Properties

Label 108.4.h.b.35.9
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 35.9
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.65391 + 2.29447i) q^{2} +(-2.52915 + 7.58969i) q^{4} +(14.4924 - 8.36717i) q^{5} +(16.7175 + 9.65186i) q^{7} +(-21.5973 + 6.74964i) q^{8} +O(q^{10})\) \(q+(1.65391 + 2.29447i) q^{2} +(-2.52915 + 7.58969i) q^{4} +(14.4924 - 8.36717i) q^{5} +(16.7175 + 9.65186i) q^{7} +(-21.5973 + 6.74964i) q^{8} +(43.1673 + 19.4137i) q^{10} +(2.44092 - 4.22780i) q^{11} +(6.03848 + 10.4590i) q^{13} +(5.50343 + 54.3211i) q^{14} +(-51.2068 - 38.3909i) q^{16} +71.2528i q^{17} +68.3003i q^{19} +(26.8509 + 131.154i) q^{20} +(13.7376 - 1.39180i) q^{22} +(-68.0491 - 117.865i) q^{23} +(77.5192 - 134.267i) q^{25} +(-14.0106 + 31.1533i) q^{26} +(-115.536 + 102.470i) q^{28} +(-190.237 - 109.833i) q^{29} +(285.221 - 164.672i) q^{31} +(3.39507 - 180.987i) q^{32} +(-163.487 + 117.846i) q^{34} +323.035 q^{35} -133.618 q^{37} +(-156.713 + 112.963i) q^{38} +(-256.520 + 278.526i) q^{40} +(29.5326 - 17.0507i) q^{41} +(0.558209 + 0.322282i) q^{43} +(25.9142 + 29.2186i) q^{44} +(157.889 - 351.074i) q^{46} +(93.4753 - 161.904i) q^{47} +(14.8169 + 25.6636i) q^{49} +(436.282 - 44.2010i) q^{50} +(-94.6525 + 19.3780i) q^{52} -266.453i q^{53} -81.6944i q^{55} +(-426.199 - 95.6168i) q^{56} +(-62.6263 - 618.147i) q^{58} +(-104.347 - 180.734i) q^{59} +(0.801886 - 1.38891i) q^{61} +(849.565 + 382.076i) q^{62} +(420.885 - 291.548i) q^{64} +(175.024 + 101.050i) q^{65} +(-371.407 + 214.432i) q^{67} +(-540.787 - 180.209i) q^{68} +(534.272 + 741.193i) q^{70} -386.365 q^{71} -776.832 q^{73} +(-220.992 - 306.582i) q^{74} +(-518.378 - 172.742i) q^{76} +(81.6122 - 47.1188i) q^{77} +(-68.5000 - 39.5485i) q^{79} +(-1063.33 - 127.919i) q^{80} +(87.9665 + 39.5613i) q^{82} +(-462.668 + 801.365i) q^{83} +(596.185 + 1032.62i) q^{85} +(0.183763 + 1.81382i) q^{86} +(-24.1811 + 107.784i) q^{88} +1044.26i q^{89} +233.130i q^{91} +(1066.66 - 218.375i) q^{92} +(526.083 - 53.2991i) q^{94} +(571.481 + 989.834i) q^{95} +(733.184 - 1269.91i) q^{97} +(-34.3784 + 76.4422i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.65391 + 2.29447i 0.584746 + 0.811216i
\(3\) 0 0
\(4\) −2.52915 + 7.58969i −0.316144 + 0.948711i
\(5\) 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 0.878063 0.478546i \(-0.158836\pi\)
0.0245984 + 0.999697i \(0.492169\pi\)
\(8\) −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 −0.830632 0.556822i \(-0.812021\pi\)
0.897538 + 0.440937i \(0.145354\pi\)
\(12\) 0 0
\(13\) 6.03848 + 10.4590i 0.128829 + 0.223138i 0.923223 0.384264i \(-0.125545\pi\)
−0.794394 + 0.607402i \(0.792212\pi\)
\(14\) 5.50343 + 54.3211i 0.105061 + 1.03699i
\(15\) 0 0
\(16\) −51.2068 38.3909i −0.800106 0.599858i
\(17\) 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 \(0.135291\pi\)
−0.911027 + 0.412347i \(0.864709\pi\)
\(20\) 26.8509 + 131.154i 0.300202 + 1.46635i
\(21\) 0 0
\(22\) 13.7376 1.39180i 0.133130 0.0134878i
\(23\) −68.0491 117.865i −0.616923 1.06854i −0.990044 0.140759i \(-0.955046\pi\)
0.373121 0.927783i \(1.62171\pi\)
\(24\) 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 \(-0.263520\pi\)
0.976044 0.217571i \(-0.0698134\pi\)
\(32\) 3.39507 180.987i 0.0187553 0.999824i
\(33\) 0 0
\(34\) −163.487 + 117.846i −0.824642 + 0.594424i
\(35\) 323.035 1.56008
\(36\) 0 0
\(37\) −133.618 −0.593693 −0.296847 0.954925i \(-0.595935\pi\)
−0.296847 + 0.954925i \(0.595935\pi\)
\(38\) −156.713 + 112.963i −0.669005 + 0.482236i
\(39\) 0 0
\(40\) −256.520 + 278.526i −1.01399 + 1.10097i
\(41\) 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 0.500990 0.865453i \(-0.332970\pi\)
−0.499010 + 0.866596i \(0.666303\pi\)
\(44\) 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 −0.683732 0.729733i \(-0.739644\pi\)
0.973834 + 0.227263i \(0.0729775\pi\)
\(48\) 0 0
\(49\) 14.8169 + 25.6636i 0.0431979 + 0.0748210i
\(50\) 436.282 44.2010i 1.23399 0.125019i
\(51\) 0 0
\(52\) −94.6525 + 19.3780i −0.252422 + 0.0516777i
\(53\) 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
\(56\) −426.199 95.6168i −1.01702 0.228167i
\(57\) 0 0
\(58\) −62.6263 618.147i −0.141780 1.39943i
\(59\) −104.347 180.734i −0.230251 0.398806i 0.727631 0.685969i \(-0.240621\pi\)
−0.957882 + 0.287163i \(0.907288\pi\)
\(60\) 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 −0.798812 0.601581i \(-0.794538\pi\)
0.121579 + 0.992582i \(0.461204\pi\)
\(68\) −540.787 180.209i −0.964412 0.321376i
\(69\) 0 0
\(70\) 534.272 + 741.193i 0.912253 + 1.26557i
\(71\) −386.365 −0.645817 −0.322909 0.946430i \(-0.604661\pi\)
−0.322909 + 0.946430i \(0.604661\pi\)
\(72\) 0 0
\(73\) −776.832 −1.24550 −0.622749 0.782422i \(-0.713984\pi\)
−0.622749 + 0.782422i \(0.713984\pi\)
\(74\) −220.992 306.582i −0.347160 0.481614i
\(75\) 0 0
\(76\) −518.378 172.742i −0.782396 0.260721i
\(77\) 81.6122 47.1188i 0.120787 0.0697362i
\(78\) 0 0
\(79\) −68.5000 39.5485i −0.0975551 0.0563235i 0.450429 0.892812i \(-0.351271\pi\)
−0.547984 + 0.836489i \(0.684604\pi\)
\(80\) −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 \(0.376245\pi\)
−0.990927 + 0.134404i \(0.957088\pi\)
\(84\) 0 0
\(85\) 596.185 + 1032.62i 0.760768 + 1.31769i
\(86\) 0.183763 + 1.81382i 0.000230415 + 0.00227429i
\(87\) 0 0
\(88\) −24.1811 + 107.784i −0.0292922 + 0.130566i
\(89\) 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
\(92\) 1066.66 218.375i 1.20877 0.247469i
\(93\) 0 0
\(94\) 526.083 53.2991i 0.577248 0.0584828i
\(95\) 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 −0.706102 0.708110i \(-0.749548\pi\)
0.260190 + 0.965557i \(0.416215\pi\)
\(104\) −201.009 185.127i −0.189525 0.174550i
\(105\) 0 0
\(106\) 611.368 440.690i 0.560201 0.403808i
\(107\) −430.456 −0.388914 −0.194457 0.980911i \(-0.562294\pi\)
−0.194457 + 0.980911i \(0.562294\pi\)
\(108\) 0 0
\(109\) 899.324 0.790272 0.395136 0.918623i \(-0.370697\pi\)
0.395136 + 0.918623i \(0.370697\pi\)
\(110\) 187.445 135.115i 0.162474 0.117116i
\(111\) 0 0
\(112\) −485.507 1136.04i −0.409608 0.958445i
\(113\) 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
\(122\) 4.51305 0.457231i 0.00334912 0.000339309i
\(123\) 0 0
\(124\) 528.446 + 2581.22i 0.382708 + 1.86936i
\(125\) 502.674i 0.359684i
\(126\) 0 0
\(127\) 1677.92i 1.17237i 0.810177 + 0.586186i \(0.199371\pi\)
−0.810177 + 0.586186i \(0.800629\pi\)
\(128\) 1365.05 + 483.512i 0.942615 + 0.333881i
\(129\) 0 0
\(130\) 57.6181 + 568.714i 0.0388727 + 0.383689i
\(131\) −712.418 1233.94i −0.475147 0.822979i 0.524448 0.851443i \(-0.324272\pi\)
−0.999595 + 0.0284637i \(0.990938\pi\)
\(132\) 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 0.00625321 0.999980i \(-0.498010\pi\)
0.869135 + 0.494575i \(0.164676\pi\)
\(140\) −817.004 + 2451.74i −0.493210 + 1.48007i
\(141\) 0 0
\(142\) −639.013 886.500i −0.377639 0.523898i
\(143\) 58.9578 0.0344776
\(144\) 0 0
\(145\) −3675.98 −2.10533
\(146\) −1284.81 1782.42i −0.728300 1.01037i
\(147\) 0 0
\(148\) 337.940 1014.12i 0.187692 0.563244i
\(149\) −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 0.801944 0.597399i \(-0.203799\pi\)
−0.116391 + 0.993203i \(0.537133\pi\)
\(152\) −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 \(-0.406196\pi\)
\(158\) −22.5503 222.581i −0.0113545 0.112073i
\(159\) 0 0
\(160\) −1465.15 2651.35i −0.723940 1.31005i
\(161\) 2627.20i 1.28604i
\(162\) 0 0
\(163\) 2186.50i 1.05067i −0.850895 0.525336i \(-0.823940\pi\)
0.850895 0.525336i \(-0.176060\pi\)
\(164\) 54.7169 + 267.267i 0.0260529 + 0.127256i
\(165\) 0 0
\(166\) −2603.92 + 263.811i −1.21749 + 0.123348i
\(167\) 1790.65 + 3101.49i 0.829726 + 1.43713i 0.898253 + 0.439479i \(0.144837\pi\)
−0.0685268 + 0.997649i \(0.521830\pi\)
\(168\) 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
\(176\) −287.301 + 122.783i −0.123046 + 0.0525858i
\(177\) 0 0
\(178\) −2396.02 + 1727.11i −1.00893 + 0.727262i
\(179\) −268.397 −0.112072 −0.0560361 0.998429i \(-0.517846\pi\)
−0.0560361 + 0.998429i \(0.517846\pi\)
\(180\) 0 0
\(181\) 898.582 0.369011 0.184506 0.982831i \(-0.440932\pi\)
0.184506 + 0.982831i \(0.440932\pi\)
\(182\) −534.910 + 385.577i −0.217858 + 0.157038i
\(183\) 0 0
\(184\) 2265.22 + 2086.25i 0.907577 + 0.835870i
\(185\) −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 −0.813157 0.582044i \(-0.802253\pi\)
0.910643 + 0.413193i \(0.135587\pi\)
\(192\) 0 0
\(193\) 1229.66 + 2129.83i 0.458616 + 0.794346i 0.998888 0.0471443i \(-0.0150121\pi\)
−0.540272 + 0.841490i \(0.681679\pi\)
\(194\) 4126.39 418.057i 1.52710 0.154715i
\(195\) 0 0
\(196\) −232.253 + 47.5485i −0.0846403 + 0.0173282i
\(197\) 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 \(0.100477\pi\)
−0.950592 + 0.310443i \(0.899523\pi\)
\(200\) −767.949 + 3423.03i −0.271511 + 1.21022i
\(201\) 0 0
\(202\) 103.469 + 1021.28i 0.0360398 + 0.355727i
\(203\) −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 −0.958379 0.285499i \(-0.907841\pi\)
−0.231940 + 0.972730i \(0.574507\pi\)
\(212\) 2022.30 + 673.900i 0.655151 + 0.218319i
\(213\) 0 0
\(214\) −711.937 987.667i −0.227416 0.315493i
\(215\) 10.7864 0.00342150
\(216\) 0 0
\(217\) 6357.58 1.98885
\(218\) 1487.40 + 2063.47i 0.462109 + 0.641081i
\(219\) 0 0
\(220\) 620.035 + 206.617i 0.190013 + 0.0633188i
\(221\) −745.230 + 430.259i −0.226831 + 0.130961i
\(222\) 0 0
\(223\) 5558.55 + 3209.23i 1.66918 + 0.963703i 0.968080 + 0.250643i \(0.0806420\pi\)
0.701103 + 0.713060i \(0.252691\pi\)
\(224\) 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 −0.982292 0.187358i \(-0.940008\pi\)
0.653403 + 0.757011i \(0.273341\pi\)
\(228\) 0 0
\(229\) −1735.36 3005.74i −0.500769 0.867357i −1.00000 0.000888202i \(-0.999717\pi\)
0.499231 0.866469i \(-0.333616\pi\)
\(230\) −649.313 6408.98i −0.186150 1.83737i
\(231\) 0 0
\(232\) 4849.94 + 1088.07i 1.37247 + 0.307911i
\(233\) 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
\(236\) 1635.62 334.857i 0.451144 0.0923615i
\(237\) 0 0
\(238\) −3870.53 + 392.135i −1.05416 + 0.106800i
\(239\) 19.9334 + 34.5257i 0.00539491 + 0.00934426i 0.868710 0.495321i \(-0.164949\pi\)
−0.863315 + 0.504665i \(0.831616\pi\)
\(240\) 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
\(248\) −5048.51 + 5481.61i −1.29267 + 1.40356i
\(249\) 0 0
\(250\) 1153.37 831.378i 0.291781 0.210324i
\(251\) 2977.61 0.748786 0.374393 0.927270i \(-0.377851\pi\)
0.374393 + 0.927270i \(0.377851\pi\)
\(252\) 0 0
\(253\) −664.410 −0.165103
\(254\) −3849.93 + 2775.13i −0.951047 + 0.685540i
\(255\) 0 0
\(256\) 1148.28 + 3931.75i 0.280341 + 0.959901i
\(257\) 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 \(0.408854\pi\)
−0.971987 + 0.235036i \(0.924479\pi\)
\(264\) 0 0
\(265\) −2229.46 3861.54i −0.516810 0.895141i
\(266\) −3710.15 + 375.886i −0.855203 + 0.0866431i
\(267\) 0 0
\(268\) −688.129 3361.20i −0.156844 0.766111i
\(269\) 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 \(-0.928559\pi\)
0.974919 0.222561i \(-0.0714415\pi\)
\(272\) 2735.46 3648.63i 0.609785 0.813348i
\(273\) 0 0
\(274\) −7.64719 75.4808i −0.00168607 0.0166422i
\(275\) −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 −0.674373 0.738391i \(-0.735586\pi\)
0.302279 + 0.953220i \(0.402253\pi\)
\(284\) 977.173 2932.39i 0.204171 0.612694i
\(285\) 0 0
\(286\) 97.5110 + 135.277i 0.0201607 + 0.0279688i
\(287\) 658.283 0.135391
\(288\) 0 0
\(289\) −163.963 −0.0333732
\(290\) −6079.75 8434.41i −1.23109 1.70788i
\(291\) 0 0
\(292\) 1964.72 5895.92i 0.393756 1.18162i
\(293\) 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
\(302\) 418.763 + 4133.36i 0.0797917 + 0.787576i
\(303\) 0 0
\(304\) 2622.11 3497.44i 0.494699 0.659842i
\(305\) 26.8381i 0.00503851i
\(306\) 0 0
\(307\) 5521.27i 1.02643i 0.858259 + 0.513217i \(0.171546\pi\)
−0.858259 + 0.513217i \(0.828454\pi\)
\(308\) 151.208 + 738.582i 0.0279736 + 0.136638i
\(309\) 0 0
\(310\) 15509.1 1571.27i 2.84148 0.287879i
\(311\) −767.330 1329.05i −0.139908 0.242327i 0.787554 0.616246i \(-0.211347\pi\)
−0.927461 + 0.373919i \(0.878014\pi\)
\(312\) 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
\(320\) 3660.19 7746.83i 0.639409 1.35332i
\(321\) 0 0
\(322\) 6028.03 4345.16i 1.04326 0.752008i
\(323\) −4866.59 −0.838342
\(324\) 0 0
\(325\) 1872.39 0.319574
\(326\) 5016.84 3616.27i 0.852323 0.614377i
\(327\) 0 0
\(328\) −522.738 + 567.582i −0.0879982 + 0.0955473i
\(329\) 3125.35 1804.42i 0.523727 0.302374i
\(330\) 0 0
\(331\) −8563.21 4943.97i −1.42198 0.820982i −0.425515 0.904951i \(-0.639907\pi\)
−0.996468 + 0.0839692i \(0.973240\pi\)
\(332\) −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 \(0.700686\pi\)
\(338\) 5771.97 584.776i 0.928858 0.0941054i
\(339\) 0 0
\(340\) −9345.12 + 1913.20i −1.49062 + 0.305170i
\(341\) 1607.81i 0.255330i
\(342\) 0 0
\(343\) 6049.14i 0.952252i
\(344\) −14.2311 3.19271i −0.00223049 0.000500405i
\(345\) 0 0
\(346\) 31.1112 + 307.080i 0.00483396 + 0.0477131i
\(347\) 3897.53 + 6750.72i 0.602969 + 1.04437i 0.992369 + 0.123305i \(0.0393493\pi\)
−0.389399 + 0.921069i \(0.627317\pi\)
\(348\) 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
\(356\) −7925.61 2641.09i −1.17993 0.393195i
\(357\) 0 0
\(358\) −443.905 615.828i −0.0655338 0.0909148i
\(359\) 5415.10 0.796095 0.398047 0.917365i \(-0.369688\pi\)
0.398047 + 0.917365i \(0.369688\pi\)
\(360\) 0 0
\(361\) 2194.06 0.319881
\(362\) 1486.18 + 2061.77i 0.215778 + 0.299348i
\(363\) 0 0
\(364\) −1769.39 589.621i −0.254783 0.0849026i
\(365\) −11258.1 + 6499.89i −1.61446 + 0.932109i
\(366\) 0 0
\(367\) 9228.51 + 5328.08i 1.31260 + 0.757830i 0.982526 0.186125i \(-0.0595928\pi\)
0.330074 + 0.943955i \(0.392926\pi\)
\(368\) −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 \(0.893564\pi\)
\(374\) 99.1695 + 978.843i 0.0137111 + 0.135334i
\(375\) 0 0
\(376\) −926.019 + 4127.61i −0.127010 + 0.566131i
\(377\) 2652.91i 0.362418i
\(378\) 0 0
\(379\) 6395.35i 0.866774i −0.901208 0.433387i \(-0.857318\pi\)
0.901208 0.433387i \(-0.142682\pi\)
\(380\) −8957.89 + 1833.93i −1.20929 + 0.247575i
\(381\) 0 0
\(382\) 1448.27 146.729i 0.193979 0.0196526i
\(383\) −682.579 1182.26i −0.0910656 0.157730i 0.816894 0.576788i \(-0.195694\pi\)
−0.907960 + 0.419057i \(0.862361\pi\)
\(384\) 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
\(392\) −493.224 454.255i −0.0635500 0.0585290i
\(393\) 0 0
\(394\) 1483.39 1069.26i 0.189675 0.136723i
\(395\) −1323.64 −0.168606
\(396\) 0 0
\(397\) 3291.69 0.416134 0.208067 0.978115i \(-0.433283\pi\)
0.208067 + 0.978115i \(0.433283\pi\)
\(398\) −3999.20 + 2882.73i −0.503672 + 0.363061i
\(399\) 0 0
\(400\) −9124.15 + 3899.36i −1.14052 + 0.487420i
\(401\) −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 \(-0.491825\pi\)
\(410\) 1605.86 162.694i 0.193434 0.0195973i
\(411\) 0 0
\(412\) −863.624 4218.41i −0.103271 0.504432i
\(413\) 4028.56i 0.479982i
\(414\) 0 0
\(415\) 15484.9i 1.83162i
\(416\) 1913.44 1057.38i 0.225515 0.124621i
\(417\) 0 0
\(418\) 95.0603 + 938.283i 0.0111233 + 0.109792i
\(419\) −3184.20 5515.19i −0.371261 0.643042i 0.618499 0.785786i \(-0.287741\pi\)
−0.989760 + 0.142743i \(0.954408\pi\)
\(420\) 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
\(428\) 1088.69 3267.03i 0.122953 0.368967i
\(429\) 0 0
\(430\) 17.8397 + 24.7489i 0.00200071 + 0.00277558i
\(431\) −10968.4 −1.22583 −0.612913 0.790150i \(-0.710002\pi\)
−0.612913 + 0.790150i \(0.710002\pi\)
\(432\) 0 0
\(433\) −1491.10 −0.165491 −0.0827457 0.996571i \(-0.526369\pi\)
−0.0827457 + 0.996571i \(0.526369\pi\)
\(434\) 10514.9 + 14587.2i 1.16297 + 1.61339i
\(435\) 0 0
\(436\) −2274.52 + 6825.59i −0.249839 + 0.749740i
\(437\) 8050.19 4647.78i 0.881219 0.508772i
\(438\) 0 0
\(439\) 1927.62 + 1112.91i 0.209567 + 0.120994i 0.601110 0.799166i \(-0.294725\pi\)
−0.391543 + 0.920160i \(0.628059\pi\)
\(440\) 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 \(-0.509073\pi\)
0.879923 0.475117i \(-0.157594\pi\)
\(444\) 0 0
\(445\) 8737.50 + 15133.8i 0.930780 + 1.61216i
\(446\) 1829.88 + 18061.7i 0.194277 + 1.91759i
\(447\) 0 0
\(448\) 9850.13 811.629i 1.03878 0.0855934i
\(449\) 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
\(452\) 613.004 + 2994.25i 0.0637905 + 0.311588i
\(453\) 0 0
\(454\) −6330.61 + 641.373i −0.654428 + 0.0663021i
\(455\) 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 −0.611136 0.791525i \(-0.709287\pi\)
0.379913 + 0.925022i \(0.375954\pi\)
\(464\) 5524.83 + 12927.6i 0.552766 + 1.29342i
\(465\) 0 0
\(466\) −8839.82 + 6371.98i −0.878749 + 0.633426i
\(467\) 32.9750 0.00326746 0.00163373 0.999999i \(-0.499480\pi\)
0.00163373 + 0.999999i \(0.499480\pi\)
\(468\) 0 0
\(469\) −8278.68 −0.815083
\(470\) 7178.23 5174.26i 0.704483 0.507810i
\(471\) 0 0
\(472\) 3473.49 + 3199.06i 0.338730 + 0.311967i
\(473\) 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 −0.604056 0.796942i \(-0.706450\pi\)
0.992200 + 0.124657i \(0.0397831\pi\)
\(480\) 0 0
\(481\) −806.850 1397.50i −0.0764848 0.132476i
\(482\) −9731.91 + 985.969i −0.919661 + 0.0931736i
\(483\) 0 0
\(484\) −10244.8 + 2097.40i −0.962138 + 0.196976i
\(485\) 24538.7i 2.29741i
\(486\) 0 0
\(487\) 1992.29i 0.185378i −0.995695 0.0926891i \(-0.970454\pi\)
0.995695 0.0926891i \(-0.0295463\pi\)
\(488\) −7.94394 + 35.4091i −0.000736896 + 0.00328462i
\(489\) 0 0
\(490\) 141.380 + 1395.48i 0.0130345 + 0.128656i
\(491\) −4407.34 7633.75i −0.405093 0.701642i 0.589239 0.807959i \(-0.299428\pi\)
−0.994332 + 0.106317i \(0.966094\pi\)
\(492\) 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 \(-0.272329\pi\)
0.981691 0.190479i \(-0.0610042\pi\)
\(500\) 3815.14 + 1271.34i 0.341236 + 0.113712i
\(501\) 0 0
\(502\) 4924.71 + 6832.04i 0.437850 + 0.607428i
\(503\) 19011.6 1.68526 0.842629 0.538494i \(-0.181006\pi\)
0.842629 + 0.538494i \(0.181006\pi\)
\(504\) 0 0
\(505\) 6073.31 0.535166
\(506\) −1098.88 1524.47i −0.0965434 0.133934i
\(507\) 0 0
\(508\) −12734.9 4243.70i −1.11224 0.370638i
\(509\) −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
\(518\) −735.357 7258.27i −0.0623740 0.615657i
\(519\) 0 0
\(520\) −4462.09 1001.06i −0.376299 0.0844218i
\(521\) 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 \(-0.780259\pi\)
0.771032 0.636796i \(-0.219741\pi\)
\(524\) 11167.1 2286.20i 0.930984 0.190598i
\(525\) 0 0
\(526\) −16552.0 + 1676.93i −1.37206 + 0.139007i
\(527\) 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
\(536\) 6574.05 7138.01i 0.529768 0.575215i
\(537\) 0 0
\(538\) −6807.83 + 4907.27i −0.545551 + 0.393248i
\(539\) 144.667 0.0115608
\(540\) 0 0
\(541\) −23075.7 −1.83383 −0.916915 0.399083i \(-0.869328\pi\)
−0.916915 + 0.399083i \(0.869328\pi\)
\(542\) 4556.31 3284.31i 0.361089 0.260283i
\(543\) 0 0
\(544\) 12895.9 + 241.908i 1.01637 + 0.0190657i
\(545\) 13033.3 7524.80i 1.02438 0.591426i
\(546\) 0 0
\(547\) 317.151 + 183.107i 0.0247905 + 0.0143128i 0.512344 0.858780i \(-0.328777\pi\)
−0.487554 + 0.873093i \(0.662111\pi\)
\(548\) 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
\(554\) −12221.2 + 1238.17i −0.937236 + 0.0949542i
\(555\) 0 0
\(556\) 2657.92 + 12982.7i 0.202736 + 0.990272i
\(557\) 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
\(560\) −16541.6 12401.6i −1.24823 0.935829i
\(561\) 0 0
\(562\) −2222.80 21940.0i −0.166839 1.64676i
\(563\) −2461.45 4263.36i −0.184259 0.319146i 0.759068 0.651012i \(-0.225655\pi\)
−0.943327 + 0.331866i \(0.892322\pi\)
\(564\) 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 −0.519032 0.854755i \(-0.673708\pi\)
0.480723 + 0.876872i \(0.340374\pi\)
\(572\) −149.113 + 447.472i −0.0108999 + 0.0327093i
\(573\) 0 0
\(574\) 1088.74 + 1510.41i 0.0791694 + 0.109831i
\(575\) −21100.5 −1.53035
\(576\) 0 0
\(577\) −6971.52 −0.502995 −0.251497 0.967858i \(-0.580923\pi\)
−0.251497 + 0.967858i \(0.580923\pi\)
\(578\) −271.180 376.207i −0.0195149 0.0270729i
\(579\) 0 0
\(580\) 9297.10 27899.5i 0.665588 1.99735i
\(581\) −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 \(0.425610\pi\)
−0.958274 + 0.285851i \(0.907724\pi\)
\(588\) 0 0
\(589\) 11247.2 + 19480.7i 0.786811 + 1.36280i
\(590\) −995.659 9827.55i −0.0694756 0.685752i
\(591\) 0 0
\(592\) 6842.15 + 5129.71i 0.475018 + 0.356132i
\(593\) 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
\(596\) −1367.87 6681.40i −0.0940100 0.459196i
\(597\) 0 0
\(598\) 4625.28 468.601i 0.316290 0.0320443i
\(599\) −14467.5 25058.4i −0.986852 1.70928i −0.633400 0.773825i \(-0.718341\pi\)
−0.353452 0.935453i \(1.38501\pi\)
\(600\) 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 −0.939112 0.343610i \(-0.888350\pi\)
−0.171981 + 0.985100i \(0.555017\pi\)
\(608\) 12361.5 + 231.885i 0.824548 + 0.0154674i
\(609\) 0 0
\(610\) 61.5791 44.3878i 0.00408732 0.00294625i
\(611\) 2257.80 0.149494
\(612\) 0 0
\(613\) 6429.22 0.423612 0.211806 0.977312i \(-0.432066\pi\)
0.211806 + 0.977312i \(0.432066\pi\)
\(614\) −12668.4 + 9131.69i −0.832660 + 0.600204i
\(615\) 0 0
\(616\) −1444.57 + 1568.49i −0.0944858 + 0.102591i
\(617\) 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 −0.277686 0.960672i \(-0.589567\pi\)
−0.970809 + 0.239853i \(0.922901\pi\)
\(620\) 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
\(626\) −24669.3 + 2499.32i −1.57505 + 0.159573i
\(627\) 0 0
\(628\) 21075.2 4314.68i 1.33916 0.274163i
\(629\) 9520.65i 0.603519i
\(630\) 0 0
\(631\) 529.250i 0.0333901i −0.999861 0.0166950i \(-0.994686\pi\)
0.999861 0.0166950i \(-0.00531444\pi\)
\(632\) 1746.35 + 391.790i 0.109915 + 0.0246591i
\(633\) 0 0
\(634\) 1999.72 + 19738.0i 0.125266 + 1.23643i
\(635\) 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 −0.565423 0.824801i \(-0.691287\pi\)
0.431587 + 0.902071i \(0.357954\pi\)
\(644\) 19939.7 + 6644.59i 1.22008 + 0.406574i
\(645\) 0 0
\(646\) −8048.91 11166.2i −0.490217 0.680076i
\(647\) 5938.61 0.360851 0.180426 0.983589i \(-0.442252\pi\)
0.180426 + 0.983589i \(0.442252\pi\)
\(648\) 0 0
\(649\) −1018.81 −0.0616205
\(650\) 3096.77 + 4296.14i 0.186870 + 0.259244i
\(651\) 0 0
\(652\) 16594.8 + 5529.97i 0.996785 + 0.332163i
\(653\) 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 \(0.482946\pi\)
−0.891558 + 0.452907i \(0.850387\pi\)
\(660\) 0 0
\(661\) 5168.04 + 8951.31i 0.304105 + 0.526725i 0.977062 0.212957i \(-0.0683093\pi\)
−0.672957 + 0.739682i \(0.734976\pi\)
\(662\) −2819.02 27824.9i −0.165505 1.63360i
\(663\) 0 0
\(664\) 4583.45 20430.2i 0.267880 1.19404i
\(665\) 22063.4i 1.28659i
\(666\) 0 0
\(667\) 29896.3i 1.73551i
\(668\) −28068.1 + 5746.32i −1.62573 + 0.332832i
\(669\) 0 0
\(670\) −20195.6 + 2046.07i −1.16451 + 0.117980i
\(671\) −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
\(680\) −19845.8 18277.8i −1.11919 1.03077i
\(681\) 0 0
\(682\) 3689.06 2659.17i 0.207128 0.149303i
\(683\) −807.274 −0.0452262 −0.0226131 0.999744i \(-0.507199\pi\)
−0.0226131 + 0.999744i \(0.507199\pi\)
\(684\) 0 0
\(685\) −448.867 −0.0250370
\(686\) 13879.5 10004.7i 0.772483 0.556826i
\(687\) 0 0
\(688\) −16.2114 37.9332i −0.000898333 0.00210202i
\(689\) 2786.82 1608.97i 0.154092 0.0889651i
\(690\) 0 0
\(691\) 19006.4 + 10973.4i 1.04636 + 0.604119i 0.921629 0.388072i \(-0.126859\pi\)
0.124735 + 0.992190i \(0.460192\pi\)
\(692\) −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
\(698\) 25555.9 2589.14i 1.38582 0.140402i
\(699\) 0 0
\(700\) 4802.09 + 23456.0i 0.259289 + 1.26651i
\(701\) 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
\(704\) −205.258 2491.06i −0.0109886 0.133360i
\(705\) 0 0
\(706\) −1298.55 12817.2i −0.0692234 0.683263i
\(707\) 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
\(716\) 678.816 2037.05i 0.0354309 0.106324i
\(717\) 0 0
\(718\) 8956.10 + 12424.8i 0.465514 + 0.645805i
\(719\) −15469.9 −0.802408 −0.401204 0.915989i \(-0.631408\pi\)
−0.401204 + 0.915989i \(0.631408\pi\)
\(720\) 0 0
\(721\) −10390.0 −0.536677
\(722\) 3628.79 + 5034.20i 0.187049 + 0.259493i
\(723\) 0 0
\(724\) −2272.65 + 6819.96i −0.116661 + 0.350085i
\(725\) −29494.0 + 17028.4i −1.51087 + 0.872301i
\(726\) 0 0
\(727\) −6900.11 3983.78i −0.352009 0.203233i 0.313561 0.949568i \(-0.398478\pi\)
−0.665570 + 0.746336i \(0.731811\pi\)
\(728\) −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 \(-0.380160\pi\)
\(734\) 3038.04 + 29986.7i 0.152774 + 1.50794i
\(735\) 0 0
\(736\) −21563.0 + 11915.9i −1.07992 + 0.596773i
\(737\) 2093.65i 0.104641i
\(738\) 0 0
\(739\) 1182.09i 0.0588414i −0.999567 0.0294207i \(-0.990634\pi\)
0.999567 0.0294207i \(-0.00936624\pi\)
\(740\) −3587.76 17524.6i −0.178228 0.870563i
\(741\) 0 0
\(742\) 14474.0 1466.41i 0.716116 0.0725519i
\(743\) −13616.4 23584.4i −0.672327 1.16450i −0.977243 0.212125i \(-0.931962\pi\)
0.304916 0.952379i \(1.59863\pi\)
\(744\) 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 −0.767870 0.640606i \(-0.778683\pi\)
0.170846 + 0.985298i \(0.445350\pi\)
\(752\) −11002.2 + 4701.99i −0.533523 + 0.228010i
\(753\) 0 0
\(754\) 6087.01 4387.68i 0.294000 0.211923i
\(755\) 24580.1 1.18485
\(756\) 0 0
\(757\) 30482.1 1.46353 0.731764 0.681559i \(-0.238698\pi\)
0.731764 + 0.681559i \(0.238698\pi\)
\(758\) 14673.9 10577.4i 0.703141 0.506843i
\(759\) 0 0
\(760\) −19023.4 17520.4i −0.907965 0.836227i
\(761\) 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 \(0.848793\pi\)
\(770\) 4437.73 449.600i 0.207694 0.0210421i
\(771\) 0 0
\(772\) −19274.8 + 3946.07i −0.898594 + 0.183967i
\(773\) 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
\(776\) −7263.34 + 32375.4i −0.336003 + 1.49769i
\(777\) 0 0
\(778\) 1771.38 + 17484.2i 0.0816285 + 0.805706i
\(779\) 1164.57 + 2017.09i 0.0535622 + 0.0927724i
\(780\) 0 0