Properties

Label 668.2.e.a.21.2
Level $668$
Weight $2$
Character 668.21
Analytic conductor $5.334$
Analytic rank $0$
Dimension $1148$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.e (of order \(83\), degree \(82\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.33400685502\)
Analytic rank: \(0\)
Dimension: \(1148\)
Relative dimension: \(14\) over \(\Q(\zeta_{83})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{83}]$

Embedding invariants

Embedding label 21.2
Character \(\chi\) \(=\) 668.21
Dual form 668.2.e.a.509.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.93125 - 0.447219i) q^{3} +(1.46272 + 1.73577i) q^{5} +(-0.690896 + 0.958545i) q^{7} +(5.52869 + 1.72722i) q^{9} +O(q^{10})\) \(q+(-2.93125 - 0.447219i) q^{3} +(1.46272 + 1.73577i) q^{5} +(-0.690896 + 0.958545i) q^{7} +(5.52869 + 1.72722i) q^{9} +(-2.12605 + 2.00864i) q^{11} +(0.538363 - 4.04003i) q^{13} +(-3.51131 - 5.74212i) q^{15} +(-0.598649 + 0.900546i) q^{17} +(-0.0363905 - 0.00840947i) q^{19} +(2.45387 - 2.50075i) q^{21} +(0.412263 + 1.95165i) q^{23} +(-0.0258384 + 0.150229i) q^{25} +(-7.43991 - 3.63256i) q^{27} +(-0.394230 + 1.86628i) q^{29} +(-6.59494 + 1.26323i) q^{31} +(7.13027 - 4.93701i) q^{33} +(-2.67440 + 0.202842i) q^{35} +(-8.98185 + 2.80603i) q^{37} +(-3.38485 + 11.6016i) q^{39} +(-7.44330 + 2.96005i) q^{41} +(-8.86584 - 3.14271i) q^{43} +(5.08883 + 12.1230i) q^{45} +(-1.64970 + 6.56947i) q^{47} +(1.77198 + 5.31632i) q^{49} +(2.15753 - 2.37199i) q^{51} +(-7.14956 - 5.36170i) q^{53} +(-6.59634 - 0.752260i) q^{55} +(0.102909 + 0.0409248i) q^{57} +(-0.837976 - 1.26056i) q^{59} +(-0.488228 - 0.625988i) q^{61} +(-5.47537 + 4.10616i) q^{63} +(7.80003 - 4.97494i) q^{65} +(5.75034 - 6.82380i) q^{67} +(-0.335629 - 5.90514i) q^{69} +(0.108184 + 1.13986i) q^{71} +(-1.61897 + 2.88767i) q^{73} +(0.142924 - 0.428802i) q^{75} +(-0.456496 - 3.42567i) q^{77} +(14.8807 + 0.563510i) q^{79} +(5.89737 + 4.08335i) q^{81} +(-3.21531 + 0.872418i) q^{83} +(-2.43879 + 0.278125i) q^{85} +(1.99022 - 5.29422i) q^{87} +(0.957123 - 1.56520i) q^{89} +(3.50060 + 3.30728i) q^{91} +(19.8963 - 0.753447i) q^{93} +(-0.0386320 - 0.0754662i) q^{95} +(-9.53417 - 1.82622i) q^{97} +(-15.2236 + 7.43298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1148q - 2q^{5} - 14q^{9} + O(q^{10}) \) \( 1148q - 2q^{5} - 14q^{9} + 2q^{11} + 4q^{13} + 14q^{15} + 2q^{17} + 2q^{19} + 14q^{23} - 6q^{25} + 2q^{29} - 2q^{31} + 16q^{33} - 2q^{35} + 10q^{37} + 6q^{39} + 4q^{41} + 4q^{43} - 2q^{45} + 2q^{47} - 30q^{49} - 2q^{51} - 6q^{55} - 4q^{57} + 6q^{59} + 2q^{61} + 14q^{63} + 22q^{65} + 12q^{67} - 14q^{69} - 8q^{71} - 18q^{73} - 26q^{75} - 2q^{79} - 6q^{81} - 22q^{83} + 34q^{85} + 2q^{87} + 14q^{89} - 6q^{91} + 32q^{93} - 8q^{95} + 44q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(335\)
\(\chi(n)\) \(e\left(\frac{23}{83}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.93125 0.447219i −1.69236 0.258202i −0.768198 0.640213i \(-0.778846\pi\)
−0.924158 + 0.382011i \(0.875232\pi\)
\(4\) 0 0
\(5\) 1.46272 + 1.73577i 0.654146 + 0.776260i 0.985941 0.167091i \(-0.0534375\pi\)
−0.331795 + 0.943351i \(0.607654\pi\)
\(6\) 0 0
\(7\) −0.690896 + 0.958545i −0.261134 + 0.362296i −0.921319 0.388807i \(-0.872887\pi\)
0.660185 + 0.751103i \(0.270478\pi\)
\(8\) 0 0
\(9\) 5.52869 + 1.72722i 1.84290 + 0.575742i
\(10\) 0 0
\(11\) −2.12605 + 2.00864i −0.641027 + 0.605628i −0.936899 0.349600i \(-0.886317\pi\)
0.295872 + 0.955228i \(0.404390\pi\)
\(12\) 0 0
\(13\) 0.538363 4.04003i 0.149315 1.12050i −0.743065 0.669219i \(-0.766629\pi\)
0.892381 0.451284i \(-0.149034\pi\)
\(14\) 0 0
\(15\) −3.51131 5.74212i −0.906616 1.48261i
\(16\) 0 0
\(17\) −0.598649 + 0.900546i −0.145194 + 0.218415i −0.898187 0.439614i \(-0.855115\pi\)
0.752993 + 0.658028i \(0.228609\pi\)
\(18\) 0 0
\(19\) −0.0363905 0.00840947i −0.00834856 0.00192927i 0.220980 0.975278i \(-0.429075\pi\)
−0.229328 + 0.973349i \(0.573653\pi\)
\(20\) 0 0
\(21\) 2.45387 2.50075i 0.535477 0.545708i
\(22\) 0 0
\(23\) 0.412263 + 1.95165i 0.0859628 + 0.406947i 0.999999 + 0.00131477i \(0.000418503\pi\)
−0.914036 + 0.405632i \(0.867051\pi\)
\(24\) 0 0
\(25\) −0.0258384 + 0.150229i −0.00516769 + 0.0300458i
\(26\) 0 0
\(27\) −7.43991 3.63256i −1.43181 0.699087i
\(28\) 0 0
\(29\) −0.394230 + 1.86628i −0.0732066 + 0.346559i −0.999546 0.0301306i \(-0.990408\pi\)
0.926339 + 0.376690i \(0.122938\pi\)
\(30\) 0 0
\(31\) −6.59494 + 1.26323i −1.18449 + 0.226882i −0.742317 0.670049i \(-0.766273\pi\)
−0.442170 + 0.896931i \(0.645791\pi\)
\(32\) 0 0
\(33\) 7.13027 4.93701i 1.24122 0.859423i
\(34\) 0 0
\(35\) −2.67440 + 0.202842i −0.452056 + 0.0342866i
\(36\) 0 0
\(37\) −8.98185 + 2.80603i −1.47661 + 0.461309i −0.927302 0.374314i \(-0.877878\pi\)
−0.549304 + 0.835622i \(0.685107\pi\)
\(38\) 0 0
\(39\) −3.38485 + 11.6016i −0.542010 + 1.85774i
\(40\) 0 0
\(41\) −7.44330 + 2.96005i −1.16245 + 0.462283i −0.869542 0.493859i \(-0.835586\pi\)
−0.292906 + 0.956141i \(0.594622\pi\)
\(42\) 0 0
\(43\) −8.86584 3.14271i −1.35203 0.479258i −0.443198 0.896424i \(-0.646156\pi\)
−0.908830 + 0.417166i \(0.863023\pi\)
\(44\) 0 0
\(45\) 5.08883 + 12.1230i 0.758598 + 1.80719i
\(46\) 0 0
\(47\) −1.64970 + 6.56947i −0.240633 + 0.958256i 0.722962 + 0.690888i \(0.242780\pi\)
−0.963595 + 0.267368i \(0.913846\pi\)
\(48\) 0 0
\(49\) 1.77198 + 5.31632i 0.253140 + 0.759474i
\(50\) 0 0
\(51\) 2.15753 2.37199i 0.302114 0.332146i
\(52\) 0 0
\(53\) −7.14956 5.36170i −0.982068 0.736486i −0.0173710 0.999849i \(-0.505530\pi\)
−0.964697 + 0.263363i \(0.915168\pi\)
\(54\) 0 0
\(55\) −6.59634 0.752260i −0.889450 0.101435i
\(56\) 0 0
\(57\) 0.102909 + 0.0409248i 0.0136306 + 0.00542062i
\(58\) 0 0
\(59\) −0.837976 1.26056i −0.109095 0.164112i 0.774182 0.632964i \(-0.218162\pi\)
−0.883277 + 0.468852i \(0.844668\pi\)
\(60\) 0 0
\(61\) −0.488228 0.625988i −0.0625112 0.0801496i 0.756254 0.654278i \(-0.227028\pi\)
−0.818765 + 0.574129i \(0.805341\pi\)
\(62\) 0 0
\(63\) −5.47537 + 4.10616i −0.689832 + 0.517328i
\(64\) 0 0
\(65\) 7.80003 4.97494i 0.967475 0.617065i
\(66\) 0 0
\(67\) 5.75034 6.82380i 0.702516 0.833659i −0.289839 0.957075i \(-0.593602\pi\)
0.992355 + 0.123416i \(0.0393849\pi\)
\(68\) 0 0
\(69\) −0.335629 5.90514i −0.0404050 0.710895i
\(70\) 0 0
\(71\) 0.108184 + 1.13986i 0.0128391 + 0.135277i 0.999645 0.0266285i \(-0.00847713\pi\)
−0.986806 + 0.161905i \(0.948236\pi\)
\(72\) 0 0
\(73\) −1.61897 + 2.88767i −0.189486 + 0.337976i −0.950482 0.310781i \(-0.899410\pi\)
0.760996 + 0.648757i \(0.224711\pi\)
\(74\) 0 0
\(75\) 0.142924 0.428802i 0.0165034 0.0495138i
\(76\) 0 0
\(77\) −0.456496 3.42567i −0.0520225 0.390392i
\(78\) 0 0
\(79\) 14.8807 + 0.563510i 1.67421 + 0.0633999i 0.857770 0.514034i \(-0.171850\pi\)
0.816437 + 0.577434i \(0.195946\pi\)
\(80\) 0 0
\(81\) 5.89737 + 4.08335i 0.655263 + 0.453705i
\(82\) 0 0
\(83\) −3.21531 + 0.872418i −0.352926 + 0.0957603i −0.433913 0.900955i \(-0.642867\pi\)
0.0809872 + 0.996715i \(0.474193\pi\)
\(84\) 0 0
\(85\) −2.43879 + 0.278125i −0.264524 + 0.0301669i
\(86\) 0 0
\(87\) 1.99022 5.29422i 0.213374 0.567600i
\(88\) 0 0
\(89\) 0.957123 1.56520i 0.101455 0.165911i −0.798364 0.602175i \(-0.794301\pi\)
0.899819 + 0.436264i \(0.143699\pi\)
\(90\) 0 0
\(91\) 3.50060 + 3.30728i 0.366962 + 0.346698i
\(92\) 0 0
\(93\) 19.8963 0.753447i 2.06315 0.0781288i
\(94\) 0 0
\(95\) −0.0386320 0.0754662i −0.00396356 0.00774267i
\(96\) 0 0
\(97\) −9.53417 1.82622i −0.968048 0.185425i −0.320331 0.947306i \(-0.603794\pi\)
−0.647717 + 0.761881i \(0.724276\pi\)
\(98\) 0 0
\(99\) −15.2236 + 7.43298i −1.53003 + 0.747043i
\(100\) 0 0
\(101\) −5.11386 + 1.81273i −0.508848 + 0.180373i −0.576126 0.817361i \(-0.695436\pi\)
0.0672778 + 0.997734i \(0.478569\pi\)
\(102\) 0 0
\(103\) 0.131761 6.96135i 0.0129828 0.685922i −0.932668 0.360737i \(-0.882525\pi\)
0.945650 0.325185i \(-0.105427\pi\)
\(104\) 0 0
\(105\) 7.93003 + 0.601461i 0.773892 + 0.0586966i
\(106\) 0 0
\(107\) −0.0971333 5.13185i −0.00939023 0.496115i −0.973256 0.229725i \(-0.926217\pi\)
0.963865 0.266390i \(-0.0858309\pi\)
\(108\) 0 0
\(109\) −6.87108 + 13.4224i −0.658130 + 1.28563i 0.286684 + 0.958025i \(0.407447\pi\)
−0.944814 + 0.327608i \(0.893758\pi\)
\(110\) 0 0
\(111\) 27.5829 4.20831i 2.61805 0.399436i
\(112\) 0 0
\(113\) 7.23477 + 6.33464i 0.680590 + 0.595913i 0.927813 0.373046i \(-0.121687\pi\)
−0.247223 + 0.968959i \(0.579518\pi\)
\(114\) 0 0
\(115\) −2.78459 + 3.57030i −0.259665 + 0.332932i
\(116\) 0 0
\(117\) 9.95448 21.4062i 0.920292 1.97900i
\(118\) 0 0
\(119\) −0.449610 1.19602i −0.0412157 0.109639i
\(120\) 0 0
\(121\) −0.138759 + 2.44136i −0.0126145 + 0.221942i
\(122\) 0 0
\(123\) 23.1419 5.34786i 2.08664 0.482200i
\(124\) 0 0
\(125\) 9.49439 5.56174i 0.849204 0.497457i
\(126\) 0 0
\(127\) 1.53757 16.2004i 0.136438 1.43755i −0.620573 0.784148i \(-0.713100\pi\)
0.757011 0.653402i \(-0.226659\pi\)
\(128\) 0 0
\(129\) 24.5825 + 13.1770i 2.16437 + 1.16017i
\(130\) 0 0
\(131\) −10.7716 11.8423i −0.941119 1.03467i −0.999339 0.0363655i \(-0.988422\pi\)
0.0582199 0.998304i \(-0.481458\pi\)
\(132\) 0 0
\(133\) 0.0332029 0.0290719i 0.00287906 0.00252085i
\(134\) 0 0
\(135\) −4.57718 18.2274i −0.393941 1.56876i
\(136\) 0 0
\(137\) 0.431461 + 1.47883i 0.0368622 + 0.126345i 0.976327 0.216302i \(-0.0693995\pi\)
−0.939464 + 0.342647i \(0.888677\pi\)
\(138\) 0 0
\(139\) −12.6773 + 5.60602i −1.07528 + 0.475496i −0.864807 0.502104i \(-0.832559\pi\)
−0.210469 + 0.977601i \(0.567499\pi\)
\(140\) 0 0
\(141\) 7.77366 18.5190i 0.654660 1.55958i
\(142\) 0 0
\(143\) 6.97038 + 9.67066i 0.582892 + 0.808702i
\(144\) 0 0
\(145\) −3.81608 + 2.04554i −0.316908 + 0.169873i
\(146\) 0 0
\(147\) −2.81655 16.3759i −0.232305 1.35066i
\(148\) 0 0
\(149\) 8.82886 + 5.63113i 0.723289 + 0.461320i 0.847405 0.530947i \(-0.178164\pi\)
−0.124116 + 0.992268i \(0.539610\pi\)
\(150\) 0 0
\(151\) 6.51529 + 11.6210i 0.530207 + 0.945703i 0.998082 + 0.0619081i \(0.0197186\pi\)
−0.467875 + 0.883795i \(0.654980\pi\)
\(152\) 0 0
\(153\) −4.86519 + 3.94484i −0.393327 + 0.318921i
\(154\) 0 0
\(155\) −11.8392 9.59957i −0.950947 0.771056i
\(156\) 0 0
\(157\) −7.20861 15.5014i −0.575310 1.23715i −0.950651 0.310263i \(-0.899583\pi\)
0.375341 0.926887i \(-0.377526\pi\)
\(158\) 0 0
\(159\) 18.5593 + 18.9139i 1.47185 + 1.49997i
\(160\) 0 0
\(161\) −2.15557 0.953214i −0.169883 0.0751238i
\(162\) 0 0
\(163\) −3.08266 1.80580i −0.241452 0.141441i 0.379755 0.925087i \(-0.376008\pi\)
−0.621208 + 0.783646i \(0.713358\pi\)
\(164\) 0 0
\(165\) 18.9991 + 5.15507i 1.47907 + 0.401321i
\(166\) 0 0
\(167\) 7.34947 10.6295i 0.568719 0.822532i
\(168\) 0 0
\(169\) −3.48564 0.945767i −0.268126 0.0727513i
\(170\) 0 0
\(171\) −0.186667 0.109348i −0.0142748 0.00836204i
\(172\) 0 0
\(173\) 3.77130 + 1.66770i 0.286727 + 0.126793i 0.542794 0.839866i \(-0.317367\pi\)
−0.256067 + 0.966659i \(0.582427\pi\)
\(174\) 0 0
\(175\) −0.126150 0.128560i −0.00953601 0.00971821i
\(176\) 0 0
\(177\) 1.89256 + 4.06978i 0.142254 + 0.305904i
\(178\) 0 0
\(179\) 19.5703 + 15.8682i 1.46276 + 1.18604i 0.943476 + 0.331440i \(0.107534\pi\)
0.519279 + 0.854605i \(0.326201\pi\)
\(180\) 0 0
\(181\) −9.64350 + 7.81923i −0.716796 + 0.581199i −0.917158 0.398523i \(-0.869523\pi\)
0.200362 + 0.979722i \(0.435788\pi\)
\(182\) 0 0
\(183\) 1.15116 + 2.05327i 0.0850964 + 0.151782i
\(184\) 0 0
\(185\) −18.0085 11.4860i −1.32401 0.844468i
\(186\) 0 0
\(187\) −0.536117 3.11707i −0.0392048 0.227943i
\(188\) 0 0
\(189\) 8.62218 4.62177i 0.627171 0.336184i
\(190\) 0 0
\(191\) 15.4325 + 21.4109i 1.11666 + 1.54924i 0.799297 + 0.600936i \(0.205205\pi\)
0.317358 + 0.948306i \(0.397204\pi\)
\(192\) 0 0
\(193\) −8.13820 + 19.3874i −0.585800 + 1.39553i 0.309854 + 0.950784i \(0.399720\pi\)
−0.895655 + 0.444751i \(0.853292\pi\)
\(194\) 0 0
\(195\) −25.0887 + 11.0944i −1.79664 + 0.794489i
\(196\) 0 0
\(197\) 3.98173 + 13.6473i 0.283686 + 0.972332i 0.969609 + 0.244658i \(0.0786757\pi\)
−0.685923 + 0.727674i \(0.740601\pi\)
\(198\) 0 0
\(199\) −2.40879 9.59235i −0.170755 0.679984i −0.993720 0.111893i \(-0.964309\pi\)
0.822966 0.568091i \(-0.192318\pi\)
\(200\) 0 0
\(201\) −19.9074 + 17.4306i −1.40416 + 1.22946i
\(202\) 0 0
\(203\) −1.51654 1.66729i −0.106440 0.117021i
\(204\) 0 0
\(205\) −16.0254 8.59014i −1.11926 0.599961i
\(206\) 0 0
\(207\) −1.09166 + 11.5021i −0.0758759 + 0.799453i
\(208\) 0 0
\(209\) 0.0942595 0.0552165i 0.00652007 0.00381940i
\(210\) 0 0
\(211\) −24.4182 + 5.64280i −1.68102 + 0.388467i −0.954390 0.298562i \(-0.903493\pi\)
−0.726630 + 0.687029i \(0.758915\pi\)
\(212\) 0 0
\(213\) 0.192654 3.38959i 0.0132004 0.232251i
\(214\) 0 0
\(215\) −7.51318 19.9859i −0.512395 1.36303i
\(216\) 0 0
\(217\) 3.34556 7.19431i 0.227111 0.488382i
\(218\) 0 0
\(219\) 6.03701 7.74043i 0.407943 0.523050i
\(220\) 0 0
\(221\) 3.31594 + 2.90338i 0.223054 + 0.195302i
\(222\) 0 0
\(223\) −0.503723 + 0.0768528i −0.0337318 + 0.00514644i −0.167668 0.985843i \(-0.553624\pi\)
0.133936 + 0.990990i \(0.457238\pi\)
\(224\) 0 0
\(225\) −0.402332 + 0.785940i −0.0268221 + 0.0523960i
\(226\) 0 0
\(227\) 0.130592 + 6.89957i 0.00866767 + 0.457940i 0.977583 + 0.210549i \(0.0675251\pi\)
−0.968916 + 0.247391i \(0.920427\pi\)
\(228\) 0 0
\(229\) −24.3453 1.84649i −1.60878 0.122019i −0.759696 0.650278i \(-0.774652\pi\)
−0.849084 + 0.528258i \(0.822845\pi\)
\(230\) 0 0
\(231\) −0.193925 + 10.2456i −0.0127593 + 0.674114i
\(232\) 0 0
\(233\) −5.70356 + 2.02176i −0.373652 + 0.132450i −0.514301 0.857610i \(-0.671949\pi\)
0.140649 + 0.990060i \(0.455081\pi\)
\(234\) 0 0
\(235\) −13.8161 + 6.74577i −0.901265 + 0.440045i
\(236\) 0 0
\(237\) −43.3669 8.30671i −2.81698 0.539579i
\(238\) 0 0
\(239\) 0.331077 + 0.646746i 0.0214156 + 0.0418345i 0.900608 0.434633i \(-0.143122\pi\)
−0.879192 + 0.476467i \(0.841917\pi\)
\(240\) 0 0
\(241\) 22.7873 0.862923i 1.46786 0.0555858i 0.708248 0.705963i \(-0.249486\pi\)
0.759611 + 0.650378i \(0.225389\pi\)
\(242\) 0 0
\(243\) 2.59412 + 2.45087i 0.166413 + 0.157223i
\(244\) 0 0
\(245\) −6.63601 + 10.8520i −0.423959 + 0.693310i
\(246\) 0 0
\(247\) −0.0535658 + 0.142491i −0.00340831 + 0.00906651i
\(248\) 0 0
\(249\) 9.81501 1.11932i 0.622001 0.0709343i
\(250\) 0 0
\(251\) 21.1228 5.73132i 1.33326 0.361758i 0.477274 0.878754i \(-0.341625\pi\)
0.855987 + 0.516997i \(0.172950\pi\)
\(252\) 0 0
\(253\) −4.79665 3.32121i −0.301563 0.208803i
\(254\) 0 0
\(255\) 7.27309 + 0.275422i 0.455458 + 0.0172476i
\(256\) 0 0
\(257\) −1.87319 14.0569i −0.116846 0.876848i −0.947432 0.319957i \(-0.896331\pi\)
0.830586 0.556891i \(-0.188006\pi\)
\(258\) 0 0
\(259\) 3.51581 10.5482i 0.218462 0.655432i
\(260\) 0 0
\(261\) −5.40306 + 9.63715i −0.334441 + 0.596525i
\(262\) 0 0
\(263\) 1.73125 + 18.2410i 0.106753 + 1.12479i 0.874830 + 0.484431i \(0.160973\pi\)
−0.768076 + 0.640359i \(0.778786\pi\)
\(264\) 0 0
\(265\) −1.15110 20.2526i −0.0707113 1.24411i
\(266\) 0 0
\(267\) −3.50555 + 4.15996i −0.214536 + 0.254585i
\(268\) 0 0
\(269\) 25.3403 16.1623i 1.54503 0.985433i 0.557112 0.830437i \(-0.311909\pi\)
0.987915 0.154996i \(-0.0495365\pi\)
\(270\) 0 0
\(271\) −12.6029 + 9.45131i −0.765569 + 0.574126i −0.909619 0.415445i \(-0.863626\pi\)
0.144050 + 0.989570i \(0.453987\pi\)
\(272\) 0 0
\(273\) −8.78203 11.2600i −0.531513 0.681486i
\(274\) 0 0
\(275\) −0.246822 0.371294i −0.0148839 0.0223898i
\(276\) 0 0
\(277\) 20.9379 + 8.32659i 1.25804 + 0.500297i 0.901010 0.433798i \(-0.142827\pi\)
0.357026 + 0.934094i \(0.383791\pi\)
\(278\) 0 0
\(279\) −38.6433 4.40696i −2.31351 0.263838i
\(280\) 0 0
\(281\) −13.1031 9.82646i −0.781666 0.586198i 0.132667 0.991161i \(-0.457646\pi\)
−0.914333 + 0.404963i \(0.867284\pi\)
\(282\) 0 0
\(283\) 2.17919 2.39581i 0.129540 0.142416i −0.671553 0.740956i \(-0.734373\pi\)
0.801093 + 0.598540i \(0.204252\pi\)
\(284\) 0 0
\(285\) 0.0794901 + 0.238487i 0.00470859 + 0.0141268i
\(286\) 0 0
\(287\) 2.30520 9.17983i 0.136071 0.541868i
\(288\) 0 0
\(289\) 6.12725 + 14.5968i 0.360427 + 0.858634i
\(290\) 0 0
\(291\) 27.1303 + 9.61697i 1.59041 + 0.563757i
\(292\) 0 0
\(293\) 23.8562 9.48715i 1.39369 0.554245i 0.452395 0.891818i \(-0.350570\pi\)
0.941299 + 0.337573i \(0.109606\pi\)
\(294\) 0 0
\(295\) 0.962331 3.29838i 0.0560291 0.192039i
\(296\) 0 0
\(297\) 23.1141 7.22111i 1.34122 0.419011i
\(298\) 0 0
\(299\) 8.10667 0.614858i 0.468821 0.0355582i
\(300\) 0 0
\(301\) 9.13780 6.32703i 0.526694 0.364684i
\(302\) 0 0
\(303\) 15.8007 3.02654i 0.907724 0.173870i
\(304\) 0 0
\(305\) 0.372433 1.76309i 0.0213255 0.100955i
\(306\) 0 0
\(307\) 2.53545 + 1.23794i 0.144706 + 0.0706531i 0.509677 0.860366i \(-0.329765\pi\)
−0.364972 + 0.931019i \(0.618921\pi\)
\(308\) 0 0
\(309\) −3.49947 + 20.3465i −0.199078 + 1.15747i
\(310\) 0 0
\(311\) 6.15596 + 29.1423i 0.349073 + 1.65251i 0.698549 + 0.715562i \(0.253829\pi\)
−0.349477 + 0.936945i \(0.613641\pi\)
\(312\) 0 0
\(313\) −4.76854 + 4.85965i −0.269534 + 0.274684i −0.835195 0.549954i \(-0.814645\pi\)
0.565661 + 0.824638i \(0.308621\pi\)
\(314\) 0 0
\(315\) −15.1363 3.49783i −0.852832 0.197081i
\(316\) 0 0
\(317\) −0.139605 + 0.210008i −0.00784100 + 0.0117952i −0.836681 0.547690i \(-0.815507\pi\)
0.828840 + 0.559485i \(0.189001\pi\)
\(318\) 0 0
\(319\) −2.91053 4.75966i −0.162959 0.266490i
\(320\) 0 0
\(321\) −2.01034 + 15.0862i −0.112206 + 0.842028i
\(322\) 0 0
\(323\) 0.0293583 0.0277370i 0.00163354 0.00154333i
\(324\) 0 0
\(325\) 0.593019 + 0.185266i 0.0328948 + 0.0102767i
\(326\) 0 0
\(327\) 26.1436 36.2715i 1.44574 2.00582i
\(328\) 0 0
\(329\) −5.15737 6.12013i −0.284335 0.337414i
\(330\) 0 0
\(331\) 4.87182 + 0.743292i 0.267780 + 0.0408550i 0.283324 0.959024i \(-0.408563\pi\)
−0.0155447 + 0.999879i \(0.504948\pi\)
\(332\) 0 0
\(333\) −54.5045 −2.98683
\(334\) 0 0
\(335\) 20.2557 1.10668
\(336\) 0 0
\(337\) 1.57216 + 0.239864i 0.0856411 + 0.0130662i 0.193503 0.981100i \(-0.438015\pi\)
−0.107862 + 0.994166i \(0.534401\pi\)
\(338\) 0 0
\(339\) −18.3739 21.8039i −0.997935 1.18423i
\(340\) 0 0
\(341\) 11.4838 15.9325i 0.621882 0.862796i
\(342\) 0 0
\(343\) −14.2150 4.44092i −0.767537 0.239787i
\(344\) 0 0
\(345\) 9.75903 9.22011i 0.525409 0.496394i
\(346\) 0 0
\(347\) 3.65094 27.3977i 0.195993 1.47078i −0.566647 0.823960i \(-0.691760\pi\)
0.762640 0.646823i \(-0.223903\pi\)
\(348\) 0 0
\(349\) −3.83711 6.27491i −0.205396 0.335888i 0.733743 0.679427i \(-0.237772\pi\)
−0.939138 + 0.343539i \(0.888374\pi\)
\(350\) 0 0
\(351\) −18.6810 + 28.1018i −0.997120 + 1.49996i
\(352\) 0 0
\(353\) 12.0875 + 2.79330i 0.643355 + 0.148673i 0.534208 0.845353i \(-0.320610\pi\)
0.109147 + 0.994026i \(0.465188\pi\)
\(354\) 0 0
\(355\) −1.82029 + 1.85507i −0.0966112 + 0.0984571i
\(356\) 0 0
\(357\) 0.783037 + 3.70689i 0.0414427 + 0.196189i
\(358\) 0 0
\(359\) −2.21185 + 12.8600i −0.116737 + 0.678727i 0.866888 + 0.498502i \(0.166116\pi\)
−0.983625 + 0.180225i \(0.942317\pi\)
\(360\) 0 0
\(361\) −17.0723 8.33562i −0.898544 0.438717i
\(362\) 0 0
\(363\) 1.49856 7.09416i 0.0786539 0.372347i
\(364\) 0 0
\(365\) −7.38042 + 1.41368i −0.386309 + 0.0739955i
\(366\) 0 0
\(367\) −3.76449 + 2.60654i −0.196505 + 0.136060i −0.663435 0.748234i \(-0.730902\pi\)
0.466930 + 0.884294i \(0.345360\pi\)
\(368\) 0 0
\(369\) −46.2643 + 3.50896i −2.40843 + 0.182669i
\(370\) 0 0
\(371\) 10.0790 3.14880i 0.523277 0.163478i
\(372\) 0 0
\(373\) −4.96726 + 17.0252i −0.257195 + 0.881533i 0.724209 + 0.689580i \(0.242205\pi\)
−0.981404 + 0.191953i \(0.938518\pi\)
\(374\) 0 0
\(375\) −30.3177 + 12.0568i −1.56560 + 0.622609i
\(376\) 0 0
\(377\) 7.32759 + 2.59744i 0.377390 + 0.133775i
\(378\) 0 0
\(379\) 6.53757 + 15.5743i 0.335812 + 0.799996i 0.998685 + 0.0512640i \(0.0163250\pi\)
−0.662873 + 0.748732i \(0.730663\pi\)
\(380\) 0 0
\(381\) −11.7521 + 46.7996i −0.602079 + 2.39762i
\(382\) 0 0
\(383\) −3.53349 10.6012i −0.180553 0.541697i 0.818929 0.573895i \(-0.194568\pi\)
−0.999481 + 0.0321985i \(0.989749\pi\)
\(384\) 0 0
\(385\) 5.27846 5.80315i 0.269015 0.295756i
\(386\) 0 0
\(387\) −43.5883 32.6883i −2.21572 1.66164i
\(388\) 0 0
\(389\) −15.8528 1.80789i −0.803768 0.0916634i −0.298259 0.954485i \(-0.596406\pi\)
−0.505509 + 0.862821i \(0.668695\pi\)
\(390\) 0 0
\(391\) −2.00435 0.797091i −0.101364 0.0403106i
\(392\) 0 0
\(393\) 26.2781 + 39.5300i 1.32555 + 1.99403i
\(394\) 0 0
\(395\) 20.7881 + 26.6537i 1.04596 + 1.34109i
\(396\) 0 0
\(397\) −6.07622 + 4.55676i −0.304957 + 0.228697i −0.741447 0.671012i \(-0.765860\pi\)
0.436490 + 0.899709i \(0.356221\pi\)
\(398\) 0 0
\(399\) −0.110327 + 0.0703679i −0.00552328 + 0.00352280i
\(400\) 0 0
\(401\) −8.10736 + 9.62082i −0.404862 + 0.480441i −0.928411 0.371555i \(-0.878825\pi\)
0.523549 + 0.851996i \(0.324608\pi\)
\(402\) 0 0
\(403\) 1.55300 + 27.3238i 0.0773605 + 1.36110i
\(404\) 0 0
\(405\) 1.53842 + 16.2093i 0.0764445 + 0.805445i
\(406\) 0 0
\(407\) 13.4595 24.0070i 0.667163 1.18998i
\(408\) 0 0
\(409\) 2.12573 6.37763i 0.105110 0.315354i −0.882940 0.469486i \(-0.844439\pi\)
0.988050 + 0.154133i \(0.0492584\pi\)
\(410\) 0 0
\(411\) −0.603357 4.52776i −0.0297614 0.223338i
\(412\) 0 0
\(413\) 1.78726 + 0.0676811i 0.0879454 + 0.00333037i
\(414\) 0 0
\(415\) −6.21739 4.30493i −0.305200 0.211321i
\(416\) 0 0
\(417\) 39.6675 10.7631i 1.94252 0.527070i
\(418\) 0 0
\(419\) −8.62334 + 0.983424i −0.421278 + 0.0480434i −0.321371 0.946953i \(-0.604144\pi\)
−0.0999069 + 0.994997i \(0.531854\pi\)
\(420\) 0 0
\(421\) 6.18624 16.4561i 0.301499 0.802023i −0.695046 0.718966i \(-0.744616\pi\)
0.996545 0.0830573i \(-0.0264684\pi\)
\(422\) 0 0
\(423\) −20.4676 + 33.4711i −0.995169 + 1.62742i
\(424\) 0 0
\(425\) −0.119820 0.113203i −0.00581212 0.00549116i
\(426\) 0 0
\(427\) 0.937353 0.0354962i 0.0453617 0.00171778i
\(428\) 0 0
\(429\) −16.1070 31.4644i −0.777652 1.51911i
\(430\) 0 0
\(431\) −22.4141 4.29331i −1.07965 0.206802i −0.382666 0.923887i \(-0.624994\pi\)
−0.696986 + 0.717085i \(0.745476\pi\)
\(432\) 0 0
\(433\) 15.0642 7.35517i 0.723941 0.353467i −0.0396087 0.999215i \(-0.512611\pi\)
0.763550 + 0.645748i \(0.223455\pi\)
\(434\) 0 0
\(435\) 12.1007 4.28937i 0.580183 0.205660i
\(436\) 0 0
\(437\) 0.00140988 0.0744884i 6.74438e−5 0.00356326i
\(438\) 0 0
\(439\) −24.1763 1.83368i −1.15387 0.0875167i −0.515253 0.857038i \(-0.672302\pi\)
−0.638621 + 0.769522i \(0.720495\pi\)
\(440\) 0 0
\(441\) 0.614252 + 32.4529i 0.0292501 + 1.54538i
\(442\) 0 0
\(443\) −16.2170 + 31.6794i −0.770495 + 1.50513i 0.0901512 + 0.995928i \(0.471265\pi\)
−0.860646 + 0.509204i \(0.829940\pi\)
\(444\) 0 0
\(445\) 4.11683 0.628104i 0.195157 0.0297750i
\(446\) 0 0
\(447\) −23.3612 20.4547i −1.10495 0.967473i
\(448\) 0 0
\(449\) 20.4355 26.2016i 0.964409 1.23653i −0.00720944 0.999974i \(-0.502295\pi\)
0.971618 0.236555i \(-0.0760184\pi\)
\(450\) 0 0
\(451\) 9.87911 21.2441i 0.465189 1.00035i
\(452\) 0 0
\(453\) −13.9008 36.9777i −0.653116 1.73737i
\(454\) 0 0
\(455\) −0.620309 + 10.9138i −0.0290805 + 0.511649i
\(456\) 0 0
\(457\) 3.64662 0.842695i 0.170582 0.0394196i −0.139001 0.990292i \(-0.544389\pi\)
0.309582 + 0.950873i \(0.399811\pi\)
\(458\) 0 0
\(459\) 7.72519 4.52536i 0.360581 0.211225i
\(460\) 0 0
\(461\) 1.55093 16.3411i 0.0722342 0.761083i −0.883807 0.467851i \(-0.845028\pi\)
0.956041 0.293232i \(-0.0947307\pi\)
\(462\) 0 0
\(463\) 17.8322 + 9.55863i 0.828731 + 0.444227i 0.831337 0.555769i \(-0.187576\pi\)
−0.00260512 + 0.999997i \(0.500829\pi\)
\(464\) 0 0
\(465\) 30.4105 + 33.4334i 1.41025 + 1.55044i
\(466\) 0 0
\(467\) −17.2597 + 15.1123i −0.798685 + 0.699314i −0.957639 0.287972i \(-0.907019\pi\)
0.158954 + 0.987286i \(0.449188\pi\)
\(468\) 0 0
\(469\) 2.56803 + 10.2265i 0.118581 + 0.472216i
\(470\) 0 0
\(471\) 14.1977 + 48.6624i 0.654194 + 2.24224i
\(472\) 0 0
\(473\) 25.1617 11.1267i 1.15694 0.511608i
\(474\) 0 0
\(475\) 0.00220362 0.00524962i 0.000101109 0.000240869i
\(476\) 0 0
\(477\) −30.2668 41.9920i −1.38582 1.92268i
\(478\) 0 0
\(479\) 7.97770 4.27631i 0.364511 0.195390i −0.279973 0.960008i \(-0.590325\pi\)
0.644483 + 0.764618i \(0.277072\pi\)
\(480\) 0 0
\(481\) 6.50095 + 37.7976i 0.296418 + 1.72342i
\(482\) 0 0
\(483\) 5.89223 + 3.75812i 0.268106 + 0.171000i
\(484\) 0 0
\(485\) −10.7759 19.2204i −0.489307 0.872752i
\(486\) 0 0
\(487\) 16.9487 13.7425i 0.768020 0.622733i −0.163450 0.986552i \(-0.552262\pi\)
0.931470 + 0.363819i \(0.118527\pi\)
\(488\) 0 0
\(489\) 8.22844 + 6.67186i 0.372103 + 0.301712i
\(490\) 0 0
\(491\) −3.12338 6.71653i −0.140956 0.303113i 0.823518 0.567290i \(-0.192008\pi\)
−0.964474 + 0.264177i \(0.914900\pi\)
\(492\) 0 0
\(493\) −1.44467 1.47227i −0.0650645 0.0663076i
\(494\) 0 0
\(495\) −35.1698 15.5524i −1.58076 0.699027i
\(496\) 0 0
\(497\) −1.16735 0.683826i −0.0523629 0.0306738i
\(498\) 0 0
\(499\) 33.7106 + 9.14678i 1.50909 + 0.409466i 0.917817 0.397004i \(-0.129950\pi\)
0.591275 + 0.806470i \(0.298625\pi\)
\(500\) 0 0
\(501\) −26.2968 + 27.8707i −1.17485 + 1.24517i
\(502\) 0 0
\(503\) 2.82760 + 0.767220i 0.126076 + 0.0342087i 0.324343 0.945939i \(-0.394857\pi\)
−0.198267 + 0.980148i \(0.563531\pi\)
\(504\) 0 0
\(505\) −10.6266 6.22498i −0.472877 0.277008i
\(506\) 0 0
\(507\) 9.79430 + 4.33112i 0.434980 + 0.192352i
\(508\) 0 0
\(509\) −18.0734 18.4187i −0.801090 0.816396i 0.184977 0.982743i \(-0.440779\pi\)
−0.986067 + 0.166347i \(0.946803\pi\)
\(510\) 0 0
\(511\) −1.64942 3.54693i −0.0729662 0.156907i
\(512\) 0 0
\(513\) 0.240194 + 0.194757i 0.0106048 + 0.00859871i
\(514\) 0 0
\(515\) 12.2760 9.95377i 0.540947 0.438615i
\(516\) 0 0
\(517\) −9.68837 17.2806i −0.426094 0.760002i
\(518\) 0 0
\(519\) −10.3088 6.57504i −0.452505 0.288612i
\(520\) 0 0
\(521\) 5.58314 + 32.4613i 0.244602 + 1.42215i 0.804677 + 0.593713i \(0.202339\pi\)
−0.560075 + 0.828442i \(0.689228\pi\)
\(522\) 0 0
\(523\) −29.4686 + 15.7962i −1.28857 + 0.690718i −0.966663 0.256053i \(-0.917578\pi\)
−0.321910 + 0.946770i \(0.604325\pi\)
\(524\) 0 0
\(525\) 0.312281 + 0.433257i 0.0136291 + 0.0189089i
\(526\) 0 0
\(527\) 2.81046 6.69528i 0.122426 0.291651i
\(528\) 0 0
\(529\) 17.3961 7.69271i 0.756353 0.334466i
\(530\) 0 0
\(531\) −2.45563 8.41664i −0.106565 0.365251i
\(532\) 0 0
\(533\) 7.95150 + 31.6647i 0.344418 + 1.37155i
\(534\) 0 0
\(535\) 8.76564 7.67504i 0.378972 0.331821i
\(536\) 0 0
\(537\) −50.2689 55.2658i −2.16926 2.38490i
\(538\) 0 0
\(539\) −14.4459 7.74347i −0.622228 0.333535i
\(540\) 0 0
\(541\) 0.291199 3.06817i 0.0125196 0.131911i −0.987079 0.160233i \(-0.948775\pi\)
0.999599 + 0.0283221i \(0.00901640\pi\)
\(542\) 0 0
\(543\) 31.7644 18.6073i 1.36314 0.798517i
\(544\) 0 0
\(545\) −33.3486 + 7.70653i −1.42850 + 0.330111i
\(546\) 0 0
\(547\) −0.601423 + 10.5816i −0.0257150 + 0.452435i 0.959565 + 0.281487i \(0.0908277\pi\)
−0.985280 + 0.170948i \(0.945317\pi\)
\(548\) 0 0
\(549\) −1.61804 4.30417i −0.0690562 0.183698i
\(550\) 0 0
\(551\) 0.0300406 0.0645996i 0.00127977 0.00275204i
\(552\) 0 0
\(553\) −10.8211 + 13.8745i −0.460162 + 0.590003i
\(554\) 0 0
\(555\) 47.6506 + 41.7220i 2.02266 + 1.77100i
\(556\) 0 0
\(557\) −6.97034 + 1.06346i −0.295343 + 0.0450603i −0.296803 0.954939i \(-0.595921\pi\)
0.00146064 + 0.999999i \(0.499535\pi\)
\(558\) 0 0
\(559\) −17.4697 + 34.1263i −0.738888 + 1.44339i
\(560\) 0 0
\(561\) 0.177477 + 9.37667i 0.00749309 + 0.395883i
\(562\) 0 0
\(563\) 0.0598335 + 0.00453813i 0.00252168 + 0.000191259i 0.0768895 0.997040i \(-0.475501\pi\)
−0.0743678 + 0.997231i \(0.523694\pi\)
\(564\) 0 0
\(565\) −0.413068 + 21.8237i −0.0173779 + 0.918129i
\(566\) 0 0
\(567\) −7.98854 + 2.83173i −0.335487 + 0.118921i
\(568\) 0 0
\(569\) 22.0804 10.7809i 0.925661 0.451957i 0.0867525 0.996230i \(-0.472351\pi\)
0.838908 + 0.544273i \(0.183194\pi\)
\(570\) 0 0
\(571\) −29.9758 5.74171i −1.25445 0.240283i −0.482459 0.875919i \(-0.660256\pi\)
−0.771989 + 0.635636i \(0.780738\pi\)
\(572\) 0 0
\(573\) −35.6610 69.6625i −1.48976 2.91019i
\(574\) 0 0
\(575\) −0.303846 + 0.0115062i −0.0126713 + 0.000479843i
\(576\) 0 0
\(577\) 33.0119 + 31.1889i 1.37430 + 1.29841i 0.911115 + 0.412152i \(0.135223\pi\)
0.463190 + 0.886259i \(0.346705\pi\)
\(578\) 0 0
\(579\) 32.5255 53.1896i 1.35171 2.21049i
\(580\) 0 0
\(581\) 1.38519 3.68477i 0.0574673 0.152870i
\(582\) 0 0
\(583\) 25.9700 2.96168i 1.07557 0.122660i
\(584\) 0 0
\(585\) 51.7168 14.0325i 2.13823 0.580171i
\(586\) 0 0
\(587\) 2.34669 + 1.62485i 0.0968581 + 0.0670647i 0.616703 0.787196i \(-0.288468\pi\)
−0.519845 + 0.854261i \(0.674010\pi\)
\(588\) 0 0
\(589\) 0.250617 + 0.00949050i 0.0103265 + 0.000391049i
\(590\) 0 0
\(591\) −5.56807 41.7844i −0.229040 1.71878i
\(592\) 0 0
\(593\) −10.8356 + 32.5090i −0.444963 + 1.33498i 0.451660 + 0.892190i \(0.350832\pi\)
−0.896624 + 0.442794i \(0.853987\pi\)
\(594\) 0 0
\(595\) 1.41836 2.52985i 0.0581470 0.103714i
\(596\) 0 0
\(597\) 2.77087 + 29.1948i 0.113404 + 1.19486i
\(598\) 0 0
\(599\) 0.299089 + 5.26224i 0.0122205 + 0.215009i 0.998694 + 0.0510894i \(0.0162693\pi\)
−0.986474 + 0.163920i \(0.947586\pi\)
\(600\) 0 0
\(601\) 21.8574 25.9376i 0.891581 1.05802i −0.106388 0.994325i \(-0.533929\pi\)
0.997969 0.0636941i \(-0.0202882\pi\)
\(602\) 0 0
\(603\) 43.5781 27.7945i 1.77464 1.13188i
\(604\) 0 0
\(605\) −4.44060 + 3.33016i −0.180536 + 0.135390i
\(606\) 0 0
\(607\) −28.2562 36.2291i −1.14688 1.47049i −0.858380 0.513014i \(-0.828529\pi\)
−0.288504 0.957479i \(-0.593158\pi\)
\(608\) 0 0
\(609\) 3.69971 + 5.56547i 0.149920 + 0.225524i
\(610\) 0 0
\(611\) 25.6527 + 10.2016i 1.03780 + 0.412712i
\(612\) 0 0
\(613\) −27.6858 3.15735i −1.11822 0.127524i −0.465445 0.885077i \(-0.654106\pi\)
−0.652774 + 0.757553i \(0.726395\pi\)
\(614\) 0 0
\(615\) 43.1327 + 32.3467i 1.73928 + 1.30434i
\(616\) 0 0
\(617\) −22.9811 + 25.2655i −0.925183 + 1.01715i 0.0746180 + 0.997212i \(0.476226\pi\)
−0.999801 + 0.0199375i \(0.993653\pi\)
\(618\) 0 0
\(619\) 2.10713 + 6.32183i 0.0846927 + 0.254096i 0.982491 0.186311i \(-0.0596533\pi\)
−0.897798 + 0.440407i \(0.854834\pi\)
\(620\) 0 0
\(621\) 4.02229 16.0177i 0.161409 0.642767i
\(622\) 0 0
\(623\) 0.839048 + 1.99884i 0.0336157 + 0.0800818i
\(624\) 0 0
\(625\) 24.2599 + 8.59949i 0.970395 + 0.343979i
\(626\) 0 0
\(627\) −0.300992 + 0.119698i −0.0120204 + 0.00478030i
\(628\) 0 0
\(629\) 2.85001 9.76839i 0.113637 0.389491i
\(630\) 0 0
\(631\) 29.6479 9.26233i 1.18026 0.368728i 0.355756 0.934579i \(-0.384224\pi\)
0.824507 + 0.565852i \(0.191452\pi\)
\(632\) 0 0
\(633\) 74.0994 5.62014i 2.94519 0.223381i
\(634\) 0 0
\(635\) 30.3692 21.0277i 1.20516 0.834457i
\(636\) 0 0
\(637\) 22.4321 4.29675i 0.888790 0.170243i
\(638\) 0 0
\(639\) −1.37068 + 6.48879i −0.0542233 + 0.256693i
\(640\) 0 0
\(641\) −16.1544 7.88744i −0.638061 0.311535i 0.0911371 0.995838i \(-0.470950\pi\)
−0.729198 + 0.684303i \(0.760106\pi\)
\(642\) 0 0
\(643\) 2.02157 11.7537i 0.0797228 0.463521i −0.918030 0.396512i \(-0.870221\pi\)
0.997752 0.0670093i \(-0.0213457\pi\)
\(644\) 0 0
\(645\) 13.0849 + 61.9438i 0.515217 + 2.43903i
\(646\) 0 0
\(647\) 11.3006 11.5165i 0.444274 0.452762i −0.454778 0.890605i \(-0.650281\pi\)
0.899052 + 0.437843i \(0.144257\pi\)
\(648\) 0 0
\(649\) 4.31359 + 0.996827i 0.169323 + 0.0391289i
\(650\) 0 0
\(651\) −13.0241 + 19.5921i −0.510454 + 0.767875i
\(652\) 0 0
\(653\) 2.27460 + 3.71971i 0.0890120 + 0.145563i 0.894530 0.447008i \(-0.147510\pi\)
−0.805518 + 0.592571i \(0.798113\pi\)
\(654\) 0 0
\(655\) 4.79979 36.0190i 0.187543 1.40738i
\(656\) 0 0
\(657\) −13.9384 + 13.1687i −0.543789 + 0.513760i
\(658\) 0 0
\(659\) 44.3325 + 13.8500i 1.72695 + 0.539518i 0.990565 0.137047i \(-0.0437610\pi\)
0.736383 + 0.676565i \(0.236532\pi\)
\(660\) 0 0
\(661\) 21.5157 29.8508i 0.836864 1.16106i −0.148214 0.988955i \(-0.547353\pi\)
0.985078 0.172106i \(-0.0550571\pi\)
\(662\) 0 0
\(663\) −8.42139 9.99347i −0.327060 0.388114i
\(664\) 0 0
\(665\) 0.0990285 + 0.0151087i 0.00384016 + 0.000585892i
\(666\) 0 0
\(667\) −3.80485 −0.147324
\(668\) 0 0
\(669\) 1.51090 0.0584150
\(670\) 0 0
\(671\) 2.29538 + 0.350205i 0.0886122 + 0.0135195i
\(672\) 0 0
\(673\) −26.0486 30.9113i −1.00410 1.19154i −0.981434 0.191801i \(-0.938567\pi\)
−0.0226676 0.999743i \(-0.507216\pi\)
\(674\) 0 0
\(675\) 0.737952 1.02383i 0.0284038 0.0394072i
\(676\) 0 0
\(677\) −37.2007 11.6219i −1.42974 0.446667i −0.517274 0.855820i \(-0.673053\pi\)
−0.912466 + 0.409153i \(0.865824\pi\)
\(678\) 0 0
\(679\) 8.33764 7.87721i 0.319969 0.302299i
\(680\) 0 0
\(681\) 2.70282 20.2827i 0.103572 0.777236i
\(682\) 0 0
\(683\) 26.6614 + 43.6001i 1.02017 + 1.66831i 0.689035 + 0.724728i \(0.258035\pi\)
0.331137 + 0.943583i \(0.392568\pi\)
\(684\) 0 0
\(685\) −1.93580 + 2.91202i −0.0739631 + 0.111263i
\(686\) 0 0
\(687\) 70.5362 + 16.3002i 2.69112 + 0.621891i
\(688\) 0 0
\(689\) −25.5105 + 25.9979i −0.971872 + 0.990441i
\(690\) 0 0
\(691\) −0.211108 0.999384i −0.00803093 0.0380183i 0.974209 0.225648i \(-0.0724498\pi\)
−0.982240 + 0.187629i \(0.939920\pi\)
\(692\) 0 0
\(693\) 3.39308 19.7279i 0.128893 0.749402i
\(694\) 0 0
\(695\) −28.2741 13.8049i −1.07250 0.523650i
\(696\) 0 0
\(697\) 1.79026 8.47506i 0.0678108 0.321016i
\(698\) 0 0
\(699\) 17.6227 3.37554i 0.666552 0.127675i
\(700\) 0 0
\(701\) −10.6518 + 7.37534i −0.402314 + 0.278563i −0.753117 0.657886i \(-0.771451\pi\)
0.350804 + 0.936449i \(0.385908\pi\)
\(702\) 0 0
\(703\) 0.350451 0.0265803i 0.0132175 0.00100250i
\(704\) 0 0
\(705\) 43.5153 13.5947i 1.63888 0.512005i
\(706\) 0 0
\(707\) 1.79556 6.15427i 0.0675290 0.231455i
\(708\) 0 0
\(709\) −26.0273 + 10.3505i −0.977476 + 0.388723i −0.803027 0.595943i \(-0.796778\pi\)
−0.174449 + 0.984666i \(0.555814\pi\)
\(710\) 0 0
\(711\) 81.2973 + 28.8177i 3.04889 + 1.08075i
\(712\) 0 0
\(713\) −5.18423 12.3502i −0.194151 0.462520i
\(714\) 0 0
\(715\) −6.59038 + 26.2444i −0.246466 + 0.981485i
\(716\) 0 0
\(717\) −0.681230 2.04384i −0.0254410 0.0763284i
\(718\) 0 0
\(719\) 13.4144 14.7478i 0.500272 0.550001i −0.436608 0.899652i \(-0.643820\pi\)
0.936880 + 0.349651i \(0.113700\pi\)
\(720\) 0 0
\(721\) 6.58174 + 4.93587i 0.245117 + 0.183821i
\(722\) 0 0
\(723\) −67.1811 7.66148i −2.49849 0.284933i
\(724\) 0 0
\(725\) −0.270183 0.107446i −0.0100343 0.00399046i
\(726\) 0 0
\(727\) −9.11096 13.7056i −0.337907 0.508312i 0.624097 0.781347i \(-0.285467\pi\)
−0.962004 + 0.273034i \(0.911973\pi\)
\(728\) 0 0
\(729\) −19.7422 25.3127i −0.731192 0.937508i
\(730\) 0 0
\(731\) 8.13768 6.10272i 0.300983 0.225717i
\(732\) 0 0
\(733\) 14.7263 9.39257i 0.543928 0.346923i −0.237034 0.971501i \(-0.576175\pi\)
0.780962 + 0.624579i \(0.214729\pi\)
\(734\) 0 0
\(735\) 24.3050 28.8422i 0.896503 1.06386i
\(736\) 0 0
\(737\) 1.48106 + 26.0581i 0.0545555 + 0.959861i
\(738\) 0 0
\(739\) −3.47419 36.6052i −0.127800 1.34654i −0.797233 0.603671i \(-0.793704\pi\)
0.669433 0.742872i \(-0.266537\pi\)
\(740\) 0 0
\(741\) 0.220739 0.393722i 0.00810907 0.0144637i
\(742\) 0 0
\(743\) −7.41765 + 22.2545i −0.272127 + 0.816439i 0.720306 + 0.693656i \(0.244001\pi\)
−0.992434 + 0.122783i \(0.960818\pi\)
\(744\) 0 0
\(745\) 3.13976 + 23.5616i 0.115032 + 0.863231i
\(746\) 0 0
\(747\) −19.2833 0.730231i −0.705538 0.0267177i
\(748\) 0 0
\(749\) 4.98622 + 3.45247i 0.182193 + 0.126151i
\(750\) 0 0
\(751\) 8.52846 2.31405i 0.311208 0.0844409i −0.102835 0.994698i \(-0.532791\pi\)
0.414042 + 0.910258i \(0.364117\pi\)
\(752\) 0 0
\(753\) −64.4794 + 7.35337i −2.34976 + 0.267972i
\(754\) 0 0
\(755\) −10.6414 + 28.3073i −0.387279 + 1.03021i
\(756\) 0 0
\(757\) −12.9260 + 21.1383i −0.469805 + 0.768283i −0.996659 0.0816725i \(-0.973974\pi\)
0.526854 + 0.849956i \(0.323371\pi\)
\(758\) 0 0
\(759\) 12.5749 + 11.8804i 0.456438 + 0.431232i
\(760\) 0 0
\(761\) −50.4871 + 1.91188i −1.83016 + 0.0693055i −0.930283 0.366843i \(-0.880439\pi\)
−0.899875 + 0.436148i \(0.856342\pi\)
\(762\) 0 0
\(763\) −8.11878 15.8597i −0.293919 0.574161i
\(764\) 0 0
\(765\) −13.9637 2.67468i −0.504859 0.0967032i
\(766\) 0 0
\(767\) −5.54385 + 2.70680i −0.200177 + 0.0977370i
\(768\) 0 0
\(769\) 8.61808 3.05488i 0.310776 0.110162i −0.174145 0.984720i \(-0.555716\pi\)
0.484920 + 0.874558i \(0.338849\pi\)
\(770\) 0 0
\(771\) −0.795752 + 42.0421i −0.0286583 + 1.51411i
\(772\) 0 0
\(773\) −3.09065 0.234413i −0.111163 0.00843126i 0.0199297 0.999801i \(-0.493656\pi\)
−0.131093 + 0.991370i \(0.541849\pi\)
\(774\) 0 0
\(775\) −0.0193703 1.02339i −0.000695800 0.0367613i
\(776\) 0 0
\(777\) −15.0231 + 29.3470i −0.538949 + 1.05282i
\(778\) 0 0
\(779\) 0.295758 0.0451237i 0.0105966 0.00161672i
\(780\) 0 0
\(781\) −2.51957 2.20609i −0.0901574 0.0789402i
\(782\) 0 0
\(783\) 9.71241 12.4529i 0.347093 0.445030i
\(784\) 0 0
\(785\) 16.3628 35.1867i 0.584014 1.25587i
\(786\) 0 0
\(787\) 2.87150 + 7.63854i 0.102358 + 0.272284i 0.977270 0.211997i \(-0.0679967\pi\)
−0.874912 + 0.484281i \(0.839081\pi\)
\(788\) 0 0
\(789\) 3.08301 54.2432i 0.109758 1.93111i
\(790\) 0 0
\(791\) −11.0705 + 2.55828i −0.393622 + 0.0909620i
\(792\) 0 0
\(793\) −2.79185 + 1.63545i −0.0991417 + 0.0580764i
\(794\) 0 0
\(795\) −5.68322 + 59.8802i −0.201563 + 2.12373i
\(796\) 0 0