Properties

Label 108.6.e.a.73.2
Level $108$
Weight $6$
Character 108.73
Analytic conductor $17.321$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{16} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 73.2
Root \(9.84603i\) of defining polynomial
Character \(\chi\) \(=\) 108.73
Dual form 108.6.e.a.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.1603 - 22.7942i) q^{5} +(-31.6287 + 54.7826i) q^{7} +O(q^{10})\) \(q+(-13.1603 - 22.7942i) q^{5} +(-31.6287 + 54.7826i) q^{7} +(49.1194 - 85.0772i) q^{11} +(369.143 + 639.374i) q^{13} -250.060 q^{17} +1102.41 q^{19} +(2204.70 + 3818.66i) q^{23} +(1216.12 - 2106.37i) q^{25} +(-3941.06 + 6826.11i) q^{29} +(2305.65 + 3993.49i) q^{31} +1664.97 q^{35} +11896.3 q^{37} +(5040.58 + 8730.55i) q^{41} +(-3518.99 + 6095.07i) q^{43} +(7459.33 - 12919.9i) q^{47} +(6402.75 + 11089.9i) q^{49} -22451.7 q^{53} -2585.69 q^{55} +(5405.25 + 9362.17i) q^{59} +(594.647 - 1029.96i) q^{61} +(9716.02 - 16828.6i) q^{65} +(-29590.2 - 51251.8i) q^{67} -14326.6 q^{71} -53098.2 q^{73} +(3107.17 + 5381.77i) q^{77} +(18695.6 - 32381.6i) q^{79} +(60439.5 - 104684. i) q^{83} +(3290.85 + 5699.93i) q^{85} -97873.2 q^{89} -46702.1 q^{91} +(-14507.9 - 25128.5i) q^{95} +(-53356.7 + 92416.4i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} + 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} + 29q^{7} - 177q^{11} - 181q^{13} - 2280q^{17} - 832q^{19} - 399q^{23} - 4778q^{25} + 6033q^{29} + 2759q^{31} - 37146q^{35} - 15172q^{37} + 18435q^{41} + 1469q^{43} + 25155q^{47} - 4056q^{49} - 116844q^{53} + 14778q^{55} + 90537q^{59} + 1403q^{61} + 148407q^{65} + 13907q^{67} - 229368q^{71} + 15200q^{73} + 211983q^{77} + 29993q^{79} + 228951q^{83} - 49662q^{85} - 598332q^{89} + 124930q^{91} + 394764q^{95} + 40541q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −13.1603 22.7942i −0.235418 0.407755i 0.723976 0.689825i \(-0.242312\pi\)
−0.959394 + 0.282069i \(0.908979\pi\)
\(6\) 0 0
\(7\) −31.6287 + 54.7826i −0.243970 + 0.422569i −0.961842 0.273607i \(-0.911783\pi\)
0.717871 + 0.696176i \(0.245117\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 49.1194 85.0772i 0.122397 0.211998i −0.798315 0.602240i \(-0.794275\pi\)
0.920712 + 0.390242i \(0.127609\pi\)
\(12\) 0 0
\(13\) 369.143 + 639.374i 0.605809 + 1.04929i 0.991923 + 0.126841i \(0.0404839\pi\)
−0.386114 + 0.922451i \(0.626183\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −250.060 −0.209856 −0.104928 0.994480i \(-0.533461\pi\)
−0.104928 + 0.994480i \(0.533461\pi\)
\(18\) 0 0
\(19\) 1102.41 0.700579 0.350290 0.936641i \(-0.386083\pi\)
0.350290 + 0.936641i \(0.386083\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2204.70 + 3818.66i 0.869022 + 1.50519i 0.862998 + 0.505208i \(0.168584\pi\)
0.00602414 + 0.999982i \(0.498082\pi\)
\(24\) 0 0
\(25\) 1216.12 2106.37i 0.389157 0.674040i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3941.06 + 6826.11i −0.870197 + 1.50723i −0.00840534 + 0.999965i \(0.502676\pi\)
−0.861792 + 0.507262i \(0.830658\pi\)
\(30\) 0 0
\(31\) 2305.65 + 3993.49i 0.430912 + 0.746361i 0.996952 0.0780167i \(-0.0248587\pi\)
−0.566040 + 0.824377i \(0.691525\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1664.97 0.229740
\(36\) 0 0
\(37\) 11896.3 1.42859 0.714297 0.699843i \(-0.246747\pi\)
0.714297 + 0.699843i \(0.246747\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5040.58 + 8730.55i 0.468297 + 0.811114i 0.999344 0.0362286i \(-0.0115344\pi\)
−0.531047 + 0.847343i \(0.678201\pi\)
\(42\) 0 0
\(43\) −3518.99 + 6095.07i −0.290233 + 0.502698i −0.973865 0.227129i \(-0.927066\pi\)
0.683632 + 0.729827i \(0.260400\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7459.33 12919.9i 0.492555 0.853131i −0.507408 0.861706i \(-0.669396\pi\)
0.999963 + 0.00857499i \(0.00272954\pi\)
\(48\) 0 0
\(49\) 6402.75 + 11089.9i 0.380957 + 0.659837i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −22451.7 −1.09789 −0.548947 0.835857i \(-0.684971\pi\)
−0.548947 + 0.835857i \(0.684971\pi\)
\(54\) 0 0
\(55\) −2585.69 −0.115258
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5405.25 + 9362.17i 0.202156 + 0.350144i 0.949223 0.314605i \(-0.101872\pi\)
−0.747067 + 0.664749i \(0.768539\pi\)
\(60\) 0 0
\(61\) 594.647 1029.96i 0.0204614 0.0354401i −0.855613 0.517615i \(-0.826820\pi\)
0.876075 + 0.482175i \(0.160153\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 9716.02 16828.6i 0.285236 0.494044i
\(66\) 0 0
\(67\) −29590.2 51251.8i −0.805307 1.39483i −0.916084 0.400988i \(-0.868667\pi\)
0.110776 0.993845i \(-0.464666\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14326.6 −0.337284 −0.168642 0.985677i \(-0.553938\pi\)
−0.168642 + 0.985677i \(0.553938\pi\)
\(72\) 0 0
\(73\) −53098.2 −1.16620 −0.583099 0.812401i \(-0.698160\pi\)
−0.583099 + 0.812401i \(0.698160\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3107.17 + 5381.77i 0.0597225 + 0.103442i
\(78\) 0 0
\(79\) 18695.6 32381.6i 0.337032 0.583756i −0.646841 0.762625i \(-0.723910\pi\)
0.983873 + 0.178869i \(0.0572438\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 60439.5 104684.i 0.962998 1.66796i 0.248097 0.968735i \(-0.420195\pi\)
0.714900 0.699226i \(-0.246472\pi\)
\(84\) 0 0
\(85\) 3290.85 + 5699.93i 0.0494039 + 0.0855701i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −97873.2 −1.30975 −0.654875 0.755737i \(-0.727279\pi\)
−0.654875 + 0.755737i \(0.727279\pi\)
\(90\) 0 0
\(91\) −46702.1 −0.591198
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −14507.9 25128.5i −0.164929 0.285665i
\(96\) 0 0
\(97\) −53356.7 + 92416.4i −0.575784 + 0.997286i 0.420172 + 0.907444i \(0.361970\pi\)
−0.995956 + 0.0898422i \(0.971364\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 48236.1 83547.3i 0.470510 0.814946i −0.528922 0.848671i \(-0.677403\pi\)
0.999431 + 0.0337242i \(0.0107368\pi\)
\(102\) 0 0
\(103\) −14972.2 25932.6i −0.139057 0.240854i 0.788083 0.615569i \(-0.211074\pi\)
−0.927140 + 0.374715i \(0.877740\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −22758.9 −0.192173 −0.0960865 0.995373i \(-0.530633\pi\)
−0.0960865 + 0.995373i \(0.530633\pi\)
\(108\) 0 0
\(109\) −2671.93 −0.0215407 −0.0107703 0.999942i \(-0.503428\pi\)
−0.0107703 + 0.999942i \(0.503428\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 65669.6 + 113743.i 0.483803 + 0.837971i 0.999827 0.0186028i \(-0.00592179\pi\)
−0.516024 + 0.856574i \(0.672588\pi\)
\(114\) 0 0
\(115\) 58028.9 100509.i 0.409166 0.708697i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7909.09 13698.9i 0.0511987 0.0886787i
\(120\) 0 0
\(121\) 75700.1 + 131116.i 0.470038 + 0.814130i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −146269. −0.837293
\(126\) 0 0
\(127\) 236012. 1.29845 0.649223 0.760598i \(-0.275094\pi\)
0.649223 + 0.760598i \(0.275094\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 180183. + 312086.i 0.917352 + 1.58890i 0.803421 + 0.595411i \(0.203011\pi\)
0.113930 + 0.993489i \(0.463656\pi\)
\(132\) 0 0
\(133\) −34867.7 + 60392.6i −0.170920 + 0.296043i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −118833. + 205825.i −0.540923 + 0.936906i 0.457929 + 0.888989i \(0.348592\pi\)
−0.998851 + 0.0479167i \(0.984742\pi\)
\(138\) 0 0
\(139\) −81673.4 141462.i −0.358545 0.621018i 0.629173 0.777265i \(-0.283394\pi\)
−0.987718 + 0.156247i \(0.950060\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 72528.2 0.296597
\(144\) 0 0
\(145\) 207461. 0.819440
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 167803. + 290644.i 0.619205 + 1.07250i 0.989631 + 0.143633i \(0.0458785\pi\)
−0.370426 + 0.928862i \(0.620788\pi\)
\(150\) 0 0
\(151\) 67788.5 117413.i 0.241943 0.419058i −0.719325 0.694674i \(-0.755549\pi\)
0.961268 + 0.275616i \(0.0888819\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 60685.7 105111.i 0.202888 0.351413i
\(156\) 0 0
\(157\) 212716. + 368435.i 0.688733 + 1.19292i 0.972248 + 0.233952i \(0.0751659\pi\)
−0.283516 + 0.958968i \(0.591501\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −278928. −0.848062
\(162\) 0 0
\(163\) −158679. −0.467789 −0.233895 0.972262i \(-0.575147\pi\)
−0.233895 + 0.972262i \(0.575147\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −259223. 448988.i −0.719254 1.24579i −0.961296 0.275519i \(-0.911150\pi\)
0.242041 0.970266i \(-0.422183\pi\)
\(168\) 0 0
\(169\) −86886.2 + 150491.i −0.234010 + 0.405317i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −76589.0 + 132656.i −0.194559 + 0.336986i −0.946756 0.321953i \(-0.895661\pi\)
0.752197 + 0.658938i \(0.228994\pi\)
\(174\) 0 0
\(175\) 76928.4 + 133244.i 0.189885 + 0.328891i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 736845. 1.71887 0.859437 0.511242i \(-0.170815\pi\)
0.859437 + 0.511242i \(0.170815\pi\)
\(180\) 0 0
\(181\) 28183.8 0.0639445 0.0319722 0.999489i \(-0.489821\pi\)
0.0319722 + 0.999489i \(0.489821\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −156559. 271168.i −0.336316 0.582517i
\(186\) 0 0
\(187\) −12282.8 + 21274.4i −0.0256858 + 0.0444891i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 49660.5 86014.5i 0.0984981 0.170604i −0.812565 0.582870i \(-0.801929\pi\)
0.911063 + 0.412267i \(0.135263\pi\)
\(192\) 0 0
\(193\) −208636. 361368.i −0.403177 0.698324i 0.590930 0.806723i \(-0.298761\pi\)
−0.994107 + 0.108399i \(0.965428\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −254565. −0.467340 −0.233670 0.972316i \(-0.575073\pi\)
−0.233670 + 0.972316i \(0.575073\pi\)
\(198\) 0 0
\(199\) −599702. −1.07350 −0.536751 0.843741i \(-0.680348\pi\)
−0.536751 + 0.843741i \(0.680348\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −249301. 431803.i −0.424604 0.735436i
\(204\) 0 0
\(205\) 132671. 229792.i 0.220491 0.381901i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 54149.4 93789.6i 0.0857488 0.148521i
\(210\) 0 0
\(211\) −378292. 655221.i −0.584953 1.01317i −0.994881 0.101051i \(-0.967779\pi\)
0.409928 0.912118i \(-0.365554\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 185243. 0.273304
\(216\) 0 0
\(217\) −291699. −0.420518
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −92307.9 159882.i −0.127133 0.220201i
\(222\) 0 0
\(223\) 55602.4 96306.2i 0.0748741 0.129686i −0.826157 0.563439i \(-0.809478\pi\)
0.901032 + 0.433754i \(0.142811\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −245380. + 425010.i −0.316063 + 0.547438i −0.979663 0.200650i \(-0.935695\pi\)
0.663600 + 0.748088i \(0.269028\pi\)
\(228\) 0 0
\(229\) −380511. 659064.i −0.479488 0.830498i 0.520235 0.854023i \(-0.325844\pi\)
−0.999723 + 0.0235249i \(0.992511\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 356267. 0.429918 0.214959 0.976623i \(-0.431038\pi\)
0.214959 + 0.976623i \(0.431038\pi\)
\(234\) 0 0
\(235\) −392667. −0.463825
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −453120. 784826.i −0.513119 0.888748i −0.999884 0.0152152i \(-0.995157\pi\)
0.486765 0.873533i \(-0.338177\pi\)
\(240\) 0 0
\(241\) −261288. + 452564.i −0.289785 + 0.501923i −0.973758 0.227584i \(-0.926917\pi\)
0.683973 + 0.729507i \(0.260251\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 168523. 291891.i 0.179368 0.310675i
\(246\) 0 0
\(247\) 406945. + 704849.i 0.424417 + 0.735113i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 625287. 0.626462 0.313231 0.949677i \(-0.398589\pi\)
0.313231 + 0.949677i \(0.398589\pi\)
\(252\) 0 0
\(253\) 433175. 0.425463
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −651106. 1.12775e6i −0.614921 1.06507i −0.990398 0.138243i \(-0.955855\pi\)
0.375478 0.926831i \(-0.377479\pi\)
\(258\) 0 0
\(259\) −376266. + 651712.i −0.348534 + 0.603679i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −716761. + 1.24147e6i −0.638977 + 1.10674i 0.346681 + 0.937983i \(0.387309\pi\)
−0.985658 + 0.168757i \(0.946025\pi\)
\(264\) 0 0
\(265\) 295471. + 511770.i 0.258464 + 0.447672i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.52329e6 1.28352 0.641758 0.766907i \(-0.278205\pi\)
0.641758 + 0.766907i \(0.278205\pi\)
\(270\) 0 0
\(271\) 1.60134e6 1.32453 0.662263 0.749271i \(-0.269596\pi\)
0.662263 + 0.749271i \(0.269596\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −119470. 206927.i −0.0952633 0.165001i
\(276\) 0 0
\(277\) 446972. 774178.i 0.350010 0.606235i −0.636241 0.771491i \(-0.719511\pi\)
0.986251 + 0.165255i \(0.0528448\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −14200.0 + 24595.2i −0.0107281 + 0.0185817i −0.871340 0.490680i \(-0.836748\pi\)
0.860612 + 0.509262i \(0.170082\pi\)
\(282\) 0 0
\(283\) 554783. + 960912.i 0.411772 + 0.713210i 0.995084 0.0990384i \(-0.0315767\pi\)
−0.583312 + 0.812248i \(0.698243\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −637709. −0.457002
\(288\) 0 0
\(289\) −1.35733e6 −0.955960
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.22884e6 + 2.12841e6i 0.836230 + 1.44839i 0.893025 + 0.450008i \(0.148579\pi\)
−0.0567942 + 0.998386i \(0.518088\pi\)
\(294\) 0 0
\(295\) 142269. 246417.i 0.0951821 0.164860i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.62770e6 + 2.81926e6i −1.05292 + 1.82372i
\(300\) 0 0
\(301\) −222602. 385559.i −0.141616 0.245287i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −31302.8 −0.0192679
\(306\) 0 0
\(307\) 1.77336e6 1.07387 0.536934 0.843624i \(-0.319583\pi\)
0.536934 + 0.843624i \(0.319583\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 752855. + 1.30398e6i 0.441378 + 0.764489i 0.997792 0.0664162i \(-0.0211565\pi\)
−0.556414 + 0.830905i \(0.687823\pi\)
\(312\) 0 0
\(313\) 406353. 703823.i 0.234446 0.406072i −0.724666 0.689100i \(-0.758006\pi\)
0.959111 + 0.283029i \(0.0913392\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 523798. 907244.i 0.292763 0.507080i −0.681699 0.731632i \(-0.738759\pi\)
0.974462 + 0.224553i \(0.0720921\pi\)
\(318\) 0 0
\(319\) 387164. + 670588.i 0.213019 + 0.368960i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −275668. −0.147021
\(324\) 0 0
\(325\) 1.79568e6 0.943020
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 471858. + 817283.i 0.240338 + 0.416277i
\(330\) 0 0
\(331\) 34002.7 58894.4i 0.0170586 0.0295463i −0.857370 0.514700i \(-0.827903\pi\)
0.874429 + 0.485154i \(0.161236\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −778830. + 1.34897e6i −0.379167 + 0.656737i
\(336\) 0 0
\(337\) 208236. + 360675.i 0.0998806 + 0.172998i 0.911635 0.411001i \(-0.134821\pi\)
−0.811755 + 0.583999i \(0.801487\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 453007. 0.210969
\(342\) 0 0
\(343\) −1.87321e6 −0.859709
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.40370e6 2.43128e6i −0.625822 1.08396i −0.988381 0.151995i \(-0.951430\pi\)
0.362559 0.931961i \(-0.381903\pi\)
\(348\) 0 0
\(349\) 240986. 417401.i 0.105908 0.183438i −0.808201 0.588907i \(-0.799558\pi\)
0.914109 + 0.405469i \(0.132892\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00019e6 3.46442e6i 0.854346 1.47977i −0.0229050 0.999738i \(-0.507292\pi\)
0.877251 0.480033i \(-0.159375\pi\)
\(354\) 0 0
\(355\) 188541. + 326563.i 0.0794027 + 0.137530i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 800858. 0.327959 0.163979 0.986464i \(-0.447567\pi\)
0.163979 + 0.986464i \(0.447567\pi\)
\(360\) 0 0
\(361\) −1.26080e6 −0.509189
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 698785. + 1.21033e6i 0.274544 + 0.475524i
\(366\) 0 0
\(367\) −1.50486e6 + 2.60649e6i −0.583218 + 1.01016i 0.411877 + 0.911239i \(0.364873\pi\)
−0.995095 + 0.0989236i \(0.968460\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 710120. 1.22996e6i 0.267853 0.463936i
\(372\) 0 0
\(373\) −796653. 1.37984e6i −0.296481 0.513520i 0.678847 0.734280i \(-0.262480\pi\)
−0.975328 + 0.220759i \(0.929147\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.81925e6 −2.10869
\(378\) 0 0
\(379\) −297930. −0.106541 −0.0532703 0.998580i \(-0.516965\pi\)
−0.0532703 + 0.998580i \(0.516965\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −645151. 1.11743e6i −0.224732 0.389247i 0.731507 0.681834i \(-0.238817\pi\)
−0.956239 + 0.292587i \(0.905484\pi\)
\(384\) 0 0
\(385\) 81782.2 141651.i 0.0281194 0.0487043i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.49937e6 4.32903e6i 0.837444 1.45050i −0.0545807 0.998509i \(-0.517382\pi\)
0.892025 0.451986i \(-0.149284\pi\)
\(390\) 0 0
\(391\) −551309. 954894.i −0.182370 0.315874i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −984153. −0.317373
\(396\) 0 0
\(397\) −558980. −0.178000 −0.0890000 0.996032i \(-0.528367\pi\)
−0.0890000 + 0.996032i \(0.528367\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 47103.6 + 81585.8i 0.0146283 + 0.0253369i 0.873247 0.487278i \(-0.162010\pi\)
−0.858619 + 0.512615i \(0.828677\pi\)
\(402\) 0 0
\(403\) −1.70222e6 + 2.94834e6i −0.522101 + 0.904305i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 584340. 1.01211e6i 0.174856 0.302859i
\(408\) 0 0
\(409\) −2.73115e6 4.73049e6i −0.807304 1.39829i −0.914724 0.404078i \(-0.867592\pi\)
0.107420 0.994214i \(-0.465741\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −683845. −0.197280
\(414\) 0 0
\(415\) −3.18159e6 −0.906827
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −418486. 724839.i −0.116452 0.201700i 0.801907 0.597448i \(-0.203819\pi\)
−0.918359 + 0.395748i \(0.870485\pi\)
\(420\) 0 0
\(421\) 3.21404e6 5.56689e6i 0.883785 1.53076i 0.0366842 0.999327i \(-0.488320\pi\)
0.847100 0.531433i \(-0.178346\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −304102. + 526720.i −0.0816671 + 0.141452i
\(426\) 0 0
\(427\) 37615.8 + 65152.5i 0.00998392 + 0.0172927i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.11509e6 1.32636 0.663178 0.748462i \(-0.269207\pi\)
0.663178 + 0.748462i \(0.269207\pi\)
\(432\) 0 0
\(433\) −1.39089e6 −0.356512 −0.178256 0.983984i \(-0.557045\pi\)
−0.178256 + 0.983984i \(0.557045\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.43048e6 + 4.20971e6i 0.608819 + 1.05450i
\(438\) 0 0
\(439\) 1.76266e6 3.05301e6i 0.436523 0.756079i −0.560896 0.827886i \(-0.689543\pi\)
0.997419 + 0.0718069i \(0.0228765\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.02216e6 1.77043e6i 0.247462 0.428617i −0.715359 0.698757i \(-0.753737\pi\)
0.962821 + 0.270140i \(0.0870701\pi\)
\(444\) 0 0
\(445\) 1.28804e6 + 2.23094e6i 0.308339 + 0.534058i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −7.70508e6 −1.80369 −0.901844 0.432062i \(-0.857786\pi\)
−0.901844 + 0.432062i \(0.857786\pi\)
\(450\) 0 0
\(451\) 990361. 0.229273
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 614611. + 1.06454e6i 0.139178 + 0.241064i
\(456\) 0 0
\(457\) −4.28846e6 + 7.42783e6i −0.960529 + 1.66369i −0.239355 + 0.970932i \(0.576936\pi\)
−0.721175 + 0.692753i \(0.756397\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 716317. 1.24070e6i 0.156983 0.271903i −0.776796 0.629752i \(-0.783157\pi\)
0.933779 + 0.357849i \(0.116490\pi\)
\(462\) 0 0
\(463\) −1.47223e6 2.54998e6i −0.319172 0.552821i 0.661144 0.750259i \(-0.270071\pi\)
−0.980315 + 0.197438i \(0.936738\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.96160e6 −1.05276 −0.526380 0.850249i \(-0.676451\pi\)
−0.526380 + 0.850249i \(0.676451\pi\)
\(468\) 0 0
\(469\) 3.74361e6 0.785884
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 345701. + 598772.i 0.0710473 + 0.123058i
\(474\) 0 0
\(475\) 1.34065e6 2.32208e6i 0.272635 0.472218i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −120757. + 209157.i −0.0240476 + 0.0416517i −0.877799 0.479030i \(-0.840989\pi\)
0.853751 + 0.520681i \(0.174322\pi\)
\(480\) 0 0
\(481\) 4.39145e6 + 7.60621e6i 0.865456 + 1.49901i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.80875e6 0.542199
\(486\) 0 0
\(487\) 325055. 0.0621061 0.0310530 0.999518i \(-0.490114\pi\)
0.0310530 + 0.999518i \(0.490114\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.49023e6 + 4.31321e6i 0.466162 + 0.807416i 0.999253 0.0386419i \(-0.0123032\pi\)
−0.533091 + 0.846058i \(0.678970\pi\)
\(492\) 0 0
\(493\) 985502. 1.70694e6i 0.182617 0.316301i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 453131. 784846.i 0.0822873 0.142526i
\(498\) 0 0
\(499\) 2.93247e6 + 5.07919e6i 0.527209 + 0.913153i 0.999497 + 0.0317085i \(0.0100948\pi\)
−0.472288 + 0.881444i \(0.656572\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.36396e6 0.240370 0.120185 0.992751i \(-0.461651\pi\)
0.120185 + 0.992751i \(0.461651\pi\)
\(504\) 0 0
\(505\) −2.53919e6 −0.443065
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.85023e6 + 3.20470e6i 0.316542 + 0.548268i 0.979764 0.200155i \(-0.0641447\pi\)
−0.663222 + 0.748423i \(0.730811\pi\)
\(510\) 0 0
\(511\) 1.67943e6 2.90885e6i 0.284517 0.492799i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −394076. + 682560.i −0.0654730 + 0.113403i
\(516\) 0 0
\(517\) −732795. 1.26924e6i −0.120575 0.208841i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 285260. 0.0460412 0.0230206 0.999735i \(-0.492672\pi\)
0.0230206 + 0.999735i \(0.492672\pi\)
\(522\) 0 0
\(523\) 8.28809e6 1.32495 0.662476 0.749083i \(-0.269506\pi\)
0.662476 + 0.749083i \(0.269506\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −576550. 998614.i −0.0904296 0.156629i
\(528\) 0 0
\(529\) −6.50327e6 + 1.12640e7i −1.01040 + 1.75006i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.72139e6 + 6.44564e6i −0.567397 + 0.982761i
\(534\) 0 0
\(535\) 299513. + 518772.i 0.0452409 + 0.0783596i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.25800e6 0.186512
\(540\) 0 0
\(541\) 1.29750e7 1.90596 0.952982 0.303028i \(-0.0979975\pi\)
0.952982 + 0.303028i \(0.0979975\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 35163.3 + 60904.6i 0.00507105 + 0.00878332i
\(546\) 0 0
\(547\) 4.65800e6 8.06790e6i 0.665628 1.15290i −0.313487 0.949593i \(-0.601497\pi\)
0.979115 0.203309i \(-0.0651696\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.34464e6 + 7.52514e6i −0.609642 + 1.05593i
\(552\) 0 0
\(553\) 1.18263e6 + 2.04838e6i 0.164451 + 0.284838i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.18234e6 0.571192 0.285596 0.958350i \(-0.407809\pi\)
0.285596 + 0.958350i \(0.407809\pi\)
\(558\) 0 0
\(559\) −5.19604e6 −0.703304
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.65660e6 2.86931e6i −0.220265 0.381511i 0.734623 0.678475i \(-0.237359\pi\)
−0.954888 + 0.296965i \(0.904026\pi\)
\(564\) 0 0
\(565\) 1.72846e6 2.99378e6i 0.227792 0.394547i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.92695e6 + 5.06963e6i −0.378996 + 0.656441i −0.990917 0.134478i \(-0.957064\pi\)
0.611920 + 0.790920i \(0.290397\pi\)
\(570\) 0 0
\(571\) −6.75429e6 1.16988e7i −0.866941 1.50159i −0.865107 0.501587i \(-0.832750\pi\)
−0.00183339 0.999998i \(-0.500584\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.07247e7 1.35274
\(576\) 0 0
\(577\) −1.12898e7 −1.41171 −0.705855 0.708356i \(-0.749437\pi\)
−0.705855 + 0.708356i \(0.749437\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.82325e6 + 6.62206e6i 0.469886 + 0.813866i
\(582\) 0 0
\(583\) −1.10282e6 + 1.91013e6i −0.134379 + 0.232751i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 991398. 1.71715e6i 0.118755 0.205690i −0.800519 0.599307i \(-0.795443\pi\)
0.919275 + 0.393617i \(0.128776\pi\)
\(588\) 0 0
\(589\) 2.54176e6 + 4.40245e6i 0.301888 + 0.522885i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.22629e7 −1.43204 −0.716021 0.698078i \(-0.754039\pi\)
−0.716021 + 0.698078i \(0.754039\pi\)
\(594\) 0 0
\(595\) −416342. −0.0482123
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.84977e6 1.35962e7i −0.893902 1.54828i −0.835158 0.550010i \(-0.814624\pi\)
−0.0587438 0.998273i \(-0.518710\pi\)
\(600\) 0 0
\(601\) 2.65972e6 4.60677e6i 0.300366 0.520248i −0.675853 0.737036i \(-0.736225\pi\)
0.976219 + 0.216788i \(0.0695580\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.99246e6 3.45105e6i 0.221311 0.383321i
\(606\) 0 0
\(607\) −2.18482e6 3.78422e6i −0.240682 0.416874i 0.720226 0.693739i \(-0.244038\pi\)
−0.960909 + 0.276865i \(0.910705\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.10142e7 1.19358
\(612\) 0 0
\(613\) −7.62875e6 −0.819978 −0.409989 0.912091i \(-0.634467\pi\)
−0.409989 + 0.912091i \(0.634467\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −7.16498e6 1.24101e7i −0.757708 1.31239i −0.944017 0.329898i \(-0.892986\pi\)
0.186309 0.982491i \(-0.440348\pi\)
\(618\) 0 0
\(619\) −5.40907e6 + 9.36878e6i −0.567408 + 0.982780i 0.429413 + 0.903108i \(0.358720\pi\)
−0.996821 + 0.0796716i \(0.974613\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.09560e6 5.36174e6i 0.319540 0.553460i
\(624\) 0 0
\(625\) −1.87542e6 3.24833e6i −0.192043 0.332629i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.97480e6 −0.299800
\(630\) 0 0
\(631\) 7.96579e6 0.796444 0.398222 0.917289i \(-0.369627\pi\)
0.398222 + 0.917289i \(0.369627\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.10597e6 5.37970e6i −0.305677 0.529448i
\(636\) 0 0
\(637\) −4.72705e6 + 8.18750e6i −0.461575 + 0.799471i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.40224e6 5.89285e6i 0.327054 0.566475i −0.654872 0.755740i \(-0.727277\pi\)
0.981926 + 0.189266i \(0.0606107\pi\)
\(642\) 0 0
\(643\) 2.66464e6 + 4.61530e6i 0.254163 + 0.440223i 0.964668 0.263469i \(-0.0848668\pi\)
−0.710505 + 0.703692i \(0.751533\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.03021e6 0.472417 0.236208 0.971702i \(-0.424095\pi\)
0.236208 + 0.971702i \(0.424095\pi\)
\(648\) 0 0
\(649\) 1.06201e6 0.0989731
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.66704e6 9.81560e6i −0.520084 0.900811i −0.999727 0.0233481i \(-0.992567\pi\)
0.479644 0.877463i \(-0.340766\pi\)
\(654\) 0 0
\(655\) 4.74251e6 8.21427e6i 0.431922 0.748110i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.91003e6 3.30828e6i 0.171328 0.296748i −0.767557 0.640981i \(-0.778528\pi\)
0.938884 + 0.344233i \(0.111861\pi\)
\(660\) 0 0
\(661\) −463286. 802435.i −0.0412426 0.0714342i 0.844667 0.535292i \(-0.179798\pi\)
−0.885910 + 0.463857i \(0.846465\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.83547e6 0.160951
\(666\) 0 0
\(667\) −3.47555e7 −3.02488
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −58417.3 101182.i −0.00500882 0.00867553i
\(672\) 0 0
\(673\) −2.45146e6 + 4.24605e6i −0.208635 + 0.361366i −0.951285 0.308314i \(-0.900235\pi\)
0.742650 + 0.669680i \(0.233569\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.37201e6 + 1.27687e7i −0.618179 + 1.07072i 0.371639 + 0.928378i \(0.378796\pi\)
−0.989818 + 0.142340i \(0.954537\pi\)
\(678\) 0 0
\(679\) −3.37521e6 5.84603e6i −0.280948 0.486616i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 6.53893e6 0.536358 0.268179 0.963369i \(-0.413578\pi\)
0.268179 + 0.963369i \(0.413578\pi\)
\(684\) 0 0
\(685\) 6.25548e6 0.509371
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −8.28790e6 1.43551e7i −0.665114 1.15201i
\(690\) 0 0
\(691\) 5.45248e6 9.44397e6i 0.434409 0.752419i −0.562838 0.826567i \(-0.690291\pi\)
0.997247 + 0.0741485i \(0.0236239\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.14968e6 + 3.72336e6i −0.168816 + 0.292397i
\(696\) 0 0
\(697\) −1.26045e6 2.18316e6i −0.0982751 0.170217i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.89162e7 1.45391 0.726957 0.686683i \(-0.240934\pi\)
0.726957 + 0.686683i \(0.240934\pi\)
\(702\) 0 0
\(703\) 1.31146e7 1.00084
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.05129e6 + 5.28499e6i 0.229581 + 0.397645i
\(708\) 0 0
\(709\) 9.63661e6 1.66911e7i 0.719960 1.24701i −0.241055 0.970512i \(-0.577493\pi\)
0.961015 0.276496i \(-0.0891733\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.01665e7 + 1.76089e7i −0.748943 + 1.29721i
\(714\) 0 0
\(715\) −954489. 1.65322e6i −0.0698242 0.120939i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.42859e7 −1.03059 −0.515293 0.857014i \(-0.672317\pi\)
−0.515293 + 0.857014i \(0.672317\pi\)
\(720\) 0 0
\(721\) 1.89421e6 0.135703
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 9.58556e6 + 1.66027e7i 0.677287 + 1.17310i
\(726\) 0 0
\(727\) −1.41386e7 + 2.44887e7i −0.992132 + 1.71842i −0.387641 + 0.921810i \(0.626710\pi\)
−0.604491 + 0.796612i \(0.706623\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 879959. 1.52413e6i 0.0609073 0.105494i
\(732\) 0 0
\(733\) −4.93850e6 8.55373e6i −0.339496 0.588025i 0.644842 0.764316i \(-0.276923\pi\)
−0.984338 + 0.176291i \(0.943590\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.81381e6 −0.394269
\(738\) 0 0
\(739\) 6.31081e6 0.425083 0.212542 0.977152i \(-0.431826\pi\)
0.212542 + 0.977152i \(0.431826\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −31529.9 54611.3i −0.00209532 0.00362920i 0.864976 0.501814i \(-0.167334\pi\)
−0.867071 + 0.498184i \(0.834000\pi\)
\(744\) 0 0
\(745\) 4.41667e6 7.64989e6i 0.291544 0.504969i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 719836. 1.24679e6i 0.0468845 0.0812063i
\(750\) 0 0
\(751\) 8.69183e6 + 1.50547e7i 0.562356 + 0.974029i 0.997290 + 0.0735670i \(0.0234383\pi\)
−0.434934 + 0.900462i \(0.643228\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.56845e6 −0.227831
\(756\) 0 0
\(757\) 9.43592e6 0.598473 0.299237 0.954179i \(-0.403268\pi\)
0.299237 + 0.954179i \(0.403268\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 8.06409e6 + 1.39674e7i 0.504771 + 0.874288i 0.999985 + 0.00551731i \(0.00175622\pi\)
−0.495214 + 0.868771i \(0.664910\pi\)
\(762\) 0 0
\(763\) 84509.8 146375.i 0.00525528 0.00910241i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.99062e6 + 6.91196e6i −0.244936 + 0.424241i
\(768\) 0 0
\(769\) 1.28431e7 + 2.22450e7i 0.783169 + 1.35649i 0.930087 + 0.367339i \(0.119731\pi\)
−0.146918 + 0.989149i \(0.546935\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.01235e7 1.21131 0.605654 0.795728i \(-0.292912\pi\)
0.605654 + 0.795728i \(0.292912\pi\)
\(774\) 0 0
\(775\) 1.12157e7 0.670769
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.55677e6 + 9.62460e6i 0.328079 + 0.568250i
\(780\) 0 0
\(781\) −703712. + 1.21886e6i −0.0412826 + 0.0715036i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.59879e6 9.69738e6i 0.324280 0.561669i
\(786\) 0 0
\(787\) −2.87640e6 4.98208e6i −0.165544 0.286730i 0.771304 0.636466i \(-0.219605\pi\)
−0.936848 + 0.349736i \(0.886271\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −8.30819e6 −0.472134
\(792\) 0 0
\(793\) 878038. 0.0495827
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.09822e6 8.83038e6i −0.284298 0.492418i 0.688141 0.725577i \(-0.258427\pi\)
−0.972439 + 0.233159i \(0.925094\pi\)
\(798\) 0 0
\(799\) −1.86528e6 + 3.23076e6i −0.103366 + 0.179035i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.60815e6 + 4.51744e6i