Properties

Label 1008.2.r.e.337.1
Level $1008$
Weight $2$
Character 1008.337
Analytic conductor $8.049$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.e.673.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.41421i) q^{3} +(-1.72474 + 2.98735i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.41421i) q^{3} +(-1.72474 + 2.98735i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-1.00000 + 2.82843i) q^{9} +(1.00000 + 1.73205i) q^{11} +(2.44949 - 4.24264i) q^{13} +(5.94949 - 0.548188i) q^{15} +2.00000 q^{17} -7.44949 q^{19} +(-0.724745 + 1.57313i) q^{21} +(-0.500000 + 0.866025i) q^{23} +(-3.44949 - 5.97469i) q^{25} +(5.00000 - 1.41421i) q^{27} +(-1.44949 - 2.51059i) q^{29} +(3.00000 - 5.19615i) q^{31} +(1.44949 - 3.14626i) q^{33} +3.44949 q^{35} -7.79796 q^{37} +(-8.44949 + 0.778539i) q^{39} +(4.89898 - 8.48528i) q^{41} +(-1.44949 - 2.51059i) q^{43} +(-6.72474 - 7.86566i) q^{45} +(-4.89898 - 8.48528i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.00000 - 2.82843i) q^{51} -1.10102 q^{53} -6.89898 q^{55} +(7.44949 + 10.5352i) q^{57} +(-1.00000 + 1.73205i) q^{59} +(-5.72474 - 9.91555i) q^{61} +(2.94949 - 0.548188i) q^{63} +(8.44949 + 14.6349i) q^{65} +(-1.55051 + 2.68556i) q^{67} +(1.72474 - 0.158919i) q^{69} -9.89898 q^{71} +2.89898 q^{73} +(-5.00000 + 10.8530i) q^{75} +(1.00000 - 1.73205i) q^{77} +(3.94949 + 6.84072i) q^{79} +(-7.00000 - 5.65685i) q^{81} +(1.00000 + 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +(-2.10102 + 4.56048i) q^{87} -7.10102 q^{89} -4.89898 q^{91} +(-10.3485 + 0.953512i) q^{93} +(12.8485 - 22.2542i) q^{95} +(3.44949 + 5.97469i) q^{97} +(-5.89898 + 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 2q^{5} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 2q^{5} - 2q^{7} - 4q^{9} + 4q^{11} + 14q^{15} + 8q^{17} - 20q^{19} + 2q^{21} - 2q^{23} - 4q^{25} + 20q^{27} + 4q^{29} + 12q^{31} - 4q^{33} + 4q^{35} + 8q^{37} - 24q^{39} + 4q^{43} - 22q^{45} - 2q^{49} - 8q^{51} - 24q^{53} - 8q^{55} + 20q^{57} - 4q^{59} - 18q^{61} + 2q^{63} + 24q^{65} - 16q^{67} + 2q^{69} - 20q^{71} - 8q^{73} - 20q^{75} + 4q^{77} + 6q^{79} - 28q^{81} + 4q^{83} - 4q^{85} - 28q^{87} - 48q^{89} - 12q^{93} + 22q^{95} + 4q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −1.00000 1.41421i −0.577350 0.816497i
\(4\) 0 0
\(5\) −1.72474 + 2.98735i −0.771329 + 1.33598i 0.165505 + 0.986209i \(0.447075\pi\)
−0.936835 + 0.349773i \(0.886259\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) −1.00000 + 2.82843i −0.333333 + 0.942809i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) 0 0
\(15\) 5.94949 0.548188i 1.53615 0.141542i
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −7.44949 −1.70903 −0.854515 0.519427i \(-0.826146\pi\)
−0.854515 + 0.519427i \(0.826146\pi\)
\(20\) 0 0
\(21\) −0.724745 + 1.57313i −0.158152 + 0.343286i
\(22\) 0 0
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) −3.44949 5.97469i −0.689898 1.19494i
\(26\) 0 0
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) 0 0
\(29\) −1.44949 2.51059i −0.269163 0.466205i 0.699483 0.714650i \(-0.253414\pi\)
−0.968646 + 0.248445i \(0.920081\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) 0 0
\(33\) 1.44949 3.14626i 0.252324 0.547694i
\(34\) 0 0
\(35\) 3.44949 0.583070
\(36\) 0 0
\(37\) −7.79796 −1.28198 −0.640988 0.767551i \(-0.721475\pi\)
−0.640988 + 0.767551i \(0.721475\pi\)
\(38\) 0 0
\(39\) −8.44949 + 0.778539i −1.35300 + 0.124666i
\(40\) 0 0
\(41\) 4.89898 8.48528i 0.765092 1.32518i −0.175106 0.984550i \(-0.556027\pi\)
0.940198 0.340629i \(-0.110640\pi\)
\(42\) 0 0
\(43\) −1.44949 2.51059i −0.221045 0.382861i 0.734080 0.679062i \(-0.237613\pi\)
−0.955126 + 0.296201i \(0.904280\pi\)
\(44\) 0 0
\(45\) −6.72474 7.86566i −1.00247 1.17254i
\(46\) 0 0
\(47\) −4.89898 8.48528i −0.714590 1.23771i −0.963118 0.269081i \(-0.913280\pi\)
0.248528 0.968625i \(-0.420053\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −2.00000 2.82843i −0.280056 0.396059i
\(52\) 0 0
\(53\) −1.10102 −0.151237 −0.0756184 0.997137i \(-0.524093\pi\)
−0.0756184 + 0.997137i \(0.524093\pi\)
\(54\) 0 0
\(55\) −6.89898 −0.930258
\(56\) 0 0
\(57\) 7.44949 + 10.5352i 0.986709 + 1.39542i
\(58\) 0 0
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) −5.72474 9.91555i −0.732978 1.26956i −0.955605 0.294652i \(-0.904796\pi\)
0.222626 0.974904i \(-0.428537\pi\)
\(62\) 0 0
\(63\) 2.94949 0.548188i 0.371601 0.0690652i
\(64\) 0 0
\(65\) 8.44949 + 14.6349i 1.04803 + 1.81524i
\(66\) 0 0
\(67\) −1.55051 + 2.68556i −0.189425 + 0.328094i −0.945059 0.326901i \(-0.893996\pi\)
0.755634 + 0.654994i \(0.227329\pi\)
\(68\) 0 0
\(69\) 1.72474 0.158919i 0.207635 0.0191316i
\(70\) 0 0
\(71\) −9.89898 −1.17479 −0.587396 0.809299i \(-0.699847\pi\)
−0.587396 + 0.809299i \(0.699847\pi\)
\(72\) 0 0
\(73\) 2.89898 0.339300 0.169650 0.985504i \(-0.445736\pi\)
0.169650 + 0.985504i \(0.445736\pi\)
\(74\) 0 0
\(75\) −5.00000 + 10.8530i −0.577350 + 1.25320i
\(76\) 0 0
\(77\) 1.00000 1.73205i 0.113961 0.197386i
\(78\) 0 0
\(79\) 3.94949 + 6.84072i 0.444352 + 0.769641i 0.998007 0.0631057i \(-0.0201005\pi\)
−0.553655 + 0.832746i \(0.686767\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 0 0
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) −3.44949 + 5.97469i −0.374150 + 0.648046i
\(86\) 0 0
\(87\) −2.10102 + 4.56048i −0.225253 + 0.488935i
\(88\) 0 0
\(89\) −7.10102 −0.752707 −0.376353 0.926476i \(-0.622822\pi\)
−0.376353 + 0.926476i \(0.622822\pi\)
\(90\) 0 0
\(91\) −4.89898 −0.513553
\(92\) 0 0
\(93\) −10.3485 + 0.953512i −1.07309 + 0.0988746i
\(94\) 0 0
\(95\) 12.8485 22.2542i 1.31823 2.28323i
\(96\) 0 0
\(97\) 3.44949 + 5.97469i 0.350243 + 0.606638i 0.986292 0.165011i \(-0.0527658\pi\)
−0.636049 + 0.771649i \(0.719432\pi\)
\(98\) 0 0
\(99\) −5.89898 + 1.09638i −0.592870 + 0.110190i
\(100\) 0 0
\(101\) −3.62372 6.27647i −0.360574 0.624533i 0.627481 0.778632i \(-0.284086\pi\)
−0.988055 + 0.154099i \(0.950753\pi\)
\(102\) 0 0
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) 0 0
\(105\) −3.44949 4.87832i −0.336636 0.476075i
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −16.6969 −1.59928 −0.799638 0.600482i \(-0.794975\pi\)
−0.799638 + 0.600482i \(0.794975\pi\)
\(110\) 0 0
\(111\) 7.79796 + 11.0280i 0.740150 + 1.04673i
\(112\) 0 0
\(113\) 7.94949 13.7689i 0.747825 1.29527i −0.201038 0.979583i \(-0.564431\pi\)
0.948863 0.315688i \(-0.102235\pi\)
\(114\) 0 0
\(115\) −1.72474 2.98735i −0.160833 0.278571i
\(116\) 0 0
\(117\) 9.55051 + 11.1708i 0.882945 + 1.03274i
\(118\) 0 0
\(119\) −1.00000 1.73205i −0.0916698 0.158777i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −16.8990 + 1.55708i −1.52373 + 0.140397i
\(124\) 0 0
\(125\) 6.55051 0.585895
\(126\) 0 0
\(127\) 3.00000 0.266207 0.133103 0.991102i \(-0.457506\pi\)
0.133103 + 0.991102i \(0.457506\pi\)
\(128\) 0 0
\(129\) −2.10102 + 4.56048i −0.184985 + 0.401528i
\(130\) 0 0
\(131\) −6.72474 + 11.6476i −0.587544 + 1.01766i 0.407009 + 0.913424i \(0.366572\pi\)
−0.994553 + 0.104232i \(0.966762\pi\)
\(132\) 0 0
\(133\) 3.72474 + 6.45145i 0.322976 + 0.559411i
\(134\) 0 0
\(135\) −4.39898 + 17.3759i −0.378604 + 1.49548i
\(136\) 0 0
\(137\) 5.89898 + 10.2173i 0.503984 + 0.872926i 0.999989 + 0.00460626i \(0.00146622\pi\)
−0.496006 + 0.868319i \(0.665200\pi\)
\(138\) 0 0
\(139\) 4.72474 8.18350i 0.400748 0.694115i −0.593069 0.805152i \(-0.702084\pi\)
0.993816 + 0.111037i \(0.0354171\pi\)
\(140\) 0 0
\(141\) −7.10102 + 15.4135i −0.598014 + 1.29805i
\(142\) 0 0
\(143\) 9.79796 0.819346
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) 0 0
\(147\) 1.72474 0.158919i 0.142255 0.0131074i
\(148\) 0 0
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i \(-0.231881\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(152\) 0 0
\(153\) −2.00000 + 5.65685i −0.161690 + 0.457330i
\(154\) 0 0
\(155\) 10.3485 + 17.9241i 0.831209 + 1.43970i
\(156\) 0 0
\(157\) −3.17423 + 5.49794i −0.253332 + 0.438783i −0.964441 0.264298i \(-0.914860\pi\)
0.711109 + 0.703081i \(0.248193\pi\)
\(158\) 0 0
\(159\) 1.10102 + 1.55708i 0.0873166 + 0.123484i
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 0.202041 0.0158251 0.00791254 0.999969i \(-0.497481\pi\)
0.00791254 + 0.999969i \(0.497481\pi\)
\(164\) 0 0
\(165\) 6.89898 + 9.75663i 0.537085 + 0.759553i
\(166\) 0 0
\(167\) 9.34847 16.1920i 0.723406 1.25298i −0.236220 0.971700i \(-0.575909\pi\)
0.959627 0.281277i \(-0.0907579\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) 0 0
\(171\) 7.44949 21.0703i 0.569677 1.61129i
\(172\) 0 0
\(173\) 6.44949 + 11.1708i 0.490346 + 0.849304i 0.999938 0.0111123i \(-0.00353722\pi\)
−0.509593 + 0.860416i \(0.670204\pi\)
\(174\) 0 0
\(175\) −3.44949 + 5.97469i −0.260757 + 0.451644i
\(176\) 0 0
\(177\) 3.44949 0.317837i 0.259280 0.0238901i
\(178\) 0 0
\(179\) 8.69694 0.650040 0.325020 0.945707i \(-0.394629\pi\)
0.325020 + 0.945707i \(0.394629\pi\)
\(180\) 0 0
\(181\) 4.34847 0.323219 0.161610 0.986855i \(-0.448331\pi\)
0.161610 + 0.986855i \(0.448331\pi\)
\(182\) 0 0
\(183\) −8.29796 + 18.0116i −0.613403 + 1.33145i
\(184\) 0 0
\(185\) 13.4495 23.2952i 0.988826 1.71270i
\(186\) 0 0
\(187\) 2.00000 + 3.46410i 0.146254 + 0.253320i
\(188\) 0 0
\(189\) −3.72474 3.62302i −0.270935 0.263536i
\(190\) 0 0
\(191\) 6.94949 + 12.0369i 0.502847 + 0.870957i 0.999995 + 0.00329106i \(0.00104758\pi\)
−0.497147 + 0.867666i \(0.665619\pi\)
\(192\) 0 0
\(193\) 4.05051 7.01569i 0.291562 0.505000i −0.682617 0.730776i \(-0.739158\pi\)
0.974179 + 0.225776i \(0.0724917\pi\)
\(194\) 0 0
\(195\) 12.2474 26.5843i 0.877058 1.90374i
\(196\) 0 0
\(197\) −12.6969 −0.904619 −0.452310 0.891861i \(-0.649400\pi\)
−0.452310 + 0.891861i \(0.649400\pi\)
\(198\) 0 0
\(199\) −6.89898 −0.489056 −0.244528 0.969642i \(-0.578633\pi\)
−0.244528 + 0.969642i \(0.578633\pi\)
\(200\) 0 0
\(201\) 5.34847 0.492810i 0.377252 0.0347601i
\(202\) 0 0
\(203\) −1.44949 + 2.51059i −0.101734 + 0.176209i
\(204\) 0 0
\(205\) 16.8990 + 29.2699i 1.18028 + 2.04430i
\(206\) 0 0
\(207\) −1.94949 2.28024i −0.135499 0.158488i
\(208\) 0 0
\(209\) −7.44949 12.9029i −0.515292 0.892512i
\(210\) 0 0
\(211\) 1.55051 2.68556i 0.106742 0.184882i −0.807707 0.589584i \(-0.799292\pi\)
0.914448 + 0.404703i \(0.132625\pi\)
\(212\) 0 0
\(213\) 9.89898 + 13.9993i 0.678267 + 0.959214i
\(214\) 0 0
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) 0 0
\(219\) −2.89898 4.09978i −0.195895 0.277037i
\(220\) 0 0
\(221\) 4.89898 8.48528i 0.329541 0.570782i
\(222\) 0 0
\(223\) −10.4495 18.0990i −0.699750 1.21200i −0.968553 0.248807i \(-0.919962\pi\)
0.268804 0.963195i \(-0.413372\pi\)
\(224\) 0 0
\(225\) 20.3485 3.78194i 1.35656 0.252129i
\(226\) 0 0
\(227\) −0.275255 0.476756i −0.0182693 0.0316434i 0.856746 0.515738i \(-0.172482\pi\)
−0.875016 + 0.484095i \(0.839149\pi\)
\(228\) 0 0
\(229\) 11.6237 20.1329i 0.768117 1.33042i −0.170465 0.985364i \(-0.554527\pi\)
0.938583 0.345055i \(-0.112140\pi\)
\(230\) 0 0
\(231\) −3.44949 + 0.317837i −0.226960 + 0.0209122i
\(232\) 0 0
\(233\) −7.00000 −0.458585 −0.229293 0.973358i \(-0.573641\pi\)
−0.229293 + 0.973358i \(0.573641\pi\)
\(234\) 0 0
\(235\) 33.7980 2.20474
\(236\) 0 0
\(237\) 5.72474 12.4261i 0.371862 0.807164i
\(238\) 0 0
\(239\) −6.39898 + 11.0834i −0.413916 + 0.716923i −0.995314 0.0966962i \(-0.969172\pi\)
0.581398 + 0.813619i \(0.302506\pi\)
\(240\) 0 0
\(241\) 4.44949 + 7.70674i 0.286617 + 0.496435i 0.973000 0.230805i \(-0.0741360\pi\)
−0.686383 + 0.727240i \(0.740803\pi\)
\(242\) 0 0
\(243\) −1.00000 + 15.5563i −0.0641500 + 0.997940i
\(244\) 0 0
\(245\) −1.72474 2.98735i −0.110190 0.190855i
\(246\) 0 0
\(247\) −18.2474 + 31.6055i −1.16106 + 2.01101i
\(248\) 0 0
\(249\) 1.44949 3.14626i 0.0918577 0.199386i
\(250\) 0 0
\(251\) −12.5505 −0.792181 −0.396091 0.918211i \(-0.629633\pi\)
−0.396091 + 0.918211i \(0.629633\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) 0 0
\(255\) 11.8990 1.09638i 0.745143 0.0686577i
\(256\) 0 0
\(257\) −13.8990 + 24.0737i −0.866995 + 1.50168i −0.00194150 + 0.999998i \(0.500618\pi\)
−0.865053 + 0.501680i \(0.832715\pi\)
\(258\) 0 0
\(259\) 3.89898 + 6.75323i 0.242271 + 0.419625i
\(260\) 0 0
\(261\) 8.55051 1.58919i 0.529263 0.0983682i
\(262\) 0 0
\(263\) 8.05051 + 13.9439i 0.496416 + 0.859817i 0.999991 0.00413383i \(-0.00131584\pi\)
−0.503576 + 0.863951i \(0.667983\pi\)
\(264\) 0 0
\(265\) 1.89898 3.28913i 0.116653 0.202050i
\(266\) 0 0
\(267\) 7.10102 + 10.0424i 0.434575 + 0.614582i
\(268\) 0 0
\(269\) −3.65153 −0.222638 −0.111319 0.993785i \(-0.535507\pi\)
−0.111319 + 0.993785i \(0.535507\pi\)
\(270\) 0 0
\(271\) −16.8990 −1.02654 −0.513270 0.858227i \(-0.671566\pi\)
−0.513270 + 0.858227i \(0.671566\pi\)
\(272\) 0 0
\(273\) 4.89898 + 6.92820i 0.296500 + 0.419314i
\(274\) 0 0
\(275\) 6.89898 11.9494i 0.416024 0.720575i
\(276\) 0 0
\(277\) −5.34847 9.26382i −0.321358 0.556609i 0.659410 0.751783i \(-0.270806\pi\)
−0.980769 + 0.195174i \(0.937473\pi\)
\(278\) 0 0
\(279\) 11.6969 + 13.6814i 0.700277 + 0.819086i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) 0 0
\(283\) −10.2753 + 17.7973i −0.610801 + 1.05794i 0.380305 + 0.924861i \(0.375819\pi\)
−0.991106 + 0.133077i \(0.957514\pi\)
\(284\) 0 0
\(285\) −44.3207 + 4.08372i −2.62533 + 0.241899i
\(286\) 0 0
\(287\) −9.79796 −0.578355
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 5.00000 10.8530i 0.293105 0.636215i
\(292\) 0 0
\(293\) −13.6237 + 23.5970i −0.795906 + 1.37855i 0.126356 + 0.991985i \(0.459672\pi\)
−0.922262 + 0.386565i \(0.873661\pi\)
\(294\) 0 0
\(295\) −3.44949 5.97469i −0.200837 0.347860i
\(296\) 0 0
\(297\) 7.44949 + 7.24604i 0.432263 + 0.420458i
\(298\) 0 0
\(299\) 2.44949 + 4.24264i 0.141658 + 0.245358i
\(300\) 0 0
\(301\) −1.44949 + 2.51059i −0.0835472 + 0.144708i
\(302\) 0 0
\(303\) −5.25255 + 11.4012i −0.301751 + 0.654982i
\(304\) 0 0
\(305\) 39.4949 2.26147
\(306\) 0 0
\(307\) −0.752551 −0.0429504 −0.0214752 0.999769i \(-0.506836\pi\)
−0.0214752 + 0.999769i \(0.506836\pi\)
\(308\) 0 0
\(309\) −24.1464 + 2.22486i −1.37364 + 0.126568i
\(310\) 0 0
\(311\) 0.651531 1.12848i 0.0369449 0.0639905i −0.846962 0.531654i \(-0.821571\pi\)
0.883907 + 0.467663i \(0.154904\pi\)
\(312\) 0 0
\(313\) −12.3485 21.3882i −0.697977 1.20893i −0.969167 0.246405i \(-0.920751\pi\)
0.271190 0.962526i \(-0.412583\pi\)
\(314\) 0 0
\(315\) −3.44949 + 9.75663i −0.194357 + 0.549724i
\(316\) 0 0
\(317\) 4.34847 + 7.53177i 0.244234 + 0.423026i 0.961916 0.273345i \(-0.0881300\pi\)
−0.717682 + 0.696371i \(0.754797\pi\)
\(318\) 0 0
\(319\) 2.89898 5.02118i 0.162312 0.281132i
\(320\) 0 0
\(321\) −12.0000 16.9706i −0.669775 0.947204i
\(322\) 0 0
\(323\) −14.8990 −0.829001
\(324\) 0 0
\(325\) −33.7980 −1.87477
\(326\) 0 0
\(327\) 16.6969 + 23.6130i 0.923343 + 1.30580i
\(328\) 0 0
\(329\) −4.89898 + 8.48528i −0.270089 + 0.467809i
\(330\) 0 0
\(331\) −12.3485 21.3882i −0.678733 1.17560i −0.975363 0.220608i \(-0.929196\pi\)
0.296629 0.954993i \(-0.404137\pi\)
\(332\) 0 0
\(333\) 7.79796 22.0560i 0.427326 1.20866i
\(334\) 0 0
\(335\) −5.34847 9.26382i −0.292218 0.506137i
\(336\) 0 0
\(337\) −17.6969 + 30.6520i −0.964014 + 1.66972i −0.251772 + 0.967787i \(0.581013\pi\)
−0.712242 + 0.701934i \(0.752320\pi\)
\(338\) 0 0
\(339\) −27.4217 + 2.52664i −1.48934 + 0.137228i
\(340\) 0 0
\(341\) 12.0000 0.649836
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −2.50000 + 5.42650i −0.134595 + 0.292153i
\(346\) 0 0
\(347\) −9.79796 + 16.9706i −0.525982 + 0.911028i 0.473560 + 0.880762i \(0.342969\pi\)
−0.999542 + 0.0302659i \(0.990365\pi\)
\(348\) 0 0
\(349\) −10.4495 18.0990i −0.559348 0.968820i −0.997551 0.0699435i \(-0.977718\pi\)
0.438203 0.898876i \(-0.355615\pi\)
\(350\) 0 0
\(351\) 6.24745 24.6773i 0.333464 1.31718i
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) 17.0732 29.5717i 0.906152 1.56950i
\(356\) 0 0
\(357\) −1.44949 + 3.14626i −0.0767151 + 0.166518i
\(358\) 0 0
\(359\) −10.7980 −0.569894 −0.284947 0.958543i \(-0.591976\pi\)
−0.284947 + 0.958543i \(0.591976\pi\)
\(360\) 0 0
\(361\) 36.4949 1.92078
\(362\) 0 0
\(363\) −12.0732 + 1.11243i −0.633679 + 0.0583875i
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) 0 0
\(367\) 2.89898 + 5.02118i 0.151325 + 0.262103i 0.931715 0.363190i \(-0.118313\pi\)
−0.780389 + 0.625294i \(0.784979\pi\)
\(368\) 0 0
\(369\) 19.1010 + 22.3417i 0.994359 + 1.16306i
\(370\) 0 0
\(371\) 0.550510 + 0.953512i 0.0285811 + 0.0495039i
\(372\) 0 0
\(373\) −1.44949 + 2.51059i −0.0750517 + 0.129993i −0.901109 0.433593i \(-0.857246\pi\)
0.826057 + 0.563587i \(0.190579\pi\)
\(374\) 0 0
\(375\) −6.55051 9.26382i −0.338267 0.478382i
\(376\) 0 0
\(377\) −14.2020 −0.731442
\(378\) 0 0
\(379\) 26.4949 1.36095 0.680476 0.732771i \(-0.261773\pi\)
0.680476 + 0.732771i \(0.261773\pi\)
\(380\) 0 0
\(381\) −3.00000 4.24264i −0.153695 0.217357i
\(382\) 0 0
\(383\) 3.44949 5.97469i 0.176261 0.305292i −0.764336 0.644818i \(-0.776933\pi\)
0.940597 + 0.339526i \(0.110266\pi\)
\(384\) 0 0
\(385\) 3.44949 + 5.97469i 0.175802 + 0.304498i
\(386\) 0 0
\(387\) 8.55051 1.58919i 0.434647 0.0807829i
\(388\) 0 0
\(389\) 7.55051 + 13.0779i 0.382826 + 0.663074i 0.991465 0.130373i \(-0.0416175\pi\)
−0.608639 + 0.793447i \(0.708284\pi\)
\(390\) 0 0
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) 23.1969 2.13737i 1.17013 0.107816i
\(394\) 0 0
\(395\) −27.2474 −1.37097
\(396\) 0 0
\(397\) 9.30306 0.466907 0.233454 0.972368i \(-0.424997\pi\)
0.233454 + 0.972368i \(0.424997\pi\)
\(398\) 0 0
\(399\) 5.39898 11.7190i 0.270287 0.586685i
\(400\) 0 0
\(401\) 5.05051 8.74774i 0.252210 0.436841i −0.711924 0.702257i \(-0.752176\pi\)
0.964134 + 0.265416i \(0.0855091\pi\)
\(402\) 0 0
\(403\) −14.6969 25.4558i −0.732107 1.26805i
\(404\) 0 0
\(405\) 28.9722 11.1548i 1.43964 0.554286i
\(406\) 0 0
\(407\) −7.79796 13.5065i −0.386530 0.669490i
\(408\) 0 0
\(409\) −2.89898 + 5.02118i −0.143345 + 0.248281i −0.928754 0.370696i \(-0.879119\pi\)
0.785409 + 0.618977i \(0.212453\pi\)
\(410\) 0 0
\(411\) 8.55051 18.5597i 0.421766 0.915485i
\(412\) 0 0
\(413\) 2.00000 0.0984136
\(414\) 0 0
\(415\) −6.89898 −0.338658
\(416\) 0 0
\(417\) −16.2980 + 1.50170i −0.798114 + 0.0735386i
\(418\) 0 0
\(419\) 12.2753 21.2614i 0.599685 1.03869i −0.393182 0.919461i \(-0.628626\pi\)
0.992867 0.119225i \(-0.0380410\pi\)
\(420\) 0 0
\(421\) −6.55051 11.3458i −0.319252 0.552961i 0.661080 0.750316i \(-0.270098\pi\)
−0.980332 + 0.197354i \(0.936765\pi\)
\(422\) 0 0
\(423\) 28.8990 5.37113i 1.40512 0.261153i
\(424\) 0 0
\(425\) −6.89898 11.9494i −0.334650 0.579630i
\(426\) 0 0
\(427\) −5.72474 + 9.91555i −0.277040 + 0.479847i
\(428\) 0 0
\(429\) −9.79796 13.8564i −0.473050 0.668994i
\(430\) 0 0
\(431\) 7.59592 0.365882 0.182941 0.983124i \(-0.441438\pi\)
0.182941 + 0.983124i \(0.441438\pi\)
\(432\) 0 0
\(433\) 11.7980 0.566974 0.283487 0.958976i \(-0.408509\pi\)
0.283487 + 0.958976i \(0.408509\pi\)
\(434\) 0 0
\(435\) −10.0000 14.1421i −0.479463 0.678064i
\(436\) 0 0
\(437\) 3.72474 6.45145i 0.178179 0.308615i
\(438\) 0 0
\(439\) 10.8990 + 18.8776i 0.520180 + 0.900978i 0.999725 + 0.0234607i \(0.00746845\pi\)
−0.479545 + 0.877517i \(0.659198\pi\)
\(440\) 0 0
\(441\) −1.94949 2.28024i −0.0928328 0.108583i
\(442\) 0 0
\(443\) −2.55051 4.41761i −0.121178 0.209887i 0.799054 0.601259i \(-0.205334\pi\)
−0.920233 + 0.391372i \(0.872001\pi\)
\(444\) 0 0
\(445\) 12.2474 21.2132i 0.580585 1.00560i
\(446\) 0 0
\(447\) −10.3485 + 0.953512i −0.489466 + 0.0450996i
\(448\) 0 0
\(449\) −18.5959 −0.877596 −0.438798 0.898586i \(-0.644596\pi\)
−0.438798 + 0.898586i \(0.644596\pi\)
\(450\) 0 0
\(451\) 19.5959 0.922736
\(452\) 0 0
\(453\) −3.62372 + 7.86566i −0.170257 + 0.369561i
\(454\) 0 0
\(455\) 8.44949 14.6349i 0.396118 0.686097i
\(456\) 0 0
\(457\) −15.7474 27.2754i −0.736635 1.27589i −0.954002 0.299799i \(-0.903080\pi\)
0.217368 0.976090i \(-0.430253\pi\)
\(458\) 0 0
\(459\) 10.0000 2.82843i 0.466760 0.132020i
\(460\) 0 0
\(461\) −10.1742 17.6223i −0.473861 0.820752i 0.525691 0.850676i \(-0.323807\pi\)
−0.999552 + 0.0299238i \(0.990474\pi\)
\(462\) 0 0
\(463\) −12.8485 + 22.2542i −0.597119 + 1.03424i 0.396125 + 0.918197i \(0.370355\pi\)
−0.993244 + 0.116044i \(0.962979\pi\)
\(464\) 0 0
\(465\) 15.0000 32.5590i 0.695608 1.50989i
\(466\) 0 0
\(467\) −10.0000 −0.462745 −0.231372 0.972865i \(-0.574322\pi\)
−0.231372 + 0.972865i \(0.574322\pi\)
\(468\) 0 0
\(469\) 3.10102 0.143192
\(470\) 0 0
\(471\) 10.9495 1.00889i 0.504526 0.0464872i
\(472\) 0 0
\(473\) 2.89898 5.02118i 0.133295 0.230874i
\(474\) 0 0
\(475\) 25.6969 + 44.5084i 1.17906 + 2.04219i
\(476\) 0 0
\(477\) 1.10102 3.11416i 0.0504123 0.142587i
\(478\) 0 0
\(479\) −14.7980 25.6308i −0.676136 1.17110i −0.976135 0.217163i \(-0.930320\pi\)
0.299999 0.953939i \(-0.403013\pi\)
\(480\) 0 0
\(481\) −19.1010 + 33.0839i −0.870932 + 1.50850i
\(482\) 0 0
\(483\) −1.00000 1.41421i −0.0455016 0.0643489i
\(484\) 0 0
\(485\) −23.7980 −1.08061
\(486\) 0 0
\(487\) −22.3939 −1.01476 −0.507382 0.861721i \(-0.669387\pi\)
−0.507382 + 0.861721i \(0.669387\pi\)
\(488\) 0 0
\(489\) −0.202041 0.285729i −0.00913661 0.0129211i
\(490\) 0 0
\(491\) −1.89898 + 3.28913i −0.0856997 + 0.148436i −0.905689 0.423942i \(-0.860646\pi\)
0.819989 + 0.572379i \(0.193979\pi\)
\(492\) 0 0
\(493\) −2.89898 5.02118i −0.130563 0.226143i
\(494\) 0 0
\(495\) 6.89898 19.5133i 0.310086 0.877056i
\(496\) 0 0
\(497\) 4.94949 + 8.57277i 0.222015 + 0.384541i
\(498\) 0 0
\(499\) 16.6969 28.9199i 0.747458 1.29463i −0.201580 0.979472i \(-0.564608\pi\)
0.949038 0.315163i \(-0.102059\pi\)
\(500\) 0 0
\(501\) −32.2474 + 2.97129i −1.44071 + 0.132748i
\(502\) 0 0
\(503\) −24.4949 −1.09217 −0.546087 0.837729i \(-0.683883\pi\)
−0.546087 + 0.837729i \(0.683883\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) 0 0
\(507\) −7.97219 + 17.3045i −0.354058 + 0.768518i
\(508\) 0 0
\(509\) 8.44949 14.6349i 0.374517 0.648683i −0.615738 0.787951i \(-0.711142\pi\)
0.990255 + 0.139269i \(0.0444752\pi\)
\(510\) 0 0
\(511\) −1.44949 2.51059i −0.0641217 0.111062i
\(512\) 0 0
\(513\) −37.2474 + 10.5352i −1.64452 + 0.465139i
\(514\) 0 0
\(515\) 24.1464 + 41.8228i 1.06402 + 1.84293i
\(516\) 0 0
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) 0 0
\(519\) 9.34847 20.2918i 0.410352 0.890711i
\(520\) 0 0
\(521\) −38.6969 −1.69534 −0.847672 0.530521i \(-0.821996\pi\)
−0.847672 + 0.530521i \(0.821996\pi\)
\(522\) 0 0
\(523\) −0.348469 −0.0152375 −0.00761875 0.999971i \(-0.502425\pi\)
−0.00761875 + 0.999971i \(0.502425\pi\)
\(524\) 0 0
\(525\) 11.8990 1.09638i 0.519314 0.0478498i
\(526\) 0 0
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) −3.89898 4.56048i −0.169201 0.197908i
\(532\) 0 0
\(533\) −24.0000 41.5692i −1.03956 1.80056i
\(534\) 0 0
\(535\) −20.6969 + 35.8481i −0.894807 + 1.54985i
\(536\) 0 0
\(537\) −8.69694 12.2993i −0.375301 0.530755i
\(538\) 0 0
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 30.4949 1.31108 0.655539 0.755161i \(-0.272441\pi\)
0.655539 + 0.755161i \(0.272441\pi\)
\(542\) 0 0
\(543\) −4.34847 6.14966i −0.186611 0.263907i
\(544\) 0 0
\(545\) 28.7980 49.8795i 1.23357 2.13660i
\(546\) 0 0
\(547\) 15.7980 + 27.3629i 0.675472 + 1.16995i 0.976331 + 0.216283i \(0.0693934\pi\)
−0.300859 + 0.953669i \(0.597273\pi\)
\(548\) 0 0
\(549\) 33.7702 6.27647i 1.44127 0.267873i
\(550\) 0 0
\(551\) 10.7980 + 18.7026i 0.460009 + 0.796758i
\(552\) 0 0
\(553\) 3.94949 6.84072i 0.167949 0.290897i
\(554\) 0 0
\(555\) −46.3939 + 4.27475i −1.96931 + 0.181453i
\(556\) 0 0
\(557\) −3.10102 −0.131394 −0.0656972 0.997840i \(-0.520927\pi\)
−0.0656972 + 0.997840i \(0.520927\pi\)
\(558\) 0 0
\(559\) −14.2020 −0.600682
\(560\) 0 0
\(561\) 2.89898 6.29253i 0.122395 0.265671i
\(562\) 0 0
\(563\) 6.97219 12.0762i 0.293843 0.508951i −0.680872 0.732402i \(-0.738399\pi\)
0.974715 + 0.223451i \(0.0717324\pi\)
\(564\) 0 0
\(565\) 27.4217 + 47.4957i 1.15364 + 1.99816i
\(566\) 0 0
\(567\) −1.39898 + 8.89060i −0.0587516 + 0.373370i
\(568\) 0 0
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 0 0
\(571\) 7.10102 12.2993i 0.297168 0.514711i −0.678319 0.734768i \(-0.737291\pi\)
0.975487 + 0.220057i \(0.0706244\pi\)
\(572\) 0 0
\(573\) 10.0732 21.8649i 0.420815 0.913421i
\(574\) 0 0
\(575\) 6.89898 0.287707
\(576\) 0 0
\(577\) 23.5959 0.982311 0.491155 0.871072i \(-0.336575\pi\)
0.491155 + 0.871072i \(0.336575\pi\)
\(578\) 0 0
\(579\) −13.9722 + 1.28740i −0.580665 + 0.0535026i
\(580\) 0 0
\(581\) 1.00000 1.73205i 0.0414870 0.0718576i
\(582\) 0 0
\(583\) −1.10102 1.90702i −0.0455996 0.0789808i
\(584\) 0 0
\(585\) −49.8434 + 9.26382i −2.06077 + 0.383012i
\(586\) 0 0
\(587\) −9.07321 15.7153i −0.374492 0.648639i 0.615759 0.787934i \(-0.288849\pi\)
−0.990251 + 0.139296i \(0.955516\pi\)
\(588\) 0 0
\(589\) −22.3485 + 38.7087i −0.920853 + 1.59496i
\(590\) 0 0
\(591\) 12.6969 + 17.9562i 0.522282 + 0.738619i
\(592\) 0 0
\(593\) −14.6969 −0.603531 −0.301765 0.953382i \(-0.597576\pi\)
−0.301765 + 0.953382i \(0.597576\pi\)
\(594\) 0 0
\(595\) 6.89898 0.282831
\(596\) 0 0
\(597\) 6.89898 + 9.75663i 0.282356 + 0.399312i
\(598\) 0 0
\(599\) −7.10102 + 12.2993i −0.290140 + 0.502537i −0.973843 0.227224i \(-0.927035\pi\)
0.683703 + 0.729761i \(0.260368\pi\)
\(600\) 0 0
\(601\) 6.34847 + 10.9959i 0.258959 + 0.448531i 0.965963 0.258679i \(-0.0832871\pi\)
−0.707004 + 0.707210i \(0.749954\pi\)
\(602\) 0 0
\(603\) −6.04541 7.07107i −0.246188 0.287956i
\(604\) 0 0
\(605\) 12.0732 + 20.9114i 0.490846 + 0.850170i
\(606\) 0 0
\(607\) −4.34847 + 7.53177i −0.176499 + 0.305705i −0.940679 0.339298i \(-0.889811\pi\)
0.764180 + 0.645003i \(0.223144\pi\)
\(608\) 0 0
\(609\) 5.00000 0.460702i 0.202610 0.0186686i
\(610\) 0 0
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 14.6969 0.593604 0.296802 0.954939i \(-0.404080\pi\)
0.296802 + 0.954939i \(0.404080\pi\)
\(614\) 0 0
\(615\) 24.4949 53.1687i 0.987730 2.14397i
\(616\) 0 0
\(617\) −21.6969 + 37.5802i −0.873486 + 1.51292i −0.0151189 + 0.999886i \(0.504813\pi\)
−0.858367 + 0.513036i \(0.828521\pi\)
\(618\) 0 0
\(619\) −2.07321 3.59091i −0.0833295 0.144331i 0.821349 0.570426i \(-0.193222\pi\)
−0.904678 + 0.426096i \(0.859889\pi\)
\(620\) 0 0
\(621\) −1.27526 + 5.03723i −0.0511742 + 0.202137i
\(622\) 0 0
\(623\) 3.55051 + 6.14966i 0.142248 + 0.246381i
\(624\) 0 0
\(625\) 5.94949 10.3048i 0.237980 0.412193i
\(626\) 0 0
\(627\) −10.7980 + 23.4381i −0.431229 + 0.936026i
\(628\) 0 0
\(629\) −15.5959 −0.621850
\(630\) 0 0
\(631\) −18.1010 −0.720590 −0.360295 0.932838i \(-0.617324\pi\)
−0.360295 + 0.932838i \(0.617324\pi\)
\(632\) 0 0
\(633\) −5.34847 + 0.492810i −0.212583 + 0.0195874i
\(634\) 0 0
\(635\) −5.17423 + 8.96204i −0.205333 + 0.355648i
\(636\) 0 0
\(637\) 2.44949 + 4.24264i 0.0970523 + 0.168100i
\(638\) 0 0
\(639\) 9.89898 27.9985i 0.391598 1.10761i
\(640\) 0 0
\(641\) −20.7474 35.9356i −0.819475 1.41937i −0.906070 0.423129i \(-0.860932\pi\)
0.0865947 0.996244i \(-0.472401\pi\)
\(642\) 0 0
\(643\) 9.69694 16.7956i 0.382410 0.662353i −0.608996 0.793173i \(-0.708428\pi\)
0.991406 + 0.130820i \(0.0417609\pi\)
\(644\) 0 0
\(645\) −10.0000 14.1421i −0.393750 0.556846i
\(646\) 0 0
\(647\) 21.3031 0.837510 0.418755 0.908099i \(-0.362467\pi\)
0.418755 + 0.908099i \(0.362467\pi\)
\(648\) 0 0
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) 6.00000 + 8.48528i 0.235159 + 0.332564i
\(652\) 0 0
\(653\) 4.89898 8.48528i 0.191712 0.332055i −0.754106 0.656753i \(-0.771929\pi\)
0.945818 + 0.324698i \(0.105263\pi\)
\(654\) 0 0
\(655\) −23.1969 40.1783i −0.906379 1.56990i
\(656\) 0 0
\(657\) −2.89898 + 8.19955i −0.113100 + 0.319895i
\(658\) 0 0
\(659\) 2.34847 + 4.06767i 0.0914834 + 0.158454i 0.908136 0.418676i \(-0.137506\pi\)
−0.816652 + 0.577130i \(0.804172\pi\)
\(660\) 0 0
\(661\) −4.72474 + 8.18350i −0.183771 + 0.318301i −0.943162 0.332334i \(-0.892164\pi\)
0.759391 + 0.650635i \(0.225497\pi\)
\(662\) 0 0
\(663\) −16.8990 + 1.55708i −0.656302 + 0.0604719i
\(664\) 0 0
\(665\) −25.6969 −0.996485
\(666\) 0 0
\(667\) 2.89898 0.112249
\(668\) 0 0
\(669\) −15.1464 + 32.8769i −0.585595 + 1.27109i
\(670\) 0 0
\(671\) 11.4495 19.8311i 0.442003 0.765571i
\(672\) 0 0
\(673\) −15.2980 26.4968i −0.589693 1.02138i −0.994272 0.106875i \(-0.965915\pi\)
0.404579 0.914503i \(-0.367418\pi\)
\(674\) 0 0
\(675\) −25.6969 24.9951i −0.989076 0.962063i
\(676\) 0 0
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 0 0
\(679\) 3.44949 5.97469i 0.132379 0.229288i
\(680\) 0 0
\(681\) −0.398979 + 0.866025i −0.0152889 + 0.0331862i
\(682\) 0 0
\(683\) −32.2020 −1.23218 −0.616088 0.787677i \(-0.711284\pi\)
−0.616088 + 0.787677i \(0.711284\pi\)
\(684\) 0 0
\(685\) −40.6969 −1.55495
\(686\) 0 0
\(687\) −40.0959 + 3.69445i −1.52975 + 0.140952i
\(688\) 0 0
\(689\) −2.69694 + 4.67123i −0.102745 + 0.177960i
\(690\) 0 0
\(691\) 3.47730 + 6.02285i 0.132283 + 0.229120i 0.924556 0.381046i \(-0.124436\pi\)
−0.792274 + 0.610166i \(0.791103\pi\)
\(692\) 0 0
\(693\) 3.89898 + 4.56048i 0.148110 + 0.173238i
\(694\) 0 0
\(695\) 16.2980 + 28.2289i 0.618217 + 1.07078i
\(696\) 0 0
\(697\) 9.79796 16.9706i 0.371124 0.642806i
\(698\) 0 0
\(699\) 7.00000 + 9.89949i 0.264764 + 0.374433i
\(700\) 0 0
\(701\) 51.3939 1.94112 0.970560 0.240860i \(-0.0774293\pi\)
0.970560 + 0.240860i \(0.0774293\pi\)
\(702\) 0 0
\(703\) 58.0908 2.19094
\(704\) 0 0
\(705\) −33.7980 47.7975i −1.27290 1.80016i
\(706\) 0 0
\(707\) −3.62372 + 6.27647i −0.136284 + 0.236051i
\(708\) 0 0
\(709\) 5.79796 + 10.0424i 0.217747 + 0.377149i 0.954119 0.299428i \(-0.0967959\pi\)
−0.736372 + 0.676577i \(0.763463\pi\)
\(710\) 0 0
\(711\) −23.2980 + 4.33013i −0.873742 + 0.162392i
\(712\) 0 0
\(713\) 3.00000 + 5.19615i 0.112351 + 0.194597i
\(714\) 0 0
\(715\) −16.8990 + 29.2699i −0.631986 + 1.09463i
\(716\) 0 0
\(717\) 22.0732 2.03383i 0.824339 0.0759549i
\(718\) 0 0
\(719\) 9.79796 0.365402 0.182701 0.983169i \(-0.441516\pi\)
0.182701 + 0.983169i \(0.441516\pi\)
\(720\) 0 0
\(721\) −14.0000 −0.521387
\(722\) 0 0
\(723\) 6.44949 13.9993i 0.239859 0.520638i
\(724\) 0 0
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) 0 0
\(727\) 20.2474 + 35.0696i 0.750936 + 1.30066i 0.947369 + 0.320143i \(0.103731\pi\)
−0.196433 + 0.980517i \(0.562936\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) 0 0
\(731\) −2.89898 5.02118i −0.107223 0.185715i
\(732\) 0 0
\(733\) 6.27526 10.8691i 0.231782 0.401458i −0.726551 0.687113i \(-0.758878\pi\)
0.958333 + 0.285655i \(0.0922111\pi\)
\(734\) 0 0
\(735\) −2.50000 + 5.42650i −0.0922139 + 0.200160i
\(736\) 0 0
\(737\) −6.20204 −0.228455
\(738\) 0 0
\(739\) 25.5959 0.941561 0.470781 0.882250i \(-0.343972\pi\)
0.470781 + 0.882250i \(0.343972\pi\)
\(740\) 0 0
\(741\) 62.9444 5.79972i 2.31232 0.213058i
\(742\) 0 0
\(743\) 18.0000 31.1769i 0.660356 1.14377i −0.320166 0.947361i \(-0.603739\pi\)
0.980522 0.196409i \(-0.0629279\pi\)
\(744\) 0 0
\(745\) 10.3485 + 17.9241i 0.379139 + 0.656687i
\(746\) 0 0
\(747\) −5.89898 + 1.09638i −0.215832 + 0.0401143i
\(748\) 0 0
\(749\) −6.00000 10.3923i −0.219235 0.379727i
\(750\) 0 0
\(751\) 20.2980 35.1571i 0.740683 1.28290i −0.211502 0.977378i \(-0.567835\pi\)
0.952185 0.305523i \(-0.0988313\pi\)
\(752\) 0 0
\(753\) 12.5505 + 17.7491i 0.457366 + 0.646813i
\(754\) 0 0
\(755\) 17.2474 0.627699
\(756\) 0 0
\(757\) 23.3939 0.850265 0.425132 0.905131i \(-0.360228\pi\)
0.425132 + 0.905131i \(0.360228\pi\)
\(758\) 0 0
\(759\) 2.00000 + 2.82843i 0.0725954 + 0.102665i
\(760\) 0 0
\(761\) −1.00000 + 1.73205i −0.0362500 + 0.0627868i −0.883581 0.468278i \(-0.844875\pi\)
0.847331 + 0.531065i \(0.178208\pi\)
\(762\) 0 0
\(763\) 8.34847 + 14.4600i 0.302235 + 0.523486i
\(764\) 0 0
\(765\) −13.4495 15.7313i −0.486267 0.568767i
\(766\) 0 0
\(767\) 4.89898 + 8.48528i 0.176892 + 0.306386i
\(768\) 0 0
\(769\) −27.0454 + 46.8440i −0.975282 + 1.68924i −0.296282 + 0.955100i \(0.595747\pi\)
−0.679000 + 0.734138i \(0.737586\pi\)
\(770\) 0 0
\(771\) 47.9444 4.41761i 1.72667 0.159096i
\(772\) 0 0
\(773\) −19.9444 −0.717350 −0.358675 0.933463i \(-0.616771\pi\)
−0.358675 + 0.933463i \(0.616771\pi\)
\(774\) 0 0
\(775\) −41.3939 −1.48691
\(776\) 0 0
\(777\) 5.65153 12.2672i 0.202748 0.440084i
\(778\) 0 0
\(779\) −36.4949 + 63.2110i −1.30757 + 2.26477i
\(780\) 0 0
\(781\) −9.89898 17.1455i −0.354213 0.613515i
\(782\) 0 0
\(783\) −10.7980 10.5031i −0.385888 0.375349i
\(784\) 0 0
\(785\) −10.9495 18.9651i −0.390804 0.676892i
\(786\) 0 0
\(787\) 23.6969 41.0443i 0.844705 1.46307i −0.0411728 0.999152i \(-0.513109\pi\)
0.885877 0.463919i \(-0.153557\pi\)
\(788\) 0 0
\(789\) 11.6691 25.3290i 0.415432 0.901737i
\(790\) 0 0
\(791\) −15.8990 −0.565303
\(792\) 0 0
\(793\) −56.0908 −1.99184
\(794\) 0 0
\(795\) −6.55051 + 0.603566i −0.232323 + 0.0214063i
\(796\) 0 0
\(797\) −17.9722 + 31.1288i −0.636608 + 1.10264i 0.349564 + 0.936912i \(0.386330\pi\)
−0.986172 + 0.165725i \(0.947004\pi\)
\(798\) 0 0
\(799\) −9.79796 16.9706i −0.346627 0.600375i
\(800\) 0 0
\(801\) 7.10102 20.0847i 0.250902 0.709659i
\(802\) 0 0
\(803\) 2.89898 + 5.02118i