Properties

Label 15.4.e.a.8.3
Level 15
Weight 4
Character 15.8
Analytic conductor 0.885
Analytic rank 0
Dimension 8
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 15.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.885028650086\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.28356903014400.8
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 8.3
Root \(1.18766 - 1.18766i\)
Character \(\chi\) = 15.8
Dual form 15.4.e.a.2.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.18766 + 1.18766i) q^{2} +(-0.932827 + 5.11173i) q^{3} -5.17891i q^{4} +(2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +O(q^{10})\) \(q+(1.18766 + 1.18766i) q^{2} +(-0.932827 + 5.11173i) q^{3} -5.17891i q^{4} +(2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +(15.8945 - 10.0000i) q^{10} +28.7164i q^{11} +(26.4732 + 4.83102i) q^{12} +(14.1789 + 14.1789i) q^{13} -31.7292 q^{14} +(53.4105 + 22.8543i) q^{15} -4.25236 q^{16} +(18.5587 + 18.5587i) q^{17} +(-18.6736 - 41.3264i) q^{18} -49.0735i q^{19} +(-56.4577 - 12.8518i) q^{20} +(-55.8211 - 80.7421i) q^{21} +(-34.1055 + 34.1055i) q^{22} +(-37.7738 + 37.7738i) q^{23} +(65.4088 + 94.6102i) q^{24} +(-112.684 - 54.1055i) q^{25} +33.6796i q^{26} +(72.3121 - 120.225i) q^{27} +(69.1789 + 69.1789i) q^{28} +125.854 q^{29} +(36.2905 + 90.5770i) q^{30} +247.367 q^{31} +(-130.267 - 130.267i) q^{32} +(-146.791 - 26.7874i) q^{33} +44.0829i q^{34} +(112.471 + 178.768i) q^{35} +(-49.3898 + 130.818i) q^{36} +(-127.463 + 127.463i) q^{37} +(58.2828 - 58.2828i) q^{38} +(-85.7053 + 59.2524i) q^{39} +(-131.789 - 209.473i) q^{40} -390.328i q^{41} +(29.5978 - 162.191i) q^{42} +(-39.3993 - 39.3993i) q^{43} +148.720 q^{44} +(-166.648 + 251.701i) q^{45} -89.7251 q^{46} +(124.560 + 124.560i) q^{47} +(3.96671 - 21.7369i) q^{48} -13.8625i q^{49} +(-69.5712 - 198.089i) q^{50} +(-112.179 + 77.5549i) q^{51} +(73.4313 - 73.4313i) q^{52} +(-160.441 + 160.441i) q^{53} +(228.669 - 56.9040i) q^{54} +(313.051 + 71.2618i) q^{55} +418.156i q^{56} +(250.850 + 45.7770i) q^{57} +(149.473 + 149.473i) q^{58} -729.423 q^{59} +(118.360 - 276.608i) q^{60} +2.00000 q^{61} +(293.789 + 293.789i) q^{62} +(464.804 - 210.024i) q^{63} -275.409i q^{64} +(189.757 - 119.385i) q^{65} +(-142.524 - 206.153i) q^{66} +(-329.987 + 329.987i) q^{67} +(96.1136 - 96.1136i) q^{68} +(-157.853 - 228.326i) q^{69} +(-78.7382 + 345.895i) q^{70} +171.760i q^{71} +(-544.637 + 246.097i) q^{72} +(-279.927 - 279.927i) q^{73} -302.767 q^{74} +(381.687 - 525.538i) q^{75} -254.147 q^{76} +(-383.589 - 383.589i) q^{77} +(-172.161 - 31.4172i) q^{78} -48.0189i q^{79} +(-10.5525 + 46.3569i) q^{80} +(547.102 + 481.789i) q^{81} +(463.578 - 463.578i) q^{82} +(144.451 - 144.451i) q^{83} +(-418.156 + 289.092i) q^{84} +(248.371 - 156.262i) q^{85} -93.5862i q^{86} +(-117.400 + 643.334i) q^{87} +(449.473 + 449.473i) q^{88} +1417.21 q^{89} +(-496.858 + 101.015i) q^{90} -378.799 q^{91} +(195.627 + 195.627i) q^{92} +(-230.751 + 1264.48i) q^{93} +295.872i q^{94} +(-534.972 - 121.779i) q^{95} +(787.409 - 544.375i) q^{96} +(908.111 - 908.111i) q^{97} +(16.4640 - 16.4640i) q^{98} +(273.861 - 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{3} - 12q^{6} - 16q^{7} + O(q^{10}) \) \( 8q - 6q^{3} - 12q^{6} - 16q^{7} - 100q^{10} + 132q^{12} + 68q^{13} + 90q^{15} + 284q^{16} - 240q^{18} - 492q^{21} - 500q^{22} - 220q^{25} + 702q^{27} + 508q^{28} + 660q^{30} + 616q^{31} - 240q^{33} - 804q^{36} - 1156q^{37} - 600q^{40} + 540q^{42} + 548q^{43} + 180q^{45} + 736q^{46} - 1116q^{48} - 852q^{51} + 224q^{52} + 460q^{55} + 684q^{57} + 60q^{58} + 540q^{60} + 16q^{61} + 1428q^{63} + 2040q^{66} + 404q^{67} - 2220q^{70} - 1800q^{72} - 2512q^{73} - 2910q^{75} - 1488q^{76} - 360q^{78} + 288q^{81} + 2800q^{82} + 4940q^{85} - 1680q^{87} + 2460q^{88} + 600q^{90} - 1304q^{91} + 3408q^{93} + 4164q^{96} + 1904q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18766 + 1.18766i 0.419903 + 0.419903i 0.885170 0.465267i \(-0.154042\pi\)
−0.465267 + 0.885170i \(0.654042\pi\)
\(3\) −0.932827 + 5.11173i −0.179523 + 0.983754i
\(4\) 5.17891i 0.647364i
\(5\) 2.48157 10.9015i 0.221958 0.975056i
\(6\) −7.17891 + 4.96314i −0.488463 + 0.337699i
\(7\) −13.3578 + 13.3578i −0.721254 + 0.721254i −0.968861 0.247606i \(-0.920356\pi\)
0.247606 + 0.968861i \(0.420356\pi\)
\(8\) 15.6521 15.6521i 0.691732 0.691732i
\(9\) −25.2597 9.53673i −0.935543 0.353212i
\(10\) 15.8945 10.0000i 0.502630 0.316228i
\(11\) 28.7164i 0.787121i 0.919299 + 0.393560i \(0.128757\pi\)
−0.919299 + 0.393560i \(0.871243\pi\)
\(12\) 26.4732 + 4.83102i 0.636846 + 0.116216i
\(13\) 14.1789 + 14.1789i 0.302502 + 0.302502i 0.841992 0.539490i \(-0.181383\pi\)
−0.539490 + 0.841992i \(0.681383\pi\)
\(14\) −31.7292 −0.605713
\(15\) 53.4105 + 22.8543i 0.919369 + 0.393397i
\(16\) −4.25236 −0.0664431
\(17\) 18.5587 + 18.5587i 0.264773 + 0.264773i 0.826990 0.562217i \(-0.190051\pi\)
−0.562217 + 0.826990i \(0.690051\pi\)
\(18\) −18.6736 41.3264i −0.244522 0.541152i
\(19\) 49.0735i 0.592538i −0.955105 0.296269i \(-0.904258\pi\)
0.955105 0.296269i \(-0.0957425\pi\)
\(20\) −56.4577 12.8518i −0.631216 0.143688i
\(21\) −55.8211 80.7421i −0.580055 0.839018i
\(22\) −34.1055 + 34.1055i −0.330514 + 0.330514i
\(23\) −37.7738 + 37.7738i −0.342451 + 0.342451i −0.857288 0.514837i \(-0.827852\pi\)
0.514837 + 0.857288i \(0.327852\pi\)
\(24\) 65.4088 + 94.6102i 0.556313 + 0.804676i
\(25\) −112.684 54.1055i −0.901469 0.432844i
\(26\) 33.6796i 0.254042i
\(27\) 72.3121 120.225i 0.515425 0.856935i
\(28\) 69.1789 + 69.1789i 0.466914 + 0.466914i
\(29\) 125.854 0.805882 0.402941 0.915226i \(-0.367988\pi\)
0.402941 + 0.915226i \(0.367988\pi\)
\(30\) 36.2905 + 90.5770i 0.220857 + 0.551234i
\(31\) 247.367 1.43318 0.716588 0.697496i \(-0.245703\pi\)
0.716588 + 0.697496i \(0.245703\pi\)
\(32\) −130.267 130.267i −0.719632 0.719632i
\(33\) −146.791 26.7874i −0.774333 0.141306i
\(34\) 44.0829i 0.222357i
\(35\) 112.471 + 178.768i 0.543175 + 0.863352i
\(36\) −49.3898 + 130.818i −0.228657 + 0.605637i
\(37\) −127.463 + 127.463i −0.566347 + 0.566347i −0.931103 0.364756i \(-0.881152\pi\)
0.364756 + 0.931103i \(0.381152\pi\)
\(38\) 58.2828 58.2828i 0.248808 0.248808i
\(39\) −85.7053 + 59.2524i −0.351893 + 0.243281i
\(40\) −131.789 209.473i −0.520942 0.828014i
\(41\) 390.328i 1.48680i −0.668845 0.743402i \(-0.733211\pi\)
0.668845 0.743402i \(-0.266789\pi\)
\(42\) 29.5978 162.191i 0.108739 0.595873i
\(43\) −39.3993 39.3993i −0.139729 0.139729i 0.633783 0.773511i \(-0.281501\pi\)
−0.773511 + 0.633783i \(0.781501\pi\)
\(44\) 148.720 0.509553
\(45\) −166.648 + 251.701i −0.552053 + 0.833809i
\(46\) −89.7251 −0.287592
\(47\) 124.560 + 124.560i 0.386575 + 0.386575i 0.873464 0.486889i \(-0.161868\pi\)
−0.486889 + 0.873464i \(0.661868\pi\)
\(48\) 3.96671 21.7369i 0.0119280 0.0653637i
\(49\) 13.8625i 0.0404155i
\(50\) −69.5712 198.089i −0.196777 0.560281i
\(51\) −112.179 + 77.5549i −0.308004 + 0.212938i
\(52\) 73.4313 73.4313i 0.195829 0.195829i
\(53\) −160.441 + 160.441i −0.415816 + 0.415816i −0.883759 0.467943i \(-0.844995\pi\)
0.467943 + 0.883759i \(0.344995\pi\)
\(54\) 228.669 56.9040i 0.576257 0.143401i
\(55\) 313.051 + 71.2618i 0.767487 + 0.174708i
\(56\) 418.156i 0.997830i
\(57\) 250.850 + 45.7770i 0.582912 + 0.106374i
\(58\) 149.473 + 149.473i 0.338392 + 0.338392i
\(59\) −729.423 −1.60954 −0.804769 0.593588i \(-0.797711\pi\)
−0.804769 + 0.593588i \(0.797711\pi\)
\(60\) 118.360 276.608i 0.254671 0.595166i
\(61\) 2.00000 0.00419793 0.00209897 0.999998i \(-0.499332\pi\)
0.00209897 + 0.999998i \(0.499332\pi\)
\(62\) 293.789 + 293.789i 0.601795 + 0.601795i
\(63\) 464.804 210.024i 0.929520 0.420009i
\(64\) 275.409i 0.537908i
\(65\) 189.757 119.385i 0.362099 0.227813i
\(66\) −142.524 206.153i −0.265810 0.384479i
\(67\) −329.987 + 329.987i −0.601706 + 0.601706i −0.940765 0.339059i \(-0.889891\pi\)
0.339059 + 0.940765i \(0.389891\pi\)
\(68\) 96.1136 96.1136i 0.171404 0.171404i
\(69\) −157.853 228.326i −0.275410 0.398365i
\(70\) −78.7382 + 345.895i −0.134443 + 0.590604i
\(71\) 171.760i 0.287100i 0.989643 + 0.143550i \(0.0458518\pi\)
−0.989643 + 0.143550i \(0.954148\pi\)
\(72\) −544.637 + 246.097i −0.891474 + 0.402817i
\(73\) −279.927 279.927i −0.448807 0.448807i 0.446151 0.894958i \(-0.352795\pi\)
−0.894958 + 0.446151i \(0.852795\pi\)
\(74\) −302.767 −0.475621
\(75\) 381.687 525.538i 0.587646 0.809118i
\(76\) −254.147 −0.383587
\(77\) −383.589 383.589i −0.567714 0.567714i
\(78\) −172.161 31.4172i −0.249915 0.0456064i
\(79\) 48.0189i 0.0683866i −0.999415 0.0341933i \(-0.989114\pi\)
0.999415 0.0341933i \(-0.0108862\pi\)
\(80\) −10.5525 + 46.3569i −0.0147476 + 0.0647858i
\(81\) 547.102 + 481.789i 0.750483 + 0.660890i
\(82\) 463.578 463.578i 0.624313 0.624313i
\(83\) 144.451 144.451i 0.191031 0.191031i −0.605111 0.796141i \(-0.706871\pi\)
0.796141 + 0.605111i \(0.206871\pi\)
\(84\) −418.156 + 289.092i −0.543150 + 0.375507i
\(85\) 248.371 156.262i 0.316937 0.199400i
\(86\) 93.5862i 0.117345i
\(87\) −117.400 + 643.334i −0.144674 + 0.792789i
\(88\) 449.473 + 449.473i 0.544477 + 0.544477i
\(89\) 1417.21 1.68790 0.843952 0.536419i \(-0.180223\pi\)
0.843952 + 0.536419i \(0.180223\pi\)
\(90\) −496.858 + 101.015i −0.581927 + 0.118310i
\(91\) −378.799 −0.436361
\(92\) 195.627 + 195.627i 0.221690 + 0.221690i
\(93\) −230.751 + 1264.48i −0.257288 + 1.40989i
\(94\) 295.872i 0.324647i
\(95\) −534.972 121.779i −0.577758 0.131519i
\(96\) 787.409 544.375i 0.837131 0.578751i
\(97\) 908.111 908.111i 0.950564 0.950564i −0.0482702 0.998834i \(-0.515371\pi\)
0.998834 + 0.0482702i \(0.0153708\pi\)
\(98\) 16.4640 16.4640i 0.0169706 0.0169706i
\(99\) 273.861 725.367i 0.278020 0.736385i
\(100\) −280.207 + 583.578i −0.280207 + 0.583578i
\(101\) 337.668i 0.332665i −0.986070 0.166333i \(-0.946807\pi\)
0.986070 0.166333i \(-0.0531926\pi\)
\(102\) −225.340 41.1217i −0.218745 0.0399182i
\(103\) −933.505 933.505i −0.893019 0.893019i 0.101787 0.994806i \(-0.467544\pi\)
−0.994806 + 0.101787i \(0.967544\pi\)
\(104\) 443.860 0.418500
\(105\) −1018.73 + 408.164i −0.946838 + 0.379359i
\(106\) −381.100 −0.349205
\(107\) −596.188 596.188i −0.538651 0.538651i 0.384481 0.923133i \(-0.374380\pi\)
−0.923133 + 0.384481i \(0.874380\pi\)
\(108\) −622.632 374.498i −0.554748 0.333667i
\(109\) 2074.60i 1.82303i 0.411264 + 0.911516i \(0.365087\pi\)
−0.411264 + 0.911516i \(0.634913\pi\)
\(110\) 287.164 + 456.434i 0.248909 + 0.395630i
\(111\) −532.657 770.460i −0.455474 0.658818i
\(112\) 56.8022 56.8022i 0.0479224 0.0479224i
\(113\) 271.193 271.193i 0.225767 0.225767i −0.585154 0.810922i \(-0.698966\pi\)
0.810922 + 0.585154i \(0.198966\pi\)
\(114\) 243.558 + 352.294i 0.200099 + 0.289433i
\(115\) 318.051 + 505.527i 0.257899 + 0.409919i
\(116\) 651.788i 0.521698i
\(117\) −222.934 493.375i −0.176156 0.389851i
\(118\) −866.309 866.309i −0.675849 0.675849i
\(119\) −495.806 −0.381937
\(120\) 1193.71 478.269i 0.908082 0.363832i
\(121\) 506.367 0.380441
\(122\) 2.37533 + 2.37533i 0.00176272 + 0.00176272i
\(123\) 1995.25 + 364.108i 1.46265 + 0.266915i
\(124\) 1281.09i 0.927786i
\(125\) −869.461 + 1094.15i −0.622135 + 0.782910i
\(126\) 801.469 + 302.593i 0.566671 + 0.213945i
\(127\) 105.588 105.588i 0.0737747 0.0737747i −0.669257 0.743031i \(-0.733387\pi\)
0.743031 + 0.669257i \(0.233387\pi\)
\(128\) −715.045 + 715.045i −0.493763 + 0.493763i
\(129\) 238.151 164.646i 0.162543 0.112374i
\(130\) 367.156 + 83.5782i 0.247706 + 0.0563868i
\(131\) 1979.28i 1.32008i 0.751231 + 0.660039i \(0.229460\pi\)
−0.751231 + 0.660039i \(0.770540\pi\)
\(132\) −138.730 + 760.216i −0.0914763 + 0.501275i
\(133\) 655.514 + 655.514i 0.427371 + 0.427371i
\(134\) −783.827 −0.505316
\(135\) −1131.18 1086.65i −0.721157 0.692772i
\(136\) 580.964 0.366304
\(137\) 507.451 + 507.451i 0.316456 + 0.316456i 0.847404 0.530948i \(-0.178164\pi\)
−0.530948 + 0.847404i \(0.678164\pi\)
\(138\) 83.6979 458.651i 0.0516293 0.282920i
\(139\) 68.4333i 0.0417585i −0.999782 0.0208793i \(-0.993353\pi\)
0.999782 0.0208793i \(-0.00664656\pi\)
\(140\) 925.823 582.479i 0.558903 0.351632i
\(141\) −752.913 + 520.527i −0.449693 + 0.310895i
\(142\) −203.993 + 203.993i −0.120554 + 0.120554i
\(143\) −407.167 + 407.167i −0.238105 + 0.238105i
\(144\) 107.413 + 40.5536i 0.0621604 + 0.0234685i
\(145\) 312.316 1372.00i 0.178872 0.785780i
\(146\) 664.917i 0.376911i
\(147\) 70.8616 + 12.9313i 0.0397590 + 0.00725550i
\(148\) 660.121 + 660.121i 0.366632 + 0.366632i
\(149\) 363.356 0.199780 0.0998902 0.994998i \(-0.468151\pi\)
0.0998902 + 0.994998i \(0.468151\pi\)
\(150\) 1077.48 170.846i 0.586505 0.0929970i
\(151\) −2083.14 −1.12267 −0.561337 0.827588i \(-0.689713\pi\)
−0.561337 + 0.827588i \(0.689713\pi\)
\(152\) −768.103 768.103i −0.409878 0.409878i
\(153\) −291.797 645.774i −0.154185 0.341227i
\(154\) 911.149i 0.476769i
\(155\) 613.859 2696.66i 0.318105 1.39743i
\(156\) 306.863 + 443.860i 0.157491 + 0.227803i
\(157\) −1208.52 + 1208.52i −0.614333 + 0.614333i −0.944072 0.329739i \(-0.893039\pi\)
0.329739 + 0.944072i \(0.393039\pi\)
\(158\) 57.0303 57.0303i 0.0287157 0.0287157i
\(159\) −670.468 969.795i −0.334412 0.483709i
\(160\) −1743.37 + 1096.84i −0.861410 + 0.541953i
\(161\) 1009.15i 0.493989i
\(162\) 77.5696 + 1221.98i 0.0376200 + 0.592639i
\(163\) 626.062 + 626.062i 0.300840 + 0.300840i 0.841343 0.540502i \(-0.181766\pi\)
−0.540502 + 0.841343i \(0.681766\pi\)
\(164\) −2021.47 −0.962502
\(165\) −656.294 + 1533.76i −0.309651 + 0.723654i
\(166\) 343.119 0.160429
\(167\) 3009.65 + 3009.65i 1.39457 + 1.39457i 0.814724 + 0.579848i \(0.196888\pi\)
0.579848 + 0.814724i \(0.303112\pi\)
\(168\) −2137.50 390.067i −0.981619 0.179133i
\(169\) 1794.92i 0.816985i
\(170\) 480.568 + 109.395i 0.216811 + 0.0493541i
\(171\) −468.000 + 1239.58i −0.209292 + 0.554345i
\(172\) −204.045 + 204.045i −0.0904552 + 0.0904552i
\(173\) 1839.23 1839.23i 0.808288 0.808288i −0.176086 0.984375i \(-0.556344\pi\)
0.984375 + 0.176086i \(0.0563438\pi\)
\(174\) −903.497 + 624.633i −0.393643 + 0.272145i
\(175\) 2227.94 782.476i 0.962379 0.337998i
\(176\) 122.113i 0.0522987i
\(177\) 680.425 3728.61i 0.288948 1.58339i
\(178\) 1683.16 + 1683.16i 0.708755 + 0.708755i
\(179\) −821.582 −0.343061 −0.171530 0.985179i \(-0.554871\pi\)
−0.171530 + 0.985179i \(0.554871\pi\)
\(180\) 1303.54 + 863.054i 0.539777 + 0.357379i
\(181\) 2314.20 0.950350 0.475175 0.879891i \(-0.342385\pi\)
0.475175 + 0.879891i \(0.342385\pi\)
\(182\) −449.885 449.885i −0.183229 0.183229i
\(183\) −1.86565 + 10.2235i −0.000753623 + 0.00412973i
\(184\) 1182.48i 0.473769i
\(185\) 1073.23 + 1705.84i 0.426515 + 0.677925i
\(186\) −1775.83 + 1227.72i −0.700053 + 0.483982i
\(187\) −532.938 + 532.938i −0.208408 + 0.208408i
\(188\) 645.087 645.087i 0.250254 0.250254i
\(189\) 640.007 + 2571.87i 0.246316 + 0.989820i
\(190\) −490.735 780.000i −0.187377 0.297827i
\(191\) 931.167i 0.352758i 0.984322 + 0.176379i \(0.0564385\pi\)
−0.984322 + 0.176379i \(0.943562\pi\)
\(192\) 1407.82 + 256.909i 0.529169 + 0.0965666i
\(193\) −2623.28 2623.28i −0.978382 0.978382i 0.0213891 0.999771i \(-0.493191\pi\)
−0.999771 + 0.0213891i \(0.993191\pi\)
\(194\) 2157.06 0.798289
\(195\) 433.254 + 1081.35i 0.159107 + 0.397114i
\(196\) −71.7928 −0.0261636
\(197\) −2995.05 2995.05i −1.08319 1.08319i −0.996210 0.0869796i \(-0.972279\pi\)
−0.0869796 0.996210i \(-0.527721\pi\)
\(198\) 1186.75 536.238i 0.425952 0.192469i
\(199\) 109.458i 0.0389912i 0.999810 + 0.0194956i \(0.00620603\pi\)
−0.999810 + 0.0194956i \(0.993794\pi\)
\(200\) −2610.60 + 916.872i −0.922987 + 0.324163i
\(201\) −1378.98 1994.63i −0.483911 0.699951i
\(202\) 401.036 401.036i 0.139687 0.139687i
\(203\) −1681.14 + 1681.14i −0.581246 + 0.581246i
\(204\) 401.650 + 580.964i 0.137849 + 0.199390i
\(205\) −4255.14 968.625i −1.44972 0.330008i
\(206\) 2217.38i 0.749962i
\(207\) 1314.39 593.915i 0.441336 0.199420i
\(208\) −60.2938 60.2938i −0.0200991 0.0200991i
\(209\) 1409.21 0.466399
\(210\) −1694.67 725.148i −0.556874 0.238286i
\(211\) 2714.94 0.885801 0.442901 0.896571i \(-0.353949\pi\)
0.442901 + 0.896571i \(0.353949\pi\)
\(212\) 830.909 + 830.909i 0.269184 + 0.269184i
\(213\) −877.989 160.222i −0.282436 0.0515409i
\(214\) 1416.14i 0.452362i
\(215\) −527.281 + 331.737i −0.167257 + 0.105229i
\(216\) −749.932 3013.61i −0.236233 0.949305i
\(217\) −3304.29 + 3304.29i −1.03368 + 1.03368i
\(218\) −2463.93 + 2463.93i −0.765496 + 0.765496i
\(219\) 1692.03 1169.79i 0.522087 0.360945i
\(220\) 369.058 1621.26i 0.113100 0.496843i
\(221\) 526.283i 0.160188i
\(222\) 282.429 1547.67i 0.0853847 0.467894i
\(223\) 2830.49 + 2830.49i 0.849971 + 0.849971i 0.990129 0.140158i \(-0.0447612\pi\)
−0.140158 + 0.990129i \(0.544761\pi\)
\(224\) 3480.17 1.03808
\(225\) 2330.36 + 2441.32i 0.690478 + 0.723354i
\(226\) 644.173 0.189601
\(227\) −1398.96 1398.96i −0.409042 0.409042i 0.472362 0.881404i \(-0.343401\pi\)
−0.881404 + 0.472362i \(0.843401\pi\)
\(228\) 237.075 1299.13i 0.0688626 0.377356i
\(229\) 3930.38i 1.13418i 0.823656 + 0.567089i \(0.191931\pi\)
−0.823656 + 0.567089i \(0.808069\pi\)
\(230\) −222.659 + 978.134i −0.0638335 + 0.280419i
\(231\) 2318.63 1602.98i 0.660408 0.456573i
\(232\) 1969.89 1969.89i 0.557454 0.557454i
\(233\) −1980.71 + 1980.71i −0.556912 + 0.556912i −0.928427 0.371515i \(-0.878838\pi\)
0.371515 + 0.928427i \(0.378838\pi\)
\(234\) 321.193 850.735i 0.0897309 0.237668i
\(235\) 1667.00 1048.79i 0.462736 0.291129i
\(236\) 3777.61i 1.04196i
\(237\) 245.460 + 44.7933i 0.0672756 + 0.0122769i
\(238\) −588.851 588.851i −0.160376 0.160376i
\(239\) −2976.20 −0.805500 −0.402750 0.915310i \(-0.631946\pi\)
−0.402750 + 0.915310i \(0.631946\pi\)
\(240\) −227.121 97.1847i −0.0610857 0.0261385i
\(241\) 1835.45 0.490587 0.245294 0.969449i \(-0.421116\pi\)
0.245294 + 0.969449i \(0.421116\pi\)
\(242\) 601.394 + 601.394i 0.159748 + 0.159748i
\(243\) −2973.13 + 2347.21i −0.784882 + 0.619645i
\(244\) 10.3578i 0.00271759i
\(245\) −151.122 34.4008i −0.0394074 0.00897057i
\(246\) 1937.25 + 2802.13i 0.502092 + 0.726248i
\(247\) 695.808 695.808i 0.179244 0.179244i
\(248\) 3871.82 3871.82i 0.991374 0.991374i
\(249\) 603.648 + 873.143i 0.153633 + 0.222222i
\(250\) −2332.11 + 266.855i −0.589982 + 0.0675095i
\(251\) 1542.14i 0.387805i −0.981021 0.193902i \(-0.937885\pi\)
0.981021 0.193902i \(-0.0621145\pi\)
\(252\) −1087.70 2407.18i −0.271898 0.601738i
\(253\) −1084.73 1084.73i −0.269550 0.269550i
\(254\) 250.805 0.0619564
\(255\) 567.082 + 1415.37i 0.139263 + 0.347584i
\(256\) −3901.74 −0.952572
\(257\) −428.853 428.853i −0.104090 0.104090i 0.653144 0.757234i \(-0.273450\pi\)
−0.757234 + 0.653144i \(0.773450\pi\)
\(258\) 478.388 + 87.2997i 0.115438 + 0.0210660i
\(259\) 3405.26i 0.816960i
\(260\) −618.283 982.733i −0.147478 0.234410i
\(261\) −3179.04 1200.24i −0.753937 0.284647i
\(262\) −2350.72 + 2350.72i −0.554304 + 0.554304i
\(263\) 5256.99 5256.99i 1.23255 1.23255i 0.269565 0.962982i \(-0.413120\pi\)
0.962982 0.269565i \(-0.0868798\pi\)
\(264\) −2716.87 + 1878.31i −0.633377 + 0.437885i
\(265\) 1350.89 + 2147.18i 0.313150 + 0.497738i
\(266\) 1557.06i 0.358908i
\(267\) −1322.01 + 7244.38i −0.303017 + 1.66048i
\(268\) 1708.97 + 1708.97i 0.389523 + 0.389523i
\(269\) −1930.34 −0.437528 −0.218764 0.975778i \(-0.570203\pi\)
−0.218764 + 0.975778i \(0.570203\pi\)
\(270\) −52.8785 2634.04i −0.0119188 0.593712i
\(271\) −3261.67 −0.731116 −0.365558 0.930789i \(-0.619122\pi\)
−0.365558 + 0.930789i \(0.619122\pi\)
\(272\) −78.9180 78.9180i −0.0175923 0.0175923i
\(273\) 353.353 1936.32i 0.0783367 0.429272i
\(274\) 1205.36i 0.265762i
\(275\) 1553.72 3235.87i 0.340700 0.709565i
\(276\) −1182.48 + 817.507i −0.257887 + 0.178290i
\(277\) 4865.57 4865.57i 1.05539 1.05539i 0.0570194 0.998373i \(-0.481840\pi\)
0.998373 0.0570194i \(-0.0181597\pi\)
\(278\) 81.2758 81.2758i 0.0175345 0.0175345i
\(279\) −6248.41 2359.07i −1.34080 0.506215i
\(280\) 4558.51 + 1037.68i 0.972940 + 0.221477i
\(281\) 3981.96i 0.845351i −0.906281 0.422676i \(-0.861091\pi\)
0.906281 0.422676i \(-0.138909\pi\)
\(282\) −1512.42 275.997i −0.319373 0.0582815i
\(283\) −4092.66 4092.66i −0.859658 0.859658i 0.131640 0.991298i \(-0.457976\pi\)
−0.991298 + 0.131640i \(0.957976\pi\)
\(284\) 889.527 0.185858
\(285\) 1121.54 2621.04i 0.233103 0.544761i
\(286\) −967.156 −0.199962
\(287\) 5213.93 + 5213.93i 1.07236 + 1.07236i
\(288\) 2048.19 + 4532.83i 0.419064 + 0.927429i
\(289\) 4224.15i 0.859791i
\(290\) 2000.40 1258.54i 0.405060 0.254842i
\(291\) 3794.91 + 5489.13i 0.764473 + 1.10577i
\(292\) −1449.71 + 1449.71i −0.290541 + 0.290541i
\(293\) −4515.35 + 4515.35i −0.900305 + 0.900305i −0.995462 0.0951570i \(-0.969665\pi\)
0.0951570 + 0.995462i \(0.469665\pi\)
\(294\) 68.8017 + 99.5179i 0.0136483 + 0.0197415i
\(295\) −1810.11 + 7951.77i −0.357250 + 1.56939i
\(296\) 3990.14i 0.783521i
\(297\) 3452.42 + 2076.54i 0.674511 + 0.405701i
\(298\) 431.545 + 431.545i 0.0838883 + 0.0838883i
\(299\) −1071.18 −0.207184
\(300\) −2721.71 1976.72i −0.523794 0.380420i
\(301\) 1052.58 0.201560
\(302\) −2474.07 2474.07i −0.471413 0.471413i
\(303\) 1726.07 + 314.986i 0.327261 + 0.0597210i
\(304\) 208.678i 0.0393701i
\(305\) 4.96314 21.8029i 0.000931766 0.00409322i
\(306\) 420.406 1113.52i 0.0785393 0.208025i
\(307\) 1831.07 1831.07i 0.340406 0.340406i −0.516114 0.856520i \(-0.672622\pi\)
0.856520 + 0.516114i \(0.172622\pi\)
\(308\) −1986.57 + 1986.57i −0.367517 + 0.367517i
\(309\) 5642.63 3901.03i 1.03883 0.718194i
\(310\) 3931.79 2473.67i 0.720357 0.453210i
\(311\) 4010.21i 0.731184i −0.930775 0.365592i \(-0.880866\pi\)
0.930775 0.365592i \(-0.119134\pi\)
\(312\) −414.044 + 2268.89i −0.0751303 + 0.411701i
\(313\) 6072.69 + 6072.69i 1.09664 + 1.09664i 0.994801 + 0.101841i \(0.0324733\pi\)
0.101841 + 0.994801i \(0.467527\pi\)
\(314\) −2870.63 −0.515920
\(315\) −1136.13 5588.23i −0.203218 0.999559i
\(316\) −248.685 −0.0442710
\(317\) 3112.10 + 3112.10i 0.551397 + 0.551397i 0.926844 0.375447i \(-0.122511\pi\)
−0.375447 + 0.926844i \(0.622511\pi\)
\(318\) 355.500 1948.08i 0.0626901 0.343531i
\(319\) 3614.09i 0.634326i
\(320\) −3002.36 683.446i −0.524490 0.119393i
\(321\) 3603.70 2491.42i 0.626600 0.433200i
\(322\) 1198.53 1198.53i 0.207427 0.207427i
\(323\) 910.737 910.737i 0.156888 0.156888i
\(324\) 2495.14 2833.39i 0.427836 0.485835i
\(325\) −830.574 2364.89i −0.141760 0.403632i
\(326\) 1487.10i 0.252647i
\(327\) −10604.8 1935.24i −1.79342 0.327275i
\(328\) −6109.45 6109.45i −1.02847 1.02847i
\(329\) −3327.71 −0.557637
\(330\) −2601.05 + 1042.13i −0.433887 + 0.173841i
\(331\) −9589.47 −1.59240 −0.796201 0.605033i \(-0.793160\pi\)
−0.796201 + 0.605033i \(0.793160\pi\)
\(332\) −748.099 748.099i −0.123666 0.123666i
\(333\) 4435.26 2004.10i 0.729883 0.329801i
\(334\) 7148.90i 1.17117i
\(335\) 2778.45 + 4416.22i 0.453144 + 0.720251i
\(336\) 237.371 + 343.345i 0.0385407 + 0.0557470i
\(337\) −2561.34 + 2561.34i −0.414021 + 0.414021i −0.883137 0.469115i \(-0.844573\pi\)
0.469115 + 0.883137i \(0.344573\pi\)
\(338\) 2131.76 2131.76i 0.343054 0.343054i
\(339\) 1133.29 + 1639.24i 0.181569 + 0.262630i
\(340\) −809.265 1286.29i −0.129084 0.205173i
\(341\) 7103.50i 1.12808i
\(342\) −2028.03 + 916.377i −0.320653 + 0.144889i
\(343\) −4396.56 4396.56i −0.692104 0.692104i
\(344\) −1233.36 −0.193310
\(345\) −2880.81 + 1154.22i −0.449558 + 0.180120i
\(346\) 4368.77 0.678805
\(347\) −8177.44 8177.44i −1.26509 1.26509i −0.948592 0.316503i \(-0.897491\pi\)
−0.316503 0.948592i \(-0.602509\pi\)
\(348\) 3331.77 + 608.005i 0.513223 + 0.0936566i
\(349\) 2766.04i 0.424249i −0.977243 0.212124i \(-0.931962\pi\)
0.977243 0.212124i \(-0.0680382\pi\)
\(350\) 3575.36 + 1716.72i 0.546032 + 0.262179i
\(351\) 2729.96 679.347i 0.415141 0.103307i
\(352\) 3740.81 3740.81i 0.566437 0.566437i
\(353\) −6338.53 + 6338.53i −0.955711 + 0.955711i −0.999060 0.0433491i \(-0.986197\pi\)
0.0433491 + 0.999060i \(0.486197\pi\)
\(354\) 5236.46 3620.23i 0.786199 0.543539i
\(355\) 1872.43 + 426.233i 0.279939 + 0.0637242i
\(356\) 7339.58i 1.09269i
\(357\) 462.501 2534.43i 0.0685663 0.375732i
\(358\) −975.763 975.763i −0.144052 0.144052i
\(359\) 8827.47 1.29776 0.648880 0.760890i \(-0.275238\pi\)
0.648880 + 0.760890i \(0.275238\pi\)
\(360\) 1331.26 + 6548.05i 0.194900 + 0.958646i
\(361\) 4450.80 0.648899
\(362\) 2748.50 + 2748.50i 0.399055 + 0.399055i
\(363\) −472.353 + 2588.42i −0.0682978 + 0.374261i
\(364\) 1961.76i 0.282484i
\(365\) −3746.27 + 2356.95i −0.537229 + 0.337996i
\(366\) −14.3578 + 9.92628i −0.00205053 + 0.00141764i
\(367\) 6191.27 6191.27i 0.880605 0.880605i −0.112991 0.993596i \(-0.536043\pi\)
0.993596 + 0.112991i \(0.0360432\pi\)
\(368\) 160.628 160.628i 0.0227535 0.0227535i
\(369\) −3722.45 + 9859.55i −0.525157 + 1.39097i
\(370\) −751.338 + 3300.60i −0.105568 + 0.463757i
\(371\) 4286.28i 0.599818i
\(372\) 6548.60 + 1195.04i 0.912713 + 0.166559i
\(373\) 3584.46 + 3584.46i 0.497577 + 0.497577i 0.910683 0.413106i \(-0.135556\pi\)
−0.413106 + 0.910683i \(0.635556\pi\)
\(374\) −1265.90 −0.175022
\(375\) −4781.95 5465.10i −0.658503 0.752578i
\(376\) 3899.27 0.534812
\(377\) 1784.48 + 1784.48i 0.243781 + 0.243781i
\(378\) −2294.40 + 3814.63i −0.312200 + 0.519057i
\(379\) 7110.48i 0.963695i 0.876255 + 0.481848i \(0.160034\pi\)
−0.876255 + 0.481848i \(0.839966\pi\)
\(380\) −630.683 + 2770.57i −0.0851404 + 0.374019i
\(381\) 441.241 + 638.231i 0.0593319 + 0.0858203i
\(382\) −1105.91 + 1105.91i −0.148124 + 0.148124i
\(383\) 1695.77 1695.77i 0.226240 0.226240i −0.584880 0.811120i \(-0.698858\pi\)
0.811120 + 0.584880i \(0.198858\pi\)
\(384\) −2988.11 4322.14i −0.397100 0.574383i
\(385\) −5133.58 + 3229.77i −0.679562 + 0.427544i
\(386\) 6231.15i 0.821650i
\(387\) 619.472 + 1370.95i 0.0813683 + 0.180076i
\(388\) −4703.02 4703.02i −0.615361 0.615361i
\(389\) 12362.2 1.61128 0.805640 0.592405i \(-0.201822\pi\)
0.805640 + 0.592405i \(0.201822\pi\)
\(390\) −769.723 + 1798.84i −0.0999395 + 0.233559i
\(391\) −1402.06 −0.181343
\(392\) −216.978 216.978i −0.0279567 0.0279567i
\(393\) −10117.5 1846.32i −1.29863 0.236984i
\(394\) 7114.22i 0.909668i
\(395\) −523.476 119.162i −0.0666808 0.0151790i
\(396\) −3756.61 1418.30i −0.476709 0.179980i
\(397\) −1340.12 + 1340.12i −0.169417 + 0.169417i −0.786723 0.617306i \(-0.788224\pi\)
0.617306 + 0.786723i \(0.288224\pi\)
\(398\) −129.999 + 129.999i −0.0163725 + 0.0163725i
\(399\) −3962.30 + 2739.33i −0.497150 + 0.343705i
\(400\) 479.171 + 230.076i 0.0598964 + 0.0287595i
\(401\) 2281.30i 0.284096i 0.989860 + 0.142048i \(0.0453688\pi\)
−0.989860 + 0.142048i \(0.954631\pi\)
\(402\) 731.175 4006.72i 0.0907156 0.497107i
\(403\) 3507.40 + 3507.40i 0.433538 + 0.433538i
\(404\) −1748.75 −0.215356
\(405\) 6609.87 4768.61i 0.810981 0.585072i
\(406\) −3993.26 −0.488133
\(407\) −3660.29 3660.29i −0.445783 0.445783i
\(408\) −541.939 + 2969.74i −0.0657597 + 0.360352i
\(409\) 4614.82i 0.557917i −0.960303 0.278959i \(-0.910011\pi\)
0.960303 0.278959i \(-0.0899892\pi\)
\(410\) −3903.28 6204.08i −0.470169 0.747311i
\(411\) −3067.32 + 2120.59i −0.368126 + 0.254504i
\(412\) −4834.54 + 4834.54i −0.578108 + 0.578108i
\(413\) 9743.49 9743.49i 1.16089 1.16089i
\(414\) 2266.43 + 855.683i 0.269055 + 0.101581i
\(415\) −1216.26 1933.19i −0.143865 0.228667i
\(416\) 3694.10i 0.435380i
\(417\) 349.813 + 63.8364i 0.0410801 + 0.00749660i
\(418\) 1673.67 + 1673.67i 0.195842 + 0.195842i
\(419\) 2142.28 0.249779 0.124889 0.992171i \(-0.460142\pi\)
0.124889 + 0.992171i \(0.460142\pi\)
\(420\) 2113.84 + 5275.92i 0.245583 + 0.612948i
\(421\) −8889.30 −1.02907 −0.514534 0.857470i \(-0.672035\pi\)
−0.514534 + 0.857470i \(0.672035\pi\)
\(422\) 3224.43 + 3224.43i 0.371950 + 0.371950i
\(423\) −1958.46 4334.26i −0.225115 0.498200i
\(424\) 5022.48i 0.575267i
\(425\) −1087.13 3095.38i −0.124079 0.353289i
\(426\) −852.466 1233.05i −0.0969534 0.140238i
\(427\) −26.7156 + 26.7156i −0.00302778 + 0.00302778i
\(428\) −3087.60 + 3087.60i −0.348703 + 0.348703i
\(429\) −1701.52 2461.15i −0.191492 0.276982i
\(430\) −1020.23 232.241i −0.114418 0.0260457i
\(431\) 15707.3i 1.75543i 0.479179 + 0.877717i \(0.340935\pi\)
−0.479179 + 0.877717i \(0.659065\pi\)
\(432\) −307.497 + 511.238i −0.0342464 + 0.0569374i
\(433\) 5430.81 + 5430.81i 0.602744 + 0.602744i 0.941040 0.338296i \(-0.109851\pi\)
−0.338296 + 0.941040i \(0.609851\pi\)
\(434\) −7848.76 −0.868094
\(435\) 6721.94 + 2876.31i 0.740902 + 0.317031i
\(436\) 10744.2 1.18016
\(437\) 1853.69 + 1853.69i 0.202915 + 0.202915i
\(438\) 3398.88 + 620.253i 0.370787 + 0.0676640i
\(439\) 8221.92i 0.893874i −0.894565 0.446937i \(-0.852515\pi\)
0.894565 0.446937i \(-0.147485\pi\)
\(440\) 6015.31 3784.51i 0.651747 0.410044i
\(441\) −132.203 + 350.163i −0.0142753 + 0.0378105i
\(442\) −625.047 + 625.047i −0.0672635 + 0.0672635i
\(443\) 1960.53 1960.53i 0.210265 0.210265i −0.594115 0.804380i \(-0.702498\pi\)
0.804380 + 0.594115i \(0.202498\pi\)
\(444\) −3990.14 + 2758.58i −0.426495 + 0.294857i
\(445\) 3516.89 15449.6i 0.374644 1.64580i
\(446\) 6723.34i 0.713810i
\(447\) −338.948 + 1857.38i −0.0358651 + 0.196535i
\(448\) 3678.86 + 3678.86i 0.387968 + 0.387968i
\(449\) −17849.2 −1.87607 −0.938036 0.346537i \(-0.887357\pi\)
−0.938036 + 0.346537i \(0.887357\pi\)
\(450\) −131.779 + 5667.15i −0.0138047 + 0.593672i
\(451\) 11208.8 1.17029
\(452\) −1404.49 1404.49i −0.146154 0.146154i
\(453\) 1943.21 10648.5i 0.201545 1.10443i
\(454\) 3323.00i 0.343516i
\(455\) −940.015 + 4129.46i −0.0968540 + 0.425477i
\(456\) 4642.85 3209.83i 0.476801 0.329636i
\(457\) −6346.80 + 6346.80i −0.649652 + 0.649652i −0.952909 0.303257i \(-0.901926\pi\)
0.303257 + 0.952909i \(0.401926\pi\)
\(458\) −4667.97 + 4667.97i −0.476245 + 0.476245i
\(459\) 3573.22 889.192i 0.363363 0.0904225i
\(460\) 2618.08 1647.16i 0.265366 0.166954i
\(461\) 8848.20i 0.893930i 0.894552 + 0.446965i \(0.147495\pi\)
−0.894552 + 0.446965i \(0.852505\pi\)
\(462\) 4657.55 + 849.944i 0.469024 + 0.0855908i
\(463\) 1329.43 + 1329.43i 0.133443 + 0.133443i 0.770673 0.637230i \(-0.219920\pi\)
−0.637230 + 0.770673i \(0.719920\pi\)
\(464\) −535.178 −0.0535453
\(465\) 13212.0 + 5653.40i 1.31762 + 0.563807i
\(466\) −4704.83 −0.467697
\(467\) 1479.96 + 1479.96i 0.146647 + 0.146647i 0.776618 0.629971i \(-0.216933\pi\)
−0.629971 + 0.776618i \(0.716933\pi\)
\(468\) −2555.14 + 1154.56i −0.252375 + 0.114037i
\(469\) 8815.81i 0.867966i
\(470\) 3225.44 + 734.227i 0.316550 + 0.0720582i
\(471\) −5050.29 7304.96i −0.494066 0.714639i
\(472\) −11417.0 + 11417.0i −1.11337 + 1.11337i
\(473\) 1131.41 1131.41i 0.109983 0.109983i
\(474\) 238.324 + 344.723i 0.0230941 + 0.0334043i
\(475\) −2655.14 + 5529.77i −0.256476 + 0.534155i
\(476\) 2567.73i 0.247252i
\(477\) 5582.76 2522.60i 0.535885 0.242143i
\(478\) −3534.73 3534.73i −0.338231 0.338231i
\(479\) 5039.60 0.480720 0.240360 0.970684i \(-0.422734\pi\)
0.240360 + 0.970684i \(0.422734\pi\)
\(480\) −3980.47 9934.81i −0.378506 0.944708i
\(481\) −3614.58 −0.342642
\(482\) 2179.89 + 2179.89i 0.205999 + 0.205999i
\(483\) 5158.51 + 941.362i 0.485963 + 0.0886821i
\(484\) 2622.43i 0.246284i
\(485\) −7646.20 12153.3i −0.715868 1.13784i
\(486\) −6318.78 743.377i −0.589765 0.0693833i
\(487\) 1292.93 1292.93i 0.120305 0.120305i −0.644391 0.764696i \(-0.722889\pi\)
0.764696 + 0.644391i \(0.222889\pi\)
\(488\) 31.3042 31.3042i 0.00290384 0.00290384i
\(489\) −3784.27 + 2616.26i −0.349961 + 0.241945i
\(490\) −138.625 220.339i −0.0127805 0.0203140i
\(491\) 13865.7i 1.27444i −0.770681 0.637221i \(-0.780084\pi\)
0.770681 0.637221i \(-0.219916\pi\)
\(492\) 1885.68 10333.2i 0.172791 0.946865i
\(493\) 2335.69 + 2335.69i 0.213375 + 0.213375i
\(494\) 1652.77 0.150530
\(495\) −7227.96 4785.53i −0.656308 0.434532i
\(496\) −1051.89 −0.0952247
\(497\) −2294.33 2294.33i −0.207072 0.207072i
\(498\) −320.070 + 1753.93i −0.0288006 + 0.157822i
\(499\) 10884.3i 0.976453i 0.872717 + 0.488226i \(0.162356\pi\)
−0.872717 + 0.488226i \(0.837644\pi\)
\(500\) 5666.50 + 4502.86i 0.506827 + 0.402748i
\(501\) −18192.0 + 12577.0i −1.62227 + 1.12156i
\(502\) 1831.54 1831.54i 0.162840 0.162840i
\(503\) −7880.86 + 7880.86i −0.698589 + 0.698589i −0.964106 0.265517i \(-0.914457\pi\)
0.265517 + 0.964106i \(0.414457\pi\)
\(504\) 3987.84 10562.5i 0.352445 0.933513i
\(505\) −3681.07 837.946i −0.324368 0.0738379i
\(506\) 2576.58i 0.226370i
\(507\) 9175.14 + 1674.35i 0.803713 + 0.146667i
\(508\) −546.829 546.829i −0.0477590 0.0477590i
\(509\) 1788.46 0.155741 0.0778704 0.996963i \(-0.475188\pi\)
0.0778704 + 0.996963i \(0.475188\pi\)
\(510\) −1007.48 + 2354.49i −0.0874747 + 0.204428i
\(511\) 7478.42 0.647408
\(512\) 1086.41 + 1086.41i 0.0937754 + 0.0937754i
\(513\) −5899.84 3548.60i −0.507766 0.305409i
\(514\) 1018.67i 0.0874153i
\(515\) −12493.1 + 7860.01i −1.06896 + 0.672531i
\(516\) −852.686 1233.36i −0.0727469 0.105224i
\(517\) −3576.93 + 3576.93i −0.304281 + 0.304281i
\(518\) 4044.31 4044.31i 0.343044 0.343044i
\(519\) 7685.96 + 11117.3i 0.650051 + 0.940263i
\(520\) 1101.47 4838.72i 0.0928896 0.408061i
\(521\) 18251.6i 1.53478i −0.641183 0.767388i \(-0.721556\pi\)
0.641183 0.767388i \(-0.278444\pi\)
\(522\) −2350.15 5201.11i −0.197056 0.436104i
\(523\) −2125.69 2125.69i −0.177725 0.177725i 0.612639 0.790363i \(-0.290108\pi\)
−0.790363 + 0.612639i \(0.790108\pi\)
\(524\) 10250.5 0.854570
\(525\) 1921.53 + 12118.5i 0.159738 + 1.00742i
\(526\) 12487.1 1.03510
\(527\) 4590.80 + 4590.80i 0.379466 + 0.379466i
\(528\) 624.207 + 113.910i 0.0514491 + 0.00938880i
\(529\) 9313.29i 0.765455i
\(530\) −945.725 + 4154.54i −0.0775088 + 0.340494i
\(531\) 18425.0 + 6956.30i 1.50579 + 0.568508i
\(532\) 3394.85 3394.85i 0.276664 0.276664i
\(533\) 5534.42 5534.42i 0.449761 0.449761i
\(534\) −10174.0 + 7033.79i −0.824478 + 0.570003i
\(535\) −7978.81 + 5019.84i −0.644774 + 0.405657i
\(536\) 10330.0i 0.832439i
\(537\) 766.393 4199.71i 0.0615872 0.337488i
\(538\) −2292.60 2292.60i −0.183719 0.183719i
\(539\) 398.082 0.0318119
\(540\) −5627.68 + 5858.26i −0.448475 + 0.466851i
\(541\) −2214.16 −0.175960 −0.0879798 0.996122i \(-0.528041\pi\)
−0.0879798 + 0.996122i \(0.528041\pi\)
\(542\) −3873.77 3873.77i −0.306998 0.306998i
\(543\) −2158.75 + 11829.6i −0.170609 + 0.934911i
\(544\) 4835.17i 0.381078i
\(545\) 22616.2 + 5148.26i 1.77756 + 0.404637i
\(546\) 2719.36 1880.03i 0.213146 0.147359i
\(547\) 12385.1 12385.1i 0.968098 0.968098i −0.0314090 0.999507i \(-0.509999\pi\)
0.999507 + 0.0314090i \(0.00999944\pi\)
\(548\) 2628.04 2628.04i 0.204862 0.204862i
\(549\) −50.5193 19.0735i −0.00392735 0.00148276i
\(550\) 5688.42 1997.84i 0.441009 0.154887i
\(551\) 6176.11i 0.477516i
\(552\) −6044.52 1103.05i −0.466072 0.0850522i
\(553\) 641.427 + 641.427i 0.0493242 + 0.0493242i
\(554\) 11557.3 0.886324
\(555\) −9720.96 + 3894.79i −0.743481 + 0.297882i
\(556\) −354.410 −0.0270329
\(557\) −8716.96 8716.96i −0.663105 0.663105i 0.293006 0.956111i \(-0.405344\pi\)
−0.956111 + 0.293006i \(0.905344\pi\)
\(558\) −4619.23 10222.8i −0.350444 0.775566i
\(559\) 1117.28i 0.0845363i
\(560\) −478.268 760.186i −0.0360902 0.0573638i
\(561\) −2227.10 3221.38i −0.167608 0.242436i
\(562\) 4729.23 4729.23i 0.354965 0.354965i
\(563\) −11697.0 + 11697.0i −0.875615 + 0.875615i −0.993077 0.117462i \(-0.962524\pi\)
0.117462 + 0.993077i \(0.462524\pi\)
\(564\) 2695.76 + 3899.27i 0.201262 + 0.291115i
\(565\) −2283.42 3629.39i −0.170025 0.270247i
\(566\) 9721.40i 0.721945i
\(567\) −13743.7 + 872.435i −1.01796 + 0.0646188i
\(568\) 2688.40 + 2688.40i 0.198596 + 0.198596i
\(569\) −11517.5 −0.848576 −0.424288 0.905527i \(-0.639476\pi\)
−0.424288 + 0.905527i \(0.639476\pi\)
\(570\) 4444.92 1780.90i 0.326627 0.130866i
\(571\) −11093.9 −0.813072 −0.406536 0.913635i \(-0.633263\pi\)
−0.406536 + 0.913635i \(0.633263\pi\)
\(572\) 2108.68 + 2108.68i 0.154141 + 0.154141i
\(573\) −4759.88 868.617i −0.347027 0.0633281i
\(574\) 12384.8i 0.900577i
\(575\) 6300.25 2212.72i 0.456937 0.160481i
\(576\) −2626.50 + 6956.73i −0.189995 + 0.503236i
\(577\) −14119.4 + 14119.4i −1.01871 + 1.01871i −0.0188920 + 0.999822i \(0.506014\pi\)
−0.999822 + 0.0188920i \(0.993986\pi\)
\(578\) 5016.87 5016.87i 0.361028 0.361028i
\(579\) 15856.6 10962.4i 1.13813 0.786846i
\(580\) −7105.44 1617.46i −0.508685 0.115795i
\(581\) 3859.10i 0.275564i
\(582\) −2012.16 + 11026.3i −0.143311 + 0.785320i
\(583\) −4607.29 4607.29i −0.327297 0.327297i
\(584\) −8762.89 −0.620909
\(585\) −5931.73 + 1205.96i −0.419226 + 0.0852316i
\(586\) −10725.4 −0.756081
\(587\) −8524.33 8524.33i −0.599381 0.599381i 0.340767 0.940148i \(-0.389313\pi\)
−0.940148 + 0.340767i \(0.889313\pi\)
\(588\) 66.9702 366.986i 0.00469695 0.0257385i
\(589\) 12139.2i 0.849211i
\(590\) −11593.8 + 7294.23i −0.809001 + 0.508981i
\(591\) 18103.8 12516.0i 1.26005 0.871135i
\(592\) 542.020 542.020i 0.0376298 0.0376298i
\(593\) 4580.53 4580.53i 0.317200 0.317200i −0.530491 0.847691i \(-0.677992\pi\)
0.847691 + 0.530491i \(0.177992\pi\)
\(594\) 1634.08 + 6566.55i 0.112874 + 0.453584i
\(595\) −1230.38 + 5405.01i −0.0847740 + 0.372410i
\(596\) 1881.79i 0.129331i
\(597\) −559.518 102.105i −0.0383577 0.00699979i
\(598\) −1272.20 1272.20i −0.0869971 0.0869971i
\(599\) 10195.8 0.695477 0.347738 0.937592i \(-0.386950\pi\)
0.347738 + 0.937592i \(0.386950\pi\)
\(600\) −2251.57 14200.0i −0.153200 0.966187i
\(601\) 18915.8 1.28385 0.641923 0.766769i \(-0.278137\pi\)
0.641923 + 0.766769i \(0.278137\pi\)
\(602\) 1250.11 + 1250.11i 0.0846355 + 0.0846355i
\(603\) 11482.4 5188.36i 0.775452 0.350392i
\(604\) 10788.4i 0.726778i
\(605\) 1256.59 5520.14i 0.0844421 0.370952i
\(606\) 1675.89 + 2424.09i 0.112341 + 0.162495i
\(607\) 12758.2 12758.2i 0.853113 0.853113i −0.137402 0.990515i \(-0.543875\pi\)
0.990515 + 0.137402i \(0.0438753\pi\)
\(608\) −6392.67 + 6392.67i −0.426409 + 0.426409i
\(609\) −7025.33 10161.8i −0.467456 0.676149i
\(610\) 31.7891 20.0000i 0.00211000 0.00132750i
\(611\) 3532.26i 0.233879i
\(612\) −3344.41 + 1511.19i −0.220898 + 0.0998140i
\(613\) 7340.02 + 7340.02i 0.483622 + 0.483622i 0.906286 0.422664i \(-0.138905\pi\)
−0.422664 + 0.906286i \(0.638905\pi\)
\(614\) 4349.39 0.285875
\(615\) 8920.67 20847.6i 0.584904 1.36692i
\(616\) −12007.9 −0.785412
\(617\) 17118.9 + 17118.9i 1.11698 + 1.11698i 0.992182 + 0.124803i \(0.0398299\pi\)
0.124803 + 0.992182i \(0.460170\pi\)
\(618\) 11334.7 + 2068.43i 0.737778 + 0.134635i
\(619\) 3176.16i 0.206237i −0.994669 0.103118i \(-0.967118\pi\)
0.994669 0.103118i \(-0.0328820\pi\)
\(620\) −13965.8 3179.12i −0.904644 0.205930i
\(621\) 1809.84 + 7272.84i 0.116950 + 0.469966i
\(622\) 4762.79 4762.79i 0.307026 0.307026i
\(623\) −18930.8 + 18930.8i −1.21741 + 1.21741i
\(624\) 364.450 251.962i 0.0233809 0.0161644i
\(625\) 9770.20 + 12193.6i 0.625293 + 0.780390i
\(626\) 14424.6i 0.920965i
\(627\) −1314.55 + 7203.53i −0.0837291 + 0.458822i
\(628\) 6258.80 + 6258.80i 0.397697 + 0.397697i
\(629\) −4731.09 −0.299906
\(630\) 5287.60 7986.28i 0.334386 0.505049i
\(631\) −11467.2 −0.723459 −0.361729 0.932283i \(-0.617814\pi\)
−0.361729 + 0.932283i \(0.617814\pi\)
\(632\) −751.597 751.597i −0.0473052 0.0473052i
\(633\) −2532.57 + 13878.0i −0.159021 + 0.871410i
\(634\) 7392.26i 0.463066i
\(635\) −889.036 1413.08i −0.0555596 0.0883094i
\(636\) −5022.48 + 3472.29i −0.313136 + 0.216486i
\(637\) 196.556 196.556i 0.0122258 0.0122258i
\(638\) −4292.32 + 4292.32i −0.266355 + 0.266355i
\(639\) 1638.02 4338.59i 0.101407 0.268595i
\(640\) 6020.60 + 9569.47i 0.371852 + 0.591042i
\(641\) 12383.2i 0.763035i 0.924362 + 0.381518i \(0.124598\pi\)
−0.924362 + 0.381518i \(0.875402\pi\)
\(642\) 7238.95 + 1321.02i 0.445013 + 0.0812092i
\(643\) −11142.9 11142.9i −0.683413 0.683413i 0.277354 0.960768i \(-0.410542\pi\)
−0.960768 + 0.277354i \(0.910542\pi\)
\(644\) −5226.29 −0.319790
\(645\) −1203.89 3004.78i −0.0734933 0.183431i
\(646\) 2163.30 0.131755
\(647\) 2391.21 + 2391.21i 0.145299 + 0.145299i 0.776014 0.630716i \(-0.217239\pi\)
−0.630716 + 0.776014i \(0.717239\pi\)
\(648\) 16104.3 1022.28i 0.976292 0.0619738i
\(649\) 20946.4i 1.26690i
\(650\) 1822.25 3795.13i 0.109961 0.229011i
\(651\) −13808.3 19973.0i −0.831322 1.20246i
\(652\) 3242.32 3242.32i 0.194753 0.194753i
\(653\) 16623.3 16623.3i 0.996201 0.996201i −0.00379136 0.999993i \(-0.501207\pi\)
0.999993 + 0.00379136i \(0.00120683\pi\)
\(654\) −10296.5 14893.4i −0.615636 0.890484i
\(655\) 21577.0 + 4911.71i 1.28715 + 0.293002i
\(656\) 1659.81i 0.0987878i
\(657\) 4401.27 + 9740.43i 0.261354 + 0.578403i
\(658\) −3952.20 3952.20i −0.234153 0.234153i
\(659\) −20089.8 −1.18754 −0.593768 0.804636i \(-0.702360\pi\)
−0.593768 + 0.804636i \(0.702360\pi\)
\(660\) 7943.19 + 3398.88i 0.468467 + 0.200457i
\(661\) 541.434 0.0318598 0.0159299 0.999873i \(-0.494929\pi\)
0.0159299 + 0.999873i \(0.494929\pi\)
\(662\) −11389.1 11389.1i −0.668654 0.668654i
\(663\) −2690.22 490.931i −0.157586 0.0287574i
\(664\) 4521.93i 0.264284i
\(665\) 8772.76 5519.36i 0.511569 0.321852i
\(666\) 7647.80 + 2887.41i 0.444964 + 0.167995i
\(667\) −4753.99 + 4753.99i −0.275975 + 0.275975i
\(668\) 15586.7 15586.7i 0.902796 0.902796i
\(669\) −17109.1 + 11828.3i −0.988751 + 0.683573i
\(670\) −1945.12 + 8544.86i −0.112159 + 0.492711i
\(671\) 57.4328i 0.00330428i
\(672\) −3246.40 + 17789.7i −0.186358 + 1.02121i
\(673\) −24314.3 24314.3i −1.39264 1.39264i −0.819354 0.573288i \(-0.805668\pi\)
−0.573288 0.819354i \(-0.694332\pi\)
\(674\) −6084.03 −0.347697
\(675\) −14653.2 + 9634.87i −0.835558 + 0.549402i
\(676\) −9295.71 −0.528887
\(677\) 14662.4 + 14662.4i 0.832380 + 0.832380i 0.987842 0.155462i \(-0.0496867\pi\)
−0.155462 + 0.987842i \(0.549687\pi\)
\(678\) −600.902 + 3292.84i −0.0340376 + 0.186520i
\(679\) 24260.8i 1.37120i
\(680\) 1441.70 6333.36i 0.0813041 0.357166i
\(681\) 8456.13 5846.14i 0.475829 0.328964i
\(682\) −8436.57 + 8436.57i −0.473685 + 0.473685i
\(683\) 15981.2 15981.2i 0.895320 0.895320i −0.0996976 0.995018i \(-0.531788\pi\)
0.995018 + 0.0996976i \(0.0317875\pi\)
\(684\) 6419.67 + 2423.73i 0.358863 + 0.135488i
\(685\) 6791.23 4272.68i 0.378803 0.238322i
\(686\) 10443.3i 0.581233i
\(687\) −20091.1 3666.36i −1.11575 0.203611i
\(688\) 167.540 + 167.540i 0.00928400 + 0.00928400i
\(689\) −4549.75 −0.251570
\(690\) −4792.26 2050.60i −0.264403 0.113138i
\(691\) −16714.9 −0.920209 −0.460105 0.887865i \(-0.652188\pi\)
−0.460105 + 0.887865i \(0.652188\pi\)
\(692\) −9525.19 9525.19i −0.523256 0.523256i
\(693\) 6031.14 + 13347.5i 0.330598 + 0.731645i
\(694\) 19424.1i 1.06243i
\(695\) −746.023 169.822i −0.0407169 0.00926865i
\(696\) 8231.98 + 11907.1i 0.448322 + 0.648474i
\(697\) 7243.96 7243.96i 0.393665 0.393665i
\(698\) 3285.13 3285.13i 0.178143 0.178143i
\(699\) −8277.19 11972.5i −0.447886 0.647842i
\(700\) −4052.37 11538.3i −0.218808 0.623009i
\(701\) 6990.49i 0.376643i 0.982107 + 0.188322i \(0.0603048\pi\)
−0.982107 + 0.188322i \(0.939695\pi\)
\(702\) 4049.11 + 2435.44i 0.217698 + 0.130940i
\(703\) 6255.06 + 6255.06i 0.335582 + 0.335582i
\(704\) 7908.75 0.423398
\(705\) 3806.09 + 9499.58i 0.203327 + 0.507482i
\(706\) −15056.1 −0.802611
\(707\) 4510.51 + 4510.51i 0.239936 + 0.239936i
\(708\) −19310.2 3523.86i −1.02503 0.187055i
\(709\) 28175.0i 1.49243i 0.665705 + 0.746215i \(0.268131\pi\)
−0.665705 + 0.746215i \(0.731869\pi\)
\(710\) 1717.60 + 2730.04i 0.0907890 + 0.144305i
\(711\) −457.943 + 1212.94i −0.0241550 + 0.0639787i
\(712\) 22182.3 22182.3i 1.16758 1.16758i
\(713\) −9343.99 + 9343.99i −0.490793 + 0.490793i
\(714\) 3559.35 2460.75i 0.186562 0.128980i
\(715\) 3428.31 + 5449.13i 0.179317 + 0.285015i
\(716\) 4254.90i 0.222085i
\(717\) 2776.28 15213.6i 0.144605 0.792414i
\(718\) 10484.1 + 10484.1i 0.544933 + 0.544933i
\(719\) 20143.8 1.04484 0.522418 0.852690i \(-0.325030\pi\)
0.522418 + 0.852690i \(0.325030\pi\)
\(720\) 708.646 1070.32i 0.0366801 0.0554008i
\(721\) 24939.2 1.28819
\(722\) 5286.05 + 5286.05i 0.272474 + 0.272474i
\(723\) −1712.15 + 9382.32i −0.0880715 + 0.482617i
\(724\) 11985.0i 0.615222i
\(725\) −14181.7 6809.41i −0.726477 0.348821i
\(726\) −3635.16 + 2513.17i −0.185831 + 0.128475i
\(727\) −9805.90 + 9805.90i −0.500249 + 0.500249i −0.911515 0.411267i \(-0.865087\pi\)
0.411267 + 0.911515i \(0.365087\pi\)
\(728\) −5929.00 + 5929.00i −0.301845 + 0.301845i
\(729\) −9224.92 17387.4i −0.468674 0.883371i
\(730\) −7248.57 1650.04i −0.367509 0.0836585i
\(731\) 1462.39i 0.0739926i
\(732\) 52.9464 + 9.66205i 0.00267344 + 0.000487868i
\(733\) 16533.1 + 16533.1i 0.833100 + 0.833100i 0.987940 0.154840i \(-0.0494861\pi\)
−0.154840 + 0.987940i \(0.549486\pi\)
\(734\) 14706.3 0.739536
\(735\) 316.818 740.405i 0.0158994 0.0371568i
\(736\) 9841.37 0.492877
\(737\) −9476.04 9476.04i −0.473615 0.473615i
\(738\) −16130.8 + 7288.81i −0.804586 + 0.363557i
\(739\) 15250.1i 0.759114i 0.925168 + 0.379557i \(0.123924\pi\)
−0.925168 + 0.379557i \(0.876076\pi\)
\(740\) 8834.41 5558.14i 0.438864 0.276110i
\(741\) 2907.72 + 4205.85i 0.144153 + 0.208510i
\(742\) 5090.66 5090.66i 0.251865 0.251865i
\(743\) 5438.49 5438.49i 0.268531 0.268531i −0.559977 0.828508i \(-0.689190\pi\)
0.828508 + 0.559977i \(0.189190\pi\)
\(744\) 16180.0 + 23403.5i 0.797294 + 1.15324i
\(745\) 901.693 3961.11i 0.0443429 0.194797i
\(746\) 8514.27i 0.417868i
\(747\) −5026.38 + 2271.20i −0.246192 + 0.111243i
\(748\) 2760.04 + 2760.04i 0.134916 + 0.134916i
\(749\) 15927.5 0.777009
\(750\) 811.363 12170.1i 0.0395024 0.592517i
\(751\) 2087.82 0.101446 0.0507228 0.998713i \(-0.483848\pi\)
0.0507228 + 0.998713i \(0.483848\pi\)
\(752\) −529.676 529.676i −0.0256852 0.0256852i
\(753\) 7883.01 + 1438.55i 0.381505 + 0.0696197i
\(754\) 4238.72i 0.204728i
\(755\) −5169.46 + 22709.3i −0.249187 + 1.09467i
\(756\) 13319.5 3314.54i 0.640774 0.159456i
\(757\) −10258.6 + 10258.6i −0.492546 + 0.492546i −0.909107 0.416562i \(-0.863235\pi\)
0.416562 + 0.909107i \(0.363235\pi\)
\(758\) −8444.86 + 8444.86i −0.404658 + 0.404658i
\(759\) 6556.70 4532.98i 0.313561 0.216781i
\(760\) −10279.5 + 6467.35i −0.490629 + 0.308678i
\(761\) 26879.5i 1.28040i −0.768210 0.640198i \(-0.778852\pi\)
0.768210 0.640198i \(-0.221148\pi\)
\(762\) −233.958 + 1282.05i −0.0111226 + 0.0609498i
\(763\) −27712.1 27712.1i −1.31487 1.31487i
\(764\) 4822.43 0.228363
\(765\) −7763.99 + 1578.48i −0.366938 + 0.0746012i
\(766\) 4028.02 0.189998
\(767\) −10342.4 10342.4i −0.486888 0.486888i
\(768\) 3639.64 19944.6i 0.171008 0.937097i
\(769\) 25180.9i 1.18082i −0.807105 0.590408i \(-0.798967\pi\)
0.807105 0.590408i \(-0.201033\pi\)
\(770\) −9932.85 2261.08i −0.464877 0.105823i
\(771\) 2592.23 1792.14i 0.121085 0.0837124i
\(772\) −13585.7 + 13585.7i −0.633369 + 0.633369i
\(773\) −18871.2 + 18871.2i −0.878072 + 0.878072i −0.993335 0.115263i \(-0.963229\pi\)
0.115263 + 0.993335i \(0.463229\pi\)
\(774\) −892.506 + 2363.96i −0.0414476 + 0.109781i
\(775\) −27874.2 13383.9i −1.29196 0.620341i
\(776\)