Properties

Label 15.4.e.a.2.3
Level 15
Weight 4
Character 15.2
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 2.3
Root \(1.18766 + 1.18766i\)
Character \(\chi\) = 15.2
Dual form 15.4.e.a.8.3

$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18766 1.18766i 0.419903 0.419903i −0.465267 0.885170i \(-0.654042\pi\)
0.885170 + 0.465267i \(0.154042\pi\)
\(3\) −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 0.247606 0.968861i \(-0.420356\pi\)
−0.968861 + 0.247606i \(0.920356\pi\)
\(8\) 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 \(-0.871243\pi\)
0.919299 0.393560i \(-0.128757\pi\)
\(12\) 26.4732 4.83102i 0.636846 0.116216i
\(13\) 14.1789 14.1789i 0.302502 0.302502i −0.539490 0.841992i \(-0.681383\pi\)
0.841992 + 0.539490i \(0.181383\pi\)
\(14\) −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 −0.562217 0.826990i \(-0.690051\pi\)
0.826990 + 0.562217i \(0.190051\pi\)
\(18\) −18.6736 + 41.3264i −0.244522 + 0.541152i
\(19\) 49.0735i 0.592538i 0.955105 + 0.296269i \(0.0957425\pi\)
−0.955105 + 0.296269i \(0.904258\pi\)
\(20\) −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 0.514837 0.857288i \(-0.327852\pi\)
−0.857288 + 0.514837i \(0.827852\pi\)
\(24\) 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 0.364756 0.931103i \(-0.381152\pi\)
−0.931103 + 0.364756i \(0.881152\pi\)
\(38\) 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 \(0.266789\pi\)
−0.668845 + 0.743402i \(0.733211\pi\)
\(42\) 29.5978 + 162.191i 0.108739 + 0.595873i
\(43\) −39.3993 + 39.3993i −0.139729 + 0.139729i −0.773511 0.633783i \(-0.781501\pi\)
0.633783 + 0.773511i \(0.281501\pi\)
\(44\) 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 −0.486889 0.873464i \(-0.661868\pi\)
0.873464 + 0.486889i \(0.161868\pi\)
\(48\) 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 0.467943 0.883759i \(-0.344995\pi\)
−0.883759 + 0.467943i \(0.844995\pi\)
\(54\) 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 0.339059 0.940765i \(-0.389891\pi\)
−0.940765 + 0.339059i \(0.889891\pi\)
\(68\) 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 \(-0.954148\pi\)
0.989643 0.143550i \(-0.0458518\pi\)
\(72\) −544.637 246.097i −0.891474 0.402817i
\(73\) −279.927 + 279.927i −0.448807 + 0.448807i −0.894958 0.446151i \(-0.852795\pi\)
0.446151 + 0.894958i \(0.352795\pi\)
\(74\) −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 \(0.0108862\pi\)
−0.999415 + 0.0341933i \(0.989114\pi\)
\(80\) −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 0.796141 0.605111i \(-0.206871\pi\)
−0.605111 + 0.796141i \(0.706871\pi\)
\(84\) −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 0.998834 0.0482702i \(-0.0153708\pi\)
−0.0482702 + 0.998834i \(0.515371\pi\)
\(98\) 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 \(0.0531926\pi\)
−0.986070 + 0.166333i \(0.946807\pi\)
\(102\) −225.340 + 41.1217i −0.218745 + 0.0399182i
\(103\) −933.505 + 933.505i −0.893019 + 0.893019i −0.994806 0.101787i \(-0.967544\pi\)
0.101787 + 0.994806i \(0.467544\pi\)
\(104\) 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 −0.923133 0.384481i \(-0.874380\pi\)
0.384481 + 0.923133i \(0.374380\pi\)
\(108\) −622.632 + 374.498i −0.554748 + 0.333667i
\(109\) 2074.60i 1.82303i −0.411264 0.911516i \(-0.634913\pi\)
0.411264 0.911516i \(-0.365087\pi\)
\(110\) 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 0.810922 0.585154i \(-0.198966\pi\)
−0.585154 + 0.810922i \(0.698966\pi\)
\(114\) 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 0.743031 0.669257i \(-0.233387\pi\)
−0.669257 + 0.743031i \(0.733387\pi\)
\(128\) −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 \(-0.770540\pi\)
0.751231 0.660039i \(-0.229460\pi\)
\(132\) −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 −0.530948 0.847404i \(-0.678164\pi\)
0.847404 + 0.530948i \(0.178164\pi\)
\(138\) 83.6979 + 458.651i 0.0516293 + 0.282920i
\(139\) 68.4333i 0.0417585i 0.999782 + 0.0208793i \(0.00664656\pi\)
−0.999782 + 0.0208793i \(0.993353\pi\)
\(140\) 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 0.329739 0.944072i \(-0.393039\pi\)
−0.944072 + 0.329739i \(0.893039\pi\)
\(158\) 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 −0.540502 0.841343i \(-0.681766\pi\)
0.841343 + 0.540502i \(0.181766\pi\)
\(164\) −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 0.579848 0.814724i \(-0.303112\pi\)
0.814724 0.579848i \(-0.196888\pi\)
\(168\) −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 0.984375 0.176086i \(-0.0563438\pi\)
−0.176086 + 0.984375i \(0.556344\pi\)
\(174\) −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 \(-0.943562\pi\)
0.984322 0.176379i \(-0.0564385\pi\)
\(192\) 1407.82 256.909i 0.529169 0.0965666i
\(193\) −2623.28 + 2623.28i −0.978382 + 0.978382i −0.999771 0.0213891i \(-0.993191\pi\)
0.0213891 + 0.999771i \(0.493191\pi\)
\(194\) 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 −0.0869796 + 0.996210i \(0.527721\pi\)
−0.996210 + 0.0869796i \(0.972279\pi\)
\(198\) 1186.75 + 536.238i 0.425952 + 0.192469i
\(199\) 109.458i 0.0389912i −0.999810 0.0194956i \(-0.993794\pi\)
0.999810 0.0194956i \(-0.00620603\pi\)
\(200\) −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 −0.140158 0.990129i \(-0.544761\pi\)
0.990129 + 0.140158i \(0.0447612\pi\)
\(224\) 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 −0.881404 0.472362i \(-0.843401\pi\)
0.472362 + 0.881404i \(0.343401\pi\)
\(228\) 237.075 + 1299.13i 0.0688626 + 0.377356i
\(229\) 3930.38i 1.13418i −0.823656 0.567089i \(-0.808069\pi\)
0.823656 0.567089i \(-0.191931\pi\)
\(230\) −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 0.371515 0.928427i \(-0.378838\pi\)
−0.928427 + 0.371515i \(0.878838\pi\)
\(234\) 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 \(0.0621145\pi\)
−0.981021 + 0.193902i \(0.937885\pi\)
\(252\) −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 −0.757234 0.653144i \(-0.773450\pi\)
0.653144 + 0.757234i \(0.273450\pi\)
\(258\) 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 0.962982 + 0.269565i \(0.0868798\pi\)
0.269565 + 0.962982i \(0.413120\pi\)
\(264\) −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 0.998373 + 0.0570194i \(0.0181597\pi\)
0.0570194 + 0.998373i \(0.481840\pi\)
\(278\) 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 \(0.138909\pi\)
−0.906281 + 0.422676i \(0.861091\pi\)
\(282\) −1512.42 + 275.997i −0.319373 + 0.0582815i
\(283\) −4092.66 + 4092.66i −0.859658 + 0.859658i −0.991298 0.131640i \(-0.957976\pi\)
0.131640 + 0.991298i \(0.457976\pi\)
\(284\) 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 0.0951570 0.995462i \(-0.469665\pi\)
−0.995462 + 0.0951570i \(0.969665\pi\)
\(294\) 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 0.856520 0.516114i \(-0.172622\pi\)
−0.516114 + 0.856520i \(0.672622\pi\)
\(308\) −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 \(0.119134\pi\)
−0.930775 + 0.365592i \(0.880866\pi\)
\(312\) −414.044 2268.89i −0.0751303 0.411701i
\(313\) 6072.69 6072.69i 1.09664 1.09664i 0.101841 0.994801i \(-0.467527\pi\)
0.994801 0.101841i \(-0.0324733\pi\)
\(314\) −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 −0.375447 0.926844i \(-0.622511\pi\)
0.926844 + 0.375447i \(0.122511\pi\)
\(318\) 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 0.469115 0.883137i \(-0.344573\pi\)
−0.883137 + 0.469115i \(0.844573\pi\)
\(338\) 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 −0.316503 + 0.948592i \(0.602509\pi\)
−0.948592 + 0.316503i \(0.897491\pi\)
\(348\) 3331.77 608.005i 0.513223 0.0936566i
\(349\) 2766.04i 0.424249i 0.977243 + 0.212124i \(0.0680382\pi\)
−0.977243 + 0.212124i \(0.931962\pi\)
\(350\) 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 0.0433491 0.999060i \(-0.486197\pi\)
−0.999060 + 0.0433491i \(0.986197\pi\)
\(354\) 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 0.993596 0.112991i \(-0.0360432\pi\)
−0.112991 + 0.993596i \(0.536043\pi\)
\(368\) 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 −0.413106 0.910683i \(-0.635556\pi\)
0.910683 + 0.413106i \(0.135556\pi\)
\(374\) −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 \(-0.839966\pi\)
0.876255 0.481848i \(-0.160034\pi\)
\(380\) −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 0.811120 0.584880i \(-0.198858\pi\)
−0.584880 + 0.811120i \(0.698858\pi\)
\(384\) −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 0.617306 0.786723i \(-0.288224\pi\)
−0.786723 + 0.617306i \(0.788224\pi\)
\(398\) −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 \(-0.954631\pi\)
0.989860 0.142048i \(-0.0453688\pi\)
\(402\) 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 \(0.0899892\pi\)
−0.960303 + 0.278959i \(0.910011\pi\)
\(410\) −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 \(-0.659065\pi\)
0.479179 0.877717i \(-0.340935\pi\)
\(432\) −307.497 511.238i −0.0342464 0.0569374i
\(433\) 5430.81 5430.81i 0.602744 0.602744i −0.338296 0.941040i \(-0.609851\pi\)
0.941040 + 0.338296i \(0.109851\pi\)
\(434\) −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 \(0.147485\pi\)
−0.894565 + 0.446937i \(0.852515\pi\)
\(440\) 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 0.804380 0.594115i \(-0.202498\pi\)
−0.594115 + 0.804380i \(0.702498\pi\)
\(444\) −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 0.303257 0.952909i \(-0.401926\pi\)
−0.952909 + 0.303257i \(0.901926\pi\)
\(458\) −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 \(-0.852505\pi\)
0.894552 0.446965i \(-0.147495\pi\)
\(462\) 4657.55 849.944i 0.469024 0.0855908i
\(463\) 1329.43 1329.43i 0.133443 0.133443i −0.637230 0.770673i \(-0.719920\pi\)
0.770673 + 0.637230i \(0.219920\pi\)
\(464\) −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 −0.629971 0.776618i \(-0.716933\pi\)
0.776618 + 0.629971i \(0.216933\pi\)
\(468\) −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 0.764696 0.644391i \(-0.222889\pi\)
−0.644391 + 0.764696i \(0.722889\pi\)
\(488\) 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 \(0.219916\pi\)
−0.770681 + 0.637221i \(0.780084\pi\)
\(492\) 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 \(-0.837644\pi\)
0.872717 0.488226i \(-0.162356\pi\)
\(500\) 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 0.265517 0.964106i \(-0.414457\pi\)
−0.964106 + 0.265517i \(0.914457\pi\)
\(504\) 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 \(0.278444\pi\)
−0.641183 + 0.767388i \(0.721556\pi\)
\(522\) −2350.15 + 5201.11i −0.197056 + 0.436104i
\(523\) −2125.69 + 2125.69i −0.177725 + 0.177725i −0.790363 0.612639i \(-0.790108\pi\)
0.612639 + 0.790363i \(0.290108\pi\)
\(524\) 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 0.999507 0.0314090i \(-0.00999944\pi\)
−0.0314090 + 0.999507i \(0.509999\pi\)
\(548\) 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 −0.956111 0.293006i \(-0.905344\pi\)
0.293006 + 0.956111i \(0.405344\pi\)
\(558\) −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 0.117462 0.993077i \(-0.462524\pi\)
−0.993077 + 0.117462i \(0.962524\pi\)
\(564\) 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 −0.999822 0.0188920i \(-0.993986\pi\)
−0.0188920 0.999822i \(-0.506014\pi\)
\(578\) 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 −0.940148 0.340767i \(-0.889313\pi\)
0.340767 + 0.940148i \(0.389313\pi\)
\(588\) 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 0.847691 0.530491i \(-0.177992\pi\)
−0.530491 + 0.847691i \(0.677992\pi\)
\(594\) 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 0.990515 0.137402i \(-0.0438753\pi\)
−0.137402 + 0.990515i \(0.543875\pi\)
\(608\) −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 −0.422664 0.906286i \(-0.638905\pi\)
0.906286 + 0.422664i \(0.138905\pi\)
\(614\) 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 0.124803 0.992182i \(-0.460170\pi\)
0.992182 0.124803i \(-0.0398299\pi\)
\(618\) 11334.7 2068.43i 0.737778 0.134635i
\(619\) 3176.16i 0.206237i 0.994669 + 0.103118i \(0.0328820\pi\)
−0.994669 + 0.103118i \(0.967118\pi\)
\(620\) −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 \(-0.875402\pi\)
0.924362 0.381518i \(-0.124598\pi\)
\(642\) 7238.95 1321.02i 0.445013 0.0812092i
\(643\) −11142.9 + 11142.9i −0.683413 + 0.683413i −0.960768 0.277354i \(-0.910542\pi\)
0.277354 + 0.960768i \(0.410542\pi\)
\(644\) −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 −0.630716 0.776014i \(-0.717239\pi\)
0.776014 + 0.630716i \(0.217239\pi\)
\(648\) 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 0.999993 0.00379136i \(-0.00120683\pi\)
−0.00379136 + 0.999993i \(0.501207\pi\)
\(654\) −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 −0.573288 + 0.819354i \(0.694332\pi\)
−0.819354 + 0.573288i \(0.805668\pi\)
\(674\) −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 −0.155462 0.987842i \(-0.549687\pi\)
0.987842 + 0.155462i \(0.0496867\pi\)
\(678\) −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 0.995018 0.0996976i \(-0.0317875\pi\)
−0.0996976 + 0.995018i \(0.531788\pi\)
\(684\) 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 \(-0.939695\pi\)
0.982107 0.188322i \(-0.0603048\pi\)
\(702\) 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 \(-0.731869\pi\)
0.665705 0.746215i \(-0.268131\pi\)
\(710\) 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 0.411267 0.911515i \(-0.365087\pi\)
−0.911515 + 0.411267i \(0.865087\pi\)
\(728\) −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 −0.154840 0.987940i \(-0.549486\pi\)
0.987940 + 0.154840i \(0.0494861\pi\)
\(734\) 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 \(-0.876076\pi\)
0.925168 0.379557i \(-0.123924\pi\)
\(740\) 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 0.828508 0.559977i \(-0.189190\pi\)
−0.559977 + 0.828508i \(0.689190\pi\)
\(744\) 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 0.416562 0.909107i \(-0.363235\pi\)
−0.909107 + 0.416562i \(0.863235\pi\)
\(758\) −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 \(0.221148\pi\)
−0.768210 + 0.640198i \(0.778852\pi\)
\(762\) −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 \(0.201033\pi\)
−0.807105 + 0.590408i \(0.798967\pi\)
\(770\) −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 0.115263 0.993335i \(-0.463229\pi\)
−0.993335 + 0.115263i \(0.963229\pi\)
\(774\) −892.506 2363.96i −0.0414476 0.109781i
\(775\) −27874.2 + 13383.9i −1.29196 + 0.620341i
\(776\)