Properties

Label 108.5.d.b.55.4
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 55.4
Root \(-1.12787 + 1.95353i\) 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.55.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.49052 + 1.95353i) q^{2} +(8.36746 - 13.6377i) q^{4} -47.1174 q^{5} +67.4003i q^{7} +(-2.56528 + 63.9486i) q^{8} +O(q^{10})\) \(q+(-3.49052 + 1.95353i) q^{2} +(8.36746 - 13.6377i) q^{4} -47.1174 q^{5} +67.4003i q^{7} +(-2.56528 + 63.9486i) q^{8} +(164.464 - 92.0451i) q^{10} -69.3981i q^{11} +3.28838 q^{13} +(-131.668 - 235.262i) q^{14} +(-115.971 - 228.225i) q^{16} +116.780 q^{17} -513.525i q^{19} +(-394.253 + 642.571i) q^{20} +(135.571 + 242.236i) q^{22} -134.254i q^{23} +1595.05 q^{25} +(-11.4782 + 6.42394i) q^{26} +(919.182 + 563.970i) q^{28} +772.602 q^{29} -1069.97i q^{31} +(850.643 + 570.072i) q^{32} +(-407.623 + 228.133i) q^{34} -3175.73i q^{35} -1034.09 q^{37} +(1003.19 + 1792.47i) q^{38} +(120.869 - 3013.09i) q^{40} +2272.62 q^{41} +2523.25i q^{43} +(-946.428 - 580.686i) q^{44} +(262.270 + 468.618i) q^{46} +694.871i q^{47} -2141.80 q^{49} +(-5567.55 + 3115.97i) q^{50} +(27.5154 - 44.8458i) q^{52} -1166.03 q^{53} +3269.86i q^{55} +(-4310.15 - 172.901i) q^{56} +(-2696.78 + 1509.30i) q^{58} -5539.90i q^{59} -3204.11 q^{61} +(2090.21 + 3734.75i) q^{62} +(-4082.84 - 328.092i) q^{64} -154.940 q^{65} -5366.14i q^{67} +(977.152 - 1592.60i) q^{68} +(6203.87 + 11084.9i) q^{70} +166.225i q^{71} +5085.51 q^{73} +(3609.51 - 2020.12i) q^{74} +(-7003.28 - 4296.90i) q^{76} +4677.46 q^{77} +724.474i q^{79} +(5464.26 + 10753.4i) q^{80} +(-7932.63 + 4439.62i) q^{82} -8153.13i q^{83} -5502.37 q^{85} +(-4929.24 - 8807.46i) q^{86} +(4437.91 + 178.026i) q^{88} -6963.40 q^{89} +221.638i q^{91} +(-1830.92 - 1123.37i) q^{92} +(-1357.45 - 2425.46i) q^{94} +24196.0i q^{95} -278.895 q^{97} +(7476.00 - 4184.07i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 28q^{4} + O(q^{10}) \) \( 16q + 28q^{4} + 176q^{10} + 176q^{13} + 88q^{16} + 384q^{22} + 2736q^{25} + 1812q^{28} + 1520q^{34} + 80q^{37} - 688q^{40} - 1824q^{46} - 7904q^{49} - 5236q^{52} - 11584q^{58} - 1648q^{61} + 5056q^{64} + 26688q^{70} + 80q^{73} - 8388q^{76} - 38464q^{82} - 16832q^{85} - 29520q^{88} - 4512q^{94} + 14864q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.49052 + 1.95353i −0.872630 + 0.488382i
\(3\) 0 0
\(4\) 8.36746 13.6377i 0.522967 0.852353i
\(5\) −47.1174 −1.88470 −0.942348 0.334634i \(-0.891387\pi\)
−0.942348 + 0.334634i \(0.891387\pi\)
\(6\) 0 0
\(7\) 67.4003i 1.37552i 0.725940 + 0.687758i \(0.241405\pi\)
−0.725940 + 0.687758i \(0.758595\pi\)
\(8\) −2.56528 + 63.9486i −0.0400825 + 0.999196i
\(9\) 0 0
\(10\) 164.464 92.0451i 1.64464 0.920451i
\(11\) 69.3981i 0.573538i −0.958000 0.286769i \(-0.907419\pi\)
0.958000 0.286769i \(-0.0925813\pi\)
\(12\) 0 0
\(13\) 3.28838 0.0194579 0.00972893 0.999953i \(-0.496903\pi\)
0.00972893 + 0.999953i \(0.496903\pi\)
\(14\) −131.668 235.262i −0.671777 1.20032i
\(15\) 0 0
\(16\) −115.971 228.225i −0.453012 0.891504i
\(17\) 116.780 0.404083 0.202041 0.979377i \(-0.435242\pi\)
0.202041 + 0.979377i \(0.435242\pi\)
\(18\) 0 0
\(19\) 513.525i 1.42251i −0.702935 0.711254i \(-0.748128\pi\)
0.702935 0.711254i \(-0.251872\pi\)
\(20\) −394.253 + 642.571i −0.985633 + 1.60643i
\(21\) 0 0
\(22\) 135.571 + 242.236i 0.280106 + 0.500487i
\(23\) 134.254i 0.253789i −0.991916 0.126895i \(-0.959499\pi\)
0.991916 0.126895i \(-0.0405010\pi\)
\(24\) 0 0
\(25\) 1595.05 2.55208
\(26\) −11.4782 + 6.42394i −0.0169795 + 0.00950287i
\(27\) 0 0
\(28\) 919.182 + 563.970i 1.17243 + 0.719349i
\(29\) 772.602 0.918671 0.459335 0.888263i \(-0.348088\pi\)
0.459335 + 0.888263i \(0.348088\pi\)
\(30\) 0 0
\(31\) 1069.97i 1.11339i −0.830717 0.556695i \(-0.812069\pi\)
0.830717 0.556695i \(-0.187931\pi\)
\(32\) 850.643 + 570.072i 0.830706 + 0.556711i
\(33\) 0 0
\(34\) −407.623 + 228.133i −0.352615 + 0.197347i
\(35\) 3175.73i 2.59243i
\(36\) 0 0
\(37\) −1034.09 −0.755362 −0.377681 0.925936i \(-0.623278\pi\)
−0.377681 + 0.925936i \(0.623278\pi\)
\(38\) 1003.19 + 1792.47i 0.694727 + 1.24132i
\(39\) 0 0
\(40\) 120.869 3013.09i 0.0755434 1.88318i
\(41\) 2272.62 1.35195 0.675973 0.736927i \(-0.263724\pi\)
0.675973 + 0.736927i \(0.263724\pi\)
\(42\) 0 0
\(43\) 2523.25i 1.36466i 0.731046 + 0.682328i \(0.239033\pi\)
−0.731046 + 0.682328i \(0.760967\pi\)
\(44\) −946.428 580.686i −0.488857 0.299941i
\(45\) 0 0
\(46\) 262.270 + 468.618i 0.123946 + 0.221464i
\(47\) 694.871i 0.314564i 0.987554 + 0.157282i \(0.0502731\pi\)
−0.987554 + 0.157282i \(0.949727\pi\)
\(48\) 0 0
\(49\) −2141.80 −0.892045
\(50\) −5567.55 + 3115.97i −2.22702 + 1.24639i
\(51\) 0 0
\(52\) 27.5154 44.8458i 0.0101758 0.0165850i
\(53\) −1166.03 −0.415106 −0.207553 0.978224i \(-0.566550\pi\)
−0.207553 + 0.978224i \(0.566550\pi\)
\(54\) 0 0
\(55\) 3269.86i 1.08095i
\(56\) −4310.15 172.901i −1.37441 0.0551342i
\(57\) 0 0
\(58\) −2696.78 + 1509.30i −0.801660 + 0.448662i
\(59\) 5539.90i 1.59147i −0.605647 0.795733i \(-0.707086\pi\)
0.605647 0.795733i \(-0.292914\pi\)
\(60\) 0 0
\(61\) −3204.11 −0.861089 −0.430544 0.902569i \(-0.641678\pi\)
−0.430544 + 0.902569i \(0.641678\pi\)
\(62\) 2090.21 + 3734.75i 0.543760 + 0.971578i
\(63\) 0 0
\(64\) −4082.84 328.092i −0.996787 0.0801006i
\(65\) −154.940 −0.0366722
\(66\) 0 0
\(67\) 5366.14i 1.19540i −0.801721 0.597699i \(-0.796082\pi\)
0.801721 0.597699i \(-0.203918\pi\)
\(68\) 977.152 1592.60i 0.211322 0.344421i
\(69\) 0 0
\(70\) 6203.87 + 11084.9i 1.26610 + 2.26223i
\(71\) 166.225i 0.0329746i 0.999864 + 0.0164873i \(0.00524832\pi\)
−0.999864 + 0.0164873i \(0.994752\pi\)
\(72\) 0 0
\(73\) 5085.51 0.954309 0.477154 0.878819i \(-0.341668\pi\)
0.477154 + 0.878819i \(0.341668\pi\)
\(74\) 3609.51 2020.12i 0.659151 0.368905i
\(75\) 0 0
\(76\) −7003.28 4296.90i −1.21248 0.743924i
\(77\) 4677.46 0.788911
\(78\) 0 0
\(79\) 724.474i 0.116083i 0.998314 + 0.0580415i \(0.0184856\pi\)
−0.998314 + 0.0580415i \(0.981514\pi\)
\(80\) 5464.26 + 10753.4i 0.853790 + 1.68021i
\(81\) 0 0
\(82\) −7932.63 + 4439.62i −1.17975 + 0.660265i
\(83\) 8153.13i 1.18350i −0.806121 0.591750i \(-0.798437\pi\)
0.806121 0.591750i \(-0.201563\pi\)
\(84\) 0 0
\(85\) −5502.37 −0.761573
\(86\) −4929.24 8807.46i −0.666473 1.19084i
\(87\) 0 0
\(88\) 4437.91 + 178.026i 0.573077 + 0.0229889i
\(89\) −6963.40 −0.879107 −0.439553 0.898217i \(-0.644863\pi\)
−0.439553 + 0.898217i \(0.644863\pi\)
\(90\) 0 0
\(91\) 221.638i 0.0267646i
\(92\) −1830.92 1123.37i −0.216318 0.132723i
\(93\) 0 0
\(94\) −1357.45 2425.46i −0.153627 0.274498i
\(95\) 24196.0i 2.68099i
\(96\) 0 0
\(97\) −278.895 −0.0296413 −0.0148207 0.999890i \(-0.504718\pi\)
−0.0148207 + 0.999890i \(0.504718\pi\)
\(98\) 7476.00 4184.07i 0.778426 0.435659i
\(99\) 0 0
\(100\) 13346.5 21752.7i 1.33465 2.17527i
\(101\) 9308.10 0.912469 0.456235 0.889860i \(-0.349198\pi\)
0.456235 + 0.889860i \(0.349198\pi\)
\(102\) 0 0
\(103\) 3271.88i 0.308406i 0.988039 + 0.154203i \(0.0492810\pi\)
−0.988039 + 0.154203i \(0.950719\pi\)
\(104\) −8.43562 + 210.287i −0.000779921 + 0.0194422i
\(105\) 0 0
\(106\) 4070.06 2277.88i 0.362234 0.202730i
\(107\) 1845.07i 0.161156i −0.996748 0.0805778i \(-0.974323\pi\)
0.996748 0.0805778i \(-0.0256765\pi\)
\(108\) 0 0
\(109\) 6021.20 0.506793 0.253396 0.967363i \(-0.418452\pi\)
0.253396 + 0.967363i \(0.418452\pi\)
\(110\) −6387.76 11413.5i −0.527914 0.943266i
\(111\) 0 0
\(112\) 15382.4 7816.49i 1.22628 0.623126i
\(113\) 8841.22 0.692398 0.346199 0.938161i \(-0.387472\pi\)
0.346199 + 0.938161i \(0.387472\pi\)
\(114\) 0 0
\(115\) 6325.72i 0.478315i
\(116\) 6464.72 10536.5i 0.480434 0.783032i
\(117\) 0 0
\(118\) 10822.3 + 19337.1i 0.777243 + 1.38876i
\(119\) 7871.00i 0.555822i
\(120\) 0 0
\(121\) 9824.90 0.671054
\(122\) 11184.0 6259.32i 0.751412 0.420540i
\(123\) 0 0
\(124\) −14591.9 8952.92i −0.949002 0.582266i
\(125\) −45706.2 −2.92520
\(126\) 0 0
\(127\) 9165.05i 0.568234i −0.958790 0.284117i \(-0.908300\pi\)
0.958790 0.284117i \(-0.0917004\pi\)
\(128\) 14892.2 6830.72i 0.908946 0.416914i
\(129\) 0 0
\(130\) 540.821 302.679i 0.0320012 0.0179100i
\(131\) 16239.9i 0.946325i 0.880975 + 0.473162i \(0.156888\pi\)
−0.880975 + 0.473162i \(0.843112\pi\)
\(132\) 0 0
\(133\) 34611.7 1.95668
\(134\) 10482.9 + 18730.6i 0.583810 + 1.04314i
\(135\) 0 0
\(136\) −299.573 + 7467.91i −0.0161967 + 0.403758i
\(137\) −30410.5 −1.62025 −0.810125 0.586257i \(-0.800601\pi\)
−0.810125 + 0.586257i \(0.800601\pi\)
\(138\) 0 0
\(139\) 32689.0i 1.69189i −0.533269 0.845946i \(-0.679037\pi\)
0.533269 0.845946i \(-0.320963\pi\)
\(140\) −43309.5 26572.8i −2.20967 1.35575i
\(141\) 0 0
\(142\) −324.725 580.212i −0.0161042 0.0287747i
\(143\) 228.207i 0.0111598i
\(144\) 0 0
\(145\) −36403.0 −1.73141
\(146\) −17751.1 + 9934.68i −0.832759 + 0.466067i
\(147\) 0 0
\(148\) −8652.71 + 14102.6i −0.395029 + 0.643835i
\(149\) 13388.8 0.603073 0.301536 0.953455i \(-0.402501\pi\)
0.301536 + 0.953455i \(0.402501\pi\)
\(150\) 0 0
\(151\) 9106.99i 0.399412i −0.979856 0.199706i \(-0.936001\pi\)
0.979856 0.199706i \(-0.0639987\pi\)
\(152\) 32839.2 + 1317.34i 1.42136 + 0.0570177i
\(153\) 0 0
\(154\) −16326.8 + 9137.54i −0.688428 + 0.385290i
\(155\) 50414.1i 2.09840i
\(156\) 0 0
\(157\) 4555.18 0.184802 0.0924009 0.995722i \(-0.470546\pi\)
0.0924009 + 0.995722i \(0.470546\pi\)
\(158\) −1415.28 2528.79i −0.0566928 0.101298i
\(159\) 0 0
\(160\) −40080.1 26860.3i −1.56563 1.04923i
\(161\) 9048.79 0.349091
\(162\) 0 0
\(163\) 466.424i 0.0175552i −0.999961 0.00877760i \(-0.997206\pi\)
0.999961 0.00877760i \(-0.00279403\pi\)
\(164\) 19016.1 30993.2i 0.707022 1.15233i
\(165\) 0 0
\(166\) 15927.4 + 28458.7i 0.578000 + 1.03276i
\(167\) 30165.9i 1.08164i −0.841138 0.540821i \(-0.818114\pi\)
0.841138 0.540821i \(-0.181886\pi\)
\(168\) 0 0
\(169\) −28550.2 −0.999621
\(170\) 19206.1 10749.0i 0.664572 0.371938i
\(171\) 0 0
\(172\) 34411.2 + 21113.2i 1.16317 + 0.713670i
\(173\) 51017.1 1.70460 0.852302 0.523051i \(-0.175206\pi\)
0.852302 + 0.523051i \(0.175206\pi\)
\(174\) 0 0
\(175\) 107507.i 3.51043i
\(176\) −15838.4 + 8048.18i −0.511312 + 0.259820i
\(177\) 0 0
\(178\) 24305.9 13603.2i 0.767135 0.429340i
\(179\) 26293.5i 0.820622i −0.911946 0.410311i \(-0.865420\pi\)
0.911946 0.410311i \(-0.134580\pi\)
\(180\) 0 0
\(181\) 3132.04 0.0956026 0.0478013 0.998857i \(-0.484779\pi\)
0.0478013 + 0.998857i \(0.484779\pi\)
\(182\) −432.975 773.631i −0.0130713 0.0233556i
\(183\) 0 0
\(184\) 8585.38 + 344.401i 0.253585 + 0.0101725i
\(185\) 48723.6 1.42363
\(186\) 0 0
\(187\) 8104.31i 0.231757i
\(188\) 9476.41 + 5814.31i 0.268119 + 0.164506i
\(189\) 0 0
\(190\) −47267.5 84456.5i −1.30935 2.33952i
\(191\) 17160.1i 0.470384i −0.971949 0.235192i \(-0.924428\pi\)
0.971949 0.235192i \(-0.0755718\pi\)
\(192\) 0 0
\(193\) −16841.7 −0.452139 −0.226070 0.974111i \(-0.572588\pi\)
−0.226070 + 0.974111i \(0.572588\pi\)
\(194\) 973.490 544.829i 0.0258659 0.0144763i
\(195\) 0 0
\(196\) −17921.4 + 29209.1i −0.466510 + 0.760338i
\(197\) −67293.3 −1.73396 −0.866981 0.498342i \(-0.833942\pi\)
−0.866981 + 0.498342i \(0.833942\pi\)
\(198\) 0 0
\(199\) 13276.3i 0.335253i 0.985851 + 0.167626i \(0.0536102\pi\)
−0.985851 + 0.167626i \(0.946390\pi\)
\(200\) −4091.75 + 102001.i −0.102294 + 2.55003i
\(201\) 0 0
\(202\) −32490.1 + 18183.6i −0.796248 + 0.445633i
\(203\) 52073.6i 1.26365i
\(204\) 0 0
\(205\) −107080. −2.54801
\(206\) −6391.71 11420.6i −0.150620 0.269124i
\(207\) 0 0
\(208\) −381.357 750.491i −0.00881465 0.0173468i
\(209\) −35637.7 −0.815863
\(210\) 0 0
\(211\) 17830.2i 0.400489i −0.979746 0.200245i \(-0.935826\pi\)
0.979746 0.200245i \(-0.0641737\pi\)
\(212\) −9756.73 + 15901.9i −0.217086 + 0.353817i
\(213\) 0 0
\(214\) 3604.39 + 6440.26i 0.0787055 + 0.140629i
\(215\) 118889.i 2.57196i
\(216\) 0 0
\(217\) 72116.2 1.53149
\(218\) −21017.1 + 11762.6i −0.442242 + 0.247508i
\(219\) 0 0
\(220\) 44593.2 + 27360.4i 0.921347 + 0.565298i
\(221\) 384.017 0.00786259
\(222\) 0 0
\(223\) 68248.8i 1.37241i −0.727406 0.686207i \(-0.759274\pi\)
0.727406 0.686207i \(-0.240726\pi\)
\(224\) −38423.0 + 57333.6i −0.765765 + 1.14265i
\(225\) 0 0
\(226\) −30860.5 + 17271.6i −0.604207 + 0.338154i
\(227\) 56672.7i 1.09982i −0.835223 0.549911i \(-0.814662\pi\)
0.835223 0.549911i \(-0.185338\pi\)
\(228\) 0 0
\(229\) 65653.5 1.25195 0.625975 0.779843i \(-0.284701\pi\)
0.625975 + 0.779843i \(0.284701\pi\)
\(230\) −12357.5 22080.1i −0.233601 0.417392i
\(231\) 0 0
\(232\) −1981.94 + 49406.8i −0.0368226 + 0.917932i
\(233\) 55652.7 1.02512 0.512559 0.858652i \(-0.328697\pi\)
0.512559 + 0.858652i \(0.328697\pi\)
\(234\) 0 0
\(235\) 32740.5i 0.592857i
\(236\) −75551.2 46354.9i −1.35649 0.832284i
\(237\) 0 0
\(238\) −15376.2 27473.9i −0.271454 0.485027i
\(239\) 13031.8i 0.228144i −0.993472 0.114072i \(-0.963611\pi\)
0.993472 0.114072i \(-0.0363895\pi\)
\(240\) 0 0
\(241\) 57972.1 0.998124 0.499062 0.866566i \(-0.333678\pi\)
0.499062 + 0.866566i \(0.333678\pi\)
\(242\) −34294.0 + 19193.2i −0.585582 + 0.327730i
\(243\) 0 0
\(244\) −26810.3 + 43696.5i −0.450321 + 0.733952i
\(245\) 100916. 1.68123
\(246\) 0 0
\(247\) 1688.67i 0.0276790i
\(248\) 68422.9 + 2744.77i 1.11250 + 0.0446275i
\(249\) 0 0
\(250\) 159538. 89288.3i 2.55262 1.42861i
\(251\) 81292.8i 1.29034i 0.764038 + 0.645171i \(0.223214\pi\)
−0.764038 + 0.645171i \(0.776786\pi\)
\(252\) 0 0
\(253\) −9317.01 −0.145558
\(254\) 17904.2 + 31990.8i 0.277515 + 0.495858i
\(255\) 0 0
\(256\) −38637.4 + 52935.0i −0.589560 + 0.807724i
\(257\) −18818.7 −0.284920 −0.142460 0.989801i \(-0.545501\pi\)
−0.142460 + 0.989801i \(0.545501\pi\)
\(258\) 0 0
\(259\) 69698.0i 1.03901i
\(260\) −1296.45 + 2113.02i −0.0191783 + 0.0312576i
\(261\) 0 0
\(262\) −31725.0 56685.6i −0.462168 0.825791i
\(263\) 96169.6i 1.39036i −0.718837 0.695179i \(-0.755325\pi\)
0.718837 0.695179i \(-0.244675\pi\)
\(264\) 0 0
\(265\) 54940.4 0.782348
\(266\) −120813. + 67615.0i −1.70746 + 0.955608i
\(267\) 0 0
\(268\) −73181.5 44901.0i −1.01890 0.625153i
\(269\) 20853.4 0.288186 0.144093 0.989564i \(-0.453974\pi\)
0.144093 + 0.989564i \(0.453974\pi\)
\(270\) 0 0
\(271\) 101517.i 1.38230i 0.722712 + 0.691149i \(0.242895\pi\)
−0.722712 + 0.691149i \(0.757105\pi\)
\(272\) −13543.1 26652.1i −0.183054 0.360242i
\(273\) 0 0
\(274\) 106148. 59407.7i 1.41388 0.791301i
\(275\) 110693.i 1.46372i
\(276\) 0 0
\(277\) 53726.5 0.700212 0.350106 0.936710i \(-0.386146\pi\)
0.350106 + 0.936710i \(0.386146\pi\)
\(278\) 63858.9 + 114102.i 0.826289 + 1.47640i
\(279\) 0 0
\(280\) 203083. + 8146.64i 2.59035 + 0.103911i
\(281\) −99500.6 −1.26012 −0.630061 0.776545i \(-0.716970\pi\)
−0.630061 + 0.776545i \(0.716970\pi\)
\(282\) 0 0
\(283\) 69719.8i 0.870529i −0.900303 0.435265i \(-0.856655\pi\)
0.900303 0.435265i \(-0.143345\pi\)
\(284\) 2266.92 + 1390.88i 0.0281060 + 0.0172446i
\(285\) 0 0
\(286\) 445.809 + 796.563i 0.00545026 + 0.00973840i
\(287\) 153175.i 1.85962i
\(288\) 0 0
\(289\) −69883.5 −0.836717
\(290\) 127065. 71114.2i 1.51088 0.845592i
\(291\) 0 0
\(292\) 42552.8 69354.4i 0.499072 0.813408i
\(293\) −12440.0 −0.144905 −0.0724526 0.997372i \(-0.523083\pi\)
−0.0724526 + 0.997372i \(0.523083\pi\)
\(294\) 0 0
\(295\) 261025.i 2.99943i
\(296\) 2652.73 66128.6i 0.0302768 0.754755i
\(297\) 0 0
\(298\) −46733.9 + 26155.4i −0.526259 + 0.294530i
\(299\) 441.480i 0.00493819i
\(300\) 0 0
\(301\) −170068. −1.87711
\(302\) 17790.8 + 31788.1i 0.195065 + 0.348539i
\(303\) 0 0
\(304\) −117199. + 59554.1i −1.26817 + 0.644413i
\(305\) 150969. 1.62289
\(306\) 0 0
\(307\) 151986.i 1.61260i −0.591504 0.806302i \(-0.701466\pi\)
0.591504 0.806302i \(-0.298534\pi\)
\(308\) 39138.4 63789.5i 0.412574 0.672431i
\(309\) 0 0
\(310\) −98485.4 175972.i −1.02482 1.83113i
\(311\) 50086.5i 0.517845i −0.965898 0.258923i \(-0.916633\pi\)
0.965898 0.258923i \(-0.0833675\pi\)
\(312\) 0 0
\(313\) 61969.9 0.632546 0.316273 0.948668i \(-0.397568\pi\)
0.316273 + 0.948668i \(0.397568\pi\)
\(314\) −15900.0 + 8898.67i −0.161264 + 0.0902539i
\(315\) 0 0
\(316\) 9880.12 + 6062.01i 0.0989437 + 0.0607075i
\(317\) −80.9272 −0.000805334 −0.000402667 1.00000i \(-0.500128\pi\)
−0.000402667 1.00000i \(0.500128\pi\)
\(318\) 0 0
\(319\) 53617.1i 0.526893i
\(320\) 192373. + 15458.9i 1.87864 + 0.150965i
\(321\) 0 0
\(322\) −31585.0 + 17677.1i −0.304627 + 0.170490i
\(323\) 59969.4i 0.574811i
\(324\) 0 0
\(325\) 5245.13 0.0496580
\(326\) 911.172 + 1628.06i 0.00857364 + 0.0153192i
\(327\) 0 0
\(328\) −5829.91 + 145331.i −0.0541894 + 1.35086i
\(329\) −46834.5 −0.432687
\(330\) 0 0
\(331\) 31123.5i 0.284074i −0.989861 0.142037i \(-0.954635\pi\)
0.989861 0.142037i \(-0.0453652\pi\)
\(332\) −111190. 68221.0i −1.00876 0.618931i
\(333\) 0 0
\(334\) 58929.9 + 105295.i 0.528254 + 0.943873i
\(335\) 252839.i 2.25296i
\(336\) 0 0
\(337\) 5863.61 0.0516304 0.0258152 0.999667i \(-0.491782\pi\)
0.0258152 + 0.999667i \(0.491782\pi\)
\(338\) 99655.0 55773.6i 0.872300 0.488197i
\(339\) 0 0
\(340\) −46040.9 + 75039.4i −0.398277 + 0.649129i
\(341\) −74253.8 −0.638572
\(342\) 0 0
\(343\) 17470.1i 0.148493i
\(344\) −161358. 6472.85i −1.36356 0.0546989i
\(345\) 0 0
\(346\) −178076. + 99663.2i −1.48749 + 0.832497i
\(347\) 138155.i 1.14738i 0.819073 + 0.573689i \(0.194488\pi\)
−0.819073 + 0.573689i \(0.805512\pi\)
\(348\) 0 0
\(349\) 180947. 1.48559 0.742797 0.669517i \(-0.233499\pi\)
0.742797 + 0.669517i \(0.233499\pi\)
\(350\) −210018. 375255.i −1.71443 3.06330i
\(351\) 0 0
\(352\) 39561.9 59033.1i 0.319295 0.476442i
\(353\) −98784.9 −0.792759 −0.396380 0.918087i \(-0.629734\pi\)
−0.396380 + 0.918087i \(0.629734\pi\)
\(354\) 0 0
\(355\) 7832.10i 0.0621472i
\(356\) −58266.0 + 94964.5i −0.459743 + 0.749309i
\(357\) 0 0
\(358\) 51365.2 + 91778.2i 0.400777 + 0.716099i
\(359\) 151427.i 1.17493i 0.809248 + 0.587467i \(0.199875\pi\)
−0.809248 + 0.587467i \(0.800125\pi\)
\(360\) 0 0
\(361\) −133387. −1.02353
\(362\) −10932.4 + 6118.52i −0.0834257 + 0.0466906i
\(363\) 0 0
\(364\) 3022.62 + 1854.55i 0.0228129 + 0.0139970i
\(365\) −239616. −1.79858
\(366\) 0 0
\(367\) 101304.i 0.752132i 0.926593 + 0.376066i \(0.122723\pi\)
−0.926593 + 0.376066i \(0.877277\pi\)
\(368\) −30640.2 + 15569.6i −0.226254 + 0.114970i
\(369\) 0 0
\(370\) −170071. + 95182.9i −1.24230 + 0.695273i
\(371\) 78590.9i 0.570985i
\(372\) 0 0
\(373\) −181796. −1.30667 −0.653336 0.757068i \(-0.726631\pi\)
−0.653336 + 0.757068i \(0.726631\pi\)
\(374\) 15832.0 + 28288.3i 0.113186 + 0.202238i
\(375\) 0 0
\(376\) −44436.0 1782.54i −0.314311 0.0126085i
\(377\) 2540.61 0.0178754
\(378\) 0 0
\(379\) 2324.09i 0.0161798i −0.999967 0.00808991i \(-0.997425\pi\)
0.999967 0.00808991i \(-0.00257513\pi\)
\(380\) 329976. + 202459.i 2.28515 + 1.40207i
\(381\) 0 0
\(382\) 33522.7 + 59897.6i 0.229727 + 0.410471i
\(383\) 129732.i 0.884402i 0.896916 + 0.442201i \(0.145802\pi\)
−0.896916 + 0.442201i \(0.854198\pi\)
\(384\) 0 0
\(385\) −220390. −1.48686
\(386\) 58786.4 32900.8i 0.394550 0.220817i
\(387\) 0 0
\(388\) −2333.65 + 3803.48i −0.0155014 + 0.0252649i
\(389\) −53603.2 −0.354235 −0.177118 0.984190i \(-0.556677\pi\)
−0.177118 + 0.984190i \(0.556677\pi\)
\(390\) 0 0
\(391\) 15678.2i 0.102552i
\(392\) 5494.32 136965.i 0.0357554 0.891329i
\(393\) 0 0
\(394\) 234889. 131459.i 1.51311 0.846835i
\(395\) 34135.3i 0.218781i
\(396\) 0 0
\(397\) 156598. 0.993584 0.496792 0.867870i \(-0.334511\pi\)
0.496792 + 0.867870i \(0.334511\pi\)
\(398\) −25935.7 46341.3i −0.163731 0.292551i
\(399\) 0 0
\(400\) −184980. 364030.i −1.15612 2.27519i
\(401\) −207347. −1.28946 −0.644731 0.764410i \(-0.723031\pi\)
−0.644731 + 0.764410i \(0.723031\pi\)
\(402\) 0 0
\(403\) 3518.46i 0.0216642i
\(404\) 77885.2 126941.i 0.477191 0.777746i
\(405\) 0 0
\(406\) −101727. 181764.i −0.617142 1.10270i
\(407\) 71763.9i 0.433229i
\(408\) 0 0
\(409\) 35322.3 0.211156 0.105578 0.994411i \(-0.466331\pi\)
0.105578 + 0.994411i \(0.466331\pi\)
\(410\) 373765. 209184.i 2.22347 1.24440i
\(411\) 0 0
\(412\) 44620.8 + 27377.3i 0.262871 + 0.161286i
\(413\) 373391. 2.18909
\(414\) 0 0
\(415\) 384154.i 2.23054i
\(416\) 2797.24 + 1874.61i 0.0161638 + 0.0108324i
\(417\) 0 0
\(418\) 124394. 69619.2i 0.711946 0.398452i
\(419\) 272874.i 1.55430i −0.629318 0.777148i \(-0.716666\pi\)
0.629318 0.777148i \(-0.283334\pi\)
\(420\) 0 0
\(421\) −223490. −1.26094 −0.630468 0.776215i \(-0.717137\pi\)
−0.630468 + 0.776215i \(0.717137\pi\)
\(422\) 34831.8 + 62236.6i 0.195592 + 0.349479i
\(423\) 0 0
\(424\) 2991.20 74566.1i 0.0166385 0.414772i
\(425\) 186270. 1.03125
\(426\) 0 0
\(427\) 215958.i 1.18444i
\(428\) −25162.4 15438.6i −0.137361 0.0842790i
\(429\) 0 0
\(430\) 232253. + 414984.i 1.25610 + 2.24437i
\(431\) 158123.i 0.851216i 0.904908 + 0.425608i \(0.139940\pi\)
−0.904908 + 0.425608i \(0.860060\pi\)
\(432\) 0 0
\(433\) 135143. 0.720803 0.360401 0.932797i \(-0.382640\pi\)
0.360401 + 0.932797i \(0.382640\pi\)
\(434\) −251723. + 140881.i −1.33642 + 0.747950i
\(435\) 0 0
\(436\) 50382.2 82115.1i 0.265036 0.431966i
\(437\) −68943.0 −0.361017
\(438\) 0 0
\(439\) 75873.6i 0.393697i 0.980434 + 0.196848i \(0.0630707\pi\)
−0.980434 + 0.196848i \(0.936929\pi\)
\(440\) −209103. 8388.11i −1.08008 0.0433270i
\(441\) 0 0
\(442\) −1340.42 + 750.187i −0.00686113 + 0.00383994i
\(443\) 99747.7i 0.508271i 0.967169 + 0.254135i \(0.0817909\pi\)
−0.967169 + 0.254135i \(0.918209\pi\)
\(444\) 0 0
\(445\) 328097. 1.65685
\(446\) 133326. + 238224.i 0.670262 + 1.19761i
\(447\) 0 0
\(448\) 22113.5 275185.i 0.110180 1.37110i
\(449\) 156931. 0.778424 0.389212 0.921148i \(-0.372747\pi\)
0.389212 + 0.921148i \(0.372747\pi\)
\(450\) 0 0
\(451\) 157716.i 0.775392i
\(452\) 73978.6 120574.i 0.362101 0.590167i
\(453\) 0 0
\(454\) 110712. + 197817.i 0.537133 + 0.959737i
\(455\) 10443.0i 0.0504432i
\(456\) 0 0
\(457\) 109830. 0.525882 0.262941 0.964812i \(-0.415308\pi\)
0.262941 + 0.964812i \(0.415308\pi\)
\(458\) −229165. + 128256.i −1.09249 + 0.611430i
\(459\) 0 0
\(460\) 86268.0 + 52930.2i 0.407694 + 0.250143i
\(461\) −172802. −0.813104 −0.406552 0.913628i \(-0.633269\pi\)
−0.406552 + 0.913628i \(0.633269\pi\)
\(462\) 0 0
\(463\) 159146.i 0.742395i 0.928554 + 0.371198i \(0.121053\pi\)
−0.928554 + 0.371198i \(0.878947\pi\)
\(464\) −89599.5 176327.i −0.416169 0.818999i
\(465\) 0 0
\(466\) −194257. + 108719.i −0.894549 + 0.500649i
\(467\) 153806.i 0.705246i 0.935765 + 0.352623i \(0.114710\pi\)
−0.935765 + 0.352623i \(0.885290\pi\)
\(468\) 0 0
\(469\) 361679. 1.64429
\(470\) 63959.5 + 114281.i 0.289540 + 0.517345i
\(471\) 0 0
\(472\) 354268. + 14211.4i 1.59019 + 0.0637900i
\(473\) 175109. 0.782683
\(474\) 0 0
\(475\) 819098.i 3.63035i
\(476\) 107342. + 65860.3i 0.473757 + 0.290677i
\(477\) 0 0
\(478\) 25458.0 + 45487.8i 0.111421 + 0.199085i
\(479\) 246496.i 1.07433i −0.843477 0.537166i \(-0.819495\pi\)
0.843477 0.537166i \(-0.180505\pi\)
\(480\) 0 0
\(481\) −3400.48 −0.0146977
\(482\) −202353. + 113250.i −0.870993 + 0.487466i
\(483\) 0 0
\(484\) 82209.5 133989.i 0.350939 0.571975i
\(485\) 13140.8 0.0558649
\(486\) 0 0
\(487\) 341810.i 1.44121i −0.693347 0.720603i \(-0.743865\pi\)
0.693347 0.720603i \(-0.256135\pi\)
\(488\) 8219.45 204898.i 0.0345146 0.860397i
\(489\) 0 0
\(490\) −352250. + 197142.i −1.46710 + 0.821084i
\(491\) 302270.i 1.25381i −0.779095 0.626906i \(-0.784321\pi\)
0.779095 0.626906i \(-0.215679\pi\)
\(492\) 0 0
\(493\) 90224.4 0.371219
\(494\) 3298.85 + 5894.32i 0.0135179 + 0.0241535i
\(495\) 0 0
\(496\) −244194. + 124085.i −0.992592 + 0.504379i
\(497\) −11203.6 −0.0453572
\(498\) 0 0
\(499\) 193507.i 0.777132i 0.921421 + 0.388566i \(0.127029\pi\)
−0.921421 + 0.388566i \(0.872971\pi\)
\(500\) −382445. + 623325.i −1.52978 + 2.49330i
\(501\) 0 0
\(502\) −158808. 283754.i −0.630179 1.12599i
\(503\) 452328.i 1.78779i −0.448273 0.893897i \(-0.647961\pi\)
0.448273 0.893897i \(-0.352039\pi\)
\(504\) 0 0
\(505\) −438573. −1.71973
\(506\) 32521.2 18201.0i 0.127018 0.0710878i
\(507\) 0 0
\(508\) −124990. 76688.2i −0.484336 0.297167i
\(509\) 232364. 0.896876 0.448438 0.893814i \(-0.351980\pi\)
0.448438 + 0.893814i \(0.351980\pi\)
\(510\) 0 0
\(511\) 342765.i 1.31267i
\(512\) 31454.7 260250.i 0.119990 0.992775i
\(513\) 0 0
\(514\) 65687.0 36762.8i 0.248630 0.139150i
\(515\) 154163.i 0.581252i
\(516\) 0 0
\(517\) 48222.8 0.180414
\(518\) 136157. + 243282.i 0.507435 + 0.906673i
\(519\) 0 0
\(520\) 397.465 9908.18i 0.00146991 0.0366427i
\(521\) −425181. −1.56638 −0.783192 0.621780i \(-0.786410\pi\)
−0.783192 + 0.621780i \(0.786410\pi\)
\(522\) 0 0
\(523\) 91819.6i 0.335685i 0.985814 + 0.167842i \(0.0536800\pi\)
−0.985814 + 0.167842i \(0.946320\pi\)
\(524\) 221474. + 135887.i 0.806603 + 0.494896i
\(525\) 0 0
\(526\) 187870. + 335682.i 0.679025 + 1.21327i
\(527\) 124951.i 0.449902i
\(528\) 0 0
\(529\) 261817. 0.935591
\(530\) −191771. + 107328.i −0.682701 + 0.382085i
\(531\) 0 0
\(532\) 289613. 472023.i 1.02328 1.66778i
\(533\) 7473.24 0.0263060
\(534\) 0 0
\(535\) 86934.9i 0.303729i
\(536\) 343157. + 13765.7i 1.19444 + 0.0479146i
\(537\) 0 0
\(538\) −72789.3 + 40737.7i −0.251480 + 0.140745i
\(539\) 148637.i 0.511622i
\(540\) 0 0
\(541\) −419310. −1.43265 −0.716326 0.697766i \(-0.754178\pi\)
−0.716326 + 0.697766i \(0.754178\pi\)
\(542\) −198317. 354349.i −0.675090 1.20624i
\(543\) 0 0
\(544\) 99338.1 + 66572.9i 0.335674 + 0.224957i
\(545\) −283703. −0.955150
\(546\) 0 0
\(547\) 372884.i 1.24623i 0.782129 + 0.623116i \(0.214134\pi\)
−0.782129 + 0.623116i \(0.785866\pi\)
\(548\) −254459. + 414727.i −0.847337 + 1.38103i
\(549\) 0 0
\(550\) 216243. + 386378.i 0.714852 + 1.27728i
\(551\) 396751.i 1.30682i
\(552\) 0 0
\(553\) −48829.8 −0.159674
\(554\) −187534. + 104956.i −0.611026 + 0.341971i
\(555\) 0 0
\(556\) −445802. 273524.i −1.44209 0.884803i
\(557\) 249244. 0.803369 0.401685 0.915778i \(-0.368425\pi\)
0.401685 + 0.915778i \(0.368425\pi\)
\(558\) 0 0
\(559\) 8297.40i 0.0265533i
\(560\) −724781. + 368293.i −2.31116 + 1.17440i
\(561\) 0 0
\(562\) 347309. 194377.i 1.09962 0.615421i
\(563\) 469821.i 1.48223i 0.671377 + 0.741116i \(0.265703\pi\)
−0.671377 + 0.741116i \(0.734297\pi\)
\(564\) 0 0
\(565\) −416575. −1.30496
\(566\) 136200. + 243358.i 0.425151 + 0.759650i
\(567\) 0 0
\(568\) −10629.9 426.415i −0.0329482 0.00132171i
\(569\) 501734. 1.54971 0.774853 0.632142i \(-0.217824\pi\)
0.774853 + 0.632142i \(0.217824\pi\)
\(570\) 0 0
\(571\) 514877.i 1.57918i 0.613636 + 0.789589i \(0.289706\pi\)
−0.613636 + 0.789589i \(0.710294\pi\)
\(572\) −3112.21 1909.52i −0.00951212 0.00583622i
\(573\) 0 0
\(574\) −299232. 534661.i −0.908206 1.62276i
\(575\) 214143.i 0.647690i
\(576\) 0 0
\(577\) 55168.5 0.165707 0.0828533 0.996562i \(-0.473597\pi\)
0.0828533 + 0.996562i \(0.473597\pi\)
\(578\) 243930. 136519.i 0.730145 0.408637i
\(579\) 0 0
\(580\) −304601. + 496451.i −0.905472 + 1.47578i
\(581\) 549524. 1.62792
\(582\) 0 0
\(583\) 80920.5i 0.238079i
\(584\) −13045.8 + 325211.i −0.0382511 + 0.953542i
\(585\) 0 0
\(586\) 43421.9 24301.8i 0.126449 0.0707690i
\(587\) 221207.i 0.641980i 0.947083 + 0.320990i \(0.104016\pi\)
−0.947083 + 0.320990i \(0.895984\pi\)
\(588\) 0 0
\(589\) −549456. −1.58381
\(590\) −509920. 911115.i −1.46487 2.61739i
\(591\) 0 0
\(592\) 119925. + 236005.i 0.342188 + 0.673408i
\(593\) 167379. 0.475982 0.237991 0.971267i \(-0.423511\pi\)
0.237991 + 0.971267i \(0.423511\pi\)
\(594\) 0 0
\(595\) 370861.i 1.04756i
\(596\) 112030. 182592.i 0.315387 0.514031i
\(597\) 0 0
\(598\) 862.442 + 1540.99i 0.00241172 + 0.00430922i
\(599\) 285002.i 0.794319i −0.917750 0.397160i \(-0.869996\pi\)
0.917750 0.397160i \(-0.130004\pi\)
\(600\) 0 0
\(601\) 30586.9 0.0846810 0.0423405 0.999103i \(-0.486519\pi\)
0.0423405 + 0.999103i \(0.486519\pi\)
\(602\) 593625. 332232.i 1.63802 0.916745i
\(603\) 0 0
\(604\) −124198. 76202.4i −0.340440 0.208879i
\(605\) −462924. −1.26473
\(606\) 0 0
\(607\) 165312.i 0.448670i 0.974512 + 0.224335i \(0.0720209\pi\)
−0.974512 + 0.224335i \(0.927979\pi\)
\(608\) 292746. 436827.i 0.791925 1.18169i
\(609\) 0 0
\(610\) −526962. + 294923.i −1.41618 + 0.792590i
\(611\) 2285.00i 0.00612074i
\(612\) 0 0
\(613\) −64752.4 −0.172320 −0.0861599 0.996281i \(-0.527460\pi\)
−0.0861599 + 0.996281i \(0.527460\pi\)
\(614\) 296909. + 530511.i 0.787566 + 1.40721i
\(615\) 0 0
\(616\) −11999.0 + 299117.i −0.0316216 + 0.788277i
\(617\) 321272. 0.843923 0.421961 0.906614i \(-0.361342\pi\)
0.421961 + 0.906614i \(0.361342\pi\)
\(618\) 0 0
\(619\) 409948.i 1.06991i −0.844880 0.534956i \(-0.820328\pi\)
0.844880 0.534956i \(-0.179672\pi\)
\(620\) 687530. + 421838.i 1.78858 + 1.09739i
\(621\) 0 0
\(622\) 97845.4 + 174828.i 0.252906 + 0.451887i
\(623\) 469335.i 1.20923i
\(624\) 0 0
\(625\) 1.15665e6 2.96103
\(626\) −216307. + 121060.i −0.551979 + 0.308924i
\(627\) 0 0
\(628\) 38115.3 62122.0i 0.0966452 0.157516i
\(629\) −120761. −0.305229
\(630\) 0 0
\(631\) 453263.i 1.13839i 0.822202 + 0.569195i \(0.192745\pi\)
−0.822202 + 0.569195i \(0.807255\pi\)
\(632\) −46329.1 1858.48i −0.115990 0.00465290i
\(633\) 0 0
\(634\) 282.478 158.093i 0.000702758 0.000393310i
\(635\) 431833.i 1.07095i
\(636\) 0 0
\(637\) −7043.05 −0.0173573
\(638\) 104743. + 187152.i 0.257325 + 0.459783i
\(639\) 0 0
\(640\) −701680. + 321846.i −1.71309 + 0.785757i
\(641\) 764363. 1.86030 0.930152 0.367175i \(-0.119675\pi\)
0.930152 + 0.367175i \(0.119675\pi\)
\(642\) 0 0
\(643\) 674655.i 1.63177i −0.578211 0.815887i \(-0.696249\pi\)
0.578211 0.815887i \(-0.303751\pi\)
\(644\) 75715.4 123404.i 0.182563 0.297549i
\(645\) 0 0
\(646\) 117152. + 209324.i 0.280727 + 0.501597i
\(647\) 372446.i 0.889723i 0.895599 + 0.444861i \(0.146747\pi\)
−0.895599 + 0.444861i \(0.853253\pi\)
\(648\) 0 0
\(649\) −384458. −0.912767
\(650\) −18308.2 + 10246.5i −0.0433331 + 0.0242521i
\(651\) 0 0
\(652\) −6360.93 3902.79i −0.0149632 0.00918078i
\(653\) −620680. −1.45560 −0.727799 0.685791i \(-0.759457\pi\)
−0.727799 + 0.685791i \(0.759457\pi\)
\(654\) 0 0
\(655\) 765181.i 1.78353i
\(656\) −263558. 518669.i −0.612447 1.20527i
\(657\) 0 0
\(658\) 163477. 91492.5i 0.377576 0.211317i
\(659\) 416907.i 0.959993i 0.877271 + 0.479996i \(0.159362\pi\)
−0.877271 + 0.479996i \(0.840638\pi\)
\(660\) 0 0
\(661\) −724690. −1.65863 −0.829315 0.558782i \(-0.811269\pi\)
−0.829315 + 0.558782i \(0.811269\pi\)
\(662\) 60800.5 + 108637.i 0.138737 + 0.247892i
\(663\) 0 0
\(664\) 521381. + 20915.1i 1.18255 + 0.0474377i
\(665\) −1.63082e6 −3.68775
\(666\) 0 0
\(667\) 103725.i 0.233149i
\(668\) −411392. 252412.i −0.921941 0.565662i
\(669\) 0 0
\(670\) −493927. 882538.i −1.10030 1.96600i
\(671\) 222359.i 0.493867i
\(672\) 0 0
\(673\) −239394. −0.528546 −0.264273 0.964448i \(-0.585132\pi\)
−0.264273 + 0.964448i \(0.585132\pi\)
\(674\) −20467.0 + 11454.7i −0.0450542 + 0.0252153i
\(675\) 0 0
\(676\) −238893. + 389357.i −0.522769 + 0.852031i
\(677\) −731049. −1.59503 −0.797515 0.603299i \(-0.793853\pi\)
−0.797515 + 0.603299i \(0.793853\pi\)
\(678\) 0 0
\(679\) 18797.6i 0.0407721i
\(680\) 14115.1 351868.i 0.0305258 0.760961i
\(681\) 0 0
\(682\) 259184. 145057.i 0.557237 0.311867i
\(683\) 804575.i 1.72475i −0.506273 0.862373i \(-0.668977\pi\)
0.506273 0.862373i \(-0.331023\pi\)
\(684\) 0 0
\(685\) 1.43286e6 3.05368
\(686\) −34128.3 60979.7i −0.0725214 0.129580i
\(687\) 0 0
\(688\) 575869. 292624.i 1.21660 0.618206i
\(689\) −3834.36 −0.00807707
\(690\) 0 0
\(691\) 734097.i 1.53744i 0.639587 + 0.768719i \(0.279105\pi\)
−0.639587 + 0.768719i \(0.720895\pi\)
\(692\) 426883. 695753.i 0.891450 1.45292i
\(693\) 0 0
\(694\) −269889. 482232.i −0.560359 1.00124i
\(695\) 1.54022e6i 3.18870i
\(696\) 0 0
\(697\) 265396. 0.546298
\(698\) −631598. + 353484.i −1.29637 + 0.725537i
\(699\) 0 0
\(700\) 1.46614e6 + 899560.i 2.99212 + 1.83584i
\(701\) 158522. 0.322592 0.161296 0.986906i \(-0.448433\pi\)
0.161296 + 0.986906i \(0.448433\pi\)
\(702\) 0 0
\(703\) 531031.i 1.07451i
\(704\) −22769.0 + 283341.i −0.0459408 + 0.571695i
\(705\) 0 0
\(706\) 344811. 192979.i 0.691785 0.387169i
\(707\) 627369.i 1.25512i
\(708\) 0 0
\(709\) 365334. 0.726770 0.363385 0.931639i \(-0.381621\pi\)
0.363385 + 0.931639i \(0.381621\pi\)
\(710\) 15300.2 + 27338.1i 0.0303516 + 0.0542315i
\(711\) 0 0
\(712\) 17863.1 445300.i 0.0352368 0.878400i
\(713\) −143648. −0.282566
\(714\) 0 0
\(715\) 10752.5i 0.0210329i
\(716\) −358582. 220010.i −0.699460 0.429158i
\(717\) 0 0
\(718\) −295816. 528558.i −0.573817 1.02528i
\(719\) 801198.i 1.54982i −0.632070 0.774911i \(-0.717795\pi\)
0.632070 0.774911i \(-0.282205\pi\)
\(720\) 0 0
\(721\) −220526. −0.424218
\(722\) 465590. 260575.i 0.893160 0.499872i
\(723\) 0 0
\(724\) 26207.2 42713.6i 0.0499970 0.0814872i
\(725\) 1.23234e6 2.34452
\(726\) 0 0
\(727\) 207794.i 0.393155i −0.980488 0.196577i \(-0.937017\pi\)
0.980488 0.196577i \(-0.0629827\pi\)
\(728\) −14173.4 568.563i −0.0267431 0.00107279i
\(729\) 0 0
\(730\) 836385. 468097.i 1.56950 0.878395i
\(731\) 294665.i 0.551434i
\(732\) 0 0
\(733\) 177976. 0.331248 0.165624 0.986189i \(-0.447036\pi\)
0.165624 + 0.986189i \(0.447036\pi\)
\(734\) −197900. 353603.i −0.367328 0.656333i
\(735\) 0 0
\(736\) 76534.7 114203.i 0.141287 0.210824i
\(737\) −372400. −0.685606
\(738\) 0 0
\(739\) 587913.i 1.07653i 0.842777 + 0.538263i \(0.180919\pi\)
−0.842777 + 0.538263i \(0.819081\pi\)
\(740\) 407693. 664476.i 0.744509 1.21343i
\(741\) 0 0
\(742\) 153530. + 274323.i 0.278859 + 0.498259i
\(743\) 675642.i 1.22388i 0.790904 + 0.611940i \(0.209611\pi\)
−0.790904 + 0.611940i \(0.790389\pi\)
\(744\) 0 0
\(745\) −630846. −1.13661
\(746\) 634562. 355143.i 1.14024 0.638155i
\(747\) 0 0
\(748\) −110524. 67812.5i −0.197539 0.121201i
\(749\) 124358. 0.221672
\(750\) 0 0
\(751\) 267589.i 0.474447i −0.971455 0.237224i \(-0.923763\pi\)
0.971455 0.237224i \(-0.0762374\pi\)
\(752\) 158587. 80584.9i 0.280435 0.142501i
\(753\) 0 0
\(754\) −8868.04 + 4963.15i −0.0155986 + 0.00873000i
\(755\) 429098.i 0.752770i
\(756\) 0 0
\(757\) 400491. 0.698878 0.349439 0.936959i \(-0.386372\pi\)
0.349439 + 0.936959i \(0.386372\pi\)
\(758\) 4540.17 + 8112.27i 0.00790193 + 0.0141190i
\(759\) 0 0
\(760\) −1.54730e6 62069.5i −2.67884 0.107461i
\(761\) 755370. 1.30434 0.652170 0.758073i \(-0.273859\pi\)
0.652170 + 0.758073i \(0.273859\pi\)
\(762\) 0 0
\(763\) 405831.i 0.697101i
\(764\) −234023. 143586.i −0.400933 0.245995i
\(765\) 0 0
\(766\) −253435. 452832.i −0.431926 0.771756i
\(767\) 18217.3i 0.0309665i
\(768\) 0 0
\(769\) −482211. −0.815427 −0.407713 0.913110i \(-0.633674\pi\)
−0.407713 + 0.913110i \(0.633674\pi\)
\(770\) 769274. 430537.i 1.29748 0.726155i
\(771\) 0 0
\(772\) −140923. + 229682.i −0.236454 + 0.385382i
\(773\) −1.06175e6 −1.77691 −0.888454 0.458965i \(-0.848220\pi\)
−0.888454 + 0.458965i \(0.848220\pi\)
\(774\) 0 0
\(775\) 1.70665e6i 2.84146i
\(776\) 715.445 17835.0i 0.00118810 0.0296175i
\(777\) 0 0
\(778\) 187103. 104715.i 0.309116 0.173002i
\(779\) 1.16705e6i 1.92315i
\(780\) 0 0
\(781\) 11535.7 0.0189122
\(782\) 30627.8 + 54725.2i 0.0500844 + 0.0894898i
\(783\) 0 0
\(784\) 248387. + 488813.i 0.404107 + 0.795262i
\(785\) −214628. −0.348295
\(786\) 0 0
\(787\) 313747.i 0.506559i −0.967393 0.253280i \(-0.918491\pi\)
0.967393 0.253280i \(-0.0815093\pi\)