Properties

Label 15.4.e.a.2.2
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 2.2
Root \(-1.18766 - 1.18766i\)
Character \(\chi\) = 15.2
Dual form 15.4.e.a.8.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.18766 + 1.18766i) q^{2} +(5.11173 + 0.932827i) q^{3} +5.17891i q^{4} +(-2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 - 13.3578i) q^{7} +(-15.6521 - 15.6521i) q^{8} +(25.2597 + 9.53673i) q^{9} +O(q^{10})\) \(q+(-1.18766 + 1.18766i) q^{2} +(5.11173 + 0.932827i) 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} +(-4.83102 + 26.4732i) q^{12} +(14.1789 - 14.1789i) q^{13} +31.7292 q^{14} +(-2.51595 - 58.0402i) q^{15} -4.25236 q^{16} +(-18.5587 + 18.5587i) q^{17} +(-41.3264 + 18.6736i) 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} +(120.225 + 72.3121i) q^{27} +(69.1789 - 69.1789i) q^{28} -125.854 q^{29} +(71.9204 + 65.9442i) q^{30} +247.367 q^{31} +(130.267 - 130.267i) q^{32} +(-26.7874 + 146.791i) 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} +(162.191 + 29.5978i) q^{42} +(-39.3993 + 39.3993i) q^{43} -148.720 q^{44} +(41.2806 - 299.033i) q^{45} -89.7251 q^{46} +(-124.560 + 124.560i) q^{47} +(-21.7369 - 3.96671i) 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} +(-45.7770 + 250.850i) q^{57} +(149.473 - 149.473i) q^{58} +729.423 q^{59} +(300.585 - 13.0299i) q^{60} +2.00000 q^{61} +(-293.789 + 293.789i) q^{62} +(-210.024 - 464.804i) 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} +(-246.097 - 544.637i) q^{72} +(-279.927 + 279.927i) q^{73} +302.767 q^{74} +(-626.480 + 171.458i) q^{75} -254.147 q^{76} +(383.589 - 383.589i) q^{77} +(-31.4172 + 172.161i) 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} +(-643.334 - 117.400i) q^{87} +(449.473 - 449.473i) q^{88} -1417.21 q^{89} +(306.124 + 404.179i) q^{90} -378.799 q^{91} +(-195.627 + 195.627i) q^{92} +(1264.48 + 230.751i) 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 −0.885170 0.465267i \(-0.845958\pi\)
0.465267 + 0.885170i \(0.345958\pi\)
\(3\) 5.11173 + 0.932827i 0.983754 + 0.179523i
\(4\) 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 \(0.128757\pi\)
−0.919299 + 0.393560i \(0.871243\pi\)
\(12\) −4.83102 + 26.4732i −0.116216 + 0.636846i
\(13\) 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
\(15\) −2.51595 58.0402i −0.0433078 0.999062i
\(16\) −4.25236 −0.0664431
\(17\) −18.5587 + 18.5587i −0.264773 + 0.264773i −0.826990 0.562217i \(-0.809949\pi\)
0.562217 + 0.826990i \(0.309949\pi\)
\(18\) −41.3264 + 18.6736i −0.541152 + 0.244522i
\(19\) 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 0.857288 0.514837i \(-0.172148\pi\)
−0.514837 + 0.857288i \(0.672148\pi\)
\(24\) −65.4088 94.6102i −0.556313 0.804676i
\(25\) −112.684 + 54.1055i −0.901469 + 0.432844i
\(26\) 33.6796i 0.254042i
\(27\) 120.225 + 72.3121i 0.856935 + 0.515425i
\(28\) 69.1789 69.1789i 0.466914 0.466914i
\(29\) −125.854 −0.805882 −0.402941 0.915226i \(-0.632012\pi\)
−0.402941 + 0.915226i \(0.632012\pi\)
\(30\) 71.9204 + 65.9442i 0.437694 + 0.401324i
\(31\) 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
\(33\) −26.7874 + 146.791i −0.141306 + 0.774333i
\(34\) 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 \(-0.733211\pi\)
0.668845 0.743402i \(-0.266789\pi\)
\(42\) 162.191 + 29.5978i 0.595873 + 0.108739i
\(43\) −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
\(45\) 41.2806 299.033i 0.136750 0.990606i
\(46\) −89.7251 −0.287592
\(47\) −124.560 + 124.560i −0.386575 + 0.386575i −0.873464 0.486889i \(-0.838132\pi\)
0.486889 + 0.873464i \(0.338132\pi\)
\(48\) −21.7369 3.96671i −0.0653637 0.0119280i
\(49\) 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 \(-0.155005\pi\)
−0.467943 + 0.883759i \(0.655005\pi\)
\(54\) −228.669 + 56.9040i −0.576257 + 0.143401i
\(55\) 313.051 71.2618i 0.767487 0.174708i
\(56\) 418.156i 0.997830i
\(57\) −45.7770 + 250.850i −0.106374 + 0.582912i
\(58\) 149.473 149.473i 0.338392 0.338392i
\(59\) 729.423 1.60954 0.804769 0.593588i \(-0.202289\pi\)
0.804769 + 0.593588i \(0.202289\pi\)
\(60\) 300.585 13.0299i 0.646756 0.0280359i
\(61\) 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
\(63\) −210.024 464.804i −0.420009 0.929520i
\(64\) 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 \(0.0458518\pi\)
−0.989643 + 0.143550i \(0.954148\pi\)
\(72\) −246.097 544.637i −0.402817 0.891474i
\(73\) −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
\(75\) −626.480 + 171.458i −0.964529 + 0.263978i
\(76\) −254.147 −0.383587
\(77\) 383.589 383.589i 0.567714 0.567714i
\(78\) −31.4172 + 172.161i −0.0456064 + 0.249915i
\(79\) 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 0.605111 0.796141i \(-0.293129\pi\)
−0.796141 + 0.605111i \(0.793129\pi\)
\(84\) 418.156 289.092i 0.543150 0.375507i
\(85\) 248.371 + 156.262i 0.316937 + 0.199400i
\(86\) 93.5862i 0.117345i
\(87\) −643.334 117.400i −0.792789 0.144674i
\(88\) 449.473 449.473i 0.544477 0.544477i
\(89\) −1417.21 −1.68790 −0.843952 0.536419i \(-0.819777\pi\)
−0.843952 + 0.536419i \(0.819777\pi\)
\(90\) 306.124 + 404.179i 0.358536 + 0.473380i
\(91\) −378.799 −0.436361
\(92\) −195.627 + 195.627i −0.221690 + 0.221690i
\(93\) 1264.48 + 230.751i 1.40989 + 0.257288i
\(94\) 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 \(-0.946807\pi\)
0.986070 0.166333i \(-0.0531926\pi\)
\(102\) 41.1217 225.340i 0.0399182 0.218745i
\(103\) −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
\(105\) −741.683 + 808.899i −0.689342 + 0.751814i
\(106\) −381.100 −0.349205
\(107\) 596.188 596.188i 0.538651 0.538651i −0.384481 0.923133i \(-0.625620\pi\)
0.923133 + 0.384481i \(0.125620\pi\)
\(108\) −374.498 + 622.632i −0.333667 + 0.554748i
\(109\) 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 0.585154 0.810922i \(-0.301034\pi\)
−0.810922 + 0.585154i \(0.801034\pi\)
\(114\) −243.558 352.294i −0.200099 0.289433i
\(115\) 318.051 505.527i 0.257899 0.409919i
\(116\) 651.788i 0.521698i
\(117\) 493.375 222.934i 0.389851 0.176156i
\(118\) −866.309 + 866.309i −0.675849 + 0.675849i
\(119\) 495.806 0.381937
\(120\) −869.073 + 947.833i −0.661126 + 0.721041i
\(121\) 506.367 0.380441
\(122\) −2.37533 + 2.37533i −0.00176272 + 0.00176272i
\(123\) 364.108 1995.25i 0.266915 1.46265i
\(124\) 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 \(0.229460\pi\)
−0.751231 + 0.660039i \(0.770540\pi\)
\(132\) −760.216 138.730i −0.501275 0.0914763i
\(133\) 655.514 655.514i 0.427371 0.427371i
\(134\) 783.827 0.505316
\(135\) 489.962 1490.07i 0.312364 0.949962i
\(136\) 580.964 0.366304
\(137\) −507.451 + 507.451i −0.316456 + 0.316456i −0.847404 0.530948i \(-0.821836\pi\)
0.530948 + 0.847404i \(0.321836\pi\)
\(138\) −458.651 83.6979i −0.282920 0.0516293i
\(139\) 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
\(147\) −12.9313 + 70.8616i −0.00725550 + 0.0397590i
\(148\) 660.121 660.121i 0.366632 0.366632i
\(149\) −363.356 −0.199780 −0.0998902 0.994998i \(-0.531849\pi\)
−0.0998902 + 0.994998i \(0.531849\pi\)
\(150\) 540.413 947.683i 0.294163 0.515853i
\(151\) −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
\(153\) −645.774 + 291.797i −0.341227 + 0.154185i
\(154\) 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
\(162\) −1221.98 + 77.5696i −0.592639 + 0.0376200i
\(163\) 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
\(165\) 1666.71 72.2492i 0.786382 0.0340884i
\(166\) 343.119 0.160429
\(167\) −3009.65 + 3009.65i −1.39457 + 1.39457i −0.579848 + 0.814724i \(0.696888\pi\)
−0.814724 + 0.579848i \(0.803112\pi\)
\(168\) −390.067 + 2137.50i −0.179133 + 0.981619i
\(169\) 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 \(-0.443656\pi\)
−0.984375 + 0.176086i \(0.943656\pi\)
\(174\) 903.497 624.633i 0.393643 0.272145i
\(175\) 2227.94 + 782.476i 0.962379 + 0.337998i
\(176\) 122.113i 0.0522987i
\(177\) 3728.61 + 680.425i 1.58339 + 0.288948i
\(178\) 1683.16 1683.16i 0.708755 0.708755i
\(179\) 821.582 0.343061 0.171530 0.985179i \(-0.445129\pi\)
0.171530 + 0.985179i \(0.445129\pi\)
\(180\) 1548.67 + 213.788i 0.641282 + 0.0885269i
\(181\) 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
\(183\) 10.2235 + 1.86565i 0.00412973 + 0.000753623i
\(184\) 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 \(0.943562\pi\)
\(192\) −256.909 + 1407.82i −0.0965666 + 0.529169i
\(193\) −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
\(195\) −858.621 787.274i −0.315319 0.289117i
\(196\) −71.7928 −0.0261636
\(197\) 2995.05 2995.05i 1.08319 1.08319i 0.0869796 0.996210i \(-0.472279\pi\)
0.996210 0.0869796i \(-0.0277215\pi\)
\(198\) −536.238 1186.75i −0.192469 0.425952i
\(199\) 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
\(207\) 593.915 + 1314.39i 0.199420 + 0.441336i
\(208\) −60.2938 + 60.2938i −0.0200991 + 0.0200991i
\(209\) −1409.21 −0.466399
\(210\) −79.8292 1841.57i −0.0262321 0.605145i
\(211\) 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
\(213\) −160.222 + 877.989i −0.0515409 + 0.282436i
\(214\) 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
\(222\) 1547.67 + 282.429i 0.467894 + 0.0853847i
\(223\) 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
\(225\) −3362.34 + 292.053i −0.996249 + 0.0865343i
\(226\) 644.173 0.189601
\(227\) 1398.96 1398.96i 0.409042 0.409042i −0.472362 0.881404i \(-0.656599\pi\)
0.881404 + 0.472362i \(0.156599\pi\)
\(228\) −1299.13 237.075i −0.377356 0.0688626i
\(229\) 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 0.928427 0.371515i \(-0.121162\pi\)
−0.371515 + 0.928427i \(0.621162\pi\)
\(234\) −321.193 + 850.735i −0.0897309 + 0.237668i
\(235\) 1667.00 + 1048.79i 0.462736 + 0.291129i
\(236\) 3777.61i 1.04196i
\(237\) −44.7933 + 245.460i −0.0122769 + 0.0672756i
\(238\) −588.851 + 588.851i −0.160376 + 0.160376i
\(239\) 2976.20 0.805500 0.402750 0.915310i \(-0.368054\pi\)
0.402750 + 0.915310i \(0.368054\pi\)
\(240\) 10.6987 + 246.808i 0.00287750 + 0.0663808i
\(241\) 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
\(243\) 2347.21 + 2973.13i 0.619645 + 0.784882i
\(244\) 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 \(-0.0621145\pi\)
\(252\) 2407.18 1087.70i 0.601738 0.271898i
\(253\) −1084.73 + 1084.73i −0.269550 + 0.269550i
\(254\) −250.805 −0.0619564
\(255\) 1123.84 + 1030.46i 0.275991 + 0.253057i
\(256\) −3901.74 −0.952572
\(257\) 428.853 428.853i 0.104090 0.104090i −0.653144 0.757234i \(-0.726550\pi\)
0.757234 + 0.653144i \(0.226550\pi\)
\(258\) 87.2997 478.388i 0.0210660 0.115438i
\(259\) 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 \(-0.913120\pi\)
−0.269565 0.962982i \(-0.586880\pi\)
\(264\) 2716.87 1878.31i 0.633377 0.437885i
\(265\) 1350.89 2147.18i 0.313150 0.497738i
\(266\) 1557.06i 0.358908i
\(267\) −7244.38 1322.01i −1.66048 0.303017i
\(268\) 1708.97 1708.97i 0.389523 0.389523i
\(269\) 1930.34 0.437528 0.218764 0.975778i \(-0.429797\pi\)
0.218764 + 0.975778i \(0.429797\pi\)
\(270\) 1187.79 + 2351.61i 0.267729 + 0.530054i
\(271\) −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
\(273\) −1936.32 353.353i −0.429272 0.0783367i
\(274\) 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 \(-0.861091\pi\)
0.906281 0.422676i \(-0.138909\pi\)
\(282\) 275.997 1512.42i 0.0582815 0.319373i
\(283\) −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
\(285\) 2848.24 123.467i 0.591982 0.0256615i
\(286\) −967.156 −0.199962
\(287\) −5213.93 + 5213.93i −1.07236 + 1.07236i
\(288\) 4532.83 2048.19i 0.927429 0.419064i
\(289\) 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 \(-0.0303353\pi\)
−0.0951570 + 0.995462i \(0.530335\pi\)
\(294\) −68.8017 99.5179i −0.0136483 0.0197415i
\(295\) −1810.11 7951.77i −0.357250 1.56939i
\(296\) 3990.14i 0.783521i
\(297\) −2076.54 + 3452.42i −0.405701 + 0.674511i
\(298\) 431.545 431.545i 0.0838883 0.0838883i
\(299\) 1071.18 0.207184
\(300\) −887.968 3244.48i −0.170889 0.624401i
\(301\) 1052.58 0.201560
\(302\) 2474.07 2474.07i 0.471413 0.471413i
\(303\) 314.986 1726.07i 0.0597210 0.327261i
\(304\) 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 \(-0.880866\pi\)
0.930775 0.365592i \(-0.119134\pi\)
\(312\) −2268.89 414.044i −0.411701 0.0751303i
\(313\) 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
\(315\) −4545.85 + 3443.01i −0.813110 + 0.615847i
\(316\) −248.685 −0.0442710
\(317\) −3112.10 + 3112.10i −0.551397 + 0.551397i −0.926844 0.375447i \(-0.877489\pi\)
0.375447 + 0.926844i \(0.377489\pi\)
\(318\) −1948.08 355.500i −0.343531 0.0626901i
\(319\) 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
\(327\) 1935.24 10604.8i 0.327275 1.79342i
\(328\) −6109.45 + 6109.45i −1.02847 + 1.02847i
\(329\) 3327.71 0.557637
\(330\) −1893.68 + 2065.30i −0.315890 + 0.344518i
\(331\) −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
\(333\) −2004.10 4435.26i −0.329801 0.729883i
\(334\) 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
\(342\) −916.377 2028.03i −0.144889 0.320653i
\(343\) −4396.56 + 4396.56i −0.692104 + 0.692104i
\(344\) 1233.36 0.193310
\(345\) 2097.36 2287.44i 0.327299 0.356960i
\(346\) 4368.77 0.678805
\(347\) 8177.44 8177.44i 1.26509 1.26509i 0.316503 0.948592i \(-0.397491\pi\)
0.948592 0.316503i \(-0.102509\pi\)
\(348\) 608.005 3331.77i 0.0936566 0.513223i
\(349\) 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 0.999060 0.0433491i \(-0.0138028\pi\)
−0.0433491 + 0.999060i \(0.513803\pi\)
\(354\) −5236.46 + 3620.23i −0.786199 + 0.543539i
\(355\) 1872.43 426.233i 0.279939 0.0637242i
\(356\) 7339.58i 1.09269i
\(357\) 2534.43 + 462.501i 0.375732 + 0.0685663i
\(358\) −975.763 + 975.763i −0.144052 + 0.144052i
\(359\) −8827.47 −1.29776 −0.648880 0.760890i \(-0.724762\pi\)
−0.648880 + 0.760890i \(0.724762\pi\)
\(360\) −5326.63 + 4034.38i −0.779828 + 0.590640i
\(361\) 4450.80 0.648899
\(362\) −2748.50 + 2748.50i −0.399055 + 0.399055i
\(363\) 2588.42 + 472.353i 0.374261 + 0.0682978i
\(364\) 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
\(372\) −1195.04 + 6548.60i −0.166559 + 0.912713i
\(373\) 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
\(375\) 3423.80 + 6404.06i 0.471478 + 0.881878i
\(376\) 3899.27 0.534812
\(377\) −1784.48 + 1784.48i −0.243781 + 0.243781i
\(378\) 3814.63 + 2294.40i 0.519057 + 0.312200i
\(379\) 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 0.584880 0.811120i \(-0.301142\pi\)
−0.811120 + 0.584880i \(0.801142\pi\)
\(384\) 2988.11 + 4322.14i 0.397100 + 0.574383i
\(385\) −5133.58 3229.77i −0.679562 0.427544i
\(386\) 6231.15i 0.821650i
\(387\) −1370.95 + 619.472i −0.180076 + 0.0813683i
\(388\) −4703.02 + 4703.02i −0.615361 + 0.615361i
\(389\) −12362.2 −1.61128 −0.805640 0.592405i \(-0.798178\pi\)
−0.805640 + 0.592405i \(0.798178\pi\)
\(390\) 1954.77 84.7362i 0.253804 0.0110020i
\(391\) −1402.06 −0.181343
\(392\) 216.978 216.978i 0.0279567 0.0279567i
\(393\) −1846.32 + 10117.5i −0.236984 + 1.29863i
\(394\) 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 \(0.0453688\pi\)
−0.989860 + 0.142048i \(0.954631\pi\)
\(402\) 4006.72 + 731.175i 0.497107 + 0.0907156i
\(403\) 3507.40 3507.40i 0.433538 0.433538i
\(404\) 1748.75 0.215356
\(405\) 3894.53 7159.80i 0.477829 0.878453i
\(406\) −3993.26 −0.488133
\(407\) 3660.29 3660.29i 0.445783 0.445783i
\(408\) 2969.74 + 541.939i 0.360352 + 0.0657597i
\(409\) 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
\(417\) −63.8364 + 349.813i −0.00749660 + 0.0410801i
\(418\) 1673.67 1673.67i 0.195842 0.195842i
\(419\) −2142.28 −0.249779 −0.124889 0.992171i \(-0.539858\pi\)
−0.124889 + 0.992171i \(0.539858\pi\)
\(420\) −4189.21 3841.11i −0.486697 0.446255i
\(421\) −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
\(423\) −4334.26 + 1958.46i −0.498200 + 0.225115i
\(424\) 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 \(0.659065\pi\)
\(432\) −511.238 307.497i −0.0569374 0.0342464i
\(433\) 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
\(435\) 316.644 + 7304.62i 0.0349009 + 0.805126i
\(436\) 10744.2 1.18016
\(437\) −1853.69 + 1853.69i −0.202915 + 0.202915i
\(438\) 620.253 3398.88i 0.0676640 0.370787i
\(439\) 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 0.594115 0.804380i \(-0.297502\pi\)
−0.804380 + 0.594115i \(0.797502\pi\)
\(444\) 3990.14 2758.58i 0.426495 0.294857i
\(445\) 3516.89 + 15449.6i 0.374644 + 1.64580i
\(446\) 6723.34i 0.713810i
\(447\) −1857.38 338.948i −0.196535 0.0358651i
\(448\) 3678.86 3678.86i 0.387968 0.387968i
\(449\) 17849.2 1.87607 0.938036 0.346537i \(-0.112643\pi\)
0.938036 + 0.346537i \(0.112643\pi\)
\(450\) 3646.47 4340.19i 0.381992 0.454664i
\(451\) 11208.8 1.17029
\(452\) 1404.49 1404.49i 0.146154 0.146154i
\(453\) −10648.5 1943.21i −1.10443 0.201545i
\(454\) 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 \(0.147495\pi\)
−0.894552 + 0.446965i \(0.852505\pi\)
\(462\) −849.944 + 4657.55i −0.0855908 + 0.469024i
\(463\) 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
\(465\) −622.365 14357.3i −0.0620677 1.43183i
\(466\) −4704.83 −0.467697
\(467\) −1479.96 + 1479.96i −0.146647 + 0.146647i −0.776618 0.629971i \(-0.783067\pi\)
0.629971 + 0.776618i \(0.283067\pi\)
\(468\) 1154.56 + 2555.14i 0.114037 + 0.252375i
\(469\) 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
\(477\) 2522.60 + 5582.76i 0.242143 + 0.535885i
\(478\) −3534.73 + 3534.73i −0.338231 + 0.338231i
\(479\) −5039.60 −0.480720 −0.240360 0.970684i \(-0.577266\pi\)
−0.240360 + 0.970684i \(0.577266\pi\)
\(480\) −7888.49 7233.00i −0.750122 0.687791i
\(481\) −3614.58 −0.342642
\(482\) −2179.89 + 2179.89i −0.205999 + 0.205999i
\(483\) 941.362 5158.51i 0.0886821 0.485963i
\(484\) 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 \(-0.780084\pi\)
0.770681 0.637221i \(-0.219916\pi\)
\(492\) 10333.2 + 1885.68i 0.946865 + 0.172791i
\(493\) 2335.69 2335.69i 0.213375 0.213375i
\(494\) −1652.77 −0.150530
\(495\) 8587.17 + 1185.43i 0.779726 + 0.107639i
\(496\) −1051.89 −0.0952247
\(497\) 2294.33 2294.33i 0.207072 0.207072i
\(498\) 1753.93 + 320.070i 0.157822 + 0.0288006i
\(499\) 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 0.964106 0.265517i \(-0.0855427\pi\)
−0.265517 + 0.964106i \(0.585543\pi\)
\(504\) −3987.84 + 10562.5i −0.352445 + 0.933513i
\(505\) −3681.07 + 837.946i −0.324368 + 0.0738379i
\(506\) 2576.58i 0.226370i
\(507\) −1674.35 + 9175.14i −0.146667 + 0.803713i
\(508\) −546.829 + 546.829i −0.0477590 + 0.0477590i
\(509\) −1788.46 −0.155741 −0.0778704 0.996963i \(-0.524812\pi\)
−0.0778704 + 0.996963i \(0.524812\pi\)
\(510\) −2558.58 + 110.911i −0.222149 + 0.00962981i
\(511\) 7478.42 0.647408
\(512\) −1086.41 + 1086.41i −0.0937754 + 0.0937754i
\(513\) −3548.60 + 5899.84i −0.305409 + 0.507766i
\(514\) 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 \(-0.278444\pi\)
\(522\) 5201.11 2350.15i 0.436104 0.197056i
\(523\) −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
\(525\) 10658.7 + 6078.09i 0.886066 + 0.505276i
\(526\) 12487.1 1.03510
\(527\) −4590.80 + 4590.80i −0.379466 + 0.379466i
\(528\) 113.910 624.207i 0.00938880 0.0514491i
\(529\) 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
\(537\) 4199.71 + 766.393i 0.337488 + 0.0615872i
\(538\) −2292.60 + 2292.60i −0.183719 + 0.183719i
\(539\) −398.082 −0.0318119
\(540\) 7716.94 + 2537.47i 0.614971 + 0.202213i
\(541\) −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
\(543\) 11829.6 + 2158.75i 0.934911 + 0.170609i
\(544\) 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
\(552\) 1103.05 6044.52i 0.0850522 0.466072i
\(553\) 641.427 641.427i 0.0493242 0.0493242i
\(554\) −11557.3 −0.886324
\(555\) −7077.31 + 7718.69i −0.541288 + 0.590343i
\(556\) −354.410 −0.0270329
\(557\) 8716.96 8716.96i 0.663105 0.663105i −0.293006 0.956111i \(-0.594656\pi\)
0.956111 + 0.293006i \(0.0946555\pi\)
\(558\) −10222.8 + 4619.23i −0.775566 + 0.350444i
\(559\) 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 \(-0.0374759\pi\)
−0.117462 + 0.993077i \(0.537476\pi\)
\(564\) −2695.76 3899.27i −0.201262 0.291115i
\(565\) −2283.42 + 3629.39i −0.170025 + 0.270247i
\(566\) 9721.40i 0.721945i
\(567\) −872.435 13743.7i −0.0646188 1.01796i
\(568\) 2688.40 2688.40i 0.198596 0.198596i
\(569\) 11517.5 0.848576 0.424288 0.905527i \(-0.360524\pi\)
0.424288 + 0.905527i \(0.360524\pi\)
\(570\) −3236.11 + 3529.38i −0.237799 + 0.259350i
\(571\) −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
\(573\) −868.617 + 4759.88i −0.0633281 + 0.347027i
\(574\) 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
\(582\) −11026.3 2012.16i −0.785320 0.143311i
\(583\) −4607.29 + 4607.29i −0.327297 + 0.327297i
\(584\) 8762.89 0.620909
\(585\) −3654.65 4825.28i −0.258293 0.341027i
\(586\) −10725.4 −0.756081
\(587\) 8524.33 8524.33i 0.599381 0.599381i −0.340767 0.940148i \(-0.610687\pi\)
0.940148 + 0.340767i \(0.110687\pi\)
\(588\) −366.986 66.9702i −0.0257385 0.00469695i
\(589\) 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 \(-0.322008\pi\)
−0.847691 + 0.530491i \(0.822008\pi\)
\(594\) −1634.08 6566.55i −0.112874 0.453584i
\(595\) −1230.38 5405.01i −0.0847740 0.372410i
\(596\) 1881.79i 0.129331i
\(597\) 102.105 559.518i 0.00699979 0.0383577i
\(598\) −1272.20 + 1272.20i −0.0869971 + 0.0869971i
\(599\) −10195.8 −0.695477 −0.347738 0.937592i \(-0.613050\pi\)
−0.347738 + 0.937592i \(0.613050\pi\)
\(600\) 12489.4 + 7122.05i 0.849798 + 0.484594i
\(601\) 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
\(603\) −5188.36 11482.4i −0.350392 0.775452i
\(604\) 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
\(612\) −1511.19 3344.41i −0.0998140 0.220898i
\(613\) 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
\(615\) −22654.7 + 982.047i −1.48541 + 0.0643902i
\(616\) −12007.9 −0.785412
\(617\) −17118.9 + 17118.9i −1.11698 + 1.11698i −0.124803 + 0.992182i \(0.539830\pi\)
−0.992182 + 0.124803i \(0.960170\pi\)
\(618\) 2068.43 11334.7i 0.134635 0.737778i
\(619\) 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
\(627\) −7203.53 1314.55i −0.458822 0.0837291i
\(628\) 6258.80 6258.80i 0.397697 0.397697i
\(629\) 4731.09 0.299906
\(630\) 1309.80 9488.09i 0.0828312 0.600023i
\(631\) −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
\(633\) 13878.0 + 2532.57i 0.871410 + 0.159021i
\(634\) 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 \(0.875402\pi\)
\(642\) −1321.02 + 7238.95i −0.0812092 + 0.445013i
\(643\) −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
\(645\) 2385.87 + 2187.62i 0.145649 + 0.133546i
\(646\) 2163.30 0.131755
\(647\) −2391.21 + 2391.21i −0.145299 + 0.145299i −0.776014 0.630716i \(-0.782761\pi\)
0.630716 + 0.776014i \(0.282761\pi\)
\(648\) −1022.28 16104.3i −0.0619738 0.976292i
\(649\) 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 \(-0.498793\pi\)
−0.999993 + 0.00379136i \(0.998793\pi\)
\(654\) 10296.5 + 14893.4i 0.615636 + 0.890484i
\(655\) 21577.0 4911.71i 1.28715 0.293002i
\(656\) 1659.81i 0.0987878i
\(657\) −9740.43 + 4401.27i −0.578403 + 0.261354i
\(658\) −3952.20 + 3952.20i −0.234153 + 0.234153i
\(659\) 20089.8 1.18754 0.593768 0.804636i \(-0.297640\pi\)
0.593768 + 0.804636i \(0.297640\pi\)
\(660\) 374.172 + 8631.73i 0.0220676 + 0.509075i
\(661\) 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
\(663\) −490.931 + 2690.22i −0.0287574 + 0.157586i
\(664\) 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
\(672\) −17789.7 3246.40i −1.02121 0.186358i
\(673\) −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
\(675\) −17459.8 1643.58i −0.995599 0.0937207i
\(676\) −9295.71 −0.528887
\(677\) −14662.4 + 14662.4i −0.832380 + 0.832380i −0.987842 0.155462i \(-0.950313\pi\)
0.155462 + 0.987842i \(0.450313\pi\)
\(678\) 3292.84 + 600.902i 0.186520 + 0.0340376i
\(679\) 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 \(-0.468212\pi\)
−0.995018 + 0.0996976i \(0.968212\pi\)
\(684\) −6419.67 2423.73i −0.358863 0.135488i
\(685\) 6791.23 + 4272.68i 0.378803 + 0.238322i
\(686\) 10443.3i 0.581233i
\(687\) 3666.36 20091.1i 0.203611 1.11575i
\(688\) 167.540 167.540i 0.00928400 0.00928400i
\(689\) 4549.75 0.251570
\(690\) 225.744 + 5207.66i 0.0124550 + 0.287322i
\(691\) −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
\(693\) 13347.5 6031.14i 0.731645 0.330598i
\(694\) 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 \(0.939695\pi\)
\(702\) −2435.44 + 4049.11i −0.130940 + 0.217698i
\(703\) 6255.06 6255.06i 0.335582 0.335582i
\(704\) −7908.75 −0.423398
\(705\) 7542.91 + 6916.13i 0.402954 + 0.369470i
\(706\) −15056.1 −0.802611
\(707\) −4510.51 + 4510.51i −0.239936 + 0.239936i
\(708\) −3523.86 + 19310.2i −0.187055 + 1.02503i
\(709\) 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
\(717\) 15213.6 + 2776.28i 0.792414 + 0.144605i
\(718\) 10484.1 10484.1i 0.544933 0.544933i
\(719\) −20143.8 −1.04484 −0.522418 0.852690i \(-0.674970\pi\)
−0.522418 + 0.852690i \(0.674970\pi\)
\(720\) −175.540 + 1271.60i −0.00908609 + 0.0658189i
\(721\) 24939.2 1.28819
\(722\) −5286.05 + 5286.05i −0.272474 + 0.272474i
\(723\) 9382.32 + 1712.15i 0.482617 + 0.0880715i
\(724\) 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
\(732\) −9.66205 + 52.9464i −0.000487868 + 0.00267344i
\(733\) 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
\(735\) 804.585 34.8775i 0.0403776 0.00175031i
\(736\) 9841.37 0.492877
\(737\) 9476.04 9476.04i 0.473615 0.473615i
\(738\) 7288.81 + 16130.8i 0.363557 + 0.804586i
\(739\) 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 0.559977 0.828508i \(-0.310810\pi\)
−0.828508 + 0.559977i \(0.810810\pi\)
\(744\) −16180.0 23403.5i −0.797294 1.15324i
\(745\) 901.693 + 3961.11i 0.0443429 + 0.194797i
\(746\) 8514.27i 0.417868i
\(747\) −2271.20 5026.38i −0.111243 0.246192i
\(748\) 2760.04 2760.04i 0.134916 0.134916i
\(749\) −15927.5 −0.777009
\(750\) −11672.2 3539.54i −0.568278 0.172328i
\(751\) 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
\(753\) 1438.55 7883.01i 0.0696197 0.381505i
\(754\) 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 \(-0.778852\pi\)
0.768210 0.640198i \(-0.221148\pi\)
\(762\) −1282.05 233.958i −0.0609498 0.0111226i
\(763\) −27712.1 + 27712.1i −1.31487 + 1.31487i
\(764\) −4822.43 −0.228363
\(765\) 4783.54 + 6315.77i 0.226078 + 0.298493i
\(766\) 4028.02 0.189998
\(767\) 10342.4 10342.4i 0.486888 0.486888i
\(768\) −19944.6 3639.64i −0.937097 0.171008i
\(769\) 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 0.993335 0.115263i \(-0.0367711\pi\)
−0.115263 + 0.993335i \(0.536771\pi\)
\(774\) 892.506 2363.96i 0.0414476 0.109781i
\(775\) −27874.2 + 13383.9i −1.29196 + 0.620341i
\(776\)