Properties

Label 637.2.c.g.246.13
Level $637$
Weight $2$
Character 637.246
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 121 x^{12} + 296 x^{10} + 3468 x^{8} - 1748 x^{6} + 40192 x^{4} - 65056 x^{2} + 228484\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 246.13
Root \(-1.41421 + 1.65552i\) of defining polynomial
Character \(\chi\) \(=\) 637.246
Dual form 637.2.c.g.246.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.65552i q^{2} -0.494977 q^{3} -0.740740 q^{4} -2.87389i q^{5} -0.819443i q^{6} +2.08473i q^{8} -2.75500 q^{9} +O(q^{10})\) \(q+1.65552i q^{2} -0.494977 q^{3} -0.740740 q^{4} -2.87389i q^{5} -0.819443i q^{6} +2.08473i q^{8} -2.75500 q^{9} +4.75778 q^{10} -2.58138i q^{11} +0.366649 q^{12} +(3.54562 - 0.654682i) q^{13} +1.42251i q^{15} -4.93278 q^{16} +2.27584 q^{17} -4.56095i q^{18} -4.39571i q^{19} +2.12881i q^{20} +4.27352 q^{22} +7.16926 q^{23} -1.03189i q^{24} -3.25926 q^{25} +(1.08384 + 5.86983i) q^{26} +2.84859 q^{27} +6.19574 q^{29} -2.35499 q^{30} -6.85404i q^{31} -3.99686i q^{32} +1.27772i q^{33} +3.76769i q^{34} +2.04074 q^{36} -5.89241i q^{37} +7.27717 q^{38} +(-1.75500 + 0.324052i) q^{39} +5.99128 q^{40} -3.98014i q^{41} +1.31425 q^{43} +1.91213i q^{44} +7.91757i q^{45} +11.8688i q^{46} -1.35208i q^{47} +2.44161 q^{48} -5.39576i q^{50} -1.12649 q^{51} +(-2.62638 + 0.484949i) q^{52} -8.28778 q^{53} +4.71589i q^{54} -7.41860 q^{55} +2.17577i q^{57} +10.2572i q^{58} +9.61085i q^{59} -1.05371i q^{60} -9.55301 q^{61} +11.3470 q^{62} -3.24870 q^{64} +(-1.88149 - 10.1897i) q^{65} -2.11529 q^{66} +15.9095i q^{67} -1.68581 q^{68} -3.54862 q^{69} +4.79396i q^{71} -5.74342i q^{72} -5.70507i q^{73} +9.75500 q^{74} +1.61326 q^{75} +3.25607i q^{76} +(-0.536475 - 2.90543i) q^{78} -2.01426 q^{79} +14.1763i q^{80} +6.85501 q^{81} +6.58920 q^{82} +3.11798i q^{83} -6.54052i q^{85} +2.17577i q^{86} -3.06675 q^{87} +5.38147 q^{88} +13.0584i q^{89} -13.1077 q^{90} -5.31056 q^{92} +3.39259i q^{93} +2.23839 q^{94} -12.6328 q^{95} +1.97835i q^{96} -14.0382i q^{97} +7.11169i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 20q^{4} + 16q^{9} + O(q^{10}) \) \( 16q - 20q^{4} + 16q^{9} + 28q^{16} - 8q^{22} - 36q^{23} - 44q^{25} + 36q^{29} + 52q^{36} + 32q^{39} - 36q^{43} - 72q^{51} + 12q^{53} - 164q^{64} - 24q^{65} + 96q^{74} + 24q^{78} + 36q^{79} + 16q^{81} + 136q^{88} + 24q^{92} - 84q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.65552i 1.17063i 0.810807 + 0.585314i \(0.199029\pi\)
−0.810807 + 0.585314i \(0.800971\pi\)
\(3\) −0.494977 −0.285775 −0.142888 0.989739i \(-0.545639\pi\)
−0.142888 + 0.989739i \(0.545639\pi\)
\(4\) −0.740740 −0.370370
\(5\) 2.87389i 1.28524i −0.766183 0.642622i \(-0.777847\pi\)
0.766183 0.642622i \(-0.222153\pi\)
\(6\) 0.819443i 0.334536i
\(7\) 0 0
\(8\) 2.08473i 0.737063i
\(9\) −2.75500 −0.918333
\(10\) 4.75778 1.50454
\(11\) 2.58138i 0.778315i −0.921171 0.389157i \(-0.872766\pi\)
0.921171 0.389157i \(-0.127234\pi\)
\(12\) 0.366649 0.105842
\(13\) 3.54562 0.654682i 0.983377 0.181576i
\(14\) 0 0
\(15\) 1.42251i 0.367291i
\(16\) −4.93278 −1.23320
\(17\) 2.27584 0.551972 0.275986 0.961162i \(-0.410996\pi\)
0.275986 + 0.961162i \(0.410996\pi\)
\(18\) 4.56095i 1.07503i
\(19\) 4.39571i 1.00844i −0.863574 0.504222i \(-0.831779\pi\)
0.863574 0.504222i \(-0.168221\pi\)
\(20\) 2.12881i 0.476016i
\(21\) 0 0
\(22\) 4.27352 0.911117
\(23\) 7.16926 1.49489 0.747447 0.664321i \(-0.231279\pi\)
0.747447 + 0.664321i \(0.231279\pi\)
\(24\) 1.03189i 0.210634i
\(25\) −3.25926 −0.651852
\(26\) 1.08384 + 5.86983i 0.212558 + 1.15117i
\(27\) 2.84859 0.548212
\(28\) 0 0
\(29\) 6.19574 1.15052 0.575260 0.817971i \(-0.304901\pi\)
0.575260 + 0.817971i \(0.304901\pi\)
\(30\) −2.35499 −0.429961
\(31\) 6.85404i 1.23102i −0.788129 0.615511i \(-0.788950\pi\)
0.788129 0.615511i \(-0.211050\pi\)
\(32\) 3.99686i 0.706551i
\(33\) 1.27772i 0.222423i
\(34\) 3.76769i 0.646154i
\(35\) 0 0
\(36\) 2.04074 0.340123
\(37\) 5.89241i 0.968707i −0.874872 0.484353i \(-0.839055\pi\)
0.874872 0.484353i \(-0.160945\pi\)
\(38\) 7.27717 1.18051
\(39\) −1.75500 + 0.324052i −0.281025 + 0.0518899i
\(40\) 5.99128 0.947305
\(41\) 3.98014i 0.621594i −0.950476 0.310797i \(-0.899404\pi\)
0.950476 0.310797i \(-0.100596\pi\)
\(42\) 0 0
\(43\) 1.31425 0.200422 0.100211 0.994966i \(-0.468048\pi\)
0.100211 + 0.994966i \(0.468048\pi\)
\(44\) 1.91213i 0.288264i
\(45\) 7.91757i 1.18028i
\(46\) 11.8688i 1.74997i
\(47\) 1.35208i 0.197221i −0.995126 0.0986106i \(-0.968560\pi\)
0.995126 0.0986106i \(-0.0314398\pi\)
\(48\) 2.44161 0.352417
\(49\) 0 0
\(50\) 5.39576i 0.763076i
\(51\) −1.12649 −0.157740
\(52\) −2.62638 + 0.484949i −0.364213 + 0.0672503i
\(53\) −8.28778 −1.13841 −0.569207 0.822194i \(-0.692750\pi\)
−0.569207 + 0.822194i \(0.692750\pi\)
\(54\) 4.71589i 0.641752i
\(55\) −7.41860 −1.00032
\(56\) 0 0
\(57\) 2.17577i 0.288188i
\(58\) 10.2572i 1.34683i
\(59\) 9.61085i 1.25123i 0.780133 + 0.625613i \(0.215151\pi\)
−0.780133 + 0.625613i \(0.784849\pi\)
\(60\) 1.05371i 0.136033i
\(61\) −9.55301 −1.22314 −0.611569 0.791191i \(-0.709461\pi\)
−0.611569 + 0.791191i \(0.709461\pi\)
\(62\) 11.3470 1.44107
\(63\) 0 0
\(64\) −3.24870 −0.406087
\(65\) −1.88149 10.1897i −0.233370 1.26388i
\(66\) −2.11529 −0.260375
\(67\) 15.9095i 1.94366i 0.235685 + 0.971830i \(0.424267\pi\)
−0.235685 + 0.971830i \(0.575733\pi\)
\(68\) −1.68581 −0.204434
\(69\) −3.54862 −0.427204
\(70\) 0 0
\(71\) 4.79396i 0.568938i 0.958685 + 0.284469i \(0.0918173\pi\)
−0.958685 + 0.284469i \(0.908183\pi\)
\(72\) 5.74342i 0.676869i
\(73\) 5.70507i 0.667728i −0.942621 0.333864i \(-0.891647\pi\)
0.942621 0.333864i \(-0.108353\pi\)
\(74\) 9.75500 1.13400
\(75\) 1.61326 0.186283
\(76\) 3.25607i 0.373497i
\(77\) 0 0
\(78\) −0.536475 2.90543i −0.0607438 0.328975i
\(79\) −2.01426 −0.226622 −0.113311 0.993560i \(-0.536146\pi\)
−0.113311 + 0.993560i \(0.536146\pi\)
\(80\) 14.1763i 1.58496i
\(81\) 6.85501 0.761667
\(82\) 6.58920 0.727655
\(83\) 3.11798i 0.342243i 0.985250 + 0.171122i \(0.0547391\pi\)
−0.985250 + 0.171122i \(0.945261\pi\)
\(84\) 0 0
\(85\) 6.54052i 0.709419i
\(86\) 2.17577i 0.234620i
\(87\) −3.06675 −0.328790
\(88\) 5.38147 0.573667
\(89\) 13.0584i 1.38418i 0.721810 + 0.692092i \(0.243311\pi\)
−0.721810 + 0.692092i \(0.756689\pi\)
\(90\) −13.1077 −1.38167
\(91\) 0 0
\(92\) −5.31056 −0.553664
\(93\) 3.39259i 0.351795i
\(94\) 2.23839 0.230873
\(95\) −12.6328 −1.29610
\(96\) 1.97835i 0.201915i
\(97\) 14.0382i 1.42536i −0.701488 0.712682i \(-0.747480\pi\)
0.701488 0.712682i \(-0.252520\pi\)
\(98\) 0 0
\(99\) 7.11169i 0.714752i
\(100\) 2.41426 0.241426
\(101\) −17.4483 −1.73617 −0.868083 0.496419i \(-0.834648\pi\)
−0.868083 + 0.496419i \(0.834648\pi\)
\(102\) 1.86492i 0.184655i
\(103\) −6.55698 −0.646078 −0.323039 0.946386i \(-0.604705\pi\)
−0.323039 + 0.946386i \(0.604705\pi\)
\(104\) 1.36483 + 7.39164i 0.133833 + 0.724810i
\(105\) 0 0
\(106\) 13.7206i 1.33266i
\(107\) 15.6020 1.50831 0.754153 0.656699i \(-0.228048\pi\)
0.754153 + 0.656699i \(0.228048\pi\)
\(108\) −2.11006 −0.203041
\(109\) 10.0171i 0.959466i −0.877414 0.479733i \(-0.840733\pi\)
0.877414 0.479733i \(-0.159267\pi\)
\(110\) 12.2816i 1.17101i
\(111\) 2.91661i 0.276832i
\(112\) 0 0
\(113\) −3.95074 −0.371654 −0.185827 0.982582i \(-0.559496\pi\)
−0.185827 + 0.982582i \(0.559496\pi\)
\(114\) −3.60203 −0.337361
\(115\) 20.6037i 1.92130i
\(116\) −4.58943 −0.426118
\(117\) −9.76816 + 1.80365i −0.903067 + 0.166747i
\(118\) −15.9109 −1.46472
\(119\) 0 0
\(120\) −2.96555 −0.270716
\(121\) 4.33649 0.394226
\(122\) 15.8152i 1.43184i
\(123\) 1.97008i 0.177636i
\(124\) 5.07706i 0.455933i
\(125\) 5.00270i 0.447455i
\(126\) 0 0
\(127\) −2.37353 −0.210616 −0.105308 0.994440i \(-0.533583\pi\)
−0.105308 + 0.994440i \(0.533583\pi\)
\(128\) 13.3720i 1.18193i
\(129\) −0.650526 −0.0572756
\(130\) 16.8693 3.11483i 1.47953 0.273189i
\(131\) −2.13546 −0.186576 −0.0932878 0.995639i \(-0.529738\pi\)
−0.0932878 + 0.995639i \(0.529738\pi\)
\(132\) 0.946460i 0.0823788i
\(133\) 0 0
\(134\) −26.3385 −2.27530
\(135\) 8.18655i 0.704586i
\(136\) 4.74451i 0.406838i
\(137\) 0.429210i 0.0366699i −0.999832 0.0183349i \(-0.994163\pi\)
0.999832 0.0183349i \(-0.00583652\pi\)
\(138\) 5.87480i 0.500096i
\(139\) 19.4858 1.65276 0.826381 0.563112i \(-0.190396\pi\)
0.826381 + 0.563112i \(0.190396\pi\)
\(140\) 0 0
\(141\) 0.669248i 0.0563609i
\(142\) −7.93648 −0.666015
\(143\) −1.68998 9.15258i −0.141323 0.765377i
\(144\) 13.5898 1.13248
\(145\) 17.8059i 1.47870i
\(146\) 9.44485 0.781661
\(147\) 0 0
\(148\) 4.36475i 0.358780i
\(149\) 22.9004i 1.87607i 0.346534 + 0.938037i \(0.387358\pi\)
−0.346534 + 0.938037i \(0.612642\pi\)
\(150\) 2.67078i 0.218068i
\(151\) 11.2207i 0.913131i −0.889690 0.456565i \(-0.849079\pi\)
0.889690 0.456565i \(-0.150921\pi\)
\(152\) 9.16385 0.743286
\(153\) −6.26993 −0.506894
\(154\) 0 0
\(155\) −19.6978 −1.58216
\(156\) 1.30000 0.240039i 0.104083 0.0192185i
\(157\) 3.78799 0.302315 0.151157 0.988510i \(-0.451700\pi\)
0.151157 + 0.988510i \(0.451700\pi\)
\(158\) 3.33464i 0.265290i
\(159\) 4.10226 0.325330
\(160\) −11.4865 −0.908091
\(161\) 0 0
\(162\) 11.3486i 0.891629i
\(163\) 19.6130i 1.53621i 0.640326 + 0.768103i \(0.278799\pi\)
−0.640326 + 0.768103i \(0.721201\pi\)
\(164\) 2.94825i 0.230220i
\(165\) 3.67204 0.285868
\(166\) −5.16188 −0.400639
\(167\) 10.2922i 0.796435i 0.917291 + 0.398217i \(0.130371\pi\)
−0.917291 + 0.398217i \(0.869629\pi\)
\(168\) 0 0
\(169\) 12.1428 4.64250i 0.934060 0.357116i
\(170\) 10.8279 0.830466
\(171\) 12.1102i 0.926087i
\(172\) −0.973521 −0.0742303
\(173\) 6.00439 0.456505 0.228253 0.973602i \(-0.426699\pi\)
0.228253 + 0.973602i \(0.426699\pi\)
\(174\) 5.07706i 0.384891i
\(175\) 0 0
\(176\) 12.7334i 0.959815i
\(177\) 4.75715i 0.357569i
\(178\) −21.6184 −1.62036
\(179\) 7.75130 0.579359 0.289680 0.957124i \(-0.406451\pi\)
0.289680 + 0.957124i \(0.406451\pi\)
\(180\) 5.86486i 0.437141i
\(181\) −19.9999 −1.48658 −0.743289 0.668970i \(-0.766735\pi\)
−0.743289 + 0.668970i \(0.766735\pi\)
\(182\) 0 0
\(183\) 4.72852 0.349542
\(184\) 14.9460i 1.10183i
\(185\) −16.9342 −1.24502
\(186\) −5.61649 −0.411821
\(187\) 5.87480i 0.429608i
\(188\) 1.00154i 0.0730448i
\(189\) 0 0
\(190\) 20.9138i 1.51725i
\(191\) 20.4835 1.48214 0.741068 0.671430i \(-0.234320\pi\)
0.741068 + 0.671430i \(0.234320\pi\)
\(192\) 1.60803 0.116050
\(193\) 12.4329i 0.894942i −0.894298 0.447471i \(-0.852325\pi\)
0.894298 0.447471i \(-0.147675\pi\)
\(194\) 23.2405 1.66857
\(195\) 0.931292 + 5.04368i 0.0666912 + 0.361185i
\(196\) 0 0
\(197\) 18.9805i 1.35231i 0.736761 + 0.676154i \(0.236354\pi\)
−0.736761 + 0.676154i \(0.763646\pi\)
\(198\) −11.7735 −0.836709
\(199\) 12.8188 0.908701 0.454350 0.890823i \(-0.349871\pi\)
0.454350 + 0.890823i \(0.349871\pi\)
\(200\) 6.79467i 0.480456i
\(201\) 7.87485i 0.555449i
\(202\) 28.8859i 2.03241i
\(203\) 0 0
\(204\) 0.834435 0.0584221
\(205\) −11.4385 −0.798900
\(206\) 10.8552i 0.756317i
\(207\) −19.7513 −1.37281
\(208\) −17.4898 + 3.22940i −1.21270 + 0.223919i
\(209\) −11.3470 −0.784887
\(210\) 0 0
\(211\) −7.86926 −0.541743 −0.270871 0.962616i \(-0.587312\pi\)
−0.270871 + 0.962616i \(0.587312\pi\)
\(212\) 6.13909 0.421634
\(213\) 2.37290i 0.162588i
\(214\) 25.8294i 1.76566i
\(215\) 3.77703i 0.257591i
\(216\) 5.93854i 0.404066i
\(217\) 0 0
\(218\) 16.5835 1.12318
\(219\) 2.82388i 0.190820i
\(220\) 5.49526 0.370490
\(221\) 8.06925 1.48995i 0.542797 0.100225i
\(222\) −4.82850 −0.324068
\(223\) 7.77059i 0.520357i −0.965560 0.260179i \(-0.916219\pi\)
0.965560 0.260179i \(-0.0837815\pi\)
\(224\) 0 0
\(225\) 8.97925 0.598617
\(226\) 6.54052i 0.435069i
\(227\) 25.5431i 1.69536i 0.530511 + 0.847678i \(0.322000\pi\)
−0.530511 + 0.847678i \(0.678000\pi\)
\(228\) 1.61168i 0.106736i
\(229\) 12.8986i 0.852362i 0.904638 + 0.426181i \(0.140141\pi\)
−0.904638 + 0.426181i \(0.859859\pi\)
\(230\) 34.1098 2.24913
\(231\) 0 0
\(232\) 12.9164i 0.848005i
\(233\) −8.14278 −0.533451 −0.266726 0.963772i \(-0.585942\pi\)
−0.266726 + 0.963772i \(0.585942\pi\)
\(234\) −2.98597 16.1714i −0.195199 1.05716i
\(235\) −3.88573 −0.253477
\(236\) 7.11914i 0.463417i
\(237\) 0.997011 0.0647628
\(238\) 0 0
\(239\) 23.8122i 1.54028i −0.637875 0.770140i \(-0.720186\pi\)
0.637875 0.770140i \(-0.279814\pi\)
\(240\) 7.01694i 0.452941i
\(241\) 0.288546i 0.0185869i −0.999957 0.00929346i \(-0.997042\pi\)
0.999957 0.00929346i \(-0.00295824\pi\)
\(242\) 7.17913i 0.461492i
\(243\) −11.9388 −0.765877
\(244\) 7.07630 0.453013
\(245\) 0 0
\(246\) −3.26150 −0.207946
\(247\) −2.87779 15.5855i −0.183109 0.991681i
\(248\) 14.2888 0.907340
\(249\) 1.54333i 0.0978045i
\(250\) 8.28206 0.523803
\(251\) −7.61843 −0.480871 −0.240435 0.970665i \(-0.577290\pi\)
−0.240435 + 0.970665i \(0.577290\pi\)
\(252\) 0 0
\(253\) 18.5066i 1.16350i
\(254\) 3.92942i 0.246554i
\(255\) 3.23741i 0.202734i
\(256\) 15.6402 0.977511
\(257\) −11.6560 −0.727082 −0.363541 0.931578i \(-0.618432\pi\)
−0.363541 + 0.931578i \(0.618432\pi\)
\(258\) 1.07696i 0.0670484i
\(259\) 0 0
\(260\) 1.39369 + 7.54793i 0.0864331 + 0.468103i
\(261\) −17.0693 −1.05656
\(262\) 3.53529i 0.218411i
\(263\) −13.5528 −0.835700 −0.417850 0.908516i \(-0.637216\pi\)
−0.417850 + 0.908516i \(0.637216\pi\)
\(264\) −2.66370 −0.163940
\(265\) 23.8182i 1.46314i
\(266\) 0 0
\(267\) 6.46359i 0.395565i
\(268\) 11.7848i 0.719873i
\(269\) 17.8332 1.08731 0.543656 0.839308i \(-0.317040\pi\)
0.543656 + 0.839308i \(0.317040\pi\)
\(270\) 13.5530 0.824808
\(271\) 30.3743i 1.84511i 0.385866 + 0.922555i \(0.373903\pi\)
−0.385866 + 0.922555i \(0.626097\pi\)
\(272\) −11.2262 −0.680690
\(273\) 0 0
\(274\) 0.710564 0.0429268
\(275\) 8.41338i 0.507346i
\(276\) 2.62860 0.158223
\(277\) −5.21425 −0.313294 −0.156647 0.987655i \(-0.550068\pi\)
−0.156647 + 0.987655i \(0.550068\pi\)
\(278\) 32.2591i 1.93477i
\(279\) 18.8829i 1.13049i
\(280\) 0 0
\(281\) 1.66255i 0.0991794i 0.998770 + 0.0495897i \(0.0157914\pi\)
−0.998770 + 0.0495897i \(0.984209\pi\)
\(282\) −1.10795 −0.0659776
\(283\) −13.7957 −0.820066 −0.410033 0.912071i \(-0.634483\pi\)
−0.410033 + 0.912071i \(0.634483\pi\)
\(284\) 3.55107i 0.210718i
\(285\) 6.25294 0.370392
\(286\) 15.1523 2.79780i 0.895972 0.165437i
\(287\) 0 0
\(288\) 11.0113i 0.648849i
\(289\) −11.8206 −0.695327
\(290\) 29.4780 1.73101
\(291\) 6.94859i 0.407333i
\(292\) 4.22597i 0.247306i
\(293\) 12.8576i 0.751149i 0.926792 + 0.375574i \(0.122555\pi\)
−0.926792 + 0.375574i \(0.877445\pi\)
\(294\) 0 0
\(295\) 27.6206 1.60813
\(296\) 12.2841 0.713998
\(297\) 7.35329i 0.426681i
\(298\) −37.9120 −2.19619
\(299\) 25.4194 4.69359i 1.47004 0.271437i
\(300\) −1.19500 −0.0689936
\(301\) 0 0
\(302\) 18.5761 1.06894
\(303\) 8.63648 0.496153
\(304\) 21.6831i 1.24361i
\(305\) 27.4543i 1.57203i
\(306\) 10.3800i 0.593384i
\(307\) 20.9016i 1.19292i −0.802644 0.596458i \(-0.796574\pi\)
0.802644 0.596458i \(-0.203426\pi\)
\(308\) 0 0
\(309\) 3.24555 0.184633
\(310\) 32.6100i 1.85212i
\(311\) 17.1392 0.971876 0.485938 0.873993i \(-0.338478\pi\)
0.485938 + 0.873993i \(0.338478\pi\)
\(312\) −0.675561 3.65869i −0.0382461 0.207133i
\(313\) 2.55266 0.144285 0.0721424 0.997394i \(-0.477016\pi\)
0.0721424 + 0.997394i \(0.477016\pi\)
\(314\) 6.27109i 0.353898i
\(315\) 0 0
\(316\) 1.49204 0.0839339
\(317\) 27.2888i 1.53269i −0.642430 0.766345i \(-0.722073\pi\)
0.642430 0.766345i \(-0.277927\pi\)
\(318\) 6.79136i 0.380841i
\(319\) 15.9936i 0.895467i
\(320\) 9.33641i 0.521921i
\(321\) −7.72264 −0.431036
\(322\) 0 0
\(323\) 10.0039i 0.556633i
\(324\) −5.07778 −0.282099
\(325\) −11.5561 + 2.13378i −0.641016 + 0.118361i
\(326\) −32.4696 −1.79833
\(327\) 4.95824i 0.274192i
\(328\) 8.29751 0.458154
\(329\) 0 0
\(330\) 6.07912i 0.334645i
\(331\) 9.69307i 0.532779i 0.963865 + 0.266390i \(0.0858308\pi\)
−0.963865 + 0.266390i \(0.914169\pi\)
\(332\) 2.30961i 0.126757i
\(333\) 16.2336i 0.889595i
\(334\) −17.0389 −0.932329
\(335\) 45.7223 2.49808
\(336\) 0 0
\(337\) 6.31370 0.343929 0.171965 0.985103i \(-0.444988\pi\)
0.171965 + 0.985103i \(0.444988\pi\)
\(338\) 7.68575 + 20.1026i 0.418049 + 1.09344i
\(339\) 1.95552 0.106210
\(340\) 4.84482i 0.262747i
\(341\) −17.6929 −0.958122
\(342\) −20.0486 −1.08410
\(343\) 0 0
\(344\) 2.73986i 0.147724i
\(345\) 10.1984i 0.549061i
\(346\) 9.94038i 0.534398i
\(347\) 29.1200 1.56324 0.781622 0.623753i \(-0.214393\pi\)
0.781622 + 0.623753i \(0.214393\pi\)
\(348\) 2.27166 0.121774
\(349\) 20.3297i 1.08822i 0.839013 + 0.544112i \(0.183133\pi\)
−0.839013 + 0.544112i \(0.816867\pi\)
\(350\) 0 0
\(351\) 10.1000 1.86492i 0.539099 0.0995421i
\(352\) −10.3174 −0.549919
\(353\) 14.1980i 0.755683i 0.925870 + 0.377841i \(0.123334\pi\)
−0.925870 + 0.377841i \(0.876666\pi\)
\(354\) 7.87555 0.418581
\(355\) 13.7773 0.731224
\(356\) 9.67285i 0.512660i
\(357\) 0 0
\(358\) 12.8324i 0.678214i
\(359\) 7.50164i 0.395921i 0.980210 + 0.197961i \(0.0634318\pi\)
−0.980210 + 0.197961i \(0.936568\pi\)
\(360\) −16.5060 −0.869941
\(361\) −0.322229 −0.0169594
\(362\) 33.1101i 1.74023i
\(363\) −2.14646 −0.112660
\(364\) 0 0
\(365\) −16.3958 −0.858193
\(366\) 7.82815i 0.409184i
\(367\) 28.5883 1.49230 0.746149 0.665779i \(-0.231901\pi\)
0.746149 + 0.665779i \(0.231901\pi\)
\(368\) −35.3644 −1.84350
\(369\) 10.9653i 0.570830i
\(370\) 28.0348i 1.45746i
\(371\) 0 0
\(372\) 2.51303i 0.130294i
\(373\) −7.91204 −0.409670 −0.204835 0.978797i \(-0.565666\pi\)
−0.204835 + 0.978797i \(0.565666\pi\)
\(374\) 9.72584 0.502911
\(375\) 2.47622i 0.127871i
\(376\) 2.81872 0.145364
\(377\) 21.9677 4.05624i 1.13139 0.208907i
\(378\) 0 0
\(379\) 1.78091i 0.0914791i 0.998953 + 0.0457395i \(0.0145644\pi\)
−0.998953 + 0.0457395i \(0.985436\pi\)
\(380\) 9.35761 0.480035
\(381\) 1.17484 0.0601889
\(382\) 33.9108i 1.73503i
\(383\) 14.1997i 0.725572i 0.931872 + 0.362786i \(0.118174\pi\)
−0.931872 + 0.362786i \(0.881826\pi\)
\(384\) 6.61883i 0.337766i
\(385\) 0 0
\(386\) 20.5829 1.04764
\(387\) −3.62077 −0.184054
\(388\) 10.3987i 0.527912i
\(389\) 6.77499 0.343506 0.171753 0.985140i \(-0.445057\pi\)
0.171753 + 0.985140i \(0.445057\pi\)
\(390\) −8.34990 + 1.54177i −0.422813 + 0.0780706i
\(391\) 16.3161 0.825140
\(392\) 0 0
\(393\) 1.05700 0.0533187
\(394\) −31.4226 −1.58305
\(395\) 5.78876i 0.291264i
\(396\) 5.26791i 0.264723i
\(397\) 29.0023i 1.45558i −0.685798 0.727792i \(-0.740547\pi\)
0.685798 0.727792i \(-0.259453\pi\)
\(398\) 21.2218i 1.06375i
\(399\) 0 0
\(400\) 16.0772 0.803861
\(401\) 21.9604i 1.09665i 0.836265 + 0.548326i \(0.184735\pi\)
−0.836265 + 0.548326i \(0.815265\pi\)
\(402\) 13.0370 0.650224
\(403\) −4.48721 24.3018i −0.223524 1.21056i
\(404\) 12.9246 0.643024
\(405\) 19.7006i 0.978928i
\(406\) 0 0
\(407\) −15.2105 −0.753959
\(408\) 2.34842i 0.116264i
\(409\) 4.00290i 0.197931i −0.995091 0.0989653i \(-0.968447\pi\)
0.995091 0.0989653i \(-0.0315533\pi\)
\(410\) 18.9366i 0.935214i
\(411\) 0.212449i 0.0104793i
\(412\) 4.85702 0.239288
\(413\) 0 0
\(414\) 32.6986i 1.60705i
\(415\) 8.96075 0.439866
\(416\) −2.61667 14.1713i −0.128293 0.694806i
\(417\) −9.64501 −0.472318
\(418\) 18.7851i 0.918811i
\(419\) −1.75047 −0.0855162 −0.0427581 0.999085i \(-0.513614\pi\)
−0.0427581 + 0.999085i \(0.513614\pi\)
\(420\) 0 0
\(421\) 16.2204i 0.790533i 0.918566 + 0.395267i \(0.129348\pi\)
−0.918566 + 0.395267i \(0.870652\pi\)
\(422\) 13.0277i 0.634179i
\(423\) 3.72498i 0.181115i
\(424\) 17.2778i 0.839082i
\(425\) −7.41755 −0.359804
\(426\) 3.92837 0.190330
\(427\) 0 0
\(428\) −11.5570 −0.558631
\(429\) 0.836502 + 4.53031i 0.0403867 + 0.218726i
\(430\) 6.25294 0.301543
\(431\) 11.6797i 0.562590i −0.959621 0.281295i \(-0.909236\pi\)
0.959621 0.281295i \(-0.0907639\pi\)
\(432\) −14.0515 −0.676052
\(433\) −31.6289 −1.51999 −0.759994 0.649930i \(-0.774798\pi\)
−0.759994 + 0.649930i \(0.774798\pi\)
\(434\) 0 0
\(435\) 8.81351i 0.422575i
\(436\) 7.42008i 0.355357i
\(437\) 31.5140i 1.50752i
\(438\) −4.67498 −0.223379
\(439\) 9.71539 0.463690 0.231845 0.972753i \(-0.425524\pi\)
0.231845 + 0.972753i \(0.425524\pi\)
\(440\) 15.4658i 0.737302i
\(441\) 0 0
\(442\) 2.46664 + 13.3588i 0.117326 + 0.635413i
\(443\) 21.1163 1.00327 0.501633 0.865081i \(-0.332733\pi\)
0.501633 + 0.865081i \(0.332733\pi\)
\(444\) 2.16045i 0.102530i
\(445\) 37.5283 1.77901
\(446\) 12.8644 0.609145
\(447\) 11.3352i 0.536135i
\(448\) 0 0
\(449\) 13.4710i 0.635735i −0.948135 0.317867i \(-0.897033\pi\)
0.948135 0.317867i \(-0.102967\pi\)
\(450\) 14.8653i 0.700758i
\(451\) −10.2743 −0.483796
\(452\) 2.92647 0.137650
\(453\) 5.55401i 0.260950i
\(454\) −42.2871 −1.98463
\(455\) 0 0
\(456\) −4.53589 −0.212413
\(457\) 9.35582i 0.437647i −0.975764 0.218823i \(-0.929778\pi\)
0.975764 0.218823i \(-0.0702218\pi\)
\(458\) −21.3538 −0.997798
\(459\) 6.48294 0.302598
\(460\) 15.2620i 0.711593i
\(461\) 8.14109i 0.379168i 0.981864 + 0.189584i \(0.0607140\pi\)
−0.981864 + 0.189584i \(0.939286\pi\)
\(462\) 0 0
\(463\) 24.3018i 1.12940i 0.825296 + 0.564700i \(0.191008\pi\)
−0.825296 + 0.564700i \(0.808992\pi\)
\(464\) −30.5623 −1.41882
\(465\) 9.74994 0.452143
\(466\) 13.4805i 0.624473i
\(467\) 32.7935 1.51750 0.758751 0.651381i \(-0.225810\pi\)
0.758751 + 0.651381i \(0.225810\pi\)
\(468\) 7.23567 1.33603i 0.334469 0.0617582i
\(469\) 0 0
\(470\) 6.43290i 0.296728i
\(471\) −1.87497 −0.0863940
\(472\) −20.0360 −0.922232
\(473\) 3.39259i 0.155991i
\(474\) 1.65057i 0.0758132i
\(475\) 14.3267i 0.657356i
\(476\) 0 0
\(477\) 22.8328 1.04544
\(478\) 39.4215 1.80310
\(479\) 2.48109i 0.113364i −0.998392 0.0566819i \(-0.981948\pi\)
0.998392 0.0566819i \(-0.0180521\pi\)
\(480\) 5.68557 0.259510
\(481\) −3.85766 20.8922i −0.175894 0.952604i
\(482\) 0.477694 0.0217584
\(483\) 0 0
\(484\) −3.21221 −0.146009
\(485\) −40.3443 −1.83194
\(486\) 19.7650i 0.896557i
\(487\) 22.9216i 1.03867i −0.854569 0.519337i \(-0.826179\pi\)
0.854569 0.519337i \(-0.173821\pi\)
\(488\) 19.9154i 0.901529i
\(489\) 9.70797i 0.439010i
\(490\) 0 0
\(491\) −22.8735 −1.03227 −0.516134 0.856508i \(-0.672629\pi\)
−0.516134 + 0.856508i \(0.672629\pi\)
\(492\) 1.45932i 0.0657910i
\(493\) 14.1005 0.635055
\(494\) 25.8020 4.76423i 1.16089 0.214353i
\(495\) 20.4382 0.918631
\(496\) 33.8095i 1.51809i
\(497\) 0 0
\(498\) 2.55501 0.114493
\(499\) 8.48087i 0.379656i 0.981817 + 0.189828i \(0.0607930\pi\)
−0.981817 + 0.189828i \(0.939207\pi\)
\(500\) 3.70570i 0.165724i
\(501\) 5.09440i 0.227601i
\(502\) 12.6124i 0.562921i
\(503\) 9.36890 0.417739 0.208869 0.977944i \(-0.433022\pi\)
0.208869 + 0.977944i \(0.433022\pi\)
\(504\) 0 0
\(505\) 50.1444i 2.23140i
\(506\) 30.6380 1.36202
\(507\) −6.01040 + 2.29793i −0.266931 + 0.102055i
\(508\) 1.75817 0.0780060
\(509\) 21.5402i 0.954753i 0.878699 + 0.477376i \(0.158412\pi\)
−0.878699 + 0.477376i \(0.841588\pi\)
\(510\) −5.35958 −0.237326
\(511\) 0 0
\(512\) 0.851388i 0.0376264i
\(513\) 12.5216i 0.552841i
\(514\) 19.2967i 0.851143i
\(515\) 18.8441i 0.830368i
\(516\) 0.481870 0.0212132
\(517\) −3.49023 −0.153500
\(518\) 0 0
\(519\) −2.97203 −0.130458
\(520\) 21.2428 3.92239i 0.931558 0.172008i
\(521\) −15.7470 −0.689889 −0.344944 0.938623i \(-0.612102\pi\)
−0.344944 + 0.938623i \(0.612102\pi\)
\(522\) 28.2585i 1.23684i
\(523\) −17.9404 −0.784477 −0.392238 0.919864i \(-0.628299\pi\)
−0.392238 + 0.919864i \(0.628299\pi\)
\(524\) 1.58182 0.0691020
\(525\) 0 0
\(526\) 22.4369i 0.978293i
\(527\) 15.5987i 0.679489i
\(528\) 6.30273i 0.274291i
\(529\) 28.3983 1.23471
\(530\) −39.4314 −1.71279
\(531\) 26.4779i 1.14904i
\(532\) 0 0
\(533\) −2.60573 14.1121i −0.112867 0.611261i
\(534\) 10.7006 0.463060
\(535\) 44.8386i 1.93854i
\(536\) −33.1671 −1.43260
\(537\) −3.83672 −0.165566
\(538\) 29.5232i 1.27284i
\(539\) 0 0
\(540\) 6.06410i 0.260957i
\(541\) 9.35582i 0.402238i −0.979567 0.201119i \(-0.935542\pi\)
0.979567 0.201119i \(-0.0644578\pi\)
\(542\) −50.2853 −2.15994
\(543\) 9.89947 0.424827
\(544\) 9.09621i 0.389997i
\(545\) −28.7881 −1.23315
\(546\) 0 0
\(547\) −33.1634 −1.41796 −0.708981 0.705227i \(-0.750845\pi\)
−0.708981 + 0.705227i \(0.750845\pi\)
\(548\) 0.317933i 0.0135814i
\(549\) 26.3185 1.12325
\(550\) −13.9285 −0.593914
\(551\) 27.2347i 1.16024i
\(552\) 7.39790i 0.314876i
\(553\) 0 0
\(554\) 8.63228i 0.366750i
\(555\) 8.38202 0.355797
\(556\) −14.4339 −0.612133
\(557\) 11.1532i 0.472578i 0.971683 + 0.236289i \(0.0759312\pi\)
−0.971683 + 0.236289i \(0.924069\pi\)
\(558\) −31.2609 −1.32338
\(559\) 4.65984 0.860419i 0.197090 0.0363918i
\(560\) 0 0
\(561\) 2.90789i 0.122771i
\(562\) −2.75238 −0.116102
\(563\) −19.1778 −0.808247 −0.404124 0.914704i \(-0.632423\pi\)
−0.404124 + 0.914704i \(0.632423\pi\)
\(564\) 0.495739i 0.0208744i
\(565\) 11.3540i 0.477666i
\(566\) 22.8389i 0.959993i
\(567\) 0 0
\(568\) −9.99409 −0.419343
\(569\) −13.4672 −0.564575 −0.282288 0.959330i \(-0.591093\pi\)
−0.282288 + 0.959330i \(0.591093\pi\)
\(570\) 10.3519i 0.433591i
\(571\) −25.1608 −1.05295 −0.526473 0.850192i \(-0.676486\pi\)
−0.526473 + 0.850192i \(0.676486\pi\)
\(572\) 1.25184 + 6.77968i 0.0523419 + 0.283473i
\(573\) −10.1389 −0.423557
\(574\) 0 0
\(575\) −23.3665 −0.974450
\(576\) 8.95016 0.372923
\(577\) 21.6484i 0.901235i 0.892717 + 0.450617i \(0.148796\pi\)
−0.892717 + 0.450617i \(0.851204\pi\)
\(578\) 19.5691i 0.813969i
\(579\) 6.15401i 0.255752i
\(580\) 13.1895i 0.547666i
\(581\) 0 0
\(582\) −11.5035 −0.476836
\(583\) 21.3939i 0.886044i
\(584\) 11.8935 0.492157
\(585\) 5.18349 + 28.0727i 0.214311 + 1.16066i
\(586\) −21.2860 −0.879316
\(587\) 34.5576i 1.42634i −0.700989 0.713172i \(-0.747258\pi\)
0.700989 0.713172i \(-0.252742\pi\)
\(588\) 0 0
\(589\) −30.1283 −1.24142
\(590\) 45.7263i 1.88252i
\(591\) 9.39493i 0.386456i
\(592\) 29.0660i 1.19461i
\(593\) 1.26839i 0.0520865i −0.999661 0.0260432i \(-0.991709\pi\)
0.999661 0.0260432i \(-0.00829075\pi\)
\(594\) 12.1735 0.499485
\(595\) 0 0
\(596\) 16.9632i 0.694842i
\(597\) −6.34501 −0.259684
\(598\) 7.77032 + 42.0824i 0.317752 + 1.72088i
\(599\) 17.5143 0.715614 0.357807 0.933796i \(-0.383525\pi\)
0.357807 + 0.933796i \(0.383525\pi\)
\(600\) 3.36320i 0.137302i
\(601\) 9.02164 0.368000 0.184000 0.982926i \(-0.441095\pi\)
0.184000 + 0.982926i \(0.441095\pi\)
\(602\) 0 0
\(603\) 43.8307i 1.78493i
\(604\) 8.31165i 0.338196i
\(605\) 12.4626i 0.506677i
\(606\) 14.2979i 0.580811i
\(607\) 15.8290 0.642479 0.321239 0.946998i \(-0.395901\pi\)
0.321239 + 0.946998i \(0.395901\pi\)
\(608\) −17.5690 −0.712517
\(609\) 0 0
\(610\) −45.4511 −1.84026
\(611\) −0.885182 4.79396i −0.0358106 0.193943i
\(612\) 4.64439 0.187738
\(613\) 17.5344i 0.708209i 0.935206 + 0.354104i \(0.115214\pi\)
−0.935206 + 0.354104i \(0.884786\pi\)
\(614\) 34.6029 1.39646
\(615\) 5.66179 0.228306
\(616\) 0 0
\(617\) 7.01448i 0.282392i −0.989982 0.141196i \(-0.954905\pi\)
0.989982 0.141196i \(-0.0450948\pi\)
\(618\) 5.37307i 0.216137i
\(619\) 38.8263i 1.56056i 0.625430 + 0.780280i \(0.284923\pi\)
−0.625430 + 0.780280i \(0.715077\pi\)
\(620\) 14.5909 0.585985
\(621\) 20.4223 0.819518
\(622\) 28.3743i 1.13771i
\(623\) 0 0
\(624\) 8.65703 1.59848i 0.346558 0.0639904i
\(625\) −30.6735 −1.22694
\(626\) 4.22597i 0.168904i
\(627\) 5.61649 0.224301
\(628\) −2.80592 −0.111968
\(629\) 13.4102i 0.534699i
\(630\) 0 0
\(631\) 12.7484i 0.507506i 0.967269 + 0.253753i \(0.0816650\pi\)
−0.967269 + 0.253753i \(0.918335\pi\)
\(632\) 4.19918i 0.167034i
\(633\) 3.89510 0.154816
\(634\) 45.1770 1.79421
\(635\) 6.82126i 0.270694i
\(636\) −3.03871 −0.120493
\(637\) 0 0
\(638\) 26.4776 1.04826
\(639\) 13.2073i 0.522474i
\(640\) −38.4297 −1.51907
\(641\) 9.71429 0.383691 0.191846 0.981425i \(-0.438553\pi\)
0.191846 + 0.981425i \(0.438553\pi\)
\(642\) 12.7850i 0.504583i
\(643\) 0.458279i 0.0180728i −0.999959 0.00903639i \(-0.997124\pi\)
0.999959 0.00903639i \(-0.00287641\pi\)
\(644\) 0 0
\(645\) 1.86954i 0.0736131i
\(646\) 16.5617 0.651610
\(647\) −6.17722 −0.242852 −0.121426 0.992601i \(-0.538747\pi\)
−0.121426 + 0.992601i \(0.538747\pi\)
\(648\) 14.2908i 0.561397i
\(649\) 24.8093 0.973848
\(650\) −3.53251 19.1313i −0.138556 0.750392i
\(651\) 0 0
\(652\) 14.5281i 0.568965i
\(653\) 28.4385 1.11289 0.556443 0.830886i \(-0.312166\pi\)
0.556443 + 0.830886i \(0.312166\pi\)
\(654\) −8.20846 −0.320976
\(655\) 6.13707i 0.239795i
\(656\) 19.6332i 0.766547i
\(657\) 15.7175i 0.613196i
\(658\) 0 0
\(659\) −25.9818 −1.01211 −0.506054 0.862502i \(-0.668897\pi\)
−0.506054 + 0.862502i \(0.668897\pi\)
\(660\) −2.72002 −0.105877
\(661\) 37.2752i 1.44984i 0.688835 + 0.724918i \(0.258122\pi\)
−0.688835 + 0.724918i \(0.741878\pi\)
\(662\) −16.0471 −0.623686
\(663\) −3.99409 + 0.737491i −0.155118 + 0.0286418i
\(664\) −6.50015 −0.252255
\(665\) 0 0
\(666\) −26.8750 −1.04139
\(667\) 44.4189 1.71991
\(668\) 7.62385i 0.294976i
\(669\) 3.84626i 0.148705i
\(670\) 75.6941i 2.92432i
\(671\) 24.6599i 0.951986i
\(672\) 0 0
\(673\) 41.7078 1.60772 0.803859 0.594820i \(-0.202777\pi\)
0.803859 + 0.594820i \(0.202777\pi\)
\(674\) 10.4525i 0.402613i
\(675\) −9.28430 −0.357353
\(676\) −8.99464 + 3.43889i −0.345948 + 0.132265i
\(677\) −18.2069 −0.699750 −0.349875 0.936796i \(-0.613776\pi\)
−0.349875 + 0.936796i \(0.613776\pi\)
\(678\) 3.23741i 0.124332i
\(679\) 0 0
\(680\) 13.6352 0.522886
\(681\) 12.6432i 0.484490i
\(682\) 29.2908i 1.12160i
\(683\) 27.3360i 1.04598i 0.852338 + 0.522991i \(0.175184\pi\)
−0.852338 + 0.522991i \(0.824816\pi\)
\(684\) 8.97048i 0.342995i
\(685\) −1.23350 −0.0471297
\(686\) 0 0
\(687\) 6.38449i 0.243584i
\(688\) −6.48294 −0.247160
\(689\) −29.3853 + 5.42586i −1.11949 + 0.206709i
\(690\) −16.8836 −0.642746
\(691\) 8.39581i 0.319392i −0.987166 0.159696i \(-0.948949\pi\)
0.987166 0.159696i \(-0.0510513\pi\)
\(692\) −4.44769 −0.169076
\(693\) 0 0
\(694\) 48.2087i 1.82998i
\(695\) 56.0000i 2.12420i
\(696\) 6.39334i 0.242339i
\(697\) 9.05817i 0.343102i
\(698\) −33.6562 −1.27391
\(699\) 4.03049 0.152447
\(700\) 0 0
\(701\) 27.4998 1.03865 0.519327 0.854576i \(-0.326183\pi\)
0.519327 + 0.854576i \(0.326183\pi\)
\(702\) 3.08741 + 16.7207i 0.116527 + 0.631084i
\(703\) −25.9013 −0.976887
\(704\) 8.38612i 0.316064i
\(705\) 1.92335 0.0724375
\(706\) −23.5050 −0.884623
\(707\) 0 0
\(708\) 3.52381i 0.132433i
\(709\) 28.9820i 1.08844i −0.838942 0.544221i \(-0.816825\pi\)
0.838942 0.544221i \(-0.183175\pi\)
\(710\) 22.8086i 0.855991i
\(711\) 5.54928 0.208114
\(712\) −27.2231 −1.02023
\(713\) 49.1384i 1.84025i
\(714\) 0 0
\(715\) −26.3035 + 4.85683i −0.983696 + 0.181635i
\(716\) −5.74170 −0.214577
\(717\) 11.7865i 0.440174i
\(718\) −12.4191 −0.463476
\(719\) −17.5522 −0.654588 −0.327294 0.944923i \(-0.606137\pi\)
−0.327294 + 0.944923i \(0.606137\pi\)
\(720\) 39.0557i 1.45552i
\(721\) 0 0
\(722\) 0.533456i 0.0198532i
\(723\) 0.142824i 0.00531168i
\(724\) 14.8147 0.550584
\(725\) −20.1935 −0.749969
\(726\) 3.55350i 0.131883i
\(727\) 22.1403 0.821139 0.410569 0.911829i \(-0.365330\pi\)
0.410569 + 0.911829i \(0.365330\pi\)
\(728\) 0 0
\(729\) −14.6556 −0.542799
\(730\) 27.1435i 1.00463i
\(731\) 2.99103 0.110627
\(732\) −3.50260 −0.129460
\(733\) 51.3414i 1.89634i −0.317768 0.948169i \(-0.602933\pi\)
0.317768 0.948169i \(-0.397067\pi\)
\(734\) 47.3285i 1.74693i
\(735\) 0 0
\(736\) 28.6545i 1.05622i
\(737\) 41.0685 1.51278
\(738\) −18.1532 −0.668229
\(739\) 22.7787i 0.837929i 0.908003 + 0.418965i \(0.137607\pi\)
−0.908003 + 0.418965i \(0.862393\pi\)
\(740\) 12.5438 0.461120
\(741\) 1.42444 + 7.71445i 0.0523281 + 0.283398i
\(742\) 0 0
\(743\) 27.6199i 1.01328i −0.862159 0.506638i \(-0.830888\pi\)
0.862159 0.506638i \(-0.169112\pi\)
\(744\) −7.07262 −0.259295
\(745\) 65.8133 2.41121
\(746\) 13.0985i 0.479571i
\(747\) 8.59004i 0.314293i
\(748\) 4.35170i 0.159114i
\(749\) 0 0
\(750\) −4.09943 −0.149690
\(751\) −41.1172 −1.50039 −0.750194 0.661218i \(-0.770040\pi\)
−0.750194 + 0.661218i \(0.770040\pi\)
\(752\) 6.66952i 0.243212i
\(753\) 3.77095 0.137421
\(754\) 6.71518 + 36.3680i 0.244552 + 1.32444i
\(755\) −32.2472 −1.17360
\(756\) 0 0
\(757\) 14.0143 0.509357 0.254678 0.967026i \(-0.418030\pi\)
0.254678 + 0.967026i \(0.418030\pi\)
\(758\) −2.94832 −0.107088
\(759\) 9.16033i 0.332499i
\(760\) 26.3359i 0.955304i
\(761\) 34.1648i 1.23847i 0.785205 + 0.619236i \(0.212558\pi\)
−0.785205 + 0.619236i \(0.787442\pi\)
\(762\) 1.94497i 0.0704588i
\(763\) 0 0
\(764\) −15.1730 −0.548938
\(765\) 18.0191i 0.651483i
\(766\) −23.5079 −0.849375
\(767\) 6.29205 + 34.0764i 0.227193 + 1.23043i
\(768\) −7.74153 −0.279348
\(769\) 52.9061i 1.90784i 0.300059 + 0.953921i \(0.402994\pi\)
−0.300059 + 0.953921i \(0.597006\pi\)
\(770\) 0 0
\(771\) 5.76946 0.207782
\(772\) 9.20957i 0.331460i
\(773\) 45.9133i 1.65139i −0.564118 0.825694i \(-0.690784\pi\)
0.564118 0.825694i \(-0.309216\pi\)
\(774\) 5.99425i 0.215459i
\(775\) 22.3391i 0.802444i
\(776\) 29.2658 1.05058
\(777\) 0 0
\(778\) 11.2161i 0.402117i
\(779\) −17.4955 −0.626843
\(780\) −0.689845 3.73605i −0.0247004 0.133772i
\(781\) 12.3750 0.442813
\(782\) 27.0116i 0.965932i
\(783\) 17.6491 0.630728
\(784\) 0 0
\(785\) 10.8863i 0.388548i
\(786\) 1.74989i 0.0624163i
\(787\) 15.1872i 0.541364i 0.962669 + 0.270682i \(0.0872492\pi\)
−0.962669 + 0.270682i \(0.912751\pi\)
\(788\) 14.0596i 0.500854i
\(789\) 6.70831 0.238822
\(790\) −9.58340 −0.340962
\(791\) 0 0
\(792\) −14.8259 −0.526817
\(793\) −33.8713 + 6.25418i −1.20281 + 0.222093i
\(794\) 48.0138 1.70395
\(795\) 11.7894i