Properties

Label 108.5.k.a.65.4
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 65.4
Character \(\chi\) \(=\) 108.65
Dual form 108.5.k.a.5.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.53499 + 7.09676i) q^{3} +(-14.0519 + 38.6073i) q^{5} +(-5.57324 + 31.6074i) q^{7} +(-19.7279 - 78.5609i) q^{9} +O(q^{10})\) \(q+(-5.53499 + 7.09676i) q^{3} +(-14.0519 + 38.6073i) q^{5} +(-5.57324 + 31.6074i) q^{7} +(-19.7279 - 78.5609i) q^{9} +(-4.11688 - 11.3110i) q^{11} +(91.3096 - 76.6178i) q^{13} +(-196.210 - 313.414i) q^{15} +(-175.368 + 101.249i) q^{17} +(98.3348 - 170.321i) q^{19} +(-193.462 - 214.499i) q^{21} +(-707.360 + 124.727i) q^{23} +(-814.293 - 683.273i) q^{25} +(666.721 + 294.829i) q^{27} +(523.078 - 623.381i) q^{29} +(28.4024 + 161.078i) q^{31} +(103.059 + 33.3899i) q^{33} +(-1141.96 - 659.313i) q^{35} +(-941.906 - 1631.43i) q^{37} +(38.3409 + 1072.08i) q^{39} +(1759.69 + 2097.12i) q^{41} +(-3246.83 + 1181.75i) q^{43} +(3310.24 + 342.290i) q^{45} +(89.3900 + 15.7619i) q^{47} +(1288.23 + 468.879i) q^{49} +(252.122 - 1804.96i) q^{51} +844.122i q^{53} +494.540 q^{55} +(664.444 + 1640.58i) q^{57} +(-1831.29 + 5031.42i) q^{59} +(860.325 - 4879.15i) q^{61} +(2593.06 - 185.709i) q^{63} +(1674.94 + 4601.85i) q^{65} +(561.501 - 471.156i) q^{67} +(3030.07 - 5710.32i) q^{69} +(-3351.53 + 1935.01i) q^{71} +(1199.32 - 2077.29i) q^{73} +(9356.12 - 1996.93i) q^{75} +(380.457 - 67.0849i) q^{77} +(3238.29 + 2717.25i) q^{79} +(-5782.62 + 3099.68i) q^{81} +(-6782.64 + 8083.24i) q^{83} +(-1444.69 - 8193.24i) q^{85} +(1528.75 + 7162.56i) q^{87} +(4410.52 + 2546.41i) q^{89} +(1912.80 + 3313.07i) q^{91} +(-1300.34 - 689.999i) q^{93} +(5193.84 + 6189.78i) q^{95} +(-14646.8 + 5331.01i) q^{97} +(-807.388 + 546.569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

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
\(3\) −5.53499 + 7.09676i −0.614998 + 0.788528i
\(4\) 0 0
\(5\) −14.0519 + 38.6073i −0.562077 + 1.54429i 0.254509 + 0.967070i \(0.418086\pi\)
−0.816586 + 0.577223i \(0.804136\pi\)
\(6\) 0 0
\(7\) −5.57324 + 31.6074i −0.113740 + 0.645050i 0.873627 + 0.486596i \(0.161762\pi\)
−0.987367 + 0.158453i \(0.949349\pi\)
\(8\) 0 0
\(9\) −19.7279 78.5609i −0.243554 0.969887i
\(10\) 0 0
\(11\) −4.11688 11.3110i −0.0340238 0.0934797i 0.921518 0.388337i \(-0.126950\pi\)
−0.955541 + 0.294857i \(0.904728\pi\)
\(12\) 0 0
\(13\) 91.3096 76.6178i 0.540293 0.453360i −0.331345 0.943510i \(-0.607502\pi\)
0.871638 + 0.490150i \(0.163058\pi\)
\(14\) 0 0
\(15\) −196.210 313.414i −0.872043 1.39295i
\(16\) 0 0
\(17\) −175.368 + 101.249i −0.606810 + 0.350342i −0.771716 0.635967i \(-0.780601\pi\)
0.164906 + 0.986309i \(0.447268\pi\)
\(18\) 0 0
\(19\) 98.3348 170.321i 0.272395 0.471803i −0.697079 0.716994i \(-0.745517\pi\)
0.969475 + 0.245191i \(0.0788508\pi\)
\(20\) 0 0
\(21\) −193.462 214.499i −0.438690 0.486391i
\(22\) 0 0
\(23\) −707.360 + 124.727i −1.33716 + 0.235778i −0.796081 0.605191i \(-0.793097\pi\)
−0.541084 + 0.840969i \(0.681986\pi\)
\(24\) 0 0
\(25\) −814.293 683.273i −1.30287 1.09324i
\(26\) 0 0
\(27\) 666.721 + 294.829i 0.914569 + 0.404430i
\(28\) 0 0
\(29\) 523.078 623.381i 0.621972 0.741237i −0.359436 0.933170i \(-0.617031\pi\)
0.981408 + 0.191932i \(0.0614754\pi\)
\(30\) 0 0
\(31\) 28.4024 + 161.078i 0.0295550 + 0.167615i 0.996013 0.0892109i \(-0.0284345\pi\)
−0.966458 + 0.256826i \(0.917323\pi\)
\(32\) 0 0
\(33\) 103.059 + 33.3899i 0.0946360 + 0.0306611i
\(34\) 0 0
\(35\) −1141.96 659.313i −0.932216 0.538215i
\(36\) 0 0
\(37\) −941.906 1631.43i −0.688025 1.19169i −0.972476 0.233004i \(-0.925145\pi\)
0.284451 0.958691i \(-0.408189\pi\)
\(38\) 0 0
\(39\) 38.3409 + 1072.08i 0.0252077 + 0.704852i
\(40\) 0 0
\(41\) 1759.69 + 2097.12i 1.04681 + 1.24754i 0.968079 + 0.250646i \(0.0806429\pi\)
0.0787328 + 0.996896i \(0.474913\pi\)
\(42\) 0 0
\(43\) −3246.83 + 1181.75i −1.75599 + 0.639129i −0.999883 0.0153148i \(-0.995125\pi\)
−0.756110 + 0.654444i \(0.772903\pi\)
\(44\) 0 0
\(45\) 3310.24 + 342.290i 1.63469 + 0.169032i
\(46\) 0 0
\(47\) 89.3900 + 15.7619i 0.0404663 + 0.00713530i 0.193845 0.981032i \(-0.437904\pi\)
−0.153378 + 0.988168i \(0.549015\pi\)
\(48\) 0 0
\(49\) 1288.23 + 468.879i 0.536540 + 0.195285i
\(50\) 0 0
\(51\) 252.122 1804.96i 0.0969326 0.693947i
\(52\) 0 0
\(53\) 844.122i 0.300506i 0.988648 + 0.150253i \(0.0480088\pi\)
−0.988648 + 0.150253i \(0.951991\pi\)
\(54\) 0 0
\(55\) 494.540 0.163484
\(56\) 0 0
\(57\) 664.444 + 1640.58i 0.204507 + 0.504950i
\(58\) 0 0
\(59\) −1831.29 + 5031.42i −0.526081 + 1.44540i 0.337568 + 0.941301i \(0.390396\pi\)
−0.863649 + 0.504094i \(0.831826\pi\)
\(60\) 0 0
\(61\) 860.325 4879.15i 0.231208 1.31125i −0.619246 0.785197i \(-0.712562\pi\)
0.850454 0.526049i \(-0.176327\pi\)
\(62\) 0 0
\(63\) 2593.06 185.709i 0.653327 0.0467898i
\(64\) 0 0
\(65\) 1674.94 + 4601.85i 0.396435 + 1.08919i
\(66\) 0 0
\(67\) 561.501 471.156i 0.125084 0.104958i −0.578100 0.815966i \(-0.696206\pi\)
0.703184 + 0.711008i \(0.251761\pi\)
\(68\) 0 0
\(69\) 3030.07 5710.32i 0.636436 1.19940i
\(70\) 0 0
\(71\) −3351.53 + 1935.01i −0.664855 + 0.383854i −0.794124 0.607756i \(-0.792070\pi\)
0.129270 + 0.991609i \(0.458737\pi\)
\(72\) 0 0
\(73\) 1199.32 2077.29i 0.225056 0.389808i −0.731280 0.682077i \(-0.761077\pi\)
0.956336 + 0.292269i \(0.0944103\pi\)
\(74\) 0 0
\(75\) 9356.12 1996.93i 1.66331 0.355010i
\(76\) 0 0
\(77\) 380.457 67.0849i 0.0641689 0.0113147i
\(78\) 0 0
\(79\) 3238.29 + 2717.25i 0.518874 + 0.435387i 0.864239 0.503082i \(-0.167801\pi\)
−0.345365 + 0.938468i \(0.612245\pi\)
\(80\) 0 0
\(81\) −5782.62 + 3099.68i −0.881363 + 0.472440i
\(82\) 0 0
\(83\) −6782.64 + 8083.24i −0.984561 + 1.17335i 0.000298097 1.00000i \(0.499905\pi\)
−0.984859 + 0.173355i \(0.944539\pi\)
\(84\) 0 0
\(85\) −1444.69 8193.24i −0.199957 1.13401i
\(86\) 0 0
\(87\) 1528.75 + 7162.56i 0.201975 + 0.946302i
\(88\) 0 0
\(89\) 4410.52 + 2546.41i 0.556813 + 0.321476i 0.751865 0.659317i \(-0.229154\pi\)
−0.195052 + 0.980793i \(0.562488\pi\)
\(90\) 0 0
\(91\) 1912.80 + 3313.07i 0.230987 + 0.400081i
\(92\) 0 0
\(93\) −1300.34 689.999i −0.150345 0.0797778i
\(94\) 0 0
\(95\) 5193.84 + 6189.78i 0.575495 + 0.685848i
\(96\) 0 0
\(97\) −14646.8 + 5331.01i −1.55668 + 0.566586i −0.969973 0.243212i \(-0.921799\pi\)
−0.586709 + 0.809798i \(0.699577\pi\)
\(98\) 0 0
\(99\) −807.388 + 546.569i −0.0823781 + 0.0557666i
\(100\) 0 0
\(101\) −13396.2 2362.10i −1.31322 0.231556i −0.527191 0.849747i \(-0.676755\pi\)
−0.786028 + 0.618191i \(0.787866\pi\)
\(102\) 0 0
\(103\) −13783.3 5016.70i −1.29921 0.472872i −0.402468 0.915434i \(-0.631848\pi\)
−0.896738 + 0.442562i \(0.854070\pi\)
\(104\) 0 0
\(105\) 10999.7 4454.95i 0.997709 0.404077i
\(106\) 0 0
\(107\) 8097.26i 0.707246i −0.935388 0.353623i \(-0.884950\pi\)
0.935388 0.353623i \(-0.115050\pi\)
\(108\) 0 0
\(109\) −13401.0 −1.12793 −0.563966 0.825798i \(-0.690725\pi\)
−0.563966 + 0.825798i \(0.690725\pi\)
\(110\) 0 0
\(111\) 16791.3 + 2345.46i 1.36282 + 0.190363i
\(112\) 0 0
\(113\) 7402.08 20337.0i 0.579691 1.59269i −0.209012 0.977913i \(-0.567025\pi\)
0.788703 0.614775i \(-0.210753\pi\)
\(114\) 0 0
\(115\) 5124.40 29061.9i 0.387479 2.19750i
\(116\) 0 0
\(117\) −7820.51 5661.85i −0.571299 0.413606i
\(118\) 0 0
\(119\) −2222.85 6107.22i −0.156970 0.431270i
\(120\) 0 0
\(121\) 11104.7 9317.92i 0.758464 0.636427i
\(122\) 0 0
\(123\) −24622.6 + 880.579i −1.62751 + 0.0582047i
\(124\) 0 0
\(125\) 15583.8 8997.30i 0.997361 0.575827i
\(126\) 0 0
\(127\) −14330.6 + 24821.3i −0.888497 + 1.53892i −0.0468449 + 0.998902i \(0.514917\pi\)
−0.841652 + 0.540020i \(0.818417\pi\)
\(128\) 0 0
\(129\) 9584.57 29582.9i 0.575961 1.77771i
\(130\) 0 0
\(131\) −7511.50 + 1324.48i −0.437707 + 0.0771796i −0.388160 0.921592i \(-0.626889\pi\)
−0.0495477 + 0.998772i \(0.515778\pi\)
\(132\) 0 0
\(133\) 4835.36 + 4057.35i 0.273354 + 0.229371i
\(134\) 0 0
\(135\) −20751.3 + 21597.4i −1.13862 + 1.18504i
\(136\) 0 0
\(137\) −18103.1 + 21574.5i −0.964524 + 1.14947i 0.0241978 + 0.999707i \(0.492297\pi\)
−0.988721 + 0.149767i \(0.952148\pi\)
\(138\) 0 0
\(139\) −2705.80 15345.3i −0.140044 0.794231i −0.971213 0.238211i \(-0.923439\pi\)
0.831169 0.556020i \(-0.187672\pi\)
\(140\) 0 0
\(141\) −606.630 + 547.137i −0.0305131 + 0.0275206i
\(142\) 0 0
\(143\) −1242.54 717.380i −0.0607628 0.0350814i
\(144\) 0 0
\(145\) 16716.8 + 28954.4i 0.795092 + 1.37714i
\(146\) 0 0
\(147\) −10457.9 + 6547.04i −0.483959 + 0.302978i
\(148\) 0 0
\(149\) 8817.28 + 10508.0i 0.397157 + 0.473313i 0.927151 0.374688i \(-0.122250\pi\)
−0.529994 + 0.848001i \(0.677806\pi\)
\(150\) 0 0
\(151\) −14397.6 + 5240.31i −0.631447 + 0.229828i −0.637861 0.770152i \(-0.720181\pi\)
0.00641405 + 0.999979i \(0.497958\pi\)
\(152\) 0 0
\(153\) 11413.8 + 11779.6i 0.487583 + 0.503210i
\(154\) 0 0
\(155\) −6617.89 1166.91i −0.275459 0.0485708i
\(156\) 0 0
\(157\) 41354.0 + 15051.6i 1.67771 + 0.610638i 0.992994 0.118168i \(-0.0377022\pi\)
0.684720 + 0.728806i \(0.259924\pi\)
\(158\) 0 0
\(159\) −5990.53 4672.20i −0.236958 0.184811i
\(160\) 0 0
\(161\) 23053.0i 0.889355i
\(162\) 0 0
\(163\) 46133.7 1.73637 0.868186 0.496239i \(-0.165286\pi\)
0.868186 + 0.496239i \(0.165286\pi\)
\(164\) 0 0
\(165\) −2737.27 + 3509.63i −0.100542 + 0.128912i
\(166\) 0 0
\(167\) −10403.4 + 28583.1i −0.373029 + 1.02489i 0.601155 + 0.799132i \(0.294707\pi\)
−0.974184 + 0.225756i \(0.927515\pi\)
\(168\) 0 0
\(169\) −2492.42 + 14135.2i −0.0872665 + 0.494913i
\(170\) 0 0
\(171\) −15320.5 4365.20i −0.523939 0.149283i
\(172\) 0 0
\(173\) −4830.95 13272.9i −0.161414 0.443480i 0.832449 0.554102i \(-0.186938\pi\)
−0.993863 + 0.110621i \(0.964716\pi\)
\(174\) 0 0
\(175\) 26134.7 21929.7i 0.853379 0.716070i
\(176\) 0 0
\(177\) −25570.6 40845.0i −0.816196 1.30375i
\(178\) 0 0
\(179\) 6081.38 3511.09i 0.189800 0.109581i −0.402089 0.915601i \(-0.631716\pi\)
0.591889 + 0.806020i \(0.298382\pi\)
\(180\) 0 0
\(181\) −5455.83 + 9449.78i −0.166534 + 0.288446i −0.937199 0.348795i \(-0.886591\pi\)
0.770665 + 0.637241i \(0.219924\pi\)
\(182\) 0 0
\(183\) 29864.2 + 33111.5i 0.891762 + 0.988728i
\(184\) 0 0
\(185\) 76220.7 13439.8i 2.22705 0.392689i
\(186\) 0 0
\(187\) 1867.20 + 1566.77i 0.0533959 + 0.0448044i
\(188\) 0 0
\(189\) −13034.6 + 19430.2i −0.364900 + 0.543943i
\(190\) 0 0
\(191\) 30575.4 36438.4i 0.838119 0.998832i −0.161809 0.986822i \(-0.551733\pi\)
0.999928 0.0120095i \(-0.00382285\pi\)
\(192\) 0 0
\(193\) 7552.68 + 42833.4i 0.202762 + 1.14992i 0.900923 + 0.433979i \(0.142891\pi\)
−0.698161 + 0.715941i \(0.745998\pi\)
\(194\) 0 0
\(195\) −41928.9 13584.6i −1.10267 0.357253i
\(196\) 0 0
\(197\) −11406.4 6585.49i −0.293911 0.169690i 0.345793 0.938311i \(-0.387610\pi\)
−0.639704 + 0.768621i \(0.720943\pi\)
\(198\) 0 0
\(199\) 17462.9 + 30246.6i 0.440971 + 0.763785i 0.997762 0.0668682i \(-0.0213007\pi\)
−0.556790 + 0.830653i \(0.687967\pi\)
\(200\) 0 0
\(201\) 235.774 + 6592.68i 0.00583585 + 0.163181i
\(202\) 0 0
\(203\) 16788.2 + 20007.4i 0.407392 + 0.485511i
\(204\) 0 0
\(205\) −105691. + 38468.4i −2.51496 + 0.915370i
\(206\) 0 0
\(207\) 23753.3 + 53110.2i 0.554350 + 1.23947i
\(208\) 0 0
\(209\) −2331.34 411.078i −0.0533719 0.00941091i
\(210\) 0 0
\(211\) 51237.9 + 18649.1i 1.15087 + 0.418883i 0.845828 0.533456i \(-0.179107\pi\)
0.305043 + 0.952339i \(0.401329\pi\)
\(212\) 0 0
\(213\) 4818.40 34495.2i 0.106205 0.760326i
\(214\) 0 0
\(215\) 141957.i 3.07101i
\(216\) 0 0
\(217\) −5249.55 −0.111481
\(218\) 0 0
\(219\) 8103.76 + 20009.0i 0.168966 + 0.417194i
\(220\) 0 0
\(221\) −8255.32 + 22681.3i −0.169024 + 0.464391i
\(222\) 0 0
\(223\) 5832.28 33076.5i 0.117281 0.665135i −0.868314 0.496015i \(-0.834796\pi\)
0.985595 0.169120i \(-0.0540927\pi\)
\(224\) 0 0
\(225\) −37614.2 + 77451.1i −0.742997 + 1.52990i
\(226\) 0 0
\(227\) 2193.22 + 6025.83i 0.0425629 + 0.116941i 0.959153 0.282887i \(-0.0912922\pi\)
−0.916590 + 0.399828i \(0.869070\pi\)
\(228\) 0 0
\(229\) 13000.1 10908.4i 0.247900 0.208013i −0.510367 0.859956i \(-0.670491\pi\)
0.758267 + 0.651944i \(0.226046\pi\)
\(230\) 0 0
\(231\) −1629.74 + 3071.33i −0.0305418 + 0.0575575i
\(232\) 0 0
\(233\) 18170.9 10491.0i 0.334706 0.193243i −0.323222 0.946323i \(-0.604766\pi\)
0.657929 + 0.753080i \(0.271433\pi\)
\(234\) 0 0
\(235\) −1864.63 + 3229.63i −0.0337642 + 0.0584812i
\(236\) 0 0
\(237\) −37207.5 + 7941.43i −0.662421 + 0.141385i
\(238\) 0 0
\(239\) 17008.7 2999.10i 0.297767 0.0525043i −0.0227689 0.999741i \(-0.507248\pi\)
0.320536 + 0.947236i \(0.396137\pi\)
\(240\) 0 0
\(241\) −27227.2 22846.4i −0.468780 0.393353i 0.377569 0.925981i \(-0.376760\pi\)
−0.846349 + 0.532628i \(0.821205\pi\)
\(242\) 0 0
\(243\) 10009.1 58194.5i 0.169504 0.985529i
\(244\) 0 0
\(245\) −36204.3 + 43146.6i −0.603154 + 0.718811i
\(246\) 0 0
\(247\) −4070.71 23086.1i −0.0667230 0.378405i
\(248\) 0 0
\(249\) −19822.9 92875.4i −0.319720 1.49797i
\(250\) 0 0
\(251\) −54334.9 31370.3i −0.862445 0.497933i 0.00238560 0.999997i \(-0.499241\pi\)
−0.864830 + 0.502065i \(0.832574\pi\)
\(252\) 0 0
\(253\) 4322.91 + 7487.50i 0.0675359 + 0.116976i
\(254\) 0 0
\(255\) 66141.7 + 35096.8i 1.01717 + 0.539744i
\(256\) 0 0
\(257\) 43512.8 + 51856.5i 0.658796 + 0.785122i 0.987212 0.159411i \(-0.0509594\pi\)
−0.328417 + 0.944533i \(0.606515\pi\)
\(258\) 0 0
\(259\) 56814.8 20678.9i 0.846958 0.308267i
\(260\) 0 0
\(261\) −59292.5 28795.5i −0.870400 0.422711i
\(262\) 0 0
\(263\) −121068. 21347.5i −1.75032 0.308628i −0.795530 0.605914i \(-0.792808\pi\)
−0.954789 + 0.297285i \(0.903919\pi\)
\(264\) 0 0
\(265\) −32589.3 11861.5i −0.464070 0.168908i
\(266\) 0 0
\(267\) −42483.4 + 17206.0i −0.595932 + 0.241356i
\(268\) 0 0
\(269\) 39540.0i 0.546427i −0.961953 0.273213i \(-0.911913\pi\)
0.961953 0.273213i \(-0.0880865\pi\)
\(270\) 0 0
\(271\) 27986.9 0.381080 0.190540 0.981679i \(-0.438976\pi\)
0.190540 + 0.981679i \(0.438976\pi\)
\(272\) 0 0
\(273\) −34099.4 4763.11i −0.457532 0.0639095i
\(274\) 0 0
\(275\) −4376.18 + 12023.5i −0.0578668 + 0.158988i
\(276\) 0 0
\(277\) −17151.2 + 97269.1i −0.223529 + 1.26770i 0.641948 + 0.766748i \(0.278126\pi\)
−0.865477 + 0.500948i \(0.832985\pi\)
\(278\) 0 0
\(279\) 12094.1 5409.04i 0.155369 0.0694883i
\(280\) 0 0
\(281\) 6829.25 + 18763.2i 0.0864890 + 0.237626i 0.975396 0.220462i \(-0.0707565\pi\)
−0.888907 + 0.458088i \(0.848534\pi\)
\(282\) 0 0
\(283\) 77950.3 65408.0i 0.973296 0.816692i −0.00976888 0.999952i \(-0.503110\pi\)
0.983064 + 0.183260i \(0.0586651\pi\)
\(284\) 0 0
\(285\) −72675.2 + 2599.09i −0.894739 + 0.0319986i
\(286\) 0 0
\(287\) −76091.7 + 43931.5i −0.923790 + 0.533350i
\(288\) 0 0
\(289\) −21257.9 + 36819.7i −0.254521 + 0.440843i
\(290\) 0 0
\(291\) 43237.1 133452.i 0.510588 1.57594i
\(292\) 0 0
\(293\) 24682.6 4352.21i 0.287512 0.0506961i −0.0280322 0.999607i \(-0.508924\pi\)
0.315544 + 0.948911i \(0.397813\pi\)
\(294\) 0 0
\(295\) −168517. 141402.i −1.93642 1.62485i
\(296\) 0 0
\(297\) 590.016 8755.09i 0.00668884 0.0992539i
\(298\) 0 0
\(299\) −55032.5 + 65585.1i −0.615569 + 0.733606i
\(300\) 0 0
\(301\) −19256.7 109210.i −0.212544 1.20540i
\(302\) 0 0
\(303\) 90910.8 81995.0i 0.990216 0.893104i
\(304\) 0 0
\(305\) 176282. + 101776.i 1.89499 + 1.09407i
\(306\) 0 0
\(307\) 35159.3 + 60897.6i 0.373046 + 0.646135i 0.990033 0.140839i \(-0.0449799\pi\)
−0.616986 + 0.786974i \(0.711647\pi\)
\(308\) 0 0
\(309\) 111893. 70049.2i 1.17188 0.733645i
\(310\) 0 0
\(311\) −49685.8 59213.2i −0.513702 0.612207i 0.445377 0.895343i \(-0.353070\pi\)
−0.959080 + 0.283136i \(0.908625\pi\)
\(312\) 0 0
\(313\) 143003. 52048.7i 1.45967 0.531277i 0.514397 0.857552i \(-0.328016\pi\)
0.945275 + 0.326275i \(0.105794\pi\)
\(314\) 0 0
\(315\) −29267.7 + 102721.i −0.294963 + 1.03523i
\(316\) 0 0
\(317\) 12789.7 + 2255.17i 0.127275 + 0.0224419i 0.236923 0.971529i \(-0.423861\pi\)
−0.109648 + 0.993970i \(0.534972\pi\)
\(318\) 0 0
\(319\) −9204.54 3350.18i −0.0904525 0.0329220i
\(320\) 0 0
\(321\) 57464.3 + 44818.2i 0.557684 + 0.434955i
\(322\) 0 0
\(323\) 39825.1i 0.381726i
\(324\) 0 0
\(325\) −126704. −1.19956
\(326\) 0 0
\(327\) 74174.1 95103.3i 0.693676 0.889406i
\(328\) 0 0
\(329\) −996.384 + 2737.54i −0.00920524 + 0.0252912i
\(330\) 0 0
\(331\) −5541.63 + 31428.2i −0.0505803 + 0.286855i −0.999598 0.0283690i \(-0.990969\pi\)
0.949017 + 0.315224i \(0.102080\pi\)
\(332\) 0 0
\(333\) −109585. + 106182.i −0.988238 + 0.957549i
\(334\) 0 0
\(335\) 10299.9 + 28298.7i 0.0917789 + 0.252161i
\(336\) 0 0
\(337\) −82087.2 + 68879.3i −0.722796 + 0.606498i −0.928157 0.372188i \(-0.878608\pi\)
0.205361 + 0.978686i \(0.434163\pi\)
\(338\) 0 0
\(339\) 103357. + 165096.i 0.899371 + 1.43660i
\(340\) 0 0
\(341\) 1705.03 984.399i 0.0146630 0.00846569i
\(342\) 0 0
\(343\) −60529.8 + 104841.i −0.514494 + 0.891131i
\(344\) 0 0
\(345\) 177882. + 197224.i 1.49449 + 1.65700i
\(346\) 0 0
\(347\) −52650.6 + 9283.71i −0.437264 + 0.0771015i −0.387947 0.921682i \(-0.626816\pi\)
−0.0493173 + 0.998783i \(0.515705\pi\)
\(348\) 0 0
\(349\) −67043.3 56256.0i −0.550433 0.461868i 0.324654 0.945833i \(-0.394752\pi\)
−0.875088 + 0.483964i \(0.839196\pi\)
\(350\) 0 0
\(351\) 83467.2 24162.0i 0.677488 0.196118i
\(352\) 0 0
\(353\) −77840.5 + 92766.7i −0.624678 + 0.744462i −0.981867 0.189570i \(-0.939291\pi\)
0.357189 + 0.934032i \(0.383735\pi\)
\(354\) 0 0
\(355\) −27610.0 156584.i −0.219084 1.24249i
\(356\) 0 0
\(357\) 55644.9 + 18028.4i 0.436605 + 0.141456i
\(358\) 0 0
\(359\) 192373. + 111067.i 1.49264 + 0.861777i 0.999964 0.00843513i \(-0.00268502\pi\)
0.492677 + 0.870212i \(0.336018\pi\)
\(360\) 0 0
\(361\) 45821.0 + 79364.4i 0.351601 + 0.608991i
\(362\) 0 0
\(363\) 4662.85 + 130382.i 0.0353865 + 0.989471i
\(364\) 0 0
\(365\) 63345.7 + 75492.5i 0.475479 + 0.566654i
\(366\) 0 0
\(367\) 29765.6 10833.8i 0.220995 0.0804356i −0.229150 0.973391i \(-0.573595\pi\)
0.450145 + 0.892956i \(0.351372\pi\)
\(368\) 0 0
\(369\) 130036. 179614.i 0.955019 1.31913i
\(370\) 0 0
\(371\) −26680.5 4704.50i −0.193841 0.0341795i
\(372\) 0 0
\(373\) −136230. 49583.8i −0.979167 0.356387i −0.197650 0.980273i \(-0.563331\pi\)
−0.781516 + 0.623885i \(0.785553\pi\)
\(374\) 0 0
\(375\) −22404.3 + 160394.i −0.159320 + 1.14058i
\(376\) 0 0
\(377\) 96997.8i 0.682463i
\(378\) 0 0
\(379\) 23022.1 0.160275 0.0801375 0.996784i \(-0.474464\pi\)
0.0801375 + 0.996784i \(0.474464\pi\)
\(380\) 0 0
\(381\) −96831.0 239086.i −0.667060 1.64704i
\(382\) 0 0
\(383\) −3524.06 + 9682.28i −0.0240240 + 0.0660055i −0.951125 0.308806i \(-0.900070\pi\)
0.927101 + 0.374812i \(0.122293\pi\)
\(384\) 0 0
\(385\) −2756.19 + 15631.1i −0.0185946 + 0.105455i
\(386\) 0 0
\(387\) 156892. + 231760.i 1.04756 + 1.54745i
\(388\) 0 0
\(389\) 7973.83 + 21907.9i 0.0526948 + 0.144778i 0.963248 0.268615i \(-0.0865659\pi\)
−0.910553 + 0.413393i \(0.864344\pi\)
\(390\) 0 0
\(391\) 111420. 93492.4i 0.728802 0.611537i
\(392\) 0 0
\(393\) 32176.5 60638.2i 0.208331 0.392610i
\(394\) 0 0
\(395\) −150410. + 86839.2i −0.964012 + 0.556573i
\(396\) 0 0
\(397\) 73141.1 126684.i 0.464067 0.803787i −0.535092 0.844794i \(-0.679723\pi\)
0.999159 + 0.0410065i \(0.0130564\pi\)
\(398\) 0 0
\(399\) −55557.7 + 11858.0i −0.348978 + 0.0744845i
\(400\) 0 0
\(401\) 8594.38 1515.42i 0.0534473 0.00942420i −0.146861 0.989157i \(-0.546917\pi\)
0.200308 + 0.979733i \(0.435806\pi\)
\(402\) 0 0
\(403\) 14934.8 + 12531.8i 0.0919582 + 0.0771621i
\(404\) 0 0
\(405\) −38413.4 266808.i −0.234192 1.62663i
\(406\) 0 0
\(407\) −14575.5 + 17370.3i −0.0879900 + 0.104862i
\(408\) 0 0
\(409\) 36219.7 + 205412.i 0.216520 + 1.22795i 0.878249 + 0.478204i \(0.158712\pi\)
−0.661729 + 0.749743i \(0.730177\pi\)
\(410\) 0 0
\(411\) −52908.2 247888.i −0.313213 1.46748i
\(412\) 0 0
\(413\) −148824. 85923.6i −0.872515 0.503747i
\(414\) 0 0
\(415\) −216763. 375445.i −1.25860 2.17997i
\(416\) 0 0
\(417\) 123879. + 65733.9i 0.712401 + 0.378022i
\(418\) 0 0
\(419\) −38386.2 45746.9i −0.218649 0.260576i 0.645559 0.763710i \(-0.276624\pi\)
−0.864208 + 0.503135i \(0.832180\pi\)
\(420\) 0 0
\(421\) 98284.1 35772.5i 0.554523 0.201830i −0.0495322 0.998773i \(-0.515773\pi\)
0.604055 + 0.796943i \(0.293551\pi\)
\(422\) 0 0
\(423\) −525.209 7333.50i −0.00293529 0.0409856i
\(424\) 0 0
\(425\) 211982. + 37378.1i 1.17360 + 0.206937i
\(426\) 0 0
\(427\) 149422. + 54385.3i 0.819521 + 0.298281i
\(428\) 0 0
\(429\) 11968.5 4847.31i 0.0650317 0.0263382i
\(430\) 0 0
\(431\) 92728.7i 0.499183i 0.968351 + 0.249591i \(0.0802963\pi\)
−0.968351 + 0.249591i \(0.919704\pi\)
\(432\) 0 0
\(433\) 48094.2 0.256517 0.128259 0.991741i \(-0.459061\pi\)
0.128259 + 0.991741i \(0.459061\pi\)
\(434\) 0 0
\(435\) −298009. 41626.9i −1.57489 0.219986i
\(436\) 0 0
\(437\) −48314.5 + 132743.i −0.252997 + 0.695103i
\(438\) 0 0
\(439\) −4555.68 + 25836.5i −0.0236387 + 0.134062i −0.994343 0.106215i \(-0.966127\pi\)
0.970705 + 0.240276i \(0.0772381\pi\)
\(440\) 0 0
\(441\) 11421.4 110455.i 0.0587276 0.567946i
\(442\) 0 0
\(443\) −11637.5 31973.7i −0.0592995 0.162924i 0.906505 0.422195i \(-0.138740\pi\)
−0.965805 + 0.259271i \(0.916518\pi\)
\(444\) 0 0
\(445\) −160287. + 134496.i −0.809426 + 0.679189i
\(446\) 0 0
\(447\) −123376. + 4412.32i −0.617472 + 0.0220827i
\(448\) 0 0
\(449\) −324556. + 187382.i −1.60989 + 0.929472i −0.620500 + 0.784206i \(0.713070\pi\)
−0.989393 + 0.145266i \(0.953596\pi\)
\(450\) 0 0
\(451\) 16476.1 28537.5i 0.0810033 0.140302i
\(452\) 0 0
\(453\) 42501.4 131181.i 0.207113 0.639258i
\(454\) 0 0
\(455\) −154787. + 27293.2i −0.747675 + 0.131835i
\(456\) 0 0
\(457\) 51282.0 + 43030.7i 0.245546 + 0.206038i 0.757252 0.653123i \(-0.226542\pi\)
−0.511706 + 0.859161i \(0.670986\pi\)
\(458\) 0 0
\(459\) −146773. + 15801.0i −0.696658 + 0.0749998i
\(460\) 0 0
\(461\) 170802. 203553.i 0.803693 0.957804i −0.196048 0.980594i \(-0.562811\pi\)
0.999740 + 0.0227907i \(0.00725514\pi\)
\(462\) 0 0
\(463\) 39061.0 + 221526.i 0.182214 + 1.03339i 0.929483 + 0.368865i \(0.120253\pi\)
−0.747269 + 0.664521i \(0.768635\pi\)
\(464\) 0 0
\(465\) 44911.2 40506.7i 0.207706 0.187336i
\(466\) 0 0
\(467\) 187102. + 108023.i 0.857916 + 0.495318i 0.863314 0.504667i \(-0.168385\pi\)
−0.00539770 + 0.999985i \(0.501718\pi\)
\(468\) 0 0
\(469\) 11762.6 + 20373.5i 0.0534760 + 0.0926231i
\(470\) 0 0
\(471\) −335711. + 210169.i −1.51330 + 0.947384i
\(472\) 0 0
\(473\) 26733.7 + 31859.9i 0.119491 + 0.142404i
\(474\) 0 0
\(475\) −196449. + 71501.5i −0.870687 + 0.316904i
\(476\) 0 0
\(477\) 66314.9 16652.7i 0.291457 0.0731895i
\(478\) 0 0
\(479\) −23419.4 4129.47i −0.102071 0.0179980i 0.122379 0.992483i \(-0.460948\pi\)
−0.224451 + 0.974485i \(0.572059\pi\)
\(480\) 0 0
\(481\) −211002. 76798.3i −0.912002 0.331942i
\(482\) 0 0
\(483\) 163601. + 127598.i 0.701281 + 0.546952i
\(484\) 0 0
\(485\) 640386.i 2.72244i
\(486\) 0 0
\(487\) 211780. 0.892951 0.446476 0.894796i \(-0.352679\pi\)
0.446476 + 0.894796i \(0.352679\pi\)
\(488\) 0 0
\(489\) −255349. + 327399.i −1.06787 + 1.36918i
\(490\) 0 0
\(491\) 104745. 287783.i 0.434479 1.19372i −0.508556 0.861029i \(-0.669821\pi\)
0.943035 0.332692i \(-0.107957\pi\)
\(492\) 0 0
\(493\) −28614.7 + 162282.i −0.117732 + 0.667693i
\(494\) 0 0
\(495\) −9756.22 38851.5i −0.0398172 0.158561i
\(496\) 0 0
\(497\) −42481.7 116718.i −0.171985 0.472524i
\(498\) 0 0
\(499\) −172810. + 145005.i −0.694015 + 0.582348i −0.920064 0.391768i \(-0.871863\pi\)
0.226049 + 0.974116i \(0.427419\pi\)
\(500\) 0 0
\(501\) −145265. 232037.i −0.578741 0.924448i
\(502\) 0 0
\(503\) −173648. + 100256.i −0.686333 + 0.396254i −0.802237 0.597006i \(-0.796357\pi\)
0.115904 + 0.993260i \(0.463023\pi\)
\(504\) 0 0
\(505\) 279436. 483998.i 1.09572 1.89784i
\(506\) 0 0
\(507\) −86518.6 95926.2i −0.336584 0.373183i
\(508\) 0 0
\(509\) −208089. + 36691.7i −0.803181 + 0.141622i −0.560145 0.828395i \(-0.689255\pi\)
−0.243036 + 0.970017i \(0.578143\pi\)
\(510\) 0 0
\(511\) 58973.6 + 49484.7i 0.225848 + 0.189509i
\(512\) 0 0
\(513\) 115777. 84564.5i 0.439936 0.321331i
\(514\) 0 0
\(515\) 387363. 461641.i 1.46051 1.74057i
\(516\) 0 0
\(517\) −189.725 1075.98i −0.000709812 0.00402555i
\(518\) 0 0
\(519\) 120934. + 39181.4i 0.448966 + 0.145460i
\(520\) 0 0
\(521\) 162900. + 94050.5i 0.600131 + 0.346486i 0.769093 0.639137i \(-0.220708\pi\)
−0.168962 + 0.985623i \(0.554041\pi\)
\(522\) 0 0
\(523\) −140142. 242732.i −0.512346 0.887410i −0.999898 0.0143156i \(-0.995443\pi\)
0.487551 0.873094i \(-0.337890\pi\)
\(524\) 0 0
\(525\) 10974.0 + 306852.i 0.0398149 + 1.11330i
\(526\) 0 0
\(527\) −21289.8 25372.2i −0.0766568 0.0913560i
\(528\) 0 0
\(529\) 221837. 80742.0i 0.792725 0.288528i
\(530\) 0 0
\(531\) 431400. + 44608.3i 1.53000 + 0.158207i
\(532\) 0 0
\(533\) 321353. + 56663.2i 1.13117 + 0.199456i
\(534\) 0 0
\(535\) 312614. + 113782.i 1.09220 + 0.397527i
\(536\) 0 0
\(537\) −8743.03 + 62591.9i −0.0303189 + 0.217055i
\(538\) 0 0
\(539\) 16501.6i 0.0568000i
\(540\) 0 0
\(541\) −438601. −1.49856 −0.749281 0.662252i \(-0.769601\pi\)
−0.749281 + 0.662252i \(0.769601\pi\)
\(542\) 0 0
\(543\) −36864.8 91023.1i −0.125030 0.308711i
\(544\) 0 0
\(545\) 188309. 517375.i 0.633984 1.74186i
\(546\) 0 0
\(547\) −22416.7 + 127132.i −0.0749200 + 0.424892i 0.924160 + 0.382006i \(0.124767\pi\)
−0.999080 + 0.0428866i \(0.986345\pi\)
\(548\) 0 0
\(549\) −400282. + 28667.3i −1.32807 + 0.0951135i
\(550\) 0 0
\(551\) −54737.9 150391.i −0.180295 0.495358i
\(552\) 0 0
\(553\) −103933. + 87210.1i −0.339862 + 0.285178i
\(554\) 0 0
\(555\) −326502. + 615309.i −1.05999 + 1.99759i
\(556\) 0 0
\(557\) −365276. + 210892.i −1.17737 + 0.679752i −0.955404 0.295303i \(-0.904579\pi\)
−0.221962 + 0.975055i \(0.571246\pi\)
\(558\) 0 0
\(559\) −205924. + 356670.i −0.658996 + 1.14141i
\(560\) 0 0
\(561\) −21453.9 + 4579.03i −0.0681679 + 0.0145495i
\(562\) 0 0
\(563\) −270231. + 47648.9i −0.852546 + 0.150327i −0.582811 0.812608i \(-0.698047\pi\)
−0.269735 + 0.962935i \(0.586936\pi\)
\(564\) 0 0
\(565\) 681145. + 571549.i 2.13375 + 1.79043i
\(566\) 0 0
\(567\) −65744.9 200049.i −0.204501 0.622258i
\(568\) 0 0
\(569\) 100787. 120113.i 0.311300 0.370993i −0.587597 0.809154i \(-0.699926\pi\)
0.898896 + 0.438162i \(0.144370\pi\)
\(570\) 0 0
\(571\) 60411.6 + 342611.i 0.185288 + 1.05082i 0.925584 + 0.378541i \(0.123574\pi\)
−0.740296 + 0.672281i \(0.765315\pi\)
\(572\) 0 0
\(573\) 89359.7 + 418672.i 0.272165 + 1.27516i
\(574\) 0 0
\(575\) 661220. + 381756.i 1.99991 + 1.15465i
\(576\) 0 0
\(577\) 288340. + 499420.i 0.866071 + 1.50008i 0.865980 + 0.500079i \(0.166696\pi\)
9.13367e−5 1.00000i \(0.499971\pi\)
\(578\) 0 0
\(579\) −345782. 183483.i −1.03144 0.547315i
\(580\) 0 0
\(581\) −217689. 259432.i −0.644888 0.768548i
\(582\) 0 0
\(583\) 9547.90 3475.15i 0.0280912 0.0102244i
\(584\) 0 0
\(585\) 328482. 222369.i 0.959843 0.649775i
\(586\) 0 0
\(587\) 318374. + 56137.9i 0.923978 + 0.162922i 0.615344 0.788259i \(-0.289017\pi\)
0.308634 + 0.951181i \(0.400128\pi\)
\(588\) 0 0
\(589\) 30227.8 + 11002.0i 0.0871318 + 0.0317134i
\(590\) 0 0
\(591\) 109870. 44497.9i 0.314560 0.127398i
\(592\) 0 0
\(593\) 101060.i 0.287388i 0.989622 + 0.143694i \(0.0458982\pi\)
−0.989622 + 0.143694i \(0.954102\pi\)
\(594\) 0 0
\(595\) 267019. 0.754237
\(596\) 0 0
\(597\) −311310. 43484.7i −0.873463 0.122008i
\(598\) 0 0
\(599\) −150516. + 413539.i −0.419497 + 1.15256i 0.532494 + 0.846434i \(0.321255\pi\)
−0.951991 + 0.306125i \(0.900967\pi\)
\(600\) 0 0
\(601\) 119609. 678335.i 0.331142 1.87800i −0.131289 0.991344i \(-0.541912\pi\)
0.462431 0.886655i \(-0.346977\pi\)
\(602\) 0 0
\(603\) −48091.6 34817.1i −0.132262 0.0957543i
\(604\) 0 0
\(605\) 203698. + 559656.i 0.556515 + 1.52901i
\(606\) 0 0
\(607\) −109880. + 92199.9i −0.298222 + 0.250238i −0.779604 0.626273i \(-0.784580\pi\)
0.481382 + 0.876511i \(0.340135\pi\)
\(608\) 0 0
\(609\) −234910. + 8401.11i −0.633384 + 0.0226518i
\(610\) 0 0
\(611\) 9369.80 5409.66i 0.0250985 0.0144906i
\(612\) 0 0
\(613\) 172287. 298409.i 0.458491 0.794130i −0.540390 0.841414i \(-0.681723\pi\)
0.998881 + 0.0472845i \(0.0150567\pi\)
\(614\) 0 0
\(615\) 311998. 962987.i 0.824900 2.54607i
\(616\) 0 0
\(617\) 678405. 119621.i 1.78204 0.314223i 0.817065 0.576546i \(-0.195600\pi\)
0.964980 + 0.262324i \(0.0844888\pi\)
\(618\) 0 0
\(619\) 499982. + 419535.i 1.30489 + 1.09493i 0.989278 + 0.146042i \(0.0466534\pi\)
0.315610 + 0.948889i \(0.397791\pi\)
\(620\) 0 0
\(621\) −508385. 125393.i −1.31828 0.325154i
\(622\) 0 0
\(623\) −105066. + 125213.i −0.270700 + 0.322608i
\(624\) 0 0
\(625\) 13014.0 + 73805.8i 0.0333157 + 0.188943i
\(626\) 0 0
\(627\) 15821.2 14269.6i 0.0402444 0.0362976i
\(628\) 0 0
\(629\) 330361. + 190734.i 0.835001 + 0.482088i
\(630\) 0 0
\(631\) 45688.2 + 79134.3i 0.114748 + 0.198749i 0.917679 0.397323i \(-0.130061\pi\)
−0.802931 + 0.596072i \(0.796727\pi\)
\(632\) 0 0
\(633\) −415949. + 260401.i −1.03808 + 0.649882i
\(634\) 0 0
\(635\) −756911. 902052.i −1.87714 2.23709i
\(636\) 0 0
\(637\) 153553. 55888.6i 0.378424 0.137735i
\(638\) 0 0
\(639\) 218135. + 225126.i 0.534223 + 0.551345i
\(640\) 0 0
\(641\) −736459. 129858.i −1.79239 0.316047i −0.824206 0.566290i \(-0.808378\pi\)
−0.968183 + 0.250243i \(0.919489\pi\)
\(642\) 0 0
\(643\) −378214. 137659.i −0.914779 0.332952i −0.158620 0.987340i \(-0.550704\pi\)
−0.756159 + 0.654387i \(0.772927\pi\)
\(644\) 0 0
\(645\) 1.00744e6 + 785732.i 2.42158 + 1.88867i
\(646\) 0 0
\(647\) 363926.i 0.869371i 0.900582 + 0.434685i \(0.143140\pi\)
−0.900582 + 0.434685i \(0.856860\pi\)
\(648\) 0 0
\(649\) 64449.8 0.153014
\(650\) 0 0
\(651\) 29056.2 37254.8i 0.0685609 0.0879063i
\(652\) 0 0
\(653\) −25486.2 + 70022.7i −0.0597693 + 0.164215i −0.965983 0.258605i \(-0.916737\pi\)
0.906214 + 0.422819i \(0.138960\pi\)
\(654\) 0 0
\(655\) 54416.3 308610.i 0.126837 0.719330i
\(656\) 0 0
\(657\) −186853. 53239.3i −0.432883 0.123339i
\(658\) 0 0
\(659\) −201632. 553979.i −0.464289 1.27562i −0.922230 0.386642i \(-0.873635\pi\)
0.457941 0.888983i \(-0.348587\pi\)
\(660\) 0 0
\(661\) −101124. + 84853.5i −0.231448 + 0.194208i −0.751135 0.660149i \(-0.770493\pi\)
0.519687 + 0.854357i \(0.326049\pi\)
\(662\) 0 0
\(663\) −115271. 184127.i −0.262236 0.418880i
\(664\) 0 0
\(665\) −224590. + 129667.i −0.507863 + 0.293215i
\(666\) 0 0
\(667\) −292253. + 506196.i −0.656911 + 1.13780i
\(668\) 0 0
\(669\) 202454. + 224468.i 0.452350 + 0.501536i
\(670\) 0 0
\(671\) −58730.1 + 10355.7i −0.130441 + 0.0230003i
\(672\) 0 0
\(673\) 338696. + 284200.i 0.747791 + 0.627471i 0.934918 0.354865i \(-0.115473\pi\)
−0.187127 + 0.982336i \(0.559918\pi\)
\(674\) 0 0
\(675\) −341457. 695629.i −0.749426 1.52676i
\(676\) 0 0
\(677\) −158293. + 188647.i −0.345370 + 0.411596i −0.910568 0.413359i \(-0.864355\pi\)
0.565198 + 0.824955i \(0.308800\pi\)
\(678\) 0 0
\(679\) −86869.1 492659.i −0.188420 1.06858i
\(680\) 0 0
\(681\) −54903.3 17788.1i −0.118387 0.0383562i
\(682\) 0 0
\(683\) 385117. + 222347.i 0.825565 + 0.476640i 0.852332 0.523002i \(-0.175188\pi\)
−0.0267669 + 0.999642i \(0.508521\pi\)
\(684\) 0 0
\(685\) −578550. 1.00208e6i −1.23299 2.13560i
\(686\) 0 0
\(687\) 5458.75 + 152636.i 0.0115659 + 0.323404i
\(688\) 0 0
\(689\) 64674.8 + 77076.4i 0.136237 + 0.162361i
\(690\) 0 0
\(691\) −260760. + 94909.0i −0.546117 + 0.198770i −0.600320 0.799760i \(-0.704960\pi\)
0.0542035 + 0.998530i \(0.482738\pi\)
\(692\) 0 0
\(693\) −12775.9 28565.6i −0.0266026 0.0594809i
\(694\) 0 0
\(695\) 630465. + 111168.i 1.30524 + 0.230149i
\(696\) 0 0
\(697\) −520924. 189601.i −1.07228 0.390279i
\(698\) 0 0
\(699\) −26123.7 + 187021.i −0.0534664 + 0.382769i
\(700\) 0 0
\(701\) 589634.i 1.19990i −0.800036 0.599952i \(-0.795186\pi\)
0.800036 0.599952i \(-0.204814\pi\)
\(702\) 0 0
\(703\) −370489. −0.749660
\(704\) 0 0
\(705\) −12599.2 31108.7i −0.0253492 0.0625899i
\(706\) 0 0
\(707\) 149320. 410253.i 0.298730 0.820755i
\(708\) 0 0
\(709\) 17459.5 99017.7i 0.0347327 0.196979i −0.962504 0.271267i \(-0.912557\pi\)
0.997237 + 0.0742880i \(0.0236684\pi\)
\(710\) 0 0
\(711\) 149585. 308008.i 0.295902 0.609289i
\(712\) 0 0
\(713\) −40181.4 110397.i −0.0790398 0.217160i
\(714\) 0 0
\(715\) 45156.2 37890.5i 0.0883294 0.0741172i
\(716\) 0 0
\(717\) −72859.2 + 137307.i −0.141725 + 0.267088i
\(718\) 0 0
\(719\) −706697. + 408012.i −1.36702 + 0.789250i −0.990547 0.137176i \(-0.956197\pi\)
−0.376475 + 0.926427i \(0.622864\pi\)
\(720\) 0 0
\(721\) 235383. 407695.i 0.452797 0.784268i
\(722\) 0 0
\(723\) 312837. 66770.7i 0.598470 0.127735i
\(724\) 0 0
\(725\) −851878. + 150209.i −1.62069 + 0.285772i
\(726\) 0 0
\(727\) −295988. 248363.i −0.560022 0.469914i 0.318296 0.947991i \(-0.396889\pi\)
−0.878318 + 0.478077i \(0.841334\pi\)
\(728\) 0 0
\(729\) 357592. + 393138.i 0.672873 + 0.739758i
\(730\) 0 0
\(731\) 449740. 535979.i 0.841640 1.00303i
\(732\) 0 0
\(733\) −21566.7 122311.i −0.0401399 0.227645i 0.958138 0.286307i \(-0.0924277\pi\)
−0.998278 + 0.0586621i \(0.981317\pi\)
\(734\) 0 0
\(735\) −105811. 495749.i −0.195864 0.917672i
\(736\) 0 0
\(737\) −7640.90 4411.47i −0.0140673 0.00812173i
\(738\) 0 0
\(739\) 42912.2 + 74326.1i 0.0785763 + 0.136098i 0.902636 0.430405i \(-0.141629\pi\)
−0.824060 + 0.566503i \(0.808296\pi\)
\(740\) 0 0
\(741\) 186368. + 98892.5i 0.339418 + 0.180106i
\(742\) 0 0
\(743\) 146820. + 174974.i 0.265956 + 0.316953i 0.882450 0.470405i \(-0.155892\pi\)
−0.616495 + 0.787359i \(0.711448\pi\)
\(744\) 0 0
\(745\) −529587. + 192754.i −0.954167 + 0.347288i
\(746\) 0 0
\(747\) 768834. + 373385.i 1.37782 + 0.669138i
\(748\) 0 0
\(749\) 255934. + 45128.0i 0.456209 + 0.0804419i
\(750\) 0 0
\(751\) −518723. 188800.i −0.919719 0.334750i −0.161592 0.986858i \(-0.551663\pi\)
−0.758127 + 0.652107i \(0.773885\pi\)
\(752\) 0 0
\(753\) 523370. 211967.i 0.923036 0.373834i
\(754\) 0 0
\(755\) 629490.i 1.10432i
\(756\) 0 0
\(757\) −291561. −0.508788 −0.254394 0.967101i \(-0.581876\pi\)
−0.254394 + 0.967101i \(0.581876\pi\)
\(758\) 0 0
\(759\) −77064.2 10764.6i −0.133773 0.0186858i
\(760\) 0 0
\(761\) 40839.4 112205.i 0.0705197 0.193751i −0.899426 0.437073i \(-0.856015\pi\)
0.969946 + 0.243322i \(0.0782372\pi\)
\(762\) 0 0
\(763\) 74686.8 423570.i 0.128291 0.727572i
\(764\) 0 0
\(765\) −615167. + 275131.i −1.05116 + 0.470129i
\(766\) 0 0
\(767\) 218283. + 599726.i 0.371046 + 1.01944i
\(768\) 0 0
\(769\) −625266. + 524661.i −1.05733 + 0.887209i −0.993846 0.110774i \(-0.964667\pi\)
−0.0634883 + 0.997983i \(0.520223\pi\)
\(770\) 0 0
\(771\) −608856. + 21774.6i −1.02425 + 0.0366303i
\(772\) 0 0
\(773\) −893014. + 515582.i −1.49451 + 0.862856i −0.999980 0.00630343i \(-0.997994\pi\)
−0.494531 + 0.869160i \(0.664660\pi\)
\(774\) 0 0
\(775\) 86932.2 150571.i 0.144736 0.250691i
\(776\) 0 0
\(777\) −167716. + 517658.i −0.277800 + 0.857434i
\(778\) 0 0
\(779\) 530221. 93492.4i 0.873740 0.154064i
\(780\) 0 0
\(781\) 35684.8 + 29943.1i 0.0585034 + 0.0490902i
\(782\) 0