Properties

Label 108.4.h.b.35.12
Level 108
Weight 4
Character 108.35
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 35.12
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.12

$q$-expansion

\(f(q)\) \(=\) \(q+(2.81402 + 0.285097i) q^{2} +(7.83744 + 1.60454i) q^{4} +(14.4924 - 8.36717i) q^{5} +(-16.7175 - 9.65186i) q^{7} +(21.5973 + 6.74964i) q^{8} +O(q^{10})\) \(q+(2.81402 + 0.285097i) q^{2} +(7.83744 + 1.60454i) q^{4} +(14.4924 - 8.36717i) q^{5} +(-16.7175 - 9.65186i) q^{7} +(21.5973 + 6.74964i) q^{8} +(43.1673 - 19.4137i) q^{10} +(-2.44092 + 4.22780i) q^{11} +(6.03848 + 10.4590i) q^{13} +(-44.2917 - 31.9267i) q^{14} +(58.8509 + 25.1509i) q^{16} +71.2528i q^{17} -68.3003i q^{19} +(127.009 - 42.3237i) q^{20} +(-8.07414 + 11.2012i) q^{22} +(68.0491 + 117.865i) q^{23} +(77.5192 - 134.267i) q^{25} +(14.0106 + 31.1533i) q^{26} +(-115.536 - 102.470i) q^{28} +(-190.237 - 109.833i) q^{29} +(-285.221 + 164.672i) q^{31} +(158.437 + 87.5535i) q^{32} +(-20.3140 + 200.507i) q^{34} -323.035 q^{35} -133.618 q^{37} +(19.4722 - 192.199i) q^{38} +(369.471 - 82.8899i) q^{40} +(29.5326 - 17.0507i) q^{41} +(-0.558209 - 0.322282i) q^{43} +(-25.9142 + 29.2186i) q^{44} +(157.889 + 351.074i) q^{46} +(-93.4753 + 161.904i) q^{47} +(14.8169 + 25.6636i) q^{49} +(256.420 - 355.730i) q^{50} +(30.5444 + 91.6604i) q^{52} -266.453i q^{53} +81.6944i q^{55} +(-295.906 - 321.291i) q^{56} +(-504.018 - 363.309i) q^{58} +(104.347 + 180.734i) q^{59} +(0.801886 - 1.38891i) q^{61} +(-849.565 + 382.076i) q^{62} +(420.885 + 291.548i) q^{64} +(175.024 + 101.050i) q^{65} +(371.407 - 214.432i) q^{67} +(-114.328 + 558.440i) q^{68} +(-909.028 - 92.0964i) q^{70} +386.365 q^{71} -776.832 q^{73} +(-376.004 - 38.0941i) q^{74} +(109.591 - 535.300i) q^{76} +(81.6122 - 47.1188i) q^{77} +(68.5000 + 39.5485i) q^{79} +(1063.33 - 127.919i) q^{80} +(87.9665 - 39.5613i) q^{82} +(462.668 - 801.365i) q^{83} +(596.185 + 1032.62i) q^{85} +(-1.47893 - 1.06605i) q^{86} +(-81.2533 + 74.8336i) q^{88} +1044.26i q^{89} -233.130i q^{91} +(344.213 + 1032.94i) q^{92} +(-309.200 + 428.952i) q^{94} +(-571.481 - 989.834i) q^{95} +(733.184 - 1269.91i) q^{97} +(34.3784 + 76.4422i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.81402 + 0.285097i 0.994907 + 0.100797i
\(3\) 0 0
\(4\) 7.83744 + 1.60454i 0.979680 + 0.200567i
\(5\) 14.4924 8.36717i 1.29624 0.748383i 0.316485 0.948598i \(-0.397497\pi\)
0.979752 + 0.200215i \(0.0641640\pi\)
\(6\) 0 0
\(7\) −16.7175 9.65186i −0.902661 0.521152i −0.0245984 0.999697i \(-0.507831\pi\)
−0.878063 + 0.478546i \(0.841164\pi\)
\(8\) 21.5973 + 6.74964i 0.954474 + 0.298295i
\(9\) 0 0
\(10\) 43.1673 19.4137i 1.36507 0.613915i
\(11\) −2.44092 + 4.22780i −0.0669059 + 0.115884i −0.897538 0.440937i \(-0.854646\pi\)
0.830632 + 0.556822i \(0.187979\pi\)
\(12\) 0 0
\(13\) 6.03848 + 10.4590i 0.128829 + 0.223138i 0.923223 0.384264i \(-0.125545\pi\)
−0.794394 + 0.607402i \(0.792212\pi\)
\(14\) −44.2917 31.9267i −0.845533 0.609483i
\(15\) 0 0
\(16\) 58.8509 + 25.1509i 0.919546 + 0.392984i
\(17\) 71.2528i 1.01655i 0.861195 + 0.508275i \(0.169717\pi\)
−0.861195 + 0.508275i \(0.830283\pi\)
\(18\) 0 0
\(19\) 68.3003i 0.824693i −0.911027 0.412347i \(-0.864709\pi\)
0.911027 0.412347i \(-0.135291\pi\)
\(20\) 127.009 42.3237i 1.42000 0.473193i
\(21\) 0 0
\(22\) −8.07414 + 11.2012i −0.0782460 + 0.108550i
\(23\) 68.0491 + 117.865i 0.616923 + 1.06854i 0.990044 + 0.140759i \(0.0449543\pi\)
−0.373121 + 0.927783i \(0.621712\pi\)
\(24\) 0 0
\(25\) 77.5192 134.267i 0.620154 1.07414i
\(26\) 14.0106 + 31.1533i 0.105681 + 0.234987i
\(27\) 0 0
\(28\) −115.536 102.470i −0.779793 0.691606i
\(29\) −190.237 109.833i −1.21814 0.703295i −0.253622 0.967303i \(-0.581622\pi\)
−0.964520 + 0.264009i \(0.914955\pi\)
\(30\) 0 0
\(31\) −285.221 + 164.672i −1.65249 + 0.954065i −0.676444 + 0.736494i \(0.736480\pi\)
−0.976044 + 0.217571i \(0.930187\pi\)
\(32\) 158.437 + 87.5535i 0.875251 + 0.483669i
\(33\) 0 0
\(34\) −20.3140 + 200.507i −0.102465 + 1.01137i
\(35\) −323.035 −1.56008
\(36\) 0 0
\(37\) −133.618 −0.593693 −0.296847 0.954925i \(-0.595935\pi\)
−0.296847 + 0.954925i \(0.595935\pi\)
\(38\) 19.4722 192.199i 0.0831266 0.820493i
\(39\) 0 0
\(40\) 369.471 82.8899i 1.46046 0.327651i
\(41\) 29.5326 17.0507i 0.112493 0.0649480i −0.442698 0.896671i \(-0.645979\pi\)
0.555191 + 0.831723i \(0.312645\pi\)
\(42\) 0 0
\(43\) −0.558209 0.322282i −0.00197967 0.00114297i 0.499010 0.866596i \(-0.333697\pi\)
−0.500990 + 0.865453i \(0.667030\pi\)
\(44\) −25.9142 + 29.2186i −0.0887890 + 0.100111i
\(45\) 0 0
\(46\) 157.889 + 351.074i 0.506075 + 1.12528i
\(47\) −93.4753 + 161.904i −0.290102 + 0.502471i −0.973834 0.227263i \(-0.927022\pi\)
0.683732 + 0.729733i \(0.260356\pi\)
\(48\) 0 0
\(49\) 14.8169 + 25.6636i 0.0431979 + 0.0748210i
\(50\) 256.420 355.730i 0.725265 1.00616i
\(51\) 0 0
\(52\) 30.5444 + 91.6604i 0.0814568 + 0.244443i
\(53\) 266.453i 0.690569i −0.938498 0.345284i \(-0.887782\pi\)
0.938498 0.345284i \(-0.112218\pi\)
\(54\) 0 0
\(55\) 81.6944i 0.200285i
\(56\) −295.906 321.291i −0.706110 0.766684i
\(57\) 0 0
\(58\) −504.018 363.309i −1.14105 0.822498i
\(59\) 104.347 + 180.734i 0.230251 + 0.398806i 0.957882 0.287163i \(-0.0927120\pi\)
−0.727631 + 0.685969i \(0.759379\pi\)
\(60\) 0 0
\(61\) 0.801886 1.38891i 0.00168313 0.00291527i −0.865183 0.501457i \(-0.832798\pi\)
0.866866 + 0.498542i \(0.166131\pi\)
\(62\) −849.565 + 382.076i −1.74024 + 0.782640i
\(63\) 0 0
\(64\) 420.885 + 291.548i 0.822041 + 0.569429i
\(65\) 175.024 + 101.050i 0.333985 + 0.192826i
\(66\) 0 0
\(67\) 371.407 214.432i 0.677233 0.391001i −0.121579 0.992582i \(-0.538796\pi\)
0.798812 + 0.601581i \(0.205462\pi\)
\(68\) −114.328 + 558.440i −0.203887 + 0.995893i
\(69\) 0 0
\(70\) −909.028 92.0964i −1.55214 0.157252i
\(71\) 386.365 0.645817 0.322909 0.946430i \(-0.395339\pi\)
0.322909 + 0.946430i \(0.395339\pi\)
\(72\) 0 0
\(73\) −776.832 −1.24550 −0.622749 0.782422i \(-0.713984\pi\)
−0.622749 + 0.782422i \(0.713984\pi\)
\(74\) −376.004 38.0941i −0.590670 0.0598425i
\(75\) 0 0
\(76\) 109.591 535.300i 0.165407 0.807935i
\(77\) 81.6122 47.1188i 0.120787 0.0697362i
\(78\) 0 0
\(79\) 68.5000 + 39.5485i 0.0975551 + 0.0563235i 0.547984 0.836489i \(-0.315396\pi\)
−0.450429 + 0.892812i \(0.648729\pi\)
\(80\) 1063.33 127.919i 1.48605 0.178772i
\(81\) 0 0
\(82\) 87.9665 39.5613i 0.118467 0.0532782i
\(83\) 462.668 801.365i 0.611861 1.05977i −0.379066 0.925370i \(-0.623755\pi\)
0.990927 0.134404i \(-0.0429121\pi\)
\(84\) 0 0
\(85\) 596.185 + 1032.62i 0.760768 + 1.31769i
\(86\) −1.47893 1.06605i −0.00185438 0.00133669i
\(87\) 0 0
\(88\) −81.2533 + 74.8336i −0.0984277 + 0.0906510i
\(89\) 1044.26i 1.24372i 0.783128 + 0.621861i \(0.213623\pi\)
−0.783128 + 0.621861i \(0.786377\pi\)
\(90\) 0 0
\(91\) 233.130i 0.268557i
\(92\) 344.213 + 1032.94i 0.390072 + 1.17056i
\(93\) 0 0
\(94\) −309.200 + 428.952i −0.339272 + 0.470670i
\(95\) −571.481 989.834i −0.617186 1.06900i
\(96\) 0 0
\(97\) 733.184 1269.91i 0.767460 1.32928i −0.171477 0.985188i \(-0.554854\pi\)
0.938936 0.344091i \(-0.111813\pi\)
\(98\) 34.3784 + 76.4422i 0.0354362 + 0.0787941i
\(99\) 0 0
\(100\) 822.989 927.929i 0.822989 0.927929i
\(101\) 314.302 + 181.462i 0.309646 + 0.178774i 0.646768 0.762687i \(-0.276120\pi\)
−0.337122 + 0.941461i \(0.609454\pi\)
\(102\) 0 0
\(103\) 466.128 269.119i 0.445912 0.257447i −0.260190 0.965557i \(-0.583785\pi\)
0.706102 + 0.708110i \(0.250452\pi\)
\(104\) 59.8206 + 266.643i 0.0564028 + 0.251408i
\(105\) 0 0
\(106\) 75.9650 749.805i 0.0696073 0.687052i
\(107\) 430.456 0.388914 0.194457 0.980911i \(-0.437706\pi\)
0.194457 + 0.980911i \(0.437706\pi\)
\(108\) 0 0
\(109\) 899.324 0.790272 0.395136 0.918623i \(-0.370697\pi\)
0.395136 + 0.918623i \(0.370697\pi\)
\(110\) −23.2908 + 229.890i −0.0201881 + 0.199265i
\(111\) 0 0
\(112\) −741.088 988.482i −0.625234 0.833953i
\(113\) 330.860 191.022i 0.275440 0.159025i −0.355917 0.934517i \(-0.615832\pi\)
0.631357 + 0.775492i \(0.282498\pi\)
\(114\) 0 0
\(115\) 1972.39 + 1138.76i 1.59936 + 0.923389i
\(116\) −1314.74 1166.05i −1.05233 0.933323i
\(117\) 0 0
\(118\) 242.107 + 538.338i 0.188880 + 0.419983i
\(119\) 687.722 1191.17i 0.529776 0.917600i
\(120\) 0 0
\(121\) 653.584 + 1132.04i 0.491047 + 0.850519i
\(122\) 2.65250 3.67980i 0.00196841 0.00273077i
\(123\) 0 0
\(124\) −2499.62 + 832.961i −1.81026 + 0.603243i
\(125\) 502.674i 0.359684i
\(126\) 0 0
\(127\) 1677.92i 1.17237i −0.810177 0.586186i \(-0.800629\pi\)
0.810177 0.586186i \(-0.199371\pi\)
\(128\) 1101.26 + 940.414i 0.760457 + 0.649388i
\(129\) 0 0
\(130\) 463.712 + 334.256i 0.312848 + 0.225509i
\(131\) 712.418 + 1233.94i 0.475147 + 0.822979i 0.999595 0.0284637i \(-0.00906150\pi\)
−0.524448 + 0.851443i \(0.675728\pi\)
\(132\) 0 0
\(133\) −659.225 + 1141.81i −0.429790 + 0.744418i
\(134\) 1106.28 497.529i 0.713196 0.320746i
\(135\) 0 0
\(136\) −480.931 + 1538.87i −0.303231 + 0.970270i
\(137\) −23.2295 13.4116i −0.0144864 0.00836370i 0.492739 0.870177i \(-0.335996\pi\)
−0.507226 + 0.861813i \(0.669329\pi\)
\(138\) 0 0
\(139\) −1434.57 + 828.252i −0.875388 + 0.505406i −0.869135 0.494575i \(-0.835324\pi\)
−0.00625321 + 0.999980i \(0.501990\pi\)
\(140\) −2531.77 518.322i −1.52838 0.312902i
\(141\) 0 0
\(142\) 1087.24 + 110.151i 0.642528 + 0.0650965i
\(143\) −58.9578 −0.0344776
\(144\) 0 0
\(145\) −3675.98 −2.10533
\(146\) −2186.02 221.473i −1.23915 0.125542i
\(147\) 0 0
\(148\) −1047.22 214.395i −0.581629 0.119075i
\(149\) −738.285 + 426.249i −0.405924 + 0.234360i −0.689037 0.724726i \(-0.741966\pi\)
0.283113 + 0.959087i \(0.408633\pi\)
\(150\) 0 0
\(151\) −1272.06 734.422i −0.685553 0.395804i 0.116391 0.993203i \(-0.462867\pi\)
−0.801944 + 0.597399i \(0.796201\pi\)
\(152\) 461.002 1475.10i 0.246002 0.787148i
\(153\) 0 0
\(154\) 243.092 109.326i 0.127201 0.0572061i
\(155\) −2755.68 + 4772.98i −1.42801 + 2.47339i
\(156\) 0 0
\(157\) −1344.52 2328.78i −0.683469 1.18380i −0.973915 0.226912i \(-0.927137\pi\)
0.290446 0.956891i \(-0.406196\pi\)
\(158\) 181.485 + 130.820i 0.0913811 + 0.0658699i
\(159\) 0 0
\(160\) 3028.71 56.8143i 1.49650 0.0280723i
\(161\) 2627.20i 1.28604i
\(162\) 0 0
\(163\) 2186.50i 1.05067i 0.850895 + 0.525336i \(0.176060\pi\)
−0.850895 + 0.525336i \(0.823940\pi\)
\(164\) 258.819 86.2473i 0.123234 0.0410658i
\(165\) 0 0
\(166\) 1530.43 2123.15i 0.715567 0.992703i
\(167\) −1790.65 3101.49i −0.829726 1.43713i −0.898253 0.439479i \(-0.855163\pi\)
0.0685268 0.997649i \(1.52183\pi\)
\(168\) 0 0
\(169\) 1025.57 1776.35i 0.466806 0.808532i
\(170\) 1383.28 + 3075.79i 0.624075 + 1.38766i
\(171\) 0 0
\(172\) −3.85781 3.42153i −0.00171021 0.00151680i
\(173\) 94.5051 + 54.5625i 0.0415323 + 0.0239787i 0.520622 0.853787i \(-0.325700\pi\)
−0.479090 + 0.877766i \(0.659033\pi\)
\(174\) 0 0
\(175\) −2591.86 + 1496.41i −1.11958 + 0.646388i
\(176\) −249.983 + 187.418i −0.107064 + 0.0802681i
\(177\) 0 0
\(178\) −297.715 + 2938.57i −0.125363 + 1.23739i
\(179\) 268.397 0.112072 0.0560361 0.998429i \(-0.482154\pi\)
0.0560361 + 0.998429i \(0.482154\pi\)
\(180\) 0 0
\(181\) 898.582 0.369011 0.184506 0.982831i \(-0.440932\pi\)
0.184506 + 0.982831i \(0.440932\pi\)
\(182\) 66.4648 656.034i 0.0270698 0.267189i
\(183\) 0 0
\(184\) 674.133 + 3004.86i 0.270096 + 1.20392i
\(185\) −1936.44 + 1118.00i −0.769567 + 0.444310i
\(186\) 0 0
\(187\) −301.242 173.922i −0.117802 0.0680132i
\(188\) −992.388 + 1118.93i −0.384986 + 0.434076i
\(189\) 0 0
\(190\) −1325.96 2948.34i −0.506291 1.12576i
\(191\) −257.331 + 445.711i −0.0974860 + 0.168851i −0.910643 0.413193i \(-0.864413\pi\)
0.813157 + 0.582044i \(0.197747\pi\)
\(192\) 0 0
\(193\) 1229.66 + 2129.83i 0.458616 + 0.794346i 0.998888 0.0471443i \(-0.0150121\pi\)
−0.540272 + 0.841490i \(0.681679\pi\)
\(194\) 2425.24 3364.53i 0.897538 1.24515i
\(195\) 0 0
\(196\) 74.9482 + 224.911i 0.0273135 + 0.0819647i
\(197\) 646.506i 0.233815i −0.993143 0.116908i \(-0.962702\pi\)
0.993143 0.116908i \(-0.0372982\pi\)
\(198\) 0 0
\(199\) 1742.98i 0.620886i −0.950592 0.310443i \(-0.899523\pi\)
0.950592 0.310443i \(-0.100477\pi\)
\(200\) 2580.46 2376.58i 0.912330 0.840248i
\(201\) 0 0
\(202\) 832.719 + 600.246i 0.290049 + 0.209075i
\(203\) 2120.19 + 3672.28i 0.733046 + 1.26967i
\(204\) 0 0
\(205\) 285.332 494.209i 0.0972119 0.168376i
\(206\) 1388.42 624.415i 0.469591 0.211190i
\(207\) 0 0
\(208\) 92.3175 + 767.393i 0.0307744 + 0.255813i
\(209\) 288.760 + 166.716i 0.0955691 + 0.0551769i
\(210\) 0 0
\(211\) 3648.27 2106.33i 1.19032 0.687231i 0.231940 0.972730i \(-0.425493\pi\)
0.958379 + 0.285499i \(0.0921593\pi\)
\(212\) 427.534 2088.31i 0.138506 0.676537i
\(213\) 0 0
\(214\) 1211.31 + 122.722i 0.386933 + 0.0392013i
\(215\) −10.7864 −0.00342150
\(216\) 0 0
\(217\) 6357.58 1.98885
\(218\) 2530.72 + 256.395i 0.786247 + 0.0796570i
\(219\) 0 0
\(220\) −131.082 + 640.275i −0.0401706 + 0.196215i
\(221\) −745.230 + 430.259i −0.226831 + 0.130961i
\(222\) 0 0
\(223\) −5558.55 3209.23i −1.66918 0.963703i −0.968080 0.250643i \(-0.919358\pi\)
−0.701103 0.713060i \(1.25269\pi\)
\(224\) −1803.62 2992.89i −0.537990 0.892728i
\(225\) 0 0
\(226\) 985.507 443.213i 0.290066 0.130452i
\(227\) 1124.83 1948.27i 0.328889 0.569653i −0.653403 0.757011i \(-0.726659\pi\)
0.982292 + 0.187358i \(0.0599924\pi\)
\(228\) 0 0
\(229\) −1735.36 3005.74i −0.500769 0.867357i −1.00000 0.000888202i \(-0.999717\pi\)
0.499231 0.866469i \(-0.333616\pi\)
\(230\) 5225.68 + 3766.81i 1.49814 + 1.07990i
\(231\) 0 0
\(232\) −3367.27 3656.13i −0.952896 1.03464i
\(233\) 3852.67i 1.08325i 0.840621 + 0.541624i \(0.182190\pi\)
−0.840621 + 0.541624i \(0.817810\pi\)
\(234\) 0 0
\(235\) 3128.50i 0.868428i
\(236\) 527.817 + 1583.92i 0.145585 + 0.436883i
\(237\) 0 0
\(238\) 2274.86 3155.91i 0.619570 0.859527i
\(239\) −19.9334 34.5257i −0.00539491 0.00934426i 0.863315 0.504665i \(-0.168384\pi\)
−0.868710 + 0.495321i \(0.835051\pi\)
\(240\) 0 0
\(241\) −1729.18 + 2995.03i −0.462184 + 0.800527i −0.999070 0.0431286i \(-0.986267\pi\)
0.536885 + 0.843655i \(0.319601\pi\)
\(242\) 1516.46 + 3371.92i 0.402817 + 0.895683i
\(243\) 0 0
\(244\) 8.51329 9.59882i 0.00223364 0.00251845i
\(245\) 429.464 + 247.951i 0.111989 + 0.0646572i
\(246\) 0 0
\(247\) 714.350 412.430i 0.184020 0.106244i
\(248\) −7271.47 + 1631.34i −1.86185 + 0.417701i
\(249\) 0 0
\(250\) 143.311 1414.53i 0.0362551 0.357852i
\(251\) −2977.61 −0.748786 −0.374393 0.927270i \(-0.622149\pi\)
−0.374393 + 0.927270i \(0.622149\pi\)
\(252\) 0 0
\(253\) −664.410 −0.165103
\(254\) 478.369 4721.70i 0.118172 1.16640i
\(255\) 0 0
\(256\) 2830.86 + 2960.31i 0.691128 + 0.722732i
\(257\) 5593.28 3229.28i 1.35758 0.783802i 0.368287 0.929712i \(-0.379944\pi\)
0.989298 + 0.145910i \(0.0466111\pi\)
\(258\) 0 0
\(259\) 2233.76 + 1289.66i 0.535904 + 0.309404i
\(260\) 1209.60 + 1072.81i 0.288524 + 0.255895i
\(261\) 0 0
\(262\) 1652.97 + 3675.46i 0.389773 + 0.866681i
\(263\) 2940.99 5093.94i 0.689540 1.19432i −0.282447 0.959283i \(-0.591146\pi\)
0.971987 0.235036i \(-0.0755207\pi\)
\(264\) 0 0
\(265\) −2229.46 3861.54i −0.516810 0.895141i
\(266\) −2180.60 + 3025.14i −0.502636 + 0.697306i
\(267\) 0 0
\(268\) 3254.95 1084.66i 0.741894 0.247225i
\(269\) 2967.07i 0.672510i 0.941771 + 0.336255i \(0.109160\pi\)
−0.941771 + 0.336255i \(0.890840\pi\)
\(270\) 0 0
\(271\) 1985.78i 0.445121i 0.974919 + 0.222561i \(0.0714415\pi\)
−0.974919 + 0.222561i \(0.928559\pi\)
\(272\) −1792.08 + 4193.29i −0.399487 + 0.934764i
\(273\) 0 0
\(274\) −61.5447 44.3631i −0.0135695 0.00978128i
\(275\) 378.436 + 655.471i 0.0829839 + 0.143732i
\(276\) 0 0
\(277\) −2171.48 + 3761.12i −0.471017 + 0.815825i −0.999450 0.0331494i \(-0.989446\pi\)
0.528433 + 0.848975i \(0.322780\pi\)
\(278\) −4273.05 + 1921.73i −0.921873 + 0.414595i
\(279\) 0 0
\(280\) −6976.68 2180.37i −1.48906 0.465365i
\(281\) −6752.10 3898.33i −1.43344 0.827597i −0.436058 0.899919i \(-0.643626\pi\)
−0.997381 + 0.0723220i \(0.976959\pi\)
\(282\) 0 0
\(283\) 1771.47 1022.76i 0.372094 0.214829i −0.302279 0.953220i \(-0.597747\pi\)
0.674373 + 0.738391i \(0.264414\pi\)
\(284\) 3028.11 + 619.937i 0.632694 + 0.129530i
\(285\) 0 0
\(286\) −165.909 16.8087i −0.0343020 0.00347524i
\(287\) −658.283 −0.135391
\(288\) 0 0
\(289\) −163.963 −0.0333732
\(290\) −10344.3 1048.01i −2.09461 0.212211i
\(291\) 0 0
\(292\) −6088.38 1246.46i −1.22019 0.249806i
\(293\) 2041.60 1178.72i 0.407070 0.235022i −0.282460 0.959279i \(-0.591151\pi\)
0.689530 + 0.724257i \(0.257817\pi\)
\(294\) 0 0
\(295\) 3024.46 + 1746.18i 0.596919 + 0.344631i
\(296\) −2885.78 901.873i −0.566665 0.177096i
\(297\) 0 0
\(298\) −2199.07 + 988.991i −0.427479 + 0.192251i
\(299\) −821.827 + 1423.45i −0.158955 + 0.275318i
\(300\) 0 0
\(301\) 6.22124 + 10.7755i 0.00119132 + 0.00206342i
\(302\) −3370.21 2429.34i −0.642165 0.462890i
\(303\) 0 0
\(304\) 1717.82 4019.54i 0.324091 0.758343i
\(305\) 26.8381i 0.00503851i
\(306\) 0 0
\(307\) 5521.27i 1.02643i −0.858259 0.513217i \(-0.828454\pi\)
0.858259 0.513217i \(-0.171546\pi\)
\(308\) 715.235 238.341i 0.132319 0.0440933i
\(309\) 0 0
\(310\) −9115.32 + 12645.6i −1.67005 + 2.31685i
\(311\) 767.330 + 1329.05i 0.139908 + 0.242327i 0.927461 0.373919i \(-0.121986\pi\)
−0.787554 + 0.616246i \(0.788653\pi\)
\(312\) 0 0
\(313\) −4383.28 + 7592.06i −0.791557 + 1.37102i 0.133446 + 0.991056i \(0.457396\pi\)
−0.925003 + 0.379961i \(0.875937\pi\)
\(314\) −3119.59 6936.57i −0.560664 1.24667i
\(315\) 0 0
\(316\) 473.408 + 419.870i 0.0842762 + 0.0747454i
\(317\) 6074.45 + 3507.08i 1.07626 + 0.621380i 0.929886 0.367849i \(-0.119906\pi\)
0.146376 + 0.989229i \(0.453239\pi\)
\(318\) 0 0
\(319\) 928.706 536.189i 0.163002 0.0941091i
\(320\) 8539.05 + 703.599i 1.49171 + 0.122914i
\(321\) 0 0
\(322\) 749.008 7393.01i 0.129629 1.27949i
\(323\) 4866.59 0.838342
\(324\) 0 0
\(325\) 1872.39 0.319574
\(326\) −623.363 + 6152.85i −0.105905 + 1.04532i
\(327\) 0 0
\(328\) 752.910 168.914i 0.126745 0.0284350i
\(329\) 3125.35 1804.42i 0.523727 0.302374i
\(330\) 0 0
\(331\) 8563.21 + 4943.97i 1.42198 + 0.820982i 0.996468 0.0839692i \(-0.0267597\pi\)
0.425515 + 0.904951i \(0.360093\pi\)
\(332\) 4911.96 5538.28i 0.811984 0.915520i
\(333\) 0 0
\(334\) −4154.69 9238.16i −0.680642 1.51344i
\(335\) 3588.38 6215.26i 0.585236 1.01366i
\(336\) 0 0
\(337\) 2504.10 + 4337.22i 0.404768 + 0.701079i 0.994294 0.106670i \(-0.0340190\pi\)
−0.589527 + 0.807749i \(0.700686\pi\)
\(338\) 3392.42 4706.29i 0.545927 0.757362i
\(339\) 0 0
\(340\) 3015.68 + 9049.71i 0.481024 + 1.44350i
\(341\) 1607.81i 0.255330i
\(342\) 0 0
\(343\) 6049.14i 0.952252i
\(344\) −9.88050 10.7281i −0.00154861 0.00168146i
\(345\) 0 0
\(346\) 250.384 + 180.483i 0.0389038 + 0.0280429i
\(347\) −3897.53 6750.72i −0.602969 1.04437i −0.992369 0.123305i \(-0.960651\pi\)
0.389399 0.921069i \(1.62732\pi\)
\(348\) 0 0
\(349\) 4540.81 7864.91i 0.696458 1.20630i −0.273228 0.961949i \(-0.588091\pi\)
0.969687 0.244352i \(-0.0785753\pi\)
\(350\) −7720.17 + 3472.00i −1.17903 + 0.530246i
\(351\) 0 0
\(352\) −756.891 + 456.130i −0.114609 + 0.0690676i
\(353\) −3944.55 2277.39i −0.594752 0.343380i 0.172222 0.985058i \(-0.444905\pi\)
−0.766974 + 0.641678i \(0.778239\pi\)
\(354\) 0 0
\(355\) 5599.34 3232.78i 0.837133 0.483319i
\(356\) −1675.55 + 8184.32i −0.249450 + 1.21845i
\(357\) 0 0
\(358\) 755.275 + 76.5192i 0.111501 + 0.0112965i
\(359\) −5415.10 −0.796095 −0.398047 0.917365i \(-0.630312\pi\)
−0.398047 + 0.917365i \(0.630312\pi\)
\(360\) 0 0
\(361\) 2194.06 0.319881
\(362\) 2528.63 + 256.183i 0.367132 + 0.0371953i
\(363\) 0 0
\(364\) 374.067 1827.15i 0.0538638 0.263100i
\(365\) −11258.1 + 6499.89i −1.61446 + 0.932109i
\(366\) 0 0
\(367\) −9228.51 5328.08i −1.31260 0.757830i −0.330074 0.943955i \(-0.607074\pi\)
−0.982526 + 0.186125i \(0.940407\pi\)
\(368\) 1040.35 + 8647.94i 0.147369 + 1.22501i
\(369\) 0 0
\(370\) −5767.93 + 2594.02i −0.810433 + 0.364477i
\(371\) −2571.77 + 4454.43i −0.359891 + 0.623350i
\(372\) 0 0
\(373\) −1354.99 2346.91i −0.188093 0.325786i 0.756522 0.653969i \(-0.226897\pi\)
−0.944614 + 0.328183i \(0.893564\pi\)
\(374\) −798.118 575.305i −0.110347 0.0795409i
\(375\) 0 0
\(376\) −3111.61 + 2865.76i −0.426779 + 0.393059i
\(377\) 2652.91i 0.362418i
\(378\) 0 0
\(379\) 6395.35i 0.866774i 0.901208 + 0.433387i \(0.142682\pi\)
−0.901208 + 0.433387i \(0.857318\pi\)
\(380\) −2890.72 8674.73i −0.390239 1.17106i
\(381\) 0 0
\(382\) −851.206 + 1180.88i −0.114009 + 0.158164i
\(383\) 682.579 + 1182.26i 0.0910656 + 0.157730i 0.907960 0.419057i \(-0.137639\pi\)
−0.816894 + 0.576788i \(0.804306\pi\)
\(384\) 0 0
\(385\) 788.503 1365.73i 0.104379 0.180789i
\(386\) 2853.08 + 6343.97i 0.376212 + 0.836528i
\(387\) 0 0
\(388\) 7783.91 8776.44i 1.01847 1.14834i
\(389\) 5380.83 + 3106.62i 0.701333 + 0.404915i 0.807844 0.589397i \(-0.200634\pi\)
−0.106510 + 0.994312i \(0.533968\pi\)
\(390\) 0 0
\(391\) −8398.18 + 4848.69i −1.08623 + 0.627133i
\(392\) 146.784 + 654.272i 0.0189126 + 0.0843004i
\(393\) 0 0
\(394\) 184.317 1819.28i 0.0235679 0.232625i
\(395\) 1323.64 0.168606
\(396\) 0 0
\(397\) 3291.69 0.416134 0.208067 0.978115i \(-0.433283\pi\)
0.208067 + 0.978115i \(0.433283\pi\)
\(398\) 496.917 4904.77i 0.0625834 0.617723i
\(399\) 0 0
\(400\) 7939.02 5952.07i 0.992378 0.744008i
\(401\) −3529.51 + 2037.76i −0.439539 + 0.253768i −0.703402 0.710792i \(-0.748337\pi\)
0.263863 + 0.964560i \(0.415003\pi\)
\(402\) 0 0
\(403\) −3444.60 1988.74i −0.425776 0.245822i
\(404\) 2172.16 + 1926.51i 0.267498 + 0.237246i
\(405\) 0 0
\(406\) 4919.31 + 10938.3i 0.601333 + 1.33710i
\(407\) 326.151 564.910i 0.0397216 0.0687998i
\(408\) 0 0
\(409\) −7054.78 12219.2i −0.852900 1.47727i −0.878579 0.477597i \(-0.841508\pi\)
0.0256787 0.999670i \(-0.491825\pi\)
\(410\) 943.828 1309.37i 0.113689 0.157720i
\(411\) 0 0
\(412\) 4085.06 1361.28i 0.488487 0.162781i
\(413\) 4028.56i 0.479982i
\(414\) 0 0
\(415\) 15484.9i 1.83162i
\(416\) 41.0022 + 2185.78i 0.00483244 + 0.257612i
\(417\) 0 0
\(418\) 765.047 + 551.466i 0.0895207 + 0.0645289i
\(419\) 3184.20 + 5515.19i 0.371261 + 0.643042i 0.989760 0.142743i \(-0.0455923\pi\)
−0.618499 + 0.785786i \(0.712259\pi\)
\(420\) 0 0
\(421\) −5406.24 + 9363.89i −0.625853 + 1.08401i 0.362522 + 0.931975i \(0.381916\pi\)
−0.988375 + 0.152034i \(0.951418\pi\)
\(422\) 10866.8 4887.15i 1.25353 0.563750i
\(423\) 0 0
\(424\) 1798.46 5754.66i 0.205993 0.659130i
\(425\) 9566.92 + 5523.46i 1.09191 + 0.630417i
\(426\) 0 0
\(427\) −26.8111 + 15.4794i −0.00303859 + 0.00175433i
\(428\) 3373.67 + 690.683i 0.381011 + 0.0780034i
\(429\) 0 0
\(430\) −30.3530 3.07516i −0.00340408 0.000344877i
\(431\) 10968.4 1.22583 0.612913 0.790150i \(-0.289998\pi\)
0.612913 + 0.790150i \(0.289998\pi\)
\(432\) 0 0
\(433\) −1491.10 −0.165491 −0.0827457 0.996571i \(-0.526369\pi\)
−0.0827457 + 0.996571i \(0.526369\pi\)
\(434\) 17890.4 + 1812.53i 1.97872 + 0.200470i
\(435\) 0 0
\(436\) 7048.40 + 1443.00i 0.774213 + 0.158503i
\(437\) 8050.19 4647.78i 0.881219 0.508772i
\(438\) 0 0
\(439\) −1927.62 1112.91i −0.209567 0.120994i 0.391543 0.920160i \(-0.371941\pi\)
−0.601110 + 0.799166i \(0.705275\pi\)
\(440\) −551.408 + 1764.38i −0.0597439 + 0.191167i
\(441\) 0 0
\(442\) −2219.76 + 998.295i −0.238876 + 0.107430i
\(443\) −7938.74 + 13750.3i −0.851425 + 1.47471i 0.0284982 + 0.999594i \(0.490927\pi\)
−0.879923 + 0.475117i \(0.842406\pi\)
\(444\) 0 0
\(445\) 8737.50 + 15133.8i 0.930780 + 1.61216i
\(446\) −14726.9 10615.6i −1.56354 1.12704i
\(447\) 0 0
\(448\) −4222.17 8936.27i −0.445265 0.942409i
\(449\) 11558.7i 1.21490i 0.794358 + 0.607450i \(0.207807\pi\)
−0.794358 + 0.607450i \(0.792193\pi\)
\(450\) 0 0
\(451\) 166.477i 0.0173816i
\(452\) 2899.60 966.246i 0.301738 0.100550i
\(453\) 0 0
\(454\) 3720.75 5161.78i 0.384633 0.533600i
\(455\) −1950.64 3378.61i −0.200984 0.348114i
\(456\) 0 0
\(457\) 5444.85 9430.75i 0.557329 0.965322i −0.440390 0.897807i \(-0.645160\pi\)
0.997718 0.0675148i \(-0.0215070\pi\)
\(458\) −4026.43 8952.96i −0.410792 0.913416i
\(459\) 0 0
\(460\) 13631.3 + 12089.7i 1.38166 + 1.22540i
\(461\) −10197.5 5887.54i −1.03025 0.594816i −0.113195 0.993573i \(-0.536108\pi\)
−0.917057 + 0.398757i \(0.869442\pi\)
\(462\) 0 0
\(463\) 2303.58 1329.97i 0.231223 0.133497i −0.379913 0.925022i \(-0.624046\pi\)
0.611136 + 0.791525i \(0.290713\pi\)
\(464\) −8433.21 11248.4i −0.843754 1.12542i
\(465\) 0 0
\(466\) −1098.39 + 10841.5i −0.109188 + 1.07773i
\(467\) −32.9750 −0.00326746 −0.00163373 0.999999i \(-0.500520\pi\)
−0.00163373 + 0.999999i \(0.500520\pi\)
\(468\) 0 0
\(469\) −8278.68 −0.815083
\(470\) −891.925 + 8803.66i −0.0875350 + 0.864006i
\(471\) 0 0
\(472\) 1033.72 + 4607.66i 0.100807 + 0.449332i
\(473\) 2.72509 1.57333i 0.000264904 0.000152942i
\(474\) 0 0
\(475\) −9170.50 5294.59i −0.885834 0.511437i
\(476\) 7301.26 8232.25i 0.703052 0.792698i
\(477\) 0 0
\(478\) −46.2499 102.839i −0.00442556 0.00984046i
\(479\) −4069.08 + 7047.85i −0.388144 + 0.672284i −0.992200 0.124657i \(-0.960217\pi\)
0.604056 + 0.796942i \(0.293550\pi\)
\(480\) 0 0
\(481\) −806.850 1397.50i −0.0764848 0.132476i
\(482\) −5719.83 + 7935.10i −0.540521 + 0.749863i
\(483\) 0 0
\(484\) 3306.02 + 9921.00i 0.310483 + 0.931724i
\(485\) 24538.7i 2.29741i
\(486\) 0 0
\(487\) 1992.29i 0.185378i 0.995695 + 0.0926891i \(0.0295463\pi\)
−0.995695 + 0.0926891i \(0.970454\pi\)
\(488\) 26.6932 24.5842i 0.00247611 0.00228048i
\(489\) 0 0
\(490\) 1137.83 + 820.178i 0.104902 + 0.0756161i
\(491\) 4407.34 + 7633.75i 0.405093 + 0.701642i 0.994332 0.106317i \(-0.0339058\pi\)
−0.589239 + 0.807959i \(0.700572\pi\)
\(492\) 0 0
\(493\) 7825.94 13554.9i 0.714934 1.23830i
\(494\) 2127.78 956.929i 0.193792 0.0871544i
\(495\) 0 0
\(496\) −20927.2 + 2517.54i −1.89447 + 0.227905i
\(497\) −6459.06 3729.14i −0.582954 0.336569i
\(498\) 0 0
\(499\) −18252.9 + 10538.3i −1.63750 + 0.945409i −0.655806 + 0.754930i \(0.727671\pi\)
−0.981691 + 0.190479i \(0.938996\pi\)
\(500\) 806.559 3939.67i 0.0721408 0.352375i
\(501\) 0 0
\(502\) −8379.07 848.909i −0.744973 0.0754754i
\(503\) −19011.6 −1.68526 −0.842629 0.538494i \(-0.818994\pi\)
−0.842629 + 0.538494i \(0.818994\pi\)
\(504\) 0 0
\(505\) 6073.31 0.535166
\(506\) −1869.66 189.421i −0.164262 0.0166419i
\(507\) 0 0
\(508\) 2692.28 13150.6i 0.235139 1.14855i
\(509\) −11096.0 + 6406.27i −0.966250 + 0.557865i −0.898091 0.439810i \(-0.855046\pi\)
−0.0681588 + 0.997674i \(0.521712\pi\)
\(510\) 0 0
\(511\) 12986.7 + 7497.88i 1.12426 + 0.649093i
\(512\) 7122.13 + 9137.45i 0.614759 + 0.788715i
\(513\) 0 0
\(514\) 16660.3 7492.64i 1.42968 0.642970i
\(515\) 4503.53 7800.35i 0.385339 0.667426i
\(516\) 0 0
\(517\) −456.332 790.390i −0.0388190 0.0672365i
\(518\) 5918.17 + 4265.98i 0.501987 + 0.361846i
\(519\) 0 0
\(520\) 3097.99 + 3363.75i 0.261261 + 0.283674i
\(521\) 14455.7i 1.21558i 0.794100 + 0.607788i \(0.207943\pi\)
−0.794100 + 0.607788i \(0.792057\pi\)
\(522\) 0 0
\(523\) 15232.9i 1.27359i 0.771032 + 0.636796i \(0.219741\pi\)
−0.771032 + 0.636796i \(0.780259\pi\)
\(524\) 3603.62 + 10814.1i 0.300429 + 0.901555i
\(525\) 0 0
\(526\) 9728.27 13496.0i 0.806412 1.11873i
\(527\) −11733.4 20322.8i −0.969854 1.67984i
\(528\) 0 0
\(529\) −3177.87 + 5504.23i −0.261187 + 0.452390i
\(530\) −5172.84 11502.1i −0.423950 0.942675i
\(531\) 0 0
\(532\) −6998.72 + 7891.13i −0.570363 + 0.643090i
\(533\) 356.664 + 205.920i 0.0289847 + 0.0167343i
\(534\) 0 0
\(535\) 6238.33 3601.70i 0.504124 0.291056i
\(536\) 9468.72 2124.29i 0.763035 0.171185i
\(537\) 0 0
\(538\) −845.902 + 8349.39i −0.0677870 + 0.669085i
\(539\) −144.667 −0.0115608
\(540\) 0 0
\(541\) −23075.7 −1.83383 −0.916915 0.399083i \(-0.869328\pi\)
−0.916915 + 0.399083i \(0.869328\pi\)
\(542\) −566.141 + 5588.04i −0.0448669 + 0.442854i
\(543\) 0 0
\(544\) −6238.43 + 11289.1i −0.491674 + 0.889736i
\(545\) 13033.3 7524.80i 1.02438 0.591426i
\(546\) 0 0
\(547\) −317.151 183.107i −0.0247905 0.0143128i 0.487554 0.873093i \(-0.337889\pi\)
−0.512344 + 0.858780i \(0.671223\pi\)
\(548\) −160.540 142.385i −0.0125145 0.0110992i
\(549\) 0 0
\(550\) 878.056 + 1952.40i 0.0680735 + 0.151365i
\(551\) −7501.66 + 12993.2i −0.580002 + 1.00459i
\(552\) 0 0
\(553\) −763.434 1322.31i −0.0587061 0.101682i
\(554\) −7182.88 + 9964.78i −0.550851 + 0.764193i
\(555\) 0 0
\(556\) −12572.3 + 4189.54i −0.958968 + 0.319562i
\(557\) 3402.66i 0.258842i 0.991590 + 0.129421i \(0.0413119\pi\)
−0.991590 + 0.129421i \(0.958688\pi\)
\(558\) 0 0
\(559\) 7.78437i 0.000588987i
\(560\) −19010.9 8124.64i −1.43457 0.613087i
\(561\) 0 0
\(562\) −17889.2 12895.0i −1.34272 0.967868i
\(563\) 2461.45 + 4263.36i 0.184259 + 0.319146i 0.943327 0.331866i \(-0.107678\pi\)
−0.759068 + 0.651012i \(0.774345\pi\)
\(564\) 0 0
\(565\) 3196.63 5536.73i 0.238023 0.412269i
\(566\) 5276.53 2373.02i 0.391854 0.176229i
\(567\) 0 0
\(568\) 8344.42 + 2607.82i 0.616416 + 0.192644i
\(569\) −10423.8 6018.16i −0.767990 0.443399i 0.0641669 0.997939i \(-0.479561\pi\)
−0.832157 + 0.554540i \(0.812894\pi\)
\(570\) 0 0
\(571\) 522.706 301.784i 0.0383092 0.0221178i −0.480723 0.876872i \(-0.659626\pi\)
0.519032 + 0.854755i \(0.326292\pi\)
\(572\) −462.078 94.6001i −0.0337770 0.00691508i
\(573\) 0 0
\(574\) −1852.42 187.674i −0.134701 0.0136470i
\(575\) 21100.5 1.53035
\(576\) 0 0
\(577\) −6971.52 −0.502995 −0.251497 0.967858i \(-0.580923\pi\)
−0.251497 + 0.967858i \(0.580923\pi\)
\(578\) −461.395 46.7453i −0.0332033 0.00336392i
\(579\) 0 0
\(580\) −28810.3 5898.25i −2.06255 0.422261i
\(581\) −15469.3 + 8931.22i −1.10461 + 0.637745i
\(582\) 0 0
\(583\) 1126.51 + 650.391i 0.0800262 + 0.0462032i
\(584\) −16777.5 5243.34i −1.18880 0.371525i
\(585\) 0 0
\(586\) 6081.15 2734.88i 0.428686 0.192793i
\(587\) 10334.9 17900.6i 0.726691 1.25867i −0.231583 0.972815i \(-0.574390\pi\)
0.958274 0.285851i \(-0.0922762\pi\)
\(588\) 0 0
\(589\) 11247.2 + 19480.7i 0.786811 + 1.36280i
\(590\) 8013.08 + 5776.04i 0.559141 + 0.403044i
\(591\) 0 0
\(592\) −7863.54 3360.62i −0.545928 0.233312i
\(593\) 2417.22i 0.167392i −0.996491 0.0836958i \(-0.973328\pi\)
0.996491 0.0836958i \(-0.0266724\pi\)
\(594\) 0 0
\(595\) 23017.2i 1.58590i
\(596\) −6470.19 + 2156.09i −0.444680 + 0.148183i
\(597\) 0 0
\(598\) −2718.46 + 3771.31i −0.185896 + 0.257893i
\(599\) 14467.5 + 25058.4i 0.986852 + 1.70928i 0.633400 + 0.773825i \(0.281659\pi\)
0.353452 + 0.935453i \(0.385008\pi\)
\(600\) 0 0
\(601\) −318.246 + 551.219i −0.0215999 + 0.0374121i −0.876623 0.481177i \(-0.840209\pi\)
0.855023 + 0.518589i \(0.173543\pi\)
\(602\) 14.4346 + 32.0962i 0.000977263 + 0.00217299i
\(603\) 0 0
\(604\) −8791.25 7797.05i −0.592237 0.525261i
\(605\) 18944.0 + 10937.3i 1.27303 + 0.734983i
\(606\) 0 0
\(607\) 16616.3 9593.41i 1.11109 0.641490i 0.171981 0.985100i \(-0.444983\pi\)
0.939112 + 0.343610i \(0.111650\pi\)
\(608\) 5979.94 10821.3i 0.398879 0.721813i
\(609\) 0 0
\(610\) 7.65146 75.5230i 0.000507866 0.00501284i
\(611\) −2257.80 −0.149494
\(612\) 0 0
\(613\) 6429.22 0.423612 0.211806 0.977312i \(-0.432066\pi\)
0.211806 + 0.977312i \(0.432066\pi\)
\(614\) 1574.10 15537.0i 0.103462 1.02121i
\(615\) 0 0
\(616\) 2080.64 466.786i 0.136090 0.0305314i
\(617\) 6024.79 3478.41i 0.393110 0.226962i −0.290397 0.956906i \(-0.593787\pi\)
0.683507 + 0.729944i \(0.260454\pi\)
\(618\) 0 0
\(619\) 19227.5 + 11101.0i 1.24850 + 0.720819i 0.970809 0.239853i \(-0.0770992\pi\)
0.277686 + 0.960672i \(0.410433\pi\)
\(620\) −29255.9 + 32986.4i −1.89508 + 2.13672i
\(621\) 0 0
\(622\) 1780.37 + 3958.75i 0.114769 + 0.255195i
\(623\) 10079.0 17457.4i 0.648168 1.12266i
\(624\) 0 0
\(625\) 5483.94 + 9498.47i 0.350972 + 0.607902i
\(626\) −14499.1 + 20114.6i −0.925720 + 1.28425i
\(627\) 0 0
\(628\) −6801.00 20409.0i −0.432149 1.29683i
\(629\) 9520.65i 0.603519i
\(630\) 0 0
\(631\) 529.250i 0.0333901i 0.999861 + 0.0166950i \(0.00531444\pi\)
−0.999861 + 0.0166950i \(0.994686\pi\)
\(632\) 1212.48 + 1316.49i 0.0763128 + 0.0828595i
\(633\) 0 0
\(634\) 16093.8 + 11600.8i 1.00815 + 0.726699i
\(635\) −14039.4 24317.0i −0.877383 1.51967i
\(636\) 0 0
\(637\) −178.943 + 309.938i −0.0111303 + 0.0192782i
\(638\) 2766.27 1244.08i 0.171658 0.0771997i
\(639\) 0 0
\(640\) 23828.5 + 4414.40i 1.47172 + 0.272648i
\(641\) 19866.3 + 11469.8i 1.22414 + 0.706755i 0.965797 0.259299i \(-0.0834915\pi\)
0.258339 + 0.966054i \(0.416825\pi\)
\(642\) 0 0
\(643\) 2182.17 1259.88i 0.133836 0.0772702i −0.431587 0.902071i \(-0.642046\pi\)
0.565423 + 0.824801i \(0.308713\pi\)
\(644\) 4215.45 20590.5i 0.257938 1.25991i
\(645\) 0 0
\(646\) 13694.7 + 1387.45i 0.834072 + 0.0845023i
\(647\) −5938.61 −0.360851 −0.180426 0.983589i \(-0.557748\pi\)
−0.180426 + 0.983589i \(0.557748\pi\)
\(648\) 0 0
\(649\) −1018.81 −0.0616205
\(650\) 5268.96 + 533.814i 0.317947 + 0.0322122i
\(651\) 0 0
\(652\) −3508.32 + 17136.5i −0.210731 + 1.02932i
\(653\) 22562.1 13026.3i 1.35210 0.780638i 0.363561 0.931571i \(-0.381561\pi\)
0.988544 + 0.150933i \(0.0482277\pi\)
\(654\) 0 0
\(655\) 20649.3 + 11921.9i 1.23181 + 0.711184i
\(656\) 2166.86 260.674i 0.128966 0.0155146i
\(657\) 0 0
\(658\) 9309.24 4186.66i 0.551538 0.248044i
\(659\) 14176.7 24554.8i 0.838008 1.45147i −0.0535504 0.998565i \(-0.517054\pi\)
0.891558 0.452907i \(-0.149613\pi\)
\(660\) 0 0
\(661\) 5168.04 + 8951.31i 0.304105 + 0.526725i 0.977062 0.212957i \(-0.0683093\pi\)
−0.672957 + 0.739682i \(0.734976\pi\)
\(662\) 22687.5 + 16353.8i 1.33199 + 0.960133i
\(663\) 0 0
\(664\) 15401.3 14184.5i 0.900130 0.829012i
\(665\) 22063.4i 1.28659i
\(666\) 0 0
\(667\) 29896.3i 1.73551i
\(668\) −9057.62 27180.9i −0.524625 1.57434i
\(669\) 0 0
\(670\) 11869.7 16466.8i 0.684430 0.949507i
\(671\) 3.91468 + 6.78042i 0.000225223 + 0.000390097i
\(672\) 0 0
\(673\) 7541.97 13063.1i 0.431979 0.748209i −0.565065 0.825046i \(-0.691149\pi\)
0.997044 + 0.0768374i \(0.0244822\pi\)
\(674\) 5810.05 + 12918.9i 0.332040 + 0.738307i
\(675\) 0 0
\(676\) 10888.1 12276.4i 0.619486 0.698477i
\(677\) 11873.7 + 6855.26i 0.674065 + 0.389172i 0.797615 0.603167i \(-0.206095\pi\)
−0.123550 + 0.992338i \(0.539428\pi\)
\(678\) 0 0
\(679\) −24514.0 + 14153.2i −1.38551 + 0.799925i
\(680\) 5906.14 + 26325.9i 0.333074 + 1.48463i
\(681\) 0 0
\(682\) 458.381 4524.41i 0.0257365 0.254030i
\(683\) 807.274 0.0452262 0.0226131 0.999744i \(-0.492801\pi\)
0.0226131 + 0.999744i \(0.492801\pi\)
\(684\) 0 0
\(685\) −448.867 −0.0250370
\(686\) −1724.59 + 17022.4i −0.0959842 + 0.947403i
\(687\) 0 0
\(688\) −24.7454 33.0061i −0.00137123 0.00182899i
\(689\) 2786.82 1608.97i 0.154092 0.0889651i
\(690\) 0 0
\(691\) −19006.4 10973.4i −1.04636 0.604119i −0.124735 0.992190i \(-0.539808\pi\)
−0.921629 + 0.388072i \(0.873141\pi\)
\(692\) 653.130 + 579.268i 0.0358790 + 0.0318215i
\(693\) 0 0
\(694\) −9043.13 20107.9i −0.494629 1.09983i
\(695\) −13860.3 + 24006.7i −0.756474 + 1.31025i
\(696\) 0 0
\(697\) 1214.91 + 2104.28i 0.0660228 + 0.114355i
\(698\) 15020.2 20837.5i 0.814503 1.12996i
\(699\) 0 0
\(700\) −22714.6 + 7569.28i −1.22647 + 0.408703i
\(701\) 3170.45i 0.170822i −0.996346 0.0854110i \(-0.972780\pi\)
0.996346 0.0854110i \(-0.0272203\pi\)
\(702\) 0 0
\(703\) 9126.15i 0.489615i
\(704\) −2259.95 + 1067.77i −0.120987 + 0.0571636i
\(705\) 0 0
\(706\) −10450.8 7533.20i −0.557111 0.401580i
\(707\) −3502.90 6067.20i −0.186337 0.322745i
\(708\) 0 0
\(709\) −1413.03 + 2447.45i −0.0748485 + 0.129641i −0.901020 0.433777i \(-0.857181\pi\)
0.826172 + 0.563418i \(0.190514\pi\)
\(710\) 16678.3 7500.76i 0.881586 0.396477i
\(711\) 0 0
\(712\) −7048.37 + 22553.2i −0.370996 + 1.18710i
\(713\) −38818.0 22411.6i −2.03892 1.17717i
\(714\) 0 0
\(715\) −854.438 + 493.310i −0.0446912 + 0.0258025i
\(716\) 2103.54 + 430.653i 0.109795 + 0.0224780i
\(717\) 0 0
\(718\) −15238.2 1543.83i −0.792040 0.0802440i
\(719\) 15469.9 0.802408 0.401204 0.915989i \(-0.368592\pi\)
0.401204 + 0.915989i \(0.368592\pi\)
\(720\) 0 0
\(721\) −10390.0 −0.536677
\(722\) 6174.14 + 625.521i 0.318252 + 0.0322430i
\(723\) 0 0
\(724\) 7042.58 + 1441.81i 0.361513 + 0.0740116i
\(725\) −29494.0 + 17028.4i −1.51087 + 0.872301i
\(726\) 0 0
\(727\) 6900.11 + 3983.78i 0.352009 + 0.203233i 0.665570 0.746336i \(-0.268189\pi\)
−0.313561 + 0.949568i \(0.601522\pi\)
\(728\) 1573.55 5034.98i 0.0801092 0.256331i
\(729\) 0 0
\(730\) −33533.8 + 15081.2i −1.70019 + 0.764629i
\(731\) 22.9635 39.7739i 0.00116188 0.00201244i
\(732\) 0 0
\(733\) −12334.6 21364.2i −0.621542 1.07654i −0.989199 0.146581i \(-0.953173\pi\)
0.367656 0.929962i \(-0.380160\pi\)
\(734\) −24450.2 17624.4i −1.22953 0.886277i
\(735\) 0 0
\(736\) 462.063 + 24632.1i 0.0231411 + 1.23363i
\(737\) 2093.65i 0.104641i
\(738\) 0 0
\(739\) 1182.09i 0.0588414i 0.999567 + 0.0294207i \(0.00936624\pi\)
−0.999567 + 0.0294207i \(0.990634\pi\)
\(740\) −16970.6 + 5655.20i −0.843044 + 0.280931i
\(741\) 0 0
\(742\) −8506.96 + 11801.7i −0.420890 + 0.583899i
\(743\) 13616.4 + 23584.4i 0.672327 + 1.16450i 0.977243 + 0.212125i \(0.0680383\pi\)
−0.304916 + 0.952379i \(0.598628\pi\)
\(744\) 0 0
\(745\) −7133.00 + 12354.7i −0.350782 + 0.607573i
\(746\) −3143.87 6990.55i −0.154296 0.343086i
\(747\) 0 0
\(748\) −2081.90 1846.46i −0.101767 0.0902584i
\(749\) −7196.16 4154.70i −0.351057 0.202683i
\(750\) 0 0
\(751\) 12287.2 7093.99i 0.597024 0.344692i −0.170846 0.985298i \(-0.554650\pi\)
0.767870 + 0.640606i \(0.221317\pi\)
\(752\) −9573.15 + 7177.21i −0.464224 + 0.348040i
\(753\) 0 0
\(754\) 756.336 7465.34i 0.0365307 0.360572i
\(755\) −24580.1 −1.18485
\(756\) 0 0
\(757\) 30482.1 1.46353 0.731764 0.681559i \(-0.238698\pi\)
0.731764 + 0.681559i \(0.238698\pi\)
\(758\) −1823.30 + 17996.7i −0.0873682 + 0.862359i
\(759\) 0 0
\(760\) −5661.41 25235.0i −0.270212 1.20443i
\(761\) 19985.7 11538.8i 0.952013 0.549645i 0.0583074 0.998299i \(-0.481430\pi\)
0.893706 + 0.448654i \(0.148096\pi\)
\(762\) 0 0
\(763\) −15034.5 8680.15i −0.713348 0.411851i
\(764\) −2731.98 + 3080.33i −0.129371 + 0.145867i
\(765\) 0 0
\(766\) 1583.73 + 3521.51i 0.0747031 + 0.166106i
\(767\) −1260.19 + 2182.72i −0.0593258 + 0.102755i
\(768\) 0 0
\(769\) −1035.31 1793.21i −0.0485491 0.0840895i 0.840730 0.541455i \(-0.182126\pi\)
−0.889279 + 0.457366i \(0.848793\pi\)
\(770\) 2608.23 3618.39i 0.122070 0.169348i
\(771\) 0 0
\(772\) 6219.99 + 18665.5i 0.289977 + 0.870188i
\(773\) 35103.0i 1.63333i 0.577110 + 0.816666i \(0.304180\pi\)
−0.577110 + 0.816666i \(0.695820\pi\)
\(774\) 0 0
\(775\) 51061.1i 2.36667i
\(776\) 24406.2 22477.9i 1.12904 1.03983i
\(777\) 0 0
\(778\) 14256.1 + 10276.2i 0.656947 + 0.473545i
\(779\) −1164.57 2017.09i −0.0535622 0.0927724i
\(780\) 0 0