Properties

Label 240.3.l.d.161.5
Level $240$
Weight $3$
Character 240.161
Analytic conductor $6.540$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53952634465\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.681615360000.5
Defining polynomial: \(x^{8} - 4 x^{7} - 2 x^{6} + 20 x^{5} + 49 x^{4} - 136 x^{3} + 168 x^{2} - 96 x + 864\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{5}\cdot 3 \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 161.5
Root \(-0.542939 + 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 240.161
Dual form 240.3.l.d.161.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.40140 - 1.79813i) q^{3} -2.23607i q^{5} +10.2132 q^{7} +(2.53346 - 8.63606i) q^{9} +O(q^{10})\) \(q+(2.40140 - 1.79813i) q^{3} -2.23607i q^{5} +10.2132 q^{7} +(2.53346 - 8.63606i) q^{9} +8.19300i q^{11} -13.5822 q^{13} +(-4.02074 - 5.36970i) q^{15} -15.4710i q^{17} +25.4934 q^{19} +(24.5261 - 18.3647i) q^{21} -17.9156i q^{23} -5.00000 q^{25} +(-9.44491 - 25.2941i) q^{27} +42.0022i q^{29} -38.4878 q^{31} +(14.7321 + 19.6747i) q^{33} -22.8375i q^{35} +11.8387 q^{37} +(-32.6163 + 24.4225i) q^{39} -46.3781i q^{41} +54.0181 q^{43} +(-19.3108 - 5.66499i) q^{45} +43.0955i q^{47} +55.3102 q^{49} +(-27.8188 - 37.1521i) q^{51} +82.7421i q^{53} +18.3201 q^{55} +(61.2199 - 45.8404i) q^{57} +45.8928i q^{59} -93.6873 q^{61} +(25.8748 - 88.2022i) q^{63} +30.3707i q^{65} -34.4995 q^{67} +(-32.2147 - 43.0227i) q^{69} +68.0061i q^{71} -44.7191 q^{73} +(-12.0070 + 8.99065i) q^{75} +83.6770i q^{77} +11.7499 q^{79} +(-68.1632 - 43.7582i) q^{81} +144.436i q^{83} -34.5942 q^{85} +(75.5255 + 100.864i) q^{87} +63.7094i q^{89} -138.718 q^{91} +(-92.4247 + 69.2061i) q^{93} -57.0050i q^{95} +63.9013 q^{97} +(70.7552 + 20.7566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} - 16 q^{7} + 20 q^{9} + O(q^{10}) \) \( 8 q + 4 q^{3} - 16 q^{7} + 20 q^{9} - 8 q^{13} + 8 q^{19} + 28 q^{21} - 40 q^{25} - 20 q^{27} - 120 q^{31} - 112 q^{33} + 8 q^{37} + 72 q^{39} + 328 q^{43} - 60 q^{45} + 64 q^{49} - 64 q^{51} + 40 q^{55} + 72 q^{57} + 8 q^{61} - 88 q^{63} - 152 q^{67} + 100 q^{69} + 32 q^{73} - 20 q^{75} - 88 q^{79} + 224 q^{81} + 152 q^{87} - 560 q^{91} - 368 q^{93} + 144 q^{97} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.40140 1.79813i 0.800467 0.599377i
\(4\) 0 0
\(5\) 2.23607i 0.447214i
\(6\) 0 0
\(7\) 10.2132 1.45903 0.729517 0.683963i \(-0.239745\pi\)
0.729517 + 0.683963i \(0.239745\pi\)
\(8\) 0 0
\(9\) 2.53346 8.63606i 0.281496 0.959563i
\(10\) 0 0
\(11\) 8.19300i 0.744818i 0.928069 + 0.372409i \(0.121468\pi\)
−0.928069 + 0.372409i \(0.878532\pi\)
\(12\) 0 0
\(13\) −13.5822 −1.04478 −0.522392 0.852705i \(-0.674960\pi\)
−0.522392 + 0.852705i \(0.674960\pi\)
\(14\) 0 0
\(15\) −4.02074 5.36970i −0.268049 0.357980i
\(16\) 0 0
\(17\) 15.4710i 0.910058i −0.890477 0.455029i \(-0.849629\pi\)
0.890477 0.455029i \(-0.150371\pi\)
\(18\) 0 0
\(19\) 25.4934 1.34176 0.670879 0.741567i \(-0.265917\pi\)
0.670879 + 0.741567i \(0.265917\pi\)
\(20\) 0 0
\(21\) 24.5261 18.3647i 1.16791 0.874511i
\(22\) 0 0
\(23\) 17.9156i 0.778941i −0.921039 0.389471i \(-0.872658\pi\)
0.921039 0.389471i \(-0.127342\pi\)
\(24\) 0 0
\(25\) −5.00000 −0.200000
\(26\) 0 0
\(27\) −9.44491 25.2941i −0.349811 0.936820i
\(28\) 0 0
\(29\) 42.0022i 1.44835i 0.689615 + 0.724177i \(0.257780\pi\)
−0.689615 + 0.724177i \(0.742220\pi\)
\(30\) 0 0
\(31\) −38.4878 −1.24154 −0.620771 0.783992i \(-0.713180\pi\)
−0.620771 + 0.783992i \(0.713180\pi\)
\(32\) 0 0
\(33\) 14.7321 + 19.6747i 0.446426 + 0.596202i
\(34\) 0 0
\(35\) 22.8375i 0.652500i
\(36\) 0 0
\(37\) 11.8387 0.319965 0.159982 0.987120i \(-0.448856\pi\)
0.159982 + 0.987120i \(0.448856\pi\)
\(38\) 0 0
\(39\) −32.6163 + 24.4225i −0.836315 + 0.626219i
\(40\) 0 0
\(41\) 46.3781i 1.13117i −0.824689 0.565587i \(-0.808650\pi\)
0.824689 0.565587i \(-0.191350\pi\)
\(42\) 0 0
\(43\) 54.0181 1.25623 0.628117 0.778119i \(-0.283826\pi\)
0.628117 + 0.778119i \(0.283826\pi\)
\(44\) 0 0
\(45\) −19.3108 5.66499i −0.429129 0.125889i
\(46\) 0 0
\(47\) 43.0955i 0.916925i 0.888714 + 0.458462i \(0.151600\pi\)
−0.888714 + 0.458462i \(0.848400\pi\)
\(48\) 0 0
\(49\) 55.3102 1.12878
\(50\) 0 0
\(51\) −27.8188 37.1521i −0.545468 0.728472i
\(52\) 0 0
\(53\) 82.7421i 1.56117i 0.625049 + 0.780586i \(0.285079\pi\)
−0.625049 + 0.780586i \(0.714921\pi\)
\(54\) 0 0
\(55\) 18.3201 0.333093
\(56\) 0 0
\(57\) 61.2199 45.8404i 1.07403 0.804218i
\(58\) 0 0
\(59\) 45.8928i 0.777844i 0.921271 + 0.388922i \(0.127152\pi\)
−0.921271 + 0.388922i \(0.872848\pi\)
\(60\) 0 0
\(61\) −93.6873 −1.53586 −0.767929 0.640535i \(-0.778713\pi\)
−0.767929 + 0.640535i \(0.778713\pi\)
\(62\) 0 0
\(63\) 25.8748 88.2022i 0.410712 1.40003i
\(64\) 0 0
\(65\) 30.3707i 0.467242i
\(66\) 0 0
\(67\) −34.4995 −0.514917 −0.257459 0.966289i \(-0.582885\pi\)
−0.257459 + 0.966289i \(0.582885\pi\)
\(68\) 0 0
\(69\) −32.2147 43.0227i −0.466879 0.623517i
\(70\) 0 0
\(71\) 68.0061i 0.957832i 0.877861 + 0.478916i \(0.158970\pi\)
−0.877861 + 0.478916i \(0.841030\pi\)
\(72\) 0 0
\(73\) −44.7191 −0.612591 −0.306295 0.951937i \(-0.599089\pi\)
−0.306295 + 0.951937i \(0.599089\pi\)
\(74\) 0 0
\(75\) −12.0070 + 8.99065i −0.160093 + 0.119875i
\(76\) 0 0
\(77\) 83.6770i 1.08671i
\(78\) 0 0
\(79\) 11.7499 0.148733 0.0743665 0.997231i \(-0.476307\pi\)
0.0743665 + 0.997231i \(0.476307\pi\)
\(80\) 0 0
\(81\) −68.1632 43.7582i −0.841521 0.540225i
\(82\) 0 0
\(83\) 144.436i 1.74020i 0.492877 + 0.870099i \(0.335945\pi\)
−0.492877 + 0.870099i \(0.664055\pi\)
\(84\) 0 0
\(85\) −34.5942 −0.406990
\(86\) 0 0
\(87\) 75.5255 + 100.864i 0.868109 + 1.15936i
\(88\) 0 0
\(89\) 63.7094i 0.715836i 0.933753 + 0.357918i \(0.116513\pi\)
−0.933753 + 0.357918i \(0.883487\pi\)
\(90\) 0 0
\(91\) −138.718 −1.52438
\(92\) 0 0
\(93\) −92.4247 + 69.2061i −0.993814 + 0.744151i
\(94\) 0 0
\(95\) 57.0050i 0.600052i
\(96\) 0 0
\(97\) 63.9013 0.658776 0.329388 0.944195i \(-0.393158\pi\)
0.329388 + 0.944195i \(0.393158\pi\)
\(98\) 0 0
\(99\) 70.7552 + 20.7566i 0.714699 + 0.209663i
\(100\) 0 0
\(101\) 50.8769i 0.503731i −0.967762 0.251866i \(-0.918956\pi\)
0.967762 0.251866i \(-0.0810441\pi\)
\(102\) 0 0
\(103\) −45.9491 −0.446108 −0.223054 0.974806i \(-0.571603\pi\)
−0.223054 + 0.974806i \(0.571603\pi\)
\(104\) 0 0
\(105\) −41.0648 54.8420i −0.391093 0.522305i
\(106\) 0 0
\(107\) 110.249i 1.03036i 0.857082 + 0.515181i \(0.172275\pi\)
−0.857082 + 0.515181i \(0.827725\pi\)
\(108\) 0 0
\(109\) −49.2797 −0.452107 −0.226054 0.974115i \(-0.572582\pi\)
−0.226054 + 0.974115i \(0.572582\pi\)
\(110\) 0 0
\(111\) 28.4295 21.2875i 0.256121 0.191779i
\(112\) 0 0
\(113\) 157.450i 1.39337i −0.717379 0.696683i \(-0.754658\pi\)
0.717379 0.696683i \(-0.245342\pi\)
\(114\) 0 0
\(115\) −40.0606 −0.348353
\(116\) 0 0
\(117\) −34.4099 + 117.297i −0.294102 + 1.00254i
\(118\) 0 0
\(119\) 158.009i 1.32781i
\(120\) 0 0
\(121\) 53.8748 0.445246
\(122\) 0 0
\(123\) −83.3939 111.373i −0.677999 0.905468i
\(124\) 0 0
\(125\) 11.1803i 0.0894427i
\(126\) 0 0
\(127\) 135.065 1.06351 0.531753 0.846900i \(-0.321534\pi\)
0.531753 + 0.846900i \(0.321534\pi\)
\(128\) 0 0
\(129\) 129.719 97.1315i 1.00557 0.752957i
\(130\) 0 0
\(131\) 150.653i 1.15002i −0.818146 0.575010i \(-0.804998\pi\)
0.818146 0.575010i \(-0.195002\pi\)
\(132\) 0 0
\(133\) 260.370 1.95767
\(134\) 0 0
\(135\) −56.5594 + 21.1195i −0.418959 + 0.156440i
\(136\) 0 0
\(137\) 139.086i 1.01523i 0.861585 + 0.507613i \(0.169472\pi\)
−0.861585 + 0.507613i \(0.830528\pi\)
\(138\) 0 0
\(139\) −110.296 −0.793496 −0.396748 0.917928i \(-0.629861\pi\)
−0.396748 + 0.917928i \(0.629861\pi\)
\(140\) 0 0
\(141\) 77.4912 + 103.490i 0.549583 + 0.733968i
\(142\) 0 0
\(143\) 111.279i 0.778174i
\(144\) 0 0
\(145\) 93.9199 0.647723
\(146\) 0 0
\(147\) 132.822 99.4549i 0.903551 0.676564i
\(148\) 0 0
\(149\) 90.8076i 0.609447i 0.952441 + 0.304723i \(0.0985640\pi\)
−0.952441 + 0.304723i \(0.901436\pi\)
\(150\) 0 0
\(151\) −111.286 −0.736992 −0.368496 0.929629i \(-0.620127\pi\)
−0.368496 + 0.929629i \(0.620127\pi\)
\(152\) 0 0
\(153\) −133.608 39.1951i −0.873258 0.256177i
\(154\) 0 0
\(155\) 86.0614i 0.555235i
\(156\) 0 0
\(157\) 142.755 0.909269 0.454635 0.890678i \(-0.349770\pi\)
0.454635 + 0.890678i \(0.349770\pi\)
\(158\) 0 0
\(159\) 148.781 + 198.697i 0.935730 + 1.24967i
\(160\) 0 0
\(161\) 182.977i 1.13650i
\(162\) 0 0
\(163\) 170.179 1.04405 0.522023 0.852932i \(-0.325178\pi\)
0.522023 + 0.852932i \(0.325178\pi\)
\(164\) 0 0
\(165\) 43.9939 32.9419i 0.266630 0.199648i
\(166\) 0 0
\(167\) 6.38780i 0.0382503i 0.999817 + 0.0191251i \(0.00608809\pi\)
−0.999817 + 0.0191251i \(0.993912\pi\)
\(168\) 0 0
\(169\) 15.4759 0.0915734
\(170\) 0 0
\(171\) 64.5865 220.163i 0.377699 1.28750i
\(172\) 0 0
\(173\) 238.403i 1.37805i −0.724736 0.689027i \(-0.758038\pi\)
0.724736 0.689027i \(-0.241962\pi\)
\(174\) 0 0
\(175\) −51.0662 −0.291807
\(176\) 0 0
\(177\) 82.5212 + 110.207i 0.466221 + 0.622638i
\(178\) 0 0
\(179\) 243.541i 1.36057i −0.732950 0.680283i \(-0.761857\pi\)
0.732950 0.680283i \(-0.238143\pi\)
\(180\) 0 0
\(181\) −325.449 −1.79806 −0.899030 0.437887i \(-0.855727\pi\)
−0.899030 + 0.437887i \(0.855727\pi\)
\(182\) 0 0
\(183\) −224.981 + 168.462i −1.22940 + 0.920557i
\(184\) 0 0
\(185\) 26.4721i 0.143093i
\(186\) 0 0
\(187\) 126.754 0.677828
\(188\) 0 0
\(189\) −96.4631 258.335i −0.510387 1.36685i
\(190\) 0 0
\(191\) 166.001i 0.869113i −0.900645 0.434556i \(-0.856905\pi\)
0.900645 0.434556i \(-0.143095\pi\)
\(192\) 0 0
\(193\) 239.408 1.24045 0.620227 0.784422i \(-0.287041\pi\)
0.620227 + 0.784422i \(0.287041\pi\)
\(194\) 0 0
\(195\) 54.6105 + 72.9323i 0.280054 + 0.374012i
\(196\) 0 0
\(197\) 257.518i 1.30720i −0.756840 0.653600i \(-0.773258\pi\)
0.756840 0.653600i \(-0.226742\pi\)
\(198\) 0 0
\(199\) 78.4735 0.394339 0.197170 0.980369i \(-0.436825\pi\)
0.197170 + 0.980369i \(0.436825\pi\)
\(200\) 0 0
\(201\) −82.8471 + 62.0345i −0.412174 + 0.308629i
\(202\) 0 0
\(203\) 428.979i 2.11320i
\(204\) 0 0
\(205\) −103.705 −0.505876
\(206\) 0 0
\(207\) −154.721 45.3886i −0.747443 0.219268i
\(208\) 0 0
\(209\) 208.867i 0.999365i
\(210\) 0 0
\(211\) 112.724 0.534237 0.267119 0.963664i \(-0.413928\pi\)
0.267119 + 0.963664i \(0.413928\pi\)
\(212\) 0 0
\(213\) 122.284 + 163.310i 0.574102 + 0.766713i
\(214\) 0 0
\(215\) 120.788i 0.561805i
\(216\) 0 0
\(217\) −393.085 −1.81145
\(218\) 0 0
\(219\) −107.389 + 80.4108i −0.490359 + 0.367172i
\(220\) 0 0
\(221\) 210.130i 0.950814i
\(222\) 0 0
\(223\) 204.686 0.917872 0.458936 0.888469i \(-0.348231\pi\)
0.458936 + 0.888469i \(0.348231\pi\)
\(224\) 0 0
\(225\) −12.6673 + 43.1803i −0.0562991 + 0.191913i
\(226\) 0 0
\(227\) 115.071i 0.506920i −0.967346 0.253460i \(-0.918431\pi\)
0.967346 0.253460i \(-0.0815685\pi\)
\(228\) 0 0
\(229\) −129.458 −0.565317 −0.282659 0.959221i \(-0.591216\pi\)
−0.282659 + 0.959221i \(0.591216\pi\)
\(230\) 0 0
\(231\) 150.462 + 200.942i 0.651351 + 0.869879i
\(232\) 0 0
\(233\) 250.150i 1.07361i −0.843708 0.536803i \(-0.819632\pi\)
0.843708 0.536803i \(-0.180368\pi\)
\(234\) 0 0
\(235\) 96.3644 0.410061
\(236\) 0 0
\(237\) 28.2162 21.1278i 0.119056 0.0891470i
\(238\) 0 0
\(239\) 49.2556i 0.206090i −0.994677 0.103045i \(-0.967141\pi\)
0.994677 0.103045i \(-0.0328586\pi\)
\(240\) 0 0
\(241\) −457.672 −1.89905 −0.949526 0.313688i \(-0.898435\pi\)
−0.949526 + 0.313688i \(0.898435\pi\)
\(242\) 0 0
\(243\) −242.370 + 17.4851i −0.997408 + 0.0719551i
\(244\) 0 0
\(245\) 123.677i 0.504806i
\(246\) 0 0
\(247\) −346.256 −1.40185
\(248\) 0 0
\(249\) 259.715 + 346.850i 1.04303 + 1.39297i
\(250\) 0 0
\(251\) 119.717i 0.476959i 0.971148 + 0.238479i \(0.0766489\pi\)
−0.971148 + 0.238479i \(0.923351\pi\)
\(252\) 0 0
\(253\) 146.783 0.580169
\(254\) 0 0
\(255\) −83.0745 + 62.2048i −0.325782 + 0.243940i
\(256\) 0 0
\(257\) 111.805i 0.435041i −0.976056 0.217520i \(-0.930203\pi\)
0.976056 0.217520i \(-0.0697969\pi\)
\(258\) 0 0
\(259\) 120.911 0.466839
\(260\) 0 0
\(261\) 362.734 + 106.411i 1.38979 + 0.407705i
\(262\) 0 0
\(263\) 55.3652i 0.210514i 0.994445 + 0.105257i \(0.0335665\pi\)
−0.994445 + 0.105257i \(0.966433\pi\)
\(264\) 0 0
\(265\) 185.017 0.698177
\(266\) 0 0
\(267\) 114.558 + 152.992i 0.429055 + 0.573003i
\(268\) 0 0
\(269\) 309.427i 1.15028i −0.818053 0.575142i \(-0.804947\pi\)
0.818053 0.575142i \(-0.195053\pi\)
\(270\) 0 0
\(271\) 194.062 0.716096 0.358048 0.933703i \(-0.383442\pi\)
0.358048 + 0.933703i \(0.383442\pi\)
\(272\) 0 0
\(273\) −333.118 + 249.433i −1.22021 + 0.913675i
\(274\) 0 0
\(275\) 40.9650i 0.148964i
\(276\) 0 0
\(277\) 5.20416 0.0187876 0.00939379 0.999956i \(-0.497010\pi\)
0.00939379 + 0.999956i \(0.497010\pi\)
\(278\) 0 0
\(279\) −97.5073 + 332.383i −0.349489 + 1.19134i
\(280\) 0 0
\(281\) 240.004i 0.854105i 0.904227 + 0.427053i \(0.140448\pi\)
−0.904227 + 0.427053i \(0.859552\pi\)
\(282\) 0 0
\(283\) −153.109 −0.541022 −0.270511 0.962717i \(-0.587193\pi\)
−0.270511 + 0.962717i \(0.587193\pi\)
\(284\) 0 0
\(285\) −102.502 136.892i −0.359657 0.480322i
\(286\) 0 0
\(287\) 473.671i 1.65042i
\(288\) 0 0
\(289\) 49.6485 0.171794
\(290\) 0 0
\(291\) 153.453 114.903i 0.527329 0.394855i
\(292\) 0 0
\(293\) 169.252i 0.577653i 0.957381 + 0.288827i \(0.0932651\pi\)
−0.957381 + 0.288827i \(0.906735\pi\)
\(294\) 0 0
\(295\) 102.619 0.347862
\(296\) 0 0
\(297\) 207.235 77.3821i 0.697760 0.260546i
\(298\) 0 0
\(299\) 243.334i 0.813825i
\(300\) 0 0
\(301\) 551.699 1.83289
\(302\) 0 0
\(303\) −91.4832 122.176i −0.301925 0.403220i
\(304\) 0 0
\(305\) 209.491i 0.686857i
\(306\) 0 0
\(307\) −330.401 −1.07623 −0.538113 0.842873i \(-0.680863\pi\)
−0.538113 + 0.842873i \(0.680863\pi\)
\(308\) 0 0
\(309\) −110.342 + 82.6224i −0.357095 + 0.267387i
\(310\) 0 0
\(311\) 133.596i 0.429570i 0.976661 + 0.214785i \(0.0689050\pi\)
−0.976661 + 0.214785i \(0.931095\pi\)
\(312\) 0 0
\(313\) −459.981 −1.46959 −0.734794 0.678290i \(-0.762721\pi\)
−0.734794 + 0.678290i \(0.762721\pi\)
\(314\) 0 0
\(315\) −197.226 57.8579i −0.626114 0.183676i
\(316\) 0 0
\(317\) 298.150i 0.940536i 0.882524 + 0.470268i \(0.155843\pi\)
−0.882524 + 0.470268i \(0.844157\pi\)
\(318\) 0 0
\(319\) −344.124 −1.07876
\(320\) 0 0
\(321\) 198.241 + 264.751i 0.617574 + 0.824771i
\(322\) 0 0
\(323\) 394.408i 1.22108i
\(324\) 0 0
\(325\) 67.9110 0.208957
\(326\) 0 0
\(327\) −118.340 + 88.6112i −0.361897 + 0.270982i
\(328\) 0 0
\(329\) 440.144i 1.33782i
\(330\) 0 0
\(331\) −397.599 −1.20120 −0.600602 0.799548i \(-0.705073\pi\)
−0.600602 + 0.799548i \(0.705073\pi\)
\(332\) 0 0
\(333\) 29.9929 102.240i 0.0900687 0.307026i
\(334\) 0 0
\(335\) 77.1432i 0.230278i
\(336\) 0 0
\(337\) −427.942 −1.26986 −0.634929 0.772571i \(-0.718970\pi\)
−0.634929 + 0.772571i \(0.718970\pi\)
\(338\) 0 0
\(339\) −283.116 378.101i −0.835151 1.11534i
\(340\) 0 0
\(341\) 315.331i 0.924723i
\(342\) 0 0
\(343\) 64.4477 0.187894
\(344\) 0 0
\(345\) −96.2016 + 72.0342i −0.278845 + 0.208795i
\(346\) 0 0
\(347\) 138.137i 0.398090i 0.979990 + 0.199045i \(0.0637840\pi\)
−0.979990 + 0.199045i \(0.936216\pi\)
\(348\) 0 0
\(349\) −301.421 −0.863669 −0.431835 0.901953i \(-0.642134\pi\)
−0.431835 + 0.901953i \(0.642134\pi\)
\(350\) 0 0
\(351\) 128.283 + 343.550i 0.365477 + 0.978775i
\(352\) 0 0
\(353\) 142.622i 0.404028i 0.979383 + 0.202014i \(0.0647487\pi\)
−0.979383 + 0.202014i \(0.935251\pi\)
\(354\) 0 0
\(355\) 152.066 0.428356
\(356\) 0 0
\(357\) −284.120 379.443i −0.795856 1.06286i
\(358\) 0 0
\(359\) 3.05663i 0.00851429i −0.999991 0.00425715i \(-0.998645\pi\)
0.999991 0.00425715i \(-0.00135510\pi\)
\(360\) 0 0
\(361\) 288.913 0.800313
\(362\) 0 0
\(363\) 129.375 96.8739i 0.356405 0.266870i
\(364\) 0 0
\(365\) 99.9950i 0.273959i
\(366\) 0 0
\(367\) 370.072 1.00837 0.504186 0.863595i \(-0.331793\pi\)
0.504186 + 0.863595i \(0.331793\pi\)
\(368\) 0 0
\(369\) −400.525 117.497i −1.08543 0.318420i
\(370\) 0 0
\(371\) 845.065i 2.27780i
\(372\) 0 0
\(373\) 455.556 1.22133 0.610665 0.791889i \(-0.290902\pi\)
0.610665 + 0.791889i \(0.290902\pi\)
\(374\) 0 0
\(375\) 20.1037 + 26.8485i 0.0536099 + 0.0715960i
\(376\) 0 0
\(377\) 570.482i 1.51322i
\(378\) 0 0
\(379\) 380.051 1.00277 0.501387 0.865223i \(-0.332823\pi\)
0.501387 + 0.865223i \(0.332823\pi\)
\(380\) 0 0
\(381\) 324.346 242.865i 0.851301 0.637440i
\(382\) 0 0
\(383\) 164.078i 0.428402i −0.976790 0.214201i \(-0.931285\pi\)
0.976790 0.214201i \(-0.0687147\pi\)
\(384\) 0 0
\(385\) 187.108 0.485994
\(386\) 0 0
\(387\) 136.853 466.503i 0.353624 1.20544i
\(388\) 0 0
\(389\) 562.622i 1.44633i −0.690676 0.723164i \(-0.742687\pi\)
0.690676 0.723164i \(-0.257313\pi\)
\(390\) 0 0
\(391\) −277.173 −0.708882
\(392\) 0 0
\(393\) −270.893 361.778i −0.689295 0.920553i
\(394\) 0 0
\(395\) 26.2736i 0.0665154i
\(396\) 0 0
\(397\) −93.4668 −0.235433 −0.117716 0.993047i \(-0.537557\pi\)
−0.117716 + 0.993047i \(0.537557\pi\)
\(398\) 0 0
\(399\) 625.253 468.179i 1.56705 1.17338i
\(400\) 0 0
\(401\) 23.4831i 0.0585613i −0.999571 0.0292807i \(-0.990678\pi\)
0.999571 0.0292807i \(-0.00932166\pi\)
\(402\) 0 0
\(403\) 522.749 1.29714
\(404\) 0 0
\(405\) −97.8464 + 152.417i −0.241596 + 0.376339i
\(406\) 0 0
\(407\) 96.9944i 0.238316i
\(408\) 0 0
\(409\) 697.472 1.70531 0.852655 0.522474i \(-0.174991\pi\)
0.852655 + 0.522474i \(0.174991\pi\)
\(410\) 0 0
\(411\) 250.095 + 334.001i 0.608503 + 0.812656i
\(412\) 0 0
\(413\) 468.714i 1.13490i
\(414\) 0 0
\(415\) 322.970 0.778240
\(416\) 0 0
\(417\) −264.865 + 198.326i −0.635167 + 0.475603i
\(418\) 0 0
\(419\) 115.537i 0.275744i 0.990450 + 0.137872i \(0.0440262\pi\)
−0.990450 + 0.137872i \(0.955974\pi\)
\(420\) 0 0
\(421\) 117.396 0.278850 0.139425 0.990233i \(-0.455475\pi\)
0.139425 + 0.990233i \(0.455475\pi\)
\(422\) 0 0
\(423\) 372.175 + 109.181i 0.879847 + 0.258110i
\(424\) 0 0
\(425\) 77.3549i 0.182012i
\(426\) 0 0
\(427\) −956.851 −2.24087
\(428\) 0 0
\(429\) −200.094 267.225i −0.466419 0.622903i
\(430\) 0 0
\(431\) 673.123i 1.56177i −0.624675 0.780885i \(-0.714768\pi\)
0.624675 0.780885i \(-0.285232\pi\)
\(432\) 0 0
\(433\) −392.655 −0.906824 −0.453412 0.891301i \(-0.649793\pi\)
−0.453412 + 0.891301i \(0.649793\pi\)
\(434\) 0 0
\(435\) 225.539 168.880i 0.518481 0.388230i
\(436\) 0 0
\(437\) 456.731i 1.04515i
\(438\) 0 0
\(439\) −409.353 −0.932468 −0.466234 0.884661i \(-0.654389\pi\)
−0.466234 + 0.884661i \(0.654389\pi\)
\(440\) 0 0
\(441\) 140.126 477.662i 0.317746 1.08313i
\(442\) 0 0
\(443\) 355.935i 0.803464i −0.915757 0.401732i \(-0.868408\pi\)
0.915757 0.401732i \(-0.131592\pi\)
\(444\) 0 0
\(445\) 142.459 0.320132
\(446\) 0 0
\(447\) 163.284 + 218.065i 0.365288 + 0.487842i
\(448\) 0 0
\(449\) 294.636i 0.656205i −0.944642 0.328103i \(-0.893591\pi\)
0.944642 0.328103i \(-0.106409\pi\)
\(450\) 0 0
\(451\) 379.976 0.842519
\(452\) 0 0
\(453\) −267.242 + 200.106i −0.589938 + 0.441736i
\(454\) 0 0
\(455\) 310.183i 0.681721i
\(456\) 0 0
\(457\) 491.814 1.07618 0.538090 0.842887i \(-0.319146\pi\)
0.538090 + 0.842887i \(0.319146\pi\)
\(458\) 0 0
\(459\) −391.325 + 146.122i −0.852561 + 0.318349i
\(460\) 0 0
\(461\) 42.6832i 0.0925883i 0.998928 + 0.0462942i \(0.0147412\pi\)
−0.998928 + 0.0462942i \(0.985259\pi\)
\(462\) 0 0
\(463\) 422.582 0.912705 0.456352 0.889799i \(-0.349156\pi\)
0.456352 + 0.889799i \(0.349156\pi\)
\(464\) 0 0
\(465\) 154.749 + 206.668i 0.332795 + 0.444447i
\(466\) 0 0
\(467\) 203.497i 0.435754i 0.975976 + 0.217877i \(0.0699131\pi\)
−0.975976 + 0.217877i \(0.930087\pi\)
\(468\) 0 0
\(469\) −352.351 −0.751282
\(470\) 0 0
\(471\) 342.813 256.693i 0.727840 0.544995i
\(472\) 0 0
\(473\) 442.570i 0.935666i
\(474\) 0 0
\(475\) −127.467 −0.268352
\(476\) 0 0
\(477\) 714.566 + 209.624i 1.49804 + 0.439463i
\(478\) 0 0
\(479\) 485.253i 1.01305i −0.862224 0.506527i \(-0.830929\pi\)
0.862224 0.506527i \(-0.169071\pi\)
\(480\) 0 0
\(481\) −160.795 −0.334294
\(482\) 0 0
\(483\) −329.016 439.401i −0.681192 0.909732i
\(484\) 0 0
\(485\) 142.888i 0.294614i
\(486\) 0 0
\(487\) −140.013 −0.287500 −0.143750 0.989614i \(-0.545916\pi\)
−0.143750 + 0.989614i \(0.545916\pi\)
\(488\) 0 0
\(489\) 408.669 306.005i 0.835724 0.625776i
\(490\) 0 0
\(491\) 20.4450i 0.0416396i 0.999783 + 0.0208198i \(0.00662763\pi\)
−0.999783 + 0.0208198i \(0.993372\pi\)
\(492\) 0 0
\(493\) 649.816 1.31809
\(494\) 0 0
\(495\) 46.4132 158.214i 0.0937641 0.319623i
\(496\) 0 0
\(497\) 694.562i 1.39751i
\(498\) 0 0
\(499\) −49.2051 −0.0986074 −0.0493037 0.998784i \(-0.515700\pi\)
−0.0493037 + 0.998784i \(0.515700\pi\)
\(500\) 0 0
\(501\) 11.4861 + 15.3397i 0.0229263 + 0.0306181i
\(502\) 0 0
\(503\) 149.060i 0.296343i −0.988962 0.148171i \(-0.952661\pi\)
0.988962 0.148171i \(-0.0473387\pi\)
\(504\) 0 0
\(505\) −113.764 −0.225275
\(506\) 0 0
\(507\) 37.1639 27.8277i 0.0733015 0.0548870i
\(508\) 0 0
\(509\) 655.375i 1.28757i −0.765205 0.643787i \(-0.777362\pi\)
0.765205 0.643787i \(-0.222638\pi\)
\(510\) 0 0
\(511\) −456.727 −0.893790
\(512\) 0 0
\(513\) −240.783 644.834i −0.469362 1.25699i
\(514\) 0 0
\(515\) 102.745i 0.199505i
\(516\) 0 0
\(517\) −353.081 −0.682942
\(518\) 0 0
\(519\) −428.680 572.502i −0.825973 1.10309i
\(520\) 0 0
\(521\) 419.868i 0.805890i 0.915224 + 0.402945i \(0.132013\pi\)
−0.915224 + 0.402945i \(0.867987\pi\)
\(522\) 0 0
\(523\) −146.678 −0.280454 −0.140227 0.990119i \(-0.544783\pi\)
−0.140227 + 0.990119i \(0.544783\pi\)
\(524\) 0 0
\(525\) −122.630 + 91.8236i −0.233582 + 0.174902i
\(526\) 0 0
\(527\) 595.444i 1.12988i
\(528\) 0 0
\(529\) 208.030 0.393251
\(530\) 0 0
\(531\) 396.333 + 116.268i 0.746390 + 0.218960i
\(532\) 0 0
\(533\) 629.917i 1.18183i
\(534\) 0 0
\(535\) 246.524 0.460792
\(536\) 0 0
\(537\) −437.919 584.840i −0.815491 1.08909i
\(538\) 0 0
\(539\) 453.156i 0.840735i
\(540\) 0 0
\(541\) 7.07300 0.0130739 0.00653697 0.999979i \(-0.497919\pi\)
0.00653697 + 0.999979i \(0.497919\pi\)
\(542\) 0 0
\(543\) −781.534 + 585.199i −1.43929 + 1.07772i
\(544\) 0 0
\(545\) 110.193i 0.202188i
\(546\) 0 0
\(547\) −3.46995 −0.00634360 −0.00317180 0.999995i \(-0.501010\pi\)
−0.00317180 + 0.999995i \(0.501010\pi\)
\(548\) 0 0
\(549\) −237.353 + 809.090i −0.432337 + 1.47375i
\(550\) 0 0
\(551\) 1070.78i 1.94334i
\(552\) 0 0
\(553\) 120.005 0.217006
\(554\) 0 0
\(555\) −47.6003 63.5702i −0.0857663 0.114541i
\(556\) 0 0
\(557\) 654.467i 1.17499i 0.809230 + 0.587493i \(0.199885\pi\)
−0.809230 + 0.587493i \(0.800115\pi\)
\(558\) 0 0
\(559\) −733.684 −1.31249
\(560\) 0 0
\(561\) 304.387 227.920i 0.542579 0.406274i
\(562\) 0 0
\(563\) 546.529i 0.970745i −0.874307 0.485373i \(-0.838684\pi\)
0.874307 0.485373i \(-0.161316\pi\)
\(564\) 0 0
\(565\) −352.070 −0.623132
\(566\) 0 0
\(567\) −696.167 446.913i −1.22781 0.788207i
\(568\) 0 0
\(569\) 746.774i 1.31243i 0.754573 + 0.656216i \(0.227844\pi\)
−0.754573 + 0.656216i \(0.772156\pi\)
\(570\) 0 0
\(571\) 230.358 0.403430 0.201715 0.979444i \(-0.435349\pi\)
0.201715 + 0.979444i \(0.435349\pi\)
\(572\) 0 0
\(573\) −298.491 398.634i −0.520926 0.695696i
\(574\) 0 0
\(575\) 89.5782i 0.155788i
\(576\) 0 0
\(577\) 525.585 0.910893 0.455446 0.890263i \(-0.349480\pi\)
0.455446 + 0.890263i \(0.349480\pi\)
\(578\) 0 0
\(579\) 574.914 430.486i 0.992943 0.743499i
\(580\) 0 0
\(581\) 1475.16i 2.53901i
\(582\) 0 0
\(583\) −677.906 −1.16279
\(584\) 0 0
\(585\) 262.283 + 76.9430i 0.448348 + 0.131526i
\(586\) 0 0
\(587\) 75.3619i 0.128385i −0.997938 0.0641924i \(-0.979553\pi\)
0.997938 0.0641924i \(-0.0204471\pi\)
\(588\) 0 0
\(589\) −981.185 −1.66585
\(590\) 0 0
\(591\) −463.051 618.405i −0.783505 1.04637i
\(592\) 0 0
\(593\) 1142.87i 1.92727i −0.267230 0.963633i \(-0.586108\pi\)
0.267230 0.963633i \(-0.413892\pi\)
\(594\) 0 0
\(595\) −353.319 −0.593813
\(596\) 0 0
\(597\) 188.446 141.106i 0.315656 0.236358i
\(598\) 0 0
\(599\) 1060.02i 1.76965i 0.465927 + 0.884823i \(0.345721\pi\)
−0.465927 + 0.884823i \(0.654279\pi\)
\(600\) 0 0
\(601\) −530.900 −0.883361 −0.441681 0.897172i \(-0.645618\pi\)
−0.441681 + 0.897172i \(0.645618\pi\)
\(602\) 0 0
\(603\) −87.4030 + 297.940i −0.144947 + 0.494095i
\(604\) 0 0
\(605\) 120.468i 0.199120i
\(606\) 0 0
\(607\) 719.995 1.18615 0.593077 0.805146i \(-0.297913\pi\)
0.593077 + 0.805146i \(0.297913\pi\)
\(608\) 0 0
\(609\) 771.360 + 1030.15i 1.26660 + 1.69154i
\(610\) 0 0
\(611\) 585.331i 0.957988i
\(612\) 0 0
\(613\) −216.348 −0.352932 −0.176466 0.984307i \(-0.556467\pi\)
−0.176466 + 0.984307i \(0.556467\pi\)
\(614\) 0 0
\(615\) −249.037 + 186.474i −0.404938 + 0.303210i
\(616\) 0 0
\(617\) 231.190i 0.374701i −0.982293 0.187350i \(-0.940010\pi\)
0.982293 0.187350i \(-0.0599900\pi\)
\(618\) 0 0
\(619\) 689.633 1.11411 0.557054 0.830476i \(-0.311932\pi\)
0.557054 + 0.830476i \(0.311932\pi\)
\(620\) 0 0
\(621\) −453.161 + 169.212i −0.729728 + 0.272482i
\(622\) 0 0
\(623\) 650.679i 1.04443i
\(624\) 0 0
\(625\) 25.0000 0.0400000
\(626\) 0 0
\(627\) 375.570 + 501.574i 0.598996 + 0.799959i
\(628\) 0 0
\(629\) 183.156i 0.291187i
\(630\) 0 0
\(631\) 616.973 0.977770 0.488885 0.872348i \(-0.337404\pi\)
0.488885 + 0.872348i \(0.337404\pi\)
\(632\) 0 0
\(633\) 270.696 202.692i 0.427639 0.320209i
\(634\) 0 0
\(635\) 302.015i 0.475614i
\(636\) 0 0
\(637\) −751.234 −1.17933
\(638\) 0 0
\(639\) 587.305 + 172.291i 0.919100 + 0.269626i
\(640\) 0 0
\(641\) 1131.85i 1.76576i −0.469598 0.882880i \(-0.655601\pi\)
0.469598 0.882880i \(-0.344399\pi\)
\(642\) 0 0
\(643\) 637.481 0.991418 0.495709 0.868489i \(-0.334908\pi\)
0.495709 + 0.868489i \(0.334908\pi\)
\(644\) 0 0
\(645\) −217.193 290.061i −0.336733 0.449706i
\(646\) 0 0
\(647\) 800.782i 1.23769i −0.785515 0.618843i \(-0.787602\pi\)
0.785515 0.618843i \(-0.212398\pi\)
\(648\) 0 0
\(649\) −375.999 −0.579352
\(650\) 0 0
\(651\) −943.955 + 706.818i −1.45001 + 1.08574i
\(652\) 0 0
\(653\) 313.185i 0.479610i 0.970821 + 0.239805i \(0.0770835\pi\)
−0.970821 + 0.239805i \(0.922916\pi\)
\(654\) 0 0
\(655\) −336.870 −0.514305
\(656\) 0 0
\(657\) −113.294 + 386.197i −0.172442 + 0.587819i
\(658\) 0 0
\(659\) 878.311i 1.33279i 0.745597 + 0.666397i \(0.232164\pi\)
−0.745597 + 0.666397i \(0.767836\pi\)
\(660\) 0 0
\(661\) 200.421 0.303208 0.151604 0.988441i \(-0.451556\pi\)
0.151604 + 0.988441i \(0.451556\pi\)
\(662\) 0 0
\(663\) 377.841 + 504.606i 0.569896 + 0.761096i
\(664\) 0 0
\(665\) 582.205i 0.875497i
\(666\) 0 0
\(667\) 752.497 1.12818
\(668\) 0 0
\(669\) 491.532 368.051i 0.734727 0.550151i
\(670\) 0 0
\(671\) 767.580i 1.14393i
\(672\) 0 0
\(673\) −60.8622 −0.0904341 −0.0452171 0.998977i \(-0.514398\pi\)
−0.0452171 + 0.998977i \(0.514398\pi\)
\(674\) 0 0
\(675\) 47.2245 + 126.471i 0.0699623 + 0.187364i
\(676\) 0 0
\(677\) 415.595i 0.613877i 0.951729 + 0.306939i \(0.0993047\pi\)
−0.951729 + 0.306939i \(0.900695\pi\)
\(678\) 0 0
\(679\) 652.639 0.961177
\(680\) 0 0
\(681\) −206.912 276.331i −0.303836 0.405772i
\(682\) 0 0
\(683\) 434.504i 0.636170i 0.948062 + 0.318085i \(0.103040\pi\)
−0.948062 + 0.318085i \(0.896960\pi\)
\(684\) 0 0
\(685\) 311.006 0.454023
\(686\) 0 0
\(687\) −310.880 + 232.782i −0.452518 + 0.338838i
\(688\) 0 0
\(689\) 1123.82i 1.63109i
\(690\) 0 0
\(691\) 166.630 0.241144 0.120572 0.992705i \(-0.461527\pi\)
0.120572 + 0.992705i \(0.461527\pi\)
\(692\) 0 0
\(693\) 722.640 + 211.992i 1.04277 + 0.305905i
\(694\) 0 0
\(695\) 246.629i 0.354862i
\(696\) 0 0
\(697\) −717.516 −1.02943
\(698\) 0 0
\(699\) −449.802 600.711i −0.643494 0.859386i
\(700\) 0 0
\(701\) 248.345i 0.354272i 0.984186 + 0.177136i \(0.0566833\pi\)
−0.984186 + 0.177136i \(0.943317\pi\)
\(702\) 0 0
\(703\) 301.809 0.429315
\(704\) 0 0
\(705\) 231.410 173.276i 0.328241 0.245781i
\(706\) 0 0
\(707\) 519.617i 0.734961i
\(708\) 0 0
\(709\) −24.1911 −0.0341200 −0.0170600 0.999854i \(-0.505431\pi\)
−0.0170600 + 0.999854i \(0.505431\pi\)
\(710\) 0 0
\(711\) 29.7679 101.473i 0.0418677 0.142719i
\(712\) 0 0
\(713\) 689.534i 0.967088i
\(714\) 0 0
\(715\) −248.827 −0.348010
\(716\) 0 0
\(717\) −88.5679 118.282i −0.123526 0.164969i
\(718\) 0 0
\(719\) 323.584i 0.450048i 0.974353 + 0.225024i \(0.0722460\pi\)
−0.974353 + 0.225024i \(0.927754\pi\)
\(720\) 0 0
\(721\) −469.289 −0.650886
\(722\) 0 0
\(723\) −1099.05 + 822.953i −1.52013 + 1.13825i
\(724\) 0 0
\(725\) 210.011i 0.289671i
\(726\) 0 0
\(727\) 454.949 0.625789 0.312895 0.949788i \(-0.398701\pi\)
0.312895 + 0.949788i \(0.398701\pi\)
\(728\) 0 0
\(729\) −550.588 + 477.802i −0.755264 + 0.655421i
\(730\) 0 0
\(731\) 835.713i 1.14325i
\(732\) 0 0
\(733\) 131.588 0.179520 0.0897600 0.995963i \(-0.471390\pi\)
0.0897600 + 0.995963i \(0.471390\pi\)
\(734\) 0 0
\(735\) −222.388 296.999i −0.302569 0.404080i
\(736\) 0 0
\(737\) 282.654i 0.383520i
\(738\) 0 0
\(739\) −1033.59 −1.39864 −0.699319 0.714810i \(-0.746513\pi\)
−0.699319 + 0.714810i \(0.746513\pi\)
\(740\) 0 0
\(741\) −831.500 + 622.613i −1.12213 + 0.840234i
\(742\) 0 0
\(743\) 439.535i 0.591569i 0.955255 + 0.295784i \(0.0955810\pi\)
−0.955255 + 0.295784i \(0.904419\pi\)
\(744\) 0 0
\(745\) 203.052 0.272553
\(746\) 0 0
\(747\) 1247.36 + 365.924i 1.66983 + 0.489858i
\(748\) 0 0
\(749\) 1126.00i 1.50333i
\(750\) 0 0
\(751\) −496.343 −0.660909 −0.330455 0.943822i \(-0.607202\pi\)
−0.330455 + 0.943822i \(0.607202\pi\)
\(752\) 0 0
\(753\) 215.266 + 287.488i 0.285878 + 0.381790i
\(754\) 0 0
\(755\) 248.843i 0.329593i
\(756\) 0 0
\(757\) 468.694 0.619147 0.309574 0.950875i \(-0.399814\pi\)
0.309574 + 0.950875i \(0.399814\pi\)
\(758\) 0 0
\(759\) 352.485 263.935i 0.464406 0.347740i
\(760\) 0 0
\(761\) 156.940i 0.206229i −0.994669 0.103115i \(-0.967119\pi\)
0.994669 0.103115i \(-0.0328808\pi\)
\(762\) 0 0
\(763\) −503.305 −0.659640
\(764\) 0 0
\(765\) −87.6430 + 298.758i −0.114566 + 0.390533i
\(766\) 0 0
\(767\) 623.325i 0.812679i
\(768\) 0 0
\(769\) 1188.63 1.54569 0.772844 0.634596i \(-0.218834\pi\)
0.772844 + 0.634596i \(0.218834\pi\)
\(770\) 0 0
\(771\) −201.041 268.490i −0.260753 0.348236i
\(772\) 0 0
\(773\) 950.291i 1.22935i −0.788779 0.614677i \(-0.789286\pi\)
0.788779 0.614677i \(-0.210714\pi\)
\(774\) 0 0
\(775\) 192.439 0.248308
\(776\) 0 0
\(777\) 290.357 217.414i 0.373690 0.279813i
\(778\) 0 0
\(779\) 1182.34i 1.51776i
\(780\) 0 0
\(781\) −557.174 −0.713411
\(782\) 0 0
\(783\) 1062.41 396.707i 1.35685 0.506650i
\(784\) 0 0
\(785\) 319.211i 0.406638i
\(786\) 0 0
\(787\) −1056.60 −1.34257 −0.671284 0.741200i \(-0.734257\pi\)
−0.671284 + 0.741200i \(0.734257\pi\)
\(788\) 0 0
\(789\) 99.5538 + 132.954i 0.126177 + 0.168510i
\(790\) 0 0
\(791\) 1608.08i 2.03297i
\(792\) 0 0
\(793\) 1272.48 1.60464
\(794\) 0 0
\(795\) 444.300 332.684i 0.558868 0.418471i
\(796\) 0 0
\(797\) 78.7126i 0.0987612i 0.998780 + 0.0493806i \(0.0157247\pi\)
−0.998780 + 0.0493806i \(0.984275\pi\)
\(798\) 0 0
\(799\) 666.730 0.834455