Properties

Label 108.4.h.b.35.10
Level 108
Weight 4
Character 108.35
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.10
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.93145 - 2.06627i) q^{2} +(-0.538974 - 7.98182i) q^{4} +(4.71466 - 2.72201i) q^{5} +(-20.9358 - 12.0873i) q^{7} +(-17.5336 - 14.3029i) q^{8} +O(q^{10})\) \(q+(1.93145 - 2.06627i) q^{2} +(-0.538974 - 7.98182i) q^{4} +(4.71466 - 2.72201i) q^{5} +(-20.9358 - 12.0873i) q^{7} +(-17.5336 - 14.3029i) q^{8} +(3.48173 - 14.9992i) q^{10} +(25.3999 - 43.9939i) q^{11} +(25.0883 + 43.4542i) q^{13} +(-65.4121 + 19.9130i) q^{14} +(-63.4190 + 8.60399i) q^{16} -51.7146i q^{17} -27.9305i q^{19} +(-24.2677 - 36.1645i) q^{20} +(-41.8447 - 137.455i) q^{22} +(-3.93548 - 6.81645i) q^{23} +(-47.6813 + 82.5864i) q^{25} +(138.245 + 32.0905i) q^{26} +(-85.1946 + 173.620i) q^{28} +(212.788 + 122.853i) q^{29} +(51.4009 - 29.6763i) q^{31} +(-104.713 + 147.659i) q^{32} +(-106.856 - 99.8843i) q^{34} -131.607 q^{35} +295.334 q^{37} +(-57.7121 - 53.9465i) q^{38} +(-121.598 - 19.7064i) q^{40} +(146.833 - 84.7741i) q^{41} +(284.968 + 164.526i) q^{43} +(-364.841 - 179.026i) q^{44} +(-21.6859 - 5.03388i) q^{46} +(-47.9742 + 83.0938i) q^{47} +(120.704 + 209.066i) q^{49} +(78.5519 + 258.034i) q^{50} +(333.322 - 223.671i) q^{52} -300.751i q^{53} -276.555i q^{55} +(194.198 + 511.375i) q^{56} +(664.839 - 202.393i) q^{58} +(113.273 + 196.195i) q^{59} +(173.722 - 300.896i) q^{61} +(37.9590 - 163.527i) q^{62} +(102.857 + 501.562i) q^{64} +(236.566 + 136.581i) q^{65} +(-904.675 + 522.314i) q^{67} +(-412.776 + 27.8728i) q^{68} +(-254.193 + 271.936i) q^{70} +243.524 q^{71} -1094.68 q^{73} +(570.424 - 610.241i) q^{74} +(-222.936 + 15.0538i) q^{76} +(-1063.53 + 614.031i) q^{77} +(530.679 + 306.388i) q^{79} +(-275.579 + 213.192i) q^{80} +(108.435 - 467.135i) q^{82} +(283.063 - 490.280i) q^{83} +(-140.768 - 243.817i) q^{85} +(890.358 - 271.046i) q^{86} +(-1074.59 + 408.082i) q^{88} +212.529i q^{89} -1213.00i q^{91} +(-52.2866 + 35.0862i) q^{92} +(79.0345 + 259.620i) q^{94} +(-76.0272 - 131.683i) q^{95} +(234.298 - 405.817i) q^{97} +(665.122 + 154.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93145 2.06627i 0.682872 0.730538i
\(3\) 0 0
\(4\) −0.538974 7.98182i −0.0673717 0.997728i
\(5\) 4.71466 2.72201i 0.421692 0.243464i −0.274109 0.961699i \(-0.588383\pi\)
0.695801 + 0.718234i \(0.255049\pi\)
\(6\) 0 0
\(7\) −20.9358 12.0873i −1.13043 0.652651i −0.186383 0.982477i \(-0.559677\pi\)
−0.944042 + 0.329826i \(0.893010\pi\)
\(8\) −17.5336 14.3029i −0.774885 0.632103i
\(9\) 0 0
\(10\) 3.48173 14.9992i 0.110102 0.474317i
\(11\) 25.3999 43.9939i 0.696214 1.20588i −0.273556 0.961856i \(-0.588200\pi\)
0.969770 0.244022i \(-0.0784669\pi\)
\(12\) 0 0
\(13\) 25.0883 + 43.4542i 0.535249 + 0.927078i 0.999151 + 0.0411921i \(0.0131156\pi\)
−0.463902 + 0.885886i \(0.653551\pi\)
\(14\) −65.4121 + 19.9130i −1.24872 + 0.380141i
\(15\) 0 0
\(16\) −63.4190 + 8.60399i −0.990922 + 0.134437i
\(17\) 51.7146i 0.737801i −0.929469 0.368901i \(-0.879734\pi\)
0.929469 0.368901i \(-0.120266\pi\)
\(18\) 0 0
\(19\) 27.9305i 0.337247i −0.985681 0.168624i \(-0.946068\pi\)
0.985681 0.168624i \(-0.0539322\pi\)
\(20\) −24.2677 36.1645i −0.271321 0.404332i
\(21\) 0 0
\(22\) −41.8447 137.455i −0.405515 1.33207i
\(23\) −3.93548 6.81645i −0.0356785 0.0617969i 0.847635 0.530580i \(-0.178026\pi\)
−0.883313 + 0.468783i \(0.844693\pi\)
\(24\) 0 0
\(25\) −47.6813 + 82.5864i −0.381450 + 0.660691i
\(26\) 138.245 + 32.0905i 1.04277 + 0.242056i
\(27\) 0 0
\(28\) −85.1946 + 173.620i −0.575010 + 1.17183i
\(29\) 212.788 + 122.853i 1.36254 + 0.786665i 0.989962 0.141335i \(-0.0451395\pi\)
0.372581 + 0.928000i \(0.378473\pi\)
\(30\) 0 0
\(31\) 51.4009 29.6763i 0.297802 0.171936i −0.343653 0.939097i \(-0.611664\pi\)
0.641455 + 0.767161i \(0.278331\pi\)
\(32\) −104.713 + 147.659i −0.578461 + 0.815710i
\(33\) 0 0
\(34\) −106.856 99.8843i −0.538992 0.503824i
\(35\) −131.607 −0.635589
\(36\) 0 0
\(37\) 295.334 1.31223 0.656116 0.754660i \(-0.272198\pi\)
0.656116 + 0.754660i \(0.272198\pi\)
\(38\) −57.7121 53.9465i −0.246372 0.230297i
\(39\) 0 0
\(40\) −121.598 19.7064i −0.480657 0.0778963i
\(41\) 146.833 84.7741i 0.559304 0.322915i −0.193562 0.981088i \(-0.562004\pi\)
0.752866 + 0.658173i \(0.228671\pi\)
\(42\) 0 0
\(43\) 284.968 + 164.526i 1.01063 + 0.583488i 0.911376 0.411574i \(-0.135021\pi\)
0.0992550 + 0.995062i \(0.468354\pi\)
\(44\) −364.841 179.026i −1.25004 0.613390i
\(45\) 0 0
\(46\) −21.6859 5.03388i −0.0695088 0.0161349i
\(47\) −47.9742 + 83.0938i −0.148888 + 0.257882i −0.930817 0.365486i \(-0.880903\pi\)
0.781928 + 0.623368i \(0.214236\pi\)
\(48\) 0 0
\(49\) 120.704 + 209.066i 0.351908 + 0.609522i
\(50\) 78.5519 + 258.034i 0.222178 + 0.729832i
\(51\) 0 0
\(52\) 333.322 223.671i 0.888911 0.596492i
\(53\) 300.751i 0.779459i −0.920929 0.389729i \(-0.872569\pi\)
0.920929 0.389729i \(-0.127431\pi\)
\(54\) 0 0
\(55\) 276.555i 0.678013i
\(56\) 194.198 + 511.375i 0.463406 + 1.22027i
\(57\) 0 0
\(58\) 664.839 202.393i 1.50513 0.458198i
\(59\) 113.273 + 196.195i 0.249947 + 0.432921i 0.963511 0.267669i \(-0.0862534\pi\)
−0.713564 + 0.700590i \(0.752920\pi\)
\(60\) 0 0
\(61\) 173.722 300.896i 0.364637 0.631570i −0.624081 0.781360i \(-0.714526\pi\)
0.988718 + 0.149790i \(0.0478597\pi\)
\(62\) 37.9590 163.527i 0.0777548 0.334966i
\(63\) 0 0
\(64\) 102.857 + 501.562i 0.200892 + 0.979613i
\(65\) 236.566 + 136.581i 0.451421 + 0.260628i
\(66\) 0 0
\(67\) −904.675 + 522.314i −1.64961 + 0.952401i −0.672378 + 0.740208i \(0.734727\pi\)
−0.977228 + 0.212193i \(0.931939\pi\)
\(68\) −412.776 + 27.8728i −0.736125 + 0.0497069i
\(69\) 0 0
\(70\) −254.193 + 271.936i −0.434026 + 0.464322i
\(71\) 243.524 0.407057 0.203528 0.979069i \(-0.434759\pi\)
0.203528 + 0.979069i \(0.434759\pi\)
\(72\) 0 0
\(73\) −1094.68 −1.75510 −0.877552 0.479481i \(-0.840825\pi\)
−0.877552 + 0.479481i \(0.840825\pi\)
\(74\) 570.424 610.241i 0.896086 0.958635i
\(75\) 0 0
\(76\) −222.936 + 15.0538i −0.336481 + 0.0227209i
\(77\) −1063.53 + 614.031i −1.57404 + 0.908770i
\(78\) 0 0
\(79\) 530.679 + 306.388i 0.755773 + 0.436346i 0.827776 0.561059i \(-0.189606\pi\)
−0.0720031 + 0.997404i \(0.522939\pi\)
\(80\) −275.579 + 213.192i −0.385134 + 0.297945i
\(81\) 0 0
\(82\) 108.435 467.135i 0.146032 0.629103i
\(83\) 283.063 490.280i 0.374340 0.648376i −0.615888 0.787834i \(-0.711203\pi\)
0.990228 + 0.139458i \(0.0445360\pi\)
\(84\) 0 0
\(85\) −140.768 243.817i −0.179628 0.311125i
\(86\) 890.358 271.046i 1.11639 0.339857i
\(87\) 0 0
\(88\) −1074.59 + 408.082i −1.30172 + 0.494337i
\(89\) 212.529i 0.253124i 0.991959 + 0.126562i \(0.0403943\pi\)
−0.991959 + 0.126562i \(0.959606\pi\)
\(90\) 0 0
\(91\) 1213.00i 1.39732i
\(92\) −52.2866 + 35.0862i −0.0592528 + 0.0397608i
\(93\) 0 0
\(94\) 79.0345 + 259.620i 0.0867211 + 0.284869i
\(95\) −76.0272 131.683i −0.0821076 0.142215i
\(96\) 0 0
\(97\) 234.298 405.817i 0.245252 0.424788i −0.716951 0.697124i \(-0.754463\pi\)
0.962202 + 0.272336i \(0.0877961\pi\)
\(98\) 665.122 + 154.393i 0.685587 + 0.159143i
\(99\) 0 0
\(100\) 684.889 + 336.072i 0.684889 + 0.336072i
\(101\) −1552.98 896.613i −1.52997 0.883330i −0.999362 0.0357140i \(-0.988629\pi\)
−0.530610 0.847616i \(-0.678037\pi\)
\(102\) 0 0
\(103\) −119.871 + 69.2074i −0.114672 + 0.0662059i −0.556239 0.831022i \(-0.687756\pi\)
0.441567 + 0.897228i \(0.354423\pi\)
\(104\) 181.630 1120.74i 0.171253 1.05671i
\(105\) 0 0
\(106\) −621.434 580.886i −0.569424 0.532271i
\(107\) −771.292 −0.696857 −0.348428 0.937335i \(-0.613285\pi\)
−0.348428 + 0.937335i \(0.613285\pi\)
\(108\) 0 0
\(109\) −275.772 −0.242332 −0.121166 0.992632i \(-0.538663\pi\)
−0.121166 + 0.992632i \(0.538663\pi\)
\(110\) −571.439 534.154i −0.495314 0.462996i
\(111\) 0 0
\(112\) 1431.72 + 586.432i 1.20790 + 0.494755i
\(113\) 542.916 313.453i 0.451976 0.260948i −0.256689 0.966494i \(-0.582631\pi\)
0.708664 + 0.705546i \(0.249298\pi\)
\(114\) 0 0
\(115\) −37.1089 21.4249i −0.0300907 0.0173729i
\(116\) 865.906 1764.65i 0.693080 1.41245i
\(117\) 0 0
\(118\) 624.173 + 144.888i 0.486947 + 0.113034i
\(119\) −625.088 + 1082.68i −0.481527 + 0.834029i
\(120\) 0 0
\(121\) −624.809 1082.20i −0.469428 0.813073i
\(122\) −286.197 940.124i −0.212385 0.697663i
\(123\) 0 0
\(124\) −264.575 394.278i −0.191609 0.285542i
\(125\) 1199.66i 0.858406i
\(126\) 0 0
\(127\) 71.3408i 0.0498463i −0.999689 0.0249231i \(-0.992066\pi\)
0.999689 0.0249231i \(-0.00793410\pi\)
\(128\) 1235.03 + 756.214i 0.852828 + 0.522191i
\(129\) 0 0
\(130\) 739.130 225.009i 0.498661 0.151805i
\(131\) −358.903 621.638i −0.239370 0.414601i 0.721164 0.692765i \(-0.243608\pi\)
−0.960534 + 0.278164i \(0.910274\pi\)
\(132\) 0 0
\(133\) −337.604 + 584.747i −0.220105 + 0.381233i
\(134\) −668.093 + 2878.13i −0.430705 + 1.85547i
\(135\) 0 0
\(136\) −739.666 + 906.744i −0.466366 + 0.571711i
\(137\) −190.925 110.231i −0.119065 0.0687420i 0.439285 0.898348i \(-0.355232\pi\)
−0.558350 + 0.829606i \(0.688565\pi\)
\(138\) 0 0
\(139\) −1214.70 + 701.309i −0.741222 + 0.427945i −0.822513 0.568746i \(-0.807429\pi\)
0.0812916 + 0.996690i \(0.474095\pi\)
\(140\) 70.9326 + 1050.46i 0.0428207 + 0.634145i
\(141\) 0 0
\(142\) 470.356 503.188i 0.277968 0.297371i
\(143\) 2548.96 1.49059
\(144\) 0 0
\(145\) 1337.63 0.766099
\(146\) −2114.32 + 2261.91i −1.19851 + 1.28217i
\(147\) 0 0
\(148\) −159.177 2357.30i −0.0884073 1.30925i
\(149\) 1289.36 744.413i 0.708917 0.409293i −0.101743 0.994811i \(-0.532442\pi\)
0.810660 + 0.585517i \(0.199109\pi\)
\(150\) 0 0
\(151\) 1704.17 + 983.903i 0.918433 + 0.530257i 0.883135 0.469120i \(-0.155429\pi\)
0.0352979 + 0.999377i \(0.488762\pi\)
\(152\) −399.486 + 489.723i −0.213175 + 0.261328i
\(153\) 0 0
\(154\) −785.408 + 3383.52i −0.410974 + 1.77047i
\(155\) 161.559 279.828i 0.0837206 0.145008i
\(156\) 0 0
\(157\) 564.122 + 977.088i 0.286763 + 0.496689i 0.973035 0.230656i \(-0.0740874\pi\)
−0.686272 + 0.727345i \(0.740754\pi\)
\(158\) 1658.06 504.755i 0.834863 0.254153i
\(159\) 0 0
\(160\) −91.7548 + 981.193i −0.0453366 + 0.484813i
\(161\) 190.277i 0.0931424i
\(162\) 0 0
\(163\) 1940.05i 0.932250i 0.884719 + 0.466125i \(0.154350\pi\)
−0.884719 + 0.466125i \(0.845650\pi\)
\(164\) −755.792 1126.31i −0.359862 0.536278i
\(165\) 0 0
\(166\) −466.329 1531.84i −0.218037 0.716227i
\(167\) 1242.52 + 2152.11i 0.575743 + 0.997217i 0.995960 + 0.0897933i \(0.0286206\pi\)
−0.420217 + 0.907424i \(0.638046\pi\)
\(168\) 0 0
\(169\) −160.344 + 277.723i −0.0729830 + 0.126410i
\(170\) −775.678 180.056i −0.349952 0.0812334i
\(171\) 0 0
\(172\) 1159.63 2363.24i 0.514075 1.04765i
\(173\) 2492.67 + 1439.15i 1.09546 + 0.632464i 0.935025 0.354583i \(-0.115377\pi\)
0.160435 + 0.987046i \(0.448710\pi\)
\(174\) 0 0
\(175\) 1996.49 1152.67i 0.862402 0.497908i
\(176\) −1232.31 + 3008.59i −0.527779 + 1.28853i
\(177\) 0 0
\(178\) 439.144 + 410.491i 0.184917 + 0.172851i
\(179\) −2965.78 −1.23840 −0.619198 0.785235i \(-0.712542\pi\)
−0.619198 + 0.785235i \(0.712542\pi\)
\(180\) 0 0
\(181\) 1250.55 0.513551 0.256776 0.966471i \(-0.417340\pi\)
0.256776 + 0.966471i \(0.417340\pi\)
\(182\) −2506.38 2342.84i −1.02080 0.954193i
\(183\) 0 0
\(184\) −28.4914 + 175.806i −0.0114153 + 0.0704379i
\(185\) 1392.40 803.902i 0.553358 0.319482i
\(186\) 0 0
\(187\) −2275.12 1313.54i −0.889698 0.513668i
\(188\) 689.097 + 338.136i 0.267327 + 0.131176i
\(189\) 0 0
\(190\) −418.936 97.2465i −0.159962 0.0371316i
\(191\) −387.763 + 671.626i −0.146898 + 0.254435i −0.930080 0.367358i \(-0.880262\pi\)
0.783181 + 0.621793i \(0.213596\pi\)
\(192\) 0 0
\(193\) 2185.71 + 3785.76i 0.815185 + 1.41194i 0.909195 + 0.416370i \(0.136698\pi\)
−0.0940101 + 0.995571i \(0.529969\pi\)
\(194\) −385.992 1267.94i −0.142848 0.469241i
\(195\) 0 0
\(196\) 1603.67 1076.12i 0.584428 0.392173i
\(197\) 1648.60i 0.596233i −0.954530 0.298116i \(-0.903642\pi\)
0.954530 0.298116i \(-0.0963584\pi\)
\(198\) 0 0
\(199\) 2946.42i 1.04958i −0.851232 0.524790i \(-0.824144\pi\)
0.851232 0.524790i \(-0.175856\pi\)
\(200\) 2017.25 766.062i 0.713205 0.270844i
\(201\) 0 0
\(202\) −4852.15 + 1477.11i −1.69008 + 0.514502i
\(203\) −2969.92 5144.05i −1.02684 1.77853i
\(204\) 0 0
\(205\) 461.513 799.363i 0.157236 0.272341i
\(206\) −88.5233 + 381.356i −0.0299403 + 0.128982i
\(207\) 0 0
\(208\) −1964.95 2539.96i −0.655024 0.846705i
\(209\) −1228.77 709.432i −0.406679 0.234796i
\(210\) 0 0
\(211\) 477.089 275.447i 0.155659 0.0898700i −0.420147 0.907456i \(-0.638021\pi\)
0.575806 + 0.817586i \(0.304688\pi\)
\(212\) −2400.54 + 162.097i −0.777688 + 0.0525135i
\(213\) 0 0
\(214\) −1489.72 + 1593.70i −0.475864 + 0.509080i
\(215\) 1791.37 0.568234
\(216\) 0 0
\(217\) −1434.82 −0.448857
\(218\) −532.642 + 569.821i −0.165482 + 0.177033i
\(219\) 0 0
\(220\) −2207.42 + 149.056i −0.676472 + 0.0456789i
\(221\) 2247.21 1297.43i 0.684000 0.394907i
\(222\) 0 0
\(223\) 1564.82 + 903.449i 0.469902 + 0.271298i 0.716199 0.697897i \(-0.245880\pi\)
−0.246297 + 0.969194i \(0.579214\pi\)
\(224\) 3977.04 1825.67i 1.18628 0.544565i
\(225\) 0 0
\(226\) 400.938 1727.23i 0.118009 0.508380i
\(227\) 752.796 1303.88i 0.220109 0.381241i −0.734732 0.678358i \(-0.762692\pi\)
0.954841 + 0.297117i \(0.0960252\pi\)
\(228\) 0 0
\(229\) −767.015 1328.51i −0.221335 0.383364i 0.733878 0.679281i \(-0.237708\pi\)
−0.955214 + 0.295917i \(0.904375\pi\)
\(230\) −115.944 + 35.2961i −0.0332396 + 0.0101189i
\(231\) 0 0
\(232\) −1973.80 5197.54i −0.558561 1.47084i
\(233\) 1257.04i 0.353440i 0.984261 + 0.176720i \(0.0565487\pi\)
−0.984261 + 0.176720i \(0.943451\pi\)
\(234\) 0 0
\(235\) 522.346i 0.144996i
\(236\) 1504.94 1009.87i 0.415098 0.278546i
\(237\) 0 0
\(238\) 1029.79 + 3382.76i 0.280469 + 0.921309i
\(239\) 916.982 + 1588.26i 0.248178 + 0.429858i 0.963020 0.269428i \(-0.0868347\pi\)
−0.714842 + 0.699286i \(0.753501\pi\)
\(240\) 0 0
\(241\) −358.771 + 621.410i −0.0958941 + 0.166094i −0.909981 0.414649i \(-0.863904\pi\)
0.814087 + 0.580743i \(0.197238\pi\)
\(242\) −3442.91 799.194i −0.914540 0.212290i
\(243\) 0 0
\(244\) −2495.33 1224.45i −0.654701 0.321259i
\(245\) 1138.16 + 657.117i 0.296794 + 0.171354i
\(246\) 0 0
\(247\) 1213.70 700.728i 0.312655 0.180511i
\(248\) −1325.70 214.846i −0.339444 0.0550109i
\(249\) 0 0
\(250\) 2478.82 + 2317.09i 0.627099 + 0.586182i
\(251\) 1053.84 0.265010 0.132505 0.991182i \(-0.457698\pi\)
0.132505 + 0.991182i \(0.457698\pi\)
\(252\) 0 0
\(253\) −399.843 −0.0993594
\(254\) −147.410 137.791i −0.0364146 0.0340386i
\(255\) 0 0
\(256\) 3947.94 1091.31i 0.963853 0.266434i
\(257\) −5985.55 + 3455.76i −1.45280 + 0.838772i −0.998639 0.0521496i \(-0.983393\pi\)
−0.454157 + 0.890922i \(0.650059\pi\)
\(258\) 0 0
\(259\) −6183.04 3569.78i −1.48338 0.856430i
\(260\) 962.665 1961.84i 0.229623 0.467954i
\(261\) 0 0
\(262\) −1977.68 459.073i −0.466341 0.108251i
\(263\) 1325.23 2295.36i 0.310712 0.538168i −0.667805 0.744336i \(-0.732766\pi\)
0.978517 + 0.206168i \(0.0660993\pi\)
\(264\) 0 0
\(265\) −818.648 1417.94i −0.189770 0.328692i
\(266\) 556.181 + 1826.99i 0.128202 + 0.421128i
\(267\) 0 0
\(268\) 4656.62 + 6939.44i 1.06137 + 1.58169i
\(269\) 2386.16i 0.540843i −0.962742 0.270422i \(-0.912837\pi\)
0.962742 0.270422i \(-0.0871631\pi\)
\(270\) 0 0
\(271\) 4287.45i 0.961048i 0.876982 + 0.480524i \(0.159554\pi\)
−0.876982 + 0.480524i \(0.840446\pi\)
\(272\) 444.951 + 3279.69i 0.0991880 + 0.731104i
\(273\) 0 0
\(274\) −596.530 + 181.598i −0.131524 + 0.0400392i
\(275\) 2422.20 + 4195.37i 0.531142 + 0.919965i
\(276\) 0 0
\(277\) −2416.58 + 4185.64i −0.524181 + 0.907909i 0.475422 + 0.879758i \(0.342295\pi\)
−0.999604 + 0.0281511i \(0.991038\pi\)
\(278\) −897.046 + 3864.46i −0.193530 + 0.833722i
\(279\) 0 0
\(280\) 2307.55 + 1882.35i 0.492508 + 0.401758i
\(281\) −1501.29 866.770i −0.318717 0.184011i 0.332104 0.943243i \(-0.392242\pi\)
−0.650821 + 0.759232i \(0.725575\pi\)
\(282\) 0 0
\(283\) −3227.63 + 1863.47i −0.677960 + 0.391420i −0.799086 0.601217i \(-0.794683\pi\)
0.121126 + 0.992637i \(0.461350\pi\)
\(284\) −131.253 1943.77i −0.0274241 0.406132i
\(285\) 0 0
\(286\) 4923.19 5266.85i 1.01788 1.08893i
\(287\) −4098.75 −0.843003
\(288\) 0 0
\(289\) 2238.61 0.455649
\(290\) 2583.57 2763.91i 0.523147 0.559664i
\(291\) 0 0
\(292\) 590.004 + 8737.54i 0.118244 + 1.75112i
\(293\) −5604.61 + 3235.82i −1.11749 + 0.645183i −0.940759 0.339076i \(-0.889886\pi\)
−0.176731 + 0.984259i \(0.556552\pi\)
\(294\) 0 0
\(295\) 1068.09 + 616.661i 0.210802 + 0.121706i
\(296\) −5178.28 4224.12i −1.01683 0.829466i
\(297\) 0 0
\(298\) 952.180 4101.97i 0.185095 0.797386i
\(299\) 197.469 342.026i 0.0381937 0.0661534i
\(300\) 0 0
\(301\) −3977.34 6888.96i −0.761629 1.31918i
\(302\) 5324.54 1620.92i 1.01454 0.308852i
\(303\) 0 0
\(304\) 240.314 + 1771.32i 0.0453386 + 0.334186i
\(305\) 1891.50i 0.355104i
\(306\) 0 0
\(307\) 7858.86i 1.46101i 0.682909 + 0.730503i \(0.260715\pi\)
−0.682909 + 0.730503i \(0.739285\pi\)
\(308\) 5474.30 + 8157.98i 1.01275 + 1.50923i
\(309\) 0 0
\(310\) −266.158 874.298i −0.0487637 0.160183i
\(311\) 3745.08 + 6486.66i 0.682842 + 1.18272i 0.974110 + 0.226075i \(0.0725896\pi\)
−0.291268 + 0.956642i \(0.594077\pi\)
\(312\) 0 0
\(313\) 4304.38 7455.41i 0.777310 1.34634i −0.156176 0.987729i \(-0.549917\pi\)
0.933487 0.358612i \(-0.116750\pi\)
\(314\) 3108.51 + 721.570i 0.558672 + 0.129683i
\(315\) 0 0
\(316\) 2159.51 4400.92i 0.384437 0.783453i
\(317\) 4705.42 + 2716.67i 0.833699 + 0.481336i 0.855117 0.518434i \(-0.173485\pi\)
−0.0214185 + 0.999771i \(0.506818\pi\)
\(318\) 0 0
\(319\) 10809.6 6240.92i 1.89724 1.09537i
\(320\) 1850.19 + 2084.72i 0.323215 + 0.364186i
\(321\) 0 0
\(322\) 393.164 + 367.511i 0.0680440 + 0.0636043i
\(323\) −1444.41 −0.248821
\(324\) 0 0
\(325\) −4784.97 −0.816684
\(326\) 4008.68 + 3747.12i 0.681044 + 0.636607i
\(327\) 0 0
\(328\) −3787.03 613.734i −0.637512 0.103316i
\(329\) 2008.75 1159.75i 0.336615 0.194344i
\(330\) 0 0
\(331\) −1367.21 789.359i −0.227035 0.131079i 0.382168 0.924093i \(-0.375177\pi\)
−0.609204 + 0.793014i \(0.708511\pi\)
\(332\) −4065.89 1995.11i −0.672122 0.329807i
\(333\) 0 0
\(334\) 6846.72 + 1589.31i 1.12166 + 0.260369i
\(335\) −2843.49 + 4925.07i −0.463751 + 0.803240i
\(336\) 0 0
\(337\) −3400.38 5889.62i −0.549645 0.952013i −0.998299 0.0583070i \(-0.981430\pi\)
0.448654 0.893706i \(-0.351904\pi\)
\(338\) 264.156 + 867.724i 0.0425095 + 0.139639i
\(339\) 0 0
\(340\) −1870.23 + 1254.99i −0.298316 + 0.200181i
\(341\) 3015.10i 0.478818i
\(342\) 0 0
\(343\) 2455.93i 0.386611i
\(344\) −2643.32 6960.59i −0.414298 1.09096i
\(345\) 0 0
\(346\) 7788.15 2370.90i 1.21010 0.368383i
\(347\) −6228.10 10787.4i −0.963522 1.66887i −0.713535 0.700620i \(-0.752907\pi\)
−0.249987 0.968249i \(1.41957\pi\)
\(348\) 0 0
\(349\) −910.729 + 1577.43i −0.139685 + 0.241942i −0.927378 0.374127i \(-0.877942\pi\)
0.787692 + 0.616069i \(0.211276\pi\)
\(350\) 1474.39 6351.63i 0.225169 0.970025i
\(351\) 0 0
\(352\) 3836.42 + 8357.25i 0.580914 + 1.26546i
\(353\) −6019.52 3475.37i −0.907611 0.524010i −0.0279495 0.999609i \(-0.508898\pi\)
−0.879662 + 0.475600i \(0.842231\pi\)
\(354\) 0 0
\(355\) 1148.14 662.877i 0.171653 0.0991038i
\(356\) 1696.37 114.548i 0.252549 0.0170534i
\(357\) 0 0
\(358\) −5728.27 + 6128.11i −0.845666 + 0.904695i
\(359\) −318.743 −0.0468597 −0.0234298 0.999725i \(-0.507459\pi\)
−0.0234298 + 0.999725i \(0.507459\pi\)
\(360\) 0 0
\(361\) 6078.89 0.886264
\(362\) 2415.38 2583.98i 0.350690 0.375169i
\(363\) 0 0
\(364\) −9681.92 + 653.773i −1.39415 + 0.0941401i
\(365\) −5161.05 + 2979.73i −0.740114 + 0.427305i
\(366\) 0 0
\(367\) −5425.21 3132.25i −0.771645 0.445510i 0.0618160 0.998088i \(-0.480311\pi\)
−0.833461 + 0.552578i \(0.813644\pi\)
\(368\) 308.233 + 398.432i 0.0436624 + 0.0564394i
\(369\) 0 0
\(370\) 1028.27 4429.78i 0.144479 0.622414i
\(371\) −3635.26 + 6296.45i −0.508715 + 0.881120i
\(372\) 0 0
\(373\) 6066.19 + 10506.9i 0.842078 + 1.45852i 0.888135 + 0.459583i \(0.152001\pi\)
−0.0460564 + 0.998939i \(0.514665\pi\)
\(374\) −7108.44 + 2163.98i −0.982804 + 0.299189i
\(375\) 0 0
\(376\) 2029.64 770.768i 0.278380 0.105716i
\(377\) 12328.7i 1.68425i
\(378\) 0 0
\(379\) 1928.72i 0.261402i −0.991422 0.130701i \(-0.958277\pi\)
0.991422 0.130701i \(-0.0417229\pi\)
\(380\) −1010.09 + 677.809i −0.136360 + 0.0915023i
\(381\) 0 0
\(382\) 638.816 + 2098.44i 0.0855619 + 0.281061i
\(383\) 2974.93 + 5152.73i 0.396898 + 0.687448i 0.993341 0.115208i \(-0.0367533\pi\)
−0.596443 + 0.802655i \(0.703420\pi\)
\(384\) 0 0
\(385\) −3342.80 + 5789.90i −0.442506 + 0.766443i
\(386\) 12044.0 + 2795.74i 1.58814 + 0.368652i
\(387\) 0 0
\(388\) −3365.44 1651.40i −0.440346 0.216076i
\(389\) −2023.11 1168.05i −0.263691 0.152242i 0.362326 0.932051i \(-0.381983\pi\)
−0.626017 + 0.779809i \(0.715316\pi\)
\(390\) 0 0
\(391\) −352.510 + 203.522i −0.0455938 + 0.0263236i
\(392\) 873.855 5392.10i 0.112593 0.694751i
\(393\) 0 0
\(394\) −3406.46 3184.19i −0.435571 0.407151i
\(395\) 3335.97 0.424938
\(396\) 0 0
\(397\) −6080.16 −0.768652 −0.384326 0.923198i \(-0.625566\pi\)
−0.384326 + 0.923198i \(0.625566\pi\)
\(398\) −6088.12 5690.88i −0.766758 0.716729i
\(399\) 0 0
\(400\) 2313.33 5647.80i 0.289166 0.705975i
\(401\) 11997.7 6926.90i 1.49411 0.862626i 0.494135 0.869385i \(-0.335485\pi\)
0.999977 + 0.00675957i \(0.00215165\pi\)
\(402\) 0 0
\(403\) 2579.12 + 1489.05i 0.318797 + 0.184057i
\(404\) −6319.59 + 12878.9i −0.778246 + 1.58601i
\(405\) 0 0
\(406\) −16365.3 3798.83i −2.00048 0.464367i
\(407\) 7501.45 12992.9i 0.913594 1.58239i
\(408\) 0 0
\(409\) 135.435 + 234.581i 0.0163737 + 0.0283601i 0.874096 0.485753i \(-0.161455\pi\)
−0.857722 + 0.514113i \(0.828121\pi\)
\(410\) −760.313 2497.54i −0.0915834 0.300841i
\(411\) 0 0
\(412\) 617.008 + 919.486i 0.0737811 + 0.109951i
\(413\) 5476.64i 0.652513i
\(414\) 0 0
\(415\) 3082.01i 0.364553i
\(416\) −9043.47 845.687i −1.06585 0.0996712i
\(417\) 0 0
\(418\) −3839.20 + 1168.74i −0.449237 + 0.136759i
\(419\) −3950.75 6842.90i −0.460637 0.797846i 0.538356 0.842718i \(-0.319046\pi\)
−0.998993 + 0.0448712i \(0.985712\pi\)
\(420\) 0 0
\(421\) 3331.91 5771.04i 0.385718 0.668083i −0.606150 0.795350i \(-0.707287\pi\)
0.991869 + 0.127267i \(0.0406204\pi\)
\(422\) 352.325 1517.81i 0.0406420 0.175085i
\(423\) 0 0
\(424\) −4301.60 + 5273.26i −0.492698 + 0.603991i
\(425\) 4270.92 + 2465.82i 0.487459 + 0.281435i
\(426\) 0 0
\(427\) −7274.02 + 4199.66i −0.824390 + 0.475962i
\(428\) 415.706 + 6156.32i 0.0469484 + 0.695273i
\(429\) 0 0
\(430\) 3459.95 3701.46i 0.388031 0.415117i
\(431\) 14773.0 1.65102 0.825509 0.564388i \(-0.190888\pi\)
0.825509 + 0.564388i \(0.190888\pi\)
\(432\) 0 0
\(433\) −2372.81 −0.263349 −0.131674 0.991293i \(-0.542035\pi\)
−0.131674 + 0.991293i \(0.542035\pi\)
\(434\) −2771.29 + 2964.74i −0.306512 + 0.327907i
\(435\) 0 0
\(436\) 148.634 + 2201.17i 0.0163263 + 0.241782i
\(437\) −190.387 + 109.920i −0.0208408 + 0.0120325i
\(438\) 0 0
\(439\) −2509.56 1448.89i −0.272835 0.157522i 0.357340 0.933974i \(-0.383684\pi\)
−0.630175 + 0.776453i \(0.717017\pi\)
\(440\) −3955.53 + 4849.02i −0.428574 + 0.525382i
\(441\) 0 0
\(442\) 1659.54 7149.28i 0.178589 0.769359i
\(443\) 3932.06 6810.53i 0.421711 0.730425i −0.574396 0.818578i \(-0.694763\pi\)
0.996107 + 0.0881526i \(0.0280963\pi\)
\(444\) 0 0
\(445\) 578.508 + 1002.00i 0.0616267 + 0.106741i
\(446\) 4889.15 1488.38i 0.519076 0.158019i
\(447\) 0 0
\(448\) 3909.13 11743.8i 0.412253 1.23849i
\(449\) 1335.91i 0.140413i −0.997532 0.0702064i \(-0.977634\pi\)
0.997532 0.0702064i \(-0.0223658\pi\)
\(450\) 0 0
\(451\) 8613.02i 0.899271i
\(452\) −2794.54 4164.52i −0.290806 0.433368i
\(453\) 0 0
\(454\) −1240.18 4073.87i −0.128204 0.421137i
\(455\) −3301.79 5718.87i −0.340198 0.589241i
\(456\) 0 0
\(457\) −8696.49 + 15062.8i −0.890164 + 1.54181i −0.0504849 + 0.998725i \(0.516077\pi\)
−0.839679 + 0.543084i \(0.817257\pi\)
\(458\) −4226.52 981.091i −0.431206 0.100095i
\(459\) 0 0
\(460\) −151.009 + 307.744i −0.0153061 + 0.0311927i
\(461\) 1933.14 + 1116.10i 0.195304 + 0.112759i 0.594463 0.804123i \(-0.297365\pi\)
−0.399159 + 0.916882i \(0.630698\pi\)
\(462\) 0 0
\(463\) −3435.96 + 1983.75i −0.344887 + 0.199121i −0.662431 0.749123i \(-0.730475\pi\)
0.317544 + 0.948244i \(0.397142\pi\)
\(464\) −14551.8 5960.41i −1.45593 0.596347i
\(465\) 0 0
\(466\) 2597.39 + 2427.92i 0.258201 + 0.241354i
\(467\) −8810.21 −0.872993 −0.436497 0.899706i \(-0.643781\pi\)
−0.436497 + 0.899706i \(0.643781\pi\)
\(468\) 0 0
\(469\) 25253.4 2.48634
\(470\) 1079.31 + 1008.89i 0.105925 + 0.0990137i
\(471\) 0 0
\(472\) 820.055 5060.13i 0.0799705 0.493456i
\(473\) 14476.3 8357.89i 1.40723 0.812466i
\(474\) 0 0
\(475\) 2306.68 + 1331.76i 0.222816 + 0.128643i
\(476\) 8978.70 + 4405.80i 0.864576 + 0.424243i
\(477\) 0 0
\(478\) 5052.89 + 1172.91i 0.483502 + 0.112234i
\(479\) −9734.00 + 16859.8i −0.928513 + 1.60823i −0.142702 + 0.989766i \(0.545579\pi\)
−0.785811 + 0.618466i \(0.787754\pi\)
\(480\) 0 0
\(481\) 7409.42 + 12833.5i 0.702371 + 1.21654i
\(482\) 591.053 + 1941.54i 0.0558542 + 0.183475i
\(483\) 0 0
\(484\) −8301.18 + 5570.39i −0.779600 + 0.523140i
\(485\) 2551.05i 0.238840i
\(486\) 0 0
\(487\) 5226.26i 0.486293i −0.969990 0.243146i \(-0.921820\pi\)
0.969990 0.243146i \(-0.0781795\pi\)
\(488\) −7349.65 + 2791.07i −0.681769 + 0.258906i
\(489\) 0 0
\(490\) 3556.09 1082.56i 0.327852 0.0998063i
\(491\) 4793.56 + 8302.69i 0.440591 + 0.763127i 0.997733 0.0672904i \(-0.0214354\pi\)
−0.557142 + 0.830417i \(0.688102\pi\)
\(492\) 0 0
\(493\) 6353.30 11004.2i 0.580402 1.00529i
\(494\) 896.303 3861.25i 0.0816327 0.351672i
\(495\) 0 0
\(496\) −3004.46 + 2324.29i −0.271984 + 0.210411i
\(497\) −5098.37 2943.55i −0.460147 0.265666i
\(498\) 0 0
\(499\) −2085.65 + 1204.15i −0.187108 + 0.108027i −0.590628 0.806944i \(-0.701120\pi\)
0.403520 + 0.914971i \(0.367787\pi\)
\(500\) 9575.47 646.585i 0.856456 0.0578323i
\(501\) 0 0
\(502\) 2035.43 2177.51i 0.180968 0.193600i
\(503\) −17192.1 −1.52397 −0.761985 0.647595i \(-0.775775\pi\)
−0.761985 + 0.647595i \(0.775775\pi\)
\(504\) 0 0
\(505\) −9762.37 −0.860237
\(506\) −772.278 + 826.185i −0.0678497 + 0.0725858i
\(507\) 0 0
\(508\) −569.430 + 38.4508i −0.0497330 + 0.00335823i
\(509\) 2562.66 1479.55i 0.223159 0.128841i −0.384253 0.923228i \(-0.625541\pi\)
0.607412 + 0.794387i \(0.292208\pi\)
\(510\) 0 0
\(511\) 22918.0 + 13231.7i 1.98401 + 1.14547i
\(512\) 5370.32 10265.4i 0.463548 0.886072i
\(513\) 0 0
\(514\) −4420.27 + 19042.4i −0.379319 + 1.63410i
\(515\) −376.767 + 652.579i −0.0322375 + 0.0558370i
\(516\) 0 0
\(517\) 2437.08 + 4221.14i 0.207316 + 0.359083i
\(518\) −19318.4 + 5880.99i −1.63861 + 0.498834i
\(519\) 0 0
\(520\) −2194.35 5778.33i −0.185055 0.487301i
\(521\) 12490.4i 1.05032i 0.851004 + 0.525159i \(0.175994\pi\)
−0.851004 + 0.525159i \(0.824006\pi\)
\(522\) 0 0
\(523\) 13273.1i 1.10974i −0.831939 0.554868i \(-0.812769\pi\)
0.831939 0.554868i \(-0.187231\pi\)
\(524\) −4768.36 + 3199.74i −0.397532 + 0.266759i
\(525\) 0 0
\(526\) −2183.23 7171.68i −0.180976 0.594487i
\(527\) −1534.70 2658.17i −0.126855 0.219719i
\(528\) 0 0
\(529\) 6052.52 10483.3i 0.497454 0.861616i
\(530\) −4511.03 1047.13i −0.369711 0.0858200i
\(531\) 0 0
\(532\) 4849.30 + 2379.53i 0.395195 + 0.193920i
\(533\) 7367.58 + 4253.68i 0.598734 + 0.345679i
\(534\) 0 0
\(535\) −3636.38 + 2099.47i −0.293859 + 0.169660i
\(536\) 23332.8 + 3781.36i 1.88027 + 0.304720i
\(537\) 0 0
\(538\) −4930.46 4608.76i −0.395107 0.369327i
\(539\) 12263.5 0.980012
\(540\) 0 0
\(541\) −12385.8 −0.984302 −0.492151 0.870510i \(-0.663789\pi\)
−0.492151 + 0.870510i \(0.663789\pi\)
\(542\) 8859.05 + 8281.01i 0.702082 + 0.656273i
\(543\) 0 0
\(544\) 7636.13 + 5415.17i 0.601832 + 0.426789i
\(545\) −1300.17 + 750.656i −0.102190 + 0.0589992i
\(546\) 0 0
\(547\) 15941.6 + 9203.89i 1.24609 + 0.719433i 0.970328 0.241792i \(-0.0777351\pi\)
0.275766 + 0.961225i \(0.411068\pi\)
\(548\) −776.939 + 1583.34i −0.0605642 + 0.123425i
\(549\) 0 0
\(550\) 13347.2 + 3098.24i 1.03477 + 0.240199i
\(551\) 3431.35 5943.28i 0.265300 0.459514i
\(552\) 0 0
\(553\) −7406.78 12828.9i −0.569563 0.986512i
\(554\) 3981.17 + 13077.7i 0.305313 + 1.00292i
\(555\) 0 0
\(556\) 6252.42 + 9317.56i 0.476910 + 0.710706i
\(557\) 13864.9i 1.05472i 0.849643 + 0.527358i \(0.176817\pi\)
−0.849643 + 0.527358i \(0.823183\pi\)
\(558\) 0 0
\(559\) 16510.7i 1.24925i
\(560\) 8346.38 1132.34i 0.629819 0.0854469i
\(561\) 0 0
\(562\) −4690.66 + 1427.95i −0.352070 + 0.107179i
\(563\) 7442.77 + 12891.3i 0.557150 + 0.965012i 0.997733 + 0.0672999i \(0.0214384\pi\)
−0.440583 + 0.897712i \(0.645228\pi\)
\(564\) 0 0
\(565\) 1706.44 2955.65i 0.127063 0.220080i
\(566\) −2383.57 + 10268.4i −0.177012 + 0.762566i
\(567\) 0 0
\(568\) −4269.87 3483.09i −0.315422 0.257302i
\(569\) −5893.56 3402.65i −0.434219 0.250697i 0.266923 0.963718i \(-0.413993\pi\)
−0.701142 + 0.713021i \(0.747326\pi\)
\(570\) 0 0
\(571\) 7163.27 4135.72i 0.524998 0.303108i −0.213979 0.976838i \(-0.568643\pi\)
0.738977 + 0.673731i \(0.235309\pi\)
\(572\) −1373.82 20345.3i −0.100424 1.48720i
\(573\) 0 0
\(574\) −7916.55 + 8469.15i −0.575663 + 0.615845i
\(575\) 750.595 0.0544382
\(576\) 0 0
\(577\) −12153.3 −0.876863 −0.438432 0.898765i \(-0.644466\pi\)
−0.438432 + 0.898765i \(0.644466\pi\)
\(578\) 4323.76 4625.57i 0.311150 0.332869i
\(579\) 0 0
\(580\) −720.949 10676.7i −0.0516134 0.764358i
\(581\) −11852.3 + 6842.92i −0.846327 + 0.488627i
\(582\) 0 0
\(583\) −13231.2 7639.04i −0.939932 0.542670i
\(584\) 19193.7 + 15657.0i 1.36000 + 1.10941i
\(585\) 0 0
\(586\) −4138.95 + 17830.5i −0.291772 + 1.25695i
\(587\) −7165.79 + 12411.5i −0.503856 + 0.872705i 0.496134 + 0.868246i \(0.334753\pi\)
−0.999990 + 0.00445871i \(0.998581\pi\)
\(588\) 0 0
\(589\) −828.874 1435.65i −0.0579850 0.100433i
\(590\) 3337.15 1015.91i 0.232862 0.0708887i
\(591\) 0 0
\(592\) −18729.8 + 2541.05i −1.30032 + 0.176413i
\(593\) 17892.9i 1.23908i −0.784966 0.619539i \(-0.787319\pi\)
0.784966 0.619539i \(-0.212681\pi\)
\(594\) 0 0
\(595\) 6805.99i 0.468938i
\(596\) −6636.71 9890.23i −0.456124 0.679731i
\(597\) 0 0
\(598\) −325.318 1068.63i −0.0222462 0.0730763i
\(599\) −5989.96 10374.9i −0.408586 0.707692i 0.586145 0.810206i \(-0.300645\pi\)
−0.994732 + 0.102514i \(0.967311\pi\)
\(600\) 0 0
\(601\) −1473.48 + 2552.14i −0.100007 + 0.173218i −0.911687 0.410885i \(-0.865220\pi\)
0.811680 + 0.584102i \(0.198553\pi\)
\(602\) −21916.5 5087.43i −1.48381 0.344432i
\(603\) 0 0
\(604\) 6934.83 14132.7i 0.467176 0.952070i
\(605\) −5891.53 3401.48i −0.395909 0.228578i
\(606\) 0 0
\(607\) −22272.8 + 12859.2i −1.48933 + 0.859866i −0.999926 0.0121903i \(-0.996120\pi\)
−0.489406 + 0.872056i \(0.662786\pi\)
\(608\) 4124.20 + 2924.68i 0.275096 + 0.195084i
\(609\) 0 0
\(610\) −3908.35 3653.34i −0.259417 0.242491i
\(611\) −4814.36 −0.318770
\(612\) 0 0
\(613\) −1851.43 −0.121988 −0.0609938 0.998138i \(-0.519427\pi\)
−0.0609938 + 0.998138i \(0.519427\pi\)
\(614\) 16238.6 + 15179.0i 1.06732 + 0.997681i
\(615\) 0 0
\(616\) 27430.0 + 4445.36i 1.79413 + 0.290761i
\(617\) −17363.4 + 10024.8i −1.13294 + 0.654103i −0.944673 0.328015i \(-0.893621\pi\)
−0.188267 + 0.982118i \(0.560287\pi\)
\(618\) 0 0
\(619\) −19210.5 11091.2i −1.24739 0.720183i −0.276805 0.960926i \(-0.589276\pi\)
−0.970589 + 0.240743i \(0.922609\pi\)
\(620\) −2320.61 1138.71i −0.150319 0.0737609i
\(621\) 0 0
\(622\) 20636.7 + 4790.34i 1.33031 + 0.308802i
\(623\) 2568.90 4449.46i 0.165202 0.286138i
\(624\) 0 0
\(625\) −2694.67 4667.31i −0.172459 0.298708i
\(626\) −7091.20 23293.8i −0.452750 1.48723i
\(627\) 0 0
\(628\) 7494.90 5029.35i 0.476240 0.319574i
\(629\) 15273.1i 0.968166i
\(630\) 0 0
\(631\) 28148.1i 1.77584i −0.459994 0.887922i \(-0.652149\pi\)
0.459994 0.887922i \(-0.347851\pi\)
\(632\) −4922.51 12962.3i −0.309821 0.815844i
\(633\) 0 0
\(634\) 14701.7 4475.55i 0.920944 0.280358i
\(635\) −194.191 336.348i −0.0121358 0.0210198i
\(636\) 0 0
\(637\) −6056.53 + 10490.2i −0.376716 + 0.652492i
\(638\) 7982.77 34389.6i 0.495362 2.13401i
\(639\) 0 0
\(640\) 7881.16 + 203.534i 0.486766 + 0.0125709i
\(641\) −6980.56 4030.23i −0.430134 0.248338i 0.269270 0.963065i \(-0.413218\pi\)
−0.699404 + 0.714727i \(0.746551\pi\)
\(642\) 0 0
\(643\) 666.166 384.611i 0.0408570 0.0235888i −0.479432 0.877579i \(-0.659157\pi\)
0.520289 + 0.853990i \(0.325824\pi\)
\(644\) 1518.76 102.554i 0.0929307 0.00627516i
\(645\) 0 0
\(646\) −2789.82 + 2984.55i −0.169913 + 0.181773i
\(647\) 25155.2 1.52852 0.764259 0.644909i \(-0.223105\pi\)
0.764259 + 0.644909i \(0.223105\pi\)
\(648\) 0 0
\(649\) 11508.5 0.696067
\(650\) −9241.94 + 9887.05i −0.557690 + 0.596619i
\(651\) 0 0
\(652\) 15485.2 1045.64i 0.930131 0.0628073i
\(653\) −17852.0 + 10306.9i −1.06984 + 0.617671i −0.928137 0.372238i \(-0.878590\pi\)
−0.141701 + 0.989910i \(0.545257\pi\)
\(654\) 0 0
\(655\) −3384.21 1953.88i −0.201881 0.116556i
\(656\) −8582.62 + 6639.64i −0.510815 + 0.395175i
\(657\) 0 0
\(658\) 1483.44 6390.65i 0.0878886 0.378622i
\(659\) 12082.8 20928.0i 0.714231 1.23708i −0.249024 0.968497i \(-0.580110\pi\)
0.963255 0.268587i \(-0.0865568\pi\)
\(660\) 0 0
\(661\) −9976.53 17279.9i −0.587053 1.01681i −0.994616 0.103629i \(-0.966955\pi\)
0.407563 0.913177i \(-0.366379\pi\)
\(662\) −4271.73 + 1300.42i −0.250794 + 0.0763478i
\(663\) 0 0
\(664\) −11975.5 + 4547.77i −0.699910 + 0.265795i
\(665\) 3675.84i 0.214351i
\(666\) 0 0
\(667\) 1933.95i 0.112268i
\(668\) 16508.1 11077.5i 0.956162 0.641620i
\(669\) 0 0
\(670\) 4684.47 + 15388.0i 0.270115 + 0.887298i
\(671\) −8825.05 15285.4i −0.507731 0.879416i
\(672\) 0 0
\(673\) 3449.60 5974.88i 0.197581 0.342221i −0.750162 0.661254i \(-0.770025\pi\)
0.947744 + 0.319033i \(0.103358\pi\)
\(674\) −18737.2 4349.43i −1.07082 0.248566i
\(675\) 0 0
\(676\) 2303.16 + 1130.15i 0.131040 + 0.0643007i
\(677\) 7812.18 + 4510.37i 0.443496 + 0.256052i 0.705079 0.709128i \(-0.250911\pi\)
−0.261584 + 0.965181i \(0.584245\pi\)
\(678\) 0 0
\(679\) −9810.44 + 5664.06i −0.554477 + 0.320128i
\(680\) −1019.11 + 6288.37i −0.0574720 + 0.354630i
\(681\) 0 0
\(682\) −6230.02 5823.52i −0.349794 0.326971i
\(683\) −7388.19 −0.413911 −0.206956 0.978350i \(-0.566356\pi\)
−0.206956 + 0.978350i \(0.566356\pi\)
\(684\) 0 0
\(685\) −1200.20 −0.0669448
\(686\) 5074.61 + 4743.51i 0.282434 + 0.264006i
\(687\) 0 0
\(688\) −19487.9 7982.23i −1.07990 0.442325i
\(689\) 13068.9 7545.32i 0.722620 0.417205i
\(690\) 0 0
\(691\) 25972.9 + 14995.5i 1.42989 + 0.825549i 0.997112 0.0759500i \(-0.0241989\pi\)
0.432781 + 0.901499i \(0.357532\pi\)
\(692\) 10143.5 20671.7i 0.557224 1.13558i
\(693\) 0 0
\(694\) −34319.0 7966.38i −1.87713 0.435734i
\(695\) −3817.95 + 6612.88i −0.208378 + 0.360922i
\(696\) 0 0
\(697\) −4384.06 7593.41i −0.238247 0.412656i
\(698\) 1500.37 + 4928.55i 0.0813608 + 0.267261i
\(699\) 0 0
\(700\) −10276.5 15314.4i −0.554878 0.826898i
\(701\) 23559.3i 1.26936i −0.772774 0.634681i \(-0.781131\pi\)
0.772774 0.634681i \(-0.218869\pi\)
\(702\) 0 0
\(703\) 8248.82i 0.442547i
\(704\) 24678.2 + 8214.55i 1.32116 + 0.439769i
\(705\) 0 0
\(706\) −18807.5 + 5725.46i −1.00259 + 0.305213i
\(707\) 21675.2 + 37542.6i 1.15301 + 1.99708i
\(708\) 0 0
\(709\) −6114.96 + 10591.4i −0.323910 + 0.561028i −0.981291 0.192530i \(-0.938331\pi\)
0.657381 + 0.753558i \(0.271664\pi\)
\(710\) 847.887 3652.68i 0.0448178 0.193074i
\(711\) 0 0
\(712\) 3039.78 3726.41i 0.160001 0.196142i
\(713\) −404.574 233.581i −0.0212502 0.0122688i
\(714\) 0 0
\(715\) 12017.5 6938.30i 0.628571 0.362906i
\(716\) 1598.48 + 23672.3i 0.0834329 + 1.23558i
\(717\) 0 0
\(718\) −615.638 + 658.611i −0.0319992 + 0.0342328i
\(719\) −37718.6 −1.95642 −0.978211 0.207613i \(-0.933431\pi\)
−0.978211 + 0.207613i \(0.933431\pi\)
\(720\) 0 0
\(721\) 3346.11 0.172837
\(722\) 11741.1 12560.6i 0.605205 0.647450i
\(723\) 0 0
\(724\) −674.014 9981.68i −0.0345988 0.512384i
\(725\) −20292.0 + 11715.6i −1.03949 + 0.600147i
\(726\) 0 0
\(727\) −7555.48 4362.16i −0.385443 0.222536i 0.294741 0.955577i \(-0.404767\pi\)
−0.680184 + 0.733041i \(0.738100\pi\)
\(728\) −17349.3 + 21268.2i −0.883252 + 1.08276i
\(729\) 0 0
\(730\) −3811.38 + 16419.4i −0.193241 + 0.832476i
\(731\) 8508.39 14737.0i 0.430498 0.745645i
\(732\) 0 0
\(733\) 7960.97 + 13788.8i 0.401153 + 0.694817i 0.993865 0.110597i \(-0.0352762\pi\)
−0.592712 + 0.805414i \(0.701943\pi\)
\(734\) −16950.6 + 5160.18i −0.852397 + 0.259490i
\(735\) 0 0
\(736\) 1418.61 + 132.659i 0.0710469 + 0.00664385i
\(737\) 53066.9i 2.65230i
\(738\) 0 0
\(739\) 21026.0i 1.04662i 0.852141 + 0.523312i \(0.175304\pi\)
−0.852141 + 0.523312i \(0.824696\pi\)
\(740\) −7167.07 10680.6i −0.356036 0.530577i
\(741\) 0 0
\(742\) 5988.86 + 19672.7i 0.296305 + 0.973328i
\(743\) −5813.11 10068.6i −0.287029 0.497148i 0.686071 0.727535i \(-0.259334\pi\)
−0.973099 + 0.230387i \(0.926001\pi\)
\(744\) 0 0
\(745\) 4052.60 7019.32i 0.199297 0.345192i
\(746\) 33426.8 + 7759.27i 1.64054 + 0.380814i
\(747\) 0 0
\(748\) −9258.24 + 18867.6i −0.452560 + 0.922284i
\(749\) 16147.6 + 9322.82i 0.787744 + 0.454804i
\(750\) 0 0
\(751\) −6096.06 + 3519.56i −0.296203 + 0.171013i −0.640736 0.767761i \(-0.721371\pi\)
0.344533 + 0.938774i \(0.388037\pi\)
\(752\) 2327.54 5682.49i 0.112868 0.275557i
\(753\) 0 0
\(754\) 25474.5 + 23812.3i 1.23041 + 1.15012i
\(755\) 10712.8 0.516395
\(756\) 0 0
\(757\) −28354.3 −1.36137 −0.680685 0.732577i \(-0.738318\pi\)
−0.680685 + 0.732577i \(0.738318\pi\)
\(758\) −3985.26 3725.23i −0.190964 0.178504i
\(759\) 0 0
\(760\) −550.409 + 3396.29i −0.0262703 + 0.162100i
\(761\) 20274.5 11705.5i 0.965771 0.557588i 0.0678265 0.997697i \(-0.478394\pi\)
0.897944 + 0.440109i \(0.145060\pi\)
\(762\) 0 0
\(763\) 5773.51 + 3333.34i 0.273939 + 0.158158i
\(764\) 5569.79 + 2733.07i 0.263754 + 0.129423i
\(765\) 0 0
\(766\) 16392.9 + 3805.24i 0.773237 + 0.179490i
\(767\) −5683.65 + 9844.37i −0.267568 + 0.463441i
\(768\) 0 0
\(769\) 12632.8 + 21880.6i 0.592392 + 1.02605i 0.993909 + 0.110202i \(0.0351498\pi\)
−0.401517 + 0.915852i \(0.631517\pi\)
\(770\) 5507.05 + 18090.1i 0.257741 + 0.846650i
\(771\) 0 0
\(772\) 29039.2 19486.4i 1.35381 0.908458i
\(773\) 31081.3i 1.44621i −0.690740 0.723103i \(-0.742715\pi\)
0.690740 0.723103i \(-0.257285\pi\)
\(774\) 0 0
\(775\) 5660.02i 0.262340i
\(776\) −9912.44 + 3764.31i −0.458551 + 0.174138i
\(777\) 0 0
\(778\) −6321.05 + 1924.28i −0.291286 + 0.0886746i
\(779\) −2367.78 4101.12i −0.108902 0.188624i
\(780\) 0