Properties

Label 16.4.e.a.13.1
Level 16
Weight 4
Character 16.13
Analytic conductor 0.944
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.944030560092\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{10} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.1
Root \(1.28199 + 1.53509i\)
Character \(\chi\) = 16.13
Dual form 16.4.e.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.81708 + 0.253099i) q^{2} +(5.49618 + 5.49618i) q^{3} +(7.87188 - 1.42600i) q^{4} +(-4.66372 + 4.66372i) q^{5} +(-16.8743 - 14.0921i) q^{6} -24.8965i q^{7} +(-21.8148 + 6.00953i) q^{8} +33.4160i q^{9} +O(q^{10})\) \(q+(-2.81708 + 0.253099i) q^{2} +(5.49618 + 5.49618i) q^{3} +(7.87188 - 1.42600i) q^{4} +(-4.66372 + 4.66372i) q^{5} +(-16.8743 - 14.0921i) q^{6} -24.8965i q^{7} +(-21.8148 + 6.00953i) q^{8} +33.4160i q^{9} +(11.9577 - 14.3185i) q^{10} +(22.3431 - 22.3431i) q^{11} +(51.1028 + 35.4277i) q^{12} +(-11.2714 - 11.2714i) q^{13} +(6.30129 + 70.1355i) q^{14} -51.2653 q^{15} +(59.9330 - 22.4506i) q^{16} -88.4846 q^{17} +(-8.45756 - 94.1356i) q^{18} +(37.8187 + 37.8187i) q^{19} +(-30.0618 + 43.3627i) q^{20} +(136.836 - 136.836i) q^{21} +(-57.2873 + 68.5974i) q^{22} +48.1224i q^{23} +(-152.928 - 86.8686i) q^{24} +81.4994i q^{25} +(34.6053 + 28.8997i) q^{26} +(-35.2635 + 35.2635i) q^{27} +(-35.5025 - 195.982i) q^{28} +(10.4432 + 10.4432i) q^{29} +(144.419 - 12.9752i) q^{30} -96.9578 q^{31} +(-163.154 + 78.4142i) q^{32} +245.604 q^{33} +(249.268 - 22.3954i) q^{34} +(116.110 + 116.110i) q^{35} +(47.6513 + 263.047i) q^{36} +(-163.279 + 163.279i) q^{37} +(-116.110 - 96.9665i) q^{38} -123.899i q^{39} +(73.7114 - 129.765i) q^{40} -360.519i q^{41} +(-350.844 + 420.110i) q^{42} +(-100.249 + 100.249i) q^{43} +(144.021 - 207.744i) q^{44} +(-155.843 - 155.843i) q^{45} +(-12.1797 - 135.565i) q^{46} +220.669 q^{47} +(452.796 + 206.010i) q^{48} -276.837 q^{49} +(-20.6274 - 229.590i) q^{50} +(-486.327 - 486.327i) q^{51} +(-104.800 - 72.6542i) q^{52} +(-175.752 + 175.752i) q^{53} +(90.4150 - 108.265i) q^{54} +208.404i q^{55} +(149.616 + 543.113i) q^{56} +415.717i q^{57} +(-32.0624 - 26.7761i) q^{58} +(405.008 - 405.008i) q^{59} +(-403.555 + 73.1044i) q^{60} +(664.576 + 664.576i) q^{61} +(273.138 - 24.5399i) q^{62} +831.942 q^{63} +(439.771 - 262.193i) q^{64} +105.133 q^{65} +(-691.885 + 62.1621i) q^{66} +(-107.377 - 107.377i) q^{67} +(-696.540 + 126.179i) q^{68} +(-264.489 + 264.489i) q^{69} +(-356.480 - 297.705i) q^{70} +215.050i q^{71} +(-200.814 - 728.964i) q^{72} -668.587i q^{73} +(418.644 - 501.296i) q^{74} +(-447.935 + 447.935i) q^{75} +(351.634 + 243.775i) q^{76} +(-556.266 - 556.266i) q^{77} +(31.3588 + 349.035i) q^{78} -822.956 q^{79} +(-174.808 + 384.215i) q^{80} +514.603 q^{81} +(91.2471 + 1015.61i) q^{82} +(326.873 + 326.873i) q^{83} +(882.027 - 1272.28i) q^{84} +(412.668 - 412.668i) q^{85} +(257.037 - 307.783i) q^{86} +114.795i q^{87} +(-353.139 + 621.682i) q^{88} -262.733i q^{89} +(478.466 + 399.578i) q^{90} +(-280.619 + 280.619i) q^{91} +(68.6226 + 378.814i) q^{92} +(-532.898 - 532.898i) q^{93} +(-621.643 + 55.8512i) q^{94} -352.752 q^{95} +(-1327.70 - 465.745i) q^{96} -150.801 q^{97} +(779.871 - 70.0671i) q^{98} +(746.618 + 746.618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} - 68q^{10} + 18q^{11} + 100q^{12} - 2q^{13} + 188q^{14} - 124q^{15} + 280q^{16} - 4q^{17} + 174q^{18} - 26q^{19} - 196q^{20} + 52q^{21} - 588q^{22} - 848q^{24} - 264q^{26} + 184q^{27} + 280q^{28} - 202q^{29} + 1236q^{30} + 368q^{31} + 968q^{32} - 4q^{33} + 436q^{34} + 476q^{35} - 596q^{36} - 10q^{37} - 1232q^{38} - 1336q^{40} - 680q^{42} - 838q^{43} + 868q^{44} + 194q^{45} + 1132q^{46} - 944q^{47} + 1768q^{48} + 94q^{49} + 726q^{50} - 1500q^{51} - 236q^{52} - 378q^{53} - 1376q^{54} - 488q^{56} + 8q^{58} + 1706q^{59} - 192q^{60} + 910q^{61} - 80q^{62} + 2628q^{63} + 512q^{64} - 492q^{65} - 428q^{66} + 1942q^{67} - 880q^{68} + 580q^{69} + 160q^{70} + 1092q^{72} - 452q^{74} - 2954q^{75} - 1228q^{76} - 268q^{77} - 772q^{78} - 4416q^{79} - 2648q^{80} + 482q^{81} - 704q^{82} - 2562q^{83} + 1960q^{84} - 12q^{85} + 3764q^{86} + 1528q^{88} + 1896q^{90} + 3332q^{91} + 632q^{92} - 2192q^{93} - 3248q^{94} + 6900q^{95} - 4432q^{96} - 4q^{97} + 314q^{98} + 4958q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81708 + 0.253099i −0.995988 + 0.0894841i
\(3\) 5.49618 + 5.49618i 1.05774 + 1.05774i 0.998228 + 0.0595129i \(0.0189548\pi\)
0.0595129 + 0.998228i \(0.481045\pi\)
\(4\) 7.87188 1.42600i 0.983985 0.178250i
\(5\) −4.66372 + 4.66372i −0.417136 + 0.417136i −0.884215 0.467079i \(-0.845306\pi\)
0.467079 + 0.884215i \(0.345306\pi\)
\(6\) −16.8743 14.0921i −1.14815 0.958846i
\(7\) 24.8965i 1.34429i −0.740422 0.672143i \(-0.765374\pi\)
0.740422 0.672143i \(-0.234626\pi\)
\(8\) −21.8148 + 6.00953i −0.964087 + 0.265586i
\(9\) 33.4160i 1.23763i
\(10\) 11.9577 14.3185i 0.378136 0.452790i
\(11\) 22.3431 22.3431i 0.612427 0.612427i −0.331151 0.943578i \(-0.607437\pi\)
0.943578 + 0.331151i \(0.107437\pi\)
\(12\) 51.1028 + 35.4277i 1.22934 + 0.852259i
\(13\) −11.2714 11.2714i −0.240471 0.240471i 0.576574 0.817045i \(-0.304389\pi\)
−0.817045 + 0.576574i \(0.804389\pi\)
\(14\) 6.30129 + 70.1355i 0.120292 + 1.33889i
\(15\) −51.2653 −0.882443
\(16\) 59.9330 22.4506i 0.936454 0.350791i
\(17\) −88.4846 −1.26239 −0.631196 0.775623i \(-0.717436\pi\)
−0.631196 + 0.775623i \(0.717436\pi\)
\(18\) −8.45756 94.1356i −0.110748 1.23266i
\(19\) 37.8187 + 37.8187i 0.456643 + 0.456643i 0.897552 0.440909i \(-0.145344\pi\)
−0.440909 + 0.897552i \(0.645344\pi\)
\(20\) −30.0618 + 43.3627i −0.336101 + 0.484810i
\(21\) 136.836 136.836i 1.42191 1.42191i
\(22\) −57.2873 + 68.5974i −0.555168 + 0.664773i
\(23\) 48.1224i 0.436270i 0.975919 + 0.218135i \(0.0699973\pi\)
−0.975919 + 0.218135i \(0.930003\pi\)
\(24\) −152.928 86.8686i −1.30068 0.738833i
\(25\) 81.4994i 0.651995i
\(26\) 34.6053 + 28.8997i 0.261025 + 0.217988i
\(27\) −35.2635 + 35.2635i −0.251351 + 0.251351i
\(28\) −35.5025 195.982i −0.239619 1.32276i
\(29\) 10.4432 + 10.4432i 0.0668705 + 0.0668705i 0.739751 0.672881i \(-0.234943\pi\)
−0.672881 + 0.739751i \(0.734943\pi\)
\(30\) 144.419 12.9752i 0.878903 0.0789646i
\(31\) −96.9578 −0.561746 −0.280873 0.959745i \(-0.590624\pi\)
−0.280873 + 0.959745i \(0.590624\pi\)
\(32\) −163.154 + 78.4142i −0.901307 + 0.433181i
\(33\) 245.604 1.29558
\(34\) 249.268 22.3954i 1.25733 0.112964i
\(35\) 116.110 + 116.110i 0.560750 + 0.560750i
\(36\) 47.6513 + 263.047i 0.220608 + 1.21781i
\(37\) −163.279 + 163.279i −0.725484 + 0.725484i −0.969717 0.244233i \(-0.921464\pi\)
0.244233 + 0.969717i \(0.421464\pi\)
\(38\) −116.110 96.9665i −0.495673 0.413949i
\(39\) 123.899i 0.508713i
\(40\) 73.7114 129.765i 0.291370 0.512941i
\(41\) 360.519i 1.37326i −0.727008 0.686629i \(-0.759090\pi\)
0.727008 0.686629i \(-0.240910\pi\)
\(42\) −350.844 + 420.110i −1.28896 + 1.54344i
\(43\) −100.249 + 100.249i −0.355531 + 0.355531i −0.862163 0.506632i \(-0.830890\pi\)
0.506632 + 0.862163i \(0.330890\pi\)
\(44\) 144.021 207.744i 0.493454 0.711785i
\(45\) −155.843 155.843i −0.516260 0.516260i
\(46\) −12.1797 135.565i −0.0390392 0.434520i
\(47\) 220.669 0.684849 0.342425 0.939545i \(-0.388752\pi\)
0.342425 + 0.939545i \(0.388752\pi\)
\(48\) 452.796 + 206.010i 1.36157 + 0.619479i
\(49\) −276.837 −0.807104
\(50\) −20.6274 229.590i −0.0583432 0.649379i
\(51\) −486.327 486.327i −1.33528 1.33528i
\(52\) −104.800 72.6542i −0.279484 0.193756i
\(53\) −175.752 + 175.752i −0.455498 + 0.455498i −0.897174 0.441676i \(-0.854384\pi\)
0.441676 + 0.897174i \(0.354384\pi\)
\(54\) 90.4150 108.265i 0.227850 0.272834i
\(55\) 208.404i 0.510931i
\(56\) 149.616 + 543.113i 0.357024 + 1.29601i
\(57\) 415.717i 0.966019i
\(58\) −32.0624 26.7761i −0.0725861 0.0606184i
\(59\) 405.008 405.008i 0.893687 0.893687i −0.101181 0.994868i \(-0.532262\pi\)
0.994868 + 0.101181i \(0.0322622\pi\)
\(60\) −403.555 + 73.1044i −0.868311 + 0.157296i
\(61\) 664.576 + 664.576i 1.39492 + 1.39492i 0.813860 + 0.581061i \(0.197362\pi\)
0.581061 + 0.813860i \(0.302638\pi\)
\(62\) 273.138 24.5399i 0.559493 0.0502674i
\(63\) 831.942 1.66373
\(64\) 439.771 262.193i 0.858928 0.512096i
\(65\) 105.133 0.200619
\(66\) −691.885 + 62.1621i −1.29038 + 0.115934i
\(67\) −107.377 107.377i −0.195794 0.195794i 0.602400 0.798194i \(-0.294211\pi\)
−0.798194 + 0.602400i \(0.794211\pi\)
\(68\) −696.540 + 126.179i −1.24218 + 0.225022i
\(69\) −264.489 + 264.489i −0.461461 + 0.461461i
\(70\) −356.480 297.705i −0.608679 0.508322i
\(71\) 215.050i 0.359461i 0.983716 + 0.179731i \(0.0575226\pi\)
−0.983716 + 0.179731i \(0.942477\pi\)
\(72\) −200.814 728.964i −0.328697 1.19318i
\(73\) 668.587i 1.07195i −0.844235 0.535974i \(-0.819945\pi\)
0.844235 0.535974i \(-0.180055\pi\)
\(74\) 418.644 501.296i 0.657654 0.787492i
\(75\) −447.935 + 447.935i −0.689642 + 0.689642i
\(76\) 351.634 + 243.775i 0.530726 + 0.367933i
\(77\) −556.266 556.266i −0.823277 0.823277i
\(78\) 31.3588 + 349.035i 0.0455217 + 0.506672i
\(79\) −822.956 −1.17202 −0.586012 0.810303i \(-0.699303\pi\)
−0.586012 + 0.810303i \(0.699303\pi\)
\(80\) −174.808 + 384.215i −0.244301 + 0.536956i
\(81\) 514.603 0.705902
\(82\) 91.2471 + 1015.61i 0.122885 + 1.36775i
\(83\) 326.873 + 326.873i 0.432277 + 0.432277i 0.889402 0.457125i \(-0.151121\pi\)
−0.457125 + 0.889402i \(0.651121\pi\)
\(84\) 882.027 1272.28i 1.14568 1.65259i
\(85\) 412.668 412.668i 0.526589 0.526589i
\(86\) 257.037 307.783i 0.322290 0.385919i
\(87\) 114.795i 0.141463i
\(88\) −353.139 + 621.682i −0.427781 + 0.753086i
\(89\) 262.733i 0.312918i −0.987684 0.156459i \(-0.949992\pi\)
0.987684 0.156459i \(-0.0500079\pi\)
\(90\) 478.466 + 399.578i 0.560386 + 0.467992i
\(91\) −280.619 + 280.619i −0.323262 + 0.323262i
\(92\) 68.6226 + 378.814i 0.0777652 + 0.429283i
\(93\) −532.898 532.898i −0.594182 0.594182i
\(94\) −621.643 + 55.8512i −0.682102 + 0.0612831i
\(95\) −352.752 −0.380964
\(96\) −1327.70 465.745i −1.41154 0.495155i
\(97\) −150.801 −0.157850 −0.0789251 0.996881i \(-0.525149\pi\)
−0.0789251 + 0.996881i \(0.525149\pi\)
\(98\) 779.871 70.0671i 0.803866 0.0722229i
\(99\) 746.618 + 746.618i 0.757958 + 0.757958i
\(100\) 116.218 + 641.553i 0.116218 + 0.641553i
\(101\) 487.985 487.985i 0.480755 0.480755i −0.424617 0.905373i \(-0.639591\pi\)
0.905373 + 0.424617i \(0.139591\pi\)
\(102\) 1493.11 + 1246.93i 1.44941 + 1.21044i
\(103\) 1840.58i 1.76075i −0.474275 0.880377i \(-0.657290\pi\)
0.474275 0.880377i \(-0.342710\pi\)
\(104\) 313.620 + 178.148i 0.295701 + 0.167970i
\(105\) 1276.33i 1.18626i
\(106\) 450.625 539.590i 0.412911 0.494431i
\(107\) −79.4098 + 79.4098i −0.0717461 + 0.0717461i −0.742069 0.670323i \(-0.766155\pi\)
0.670323 + 0.742069i \(0.266155\pi\)
\(108\) −227.304 + 327.876i −0.202522 + 0.292129i
\(109\) 952.979 + 952.979i 0.837421 + 0.837421i 0.988519 0.151098i \(-0.0482809\pi\)
−0.151098 + 0.988519i \(0.548281\pi\)
\(110\) −52.7469 587.091i −0.0457202 0.508881i
\(111\) −1794.82 −1.53475
\(112\) −558.942 1492.12i −0.471563 1.25886i
\(113\) −720.469 −0.599788 −0.299894 0.953973i \(-0.596951\pi\)
−0.299894 + 0.953973i \(0.596951\pi\)
\(114\) −105.218 1171.11i −0.0864433 0.962144i
\(115\) −224.430 224.430i −0.181984 0.181984i
\(116\) 97.0993 + 67.3153i 0.0777193 + 0.0538799i
\(117\) 376.646 376.646i 0.297615 0.297615i
\(118\) −1038.43 + 1243.45i −0.810131 + 0.970072i
\(119\) 2202.96i 1.69702i
\(120\) 1118.34 308.080i 0.850752 0.234365i
\(121\) 332.571i 0.249865i
\(122\) −2040.37 1703.96i −1.51415 1.26450i
\(123\) 1981.48 1981.48i 1.45255 1.45255i
\(124\) −763.240 + 138.262i −0.552750 + 0.100131i
\(125\) −963.056 963.056i −0.689107 0.689107i
\(126\) −2343.65 + 210.564i −1.65705 + 0.148877i
\(127\) 2622.35 1.83225 0.916124 0.400895i \(-0.131301\pi\)
0.916124 + 0.400895i \(0.131301\pi\)
\(128\) −1172.51 + 849.925i −0.809658 + 0.586902i
\(129\) −1101.97 −0.752119
\(130\) −296.169 + 26.6092i −0.199814 + 0.0179522i
\(131\) 657.574 + 657.574i 0.438569 + 0.438569i 0.891530 0.452961i \(-0.149632\pi\)
−0.452961 + 0.891530i \(0.649632\pi\)
\(132\) 1933.36 350.231i 1.27483 0.230937i
\(133\) 941.555 941.555i 0.613858 0.613858i
\(134\) 329.666 + 275.312i 0.212529 + 0.177488i
\(135\) 328.919i 0.209695i
\(136\) 1930.27 531.751i 1.21706 0.335274i
\(137\) 2511.52i 1.56623i 0.621874 + 0.783117i \(0.286371\pi\)
−0.621874 + 0.783117i \(0.713629\pi\)
\(138\) 678.146 812.030i 0.418316 0.500903i
\(139\) −1086.02 + 1086.02i −0.662697 + 0.662697i −0.956015 0.293318i \(-0.905241\pi\)
0.293318 + 0.956015i \(0.405241\pi\)
\(140\) 1079.58 + 748.434i 0.651723 + 0.451816i
\(141\) 1212.84 + 1212.84i 0.724393 + 0.724393i
\(142\) −54.4290 605.813i −0.0321661 0.358019i
\(143\) −503.677 −0.294543
\(144\) 750.210 + 2002.72i 0.434149 + 1.15898i
\(145\) −97.4080 −0.0557882
\(146\) 169.219 + 1883.46i 0.0959222 + 1.06765i
\(147\) −1521.54 1521.54i −0.853706 0.853706i
\(148\) −1052.48 + 1518.15i −0.584547 + 0.843183i
\(149\) −2284.63 + 2284.63i −1.25614 + 1.25614i −0.303214 + 0.952922i \(0.598060\pi\)
−0.952922 + 0.303214i \(0.901940\pi\)
\(150\) 1148.50 1375.24i 0.625163 0.748587i
\(151\) 2814.39i 1.51677i −0.651809 0.758383i \(-0.725990\pi\)
0.651809 0.758383i \(-0.274010\pi\)
\(152\) −1052.28 597.735i −0.561521 0.318965i
\(153\) 2956.80i 1.56237i
\(154\) 1707.84 + 1426.25i 0.893645 + 0.746304i
\(155\) 452.184 452.184i 0.234325 0.234325i
\(156\) −176.681 975.322i −0.0906781 0.500566i
\(157\) −906.308 906.308i −0.460709 0.460709i 0.438179 0.898888i \(-0.355624\pi\)
−0.898888 + 0.438179i \(0.855624\pi\)
\(158\) 2318.33 208.290i 1.16732 0.104877i
\(159\) −1931.93 −0.963598
\(160\) 395.203 1126.61i 0.195272 0.556663i
\(161\) 1198.08 0.586472
\(162\) −1449.68 + 130.246i −0.703070 + 0.0631670i
\(163\) 1392.36 + 1392.36i 0.669067 + 0.669067i 0.957500 0.288433i \(-0.0931342\pi\)
−0.288433 + 0.957500i \(0.593134\pi\)
\(164\) −514.101 2837.96i −0.244784 1.35127i
\(165\) −1145.43 + 1145.43i −0.540433 + 0.540433i
\(166\) −1003.56 838.097i −0.469225 0.391861i
\(167\) 1221.66i 0.566075i −0.959109 0.283038i \(-0.908658\pi\)
0.959109 0.283038i \(-0.0913421\pi\)
\(168\) −2162.73 + 3807.36i −0.993202 + 1.74848i
\(169\) 1942.91i 0.884347i
\(170\) −1058.07 + 1266.96i −0.477356 + 0.571598i
\(171\) −1263.75 + 1263.75i −0.565155 + 0.565155i
\(172\) −646.193 + 932.104i −0.286464 + 0.413211i
\(173\) −563.418 563.418i −0.247606 0.247606i 0.572381 0.819988i \(-0.306020\pi\)
−0.819988 + 0.572381i \(0.806020\pi\)
\(174\) −29.0545 323.387i −0.0126587 0.140896i
\(175\) 2029.05 0.876468
\(176\) 837.474 1840.71i 0.358676 0.788344i
\(177\) 4451.99 1.89058
\(178\) 66.4976 + 740.141i 0.0280012 + 0.311662i
\(179\) −2202.23 2202.23i −0.919565 0.919565i 0.0774329 0.996998i \(-0.475328\pi\)
−0.996998 + 0.0774329i \(0.975328\pi\)
\(180\) −1449.01 1004.55i −0.600016 0.415969i
\(181\) 121.294 121.294i 0.0498104 0.0498104i −0.681763 0.731573i \(-0.738786\pi\)
0.731573 + 0.681763i \(0.238786\pi\)
\(182\) 719.502 861.551i 0.293039 0.350892i
\(183\) 7305.26i 2.95093i
\(184\) −289.193 1049.78i −0.115867 0.420602i
\(185\) 1522.98i 0.605251i
\(186\) 1636.09 + 1366.34i 0.644968 + 0.538628i
\(187\) −1977.02 + 1977.02i −0.773124 + 0.773124i
\(188\) 1737.08 314.675i 0.673882 0.122074i
\(189\) 877.939 + 877.939i 0.337887 + 0.337887i
\(190\) 993.731 89.2813i 0.379436 0.0340902i
\(191\) 3927.65 1.48793 0.743966 0.668218i \(-0.232942\pi\)
0.743966 + 0.668218i \(0.232942\pi\)
\(192\) 3858.12 + 976.000i 1.45019 + 0.366858i
\(193\) −3249.02 −1.21176 −0.605880 0.795556i \(-0.707179\pi\)
−0.605880 + 0.795556i \(0.707179\pi\)
\(194\) 424.817 38.1675i 0.157217 0.0141251i
\(195\) 577.833 + 577.833i 0.212202 + 0.212202i
\(196\) −2179.23 + 394.769i −0.794178 + 0.143866i
\(197\) 2420.90 2420.90i 0.875545 0.875545i −0.117525 0.993070i \(-0.537496\pi\)
0.993070 + 0.117525i \(0.0374961\pi\)
\(198\) −2292.25 1914.31i −0.822743 0.687093i
\(199\) 1371.30i 0.488488i 0.969714 + 0.244244i \(0.0785397\pi\)
−0.969714 + 0.244244i \(0.921460\pi\)
\(200\) −489.773 1777.89i −0.173161 0.628580i
\(201\) 1180.33i 0.414198i
\(202\) −1251.18 + 1498.20i −0.435807 + 0.521847i
\(203\) 259.998 259.998i 0.0898931 0.0898931i
\(204\) −4521.82 3134.81i −1.55191 1.07588i
\(205\) 1681.36 + 1681.36i 0.572836 + 0.572836i
\(206\) 465.849 + 5185.06i 0.157559 + 1.75369i
\(207\) −1608.06 −0.539941
\(208\) −928.580 422.480i −0.309546 0.140835i
\(209\) 1689.98 0.559321
\(210\) −323.038 3595.52i −0.106151 1.18150i
\(211\) −1620.50 1620.50i −0.528719 0.528719i 0.391471 0.920190i \(-0.371966\pi\)
−0.920190 + 0.391471i \(0.871966\pi\)
\(212\) −1132.88 + 1634.12i −0.367011 + 0.529396i
\(213\) −1181.95 + 1181.95i −0.380217 + 0.380217i
\(214\) 203.605 243.802i 0.0650382 0.0778784i
\(215\) 935.068i 0.296610i
\(216\) 557.350 981.184i 0.175569 0.309079i
\(217\) 2413.91i 0.755148i
\(218\) −2925.82 2443.42i −0.908997 0.759125i
\(219\) 3674.67 3674.67i 1.13384 1.13384i
\(220\) 297.185 + 1640.53i 0.0910736 + 0.502749i
\(221\) 997.347 + 997.347i 0.303569 + 0.303569i
\(222\) 5056.15 454.268i 1.52859 0.137335i
\(223\) −419.617 −0.126007 −0.0630036 0.998013i \(-0.520068\pi\)
−0.0630036 + 0.998013i \(0.520068\pi\)
\(224\) 1952.24 + 4061.97i 0.582320 + 1.21161i
\(225\) −2723.38 −0.806929
\(226\) 2029.62 182.350i 0.597381 0.0536714i
\(227\) −2133.64 2133.64i −0.623853 0.623853i 0.322661 0.946515i \(-0.395423\pi\)
−0.946515 + 0.322661i \(0.895423\pi\)
\(228\) 592.813 + 3272.48i 0.172193 + 0.950548i
\(229\) −1574.42 + 1574.42i −0.454325 + 0.454325i −0.896787 0.442462i \(-0.854105\pi\)
0.442462 + 0.896787i \(0.354105\pi\)
\(230\) 689.039 + 575.433i 0.197539 + 0.164969i
\(231\) 6114.67i 1.74163i
\(232\) −290.574 165.057i −0.0822289 0.0467091i
\(233\) 1194.86i 0.335957i 0.985791 + 0.167978i \(0.0537239\pi\)
−0.985791 + 0.167978i \(0.946276\pi\)
\(234\) −965.712 + 1156.37i −0.269789 + 0.323052i
\(235\) −1029.14 + 1029.14i −0.285675 + 0.285675i
\(236\) 2610.63 3765.71i 0.720075 1.03867i
\(237\) −4523.12 4523.12i −1.23970 1.23970i
\(238\) −557.567 6205.91i −0.151856 1.69021i
\(239\) −4241.03 −1.14782 −0.573911 0.818917i \(-0.694575\pi\)
−0.573911 + 0.818917i \(0.694575\pi\)
\(240\) −3072.49 + 1150.94i −0.826367 + 0.309553i
\(241\) −5571.19 −1.48910 −0.744548 0.667569i \(-0.767335\pi\)
−0.744548 + 0.667569i \(0.767335\pi\)
\(242\) −84.1734 936.878i −0.0223590 0.248863i
\(243\) 3780.46 + 3780.46i 0.998012 + 0.998012i
\(244\) 6179.15 + 4283.77i 1.62123 + 1.12394i
\(245\) 1291.09 1291.09i 0.336672 0.336672i
\(246\) −5080.47 + 6083.49i −1.31674 + 1.57670i
\(247\) 852.541i 0.219619i
\(248\) 2115.12 582.671i 0.541572 0.149192i
\(249\) 3593.11i 0.914474i
\(250\) 2956.75 + 2469.26i 0.748006 + 0.624678i
\(251\) −482.728 + 482.728i −0.121393 + 0.121393i −0.765193 0.643801i \(-0.777357\pi\)
0.643801 + 0.765193i \(0.277357\pi\)
\(252\) 6548.95 1186.35i 1.63708 0.296560i
\(253\) 1075.20 + 1075.20i 0.267184 + 0.267184i
\(254\) −7387.36 + 663.713i −1.82490 + 0.163957i
\(255\) 4536.19 1.11399
\(256\) 3087.94 2691.07i 0.753891 0.656999i
\(257\) 8093.12 1.96434 0.982169 0.188002i \(-0.0602013\pi\)
0.982169 + 0.188002i \(0.0602013\pi\)
\(258\) 3104.35 278.909i 0.749102 0.0673027i
\(259\) 4065.08 + 4065.08i 0.975257 + 0.975257i
\(260\) 827.598 149.921i 0.197406 0.0357603i
\(261\) −348.969 + 348.969i −0.0827610 + 0.0827610i
\(262\) −2018.87 1686.01i −0.476054 0.397564i
\(263\) 410.300i 0.0961984i −0.998843 0.0480992i \(-0.984684\pi\)
0.998843 0.0480992i \(-0.0153164\pi\)
\(264\) −5357.79 + 1475.96i −1.24905 + 0.344088i
\(265\) 1639.32i 0.380009i
\(266\) −2414.13 + 2890.74i −0.556465 + 0.666326i
\(267\) 1444.03 1444.03i 0.330986 0.330986i
\(268\) −998.378 692.139i −0.227558 0.157758i
\(269\) −4.77962 4.77962i −0.00108334 0.00108334i 0.706565 0.707648i \(-0.250244\pi\)
−0.707648 + 0.706565i \(0.750244\pi\)
\(270\) 83.2490 + 926.590i 0.0187643 + 0.208854i
\(271\) −2833.98 −0.635247 −0.317623 0.948217i \(-0.602885\pi\)
−0.317623 + 0.948217i \(0.602885\pi\)
\(272\) −5303.15 + 1986.54i −1.18217 + 0.442836i
\(273\) −3084.67 −0.683855
\(274\) −635.665 7075.17i −0.140153 1.55995i
\(275\) 1820.95 + 1820.95i 0.399300 + 0.399300i
\(276\) −1704.87 + 2459.19i −0.371815 + 0.536326i
\(277\) 1525.80 1525.80i 0.330962 0.330962i −0.521989 0.852952i \(-0.674810\pi\)
0.852952 + 0.521989i \(0.174810\pi\)
\(278\) 2784.53 3334.27i 0.600738 0.719339i
\(279\) 3239.94i 0.695234i
\(280\) −3230.70 1835.16i −0.689539 0.391684i
\(281\) 4750.23i 1.00845i 0.863572 + 0.504226i \(0.168222\pi\)
−0.863572 + 0.504226i \(0.831778\pi\)
\(282\) −3723.63 3109.69i −0.786308 0.656665i
\(283\) 644.104 644.104i 0.135293 0.135293i −0.636217 0.771510i \(-0.719502\pi\)
0.771510 + 0.636217i \(0.219502\pi\)
\(284\) 306.662 + 1692.85i 0.0640740 + 0.353705i
\(285\) −1938.79 1938.79i −0.402961 0.402961i
\(286\) 1418.90 127.480i 0.293361 0.0263569i
\(287\) −8975.67 −1.84605
\(288\) −2620.29 5451.95i −0.536118 1.11548i
\(289\) 2916.53 0.593635
\(290\) 274.406 24.6539i 0.0555644 0.00499216i
\(291\) −828.827 828.827i −0.166965 0.166965i
\(292\) −953.405 5263.03i −0.191075 1.05478i
\(293\) −1433.16 + 1433.16i −0.285755 + 0.285755i −0.835399 0.549644i \(-0.814763\pi\)
0.549644 + 0.835399i \(0.314763\pi\)
\(294\) 4671.41 + 3901.21i 0.926675 + 0.773888i
\(295\) 3777.69i 0.745578i
\(296\) 2580.67 4543.13i 0.506751 0.892108i
\(297\) 1575.79i 0.307868i
\(298\) 5857.75 7014.23i 1.13869 1.36350i
\(299\) 542.407 542.407i 0.104910 0.104910i
\(300\) −2887.34 + 4164.85i −0.555668 + 0.801526i
\(301\) 2495.85 + 2495.85i 0.477935 + 0.477935i
\(302\) 712.319 + 7928.36i 0.135726 + 1.51068i
\(303\) 5364.10 1.01703
\(304\) 3115.65 + 1417.54i 0.587811 + 0.267439i
\(305\) −6198.79 −1.16374
\(306\) 748.364 + 8329.55i 0.139808 + 1.55611i
\(307\) −231.211 231.211i −0.0429834 0.0429834i 0.685288 0.728272i \(-0.259676\pi\)
−0.728272 + 0.685288i \(0.759676\pi\)
\(308\) −5172.09 3585.62i −0.956842 0.663343i
\(309\) 10116.2 10116.2i 1.86242 1.86242i
\(310\) −1159.39 + 1388.29i −0.212416 + 0.254353i
\(311\) 871.410i 0.158885i 0.996839 + 0.0794423i \(0.0253140\pi\)
−0.996839 + 0.0794423i \(0.974686\pi\)
\(312\) 744.577 + 2702.84i 0.135107 + 0.490443i
\(313\) 3515.02i 0.634762i −0.948298 0.317381i \(-0.897197\pi\)
0.948298 0.317381i \(-0.102803\pi\)
\(314\) 2782.53 + 2323.76i 0.500087 + 0.417634i
\(315\) −3879.95 + 3879.95i −0.694001 + 0.694001i
\(316\) −6478.22 + 1173.54i −1.15325 + 0.208913i
\(317\) 4723.77 + 4723.77i 0.836951 + 0.836951i 0.988456 0.151506i \(-0.0484121\pi\)
−0.151506 + 0.988456i \(0.548412\pi\)
\(318\) 5442.40 488.970i 0.959732 0.0862266i
\(319\) 466.665 0.0819067
\(320\) −828.174 + 3273.77i −0.144676 + 0.571904i
\(321\) −872.901 −0.151778
\(322\) −3375.09 + 303.233i −0.584119 + 0.0524799i
\(323\) −3346.38 3346.38i −0.576462 0.576462i
\(324\) 4050.89 733.824i 0.694597 0.125827i
\(325\) 918.613 918.613i 0.156786 0.156786i
\(326\) −4274.79 3569.98i −0.726254 0.606512i
\(327\) 10475.5i 1.77155i
\(328\) 2166.55 + 7864.65i 0.364718 + 1.32394i
\(329\) 5493.90i 0.920633i
\(330\) 2936.85 3516.67i 0.489904 0.586625i
\(331\) −1820.26 + 1820.26i −0.302268 + 0.302268i −0.841901 0.539633i \(-0.818563\pi\)
0.539633 + 0.841901i \(0.318563\pi\)
\(332\) 3039.23 + 2106.99i 0.502408 + 0.348301i
\(333\) −5456.13 5456.13i −0.897880 0.897880i
\(334\) 309.200 + 3441.50i 0.0506547 + 0.563804i
\(335\) 1001.55 0.163345
\(336\) 5128.93 11273.0i 0.832757 1.83034i
\(337\) 74.0970 0.0119772 0.00598861 0.999982i \(-0.498094\pi\)
0.00598861 + 0.999982i \(0.498094\pi\)
\(338\) 491.749 + 5473.33i 0.0791350 + 0.880799i
\(339\) −3959.83 3959.83i −0.634420 0.634420i
\(340\) 2660.01 3836.94i 0.424292 0.612021i
\(341\) −2166.34 + 2166.34i −0.344029 + 0.344029i
\(342\) 3240.23 3879.94i 0.512315 0.613460i
\(343\) 1647.24i 0.259307i
\(344\) 1584.46 2789.36i 0.248339 0.437187i
\(345\) 2467.01i 0.384984i
\(346\) 1729.80 + 1444.59i 0.268770 + 0.224456i
\(347\) 2102.73 2102.73i 0.325305 0.325305i −0.525493 0.850798i \(-0.676119\pi\)
0.850798 + 0.525493i \(0.176119\pi\)
\(348\) 163.698 + 903.652i 0.0252159 + 0.139198i
\(349\) −6612.85 6612.85i −1.01426 1.01426i −0.999897 0.0143661i \(-0.995427\pi\)
−0.0143661 0.999897i \(-0.504573\pi\)
\(350\) −5716.00 + 513.551i −0.872951 + 0.0784299i
\(351\) 794.940 0.120885
\(352\) −1893.35 + 5397.38i −0.286693 + 0.817277i
\(353\) 2216.90 0.334259 0.167130 0.985935i \(-0.446550\pi\)
0.167130 + 0.985935i \(0.446550\pi\)
\(354\) −12541.6 + 1126.80i −1.88299 + 0.169177i
\(355\) −1002.93 1002.93i −0.149944 0.149944i
\(356\) −374.658 2068.21i −0.0557776 0.307906i
\(357\) −12107.9 + 12107.9i −1.79500 + 1.79500i
\(358\) 6761.23 + 5646.46i 0.998162 + 0.833589i
\(359\) 2082.23i 0.306117i −0.988217 0.153059i \(-0.951088\pi\)
0.988217 0.153059i \(-0.0489123\pi\)
\(360\) 4336.23 + 2463.14i 0.634831 + 0.360608i
\(361\) 3998.49i 0.582955i
\(362\) −310.995 + 372.393i −0.0451533 + 0.0540678i
\(363\) −1827.87 + 1827.87i −0.264293 + 0.264293i
\(364\) −1808.84 + 2609.16i −0.260464 + 0.375707i
\(365\) 3118.10 + 3118.10i 0.447148 + 0.447148i
\(366\) −1848.95 20579.5i −0.264061 2.93909i
\(367\) 4509.22 0.641360 0.320680 0.947188i \(-0.396089\pi\)
0.320680 + 0.947188i \(0.396089\pi\)
\(368\) 1080.38 + 2884.12i 0.153040 + 0.408547i
\(369\) 12047.1 1.69959
\(370\) 385.464 + 4290.34i 0.0541603 + 0.602823i
\(371\) 4375.61 + 4375.61i 0.612320 + 0.612320i
\(372\) −4954.82 3434.99i −0.690579 0.478753i
\(373\) −8661.56 + 8661.56i −1.20236 + 1.20236i −0.228908 + 0.973448i \(0.573515\pi\)
−0.973448 + 0.228908i \(0.926485\pi\)
\(374\) 5069.05 6069.81i 0.700840 0.839205i
\(375\) 10586.3i 1.45779i
\(376\) −4813.86 + 1326.12i −0.660254 + 0.181886i
\(377\) 235.418i 0.0321609i
\(378\) −2695.43 2251.02i −0.366767 0.306296i
\(379\) 3522.46 3522.46i 0.477405 0.477405i −0.426896 0.904301i \(-0.640393\pi\)
0.904301 + 0.426896i \(0.140393\pi\)
\(380\) −2776.82 + 503.025i −0.374863 + 0.0679069i
\(381\) 14412.9 + 14412.9i 1.93804 + 1.93804i
\(382\) −11064.5 + 994.086i −1.48196 + 0.133146i
\(383\) 3044.88 0.406229 0.203115 0.979155i \(-0.434894\pi\)
0.203115 + 0.979155i \(0.434894\pi\)
\(384\) −11115.7 1772.98i −1.47720 0.235618i
\(385\) 5188.54 0.686837
\(386\) 9152.75 822.325i 1.20690 0.108433i
\(387\) −3349.92 3349.92i −0.440016 0.440016i
\(388\) −1187.08 + 215.042i −0.155322 + 0.0281368i
\(389\) 1932.73 1932.73i 0.251911 0.251911i −0.569843 0.821754i \(-0.692996\pi\)
0.821754 + 0.569843i \(0.192996\pi\)
\(390\) −1774.05 1481.55i −0.230340 0.192362i
\(391\) 4258.09i 0.550744i
\(392\) 6039.14 1663.66i 0.778119 0.214356i
\(393\) 7228.29i 0.927784i
\(394\) −6207.15 + 7432.61i −0.793685 + 0.950379i
\(395\) 3838.04 3838.04i 0.488893 0.488893i
\(396\) 6941.96 + 4812.61i 0.880926 + 0.610714i
\(397\) −672.457 672.457i −0.0850117 0.0850117i 0.663322 0.748334i \(-0.269146\pi\)
−0.748334 + 0.663322i \(0.769146\pi\)
\(398\) −347.075 3863.07i −0.0437119 0.486528i
\(399\) 10349.9 1.29861
\(400\) 1829.71 + 4884.51i 0.228714 + 0.610563i
\(401\) −7606.74 −0.947288 −0.473644 0.880716i \(-0.657062\pi\)
−0.473644 + 0.880716i \(0.657062\pi\)
\(402\) 298.740 + 3325.07i 0.0370641 + 0.412536i
\(403\) 1092.85 + 1092.85i 0.135084 + 0.135084i
\(404\) 3145.49 4537.23i 0.387361 0.558751i
\(405\) −2399.96 + 2399.96i −0.294457 + 0.294457i
\(406\) −666.631 + 798.241i −0.0814885 + 0.0975765i
\(407\) 7296.32i 0.888612i
\(408\) 13531.7 + 7686.54i 1.64196 + 0.932697i
\(409\) 4981.58i 0.602257i 0.953584 + 0.301129i \(0.0973634\pi\)
−0.953584 + 0.301129i \(0.902637\pi\)
\(410\) −5162.08 4310.98i −0.621797 0.519278i
\(411\) −13803.8 + 13803.8i −1.65667 + 1.65667i
\(412\) −2624.67 14488.8i −0.313855 1.73256i
\(413\) −10083.3 10083.3i −1.20137 1.20137i
\(414\) 4530.03 406.998i 0.537775 0.0483161i
\(415\) −3048.89 −0.360637
\(416\) 2722.81 + 955.136i 0.320906 + 0.112571i
\(417\) −11937.9 −1.40192
\(418\) −4760.80 + 427.732i −0.557077 + 0.0500503i
\(419\) −3433.38 3433.38i −0.400314 0.400314i 0.478030 0.878344i \(-0.341351\pi\)
−0.878344 + 0.478030i \(0.841351\pi\)
\(420\) 1820.05 + 10047.1i 0.211450 + 1.16726i
\(421\) 7973.72 7973.72i 0.923077 0.923077i −0.0741686 0.997246i \(-0.523630\pi\)
0.997246 + 0.0741686i \(0.0236303\pi\)
\(422\) 4975.22 + 4154.93i 0.573910 + 0.479286i
\(423\) 7373.88i 0.847590i
\(424\) 2777.81 4890.18i 0.318166 0.560114i
\(425\) 7211.44i 0.823074i
\(426\) 3030.51 3628.81i 0.344668 0.412715i
\(427\) 16545.6 16545.6i 1.87517 1.87517i
\(428\) −511.866 + 738.343i −0.0578084 + 0.0833859i
\(429\) −2768.30 2768.30i −0.311550 0.311550i
\(430\) 236.665 + 2634.16i 0.0265418 + 0.295420i
\(431\) 4800.16 0.536463 0.268232 0.963354i \(-0.413561\pi\)
0.268232 + 0.963354i \(0.413561\pi\)
\(432\) −1321.76 + 2905.14i −0.147207 + 0.323550i
\(433\) 6242.32 0.692810 0.346405 0.938085i \(-0.387402\pi\)
0.346405 + 0.938085i \(0.387402\pi\)
\(434\) −610.959 6800.18i −0.0675737 0.752118i
\(435\) −535.372 535.372i −0.0590095 0.0590095i
\(436\) 8860.69 + 6142.79i 0.973280 + 0.674739i
\(437\) −1819.93 + 1819.93i −0.199220 + 0.199220i
\(438\) −9421.79 + 11281.9i −1.02783 + 1.23075i
\(439\) 4929.27i 0.535903i 0.963432 + 0.267951i \(0.0863466\pi\)
−0.963432 + 0.267951i \(0.913653\pi\)
\(440\) −1252.41 4546.30i −0.135696 0.492582i
\(441\) 9250.77i 0.998896i
\(442\) −3062.03 2557.18i −0.329516 0.275187i
\(443\) −7670.67 + 7670.67i −0.822674 + 0.822674i −0.986491 0.163817i \(-0.947619\pi\)
0.163817 + 0.986491i \(0.447619\pi\)
\(444\) −14128.6 + 2559.42i −1.51017 + 0.273569i
\(445\) 1225.32 + 1225.32i 0.130529 + 0.130529i
\(446\) 1182.09 106.205i 0.125502 0.0112756i
\(447\) −25113.5 −2.65733
\(448\) −6527.70 10948.8i −0.688404 1.15464i
\(449\) −11515.2 −1.21032 −0.605162 0.796102i \(-0.706892\pi\)
−0.605162 + 0.796102i \(0.706892\pi\)
\(450\) 7671.99 689.286i 0.803691 0.0722073i
\(451\) −8055.12 8055.12i −0.841021 0.841021i
\(452\) −5671.44 + 1027.39i −0.590182 + 0.106912i
\(453\) 15468.4 15468.4i 1.60434 1.60434i
\(454\) 6550.66 + 5470.61i 0.677176 + 0.565526i
\(455\) 2617.46i 0.269689i
\(456\) −2498.26 9068.79i −0.256561 0.931326i
\(457\) 4829.89i 0.494383i 0.968967 + 0.247191i \(0.0795076\pi\)
−0.968967 + 0.247191i \(0.920492\pi\)
\(458\) 4036.78 4833.74i 0.411848 0.493157i
\(459\) 3120.28 3120.28i 0.317303 0.317303i
\(460\) −2086.72 1446.65i −0.211508 0.146631i
\(461\) 8265.79 + 8265.79i 0.835090 + 0.835090i 0.988208 0.153118i \(-0.0489315\pi\)
−0.153118 + 0.988208i \(0.548931\pi\)
\(462\) 1547.62 + 17225.5i 0.155848 + 1.73464i
\(463\) −5043.86 −0.506281 −0.253141 0.967430i \(-0.581464\pi\)
−0.253141 + 0.967430i \(0.581464\pi\)
\(464\) 860.346 + 391.435i 0.0860788 + 0.0391636i
\(465\) 4970.57 0.495709
\(466\) −302.418 3366.02i −0.0300628 0.334609i
\(467\) 12438.8 + 12438.8i 1.23255 + 1.23255i 0.962982 + 0.269564i \(0.0868796\pi\)
0.269564 + 0.962982i \(0.413120\pi\)
\(468\) 2427.81 3502.01i 0.239798 0.345898i
\(469\) −2673.31 + 2673.31i −0.263203 + 0.263203i
\(470\) 2638.70 3159.64i 0.258966 0.310093i
\(471\) 9962.47i 0.974621i
\(472\) −6401.26 + 11269.1i −0.624241 + 1.09894i
\(473\) 4479.75i 0.435474i
\(474\) 13886.8 + 11597.2i 1.34566 + 1.12379i
\(475\) −3082.20 + 3082.20i −0.297729 + 0.297729i
\(476\) 3141.42 + 17341.4i 0.302493 + 1.66984i
\(477\) −5872.93 5872.93i −0.563738 0.563738i
\(478\) 11947.3 1073.40i 1.14322 0.102712i
\(479\) 13059.7 1.24575 0.622875 0.782321i \(-0.285964\pi\)
0.622875 + 0.782321i \(0.285964\pi\)
\(480\) 8364.14 4019.93i 0.795352 0.382258i
\(481\) 3680.77 0.348916
\(482\) 15694.5 1410.06i 1.48312 0.133250i
\(483\) 6584.87 + 6584.87i 0.620335 + 0.620335i
\(484\) 474.246 + 2617.96i 0.0445385 + 0.245864i
\(485\) 703.292 703.292i 0.0658450 0.0658450i
\(486\) −11606.7 9693.04i −1.08331 0.904702i
\(487\) 15549.3i 1.44683i 0.690414 + 0.723414i \(0.257428\pi\)
−0.690414 + 0.723414i \(0.742572\pi\)
\(488\) −18491.4 10503.8i −1.71530 0.974354i
\(489\) 15305.3i 1.41540i
\(490\) −3310.33 + 3963.88i −0.305195 + 0.365448i
\(491\) −8628.34 + 8628.34i −0.793058 + 0.793058i −0.981990 0.188932i \(-0.939497\pi\)
0.188932 + 0.981990i \(0.439497\pi\)
\(492\) 12772.4 18423.5i 1.17037 1.68821i
\(493\) −924.059 924.059i −0.0844169 0.0844169i
\(494\) 215.777 + 2401.68i 0.0196524 + 0.218738i
\(495\) −6964.03 −0.632344
\(496\) −5810.98 + 2176.76i −0.526049 + 0.197056i
\(497\) 5354.00 0.483219
\(498\) −909.413 10122.1i −0.0818309 0.910806i
\(499\) 1732.42 + 1732.42i 0.155418 + 0.155418i 0.780533 0.625115i \(-0.214948\pi\)
−0.625115 + 0.780533i \(0.714948\pi\)
\(500\) −8954.38 6207.74i −0.800904 0.555237i
\(501\) 6714.44 6714.44i 0.598761 0.598761i
\(502\) 1237.71 1482.06i 0.110043 0.131768i
\(503\) 16579.6i 1.46968i −0.678241 0.734839i \(-0.737258\pi\)
0.678241 0.734839i \(-0.262742\pi\)
\(504\) −18148.7 + 4999.58i −1.60398 + 0.441863i
\(505\) 4551.65i 0.401081i
\(506\) −3301.07 2756.80i −0.290021 0.242203i
\(507\) 10678.6 10678.6i 0.935410 0.935410i
\(508\) 20642.8 3739.47i 1.80291 0.326599i
\(509\) −7830.92 7830.92i −0.681924 0.681924i 0.278509 0.960434i \(-0.410160\pi\)
−0.960434 + 0.278509i \(0.910160\pi\)
\(510\) −12778.8 + 1148.11i −1.10952 + 0.0996844i
\(511\) −16645.5 −1.44100
\(512\) −8017.86 + 8362.51i −0.692076 + 0.721825i
\(513\) −2667.24 −0.229555
\(514\) −22799.0 + 2048.36i −1.95646 + 0.175777i
\(515\) 8583.95 + 8583.95i 0.734474 + 0.734474i
\(516\) −8674.61 + 1571.42i −0.740074 + 0.134065i
\(517\) 4930.44 4930.44i 0.419420 0.419420i
\(518\) −12480.5 10422.8i −1.05861 0.884075i
\(519\) 6193.30i 0.523807i
\(520\) −2293.47 + 631.803i −0.193414 + 0.0532815i
\(521\) 3400.02i 0.285907i −0.989729 0.142953i \(-0.954340\pi\)
0.989729 0.142953i \(-0.0456599\pi\)
\(522\) 894.749 1071.40i 0.0750232 0.0898348i
\(523\) −2019.50 + 2019.50i −0.168847 + 0.168847i −0.786472 0.617626i \(-0.788095\pi\)
0.617626 + 0.786472i \(0.288095\pi\)
\(524\) 6114.05 + 4238.64i 0.509720 + 0.353370i
\(525\) 11152.0 + 11152.0i 0.927075 + 0.927075i
\(526\) 103.847 + 1155.85i 0.00860822 + 0.0958124i
\(527\) 8579.28 0.709144
\(528\) 14719.8 5513.95i 1.21325 0.454477i
\(529\) 9851.23 0.809668
\(530\) 414.910 + 4618.09i 0.0340048 + 0.378485i
\(531\) 13533.7 + 13533.7i 1.10605 + 1.10605i
\(532\) 6069.15 8754.47i 0.494607 0.713448i
\(533\) −4063.56 + 4063.56i −0.330229 + 0.330229i
\(534\) −3702.47 + 4433.43i −0.300040 + 0.359276i
\(535\) 740.691i 0.0598558i
\(536\) 2987.69 + 1697.12i 0.240762 + 0.136762i
\(537\) 24207.7i 1.94532i
\(538\) 14.6743 + 12.2548i 0.00117594 + 0.000982052i
\(539\) −6185.39 + 6185.39i −0.494293 + 0.494293i
\(540\) −469.038 2589.21i −0.0373781 0.206337i
\(541\) −13432.6 13432.6i −1.06749 1.06749i −0.997551 0.0699388i \(-0.977720\pi\)
−0.0699388 0.997551i \(-0.522280\pi\)
\(542\) 7983.54 717.278i 0.632699 0.0568445i
\(543\) 1333.30 0.105373
\(544\) 14436.6 6938.45i 1.13780 0.546845i
\(545\) −8888.86 −0.698637
\(546\) 8689.75 780.726i 0.681112 0.0611941i
\(547\) −5376.46 5376.46i −0.420257 0.420257i 0.465035 0.885292i \(-0.346042\pi\)
−0.885292 + 0.465035i \(0.846042\pi\)
\(548\) 3581.44 + 19770.4i 0.279181 + 1.54115i
\(549\) −22207.5 + 22207.5i −1.72640 + 1.72640i
\(550\) −5590.64 4668.88i −0.433429 0.361967i
\(551\) 789.894i 0.0610719i
\(552\) 4180.33 7359.24i 0.322331 0.567446i
\(553\) 20488.7i 1.57553i
\(554\) −3912.13 + 4684.49i −0.300019 + 0.359251i
\(555\) 8370.55 8370.55i 0.640198 0.640198i
\(556\) −7000.34 + 10097.7i −0.533958 + 0.770210i
\(557\) −2076.28 2076.28i −0.157944 0.157944i 0.623711 0.781655i \(-0.285624\pi\)
−0.781655 + 0.623711i \(0.785624\pi\)
\(558\) 820.027 + 9127.18i 0.0622124 + 0.692445i
\(559\) 2259.90 0.170990
\(560\) 9565.61 + 4352.10i 0.721823 + 0.328410i
\(561\) −21732.1 −1.63553
\(562\) −1202.28 13381.8i −0.0902405 1.00441i
\(563\) −16643.1 16643.1i −1.24587 1.24587i −0.957528 0.288339i \(-0.906897\pi\)
−0.288339 0.957528i \(-0.593103\pi\)
\(564\) 11276.8 + 7817.81i 0.841915 + 0.583669i
\(565\) 3360.07 3360.07i 0.250193 0.250193i
\(566\) −1651.47 + 1977.51i −0.122644 + 0.146857i
\(567\) 12811.8i 0.948934i
\(568\) −1292.35 4691.28i −0.0954679 0.346552i
\(569\) 5659.60i 0.416982i 0.978024 + 0.208491i \(0.0668551\pi\)
−0.978024 + 0.208491i \(0.933145\pi\)
\(570\) 5952.43 + 4971.02i 0.437403 + 0.365286i
\(571\) 4872.67 4872.67i 0.357119 0.357119i −0.505631 0.862750i \(-0.668740\pi\)
0.862750 + 0.505631i \(0.168740\pi\)
\(572\) −3964.89 + 718.244i −0.289825 + 0.0525023i
\(573\) 21587.1 + 21587.1i 1.57385 + 1.57385i
\(574\) 25285.2 2271.73i 1.83865 0.165192i
\(575\) −3921.95 −0.284446
\(576\) 8761.45 + 14695.4i 0.633786 + 1.06303i
\(577\) 10652.2 0.768556 0.384278 0.923217i \(-0.374450\pi\)
0.384278 + 0.923217i \(0.374450\pi\)
\(578\) −8216.10 + 738.171i −0.591254 + 0.0531209i
\(579\) −17857.2 17857.2i −1.28173 1.28173i
\(580\) −766.784 + 138.904i −0.0548948 + 0.00994426i
\(581\) 8138.01 8138.01i 0.581104 0.581104i
\(582\) 2544.65 + 2125.10i 0.181235 + 0.151354i
\(583\) 7853.69i 0.557919i
\(584\) 4017.89 + 14585.1i 0.284694 + 1.03345i
\(585\) 3513.14i 0.248291i
\(586\) 3674.61 4400.07i 0.259039 0.310180i
\(587\) 9903.95 9903.95i 0.696388 0.696388i −0.267242 0.963630i \(-0.586112\pi\)
0.963630 + 0.267242i \(0.0861122\pi\)
\(588\) −14147.1 9807.69i −0.992208 0.687861i
\(589\) −3666.82 3666.82i −0.256517 0.256517i
\(590\) −956.129 10642.0i −0.0667173 0.742587i
\(591\) 26611.5 1.85220
\(592\) −6120.09 + 13451.5i −0.424889 + 0.933875i
\(593\) −3528.04 −0.244316 −0.122158 0.992511i \(-0.538981\pi\)
−0.122158 + 0.992511i \(0.538981\pi\)
\(594\) −398.832 4439.14i −0.0275493 0.306633i
\(595\) −10274.0 10274.0i −0.707887 0.707887i
\(596\) −14726.5 + 21242.2i −1.01211 + 1.45993i
\(597\) −7536.93 + 7536.93i −0.516693 + 0.516693i
\(598\) −1390.72 + 1665.29i −0.0951018 + 0.113877i
\(599\) 19024.9i 1.29772i 0.760907 + 0.648861i \(0.224754\pi\)
−0.760907 + 0.648861i \(0.775246\pi\)
\(600\) 7079.74 12463.5i 0.481715 0.848034i
\(601\) 1065.92i 0.0723460i 0.999346 + 0.0361730i \(0.0115167\pi\)
−0.999346 + 0.0361730i \(0.988483\pi\)
\(602\) −7662.72 6399.32i −0.518786 0.433250i
\(603\) 3588.11 3588.11i 0.242320 0.242320i
\(604\) −4013.32 22154.5i −0.270364 1.49248i
\(605\) −1551.02 1551.02i −0.104228 0.104228i
\(606\) −15111.1 + 1357.65i −1.01295 + 0.0910079i
\(607\) 12909.7 0.863242 0.431621 0.902055i \(-0.357942\pi\)
0.431621 + 0.902055i \(0.357942\pi\)
\(608\) −9135.80 3204.75i −0.609384 0.213766i
\(609\) 2858.00 0.190167
\(610\) 17462.5 1568.91i 1.15908 0.104137i
\(611\) −2487.25 2487.25i −0.164687 0.164687i
\(612\) −4216.40 23275.6i −0.278494 1.53735i
\(613\) −8763.41 + 8763.41i −0.577408 + 0.577408i −0.934188 0.356781i \(-0.883874\pi\)
0.356781 + 0.934188i \(0.383874\pi\)
\(614\) 709.859 + 592.820i 0.0466573 + 0.0389646i
\(615\) 18482.1i 1.21182i
\(616\) 15477.7 + 8791.93i 1.01236 + 0.575060i
\(617\) 18921.2i 1.23459i −0.786733 0.617293i \(-0.788229\pi\)
0.786733 0.617293i \(-0.211771\pi\)
\(618\) −25937.6 + 31058.4i −1.68829 + 2.02161i
\(619\) −15116.6 + 15116.6i −0.981565 + 0.981565i −0.999833 0.0182677i \(-0.994185\pi\)
0.0182677 + 0.999833i \(0.494185\pi\)
\(620\) 2914.73 4204.36i 0.188804 0.272340i
\(621\) −1696.97 1696.97i −0.109657 0.109657i
\(622\) −220.553 2454.83i −0.0142176 0.158247i
\(623\) −6541.15 −0.420651
\(624\) −2781.62 7425.67i −0.178452 0.476386i
\(625\) −1204.57 −0.0770926
\(626\) 889.648 + 9902.09i 0.0568011 + 0.632216i
\(627\) 9288.42 + 9288.42i 0.591617 + 0.591617i
\(628\) −8426.75 5841.95i −0.535452 0.371209i
\(629\) 14447.7 14447.7i 0.915845 0.915845i
\(630\) 9948.11 11912.1i 0.629115 0.753319i
\(631\) 9602.80i 0.605834i −0.953017 0.302917i \(-0.902039\pi\)
0.953017 0.302917i \(-0.0979605\pi\)
\(632\) 17952.6 4945.58i 1.12993 0.311273i
\(633\) 17813.1i 1.11849i
\(634\) −14502.8 12111.7i −0.908487 0.758699i
\(635\) −12229.9 + 12229.9i −0.764297 + 0.764297i
\(636\) −15207.9 + 2754.93i −0.948166 + 0.171761i
\(637\) 3120.34 + 3120.34i 0.194085 + 0.194085i
\(638\) −1314.63 + 118.113i −0.0815781 + 0.00732935i
\(639\) −7186.12 −0.444880
\(640\) 1504.44 9432.08i 0.0929194 0.582556i
\(641\) 4450.84 0.274256 0.137128 0.990553i \(-0.456213\pi\)
0.137128 + 0.990553i \(0.456213\pi\)
\(642\) 2459.03 220.931i 0.151169 0.0135817i
\(643\) 6491.27 + 6491.27i 0.398119 + 0.398119i 0.877569 0.479450i \(-0.159164\pi\)
−0.479450 + 0.877569i \(0.659164\pi\)
\(644\) 9431.15 1708.46i 0.577080 0.104539i
\(645\) 5139.30 5139.30i 0.313736 0.313736i
\(646\) 10274.0 + 8580.05i 0.625734 + 0.522566i
\(647\) 5546.17i 0.337005i −0.985701 0.168503i \(-0.946107\pi\)
0.985701 0.168503i \(-0.0538932\pi\)
\(648\) −11226.0 + 3092.52i −0.680551 + 0.187478i
\(649\) 18098.3i 1.09464i
\(650\) −2355.31 + 2820.31i −0.142127 + 0.170187i
\(651\) −13267.3 + 13267.3i −0.798750 + 0.798750i
\(652\) 12946.0 + 8974.98i 0.777613 + 0.539091i
\(653\) 6327.58 + 6327.58i 0.379200 + 0.379200i 0.870813 0.491614i \(-0.163593\pi\)
−0.491614 + 0.870813i \(0.663593\pi\)
\(654\) −2651.34 29510.3i −0.158525 1.76444i
\(655\) −6133.49 −0.365886
\(656\) −8093.88 21607.0i −0.481727 1.28599i
\(657\) 22341.5 1.32667
\(658\) 1390.50 + 15476.7i 0.0823820 + 0.916940i
\(659\) 15135.2 + 15135.2i 0.894663 + 0.894663i 0.994958 0.100294i \(-0.0319785\pi\)
−0.100294 + 0.994958i \(0.531978\pi\)
\(660\) −7383.28 + 10650.0i −0.435445 + 0.628110i
\(661\) −23460.1 + 23460.1i −1.38047 + 1.38047i −0.536694 + 0.843777i \(0.680327\pi\)
−0.843777 + 0.536694i \(0.819673\pi\)
\(662\) 4667.12 5588.53i 0.274007 0.328103i
\(663\) 10963.2i 0.642195i
\(664\) −9095.03 5166.32i −0.531560 0.301946i
\(665\) 8782.30i 0.512125i
\(666\) 16751.3 + 13989.4i 0.974624 + 0.813932i
\(667\) −502.550 + 502.550i −0.0291736 + 0.0291736i
\(668\) −1742.08 9616.73i −0.100903 0.557009i
\(669\) −2306.29 2306.29i −0.133283 0.133283i
\(670\) −2821.45 + 253.492i −0.162690 + 0.0146168i
\(671\) 29697.4 1.70858
\(672\) −11595.4 + 33055.2i −0.665630 + 1.89752i
\(673\) 30638.5 1.75487 0.877436 0.479694i \(-0.159252\pi\)
0.877436 + 0.479694i \(0.159252\pi\)
\(674\) −208.737 + 18.7539i −0.0119292 + 0.00107177i
\(675\) −2873.96 2873.96i −0.163879 0.163879i
\(676\) −2770.59 15294.4i −0.157635 0.870184i
\(677\) −12468.9 + 12468.9i −0.707855 + 0.707855i −0.966084 0.258229i \(-0.916861\pi\)
0.258229 + 0.966084i \(0.416861\pi\)
\(678\) 12157.4 + 10152.9i 0.688645 + 0.575104i
\(679\) 3754.41i 0.212196i
\(680\) −6522.33 + 11482.2i −0.367823 + 0.647533i
\(681\) 23453.8i 1.31975i
\(682\) 5554.45 6651.05i 0.311864 0.373434i
\(683\) 13838.5 13838.5i 0.775280 0.775280i −0.203744 0.979024i \(-0.565311\pi\)
0.979024 + 0.203744i \(0.0653111\pi\)
\(684\) −8145.99 + 11750.2i −0.455365 + 0.656843i
\(685\) −11713.1 11713.1i −0.653333 0.653333i
\(686\) 416.914 + 4640.40i 0.0232039 + 0.258267i
\(687\) −17306.6 −0.961116
\(688\) −3757.58 + 8258.89i −0.208221 + 0.457656i
\(689\) 3961.95 0.219068
\(690\) 624.398 + 6949.77i 0.0344499 + 0.383439i
\(691\) −106.012 106.012i −0.00583628 0.00583628i 0.704183 0.710019i \(-0.251314\pi\)
−0.710019 + 0.704183i \(0.751314\pi\)
\(692\) −5238.60 3631.73i −0.287777 0.199505i
\(693\) 18588.2 18588.2i 1.01891 1.01891i
\(694\) −5391.37 + 6455.77i −0.294890 + 0.353109i
\(695\) 10129.8i 0.552870i
\(696\) −689.863 2504.23i −0.0375707 0.136383i
\(697\) 31900.4i 1.73359i
\(698\) 20302.6 + 16955.2i 1.10095 + 0.919434i
\(699\) −6567.17 + 6567.17i −0.355355 + 0.355355i
\(700\) 15972.4 2893.43i 0.862431 0.156231i
\(701\) 7839.35 + 7839.35i 0.422380 + 0.422380i 0.886022 0.463643i \(-0.153458\pi\)
−0.463643 + 0.886022i \(0.653458\pi\)
\(702\) −2239.41 + 201.199i −0.120400 + 0.0108173i
\(703\) −12350.0 −0.662574
\(704\) 3967.64 15684.1i 0.212409 0.839653i
\(705\) −11312.7 −0.604341
\(706\) −6245.17 + 561.095i −0.332918 + 0.0299109i
\(707\) −12149.1 12149.1i −0.646273 0.646273i
\(708\) 35045.5 6348.55i 1.86030 0.336996i
\(709\) 2728.30 2728.30i 0.144518 0.144518i −0.631146 0.775664i \(-0.717415\pi\)
0.775664 + 0.631146i \(0.217415\pi\)
\(710\) 3079.19 + 2571.50i 0.162760 + 0.135925i
\(711\) 27499.9i 1.45053i
\(712\) 1578.90 + 5731.48i 0.0831066 + 0.301680i
\(713\) 4665.84i 0.245073i
\(714\) 31044.3 37173.3i 1.62718 1.94843i
\(715\) 2349.01 2349.01i 0.122864 0.122864i
\(716\) −20476.0 14195.3i −1.06875 0.740925i
\(717\) −23309.5 23309.5i −1.21410 1.21410i
\(718\) 527.011 + 5865.82i 0.0273926 + 0.304889i
\(719\) −32717.8 −1.69704 −0.848519 0.529166i \(-0.822505\pi\)
−0.848519 + 0.529166i \(0.822505\pi\)
\(720\) −12838.9 5841.37i −0.664553 0.302354i
\(721\) −45824.0 −2.36696
\(722\) 1012.01 + 11264.1i 0.0521652 + 0.580616i
\(723\) −30620.3 30620.3i −1.57508 1.57508i
\(724\) 781.844 1127.77i 0.0401340 0.0578914i
\(725\) −851.111 + 851.111i −0.0435993 + 0.0435993i
\(726\) 4686.62 5611.88i 0.239582 0.286882i
\(727\) 25847.2i 1.31859i 0.751883 + 0.659297i \(0.229146\pi\)
−0.751883 + 0.659297i \(0.770854\pi\)
\(728\) 4435.26 7808.03i 0.225799 0.397507i
\(729\) 27662.0i 1.40537i
\(730\) −9573.13 7994.75i −0.485366 0.405341i
\(731\) 8870.50 8870.50i 0.448820 0.448820i
\(732\) 10417.3 + 57506.1i 0.526004 + 2.90367i
\(733\) 10131.9 + 10131.9i 0.510547 + 0.510547i 0.914694 0.404147i \(-0.132432\pi\)
−0.404147 + 0.914694i \(0.632432\pi\)
\(734\) −12702.8 + 1141.28i −0.638787 + 0.0573915i
\(735\) 14192.1 0.712223
\(736\) −3773.48 7851.36i −0.188984 0.393213i
\(737\) −4798.27 −0.239819
\(738\) −33937.7 + 3049.11i −1.69277 + 0.152086i
\(739\) 19163.7 + 19163.7i 0.953921 + 0.953921i 0.998984 0.0450633i \(-0.0143490\pi\)
−0.0450633 + 0.998984i \(0.514349\pi\)
\(740\) −2171.76 11988.7i −0.107886 0.595558i
\(741\) 4685.72 4685.72i 0.232300 0.232300i
\(742\) −13433.9 11219.0i −0.664656 0.555070i
\(743\) 23322.1i 1.15155i −0.817607 0.575777i \(-0.804699\pi\)
0.817607 0.575777i \(-0.195301\pi\)
\(744\) 14827.5 + 8422.59i 0.730650 + 0.415037i
\(745\) 21309.8i 1.04796i
\(746\) 22208.1 26592.5i 1.08994 1.30512i
\(747\) −10922.8 + 10922.8i −0.534999 + 0.534999i
\(748\) −12743.6 + 18382.1i −0.622933 + 0.898552i
\(749\) 1977.03 + 1977.03i 0.0964473 + 0.0964473i
\(750\) 2679.37 + 29822.3i 0.130449 + 1.45194i
\(751\) 25994.0 1.26303 0.631515 0.775364i \(-0.282434\pi\)
0.631515 + 0.775364i \(0.282434\pi\)
\(752\) 13225.4 4954.16i 0.641330 0.240239i
\(753\) −5306.32 −0.256804
\(754\) 59.5842 + 663.192i 0.00287789 + 0.0320319i
\(755\) 13125.5 + 13125.5i 0.632698 + 0.632698i
\(756\) 8162.97 + 5659.09i 0.392704 + 0.272247i
\(757\) 22145.0 22145.0i 1.06324 1.06324i 0.0653808 0.997860i \(-0.479174\pi\)
0.997860 0.0653808i \(-0.0208262\pi\)
\(758\) −9031.52 + 10814.6i −0.432770 + 0.518210i
\(759\) 11819.0i 0.565222i
\(760\) 7695.22 2119.87i 0.367283 0.101179i
\(761\) 16497.5i 0.785853i 0.919570 + 0.392926i \(0.128537\pi\)
−0.919570 + 0.392926i \(0.871463\pi\)
\(762\) −44250.1 36954.4i −2.10369 1.75684i
\(763\) 23725.9 23725.9i 1.12573 1.12573i
\(764\) 30918.0 5600.84i 1.46410 0.265224i
\(765\) 13789.7 + 13789.7i 0.651723 + 0.651723i
\(766\) −8577.66 + 770.656i −0.404600 + 0.0363511i
\(767\) −9130.02 −0.429812
\(768\) 31762.5 + 2181.27i 1.49236 + 0.102487i
\(769\) −24867.3 −1.16611 −0.583055 0.812433i \(-0.698143\pi\)
−0.583055 + 0.812433i \(0.698143\pi\)
\(770\) −14616.5 + 1313.21i −0.684082 + 0.0614610i
\(771\) 44481.2 + 44481.2i 2.07776 + 2.07776i
\(772\) −25575.9 + 4633.11i −1.19235 + 0.215996i
\(773\) 1881.72 1881.72i 0.0875559 0.0875559i −0.661972 0.749528i \(-0.730280\pi\)