Properties

Label 108.4.h.b.71.5
Level 108
Weight 4
Character 108.71
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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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 71.5
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.823719 - 2.70582i) q^{2} +(-6.64298 + 4.45768i) q^{4} +(4.71466 + 2.72201i) q^{5} +(20.9358 - 12.0873i) q^{7} +(17.5336 + 14.3029i) q^{8} +O(q^{10})\) \(q+(-0.823719 - 2.70582i) q^{2} +(-6.64298 + 4.45768i) q^{4} +(4.71466 + 2.72201i) q^{5} +(20.9358 - 12.0873i) q^{7} +(17.5336 + 14.3029i) q^{8} +(3.48173 - 14.9992i) q^{10} +(-25.3999 - 43.9939i) q^{11} +(25.0883 - 43.4542i) q^{13} +(-49.9512 - 46.6920i) q^{14} +(24.2582 - 59.2245i) q^{16} +51.7146i q^{17} -27.9305i q^{19} +(-43.4533 + 2.93419i) q^{20} +(-98.1174 + 104.966i) q^{22} +(3.93548 - 6.81645i) q^{23} +(-47.6813 - 82.5864i) q^{25} +(-138.245 - 32.0905i) q^{26} +(-85.1946 + 173.620i) q^{28} +(212.788 - 122.853i) q^{29} +(-51.4009 - 29.6763i) q^{31} +(-180.233 - 16.8542i) q^{32} +(139.931 - 42.5982i) q^{34} +131.607 q^{35} +295.334 q^{37} +(-75.5750 + 23.0069i) q^{38} +(43.7327 + 115.160i) q^{40} +(146.833 + 84.7741i) q^{41} +(-284.968 + 164.526i) q^{43} +(364.841 + 179.026i) q^{44} +(-21.6859 - 5.03388i) q^{46} +(47.9742 + 83.0938i) q^{47} +(120.704 - 209.066i) q^{49} +(-184.188 + 197.045i) q^{50} +(27.0439 + 400.500i) q^{52} +300.751i q^{53} -276.555i q^{55} +(539.963 + 87.5075i) q^{56} +(-507.697 - 474.571i) q^{58} +(-113.273 + 196.195i) q^{59} +(173.722 + 300.896i) q^{61} +(-37.9590 + 163.527i) q^{62} +(102.857 + 501.562i) q^{64} +(236.566 - 136.581i) q^{65} +(904.675 + 522.314i) q^{67} +(-230.527 - 343.538i) q^{68} +(-108.407 - 356.105i) q^{70} -243.524 q^{71} -1094.68 q^{73} +(-243.272 - 799.122i) q^{74} +(124.505 + 185.542i) q^{76} +(-1063.53 - 614.031i) q^{77} +(-530.679 + 306.388i) q^{79} +(275.579 - 213.192i) q^{80} +(108.435 - 467.135i) q^{82} +(-283.063 - 490.280i) q^{83} +(-140.768 + 243.817i) q^{85} +(679.912 + 635.549i) q^{86} +(183.886 - 1134.66i) q^{88} -212.529i q^{89} -1213.00i q^{91} +(4.24224 + 62.8246i) q^{92} +(185.320 - 198.256i) q^{94} +(76.0272 - 131.683i) q^{95} +(234.298 + 405.817i) q^{97} +(-665.122 - 154.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.823719 2.70582i −0.291229 0.956654i
\(3\) 0 0
\(4\) −6.64298 + 4.45768i −0.830372 + 0.557210i
\(5\) 4.71466 + 2.72201i 0.421692 + 0.243464i 0.695801 0.718234i \(-0.255049\pi\)
−0.274109 + 0.961699i \(0.588383\pi\)
\(6\) 0 0
\(7\) 20.9358 12.0873i 1.13043 0.652651i 0.186383 0.982477i \(-0.440323\pi\)
0.944042 + 0.329826i \(0.106990\pi\)
\(8\) 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 −0.969770 0.244022i \(-0.921533\pi\)
0.273556 0.961856i \(1.58820\pi\)
\(12\) 0 0
\(13\) 25.0883 43.4542i 0.535249 0.927078i −0.463902 0.885886i \(-0.653551\pi\)
0.999151 0.0411921i \(-0.0131156\pi\)
\(14\) −49.9512 46.6920i −0.953573 0.891355i
\(15\) 0 0
\(16\) 24.2582 59.2245i 0.379035 0.925382i
\(17\) 51.7146i 0.737801i 0.929469 + 0.368901i \(0.120266\pi\)
−0.929469 + 0.368901i \(0.879734\pi\)
\(18\) 0 0
\(19\) 27.9305i 0.337247i −0.985681 0.168624i \(-0.946068\pi\)
0.985681 0.168624i \(-0.0539322\pi\)
\(20\) −43.4533 + 2.93419i −0.485822 + 0.0328052i
\(21\) 0 0
\(22\) −98.1174 + 104.966i −0.950850 + 1.01722i
\(23\) 3.93548 6.81645i 0.0356785 0.0617969i −0.847635 0.530580i \(-0.821974\pi\)
0.883313 + 0.468783i \(0.155307\pi\)
\(24\) 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 0.372581 0.928000i \(-0.378473\pi\)
0.989962 + 0.141335i \(0.0451395\pi\)
\(30\) 0 0
\(31\) −51.4009 29.6763i −0.297802 0.171936i 0.343653 0.939097i \(-0.388336\pi\)
−0.641455 + 0.767161i \(0.721669\pi\)
\(32\) −180.233 16.8542i −0.995656 0.0931073i
\(33\) 0 0
\(34\) 139.931 42.5982i 0.705820 0.214869i
\(35\) 131.607 0.635589
\(36\) 0 0
\(37\) 295.334 1.31223 0.656116 0.754660i \(-0.272198\pi\)
0.656116 + 0.754660i \(0.272198\pi\)
\(38\) −75.5750 + 23.0069i −0.322629 + 0.0982160i
\(39\) 0 0
\(40\) 43.7327 + 115.160i 0.172868 + 0.455210i
\(41\) 146.833 + 84.7741i 0.559304 + 0.322915i 0.752866 0.658173i \(-0.228671\pi\)
−0.193562 + 0.981088i \(0.562004\pi\)
\(42\) 0 0
\(43\) −284.968 + 164.526i −1.01063 + 0.583488i −0.911376 0.411574i \(-0.864979\pi\)
−0.0992550 + 0.995062i \(0.531646\pi\)
\(44\) 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 \(-0.119097\pi\)
−0.781928 + 0.623368i \(0.785764\pi\)
\(48\) 0 0
\(49\) 120.704 209.066i 0.351908 0.609522i
\(50\) −184.188 + 197.045i −0.520964 + 0.557328i
\(51\) 0 0
\(52\) 27.0439 + 400.500i 0.0721213 + 1.06807i
\(53\) 300.751i 0.779459i 0.920929 + 0.389729i \(0.127431\pi\)
−0.920929 + 0.389729i \(0.872569\pi\)
\(54\) 0 0
\(55\) 276.555i 0.678013i
\(56\) 539.963 + 87.5075i 1.28849 + 0.208816i
\(57\) 0 0
\(58\) −507.697 474.571i −1.14938 1.07438i
\(59\) −113.273 + 196.195i −0.249947 + 0.432921i −0.963511 0.267669i \(-0.913747\pi\)
0.713564 + 0.700590i \(0.247080\pi\)
\(60\) 0 0
\(61\) 173.722 + 300.896i 0.364637 + 0.631570i 0.988718 0.149790i \(-0.0478597\pi\)
−0.624081 + 0.781360i \(0.714526\pi\)
\(62\) −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 0.977228 + 0.212193i \(0.0680605\pi\)
0.672378 + 0.740208i \(0.265273\pi\)
\(68\) −230.527 343.538i −0.411110 0.612649i
\(69\) 0 0
\(70\) −108.407 356.105i −0.185102 0.608038i
\(71\) −243.524 −0.407057 −0.203528 0.979069i \(-0.565241\pi\)
−0.203528 + 0.979069i \(0.565241\pi\)
\(72\) 0 0
\(73\) −1094.68 −1.75510 −0.877552 0.479481i \(-0.840825\pi\)
−0.877552 + 0.479481i \(0.840825\pi\)
\(74\) −243.272 799.122i −0.382159 1.25535i
\(75\) 0 0
\(76\) 124.505 + 185.542i 0.187917 + 0.280041i
\(77\) −1063.53 614.031i −1.57404 0.908770i
\(78\) 0 0
\(79\) −530.679 + 306.388i −0.755773 + 0.436346i −0.827776 0.561059i \(-0.810394\pi\)
0.0720031 + 0.997404i \(0.477061\pi\)
\(80\) 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 \(-0.288797\pi\)
−0.990228 + 0.139458i \(0.955464\pi\)
\(84\) 0 0
\(85\) −140.768 + 243.817i −0.179628 + 0.311125i
\(86\) 679.912 + 635.549i 0.852521 + 0.796896i
\(87\) 0 0
\(88\) 183.886 1134.66i 0.222754 1.37450i
\(89\) 212.529i 0.253124i −0.991959 0.126562i \(-0.959606\pi\)
0.991959 0.126562i \(-0.0403943\pi\)
\(90\) 0 0
\(91\) 1213.00i 1.39732i
\(92\) 4.24224 + 62.8246i 0.00480744 + 0.0711948i
\(93\) 0 0
\(94\) 185.320 198.256i 0.203343 0.217537i
\(95\) 76.0272 131.683i 0.0821076 0.142215i
\(96\) 0 0
\(97\) 234.298 + 405.817i 0.245252 + 0.424788i 0.962202 0.272336i \(-0.0877961\pi\)
−0.716951 + 0.697124i \(0.754463\pi\)
\(98\) −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 −0.530610 + 0.847616i \(0.678037\pi\)
−0.999362 + 0.0357140i \(0.988629\pi\)
\(102\) 0 0
\(103\) 119.871 + 69.2074i 0.114672 + 0.0662059i 0.556239 0.831022i \(-0.312244\pi\)
−0.441567 + 0.897228i \(0.645577\pi\)
\(104\) 1061.41 403.076i 1.00077 0.380046i
\(105\) 0 0
\(106\) 813.779 247.734i 0.745672 0.227001i
\(107\) 771.292 0.696857 0.348428 0.937335i \(-0.386715\pi\)
0.348428 + 0.937335i \(0.386715\pi\)
\(108\) 0 0
\(109\) −275.772 −0.242332 −0.121166 0.992632i \(-0.538663\pi\)
−0.121166 + 0.992632i \(0.538663\pi\)
\(110\) −748.310 + 227.804i −0.648623 + 0.197457i
\(111\) 0 0
\(112\) −207.998 1533.13i −0.175481 1.29345i
\(113\) 542.916 + 313.453i 0.451976 + 0.260948i 0.708664 0.705546i \(-0.249298\pi\)
−0.256689 + 0.966494i \(0.582631\pi\)
\(114\) 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
\(122\) 671.073 717.916i 0.498001 0.532762i
\(123\) 0 0
\(124\) 473.742 31.9895i 0.343091 0.0231673i
\(125\) 1199.66i 0.858406i
\(126\) 0 0
\(127\) 71.3408i 0.0498463i −0.999689 0.0249231i \(-0.992066\pi\)
0.999689 0.0249231i \(-0.00793410\pi\)
\(128\) 1272.41 691.458i 0.878645 0.477475i
\(129\) 0 0
\(130\) −564.428 527.601i −0.380797 0.355951i
\(131\) 358.903 621.638i 0.239370 0.414601i −0.721164 0.692765i \(-0.756392\pi\)
0.960534 + 0.278164i \(0.0897258\pi\)
\(132\) 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 −0.558350 0.829606i \(-0.688565\pi\)
0.439285 + 0.898348i \(0.355232\pi\)
\(138\) 0 0
\(139\) 1214.70 + 701.309i 0.741222 + 0.427945i 0.822513 0.568746i \(-0.192571\pi\)
−0.0812916 + 0.996690i \(0.525905\pi\)
\(140\) −874.261 + 586.661i −0.527775 + 0.354156i
\(141\) 0 0
\(142\) 200.596 + 658.934i 0.118547 + 0.389412i
\(143\) −2548.96 −1.49059
\(144\) 0 0
\(145\) 1337.63 0.766099
\(146\) 901.708 + 2962.01i 0.511136 + 1.67903i
\(147\) 0 0
\(148\) −1961.90 + 1316.50i −1.08964 + 0.731188i
\(149\) 1289.36 + 744.413i 0.708917 + 0.409293i 0.810660 0.585517i \(-0.199109\pi\)
−0.101743 + 0.994811i \(0.532442\pi\)
\(150\) 0 0
\(151\) −1704.17 + 983.903i −0.918433 + 0.530257i −0.883135 0.469120i \(-0.844571\pi\)
−0.0352979 + 0.999377i \(0.511238\pi\)
\(152\) 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 −0.686272 0.727345i \(-0.740754\pi\)
0.973035 + 0.230656i \(0.0740874\pi\)
\(158\) 1266.16 + 1183.55i 0.637534 + 0.595937i
\(159\) 0 0
\(160\) −803.861 570.059i −0.397192 0.281669i
\(161\) 190.277i 0.0931424i
\(162\) 0 0
\(163\) 1940.05i 0.932250i 0.884719 + 0.466125i \(0.154350\pi\)
−0.884719 + 0.466125i \(0.845650\pi\)
\(164\) −1353.30 + 91.3821i −0.644362 + 0.0435106i
\(165\) 0 0
\(166\) −1093.45 + 1169.77i −0.511252 + 0.546939i
\(167\) −1242.52 + 2152.11i −0.575743 + 0.997217i 0.420217 + 0.907424i \(0.361954\pi\)
−0.995960 + 0.0897933i \(0.971379\pi\)
\(168\) 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 0.160435 0.987046i \(-0.448710\pi\)
0.935025 + 0.354583i \(0.115377\pi\)
\(174\) 0 0
\(175\) −1996.49 1152.67i −0.862402 0.497908i
\(176\) −3221.67 + 437.081i −1.37979 + 0.187194i
\(177\) 0 0
\(178\) −575.067 + 175.064i −0.242152 + 0.0737170i
\(179\) 2965.78 1.23840 0.619198 0.785235i \(-0.287458\pi\)
0.619198 + 0.785235i \(0.287458\pi\)
\(180\) 0 0
\(181\) 1250.55 0.513551 0.256776 0.966471i \(-0.417340\pi\)
0.256776 + 0.966471i \(0.417340\pi\)
\(182\) −3282.15 + 999.167i −1.33675 + 0.406941i
\(183\) 0 0
\(184\) 166.498 63.2286i 0.0667087 0.0253330i
\(185\) 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 \(-0.119738\pi\)
−0.783181 + 0.621793i \(0.786404\pi\)
\(192\) 0 0
\(193\) 2185.71 3785.76i 0.815185 1.41194i −0.0940101 0.995571i \(-0.529969\pi\)
0.909195 0.416370i \(-0.136698\pi\)
\(194\) 905.073 968.249i 0.334951 0.358331i
\(195\) 0 0
\(196\) 130.113 + 1926.88i 0.0474173 + 0.702216i
\(197\) 1648.60i 0.596233i 0.954530 + 0.298116i \(0.0963584\pi\)
−0.954530 + 0.298116i \(0.903642\pi\)
\(198\) 0 0
\(199\) 2946.42i 1.04958i −0.851232 0.524790i \(-0.824144\pi\)
0.851232 0.524790i \(-0.175856\pi\)
\(200\) 345.195 2130.02i 0.122045 0.753075i
\(201\) 0 0
\(202\) 3705.30 + 3463.53i 1.29061 + 1.20640i
\(203\) 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 \(-0.361979\pi\)
−0.575806 + 0.817586i \(0.695312\pi\)
\(212\) −1340.65 1997.88i −0.434322 0.647241i
\(213\) 0 0
\(214\) −635.328 2086.98i −0.202945 0.666650i
\(215\) −1791.37 −0.568234
\(216\) 0 0
\(217\) −1434.82 −0.448857
\(218\) 227.159 + 746.192i 0.0705741 + 0.231828i
\(219\) 0 0
\(220\) 1232.79 + 1837.15i 0.377795 + 0.563003i
\(221\) 2247.21 + 1297.43i 0.684000 + 0.394907i
\(222\) 0 0
\(223\) −1564.82 + 903.449i −0.469902 + 0.271298i −0.716199 0.697897i \(-0.754120\pi\)
0.246297 + 0.969194i \(0.420786\pi\)
\(224\) −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 \(-0.237308\pi\)
−0.954841 + 0.297117i \(0.903975\pi\)
\(228\) 0 0
\(229\) −767.015 + 1328.51i −0.221335 + 0.383364i −0.955214 0.295917i \(-0.904375\pi\)
0.733878 + 0.679281i \(0.237708\pi\)
\(230\) −88.5392 82.7622i −0.0253831 0.0237269i
\(231\) 0 0
\(232\) 5488.10 + 889.413i 1.55307 + 0.251693i
\(233\) 1257.04i 0.353440i −0.984261 0.176720i \(-0.943451\pi\)
0.984261 0.176720i \(-0.0565487\pi\)
\(234\) 0 0
\(235\) 522.346i 0.144996i
\(236\) −122.102 1808.25i −0.0336787 0.498759i
\(237\) 0 0
\(238\) 2414.66 2583.21i 0.657643 0.703548i
\(239\) −916.982 + 1588.26i −0.248178 + 0.429858i −0.963020 0.269428i \(-0.913165\pi\)
0.714842 + 0.699286i \(0.246499\pi\)
\(240\) 0 0
\(241\) −358.771 621.410i −0.0958941 0.166094i 0.814087 0.580743i \(-0.197238\pi\)
−0.909981 + 0.414649i \(0.863904\pi\)
\(242\) 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
\(248\) −476.788 1255.51i −0.122081 0.321472i
\(249\) 0 0
\(250\) −3246.07 + 988.182i −0.821198 + 0.249992i
\(251\) −1053.84 −0.265010 −0.132505 0.991182i \(-0.542302\pi\)
−0.132505 + 0.991182i \(0.542302\pi\)
\(252\) 0 0
\(253\) −399.843 −0.0993594
\(254\) −193.036 + 58.7648i −0.0476856 + 0.0145167i
\(255\) 0 0
\(256\) −2919.08 2873.36i −0.712665 0.701504i
\(257\) −5985.55 3455.76i −1.45280 0.838772i −0.454157 0.890922i \(-0.650059\pi\)
−0.998639 + 0.0521496i \(0.983393\pi\)
\(258\) 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 \(-0.267234\pi\)
−0.978517 + 0.206168i \(0.933901\pi\)
\(264\) 0 0
\(265\) −818.648 + 1417.94i −0.189770 + 0.328692i
\(266\) −1304.13 + 1395.16i −0.300607 + 0.321590i
\(267\) 0 0
\(268\) −8338.04 + 563.027i −1.90047 + 0.128330i
\(269\) 2386.16i 0.540843i 0.962742 + 0.270422i \(0.0871631\pi\)
−0.962742 + 0.270422i \(0.912837\pi\)
\(270\) 0 0
\(271\) 4287.45i 0.961048i 0.876982 + 0.480524i \(0.159554\pi\)
−0.876982 + 0.480524i \(0.840446\pi\)
\(272\) 3062.77 + 1254.50i 0.682748 + 0.279652i
\(273\) 0 0
\(274\) 455.534 + 425.811i 0.100437 + 0.0938839i
\(275\) −2422.20 + 4195.37i −0.531142 + 0.919965i
\(276\) 0 0
\(277\) −2416.58 4185.64i −0.524181 0.907909i −0.999604 0.0281511i \(-0.991038\pi\)
0.475422 0.879758i \(-0.342295\pi\)
\(278\) 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 −0.650821 0.759232i \(-0.725575\pi\)
0.332104 + 0.943243i \(0.392242\pi\)
\(282\) 0 0
\(283\) 3227.63 + 1863.47i 0.677960 + 0.391420i 0.799086 0.601217i \(-0.205317\pi\)
−0.121126 + 0.992637i \(0.538650\pi\)
\(284\) 1617.73 1085.55i 0.338009 0.226816i
\(285\) 0 0
\(286\) 2099.62 + 6897.03i 0.434103 + 1.42598i
\(287\) 4098.75 0.843003
\(288\) 0 0
\(289\) 2238.61 0.455649
\(290\) −1101.83 3619.40i −0.223110 0.732891i
\(291\) 0 0
\(292\) 7271.93 4879.73i 1.45739 0.977961i
\(293\) −5604.61 3235.82i −1.11749 0.645183i −0.176731 0.984259i \(-0.556552\pi\)
−0.940759 + 0.339076i \(0.889886\pi\)
\(294\) 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
\(302\) 4066.02 + 3800.72i 0.774746 + 0.724196i
\(303\) 0 0
\(304\) −1654.17 677.545i −0.312083 0.127828i
\(305\) 1891.50i 0.355104i
\(306\) 0 0
\(307\) 7858.86i 1.46101i 0.682909 + 0.730503i \(0.260715\pi\)
−0.682909 + 0.730503i \(0.739285\pi\)
\(308\) 9802.17 661.893i 1.81341 0.122451i
\(309\) 0 0
\(310\) −624.086 + 667.648i −0.114341 + 0.122322i
\(311\) −3745.08 + 6486.66i −0.682842 + 1.18272i 0.291268 + 0.956642i \(0.405923\pi\)
−0.974110 + 0.226075i \(0.927410\pi\)
\(312\) 0 0
\(313\) 4304.38 + 7455.41i 0.777310 + 1.34634i 0.933487 + 0.358612i \(0.116750\pi\)
−0.156176 + 0.987729i \(0.549917\pi\)
\(314\) −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 −0.0214185 0.999771i \(-0.506818\pi\)
0.855117 + 0.518434i \(0.173485\pi\)
\(318\) 0 0
\(319\) −10809.6 6240.92i −1.89724 1.09537i
\(320\) −880.323 + 2644.67i −0.153786 + 0.462006i
\(321\) 0 0
\(322\) −514.856 + 156.735i −0.0891050 + 0.0271257i
\(323\) 1444.41 0.248821
\(324\) 0 0
\(325\) −4784.97 −0.816684
\(326\) 5249.44 1598.06i 0.891840 0.271498i
\(327\) 0 0
\(328\) 1362.01 + 3586.53i 0.229281 + 0.603759i
\(329\) 2008.75 + 1159.75i 0.336615 + 0.194344i
\(330\) 0 0
\(331\) 1367.21 789.359i 0.227035 0.131079i −0.382168 0.924093i \(-0.624823\pi\)
0.609204 + 0.793014i \(0.291489\pi\)
\(332\) 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 0.448654 + 0.893706i \(0.351904\pi\)
−0.998299 + 0.0583070i \(0.981430\pi\)
\(338\) −619.393 + 662.628i −0.0996761 + 0.106634i
\(339\) 0 0
\(340\) −151.740 2247.17i −0.0242037 0.358440i
\(341\) 3015.10i 0.478818i
\(342\) 0 0
\(343\) 2455.93i 0.386611i
\(344\) −7349.71 1191.11i −1.15195 0.186687i
\(345\) 0 0
\(346\) −5947.34 5559.29i −0.924078 0.863784i
\(347\) 6228.10 10787.4i 0.963522 1.66887i 0.249987 0.968249i \(-0.419573\pi\)
0.713535 0.700620i \(-0.247093\pi\)
\(348\) 0 0
\(349\) −910.729 1577.43i −0.139685 0.241942i 0.787692 0.616069i \(-0.211276\pi\)
−0.927378 + 0.374127i \(0.877942\pi\)
\(350\) −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 −0.879662 0.475600i \(-0.842231\pi\)
−0.0279495 + 0.999609i \(0.508898\pi\)
\(354\) 0 0
\(355\) −1148.14 662.877i −0.171653 0.0991038i
\(356\) 947.387 + 1411.83i 0.141043 + 0.210187i
\(357\) 0 0
\(358\) −2442.97 8024.88i −0.360656 1.18472i
\(359\) 318.743 0.0468597 0.0234298 0.999725i \(-0.492541\pi\)
0.0234298 + 0.999725i \(0.492541\pi\)
\(360\) 0 0
\(361\) 6078.89 0.886264
\(362\) −1030.10 3383.77i −0.149561 0.491290i
\(363\) 0 0
\(364\) 5407.14 + 8057.90i 0.778602 + 1.16030i
\(365\) −5161.05 2979.73i −0.740114 0.427305i
\(366\) 0 0
\(367\) 5425.21 3132.25i 0.771645 0.445510i −0.0618160 0.998088i \(-0.519689\pi\)
0.833461 + 0.552578i \(0.186356\pi\)
\(368\) −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 −0.0460564 0.998939i \(-0.514665\pi\)
0.888135 0.459583i \(-0.152001\pi\)
\(374\) −5428.28 5074.10i −0.750508 0.701538i
\(375\) 0 0
\(376\) −347.316 + 2143.10i −0.0476368 + 0.293942i
\(377\) 12328.7i 1.68425i
\(378\) 0 0
\(379\) 1928.72i 0.261402i −0.991422 0.130701i \(-0.958277\pi\)
0.991422 0.130701i \(-0.0417229\pi\)
\(380\) 81.9533 + 1213.67i 0.0110635 + 0.163842i
\(381\) 0 0
\(382\) 1497.89 1602.45i 0.200625 0.214630i
\(383\) −2974.93 + 5152.73i −0.396898 + 0.687448i −0.993341 0.115208i \(-0.963247\pi\)
0.596443 + 0.802655i \(0.296580\pi\)
\(384\) 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 −0.626017 0.779809i \(-0.715316\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(390\) 0 0
\(391\) 352.510 + 203.522i 0.0455938 + 0.0263236i
\(392\) 5106.63 1939.27i 0.657968 0.249867i
\(393\) 0 0
\(394\) 4460.82 1357.98i 0.570388 0.173640i
\(395\) −3335.97 −0.424938
\(396\) 0 0
\(397\) −6080.16 −0.768652 −0.384326 0.923198i \(-0.625566\pi\)
−0.384326 + 0.923198i \(0.625566\pi\)
\(398\) −7972.51 + 2427.02i −1.00408 + 0.305668i
\(399\) 0 0
\(400\) −6047.80 + 820.499i −0.755975 + 0.102562i
\(401\) 11997.7 + 6926.90i 1.49411 + 0.862626i 0.999977 0.00675957i \(-0.00215165\pi\)
0.494135 + 0.869385i \(0.335485\pi\)
\(402\) 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 −0.857722 0.514113i \(-0.828121\pi\)
0.874096 + 0.485753i \(0.161455\pi\)
\(410\) 1782.78 1907.22i 0.214745 0.229734i
\(411\) 0 0
\(412\) −1104.80 + 74.6019i −0.132111 + 0.00892081i
\(413\) 5476.64i 0.652513i
\(414\) 0 0
\(415\) 3082.01i 0.364553i
\(416\) −5254.12 + 7409.03i −0.619242 + 0.873216i
\(417\) 0 0
\(418\) 2931.76 + 2740.47i 0.343055 + 0.320672i
\(419\) 3950.75 6842.90i 0.460637 0.797846i −0.538356 0.842718i \(-0.680954\pi\)
0.998993 + 0.0448712i \(0.0142877\pi\)
\(420\) 0 0
\(421\) 3331.91 + 5771.04i 0.385718 + 0.668083i 0.991869 0.127267i \(-0.0406204\pi\)
−0.606150 + 0.795350i \(0.707287\pi\)
\(422\) −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
\(428\) −5123.68 + 3438.17i −0.578650 + 0.388295i
\(429\) 0 0
\(430\) 1475.58 + 4847.13i 0.165486 + 0.543603i
\(431\) −14773.0 −1.65102 −0.825509 0.564388i \(-0.809112\pi\)
−0.825509 + 0.564388i \(0.809112\pi\)
\(432\) 0 0
\(433\) −2372.81 −0.263349 −0.131674 0.991293i \(-0.542035\pi\)
−0.131674 + 0.991293i \(0.542035\pi\)
\(434\) 1181.89 + 3882.38i 0.130720 + 0.429401i
\(435\) 0 0
\(436\) 1831.95 1229.30i 0.201226 0.135030i
\(437\) −190.387 109.920i −0.0208408 0.0120325i
\(438\) 0 0
\(439\) 2509.56 1448.89i 0.272835 0.157522i −0.357340 0.933974i \(-0.616316\pi\)
0.630175 + 0.776453i \(0.282983\pi\)
\(440\) 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 \(-0.305237\pi\)
−0.996107 + 0.0881526i \(0.971904\pi\)
\(444\) 0 0
\(445\) 578.508 1002.00i 0.0616267 0.106741i
\(446\) 3733.55 + 3489.94i 0.396387 + 0.370523i
\(447\) 0 0
\(448\) 8215.90 + 9257.33i 0.866439 + 0.976267i
\(449\) 1335.91i 0.140413i 0.997532 + 0.0702064i \(0.0223658\pi\)
−0.997532 + 0.0702064i \(0.977634\pi\)
\(450\) 0 0
\(451\) 8613.02i 0.899271i
\(452\) −5003.85 + 337.886i −0.520711 + 0.0351611i
\(453\) 0 0
\(454\) −2907.98 + 3110.97i −0.300613 + 0.321597i
\(455\) 3301.79 5718.87i 0.340198 0.589241i
\(456\) 0 0
\(457\) −8696.49 15062.8i −0.890164 1.54181i −0.839679 0.543084i \(-0.817257\pi\)
−0.0504849 0.998725i \(-0.516077\pi\)
\(458\) 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 −0.399159 0.916882i \(-0.630698\pi\)
0.594463 + 0.804123i \(0.297365\pi\)
\(462\) 0 0
\(463\) 3435.96 + 1983.75i 0.344887 + 0.199121i 0.662431 0.749123i \(-0.269525\pi\)
−0.317544 + 0.948244i \(0.602858\pi\)
\(464\) −2114.06 15582.5i −0.211514 1.55905i
\(465\) 0 0
\(466\) −3401.33 + 1035.45i −0.338120 + 0.102932i
\(467\) 8810.21 0.872993 0.436497 0.899706i \(-0.356219\pi\)
0.436497 + 0.899706i \(0.356219\pi\)
\(468\) 0 0
\(469\) 25253.4 2.48634
\(470\) 1413.38 430.266i 0.138711 0.0422270i
\(471\) 0 0
\(472\) −4792.23 + 1819.88i −0.467331 + 0.177472i
\(473\) 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 0.785811 + 0.618466i \(0.212246\pi\)
0.142702 + 0.989766i \(0.454421\pi\)
\(480\) 0 0
\(481\) 7409.42 12833.5i 0.702371 1.21654i
\(482\) −1385.90 + 1482.64i −0.130967 + 0.140109i
\(483\) 0 0
\(484\) −673.511 9974.23i −0.0632524 0.936723i
\(485\) 2551.05i 0.238840i
\(486\) 0 0
\(487\) 5226.26i 0.486293i −0.969990 0.243146i \(-0.921820\pi\)
0.969990 0.243146i \(-0.0781795\pi\)
\(488\) −1257.69 + 7760.52i −0.116666 + 0.719882i
\(489\) 0 0
\(490\) −2715.57 2538.38i −0.250361 0.234025i
\(491\) −4793.56 + 8302.69i −0.440591 + 0.763127i −0.997733 0.0672904i \(-0.978565\pi\)
0.557142 + 0.830417i \(0.311898\pi\)
\(492\) 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 \(-0.298880\pi\)
−0.403520 + 0.914971i \(0.632213\pi\)
\(500\) 5347.69 + 7969.31i 0.478312 + 0.712797i
\(501\) 0 0
\(502\) 868.064 + 2851.49i 0.0771785 + 0.253523i
\(503\) 17192.1 1.52397 0.761985 0.647595i \(-0.224225\pi\)
0.761985 + 0.647595i \(0.224225\pi\)
\(504\) 0 0
\(505\) −9762.37 −0.860237
\(506\) 329.358 + 1081.91i 0.0289363 + 0.0950525i
\(507\) 0 0
\(508\) 318.014 + 473.915i 0.0277748 + 0.0413909i
\(509\) 2562.66 + 1479.55i 0.223159 + 0.128841i 0.607412 0.794387i \(-0.292208\pi\)
−0.384253 + 0.923228i \(0.625541\pi\)
\(510\) 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
\(518\) −14752.3 13789.7i −1.25131 1.16966i
\(519\) 0 0
\(520\) 6101.36 + 988.798i 0.514543 + 0.0833878i
\(521\) 12490.4i 1.05032i −0.851004 0.525159i \(-0.824006\pi\)
0.851004 0.525159i \(-0.175994\pi\)
\(522\) 0 0
\(523\) 13273.1i 1.10974i −0.831939 0.554868i \(-0.812769\pi\)
0.831939 0.554868i \(-0.187231\pi\)
\(524\) 386.878 + 5729.40i 0.0322535 + 0.477652i
\(525\) 0 0
\(526\) −5119.24 + 5476.57i −0.424352 + 0.453973i
\(527\) 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
\(536\) 8391.65 + 22097.5i 0.676239 + 1.78072i
\(537\) 0 0
\(538\) 6456.53 1965.53i 0.517400 0.157509i
\(539\) −12263.5 −0.980012
\(540\) 0 0
\(541\) −12385.8 −0.984302 −0.492151 0.870510i \(-0.663789\pi\)
−0.492151 + 0.870510i \(0.663789\pi\)
\(542\) 11601.1 3531.65i 0.919390 0.279885i
\(543\) 0 0
\(544\) 871.609 9320.67i 0.0686947 0.734596i
\(545\) −1300.17 750.656i −0.102190 0.0589992i
\(546\) 0 0
\(547\) −15941.6 + 9203.89i −1.24609 + 0.719433i −0.970328 0.241792i \(-0.922265\pi\)
−0.275766 + 0.961225i \(0.588932\pi\)
\(548\) 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
\(554\) −9335.03 + 9986.63i −0.715898 + 0.765869i
\(555\) 0 0
\(556\) −11195.5 + 755.975i −0.853944 + 0.0576627i
\(557\) 13864.9i 1.05472i −0.849643 0.527358i \(-0.823183\pi\)
0.849643 0.527358i \(-0.176817\pi\)
\(558\) 0 0
\(559\) 16510.7i 1.24925i
\(560\) 3192.55 7794.35i 0.240910 0.588163i
\(561\) 0 0
\(562\) 3581.97 + 3348.25i 0.268854 + 0.251312i
\(563\) −7442.77 + 12891.3i −0.557150 + 0.965012i 0.440583 + 0.897712i \(0.354772\pi\)
−0.997733 + 0.0672999i \(0.978562\pi\)
\(564\) 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 −0.701142 0.713021i \(-0.747326\pi\)
0.266923 + 0.963718i \(0.413993\pi\)
\(570\) 0 0
\(571\) −7163.27 4135.72i −0.524998 0.303108i 0.213979 0.976838i \(-0.431357\pi\)
−0.738977 + 0.673731i \(0.764691\pi\)
\(572\) 16932.7 11362.4i 1.23775 0.830572i
\(573\) 0 0
\(574\) −3376.22 11090.5i −0.245506 0.806461i
\(575\) −750.595 −0.0544382
\(576\) 0 0
\(577\) −12153.3 −0.876863 −0.438432 0.898765i \(-0.644466\pi\)
−0.438432 + 0.898765i \(0.644466\pi\)
\(578\) −1843.98 6057.27i −0.132698 0.435899i
\(579\) 0 0
\(580\) −8885.86 + 5962.73i −0.636147 + 0.426878i
\(581\) −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 0.999990 + 0.00445871i \(0.00141926\pi\)
−0.496134 + 0.868246i \(0.665247\pi\)
\(588\) 0 0
\(589\) −828.874 + 1435.65i −0.0579850 + 0.100433i
\(590\) 2548.38 + 2382.10i 0.177822 + 0.166220i
\(591\) 0 0
\(592\) 7164.28 17491.0i 0.497382 1.21432i
\(593\) 17892.9i 1.23908i 0.784966 + 0.619539i \(0.212681\pi\)
−0.784966 + 0.619539i \(0.787319\pi\)
\(594\) 0 0
\(595\) 6805.99i 0.468938i
\(596\) −11883.5 + 802.438i −0.816727 + 0.0551496i
\(597\) 0 0
\(598\) −762.804 + 816.049i −0.0521628 + 0.0558039i
\(599\) 5989.96 10374.9i 0.408586 0.707692i −0.586145 0.810206i \(-0.699355\pi\)
0.994732 + 0.102514i \(0.0326886\pi\)
\(600\) 0 0
\(601\) −1473.48 2552.14i −0.100007 0.173218i 0.811680 0.584102i \(-0.198553\pi\)
−0.911687 + 0.410885i \(0.865220\pi\)
\(602\) 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 \(-0.00388040\pi\)
0.489406 + 0.872056i \(0.337214\pi\)
\(608\) −470.747 + 5034.00i −0.0314002 + 0.335782i
\(609\) 0 0
\(610\) 5118.06 1558.06i 0.339712 0.103417i
\(611\) 4814.36 0.318770
\(612\) 0 0
\(613\) −1851.43 −0.121988 −0.0609938 0.998138i \(-0.519427\pi\)
−0.0609938 + 0.998138i \(0.519427\pi\)
\(614\) 21264.7 6473.49i 1.39768 0.425487i
\(615\) 0 0
\(616\) −9865.20 25977.7i −0.645260 1.69914i
\(617\) −17363.4 10024.8i −1.13294 0.654103i −0.188267 0.982118i \(-0.560287\pi\)
−0.944673 + 0.328015i \(0.893621\pi\)
\(618\) 0 0
\(619\) 19210.5 11091.2i 1.24739 0.720183i 0.276805 0.960926i \(-0.410724\pi\)
0.970589 + 0.240743i \(0.0773911\pi\)
\(620\) 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
\(626\) 16627.4 17788.1i 1.06161 1.13571i
\(627\) 0 0
\(628\) 608.094 + 9005.44i 0.0386395 + 0.572223i
\(629\) 15273.1i 0.968166i
\(630\) 0 0
\(631\) 28148.1i 1.77584i −0.459994 0.887922i \(-0.652149\pi\)
0.459994 0.887922i \(-0.347851\pi\)
\(632\) −13687.0 2218.14i −0.861452 0.139609i
\(633\) 0 0
\(634\) −11226.8 10494.3i −0.703269 0.657382i
\(635\) 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 −0.699404 0.714727i \(-0.746551\pi\)
0.269270 + 0.963065i \(0.413218\pi\)
\(642\) 0 0
\(643\) −666.166 384.611i −0.0408570 0.0235888i 0.479432 0.877579i \(-0.340843\pi\)
−0.520289 + 0.853990i \(0.674176\pi\)
\(644\) 848.193 + 1264.00i 0.0518998 + 0.0773428i
\(645\) 0 0
\(646\) −1189.79 3908.33i −0.0724639 0.238036i
\(647\) −25155.2 −1.52852 −0.764259 0.644909i \(-0.776895\pi\)
−0.764259 + 0.644909i \(0.776895\pi\)
\(648\) 0 0
\(649\) 11508.5 0.696067
\(650\) 3941.47 + 12947.3i 0.237842 + 0.781283i
\(651\) 0 0
\(652\) −8648.13 12887.7i −0.519458 0.774114i
\(653\) −17852.0 10306.9i −1.06984 0.617671i −0.141701 0.989910i \(-0.545257\pi\)
−0.928137 + 0.372238i \(0.878590\pi\)
\(654\) 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 −0.963255 0.268587i \(-0.913443\pi\)
0.249024 0.968497i \(1.58011\pi\)
\(660\) 0 0
\(661\) −9976.53 + 17279.9i −0.587053 + 1.01681i 0.407563 + 0.913177i \(0.366379\pi\)
−0.994616 + 0.103629i \(0.966955\pi\)
\(662\) −3262.06 3049.22i −0.191516 0.179020i
\(663\) 0 0
\(664\) 2049.27 12645.0i 0.119770 0.739038i
\(665\) 3675.84i 0.214351i
\(666\) 0 0
\(667\) 1933.95i 0.112268i
\(668\) −1339.37 19835.2i −0.0775777 1.14887i
\(669\) 0 0
\(670\) 10984.1 11750.9i 0.633365 0.677575i
\(671\) 8825.05 15285.4i 0.507731 0.879416i
\(672\) 0 0
\(673\) 3449.60 + 5974.88i 0.197581 + 0.342221i 0.947744 0.319033i \(-0.103358\pi\)
−0.750162 + 0.661254i \(0.770025\pi\)
\(674\) 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 −0.261584 0.965181i \(-0.584245\pi\)
0.705079 + 0.709128i \(0.250911\pi\)
\(678\) 0 0
\(679\) 9810.44 + 5664.06i 0.554477 + 0.320128i
\(680\) −5955.44 + 2261.61i −0.335854 + 0.127543i
\(681\) 0 0
\(682\) 8158.33 2483.59i 0.458062 0.139445i
\(683\) 7388.19 0.413911 0.206956 0.978350i \(-0.433644\pi\)
0.206956 + 0.978350i \(0.433644\pi\)
\(684\) 0 0
\(685\) −1200.20 −0.0669448
\(686\) 6645.30 2022.99i 0.369853 0.112592i
\(687\) 0 0
\(688\) 2831.16 + 20868.2i 0.156885 + 1.15638i
\(689\) 13068.9 + 7545.32i 0.722620 + 0.417205i
\(690\) 0 0
\(691\) −25972.9 + 14995.5i −1.42989 + 0.825549i −0.997112 0.0759500i \(-0.975801\pi\)
−0.432781 + 0.901499i \(0.642468\pi\)
\(692\) −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
\(698\) −3518.06 + 3763.63i −0.190775 + 0.204091i
\(699\) 0 0
\(700\) 18400.9 1242.52i 0.993554 0.0670899i
\(701\) 23559.3i 1.26936i 0.772774 + 0.634681i \(0.218869\pi\)
−0.772774 + 0.634681i \(0.781131\pi\)
\(702\) 0 0
\(703\) 8248.82i 0.442547i
\(704\) 19453.1 17264.7i 1.04143 0.924272i
\(705\) 0 0
\(706\) 14362.1 + 13425.0i 0.765618 + 0.715663i
\(707\) −21675.2 + 37542.6i −1.15301 + 1.99708i
\(708\) 0 0
\(709\) −6114.96 10591.4i −0.323910 0.561028i 0.657381 0.753558i \(-0.271664\pi\)
−0.981291 + 0.192530i \(0.938331\pi\)
\(710\) −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
\(716\) −19701.6 + 13220.5i −1.02833 + 0.690046i
\(717\) 0 0
\(718\) −262.555 862.464i −0.0136469 0.0448285i
\(719\) 37718.6 1.95642 0.978211 0.207613i \(-0.0665694\pi\)
0.978211 + 0.207613i \(0.0665694\pi\)
\(720\) 0 0
\(721\) 3346.11 0.172837
\(722\) −5007.29 16448.4i −0.258105 0.847848i
\(723\) 0 0
\(724\) −8307.38 + 5574.55i −0.426438 + 0.286156i
\(725\) −20292.0 11715.6i −1.03949 0.600147i
\(726\) 0 0
\(727\) 7555.48 4362.16i 0.385443 0.222536i −0.294741 0.955577i \(-0.595233\pi\)
0.680184 + 0.733041i \(0.261900\pi\)
\(728\) 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 −0.592712 0.805414i \(-0.701943\pi\)
0.993865 + 0.110597i \(0.0352762\pi\)
\(734\) −12944.2 12099.6i −0.650923 0.608452i
\(735\) 0 0
\(736\) −824.189 + 1162.22i −0.0412772 + 0.0582065i
\(737\) 53066.9i 2.65230i
\(738\) 0 0
\(739\) 21026.0i 1.04662i 0.852141 + 0.523312i \(0.175304\pi\)
−0.852141 + 0.523312i \(0.824696\pi\)
\(740\) −12833.2 + 866.565i −0.637511 + 0.0430480i
\(741\) 0 0
\(742\) 14042.7 15022.9i 0.694774 0.743271i
\(743\) 5813.11 10068.6i 0.287029 0.497148i −0.686071 0.727535i \(-0.740666\pi\)
0.973099 + 0.230387i \(0.0739992\pi\)
\(744\) 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 \(-0.278629\pi\)
−0.344533 + 0.938774i \(0.611963\pi\)
\(752\) 6084.95 825.539i 0.295074 0.0400323i
\(753\) 0 0
\(754\) −33359.3 + 10155.4i −1.61124 + 0.490500i
\(755\) −10712.8 −0.516395
\(756\) 0 0
\(757\) −28354.3 −1.36137 −0.680685 0.732577i \(-0.738318\pi\)
−0.680685 + 0.732577i \(0.738318\pi\)
\(758\) −5218.77 + 1588.72i −0.250072 + 0.0761279i
\(759\) 0 0
\(760\) 3216.47 1221.47i 0.153518 0.0582994i
\(761\) 20274.5 + 11705.5i 0.965771 + 0.557588i 0.897944 0.440109i \(-0.145060\pi\)
0.0678265 + 0.997697i \(0.478394\pi\)
\(762\) 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 −0.401517 0.915852i \(-0.631517\pi\)
0.993909 0.110202i \(-0.0351498\pi\)
\(770\) −12912.9 + 13814.3i −0.604350 + 0.646535i
\(771\) 0 0
\(772\) 2356.08 + 34891.9i 0.109841 + 1.62667i
\(773\) 31081.3i 1.44621i 0.690740 + 0.723103i \(0.257285\pi\)
−0.690740 + 0.723103i \(0.742715\pi\)
\(774\) 0 0
\(775\) 5660.02i 0.262340i
\(776\) −1696.24 + 10466.6i −0.0784682 + 0.484186i
\(777\) 0 0
\(778\) 4827.00 + 4512.05i 0.222438 + 0.207924i
\(779\) 2367.78 4101.12i 0.108902 0.188624i
\(780\) 0 0