Properties

Label 624.2.cn.f.353.2
Level $624$
Weight $2$
Character 624.353
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 353.2
Character \(\chi\) \(=\) 624.353
Dual form 624.2.cn.f.449.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.55814 - 0.756439i) q^{3} +(-3.14772 - 3.14772i) q^{5} +(-2.26593 + 0.607154i) q^{7} +(1.85560 + 2.35728i) q^{9} +O(q^{10})\) \(q+(-1.55814 - 0.756439i) q^{3} +(-3.14772 - 3.14772i) q^{5} +(-2.26593 + 0.607154i) q^{7} +(1.85560 + 2.35728i) q^{9} +(-3.54906 - 0.950969i) q^{11} +(2.62122 - 2.47572i) q^{13} +(2.52353 + 7.28565i) q^{15} +(0.814572 - 1.41088i) q^{17} +(1.43802 + 5.36676i) q^{19} +(3.98991 + 0.768007i) q^{21} +(0.495519 + 0.858264i) q^{23} +14.8163i q^{25} +(-1.10815 - 5.07661i) q^{27} +(-3.01980 + 1.74348i) q^{29} +(4.72615 - 4.72615i) q^{31} +(4.81059 + 4.16639i) q^{33} +(9.04366 + 5.22136i) q^{35} +(0.485423 - 1.81162i) q^{37} +(-5.95697 + 1.87472i) q^{39} +(-1.42485 + 5.31761i) q^{41} +(2.75816 + 1.59242i) q^{43} +(1.57914 - 13.2610i) q^{45} +(1.43015 - 1.43015i) q^{47} +(-1.29638 + 0.748468i) q^{49} +(-2.33646 + 1.58217i) q^{51} +9.03162i q^{53} +(8.17808 + 14.1648i) q^{55} +(1.81899 - 9.44994i) q^{57} +(-0.206728 - 0.771519i) q^{59} +(-0.868812 + 1.50483i) q^{61} +(-5.63588 - 4.21478i) q^{63} +(-16.0438 - 0.458014i) q^{65} +(-12.5951 - 3.37485i) q^{67} +(-0.122863 - 1.71213i) q^{69} +(-4.81283 + 1.28959i) q^{71} +(-5.36519 - 5.36519i) q^{73} +(11.2076 - 23.0859i) q^{75} +8.61930 q^{77} -4.28909 q^{79} +(-2.11350 + 8.74832i) q^{81} +(5.71245 + 5.71245i) q^{83} +(-7.00511 + 1.87701i) q^{85} +(6.02411 - 0.432294i) q^{87} +(-5.12406 - 1.37299i) q^{89} +(-4.43637 + 7.20128i) q^{91} +(-10.9390 + 3.78895i) q^{93} +(12.3666 - 21.4196i) q^{95} +(1.80454 + 6.73465i) q^{97} +(-4.34394 - 10.1307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.55814 0.756439i −0.899592 0.436730i
\(4\) 0 0
\(5\) −3.14772 3.14772i −1.40770 1.40770i −0.771619 0.636085i \(-0.780553\pi\)
−0.636085 0.771619i \(-0.719447\pi\)
\(6\) 0 0
\(7\) −2.26593 + 0.607154i −0.856440 + 0.229482i −0.660215 0.751076i \(-0.729535\pi\)
−0.196225 + 0.980559i \(0.562868\pi\)
\(8\) 0 0
\(9\) 1.85560 + 2.35728i 0.618533 + 0.785759i
\(10\) 0 0
\(11\) −3.54906 0.950969i −1.07008 0.286728i −0.319556 0.947567i \(-0.603534\pi\)
−0.750527 + 0.660840i \(0.770200\pi\)
\(12\) 0 0
\(13\) 2.62122 2.47572i 0.726997 0.686641i
\(14\) 0 0
\(15\) 2.52353 + 7.28565i 0.651573 + 1.88115i
\(16\) 0 0
\(17\) 0.814572 1.41088i 0.197563 0.342189i −0.750175 0.661240i \(-0.770031\pi\)
0.947738 + 0.319051i \(0.103364\pi\)
\(18\) 0 0
\(19\) 1.43802 + 5.36676i 0.329904 + 1.23122i 0.909289 + 0.416165i \(0.136626\pi\)
−0.579385 + 0.815054i \(0.696707\pi\)
\(20\) 0 0
\(21\) 3.98991 + 0.768007i 0.870669 + 0.167593i
\(22\) 0 0
\(23\) 0.495519 + 0.858264i 0.103323 + 0.178961i 0.913052 0.407844i \(-0.133719\pi\)
−0.809729 + 0.586804i \(0.800386\pi\)
\(24\) 0 0
\(25\) 14.8163i 2.96326i
\(26\) 0 0
\(27\) −1.10815 5.07661i −0.213263 0.976995i
\(28\) 0 0
\(29\) −3.01980 + 1.74348i −0.560763 + 0.323757i −0.753452 0.657503i \(-0.771613\pi\)
0.192689 + 0.981260i \(0.438279\pi\)
\(30\) 0 0
\(31\) 4.72615 4.72615i 0.848841 0.848841i −0.141148 0.989989i \(-0.545079\pi\)
0.989989 + 0.141148i \(0.0450793\pi\)
\(32\) 0 0
\(33\) 4.81059 + 4.16639i 0.837416 + 0.725276i
\(34\) 0 0
\(35\) 9.04366 + 5.22136i 1.52866 + 0.882571i
\(36\) 0 0
\(37\) 0.485423 1.81162i 0.0798031 0.297829i −0.914476 0.404639i \(-0.867397\pi\)
0.994279 + 0.106810i \(0.0340637\pi\)
\(38\) 0 0
\(39\) −5.95697 + 1.87472i −0.953878 + 0.300195i
\(40\) 0 0
\(41\) −1.42485 + 5.31761i −0.222524 + 0.830471i 0.760857 + 0.648919i \(0.224779\pi\)
−0.983381 + 0.181552i \(0.941888\pi\)
\(42\) 0 0
\(43\) 2.75816 + 1.59242i 0.420615 + 0.242842i 0.695341 0.718680i \(-0.255254\pi\)
−0.274725 + 0.961523i \(0.588587\pi\)
\(44\) 0 0
\(45\) 1.57914 13.2610i 0.235404 1.97683i
\(46\) 0 0
\(47\) 1.43015 1.43015i 0.208609 0.208609i −0.595067 0.803676i \(-0.702875\pi\)
0.803676 + 0.595067i \(0.202875\pi\)
\(48\) 0 0
\(49\) −1.29638 + 0.748468i −0.185198 + 0.106924i
\(50\) 0 0
\(51\) −2.33646 + 1.58217i −0.327170 + 0.221549i
\(52\) 0 0
\(53\) 9.03162i 1.24059i 0.784369 + 0.620294i \(0.212987\pi\)
−0.784369 + 0.620294i \(0.787013\pi\)
\(54\) 0 0
\(55\) 8.17808 + 14.1648i 1.10273 + 1.90999i
\(56\) 0 0
\(57\) 1.81899 9.44994i 0.240932 1.25168i
\(58\) 0 0
\(59\) −0.206728 0.771519i −0.0269137 0.100443i 0.951163 0.308691i \(-0.0998907\pi\)
−0.978076 + 0.208247i \(0.933224\pi\)
\(60\) 0 0
\(61\) −0.868812 + 1.50483i −0.111240 + 0.192673i −0.916270 0.400560i \(-0.868816\pi\)
0.805030 + 0.593233i \(0.202149\pi\)
\(62\) 0 0
\(63\) −5.63588 4.21478i −0.710055 0.531013i
\(64\) 0 0
\(65\) −16.0438 0.458014i −1.98998 0.0568096i
\(66\) 0 0
\(67\) −12.5951 3.37485i −1.53874 0.412303i −0.612879 0.790176i \(-0.709989\pi\)
−0.925857 + 0.377873i \(0.876656\pi\)
\(68\) 0 0
\(69\) −0.122863 1.71213i −0.0147910 0.206116i
\(70\) 0 0
\(71\) −4.81283 + 1.28959i −0.571178 + 0.153047i −0.532837 0.846218i \(-0.678874\pi\)
−0.0383409 + 0.999265i \(0.512207\pi\)
\(72\) 0 0
\(73\) −5.36519 5.36519i −0.627948 0.627948i 0.319604 0.947551i \(-0.396450\pi\)
−0.947551 + 0.319604i \(0.896450\pi\)
\(74\) 0 0
\(75\) 11.2076 23.0859i 1.29415 2.66573i
\(76\) 0 0
\(77\) 8.61930 0.982261
\(78\) 0 0
\(79\) −4.28909 −0.482561 −0.241280 0.970455i \(-0.577567\pi\)
−0.241280 + 0.970455i \(0.577567\pi\)
\(80\) 0 0
\(81\) −2.11350 + 8.74832i −0.234834 + 0.972036i
\(82\) 0 0
\(83\) 5.71245 + 5.71245i 0.627023 + 0.627023i 0.947318 0.320295i \(-0.103782\pi\)
−0.320295 + 0.947318i \(0.603782\pi\)
\(84\) 0 0
\(85\) −7.00511 + 1.87701i −0.759811 + 0.203591i
\(86\) 0 0
\(87\) 6.02411 0.432294i 0.645853 0.0463468i
\(88\) 0 0
\(89\) −5.12406 1.37299i −0.543150 0.145536i −0.0231959 0.999731i \(-0.507384\pi\)
−0.519954 + 0.854194i \(0.674051\pi\)
\(90\) 0 0
\(91\) −4.43637 + 7.20128i −0.465057 + 0.754900i
\(92\) 0 0
\(93\) −10.9390 + 3.78895i −1.13433 + 0.392896i
\(94\) 0 0
\(95\) 12.3666 21.4196i 1.26879 2.19760i
\(96\) 0 0
\(97\) 1.80454 + 6.73465i 0.183224 + 0.683800i 0.995004 + 0.0998369i \(0.0318321\pi\)
−0.811780 + 0.583963i \(0.801501\pi\)
\(98\) 0 0
\(99\) −4.34394 10.1307i −0.436583 1.01818i
\(100\) 0 0
\(101\) 2.74059 + 4.74684i 0.272699 + 0.472328i 0.969552 0.244886i \(-0.0787504\pi\)
−0.696853 + 0.717214i \(0.745417\pi\)
\(102\) 0 0
\(103\) 1.08980i 0.107381i 0.998558 + 0.0536906i \(0.0170985\pi\)
−0.998558 + 0.0536906i \(0.982902\pi\)
\(104\) 0 0
\(105\) −10.1416 14.9766i −0.989723 1.46157i
\(106\) 0 0
\(107\) 3.10085 1.79028i 0.299771 0.173073i −0.342569 0.939493i \(-0.611297\pi\)
0.642340 + 0.766420i \(0.277964\pi\)
\(108\) 0 0
\(109\) 0.882554 0.882554i 0.0845333 0.0845333i −0.663576 0.748109i \(-0.730962\pi\)
0.748109 + 0.663576i \(0.230962\pi\)
\(110\) 0 0
\(111\) −2.12674 + 2.45557i −0.201861 + 0.233073i
\(112\) 0 0
\(113\) 10.0012 + 5.77419i 0.940832 + 0.543190i 0.890221 0.455529i \(-0.150550\pi\)
0.0506112 + 0.998718i \(0.483883\pi\)
\(114\) 0 0
\(115\) 1.14182 4.26133i 0.106475 0.397371i
\(116\) 0 0
\(117\) 10.6999 + 1.58501i 0.989206 + 0.146534i
\(118\) 0 0
\(119\) −0.989141 + 3.69152i −0.0906744 + 0.338401i
\(120\) 0 0
\(121\) 2.16523 + 1.25010i 0.196839 + 0.113645i
\(122\) 0 0
\(123\) 6.24256 7.20776i 0.562873 0.649902i
\(124\) 0 0
\(125\) 30.8990 30.8990i 2.76369 2.76369i
\(126\) 0 0
\(127\) 6.03332 3.48334i 0.535371 0.309096i −0.207830 0.978165i \(-0.566640\pi\)
0.743201 + 0.669069i \(0.233307\pi\)
\(128\) 0 0
\(129\) −3.09303 4.56760i −0.272326 0.402155i
\(130\) 0 0
\(131\) 3.81151i 0.333013i 0.986040 + 0.166507i \(0.0532487\pi\)
−0.986040 + 0.166507i \(0.946751\pi\)
\(132\) 0 0
\(133\) −6.51690 11.2876i −0.565087 0.978759i
\(134\) 0 0
\(135\) −12.4916 + 19.4679i −1.07511 + 1.67553i
\(136\) 0 0
\(137\) −1.45242 5.42052i −0.124089 0.463106i 0.875717 0.482825i \(-0.160389\pi\)
−0.999806 + 0.0197193i \(0.993723\pi\)
\(138\) 0 0
\(139\) −9.44568 + 16.3604i −0.801172 + 1.38767i 0.117672 + 0.993052i \(0.462457\pi\)
−0.918845 + 0.394619i \(0.870877\pi\)
\(140\) 0 0
\(141\) −3.31020 + 1.14655i −0.278769 + 0.0965571i
\(142\) 0 0
\(143\) −11.6572 + 6.29378i −0.974826 + 0.526312i
\(144\) 0 0
\(145\) 14.9935 + 4.01750i 1.24514 + 0.333635i
\(146\) 0 0
\(147\) 2.58612 0.185582i 0.213299 0.0153065i
\(148\) 0 0
\(149\) −8.75010 + 2.34458i −0.716836 + 0.192076i −0.598760 0.800929i \(-0.704339\pi\)
−0.118077 + 0.993004i \(0.537673\pi\)
\(150\) 0 0
\(151\) −15.1312 15.1312i −1.23136 1.23136i −0.963441 0.267919i \(-0.913664\pi\)
−0.267919 0.963441i \(-0.586336\pi\)
\(152\) 0 0
\(153\) 4.83736 0.697857i 0.391077 0.0564184i
\(154\) 0 0
\(155\) −29.7532 −2.38983
\(156\) 0 0
\(157\) −14.0150 −1.11852 −0.559258 0.828994i \(-0.688914\pi\)
−0.559258 + 0.828994i \(0.688914\pi\)
\(158\) 0 0
\(159\) 6.83187 14.0725i 0.541803 1.11602i
\(160\) 0 0
\(161\) −1.64391 1.64391i −0.129558 0.129558i
\(162\) 0 0
\(163\) 9.97023 2.67152i 0.780929 0.209249i 0.153735 0.988112i \(-0.450870\pi\)
0.627194 + 0.778863i \(0.284203\pi\)
\(164\) 0 0
\(165\) −2.02774 28.2570i −0.157860 2.19981i
\(166\) 0 0
\(167\) 7.72646 + 2.07030i 0.597891 + 0.160204i 0.545057 0.838399i \(-0.316508\pi\)
0.0528340 + 0.998603i \(0.483175\pi\)
\(168\) 0 0
\(169\) 0.741638 12.9788i 0.0570491 0.998371i
\(170\) 0 0
\(171\) −9.98255 + 13.3484i −0.763385 + 1.02078i
\(172\) 0 0
\(173\) 0.913430 1.58211i 0.0694468 0.120285i −0.829211 0.558936i \(-0.811210\pi\)
0.898658 + 0.438650i \(0.144543\pi\)
\(174\) 0 0
\(175\) −8.99577 33.5727i −0.680016 2.53786i
\(176\) 0 0
\(177\) −0.261496 + 1.35851i −0.0196553 + 0.102112i
\(178\) 0 0
\(179\) 6.73189 + 11.6600i 0.503165 + 0.871508i 0.999993 + 0.00365865i \(0.00116459\pi\)
−0.496828 + 0.867849i \(0.665502\pi\)
\(180\) 0 0
\(181\) 7.13395i 0.530262i 0.964212 + 0.265131i \(0.0854153\pi\)
−0.964212 + 0.265131i \(0.914585\pi\)
\(182\) 0 0
\(183\) 2.49204 1.68753i 0.184217 0.124746i
\(184\) 0 0
\(185\) −7.23047 + 4.17451i −0.531595 + 0.306916i
\(186\) 0 0
\(187\) −4.23267 + 4.23267i −0.309524 + 0.309524i
\(188\) 0 0
\(189\) 5.59327 + 10.8304i 0.406850 + 0.787798i
\(190\) 0 0
\(191\) −14.4696 8.35404i −1.04699 0.604477i −0.125182 0.992134i \(-0.539951\pi\)
−0.921804 + 0.387656i \(0.873285\pi\)
\(192\) 0 0
\(193\) −5.47749 + 20.4423i −0.394278 + 1.47147i 0.428728 + 0.903434i \(0.358962\pi\)
−0.823006 + 0.568033i \(0.807705\pi\)
\(194\) 0 0
\(195\) 24.6520 + 12.8498i 1.76536 + 0.920192i
\(196\) 0 0
\(197\) −2.43576 + 9.09039i −0.173541 + 0.647664i 0.823255 + 0.567672i \(0.192156\pi\)
−0.996796 + 0.0799913i \(0.974511\pi\)
\(198\) 0 0
\(199\) 3.91265 + 2.25897i 0.277360 + 0.160134i 0.632228 0.774783i \(-0.282141\pi\)
−0.354867 + 0.934917i \(0.615474\pi\)
\(200\) 0 0
\(201\) 17.0721 + 14.7859i 1.20417 + 1.04292i
\(202\) 0 0
\(203\) 5.78409 5.78409i 0.405964 0.405964i
\(204\) 0 0
\(205\) 21.2234 12.2533i 1.48230 0.855809i
\(206\) 0 0
\(207\) −1.10368 + 2.76067i −0.0767111 + 0.191880i
\(208\) 0 0
\(209\) 20.4145i 1.41210i
\(210\) 0 0
\(211\) 2.80684 + 4.86160i 0.193231 + 0.334686i 0.946319 0.323234i \(-0.104770\pi\)
−0.753088 + 0.657920i \(0.771437\pi\)
\(212\) 0 0
\(213\) 8.47456 + 1.63124i 0.580667 + 0.111771i
\(214\) 0 0
\(215\) −3.66941 13.6944i −0.250252 0.933952i
\(216\) 0 0
\(217\) −7.83961 + 13.5786i −0.532187 + 0.921775i
\(218\) 0 0
\(219\) 4.30127 + 12.4181i 0.290653 + 0.839141i
\(220\) 0 0
\(221\) −1.35777 5.71489i −0.0913332 0.384425i
\(222\) 0 0
\(223\) 20.3206 + 5.44489i 1.36077 + 0.364617i 0.864099 0.503322i \(-0.167889\pi\)
0.496671 + 0.867939i \(0.334556\pi\)
\(224\) 0 0
\(225\) −34.9261 + 27.4931i −2.32841 + 1.83288i
\(226\) 0 0
\(227\) −21.0863 + 5.65005i −1.39954 + 0.375007i −0.878181 0.478328i \(-0.841243\pi\)
−0.521363 + 0.853335i \(0.674576\pi\)
\(228\) 0 0
\(229\) −2.87926 2.87926i −0.190267 0.190267i 0.605545 0.795811i \(-0.292955\pi\)
−0.795811 + 0.605545i \(0.792955\pi\)
\(230\) 0 0
\(231\) −13.4301 6.51998i −0.883635 0.428983i
\(232\) 0 0
\(233\) 23.3765 1.53145 0.765724 0.643169i \(-0.222381\pi\)
0.765724 + 0.643169i \(0.222381\pi\)
\(234\) 0 0
\(235\) −9.00343 −0.587319
\(236\) 0 0
\(237\) 6.68301 + 3.24444i 0.434108 + 0.210749i
\(238\) 0 0
\(239\) 16.6210 + 16.6210i 1.07512 + 1.07512i 0.996939 + 0.0781813i \(0.0249113\pi\)
0.0781813 + 0.996939i \(0.475089\pi\)
\(240\) 0 0
\(241\) −20.0852 + 5.38182i −1.29380 + 0.346673i −0.839103 0.543972i \(-0.816920\pi\)
−0.454699 + 0.890645i \(0.650253\pi\)
\(242\) 0 0
\(243\) 9.91070 12.0324i 0.635772 0.771877i
\(244\) 0 0
\(245\) 6.43662 + 1.72469i 0.411221 + 0.110186i
\(246\) 0 0
\(247\) 17.0560 + 10.5074i 1.08524 + 0.668567i
\(248\) 0 0
\(249\) −4.57968 13.2219i −0.290225 0.837906i
\(250\) 0 0
\(251\) −4.45550 + 7.71715i −0.281228 + 0.487102i −0.971688 0.236269i \(-0.924075\pi\)
0.690459 + 0.723371i \(0.257409\pi\)
\(252\) 0 0
\(253\) −0.942446 3.51726i −0.0592511 0.221128i
\(254\) 0 0
\(255\) 12.3348 + 2.37429i 0.772434 + 0.148684i
\(256\) 0 0
\(257\) 14.4003 + 24.9421i 0.898269 + 1.55585i 0.829706 + 0.558201i \(0.188508\pi\)
0.0685631 + 0.997647i \(0.478159\pi\)
\(258\) 0 0
\(259\) 4.39974i 0.273386i
\(260\) 0 0
\(261\) −9.71342 3.88330i −0.601245 0.240370i
\(262\) 0 0
\(263\) −9.48931 + 5.47865i −0.585136 + 0.337828i −0.763172 0.646196i \(-0.776359\pi\)
0.178036 + 0.984024i \(0.443026\pi\)
\(264\) 0 0
\(265\) 28.4290 28.4290i 1.74638 1.74638i
\(266\) 0 0
\(267\) 6.94542 + 6.01535i 0.425053 + 0.368133i
\(268\) 0 0
\(269\) −18.8477 10.8817i −1.14917 0.663472i −0.200483 0.979697i \(-0.564251\pi\)
−0.948684 + 0.316225i \(0.897584\pi\)
\(270\) 0 0
\(271\) −5.65767 + 21.1147i −0.343679 + 1.28263i 0.550469 + 0.834855i \(0.314449\pi\)
−0.894148 + 0.447771i \(0.852218\pi\)
\(272\) 0 0
\(273\) 12.3598 7.86477i 0.748050 0.475997i
\(274\) 0 0
\(275\) 14.0898 52.5840i 0.849649 3.17093i
\(276\) 0 0
\(277\) −18.0419 10.4165i −1.08403 0.625867i −0.152051 0.988373i \(-0.548588\pi\)
−0.931981 + 0.362506i \(0.881921\pi\)
\(278\) 0 0
\(279\) 19.9107 + 2.37100i 1.19202 + 0.141948i
\(280\) 0 0
\(281\) −12.8134 + 12.8134i −0.764385 + 0.764385i −0.977112 0.212727i \(-0.931766\pi\)
0.212727 + 0.977112i \(0.431766\pi\)
\(282\) 0 0
\(283\) −4.75138 + 2.74321i −0.282440 + 0.163067i −0.634528 0.772900i \(-0.718805\pi\)
0.352087 + 0.935967i \(0.385472\pi\)
\(284\) 0 0
\(285\) −35.4715 + 24.0201i −2.10115 + 1.42283i
\(286\) 0 0
\(287\) 12.9144i 0.762314i
\(288\) 0 0
\(289\) 7.17294 + 12.4239i 0.421938 + 0.730818i
\(290\) 0 0
\(291\) 2.28262 11.8586i 0.133810 0.695161i
\(292\) 0 0
\(293\) 3.84609 + 14.3538i 0.224691 + 0.838557i 0.982528 + 0.186114i \(0.0595893\pi\)
−0.757837 + 0.652443i \(0.773744\pi\)
\(294\) 0 0
\(295\) −1.77780 + 3.07925i −0.103508 + 0.179281i
\(296\) 0 0
\(297\) −0.894816 + 19.0710i −0.0519225 + 1.10661i
\(298\) 0 0
\(299\) 3.42369 + 1.02294i 0.197997 + 0.0591580i
\(300\) 0 0
\(301\) −7.21664 1.93369i −0.415960 0.111456i
\(302\) 0 0
\(303\) −0.679526 9.46933i −0.0390377 0.543999i
\(304\) 0 0
\(305\) 7.47155 2.00200i 0.427820 0.114634i
\(306\) 0 0
\(307\) −13.9068 13.9068i −0.793705 0.793705i 0.188390 0.982094i \(-0.439673\pi\)
−0.982094 + 0.188390i \(0.939673\pi\)
\(308\) 0 0
\(309\) 0.824368 1.69806i 0.0468967 0.0965994i
\(310\) 0 0
\(311\) −14.2047 −0.805475 −0.402737 0.915316i \(-0.631941\pi\)
−0.402737 + 0.915316i \(0.631941\pi\)
\(312\) 0 0
\(313\) 15.6942 0.887091 0.443546 0.896252i \(-0.353720\pi\)
0.443546 + 0.896252i \(0.353720\pi\)
\(314\) 0 0
\(315\) 4.47322 + 31.0072i 0.252038 + 1.74706i
\(316\) 0 0
\(317\) −7.57231 7.57231i −0.425304 0.425304i 0.461721 0.887025i \(-0.347232\pi\)
−0.887025 + 0.461721i \(0.847232\pi\)
\(318\) 0 0
\(319\) 12.3755 3.31600i 0.692893 0.185660i
\(320\) 0 0
\(321\) −6.18580 + 0.443897i −0.345258 + 0.0247759i
\(322\) 0 0
\(323\) 8.74323 + 2.34274i 0.486486 + 0.130354i
\(324\) 0 0
\(325\) 36.6810 + 38.8369i 2.03470 + 2.15428i
\(326\) 0 0
\(327\) −2.04274 + 0.707544i −0.112964 + 0.0391273i
\(328\) 0 0
\(329\) −2.37230 + 4.10894i −0.130789 + 0.226533i
\(330\) 0 0
\(331\) 2.39175 + 8.92612i 0.131462 + 0.490624i 0.999987 0.00502131i \(-0.00159834\pi\)
−0.868525 + 0.495645i \(0.834932\pi\)
\(332\) 0 0
\(333\) 5.17125 2.21737i 0.283383 0.121511i
\(334\) 0 0
\(335\) 29.0228 + 50.2690i 1.58569 + 2.74649i
\(336\) 0 0
\(337\) 28.4642i 1.55054i −0.631629 0.775271i \(-0.717613\pi\)
0.631629 0.775271i \(-0.282387\pi\)
\(338\) 0 0
\(339\) −11.2154 16.5623i −0.609138 0.899539i
\(340\) 0 0
\(341\) −21.2678 + 12.2790i −1.15172 + 0.664944i
\(342\) 0 0
\(343\) 14.0945 14.0945i 0.761031 0.761031i
\(344\) 0 0
\(345\) −5.00256 + 5.77604i −0.269329 + 0.310971i
\(346\) 0 0
\(347\) −2.09837 1.21149i −0.112646 0.0650363i 0.442618 0.896710i \(-0.354050\pi\)
−0.555265 + 0.831674i \(0.687383\pi\)
\(348\) 0 0
\(349\) 3.83210 14.3016i 0.205128 0.765547i −0.784283 0.620404i \(-0.786969\pi\)
0.989411 0.145144i \(-0.0463645\pi\)
\(350\) 0 0
\(351\) −15.4730 10.5635i −0.825886 0.563837i
\(352\) 0 0
\(353\) 4.21638 15.7357i 0.224415 0.837529i −0.758223 0.651996i \(-0.773932\pi\)
0.982638 0.185533i \(-0.0594013\pi\)
\(354\) 0 0
\(355\) 19.2087 + 11.0902i 1.01949 + 0.588605i
\(356\) 0 0
\(357\) 4.33363 5.00369i 0.229360 0.264823i
\(358\) 0 0
\(359\) −23.4805 + 23.4805i −1.23926 + 1.23926i −0.278950 + 0.960306i \(0.589986\pi\)
−0.960306 + 0.278950i \(0.910014\pi\)
\(360\) 0 0
\(361\) −10.2798 + 5.93502i −0.541040 + 0.312369i
\(362\) 0 0
\(363\) −2.42811 3.58569i −0.127443 0.188200i
\(364\) 0 0
\(365\) 33.7762i 1.76793i
\(366\) 0 0
\(367\) −9.40635 16.2923i −0.491007 0.850450i 0.508939 0.860803i \(-0.330038\pi\)
−0.999946 + 0.0103530i \(0.996704\pi\)
\(368\) 0 0
\(369\) −15.1790 + 6.50859i −0.790188 + 0.338823i
\(370\) 0 0
\(371\) −5.48358 20.4650i −0.284693 1.06249i
\(372\) 0 0
\(373\) 2.40324 4.16253i 0.124435 0.215528i −0.797077 0.603878i \(-0.793622\pi\)
0.921512 + 0.388350i \(0.126955\pi\)
\(374\) 0 0
\(375\) −71.5182 + 24.7717i −3.69318 + 1.27921i
\(376\) 0 0
\(377\) −3.59921 + 12.0462i −0.185369 + 0.620413i
\(378\) 0 0
\(379\) 21.9656 + 5.88567i 1.12830 + 0.302326i 0.774237 0.632896i \(-0.218134\pi\)
0.354061 + 0.935222i \(0.384801\pi\)
\(380\) 0 0
\(381\) −12.0357 + 0.863689i −0.616607 + 0.0442481i
\(382\) 0 0
\(383\) 1.79837 0.481871i 0.0918923 0.0246225i −0.212580 0.977144i \(-0.568187\pi\)
0.304472 + 0.952521i \(0.401520\pi\)
\(384\) 0 0
\(385\) −27.1312 27.1312i −1.38273 1.38273i
\(386\) 0 0
\(387\) 1.36426 + 9.45665i 0.0693490 + 0.480708i
\(388\) 0 0
\(389\) −7.43410 −0.376924 −0.188462 0.982081i \(-0.560350\pi\)
−0.188462 + 0.982081i \(0.560350\pi\)
\(390\) 0 0
\(391\) 1.61455 0.0816511
\(392\) 0 0
\(393\) 2.88318 5.93887i 0.145437 0.299576i
\(394\) 0 0
\(395\) 13.5009 + 13.5009i 0.679303 + 0.679303i
\(396\) 0 0
\(397\) −2.45026 + 0.656546i −0.122975 + 0.0329511i −0.319782 0.947491i \(-0.603610\pi\)
0.196806 + 0.980442i \(0.436943\pi\)
\(398\) 0 0
\(399\) 1.61586 + 22.5173i 0.0808940 + 1.12727i
\(400\) 0 0
\(401\) −19.8434 5.31703i −0.990933 0.265520i −0.273291 0.961931i \(-0.588112\pi\)
−0.717643 + 0.696412i \(0.754779\pi\)
\(402\) 0 0
\(403\) 0.687685 24.0889i 0.0342560 1.19995i
\(404\) 0 0
\(405\) 34.1900 20.8846i 1.69891 1.03776i
\(406\) 0 0
\(407\) −3.44560 + 5.96795i −0.170792 + 0.295820i
\(408\) 0 0
\(409\) −2.36833 8.83872i −0.117106 0.437047i 0.882330 0.470632i \(-0.155974\pi\)
−0.999436 + 0.0335855i \(0.989307\pi\)
\(410\) 0 0
\(411\) −1.83721 + 9.54459i −0.0906231 + 0.470800i
\(412\) 0 0
\(413\) 0.936860 + 1.62269i 0.0460999 + 0.0798473i
\(414\) 0 0
\(415\) 35.9624i 1.76533i
\(416\) 0 0
\(417\) 27.0933 18.3467i 1.32677 0.898442i
\(418\) 0 0
\(419\) −5.18334 + 2.99260i −0.253223 + 0.146198i −0.621239 0.783621i \(-0.713370\pi\)
0.368016 + 0.929819i \(0.380037\pi\)
\(420\) 0 0
\(421\) −18.8397 + 18.8397i −0.918191 + 0.918191i −0.996898 0.0787065i \(-0.974921\pi\)
0.0787065 + 0.996898i \(0.474921\pi\)
\(422\) 0 0
\(423\) 6.02505 + 0.717473i 0.292948 + 0.0348847i
\(424\) 0 0
\(425\) 20.9040 + 12.0690i 1.01399 + 0.585430i
\(426\) 0 0
\(427\) 1.05500 3.93733i 0.0510553 0.190541i
\(428\) 0 0
\(429\) 22.9244 0.988606i 1.10680 0.0477303i
\(430\) 0 0
\(431\) −5.32426 + 19.8704i −0.256461 + 0.957124i 0.710811 + 0.703383i \(0.248328\pi\)
−0.967272 + 0.253742i \(0.918339\pi\)
\(432\) 0 0
\(433\) 12.9674 + 7.48671i 0.623172 + 0.359788i 0.778103 0.628137i \(-0.216182\pi\)
−0.154931 + 0.987925i \(0.549516\pi\)
\(434\) 0 0
\(435\) −20.3230 17.6015i −0.974412 0.843927i
\(436\) 0 0
\(437\) −3.89353 + 3.89353i −0.186253 + 0.186253i
\(438\) 0 0
\(439\) 25.4738 14.7073i 1.21580 0.701941i 0.251781 0.967784i \(-0.418984\pi\)
0.964016 + 0.265843i \(0.0856504\pi\)
\(440\) 0 0
\(441\) −4.16991 1.66708i −0.198567 0.0793847i
\(442\) 0 0
\(443\) 13.4346i 0.638296i −0.947705 0.319148i \(-0.896603\pi\)
0.947705 0.319148i \(-0.103397\pi\)
\(444\) 0 0
\(445\) 11.8073 + 20.4509i 0.559722 + 0.969466i
\(446\) 0 0
\(447\) 15.4074 + 2.96573i 0.728746 + 0.140274i
\(448\) 0 0
\(449\) −9.13607 34.0963i −0.431158 1.60910i −0.750097 0.661328i \(-0.769993\pi\)
0.318939 0.947775i \(-0.396673\pi\)
\(450\) 0 0
\(451\) 10.1138 17.5175i 0.476238 0.824869i
\(452\) 0 0
\(453\) 12.1307 + 35.0224i 0.569950 + 1.64550i
\(454\) 0 0
\(455\) 36.6321 8.70320i 1.71734 0.408012i
\(456\) 0 0
\(457\) −5.37186 1.43938i −0.251285 0.0673316i 0.130978 0.991385i \(-0.458188\pi\)
−0.382263 + 0.924054i \(0.624855\pi\)
\(458\) 0 0
\(459\) −8.06516 2.57181i −0.376450 0.120042i
\(460\) 0 0
\(461\) 15.4331 4.13530i 0.718793 0.192600i 0.119160 0.992875i \(-0.461980\pi\)
0.599633 + 0.800275i \(0.295313\pi\)
\(462\) 0 0
\(463\) −19.1882 19.1882i −0.891750 0.891750i 0.102938 0.994688i \(-0.467176\pi\)
−0.994688 + 0.102938i \(0.967176\pi\)
\(464\) 0 0
\(465\) 46.3596 + 22.5065i 2.14988 + 1.04371i
\(466\) 0 0
\(467\) 13.2438 0.612849 0.306425 0.951895i \(-0.400867\pi\)
0.306425 + 0.951895i \(0.400867\pi\)
\(468\) 0 0
\(469\) 30.5886 1.41245
\(470\) 0 0
\(471\) 21.8373 + 10.6015i 1.00621 + 0.488490i
\(472\) 0 0
\(473\) −8.27454 8.27454i −0.380464 0.380464i
\(474\) 0 0
\(475\) −79.5156 + 21.3061i −3.64843 + 0.977593i
\(476\) 0 0
\(477\) −21.2900 + 16.7591i −0.974803 + 0.767345i
\(478\) 0 0
\(479\) 35.0689 + 9.39667i 1.60234 + 0.429345i 0.945747 0.324903i \(-0.105332\pi\)
0.656590 + 0.754248i \(0.271998\pi\)
\(480\) 0 0
\(481\) −3.21267 5.95045i −0.146485 0.271317i
\(482\) 0 0
\(483\) 1.31792 + 3.80496i 0.0599676 + 0.173132i
\(484\) 0 0
\(485\) 15.5186 26.8790i 0.704663 1.22051i
\(486\) 0 0
\(487\) 7.12944 + 26.6074i 0.323066 + 1.20570i 0.916242 + 0.400625i \(0.131207\pi\)
−0.593176 + 0.805073i \(0.702126\pi\)
\(488\) 0 0
\(489\) −17.5559 3.37928i −0.793903 0.152816i
\(490\) 0 0
\(491\) 5.49069 + 9.51015i 0.247791 + 0.429187i 0.962913 0.269813i \(-0.0869620\pi\)
−0.715121 + 0.699000i \(0.753629\pi\)
\(492\) 0 0
\(493\) 5.68077i 0.255849i
\(494\) 0 0
\(495\) −18.2152 + 45.5623i −0.818713 + 2.04787i
\(496\) 0 0
\(497\) 10.1225 5.84425i 0.454058 0.262150i
\(498\) 0 0
\(499\) −15.2819 + 15.2819i −0.684112 + 0.684112i −0.960924 0.276812i \(-0.910722\pi\)
0.276812 + 0.960924i \(0.410722\pi\)
\(500\) 0 0
\(501\) −10.4728 9.07041i −0.467892 0.405236i
\(502\) 0 0
\(503\) −27.8209 16.0624i −1.24047 0.716186i −0.271281 0.962500i \(-0.587447\pi\)
−0.969190 + 0.246314i \(0.920781\pi\)
\(504\) 0 0
\(505\) 6.31512 23.5684i 0.281019 1.04878i
\(506\) 0 0
\(507\) −10.9733 + 19.6618i −0.487340 + 0.873212i
\(508\) 0 0
\(509\) 0.274449 1.02426i 0.0121647 0.0453994i −0.959577 0.281447i \(-0.909186\pi\)
0.971741 + 0.236048i \(0.0758522\pi\)
\(510\) 0 0
\(511\) 15.4146 + 8.89963i 0.681903 + 0.393697i
\(512\) 0 0
\(513\) 25.6514 13.2474i 1.13254 0.584888i
\(514\) 0 0
\(515\) 3.43039 3.43039i 0.151161 0.151161i
\(516\) 0 0
\(517\) −6.43572 + 3.71567i −0.283043 + 0.163415i
\(518\) 0 0
\(519\) −2.62002 + 1.77419i −0.115006 + 0.0778783i
\(520\) 0 0
\(521\) 14.8230i 0.649407i −0.945816 0.324704i \(-0.894735\pi\)
0.945816 0.324704i \(-0.105265\pi\)
\(522\) 0 0
\(523\) 0.156423 + 0.270933i 0.00683991 + 0.0118471i 0.869425 0.494065i \(-0.164489\pi\)
−0.862585 + 0.505912i \(0.831156\pi\)
\(524\) 0 0
\(525\) −11.3790 + 59.1157i −0.496621 + 2.58002i
\(526\) 0 0
\(527\) −2.81824 10.5178i −0.122764 0.458163i
\(528\) 0 0
\(529\) 11.0089 19.0680i 0.478649 0.829044i
\(530\) 0 0
\(531\) 1.43508 1.91894i 0.0622771 0.0832751i
\(532\) 0 0
\(533\) 9.43005 + 17.4662i 0.408461 + 0.756544i
\(534\) 0 0
\(535\) −15.3959 4.12533i −0.665624 0.178353i
\(536\) 0 0
\(537\) −1.66916 23.2601i −0.0720297 1.00375i
\(538\) 0 0
\(539\) 5.31272 1.42354i 0.228835 0.0613161i
\(540\) 0 0
\(541\) 1.64054 + 1.64054i 0.0705322 + 0.0705322i 0.741493 0.670961i \(-0.234118\pi\)
−0.670961 + 0.741493i \(0.734118\pi\)
\(542\) 0 0
\(543\) 5.39640 11.1157i 0.231582 0.477020i
\(544\) 0 0
\(545\) −5.55607 −0.237996
\(546\) 0 0
\(547\) −2.92991 −0.125274 −0.0626369 0.998036i \(-0.519951\pi\)
−0.0626369 + 0.998036i \(0.519951\pi\)
\(548\) 0 0
\(549\) −5.15946 + 0.744325i −0.220200 + 0.0317670i
\(550\) 0 0
\(551\) −13.6994 13.6994i −0.583614 0.583614i
\(552\) 0 0
\(553\) 9.71878 2.60414i 0.413285 0.110739i
\(554\) 0 0
\(555\) 14.4238 1.03506i 0.612258 0.0439361i
\(556\) 0 0
\(557\) −37.5546 10.0627i −1.59124 0.426371i −0.648857 0.760910i \(-0.724753\pi\)
−0.942382 + 0.334539i \(0.891419\pi\)
\(558\) 0 0
\(559\) 11.1722 2.65432i 0.472532 0.112266i
\(560\) 0 0
\(561\) 9.79685 3.39334i 0.413623 0.143267i
\(562\) 0 0
\(563\) −8.43667 + 14.6127i −0.355563 + 0.615854i −0.987214 0.159399i \(-0.949044\pi\)
0.631651 + 0.775253i \(0.282378\pi\)
\(564\) 0 0
\(565\) −13.3054 49.6565i −0.559763 2.08906i
\(566\) 0 0
\(567\) −0.522531 21.1063i −0.0219443 0.886381i
\(568\) 0 0
\(569\) −9.07218 15.7135i −0.380326 0.658743i 0.610783 0.791798i \(-0.290855\pi\)
−0.991109 + 0.133055i \(0.957521\pi\)
\(570\) 0 0
\(571\) 32.6819i 1.36769i 0.729626 + 0.683847i \(0.239694\pi\)
−0.729626 + 0.683847i \(0.760306\pi\)
\(572\) 0 0
\(573\) 16.2264 + 23.9622i 0.677867 + 1.00103i
\(574\) 0 0
\(575\) −12.7163 + 7.34176i −0.530307 + 0.306173i
\(576\) 0 0
\(577\) 20.9504 20.9504i 0.872178 0.872178i −0.120531 0.992710i \(-0.538460\pi\)
0.992710 + 0.120531i \(0.0384597\pi\)
\(578\) 0 0
\(579\) 23.9980 27.7085i 0.997324 1.15153i
\(580\) 0 0
\(581\) −16.4123 9.47567i −0.680899 0.393117i
\(582\) 0 0
\(583\) 8.58879 32.0538i 0.355711 1.32753i
\(584\) 0 0
\(585\) −28.6911 38.6695i −1.18623 1.59879i
\(586\) 0 0
\(587\) 10.2200 38.1416i 0.421825 1.57427i −0.348935 0.937147i \(-0.613457\pi\)
0.770760 0.637126i \(-0.219877\pi\)
\(588\) 0 0
\(589\) 32.1604 + 18.5678i 1.32515 + 0.765073i
\(590\) 0 0
\(591\) 10.6716 12.3216i 0.438971 0.506843i
\(592\) 0 0
\(593\) 9.44894 9.44894i 0.388022 0.388022i −0.485960 0.873981i \(-0.661530\pi\)
0.873981 + 0.485960i \(0.161530\pi\)
\(594\) 0 0
\(595\) 14.7334 8.50635i 0.604012 0.348726i
\(596\) 0 0
\(597\) −4.38768 6.47947i −0.179576 0.265187i
\(598\) 0 0
\(599\) 32.9682i 1.34704i −0.739167 0.673522i \(-0.764780\pi\)
0.739167 0.673522i \(-0.235220\pi\)
\(600\) 0 0
\(601\) 0.969322 + 1.67891i 0.0395395 + 0.0684844i 0.885118 0.465367i \(-0.154078\pi\)
−0.845578 + 0.533851i \(0.820744\pi\)
\(602\) 0 0
\(603\) −15.4160 35.9525i −0.627789 1.46410i
\(604\) 0 0
\(605\) −2.88058 10.7505i −0.117112 0.437069i
\(606\) 0 0
\(607\) −4.67064 + 8.08978i −0.189575 + 0.328354i −0.945109 0.326756i \(-0.894044\pi\)
0.755533 + 0.655110i \(0.227378\pi\)
\(608\) 0 0
\(609\) −13.3877 + 4.63711i −0.542498 + 0.187905i
\(610\) 0 0
\(611\) 0.208096 7.28940i 0.00841867 0.294897i
\(612\) 0 0
\(613\) −31.7571 8.50929i −1.28266 0.343687i −0.447790 0.894139i \(-0.647789\pi\)
−0.834867 + 0.550452i \(0.814455\pi\)
\(614\) 0 0
\(615\) −42.3379 + 3.03819i −1.70723 + 0.122512i
\(616\) 0 0
\(617\) −24.1659 + 6.47523i −0.972881 + 0.260683i −0.710044 0.704157i \(-0.751325\pi\)
−0.262837 + 0.964840i \(0.584658\pi\)
\(618\) 0 0
\(619\) −12.3512 12.3512i −0.496437 0.496437i 0.413890 0.910327i \(-0.364170\pi\)
−0.910327 + 0.413890i \(0.864170\pi\)
\(620\) 0 0
\(621\) 3.80797 3.46664i 0.152809 0.139112i
\(622\) 0 0
\(623\) 12.4444 0.498573
\(624\) 0 0
\(625\) −120.441 −4.81766
\(626\) 0 0
\(627\) −15.4423 + 31.8086i −0.616707 + 1.27031i
\(628\) 0 0
\(629\) −2.16057 2.16057i −0.0861477 0.0861477i
\(630\) 0 0
\(631\) −32.6451 + 8.74723i −1.29958 + 0.348222i −0.841292 0.540581i \(-0.818204\pi\)
−0.458289 + 0.888803i \(0.651538\pi\)
\(632\) 0 0
\(633\) −0.695953 9.69825i −0.0276616 0.385471i
\(634\) 0 0
\(635\) −29.9558 8.02663i −1.18876 0.318527i
\(636\) 0 0
\(637\) −1.54512 + 5.17138i −0.0612198 + 0.204898i
\(638\) 0 0
\(639\) −11.9706 8.95219i −0.473550 0.354143i
\(640\) 0 0
\(641\) 11.3280 19.6207i 0.447430 0.774971i −0.550788 0.834645i \(-0.685673\pi\)
0.998218 + 0.0596740i \(0.0190061\pi\)
\(642\) 0 0
\(643\) −11.8724 44.3085i −0.468203 1.74736i −0.646046 0.763299i \(-0.723579\pi\)
0.177843 0.984059i \(-0.443088\pi\)
\(644\) 0 0
\(645\) −4.64155 + 24.1135i −0.182761 + 0.949469i
\(646\) 0 0
\(647\) −23.7381 41.1155i −0.933239 1.61642i −0.777744 0.628581i \(-0.783636\pi\)
−0.155495 0.987837i \(-0.549697\pi\)
\(648\) 0 0
\(649\) 2.93476i 0.115199i
\(650\) 0 0
\(651\) 22.4866 15.2272i 0.881319 0.596800i
\(652\) 0 0
\(653\) −28.5462 + 16.4812i −1.11710 + 0.644958i −0.940659 0.339353i \(-0.889792\pi\)
−0.176441 + 0.984311i \(0.556458\pi\)
\(654\) 0 0
\(655\) 11.9976 11.9976i 0.468784 0.468784i
\(656\) 0 0
\(657\) 2.69159 22.6029i 0.105009 0.881822i
\(658\) 0 0
\(659\) 14.6160 + 8.43857i 0.569360 + 0.328720i 0.756894 0.653538i \(-0.226716\pi\)
−0.187534 + 0.982258i \(0.560049\pi\)
\(660\) 0 0
\(661\) −3.30272 + 12.3259i −0.128461 + 0.479423i −0.999939 0.0110108i \(-0.996495\pi\)
0.871478 + 0.490434i \(0.163162\pi\)
\(662\) 0 0
\(663\) −2.20738 + 9.93166i −0.0857274 + 0.385714i
\(664\) 0 0
\(665\) −15.0168 + 56.0436i −0.582328 + 2.17328i
\(666\) 0 0
\(667\) −2.99274 1.72786i −0.115879 0.0669030i
\(668\) 0 0
\(669\) −27.5436 23.8552i −1.06490 0.922296i
\(670\) 0 0
\(671\) 4.51451 4.51451i 0.174281 0.174281i
\(672\) 0 0
\(673\) −13.3091 + 7.68401i −0.513028 + 0.296197i −0.734077 0.679066i \(-0.762385\pi\)
0.221049 + 0.975263i \(0.429052\pi\)
\(674\) 0 0
\(675\) 75.2167 16.4186i 2.89509 0.631954i
\(676\) 0 0
\(677\) 4.08973i 0.157181i 0.996907 + 0.0785906i \(0.0250420\pi\)
−0.996907 + 0.0785906i \(0.974958\pi\)
\(678\) 0 0
\(679\) −8.17793 14.1646i −0.313840 0.543587i
\(680\) 0 0
\(681\) 37.1293 + 7.14691i 1.42280 + 0.273870i
\(682\) 0 0
\(683\) 9.15575 + 34.1697i 0.350335 + 1.30747i 0.886254 + 0.463199i \(0.153299\pi\)
−0.535919 + 0.844269i \(0.680035\pi\)
\(684\) 0 0
\(685\) −12.4905 + 21.6341i −0.477236 + 0.826597i
\(686\) 0 0
\(687\) 2.30830 + 6.66427i 0.0880672 + 0.254258i
\(688\) 0 0
\(689\) 22.3597 + 23.6739i 0.851838 + 0.901904i
\(690\) 0 0
\(691\) 2.30242 + 0.616931i 0.0875881 + 0.0234692i 0.302347 0.953198i \(-0.402230\pi\)
−0.214759 + 0.976667i \(0.568897\pi\)
\(692\) 0 0
\(693\) 15.9940 + 20.3181i 0.607561 + 0.771820i
\(694\) 0 0
\(695\) 81.2304 21.7656i 3.08124 0.825617i
\(696\) 0 0
\(697\) 6.34187 + 6.34187i 0.240215 + 0.240215i
\(698\) 0 0
\(699\) −36.4239 17.6829i −1.37768 0.668830i
\(700\) 0 0
\(701\) 44.9525 1.69783 0.848916 0.528528i \(-0.177256\pi\)
0.848916 + 0.528528i \(0.177256\pi\)
\(702\) 0 0
\(703\) 10.4206 0.393021
\(704\) 0 0
\(705\) 14.0286 + 6.81055i 0.528348 + 0.256500i
\(706\) 0 0
\(707\) −9.09204 9.09204i −0.341941 0.341941i
\(708\) 0 0
\(709\) −26.4355 + 7.08337i −0.992807 + 0.266022i −0.718429 0.695600i \(-0.755138\pi\)
−0.274378 + 0.961622i \(0.588472\pi\)
\(710\) 0 0
\(711\) −7.95884 10.1106i −0.298480 0.379176i
\(712\) 0 0
\(713\) 6.39818 + 1.71439i 0.239614 + 0.0642043i
\(714\) 0 0
\(715\) 56.5048 + 16.8826i 2.11316 + 0.631375i
\(716\) 0 0
\(717\) −13.3250 38.4705i −0.497632 1.43671i
\(718\) 0 0
\(719\) 5.57711 9.65984i 0.207991 0.360251i −0.743090 0.669191i \(-0.766641\pi\)
0.951082 + 0.308940i \(0.0999741\pi\)
\(720\) 0 0
\(721\) −0.661676 2.46941i −0.0246421 0.0919656i
\(722\) 0 0
\(723\) 35.3666 + 6.80762i 1.31530 + 0.253178i
\(724\) 0 0
\(725\) −25.8320 44.7423i −0.959376 1.66169i
\(726\) 0 0
\(727\) 29.1867i 1.08247i 0.840870 + 0.541237i \(0.182044\pi\)
−0.840870 + 0.541237i \(0.817956\pi\)
\(728\) 0 0
\(729\) −24.5440 + 11.2513i −0.909038 + 0.416714i
\(730\) 0 0
\(731\) 4.49344 2.59429i 0.166196 0.0959533i
\(732\) 0 0
\(733\) 30.3088 30.3088i 1.11948 1.11948i 0.127663 0.991818i \(-0.459252\pi\)
0.991818 0.127663i \(-0.0407476\pi\)
\(734\) 0 0
\(735\) −8.72454 7.55622i −0.321809 0.278715i
\(736\) 0 0
\(737\) 41.4914 + 23.9551i 1.52836 + 0.882397i
\(738\) 0 0
\(739\) −6.82020 + 25.4533i −0.250885 + 0.936316i 0.719448 + 0.694546i \(0.244395\pi\)
−0.970334 + 0.241770i \(0.922272\pi\)
\(740\) 0 0
\(741\) −18.6274 29.2737i −0.684295 1.07540i
\(742\) 0 0
\(743\) −6.56318 + 24.4941i −0.240780 + 0.898602i 0.734678 + 0.678416i \(0.237333\pi\)
−0.975458 + 0.220186i \(0.929333\pi\)
\(744\) 0 0
\(745\) 34.9230 + 20.1628i 1.27948 + 0.738707i
\(746\) 0 0
\(747\) −2.86581 + 24.0659i −0.104854 + 0.880524i
\(748\) 0 0
\(749\) −5.93934 + 5.93934i −0.217019 + 0.217019i
\(750\) 0 0
\(751\) −16.1198 + 9.30675i −0.588219 + 0.339608i −0.764393 0.644751i \(-0.776961\pi\)
0.176174 + 0.984359i \(0.443628\pi\)
\(752\) 0 0
\(753\) 12.7798 8.65408i 0.465723 0.315372i
\(754\) 0 0
\(755\) 95.2577i 3.46678i
\(756\) 0 0
\(757\) −1.20008 2.07859i −0.0436175 0.0755478i 0.843392 0.537298i \(-0.180555\pi\)
−0.887010 + 0.461750i \(0.847222\pi\)
\(758\) 0 0
\(759\) −1.19213 + 6.19328i −0.0432715 + 0.224802i
\(760\) 0 0
\(761\) −2.70569 10.0978i −0.0980811 0.366044i 0.899387 0.437152i \(-0.144013\pi\)
−0.997469 + 0.0711086i \(0.977346\pi\)
\(762\) 0 0
\(763\) −1.46396 + 2.53565i −0.0529988 + 0.0917967i
\(764\) 0 0
\(765\) −17.4233 13.0300i −0.629941 0.471100i
\(766\) 0 0
\(767\) −2.45194 1.51052i −0.0885345 0.0545419i
\(768\) 0 0
\(769\) 31.6831 + 8.48946i 1.14252 + 0.306138i 0.779964 0.625824i \(-0.215237\pi\)
0.362557 + 0.931962i \(0.381904\pi\)
\(770\) 0 0
\(771\) −3.57055 49.7563i −0.128590 1.79193i
\(772\) 0 0
\(773\) 30.9596 8.29561i 1.11354 0.298372i 0.345274 0.938502i \(-0.387786\pi\)
0.768267 + 0.640130i \(0.221119\pi\)
\(774\) 0 0
\(775\) 70.0240 + 70.0240i 2.51534 + 2.51534i
\(776\) 0 0
\(777\) 3.32813 6.85541i 0.119396 0.245936i
\(778\) 0 0
\(779\) −30.5873 −1.09590
\(780\) 0 0
\(781\) 18.3074 0.655090
\(782\) 0 0
\(783\) 12.1974 + 13.3983i 0.435899 + 0.478817i
\(784\) 0 0
\(785\) 44.1152 + 44.1152i 1.57454 + 1.57454i
\(786\) 0 0
\(787\) −0.821024 + 0.219993i −0.0292663 + 0.00784189i −0.273423 0.961894i \(-0.588156\pi\)
0.244156 + 0.969736i \(0.421489\pi\)
\(788\) 0 0
\(789\) 18.9299 1.35842i 0.673923 0.0483612i
\(790\) 0 0
\(791\) −26.1678 7.01164i −0.930419 0.249305i
\(792\) 0 0
\(793\) 1.44817 + 6.09542i 0.0514262 + 0.216455i
\(794\) 0 0
\(795\) −65.8012 + 22.7916i −2.33373 + 0.808333i
\(796\) 0 0
\(797\) −10.3419