51015	+	6.50182i	0.469830	+	0.469229i
$193$	−7.20767	−	12.4840i	−0.518819	−	0.898621i	−0.999761	−	0.0218687i	$-0.993038\pi$
$193$	−7.20767	−	12.4840i	−0.518819	−	0.898621i	0.480942	−	0.876753i	$-0.340295\pi$
$194$	1.47179	+	2.54922i	0.105669	+	0.183023i
$195$	−36.0998	+	9.69767i	−2.58516	+	0.694464i
$196$	−2.93663	+	5.08639i	−0.209759	+	0.363314i
$197$	−18.3267			−1.30572			−0.652860	−	0.757478i	$-0.726431\pi$
$197$	−18.3267			−1.30572			−0.652860	+	0.757478i	$0.726431\pi$
$198$	−2.32209	+	1.34462i	−0.165024	+	0.0955583i
$199$	−1.51211			−0.107190			−0.0535951	−	0.998563i	$-0.517068\pi$
$199$	−1.51211			−0.107190			−0.0535951	+	0.998563i	$0.517068\pi$
$200$	−12.9578	+	22.4435i	−0.916253	+	1.58700i
$201$	3.99867	−	14.9615i	0.282045	−	1.05531i
$202$	6.34738	+	10.9940i	0.446600	+	0.773534i
$203$	3.12380	+	5.41058i	0.219248	+	0.379749i
$204$	2.57409	−	9.63129i	0.180222	−	0.674325i
$205$	−7.96199	+	13.7906i	−0.556089	+	0.963175i
$206$	−17.1532			−1.19512
$207$	−4.28637	+	2.48206i	−0.297923	+	0.172515i
$208$	−0.921357			−0.0638846
$209$	−0.351063	+	0.608059i	−0.0242835	+	0.0420603i
$210$	8.13898	−	2.18642i	0.561643	−	0.150877i
$211$	5.51111	+	9.54553i	0.379401	+	0.657141i	0.990975	−	0.134045i	$-0.0427968\pi$
$211$	5.51111	+	9.54553i	0.379401	+	0.657141i	−0.611574	+	0.791187i	$0.709463\pi$
$212$	−0.691903	−	1.19841i	−0.0475201	−	0.0823072i
$213$	6.30171	+	6.29365i	0.431786	+	0.431234i
$214$	−4.47369	+	7.74866i	−0.305815	+	0.529688i
$215$	−15.3915			−1.04969
$216$	−10.4961	+	10.5365i	−0.714169	+	0.716917i
$217$	−4.79655			−0.325611
$218$	−3.31283	+	5.73799i	−0.224373	+	0.388626i
$219$	12.9144	+	12.8979i	0.872672	+	0.871556i
$220$	2.24934	+	3.89597i	0.151650	+	0.262666i
$221$	13.8059	+	23.9126i	0.928687	+	1.60853i
$222$	14.5693	−	3.91382i	0.977827	−	0.262679i
$223$	11.6566	−	20.1899i	0.780585	−	1.35201i	−0.151017	−	0.988531i	$-0.548255\pi$
$223$	11.6566	−	20.1899i	0.780585	−	1.35201i	0.931601	−	0.363481i	$-0.118412\pi$
$224$	−8.09864			−0.541113
$225$	−23.5416	−	13.5516i	−1.56944	−	0.903440i
$226$	−1.46988			−0.0977750
$227$	−2.98944	+	5.17787i	−0.198416	+	0.343667i	−0.948015	−	0.318225i	$-0.896913\pi$
$227$	−2.98944	+	5.17787i	−0.198416	+	0.343667i	0.749599	+	0.661893i	$0.230246\pi$
$228$	−0.376799	+	1.40984i	−0.0249541	+	0.0933691i
$229$	−4.71228	−	8.16190i	−0.311396	−	0.539354i	0.667269	−	0.744817i	$-0.267463\pi$
$229$	−4.71228	−	8.16190i	−0.311396	−	0.539354i	−0.978665	+	0.205463i	$0.934130\pi$
$230$	−2.76812	−	4.79452i	−0.182524	−	0.316141i
$231$	0.648937	−	2.42808i	0.0426969	−	0.159756i
$232$	6.16163	−	10.6723i	0.404531	−	0.700668i
$233$	27.1685			1.77987			0.889933	−	0.456091i	$-0.150751\pi$
$233$	27.1685			1.77987			0.889933	+	0.456091i	$0.150751\pi$
$234$	−0.0197720	−	15.4467i	−0.00129254	−	1.00978i
$235$	6.73513			0.439352
$236$	−2.79060	+	4.83346i	−0.181653	+	0.314631i
$237$	1.81784	−	0.488337i	0.118082	−	0.0317209i
$238$	−3.11266	−	5.39128i	−0.201764	−	0.349465i
$239$	−0.121289	−	0.210079i	−0.00784553	−	0.0135889i	0.862076	−	0.506779i	$-0.169164\pi$
$239$	−0.121289	−	0.210079i	−0.00784553	−	0.0135889i	−0.869922	+	0.493190i	$0.835831\pi$
$240$	−0.735346	−	0.734405i	−0.0474664	−	0.0474057i
$241$	6.35528	−	11.0077i	0.409379	−	0.709066i	−0.585441	−	0.810715i	$-0.699079\pi$
$241$	6.35528	−	11.0077i	0.409379	−	0.709066i	0.994820	+	0.101649i	$0.0324119\pi$
$242$	−0.894434			−0.0574964
$243$	−11.0579	−	10.9874i	−0.709366	−	0.704840i
$244$	−3.05870			−0.195813
$245$	9.17445	−	15.8906i	0.586134	−	1.01521i
$246$	−4.65603	−	4.65007i	−0.296858	−	0.296478i
$247$	−2.02093	−	3.50036i	−0.128589	−	0.222722i
$248$	4.73054	+	8.19354i	0.300390	+	0.520290i
$249$	6.36215	−	1.70910i	0.403185	−	0.108310i
$250$	6.79769	−	11.7739i	0.429924	−	0.744650i
$251$	23.6134			1.49046			0.745232	−	0.666805i	$-0.232339\pi$
$251$	23.6134			1.49046			0.745232	+	0.666805i	$0.232339\pi$
$252$	−0.00668647	−	5.22375i	−0.000421208	−	0.329065i
$253$	−1.65105			−0.103800
$254$	−9.98675	+	17.2976i	−0.626624	+	1.08535i
$255$	−8.04182	+	30.0895i	−0.503598	+	1.88428i
$256$	8.17925	+	14.1669i	0.511203	+	0.885430i
$257$	−2.05836	−	3.56518i	−0.128397	−	0.222390i	0.794659	−	0.607056i	$-0.207650\pi$
$257$	−2.05836	−	3.56518i	−0.128397	−	0.222390i	−0.923056	+	0.384667i	$0.874316\pi$
$258$	1.64225	−	6.14469i	0.102242	−	0.382552i
$259$	−7.06504	+	12.2370i	−0.439000	+	0.760371i
$260$	−25.8971			−1.60607
$261$	11.1944	+	6.44401i	0.692917	+	0.398874i
$262$	8.75549			0.540916
$263$	5.79614	−	10.0392i	0.357405	−	0.619044i	−0.630121	−	0.776497i	$-0.716995\pi$
$263$	5.79614	−	10.0392i	0.357405	−	0.619044i	0.987527	+	0.157452i	$0.0503281\pi$
$264$	−4.78769	+	1.28614i	−0.294662	+	0.0791567i
$265$	2.16160	+	3.74400i	0.132786	+	0.229992i
$266$	0.455635	+	0.789184i	0.0279368	+	0.0483880i
$267$	−4.92094	−	4.91464i	−0.301157	−	0.300771i
$268$	5.36469	−	9.29192i	0.327701	−	0.567594i
$269$	−6.82534			−0.416148			−0.208074	−	0.978113i	$-0.566720\pi$
$269$	−6.82534			−0.416148			−0.208074	+	0.978113i	$0.566720\pi$
$270$	12.2967	−	12.3440i	0.748351	−	0.751230i
$271$	−7.57539			−0.460172			−0.230086	−	0.973170i	$-0.573901\pi$
$271$	−7.57539			−0.460172			−0.230086	+	0.973170i	$0.573901\pi$
$272$	−0.383848	+	0.664845i	−0.0232742	+	0.0403121i
$273$	10.2370	+	10.2240i	0.619574	+	0.618782i
$274$	−1.06268	−	1.84062i	−0.0641989	−	0.111196i
$275$	−4.52724	−	7.84141i	−0.273003	−	0.472855i
$276$	−3.31410	+	0.890284i	−0.199485	+	0.0535888i
$277$	9.40168	−	16.2842i	0.564892	−	0.978422i	−0.432168	−	0.901793i	$-0.642251\pi$
$277$	9.40168	−	16.2842i	0.564892	−	0.978422i	0.997060	−	0.0766286i	$-0.0244156\pi$
$278$	10.2741			0.616200
$279$	−8.58173	+	4.96932i	−0.513775	+	0.297505i
$280$	15.5700			0.930485
$281$	−12.4416	+	21.5495i	−0.742205	+	1.28554i	0.209285	+	0.977855i	$0.432886\pi$
$281$	−12.4416	+	21.5495i	−0.742205	+	1.28554i	−0.951489	+	0.307681i	$0.900447\pi$
$282$	−0.718630	+	2.68884i	−0.0427938	+	0.160118i
$283$	9.07061	+	15.7108i	0.539192	+	0.933908i	0.998948	+	0.0458626i	$0.0146036\pi$
$283$	9.07061	+	15.7108i	0.539192	+	0.933908i	−0.459756	+	0.888045i	$0.652063\pi$
$284$	3.08519	+	5.34371i	0.183073	+	0.317091i
$285$	1.17717	−	4.40455i	0.0697297	−	0.260903i
$286$	2.57445	−	4.45908i	0.152231	−	0.263671i
$287$	6.16352			0.363821
$288$	−14.4897	+	8.39035i	−0.853811	+	0.494406i
$289$	6.00687			0.353345
$290$	−7.21863	+	12.5030i	−0.423893	+	0.734203i
$291$	−5.50501	+	1.47884i	−0.322710	+	0.0866912i
$292$	6.32262	+	10.9511i	0.370003	+	0.640864i
$293$	8.03876	+	13.9235i	0.469630	+	0.813422i	0.999397	−	0.0347207i	$-0.0110542\pi$
$293$	8.03876	+	13.9235i	0.469630	+	0.813422i	−0.529768	+	0.848143i	$0.677721\pi$
$294$	5.36505	+	5.35819i	0.312896	+	0.312496i
$295$	8.71822	−	15.1004i	0.507595	−	0.879180i
$296$	27.8713			1.61998
$297$	−1.35450	−	5.01651i	−0.0785959	−	0.291087i
$298$	0.627280			0.0363373
$299$	4.75221	−	8.23107i	0.274828	−	0.476015i
$300$	−13.3157	−	13.2987i	−0.768783	−	0.767799i
$301$	2.97871	+	5.15927i	0.171690	+	0.297375i
$302$	−1.12052	−	1.94080i	−0.0644787	−	0.111680i
$303$	−23.7414	+	6.37777i	−1.36391	+	0.366393i
$304$	0.0561883	−	0.0973209i	0.00322262	−	0.00558174i
$305$	9.55581			0.547164
$306$	−11.1545	−	6.42102i	−0.637659	−	0.367065i
$307$	−20.1343			−1.14913			−0.574563	−	0.818461i	$-0.694828\pi$
$307$	−20.1343			−1.14913			−0.574563	+	0.818461i	$0.694828\pi$
$308$	0.870626	−	1.50797i	0.0496085	−	0.0859244i
$309$	8.57659	−	32.0904i	0.487905	−	1.82556i
$310$	−5.54204	−	9.59910i	−0.314767	−	0.545192i
$311$	6.51226	+	11.2796i	0.369276	+	0.639605i	0.989453	−	0.144857i	$-0.0462723\pi$
$311$	6.51226	+	11.2796i	0.369276	+	0.639605i	−0.620176	+	0.784462i	$0.712939\pi$
$312$	7.36854	−	27.5703i	0.417162	−	1.56086i
$313$	−5.12591	+	8.87834i	−0.289734	+	0.501833i	−0.973746	−	0.227637i	$-0.926900\pi$
$313$	−5.12591	+	8.87834i	−0.289734	+	0.501833i	0.684012	+	0.729470i	$0.260233\pi$
$314$	−3.96744			−0.223895
$315$	0.0208895	+	16.3197i	0.00117699	+	0.919512i
$316$	1.30408			0.0733601
$317$	5.50882	−	9.54156i	0.309406	−	0.535908i	−0.668826	−	0.743419i	$-0.733203\pi$
$317$	5.50882	−	9.54156i	0.309406	−	0.535908i	0.978233	+	0.207511i	$0.0665363\pi$
$318$	−1.72535	+	0.463489i	−0.0967526	+	0.0259912i
$319$	2.15278	+	3.72872i	0.120532	+	0.208768i
$320$	−9.95738	−	17.2467i	−0.556635	−	0.964119i
$321$	−12.2595	−	12.2438i	−0.684256	−	0.683381i
$322$	−1.07142	+	1.85576i	−0.0597082	+	0.103418i
$323$	−3.36778			−0.187388
$324$	−5.42387	−	9.33913i	−0.301326	−	0.518840i
$325$	52.1232			2.89127
$326$	7.91511	−	13.7094i	0.438378	−	0.759292i
$327$	−9.07829	−	9.06668i	−0.502031	−	0.501389i
$328$	−6.07870	−	10.5286i	−0.335640	−	0.581346i
$329$	−1.30345	−	2.25764i	−0.0718613	−	0.124467i
$330$	5.60900	−	1.50678i	0.308765	−	0.0829453i
$331$	9.07216	−	15.7134i	0.498651	−	0.863689i	−0.501348	−	0.865246i	$-0.667162\pi$
$331$	9.07216	−	15.7134i	0.498651	−	0.863689i	0.999999	+	0.00155679i	$0.000495541\pi$
$332$	4.56406			0.250485
$333$	0.0373935	+	29.2133i	0.00204915	+	1.60088i
$334$	7.96163			0.435641
$335$	−16.7600	+	29.0293i	−0.915699	+	1.58604i
$336$	−0.103864	+	0.388619i	−0.00566623	+	0.0212009i
$337$	0.839543	+	1.45413i	0.0457328	+	0.0792115i	0.887986	−	0.459871i	$-0.152104\pi$
$337$	0.839543	+	1.45413i	0.0457328	+	0.0792115i	−0.842253	+	0.539083i	$0.818771\pi$
$338$	9.00631	+	15.5994i	0.489879	+	0.848495i
$339$	0.734941	−	2.74987i	0.0399165	−	0.149353i
$340$	−10.7891	+	18.6872i	−0.585118	+	1.01345i
$341$	−3.30555			−0.179006
$342$	1.63281	+	0.939918i	0.0882922	+	0.0508250i
$343$	−17.2595			−0.931925
$344$	5.87543	−	10.1765i	0.316782	−	0.548682i
$345$	10.3537	−	2.78137i	0.557425	−	0.149744i
$346$	−11.0601	−	19.1566i	−0.594592	−	1.02986i
$347$	9.39059	+	16.2650i	0.504113	+	0.873150i	0.999989	+	0.00475637i	$0.00151401\pi$
$347$	9.39059	+	16.2650i	0.504113	+	0.873150i	−0.495875	+	0.868394i	$0.665153\pi$
$348$	6.33183	+	6.32373i	0.339422	+	0.338988i
$349$	−16.2545	+	28.1536i	−0.870082	+	1.50703i	−0.00817109	+	0.999967i	$0.502601\pi$
$349$	−16.2545	+	28.1536i	−0.870082	+	1.50703i	−0.861911	+	0.507060i	$0.830732\pi$
$350$	−11.7516			−0.628149
$351$	28.9078	+	7.68637i	1.54298	+	0.410268i
$352$	−5.58120			−0.297479
$353$	−3.35487	+	5.81081i	−0.178562	+	0.309278i	−0.941388	−	0.337325i	$-0.890478\pi$
$353$	−3.35487	+	5.81081i	−0.178562	+	0.309278i	0.762826	+	0.646603i	$0.223811\pi$
$354$	5.09826	+	5.09174i	0.270970	+	0.270623i
$355$	−9.63857	−	16.6945i	−0.511562	−	0.886052i
$356$	−2.40919	−	4.17284i	−0.127687	−	0.221160i
$357$	11.6424	−	3.12756i	0.616182	−	0.165528i
$358$	−5.30342	+	9.18579i	−0.280294	+	0.485484i
$359$	14.7797			0.780040			0.390020	−	0.920806i	$-0.372468\pi$
$359$	14.7797			0.780040			0.390020	+	0.920806i	$0.372468\pi$
$360$	27.8570	−	16.1308i	1.46819	−	0.850169i
$361$	−18.5070			−0.974054
$362$	−2.21169	+	3.83076i	−0.116244	+	0.201340i
$363$	0.447217	−	1.67332i	0.0234728	−	0.0878265i
$364$	5.01185	+	8.68078i	0.262692	+	0.454997i
$365$	−19.7527	−	34.2128i	−1.03391	−	1.79078i
$366$	−1.01959	+	3.81493i	−0.0532949	+	0.199410i
$367$	−13.2934	+	23.0249i	−0.693912	+	1.20189i	0.276634	+	0.960975i	$0.410781\pi$
$367$	−13.2934	+	23.0249i	−0.693912	+	1.20189i	−0.970546	+	0.240916i	$0.922552\pi$
$368$	0.264253			0.0137751
$369$	11.0274	−	6.38553i	0.574065	−	0.332417i
$370$	−32.6525			−1.69752
$371$	0.836667	−	1.44915i	0.0434376	−	0.0752361i
$372$	−6.63516	+	1.78244i	−0.344017	+	0.0924150i
$373$	−11.7781	−	20.4003i	−0.609848	−	1.05629i	−0.991265	−	0.131885i	$-0.957897\pi$
$373$	−11.7781	−	20.4003i	−0.609848	−	1.05629i	0.381417	−	0.924403i	$-0.375436\pi$
$374$	−2.14510	−	3.71542i	−0.110920	−	0.192120i
$375$	18.6280	+	18.6042i	0.961947	+	0.960716i
$376$	−2.57102	+	4.45314i	−0.132590	+	0.229653i
$377$	−24.7854			−1.27651
$378$	−6.51750	−	1.73295i	−0.335224	−	0.0891335i
$379$	31.6536			1.62594			0.812969	−	0.582307i	$-0.197850\pi$
$379$	31.6536			1.62594			0.812969	+	0.582307i	$0.197850\pi$
$380$	1.57932	−	2.73546i	0.0810173	−	0.140326i
$381$	−27.3671	−	27.3321i	−1.40206	−	1.40027i
$382$	0.144705	+	0.250637i	0.00740375	+	0.0128237i
$383$	17.9220	+	31.0419i	0.915773	+	1.58616i	0.805766	+	0.592234i	$0.201754\pi$
$383$	17.9220	+	31.0419i	0.915773	+	1.58616i	0.110006	+	0.993931i	$0.464913\pi$
$384$	−10.7241	+	2.88086i	−0.547261	+	0.147013i
$385$	−2.71996	+	4.71110i	−0.138622	+	0.240100i
$386$	−12.8936			−0.656265
$387$	10.6744	+	6.14469i	0.542613	+	0.312352i
$388$	−3.94917			−0.200489
$389$	−1.96084	+	3.39628i	−0.0994188	+	0.172198i	−0.911444	−	0.411424i	$-0.865032\pi$
$389$	−1.96084	+	3.39628i	−0.0994188	+	0.172198i	0.812025	+	0.583622i	$0.198365\pi$
$390$	−8.63258	+	32.2999i	−0.437128	+	1.63557i
$391$	−3.95966	−	6.85833i	−0.200249	−	0.346841i
$392$	7.00437	+	12.1319i	0.353774	+	0.612755i
$393$	−4.37775	+	16.3799i	−0.220828	+	0.826257i
$394$	−8.19599	+	14.1959i	−0.412908	+	0.715178i
$395$	−4.07412			−0.204991
$396$	−0.00460800	−	3.59996i	−0.000231561	−	0.180905i
$397$	−3.90292			−0.195882			−0.0979411	−	0.995192i	$-0.531226\pi$
$397$	−3.90292			−0.195882			−0.0979411	+	0.995192i	$0.531226\pi$
$398$	−0.676239	+	1.17128i	−0.0338968	+	0.0587110i
$399$	−1.70423	+	0.457817i	−0.0853184	+	0.0229195i
$400$	0.724594	+	1.25503i	0.0362297	+	0.0627517i
$401$	−15.8378	−	27.4318i	−0.790900	−	1.36988i	−0.925411	−	0.378966i	$-0.876280\pi$
$401$	−15.8378	−	27.4318i	−0.790900	−	1.36988i	0.134511	−	0.990912i	$-0.457054\pi$
$402$	−9.80098	−	9.78844i	−0.488828	−	0.488203i
$403$	9.51440	−	16.4794i	0.473946	−	0.820898i
$404$	−17.0315			−0.847349
$405$	16.9449	+	29.1767i	0.842001	+	1.44980i
$406$	5.58807			0.277331
$407$	−4.86889	+	8.43317i	−0.241342	+	0.418017i
$408$	−16.8248	−	16.8032i	−0.832949	−	0.831884i
$409$	6.45815	+	11.1858i	0.319335	+	0.553104i	0.980349	−	0.197269i	$-0.0632072\pi$
$409$	6.45815	+	11.1858i	0.319335	+	0.553104i	−0.661015	+	0.750373i	$0.729874\pi$
$410$	7.12147	+	12.3348i	0.351704	+	0.609170i
$411$	3.97480	−	1.06777i	0.196062	−	0.0526692i
$412$	11.5065	−	19.9299i	0.566885	−	0.981873i
$413$	−6.74893			−0.332093
$414$	0.00567078	+	4.43025i	0.000278703	+	0.217735i
$415$	−14.2587			−0.699934
$416$	16.0644	−	27.8244i	0.787622	−	1.36420i
$417$	−5.13705	+	19.2209i	−0.251563	+	0.941254i
$418$	0.314002	+	0.543868i	0.0153584	+	0.0266015i
$419$	−13.6804	−	23.6951i	−0.668331	−	1.15758i	−0.978371	−	0.206860i	$-0.933676\pi$
$419$	−13.6804	−	23.6951i	−0.668331	−	1.15758i	0.310040	−	0.950724i	$-0.399658\pi$
$420$	−2.91936	+	10.9231i	−0.142450	+	0.532995i
$421$	9.78884	−	16.9548i	0.477079	−	0.826325i	−0.522576	−	0.852593i	$-0.675029\pi$
$421$	9.78884	−	16.9548i	0.477079	−	0.826325i	0.999655	+	0.0262679i	$0.00836230\pi$
$422$	9.85865			0.479912
$423$	−4.67101	−	2.68884i	−0.227112	−	0.130736i
$424$	−3.30061			−0.160292
$425$	21.7151	−	37.6117i	1.05334	−	1.82444i
$426$	7.69331	−	2.06669i	0.372742	−	0.100132i
$427$	−1.84933	−	3.20313i	−0.0894954	−	0.155011i
$428$	−6.00198	−	10.3957i	−0.290117	−	0.502497i
$429$	7.05489	+	7.04587i	0.340613	+	0.340178i
$430$	−6.88333	+	11.9223i	−0.331944	+	0.574943i
$431$	9.80495			0.472288			0.236144	−	0.971718i	$-0.424116\pi$
$431$	9.80495			0.472288			0.236144	+	0.971718i	$0.424116\pi$
$432$	0.216790	+	0.802901i	0.0104303	+	0.0386296i
$433$	−1.98391			−0.0953409			−0.0476704	−	0.998863i	$-0.515180\pi$
$433$	−1.98391			−0.0953409			−0.0476704	+	0.998863i	$0.515180\pi$
$434$	−2.14510	+	3.71542i	−0.102968	+	0.178346i
$435$	−19.7815	−	19.7562i	−0.948452	−	0.947239i
$436$	−4.44455	−	7.69819i	−0.212855	−	0.368676i
$437$	0.579621	+	1.00393i	0.0277270	+	0.0480246i
$438$	15.7662	−	4.23537i	0.753340	−	0.202374i
$439$	−17.5309	+	30.3644i	−0.836703	+	1.44921i	0.0559337	+	0.998434i	$0.482186\pi$
$439$	−17.5309	+	30.3644i	−0.836703	+	1.44921i	−0.892636	+	0.450777i	$0.851147\pi$
$440$	10.7301			0.511538
$441$	−12.7067	+	7.35792i	−0.605081	+	0.350377i
$442$	24.6970			1.17472
$443$	−11.8560	+	20.5353i	−0.563298	+	0.975660i	0.433908	+	0.900957i	$0.357134\pi$
$443$	−11.8560	+	20.5353i	−0.563298	+	0.975660i	−0.997206	+	0.0747032i	$0.976199\pi$
$444$	−5.22583	+	19.5531i	−0.248007	+	0.927950i
$445$	7.52665	+	13.0365i	0.356798	+	0.617992i
$446$	−10.4261	−	18.0585i	−0.493689	−	0.855094i
$447$	−0.313640	+	1.17352i	−0.0148347	+	0.0555058i
$448$	−3.85409	+	6.67548i	−0.182089	+	0.315387i
$449$	−11.6575			−0.550154			−0.275077	−	0.961422i	$-0.588703\pi$
$449$	−11.6575			−0.550154			−0.275077	+	0.961422i	$0.588703\pi$
$450$	−21.0253	+	12.1749i	−0.991143	+	0.573929i
$451$	4.24760			0.200012
$452$	0.986009	−	1.70782i	0.0463780	−	0.0803290i
$453$	4.19113	−	1.12589i	0.196917	−	0.0528988i
$454$	2.67386	+	4.63126i	0.125490	+	0.217356i
$455$	−15.6577	−	27.1200i	−0.734046	−	1.27140i
$456$	2.46283	+	2.45968i	0.115333	+	0.115185i
$457$	−6.60015	+	11.4318i	−0.308742	+	0.534757i	−0.978087	−	0.208195i	$-0.933241\pi$
$457$	−6.60015	+	11.4318i	−0.308742	+	0.534757i	0.669346	+	0.742951i	$0.266575\pi$
$458$	−8.42964			−0.393891
$459$	17.5898	−	17.6574i	0.821020	−	0.824179i
$460$	7.42751			0.346310
$461$	15.1456	−	26.2330i	0.705402	−	1.22179i	−0.261144	−	0.965300i	$-0.584100\pi$
$461$	15.1456	−	26.2330i	0.705402	−	1.22179i	0.966546	−	0.256493i	$-0.0825669\pi$
$462$	−1.59058	−	1.58855i	−0.0740006	−	0.0739059i
$463$	13.6059	+	23.5662i	0.632322	+	1.09521i	0.987076	+	0.160254i	$0.0512313\pi$
$463$	13.6059	+	23.5662i	0.632322	+	1.09521i	−0.354754	+	0.934960i	$0.615435\pi$
$464$	−0.344556	−	0.596789i	−0.0159956	−	0.0277052i
$465$	20.7292	−	5.56858i	0.961292	−	0.258237i
$466$	12.1502	−	21.0448i	0.562847	−	0.974880i
$467$	31.1873			1.44318			0.721588	−	0.692322i	$-0.243412\pi$
$467$	31.1873			1.44318			0.721588	+	0.692322i	$0.243412\pi$
$468$	17.9604	+	10.3388i	0.830220	+	0.477912i
$469$	12.9742			0.599095
$470$	3.01207	−	5.21705i	0.138936	−	0.240645i
$471$	1.98372	−	7.42234i	0.0914049	−	0.342003i
$472$	6.65606	+	11.5286i	0.306370	+	0.530648i
$473$	2.05278	+	3.55552i	0.0943871	+	0.163483i
$474$	0.434703	−	1.62650i	0.0199666	−	0.0747075i
$475$	−3.17869	+	5.50566i	−0.145848	+	0.252617i
$476$	8.35199			0.382813
$477$	−0.00442826	−	3.45954i	−0.000202756	−	0.158402i
$478$	−0.216970			−0.00992397
$479$	19.1386	−	33.1490i	0.874464	−	1.51462i	0.0171309	−	0.999853i	$-0.494547\pi$
$479$	19.1386	−	33.1490i	0.874464	−	1.51462i	0.857333	−	0.514762i	$-0.172120\pi$
$480$	34.9997	−	9.40217i	1.59751	−	0.429148i
$481$	−28.0283	−	48.5465i	−1.27798	−	2.21353i
$482$	−5.68438	−	9.84563i	−0.258916	−	0.448456i
$483$	−2.93607	−	2.93232i	−0.133596	−	0.133425i
$484$	0.599994	−	1.03922i	0.0272725	−	0.0472373i
$485$	12.3378			0.560228
$486$	−13.4561	+	3.65175i	−0.610383	+	0.165647i
$487$	−15.8602			−0.718697			−0.359348	−	0.933204i	$-0.617001\pi$
$487$	−15.8602			−0.718697			−0.359348	+	0.933204i	$0.617001\pi$
$488$	−3.64776	+	6.31811i	−0.165127	+	0.286008i
$489$	21.6901	+	21.6624i	0.980862	+	0.979607i
$490$	−8.20594	−	14.2131i	−0.370706	−	0.642082i
$491$	3.50114	+	6.06416i	0.158004	+	0.273672i	0.934149	−	0.356883i	$-0.116161\pi$
$491$	3.50114	+	6.06416i	0.158004	+	0.273672i	−0.776145	+	0.630555i	$0.782827\pi$
$492$	8.52611	−	2.29041i	0.384387	−	0.103260i
$493$	−10.3259	+	17.8850i	−0.465055	+	0.805499i
$494$	−3.61518			−0.162655
$495$	0.0143960	+	11.2468i	0.000647054	+	0.505505i
$496$	0.529060			0.0237555
$497$	−3.73070	+	6.46175i	−0.167345	+	0.289849i
$498$	1.52139	−	5.69247i	0.0681751	−	0.255086i
$499$	−12.3353	−	21.3653i	−0.552202	−	0.956443i	−0.998115	−	0.0613663i	$-0.980454\pi$
$499$	−12.3353	−	21.3653i	−0.552202	−	0.956443i	0.445913	−	0.895076i	$-0.352879\pi$
$500$	9.11990	+	15.7961i	0.407854	+	0.706425i
$501$	−3.98081	+	14.8947i	−0.177850	+	0.665447i
$502$	10.5603	−	18.2910i	0.471330	−	0.816367i
$503$	6.05183			0.269838			0.134919	−	0.990857i	$-0.456923\pi$
$503$	6.05183			0.269838			0.134919	+	0.990857i	$0.456923\pi$
$504$	−10.7983	−	6.21596i	−0.480992	−	0.276881i
$505$	53.2088			2.36776
$506$	−0.738375	+	1.27890i	−0.0328248	+	0.0568542i
$507$	−33.6867	+	9.04944i	−1.49608	+	0.401900i
$508$	−13.3984	−	23.2067i	−0.594458	−	1.02963i
$509$	10.0280	+	17.3690i	0.444482	+	0.769866i	0.998016	−	0.0629607i	$-0.0200543\pi$
$509$	10.0280	+	17.3690i	0.444482	+	0.769866i	−0.553534	+	0.832827i	$0.686721\pi$
$510$	19.7110	+	19.6857i	0.872816	+	0.871700i
$511$	−7.64547	+	13.2423i	−0.338216	+	0.585807i
$512$	1.80948			0.0799683
$513$	−2.57482	+	2.58472i	−0.113681	+	0.114118i
$514$	−3.68212			−0.162412
$515$	−35.9479	+	62.2637i	−1.58406	+	2.74366i
$516$	6.03773	+	6.03000i	0.265796	+	0.265456i
$517$	−0.898274	−	1.55586i	−0.0395060	−	0.0684265i
$518$	6.31921	+	10.9452i	0.277650	+	0.480904i
$519$	41.3684	−	11.1130i	1.81587	−	0.487807i
$520$	−30.8845	+	53.4936i	−1.35438	+	2.34585i
$521$	18.8721			0.826804			0.413402	−	0.910549i	$-0.364340\pi$
$521$	18.8721			0.826804			0.413402	+	0.910549i	$0.364340\pi$
$522$	9.99788	−	5.78935i	0.437595	−	0.253393i
$523$	−16.0568			−0.702114			−0.351057	−	0.936354i	$-0.614178\pi$
$523$	−16.0568			−0.702114			−0.351057	+	0.936354i	$0.614178\pi$
$524$	−5.87326	+	10.1728i	−0.256575	+	0.444400i
$525$	5.87579	−	21.9850i	0.256441	−	0.959505i
$526$	−5.18427	−	8.97941i	−0.226045	−	0.391521i
$527$	−7.92762	−	13.7310i	−0.345333	−	0.598134i
$528$	−0.0715779	+	0.267818i	−0.00311503	+	0.0116553i
$529$	10.1370	−	17.5578i	0.440740	−	0.763384i
$530$	3.86682			0.167964
$531$	−12.0748	+	6.99203i	−0.524003	+	0.303428i
$532$	−1.22258			−0.0530054
$533$	−12.2259	+	21.1759i	−0.529563	+	0.917230i
$534$	−6.00762	+	1.61386i	−0.259975	+	0.0698385i
$535$	18.7510	+	32.4778i	0.810678	+	1.40414i
$536$	−12.7957	−	22.1628i	−0.552690	−	0.957288i
$537$	−14.5332	−	14.5146i	−0.627153	−	0.626351i
$538$	−3.05241	+	5.28692i	−0.131599	+	0.227935i
$539$	−4.89443			−0.210818
$540$	6.09344	+	22.5676i	0.262220	+	0.971156i
$541$	18.4357			0.792614			0.396307	−	0.918118i	$-0.370292\pi$
$541$	18.4357			0.792614			0.396307	+	0.918118i	$0.370292\pi$
$542$	−3.38784	+	5.86791i	−0.145520	+	0.252048i
$543$	−6.06080	−	6.05304i	−0.260094	−	0.259761i
$544$	−13.3852	−	23.1839i	−0.573888	−	0.994002i
$545$	13.8854	+	24.0502i	0.594785	+	1.03020i
$546$	12.4977	−	3.35732i	0.534851	−	0.143680i
$547$	14.4834	−	25.0860i	0.619267	−	1.07260i	−0.370353	−	0.928891i	$-0.620763\pi$
$547$	14.4834	−	25.0860i	0.619267	−	1.07260i	0.989620	−	0.143711i	$-0.0459035\pi$
$548$	2.85143			0.121807
$549$	−6.62724	−	3.81493i	−0.282844	−	0.162817i
$550$	−8.09864			−0.345327
$551$	1.51152	−	2.61803i	0.0643929	−	0.111532i
$552$	−2.11336	+	7.90741i	−0.0899506	+	0.336562i
$553$	0.788462	+	1.36566i	0.0335288	+	0.0580736i
$554$	−8.40918	−	14.5651i	−0.357272	−	0.618813i
$555$	16.3262	−	61.0867i	0.693010	−	2.59299i
$556$	−6.89196	+	11.9372i	−0.292284	+	0.506251i
$557$	−11.7584			−0.498219			−0.249110	−	0.968475i	$-0.580138\pi$
$557$	−11.7584			−0.498219			−0.249110	+	0.968475i	$0.580138\pi$
$558$	0.0113535	+	8.86979i	0.000480630	+	0.375488i
$559$	−23.6341			−0.999618
$560$	0.435334	−	0.754021i	0.0183962	−	0.0318632i
$561$	8.02340	−	2.15537i	0.338748	−	0.0909997i
$562$	11.1282	+	19.2746i	0.469415	+	0.813050i
$563$	0.282557	+	0.489403i	0.0119084	+	0.0206259i	0.871918	−	0.489652i	$-0.162876\pi$
$563$	0.282557	+	0.489403i	0.0119084	+	0.0206259i	−0.860010	+	0.510277i	$0.829543\pi$
$564$	−2.64204	−	2.63866i	−0.111250	−	0.111108i
$565$	−3.08043	+	5.33546i	−0.129595	+	0.224465i
$566$	16.2261			0.682035
$567$	6.50078	−	11.3265i	0.273007	−	0.475670i
$568$	14.7174			0.617530
$569$	−3.11671	+	5.39830i	−0.130659	+	0.226309i	−0.923931	−	0.382559i	$-0.875043\pi$
$569$	−3.11671	+	5.39830i	−0.130659	+	0.226309i	0.793272	+	0.608868i	$0.208376\pi$
$570$	−2.88532	−	2.88163i	−0.120853	−	0.120698i
$571$	14.1967	+	24.5894i	0.594114	+	1.02904i	0.993671	+	0.112327i	$0.0358304\pi$
$571$	14.1967	+	24.5894i	0.594114	+	1.02904i	−0.399558	+	0.916708i	$0.630836\pi$
$572$	3.45393	+	5.98239i	0.144416	+	0.250136i
$573$	−0.541247	+	0.145398i	−0.0226109	+	0.00607409i
$574$	2.75643	−	4.77427i	0.115051	−	0.199274i
$575$	−14.9494			−0.623432
$576$	0.0203987	+	15.9363i	0.000849947	+	0.664014i
$577$	−25.5623			−1.06417			−0.532087	−	0.846690i	$-0.678592\pi$
$577$	−25.5623			−1.06417			−0.532087	+	0.846690i	$0.678592\pi$
$578$	2.68637	−	4.65294i	0.111738	−	0.193537i
$579$	6.44678	−	24.1215i	0.267919	−	1.00245i
$580$	−9.68464	−	16.7743i	−0.402133	−	0.696515i
$581$	2.75949	+	4.77957i	0.114483	+	0.198290i
$582$	−1.31642	+	4.92556i	−0.0545674	+	0.204171i
$583$	0.576591	−	0.998685i	0.0238800	−	0.0413613i
$584$	30.1611			1.24807
$585$	−56.1108	−	32.2999i	−2.31990	−	1.33544i
$586$	14.3803			0.594044
$587$	17.5932	−	30.4724i	0.726151	−	1.25773i	−0.232347	−	0.972633i	$-0.574641\pi$
$587$	17.5932	−	30.4724i	0.726151	−	1.25773i	0.958498	−	0.285098i	$-0.0920260\pi$
$588$	−9.82447	+	2.63920i	−0.405154	+	0.108839i
$589$	1.16046	+	2.00997i	0.0478158	+	0.0828194i
$590$	−7.79787	−	13.5063i	−0.321033	−	0.556046i
$591$	−22.4599	−	22.4311i	−0.923875	−	0.922693i
$592$	0.779276	−	1.34975i	0.0320280	−	0.0554742i
$593$	−40.8141			−1.67604			−0.838018	−	0.545643i	$-0.816286\pi$
$593$	−40.8141			−1.67604			−0.838018	+	0.545643i	$0.816286\pi$
$594$	−4.49155	−	1.19427i	−0.184291	−	0.0490015i
$595$	−26.0928			−1.06970
$596$	−0.420785	+	0.728821i	−0.0172360	+	0.0298537i
$597$	−1.85313	−	1.85076i	−0.0758435	−	0.0757465i
$598$	−4.25054	−	7.36215i	−0.173817	−	0.301061i
$599$	−23.2063	−	40.1945i	−0.948184	−	1.64230i	−0.749247	−	0.662291i	$-0.769584\pi$
$599$	−23.2063	−	40.1945i	−0.948184	−	1.64230i	−0.198938	−	0.980012i	$-0.563749\pi$
$600$	−43.3501	+	11.6454i	−1.76976	+	0.475420i
$601$	−7.64723	+	13.2454i	−0.311937	+	0.540291i	−0.978782	−	0.204906i	$-0.934311\pi$
$601$	−7.64723	+	13.2454i	−0.311937	+	0.540291i	0.666844	+	0.745197i	$0.267645\pi$
$602$	5.32851			0.217174
$603$	23.2128	−	13.4416i	0.945300	−	0.547384i
$604$	3.00662			0.122338
$605$	−1.87447	+	3.24667i	−0.0762079	+	0.131996i
$606$	−5.67731	+	21.2424i	−0.230625	+	0.862912i
$607$	17.2474	+	29.8734i	0.700051	+	1.21252i	0.968448	+	0.249216i	$0.0801729\pi$
$607$	17.2474	+	29.8734i	0.700051	+	1.21252i	−0.268397	+	0.963308i	$0.586494\pi$
$608$	1.95935	+	3.39370i	0.0794622	+	0.137633i
$609$	−2.79403	+	10.4542i	−0.113220	+	0.423627i
$610$	4.27352	−	7.40196i	0.173030	−	0.299696i
$611$	10.3420			0.418394
$612$	14.9429	−	8.65284i	0.604033	−	0.349770i
$613$	19.6568			0.793931			0.396965	−	0.917834i	$-0.370063\pi$
$613$	19.6568			0.793931			0.396965	+	0.917834i	$0.370063\pi$
$614$	−9.00440	+	15.5961i	−0.363388	+	0.629406i
$615$	−26.6368	+	7.15557i	−1.07410	+	0.288541i
$616$	−2.07659	−	3.59676i	−0.0836682	−	0.144918i
$617$	18.0267	+	31.2231i	0.725726	+	1.25699i	0.958675	+	0.284505i	$0.0918292\pi$
$617$	18.0267	+	31.2231i	0.725726	+	1.25699i	−0.232949	+	0.972489i	$0.574837\pi$
$618$	−21.0217	−	20.9948i	−0.845617	−	0.844536i
$619$	4.40997	−	7.63830i	0.177252	−	0.307009i	−0.763686	−	0.645587i	$-0.776613\pi$
$619$	4.40997	−	7.63830i	0.177252	−	0.307009i	0.940938	+	0.338578i	$0.109946\pi$
$620$	14.8706			0.597218
$621$	−8.29101	−	2.20452i	−0.332707	−	0.0884641i
$622$	11.6496			0.467105
$623$	2.91326	−	5.04591i	0.116717	−	0.202160i
$624$	−1.12915	−	1.12770i	−0.0452021	−	0.0451443i
$625$	−5.85564	−	10.1423i	−0.234226	−	0.405691i
$626$	4.58479	+	7.94108i	0.183245	+	0.317390i
$627$	−1.17448	+	0.315506i	−0.0469041	+	0.0126001i
$628$	2.66139	−	4.60967i	0.106201	−	0.183946i
$629$	−46.7078			−1.86236
$630$	12.6506	+	7.28228i	0.504014	+	0.290133i
$631$	−0.823111			−0.0327675			−0.0163838	−	0.999866i	$-0.505215\pi$
$631$	−0.823111			−0.0327675			−0.0163838	+	0.999866i	$0.505215\pi$
$632$	1.55522	−	2.69373i	0.0618635	−	0.107151i
$633$	−4.92933	+	18.4437i	−0.195923	+	0.733072i
$634$	−4.92728	−	8.53430i	−0.195687	−	0.338940i
$635$	41.8585	+	72.5010i	1.66110	+	2.87711i
$636$	0.618861	−	2.31555i	0.0245394	−	0.0918175i
$637$	14.0877	−	24.4006i	0.558174	−	0.966786i
$638$	3.85103			0.152464
$639$	0.0197456	+	15.4261i	0.000781125	+	0.610247i
$640$	24.0346			0.950052
$641$	−15.5236	+	26.8877i	−0.613145	+	1.06200i	0.377562	+	0.925984i	$0.376763\pi$
$641$	−15.5236	+	26.8877i	−0.613145	+	1.06200i	−0.990707	+	0.136014i	$0.956571\pi$
$642$	−14.9667	+	4.02058i	−0.590688	+	0.158680i
$643$	0.282962	+	0.490105i	0.0111589	+	0.0193279i	0.871551	−	0.490305i	$-0.163115\pi$
$643$	0.282962	+	0.490105i	0.0111589	+	0.0193279i	−0.860392	+	0.509633i	$0.829781\pi$
$644$	−1.43744	−	2.48972i	−0.0566432	−	0.0981088i
$645$	−18.8627	−	18.8386i	−0.742718	−	0.741768i
$646$	−1.50613	+	2.60869i	−0.0592578	+	0.102638i
$647$	−32.7343			−1.28692			−0.643458	−	0.765481i	$-0.722501\pi$
$647$	−32.7343			−1.28692			−0.643458	+	0.765481i	$0.722501\pi$
$648$	−25.7595	+	0.0659452i	−1.01193	+	0.00259057i
$649$	−4.65105			−0.182569
$650$	23.3104	−	40.3747i	0.914307	−	1.58363i
$651$	−5.87831	−	5.87079i	−0.230389	−	0.230094i
$652$	10.6191	+	18.3927i	0.415874	+	0.720316i
$653$	3.61631	+	6.26362i	0.141517	+	0.245115i	0.928068	−	0.372411i	$-0.121469\pi$
$653$	3.61631	+	6.26362i	0.141517	+	0.245115i	−0.786551	+	0.617525i	$0.788135\pi$
$654$	−11.0830	+	2.97730i	−0.433381	+	0.116421i
$655$	18.3489	−	31.7812i	0.716951	−	1.24180i
$656$	−0.679837			−0.0265432
$657$	0.0404655	+	31.6134i	0.00157871	+	1.23336i
$658$	−2.33169			−0.0908989
$659$	−18.2545	+	31.6177i	−0.711093	+	1.23165i	0.253354	+	0.967374i	$0.418466\pi$
$659$	−18.2545	+	31.6177i	−0.711093	+	1.23165i	−0.964447	+	0.264276i	$0.914867\pi$
$660$	−2.01188	+	7.52772i	−0.0783124	+	0.293016i
$661$	−7.07158	−	12.2483i	−0.275053	−	0.476405i	0.695096	−	0.718917i	$-0.255362\pi$
$661$	−7.07158	−	12.2483i	−0.275053	−	0.476405i	−0.970148	+	0.242512i	$0.922029\pi$
$662$	−8.11445	−	14.0546i	−0.315377	−	0.546249i
$663$	−12.3485	+	46.2035i	−0.479576	+	1.79439i
$664$	5.44303	−	9.42760i	0.211230	−	0.365862i
$665$	3.81950			0.148114
$666$	22.6454	+	13.0357i	0.877493	+	0.505124i
$667$	7.10866			0.275249
$668$	−5.34073	+	9.25041i	−0.206639	+	0.357909i
$669$	38.9971	−	10.4760i	1.50772	−	0.405025i
$670$	14.9908	+	25.9647i	0.579143	+	1.00311i
$671$	−1.27447	−	2.20745i	−0.0492004	−	0.0852176i
$672$	−9.92511	−	9.91242i	−0.382869	−	0.382380i
$673$	−7.78212	+	13.4790i	−0.299979	+	0.519578i	−0.976131	−	0.217184i	$-0.930313\pi$
$673$	−7.78212	+	13.4790i	−0.299979	+	0.519578i	0.676152	+	0.736762i	$0.263646\pi$
$674$	1.50183			0.0578484
$675$	−12.2643	−	45.4219i	−0.472052	−	1.74829i
$676$	−24.1661			−0.929464
$677$	17.0779	−	29.5798i	0.656357	−	1.13684i	−0.325195	−	0.945647i	$-0.605430\pi$
$677$	17.0779	−	29.5798i	0.656357	−	1.13684i	0.981552	−	0.191196i	$-0.0612366\pi$
$678$	−1.80138	−	1.79908i	−0.0691816	−	0.0690931i
$679$	−2.38772	−	4.13565i	−0.0916322	−	0.158712i
$680$	25.7337	+	44.5721i	0.986844	+	1.70926i
$681$	−10.0012	+	2.68666i	−0.383245	+	0.102953i
$682$	−1.47830	+	2.56049i	−0.0566070	+	0.0980462i
$683$	−48.8978			−1.87102			−0.935512	−	0.353295i	$-0.885061\pi$
$683$	−48.8978			−1.87102			−0.935512	+	0.353295i	$0.885061\pi$
$684$	−2.18737	+	1.26661i	−0.0836362	+	0.0484302i
$685$	−8.90825			−0.340367
$686$	−7.71874	+	13.3693i	−0.294703	+	0.510440i
$687$	4.21482	−	15.7703i	0.160805	−	0.601674i
$688$	−0.328552	−	0.569068i	−0.0125259	−	0.0216955i
$689$	3.31921	+	5.74904i	0.126452	+	0.219021i
$690$	2.47590	−	9.26389i	0.0942558	−	0.352670i
$691$	17.0662	−	29.5596i	0.649230	−	1.12450i	−0.334077	−	0.942546i	$-0.608425\pi$
$691$	17.0662	−	29.5596i	0.649230	−	1.12450i	0.983307	−	0.181954i	$-0.0582420\pi$
$692$	29.6767			1.12814
$693$	3.76717	−	2.18141i	0.143103	−	0.0828649i
$694$	16.7985			0.637663
$695$	21.5315	−	37.2936i	0.816735	−	1.41463i
$696$	20.6137	−	5.53756i	0.781359	−	0.209901i
$697$	10.1869	+	17.6443i	0.385857	+	0.668324i
$698$	14.5386	+	25.1815i	0.550292	+	0.953134i
$699$	33.2958	+	33.2532i	1.25936	+	1.25775i
$700$	7.88307	−	13.6539i	0.297952	−	0.516068i
$701$	−22.2291			−0.839581			−0.419791	−	0.907621i	$-0.637896\pi$
$701$	−22.2291			−0.839581			−0.419791	+	0.907621i	$0.637896\pi$
$702$	18.8819	−	18.9546i	0.712653	−	0.715395i
$703$	6.83715			0.257868
$704$	−2.65606	+	4.60043i	−0.100104	+	0.173385i
$705$	8.25410	+	8.24354i	0.310867	+	0.310470i
$706$	3.00071	+	5.19739i	0.112933	+	0.195606i
$707$	−10.2975	−	17.8357i	−0.387276	−	0.670782i
$708$	−9.33593	+	2.50796i	−0.350866	+	0.0942549i
$709$	10.2198	−	17.7012i	0.383812	−	0.664781i	−0.607792	−	0.794096i	$-0.707945\pi$
$709$	10.2198	−	17.7012i	0.383812	−	0.664781i	0.991604	+	0.129315i	$0.0412779\pi$
$710$	−17.2421			−0.647086
$711$	2.82552	+	1.62650i	0.105965	+	0.0609984i
$712$	−11.4927			−0.430706
$713$	−2.72881	+	4.72644i	−0.102195	+	0.177006i
$714$	2.78407	−	10.4169i	0.104191	−	0.389844i
$715$	−10.7906	−	18.6898i	−0.403544	−	0.698959i
$716$	−7.11516	−	12.3238i	−0.265906	−	0.460563i
$717$	0.108485	−	0.405910i	0.00405144	−	0.0151590i
$718$	6.60971	−	11.4484i	0.246672	−	0.427249i
$719$	19.8844			0.741563			0.370782	−	0.928720i	$-0.379090\pi$
$719$	19.8844			0.741563			0.370782	+	0.928720i	$0.379090\pi$
$720$	−0.00230411	−	1.80007i	−8.58692e−5	−	0.0670846i
$721$	27.8279			1.03637
$722$	−8.27665	+	14.3356i	−0.308025	+	0.533515i
$723$	21.2615	−	5.71160i	0.790725	−	0.212417i
$724$	−2.96724	−	5.13942i	−0.110277	−	0.191005i
$725$	19.4923	+	33.7616i	0.723925	+	1.25388i
$726$	−1.09615	−	1.09475i	−0.0406821	−	0.0406301i
$727$	−0.143365	+	0.248316i	−0.00531712	+	0.00920951i	−0.868672	−	0.495388i	$-0.835026\pi$
$727$	−0.143365	+	0.248316i	−0.00531712	+	0.00920951i	0.863355	+	0.504598i	$0.168359\pi$
$728$	23.9083			0.886099
$729$	−0.103681	−	26.9998i	−0.00384003	−	0.999993i
$730$	−35.3350			−1.30781
$731$	−9.84627	+	17.0542i	−0.364178	+	0.630774i
$732$	−3.74853	−	3.74373i	−0.138550	−	0.138372i
$733$	−5.10058	−	8.83447i	−0.188394	−	0.326309i	0.756321	−	0.654201i	$-0.226995\pi$
$733$	−5.10058	−	8.83447i	−0.188394	−	0.326309i	−0.944715	+	0.327892i	$0.893662\pi$
$734$	11.8901	+	20.5943i	0.438872	+	0.760148i
$735$	30.6930	−	8.24523i	1.13213	−	0.304130i
$736$	−4.60741	+	7.98026i	−0.169831	+	0.294156i
$737$	8.94124			0.329355
$738$	−0.0145891	−	11.3976i	−0.000537031	−	0.419551i
$739$	29.3420			1.07936			0.539681	−	0.841870i	$-0.318545\pi$
$739$	29.3420			1.07936			0.539681	+	0.841870i	$0.318545\pi$
$740$	21.9036	−	37.9381i	0.805191	−	1.39463i
$741$	1.80759	−	6.76333i	0.0664035	−	0.248457i
$742$	−0.748343	−	1.29617i	−0.0274725	−	0.0475838i
$743$	−23.9113	−	41.4155i	−0.877219	−	1.51939i	−0.854380	−	0.519650i	$-0.826063\pi$
$743$	−23.9113	−	41.4155i	−0.877219	−	1.51939i	−0.0228399	−	0.999739i	$-0.507271\pi$
$744$	−4.23116	+	15.8314i	−0.155122	+	0.580408i
$745$	1.31459	−	2.27694i	0.0481629	−	0.0834205i
$746$	−21.0695			−0.771410
$747$	9.88886	+	5.69247i	0.361815	+	0.208277i
$748$	5.75580			0.210453
$749$	7.25776	−	12.5708i	0.265193	−	0.459327i
$750$	22.7416	−	6.10920i	0.830406	−	0.223076i
$751$	10.0234	+	17.3610i	0.365758	+	0.633512i	0.988898	−	0.148599i	$-0.0474764\pi$
$751$	10.0234	+	17.3610i	0.365758	+	0.633512i	−0.623139	+	0.782111i	$0.714143\pi$
$752$	0.143770	+	0.249018i	0.00524277	+	0.00908074i
$753$	28.9389	+	28.9019i	1.05459	+	1.05324i
$754$	−11.0845	+	19.1988i	−0.403672	+	0.699180i
$755$	−9.39311			−0.341850
$756$	6.38547	−	6.41004i	0.232237	−	0.233131i
$757$	−34.7845			−1.26427			−0.632133	−	0.774860i	$-0.717820\pi$
$757$	−34.7845			−1.26427			−0.632133	+	0.774860i	$0.717820\pi$
$758$	14.1560	−	24.5190i	0.514171	−	0.890570i
$759$	−2.02340	−	2.02081i	−0.0734449	−	0.0733509i
$760$	−3.76694	−	6.52453i	−0.136641	−	0.236670i
$761$	3.27617	+	5.67450i	0.118761	+	0.205700i	0.919277	−	0.393611i	$-0.128774\pi$
$761$	3.27617	+	5.67450i	0.118761	+	0.205700i	−0.800516	+	0.599312i	$0.795441\pi$
$762$	−33.4106	+	8.97526i	−1.21034	+	0.325139i
$763$	5.37447	−	9.30885i	0.194569	−	0.337003i
$764$	−0.388278			−0.0140474
$765$	−46.6839	+	27.0327i	−1.68786	+	0.977368i
$766$	32.0601			1.15838
$767$	13.3871	−	23.1872i	0.483381	−	0.837241i
$768$	−7.31580	+	27.3730i	−0.263986	+	0.987738i
$769$	17.0111	+	29.4641i	0.613435	+	1.06250i	0.990657	+	0.136378i	$0.0435462\pi$
$769$	17.0111	+	29.4641i	0.613435	+	1.06250i	−0.377221	+	0.926123i	$0.623120\pi$
$770$	2.43282	+	4.21377i	0.0876728	+	0.151854i
$771$	1.84106	−	6.88857i	0.0663042	−	0.248086i
$772$	8.64912	−	14.9807i	0.311289	−	0.539168i
$773$	5.09752			0.183345			0.0916725	−	0.995789i	$-0.470779\pi$
$773$	5.09752			0.183345			0.0916725	+	0.995789i	$0.470779\pi$
$774$	9.53349	−	5.52044i	0.342674	−	0.198428i
$775$	−29.9301			−1.07512
$776$	−4.70972	+	8.15747i	−0.169069	+	0.292836i
$777$	−23.6360	+	6.34947i	−0.847938	+	0.227786i
$778$	1.75385	+	3.03775i	0.0628784	+	0.108909i
$779$	−1.49118	−	2.58279i	−0.0534269	−	0.0925382i
$780$	−31.7377	−	31.6971i	−1.13639	−	1.13494i
$781$	−2.57102	+	4.45314i	−0.0919983	+	0.159346i
$782$	−7.08330			−0.253298
$783$	5.83186	+	21.5988i	0.208414	+	0.771880i
$784$	0.783363			0.0279773
$785$	−8.31456	+	14.4012i	−0.296759	+	0.514002i
$786$	10.7301	+	10.7164i	0.382730	+	0.382241i
$787$	12.5535	+	21.7433i	0.447485	+	0.775066i	0.998222	−	0.0596127i	$-0.0189866\pi$
$787$	12.5535	+	21.7433i	0.447485	+	0.775066i	−0.550737	+	0.834679i	$0.685653\pi$
$788$	−10.9959	−	19.0454i	−0.391712	−	0.678466i
$789$	19.3909	−	5.20909i	0.690336	−	0.185449i
$790$	−1.82202	+	3.15582i	−0.0648244	+	0.112279i
$791$	2.38462			0.0847872
$792$	−7.44164	−	4.28374i	−0.264427	−	0.152216i
$793$	14.6733			0.521063
$794$	−1.74545	+	3.02321i	−0.0619438	+	0.107290i
$795$	−1.93341	+	7.23410i	−0.0685710	+	0.256567i
$796$	−0.907254	−	1.57141i	−0.0321568	−	0.0556972i
$797$	3.39784	+	5.88523i	0.120358	+	0.208466i	0.919909	−	0.392133i	$-0.128263\pi$
$797$	3.39784	+	5.88523i	0.120358	+	0.208466i	−0.799551	+	0.600598i	$0.794929\pi$
$798$	−0.407536	+	1.52485i	−0.0144266	+	0.0539790i
$799$	4.30861	−	7.46274i	0.152428	−	0.264013i
$800$	−50.5349			−1.78668
$801$	−0.0154191	−	12.0461i	−0.000544808	−	0.425627i
$802$	−28.3316			−1.00042
$803$	−5.26890	+	9.12600i	−0.185935	+	0.322050i
$804$	17.9475	−	4.82134i	0.632960	−	0.170035i
$805$	4.49077	+	7.77824i	0.158279	+	0.274147i
$806$	−8.51000	−	14.7397i	−0.299752	−	0.519185i
$807$	−8.36465	−	8.35395i	−0.294450	−	0.294073i
$808$	−20.3115	+	35.1806i	−0.714557	+	1.23765i
$809$	17.0314			0.598792			0.299396	−	0.954129i	$-0.403215\pi$
$809$	17.0314			0.598792			0.299396	+	0.954129i	$0.403215\pi$
$810$	30.1784	−	0.0772577i	1.06036	−	0.00271456i
$811$	2.28561			0.0802587			0.0401294	−	0.999194i	$-0.487223\pi$
$811$	2.28561			0.0802587			0.0401294	+	0.999194i	$0.487223\pi$
$812$	−3.74853	+	6.49264i	−0.131547	+	0.227847i
$813$	−9.28385	−	9.27198i	−0.325599	−	0.325182i
$814$	4.35490	+	7.54291i	0.152639	+	0.264379i
$815$	−33.1754	−	57.4615i	−1.16208	−	2.01279i
$816$	−1.28416	+	0.344971i	−0.0449546	+	0.0120764i
$817$	1.44131	−	2.49643i	0.0504251	−	0.0873389i
$818$	11.5528			0.403933
$819$	0.0320765	+	25.0595i	0.00112084	+	0.875650i
$820$	−19.1086			−0.667301
$821$	−11.0263	+	19.0981i	−0.384821	+	0.666530i	−0.991744	−	0.128231i	$-0.959070\pi$
$821$	−11.0263	+	19.0981i	−0.384821	+	0.666530i	0.606923	+	0.794761i	$0.292404\pi$
$822$	0.950498	−	3.55641i	0.0331524	−	0.124044i
$823$	12.3556	+	21.4006i	0.430691	+	0.745978i	0.996933	−	0.0782608i	$-0.0249367\pi$
$823$	12.3556	+	21.4006i	0.430691	+	0.745978i	−0.566242	+	0.824239i	$0.691603\pi$
$824$	−27.4450	−	47.5361i	−0.956092	−	1.65600i
$825$	4.04932	−	15.1510i	0.140979	−	0.527492i
$826$	−3.01824	+	5.22774i	−0.105018	+	0.181896i
$827$	19.8452			0.690085			0.345043	−	0.938587i	$-0.387864\pi$
$827$	19.8452			0.690085			0.345043	+	0.938587i	$0.387864\pi$
$828$	−5.15120	−	2.96526i	−0.179017	−	0.103050i
$829$	32.9988			1.14610			0.573048	−	0.819522i	$-0.305761\pi$
$829$	32.9988			1.14610			0.573048	+	0.819522i	$0.305761\pi$
$830$	−6.37675	+	11.0449i	−0.221340	+	0.383373i
$831$	31.4532	−	8.44945i	1.09110	−	0.293108i
$832$	−15.2899	−	26.4829i	−0.530082	−	0.918129i
$833$	−11.7382	−	20.3311i	−0.406704	−	0.704432i
$834$	12.5912	+	12.5751i	0.435998	+	0.435440i
$835$	16.6852	−	28.8996i	0.577415	−	1.00011i
$836$	−0.842543			−0.0291399
$837$	−16.5994	−	4.41366i	−0.573759	−	0.152558i
$838$	−24.4724			−0.845386
$839$	10.1382	−	17.5598i	0.350008	−	0.606232i	−0.636242	−	0.771489i	$-0.719512\pi$
$839$	10.1382	−	17.5598i	0.350008	−	0.606232i	0.986251	+	0.165257i	$0.0528454\pi$
$840$	19.0815	+	19.0571i	0.658373	+	0.657531i
$841$	5.23110	+	9.06053i	0.180383	+	0.312432i
$842$	−8.75547	−	15.1649i	−0.301733	−	0.522617i
$843$	−41.6233	+	11.1815i	−1.43358	+	0.385111i
$844$	−6.61327	+	11.4545i	−0.227638	+	0.394281i
$845$	75.4981			2.59721
$846$	−4.17174	+	2.41568i	−0.143427	+	0.0830528i
$847$	1.45106			0.0498589
$848$	−0.0922845	+	0.159842i	−0.00316906	+	0.00548898i
$849$	−8.11306	+	30.3561i	−0.278440	+	1.04182i
$850$	−19.4228	−	33.6412i	−0.666195	−	1.15388i
$851$	8.03876	+	13.9235i	0.275565	+	0.477293i
$852$	−2.75950	+	10.3250i	−0.0945389	+	0.353729i
$853$	3.76447	−	6.52026i	0.128893	−	0.223249i	−0.794355	−	0.607454i	$-0.792191\pi$
$853$	3.76447	−	6.52026i	0.128893	−	0.223249i	0.923248	+	0.384205i	$0.125524\pi$
$854$	−3.30821			−0.113205
$855$	6.83365	−	3.95708i	0.233706	−	0.135329i
$856$	−28.6315			−0.978605
$857$	5.76395	−	9.98345i	0.196893	−	0.341028i	−0.750627	−	0.660727i	$-0.770248\pi$
$857$	5.76395	−	9.98345i	0.196893	−	0.341028i	0.947519	+	0.319699i	$0.103582\pi$
$858$	8.61281	−	2.31370i	0.294037	−	0.0789886i
$859$	1.31075	+	2.27029i	0.0447222	+	0.0774612i	0.887520	−	0.460769i	$-0.152426\pi$
$859$	1.31075	+	2.27029i	0.0447222	+	0.0774612i	−0.842798	+	0.538230i	$0.819093\pi$
$860$	−9.23480	−	15.9951i	−0.314904	−	0.545430i
$861$	7.55356	+	7.54390i	0.257425	+	0.257095i
$862$	4.38494	−	7.59494i	0.149352	−	0.258685i
$863$	29.7385			1.01231			0.506156	−	0.862442i	$-0.331066\pi$
$863$	29.7385			1.01231			0.506156	+	0.862442i	$0.331066\pi$
$864$	−28.0269	−	7.45215i	−0.953496	−	0.253527i
$865$	−92.7143			−3.15238
$866$	−0.887240	+	1.53675i	−0.0301496	+	0.0522207i
$867$	7.36159	+	7.35217i	0.250013	+	0.249693i
$868$	−2.87790	−	4.98467i	−0.0976823	−	0.169191i
$869$	0.543371	+	0.941146i	0.0184326	+	0.0319262i
$870$	−24.1499	+	6.48750i	−0.818757	+	0.219947i
$871$	−25.7356	+	44.5754i	−0.872018	+	1.51038i
$872$	−21.2020			−0.717991
$873$	−8.55659	−	4.92556i	−0.289597	−	0.166705i
$874$	1.03686			0.0350725
$875$	−11.0280	+	19.1011i	−0.372815	+	0.645735i
$876$	−5.65516	+	21.1595i	−0.191070	+	0.714914i
$877$	−1.06123	−	1.83811i	−0.0358352	−	0.0620684i	0.847552	−	0.530713i	$-0.178076\pi$
$877$	−1.06123	−	1.83811i	−0.0358352	−	0.0620684i	−0.883387	+	0.468645i	$0.844742\pi$
$878$	15.6802	+	27.1589i	0.529181	+	0.916569i
$879$	−7.19014	+	26.9028i	−0.242517	+	0.907410i
$880$	0.300012	−	0.519636i	0.0101134	−	0.0175169i
$881$	14.0627			0.473783			0.236892	−	0.971536i	$-0.423871\pi$
$881$	14.0627			0.473783			0.236892	+	0.971536i	$0.423871\pi$
$882$	0.0168107	+	13.1332i	0.000566046	+	0.442219i
$883$	−20.5227			−0.690645			−0.345323	−	0.938484i	$-0.612231\pi$
$883$	−20.5227			−0.690645			−0.345323	+	0.938484i	$0.612231\pi$
$884$	−16.5670	+	28.6948i	−0.557207	+	0.965111i
$885$	29.1667	−	7.83521i	0.980429	−	0.263378i
$886$	10.6044	+	18.3674i	0.356263	+	0.617066i
$887$	−1.25686	−	2.17695i	−0.0422013	−	0.0730949i	0.844153	−	0.536102i	$-0.180104\pi$
$887$	−1.25686	−	2.17695i	−0.0422013	−	0.0730949i	−0.886355	+	0.463007i	$0.846770\pi$
$888$	34.1570	+	34.1133i	1.14624	+	1.14477i
$889$	16.2017	−	28.0622i	0.543387	−	0.941174i
$890$	13.4642			0.451321
$891$	4.48003	−	7.80572i	0.150087	−	0.261502i
$892$	27.9756			0.936693
$893$	−0.630701	+	1.09241i	−0.0211056	+	0.0365560i
$894$	0.768749	+	0.767766i	0.0257108	+	0.0256779i
$895$	22.2288	+	38.5013i	0.743025	+	1.28696i
$896$	−4.65141	−	8.05647i	−0.155393	−	0.269148i
$897$	15.8985	−	4.27089i	0.530835	−	0.142601i
$898$	−5.21345	+	9.02997i	−0.173975	+	0.301334i
$899$	14.2322			0.474672
$900$	−0.0417231	−	32.5958i	−0.00139077	−	1.08653i
$901$	5.53130			0.184274
$902$	1.89960	−	3.29020i	0.0632498	−	0.109552i
$903$	−2.66425	+	9.96865i	−0.0886608	+	0.331736i
$904$	−2.35180	−	4.07344i	−0.0782197	−	0.135481i
$905$	9.27009	+	16.0563i	0.308148	+	0.533728i
$906$	1.00223	−	3.74998i	0.0332969	−	0.124585i
$907$	−16.6153	+	28.7786i	−0.551703	+	0.955577i	0.446449	+	0.894809i	$0.352688\pi$
$907$	−16.6153	+	28.7786i	−0.551703	+	0.955577i	−0.998152	+	0.0607683i	$0.980645\pi$
$908$	−7.17460			−0.238097
$909$	−36.9019	−	21.2424i	−1.22396	−	0.704565i
$910$	−28.0096			−0.928509
$911$	−2.77447	+	4.80553i	−0.0919223	+	0.159214i	−0.908320	−	0.418276i	$-0.862634\pi$
$911$	−2.77447	+	4.80553i	−0.0919223	+	0.159214i	0.816398	+	0.577490i	$0.195968\pi$
$912$	0.187977	−	0.0504973i	0.00622455	−	0.00167213i
$913$	1.90171	+	3.29386i	0.0629374	+	0.109011i
$914$	5.90339	+	10.2250i	0.195267	+	0.338212i
$915$	11.7109	+	11.6959i	0.387151	+	0.386656i
$916$	5.65468	−	9.79419i	0.186836	−	0.323609i
$917$	−14.2042			−0.469064
$918$	−5.81106	−	21.5218i	−0.191793	−	0.710325i
$919$	−46.9009			−1.54712			−0.773560	−	0.633724i	$-0.781526\pi$
$919$	−46.9009			−1.54712			−0.773560	+	0.633724i	$0.781526\pi$
$920$	8.85795	−	15.3424i	0.292038	−	0.505824i
$921$	−24.6752	−	24.6436i	−0.813074	−	0.812034i
$922$	−13.5468	−	23.4637i	−0.446139	−	0.772735i
$923$	−14.8004	−	25.6350i	−0.487160	−	0.843785i
$924$	2.91267	−	0.782446i	0.0958198	−	0.0257406i
$925$	−44.0853	+	76.3580i	−1.44952	+	2.51064i
$926$	24.3392			0.799837
$927$	49.7883	−	28.8303i	1.63526	−	0.946911i
$928$	24.0302			0.788829
$929$	15.5050	−	26.8554i	0.508702	−	0.881098i	−0.491247	−	0.871020i	$-0.663459\pi$
$929$	15.5050	−	26.8554i	0.508702	−	0.881098i	0.999949	−	0.0100775i	$-0.00320784\pi$
$930$	4.95699	−	18.5472i	0.162546	−	0.608187i
$931$	1.71825	+	2.97610i	0.0563135	+	0.0975378i
$932$	16.3009	+	28.2340i	0.533955	+	0.924837i
$933$	−5.82478	+	21.7942i	−0.190695	+	0.713509i
$934$	13.9475	−	24.1578i	0.456376	−	0.790466i
$935$	−17.9819			−0.588072
$936$	42.7754	−	24.7694i	1.39816	−	0.809614i
$937$	−44.0640			−1.43951			−0.719755	−	0.694229i	$-0.755746\pi$
$937$	−44.0640			−1.43951			−0.719755	+	0.694229i	$0.755746\pi$
$938$	5.80230	−	10.0499i	0.189452	−	0.328140i
$939$	−17.1487	+	4.60674i	−0.559626	+	0.150335i
$940$	4.04104	+	6.99929i	0.131804	+	0.228292i
$941$	−1.06028	−	1.83646i	−0.0345642	−	0.0598669i	0.848226	−	0.529635i	$-0.177671\pi$
$941$	−1.06028	−	1.83646i	−0.0345642	−	0.0598669i	−0.882790	+	0.469768i	$0.844338\pi$
$942$	−4.86221	−	4.85599i	−0.158419	−	0.158217i
$943$	3.50649	−	6.07342i	0.114187	−	0.197778i
$944$	0.744409			0.0242284
$945$	−19.9491	+	20.0259i	−0.648944	+	0.651441i
$946$	3.67216			0.119392
$947$	7.66234	−	13.2716i	0.248993	−	0.431268i	−0.714254	−	0.699887i	$-0.753234\pi$
$947$	7.66234	−	13.2716i	0.248993	−	0.431268i	0.963247	+	0.268619i	$0.0865672\pi$
$948$	1.59818	+	1.59614i	0.0519066	+	0.0518402i
$949$	−30.3310	−	52.5348i	−0.984586	−	1.70535i
$950$	2.84313	+	4.92445i	0.0922433	+	0.159770i
$951$	18.4297	−	4.95087i	0.597625	−	0.160543i
$952$	9.96047	−	17.2520i	0.322821	−	0.559142i
$953$	31.7696			1.02912			0.514559	−	0.857455i	$-0.327955\pi$
$953$	31.7696			1.02912			0.514559	+	0.857455i	$0.327955\pi$
$954$	−2.68175	−	1.54374i	−0.0868249	−	0.0499803i
$955$	1.21303			0.0392529
$956$	0.145545	−	0.252092i	0.00470727	−	0.00815323i
$957$	−1.92552	+	7.20457i	−0.0622431	+	0.232891i
$958$	−17.1182	−	29.6496i	−0.553064	−	0.957934i
$959$	1.72401	+	2.98607i	0.0556711	+	0.0964253i
$960$	8.90622	−	33.3238i	0.287447	−	1.07552i
$961$	10.0367	−	17.3840i	0.323763	−	0.560774i
$962$	−50.1390			−1.61655
$963$	−0.0384134	−	30.0102i	−0.00123786	−	0.967065i
$964$	15.2525			0.491251
$965$	−27.0211	+	46.8018i	−0.869838	+	1.50660i
$966$	−3.58444	+	0.962907i	−0.115327	+	0.0309810i
$967$	−2.35911	−	4.08609i	−0.0758637	−	0.131400i	0.825598	−	0.564259i	$-0.190838\pi$
$967$	−2.35911	−	4.08609i	−0.0758637	−	0.131400i	−0.901462	+	0.432859i	$0.857505\pi$
$968$	−1.43109	−	2.47872i	−0.0459969	−	0.0796690i
$969$	−4.12731	−	4.12203i	−0.132588	−	0.132419i
$970$	5.51765	−	9.55685i	0.177161	−	0.306852i
$971$	−2.48946			−0.0798905			−0.0399452	−	0.999202i	$-0.512718\pi$
$971$	−2.48946			−0.0798905			−0.0399452	+	0.999202i	$0.512718\pi$
$972$	4.78362	−	18.0840i	0.153435	−	0.580044i
$973$	−16.6679			−0.534348
$974$	−7.09297	+	12.2854i	−0.227273	+	0.393649i
$975$	63.8784	+	63.7967i	2.04575	+	2.04313i
$976$	0.203982	+	0.353306i	0.00652929	+	0.0113091i
$977$	−23.9951	−	41.5608i	−0.767672	−	1.32965i	−0.938822	−	0.344403i	$-0.888081\pi$
$977$	−23.9951	−	41.5608i	−0.767672	−	1.32965i	0.171150	−	0.985245i	$-0.445252\pi$
$978$	26.4799	−	7.11345i	0.846735	−	0.227463i
$979$	2.00768	−	3.47740i	0.0641657	−	0.111138i
$980$	22.0185			0.703354
$981$	−0.0284457	−	22.2230i	−0.000908201	−	0.709524i
$982$	6.26308			0.199863
$983$	0.248569	−	0.430534i	0.00792811	−	0.0137319i	−0.862034	−	0.506850i	$-0.830810\pi$
$983$	0.248569	−	0.430534i	0.00792811	−	0.0137319i	0.869962	+	0.493118i	$0.164143\pi$
$984$	5.43699	−	20.3432i	0.173325	−	0.648518i
$985$	34.3527	+	59.5006i	1.09457	+	1.89585i
$986$	9.23583	+	15.9969i	0.294129	+	0.509446i
$987$	1.16585	−	4.36216i	0.0371093	−	0.138849i
$988$	2.42509	−	4.20039i	0.0771525	−	0.133632i
$989$	6.77848			0.215543
$990$	8.71822	+	5.01860i	0.277083	+	0.159502i
$991$	56.7182			1.80171			0.900856	−	0.434118i	$-0.142940\pi$
$991$	56.7182			1.80171			0.900856	+	0.434118i	$0.142940\pi$
$992$	−9.22448	+	15.9773i	−0.292878	+	0.507279i
$993$	30.3508	−	8.15331i	0.963155	−	0.258737i
$994$	3.33686	+	5.77961i	0.105839	+	0.183318i
$995$	2.83439	+	4.90931i	0.0898562	+	0.155635i
$996$	5.59338	+	5.58622i	0.177233	+	0.177006i
$997$	−25.5948	+	44.3314i	−0.810594	+	1.40399i	0.101855	+	0.994799i	$0.467522\pi$
$997$	−25.5948	+	44.3314i	−0.810594	+	1.40399i	−0.912449	+	0.409191i	$0.865811\pi$
$998$	−22.0662			−0.698492
$999$	−35.7102	+	35.8475i	−1.12982	+	1.13417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.e.e.34.3	✓	8
3.2	odd	2		297.2.e.e.100.2		8
9.2	odd	6		891.2.a.p.1.3		4
9.4	even	3	inner	99.2.e.e.67.3	yes	8
9.5	odd	6		297.2.e.e.199.2		8
9.7	even	3		891.2.a.q.1.2		4
11.10	odd	2		1089.2.e.i.727.2		8
99.43	odd	6		9801.2.a.bi.1.3		4
99.65	even	6		9801.2.a.bl.1.2		4
99.76	odd	6		1089.2.e.i.364.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.3	✓	8	1.1	even	1	trivial
99.2.e.e.67.3	yes	8	9.4	even	3	inner
297.2.e.e.100.2		8	3.2	odd	2
297.2.e.e.199.2		8	9.5	odd	6
891.2.a.p.1.3		4	9.2	odd	6
891.2.a.q.1.2		4	9.7	even	3
1089.2.e.i.364.2		8	99.76	odd	6
1089.2.e.i.727.2		8	11.10	odd	2
9801.2.a.bi.1.3		4	99.43	odd	6
9801.2.a.bl.1.2		4	99.65	even	6

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.447217 - 0.774602i) q^{2} +(1.22553 + 1.22396i) q^{3} +(0.599994 + 1.03922i) q^{4} +(-1.87447 - 3.24667i) q^{5} +(1.49616 - 0.401921i) q^{6} +(-0.725528 + 1.25665i) q^{7} +2.86218 q^{8} +(0.00384004 + 3.00000i) q^{9} +O(q^{10})\)	\(q+(0.447217 - 0.774602i) q^{2} +(1.22553 + 1.22396i) q^{3} +(0.599994 + 1.03922i) q^{4} +(-1.87447 - 3.24667i) q^{5} +(1.49616 - 0.401921i) q^{6} +(-0.725528 + 1.25665i) q^{7} +2.86218 q^{8} +(0.00384004 + 3.00000i) q^{9} -3.35317 q^{10} +(-0.500000 + 0.866025i) q^{11} +(-0.536655 + 2.00796i) q^{12} +(-2.87831 - 4.98537i) q^{13} +(0.648937 + 1.12399i) q^{14} +(1.67659 - 6.27316i) q^{15} +(0.0800260 - 0.138609i) q^{16} -4.79655 q^{17} +(2.32552 + 1.33868i) q^{18} +0.702126 q^{19} +(2.24934 - 3.89597i) q^{20} +(-2.42725 + 0.652045i) q^{21} +(0.447217 + 0.774602i) q^{22} +(0.825523 + 1.42985i) q^{23} +(3.50768 + 3.50319i) q^{24} +(-4.52724 + 7.84141i) q^{25} -5.14891 q^{26} +(-3.66717 + 3.68128i) q^{27} -1.74125 q^{28} +(2.15278 - 3.72872i) q^{29} +(-4.10941 - 4.10415i) q^{30} +(1.65278 + 2.86269i) q^{31} +(2.79060 + 4.83346i) q^{32} +(-1.67275 + 0.449358i) q^{33} +(-2.14510 + 3.71542i) q^{34} +5.43991 q^{35} +(-3.11535 + 1.80397i) q^{36} +9.73779 q^{37} +(0.314002 - 0.543868i) q^{38} +(2.57445 - 9.63265i) q^{39} +(-5.36505 - 9.29255i) q^{40} +(-2.12380 - 3.67853i) q^{41} +(-0.580431 + 2.17176i) q^{42} +(2.05278 - 3.55552i) q^{43} -1.19999 q^{44} +(9.73280 - 5.63586i) q^{45} +1.47675 q^{46} +(-0.898274 + 1.55586i) q^{47} +(0.267726 - 0.0719207i) q^{48} +(2.44722 + 4.23870i) q^{49} +(4.04932 + 7.01363i) q^{50} +(-5.87831 - 5.87079i) q^{51} +(3.45393 - 5.98239i) q^{52} -1.15318 q^{53} +(1.21151 + 4.48693i) q^{54} +3.74893 q^{55} +(-2.07659 + 3.59676i) q^{56} +(0.860475 + 0.859374i) q^{57} +(-1.92552 - 3.33509i) q^{58} +(2.32552 + 4.02792i) q^{59} +(7.52513 - 2.02152i) q^{60} +(-1.27447 + 2.20745i) q^{61} +2.95660 q^{62} +(-3.77274 - 2.17176i) q^{63} +5.31212 q^{64} +(-10.7906 + 18.6898i) q^{65} +(-0.400006 + 1.49667i) q^{66} +(-4.47062 - 7.74334i) q^{67} +(-2.87790 - 4.98467i) q^{68} +(-0.738375 + 2.76273i) q^{69} +(2.43282 - 4.21377i) q^{70} +5.14204 q^{71} +(0.0109909 + 8.58653i) q^{72} +10.5378 q^{73} +(4.35490 - 7.54291i) q^{74} +(-15.1458 + 4.06871i) q^{75} +(0.421271 + 0.729663i) q^{76} +(-0.725528 - 1.25665i) q^{77} +(-6.31013 - 6.30206i) q^{78} +(0.543371 - 0.941146i) q^{79} -0.600024 q^{80} +(-8.99997 + 0.0230402i) q^{81} -3.79920 q^{82} +(1.90171 - 3.29386i) q^{83} +(-2.13395 - 2.13122i) q^{84} +(8.99096 + 15.5728i) q^{85} +(-1.83608 - 3.18018i) q^{86} +(7.20210 - 1.93474i) q^{87} +(-1.43109 + 2.47872i) q^{88} -4.01536 q^{89} +(-0.0128763 - 10.0595i) q^{90} +8.35317 q^{91} +(-0.990617 + 1.71580i) q^{92} +(-1.47830 + 5.53125i) q^{93} +(0.803446 + 1.39161i) q^{94} +(-1.31611 - 2.27957i) q^{95} +(-2.49601 + 9.33913i) q^{96} +(-1.64550 + 2.85009i) q^{97} +4.37775 q^{98} +(-2.59999 - 1.49667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9	\( 8 q - q^{2} + 5 q^{3} - 11 q^{4} - 4 q^{5} + 17 q^{6} - q^{7} - 5 q^{9} + 2 q^{10} - 4 q^{11} - 2 q^{12} - 7 q^{13} - q^{14} - q^{15} - 17 q^{16} - 10 q^{17} - 2 q^{18} + 18 q^{19} + 10 q^{20} - 13 q^{21} - q^{22} - 14 q^{23} + 18 q^{24} - 14 q^{25} + 44 q^{26} + 5 q^{27} - 2 q^{28} + 6 q^{29} - 37 q^{30} + 2 q^{31} + 34 q^{32} - 4 q^{33} - 16 q^{34} - 16 q^{35} + 11 q^{36} + 6 q^{37} - 3 q^{38} - 22 q^{39} - 12 q^{40} + 2 q^{41} - q^{42} + 21 q^{43} + 22 q^{44} + 49 q^{45} + 4 q^{46} + 7 q^{47} - 59 q^{48} + 15 q^{49} - 23 q^{50} - 31 q^{51} + 10 q^{52} - 12 q^{53} - 37 q^{54} + 8 q^{55} - 18 q^{56} + 33 q^{57} + 21 q^{58} - 2 q^{59} + 73 q^{60} - 15 q^{61} - 40 q^{62} - 5 q^{63} + 32 q^{64} - 19 q^{65} - 19 q^{66} - 14 q^{67} + 7 q^{68} - 2 q^{69} + 38 q^{70} - 6 q^{71} + 75 q^{72} + 44 q^{73} + 36 q^{74} + 10 q^{75} - 42 q^{76} - q^{77} + 29 q^{78} - 11 q^{79} - 68 q^{80} + 7 q^{81} - 34 q^{82} - 18 q^{83} + 34 q^{84} - 13 q^{85} + 24 q^{86} - 9 q^{87} - 12 q^{89} - 80 q^{90} + 38 q^{91} - 67 q^{92} + 20 q^{93} + 19 q^{94} + 30 q^{95} - 50 q^{96} - 26 q^{97} + 30 q^{98} - 5 q^{99}+O(q^{100}) \) 8 * q - q^2 + 5 * q^3 - 11 * q^4 - 4 * q^5 + 17 * q^6 - q^7 - 5 * q^9 + 2 * q^10 - 4 * q^11 - 2 * q^12 - 7 * q^13 - q^14 - q^15 - 17 * q^16 - 10 * q^17 - 2 * q^18 + 18 * q^19 + 10 * q^20 - 13 * q^21 - q^22 - 14 * q^23 + 18 * q^24 - 14 * q^25 + 44 * q^26 + 5 * q^27 - 2 * q^28 + 6 * q^29 - 37 * q^30 + 2 * q^31 + 34 * q^32 - 4 * q^33 - 16 * q^34 - 16 * q^35 + 11 * q^36 + 6 * q^37 - 3 * q^38 - 22 * q^39 - 12 * q^40 + 2 * q^41 - q^42 + 21 * q^43 + 22 * q^44 + 49 * q^45 + 4 * q^46 + 7 * q^47 - 59 * q^48 + 15 * q^49 - 23 * q^50 - 31 * q^51 + 10 * q^52 - 12 * q^53 - 37 * q^54 + 8 * q^55 - 18 * q^56 + 33 * q^57 + 21 * q^58 - 2 * q^59 + 73 * q^60 - 15 * q^61 - 40 * q^62 - 5 * q^63 + 32 * q^64 - 19 * q^65 - 19 * q^66 - 14 * q^67 + 7 * q^68 - 2 * q^69 + 38 * q^70 - 6 * q^71 + 75 * q^72 + 44 * q^73 + 36 * q^74 + 10 * q^75 - 42 * q^76 - q^77 + 29 * q^78 - 11 * q^79 - 68 * q^80 + 7 * q^81 - 34 * q^82 - 18 * q^83 + 34 * q^84 - 13 * q^85 + 24 * q^86 - 9 * q^87 - 12 * q^89 - 80 * q^90 + 38 * q^91 - 67 * q^92 + 20 * q^93 + 19 * q^94 + 30 * q^95 - 50 * q^96 - 26 * q^97 + 30 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more