Properties

Label 91.2.i.a.83.3
Level $91$
Weight $2$
Character 91.83
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 83.3
Root \(1.52891 + 1.52891i\) of defining polynomial
Character \(\chi\) \(=\) 91.83
Dual form 91.2.i.a.34.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.403032 + 0.403032i) q^{2} -1.23240i q^{3} +1.67513i q^{4} +(1.03221 + 1.03221i) q^{5} +(0.496696 + 0.496696i) q^{6} +(2.60707 - 0.450747i) q^{7} +(-1.48119 - 1.48119i) q^{8} +1.48119 q^{9} +O(q^{10})\) \(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} +(2.60707 - 0.450747i) 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} +(-0.555500 - 3.21295i) 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} +(0.755061 + 4.36719i) 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} +(3.86158 - 0.667644i) 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} +(-2.16916 + 0.375035i) 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} +(5.38211 - 0.930536i) 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} +(-9.50175 + 0.846661i) 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} +(-1.71022 + 3.60468i) q^{98} +(-0.884226 - 0.884226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - 8q^{7} + 4q^{8} - 4q^{9} - 8q^{11} + 8q^{14} - 4q^{15} + 16q^{16} - 8q^{18} - 16q^{22} - 20q^{28} - 4q^{29} - 16q^{32} - 4q^{35} + 12q^{37} + 40q^{39} + 40q^{42} + 12q^{44} + 24q^{46} - 28q^{50} - 12q^{53} - 8q^{57} - 44q^{58} + 44q^{60} + 20q^{63} - 40q^{65} + 60q^{67} + 4q^{70} - 28q^{72} - 48q^{74} + 44q^{78} - 4q^{79} - 92q^{81} - 4q^{84} + 12q^{85} + 36q^{86} - 32q^{91} + 24q^{92} - 28q^{93} - 28q^{98} + 12q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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 −0.835094 0.550107i \(-0.814587\pi\)
0.550107 + 0.835094i \(0.314587\pi\)
\(3\) 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 \(-0.144159\pi\)
−0.437566 + 0.899186i \(0.644159\pi\)
\(6\) 0.496696 + 0.496696i 0.202775 + 0.202775i
\(7\) 2.60707 0.450747i 0.985381 0.170366i
\(8\) −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 0.611360 0.791353i \(-0.290623\pi\)
−0.791353 + 0.611360i \(0.790623\pi\)
\(12\) 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 \(-0.850052\pi\)
−0.891080 + 0.453845i \(0.850052\pi\)
\(18\) −0.596968 + 0.596968i −0.140707 + 0.140707i
\(19\) 3.59334 + 3.59334i 0.824368 + 0.824368i 0.986731 0.162363i \(-0.0519115\pi\)
−0.162363 + 0.986731i \(0.551911\pi\)
\(20\) −1.72909 + 1.72909i −0.386637 + 0.386637i
\(21\) −0.555500 3.21295i −0.121220 0.701124i
\(22\) 0.481194 0.102591
\(23\) 4.44358i 0.926551i −0.886214 0.463276i \(-0.846674\pi\)
0.886214 0.463276i \(-0.153326\pi\)
\(24\) −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
\(28\) 0.755061 + 4.36719i 0.142693 + 0.825321i
\(29\) −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 \(-0.301616\pi\)
−0.811990 + 0.583672i \(0.801616\pi\)
\(32\) 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 0.903259 0.429095i \(-0.141168\pi\)
−0.429095 + 0.903259i \(0.641168\pi\)
\(38\) −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 \(-0.206545\pi\)
−0.604294 + 0.796762i \(0.706545\pi\)
\(42\) 1.51881 + 1.07104i 0.234357 + 0.165265i
\(43\) 8.66291i 1.32108i 0.750790 + 0.660541i \(0.229673\pi\)
−0.750790 + 0.660541i \(0.770327\pi\)
\(44\) 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 \(-0.666226\pi\)
0.866717 + 0.498801i \(0.166226\pi\)
\(48\) 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 \(-0.781986\pi\)
0.632605 + 0.774474i \(0.281986\pi\)
\(60\) 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
\(63\) 3.86158 0.667644i 0.486513 0.0841153i
\(64\) 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 0.0739770 0.997260i \(-0.476431\pi\)
0.997260 0.0739770i \(-0.0235691\pi\)
\(68\) 12.3089i 1.49268i
\(69\) −5.47626 −0.659265
\(70\) −2.16916 + 0.375035i −0.259265 + 0.0448253i
\(71\) −1.46604 + 1.46604i −0.173986 + 0.173986i −0.788728 0.614742i \(-0.789260\pi\)
0.614742 + 0.788728i \(0.289260\pi\)
\(72\) −2.19394 2.19394i −0.258558 0.258558i
\(73\) −0.103857 + 0.103857i −0.0121555 + 0.0121555i −0.713158 0.701003i \(-0.752736\pi\)
0.701003 + 0.713158i \(0.252736\pi\)
\(74\) −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 0.883528 + 0.468379i \(0.155162\pi\)
0.468379 + 0.883528i \(0.344838\pi\)
\(84\) 5.38211 0.930536i 0.587237 0.101530i
\(85\) −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 \(-0.922743\pi\)
0.240334 + 0.970690i \(0.422743\pi\)
\(90\) −1.23240 −0.129906
\(91\) −9.50175 + 0.846661i −0.996054 + 0.0887541i
\(92\) 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 \(-0.393234\pi\)
−0.944273 + 0.329163i \(0.893234\pi\)
\(98\) −1.71022 + 3.60468i −0.172758 + 0.364128i
\(99\) −0.884226 0.884226i −0.0888681 0.0888681i
\(100\) 4.80606 0.480606
\(101\) 12.8707 1.28068 0.640339 0.768092i \(-0.278794\pi\)
0.640339 + 0.768092i \(0.278794\pi\)
\(102\) −3.64974 3.64974i −0.361378 0.361378i
\(103\) −6.11564 −0.602592 −0.301296 0.953531i \(-0.597419\pi\)
−0.301296 + 0.953531i \(0.597419\pi\)
\(104\) 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 −0.892116 0.451806i \(-0.850780\pi\)
0.451806 + 0.892116i \(0.350780\pi\)
\(110\) 0.496696 + 0.496696i 0.0473581 + 0.0473581i
\(111\) 3.55452 3.55452i 0.337380 0.337380i
\(112\) −5.62170 + 0.971958i −0.531200 + 0.0918414i
\(113\) 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
\(119\) −19.1569 + 3.31211i −1.75611 + 0.303620i
\(120\) −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 \(0.0218951\pi\)
−0.997635 + 0.0687312i \(0.978105\pi\)
\(128\) 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 0.995899 + 0.0904753i \(0.0288386\pi\)
0.0904753 + 0.995899i \(0.471161\pi\)
\(138\) 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 −0.995287 0.0969724i \(-0.969084\pi\)
0.0969724 + 0.995287i \(0.469084\pi\)
\(150\) 1.42505 1.42505i 0.116355 0.116355i
\(151\) 6.14117 + 6.14117i 0.499761 + 0.499761i 0.911363 0.411602i \(-0.135031\pi\)
−0.411602 + 0.911363i \(0.635031\pi\)
\(152\) 10.6449i 0.863413i
\(153\) −10.8839 −0.879909
\(154\) 1.25451 0.216897i 0.101091 0.0174781i
\(155\) 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
\(161\) −2.00293 11.5847i −0.157853 0.913006i
\(162\) 0.952155 0.952155i 0.0748083 0.0748083i
\(163\) −5.41327 5.41327i −0.424000 0.424000i 0.462579 0.886578i \(-0.346924\pi\)
−0.886578 + 0.462579i \(0.846924\pi\)
\(164\) −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 \(-0.587932\pi\)
0.962086 + 0.272746i \(0.0879318\pi\)
\(168\) −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 \(-0.412313\pi\)
0.272007 + 0.962295i \(0.412313\pi\)
\(174\) −1.76039 1.76039i −0.133455 0.133455i
\(175\) −1.29322 7.47987i −0.0977586 0.565425i
\(176\) 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 \(-0.827355\pi\)
0.856482 0.516177i \(-0.172645\pi\)
\(180\) −2.56112 + 2.56112i −0.190895 + 0.190895i
\(181\) −4.56052 −0.338981 −0.169490 0.985532i \(-0.554212\pi\)
−0.169490 + 0.985532i \(0.554212\pi\)
\(182\) 3.48827 4.17074i 0.258568 0.309156i
\(183\) 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
\(189\) −2.48930 14.3979i −0.181070 1.04729i
\(190\) −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 −0.964965 0.262377i \(-0.915494\pi\)
−0.262377 0.964965i \(-0.584506\pi\)
\(194\) 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 −0.932482 0.361216i \(-0.882362\pi\)
0.361216 + 0.932482i \(0.382362\pi\)
\(198\) 0.712742 0.0506524
\(199\) −4.57558 −0.324354 −0.162177 0.986762i \(-0.551852\pi\)
−0.162177 + 0.986762i \(0.551852\pi\)
\(200\) −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
\(203\) −9.23998 + 1.59754i −0.648520 + 0.112125i
\(204\) −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
\(210\) 0.462193 + 2.67327i 0.0318943 + 0.184473i
\(211\) −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 \(-0.206796\pi\)
−0.604923 + 0.796284i \(0.706796\pi\)
\(224\) 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 −0.925201 0.379477i \(-0.876104\pi\)
−0.379477 0.925201i \(-0.623896\pi\)
\(228\) 7.41819 + 7.41819i 0.491282 + 0.491282i
\(229\) −13.2060 + 13.2060i −0.872676 + 0.872676i −0.992763 0.120087i \(-0.961683\pi\)
0.120087 + 0.992763i \(0.461683\pi\)
\(230\) 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 \(0.178350\pi\)
−0.847094 + 0.531443i \(0.821650\pi\)
\(234\) 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 −0.733867 0.679294i \(-0.762286\pi\)
0.679294 + 0.733867i \(0.262286\pi\)
\(240\) −2.74306 + 2.74306i −0.177064 + 0.177064i
\(241\) 15.2966 15.2966i 0.985342 0.985342i −0.0145517 0.999894i \(-0.504632\pi\)
0.999894 + 0.0145517i \(0.00463211\pi\)
\(242\) 4.14609 + 4.14609i 0.266521 + 0.266521i
\(243\) 13.6563i 0.876054i
\(244\) −11.9086 −0.762367
\(245\) 9.23204 + 4.38009i 0.589813 + 0.279834i
\(246\) 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 \(-0.166751\pi\)
0.865893 + 0.500229i \(0.166751\pi\)
\(252\) 1.11839 + 6.46865i 0.0704521 + 0.407487i
\(253\) −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 \(-0.278252\pi\)
0.641645 + 0.767002i \(0.278252\pi\)
\(258\) −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
\(266\) −7.55128 + 1.30557i −0.462999 + 0.0800497i
\(267\) 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 0.322301 0.946637i \(-0.395544\pi\)
0.946637 0.322301i \(-0.104456\pi\)
\(272\) 15.8448 0.960730
\(273\) 1.04342 + 11.7099i 0.0631508 + 0.708718i
\(274\) −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 \(0.282695\pi\)
−0.630877 + 0.775883i \(0.717305\pi\)
\(278\) 2.80013 + 2.80013i 0.167941 + 0.167941i
\(279\) −1.88293 1.88293i −0.112728 0.112728i
\(280\) −1.37830 7.97196i −0.0823694 0.476416i
\(281\) 12.0782 + 12.0782i 0.720523 + 0.720523i 0.968712 0.248189i \(-0.0798354\pi\)
−0.248189 + 0.968712i \(0.579835\pi\)
\(282\) 2.50563 0.149208
\(283\) −15.3667 −0.913458 −0.456729 0.889606i \(-0.650979\pi\)
−0.456729 + 0.889606i \(0.650979\pi\)
\(284\) −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 \(-0.882478\pi\)
0.360874 + 0.932615i \(0.382478\pi\)
\(294\) 4.44240 + 2.10767i 0.259086 + 0.122922i
\(295\) −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
\(301\) 3.90478 + 22.5848i 0.225068 + 1.30177i
\(302\) −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 \(-0.856561\pi\)
0.435529 + 0.900175i \(0.356561\pi\)
\(308\) 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 \(-0.872562\pi\)
−0.920922 + 0.389747i \(0.872562\pi\)
\(312\) 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 −0.897337 0.441345i \(-0.854501\pi\)
0.441345 + 0.897337i \(0.354501\pi\)
\(318\) −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 −0.728912 0.684607i \(-0.759974\pi\)
0.684607 + 0.728912i \(0.259974\pi\)
\(332\) −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
\(336\) 1.19784 + 6.92817i 0.0653475 + 0.377963i
\(337\) 26.6058i 1.44931i −0.689112 0.724655i \(-0.741999\pi\)
0.689112 0.724655i \(-0.258001\pi\)
\(338\) −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
\(343\) 16.1308 9.09937i 0.870979 0.491320i
\(344\) 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 \(-0.777922\pi\)
0.642439 + 0.766336i \(0.277922\pi\)
\(350\) 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 \(-0.382467\pi\)
−0.932602 + 0.360906i \(0.882467\pi\)
\(354\) −1.08252 −0.0575351
\(355\) −3.02653 −0.160631
\(356\) −11.5419 11.5419i −0.611721 0.611721i
\(357\) 4.08184 + 23.6089i 0.216034 + 1.24952i
\(358\) 5.56665 + 5.56665i 0.294207 + 0.294207i
\(359\) −16.9726 16.9726i −0.895781 0.895781i 0.0992789 0.995060i \(-0.468346\pi\)
−0.995060 + 0.0992789i \(0.968346\pi\)
\(360\) 4.52923i 0.238711i
\(361\) 6.82416i 0.359166i
\(362\) 1.83803 1.83803i 0.0966049 0.0966049i
\(363\) −12.6780 −0.665422
\(364\) −1.41827 15.9167i −0.0743374 0.834260i
\(365\) −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
\(371\) −25.5333 + 4.41455i −1.32562 + 0.229192i
\(372\) −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 −0.649973 0.759957i \(-0.725220\pi\)
0.759957 + 0.649973i \(0.225220\pi\)
\(380\) −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 \(-0.216453\pi\)
−0.628798 + 0.777569i \(0.716453\pi\)
\(384\) 10.0518 10.0518i 0.512956 0.512956i
\(385\) −0.555500 3.21295i −0.0283109 0.163747i
\(386\) 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 \(-0.854194\pi\)
0.896910 0.442212i \(-0.145806\pi\)
\(390\) 0.304041 3.68458i 0.0153957 0.186576i
\(391\) 32.6516i 1.65126i
\(392\) −13.2477 6.28529i −0.669109 0.317455i
\(393\) 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 \(-0.632257\pi\)
0.914916 + 0.403645i \(0.132257\pi\)
\(398\) 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 0.979623 0.200846i \(-0.0643692\pi\)
−0.200846 + 0.979623i \(0.564369\pi\)
\(402\) 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 \(-0.229963\pi\)
−0.661224 + 0.750189i \(0.729963\pi\)
\(410\) −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 −0.883811 0.467844i \(-0.845031\pi\)
0.467844 + 0.883811i \(0.345031\pi\)
\(422\) 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
\(427\) 3.20438 + 18.5338i 0.155071 + 0.896911i
\(428\) 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 0.182880 0.983135i \(-0.441458\pi\)
0.983135 0.182880i \(-0.0585421\pi\)
\(432\) 11.9086i 0.572951i
\(433\) −35.8708 −1.72384 −0.861920 0.507044i \(-0.830738\pi\)
−0.861920 + 0.507044i \(0.830738\pi\)
\(434\) 2.67143 0.461874i 0.128233 0.0221707i
\(435\) −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 \(-0.419148\pi\)
0.251281 + 0.967914i \(0.419148\pi\)
\(440\) −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
\(448\) −0.551829 3.19172i −0.0260715 0.150795i
\(449\) 9.65069 + 9.65069i 0.455444 + 0.455444i 0.897157 0.441712i \(-0.145629\pi\)
−0.441712 + 0.897157i \(0.645629\pi\)
\(450\) 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
\(455\) −10.6818 8.93390i −0.500769 0.418828i
\(456\) −13.1187 −0.614340
\(457\) −22.1217 + 22.1217i −1.03481 + 1.03481i −0.0354353 + 0.999372i \(0.511282\pi\)
−0.999372 + 0.0354353i \(0.988718\pi\)
\(458\) 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 \(-0.243783\pi\)
−0.693162 + 0.720782i \(0.743783\pi\)
\(462\) −0.267304 1.54605i −0.0124361 0.0719289i
\(463\) 2.47096 + 2.47096i 0.114835 + 0.114835i 0.762189 0.647354i \(-0.224124\pi\)
−0.647354 + 0.762189i \(0.724124\pi\)
\(464\) 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 \(-0.600234\pi\)
−0.309716 + 0.950829i \(0.600234\pi\)
\(468\) 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
\(476\) −5.54821 32.0903i −0.254302 1.47085i
\(477\) −14.5066 −0.664211
\(478\) 0.680055i 0.0311050i
\(479\) −8.85827 + 8.85827i −0.404745 + 0.404745i −0.879901 0.475157i \(-0.842391\pi\)
0.475157 + 0.879901i \(0.342391\pi\)
\(480\) 9.74798i 0.444933i
\(481\) −9.50879 11.2192i −0.433564 0.511552i
\(482\) 12.3301i 0.561619i
\(483\) −14.2770 + 2.46841i −0.649627 + 0.112317i
\(484\) 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 −0.170572 0.985345i \(-0.554561\pi\)
0.985345 + 0.170572i \(0.0545614\pi\)
\(488\) 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 \(-0.855019\pi\)
0.898054 0.439884i \(-0.144981\pi\)
\(492\) 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 −0.440478 0.897763i \(-0.645191\pi\)
0.897763 + 0.440478i \(0.145191\pi\)
\(500\) 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 \(-0.390319\pi\)
−0.941220 + 0.337795i \(0.890319\pi\)
\(510\) 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
\(518\) −6.06110 + 1.04793i −0.266310 + 0.0460433i
\(519\) 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
\(525\) −9.21818 + 1.59377i −0.402314 + 0.0695577i
\(526\) 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
\(539\) −5.33923 2.53317i −0.229977 0.109111i
\(540\) 9.54912 + 9.54912i 0.410929 + 0.410929i
\(541\) −23.2853 23.2853i −1.00111 1.00111i −0.999999 0.00111270i \(-0.999646\pi\)
−0.00111270 0.999999i \(-0.500354\pi\)
\(542\) 16.8382i 0.723260i
\(543\) 5.62038i 0.241193i
\(544\) −28.1537 + 28.1537i −1.20708 + 1.20708i
\(545\) −9.49011 −0.406512
\(546\) −5.14001 4.29894i −0.219972 0.183978i
\(547\) −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
\(553\) −12.5107 + 2.16303i −0.532011 + 0.0919815i
\(554\) −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 0.863195 0.504871i \(-0.168460\pi\)
−0.504871 + 0.863195i \(0.668460\pi\)
\(558\) 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 \(-0.457288\pi\)
0.133780 + 0.991011i \(0.457288\pi\)
\(564\) 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
\(567\) −6.15916 + 1.06488i −0.258660 + 0.0447208i
\(568\) 4.34297 0.182227
\(569\) 36.6140i 1.53494i −0.641085 0.767470i \(-0.721515\pi\)
0.641085 0.767470i \(-0.278485\pi\)
\(570\) −3.68458 + 3.68458i −0.154330 + 0.154330i
\(571\) 18.8070i 0.787049i 0.919314 + 0.393525i \(0.128744\pi\)
−0.919314 + 0.393525i \(0.871256\pi\)
\(572\) −3.88985 + 3.29683i −0.162643 + 0.137847i
\(573\) 4.56659i 0.190772i
\(574\) −2.58984 + 0.447768i −0.108098 + 0.0186895i
\(575\) −12.7489 −0.531668
\(576\) 1.81336i 0.0755566i
\(577\) 31.3416 + 31.3416i 1.30477 + 1.30477i 0.925140 + 0.379627i \(0.123948\pi\)
0.379627 + 0.925140i \(0.376052\pi\)
\(578\) −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 \(-0.218671\pi\)
−0.634200 + 0.773169i \(0.718671\pi\)
\(588\) 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 \(-0.649595\pi\)
0.891583 + 0.452857i \(0.149595\pi\)
\(594\) 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
\(609\) 1.96880 + 11.3873i 0.0797799 + 0.461438i
\(610\) 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 −0.159276 0.987234i \(-0.550916\pi\)
0.987234 + 0.159276i \(0.0509158\pi\)
\(614\) 6.56236i 0.264835i
\(615\) 3.13547 0.126434
\(616\) 0.797125 + 4.61048i 0.0321171 + 0.185762i
\(617\) 8.21440 8.21440i 0.330699 0.330699i −0.522153 0.852852i \(-0.674871\pi\)
0.852852 + 0.522153i \(0.174871\pi\)
\(618\) −3.03761 3.03761i −0.122191 0.122191i
\(619\) 26.6973 26.6973i 1.07306 1.07306i 0.0759445 0.997112i \(-0.475803\pi\)
0.997112 0.0759445i \(-0.0241972\pi\)
\(620\) 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
\(630\) −3.21295 + 0.555500i −0.128007 + 0.0221317i
\(631\) 5.13093 + 5.13093i 0.204259 + 0.204259i 0.801822 0.597563i \(-0.203864\pi\)
−0.597563 + 0.801822i \(0.703864\pi\)
\(632\) 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
\(637\) −24.3901 + 6.49019i −0.966371 + 0.257151i
\(638\) −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 \(0.104560\pi\)
−0.946532 + 0.322610i \(0.895440\pi\)
\(642\) 4.40523 + 4.40523i 0.173860 + 0.173860i
\(643\) 28.1910 + 28.1910i 1.11175 + 1.11175i 0.992914 + 0.118832i \(0.0379150\pi\)
0.118832 + 0.992914i \(0.462085\pi\)
\(644\) 19.4060 3.35517i 0.764702 0.132212i
\(645\) 11.0201 + 11.0201i 0.433915 + 0.433915i
\(646\) 21.2833 0.837380
\(647\) 11.1139 0.436932 0.218466 0.975845i \(-0.429895\pi\)
0.218466 + 0.975845i \(0.429895\pi\)
\(648\) 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
\(658\) 0.916430 + 5.30053i 0.0357262 + 0.206636i
\(659\) 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 \(-0.960064\pi\)
0.125134 + 0.992140i \(0.460064\pi\)
\(662\) 0.649738i 0.0252528i
\(663\) 2.68512 32.5402i 0.104282 1.26376i
\(664\) 36.4861i 1.41594i
\(665\) 3.34373 + 19.3398i 0.129664 + 0.749964i
\(666\) −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 \(-0.991499\pi\)
0.999643 0.0267036i \(-0.00850104\pi\)
\(674\) 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 0.998979 + 0.0451754i \(0.0143847\pi\)
0.0451754 + 0.998979i \(0.485615\pi\)
\(684\) −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 \(-0.106535\pi\)
−0.328475 + 0.944513i \(0.606535\pi\)
\(692\) 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
\(700\) 12.5298 2.16632i 0.473580 0.0818792i
\(701\) 15.2981i 0.577800i 0.957359 + 0.288900i \(0.0932895\pi\)
−0.957359 + 0.288900i \(0.906711\pi\)
\(702\) −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
\(707\) 33.5547 5.80141i 1.26196 0.218185i
\(708\) −2.24965 + 2.24965i −0.0845469 + 0.0845469i
\(709\) −2.74107 2.74107i −0.102943 0.102943i 0.653759 0.756703i \(-0.273191\pi\)
−0.756703 + 0.653759i \(0.773191\pi\)
\(710\) 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 \(-0.535655\pi\)
−0.111780 + 0.993733i \(0.535655\pi\)
\(720\) −3.29683 3.29683i −0.122865 0.122865i
\(721\) −15.9439 + 2.75661i −0.593782 + 0.102661i
\(722\) −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 \(-0.412618\pi\)
0.271084 + 0.962556i \(0.412618\pi\)
\(728\) 15.3280 + 12.8199i 0.568093 + 0.475136i
\(729\) −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 −0.999299 0.0374350i \(-0.988081\pi\)
−0.0374350 0.999299i \(-0.511919\pi\)
\(734\) −3.94881 3.94881i −0.145753 0.145753i
\(735\) 5.39802 11.3775i 0.199109 0.419667i
\(736\) −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 0.332395 0.943140i \(-0.392143\pi\)
−0.943140 + 0.332395i \(0.892143\pi\)
\(740\) −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 −0.757897 0.652374i \(-0.773773\pi\)
0.652374 + 0.757897i \(0.273773\pi\)
\(744\) 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
\(749\) 23.1223 3.99771i 0.844871 0.146073i
\(750\) 8.06888 0.294634
\(751\) 45.9438i 1.67651i 0.545275 + 0.838257i \(0.316425\pi\)
−0.545275 + 0.838257i \(0.683575\pi\)
\(752\) −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
\(756\) 24.1183 4.16991i 0.877174 0.151658i
\(757\) −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 \(-0.660333\pi\)
0.875802 + 0.482670i \(0.160333\pi\)
\(762\) −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 \(-0.287722\pi\)
−0.785749 + 0.618545i \(0.787722\pi\)
\(770\) 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 \(-0.296177\pi\)
−0.801899 + 0.597460i \(0.796177\pi\)
\(774\) −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