Properties

Label 108.6.e.a.37.1
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 37.1
Root \(3.71922i\) 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.73.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-40.7270 + 70.5412i) q^{5} +(89.6312 + 155.246i) q^{7} +O(q^{10})\) \(q+(-40.7270 + 70.5412i) q^{5} +(89.6312 + 155.246i) q^{7} +(-250.250 - 433.446i) q^{11} +(275.245 - 476.739i) q^{13} -753.636 q^{17} -2570.83 q^{19} +(-1372.72 + 2377.63i) q^{23} +(-1754.87 - 3039.53i) q^{25} +(1954.86 + 3385.92i) q^{29} +(1552.42 - 2688.87i) q^{31} -14601.6 q^{35} -9568.10 q^{37} +(1113.47 - 1928.59i) q^{41} +(-7143.42 - 12372.8i) q^{43} +(-3236.07 - 5605.04i) q^{47} +(-7664.00 + 13274.4i) q^{49} -13692.2 q^{53} +40767.8 q^{55} +(2854.22 - 4943.65i) q^{59} +(5899.59 + 10218.4i) q^{61} +(22419.8 + 38832.3i) q^{65} +(1771.66 - 3068.60i) q^{67} +58429.0 q^{71} -60181.3 q^{73} +(44860.5 - 77700.6i) q^{77} +(27811.7 + 48171.3i) q^{79} +(19990.3 + 34624.2i) q^{83} +(30693.3 - 53162.4i) q^{85} -103171. q^{89} +98682.3 q^{91} +(104702. - 181349. i) q^{95} +(82996.9 + 143755. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 21q^{5} + 29q^{7} + O(q^{10}) \) \( 10q + 21q^{5} + 29q^{7} - 177q^{11} - 181q^{13} - 2280q^{17} - 832q^{19} - 399q^{23} - 4778q^{25} + 6033q^{29} + 2759q^{31} - 37146q^{35} - 15172q^{37} + 18435q^{41} + 1469q^{43} + 25155q^{47} - 4056q^{49} - 116844q^{53} + 14778q^{55} + 90537q^{59} + 1403q^{61} + 148407q^{65} + 13907q^{67} - 229368q^{71} + 15200q^{73} + 211983q^{77} + 29993q^{79} + 228951q^{83} - 49662q^{85} - 598332q^{89} + 124930q^{91} + 394764q^{95} + 40541q^{97} + O(q^{100}) \)

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
\(5\) −40.7270 + 70.5412i −0.728546 + 1.26188i 0.228951 + 0.973438i \(0.426470\pi\)
−0.957498 + 0.288441i \(0.906863\pi\)
\(6\) 0 0
\(7\) 89.6312 + 155.246i 0.691376 + 1.19750i 0.971387 + 0.237501i \(0.0763283\pi\)
−0.280012 + 0.959997i \(0.590338\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −250.250 433.446i −0.623581 1.08007i −0.988813 0.149158i \(-0.952344\pi\)
0.365232 0.930916i \(-0.380990\pi\)
\(12\) 0 0
\(13\) 275.245 476.739i 0.451712 0.782388i −0.546780 0.837276i \(-0.684147\pi\)
0.998493 + 0.0548877i \(0.0174801\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −753.636 −0.632469 −0.316234 0.948681i \(-0.602419\pi\)
−0.316234 + 0.948681i \(0.602419\pi\)
\(18\) 0 0
\(19\) −2570.83 −1.63376 −0.816882 0.576805i \(-0.804299\pi\)
−0.816882 + 0.576805i \(0.804299\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1372.72 + 2377.63i −0.541083 + 0.937183i 0.457759 + 0.889076i \(0.348652\pi\)
−0.998842 + 0.0481071i \(0.984681\pi\)
\(24\) 0 0
\(25\) −1754.87 3039.53i −0.561560 0.972650i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1954.86 + 3385.92i 0.431639 + 0.747621i 0.997015 0.0772128i \(-0.0246021\pi\)
−0.565376 + 0.824834i \(0.691269\pi\)
\(30\) 0 0
\(31\) 1552.42 2688.87i 0.290138 0.502534i −0.683704 0.729759i \(-0.739632\pi\)
0.973842 + 0.227226i \(0.0729655\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −14601.6 −2.01480
\(36\) 0 0
\(37\) −9568.10 −1.14900 −0.574502 0.818503i \(-0.694804\pi\)
−0.574502 + 0.818503i \(0.694804\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1113.47 1928.59i 0.103447 0.179176i −0.809656 0.586905i \(-0.800346\pi\)
0.913103 + 0.407730i \(0.133679\pi\)
\(42\) 0 0
\(43\) −7143.42 12372.8i −0.589162 1.02046i −0.994342 0.106222i \(-0.966125\pi\)
0.405180 0.914237i \(-0.367209\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3236.07 5605.04i −0.213685 0.370112i 0.739180 0.673508i \(-0.235213\pi\)
−0.952865 + 0.303395i \(0.901880\pi\)
\(48\) 0 0
\(49\) −7664.00 + 13274.4i −0.456000 + 0.789816i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −13692.2 −0.669553 −0.334777 0.942298i \(-0.608661\pi\)
−0.334777 + 0.942298i \(0.608661\pi\)
\(54\) 0 0
\(55\) 40767.8 1.81723
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2854.22 4943.65i 0.106747 0.184892i −0.807703 0.589589i \(-0.799290\pi\)
0.914451 + 0.404697i \(0.132623\pi\)
\(60\) 0 0
\(61\) 5899.59 + 10218.4i 0.203000 + 0.351607i 0.949494 0.313786i \(-0.101597\pi\)
−0.746493 + 0.665393i \(0.768264\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 22419.8 + 38832.3i 0.658186 + 1.14001i
\(66\) 0 0
\(67\) 1771.66 3068.60i 0.0482162 0.0835129i −0.840910 0.541175i \(-0.817980\pi\)
0.889126 + 0.457662i \(0.151313\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 58429.0 1.37557 0.687785 0.725914i \(-0.258583\pi\)
0.687785 + 0.725914i \(0.258583\pi\)
\(72\) 0 0
\(73\) −60181.3 −1.32176 −0.660882 0.750490i \(-0.729818\pi\)
−0.660882 + 0.750490i \(0.729818\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 44860.5 77700.6i 0.862258 1.49347i
\(78\) 0 0
\(79\) 27811.7 + 48171.3i 0.501372 + 0.868401i 0.999999 + 0.00158440i \(0.000504331\pi\)
−0.498627 + 0.866817i \(0.666162\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 19990.3 + 34624.2i 0.318511 + 0.551677i 0.980178 0.198121i \(-0.0634839\pi\)
−0.661667 + 0.749798i \(0.730151\pi\)
\(84\) 0 0
\(85\) 30693.3 53162.4i 0.460783 0.798099i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −103171. −1.38065 −0.690327 0.723498i \(-0.742533\pi\)
−0.690327 + 0.723498i \(0.742533\pi\)
\(90\) 0 0
\(91\) 98682.3 1.24921
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 104702. 181349.i 1.19027 2.06161i
\(96\) 0 0
\(97\) 82996.9 + 143755.i 0.895638 + 1.55129i 0.833013 + 0.553254i \(0.186614\pi\)
0.0626259 + 0.998037i \(0.480053\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 82524.4 + 142936.i 0.804969 + 1.39425i 0.916312 + 0.400464i \(0.131151\pi\)
−0.111344 + 0.993782i \(0.535515\pi\)
\(102\) 0 0
\(103\) −36430.5 + 63099.4i −0.338354 + 0.586047i −0.984123 0.177486i \(-0.943204\pi\)
0.645769 + 0.763533i \(0.276537\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −123024. −1.03880 −0.519399 0.854532i \(-0.673844\pi\)
−0.519399 + 0.854532i \(0.673844\pi\)
\(108\) 0 0
\(109\) 24274.5 0.195697 0.0978486 0.995201i \(-0.468804\pi\)
0.0978486 + 0.995201i \(0.468804\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −100686. + 174394.i −0.741778 + 1.28480i 0.209908 + 0.977721i \(0.432684\pi\)
−0.951685 + 0.307075i \(0.900650\pi\)
\(114\) 0 0
\(115\) −111814. 193667.i −0.788408 1.36556i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −67549.3 116999.i −0.437274 0.757380i
\(120\) 0 0
\(121\) −44725.0 + 77465.9i −0.277707 + 0.481002i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 31339.2 0.179396
\(126\) 0 0
\(127\) −104163. −0.573067 −0.286534 0.958070i \(-0.592503\pi\)
−0.286534 + 0.958070i \(0.592503\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 89424.9 154888.i 0.455282 0.788571i −0.543423 0.839459i \(-0.682872\pi\)
0.998704 + 0.0508883i \(0.0162053\pi\)
\(132\) 0 0
\(133\) −230426. 399110.i −1.12954 1.95643i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 67651.3 + 117176.i 0.307946 + 0.533378i 0.977913 0.209013i \(-0.0670250\pi\)
−0.669967 + 0.742391i \(0.733692\pi\)
\(138\) 0 0
\(139\) 113083. 195866.i 0.496434 0.859848i −0.503558 0.863961i \(-0.667976\pi\)
0.999992 + 0.00411320i \(0.00130927\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −275521. −1.12672
\(144\) 0 0
\(145\) −318462. −1.25788
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −171449. + 296958.i −0.632657 + 1.09579i 0.354350 + 0.935113i \(0.384702\pi\)
−0.987006 + 0.160680i \(0.948631\pi\)
\(150\) 0 0
\(151\) 121970. + 211258.i 0.435322 + 0.754000i 0.997322 0.0731373i \(-0.0233011\pi\)
−0.562000 + 0.827137i \(0.689968\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 126451. + 219019.i 0.422758 + 0.732238i
\(156\) 0 0
\(157\) −174438. + 302136.i −0.564797 + 0.978257i 0.432272 + 0.901743i \(0.357712\pi\)
−0.997069 + 0.0765136i \(0.975621\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −492156. −1.49637
\(162\) 0 0
\(163\) 303629. 0.895107 0.447553 0.894257i \(-0.352295\pi\)
0.447553 + 0.894257i \(0.352295\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −16387.7 + 28384.4i −0.0454703 + 0.0787568i −0.887865 0.460104i \(-0.847812\pi\)
0.842395 + 0.538861i \(0.181145\pi\)
\(168\) 0 0
\(169\) 34126.4 + 59108.7i 0.0919123 + 0.159197i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −177651. 307701.i −0.451287 0.781652i 0.547179 0.837015i \(-0.315702\pi\)
−0.998466 + 0.0553636i \(0.982368\pi\)
\(174\) 0 0
\(175\) 314583. 544873.i 0.776497 1.34493i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 459272. 1.07137 0.535683 0.844419i \(-0.320054\pi\)
0.535683 + 0.844419i \(0.320054\pi\)
\(180\) 0 0
\(181\) −190088. −0.431279 −0.215640 0.976473i \(-0.569184\pi\)
−0.215640 + 0.976473i \(0.569184\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 389680. 674945.i 0.837103 1.44990i
\(186\) 0 0
\(187\) 188598. + 326661.i 0.394396 + 0.683113i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −344280. 596310.i −0.682854 1.18274i −0.974106 0.226092i \(-0.927405\pi\)
0.291252 0.956646i \(-0.405928\pi\)
\(192\) 0 0
\(193\) −172138. + 298152.i −0.332648 + 0.576163i −0.983030 0.183444i \(-0.941275\pi\)
0.650382 + 0.759607i \(0.274609\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 596238. 1.09460 0.547298 0.836938i \(-0.315656\pi\)
0.547298 + 0.836938i \(0.315656\pi\)
\(198\) 0 0
\(199\) −49436.6 −0.0884945 −0.0442473 0.999021i \(-0.514089\pi\)
−0.0442473 + 0.999021i \(0.514089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −350433. + 606968.i −0.596849 + 1.03377i
\(204\) 0 0
\(205\) 90696.5 + 157091.i 0.150732 + 0.261076i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 643351. + 1.11432e6i 1.01878 + 1.76459i
\(210\) 0 0
\(211\) 75999.1 131634.i 0.117518 0.203546i −0.801266 0.598309i \(-0.795840\pi\)
0.918783 + 0.394762i \(0.129173\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.16372e6 1.71693
\(216\) 0 0
\(217\) 556580. 0.802377
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −207435. + 359288.i −0.285694 + 0.494836i
\(222\) 0 0
\(223\) 281057. + 486805.i 0.378471 + 0.655531i 0.990840 0.135041i \(-0.0431167\pi\)
−0.612369 + 0.790572i \(0.709783\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −630493. 1.09205e6i −0.812111 1.40662i −0.911384 0.411558i \(-0.864985\pi\)
0.0992724 0.995060i \(-0.468348\pi\)
\(228\) 0 0
\(229\) −69803.7 + 120904.i −0.0879609 + 0.152353i −0.906649 0.421886i \(-0.861368\pi\)
0.818688 + 0.574238i \(0.194702\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.18799e6 1.43358 0.716790 0.697289i \(-0.245610\pi\)
0.716790 + 0.697289i \(0.245610\pi\)
\(234\) 0 0
\(235\) 527181. 0.622716
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −164952. + 285705.i −0.186794 + 0.323536i −0.944179 0.329432i \(-0.893143\pi\)
0.757386 + 0.652968i \(0.226476\pi\)
\(240\) 0 0
\(241\) −84372.3 146137.i −0.0935745 0.162076i 0.815438 0.578844i \(-0.196496\pi\)
−0.909013 + 0.416768i \(0.863163\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −624263. 1.08126e6i −0.664435 1.15083i
\(246\) 0 0
\(247\) −707609. + 1.22561e6i −0.737991 + 1.27824i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 224796. 0.225218 0.112609 0.993639i \(-0.464079\pi\)
0.112609 + 0.993639i \(0.464079\pi\)
\(252\) 0 0
\(253\) 1.37410e6 1.34964
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 347968. 602698.i 0.328629 0.569203i −0.653611 0.756831i \(-0.726747\pi\)
0.982240 + 0.187628i \(0.0600799\pi\)
\(258\) 0 0
\(259\) −857600. 1.48541e6i −0.794393 1.37593i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −241366. 418057.i −0.215172 0.372689i 0.738154 0.674633i \(-0.235698\pi\)
−0.953326 + 0.301944i \(0.902365\pi\)
\(264\) 0 0
\(265\) 557644. 965867.i 0.487800 0.844895i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.23733e6 −1.88516 −0.942581 0.333978i \(-0.891609\pi\)
−0.942581 + 0.333978i \(0.891609\pi\)
\(270\) 0 0
\(271\) −1.74480e6 −1.44318 −0.721592 0.692318i \(-0.756589\pi\)
−0.721592 + 0.692318i \(0.756589\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −878315. + 1.52129e6i −0.700356 + 1.21305i
\(276\) 0 0
\(277\) 378971. + 656397.i 0.296761 + 0.514005i 0.975393 0.220474i \(-0.0707603\pi\)
−0.678632 + 0.734478i \(0.737427\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 215216. + 372764.i 0.162595 + 0.281623i 0.935799 0.352535i \(-0.114680\pi\)
−0.773203 + 0.634158i \(0.781347\pi\)
\(282\) 0 0
\(283\) −478649. + 829044.i −0.355264 + 0.615335i −0.987163 0.159716i \(-0.948942\pi\)
0.631899 + 0.775051i \(0.282276\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 399206. 0.286083
\(288\) 0 0
\(289\) −851890. −0.599983
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −283147. + 490425.i −0.192683 + 0.333737i −0.946138 0.323762i \(-0.895052\pi\)
0.753456 + 0.657499i \(0.228386\pi\)
\(294\) 0 0
\(295\) 232487. + 402680.i 0.155541 + 0.269404i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 755673. + 1.30886e6i 0.488828 + 0.846674i
\(300\) 0 0
\(301\) 1.28055e6 2.21797e6i 0.814665 1.41104i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −961090. −0.591581
\(306\) 0 0
\(307\) −2.00565e6 −1.21453 −0.607265 0.794499i \(-0.707733\pi\)
−0.607265 + 0.794499i \(0.707733\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.05835e6 + 1.83312e6i −0.620481 + 1.07471i 0.368915 + 0.929463i \(0.379729\pi\)
−0.989396 + 0.145242i \(0.953604\pi\)
\(312\) 0 0
\(313\) −606669. 1.05078e6i −0.350018 0.606249i 0.636234 0.771496i \(-0.280491\pi\)
−0.986252 + 0.165247i \(0.947158\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.28378e6 2.22357e6i −0.717533 1.24280i −0.961974 0.273140i \(-0.911938\pi\)
0.244441 0.969664i \(-0.421396\pi\)
\(318\) 0 0
\(319\) 978409. 1.69465e6i 0.538324 0.932404i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.93747e6 1.03330
\(324\) 0 0
\(325\) −1.93208e6 −1.01465
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 580105. 1.00477e6i 0.295473 0.511773i
\(330\) 0 0
\(331\) −721129. 1.24903e6i −0.361778 0.626619i 0.626475 0.779441i \(-0.284497\pi\)
−0.988254 + 0.152823i \(0.951164\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 144309. + 249950.i 0.0702555 + 0.121686i
\(336\) 0 0
\(337\) −790934. + 1.36994e6i −0.379372 + 0.657092i −0.990971 0.134076i \(-0.957193\pi\)
0.611599 + 0.791168i \(0.290527\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.55397e6 −0.723698
\(342\) 0 0
\(343\) 265129. 0.121681
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −824985. + 1.42892e6i −0.367809 + 0.637064i −0.989223 0.146419i \(-0.953225\pi\)
0.621414 + 0.783483i \(0.286559\pi\)
\(348\) 0 0
\(349\) −325183. 563234.i −0.142911 0.247528i 0.785681 0.618632i \(-0.212313\pi\)
−0.928591 + 0.371104i \(0.878979\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 590817. + 1.02333e6i 0.252358 + 0.437096i 0.964174 0.265269i \(-0.0854607\pi\)
−0.711817 + 0.702365i \(0.752127\pi\)
\(354\) 0 0
\(355\) −2.37964e6 + 4.12165e6i −1.00217 + 1.73580i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −985030. −0.403379 −0.201690 0.979449i \(-0.564643\pi\)
−0.201690 + 0.979449i \(0.564643\pi\)
\(360\) 0 0
\(361\) 4.13306e6 1.66918
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.45100e6 4.24526e6i 0.962967 1.66791i
\(366\) 0 0
\(367\) 598436. + 1.03652e6i 0.231928 + 0.401711i 0.958375 0.285511i \(-0.0921634\pi\)
−0.726448 + 0.687222i \(0.758830\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.22725e6 2.12566e6i −0.462913 0.801788i
\(372\) 0 0
\(373\) 1.23230e6 2.13441e6i 0.458611 0.794337i −0.540277 0.841487i \(-0.681681\pi\)
0.998888 + 0.0471500i \(0.0150139\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.15227e6 0.779906
\(378\) 0 0
\(379\) 5.33540e6 1.90796 0.953979 0.299875i \(-0.0969449\pi\)
0.953979 + 0.299875i \(0.0969449\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 826117. 1.43088e6i 0.287770 0.498432i −0.685507 0.728066i \(-0.740420\pi\)
0.973277 + 0.229634i \(0.0737529\pi\)
\(384\) 0 0
\(385\) 3.65406e6 + 6.32902e6i 1.25639 + 2.17613i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.83443e6 + 4.90938e6i 0.949712 + 1.64495i 0.746029 + 0.665913i \(0.231958\pi\)
0.203683 + 0.979037i \(0.434709\pi\)
\(390\) 0 0
\(391\) 1.03453e6 1.79187e6i 0.342218 0.592739i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.53074e6 −1.46109
\(396\) 0 0
\(397\) 418875. 0.133385 0.0666927 0.997774i \(-0.478755\pi\)
0.0666927 + 0.997774i \(0.478755\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.43256e6 2.48126e6i 0.444889 0.770570i −0.553156 0.833078i \(-0.686577\pi\)
0.998044 + 0.0625082i \(0.0199100\pi\)
\(402\) 0 0
\(403\) −854592. 1.48020e6i −0.262118 0.454001i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.39442e6 + 4.14726e6i 0.716497 + 1.24101i
\(408\) 0 0
\(409\) −2.65238e6 + 4.59406e6i −0.784021 + 1.35796i 0.145561 + 0.989349i \(0.453501\pi\)
−0.929582 + 0.368615i \(0.879832\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.02331e6 0.295210
\(414\) 0 0
\(415\) −3.25658e6 −0.928200
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.42136e6 4.19393e6i 0.673791 1.16704i −0.303030 0.952981i \(-0.597998\pi\)
0.976821 0.214059i \(-0.0686684\pi\)
\(420\) 0 0
\(421\) −2.28969e6 3.96586e6i −0.629610 1.09052i −0.987630 0.156803i \(-0.949881\pi\)
0.358019 0.933714i \(-0.383452\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.32254e6 + 2.29070e6i 0.355169 + 0.615171i
\(426\) 0 0
\(427\) −1.05757e6 + 1.83177e6i −0.280699 + 0.486185i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.09717e6 0.803105 0.401552 0.915836i \(-0.368471\pi\)
0.401552 + 0.915836i \(0.368471\pi\)
\(432\) 0 0
\(433\) −992453. −0.254384 −0.127192 0.991878i \(-0.540596\pi\)
−0.127192 + 0.991878i \(0.540596\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.52904e6 6.11248e6i 0.884002 1.53114i
\(438\) 0 0
\(439\) 442686. + 766755.i 0.109631 + 0.189887i 0.915621 0.402043i \(-0.131700\pi\)
−0.805990 + 0.591930i \(0.798366\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −270389. 468327.i −0.0654605 0.113381i 0.831438 0.555618i \(-0.187518\pi\)
−0.896898 + 0.442237i \(0.854185\pi\)
\(444\) 0 0
\(445\) 4.20186e6 7.27784e6i 1.00587 1.74222i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.22193e6 −0.520132 −0.260066 0.965591i \(-0.583744\pi\)
−0.260066 + 0.965591i \(0.583744\pi\)
\(450\) 0 0
\(451\) −1.11458e6 −0.258031
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.01903e6 + 6.96117e6i −0.910108 + 1.57635i
\(456\) 0 0
\(457\) 288892. + 500376.i 0.0647061 + 0.112074i 0.896564 0.442915i \(-0.146056\pi\)
−0.831857 + 0.554989i \(0.812722\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.70719e6 2.95694e6i −0.374137 0.648023i 0.616061 0.787699i \(-0.288728\pi\)
−0.990197 + 0.139675i \(0.955394\pi\)
\(462\) 0 0
\(463\) 927775. 1.60695e6i 0.201136 0.348378i −0.747759 0.663971i \(-0.768870\pi\)
0.948895 + 0.315593i \(0.102203\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.73338e6 0.792154 0.396077 0.918217i \(-0.370371\pi\)
0.396077 + 0.918217i \(0.370371\pi\)
\(468\) 0 0
\(469\) 635184. 0.133342
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.57528e6 + 6.19258e6i −0.734781 + 1.27268i
\(474\) 0 0
\(475\) 4.51148e6 + 7.81411e6i 0.917455 + 1.58908i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.99246e6 3.45105e6i −0.396782 0.687246i 0.596545 0.802579i \(-0.296540\pi\)
−0.993327 + 0.115334i \(0.963206\pi\)
\(480\) 0 0
\(481\) −2.63358e6 + 4.56149e6i −0.519019 + 0.898967i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.35209e7 −2.61006
\(486\) 0 0
\(487\) 4.19007e6 0.800570 0.400285 0.916391i \(-0.368911\pi\)
0.400285 + 0.916391i \(0.368911\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.09606e6 3.63049e6i 0.392374 0.679612i −0.600388 0.799709i \(-0.704987\pi\)
0.992762 + 0.120097i \(0.0383204\pi\)
\(492\) 0 0
\(493\) −1.47325e6 2.55175e6i −0.272998 0.472847i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.23706e6 + 9.07086e6i 0.951036 + 1.64724i
\(498\) 0 0
\(499\) 1.85169e6 3.20722e6i 0.332903 0.576604i −0.650177 0.759783i \(-0.725305\pi\)
0.983080 + 0.183178i \(0.0586386\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.03820e6 −0.711653 −0.355827 0.934552i \(-0.615801\pi\)
−0.355827 + 0.934552i \(0.615801\pi\)
\(504\) 0 0
\(505\) −1.34439e7 −2.34583
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 83980.3 145458.i 0.0143676 0.0248853i −0.858752 0.512391i \(-0.828760\pi\)
0.873120 + 0.487506i \(0.162093\pi\)
\(510\) 0 0
\(511\) −5.39412e6 9.34289e6i −0.913836 1.58281i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.96741e6 5.13970e6i −0.493014 0.853925i
\(516\) 0 0
\(517\) −1.61965e6 + 2.80532e6i −0.266499 + 0.461590i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.98731e6 −0.643555 −0.321777 0.946815i \(-0.604280\pi\)
−0.321777 + 0.946815i \(0.604280\pi\)
\(522\) 0 0
\(523\) −4.41694e6 −0.706102 −0.353051 0.935604i \(-0.614856\pi\)
−0.353051 + 0.935604i \(0.614856\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.16996e6 + 2.02643e6i −0.183503 + 0.317837i
\(528\) 0 0
\(529\) −550576. 953626.i −0.0855418 0.148163i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −612955. 1.06167e6i −0.0934567 0.161872i
\(534\) 0 0
\(535\) 5.01040e6 8.67827e6i 0.756812 1.31084i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.67167e6 1.13741
\(540\) 0 0
\(541\) 9.24640e6 1.35825 0.679125 0.734023i \(-0.262360\pi\)
0.679125 + 0.734023i \(0.262360\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −988628. + 1.71235e6i −0.142574 + 0.246946i
\(546\) 0 0
\(547\) −762888. 1.32136e6i −0.109017 0.188822i 0.806356 0.591431i \(-0.201437\pi\)
−0.915372 + 0.402609i \(0.868103\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.02561e6 8.70461e6i −0.705196 1.22144i
\(552\) 0 0
\(553\) −4.98559e6 + 8.63529e6i −0.693272 + 1.20078i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.86988e6 −0.801662 −0.400831 0.916152i \(-0.631279\pi\)
−0.400831 + 0.916152i \(0.631279\pi\)
\(558\) 0 0
\(559\) −7.86477e6 −1.06453
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −106686. + 184785.i −0.0141852 + 0.0245695i −0.873031 0.487665i \(-0.837849\pi\)
0.858846 + 0.512234i \(0.171182\pi\)
\(564\) 0 0
\(565\) −8.20129e6 1.42050e7i −1.08084 1.87207i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.64514e6 + 9.77767e6i 0.730961 + 1.26606i 0.956473 + 0.291821i \(0.0942612\pi\)
−0.225512 + 0.974240i \(0.572405\pi\)
\(570\) 0 0
\(571\) 232342. 402427.i 0.0298220 0.0516532i −0.850729 0.525604i \(-0.823839\pi\)
0.880551 + 0.473951i \(0.157173\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.63583e6 1.21540
\(576\) 0 0
\(577\) 8.78227e6 1.09816 0.549082 0.835769i \(-0.314978\pi\)
0.549082 + 0.835769i \(0.314978\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.58351e6 + 6.20682e6i −0.440421 + 0.762832i
\(582\) 0 0
\(583\) 3.42649e6 + 5.93485e6i 0.417521 + 0.723167i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.02083e6 + 8.69633e6i 0.601423 + 1.04170i 0.992606 + 0.121382i \(0.0387327\pi\)
−0.391183 + 0.920313i \(0.627934\pi\)
\(588\) 0 0
\(589\) −3.99100e6 + 6.91262e6i −0.474017 + 0.821021i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.15945e7 1.35399 0.676995 0.735988i \(-0.263282\pi\)
0.676995 + 0.735988i \(0.263282\pi\)
\(594\) 0 0
\(595\) 1.10043e7 1.27430
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −744422. + 1.28938e6i −0.0847720 + 0.146829i −0.905294 0.424786i \(-0.860350\pi\)
0.820522 + 0.571615i \(0.193683\pi\)
\(600\) 0 0
\(601\) 4.75503e6 + 8.23596e6i 0.536992 + 0.930097i 0.999064 + 0.0432545i \(0.0137726\pi\)
−0.462073 + 0.886842i \(0.652894\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.64303e6 6.30991e6i −0.404645 0.700865i
\(606\) 0 0
\(607\) −3.70203e6 + 6.41210e6i −0.407819 + 0.706364i −0.994645 0.103349i \(-0.967044\pi\)
0.586826 + 0.809713i \(0.300377\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.56285e6 −0.386096
\(612\) 0 0
\(613\) −7.14368e6 −0.767840 −0.383920 0.923366i \(-0.625426\pi\)
−0.383920 + 0.923366i \(0.625426\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −502021. + 869525.i −0.0530895 + 0.0919537i −0.891349 0.453318i \(-0.850240\pi\)
0.838259 + 0.545272i \(0.183574\pi\)
\(618\) 0 0
\(619\) 3.74328e6 + 6.48355e6i 0.392668 + 0.680121i 0.992801 0.119779i \(-0.0382187\pi\)
−0.600132 + 0.799901i \(0.704885\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9.24738e6 1.60169e7i −0.954550 1.65333i
\(624\) 0 0
\(625\) 4.20763e6 7.28783e6i 0.430861 0.746274i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.21086e6 0.726709
\(630\) 0 0
\(631\) 1.34648e7 1.34626 0.673128 0.739526i \(-0.264950\pi\)
0.673128 + 0.739526i \(0.264950\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.24226e6 7.34781e6i 0.417506 0.723142i
\(636\) 0 0
\(637\) 4.21896e6 + 7.30746e6i 0.411962 + 0.713539i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8.13083e6 1.40830e7i −0.781610 1.35379i −0.931004 0.365010i \(-0.881065\pi\)
0.149394 0.988778i \(-0.452268\pi\)
\(642\) 0 0
\(643\) 5.68437e6 9.84561e6i 0.542194 0.939108i −0.456584 0.889680i \(-0.650927\pi\)
0.998778 0.0494272i \(-0.0157396\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.18311e7 1.11113 0.555563 0.831474i \(-0.312503\pi\)
0.555563 + 0.831474i \(0.312503\pi\)
\(648\) 0 0
\(649\) −2.85707e6 −0.266262
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.67300e6 + 4.62977e6i −0.245310 + 0.424890i −0.962219 0.272278i \(-0.912223\pi\)
0.716909 + 0.697167i \(0.245556\pi\)
\(654\) 0 0
\(655\) 7.28401e6 + 1.26163e7i 0.663387 + 1.14902i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6.18681e6 1.07159e7i −0.554949 0.961200i −0.997907 0.0646581i \(-0.979404\pi\)
0.442958 0.896542i \(-0.353929\pi\)
\(660\) 0 0
\(661\) 1.04915e7 1.81718e7i 0.933974 1.61769i 0.157520 0.987516i \(-0.449650\pi\)
0.776454 0.630174i \(-0.217016\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.75383e7 3.29170
\(666\) 0 0
\(667\) −1.07339e7 −0.934210
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.95275e6 5.11431e6i 0.253175 0.438511i
\(672\) 0 0
\(673\) 6.30874e6 + 1.09271e7i 0.536915 + 0.929963i 0.999068 + 0.0431633i \(0.0137436\pi\)
−0.462154 + 0.886800i \(0.652923\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.99728e6 + 6.92349e6i 0.335192 + 0.580569i 0.983522 0.180791i \(-0.0578656\pi\)
−0.648330 + 0.761359i \(0.724532\pi\)
\(678\) 0 0
\(679\) −1.48782e7 + 2.57698e7i −1.23845 + 2.14505i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.23985e7 −1.01699 −0.508496 0.861064i \(-0.669798\pi\)
−0.508496 + 0.861064i \(0.669798\pi\)
\(684\) 0 0
\(685\) −1.10209e7 −0.897412
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.76873e6 + 6.52763e6i −0.302445 + 0.523851i
\(690\) 0 0
\(691\) −1.03172e7 1.78699e7i −0.821990 1.42373i −0.904198 0.427113i \(-0.859530\pi\)
0.0822079 0.996615i \(-0.473803\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.21108e6 + 1.59541e7i 0.723350 + 1.25288i
\(696\) 0 0
\(697\) −839150. + 1.45345e6i −0.0654271 + 0.113323i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.28362e7 −1.75521 −0.877603 0.479388i \(-0.840859\pi\)
−0.877603 + 0.479388i \(0.840859\pi\)
\(702\) 0 0
\(703\) 2.45980e7 1.87720
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.47935e7 + 2.56231e7i −1.11307 + 1.92790i
\(708\) 0 0
\(709\) 8.91237e6 + 1.54367e7i 0.665852 + 1.15329i 0.979054 + 0.203603i \(0.0652651\pi\)
−0.313202 + 0.949687i \(0.601402\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.26209e6 + 7.38215e6i 0.313978 + 0.543825i
\(714\) 0 0
\(715\) 1.12211e7 1.94356e7i 0.820865 1.42178i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.10161e7 0.794702 0.397351 0.917667i \(-0.369929\pi\)
0.397351 + 0.917667i \(0.369929\pi\)
\(720\) 0 0
\(721\) −1.30612e7 −0.935720
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.86107e6 1.18837e7i 0.484782 0.839667i
\(726\) 0 0
\(727\) −1.30016e7 2.25195e7i −0.912351 1.58024i −0.810734 0.585414i \(-0.800932\pi\)
−0.101616 0.994824i \(-0.532401\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.38353e6 + 9.32456e6i 0.372627 + 0.645409i
\(732\) 0 0
\(733\) −1.33355e7 + 2.30978e7i −0.916750 + 1.58786i −0.112431 + 0.993660i \(0.535864\pi\)
−0.804319 + 0.594198i \(0.797470\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.77343e6 −0.120267
\(738\) 0 0
\(739\) 1.31065e6 0.0882829 0.0441414 0.999025i \(-0.485945\pi\)
0.0441414 + 0.999025i \(0.485945\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.02502e7 1.77539e7i 0.681178 1.17983i −0.293444 0.955976i \(-0.594801\pi\)
0.974622 0.223858i \(-0.0718653\pi\)
\(744\) 0 0
\(745\) −1.39652e7 2.41884e7i −0.921839 1.59667i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.10268e7 1.90990e7i −0.718199 1.24396i
\(750\) 0 0
\(751\) 6.78701e6 1.17554e7i 0.439115 0.760570i −0.558506 0.829500i \(-0.688625\pi\)
0.997621 + 0.0689306i \(0.0219587\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.98699e7 −1.26861
\(756\) 0 0
\(757\) −470115. −0.0298171 −0.0149085 0.999889i \(-0.504746\pi\)
−0.0149085 + 0.999889i \(0.504746\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.02690e6 + 1.77865e6i −0.0642789 + 0.111334i −0.896374 0.443299i \(-0.853808\pi\)
0.832095 + 0.554633i \(0.187141\pi\)
\(762\) 0 0
\(763\) 2.17575e6 + 3.76852e6i 0.135300 + 0.234347i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.57122e6 2.72143e6i −0.0964381 0.167036i
\(768\) 0 0
\(769\) −1.25600e6 + 2.17546e6i −0.0765905 + 0.132659i −0.901777 0.432202i \(-0.857737\pi\)
0.825186 + 0.564861i \(0.191070\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.03339e6 0.483560 0.241780 0.970331i \(-0.422269\pi\)
0.241780 + 0.970331i \(0.422269\pi\)
\(774\) 0 0
\(775\) −1.08972e7 −0.651719
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.86254e6 + 4.95806e6i −0.169008 + 0.292731i
\(780\) 0 0
\(781\) −1.46219e7 2.53258e7i −0.857780 1.48572i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.42087e7 2.46102e7i −0.822962 1.42541i
\(786\) 0 0
\(787\) −1.57883e7 + 2.73461e7i −0.908653 + 1.57383i −0.0927148 + 0.995693i \(0.529554\pi\)
−0.815938 + 0.578140i \(0.803779\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.60985e7 −2.05139
\(792\) 0 0
\(793\) 6.49534e6 0.366791
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.33523e7 + 2.31268e7i −0.744577 + 1.28965i 0.205815 + 0.978591i \(0.434016\pi\)
−0.950392 + 0.311055i \(0.899318\pi\)
\(798\) 0 0
\(799\) 2.43882e6 + 4.22416e6i 0.135149 + 0.234085i
\(800\) 0 0
\(801\) 0 0