Properties

Label 108.4.b.a.107.10
Level 108
Weight 4
Character 108.107
Analytic conductor 6.372
Analytic rank 0
Dimension 12
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.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{18}\cdot 3^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.10
Root \(-0.456937 + 0.263813i\) of \(x^{12} - 12 x^{10} + 112 x^{8} - 368 x^{6} + 928 x^{4} - 256 x^{2} + 64\)
Character \(\chi\) \(=\) 108.107
Dual form 108.4.b.a.107.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.51859 + 2.38619i) q^{2} +(-3.38780 + 7.24726i) q^{4} +13.1987i q^{5} -4.49091i q^{7} +(-22.4380 + 2.92167i) q^{8} +O(q^{10})\) \(q+(1.51859 + 2.38619i) q^{2} +(-3.38780 + 7.24726i) q^{4} +13.1987i q^{5} -4.49091i q^{7} +(-22.4380 + 2.92167i) q^{8} +(-31.4945 + 20.0433i) q^{10} +22.3519 q^{11} -73.5402 q^{13} +(10.7162 - 6.81984i) q^{14} +(-41.0457 - 49.1045i) q^{16} +42.6199i q^{17} +122.563i q^{19} +(-95.6542 - 44.7144i) q^{20} +(33.9433 + 53.3359i) q^{22} +197.965 q^{23} -49.2047 q^{25} +(-111.677 - 175.481i) q^{26} +(32.5468 + 15.2143i) q^{28} -14.6816i q^{29} -147.133i q^{31} +(54.8412 - 172.512i) q^{32} +(-101.699 + 64.7220i) q^{34} +59.2740 q^{35} +234.154 q^{37} +(-292.458 + 186.122i) q^{38} +(-38.5622 - 296.152i) q^{40} +396.340i q^{41} -280.764i q^{43} +(-75.7238 + 161.990i) q^{44} +(300.627 + 472.382i) q^{46} +534.237 q^{47} +322.832 q^{49} +(-74.7216 - 117.412i) q^{50} +(249.139 - 532.965i) q^{52} +337.497i q^{53} +295.016i q^{55} +(13.1210 + 100.767i) q^{56} +(35.0330 - 22.2952i) q^{58} -672.928 q^{59} -80.8693 q^{61} +(351.087 - 223.434i) q^{62} +(494.928 - 131.113i) q^{64} -970.632i q^{65} +251.791i q^{67} +(-308.878 - 144.388i) q^{68} +(90.0127 + 141.439i) q^{70} -95.8124 q^{71} -251.422 q^{73} +(355.583 + 558.737i) q^{74} +(-888.245 - 415.218i) q^{76} -100.381i q^{77} -499.839i q^{79} +(648.114 - 541.748i) q^{80} +(-945.742 + 601.876i) q^{82} +16.1731 q^{83} -562.526 q^{85} +(669.957 - 426.365i) q^{86} +(-501.533 + 65.3050i) q^{88} -321.011i q^{89} +330.263i q^{91} +(-670.665 + 1434.71i) q^{92} +(811.285 + 1274.79i) q^{94} -1617.67 q^{95} -210.036 q^{97} +(490.248 + 770.337i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{4} + O(q^{10}) \) \( 12q - 12q^{4} + 24q^{10} + 36q^{13} + 24q^{16} + 120q^{22} - 132q^{25} + 420q^{28} - 360q^{34} + 516q^{37} - 1152q^{40} - 696q^{46} - 720q^{49} + 204q^{52} + 2832q^{58} - 972q^{61} + 2496q^{64} - 1848q^{70} + 660q^{73} - 5004q^{76} - 3888q^{82} + 1056q^{85} + 3168q^{88} + 7608q^{94} + 2532q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51859 + 2.38619i 0.536901 + 0.843645i
\(3\) 0 0
\(4\) −3.38780 + 7.24726i −0.423474 + 0.905908i
\(5\) 13.1987i 1.18052i 0.807212 + 0.590262i \(0.200976\pi\)
−0.807212 + 0.590262i \(0.799024\pi\)
\(6\) 0 0
\(7\) 4.49091i 0.242486i −0.992623 0.121243i \(-0.961312\pi\)
0.992623 0.121243i \(-0.0386881\pi\)
\(8\) −22.4380 + 2.92167i −0.991629 + 0.129121i
\(9\) 0 0
\(10\) −31.4945 + 20.0433i −0.995944 + 0.633825i
\(11\) 22.3519 0.612669 0.306335 0.951924i \(-0.400897\pi\)
0.306335 + 0.951924i \(0.400897\pi\)
\(12\) 0 0
\(13\) −73.5402 −1.56895 −0.784476 0.620159i \(-0.787068\pi\)
−0.784476 + 0.620159i \(0.787068\pi\)
\(14\) 10.7162 6.81984i 0.204573 0.130191i
\(15\) 0 0
\(16\) −41.0457 49.1045i −0.641339 0.767258i
\(17\) 42.6199i 0.608050i 0.952664 + 0.304025i \(0.0983307\pi\)
−0.952664 + 0.304025i \(0.901669\pi\)
\(18\) 0 0
\(19\) 122.563i 1.47989i 0.672669 + 0.739943i \(0.265148\pi\)
−0.672669 + 0.739943i \(0.734852\pi\)
\(20\) −95.6542 44.7144i −1.06945 0.499922i
\(21\) 0 0
\(22\) 33.9433 + 53.3359i 0.328943 + 0.516875i
\(23\) 197.965 1.79472 0.897360 0.441299i \(-0.145482\pi\)
0.897360 + 0.441299i \(0.145482\pi\)
\(24\) 0 0
\(25\) −49.2047 −0.393638
\(26\) −111.677 175.481i −0.842372 1.32364i
\(27\) 0 0
\(28\) 32.5468 + 15.2143i 0.219670 + 0.102687i
\(29\) 14.6816i 0.0940102i −0.998895 0.0470051i \(-0.985032\pi\)
0.998895 0.0470051i \(-0.0149677\pi\)
\(30\) 0 0
\(31\) 147.133i 0.852448i −0.904618 0.426224i \(-0.859844\pi\)
0.904618 0.426224i \(-0.140156\pi\)
\(32\) 54.8412 172.512i 0.302958 0.953004i
\(33\) 0 0
\(34\) −101.699 + 64.7220i −0.512979 + 0.326463i
\(35\) 59.2740 0.286261
\(36\) 0 0
\(37\) 234.154 1.04040 0.520199 0.854045i \(-0.325858\pi\)
0.520199 + 0.854045i \(0.325858\pi\)
\(38\) −292.458 + 186.122i −1.24850 + 0.794553i
\(39\) 0 0
\(40\) −38.5622 296.152i −0.152430 1.17064i
\(41\) 396.340i 1.50970i 0.655895 + 0.754852i \(0.272292\pi\)
−0.655895 + 0.754852i \(0.727708\pi\)
\(42\) 0 0
\(43\) 280.764i 0.995725i −0.867256 0.497863i \(-0.834118\pi\)
0.867256 0.497863i \(-0.165882\pi\)
\(44\) −75.7238 + 161.990i −0.259450 + 0.555022i
\(45\) 0 0
\(46\) 300.627 + 472.382i 0.963587 + 1.51411i
\(47\) 534.237 1.65801 0.829006 0.559240i \(-0.188907\pi\)
0.829006 + 0.559240i \(0.188907\pi\)
\(48\) 0 0
\(49\) 322.832 0.941200
\(50\) −74.7216 117.412i −0.211345 0.332091i
\(51\) 0 0
\(52\) 249.139 532.965i 0.664411 1.42133i
\(53\) 337.497i 0.874695i 0.899293 + 0.437347i \(0.144082\pi\)
−0.899293 + 0.437347i \(0.855918\pi\)
\(54\) 0 0
\(55\) 295.016i 0.723271i
\(56\) 13.1210 + 100.767i 0.0313101 + 0.240457i
\(57\) 0 0
\(58\) 35.0330 22.2952i 0.0793113 0.0504742i
\(59\) −672.928 −1.48488 −0.742439 0.669914i \(-0.766331\pi\)
−0.742439 + 0.669914i \(0.766331\pi\)
\(60\) 0 0
\(61\) −80.8693 −0.169742 −0.0848709 0.996392i \(-0.527048\pi\)
−0.0848709 + 0.996392i \(0.527048\pi\)
\(62\) 351.087 223.434i 0.719164 0.457680i
\(63\) 0 0
\(64\) 494.928 131.113i 0.966656 0.256080i
\(65\) 970.632i 1.85219i
\(66\) 0 0
\(67\) 251.791i 0.459121i 0.973294 + 0.229560i \(0.0737289\pi\)
−0.973294 + 0.229560i \(0.926271\pi\)
\(68\) −308.878 144.388i −0.550838 0.257494i
\(69\) 0 0
\(70\) 90.0127 + 141.439i 0.153694 + 0.241503i
\(71\) −95.8124 −0.160153 −0.0800763 0.996789i \(-0.525516\pi\)
−0.0800763 + 0.996789i \(0.525516\pi\)
\(72\) 0 0
\(73\) −251.422 −0.403106 −0.201553 0.979478i \(-0.564599\pi\)
−0.201553 + 0.979478i \(0.564599\pi\)
\(74\) 355.583 + 558.737i 0.558591 + 0.877727i
\(75\) 0 0
\(76\) −888.245 415.218i −1.34064 0.626694i
\(77\) 100.381i 0.148564i
\(78\) 0 0
\(79\) 499.839i 0.711852i −0.934514 0.355926i \(-0.884165\pi\)
0.934514 0.355926i \(-0.115835\pi\)
\(80\) 648.114 541.748i 0.905766 0.757116i
\(81\) 0 0
\(82\) −945.742 + 601.876i −1.27366 + 0.810562i
\(83\) 16.1731 0.0213882 0.0106941 0.999943i \(-0.496596\pi\)
0.0106941 + 0.999943i \(0.496596\pi\)
\(84\) 0 0
\(85\) −562.526 −0.717818
\(86\) 669.957 426.365i 0.840039 0.534606i
\(87\) 0 0
\(88\) −501.533 + 65.3050i −0.607540 + 0.0791084i
\(89\) 321.011i 0.382327i −0.981558 0.191164i \(-0.938774\pi\)
0.981558 0.191164i \(-0.0612261\pi\)
\(90\) 0 0
\(91\) 330.263i 0.380450i
\(92\) −670.665 + 1434.71i −0.760018 + 1.62585i
\(93\) 0 0
\(94\) 811.285 + 1274.79i 0.890188 + 1.39877i
\(95\) −1617.67 −1.74704
\(96\) 0 0
\(97\) −210.036 −0.219855 −0.109928 0.993940i \(-0.535062\pi\)
−0.109928 + 0.993940i \(0.535062\pi\)
\(98\) 490.248 + 770.337i 0.505331 + 0.794039i
\(99\) 0 0
\(100\) 166.696 356.600i 0.166696 0.356600i
\(101\) 1568.74i 1.54550i −0.634713 0.772748i \(-0.718882\pi\)
0.634713 0.772748i \(-0.281118\pi\)
\(102\) 0 0
\(103\) 544.057i 0.520462i −0.965546 0.260231i \(-0.916201\pi\)
0.965546 0.260231i \(-0.0837987\pi\)
\(104\) 1650.09 214.860i 1.55582 0.202585i
\(105\) 0 0
\(106\) −805.333 + 512.519i −0.737932 + 0.469625i
\(107\) −1105.78 −0.999064 −0.499532 0.866295i \(-0.666495\pi\)
−0.499532 + 0.866295i \(0.666495\pi\)
\(108\) 0 0
\(109\) 17.6601 0.0155186 0.00775932 0.999970i \(-0.497530\pi\)
0.00775932 + 0.999970i \(0.497530\pi\)
\(110\) −703.963 + 448.007i −0.610184 + 0.388325i
\(111\) 0 0
\(112\) −220.524 + 184.333i −0.186050 + 0.155516i
\(113\) 1603.29i 1.33473i 0.744729 + 0.667367i \(0.232579\pi\)
−0.744729 + 0.667367i \(0.767421\pi\)
\(114\) 0 0
\(115\) 2612.87i 2.11871i
\(116\) 106.401 + 49.7381i 0.0851646 + 0.0398109i
\(117\) 0 0
\(118\) −1021.90 1605.73i −0.797233 1.25271i
\(119\) 191.402 0.147444
\(120\) 0 0
\(121\) −831.391 −0.624636
\(122\) −122.807 192.969i −0.0911345 0.143202i
\(123\) 0 0
\(124\) 1066.31 + 498.457i 0.772240 + 0.360990i
\(125\) 1000.40i 0.715825i
\(126\) 0 0
\(127\) 2080.04i 1.45334i −0.686988 0.726669i \(-0.741068\pi\)
0.686988 0.726669i \(-0.258932\pi\)
\(128\) 1064.45 + 981.885i 0.735039 + 0.678025i
\(129\) 0 0
\(130\) 2316.11 1473.99i 1.56259 0.994441i
\(131\) 1093.35 0.729213 0.364606 0.931162i \(-0.381204\pi\)
0.364606 + 0.931162i \(0.381204\pi\)
\(132\) 0 0
\(133\) 550.419 0.358853
\(134\) −600.820 + 382.365i −0.387335 + 0.246503i
\(135\) 0 0
\(136\) −124.521 956.306i −0.0785120 0.602960i
\(137\) 1344.61i 0.838522i −0.907866 0.419261i \(-0.862289\pi\)
0.907866 0.419261i \(-0.137711\pi\)
\(138\) 0 0
\(139\) 805.378i 0.491448i 0.969340 + 0.245724i \(0.0790257\pi\)
−0.969340 + 0.245724i \(0.920974\pi\)
\(140\) −200.808 + 429.575i −0.121224 + 0.259326i
\(141\) 0 0
\(142\) −145.499 228.627i −0.0859862 0.135112i
\(143\) −1643.77 −0.961249
\(144\) 0 0
\(145\) 193.777 0.110981
\(146\) −381.806 599.941i −0.216428 0.340079i
\(147\) 0 0
\(148\) −793.267 + 1696.98i −0.440582 + 0.942505i
\(149\) 879.365i 0.483493i −0.970339 0.241746i \(-0.922280\pi\)
0.970339 0.241746i \(-0.0777202\pi\)
\(150\) 0 0
\(151\) 1826.20i 0.984197i −0.870540 0.492098i \(-0.836230\pi\)
0.870540 0.492098i \(-0.163770\pi\)
\(152\) −358.089 2750.07i −0.191084 1.46750i
\(153\) 0 0
\(154\) 239.527 152.437i 0.125335 0.0797642i
\(155\) 1941.96 1.00634
\(156\) 0 0
\(157\) 3417.81 1.73740 0.868698 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(158\) 1192.71 759.049i 0.600551 0.382194i
\(159\) 0 0
\(160\) 2276.93 + 723.831i 1.12504 + 0.357649i
\(161\) 889.044i 0.435195i
\(162\) 0 0
\(163\) 1190.78i 0.572204i −0.958199 0.286102i \(-0.907640\pi\)
0.958199 0.286102i \(-0.0923596\pi\)
\(164\) −2872.38 1342.72i −1.36765 0.639321i
\(165\) 0 0
\(166\) 24.5602 + 38.5920i 0.0114834 + 0.0180441i
\(167\) 2123.75 0.984077 0.492039 0.870573i \(-0.336252\pi\)
0.492039 + 0.870573i \(0.336252\pi\)
\(168\) 0 0
\(169\) 3211.16 1.46161
\(170\) −854.244 1342.29i −0.385397 0.605584i
\(171\) 0 0
\(172\) 2034.77 + 951.173i 0.902035 + 0.421664i
\(173\) 1769.12i 0.777477i 0.921348 + 0.388738i \(0.127089\pi\)
−0.921348 + 0.388738i \(0.872911\pi\)
\(174\) 0 0
\(175\) 220.974i 0.0954519i
\(176\) −917.450 1097.58i −0.392929 0.470075i
\(177\) 0 0
\(178\) 765.993 487.483i 0.322548 0.205272i
\(179\) 3685.89 1.53909 0.769543 0.638595i \(-0.220484\pi\)
0.769543 + 0.638595i \(0.220484\pi\)
\(180\) 0 0
\(181\) −2425.51 −0.996059 −0.498030 0.867160i \(-0.665943\pi\)
−0.498030 + 0.867160i \(0.665943\pi\)
\(182\) −788.069 + 501.532i −0.320965 + 0.204264i
\(183\) 0 0
\(184\) −4441.94 + 578.389i −1.77970 + 0.231736i
\(185\) 3090.52i 1.22822i
\(186\) 0 0
\(187\) 952.638i 0.372534i
\(188\) −1809.89 + 3871.76i −0.702125 + 1.50201i
\(189\) 0 0
\(190\) −2456.56 3860.06i −0.937989 1.47388i
\(191\) −1367.60 −0.518096 −0.259048 0.965865i \(-0.583409\pi\)
−0.259048 + 0.965865i \(0.583409\pi\)
\(192\) 0 0
\(193\) −1240.32 −0.462591 −0.231296 0.972883i \(-0.574296\pi\)
−0.231296 + 0.972883i \(0.574296\pi\)
\(194\) −318.958 501.187i −0.118041 0.185480i
\(195\) 0 0
\(196\) −1093.69 + 2339.65i −0.398574 + 0.852641i
\(197\) 2889.56i 1.04504i 0.852628 + 0.522519i \(0.175008\pi\)
−0.852628 + 0.522519i \(0.824992\pi\)
\(198\) 0 0
\(199\) 1851.53i 0.659555i −0.944059 0.329777i \(-0.893026\pi\)
0.944059 0.329777i \(-0.106974\pi\)
\(200\) 1104.06 143.760i 0.390343 0.0508269i
\(201\) 0 0
\(202\) 3743.30 2382.26i 1.30385 0.829778i
\(203\) −65.9336 −0.0227962
\(204\) 0 0
\(205\) −5231.16 −1.78224
\(206\) 1298.22 826.198i 0.439085 0.279437i
\(207\) 0 0
\(208\) 3018.51 + 3611.15i 1.00623 + 1.20379i
\(209\) 2739.52i 0.906681i
\(210\) 0 0
\(211\) 4177.37i 1.36295i 0.731843 + 0.681474i \(0.238661\pi\)
−0.731843 + 0.681474i \(0.761339\pi\)
\(212\) −2445.93 1143.37i −0.792393 0.370411i
\(213\) 0 0
\(214\) −1679.22 2638.60i −0.536399 0.842856i
\(215\) 3705.72 1.17548
\(216\) 0 0
\(217\) −660.762 −0.206707
\(218\) 26.8184 + 42.1404i 0.00833198 + 0.0130922i
\(219\) 0 0
\(220\) −2138.06 999.453i −0.655217 0.306287i
\(221\) 3134.28i 0.954002i
\(222\) 0 0
\(223\) 1155.67i 0.347039i 0.984830 + 0.173519i \(0.0555139\pi\)
−0.984830 + 0.173519i \(0.944486\pi\)
\(224\) −774.737 246.287i −0.231091 0.0734632i
\(225\) 0 0
\(226\) −3825.76 + 2434.74i −1.12604 + 0.716620i
\(227\) 1499.50 0.438437 0.219218 0.975676i \(-0.429649\pi\)
0.219218 + 0.975676i \(0.429649\pi\)
\(228\) 0 0
\(229\) −320.011 −0.0923445 −0.0461723 0.998933i \(-0.514702\pi\)
−0.0461723 + 0.998933i \(0.514702\pi\)
\(230\) −6234.81 + 3967.87i −1.78744 + 1.13754i
\(231\) 0 0
\(232\) 42.8947 + 329.425i 0.0121387 + 0.0932233i
\(233\) 1446.64i 0.406749i −0.979101 0.203374i \(-0.934809\pi\)
0.979101 0.203374i \(-0.0651909\pi\)
\(234\) 0 0
\(235\) 7051.22i 1.95732i
\(236\) 2279.74 4876.89i 0.628808 1.34516i
\(237\) 0 0
\(238\) 290.661 + 456.722i 0.0791628 + 0.124390i
\(239\) −1432.06 −0.387582 −0.193791 0.981043i \(-0.562078\pi\)
−0.193791 + 0.981043i \(0.562078\pi\)
\(240\) 0 0
\(241\) −1148.97 −0.307102 −0.153551 0.988141i \(-0.549071\pi\)
−0.153551 + 0.988141i \(0.549071\pi\)
\(242\) −1262.54 1983.86i −0.335368 0.526972i
\(243\) 0 0
\(244\) 273.968 586.081i 0.0718813 0.153770i
\(245\) 4260.95i 1.11111i
\(246\) 0 0
\(247\) 9013.30i 2.32187i
\(248\) 429.875 + 3301.37i 0.110069 + 0.845312i
\(249\) 0 0
\(250\) −2387.13 + 1519.19i −0.603903 + 0.384327i
\(251\) −3652.62 −0.918531 −0.459266 0.888299i \(-0.651887\pi\)
−0.459266 + 0.888299i \(0.651887\pi\)
\(252\) 0 0
\(253\) 4424.90 1.09957
\(254\) 4963.37 3158.72i 1.22610 0.780298i
\(255\) 0 0
\(256\) −726.503 + 4031.06i −0.177369 + 0.984144i
\(257\) 5362.37i 1.30154i −0.759275 0.650770i \(-0.774446\pi\)
0.759275 0.650770i \(-0.225554\pi\)
\(258\) 0 0
\(259\) 1051.57i 0.252283i
\(260\) 7034.43 + 3288.30i 1.67791 + 0.784354i
\(261\) 0 0
\(262\) 1660.35 + 2608.95i 0.391515 + 0.615197i
\(263\) −1096.98 −0.257196 −0.128598 0.991697i \(-0.541048\pi\)
−0.128598 + 0.991697i \(0.541048\pi\)
\(264\) 0 0
\(265\) −4454.51 −1.03260
\(266\) 835.859 + 1313.40i 0.192668 + 0.302744i
\(267\) 0 0
\(268\) −1824.79 853.015i −0.415921 0.194426i
\(269\) 5602.35i 1.26982i −0.772586 0.634910i \(-0.781037\pi\)
0.772586 0.634910i \(-0.218963\pi\)
\(270\) 0 0
\(271\) 1051.62i 0.235725i −0.993030 0.117862i \(-0.962396\pi\)
0.993030 0.117862i \(-0.0376041\pi\)
\(272\) 2092.83 1749.36i 0.466531 0.389966i
\(273\) 0 0
\(274\) 3208.48 2041.90i 0.707415 0.450203i
\(275\) −1099.82 −0.241170
\(276\) 0 0
\(277\) 2739.10 0.594139 0.297069 0.954856i \(-0.403991\pi\)
0.297069 + 0.954856i \(0.403991\pi\)
\(278\) −1921.78 + 1223.04i −0.414608 + 0.263859i
\(279\) 0 0
\(280\) −1329.99 + 173.179i −0.283865 + 0.0369623i
\(281\) 423.244i 0.0898528i −0.998990 0.0449264i \(-0.985695\pi\)
0.998990 0.0449264i \(-0.0143053\pi\)
\(282\) 0 0
\(283\) 1630.51i 0.342486i 0.985229 + 0.171243i \(0.0547783\pi\)
−0.985229 + 0.171243i \(0.945222\pi\)
\(284\) 324.593 694.378i 0.0678206 0.145084i
\(285\) 0 0
\(286\) −2496.20 3922.33i −0.516096 0.810953i
\(287\) 1779.93 0.366083
\(288\) 0 0
\(289\) 3096.54 0.630275
\(290\) 294.267 + 462.388i 0.0595860 + 0.0936289i
\(291\) 0 0
\(292\) 851.767 1822.12i 0.170705 0.365177i
\(293\) 2352.75i 0.469109i −0.972103 0.234554i \(-0.924637\pi\)
0.972103 0.234554i \(-0.0753631\pi\)
\(294\) 0 0
\(295\) 8881.76i 1.75293i
\(296\) −5253.96 + 684.122i −1.03169 + 0.134337i
\(297\) 0 0
\(298\) 2098.33 1335.39i 0.407896 0.259588i
\(299\) −14558.4 −2.81583
\(300\) 0 0
\(301\) −1260.89 −0.241450
\(302\) 4357.65 2773.23i 0.830313 0.528416i
\(303\) 0 0
\(304\) 6018.39 5030.68i 1.13545 0.949109i
\(305\) 1067.37i 0.200384i
\(306\) 0 0
\(307\) 10088.6i 1.87554i 0.347263 + 0.937768i \(0.387111\pi\)
−0.347263 + 0.937768i \(0.612889\pi\)
\(308\) 727.485 + 340.069i 0.134585 + 0.0629131i
\(309\) 0 0
\(310\) 2949.03 + 4633.89i 0.540303 + 0.848990i
\(311\) 3970.97 0.724029 0.362015 0.932172i \(-0.382089\pi\)
0.362015 + 0.932172i \(0.382089\pi\)
\(312\) 0 0
\(313\) 4539.33 0.819738 0.409869 0.912144i \(-0.365574\pi\)
0.409869 + 0.912144i \(0.365574\pi\)
\(314\) 5190.24 + 8155.55i 0.932810 + 1.46575i
\(315\) 0 0
\(316\) 3622.47 + 1693.35i 0.644873 + 0.301451i
\(317\) 4211.47i 0.746181i 0.927795 + 0.373091i \(0.121702\pi\)
−0.927795 + 0.373091i \(0.878298\pi\)
\(318\) 0 0
\(319\) 328.161i 0.0575972i
\(320\) 1730.52 + 6532.38i 0.302309 + 1.14116i
\(321\) 0 0
\(322\) 2121.43 1350.09i 0.367151 0.233657i
\(323\) −5223.62 −0.899846
\(324\) 0 0
\(325\) 3618.52 0.617599
\(326\) 2841.43 1808.30i 0.482737 0.307217i
\(327\) 0 0
\(328\) −1157.98 8893.08i −0.194934 1.49707i
\(329\) 2399.21i 0.402045i
\(330\) 0 0
\(331\) 3143.43i 0.521990i 0.965340 + 0.260995i \(0.0840506\pi\)
−0.965340 + 0.260995i \(0.915949\pi\)
\(332\) −54.7910 + 117.210i −0.00905738 + 0.0193758i
\(333\) 0 0
\(334\) 3225.10 + 5067.68i 0.528352 + 0.830212i
\(335\) −3323.30 −0.542004
\(336\) 0 0
\(337\) 7102.24 1.14802 0.574012 0.818847i \(-0.305386\pi\)
0.574012 + 0.818847i \(0.305386\pi\)
\(338\) 4876.42 + 7662.43i 0.784741 + 1.23308i
\(339\) 0 0
\(340\) 1905.72 4076.78i 0.303978 0.650277i
\(341\) 3288.71i 0.522269i
\(342\) 0 0
\(343\) 2990.19i 0.470715i
\(344\) 820.302 + 6299.79i 0.128569 + 0.987390i
\(345\) 0 0
\(346\) −4221.45 + 2686.56i −0.655915 + 0.417428i
\(347\) 4871.70 0.753678 0.376839 0.926279i \(-0.377011\pi\)
0.376839 + 0.926279i \(0.377011\pi\)
\(348\) 0 0
\(349\) −7245.91 −1.11136 −0.555680 0.831396i \(-0.687542\pi\)
−0.555680 + 0.831396i \(0.687542\pi\)
\(350\) −527.286 + 335.568i −0.0805275 + 0.0512482i
\(351\) 0 0
\(352\) 1225.81 3855.98i 0.185613 0.583876i
\(353\) 9352.32i 1.41012i 0.709146 + 0.705062i \(0.249081\pi\)
−0.709146 + 0.705062i \(0.750919\pi\)
\(354\) 0 0
\(355\) 1264.60i 0.189064i
\(356\) 2326.45 + 1087.52i 0.346353 + 0.161906i
\(357\) 0 0
\(358\) 5597.34 + 8795.24i 0.826337 + 1.29844i
\(359\) −5162.08 −0.758898 −0.379449 0.925213i \(-0.623886\pi\)
−0.379449 + 0.925213i \(0.623886\pi\)
\(360\) 0 0
\(361\) −8162.66 −1.19006
\(362\) −3683.34 5787.73i −0.534785 0.840321i
\(363\) 0 0
\(364\) −2393.50 1118.86i −0.344652 0.161111i
\(365\) 3318.44i 0.475877i
\(366\) 0 0
\(367\) 3138.93i 0.446460i −0.974766 0.223230i \(-0.928340\pi\)
0.974766 0.223230i \(-0.0716600\pi\)
\(368\) −8125.61 9720.97i −1.15102 1.37701i
\(369\) 0 0
\(370\) −7374.58 + 4693.23i −1.03618 + 0.659430i
\(371\) 1515.67 0.212102
\(372\) 0 0
\(373\) 3085.24 0.428278 0.214139 0.976803i \(-0.431305\pi\)
0.214139 + 0.976803i \(0.431305\pi\)
\(374\) −2273.17 + 1446.66i −0.314286 + 0.200014i
\(375\) 0 0
\(376\) −11987.2 + 1560.87i −1.64413 + 0.214084i
\(377\) 1079.68i 0.147498i
\(378\) 0 0
\(379\) 13468.6i 1.82542i −0.408611 0.912709i \(-0.633987\pi\)
0.408611 0.912709i \(-0.366013\pi\)
\(380\) 5480.32 11723.7i 0.739828 1.58266i
\(381\) 0 0
\(382\) −2076.82 3263.36i −0.278166 0.437089i
\(383\) 1100.69 0.146847 0.0734235 0.997301i \(-0.476608\pi\)
0.0734235 + 0.997301i \(0.476608\pi\)
\(384\) 0 0
\(385\) 1324.89 0.175383
\(386\) −1883.53 2959.64i −0.248366 0.390263i
\(387\) 0 0
\(388\) 711.560 1522.19i 0.0931031 0.199169i
\(389\) 10089.1i 1.31501i −0.753452 0.657503i \(-0.771613\pi\)
0.753452 0.657503i \(-0.228387\pi\)
\(390\) 0 0
\(391\) 8437.26i 1.09128i
\(392\) −7243.70 + 943.208i −0.933321 + 0.121529i
\(393\) 0 0
\(394\) −6895.03 + 4388.04i −0.881641 + 0.561082i
\(395\) 6597.21 0.840359
\(396\) 0 0
\(397\) 1596.47 0.201825 0.100912 0.994895i \(-0.467824\pi\)
0.100912 + 0.994895i \(0.467824\pi\)
\(398\) 4418.10 2811.70i 0.556430 0.354116i
\(399\) 0 0
\(400\) 2019.64 + 2416.17i 0.252455 + 0.302022i
\(401\) 4818.54i 0.600066i −0.953929 0.300033i \(-0.903002\pi\)
0.953929 0.300033i \(-0.0969977\pi\)
\(402\) 0 0
\(403\) 10820.2i 1.33745i
\(404\) 11369.0 + 5314.56i 1.40008 + 0.654478i
\(405\) 0 0
\(406\) −100.126 157.330i −0.0122393 0.0192319i
\(407\) 5233.80 0.637420
\(408\) 0 0
\(409\) −4223.57 −0.510617 −0.255308 0.966860i \(-0.582177\pi\)
−0.255308 + 0.966860i \(0.582177\pi\)
\(410\) −7943.96 12482.5i −0.956888 1.50358i
\(411\) 0 0
\(412\) 3942.93 + 1843.16i 0.471491 + 0.220402i
\(413\) 3022.06i 0.360063i
\(414\) 0 0
\(415\) 213.463i 0.0252493i
\(416\) −4033.03 + 12686.6i −0.475326 + 1.49522i
\(417\) 0 0
\(418\) −6537.00 + 4160.19i −0.764917 + 0.486798i
\(419\) −1165.75 −0.135921 −0.0679604 0.997688i \(-0.521649\pi\)
−0.0679604 + 0.997688i \(0.521649\pi\)
\(420\) 0 0
\(421\) −9114.56 −1.05515 −0.527573 0.849510i \(-0.676898\pi\)
−0.527573 + 0.849510i \(0.676898\pi\)
\(422\) −9967.99 + 6343.69i −1.14984 + 0.731768i
\(423\) 0 0
\(424\) −986.057 7572.77i −0.112941 0.867373i
\(425\) 2097.10i 0.239352i
\(426\) 0 0
\(427\) 363.177i 0.0411601i
\(428\) 3746.16 8013.88i 0.423078 0.905060i
\(429\) 0 0
\(430\) 5627.45 + 8842.54i 0.631115 + 0.991686i
\(431\) 6631.38 0.741120 0.370560 0.928809i \(-0.379166\pi\)
0.370560 + 0.928809i \(0.379166\pi\)
\(432\) 0 0
\(433\) −15681.8 −1.74046 −0.870230 0.492646i \(-0.836030\pi\)
−0.870230 + 0.492646i \(0.836030\pi\)
\(434\) −1003.42 1576.70i −0.110981 0.174388i
\(435\) 0 0
\(436\) −59.8289 + 127.988i −0.00657175 + 0.0140585i
\(437\) 24263.2i 2.65598i
\(438\) 0 0
\(439\) 7923.17i 0.861395i 0.902496 + 0.430697i \(0.141732\pi\)
−0.902496 + 0.430697i \(0.858268\pi\)
\(440\) −861.939 6619.56i −0.0933894 0.717216i
\(441\) 0 0
\(442\) 7478.98 4759.67i 0.804839 0.512205i
\(443\) 14013.0 1.50289 0.751445 0.659796i \(-0.229357\pi\)
0.751445 + 0.659796i \(0.229357\pi\)
\(444\) 0 0
\(445\) 4236.92 0.451346
\(446\) −2757.65 + 1754.99i −0.292777 + 0.186325i
\(447\) 0 0
\(448\) −588.817 2222.68i −0.0620959 0.234401i
\(449\) 5967.60i 0.627235i 0.949549 + 0.313617i \(0.101541\pi\)
−0.949549 + 0.313617i \(0.898459\pi\)
\(450\) 0 0
\(451\) 8858.96i 0.924950i
\(452\) −11619.5 5431.62i −1.20915 0.565226i
\(453\) 0 0
\(454\) 2277.12 + 3578.09i 0.235397 + 0.369885i
\(455\) −4359.02 −0.449130
\(456\) 0 0
\(457\) 12901.4 1.32057 0.660285 0.751015i \(-0.270435\pi\)
0.660285 + 0.751015i \(0.270435\pi\)
\(458\) −485.963 763.606i −0.0495799 0.0779060i
\(459\) 0 0
\(460\) −18936.2 8851.88i −1.91936 0.897220i
\(461\) 9801.20i 0.990212i 0.868833 + 0.495106i \(0.164871\pi\)
−0.868833 + 0.495106i \(0.835129\pi\)
\(462\) 0 0
\(463\) 3427.68i 0.344056i −0.985092 0.172028i \(-0.944968\pi\)
0.985092 0.172028i \(-0.0550320\pi\)
\(464\) −720.930 + 602.615i −0.0721301 + 0.0602924i
\(465\) 0 0
\(466\) 3451.96 2196.85i 0.343152 0.218384i
\(467\) 13777.2 1.36517 0.682583 0.730808i \(-0.260856\pi\)
0.682583 + 0.730808i \(0.260856\pi\)
\(468\) 0 0
\(469\) 1130.77 0.111331
\(470\) −16825.5 + 10707.9i −1.65129 + 1.05089i
\(471\) 0 0
\(472\) 15099.2 1966.08i 1.47245 0.191729i
\(473\) 6275.63i 0.610050i
\(474\) 0 0
\(475\) 6030.67i 0.582539i
\(476\) −648.432 + 1387.14i −0.0624387 + 0.133571i
\(477\) 0 0
\(478\) −2174.70 3417.16i −0.208093 0.326982i
\(479\) 2793.91 0.266507 0.133254 0.991082i \(-0.457458\pi\)
0.133254 + 0.991082i \(0.457458\pi\)
\(480\) 0 0
\(481\) −17219.8 −1.63234
\(482\) −1744.81 2741.66i −0.164883 0.259085i
\(483\) 0 0
\(484\) 2816.58 6025.31i 0.264518 0.565863i
\(485\) 2772.20i 0.259545i
\(486\) 0 0
\(487\) 17643.8i 1.64172i −0.571131 0.820859i \(-0.693495\pi\)
0.571131 0.820859i \(-0.306505\pi\)
\(488\) 1814.54 236.273i 0.168321 0.0219172i
\(489\) 0 0
\(490\) −10167.4 + 6470.61i −0.937383 + 0.596556i
\(491\) −4816.53 −0.442703 −0.221351 0.975194i \(-0.571047\pi\)
−0.221351 + 0.975194i \(0.571047\pi\)
\(492\) 0 0
\(493\) 625.727 0.0571629
\(494\) 21507.4 13687.5i 1.95884 1.24662i
\(495\) 0 0
\(496\) −7224.90 + 6039.18i −0.654047 + 0.546708i
\(497\) 430.285i 0.0388349i
\(498\) 0 0
\(499\) 9504.01i 0.852621i 0.904577 + 0.426311i \(0.140187\pi\)
−0.904577 + 0.426311i \(0.859813\pi\)
\(500\) −7250.14 3389.14i −0.648472 0.303134i
\(501\) 0 0
\(502\) −5546.82 8715.84i −0.493161 0.774915i
\(503\) −13840.8 −1.22690 −0.613452 0.789732i \(-0.710220\pi\)
−0.613452 + 0.789732i \(0.710220\pi\)
\(504\) 0 0
\(505\) 20705.2 1.82450
\(506\) 6719.59 + 10558.7i 0.590360 + 0.927647i
\(507\) 0 0
\(508\) 15074.6 + 7046.75i 1.31659 + 0.615451i
\(509\) 8144.19i 0.709204i 0.935017 + 0.354602i \(0.115384\pi\)
−0.935017 + 0.354602i \(0.884616\pi\)
\(510\) 0 0
\(511\) 1129.12i 0.0977478i
\(512\) −10722.1 + 4387.93i −0.925498 + 0.378752i
\(513\) 0 0
\(514\) 12795.6 8143.22i 1.09804 0.698798i
\(515\) 7180.83 0.614418
\(516\) 0 0
\(517\) 11941.2 1.01581
\(518\) 2509.24 1596.89i 0.212837 0.135451i
\(519\) 0 0
\(520\) 2835.87 + 21779.0i 0.239156 + 1.83668i
\(521\) 21121.1i 1.77607i 0.459779 + 0.888034i \(0.347929\pi\)
−0.459779 + 0.888034i \(0.652071\pi\)
\(522\) 0 0
\(523\) 15414.6i 1.28878i −0.764696 0.644391i \(-0.777111\pi\)
0.764696 0.644391i \(-0.222889\pi\)
\(524\) −3704.06 + 7923.83i −0.308803 + 0.660600i
\(525\) 0 0
\(526\) −1665.85 2617.59i −0.138089 0.216982i
\(527\) 6270.81 0.518331
\(528\) 0 0
\(529\) 27023.2 2.22102
\(530\) −6764.56 10629.3i −0.554403 0.871147i
\(531\) 0 0
\(532\) −1864.71 + 3989.03i −0.151965 + 0.325087i
\(533\) 29146.9i 2.36865i
\(534\) 0 0
\(535\) 14594.8i 1.17942i
\(536\) −735.649 5649.68i −0.0592821 0.455278i
\(537\) 0 0
\(538\) 13368.3 8507.65i 1.07128 0.681767i
\(539\) 7215.91 0.576644
\(540\) 0 0
\(541\) −3269.66 −0.259840 −0.129920 0.991524i \(-0.541472\pi\)
−0.129920 + 0.991524i \(0.541472\pi\)
\(542\) 2509.36 1596.97i 0.198868 0.126561i
\(543\) 0 0
\(544\) 7352.46 + 2337.33i 0.579474 + 0.184214i
\(545\) 233.090i 0.0183201i
\(546\) 0 0
\(547\) 2028.46i 0.158557i 0.996853 + 0.0792784i \(0.0252616\pi\)
−0.996853 + 0.0792784i \(0.974738\pi\)
\(548\) 9744.72 + 4555.25i 0.759624 + 0.355092i
\(549\) 0 0
\(550\) −1670.17 2624.38i −0.129484 0.203462i
\(551\) 1799.41 0.139124
\(552\) 0 0
\(553\) −2244.74 −0.172615
\(554\) 4159.56 + 6536.01i 0.318994 + 0.501242i
\(555\) 0 0
\(556\) −5836.79 2728.45i −0.445207 0.208116i
\(557\) 5968.99i 0.454065i −0.973887 0.227032i \(-0.927098\pi\)
0.973887 0.227032i \(-0.0729023\pi\)
\(558\) 0 0
\(559\) 20647.5i 1.56225i
\(560\) −2432.94 2910.62i −0.183590 0.219636i
\(561\) 0 0
\(562\) 1009.94 642.733i 0.0758039 0.0482421i
\(563\) −13107.0 −0.981161 −0.490581 0.871396i \(-0.663215\pi\)
−0.490581 + 0.871396i \(0.663215\pi\)
\(564\) 0 0
\(565\) −21161.3 −1.57569
\(566\) −3890.70 + 2476.06i −0.288937 + 0.183881i
\(567\) 0 0
\(568\) 2149.84 279.932i 0.158812 0.0206791i
\(569\) 20162.7i 1.48553i −0.669553 0.742764i \(-0.733514\pi\)
0.669553 0.742764i \(-0.266486\pi\)
\(570\) 0 0
\(571\) 9396.23i 0.688652i −0.938850 0.344326i \(-0.888108\pi\)
0.938850 0.344326i \(-0.111892\pi\)
\(572\) 5568.74 11912.8i 0.407064 0.870803i
\(573\) 0 0
\(574\) 2702.97 + 4247.24i 0.196550 + 0.308844i
\(575\) −9740.82 −0.706470
\(576\) 0 0
\(577\) −3349.25 −0.241648 −0.120824 0.992674i \(-0.538554\pi\)
−0.120824 + 0.992674i \(0.538554\pi\)
\(578\) 4702.36 + 7388.93i 0.338395 + 0.531728i
\(579\) 0 0
\(580\) −656.477 + 1404.35i −0.0469978 + 0.100539i
\(581\) 72.6318i 0.00518636i
\(582\) 0 0
\(583\) 7543.72i 0.535899i
\(584\) 5641.41 734.573i 0.399732 0.0520494i
\(585\) 0 0
\(586\) 5614.10 3572.85i 0.395762 0.251865i
\(587\) 5156.24 0.362557 0.181278 0.983432i \(-0.441977\pi\)
0.181278 + 0.983432i \(0.441977\pi\)
\(588\) 0 0
\(589\) 18033.1 1.26153
\(590\) 21193.5 13487.7i 1.47886 0.941153i
\(591\) 0 0
\(592\) −9611.03 11498.0i −0.667248 0.798254i
\(593\) 19449.0i 1.34684i −0.739261 0.673419i \(-0.764825\pi\)
0.739261 0.673419i \(-0.235175\pi\)
\(594\) 0 0
\(595\) 2526.26i 0.174061i
\(596\) 6372.99 + 2979.11i 0.438000 + 0.204747i
\(597\) 0 0
\(598\) −22108.2 34739.1i −1.51182 2.37556i
\(599\) −25726.7 −1.75486 −0.877432 0.479701i \(-0.840745\pi\)
−0.877432 + 0.479701i \(0.840745\pi\)
\(600\) 0 0
\(601\) −11668.4 −0.791952 −0.395976 0.918261i \(-0.629594\pi\)
−0.395976 + 0.918261i \(0.629594\pi\)
\(602\) −1914.77 3008.72i −0.129635 0.203698i
\(603\) 0 0
\(604\) 13234.9 + 6186.78i 0.891592 + 0.416782i
\(605\) 10973.3i 0.737399i
\(606\) 0 0
\(607\) 26441.9i 1.76811i 0.467382 + 0.884055i \(0.345197\pi\)
−0.467382 + 0.884055i \(0.654803\pi\)
\(608\) 21143.6 + 6721.50i 1.41034 + 0.448343i
\(609\) 0 0
\(610\) 2546.94 1620.89i 0.169053 0.107587i
\(611\) −39287.9 −2.60134
\(612\) 0 0
\(613\) −4001.56 −0.263656 −0.131828 0.991273i \(-0.542085\pi\)
−0.131828 + 0.991273i \(0.542085\pi\)
\(614\) −24073.4 + 15320.5i −1.58229 + 1.00698i
\(615\) 0 0
\(616\) 293.279 + 2252.34i 0.0191827 + 0.147320i
\(617\) 25511.2i 1.66457i 0.554347 + 0.832286i \(0.312968\pi\)
−0.554347 + 0.832286i \(0.687032\pi\)
\(618\) 0 0
\(619\) 25105.1i 1.63014i −0.579361 0.815071i \(-0.696698\pi\)
0.579361 0.815071i \(-0.303302\pi\)
\(620\) −6578.97 + 14073.9i −0.426157 + 0.911648i
\(621\) 0 0
\(622\) 6030.26 + 9475.48i 0.388732 + 0.610824i
\(623\) −1441.63 −0.0927091
\(624\) 0 0
\(625\) −19354.5 −1.23869
\(626\) 6893.36 + 10831.7i 0.440118 + 0.691568i
\(627\) 0 0
\(628\) −11578.8 + 24769.8i −0.735743 + 1.57392i
\(629\) 9979.65i 0.632614i
\(630\) 0 0
\(631\) 10090.6i 0.636612i 0.947988 + 0.318306i \(0.103114\pi\)
−0.947988 + 0.318306i \(0.896886\pi\)
\(632\) 1460.37 + 11215.4i 0.0919150 + 0.705893i
\(633\) 0 0
\(634\) −10049.4 + 6395.47i −0.629512 + 0.400626i
\(635\) 27453.8 1.71570
\(636\) 0 0
\(637\) −23741.1 −1.47670
\(638\) 783.055 498.341i 0.0485916 0.0309240i
\(639\) 0 0
\(640\) −12959.6 + 14049.3i −0.800425 + 0.867732i
\(641\) 155.209i 0.00956376i −0.999989 0.00478188i \(-0.998478\pi\)
0.999989 0.00478188i \(-0.00152213\pi\)
\(642\) 0 0
\(643\) 8048.26i 0.493612i −0.969065 0.246806i \(-0.920619\pi\)
0.969065 0.246806i \(-0.0793810\pi\)
\(644\) 6443.14 + 3011.90i 0.394247 + 0.184294i
\(645\) 0 0
\(646\) −7932.52 12464.5i −0.483128 0.759150i
\(647\) 17128.5 1.04079 0.520394 0.853926i \(-0.325785\pi\)
0.520394 + 0.853926i \(0.325785\pi\)
\(648\) 0 0
\(649\) −15041.2 −0.909739
\(650\) 5495.04 + 8634.48i 0.331590 + 0.521034i
\(651\) 0 0
\(652\) 8629.91 + 4034.13i 0.518364 + 0.242314i
\(653\) 5854.10i 0.350825i −0.984495 0.175412i \(-0.943874\pi\)
0.984495 0.175412i \(-0.0561259\pi\)
\(654\) 0 0
\(655\) 14430.8i 0.860853i
\(656\) 19462.1 16268.0i 1.15833 0.968232i
\(657\) 0 0
\(658\) 5724.98 3643.41i 0.339184 0.215859i
\(659\) −22130.6 −1.30817 −0.654086 0.756420i \(-0.726947\pi\)
−0.654086 + 0.756420i \(0.726947\pi\)
\(660\) 0 0
\(661\) 19160.0 1.12744 0.563721 0.825965i \(-0.309369\pi\)
0.563721 + 0.825965i \(0.309369\pi\)
\(662\) −7500.82 + 4773.57i −0.440374 + 0.280257i
\(663\) 0 0
\(664\) −362.891 + 47.2524i −0.0212092 + 0.00276167i
\(665\) 7264.80i 0.423634i
\(666\) 0 0
\(667\) 2906.44i 0.168722i
\(668\) −7194.84 + 15391.4i −0.416732 + 0.891484i
\(669\) 0 0
\(670\) −5046.71 7930.02i −0.291002 0.457259i
\(671\) −1807.58 −0.103996
\(672\) 0 0
\(673\) 24302.6 1.39197 0.695984 0.718057i \(-0.254968\pi\)
0.695984 + 0.718057i \(0.254968\pi\)
\(674\) 10785.4 + 16947.3i 0.616375 + 0.968524i
\(675\) 0 0
\(676\) −10878.8 + 23272.1i −0.618955 + 1.32409i
\(677\) 16656.4i 0.945581i 0.881175 + 0.472791i \(0.156753\pi\)
−0.881175 + 0.472791i \(0.843247\pi\)
\(678\) 0 0
\(679\) 943.255i 0.0533120i
\(680\) 12622.0 1643.52i 0.711809 0.0926853i
\(681\) 0 0
\(682\) 7847.48 4994.19i 0.440610 0.280407i
\(683\) −24952.6 −1.39793 −0.698964 0.715157i \(-0.746355\pi\)
−0.698964 + 0.715157i \(0.746355\pi\)
\(684\) 0 0
\(685\) 17747.0 0.989895
\(686\) 7135.16 4540.86i 0.397116 0.252727i
\(687\) 0 0
\(688\) −13786.8 + 11524.2i −0.763978 + 0.638597i
\(689\) 24819.6i 1.37235i
\(690\) 0 0
\(691\) 15536.7i 0.855346i −0.903934 0.427673i \(-0.859334\pi\)
0.903934 0.427673i \(-0.140666\pi\)
\(692\) −12821.3 5993.41i −0.704323 0.329242i
\(693\) 0 0
\(694\) 7398.09 + 11624.8i 0.404651 + 0.635837i
\(695\) −10629.9 −0.580166
\(696\) 0 0
\(697\) −16892.0 −0.917976
\(698\) −11003.5 17290.1i −0.596691 0.937594i
\(699\) 0 0
\(700\) −1601.46 748.615i −0.0864706 0.0404214i
\(701\) 9683.38i 0.521735i −0.965375 0.260868i \(-0.915991\pi\)
0.965375 0.260868i \(-0.0840086\pi\)
\(702\) 0 0
\(703\) 28698.6i 1.53967i
\(704\) 11062.6 2930.63i 0.592240 0.156892i
\(705\) 0 0
\(706\) −22316.4 + 14202.3i −1.18964 + 0.757097i
\(707\) −7045.06 −0.374762
\(708\) 0 0
\(709\) −15665.5 −0.829801 −0.414901 0.909867i \(-0.636184\pi\)
−0.414901 + 0.909867i \(0.636184\pi\)
\(710\) 3017.56 1920.40i 0.159503 0.101509i
\(711\) 0 0
\(712\) 937.889 + 7202.85i 0.0493664 + 0.379127i
\(713\) 29127.2i 1.52991i
\(714\) 0 0
\(715\) 21695.5i 1.13478i
\(716\) −12487.0 + 26712.6i −0.651764 + 1.39427i
\(717\) 0 0
\(718\) −7839.06 12317.7i −0.407453 0.640240i
\(719\) 15944.3 0.827015 0.413507 0.910501i \(-0.364304\pi\)
0.413507 + 0.910501i \(0.364304\pi\)
\(720\) 0 0
\(721\) −2443.31 −0.126205
\(722\) −12395.7 19477.6i −0.638947 1.00399i
\(723\) 0 0
\(724\) 8217.13 17578.3i 0.421806 0.902338i
\(725\) 722.402i 0.0370060i
\(726\) 0 0
\(727\) 23773.6i 1.21281i −0.795156 0.606405i \(-0.792611\pi\)
0.795156 0.606405i \(-0.207389\pi\)
\(728\) −964.919 7410.43i −0.0491240 0.377265i
\(729\) 0 0
\(730\) 7918.42 5039.33i 0.401471 0.255499i
\(731\) 11966.2 0.605451
\(732\) 0 0
\(733\) −16190.1 −0.815818 −0.407909 0.913023i \(-0.633742\pi\)
−0.407909 + 0.913023i \(0.633742\pi\)
\(734\) 7490.07 4766.73i 0.376653 0.239705i
\(735\) 0 0
\(736\) 10856.6 34151.4i 0.543724 1.71038i
\(737\) 5628.00i 0.281289i
\(738\) 0 0
\(739\) 3013.13i 0.149986i 0.997184 + 0.0749930i \(0.0238934\pi\)
−0.997184 + 0.0749930i \(0.976107\pi\)
\(740\) −22397.9 10470.1i −1.11265 0.520118i
\(741\) 0 0
\(742\) 2301.68 + 3616.68i 0.113878 + 0.178939i
\(743\) 14363.7 0.709225 0.354613 0.935013i \(-0.384613\pi\)
0.354613 + 0.935013i \(0.384613\pi\)
\(744\) 0 0
\(745\) 11606.4 0.570775
\(746\) 4685.20 + 7361.97i 0.229943 + 0.361315i
\(747\) 0 0
\(748\) −6904.02 3227.34i −0.337481 0.157758i
\(749\) 4965.96i 0.242260i
\(750\) 0 0
\(751\) 21754.9i 1.05705i 0.848917 + 0.528526i \(0.177255\pi\)
−0.848917 + 0.528526i \(0.822745\pi\)
\(752\) −21928.1 26233.5i −1.06335 1.27212i
\(753\) 0 0
\(754\) −2576.33 + 1639.59i −0.124436 + 0.0791916i
\(755\) 24103.3 1.16187
\(756\) 0 0
\(757\) 25070.4 1.20370 0.601848 0.798611i \(-0.294431\pi\)
0.601848 + 0.798611i \(0.294431\pi\)
\(758\) 32138.5 20453.2i 1.54000 0.980069i
\(759\) 0 0
\(760\) 36297.2 4726.29i 1.73242 0.225580i
\(761\) 20326.9i 0.968263i 0.874995 + 0.484132i \(0.160864\pi\)
−0.874995 + 0.484132i \(0.839136\pi\)
\(762\) 0 0
\(763\) 79.3101i 0.00376306i
\(764\) 4633.16 9911.38i 0.219400 0.469347i
\(765\) 0 0
\(766\) 1671.48 + 2626.44i 0.0788423 + 0.123887i
\(767\) 49487.3 2.32970
\(768\) 0 0
\(769\) −4680.89 −0.219502 −0.109751 0.993959i \(-0.535005\pi\)
−0.109751 + 0.993959i \(0.535005\pi\)
\(770\) 2011.96 + 3161.44i 0.0941636 + 0.147961i
\(771\) 0 0
\(772\) 4201.95 8988.92i 0.195896 0.419065i
\(773\) 2385.68i 0.111005i 0.998459 + 0.0555025i \(0.0176761\pi\)
−0.998459 + 0.0555025i \(0.982324\pi\)
\(774\) 0 0
\(775\) 7239.65i 0.335556i
\(776\) 4712.80 613.658i 0.218015 0.0283879i
\(777\) 0 0
\(778\) 24074.5 15321.2i 1.10940 0.706028i
\(779\) −48576.6 −2.23419
\(780\) 0 0
\(781\) −2141.59 −0.0981206
\(782\) −20132.9 + 12812.7i −0.920653 + 0.585909i
\(783\) 0 0
\(784\) −13250.8 15852.5i −0.603628 0.722143i
\(785\) 45110.6i 2.05104i
\(786\) 0 0
\(787\) 8714.78i 0.394725i −0.980331 0.197362i \(-0.936762\pi\)
0.980331 0.197362i \(-0.0632375\pi\)
\(788\) −20941.4 9789.23i −0.946708 0.442547i
\(789\) 0 0
\(790\) 10018.4 +