Properties

Label 108.6.b.b.107.4
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 107.4
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.107.3

$q$-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 \(-0.926415\pi\)
0.973398 0.229121i \(-0.0735851\pi\)
\(8\) −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 \(-0.428354\pi\)
0.223187 + 0.974776i \(0.428354\pi\)
\(12\) 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 \(-0.828191\pi\)
0.857835 0.513925i \(-0.171809\pi\)
\(20\) 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 \(-0.342139\pi\)
0.475854 + 0.879524i \(0.342139\pi\)
\(24\) 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 \(0.145627\pi\)
−0.897160 + 0.441706i \(0.854373\pi\)
\(32\) 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 \(0.298078\pi\)
−0.592659 + 0.805454i \(0.701922\pi\)
\(44\) 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 \(-0.421726\pi\)
0.243435 + 0.969917i \(0.421726\pi\)
\(48\) 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 \(-0.463344\pi\)
0.114904 + 0.993377i \(0.463344\pi\)
\(60\) 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 \(-0.822499\pi\)
0.848509 0.529182i \(-0.177501\pi\)
\(68\) −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 \(-0.678926\pi\)
−0.532976 + 0.846131i \(0.678926\pi\)
\(72\) 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 \(0.242034\pi\)
−0.724580 + 0.689191i \(0.757966\pi\)
\(80\) 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 \(-0.654368\pi\)
−0.466174 + 0.884693i \(0.654368\pi\)
\(84\) 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 \(0.0575096\pi\)
−0.983723 + 0.179690i \(0.942490\pi\)
\(104\) 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 \(-0.557948\pi\)
−0.181046 + 0.983475i \(0.557948\pi\)
\(108\) 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 \(-0.931918\pi\)
0.977214 0.212258i \(-0.0680816\pi\)
\(128\) 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 \(-0.211426\pi\)
0.787401 + 0.616441i \(0.211426\pi\)
\(132\) 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 \(-0.744650\pi\)
0.695122 0.718891i \(-0.255350\pi\)
\(140\) 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 \(-0.981317\pi\)
0.998278 0.0586602i \(-0.0186829\pi\)
\(152\) 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 \(-0.841055\pi\)
0.877898 0.478848i \(-0.158945\pi\)
\(164\) 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 \(-0.214189\pi\)
0.782021 + 0.623251i \(0.214189\pi\)
\(168\) 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 \(-0.817272\pi\)
−0.839705 + 0.543043i \(0.817272\pi\)
\(180\) 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 \(-0.529794\pi\)
−0.0934655 + 0.995623i \(0.529794\pi\)
\(192\) 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 \(0.0925468\pi\)
−0.958031 + 0.286665i \(0.907453\pi\)
\(200\) −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 \(0.322500\pi\)
−0.529178 + 0.848511i \(0.677500\pi\)
\(212\) −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 \(-0.719554\pi\)
0.636344 0.771406i \(-0.280446\pi\)
\(224\) 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 \(-0.678851\pi\)
−0.532774 + 0.846257i \(0.678851\pi\)
\(228\) 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 \(-0.324649\pi\)
0.523439 + 0.852063i \(0.324649\pi\)
\(240\) 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 \(-0.608233\pi\)
−0.333511 + 0.942746i \(0.608233\pi\)
\(252\) 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 \(-0.456265\pi\)
0.136965 + 0.990576i \(0.456265\pi\)
\(264\) 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 \(0.0848598\pi\)
−0.964674 + 0.263448i \(0.915140\pi\)
\(272\) −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 \(-0.967970\pi\)
0.994942 0.100454i \(-0.0320296\pi\)
\(284\) −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 \(0.232058\pi\)
−0.745820 + 0.666147i \(0.767942\pi\)
\(308\) −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 \(-0.247611\pi\)
0.712395 + 0.701779i \(0.247611\pi\)
\(312\) 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 \(0.221811\pi\)
−0.766875 + 0.641797i \(0.778189\pi\)
\(332\) −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 \(-0.792902\pi\)
−0.795710 + 0.605678i \(0.792902\pi\)
\(348\) 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 \(-0.371761\pi\)
0.392065 + 0.919937i \(0.371761\pi\)
\(360\) 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 \(-0.945308\pi\)
0.985275 0.170974i \(-0.0546916\pi\)
\(368\) −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 \(-0.699142\pi\)
0.585602 0.810599i \(-0.300858\pi\)
\(380\) 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 \(-0.598859\pi\)
−0.305605 + 0.952158i \(0.598859\pi\)
\(384\) 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 \(-0.763786\pi\)
−0.737060 + 0.675827i \(0.763786\pi\)
\(420\) 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 \(-0.215400\pi\)
0.779645 + 0.626222i \(0.215400\pi\)
\(432\) 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 \(0.340923\pi\)
−0.479211 + 0.877700i \(0.659077\pi\)
\(440\) −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 \(-0.484368\pi\)
0.0490893 + 0.998794i \(0.484368\pi\)
\(444\) 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 \(-0.781695\pi\)
0.773896 0.633313i \(-0.218305\pi\)
\(464\) 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 \(-0.554633\pi\)
−0.170793 + 0.985307i \(0.554633\pi\)
\(468\) 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 \(-0.368333\pi\)
0.401949 + 0.915662i \(0.368333\pi\)
\(480\) 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 \(0.205173\pi\)
−0.799359 + 0.600854i \(0.794827\pi\)
\(488\) −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 \(-0.664087\pi\)
−0.492964 + 0.870050i \(0.664087\pi\)
\(492\) 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 \(0.0647385\pi\)
−0.979389 + 0.201983i \(0.935261\pi\)
\(500\) 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 \(-0.252376\pi\)
0.701809 + 0.712365i \(0.252376\pi\)
\(504\) 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 \(-0.919101\pi\)
0.967877 0.251423i \(-0.0808986\pi\)
\(524\) 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 \(0.0386719\pi\)
−0.992629 + 0.121193i \(0.961328\pi\)
\(548\) 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 \(-0.825303\pi\)
−0.853137 + 0.521687i \(0.825303\pi\)
\(564\) 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 \(0.176624\pi\)
−0.849963 + 0.526842i \(0.823376\pi\)
\(572\) −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 \(-0.667631\pi\)
−0.502621 + 0.864507i \(0.667631\pi\)
\(588\) 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 \(-0.542486\pi\)
−0.133077 + 0.991106i \(0.542486\pi\)
\(600\) 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 \(0.276430\pi\)
−0.646026 + 0.763316i \(0.723570\pi\)
\(608\) 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 \(-0.902729\pi\)
0.953671 0.300852i \(-0.0972710\pi\)
\(620\) −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 \(0.0565370\pi\)
−0.984268 + 0.176684i \(0.943463\pi\)
\(632\) −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 \(0.111449\pi\)
−0.939329 + 0.343017i \(0.888551\pi\)
\(644\) −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 \(-0.520273\pi\)
−0.0636472 + 0.997972i \(0.520273\pi\)
\(648\) 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 \(-0.755304\pi\)
−0.718792 + 0.695226i \(0.755304\pi\)
\(660\) 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 \(-0.698666\pi\)
−0.584389 + 0.811473i \(0.698666\pi\)
\(684\) 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 \(-0.910698\pi\)
0.960904 0.276883i \(-0.0893016\pi\)
\(692\) −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 \(-0.528983\pi\)
−0.0909281 + 0.995857i \(0.528983\pi\)
\(720\) 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 \(-0.704688\pi\)
0.599637 0.800272i \(-0.295312\pi\)
\(728\) −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 \(0.0221396\pi\)
−0.997582 + 0.0694974i \(0.977860\pi\)
\(740\) 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 \(-0.247885\pi\)
0.711789 + 0.702393i \(0.247885\pi\)
\(744\) 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 \(-0.874562\pi\)
0.923352 0.383955i \(-0.125438\pi\)
\(752\) −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