Properties

Label 16.4.e.a.5.1
Level 16
Weight 4
Character 16.5
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 5.1
Root \(1.28199 - 1.53509i\)
Character \(\chi\) = 16.5
Dual form 16.4.e.a.13.1

$q$-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 \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81708 0.253099i −0.995988 0.0894841i
\(3\) 5.49618 5.49618i 1.05774 1.05774i 0.0595129 0.998228i \(-0.481045\pi\)
0.998228 0.0595129i \(-0.0189548\pi\)
\(4\) 7.87188 + 1.42600i 0.983985 + 0.178250i
\(5\) −4.66372 4.66372i −0.417136 0.417136i 0.467079 0.884215i \(-0.345306\pi\)
−0.884215 + 0.467079i \(0.845306\pi\)
\(6\) −16.8743 + 14.0921i −1.14815 + 0.958846i
\(7\) 24.8965i 1.34429i 0.740422 + 0.672143i \(0.234626\pi\)
−0.740422 + 0.672143i \(0.765374\pi\)
\(8\) −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 0.943578 0.331151i \(-0.107437\pi\)
−0.331151 + 0.943578i \(0.607437\pi\)
\(12\) 51.1028 35.4277i 1.22934 0.852259i
\(13\) −11.2714 + 11.2714i −0.240471 + 0.240471i −0.817045 0.576574i \(-0.804389\pi\)
0.576574 + 0.817045i \(0.304389\pi\)
\(14\) 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 −0.440909 0.897552i \(-0.645344\pi\)
0.897552 + 0.440909i \(0.145344\pi\)
\(20\) −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 \(-0.930003\pi\)
0.975919 0.218135i \(-0.0699973\pi\)
\(24\) −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 −0.672881 0.739751i \(-0.734943\pi\)
0.739751 + 0.672881i \(0.234943\pi\)
\(30\) 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 0.244233 0.969717i \(-0.421464\pi\)
−0.969717 + 0.244233i \(0.921464\pi\)
\(38\) −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 \(0.240910\pi\)
−0.727008 + 0.686629i \(0.759090\pi\)
\(42\) −350.844 420.110i −1.28896 1.54344i
\(43\) −100.249 100.249i −0.355531 0.355531i 0.506632 0.862163i \(-0.330890\pi\)
−0.862163 + 0.506632i \(0.830890\pi\)
\(44\) 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 0.441676 0.897174i \(-0.354384\pi\)
−0.897174 + 0.441676i \(0.854384\pi\)
\(54\) 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 0.994868 0.101181i \(-0.0322622\pi\)
−0.101181 + 0.994868i \(0.532262\pi\)
\(60\) −403.555 73.1044i −0.868311 0.157296i
\(61\) 664.576 664.576i 1.39492 1.39492i 0.581061 0.813860i \(-0.302638\pi\)
0.813860 0.581061i \(-0.197362\pi\)
\(62\) 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 −0.798194 0.602400i \(-0.794211\pi\)
0.602400 + 0.798194i \(0.294211\pi\)
\(68\) −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 \(-0.942477\pi\)
0.983716 0.179731i \(-0.0575226\pi\)
\(72\) −200.814 + 728.964i −0.328697 + 1.19318i
\(73\) 668.587i 1.07195i 0.844235 + 0.535974i \(0.180055\pi\)
−0.844235 + 0.535974i \(0.819945\pi\)
\(74\) 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 −0.457125 0.889402i \(-0.651121\pi\)
0.889402 + 0.457125i \(0.151121\pi\)
\(84\) 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 \(0.0500079\pi\)
−0.987684 + 0.156459i \(0.949992\pi\)
\(90\) 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 0.905373 0.424617i \(-0.139591\pi\)
−0.424617 + 0.905373i \(0.639591\pi\)
\(102\) 1493.11 1246.93i 1.44941 1.21044i
\(103\) 1840.58i 1.76075i 0.474275 + 0.880377i \(0.342710\pi\)
−0.474275 + 0.880377i \(0.657290\pi\)
\(104\) 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 0.670323 0.742069i \(-0.266155\pi\)
−0.742069 + 0.670323i \(0.766155\pi\)
\(108\) −227.304 327.876i −0.202522 0.292129i
\(109\) 952.979 952.979i 0.837421 0.837421i −0.151098 0.988519i \(-0.548281\pi\)
0.988519 + 0.151098i \(0.0482809\pi\)
\(110\) −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 −0.452961 0.891530i \(-0.649632\pi\)
0.891530 + 0.452961i \(0.149632\pi\)
\(132\) 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 \(-0.713629\pi\)
0.621874 0.783117i \(-0.286371\pi\)
\(138\) 678.146 + 812.030i 0.418316 + 0.500903i
\(139\) −1086.02 1086.02i −0.662697 0.662697i 0.293318 0.956015i \(-0.405241\pi\)
−0.956015 + 0.293318i \(0.905241\pi\)
\(140\) 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 −0.952922 0.303214i \(-0.901940\pi\)
−0.303214 0.952922i \(-0.598060\pi\)
\(150\) 1148.50 + 1375.24i 0.625163 + 0.748587i
\(151\) 2814.39i 1.51677i 0.651809 + 0.758383i \(0.274010\pi\)
−0.651809 + 0.758383i \(0.725990\pi\)
\(152\) −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 −0.898888 0.438179i \(-0.855624\pi\)
0.438179 + 0.898888i \(0.355624\pi\)
\(158\) 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 −0.288433 0.957500i \(-0.593134\pi\)
0.957500 + 0.288433i \(0.0931342\pi\)
\(164\) −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 \(0.0913421\pi\)
−0.959109 + 0.283038i \(0.908658\pi\)
\(168\) −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 −0.819988 0.572381i \(-0.806020\pi\)
0.572381 + 0.819988i \(0.306020\pi\)
\(174\) −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 −0.996998 0.0774329i \(-0.975328\pi\)
0.0774329 + 0.996998i \(0.475328\pi\)
\(180\) −1449.01 + 1004.55i −0.600016 + 0.415969i
\(181\) 121.294 + 121.294i 0.0498104 + 0.0498104i 0.731573 0.681763i \(-0.238786\pi\)
−0.681763 + 0.731573i \(0.738786\pi\)
\(182\) 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 0.993070 0.117525i \(-0.0374961\pi\)
−0.117525 + 0.993070i \(0.537496\pi\)
\(198\) −2292.25 + 1914.31i −0.822743 + 0.687093i
\(199\) 1371.30i 0.488488i −0.969714 0.244244i \(-0.921460\pi\)
0.969714 0.244244i \(-0.0785397\pi\)
\(200\) −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 −0.920190 0.391471i \(-0.871966\pi\)
0.391471 + 0.920190i \(0.371966\pi\)
\(212\) −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 −0.946515 0.322661i \(-0.895423\pi\)
0.322661 + 0.946515i \(0.395423\pi\)
\(228\) 592.813 3272.48i 0.172193 0.950548i
\(229\) −1574.42 1574.42i −0.454325 0.454325i 0.442462 0.896787i \(-0.354105\pi\)
−0.896787 + 0.442462i \(0.854105\pi\)
\(230\) 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 \(-0.946276\pi\)
0.985791 0.167978i \(-0.0537239\pi\)
\(234\) −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 0.643801 0.765193i \(-0.277357\pi\)
−0.765193 + 0.643801i \(0.777357\pi\)
\(252\) 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 \(0.0153164\pi\)
−0.998843 + 0.0480992i \(0.984684\pi\)
\(264\) −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 −0.707648 0.706565i \(-0.750244\pi\)
0.706565 + 0.707648i \(0.250244\pi\)
\(270\) 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 0.852952 0.521989i \(-0.174810\pi\)
−0.521989 + 0.852952i \(0.674810\pi\)
\(278\) 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 \(-0.831778\pi\)
0.863572 0.504226i \(-0.168222\pi\)
\(282\) −3723.63 + 3109.69i −0.786308 + 0.656665i
\(283\) 644.104 + 644.104i 0.135293 + 0.135293i 0.771510 0.636217i \(-0.219502\pi\)
−0.636217 + 0.771510i \(0.719502\pi\)
\(284\) 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 0.549644 0.835399i \(-0.314763\pi\)
−0.835399 + 0.549644i \(0.814763\pi\)
\(294\) 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 −0.728272 0.685288i \(-0.759676\pi\)
0.685288 + 0.728272i \(0.259676\pi\)
\(308\) −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 \(-0.974686\pi\)
0.996839 0.0794423i \(-0.0253140\pi\)
\(312\) 744.577 2702.84i 0.135107 0.490443i
\(313\) 3515.02i 0.634762i 0.948298 + 0.317381i \(0.102803\pi\)
−0.948298 + 0.317381i \(0.897197\pi\)
\(314\) 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 −0.151506 0.988456i \(-0.548412\pi\)
0.988456 + 0.151506i \(0.0484121\pi\)
\(318\) 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 0.539633 0.841901i \(-0.318563\pi\)
−0.841901 + 0.539633i \(0.818563\pi\)
\(332\) 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 0.850798 0.525493i \(-0.176119\pi\)
−0.525493 + 0.850798i \(0.676119\pi\)
\(348\) 163.698 903.652i 0.0252159 0.139198i
\(349\) −6612.85 + 6612.85i −1.01426 + 1.01426i −0.0143661 + 0.999897i \(0.504573\pi\)
−0.999897 + 0.0143661i \(0.995427\pi\)
\(350\) −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 \(0.0489123\pi\)
−0.988217 + 0.153059i \(0.951088\pi\)
\(360\) 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 −0.973448 0.228908i \(-0.926485\pi\)
−0.228908 0.973448i \(-0.573515\pi\)
\(374\) 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 0.904301 0.426896i \(-0.140393\pi\)
−0.426896 + 0.904301i \(0.640393\pi\)
\(380\) −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 0.821754 0.569843i \(-0.192996\pi\)
−0.569843 + 0.821754i \(0.692996\pi\)
\(390\) −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 −0.748334 0.663322i \(-0.769146\pi\)
0.663322 + 0.748334i \(0.269146\pi\)
\(398\) −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 \(-0.902637\pi\)
0.953584 0.301129i \(-0.0973634\pi\)
\(410\) −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 −0.878344 0.478030i \(-0.841351\pi\)
0.478030 + 0.878344i \(0.341351\pi\)
\(420\) 1820.05 10047.1i 0.211450 1.16726i
\(421\) 7973.72 + 7973.72i 0.923077 + 0.923077i 0.997246 0.0741686i \(-0.0236303\pi\)
−0.0741686 + 0.997246i \(0.523630\pi\)
\(422\) 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 \(-0.913653\pi\)
0.963432 0.267951i \(-0.0863466\pi\)
\(440\) −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 0.163817 0.986491i \(-0.447619\pi\)
−0.986491 + 0.163817i \(0.947619\pi\)
\(444\) −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 \(-0.920492\pi\)
0.968967 0.247191i \(-0.0795076\pi\)
\(458\) 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 −0.153118 0.988208i \(-0.548931\pi\)
0.988208 + 0.153118i \(0.0489315\pi\)
\(462\) 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 0.269564 0.962982i \(-0.413120\pi\)
0.962982 0.269564i \(-0.0868796\pi\)
\(468\) 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 \(-0.742572\pi\)
0.690414 0.723414i \(-0.257428\pi\)
\(488\) −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 0.188932 0.981990i \(-0.439497\pi\)
−0.981990 + 0.188932i \(0.939497\pi\)
\(492\) 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 −0.625115 0.780533i \(-0.714948\pi\)
0.780533 + 0.625115i \(0.214948\pi\)
\(500\) −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 \(0.262742\pi\)
−0.678241 + 0.734839i \(0.737258\pi\)
\(504\) −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 −0.960434 0.278509i \(-0.910160\pi\)
0.278509 + 0.960434i \(0.410160\pi\)
\(510\) −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 \(0.0456599\pi\)
−0.989729 + 0.142953i \(0.954340\pi\)
\(522\) 894.749 + 1071.40i 0.0750232 + 0.0898348i
\(523\) −2019.50 2019.50i −0.168847 0.168847i 0.617626 0.786472i \(-0.288095\pi\)
−0.786472 + 0.617626i \(0.788095\pi\)
\(524\) 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 −0.0699388 + 0.997551i \(0.522280\pi\)
−0.997551 + 0.0699388i \(0.977720\pi\)
\(542\) 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 −0.885292 0.465035i \(-0.846042\pi\)
0.465035 + 0.885292i \(0.346042\pi\)
\(548\) 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 −0.781655 0.623711i \(-0.785624\pi\)
0.623711 + 0.781655i \(0.285624\pi\)
\(558\) 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 −0.288339 + 0.957528i \(0.593103\pi\)
−0.957528 + 0.288339i \(0.906897\pi\)
\(564\) 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 \(-0.933145\pi\)
0.978024 0.208491i \(-0.0668551\pi\)
\(570\) 5952.43 4971.02i 0.437403 0.365286i
\(571\) 4872.67 + 4872.67i 0.357119 + 0.357119i 0.862750 0.505631i \(-0.168740\pi\)
−0.505631 + 0.862750i \(0.668740\pi\)
\(572\) −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 0.963630 0.267242i \(-0.0861122\pi\)
−0.267242 + 0.963630i \(0.586112\pi\)
\(588\) −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 \(-0.775246\pi\)
0.760907 0.648861i \(-0.224754\pi\)
\(600\) 7079.74 + 12463.5i 0.481715 + 0.848034i
\(601\) 1065.92i 0.0723460i −0.999346 0.0361730i \(-0.988483\pi\)
0.999346 0.0361730i \(-0.0115167\pi\)
\(602\) −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 0.356781 0.934188i \(-0.383874\pi\)
−0.934188 + 0.356781i \(0.883874\pi\)
\(614\) 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 \(0.211771\pi\)
−0.786733 + 0.617293i \(0.788229\pi\)
\(618\) −25937.6 31058.4i −1.68829 2.02161i
\(619\) −15116.6 15116.6i −0.981565 0.981565i 0.0182677 0.999833i \(-0.494185\pi\)
−0.999833 + 0.0182677i \(0.994185\pi\)
\(620\) 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 \(0.0979605\pi\)
−0.953017 + 0.302917i \(0.902039\pi\)
\(632\) 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 −0.479450 0.877569i \(-0.659164\pi\)
0.877569 + 0.479450i \(0.159164\pi\)
\(644\) 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 \(0.0538932\pi\)
−0.985701 + 0.168503i \(0.946107\pi\)
\(648\) −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 −0.491614 0.870813i \(-0.663593\pi\)
0.870813 + 0.491614i \(0.163593\pi\)
\(654\) −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 −0.100294 0.994958i \(-0.531978\pi\)
0.994958 + 0.100294i \(0.0319785\pi\)
\(660\) −7383.28 10650.0i −0.435445 0.628110i
\(661\) −23460.1 23460.1i −1.38047 1.38047i −0.843777 0.536694i \(-0.819673\pi\)
−0.536694 0.843777i \(-0.680327\pi\)
\(662\) 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 0.258229 0.966084i \(-0.416861\pi\)
−0.966084 + 0.258229i \(0.916861\pi\)
\(678\) 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 0.979024 0.203744i \(-0.0653111\pi\)
−0.203744 + 0.979024i \(0.565311\pi\)
\(684\) −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 −0.710019 0.704183i \(-0.751314\pi\)
0.704183 + 0.710019i \(0.251314\pi\)
\(692\) −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 −0.463643 0.886022i \(-0.653458\pi\)
0.886022 + 0.463643i \(0.153458\pi\)
\(702\) −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 0.775664 0.631146i \(-0.217415\pi\)
−0.631146 + 0.775664i \(0.717415\pi\)
\(710\) 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 \(-0.770854\pi\)
0.751883 0.659297i \(-0.229146\pi\)
\(728\) 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 −0.404147 0.914694i \(-0.632432\pi\)
0.914694 + 0.404147i \(0.132432\pi\)
\(734\) −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 −0.0450633 0.998984i \(-0.514349\pi\)
0.998984 + 0.0450633i \(0.0143490\pi\)
\(740\) −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 \(0.195301\pi\)
−0.817607 + 0.575777i \(0.804699\pi\)
\(744\) 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 0.997860 + 0.0653808i \(0.0208262\pi\)
0.0653808 + 0.997860i \(0.479174\pi\)
\(758\) −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 \(-0.871463\pi\)
0.919570 0.392926i \(-0.128537\pi\)
\(762\) −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 0.749528 0.661972i \(-0.230280\pi\)