Properties

Label 1950.2.bc.i.751.6
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.6
Root \(1.40719 + 0.536449i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.i.901.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.42916 + 1.40247i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(2.42916 + 1.40247i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.515171 + 0.297434i) q^{11} -1.00000 q^{12} +(3.43052 + 1.10975i) q^{13} +2.80495 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.87649 + 4.98222i) q^{17} +1.00000i q^{18} +(6.59574 + 3.80805i) q^{19} -2.80495i q^{21} +(-0.297434 + 0.515171i) q^{22} +(-2.32278 - 4.02317i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(3.52579 - 0.754186i) q^{26} +1.00000 q^{27} +(2.42916 - 1.40247i) q^{28} +(1.26235 + 2.18645i) q^{29} +6.59309i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.515171 + 0.297434i) q^{33} +5.75297i q^{34} +(0.500000 + 0.866025i) q^{36} +(8.98379 - 5.18679i) q^{37} +7.61611 q^{38} +(-0.754186 - 3.52579i) q^{39} +(-4.98222 + 2.87649i) q^{41} +(-1.40247 - 2.42916i) q^{42} +(-2.12230 + 3.67593i) q^{43} +0.594869i q^{44} +(-4.02317 - 2.32278i) q^{46} +2.89798i q^{47} +(-0.500000 + 0.866025i) q^{48} +(0.433868 + 0.751482i) q^{49} +5.75297 q^{51} +(2.67633 - 2.41604i) q^{52} +13.8960 q^{53} +(0.866025 - 0.500000i) q^{54} +(1.40247 - 2.42916i) q^{56} -7.61611i q^{57} +(2.18645 + 1.26235i) q^{58} +(-8.40299 - 4.85147i) q^{59} +(-3.41309 + 5.91165i) q^{61} +(3.29654 + 5.70978i) q^{62} +(-2.42916 + 1.40247i) q^{63} -1.00000 q^{64} +0.594869 q^{66} +(6.80906 - 3.93121i) q^{67} +(2.87649 + 4.98222i) q^{68} +(-2.32278 + 4.02317i) q^{69} +(-1.11257 - 0.642342i) q^{71} +(0.866025 + 0.500000i) q^{72} -14.5400i q^{73} +(5.18679 - 8.98379i) q^{74} +(6.59574 - 3.80805i) q^{76} -1.66858 q^{77} +(-2.41604 - 2.67633i) q^{78} +1.83150 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.87649 + 4.98222i) q^{82} -4.19184i q^{83} +(-2.42916 - 1.40247i) q^{84} +4.24460i q^{86} +(1.26235 - 2.18645i) q^{87} +(0.297434 + 0.515171i) q^{88} +(5.24333 - 3.02724i) q^{89} +(6.77687 + 7.50697i) q^{91} -4.64555 q^{92} +(5.70978 - 3.29654i) q^{93} +(1.44899 + 2.50973i) q^{94} +1.00000i q^{96} +(-14.6413 - 8.45318i) q^{97} +(0.751482 + 0.433868i) q^{98} -0.594869i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 6q^{4} + 12q^{7} - 6q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 6q^{4} + 12q^{7} - 6q^{9} + 6q^{11} - 12q^{12} - 4q^{13} - 4q^{14} - 6q^{16} - 8q^{17} + 6q^{19} + 6q^{22} - 16q^{23} - 2q^{26} + 12q^{27} + 12q^{28} - 14q^{29} - 6q^{33} + 6q^{36} + 6q^{37} + 8q^{38} + 2q^{39} - 18q^{41} + 2q^{42} - 10q^{43} - 6q^{46} - 6q^{48} - 8q^{49} + 16q^{51} - 2q^{52} - 2q^{56} - 6q^{58} + 36q^{59} + 10q^{61} - 16q^{62} - 12q^{63} - 12q^{64} - 12q^{66} - 24q^{67} + 8q^{68} - 16q^{69} - 12q^{71} + 12q^{74} + 6q^{76} - 24q^{77} + 10q^{78} - 4q^{79} - 6q^{81} - 8q^{82} - 12q^{84} - 14q^{87} - 6q^{88} - 18q^{89} + 2q^{91} - 32q^{92} + 6q^{93} + 8q^{94} + 24q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 2.42916 + 1.40247i 0.918135 + 0.530085i 0.883040 0.469299i \(-0.155493\pi\)
0.0350954 + 0.999384i \(0.488827\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.515171 + 0.297434i −0.155330 + 0.0896798i −0.575650 0.817696i \(-0.695251\pi\)
0.420320 + 0.907376i \(0.361918\pi\)
\(12\) −1.00000 −0.288675
\(13\) 3.43052 + 1.10975i 0.951454 + 0.307790i
\(14\) 2.80495 0.749654
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.87649 + 4.98222i −0.697650 + 1.20837i 0.271629 + 0.962402i \(0.412438\pi\)
−0.969279 + 0.245963i \(0.920896\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.59574 + 3.80805i 1.51317 + 0.873628i 0.999881 + 0.0154099i \(0.00490533\pi\)
0.513286 + 0.858218i \(0.328428\pi\)
\(20\) 0 0
\(21\) 2.80495i 0.612090i
\(22\) −0.297434 + 0.515171i −0.0634132 + 0.109835i
\(23\) −2.32278 4.02317i −0.484332 0.838888i 0.515506 0.856886i \(-0.327604\pi\)
−0.999838 + 0.0179978i \(0.994271\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.52579 0.754186i 0.691465 0.147908i
\(27\) 1.00000 0.192450
\(28\) 2.42916 1.40247i 0.459067 0.265043i
\(29\) 1.26235 + 2.18645i 0.234412 + 0.406013i 0.959102 0.283062i \(-0.0913502\pi\)
−0.724690 + 0.689075i \(0.758017\pi\)
\(30\) 0 0
\(31\) 6.59309i 1.18415i 0.805882 + 0.592077i \(0.201692\pi\)
−0.805882 + 0.592077i \(0.798308\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0.515171 + 0.297434i 0.0896798 + 0.0517767i
\(34\) 5.75297i 0.986626i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 8.98379 5.18679i 1.47693 0.852703i 0.477265 0.878759i \(-0.341628\pi\)
0.999660 + 0.0260561i \(0.00829487\pi\)
\(38\) 7.61611 1.23550
\(39\) −0.754186 3.52579i −0.120766 0.564578i
\(40\) 0 0
\(41\) −4.98222 + 2.87649i −0.778092 + 0.449232i −0.835754 0.549105i \(-0.814969\pi\)
0.0576618 + 0.998336i \(0.481636\pi\)
\(42\) −1.40247 2.42916i −0.216406 0.374827i
\(43\) −2.12230 + 3.67593i −0.323648 + 0.560574i −0.981238 0.192802i \(-0.938243\pi\)
0.657590 + 0.753376i \(0.271576\pi\)
\(44\) 0.594869i 0.0896798i
\(45\) 0 0
\(46\) −4.02317 2.32278i −0.593184 0.342475i
\(47\) 2.89798i 0.422715i 0.977409 + 0.211357i \(0.0677884\pi\)
−0.977409 + 0.211357i \(0.932212\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 0.433868 + 0.751482i 0.0619812 + 0.107355i
\(50\) 0 0
\(51\) 5.75297 0.805577
\(52\) 2.67633 2.41604i 0.371140 0.335044i
\(53\) 13.8960 1.90876 0.954379 0.298598i \(-0.0965189\pi\)
0.954379 + 0.298598i \(0.0965189\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.40247 2.42916i 0.187414 0.324610i
\(57\) 7.61611i 1.00878i
\(58\) 2.18645 + 1.26235i 0.287095 + 0.165754i
\(59\) −8.40299 4.85147i −1.09398 0.631607i −0.159344 0.987223i \(-0.550938\pi\)
−0.934632 + 0.355616i \(0.884271\pi\)
\(60\) 0 0
\(61\) −3.41309 + 5.91165i −0.437002 + 0.756910i −0.997457 0.0712755i \(-0.977293\pi\)
0.560455 + 0.828185i \(0.310626\pi\)
\(62\) 3.29654 + 5.70978i 0.418661 + 0.725143i
\(63\) −2.42916 + 1.40247i −0.306045 + 0.176695i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0.594869 0.0732233
\(67\) 6.80906 3.93121i 0.831859 0.480274i −0.0226299 0.999744i \(-0.507204\pi\)
0.854489 + 0.519470i \(0.173871\pi\)
\(68\) 2.87649 + 4.98222i 0.348825 + 0.604183i
\(69\) −2.32278 + 4.02317i −0.279629 + 0.484332i
\(70\) 0 0
\(71\) −1.11257 0.642342i −0.132038 0.0762320i 0.432526 0.901621i \(-0.357622\pi\)
−0.564564 + 0.825389i \(0.690956\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 14.5400i 1.70178i −0.525341 0.850892i \(-0.676062\pi\)
0.525341 0.850892i \(-0.323938\pi\)
\(74\) 5.18679 8.98379i 0.602952 1.04434i
\(75\) 0 0
\(76\) 6.59574 3.80805i 0.756584 0.436814i
\(77\) −1.66858 −0.190152
\(78\) −2.41604 2.67633i −0.273563 0.303035i
\(79\) 1.83150 0.206060 0.103030 0.994678i \(-0.467146\pi\)
0.103030 + 0.994678i \(0.467146\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.87649 + 4.98222i −0.317655 + 0.550194i
\(83\) 4.19184i 0.460114i −0.973177 0.230057i \(-0.926109\pi\)
0.973177 0.230057i \(-0.0738913\pi\)
\(84\) −2.42916 1.40247i −0.265043 0.153022i
\(85\) 0 0
\(86\) 4.24460i 0.457707i
\(87\) 1.26235 2.18645i 0.135338 0.234412i
\(88\) 0.297434 + 0.515171i 0.0317066 + 0.0549175i
\(89\) 5.24333 3.02724i 0.555792 0.320886i −0.195663 0.980671i \(-0.562686\pi\)
0.751455 + 0.659785i \(0.229353\pi\)
\(90\) 0 0
\(91\) 6.77687 + 7.50697i 0.710409 + 0.786945i
\(92\) −4.64555 −0.484332
\(93\) 5.70978 3.29654i 0.592077 0.341836i
\(94\) 1.44899 + 2.50973i 0.149452 + 0.258859i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −14.6413 8.45318i −1.48660 0.858291i −0.486719 0.873558i \(-0.661807\pi\)
−0.999883 + 0.0152677i \(0.995140\pi\)
\(98\) 0.751482 + 0.433868i 0.0759111 + 0.0438273i
\(99\) 0.594869i 0.0597866i
\(100\) 0 0
\(101\) 2.72360 + 4.71741i 0.271008 + 0.469400i 0.969120 0.246589i \(-0.0793096\pi\)
−0.698112 + 0.715988i \(0.745976\pi\)
\(102\) 4.98222 2.87649i 0.493313 0.284814i
\(103\) 13.7529 1.35511 0.677556 0.735471i \(-0.263039\pi\)
0.677556 + 0.735471i \(0.263039\pi\)
\(104\) 1.10975 3.43052i 0.108820 0.336390i
\(105\) 0 0
\(106\) 12.0343 6.94798i 1.16887 0.674848i
\(107\) 2.11545 + 3.66407i 0.204509 + 0.354219i 0.949976 0.312323i \(-0.101107\pi\)
−0.745468 + 0.666542i \(0.767774\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 0.447358i 0.0428491i −0.999770 0.0214246i \(-0.993180\pi\)
0.999770 0.0214246i \(-0.00682017\pi\)
\(110\) 0 0
\(111\) −8.98379 5.18679i −0.852703 0.492308i
\(112\) 2.80495i 0.265043i
\(113\) 4.68350 8.11206i 0.440587 0.763119i −0.557146 0.830414i \(-0.688104\pi\)
0.997733 + 0.0672956i \(0.0214371\pi\)
\(114\) −3.80805 6.59574i −0.356657 0.617748i
\(115\) 0 0
\(116\) 2.52469 0.234412
\(117\) −2.67633 + 2.41604i −0.247427 + 0.223363i
\(118\) −9.70293 −0.893227
\(119\) −13.9749 + 8.06839i −1.28107 + 0.739628i
\(120\) 0 0
\(121\) −5.32307 + 9.21982i −0.483915 + 0.838165i
\(122\) 6.82619i 0.618014i
\(123\) 4.98222 + 2.87649i 0.449232 + 0.259364i
\(124\) 5.70978 + 3.29654i 0.512753 + 0.296038i
\(125\) 0 0
\(126\) −1.40247 + 2.42916i −0.124942 + 0.216406i
\(127\) −3.34395 5.79190i −0.296728 0.513948i 0.678658 0.734455i \(-0.262562\pi\)
−0.975385 + 0.220507i \(0.929229\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 4.24460 0.373716
\(130\) 0 0
\(131\) −11.6724 −1.01982 −0.509911 0.860227i \(-0.670322\pi\)
−0.509911 + 0.860227i \(0.670322\pi\)
\(132\) 0.515171 0.297434i 0.0448399 0.0258883i
\(133\) 10.6814 + 18.5007i 0.926194 + 1.60422i
\(134\) 3.93121 6.80906i 0.339605 0.588213i
\(135\) 0 0
\(136\) 4.98222 + 2.87649i 0.427222 + 0.246657i
\(137\) 5.89144 + 3.40142i 0.503339 + 0.290603i 0.730092 0.683349i \(-0.239477\pi\)
−0.226752 + 0.973953i \(0.572811\pi\)
\(138\) 4.64555i 0.395456i
\(139\) 3.54908 6.14719i 0.301029 0.521397i −0.675340 0.737506i \(-0.736003\pi\)
0.976369 + 0.216109i \(0.0693366\pi\)
\(140\) 0 0
\(141\) 2.50973 1.44899i 0.211357 0.122027i
\(142\) −1.28468 −0.107808
\(143\) −2.09738 + 0.448642i −0.175392 + 0.0375173i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −7.27002 12.5920i −0.601671 1.04213i
\(147\) 0.433868 0.751482i 0.0357848 0.0619812i
\(148\) 10.3736i 0.852703i
\(149\) 3.02342 + 1.74557i 0.247688 + 0.143003i 0.618705 0.785623i \(-0.287658\pi\)
−0.371017 + 0.928626i \(0.620991\pi\)
\(150\) 0 0
\(151\) 4.54988i 0.370264i −0.982714 0.185132i \(-0.940729\pi\)
0.982714 0.185132i \(-0.0592713\pi\)
\(152\) 3.80805 6.59574i 0.308874 0.534985i
\(153\) −2.87649 4.98222i −0.232550 0.402789i
\(154\) −1.44503 + 0.834288i −0.116444 + 0.0672288i
\(155\) 0 0
\(156\) −3.43052 1.10975i −0.274661 0.0888512i
\(157\) −11.4957 −0.917460 −0.458730 0.888576i \(-0.651695\pi\)
−0.458730 + 0.888576i \(0.651695\pi\)
\(158\) 1.58613 0.915751i 0.126186 0.0728532i
\(159\) −6.94798 12.0343i −0.551011 0.954379i
\(160\) 0 0
\(161\) 13.0305i 1.02695i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −11.9762 6.91443i −0.938045 0.541580i −0.0486977 0.998814i \(-0.515507\pi\)
−0.889347 + 0.457233i \(0.848840\pi\)
\(164\) 5.75297i 0.449232i
\(165\) 0 0
\(166\) −2.09592 3.63024i −0.162675 0.281761i
\(167\) 18.6542 10.7700i 1.44351 0.833409i 0.445425 0.895319i \(-0.353052\pi\)
0.998082 + 0.0619099i \(0.0197191\pi\)
\(168\) −2.80495 −0.216406
\(169\) 10.5369 + 7.61404i 0.810531 + 0.585696i
\(170\) 0 0
\(171\) −6.59574 + 3.80805i −0.504389 + 0.291209i
\(172\) 2.12230 + 3.67593i 0.161824 + 0.280287i
\(173\) −6.83251 + 11.8342i −0.519466 + 0.899741i 0.480278 + 0.877116i \(0.340536\pi\)
−0.999744 + 0.0226249i \(0.992798\pi\)
\(174\) 2.52469i 0.191396i
\(175\) 0 0
\(176\) 0.515171 + 0.297434i 0.0388325 + 0.0224200i
\(177\) 9.70293i 0.729317i
\(178\) 3.02724 5.24333i 0.226901 0.393004i
\(179\) −5.37886 9.31647i −0.402035 0.696345i 0.591936 0.805985i \(-0.298364\pi\)
−0.993971 + 0.109639i \(0.965030\pi\)
\(180\) 0 0
\(181\) 5.86469 0.435919 0.217959 0.975958i \(-0.430060\pi\)
0.217959 + 0.975958i \(0.430060\pi\)
\(182\) 9.62243 + 3.11280i 0.713262 + 0.230736i
\(183\) 6.82619 0.504606
\(184\) −4.02317 + 2.32278i −0.296592 + 0.171237i
\(185\) 0 0
\(186\) 3.29654 5.70978i 0.241714 0.418661i
\(187\) 3.42226i 0.250261i
\(188\) 2.50973 + 1.44899i 0.183041 + 0.105679i
\(189\) 2.42916 + 1.40247i 0.176695 + 0.102015i
\(190\) 0 0
\(191\) 6.91728 11.9811i 0.500517 0.866921i −0.499483 0.866324i \(-0.666477\pi\)
1.00000 0.000597179i \(-0.000190088\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 14.7280 8.50322i 1.06014 0.612075i 0.134673 0.990890i \(-0.457002\pi\)
0.925472 + 0.378815i \(0.123668\pi\)
\(194\) −16.9064 −1.21381
\(195\) 0 0
\(196\) 0.867736 0.0619812
\(197\) −5.48171 + 3.16487i −0.390556 + 0.225487i −0.682401 0.730978i \(-0.739064\pi\)
0.291845 + 0.956466i \(0.405731\pi\)
\(198\) −0.297434 0.515171i −0.0211377 0.0366116i
\(199\) −8.31782 + 14.4069i −0.589634 + 1.02128i 0.404646 + 0.914473i \(0.367395\pi\)
−0.994280 + 0.106803i \(0.965939\pi\)
\(200\) 0 0
\(201\) −6.80906 3.93121i −0.480274 0.277286i
\(202\) 4.71741 + 2.72360i 0.331916 + 0.191632i
\(203\) 7.08163i 0.497033i
\(204\) 2.87649 4.98222i 0.201394 0.348825i
\(205\) 0 0
\(206\) 11.9104 6.87645i 0.829834 0.479105i
\(207\) 4.64555 0.322888
\(208\) −0.754186 3.52579i −0.0522934 0.244470i
\(209\) −4.53058 −0.313387
\(210\) 0 0
\(211\) −8.27443 14.3317i −0.569635 0.986637i −0.996602 0.0823697i \(-0.973751\pi\)
0.426967 0.904267i \(-0.359582\pi\)
\(212\) 6.94798 12.0343i 0.477190 0.826516i
\(213\) 1.28468i 0.0880251i
\(214\) 3.66407 + 2.11545i 0.250471 + 0.144609i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −9.24663 + 16.0156i −0.627702 + 1.08721i
\(218\) −0.223679 0.387423i −0.0151495 0.0262396i
\(219\) −12.5920 + 7.27002i −0.850892 + 0.491262i
\(220\) 0 0
\(221\) −15.3969 + 13.8994i −1.03570 + 0.934975i
\(222\) −10.3736 −0.696229
\(223\) −14.4242 + 8.32779i −0.965913 + 0.557670i −0.897988 0.440020i \(-0.854971\pi\)
−0.0679254 + 0.997690i \(0.521638\pi\)
\(224\) −1.40247 2.42916i −0.0937068 0.162305i
\(225\) 0 0
\(226\) 9.36701i 0.623084i
\(227\) −2.61722 1.51105i −0.173711 0.100292i 0.410624 0.911805i \(-0.365311\pi\)
−0.584334 + 0.811513i \(0.698644\pi\)
\(228\) −6.59574 3.80805i −0.436814 0.252195i
\(229\) 16.4472i 1.08686i 0.839453 + 0.543432i \(0.182875\pi\)
−0.839453 + 0.543432i \(0.817125\pi\)
\(230\) 0 0
\(231\) 0.834288 + 1.44503i 0.0548921 + 0.0950759i
\(232\) 2.18645 1.26235i 0.143547 0.0828771i
\(233\) −13.8289 −0.905959 −0.452980 0.891521i \(-0.649639\pi\)
−0.452980 + 0.891521i \(0.649639\pi\)
\(234\) −1.10975 + 3.43052i −0.0725467 + 0.224260i
\(235\) 0 0
\(236\) −8.40299 + 4.85147i −0.546988 + 0.315804i
\(237\) −0.915751 1.58613i −0.0594844 0.103030i
\(238\) −8.06839 + 13.9749i −0.522996 + 0.905856i
\(239\) 4.60216i 0.297689i 0.988861 + 0.148845i \(0.0475554\pi\)
−0.988861 + 0.148845i \(0.952445\pi\)
\(240\) 0 0
\(241\) 5.38108 + 3.10677i 0.346626 + 0.200125i 0.663198 0.748444i \(-0.269199\pi\)
−0.316572 + 0.948568i \(0.602532\pi\)
\(242\) 10.6461i 0.684359i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.41309 + 5.91165i 0.218501 + 0.378455i
\(245\) 0 0
\(246\) 5.75297 0.366796
\(247\) 18.4008 + 20.3832i 1.17082 + 1.29695i
\(248\) 6.59309 0.418661
\(249\) −3.63024 + 2.09592i −0.230057 + 0.132824i
\(250\) 0 0
\(251\) 8.19386 14.1922i 0.517192 0.895802i −0.482609 0.875836i \(-0.660311\pi\)
0.999801 0.0199663i \(-0.00635591\pi\)
\(252\) 2.80495i 0.176695i
\(253\) 2.39326 + 1.38175i 0.150463 + 0.0868697i
\(254\) −5.79190 3.34395i −0.363416 0.209818i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.20466 + 7.28269i 0.262280 + 0.454282i 0.966847 0.255355i \(-0.0821924\pi\)
−0.704568 + 0.709637i \(0.748859\pi\)
\(258\) 3.67593 2.12230i 0.228853 0.132129i
\(259\) 29.0974 1.80802
\(260\) 0 0
\(261\) −2.52469 −0.156275
\(262\) −10.1086 + 5.83620i −0.624511 + 0.360562i
\(263\) 2.94536 + 5.10152i 0.181619 + 0.314573i 0.942432 0.334398i \(-0.108533\pi\)
−0.760813 + 0.648971i \(0.775200\pi\)
\(264\) 0.297434 0.515171i 0.0183058 0.0317066i
\(265\) 0 0
\(266\) 18.5007 + 10.6814i 1.13435 + 0.654918i
\(267\) −5.24333 3.02724i −0.320886 0.185264i
\(268\) 7.86242i 0.480274i
\(269\) −11.4228 + 19.7848i −0.696459 + 1.20630i 0.273228 + 0.961949i \(0.411909\pi\)
−0.969686 + 0.244352i \(0.921425\pi\)
\(270\) 0 0
\(271\) −23.2565 + 13.4271i −1.41273 + 0.815639i −0.995645 0.0932285i \(-0.970281\pi\)
−0.417084 + 0.908868i \(0.636948\pi\)
\(272\) 5.75297 0.348825
\(273\) 3.11280 9.62243i 0.188395 0.582376i
\(274\) 6.80285 0.410975
\(275\) 0 0
\(276\) 2.32278 + 4.02317i 0.139815 + 0.242166i
\(277\) 5.31249 9.20150i 0.319197 0.552865i −0.661124 0.750277i \(-0.729920\pi\)
0.980321 + 0.197412i \(0.0632537\pi\)
\(278\) 7.09816i 0.425719i
\(279\) −5.70978 3.29654i −0.341836 0.197359i
\(280\) 0 0
\(281\) 28.3732i 1.69260i 0.532705 + 0.846301i \(0.321176\pi\)
−0.532705 + 0.846301i \(0.678824\pi\)
\(282\) 1.44899 2.50973i 0.0862862 0.149452i
\(283\) −2.83482 4.91005i −0.168512 0.291872i 0.769385 0.638786i \(-0.220563\pi\)
−0.937897 + 0.346914i \(0.887230\pi\)
\(284\) −1.11257 + 0.642342i −0.0660188 + 0.0381160i
\(285\) 0 0
\(286\) −1.59207 + 1.43723i −0.0941408 + 0.0849850i
\(287\) −16.1368 −0.952524
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −8.04834 13.9401i −0.473431 0.820007i
\(290\) 0 0
\(291\) 16.9064i 0.991069i
\(292\) −12.5920 7.27002i −0.736894 0.425446i
\(293\) −1.43617 0.829176i −0.0839022 0.0484410i 0.457462 0.889229i \(-0.348759\pi\)
−0.541364 + 0.840788i \(0.682092\pi\)
\(294\) 0.867736i 0.0506074i
\(295\) 0 0
\(296\) −5.18679 8.98379i −0.301476 0.522172i
\(297\) −0.515171 + 0.297434i −0.0298933 + 0.0172589i
\(298\) 3.49115 0.202237
\(299\) −3.50361 16.3793i −0.202619 0.947237i
\(300\) 0 0
\(301\) −10.3108 + 5.95294i −0.594304 + 0.343122i
\(302\) −2.27494 3.94031i −0.130908 0.226740i
\(303\) 2.72360 4.71741i 0.156467 0.271008i
\(304\) 7.61611i 0.436814i
\(305\) 0 0
\(306\) −4.98222 2.87649i −0.284814 0.164438i
\(307\) 0.384087i 0.0219210i −0.999940 0.0109605i \(-0.996511\pi\)
0.999940 0.0109605i \(-0.00348891\pi\)
\(308\) −0.834288 + 1.44503i −0.0475380 + 0.0823382i
\(309\) −6.87645 11.9104i −0.391187 0.677556i
\(310\) 0 0
\(311\) −11.6920 −0.662993 −0.331497 0.943456i \(-0.607554\pi\)
−0.331497 + 0.943456i \(0.607554\pi\)
\(312\) −3.52579 + 0.754186i −0.199609 + 0.0426974i
\(313\) 10.5788 0.597948 0.298974 0.954261i \(-0.403356\pi\)
0.298974 + 0.954261i \(0.403356\pi\)
\(314\) −9.95560 + 5.74787i −0.561827 + 0.324371i
\(315\) 0 0
\(316\) 0.915751 1.58613i 0.0515150 0.0892266i
\(317\) 22.1023i 1.24139i −0.784052 0.620695i \(-0.786850\pi\)
0.784052 0.620695i \(-0.213150\pi\)
\(318\) −12.0343 6.94798i −0.674848 0.389624i
\(319\) −1.30065 0.750930i −0.0728224 0.0420440i
\(320\) 0 0
\(321\) 2.11545 3.66407i 0.118073 0.204509i
\(322\) −6.51527 11.2848i −0.363082 0.628876i
\(323\) −37.9451 + 21.9076i −2.11132 + 1.21897i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −13.8289 −0.765910
\(327\) −0.387423 + 0.223679i −0.0214246 + 0.0123695i
\(328\) 2.87649 + 4.98222i 0.158827 + 0.275097i
\(329\) −4.06435 + 7.03966i −0.224075 + 0.388109i
\(330\) 0 0
\(331\) −5.28809 3.05308i −0.290660 0.167812i 0.347580 0.937650i \(-0.387004\pi\)
−0.638239 + 0.769838i \(0.720337\pi\)
\(332\) −3.63024 2.09592i −0.199235 0.115029i
\(333\) 10.3736i 0.568469i
\(334\) 10.7700 18.6542i 0.589309 1.02071i
\(335\) 0 0
\(336\) −2.42916 + 1.40247i −0.132521 + 0.0765112i
\(337\) 4.29852 0.234155 0.117078 0.993123i \(-0.462647\pi\)
0.117078 + 0.993123i \(0.462647\pi\)
\(338\) 12.9322 + 1.32550i 0.703422 + 0.0720979i
\(339\) −9.36701 −0.508746
\(340\) 0 0
\(341\) −1.96101 3.39657i −0.106195 0.183935i
\(342\) −3.80805 + 6.59574i −0.205916 + 0.356657i
\(343\) 17.2007i 0.928750i
\(344\) 3.67593 + 2.12230i 0.198193 + 0.114427i
\(345\) 0 0
\(346\) 13.6650i 0.734636i
\(347\) −17.1730 + 29.7444i −0.921893 + 1.59677i −0.125409 + 0.992105i \(0.540024\pi\)
−0.796484 + 0.604660i \(0.793309\pi\)
\(348\) −1.26235 2.18645i −0.0676689 0.117206i
\(349\) −13.8581 + 8.00099i −0.741808 + 0.428283i −0.822726 0.568438i \(-0.807548\pi\)
0.0809181 + 0.996721i \(0.474215\pi\)
\(350\) 0 0
\(351\) 3.43052 + 1.10975i 0.183107 + 0.0592341i
\(352\) 0.594869 0.0317066
\(353\) −16.7941 + 9.69607i −0.893859 + 0.516070i −0.875203 0.483756i \(-0.839272\pi\)
−0.0186563 + 0.999826i \(0.505939\pi\)
\(354\) 4.85147 + 8.40299i 0.257853 + 0.446614i
\(355\) 0 0
\(356\) 6.05447i 0.320886i
\(357\) 13.9749 + 8.06839i 0.739628 + 0.427025i
\(358\) −9.31647 5.37886i −0.492391 0.284282i
\(359\) 15.8342i 0.835699i −0.908516 0.417850i \(-0.862784\pi\)
0.908516 0.417850i \(-0.137216\pi\)
\(360\) 0 0
\(361\) 19.5026 + 33.7794i 1.02645 + 1.77786i
\(362\) 5.07897 2.93234i 0.266945 0.154121i
\(363\) 10.6461 0.558777
\(364\) 9.88966 2.11545i 0.518359 0.110880i
\(365\) 0 0
\(366\) 5.91165 3.41309i 0.309007 0.178405i
\(367\) −7.64645 13.2440i −0.399141 0.691333i 0.594479 0.804111i \(-0.297358\pi\)
−0.993620 + 0.112778i \(0.964025\pi\)
\(368\) −2.32278 + 4.02317i −0.121083 + 0.209722i
\(369\) 5.75297i 0.299488i
\(370\) 0 0
\(371\) 33.7555 + 19.4887i 1.75250 + 1.01180i
\(372\) 6.59309i 0.341836i
\(373\) −10.8258 + 18.7508i −0.560538 + 0.970881i 0.436911 + 0.899505i \(0.356072\pi\)
−0.997449 + 0.0713760i \(0.977261\pi\)
\(374\) −1.71113 2.96377i −0.0884805 0.153253i
\(375\) 0 0
\(376\) 2.89798 0.149452
\(377\) 1.90409 + 8.90154i 0.0980655 + 0.458453i
\(378\) 2.80495 0.144271
\(379\) −7.81479 + 4.51187i −0.401419 + 0.231759i −0.687096 0.726567i \(-0.741115\pi\)
0.285677 + 0.958326i \(0.407782\pi\)
\(380\) 0 0
\(381\) −3.34395 + 5.79190i −0.171316 + 0.296728i
\(382\) 13.8346i 0.707838i
\(383\) −8.72439 5.03703i −0.445795 0.257380i 0.260257 0.965539i \(-0.416193\pi\)
−0.706053 + 0.708159i \(0.749526\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 8.50322 14.7280i 0.432802 0.749636i
\(387\) −2.12230 3.67593i −0.107883 0.186858i
\(388\) −14.6413 + 8.45318i −0.743301 + 0.429145i
\(389\) 24.3591 1.23505 0.617527 0.786550i \(-0.288135\pi\)
0.617527 + 0.786550i \(0.288135\pi\)
\(390\) 0 0
\(391\) 26.7257 1.35158
\(392\) 0.751482 0.433868i 0.0379556 0.0219137i
\(393\) 5.83620 + 10.1086i 0.294397 + 0.509911i
\(394\) −3.16487 + 5.48171i −0.159444 + 0.276165i
\(395\) 0 0
\(396\) −0.515171 0.297434i −0.0258883 0.0149466i
\(397\) 26.0137 + 15.0190i 1.30559 + 0.753784i 0.981357 0.192193i \(-0.0615601\pi\)
0.324234 + 0.945977i \(0.394893\pi\)
\(398\) 16.6356i 0.833869i
\(399\) 10.6814 18.5007i 0.534739 0.926194i
\(400\) 0 0
\(401\) 2.35786 1.36131i 0.117746 0.0679807i −0.439970 0.898012i \(-0.645011\pi\)
0.557716 + 0.830032i \(0.311678\pi\)
\(402\) −7.86242 −0.392142
\(403\) −7.31669 + 22.6177i −0.364470 + 1.12667i
\(404\) 5.44720 0.271008
\(405\) 0 0
\(406\) 3.54082 + 6.13287i 0.175728 + 0.304369i
\(407\) −3.08546 + 5.34417i −0.152941 + 0.264901i
\(408\) 5.75297i 0.284814i
\(409\) 33.1032 + 19.1121i 1.63685 + 0.945034i 0.981909 + 0.189352i \(0.0606386\pi\)
0.654938 + 0.755683i \(0.272695\pi\)
\(410\) 0 0
\(411\) 6.80285i 0.335560i
\(412\) 6.87645 11.9104i 0.338778 0.586781i
\(413\) −13.6081 23.5699i −0.669612 1.15980i
\(414\) 4.02317 2.32278i 0.197728 0.114158i
\(415\) 0 0
\(416\) −2.41604 2.67633i −0.118456 0.131218i
\(417\) −7.09816 −0.347598
\(418\) −3.92360 + 2.26529i −0.191910 + 0.110799i
\(419\) −14.9365 25.8708i −0.729695 1.26387i −0.957012 0.290048i \(-0.906329\pi\)
0.227317 0.973821i \(-0.427005\pi\)
\(420\) 0 0
\(421\) 14.2033i 0.692226i −0.938193 0.346113i \(-0.887501\pi\)
0.938193 0.346113i \(-0.112499\pi\)
\(422\) −14.3317 8.27443i −0.697658 0.402793i
\(423\) −2.50973 1.44899i −0.122027 0.0704524i
\(424\) 13.8960i 0.674848i
\(425\) 0 0
\(426\) 0.642342 + 1.11257i 0.0311216 + 0.0539042i
\(427\) −16.5819 + 9.57355i −0.802453 + 0.463297i
\(428\) 4.23091 0.204509
\(429\) 1.43723 + 1.59207i 0.0693899 + 0.0768657i
\(430\) 0 0
\(431\) −8.09901 + 4.67596i −0.390115 + 0.225233i −0.682210 0.731156i \(-0.738981\pi\)
0.292095 + 0.956389i \(0.405648\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −1.98005 + 3.42954i −0.0951549 + 0.164813i −0.909673 0.415325i \(-0.863668\pi\)
0.814518 + 0.580138i \(0.197001\pi\)
\(434\) 18.4933i 0.887705i
\(435\) 0 0
\(436\) −0.387423 0.223679i −0.0185542 0.0107123i
\(437\) 35.3810i 1.69250i
\(438\) −7.27002 + 12.5920i −0.347375 + 0.601671i
\(439\) 11.2992 + 19.5708i 0.539281 + 0.934062i 0.998943 + 0.0459680i \(0.0146372\pi\)
−0.459662 + 0.888094i \(0.652029\pi\)
\(440\) 0 0
\(441\) −0.867736 −0.0413208
\(442\) −6.38437 + 19.7357i −0.303673 + 0.938730i
\(443\) −29.0428 −1.37987 −0.689933 0.723873i \(-0.742360\pi\)
−0.689933 + 0.723873i \(0.742360\pi\)
\(444\) −8.98379 + 5.18679i −0.426352 + 0.246154i
\(445\) 0 0
\(446\) −8.32779 + 14.4242i −0.394332 + 0.683004i
\(447\) 3.49115i 0.165125i
\(448\) −2.42916 1.40247i −0.114767 0.0662607i
\(449\) −23.7886 13.7343i −1.12265 0.648164i −0.180576 0.983561i \(-0.557796\pi\)
−0.942077 + 0.335397i \(0.891130\pi\)
\(450\) 0 0
\(451\) 1.71113 2.96377i 0.0805740 0.139558i
\(452\) −4.68350 8.11206i −0.220293 0.381559i
\(453\) −3.94031 + 2.27494i −0.185132 + 0.106886i
\(454\) −3.02210 −0.141834
\(455\) 0 0
\(456\) −7.61611 −0.356657
\(457\) −3.79470 + 2.19087i −0.177508 + 0.102485i −0.586122 0.810223i \(-0.699346\pi\)
0.408613 + 0.912708i \(0.366013\pi\)
\(458\) 8.22361 + 14.2437i 0.384264 + 0.665565i
\(459\) −2.87649 + 4.98222i −0.134263 + 0.232550i
\(460\) 0 0
\(461\) −21.0593 12.1586i −0.980829 0.566282i −0.0783090 0.996929i \(-0.524952\pi\)
−0.902520 + 0.430647i \(0.858285\pi\)
\(462\) 1.44503 + 0.834288i 0.0672288 + 0.0388146i
\(463\) 19.0660i 0.886071i −0.896504 0.443035i \(-0.853902\pi\)
0.896504 0.443035i \(-0.146098\pi\)
\(464\) 1.26235 2.18645i 0.0586030 0.101503i
\(465\) 0 0
\(466\) −11.9762 + 6.91443i −0.554784 + 0.320305i
\(467\) −10.1176 −0.468188 −0.234094 0.972214i \(-0.575212\pi\)
−0.234094 + 0.972214i \(0.575212\pi\)
\(468\) 0.754186 + 3.52579i 0.0348623 + 0.162980i
\(469\) 22.0537 1.01834
\(470\) 0 0
\(471\) 5.74787 + 9.95560i 0.264848 + 0.458730i
\(472\) −4.85147 + 8.40299i −0.223307 + 0.386779i
\(473\) 2.52498i 0.116099i
\(474\) −1.58613 0.915751i −0.0728532 0.0420618i
\(475\) 0 0
\(476\) 16.1368i 0.739628i
\(477\) −6.94798 + 12.0343i −0.318126 + 0.551011i
\(478\) 2.30108 + 3.98559i 0.105249 + 0.182297i
\(479\) 24.8215 14.3307i 1.13412 0.654786i 0.189155 0.981947i \(-0.439425\pi\)
0.944969 + 0.327161i \(0.106092\pi\)
\(480\) 0 0
\(481\) 36.5751 7.82361i 1.66768 0.356726i
\(482\) 6.21354 0.283019
\(483\) −11.2848 + 6.51527i −0.513475 + 0.296455i
\(484\) 5.32307 + 9.21982i 0.241958 + 0.419083i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 15.1033 + 8.71990i 0.684396 + 0.395136i 0.801509 0.597982i \(-0.204031\pi\)
−0.117113 + 0.993119i \(0.537364\pi\)
\(488\) 5.91165 + 3.41309i 0.267608 + 0.154504i
\(489\) 13.8289i 0.625363i
\(490\) 0 0
\(491\) −11.2233 19.4394i −0.506503 0.877288i −0.999972 0.00752493i \(-0.997605\pi\)
0.493469 0.869763i \(-0.335729\pi\)
\(492\) 4.98222 2.87649i 0.224616 0.129682i
\(493\) −14.5245 −0.654150
\(494\) 26.1272 + 8.45199i 1.17552 + 0.380273i
\(495\) 0 0
\(496\) 5.70978 3.29654i 0.256377 0.148019i
\(497\) −1.80174 3.12070i −0.0808189 0.139983i
\(498\) −2.09592 + 3.63024i −0.0939204 + 0.162675i
\(499\) 10.4136i 0.466177i −0.972456 0.233088i \(-0.925117\pi\)
0.972456 0.233088i \(-0.0748832\pi\)
\(500\) 0 0
\(501\) −18.6542 10.7700i −0.833409 0.481169i
\(502\) 16.3877i 0.731420i
\(503\) 2.88899 5.00387i 0.128814 0.223112i −0.794404 0.607390i \(-0.792216\pi\)
0.923217 + 0.384279i \(0.125550\pi\)
\(504\) 1.40247 + 2.42916i 0.0624712 + 0.108203i
\(505\) 0 0
\(506\) 2.76349 0.122852
\(507\) 1.32550 12.9322i 0.0588677 0.574341i
\(508\) −6.68791 −0.296728
\(509\) 6.18024 3.56816i 0.273934 0.158156i −0.356740 0.934204i \(-0.616112\pi\)
0.630674 + 0.776048i \(0.282778\pi\)
\(510\) 0 0
\(511\) 20.3920 35.3200i 0.902090 1.56247i
\(512\) 1.00000i 0.0441942i
\(513\) 6.59574 + 3.80805i 0.291209 + 0.168130i
\(514\) 7.28269 + 4.20466i 0.321226 + 0.185460i
\(515\) 0 0
\(516\) 2.12230 3.67593i 0.0934290 0.161824i
\(517\) −0.861960 1.49296i −0.0379090 0.0656603i
\(518\) 25.1991 14.5487i 1.10718 0.639232i
\(519\) 13.6650 0.599827
\(520\) 0 0
\(521\) 1.09782 0.0480965 0.0240483 0.999711i \(-0.492344\pi\)
0.0240483 + 0.999711i \(0.492344\pi\)
\(522\) −2.18645 + 1.26235i −0.0956982 + 0.0552514i
\(523\) −7.47153 12.9411i −0.326707 0.565873i 0.655149 0.755499i \(-0.272606\pi\)
−0.981856 + 0.189626i \(0.939272\pi\)
\(524\) −5.83620 + 10.1086i −0.254956 + 0.441596i
\(525\) 0 0
\(526\) 5.10152 + 2.94536i 0.222437 + 0.128424i
\(527\) −32.8482 18.9649i −1.43089 0.826125i
\(528\) 0.594869i 0.0258883i
\(529\) 0.709414 1.22874i 0.0308441 0.0534235i
\(530\) 0 0
\(531\) 8.40299 4.85147i 0.364659 0.210536i
\(532\) 21.3628 0.926194
\(533\) −20.2838 + 4.33881i −0.878588 + 0.187935i
\(534\) −6.05447 −0.262003
\(535\) 0 0
\(536\) −3.93121 6.80906i −0.169802 0.294106i
\(537\) −5.37886 + 9.31647i −0.232115 + 0.402035i
\(538\) 22.8455i 0.984941i
\(539\) −0.447033 0.258095i −0.0192551 0.0111169i
\(540\) 0 0
\(541\) 19.3888i 0.833589i −0.909001 0.416794i \(-0.863154\pi\)
0.909001 0.416794i \(-0.136846\pi\)
\(542\) −13.4271 + 23.2565i −0.576744 + 0.998950i
\(543\) −2.93234 5.07897i −0.125839 0.217959i
\(544\) 4.98222 2.87649i 0.213611 0.123328i
\(545\) 0 0
\(546\) −2.11545 9.88966i −0.0905330 0.423239i
\(547\) −26.1335 −1.11739 −0.558693 0.829374i \(-0.688697\pi\)
−0.558693 + 0.829374i \(0.688697\pi\)
\(548\) 5.89144 3.40142i 0.251670 0.145302i
\(549\) −3.41309 5.91165i −0.145667 0.252303i
\(550\) 0 0
\(551\) 19.2283i 0.819155i
\(552\) 4.02317 + 2.32278i 0.171237 + 0.0988640i
\(553\) 4.44901 + 2.56863i 0.189191 + 0.109229i
\(554\) 10.6250i 0.451412i
\(555\) 0 0
\(556\) −3.54908 6.14719i −0.150514 0.260699i
\(557\) 30.6446 17.6927i 1.29846 0.749663i 0.318318 0.947984i \(-0.396882\pi\)
0.980137 + 0.198321i \(0.0635487\pi\)
\(558\) −6.59309 −0.279108
\(559\) −11.3600 + 10.2551i −0.480475 + 0.433745i
\(560\) 0 0
\(561\) −2.96377 + 1.71113i −0.125130 + 0.0722440i
\(562\) 14.1866 + 24.5719i 0.598425 + 1.03650i
\(563\) 14.8963 25.8011i 0.627804 1.08739i −0.360187 0.932880i \(-0.617287\pi\)
0.987991 0.154509i \(-0.0493794\pi\)
\(564\) 2.89798i 0.122027i
\(565\) 0 0
\(566\) −4.91005 2.83482i −0.206385 0.119156i
\(567\) 2.80495i 0.117797i
\(568\) −0.642342 + 1.11257i −0.0269521 + 0.0466824i
\(569\) 7.14388 + 12.3736i 0.299487 + 0.518727i 0.976019 0.217687i \(-0.0698511\pi\)
−0.676532 + 0.736414i \(0.736518\pi\)
\(570\) 0 0
\(571\) −37.4439 −1.56698 −0.783490 0.621404i \(-0.786562\pi\)
−0.783490 + 0.621404i \(0.786562\pi\)
\(572\) −0.660156 + 2.04071i −0.0276025 + 0.0853263i
\(573\) −13.8346 −0.577947
\(574\) −13.9749 + 8.06839i −0.583300 + 0.336768i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 47.6052i 1.98183i 0.134485 + 0.990916i \(0.457062\pi\)
−0.134485 + 0.990916i \(0.542938\pi\)
\(578\) −13.9401 8.04834i −0.579833 0.334767i
\(579\) −14.7280 8.50322i −0.612075 0.353382i
\(580\) 0 0
\(581\) 5.87895 10.1826i 0.243900 0.422447i
\(582\) 8.45318 + 14.6413i 0.350396 + 0.606903i
\(583\) −7.15881 + 4.13314i −0.296487 + 0.171177i
\(584\) −14.5400 −0.601671
\(585\) 0 0
\(586\) −1.65835 −0.0685059
\(587\) −32.5654 + 18.8016i −1.34412 + 0.776027i −0.987409 0.158189i \(-0.949435\pi\)
−0.356709 + 0.934216i \(0.616101\pi\)
\(588\) −0.433868 0.751482i −0.0178924 0.0309906i
\(589\) −25.1068 + 43.4863i −1.03451 + 1.79182i
\(590\) 0 0
\(591\) 5.48171 + 3.16487i 0.225487 + 0.130185i
\(592\) −8.98379 5.18679i −0.369231 0.213176i
\(593\) 24.0046i 0.985752i −0.870100 0.492876i \(-0.835946\pi\)
0.870100 0.492876i \(-0.164054\pi\)
\(594\) −0.297434 + 0.515171i −0.0122039 + 0.0211377i
\(595\) 0 0
\(596\) 3.02342 1.74557i 0.123844 0.0715014i
\(597\) 16.6356 0.680851
\(598\) −11.2238 12.4330i −0.458977 0.508425i
\(599\) 23.7092 0.968731 0.484365 0.874866i \(-0.339051\pi\)
0.484365 + 0.874866i \(0.339051\pi\)
\(600\) 0 0
\(601\) 0.918249 + 1.59045i 0.0374562 + 0.0648760i 0.884146 0.467211i \(-0.154741\pi\)
−0.846690 + 0.532087i \(0.821408\pi\)
\(602\) −5.95294 + 10.3108i −0.242624 + 0.420237i
\(603\) 7.86242i 0.320183i
\(604\) −3.94031 2.27494i −0.160329 0.0925661i
\(605\) 0 0
\(606\) 5.44720i 0.221277i
\(607\) 17.4483 30.2214i 0.708206 1.22665i −0.257316 0.966327i \(-0.582838\pi\)
0.965522 0.260321i \(-0.0838284\pi\)
\(608\) −3.80805 6.59574i −0.154437 0.267493i
\(609\) 6.13287 3.54082i 0.248517 0.143481i
\(610\) 0 0
\(611\) −3.21604 + 9.94159i −0.130107 + 0.402194i
\(612\) −5.75297 −0.232550
\(613\) −8.15061 + 4.70575i −0.329200 + 0.190064i −0.655486 0.755207i \(-0.727536\pi\)
0.326286 + 0.945271i \(0.394203\pi\)
\(614\) −0.192044 0.332629i −0.00775025 0.0134238i
\(615\) 0 0
\(616\) 1.66858i 0.0672288i
\(617\) 9.48432 + 5.47577i 0.381824 + 0.220446i 0.678612 0.734497i \(-0.262582\pi\)
−0.296787 + 0.954944i \(0.595915\pi\)
\(618\) −11.9104 6.87645i −0.479105 0.276611i
\(619\) 1.00216i 0.0402803i −0.999797 0.0201402i \(-0.993589\pi\)
0.999797 0.0201402i \(-0.00641125\pi\)
\(620\) 0 0
\(621\) −2.32278 4.02317i −0.0932098 0.161444i
\(622\) −10.1256 + 5.84601i −0.405999 + 0.234404i
\(623\) 16.9825 0.680389
\(624\) −2.67633 + 2.41604i −0.107139 + 0.0967190i
\(625\) 0 0
\(626\) 9.16150 5.28939i 0.366167 0.211407i
\(627\) 2.26529 + 3.92360i 0.0904671 + 0.156694i
\(628\) −5.74787 + 9.95560i −0.229365 + 0.397272i
\(629\) 59.6789i 2.37955i
\(630\) 0 0
\(631\) −33.5167 19.3509i −1.33428 0.770346i −0.348327 0.937373i \(-0.613250\pi\)
−0.985952 + 0.167027i \(0.946583\pi\)
\(632\) 1.83150i 0.0728532i
\(633\) −8.27443 + 14.3317i −0.328879 + 0.569635i
\(634\) −11.0512 19.1412i −0.438898 0.760193i
\(635\) 0 0
\(636\) −13.8960 −0.551011
\(637\) 0.654435 + 3.05946i 0.0259296 + 0.121220i
\(638\) −1.50186 −0.0594592
\(639\) 1.11257 0.642342i 0.0440126 0.0254107i
\(640\) 0 0
\(641\) 4.99961 8.65957i 0.197473 0.342033i −0.750236 0.661170i \(-0.770060\pi\)
0.947708 + 0.319138i \(0.103393\pi\)
\(642\) 4.23091i 0.166981i
\(643\) 5.86694 + 3.38728i 0.231369 + 0.133581i 0.611204 0.791473i \(-0.290686\pi\)
−0.379834 + 0.925055i \(0.624019\pi\)
\(644\) −11.2848 6.51527i −0.444683 0.256738i
\(645\) 0 0
\(646\) −21.9076 + 37.9451i −0.861944 + 1.49293i
\(647\) −8.59384 14.8850i −0.337859 0.585188i 0.646171 0.763193i \(-0.276369\pi\)
−0.984030 + 0.178004i \(0.943036\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 5.77197 0.226570
\(650\) 0 0
\(651\) 18.4933 0.724808
\(652\) −11.9762 + 6.91443i −0.469022 + 0.270790i
\(653\) −12.4362 21.5401i −0.486666 0.842930i 0.513217 0.858259i \(-0.328454\pi\)
−0.999883 + 0.0153292i \(0.995120\pi\)
\(654\) −0.223679 + 0.387423i −0.00874654 + 0.0151495i
\(655\) 0 0
\(656\) 4.98222 + 2.87649i 0.194523 + 0.112308i
\(657\) 12.5920 + 7.27002i 0.491262 + 0.283631i
\(658\) 8.12870i 0.316890i
\(659\) 4.12151 7.13867i 0.160551 0.278083i −0.774515 0.632555i \(-0.782006\pi\)
0.935067 + 0.354472i \(0.115339\pi\)
\(660\) 0 0
\(661\) 22.3962 12.9305i 0.871112 0.502937i 0.00339467 0.999994i \(-0.498919\pi\)
0.867718 + 0.497057i \(0.165586\pi\)
\(662\) −6.10616 −0.237323
\(663\) 19.7357 + 6.38437i 0.766470 + 0.247948i
\(664\) −4.19184 −0.162675
\(665\) 0 0
\(666\) 5.18679 + 8.98379i 0.200984 + 0.348115i
\(667\) 5.86430 10.1573i 0.227067 0.393291i
\(668\) 21.5400i 0.833409i
\(669\) 14.4242 + 8.32779i 0.557670 + 0.321971i
\(670\) 0 0
\(671\) 4.06069i 0.156761i
\(672\) −1.40247 + 2.42916i −0.0541016 + 0.0937068i
\(673\) 3.46306 + 5.99820i 0.133491 + 0.231213i 0.925020 0.379918i \(-0.124048\pi\)
−0.791529 + 0.611132i \(0.790715\pi\)
\(674\) 3.72263 2.14926i 0.143390 0.0827864i
\(675\) 0 0
\(676\) 11.8624 5.31820i 0.456246 0.204546i
\(677\) 4.72639 0.181650 0.0908250 0.995867i \(-0.471050\pi\)
0.0908250 + 0.995867i \(0.471050\pi\)
\(678\) −8.11206 + 4.68350i −0.311542 + 0.179869i
\(679\) −23.7107 41.0682i −0.909935 1.57605i
\(680\) 0 0
\(681\) 3.02210i 0.115807i
\(682\) −3.39657 1.96101i −0.130061 0.0750910i
\(683\) 16.9567 + 9.78995i 0.648830 + 0.374602i 0.788008 0.615665i \(-0.211113\pi\)
−0.139178 + 0.990267i \(0.544446\pi\)
\(684\) 7.61611i 0.291209i
\(685\) 0 0
\(686\) −8.60034 14.8962i −0.328363 0.568741i
\(687\) 14.2437 8.22361i 0.543432 0.313750i
\(688\) 4.24460 0.161824
\(689\) 47.6704 + 15.4211i 1.81610 + 0.587496i
\(690\) 0 0
\(691\) −10.7079 + 6.18224i −0.407350 + 0.235183i −0.689650 0.724143i \(-0.742236\pi\)
0.282301 + 0.959326i \(0.408902\pi\)
\(692\) 6.83251 + 11.8342i 0.259733 + 0.449871i
\(693\) 0.834288 1.44503i 0.0316920 0.0548921i
\(694\) 34.3459i 1.30375i
\(695\) 0 0
\(696\) −2.18645 1.26235i −0.0828771 0.0478491i
\(697\) 33.0967i 1.25363i
\(698\) −8.00099 + 13.8581i −0.302842 + 0.524538i
\(699\) 6.91443 + 11.9762i 0.261528 + 0.452980i
\(700\) 0 0
\(701\) 43.7550 1.65260 0.826302 0.563227i \(-0.190441\pi\)
0.826302 + 0.563227i \(0.190441\pi\)
\(702\) 3.52579 0.754186i 0.133072 0.0284649i
\(703\) 79.0063 2.97978
\(704\) 0.515171 0.297434i 0.0194163 0.0112100i
\(705\) 0 0
\(706\) −9.69607 + 16.7941i −0.364916 + 0.632054i
\(707\) 15.2791i 0.574630i
\(708\) 8.40299 + 4.85147i 0.315804 + 0.182329i
\(709\) −16.4104 9.47457i −0.616307 0.355825i 0.159123 0.987259i \(-0.449133\pi\)
−0.775430 + 0.631434i \(0.782467\pi\)
\(710\) 0 0
\(711\) −0.915751 + 1.58613i −0.0343434 + 0.0594844i
\(712\) −3.02724 5.24333i −0.113451 0.196502i
\(713\) 26.5251 15.3143i 0.993372 0.573524i
\(714\) 16.1368 0.603904
\(715\) 0 0
\(716\) −10.7577 −0.402035
\(717\) 3.98559 2.30108i 0.148845 0.0859355i
\(718\) −7.91712 13.7129i −0.295464 0.511759i
\(719\) 23.5155 40.7301i 0.876981 1.51898i 0.0223436 0.999750i \(-0.492887\pi\)
0.854637 0.519225i \(-0.173779\pi\)
\(720\) 0 0
\(721\) 33.4079 + 19.2881i 1.24418 + 0.718326i
\(722\) 33.7794 + 19.5026i 1.25714 + 0.725810i
\(723\) 6.21354i 0.231084i
\(724\) 2.93234 5.07897i 0.108980 0.188758i
\(725\) 0 0
\(726\) 9.21982 5.32307i 0.342180 0.197557i
\(727\) 4.10440 0.152224 0.0761119 0.997099i \(-0.475749\pi\)
0.0761119 + 0.997099i \(0.475749\pi\)
\(728\) 7.50697 6.77687i 0.278227 0.251167i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.2095 21.1475i −0.451586 0.782169i
\(732\) 3.41309 5.91165i 0.126152 0.218501i
\(733\) 24.2968i 0.897421i 0.893677 + 0.448711i \(0.148117\pi\)
−0.893677 + 0.448711i \(0.851883\pi\)
\(734\) −13.2440 7.64645i −0.488847 0.282236i
\(735\) 0 0
\(736\) 4.64555i 0.171237i
\(737\) −2.33855 + 4.05050i −0.0861418 + 0.149202i
\(738\) −2.87649 4.98222i −0.105885 0.183398i
\(739\) 35.0414 20.2311i 1.28902 0.744215i 0.310539 0.950561i \(-0.399491\pi\)
0.978479 + 0.206346i \(0.0661572\pi\)
\(740\) 0 0
\(741\) 8.45199 26.1272i 0.310492 0.959806i
\(742\) 38.9775 1.43091
\(743\) −27.2794 + 15.7497i −1.00078 + 0.577802i −0.908480 0.417929i \(-0.862756\pi\)
−0.0923027 + 0.995731i \(0.529423\pi\)
\(744\) −3.29654 5.70978i −0.120857 0.209331i
\(745\) 0 0
\(746\) 21.6516i 0.792721i
\(747\) 3.63024 + 2.09592i 0.132824 + 0.0766857i
\(748\) −2.96377 1.71113i −0.108366 0.0625651i
\(749\) 11.8675i 0.433628i
\(750\) 0 0
\(751\) −8.37551 14.5068i −0.305627 0.529361i 0.671774 0.740756i \(-0.265533\pi\)
−0.977401 + 0.211395i \(0.932199\pi\)
\(752\) 2.50973 1.44899i 0.0915204 0.0528393i
\(753\) −16.3877 −0.597202
\(754\) 6.09976 + 6.75692i 0.222140 + 0.246072i
\(755\) 0 0
\(756\) 2.42916 1.40247i 0.0883476 0.0510075i
\(757\) −13.3892 23.1908i −0.486640 0.842885i 0.513242 0.858244i \(-0.328444\pi\)
−0.999882 + 0.0153589i \(0.995111\pi\)
\(758\) −4.51187 + 7.81479i −0.163879 + 0.283846i
\(759\) 2.76349i 0.100308i
\(760\) 0 0
\(761\) −0.217029 0.125302i −0.00786729 0.00454218i 0.496061 0.868288i \(-0.334779\pi\)
−0.503928 + 0.863745i \(0.668112\pi\)
\(762\) 6.68791i 0.242277i
\(763\) 0.627408 1.08670i 0.0227137 0.0393413i
\(764\) −6.91728 11.9811i −0.250259 0.433461i
\(765\) 0 0
\(766\) −10.0741 −0.363990
\(767\) −23.4427 25.9683i −0.846466 0.937660i
\(768\) 1.00000 0.0360844
\(769\) −17.1777 + 9.91755i −0.619444 + 0.357636i −0.776652 0.629929i \(-0.783084\pi\)
0.157209 + 0.987565i \(0.449750\pi\)
\(770\) 0 0
\(771\) 4.20466 7.28269i 0.151427 0.262280i
\(772\) 17.0064i 0.612075i
\(773\) 31.7285 + 18.3185i 1.14120 + 0.658869i 0.946726 0.322039i \(-0.104368\pi\)
0.194469 + 0.980909i \(0.437702\pi\)
\(774\) −3.67593 2.12230i −0.132129 0.0762845i
\(775\) 0 0
\(776\) −8.45318 + 14.6413i −0.303452 + 0.525594i
\(777\) −14.5487 25.1991i −0.521931 0.904011i
\(778\) 21.0956 12.1795i 0.756313 0.436658i
\(779\) −43.8152 −1.56984
\(780\) 0 0
\(781\) 0.764218 0.0273459
\(782\) 23.1452 13.3629i 0.827669 0.477855i
\(783\) 1.26235 + 2.18645i 0.0451126 + 0.0781373i