Properties

Label 108.6.e.a.73.4
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: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
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 73.4
Root \(2.13639i\) of \(x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368\)
Character \(\chi\) \(=\) 108.73
Dual form 108.6.e.a.37.4

$q$-expansion

\(f(q)\) \(=\) \(q+(14.0718 + 24.3731i) q^{5} +(75.7039 - 131.123i) q^{7} +O(q^{10})\) \(q+(14.0718 + 24.3731i) q^{5} +(75.7039 - 131.123i) q^{7} +(-138.873 + 240.536i) q^{11} +(-291.929 - 505.636i) q^{13} +1612.01 q^{17} +1368.76 q^{19} +(428.014 + 741.342i) q^{23} +(1166.47 - 2020.38i) q^{25} +(4267.49 - 7391.50i) q^{29} +(-1469.19 - 2544.71i) q^{31} +4261.17 q^{35} +4036.80 q^{37} +(9449.81 + 16367.5i) q^{41} +(10158.6 - 17595.1i) q^{43} +(-147.890 + 256.152i) q^{47} +(-3058.67 - 5297.78i) q^{49} -3039.13 q^{53} -7816.81 q^{55} +(-8618.31 - 14927.4i) q^{59} +(-12826.2 + 22215.7i) q^{61} +(8215.95 - 14230.4i) q^{65} +(13140.1 + 22759.4i) q^{67} -76665.7 q^{71} +1496.33 q^{73} +(21026.5 + 36419.0i) q^{77} +(-49637.1 + 85974.0i) q^{79} +(25025.7 - 43345.7i) q^{83} +(22683.8 + 39289.6i) q^{85} -136635. q^{89} -88400.8 q^{91} +(19261.0 + 33361.0i) q^{95} +(33325.0 - 57720.5i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} + 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} + 29q^{7} - 177q^{11} - 181q^{13} - 2280q^{17} - 832q^{19} - 399q^{23} - 4778q^{25} + 6033q^{29} + 2759q^{31} - 37146q^{35} - 15172q^{37} + 18435q^{41} + 1469q^{43} + 25155q^{47} - 4056q^{49} - 116844q^{53} + 14778q^{55} + 90537q^{59} + 1403q^{61} + 148407q^{65} + 13907q^{67} - 229368q^{71} + 15200q^{73} + 211983q^{77} + 29993q^{79} + 228951q^{83} - 49662q^{85} - 598332q^{89} + 124930q^{91} + 394764q^{95} + 40541q^{97} + O(q^{100}) \)

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
\(5\) 14.0718 + 24.3731i 0.251724 + 0.435999i 0.964001 0.265900i \(-0.0856690\pi\)
−0.712276 + 0.701899i \(0.752336\pi\)
\(6\) 0 0
\(7\) 75.7039 131.123i 0.583947 1.01143i −0.411059 0.911609i \(-0.634841\pi\)
0.995006 0.0998170i \(-0.0318257\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −138.873 + 240.536i −0.346049 + 0.599374i −0.985544 0.169421i \(-0.945810\pi\)
0.639495 + 0.768795i \(0.279144\pi\)
\(12\) 0 0
\(13\) −291.929 505.636i −0.479092 0.829812i 0.520620 0.853788i \(-0.325701\pi\)
−0.999713 + 0.0239762i \(0.992367\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1612.01 1.35283 0.676417 0.736519i \(-0.263532\pi\)
0.676417 + 0.736519i \(0.263532\pi\)
\(18\) 0 0
\(19\) 1368.76 0.869851 0.434925 0.900467i \(-0.356775\pi\)
0.434925 + 0.900467i \(0.356775\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 428.014 + 741.342i 0.168709 + 0.292213i 0.937966 0.346727i \(-0.112707\pi\)
−0.769257 + 0.638939i \(0.779373\pi\)
\(24\) 0 0
\(25\) 1166.47 2020.38i 0.373270 0.646522i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4267.49 7391.50i 0.942274 1.63207i 0.181154 0.983455i \(-0.442017\pi\)
0.761120 0.648611i \(-0.224650\pi\)
\(30\) 0 0
\(31\) −1469.19 2544.71i −0.274583 0.475591i 0.695447 0.718577i \(-0.255206\pi\)
−0.970030 + 0.242986i \(0.921873\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4261.17 0.587975
\(36\) 0 0
\(37\) 4036.80 0.484767 0.242383 0.970181i \(-0.422071\pi\)
0.242383 + 0.970181i \(0.422071\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9449.81 + 16367.5i 0.877937 + 1.52063i 0.853601 + 0.520928i \(0.174414\pi\)
0.0243361 + 0.999704i \(0.492253\pi\)
\(42\) 0 0
\(43\) 10158.6 17595.1i 0.837840 1.45118i −0.0538576 0.998549i \(-0.517152\pi\)
0.891697 0.452632i \(-0.149515\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −147.890 + 256.152i −0.00976546 + 0.0169143i −0.870867 0.491519i \(-0.836442\pi\)
0.861101 + 0.508433i \(0.169775\pi\)
\(48\) 0 0
\(49\) −3058.67 5297.78i −0.181988 0.315213i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3039.13 −0.148614 −0.0743069 0.997235i \(-0.523674\pi\)
−0.0743069 + 0.997235i \(0.523674\pi\)
\(54\) 0 0
\(55\) −7816.81 −0.348436
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8618.31 14927.4i −0.322324 0.558281i 0.658643 0.752455i \(-0.271131\pi\)
−0.980967 + 0.194174i \(0.937797\pi\)
\(60\) 0 0
\(61\) −12826.2 + 22215.7i −0.441342 + 0.764426i −0.997789 0.0664565i \(-0.978831\pi\)
0.556448 + 0.830883i \(0.312164\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 8215.95 14230.4i 0.241198 0.417768i
\(66\) 0 0
\(67\) 13140.1 + 22759.4i 0.357613 + 0.619403i 0.987561 0.157233i \(-0.0502575\pi\)
−0.629949 + 0.776637i \(0.716924\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −76665.7 −1.80491 −0.902454 0.430786i \(-0.858236\pi\)
−0.902454 + 0.430786i \(0.858236\pi\)
\(72\) 0 0
\(73\) 1496.33 0.0328640 0.0164320 0.999865i \(-0.494769\pi\)
0.0164320 + 0.999865i \(0.494769\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 21026.5 + 36419.0i 0.404148 + 0.700006i
\(78\) 0 0
\(79\) −49637.1 + 85974.0i −0.894826 + 1.54988i −0.0608070 + 0.998150i \(0.519367\pi\)
−0.834019 + 0.551735i \(0.813966\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 25025.7 43345.7i 0.398740 0.690639i −0.594830 0.803851i \(-0.702781\pi\)
0.993571 + 0.113213i \(0.0361141\pi\)
\(84\) 0 0
\(85\) 22683.8 + 39289.6i 0.340541 + 0.589834i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −136635. −1.82847 −0.914235 0.405185i \(-0.867207\pi\)
−0.914235 + 0.405185i \(0.867207\pi\)
\(90\) 0 0
\(91\) −88400.8 −1.11906
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 19261.0 + 33361.0i 0.218963 + 0.379254i
\(96\) 0 0
\(97\) 33325.0 57720.5i 0.359617 0.622875i −0.628280 0.777987i \(-0.716241\pi\)
0.987897 + 0.155113i \(0.0495740\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12338.7 + 21371.2i −0.120355 + 0.208462i −0.919908 0.392135i \(-0.871737\pi\)
0.799552 + 0.600596i \(0.205070\pi\)
\(102\) 0 0
\(103\) −57883.5 100257.i −0.537603 0.931155i −0.999032 0.0439785i \(-0.985997\pi\)
0.461430 0.887177i \(-0.347337\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −84364.3 −0.712360 −0.356180 0.934417i \(-0.615921\pi\)
−0.356180 + 0.934417i \(0.615921\pi\)
\(108\) 0 0
\(109\) 198400. 1.59947 0.799735 0.600354i \(-0.204973\pi\)
0.799735 + 0.600354i \(0.204973\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 114453. + 198238.i 0.843199 + 1.46046i 0.887176 + 0.461430i \(0.152664\pi\)
−0.0439777 + 0.999033i \(0.514003\pi\)
\(114\) 0 0
\(115\) −12045.9 + 20864.1i −0.0849364 + 0.147114i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 122035. 211371.i 0.789983 1.36829i
\(120\) 0 0
\(121\) 41953.8 + 72666.2i 0.260500 + 0.451200i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 153606. 0.879293
\(126\) 0 0
\(127\) −246629. −1.35686 −0.678430 0.734665i \(-0.737339\pi\)
−0.678430 + 0.734665i \(0.737339\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −84612.6 146553.i −0.430781 0.746135i 0.566159 0.824296i \(-0.308429\pi\)
−0.996941 + 0.0781606i \(0.975095\pi\)
\(132\) 0 0
\(133\) 103621. 179477.i 0.507947 0.879789i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 49985.3 86577.0i 0.227531 0.394095i −0.729545 0.683933i \(-0.760268\pi\)
0.957076 + 0.289838i \(0.0936013\pi\)
\(138\) 0 0
\(139\) 18699.4 + 32388.2i 0.0820899 + 0.142184i 0.904147 0.427221i \(-0.140507\pi\)
−0.822058 + 0.569404i \(0.807174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 162165. 0.663158
\(144\) 0 0
\(145\) 240205. 0.948773
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 127267. + 220433.i 0.469623 + 0.813411i 0.999397 0.0347281i \(-0.0110565\pi\)
−0.529774 + 0.848139i \(0.677723\pi\)
\(150\) 0 0
\(151\) 118363. 205010.i 0.422448 0.731701i −0.573731 0.819044i \(-0.694504\pi\)
0.996178 + 0.0873434i \(0.0278377\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 41348.3 71617.4i 0.138238 0.239436i
\(156\) 0 0
\(157\) −127406. 220673.i −0.412515 0.714497i 0.582649 0.812724i \(-0.302016\pi\)
−0.995164 + 0.0982266i \(0.968683\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 129609. 0.394069
\(162\) 0 0
\(163\) 215050. 0.633973 0.316987 0.948430i \(-0.397329\pi\)
0.316987 + 0.948430i \(0.397329\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 96168.5 + 166569.i 0.266834 + 0.462171i 0.968043 0.250786i \(-0.0806890\pi\)
−0.701208 + 0.712956i \(0.747356\pi\)
\(168\) 0 0
\(169\) 15201.2 26329.2i 0.0409411 0.0709121i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4150.57 + 7189.00i −0.0105437 + 0.0182622i −0.871249 0.490841i \(-0.836690\pi\)
0.860705 + 0.509103i \(0.170023\pi\)
\(174\) 0 0
\(175\) −176612. 305902.i −0.435939 0.755069i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −574496. −1.34015 −0.670077 0.742292i \(-0.733739\pi\)
−0.670077 + 0.742292i \(0.733739\pi\)
\(180\) 0 0
\(181\) −224707. −0.509823 −0.254912 0.966964i \(-0.582046\pi\)
−0.254912 + 0.966964i \(0.582046\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 56805.1 + 98389.3i 0.122028 + 0.211358i
\(186\) 0 0
\(187\) −223865. + 387745.i −0.468147 + 0.810854i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −239041. + 414031.i −0.474121 + 0.821201i −0.999561 0.0296294i \(-0.990567\pi\)
0.525440 + 0.850830i \(0.323901\pi\)
\(192\) 0 0
\(193\) 263025. + 455572.i 0.508281 + 0.880368i 0.999954 + 0.00958824i \(0.00305208\pi\)
−0.491673 + 0.870780i \(0.663615\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 222278. 0.408067 0.204034 0.978964i \(-0.434595\pi\)
0.204034 + 0.978964i \(0.434595\pi\)
\(198\) 0 0
\(199\) −109696. −0.196363 −0.0981813 0.995169i \(-0.531303\pi\)
−0.0981813 + 0.995169i \(0.531303\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −646131. 1.11913e6i −1.10048 1.90608i
\(204\) 0 0
\(205\) −265952. + 460642.i −0.441996 + 0.765560i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −190085. + 329237.i −0.301011 + 0.521366i
\(210\) 0 0
\(211\) 309436. + 535959.i 0.478482 + 0.828754i 0.999696 0.0246717i \(-0.00785404\pi\)
−0.521214 + 0.853426i \(0.674521\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 571797. 0.843618
\(216\) 0 0
\(217\) −444893. −0.641367
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −470592. 815089.i −0.648132 1.12260i
\(222\) 0 0
\(223\) −231653. + 401234.i −0.311943 + 0.540301i −0.978783 0.204900i \(-0.934313\pi\)
0.666840 + 0.745201i \(0.267646\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −573326. + 993029.i −0.738477 + 1.27908i 0.214704 + 0.976679i \(0.431121\pi\)
−0.953181 + 0.302400i \(0.902212\pi\)
\(228\) 0 0
\(229\) 175527. + 304022.i 0.221185 + 0.383104i 0.955168 0.296064i \(-0.0956741\pi\)
−0.733983 + 0.679168i \(0.762341\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −814275. −0.982610 −0.491305 0.870988i \(-0.663480\pi\)
−0.491305 + 0.870988i \(0.663480\pi\)
\(234\) 0 0
\(235\) −8324.30 −0.00983281
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −357452. 619124.i −0.404783 0.701105i 0.589513 0.807759i \(-0.299320\pi\)
−0.994296 + 0.106654i \(0.965986\pi\)
\(240\) 0 0
\(241\) −22648.5 + 39228.3i −0.0251186 + 0.0435068i −0.878311 0.478089i \(-0.841330\pi\)
0.853193 + 0.521596i \(0.174663\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 86082.2 149099.i 0.0916216 0.158693i
\(246\) 0 0
\(247\) −399582. 692097.i −0.416739 0.721813i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.35110e6 1.35364 0.676822 0.736147i \(-0.263357\pi\)
0.676822 + 0.736147i \(0.263357\pi\)
\(252\) 0 0
\(253\) −237759. −0.233526
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 600097. + 1.03940e6i 0.566747 + 0.981634i 0.996885 + 0.0788708i \(0.0251315\pi\)
−0.430138 + 0.902763i \(0.641535\pi\)
\(258\) 0 0
\(259\) 305602. 529318.i 0.283078 0.490306i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −656802. + 1.13761e6i −0.585525 + 1.01416i 0.409285 + 0.912407i \(0.365778\pi\)
−0.994810 + 0.101752i \(0.967555\pi\)
\(264\) 0 0
\(265\) −42766.1 74073.0i −0.0374097 0.0647956i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −321363. −0.270779 −0.135389 0.990792i \(-0.543229\pi\)
−0.135389 + 0.990792i \(0.543229\pi\)
\(270\) 0 0
\(271\) 384928. 0.318388 0.159194 0.987247i \(-0.449110\pi\)
0.159194 + 0.987247i \(0.449110\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 323983. + 561155.i 0.258339 + 0.447457i
\(276\) 0 0
\(277\) 847964. 1.46872e6i 0.664015 1.15011i −0.315536 0.948913i \(-0.602184\pi\)
0.979551 0.201194i \(-0.0644822\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 530669. 919146.i 0.400920 0.694415i −0.592917 0.805264i \(-0.702024\pi\)
0.993837 + 0.110849i \(0.0353570\pi\)
\(282\) 0 0
\(283\) 192313. + 333096.i 0.142739 + 0.247231i 0.928527 0.371265i \(-0.121076\pi\)
−0.785788 + 0.618496i \(0.787742\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.86155e6 2.05067
\(288\) 0 0
\(289\) 1.17871e6 0.830158
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −667643. 1.15639e6i −0.454334 0.786929i 0.544316 0.838880i \(-0.316789\pi\)
−0.998650 + 0.0519513i \(0.983456\pi\)
\(294\) 0 0
\(295\) 242551. 420110.i 0.162273 0.281066i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 249900. 432839.i 0.161655 0.279994i
\(300\) 0 0
\(301\) −1.53809e6 2.66404e6i −0.978508 1.69483i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −721954. −0.444386
\(306\) 0 0
\(307\) 636269. 0.385296 0.192648 0.981268i \(-0.438292\pi\)
0.192648 + 0.981268i \(0.438292\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −269890. 467464.i −0.158229 0.274061i 0.776001 0.630732i \(-0.217245\pi\)
−0.934230 + 0.356671i \(0.883912\pi\)
\(312\) 0 0
\(313\) −976605. + 1.69153e6i −0.563454 + 0.975931i 0.433738 + 0.901039i \(0.357194\pi\)
−0.997192 + 0.0748915i \(0.976139\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 781983. 1.35443e6i 0.437068 0.757024i −0.560394 0.828226i \(-0.689350\pi\)
0.997462 + 0.0712021i \(0.0226835\pi\)
\(318\) 0 0
\(319\) 1.18528e6 + 2.05297e6i 0.652146 + 1.12955i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.20646e6 1.17676
\(324\) 0 0
\(325\) −1.36210e6 −0.715323
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 22391.6 + 38783.5i 0.0114050 + 0.0197541i
\(330\) 0 0
\(331\) 1.28000e6 2.21702e6i 0.642154 1.11224i −0.342796 0.939410i \(-0.611374\pi\)
0.984951 0.172834i \(-0.0552925\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −369811. + 640532.i −0.180040 + 0.311838i
\(336\) 0 0
\(337\) 299646. + 519002.i 0.143725 + 0.248940i 0.928897 0.370339i \(-0.120758\pi\)
−0.785171 + 0.619279i \(0.787425\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 816125. 0.380076
\(342\) 0 0
\(343\) 1.61850e6 0.742808
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.34386e6 + 2.32764e6i 0.599144 + 1.03775i 0.992948 + 0.118553i \(0.0378256\pi\)
−0.393804 + 0.919195i \(0.628841\pi\)
\(348\) 0 0
\(349\) −335807. + 581635.i −0.147580 + 0.255615i −0.930332 0.366717i \(-0.880482\pi\)
0.782753 + 0.622333i \(0.213815\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −764881. + 1.32481e6i −0.326706 + 0.565871i −0.981856 0.189627i \(-0.939272\pi\)
0.655150 + 0.755499i \(0.272605\pi\)
\(354\) 0 0
\(355\) −1.07883e6 1.86858e6i −0.454339 0.786939i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.27210e6 −1.33996 −0.669978 0.742381i \(-0.733697\pi\)
−0.669978 + 0.742381i \(0.733697\pi\)
\(360\) 0 0
\(361\) −602583. −0.243360
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 21056.1 + 36470.2i 0.00827267 + 0.0143287i
\(366\) 0 0
\(367\) −313571. + 543121.i −0.121526 + 0.210490i −0.920370 0.391049i \(-0.872112\pi\)
0.798843 + 0.601539i \(0.205446\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −230074. + 398500.i −0.0867826 + 0.150312i
\(372\) 0 0
\(373\) −66186.8 114639.i −0.0246320 0.0426638i 0.853447 0.521180i \(-0.174508\pi\)
−0.878079 + 0.478516i \(0.841175\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.98322e6 −1.80574
\(378\) 0 0
\(379\) −163225. −0.0583700 −0.0291850 0.999574i \(-0.509291\pi\)
−0.0291850 + 0.999574i \(0.509291\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −398301. 689877.i −0.138744 0.240312i 0.788277 0.615320i \(-0.210973\pi\)
−0.927021 + 0.375008i \(0.877640\pi\)
\(384\) 0 0
\(385\) −591763. + 1.02496e6i −0.203468 + 0.352417i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.04745e6 3.54629e6i 0.686024 1.18823i −0.287089 0.957904i \(-0.592688\pi\)
0.973114 0.230325i \(-0.0739790\pi\)
\(390\) 0 0
\(391\) 689961. + 1.19505e6i 0.228235 + 0.395315i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.79394e6 −0.900998
\(396\) 0 0
\(397\) −5.58867e6 −1.77964 −0.889820 0.456312i \(-0.849170\pi\)
−0.889820 + 0.456312i \(0.849170\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.11676e6 + 1.93429e6i 0.346817 + 0.600705i 0.985682 0.168614i \(-0.0539291\pi\)
−0.638865 + 0.769319i \(0.720596\pi\)
\(402\) 0 0
\(403\) −857798. + 1.48575e6i −0.263101 + 0.455704i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −560604. + 970995.i −0.167753 + 0.290557i
\(408\) 0 0
\(409\) 2.30256e6 + 3.98815e6i 0.680617 + 1.17886i 0.974793 + 0.223111i \(0.0716214\pi\)
−0.294176 + 0.955751i \(0.595045\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.60976e6 −0.752880
\(414\) 0 0
\(415\) 1.40863e6 0.401491
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 571064. + 989112.i 0.158909 + 0.275239i 0.934476 0.356027i \(-0.115869\pi\)
−0.775566 + 0.631266i \(0.782536\pi\)
\(420\) 0 0
\(421\) −962383. + 1.66690e6i −0.264632 + 0.458356i −0.967467 0.252996i \(-0.918584\pi\)
0.702835 + 0.711353i \(0.251917\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.88035e6 3.25687e6i 0.504972 0.874637i
\(426\) 0 0
\(427\) 1.94199e6 + 3.36363e6i 0.515440 + 0.892769i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.21303e6 −0.573843 −0.286922 0.957954i \(-0.592632\pi\)
−0.286922 + 0.957954i \(0.592632\pi\)
\(432\) 0 0
\(433\) 3.00235e6 0.769558 0.384779 0.923009i \(-0.374278\pi\)
0.384779 + 0.923009i \(0.374278\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 585851. + 1.01472e6i 0.146752 + 0.254181i
\(438\) 0 0
\(439\) −960857. + 1.66425e6i −0.237956 + 0.412153i −0.960128 0.279562i \(-0.909811\pi\)
0.722171 + 0.691714i \(0.243144\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −924258. + 1.60086e6i −0.223761 + 0.387565i −0.955947 0.293540i \(-0.905167\pi\)
0.732186 + 0.681105i \(0.238500\pi\)
\(444\) 0 0
\(445\) −1.92271e6 3.33022e6i −0.460270 0.797211i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.45640e6 −0.809110 −0.404555 0.914514i \(-0.632574\pi\)
−0.404555 + 0.914514i \(0.632574\pi\)
\(450\) 0 0
\(451\) −5.24931e6 −1.21524
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.24396e6 2.15460e6i −0.281694 0.487908i
\(456\) 0 0
\(457\) −1.79319e6 + 3.10589e6i −0.401638 + 0.695658i −0.993924 0.110070i \(-0.964892\pi\)
0.592286 + 0.805728i \(0.298226\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.21775e6 7.30536e6i 0.924333 1.60099i 0.131703 0.991289i \(-0.457955\pi\)
0.792630 0.609703i \(-0.208711\pi\)
\(462\) 0 0
\(463\) −2.47237e6 4.28227e6i −0.535995 0.928370i −0.999114 0.0420745i \(-0.986603\pi\)
0.463120 0.886296i \(-0.346730\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.12589e6 0.875438 0.437719 0.899112i \(-0.355787\pi\)
0.437719 + 0.899112i \(0.355787\pi\)
\(468\) 0 0
\(469\) 3.97904e6 0.835307
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.82151e6 + 4.88700e6i 0.579867 + 1.00436i
\(474\) 0 0
\(475\) 1.59662e6 2.76543e6i 0.324689 0.562378i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −561301. + 972203.i −0.111778 + 0.193606i −0.916487 0.400064i \(-0.868988\pi\)
0.804709 + 0.593669i \(0.202321\pi\)
\(480\) 0 0
\(481\) −1.17846e6 2.04115e6i −0.232248 0.402265i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.87577e6 0.362097
\(486\) 0 0
\(487\) 8.11380e6 1.55025 0.775126 0.631807i \(-0.217687\pi\)
0.775126 + 0.631807i \(0.217687\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.66481e6 2.88353e6i −0.311645 0.539786i 0.667073 0.744992i \(-0.267547\pi\)
−0.978719 + 0.205207i \(0.934213\pi\)
\(492\) 0 0
\(493\) 6.87921e6 1.19151e7i 1.27474 2.20791i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.80389e6 + 1.00526e7i −1.05397 + 1.82553i
\(498\) 0 0
\(499\) −940630. 1.62922e6i −0.169109 0.292906i 0.768998 0.639252i \(-0.220756\pi\)
−0.938107 + 0.346346i \(0.887422\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.96749e6 1.40411 0.702056 0.712122i \(-0.252266\pi\)
0.702056 + 0.712122i \(0.252266\pi\)
\(504\) 0 0
\(505\) −694511. −0.121186
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.40561e6 + 9.36279e6i 0.924805 + 1.60181i 0.791874 + 0.610684i \(0.209106\pi\)
0.132931 + 0.991125i \(0.457561\pi\)
\(510\) 0 0
\(511\) 113278. 196204.i 0.0191908 0.0332395i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.62905e6 2.82160e6i 0.270655 0.468789i
\(516\) 0 0
\(517\) −41075.9 71145.5i −0.00675865 0.0117063i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.19670e6 0.193148 0.0965740 0.995326i \(-0.469212\pi\)
0.0965740 + 0.995326i \(0.469212\pi\)
\(522\) 0 0
\(523\) −6.43371e6 −1.02851 −0.514254 0.857638i \(-0.671931\pi\)
−0.514254 + 0.857638i \(0.671931\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.36834e6 4.10209e6i −0.371465 0.643396i
\(528\) 0 0
\(529\) 2.85178e6 4.93943e6i 0.443074 0.767427i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.51735e6 9.55633e6i 0.841226 1.45705i
\(534\) 0 0
\(535\) −1.18716e6 2.05622e6i −0.179318 0.310588i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.69907e6 0.251907
\(540\) 0 0
\(541\) 5.85989e6 0.860788 0.430394 0.902641i \(-0.358375\pi\)
0.430394 + 0.902641i \(0.358375\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.79185e6 + 4.83563e6i 0.402625 + 0.697368i
\(546\) 0 0
\(547\) −2.59436e6 + 4.49357e6i −0.370734 + 0.642130i −0.989679 0.143305i \(-0.954227\pi\)
0.618945 + 0.785434i \(0.287560\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.84118e6 1.01172e7i 0.819637 1.41965i
\(552\) 0 0
\(553\) 7.51545e6 + 1.30171e7i 1.04506 + 1.81010i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.07405e6 −0.692973 −0.346487 0.938055i \(-0.612625\pi\)
−0.346487 + 0.938055i \(0.612625\pi\)
\(558\) 0 0
\(559\) −1.18623e7 −1.60561
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.05439e6 5.29036e6i −0.406119 0.703419i 0.588332 0.808620i \(-0.299785\pi\)
−0.994451 + 0.105200i \(0.966452\pi\)
\(564\) 0 0
\(565\) −3.22111e6 + 5.57913e6i −0.424507 + 0.735268i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.40483e6 + 9.36143e6i −0.699844 + 1.21216i 0.268677 + 0.963230i \(0.413414\pi\)
−0.968520 + 0.248934i \(0.919920\pi\)
\(570\) 0 0
\(571\) −6.02796e6 1.04407e7i −0.773714 1.34011i −0.935515 0.353288i \(-0.885063\pi\)
0.161801 0.986823i \(-0.448270\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.99706e6 0.251896
\(576\) 0 0
\(577\) 1.22323e7 1.52957 0.764786 0.644285i \(-0.222845\pi\)
0.764786 + 0.644285i \(0.222845\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.78908e6 6.56288e6i −0.465686 0.806593i
\(582\) 0 0
\(583\) 422054. 731019.i 0.0514277 0.0890754i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.29817e6 + 7.44465e6i −0.514859 + 0.891762i 0.484992 + 0.874519i \(0.338823\pi\)
−0.999851 + 0.0172439i \(0.994511\pi\)
\(588\) 0 0
\(589\) −2.01097e6 3.48311e6i −0.238846 0.413693i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.78455e6 0.675511 0.337756 0.941234i \(-0.390332\pi\)
0.337756 + 0.941234i \(0.390332\pi\)
\(594\) 0 0
\(595\) 6.86903e6 0.795432
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.62557e6 4.54761e6i −0.298989 0.517865i 0.676916 0.736061i \(-0.263316\pi\)
−0.975905 + 0.218196i \(0.929983\pi\)
\(600\) 0 0
\(601\) 3.11169e6 5.38960e6i 0.351407 0.608654i −0.635090 0.772439i \(-0.719037\pi\)
0.986496 + 0.163784i \(0.0523701\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.18073e6 + 2.04509e6i −0.131148 + 0.227156i
\(606\) 0 0
\(607\) 7.94049e6 + 1.37533e7i 0.874733 + 1.51508i 0.857046 + 0.515239i \(0.172297\pi\)
0.0176871 + 0.999844i \(0.494370\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 172693. 0.0187142
\(612\) 0 0
\(613\) −1.28661e7 −1.38292 −0.691458 0.722417i \(-0.743031\pi\)
−0.691458 + 0.722417i \(0.743031\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.43797e6 5.95473e6i −0.363571 0.629723i 0.624975 0.780645i \(-0.285109\pi\)
−0.988546 + 0.150922i \(0.951776\pi\)
\(618\) 0 0
\(619\) −6.52408e6 + 1.13000e7i −0.684373 + 1.18537i 0.289261 + 0.957250i \(0.406591\pi\)
−0.973633 + 0.228118i \(0.926743\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.03438e7 + 1.79160e7i −1.06773 + 1.84936i
\(624\) 0 0
\(625\) −1.48369e6 2.56983e6i −0.151930 0.263151i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.50734e6 0.655809
\(630\) 0 0
\(631\) −1.52784e7 −1.52758 −0.763790 0.645464i \(-0.776664\pi\)
−0.763790 + 0.645464i \(0.776664\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3.47052e6 6.01111e6i −0.341554 0.591590i
\(636\) 0 0
\(637\) −1.78583e6 + 3.09315e6i −0.174378 + 0.302032i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −5.96157e6 + 1.03257e7i −0.573080 + 0.992604i 0.423167 + 0.906052i \(0.360918\pi\)
−0.996247 + 0.0865524i \(0.972415\pi\)
\(642\) 0 0
\(643\) 3.00302e6 + 5.20137e6i 0.286438 + 0.496125i 0.972957 0.230987i \(-0.0741955\pi\)
−0.686519 + 0.727112i \(0.740862\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.19440e7 −1.12173 −0.560864 0.827908i \(-0.689531\pi\)
−0.560864 + 0.827908i \(0.689531\pi\)
\(648\) 0 0
\(649\) 4.78742e6 0.446159
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.53297e6 2.65518e6i −0.140686 0.243675i 0.787069 0.616864i \(-0.211597\pi\)
−0.927755 + 0.373190i \(0.878264\pi\)
\(654\) 0 0
\(655\) 2.38131e6 4.12454e6i 0.216876 0.375641i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.55065e6 + 2.68581e6i −0.139092 + 0.240914i −0.927153 0.374683i \(-0.877752\pi\)
0.788061 + 0.615597i \(0.211085\pi\)
\(660\) 0 0
\(661\) −6.48853e6 1.12385e7i −0.577621 1.00047i −0.995751 0.0920819i \(-0.970648\pi\)
0.418130 0.908387i \(-0.362685\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.83253e6 0.511450
\(666\) 0 0
\(667\) 7.30618e6 0.635881
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.56245e6 6.17034e6i −0.305452 0.529058i
\(672\) 0 0
\(673\) −1.10703e7 + 1.91743e7i −0.942154 + 1.63186i −0.180801 + 0.983520i \(0.557869\pi\)
−0.761352 + 0.648338i \(0.775464\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 799850. 1.38538e6i 0.0670713 0.116171i −0.830540 0.556960i \(-0.811968\pi\)
0.897611 + 0.440789i \(0.145301\pi\)
\(678\) 0 0
\(679\) −5.04566e6 8.73934e6i −0.419994 0.727452i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.36986e7 −1.12363 −0.561816 0.827262i \(-0.689897\pi\)
−0.561816 + 0.827262i \(0.689897\pi\)
\(684\) 0 0
\(685\) 2.81353e6 0.229100
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 887210. + 1.53669e6i 0.0711998 + 0.123322i
\(690\) 0 0
\(691\) 2.09107e6 3.62183e6i 0.166599 0.288558i −0.770623 0.637291i \(-0.780055\pi\)
0.937222 + 0.348733i \(0.113388\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −526268. + 911522.i −0.0413280 + 0.0715822i
\(696\) 0 0
\(697\) 1.52331e7 + 2.63846e7i 1.18770 + 2.05716i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.47134e7 1.13089 0.565443 0.824788i \(-0.308705\pi\)
0.565443 + 0.824788i \(0.308705\pi\)
\(702\) 0 0
\(703\) 5.52543e6 0.421675
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.86818e6 + 3.23577e6i 0.140562 + 0.243461i
\(708\) 0 0
\(709\) 4.25908e6 7.37694e6i 0.318200 0.551139i −0.661913 0.749581i \(-0.730255\pi\)
0.980113 + 0.198442i \(0.0635883\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.25767e6 2.17834e6i 0.0926493 0.160473i
\(714\) 0 0
\(715\) 2.28195e6 + 3.95246e6i 0.166933 + 0.289136i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.20183e7 0.867003 0.433502 0.901153i \(-0.357278\pi\)
0.433502 + 0.901153i \(0.357278\pi\)
\(720\) 0 0
\(721\) −1.75280e7 −1.25573
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9.95577e6 1.72439e7i −0.703445 1.21840i
\(726\) 0 0
\(727\) −1.49257e6 + 2.58521e6i −0.104737 + 0.181409i −0.913631 0.406545i \(-0.866733\pi\)
0.808894 + 0.587955i \(0.200067\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.63757e7 2.83635e7i 1.13346 1.96321i
\(732\) 0 0
\(733\) −1.05675e7 1.83035e7i −0.726464 1.25827i −0.958369 0.285534i \(-0.907829\pi\)
0.231905 0.972739i \(-0.425504\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.29926e6 −0.495006
\(738\) 0 0
\(739\) 1.33961e7 0.902337 0.451168 0.892439i \(-0.351007\pi\)
0.451168 + 0.892439i \(0.351007\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 5.95418e6 + 1.03129e7i 0.395685 + 0.685347i 0.993188 0.116519i \(-0.0371737\pi\)
−0.597503 + 0.801867i \(0.703840\pi\)
\(744\) 0 0
\(745\) −3.58175e6 + 6.20377e6i −0.236431 + 0.409511i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −6.38671e6 + 1.10621e7i −0.415980 + 0.720499i
\(750\) 0 0
\(751\) −2.33184e6 4.03886e6i −0.150868 0.261312i 0.780679 0.624933i \(-0.214874\pi\)
−0.931547 + 0.363621i \(0.881540\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.66232e6 0.425361
\(756\) 0 0
\(757\) 138599. 0.00879065 0.00439532 0.999990i \(-0.498601\pi\)
0.00439532 + 0.999990i \(0.498601\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.19856e6 + 2.07597e6i 0.0750237 + 0.129945i 0.901097 0.433618i \(-0.142763\pi\)
−0.826073 + 0.563563i \(0.809430\pi\)
\(762\) 0 0
\(763\) 1.50197e7 2.60148e7i 0.934005 1.61774i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.03188e6 + 8.71546e6i −0.308846 + 0.534936i
\(768\) 0 0
\(769\) −399739. 692369.i −0.0243759 0.0422203i 0.853580 0.520962i \(-0.174427\pi\)
−0.877956 + 0.478741i \(0.841093\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.07743e6 −0.0648546 −0.0324273 0.999474i \(-0.510324\pi\)
−0.0324273 + 0.999474i \(0.510324\pi\)
\(774\) 0 0
\(775\) −6.85505e6 −0.409974
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.29346e7 + 2.24033e7i 0.763674 + 1.32272i
\(780\) 0 0
\(781\) 1.06468e7 1.84408e7i 0.624586 1.08182i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.58566e6 6.21055e6i 0.207680 0.359713i
\(786\) 0 0
\(787\) −1.53546e6 2.65949e6i −0.0883692 0.153060i 0.818453 0.574574i \(-0.194832\pi\)
−0.906822 + 0.421514i \(0.861499\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.46581e7 1.96953
\(792\) 0 0
\(793\) 1.49774e7 0.845774
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.49242e6 + 1.29772e7i 0.417808 + 0.723664i 0.995719 0.0924359i \(-0.0294653\pi\)
−0.577911 + 0.816100i \(0.696132\pi\)
\(798\) 0 0
\(799\) −238399. + 412919.i −0.0132110 + 0.0228822i
\(800\) 0 0
\(801\) 0 0
\(802\)