Properties

Label 930.4.d.c.559.15
Level $930$
Weight $4$
Character 930.559
Analytic conductor $54.872$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(54.8717763053\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 2763 x^{18} + 2652899 x^{16} + 1161420105 x^{14} + 247831438280 x^{12} + 26461073949176 x^{10} + 1433368340491408 x^{8} + 37536884921183444 x^{6} + 414170668954972900 x^{4} + 1987578737873500000 x^{2} + 3460065015625000000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.15
Root \(2.45273i\) of defining polynomial
Character \(\chi\) \(=\) 930.559
Dual form 930.4.d.c.559.5

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(1.65380 - 11.0573i) q^{5} +6.00000 q^{6} +2.45273i q^{7} -8.00000i q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+2.00000i q^{2} -3.00000i q^{3} -4.00000 q^{4} +(1.65380 - 11.0573i) q^{5} +6.00000 q^{6} +2.45273i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(22.1147 + 3.30759i) q^{10} -35.2532 q^{11} +12.0000i q^{12} +31.1443i q^{13} -4.90546 q^{14} +(-33.1720 - 4.96139i) q^{15} +16.0000 q^{16} +47.1144i q^{17} -18.0000i q^{18} +118.399 q^{19} +(-6.61519 + 44.2294i) q^{20} +7.35819 q^{21} -70.5064i q^{22} -57.1501i q^{23} -24.0000 q^{24} +(-119.530 - 36.5732i) q^{25} -62.2886 q^{26} +27.0000i q^{27} -9.81092i q^{28} -298.374 q^{29} +(9.92278 - 66.3441i) q^{30} -31.0000 q^{31} +32.0000i q^{32} +105.760i q^{33} -94.2289 q^{34} +(27.1207 + 4.05632i) q^{35} +36.0000 q^{36} -82.3944i q^{37} +236.798i q^{38} +93.4329 q^{39} +(-88.4588 - 13.2304i) q^{40} -25.0717 q^{41} +14.7164i q^{42} +264.775i q^{43} +141.013 q^{44} +(-14.8842 + 99.5161i) q^{45} +114.300 q^{46} +344.703i q^{47} -48.0000i q^{48} +336.984 q^{49} +(73.1465 - 239.060i) q^{50} +141.343 q^{51} -124.577i q^{52} +422.169i q^{53} -54.0000 q^{54} +(-58.3016 + 389.807i) q^{55} +19.6218 q^{56} -355.198i q^{57} -596.749i q^{58} -43.3724 q^{59} +(132.688 + 19.8456i) q^{60} +96.2068 q^{61} -62.0000i q^{62} -22.0746i q^{63} -64.0000 q^{64} +(344.373 + 51.5064i) q^{65} -211.519 q^{66} -706.568i q^{67} -188.458i q^{68} -171.450 q^{69} +(-8.11264 + 54.2414i) q^{70} +1110.36 q^{71} +72.0000i q^{72} -94.3706i q^{73} +164.789 q^{74} +(-109.720 + 358.590i) q^{75} -473.597 q^{76} -86.4666i q^{77} +186.866i q^{78} +607.265 q^{79} +(26.4608 - 176.918i) q^{80} +81.0000 q^{81} -50.1434i q^{82} +604.212i q^{83} -29.4328 q^{84} +(520.961 + 77.9177i) q^{85} -529.549 q^{86} +895.123i q^{87} +282.026i q^{88} +391.745 q^{89} +(-199.032 - 29.7684i) q^{90} -76.3886 q^{91} +228.600i q^{92} +93.0000i q^{93} -689.405 q^{94} +(195.808 - 1309.18i) q^{95} +96.0000 q^{96} +1048.85i q^{97} +673.968i q^{98} +317.279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 80q^{4} - 2q^{5} + 120q^{6} - 180q^{9} + O(q^{10}) \) \( 20q - 80q^{4} - 2q^{5} + 120q^{6} - 180q^{9} + 8q^{10} - 114q^{11} + 52q^{14} - 12q^{15} + 320q^{16} + 370q^{19} + 8q^{20} - 78q^{21} - 480q^{24} - 90q^{25} - 368q^{26} + 368q^{29} - 12q^{30} - 620q^{31} + 712q^{34} + 374q^{35} + 720q^{36} + 552q^{39} - 32q^{40} - 872q^{41} + 456q^{44} + 18q^{45} - 1236q^{46} + 1334q^{49} + 416q^{50} - 1068q^{51} - 1080q^{54} - 1290q^{55} - 208q^{56} + 3228q^{59} + 48q^{60} - 2604q^{61} - 1280q^{64} + 44q^{65} - 684q^{66} + 1854q^{69} - 852q^{70} - 2290q^{71} + 2008q^{74} - 624q^{75} - 1480q^{76} + 4342q^{79} - 32q^{80} + 1620q^{81} + 312q^{84} + 500q^{85} - 4q^{86} + 1390q^{89} - 72q^{90} - 5744q^{91} + 2608q^{94} - 1136q^{95} + 1920q^{96} + 1026q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 3.00000i 0.577350i
\(4\) −4.00000 −0.500000
\(5\) 1.65380 11.0573i 0.147920 0.988999i
\(6\) 6.00000 0.408248
\(7\) 2.45273i 0.132435i 0.997805 + 0.0662175i \(0.0210931\pi\)
−0.997805 + 0.0662175i \(0.978907\pi\)
\(8\) 8.00000i 0.353553i
\(9\) −9.00000 −0.333333
\(10\) 22.1147 + 3.30759i 0.699328 + 0.104595i
\(11\) −35.2532 −0.966295 −0.483147 0.875539i \(-0.660506\pi\)
−0.483147 + 0.875539i \(0.660506\pi\)
\(12\) 12.0000i 0.288675i
\(13\) 31.1443i 0.664452i 0.943200 + 0.332226i \(0.107800\pi\)
−0.943200 + 0.332226i \(0.892200\pi\)
\(14\) −4.90546 −0.0936457
\(15\) −33.1720 4.96139i −0.570999 0.0854017i
\(16\) 16.0000 0.250000
\(17\) 47.1144i 0.672172i 0.941831 + 0.336086i \(0.109103\pi\)
−0.941831 + 0.336086i \(0.890897\pi\)
\(18\) 18.0000i 0.235702i
\(19\) 118.399 1.42961 0.714806 0.699323i \(-0.246515\pi\)
0.714806 + 0.699323i \(0.246515\pi\)
\(20\) −6.61519 + 44.2294i −0.0739601 + 0.494500i
\(21\) 7.35819 0.0764614
\(22\) 70.5064i 0.683273i
\(23\) 57.1501i 0.518114i −0.965862 0.259057i \(-0.916588\pi\)
0.965862 0.259057i \(-0.0834117\pi\)
\(24\) −24.0000 −0.204124
\(25\) −119.530 36.5732i −0.956239 0.292586i
\(26\) −62.2886 −0.469839
\(27\) 27.0000i 0.192450i
\(28\) 9.81092i 0.0662175i
\(29\) −298.374 −1.91058 −0.955288 0.295676i \(-0.904455\pi\)
−0.955288 + 0.295676i \(0.904455\pi\)
\(30\) 9.92278 66.3441i 0.0603881 0.403757i
\(31\) −31.0000 −0.179605
\(32\) 32.0000i 0.176777i
\(33\) 105.760i 0.557890i
\(34\) −94.2289 −0.475298
\(35\) 27.1207 + 4.05632i 0.130978 + 0.0195898i
\(36\) 36.0000 0.166667
\(37\) 82.3944i 0.366096i −0.983104 0.183048i \(-0.941404\pi\)
0.983104 0.183048i \(-0.0585964\pi\)
\(38\) 236.798i 1.01089i
\(39\) 93.4329 0.383622
\(40\) −88.4588 13.2304i −0.349664 0.0522977i
\(41\) −25.0717 −0.0955009 −0.0477505 0.998859i \(-0.515205\pi\)
−0.0477505 + 0.998859i \(0.515205\pi\)
\(42\) 14.7164i 0.0540664i
\(43\) 264.775i 0.939018i 0.882928 + 0.469509i \(0.155569\pi\)
−0.882928 + 0.469509i \(0.844431\pi\)
\(44\) 141.013 0.483147
\(45\) −14.8842 + 99.5161i −0.0493067 + 0.329666i
\(46\) 114.300 0.366362
\(47\) 344.703i 1.06979i 0.844919 + 0.534894i \(0.179648\pi\)
−0.844919 + 0.534894i \(0.820352\pi\)
\(48\) 48.0000i 0.144338i
\(49\) 336.984 0.982461
\(50\) 73.1465 239.060i 0.206889 0.676163i
\(51\) 141.343 0.388079
\(52\) 124.577i 0.332226i
\(53\) 422.169i 1.09414i 0.837087 + 0.547069i \(0.184257\pi\)
−0.837087 + 0.547069i \(0.815743\pi\)
\(54\) −54.0000 −0.136083
\(55\) −58.3016 + 389.807i −0.142934 + 0.955665i
\(56\) 19.6218 0.0468228
\(57\) 355.198i 0.825387i
\(58\) 596.749i 1.35098i
\(59\) −43.3724 −0.0957051 −0.0478526 0.998854i \(-0.515238\pi\)
−0.0478526 + 0.998854i \(0.515238\pi\)
\(60\) 132.688 + 19.8456i 0.285500 + 0.0427009i
\(61\) 96.2068 0.201935 0.100967 0.994890i \(-0.467806\pi\)
0.100967 + 0.994890i \(0.467806\pi\)
\(62\) 62.0000i 0.127000i
\(63\) 22.0746i 0.0441450i
\(64\) −64.0000 −0.125000
\(65\) 344.373 + 51.5064i 0.657143 + 0.0982858i
\(66\) −211.519 −0.394488
\(67\) 706.568i 1.28837i −0.764868 0.644186i \(-0.777196\pi\)
0.764868 0.644186i \(-0.222804\pi\)
\(68\) 188.458i 0.336086i
\(69\) −171.450 −0.299133
\(70\) −8.11264 + 54.2414i −0.0138521 + 0.0926155i
\(71\) 1110.36 1.85600 0.928000 0.372580i \(-0.121527\pi\)
0.928000 + 0.372580i \(0.121527\pi\)
\(72\) 72.0000i 0.117851i
\(73\) 94.3706i 0.151305i −0.997134 0.0756524i \(-0.975896\pi\)
0.997134 0.0756524i \(-0.0241039\pi\)
\(74\) 164.789 0.258869
\(75\) −109.720 + 358.590i −0.168924 + 0.552085i
\(76\) −473.597 −0.714806
\(77\) 86.4666i 0.127971i
\(78\) 186.866i 0.271261i
\(79\) 607.265 0.864843 0.432422 0.901672i \(-0.357659\pi\)
0.432422 + 0.901672i \(0.357659\pi\)
\(80\) 26.4608 176.918i 0.0369800 0.247250i
\(81\) 81.0000 0.111111
\(82\) 50.1434i 0.0675294i
\(83\) 604.212i 0.799047i 0.916723 + 0.399523i \(0.130824\pi\)
−0.916723 + 0.399523i \(0.869176\pi\)
\(84\) −29.4328 −0.0382307
\(85\) 520.961 + 77.9177i 0.664778 + 0.0994278i
\(86\) −529.549 −0.663986
\(87\) 895.123i 1.10307i
\(88\) 282.026i 0.341637i
\(89\) 391.745 0.466572 0.233286 0.972408i \(-0.425052\pi\)
0.233286 + 0.972408i \(0.425052\pi\)
\(90\) −199.032 29.7684i −0.233109 0.0348651i
\(91\) −76.3886 −0.0879967
\(92\) 228.600i 0.259057i
\(93\) 93.0000i 0.103695i
\(94\) −689.405 −0.756454
\(95\) 195.808 1309.18i 0.211468 1.41389i
\(96\) 96.0000 0.102062
\(97\) 1048.85i 1.09788i 0.835861 + 0.548942i \(0.184969\pi\)
−0.835861 + 0.548942i \(0.815031\pi\)
\(98\) 673.968i 0.694705i
\(99\) 317.279 0.322098
\(100\) 478.120 + 146.293i 0.478120 + 0.146293i
\(101\) 1284.24 1.26521 0.632605 0.774474i \(-0.281986\pi\)
0.632605 + 0.774474i \(0.281986\pi\)
\(102\) 282.687i 0.274413i
\(103\) 1975.76i 1.89007i 0.326970 + 0.945035i \(0.393972\pi\)
−0.326970 + 0.945035i \(0.606028\pi\)
\(104\) 249.154 0.234919
\(105\) 12.1690 81.3621i 0.0113102 0.0756202i
\(106\) −844.338 −0.773673
\(107\) 1618.89i 1.46266i 0.682026 + 0.731328i \(0.261099\pi\)
−0.682026 + 0.731328i \(0.738901\pi\)
\(108\) 108.000i 0.0962250i
\(109\) 2039.14 1.79187 0.895936 0.444182i \(-0.146506\pi\)
0.895936 + 0.444182i \(0.146506\pi\)
\(110\) −779.614 116.603i −0.675757 0.101070i
\(111\) −247.183 −0.211366
\(112\) 39.2437i 0.0331087i
\(113\) 895.966i 0.745888i 0.927854 + 0.372944i \(0.121652\pi\)
−0.927854 + 0.372944i \(0.878348\pi\)
\(114\) 710.395 0.583637
\(115\) −631.928 94.5146i −0.512414 0.0766394i
\(116\) 1193.50 0.955288
\(117\) 280.299i 0.221484i
\(118\) 86.7447i 0.0676737i
\(119\) −115.559 −0.0890191
\(120\) −39.6911 + 265.376i −0.0301941 + 0.201879i
\(121\) −88.2119 −0.0662749
\(122\) 192.414i 0.142789i
\(123\) 75.2150i 0.0551375i
\(124\) 124.000 0.0898027
\(125\) −602.081 + 1261.20i −0.430814 + 0.902441i
\(126\) 44.1491 0.0312152
\(127\) 920.890i 0.643431i −0.946836 0.321716i \(-0.895740\pi\)
0.946836 0.321716i \(-0.104260\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 794.324 0.542142
\(130\) −103.013 + 688.747i −0.0694986 + 0.464670i
\(131\) −2612.31 −1.74228 −0.871141 0.491034i \(-0.836619\pi\)
−0.871141 + 0.491034i \(0.836619\pi\)
\(132\) 423.038i 0.278945i
\(133\) 290.401i 0.189331i
\(134\) 1413.14 0.911017
\(135\) 298.548 + 44.6525i 0.190333 + 0.0284672i
\(136\) 376.916 0.237649
\(137\) 2194.36i 1.36845i −0.729273 0.684223i \(-0.760141\pi\)
0.729273 0.684223i \(-0.239859\pi\)
\(138\) 342.900i 0.211519i
\(139\) 783.660 0.478196 0.239098 0.970995i \(-0.423148\pi\)
0.239098 + 0.970995i \(0.423148\pi\)
\(140\) −108.483 16.2253i −0.0654891 0.00979490i
\(141\) 1034.11 0.617642
\(142\) 2220.73i 1.31239i
\(143\) 1097.94i 0.642056i
\(144\) −144.000 −0.0833333
\(145\) −493.451 + 3299.23i −0.282613 + 1.88956i
\(146\) 188.741 0.106989
\(147\) 1010.95i 0.567224i
\(148\) 329.578i 0.183048i
\(149\) −256.065 −0.140790 −0.0703949 0.997519i \(-0.522426\pi\)
−0.0703949 + 0.997519i \(0.522426\pi\)
\(150\) −717.179 219.439i −0.390383 0.119448i
\(151\) −3553.83 −1.91528 −0.957638 0.287973i \(-0.907019\pi\)
−0.957638 + 0.287973i \(0.907019\pi\)
\(152\) 947.193i 0.505444i
\(153\) 424.030i 0.224057i
\(154\) 172.933 0.0904893
\(155\) −51.2677 + 342.778i −0.0265672 + 0.177630i
\(156\) −373.732 −0.191811
\(157\) 345.400i 0.175579i 0.996139 + 0.0877896i \(0.0279803\pi\)
−0.996139 + 0.0877896i \(0.972020\pi\)
\(158\) 1214.53i 0.611537i
\(159\) 1266.51 0.631701
\(160\) 353.835 + 52.9215i 0.174832 + 0.0261488i
\(161\) 140.174 0.0686164
\(162\) 162.000i 0.0785674i
\(163\) 1410.83i 0.677945i 0.940796 + 0.338972i \(0.110079\pi\)
−0.940796 + 0.338972i \(0.889921\pi\)
\(164\) 100.287 0.0477505
\(165\) 1169.42 + 174.905i 0.551753 + 0.0825232i
\(166\) −1208.42 −0.565011
\(167\) 1809.73i 0.838569i 0.907855 + 0.419285i \(0.137719\pi\)
−0.907855 + 0.419285i \(0.862281\pi\)
\(168\) 58.8655i 0.0270332i
\(169\) 1227.03 0.558503
\(170\) −155.835 + 1041.92i −0.0703061 + 0.470069i
\(171\) −1065.59 −0.476537
\(172\) 1059.10i 0.469509i
\(173\) 3916.63i 1.72125i 0.509243 + 0.860623i \(0.329925\pi\)
−0.509243 + 0.860623i \(0.670075\pi\)
\(174\) −1790.25 −0.779990
\(175\) 89.7043 293.175i 0.0387486 0.126640i
\(176\) −564.051 −0.241574
\(177\) 130.117i 0.0552554i
\(178\) 783.490i 0.329916i
\(179\) −265.024 −0.110664 −0.0553320 0.998468i \(-0.517622\pi\)
−0.0553320 + 0.998468i \(0.517622\pi\)
\(180\) 59.5367 398.065i 0.0246534 0.164833i
\(181\) 2535.64 1.04128 0.520642 0.853775i \(-0.325693\pi\)
0.520642 + 0.853775i \(0.325693\pi\)
\(182\) 152.777i 0.0622231i
\(183\) 288.620i 0.116587i
\(184\) −457.201 −0.183181
\(185\) −911.064 136.264i −0.362069 0.0541530i
\(186\) −186.000 −0.0733236
\(187\) 1660.93i 0.649516i
\(188\) 1378.81i 0.534894i
\(189\) −66.2237 −0.0254871
\(190\) 2618.36 + 391.617i 0.999768 + 0.149531i
\(191\) −634.288 −0.240290 −0.120145 0.992756i \(-0.538336\pi\)
−0.120145 + 0.992756i \(0.538336\pi\)
\(192\) 192.000i 0.0721688i
\(193\) 4931.48i 1.83925i 0.392796 + 0.919626i \(0.371508\pi\)
−0.392796 + 0.919626i \(0.628492\pi\)
\(194\) −2097.70 −0.776321
\(195\) 154.519 1033.12i 0.0567454 0.379401i
\(196\) −1347.94 −0.491230
\(197\) 4890.76i 1.76879i −0.466737 0.884396i \(-0.654570\pi\)
0.466737 0.884396i \(-0.345430\pi\)
\(198\) 634.558i 0.227758i
\(199\) 2738.39 0.975474 0.487737 0.872991i \(-0.337823\pi\)
0.487737 + 0.872991i \(0.337823\pi\)
\(200\) −292.586 + 956.239i −0.103445 + 0.338082i
\(201\) −2119.70 −0.743842
\(202\) 2568.47i 0.894639i
\(203\) 731.832i 0.253027i
\(204\) −565.373 −0.194039
\(205\) −41.4635 + 277.226i −0.0141265 + 0.0944504i
\(206\) −3951.51 −1.33648
\(207\) 514.351i 0.172705i
\(208\) 498.309i 0.166113i
\(209\) −4173.95 −1.38143
\(210\) 162.724 + 24.3379i 0.0534716 + 0.00799750i
\(211\) 5556.03 1.81276 0.906381 0.422460i \(-0.138833\pi\)
0.906381 + 0.422460i \(0.138833\pi\)
\(212\) 1688.68i 0.547069i
\(213\) 3331.09i 1.07156i
\(214\) −3237.78 −1.03425
\(215\) 2927.71 + 437.884i 0.928688 + 0.138900i
\(216\) 216.000 0.0680414
\(217\) 76.0346i 0.0237860i
\(218\) 4078.28i 1.26705i
\(219\) −283.112 −0.0873559
\(220\) 233.207 1559.23i 0.0714672 0.477832i
\(221\) −1467.35 −0.446626
\(222\) 494.366i 0.149458i
\(223\) 6505.89i 1.95366i −0.214014 0.976831i \(-0.568654\pi\)
0.214014 0.976831i \(-0.431346\pi\)
\(224\) −78.4874 −0.0234114
\(225\) 1075.77 + 329.159i 0.318746 + 0.0975286i
\(226\) −1791.93 −0.527423
\(227\) 1721.52i 0.503354i 0.967811 + 0.251677i \(0.0809821\pi\)
−0.967811 + 0.251677i \(0.919018\pi\)
\(228\) 1420.79i 0.412694i
\(229\) −2074.96 −0.598764 −0.299382 0.954133i \(-0.596781\pi\)
−0.299382 + 0.954133i \(0.596781\pi\)
\(230\) 189.029 1263.86i 0.0541923 0.362331i
\(231\) −259.400 −0.0738842
\(232\) 2386.99i 0.675491i
\(233\) 4235.01i 1.19075i 0.803448 + 0.595375i \(0.202997\pi\)
−0.803448 + 0.595375i \(0.797003\pi\)
\(234\) 560.598 0.156613
\(235\) 3811.50 + 570.068i 1.05802 + 0.158243i
\(236\) 173.489 0.0478526
\(237\) 1821.79i 0.499318i
\(238\) 231.118i 0.0629460i
\(239\) −6106.61 −1.65274 −0.826368 0.563131i \(-0.809597\pi\)
−0.826368 + 0.563131i \(0.809597\pi\)
\(240\) −530.753 79.3823i −0.142750 0.0213504i
\(241\) −3008.74 −0.804190 −0.402095 0.915598i \(-0.631718\pi\)
−0.402095 + 0.915598i \(0.631718\pi\)
\(242\) 176.424i 0.0468635i
\(243\) 243.000i 0.0641500i
\(244\) −384.827 −0.100967
\(245\) 557.303 3726.15i 0.145326 0.971653i
\(246\) −150.430 −0.0389881
\(247\) 3687.46i 0.949909i
\(248\) 248.000i 0.0635001i
\(249\) 1812.64 0.461330
\(250\) −2522.40 1204.16i −0.638122 0.304632i
\(251\) −4410.77 −1.10918 −0.554592 0.832122i \(-0.687126\pi\)
−0.554592 + 0.832122i \(0.687126\pi\)
\(252\) 88.2983i 0.0220725i
\(253\) 2014.72i 0.500650i
\(254\) 1841.78 0.454975
\(255\) 233.753 1562.88i 0.0574047 0.383810i
\(256\) 256.000 0.0625000
\(257\) 4828.05i 1.17185i −0.810365 0.585925i \(-0.800731\pi\)
0.810365 0.585925i \(-0.199269\pi\)
\(258\) 1588.65i 0.383352i
\(259\) 202.091 0.0484839
\(260\) −1377.49 206.026i −0.328571 0.0491429i
\(261\) 2685.37 0.636859
\(262\) 5224.63i 1.23198i
\(263\) 4853.47i 1.13794i −0.822359 0.568970i \(-0.807342\pi\)
0.822359 0.568970i \(-0.192658\pi\)
\(264\) 846.077 0.197244
\(265\) 4668.07 + 698.182i 1.08210 + 0.161845i
\(266\) −580.803 −0.133877
\(267\) 1175.23i 0.269375i
\(268\) 2826.27i 0.644186i
\(269\) 1124.63 0.254906 0.127453 0.991845i \(-0.459320\pi\)
0.127453 + 0.991845i \(0.459320\pi\)
\(270\) −89.3051 + 597.097i −0.0201294 + 0.134586i
\(271\) −2424.69 −0.543503 −0.271751 0.962367i \(-0.587603\pi\)
−0.271751 + 0.962367i \(0.587603\pi\)
\(272\) 753.831i 0.168043i
\(273\) 229.166i 0.0508049i
\(274\) 4388.73 0.967638
\(275\) 4213.81 + 1289.32i 0.924009 + 0.282724i
\(276\) 685.801 0.149567
\(277\) 5668.85i 1.22963i 0.788671 + 0.614816i \(0.210770\pi\)
−0.788671 + 0.614816i \(0.789230\pi\)
\(278\) 1567.32i 0.338135i
\(279\) 279.000 0.0598684
\(280\) 32.4506 216.966i 0.00692604 0.0463078i
\(281\) −3211.25 −0.681733 −0.340866 0.940112i \(-0.610720\pi\)
−0.340866 + 0.940112i \(0.610720\pi\)
\(282\) 2068.22i 0.436739i
\(283\) 1030.37i 0.216428i −0.994128 0.108214i \(-0.965487\pi\)
0.994128 0.108214i \(-0.0345132\pi\)
\(284\) −4441.46 −0.928000
\(285\) −3927.54 587.425i −0.816307 0.122091i
\(286\) 2195.87 0.454002
\(287\) 61.4941i 0.0126477i
\(288\) 288.000i 0.0589256i
\(289\) 2693.23 0.548184
\(290\) −6598.46 986.901i −1.33612 0.199837i
\(291\) 3146.55 0.633864
\(292\) 377.483i 0.0756524i
\(293\) 899.072i 0.179264i 0.995975 + 0.0896320i \(0.0285691\pi\)
−0.995975 + 0.0896320i \(0.971431\pi\)
\(294\) 2021.90 0.401088
\(295\) −71.7291 + 479.583i −0.0141567 + 0.0946523i
\(296\) −659.155 −0.129435
\(297\) 951.836i 0.185963i
\(298\) 512.130i 0.0995534i
\(299\) 1779.90 0.344262
\(300\) 438.879 1434.36i 0.0844622 0.276042i
\(301\) −649.421 −0.124359
\(302\) 7107.67i 1.35431i
\(303\) 3852.71i 0.730470i
\(304\) 1894.39 0.357403
\(305\) 159.107 1063.79i 0.0298702 0.199713i
\(306\) 848.060 0.158433
\(307\) 7269.78i 1.35149i 0.737135 + 0.675746i \(0.236178\pi\)
−0.737135 + 0.675746i \(0.763822\pi\)
\(308\) 345.866i 0.0639856i
\(309\) 5927.27 1.09123
\(310\) −685.556 102.535i −0.125603 0.0187859i
\(311\) −3473.70 −0.633362 −0.316681 0.948532i \(-0.602568\pi\)
−0.316681 + 0.948532i \(0.602568\pi\)
\(312\) 747.463i 0.135631i
\(313\) 3467.92i 0.626257i 0.949711 + 0.313128i \(0.101377\pi\)
−0.949711 + 0.313128i \(0.898623\pi\)
\(314\) −690.800 −0.124153
\(315\) −244.086 36.5069i −0.0436594 0.00652993i
\(316\) −2429.06 −0.432422
\(317\) 1696.27i 0.300542i 0.988645 + 0.150271i \(0.0480147\pi\)
−0.988645 + 0.150271i \(0.951985\pi\)
\(318\) 2533.01i 0.446680i
\(319\) 10518.7 1.84618
\(320\) −105.843 + 707.670i −0.0184900 + 0.123625i
\(321\) 4856.67 0.844465
\(322\) 280.347i 0.0485191i
\(323\) 5578.31i 0.960946i
\(324\) −324.000 −0.0555556
\(325\) 1139.05 3722.68i 0.194409 0.635375i
\(326\) −2821.67 −0.479379
\(327\) 6117.42i 1.03454i
\(328\) 200.573i 0.0337647i
\(329\) −845.462 −0.141677
\(330\) −349.810 + 2338.84i −0.0583527 + 0.390148i
\(331\) 5986.62 0.994122 0.497061 0.867715i \(-0.334412\pi\)
0.497061 + 0.867715i \(0.334412\pi\)
\(332\) 2416.85i 0.399523i
\(333\) 741.550i 0.122032i
\(334\) −3619.46 −0.592958
\(335\) −7812.77 1168.52i −1.27420 0.190576i
\(336\) 117.731 0.0191153
\(337\) 2762.05i 0.446464i −0.974765 0.223232i \(-0.928339\pi\)
0.974765 0.223232i \(-0.0716608\pi\)
\(338\) 2454.06i 0.394922i
\(339\) 2687.90 0.430639
\(340\) −2083.84 311.671i −0.332389 0.0497139i
\(341\) 1092.85 0.173552
\(342\) 2131.19i 0.336963i
\(343\) 1667.82i 0.262547i
\(344\) 2118.20 0.331993
\(345\) −283.544 + 1895.78i −0.0442478 + 0.295842i
\(346\) −7833.25 −1.21710
\(347\) 348.734i 0.0539511i −0.999636 0.0269756i \(-0.991412\pi\)
0.999636 0.0269756i \(-0.00858763\pi\)
\(348\) 3580.49i 0.551536i
\(349\) −3247.11 −0.498034 −0.249017 0.968499i \(-0.580108\pi\)
−0.249017 + 0.968499i \(0.580108\pi\)
\(350\) 586.349 + 179.409i 0.0895477 + 0.0273994i
\(351\) −840.896 −0.127874
\(352\) 1128.10i 0.170818i
\(353\) 8034.97i 1.21150i −0.795656 0.605749i \(-0.792874\pi\)
0.795656 0.605749i \(-0.207126\pi\)
\(354\) −260.234 −0.0390714
\(355\) 1836.32 12277.7i 0.274540 1.83558i
\(356\) −1566.98 −0.233286
\(357\) 346.677i 0.0513952i
\(358\) 530.049i 0.0782512i
\(359\) −5821.40 −0.855826 −0.427913 0.903820i \(-0.640751\pi\)
−0.427913 + 0.903820i \(0.640751\pi\)
\(360\) 796.129 + 119.073i 0.116555 + 0.0174326i
\(361\) 7159.37 1.04379
\(362\) 5071.27i 0.736299i
\(363\) 264.636i 0.0382639i
\(364\) 305.554 0.0439984
\(365\) −1043.49 156.070i −0.149640 0.0223810i
\(366\) 577.241 0.0824395
\(367\) 5139.43i 0.730997i 0.930812 + 0.365499i \(0.119102\pi\)
−0.930812 + 0.365499i \(0.880898\pi\)
\(368\) 914.401i 0.129528i
\(369\) 225.645 0.0318336
\(370\) 272.527 1822.13i 0.0382919 0.256021i
\(371\) −1035.47 −0.144902
\(372\) 372.000i 0.0518476i
\(373\) 895.837i 0.124356i 0.998065 + 0.0621779i \(0.0198046\pi\)
−0.998065 + 0.0621779i \(0.980195\pi\)
\(374\) 3321.87 0.459277
\(375\) 3783.60 + 1806.24i 0.521024 + 0.248731i
\(376\) 2757.62 0.378227
\(377\) 9292.66i 1.26949i
\(378\) 132.447i 0.0180221i
\(379\) −14266.0 −1.93350 −0.966748 0.255732i \(-0.917684\pi\)
−0.966748 + 0.255732i \(0.917684\pi\)
\(380\) −783.233 + 5236.72i −0.105734 + 0.706943i
\(381\) −2762.67 −0.371485
\(382\) 1268.58i 0.169911i
\(383\) 7255.84i 0.968032i 0.875059 + 0.484016i \(0.160822\pi\)
−0.875059 + 0.484016i \(0.839178\pi\)
\(384\) −384.000 −0.0510310
\(385\) −956.091 142.998i −0.126563 0.0189295i
\(386\) −9862.96 −1.30055
\(387\) 2382.97i 0.313006i
\(388\) 4195.41i 0.548942i
\(389\) 4258.04 0.554990 0.277495 0.960727i \(-0.410496\pi\)
0.277495 + 0.960727i \(0.410496\pi\)
\(390\) 2066.24 + 309.038i 0.268277 + 0.0401250i
\(391\) 2692.59 0.348262
\(392\) 2695.87i 0.347352i
\(393\) 7836.94i 1.00591i
\(394\) 9781.52 1.25073
\(395\) 1004.29 6714.74i 0.127928 0.855329i
\(396\) −1269.12 −0.161049
\(397\) 2197.33i 0.277786i −0.990307 0.138893i \(-0.955646\pi\)
0.990307 0.138893i \(-0.0443544\pi\)
\(398\) 5476.78i 0.689764i
\(399\) 871.204 0.109310
\(400\) −1912.48 585.172i −0.239060 0.0731465i
\(401\) −1315.27 −0.163794 −0.0818970 0.996641i \(-0.526098\pi\)
−0.0818970 + 0.996641i \(0.526098\pi\)
\(402\) 4239.41i 0.525976i
\(403\) 965.474i 0.119339i
\(404\) −5136.95 −0.632605
\(405\) 133.958 895.645i 0.0164356 0.109889i
\(406\) 1463.66 0.178917
\(407\) 2904.67i 0.353757i
\(408\) 1130.75i 0.137207i
\(409\) 4484.14 0.542118 0.271059 0.962563i \(-0.412626\pi\)
0.271059 + 0.962563i \(0.412626\pi\)
\(410\) −554.453 82.9270i −0.0667865 0.00998895i
\(411\) −6583.09 −0.790073
\(412\) 7903.03i 0.945035i
\(413\) 106.381i 0.0126747i
\(414\) −1028.70 −0.122121
\(415\) 6680.98 + 999.244i 0.790256 + 0.118195i
\(416\) −996.618 −0.117460
\(417\) 2350.98i 0.276086i
\(418\) 8347.90i 0.976816i
\(419\) 3807.12 0.443891 0.221945 0.975059i \(-0.428759\pi\)
0.221945 + 0.975059i \(0.428759\pi\)
\(420\) −48.6758 + 325.448i −0.00565509 + 0.0378101i
\(421\) 3033.45 0.351167 0.175584 0.984465i \(-0.443819\pi\)
0.175584 + 0.984465i \(0.443819\pi\)
\(422\) 11112.1i 1.28182i
\(423\) 3102.32i 0.356596i
\(424\) 3377.35 0.386837
\(425\) 1723.13 5631.58i 0.196668 0.642758i
\(426\) 6662.19 0.757709
\(427\) 235.969i 0.0267432i
\(428\) 6475.57i 0.731328i
\(429\) −3293.81 −0.370691
\(430\) −875.767 + 5855.41i −0.0982169 + 0.656681i
\(431\) 5569.05 0.622393 0.311197 0.950346i \(-0.399270\pi\)
0.311197 + 0.950346i \(0.399270\pi\)
\(432\) 432.000i 0.0481125i
\(433\) 11093.0i 1.23116i −0.788073 0.615582i \(-0.788921\pi\)
0.788073 0.615582i \(-0.211079\pi\)
\(434\) 152.069 0.0168193
\(435\) 9897.69 + 1480.35i 1.09094 + 0.163167i
\(436\) −8156.56 −0.895936
\(437\) 6766.52i 0.740702i
\(438\) 566.224i 0.0617699i
\(439\) −2915.40 −0.316958 −0.158479 0.987362i \(-0.550659\pi\)
−0.158479 + 0.987362i \(0.550659\pi\)
\(440\) 3118.46 + 466.413i 0.337878 + 0.0505349i
\(441\) −3032.86 −0.327487
\(442\) 2934.69i 0.315812i
\(443\) 1390.52i 0.149132i −0.997216 0.0745661i \(-0.976243\pi\)
0.997216 0.0745661i \(-0.0237572\pi\)
\(444\) 988.733 0.105683
\(445\) 647.867 4331.66i 0.0690153 0.461439i
\(446\) 13011.8 1.38145
\(447\) 768.195i 0.0812850i
\(448\) 156.975i 0.0165544i
\(449\) 11386.2 1.19677 0.598383 0.801210i \(-0.295810\pi\)
0.598383 + 0.801210i \(0.295810\pi\)
\(450\) −658.318 + 2151.54i −0.0689631 + 0.225388i
\(451\) 883.857 0.0922820
\(452\) 3583.86i 0.372944i
\(453\) 10661.5i 1.10579i
\(454\) −3443.04 −0.355925
\(455\) −126.331 + 844.655i −0.0130165 + 0.0870287i
\(456\) −2841.58 −0.291818
\(457\) 18212.5i 1.86421i −0.362191 0.932104i \(-0.617971\pi\)
0.362191 0.932104i \(-0.382029\pi\)
\(458\) 4149.92i 0.423390i
\(459\) −1272.09 −0.129360
\(460\) 2527.71 + 378.059i 0.256207 + 0.0383197i
\(461\) 8974.30 0.906670 0.453335 0.891340i \(-0.350234\pi\)
0.453335 + 0.891340i \(0.350234\pi\)
\(462\) 518.800i 0.0522440i
\(463\) 10970.1i 1.10113i 0.834792 + 0.550566i \(0.185588\pi\)
−0.834792 + 0.550566i \(0.814412\pi\)
\(464\) −4773.99 −0.477644
\(465\) 1028.33 + 153.803i 0.102554 + 0.0153386i
\(466\) −8470.02 −0.841988
\(467\) 4721.07i 0.467805i 0.972260 + 0.233903i \(0.0751497\pi\)
−0.972260 + 0.233903i \(0.924850\pi\)
\(468\) 1121.20i 0.110742i
\(469\) 1733.02 0.170626
\(470\) −1140.14 + 7622.99i −0.111895 + 0.748133i
\(471\) 1036.20 0.101371
\(472\) 346.979i 0.0338369i
\(473\) 9334.15i 0.907368i
\(474\) 3643.59 0.353071
\(475\) −14152.2 4330.24i −1.36705 0.418284i
\(476\) 462.236 0.0445096
\(477\) 3799.52i 0.364713i
\(478\) 12213.2i 1.16866i
\(479\) −18909.3 −1.80373 −0.901865 0.432018i \(-0.857802\pi\)
−0.901865 + 0.432018i \(0.857802\pi\)
\(480\) 158.765 1061.51i 0.0150970 0.100939i
\(481\) 2566.12 0.243253
\(482\) 6017.47i 0.568648i
\(483\) 420.521i 0.0396157i
\(484\) 352.848 0.0331375
\(485\) 11597.5 + 1734.59i 1.08581 + 0.162399i
\(486\) 486.000 0.0453609
\(487\) 5928.26i 0.551612i 0.961213 + 0.275806i \(0.0889448\pi\)
−0.961213 + 0.275806i \(0.911055\pi\)
\(488\) 769.654i 0.0713947i
\(489\) 4232.50 0.391412
\(490\) 7452.30 + 1114.61i 0.687063 + 0.102761i
\(491\) −16523.9 −1.51876 −0.759382 0.650645i \(-0.774498\pi\)
−0.759382 + 0.650645i \(0.774498\pi\)
\(492\) 300.860i 0.0275687i
\(493\) 14057.7i 1.28424i
\(494\) −7374.92 −0.671687
\(495\) 524.715 3508.26i 0.0476448 0.318555i
\(496\) −496.000 −0.0449013
\(497\) 2723.42i 0.245799i
\(498\) 3625.27i 0.326209i
\(499\) 874.688 0.0784698 0.0392349 0.999230i \(-0.487508\pi\)
0.0392349 + 0.999230i \(0.487508\pi\)
\(500\) 2408.32 5044.80i 0.215407 0.451220i
\(501\) 5429.19 0.484148
\(502\) 8821.54i 0.784312i
\(503\) 15289.9i 1.35536i −0.735359 0.677678i \(-0.762986\pi\)
0.735359 0.677678i \(-0.237014\pi\)
\(504\) −176.597 −0.0156076
\(505\) 2123.87 14200.2i 0.187150 1.25129i
\(506\) −4029.45 −0.354013
\(507\) 3681.10i 0.322452i
\(508\) 3683.56i 0.321716i
\(509\) −17458.2 −1.52027 −0.760137 0.649763i \(-0.774868\pi\)
−0.760137 + 0.649763i \(0.774868\pi\)
\(510\) 3125.76 + 467.506i 0.271394 + 0.0405912i
\(511\) 231.466 0.0200380
\(512\) 512.000i 0.0441942i
\(513\) 3196.78i 0.275129i
\(514\) 9656.10 0.828623
\(515\) 21846.6 + 3267.50i 1.86928 + 0.279579i
\(516\) −3177.30 −0.271071
\(517\) 12151.9i 1.03373i
\(518\) 404.182i 0.0342833i
\(519\) 11749.9 0.993762
\(520\) 412.051 2754.99i 0.0347493 0.232335i
\(521\) −7380.17 −0.620597 −0.310298 0.950639i \(-0.600429\pi\)
−0.310298 + 0.950639i \(0.600429\pi\)
\(522\) 5370.74i 0.450327i
\(523\) 7990.31i 0.668053i 0.942564 + 0.334027i \(0.108408\pi\)
−0.942564 + 0.334027i \(0.891592\pi\)
\(524\) 10449.3 0.871141
\(525\) −879.524 269.113i −0.0731154 0.0223715i
\(526\) 9706.95 0.804645
\(527\) 1460.55i 0.120726i
\(528\) 1692.15i 0.139473i
\(529\) 8900.87 0.731558
\(530\) −1396.36 + 9336.14i −0.114442 + 0.765162i
\(531\) 390.351 0.0319017
\(532\) 1161.61i 0.0946654i
\(533\) 780.840i 0.0634558i
\(534\) 2350.47 0.190477
\(535\) 17900.6 + 2677.32i 1.44657 + 0.216356i
\(536\) −5652.54 −0.455509
\(537\) 795.073i 0.0638919i
\(538\) 2249.25i 0.180246i
\(539\) −11879.8 −0.949347
\(540\) −1194.19 178.610i −0.0951665 0.0142336i
\(541\) 5396.99 0.428900 0.214450 0.976735i \(-0.431204\pi\)
0.214450 + 0.976735i \(0.431204\pi\)
\(542\) 4849.37i 0.384315i
\(543\) 7606.91i 0.601185i
\(544\) −1507.66 −0.118824
\(545\) 3372.32 22547.5i 0.265054 1.77216i
\(546\) −458.332 −0.0359245
\(547\) 9629.59i 0.752708i −0.926476 0.376354i \(-0.877178\pi\)
0.926476 0.376354i \(-0.122822\pi\)
\(548\) 8777.45i 0.684223i
\(549\) −865.861 −0.0673116
\(550\) −2578.65 + 8427.62i −0.199916 + 0.653373i
\(551\) −35327.3 −2.73138
\(552\) 1371.60i 0.105760i
\(553\) 1489.46i 0.114536i
\(554\) −11337.7 −0.869481
\(555\) −408.791 + 2733.19i −0.0312652 + 0.209041i
\(556\) −3134.64 −0.239098
\(557\) 22557.4i 1.71596i 0.513684 + 0.857980i \(0.328281\pi\)
−0.513684 + 0.857980i \(0.671719\pi\)
\(558\) 558.000i 0.0423334i
\(559\) −8246.22 −0.623932
\(560\) 433.931 + 64.9011i 0.0327445 + 0.00489745i
\(561\) −4982.80 −0.374998
\(562\) 6422.49i 0.482058i
\(563\) 19572.7i 1.46517i 0.680677 + 0.732584i \(0.261686\pi\)
−0.680677 + 0.732584i \(0.738314\pi\)
\(564\) −4136.43 −0.308821
\(565\) 9907.00 + 1481.75i 0.737683 + 0.110332i
\(566\) 2060.74 0.153038
\(567\) 198.671i 0.0147150i
\(568\) 8882.92i 0.656195i
\(569\) 20027.6 1.47557 0.737784 0.675036i \(-0.235872\pi\)
0.737784 + 0.675036i \(0.235872\pi\)
\(570\) 1174.85 7855.09i 0.0863316 0.577216i
\(571\) 2789.72 0.204459 0.102230 0.994761i \(-0.467402\pi\)
0.102230 + 0.994761i \(0.467402\pi\)
\(572\) 4391.75i 0.321028i
\(573\) 1902.86i 0.138732i
\(574\) 122.988 0.00894325
\(575\) −2090.16 + 6831.14i −0.151593 + 0.495441i
\(576\) 576.000 0.0416667
\(577\) 24541.5i 1.77067i 0.464955 + 0.885335i \(0.346071\pi\)
−0.464955 + 0.885335i \(0.653929\pi\)
\(578\) 5386.46i 0.387625i
\(579\) 14794.4 1.06189
\(580\) 1973.80 13196.9i 0.141306 0.944780i
\(581\) −1481.97 −0.105822
\(582\) 6293.11i 0.448209i
\(583\) 14882.8i 1.05726i
\(584\) −754.965 −0.0534943
\(585\) −3099.36 463.557i −0.219048 0.0327619i
\(586\) −1798.14 −0.126759
\(587\) 10482.0i 0.737030i −0.929622 0.368515i \(-0.879866\pi\)
0.929622 0.368515i \(-0.120134\pi\)
\(588\) 4043.81i 0.283612i
\(589\) −3670.37 −0.256766
\(590\) −959.167 143.458i −0.0669293 0.0100103i
\(591\) −14672.3 −1.02121
\(592\) 1318.31i 0.0915240i
\(593\) 15003.7i 1.03900i 0.854469 + 0.519502i \(0.173882\pi\)
−0.854469 + 0.519502i \(0.826118\pi\)
\(594\) 1903.67 0.131496
\(595\) −191.111 + 1277.78i −0.0131677 + 0.0880399i
\(596\) 1024.26 0.0703949
\(597\) 8215.17i 0.563190i
\(598\) 3559.80i 0.243430i
\(599\) 11891.8 0.811164 0.405582 0.914059i \(-0.367069\pi\)
0.405582 + 0.914059i \(0.367069\pi\)
\(600\) 2868.72 + 877.757i 0.195192 + 0.0597238i
\(601\) −20918.4 −1.41976 −0.709882 0.704321i \(-0.751252\pi\)
−0.709882 + 0.704321i \(0.751252\pi\)
\(602\) 1298.84i 0.0879349i
\(603\) 6359.11i 0.429458i
\(604\) 14215.3 0.957638
\(605\) −145.885 + 975.390i −0.00980340 + 0.0655459i
\(606\) 7705.42 0.516520
\(607\) 5661.21i 0.378553i 0.981924 + 0.189276i \(0.0606142\pi\)
−0.981924 + 0.189276i \(0.939386\pi\)
\(608\) 3788.77i 0.252722i
\(609\) −2195.50 −0.146085
\(610\) 2127.58 + 318.213i 0.141219 + 0.0211214i
\(611\) −10735.5 −0.710823
\(612\) 1696.12i 0.112029i
\(613\) 7829.80i 0.515893i 0.966159 + 0.257947i \(0.0830459\pi\)
−0.966159 + 0.257947i \(0.916954\pi\)
\(614\) −14539.6 −0.955649
\(615\) 831.679 + 124.390i 0.0545309 + 0.00815595i
\(616\) −691.733 −0.0452447
\(617\) 11841.8i 0.772662i −0.922360 0.386331i \(-0.873742\pi\)
0.922360 0.386331i \(-0.126258\pi\)
\(618\) 11854.5i 0.771618i
\(619\) 21332.4 1.38517 0.692585 0.721337i \(-0.256472\pi\)
0.692585 + 0.721337i \(0.256472\pi\)
\(620\) 205.071 1371.11i 0.0132836 0.0888148i
\(621\) 1543.05 0.0997110
\(622\) 6947.40i 0.447854i
\(623\) 960.844i 0.0617904i
\(624\) 1494.93 0.0959054
\(625\) 12949.8 + 8743.19i 0.828787 + 0.559564i
\(626\) −6935.84 −0.442830
\(627\) 12521.9i 0.797567i
\(628\) 1381.60i 0.0877896i
\(629\) 3881.97 0.246080
\(630\) 73.0137 488.172i 0.00461736 0.0308718i
\(631\) −19975.5 −1.26024 −0.630121 0.776497i \(-0.716995\pi\)
−0.630121 + 0.776497i \(0.716995\pi\)
\(632\) 4858.12i 0.305768i
\(633\) 16668.1i 1.04660i
\(634\) −3392.54 −0.212516
\(635\) −10182.6 1522.97i −0.636353 0.0951765i
\(636\) −5066.03 −0.315851
\(637\) 10495.1i 0.652798i
\(638\) 21037.3i 1.30545i
\(639\) −9993.28 −0.618667
\(640\) −1415.34 211.686i −0.0874160 0.0130744i
\(641\) −642.218 −0.0395727 −0.0197863 0.999804i \(-0.506299\pi\)
−0.0197863 + 0.999804i \(0.506299\pi\)
\(642\) 9713.35i 0.597127i
\(643\) 14350.3i 0.880125i 0.897967 + 0.440063i \(0.145044\pi\)
−0.897967 + 0.440063i \(0.854956\pi\)
\(644\) −560.695 −0.0343082
\(645\) 1313.65 8783.12i 0.0801937 0.536178i
\(646\) −11156.6 −0.679491
\(647\) 9666.18i 0.587352i −0.955905 0.293676i \(-0.905121\pi\)
0.955905 0.293676i \(-0.0948787\pi\)
\(648\) 648.000i 0.0392837i
\(649\) 1529.01 0.0924793
\(650\) 7445.35 + 2278.10i 0.449278 + 0.137468i
\(651\) −228.104 −0.0137329
\(652\) 5643.33i 0.338972i
\(653\) 3146.94i 0.188590i −0.995544 0.0942950i \(-0.969940\pi\)
0.995544 0.0942950i \(-0.0300597\pi\)
\(654\) 12234.8 0.731529
\(655\) −4320.24 + 28885.3i −0.257718 + 1.72312i
\(656\) −401.147 −0.0238752
\(657\) 849.336i 0.0504349i
\(658\) 1690.92i 0.100181i
\(659\) −33398.3 −1.97422 −0.987111 0.160040i \(-0.948838\pi\)
−0.987111 + 0.160040i \(0.948838\pi\)
\(660\) −4677.68 699.620i −0.275877 0.0412616i
\(661\) −28820.2 −1.69588 −0.847939 0.530094i \(-0.822157\pi\)
−0.847939 + 0.530094i \(0.822157\pi\)
\(662\) 11973.2i 0.702951i
\(663\) 4402.04i 0.257860i
\(664\) 4833.69 0.282506
\(665\) 3211.07 + 480.265i 0.187248 + 0.0280058i
\(666\) −1483.10 −0.0862897
\(667\) 17052.1i 0.989896i
\(668\) 7238.92i 0.419285i
\(669\) −19517.7 −1.12795
\(670\) 2337.04 15625.5i 0.134758 0.900995i
\(671\) −3391.60 −0.195128
\(672\) 235.462i 0.0135166i
\(673\) 7808.13i 0.447223i −0.974678 0.223612i \(-0.928215\pi\)
0.974678 0.223612i \(-0.0717847\pi\)
\(674\) 5524.10 0.315698
\(675\) 987.477 3227.31i 0.0563082 0.184028i
\(676\) −4908.13 −0.279252
\(677\) 21793.5i 1.23721i 0.785702 + 0.618606i \(0.212302\pi\)
−0.785702 + 0.618606i \(0.787698\pi\)
\(678\) 5375.79i 0.304508i
\(679\) −2572.55 −0.145398
\(680\) 623.342 4167.69i 0.0351530 0.235035i
\(681\) 5164.57 0.290612
\(682\) 2185.70i 0.122720i
\(683\) 4067.07i 0.227851i 0.993489 + 0.113925i \(0.0363425\pi\)
−0.993489 + 0.113925i \(0.963658\pi\)
\(684\) 4262.37 0.238269
\(685\) −24263.8 3629.03i −1.35339 0.202421i
\(686\) −3335.64 −0.185649
\(687\) 6224.87i 0.345697i
\(688\) 4236.39i 0.234754i
\(689\) −13148.2 −0.727003
\(690\) −3791.57 567.088i −0.209192 0.0312879i
\(691\) −12621.9 −0.694878 −0.347439 0.937703i \(-0.612949\pi\)
−0.347439 + 0.937703i \(0.612949\pi\)
\(692\) 15666.5i 0.860623i
\(693\) 778.199i 0.0426571i
\(694\) 697.469 0.0381492
\(695\) 1296.02 8665.20i 0.0707348 0.472935i
\(696\) 7160.98 0.389995
\(697\) 1181.24i 0.0641931i
\(698\) 6494.23i 0.352164i
\(699\) 12705.0 0.687480
\(700\) −358.817 + 1172.70i −0.0193743 + 0.0633198i
\(701\) 5058.76 0.272563 0.136282 0.990670i \(-0.456485\pi\)
0.136282 + 0.990670i \(0.456485\pi\)
\(702\) 1681.79i 0.0904205i
\(703\) 9755.43i 0.523376i
\(704\) 2256.20 0.120787
\(705\) 1710.20 11434.5i 0.0913617 0.610848i
\(706\) 16069.9 0.856658
\(707\) 3149.89i 0.167558i
\(708\) 520.468i 0.0276277i
\(709\) −13023.0 −0.689829 −0.344915 0.938634i \(-0.612092\pi\)
−0.344915 + 0.938634i \(0.612092\pi\)
\(710\) 24555.4 + 3672.64i 1.29795 + 0.194129i
\(711\) −5465.38 −0.288281
\(712\) 3133.96i 0.164958i
\(713\) 1771.65i 0.0930560i
\(714\) −693.354 −0.0363419
\(715\) −12140.3 1815.76i −0.634993 0.0949731i
\(716\) 1060.10 0.0553320
\(717\) 18319.8i 0.954207i
\(718\) 11642.8i 0.605161i
\(719\) 17673.7 0.916717 0.458358 0.888767i \(-0.348438\pi\)
0.458358 + 0.888767i \(0.348438\pi\)
\(720\) −238.147 + 1592.26i −0.0123267 + 0.0824166i
\(721\) −4846.00 −0.250311
\(722\) 14318.7i 0.738072i
\(723\) 9026.21i 0.464299i
\(724\) −10142.5 −0.520642
\(725\) 35664.7 + 10912.5i 1.82697 + 0.559008i
\(726\) −529.272 −0.0270566
\(727\) 26012.9i 1.32705i 0.748155 + 0.663524i \(0.230940\pi\)
−0.748155 + 0.663524i \(0.769060\pi\)
\(728\) 611.109i 0.0311115i
\(729\) −729.000 −0.0370370
\(730\) 312.140 2086.98i 0.0158258 0.105812i
\(731\) −12474.7 −0.631182
\(732\) 1154.48i 0.0582935i
\(733\) 15642.6i 0.788229i −0.919061 0.394115i \(-0.871051\pi\)
0.919061 0.394115i \(-0.128949\pi\)
\(734\) −10278.9 −0.516893
\(735\) −11178.5 1671.91i −0.560984 0.0839039i
\(736\) 1828.80 0.0915904
\(737\) 24908.8i 1.24495i
\(738\) 451.290i 0.0225098i
\(739\) −17297.5 −0.861028 −0.430514 0.902584i \(-0.641668\pi\)
−0.430514 + 0.902584i \(0.641668\pi\)
\(740\) 3644.25 + 545.055i 0.181034 + 0.0270765i
\(741\) 11062.4 0.548430
\(742\) 2070.93i 0.102461i
\(743\) 20564.7i 1.01540i −0.861533 0.507702i \(-0.830495\pi\)
0.861533 0.507702i \(-0.169505\pi\)
\(744\) 744.000 0.0366618
\(745\) −423.480 + 2831.40i −0.0208256 + 0.139241i
\(746\) −1791.67 −0.0879328
\(747\) 5437.91i 0.266349i
\(748\) 6643.74i 0.324758i
\(749\) −3970.70 −0.193707
\(750\) −3612.49 + 7567.19i −0.175879 + 0.368420i
\(751\) −27970.2 −1.35905 −0.679526 0.733652i \(-0.737814\pi\)
−0.679526 + 0.733652i \(0.737814\pi\)
\(752\) 5515.24i 0.267447i
\(753\) 13232.3i 0.640388i
\(754\) 18585.3 0.897663
\(755\) −5877.32 + 39296.0i −0.283308 + 1.89421i
\(756\) 264.895 0.0127436
\(757\) 16261.9i 0.780780i 0.920650 + 0.390390i \(0.127660\pi\)
−0.920650 + 0.390390i \(0.872340\pi\)
\(758\) 28532.0i 1.36719i
\(759\) 6044.17 0.289051
\(760\) −10473.4 1566.47i −0.499884 0.0747654i
\(761\) −23922.9 −1.13956 −0.569779 0.821798i \(-0.692971\pi\)
−0.569779 + 0.821798i \(0.692971\pi\)
\(762\) 5525.34i 0.262680i
\(763\) 5001.46i 0.237307i
\(764\) 2537.15 0.120145
\(765\) −4688.65 701.260i −0.221593 0.0331426i
\(766\) −14511.7 −0.684502
\(767\) 1350.80i 0.0635915i
\(768\) 768.000i 0.0360844i
\(769\) 31811.9 1.49176 0.745881 0.666079i \(-0.232029\pi\)
0.745881 + 0.666079i \(0.232029\pi\)
\(770\) 285.996 1912.18i 0.0133852 0.0894939i
\(771\) −14484.1 −0.676568
\(772\) 19725.9i 0.919626i
\(773\) 22660.3i 1.05438i −0.849747 0.527190i \(-0.823246\pi\)
0.849747 0.527190i \(-0.176754\pi\)
\(774\) 4765.94 0.221329
\(775\) 3705.43 + 1133.77i 0.171746 + 0.0525500i
\(776\) 8390.81 0.388161
\(777\) 606.274i 0.0279922i
\(778\) 8516.08i 0.392437i
\(779\) −2968.47 −0.136529
\(780\) −618.077 + 4132.48i −0.0283727 + 0.189701i
\(781\) −39143.9 −1.79344
\(782\) 5385.19i 0.246258i
\(783\) 8056.11i 0.367691i
\(784\) 5391.75