Properties

Label 108.5.k.a.65.10
Level 108
Weight 5
Character 108.65
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 65.10
Character \(\chi\) \(=\) 108.65
Dual form 108.5.k.a.5.10

$q$-expansion

\(f(q)\) \(=\) \(q+(6.98131 + 5.67991i) q^{3} +(-8.75895 + 24.0650i) q^{5} +(-0.632293 + 3.58591i) q^{7} +(16.4774 + 79.3063i) q^{9} +O(q^{10})\) \(q+(6.98131 + 5.67991i) q^{3} +(-8.75895 + 24.0650i) q^{5} +(-0.632293 + 3.58591i) q^{7} +(16.4774 + 79.3063i) q^{9} +(-22.6368 - 62.1941i) q^{11} +(-236.237 + 198.227i) q^{13} +(-197.836 + 118.255i) q^{15} +(205.336 - 118.551i) q^{17} +(25.2661 - 43.7622i) q^{19} +(-24.7819 + 21.4430i) q^{21} +(-330.376 + 58.2542i) q^{23} +(-23.6276 - 19.8259i) q^{25} +(-335.419 + 647.252i) q^{27} +(-402.857 + 480.107i) q^{29} +(111.849 + 634.330i) q^{31} +(195.222 - 562.771i) q^{33} +(-80.7568 - 46.6249i) q^{35} +(978.384 + 1694.61i) q^{37} +(-2775.15 + 42.0759i) q^{39} +(-724.003 - 862.834i) q^{41} +(296.362 - 107.867i) q^{43} +(-2052.83 - 298.112i) q^{45} +(3610.79 + 636.681i) q^{47} +(2243.74 + 816.656i) q^{49} +(2106.87 + 338.649i) q^{51} -3927.39i q^{53} +1694.98 q^{55} +(424.955 - 162.008i) q^{57} +(662.491 - 1820.18i) q^{59} +(633.851 - 3594.75i) q^{61} +(-294.804 + 8.94148i) q^{63} +(-2701.14 - 7421.31i) q^{65} +(-1252.37 + 1050.86i) q^{67} +(-2637.34 - 1469.81i) q^{69} +(6356.50 - 3669.93i) q^{71} +(-832.121 + 1441.28i) q^{73} +(-52.3423 - 272.614i) q^{75} +(237.336 - 41.8487i) q^{77} +(8242.86 + 6916.58i) q^{79} +(-6017.99 + 2613.52i) q^{81} +(4039.89 - 4814.55i) q^{83} +(1054.40 + 5979.79i) q^{85} +(-5539.43 + 1063.58i) q^{87} +(4492.85 + 2593.95i) q^{89} +(-561.452 - 972.463i) q^{91} +(-2822.08 + 5063.75i) q^{93} +(831.832 + 991.339i) q^{95} +(-3954.60 + 1439.36i) q^{97} +(4559.39 - 2820.04i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{13}{18}\right)\) \(1\)

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
\(3\) 6.98131 + 5.67991i 0.775701 + 0.631101i
\(4\) 0 0
\(5\) −8.75895 + 24.0650i −0.350358 + 0.962600i 0.631898 + 0.775052i \(0.282276\pi\)
−0.982255 + 0.187548i \(0.939946\pi\)
\(6\) 0 0
\(7\) −0.632293 + 3.58591i −0.0129039 + 0.0731819i −0.990580 0.136937i \(-0.956274\pi\)
0.977676 + 0.210119i \(0.0673852\pi\)
\(8\) 0 0
\(9\) 16.4774 + 79.3063i 0.203424 + 0.979091i
\(10\) 0 0
\(11\) −22.6368 62.1941i −0.187081 0.514001i 0.810325 0.585981i \(-0.199291\pi\)
−0.997406 + 0.0719797i \(0.977068\pi\)
\(12\) 0 0
\(13\) −236.237 + 198.227i −1.39785 + 1.17294i −0.435812 + 0.900038i \(0.643539\pi\)
−0.962042 + 0.272901i \(0.912017\pi\)
\(14\) 0 0
\(15\) −197.836 + 118.255i −0.879271 + 0.525579i
\(16\) 0 0
\(17\) 205.336 118.551i 0.710505 0.410210i −0.100743 0.994912i \(-0.532122\pi\)
0.811248 + 0.584702i \(0.198789\pi\)
\(18\) 0 0
\(19\) 25.2661 43.7622i 0.0699892 0.121225i −0.828907 0.559386i \(-0.811037\pi\)
0.898896 + 0.438161i \(0.144370\pi\)
\(20\) 0 0
\(21\) −24.7819 + 21.4430i −0.0561947 + 0.0486236i
\(22\) 0 0
\(23\) −330.376 + 58.2542i −0.624530 + 0.110121i −0.476952 0.878929i \(-0.658259\pi\)
−0.147577 + 0.989051i \(0.547147\pi\)
\(24\) 0 0
\(25\) −23.6276 19.8259i −0.0378042 0.0317215i
\(26\) 0 0
\(27\) −335.419 + 647.252i −0.460108 + 0.887863i
\(28\) 0 0
\(29\) −402.857 + 480.107i −0.479022 + 0.570876i −0.950390 0.311060i \(-0.899316\pi\)
0.471368 + 0.881936i \(0.343760\pi\)
\(30\) 0 0
\(31\) 111.849 + 634.330i 0.116389 + 0.660073i 0.986053 + 0.166430i \(0.0532239\pi\)
−0.869665 + 0.493643i \(0.835665\pi\)
\(32\) 0 0
\(33\) 195.222 562.771i 0.179267 0.516778i
\(34\) 0 0
\(35\) −80.7568 46.6249i −0.0659239 0.0380612i
\(36\) 0 0
\(37\) 978.384 + 1694.61i 0.714671 + 1.23785i 0.963086 + 0.269193i \(0.0867568\pi\)
−0.248416 + 0.968654i \(0.579910\pi\)
\(38\) 0 0
\(39\) −2775.15 + 42.0759i −1.82456 + 0.0276633i
\(40\) 0 0
\(41\) −724.003 862.834i −0.430698 0.513286i 0.506426 0.862284i \(-0.330967\pi\)
−0.937124 + 0.348998i \(0.886522\pi\)
\(42\) 0 0
\(43\) 296.362 107.867i 0.160282 0.0583380i −0.260633 0.965438i \(-0.583931\pi\)
0.420915 + 0.907100i \(0.361709\pi\)
\(44\) 0 0
\(45\) −2052.83 298.112i −1.01374 0.147216i
\(46\) 0 0
\(47\) 3610.79 + 636.681i 1.63458 + 0.288221i 0.914172 0.405326i \(-0.132842\pi\)
0.720411 + 0.693547i \(0.243953\pi\)
\(48\) 0 0
\(49\) 2243.74 + 816.656i 0.934504 + 0.340131i
\(50\) 0 0
\(51\) 2106.87 + 338.649i 0.810023 + 0.130200i
\(52\) 0 0
\(53\) 3927.39i 1.39815i −0.715051 0.699073i \(-0.753596\pi\)
0.715051 0.699073i \(-0.246404\pi\)
\(54\) 0 0
\(55\) 1694.98 0.560323
\(56\) 0 0
\(57\) 424.955 162.008i 0.130796 0.0498640i
\(58\) 0 0
\(59\) 662.491 1820.18i 0.190316 0.522890i −0.807432 0.589961i \(-0.799143\pi\)
0.997748 + 0.0670710i \(0.0213654\pi\)
\(60\) 0 0
\(61\) 633.851 3594.75i 0.170344 0.966070i −0.773037 0.634361i \(-0.781263\pi\)
0.943382 0.331710i \(-0.107625\pi\)
\(62\) 0 0
\(63\) −294.804 + 8.94148i −0.0742766 + 0.00225283i
\(64\) 0 0
\(65\) −2701.14 7421.31i −0.639322 1.75652i
\(66\) 0 0
\(67\) −1252.37 + 1050.86i −0.278986 + 0.234097i −0.771534 0.636188i \(-0.780510\pi\)
0.492548 + 0.870285i \(0.336066\pi\)
\(68\) 0 0
\(69\) −2637.34 1469.81i −0.553946 0.308720i
\(70\) 0 0
\(71\) 6356.50 3669.93i 1.26096 0.728016i 0.287700 0.957721i \(-0.407109\pi\)
0.973260 + 0.229705i \(0.0737761\pi\)
\(72\) 0 0
\(73\) −832.121 + 1441.28i −0.156150 + 0.270459i −0.933477 0.358637i \(-0.883242\pi\)
0.777327 + 0.629096i \(0.216575\pi\)
\(74\) 0 0
\(75\) −52.3423 272.614i −0.00930530 0.0484646i
\(76\) 0 0
\(77\) 237.336 41.8487i 0.0400296 0.00705830i
\(78\) 0 0
\(79\) 8242.86 + 6916.58i 1.32076 + 1.10825i 0.986143 + 0.165895i \(0.0530513\pi\)
0.334617 + 0.942354i \(0.391393\pi\)
\(80\) 0 0
\(81\) −6017.99 + 2613.52i −0.917237 + 0.398341i
\(82\) 0 0
\(83\) 4039.89 4814.55i 0.586426 0.698875i −0.388489 0.921453i \(-0.627003\pi\)
0.974915 + 0.222578i \(0.0714473\pi\)
\(84\) 0 0
\(85\) 1054.40 + 5979.79i 0.145937 + 0.827652i
\(86\) 0 0
\(87\) −5539.43 + 1063.58i −0.731858 + 0.140518i
\(88\) 0 0
\(89\) 4492.85 + 2593.95i 0.567207 + 0.327477i 0.756033 0.654533i \(-0.227135\pi\)
−0.188826 + 0.982011i \(0.560468\pi\)
\(90\) 0 0
\(91\) −561.452 972.463i −0.0678000 0.117433i
\(92\) 0 0
\(93\) −2822.08 + 5063.75i −0.326289 + 0.585472i
\(94\) 0 0
\(95\) 831.832 + 991.339i 0.0921698 + 0.109844i
\(96\) 0 0
\(97\) −3954.60 + 1439.36i −0.420300 + 0.152977i −0.543507 0.839404i \(-0.682904\pi\)
0.123208 + 0.992381i \(0.460682\pi\)
\(98\) 0 0
\(99\) 4559.39 2820.04i 0.465197 0.287730i
\(100\) 0 0
\(101\) −15898.8 2803.39i −1.55856 0.274815i −0.673104 0.739548i \(-0.735039\pi\)
−0.885451 + 0.464732i \(0.846151\pi\)
\(102\) 0 0
\(103\) 13317.2 + 4847.05i 1.25527 + 0.456881i 0.882179 0.470914i \(-0.156076\pi\)
0.373091 + 0.927795i \(0.378298\pi\)
\(104\) 0 0
\(105\) −298.963 784.194i −0.0271168 0.0711287i
\(106\) 0 0
\(107\) 5472.24i 0.477967i 0.971024 + 0.238984i \(0.0768142\pi\)
−0.971024 + 0.238984i \(0.923186\pi\)
\(108\) 0 0
\(109\) −8864.19 −0.746081 −0.373041 0.927815i \(-0.621685\pi\)
−0.373041 + 0.927815i \(0.621685\pi\)
\(110\) 0 0
\(111\) −2794.83 + 17387.7i −0.226835 + 1.41123i
\(112\) 0 0
\(113\) −1907.44 + 5240.66i −0.149381 + 0.410421i −0.991702 0.128555i \(-0.958966\pi\)
0.842322 + 0.538975i \(0.181188\pi\)
\(114\) 0 0
\(115\) 1491.86 8460.75i 0.112806 0.639754i
\(116\) 0 0
\(117\) −19613.2 15468.9i −1.43277 1.13002i
\(118\) 0 0
\(119\) 295.280 + 811.275i 0.0208516 + 0.0572894i
\(120\) 0 0
\(121\) 7859.97 6595.30i 0.536847 0.450468i
\(122\) 0 0
\(123\) −153.678 10136.0i −0.0101578 0.669970i
\(124\) 0 0
\(125\) −13177.5 + 7608.01i −0.843357 + 0.486912i
\(126\) 0 0
\(127\) −12709.1 + 22012.8i −0.787967 + 1.36480i 0.139244 + 0.990258i \(0.455533\pi\)
−0.927211 + 0.374540i \(0.877800\pi\)
\(128\) 0 0
\(129\) 2681.67 + 930.255i 0.161148 + 0.0559014i
\(130\) 0 0
\(131\) −6066.88 + 1069.75i −0.353527 + 0.0623364i −0.347592 0.937646i \(-0.613000\pi\)
−0.00593554 + 0.999982i \(0.501889\pi\)
\(132\) 0 0
\(133\) 140.952 + 118.272i 0.00796832 + 0.00668622i
\(134\) 0 0
\(135\) −12638.2 13741.1i −0.693454 0.753970i
\(136\) 0 0
\(137\) 13079.1 15587.0i 0.696845 0.830467i −0.295321 0.955398i \(-0.595426\pi\)
0.992165 + 0.124931i \(0.0398709\pi\)
\(138\) 0 0
\(139\) 1564.03 + 8870.06i 0.0809498 + 0.459089i 0.998157 + 0.0606794i \(0.0193267\pi\)
−0.917207 + 0.398410i \(0.869562\pi\)
\(140\) 0 0
\(141\) 21591.8 + 24953.8i 1.08605 + 1.25516i
\(142\) 0 0
\(143\) 17676.2 + 10205.4i 0.864404 + 0.499064i
\(144\) 0 0
\(145\) −8025.16 13900.0i −0.381696 0.661117i
\(146\) 0 0
\(147\) 11025.7 + 18445.6i 0.510238 + 0.853606i
\(148\) 0 0
\(149\) 9361.36 + 11156.4i 0.421664 + 0.502519i 0.934498 0.355968i \(-0.115849\pi\)
−0.512834 + 0.858488i \(0.671404\pi\)
\(150\) 0 0
\(151\) −4398.99 + 1601.10i −0.192930 + 0.0702207i −0.436678 0.899618i \(-0.643845\pi\)
0.243748 + 0.969839i \(0.421623\pi\)
\(152\) 0 0
\(153\) 12785.2 + 14331.0i 0.546167 + 0.612202i
\(154\) 0 0
\(155\) −16244.8 2864.40i −0.676164 0.119226i
\(156\) 0 0
\(157\) −4131.63 1503.79i −0.167619 0.0610082i 0.256848 0.966452i \(-0.417316\pi\)
−0.424466 + 0.905444i \(0.639538\pi\)
\(158\) 0 0
\(159\) 22307.2 27418.3i 0.882370 1.08454i
\(160\) 0 0
\(161\) 1221.53i 0.0471252i
\(162\) 0 0
\(163\) −48545.4 −1.82714 −0.913572 0.406677i \(-0.866688\pi\)
−0.913572 + 0.406677i \(0.866688\pi\)
\(164\) 0 0
\(165\) 11833.2 + 9627.31i 0.434643 + 0.353620i
\(166\) 0 0
\(167\) −14935.4 + 41034.8i −0.535532 + 1.47136i 0.316868 + 0.948470i \(0.397369\pi\)
−0.852399 + 0.522891i \(0.824853\pi\)
\(168\) 0 0
\(169\) 11554.7 65530.0i 0.404562 2.29439i
\(170\) 0 0
\(171\) 3886.94 + 1282.68i 0.132928 + 0.0438657i
\(172\) 0 0
\(173\) −7728.43 21233.7i −0.258225 0.709469i −0.999277 0.0380204i \(-0.987895\pi\)
0.741051 0.671448i \(-0.234327\pi\)
\(174\) 0 0
\(175\) 86.0336 72.1907i 0.00280926 0.00235725i
\(176\) 0 0
\(177\) 14963.5 8944.35i 0.477625 0.285497i
\(178\) 0 0
\(179\) 47920.0 27666.6i 1.49558 0.863476i 0.495597 0.868553i \(-0.334949\pi\)
0.999987 + 0.00507689i \(0.00161603\pi\)
\(180\) 0 0
\(181\) 20301.3 35162.8i 0.619678 1.07331i −0.369866 0.929085i \(-0.620596\pi\)
0.989544 0.144229i \(-0.0460702\pi\)
\(182\) 0 0
\(183\) 24842.9 21495.8i 0.741824 0.641877i
\(184\) 0 0
\(185\) −49350.4 + 8701.82i −1.44194 + 0.254253i
\(186\) 0 0
\(187\) −12021.3 10087.1i −0.343770 0.288458i
\(188\) 0 0
\(189\) −2108.90 1612.04i −0.0590382 0.0451285i
\(190\) 0 0
\(191\) −10391.8 + 12384.5i −0.284856 + 0.339478i −0.889430 0.457071i \(-0.848899\pi\)
0.604575 + 0.796549i \(0.293343\pi\)
\(192\) 0 0
\(193\) 5546.95 + 31458.3i 0.148915 + 0.844542i 0.964140 + 0.265396i \(0.0855027\pi\)
−0.815224 + 0.579146i \(0.803386\pi\)
\(194\) 0 0
\(195\) 23294.9 67152.7i 0.612620 1.76601i
\(196\) 0 0
\(197\) 50661.7 + 29249.5i 1.30541 + 0.753679i 0.981326 0.192350i \(-0.0616108\pi\)
0.324083 + 0.946028i \(0.394944\pi\)
\(198\) 0 0
\(199\) −8677.79 15030.4i −0.219131 0.379545i 0.735412 0.677620i \(-0.236989\pi\)
−0.954542 + 0.298075i \(0.903655\pi\)
\(200\) 0 0
\(201\) −14712.0 + 223.057i −0.364148 + 0.00552109i
\(202\) 0 0
\(203\) −1466.90 1748.18i −0.0355965 0.0424223i
\(204\) 0 0
\(205\) 27105.6 9865.63i 0.644988 0.234756i
\(206\) 0 0
\(207\) −10063.7 25241.0i −0.234863 0.589070i
\(208\) 0 0
\(209\) −3293.69 580.767i −0.0754033 0.0132956i
\(210\) 0 0
\(211\) 6345.41 + 2309.54i 0.142526 + 0.0518753i 0.412298 0.911049i \(-0.364726\pi\)
−0.269772 + 0.962924i \(0.586948\pi\)
\(212\) 0 0
\(213\) 65221.5 + 10483.4i 1.43758 + 0.231070i
\(214\) 0 0
\(215\) 8076.75i 0.174727i
\(216\) 0 0
\(217\) −2345.37 −0.0498072
\(218\) 0 0
\(219\) −13995.6 + 5335.62i −0.291812 + 0.111249i
\(220\) 0 0
\(221\) −25008.1 + 68709.2i −0.512031 + 1.40679i
\(222\) 0 0
\(223\) 14045.2 79654.1i 0.282434 1.60176i −0.431876 0.901933i \(-0.642148\pi\)
0.714310 0.699830i \(-0.246741\pi\)
\(224\) 0 0
\(225\) 1183.00 2200.50i 0.0233679 0.0434666i
\(226\) 0 0
\(227\) −4625.90 12709.6i −0.0897728 0.246649i 0.886679 0.462386i \(-0.153007\pi\)
−0.976451 + 0.215738i \(0.930784\pi\)
\(228\) 0 0
\(229\) −14498.7 + 12165.9i −0.276477 + 0.231992i −0.770473 0.637472i \(-0.779980\pi\)
0.493996 + 0.869464i \(0.335536\pi\)
\(230\) 0 0
\(231\) 1894.61 + 1055.89i 0.0355055 + 0.0197876i
\(232\) 0 0
\(233\) −46376.2 + 26775.3i −0.854247 + 0.493200i −0.862081 0.506770i \(-0.830839\pi\)
0.00783474 + 0.999969i \(0.497506\pi\)
\(234\) 0 0
\(235\) −46948.5 + 81317.1i −0.850131 + 1.47247i
\(236\) 0 0
\(237\) 18260.4 + 95105.5i 0.325098 + 1.69320i
\(238\) 0 0
\(239\) −41032.0 + 7235.05i −0.718335 + 0.126662i −0.520855 0.853645i \(-0.674387\pi\)
−0.197480 + 0.980307i \(0.563276\pi\)
\(240\) 0 0
\(241\) −71951.4 60374.4i −1.23881 1.03949i −0.997616 0.0690098i \(-0.978016\pi\)
−0.241196 0.970477i \(-0.577540\pi\)
\(242\) 0 0
\(243\) −56858.0 15935.9i −0.962895 0.269875i
\(244\) 0 0
\(245\) −39305.6 + 46842.6i −0.654821 + 0.780386i
\(246\) 0 0
\(247\) 2706.03 + 15346.7i 0.0443546 + 0.251548i
\(248\) 0 0
\(249\) 55549.9 10665.7i 0.895952 0.172024i
\(250\) 0 0
\(251\) 53554.3 + 30919.6i 0.850054 + 0.490779i 0.860669 0.509165i \(-0.170046\pi\)
−0.0106150 + 0.999944i \(0.503379\pi\)
\(252\) 0 0
\(253\) 11101.7 + 19228.8i 0.173440 + 0.300407i
\(254\) 0 0
\(255\) −26603.6 + 47735.6i −0.409128 + 0.734112i
\(256\) 0 0
\(257\) 6611.38 + 7879.13i 0.100098 + 0.119292i 0.813768 0.581190i \(-0.197413\pi\)
−0.713670 + 0.700482i \(0.752968\pi\)
\(258\) 0 0
\(259\) −6695.35 + 2436.91i −0.0998099 + 0.0363278i
\(260\) 0 0
\(261\) −44713.5 24038.3i −0.656384 0.352876i
\(262\) 0 0
\(263\) 64659.5 + 11401.2i 0.934805 + 0.164831i 0.620247 0.784407i \(-0.287032\pi\)
0.314558 + 0.949238i \(0.398144\pi\)
\(264\) 0 0
\(265\) 94512.7 + 34399.8i 1.34586 + 0.489851i
\(266\) 0 0
\(267\) 16632.6 + 43628.1i 0.233312 + 0.611989i
\(268\) 0 0
\(269\) 78857.5i 1.08978i −0.838508 0.544890i \(-0.816572\pi\)
0.838508 0.544890i \(-0.183428\pi\)
\(270\) 0 0
\(271\) −85836.1 −1.16878 −0.584388 0.811474i \(-0.698666\pi\)
−0.584388 + 0.811474i \(0.698666\pi\)
\(272\) 0 0
\(273\) 1603.83 9978.06i 0.0215195 0.133882i
\(274\) 0 0
\(275\) −698.202 + 1918.29i −0.00923242 + 0.0253659i
\(276\) 0 0
\(277\) −12768.2 + 72412.3i −0.166407 + 0.943741i 0.781195 + 0.624287i \(0.214611\pi\)
−0.947602 + 0.319454i \(0.896501\pi\)
\(278\) 0 0
\(279\) −48463.4 + 19322.4i −0.622595 + 0.248230i
\(280\) 0 0
\(281\) −50983.9 140077.i −0.645685 1.77401i −0.633082 0.774084i \(-0.718211\pi\)
−0.0126027 0.999921i \(-0.504012\pi\)
\(282\) 0 0
\(283\) −43283.8 + 36319.5i −0.540447 + 0.453489i −0.871691 0.490056i \(-0.836976\pi\)
0.331244 + 0.943545i \(0.392532\pi\)
\(284\) 0 0
\(285\) 176.566 + 11645.6i 0.00217379 + 0.143374i
\(286\) 0 0
\(287\) 3551.83 2050.65i 0.0431209 0.0248959i
\(288\) 0 0
\(289\) −13651.9 + 23645.9i −0.163455 + 0.283113i
\(290\) 0 0
\(291\) −35783.7 12413.2i −0.422570 0.146587i
\(292\) 0 0
\(293\) −8976.28 + 1582.76i −0.104559 + 0.0184366i −0.225683 0.974201i \(-0.572461\pi\)
0.121124 + 0.992637i \(0.461350\pi\)
\(294\) 0 0
\(295\) 37999.9 + 31885.7i 0.436655 + 0.366397i
\(296\) 0 0
\(297\) 47848.1 + 6209.38i 0.542440 + 0.0703939i
\(298\) 0 0
\(299\) 66499.6 79251.2i 0.743835 0.886469i
\(300\) 0 0
\(301\) 199.414 + 1130.93i 0.00220101 + 0.0124825i
\(302\) 0 0
\(303\) −95071.6 109875.i −1.03554 1.19678i
\(304\) 0 0
\(305\) 80955.7 + 46739.8i 0.870258 + 0.502444i
\(306\) 0 0
\(307\) −55967.7 96939.0i −0.593829 1.02854i −0.993711 0.111975i \(-0.964282\pi\)
0.399882 0.916566i \(-0.369051\pi\)
\(308\) 0 0
\(309\) 65440.4 + 109479.i 0.685376 + 1.14660i
\(310\) 0 0
\(311\) 15433.3 + 18392.6i 0.159565 + 0.190162i 0.839903 0.542736i \(-0.182612\pi\)
−0.680338 + 0.732898i \(0.738167\pi\)
\(312\) 0 0
\(313\) 166946. 60763.3i 1.70407 0.620230i 0.707790 0.706423i \(-0.249692\pi\)
0.996278 + 0.0861930i \(0.0274702\pi\)
\(314\) 0 0
\(315\) 2367.00 7172.78i 0.0238548 0.0722880i
\(316\) 0 0
\(317\) −168850. 29772.9i −1.68029 0.296280i −0.749544 0.661954i \(-0.769727\pi\)
−0.930743 + 0.365674i \(0.880838\pi\)
\(318\) 0 0
\(319\) 38979.2 + 14187.3i 0.383047 + 0.139418i
\(320\) 0 0
\(321\) −31081.8 + 38203.4i −0.301645 + 0.370760i
\(322\) 0 0
\(323\) 11981.3i 0.114841i
\(324\) 0 0
\(325\) 9511.75 0.0900521
\(326\) 0 0
\(327\) −61883.7 50347.8i −0.578736 0.470852i
\(328\) 0 0
\(329\) −4566.16 + 12545.4i −0.0421851 + 0.115903i
\(330\) 0 0
\(331\) −21564.0 + 122296.i −0.196822 + 1.11623i 0.712978 + 0.701186i \(0.247346\pi\)
−0.909800 + 0.415047i \(0.863765\pi\)
\(332\) 0 0
\(333\) −118272. + 105515.i −1.06658 + 0.951535i
\(334\) 0 0
\(335\) −14319.6 39342.7i −0.127597 0.350570i
\(336\) 0 0
\(337\) 144069. 120888.i 1.26856 1.06445i 0.273845 0.961774i \(-0.411704\pi\)
0.994715 0.102674i \(-0.0327400\pi\)
\(338\) 0 0
\(339\) −43082.9 + 25752.6i −0.374892 + 0.224089i
\(340\) 0 0
\(341\) 36919.7 21315.6i 0.317504 0.183311i
\(342\) 0 0
\(343\) −8718.45 + 15100.8i −0.0741056 + 0.128355i
\(344\) 0 0
\(345\) 58471.4 50593.5i 0.491253 0.425066i
\(346\) 0 0
\(347\) 126703. 22341.2i 1.05227 0.185544i 0.379347 0.925254i \(-0.376149\pi\)
0.672925 + 0.739710i \(0.265037\pi\)
\(348\) 0 0
\(349\) 36525.7 + 30648.7i 0.299881 + 0.251630i 0.780295 0.625412i \(-0.215069\pi\)
−0.480414 + 0.877042i \(0.659514\pi\)
\(350\) 0 0
\(351\) −49064.1 219394.i −0.398244 1.78078i
\(352\) 0 0
\(353\) 94657.4 112808.i 0.759635 0.905298i −0.238190 0.971219i \(-0.576554\pi\)
0.997825 + 0.0659209i \(0.0209985\pi\)
\(354\) 0 0
\(355\) 32640.6 + 185114.i 0.259001 + 1.46887i
\(356\) 0 0
\(357\) −2546.52 + 7340.92i −0.0199807 + 0.0575989i
\(358\) 0 0
\(359\) 65225.6 + 37658.0i 0.506092 + 0.292192i 0.731226 0.682136i \(-0.238949\pi\)
−0.225134 + 0.974328i \(0.572282\pi\)
\(360\) 0 0
\(361\) 63883.7 + 110650.i 0.490203 + 0.849057i
\(362\) 0 0
\(363\) 92333.6 1399.93i 0.700723 0.0106241i
\(364\) 0 0
\(365\) −27395.8 32649.1i −0.205636 0.245067i
\(366\) 0 0
\(367\) 107072. 38970.8i 0.794954 0.289339i 0.0875599 0.996159i \(-0.472093\pi\)
0.707394 + 0.706820i \(0.249871\pi\)
\(368\) 0 0
\(369\) 56498.5 71635.3i 0.414939 0.526107i
\(370\) 0 0
\(371\) 14083.3 + 2483.26i 0.102319 + 0.0180416i
\(372\) 0 0
\(373\) 51753.2 + 18836.6i 0.371980 + 0.135390i 0.521244 0.853408i \(-0.325468\pi\)
−0.149264 + 0.988797i \(0.547690\pi\)
\(374\) 0 0
\(375\) −135209. 21732.8i −0.961484 0.154545i
\(376\) 0 0
\(377\) 193276.i 1.35986i
\(378\) 0 0
\(379\) 129313. 0.900249 0.450125 0.892966i \(-0.351380\pi\)
0.450125 + 0.892966i \(0.351380\pi\)
\(380\) 0 0
\(381\) −213757. + 81491.8i −1.47255 + 0.561389i
\(382\) 0 0
\(383\) 83657.1 229846.i 0.570303 1.56689i −0.233726 0.972303i \(-0.575092\pi\)
0.804028 0.594591i \(-0.202686\pi\)
\(384\) 0 0
\(385\) −1071.72 + 6078.03i −0.00723037 + 0.0410055i
\(386\) 0 0
\(387\) 13437.8 + 21726.0i 0.0897234 + 0.145063i
\(388\) 0 0
\(389\) 43560.0 + 119680.i 0.287865 + 0.790903i 0.996365 + 0.0851915i \(0.0271502\pi\)
−0.708500 + 0.705711i \(0.750628\pi\)
\(390\) 0 0
\(391\) −60932.0 + 51128.0i −0.398558 + 0.334430i
\(392\) 0 0
\(393\) −48430.9 26991.0i −0.313572 0.174757i
\(394\) 0 0
\(395\) −238646. + 137783.i −1.52954 + 0.883080i
\(396\) 0 0
\(397\) 48666.8 84293.3i 0.308782 0.534825i −0.669314 0.742979i \(-0.733412\pi\)
0.978096 + 0.208154i \(0.0667454\pi\)
\(398\) 0 0
\(399\) 312.251 + 1626.29i 0.00196136 + 0.0102153i
\(400\) 0 0
\(401\) −20496.9 + 3614.15i −0.127467 + 0.0224759i −0.237018 0.971505i \(-0.576170\pi\)
0.109551 + 0.993981i \(0.465059\pi\)
\(402\) 0 0
\(403\) −152164. 127681.i −0.936919 0.786168i
\(404\) 0 0
\(405\) −10183.0 167715.i −0.0620821 1.02249i
\(406\) 0 0
\(407\) 83247.4 99210.3i 0.502553 0.598919i
\(408\) 0 0
\(409\) −50897.1 288652.i −0.304261 1.72555i −0.626963 0.779049i \(-0.715702\pi\)
0.322702 0.946501i \(-0.395409\pi\)
\(410\) 0 0
\(411\) 179842. 34530.0i 1.06465 0.204415i
\(412\) 0 0
\(413\) 6108.11 + 3526.52i 0.0358102 + 0.0206750i
\(414\) 0 0
\(415\) 80477.0 + 139390.i 0.467278 + 0.809350i
\(416\) 0 0
\(417\) −39462.1 + 70808.2i −0.226939 + 0.407203i
\(418\) 0 0
\(419\) −39138.7 46643.7i −0.222935 0.265684i 0.642971 0.765891i \(-0.277702\pi\)
−0.865906 + 0.500207i \(0.833257\pi\)
\(420\) 0 0
\(421\) −210167. + 76494.4i −1.18577 + 0.431584i −0.858236 0.513256i \(-0.828439\pi\)
−0.327533 + 0.944840i \(0.606217\pi\)
\(422\) 0 0
\(423\) 9003.53 + 296850.i 0.0503190 + 1.65904i
\(424\) 0 0
\(425\) −7201.98 1269.90i −0.0398725 0.00703060i
\(426\) 0 0
\(427\) 12489.7 + 4545.87i 0.0685007 + 0.0249322i
\(428\) 0 0
\(429\) 65437.5 + 171646.i 0.355559 + 0.932650i
\(430\) 0 0
\(431\) 244624.i 1.31687i −0.752635 0.658437i \(-0.771218\pi\)
0.752635 0.658437i \(-0.228782\pi\)
\(432\) 0 0
\(433\) −119238. −0.635971 −0.317986 0.948096i \(-0.603006\pi\)
−0.317986 + 0.948096i \(0.603006\pi\)
\(434\) 0 0
\(435\) 22924.5 142622.i 0.121149 0.753718i
\(436\) 0 0
\(437\) −5797.98 + 15929.8i −0.0303609 + 0.0834158i
\(438\) 0 0
\(439\) −16161.5 + 91656.5i −0.0838597 + 0.475592i 0.913737 + 0.406306i \(0.133183\pi\)
−0.997597 + 0.0692860i \(0.977928\pi\)
\(440\) 0 0
\(441\) −27795.0 + 191399.i −0.142919 + 0.984155i
\(442\) 0 0
\(443\) 94532.4 + 259726.i 0.481696 + 1.32345i 0.908038 + 0.418887i \(0.137580\pi\)
−0.426342 + 0.904562i \(0.640198\pi\)
\(444\) 0 0
\(445\) −101776. + 85400.2i −0.513955 + 0.431259i
\(446\) 0 0
\(447\) 1987.06 + 131058.i 0.00994477 + 0.655917i
\(448\) 0 0
\(449\) −84746.9 + 48928.6i −0.420369 + 0.242700i −0.695235 0.718782i \(-0.744700\pi\)
0.274866 + 0.961483i \(0.411366\pi\)
\(450\) 0 0
\(451\) −37274.0 + 64560.5i −0.183254 + 0.317405i
\(452\) 0 0
\(453\) −39804.8 13808.1i −0.193972 0.0672878i
\(454\) 0 0
\(455\) 28320.1 4993.59i 0.136795 0.0241207i
\(456\) 0 0
\(457\) 132440. + 111130.i 0.634141 + 0.532107i 0.902212 0.431292i \(-0.141942\pi\)
−0.268072 + 0.963399i \(0.586387\pi\)
\(458\) 0 0
\(459\) 7858.62 + 172668.i 0.0373010 + 0.819572i
\(460\) 0 0
\(461\) −207164. + 246888.i −0.974793 + 1.16171i 0.0120331 + 0.999928i \(0.496170\pi\)
−0.986826 + 0.161785i \(0.948275\pi\)
\(462\) 0 0
\(463\) 42566.1 + 241404.i 0.198564 + 1.12611i 0.907250 + 0.420591i \(0.138177\pi\)
−0.708686 + 0.705524i \(0.750712\pi\)
\(464\) 0 0
\(465\) −97140.7 112266.i −0.449257 0.519211i
\(466\) 0 0
\(467\) 199445. + 115149.i 0.914510 + 0.527992i 0.881879 0.471475i \(-0.156278\pi\)
0.0326303 + 0.999467i \(0.489612\pi\)
\(468\) 0 0
\(469\) −2976.43 5155.33i −0.0135316 0.0234375i
\(470\) 0 0
\(471\) −20302.8 33965.7i −0.0915197 0.153108i
\(472\) 0 0
\(473\) −13417.4 15990.2i −0.0599715 0.0714713i
\(474\) 0 0
\(475\) −1464.60 + 533.072i −0.00649131 + 0.00236264i
\(476\) 0 0
\(477\) 311467. 64713.0i 1.36891 0.284416i
\(478\) 0 0
\(479\) 133421. + 23525.7i 0.581505 + 0.102535i 0.456660 0.889641i \(-0.349046\pi\)
0.124845 + 0.992176i \(0.460157\pi\)
\(480\) 0 0
\(481\) −567048. 206389.i −2.45092 0.892063i
\(482\) 0 0
\(483\) 6938.19 8527.90i 0.0297408 0.0365551i
\(484\) 0 0
\(485\) 107775.i 0.458177i
\(486\) 0 0
\(487\) 253009. 1.06679 0.533393 0.845868i \(-0.320917\pi\)
0.533393 + 0.845868i \(0.320917\pi\)
\(488\) 0 0
\(489\) −338910. 275733.i −1.41732 1.15311i
\(490\) 0 0
\(491\) −86121.8 + 236618.i −0.357232 + 0.981487i 0.622754 + 0.782418i \(0.286014\pi\)
−0.979986 + 0.199069i \(0.936208\pi\)
\(492\) 0 0
\(493\) −25804.1 + 146342.i −0.106168 + 0.602110i
\(494\) 0 0
\(495\) 27928.7 + 134422.i 0.113983 + 0.548607i
\(496\) 0 0
\(497\) 9140.86 + 25114.3i 0.0370062 + 0.101674i
\(498\) 0 0
\(499\) 49665.0 41673.9i 0.199457 0.167364i −0.537589 0.843207i \(-0.680665\pi\)
0.737046 + 0.675843i \(0.236220\pi\)
\(500\) 0 0
\(501\) −337343. + 201645.i −1.34399 + 0.803362i
\(502\) 0 0
\(503\) −420415. + 242727.i −1.66166 + 0.959360i −0.689737 + 0.724060i \(0.742274\pi\)
−0.971923 + 0.235300i \(0.924393\pi\)
\(504\) 0 0
\(505\) 206721. 358051.i 0.810589 1.40398i
\(506\) 0 0
\(507\) 452871. 391855.i 1.76181 1.52444i
\(508\) 0 0
\(509\) −287186. + 50638.7i −1.10848 + 0.195455i −0.697778 0.716314i \(-0.745828\pi\)
−0.410703 + 0.911769i \(0.634717\pi\)
\(510\) 0 0
\(511\) −4642.14 3895.22i −0.0177777 0.0149173i
\(512\) 0 0
\(513\) 19850.4 + 31032.2i 0.0754284 + 0.117917i
\(514\) 0 0
\(515\) −233289. + 278023.i −0.879587 + 1.04825i
\(516\) 0 0
\(517\) −42139.1 238983.i −0.157654 0.894098i
\(518\) 0 0
\(519\) 66650.8 192136.i 0.247440 0.713302i
\(520\) 0 0
\(521\) −41930.4 24208.5i −0.154473 0.0891853i 0.420771 0.907167i \(-0.361760\pi\)
−0.575244 + 0.817982i \(0.695093\pi\)
\(522\) 0 0
\(523\) −155771. 269804.i −0.569488 0.986382i −0.996617 0.0821910i \(-0.973808\pi\)
0.427129 0.904191i \(-0.359525\pi\)
\(524\) 0 0
\(525\) 1010.66 15.3233i 0.00366681 5.55948e-5i
\(526\) 0 0
\(527\) 98167.0 + 116991.i 0.353463 + 0.421241i
\(528\) 0 0
\(529\) −157210. + 57219.7i −0.561782 + 0.204472i
\(530\) 0 0
\(531\) 155268. + 22548.0i 0.550672 + 0.0799686i
\(532\) 0 0
\(533\) 342073. + 60316.7i 1.20411 + 0.212316i
\(534\) 0 0
\(535\) −131690. 47931.1i −0.460091 0.167460i
\(536\) 0 0
\(537\) 491688. + 79031.8i 1.70507 + 0.274065i
\(538\) 0 0
\(539\) 158034.i 0.543968i
\(540\) 0 0
\(541\) 333475. 1.13938 0.569690 0.821860i \(-0.307063\pi\)
0.569690 + 0.821860i \(0.307063\pi\)
\(542\) 0 0
\(543\) 341451. 130173.i 1.15805 0.441492i
\(544\) 0 0
\(545\) 77641.0 213317.i 0.261395 0.718178i
\(546\) 0 0
\(547\) 58942.6 334280.i 0.196995 1.11721i −0.712554 0.701617i \(-0.752462\pi\)
0.909549 0.415596i \(-0.136427\pi\)
\(548\) 0 0
\(549\) 295530. 8963.51i 0.980522 0.0297395i
\(550\) 0 0
\(551\) 10831.9 + 29760.3i 0.0356780 + 0.0980245i
\(552\) 0 0
\(553\) −30014.2 + 25184.9i −0.0981468 + 0.0823549i
\(554\) 0 0
\(555\) −393956. 219556.i −1.27897 0.712786i
\(556\) 0 0
\(557\) −211847. + 122310.i −0.682828 + 0.394231i −0.800920 0.598772i \(-0.795656\pi\)
0.118092 + 0.993003i \(0.462322\pi\)
\(558\) 0 0
\(559\) −48629.6 + 84229.0i −0.155624 + 0.269549i
\(560\) 0 0
\(561\) −26630.8 138701.i −0.0846173 0.440711i
\(562\) 0 0
\(563\) 465712. 82117.5i 1.46927 0.259071i 0.618986 0.785402i \(-0.287544\pi\)
0.850280 + 0.526331i \(0.176433\pi\)
\(564\) 0 0
\(565\) −109409. 91805.3i −0.342734 0.287588i
\(566\) 0 0
\(567\) −5566.71 23232.5i −0.0173154 0.0722653i
\(568\) 0 0
\(569\) −190547. + 227085.i −0.588542 + 0.701397i −0.975325 0.220774i \(-0.929142\pi\)
0.386783 + 0.922171i \(0.373586\pi\)
\(570\) 0 0
\(571\) −96134.7 545207.i −0.294855 1.67220i −0.667792 0.744347i \(-0.732761\pi\)
0.372938 0.927856i \(-0.378350\pi\)
\(572\) 0 0
\(573\) −142891. + 27435.4i −0.435208 + 0.0835607i
\(574\) 0 0
\(575\) 8960.94 + 5173.60i 0.0271030 + 0.0156479i
\(576\) 0 0
\(577\) 127612. + 221030.i 0.383300 + 0.663895i 0.991532 0.129864i \(-0.0414542\pi\)
−0.608232 + 0.793760i \(0.708121\pi\)
\(578\) 0 0
\(579\) −139955. + 251127.i −0.417477 + 0.749092i
\(580\) 0 0
\(581\) 14710.2 + 17530.9i 0.0435778 + 0.0519340i
\(582\) 0 0
\(583\) −244261. + 88903.6i −0.718648 + 0.261567i
\(584\) 0 0
\(585\) 544049. 336501.i 1.58974 0.983273i
\(586\) 0 0
\(587\) 390885. + 68923.6i 1.13442 + 0.200029i 0.709163 0.705045i \(-0.249073\pi\)
0.425255 + 0.905073i \(0.360184\pi\)
\(588\) 0 0
\(589\) 30585.6 + 11132.3i 0.0881631 + 0.0320887i
\(590\) 0 0
\(591\) 187550. + 491953.i 0.536961 + 1.40847i
\(592\) 0 0
\(593\) 141628.i 0.402754i −0.979514 0.201377i \(-0.935458\pi\)
0.979514 0.201377i \(-0.0645416\pi\)
\(594\) 0 0
\(595\) −22109.7 −0.0624523
\(596\) 0 0
\(597\) 24788.8 154221.i 0.0695515 0.432707i
\(598\) 0 0
\(599\) 205094. 563492.i 0.571611 1.57049i −0.230348 0.973108i \(-0.573987\pi\)
0.801959 0.597379i \(-0.203791\pi\)
\(600\) 0 0
\(601\) −67002.3 + 379989.i −0.185499 + 1.05202i 0.739814 + 0.672811i \(0.234913\pi\)
−0.925313 + 0.379204i \(0.876198\pi\)
\(602\) 0 0
\(603\) −103976. 82005.3i −0.285955 0.225532i
\(604\) 0 0
\(605\) 89870.9 + 246918.i 0.245532 + 0.674594i
\(606\) 0 0
\(607\) 109301. 91714.6i 0.296652 0.248921i −0.482297 0.876008i \(-0.660197\pi\)
0.778949 + 0.627087i \(0.215753\pi\)
\(608\) 0 0
\(609\) −311.366 20536.4i −0.000839529 0.0553720i
\(610\) 0 0
\(611\) −979212. + 565348.i −2.62297 + 1.51438i
\(612\) 0 0
\(613\) 67410.6 116759.i 0.179394 0.310719i −0.762279 0.647248i \(-0.775920\pi\)
0.941673 + 0.336529i \(0.109253\pi\)
\(614\) 0 0
\(615\) 245268. + 85082.2i 0.648472 + 0.224951i
\(616\) 0 0
\(617\) 550083. 96994.6i 1.44497 0.254787i 0.604481 0.796619i \(-0.293380\pi\)
0.840487 + 0.541832i \(0.182269\pi\)
\(618\) 0 0
\(619\) 206114. + 172950.i 0.537931 + 0.451377i 0.870830 0.491585i \(-0.163582\pi\)
−0.332899 + 0.942963i \(0.608027\pi\)
\(620\) 0 0
\(621\) 73109.3 233376.i 0.189579 0.605164i
\(622\) 0 0
\(623\) −12142.5 + 14470.8i −0.0312846 + 0.0372835i
\(624\) 0 0
\(625\) −71013.6 402738.i −0.181795 1.03101i
\(626\) 0 0
\(627\) −19695.6 22762.4i −0.0500995 0.0579005i
\(628\) 0 0
\(629\) 401795. + 231976.i 1.01555 + 0.586330i
\(630\) 0 0
\(631\) −263153. 455795.i −0.660922 1.14475i −0.980374 0.197148i \(-0.936832\pi\)
0.319451 0.947603i \(-0.396501\pi\)
\(632\) 0 0
\(633\) 31181.3 + 52165.0i 0.0778192 + 0.130188i
\(634\) 0 0
\(635\) −418421. 498654.i −1.03769 1.23666i
\(636\) 0 0
\(637\) −691939. + 251845.i −1.70525 + 0.620661i
\(638\) 0 0
\(639\) 395787. + 443640.i 0.969303 + 1.08650i
\(640\) 0 0
\(641\) −505241. 89087.6i −1.22965 0.216821i −0.479176 0.877719i \(-0.659065\pi\)
−0.750476 + 0.660898i \(0.770176\pi\)
\(642\) 0 0
\(643\) −20896.4 7605.67i −0.0505417 0.0183957i 0.316626 0.948551i \(-0.397450\pi\)
−0.367167 + 0.930155i \(0.619672\pi\)
\(644\) 0 0
\(645\) −45875.2 + 56386.3i −0.110270 + 0.135536i
\(646\) 0 0
\(647\) 341326.i 0.815381i −0.913120 0.407690i \(-0.866334\pi\)
0.913120 0.407690i \(-0.133666\pi\)
\(648\) 0 0
\(649\) −128201. −0.304370
\(650\) 0 0
\(651\) −16373.8 13321.5i −0.0386355 0.0314334i
\(652\) 0 0
\(653\) −25633.4 + 70427.1i −0.0601145 + 0.165163i −0.966114 0.258115i \(-0.916899\pi\)
0.906000 + 0.423278i \(0.139121\pi\)
\(654\) 0 0
\(655\) 27395.8 155369.i 0.0638560 0.362145i
\(656\) 0 0
\(657\) −128013. 42244.1i −0.296568 0.0978667i
\(658\) 0 0
\(659\) 97130.3 + 266863.i 0.223658 + 0.614495i 0.999872 0.0159741i \(-0.00508493\pi\)
−0.776215 + 0.630469i \(0.782863\pi\)
\(660\) 0 0
\(661\) 118548. 99473.7i 0.271326 0.227670i −0.496964 0.867771i \(-0.665552\pi\)
0.768291 + 0.640101i \(0.221108\pi\)
\(662\) 0 0
\(663\) −564851. + 337636.i −1.28501 + 0.768108i
\(664\) 0 0
\(665\) −4080.82 + 2356.06i −0.00922792 + 0.00532774i
\(666\) 0 0
\(667\) 105126. 182084.i 0.236298 0.409279i
\(668\) 0 0
\(669\) 550481. 476314.i 1.22996 1.06424i
\(670\) 0 0
\(671\) −237920. + 41951.8i −0.528429 + 0.0931763i
\(672\) 0 0
\(673\) 606326. + 508768.i 1.33868 + 1.12328i 0.981963 + 0.189071i \(0.0605478\pi\)
0.356715 + 0.934213i \(0.383897\pi\)
\(674\) 0 0
\(675\) 20757.5 8643.03i 0.0455583 0.0189696i
\(676\) 0 0
\(677\) 319117. 380309.i 0.696262 0.829773i −0.295836 0.955239i \(-0.595598\pi\)
0.992098 + 0.125466i \(0.0400426\pi\)
\(678\) 0 0
\(679\) −2660.94 15090.9i −0.00577159 0.0327323i
\(680\) 0 0
\(681\) 39894.3 115004.i 0.0860233 0.247981i
\(682\) 0 0
\(683\) 54865.2 + 31676.5i 0.117613 + 0.0679040i 0.557653 0.830074i \(-0.311702\pi\)
−0.440039 + 0.897978i \(0.645036\pi\)
\(684\) 0 0
\(685\) 260543. + 451274.i 0.555263 + 0.961744i
\(686\) 0 0
\(687\) −170321. + 2582.35i −0.360874 + 0.00547144i
\(688\) 0 0
\(689\) 778514. + 927796.i 1.63994 + 1.95440i
\(690\) 0 0
\(691\) 205774. 74895.6i 0.430958 0.156856i −0.117428 0.993081i \(-0.537465\pi\)
0.548385 + 0.836226i \(0.315243\pi\)
\(692\) 0 0
\(693\) 7229.53 + 18132.7i 0.0150537 + 0.0377568i
\(694\) 0 0
\(695\) −227157. 40054.0i −0.470281 0.0829232i
\(696\) 0 0
\(697\) −250953. 91339.6i −0.516568 0.188015i
\(698\) 0 0
\(699\) −475848. 76485.7i −0.973899 0.156540i
\(700\) 0 0
\(701\) 484481.i 0.985919i −0.870052 0.492959i \(-0.835915\pi\)
0.870052 0.492959i \(-0.164085\pi\)
\(702\) 0 0
\(703\) 98879.8 0.200077
\(704\) 0 0
\(705\) −789636. + 301037.i −1.58872 + 0.605678i
\(706\) 0 0
\(707\) 20105.4 55239.2i 0.0402230 0.110512i
\(708\) 0 0
\(709\) −68351.0 + 387638.i −0.135973 + 0.771140i 0.838205 + 0.545356i \(0.183606\pi\)
−0.974177 + 0.225784i \(0.927506\pi\)
\(710\) 0 0
\(711\) −412708. + 767678.i −0.816402 + 1.51859i
\(712\) 0 0
\(713\) −73904.8 203052.i −0.145376 0.399418i
\(714\) 0 0
\(715\) −400417. + 335990.i −0.783249 + 0.657224i
\(716\) 0 0
\(717\) −327552. 182548.i −0.637150 0.355090i
\(718\) 0 0
\(719\) −643290. + 371404.i −1.24437 + 0.718437i −0.969981 0.243182i \(-0.921809\pi\)
−0.274389 + 0.961619i \(0.588475\pi\)
\(720\) 0 0
\(721\) −25801.4 + 44689.4i −0.0496333 + 0.0859674i
\(722\) 0 0
\(723\) −159394. 830170.i −0.304927 1.58815i
\(724\) 0 0
\(725\) 19037.1 3356.76i 0.0362181 0.00638622i
\(726\) 0 0
\(727\) 511540. + 429233.i 0.967856 + 0.812128i 0.982213 0.187769i \(-0.0601256\pi\)
−0.0143568 + 0.999897i \(0.504570\pi\)
\(728\) 0 0
\(729\) −306429. 434201.i −0.576600 0.817026i
\(730\) 0 0
\(731\) 48066.0 57282.9i 0.0899505 0.107199i
\(732\) 0 0
\(733\) 90190.3 + 511495.i 0.167862 + 0.951991i 0.946065 + 0.323978i \(0.105020\pi\)
−0.778203 + 0.628013i \(0.783868\pi\)
\(734\) 0 0
\(735\) −540467. + 103771.i −1.00045 + 0.192088i
\(736\) 0 0
\(737\) 93707.0 + 54101.8i 0.172519 + 0.0996039i
\(738\) 0 0
\(739\) −18612.0 32237.0i −0.0340804 0.0590290i 0.848482 0.529224i \(-0.177517\pi\)
−0.882563 + 0.470195i \(0.844184\pi\)
\(740\) 0 0
\(741\) −68276.0 + 122510.i −0.124346 + 0.223118i
\(742\) 0 0
\(743\) −533099. 635323.i −0.965674 1.15085i −0.988517 0.151107i \(-0.951716\pi\)
0.0228434 0.999739i \(-0.492728\pi\)
\(744\) 0 0
\(745\) −350475. + 127563.i −0.631458 + 0.229832i
\(746\) 0 0
\(747\) 448391. + 241058.i 0.803555 + 0.431996i
\(748\) 0 0
\(749\) −19623.0 3460.06i −0.0349785 0.00616766i
\(750\) 0 0
\(751\) 410674. + 149473.i 0.728144 + 0.265023i 0.679379 0.733787i \(-0.262249\pi\)
0.0487651 + 0.998810i \(0.484471\pi\)
\(752\) 0 0
\(753\) 198259. + 520042.i 0.349657 + 0.917167i
\(754\) 0 0
\(755\) 119886.i 0.210317i
\(756\) 0 0
\(757\) 515657. 0.899848 0.449924 0.893067i \(-0.351451\pi\)
0.449924 + 0.893067i \(0.351451\pi\)
\(758\) 0 0
\(759\) −31712.9 + 197299.i −0.0550494 + 0.342484i
\(760\) 0 0
\(761\) −194402. + 534114.i −0.335684 + 0.922284i 0.650920 + 0.759147i \(0.274383\pi\)
−0.986603 + 0.163137i \(0.947839\pi\)
\(762\) 0 0
\(763\) 5604.77 31786.2i 0.00962739 0.0545996i
\(764\) 0 0
\(765\) −456862. + 182152.i −0.780660 + 0.311250i
\(766\) 0 0
\(767\) 204303. + 561318.i 0.347283 + 0.954153i
\(768\) 0 0
\(769\) −61792.2 + 51849.8i −0.104491 + 0.0876788i −0.693537 0.720421i \(-0.743948\pi\)
0.589045 + 0.808100i \(0.299504\pi\)
\(770\) 0 0
\(771\) 1403.34 + 92558.7i 0.00236077 + 0.155707i
\(772\) 0 0
\(773\) 418443. 241588.i 0.700288 0.404312i −0.107167 0.994241i \(-0.534178\pi\)
0.807455 + 0.589930i \(0.200844\pi\)
\(774\) 0 0
\(775\) 9933.44 17205.2i 0.0165385 0.0286455i
\(776\) 0 0
\(777\) −60583.7 21016.1i −0.100349 0.0348106i
\(778\) 0 0
\(779\) −56052.2 + 9883.51i −0.0923672 + 0.0162868i
\(780\) 0 0