Properties

Label 108.6.e.a.37.3
Level 108
Weight 6
Character 108.37
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: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
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 37.3
Root \(7.64342i\) of \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Character \(\chi\) \(=\) 108.37
Dual form 108.6.e.a.73.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-4.88422 + 8.45972i) q^{5} +(-68.3340 - 118.358i) q^{7} +O(q^{10})\) \(q+(-4.88422 + 8.45972i) q^{5} +(-68.3340 - 118.358i) q^{7} +(326.660 + 565.792i) q^{11} +(-125.247 + 216.934i) q^{13} -249.768 q^{17} -1754.03 q^{19} +(-827.440 + 1433.17i) q^{23} +(1514.79 + 2623.69i) q^{25} +(2123.96 + 3678.81i) q^{29} +(-4493.72 + 7783.34i) q^{31} +1335.03 q^{35} -6000.33 q^{37} +(-5372.59 + 9305.61i) q^{41} +(-5023.30 - 8700.62i) q^{43} +(11743.3 + 20340.0i) q^{47} +(-935.582 + 1620.48i) q^{49} -9411.34 q^{53} -6381.93 q^{55} +(22083.4 - 38249.5i) q^{59} +(11202.4 + 19403.2i) q^{61} +(-1223.47 - 2119.11i) q^{65} +(18001.5 - 31179.5i) q^{67} -78538.5 q^{71} +61305.5 q^{73} +(44644.1 - 77325.8i) q^{77} +(-13745.0 - 23807.1i) q^{79} +(-32403.2 - 56124.0i) q^{83} +(1219.92 - 2112.97i) q^{85} +34652.4 q^{89} +34234.5 q^{91} +(8567.06 - 14838.6i) q^{95} +(-8056.14 - 13953.6i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} + 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} + 29q^{7} - 177q^{11} - 181q^{13} - 2280q^{17} - 832q^{19} - 399q^{23} - 4778q^{25} + 6033q^{29} + 2759q^{31} - 37146q^{35} - 15172q^{37} + 18435q^{41} + 1469q^{43} + 25155q^{47} - 4056q^{49} - 116844q^{53} + 14778q^{55} + 90537q^{59} + 1403q^{61} + 148407q^{65} + 13907q^{67} - 229368q^{71} + 15200q^{73} + 211983q^{77} + 29993q^{79} + 228951q^{83} - 49662q^{85} - 598332q^{89} + 124930q^{91} + 394764q^{95} + 40541q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −4.88422 + 8.45972i −0.0873716 + 0.151332i −0.906399 0.422422i \(-0.861180\pi\)
0.819028 + 0.573754i \(0.194513\pi\)
\(6\) 0 0
\(7\) −68.3340 118.358i −0.527099 0.912962i −0.999501 0.0315789i \(-0.989946\pi\)
0.472403 0.881383i \(-0.343387\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 326.660 + 565.792i 0.813982 + 1.40986i 0.910057 + 0.414484i \(0.136038\pi\)
−0.0960745 + 0.995374i \(0.530629\pi\)
\(12\) 0 0
\(13\) −125.247 + 216.934i −0.205546 + 0.356016i −0.950307 0.311316i \(-0.899230\pi\)
0.744761 + 0.667332i \(0.232564\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −249.768 −0.209611 −0.104806 0.994493i \(-0.533422\pi\)
−0.104806 + 0.994493i \(0.533422\pi\)
\(18\) 0 0
\(19\) −1754.03 −1.11469 −0.557343 0.830282i \(-0.688179\pi\)
−0.557343 + 0.830282i \(0.688179\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −827.440 + 1433.17i −0.326150 + 0.564908i −0.981744 0.190205i \(-0.939085\pi\)
0.655595 + 0.755113i \(0.272418\pi\)
\(24\) 0 0
\(25\) 1514.79 + 2623.69i 0.484732 + 0.839581i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2123.96 + 3678.81i 0.468977 + 0.812292i 0.999371 0.0354595i \(-0.0112895\pi\)
−0.530394 + 0.847751i \(0.677956\pi\)
\(30\) 0 0
\(31\) −4493.72 + 7783.34i −0.839849 + 1.45466i 0.0501712 + 0.998741i \(0.484023\pi\)
−0.890020 + 0.455921i \(0.849310\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1335.03 0.184214
\(36\) 0 0
\(37\) −6000.33 −0.720561 −0.360280 0.932844i \(-0.617319\pi\)
−0.360280 + 0.932844i \(0.617319\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5372.59 + 9305.61i −0.499142 + 0.864540i −1.00000 0.000990010i \(-0.999685\pi\)
0.500857 + 0.865530i \(0.333018\pi\)
\(42\) 0 0
\(43\) −5023.30 8700.62i −0.414303 0.717594i 0.581052 0.813867i \(-0.302641\pi\)
−0.995355 + 0.0962724i \(0.969308\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11743.3 + 20340.0i 0.775435 + 1.34309i 0.934550 + 0.355833i \(0.115803\pi\)
−0.159114 + 0.987260i \(0.550864\pi\)
\(48\) 0 0
\(49\) −935.582 + 1620.48i −0.0556662 + 0.0964167i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9411.34 −0.460216 −0.230108 0.973165i \(-0.573908\pi\)
−0.230108 + 0.973165i \(0.573908\pi\)
\(54\) 0 0
\(55\) −6381.93 −0.284476
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 22083.4 38249.5i 0.825915 1.43053i −0.0753026 0.997161i \(-0.523992\pi\)
0.901218 0.433366i \(-0.142674\pi\)
\(60\) 0 0
\(61\) 11202.4 + 19403.2i 0.385467 + 0.667649i 0.991834 0.127536i \(-0.0407069\pi\)
−0.606366 + 0.795185i \(0.707374\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1223.47 2119.11i −0.0359177 0.0622113i
\(66\) 0 0
\(67\) 18001.5 31179.5i 0.489916 0.848560i −0.510016 0.860165i \(-0.670361\pi\)
0.999933 + 0.0116049i \(0.00369404\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −78538.5 −1.84900 −0.924499 0.381184i \(-0.875517\pi\)
−0.924499 + 0.381184i \(0.875517\pi\)
\(72\) 0 0
\(73\) 61305.5 1.34646 0.673229 0.739434i \(-0.264907\pi\)
0.673229 + 0.739434i \(0.264907\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 44644.1 77325.8i 0.858098 1.48627i
\(78\) 0 0
\(79\) −13745.0 23807.1i −0.247787 0.429180i 0.715125 0.698997i \(-0.246370\pi\)
−0.962911 + 0.269817i \(0.913037\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −32403.2 56124.0i −0.516289 0.894238i −0.999821 0.0189117i \(-0.993980\pi\)
0.483533 0.875326i \(-0.339353\pi\)
\(84\) 0 0
\(85\) 1219.92 2112.97i 0.0183141 0.0317209i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 34652.4 0.463722 0.231861 0.972749i \(-0.425518\pi\)
0.231861 + 0.972749i \(0.425518\pi\)
\(90\) 0 0
\(91\) 34234.5 0.433372
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 8567.06 14838.6i 0.0973919 0.168688i
\(96\) 0 0
\(97\) −8056.14 13953.6i −0.0869356 0.150577i 0.819279 0.573395i \(-0.194374\pi\)
−0.906214 + 0.422819i \(0.861041\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 93469.6 + 161894.i 0.911731 + 1.57916i 0.811618 + 0.584189i \(0.198587\pi\)
0.100113 + 0.994976i \(0.468079\pi\)
\(102\) 0 0
\(103\) 84293.8 146001.i 0.782893 1.35601i −0.147357 0.989083i \(-0.547077\pi\)
0.930250 0.366927i \(-0.119590\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −155131. −1.30991 −0.654953 0.755669i \(-0.727312\pi\)
−0.654953 + 0.755669i \(0.727312\pi\)
\(108\) 0 0
\(109\) −115289. −0.929439 −0.464720 0.885458i \(-0.653845\pi\)
−0.464720 + 0.885458i \(0.653845\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 62693.8 108589.i 0.461880 0.799999i −0.537175 0.843471i \(-0.680509\pi\)
0.999055 + 0.0434719i \(0.0138419\pi\)
\(114\) 0 0
\(115\) −8082.80 13999.8i −0.0569924 0.0987138i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 17067.7 + 29562.1i 0.110486 + 0.191367i
\(120\) 0 0
\(121\) −132889. + 230170.i −0.825134 + 1.42917i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −60120.6 −0.344151
\(126\) 0 0
\(127\) 17459.4 0.0960548 0.0480274 0.998846i \(-0.484707\pi\)
0.0480274 + 0.998846i \(0.484707\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −14464.0 + 25052.4i −0.0736395 + 0.127547i −0.900494 0.434869i \(-0.856795\pi\)
0.826854 + 0.562416i \(0.190128\pi\)
\(132\) 0 0
\(133\) 119860. + 207603.i 0.587549 + 1.01767i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 204277. + 353818.i 0.929862 + 1.61057i 0.783550 + 0.621329i \(0.213407\pi\)
0.146312 + 0.989239i \(0.453260\pi\)
\(138\) 0 0
\(139\) −144577. + 250415.i −0.634693 + 1.09932i 0.351888 + 0.936042i \(0.385540\pi\)
−0.986580 + 0.163278i \(0.947793\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −163653. −0.669243
\(144\) 0 0
\(145\) −41495.6 −0.163901
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −169.673 + 293.882i −0.000626104 + 0.00108444i −0.866338 0.499458i \(-0.833533\pi\)
0.865712 + 0.500542i \(0.166866\pi\)
\(150\) 0 0
\(151\) −178737. 309581.i −0.637928 1.10492i −0.985887 0.167414i \(-0.946458\pi\)
0.347958 0.937510i \(-0.386875\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −43896.6 76031.1i −0.146758 0.254192i
\(156\) 0 0
\(157\) 376.310 651.789i 0.00121842 0.00211037i −0.865416 0.501055i \(-0.832945\pi\)
0.866634 + 0.498944i \(0.166279\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 226169. 0.687653
\(162\) 0 0
\(163\) −358488. −1.05683 −0.528416 0.848986i \(-0.677214\pi\)
−0.528416 + 0.848986i \(0.677214\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −246875. + 427601.i −0.684994 + 1.18644i 0.288445 + 0.957496i \(0.406862\pi\)
−0.973439 + 0.228948i \(0.926472\pi\)
\(168\) 0 0
\(169\) 154273. + 267209.i 0.415502 + 0.719670i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 83924.6 + 145362.i 0.213193 + 0.369262i 0.952712 0.303874i \(-0.0982802\pi\)
−0.739519 + 0.673136i \(0.764947\pi\)
\(174\) 0 0
\(175\) 207023. 358575.i 0.511004 0.885084i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 483862. 1.12873 0.564364 0.825526i \(-0.309122\pi\)
0.564364 + 0.825526i \(0.309122\pi\)
\(180\) 0 0
\(181\) 74732.3 0.169555 0.0847777 0.996400i \(-0.472982\pi\)
0.0847777 + 0.996400i \(0.472982\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 29306.9 50761.1i 0.0629565 0.109044i
\(186\) 0 0
\(187\) −81589.4 141317.i −0.170620 0.295522i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −297130. 514645.i −0.589337 1.02076i −0.994319 0.106437i \(-0.966056\pi\)
0.404983 0.914324i \(-0.367277\pi\)
\(192\) 0 0
\(193\) 44949.8 77855.4i 0.0868630 0.150451i −0.819321 0.573336i \(-0.805649\pi\)
0.906184 + 0.422885i \(0.138982\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −425161. −0.780527 −0.390263 0.920703i \(-0.627616\pi\)
−0.390263 + 0.920703i \(0.627616\pi\)
\(198\) 0 0
\(199\) 374339. 0.670089 0.335044 0.942202i \(-0.391249\pi\)
0.335044 + 0.942202i \(0.391249\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 290278. 502775.i 0.494394 0.856316i
\(204\) 0 0
\(205\) −52481.9 90901.3i −0.0872217 0.151072i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −572971. 992416.i −0.907334 1.57155i
\(210\) 0 0
\(211\) 82302.7 142552.i 0.127265 0.220429i −0.795351 0.606149i \(-0.792714\pi\)
0.922616 + 0.385720i \(0.126047\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 98139.7 0.144793
\(216\) 0 0
\(217\) 1.22829e6 1.77073
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 31282.7 54183.2i 0.0430848 0.0746250i
\(222\) 0 0
\(223\) 162339. + 281179.i 0.218605 + 0.378635i 0.954382 0.298589i \(-0.0965160\pi\)
−0.735777 + 0.677224i \(0.763183\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −354884. 614677.i −0.457111 0.791739i 0.541696 0.840575i \(-0.317782\pi\)
−0.998807 + 0.0488351i \(0.984449\pi\)
\(228\) 0 0
\(229\) 126953. 219889.i 0.159976 0.277086i −0.774884 0.632104i \(-0.782192\pi\)
0.934860 + 0.355017i \(0.115525\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 557666. 0.672952 0.336476 0.941692i \(-0.390765\pi\)
0.336476 + 0.941692i \(0.390765\pi\)
\(234\) 0 0
\(235\) −229427. −0.271004
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −266147. + 460981.i −0.301389 + 0.522021i −0.976451 0.215740i \(-0.930784\pi\)
0.675062 + 0.737761i \(0.264117\pi\)
\(240\) 0 0
\(241\) −332544. 575984.i −0.368814 0.638804i 0.620567 0.784154i \(-0.286903\pi\)
−0.989380 + 0.145350i \(0.953569\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9139.17 15829.5i −0.00972729 0.0168482i
\(246\) 0 0
\(247\) 219687. 380508.i 0.229119 0.396846i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 906446. 0.908150 0.454075 0.890963i \(-0.349970\pi\)
0.454075 + 0.890963i \(0.349970\pi\)
\(252\) 0 0
\(253\) −1.08117e6 −1.06192
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −362420. + 627731.i −0.342279 + 0.592844i −0.984855 0.173377i \(-0.944532\pi\)
0.642577 + 0.766221i \(0.277865\pi\)
\(258\) 0 0
\(259\) 410027. + 710187.i 0.379807 + 0.657844i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 126262. + 218692.i 0.112560 + 0.194959i 0.916802 0.399343i \(-0.130762\pi\)
−0.804242 + 0.594302i \(0.797428\pi\)
\(264\) 0 0
\(265\) 45967.1 79617.3i 0.0402098 0.0696455i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 191107. 0.161026 0.0805131 0.996754i \(-0.474344\pi\)
0.0805131 + 0.996754i \(0.474344\pi\)
\(270\) 0 0
\(271\) 86694.8 0.0717084 0.0358542 0.999357i \(-0.488585\pi\)
0.0358542 + 0.999357i \(0.488585\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −989643. + 1.71411e6i −0.789127 + 1.36681i
\(276\) 0 0
\(277\) −635239. 1.10027e6i −0.497437 0.861586i 0.502559 0.864543i \(-0.332392\pi\)
−0.999996 + 0.00295734i \(0.999059\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −28414.8 49215.9i −0.0214674 0.0371826i 0.855092 0.518476i \(-0.173500\pi\)
−0.876560 + 0.481293i \(0.840167\pi\)
\(282\) 0 0
\(283\) −676798. + 1.17225e6i −0.502335 + 0.870069i 0.497662 + 0.867371i \(0.334192\pi\)
−0.999996 + 0.00269796i \(0.999141\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.46852e6 1.05239
\(288\) 0 0
\(289\) −1.35747e6 −0.956063
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −263851. + 457003.i −0.179552 + 0.310993i −0.941727 0.336378i \(-0.890798\pi\)
0.762175 + 0.647371i \(0.224131\pi\)
\(294\) 0 0
\(295\) 215720. + 373638.i 0.144323 + 0.249975i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −207269. 359000.i −0.134077 0.232229i
\(300\) 0 0
\(301\) −686525. + 1.18910e6i −0.436757 + 0.756486i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −218861. −0.134716
\(306\) 0 0
\(307\) 1.15348e6 0.698497 0.349249 0.937030i \(-0.386437\pi\)
0.349249 + 0.937030i \(0.386437\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −758833. + 1.31434e6i −0.444883 + 0.770559i −0.998044 0.0625148i \(-0.980088\pi\)
0.553161 + 0.833074i \(0.313421\pi\)
\(312\) 0 0
\(313\) 979958. + 1.69734e6i 0.565388 + 0.979281i 0.997013 + 0.0772280i \(0.0246069\pi\)
−0.431625 + 0.902053i \(0.642060\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 916140. + 1.58680e6i 0.512052 + 0.886899i 0.999902 + 0.0139724i \(0.00444770\pi\)
−0.487851 + 0.872927i \(0.662219\pi\)
\(318\) 0 0
\(319\) −1.38763e6 + 2.40344e6i −0.763477 + 1.32238i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 438100. 0.233651
\(324\) 0 0
\(325\) −758891. −0.398539
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.60493e6 2.77983e6i 0.817462 1.41589i
\(330\) 0 0
\(331\) 360056. + 623635.i 0.180634 + 0.312868i 0.942097 0.335341i \(-0.108852\pi\)
−0.761462 + 0.648209i \(0.775518\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 175847. + 304575.i 0.0856095 + 0.148280i
\(336\) 0 0
\(337\) 1.55433e6 2.69218e6i 0.745537 1.29131i −0.204406 0.978886i \(-0.565526\pi\)
0.949943 0.312422i \(-0.101140\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −5.87168e6 −2.73449
\(342\) 0 0
\(343\) −2.04125e6 −0.936831
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 136034. 235618.i 0.0606490 0.105047i −0.834107 0.551603i \(-0.814016\pi\)
0.894756 + 0.446556i \(0.147350\pi\)
\(348\) 0 0
\(349\) −1.51024e6 2.61582e6i −0.663718 1.14959i −0.979631 0.200805i \(-0.935644\pi\)
0.315913 0.948788i \(-0.397689\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 526944. + 912695.i 0.225075 + 0.389842i 0.956342 0.292250i \(-0.0944038\pi\)
−0.731267 + 0.682092i \(0.761070\pi\)
\(354\) 0 0
\(355\) 383599. 664413.i 0.161550 0.279813i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.26085e6 1.74486 0.872430 0.488739i \(-0.162543\pi\)
0.872430 + 0.488739i \(0.162543\pi\)
\(360\) 0 0
\(361\) 600514. 0.242524
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −299430. + 518628.i −0.117642 + 0.203762i
\(366\) 0 0
\(367\) 155650. + 269594.i 0.0603231 + 0.104483i 0.894610 0.446848i \(-0.147454\pi\)
−0.834287 + 0.551331i \(0.814120\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 643115. + 1.11391e6i 0.242579 + 0.420160i
\(372\) 0 0
\(373\) 1.13768e6 1.97052e6i 0.423397 0.733345i −0.572872 0.819645i \(-0.694171\pi\)
0.996269 + 0.0862997i \(0.0275043\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.06408e6 −0.385585
\(378\) 0 0
\(379\) 3.28710e6 1.17548 0.587739 0.809050i \(-0.300018\pi\)
0.587739 + 0.809050i \(0.300018\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.12336e6 1.94572e6i 0.391311 0.677770i −0.601312 0.799014i \(-0.705355\pi\)
0.992623 + 0.121244i \(0.0386885\pi\)
\(384\) 0 0
\(385\) 436103. + 755352.i 0.149947 + 0.259715i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −683723. 1.18424e6i −0.229090 0.396796i 0.728449 0.685100i \(-0.240242\pi\)
−0.957539 + 0.288305i \(0.906908\pi\)
\(390\) 0 0
\(391\) 206668. 357960.i 0.0683647 0.118411i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 268535. 0.0865982
\(396\) 0 0
\(397\) 1.52652e6 0.486099 0.243050 0.970014i \(-0.421852\pi\)
0.243050 + 0.970014i \(0.421852\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.36998e6 4.10493e6i 0.736011 1.27481i −0.218267 0.975889i \(-0.570040\pi\)
0.954278 0.298920i \(-0.0966263\pi\)
\(402\) 0 0
\(403\) −1.12565e6 1.94968e6i −0.345255 0.597999i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.96007e6 3.39494e6i −0.586523 1.01589i
\(408\) 0 0
\(409\) −478468. + 828731.i −0.141431 + 0.244966i −0.928036 0.372491i \(-0.878504\pi\)
0.786605 + 0.617457i \(0.211837\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6.03619e6 −1.74136
\(414\) 0 0
\(415\) 633057. 0.180436
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 885418. 1.53359e6i 0.246384 0.426750i −0.716135 0.697961i \(-0.754091\pi\)
0.962520 + 0.271211i \(0.0874241\pi\)
\(420\) 0 0
\(421\) −1.54265e6 2.67194e6i −0.424190 0.734719i 0.572154 0.820146i \(-0.306108\pi\)
−0.996344 + 0.0854269i \(0.972775\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −378346. 655315.i −0.101605 0.175986i
\(426\) 0 0
\(427\) 1.53101e6 2.65180e6i 0.406359 0.703834i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.16873e6 −0.562356 −0.281178 0.959656i \(-0.590725\pi\)
−0.281178 + 0.959656i \(0.590725\pi\)
\(432\) 0 0
\(433\) 6.69677e6 1.71651 0.858253 0.513226i \(-0.171550\pi\)
0.858253 + 0.513226i \(0.171550\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.45135e6 2.51382e6i 0.363554 0.629695i
\(438\) 0 0
\(439\) 3.23130e6 + 5.59677e6i 0.800231 + 1.38604i 0.919464 + 0.393175i \(0.128623\pi\)
−0.119232 + 0.992866i \(0.538043\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 877362. + 1.51964e6i 0.212407 + 0.367900i 0.952467 0.304640i \(-0.0985363\pi\)
−0.740060 + 0.672541i \(0.765203\pi\)
\(444\) 0 0
\(445\) −169250. + 293149.i −0.0405162 + 0.0701761i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 515131. 0.120587 0.0602937 0.998181i \(-0.480796\pi\)
0.0602937 + 0.998181i \(0.480796\pi\)
\(450\) 0 0
\(451\) −7.02006e6 −1.62517
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −167209. + 289614.i −0.0378644 + 0.0655830i
\(456\) 0 0
\(457\) 2.46694e6 + 4.27287e6i 0.552546 + 0.957038i 0.998090 + 0.0617782i \(0.0196771\pi\)
−0.445543 + 0.895260i \(0.646990\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.12932e6 + 7.15219e6i 0.904953 + 1.56742i 0.820981 + 0.570956i \(0.193427\pi\)
0.0839718 + 0.996468i \(0.473239\pi\)
\(462\) 0 0
\(463\) −1.09543e6 + 1.89734e6i −0.237482 + 0.411331i −0.959991 0.280030i \(-0.909655\pi\)
0.722509 + 0.691362i \(0.242989\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.29374e6 −0.486691 −0.243345 0.969940i \(-0.578245\pi\)
−0.243345 + 0.969940i \(0.578245\pi\)
\(468\) 0 0
\(469\) −4.92046e6 −1.03294
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.28183e6 5.68429e6i 0.674471 1.16822i
\(474\) 0 0
\(475\) −2.65698e6 4.60203e6i −0.540324 0.935869i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 46443.2 + 80442.0i 0.00924876 + 0.0160193i 0.870613 0.491969i \(-0.163723\pi\)
−0.861364 + 0.507988i \(0.830389\pi\)
\(480\) 0 0
\(481\) 751522. 1.30168e6i 0.148108 0.256531i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 157392. 0.0303828
\(486\) 0 0
\(487\) −1.13899e6 −0.217620 −0.108810 0.994063i \(-0.534704\pi\)
−0.108810 + 0.994063i \(0.534704\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.36473e6 + 7.55993e6i −0.817060 + 1.41519i 0.0907800 + 0.995871i \(0.471064\pi\)
−0.907840 + 0.419318i \(0.862269\pi\)
\(492\) 0 0
\(493\) −530498. 918849.i −0.0983029 0.170266i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.36685e6 + 9.29566e6i 0.974605 + 1.68807i
\(498\) 0 0
\(499\) 738810. 1.27966e6i 0.132825 0.230061i −0.791939 0.610600i \(-0.790928\pi\)
0.924765 + 0.380539i \(0.124262\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 743514. 0.131029 0.0655147 0.997852i \(-0.479131\pi\)
0.0655147 + 0.997852i \(0.479131\pi\)
\(504\) 0 0
\(505\) −1.82610e6 −0.318638
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.43560e6 + 7.68269e6i −0.758854 + 1.31437i 0.184582 + 0.982817i \(0.440907\pi\)
−0.943435 + 0.331556i \(0.892426\pi\)
\(510\) 0 0
\(511\) −4.18926e6 7.25600e6i −0.709716 1.22926i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 823419. + 1.42620e6i 0.136805 + 0.236954i
\(516\) 0 0
\(517\) −7.67214e6 + 1.32885e7i −1.26238 + 2.18651i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.00935e6 0.324311 0.162155 0.986765i \(-0.448155\pi\)
0.162155 + 0.986765i \(0.448155\pi\)
\(522\) 0 0
\(523\) 6.39895e6 1.02295 0.511475 0.859298i \(-0.329099\pi\)
0.511475 + 0.859298i \(0.329099\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.12239e6 1.94403e6i 0.176042 0.304914i
\(528\) 0 0
\(529\) 1.84886e6 + 3.20231e6i 0.287253 + 0.497536i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.34580e6 2.33100e6i −0.205193 0.355405i
\(534\) 0 0
\(535\) 757696. 1.31237e6i 0.114449 0.198231i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.22247e6 −0.181245
\(540\) 0 0
\(541\) −1.26335e7 −1.85580 −0.927899 0.372832i \(-0.878387\pi\)
−0.927899 + 0.372832i \(0.878387\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 563096. 975311.i 0.0812066 0.140654i
\(546\) 0 0
\(547\) 5.51776e6 + 9.55704e6i 0.788487 + 1.36570i 0.926894 + 0.375323i \(0.122468\pi\)
−0.138407 + 0.990375i \(0.544198\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.72548e6 6.45273e6i −0.522762 0.905450i
\(552\) 0 0
\(553\) −1.87851e6 + 3.25367e6i −0.261216 + 0.452440i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.08374e7 1.48009 0.740046 0.672557i \(-0.234804\pi\)
0.740046 + 0.672557i \(0.234804\pi\)
\(558\) 0 0
\(559\) 2.51661e6 0.340633
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.65688e6 + 2.86981e6i −0.220303 + 0.381577i −0.954900 0.296927i \(-0.904038\pi\)
0.734597 + 0.678504i \(0.237371\pi\)
\(564\) 0 0
\(565\) 612421. + 1.06074e6i 0.0807103 + 0.139794i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −774757. 1.34192e6i −0.100319 0.173758i 0.811497 0.584357i \(-0.198653\pi\)
−0.911816 + 0.410599i \(0.865320\pi\)
\(570\) 0 0
\(571\) −1.59557e6 + 2.76361e6i −0.204798 + 0.354720i −0.950068 0.312042i \(-0.898987\pi\)
0.745271 + 0.666762i \(0.232320\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.01359e6 −0.632381
\(576\) 0 0
\(577\) 9.55234e6 1.19446 0.597228 0.802072i \(-0.296269\pi\)
0.597228 + 0.802072i \(0.296269\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.42848e6 + 7.67035e6i −0.544270 + 0.942704i
\(582\) 0 0
\(583\) −3.07431e6 5.32487e6i −0.374608 0.648840i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.64410e6 9.77587e6i −0.676083 1.17101i −0.976151 0.217092i \(-0.930343\pi\)
0.300069 0.953918i \(-0.402990\pi\)
\(588\) 0 0
\(589\) 7.88210e6 1.36522e7i 0.936168 1.62149i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.91815e6 0.924671 0.462336 0.886705i \(-0.347012\pi\)
0.462336 + 0.886705i \(0.347012\pi\)
\(594\) 0 0
\(595\) −333449. −0.0386133
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.60914e6 + 2.78711e6i −0.183242 + 0.317385i −0.942983 0.332841i \(-0.891993\pi\)
0.759740 + 0.650227i \(0.225326\pi\)
\(600\) 0 0
\(601\) 3.74304e6 + 6.48314e6i 0.422706 + 0.732149i 0.996203 0.0870589i \(-0.0277468\pi\)
−0.573497 + 0.819208i \(0.694414\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.29811e6 2.24840e6i −0.144186 0.249738i
\(606\) 0 0
\(607\) 5.06061e6 8.76524e6i 0.557483 0.965588i −0.440223 0.897888i \(-0.645101\pi\)
0.997706 0.0676999i \(-0.0215661\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.88325e6 −0.637550
\(612\) 0 0
\(613\) −4.34715e6 −0.467254 −0.233627 0.972326i \(-0.575059\pi\)
−0.233627 + 0.972326i \(0.575059\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 9.29590e6 1.61010e7i 0.983056 1.70270i 0.332781 0.943004i \(-0.392013\pi\)
0.650275 0.759699i \(-0.274654\pi\)
\(618\) 0 0
\(619\) −6.83014e6 1.18301e7i −0.716478 1.24098i −0.962387 0.271683i \(-0.912420\pi\)
0.245909 0.969293i \(-0.420914\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.36794e6 4.10139e6i −0.244428 0.423361i
\(624\) 0 0
\(625\) −4.44007e6 + 7.69043e6i −0.454663 + 0.787500i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.49869e6 0.151038
\(630\) 0 0
\(631\) −3.33121e6 −0.333065 −0.166532 0.986036i \(-0.553257\pi\)
−0.166532 + 0.986036i \(0.553257\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −85275.4 + 147701.i −0.00839246 + 0.0145362i
\(636\) 0 0
\(637\) −234358. 405919.i −0.0228839 0.0396361i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.14477e6 + 1.98280e6i 0.110046 + 0.190604i 0.915788 0.401661i \(-0.131567\pi\)
−0.805743 + 0.592266i \(0.798234\pi\)
\(642\) 0 0
\(643\) 3.40519e6 5.89797e6i 0.324799 0.562568i −0.656673 0.754176i \(-0.728037\pi\)
0.981472 + 0.191608i \(0.0613701\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.48250e7 1.39231 0.696153 0.717894i \(-0.254894\pi\)
0.696153 + 0.717894i \(0.254894\pi\)
\(648\) 0 0
\(649\) 2.88551e7 2.68912
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.06356e6 + 7.03829e6i −0.372927 + 0.645928i −0.990014 0.140966i \(-0.954979\pi\)
0.617088 + 0.786894i \(0.288312\pi\)
\(654\) 0 0
\(655\) −141291. 244723.i −0.0128680 0.0222880i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −4.07616e6 7.06011e6i −0.365626 0.633283i 0.623250 0.782023i \(-0.285812\pi\)
−0.988876 + 0.148739i \(0.952478\pi\)
\(660\) 0 0
\(661\) 4.37958e6 7.58565e6i 0.389878 0.675288i −0.602555 0.798077i \(-0.705851\pi\)
0.992433 + 0.122789i \(0.0391839\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.34169e6 −0.205341
\(666\) 0 0
\(667\) −7.02980e6 −0.611827
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.31878e6 + 1.26765e7i −0.627527 + 1.08691i
\(672\) 0 0
\(673\) −4.26745e6 7.39143e6i −0.363187 0.629058i 0.625296 0.780387i \(-0.284978\pi\)
−0.988483 + 0.151329i \(0.951645\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.58162e6 1.31317e7i −0.635755 1.10116i −0.986355 0.164635i \(-0.947355\pi\)
0.350599 0.936526i \(-0.385978\pi\)
\(678\) 0 0
\(679\) −1.10102e6 + 1.90702e6i −0.0916473 + 0.158738i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.33221e7 1.09275 0.546376 0.837540i \(-0.316007\pi\)
0.546376 + 0.837540i \(0.316007\pi\)
\(684\) 0 0
\(685\) −3.99094e6 −0.324974
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.17874e6 2.04164e6i 0.0945956 0.163844i
\(690\) 0 0
\(691\) 981739. + 1.70042e6i 0.0782169 + 0.135476i 0.902481 0.430730i \(-0.141744\pi\)
−0.824264 + 0.566206i \(0.808411\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.41230e6 2.44617e6i −0.110908 0.192099i
\(696\) 0 0
\(697\) 1.34190e6 2.32425e6i 0.104626 0.181217i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.36605e7 −1.81856 −0.909282 0.416180i \(-0.863369\pi\)
−0.909282 + 0.416180i \(0.863369\pi\)
\(702\) 0 0
\(703\) 1.05247e7 0.803199
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.27743e7 2.21257e7i 0.961145 1.66475i
\(708\) 0 0
\(709\) 8.39194e6 + 1.45353e7i 0.626970 + 1.08594i 0.988156 + 0.153451i \(0.0490386\pi\)
−0.361186 + 0.932494i \(0.617628\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.43656e6 1.28805e7i −0.547833 0.948875i
\(714\) 0 0
\(715\) 799317. 1.38446e6i 0.0584728 0.101278i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 5.89621e6 0.425355 0.212677 0.977123i \(-0.431782\pi\)
0.212677 + 0.977123i \(0.431782\pi\)
\(720\) 0 0
\(721\) −2.30405e7 −1.65065
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.43470e6 + 1.11452e7i −0.454656 + 0.787488i
\(726\) 0 0
\(727\) 5.15459e6 + 8.92800e6i 0.361708 + 0.626496i 0.988242 0.152898i \(-0.0488605\pi\)
−0.626534 + 0.779394i \(0.715527\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.25466e6 + 2.17314e6i 0.0868427 + 0.150416i
\(732\) 0 0
\(733\) −7.66868e6 + 1.32825e7i −0.527182 + 0.913106i 0.472316 + 0.881429i \(0.343418\pi\)
−0.999498 + 0.0316768i \(0.989915\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.35215e7 1.59513
\(738\) 0 0
\(739\) −1.97929e6 −0.133321 −0.0666606 0.997776i \(-0.521234\pi\)
−0.0666606 + 0.997776i \(0.521234\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.44874e7 + 2.50929e7i −0.962758 + 1.66755i −0.247238 + 0.968955i \(0.579523\pi\)
−0.715520 + 0.698592i \(0.753810\pi\)
\(744\) 0 0
\(745\) −1657.44 2870.77i −0.000109407 0.000189499i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.06008e7 + 1.83611e7i 0.690450 + 1.19589i
\(750\) 0 0
\(751\) −5.21827e6 + 9.03831e6i −0.337619 + 0.584773i −0.983984 0.178255i \(-0.942955\pi\)
0.646366 + 0.763028i \(0.276288\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 3.49196e6 0.222947
\(756\) 0 0
\(757\) 1.51464e7 0.960661 0.480331 0.877087i \(-0.340517\pi\)
0.480331 + 0.877087i \(0.340517\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.10900e7 + 1.92084e7i −0.694176 + 1.20235i 0.276282 + 0.961077i \(0.410898\pi\)
−0.970458 + 0.241271i \(0.922436\pi\)
\(762\) 0 0
\(763\) 7.87815e6 + 1.36454e7i 0.489906 + 0.848542i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.53175e6 + 9.58127e6i 0.339527 + 0.588078i
\(768\) 0 0
\(769\) 3.21191e6 5.56319e6i 0.195861 0.339241i −0.751322 0.659936i \(-0.770583\pi\)
0.947182 + 0.320695i \(0.103917\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.34346e6 −0.141062 −0.0705308 0.997510i \(-0.522469\pi\)
−0.0705308 + 0.997510i \(0.522469\pi\)
\(774\) 0 0
\(775\) −2.72281e7 −1.62841
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.42368e6 1.63223e7i 0.556387 0.963690i
\(780\) 0 0
\(781\) −2.56554e7 4.44365e7i −1.50505 2.60683i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3675.97 + 6366.96i 0.000212911 + 0.000368772i
\(786\) 0 0
\(787\) −1.42540e7 + 2.46887e7i −0.820354 + 1.42089i 0.0850650 + 0.996375i \(0.472890\pi\)
−0.905419 + 0.424519i \(0.860443\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.71365e7 −0.973824
\(792\) 0 0
\(793\) −5.61228e6 −0.316925
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.77498e6 6.53845e6i 0.210508 0.364611i −0.741366 0.671101i \(-0.765822\pi\)
0.951874 + 0.306491i \(0.0991549\pi\)
\(798\) 0 0
\(799\) −2.93310e6 5.08028e6i −0.162540 0.281528i
\(800\) 0 0
\(801\) 0 0
\(802\)