Properties

Label 108.5.d.b.55.1
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{24} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.1
Root \(-0.222504 - 0.385387i\) of \(x^{16} + 38 x^{14} + 1016 x^{12} + 13512 x^{10} + 130640 x^{8} + 569472 x^{6} + 1783808 x^{4} + 352256 x^{2} + 65536\)
Character \(\chi\) \(=\) 108.55
Dual form 108.5.d.b.55.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.98139 - 0.385387i) q^{2} +(15.7030 + 3.06876i) q^{4} +22.8093 q^{5} +82.1204i q^{7} +(-61.3369 - 18.2696i) q^{8} +O(q^{10})\) \(q+(-3.98139 - 0.385387i) q^{2} +(15.7030 + 3.06876i) q^{4} +22.8093 q^{5} +82.1204i q^{7} +(-61.3369 - 18.2696i) q^{8} +(-90.8127 - 8.79041i) q^{10} -107.306i q^{11} +57.1351 q^{13} +(31.6482 - 326.954i) q^{14} +(237.165 + 96.3771i) q^{16} -291.903 q^{17} +304.924i q^{19} +(358.173 + 69.9961i) q^{20} +(-41.3543 + 427.227i) q^{22} +982.813i q^{23} -104.737 q^{25} +(-227.477 - 22.0191i) q^{26} +(-252.008 + 1289.53i) q^{28} +1049.98 q^{29} +783.041i q^{31} +(-907.106 - 475.115i) q^{32} +(1162.18 + 112.496i) q^{34} +1873.11i q^{35} +1404.40 q^{37} +(117.514 - 1214.02i) q^{38} +(-1399.05 - 416.717i) q^{40} +363.412 q^{41} -64.7059i q^{43} +(329.295 - 1685.02i) q^{44} +(378.764 - 3912.96i) q^{46} +3495.66i q^{47} -4342.77 q^{49} +(416.998 + 40.3642i) q^{50} +(897.189 + 175.334i) q^{52} -3268.87 q^{53} -2447.57i q^{55} +(1500.31 - 5037.02i) q^{56} +(-4180.37 - 404.648i) q^{58} -867.469i q^{59} +6034.94 q^{61} +(301.774 - 3117.59i) q^{62} +(3428.44 + 2241.21i) q^{64} +1303.21 q^{65} -3421.54i q^{67} +(-4583.74 - 895.780i) q^{68} +(721.872 - 7457.58i) q^{70} +3188.67i q^{71} -4267.98 q^{73} +(-5591.47 - 541.239i) q^{74} +(-935.737 + 4788.20i) q^{76} +8812.00 q^{77} -7530.43i q^{79} +(5409.57 + 2198.29i) q^{80} +(-1446.89 - 140.055i) q^{82} -586.258i q^{83} -6658.11 q^{85} +(-24.9368 + 257.619i) q^{86} +(-1960.44 + 6581.81i) q^{88} -5789.27 q^{89} +4691.96i q^{91} +(-3016.01 + 15433.1i) q^{92} +(1347.18 - 13917.6i) q^{94} +6955.09i q^{95} +10837.8 q^{97} +(17290.3 + 1673.65i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 28q^{4} + O(q^{10}) \) \( 16q + 28q^{4} + 176q^{10} + 176q^{13} + 88q^{16} + 384q^{22} + 2736q^{25} + 1812q^{28} + 1520q^{34} + 80q^{37} - 688q^{40} - 1824q^{46} - 7904q^{49} - 5236q^{52} - 11584q^{58} - 1648q^{61} + 5056q^{64} + 26688q^{70} + 80q^{73} - 8388q^{76} - 38464q^{82} - 16832q^{85} - 29520q^{88} - 4512q^{94} + 14864q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.98139 0.385387i −0.995348 0.0963469i
\(3\) 0 0
\(4\) 15.7030 + 3.06876i 0.981435 + 0.191797i
\(5\) 22.8093 0.912371 0.456186 0.889885i \(-0.349215\pi\)
0.456186 + 0.889885i \(0.349215\pi\)
\(6\) 0 0
\(7\) 82.1204i 1.67593i 0.545726 + 0.837964i \(0.316254\pi\)
−0.545726 + 0.837964i \(0.683746\pi\)
\(8\) −61.3369 18.2696i −0.958390 0.285463i
\(9\) 0 0
\(10\) −90.8127 8.79041i −0.908127 0.0879041i
\(11\) 107.306i 0.886825i −0.896318 0.443413i \(-0.853768\pi\)
0.896318 0.443413i \(-0.146232\pi\)
\(12\) 0 0
\(13\) 57.1351 0.338077 0.169039 0.985609i \(-0.445934\pi\)
0.169039 + 0.985609i \(0.445934\pi\)
\(14\) 31.6482 326.954i 0.161470 1.66813i
\(15\) 0 0
\(16\) 237.165 + 96.3771i 0.926428 + 0.376473i
\(17\) −291.903 −1.01005 −0.505023 0.863106i \(-0.668516\pi\)
−0.505023 + 0.863106i \(0.668516\pi\)
\(18\) 0 0
\(19\) 304.924i 0.844664i 0.906441 + 0.422332i \(0.138788\pi\)
−0.906441 + 0.422332i \(0.861212\pi\)
\(20\) 358.173 + 69.9961i 0.895433 + 0.174990i
\(21\) 0 0
\(22\) −41.3543 + 427.227i −0.0854428 + 0.882699i
\(23\) 982.813i 1.85787i 0.370243 + 0.928935i \(0.379274\pi\)
−0.370243 + 0.928935i \(0.620726\pi\)
\(24\) 0 0
\(25\) −104.737 −0.167579
\(26\) −227.477 22.0191i −0.336505 0.0325727i
\(27\) 0 0
\(28\) −252.008 + 1289.53i −0.321438 + 1.64481i
\(29\) 1049.98 1.24849 0.624244 0.781230i \(-0.285407\pi\)
0.624244 + 0.781230i \(0.285407\pi\)
\(30\) 0 0
\(31\) 783.041i 0.814819i 0.913246 + 0.407409i \(0.133568\pi\)
−0.913246 + 0.407409i \(0.866432\pi\)
\(32\) −907.106 475.115i −0.885846 0.463980i
\(33\) 0 0
\(34\) 1162.18 + 112.496i 1.00535 + 0.0973148i
\(35\) 1873.11i 1.52907i
\(36\) 0 0
\(37\) 1404.40 1.02586 0.512930 0.858431i \(-0.328560\pi\)
0.512930 + 0.858431i \(0.328560\pi\)
\(38\) 117.514 1214.02i 0.0813808 0.840735i
\(39\) 0 0
\(40\) −1399.05 416.717i −0.874407 0.260448i
\(41\) 363.412 0.216188 0.108094 0.994141i \(-0.465525\pi\)
0.108094 + 0.994141i \(0.465525\pi\)
\(42\) 0 0
\(43\) 64.7059i 0.0349951i −0.999847 0.0174975i \(-0.994430\pi\)
0.999847 0.0174975i \(-0.00556992\pi\)
\(44\) 329.295 1685.02i 0.170091 0.870361i
\(45\) 0 0
\(46\) 378.764 3912.96i 0.179000 1.84923i
\(47\) 3495.66i 1.58246i 0.611518 + 0.791230i \(0.290559\pi\)
−0.611518 + 0.791230i \(0.709441\pi\)
\(48\) 0 0
\(49\) −4342.77 −1.80873
\(50\) 416.998 + 40.3642i 0.166799 + 0.0161457i
\(51\) 0 0
\(52\) 897.189 + 175.334i 0.331801 + 0.0648423i
\(53\) −3268.87 −1.16371 −0.581856 0.813292i \(-0.697673\pi\)
−0.581856 + 0.813292i \(0.697673\pi\)
\(54\) 0 0
\(55\) 2447.57i 0.809114i
\(56\) 1500.31 5037.02i 0.478415 1.60619i
\(57\) 0 0
\(58\) −4180.37 404.648i −1.24268 0.120288i
\(59\) 867.469i 0.249201i −0.992207 0.124601i \(-0.960235\pi\)
0.992207 0.124601i \(-0.0397650\pi\)
\(60\) 0 0
\(61\) 6034.94 1.62186 0.810929 0.585144i \(-0.198962\pi\)
0.810929 + 0.585144i \(0.198962\pi\)
\(62\) 301.774 3117.59i 0.0785052 0.811028i
\(63\) 0 0
\(64\) 3428.44 + 2241.21i 0.837022 + 0.547170i
\(65\) 1303.21 0.308452
\(66\) 0 0
\(67\) 3421.54i 0.762205i −0.924533 0.381103i \(-0.875544\pi\)
0.924533 0.381103i \(-0.124456\pi\)
\(68\) −4583.74 895.780i −0.991294 0.193724i
\(69\) 0 0
\(70\) 721.872 7457.58i 0.147321 1.52195i
\(71\) 3188.67i 0.632547i 0.948668 + 0.316273i \(0.102432\pi\)
−0.948668 + 0.316273i \(0.897568\pi\)
\(72\) 0 0
\(73\) −4267.98 −0.800896 −0.400448 0.916319i \(-0.631146\pi\)
−0.400448 + 0.916319i \(0.631146\pi\)
\(74\) −5591.47 541.239i −1.02109 0.0988383i
\(75\) 0 0
\(76\) −935.737 + 4788.20i −0.162004 + 0.828983i
\(77\) 8812.00 1.48625
\(78\) 0 0
\(79\) 7530.43i 1.20661i −0.797512 0.603303i \(-0.793851\pi\)
0.797512 0.603303i \(-0.206149\pi\)
\(80\) 5409.57 + 2198.29i 0.845246 + 0.343483i
\(81\) 0 0
\(82\) −1446.89 140.055i −0.215182 0.0208290i
\(83\) 586.258i 0.0851006i −0.999094 0.0425503i \(-0.986452\pi\)
0.999094 0.0425503i \(-0.0135483\pi\)
\(84\) 0 0
\(85\) −6658.11 −0.921537
\(86\) −24.9368 + 257.619i −0.00337167 + 0.0348323i
\(87\) 0 0
\(88\) −1960.44 + 6581.81i −0.253156 + 0.849924i
\(89\) −5789.27 −0.730876 −0.365438 0.930836i \(-0.619081\pi\)
−0.365438 + 0.930836i \(0.619081\pi\)
\(90\) 0 0
\(91\) 4691.96i 0.566593i
\(92\) −3016.01 + 15433.1i −0.356334 + 1.82338i
\(93\) 0 0
\(94\) 1347.18 13917.6i 0.152465 1.57510i
\(95\) 6955.09i 0.770647i
\(96\) 0 0
\(97\) 10837.8 1.15185 0.575927 0.817501i \(-0.304641\pi\)
0.575927 + 0.817501i \(0.304641\pi\)
\(98\) 17290.3 + 1673.65i 1.80032 + 0.174266i
\(99\) 0 0
\(100\) −1644.68 321.411i −0.164468 0.0321411i
\(101\) −11502.9 −1.12763 −0.563813 0.825903i \(-0.690666\pi\)
−0.563813 + 0.825903i \(0.690666\pi\)
\(102\) 0 0
\(103\) 13839.0i 1.30446i 0.758020 + 0.652231i \(0.226167\pi\)
−0.758020 + 0.652231i \(0.773833\pi\)
\(104\) −3504.49 1043.84i −0.324010 0.0965086i
\(105\) 0 0
\(106\) 13014.6 + 1259.78i 1.15830 + 0.112120i
\(107\) 14731.9i 1.28674i −0.765555 0.643371i \(-0.777535\pi\)
0.765555 0.643371i \(-0.222465\pi\)
\(108\) 0 0
\(109\) 3545.18 0.298391 0.149195 0.988808i \(-0.452332\pi\)
0.149195 + 0.988808i \(0.452332\pi\)
\(110\) −943.262 + 9744.73i −0.0779556 + 0.805350i
\(111\) 0 0
\(112\) −7914.53 + 19476.1i −0.630941 + 1.55263i
\(113\) 12472.0 0.976742 0.488371 0.872636i \(-0.337591\pi\)
0.488371 + 0.872636i \(0.337591\pi\)
\(114\) 0 0
\(115\) 22417.3i 1.69507i
\(116\) 16487.8 + 3222.13i 1.22531 + 0.239456i
\(117\) 0 0
\(118\) −334.312 + 3453.73i −0.0240098 + 0.248042i
\(119\) 23971.2i 1.69276i
\(120\) 0 0
\(121\) 3126.46 0.213541
\(122\) −24027.4 2325.79i −1.61431 0.156261i
\(123\) 0 0
\(124\) −2402.96 + 12296.1i −0.156280 + 0.799691i
\(125\) −16644.8 −1.06527
\(126\) 0 0
\(127\) 1002.07i 0.0621284i −0.999517 0.0310642i \(-0.990110\pi\)
0.999517 0.0310642i \(-0.00988964\pi\)
\(128\) −12786.2 10244.4i −0.780410 0.625269i
\(129\) 0 0
\(130\) −5188.59 502.241i −0.307017 0.0297184i
\(131\) 33549.8i 1.95500i −0.210933 0.977501i \(-0.567650\pi\)
0.210933 0.977501i \(-0.432350\pi\)
\(132\) 0 0
\(133\) −25040.5 −1.41560
\(134\) −1318.62 + 13622.5i −0.0734361 + 0.758659i
\(135\) 0 0
\(136\) 17904.5 + 5332.97i 0.968018 + 0.288331i
\(137\) 19700.7 1.04964 0.524821 0.851213i \(-0.324132\pi\)
0.524821 + 0.851213i \(0.324132\pi\)
\(138\) 0 0
\(139\) 12634.4i 0.653922i −0.945038 0.326961i \(-0.893975\pi\)
0.945038 0.326961i \(-0.106025\pi\)
\(140\) −5748.11 + 29413.3i −0.293271 + 1.50068i
\(141\) 0 0
\(142\) 1228.87 12695.3i 0.0609439 0.629604i
\(143\) 6130.93i 0.299816i
\(144\) 0 0
\(145\) 23949.2 1.13908
\(146\) 16992.5 + 1644.82i 0.797171 + 0.0771639i
\(147\) 0 0
\(148\) 22053.2 + 4309.76i 1.00681 + 0.196757i
\(149\) 24054.7 1.08350 0.541749 0.840541i \(-0.317762\pi\)
0.541749 + 0.840541i \(0.317762\pi\)
\(150\) 0 0
\(151\) 29000.6i 1.27190i −0.771730 0.635951i \(-0.780608\pi\)
0.771730 0.635951i \(-0.219392\pi\)
\(152\) 5570.85 18703.1i 0.241121 0.809518i
\(153\) 0 0
\(154\) −35084.0 3396.04i −1.47934 0.143196i
\(155\) 17860.6i 0.743417i
\(156\) 0 0
\(157\) 11143.2 0.452074 0.226037 0.974119i \(-0.427423\pi\)
0.226037 + 0.974119i \(0.427423\pi\)
\(158\) −2902.13 + 29981.6i −0.116253 + 1.20099i
\(159\) 0 0
\(160\) −20690.4 10837.0i −0.808220 0.423322i
\(161\) −80709.0 −3.11365
\(162\) 0 0
\(163\) 3212.14i 0.120898i 0.998171 + 0.0604490i \(0.0192533\pi\)
−0.998171 + 0.0604490i \(0.980747\pi\)
\(164\) 5706.65 + 1115.22i 0.212175 + 0.0414643i
\(165\) 0 0
\(166\) −225.937 + 2334.12i −0.00819918 + 0.0847047i
\(167\) 22589.6i 0.809983i −0.914320 0.404992i \(-0.867274\pi\)
0.914320 0.404992i \(-0.132726\pi\)
\(168\) 0 0
\(169\) −25296.6 −0.885704
\(170\) 26508.5 + 2565.95i 0.917250 + 0.0887872i
\(171\) 0 0
\(172\) 198.567 1016.07i 0.00671196 0.0343454i
\(173\) 20741.2 0.693013 0.346506 0.938048i \(-0.387368\pi\)
0.346506 + 0.938048i \(0.387368\pi\)
\(174\) 0 0
\(175\) 8601.02i 0.280850i
\(176\) 10341.8 25449.2i 0.333866 0.821579i
\(177\) 0 0
\(178\) 23049.3 + 2231.11i 0.727476 + 0.0704176i
\(179\) 37551.2i 1.17197i 0.810321 + 0.585986i \(0.199293\pi\)
−0.810321 + 0.585986i \(0.800707\pi\)
\(180\) 0 0
\(181\) −38019.3 −1.16050 −0.580252 0.814437i \(-0.697046\pi\)
−0.580252 + 0.814437i \(0.697046\pi\)
\(182\) 1808.22 18680.5i 0.0545895 0.563957i
\(183\) 0 0
\(184\) 17955.6 60282.7i 0.530353 1.78056i
\(185\) 32033.4 0.935964
\(186\) 0 0
\(187\) 31322.9i 0.895734i
\(188\) −10727.3 + 54892.1i −0.303512 + 1.55308i
\(189\) 0 0
\(190\) 2680.41 27690.9i 0.0742495 0.767062i
\(191\) 7313.44i 0.200473i 0.994964 + 0.100236i \(0.0319599\pi\)
−0.994964 + 0.100236i \(0.968040\pi\)
\(192\) 0 0
\(193\) 60987.7 1.63730 0.818649 0.574294i \(-0.194724\pi\)
0.818649 + 0.574294i \(0.194724\pi\)
\(194\) −43149.5 4176.75i −1.14650 0.110978i
\(195\) 0 0
\(196\) −68194.3 13326.9i −1.77515 0.346910i
\(197\) 13891.0 0.357934 0.178967 0.983855i \(-0.442725\pi\)
0.178967 + 0.983855i \(0.442725\pi\)
\(198\) 0 0
\(199\) 43065.2i 1.08748i −0.839255 0.543738i \(-0.817008\pi\)
0.839255 0.543738i \(-0.182992\pi\)
\(200\) 6424.23 + 1913.50i 0.160606 + 0.0478375i
\(201\) 0 0
\(202\) 45797.6 + 4433.08i 1.12238 + 0.108643i
\(203\) 86224.6i 2.09237i
\(204\) 0 0
\(205\) 8289.17 0.197244
\(206\) 5333.39 55098.6i 0.125681 1.29839i
\(207\) 0 0
\(208\) 13550.5 + 5506.51i 0.313204 + 0.127277i
\(209\) 32720.1 0.749070
\(210\) 0 0
\(211\) 23061.3i 0.517987i −0.965879 0.258993i \(-0.916609\pi\)
0.965879 0.258993i \(-0.0833908\pi\)
\(212\) −51330.9 10031.4i −1.14211 0.223197i
\(213\) 0 0
\(214\) −5677.49 + 58653.5i −0.123973 + 1.28076i
\(215\) 1475.89i 0.0319285i
\(216\) 0 0
\(217\) −64303.6 −1.36558
\(218\) −14114.8 1366.27i −0.297003 0.0287490i
\(219\) 0 0
\(220\) 7510.99 38434.1i 0.155186 0.794092i
\(221\) −16677.9 −0.341474
\(222\) 0 0
\(223\) 59739.3i 1.20130i −0.799514 0.600648i \(-0.794909\pi\)
0.799514 0.600648i \(-0.205091\pi\)
\(224\) 39016.7 74491.9i 0.777597 1.48461i
\(225\) 0 0
\(226\) −49656.0 4806.56i −0.972198 0.0941060i
\(227\) 33998.0i 0.659784i −0.944019 0.329892i \(-0.892988\pi\)
0.944019 0.329892i \(-0.107012\pi\)
\(228\) 0 0
\(229\) 14052.1 0.267959 0.133980 0.990984i \(-0.457224\pi\)
0.133980 + 0.990984i \(0.457224\pi\)
\(230\) 8639.33 89251.9i 0.163314 1.68718i
\(231\) 0 0
\(232\) −64402.4 19182.7i −1.19654 0.356397i
\(233\) −9622.25 −0.177241 −0.0886206 0.996065i \(-0.528246\pi\)
−0.0886206 + 0.996065i \(0.528246\pi\)
\(234\) 0 0
\(235\) 79733.4i 1.44379i
\(236\) 2662.05 13621.8i 0.0477961 0.244575i
\(237\) 0 0
\(238\) −9238.21 + 95438.9i −0.163092 + 1.68489i
\(239\) 28426.1i 0.497647i 0.968549 + 0.248824i \(0.0800439\pi\)
−0.968549 + 0.248824i \(0.919956\pi\)
\(240\) 0 0
\(241\) −9489.78 −0.163389 −0.0816943 0.996657i \(-0.526033\pi\)
−0.0816943 + 0.996657i \(0.526033\pi\)
\(242\) −12447.6 1204.90i −0.212548 0.0205740i
\(243\) 0 0
\(244\) 94766.3 + 18519.7i 1.59175 + 0.311068i
\(245\) −99055.4 −1.65024
\(246\) 0 0
\(247\) 17421.8i 0.285562i
\(248\) 14305.9 48029.3i 0.232601 0.780914i
\(249\) 0 0
\(250\) 66269.3 + 6414.68i 1.06031 + 0.102635i
\(251\) 29529.8i 0.468720i 0.972150 + 0.234360i \(0.0752994\pi\)
−0.972150 + 0.234360i \(0.924701\pi\)
\(252\) 0 0
\(253\) 105462. 1.64761
\(254\) −386.185 + 3989.63i −0.00598588 + 0.0618394i
\(255\) 0 0
\(256\) 46958.9 + 45714.6i 0.716536 + 0.697550i
\(257\) 14174.7 0.214609 0.107304 0.994226i \(-0.465778\pi\)
0.107304 + 0.994226i \(0.465778\pi\)
\(258\) 0 0
\(259\) 115330.i 1.71927i
\(260\) 20464.2 + 3999.23i 0.302726 + 0.0591603i
\(261\) 0 0
\(262\) −12929.7 + 133575.i −0.188358 + 1.94591i
\(263\) 106157.i 1.53475i 0.641197 + 0.767377i \(0.278438\pi\)
−0.641197 + 0.767377i \(0.721562\pi\)
\(264\) 0 0
\(265\) −74560.5 −1.06174
\(266\) 99695.9 + 9650.29i 1.40901 + 0.136388i
\(267\) 0 0
\(268\) 10499.9 53728.3i 0.146189 0.748055i
\(269\) 57391.1 0.793122 0.396561 0.918008i \(-0.370204\pi\)
0.396561 + 0.918008i \(0.370204\pi\)
\(270\) 0 0
\(271\) 22027.2i 0.299930i −0.988691 0.149965i \(-0.952084\pi\)
0.988691 0.149965i \(-0.0479161\pi\)
\(272\) −69229.4 28132.8i −0.935735 0.380255i
\(273\) 0 0
\(274\) −78436.3 7592.41i −1.04476 0.101130i
\(275\) 11238.9i 0.148613i
\(276\) 0 0
\(277\) 30261.0 0.394388 0.197194 0.980364i \(-0.436817\pi\)
0.197194 + 0.980364i \(0.436817\pi\)
\(278\) −4869.15 + 50302.6i −0.0630034 + 0.650880i
\(279\) 0 0
\(280\) 34221.0 114891.i 0.436492 1.46544i
\(281\) 30448.5 0.385615 0.192807 0.981237i \(-0.438241\pi\)
0.192807 + 0.981237i \(0.438241\pi\)
\(282\) 0 0
\(283\) 102769.i 1.28318i 0.767046 + 0.641592i \(0.221726\pi\)
−0.767046 + 0.641592i \(0.778274\pi\)
\(284\) −9785.25 + 50071.5i −0.121321 + 0.620803i
\(285\) 0 0
\(286\) −2362.78 + 24409.6i −0.0288863 + 0.298421i
\(287\) 29843.6i 0.362316i
\(288\) 0 0
\(289\) 1686.57 0.0201934
\(290\) −95351.3 9229.73i −1.13378 0.109747i
\(291\) 0 0
\(292\) −67019.8 13097.4i −0.786027 0.153610i
\(293\) 40053.4 0.466557 0.233278 0.972410i \(-0.425055\pi\)
0.233278 + 0.972410i \(0.425055\pi\)
\(294\) 0 0
\(295\) 19786.4i 0.227364i
\(296\) −86141.7 25657.9i −0.983173 0.292845i
\(297\) 0 0
\(298\) −95771.3 9270.39i −1.07846 0.104392i
\(299\) 56153.1i 0.628104i
\(300\) 0 0
\(301\) 5313.68 0.0586492
\(302\) −11176.5 + 115463.i −0.122544 + 1.26598i
\(303\) 0 0
\(304\) −29387.7 + 72317.4i −0.317993 + 0.782520i
\(305\) 137653. 1.47974
\(306\) 0 0
\(307\) 17196.5i 0.182458i 0.995830 + 0.0912291i \(0.0290796\pi\)
−0.995830 + 0.0912291i \(0.970920\pi\)
\(308\) 138374. + 27041.9i 1.45866 + 0.285060i
\(309\) 0 0
\(310\) 6883.25 71110.0i 0.0716259 0.739958i
\(311\) 135448.i 1.40039i −0.713949 0.700197i \(-0.753095\pi\)
0.713949 0.700197i \(-0.246905\pi\)
\(312\) 0 0
\(313\) −29263.8 −0.298705 −0.149352 0.988784i \(-0.547719\pi\)
−0.149352 + 0.988784i \(0.547719\pi\)
\(314\) −44365.3 4294.44i −0.449971 0.0435559i
\(315\) 0 0
\(316\) 23109.0 118250.i 0.231424 1.18420i
\(317\) −58389.3 −0.581051 −0.290526 0.956867i \(-0.593830\pi\)
−0.290526 + 0.956867i \(0.593830\pi\)
\(318\) 0 0
\(319\) 112669.i 1.10719i
\(320\) 78200.3 + 51120.3i 0.763674 + 0.499222i
\(321\) 0 0
\(322\) 321334. + 31104.2i 3.09917 + 0.299991i
\(323\) 89008.3i 0.853150i
\(324\) 0 0
\(325\) −5984.14 −0.0566546
\(326\) 1237.92 12788.8i 0.0116481 0.120336i
\(327\) 0 0
\(328\) −22290.6 6639.41i −0.207193 0.0617137i
\(329\) −287065. −2.65209
\(330\) 0 0
\(331\) 92155.6i 0.841135i −0.907261 0.420568i \(-0.861831\pi\)
0.907261 0.420568i \(-0.138169\pi\)
\(332\) 1799.08 9205.98i 0.0163221 0.0835207i
\(333\) 0 0
\(334\) −8705.76 + 89938.1i −0.0780393 + 0.806215i
\(335\) 78042.8i 0.695414i
\(336\) 0 0
\(337\) −44787.4 −0.394363 −0.197182 0.980367i \(-0.563179\pi\)
−0.197182 + 0.980367i \(0.563179\pi\)
\(338\) 100716. + 9748.98i 0.881583 + 0.0853348i
\(339\) 0 0
\(340\) −104552. 20432.1i −0.904428 0.176748i
\(341\) 84024.8 0.722602
\(342\) 0 0
\(343\) 159459.i 1.35538i
\(344\) −1182.15 + 3968.86i −0.00998980 + 0.0335389i
\(345\) 0 0
\(346\) −82578.8 7993.39i −0.689789 0.0667696i
\(347\) 105966.i 0.880049i −0.897986 0.440024i \(-0.854970\pi\)
0.897986 0.440024i \(-0.145030\pi\)
\(348\) 0 0
\(349\) 66799.1 0.548428 0.274214 0.961669i \(-0.411582\pi\)
0.274214 + 0.961669i \(0.411582\pi\)
\(350\) −3314.73 + 34244.0i −0.0270590 + 0.279543i
\(351\) 0 0
\(352\) −50982.7 + 97337.8i −0.411469 + 0.785590i
\(353\) −37451.3 −0.300551 −0.150275 0.988644i \(-0.548016\pi\)
−0.150275 + 0.988644i \(0.548016\pi\)
\(354\) 0 0
\(355\) 72731.2i 0.577118i
\(356\) −90908.6 17765.8i −0.717307 0.140180i
\(357\) 0 0
\(358\) 14471.7 149506.i 0.112916 1.16652i
\(359\) 117783.i 0.913893i −0.889494 0.456947i \(-0.848943\pi\)
0.889494 0.456947i \(-0.151057\pi\)
\(360\) 0 0
\(361\) 37342.4 0.286542
\(362\) 151370. + 14652.2i 1.15511 + 0.111811i
\(363\) 0 0
\(364\) −14398.5 + 73677.6i −0.108671 + 0.556074i
\(365\) −97349.5 −0.730715
\(366\) 0 0
\(367\) 119975.i 0.890753i −0.895343 0.445376i \(-0.853070\pi\)
0.895343 0.445376i \(-0.146930\pi\)
\(368\) −94720.6 + 233089.i −0.699438 + 1.72118i
\(369\) 0 0
\(370\) −127537. 12345.3i −0.931610 0.0901772i
\(371\) 268441.i 1.95030i
\(372\) 0 0
\(373\) −261060. −1.87638 −0.938192 0.346114i \(-0.887501\pi\)
−0.938192 + 0.346114i \(0.887501\pi\)
\(374\) 12071.5 124709.i 0.0863012 0.891567i
\(375\) 0 0
\(376\) 63864.4 214413.i 0.451734 1.51661i
\(377\) 59990.6 0.422085
\(378\) 0 0
\(379\) 138313.i 0.962907i 0.876472 + 0.481454i \(0.159891\pi\)
−0.876472 + 0.481454i \(0.840109\pi\)
\(380\) −21343.5 + 109216.i −0.147808 + 0.756340i
\(381\) 0 0
\(382\) 2818.51 29117.7i 0.0193149 0.199540i
\(383\) 182153.i 1.24176i 0.783905 + 0.620880i \(0.213225\pi\)
−0.783905 + 0.620880i \(0.786775\pi\)
\(384\) 0 0
\(385\) 200995. 1.35602
\(386\) −242816. 23503.9i −1.62968 0.157748i
\(387\) 0 0
\(388\) 170185. + 33258.6i 1.13047 + 0.220922i
\(389\) 143024. 0.945171 0.472586 0.881285i \(-0.343321\pi\)
0.472586 + 0.881285i \(0.343321\pi\)
\(390\) 0 0
\(391\) 286886.i 1.87653i
\(392\) 266372. + 79340.8i 1.73347 + 0.516326i
\(393\) 0 0
\(394\) −55305.7 5353.43i −0.356268 0.0344858i
\(395\) 171764.i 1.10087i
\(396\) 0 0
\(397\) −55426.8 −0.351673 −0.175837 0.984419i \(-0.556263\pi\)
−0.175837 + 0.984419i \(0.556263\pi\)
\(398\) −16596.8 + 171459.i −0.104775 + 1.08242i
\(399\) 0 0
\(400\) −24839.9 10094.2i −0.155250 0.0630889i
\(401\) 70455.5 0.438154 0.219077 0.975708i \(-0.429695\pi\)
0.219077 + 0.975708i \(0.429695\pi\)
\(402\) 0 0
\(403\) 44739.1i 0.275472i
\(404\) −180630. 35299.6i −1.10669 0.216275i
\(405\) 0 0
\(406\) 33229.9 343294.i 0.201594 2.08264i
\(407\) 150700.i 0.909758i
\(408\) 0 0
\(409\) 157877. 0.943785 0.471892 0.881656i \(-0.343571\pi\)
0.471892 + 0.881656i \(0.343571\pi\)
\(410\) −33002.4 3194.54i −0.196326 0.0190038i
\(411\) 0 0
\(412\) −42468.6 + 217314.i −0.250192 + 1.28024i
\(413\) 71237.0 0.417643
\(414\) 0 0
\(415\) 13372.1i 0.0776434i
\(416\) −51827.6 27145.8i −0.299484 0.156861i
\(417\) 0 0
\(418\) −130272. 12609.9i −0.745585 0.0721705i
\(419\) 22310.6i 0.127082i −0.997979 0.0635409i \(-0.979761\pi\)
0.997979 0.0635409i \(-0.0202393\pi\)
\(420\) 0 0
\(421\) −106342. −0.599985 −0.299992 0.953942i \(-0.596984\pi\)
−0.299992 + 0.953942i \(0.596984\pi\)
\(422\) −8887.53 + 91816.0i −0.0499064 + 0.515577i
\(423\) 0 0
\(424\) 200502. + 59721.0i 1.11529 + 0.332197i
\(425\) 30573.0 0.169262
\(426\) 0 0
\(427\) 495592.i 2.71812i
\(428\) 45208.6 231334.i 0.246793 1.26285i
\(429\) 0 0
\(430\) −568.791 + 5876.12i −0.00307621 + 0.0317800i
\(431\) 270251.i 1.45483i 0.686197 + 0.727416i \(0.259279\pi\)
−0.686197 + 0.727416i \(0.740721\pi\)
\(432\) 0 0
\(433\) −115964. −0.618513 −0.309256 0.950979i \(-0.600080\pi\)
−0.309256 + 0.950979i \(0.600080\pi\)
\(434\) 256018. + 24781.8i 1.35922 + 0.131569i
\(435\) 0 0
\(436\) 55669.8 + 10879.3i 0.292851 + 0.0572306i
\(437\) −299683. −1.56928
\(438\) 0 0
\(439\) 285409.i 1.48095i 0.672087 + 0.740473i \(0.265398\pi\)
−0.672087 + 0.740473i \(0.734602\pi\)
\(440\) −44716.2 + 150126.i −0.230972 + 0.775446i
\(441\) 0 0
\(442\) 66401.3 + 6427.46i 0.339885 + 0.0328999i
\(443\) 269606.i 1.37380i 0.726753 + 0.686899i \(0.241028\pi\)
−0.726753 + 0.686899i \(0.758972\pi\)
\(444\) 0 0
\(445\) −132049. −0.666830
\(446\) −23022.8 + 237845.i −0.115741 + 1.19571i
\(447\) 0 0
\(448\) −184049. + 281545.i −0.917017 + 1.40279i
\(449\) −12218.4 −0.0606070 −0.0303035 0.999541i \(-0.509647\pi\)
−0.0303035 + 0.999541i \(0.509647\pi\)
\(450\) 0 0
\(451\) 38996.3i 0.191721i
\(452\) 195848. + 38273.6i 0.958608 + 0.187336i
\(453\) 0 0
\(454\) −13102.4 + 135359.i −0.0635681 + 0.656715i
\(455\) 107020.i 0.516943i
\(456\) 0 0
\(457\) 296484. 1.41961 0.709805 0.704398i \(-0.248783\pi\)
0.709805 + 0.704398i \(0.248783\pi\)
\(458\) −55946.8 5415.49i −0.266713 0.0258171i
\(459\) 0 0
\(460\) −68793.1 + 352017.i −0.325109 + 1.66360i
\(461\) −38233.3 −0.179904 −0.0899519 0.995946i \(-0.528671\pi\)
−0.0899519 + 0.995946i \(0.528671\pi\)
\(462\) 0 0
\(463\) 210426.i 0.981607i −0.871270 0.490804i \(-0.836703\pi\)
0.871270 0.490804i \(-0.163297\pi\)
\(464\) 249018. + 101194.i 1.15663 + 0.470022i
\(465\) 0 0
\(466\) 38309.9 + 3708.29i 0.176417 + 0.0170766i
\(467\) 58599.8i 0.268697i 0.990934 + 0.134348i \(0.0428941\pi\)
−0.990934 + 0.134348i \(0.957106\pi\)
\(468\) 0 0
\(469\) 280978. 1.27740
\(470\) 30728.2 317450.i 0.139105 1.43707i
\(471\) 0 0
\(472\) −15848.4 + 53207.9i −0.0711378 + 0.238832i
\(473\) −6943.32 −0.0310345
\(474\) 0 0
\(475\) 31936.7i 0.141548i
\(476\) 73561.9 376419.i 0.324668 1.66134i
\(477\) 0 0
\(478\) 10955.1 113175.i 0.0479467 0.495332i
\(479\) 123721.i 0.539227i 0.962969 + 0.269614i \(0.0868960\pi\)
−0.962969 + 0.269614i \(0.913104\pi\)
\(480\) 0 0
\(481\) 80240.6 0.346820
\(482\) 37782.5 + 3657.24i 0.162629 + 0.0157420i
\(483\) 0 0
\(484\) 49094.6 + 9594.33i 0.209577 + 0.0409566i
\(485\) 247202. 1.05092
\(486\) 0 0
\(487\) 39541.5i 0.166723i 0.996519 + 0.0833614i \(0.0265656\pi\)
−0.996519 + 0.0833614i \(0.973434\pi\)
\(488\) −370164. 110256.i −1.55437 0.462981i
\(489\) 0 0
\(490\) 394378. + 38174.7i 1.64256 + 0.158995i
\(491\) 97311.7i 0.403647i −0.979422 0.201824i \(-0.935313\pi\)
0.979422 0.201824i \(-0.0646868\pi\)
\(492\) 0 0
\(493\) −306492. −1.26103
\(494\) 6714.16 69363.2i 0.0275130 0.284233i
\(495\) 0 0
\(496\) −75467.2 + 185710.i −0.306757 + 0.754870i
\(497\) −261855. −1.06010
\(498\) 0 0
\(499\) 217620.i 0.873974i 0.899468 + 0.436987i \(0.143954\pi\)
−0.899468 + 0.436987i \(0.856046\pi\)
\(500\) −261372. 51078.7i −1.04549 0.204315i
\(501\) 0 0
\(502\) 11380.4 117570.i 0.0451597 0.466539i
\(503\) 190305.i 0.752169i −0.926585 0.376084i \(-0.877270\pi\)
0.926585 0.376084i \(-0.122730\pi\)
\(504\) 0 0
\(505\) −262373. −1.02881
\(506\) −419884. 40643.6i −1.63994 0.158742i
\(507\) 0 0
\(508\) 3075.11 15735.4i 0.0119161 0.0609750i
\(509\) 100460. 0.387755 0.193878 0.981026i \(-0.437894\pi\)
0.193878 + 0.981026i \(0.437894\pi\)
\(510\) 0 0
\(511\) 350488.i 1.34224i
\(512\) −169344. 200105.i −0.645996 0.763341i
\(513\) 0 0
\(514\) −56435.1 5462.75i −0.213611 0.0206769i
\(515\) 315658.i 1.19015i
\(516\) 0 0
\(517\) 375104. 1.40337
\(518\) 44446.7 459174.i 0.165646 1.71127i
\(519\) 0 0
\(520\) −79934.9 23809.2i −0.295617 0.0880517i
\(521\) 417246. 1.53715 0.768575 0.639759i \(-0.220966\pi\)
0.768575 + 0.639759i \(0.220966\pi\)
\(522\) 0 0
\(523\) 246542.i 0.901339i 0.892691 + 0.450669i \(0.148815\pi\)
−0.892691 + 0.450669i \(0.851185\pi\)
\(524\) 102956. 526831.i 0.374964 1.91871i
\(525\) 0 0
\(526\) 40911.7 422654.i 0.147869 1.52761i
\(527\) 228572.i 0.823004i
\(528\) 0 0
\(529\) −686081. −2.45168
\(530\) 296855. + 28734.7i 1.05680 + 0.102295i
\(531\) 0 0
\(532\) −393209. 76843.1i −1.38931 0.271507i
\(533\) 20763.6 0.0730883
\(534\) 0 0
\(535\) 336024.i 1.17399i
\(536\) −62510.3 + 209867.i −0.217581 + 0.730490i
\(537\) 0 0
\(538\) −228496. 22117.8i −0.789432 0.0764148i
\(539\) 466004.i 1.60403i
\(540\) 0 0
\(541\) 65384.7 0.223399 0.111700 0.993742i \(-0.464371\pi\)
0.111700 + 0.993742i \(0.464371\pi\)
\(542\) −8489.00 + 87698.8i −0.0288973 + 0.298535i
\(543\) 0 0
\(544\) 264787. + 138688.i 0.894745 + 0.468641i
\(545\) 80863.1 0.272243
\(546\) 0 0
\(547\) 238533.i 0.797213i 0.917122 + 0.398607i \(0.130506\pi\)
−0.917122 + 0.398607i \(0.869494\pi\)
\(548\) 309360. + 60456.7i 1.03016 + 0.201318i
\(549\) 0 0
\(550\) 4331.32 44746.3i 0.0143184 0.147922i
\(551\) 320163.i 1.05455i
\(552\) 0 0
\(553\) 618402. 2.02218
\(554\) −120481. 11662.2i −0.392554 0.0379981i
\(555\) 0 0
\(556\) 38772.0 198398.i 0.125421 0.641782i
\(557\) −412118. −1.32835 −0.664173 0.747579i \(-0.731216\pi\)
−0.664173 + 0.747579i \(0.731216\pi\)
\(558\) 0 0
\(559\) 3696.98i 0.0118310i
\(560\) −180525. + 444237.i −0.575653 + 1.41657i
\(561\) 0 0
\(562\) −121227. 11734.5i −0.383821 0.0371528i
\(563\) 451490.i 1.42440i 0.701978 + 0.712199i \(0.252301\pi\)
−0.701978 + 0.712199i \(0.747699\pi\)
\(564\) 0 0
\(565\) 284478. 0.891151
\(566\) 39605.8 409163.i 0.123631 1.27721i
\(567\) 0 0
\(568\) 58255.8 195583.i 0.180569 0.606226i
\(569\) −125491. −0.387603 −0.193801 0.981041i \(-0.562082\pi\)
−0.193801 + 0.981041i \(0.562082\pi\)
\(570\) 0 0
\(571\) 295508.i 0.906352i −0.891421 0.453176i \(-0.850291\pi\)
0.891421 0.453176i \(-0.149709\pi\)
\(572\) 18814.3 96273.7i 0.0575038 0.294249i
\(573\) 0 0
\(574\) 11501.3 118819.i 0.0349080 0.360630i
\(575\) 102937.i 0.311339i
\(576\) 0 0
\(577\) −169123. −0.507986 −0.253993 0.967206i \(-0.581744\pi\)
−0.253993 + 0.967206i \(0.581744\pi\)
\(578\) −6714.89 649.983i −0.0200994 0.00194557i
\(579\) 0 0
\(580\) 376074. + 73494.4i 1.11794 + 0.218473i
\(581\) 48143.8 0.142622
\(582\) 0 0
\(583\) 350769.i 1.03201i
\(584\) 261785. + 77974.4i 0.767571 + 0.228626i
\(585\) 0 0
\(586\) −159468. 15436.1i −0.464386 0.0449513i
\(587\) 287012.i 0.832959i −0.909145 0.416480i \(-0.863264\pi\)
0.909145 0.416480i \(-0.136736\pi\)
\(588\) 0 0
\(589\) −238768. −0.688248
\(590\) −7625.41 + 78777.2i −0.0219058 + 0.226306i
\(591\) 0 0
\(592\) 333075. + 135352.i 0.950384 + 0.386208i
\(593\) −275747. −0.784155 −0.392078 0.919932i \(-0.628244\pi\)
−0.392078 + 0.919932i \(0.628244\pi\)
\(594\) 0 0
\(595\) 546767.i 1.54443i
\(596\) 377730. + 73818.1i 1.06338 + 0.207812i
\(597\) 0 0
\(598\) 21640.7 223567.i 0.0605158 0.625182i
\(599\) 498296.i 1.38878i 0.719598 + 0.694391i \(0.244326\pi\)
−0.719598 + 0.694391i \(0.755674\pi\)
\(600\) 0 0
\(601\) −382620. −1.05930 −0.529650 0.848216i \(-0.677677\pi\)
−0.529650 + 0.848216i \(0.677677\pi\)
\(602\) −21155.8 2047.82i −0.0583764 0.00565067i
\(603\) 0 0
\(604\) 88995.9 455395.i 0.243947 1.24829i
\(605\) 71312.2 0.194829
\(606\) 0 0
\(607\) 11197.4i 0.0303907i 0.999885 + 0.0151954i \(0.00483702\pi\)
−0.999885 + 0.0151954i \(0.995163\pi\)
\(608\) 144874. 276598.i 0.391907 0.748242i
\(609\) 0 0
\(610\) −548049. 53049.6i −1.47285 0.142568i
\(611\) 199725.i 0.534994i
\(612\) 0 0
\(613\) 289927. 0.771558 0.385779 0.922591i \(-0.373933\pi\)
0.385779 + 0.922591i \(0.373933\pi\)
\(614\) 6627.32 68466.0i 0.0175793 0.181609i
\(615\) 0 0
\(616\) −540501. 160992.i −1.42441 0.424271i
\(617\) 477462. 1.25420 0.627102 0.778937i \(-0.284241\pi\)
0.627102 + 0.778937i \(0.284241\pi\)
\(618\) 0 0
\(619\) 254686.i 0.664698i −0.943156 0.332349i \(-0.892159\pi\)
0.943156 0.332349i \(-0.107841\pi\)
\(620\) −54809.8 + 280464.i −0.142585 + 0.729615i
\(621\) 0 0
\(622\) −52199.8 + 539270.i −0.134924 + 1.39388i
\(623\) 475417.i 1.22489i
\(624\) 0 0
\(625\) −314195. −0.804339
\(626\) 116511. + 11277.9i 0.297315 + 0.0287793i
\(627\) 0 0
\(628\) 174981. + 34195.7i 0.443681 + 0.0867065i
\(629\) −409949. −1.03617
\(630\) 0 0
\(631\) 522734.i 1.31287i −0.754383 0.656435i \(-0.772064\pi\)
0.754383 0.656435i \(-0.227936\pi\)
\(632\) −137578. + 461893.i −0.344441 + 1.15640i
\(633\) 0 0
\(634\) 232471. + 22502.5i 0.578348 + 0.0559825i
\(635\) 22856.5i 0.0566842i
\(636\) 0 0
\(637\) −248124. −0.611492
\(638\) −43421.1 + 448578.i −0.106674 + 1.10204i
\(639\) 0 0
\(640\) −291645. 233667.i −0.712023 0.570477i
\(641\) 399966. 0.973434 0.486717 0.873560i \(-0.338194\pi\)
0.486717 + 0.873560i \(0.338194\pi\)
\(642\) 0 0
\(643\) 95576.4i 0.231169i −0.993298 0.115584i \(-0.963126\pi\)
0.993298 0.115584i \(-0.0368740\pi\)
\(644\) −1.26737e6 247676.i −3.05585 0.597190i
\(645\) 0 0
\(646\) −34302.7 + 354377.i −0.0821983 + 0.849181i
\(647\) 310762.i 0.742367i −0.928560 0.371184i \(-0.878952\pi\)
0.928560 0.371184i \(-0.121048\pi\)
\(648\) 0 0
\(649\) −93084.5 −0.220998
\(650\) 23825.2 + 2306.21i 0.0563910 + 0.00545849i
\(651\) 0 0
\(652\) −9857.28 + 50440.1i −0.0231879 + 0.118654i
\(653\) 648837. 1.52163 0.760815 0.648969i \(-0.224799\pi\)
0.760815 + 0.648969i \(0.224799\pi\)
\(654\) 0 0
\(655\) 765246.i 1.78369i
\(656\) 86188.8 + 35024.6i 0.200283 + 0.0813890i
\(657\) 0 0
\(658\) 1.14292e6 + 110631.i 2.63975 + 0.255520i
\(659\) 149570.i 0.344408i −0.985061 0.172204i \(-0.944911\pi\)
0.985061 0.172204i \(-0.0550889\pi\)
\(660\) 0 0
\(661\) 170849. 0.391029 0.195515 0.980701i \(-0.437362\pi\)
0.195515 + 0.980701i \(0.437362\pi\)
\(662\) −35515.6 + 366907.i −0.0810407 + 0.837222i
\(663\) 0 0
\(664\) −10710.7 + 35959.3i −0.0242931 + 0.0815596i
\(665\) −571155. −1.29155
\(666\) 0 0
\(667\) 1.03193e6i 2.31953i
\(668\) 69322.0 354724.i 0.155353 0.794945i
\(669\) 0 0
\(670\) −30076.7 + 310719.i −0.0670010 + 0.692179i
\(671\) 647584.i 1.43830i
\(672\) 0 0
\(673\) 782980. 1.72870 0.864351 0.502888i \(-0.167729\pi\)
0.864351 + 0.502888i \(0.167729\pi\)
\(674\) 178316. + 17260.5i 0.392528 + 0.0379956i
\(675\) 0 0
\(676\) −397231. 77629.0i −0.869260 0.169876i
\(677\) 458234. 0.999792 0.499896 0.866085i \(-0.333372\pi\)
0.499896 + 0.866085i \(0.333372\pi\)
\(678\) 0 0
\(679\) 890005.i 1.93042i
\(680\) 408388. + 121641.i 0.883192 + 0.263065i
\(681\) 0 0
\(682\) −334536. 32382.1i −0.719240 0.0696204i
\(683\) 444767.i 0.953434i −0.879057 0.476717i \(-0.841827\pi\)
0.879057 0.476717i \(-0.158173\pi\)
\(684\) 0 0
\(685\) 449360. 0.957663
\(686\) −61453.4 + 634868.i −0.130586 + 1.34907i
\(687\) 0 0
\(688\) 6236.16 15346.0i 0.0131747 0.0324204i
\(689\) −186767. −0.393425
\(690\) 0 0
\(691\) 373248.i 0.781702i 0.920454 + 0.390851i \(0.127819\pi\)
−0.920454 + 0.390851i \(0.872181\pi\)
\(692\) 325698. + 63649.6i 0.680147 + 0.132918i
\(693\) 0 0
\(694\) −40837.9 + 421891.i −0.0847899 + 0.875955i
\(695\) 288182.i 0.596620i
\(696\) 0 0
\(697\) −106081. −0.218360
\(698\) −265953. 25743.5i −0.545877 0.0528393i
\(699\) 0 0
\(700\) 26394.4 135061.i 0.0538662 0.275636i
\(701\) −699890. −1.42427 −0.712137 0.702041i \(-0.752273\pi\)
−0.712137 + 0.702041i \(0.752273\pi\)
\(702\) 0 0
\(703\) 428235.i 0.866507i
\(704\) 240495. 367892.i 0.485244 0.742292i
\(705\) 0 0
\(706\) 149108. + 14433.3i 0.299153 + 0.0289571i
\(707\) 944624.i 1.88982i
\(708\) 0 0
\(709\) 305897. 0.608531 0.304265 0.952587i \(-0.401589\pi\)
0.304265 + 0.952587i \(0.401589\pi\)
\(710\) 28029.7 289571.i 0.0556035 0.574433i
\(711\) 0 0
\(712\) 355096. + 105768.i 0.700464 + 0.208638i
\(713\) −769583. −1.51383
\(714\) 0 0
\(715\) 139842.i 0.273543i
\(716\) −115235. + 589664.i −0.224781 + 1.15021i
\(717\) 0 0
\(718\) −45392.3 + 468942.i −0.0880507 + 0.909641i
\(719\) 265534.i 0.513644i 0.966459 + 0.256822i \(0.0826755\pi\)
−0.966459 + 0.256822i \(0.917325\pi\)
\(720\) 0 0
\(721\) −1.13647e6 −2.18618
\(722\) −148675. 14391.3i −0.285209 0.0276074i
\(723\) 0 0
\(724\) −597015. 116672.i −1.13896 0.222582i
\(725\) −109971. −0.209220
\(726\) 0 0
\(727\) 901047.i 1.70482i 0.522874 + 0.852410i \(0.324860\pi\)
−0.522874 + 0.852410i \(0.675140\pi\)
\(728\) 85720.4 287790.i 0.161741 0.543017i
\(729\) 0 0
\(730\) 387586. + 37517.3i 0.727315 + 0.0704021i
\(731\) 18887.9i 0.0353466i
\(732\) 0 0
\(733\) −887881. −1.65252 −0.826261 0.563288i \(-0.809536\pi\)
−0.826261 + 0.563288i \(0.809536\pi\)
\(734\) −46236.7 + 477666.i −0.0858212 + 0.886609i
\(735\) 0 0
\(736\) 466950. 891516.i 0.862014 1.64579i
\(737\) −367151. −0.675943
\(738\) 0 0
\(739\) 401381.i 0.734966i −0.930030 0.367483i \(-0.880220\pi\)
0.930030 0.367483i \(-0.119780\pi\)
\(740\) 503019. + 98302.6i 0.918588 + 0.179515i
\(741\) 0 0
\(742\) −103454. + 1.06877e6i −0.187905 + 1.94122i
\(743\) 314050.i 0.568880i −0.958694 0.284440i \(-0.908192\pi\)
0.958694 0.284440i \(-0.0918077\pi\)
\(744\) 0 0
\(745\) 548671. 0.988552
\(746\) 1.03938e6 + 100609.i 1.86766 + 0.180784i
\(747\) 0 0
\(748\) −96122.5 + 491863.i −0.171799 + 0.879105i
\(749\) 1.20979e6 2.15648
\(750\) 0 0
\(751\) 331743.i 0.588195i 0.955775 + 0.294098i \(0.0950191\pi\)
−0.955775 + 0.294098i \(0.904981\pi\)
\(752\) −336901. + 829049.i −0.595754 + 1.46604i
\(753\) 0 0
\(754\) −238846. 23119.6i −0.420122 0.0406666i
\(755\) 661483.i 1.16045i
\(756\) 0 0
\(757\) 300610. 0.524581 0.262290 0.964989i \(-0.415522\pi\)
0.262290 + 0.964989i \(0.415522\pi\)
\(758\) 53304.1 550678.i 0.0927731 0.958428i
\(759\) 0 0
\(760\) 127067. 426604.i 0.219991 0.738581i
\(761\) 78374.5 0.135334 0.0676668 0.997708i \(-0.478445\pi\)
0.0676668 + 0.997708i \(0.478445\pi\)
\(762\) 0 0
\(763\) 291132.i 0.500081i
\(764\) −22443.2 + 114843.i −0.0384501 + 0.196751i
\(765\) 0 0
\(766\) 70199.3 725221.i 0.119640 1.23598i
\(767\) 49562.9i 0.0842493i
\(768\) 0 0
\(769\) 987499. 1.66988 0.834938 0.550345i \(-0.185504\pi\)
0.834938 + 0.550345i \(0.185504\pi\)
\(770\) −800242. 77461.1i −1.34971 0.130648i
\(771\) 0 0
\(772\) 957687. + 187156.i 1.60690 + 0.314029i
\(773\) −622600. −1.04196 −0.520979 0.853569i \(-0.674433\pi\)
−0.520979 + 0.853569i \(0.674433\pi\)
\(774\) 0 0
\(775\) 82013.1i 0.136546i
\(776\) −664757. 198003.i −1.10393 0.328812i
\(777\) 0 0
\(778\) −569436. 55119.8i −0.940774 0.0910643i
\(779\) 110813.i 0.182606i
\(780\) 0 0
\(781\) 342163. 0.560958
\(782\) −110562. + 1.14221e6i −0.180798 + 1.86780i
\(783\) 0 0
\(784\) −1.02995e6 418543.i −1.67566 0.680939i
\(785\) 254168. 0.412459
\(786\) 0 0
\(787\) 1.09638e6i 1.77016i −0.465437 0.885081i \(-0.654103\pi\)
0.465437 0.885081i \(-0.345897\pi\)
\(788