Properties

Label 108.6.b.b.107.14
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
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: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{30}\cdot 3^{32}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.14
Root \(-1.73205 - 0.353400i\) of \(x^{16} + 30 x^{14} + 619 x^{12} + 5604 x^{10} + 40971 x^{8} - 4866 x^{6} + 568069 x^{4} - 7909632 x^{2} + 20340100\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.b.107.13

$q$-expansion

\(f(q)\) \(=\) \(q+(5.08799 + 2.47231i) q^{2} +(19.7753 + 25.1582i) q^{4} +33.1536i q^{5} +59.4073i q^{7} +(38.4178 + 176.896i) q^{8} +O(q^{10})\) \(q+(5.08799 + 2.47231i) q^{2} +(19.7753 + 25.1582i) q^{4} +33.1536i q^{5} +59.4073i q^{7} +(38.4178 + 176.896i) q^{8} +(-81.9660 + 168.685i) q^{10} -179.135 q^{11} -143.222 q^{13} +(-146.873 + 302.264i) q^{14} +(-241.872 + 995.025i) q^{16} -93.8221i q^{17} +1617.39i q^{19} +(-834.085 + 655.624i) q^{20} +(-911.438 - 442.878i) q^{22} -2414.48 q^{23} +2025.84 q^{25} +(-728.711 - 354.089i) q^{26} +(-1494.58 + 1174.80i) q^{28} +7910.14i q^{29} -4726.80i q^{31} +(-3690.65 + 4464.70i) q^{32} +(231.958 - 477.366i) q^{34} -1969.56 q^{35} +9387.10 q^{37} +(-3998.68 + 8229.25i) q^{38} +(-5864.73 + 1273.69i) q^{40} +11838.5i q^{41} -19531.8i q^{43} +(-3542.46 - 4506.72i) q^{44} +(-12284.8 - 5969.34i) q^{46} -7373.21 q^{47} +13277.8 q^{49} +(10307.5 + 5008.51i) q^{50} +(-2832.26 - 3603.20i) q^{52} -26895.4i q^{53} -5938.97i q^{55} +(-10508.9 + 2282.30i) q^{56} +(-19556.3 + 40246.7i) q^{58} -6144.64 q^{59} +55252.3 q^{61} +(11686.1 - 24049.9i) q^{62} +(-29816.1 + 13591.9i) q^{64} -4748.31i q^{65} +38888.6i q^{67} +(2360.40 - 1855.36i) q^{68} +(-10021.1 - 4869.38i) q^{70} +45277.6 q^{71} +21000.4 q^{73} +(47761.5 + 23207.8i) q^{74} +(-40690.5 + 31984.4i) q^{76} -10641.9i q^{77} -76460.5i q^{79} +(-32988.6 - 8018.91i) q^{80} +(-29268.4 + 60234.0i) q^{82} +58515.8 q^{83} +3110.54 q^{85} +(48288.6 - 99377.5i) q^{86} +(-6881.99 - 31688.2i) q^{88} -18558.5i q^{89} -8508.41i q^{91} +(-47747.1 - 60744.0i) q^{92} +(-37514.9 - 18228.9i) q^{94} -53622.2 q^{95} +137248. q^{97} +(67557.2 + 32826.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 94q^{4} + O(q^{10}) \) \( 16q + 94q^{4} + 1454q^{10} + 896q^{13} + 178q^{16} + 30q^{22} + 9888q^{25} + 11454q^{28} - 6172q^{34} - 71008q^{37} - 16618q^{40} + 35304q^{46} - 49376q^{49} + 14876q^{52} - 10492q^{58} + 77888q^{61} + 89206q^{64} + 229398q^{70} - 38032q^{73} + 48960q^{76} - 224488q^{82} - 371264q^{85} + 249102q^{88} + 68772q^{94} - 976q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.08799 + 2.47231i 0.899439 + 0.437047i
\(3\) 0 0
\(4\) 19.7753 + 25.1582i 0.617979 + 0.786194i
\(5\) 33.1536i 0.593069i 0.955022 + 0.296535i \(0.0958310\pi\)
−0.955022 + 0.296535i \(0.904169\pi\)
\(6\) 0 0
\(7\) 59.4073i 0.458242i 0.973398 + 0.229121i \(0.0735851\pi\)
−0.973398 + 0.229121i \(0.926415\pi\)
\(8\) 38.4178 + 176.896i 0.212231 + 0.977220i
\(9\) 0 0
\(10\) −81.9660 + 168.685i −0.259199 + 0.533430i
\(11\) −179.135 −0.446374 −0.223187 0.974776i \(-0.571646\pi\)
−0.223187 + 0.974776i \(0.571646\pi\)
\(12\) 0 0
\(13\) −143.222 −0.235045 −0.117522 0.993070i \(-0.537495\pi\)
−0.117522 + 0.993070i \(0.537495\pi\)
\(14\) −146.873 + 302.264i −0.200273 + 0.412160i
\(15\) 0 0
\(16\) −241.872 + 995.025i −0.236203 + 0.971704i
\(17\) 93.8221i 0.0787377i −0.999225 0.0393689i \(-0.987465\pi\)
0.999225 0.0393689i \(-0.0125347\pi\)
\(18\) 0 0
\(19\) 1617.39i 1.02785i 0.857835 + 0.513925i \(0.171809\pi\)
−0.857835 + 0.513925i \(0.828191\pi\)
\(20\) −834.085 + 655.624i −0.466268 + 0.366505i
\(21\) 0 0
\(22\) −911.438 442.878i −0.401486 0.195087i
\(23\) −2414.48 −0.951708 −0.475854 0.879524i \(-0.657861\pi\)
−0.475854 + 0.879524i \(0.657861\pi\)
\(24\) 0 0
\(25\) 2025.84 0.648269
\(26\) −728.711 354.089i −0.211408 0.102726i
\(27\) 0 0
\(28\) −1494.58 + 1174.80i −0.360267 + 0.283184i
\(29\) 7910.14i 1.74658i 0.487198 + 0.873291i \(0.338019\pi\)
−0.487198 + 0.873291i \(0.661981\pi\)
\(30\) 0 0
\(31\) 4726.80i 0.883412i −0.897160 0.441706i \(-0.854373\pi\)
0.897160 0.441706i \(-0.145627\pi\)
\(32\) −3690.65 + 4464.70i −0.637130 + 0.770756i
\(33\) 0 0
\(34\) 231.958 477.366i 0.0344121 0.0708198i
\(35\) −1969.56 −0.271769
\(36\) 0 0
\(37\) 9387.10 1.12727 0.563634 0.826025i \(-0.309403\pi\)
0.563634 + 0.826025i \(0.309403\pi\)
\(38\) −3998.68 + 8229.25i −0.449219 + 0.924488i
\(39\) 0 0
\(40\) −5864.73 + 1273.69i −0.579559 + 0.125867i
\(41\) 11838.5i 1.09986i 0.835212 + 0.549928i \(0.185345\pi\)
−0.835212 + 0.549928i \(0.814655\pi\)
\(42\) 0 0
\(43\) 19531.8i 1.61091i −0.592659 0.805454i \(-0.701922\pi\)
0.592659 0.805454i \(-0.298078\pi\)
\(44\) −3542.46 4506.72i −0.275850 0.350937i
\(45\) 0 0
\(46\) −12284.8 5969.34i −0.856003 0.415941i
\(47\) −7373.21 −0.486869 −0.243435 0.969917i \(-0.578274\pi\)
−0.243435 + 0.969917i \(0.578274\pi\)
\(48\) 0 0
\(49\) 13277.8 0.790015
\(50\) 10307.5 + 5008.51i 0.583078 + 0.283324i
\(51\) 0 0
\(52\) −2832.26 3603.20i −0.145253 0.184791i
\(53\) 26895.4i 1.31519i −0.753372 0.657594i \(-0.771574\pi\)
0.753372 0.657594i \(-0.228426\pi\)
\(54\) 0 0
\(55\) 5938.97i 0.264731i
\(56\) −10508.9 + 2282.30i −0.447803 + 0.0972529i
\(57\) 0 0
\(58\) −19556.3 + 40246.7i −0.763339 + 1.57094i
\(59\) −6144.64 −0.229809 −0.114904 0.993377i \(-0.536656\pi\)
−0.114904 + 0.993377i \(0.536656\pi\)
\(60\) 0 0
\(61\) 55252.3 1.90119 0.950596 0.310430i \(-0.100473\pi\)
0.950596 + 0.310430i \(0.100473\pi\)
\(62\) 11686.1 24049.9i 0.386093 0.794575i
\(63\) 0 0
\(64\) −29816.1 + 13591.9i −0.909916 + 0.414792i
\(65\) 4748.31i 0.139398i
\(66\) 0 0
\(67\) 38888.6i 1.05836i 0.848509 + 0.529182i \(0.177501\pi\)
−0.848509 + 0.529182i \(0.822499\pi\)
\(68\) 2360.40 1855.36i 0.0619032 0.0486583i
\(69\) 0 0
\(70\) −10021.1 4869.38i −0.244440 0.118776i
\(71\) 45277.6 1.06595 0.532976 0.846131i \(-0.321074\pi\)
0.532976 + 0.846131i \(0.321074\pi\)
\(72\) 0 0
\(73\) 21000.4 0.461233 0.230617 0.973045i \(-0.425926\pi\)
0.230617 + 0.973045i \(0.425926\pi\)
\(74\) 47761.5 + 23207.8i 1.01391 + 0.492669i
\(75\) 0 0
\(76\) −40690.5 + 31984.4i −0.808090 + 0.635190i
\(77\) 10641.9i 0.204547i
\(78\) 0 0
\(79\) 76460.5i 1.37838i −0.724580 0.689191i \(-0.757966\pi\)
0.724580 0.689191i \(-0.242034\pi\)
\(80\) −32988.6 8018.91i −0.576288 0.140085i
\(81\) 0 0
\(82\) −29268.4 + 60234.0i −0.480689 + 0.989253i
\(83\) 58515.8 0.932347 0.466174 0.884693i \(-0.345632\pi\)
0.466174 + 0.884693i \(0.345632\pi\)
\(84\) 0 0
\(85\) 3110.54 0.0466969
\(86\) 48288.6 99377.5i 0.704042 1.44891i
\(87\) 0 0
\(88\) −6881.99 31688.2i −0.0947343 0.436206i
\(89\) 18558.5i 0.248352i −0.992260 0.124176i \(-0.960371\pi\)
0.992260 0.124176i \(-0.0396287\pi\)
\(90\) 0 0
\(91\) 8508.41i 0.107707i
\(92\) −47747.1 60744.0i −0.588136 0.748227i
\(93\) 0 0
\(94\) −37514.9 18228.9i −0.437909 0.212785i
\(95\) −53622.2 −0.609586
\(96\) 0 0
\(97\) 137248. 1.48107 0.740536 0.672017i \(-0.234572\pi\)
0.740536 + 0.672017i \(0.234572\pi\)
\(98\) 67557.2 + 32826.8i 0.710570 + 0.345274i
\(99\) 0 0
\(100\) 40061.7 + 50966.5i 0.400617 + 0.509665i
\(101\) 97319.1i 0.949280i −0.880180 0.474640i \(-0.842578\pi\)
0.880180 0.474640i \(-0.157422\pi\)
\(102\) 0 0
\(103\) 38694.4i 0.359381i −0.983723 0.179690i \(-0.942490\pi\)
0.983723 0.179690i \(-0.0575096\pi\)
\(104\) −5502.27 25335.3i −0.0498837 0.229690i
\(105\) 0 0
\(106\) 66493.8 136844.i 0.574799 1.18293i
\(107\) 42882.4 0.362093 0.181046 0.983475i \(-0.442052\pi\)
0.181046 + 0.983475i \(0.442052\pi\)
\(108\) 0 0
\(109\) −41832.7 −0.337248 −0.168624 0.985680i \(-0.553932\pi\)
−0.168624 + 0.985680i \(0.553932\pi\)
\(110\) 14683.0 30217.5i 0.115700 0.238109i
\(111\) 0 0
\(112\) −59111.7 14368.9i −0.445275 0.108238i
\(113\) 30797.2i 0.226890i 0.993544 + 0.113445i \(0.0361885\pi\)
−0.993544 + 0.113445i \(0.963811\pi\)
\(114\) 0 0
\(115\) 80048.6i 0.564429i
\(116\) −199005. + 156426.i −1.37315 + 1.07935i
\(117\) 0 0
\(118\) −31263.9 15191.5i −0.206699 0.100437i
\(119\) 5573.72 0.0360809
\(120\) 0 0
\(121\) −128962. −0.800750
\(122\) 281123. + 136601.i 1.71001 + 0.830911i
\(123\) 0 0
\(124\) 118918. 93474.2i 0.694534 0.545931i
\(125\) 170769.i 0.977538i
\(126\) 0 0
\(127\) 77161.9i 0.424515i 0.977214 + 0.212258i \(0.0680816\pi\)
−0.977214 + 0.212258i \(0.931918\pi\)
\(128\) −185308. 4559.32i −0.999697 0.0245966i
\(129\) 0 0
\(130\) 11739.3 24159.4i 0.0609234 0.125380i
\(131\) −309317. −1.57480 −0.787401 0.616441i \(-0.788574\pi\)
−0.787401 + 0.616441i \(0.788574\pi\)
\(132\) 0 0
\(133\) −96084.5 −0.471004
\(134\) −96144.6 + 197865.i −0.462555 + 0.951933i
\(135\) 0 0
\(136\) 16596.7 3604.44i 0.0769441 0.0167106i
\(137\) 69310.1i 0.315497i 0.987479 + 0.157749i \(0.0504236\pi\)
−0.987479 + 0.157749i \(0.949576\pi\)
\(138\) 0 0
\(139\) 327514.i 1.43778i 0.695122 + 0.718891i \(0.255350\pi\)
−0.695122 + 0.718891i \(0.744650\pi\)
\(140\) −38948.8 49550.7i −0.167948 0.213663i
\(141\) 0 0
\(142\) 230372. + 111940.i 0.958758 + 0.465871i
\(143\) 25656.0 0.104918
\(144\) 0 0
\(145\) −262250. −1.03584
\(146\) 106850. + 51919.6i 0.414851 + 0.201581i
\(147\) 0 0
\(148\) 185633. + 236163.i 0.696628 + 0.886251i
\(149\) 317624.i 1.17205i 0.810292 + 0.586026i \(0.199308\pi\)
−0.810292 + 0.586026i \(0.800692\pi\)
\(150\) 0 0
\(151\) 32871.2i 0.117320i 0.998278 + 0.0586602i \(0.0186829\pi\)
−0.998278 + 0.0586602i \(0.981317\pi\)
\(152\) −286109. + 62136.5i −1.00444 + 0.218141i
\(153\) 0 0
\(154\) 26310.2 54146.1i 0.0893968 0.183978i
\(155\) 156711. 0.523925
\(156\) 0 0
\(157\) −292389. −0.946700 −0.473350 0.880874i \(-0.656955\pi\)
−0.473350 + 0.880874i \(0.656955\pi\)
\(158\) 189034. 389031.i 0.602418 1.23977i
\(159\) 0 0
\(160\) −148021. 122358.i −0.457112 0.377862i
\(161\) 143438.i 0.436112i
\(162\) 0 0
\(163\) 324860.i 0.957695i 0.877898 + 0.478848i \(0.158945\pi\)
−0.877898 + 0.478848i \(0.841055\pi\)
\(164\) −297835. + 234110.i −0.864701 + 0.679689i
\(165\) 0 0
\(166\) 297728. + 144669.i 0.838589 + 0.407480i
\(167\) −563689. −1.56404 −0.782021 0.623251i \(-0.785811\pi\)
−0.782021 + 0.623251i \(0.785811\pi\)
\(168\) 0 0
\(169\) −350781. −0.944754
\(170\) 15826.4 + 7690.23i 0.0420010 + 0.0204088i
\(171\) 0 0
\(172\) 491384. 386247.i 1.26649 0.995508i
\(173\) 126447.i 0.321214i −0.987018 0.160607i \(-0.948655\pi\)
0.987018 0.160607i \(-0.0513452\pi\)
\(174\) 0 0
\(175\) 120350.i 0.297064i
\(176\) 43327.7 178244.i 0.105435 0.433744i
\(177\) 0 0
\(178\) 45882.4 94425.4i 0.108541 0.223377i
\(179\) 719928. 1.67941 0.839705 0.543043i \(-0.182728\pi\)
0.839705 + 0.543043i \(0.182728\pi\)
\(180\) 0 0
\(181\) −51023.8 −0.115765 −0.0578823 0.998323i \(-0.518435\pi\)
−0.0578823 + 0.998323i \(0.518435\pi\)
\(182\) 21035.5 43290.7i 0.0470732 0.0968761i
\(183\) 0 0
\(184\) −92759.1 427111.i −0.201982 0.930028i
\(185\) 311216.i 0.668548i
\(186\) 0 0
\(187\) 16806.8i 0.0351465i
\(188\) −145808. 185497.i −0.300875 0.382774i
\(189\) 0 0
\(190\) −272829. 132571.i −0.548285 0.266418i
\(191\) 94246.4 0.186931 0.0934655 0.995623i \(-0.470206\pi\)
0.0934655 + 0.995623i \(0.470206\pi\)
\(192\) 0 0
\(193\) −17335.4 −0.0334997 −0.0167498 0.999860i \(-0.505332\pi\)
−0.0167498 + 0.999860i \(0.505332\pi\)
\(194\) 698316. + 339319.i 1.33213 + 0.647298i
\(195\) 0 0
\(196\) 262573. + 334045.i 0.488213 + 0.621105i
\(197\) 680902.i 1.25003i −0.780614 0.625013i \(-0.785094\pi\)
0.780614 0.625013i \(-0.214906\pi\)
\(198\) 0 0
\(199\) 320286.i 0.573331i −0.958031 0.286665i \(-0.907453\pi\)
0.958031 0.286665i \(-0.0925468\pi\)
\(200\) 77828.4 + 358362.i 0.137582 + 0.633501i
\(201\) 0 0
\(202\) 240603. 495159.i 0.414880 0.853819i
\(203\) −469920. −0.800357
\(204\) 0 0
\(205\) −392488. −0.652291
\(206\) 95664.5 196877.i 0.157066 0.323241i
\(207\) 0 0
\(208\) 34641.3 142509.i 0.0555182 0.228394i
\(209\) 289731.i 0.458806i
\(210\) 0 0
\(211\) 1.09747e6i 1.69702i −0.529178 0.848511i \(-0.677500\pi\)
0.529178 0.848511i \(-0.322500\pi\)
\(212\) 676640. 531865.i 1.03399 0.812760i
\(213\) 0 0
\(214\) 218186. + 106019.i 0.325680 + 0.158252i
\(215\) 647548. 0.955380
\(216\) 0 0
\(217\) 280807. 0.404816
\(218\) −212845. 103424.i −0.303334 0.147393i
\(219\) 0 0
\(220\) 149414. 117445.i 0.208130 0.163598i
\(221\) 13437.4i 0.0185069i
\(222\) 0 0
\(223\) 1.14571e6i 1.54281i 0.636344 + 0.771406i \(0.280446\pi\)
−0.636344 + 0.771406i \(0.719554\pi\)
\(224\) −265235. 219252.i −0.353193 0.291960i
\(225\) 0 0
\(226\) −76140.3 + 156696.i −0.0991615 + 0.204073i
\(227\) 827252. 1.06555 0.532774 0.846257i \(-0.321149\pi\)
0.532774 + 0.846257i \(0.321149\pi\)
\(228\) 0 0
\(229\) 800776. 1.00907 0.504536 0.863390i \(-0.331663\pi\)
0.504536 + 0.863390i \(0.331663\pi\)
\(230\) 197905. 407287.i 0.246682 0.507669i
\(231\) 0 0
\(232\) −1.39927e6 + 303891.i −1.70680 + 0.370678i
\(233\) 1.65496e6i 1.99709i −0.0539626 0.998543i \(-0.517185\pi\)
0.0539626 0.998543i \(-0.482815\pi\)
\(234\) 0 0
\(235\) 244449.i 0.288747i
\(236\) −121512. 154588.i −0.142017 0.180674i
\(237\) 0 0
\(238\) 28359.0 + 13780.0i 0.0324526 + 0.0157691i
\(239\) −924466. −1.04688 −0.523439 0.852063i \(-0.675351\pi\)
−0.523439 + 0.852063i \(0.675351\pi\)
\(240\) 0 0
\(241\) −108394. −0.120216 −0.0601082 0.998192i \(-0.519145\pi\)
−0.0601082 + 0.998192i \(0.519145\pi\)
\(242\) −656156. 318833.i −0.720225 0.349966i
\(243\) 0 0
\(244\) 1.09263e6 + 1.39005e6i 1.17490 + 1.49471i
\(245\) 440206.i 0.468533i
\(246\) 0 0
\(247\) 231645.i 0.241591i
\(248\) 836151. 181594.i 0.863288 0.187487i
\(249\) 0 0
\(250\) −422194. + 868871.i −0.427230 + 0.879235i
\(251\) 665770. 0.667022 0.333511 0.942746i \(-0.391767\pi\)
0.333511 + 0.942746i \(0.391767\pi\)
\(252\) 0 0
\(253\) 432518. 0.424818
\(254\) −190768. + 392599.i −0.185533 + 0.381826i
\(255\) 0 0
\(256\) −931572. 481336.i −0.888417 0.459038i
\(257\) 1.17372e6i 1.10849i 0.832354 + 0.554244i \(0.186993\pi\)
−0.832354 + 0.554244i \(0.813007\pi\)
\(258\) 0 0
\(259\) 557662.i 0.516561i
\(260\) 119459. 93899.5i 0.109594 0.0861450i
\(261\) 0 0
\(262\) −1.57381e6 764729.i −1.41644 0.688263i
\(263\) −307275. −0.273929 −0.136965 0.990576i \(-0.543735\pi\)
−0.136965 + 0.990576i \(0.543735\pi\)
\(264\) 0 0
\(265\) 891678. 0.779998
\(266\) −488877. 237551.i −0.423639 0.205851i
\(267\) 0 0
\(268\) −978366. + 769034.i −0.832079 + 0.654047i
\(269\) 1.40037e6i 1.17994i 0.807424 + 0.589972i \(0.200861\pi\)
−0.807424 + 0.589972i \(0.799139\pi\)
\(270\) 0 0
\(271\) 637013.i 0.526896i −0.964674 0.263448i \(-0.915140\pi\)
0.964674 0.263448i \(-0.0848598\pi\)
\(272\) 93355.3 + 22692.9i 0.0765098 + 0.0185981i
\(273\) 0 0
\(274\) −171356. + 352650.i −0.137887 + 0.283770i
\(275\) −362899. −0.289370
\(276\) 0 0
\(277\) 820888. 0.642813 0.321406 0.946941i \(-0.395844\pi\)
0.321406 + 0.946941i \(0.395844\pi\)
\(278\) −809718. + 1.66639e6i −0.628379 + 1.29320i
\(279\) 0 0
\(280\) −75666.4 348407.i −0.0576777 0.265578i
\(281\) 446685.i 0.337470i 0.985661 + 0.168735i \(0.0539683\pi\)
−0.985661 + 0.168735i \(0.946032\pi\)
\(282\) 0 0
\(283\) 270685.i 0.200908i 0.994942 + 0.100454i \(0.0320296\pi\)
−0.994942 + 0.100454i \(0.967970\pi\)
\(284\) 895380. + 1.13910e6i 0.658736 + 0.838045i
\(285\) 0 0
\(286\) 130538. + 63429.8i 0.0943672 + 0.0458541i
\(287\) −703291. −0.504000
\(288\) 0 0
\(289\) 1.41105e6 0.993800
\(290\) −1.33432e6 648363.i −0.931679 0.452713i
\(291\) 0 0
\(292\) 415290. + 528333.i 0.285033 + 0.362619i
\(293\) 384363.i 0.261561i −0.991411 0.130781i \(-0.958252\pi\)
0.991411 0.130781i \(-0.0417483\pi\)
\(294\) 0 0
\(295\) 203717.i 0.136293i
\(296\) 360632. + 1.66054e6i 0.239241 + 1.10159i
\(297\) 0 0
\(298\) −785265. + 1.61607e6i −0.512242 + 1.05419i
\(299\) 345806. 0.223694
\(300\) 0 0
\(301\) 1.16033e6 0.738185
\(302\) −81268.0 + 167249.i −0.0512746 + 0.105523i
\(303\) 0 0
\(304\) −1.60934e6 391200.i −0.998766 0.242781i
\(305\) 1.83181e6i 1.12754i
\(306\) 0 0
\(307\) 2.20012e6i 1.33229i −0.745820 0.666147i \(-0.767942\pi\)
0.745820 0.666147i \(-0.232058\pi\)
\(308\) 267732. 210448.i 0.160814 0.126406i
\(309\) 0 0
\(310\) 797342. + 387437.i 0.471238 + 0.228980i
\(311\) −2.43025e6 −1.42479 −0.712395 0.701779i \(-0.752389\pi\)
−0.712395 + 0.701779i \(0.752389\pi\)
\(312\) 0 0
\(313\) 406568. 0.234570 0.117285 0.993098i \(-0.462581\pi\)
0.117285 + 0.993098i \(0.462581\pi\)
\(314\) −1.48767e6 722878.i −0.851498 0.413753i
\(315\) 0 0
\(316\) 1.92361e6 1.51203e6i 1.08368 0.851812i
\(317\) 2.49960e6i 1.39709i −0.715568 0.698543i \(-0.753832\pi\)
0.715568 0.698543i \(-0.246168\pi\)
\(318\) 0 0
\(319\) 1.41698e6i 0.779630i
\(320\) −450620. 988512.i −0.246000 0.539644i
\(321\) 0 0
\(322\) 354623. 729809.i 0.190602 0.392256i
\(323\) 151747. 0.0809306
\(324\) 0 0
\(325\) −290144. −0.152372
\(326\) −803155. + 1.65289e6i −0.418558 + 0.861388i
\(327\) 0 0
\(328\) −2.09417e6 + 454809.i −1.07480 + 0.233423i
\(329\) 438023.i 0.223104i
\(330\) 0 0
\(331\) 2.55857e6i 1.28359i −0.766875 0.641797i \(-0.778189\pi\)
0.766875 0.641797i \(-0.221811\pi\)
\(332\) 1.15717e6 + 1.47215e6i 0.576171 + 0.733006i
\(333\) 0 0
\(334\) −2.86805e6 1.39362e6i −1.40676 0.683561i
\(335\) −1.28929e6 −0.627683
\(336\) 0 0
\(337\) 320043. 0.153509 0.0767544 0.997050i \(-0.475544\pi\)
0.0767544 + 0.997050i \(0.475544\pi\)
\(338\) −1.78477e6 867239.i −0.849748 0.412902i
\(339\) 0 0
\(340\) 61512.0 + 78255.6i 0.0288578 + 0.0367129i
\(341\) 846737.i 0.394332i
\(342\) 0 0
\(343\) 1.78725e6i 0.820259i
\(344\) 3.45509e6 750369.i 1.57421 0.341884i
\(345\) 0 0
\(346\) 312617. 643363.i 0.140386 0.288912i
\(347\) 3.56951e6 1.59142 0.795710 0.605678i \(-0.207098\pi\)
0.795710 + 0.605678i \(0.207098\pi\)
\(348\) 0 0
\(349\) −319652. −0.140480 −0.0702400 0.997530i \(-0.522377\pi\)
−0.0702400 + 0.997530i \(0.522377\pi\)
\(350\) −297542. + 612338.i −0.129831 + 0.267191i
\(351\) 0 0
\(352\) 661126. 799784.i 0.284399 0.344046i
\(353\) 1.78942e6i 0.764320i 0.924096 + 0.382160i \(0.124820\pi\)
−0.924096 + 0.382160i \(0.875180\pi\)
\(354\) 0 0
\(355\) 1.50111e6i 0.632183i
\(356\) 466898. 367000.i 0.195253 0.153476i
\(357\) 0 0
\(358\) 3.66299e6 + 1.77989e6i 1.51053 + 0.733981i
\(359\) −1.91480e6 −0.784130 −0.392065 0.919937i \(-0.628239\pi\)
−0.392065 + 0.919937i \(0.628239\pi\)
\(360\) 0 0
\(361\) −139839. −0.0564754
\(362\) −259609. 126147.i −0.104123 0.0505946i
\(363\) 0 0
\(364\) 214056. 168257.i 0.0846788 0.0665609i
\(365\) 696239.i 0.273543i
\(366\) 0 0
\(367\) 882321.i 0.341949i 0.985275 + 0.170974i \(0.0546916\pi\)
−0.985275 + 0.170974i \(0.945308\pi\)
\(368\) 583994. 2.40247e6i 0.224796 0.924778i
\(369\) 0 0
\(370\) −769423. + 1.58346e6i −0.292187 + 0.601318i
\(371\) 1.59778e6 0.602674
\(372\) 0 0
\(373\) −2.86790e6 −1.06731 −0.533657 0.845701i \(-0.679183\pi\)
−0.533657 + 0.845701i \(0.679183\pi\)
\(374\) −41551.8 + 85513.1i −0.0153607 + 0.0316121i
\(375\) 0 0
\(376\) −283263. 1.30429e6i −0.103329 0.475778i
\(377\) 1.13290e6i 0.410525i
\(378\) 0 0
\(379\) 4.53351e6i 1.62120i 0.585602 + 0.810599i \(0.300858\pi\)
−0.585602 + 0.810599i \(0.699142\pi\)
\(380\) −1.06040e6 1.34904e6i −0.376712 0.479253i
\(381\) 0 0
\(382\) 479525. + 233007.i 0.168133 + 0.0816977i
\(383\) 1.75464e6 0.611210 0.305605 0.952158i \(-0.401141\pi\)
0.305605 + 0.952158i \(0.401141\pi\)
\(384\) 0 0
\(385\) 352818. 0.121311
\(386\) −88202.4 42858.5i −0.0301309 0.0146409i
\(387\) 0 0
\(388\) 2.71412e6 + 3.45291e6i 0.915272 + 1.16441i
\(389\) 1.84834e6i 0.619311i −0.950849 0.309656i \(-0.899786\pi\)
0.950849 0.309656i \(-0.100214\pi\)
\(390\) 0 0
\(391\) 226531.i 0.0749353i
\(392\) 510104. + 2.34878e6i 0.167665 + 0.772018i
\(393\) 0 0
\(394\) 1.68340e6 3.46443e6i 0.546321 1.12432i
\(395\) 2.53494e6 0.817476
\(396\) 0 0
\(397\) −1.30700e6 −0.416198 −0.208099 0.978108i \(-0.566728\pi\)
−0.208099 + 0.978108i \(0.566728\pi\)
\(398\) 791847. 1.62961e6i 0.250573 0.515676i
\(399\) 0 0
\(400\) −489993. + 2.01576e6i −0.153123 + 0.629925i
\(401\) 3.45140e6i 1.07185i −0.844265 0.535925i \(-0.819963\pi\)
0.844265 0.535925i \(-0.180037\pi\)
\(402\) 0 0
\(403\) 676981.i 0.207641i
\(404\) 2.44837e6 1.92452e6i 0.746319 0.586636i
\(405\) 0 0
\(406\) −2.39095e6 1.16179e6i −0.719872 0.349794i
\(407\) −1.68156e6 −0.503183
\(408\) 0 0
\(409\) −5.83836e6 −1.72577 −0.862884 0.505402i \(-0.831344\pi\)
−0.862884 + 0.505402i \(0.831344\pi\)
\(410\) −1.99697e6 970352.i −0.586696 0.285082i
\(411\) 0 0
\(412\) 973481. 765194.i 0.282543 0.222090i
\(413\) 365036.i 0.105308i
\(414\) 0 0
\(415\) 1.94001e6i 0.552947i
\(416\) 528582. 639442.i 0.149754 0.181162i
\(417\) 0 0
\(418\) 716305. 1.47415e6i 0.200520 0.412668i
\(419\) 5.29746e6 1.47412 0.737060 0.675827i \(-0.236214\pi\)
0.737060 + 0.675827i \(0.236214\pi\)
\(420\) 0 0
\(421\) −631619. −0.173680 −0.0868400 0.996222i \(-0.527677\pi\)
−0.0868400 + 0.996222i \(0.527677\pi\)
\(422\) 2.71329e6 5.58393e6i 0.741679 1.52637i
\(423\) 0 0
\(424\) 4.75768e6 1.03326e6i 1.28523 0.279123i
\(425\) 190069.i 0.0510432i
\(426\) 0 0
\(427\) 3.28239e6i 0.871205i
\(428\) 848015. + 1.07885e6i 0.223766 + 0.284675i
\(429\) 0 0
\(430\) 3.29472e6 + 1.60094e6i 0.859305 + 0.417546i
\(431\) −6.01340e6 −1.55929 −0.779645 0.626222i \(-0.784600\pi\)
−0.779645 + 0.626222i \(0.784600\pi\)
\(432\) 0 0
\(433\) −5.60717e6 −1.43722 −0.718611 0.695412i \(-0.755222\pi\)
−0.718611 + 0.695412i \(0.755222\pi\)
\(434\) 1.42874e6 + 694242.i 0.364107 + 0.176924i
\(435\) 0 0
\(436\) −827256. 1.05244e6i −0.208413 0.265143i
\(437\) 3.90514e6i 0.978213i
\(438\) 0 0
\(439\) 7.08822e6i 1.75540i −0.479211 0.877700i \(-0.659077\pi\)
0.479211 0.877700i \(-0.340923\pi\)
\(440\) 1.05058e6 228163.i 0.258700 0.0561840i
\(441\) 0 0
\(442\) −33221.4 + 68369.2i −0.00808838 + 0.0166458i
\(443\) −405533. −0.0981786 −0.0490893 0.998794i \(-0.515632\pi\)
−0.0490893 + 0.998794i \(0.515632\pi\)
\(444\) 0 0
\(445\) 615280. 0.147290
\(446\) −2.83255e6 + 5.82937e6i −0.674281 + 1.38766i
\(447\) 0 0
\(448\) −807458. 1.77130e6i −0.190075 0.416962i
\(449\) 5.81570e6i 1.36140i −0.732561 0.680701i \(-0.761675\pi\)
0.732561 0.680701i \(-0.238325\pi\)
\(450\) 0 0
\(451\) 2.12069e6i 0.490947i
\(452\) −774802. + 609025.i −0.178379 + 0.140213i
\(453\) 0 0
\(454\) 4.20905e6 + 2.04523e6i 0.958395 + 0.465695i
\(455\) 282084. 0.0638779
\(456\) 0 0
\(457\) 1.51155e6 0.338558 0.169279 0.985568i \(-0.445856\pi\)
0.169279 + 0.985568i \(0.445856\pi\)
\(458\) 4.07434e6 + 1.97977e6i 0.907599 + 0.441012i
\(459\) 0 0
\(460\) 2.01388e6 1.58299e6i 0.443751 0.348805i
\(461\) 8.52192e6i 1.86761i 0.357787 + 0.933803i \(0.383531\pi\)
−0.357787 + 0.933803i \(0.616469\pi\)
\(462\) 0 0
\(463\) 5.84253e6i 1.26663i 0.773896 + 0.633313i \(0.218305\pi\)
−0.773896 + 0.633313i \(0.781695\pi\)
\(464\) −7.87079e6 1.91324e6i −1.69716 0.412548i
\(465\) 0 0
\(466\) 4.09157e6 8.42041e6i 0.872821 1.79626i
\(467\) 1.60988e6 0.341586 0.170793 0.985307i \(-0.445367\pi\)
0.170793 + 0.985307i \(0.445367\pi\)
\(468\) 0 0
\(469\) −2.31026e6 −0.484986
\(470\) 604353. 1.24375e6i 0.126196 0.259710i
\(471\) 0 0
\(472\) −236064. 1.08696e6i −0.0487724 0.224574i
\(473\) 3.49883e6i 0.719067i
\(474\) 0 0
\(475\) 3.27656e6i 0.666323i
\(476\) 110222. + 140225.i 0.0222973 + 0.0283666i
\(477\) 0 0
\(478\) −4.70367e6 2.28557e6i −0.941602 0.457535i
\(479\) −4.03682e6 −0.803898 −0.401949 0.915662i \(-0.631667\pi\)
−0.401949 + 0.915662i \(0.631667\pi\)
\(480\) 0 0
\(481\) −1.34444e6 −0.264958
\(482\) −551509. 267984.i −0.108127 0.0525402i
\(483\) 0 0
\(484\) −2.55026e6 3.24444e6i −0.494847 0.629545i
\(485\) 4.55026e6i 0.878378i
\(486\) 0 0
\(487\) 6.28957e6i 1.20171i −0.799359 0.600854i \(-0.794827\pi\)
0.799359 0.600854i \(-0.205173\pi\)
\(488\) 2.12268e6 + 9.77390e6i 0.403491 + 1.85788i
\(489\) 0 0
\(490\) −1.08833e6 + 2.23976e6i −0.204771 + 0.421417i
\(491\) 5.26683e6 0.985928 0.492964 0.870050i \(-0.335913\pi\)
0.492964 + 0.870050i \(0.335913\pi\)
\(492\) 0 0
\(493\) 742146. 0.137522
\(494\) 572698. 1.17861e6i 0.105587 0.217296i
\(495\) 0 0
\(496\) 4.70329e6 + 1.14328e6i 0.858415 + 0.208664i
\(497\) 2.68982e6i 0.488463i
\(498\) 0 0
\(499\) 2.24696e6i 0.403966i −0.979389 0.201983i \(-0.935261\pi\)
0.979389 0.201983i \(-0.0647385\pi\)
\(500\) −4.29624e6 + 3.37701e6i −0.768535 + 0.604098i
\(501\) 0 0
\(502\) 3.38744e6 + 1.64599e6i 0.599945 + 0.291520i
\(503\) −7.96470e6 −1.40362 −0.701809 0.712365i \(-0.747624\pi\)
−0.701809 + 0.712365i \(0.747624\pi\)
\(504\) 0 0
\(505\) 3.22648e6 0.562989
\(506\) 2.20065e6 + 1.06932e6i 0.382098 + 0.185665i
\(507\) 0 0
\(508\) −1.94125e6 + 1.52590e6i −0.333752 + 0.262342i
\(509\) 2.49761e6i 0.427297i −0.976911 0.213648i \(-0.931465\pi\)
0.976911 0.213648i \(-0.0685347\pi\)
\(510\) 0 0
\(511\) 1.24758e6i 0.211356i
\(512\) −3.54982e6 4.75217e6i −0.598455 0.801157i
\(513\) 0 0
\(514\) −2.90180e6 + 5.97187e6i −0.484462 + 0.997017i
\(515\) 1.28286e6 0.213138
\(516\) 0 0
\(517\) 1.32080e6 0.217326
\(518\) −1.37871e6 + 2.83738e6i −0.225761 + 0.464615i
\(519\) 0 0
\(520\) 839956. 182420.i 0.136222 0.0295845i
\(521\) 9.44582e6i 1.52456i 0.647246 + 0.762281i \(0.275921\pi\)
−0.647246 + 0.762281i \(0.724079\pi\)
\(522\) 0 0
\(523\) 3.14550e6i 0.502846i 0.967877 + 0.251423i \(0.0808986\pi\)
−0.967877 + 0.251423i \(0.919101\pi\)
\(524\) −6.11686e6 7.78188e6i −0.973196 1.23810i
\(525\) 0 0
\(526\) −1.56341e6 759680.i −0.246382 0.119720i
\(527\) −443479. −0.0695579
\(528\) 0 0
\(529\) −606637. −0.0942519
\(530\) 4.53685e6 + 2.20451e6i 0.701560 + 0.340896i
\(531\) 0 0
\(532\) −1.90010e6 2.41731e6i −0.291071 0.370300i
\(533\) 1.69553e6i 0.258515i
\(534\) 0 0
\(535\) 1.42171e6i 0.214746i
\(536\) −6.87922e6 + 1.49401e6i −1.03425 + 0.224617i
\(537\) 0 0
\(538\) −3.46215e6 + 7.12506e6i −0.515691 + 1.06129i
\(539\) −2.37852e6 −0.352642
\(540\) 0 0
\(541\) −1.17569e6 −0.172703 −0.0863515 0.996265i \(-0.527521\pi\)
−0.0863515 + 0.996265i \(0.527521\pi\)
\(542\) 1.57490e6 3.24112e6i 0.230279 0.473911i
\(543\) 0 0
\(544\) 418887. + 346265.i 0.0606876 + 0.0501662i
\(545\) 1.38690e6i 0.200012i
\(546\) 0 0
\(547\) 1.69619e6i 0.242386i −0.992629 0.121193i \(-0.961328\pi\)
0.992629 0.121193i \(-0.0386719\pi\)
\(548\) −1.74372e6 + 1.37063e6i −0.248042 + 0.194971i
\(549\) 0 0
\(550\) −1.84643e6 897200.i −0.260271 0.126469i
\(551\) −1.27938e7 −1.79523
\(552\) 0 0
\(553\) 4.54231e6 0.631632
\(554\) 4.17667e6 + 2.02949e6i 0.578171 + 0.280939i
\(555\) 0 0
\(556\) −8.23968e6 + 6.47671e6i −1.13038 + 0.888520i
\(557\) 713498.i 0.0974440i −0.998812 0.0487220i \(-0.984485\pi\)
0.998812 0.0487220i \(-0.0155148\pi\)
\(558\) 0 0
\(559\) 2.79737e6i 0.378635i
\(560\) 476382. 1.95977e6i 0.0641926 0.264079i
\(561\) 0 0
\(562\) −1.10435e6 + 2.27273e6i −0.147491 + 0.303534i
\(563\) 1.28328e7 1.70627 0.853137 0.521687i \(-0.174697\pi\)
0.853137 + 0.521687i \(0.174697\pi\)
\(564\) 0 0
\(565\) −1.02104e6 −0.134561
\(566\) −669217. + 1.37724e6i −0.0878064 + 0.180705i
\(567\) 0 0
\(568\) 1.73947e6 + 8.00941e6i 0.226227 + 1.04167i
\(569\) 7.48951e6i 0.969779i −0.874575 0.484890i \(-0.838860\pi\)
0.874575 0.484890i \(-0.161140\pi\)
\(570\) 0 0
\(571\) 8.20920e6i 1.05368i −0.849963 0.526842i \(-0.823376\pi\)
0.849963 0.526842i \(-0.176624\pi\)
\(572\) 507357. + 645460.i 0.0648371 + 0.0824859i
\(573\) 0 0
\(574\) −3.57834e6 1.73876e6i −0.453317 0.220272i
\(575\) −4.89135e6 −0.616962
\(576\) 0 0
\(577\) 1.12522e7 1.40701 0.703505 0.710691i \(-0.251617\pi\)
0.703505 + 0.710691i \(0.251617\pi\)
\(578\) 7.17943e6 + 3.48857e6i 0.893862 + 0.434338i
\(579\) 0 0
\(580\) −5.18607e6 6.59773e6i −0.640131 0.814375i
\(581\) 3.47626e6i 0.427240i
\(582\) 0 0
\(583\) 4.81791e6i 0.587066i
\(584\) 806791. + 3.71488e6i 0.0978879 + 0.450726i
\(585\) 0 0
\(586\) 950266. 1.95564e6i 0.114315 0.235258i
\(587\) 8.39201e6 1.00524 0.502621 0.864507i \(-0.332369\pi\)
0.502621 + 0.864507i \(0.332369\pi\)
\(588\) 0 0
\(589\) 7.64507e6 0.908015
\(590\) 503652. 1.03651e6i 0.0595663 0.122587i
\(591\) 0 0
\(592\) −2.27047e6 + 9.34039e6i −0.266264 + 1.09537i
\(593\) 5.97649e6i 0.697926i 0.937137 + 0.348963i \(0.113466\pi\)
−0.937137 + 0.348963i \(0.886534\pi\)
\(594\) 0 0
\(595\) 184789.i 0.0213985i
\(596\) −7.99084e6 + 6.28112e6i −0.921461 + 0.724305i
\(597\) 0 0
\(598\) 1.75946e6 + 854940.i 0.201199 + 0.0977648i
\(599\) 2.33722e6 0.266153 0.133077 0.991106i \(-0.457514\pi\)
0.133077 + 0.991106i \(0.457514\pi\)
\(600\) 0 0
\(601\) 5.95099e6 0.672052 0.336026 0.941853i \(-0.390917\pi\)
0.336026 + 0.941853i \(0.390917\pi\)
\(602\) 5.90375e6 + 2.86870e6i 0.663952 + 0.322622i
\(603\) 0 0
\(604\) −826982. + 650040.i −0.0922367 + 0.0725016i
\(605\) 4.27554e6i 0.474900i
\(606\) 0 0
\(607\) 1.38582e7i 1.52663i −0.646026 0.763316i \(-0.723570\pi\)
0.646026 0.763316i \(-0.276430\pi\)
\(608\) −7.22114e6 5.96921e6i −0.792222 0.654874i
\(609\) 0 0
\(610\) −4.52881e6 + 9.32025e6i −0.492788 + 1.01415i
\(611\) 1.05600e6 0.114436
\(612\) 0 0
\(613\) 8.69155e6 0.934214 0.467107 0.884201i \(-0.345296\pi\)
0.467107 + 0.884201i \(0.345296\pi\)
\(614\) 5.43938e6 1.11942e7i 0.582276 1.19832i
\(615\) 0 0
\(616\) 1.88251e6 408840.i 0.199888 0.0434112i
\(617\) 1.37669e7i 1.45587i −0.685646 0.727936i \(-0.740480\pi\)
0.685646 0.727936i \(-0.259520\pi\)
\(618\) 0 0
\(619\) 5.73601e6i 0.601704i 0.953671 + 0.300852i \(0.0972710\pi\)
−0.953671 + 0.300852i \(0.902729\pi\)
\(620\) 3.09900e6 + 3.94256e6i 0.323775 + 0.411907i
\(621\) 0 0
\(622\) −1.23651e7 6.00834e6i −1.28151 0.622700i
\(623\) 1.10251e6 0.113805
\(624\) 0 0
\(625\) 669150. 0.0685209
\(626\) 2.06862e6 + 1.00516e6i 0.210981 + 0.102518i
\(627\) 0 0
\(628\) −5.78210e6 7.35599e6i −0.585041 0.744290i
\(629\) 880717.i 0.0887585i
\(630\) 0 0
\(631\) 3.53427e6i 0.353368i −0.984268 0.176684i \(-0.943463\pi\)
0.984268 0.176684i \(-0.0565370\pi\)
\(632\) 1.35255e7 2.93745e6i 1.34698 0.292535i
\(633\) 0 0
\(634\) 6.17980e6 1.27180e7i 0.610592 1.25659i
\(635\) −2.55819e6 −0.251767
\(636\) 0 0
\(637\) −1.90167e6 −0.185689
\(638\) 3.50323e6 7.20961e6i 0.340735 0.701229i
\(639\) 0 0
\(640\) 151158. 6.14362e6i 0.0145875 0.592890i
\(641\) 717761.i 0.0689978i 0.999405 + 0.0344989i \(0.0109835\pi\)
−0.999405 + 0.0344989i \(0.989016\pi\)
\(642\) 0 0
\(643\) 7.19240e6i 0.686035i −0.939329 0.343017i \(-0.888551\pi\)
0.939329 0.343017i \(-0.111449\pi\)
\(644\) 3.60863e6 2.83653e6i 0.342869 0.269508i
\(645\) 0 0
\(646\) 772086. + 375165.i 0.0727921 + 0.0353705i
\(647\) 1.35541e6 0.127294 0.0636472 0.997972i \(-0.479727\pi\)
0.0636472 + 0.997972i \(0.479727\pi\)
\(648\) 0 0
\(649\) 1.10072e6 0.102581
\(650\) −1.47625e6 717327.i −0.137049 0.0665938i
\(651\) 0 0
\(652\) −8.17290e6 + 6.42422e6i −0.752934 + 0.591836i
\(653\) 7.90801e6i 0.725745i −0.931839 0.362873i \(-0.881796\pi\)
0.931839 0.362873i \(-0.118204\pi\)
\(654\) 0 0
\(655\) 1.02550e7i 0.933967i
\(656\) −1.17796e7 2.86339e6i −1.06873 0.259789i
\(657\) 0 0
\(658\) 1.08293e6 2.22866e6i 0.0975068 0.200668i
\(659\) 1.60268e7 1.43758 0.718792 0.695226i \(-0.244696\pi\)
0.718792 + 0.695226i \(0.244696\pi\)
\(660\) 0 0
\(661\) 1.22510e7 1.09061 0.545303 0.838239i \(-0.316415\pi\)
0.545303 + 0.838239i \(0.316415\pi\)
\(662\) 6.32558e6 1.30180e7i 0.560991 1.15451i
\(663\) 0 0
\(664\) 2.24805e6 + 1.03512e7i 0.197873 + 0.911108i
\(665\) 3.18555e6i 0.279338i
\(666\) 0 0
\(667\) 1.90989e7i 1.66224i
\(668\) −1.11472e7 1.41814e7i −0.966546 1.22964i
\(669\) 0 0
\(670\) −6.55992e6 3.18754e6i −0.564562 0.274327i
\(671\) −9.89764e6 −0.848643
\(672\) 0 0
\(673\) −8.62568e6 −0.734101 −0.367051 0.930201i \(-0.619632\pi\)
−0.367051 + 0.930201i \(0.619632\pi\)
\(674\) 1.62838e6 + 791246.i 0.138072 + 0.0670906i
\(675\) 0 0
\(676\) −6.93681e6 8.82501e6i −0.583839 0.742760i
\(677\) 3.13206e6i 0.262638i −0.991340 0.131319i \(-0.958079\pi\)
0.991340 0.131319i \(-0.0419213\pi\)
\(678\) 0 0
\(679\) 8.15352e6i 0.678689i
\(680\) 119500. + 550241.i 0.00991052 + 0.0456332i
\(681\) 0 0
\(682\) −2.09340e6 + 4.30819e6i −0.172342 + 0.354678i
\(683\) 1.42490e7 1.16878 0.584389 0.811473i \(-0.301334\pi\)
0.584389 + 0.811473i \(0.301334\pi\)
\(684\) 0 0
\(685\) −2.29788e6 −0.187112
\(686\) −4.41865e6 + 9.09354e6i −0.358492 + 0.737773i
\(687\) 0 0
\(688\) 1.94346e7 + 4.72418e6i 1.56532 + 0.380501i
\(689\) 3.85200e6i 0.309128i
\(690\) 0 0
\(691\) 6.95060e6i 0.553767i 0.960904 + 0.276883i \(0.0893016\pi\)
−0.960904 + 0.276883i \(0.910698\pi\)
\(692\) 3.18119e6 2.50054e6i 0.252537 0.198504i
\(693\) 0 0
\(694\) 1.81616e7 + 8.82494e6i 1.43138 + 0.695526i
\(695\) −1.08583e7 −0.852705
\(696\) 0 0
\(697\) 1.11071e6 0.0866002
\(698\) −1.62639e6 790281.i −0.126353 0.0613964i
\(699\) 0 0
\(700\) −3.02778e6 + 2.37996e6i −0.233550 + 0.183579i
\(701\) 4.21552e6i 0.324008i −0.986790 0.162004i \(-0.948204\pi\)
0.986790 0.162004i \(-0.0517958\pi\)
\(702\) 0 0
\(703\) 1.51826e7i 1.15866i
\(704\) 5.34112e6 2.43479e6i 0.406163 0.185152i
\(705\) 0 0
\(706\) −4.42400e6 + 9.10455e6i −0.334044 + 0.687459i
\(707\) 5.78146e6 0.435000
\(708\) 0 0
\(709\) −5.08494e6 −0.379901 −0.189950 0.981794i \(-0.560833\pi\)
−0.189950 + 0.981794i \(0.560833\pi\)
\(710\) −3.71122e6 + 7.63766e6i −0.276294 + 0.568610i
\(711\) 0 0
\(712\) 3.28291e6 712977.i 0.242694 0.0527079i
\(713\) 1.14128e7i 0.840750i
\(714\) 0 0
\(715\) 850590.i 0.0622236i
\(716\) 1.42368e7 + 1.81121e7i 1.03784 + 1.32034i
\(717\) 0 0
\(718\) −9.74251e6 4.73399e6i −0.705277 0.342702i
\(719\) 2.52087e6 0.181856 0.0909281 0.995857i \(-0.471017\pi\)
0.0909281 + 0.995857i \(0.471017\pi\)
\(720\) 0 0
\(721\) 2.29873e6 0.164683
\(722\) −711498. 345725.i −0.0507962 0.0246824i
\(723\) 0 0
\(724\) −1.00901e6 1.28367e6i −0.0715402 0.0910135i
\(725\) 1.60247e7i 1.13225i
\(726\) 0 0
\(727\) 2.28089e7i 1.60054i 0.599637 + 0.800272i \(0.295312\pi\)
−0.599637 + 0.800272i \(0.704688\pi\)
\(728\) 1.50510e6 326875.i 0.105254 0.0228588i
\(729\) 0 0
\(730\) −1.72132e6 + 3.54246e6i −0.119551 + 0.246036i
\(731\) −1.83251e6 −0.126839
\(732\) 0 0
\(733\) −4.13592e6 −0.284323 −0.142161 0.989843i \(-0.545405\pi\)
−0.142161 + 0.989843i \(0.545405\pi\)
\(734\) −2.18137e6 + 4.48924e6i −0.149448 + 0.307562i
\(735\) 0 0
\(736\) 8.91100e6 1.07799e7i 0.606362 0.733535i
\(737\) 6.96631e6i 0.472426i
\(738\) 0 0
\(739\) 2.06353e6i 0.138995i −0.997582 0.0694974i \(-0.977860\pi\)
0.997582 0.0694974i \(-0.0221396\pi\)
\(740\) −7.82964e6 + 6.15440e6i −0.525608 + 0.413149i
\(741\) 0 0
\(742\) 8.12950e6 + 3.95021e6i 0.542068 + 0.263397i
\(743\) −2.14217e7 −1.42358 −0.711789 0.702393i \(-0.752115\pi\)
−0.711789 + 0.702393i \(0.752115\pi\)
\(744\) 0 0
\(745\) −1.05304e7 −0.695109
\(746\) −1.45919e7 7.09035e6i −0.959984 0.466467i
\(747\) 0 0
\(748\) −422830. + 332361.i −0.0276320 + 0.0217198i
\(749\) 2.54753e6i 0.165926i
\(750\) 0 0
\(751\) 1.18689e7i 0.767910i 0.923352 + 0.383955i \(0.125438\pi\)
−0.923352 + 0.383955i \(0.874562\pi\)
\(752\) 1.78337e6 7.33653e6i 0.115000 0.473093i
\(753\) 0 0
\(754\) 2.80089e6 5.76421e6i 0.179419 0.369242i
\(755\) −1.08980e6 −0.0695792
\(756\) 0 0
\(757\) −1.89960e7 −1.20482 −0.602412 0.798186i \(-0.705793\pi\)
−0.602412 + 0.798186i \(0.705793\pi\)
\(758\) −1.12082e7 + 2.30664e7i −0.708540 + 1.45817i
\(759\) 0 0
\(760\) −2.06005e6 9.48553e6i −0.129373 0.595700i
\(761\) 2.59190e7i 1.62240i 0.584771 + 0.811198i \(0.301184\pi\)
−0.584771 + 0.811198i \(0.698816\pi\)
\(762\) 0 0
\(763\) 2.48517e6i 0.154541i
\(764\) 1.86375e6 + 2.37107e6i 0.115520 + 0.146964i
\(765\) 0 0
\(766\) 8.92758e6 + 4.33801e6i 0.549746 + 0.267128i
\(767\) 880046. 0.0540153
\(768\) 0 0
\(769\) −2.19627e7 −1.33927 −0.669637 0.742689i \(-0.733550\pi\)
−0.669637 + 0.742689i \(0.733550\pi\)
\(770\) 1.79514e6 + 872277.i 0.109112 + 0.0530185i
\(771\) 0 0
\(772\) −342814. 436128.i −0.0207021 0.0263373i
\(773\) 1.80022e7i 1.08362i −0.840501 0.541810i \(-0.817739\pi\)
0.840501 0.541810i \(-0.182261\pi\)
\(774\) 0 0
\(775\) 9.57575e6i 0.572688i
\(776\) 5.27276e6 + 2.42785e7i 0.314329 + 1.44733i
\(777\) 0 0
\(778\) 4.56969e6 9.40436e6i 0.270668 0.557032i
\(779\) −1.91474e7 −1.13049
\(780\) 0 0
\(781\) −8.11081e6 −0.475813
\(782\) −560057. + 1.15259e6i −0.0327503 + 0.0673997i
\(783\) 0 0
\(784\) −3.21152e6 + 1.32117e7i −0.186604 + 0.767660i
\(785\) 9.69375e6i 0.561459i
\(786\) 0 0
\(787\)