Properties

Label 108.5.k.a.5.4
Level 108
Weight 5
Character 108.5
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 5.4
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.4

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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 −0.816586 0.577223i \(-0.804136\pi\)
0.254509 0.967070i \(-0.418086\pi\)
\(6\) 0 0
\(7\) −5.57324 31.6074i −0.113740 0.645050i −0.987367 0.158453i \(-0.949349\pi\)
0.873627 0.486596i \(-0.161762\pi\)
\(8\) 0 0
\(9\) −19.7279 + 78.5609i −0.243554 + 0.969887i
\(10\) 0 0
\(11\) −4.11688 + 11.3110i −0.0340238 + 0.0934797i −0.955541 0.294857i \(-0.904728\pi\)
0.921518 + 0.388337i \(0.126950\pi\)
\(12\) 0 0
\(13\) 91.3096 + 76.6178i 0.540293 + 0.453360i 0.871638 0.490150i \(-0.163058\pi\)
−0.331345 + 0.943510i \(0.607502\pi\)
\(14\) 0 0
\(15\) −196.210 + 313.414i −0.872043 + 1.39295i
\(16\) 0 0
\(17\) −175.368 101.249i −0.606810 0.350342i 0.164906 0.986309i \(-0.447268\pi\)
−0.771716 + 0.635967i \(0.780601\pi\)
\(18\) 0 0
\(19\) 98.3348 + 170.321i 0.272395 + 0.471803i 0.969475 0.245191i \(-0.0788508\pi\)
−0.697079 + 0.716994i \(0.745517\pi\)
\(20\) 0 0
\(21\) −193.462 + 214.499i −0.438690 + 0.486391i
\(22\) 0 0
\(23\) −707.360 124.727i −1.33716 0.235778i −0.541084 0.840969i \(-0.681986\pi\)
−0.796081 + 0.605191i \(0.793097\pi\)
\(24\) 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 0.981408 0.191932i \(-0.0614754\pi\)
−0.359436 + 0.933170i \(0.617031\pi\)
\(30\) 0 0
\(31\) 28.4024 161.078i 0.0295550 0.167615i −0.966458 0.256826i \(-0.917323\pi\)
0.996013 + 0.0892109i \(0.0284345\pi\)
\(32\) 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 0.284451 + 0.958691i \(0.408189\pi\)
−0.972476 + 0.233004i \(0.925145\pi\)
\(38\) 0 0
\(39\) 38.3409 1072.08i 0.0252077 0.704852i
\(40\) 0 0
\(41\) 1759.69 2097.12i 1.04681 1.24754i 0.0787328 0.996896i \(-0.474913\pi\)
0.968079 0.250646i \(-0.0806429\pi\)
\(42\) 0 0
\(43\) −3246.83 1181.75i −1.75599 0.639129i −0.756110 0.654444i \(-0.772903\pi\)
−0.999883 + 0.0153148i \(0.995125\pi\)
\(44\) 0 0
\(45\) 3310.24 342.290i 1.63469 0.169032i
\(46\) 0 0
\(47\) 89.3900 15.7619i 0.0404663 0.00713530i −0.153378 0.988168i \(-0.549015\pi\)
0.193845 + 0.981032i \(0.437904\pi\)
\(48\) 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 \(-0.951991\pi\)
0.988648 0.150253i \(-0.0480088\pi\)
\(54\) 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 −0.863649 0.504094i \(-0.831826\pi\)
0.337568 0.941301i \(-0.390396\pi\)
\(60\) 0 0
\(61\) 860.325 + 4879.15i 0.231208 + 1.31125i 0.850454 + 0.526049i \(0.176327\pi\)
−0.619246 + 0.785197i \(0.712562\pi\)
\(62\) 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 0.703184 0.711008i \(-0.251761\pi\)
−0.578100 + 0.815966i \(0.696206\pi\)
\(68\) 0 0
\(69\) 3030.07 + 5710.32i 0.636436 + 1.19940i
\(70\) 0 0
\(71\) −3351.53 1935.01i −0.664855 0.383854i 0.129270 0.991609i \(-0.458737\pi\)
−0.794124 + 0.607756i \(0.792070\pi\)
\(72\) 0 0
\(73\) 1199.32 + 2077.29i 0.225056 + 0.389808i 0.956336 0.292269i \(-0.0944103\pi\)
−0.731280 + 0.682077i \(0.761077\pi\)
\(74\) 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 −0.345365 0.938468i \(-0.612245\pi\)
0.864239 + 0.503082i \(0.167801\pi\)
\(80\) 0 0
\(81\) −5782.62 3099.68i −0.881363 0.472440i
\(82\) 0 0
\(83\) −6782.64 8083.24i −0.984561 1.17335i −0.984859 0.173355i \(-0.944539\pi\)
0.000298097 1.00000i \(-0.499905\pi\)
\(84\) 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 −0.195052 0.980793i \(-0.562488\pi\)
0.751865 + 0.659317i \(0.229154\pi\)
\(90\) 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 −0.586709 0.809798i \(-0.699577\pi\)
−0.969973 + 0.243212i \(0.921799\pi\)
\(98\) 0 0
\(99\) −807.388 546.569i −0.0823781 0.0557666i
\(100\) 0 0
\(101\) −13396.2 + 2362.10i −1.31322 + 0.231556i −0.786028 0.618191i \(-0.787866\pi\)
−0.527191 + 0.849747i \(0.676755\pi\)
\(102\) 0 0
\(103\) −13783.3 + 5016.70i −1.29921 + 0.472872i −0.896738 0.442562i \(-0.854070\pi\)
−0.402468 + 0.915434i \(0.631848\pi\)
\(104\) 0 0
\(105\) 10999.7 + 4454.95i 0.997709 + 0.404077i
\(106\) 0 0
\(107\) 8097.26i 0.707246i 0.935388 + 0.353623i \(0.115050\pi\)
−0.935388 + 0.353623i \(0.884950\pi\)
\(108\) 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 0.788703 + 0.614775i \(0.210753\pi\)
−0.209012 + 0.977913i \(0.567025\pi\)
\(114\) 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 −0.841652 0.540020i \(-0.818417\pi\)
−0.0468449 0.998902i \(-0.514917\pi\)
\(128\) 0 0
\(129\) 9584.57 + 29582.9i 0.575961 + 1.77771i
\(130\) 0 0
\(131\) −7511.50 1324.48i −0.437707 0.0771796i −0.0495477 0.998772i \(-0.515778\pi\)
−0.388160 + 0.921592i \(0.626889\pi\)
\(132\) 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 −0.988721 0.149767i \(-0.952148\pi\)
0.0241978 0.999707i \(-0.492297\pi\)
\(138\) 0 0
\(139\) −2705.80 + 15345.3i −0.140044 + 0.794231i 0.831169 + 0.556020i \(0.187672\pi\)
−0.971213 + 0.238211i \(0.923439\pi\)
\(140\) 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 −0.529994 0.848001i \(-0.677806\pi\)
0.927151 + 0.374688i \(0.122250\pi\)
\(150\) 0 0
\(151\) −14397.6 5240.31i −0.631447 0.229828i 0.00641405 0.999979i \(-0.497958\pi\)
−0.637861 + 0.770152i \(0.720181\pi\)
\(152\) 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 0.684720 0.728806i \(-0.259924\pi\)
0.992994 + 0.118168i \(0.0377022\pi\)
\(158\) 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 −0.974184 0.225756i \(-0.927515\pi\)
0.601155 0.799132i \(-0.294707\pi\)
\(168\) 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 −0.993863 0.110621i \(-0.964716\pi\)
0.832449 + 0.554102i \(0.186938\pi\)
\(174\) 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 0.591889 0.806020i \(-0.298382\pi\)
−0.402089 + 0.915601i \(0.631716\pi\)
\(180\) 0 0
\(181\) −5455.83 9449.78i −0.166534 0.288446i 0.770665 0.637241i \(-0.219924\pi\)
−0.937199 + 0.348795i \(0.886591\pi\)
\(182\) 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 0.999928 + 0.0120095i \(0.00382285\pi\)
−0.161809 + 0.986822i \(0.551733\pi\)
\(192\) 0 0
\(193\) 7552.68 42833.4i 0.202762 1.14992i −0.698161 0.715941i \(-0.745998\pi\)
0.900923 0.433979i \(-0.142891\pi\)
\(194\) 0 0
\(195\) −41928.9 + 13584.6i −1.10267 + 0.357253i
\(196\) 0 0
\(197\) −11406.4 + 6585.49i −0.293911 + 0.169690i −0.639704 0.768621i \(-0.720943\pi\)
0.345793 + 0.938311i \(0.387610\pi\)
\(198\) 0 0
\(199\) 17462.9 30246.6i 0.440971 0.763785i −0.556790 0.830653i \(-0.687967\pi\)
0.997762 + 0.0668682i \(0.0213007\pi\)
\(200\) 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 0.305043 0.952339i \(-0.401329\pi\)
0.845828 + 0.533456i \(0.179107\pi\)
\(212\) 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 0.985595 + 0.169120i \(0.0540927\pi\)
−0.868314 + 0.496015i \(0.834796\pi\)
\(224\) 0 0
\(225\) −37614.2 77451.1i −0.742997 1.52990i
\(226\) 0 0
\(227\) 2193.22 6025.83i 0.0425629 0.116941i −0.916590 0.399828i \(-0.869070\pi\)
0.959153 + 0.282887i \(0.0912922\pi\)
\(228\) 0 0
\(229\) 13000.1 + 10908.4i 0.247900 + 0.208013i 0.758267 0.651944i \(-0.226046\pi\)
−0.510367 + 0.859956i \(0.670491\pi\)
\(230\) 0 0
\(231\) −1629.74 3071.33i −0.0305418 0.0575575i
\(232\) 0 0
\(233\) 18170.9 + 10491.0i 0.334706 + 0.193243i 0.657929 0.753080i \(-0.271433\pi\)
−0.323222 + 0.946323i \(0.604766\pi\)
\(234\) 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 0.320536 0.947236i \(-0.396137\pi\)
−0.0227689 + 0.999741i \(0.507248\pi\)
\(240\) 0 0
\(241\) −27227.2 + 22846.4i −0.468780 + 0.393353i −0.846349 0.532628i \(-0.821205\pi\)
0.377569 + 0.925981i \(0.376760\pi\)
\(242\) 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 −0.864830 0.502065i \(-0.832574\pi\)
0.00238560 + 0.999997i \(0.499241\pi\)
\(252\) 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 −0.328417 0.944533i \(-0.606515\pi\)
0.987212 + 0.159411i \(0.0509594\pi\)
\(258\) 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 −0.954789 0.297285i \(-0.903919\pi\)
−0.795530 + 0.605914i \(0.792808\pi\)
\(264\) 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 \(0.0880865\pi\)
−0.961953 + 0.273213i \(0.911913\pi\)
\(270\) 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 −0.865477 0.500948i \(-0.832985\pi\)
0.641948 0.766748i \(-0.278126\pi\)
\(278\) 0 0
\(279\) 12094.1 + 5409.04i 0.155369 + 0.0694883i
\(280\) 0 0
\(281\) 6829.25 18763.2i 0.0864890 0.237626i −0.888907 0.458088i \(-0.848534\pi\)
0.975396 + 0.220462i \(0.0707565\pi\)
\(282\) 0 0
\(283\) 77950.3 + 65408.0i 0.973296 + 0.816692i 0.983064 0.183260i \(-0.0586651\pi\)
−0.00976888 + 0.999952i \(0.503110\pi\)
\(284\) 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 0.315544 0.948911i \(-0.397813\pi\)
−0.0280322 + 0.999607i \(0.508924\pi\)
\(294\) 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 −0.616986 0.786974i \(-0.711647\pi\)
0.990033 + 0.140839i \(0.0449799\pi\)
\(308\) 0 0
\(309\) 111893. + 70049.2i 1.17188 + 0.733645i
\(310\) 0 0
\(311\) −49685.8 + 59213.2i −0.513702 + 0.612207i −0.959080 0.283136i \(-0.908625\pi\)
0.445377 + 0.895343i \(0.353070\pi\)
\(312\) 0 0
\(313\) 143003. + 52048.7i 1.45967 + 0.531277i 0.945275 0.326275i \(-0.105794\pi\)
0.514397 + 0.857552i \(0.328016\pi\)
\(314\) 0 0
\(315\) −29267.7 102721.i −0.294963 1.03523i
\(316\) 0 0
\(317\) 12789.7 2255.17i 0.127275 0.0224419i −0.109648 0.993970i \(-0.534972\pi\)
0.236923 + 0.971529i \(0.423861\pi\)
\(318\) 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 0.949017 0.315224i \(-0.102080\pi\)
−0.999598 + 0.0283690i \(0.990969\pi\)
\(332\) 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 0.205361 0.978686i \(-0.434163\pi\)
−0.928157 + 0.372188i \(0.878608\pi\)
\(338\) 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 −0.0493173 0.998783i \(-0.515705\pi\)
−0.387947 + 0.921682i \(0.626816\pi\)
\(348\) 0 0
\(349\) −67043.3 + 56256.0i −0.550433 + 0.461868i −0.875088 0.483964i \(-0.839196\pi\)
0.324654 + 0.945833i \(0.394752\pi\)
\(350\) 0 0
\(351\) 83467.2 + 24162.0i 0.677488 + 0.196118i
\(352\) 0 0
\(353\) −77840.5 92766.7i −0.624678 0.744462i 0.357189 0.934032i \(-0.383735\pi\)
−0.981867 + 0.189570i \(0.939291\pi\)
\(354\) 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 0.492677 0.870212i \(-0.336018\pi\)
0.999964 + 0.00843513i \(0.00268502\pi\)
\(360\) 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 0.450145 0.892956i \(-0.351372\pi\)
−0.229150 + 0.973391i \(0.573595\pi\)
\(368\) 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 −0.781516 0.623885i \(-0.785553\pi\)
−0.197650 + 0.980273i \(0.563331\pi\)
\(374\) 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 0.927101 0.374812i \(-0.122293\pi\)
−0.951125 + 0.308806i \(0.900070\pi\)
\(384\) 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 −0.910553 0.413393i \(-0.864344\pi\)
0.963248 + 0.268615i \(0.0865659\pi\)
\(390\) 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 0.999159 0.0410065i \(-0.0130564\pi\)
−0.535092 + 0.844794i \(0.679723\pi\)
\(398\) 0 0
\(399\) −55557.7 11858.0i −0.348978 0.0744845i
\(400\) 0 0
\(401\) 8594.38 + 1515.42i 0.0534473 + 0.00942420i 0.200308 0.979733i \(-0.435806\pi\)
−0.146861 + 0.989157i \(0.546917\pi\)
\(402\) 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 −0.661729 0.749743i \(-0.730177\pi\)
0.878249 0.478204i \(-0.158712\pi\)
\(410\) 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 −0.864208 0.503135i \(-0.832180\pi\)
0.645559 + 0.763710i \(0.276624\pi\)
\(420\) 0 0
\(421\) 98284.1 + 35772.5i 0.554523 + 0.201830i 0.604055 0.796943i \(-0.293551\pi\)
−0.0495322 + 0.998773i \(0.515773\pi\)
\(422\) 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 \(-0.919704\pi\)
0.968351 0.249591i \(-0.0802963\pi\)
\(432\) 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 0.970705 0.240276i \(-0.0772381\pi\)
−0.994343 + 0.106215i \(0.966127\pi\)
\(440\) 0 0
\(441\) 11421.4 + 110455.i 0.0587276 + 0.567946i
\(442\) 0 0
\(443\) −11637.5 + 31973.7i −0.0592995 + 0.162924i −0.965805 0.259271i \(-0.916518\pi\)
0.906505 + 0.422195i \(0.138740\pi\)
\(444\) 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 −0.989393 0.145266i \(-0.953596\pi\)
−0.620500 0.784206i \(-0.713070\pi\)
\(450\) 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 −0.511706 0.859161i \(-0.670986\pi\)
0.757252 + 0.653123i \(0.226542\pi\)
\(458\) 0 0
\(459\) −146773. 15801.0i −0.696658 0.0749998i
\(460\) 0 0
\(461\) 170802. + 203553.i 0.803693 + 0.957804i 0.999740 0.0227907i \(-0.00725514\pi\)
−0.196048 + 0.980594i \(0.562811\pi\)
\(462\) 0 0
\(463\) 39061.0 221526.i 0.182214 1.03339i −0.747269 0.664521i \(-0.768635\pi\)
0.929483 0.368865i \(-0.120253\pi\)
\(464\) 0 0
\(465\) 44911.2 + 40506.7i 0.207706 + 0.187336i
\(466\) 0 0
\(467\) 187102. 108023.i 0.857916 0.495318i −0.00539770 0.999985i \(-0.501718\pi\)
0.863314 + 0.504667i \(0.168385\pi\)
\(468\) 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 −0.224451 0.974485i \(-0.572059\pi\)
0.122379 + 0.992483i \(0.460948\pi\)
\(480\) 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 0.943035 + 0.332692i \(0.107957\pi\)
−0.508556 + 0.861029i \(0.669821\pi\)
\(492\) 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 0.226049 0.974116i \(-0.427419\pi\)
−0.920064 + 0.391768i \(0.871863\pi\)
\(500\) 0 0
\(501\) −145265. + 232037.i −0.578741 + 0.924448i
\(502\) 0 0
\(503\) −173648. 100256.i −0.686333 0.396254i 0.115904 0.993260i \(-0.463023\pi\)
−0.802237 + 0.597006i \(0.796357\pi\)
\(504\) 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 −0.243036 0.970017i \(-0.578143\pi\)
−0.560145 + 0.828395i \(0.689255\pi\)
\(510\) 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 −0.168962 0.985623i \(-0.554041\pi\)
0.769093 + 0.639137i \(0.220708\pi\)
\(522\) 0 0
\(523\) −140142. + 242732.i −0.512346 + 0.887410i 0.487551 + 0.873094i \(0.337890\pi\)
−0.999898 + 0.0143156i \(0.995443\pi\)
\(524\) 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 −0.999080 0.0428866i \(-0.986345\pi\)
0.924160 0.382006i \(-0.124767\pi\)
\(548\) 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 −0.221962 0.975055i \(-0.571246\pi\)
−0.955404 + 0.295303i \(0.904579\pi\)
\(558\) 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 −0.269735 0.962935i \(-0.586936\pi\)
−0.582811 + 0.812608i \(0.698047\pi\)
\(564\) 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 0.898896 0.438162i \(-0.144370\pi\)
−0.587597 + 0.809154i \(0.699926\pi\)
\(570\) 0 0
\(571\) 60411.6 342611.i 0.185288 1.05082i −0.740296 0.672281i \(-0.765315\pi\)
0.925584 0.378541i \(-0.123574\pi\)
\(572\) 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 9.13367e−5 1.00000i \(-0.499971\pi\)
0.865980 0.500079i \(-0.166696\pi\)
\(578\) 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 0.308634 0.951181i \(-0.400128\pi\)
0.615344 + 0.788259i \(0.289017\pi\)
\(588\) 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 \(-0.954102\pi\)
0.989622 0.143694i \(-0.0458982\pi\)
\(594\) 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 −0.951991 0.306125i \(-0.900967\pi\)
0.532494 0.846434i \(-0.321255\pi\)
\(600\) 0 0
\(601\) 119609. + 678335.i 0.331142 + 1.87800i 0.462431 + 0.886655i \(0.346977\pi\)
−0.131289 + 0.991344i \(0.541912\pi\)
\(602\) 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 0.481382 0.876511i \(-0.340135\pi\)
−0.779604 + 0.626273i \(0.784580\pi\)
\(608\) 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 0.998881 0.0472845i \(-0.0150567\pi\)
−0.540390 + 0.841414i \(0.681723\pi\)
\(614\) 0 0
\(615\) 311998. + 962987.i 0.824900 + 2.54607i
\(616\) 0 0
\(617\) 678405. + 119621.i 1.78204 + 0.314223i 0.964980 0.262324i \(-0.0844888\pi\)
0.817065 + 0.576546i \(0.195600\pi\)
\(618\) 0 0
\(619\) 499982. 419535.i 1.30489 1.09493i 0.315610 0.948889i \(-0.397791\pi\)
0.989278 0.146042i \(-0.0466534\pi\)
\(620\) 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 −0.802931 0.596072i \(-0.796727\pi\)
0.917679 + 0.397323i \(0.130061\pi\)
\(632\) 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 −0.968183 0.250243i \(-0.919489\pi\)
−0.824206 + 0.566290i \(0.808378\pi\)
\(642\) 0 0
\(643\) −378214. + 137659.i −0.914779 + 0.332952i −0.756159 0.654387i \(-0.772927\pi\)
−0.158620 + 0.987340i \(0.550704\pi\)
\(644\) 0 0
\(645\) 1.00744e6 785732.i 2.42158 1.88867i
\(646\) 0 0
\(647\) 363926.i 0.869371i −0.900582 0.434685i \(-0.856860\pi\)
0.900582 0.434685i \(-0.143140\pi\)
\(648\) 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 0.906214 0.422819i \(-0.138960\pi\)
−0.965983 + 0.258605i \(0.916737\pi\)
\(654\) 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 0.457941 + 0.888983i \(0.348587\pi\)
−0.922230 + 0.386642i \(0.873635\pi\)
\(660\) 0 0
\(661\) −101124. 84853.5i −0.231448 0.194208i 0.519687 0.854357i \(-0.326049\pi\)
−0.751135 + 0.660149i \(0.770493\pi\)
\(662\) 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 −0.187127 0.982336i \(-0.559918\pi\)
0.934918 + 0.354865i \(0.115473\pi\)
\(674\) 0 0
\(675\) −341457. + 695629.i −0.749426 + 1.52676i
\(676\) 0 0
\(677\) −158293. 188647.i −0.345370 0.411596i 0.565198 0.824955i \(-0.308800\pi\)
−0.910568 + 0.413359i \(0.864355\pi\)
\(678\) 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 −0.0267669 0.999642i \(-0.508521\pi\)
0.852332 + 0.523002i \(0.175188\pi\)
\(684\) 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 0.0542035 0.998530i \(-0.482738\pi\)
−0.600320 + 0.799760i \(0.704960\pi\)
\(692\) 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 \(0.204814\pi\)
−0.800036 + 0.599952i \(0.795186\pi\)
\(702\) 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 0.997237 0.0742880i \(-0.0236684\pi\)
−0.962504 + 0.271267i \(0.912557\pi\)
\(710\) 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 −0.376475 0.926427i \(-0.622864\pi\)
−0.990547 + 0.137176i \(0.956197\pi\)
\(720\) 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 −0.878318 0.478077i \(-0.841334\pi\)
0.318296 + 0.947991i \(0.396889\pi\)
\(728\) 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 −0.998278 0.0586621i \(-0.981317\pi\)
0.958138 + 0.286307i \(0.0924277\pi\)
\(734\) 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 −0.824060 0.566503i \(-0.808296\pi\)
0.902636 + 0.430405i \(0.141629\pi\)
\(740\) 0 0
\(741\) 186368. 98892.5i 0.339418 0.180106i
\(742\) 0 0
\(743\) 146820. 174974.i 0.265956 0.316953i −0.616495 0.787359i \(-0.711448\pi\)
0.882450 + 0.470405i \(0.155892\pi\)
\(744\) 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 −0.758127 0.652107i \(-0.773885\pi\)
−0.161592 + 0.986858i \(0.551663\pi\)
\(752\) 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 0.969946 0.243322i \(-0.0782372\pi\)
−0.899426 + 0.437073i \(0.856015\pi\)
\(762\) 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 −0.0634883 0.997983i \(-0.520223\pi\)
−0.993846 + 0.110774i \(0.964667\pi\)
\(770\) 0 0
\(771\) −608856. 21774.6i −1.02425 0.0366303i
\(772\) 0 0
\(773\) −893014. 515582.i −1.49451 0.862856i −0.494531 0.869160i \(-0.664660\pi\)
−0.999980 + 0.00630343i \(0.997994\pi\)
\(774\) 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