LMFDB - Embedded newform 349.2.e.a.123.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(123,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("349.123");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			123.3
Character	$\chi$	$=$	349.123
Dual form			349.2.e.a.227.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10033 + 1.21263i) q^{2} +(0.180949 - 0.313412i) q^{3} +(1.94093 - 3.36178i) q^{4} +(-1.51394 + 2.62221i) q^{5} +0.877693i q^{6} +(0.636711 - 0.367605i) q^{7} +4.56397i q^{8} +(1.43452 + 2.48465i) q^{9} +O(q^{10})$	\(q+(-2.10033 + 1.21263i) q^{2} +(0.180949 - 0.313412i) q^{3} +(1.94093 - 3.36178i) q^{4} +(-1.51394 + 2.62221i) q^{5} +0.877693i q^{6} +(0.636711 - 0.367605i) q^{7} +4.56397i q^{8} +(1.43452 + 2.48465i) q^{9} -7.34336i q^{10} -0.521449i q^{11} +(-0.702417 - 1.21662i) q^{12} +(2.12237 - 1.22535i) q^{13} +(-0.891536 + 1.54419i) q^{14} +(0.547890 + 0.948973i) q^{15} +(-1.65254 - 2.86229i) q^{16} -3.97105 q^{17} +(-6.02591 - 3.47906i) q^{18} +(-1.80811 + 3.13175i) q^{19} +(5.87688 + 10.1791i) q^{20} -0.266071i q^{21} +(0.632323 + 1.09522i) q^{22} +(1.71639 + 2.97288i) q^{23} +(1.43041 + 0.825845i) q^{24} +(-2.08401 - 3.60961i) q^{25} +(-2.97179 + 5.14729i) q^{26} +2.12399 q^{27} -2.85398i q^{28} +(-4.59276 + 7.95490i) q^{29} +(-2.30150 - 1.32877i) q^{30} -7.18488 q^{31} +(-0.963261 - 0.556139i) q^{32} +(-0.163429 - 0.0943555i) q^{33} +(8.34052 - 4.81540i) q^{34} +2.22613i q^{35} +11.1372 q^{36} -0.220912 q^{37} -8.77027i q^{38} -0.886904i q^{39} +(-11.9677 - 6.90957i) q^{40} -6.02009 q^{41} +(0.322645 + 0.558837i) q^{42} +(-3.30643 - 1.90897i) q^{43} +(-1.75300 - 1.01209i) q^{44} -8.68706 q^{45} +(-7.20998 - 4.16268i) q^{46} -11.2183i q^{47} -1.19610 q^{48} +(-3.22973 + 5.59406i) q^{49} +(8.75421 + 5.05424i) q^{50} +(-0.718556 + 1.24458i) q^{51} -9.51328i q^{52} +4.18955i q^{53} +(-4.46108 + 2.57560i) q^{54} +(1.36735 + 0.789441i) q^{55} +(1.67774 + 2.90593i) q^{56} +(0.654352 + 1.13337i) q^{57} -22.2772i q^{58} +(7.00991 + 4.04717i) q^{59} +4.25366 q^{60} +2.04793i q^{61} +(15.0906 - 8.71258i) q^{62} +(1.82674 + 1.05467i) q^{63} +9.30773 q^{64} +7.42042i q^{65} +0.457672 q^{66} +5.86487 q^{67} +(-7.70752 + 13.3498i) q^{68} +1.24232 q^{69} +(-2.69946 - 4.67560i) q^{70} +(5.57107 - 3.21646i) q^{71} +(-11.3399 + 6.54709i) q^{72} +(-2.09291 + 3.62502i) q^{73} +(0.463987 - 0.267883i) q^{74} -1.50839 q^{75} +(7.01884 + 12.1570i) q^{76} +(-0.191687 - 0.332012i) q^{77} +(1.07548 + 1.86279i) q^{78} +8.38030i q^{79} +10.0074 q^{80} +(-3.91921 + 6.78828i) q^{81} +(12.6442 - 7.30012i) q^{82} +(6.22161 + 10.7761i) q^{83} +(-0.894473 - 0.516424i) q^{84} +(6.01192 - 10.4129i) q^{85} +9.25947 q^{86} +(1.66211 + 2.87886i) q^{87} +2.37988 q^{88} +(1.77931 + 1.02729i) q^{89} +(18.2457 - 10.5342i) q^{90} +(0.900892 - 1.56039i) q^{91} +13.3256 q^{92} +(-1.30009 + 2.25183i) q^{93} +(13.6036 + 23.5621i) q^{94} +(-5.47474 - 9.48253i) q^{95} +(-0.348602 + 0.201265i) q^{96} +(-1.50118 + 0.866708i) q^{97} -15.6658i q^{98} +(1.29562 - 0.748026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	$ 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) $ 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.10033	+	1.21263i	−1.48516	+	0.857457i	−0.999857	−	0.0168905i	$-0.994623\pi$
$2$	−2.10033	+	1.21263i	−1.48516	+	0.857457i	−0.485301	+	0.874347i	$0.661290\pi$
$3$	0.180949	−	0.313412i	0.104471	−	0.180949i	−0.809051	−	0.587738i	$-0.800018\pi$
$3$	0.180949	−	0.313412i	0.104471	−	0.180949i	0.913522	+	0.406790i	$0.133352\pi$
$4$	1.94093	−	3.36178i	0.970464	−	1.68089i
$5$	−1.51394	+	2.62221i	−0.677053	+	1.17269i	0.298811	+	0.954312i	$0.403410\pi$
$5$	−1.51394	+	2.62221i	−0.677053	+	1.17269i	−0.975864	+	0.218378i	$0.929923\pi$
$6$			0.877693i			0.358317i
$7$	0.636711	−	0.367605i	0.240654	−	0.138942i	−0.374823	−	0.927096i	$-0.622297\pi$
$7$	0.636711	−	0.367605i	0.240654	−	0.138942i	0.615477	+	0.788155i	$0.288963\pi$
$8$			4.56397i			1.61361i
$9$	1.43452	+	2.48465i	0.478172	+	0.828218i
$10$		−	7.34336i		−	2.32217i
$11$		−	0.521449i		−	0.157223i	−0.996905	−	0.0786114i	$-0.974951\pi$
$11$		−	0.521449i		−	0.157223i	0.996905	−	0.0786114i	$-0.0250486\pi$
$12$	−0.702417	−	1.21662i	−0.202770	−	0.351208i
$13$	2.12237	−	1.22535i	0.588640	−	0.339852i	−0.175919	−	0.984405i	$-0.556290\pi$
$13$	2.12237	−	1.22535i	0.588640	−	0.339852i	0.764560	+	0.644553i	$0.222956\pi$
$14$	−0.891536	+	1.54419i	−0.238273	+	0.412701i
$15$	0.547890	+	0.948973i	0.141464	+	0.245024i
$16$	−1.65254	−	2.86229i	−0.413136	−	0.715572i
$17$	−3.97105			−0.963121			−0.481561	−	0.876413i	$-0.659930\pi$
$17$	−3.97105			−0.963121			−0.481561	+	0.876413i	$0.659930\pi$
$18$	−6.02591	−	3.47906i	−1.42032	−	0.820023i
$19$	−1.80811	+	3.13175i	−0.414810	+	0.718472i	−0.995408	−	0.0957181i	$-0.969485\pi$
$19$	−1.80811	+	3.13175i	−0.414810	+	0.718472i	0.580599	+	0.814190i	$0.302819\pi$
$20$	5.87688	+	10.1791i	1.31411	+	2.27611i
$21$		−	0.266071i		−	0.0580614i
$22$	0.632323	+	1.09522i	0.134812	+	0.233501i
$23$	1.71639	+	2.97288i	0.357892	+	0.619888i	0.987609	−	0.156937i	$-0.0501621\pi$
$23$	1.71639	+	2.97288i	0.357892	+	0.619888i	−0.629716	+	0.776825i	$0.716829\pi$
$24$	1.43041	+	0.825845i	0.291980	+	0.168575i
$25$	−2.08401	−	3.60961i	−0.416801	−	0.721921i
$26$	−2.97179	+	5.14729i	−0.582816	+	1.00947i
$27$	2.12399			0.408761
$28$		−	2.85398i		−	0.539352i
$29$	−4.59276	+	7.95490i	−0.852855	+	1.47719i	0.0257663	+	0.999668i	$0.491797\pi$
$29$	−4.59276	+	7.95490i	−0.852855	+	1.47719i	−0.878621	+	0.477520i	$0.841536\pi$
$30$	−2.30150	−	1.32877i	−0.420194	−	0.242599i
$31$	−7.18488			−1.29044			−0.645221	−	0.763996i	$-0.723235\pi$
$31$	−7.18488			−1.29044			−0.645221	+	0.763996i	$0.723235\pi$
$32$	−0.963261	−	0.556139i	−0.170282	−	0.0983125i
$33$	−0.163429	−	0.0943555i	−0.0284493	−	0.0164252i
$34$	8.34052	−	4.81540i	1.43039	−	0.825835i
$35$			2.22613i			0.376284i
$36$	11.1372			1.85619
$37$	−0.220912			−0.0363176			−0.0181588	−	0.999835i	$-0.505780\pi$
$37$	−0.220912			−0.0363176			−0.0181588	+	0.999835i	$0.505780\pi$
$38$		−	8.77027i		−	1.42273i
$39$		−	0.886904i		−	0.142018i
$40$	−11.9677	−	6.90957i	−1.89226	−	1.09250i
$41$	−6.02009			−0.940180			−0.470090	−	0.882619i	$-0.655778\pi$
$41$	−6.02009			−0.940180			−0.470090	+	0.882619i	$0.655778\pi$
$42$	0.322645	+	0.558837i	0.0497852	+	0.0862304i
$43$	−3.30643	−	1.90897i	−0.504226	−	0.291115i	0.226231	−	0.974074i	$-0.427360\pi$
$43$	−3.30643	−	1.90897i	−0.504226	−	0.291115i	−0.730457	+	0.682959i	$0.760693\pi$
$44$	−1.75300	−	1.01209i	−0.264275	−	0.152579i
$45$	−8.68706			−1.29499
$46$	−7.20998	−	4.16268i	−1.06305	−	0.613754i
$47$		−	11.2183i		−	1.63636i	−0.574966	−	0.818178i	$-0.694985\pi$
$47$		−	11.2183i		−	1.63636i	0.574966	−	0.818178i	$-0.305015\pi$
$48$	−1.19610			−0.172642
$49$	−3.22973	+	5.59406i	−0.461390	+	0.799152i
$50$	8.75421	+	5.05424i	1.23803	+	0.714778i
$51$	−0.718556	+	1.24458i	−0.100618	+	0.174276i
$52$		−	9.51328i		−	1.31925i
$53$			4.18955i			0.575479i	0.957709	+	0.287739i	$0.0929037\pi$
$53$			4.18955i			0.575479i	−0.957709	+	0.287739i	$0.907096\pi$
$54$	−4.46108	+	2.57560i	−0.607075	+	0.350495i
$55$	1.36735	+	0.789441i	0.184374	+	0.106448i
$56$	1.67774	+	2.90593i	0.224198	+	0.388322i
$57$	0.654352	+	1.13337i	0.0866710	+	0.150119i
$58$		−	22.2772i		−	2.92514i
$59$	7.00991	+	4.04717i	0.912612	+	0.526897i	0.881271	−	0.472612i	$-0.156689\pi$
$59$	7.00991	+	4.04717i	0.912612	+	0.526897i	0.0313417	+	0.999509i	$0.490022\pi$
$60$	4.25366			0.549145
$61$			2.04793i			0.262211i	0.991368	+	0.131105i	$0.0418526\pi$
$61$			2.04793i			0.262211i	−0.991368	+	0.131105i	$0.958147\pi$
$62$	15.0906	−	8.71258i	1.91651	−	1.10650i
$63$	1.82674	+	1.05467i	0.230148	+	0.132876i
$64$	9.30773			1.16347
$65$			7.42042i			0.920390i
$66$	0.457672			0.0563355
$67$	5.86487			0.716507			0.358254	−	0.933624i	$-0.383372\pi$
$67$	5.86487			0.716507			0.358254	+	0.933624i	$0.383372\pi$
$68$	−7.70752	+	13.3498i	−0.934674	+	1.61890i
$69$	1.24232			0.149557
$70$	−2.69946	−	4.67560i	−0.322647	−	0.558841i
$71$	5.57107	−	3.21646i	0.661164	−	0.381723i	−0.131556	−	0.991309i	$-0.541997\pi$
$71$	5.57107	−	3.21646i	0.661164	−	0.381723i	0.792720	+	0.609585i	$0.208664\pi$
$72$	−11.3399	+	6.54709i	−1.33642	+	0.771582i
$73$	−2.09291	+	3.62502i	−0.244956	+	0.424276i	−0.962119	−	0.272629i	$-0.912107\pi$
$73$	−2.09291	+	3.62502i	−0.244956	+	0.424276i	0.717163	+	0.696905i	$0.245440\pi$
$74$	0.463987	−	0.267883i	0.0539374	−	0.0311408i
$75$	−1.50839			−0.174174
$76$	7.01884	+	12.1570i	0.805116	+	1.39450i
$77$	−0.191687	−	0.332012i	−0.0218448	−	0.0378363i
$78$	1.07548	+	1.86279i	0.121774	+	0.210920i
$79$			8.38030i			0.942857i	0.881904	+	0.471429i	$0.156261\pi$
$79$			8.38030i			0.942857i	−0.881904	+	0.471429i	$0.843739\pi$
$80$	10.0074			1.11886
$81$	−3.91921	+	6.78828i	−0.435468	+	0.754253i
$82$	12.6442	−	7.30012i	1.39632	−	0.806163i
$83$	6.22161	+	10.7761i	0.682910	+	1.18284i	0.974089	+	0.226166i	$0.0726193\pi$
$83$	6.22161	+	10.7761i	0.682910	+	1.18284i	−0.291178	+	0.956669i	$0.594047\pi$
$84$	−0.894473	−	0.516424i	−0.0975950	−	0.0563465i
$85$	6.01192	−	10.4129i	0.652084	−	1.12944i
$86$	9.25947			0.998475
$87$	1.66211	+	2.87886i	0.178197	+	0.308646i
$88$	2.37988			0.253696
$89$	1.77931	+	1.02729i	0.188607	+	0.108892i	0.591330	−	0.806430i	$-0.298603\pi$
$89$	1.77931	+	1.02729i	0.188607	+	0.108892i	−0.402723	+	0.915322i	$0.631936\pi$
$90$	18.2457	−	10.5342i	1.92327	−	1.11040i
$91$	0.900892	−	1.56039i	0.0944392	−	0.163573i
$92$	13.3256			1.38929
$93$	−1.30009	+	2.25183i	−0.134814	+	0.233504i
$94$	13.6036	+	23.5621i	1.40310	+	2.43025i
$95$	−5.47474	−	9.48253i	−0.561697	−	0.972887i
$96$	−0.348602	+	0.201265i	−0.0355790	+	0.0205416i
$97$	−1.50118	+	0.866708i	−0.152422	+	0.0880008i	−0.574271	−	0.818665i	$-0.694714\pi$
$97$	−1.50118	+	0.866708i	−0.152422	+	0.0880008i	0.421849	+	0.906666i	$0.361381\pi$
$98$		−	15.6658i		−	1.58249i
$99$	1.29562	−	0.748026i	0.130215	−	0.0751795i
$100$	−16.1796			−1.61796
$101$		−	13.2211i		−	1.31555i	−0.753216	−	0.657773i	$-0.771499\pi$
$101$		−	13.2211i		−	1.31555i	0.753216	−	0.657773i	$-0.228501\pi$
$102$		−	3.48536i		−	0.345102i
$103$			5.15375i			0.507814i	0.967229	+	0.253907i	$0.0817158\pi$
$103$			5.15375i			0.507814i	−0.967229	+	0.253907i	$0.918284\pi$
$104$	5.59248	+	9.68645i	0.548387	+	0.949835i
$105$	0.697695	+	0.402814i	0.0680881	+	0.0393107i
$106$	−5.08036	−	8.79944i	−0.493448	−	0.854677i
$107$	9.00541	−	5.19928i	0.870586	−	0.502633i	0.00304313	−	0.999995i	$-0.499031\pi$
$107$	9.00541	−	5.19928i	0.870586	−	0.502633i	0.867543	+	0.497362i	$0.165698\pi$
$108$	4.12250	−	7.14039i	0.396688	−	0.687084i
$109$	1.04215	−	1.80505i	0.0998196	−	0.172893i	−0.811790	−	0.583949i	$-0.801507\pi$
$109$	1.04215	−	1.80505i	0.0998196	−	0.172893i	0.911610	+	0.411056i	$0.134840\pi$
$110$	−3.82919			−0.365099
$111$	−0.0399736	+	0.0692364i	−0.00379413	+	0.00657163i
$112$	−2.10439	−	1.21497i	−0.198846	−	0.114804i
$113$	15.0613	−	8.69564i	1.41685	−	0.818017i	0.420827	−	0.907141i	$-0.361740\pi$
$113$	15.0613	−	8.69564i	1.41685	−	0.818017i	0.996021	+	0.0891237i	$0.0284066\pi$
$114$	−2.74871	−	1.58697i	−0.257440	−	0.148633i
$115$	−10.3940			−0.969248
$116$	17.8284	+	30.8798i	1.65533	+	2.86711i
$117$	6.08915	+	3.51557i	0.562942	+	0.325015i
$118$	−19.6308			−1.80717
$119$	−2.52841	+	1.45978i	−0.231779	+	0.133818i
$120$	−4.33109	+	2.50055i	−0.395372	+	0.228268i
$121$	10.7281			0.975281
$122$	−2.48338	−	4.30133i	−0.224834	−	0.389424i
$123$	−1.08933	+	1.88677i	−0.0982213	+	0.170124i
$124$	−13.9453	+	24.1540i	−1.25233	+	2.16910i
$125$	−2.51915			−0.225320
$126$	−5.11569			−0.455742
$127$			3.28802i			0.291764i	0.989302	+	0.145882i	$0.0466020\pi$
$127$			3.28802i			0.291764i	−0.989302	+	0.145882i	$0.953398\pi$
$128$	−17.6228	+	10.1745i	−1.55765	+	0.899309i
$129$	−1.19659	+	0.690851i	−0.105354	+	0.0608261i
$130$	−8.99820	−	15.5853i	−0.789195	−	1.36693i
$131$		−	9.11661i		−	0.796522i	−0.917272	−	0.398261i	$-0.869614\pi$
$131$		−	9.11661i		−	0.796522i	0.917272	−	0.398261i	$-0.130386\pi$
$132$	−0.634406	+	0.366274i	−0.0552179	+	0.0318801i
$133$			2.65869i			0.230538i
$134$	−12.3182	+	7.11189i	−1.06413	+	0.614374i
$135$	−3.21558	+	5.56955i	−0.276753	+	0.479350i
$136$		−	18.1238i		−	1.55410i
$137$	−6.00394	−	3.46638i	−0.512951	−	0.296153i	0.221095	−	0.975252i	$-0.429037\pi$
$137$	−6.00394	−	3.46638i	−0.512951	−	0.296153i	−0.734046	+	0.679100i	$0.762370\pi$
$138$	−2.60927	+	1.50646i	−0.222116	+	0.128239i
$139$	4.30215			0.364904			0.182452	−	0.983215i	$-0.441597\pi$
$139$	4.30215			0.364904			0.182452	+	0.983215i	$0.441597\pi$
$140$	7.48375	+	4.32075i	0.632493	+	0.365170i
$141$	−3.51595	−	2.02993i	−0.296096	−	0.170951i
$142$	−7.80073	+	13.5113i	−0.654623	+	1.13384i
$143$	−0.638959	−	1.10671i	−0.0534324	−	0.0925477i
$144$	4.74120	−	8.21199i	0.395100	−	0.684333i
$145$	−13.9063	−	24.0864i	−1.15486	−	2.00027i
$146$		−	10.1517i		−	0.840157i
$147$	1.16883	+	2.02448i	0.0964036	+	0.166976i
$148$	−0.428773	+	0.742657i	−0.0352449	+	0.0610460i
$149$	−10.5014	+	6.06299i	−0.860308	+	0.496699i	−0.864115	−	0.503294i	$-0.832121\pi$
$149$	−10.5014	+	6.06299i	−0.860308	+	0.496699i	0.00380732	+	0.999993i	$0.498788\pi$
$150$	3.16812	−	1.82912i	0.258676	−	0.149347i
$151$	−9.13473	+	15.8218i	−0.743374	+	1.28756i	0.207577	+	0.978219i	$0.433442\pi$
$151$	−9.13473	+	15.8218i	−0.743374	+	1.28756i	−0.950951	+	0.309343i	$0.899891\pi$
$152$	−14.2932	−	8.25219i	−1.15933	−	0.669341i
$153$	−5.69653	−	9.86668i	−0.460537	−	0.797674i
$154$	0.805214	+	0.464891i	0.0648860	+	0.0374620i
$155$	10.8775	−	18.8403i	0.873698	−	1.51329i
$156$	−2.98158	−	1.72142i	−0.238717	−	0.137824i
$157$	11.6174	−	20.1219i	0.927170	−	1.60591i	0.139137	−	0.990273i	$-0.455567\pi$
$157$	11.6174	−	20.1219i	0.927170	−	1.60591i	0.788033	−	0.615633i	$-0.211099\pi$
$158$	−10.1622	−	17.6014i	−0.808459	−	1.40029i
$159$	1.31306	+	0.758093i	0.104132	+	0.0601207i
$160$	2.91663	−	1.68392i	0.230580	−	0.133125i
$161$	2.18569	+	1.26191i	0.172257	+	0.0994524i
$162$		−	19.0102i		−	1.49358i
$163$		−	6.19983i		−	0.485608i	−0.970075	−	0.242804i	$-0.921933\pi$
$163$		−	6.19983i		−	0.485608i	0.970075	−	0.242804i	$-0.0780672\pi$
$164$	−11.6845	+	20.2382i	−0.912410	+	1.58034i
$165$	0.494841	−	0.285696i	0.0385233	−	0.0222414i
$166$	−26.1349	−	15.0890i	−2.02846	−	1.17113i
$167$		−	3.13488i		−	0.242584i	−0.992617	−	0.121292i	$-0.961296\pi$
$167$		−	3.13488i		−	0.242584i	0.992617	−	0.121292i	$-0.0387037\pi$
$168$	1.21434			0.0936884
$169$	−3.49702	+	6.05702i	−0.269002	+	0.465925i
$170$			29.1608i			2.23653i
$171$	−10.3751			−0.793402
$172$	−12.8351	+	7.41034i	−0.978667	+	0.565033i
$173$	1.11384	−	0.643075i	0.0846836	−	0.0488921i	−0.457060	−	0.889436i	$-0.651098\pi$
$173$	1.11384	−	0.643075i	0.0846836	−	0.0488921i	0.541744	+	0.840544i	$0.317764\pi$
$174$	−6.98196	−	4.03104i	−0.529301	−	0.305592i
$175$	−2.65382	−	1.53218i	−0.200610	−	0.115822i
$176$	−1.49254	+	0.861717i	−0.112504	+	0.0649543i
$177$	2.53687	−	1.46466i	0.190683	−	0.110091i
$178$	−4.98286			−0.373481
$179$			15.5840i			1.16480i	0.812901	+	0.582402i	$0.197887\pi$
$179$			15.5840i			1.16480i	−0.812901	+	0.582402i	$0.802113\pi$
$180$	−16.8609	+	29.2040i	−1.25674	+	2.17674i
$181$	21.6112			1.60635			0.803174	−	0.595745i	$-0.203143\pi$
$181$	21.6112			1.60635			0.803174	+	0.595745i	$0.203143\pi$
$182$			4.36979i			0.323910i
$183$	0.641847	+	0.370571i	0.0474467	+	0.0273934i
$184$	−13.5681	+	7.83357i	−1.00026	+	0.577498i
$185$	0.334446	−	0.579277i	0.0245890	−	0.0425893i
$186$		−	6.30612i		−	0.462387i
$187$			2.07070i			0.151425i
$188$	−37.7135	−	21.7739i	−2.75054	−	1.58802i
$189$	1.35237	−	0.780789i	0.0983702	−	0.0567941i
$190$	22.9975	+	13.2776i	1.66842	+	0.963261i
$191$	9.91040	+	17.1653i	0.717092	+	1.24204i	0.962147	+	0.272530i	$0.0878604\pi$
$191$	9.91040	+	17.1653i	0.717092	+	1.24204i	−0.245056	+	0.969509i	$0.578806\pi$
$192$	1.68422	−	2.91716i	0.121548	−	0.210528i
$193$	9.22880	+	5.32825i	0.664303	+	0.383536i	0.793915	−	0.608029i	$-0.208040\pi$
$193$	9.22880	+	5.32825i	0.664303	+	0.383536i	−0.129611	+	0.991565i	$0.541373\pi$
$194$	2.10199	−	3.64075i	0.150914	−	0.261390i
$195$	2.32565	+	1.34272i	0.166543	+	0.0961539i
$196$	12.5374	+	21.7153i	0.895525	+	1.55109i
$197$	−8.39184	−	4.84503i	−0.597894	−	0.345194i	0.170319	−	0.985389i	$-0.445520\pi$
$197$	−8.39184	−	4.84503i	−0.597894	−	0.345194i	−0.768213	+	0.640195i	$0.778854\pi$
$198$	−1.81415	+	3.14221i	−0.128926	+	0.223307i
$199$	6.82940	−	3.94295i	0.484123	−	0.279509i	−0.238010	−	0.971263i	$-0.576495\pi$
$199$	6.82940	−	3.94295i	0.484123	−	0.279509i	0.722133	+	0.691754i	$0.243162\pi$
$200$	16.4741	−	9.51135i	1.16490	−	0.672554i
$201$	1.06124	−	1.83812i	0.0748541	−	0.129651i
$202$	16.0322	+	27.7686i	1.12802	+	1.95379i
$203$			6.75330i			0.473989i
$204$	2.78933	+	4.83126i	0.195292	+	0.338256i
$205$	9.11403	−	15.7860i	0.636551	−	1.10254i
$206$	−6.24958	−	10.8246i	−0.435429	−	0.754185i
$207$	−4.92438	+	8.52928i	−0.342268	+	0.592826i
$208$	−7.01462	−	4.04989i	−0.486377	−	0.280810i
$209$	1.63305	+	0.942840i	0.112960	+	0.0652176i
$210$	−1.95385			−0.134829
$211$	23.0086	−	13.2840i	1.58398	−	0.914512i	0.589711	−	0.807615i	$-0.299242\pi$
$211$	23.0086	−	13.2840i	1.58398	−	0.914512i	0.994270	−	0.106897i	$-0.0340915\pi$
$212$	14.0844	+	8.13161i	0.967318	+	0.558481i
$213$		−	2.32806i		−	0.159516i
$214$	−12.6096	+	21.8404i	−0.861972	+	1.49298i
$215$	10.0115	−	5.78012i	0.682776	−	0.394201i
$216$			9.69382i			0.659581i
$217$	−4.57469	+	2.64120i	−0.310551	+	0.179296i
$218$			5.05494i			0.342364i
$219$	0.757417	+	1.31189i	0.0511815	+	0.0886490i
$220$	5.30786	−	3.06449i	0.357856	−	0.206608i
$221$	−8.42805	+	4.86594i	−0.566932	+	0.327318i
$222$		−	0.193892i		−	0.0130132i
$223$	−16.4911			−1.10432			−0.552162	−	0.833737i	$-0.686197\pi$
$223$	−16.4911			−1.10432			−0.552162	+	0.833737i	$0.686197\pi$
$224$	−0.817759			−0.0546388
$225$	5.97908	−	10.3561i	0.398605	−	0.690404i
$226$	−21.0891	+	36.5275i	−1.40283	+	2.42977i
$227$	6.11344	+	10.5888i	0.405763	+	0.702803i	0.994410	−	0.105588i	$-0.0336724\pi$
$227$	6.11344	+	10.5888i	0.405763	+	0.702803i	−0.588647	+	0.808390i	$0.700339\pi$
$228$	5.08020			0.336444
$229$	−8.88316	+	5.12869i	−0.587016	+	0.338914i	−0.763917	−	0.645315i	$-0.776726\pi$
$229$	−8.88316	+	5.12869i	−0.587016	+	0.338914i	0.176901	+	0.984229i	$0.443393\pi$
$230$	21.8309	−	12.6041i	1.43949	−	0.831088i
$231$	−0.138742			−0.00912858
$232$	−36.3060	−	20.9613i	−2.38360	−	1.37617i
$233$	−5.22137	−	9.04367i	−0.342063	−	0.592471i	0.642753	−	0.766074i	$-0.277792\pi$
$233$	−5.22137	−	9.04367i	−0.342063	−	0.592471i	−0.984816	+	0.173603i	$0.944459\pi$
$234$	−17.0523			−1.11474
$235$	29.4168	+	16.9838i	1.91894	+	1.10790i
$236$	27.2114	−	15.7105i	1.77131	−	1.02267i
$237$	2.62649	+	1.51640i	0.170609	+	0.0985010i
$238$	3.54034	−	6.13204i	0.229486	−	0.397481i
$239$	9.22397			0.596649			0.298325	−	0.954464i	$-0.403572\pi$
$239$	9.22397			0.596649			0.298325	+	0.954464i	$0.403572\pi$
$240$	1.81082	−	3.13644i	0.116888	−	0.202456i
$241$	11.2243	−	19.4410i	0.723018	−	1.25230i	−0.236767	−	0.971567i	$-0.576088\pi$
$241$	11.2243	−	19.4410i	0.723018	−	1.25230i	0.959785	−	0.280737i	$-0.0905790\pi$
$242$	−22.5325	+	13.0092i	−1.44845	+	0.836261i
$243$	4.60433	+	7.97494i	0.295368	+	0.511593i
$244$	6.88470	+	3.97489i	0.440748	+	0.254466i
$245$	−9.77922	−	16.9381i	−0.624771	−	1.08214i
$246$		−	5.28379i		−	0.336882i
$247$			8.86231i			0.563895i
$248$		−	32.7916i		−	2.08227i
$249$	4.50317			0.285377
$250$	5.29105	−	3.05479i	0.334635	−	0.193202i
$251$			6.35574i			0.401171i	0.979676	+	0.200585i	$0.0642844\pi$
$251$			6.35574i			0.401171i	−0.979676	+	0.200585i	$0.935716\pi$
$252$	7.09115	−	4.09408i	0.446701	−	0.257903i
$253$	1.55020	−	0.895011i	0.0974605	−	0.0562688i
$254$	−3.98714	−	6.90592i	−0.250175	−	0.433316i
$255$	−2.17570	−	3.76842i	−0.136247	−	0.235987i
$256$	15.3681	−	26.6183i	0.960504	−	1.66364i
$257$	−21.2274			−1.32413			−0.662063	−	0.749448i	$-0.730319\pi$
$257$	−21.2274			−1.32413			−0.662063	+	0.749448i	$0.730319\pi$
$258$	1.67549	−	2.90203i	0.104311	−	0.180673i
$259$	−0.140657	+	0.0812083i	−0.00873999	+	0.00504604i
$260$	24.9459	+	14.4025i	1.54708	+	0.893205i
$261$	−26.3536			−1.63124
$262$	11.0550	+	19.1479i	0.682983	+	1.18296i
$263$	−22.0470			−1.35947			−0.679737	−	0.733456i	$-0.737906\pi$
$263$	−22.0470			−1.35947			−0.679737	+	0.733456i	$0.737906\pi$
$264$	0.430636	−	0.745884i	0.0265038	−	0.0459060i
$265$	−10.9859	−	6.34271i	−0.674858	−	0.389630i
$266$	−3.22400	−	5.58413i	−0.197676	−	0.342385i
$267$	0.643928	−	0.371772i	0.0394078	−	0.0227521i
$268$	11.3833	−	19.7164i	0.695344	−	1.20437i
$269$	28.4222			1.73293			0.866467	−	0.499234i	$-0.166385\pi$
$269$	28.4222			1.73293			0.866467	+	0.499234i	$0.166385\pi$
$270$		−	15.5972i		−	0.949215i
$271$	−12.7708	−	22.1197i	−0.775772	−	1.34368i	−0.934360	−	0.356331i	$-0.884027\pi$
$271$	−12.7708	−	22.1197i	−0.775772	−	1.34368i	0.158588	−	0.987345i	$-0.449306\pi$
$272$	6.56233	+	11.3663i	0.397900	+	0.689182i
$273$	−0.326031	−	0.564702i	−0.0197323	−	0.0341773i
$274$	16.8137			1.01575
$275$	−1.88222	+	1.08670i	−0.113502	+	0.0655307i
$276$	2.41124	−	4.17640i	0.145140	−	0.251390i
$277$	−22.7261	+	13.1209i	−1.36548	+	0.788360i	−0.990347	−	0.138611i	$-0.955736\pi$
$277$	−22.7261	+	13.1209i	−1.36548	+	0.788360i	−0.375133	+	0.926971i	$0.622403\pi$
$278$	−9.03594	+	5.21690i	−0.541940	+	0.312889i
$279$	−10.3068	−	17.8519i	−0.617053	−	1.06877i
$280$	−10.1600			−0.607175
$281$	−3.09788	+	5.36568i	−0.184804	+	0.320090i	−0.943510	−	0.331343i	$-0.892498\pi$
$281$	−3.09788	+	5.36568i	−0.184804	+	0.320090i	0.758707	+	0.651433i	$0.225832\pi$
$282$	9.84621			0.586333
$283$	25.6860			1.52688			0.763438	−	0.645881i	$-0.223510\pi$
$283$	25.6860			1.52688			0.763438	+	0.645881i	$0.223510\pi$
$284$		−	24.9717i		−	1.48179i
$285$	−3.96259			−0.234724
$286$	2.68405	+	1.54964i	0.158711	+	0.0916320i
$287$	−3.83306	+	2.21302i	−0.226258	+	0.130630i
$288$		−	3.19116i		−	0.188041i
$289$	−1.23076			−0.0723978
$290$	58.4157	+	33.7263i	3.43029	+	1.98048i
$291$			0.627319i			0.0367741i
$292$	8.12436	+	14.0718i	0.475442	+	0.823490i
$293$	−7.60089	−	13.1651i	−0.444049	−	0.769115i	0.553936	−	0.832559i	$-0.313125\pi$
$293$	−7.60089	−	13.1651i	−0.444049	−	0.769115i	−0.997985	+	0.0634435i	$0.979792\pi$
$294$	−4.90987	−	2.83471i	−0.286349	−	0.165324i
$295$	−21.2251	+	12.2543i	−1.23577	+	0.713474i
$296$		−	1.00823i		−	0.0586024i
$297$		−	1.10755i		−	0.0642666i
$298$	14.7043	−	25.4686i	0.851796	−	1.47535i
$299$	7.28565	+	4.20637i	0.421340	+	0.243261i
$300$	−2.92768	+	5.07089i	−0.169030	+	0.292768i
$301$	−2.80699			−0.161792
$302$		−	44.3081i		−	2.54964i
$303$	−4.14365	−	2.39234i	−0.238046	−	0.137436i
$304$	11.9519			0.685491
$305$	−5.37012	−	3.10044i	−0.307492	−	0.177531i
$306$	23.9292	+	13.8155i	1.36794	+	0.789781i
$307$	10.9489	+	18.9641i	0.624887	+	1.08234i	0.988563	+	0.150811i	$0.0481885\pi$
$307$	10.9489	+	18.9641i	0.624887	+	1.08234i	−0.363675	+	0.931526i	$0.618478\pi$
$308$	−1.48821			−0.0847984
$309$	1.61525	+	0.932565i	0.0918883	+	0.0530518i
$310$			52.7612i			2.99663i
$311$			13.1461i			0.745445i	0.927943	+	0.372723i	$0.121576\pi$
$311$			13.1461i			0.745445i	−0.927943	+	0.372723i	$0.878424\pi$
$312$	4.04781			0.229162
$313$	−6.70566			−0.379026			−0.189513	−	0.981878i	$-0.560691\pi$
$313$	−6.70566			−0.379026			−0.189513	+	0.981878i	$0.560691\pi$
$314$			56.3503i			3.18003i
$315$	−5.53115	+	3.19341i	−0.311645	+	0.179928i
$316$	28.1728	+	16.2655i	1.58484	+	0.915009i
$317$	0.958606	+	0.553452i	0.0538407	+	0.0310849i	0.526679	−	0.850064i	$-0.323437\pi$
$317$	0.958606	+	0.553452i	0.0538407	+	0.0310849i	−0.472838	+	0.881149i	$0.656770\pi$
$318$	−3.67714			−0.206204
$319$	4.14807	+	2.39489i	0.232248	+	0.134088i
$320$	−14.0913	+	24.4069i	−0.787728	+	1.36439i
$321$		−	3.76321i		−	0.210042i
$322$	−6.12090			−0.341105
$323$	7.18011	−	12.4363i	0.399512	−	0.691975i
$324$	15.2138	+	26.3511i	0.845212	+	1.46395i
$325$	−8.84608	−	5.10728i	−0.490692	−	0.283301i
$326$	7.51808	+	13.0217i	0.416388	+	0.721205i
$327$	−0.377150	−	0.653244i	−0.0208565	−	0.0361245i
$328$		−	27.4755i		−	1.51708i
$329$	−4.12390	−	7.14281i	−0.227358	−	0.393796i
$330$	−0.692886	+	1.20011i	−0.0381421	+	0.0660641i
$331$	−7.82194	−	4.51600i	−0.429933	−	0.248222i	0.269385	−	0.963033i	$-0.413180\pi$
$331$	−7.82194	−	4.51600i	−0.429933	−	0.248222i	−0.699318	+	0.714811i	$0.746513\pi$
$332$	48.3028			2.65096
$333$	−0.316901	−	0.548888i	−0.0173661	−	0.0300789i
$334$	3.80143	+	6.58428i	0.208005	+	0.360276i
$335$	−8.87903	+	15.3789i	−0.485113	+	0.840241i
$336$	−0.761572	+	0.439694i	−0.0415471	+	0.0239872i
$337$	8.11116	+	14.0489i	0.441843	+	0.765295i	0.997826	−	0.0658988i	$-0.0209914\pi$
$337$	8.11116	+	14.0489i	0.441843	+	0.765295i	−0.555983	+	0.831194i	$0.687658\pi$
$338$		−	16.9623i		−	0.922629i
$339$		−	6.29386i		−	0.341836i
$340$	−23.3374	−	40.4215i	−1.26565	−	2.19217i
$341$			3.74655i			0.202887i
$342$	21.7911	−	12.5811i	1.17833	−	0.680307i
$343$			9.89555i			0.534309i
$344$	8.71249	−	15.0905i	0.469746	−	0.813624i
$345$	−1.88079	+	3.25762i	−0.101258	+	0.175384i
$346$	−1.55962	+	2.70134i	−0.0838457	+	0.145225i
$347$	18.4115	−	10.6299i	0.988380	−	0.570641i	0.0835902	−	0.996500i	$-0.473361\pi$
$347$	18.4115	−	10.6299i	0.988380	−	0.570641i	0.904790	+	0.425859i	$0.140028\pi$
$348$	12.9041			0.691734
$349$	−11.6439	+	14.6089i	−0.623282	+	0.781997i
$349$	−11.6439	+	14.6089i	−0.623282	+	0.781997i
$350$	7.43187			0.397250
$351$	4.50789	−	2.60263i	0.240613	−	0.138918i
$352$	−0.289998	+	0.502292i	−0.0154570	+	0.0267722i
$353$	3.12925	−	5.42003i	0.166553	−	0.288479i	−0.770652	−	0.637256i	$-0.780070\pi$
$353$	3.12925	−	5.42003i	0.166553	−	0.288479i	0.937206	+	0.348777i	$0.113403\pi$
$354$	−3.55218	+	6.15255i	−0.188796	+	0.327004i
$355$			19.4781i			1.03379i
$356$	6.90703	−	3.98778i	0.366072	−	0.211352i
$357$			1.05658i			0.0559202i
$358$	−18.8976	−	32.7316i	−0.998769	−	1.72992i
$359$		−	31.8355i		−	1.68021i	−0.542422	−	0.840106i	$-0.682493\pi$
$359$		−	31.8355i		−	1.68021i	0.542422	−	0.840106i	$-0.317507\pi$
$360$		−	39.6475i		−	2.08961i
$361$	2.96144	+	5.12937i	0.155865	+	0.269967i
$362$	−45.3907	+	26.2063i	−2.38568	+	1.37737i
$363$	1.94123	−	3.36232i	0.101888	−	0.176476i
$364$	−3.49713	−	6.05721i	−0.183300	−	0.317484i
$365$	−6.33705	−	10.9761i	−0.331697	−	0.574515i
$366$	−1.79745			−0.0939545
$367$	7.70111	+	4.44624i	0.401995	+	0.232092i	0.687344	−	0.726332i	$-0.258776\pi$
$367$	7.70111	+	4.44624i	0.401995	+	0.232092i	−0.285350	+	0.958424i	$0.592110\pi$
$368$	5.67282	−	9.82561i	0.295716	−	0.512196i
$369$	−8.63590	−	14.9578i	−0.449567	−	0.778673i
$370$			1.62223i			0.0843358i
$371$	1.54010	+	2.66753i	0.0799580	+	0.138491i
$372$	5.04678	+	8.74128i	0.261663	+	0.453214i
$373$	−22.3071	−	12.8790i	−1.15502	−	0.666851i	−0.204914	−	0.978780i	$-0.565691\pi$
$373$	−22.3071	−	12.8790i	−1.15502	−	0.666851i	−0.950105	+	0.311929i	$0.899025\pi$
$374$	−2.51099	−	4.34916i	−0.129840	−	0.224889i
$375$	−0.455837	+	0.789533i	−0.0235393	+	0.0407713i
$376$	51.2000			2.64044
$377$			22.5110i			1.15938i
$378$	−1.89361	+	3.27983i	−0.0973969	+	0.168696i
$379$	16.6729	+	9.62609i	0.856428	+	0.494459i	0.862814	−	0.505521i	$-0.168700\pi$
$379$	16.6729	+	9.62609i	0.856428	+	0.494459i	−0.00638661	+	0.999980i	$0.502033\pi$
$380$	−42.5043			−2.18042
$381$	1.03051	+	0.594962i	0.0527944	+	0.0304808i
$382$	−41.6303	−	24.0352i	−2.12999	−	1.22975i
$383$	−12.0088	+	6.93326i	−0.613619	+	0.354273i	−0.774381	−	0.632720i	$-0.781938\pi$
$383$	−12.0088	+	6.93326i	−0.613619	+	0.354273i	0.160761	+	0.986993i	$0.448605\pi$
$384$			7.36427i			0.375806i
$385$	1.16081			0.0591604
$386$	−25.8447			−1.31546
$387$		−	10.9538i		−	0.556812i
$388$			6.72887i			0.341606i
$389$	31.4674	+	18.1677i	1.59546	+	0.921139i	0.992347	+	0.123483i	$0.0394065\pi$
$389$	31.4674	+	18.1677i	1.59546	+	0.921139i	0.603113	+	0.797656i	$0.293927\pi$
$390$	−6.51285			−0.329791
$391$	−6.81588	−	11.8054i	−0.344694	−	0.597027i
$392$	−25.5311	−	14.7404i	−1.28952	−	0.744503i
$393$	−2.85726	−	1.64964i	−0.144130	−	0.0832132i
$394$	23.5009			1.18396
$395$	−21.9749	−	12.6872i	−1.10568	−	0.638364i
$396$		−	5.80746i		−	0.291836i
$397$	26.0140			1.30561			0.652803	−	0.757528i	$-0.273593\pi$
$397$	26.0140			1.30561			0.652803	+	0.757528i	$0.273593\pi$
$398$	−9.56267	+	16.5630i	−0.479333	+	0.830229i
$399$	0.833267	+	0.481087i	0.0417155	+	0.0240845i
$400$	−6.88782	+	11.9301i	−0.344391	+	0.596503i
$401$		−	25.0199i		−	1.24943i	−0.780851	−	0.624717i	$-0.785214\pi$
$401$		−	25.0199i		−	1.24943i	0.780851	−	0.624717i	$-0.214786\pi$
$402$			5.14755i			0.256737i
$403$	−15.2490	+	8.80401i	−0.759607	+	0.438559i
$404$	−44.4464	−	25.6611i	−2.21129	−	1.27669i
$405$	−11.8669	−	20.5540i	−0.589670	−	1.02134i
$406$	−8.18923	−	14.1842i	−0.406425	−	0.703948i
$407$			0.115194i			0.00570996i
$408$	−5.68021	−	3.27947i	−0.281212	−	0.162358i
$409$	29.9009			1.47850			0.739252	−	0.673429i	$-0.235179\pi$
$409$	29.9009			1.47850			0.739252	+	0.673429i	$0.235179\pi$
$410$			44.2077i			2.18326i
$411$	−2.17281	+	1.25447i	−0.107177	+	0.0618786i
$412$	17.3258	+	10.0031i	0.853581	+	0.492815i
$413$	5.95105			0.292832
$414$		−	23.8857i		−	1.17392i
$415$	−37.6765			−1.84947
$416$	−2.72587			−0.133647
$417$	0.778469	−	1.34835i	0.0381218	−	0.0660288i
$418$	−4.57325			−0.223685
$419$	1.61419	+	2.79586i	0.0788583	+	0.136587i	0.902758	−	0.430150i	$-0.141539\pi$
$419$	1.61419	+	2.79586i	0.0788583	+	0.136587i	−0.823899	+	0.566736i	$0.808206\pi$
$420$	2.70835	−	1.56367i	0.132154	−	0.0762991i
$421$	−18.3736	+	10.6080i	−0.895473	+	0.517002i	−0.875729	−	0.482804i	$-0.839619\pi$
$421$	−18.3736	+	10.6080i	−0.895473	+	0.517002i	−0.0197442	+	0.999805i	$0.506285\pi$
$422$	−32.2172	+	55.8018i	−1.56831	+	2.71639i
$423$	27.8735	−	16.0928i	1.35526	−	0.782459i
$424$	−19.1210			−0.928597
$425$	8.27569	+	14.3339i	0.401430	+	0.695297i
$426$	2.82306	+	4.88969i	0.136778	+	0.236906i
$427$	0.752831	+	1.30394i	0.0364320	+	0.0631021i
$428$		−	40.3657i		−	1.95115i
$429$	−0.462475			−0.0223285
$430$	−14.0183	+	24.2803i	−0.676020	+	1.17090i
$431$	9.42400	−	5.44095i	0.453938	−	0.262081i	−0.255554	−	0.966795i	$-0.582258\pi$
$431$	9.42400	−	5.44095i	0.453938	−	0.262081i	0.709492	+	0.704713i	$0.248924\pi$
$432$	−3.50998	−	6.07946i	−0.168874	−	0.292498i
$433$	27.3923	+	15.8149i	1.31639	+	0.760018i	0.983146	−	0.182823i	$-0.0585235\pi$
$433$	27.3923	+	15.8149i	1.31639	+	0.760018i	0.333244	+	0.942841i	$0.391857\pi$
$434$	6.40558	−	11.0948i	0.307478	−	0.532567i
$435$	−10.0653			−0.482595
$436$	−4.04547	−	7.00695i	−0.193743	−	0.335572i
$437$	−12.4137			−0.593829
$438$	−3.18165	−	1.83693i	−0.152025	−	0.0877719i
$439$	21.9273	−	12.6597i	1.04653	−	0.604215i	0.124855	−	0.992175i	$-0.460153\pi$
$439$	21.9273	−	12.6597i	1.04653	−	0.604215i	0.921676	+	0.387960i	$0.126820\pi$
$440$	−3.60299	+	6.24056i	−0.171766	+	0.297507i
$441$	−18.5324			−0.882495
$442$	11.8011	−	20.4402i	0.561322	−	0.972239i
$443$	19.6701	+	34.0696i	0.934554	+	1.61869i	0.775428	+	0.631436i	$0.217534\pi$
$443$	19.6701	+	34.0696i	0.934554	+	1.61869i	0.159126	+	0.987258i	$0.449132\pi$
$444$	0.155172	+	0.268766i	0.00736413	+	0.0127551i
$445$	−5.38753	+	3.11049i	−0.255393	+	0.147451i
$446$	34.6367	−	19.9975i	1.64010	−	0.946910i
$447$			4.38836i			0.207562i
$448$	5.92634	−	3.42157i	0.279993	−	0.161654i
$449$	−1.85843			−0.0877046			−0.0438523	−	0.999038i	$-0.513963\pi$
$449$	−1.85843			−0.0877046			−0.0438523	+	0.999038i	$0.513963\pi$
$450$			29.0016i			1.36715i
$451$			3.13917i			0.147818i
$452$		−	67.5104i		−	3.17542i
$453$	3.30584	+	5.72588i	0.155322	+	0.269025i
$454$	−25.6805	−	14.8266i	−1.20525	−	0.695849i
$455$	2.72779	+	4.72467i	0.127881	+	0.221496i
$456$	−5.17268	+	2.98645i	−0.242233	+	0.139853i
$457$	2.49905	−	4.32848i	0.116900	−	0.202478i	−0.801637	−	0.597811i	$-0.796037\pi$
$457$	2.49905	−	4.32848i	0.116900	−	0.202478i	0.918538	+	0.395333i	$0.129371\pi$
$458$	12.4384	−	21.5439i	0.581207	−	1.00668i
$459$	−8.43446			−0.393687
$460$	−20.1741	+	34.9425i	−0.940620	+	1.62920i
$461$	−12.3731	−	7.14359i	−0.576271	−	0.332710i	0.183379	−	0.983042i	$-0.441296\pi$
$461$	−12.3731	−	7.14359i	−0.576271	−	0.332710i	−0.759650	+	0.650332i	$0.774630\pi$
$462$	0.291405	−	0.168243i	0.0135574	−	0.00782736i
$463$	−0.874914	−	0.505132i	−0.0406607	−	0.0234755i	0.479532	−	0.877524i	$-0.340806\pi$
$463$	−0.874914	−	0.505132i	−0.0406607	−	0.0234755i	−0.520193	+	0.854049i	$0.674140\pi$
$464$	30.3589			1.40938
$465$	−3.93652	−	6.81826i	−0.182552	−	0.316189i
$466$	21.9332	+	12.6631i	1.01604	+	0.586608i
$467$	39.1229			1.81039			0.905195	−	0.424996i	$-0.139724\pi$
$467$	39.1229			1.81039			0.905195	+	0.424996i	$0.139724\pi$
$468$	23.6372	−	13.6469i	1.09263	−	0.630830i
$469$	3.73423	−	2.15596i	0.172431	−	0.0995528i
$470$	−82.3799			−3.79990
$471$	−4.20431	−	7.28208i	−0.193724	−	0.335540i
$472$	−18.4712	+	31.9930i	−0.850206	+	1.47260i
$473$	−0.995431	+	1.72414i	−0.0457699	+	0.0792759i
$474$	−7.35533			−0.337841
$475$	15.0725			0.691573
$476$			11.3333i			0.519461i
$477$	−10.4096	+	6.00997i	−0.476622	+	0.275178i
$478$	−19.3734	+	11.1852i	−0.886118	+	0.511601i
$479$	−7.93792	−	13.7489i	−0.362693	−	0.628202i	0.625710	−	0.780056i	$-0.284809\pi$
$479$	−7.93792	−	13.7489i	−0.362693	−	0.628202i	−0.988403	+	0.151853i	$0.951476\pi$
$480$		−	1.21881i		−	0.0556309i
$481$	−0.468857	+	0.270694i	−0.0213780	+	0.0123426i
$482$			54.4433i			2.47983i
$483$	0.790996	−	0.456682i	0.0359916	−	0.0207797i
$484$	20.8224	−	36.0655i	0.946475	−	1.63934i
$485$		−	5.24856i		−	0.238325i
$486$	−19.3412	−	11.1667i	−0.877337	−	0.506531i
$487$	−22.8934	+	13.2175i	−1.03740	+	0.598943i	−0.919096	−	0.394034i	$-0.871079\pi$
$487$	−22.8934	+	13.2175i	−1.03740	+	0.598943i	−0.118305	+	0.992977i	$0.537746\pi$
$488$	−9.34671			−0.423106
$489$	−1.94310	−	1.12185i	−0.0878702	−	0.0507319i
$490$	41.0792	+	23.7171i	1.85577	+	1.07143i
$491$	−16.3994	+	28.4046i	−0.740094	+	1.28188i	0.212359	+	0.977192i	$0.431885\pi$
$491$	−16.3994	+	28.4046i	−0.740094	+	1.28188i	−0.952452	+	0.304688i	$0.901448\pi$
$492$	4.22861	+	7.32416i	0.190640	+	0.330199i
$493$	18.2381	−	31.5893i	0.821402	−	1.42271i
$494$	−10.7467	−	18.6138i	−0.483516	−	0.837474i
$495$			4.52986i			0.203602i
$496$	11.8733	+	20.5652i	0.533128	+	0.923405i
$497$	2.36478	−	4.09591i	0.106075	−	0.183727i
$498$	−9.45814	+	5.46066i	−0.423830	+	0.244698i
$499$	28.7892	−	16.6214i	1.28878	−	0.744078i	0.310343	−	0.950624i	$-0.399556\pi$
$499$	28.7892	−	16.6214i	1.28878	−	0.744078i	0.978437	+	0.206547i	$0.0662226\pi$
$500$	−4.88949	+	8.46884i	−0.218665	+	0.378738i
$501$	−0.982509	−	0.567252i	−0.0438953	−	0.0253429i
$502$	−7.70714	−	13.3492i	−0.343986	−	0.595802i
$503$	−23.9983	−	13.8554i	−1.07003	−	0.617782i	−0.141840	−	0.989890i	$-0.545302\pi$
$503$	−23.9983	−	13.8554i	−1.07003	−	0.617782i	−0.928190	+	0.372107i	$0.878635\pi$
$504$	−4.81349	+	8.33721i	−0.214410	+	0.371369i
$505$	34.6685	+	20.0159i	1.54273	+	0.890694i
$506$	−2.17063	+	3.75964i	−0.0964962	+	0.167136i
$507$	1.26556	+	2.19202i	0.0562056	+	0.0973510i
$508$	11.0536	+	6.38180i	0.490424	+	0.283147i
$509$	32.1348	−	18.5530i	1.42435	−	0.822348i	0.427682	−	0.903929i	$-0.359330\pi$
$509$	32.1348	−	18.5530i	1.42435	−	0.822348i	0.996667	+	0.0815813i	$0.0259970\pi$
$510$	9.13937	+	5.27662i	0.404698	+	0.233653i
$511$			3.07745i			0.136139i
$512$			33.8448i			1.49574i
$513$	−3.84041	+	6.65179i	−0.169558	+	0.293684i
$514$	44.5845	−	25.7409i	1.96654	−	1.13538i
$515$	−13.5142	−	7.80245i	−0.595509	−	0.343817i
$516$			5.36357i			0.236118i
$517$	−5.84976			−0.257272
$518$	0.196951	−	0.341129i	0.00865351	−	0.0149883i
$519$		−	0.465455i		−	0.0204312i
$520$	−33.8666			−1.48515
$521$	−15.4685	+	8.93072i	−0.677686	+	0.391262i	−0.798982	−	0.601354i	$-0.794628\pi$
$521$	−15.4685	+	8.93072i	−0.677686	+	0.391262i	0.121297	+	0.992616i	$0.461295\pi$
$522$	55.3512	−	31.9570i	2.42266	−	1.39872i
$523$	2.30768	+	1.33234i	0.100908	+	0.0582590i	0.549605	−	0.835425i	$-0.314778\pi$
$523$	2.30768	+	1.33234i	0.100908	+	0.0582590i	−0.448697	+	0.893684i	$0.648112\pi$
$524$	−30.6481	−	17.6947i	−1.33887	−	0.772995i
$525$	−0.960411	+	0.554494i	−0.0419158	+	0.0242001i
$526$	46.3059	−	26.7347i	2.01903	−	1.16569i
$527$	28.5315			1.24285
$528$			0.623706i			0.0271433i
$529$	5.60800	−	9.71334i	0.243826	−	0.422319i
$530$	30.7654			1.33636
$531$			23.2229i			1.00779i
$532$	8.93795	+	5.16033i	0.387509	+	0.223729i
$533$	−12.7769	+	7.37673i	−0.553428	+	0.319522i
$534$	−0.901642	+	1.56169i	−0.0390179	+	0.0675809i
$535$			31.4855i			1.36124i
$536$			26.7671i			1.15616i
$537$	4.88422	+	2.81991i	0.210770	+	0.121688i
$538$	−59.6961	+	34.4656i	−2.57368	+	1.48592i
$539$	2.91702	+	1.68414i	0.125645	+	0.0725411i
$540$	12.4824	+	21.6202i	0.537158	+	0.930384i
$541$	−10.8052	+	18.7152i	−0.464554	+	0.804631i	−0.999181	−	0.0404571i	$-0.987119\pi$
$541$	−10.8052	+	18.7152i	−0.464554	+	0.804631i	0.534628	+	0.845088i	$0.320452\pi$
$542$	53.6459	+	30.9725i	2.30429	+	1.33038i
$543$	3.91052	−	6.77322i	0.167816	−	0.290667i
$544$	3.82516	+	2.20846i	0.164002	+	0.0946868i
$545$	3.15549	+	5.46547i	0.135166	+	0.234115i
$546$	1.36954	+	0.790707i	0.0586111	+	0.0338391i
$547$	−6.75459	+	11.6993i	−0.288806	+	0.500226i	−0.973525	−	0.228581i	$-0.926591\pi$
$547$	−6.75459	+	11.6993i	−0.288806	+	0.500226i	0.684719	+	0.728807i	$0.259925\pi$
$548$	−23.3064	+	13.4560i	−0.995601	+	0.574811i
$549$	−5.08840	+	2.93779i	−0.217168	+	0.125382i
$550$	2.63553	−	4.56487i	0.112379	−	0.194647i
$551$	−16.6085	−	28.7667i	−0.707545	−	1.22550i
$552$			5.66990i			0.241327i
$553$	3.08064	+	5.33583i	0.131002	+	0.226903i
$554$	31.8216	−	55.1166i	1.35197	−	2.34168i
$555$	−0.121035	−	0.209639i	−0.00513765	−	0.00889868i
$556$	8.35016	−	14.4629i	0.354126	−	0.613364i
$557$	2.27924	+	1.31592i	0.0965745	+	0.0557573i	0.547509	−	0.836800i	$-0.315576\pi$
$557$	2.27924	+	1.31592i	0.0965745	+	0.0557573i	−0.450935	+	0.892557i	$0.648909\pi$
$558$	43.2955	+	24.9967i	1.83284	+	1.05819i
$559$	−9.35664			−0.395744
$560$	6.37181	−	3.67877i	0.269258	−	0.155456i
$561$	0.648983	+	0.374690i	0.0274001	+	0.0158194i
$562$		−	15.0263i		−	0.633845i
$563$	2.68767	−	4.65518i	0.113272	−	0.196193i	−0.803816	−	0.594878i	$-0.797200\pi$
$563$	2.68767	−	4.65518i	0.113272	−	0.196193i	0.917088	+	0.398686i	$0.130534\pi$
$564$	−13.6484	+	7.87991i	−0.574701	+	0.331804i
$565$			52.6586i			2.21536i
$566$	−53.9492	+	31.1476i	−2.26765	+	1.30923i
$567$			5.76290i			0.242019i
$568$	14.6798	+	25.4262i	0.615952	+	1.06686i
$569$	−39.3688	+	22.7296i	−1.65043	+	0.952874i	−0.673531	+	0.739159i	$0.735223\pi$
$569$	−39.3688	+	22.7296i	−1.65043	+	0.952874i	−0.976896	+	0.213715i	$0.931444\pi$
$570$	8.32275	−	4.80514i	0.348602	−	0.201265i
$571$		−	45.0105i		−	1.88363i	−0.336131	−	0.941815i	$-0.609118\pi$
$571$		−	45.0105i		−	1.88363i	0.336131	−	0.941815i	$-0.390882\pi$
$572$	−4.96069			−0.207417
$573$	7.17310			0.299660
$574$	5.36713	−	9.29614i	0.224020	−	0.388013i
$575$	7.15394	−	12.3910i	0.298340	−	0.516740i
$576$	13.3521	+	23.1265i	0.556337	+	0.963603i
$577$	−19.7927			−0.823983			−0.411991	−	0.911188i	$-0.635167\pi$
$577$	−19.7927			−0.823983			−0.411991	+	0.911188i	$0.635167\pi$
$578$	2.58501	−	1.49246i	0.107522	−	0.0620779i
$579$	3.33988	−	1.92828i	0.138801	−	0.0801365i
$580$	−107.964			−4.48298
$581$	7.92274	+	4.57419i	0.328691	+	0.189770i
$582$	−0.760703	−	1.31758i	−0.0315322	−	0.0546153i
$583$	2.18464			0.0904784
$584$	−16.5445	−	9.55197i	−0.684616	−	0.395263i
$585$	−18.4372	+	10.6447i	−0.762283	+	0.440105i
$586$	31.9288	+	18.4341i	1.31897	+	0.761506i
$587$	11.7353	−	20.3262i	0.484368	−	0.838950i	−0.515470	−	0.856907i	$-0.672383\pi$
$587$	11.7353	−	20.3262i	0.484368	−	0.838950i	0.999839	+	0.0179569i	$0.00571616\pi$
$588$	9.07447			0.374225
$589$	12.9911	−	22.5012i	0.535288	−	0.927147i
$590$	29.7198	−	51.4763i	1.22355	−	2.11924i
$591$	−3.03699	+	1.75340i	−0.124925	+	0.0721254i
$592$	0.365066	+	0.632312i	0.0150041	+	0.0259879i
$593$	−1.11329	−	0.642757i	−0.0457172	−	0.0263949i	0.476967	−	0.878921i	$-0.341736\pi$
$593$	−1.11329	−	0.642757i	−0.0457172	−	0.0263949i	−0.522684	+	0.852526i	$0.675069\pi$
$594$	1.34305	+	2.32622i	0.0551058	+	0.0954461i
$595$		−	8.84005i		−	0.362407i
$596$			47.0713i			1.92811i
$597$		−	2.85389i		−	0.116802i
$598$	−20.4030			−0.834342
$599$	−13.2550	+	7.65277i	−0.541584	+	0.312684i	−0.745721	−	0.666259i	$-0.767895\pi$
$599$	−13.2550	+	7.65277i	−0.541584	+	0.312684i	0.204136	+	0.978942i	$0.434561\pi$
$600$		−	6.88427i		−	0.281049i
$601$	−29.6757	+	17.1332i	−1.21050	+	0.698880i	−0.962867	−	0.269975i	$-0.912984\pi$
$601$	−29.6757	+	17.1332i	−1.21050	+	0.698880i	−0.247628	+	0.968855i	$0.579651\pi$
$602$	5.89561	−	3.40383i	0.240287	−	0.138730i
$603$	8.41324	+	14.5722i	0.342614	+	0.593424i
$604$	35.4597	+	61.4180i	1.44283	+	2.49906i
$605$	−16.2416	+	28.1314i	−0.660317	+	1.14370i
$606$	11.6040			0.471382
$607$	15.2307	−	26.3803i	0.618195	−	1.07075i	−0.371620	−	0.928385i	$-0.621198\pi$
$607$	15.2307	−	26.3803i	0.618195	−	1.07075i	0.989815	−	0.142360i	$-0.0454691\pi$
$608$	3.48337	−	2.01113i	0.141269	−	0.0815620i
$609$	2.11657	+	1.22200i	0.0857676	+	0.0495180i
$610$	15.0387			0.608899
$611$	−13.7464	−	23.8094i	−0.556118	−	0.963224i
$612$	−44.2262			−1.78774
$613$	10.4814	−	18.1543i	0.423340	−	0.733247i	−0.572924	−	0.819609i	$-0.694191\pi$
$613$	10.4814	−	18.1543i	0.423340	−	0.733247i	0.996264	+	0.0863619i	$0.0275241\pi$
$614$	−45.9927	−	26.5539i	−1.85611	−	1.07163i
$615$	−3.29834	−	5.71290i	−0.133002	−	0.230366i
$616$	1.51530	−	0.874857i	0.0610530	−	0.0352490i
$617$	18.5830	−	32.1867i	0.748122	−	1.29579i	−0.200599	−	0.979673i	$-0.564289\pi$
$617$	18.5830	−	32.1867i	0.748122	−	1.29579i	0.948722	−	0.316113i	$-0.102378\pi$
$618$	−4.52341			−0.181958
$619$		−	21.8856i		−	0.879656i	−0.898082	−	0.439828i	$-0.855039\pi$
$619$		−	21.8856i		−	0.879656i	0.898082	−	0.439828i	$-0.144961\pi$
$620$	−42.2247	−	73.1353i	−1.69578	−	2.93718i
$621$	3.64559	+	6.31435i	0.146293	+	0.253386i
$622$	−15.9413	−	27.6111i	−0.639187	−	1.10710i
$623$	1.51054			0.0605187
$624$	−2.53857	+	1.46565i	−0.101624	+	0.0586728i
$625$	14.2339	−	24.6538i	0.569355	−	0.986151i
$626$	14.0841	−	8.13146i	0.562914	−	0.324999i
$627$	0.590995	−	0.341211i	0.0236021	−	0.0136267i
$628$	−45.0971	−	78.1105i	−1.79957	−	3.11695i
$629$	0.877251			0.0349783
$630$	7.74483	−	13.4144i	0.308561	−	0.534444i
$631$	−20.1531			−0.802282			−0.401141	−	0.916016i	$-0.631386\pi$
$631$	−20.1531			−0.802282			−0.401141	+	0.916016i	$0.631386\pi$
$632$	−38.2475			−1.52140
$633$		−	9.61493i		−	0.382159i
$634$	−2.68452			−0.106616
$635$	−8.62189	−	4.97785i	−0.342149	−	0.197540i
$636$	5.09709	−	2.94281i	0.202113	−	0.116690i
$637$			15.8302i			0.627217i
$638$	−11.6164			−0.459899
$639$	15.9836	+	9.22812i	0.632300	+	0.365059i
$640$		−	61.6143i		−	2.43552i
$641$	11.0077	+	19.0658i	0.434776	+	0.753054i	0.997277	−	0.0737420i	$-0.0234941\pi$
$641$	11.0077	+	19.0658i	0.434776	+	0.753054i	−0.562501	+	0.826797i	$0.690161\pi$
$642$	4.56337	+	7.90399i	0.180102	+	0.311945i
$643$	−9.99492	−	5.77057i	−0.394161	−	0.227569i	0.289800	−	0.957087i	$-0.406411\pi$
$643$	−9.99492	−	5.77057i	−0.394161	−	0.227569i	−0.683962	+	0.729518i	$0.739744\pi$
$644$	8.48454	−	4.89855i	0.334338	−	0.193030i
$645$		−	4.18362i		−	0.164730i
$646$			34.8272i			1.37026i
$647$	−7.33821	+	12.7102i	−0.288495	+	0.499688i	−0.973451	−	0.228897i	$-0.926488\pi$
$647$	−7.33821	+	12.7102i	−0.288495	+	0.499688i	0.684956	+	0.728585i	$0.259822\pi$
$648$	−30.9815	−	17.8872i	−1.21707	−	0.702675i
$649$	2.11039	−	3.65531i	0.0828402	−	0.143483i
$650$	24.7729			0.971674
$651$			1.91169i			0.0749249i
$652$	−20.8425	−	12.0334i	−0.816255	−	0.471265i
$653$	14.3875			0.563025			0.281513	−	0.959557i	$-0.409164\pi$
$653$	14.3875			0.563025			0.281513	+	0.959557i	$0.409164\pi$
$654$	1.58428	+	0.914686i	0.0619503	+	0.0357670i
$655$	23.9057	+	13.8020i	0.934073	+	0.539287i
$656$	9.94845	+	17.2312i	0.388422	+	0.672766i
$657$	−12.0092			−0.468524
$658$	17.3231	+	10.0015i	0.675326	+	0.389899i
$659$		−	20.9536i		−	0.816237i	−0.912929	−	0.408118i	$-0.866185\pi$
$659$		−	20.9536i		−	0.816237i	0.912929	−	0.408118i	$-0.133815\pi$
$660$		−	2.21806i		−	0.0863380i
$661$	−21.7182			−0.844741			−0.422371	−	0.906423i	$-0.638802\pi$
$661$	−21.7182			−0.844741			−0.422371	+	0.906423i	$0.638802\pi$
$662$	21.9049			0.851358
$663$			3.52194i			0.136781i
$664$	−49.1820	+	28.3953i	−1.90863	+	1.10195i
$665$	−6.97166	−	4.02509i	−0.270349	−	0.156086i
$666$	1.33119	+	0.768565i	0.0515827	+	0.0297813i
$667$	−31.5319			−1.22092
$668$	−10.5388	−	6.08457i	−0.407758	−	0.235419i
$669$	−2.98404	+	5.16851i	−0.115370	+	0.199826i
$670$		−	43.0678i		−	1.66385i
$671$	1.06789			0.0412255
$672$	−0.147972	+	0.256296i	−0.00570816	+	0.00988683i
$673$	3.77092	+	6.53143i	0.145358	+	0.251768i	0.929507	−	0.368805i	$-0.120233\pi$
$673$	3.77092	+	6.53143i	0.145358	+	0.251768i	−0.784148	+	0.620574i	$0.786900\pi$
$674$	−34.0723	−	19.6716i	−1.31241	−	0.757723i
$675$	−4.42640	−	7.66675i	−0.170372	−	0.295093i
$676$	13.5749	+	23.5125i	0.522113	+	0.904326i
$677$		−	0.154122i		−	0.00592337i	−0.999996	−	0.00296169i	$-0.999057\pi$
$677$		−	0.154122i		−	0.00592337i	0.999996	−	0.00296169i	$-0.000942735\pi$
$678$	7.63210	+	13.2192i	0.293109	+	0.507680i
$679$	−0.637213	+	1.10369i	−0.0244540	+	0.0423556i
$680$	47.5244	+	27.4382i	1.82248	+	1.05221i
$681$	4.42488			0.169562
$682$	−4.54317	−	7.86899i	−0.173967	−	0.301319i
$683$	18.6919	+	32.3754i	0.715228	+	1.23881i	0.962872	+	0.269959i	$0.0870103\pi$
$683$	18.6919	+	32.3754i	0.715228	+	1.23881i	−0.247644	+	0.968851i	$0.579656\pi$
$684$	−20.1373	+	34.8788i	−0.769967	+	1.33362i
$685$	18.1792	−	10.4958i	0.694590	−	0.401022i
$686$	−11.9996	−	20.7839i	−0.458147	−	0.793534i
$687$			3.71212i			0.141626i
$688$			12.6186i			0.481080i
$689$	5.13367	+	8.89178i	0.195577	+	0.338750i
$690$		−	9.12277i		−	0.347298i
$691$	−27.5523	+	15.9073i	−1.04814	+	0.605143i	−0.922128	−	0.386885i	$-0.873551\pi$
$691$	−27.5523	+	15.9073i	−1.04814	+	0.605143i	−0.126011	+	0.992029i	$0.540218\pi$
$692$		−	4.99265i		−	0.189792i
$693$	0.549957	−	0.952554i	0.0208911	−	0.0361845i
$694$	−25.7801	+	44.6525i	−0.978600	+	1.69499i
$695$	−6.51318	+	11.2812i	−0.247059	+	0.427919i
$696$	−13.1390	+	7.58582i	−0.498034	+	0.287540i
$697$	23.9061			0.905507
$698$	6.74080	−	44.8032i	0.255143	−	1.69583i
$699$	−3.77920			−0.142942
$700$	−10.3017	+	5.94772i	−0.389369	+	0.224803i
$701$	20.3238	−	35.2018i	0.767619	−	1.32956i	−0.171232	−	0.985231i	$-0.554775\pi$
$701$	20.3238	−	35.2018i	0.767619	−	1.32956i	0.938851	−	0.344324i	$-0.111892\pi$
$702$	−6.31204	+	10.9328i	−0.238233	+	0.412631i
$703$	0.399433	−	0.691839i	0.0150649	−	0.0260932i
$704$		−	4.85351i		−	0.182923i
$705$	10.6458	−	6.14638i	0.400946	−	0.231486i
$706$			15.1785i			0.571249i
$707$	−4.86014	−	8.41800i	−0.182784	−	0.316592i
$708$		−	11.3712i		−	0.427356i
$709$			9.70847i			0.364609i	0.983242	+	0.182305i	$0.0583557\pi$
$709$			9.70847i			0.364609i	−0.983242	+	0.182305i	$0.941644\pi$
$710$	−23.6196	−	40.9104i	−0.886428	−	1.53534i
$711$	−20.8221	+	12.0217i	−0.780891	+	0.450848i
$712$	−4.68851	+	8.12073i	−0.175709	+	0.304337i
$713$	−12.3321	−	21.3598i	−0.461840	−	0.799930i
$714$	−1.28124	−	2.21917i	−0.0479491	−	0.0830503i
$715$	3.86937			0.144706
$716$	52.3901	+	30.2474i	1.95791	+	1.13040i
$717$	1.66907	−	2.89091i	0.0623324	−	0.107963i
$718$	38.6045	+	66.8650i	1.44071	+	2.49538i
$719$		−	41.3961i		−	1.54381i	−0.635736	−	0.771907i	$-0.719303\pi$
$719$		−	41.3961i		−	1.54381i	0.635736	−	0.771907i	$-0.280697\pi$
$720$	14.3557	+	24.8649i	0.535007	+	0.926659i
$721$	1.89455	+	3.28145i	0.0705566	+	0.122208i
$722$	−12.4400	−	7.18225i	−0.462970	−	0.267296i
$723$	−4.06203	−	7.03564i	−0.151068	−	0.261658i
$724$	41.9458	−	72.6522i	1.55890	−	2.70010i
$725$	38.2854			1.42188
$726$			9.41597i			0.349459i
$727$	−15.6259	+	27.0648i	−0.579531	+	1.00378i	0.416002	+	0.909364i	$0.363431\pi$
$727$	−15.6259	+	27.0648i	−0.579531	+	1.00378i	−0.995533	+	0.0944133i	$0.969902\pi$
$728$	7.12159	+	4.11165i	0.263944	+	0.152388i
$729$	−20.1827			−0.747507
$730$	26.6198	+	15.3690i	0.985244	+	0.568831i
$731$	13.1300	+	7.58062i	0.485631	+	0.280379i
$732$	2.49156	−	1.43850i	0.0920906	−	0.0531685i
$733$			38.8971i			1.43670i	0.695684	+	0.718348i	$0.255102\pi$
$733$			38.8971i			1.43670i	−0.695684	+	0.718348i	$0.744898\pi$
$734$	−21.5665			−0.796034
$735$	−7.07815			−0.261081
$736$		−	3.81821i		−	0.140741i
$737$		−	3.05823i		−	0.112651i
$738$	36.2765	+	20.9443i	1.33536	+	0.770969i
$739$	27.2513			1.00246			0.501228	−	0.865315i	$-0.332882\pi$
$739$	27.2513			1.00246			0.501228	+	0.865315i	$0.332882\pi$
$740$	−1.29827	−	2.24867i	−0.0477254	−	0.0826628i
$741$	2.77756	+	1.60362i	0.102036	+	0.0589106i
$742$	−6.46944	−	3.73513i	−0.237501	−	0.137121i
$743$	30.3423			1.11315			0.556575	−	0.830797i	$-0.312115\pi$
$743$	30.3423			1.11315			0.556575	+	0.830797i	$0.312115\pi$
$744$	−10.2773	−	5.93360i	−0.376784	−	0.217536i
$745$		−	36.7159i		−	1.34517i
$746$	62.4698			2.28718
$747$	−17.8500	+	30.9171i	−0.653097	+	1.13120i
$748$	6.96125	+	4.01908i	0.254528	+	0.146952i
$749$	3.82257	−	6.62088i	0.139674	−	0.241922i
$750$		−	2.21104i		−	0.0807358i
$751$			32.8675i			1.19935i	0.800242	+	0.599677i	$0.204704\pi$
$751$			32.8675i			1.19935i	−0.800242	+	0.599677i	$0.795296\pi$
$752$	−32.1100	+	18.5387i	−1.17093	+	0.676037i
$753$	1.99197	+	1.15006i	0.0725913	+	0.0419106i
$754$	−27.2975	−	47.2806i	−0.994115	−	1.72186i
$755$	−27.6588	−	47.9065i	−1.00661	−	1.74349i
$756$		−	6.06182i		−	0.220466i
$757$	−19.9983	−	11.5460i	−0.726849	−	0.419647i	0.0904192	−	0.995904i	$-0.471179\pi$
$757$	−19.9983	−	11.5460i	−0.726849	−	0.419647i	−0.817268	+	0.576257i	$0.804513\pi$
$758$	−46.6914			−1.69591
$759$		−	0.647804i		−	0.0235138i
$760$	43.2780	−	24.9866i	1.56986	−	0.906358i
$761$	27.4598	+	15.8539i	0.995417	+	0.574705i	0.906889	−	0.421369i	$-0.138450\pi$
$761$	27.4598	+	15.8539i	0.995417	+	0.574705i	0.0885282	+	0.996074i	$0.471784\pi$
$762$	−2.88587			−0.104544
$763$		−	1.53240i		−	0.0554765i
$764$	76.9415			2.78365
$765$	34.4967			1.24723
$766$	16.8149	−	29.1243i	0.607548	−	1.05230i
$767$	19.8369			0.716267
$768$	−5.56166	−	9.63308i	−0.200689	−	0.347604i
$769$	−20.8049	+	12.0117i	−0.750245	+	0.433154i	−0.825783	−	0.563989i	$-0.809266\pi$
$769$	−20.8049	+	12.0117i	−0.750245	+	0.433154i	0.0755372	+	0.997143i	$0.475933\pi$
$770$	−2.43809	+	1.40763i	−0.0878625	+	0.0507275i
$771$	−3.84106	+	6.65292i	−0.138333	+	0.239599i
$772$	35.8248	−	20.6835i	1.28936	−	0.744415i
$773$	−45.9421			−1.65242			−0.826211	−	0.563360i	$-0.809508\pi$
$773$	−45.9421			−1.65242			−0.826211	+	0.563360i	$0.809508\pi$
$774$	13.2829	+	23.0066i	0.477442	+	0.826954i
$775$	14.9733	+	25.9346i	0.537858	+	0.931598i
$776$	−3.95563	−	6.85136i	−0.141999	−	0.245949i
$777$			0.0587781i			0.00210865i
$778$	−88.1226			−3.15935
$779$	10.8850	−	18.8534i	0.389996	−	0.675493i
$780$	9.02784	−	5.21223i	0.323249	−	0.186628i
$781$	−1.67722	−	2.90503i	−0.0600156	−	0.103950i
$782$	28.6312	+	16.5302i	1.02385	+	0.591120i
$783$	−9.75497	+	16.8961i	−0.348614	+	0.603817i
$784$	21.3491			0.762467
$785$	35.1760	+	60.9267i	1.25549	+	2.17457i
$786$	8.00158			0.285407
$787$	−0.0533657	−	0.0308107i	−0.00190228	−	0.00109828i	0.499049	−	0.866574i	$-0.333683\pi$
$787$	−0.0533657	−	0.0308107i	−0.00190228	−	0.00109828i	−0.500951	+	0.865476i	$0.667016\pi$
$788$	−32.5759	+	18.8077i	−1.16047	+	0.669997i
$789$	−3.98937	+	6.90979i	−0.142025	+	0.245995i
$790$	61.5395			2.18948
$791$	6.39313	−	11.0732i	0.227314	−	0.393719i
$792$	3.41397	+	5.91318i	0.121310	+	0.210116i
$793$	2.50944	+	4.34647i	0.0891127	+	0.154348i
$794$	−54.6380	+	31.5453i	−1.93903	+	1.11950i
$795$	−3.97577	+	2.29541i	−0.141006	+	0.0814098i
$796$		−	30.6120i		−	1.08501i
$797$	26.5157	−	15.3089i	0.939235	−	0.542268i	0.0495147	−	0.998773i	$-0.484233\pi$
$797$	26.5157	−	15.3089i	0.939235	−	0.542268i	0.889720	+	0.456506i	$0.150899\pi$
$798$	−2.33351			−0.0826055
$799$			44.5484i			1.57601i
$800$			4.63599i			0.163907i
$801$			5.89463i			0.208277i
$802$	30.3398	+	52.5501i	1.07134	+	1.85561i
$803$	1.89026	+	1.09134i	0.0667059	+	0.0385127i
$804$	−4.11958	−	7.13532i	−0.145286	−	0.251643i
$805$	−6.61800	+	3.82090i	−0.233254	+	0.134669i
$806$	21.3520	−	36.9827i	0.752091	−	1.30266i
$807$	5.14297	−	8.90788i	0.181041	−	0.313572i
$808$	60.3406			2.12278
$809$	−18.4745	+	31.9988i	−0.649529	+	1.12502i	0.333706	+	0.942677i	$0.391701\pi$
$809$	−18.4745	+	31.9988i	−0.649529	+	1.12502i	−0.983235	+	0.182340i	$0.941633\pi$
$810$	49.8487	+	28.7802i	1.75151	+	1.01123i
$811$	35.0309	−	20.2251i	1.23010	−	0.710200i	0.263052	−	0.964782i	$-0.415271\pi$
$811$	35.0309	−	20.2251i	1.23010	−	0.710200i	0.967051	+	0.254582i	$0.0819377\pi$
$812$	22.7031	+	13.1077i	0.796724	+	0.459989i
$813$	−9.24345			−0.324182
$814$	−0.139687	−	0.241946i	−0.00489604	−	0.00848019i
$815$	16.2573	+	9.38615i	0.569468	+	0.328782i
$816$	4.74978			0.166276
$817$	11.9568	−	6.90327i	0.418316	−	0.241515i
$818$	−62.8018	+	36.2586i	−2.19581	+	1.26775i
$819$	5.16938			0.180633
$820$	−35.3793	−	61.2788i	−1.23550	−	2.13995i
$821$	−7.18174	+	12.4391i	−0.250644	+	0.434129i	−0.963703	−	0.266975i	$-0.913976\pi$
$821$	−7.18174	+	12.4391i	−0.250644	+	0.434129i	0.713059	+	0.701104i	$0.247309\pi$
$822$	3.04242	−	5.26962i	0.106116	−	0.183799i
$823$	21.5492			0.751158			0.375579	−	0.926790i	$-0.377444\pi$
$823$	21.5492			0.751158			0.375579	+	0.926790i	$0.377444\pi$
$824$	−23.5216			−0.819414
$825$			0.786550i			0.0273842i
$826$	−12.4992	+	7.21640i	−0.434902	+	0.251091i
$827$	−24.3316	+	14.0479i	−0.846093	+	0.488492i	−0.859331	−	0.511420i	$-0.829120\pi$
$827$	−24.3316	+	14.0479i	−0.846093	+	0.488492i	0.0132374	+	0.999912i	$0.495786\pi$
$828$	19.1157	+	33.1094i	0.664317	+	1.15063i
$829$			25.1361i			0.873014i	0.899701	+	0.436507i	$0.143785\pi$
$829$			25.1361i			0.873014i	−0.899701	+	0.436507i	$0.856215\pi$
$830$	79.1331	−	45.6875i	2.74675	−	1.58584i
$831$			9.49686i			0.329442i
$832$	19.7545	−	11.4052i	0.684863	−	0.395406i
$833$	12.8254	−	22.2143i	0.444375	−	0.769680i
$834$			3.77597i			0.130751i
$835$	8.22032	+	4.74600i	0.284476	+	0.164242i
$836$	6.33925	−	3.65997i	0.219247	−	0.126583i
$837$	−15.2606			−0.527483
$838$	−6.78066	−	3.91482i	−0.234234	−	0.135235i
$839$	16.5889	+	9.57759i	0.572712	+	0.330655i	0.758232	−	0.651985i	$-0.226064\pi$
$839$	16.5889	+	9.57759i	0.572712	+	0.330655i	−0.185520	+	0.982640i	$0.559397\pi$
$840$	−1.83843	+	3.18426i	−0.0634320	+	0.109867i
$841$	−27.6869	−	47.9552i	−0.954722	−	1.65363i
$842$	25.7271	−	44.5606i	0.886613	−	1.53566i
$843$	1.12111	+	1.94183i	0.0386132	+	0.0668800i
$844$		−	103.133i		−	3.55000i
$845$	−10.5885	−	18.3399i	−0.364257	−	0.630911i
$846$	−39.0291	+	67.6004i	−1.34185	+	2.32415i
$847$	6.83070	−	3.94370i	0.234706	−	0.135507i
$848$	11.9917	−	6.92341i	0.411796	−	0.237751i
$849$	4.64786	−	8.05032i	0.159514	−	0.276286i
$850$	−34.7634	−	20.0707i	−1.19237	−	0.688418i
$851$	−0.379171	−	0.656743i	−0.0129978	−	0.0225129i
$852$	−7.82642	−	4.51859i	−0.268129	−	0.154804i
$853$	−6.05014	+	10.4792i	−0.207153	+	0.358800i	−0.950817	−	0.309755i	$-0.899753\pi$
$853$	−6.05014	+	10.4792i	−0.207153	+	0.358800i	0.743664	+	0.668554i	$0.233086\pi$
$854$	−3.16239	−	1.82581i	−0.108215	−	0.0624778i
$855$	15.7072	−	27.2057i	0.537175	−	0.930414i
$856$	23.7294	+	41.1005i	0.811053	+	1.40479i
$857$	−31.4399	−	18.1518i	−1.07396	−	0.620054i	−0.144703	−	0.989475i	$-0.546223\pi$
$857$	−31.4399	−	18.1518i	−1.07396	−	0.620054i	−0.929262	+	0.369421i	$0.879556\pi$
$858$	0.971351	−	0.560810i	0.0331614	−	0.0191457i
$859$	−27.2479	−	15.7316i	−0.929688	−	0.536756i	−0.0429751	−	0.999076i	$-0.513684\pi$
$859$	−27.2479	−	15.7316i	−0.929688	−	0.536756i	−0.886713	+	0.462321i	$0.847017\pi$
$860$		−	44.8752i		−	1.53023i
$861$			1.60177i			0.0545882i
$862$	−13.1957	+	22.8556i	−0.449447	+	0.778465i
$863$	11.7142	−	6.76321i	0.398757	−	0.230222i	−0.287191	−	0.957873i	$-0.592721\pi$
$863$	11.7142	−	6.76321i	0.398757	−	0.230222i	0.685947	+	0.727651i	$0.259388\pi$
$864$	−2.04595	−	1.18123i	−0.0696048	−	0.0401863i
$865$			3.89430i			0.132410i
$866$	−76.7105			−2.60673
$867$	−0.222705	+	0.385736i	−0.00756345	+	0.0131003i
$868$			20.5055i			0.696003i
$869$	4.36990			0.148239
$870$	21.1405	−	12.2055i	0.716729	−	0.413804i
$871$	12.4474	−	7.18653i	0.421765	−	0.243506i
$872$	8.23821	+	4.75633i	0.278981	+	0.161070i
$873$	−4.30694	−	2.48661i	−0.145768	−	0.0841590i
$874$	26.0729	−	15.0532i	0.881931	−	0.509183i
$875$	−1.60397	+	0.926054i	−0.0542241	+	0.0313063i
$876$	5.88037			0.198679
$877$			13.4228i			0.453257i	0.973981	+	0.226629i	$0.0727704\pi$
$877$			13.4228i			0.453257i	−0.973981	+	0.226629i	$0.927230\pi$
$878$	−30.7030	+	53.1792i	−1.03618	+	1.79471i
$879$	−5.50149			−0.185561
$880$		−	5.21834i		−	0.175910i
$881$	8.29007	+	4.78627i	0.279299	+	0.161254i	0.633106	−	0.774065i	$-0.281780\pi$
$881$	8.29007	+	4.78627i	0.279299	+	0.161254i	−0.353807	+	0.935319i	$0.615113\pi$
$882$	38.9242	−	22.4729i	1.31065	−	0.756701i
$883$	11.0588	−	19.1544i	0.372159	−	0.644598i	−0.617739	−	0.786384i	$-0.711951\pi$
$883$	11.0588	−	19.1544i	0.372159	−	0.644598i	0.989897	+	0.141786i	$0.0452843\pi$
$884$			37.7777i			1.27060i
$885$			8.86962i			0.298149i
$886$	−82.6274	−	47.7049i	−2.77592	−	1.60268i
$887$	−13.7868	+	7.95982i	−0.462916	+	0.267265i	−0.713270	−	0.700890i	$-0.752786\pi$
$887$	−13.7868	+	7.95982i	−0.462916	+	0.267265i	0.250354	+	0.968154i	$0.419453\pi$
$888$	−0.315993	−	0.182439i	−0.0106040	−	0.00612224i
$889$	1.20869	+	2.09352i	0.0405383	+	0.0702143i
$890$	7.54373	−	13.0661i	0.252866	−	0.437978i
$891$	3.53974	+	2.04367i	0.118586	+	0.0684655i
$892$	−32.0080	+	55.4395i	−1.07171	+	1.85625i
$893$	35.1328	+	20.2839i	1.17568	+	0.678776i
$894$	−5.32144	−	9.21700i	−0.177976	−	0.308263i
$895$	−40.8646	−	23.5932i	−1.36595	−	0.788634i
$896$	−7.48042	+	12.9565i	−0.249903	+	0.432845i
$897$	2.63666	−	1.52227i	0.0880354	−	0.0508273i
$898$	3.90331	−	2.25358i	0.130255	−	0.0752029i
$899$	32.9985	−	57.1550i	1.10056	−	1.90623i
$900$	−23.2099	−	40.2007i	−0.773664	−	1.34002i
$901$		−	16.6369i		−	0.554256i
$902$	−3.80664	−	6.59329i	−0.126747	−	0.219533i
$903$	−0.507921	+	0.879746i	−0.0169026	+	0.0292761i
$904$	39.6867	+	68.7394i	1.31996	+	2.28624i
$905$	−32.7180	+	56.6692i	−1.08758	+	1.88375i
$906$	−13.8867	−	8.01749i	−0.461355	−	0.266363i
$907$	−11.8512	−	6.84227i	−0.393512	−	0.227194i	0.290169	−	0.956975i	$-0.406288\pi$
$907$	−11.8512	−	6.84227i	−0.393512	−	0.227194i	−0.683681	+	0.729781i	$0.739622\pi$
$908$	47.4630			1.57511
$909$	32.8498	−	18.9658i	1.08956	−	0.629057i
$910$	−11.4585	−	6.61558i	−0.379846	−	0.219304i
$911$			41.2145i			1.36550i	0.730654	+	0.682748i	$0.239215\pi$
$911$			41.2145i			1.36550i	−0.730654	+	0.682748i	$0.760785\pi$
$912$	2.16269	−	3.74589i	0.0716138	−	0.124039i
$913$	5.61921	−	3.24425i	0.185969	−	0.107369i
$914$			12.1216i			0.400948i
$915$	−1.94343	+	1.12204i	−0.0642478	+	0.0370935i
$916$			39.8177i			1.31561i
$917$	−3.35131	−	5.80465i	−0.110670	−	0.191686i
$918$	17.7152	−	10.2278i	0.584687	−	0.337569i
$919$	−32.1867	+	18.5830i	−1.06174	+	0.612996i	−0.925913	−	0.377736i	$-0.876703\pi$
$919$	−32.1867	+	18.5830i	−1.06174	+	0.612996i	−0.135828	+	0.990732i	$0.543369\pi$
$920$		−	47.4381i		−	1.56399i
$921$	7.92477			0.261130
$922$	34.6500			1.14114
$923$	7.88259	−	13.6530i	0.259459	−	0.449396i
$924$	−0.269289	+	0.466422i	−0.00885896	+	0.0153442i
$925$	0.460381	+	0.797403i	0.0151372	+	0.0262185i
$926$	2.45015			0.0805168
$927$	−12.8053	+	7.39314i	−0.420581	+	0.242822i
$928$	8.84806	−	5.10843i	0.290452	−	0.167692i
$929$	−20.7891			−0.682067			−0.341034	−	0.940051i	$-0.610777\pi$
$929$	−20.7891			−0.682067			−0.341034	+	0.940051i	$0.610777\pi$
$930$	16.5360	+	9.54706i	0.542237	+	0.313061i
$931$	−11.6795	−	20.2294i	−0.382779	−	0.662992i
$932$	−40.5372			−1.32784
$933$	4.12014	+	2.37876i	0.134887	+	0.0778772i
$934$	−82.1710	+	47.4414i	−2.68872	+	1.55233i
$935$	−5.42982	−	3.13491i	−0.177574	−	0.102522i
$936$	−16.0450	+	27.7907i	−0.524447	+	0.908368i
$937$	−54.1220			−1.76809			−0.884045	−	0.467402i	$-0.845190\pi$
$937$	−54.1220			−1.76809			−0.884045	+	0.467402i	$0.845190\pi$
$938$	−5.22874	+	9.05645i	−0.170724	+	0.295703i
$939$	−1.21338	+	2.10164i	−0.0395972	+	0.0685843i
$940$	114.192	−	65.9285i	3.72452	−	2.15035i
$941$	−11.0542	−	19.1464i	−0.360357	−	0.624156i	0.627663	−	0.778485i	$-0.284012\pi$
$941$	−11.0542	−	19.1464i	−0.360357	−	0.624156i	−0.988019	+	0.154329i	$0.950678\pi$
$942$	17.6609	+	10.1965i	0.575423	+	0.332220i
$943$	−10.3328	−	17.8970i	−0.336483	−	0.582806i
$944$		−	26.7525i		−	0.870720i
$945$			4.72826i			0.153810i
$946$		−	4.82834i		−	0.156983i
$947$	40.7579			1.32445			0.662226	−	0.749304i	$-0.269612\pi$
$947$	40.7579			1.32445			0.662226	+	0.749304i	$0.269612\pi$
$948$	10.1956	−	5.88646i	0.331139	−	0.191183i
$949$			10.2582i			0.332995i
$950$	−31.6572	+	18.2773i	−1.02710	+	0.592994i
$951$	0.346917	−	0.200293i	0.0112496	−	0.00649493i
$952$	−6.66240	−	11.5396i	−0.215930	−	0.374001i
$953$	10.0529	+	17.4121i	0.325645	+	0.564034i	0.981643	−	0.190729i	$-0.0610851\pi$
$953$	10.0529	+	17.4121i	0.325645	+	0.564034i	−0.655997	+	0.754763i	$0.727752\pi$
$954$	14.5757	−	25.2459i	0.471906	−	0.817365i
$955$	−60.0149			−1.94204
$956$	17.9031	−	31.0090i	0.579026	−	1.00290i
$957$	1.50118	−	0.866705i	0.0485262	−	0.0280166i
$958$	33.3445	+	19.2515i	1.07731	+	0.621987i
$959$	−5.09704			−0.164592
$960$	5.09961	+	8.83278i	0.164589	+	0.285077i
$961$	20.6225			0.665242
$962$	0.656503	−	1.13710i	0.0211665	−	0.0366614i
$963$	25.8368	+	14.9169i	0.832579	+	0.480690i
$964$	−43.5709	−	75.4671i	−1.40333	−	2.43063i
$965$	−27.9436	+	16.1333i	−0.899537	+	0.519348i
$966$	−1.10757	+	1.91837i	−0.0356355	+	0.0617224i
$967$	−32.6511			−1.04999			−0.524994	−	0.851106i	$-0.675932\pi$
$967$	−32.6511			−1.04999			−0.524994	+	0.851106i	$0.675932\pi$
$968$			48.9627i			1.57372i
$969$	−2.59846	−	4.50067i	−0.0834747	−	0.144582i
$970$	6.36455	+	11.0237i	0.204353	+	0.353950i
$971$	−18.2734	−	31.6505i	−0.586422	−	1.01571i	−0.994697	−	0.102853i	$-0.967203\pi$
$971$	−18.2734	−	31.6505i	−0.586422	−	1.01571i	0.408275	−	0.912859i	$-0.366131\pi$
$972$	35.7467			1.14658
$973$	2.73923	−	1.58149i	0.0878156	−	0.0507004i
$974$	32.0559	−	55.5224i	1.02714	−	1.77905i
$975$	−3.20137	+	1.84831i	−0.102526	+	0.0591934i
$976$	5.86177	−	3.38429i	0.187631	−	0.108329i
$977$	21.0897	+	36.5285i	0.674721	+	1.16865i	0.976550	+	0.215289i	$0.0690693\pi$
$977$	21.0897	+	36.5285i	0.674721	+	1.16865i	−0.301830	+	0.953362i	$0.597597\pi$
$978$	5.44155			0.174001
$979$	0.535677	−	0.927820i	0.0171203	−	0.0296533i
$980$	−75.9230			−2.42527
$981$	5.97991			0.190924
$982$		−	79.5453i		−	2.53839i
$983$	5.84405			0.186396			0.0931982	−	0.995648i	$-0.470291\pi$
$983$	5.84405			0.186396			0.0931982	+	0.995648i	$0.470291\pi$
$984$	−8.61117	−	4.97166i	−0.274514	−	0.158491i
$985$	25.4094	−	14.6701i	0.809612	−	0.467429i
$986$			88.4640i			2.81727i
$987$	−2.98486			−0.0950091
$988$	29.7932	+	17.2011i	0.947847	+	0.547240i
$989$		−	13.1062i		−	0.416752i
$990$	−5.49303	−	9.51420i	−0.174580	−	0.302381i
$991$	−0.627059	−	1.08610i	−0.0199192	−	0.0345010i	0.855894	−	0.517151i	$-0.173008\pi$
$991$	−0.627059	−	1.08610i	−0.0199192	−	0.0345010i	−0.875813	+	0.482650i	$0.839674\pi$
$992$	6.92092	+	3.99579i	0.219739	+	0.126867i
$993$	−2.83074	+	1.63433i	−0.0898308	+	0.0518639i
$994$			11.4704i			0.363818i
$995$			23.8775i			0.756969i
$996$	8.74032	−	15.1387i	0.276948	−	0.479687i
$997$	14.4316	+	8.33211i	0.457054	+	0.263880i	0.710805	−	0.703389i	$-0.248331\pi$
$997$	14.4316	+	8.33211i	0.457054	+	0.263880i	−0.253751	+	0.967270i	$0.581664\pi$
$998$	−40.3112	+	69.8210i	−1.27603	+	2.21015i
$999$	−0.469213			−0.0148452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.e.a.123.3	✓	58
349.227	even	6	inner	349.2.e.a.227.3	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.e.a.123.3	✓	58	1.1	even	1	trivial
349.2.e.a.227.3	yes	58	349.227	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10033 + 1.21263i) q^{2} +(0.180949 - 0.313412i) q^{3} +(1.94093 - 3.36178i) q^{4} +(-1.51394 + 2.62221i) q^{5} +0.877693i q^{6} +(0.636711 - 0.367605i) q^{7} +4.56397i q^{8} +(1.43452 + 2.48465i) q^{9} +O(q^{10})\)	\(q+(-2.10033 + 1.21263i) q^{2} +(0.180949 - 0.313412i) q^{3} +(1.94093 - 3.36178i) q^{4} +(-1.51394 + 2.62221i) q^{5} +0.877693i q^{6} +(0.636711 - 0.367605i) q^{7} +4.56397i q^{8} +(1.43452 + 2.48465i) q^{9} -7.34336i q^{10} -0.521449i q^{11} +(-0.702417 - 1.21662i) q^{12} +(2.12237 - 1.22535i) q^{13} +(-0.891536 + 1.54419i) q^{14} +(0.547890 + 0.948973i) q^{15} +(-1.65254 - 2.86229i) q^{16} -3.97105 q^{17} +(-6.02591 - 3.47906i) q^{18} +(-1.80811 + 3.13175i) q^{19} +(5.87688 + 10.1791i) q^{20} -0.266071i q^{21} +(0.632323 + 1.09522i) q^{22} +(1.71639 + 2.97288i) q^{23} +(1.43041 + 0.825845i) q^{24} +(-2.08401 - 3.60961i) q^{25} +(-2.97179 + 5.14729i) q^{26} +2.12399 q^{27} -2.85398i q^{28} +(-4.59276 + 7.95490i) q^{29} +(-2.30150 - 1.32877i) q^{30} -7.18488 q^{31} +(-0.963261 - 0.556139i) q^{32} +(-0.163429 - 0.0943555i) q^{33} +(8.34052 - 4.81540i) q^{34} +2.22613i q^{35} +11.1372 q^{36} -0.220912 q^{37} -8.77027i q^{38} -0.886904i q^{39} +(-11.9677 - 6.90957i) q^{40} -6.02009 q^{41} +(0.322645 + 0.558837i) q^{42} +(-3.30643 - 1.90897i) q^{43} +(-1.75300 - 1.01209i) q^{44} -8.68706 q^{45} +(-7.20998 - 4.16268i) q^{46} -11.2183i q^{47} -1.19610 q^{48} +(-3.22973 + 5.59406i) q^{49} +(8.75421 + 5.05424i) q^{50} +(-0.718556 + 1.24458i) q^{51} -9.51328i q^{52} +4.18955i q^{53} +(-4.46108 + 2.57560i) q^{54} +(1.36735 + 0.789441i) q^{55} +(1.67774 + 2.90593i) q^{56} +(0.654352 + 1.13337i) q^{57} -22.2772i q^{58} +(7.00991 + 4.04717i) q^{59} +4.25366 q^{60} +2.04793i q^{61} +(15.0906 - 8.71258i) q^{62} +(1.82674 + 1.05467i) q^{63} +9.30773 q^{64} +7.42042i q^{65} +0.457672 q^{66} +5.86487 q^{67} +(-7.70752 + 13.3498i) q^{68} +1.24232 q^{69} +(-2.69946 - 4.67560i) q^{70} +(5.57107 - 3.21646i) q^{71} +(-11.3399 + 6.54709i) q^{72} +(-2.09291 + 3.62502i) q^{73} +(0.463987 - 0.267883i) q^{74} -1.50839 q^{75} +(7.01884 + 12.1570i) q^{76} +(-0.191687 - 0.332012i) q^{77} +(1.07548 + 1.86279i) q^{78} +8.38030i q^{79} +10.0074 q^{80} +(-3.91921 + 6.78828i) q^{81} +(12.6442 - 7.30012i) q^{82} +(6.22161 + 10.7761i) q^{83} +(-0.894473 - 0.516424i) q^{84} +(6.01192 - 10.4129i) q^{85} +9.25947 q^{86} +(1.66211 + 2.87886i) q^{87} +2.37988 q^{88} +(1.77931 + 1.02729i) q^{89} +(18.2457 - 10.5342i) q^{90} +(0.900892 - 1.56039i) q^{91} +13.3256 q^{92} +(-1.30009 + 2.25183i) q^{93} +(13.6036 + 23.5621i) q^{94} +(-5.47474 - 9.48253i) q^{95} +(-0.348602 + 0.201265i) q^{96} +(-1.50118 + 0.866708i) q^{97} -15.6658i q^{98} +(1.29562 - 0.748026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9}+O(q^{10}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9	\( 58 q - 3 q^{2} + 27 q^{4} + 2 q^{5} - 29 q^{9} - q^{12} - 3 q^{13} - 10 q^{14} + q^{15} - 29 q^{16} - 10 q^{17} + 15 q^{18} - 9 q^{19} - 3 q^{22} - 17 q^{23} - 48 q^{24} - 29 q^{25} - 4 q^{26} + 18 q^{27} - 2 q^{29} + 9 q^{30} + 32 q^{31} + 9 q^{32} - 12 q^{33} - 63 q^{34} + 24 q^{36} - 16 q^{37} + 54 q^{40} - 10 q^{41} - 15 q^{42} - 45 q^{43} + 18 q^{44} - 2 q^{45} + 27 q^{46} + 6 q^{48} + 35 q^{49} + 6 q^{50} - 14 q^{51} + 27 q^{54} + 24 q^{55} + 11 q^{56} - 29 q^{57} - 18 q^{59} + 116 q^{60} - 9 q^{62} - 21 q^{63} - 132 q^{64} + 130 q^{66} + 58 q^{67} + 42 q^{69} + 40 q^{70} - 24 q^{71} + 72 q^{72} - 6 q^{73} + 30 q^{74} - 58 q^{75} + 37 q^{76} - 4 q^{77} - 33 q^{78} - 40 q^{80} - 81 q^{81} + 21 q^{82} + 12 q^{83} + 18 q^{84} - 11 q^{85} - 126 q^{86} - 42 q^{87} - 50 q^{88} + 3 q^{89} - 12 q^{90} - 28 q^{91} - 120 q^{92} + 31 q^{93} + 29 q^{94} + 60 q^{95} - 120 q^{96} - 15 q^{97} + 39 q^{99}+O(q^{100}) \) 58 * q - 3 * q^2 + 27 * q^4 + 2 * q^5 - 29 * q^9 - q^12 - 3 * q^13 - 10 * q^14 + q^15 - 29 * q^16 - 10 * q^17 + 15 * q^18 - 9 * q^19 - 3 * q^22 - 17 * q^23 - 48 * q^24 - 29 * q^25 - 4 * q^26 + 18 * q^27 - 2 * q^29 + 9 * q^30 + 32 * q^31 + 9 * q^32 - 12 * q^33 - 63 * q^34 + 24 * q^36 - 16 * q^37 + 54 * q^40 - 10 * q^41 - 15 * q^42 - 45 * q^43 + 18 * q^44 - 2 * q^45 + 27 * q^46 + 6 * q^48 + 35 * q^49 + 6 * q^50 - 14 * q^51 + 27 * q^54 + 24 * q^55 + 11 * q^56 - 29 * q^57 - 18 * q^59 + 116 * q^60 - 9 * q^62 - 21 * q^63 - 132 * q^64 + 130 * q^66 + 58 * q^67 + 42 * q^69 + 40 * q^70 - 24 * q^71 + 72 * q^72 - 6 * q^73 + 30 * q^74 - 58 * q^75 + 37 * q^76 - 4 * q^77 - 33 * q^78 - 40 * q^80 - 81 * q^81 + 21 * q^82 + 12 * q^83 + 18 * q^84 - 11 * q^85 - 126 * q^86 - 42 * q^87 - 50 * q^88 + 3 * q^89 - 12 * q^90 - 28 * q^91 - 120 * q^92 + 31 * q^93 + 29 * q^94 + 60 * q^95 - 120 * q^96 - 15 * q^97 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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