Properties

Label 108.6.b.a.107.4
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 4
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: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{-29})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.4
Root \(0.866025 - 2.69258i\) of \(x^{4} + 13 x^{2} + 64\)
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.a.107.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 + 5.38516i) q^{2} +(-26.0000 + 18.6548i) q^{4} +91.5478i q^{5} +158.565i q^{7} +(-145.492 - 107.703i) q^{8} +O(q^{10})\) \(q+(1.73205 + 5.38516i) q^{2} +(-26.0000 + 18.6548i) q^{4} +91.5478i q^{5} +158.565i q^{7} +(-145.492 - 107.703i) q^{8} +(-493.000 + 158.565i) q^{10} +580.237 q^{11} -166.000 q^{13} +(-853.901 + 274.643i) q^{14} +(328.000 - 970.047i) q^{16} -829.315i q^{17} +671.571i q^{19} +(-1707.80 - 2380.24i) q^{20} +(1005.00 + 3124.67i) q^{22} -3859.01 q^{23} -5256.00 q^{25} +(-287.520 - 893.937i) q^{26} +(-2958.00 - 4122.70i) q^{28} -3414.19i q^{29} +6333.29i q^{31} +(5791.98 + 86.1626i) q^{32} +(4466.00 - 1436.42i) q^{34} -14516.3 q^{35} +15332.0 q^{37} +(-3616.52 + 1163.20i) q^{38} +(9860.00 - 13319.5i) q^{40} -10102.6i q^{41} -3003.42i q^{43} +(-15086.2 + 10824.2i) q^{44} +(-6684.00 - 20781.4i) q^{46} +7070.23 q^{47} -8336.00 q^{49} +(-9103.66 - 28304.4i) q^{50} +(4316.00 - 3096.69i) q^{52} +17281.0i q^{53} +53119.4i q^{55} +(17078.0 - 23070.0i) q^{56} +(18386.0 - 5913.56i) q^{58} +28429.9 q^{59} -53188.0 q^{61} +(-34105.8 + 10969.6i) q^{62} +(9568.00 + 31340.0i) q^{64} -15196.9i q^{65} +41059.1i q^{67} +(15470.7 + 21562.2i) q^{68} +(-25143.0 - 78172.8i) q^{70} +26822.5 q^{71} -30739.0 q^{73} +(26555.8 + 82565.3i) q^{74} +(-12528.0 - 17460.9i) q^{76} +92005.5i q^{77} +70197.9i q^{79} +(88805.7 + 30027.7i) q^{80} +(54404.0 - 17498.2i) q^{82} -11402.1 q^{83} +75922.0 q^{85} +(16173.9 - 5202.07i) q^{86} +(-84420.0 - 62493.4i) q^{88} -68682.4i q^{89} -26321.9i q^{91} +(100334. - 71988.9i) q^{92} +(12246.0 + 38074.4i) q^{94} -61480.9 q^{95} -13717.0 q^{97} +(-14438.4 - 44890.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 104q^{4} + O(q^{10}) \) \( 4q - 104q^{4} - 1972q^{10} - 664q^{13} + 1312q^{16} + 4020q^{22} - 21024q^{25} - 11832q^{28} + 17864q^{34} + 61328q^{37} + 39440q^{40} - 26736q^{46} - 33344q^{49} + 17264q^{52} + 73544q^{58} - 212752q^{61} + 38272q^{64} - 100572q^{70} - 122956q^{73} - 50112q^{76} + 217616q^{82} + 303688q^{85} - 337680q^{88} + 48984q^{94} - 54868q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 + 5.38516i 0.306186 + 0.951972i
\(3\) 0 0
\(4\) −26.0000 + 18.6548i −0.812500 + 0.582961i
\(5\) 91.5478i 1.63766i 0.574038 + 0.818828i \(0.305376\pi\)
−0.574038 + 0.818828i \(0.694624\pi\)
\(6\) 0 0
\(7\) 158.565i 1.22310i 0.791204 + 0.611552i \(0.209455\pi\)
−0.791204 + 0.611552i \(0.790545\pi\)
\(8\) −145.492 107.703i −0.803739 0.594982i
\(9\) 0 0
\(10\) −493.000 + 158.565i −1.55900 + 0.501428i
\(11\) 580.237 1.44585 0.722926 0.690926i \(-0.242797\pi\)
0.722926 + 0.690926i \(0.242797\pi\)
\(12\) 0 0
\(13\) −166.000 −0.272427 −0.136213 0.990680i \(-0.543493\pi\)
−0.136213 + 0.990680i \(0.543493\pi\)
\(14\) −853.901 + 274.643i −1.16436 + 0.374498i
\(15\) 0 0
\(16\) 328.000 970.047i 0.320312 0.947312i
\(17\) 829.315i 0.695981i −0.937498 0.347991i \(-0.886864\pi\)
0.937498 0.347991i \(-0.113136\pi\)
\(18\) 0 0
\(19\) 671.571i 0.426784i 0.976967 + 0.213392i \(0.0684511\pi\)
−0.976967 + 0.213392i \(0.931549\pi\)
\(20\) −1707.80 2380.24i −0.954690 1.33060i
\(21\) 0 0
\(22\) 1005.00 + 3124.67i 0.442700 + 1.37641i
\(23\) −3859.01 −1.52109 −0.760547 0.649283i \(-0.775069\pi\)
−0.760547 + 0.649283i \(0.775069\pi\)
\(24\) 0 0
\(25\) −5256.00 −1.68192
\(26\) −287.520 893.937i −0.0834133 0.259343i
\(27\) 0 0
\(28\) −2958.00 4122.70i −0.713022 0.993772i
\(29\) 3414.19i 0.753864i −0.926241 0.376932i \(-0.876979\pi\)
0.926241 0.376932i \(-0.123021\pi\)
\(30\) 0 0
\(31\) 6333.29i 1.18366i 0.806065 + 0.591828i \(0.201593\pi\)
−0.806065 + 0.591828i \(0.798407\pi\)
\(32\) 5791.98 + 86.1626i 0.999889 + 0.0148746i
\(33\) 0 0
\(34\) 4466.00 1436.42i 0.662554 0.213100i
\(35\) −14516.3 −2.00302
\(36\) 0 0
\(37\) 15332.0 1.84117 0.920586 0.390539i \(-0.127711\pi\)
0.920586 + 0.390539i \(0.127711\pi\)
\(38\) −3616.52 + 1163.20i −0.406286 + 0.130675i
\(39\) 0 0
\(40\) 9860.00 13319.5i 0.974377 1.31625i
\(41\) 10102.6i 0.938582i −0.883044 0.469291i \(-0.844510\pi\)
0.883044 0.469291i \(-0.155490\pi\)
\(42\) 0 0
\(43\) 3003.42i 0.247710i −0.992300 0.123855i \(-0.960474\pi\)
0.992300 0.123855i \(-0.0395258\pi\)
\(44\) −15086.2 + 10824.2i −1.17475 + 0.842875i
\(45\) 0 0
\(46\) −6684.00 20781.4i −0.465738 1.44804i
\(47\) 7070.23 0.466862 0.233431 0.972373i \(-0.425005\pi\)
0.233431 + 0.972373i \(0.425005\pi\)
\(48\) 0 0
\(49\) −8336.00 −0.495984
\(50\) −9103.66 28304.4i −0.514981 1.60114i
\(51\) 0 0
\(52\) 4316.00 3096.69i 0.221347 0.158814i
\(53\) 17281.0i 0.845043i 0.906353 + 0.422522i \(0.138855\pi\)
−0.906353 + 0.422522i \(0.861145\pi\)
\(54\) 0 0
\(55\) 53119.4i 2.36781i
\(56\) 17078.0 23070.0i 0.727725 0.983056i
\(57\) 0 0
\(58\) 18386.0 5913.56i 0.717658 0.230823i
\(59\) 28429.9 1.06327 0.531637 0.846972i \(-0.321577\pi\)
0.531637 + 0.846972i \(0.321577\pi\)
\(60\) 0 0
\(61\) −53188.0 −1.83016 −0.915080 0.403272i \(-0.867873\pi\)
−0.915080 + 0.403272i \(0.867873\pi\)
\(62\) −34105.8 + 10969.6i −1.12681 + 0.362419i
\(63\) 0 0
\(64\) 9568.00 + 31340.0i 0.291992 + 0.956421i
\(65\) 15196.9i 0.446141i
\(66\) 0 0
\(67\) 41059.1i 1.11744i 0.829358 + 0.558718i \(0.188707\pi\)
−0.829358 + 0.558718i \(0.811293\pi\)
\(68\) 15470.7 + 21562.2i 0.405730 + 0.565485i
\(69\) 0 0
\(70\) −25143.0 78172.8i −0.613299 1.90682i
\(71\) 26822.5 0.631472 0.315736 0.948847i \(-0.397749\pi\)
0.315736 + 0.948847i \(0.397749\pi\)
\(72\) 0 0
\(73\) −30739.0 −0.675123 −0.337561 0.941304i \(-0.609602\pi\)
−0.337561 + 0.941304i \(0.609602\pi\)
\(74\) 26555.8 + 82565.3i 0.563742 + 1.75274i
\(75\) 0 0
\(76\) −12528.0 17460.9i −0.248799 0.346762i
\(77\) 92005.5i 1.76843i
\(78\) 0 0
\(79\) 70197.9i 1.26548i 0.774363 + 0.632741i \(0.218070\pi\)
−0.774363 + 0.632741i \(0.781930\pi\)
\(80\) 88805.7 + 30027.7i 1.55137 + 0.524562i
\(81\) 0 0
\(82\) 54404.0 17498.2i 0.893503 0.287381i
\(83\) −11402.1 −0.181673 −0.0908363 0.995866i \(-0.528954\pi\)
−0.0908363 + 0.995866i \(0.528954\pi\)
\(84\) 0 0
\(85\) 75922.0 1.13978
\(86\) 16173.9 5202.07i 0.235813 0.0758455i
\(87\) 0 0
\(88\) −84420.0 62493.4i −1.16209 0.860256i
\(89\) 68682.4i 0.919116i −0.888148 0.459558i \(-0.848008\pi\)
0.888148 0.459558i \(-0.151992\pi\)
\(90\) 0 0
\(91\) 26321.9i 0.333206i
\(92\) 100334. 71988.9i 1.23589 0.886739i
\(93\) 0 0
\(94\) 12246.0 + 38074.4i 0.142947 + 0.444440i
\(95\) −61480.9 −0.698926
\(96\) 0 0
\(97\) −13717.0 −0.148023 −0.0740116 0.997257i \(-0.523580\pi\)
−0.0740116 + 0.997257i \(0.523580\pi\)
\(98\) −14438.4 44890.7i −0.151863 0.472163i
\(99\) 0 0
\(100\) 136656. 98049.4i 1.36656 0.980494i
\(101\) 8492.40i 0.0828376i 0.999142 + 0.0414188i \(0.0131878\pi\)
−0.999142 + 0.0414188i \(0.986812\pi\)
\(102\) 0 0
\(103\) 167986.i 1.56020i 0.625655 + 0.780100i \(0.284832\pi\)
−0.625655 + 0.780100i \(0.715168\pi\)
\(104\) 24151.7 + 17878.7i 0.218960 + 0.162089i
\(105\) 0 0
\(106\) −93061.0 + 29931.6i −0.804457 + 0.258741i
\(107\) 108875. 0.919324 0.459662 0.888094i \(-0.347971\pi\)
0.459662 + 0.888094i \(0.347971\pi\)
\(108\) 0 0
\(109\) −87628.0 −0.706442 −0.353221 0.935540i \(-0.614914\pi\)
−0.353221 + 0.935540i \(0.614914\pi\)
\(110\) −286057. + 92005.5i −2.25409 + 0.724990i
\(111\) 0 0
\(112\) 153816. + 52009.5i 1.15866 + 0.391776i
\(113\) 98139.2i 0.723014i 0.932369 + 0.361507i \(0.117738\pi\)
−0.932369 + 0.361507i \(0.882262\pi\)
\(114\) 0 0
\(115\) 353284.i 2.49103i
\(116\) 63691.0 + 88769.1i 0.439474 + 0.612515i
\(117\) 0 0
\(118\) 49242.0 + 153100.i 0.325560 + 1.01221i
\(119\) 131501. 0.851257
\(120\) 0 0
\(121\) 175624. 1.09049
\(122\) −92124.3 286426.i −0.560370 1.74226i
\(123\) 0 0
\(124\) −118146. 164666.i −0.690025 0.961720i
\(125\) 195088.i 1.11675i
\(126\) 0 0
\(127\) 6240.02i 0.0343302i −0.999853 0.0171651i \(-0.994536\pi\)
0.999853 0.0171651i \(-0.00546409\pi\)
\(128\) −152199. + 105808.i −0.821081 + 0.570811i
\(129\) 0 0
\(130\) 81838.0 26321.9i 0.424714 0.136602i
\(131\) −177727. −0.904849 −0.452425 0.891803i \(-0.649441\pi\)
−0.452425 + 0.891803i \(0.649441\pi\)
\(132\) 0 0
\(133\) −106488. −0.522001
\(134\) −221110. + 71116.5i −1.06377 + 0.342144i
\(135\) 0 0
\(136\) −89320.0 + 120659.i −0.414096 + 0.559387i
\(137\) 23339.3i 0.106240i 0.998588 + 0.0531198i \(0.0169165\pi\)
−0.998588 + 0.0531198i \(0.983083\pi\)
\(138\) 0 0
\(139\) 209717.i 0.920653i −0.887750 0.460327i \(-0.847732\pi\)
0.887750 0.460327i \(-0.152268\pi\)
\(140\) 377424. 270798.i 1.62746 1.16769i
\(141\) 0 0
\(142\) 46458.0 + 144444.i 0.193348 + 0.601143i
\(143\) −96319.3 −0.393889
\(144\) 0 0
\(145\) 312562. 1.23457
\(146\) −53241.5 165535.i −0.206713 0.642697i
\(147\) 0 0
\(148\) −398632. + 286015.i −1.49595 + 1.07333i
\(149\) 186591.i 0.688532i 0.938872 + 0.344266i \(0.111872\pi\)
−0.938872 + 0.344266i \(0.888128\pi\)
\(150\) 0 0
\(151\) 145890.i 0.520693i 0.965515 + 0.260347i \(0.0838368\pi\)
−0.965515 + 0.260347i \(0.916163\pi\)
\(152\) 72330.4 97708.4i 0.253929 0.343023i
\(153\) 0 0
\(154\) −495465. + 159358.i −1.68349 + 0.541468i
\(155\) −579799. −1.93842
\(156\) 0 0
\(157\) −223132. −0.722458 −0.361229 0.932477i \(-0.617643\pi\)
−0.361229 + 0.932477i \(0.617643\pi\)
\(158\) −378027. + 121586.i −1.20470 + 0.387473i
\(159\) 0 0
\(160\) −7888.00 + 530243.i −0.0243594 + 1.63748i
\(161\) 611906.i 1.86046i
\(162\) 0 0
\(163\) 88927.2i 0.262160i −0.991372 0.131080i \(-0.958156\pi\)
0.991372 0.131080i \(-0.0418444\pi\)
\(164\) 188461. + 262667.i 0.547157 + 0.762598i
\(165\) 0 0
\(166\) −19749.0 61402.1i −0.0556256 0.172947i
\(167\) −309029. −0.857449 −0.428724 0.903435i \(-0.641037\pi\)
−0.428724 + 0.903435i \(0.641037\pi\)
\(168\) 0 0
\(169\) −343737. −0.925784
\(170\) 131501. + 408852.i 0.348984 + 1.08504i
\(171\) 0 0
\(172\) 56028.0 + 78088.8i 0.144406 + 0.201265i
\(173\) 772238.i 1.96172i −0.194727 0.980858i \(-0.562382\pi\)
0.194727 0.980858i \(-0.437618\pi\)
\(174\) 0 0
\(175\) 833420.i 2.05716i
\(176\) 190318. 562857.i 0.463124 1.36967i
\(177\) 0 0
\(178\) 369866. 118961.i 0.874973 0.281421i
\(179\) 302910. 0.706611 0.353306 0.935508i \(-0.385058\pi\)
0.353306 + 0.935508i \(0.385058\pi\)
\(180\) 0 0
\(181\) 719552. 1.63255 0.816274 0.577665i \(-0.196036\pi\)
0.816274 + 0.577665i \(0.196036\pi\)
\(182\) 141748. 45590.8i 0.317203 0.102023i
\(183\) 0 0
\(184\) 561456. + 415628.i 1.22256 + 0.905024i
\(185\) 1.40361e6i 3.01521i
\(186\) 0 0
\(187\) 481199.i 1.00629i
\(188\) −183826. + 131893.i −0.379326 + 0.272163i
\(189\) 0 0
\(190\) −106488. 331085.i −0.214001 0.665357i
\(191\) 970416. 1.92475 0.962376 0.271723i \(-0.0875934\pi\)
0.962376 + 0.271723i \(0.0875934\pi\)
\(192\) 0 0
\(193\) −100561. −0.194328 −0.0971642 0.995268i \(-0.530977\pi\)
−0.0971642 + 0.995268i \(0.530977\pi\)
\(194\) −23758.5 73868.3i −0.0453227 0.140914i
\(195\) 0 0
\(196\) 216736. 155506.i 0.402987 0.289139i
\(197\) 453932.i 0.833345i 0.909057 + 0.416673i \(0.136804\pi\)
−0.909057 + 0.416673i \(0.863196\pi\)
\(198\) 0 0
\(199\) 529674.i 0.948147i −0.880485 0.474074i \(-0.842783\pi\)
0.880485 0.474074i \(-0.157217\pi\)
\(200\) 764707. + 566089.i 1.35182 + 1.00071i
\(201\) 0 0
\(202\) −45733.0 + 14709.3i −0.0788590 + 0.0253637i
\(203\) 541373. 0.922055
\(204\) 0 0
\(205\) 924868. 1.53708
\(206\) −904633. + 290960.i −1.48527 + 0.477712i
\(207\) 0 0
\(208\) −54448.0 + 161028.i −0.0872617 + 0.258073i
\(209\) 389671.i 0.617066i
\(210\) 0 0
\(211\) 823831.i 1.27389i 0.770909 + 0.636945i \(0.219802\pi\)
−0.770909 + 0.636945i \(0.780198\pi\)
\(212\) −322373. 449306.i −0.492628 0.686598i
\(213\) 0 0
\(214\) 188577. + 586310.i 0.281484 + 0.875170i
\(215\) 274956. 0.405665
\(216\) 0 0
\(217\) −1.00424e6 −1.44773
\(218\) −151776. 471891.i −0.216303 0.672513i
\(219\) 0 0
\(220\) −990930. 1.38111e6i −1.38034 1.92384i
\(221\) 137666.i 0.189604i
\(222\) 0 0
\(223\) 278385.i 0.374873i 0.982277 + 0.187436i \(0.0600178\pi\)
−0.982277 + 0.187436i \(0.939982\pi\)
\(224\) −13662.4 + 918408.i −0.0181931 + 1.22297i
\(225\) 0 0
\(226\) −528496. + 169982.i −0.688289 + 0.221377i
\(227\) 309112. 0.398154 0.199077 0.979984i \(-0.436206\pi\)
0.199077 + 0.979984i \(0.436206\pi\)
\(228\) 0 0
\(229\) 140882. 0.177528 0.0887640 0.996053i \(-0.471708\pi\)
0.0887640 + 0.996053i \(0.471708\pi\)
\(230\) 1.90249e6 611906.i 2.37139 0.762719i
\(231\) 0 0
\(232\) −367720. + 496739.i −0.448536 + 0.605910i
\(233\) 886021.i 1.06919i −0.845109 0.534594i \(-0.820464\pi\)
0.845109 0.534594i \(-0.179536\pi\)
\(234\) 0 0
\(235\) 647264.i 0.764561i
\(236\) −739177. + 530353.i −0.863910 + 0.619847i
\(237\) 0 0
\(238\) 227766. + 708153.i 0.260643 + 0.810373i
\(239\) 210368. 0.238224 0.119112 0.992881i \(-0.461995\pi\)
0.119112 + 0.992881i \(0.461995\pi\)
\(240\) 0 0
\(241\) 1.40339e6 1.55645 0.778226 0.627984i \(-0.216120\pi\)
0.778226 + 0.627984i \(0.216120\pi\)
\(242\) 304190. + 945764.i 0.333892 + 1.03811i
\(243\) 0 0
\(244\) 1.38289e6 992209.i 1.48701 1.06691i
\(245\) 763142.i 0.812251i
\(246\) 0 0
\(247\) 111481.i 0.116267i
\(248\) 682116. 921445.i 0.704254 0.951350i
\(249\) 0 0
\(250\) 1.05058e6 337903.i 1.06312 0.341934i
\(251\) −1.37851e6 −1.38110 −0.690550 0.723285i \(-0.742631\pi\)
−0.690550 + 0.723285i \(0.742631\pi\)
\(252\) 0 0
\(253\) −2.23914e6 −2.19928
\(254\) 33603.5 10808.0i 0.0326814 0.0105114i
\(255\) 0 0
\(256\) −833408. 636351.i −0.794800 0.606872i
\(257\) 466581.i 0.440651i 0.975426 + 0.220325i \(0.0707119\pi\)
−0.975426 + 0.220325i \(0.929288\pi\)
\(258\) 0 0
\(259\) 2.43113e6i 2.25195i
\(260\) 283495. + 395120.i 0.260083 + 0.362490i
\(261\) 0 0
\(262\) −307833. 957092.i −0.277052 0.861391i
\(263\) −209308. −0.186593 −0.0932967 0.995638i \(-0.529741\pi\)
−0.0932967 + 0.995638i \(0.529741\pi\)
\(264\) 0 0
\(265\) −1.58204e6 −1.38389
\(266\) −184443. 573455.i −0.159830 0.496930i
\(267\) 0 0
\(268\) −765948. 1.06754e6i −0.651422 0.907917i
\(269\) 566035.i 0.476938i 0.971150 + 0.238469i \(0.0766456\pi\)
−0.971150 + 0.238469i \(0.923354\pi\)
\(270\) 0 0
\(271\) 909503.i 0.752283i −0.926562 0.376141i \(-0.877251\pi\)
0.926562 0.376141i \(-0.122749\pi\)
\(272\) −804475. 272015.i −0.659311 0.222931i
\(273\) 0 0
\(274\) −125686. + 40424.9i −0.101137 + 0.0325291i
\(275\) −3.04973e6 −2.43181
\(276\) 0 0
\(277\) −808732. −0.633294 −0.316647 0.948543i \(-0.602557\pi\)
−0.316647 + 0.948543i \(0.602557\pi\)
\(278\) 1.12936e6 363240.i 0.876436 0.281891i
\(279\) 0 0
\(280\) 2.11201e6 + 1.56346e6i 1.60991 + 1.19176i
\(281\) 370359.i 0.279806i 0.990165 + 0.139903i \(0.0446791\pi\)
−0.990165 + 0.139903i \(0.955321\pi\)
\(282\) 0 0
\(283\) 866028.i 0.642786i 0.946946 + 0.321393i \(0.104151\pi\)
−0.946946 + 0.321393i \(0.895849\pi\)
\(284\) −697386. + 500368.i −0.513071 + 0.368124i
\(285\) 0 0
\(286\) −166830. 518696.i −0.120603 0.374971i
\(287\) 1.60192e6 1.14798
\(288\) 0 0
\(289\) 732093. 0.515610
\(290\) 541373. + 1.68320e6i 0.378009 + 1.17528i
\(291\) 0 0
\(292\) 799214. 573429.i 0.548537 0.393570i
\(293\) 965980.i 0.657354i 0.944442 + 0.328677i \(0.106603\pi\)
−0.944442 + 0.328677i \(0.893397\pi\)
\(294\) 0 0
\(295\) 2.60269e6i 1.74128i
\(296\) −2.23069e6 1.65131e6i −1.47982 1.09547i
\(297\) 0 0
\(298\) −1.00482e6 + 323184.i −0.655463 + 0.210819i
\(299\) 640596. 0.414387
\(300\) 0 0
\(301\) 476238. 0.302976
\(302\) −785639. + 252688.i −0.495685 + 0.159429i
\(303\) 0 0
\(304\) 651456. + 220275.i 0.404298 + 0.136704i
\(305\) 4.86924e6i 2.99717i
\(306\) 0 0
\(307\) 2.39913e6i 1.45281i 0.687268 + 0.726404i \(0.258810\pi\)
−0.687268 + 0.726404i \(0.741190\pi\)
\(308\) −1.71634e6 2.39214e6i −1.03092 1.43685i
\(309\) 0 0
\(310\) −1.00424e6 3.12231e6i −0.593518 1.84532i
\(311\) 1.35847e6 0.796432 0.398216 0.917292i \(-0.369630\pi\)
0.398216 + 0.917292i \(0.369630\pi\)
\(312\) 0 0
\(313\) 1.55077e6 0.894716 0.447358 0.894355i \(-0.352365\pi\)
0.447358 + 0.894355i \(0.352365\pi\)
\(314\) −386476. 1.20160e6i −0.221207 0.687760i
\(315\) 0 0
\(316\) −1.30952e6 1.82514e6i −0.737727 1.02820i
\(317\) 1.13244e6i 0.632947i −0.948601 0.316474i \(-0.897501\pi\)
0.948601 0.316474i \(-0.102499\pi\)
\(318\) 0 0
\(319\) 1.98104e6i 1.08998i
\(320\) −2.86911e6 + 875929.i −1.56629 + 0.478183i
\(321\) 0 0
\(322\) 3.29521e6 1.05985e6i 1.77110 0.569646i
\(323\) 556944. 0.297034
\(324\) 0 0
\(325\) 872496. 0.458200
\(326\) 478888. 154026.i 0.249569 0.0802697i
\(327\) 0 0
\(328\) −1.08808e6 + 1.46985e6i −0.558440 + 0.754375i
\(329\) 1.12109e6i 0.571021i
\(330\) 0 0
\(331\) 3.69262e6i 1.85253i −0.376878 0.926263i \(-0.623003\pi\)
0.376878 0.926263i \(-0.376997\pi\)
\(332\) 296454. 212703.i 0.147609 0.105908i
\(333\) 0 0
\(334\) −535254. 1.66417e6i −0.262539 0.816267i
\(335\) −3.75887e6 −1.82998
\(336\) 0 0
\(337\) 498854. 0.239276 0.119638 0.992818i \(-0.461827\pi\)
0.119638 + 0.992818i \(0.461827\pi\)
\(338\) −595370. 1.85108e6i −0.283462 0.881320i
\(339\) 0 0
\(340\) −1.97397e6 + 1.41631e6i −0.926070 + 0.664446i
\(341\) 3.67481e6i 1.71139i
\(342\) 0 0
\(343\) 1.34321e6i 0.616464i
\(344\) −323478. + 436974.i −0.147383 + 0.199095i
\(345\) 0 0
\(346\) 4.15863e6 1.33756e6i 1.86750 0.600650i
\(347\) −547933. −0.244289 −0.122144 0.992512i \(-0.538977\pi\)
−0.122144 + 0.992512i \(0.538977\pi\)
\(348\) 0 0
\(349\) −1.64807e6 −0.724290 −0.362145 0.932122i \(-0.617956\pi\)
−0.362145 + 0.932122i \(0.617956\pi\)
\(350\) 4.48810e6 1.44353e6i 1.95836 0.629875i
\(351\) 0 0
\(352\) 3.36072e6 + 49994.8i 1.44569 + 0.0215064i
\(353\) 1.17939e6i 0.503758i 0.967759 + 0.251879i \(0.0810485\pi\)
−0.967759 + 0.251879i \(0.918951\pi\)
\(354\) 0 0
\(355\) 2.45554e6i 1.03413i
\(356\) 1.28125e6 + 1.78574e6i 0.535809 + 0.746782i
\(357\) 0 0
\(358\) 524655. + 1.63122e6i 0.216355 + 0.672674i
\(359\) 2.81312e6 1.15200 0.576000 0.817449i \(-0.304613\pi\)
0.576000 + 0.817449i \(0.304613\pi\)
\(360\) 0 0
\(361\) 2.02509e6 0.817855
\(362\) 1.24630e6 + 3.87491e6i 0.499863 + 1.55414i
\(363\) 0 0
\(364\) 491028. + 684368.i 0.194246 + 0.270730i
\(365\) 2.81409e6i 1.10562i
\(366\) 0 0
\(367\) 2.94104e6i 1.13982i −0.821707 0.569910i \(-0.806978\pi\)
0.821707 0.569910i \(-0.193022\pi\)
\(368\) −1.26576e6 + 3.74342e6i −0.487226 + 1.44095i
\(369\) 0 0
\(370\) −7.55868e6 + 2.43113e6i −2.87039 + 0.923215i
\(371\) −2.74017e6 −1.03358
\(372\) 0 0
\(373\) −2.11698e6 −0.787851 −0.393926 0.919142i \(-0.628883\pi\)
−0.393926 + 0.919142i \(0.628883\pi\)
\(374\) 2.59134e6 833462.i 0.957955 0.308111i
\(375\) 0 0
\(376\) −1.02866e6 761487.i −0.375236 0.277775i
\(377\) 566756.i 0.205373i
\(378\) 0 0
\(379\) 2.75613e6i 0.985602i −0.870142 0.492801i \(-0.835973\pi\)
0.870142 0.492801i \(-0.164027\pi\)
\(380\) 1.59850e6 1.14691e6i 0.567877 0.407447i
\(381\) 0 0
\(382\) 1.68081e6 + 5.22585e6i 0.589332 + 1.83231i
\(383\) 4.51402e6 1.57241 0.786206 0.617964i \(-0.212042\pi\)
0.786206 + 0.617964i \(0.212042\pi\)
\(384\) 0 0
\(385\) −8.42291e6 −2.89608
\(386\) −174177. 541538.i −0.0595007 0.184995i
\(387\) 0 0
\(388\) 356642. 255887.i 0.120269 0.0862918i
\(389\) 1.56097e6i 0.523023i 0.965200 + 0.261511i \(0.0842209\pi\)
−0.965200 + 0.261511i \(0.915779\pi\)
\(390\) 0 0
\(391\) 3.20034e6i 1.05865i
\(392\) 1.21282e6 + 897815.i 0.398641 + 0.295102i
\(393\) 0 0
\(394\) −2.44450e6 + 786233.i −0.793321 + 0.255159i
\(395\) −6.42646e6 −2.07243
\(396\) 0 0
\(397\) 3.93330e6 1.25251 0.626255 0.779618i \(-0.284587\pi\)
0.626255 + 0.779618i \(0.284587\pi\)
\(398\) 2.85238e6 917422.i 0.902609 0.290310i
\(399\) 0 0
\(400\) −1.72397e6 + 5.09857e6i −0.538740 + 1.59330i
\(401\) 4.10604e6i 1.27515i −0.770387 0.637576i \(-0.779937\pi\)
0.770387 0.637576i \(-0.220063\pi\)
\(402\) 0 0
\(403\) 1.05133e6i 0.322459i
\(404\) −158424. 220803.i −0.0482911 0.0673055i
\(405\) 0 0
\(406\) 937686. + 2.91538e6i 0.282320 + 0.877770i
\(407\) 8.89619e6 2.66206
\(408\) 0 0
\(409\) 4.42833e6 1.30898 0.654488 0.756072i \(-0.272884\pi\)
0.654488 + 0.756072i \(0.272884\pi\)
\(410\) 1.60192e6 + 4.98057e6i 0.470631 + 1.46325i
\(411\) 0 0
\(412\) −3.13374e6 4.36764e6i −0.909536 1.26766i
\(413\) 4.50800e6i 1.30049i
\(414\) 0 0
\(415\) 1.04384e6i 0.297517i
\(416\) −961468. 14303.0i −0.272397 0.00405223i
\(417\) 0 0
\(418\) −2.09844e6 + 674929.i −0.587430 + 0.188937i
\(419\) −585360. −0.162888 −0.0814439 0.996678i \(-0.525953\pi\)
−0.0814439 + 0.996678i \(0.525953\pi\)
\(420\) 0 0
\(421\) 3.61291e6 0.993463 0.496731 0.867904i \(-0.334533\pi\)
0.496731 + 0.867904i \(0.334533\pi\)
\(422\) −4.43647e6 + 1.42692e6i −1.21271 + 0.390048i
\(423\) 0 0
\(424\) 1.86122e6 2.51425e6i 0.502786 0.679194i
\(425\) 4.35888e6i 1.17058i
\(426\) 0 0
\(427\) 8.43378e6i 2.23848i
\(428\) −2.83075e6 + 2.03104e6i −0.746951 + 0.535930i
\(429\) 0 0
\(430\) 476238. + 1.48068e6i 0.124209 + 0.386181i
\(431\) 1.66336e6 0.431314 0.215657 0.976469i \(-0.430811\pi\)
0.215657 + 0.976469i \(0.430811\pi\)
\(432\) 0 0
\(433\) −783805. −0.200904 −0.100452 0.994942i \(-0.532029\pi\)
−0.100452 + 0.994942i \(0.532029\pi\)
\(434\) −1.73940e6 5.40800e6i −0.443276 1.37820i
\(435\) 0 0
\(436\) 2.27833e6 1.63468e6i 0.573984 0.411828i
\(437\) 2.59160e6i 0.649179i
\(438\) 0 0
\(439\) 1.91382e6i 0.473958i −0.971515 0.236979i \(-0.923843\pi\)
0.971515 0.236979i \(-0.0761572\pi\)
\(440\) 5.72114e6 7.72847e6i 1.40880 1.90310i
\(441\) 0 0
\(442\) −741356. + 238445.i −0.180497 + 0.0580541i
\(443\) 2.53916e6 0.614724 0.307362 0.951593i \(-0.400554\pi\)
0.307362 + 0.951593i \(0.400554\pi\)
\(444\) 0 0
\(445\) 6.28772e6 1.50520
\(446\) −1.49915e6 + 482177.i −0.356868 + 0.114781i
\(447\) 0 0
\(448\) −4.96944e6 + 1.51715e6i −1.16980 + 0.357137i
\(449\) 6.05887e6i 1.41833i 0.705045 + 0.709163i \(0.250927\pi\)
−0.705045 + 0.709163i \(0.749073\pi\)
\(450\) 0 0
\(451\) 5.86188e6i 1.35705i
\(452\) −1.83076e6 2.55162e6i −0.421489 0.587449i
\(453\) 0 0
\(454\) 535398. + 1.66462e6i 0.121909 + 0.379032i
\(455\) 2.40971e6 0.545678
\(456\) 0 0
\(457\) 3.29032e6 0.736967 0.368483 0.929634i \(-0.379877\pi\)
0.368483 + 0.929634i \(0.379877\pi\)
\(458\) 244015. + 758673.i 0.0543566 + 0.169002i
\(459\) 0 0
\(460\) 6.59042e6 + 9.18538e6i 1.45217 + 2.02396i
\(461\) 6.41710e6i 1.40633i −0.711028 0.703163i \(-0.751770\pi\)
0.711028 0.703163i \(-0.248230\pi\)
\(462\) 0 0
\(463\) 1.34410e6i 0.291394i 0.989329 + 0.145697i \(0.0465424\pi\)
−0.989329 + 0.145697i \(0.953458\pi\)
\(464\) −3.31193e6 1.11986e6i −0.714145 0.241472i
\(465\) 0 0
\(466\) 4.77137e6 1.53463e6i 1.01784 0.327371i
\(467\) −256155. −0.0543513 −0.0271757 0.999631i \(-0.508651\pi\)
−0.0271757 + 0.999631i \(0.508651\pi\)
\(468\) 0 0
\(469\) −6.51056e6 −1.36674
\(470\) −3.48562e6 + 1.12109e6i −0.727840 + 0.234098i
\(471\) 0 0
\(472\) −4.13633e6 3.06199e6i −0.854594 0.632629i
\(473\) 1.74269e6i 0.358153i
\(474\) 0 0
\(475\) 3.52978e6i 0.717817i
\(476\) −3.41902e6 + 2.45311e6i −0.691647 + 0.496250i
\(477\) 0 0
\(478\) 364368. + 1.13287e6i 0.0729408 + 0.226782i
\(479\) −9661.38 −0.00192398 −0.000961990 1.00000i \(-0.500306\pi\)
−0.000961990 1.00000i \(0.500306\pi\)
\(480\) 0 0
\(481\) −2.54511e6 −0.501585
\(482\) 2.43074e6 + 7.55749e6i 0.476564 + 1.48170i
\(483\) 0 0
\(484\) −4.56622e6 + 3.27622e6i −0.886021 + 0.635712i
\(485\) 1.25576e6i 0.242411i
\(486\) 0 0
\(487\) 7.37413e6i 1.40893i 0.709740 + 0.704464i \(0.248812\pi\)
−0.709740 + 0.704464i \(0.751188\pi\)
\(488\) 7.73844e6 + 5.72852e6i 1.47097 + 1.08891i
\(489\) 0 0
\(490\) 4.10965e6 1.32180e6i 0.773240 0.248700i
\(491\) −4.96250e6 −0.928960 −0.464480 0.885584i \(-0.653759\pi\)
−0.464480 + 0.885584i \(0.653759\pi\)
\(492\) 0 0
\(493\) −2.83144e6 −0.524675
\(494\) 600343. 193090.i 0.110683 0.0355995i
\(495\) 0 0
\(496\) 6.14359e6 + 2.07732e6i 1.12129 + 0.379140i
\(497\) 4.25313e6i 0.772356i
\(498\) 0 0
\(499\) 2.22135e6i 0.399361i −0.979861 0.199681i \(-0.936010\pi\)
0.979861 0.199681i \(-0.0639905\pi\)
\(500\) 3.63933e6 + 5.07230e6i 0.651022 + 0.907360i
\(501\) 0 0
\(502\) −2.38765e6 7.42349e6i −0.422874 1.31477i
\(503\) −1.01231e7 −1.78400 −0.891999 0.452037i \(-0.850698\pi\)
−0.891999 + 0.452037i \(0.850698\pi\)
\(504\) 0 0
\(505\) −777461. −0.135659
\(506\) −3.87830e6 1.20581e7i −0.673388 2.09365i
\(507\) 0 0
\(508\) 116406. + 162240.i 0.0200132 + 0.0278933i
\(509\) 1.04816e7i 1.79322i −0.442819 0.896611i \(-0.646021\pi\)
0.442819 0.896611i \(-0.353979\pi\)
\(510\) 0 0
\(511\) 4.87414e6i 0.825745i
\(512\) 1.98335e6 5.59023e6i 0.334368 0.942443i
\(513\) 0 0
\(514\) −2.51262e6 + 808143.i −0.419487 + 0.134921i
\(515\) −1.53788e7 −2.55507
\(516\) 0 0
\(517\) 4.10241e6 0.675014
\(518\) −1.30920e7 + 4.21083e6i −2.14379 + 0.689515i
\(519\) 0 0
\(520\) −1.63676e6 + 2.21104e6i −0.265446 + 0.358581i
\(521\) 1.59021e6i 0.256661i −0.991731 0.128330i \(-0.959038\pi\)
0.991731 0.128330i \(-0.0409618\pi\)
\(522\) 0 0
\(523\) 2.90818e6i 0.464909i −0.972607 0.232454i \(-0.925324\pi\)
0.972607 0.232454i \(-0.0746756\pi\)
\(524\) 4.62091e6 3.31546e6i 0.735190 0.527492i
\(525\) 0 0
\(526\) −362532. 1.12716e6i −0.0571323 0.177632i
\(527\) 5.25230e6 0.823802
\(528\) 0 0
\(529\) 8.45561e6 1.31373
\(530\) −2.74017e6 8.51953e6i −0.423728 1.31743i
\(531\) 0 0
\(532\) 2.76869e6 1.98651e6i 0.424126 0.304306i
\(533\) 1.67703e6i 0.255695i
\(534\) 0 0
\(535\) 9.96727e6i 1.50554i
\(536\) 4.42220e6 5.97378e6i 0.664855 0.898127i
\(537\) 0 0
\(538\) −3.04819e6 + 980401.i −0.454032 + 0.146032i
\(539\) −4.83686e6 −0.717119
\(540\) 0 0
\(541\) 1.04918e6 0.154119 0.0770596 0.997026i \(-0.475447\pi\)
0.0770596 + 0.997026i \(0.475447\pi\)
\(542\) 4.89783e6 1.57531e6i 0.716152 0.230339i
\(543\) 0 0
\(544\) 71456.0 4.80338e6i 0.0103524 0.695904i
\(545\) 8.02215e6i 1.15691i
\(546\) 0 0
\(547\) 1.32733e7i 1.89675i 0.317150 + 0.948375i \(0.397274\pi\)
−0.317150 + 0.948375i \(0.602726\pi\)
\(548\) −435389. 606822.i −0.0619336 0.0863197i
\(549\) 0 0
\(550\) −5.28228e6 1.64233e7i −0.744586 2.31501i
\(551\) 2.29288e6 0.321737
\(552\) 0 0
\(553\) −1.11310e7 −1.54782
\(554\) −1.40076e6 4.35516e6i −0.193906 0.602878i
\(555\) 0 0
\(556\) 3.91222e6 + 5.45264e6i 0.536705 + 0.748031i
\(557\) 7.30021e6i 0.997005i 0.866888 + 0.498503i \(0.166117\pi\)
−0.866888 + 0.498503i \(0.833883\pi\)
\(558\) 0 0
\(559\) 498567.i 0.0674830i
\(560\) −4.76135e6 + 1.40815e7i −0.641594 + 1.89749i
\(561\) 0 0
\(562\) −1.99445e6 + 641481.i −0.266368 + 0.0856728i
\(563\) −262653. −0.0349230 −0.0174615 0.999848i \(-0.505558\pi\)
−0.0174615 + 0.999848i \(0.505558\pi\)
\(564\) 0 0
\(565\) −8.98443e6 −1.18405
\(566\) −4.66371e6 + 1.50001e6i −0.611914 + 0.196812i
\(567\) 0 0
\(568\) −3.90247e6 2.88888e6i −0.507538 0.375715i
\(569\) 4.86509e6i 0.629956i −0.949099 0.314978i \(-0.898003\pi\)
0.949099 0.314978i \(-0.101997\pi\)
\(570\) 0 0
\(571\) 3.80253e6i 0.488070i 0.969766 + 0.244035i \(0.0784712\pi\)
−0.969766 + 0.244035i \(0.921529\pi\)
\(572\) 2.50430e6 1.79681e6i 0.320035 0.229622i
\(573\) 0 0
\(574\) 2.77460e6 + 8.62659e6i 0.351497 + 1.09285i
\(575\) 2.02830e7 2.55836
\(576\) 0 0
\(577\) −123970. −0.0155016 −0.00775081 0.999970i \(-0.502467\pi\)
−0.00775081 + 0.999970i \(0.502467\pi\)
\(578\) 1.26802e6 + 3.94244e6i 0.157873 + 0.490846i
\(579\) 0 0
\(580\) −8.12661e6 + 5.83077e6i −1.00309 + 0.719707i
\(581\) 1.80798e6i 0.222204i
\(582\) 0 0
\(583\) 1.00271e7i 1.22181i
\(584\) 4.47229e6 + 3.31069e6i 0.542622 + 0.401686i
\(585\) 0 0
\(586\) −5.20196e6 + 1.67313e6i −0.625782 + 0.201273i
\(587\) −5.68744e6 −0.681274 −0.340637 0.940195i \(-0.610643\pi\)
−0.340637 + 0.940195i \(0.610643\pi\)
\(588\) 0 0
\(589\) −4.25326e6 −0.505165
\(590\) −1.40159e7 + 4.50800e6i −1.65765 + 0.533155i
\(591\) 0 0
\(592\) 5.02890e6 1.48728e7i 0.589751 1.74416i
\(593\) 8.77471e6i 1.02470i 0.858777 + 0.512349i \(0.171225\pi\)
−0.858777 + 0.512349i \(0.828775\pi\)
\(594\) 0 0
\(595\) 1.20386e7i 1.39407i
\(596\) −3.48080e6 4.85135e6i −0.401387 0.559432i
\(597\) 0 0
\(598\) 1.10954e6 + 3.44971e6i 0.126880 + 0.394484i
\(599\) 1.28831e7 1.46707 0.733537 0.679649i \(-0.237868\pi\)
0.733537 + 0.679649i \(0.237868\pi\)
\(600\) 0 0
\(601\) −2.62469e6 −0.296410 −0.148205 0.988957i \(-0.547350\pi\)
−0.148205 + 0.988957i \(0.547350\pi\)
\(602\) 824868. + 2.56462e6i 0.0927670 + 0.288424i
\(603\) 0 0
\(604\) −2.72153e6 3.79313e6i −0.303544 0.423063i
\(605\) 1.60780e7i 1.78584i
\(606\) 0 0
\(607\) 5.78348e6i 0.637114i −0.947904 0.318557i \(-0.896802\pi\)
0.947904 0.318557i \(-0.103198\pi\)
\(608\) −57864.4 + 3.88973e6i −0.00634822 + 0.426737i
\(609\) 0 0
\(610\) 2.62217e7 8.43378e6i 2.85322 0.917693i
\(611\) −1.17366e6 −0.127186
\(612\) 0 0
\(613\) −1.67367e6 −0.179895 −0.0899476 0.995946i \(-0.528670\pi\)
−0.0899476 + 0.995946i \(0.528670\pi\)
\(614\) −1.29197e7 + 4.15542e6i −1.38303 + 0.444830i
\(615\) 0 0
\(616\) 9.90930e6 1.33861e7i 1.05218 1.42135i
\(617\) 8.52976e6i 0.902036i 0.892515 + 0.451018i \(0.148939\pi\)
−0.892515 + 0.451018i \(0.851061\pi\)
\(618\) 0 0
\(619\) 9.46604e6i 0.992983i 0.868042 + 0.496491i \(0.165379\pi\)
−0.868042 + 0.496491i \(0.834621\pi\)
\(620\) 1.50748e7 1.08160e7i 1.57497 1.13002i
\(621\) 0 0
\(622\) 2.35294e6 + 7.31558e6i 0.243856 + 0.758180i
\(623\) 1.08907e7 1.12417
\(624\) 0 0
\(625\) 1.43491e6 0.146935
\(626\) 2.68600e6 + 8.35113e6i 0.273950 + 0.851744i
\(627\) 0 0
\(628\) 5.80143e6 4.16247e6i 0.586997 0.421165i
\(629\) 1.27151e7i 1.28142i
\(630\) 0 0
\(631\) 1.04052e7i 1.04035i −0.854060 0.520174i \(-0.825867\pi\)
0.854060 0.520174i \(-0.174133\pi\)
\(632\) 7.56054e6 1.02132e7i 0.752940 1.01712i
\(633\) 0 0
\(634\) 6.09838e6 1.96145e6i 0.602548 0.193800i
\(635\) 571260. 0.0562211
\(636\) 0 0
\(637\) 1.38378e6 0.135119
\(638\) 1.06682e7 3.43127e6i 1.03763 0.333736i
\(639\) 0 0
\(640\) −9.68646e6 1.39335e7i −0.934793 1.34465i
\(641\) 360957.i 0.0346985i 0.999849 + 0.0173492i \(0.00552271\pi\)
−0.999849 + 0.0173492i \(0.994477\pi\)
\(642\) 0 0
\(643\) 557777.i 0.0532027i 0.999646 + 0.0266013i \(0.00846847\pi\)
−0.999646 + 0.0266013i \(0.991532\pi\)
\(644\) 1.14149e7 + 1.59095e7i 1.08457 + 1.51162i
\(645\) 0 0
\(646\) 964656. + 2.99924e6i 0.0909476 + 0.282768i
\(647\) 6.76712e6 0.635540 0.317770 0.948168i \(-0.397066\pi\)
0.317770 + 0.948168i \(0.397066\pi\)
\(648\) 0 0
\(649\) 1.64961e7 1.53734
\(650\) 1.51121e6 + 4.69853e6i 0.140295 + 0.436193i
\(651\) 0 0
\(652\) 1.65892e6 + 2.31211e6i 0.152829 + 0.213005i
\(653\) 9.16397e6i 0.841009i 0.907290 + 0.420505i \(0.138147\pi\)
−0.907290 + 0.420505i \(0.861853\pi\)
\(654\) 0 0
\(655\) 1.62706e7i 1.48183i
\(656\) −9.79997e6 3.31364e6i −0.889130 0.300640i
\(657\) 0 0
\(658\) −6.03728e6 + 1.94179e6i −0.543596 + 0.174839i
\(659\) −3.33571e6 −0.299209 −0.149605 0.988746i \(-0.547800\pi\)
−0.149605 + 0.988746i \(0.547800\pi\)
\(660\) 0 0
\(661\) −1.08460e7 −0.965528 −0.482764 0.875750i \(-0.660367\pi\)
−0.482764 + 0.875750i \(0.660367\pi\)
\(662\) 1.98853e7 6.39580e6i 1.76355 0.567218i
\(663\) 0 0
\(664\) 1.65892e6 + 1.22804e6i 0.146017 + 0.108092i
\(665\) 9.74874e6i 0.854859i
\(666\) 0 0
\(667\) 1.31754e7i 1.14670i
\(668\) 8.03476e6 5.76486e6i 0.696677 0.499859i
\(669\) 0 0
\(670\) −6.51056e6 2.02421e7i −0.560314 1.74209i
\(671\) −3.08616e7 −2.64614
\(672\) 0 0
\(673\) 1.59743e7 1.35952 0.679759 0.733436i \(-0.262084\pi\)
0.679759 + 0.733436i \(0.262084\pi\)
\(674\) 864040. + 2.68641e6i 0.0732629 + 0.227784i
\(675\) 0 0
\(676\) 8.93716e6 6.41233e6i 0.752199 0.539696i
\(677\) 587812.i 0.0492909i 0.999696 + 0.0246455i \(0.00784569\pi\)
−0.999696 + 0.0246455i \(0.992154\pi\)
\(678\) 0 0
\(679\) 2.17504e6i 0.181048i
\(680\) −1.10461e7 8.17705e6i −0.916084 0.678148i
\(681\) 0 0
\(682\) −1.97895e7 + 6.36496e6i −1.62919 + 0.524004i
\(683\) −8.64998e6 −0.709518 −0.354759 0.934958i \(-0.615437\pi\)
−0.354759 + 0.934958i \(0.615437\pi\)
\(684\) 0 0
\(685\) −2.13666e6 −0.173984
\(686\) −7.23340e6 + 2.32650e6i −0.586857 + 0.188753i
\(687\) 0 0
\(688\) −2.91346e6 985120.i −0.234659 0.0793448i
\(689\) 2.86864e6i 0.230212i
\(690\) 0 0
\(691\) 1.81129e7i 1.44309i 0.692368 + 0.721545i \(0.256568\pi\)
−0.692368 + 0.721545i \(0.743432\pi\)
\(692\) 1.44059e7 + 2.00782e7i 1.14360 + 1.59389i
\(693\) 0 0
\(694\) −949047. 2.95071e6i −0.0747978 0.232556i
\(695\) 1.91991e7 1.50771
\(696\) 0 0
\(697\) −8.37822e6 −0.653235
\(698\) −2.85454e6 8.87514e6i −0.221768 0.689504i
\(699\) 0 0
\(700\) 1.55472e7 + 2.16689e7i 1.19925 + 1.67145i
\(701\) 3.00066e6i 0.230633i −0.993329 0.115317i \(-0.963212\pi\)
0.993329 0.115317i \(-0.0367883\pi\)
\(702\) 0 0
\(703\) 1.02965e7i 0.785783i
\(704\) 5.55171e6 + 1.81846e7i 0.422177 + 1.38284i
\(705\) 0 0
\(706\) −6.35123e6 + 2.04277e6i −0.479564 + 0.154244i
\(707\) −1.34660e6 −0.101319
\(708\) 0 0
\(709\) 1.58384e7 1.18330 0.591651 0.806194i \(-0.298476\pi\)
0.591651 + 0.806194i \(0.298476\pi\)
\(710\) −1.32235e7 + 4.25313e6i −0.984466 + 0.316638i
\(711\) 0 0
\(712\) −7.39732e6 + 9.99276e6i −0.546858 + 0.738729i
\(713\) 2.44402e7i 1.80045i
\(714\) 0 0
\(715\) 8.81782e6i 0.645054i
\(716\) −7.87565e6 + 5.65071e6i −0.574122 + 0.411927i
\(717\) 0 0
\(718\) 4.87247e6 + 1.51491e7i 0.352727 + 1.09667i
\(719\) 2.87578e6 0.207460 0.103730 0.994606i \(-0.466922\pi\)
0.103730 + 0.994606i \(0.466922\pi\)
\(720\) 0 0
\(721\) −2.66368e7 −1.90829
\(722\) 3.50756e6 + 1.09054e7i 0.250416 + 0.778575i
\(723\) 0 0
\(724\) −1.87084e7 + 1.34231e7i −1.32644 + 0.951712i
\(725\) 1.79450e7i 1.26794i
\(726\) 0 0
\(727\) 2.80274e6i 0.196674i 0.995153 + 0.0983369i \(0.0313523\pi\)
−0.995153 + 0.0983369i \(0.968648\pi\)
\(728\) −2.83495e6 + 3.82963e6i −0.198252 + 0.267811i
\(729\) 0 0
\(730\) 1.51543e7 4.87414e6i 1.05252 0.338525i
\(731\) −2.49078e6 −0.172402
\(732\) 0 0
\(733\) 1.04544e7 0.718685 0.359342 0.933206i \(-0.383001\pi\)
0.359342 + 0.933206i \(0.383001\pi\)
\(734\) 1.58380e7 5.09404e6i 1.08508 0.348997i
\(735\) 0 0
\(736\) −2.23513e7 332502.i −1.52093 0.0226256i
\(737\) 2.38240e7i 1.61565i
\(738\) 0 0
\(739\) 2.46827e7i 1.66257i −0.555844 0.831286i \(-0.687605\pi\)
0.555844 0.831286i \(-0.312395\pi\)
\(740\) −2.61840e7 3.64939e7i −1.75775 2.44986i
\(741\) 0 0
\(742\) −4.74611e6 1.47563e7i −0.316467 0.983935i
\(743\) 2.00401e7 1.33177 0.665884 0.746056i \(-0.268055\pi\)
0.665884 + 0.746056i \(0.268055\pi\)
\(744\) 0 0
\(745\) −1.70820e7 −1.12758
\(746\) −3.66671e6 1.14003e7i −0.241229 0.750012i
\(747\) 0 0
\(748\) 8.97666e6 + 1.25112e7i 0.586625 + 0.817607i
\(749\) 1.72638e7i 1.12443i
\(750\) 0 0
\(751\) 8.22982e6i 0.532464i −0.963909 0.266232i \(-0.914221\pi\)
0.963909 0.266232i \(-0.0857787\pi\)
\(752\) 2.31904e6 6.85846e6i 0.149542 0.442264i
\(753\) 0 0
\(754\) −3.05208e6 + 981651.i −0.195509 + 0.0628823i
\(755\) −1.33559e7 −0.852717
\(756\) 0 0
\(757\) −5.34992e6 −0.339319 −0.169659 0.985503i \(-0.554267\pi\)
−0.169659 + 0.985503i \(0.554267\pi\)
\(758\) 1.48422e7 4.77375e6i 0.938265 0.301778i
\(759\) 0 0
\(760\) 8.94499e6 + 6.62169e6i 0.561754 + 0.415848i
\(761\) 1.17630e7i 0.736301i −0.929766 0.368150i \(-0.879991\pi\)
0.929766 0.368150i \(-0.120009\pi\)
\(762\) 0 0
\(763\) 1.38948e7i 0.864052i
\(764\) −2.52308e7 + 1.81029e7i −1.56386 + 1.12206i
\(765\) 0 0
\(766\) 7.81851e6 + 2.43087e7i 0.481451 + 1.49689i
\(767\) −4.71936e6 −0.289664
\(768\) 0 0
\(769\) −1.34112e7 −0.817807 −0.408903 0.912578i \(-0.634089\pi\)
−0.408903 + 0.912578i \(0.634089\pi\)
\(770\) −1.45889e7 4.53587e7i −0.886739 2.75698i
\(771\) 0 0
\(772\) 2.61459e6 1.87594e6i 0.157892 0.113286i
\(773\) 2.94018e7i 1.76980i −0.465779 0.884901i \(-0.654226\pi\)
0.465779 0.884901i \(-0.345774\pi\)
\(774\) 0 0
\(775\) 3.32878e7i 1.99081i
\(776\) 1.99572e6 + 1.47737e6i 0.118972 + 0.0880712i
\(777\) 0 0
\(778\) −8.40609e6 + 2.70368e6i −0.497903 + 0.160142i
\(779\) 6.78460e6 0.400572
\(780\) 0 0
\(781\) 1.55634e7 0.913015
\(782\) −1.72343e7 + 5.54314e6i −1.00781 + 0.324145i
\(783\) 0 0
\(784\) −2.73421e6 + 8.08632e6i −0.158870 + 0.469851i
\(785\) 2.04272e7i 1.18314i
\(786\) 0 0
\(787\) 1.80678e7i 1.03984i 0.854214 + 0.519921i \(0.174039\pi\)
−0.854214 + 0.519921i \(0.825961\pi\)
\(788\) −8.46799e6 1.18022e7i −0.485808 0.677093i
\(789\) 0 0
\(790\) −1.11310e7 3.46075e7i −0.634548 1.97289i
\(791\) −1.55615e7 −0.884321
\(792\) 0 0
\(793\) 8.82921e6 0.498585
\(794\) 6.81268e6 + 2.11815e7i