Properties

Label 91.2.i.a.34.3
Level $91$
Weight $2$
Character 91.34
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 35 x^{8} + 295 x^{4} + 169\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 34.3
Root \(-1.52891 + 1.52891i\) of defining polynomial
Character \(\chi\) \(=\) 91.34
Dual form 91.2.i.a.83.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.403032 - 0.403032i) q^{2} -1.23240i q^{3} -1.67513i q^{4} +(-1.03221 + 1.03221i) q^{5} +(-0.496696 + 0.496696i) q^{6} +(-0.450747 - 2.60707i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})\) \(q+(-0.403032 - 0.403032i) q^{2} -1.23240i q^{3} -1.67513i q^{4} +(-1.03221 + 1.03221i) q^{5} +(-0.496696 + 0.496696i) q^{6} +(-0.450747 - 2.60707i) q^{7} +(-1.48119 + 1.48119i) q^{8} +1.48119 q^{9} +0.832030 q^{10} +(-0.596968 + 0.596968i) q^{11} -2.06443 q^{12} +(3.59334 - 0.296512i) q^{13} +(-0.869067 + 1.23240i) q^{14} +(1.27210 + 1.27210i) q^{15} -2.15633 q^{16} +7.34804 q^{17} +(-0.596968 - 0.596968i) q^{18} +(-3.59334 + 3.59334i) q^{19} +(1.72909 + 1.72909i) q^{20} +(-3.21295 + 0.555500i) q^{21} +0.481194 q^{22} +4.44358i q^{23} +(1.82542 + 1.82542i) q^{24} +2.86907i q^{25} +(-1.56773 - 1.32873i) q^{26} -5.52262i q^{27} +(-4.36719 + 0.755061i) q^{28} -3.54420 q^{29} -1.02539i q^{30} +(1.27122 - 1.27122i) q^{31} +(3.83146 + 3.83146i) q^{32} +(0.735703 + 0.735703i) q^{33} +(-2.96149 - 2.96149i) q^{34} +(3.15633 + 2.22579i) q^{35} -2.48119i q^{36} +(2.88423 - 2.88423i) q^{37} +2.89646 q^{38} +(-0.365420 - 4.42842i) q^{39} -3.05782i q^{40} +(-1.23240 + 1.23240i) q^{41} +(1.51881 + 1.07104i) q^{42} -8.66291i q^{43} +(1.00000 + 1.00000i) q^{44} +(-1.52891 + 1.52891i) q^{45} +(1.79090 - 1.79090i) q^{46} +(-2.52230 - 2.52230i) q^{47} +2.65745i q^{48} +(-6.59365 + 2.35026i) q^{49} +(1.15633 - 1.15633i) q^{50} -9.05571i q^{51} +(-0.496696 - 6.01931i) q^{52} -9.79384 q^{53} +(-2.22579 + 2.22579i) q^{54} -1.23240i q^{55} +(4.52923 + 3.19394i) q^{56} +(4.42842 + 4.42842i) q^{57} +(1.42842 + 1.42842i) q^{58} +(1.08972 + 1.08972i) q^{59} +(2.13093 - 2.13093i) q^{60} +7.10903i q^{61} -1.02469 q^{62} +(-0.667644 - 3.86158i) q^{63} +1.22425i q^{64} +(-3.40303 + 4.01516i) q^{65} -0.593023i q^{66} +(8.76845 + 8.76845i) q^{67} -12.3089i q^{68} +5.47626 q^{69} +(-0.375035 - 2.16916i) q^{70} +(-1.46604 - 1.46604i) q^{71} +(-2.19394 + 2.19394i) q^{72} +(0.103857 + 0.103857i) q^{73} -2.32487 q^{74} +3.53583 q^{75} +(6.01931 + 6.01931i) q^{76} +(1.82542 + 1.28726i) q^{77} +(-1.63752 + 1.93207i) q^{78} -4.79877 q^{79} +(2.22579 - 2.22579i) q^{80} -2.36248 q^{81} +0.993391 q^{82} +(-12.3165 + 12.3165i) q^{83} +(0.930536 + 5.38211i) q^{84} +(-7.58475 + 7.58475i) q^{85} +(-3.49143 + 3.49143i) q^{86} +4.36786i q^{87} -1.76845i q^{88} +(6.89017 + 6.89017i) q^{89} +1.23240 q^{90} +(-2.39271 - 9.23444i) q^{91} +7.44358 q^{92} +(-1.56665 - 1.56665i) q^{93} +2.03313i q^{94} -7.41819i q^{95} +(4.72188 - 4.72188i) q^{96} +(6.05814 - 6.05814i) q^{97} +(3.60468 + 1.71022i) q^{98} +(-0.884226 + 0.884226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{2} - 8 q^{7} + 4 q^{8} - 4 q^{9} - 8 q^{11} + 8 q^{14} - 4 q^{15} + 16 q^{16} - 8 q^{18} - 16 q^{22} - 20 q^{28} - 4 q^{29} - 16 q^{32} - 4 q^{35} + 12 q^{37} + 40 q^{39} + 40 q^{42} + 12 q^{44} + 24 q^{46} - 28 q^{50} - 12 q^{53} - 8 q^{57} - 44 q^{58} + 44 q^{60} + 20 q^{63} - 40 q^{65} + 60 q^{67} + 4 q^{70} - 28 q^{72} - 48 q^{74} + 44 q^{78} - 4 q^{79} - 92 q^{81} - 4 q^{84} + 12 q^{85} + 36 q^{86} - 32 q^{91} + 24 q^{92} - 28 q^{93} - 28 q^{98} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.403032 0.403032i −0.284986 0.284986i 0.550107 0.835094i \(-0.314587\pi\)
−0.835094 + 0.550107i \(0.814587\pi\)
\(3\) 1.23240i 0.711526i −0.934576 0.355763i \(-0.884221\pi\)
0.934576 0.355763i \(-0.115779\pi\)
\(4\) 1.67513i 0.837565i
\(5\) −1.03221 + 1.03221i −0.461620 + 0.461620i −0.899186 0.437566i \(-0.855841\pi\)
0.437566 + 0.899186i \(0.355841\pi\)
\(6\) −0.496696 + 0.496696i −0.202775 + 0.202775i
\(7\) −0.450747 2.60707i −0.170366 0.985381i
\(8\) −1.48119 + 1.48119i −0.523681 + 0.523681i
\(9\) 1.48119 0.493731
\(10\) 0.832030 0.263111
\(11\) −0.596968 + 0.596968i −0.179993 + 0.179993i −0.791353 0.611360i \(-0.790623\pi\)
0.611360 + 0.791353i \(0.290623\pi\)
\(12\) −2.06443 −0.595949
\(13\) 3.59334 0.296512i 0.996613 0.0822375i
\(14\) −0.869067 + 1.23240i −0.232268 + 0.329372i
\(15\) 1.27210 + 1.27210i 0.328455 + 0.328455i
\(16\) −2.15633 −0.539081
\(17\) 7.34804 1.78216 0.891080 0.453845i \(-0.149948\pi\)
0.891080 + 0.453845i \(0.149948\pi\)
\(18\) −0.596968 0.596968i −0.140707 0.140707i
\(19\) −3.59334 + 3.59334i −0.824368 + 0.824368i −0.986731 0.162363i \(-0.948089\pi\)
0.162363 + 0.986731i \(0.448089\pi\)
\(20\) 1.72909 + 1.72909i 0.386637 + 0.386637i
\(21\) −3.21295 + 0.555500i −0.701124 + 0.121220i
\(22\) 0.481194 0.102591
\(23\) 4.44358i 0.926551i 0.886214 + 0.463276i \(0.153326\pi\)
−0.886214 + 0.463276i \(0.846674\pi\)
\(24\) 1.82542 + 1.82542i 0.372613 + 0.372613i
\(25\) 2.86907i 0.573813i
\(26\) −1.56773 1.32873i −0.307458 0.260585i
\(27\) 5.52262i 1.06283i
\(28\) −4.36719 + 0.755061i −0.825321 + 0.142693i
\(29\) −3.54420 −0.658141 −0.329071 0.944305i \(-0.606735\pi\)
−0.329071 + 0.944305i \(0.606735\pi\)
\(30\) 1.02539i 0.187210i
\(31\) 1.27122 1.27122i 0.228318 0.228318i −0.583672 0.811990i \(-0.698384\pi\)
0.811990 + 0.583672i \(0.198384\pi\)
\(32\) 3.83146 + 3.83146i 0.677312 + 0.677312i
\(33\) 0.735703 + 0.735703i 0.128069 + 0.128069i
\(34\) −2.96149 2.96149i −0.507892 0.507892i
\(35\) 3.15633 + 2.22579i 0.533516 + 0.376227i
\(36\) 2.48119i 0.413532i
\(37\) 2.88423 2.88423i 0.474164 0.474164i −0.429095 0.903259i \(-0.641168\pi\)
0.903259 + 0.429095i \(0.141168\pi\)
\(38\) 2.89646 0.469868
\(39\) −0.365420 4.42842i −0.0585141 0.709115i
\(40\) 3.05782i 0.483484i
\(41\) −1.23240 + 1.23240i −0.192468 + 0.192468i −0.796762 0.604294i \(-0.793455\pi\)
0.604294 + 0.796762i \(0.293455\pi\)
\(42\) 1.51881 + 1.07104i 0.234357 + 0.165265i
\(43\) 8.66291i 1.32108i −0.750790 0.660541i \(-0.770327\pi\)
0.750790 0.660541i \(-0.229673\pi\)
\(44\) 1.00000 + 1.00000i 0.150756 + 0.150756i
\(45\) −1.52891 + 1.52891i −0.227916 + 0.227916i
\(46\) 1.79090 1.79090i 0.264055 0.264055i
\(47\) −2.52230 2.52230i −0.367915 0.367915i 0.498801 0.866717i \(-0.333774\pi\)
−0.866717 + 0.498801i \(0.833774\pi\)
\(48\) 2.65745i 0.383570i
\(49\) −6.59365 + 2.35026i −0.941951 + 0.335752i
\(50\) 1.15633 1.15633i 0.163529 0.163529i
\(51\) 9.05571i 1.26805i
\(52\) −0.496696 6.01931i −0.0688793 0.834728i
\(53\) −9.79384 −1.34529 −0.672644 0.739966i \(-0.734841\pi\)
−0.672644 + 0.739966i \(0.734841\pi\)
\(54\) −2.22579 + 2.22579i −0.302892 + 0.302892i
\(55\) 1.23240i 0.166177i
\(56\) 4.52923 + 3.19394i 0.605243 + 0.426808i
\(57\) 4.42842 + 4.42842i 0.586559 + 0.586559i
\(58\) 1.42842 + 1.42842i 0.187561 + 0.187561i
\(59\) 1.08972 + 1.08972i 0.141869 + 0.141869i 0.774474 0.632605i \(-0.218014\pi\)
−0.632605 + 0.774474i \(0.718014\pi\)
\(60\) 2.13093 2.13093i 0.275102 0.275102i
\(61\) 7.10903i 0.910218i 0.890436 + 0.455109i \(0.150400\pi\)
−0.890436 + 0.455109i \(0.849600\pi\)
\(62\) −1.02469 −0.130135
\(63\) −0.667644 3.86158i −0.0841153 0.486513i
\(64\) 1.22425i 0.153032i
\(65\) −3.40303 + 4.01516i −0.422094 + 0.498019i
\(66\) 0.593023i 0.0729961i
\(67\) 8.76845 + 8.76845i 1.07124 + 1.07124i 0.997260 + 0.0739770i \(0.0235691\pi\)
0.0739770 + 0.997260i \(0.476431\pi\)
\(68\) 12.3089i 1.49268i
\(69\) 5.47626 0.659265
\(70\) −0.375035 2.16916i −0.0448253 0.259265i
\(71\) −1.46604 1.46604i −0.173986 0.173986i 0.614742 0.788728i \(-0.289260\pi\)
−0.788728 + 0.614742i \(0.789260\pi\)
\(72\) −2.19394 + 2.19394i −0.258558 + 0.258558i
\(73\) 0.103857 + 0.103857i 0.0121555 + 0.0121555i 0.713158 0.701003i \(-0.247264\pi\)
−0.701003 + 0.713158i \(0.747264\pi\)
\(74\) −2.32487 −0.270261
\(75\) 3.53583 0.408283
\(76\) 6.01931 + 6.01931i 0.690462 + 0.690462i
\(77\) 1.82542 + 1.28726i 0.208026 + 0.146697i
\(78\) −1.63752 + 1.93207i −0.185413 + 0.218764i
\(79\) −4.79877 −0.539904 −0.269952 0.962874i \(-0.587008\pi\)
−0.269952 + 0.962874i \(0.587008\pi\)
\(80\) 2.22579 2.22579i 0.248851 0.248851i
\(81\) −2.36248 −0.262498
\(82\) 0.993391 0.109702
\(83\) −12.3165 + 12.3165i −1.35191 + 1.35191i −0.468379 + 0.883528i \(0.655162\pi\)
−0.883528 + 0.468379i \(0.844838\pi\)
\(84\) 0.930536 + 5.38211i 0.101530 + 0.587237i
\(85\) −7.58475 + 7.58475i −0.822682 + 0.822682i
\(86\) −3.49143 + 3.49143i −0.376490 + 0.376490i
\(87\) 4.36786i 0.468284i
\(88\) 1.76845i 0.188518i
\(89\) 6.89017 + 6.89017i 0.730356 + 0.730356i 0.970690 0.240334i \(-0.0772570\pi\)
−0.240334 + 0.970690i \(0.577257\pi\)
\(90\) 1.23240 0.129906
\(91\) −2.39271 9.23444i −0.250825 0.968033i
\(92\) 7.44358 0.776047
\(93\) −1.56665 1.56665i −0.162454 0.162454i
\(94\) 2.03313i 0.209702i
\(95\) 7.41819i 0.761090i
\(96\) 4.72188 4.72188i 0.481925 0.481925i
\(97\) 6.05814 6.05814i 0.615110 0.615110i −0.329163 0.944273i \(-0.606766\pi\)
0.944273 + 0.329163i \(0.106766\pi\)
\(98\) 3.60468 + 1.71022i 0.364128 + 0.172758i
\(99\) −0.884226 + 0.884226i −0.0888681 + 0.0888681i
\(100\) 4.80606 0.480606
\(101\) −12.8707 −1.28068 −0.640339 0.768092i \(-0.721206\pi\)
−0.640339 + 0.768092i \(0.721206\pi\)
\(102\) −3.64974 + 3.64974i −0.361378 + 0.361378i
\(103\) 6.11564 0.602592 0.301296 0.953531i \(-0.402581\pi\)
0.301296 + 0.953531i \(0.402581\pi\)
\(104\) −4.88324 + 5.76162i −0.478841 + 0.564974i
\(105\) 2.74306 3.88985i 0.267695 0.379610i
\(106\) 3.94723 + 3.94723i 0.383389 + 0.383389i
\(107\) 8.86907 0.857405 0.428703 0.903446i \(-0.358971\pi\)
0.428703 + 0.903446i \(0.358971\pi\)
\(108\) −9.25111 −0.890188
\(109\) −4.59697 4.59697i −0.440310 0.440310i 0.451806 0.892116i \(-0.350780\pi\)
−0.892116 + 0.451806i \(0.850780\pi\)
\(110\) −0.496696 + 0.496696i −0.0473581 + 0.0473581i
\(111\) −3.55452 3.55452i −0.337380 0.337380i
\(112\) 0.971958 + 5.62170i 0.0918414 + 0.531200i
\(113\) 1.60720 0.151193 0.0755964 0.997138i \(-0.475914\pi\)
0.0755964 + 0.997138i \(0.475914\pi\)
\(114\) 3.56959i 0.334323i
\(115\) −4.58673 4.58673i −0.427715 0.427715i
\(116\) 5.93700i 0.551236i
\(117\) 5.32243 0.439191i 0.492059 0.0406032i
\(118\) 0.878382i 0.0808617i
\(119\) −3.31211 19.1569i −0.303620 1.75611i
\(120\) −3.76845 −0.344011
\(121\) 10.2873i 0.935205i
\(122\) 2.86516 2.86516i 0.259400 0.259400i
\(123\) 1.51881 + 1.51881i 0.136946 + 0.136946i
\(124\) −2.12946 2.12946i −0.191231 0.191231i
\(125\) −8.12256 8.12256i −0.726504 0.726504i
\(126\) −1.28726 + 1.82542i −0.114678 + 0.162621i
\(127\) 1.54912i 0.137462i −0.997635 0.0687312i \(-0.978105\pi\)
0.997635 0.0687312i \(-0.0218951\pi\)
\(128\) 8.15633 8.15633i 0.720924 0.720924i
\(129\) −10.6762 −0.939983
\(130\) 2.98977 0.246707i 0.262220 0.0216376i
\(131\) 5.31490i 0.464365i 0.972672 + 0.232183i \(0.0745867\pi\)
−0.972672 + 0.232183i \(0.925413\pi\)
\(132\) 1.23240 1.23240i 0.107267 0.107267i
\(133\) 10.9878 + 7.74841i 0.952761 + 0.671872i
\(134\) 7.06793i 0.610576i
\(135\) 5.70052 + 5.70052i 0.490623 + 0.490623i
\(136\) −10.8839 + 10.8839i −0.933284 + 0.933284i
\(137\) 12.7157 12.7157i 1.08637 1.08637i 0.0904753 0.995899i \(-0.471161\pi\)
0.995899 0.0904753i \(-0.0288386\pi\)
\(138\) −2.20711 2.20711i −0.187882 0.187882i
\(139\) 6.94767i 0.589294i −0.955606 0.294647i \(-0.904798\pi\)
0.955606 0.294647i \(-0.0952020\pi\)
\(140\) 3.72849 5.28726i 0.315115 0.446855i
\(141\) −3.10848 + 3.10848i −0.261781 + 0.261781i
\(142\) 1.18172i 0.0991676i
\(143\) −1.96810 + 2.32212i −0.164581 + 0.194185i
\(144\) −3.19394 −0.266161
\(145\) 3.65837 3.65837i 0.303811 0.303811i
\(146\) 0.0837150i 0.00692831i
\(147\) 2.89646 + 8.12601i 0.238896 + 0.670222i
\(148\) −4.83146 4.83146i −0.397143 0.397143i
\(149\) −10.9653 10.9653i −0.898315 0.898315i 0.0969724 0.995287i \(-0.469084\pi\)
−0.995287 + 0.0969724i \(0.969084\pi\)
\(150\) −1.42505 1.42505i −0.116355 0.116355i
\(151\) 6.14117 6.14117i 0.499761 0.499761i −0.411602 0.911363i \(-0.635031\pi\)
0.911363 + 0.411602i \(0.135031\pi\)
\(152\) 10.6449i 0.863413i
\(153\) 10.8839 0.879909
\(154\) −0.216897 1.25451i −0.0174781 0.101091i
\(155\) 2.62435i 0.210793i
\(156\) −7.41819 + 0.612127i −0.593931 + 0.0490094i
\(157\) 9.69783i 0.773971i 0.922086 + 0.386985i \(0.126484\pi\)
−0.922086 + 0.386985i \(0.873516\pi\)
\(158\) 1.93406 + 1.93406i 0.153865 + 0.153865i
\(159\) 12.0699i 0.957207i
\(160\) −7.90977 −0.625322
\(161\) 11.5847 2.00293i 0.913006 0.157853i
\(162\) 0.952155 + 0.952155i 0.0748083 + 0.0748083i
\(163\) −5.41327 + 5.41327i −0.424000 + 0.424000i −0.886578 0.462579i \(-0.846924\pi\)
0.462579 + 0.886578i \(0.346924\pi\)
\(164\) 2.06443 + 2.06443i 0.161205 + 0.161205i
\(165\) −1.51881 −0.118239
\(166\) 9.92784 0.770550
\(167\) −8.90824 8.90824i −0.689340 0.689340i 0.272746 0.962086i \(-0.412068\pi\)
−0.962086 + 0.272746i \(0.912068\pi\)
\(168\) 3.93620 5.58181i 0.303685 0.430646i
\(169\) 12.8242 2.13093i 0.986474 0.163918i
\(170\) 6.11379 0.468906
\(171\) −5.32243 + 5.32243i −0.407017 + 0.407017i
\(172\) −14.5115 −1.10649
\(173\) −7.15538 −0.544014 −0.272007 0.962295i \(-0.587687\pi\)
−0.272007 + 0.962295i \(0.587687\pi\)
\(174\) 1.76039 1.76039i 0.133455 0.133455i
\(175\) 7.47987 1.29322i 0.565425 0.0977586i
\(176\) 1.28726 1.28726i 0.0970307 0.0970307i
\(177\) 1.34297 1.34297i 0.100944 0.100944i
\(178\) 5.55391i 0.416283i
\(179\) 13.8119i 1.03235i 0.856482 + 0.516177i \(0.172645\pi\)
−0.856482 + 0.516177i \(0.827355\pi\)
\(180\) 2.56112 + 2.56112i 0.190895 + 0.190895i
\(181\) 4.56052 0.338981 0.169490 0.985532i \(-0.445788\pi\)
0.169490 + 0.985532i \(0.445788\pi\)
\(182\) −2.75743 + 4.68611i −0.204395 + 0.347358i
\(183\) 8.76116 0.647643
\(184\) −6.58181 6.58181i −0.485217 0.485217i
\(185\) 5.95428i 0.437767i
\(186\) 1.26282i 0.0925945i
\(187\) −4.38655 + 4.38655i −0.320776 + 0.320776i
\(188\) −4.22518 + 4.22518i −0.308153 + 0.308153i
\(189\) −14.3979 + 2.48930i −1.04729 + 0.181070i
\(190\) −2.98977 + 2.98977i −0.216900 + 0.216900i
\(191\) 3.70545 0.268117 0.134058 0.990973i \(-0.457199\pi\)
0.134058 + 0.990973i \(0.457199\pi\)
\(192\) 1.50877 0.108886
\(193\) −17.0508 + 17.0508i −1.22734 + 1.22734i −0.262377 + 0.964965i \(0.584506\pi\)
−0.964965 + 0.262377i \(0.915494\pi\)
\(194\) −4.88324 −0.350596
\(195\) 4.94827 + 4.19389i 0.354353 + 0.300331i
\(196\) 3.93700 + 11.0452i 0.281214 + 0.788945i
\(197\) −8.01810 8.01810i −0.571266 0.571266i 0.361216 0.932482i \(-0.382362\pi\)
−0.932482 + 0.361216i \(0.882362\pi\)
\(198\) 0.712742 0.0506524
\(199\) 4.57558 0.324354 0.162177 0.986762i \(-0.448148\pi\)
0.162177 + 0.986762i \(0.448148\pi\)
\(200\) −4.24965 4.24965i −0.300495 0.300495i
\(201\) 10.8062 10.8062i 0.762212 0.762212i
\(202\) 5.18728 + 5.18728i 0.364976 + 0.364976i
\(203\) 1.59754 + 9.23998i 0.112125 + 0.648520i
\(204\) −15.1695 −1.06208
\(205\) 2.54420i 0.177695i
\(206\) −2.46480 2.46480i −0.171731 0.171731i
\(207\) 6.58181i 0.457467i
\(208\) −7.74841 + 0.639375i −0.537255 + 0.0443327i
\(209\) 4.29022i 0.296761i
\(210\) −2.67327 + 0.462193i −0.184473 + 0.0318943i
\(211\) −0.594028 −0.0408946 −0.0204473 0.999791i \(-0.506509\pi\)
−0.0204473 + 0.999791i \(0.506509\pi\)
\(212\) 16.4060i 1.12677i
\(213\) −1.80674 + 1.80674i −0.123796 + 0.123796i
\(214\) −3.57452 3.57452i −0.244349 0.244349i
\(215\) 8.94198 + 8.94198i 0.609838 + 0.609838i
\(216\) 8.18007 + 8.18007i 0.556583 + 0.556583i
\(217\) −3.88717 2.74117i −0.263878 0.186083i
\(218\) 3.70545i 0.250965i
\(219\) 0.127993 0.127993i 0.00864895 0.00864895i
\(220\) −2.06443 −0.139184
\(221\) 26.4040 2.17878i 1.77612 0.146560i
\(222\) 2.86516i 0.192297i
\(223\) −2.85764 + 2.85764i −0.191361 + 0.191361i −0.796284 0.604923i \(-0.793204\pi\)
0.604923 + 0.796284i \(0.293204\pi\)
\(224\) 8.26187 11.7159i 0.552019 0.782802i
\(225\) 4.24965i 0.283310i
\(226\) −0.647754 0.647754i −0.0430879 0.0430879i
\(227\) 19.6570 19.6570i 1.30468 1.30468i 0.379477 0.925201i \(-0.376104\pi\)
0.925201 0.379477i \(-0.123896\pi\)
\(228\) 7.41819 7.41819i 0.491282 0.491282i
\(229\) 13.2060 + 13.2060i 0.872676 + 0.872676i 0.992763 0.120087i \(-0.0383174\pi\)
−0.120087 + 0.992763i \(0.538317\pi\)
\(230\) 3.69720i 0.243786i
\(231\) 1.58641 2.24965i 0.104378 0.148016i
\(232\) 5.24965 5.24965i 0.344656 0.344656i
\(233\) 16.2243i 1.06289i −0.847094 0.531443i \(-0.821650\pi\)
0.847094 0.531443i \(-0.178350\pi\)
\(234\) −2.32212 1.96810i −0.151802 0.128659i
\(235\) 5.20711 0.339674
\(236\) 1.82542 1.82542i 0.118825 0.118825i
\(237\) 5.91400i 0.384155i
\(238\) −6.38594 + 9.05571i −0.413939 + 0.586994i
\(239\) −0.843675 0.843675i −0.0545728 0.0545728i 0.679294 0.733867i \(-0.262286\pi\)
−0.733867 + 0.679294i \(0.762286\pi\)
\(240\) −2.74306 2.74306i −0.177064 0.177064i
\(241\) −15.2966 15.2966i −0.985342 0.985342i 0.0145517 0.999894i \(-0.495368\pi\)
−0.999894 + 0.0145517i \(0.995368\pi\)
\(242\) 4.14609 4.14609i 0.266521 0.266521i
\(243\) 13.6563i 0.876054i
\(244\) 11.9086 0.762367
\(245\) 4.38009 9.23204i 0.279834 0.589813i
\(246\) 1.22425i 0.0780556i
\(247\) −11.8466 + 13.9775i −0.753782 + 0.889370i
\(248\) 3.76585i 0.239132i
\(249\) 15.1788 + 15.1788i 0.961916 + 0.961916i
\(250\) 6.54730i 0.414088i
\(251\) −27.4367 −1.73179 −0.865893 0.500229i \(-0.833249\pi\)
−0.865893 + 0.500229i \(0.833249\pi\)
\(252\) −6.46865 + 1.11839i −0.407487 + 0.0704521i
\(253\) −2.65268 2.65268i −0.166772 0.166772i
\(254\) −0.624346 + 0.624346i −0.0391749 + 0.0391749i
\(255\) 9.34743 + 9.34743i 0.585359 + 0.585359i
\(256\) −4.12601 −0.257876
\(257\) −20.5727 −1.28329 −0.641645 0.767002i \(-0.721748\pi\)
−0.641645 + 0.767002i \(0.721748\pi\)
\(258\) 4.30283 + 4.30283i 0.267883 + 0.267883i
\(259\) −8.81944 6.21933i −0.548014 0.386450i
\(260\) 6.72592 + 5.70052i 0.417124 + 0.353531i
\(261\) −5.24965 −0.324945
\(262\) 2.14207 2.14207i 0.132338 0.132338i
\(263\) −23.8568 −1.47108 −0.735538 0.677483i \(-0.763071\pi\)
−0.735538 + 0.677483i \(0.763071\pi\)
\(264\) −2.17944 −0.134135
\(265\) 10.1093 10.1093i 0.621012 0.621012i
\(266\) −1.30557 7.55128i −0.0800497 0.462999i
\(267\) 8.49143 8.49143i 0.519667 0.519667i
\(268\) 14.6883 14.6883i 0.897231 0.897231i
\(269\) 1.10840i 0.0675803i 0.999429 + 0.0337902i \(0.0107578\pi\)
−0.999429 + 0.0337902i \(0.989242\pi\)
\(270\) 4.59498i 0.279642i
\(271\) −20.8894 20.8894i −1.26894 1.26894i −0.946637 0.322301i \(-0.895544\pi\)
−0.322301 0.946637i \(-0.604456\pi\)
\(272\) −15.8448 −0.960730
\(273\) −11.3805 + 2.94878i −0.688780 + 0.178468i
\(274\) −10.2496 −0.619204
\(275\) −1.71274 1.71274i −0.103282 0.103282i
\(276\) 9.17346i 0.552177i
\(277\) 25.8265i 1.55177i −0.630877 0.775883i \(-0.717305\pi\)
0.630877 0.775883i \(-0.282695\pi\)
\(278\) −2.80013 + 2.80013i −0.167941 + 0.167941i
\(279\) 1.88293 1.88293i 0.112728 0.112728i
\(280\) −7.97196 + 1.37830i −0.476416 + 0.0823694i
\(281\) 12.0782 12.0782i 0.720523 0.720523i −0.248189 0.968712i \(-0.579835\pi\)
0.968712 + 0.248189i \(0.0798354\pi\)
\(282\) 2.50563 0.149208
\(283\) 15.3667 0.913458 0.456729 0.889606i \(-0.349021\pi\)
0.456729 + 0.889606i \(0.349021\pi\)
\(284\) −2.45580 + 2.45580i −0.145725 + 0.145725i
\(285\) −9.14217 −0.541535
\(286\) 1.72909 0.142680i 0.102243 0.00843683i
\(287\) 3.76845 + 2.65745i 0.222445 + 0.156864i
\(288\) 5.67513 + 5.67513i 0.334410 + 0.334410i
\(289\) 36.9937 2.17610
\(290\) −2.94888 −0.173164
\(291\) −7.46604 7.46604i −0.437667 0.437667i
\(292\) 0.173973 0.173973i 0.0101810 0.0101810i
\(293\) 9.78662 + 9.78662i 0.571741 + 0.571741i 0.932615 0.360874i \(-0.117522\pi\)
−0.360874 + 0.932615i \(0.617522\pi\)
\(294\) 2.10767 4.44240i 0.122922 0.259086i
\(295\) −2.24965 −0.130979
\(296\) 8.54420i 0.496621i
\(297\) 3.29683 + 3.29683i 0.191301 + 0.191301i
\(298\) 8.83875i 0.512015i
\(299\) 1.31757 + 15.9673i 0.0761972 + 0.923413i
\(300\) 5.92298i 0.341964i
\(301\) −22.5848 + 3.90478i −1.30177 + 0.225068i
\(302\) −4.95017 −0.284850
\(303\) 15.8618i 0.911235i
\(304\) 7.74841 7.74841i 0.444402 0.444402i
\(305\) −7.33804 7.33804i −0.420175 0.420175i
\(306\) −4.38655 4.38655i −0.250762 0.250762i
\(307\) 8.14125 + 8.14125i 0.464645 + 0.464645i 0.900175 0.435529i \(-0.143439\pi\)
−0.435529 + 0.900175i \(0.643439\pi\)
\(308\) 2.15633 3.05782i 0.122868 0.174235i
\(309\) 7.53690i 0.428759i
\(310\) 1.05769 1.05769i 0.0600730 0.0600730i
\(311\) 32.4813 1.84184 0.920922 0.389747i \(-0.127438\pi\)
0.920922 + 0.389747i \(0.127438\pi\)
\(312\) 7.10062 + 6.01810i 0.401993 + 0.340708i
\(313\) 19.7346i 1.11547i −0.830020 0.557733i \(-0.811671\pi\)
0.830020 0.557733i \(-0.188329\pi\)
\(314\) 3.90853 3.90853i 0.220571 0.220571i
\(315\) 4.67513 + 3.29683i 0.263414 + 0.185755i
\(316\) 8.03857i 0.452205i
\(317\) −8.11871 8.11871i −0.455992 0.455992i 0.441345 0.897337i \(-0.354501\pi\)
−0.897337 + 0.441345i \(0.854501\pi\)
\(318\) 4.86456 4.86456i 0.272791 0.272791i
\(319\) 2.11577 2.11577i 0.118461 0.118461i
\(320\) −1.26369 1.26369i −0.0706425 0.0706425i
\(321\) 10.9302i 0.610066i
\(322\) −5.47626 3.86177i −0.305180 0.215208i
\(323\) −26.4040 + 26.4040i −1.46916 + 1.46916i
\(324\) 3.95746i 0.219859i
\(325\) 0.850712 + 10.3095i 0.0471890 + 0.571870i
\(326\) 4.36344 0.241668
\(327\) −5.66530 + 5.66530i −0.313292 + 0.313292i
\(328\) 3.65084i 0.201584i
\(329\) −5.43890 + 7.71274i −0.299856 + 0.425217i
\(330\) 0.612127 + 0.612127i 0.0336965 + 0.0336965i
\(331\) −0.806063 0.806063i −0.0443053 0.0443053i 0.684607 0.728912i \(-0.259974\pi\)
−0.728912 + 0.684607i \(0.759974\pi\)
\(332\) 20.6317 + 20.6317i 1.13231 + 1.13231i
\(333\) 4.27210 4.27210i 0.234110 0.234110i
\(334\) 7.18061i 0.392905i
\(335\) −18.1018 −0.989009
\(336\) 6.92817 1.19784i 0.377963 0.0653475i
\(337\) 26.6058i 1.44931i 0.689112 + 0.724655i \(0.258001\pi\)
−0.689112 + 0.724655i \(0.741999\pi\)
\(338\) −6.02738 4.30971i −0.327846 0.234417i
\(339\) 1.98071i 0.107578i
\(340\) 12.7054 + 12.7054i 0.689050 + 0.689050i
\(341\) 1.51776i 0.0821912i
\(342\) 4.29022 0.231988
\(343\) 9.09937 + 16.1308i 0.491320 + 0.870979i
\(344\) 12.8315 + 12.8315i 0.691826 + 0.691826i
\(345\) −5.65268 + 5.65268i −0.304330 + 0.304330i
\(346\) 2.88385 + 2.88385i 0.155037 + 0.155037i
\(347\) −20.2071 −1.08477 −0.542387 0.840129i \(-0.682479\pi\)
−0.542387 + 0.840129i \(0.682479\pi\)
\(348\) 7.31674 0.392219
\(349\) 2.31459 + 2.31459i 0.123897 + 0.123897i 0.766336 0.642439i \(-0.222078\pi\)
−0.642439 + 0.766336i \(0.722078\pi\)
\(350\) −3.53583 2.49341i −0.188998 0.133279i
\(351\) −1.63752 19.8446i −0.0874043 1.05923i
\(352\) −4.57452 −0.243822
\(353\) 10.7412 10.7412i 0.571696 0.571696i −0.360906 0.932602i \(-0.617533\pi\)
0.932602 + 0.360906i \(0.117533\pi\)
\(354\) −1.08252 −0.0575351
\(355\) 3.02653 0.160631
\(356\) 11.5419 11.5419i 0.611721 0.611721i
\(357\) −23.6089 + 4.08184i −1.24952 + 0.216034i
\(358\) 5.56665 5.56665i 0.294207 0.294207i
\(359\) −16.9726 + 16.9726i −0.895781 + 0.895781i −0.995060 0.0992789i \(-0.968346\pi\)
0.0992789 + 0.995060i \(0.468346\pi\)
\(360\) 4.52923i 0.238711i
\(361\) 6.82416i 0.359166i
\(362\) −1.83803 1.83803i −0.0966049 0.0966049i
\(363\) 12.6780 0.665422
\(364\) −15.4689 + 4.00811i −0.810791 + 0.210082i
\(365\) −0.214405 −0.0112225
\(366\) −3.53102 3.53102i −0.184570 0.184570i
\(367\) 9.79778i 0.511440i 0.966751 + 0.255720i \(0.0823125\pi\)
−0.966751 + 0.255720i \(0.917688\pi\)
\(368\) 9.58181i 0.499486i
\(369\) −1.82542 + 1.82542i −0.0950276 + 0.0950276i
\(370\) 2.39976 2.39976i 0.124758 0.124758i
\(371\) 4.41455 + 25.5333i 0.229192 + 1.32562i
\(372\) −2.62435 + 2.62435i −0.136066 + 0.136066i
\(373\) −5.96731 −0.308976 −0.154488 0.987995i \(-0.549373\pi\)
−0.154488 + 0.987995i \(0.549373\pi\)
\(374\) 3.53583 0.182834
\(375\) −10.0102 + 10.0102i −0.516926 + 0.516926i
\(376\) 7.47204 0.385341
\(377\) −12.7355 + 1.05090i −0.655912 + 0.0541239i
\(378\) 6.80606 + 4.79953i 0.350066 + 0.246861i
\(379\) 2.14117 + 2.14117i 0.109984 + 0.109984i 0.759957 0.649973i \(-0.225220\pi\)
−0.649973 + 0.759957i \(0.725220\pi\)
\(380\) −12.4264 −0.637463
\(381\) −1.90914 −0.0978080
\(382\) −1.49341 1.49341i −0.0764097 0.0764097i
\(383\) −2.91152 + 2.91152i −0.148772 + 0.148772i −0.777569 0.628798i \(-0.783547\pi\)
0.628798 + 0.777569i \(0.283547\pi\)
\(384\) −10.0518 10.0518i −0.512956 0.512956i
\(385\) −3.21295 + 0.555500i −0.163747 + 0.0283109i
\(386\) 13.7440 0.699552
\(387\) 12.8315i 0.652260i
\(388\) −10.1482 10.1482i −0.515195 0.515195i
\(389\) 17.4436i 0.884425i 0.896910 + 0.442212i \(0.145806\pi\)
−0.896910 + 0.442212i \(0.854194\pi\)
\(390\) −0.304041 3.68458i −0.0153957 0.186576i
\(391\) 32.6516i 1.65126i
\(392\) 6.28529 13.2477i 0.317455 0.669109i
\(393\) 6.55008 0.330408
\(394\) 6.46310i 0.325606i
\(395\) 4.95336 4.95336i 0.249230 0.249230i
\(396\) 1.48119 + 1.48119i 0.0744328 + 0.0744328i
\(397\) −10.1870 10.1870i −0.511270 0.511270i 0.403645 0.914916i \(-0.367743\pi\)
−0.914916 + 0.403645i \(0.867743\pi\)
\(398\) −1.84410 1.84410i −0.0924365 0.0924365i
\(399\) 9.54912 13.5413i 0.478054 0.677914i
\(400\) 6.18664i 0.309332i
\(401\) 15.5950 15.5950i 0.778776 0.778776i −0.200846 0.979623i \(-0.564369\pi\)
0.979623 + 0.200846i \(0.0643692\pi\)
\(402\) −8.71050 −0.434440
\(403\) 4.19100 4.94486i 0.208768 0.246321i
\(404\) 21.5600i 1.07265i
\(405\) 2.43859 2.43859i 0.121174 0.121174i
\(406\) 3.08015 4.36786i 0.152865 0.216773i
\(407\) 3.44358i 0.170692i
\(408\) 13.4133 + 13.4133i 0.664056 + 0.664056i
\(409\) −1.79921 + 1.79921i −0.0889652 + 0.0889652i −0.750189 0.661224i \(-0.770037\pi\)
0.661224 + 0.750189i \(0.270037\pi\)
\(410\) −1.02539 + 1.02539i −0.0506405 + 0.0506405i
\(411\) −15.6708 15.6708i −0.772983 0.772983i
\(412\) 10.2445i 0.504710i
\(413\) 2.34979 3.33216i 0.115626 0.163965i
\(414\) 2.65268 2.65268i 0.130372 0.130372i
\(415\) 25.4264i 1.24813i
\(416\) 14.9038 + 12.6316i 0.730718 + 0.619317i
\(417\) −8.56230 −0.419297
\(418\) −1.72909 + 1.72909i −0.0845728 + 0.0845728i
\(419\) 16.5064i 0.806392i −0.915114 0.403196i \(-0.867899\pi\)
0.915114 0.403196i \(-0.132101\pi\)
\(420\) −6.51601 4.59498i −0.317949 0.224212i
\(421\) −8.53492 8.53492i −0.415967 0.415967i 0.467844 0.883811i \(-0.345031\pi\)
−0.883811 + 0.467844i \(0.845031\pi\)
\(422\) 0.239412 + 0.239412i 0.0116544 + 0.0116544i
\(423\) −3.73602 3.73602i −0.181651 0.181651i
\(424\) 14.5066 14.5066i 0.704502 0.704502i
\(425\) 21.0820i 1.02263i
\(426\) 1.45635 0.0705602
\(427\) 18.5338 3.20438i 0.896911 0.155071i
\(428\) 14.8568i 0.718133i
\(429\) 2.86177 + 2.42548i 0.138168 + 0.117103i
\(430\) 7.20780i 0.347591i
\(431\) 24.2071 + 24.2071i 1.16602 + 1.16602i 0.983135 + 0.182880i \(0.0585421\pi\)
0.182880 + 0.983135i \(0.441458\pi\)
\(432\) 11.9086i 0.572951i
\(433\) 35.8708 1.72384 0.861920 0.507044i \(-0.169262\pi\)
0.861920 + 0.507044i \(0.169262\pi\)
\(434\) 0.461874 + 2.67143i 0.0221707 + 0.128233i
\(435\) −4.50857 4.50857i −0.216169 0.216169i
\(436\) −7.70052 + 7.70052i −0.368788 + 0.368788i
\(437\) −15.9673 15.9673i −0.763819 0.763819i
\(438\) −0.103170 −0.00492967
\(439\) −10.5299 −0.502563 −0.251281 0.967914i \(-0.580852\pi\)
−0.251281 + 0.967914i \(0.580852\pi\)
\(440\) 1.82542 + 1.82542i 0.0870236 + 0.0870236i
\(441\) −9.76648 + 3.48119i −0.465071 + 0.165771i
\(442\) −11.5198 9.76353i −0.547939 0.464404i
\(443\) 12.8618 0.611081 0.305541 0.952179i \(-0.401163\pi\)
0.305541 + 0.952179i \(0.401163\pi\)
\(444\) −5.95428 + 5.95428i −0.282578 + 0.282578i
\(445\) −14.2243 −0.674294
\(446\) 2.30344 0.109071
\(447\) −13.5137 + 13.5137i −0.639174 + 0.639174i
\(448\) 3.19172 0.551829i 0.150795 0.0260715i
\(449\) 9.65069 9.65069i 0.455444 0.455444i −0.441712 0.897157i \(-0.645629\pi\)
0.897157 + 0.441712i \(0.145629\pi\)
\(450\) 1.71274 1.71274i 0.0807394 0.0807394i
\(451\) 1.47141i 0.0692858i
\(452\) 2.69227i 0.126634i
\(453\) −7.56836 7.56836i −0.355593 0.355593i
\(454\) −15.8448 −0.743631
\(455\) 12.0017 + 7.06213i 0.562649 + 0.331078i
\(456\) −13.1187 −0.614340
\(457\) −22.1217 22.1217i −1.03481 1.03481i −0.999372 0.0354353i \(-0.988718\pi\)
−0.0354353 0.999372i \(-0.511282\pi\)
\(458\) 10.6449i 0.497402i
\(459\) 40.5804i 1.89413i
\(460\) −7.68337 + 7.68337i −0.358239 + 0.358239i
\(461\) −0.593023 + 0.593023i −0.0276198 + 0.0276198i −0.720782 0.693162i \(-0.756217\pi\)
0.693162 + 0.720782i \(0.256217\pi\)
\(462\) −1.54605 + 0.267304i −0.0719289 + 0.0124361i
\(463\) 2.47096 2.47096i 0.114835 0.114835i −0.647354 0.762189i \(-0.724124\pi\)
0.762189 + 0.647354i \(0.224124\pi\)
\(464\) 7.64244 0.354792
\(465\) 3.23424 0.149984
\(466\) −6.53889 + 6.53889i −0.302908 + 0.302908i
\(467\) 13.3860 0.619432 0.309716 0.950829i \(-0.399766\pi\)
0.309716 + 0.950829i \(0.399766\pi\)
\(468\) −0.735703 8.91577i −0.0340079 0.412132i
\(469\) 18.9076 26.8123i 0.873073 1.23808i
\(470\) −2.09863 2.09863i −0.0968026 0.0968026i
\(471\) 11.9516 0.550700
\(472\) −3.22817 −0.148589
\(473\) 5.17148 + 5.17148i 0.237785 + 0.237785i
\(474\) 2.38353 2.38353i 0.109479 0.109479i
\(475\) −10.3095 10.3095i −0.473034 0.473034i
\(476\) −32.0903 + 5.54821i −1.47085 + 0.254302i
\(477\) −14.5066 −0.664211
\(478\) 0.680055i 0.0311050i
\(479\) 8.85827 + 8.85827i 0.404745 + 0.404745i 0.879901 0.475157i \(-0.157609\pi\)
−0.475157 + 0.879901i \(0.657609\pi\)
\(480\) 9.74798i 0.444933i
\(481\) 9.50879 11.2192i 0.433564 0.511552i
\(482\) 12.3301i 0.561619i
\(483\) −2.46841 14.2770i −0.112317 0.649627i
\(484\) 17.2325 0.783296
\(485\) 12.5066i 0.567895i
\(486\) −5.50394 + 5.50394i −0.249664 + 0.249664i
\(487\) 17.9805 + 17.9805i 0.814774 + 0.814774i 0.985345 0.170572i \(-0.0545614\pi\)
−0.170572 + 0.985345i \(0.554561\pi\)
\(488\) −10.5299 10.5299i −0.476664 0.476664i
\(489\) 6.67130 + 6.67130i 0.301687 + 0.301687i
\(490\) −5.48612 + 1.95549i −0.247838 + 0.0883400i
\(491\) 19.4944i 0.879769i 0.898054 + 0.439884i \(0.144981\pi\)
−0.898054 + 0.439884i \(0.855019\pi\)
\(492\) 2.54420 2.54420i 0.114701 0.114701i
\(493\) −26.0429 −1.17291
\(494\) 10.4080 0.858833i 0.468276 0.0386407i
\(495\) 1.82542i 0.0820466i
\(496\) −2.74117 + 2.74117i −0.123082 + 0.123082i
\(497\) −3.16125 + 4.48287i −0.141801 + 0.201084i
\(498\) 12.2351i 0.548266i
\(499\) 10.2150 + 10.2150i 0.457285 + 0.457285i 0.897763 0.440478i \(-0.145191\pi\)
−0.440478 + 0.897763i \(0.645191\pi\)
\(500\) −13.6064 + 13.6064i −0.608495 + 0.608495i
\(501\) −10.9785 + 10.9785i −0.490483 + 0.490483i
\(502\) 11.0578 + 11.0578i 0.493536 + 0.493536i
\(503\) 31.8196i 1.41877i 0.704824 + 0.709383i \(0.251026\pi\)
−0.704824 + 0.709383i \(0.748974\pi\)
\(504\) 6.70866 + 4.73084i 0.298828 + 0.210728i
\(505\) 13.2853 13.2853i 0.591187 0.591187i
\(506\) 2.13823i 0.0950558i
\(507\) −2.62616 15.8045i −0.116632 0.701901i
\(508\) −2.59498 −0.115134
\(509\) 13.6139 13.6139i 0.603425 0.603425i −0.337795 0.941220i \(-0.609681\pi\)
0.941220 + 0.337795i \(0.109681\pi\)
\(510\) 7.53462i 0.333639i
\(511\) 0.223949 0.317575i 0.00990691 0.0140487i
\(512\) −14.6497 14.6497i −0.647433 0.647433i
\(513\) 19.8446 + 19.8446i 0.876162 + 0.876162i
\(514\) 8.29145 + 8.29145i 0.365720 + 0.365720i
\(515\) −6.31265 + 6.31265i −0.278169 + 0.278169i
\(516\) 17.8840i 0.787298i
\(517\) 3.01147 0.132444
\(518\) 1.04793 + 6.06110i 0.0460433 + 0.266310i
\(519\) 8.81828i 0.387080i
\(520\) −0.906679 10.9878i −0.0397605 0.481846i
\(521\) 21.6750i 0.949601i −0.880094 0.474800i \(-0.842520\pi\)
0.880094 0.474800i \(-0.157480\pi\)
\(522\) 2.11577 + 2.11577i 0.0926049 + 0.0926049i
\(523\) 8.77309i 0.383620i −0.981432 0.191810i \(-0.938564\pi\)
0.981432 0.191810i \(-0.0614358\pi\)
\(524\) 8.90316 0.388936
\(525\) −1.59377 9.21818i −0.0695577 0.402314i
\(526\) 9.61507 + 9.61507i 0.419237 + 0.419237i
\(527\) 9.34098 9.34098i 0.406900 0.406900i
\(528\) −1.58641 1.58641i −0.0690398 0.0690398i
\(529\) 3.25457 0.141503
\(530\) −8.14877 −0.353960
\(531\) 1.61409 + 1.61409i 0.0700453 + 0.0700453i
\(532\) 12.9796 18.4060i 0.562737 0.798000i
\(533\) −4.06300 + 4.79384i −0.175988 + 0.207644i
\(534\) −6.84463 −0.296196
\(535\) −9.15478 + 9.15478i −0.395796 + 0.395796i
\(536\) −25.9756 −1.12197
\(537\) 17.0218 0.734546
\(538\) 0.446720 0.446720i 0.0192595 0.0192595i
\(539\) 2.53317 5.33923i 0.109111 0.229977i
\(540\) 9.54912 9.54912i 0.410929 0.410929i
\(541\) −23.2853 + 23.2853i −1.00111 + 1.00111i −0.00111270 + 0.999999i \(0.500354\pi\)
−0.999999 + 0.00111270i \(0.999646\pi\)
\(542\) 16.8382i 0.723260i
\(543\) 5.62038i 0.241193i
\(544\) 28.1537 + 28.1537i 1.20708 + 1.20708i
\(545\) 9.49011 0.406512
\(546\) 5.77516 + 3.39826i 0.247154 + 0.145432i
\(547\) −15.1744 −0.648812 −0.324406 0.945918i \(-0.605164\pi\)
−0.324406 + 0.945918i \(0.605164\pi\)
\(548\) −21.3004 21.3004i −0.909909 0.909909i
\(549\) 10.5299i 0.449403i
\(550\) 1.38058i 0.0588681i
\(551\) 12.7355 12.7355i 0.542551 0.542551i
\(552\) −8.11141 + 8.11141i −0.345245 + 0.345245i
\(553\) 2.16303 + 12.5107i 0.0919815 + 0.532011i
\(554\) −10.4089 + 10.4089i −0.442232 + 0.442232i
\(555\) 7.33804 0.311483
\(556\) −11.6383 −0.493572
\(557\) 8.45676 8.45676i 0.358324 0.358324i −0.504871 0.863195i \(-0.668460\pi\)
0.863195 + 0.504871i \(0.168460\pi\)
\(558\) −1.51776 −0.0642518
\(559\) −2.56865 31.1288i −0.108642 1.31661i
\(560\) −6.80606 4.79953i −0.287609 0.202817i
\(561\) 5.40597 + 5.40597i 0.228240 + 0.228240i
\(562\) −9.73577 −0.410678
\(563\) −6.34858 −0.267561 −0.133780 0.991011i \(-0.542712\pi\)
−0.133780 + 0.991011i \(0.542712\pi\)
\(564\) 5.20711 + 5.20711i 0.219259 + 0.219259i
\(565\) −1.65898 + 1.65898i −0.0697937 + 0.0697937i
\(566\) −6.19329 6.19329i −0.260323 0.260323i
\(567\) 1.06488 + 6.15916i 0.0447208 + 0.258660i
\(568\) 4.34297 0.182227
\(569\) 36.6140i 1.53494i 0.641085 + 0.767470i \(0.278485\pi\)
−0.641085 + 0.767470i \(0.721515\pi\)
\(570\) 3.68458 + 3.68458i 0.154330 + 0.154330i
\(571\) 18.8070i 0.787049i −0.919314 0.393525i \(-0.871256\pi\)
0.919314 0.393525i \(-0.128744\pi\)
\(572\) 3.88985 + 3.29683i 0.162643 + 0.137847i
\(573\) 4.56659i 0.190772i
\(574\) −0.447768 2.58984i −0.0186895 0.108098i
\(575\) −12.7489 −0.531668
\(576\) 1.81336i 0.0755566i
\(577\) −31.3416 + 31.3416i −1.30477 + 1.30477i −0.379627 + 0.925140i \(0.623948\pi\)
−0.925140 + 0.379627i \(0.876052\pi\)
\(578\) −14.9096 14.9096i −0.620158 0.620158i
\(579\) 21.0134 + 21.0134i 0.873285 + 0.873285i
\(580\) −6.12825 6.12825i −0.254462 0.254462i
\(581\) 37.6615 + 26.5583i 1.56246 + 1.10182i
\(582\) 6.01810i 0.249458i
\(583\) 5.84661 5.84661i 0.242142 0.242142i
\(584\) −0.307664 −0.0127312
\(585\) −5.04055 + 5.94723i −0.208401 + 0.245888i
\(586\) 7.88864i 0.325877i
\(587\) −3.36694 + 3.36694i −0.138969 + 0.138969i −0.773169 0.634200i \(-0.781329\pi\)
0.634200 + 0.773169i \(0.281329\pi\)
\(588\) 13.6121 4.85195i 0.561355 0.200091i
\(589\) 9.13586i 0.376436i
\(590\) 0.906679 + 0.906679i 0.0373274 + 0.0373274i
\(591\) −9.88149 + 9.88149i −0.406470 + 0.406470i
\(592\) −6.21933 + 6.21933i −0.255613 + 0.255613i
\(593\) −10.6837 10.6837i −0.438726 0.438726i 0.452857 0.891583i \(-0.350405\pi\)
−0.891583 + 0.452857i \(0.850405\pi\)
\(594\) 2.65745i 0.109037i
\(595\) 23.1928 + 16.3552i 0.950812 + 0.670497i
\(596\) −18.3684 + 18.3684i −0.752397 + 0.752397i
\(597\) 5.63893i 0.230786i
\(598\) 5.90430 6.96635i 0.241445 0.284875i
\(599\) −12.8437 −0.524778 −0.262389 0.964962i \(-0.584510\pi\)
−0.262389 + 0.964962i \(0.584510\pi\)
\(600\) −5.23726 + 5.23726i −0.213810 + 0.213810i
\(601\) 19.5732i 0.798409i 0.916862 + 0.399205i \(0.130714\pi\)
−0.916862 + 0.399205i \(0.869286\pi\)
\(602\) 10.6762 + 7.52865i 0.435128 + 0.306845i
\(603\) 12.9878 + 12.9878i 0.528903 + 0.528903i
\(604\) −10.2873 10.2873i −0.418583 0.418583i
\(605\) −10.6187 10.6187i −0.431710 0.431710i
\(606\) 6.39280 6.39280i 0.259690 0.259690i
\(607\) 41.9804i 1.70393i −0.523598 0.851965i \(-0.675411\pi\)
0.523598 0.851965i \(-0.324589\pi\)
\(608\) −27.5354 −1.11671
\(609\) 11.3873 1.96880i 0.461438 0.0797799i
\(610\) 5.91493i 0.239488i
\(611\) −9.81137 8.31559i −0.396926 0.336413i
\(612\) 18.2319i 0.736981i
\(613\) 20.4993 + 20.4993i 0.827959 + 0.827959i 0.987234 0.159276i \(-0.0509158\pi\)
−0.159276 + 0.987234i \(0.550916\pi\)
\(614\) 6.56236i 0.264835i
\(615\) −3.13547 −0.126434
\(616\) −4.61048 + 0.797125i −0.185762 + 0.0321171i
\(617\) 8.21440 + 8.21440i 0.330699 + 0.330699i 0.852852 0.522153i \(-0.174871\pi\)
−0.522153 + 0.852852i \(0.674871\pi\)
\(618\) −3.03761 + 3.03761i −0.122191 + 0.122191i
\(619\) −26.6973 26.6973i −1.07306 1.07306i −0.997112 0.0759445i \(-0.975803\pi\)
−0.0759445 0.997112i \(-0.524197\pi\)
\(620\) 4.39612 0.176553
\(621\) 24.5402 0.984764
\(622\) −13.0910 13.0910i −0.524900 0.524900i
\(623\) 14.8574 21.0689i 0.595251 0.844107i
\(624\) 0.787965 + 9.54912i 0.0315438 + 0.382271i
\(625\) 2.42311 0.0969246
\(626\) −7.95367 + 7.95367i −0.317893 + 0.317893i
\(627\) −5.28726 −0.211153
\(628\) 16.2451 0.648251
\(629\) 21.1934 21.1934i 0.845036 0.845036i
\(630\) −0.555500 3.21295i −0.0221317 0.128007i
\(631\) 5.13093 5.13093i 0.204259 0.204259i −0.597563 0.801822i \(-0.703864\pi\)
0.801822 + 0.597563i \(0.203864\pi\)
\(632\) 7.10791 7.10791i 0.282737 0.282737i
\(633\) 0.732080i 0.0290976i
\(634\) 6.54420i 0.259903i
\(635\) 1.59903 + 1.59903i 0.0634554 + 0.0634554i
\(636\) 20.2187 0.801723
\(637\) −22.9963 + 10.4004i −0.911149 + 0.412078i
\(638\) −1.70545 −0.0675193
\(639\) −2.17148 2.17148i −0.0859026 0.0859026i
\(640\) 16.8382i 0.665586i
\(641\) 16.3357i 0.645220i −0.946532 0.322610i \(-0.895440\pi\)
0.946532 0.322610i \(-0.104560\pi\)
\(642\) −4.40523 + 4.40523i −0.173860 + 0.173860i
\(643\) −28.1910 + 28.1910i −1.11175 + 1.11175i −0.118832 + 0.992914i \(0.537915\pi\)
−0.992914 + 0.118832i \(0.962085\pi\)
\(644\) −3.35517 19.4060i −0.132212 0.764702i
\(645\) 11.0201 11.0201i 0.433915 0.433915i
\(646\) 21.2833 0.837380
\(647\) −11.1139 −0.436932 −0.218466 0.975845i \(-0.570105\pi\)
−0.218466 + 0.975845i \(0.570105\pi\)
\(648\) 3.49929 3.49929i 0.137465 0.137465i
\(649\) −1.30105 −0.0510709
\(650\) 3.81220 4.49793i 0.149527 0.176423i
\(651\) −3.37821 + 4.79054i −0.132402 + 0.187756i
\(652\) 9.06793 + 9.06793i 0.355127 + 0.355127i
\(653\) 4.95651 0.193963 0.0969816 0.995286i \(-0.469081\pi\)
0.0969816 + 0.995286i \(0.469081\pi\)
\(654\) 4.56659 0.178568
\(655\) −5.48612 5.48612i −0.214360 0.214360i
\(656\) 2.65745 2.65745i 0.103756 0.103756i
\(657\) 0.153832 + 0.153832i 0.00600155 + 0.00600155i
\(658\) 5.30053 0.916430i 0.206636 0.0357262i
\(659\) 26.1514 1.01871 0.509357 0.860555i \(-0.329883\pi\)
0.509357 + 0.860555i \(0.329883\pi\)
\(660\) 2.54420i 0.0990328i
\(661\) 22.2906 + 22.2906i 0.867006 + 0.867006i 0.992140 0.125134i \(-0.0399361\pi\)
−0.125134 + 0.992140i \(0.539936\pi\)
\(662\) 0.649738i 0.0252528i
\(663\) −2.68512 32.5402i −0.104282 1.26376i
\(664\) 36.4861i 1.41594i
\(665\) −19.3398 + 3.34373i −0.749964 + 0.129664i
\(666\) −3.44358 −0.133436
\(667\) 15.7489i 0.609801i
\(668\) −14.9225 + 14.9225i −0.577368 + 0.577368i
\(669\) 3.52175 + 3.52175i 0.136159 + 0.136159i
\(670\) 7.29562 + 7.29562i 0.281854 + 0.281854i
\(671\) −4.24387 4.24387i −0.163833 0.163833i
\(672\) −14.4387 10.1819i −0.556983 0.392776i
\(673\) 1.38550i 0.0534072i 0.999643 + 0.0267036i \(0.00850104\pi\)
−0.999643 + 0.0267036i \(0.991499\pi\)
\(674\) 10.7230 10.7230i 0.413034 0.413034i
\(675\) 15.8448 0.609865
\(676\) −3.56959 21.4821i −0.137292 0.826237i
\(677\) 14.1868i 0.545242i −0.962122 0.272621i \(-0.912110\pi\)
0.962122 0.272621i \(-0.0878905\pi\)
\(678\) −0.798290 + 0.798290i −0.0306582 + 0.0306582i
\(679\) −18.5247 13.0633i −0.710912 0.501324i
\(680\) 22.4690i 0.861646i
\(681\) −24.2252 24.2252i −0.928312 0.928312i
\(682\) 0.611704 0.611704i 0.0234234 0.0234234i
\(683\) 27.2882 27.2882i 1.04415 1.04415i 0.0451754 0.998979i \(-0.485615\pi\)
0.998979 0.0451754i \(-0.0143847\pi\)
\(684\) 8.91577 + 8.91577i 0.340903 + 0.340903i
\(685\) 26.2506i 1.00298i
\(686\) 2.83387 10.1685i 0.108198 0.388237i
\(687\) 16.2750 16.2750i 0.620931 0.620931i
\(688\) 18.6801i 0.712170i
\(689\) −35.1926 + 2.90399i −1.34073 + 0.110633i
\(690\) 4.55642 0.173460
\(691\) −16.1937 + 16.1937i −0.616037 + 0.616037i −0.944513 0.328475i \(-0.893465\pi\)
0.328475 + 0.944513i \(0.393465\pi\)
\(692\) 11.9862i 0.455647i
\(693\) 2.70380 + 1.90668i 0.102709 + 0.0724287i
\(694\) 8.14411 + 8.14411i 0.309146 + 0.309146i
\(695\) 7.17148 + 7.17148i 0.272030 + 0.272030i
\(696\) −6.46966 6.46966i −0.245232 0.245232i
\(697\) −9.05571 + 9.05571i −0.343009 + 0.343009i
\(698\) 1.86570i 0.0706180i
\(699\) −19.9947 −0.756271
\(700\) −2.16632 12.5298i −0.0818792 0.473580i
\(701\) 15.2981i 0.577800i −0.957359 0.288900i \(-0.906711\pi\)
0.957359 0.288900i \(-0.0932895\pi\)
\(702\) −7.33804 + 8.65799i −0.276957 + 0.326775i
\(703\) 20.7280i 0.781771i
\(704\) −0.730841 0.730841i −0.0275446 0.0275446i
\(705\) 6.41723i 0.241687i
\(706\) −8.65808 −0.325851
\(707\) 5.80141 + 33.5547i 0.218185 + 1.26196i
\(708\) −2.24965 2.24965i −0.0845469 0.0845469i
\(709\) −2.74107 + 2.74107i −0.102943 + 0.102943i −0.756703 0.653759i \(-0.773191\pi\)
0.653759 + 0.756703i \(0.273191\pi\)
\(710\) −1.21979 1.21979i −0.0457778 0.0457778i
\(711\) −7.10791 −0.266567
\(712\) −20.4113 −0.764948
\(713\) 5.64878 + 5.64878i 0.211548 + 0.211548i
\(714\) 11.1602 + 7.87002i 0.417662 + 0.294528i
\(715\) −0.365420 4.42842i −0.0136659 0.165614i
\(716\) 23.1368 0.864663
\(717\) −1.03974 + 1.03974i −0.0388299 + 0.0388299i
\(718\) 13.6810 0.510571
\(719\) 5.99456 0.223559 0.111780 0.993733i \(-0.464345\pi\)
0.111780 + 0.993733i \(0.464345\pi\)
\(720\) 3.29683 3.29683i 0.122865 0.122865i
\(721\) −2.75661 15.9439i −0.102661 0.593782i
\(722\) −2.75035 + 2.75035i −0.102358 + 0.102358i
\(723\) −18.8515 + 18.8515i −0.701096 + 0.701096i
\(724\) 7.63947i 0.283919i
\(725\) 10.1685i 0.377650i
\(726\) −5.10964 5.10964i −0.189636 0.189636i
\(727\) −14.6184 −0.542168 −0.271084 0.962556i \(-0.587382\pi\)
−0.271084 + 0.962556i \(0.587382\pi\)
\(728\) 17.2221 + 10.1339i 0.638293 + 0.375588i
\(729\) −23.9175 −0.885833
\(730\) 0.0864119 + 0.0864119i 0.00319825 + 0.00319825i
\(731\) 63.6554i 2.35438i
\(732\) 14.6761i 0.542444i
\(733\) 28.0685 28.0685i 1.03673 1.03673i 0.0374350 0.999299i \(-0.488081\pi\)
0.999299 0.0374350i \(-0.0119187\pi\)
\(734\) 3.94881 3.94881i 0.145753 0.145753i
\(735\) −11.3775 5.39802i −0.419667 0.199109i
\(736\) −17.0254 + 17.0254i −0.627564 + 0.627564i
\(737\) −10.4690 −0.385630
\(738\) 1.47141 0.0541632
\(739\) −16.6028 + 16.6028i −0.610746 + 0.610746i −0.943140 0.332395i \(-0.892143\pi\)
0.332395 + 0.943140i \(0.392143\pi\)
\(740\) 9.97420 0.366659
\(741\) 17.2259 + 14.5997i 0.632809 + 0.536335i
\(742\) 8.51151 12.0699i 0.312467 0.443101i
\(743\) −2.87636 2.87636i −0.105523 0.105523i 0.652374 0.757897i \(-0.273773\pi\)
−0.757897 + 0.652374i \(0.773773\pi\)
\(744\) 4.64103 0.170148
\(745\) 22.6371 0.829361
\(746\) 2.40502 + 2.40502i 0.0880539 + 0.0880539i
\(747\) −18.2431 + 18.2431i −0.667479 + 0.667479i
\(748\) 7.34804 + 7.34804i 0.268671 + 0.268671i
\(749\) −3.99771 23.1223i −0.146073 0.844871i
\(750\) 8.06888 0.294634
\(751\) 45.9438i 1.67651i −0.545275 0.838257i \(-0.683575\pi\)
0.545275 0.838257i \(-0.316425\pi\)
\(752\) 5.43890 + 5.43890i 0.198336 + 0.198336i
\(753\) 33.8129i 1.23221i
\(754\) 5.55636 + 4.70927i 0.202351 + 0.171501i
\(755\) 12.6780i 0.461400i
\(756\) 4.16991 + 24.1183i 0.151658 + 0.877174i
\(757\) −24.7889 −0.900969 −0.450484 0.892784i \(-0.648749\pi\)
−0.450484 + 0.892784i \(0.648749\pi\)
\(758\) 1.72592i 0.0626881i
\(759\) −3.26916 + 3.26916i −0.118663 + 0.118663i
\(760\) 10.9878 + 10.9878i 0.398569 + 0.398569i
\(761\) −10.8450 10.8450i −0.393133 0.393133i 0.482670 0.875802i \(-0.339667\pi\)
−0.875802 + 0.482670i \(0.839667\pi\)
\(762\) 0.769443 + 0.769443i 0.0278740 + 0.0278740i
\(763\) −9.91256 + 14.0567i −0.358859 + 0.508887i
\(764\) 6.20711i 0.224565i
\(765\) −11.2345 + 11.2345i −0.406184 + 0.406184i
\(766\) 2.34687 0.0847958
\(767\) 4.23884 + 3.59261i 0.153056 + 0.129722i
\(768\) 5.08489i 0.183485i
\(769\) 4.63670 4.63670i 0.167204 0.167204i −0.618545 0.785749i \(-0.712278\pi\)
0.785749 + 0.618545i \(0.212278\pi\)
\(770\) 1.51881 + 1.07104i 0.0547340 + 0.0385975i
\(771\) 25.3538i 0.913094i
\(772\) 28.5623 + 28.5623i 1.02798 + 1.02798i
\(773\) 5.68398 5.68398i 0.204438 0.204438i −0.597460 0.801899i \(-0.703823\pi\)
0.801899 + 0.597460i \(0.203823\pi\)
\(774\) −5.17148 + 5.17148i −0.185885 + 0.185885i
\(775\) 3.64722 + 3.64722i 0.131012 + 0.131012i
\(776\) 17.9466i 0.644244i
\(777\) −7.66469 + 10.8691i −0.274969 + 0.389926i
\(778\) 7.03032 7.03032i 0.252049 0.252049i
\(779\)