Properties

Label 684.3.g.b.343.2
Level $684$
Weight $3$
Character 684.343
Analytic conductor $18.638$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 76)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 343.2
Root \(1.94929 - 0.447510i\) of defining polynomial
Character \(\chi\) \(=\) 684.343
Dual form 684.3.g.b.343.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.94929 + 0.447510i) q^{2} +(3.59947 - 1.74465i) q^{4} +3.90374 q^{5} +2.64664i q^{7} +(-6.23566 + 5.01164i) q^{8} +O(q^{10})\) \(q+(-1.94929 + 0.447510i) q^{2} +(3.59947 - 1.74465i) q^{4} +3.90374 q^{5} +2.64664i q^{7} +(-6.23566 + 5.01164i) q^{8} +(-7.60953 + 1.74696i) q^{10} -13.2532i q^{11} +1.60050 q^{13} +(-1.18440 - 5.15907i) q^{14} +(9.91236 - 12.5597i) q^{16} -8.10013 q^{17} -4.35890i q^{19} +(14.0514 - 6.81068i) q^{20} +(5.93094 + 25.8343i) q^{22} -38.2047i q^{23} -9.76079 q^{25} +(-3.11984 + 0.716239i) q^{26} +(4.61747 + 9.52650i) q^{28} +51.1656 q^{29} -13.6518i q^{31} +(-13.7015 + 28.9183i) q^{32} +(15.7895 - 3.62489i) q^{34} +10.3318i q^{35} -35.3910 q^{37} +(1.95065 + 8.49676i) q^{38} +(-24.3424 + 19.5641i) q^{40} -8.06155 q^{41} -16.2115i q^{43} +(-23.1223 - 47.7045i) q^{44} +(17.0970 + 74.4721i) q^{46} +1.59429i q^{47} +41.9953 q^{49} +(19.0266 - 4.36805i) q^{50} +(5.76095 - 2.79232i) q^{52} -56.8772 q^{53} -51.7371i q^{55} +(-13.2640 - 16.5036i) q^{56} +(-99.7366 + 22.8971i) q^{58} +106.526i q^{59} -35.9021 q^{61} +(6.10933 + 26.6114i) q^{62} +(13.7670 - 62.5018i) q^{64} +6.24794 q^{65} -47.5191i q^{67} +(-29.1562 + 14.1319i) q^{68} +(-4.62359 - 20.1397i) q^{70} -125.941i q^{71} +34.2172 q^{73} +(68.9874 - 15.8378i) q^{74} +(-7.60477 - 15.6897i) q^{76} +35.0765 q^{77} -71.1726i q^{79} +(38.6953 - 49.0297i) q^{80} +(15.7143 - 3.60763i) q^{82} -149.310i q^{83} -31.6208 q^{85} +(7.25479 + 31.6008i) q^{86} +(66.4202 + 82.6425i) q^{88} +169.809 q^{89} +4.23595i q^{91} +(-66.6541 - 137.517i) q^{92} +(-0.713460 - 3.10773i) q^{94} -17.0160i q^{95} +109.526 q^{97} +(-81.8610 + 18.7933i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} + O(q^{10}) \) \( 14 q - 2 q^{2} + 2 q^{4} + 40 q^{8} - 12 q^{10} + 54 q^{13} - 30 q^{14} + 58 q^{16} - 34 q^{17} - 32 q^{20} + 36 q^{22} - 86 q^{25} + 16 q^{26} + 18 q^{28} - 54 q^{29} - 72 q^{32} - 82 q^{34} + 100 q^{37} - 148 q^{40} - 224 q^{41} + 96 q^{44} + 46 q^{46} - 220 q^{49} + 58 q^{50} - 288 q^{52} - 14 q^{53} - 12 q^{56} - 72 q^{58} + 28 q^{61} - 396 q^{62} - 118 q^{64} + 472 q^{65} - 30 q^{68} + 156 q^{70} + 70 q^{73} + 224 q^{74} - 228 q^{77} + 348 q^{80} - 400 q^{82} + 48 q^{85} + 124 q^{86} + 472 q^{88} - 126 q^{92} - 88 q^{94} + 308 q^{97} - 68 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.94929 + 0.447510i −0.974645 + 0.223755i
\(3\) 0 0
\(4\) 3.59947 1.74465i 0.899867 0.436164i
\(5\) 3.90374 0.780749 0.390374 0.920656i \(-0.372346\pi\)
0.390374 + 0.920656i \(0.372346\pi\)
\(6\) 0 0
\(7\) 2.64664i 0.378092i 0.981968 + 0.189046i \(0.0605395\pi\)
−0.981968 + 0.189046i \(0.939461\pi\)
\(8\) −6.23566 + 5.01164i −0.779458 + 0.626455i
\(9\) 0 0
\(10\) −7.60953 + 1.74696i −0.760953 + 0.174696i
\(11\) 13.2532i 1.20484i −0.798181 0.602418i \(-0.794204\pi\)
0.798181 0.602418i \(-0.205796\pi\)
\(12\) 0 0
\(13\) 1.60050 0.123115 0.0615576 0.998104i \(-0.480393\pi\)
0.0615576 + 0.998104i \(0.480393\pi\)
\(14\) −1.18440 5.15907i −0.0845999 0.368505i
\(15\) 0 0
\(16\) 9.91236 12.5597i 0.619523 0.784979i
\(17\) −8.10013 −0.476478 −0.238239 0.971207i \(-0.576570\pi\)
−0.238239 + 0.971207i \(0.576570\pi\)
\(18\) 0 0
\(19\) 4.35890i 0.229416i
\(20\) 14.0514 6.81068i 0.702570 0.340534i
\(21\) 0 0
\(22\) 5.93094 + 25.8343i 0.269588 + 1.17429i
\(23\) 38.2047i 1.66108i −0.556962 0.830538i \(-0.688033\pi\)
0.556962 0.830538i \(-0.311967\pi\)
\(24\) 0 0
\(25\) −9.76079 −0.390431
\(26\) −3.11984 + 0.716239i −0.119994 + 0.0275477i
\(27\) 0 0
\(28\) 4.61747 + 9.52650i 0.164910 + 0.340232i
\(29\) 51.1656 1.76433 0.882165 0.470940i \(-0.156085\pi\)
0.882165 + 0.470940i \(0.156085\pi\)
\(30\) 0 0
\(31\) 13.6518i 0.440381i −0.975457 0.220191i \(-0.929332\pi\)
0.975457 0.220191i \(-0.0706679\pi\)
\(32\) −13.7015 + 28.9183i −0.428172 + 0.903697i
\(33\) 0 0
\(34\) 15.7895 3.62489i 0.464397 0.106614i
\(35\) 10.3318i 0.295195i
\(36\) 0 0
\(37\) −35.3910 −0.956514 −0.478257 0.878220i \(-0.658731\pi\)
−0.478257 + 0.878220i \(0.658731\pi\)
\(38\) 1.95065 + 8.49676i 0.0513329 + 0.223599i
\(39\) 0 0
\(40\) −24.3424 + 19.5641i −0.608561 + 0.489104i
\(41\) −8.06155 −0.196623 −0.0983116 0.995156i \(-0.531344\pi\)
−0.0983116 + 0.995156i \(0.531344\pi\)
\(42\) 0 0
\(43\) 16.2115i 0.377010i −0.982072 0.188505i \(-0.939636\pi\)
0.982072 0.188505i \(-0.0603643\pi\)
\(44\) −23.1223 47.7045i −0.525506 1.08419i
\(45\) 0 0
\(46\) 17.0970 + 74.4721i 0.371674 + 1.61896i
\(47\) 1.59429i 0.0339210i 0.999856 + 0.0169605i \(0.00539895\pi\)
−0.999856 + 0.0169605i \(0.994601\pi\)
\(48\) 0 0
\(49\) 41.9953 0.857047
\(50\) 19.0266 4.36805i 0.380532 0.0873610i
\(51\) 0 0
\(52\) 5.76095 2.79232i 0.110787 0.0536984i
\(53\) −56.8772 −1.07315 −0.536577 0.843851i \(-0.680283\pi\)
−0.536577 + 0.843851i \(0.680283\pi\)
\(54\) 0 0
\(55\) 51.7371i 0.940675i
\(56\) −13.2640 16.5036i −0.236857 0.294706i
\(57\) 0 0
\(58\) −99.7366 + 22.8971i −1.71960 + 0.394778i
\(59\) 106.526i 1.80553i 0.430135 + 0.902765i \(0.358466\pi\)
−0.430135 + 0.902765i \(0.641534\pi\)
\(60\) 0 0
\(61\) −35.9021 −0.588558 −0.294279 0.955720i \(-0.595080\pi\)
−0.294279 + 0.955720i \(0.595080\pi\)
\(62\) 6.10933 + 26.6114i 0.0985375 + 0.429216i
\(63\) 0 0
\(64\) 13.7670 62.5018i 0.215109 0.976590i
\(65\) 6.24794 0.0961221
\(66\) 0 0
\(67\) 47.5191i 0.709240i −0.935011 0.354620i \(-0.884610\pi\)
0.935011 0.354620i \(-0.115390\pi\)
\(68\) −29.1562 + 14.1319i −0.428767 + 0.207822i
\(69\) 0 0
\(70\) −4.62359 20.1397i −0.0660513 0.287710i
\(71\) 125.941i 1.77382i −0.461941 0.886911i \(-0.652847\pi\)
0.461941 0.886911i \(-0.347153\pi\)
\(72\) 0 0
\(73\) 34.2172 0.468729 0.234364 0.972149i \(-0.424699\pi\)
0.234364 + 0.972149i \(0.424699\pi\)
\(74\) 68.9874 15.8378i 0.932262 0.214025i
\(75\) 0 0
\(76\) −7.60477 15.6897i −0.100063 0.206444i
\(77\) 35.0765 0.455539
\(78\) 0 0
\(79\) 71.1726i 0.900919i −0.892797 0.450460i \(-0.851260\pi\)
0.892797 0.450460i \(-0.148740\pi\)
\(80\) 38.6953 49.0297i 0.483692 0.612871i
\(81\) 0 0
\(82\) 15.7143 3.60763i 0.191638 0.0439954i
\(83\) 149.310i 1.79891i −0.437010 0.899457i \(-0.643962\pi\)
0.437010 0.899457i \(-0.356038\pi\)
\(84\) 0 0
\(85\) −31.6208 −0.372010
\(86\) 7.25479 + 31.6008i 0.0843580 + 0.367452i
\(87\) 0 0
\(88\) 66.4202 + 82.6425i 0.754776 + 0.939119i
\(89\) 169.809 1.90797 0.953983 0.299861i \(-0.0969405\pi\)
0.953983 + 0.299861i \(0.0969405\pi\)
\(90\) 0 0
\(91\) 4.23595i 0.0465488i
\(92\) −66.6541 137.517i −0.724501 1.49475i
\(93\) 0 0
\(94\) −0.713460 3.10773i −0.00758999 0.0330610i
\(95\) 17.0160i 0.179116i
\(96\) 0 0
\(97\) 109.526 1.12914 0.564569 0.825386i \(-0.309042\pi\)
0.564569 + 0.825386i \(0.309042\pi\)
\(98\) −81.8610 + 18.7933i −0.835317 + 0.191769i
\(99\) 0 0
\(100\) −35.1336 + 17.0292i −0.351336 + 0.170292i
\(101\) 118.435 1.17263 0.586313 0.810084i \(-0.300579\pi\)
0.586313 + 0.810084i \(0.300579\pi\)
\(102\) 0 0
\(103\) 34.5985i 0.335908i −0.985795 0.167954i \(-0.946284\pi\)
0.985795 0.167954i \(-0.0537160\pi\)
\(104\) −9.98017 + 8.02112i −0.0959632 + 0.0771261i
\(105\) 0 0
\(106\) 110.870 25.4531i 1.04595 0.240124i
\(107\) 85.2253i 0.796498i −0.917277 0.398249i \(-0.869618\pi\)
0.917277 0.398249i \(-0.130382\pi\)
\(108\) 0 0
\(109\) 146.541 1.34442 0.672208 0.740362i \(-0.265346\pi\)
0.672208 + 0.740362i \(0.265346\pi\)
\(110\) 23.1529 + 100.851i 0.210481 + 0.916824i
\(111\) 0 0
\(112\) 33.2409 + 26.2345i 0.296794 + 0.234236i
\(113\) −36.0565 −0.319084 −0.159542 0.987191i \(-0.551002\pi\)
−0.159542 + 0.987191i \(0.551002\pi\)
\(114\) 0 0
\(115\) 149.141i 1.29688i
\(116\) 184.169 89.2662i 1.58766 0.769537i
\(117\) 0 0
\(118\) −47.6716 207.651i −0.403996 1.75975i
\(119\) 21.4381i 0.180152i
\(120\) 0 0
\(121\) −54.6474 −0.451631
\(122\) 69.9836 16.0665i 0.573636 0.131693i
\(123\) 0 0
\(124\) −23.8177 49.1393i −0.192078 0.396285i
\(125\) −135.697 −1.08558
\(126\) 0 0
\(127\) 103.364i 0.813890i 0.913453 + 0.406945i \(0.133406\pi\)
−0.913453 + 0.406945i \(0.866594\pi\)
\(128\) 1.13432 + 127.995i 0.00886188 + 0.999961i
\(129\) 0 0
\(130\) −12.1790 + 2.79601i −0.0936850 + 0.0215078i
\(131\) 85.6520i 0.653832i 0.945053 + 0.326916i \(0.106009\pi\)
−0.945053 + 0.326916i \(0.893991\pi\)
\(132\) 0 0
\(133\) 11.5364 0.0867402
\(134\) 21.2653 + 92.6285i 0.158696 + 0.691257i
\(135\) 0 0
\(136\) 50.5097 40.5949i 0.371395 0.298492i
\(137\) −89.4114 −0.652638 −0.326319 0.945260i \(-0.605808\pi\)
−0.326319 + 0.945260i \(0.605808\pi\)
\(138\) 0 0
\(139\) 175.314i 1.26125i −0.776087 0.630625i \(-0.782799\pi\)
0.776087 0.630625i \(-0.217201\pi\)
\(140\) 18.0254 + 37.1890i 0.128753 + 0.265636i
\(141\) 0 0
\(142\) 56.3600 + 245.496i 0.396901 + 1.72885i
\(143\) 21.2117i 0.148334i
\(144\) 0 0
\(145\) 199.737 1.37750
\(146\) −66.6993 + 15.3125i −0.456844 + 0.104880i
\(147\) 0 0
\(148\) −127.389 + 61.7451i −0.860736 + 0.417197i
\(149\) −207.665 −1.39372 −0.696862 0.717205i \(-0.745421\pi\)
−0.696862 + 0.717205i \(0.745421\pi\)
\(150\) 0 0
\(151\) 33.2962i 0.220504i −0.993904 0.110252i \(-0.964834\pi\)
0.993904 0.110252i \(-0.0351659\pi\)
\(152\) 21.8452 + 27.1806i 0.143719 + 0.178820i
\(153\) 0 0
\(154\) −68.3742 + 15.6971i −0.443989 + 0.101929i
\(155\) 53.2932i 0.343827i
\(156\) 0 0
\(157\) −232.843 −1.48308 −0.741539 0.670910i \(-0.765904\pi\)
−0.741539 + 0.670910i \(0.765904\pi\)
\(158\) 31.8505 + 138.736i 0.201585 + 0.878077i
\(159\) 0 0
\(160\) −53.4872 + 112.890i −0.334295 + 0.705561i
\(161\) 101.114 0.628039
\(162\) 0 0
\(163\) 133.148i 0.816858i −0.912790 0.408429i \(-0.866077\pi\)
0.912790 0.408429i \(-0.133923\pi\)
\(164\) −29.0173 + 14.0646i −0.176935 + 0.0857599i
\(165\) 0 0
\(166\) 66.8177 + 291.048i 0.402516 + 1.75330i
\(167\) 84.0944i 0.503559i −0.967785 0.251780i \(-0.918984\pi\)
0.967785 0.251780i \(-0.0810158\pi\)
\(168\) 0 0
\(169\) −166.438 −0.984843
\(170\) 61.6382 14.1506i 0.362578 0.0832390i
\(171\) 0 0
\(172\) −28.2834 58.3526i −0.164438 0.339259i
\(173\) −40.8353 −0.236042 −0.118021 0.993011i \(-0.537655\pi\)
−0.118021 + 0.993011i \(0.537655\pi\)
\(174\) 0 0
\(175\) 25.8333i 0.147619i
\(176\) −166.456 131.371i −0.945771 0.746424i
\(177\) 0 0
\(178\) −331.007 + 75.9912i −1.85959 + 0.426917i
\(179\) 94.3723i 0.527219i 0.964629 + 0.263610i \(0.0849131\pi\)
−0.964629 + 0.263610i \(0.915087\pi\)
\(180\) 0 0
\(181\) 101.869 0.562811 0.281405 0.959589i \(-0.409199\pi\)
0.281405 + 0.959589i \(0.409199\pi\)
\(182\) −1.89563 8.25709i −0.0104155 0.0453686i
\(183\) 0 0
\(184\) 191.468 + 238.232i 1.04059 + 1.29474i
\(185\) −138.157 −0.746797
\(186\) 0 0
\(187\) 107.353i 0.574078i
\(188\) 2.78148 + 5.73859i 0.0147951 + 0.0305244i
\(189\) 0 0
\(190\) 7.61484 + 33.1692i 0.0400781 + 0.174575i
\(191\) 96.9894i 0.507798i 0.967231 + 0.253899i \(0.0817131\pi\)
−0.967231 + 0.253899i \(0.918287\pi\)
\(192\) 0 0
\(193\) 218.158 1.13035 0.565177 0.824970i \(-0.308808\pi\)
0.565177 + 0.824970i \(0.308808\pi\)
\(194\) −213.499 + 49.0142i −1.10051 + 0.252650i
\(195\) 0 0
\(196\) 151.161 73.2673i 0.771228 0.373813i
\(197\) 0.646370 0.00328107 0.00164053 0.999999i \(-0.499478\pi\)
0.00164053 + 0.999999i \(0.499478\pi\)
\(198\) 0 0
\(199\) 20.5908i 0.103471i 0.998661 + 0.0517356i \(0.0164753\pi\)
−0.998661 + 0.0517356i \(0.983525\pi\)
\(200\) 60.8650 48.9175i 0.304325 0.244588i
\(201\) 0 0
\(202\) −230.865 + 53.0010i −1.14290 + 0.262381i
\(203\) 135.417i 0.667078i
\(204\) 0 0
\(205\) −31.4702 −0.153513
\(206\) 15.4832 + 67.4426i 0.0751611 + 0.327391i
\(207\) 0 0
\(208\) 15.8647 20.1017i 0.0762727 0.0966429i
\(209\) −57.7694 −0.276408
\(210\) 0 0
\(211\) 161.772i 0.766690i 0.923605 + 0.383345i \(0.125228\pi\)
−0.923605 + 0.383345i \(0.874772\pi\)
\(212\) −204.728 + 99.2311i −0.965697 + 0.468071i
\(213\) 0 0
\(214\) 38.1392 + 166.129i 0.178221 + 0.776303i
\(215\) 63.2854i 0.294350i
\(216\) 0 0
\(217\) 36.1315 0.166504
\(218\) −285.652 + 65.5787i −1.31033 + 0.300820i
\(219\) 0 0
\(220\) −90.2634 186.226i −0.410288 0.846482i
\(221\) −12.9642 −0.0586617
\(222\) 0 0
\(223\) 171.167i 0.767567i 0.923423 + 0.383784i \(0.125379\pi\)
−0.923423 + 0.383784i \(0.874621\pi\)
\(224\) −76.5364 36.2630i −0.341680 0.161888i
\(225\) 0 0
\(226\) 70.2845 16.1356i 0.310994 0.0713966i
\(227\) 110.173i 0.485343i 0.970109 + 0.242672i \(0.0780237\pi\)
−0.970109 + 0.242672i \(0.921976\pi\)
\(228\) 0 0
\(229\) 184.830 0.807120 0.403560 0.914953i \(-0.367773\pi\)
0.403560 + 0.914953i \(0.367773\pi\)
\(230\) 66.7423 + 290.720i 0.290184 + 1.26400i
\(231\) 0 0
\(232\) −319.051 + 256.423i −1.37522 + 1.10527i
\(233\) 226.138 0.970550 0.485275 0.874362i \(-0.338719\pi\)
0.485275 + 0.874362i \(0.338719\pi\)
\(234\) 0 0
\(235\) 6.22369i 0.0264838i
\(236\) 185.851 + 383.438i 0.787506 + 1.62474i
\(237\) 0 0
\(238\) 9.59378 + 41.7891i 0.0403100 + 0.175585i
\(239\) 282.285i 1.18111i 0.806999 + 0.590553i \(0.201090\pi\)
−0.806999 + 0.590553i \(0.798910\pi\)
\(240\) 0 0
\(241\) −8.68875 −0.0360529 −0.0180265 0.999838i \(-0.505738\pi\)
−0.0180265 + 0.999838i \(0.505738\pi\)
\(242\) 106.524 24.4552i 0.440180 0.101055i
\(243\) 0 0
\(244\) −129.228 + 62.6367i −0.529624 + 0.256708i
\(245\) 163.939 0.669138
\(246\) 0 0
\(247\) 6.97641i 0.0282446i
\(248\) 68.4180 + 85.1281i 0.275879 + 0.343259i
\(249\) 0 0
\(250\) 264.513 60.7259i 1.05805 0.242903i
\(251\) 273.275i 1.08874i −0.838844 0.544372i \(-0.816768\pi\)
0.838844 0.544372i \(-0.183232\pi\)
\(252\) 0 0
\(253\) −506.335 −2.00132
\(254\) −46.2565 201.487i −0.182112 0.793255i
\(255\) 0 0
\(256\) −59.4902 248.992i −0.232383 0.972624i
\(257\) −225.614 −0.877877 −0.438938 0.898517i \(-0.644645\pi\)
−0.438938 + 0.898517i \(0.644645\pi\)
\(258\) 0 0
\(259\) 93.6673i 0.361650i
\(260\) 22.4893 10.9005i 0.0864971 0.0419250i
\(261\) 0 0
\(262\) −38.3301 166.961i −0.146298 0.637255i
\(263\) 153.711i 0.584454i 0.956349 + 0.292227i \(0.0943962\pi\)
−0.956349 + 0.292227i \(0.905604\pi\)
\(264\) 0 0
\(265\) −222.034 −0.837864
\(266\) −22.4879 + 5.16267i −0.0845409 + 0.0194085i
\(267\) 0 0
\(268\) −82.9044 171.043i −0.309345 0.638222i
\(269\) 266.196 0.989575 0.494788 0.869014i \(-0.335246\pi\)
0.494788 + 0.869014i \(0.335246\pi\)
\(270\) 0 0
\(271\) 420.472i 1.55156i −0.631005 0.775778i \(-0.717357\pi\)
0.631005 0.775778i \(-0.282643\pi\)
\(272\) −80.2914 + 101.735i −0.295189 + 0.374025i
\(273\) 0 0
\(274\) 174.289 40.0125i 0.636091 0.146031i
\(275\) 129.362i 0.470406i
\(276\) 0 0
\(277\) −51.6625 −0.186507 −0.0932536 0.995642i \(-0.529727\pi\)
−0.0932536 + 0.995642i \(0.529727\pi\)
\(278\) 78.4547 + 341.738i 0.282211 + 1.22927i
\(279\) 0 0
\(280\) −51.7793 64.4257i −0.184926 0.230092i
\(281\) −412.087 −1.46650 −0.733251 0.679958i \(-0.761998\pi\)
−0.733251 + 0.679958i \(0.761998\pi\)
\(282\) 0 0
\(283\) 492.048i 1.73868i 0.494211 + 0.869342i \(0.335457\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(284\) −219.724 453.322i −0.773676 1.59620i
\(285\) 0 0
\(286\) 9.49246 + 41.3478i 0.0331904 + 0.144573i
\(287\) 21.3360i 0.0743416i
\(288\) 0 0
\(289\) −223.388 −0.772969
\(290\) −389.346 + 89.3844i −1.34257 + 0.308222i
\(291\) 0 0
\(292\) 123.164 59.6972i 0.421794 0.204442i
\(293\) 462.881 1.57980 0.789899 0.613237i \(-0.210133\pi\)
0.789899 + 0.613237i \(0.210133\pi\)
\(294\) 0 0
\(295\) 415.851i 1.40966i
\(296\) 220.686 177.367i 0.745562 0.599213i
\(297\) 0 0
\(298\) 404.799 92.9321i 1.35839 0.311853i
\(299\) 61.1466i 0.204504i
\(300\) 0 0
\(301\) 42.9059 0.142544
\(302\) 14.9004 + 64.9039i 0.0493390 + 0.214914i
\(303\) 0 0
\(304\) −54.7463 43.2070i −0.180086 0.142128i
\(305\) −140.152 −0.459516
\(306\) 0 0
\(307\) 477.735i 1.55614i 0.628178 + 0.778070i \(0.283801\pi\)
−0.628178 + 0.778070i \(0.716199\pi\)
\(308\) 126.257 61.1963i 0.409924 0.198689i
\(309\) 0 0
\(310\) 23.8492 + 103.884i 0.0769330 + 0.335109i
\(311\) 397.518i 1.27819i 0.769127 + 0.639096i \(0.220691\pi\)
−0.769127 + 0.639096i \(0.779309\pi\)
\(312\) 0 0
\(313\) −249.717 −0.797818 −0.398909 0.916991i \(-0.630611\pi\)
−0.398909 + 0.916991i \(0.630611\pi\)
\(314\) 453.879 104.200i 1.44548 0.331846i
\(315\) 0 0
\(316\) −124.172 256.184i −0.392948 0.810708i
\(317\) −17.5401 −0.0553317 −0.0276658 0.999617i \(-0.508807\pi\)
−0.0276658 + 0.999617i \(0.508807\pi\)
\(318\) 0 0
\(319\) 678.108i 2.12573i
\(320\) 53.7428 243.991i 0.167946 0.762471i
\(321\) 0 0
\(322\) −197.101 + 45.2496i −0.612115 + 0.140527i
\(323\) 35.3076i 0.109312i
\(324\) 0 0
\(325\) −15.6221 −0.0480681
\(326\) 59.5850 + 259.544i 0.182776 + 0.796147i
\(327\) 0 0
\(328\) 50.2691 40.4016i 0.153260 0.123176i
\(329\) −4.21951 −0.0128252
\(330\) 0 0
\(331\) 524.291i 1.58396i 0.610546 + 0.791981i \(0.290950\pi\)
−0.610546 + 0.791981i \(0.709050\pi\)
\(332\) −260.494 537.436i −0.784621 1.61878i
\(333\) 0 0
\(334\) 37.6331 + 163.924i 0.112674 + 0.490792i
\(335\) 185.502i 0.553738i
\(336\) 0 0
\(337\) −10.3787 −0.0307974 −0.0153987 0.999881i \(-0.504902\pi\)
−0.0153987 + 0.999881i \(0.504902\pi\)
\(338\) 324.437 74.4829i 0.959872 0.220363i
\(339\) 0 0
\(340\) −113.818 + 55.1674i −0.334759 + 0.162257i
\(341\) −180.930 −0.530587
\(342\) 0 0
\(343\) 240.832i 0.702134i
\(344\) 81.2459 + 101.089i 0.236180 + 0.293864i
\(345\) 0 0
\(346\) 79.5998 18.2742i 0.230057 0.0528156i
\(347\) 140.835i 0.405864i −0.979193 0.202932i \(-0.934953\pi\)
0.979193 0.202932i \(-0.0650470\pi\)
\(348\) 0 0
\(349\) 588.176 1.68532 0.842659 0.538447i \(-0.180989\pi\)
0.842659 + 0.538447i \(0.180989\pi\)
\(350\) 11.5607 + 50.3566i 0.0330305 + 0.143876i
\(351\) 0 0
\(352\) 383.260 + 181.589i 1.08881 + 0.515877i
\(353\) 67.7579 0.191949 0.0959744 0.995384i \(-0.469403\pi\)
0.0959744 + 0.995384i \(0.469403\pi\)
\(354\) 0 0
\(355\) 491.643i 1.38491i
\(356\) 611.222 296.258i 1.71692 0.832185i
\(357\) 0 0
\(358\) −42.2325 183.959i −0.117968 0.513852i
\(359\) 136.276i 0.379598i −0.981823 0.189799i \(-0.939216\pi\)
0.981823 0.189799i \(-0.0607836\pi\)
\(360\) 0 0
\(361\) −19.0000 −0.0526316
\(362\) −198.572 + 45.5873i −0.548541 + 0.125932i
\(363\) 0 0
\(364\) 7.39026 + 15.2472i 0.0203029 + 0.0418878i
\(365\) 133.575 0.365959
\(366\) 0 0
\(367\) 274.645i 0.748352i 0.927358 + 0.374176i \(0.122074\pi\)
−0.927358 + 0.374176i \(0.877926\pi\)
\(368\) −479.838 378.699i −1.30391 1.02907i
\(369\) 0 0
\(370\) 269.309 61.8268i 0.727862 0.167100i
\(371\) 150.534i 0.405751i
\(372\) 0 0
\(373\) 7.96701 0.0213593 0.0106796 0.999943i \(-0.496601\pi\)
0.0106796 + 0.999943i \(0.496601\pi\)
\(374\) −48.0414 209.261i −0.128453 0.559523i
\(375\) 0 0
\(376\) −7.98999 9.94144i −0.0212500 0.0264400i
\(377\) 81.8904 0.217216
\(378\) 0 0
\(379\) 514.957i 1.35873i −0.733803 0.679363i \(-0.762256\pi\)
0.733803 0.679363i \(-0.237744\pi\)
\(380\) −29.6871 61.2487i −0.0781239 0.161181i
\(381\) 0 0
\(382\) −43.4037 189.061i −0.113622 0.494923i
\(383\) 669.698i 1.74856i 0.485424 + 0.874279i \(0.338665\pi\)
−0.485424 + 0.874279i \(0.661335\pi\)
\(384\) 0 0
\(385\) 136.930 0.355661
\(386\) −425.254 + 97.6280i −1.10169 + 0.252922i
\(387\) 0 0
\(388\) 394.237 191.086i 1.01607 0.492489i
\(389\) 374.922 0.963809 0.481905 0.876224i \(-0.339945\pi\)
0.481905 + 0.876224i \(0.339945\pi\)
\(390\) 0 0
\(391\) 309.463i 0.791466i
\(392\) −261.868 + 210.465i −0.668032 + 0.536901i
\(393\) 0 0
\(394\) −1.25996 + 0.289257i −0.00319788 + 0.000734155i
\(395\) 277.840i 0.703391i
\(396\) 0 0
\(397\) −32.0134 −0.0806384 −0.0403192 0.999187i \(-0.512837\pi\)
−0.0403192 + 0.999187i \(0.512837\pi\)
\(398\) −9.21458 40.1374i −0.0231522 0.100848i
\(399\) 0 0
\(400\) −96.7524 + 122.592i −0.241881 + 0.306480i
\(401\) −380.066 −0.947796 −0.473898 0.880580i \(-0.657153\pi\)
−0.473898 + 0.880580i \(0.657153\pi\)
\(402\) 0 0
\(403\) 21.8497i 0.0542177i
\(404\) 426.304 206.629i 1.05521 0.511457i
\(405\) 0 0
\(406\) −60.6004 263.967i −0.149262 0.650165i
\(407\) 469.044i 1.15244i
\(408\) 0 0
\(409\) 116.916 0.285858 0.142929 0.989733i \(-0.454348\pi\)
0.142929 + 0.989733i \(0.454348\pi\)
\(410\) 61.3446 14.0832i 0.149621 0.0343494i
\(411\) 0 0
\(412\) −60.3625 124.536i −0.146511 0.302273i
\(413\) −281.937 −0.682655
\(414\) 0 0
\(415\) 582.867i 1.40450i
\(416\) −21.9292 + 46.2837i −0.0527145 + 0.111259i
\(417\) 0 0
\(418\) 112.609 25.8524i 0.269400 0.0618478i
\(419\) 0.146671i 0.000350050i 1.00000 0.000175025i \(5.57122e-5\pi\)
−1.00000 0.000175025i \(0.999944\pi\)
\(420\) 0 0
\(421\) −613.336 −1.45686 −0.728428 0.685123i \(-0.759749\pi\)
−0.728428 + 0.685123i \(0.759749\pi\)
\(422\) −72.3944 315.340i −0.171551 0.747251i
\(423\) 0 0
\(424\) 354.667 285.048i 0.836479 0.672283i
\(425\) 79.0636 0.186032
\(426\) 0 0
\(427\) 95.0199i 0.222529i
\(428\) −148.689 306.766i −0.347404 0.716743i
\(429\) 0 0
\(430\) 28.3208 + 123.362i 0.0658624 + 0.286887i
\(431\) 310.234i 0.719800i 0.932991 + 0.359900i \(0.117189\pi\)
−0.932991 + 0.359900i \(0.882811\pi\)
\(432\) 0 0
\(433\) −194.780 −0.449838 −0.224919 0.974378i \(-0.572212\pi\)
−0.224919 + 0.974378i \(0.572212\pi\)
\(434\) −70.4307 + 16.1692i −0.162283 + 0.0372562i
\(435\) 0 0
\(436\) 527.471 255.664i 1.20980 0.586385i
\(437\) −166.531 −0.381077
\(438\) 0 0
\(439\) 340.063i 0.774631i 0.921947 + 0.387315i \(0.126598\pi\)
−0.921947 + 0.387315i \(0.873402\pi\)
\(440\) 259.288 + 322.615i 0.589290 + 0.733216i
\(441\) 0 0
\(442\) 25.2711 5.80163i 0.0571744 0.0131259i
\(443\) 643.348i 1.45225i −0.687561 0.726127i \(-0.741318\pi\)
0.687561 0.726127i \(-0.258682\pi\)
\(444\) 0 0
\(445\) 662.891 1.48964
\(446\) −76.5992 333.655i −0.171747 0.748106i
\(447\) 0 0
\(448\) 165.420 + 36.4363i 0.369240 + 0.0813309i
\(449\) 416.379 0.927348 0.463674 0.886006i \(-0.346531\pi\)
0.463674 + 0.886006i \(0.346531\pi\)
\(450\) 0 0
\(451\) 106.841i 0.236899i
\(452\) −129.784 + 62.9061i −0.287133 + 0.139173i
\(453\) 0 0
\(454\) −49.3035 214.759i −0.108598 0.473037i
\(455\) 16.5360i 0.0363430i
\(456\) 0 0
\(457\) 814.576 1.78244 0.891221 0.453568i \(-0.149849\pi\)
0.891221 + 0.453568i \(0.149849\pi\)
\(458\) −360.288 + 82.7134i −0.786655 + 0.180597i
\(459\) 0 0
\(460\) −260.200 536.830i −0.565653 1.16702i
\(461\) −122.745 −0.266259 −0.133129 0.991099i \(-0.542503\pi\)
−0.133129 + 0.991099i \(0.542503\pi\)
\(462\) 0 0
\(463\) 348.734i 0.753206i 0.926375 + 0.376603i \(0.122908\pi\)
−0.926375 + 0.376603i \(0.877092\pi\)
\(464\) 507.172 642.622i 1.09304 1.38496i
\(465\) 0 0
\(466\) −440.809 + 101.199i −0.945942 + 0.217165i
\(467\) 41.9400i 0.0898072i 0.998991 + 0.0449036i \(0.0142981\pi\)
−0.998991 + 0.0449036i \(0.985702\pi\)
\(468\) 0 0
\(469\) 125.766 0.268158
\(470\) −2.78516 12.1318i −0.00592588 0.0258123i
\(471\) 0 0
\(472\) −533.871 664.262i −1.13108 1.40733i
\(473\) −214.854 −0.454236
\(474\) 0 0
\(475\) 42.5463i 0.0895711i
\(476\) −37.4021 77.1659i −0.0785759 0.162113i
\(477\) 0 0
\(478\) −126.325 550.255i −0.264279 1.15116i
\(479\) 257.365i 0.537297i −0.963238 0.268648i \(-0.913423\pi\)
0.963238 0.268648i \(-0.0865770\pi\)
\(480\) 0 0
\(481\) −56.6433 −0.117761
\(482\) 16.9369 3.88830i 0.0351388 0.00806702i
\(483\) 0 0
\(484\) −196.702 + 95.3408i −0.406408 + 0.196985i
\(485\) 427.563 0.881573
\(486\) 0 0
\(487\) 312.131i 0.640927i 0.947261 + 0.320463i \(0.103839\pi\)
−0.947261 + 0.320463i \(0.896161\pi\)
\(488\) 223.873 179.928i 0.458756 0.368705i
\(489\) 0 0
\(490\) −319.565 + 73.3643i −0.652172 + 0.149723i
\(491\) 855.711i 1.74279i −0.490581 0.871396i \(-0.663215\pi\)
0.490581 0.871396i \(-0.336785\pi\)
\(492\) 0 0
\(493\) −414.448 −0.840665
\(494\) 3.12201 + 13.5991i 0.00631987 + 0.0275285i
\(495\) 0 0
\(496\) −171.462 135.322i −0.345690 0.272826i
\(497\) 333.321 0.670667
\(498\) 0 0
\(499\) 437.337i 0.876427i 0.898871 + 0.438214i \(0.144389\pi\)
−0.898871 + 0.438214i \(0.855611\pi\)
\(500\) −488.438 + 236.745i −0.976876 + 0.473489i
\(501\) 0 0
\(502\) 122.293 + 532.692i 0.243612 + 1.06114i
\(503\) 454.628i 0.903834i −0.892060 0.451917i \(-0.850740\pi\)
0.892060 0.451917i \(-0.149260\pi\)
\(504\) 0 0
\(505\) 462.341 0.915527
\(506\) 986.994 226.590i 1.95058 0.447806i
\(507\) 0 0
\(508\) 180.335 + 372.056i 0.354989 + 0.732393i
\(509\) −330.296 −0.648912 −0.324456 0.945901i \(-0.605181\pi\)
−0.324456 + 0.945901i \(0.605181\pi\)
\(510\) 0 0
\(511\) 90.5606i 0.177222i
\(512\) 227.390 + 458.735i 0.444121 + 0.895967i
\(513\) 0 0
\(514\) 439.788 100.965i 0.855619 0.196429i
\(515\) 135.064i 0.262260i
\(516\) 0 0
\(517\) 21.1294 0.0408693
\(518\) 41.9171 + 182.585i 0.0809210 + 0.352480i
\(519\) 0 0
\(520\) −38.9600 + 31.3124i −0.0749231 + 0.0602161i
\(521\) 156.351 0.300098 0.150049 0.988679i \(-0.452057\pi\)
0.150049 + 0.988679i \(0.452057\pi\)
\(522\) 0 0
\(523\) 383.630i 0.733518i 0.930316 + 0.366759i \(0.119533\pi\)
−0.930316 + 0.366759i \(0.880467\pi\)
\(524\) 149.433 + 308.302i 0.285178 + 0.588362i
\(525\) 0 0
\(526\) −68.7874 299.628i −0.130774 0.569635i
\(527\) 110.581i 0.209832i
\(528\) 0 0
\(529\) −930.602 −1.75917
\(530\) 432.809 99.3624i 0.816620 0.187476i
\(531\) 0 0
\(532\) 41.5251 20.1271i 0.0780546 0.0378329i
\(533\) −12.9025 −0.0242073
\(534\) 0 0
\(535\) 332.698i 0.621865i
\(536\) 238.148 + 296.313i 0.444307 + 0.552823i
\(537\) 0 0
\(538\) −518.893 + 119.125i −0.964485 + 0.221422i
\(539\) 556.572i 1.03260i
\(540\) 0 0
\(541\) −167.893 −0.310337 −0.155169 0.987888i \(-0.549592\pi\)
−0.155169 + 0.987888i \(0.549592\pi\)
\(542\) 188.165 + 819.622i 0.347169 + 1.51222i
\(543\) 0 0
\(544\) 110.984 234.242i 0.204015 0.430592i
\(545\) 572.060 1.04965
\(546\) 0 0
\(547\) 93.9282i 0.171715i −0.996307 0.0858576i \(-0.972637\pi\)
0.996307 0.0858576i \(-0.0273630\pi\)
\(548\) −321.834 + 155.992i −0.587288 + 0.284657i
\(549\) 0 0
\(550\) −57.8906 252.164i −0.105256 0.458479i
\(551\) 223.026i 0.404765i
\(552\) 0 0
\(553\) 188.368 0.340630
\(554\) 100.705 23.1195i 0.181778 0.0417319i
\(555\) 0 0
\(556\) −305.862 631.037i −0.550112 1.13496i
\(557\) −658.999 −1.18312 −0.591561 0.806260i \(-0.701488\pi\)
−0.591561 + 0.806260i \(0.701488\pi\)
\(558\) 0 0
\(559\) 25.9464i 0.0464158i
\(560\) 129.764 + 102.413i 0.231721 + 0.182880i
\(561\) 0 0
\(562\) 803.277 184.413i 1.42932 0.328137i
\(563\) 709.470i 1.26016i 0.776531 + 0.630079i \(0.216978\pi\)
−0.776531 + 0.630079i \(0.783022\pi\)
\(564\) 0 0
\(565\) −140.755 −0.249124
\(566\) −220.196 959.144i −0.389039 1.69460i
\(567\) 0 0
\(568\) 631.172 + 785.328i 1.11122 + 1.38262i
\(569\) −613.773 −1.07869 −0.539344 0.842086i \(-0.681328\pi\)
−0.539344 + 0.842086i \(0.681328\pi\)
\(570\) 0 0
\(571\) 436.257i 0.764022i −0.924158 0.382011i \(-0.875232\pi\)
0.924158 0.382011i \(-0.124768\pi\)
\(572\) −37.0071 76.3510i −0.0646978 0.133481i
\(573\) 0 0
\(574\) 9.54809 + 41.5901i 0.0166343 + 0.0724567i
\(575\) 372.908i 0.648536i
\(576\) 0 0
\(577\) 356.629 0.618074 0.309037 0.951050i \(-0.399993\pi\)
0.309037 + 0.951050i \(0.399993\pi\)
\(578\) 435.448 99.9683i 0.753370 0.172956i
\(579\) 0 0
\(580\) 718.948 348.473i 1.23957 0.600815i
\(581\) 395.170 0.680154
\(582\) 0 0
\(583\) 753.805i 1.29298i
\(584\) −213.367 + 171.484i −0.365354 + 0.293637i
\(585\) 0 0
\(586\) −902.290 + 207.144i −1.53974 + 0.353488i
\(587\) 411.394i 0.700842i −0.936592 0.350421i \(-0.886039\pi\)
0.936592 0.350421i \(-0.113961\pi\)
\(588\) 0 0
\(589\) −59.5069 −0.101030
\(590\) −186.098 810.615i −0.315420 1.37392i
\(591\) 0 0
\(592\) −350.809 + 444.499i −0.592582 + 0.750843i
\(593\) −110.332 −0.186057 −0.0930285 0.995663i \(-0.529655\pi\)
−0.0930285 + 0.995663i \(0.529655\pi\)
\(594\) 0 0
\(595\) 83.6890i 0.140654i
\(596\) −747.483 + 362.303i −1.25417 + 0.607892i
\(597\) 0 0
\(598\) 27.3637 + 119.193i 0.0457587 + 0.199319i
\(599\) 679.317i 1.13408i 0.823689 + 0.567042i \(0.191912\pi\)
−0.823689 + 0.567042i \(0.808088\pi\)
\(600\) 0 0
\(601\) −873.422 −1.45328 −0.726641 0.687018i \(-0.758920\pi\)
−0.726641 + 0.687018i \(0.758920\pi\)
\(602\) −83.6361 + 19.2008i −0.138930 + 0.0318950i
\(603\) 0 0
\(604\) −58.0903 119.849i −0.0961760 0.198425i
\(605\) −213.329 −0.352610
\(606\) 0 0
\(607\) 14.0258i 0.0231067i −0.999933 0.0115534i \(-0.996322\pi\)
0.999933 0.0115534i \(-0.00367763\pi\)
\(608\) 126.052 + 59.7235i 0.207322 + 0.0982294i
\(609\) 0 0
\(610\) 273.198 62.7196i 0.447865 0.102819i
\(611\) 2.55165i 0.00417619i
\(612\) 0 0
\(613\) 22.8620 0.0372953 0.0186477 0.999826i \(-0.494064\pi\)
0.0186477 + 0.999826i \(0.494064\pi\)
\(614\) −213.791 931.244i −0.348194 1.51668i
\(615\) 0 0
\(616\) −218.725 + 175.791i −0.355073 + 0.285374i
\(617\) −935.677 −1.51649 −0.758247 0.651968i \(-0.773944\pi\)
−0.758247 + 0.651968i \(0.773944\pi\)
\(618\) 0 0
\(619\) 256.561i 0.414476i 0.978291 + 0.207238i \(0.0664475\pi\)
−0.978291 + 0.207238i \(0.933553\pi\)
\(620\) −92.9782 191.827i −0.149965 0.309399i
\(621\) 0 0
\(622\) −177.893 774.877i −0.286002 1.24578i
\(623\) 449.423i 0.721386i
\(624\) 0 0
\(625\) −285.707 −0.457132
\(626\) 486.771 111.751i 0.777589 0.178516i
\(627\) 0 0
\(628\) −838.112 + 406.231i −1.33457 + 0.646865i
\(629\) 286.672 0.455758
\(630\) 0 0
\(631\) 530.971i 0.841476i 0.907182 + 0.420738i \(0.138229\pi\)
−0.907182 + 0.420738i \(0.861771\pi\)
\(632\) 356.691 + 443.808i 0.564385 + 0.702228i
\(633\) 0 0
\(634\) 34.1908 7.84939i 0.0539288 0.0123807i
\(635\) 403.507i 0.635444i
\(636\) 0 0
\(637\) 67.2134 0.105516
\(638\) 303.460 + 1321.83i 0.475643 + 2.07183i
\(639\) 0 0
\(640\) 4.42810 + 499.660i 0.00691890 + 0.780718i
\(641\) 394.362 0.615230 0.307615 0.951511i \(-0.400469\pi\)
0.307615 + 0.951511i \(0.400469\pi\)
\(642\) 0 0
\(643\) 4.02353i 0.00625743i −0.999995 0.00312871i \(-0.999004\pi\)
0.999995 0.00312871i \(-0.000995902\pi\)
\(644\) 363.958 176.409i 0.565151 0.273928i
\(645\) 0 0
\(646\) −15.8005 68.8249i −0.0244590 0.106540i
\(647\) 627.845i 0.970394i 0.874405 + 0.485197i \(0.161252\pi\)
−0.874405 + 0.485197i \(0.838748\pi\)
\(648\) 0 0
\(649\) 1411.81 2.17537
\(650\) 30.4521 6.99106i 0.0468493 0.0107555i
\(651\) 0 0
\(652\) −232.297 479.262i −0.356284 0.735064i
\(653\) 548.722 0.840309 0.420155 0.907453i \(-0.361976\pi\)
0.420155 + 0.907453i \(0.361976\pi\)
\(654\) 0 0
\(655\) 334.364i 0.510479i
\(656\) −79.9090 + 101.250i −0.121813 + 0.154345i
\(657\) 0 0
\(658\) 8.22504 1.88827i 0.0125001 0.00286971i
\(659\) 499.633i 0.758168i −0.925362 0.379084i \(-0.876239\pi\)
0.925362 0.379084i \(-0.123761\pi\)
\(660\) 0 0
\(661\) −655.267 −0.991326 −0.495663 0.868515i \(-0.665075\pi\)
−0.495663 + 0.868515i \(0.665075\pi\)
\(662\) −234.626 1022.00i −0.354419 1.54380i
\(663\) 0 0
\(664\) 748.287 + 931.046i 1.12694 + 1.40218i
\(665\) 45.0353 0.0677223
\(666\) 0 0
\(667\) 1954.77i 2.93069i
\(668\) −146.716 302.695i −0.219634 0.453136i
\(669\) 0 0
\(670\) 83.0141 + 361.598i 0.123902 + 0.539698i
\(671\) 475.817i 0.709117i
\(672\) 0 0
\(673\) 686.513 1.02008 0.510039 0.860151i \(-0.329631\pi\)
0.510039 + 0.860151i \(0.329631\pi\)
\(674\) 20.2311 4.64458i 0.0300165 0.00689107i
\(675\) 0 0
\(676\) −599.090 + 290.377i −0.886228 + 0.429553i
\(677\) 639.146 0.944085 0.472043 0.881576i \(-0.343517\pi\)
0.472043 + 0.881576i \(0.343517\pi\)
\(678\) 0 0
\(679\) 289.877i 0.426918i
\(680\) 197.177 158.472i 0.289966 0.233047i
\(681\) 0 0
\(682\) 352.686 80.9681i 0.517135 0.118722i
\(683\) 839.655i 1.22936i 0.788775 + 0.614682i \(0.210716\pi\)
−0.788775 + 0.614682i \(0.789284\pi\)
\(684\) 0 0
\(685\) −349.039 −0.509546
\(686\) −107.775 469.451i −0.157106 0.684331i
\(687\) 0 0
\(688\) −203.610 160.694i −0.295945 0.233567i
\(689\) −91.0319 −0.132122
\(690\) 0 0
\(691\) 1091.05i 1.57895i 0.613783 + 0.789475i \(0.289647\pi\)
−0.613783 + 0.789475i \(0.710353\pi\)
\(692\) −146.985 + 71.2434i −0.212406 + 0.102953i
\(693\) 0 0
\(694\) 63.0249 + 274.528i 0.0908140 + 0.395573i
\(695\) 684.380i 0.984720i
\(696\) 0 0
\(697\) 65.2996 0.0936867
\(698\) −1146.53 + 263.215i −1.64259 + 0.377098i
\(699\) 0 0
\(700\) −45.0702 92.9862i −0.0643860 0.132837i
\(701\) −431.165 −0.615071 −0.307536 0.951537i \(-0.599504\pi\)
−0.307536 + 0.951537i \(0.599504\pi\)
\(702\) 0 0
\(703\) 154.266i 0.219439i
\(704\) −828.349 182.457i −1.17663 0.259171i
\(705\) 0 0
\(706\) −132.080 + 30.3223i −0.187082 + 0.0429495i
\(707\) 313.456i 0.443360i
\(708\) 0 0
\(709\) −197.989 −0.279251 −0.139626 0.990204i \(-0.544590\pi\)
−0.139626 + 0.990204i \(0.544590\pi\)
\(710\) 220.015 + 958.355i 0.309880 + 1.34980i
\(711\) 0 0
\(712\) −1058.87 + 851.021i −1.48718 + 1.19525i
\(713\) −521.564 −0.731506
\(714\) 0 0
\(715\) 82.8052i 0.115811i
\(716\) 164.647 + 339.690i 0.229954 + 0.474427i
\(717\) 0 0
\(718\) 60.9847 + 265.641i 0.0849369 + 0.369973i
\(719\) 555.460i 0.772545i 0.922385 + 0.386273i \(0.126238\pi\)
−0.922385 + 0.386273i \(0.873762\pi\)
\(720\) 0 0
\(721\) 91.5699 0.127004
\(722\) 37.0365 8.50269i 0.0512971 0.0117766i
\(723\) 0 0
\(724\) 366.674 177.726i 0.506455 0.245478i
\(725\) −499.416 −0.688850
\(726\) 0 0
\(727\) 8.18995i 0.0112654i 0.999984 + 0.00563271i \(0.00179296\pi\)
−0.999984 + 0.00563271i \(0.998207\pi\)
\(728\) −21.2290 26.4139i −0.0291607 0.0362829i
\(729\) 0 0
\(730\) −260.377 + 59.7762i −0.356681 + 0.0818852i
\(731\) 131.315i 0.179637i
\(732\) 0 0
\(733\) −491.152 −0.670058 −0.335029 0.942208i \(-0.608746\pi\)
−0.335029 + 0.942208i \(0.608746\pi\)
\(734\) −122.907 535.364i −0.167448 0.729378i
\(735\) 0 0
\(736\) 1104.82 + 523.462i 1.50111 + 0.711226i
\(737\) −629.780 −0.854518
\(738\) 0 0
\(739\) 1037.82i 1.40436i −0.712000 0.702180i \(-0.752210\pi\)
0.712000 0.702180i \(-0.247790\pi\)
\(740\) −497.294 + 241.037i −0.672018 + 0.325726i
\(741\) 0 0
\(742\) 67.3653 + 293.434i 0.0907888 + 0.395463i
\(743\) 148.421i 0.199759i 0.995000 + 0.0998795i \(0.0318457\pi\)
−0.995000 + 0.0998795i \(0.968154\pi\)
\(744\) 0 0
\(745\) −810.670 −1.08815
\(746\) −15.5300 + 3.56532i −0.0208177 + 0.00477925i
\(747\) 0 0
\(748\) 187.293 + 386.413i 0.250392 + 0.516594i
\(749\) 225.561 0.301149
\(750\) 0 0
\(751\) 443.027i 0.589916i 0.955510 + 0.294958i \(0.0953056\pi\)
−0.955510 + 0.294958i \(0.904694\pi\)
\(752\) 20.0237 + 15.8032i 0.0266273 + 0.0210148i
\(753\) 0 0
\(754\) −159.628 + 36.6468i −0.211709 + 0.0486032i
\(755\) 129.980i 0.172159i
\(756\) 0 0
\(757\) 878.626 1.16067 0.580334 0.814379i \(-0.302922\pi\)
0.580334 + 0.814379i \(0.302922\pi\)
\(758\) 230.448 + 1003.80i 0.304022 + 1.32428i
\(759\) 0 0
\(760\) 85.2781 + 106.106i 0.112208 + 0.139613i
\(761\) 750.924 0.986760 0.493380 0.869814i \(-0.335761\pi\)
0.493380 + 0.869814i \(0.335761\pi\)
\(762\) 0 0
\(763\) 387.842i 0.508312i
\(764\) 169.213 + 349.111i 0.221483 + 0.456951i
\(765\) 0 0
\(766\) −299.696 1305.44i −0.391249 1.70422i
\(767\) 170.495i 0.222288i
\(768\) 0 0
\(769\) −315.536 −0.410319 −0.205160 0.978729i \(-0.565771\pi\)
−0.205160 + 0.978729i \(0.565771\pi\)
\(770\) −266.916 + 61.2773i −0.346644 + 0.0795810i
\(771\) 0 0
\(772\) 785.254 380.611i 1.01717 0.493019i
\(773\) 110.053 0.142371 0.0711853 0.997463i \(-0.477322\pi\)
0.0711853 + 0.997463i \(0.477322\pi\)
\(774\) 0 0
\(775\) 133.252i 0.171939i
\(776\) −682.970 + 548.907i −0.880116 + 0.707354i
\(777\) 0 0
\(778\) −730.832 + 167.781i −0.939372 + 0.215657i
\(779\) 35.1395i 0.0451085i
\(780\) 0 0
\(781\) −1669.13 −2.13716
\(782\) −138.488 603.234i −0.177094 0.771399i
\(783\) 0 0
\(784\) 416.273 527.447i 0.530960 0.672764i
\(785\) −908.961 −1.15791
\(786\) 0 0
\(787\) 660.023i 0.838657i −0.907834 0.419329i \(-0.862265\pi\)
0.907834 0.419329i \(-0.137735\pi\)
\(788\) 2.32659 1.12769i 0.00295253 0.00143108i
\(789\) 0 0
\(790\) 124.336 + 541.590i 0.157387 + 0.685557i
\(791\)