Properties

Label 1110.2.o.b.253.15
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(253,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1110.253");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), 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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.15
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.b.487.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.314477 - 2.21384i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.376687 + 0.376687i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-0.314477 - 2.21384i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-0.376687 + 0.376687i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-0.314477 - 2.21384i) q^{10} -1.28566i q^{11} +(0.707107 - 0.707107i) q^{12} +5.12767 q^{13} +(-0.376687 + 0.376687i) q^{14} +(-1.78779 - 1.34306i) q^{15} +1.00000 q^{16} +2.31038i q^{17} -1.00000i q^{18} +(-3.87466 - 3.87466i) q^{19} +(-0.314477 - 2.21384i) q^{20} +0.532716i q^{21} -1.28566i q^{22} +6.29757 q^{23} +(0.707107 - 0.707107i) q^{24} +(-4.80221 + 1.39241i) q^{25} +5.12767 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.376687 + 0.376687i) q^{28} +(1.15504 - 1.15504i) q^{29} +(-1.78779 - 1.34306i) q^{30} +(-7.11133 - 7.11133i) q^{31} +1.00000 q^{32} +(-0.909099 - 0.909099i) q^{33} +2.31038i q^{34} +(0.952386 + 0.715467i) q^{35} -1.00000i q^{36} +(-3.20192 - 5.17182i) q^{37} +(-3.87466 - 3.87466i) q^{38} +(3.62581 - 3.62581i) q^{39} +(-0.314477 - 2.21384i) q^{40} +2.12896i q^{41} +0.532716i q^{42} +2.56124 q^{43} -1.28566i q^{44} +(-2.21384 + 0.314477i) q^{45} +6.29757 q^{46} +(2.64523 - 2.64523i) q^{47} +(0.707107 - 0.707107i) q^{48} +6.71621i q^{49} +(-4.80221 + 1.39241i) q^{50} +(1.63368 + 1.63368i) q^{51} +5.12767 q^{52} +(0.572887 + 0.572887i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(-2.84625 + 0.404311i) q^{55} +(-0.376687 + 0.376687i) q^{56} -5.47960 q^{57} +(1.15504 - 1.15504i) q^{58} +(1.04438 + 1.04438i) q^{59} +(-1.78779 - 1.34306i) q^{60} +(3.44882 + 3.44882i) q^{61} +(-7.11133 - 7.11133i) q^{62} +(0.376687 + 0.376687i) q^{63} +1.00000 q^{64} +(-1.61253 - 11.3519i) q^{65} +(-0.909099 - 0.909099i) q^{66} +(-5.32260 - 5.32260i) q^{67} +2.31038i q^{68} +(4.45305 - 4.45305i) q^{69} +(0.952386 + 0.715467i) q^{70} +4.38568 q^{71} -1.00000i q^{72} +(-9.81049 + 9.81049i) q^{73} +(-3.20192 - 5.17182i) q^{74} +(-2.41109 + 4.38025i) q^{75} +(-3.87466 - 3.87466i) q^{76} +(0.484292 + 0.484292i) q^{77} +(3.62581 - 3.62581i) q^{78} +(11.4000 + 11.4000i) q^{79} +(-0.314477 - 2.21384i) q^{80} -1.00000 q^{81} +2.12896i q^{82} +(11.5202 + 11.5202i) q^{83} +0.532716i q^{84} +(5.11482 - 0.726561i) q^{85} +2.56124 q^{86} -1.63348i q^{87} -1.28566i q^{88} +(-8.09354 + 8.09354i) q^{89} +(-2.21384 + 0.314477i) q^{90} +(-1.93153 + 1.93153i) q^{91} +6.29757 q^{92} -10.0569 q^{93} +(2.64523 - 2.64523i) q^{94} +(-7.35940 + 9.79638i) q^{95} +(0.707107 - 0.707107i) q^{96} -8.07546i q^{97} +6.71621i q^{98} -1.28566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000 0.500000
\(5\) −0.314477 2.21384i −0.140638 0.990061i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) −0.376687 + 0.376687i −0.142374 + 0.142374i −0.774702 0.632327i \(-0.782100\pi\)
0.632327 + 0.774702i \(0.282100\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000i 0.333333i
\(10\) −0.314477 2.21384i −0.0994464 0.700079i
\(11\) 1.28566i 0.387641i −0.981037 0.193821i \(-0.937912\pi\)
0.981037 0.193821i \(-0.0620880\pi\)
\(12\) 0.707107 0.707107i 0.204124 0.204124i
\(13\) 5.12767 1.42216 0.711080 0.703112i \(-0.248207\pi\)
0.711080 + 0.703112i \(0.248207\pi\)
\(14\) −0.376687 + 0.376687i −0.100674 + 0.100674i
\(15\) −1.78779 1.34306i −0.461606 0.346775i
\(16\) 1.00000 0.250000
\(17\) 2.31038i 0.560349i 0.959949 + 0.280175i \(0.0903924\pi\)
−0.959949 + 0.280175i \(0.909608\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.87466 3.87466i −0.888908 0.888908i 0.105510 0.994418i \(-0.466352\pi\)
−0.994418 + 0.105510i \(0.966352\pi\)
\(20\) −0.314477 2.21384i −0.0703192 0.495031i
\(21\) 0.532716i 0.116248i
\(22\) 1.28566i 0.274104i
\(23\) 6.29757 1.31313 0.656567 0.754268i \(-0.272008\pi\)
0.656567 + 0.754268i \(0.272008\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) −4.80221 + 1.39241i −0.960442 + 0.278481i
\(26\) 5.12767 1.00562
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −0.376687 + 0.376687i −0.0711872 + 0.0711872i
\(29\) 1.15504 1.15504i 0.214486 0.214486i −0.591684 0.806170i \(-0.701537\pi\)
0.806170 + 0.591684i \(0.201537\pi\)
\(30\) −1.78779 1.34306i −0.326405 0.245207i
\(31\) −7.11133 7.11133i −1.27723 1.27723i −0.942210 0.335023i \(-0.891256\pi\)
−0.335023 0.942210i \(-0.608744\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.909099 0.909099i −0.158254 0.158254i
\(34\) 2.31038i 0.396227i
\(35\) 0.952386 + 0.715467i 0.160983 + 0.120936i
\(36\) 1.00000i 0.166667i
\(37\) −3.20192 5.17182i −0.526392 0.850242i
\(38\) −3.87466 3.87466i −0.628553 0.628553i
\(39\) 3.62581 3.62581i 0.580594 0.580594i
\(40\) −0.314477 2.21384i −0.0497232 0.350039i
\(41\) 2.12896i 0.332487i 0.986085 + 0.166244i \(0.0531638\pi\)
−0.986085 + 0.166244i \(0.946836\pi\)
\(42\) 0.532716i 0.0821999i
\(43\) 2.56124 0.390585 0.195292 0.980745i \(-0.437434\pi\)
0.195292 + 0.980745i \(0.437434\pi\)
\(44\) 1.28566i 0.193821i
\(45\) −2.21384 + 0.314477i −0.330020 + 0.0468795i
\(46\) 6.29757 0.928526
\(47\) 2.64523 2.64523i 0.385847 0.385847i −0.487356 0.873203i \(-0.662039\pi\)
0.873203 + 0.487356i \(0.162039\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 6.71621i 0.959459i
\(50\) −4.80221 + 1.39241i −0.679135 + 0.196916i
\(51\) 1.63368 + 1.63368i 0.228762 + 0.228762i
\(52\) 5.12767 0.711080
\(53\) 0.572887 + 0.572887i 0.0786920 + 0.0786920i 0.745357 0.666665i \(-0.232279\pi\)
−0.666665 + 0.745357i \(0.732279\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) −2.84625 + 0.404311i −0.383788 + 0.0545172i
\(56\) −0.376687 + 0.376687i −0.0503369 + 0.0503369i
\(57\) −5.47960 −0.725790
\(58\) 1.15504 1.15504i 0.151664 0.151664i
\(59\) 1.04438 + 1.04438i 0.135966 + 0.135966i 0.771814 0.635848i \(-0.219349\pi\)
−0.635848 + 0.771814i \(0.719349\pi\)
\(60\) −1.78779 1.34306i −0.230803 0.173388i
\(61\) 3.44882 + 3.44882i 0.441576 + 0.441576i 0.892542 0.450965i \(-0.148920\pi\)
−0.450965 + 0.892542i \(0.648920\pi\)
\(62\) −7.11133 7.11133i −0.903140 0.903140i
\(63\) 0.376687 + 0.376687i 0.0474581 + 0.0474581i
\(64\) 1.00000 0.125000
\(65\) −1.61253 11.3519i −0.200010 1.40802i
\(66\) −0.909099 0.909099i −0.111902 0.111902i
\(67\) −5.32260 5.32260i −0.650259 0.650259i 0.302797 0.953055i \(-0.402080\pi\)
−0.953055 + 0.302797i \(0.902080\pi\)
\(68\) 2.31038i 0.280175i
\(69\) 4.45305 4.45305i 0.536085 0.536085i
\(70\) 0.952386 + 0.715467i 0.113832 + 0.0855147i
\(71\) 4.38568 0.520484 0.260242 0.965543i \(-0.416198\pi\)
0.260242 + 0.965543i \(0.416198\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −9.81049 + 9.81049i −1.14823 + 1.14823i −0.161330 + 0.986901i \(0.551578\pi\)
−0.986901 + 0.161330i \(0.948422\pi\)
\(74\) −3.20192 5.17182i −0.372215 0.601212i
\(75\) −2.41109 + 4.38025i −0.278409 + 0.505788i
\(76\) −3.87466 3.87466i −0.444454 0.444454i
\(77\) 0.484292 + 0.484292i 0.0551902 + 0.0551902i
\(78\) 3.62581 3.62581i 0.410542 0.410542i
\(79\) 11.4000 + 11.4000i 1.28259 + 1.28259i 0.939186 + 0.343409i \(0.111582\pi\)
0.343409 + 0.939186i \(0.388418\pi\)
\(80\) −0.314477 2.21384i −0.0351596 0.247515i
\(81\) −1.00000 −0.111111
\(82\) 2.12896i 0.235104i
\(83\) 11.5202 + 11.5202i 1.26450 + 1.26450i 0.948887 + 0.315617i \(0.102212\pi\)
0.315617 + 0.948887i \(0.397788\pi\)
\(84\) 0.532716i 0.0581241i
\(85\) 5.11482 0.726561i 0.554780 0.0788066i
\(86\) 2.56124 0.276185
\(87\) 1.63348i 0.175127i
\(88\) 1.28566i 0.137052i
\(89\) −8.09354 + 8.09354i −0.857914 + 0.857914i −0.991092 0.133179i \(-0.957482\pi\)
0.133179 + 0.991092i \(0.457482\pi\)
\(90\) −2.21384 + 0.314477i −0.233360 + 0.0331488i
\(91\) −1.93153 + 1.93153i −0.202479 + 0.202479i
\(92\) 6.29757 0.656567
\(93\) −10.0569 −1.04286
\(94\) 2.64523 2.64523i 0.272835 0.272835i
\(95\) −7.35940 + 9.79638i −0.755059 + 1.00509i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 8.07546i 0.819939i −0.912099 0.409969i \(-0.865539\pi\)
0.912099 0.409969i \(-0.134461\pi\)
\(98\) 6.71621i 0.678440i
\(99\) −1.28566 −0.129214
\(100\) −4.80221 + 1.39241i −0.480221 + 0.139241i
\(101\) 15.8768i 1.57980i 0.613233 + 0.789902i \(0.289869\pi\)
−0.613233 + 0.789902i \(0.710131\pi\)
\(102\) 1.63368 + 1.63368i 0.161759 + 0.161759i
\(103\) 9.00947i 0.887729i −0.896094 0.443865i \(-0.853607\pi\)
0.896094 0.443865i \(-0.146393\pi\)
\(104\) 5.12767 0.502809
\(105\) 1.17935 0.167527i 0.115093 0.0163490i
\(106\) 0.572887 + 0.572887i 0.0556437 + 0.0556437i
\(107\) 1.41163 1.41163i 0.136468 0.136468i −0.635573 0.772041i \(-0.719236\pi\)
0.772041 + 0.635573i \(0.219236\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 1.15892 + 1.15892i 0.111004 + 0.111004i 0.760427 0.649423i \(-0.224990\pi\)
−0.649423 + 0.760427i \(0.724990\pi\)
\(110\) −2.84625 + 0.404311i −0.271379 + 0.0385495i
\(111\) −5.92113 1.39293i −0.562009 0.132211i
\(112\) −0.376687 + 0.376687i −0.0355936 + 0.0355936i
\(113\) 2.77598i 0.261142i 0.991439 + 0.130571i \(0.0416811\pi\)
−0.991439 + 0.130571i \(0.958319\pi\)
\(114\) −5.47960 −0.513211
\(115\) −1.98044 13.9418i −0.184677 1.30008i
\(116\) 1.15504 1.15504i 0.107243 0.107243i
\(117\) 5.12767i 0.474053i
\(118\) 1.04438 + 1.04438i 0.0961427 + 0.0961427i
\(119\) −0.870290 0.870290i −0.0797794 0.0797794i
\(120\) −1.78779 1.34306i −0.163202 0.122604i
\(121\) 9.34708 0.849734
\(122\) 3.44882 + 3.44882i 0.312242 + 0.312242i
\(123\) 1.50540 + 1.50540i 0.135737 + 0.135737i
\(124\) −7.11133 7.11133i −0.638616 0.638616i
\(125\) 4.59275 + 10.1935i 0.410788 + 0.911731i
\(126\) 0.376687 + 0.376687i 0.0335580 + 0.0335580i
\(127\) −10.6282 + 10.6282i −0.943105 + 0.943105i −0.998466 0.0553618i \(-0.982369\pi\)
0.0553618 + 0.998466i \(0.482369\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.81107 1.81107i 0.159456 0.159456i
\(130\) −1.61253 11.3519i −0.141429 0.995623i
\(131\) 10.6555 + 10.6555i 0.930972 + 0.930972i 0.997767 0.0667945i \(-0.0212772\pi\)
−0.0667945 + 0.997767i \(0.521277\pi\)
\(132\) −0.909099 0.909099i −0.0791269 0.0791269i
\(133\) 2.91907 0.253115
\(134\) −5.32260 5.32260i −0.459802 0.459802i
\(135\) −1.34306 + 1.78779i −0.115592 + 0.153869i
\(136\) 2.31038i 0.198113i
\(137\) 8.98795 8.98795i 0.767892 0.767892i −0.209843 0.977735i \(-0.567295\pi\)
0.977735 + 0.209843i \(0.0672953\pi\)
\(138\) 4.45305 4.45305i 0.379069 0.379069i
\(139\) 19.4517 1.64987 0.824937 0.565225i \(-0.191211\pi\)
0.824937 + 0.565225i \(0.191211\pi\)
\(140\) 0.952386 + 0.715467i 0.0804913 + 0.0604680i
\(141\) 3.74092i 0.315042i
\(142\) 4.38568 0.368038
\(143\) 6.59244i 0.551287i
\(144\) 1.00000i 0.0833333i
\(145\) −2.92032 2.19385i −0.242519 0.182189i
\(146\) −9.81049 + 9.81049i −0.811922 + 0.811922i
\(147\) 4.74908 + 4.74908i 0.391698 + 0.391698i
\(148\) −3.20192 5.17182i −0.263196 0.425121i
\(149\) 15.6534i 1.28238i −0.767382 0.641190i \(-0.778441\pi\)
0.767382 0.641190i \(-0.221559\pi\)
\(150\) −2.41109 + 4.38025i −0.196865 + 0.357646i
\(151\) 3.10992i 0.253082i 0.991961 + 0.126541i \(0.0403875\pi\)
−0.991961 + 0.126541i \(0.959612\pi\)
\(152\) −3.87466 3.87466i −0.314276 0.314276i
\(153\) 2.31038 0.186783
\(154\) 0.484292 + 0.484292i 0.0390253 + 0.0390253i
\(155\) −13.5070 + 17.9797i −1.08491 + 1.44417i
\(156\) 3.62581 3.62581i 0.290297 0.290297i
\(157\) −12.5025 + 12.5025i −0.997805 + 0.997805i −0.999998 0.00219308i \(-0.999302\pi\)
0.00219308 + 0.999998i \(0.499302\pi\)
\(158\) 11.4000 + 11.4000i 0.906931 + 0.906931i
\(159\) 0.810184 0.0642518
\(160\) −0.314477 2.21384i −0.0248616 0.175020i
\(161\) −2.37221 + 2.37221i −0.186957 + 0.186957i
\(162\) −1.00000 −0.0785674
\(163\) 8.61293i 0.674617i −0.941394 0.337308i \(-0.890483\pi\)
0.941394 0.337308i \(-0.109517\pi\)
\(164\) 2.12896i 0.166244i
\(165\) −1.72671 + 2.29849i −0.134424 + 0.178938i
\(166\) 11.5202 + 11.5202i 0.894139 + 0.894139i
\(167\) 21.8398i 1.69001i 0.534755 + 0.845007i \(0.320404\pi\)
−0.534755 + 0.845007i \(0.679596\pi\)
\(168\) 0.532716i 0.0410999i
\(169\) 13.2930 1.02254
\(170\) 5.11482 0.726561i 0.392289 0.0557247i
\(171\) −3.87466 + 3.87466i −0.296303 + 0.296303i
\(172\) 2.56124 0.195292
\(173\) −1.32378 + 1.32378i −0.100645 + 0.100645i −0.755636 0.654991i \(-0.772672\pi\)
0.654991 + 0.755636i \(0.272672\pi\)
\(174\) 1.63348i 0.123833i
\(175\) 1.28443 2.33343i 0.0970937 0.176391i
\(176\) 1.28566i 0.0969103i
\(177\) 1.47697 0.111016
\(178\) −8.09354 + 8.09354i −0.606636 + 0.606636i
\(179\) 17.8003 17.8003i 1.33046 1.33046i 0.425501 0.904958i \(-0.360098\pi\)
0.904958 0.425501i \(-0.139902\pi\)
\(180\) −2.21384 + 0.314477i −0.165010 + 0.0234397i
\(181\) −1.98719 −0.147707 −0.0738533 0.997269i \(-0.523530\pi\)
−0.0738533 + 0.997269i \(0.523530\pi\)
\(182\) −1.93153 + 1.93153i −0.143174 + 0.143174i
\(183\) 4.87737 0.360546
\(184\) 6.29757 0.464263
\(185\) −10.4427 + 8.71497i −0.767760 + 0.640737i
\(186\) −10.0569 −0.737411
\(187\) 2.97036 0.217214
\(188\) 2.64523 2.64523i 0.192923 0.192923i
\(189\) 0.532716 0.0387494
\(190\) −7.35940 + 9.79638i −0.533907 + 0.710704i
\(191\) −4.41456 + 4.41456i −0.319426 + 0.319426i −0.848547 0.529120i \(-0.822522\pi\)
0.529120 + 0.848547i \(0.322522\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) −2.09366 −0.150705 −0.0753524 0.997157i \(-0.524008\pi\)
−0.0753524 + 0.997157i \(0.524008\pi\)
\(194\) 8.07546i 0.579784i
\(195\) −9.16721 6.88674i −0.656477 0.493170i
\(196\) 6.71621i 0.479730i
\(197\) −4.75052 + 4.75052i −0.338460 + 0.338460i −0.855788 0.517327i \(-0.826927\pi\)
0.517327 + 0.855788i \(0.326927\pi\)
\(198\) −1.28566 −0.0913679
\(199\) −4.93690 + 4.93690i −0.349968 + 0.349968i −0.860097 0.510130i \(-0.829597\pi\)
0.510130 + 0.860097i \(0.329597\pi\)
\(200\) −4.80221 + 1.39241i −0.339567 + 0.0984580i
\(201\) −7.52729 −0.530934
\(202\) 15.8768i 1.11709i
\(203\) 0.870179i 0.0610746i
\(204\) 1.63368 + 1.63368i 0.114381 + 0.114381i
\(205\) 4.71318 0.669508i 0.329183 0.0467605i
\(206\) 9.00947i 0.627719i
\(207\) 6.29757i 0.437711i
\(208\) 5.12767 0.355540
\(209\) −4.98150 + 4.98150i −0.344577 + 0.344577i
\(210\) 1.17935 0.167527i 0.0813829 0.0115605i
\(211\) −13.1658 −0.906374 −0.453187 0.891416i \(-0.649713\pi\)
−0.453187 + 0.891416i \(0.649713\pi\)
\(212\) 0.572887 + 0.572887i 0.0393460 + 0.0393460i
\(213\) 3.10114 3.10114i 0.212487 0.212487i
\(214\) 1.41163 1.41163i 0.0964974 0.0964974i
\(215\) −0.805450 5.67018i −0.0549312 0.386703i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) 5.35750 0.363690
\(218\) 1.15892 + 1.15892i 0.0784919 + 0.0784919i
\(219\) 13.8741i 0.937526i
\(220\) −2.84625 + 0.404311i −0.191894 + 0.0272586i
\(221\) 11.8469i 0.796906i
\(222\) −5.92113 1.39293i −0.397400 0.0934874i
\(223\) −13.0670 13.0670i −0.875031 0.875031i 0.117984 0.993015i \(-0.462357\pi\)
−0.993015 + 0.117984i \(0.962357\pi\)
\(224\) −0.376687 + 0.376687i −0.0251685 + 0.0251685i
\(225\) 1.39241 + 4.80221i 0.0928271 + 0.320147i
\(226\) 2.77598i 0.184655i
\(227\) 16.0865i 1.06770i −0.845580 0.533848i \(-0.820745\pi\)
0.845580 0.533848i \(-0.179255\pi\)
\(228\) −5.47960 −0.362895
\(229\) 6.71533i 0.443762i −0.975074 0.221881i \(-0.928780\pi\)
0.975074 0.221881i \(-0.0712196\pi\)
\(230\) −1.98044 13.9418i −0.130586 0.919297i
\(231\) 0.684892 0.0450626
\(232\) 1.15504 1.15504i 0.0758322 0.0758322i
\(233\) −4.61749 + 4.61749i −0.302502 + 0.302502i −0.841992 0.539490i \(-0.818617\pi\)
0.539490 + 0.841992i \(0.318617\pi\)
\(234\) 5.12767i 0.335206i
\(235\) −6.68799 5.02426i −0.436277 0.327747i
\(236\) 1.04438 + 1.04438i 0.0679832 + 0.0679832i
\(237\) 16.1220 1.04723
\(238\) −0.870290 0.870290i −0.0564125 0.0564125i
\(239\) −13.1078 13.1078i −0.847873 0.847873i 0.141995 0.989867i \(-0.454648\pi\)
−0.989867 + 0.141995i \(0.954648\pi\)
\(240\) −1.78779 1.34306i −0.115402 0.0866938i
\(241\) −12.6538 + 12.6538i −0.815103 + 0.815103i −0.985394 0.170291i \(-0.945529\pi\)
0.170291 + 0.985394i \(0.445529\pi\)
\(242\) 9.34708 0.600853
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 3.44882 + 3.44882i 0.220788 + 0.220788i
\(245\) 14.8686 2.11209i 0.949923 0.134937i
\(246\) 1.50540 + 1.50540i 0.0959808 + 0.0959808i
\(247\) −19.8680 19.8680i −1.26417 1.26417i
\(248\) −7.11133 7.11133i −0.451570 0.451570i
\(249\) 16.2920 1.03246
\(250\) 4.59275 + 10.1935i 0.290471 + 0.644691i
\(251\) −0.829972 0.829972i −0.0523874 0.0523874i 0.680428 0.732815i \(-0.261794\pi\)
−0.732815 + 0.680428i \(0.761794\pi\)
\(252\) 0.376687 + 0.376687i 0.0237291 + 0.0237291i
\(253\) 8.09653i 0.509025i
\(254\) −10.6282 + 10.6282i −0.666876 + 0.666876i
\(255\) 3.10297 4.13048i 0.194315 0.258661i
\(256\) 1.00000 0.0625000
\(257\) 9.61238i 0.599604i 0.954001 + 0.299802i \(0.0969206\pi\)
−0.954001 + 0.299802i \(0.903079\pi\)
\(258\) 1.81107 1.81107i 0.112752 0.112752i
\(259\) 3.15428 + 0.742037i 0.195997 + 0.0461079i
\(260\) −1.61253 11.3519i −0.100005 0.704012i
\(261\) −1.15504 1.15504i −0.0714953 0.0714953i
\(262\) 10.6555 + 10.6555i 0.658297 + 0.658297i
\(263\) −11.2512 + 11.2512i −0.693779 + 0.693779i −0.963061 0.269283i \(-0.913213\pi\)
0.269283 + 0.963061i \(0.413213\pi\)
\(264\) −0.909099 0.909099i −0.0559512 0.0559512i
\(265\) 1.08812 1.44844i 0.0668428 0.0889770i
\(266\) 2.91907 0.178980
\(267\) 11.4460i 0.700483i
\(268\) −5.32260 5.32260i −0.325129 0.325129i
\(269\) 23.2912i 1.42009i 0.704158 + 0.710043i \(0.251325\pi\)
−0.704158 + 0.710043i \(0.748675\pi\)
\(270\) −1.34306 + 1.78779i −0.0817357 + 0.108802i
\(271\) 13.8775 0.842996 0.421498 0.906829i \(-0.361504\pi\)
0.421498 + 0.906829i \(0.361504\pi\)
\(272\) 2.31038i 0.140087i
\(273\) 2.73159i 0.165323i
\(274\) 8.98795 8.98795i 0.542982 0.542982i
\(275\) 1.79016 + 6.17401i 0.107951 + 0.372307i
\(276\) 4.45305 4.45305i 0.268042 0.268042i
\(277\) −6.57502 −0.395055 −0.197527 0.980297i \(-0.563291\pi\)
−0.197527 + 0.980297i \(0.563291\pi\)
\(278\) 19.4517 1.16664
\(279\) −7.11133 + 7.11133i −0.425744 + 0.425744i
\(280\) 0.952386 + 0.715467i 0.0569160 + 0.0427573i
\(281\) −13.5903 + 13.5903i −0.810729 + 0.810729i −0.984743 0.174015i \(-0.944326\pi\)
0.174015 + 0.984743i \(0.444326\pi\)
\(282\) 3.74092i 0.222769i
\(283\) 8.54984i 0.508235i 0.967173 + 0.254118i \(0.0817850\pi\)
−0.967173 + 0.254118i \(0.918215\pi\)
\(284\) 4.38568 0.260242
\(285\) 1.72321 + 12.1310i 0.102074 + 0.718577i
\(286\) 6.59244i 0.389819i
\(287\) −0.801951 0.801951i −0.0473377 0.0473377i
\(288\) 1.00000i 0.0589256i
\(289\) 11.6621 0.686009
\(290\) −2.92032 2.19385i −0.171487 0.128827i
\(291\) −5.71021 5.71021i −0.334739 0.334739i
\(292\) −9.81049 + 9.81049i −0.574115 + 0.574115i
\(293\) 7.61554 + 7.61554i 0.444905 + 0.444905i 0.893656 0.448752i \(-0.148131\pi\)
−0.448752 + 0.893656i \(0.648131\pi\)
\(294\) 4.74908 + 4.74908i 0.276972 + 0.276972i
\(295\) 1.98366 2.64052i 0.115493 0.153737i
\(296\) −3.20192 5.17182i −0.186108 0.300606i
\(297\) −0.909099 + 0.909099i −0.0527513 + 0.0527513i
\(298\) 15.6534i 0.906779i
\(299\) 32.2918 1.86749
\(300\) −2.41109 + 4.38025i −0.139205 + 0.252894i
\(301\) −0.964785 + 0.964785i −0.0556093 + 0.0556093i
\(302\) 3.10992i 0.178956i
\(303\) 11.2266 + 11.2266i 0.644952 + 0.644952i
\(304\) −3.87466 3.87466i −0.222227 0.222227i
\(305\) 6.55058 8.71973i 0.375085 0.499290i
\(306\) 2.31038 0.132076
\(307\) −19.6731 19.6731i −1.12280 1.12280i −0.991319 0.131482i \(-0.958026\pi\)
−0.131482 0.991319i \(-0.541974\pi\)
\(308\) 0.484292 + 0.484292i 0.0275951 + 0.0275951i
\(309\) −6.37065 6.37065i −0.362414 0.362414i
\(310\) −13.5070 + 17.9797i −0.767147 + 1.02118i
\(311\) −3.86047 3.86047i −0.218907 0.218907i 0.589131 0.808038i \(-0.299470\pi\)
−0.808038 + 0.589131i \(0.799470\pi\)
\(312\) 3.62581 3.62581i 0.205271 0.205271i
\(313\) 18.9968 1.07376 0.536880 0.843659i \(-0.319603\pi\)
0.536880 + 0.843659i \(0.319603\pi\)
\(314\) −12.5025 + 12.5025i −0.705554 + 0.705554i
\(315\) 0.715467 0.952386i 0.0403120 0.0536609i
\(316\) 11.4000 + 11.4000i 0.641297 + 0.641297i
\(317\) 17.8153 + 17.8153i 1.00061 + 1.00061i 1.00000 0.000608272i \(0.000193619\pi\)
0.000608272 1.00000i \(0.499806\pi\)
\(318\) 0.810184 0.0454329
\(319\) −1.48499 1.48499i −0.0831435 0.0831435i
\(320\) −0.314477 2.21384i −0.0175798 0.123758i
\(321\) 1.99635i 0.111426i
\(322\) −2.37221 + 2.37221i −0.132198 + 0.132198i
\(323\) 8.95194 8.95194i 0.498099 0.498099i
\(324\) −1.00000 −0.0555556
\(325\) −24.6241 + 7.13980i −1.36590 + 0.396045i
\(326\) 8.61293i 0.477026i
\(327\) 1.63896 0.0906347
\(328\) 2.12896i 0.117552i
\(329\) 1.99285i 0.109869i
\(330\) −1.72671 + 2.29849i −0.0950524 + 0.126528i
\(331\) −1.11563 + 1.11563i −0.0613208 + 0.0613208i −0.737102 0.675781i \(-0.763806\pi\)
0.675781 + 0.737102i \(0.263806\pi\)
\(332\) 11.5202 + 11.5202i 0.632252 + 0.632252i
\(333\) −5.17182 + 3.20192i −0.283414 + 0.175464i
\(334\) 21.8398i 1.19502i
\(335\) −10.1096 + 13.4572i −0.552344 + 0.735247i
\(336\) 0.532716i 0.0290621i
\(337\) −19.6821 19.6821i −1.07215 1.07215i −0.997186 0.0749653i \(-0.976115\pi\)
−0.0749653 0.997186i \(-0.523885\pi\)
\(338\) 13.2930 0.723042
\(339\) 1.96291 + 1.96291i 0.106611 + 0.106611i
\(340\) 5.11482 0.726561i 0.277390 0.0394033i
\(341\) −9.14275 + 9.14275i −0.495108 + 0.495108i
\(342\) −3.87466 + 3.87466i −0.209518 + 0.209518i
\(343\) −5.16672 5.16672i −0.278977 0.278977i
\(344\) 2.56124 0.138093
\(345\) −11.2587 8.45798i −0.606151 0.455362i
\(346\) −1.32378 + 1.32378i −0.0711669 + 0.0711669i
\(347\) −3.98304 −0.213821 −0.106910 0.994269i \(-0.534096\pi\)
−0.106910 + 0.994269i \(0.534096\pi\)
\(348\) 1.63348i 0.0875635i
\(349\) 7.69090i 0.411684i −0.978585 0.205842i \(-0.934007\pi\)
0.978585 0.205842i \(-0.0659934\pi\)
\(350\) 1.28443 2.33343i 0.0686556 0.124727i
\(351\) −3.62581 3.62581i −0.193531 0.193531i
\(352\) 1.28566i 0.0685259i
\(353\) 21.0577i 1.12079i −0.828226 0.560395i \(-0.810649\pi\)
0.828226 0.560395i \(-0.189351\pi\)
\(354\) 1.47697 0.0785002
\(355\) −1.37919 9.70920i −0.0732000 0.515311i
\(356\) −8.09354 + 8.09354i −0.428957 + 0.428957i
\(357\) −1.23078 −0.0651396
\(358\) 17.8003 17.8003i 0.940777 0.940777i
\(359\) 19.0802i 1.00701i −0.863992 0.503506i \(-0.832043\pi\)
0.863992 0.503506i \(-0.167957\pi\)
\(360\) −2.21384 + 0.314477i −0.116680 + 0.0165744i
\(361\) 11.0260i 0.580315i
\(362\) −1.98719 −0.104444
\(363\) 6.60938 6.60938i 0.346903 0.346903i
\(364\) −1.93153 + 1.93153i −0.101240 + 0.101240i
\(365\) 24.8041 + 18.6337i 1.29830 + 0.975333i
\(366\) 4.87737 0.254944
\(367\) 13.0910 13.0910i 0.683346 0.683346i −0.277407 0.960753i \(-0.589475\pi\)
0.960753 + 0.277407i \(0.0894750\pi\)
\(368\) 6.29757 0.328283
\(369\) 2.12896 0.110829
\(370\) −10.4427 + 8.71497i −0.542889 + 0.453070i
\(371\) −0.431598 −0.0224075
\(372\) −10.0569 −0.521428
\(373\) −17.5157 + 17.5157i −0.906927 + 0.906927i −0.996023 0.0890959i \(-0.971602\pi\)
0.0890959 + 0.996023i \(0.471602\pi\)
\(374\) 2.97036 0.153594
\(375\) 10.4554 + 3.96030i 0.539916 + 0.204509i
\(376\) 2.64523 2.64523i 0.136417 0.136417i
\(377\) 5.92267 5.92267i 0.305033 0.305033i
\(378\) 0.532716 0.0274000
\(379\) 21.8739i 1.12358i −0.827278 0.561792i \(-0.810112\pi\)
0.827278 0.561792i \(-0.189888\pi\)
\(380\) −7.35940 + 9.79638i −0.377529 + 0.502544i
\(381\) 15.0306i 0.770042i
\(382\) −4.41456 + 4.41456i −0.225868 + 0.225868i
\(383\) −5.61751 −0.287042 −0.143521 0.989647i \(-0.545842\pi\)
−0.143521 + 0.989647i \(0.545842\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 0.919848 1.22444i 0.0468798 0.0624035i
\(386\) −2.09366 −0.106564
\(387\) 2.56124i 0.130195i
\(388\) 8.07546i 0.409969i
\(389\) 5.37334 + 5.37334i 0.272439 + 0.272439i 0.830081 0.557642i \(-0.188294\pi\)
−0.557642 + 0.830081i \(0.688294\pi\)
\(390\) −9.16721 6.88674i −0.464200 0.348724i
\(391\) 14.5498i 0.735814i
\(392\) 6.71621i 0.339220i
\(393\) 15.0691 0.760136
\(394\) −4.75052 + 4.75052i −0.239328 + 0.239328i
\(395\) 21.6527 28.8227i 1.08946 1.45023i
\(396\) −1.28566 −0.0646069
\(397\) 17.9874 + 17.9874i 0.902761 + 0.902761i 0.995674 0.0929128i \(-0.0296178\pi\)
−0.0929128 + 0.995674i \(0.529618\pi\)
\(398\) −4.93690 + 4.93690i −0.247465 + 0.247465i
\(399\) 2.06409 2.06409i 0.103334 0.103334i
\(400\) −4.80221 + 1.39241i −0.240110 + 0.0696203i
\(401\) 15.1996 + 15.1996i 0.759033 + 0.759033i 0.976146 0.217113i \(-0.0696641\pi\)
−0.217113 + 0.976146i \(0.569664\pi\)
\(402\) −7.52729 −0.375427
\(403\) −36.4645 36.4645i −1.81643 1.81643i
\(404\) 15.8768i 0.789902i
\(405\) 0.314477 + 2.21384i 0.0156265 + 0.110007i
\(406\) 0.870179i 0.0431863i
\(407\) −6.64920 + 4.11658i −0.329589 + 0.204051i
\(408\) 1.63368 + 1.63368i 0.0808795 + 0.0808795i
\(409\) −27.1312 + 27.1312i −1.34155 + 1.34155i −0.447033 + 0.894517i \(0.647519\pi\)
−0.894517 + 0.447033i \(0.852481\pi\)
\(410\) 4.71318 0.669508i 0.232767 0.0330646i
\(411\) 12.7109i 0.626981i
\(412\) 9.00947i 0.443865i
\(413\) −0.786807 −0.0387163
\(414\) 6.29757i 0.309509i
\(415\) 21.8810 29.1267i 1.07410 1.42977i
\(416\) 5.12767 0.251405
\(417\) 13.7544 13.7544i 0.673558 0.673558i
\(418\) −4.98150 + 4.98150i −0.243653 + 0.243653i
\(419\) 7.19965i 0.351726i −0.984415 0.175863i \(-0.943728\pi\)
0.984415 0.175863i \(-0.0562716\pi\)
\(420\) 1.17935 0.167527i 0.0575464 0.00817448i
\(421\) 6.17926 + 6.17926i 0.301159 + 0.301159i 0.841467 0.540308i \(-0.181692\pi\)
−0.540308 + 0.841467i \(0.681692\pi\)
\(422\) −13.1658 −0.640903
\(423\) −2.64523 2.64523i −0.128616 0.128616i
\(424\) 0.572887 + 0.572887i 0.0278218 + 0.0278218i
\(425\) −3.21699 11.0949i −0.156047 0.538183i
\(426\) 3.10114 3.10114i 0.150251 0.150251i
\(427\) −2.59825 −0.125738
\(428\) 1.41163 1.41163i 0.0682340 0.0682340i
\(429\) −4.66156 4.66156i −0.225062 0.225062i
\(430\) −0.805450 5.67018i −0.0388423 0.273440i
\(431\) 19.0871 + 19.0871i 0.919394 + 0.919394i 0.996985 0.0775910i \(-0.0247228\pi\)
−0.0775910 + 0.996985i \(0.524723\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) −27.0193 27.0193i −1.29847 1.29847i −0.929405 0.369061i \(-0.879679\pi\)
−0.369061 0.929405i \(-0.620321\pi\)
\(434\) 5.35750 0.257168
\(435\) −3.61626 + 0.513691i −0.173386 + 0.0246296i
\(436\) 1.15892 + 1.15892i 0.0555022 + 0.0555022i
\(437\) −24.4009 24.4009i −1.16726 1.16726i
\(438\) 13.8741i 0.662931i
\(439\) −8.21948 + 8.21948i −0.392294 + 0.392294i −0.875504 0.483210i \(-0.839471\pi\)
0.483210 + 0.875504i \(0.339471\pi\)
\(440\) −2.84625 + 0.404311i −0.135690 + 0.0192748i
\(441\) 6.71621 0.319820
\(442\) 11.8469i 0.563497i
\(443\) 7.35664 7.35664i 0.349525 0.349525i −0.510408 0.859932i \(-0.670506\pi\)
0.859932 + 0.510408i \(0.170506\pi\)
\(444\) −5.92113 1.39293i −0.281004 0.0661055i
\(445\) 20.4631 + 15.3726i 0.970042 + 0.728731i
\(446\) −13.0670 13.0670i −0.618740 0.618740i
\(447\) −11.0687 11.0687i −0.523529 0.523529i
\(448\) −0.376687 + 0.376687i −0.0177968 + 0.0177968i
\(449\) −15.3192 15.3192i −0.722956 0.722956i 0.246250 0.969206i \(-0.420801\pi\)
−0.969206 + 0.246250i \(0.920801\pi\)
\(450\) 1.39241 + 4.80221i 0.0656387 + 0.226378i
\(451\) 2.73711 0.128886
\(452\) 2.77598i 0.130571i
\(453\) 2.19905 + 2.19905i 0.103320 + 0.103320i
\(454\) 16.0865i 0.754975i
\(455\) 4.88352 + 3.66868i 0.228943 + 0.171990i
\(456\) −5.47960 −0.256606
\(457\) 11.9041i 0.556852i −0.960458 0.278426i \(-0.910187\pi\)
0.960458 0.278426i \(-0.0898127\pi\)
\(458\) 6.71533i 0.313787i
\(459\) 1.63368 1.63368i 0.0762539 0.0762539i
\(460\) −1.98044 13.9418i −0.0923385 0.650041i
\(461\) −21.6193 + 21.6193i −1.00691 + 1.00691i −0.00693591 + 0.999976i \(0.502208\pi\)
−0.999976 + 0.00693591i \(0.997792\pi\)
\(462\) 0.684892 0.0318641
\(463\) 7.74140 0.359773 0.179887 0.983687i \(-0.442427\pi\)
0.179887 + 0.983687i \(0.442427\pi\)
\(464\) 1.15504 1.15504i 0.0536215 0.0536215i
\(465\) 3.16268 + 22.2645i 0.146666 + 1.03249i
\(466\) −4.61749 + 4.61749i −0.213901 + 0.213901i
\(467\) 40.6171i 1.87954i −0.341813 0.939768i \(-0.611041\pi\)
0.341813 0.939768i \(-0.388959\pi\)
\(468\) 5.12767i 0.237027i
\(469\) 4.00991 0.185160
\(470\) −6.68799 5.02426i −0.308494 0.231752i
\(471\) 17.6811i 0.814704i
\(472\) 1.04438 + 1.04438i 0.0480714 + 0.0480714i
\(473\) 3.29288i 0.151407i
\(474\) 16.1220 0.740506
\(475\) 24.0020 + 13.2118i 1.10129 + 0.606200i
\(476\) −0.870290 0.870290i −0.0398897 0.0398897i
\(477\) 0.572887 0.572887i 0.0262307 0.0262307i
\(478\) −13.1078 13.1078i −0.599537 0.599537i
\(479\) −4.76750 4.76750i −0.217833 0.217833i 0.589752 0.807585i \(-0.299226\pi\)
−0.807585 + 0.589752i \(0.799226\pi\)
\(480\) −1.78779 1.34306i −0.0816012 0.0613018i
\(481\) −16.4184 26.5194i −0.748613 1.20918i
\(482\) −12.6538 + 12.6538i −0.576365 + 0.576365i
\(483\) 3.35482i 0.152649i
\(484\) 9.34708 0.424867
\(485\) −17.8778 + 2.53955i −0.811789 + 0.115315i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 16.5284i 0.748971i 0.927233 + 0.374486i \(0.122181\pi\)
−0.927233 + 0.374486i \(0.877819\pi\)
\(488\) 3.44882 + 3.44882i 0.156121 + 0.156121i
\(489\) −6.09026 6.09026i −0.275411 0.275411i
\(490\) 14.8686 2.11209i 0.671697 0.0954147i
\(491\) −11.4600 −0.517185 −0.258592 0.965987i \(-0.583259\pi\)
−0.258592 + 0.965987i \(0.583259\pi\)
\(492\) 1.50540 + 1.50540i 0.0678687 + 0.0678687i
\(493\) 2.66858 + 2.66858i 0.120187 + 0.120187i
\(494\) −19.8680 19.8680i −0.893902 0.893902i
\(495\) 0.404311 + 2.84625i 0.0181724 + 0.127929i
\(496\) −7.11133 7.11133i −0.319308 0.319308i
\(497\) −1.65203 + 1.65203i −0.0741036 + 0.0741036i
\(498\) 16.2920 0.730062
\(499\) −11.0278 + 11.0278i −0.493674 + 0.493674i −0.909462 0.415788i \(-0.863506\pi\)
0.415788 + 0.909462i \(0.363506\pi\)
\(500\) 4.59275 + 10.1935i 0.205394 + 0.455865i
\(501\) 15.4431 + 15.4431i 0.689946 + 0.689946i
\(502\) −0.829972 0.829972i −0.0370435 0.0370435i
\(503\) 17.9392 0.799870 0.399935 0.916543i \(-0.369033\pi\)
0.399935 + 0.916543i \(0.369033\pi\)
\(504\) 0.376687 + 0.376687i 0.0167790 + 0.0167790i
\(505\) 35.1488 4.99290i 1.56410 0.222181i
\(506\) 8.09653i 0.359935i
\(507\) 9.39955 9.39955i 0.417449 0.417449i
\(508\) −10.6282 + 10.6282i −0.471552 + 0.471552i
\(509\) −10.1276 −0.448897 −0.224448 0.974486i \(-0.572058\pi\)
−0.224448 + 0.974486i \(0.572058\pi\)
\(510\) 3.10297 4.13048i 0.137402 0.182901i
\(511\) 7.39097i 0.326957i
\(512\) 1.00000 0.0441942
\(513\) 5.47960i 0.241930i
\(514\) 9.61238i 0.423984i
\(515\) −19.9455 + 2.83327i −0.878906 + 0.124849i
\(516\) 1.81107 1.81107i 0.0797278 0.0797278i
\(517\) −3.40087 3.40087i −0.149570 0.149570i
\(518\) 3.15428 + 0.742037i 0.138591 + 0.0326032i
\(519\) 1.87211i 0.0821764i
\(520\) −1.61253 11.3519i −0.0707143 0.497812i
\(521\) 2.42962i 0.106444i −0.998583 0.0532219i \(-0.983051\pi\)
0.998583 0.0532219i \(-0.0169491\pi\)
\(522\) −1.15504 1.15504i −0.0505548 0.0505548i
\(523\) −27.3470 −1.19580 −0.597901 0.801570i \(-0.703998\pi\)
−0.597901 + 0.801570i \(0.703998\pi\)
\(524\) 10.6555 + 10.6555i 0.465486 + 0.465486i
\(525\) −0.741757 2.55821i −0.0323729 0.111650i
\(526\) −11.2512 + 11.2512i −0.490576 + 0.490576i
\(527\) 16.4299 16.4299i 0.715696 0.715696i
\(528\) −0.909099 0.909099i −0.0395635 0.0395635i
\(529\) 16.6594 0.724321
\(530\) 1.08812 1.44844i 0.0472650 0.0629163i
\(531\) 1.04438 1.04438i 0.0453221 0.0453221i
\(532\) 2.91907 0.126558
\(533\) 10.9166i 0.472850i
\(534\) 11.4460i 0.495317i
\(535\) −3.56907 2.68121i −0.154304 0.115919i
\(536\) −5.32260 5.32260i −0.229901 0.229901i
\(537\) 25.1735i 1.08632i
\(538\) 23.2912i 1.00415i
\(539\) 8.63477 0.371926
\(540\) −1.34306 + 1.78779i −0.0577959 + 0.0769344i
\(541\) 24.0214 24.0214i 1.03276 1.03276i 0.0333158 0.999445i \(-0.489393\pi\)
0.999445 0.0333158i \(-0.0106067\pi\)
\(542\) 13.8775 0.596088
\(543\) −1.40516 + 1.40516i −0.0603010 + 0.0603010i
\(544\) 2.31038i 0.0990567i
\(545\) 2.20121 2.93012i 0.0942896 0.125513i
\(546\) 2.73159i 0.116901i
\(547\) 37.8077 1.61654 0.808271 0.588810i \(-0.200404\pi\)
0.808271 + 0.588810i \(0.200404\pi\)
\(548\) 8.98795 8.98795i 0.383946 0.383946i
\(549\) 3.44882 3.44882i 0.147192 0.147192i
\(550\) 1.79016 + 6.17401i 0.0763327 + 0.263261i
\(551\) −8.95079 −0.381316
\(552\) 4.45305 4.45305i 0.189535 0.189535i
\(553\) −8.58843 −0.365217
\(554\) −6.57502 −0.279346
\(555\) −1.22167 + 13.5465i −0.0518571 + 0.575017i
\(556\) 19.4517 0.824937
\(557\) −18.1545 −0.769231 −0.384615 0.923077i \(-0.625666\pi\)
−0.384615 + 0.923077i \(0.625666\pi\)
\(558\) −7.11133 + 7.11133i −0.301047 + 0.301047i
\(559\) 13.1332 0.555474
\(560\) 0.952386 + 0.715467i 0.0402457 + 0.0302340i
\(561\) 2.10036 2.10036i 0.0886774 0.0886774i
\(562\) −13.5903 + 13.5903i −0.573272 + 0.573272i
\(563\) 19.8695 0.837398 0.418699 0.908125i \(-0.362486\pi\)
0.418699 + 0.908125i \(0.362486\pi\)
\(564\) 3.74092i 0.157521i
\(565\) 6.14558 0.872982i 0.258547 0.0367266i
\(566\) 8.54984i 0.359376i
\(567\) 0.376687 0.376687i 0.0158194 0.0158194i
\(568\) 4.38568 0.184019
\(569\) 6.05236 6.05236i 0.253728 0.253728i −0.568769 0.822497i \(-0.692580\pi\)
0.822497 + 0.568769i \(0.192580\pi\)
\(570\) 1.72321 + 12.1310i 0.0721772 + 0.508111i
\(571\) 12.1222 0.507297 0.253648 0.967296i \(-0.418369\pi\)
0.253648 + 0.967296i \(0.418369\pi\)
\(572\) 6.59244i 0.275644i
\(573\) 6.24313i 0.260810i
\(574\) −0.801951 0.801951i −0.0334728 0.0334728i
\(575\) −30.2422 + 8.76877i −1.26119 + 0.365683i
\(576\) 1.00000i 0.0416667i
\(577\) 36.8080i 1.53234i −0.642641 0.766168i \(-0.722161\pi\)
0.642641 0.766168i \(-0.277839\pi\)
\(578\) 11.6621 0.485081
\(579\) −1.48044 + 1.48044i −0.0615249 + 0.0615249i
\(580\) −2.92032 2.19385i −0.121260 0.0910946i
\(581\) −8.67901 −0.360066
\(582\) −5.71021 5.71021i −0.236696 0.236696i
\(583\) 0.736538 0.736538i 0.0305043 0.0305043i
\(584\) −9.81049 + 9.81049i −0.405961 + 0.405961i
\(585\) −11.3519 + 1.61253i −0.469341 + 0.0666701i
\(586\) 7.61554 + 7.61554i 0.314595 + 0.314595i
\(587\) −14.5475 −0.600439 −0.300220 0.953870i \(-0.597060\pi\)
−0.300220 + 0.953870i \(0.597060\pi\)
\(588\) 4.74908 + 4.74908i 0.195849 + 0.195849i
\(589\) 55.1080i 2.27068i
\(590\) 1.98366 2.64052i 0.0816658 0.108709i
\(591\) 6.71825i 0.276352i
\(592\) −3.20192 5.17182i −0.131598 0.212560i
\(593\) −16.6115 16.6115i −0.682153 0.682153i 0.278332 0.960485i \(-0.410219\pi\)
−0.960485 + 0.278332i \(0.910219\pi\)
\(594\) −0.909099 + 0.909099i −0.0373008 + 0.0373008i
\(595\) −1.65300 + 2.20037i −0.0677664 + 0.0902065i
\(596\) 15.6534i 0.641190i
\(597\) 6.98183i 0.285747i
\(598\) 32.2918 1.32051
\(599\) 13.5361i 0.553069i −0.961004 0.276535i \(-0.910814\pi\)
0.961004 0.276535i \(-0.0891861\pi\)
\(600\) −2.41109 + 4.38025i −0.0984325 + 0.178823i
\(601\) 8.79388 0.358710 0.179355 0.983784i \(-0.442599\pi\)
0.179355 + 0.983784i \(0.442599\pi\)
\(602\) −0.964785 + 0.964785i −0.0393217 + 0.0393217i
\(603\) −5.32260 + 5.32260i −0.216753 + 0.216753i
\(604\) 3.10992i 0.126541i
\(605\) −2.93944 20.6930i −0.119505 0.841289i
\(606\) 11.2266 + 11.2266i 0.456050 + 0.456050i
\(607\) −1.05689 −0.0428979 −0.0214489 0.999770i \(-0.506828\pi\)
−0.0214489 + 0.999770i \(0.506828\pi\)
\(608\) −3.87466 3.87466i −0.157138 0.157138i
\(609\) 0.615309 + 0.615309i 0.0249336 + 0.0249336i
\(610\) 6.55058 8.71973i 0.265225 0.353051i
\(611\) 13.5639 13.5639i 0.548735 0.548735i
\(612\) 2.31038 0.0933915
\(613\) 31.3429 31.3429i 1.26593 1.26593i 0.317753 0.948174i \(-0.397072\pi\)
0.948174 0.317753i \(-0.102928\pi\)
\(614\) −19.6731 19.6731i −0.793940 0.793940i
\(615\) 2.85931 3.80613i 0.115298 0.153478i
\(616\) 0.484292 + 0.484292i 0.0195127 + 0.0195127i
\(617\) −18.9748 18.9748i −0.763896 0.763896i 0.213128 0.977024i \(-0.431635\pi\)
−0.977024 + 0.213128i \(0.931635\pi\)
\(618\) −6.37065 6.37065i −0.256265 0.256265i
\(619\) −14.1356 −0.568157 −0.284079 0.958801i \(-0.591688\pi\)
−0.284079 + 0.958801i \(0.591688\pi\)
\(620\) −13.5070 + 17.9797i −0.542455 + 0.722083i
\(621\) −4.45305 4.45305i −0.178695 0.178695i
\(622\) −3.86047 3.86047i −0.154791 0.154791i
\(623\) 6.09747i 0.244290i
\(624\) 3.62581 3.62581i 0.145149 0.145149i
\(625\) 21.1224 13.3732i 0.844896 0.534930i
\(626\) 18.9968 0.759263
\(627\) 7.04490i 0.281346i
\(628\) −12.5025 + 12.5025i −0.498902 + 0.498902i
\(629\) 11.9489 7.39765i 0.476432 0.294963i
\(630\) 0.715467 0.952386i 0.0285049 0.0379440i
\(631\) −13.8331 13.8331i −0.550688 0.550688i 0.375951 0.926639i \(-0.377316\pi\)
−0.926639 + 0.375951i \(0.877316\pi\)
\(632\) 11.4000 + 11.4000i 0.453466 + 0.453466i
\(633\) −9.30966 + 9.30966i −0.370026 + 0.370026i
\(634\) 17.8153 + 17.8153i 0.707537 + 0.707537i
\(635\) 26.8716 + 20.1869i 1.06637 + 0.801094i
\(636\) 0.810184 0.0321259
\(637\) 34.4385i 1.36450i
\(638\) −1.48499 1.48499i −0.0587914 0.0587914i
\(639\) 4.38568i 0.173495i
\(640\) −0.314477 2.21384i −0.0124308 0.0875099i
\(641\) 24.5047 0.967877 0.483938 0.875102i \(-0.339206\pi\)
0.483938 + 0.875102i \(0.339206\pi\)
\(642\) 1.99635i 0.0787898i
\(643\) 1.49125i 0.0588093i −0.999568 0.0294046i \(-0.990639\pi\)
0.999568 0.0294046i \(-0.00936114\pi\)
\(644\) −2.37221 + 2.37221i −0.0934783 + 0.0934783i
\(645\) −4.57896 3.43988i −0.180296 0.135445i
\(646\) 8.95194 8.95194i 0.352209 0.352209i
\(647\) 32.4023 1.27386 0.636932 0.770920i \(-0.280203\pi\)
0.636932 + 0.770920i \(0.280203\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 1.34271 1.34271i 0.0527062 0.0527062i
\(650\) −24.6241 + 7.13980i −0.965838 + 0.280046i
\(651\) 3.78832 3.78832i 0.148476 0.148476i
\(652\) 8.61293i 0.337308i
\(653\) 49.0619i 1.91994i −0.280099 0.959971i \(-0.590367\pi\)
0.280099 0.959971i \(-0.409633\pi\)
\(654\) 1.63896 0.0640884
\(655\) 20.2386 26.9404i 0.790789 1.05265i
\(656\) 2.12896i 0.0831218i
\(657\) 9.81049 + 9.81049i 0.382743 + 0.382743i
\(658\) 1.99285i 0.0776894i
\(659\) −11.1464 −0.434200 −0.217100 0.976149i \(-0.569660\pi\)
−0.217100 + 0.976149i \(0.569660\pi\)
\(660\) −1.72671 + 2.29849i −0.0672122 + 0.0894688i
\(661\) 31.4369 + 31.4369i 1.22275 + 1.22275i 0.966649 + 0.256103i \(0.0824386\pi\)
0.256103 + 0.966649i \(0.417561\pi\)
\(662\) −1.11563 + 1.11563i −0.0433603 + 0.0433603i
\(663\) 8.37699 + 8.37699i 0.325335 + 0.325335i
\(664\) 11.5202 + 11.5202i 0.447070 + 0.447070i
\(665\) −0.917981 6.46237i −0.0355978 0.250600i
\(666\) −5.17182 + 3.20192i −0.200404 + 0.124072i
\(667\) 7.27396 7.27396i 0.281649 0.281649i
\(668\) 21.8398i 0.845007i
\(669\) −18.4795 −0.714460
\(670\) −10.1096 + 13.4572i −0.390566 + 0.519898i
\(671\) 4.43401 4.43401i 0.171173 0.171173i
\(672\) 0.532716i 0.0205500i
\(673\) −1.81889 1.81889i −0.0701132 0.0701132i 0.671181 0.741294i \(-0.265787\pi\)
−0.741294 + 0.671181i \(0.765787\pi\)
\(674\) −19.6821 19.6821i −0.758126 0.758126i
\(675\) 4.38025 + 2.41109i 0.168596 + 0.0928031i
\(676\) 13.2930 0.511268
\(677\) −9.38604 9.38604i −0.360735 0.360735i 0.503349 0.864083i \(-0.332101\pi\)
−0.864083 + 0.503349i \(0.832101\pi\)
\(678\) 1.96291 + 1.96291i 0.0753853 + 0.0753853i
\(679\) 3.04192 + 3.04192i 0.116738 + 0.116738i
\(680\) 5.11482 0.726561i 0.196144 0.0278624i
\(681\) −11.3749 11.3749i −0.435885 0.435885i
\(682\) −9.14275 + 9.14275i −0.350094 + 0.350094i
\(683\) −0.539905 −0.0206589 −0.0103295 0.999947i \(-0.503288\pi\)
−0.0103295 + 0.999947i \(0.503288\pi\)
\(684\) −3.87466 + 3.87466i −0.148151 + 0.148151i
\(685\) −22.7244 17.0714i −0.868255 0.652265i
\(686\) −5.16672 5.16672i −0.197266 0.197266i
\(687\) −4.74846 4.74846i −0.181165 0.181165i
\(688\) 2.56124 0.0976462
\(689\) 2.93757 + 2.93757i 0.111913 + 0.111913i
\(690\) −11.2587 8.45798i −0.428613 0.321990i
\(691\) 40.4342i 1.53819i −0.639135 0.769094i \(-0.720708\pi\)
0.639135 0.769094i \(-0.279292\pi\)
\(692\) −1.32378 + 1.32378i −0.0503226 + 0.0503226i
\(693\) 0.484292 0.484292i 0.0183967 0.0183967i
\(694\) −3.98304 −0.151194
\(695\) −6.11712 43.0631i −0.232036 1.63348i
\(696\) 1.63348i 0.0619167i
\(697\) −4.91870 −0.186309
\(698\) 7.69090i 0.291105i
\(699\) 6.53012i 0.246992i
\(700\) 1.28443 2.33343i 0.0485469 0.0881954i
\(701\) 23.7123 23.7123i 0.895601 0.895601i −0.0994419 0.995043i \(-0.531706\pi\)
0.995043 + 0.0994419i \(0.0317057\pi\)
\(702\) −3.62581 3.62581i −0.136847 0.136847i
\(703\) −7.63270 + 32.4454i −0.287873 + 1.22370i
\(704\) 1.28566i 0.0484551i
\(705\) −8.28182 + 1.17643i −0.311911 + 0.0443071i
\(706\) 21.0577i 0.792518i
\(707\) −5.98060 5.98060i −0.224924 0.224924i
\(708\) 1.47697 0.0555080
\(709\) 16.8933 + 16.8933i 0.634441 + 0.634441i 0.949179 0.314738i \(-0.101917\pi\)
−0.314738 + 0.949179i \(0.601917\pi\)
\(710\) −1.37919 9.70920i −0.0517602 0.364380i
\(711\) 11.4000 11.4000i 0.427532 0.427532i
\(712\) −8.09354 + 8.09354i −0.303318 + 0.303318i
\(713\) −44.7841 44.7841i −1.67718 1.67718i
\(714\) −1.23078 −0.0460607
\(715\) −14.5946 + 2.07317i −0.545808 + 0.0775322i
\(716\) 17.8003 17.8003i 0.665230 0.665230i
\(717\) −18.5372 −0.692285
\(718\) 19.0802i 0.712065i
\(719\) 13.6649i 0.509614i 0.966992 + 0.254807i \(0.0820120\pi\)
−0.966992 + 0.254807i \(0.917988\pi\)
\(720\) −2.21384 + 0.314477i −0.0825051 + 0.0117199i
\(721\) 3.39375 + 3.39375i 0.126390 + 0.126390i
\(722\) 11.0260i 0.410345i
\(723\) 17.8952i 0.665529i
\(724\) −1.98719 −0.0738533
\(725\) −3.93846 + 7.15504i −0.146271 + 0.265731i
\(726\) 6.60938 6.60938i 0.245297 0.245297i
\(727\) −6.24565 −0.231638 −0.115819 0.993270i \(-0.536949\pi\)
−0.115819 + 0.993270i \(0.536949\pi\)
\(728\) −1.93153 + 1.93153i −0.0715871 + 0.0715871i
\(729\) 1.00000i 0.0370370i
\(730\) 24.8041 + 18.6337i 0.918039 + 0.689665i
\(731\) 5.91743i 0.218864i
\(732\) 4.87737 0.180273
\(733\) −11.6047 + 11.6047i −0.428628 + 0.428628i −0.888161 0.459533i \(-0.848017\pi\)
0.459533 + 0.888161i \(0.348017\pi\)
\(734\) 13.0910 13.0910i 0.483198 0.483198i
\(735\) 9.02024 12.0072i 0.332717 0.442892i
\(736\) 6.29757 0.232131
\(737\) −6.84305 + 6.84305i −0.252067 + 0.252067i
\(738\) 2.12896 0.0783680
\(739\) −26.9960 −0.993065 −0.496533 0.868018i \(-0.665394\pi\)
−0.496533 + 0.868018i \(0.665394\pi\)
\(740\) −10.4427 + 8.71497i −0.383880 + 0.320369i
\(741\) −28.0976 −1.03219
\(742\) −0.431598 −0.0158445
\(743\) 2.59470 2.59470i 0.0951901 0.0951901i −0.657908 0.753098i \(-0.728558\pi\)
0.753098 + 0.657908i \(0.228558\pi\)
\(744\) −10.0569 −0.368705
\(745\) −34.6543 + 4.92265i −1.26963 + 0.180352i
\(746\) −17.5157 + 17.5157i −0.641294 + 0.641294i
\(747\) 11.5202 11.5202i 0.421501 0.421501i
\(748\) 2.97036 0.108607
\(749\) 1.06349i 0.0388591i
\(750\) 10.4554 + 3.96030i 0.381778 + 0.144610i
\(751\) 37.6977i 1.37561i −0.725897 0.687803i \(-0.758575\pi\)
0.725897 0.687803i \(-0.241425\pi\)
\(752\) 2.64523 2.64523i 0.0964617 0.0964617i
\(753\) −1.17376 −0.0427741
\(754\) 5.92267 5.92267i 0.215691 0.215691i
\(755\) 6.88488 0.977999i 0.250566 0.0355930i
\(756\) 0.532716 0.0193747
\(757\) 27.3872i 0.995406i 0.867347 + 0.497703i \(0.165823\pi\)
−0.867347 + 0.497703i \(0.834177\pi\)
\(758\) 21.8739i 0.794494i
\(759\) −5.72511 5.72511i −0.207808 0.207808i
\(760\) −7.35940 + 9.79638i −0.266954 + 0.355352i
\(761\) 41.7778i 1.51444i 0.653157 + 0.757222i \(0.273444\pi\)
−0.653157 + 0.757222i \(0.726556\pi\)
\(762\) 15.0306i 0.544502i
\(763\) −0.873100 −0.0316083
\(764\) −4.41456 + 4.41456i −0.159713 + 0.159713i
\(765\) −0.726561 5.11482i −0.0262689 0.184927i
\(766\) −5.61751 −0.202969
\(767\) 5.35522 + 5.35522i 0.193366 + 0.193366i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −27.6843 + 27.6843i −0.998322 + 0.998322i −0.999999 0.00167616i \(-0.999466\pi\)
0.00167616 + 0.999999i \(0.499466\pi\)
\(770\) 0.919848 1.22444i 0.0331490 0.0441259i
\(771\) 6.79698 + 6.79698i 0.244787 + 0.244787i
\(772\) −2.09366 −0.0753524
\(773\) 19.1232 + 19.1232i 0.687812 + 0.687812i 0.961748 0.273936i \(-0.0883256\pi\)
−0.273936 + 0.961748i \(0.588326\pi\)
\(774\) 2.56124i 0.0920618i
\(775\) 44.0520 + 24.2482i 1.58239 + 0.871022i
\(776\) 8.07546i 0.289892i
\(777\) 2.75511 1.70571i 0.0988391 0.0611921i
\(778\) 5.37334 + 5.37334i 0.192644 + 0.192644i
\(779\) 8.24898 8.24898i 0.295551 0.295551i
\(780\) −9.16721 6.88674i −0.328239 0.246585i
\(781\) 5.63849i 0.201761i
\(782\) 14.5498i 0.520299i
\(783\) −1.63348 −0.0583757
\(784\) 6.71621i 0.239865i
\(785\) 31.6102 + 23.7467i 1.12822 + 0.847558i
\(786\) 15.0691 0.537497
\(787\) −5.34065 + 5.34065i −0.190374 + 0.190374i −0.795858 0.605484i \(-0.792980\pi\)
0.605484 + 0.795858i \(0.292980\pi\)
\(788\) −4.75052 + 4.75052i −0.169230 + 0.169230i
\(789\) 15.9116i 0.566468i
\(790\) 21.6527 28.8227i 0.770368 1.02547i
\(791\) −1.04568 1.04568i −0.0371800 0.0371800i
\(792\) −1.28566 −0.0456839
\(793\) 17.6844 + 17.6844i 0.627992 + 0.627992i
\(794\) 17.9874 + 17.9874i 0.638349 + 0.638349i
\(795\) −0.254784 1.79362i −0.00903627 0.0636132i
\(796\) −4.93690 + 4.93690i −0.174984 + 0.174984i
\(797\) −25.8297 −0.914934 −0.457467 0.889227i \(-0.651243\pi\)
−0.457467 + 0.889227i \(0.651243\pi\)
\(798\) 2.06409 2.06409i 0.0730682 0.0730682i
\(799\) 6.11149 + 6.11149i 0.216209 + 0.216209i
\(800\) −4.80221 + 1.39241i −0.169784 + 0.0492290i
\(801\) 8.09354 + 8.09354i 0.285971 + 0.285971i
\(802\) 15.1996 + 15.1996i 0.536718 + 0.536718i
\(803\) 12.6129 + 12.6129i 0.445101 + 0.445101i
\(804\) −7.52729 −0.265467
\(805\) 5.99772 + 4.50570i 0.211392 + 0.158805i
\(806\) −36.4645 36.4645i −1.28441 1.28441i
\(807\) 16.4693 + 16.4693i 0.579748 + 0.579748i
\(808\) 15.8768i 0.558545i
\(809\) 32.2660 32.2660i 1.13441 1.13441i 0.144976 0.989435i \(-0.453689\pi\)
0.989435 0.144976i \(-0.0463105\pi\)
\(810\) 0.314477 + 2.21384i 0.0110496 + 0.0777865i
\(811\) −16.4212 −0.576628 −0.288314 0.957536i \(-0.593095\pi\)
−0.288314 + 0.957536i \(0.593095\pi\)
\(812\) 0.870179i 0.0305373i
\(813\) 9.81285 9.81285i 0.344152 0.344152i
\(814\) −6.64920 + 4.11658i −0.233054 + 0.144286i
\(815\) −19.0677 + 2.70857i −0.667912 + 0.0948770i
\(816\) 1.63368 + 1.63368i 0.0571904 + 0.0571904i
\(817\) −9.92392 9.92392i −0.347194 0.347194i
\(818\) −27.1312 + 27.1312i −0.948620 + 0.948620i
\(819\) 1.93153 + 1.93153i 0.0674930 + 0.0674930i
\(820\) 4.71318 0.669508i 0.164591 0.0233802i
\(821\) −31.7926 −1.10957 −0.554784 0.831994i \(-0.687199\pi\)
−0.554784 + 0.831994i \(0.687199\pi\)
\(822\) 12.7109i 0.443343i
\(823\) −25.1623 25.1623i −0.877102 0.877102i 0.116132 0.993234i \(-0.462951\pi\)
−0.993234 + 0.116132i \(0.962951\pi\)
\(824\) 9.00947i 0.313860i
\(825\) 5.63152 + 3.09985i 0.196064 + 0.107923i
\(826\) −0.786807 −0.0273765
\(827\) 13.8706i 0.482329i −0.970484 0.241165i \(-0.922471\pi\)
0.970484 0.241165i \(-0.0775294\pi\)
\(828\) 6.29757i 0.218856i
\(829\) −19.5830 + 19.5830i −0.680147 + 0.680147i −0.960033 0.279886i \(-0.909703\pi\)
0.279886 + 0.960033i \(0.409703\pi\)
\(830\) 21.8810 29.1267i 0.759502 1.01100i
\(831\) −4.64924 + 4.64924i −0.161280 + 0.161280i
\(832\) 5.12767 0.177770
\(833\) −15.5170 −0.537632
\(834\) 13.7544 13.7544i 0.476277 0.476277i
\(835\) 48.3499 6.86812i 1.67322 0.237681i
\(836\) −4.98150 + 4.98150i −0.172289 + 0.172289i
\(837\) 10.0569i 0.347619i
\(838\) 7.19965i 0.248708i
\(839\) −29.1983 −1.00804 −0.504019 0.863692i \(-0.668146\pi\)
−0.504019 + 0.863692i \(0.668146\pi\)
\(840\) 1.17935 0.167527i 0.0406915 0.00578023i
\(841\) 26.3318i 0.907992i
\(842\) 6.17926 + 6.17926i 0.212951 + 0.212951i
\(843\) 19.2196i 0.661957i
\(844\) −13.1658 −0.453187
\(845\) −4.18033 29.4286i −0.143808 1.01237i
\(846\) −2.64523 2.64523i −0.0909449 0.0909449i
\(847\) −3.52093 + 3.52093i −0.120980 + 0.120980i
\(848\) 0.572887 + 0.572887i 0.0196730 + 0.0196730i
\(849\) 6.04565 + 6.04565i 0.207486 + 0.207486i
\(850\) −3.21699 11.0949i −0.110342 0.380553i
\(851\) −20.1643 32.5699i −0.691223 1.11648i
\(852\) 3.10114 3.10114i 0.106243 0.106243i
\(853\) 6.30510i 0.215883i 0.994157 + 0.107941i \(0.0344259\pi\)
−0.994157 + 0.107941i \(0.965574\pi\)
\(854\) −2.59825 −0.0889104
\(855\) 9.79638 + 7.35940i 0.335029 + 0.251686i
\(856\) 1.41163 1.41163i 0.0482487 0.0482487i
\(857\) 5.70445i 0.194860i 0.995242 + 0.0974302i \(0.0310623\pi\)
−0.995242 + 0.0974302i \(0.968938\pi\)
\(858\) −4.66156 4.66156i −0.159143 0.159143i
\(859\) 9.67146 + 9.67146i 0.329986 + 0.329986i 0.852581 0.522595i \(-0.175036\pi\)
−0.522595 + 0.852581i \(0.675036\pi\)
\(860\) −0.805450 5.67018i −0.0274656 0.193351i
\(861\) −1.13413 −0.0386510
\(862\) 19.0871 + 19.0871i 0.650110 + 0.650110i
\(863\) −11.4917 11.4917i −0.391181 0.391181i 0.483928 0.875108i \(-0.339210\pi\)
−0.875108 + 0.483928i \(0.839210\pi\)
\(864\) −0.707107 0.707107i −0.0240563 0.0240563i
\(865\) 3.34694 + 2.51434i 0.113799 + 0.0854903i
\(866\) −27.0193 27.0193i −0.918154 0.918154i
\(867\) 8.24638 8.24638i 0.280062 0.280062i
\(868\) 5.35750 0.181845
\(869\) 14.6565 14.6565i 0.497186 0.497186i
\(870\) −3.61626 + 0.513691i −0.122603 + 0.0174157i
\(871\) −27.2925 27.2925i −0.924771 0.924771i
\(872\) 1.15892 + 1.15892i 0.0392460 + 0.0392460i
\(873\) −8.07546 −0.273313
\(874\) −24.4009 24.4009i −0.825374 0.825374i
\(875\) −5.56978 2.10971i −0.188293 0.0713214i
\(876\) 13.8741i 0.468763i
\(877\) 9.10608 9.10608i 0.307490 0.307490i −0.536445 0.843935i \(-0.680233\pi\)
0.843935 + 0.536445i \(0.180233\pi\)
\(878\) −8.21948 + 8.21948i −0.277394 + 0.277394i
\(879\) 10.7700 0.363263
\(880\) −2.84625 + 0.404311i −0.0959471 + 0.0136293i
\(881\) 2.47471i 0.0833752i −0.999131 0.0416876i \(-0.986727\pi\)
0.999131 0.0416876i \(-0.0132734\pi\)
\(882\) 6.71621 0.226147
\(883\) 42.6117i 1.43400i 0.697075 + 0.716999i \(0.254485\pi\)
−0.697075 + 0.716999i \(0.745515\pi\)
\(884\) 11.8469i 0.398453i
\(885\) −0.464474 3.26979i −0.0156131 0.109913i
\(886\) 7.35664 7.35664i 0.247151 0.247151i
\(887\) −14.4378 14.4378i −0.484774 0.484774i 0.421878 0.906652i \(-0.361371\pi\)
−0.906652 + 0.421878i \(0.861371\pi\)
\(888\) −5.92113 1.39293i −0.198700 0.0467437i
\(889\) 8.00705i 0.268548i
\(890\) 20.4631 + 15.3726i 0.685924 + 0.515291i
\(891\) 1.28566i 0.0430712i
\(892\) −13.0670 13.0670i −0.437516 0.437516i
\(893\) −20.4987 −0.685964
\(894\) −11.0687 11.0687i −0.370191 0.370191i
\(895\) −45.0049 33.8094i −1.50435 1.13012i
\(896\) −0.376687 + 0.376687i −0.0125842 + 0.0125842i
\(897\) 22.8338 22.8338i 0.762398 0.762398i
\(898\) −15.3192 15.3192i −0.511207 0.511207i
\(899\) −16.4278 −0.547897
\(900\) 1.39241 + 4.80221i 0.0464135 + 0.160074i
\(901\) −1.32359 + 1.32359i −0.0440950 + 0.0440950i
\(902\) 2.73711 0.0911359
\(903\) 1.36441i 0.0454048i
\(904\) 2.77598i 0.0923277i
\(905\) 0.624925 + 4.39933i 0.0207732 + 0.146239i
\(906\) 2.19905 + 2.19905i 0.0730584 + 0.0730584i
\(907\) 20.9996i 0.697281i 0.937256 + 0.348641i \(0.113357\pi\)
−0.937256 + 0.348641i \(0.886643\pi\)
\(908\) 16.0865i 0.533848i
\(909\) 15.8768 0.526601
\(910\) 4.88352 + 3.66868i 0.161887 + 0.121615i
\(911\) 2.09529 2.09529i 0.0694199 0.0694199i −0.671544 0.740964i \(-0.734369\pi\)
0.740964 + 0.671544i \(0.234369\pi\)
\(912\) −5.47960 −0.181448
\(913\) 14.8110 14.8110i 0.490174 0.490174i
\(914\) 11.9041i 0.393754i
\(915\) −1.53382 10.7977i −0.0507066 0.356962i
\(916\) 6.71533i 0.221881i
\(917\) −8.02756 −0.265093
\(918\) 1.63368 1.63368i 0.0539196 0.0539196i
\(919\) 26.2479 26.2479i 0.865840 0.865840i −0.126169 0.992009i \(-0.540268\pi\)
0.992009 + 0.126169i \(0.0402681\pi\)
\(920\) −1.98044 13.9418i −0.0652932 0.459649i
\(921\) −27.8219 −0.916763
\(922\) −21.6193 + 21.6193i −0.711994 + 0.711994i
\(923\) 22.4883 0.740211
\(924\) 0.684892 0.0225313
\(925\) 22.5776 + 20.3778i 0.742345 + 0.670017i
\(926\) 7.74140 0.254398
\(927\) −9.00947 −0.295910
\(928\) 1.15504 1.15504i 0.0379161 0.0379161i
\(929\) −36.8972 −1.21056 −0.605279 0.796014i \(-0.706938\pi\)
−0.605279 + 0.796014i \(0.706938\pi\)
\(930\) 3.16268 + 22.2645i 0.103708 + 0.730082i
\(931\) 26.0230 26.0230i 0.852871 0.852871i
\(932\) −4.61749 + 4.61749i −0.151251 + 0.151251i
\(933\) −5.45953 −0.178737
\(934\) 40.6171i 1.32903i
\(935\) −0.934111 6.57592i −0.0305487 0.215056i
\(936\) 5.12767i 0.167603i
\(937\) −6.68552 + 6.68552i −0.218406 + 0.218406i −0.807827 0.589420i \(-0.799356\pi\)
0.589420 + 0.807827i \(0.299356\pi\)
\(938\) 4.00991 0.130928
\(939\) 13.4327 13.4327i 0.438361 0.438361i
\(940\) −6.68799 5.02426i −0.218138 0.163873i
\(941\) −5.71005 −0.186142 −0.0930711 0.995659i \(-0.529668\pi\)
−0.0930711 + 0.995659i \(0.529668\pi\)
\(942\) 17.6811i 0.576083i
\(943\) 13.4073i 0.436600i
\(944\) 1.04438 + 1.04438i 0.0339916 + 0.0339916i
\(945\) −0.167527 1.17935i −0.00544965 0.0383643i
\(946\) 3.29288i 0.107061i
\(947\) 31.5411i 1.02495i 0.858703 + 0.512474i \(0.171271\pi\)
−0.858703 + 0.512474i \(0.828729\pi\)
\(948\) 16.1220 0.523617
\(949\) −50.3049 + 50.3049i −1.63297 + 1.63297i
\(950\) 24.0020 + 13.2118i 0.778729 + 0.428648i
\(951\) 25.1947 0.816993
\(952\) −0.870290 0.870290i −0.0282063 0.0282063i
\(953\) 41.8752 41.8752i 1.35647 1.35647i 0.478245 0.878227i \(-0.341273\pi\)
0.878227 0.478245i \(-0.158727\pi\)
\(954\) 0.572887 0.572887i 0.0185479 0.0185479i
\(955\) 11.1614 + 8.38487i 0.361175 + 0.271328i
\(956\) −13.1078 13.1078i −0.423936 0.423936i
\(957\) −2.10009 −0.0678864
\(958\) −4.76750 4.76750i −0.154031 0.154031i
\(959\) 6.77129i 0.218656i
\(960\) −1.78779 1.34306i −0.0577008 0.0433469i
\(961\) 70.1421i 2.26265i
\(962\) −16.4184 26.5194i −0.529350 0.855019i
\(963\) −1.41163 1.41163i −0.0454893 0.0454893i
\(964\) −12.6538 + 12.6538i −0.407552 + 0.407552i
\(965\) 0.658407 + 4.63503i 0.0211949 + 0.149207i
\(966\) 3.35482i 0.107939i
\(967\) 20.2774i 0.652076i −0.945357 0.326038i \(-0.894286\pi\)
0.945357 0.326038i \(-0.105714\pi\)
\(968\) 9.34708 0.300426
\(969\) 12.6599i 0.406696i
\(970\) −17.8778 + 2.53955i −0.574022 + 0.0815399i
\(971\) 16.4316 0.527316 0.263658 0.964616i \(-0.415071\pi\)
0.263658 + 0.964616i \(0.415071\pi\)
\(972\) −0.707107 + 0.707107i −0.0226805 + 0.0226805i
\(973\) −7.32722 + 7.32722i −0.234900 + 0.234900i
\(974\) 16.5284i 0.529603i
\(975\) −12.3633 + 22.4605i −0.395942 + 0.719311i
\(976\) 3.44882 + 3.44882i 0.110394 + 0.110394i
\(977\) 45.6145 1.45934 0.729669 0.683801i \(-0.239674\pi\)
0.729669 + 0.683801i \(0.239674\pi\)
\(978\) −6.09026 6.09026i −0.194745 0.194745i
\(979\) 10.4055 + 10.4055i 0.332563 + 0.332563i
\(980\) 14.8686 2.11209i 0.474962 0.0674684i
\(981\) 1.15892 1.15892i 0.0370014 0.0370014i
\(982\) −11.4600 −0.365705
\(983\) −18.8451 + 18.8451i −0.601066 + 0.601066i −0.940595 0.339530i \(-0.889732\pi\)
0.339530 + 0.940595i \(0.389732\pi\)
\(984\) 1.50540 + 1.50540i 0.0479904 + 0.0479904i
\(985\) 12.0108 + 9.02298i 0.382697 + 0.287496i
\(986\) 2.66858 + 2.66858i 0.0849850 + 0.0849850i
\(987\) 1.40916 + 1.40916i 0.0448540 + 0.0448540i
\(988\) −19.8680 19.8680i −0.632084 0.632084i
\(989\) 16.1296 0.512890
\(990\) 0.404311 + 2.84625i 0.0128498 + 0.0904598i
\(991\) 28.3442 + 28.3442i 0.900383 + 0.900383i 0.995469 0.0950859i \(-0.0303126\pi\)
−0.0950859 + 0.995469i \(0.530313\pi\)
\(992\) −7.11133 7.11133i −0.225785 0.225785i
\(993\) 1.57774i 0.0500682i
\(994\) −1.65203 + 1.65203i −0.0523992 + 0.0523992i
\(995\) 12.4821 + 9.37699i 0.395708 + 0.297270i
\(996\) 16.2920 0.516232
\(997\) 34.7231i 1.09969i 0.835266 + 0.549846i \(0.185313\pi\)
−0.835266 + 0.549846i \(0.814687\pi\)
\(998\) −11.0278 + 11.0278i −0.349080 + 0.349080i
\(999\) −1.39293 + 5.92113i −0.0440704 + 0.187336i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1110.2.o.b.253.15 yes 40
5.2 odd 4 1110.2.l.b.697.6 yes 40
37.6 odd 4 1110.2.l.b.43.6 40
185.117 even 4 inner 1110.2.o.b.487.15 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.2.l.b.43.6 40 37.6 odd 4
1110.2.l.b.697.6 yes 40 5.2 odd 4
1110.2.o.b.253.15 yes 40 1.1 even 1 trivial
1110.2.o.b.487.15 yes 40 185.117 even 4 inner