Properties

Label 688.2.i.e.337.2
Level 688
Weight 2
Character 688.337
Analytic conductor 5.494
Analytic rank 0
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 688 = 2^{4} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 688.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.49370765906\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 43)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 688.337
Dual form 688.2.i.e.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 - 0.330792i) q^{3} +(1.61803 + 2.80252i) q^{5} +(0.118034 - 0.204441i) q^{7} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.330792i) q^{3} +(1.61803 + 2.80252i) q^{5} +(0.118034 - 0.204441i) q^{7} +(1.42705 - 2.47172i) q^{9} +1.38197 q^{11} +(-1.80902 + 3.13331i) q^{13} +(0.618034 - 1.07047i) q^{15} +(2.54508 - 4.40822i) q^{17} +(1.61803 + 2.80252i) q^{19} -0.0901699 q^{21} +(3.30902 + 5.73139i) q^{23} +(-2.73607 + 4.73901i) q^{25} -2.23607 q^{27} +(-1.50000 + 2.59808i) q^{29} +(-0.263932 - 0.457144i) q^{33} +0.763932 q^{35} +(-0.927051 - 1.60570i) q^{37} +1.38197 q^{39} +0.527864 q^{41} +(6.50000 + 0.866025i) q^{43} +9.23607 q^{45} -7.85410 q^{47} +(3.47214 + 6.01392i) q^{49} -1.94427 q^{51} +(1.80902 + 3.13331i) q^{53} +(2.23607 + 3.87298i) q^{55} +(0.618034 - 1.07047i) q^{57} +6.09017 q^{59} +(1.92705 - 3.33775i) q^{61} +(-0.336881 - 0.583495i) q^{63} -11.7082 q^{65} +(1.42705 + 2.47172i) q^{67} +(1.26393 - 2.18919i) q^{69} +(6.89919 - 11.9497i) q^{71} +(2.42705 - 4.20378i) q^{73} +2.09017 q^{75} +(0.163119 - 0.282530i) q^{77} +(-1.80902 + 3.13331i) q^{79} +(-3.85410 - 6.67550i) q^{81} +(-6.51722 - 11.2882i) q^{83} +16.4721 q^{85} +1.14590 q^{87} +(-2.42705 - 4.20378i) q^{89} +(0.427051 + 0.739674i) q^{91} +(-5.23607 + 9.06914i) q^{95} -4.76393 q^{97} +(1.97214 - 3.41584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{3} + 2q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 4q - 3q^{3} + 2q^{5} - 4q^{7} - q^{9} + 10q^{11} - 5q^{13} - 2q^{15} - q^{17} + 2q^{19} + 22q^{21} + 11q^{23} - 2q^{25} - 6q^{29} - 10q^{33} + 12q^{35} + 3q^{37} + 10q^{39} + 20q^{41} + 26q^{43} + 28q^{45} - 18q^{47} - 4q^{49} + 28q^{51} + 5q^{53} - 2q^{57} + 2q^{59} + q^{61} - 17q^{63} - 20q^{65} - q^{67} + 14q^{69} + 3q^{71} + 3q^{73} - 14q^{75} - 15q^{77} - 5q^{79} - 2q^{81} + 3q^{83} + 48q^{85} + 18q^{87} - 3q^{89} - 5q^{91} - 12q^{95} - 28q^{97} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).

\(n\) \(431\) \(433\) \(517\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −0.190983 0.330792i −0.110264 0.190983i 0.805613 0.592443i \(-0.201836\pi\)
−0.915877 + 0.401460i \(0.868503\pi\)
\(4\) 0 0
\(5\) 1.61803 + 2.80252i 0.723607 + 1.25332i 0.959545 + 0.281556i \(0.0908504\pi\)
−0.235938 + 0.971768i \(0.575816\pi\)
\(6\) 0 0
\(7\) 0.118034 0.204441i 0.0446127 0.0772714i −0.842857 0.538138i \(-0.819128\pi\)
0.887469 + 0.460866i \(0.152461\pi\)
\(8\) 0 0
\(9\) 1.42705 2.47172i 0.475684 0.823908i
\(10\) 0 0
\(11\) 1.38197 0.416678 0.208339 0.978057i \(-0.433194\pi\)
0.208339 + 0.978057i \(0.433194\pi\)
\(12\) 0 0
\(13\) −1.80902 + 3.13331i −0.501731 + 0.869024i 0.498267 + 0.867024i \(0.333970\pi\)
−0.999998 + 0.00199999i \(0.999363\pi\)
\(14\) 0 0
\(15\) 0.618034 1.07047i 0.159576 0.276393i
\(16\) 0 0
\(17\) 2.54508 4.40822i 0.617274 1.06915i −0.372707 0.927949i \(-0.621570\pi\)
0.989981 0.141201i \(-0.0450962\pi\)
\(18\) 0 0
\(19\) 1.61803 + 2.80252i 0.371202 + 0.642942i 0.989751 0.142805i \(-0.0456123\pi\)
−0.618548 + 0.785747i \(0.712279\pi\)
\(20\) 0 0
\(21\) −0.0901699 −0.0196767
\(22\) 0 0
\(23\) 3.30902 + 5.73139i 0.689978 + 1.19508i 0.971845 + 0.235623i \(0.0757130\pi\)
−0.281867 + 0.959454i \(0.590954\pi\)
\(24\) 0 0
\(25\) −2.73607 + 4.73901i −0.547214 + 0.947802i
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) −0.263932 0.457144i −0.0459447 0.0795785i
\(34\) 0 0
\(35\) 0.763932 0.129128
\(36\) 0 0
\(37\) −0.927051 1.60570i −0.152406 0.263975i 0.779705 0.626147i \(-0.215369\pi\)
−0.932112 + 0.362171i \(0.882036\pi\)
\(38\) 0 0
\(39\) 1.38197 0.221292
\(40\) 0 0
\(41\) 0.527864 0.0824385 0.0412193 0.999150i \(-0.486876\pi\)
0.0412193 + 0.999150i \(0.486876\pi\)
\(42\) 0 0
\(43\) 6.50000 + 0.866025i 0.991241 + 0.132068i
\(44\) 0 0
\(45\) 9.23607 1.37683
\(46\) 0 0
\(47\) −7.85410 −1.14564 −0.572819 0.819682i \(-0.694150\pi\)
−0.572819 + 0.819682i \(0.694150\pi\)
\(48\) 0 0
\(49\) 3.47214 + 6.01392i 0.496019 + 0.859131i
\(50\) 0 0
\(51\) −1.94427 −0.272253
\(52\) 0 0
\(53\) 1.80902 + 3.13331i 0.248488 + 0.430393i 0.963106 0.269121i \(-0.0867331\pi\)
−0.714619 + 0.699514i \(0.753400\pi\)
\(54\) 0 0
\(55\) 2.23607 + 3.87298i 0.301511 + 0.522233i
\(56\) 0 0
\(57\) 0.618034 1.07047i 0.0818606 0.141787i
\(58\) 0 0
\(59\) 6.09017 0.792873 0.396436 0.918062i \(-0.370247\pi\)
0.396436 + 0.918062i \(0.370247\pi\)
\(60\) 0 0
\(61\) 1.92705 3.33775i 0.246734 0.427355i −0.715884 0.698219i \(-0.753976\pi\)
0.962618 + 0.270864i \(0.0873094\pi\)
\(62\) 0 0
\(63\) −0.336881 0.583495i −0.0424430 0.0735135i
\(64\) 0 0
\(65\) −11.7082 −1.45222
\(66\) 0 0
\(67\) 1.42705 + 2.47172i 0.174342 + 0.301969i 0.939933 0.341358i \(-0.110887\pi\)
−0.765591 + 0.643327i \(0.777553\pi\)
\(68\) 0 0
\(69\) 1.26393 2.18919i 0.152160 0.263548i
\(70\) 0 0
\(71\) 6.89919 11.9497i 0.818783 1.41817i −0.0877966 0.996138i \(-0.527983\pi\)
0.906580 0.422035i \(-0.138684\pi\)
\(72\) 0 0
\(73\) 2.42705 4.20378i 0.284065 0.492015i −0.688317 0.725410i \(-0.741650\pi\)
0.972382 + 0.233395i \(0.0749836\pi\)
\(74\) 0 0
\(75\) 2.09017 0.241352
\(76\) 0 0
\(77\) 0.163119 0.282530i 0.0185891 0.0321973i
\(78\) 0 0
\(79\) −1.80902 + 3.13331i −0.203530 + 0.352525i −0.949663 0.313272i \(-0.898575\pi\)
0.746133 + 0.665797i \(0.231908\pi\)
\(80\) 0 0
\(81\) −3.85410 6.67550i −0.428234 0.741722i
\(82\) 0 0
\(83\) −6.51722 11.2882i −0.715358 1.23904i −0.962821 0.270139i \(-0.912930\pi\)
0.247463 0.968897i \(-0.420403\pi\)
\(84\) 0 0
\(85\) 16.4721 1.78665
\(86\) 0 0
\(87\) 1.14590 0.122853
\(88\) 0 0
\(89\) −2.42705 4.20378i −0.257267 0.445599i 0.708242 0.705970i \(-0.249489\pi\)
−0.965509 + 0.260371i \(0.916155\pi\)
\(90\) 0 0
\(91\) 0.427051 + 0.739674i 0.0447671 + 0.0775389i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.23607 + 9.06914i −0.537209 + 0.930474i
\(96\) 0 0
\(97\) −4.76393 −0.483704 −0.241852 0.970313i \(-0.577755\pi\)
−0.241852 + 0.970313i \(0.577755\pi\)
\(98\) 0 0
\(99\) 1.97214 3.41584i 0.198207 0.343305i
\(100\) 0 0
\(101\) −4.11803 + 7.13264i −0.409760 + 0.709725i −0.994863 0.101234i \(-0.967721\pi\)
0.585103 + 0.810959i \(0.301054\pi\)
\(102\) 0 0
\(103\) 5.20820 9.02087i 0.513180 0.888853i −0.486704 0.873567i \(-0.661801\pi\)
0.999883 0.0152859i \(-0.00486585\pi\)
\(104\) 0 0
\(105\) −0.145898 0.252703i −0.0142382 0.0246613i
\(106\) 0 0
\(107\) −16.4721 −1.59242 −0.796211 0.605019i \(-0.793165\pi\)
−0.796211 + 0.605019i \(0.793165\pi\)
\(108\) 0 0
\(109\) 3.57295 + 6.18853i 0.342226 + 0.592754i 0.984846 0.173432i \(-0.0554857\pi\)
−0.642619 + 0.766186i \(0.722152\pi\)
\(110\) 0 0
\(111\) −0.354102 + 0.613323i −0.0336099 + 0.0582140i
\(112\) 0 0
\(113\) −13.3820 −1.25887 −0.629435 0.777053i \(-0.716714\pi\)
−0.629435 + 0.777053i \(0.716714\pi\)
\(114\) 0 0
\(115\) −10.7082 + 18.5472i −0.998545 + 1.72953i
\(116\) 0 0
\(117\) 5.16312 + 8.94278i 0.477331 + 0.826761i
\(118\) 0 0
\(119\) −0.600813 1.04064i −0.0550764 0.0953952i
\(120\) 0 0
\(121\) −9.09017 −0.826379
\(122\) 0 0
\(123\) −0.100813 0.174613i −0.00909001 0.0157444i
\(124\) 0 0
\(125\) −1.52786 −0.136656
\(126\) 0 0
\(127\) −16.6525 −1.47767 −0.738834 0.673887i \(-0.764623\pi\)
−0.738834 + 0.673887i \(0.764623\pi\)
\(128\) 0 0
\(129\) −0.954915 2.31555i −0.0840756 0.203872i
\(130\) 0 0
\(131\) 7.94427 0.694094 0.347047 0.937848i \(-0.387184\pi\)
0.347047 + 0.937848i \(0.387184\pi\)
\(132\) 0 0
\(133\) 0.763932 0.0662413
\(134\) 0 0
\(135\) −3.61803 6.26662i −0.311391 0.539345i
\(136\) 0 0
\(137\) −9.70820 −0.829428 −0.414714 0.909952i \(-0.636118\pi\)
−0.414714 + 0.909952i \(0.636118\pi\)
\(138\) 0 0
\(139\) −9.35410 16.2018i −0.793405 1.37422i −0.923847 0.382761i \(-0.874973\pi\)
0.130443 0.991456i \(-0.458360\pi\)
\(140\) 0 0
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) 0 0
\(143\) −2.50000 + 4.33013i −0.209061 + 0.362103i
\(144\) 0 0
\(145\) −9.70820 −0.806222
\(146\) 0 0
\(147\) 1.32624 2.29711i 0.109386 0.189463i
\(148\) 0 0
\(149\) −4.50000 7.79423i −0.368654 0.638528i 0.620701 0.784047i \(-0.286848\pi\)
−0.989355 + 0.145519i \(0.953515\pi\)
\(150\) 0 0
\(151\) 2.14590 0.174631 0.0873154 0.996181i \(-0.472171\pi\)
0.0873154 + 0.996181i \(0.472171\pi\)
\(152\) 0 0
\(153\) −7.26393 12.5815i −0.587254 1.01715i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.92705 10.2660i 0.473030 0.819312i −0.526493 0.850179i \(-0.676493\pi\)
0.999524 + 0.0308670i \(0.00982682\pi\)
\(158\) 0 0
\(159\) 0.690983 1.19682i 0.0547985 0.0949138i
\(160\) 0 0
\(161\) 1.56231 0.123127
\(162\) 0 0
\(163\) 7.00000 12.1244i 0.548282 0.949653i −0.450110 0.892973i \(-0.648615\pi\)
0.998392 0.0566798i \(-0.0180514\pi\)
\(164\) 0 0
\(165\) 0.854102 1.47935i 0.0664917 0.115167i
\(166\) 0 0
\(167\) 4.88197 + 8.45581i 0.377778 + 0.654330i 0.990739 0.135783i \(-0.0433550\pi\)
−0.612961 + 0.790113i \(0.710022\pi\)
\(168\) 0 0
\(169\) −0.0450850 0.0780895i −0.00346807 0.00600688i
\(170\) 0 0
\(171\) 9.23607 0.706300
\(172\) 0 0
\(173\) −8.23607 −0.626177 −0.313088 0.949724i \(-0.601364\pi\)
−0.313088 + 0.949724i \(0.601364\pi\)
\(174\) 0 0
\(175\) 0.645898 + 1.11873i 0.0488253 + 0.0845679i
\(176\) 0 0
\(177\) −1.16312 2.01458i −0.0874254 0.151425i
\(178\) 0 0
\(179\) −10.8262 + 18.7516i −0.809191 + 1.40156i 0.104234 + 0.994553i \(0.466761\pi\)
−0.913425 + 0.407007i \(0.866572\pi\)
\(180\) 0 0
\(181\) 10.8090 18.7218i 0.803428 1.39158i −0.113919 0.993490i \(-0.536341\pi\)
0.917347 0.398088i \(-0.130326\pi\)
\(182\) 0 0
\(183\) −1.47214 −0.108823
\(184\) 0 0
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 0 0
\(187\) 3.51722 6.09201i 0.257205 0.445492i
\(188\) 0 0
\(189\) −0.263932 + 0.457144i −0.0191982 + 0.0332523i
\(190\) 0 0
\(191\) −11.7361 20.3275i −0.849192 1.47084i −0.881930 0.471380i \(-0.843756\pi\)
0.0327382 0.999464i \(-0.489577\pi\)
\(192\) 0 0
\(193\) −10.7082 −0.770793 −0.385397 0.922751i \(-0.625935\pi\)
−0.385397 + 0.922751i \(0.625935\pi\)
\(194\) 0 0
\(195\) 2.23607 + 3.87298i 0.160128 + 0.277350i
\(196\) 0 0
\(197\) −7.47214 + 12.9421i −0.532368 + 0.922088i 0.466918 + 0.884301i \(0.345364\pi\)
−0.999286 + 0.0377873i \(0.987969\pi\)
\(198\) 0 0
\(199\) 15.9443 1.13026 0.565130 0.825002i \(-0.308826\pi\)
0.565130 + 0.825002i \(0.308826\pi\)
\(200\) 0 0
\(201\) 0.545085 0.944115i 0.0384473 0.0665927i
\(202\) 0 0
\(203\) 0.354102 + 0.613323i 0.0248531 + 0.0430468i
\(204\) 0 0
\(205\) 0.854102 + 1.47935i 0.0596531 + 0.103322i
\(206\) 0 0
\(207\) 18.8885 1.31284
\(208\) 0 0
\(209\) 2.23607 + 3.87298i 0.154672 + 0.267900i
\(210\) 0 0
\(211\) 4.76393 0.327963 0.163981 0.986463i \(-0.447566\pi\)
0.163981 + 0.986463i \(0.447566\pi\)
\(212\) 0 0
\(213\) −5.27051 −0.361129
\(214\) 0 0
\(215\) 8.09017 + 19.6176i 0.551745 + 1.33791i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −1.85410 −0.125289
\(220\) 0 0
\(221\) 9.20820 + 15.9491i 0.619411 + 1.07285i
\(222\) 0 0
\(223\) −7.23607 −0.484563 −0.242281 0.970206i \(-0.577896\pi\)
−0.242281 + 0.970206i \(0.577896\pi\)
\(224\) 0 0
\(225\) 7.80902 + 13.5256i 0.520601 + 0.901708i
\(226\) 0 0
\(227\) 3.73607 + 6.47106i 0.247972 + 0.429499i 0.962963 0.269634i \(-0.0869027\pi\)
−0.714991 + 0.699133i \(0.753569\pi\)
\(228\) 0 0
\(229\) 7.85410 13.6037i 0.519014 0.898958i −0.480742 0.876862i \(-0.659633\pi\)
0.999756 0.0220961i \(-0.00703396\pi\)
\(230\) 0 0
\(231\) −0.124612 −0.00819885
\(232\) 0 0
\(233\) 5.51722 9.55611i 0.361445 0.626041i −0.626754 0.779217i \(-0.715617\pi\)
0.988199 + 0.153176i \(0.0489501\pi\)
\(234\) 0 0
\(235\) −12.7082 22.0113i −0.828992 1.43586i
\(236\) 0 0
\(237\) 1.38197 0.0897683
\(238\) 0 0
\(239\) −10.8541 18.7999i −0.702093 1.21606i −0.967730 0.251988i \(-0.918916\pi\)
0.265637 0.964073i \(-0.414418\pi\)
\(240\) 0 0
\(241\) 14.6353 25.3490i 0.942740 1.63287i 0.182525 0.983201i \(-0.441573\pi\)
0.760215 0.649672i \(-0.225094\pi\)
\(242\) 0 0
\(243\) −4.82624 + 8.35929i −0.309603 + 0.536249i
\(244\) 0 0
\(245\) −11.2361 + 19.4614i −0.717846 + 1.24335i
\(246\) 0 0
\(247\) −11.7082 −0.744975
\(248\) 0 0
\(249\) −2.48936 + 4.31169i −0.157757 + 0.273242i
\(250\) 0 0
\(251\) −3.40983 + 5.90600i −0.215227 + 0.372783i −0.953343 0.301890i \(-0.902382\pi\)
0.738116 + 0.674674i \(0.235716\pi\)
\(252\) 0 0
\(253\) 4.57295 + 7.92058i 0.287499 + 0.497963i
\(254\) 0 0
\(255\) −3.14590 5.44886i −0.197004 0.341221i
\(256\) 0 0
\(257\) 23.5623 1.46978 0.734888 0.678188i \(-0.237235\pi\)
0.734888 + 0.678188i \(0.237235\pi\)
\(258\) 0 0
\(259\) −0.437694 −0.0271970
\(260\) 0 0
\(261\) 4.28115 + 7.41517i 0.264997 + 0.458988i
\(262\) 0 0
\(263\) −5.25329 9.09896i −0.323932 0.561066i 0.657364 0.753573i \(-0.271671\pi\)
−0.981296 + 0.192507i \(0.938338\pi\)
\(264\) 0 0
\(265\) −5.85410 + 10.1396i −0.359615 + 0.622871i
\(266\) 0 0
\(267\) −0.927051 + 1.60570i −0.0567346 + 0.0982672i
\(268\) 0 0
\(269\) −8.56231 −0.522053 −0.261027 0.965332i \(-0.584061\pi\)
−0.261027 + 0.965332i \(0.584061\pi\)
\(270\) 0 0
\(271\) 3.57295 6.18853i 0.217041 0.375926i −0.736861 0.676044i \(-0.763693\pi\)
0.953902 + 0.300118i \(0.0970261\pi\)
\(272\) 0 0
\(273\) 0.163119 0.282530i 0.00987241 0.0170995i
\(274\) 0 0
\(275\) −3.78115 + 6.54915i −0.228012 + 0.394929i
\(276\) 0 0
\(277\) 1.76393 + 3.05522i 0.105984 + 0.183570i 0.914140 0.405399i \(-0.132867\pi\)
−0.808156 + 0.588969i \(0.799534\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.736068 + 1.27491i 0.0439101 + 0.0760546i 0.887145 0.461490i \(-0.152685\pi\)
−0.843235 + 0.537545i \(0.819352\pi\)
\(282\) 0 0
\(283\) 7.61803 13.1948i 0.452845 0.784351i −0.545716 0.837970i \(-0.683742\pi\)
0.998561 + 0.0536192i \(0.0170757\pi\)
\(284\) 0 0
\(285\) 4.00000 0.236940
\(286\) 0 0
\(287\) 0.0623059 0.107917i 0.00367780 0.00637014i
\(288\) 0 0
\(289\) −4.45492 7.71614i −0.262054 0.453891i
\(290\) 0 0
\(291\) 0.909830 + 1.57587i 0.0533352 + 0.0923792i
\(292\) 0 0
\(293\) −0.909830 −0.0531528 −0.0265764 0.999647i \(-0.508461\pi\)
−0.0265764 + 0.999647i \(0.508461\pi\)
\(294\) 0 0
\(295\) 9.85410 + 17.0678i 0.573728 + 0.993726i
\(296\) 0 0
\(297\) −3.09017 −0.179310
\(298\) 0 0
\(299\) −23.9443 −1.38473
\(300\) 0 0
\(301\) 0.944272 1.22665i 0.0544269 0.0707027i
\(302\) 0 0
\(303\) 3.14590 0.180727
\(304\) 0 0
\(305\) 12.4721 0.714152
\(306\) 0 0
\(307\) 14.1074 + 24.4347i 0.805151 + 1.39456i 0.916189 + 0.400747i \(0.131249\pi\)
−0.111038 + 0.993816i \(0.535417\pi\)
\(308\) 0 0
\(309\) −3.97871 −0.226341
\(310\) 0 0
\(311\) 11.9164 + 20.6398i 0.675717 + 1.17038i 0.976259 + 0.216608i \(0.0694994\pi\)
−0.300541 + 0.953769i \(0.597167\pi\)
\(312\) 0 0
\(313\) 13.5623 + 23.4906i 0.766587 + 1.32777i 0.939404 + 0.342813i \(0.111380\pi\)
−0.172817 + 0.984954i \(0.555287\pi\)
\(314\) 0 0
\(315\) 1.09017 1.88823i 0.0614241 0.106390i
\(316\) 0 0
\(317\) −29.3050 −1.64593 −0.822965 0.568092i \(-0.807682\pi\)
−0.822965 + 0.568092i \(0.807682\pi\)
\(318\) 0 0
\(319\) −2.07295 + 3.59045i −0.116063 + 0.201027i
\(320\) 0 0
\(321\) 3.14590 + 5.44886i 0.175587 + 0.304125i
\(322\) 0 0
\(323\) 16.4721 0.916534
\(324\) 0 0
\(325\) −9.89919 17.1459i −0.549108 0.951083i
\(326\) 0 0
\(327\) 1.36475 2.36381i 0.0754706 0.130719i
\(328\) 0 0
\(329\) −0.927051 + 1.60570i −0.0511100 + 0.0885251i
\(330\) 0 0
\(331\) 1.73607 3.00696i 0.0954229 0.165277i −0.814362 0.580357i \(-0.802913\pi\)
0.909785 + 0.415080i \(0.136246\pi\)
\(332\) 0 0
\(333\) −5.29180 −0.289989
\(334\) 0 0
\(335\) −4.61803 + 7.99867i −0.252310 + 0.437014i
\(336\) 0 0
\(337\) −14.0000 + 24.2487i −0.762629 + 1.32091i 0.178863 + 0.983874i \(0.442758\pi\)
−0.941491 + 0.337037i \(0.890575\pi\)
\(338\) 0 0
\(339\) 2.55573 + 4.42665i 0.138808 + 0.240423i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 3.29180 0.177740
\(344\) 0 0
\(345\) 8.18034 0.440415
\(346\) 0 0
\(347\) −0.545085 0.944115i −0.0292617 0.0506827i 0.851024 0.525127i \(-0.175982\pi\)
−0.880285 + 0.474445i \(0.842649\pi\)
\(348\) 0 0
\(349\) −3.64590 6.31488i −0.195160 0.338028i 0.751793 0.659400i \(-0.229189\pi\)
−0.946953 + 0.321372i \(0.895856\pi\)
\(350\) 0 0
\(351\) 4.04508 7.00629i 0.215911 0.373968i
\(352\) 0 0
\(353\) 6.38197 11.0539i 0.339678 0.588339i −0.644694 0.764441i \(-0.723015\pi\)
0.984372 + 0.176101i \(0.0563486\pi\)
\(354\) 0 0
\(355\) 44.6525 2.36991
\(356\) 0 0
\(357\) −0.229490 + 0.397489i −0.0121459 + 0.0210373i
\(358\) 0 0
\(359\) −18.3262 + 31.7420i −0.967222 + 1.67528i −0.263699 + 0.964605i \(0.584942\pi\)
−0.703523 + 0.710672i \(0.748391\pi\)
\(360\) 0 0
\(361\) 4.26393 7.38535i 0.224417 0.388702i
\(362\) 0 0
\(363\) 1.73607 + 3.00696i 0.0911199 + 0.157824i
\(364\) 0 0
\(365\) 15.7082 0.822205
\(366\) 0 0
\(367\) −1.59017 2.75426i −0.0830062 0.143771i 0.821534 0.570160i \(-0.193119\pi\)
−0.904540 + 0.426389i \(0.859785\pi\)
\(368\) 0 0
\(369\) 0.753289 1.30473i 0.0392147 0.0679218i
\(370\) 0 0
\(371\) 0.854102 0.0443428
\(372\) 0 0
\(373\) −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) 0 0
\(375\) 0.291796 + 0.505406i 0.0150683 + 0.0260990i
\(376\) 0 0
\(377\) −5.42705 9.39993i −0.279507 0.484121i
\(378\) 0 0
\(379\) −17.3607 −0.891758 −0.445879 0.895093i \(-0.647109\pi\)
−0.445879 + 0.895093i \(0.647109\pi\)
\(380\) 0 0
\(381\) 3.18034 + 5.50851i 0.162934 + 0.282210i
\(382\) 0 0
\(383\) 2.12461 0.108563 0.0542813 0.998526i \(-0.482713\pi\)
0.0542813 + 0.998526i \(0.482713\pi\)
\(384\) 0 0
\(385\) 1.05573 0.0538049
\(386\) 0 0
\(387\) 11.4164 14.8303i 0.580329 0.753869i
\(388\) 0 0
\(389\) 23.0689 1.16964 0.584819 0.811164i \(-0.301165\pi\)
0.584819 + 0.811164i \(0.301165\pi\)
\(390\) 0 0
\(391\) 33.6869 1.70362
\(392\) 0 0
\(393\) −1.51722 2.62790i −0.0765337 0.132560i
\(394\) 0 0
\(395\) −11.7082 −0.589104
\(396\) 0 0
\(397\) −2.79180 4.83553i −0.140116 0.242688i 0.787424 0.616412i \(-0.211414\pi\)
−0.927540 + 0.373723i \(0.878081\pi\)
\(398\) 0 0
\(399\) −0.145898 0.252703i −0.00730404 0.0126510i
\(400\) 0 0
\(401\) −0.708204 + 1.22665i −0.0353660 + 0.0612557i −0.883167 0.469059i \(-0.844593\pi\)
0.847801 + 0.530315i \(0.177926\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 12.4721 21.6024i 0.619745 1.07343i
\(406\) 0 0
\(407\) −1.28115 2.21902i −0.0635044 0.109993i
\(408\) 0 0
\(409\) 20.0902 0.993395 0.496697 0.867924i \(-0.334546\pi\)
0.496697 + 0.867924i \(0.334546\pi\)
\(410\) 0 0
\(411\) 1.85410 + 3.21140i 0.0914561 + 0.158407i
\(412\) 0 0
\(413\) 0.718847 1.24508i 0.0353722 0.0612664i
\(414\) 0 0
\(415\) 21.0902 36.5292i 1.03528 1.79315i
\(416\) 0 0
\(417\) −3.57295 + 6.18853i −0.174968 + 0.303054i
\(418\) 0 0
\(419\) 5.76393 0.281587 0.140793 0.990039i \(-0.455035\pi\)
0.140793 + 0.990039i \(0.455035\pi\)
\(420\) 0 0
\(421\) −11.8262 + 20.4836i −0.576376 + 0.998312i 0.419515 + 0.907748i \(0.362200\pi\)
−0.995891 + 0.0905634i \(0.971133\pi\)
\(422\) 0 0
\(423\) −11.2082 + 19.4132i −0.544962 + 0.943901i
\(424\) 0 0
\(425\) 13.9271 + 24.1224i 0.675561 + 1.17011i
\(426\) 0 0
\(427\) −0.454915 0.787936i −0.0220149 0.0381309i
\(428\) 0 0
\(429\) 1.90983 0.0922075
\(430\) 0 0
\(431\) 0.201626 0.00971199 0.00485599 0.999988i \(-0.498454\pi\)
0.00485599 + 0.999988i \(0.498454\pi\)
\(432\) 0 0
\(433\) 10.6459 + 18.4392i 0.511609 + 0.886133i 0.999909 + 0.0134574i \(0.00428377\pi\)
−0.488300 + 0.872676i \(0.662383\pi\)
\(434\) 0 0
\(435\) 1.85410 + 3.21140i 0.0888974 + 0.153975i
\(436\) 0 0
\(437\) −10.7082 + 18.5472i −0.512243 + 0.887231i
\(438\) 0 0
\(439\) 3.92705 6.80185i 0.187428 0.324635i −0.756964 0.653457i \(-0.773318\pi\)
0.944392 + 0.328822i \(0.106652\pi\)
\(440\) 0 0
\(441\) 19.8197 0.943793
\(442\) 0 0
\(443\) −3.23607 + 5.60503i −0.153750 + 0.266303i −0.932603 0.360903i \(-0.882468\pi\)
0.778853 + 0.627206i \(0.215802\pi\)
\(444\) 0 0
\(445\) 7.85410 13.6037i 0.372320 0.644877i
\(446\) 0 0
\(447\) −1.71885 + 2.97713i −0.0812987 + 0.140813i
\(448\) 0 0
\(449\) −10.4164 18.0417i −0.491581 0.851443i 0.508372 0.861137i \(-0.330247\pi\)
−0.999953 + 0.00969466i \(0.996914\pi\)
\(450\) 0 0
\(451\) 0.729490 0.0343504
\(452\) 0 0
\(453\) −0.409830 0.709846i −0.0192555 0.0333515i
\(454\) 0 0
\(455\) −1.38197 + 2.39364i −0.0647876 + 0.112215i
\(456\) 0 0
\(457\) −2.29180 −0.107206 −0.0536028 0.998562i \(-0.517070\pi\)
−0.0536028 + 0.998562i \(0.517070\pi\)
\(458\) 0 0
\(459\) −5.69098 + 9.85707i −0.265632 + 0.460089i
\(460\) 0 0
\(461\) −8.79837 15.2392i −0.409781 0.709762i 0.585084 0.810973i \(-0.301062\pi\)
−0.994865 + 0.101211i \(0.967728\pi\)
\(462\) 0 0
\(463\) 11.9164 + 20.6398i 0.553802 + 0.959214i 0.997996 + 0.0632829i \(0.0201571\pi\)
−0.444193 + 0.895931i \(0.646510\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.4721 28.5306i −0.762240 1.32024i −0.941694 0.336471i \(-0.890766\pi\)
0.179454 0.983766i \(-0.442567\pi\)
\(468\) 0 0
\(469\) 0.673762 0.0311114
\(470\) 0 0
\(471\) −4.52786 −0.208633
\(472\) 0 0
\(473\) 8.98278 + 1.19682i 0.413029 + 0.0550297i
\(474\) 0 0
\(475\) −17.7082 −0.812508
\(476\) 0 0
\(477\) 10.3262 0.472806
\(478\) 0 0
\(479\) −18.0902 31.3331i −0.826561 1.43165i −0.900720 0.434399i \(-0.856961\pi\)
0.0741595 0.997246i \(-0.476373\pi\)
\(480\) 0 0
\(481\) 6.70820 0.305868
\(482\) 0 0
\(483\) −0.298374 0.516799i −0.0135765 0.0235152i
\(484\) 0 0
\(485\) −7.70820 13.3510i −0.350012 0.606238i
\(486\) 0 0
\(487\) −7.16312 + 12.4069i −0.324592 + 0.562210i −0.981430 0.191822i \(-0.938560\pi\)
0.656838 + 0.754032i \(0.271894\pi\)
\(488\) 0 0
\(489\) −5.34752 −0.241823
\(490\) 0 0
\(491\) −4.82624 + 8.35929i −0.217805 + 0.377249i −0.954137 0.299371i \(-0.903223\pi\)
0.736332 + 0.676621i \(0.236556\pi\)
\(492\) 0 0
\(493\) 7.63525 + 13.2246i 0.343875 + 0.595608i
\(494\) 0 0
\(495\) 12.7639 0.573696
\(496\) 0 0
\(497\) −1.62868 2.82095i −0.0730562 0.126537i
\(498\) 0 0
\(499\) 3.57295 6.18853i 0.159947 0.277037i −0.774902 0.632081i \(-0.782201\pi\)
0.934849 + 0.355044i \(0.115534\pi\)
\(500\) 0 0
\(501\) 1.86475 3.22983i 0.0833107 0.144298i
\(502\) 0 0
\(503\) −2.26393 + 3.92125i −0.100944 + 0.174840i −0.912074 0.410026i \(-0.865520\pi\)
0.811130 + 0.584866i \(0.198853\pi\)
\(504\) 0 0
\(505\) −26.6525 −1.18602
\(506\) 0 0
\(507\) −0.0172209 + 0.0298275i −0.000764808 + 0.00132469i
\(508\) 0 0
\(509\) −2.64590 + 4.58283i −0.117277 + 0.203130i −0.918688 0.394984i \(-0.870750\pi\)
0.801410 + 0.598115i \(0.204083\pi\)
\(510\) 0 0
\(511\) −0.572949 0.992377i −0.0253458 0.0439002i
\(512\) 0 0
\(513\) −3.61803 6.26662i −0.159740 0.276678i
\(514\) 0 0
\(515\) 33.7082 1.48536
\(516\) 0 0
\(517\) −10.8541 −0.477363
\(518\) 0 0
\(519\) 1.57295 + 2.72443i 0.0690448 + 0.119589i
\(520\) 0 0
\(521\) −3.51722 6.09201i −0.154092 0.266896i 0.778636 0.627476i \(-0.215912\pi\)
−0.932728 + 0.360580i \(0.882579\pi\)
\(522\) 0 0
\(523\) −8.91641 + 15.4437i −0.389887 + 0.675305i −0.992434 0.122779i \(-0.960819\pi\)
0.602547 + 0.798084i \(0.294153\pi\)
\(524\) 0 0
\(525\) 0.246711 0.427316i 0.0107674 0.0186496i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −10.3992 + 18.0119i −0.452139 + 0.783127i
\(530\) 0 0
\(531\) 8.69098 15.0532i 0.377157 0.653254i
\(532\) 0 0
\(533\) −0.954915 + 1.65396i −0.0413620 + 0.0716410i
\(534\) 0 0
\(535\) −26.6525 46.1634i −1.15229 1.99582i
\(536\) 0 0
\(537\) 8.27051 0.356899
\(538\) 0 0
\(539\) 4.79837 + 8.31103i 0.206681 + 0.357981i
\(540\) 0 0
\(541\) 10.0279 17.3688i 0.431132 0.746742i −0.565839 0.824515i \(-0.691448\pi\)
0.996971 + 0.0777737i \(0.0247812\pi\)
\(542\) 0 0
\(543\) −8.25735 −0.354357
\(544\) 0 0
\(545\) −11.5623 + 20.0265i −0.495275 + 0.857841i
\(546\) 0 0
\(547\) 10.5000 + 18.1865i 0.448948 + 0.777600i 0.998318 0.0579790i \(-0.0184657\pi\)
−0.549370 + 0.835579i \(0.685132\pi\)
\(548\) 0 0
\(549\) −5.50000 9.52628i −0.234734 0.406572i
\(550\) 0 0
\(551\) −9.70820 −0.413583
\(552\) 0 0
\(553\) 0.427051 + 0.739674i 0.0181601 + 0.0314541i
\(554\) 0 0
\(555\) −2.29180 −0.0972813
\(556\) 0 0
\(557\) −18.4377 −0.781230 −0.390615 0.920554i \(-0.627738\pi\)
−0.390615 + 0.920554i \(0.627738\pi\)
\(558\) 0 0
\(559\) −14.4721 + 18.7999i −0.612106 + 0.795149i
\(560\) 0 0
\(561\) −2.68692 −0.113442
\(562\) 0 0
\(563\) −14.3262 −0.603779 −0.301889 0.953343i \(-0.597617\pi\)
−0.301889 + 0.953343i \(0.597617\pi\)
\(564\) 0 0
\(565\) −21.6525 37.5032i −0.910927 1.57777i
\(566\) 0 0
\(567\) −1.81966 −0.0764185
\(568\) 0 0
\(569\) 4.02786 + 6.97647i 0.168857 + 0.292469i 0.938018 0.346586i \(-0.112659\pi\)
−0.769161 + 0.639055i \(0.779326\pi\)
\(570\) 0 0
\(571\) −10.4098 18.0304i −0.435638 0.754547i 0.561710 0.827334i \(-0.310144\pi\)
−0.997347 + 0.0727876i \(0.976810\pi\)
\(572\) 0 0
\(573\) −4.48278 + 7.76440i −0.187271 + 0.324363i
\(574\) 0 0
\(575\) −36.2148 −1.51026
\(576\) 0 0
\(577\) −11.6074 + 20.1046i −0.483222 + 0.836965i −0.999814 0.0192664i \(-0.993867\pi\)
0.516592 + 0.856231i \(0.327200\pi\)
\(578\) 0 0
\(579\) 2.04508 + 3.54219i 0.0849908 + 0.147208i
\(580\) 0 0
\(581\) −3.07701 −0.127656
\(582\) 0 0
\(583\) 2.50000 + 4.33013i 0.103539 + 0.179336i
\(584\) 0 0
\(585\) −16.7082 + 28.9395i −0.690799 + 1.19650i
\(586\) 0 0
\(587\) −13.3713 + 23.1598i −0.551894 + 0.955908i 0.446244 + 0.894911i \(0.352761\pi\)
−0.998138 + 0.0609966i \(0.980572\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 5.70820 0.234804
\(592\) 0 0
\(593\) 10.7639 18.6437i 0.442022 0.765604i −0.555818 0.831304i \(-0.687595\pi\)
0.997839 + 0.0657001i \(0.0209281\pi\)
\(594\) 0 0
\(595\) 1.94427 3.36758i 0.0797074 0.138057i
\(596\) 0 0
\(597\) −3.04508 5.27424i −0.124627 0.215860i
\(598\) 0 0
\(599\) 15.8820 + 27.5084i 0.648920 + 1.12396i 0.983381 + 0.181552i \(0.0581122\pi\)
−0.334462 + 0.942409i \(0.608555\pi\)
\(600\) 0 0
\(601\) 2.58359 0.105387 0.0526935 0.998611i \(-0.483219\pi\)
0.0526935 + 0.998611i \(0.483219\pi\)
\(602\) 0 0
\(603\) 8.14590 0.331727
\(604\) 0 0
\(605\) −14.7082 25.4754i −0.597974 1.03572i
\(606\) 0 0
\(607\) −8.57295 14.8488i −0.347965 0.602694i 0.637923 0.770100i \(-0.279794\pi\)
−0.985888 + 0.167407i \(0.946461\pi\)
\(608\) 0 0
\(609\) 0.135255 0.234268i 0.00548081 0.00949303i
\(610\) 0 0
\(611\) 14.2082 24.6093i 0.574802 0.995587i
\(612\) 0 0
\(613\) 29.7984 1.20354 0.601772 0.798668i \(-0.294461\pi\)
0.601772 + 0.798668i \(0.294461\pi\)
\(614\) 0 0
\(615\) 0.326238 0.565061i 0.0131552 0.0227854i
\(616\) 0 0
\(617\) 1.85410 3.21140i 0.0746433 0.129286i −0.826288 0.563248i \(-0.809552\pi\)
0.900931 + 0.433962i \(0.142885\pi\)
\(618\) 0 0
\(619\) 1.63525 2.83234i 0.0657264 0.113842i −0.831290 0.555840i \(-0.812397\pi\)
0.897016 + 0.441998i \(0.145730\pi\)
\(620\) 0 0
\(621\) −7.39919 12.8158i −0.296919 0.514279i
\(622\) 0 0
\(623\) −1.14590 −0.0459094
\(624\) 0 0
\(625\) 11.2082 + 19.4132i 0.448328 + 0.776527i
\(626\) 0 0
\(627\) 0.854102 1.47935i 0.0341095 0.0590795i
\(628\) 0 0
\(629\) −9.43769 −0.376306
\(630\) 0 0
\(631\) −7.95492 + 13.7783i −0.316680 + 0.548506i −0.979793 0.200013i \(-0.935902\pi\)
0.663113 + 0.748519i \(0.269235\pi\)
\(632\) 0 0
\(633\) −0.909830 1.57587i −0.0361625 0.0626353i
\(634\) 0 0
\(635\) −26.9443 46.6688i −1.06925 1.85200i
\(636\) 0 0
\(637\) −25.1246 −0.995473
\(638\) 0 0
\(639\) −19.6910 34.1058i −0.778963 1.34920i
\(640\) 0 0
\(641\) 33.1803 1.31054 0.655272 0.755393i \(-0.272554\pi\)
0.655272 + 0.755393i \(0.272554\pi\)
\(642\) 0 0
\(643\) −29.5623 −1.16582 −0.582912 0.812535i \(-0.698087\pi\)
−0.582912 + 0.812535i \(0.698087\pi\)
\(644\) 0 0
\(645\) 4.94427 6.42280i 0.194681 0.252897i
\(646\) 0 0
\(647\) 37.3262 1.46745 0.733723 0.679449i \(-0.237781\pi\)
0.733723 + 0.679449i \(0.237781\pi\)
\(648\) 0 0
\(649\) 8.41641 0.330373
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.88854 0.113037 0.0565187 0.998402i \(-0.482000\pi\)
0.0565187 + 0.998402i \(0.482000\pi\)
\(654\) 0 0
\(655\) 12.8541 + 22.2640i 0.502251 + 0.869925i
\(656\) 0 0
\(657\) −6.92705 11.9980i −0.270250 0.468087i
\(658\) 0 0
\(659\) 7.68034 13.3027i 0.299184 0.518201i −0.676766 0.736198i \(-0.736619\pi\)
0.975949 + 0.217997i \(0.0699524\pi\)
\(660\) 0 0
\(661\) 30.3951 1.18223 0.591117 0.806586i \(-0.298687\pi\)
0.591117 + 0.806586i \(0.298687\pi\)
\(662\) 0 0
\(663\) 3.51722 6.09201i 0.136598 0.236594i
\(664\) 0 0
\(665\) 1.23607 + 2.14093i 0.0479327 + 0.0830218i
\(666\) 0 0
\(667\) −19.8541 −0.768754
\(668\) 0 0
\(669\) 1.38197 + 2.39364i 0.0534299 + 0.0925433i
\(670\) 0 0
\(671\) 2.66312 4.61266i 0.102809 0.178070i
\(672\) 0 0
\(673\) 19.9164 34.4962i 0.767721 1.32973i −0.171075 0.985258i \(-0.554724\pi\)
0.938796 0.344474i \(-0.111943\pi\)
\(674\) 0 0
\(675\) 6.11803 10.5967i 0.235483 0.407869i
\(676\) 0 0
\(677\) −36.2361 −1.39267 −0.696333 0.717719i \(-0.745186\pi\)
−0.696333 + 0.717719i \(0.745186\pi\)
\(678\) 0 0
\(679\) −0.562306 + 0.973942i −0.0215793 + 0.0373765i
\(680\) 0 0
\(681\) 1.42705 2.47172i 0.0546847 0.0947167i
\(682\) 0 0
\(683\) 14.5623 + 25.2227i 0.557211 + 0.965118i 0.997728 + 0.0673736i \(0.0214619\pi\)
−0.440517 + 0.897744i \(0.645205\pi\)
\(684\) 0 0
\(685\) −15.7082 27.2074i −0.600180 1.03954i
\(686\) 0 0
\(687\) −6.00000 −0.228914
\(688\) 0 0
\(689\) −13.0902 −0.498696
\(690\) 0 0
\(691\) 24.6353 + 42.6695i 0.937169 + 1.62322i 0.770719 + 0.637175i \(0.219897\pi\)
0.166450 + 0.986050i \(0.446770\pi\)
\(692\) 0 0
\(693\) −0.465558 0.806370i −0.0176851 0.0306315i
\(694\) 0 0
\(695\) 30.2705 52.4301i 1.14823 1.98879i
\(696\) 0 0
\(697\) 1.34346 2.32694i 0.0508871 0.0881391i
\(698\) 0 0
\(699\) −4.21478 −0.159418
\(700\) 0 0
\(701\) −11.7533 + 20.3573i −0.443916 + 0.768884i −0.997976 0.0635921i \(-0.979744\pi\)
0.554060 + 0.832476i \(0.313078\pi\)
\(702\) 0 0
\(703\) 3.00000 5.19615i 0.113147 0.195977i
\(704\) 0 0
\(705\) −4.85410 + 8.40755i −0.182816 + 0.316647i
\(706\) 0 0
\(707\) 0.972136 + 1.68379i 0.0365609 + 0.0633254i
\(708\) 0 0
\(709\) −6.88854 −0.258705 −0.129352 0.991599i \(-0.541290\pi\)
−0.129352 + 0.991599i \(0.541290\pi\)
\(710\) 0 0
\(711\) 5.16312 + 8.94278i 0.193632 + 0.335381i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −16.1803 −0.605110
\(716\) 0 0
\(717\) −4.14590 + 7.18091i −0.154831 + 0.268176i
\(718\) 0 0
\(719\) 6.89919 + 11.9497i 0.257296 + 0.445650i 0.965517 0.260341i \(-0.0838350\pi\)
−0.708220 + 0.705991i \(0.750502\pi\)
\(720\) 0 0
\(721\) −1.22949 2.12954i −0.0457886 0.0793082i
\(722\) 0 0
\(723\) −11.1803 −0.415801
\(724\) 0 0
\(725\) −8.20820 14.2170i −0.304845 0.528007i
\(726\) 0 0
\(727\) −28.9787 −1.07476 −0.537381 0.843340i \(-0.680586\pi\)
−0.537381 + 0.843340i \(0.680586\pi\)
\(728\) 0 0
\(729\) −19.4377 −0.719915
\(730\) 0 0
\(731\) 20.3607 26.4493i 0.753067 0.978263i
\(732\) 0 0
\(733\) −42.5410 −1.57129 −0.785644 0.618679i \(-0.787668\pi\)
−0.785644 + 0.618679i \(0.787668\pi\)
\(734\) 0 0
\(735\) 8.58359 0.316611
\(736\) 0 0
\(737\) 1.97214 + 3.41584i 0.0726446 + 0.125824i
\(738\) 0 0
\(739\) 17.5410 0.645257 0.322628 0.946526i \(-0.395434\pi\)
0.322628 + 0.946526i \(0.395434\pi\)
\(740\) 0 0
\(741\) 2.23607 + 3.87298i 0.0821440 + 0.142278i
\(742\) 0 0
\(743\) −5.68034 9.83864i −0.208391 0.360945i 0.742817 0.669495i \(-0.233489\pi\)
−0.951208 + 0.308550i \(0.900156\pi\)
\(744\) 0 0
\(745\) 14.5623 25.2227i 0.533522 0.924087i
\(746\) 0 0
\(747\) −37.2016 −1.36114
\(748\) 0 0
\(749\) −1.94427 + 3.36758i −0.0710421 + 0.123049i
\(750\) 0 0
\(751\) 4.48936 + 7.77579i 0.163819 + 0.283743i 0.936235 0.351374i \(-0.114285\pi\)
−0.772416 + 0.635117i \(0.780952\pi\)
\(752\) 0 0
\(753\) 2.60488 0.0949270
\(754\) 0 0
\(755\) 3.47214 + 6.01392i 0.126364 + 0.218869i
\(756\) 0 0
\(757\) −7.98936 + 13.8380i −0.290378 + 0.502950i −0.973899 0.226981i \(-0.927114\pi\)
0.683521 + 0.729931i \(0.260448\pi\)
\(758\) 0 0
\(759\) 1.74671 3.02539i 0.0634016 0.109815i
\(760\) 0 0
\(761\) 5.04508 8.73834i 0.182884 0.316765i −0.759977 0.649950i \(-0.774790\pi\)
0.942862 + 0.333185i \(0.108123\pi\)
\(762\) 0 0
\(763\) 1.68692 0.0610705
\(764\) 0 0
\(765\) 23.5066 40.7146i 0.849882 1.47204i
\(766\) 0 0
\(767\) −11.0172 + 19.0824i −0.397809 + 0.689025i
\(768\) 0 0
\(769\) 7.94427 + 13.7599i 0.286478 + 0.496194i 0.972966 0.230946i \(-0.0741822\pi\)
−0.686489 + 0.727140i \(0.740849\pi\)
\(770\) 0 0
\(771\) −4.50000 7.79423i −0.162064 0.280702i
\(772\) 0 0
\(773\) −33.5967 −1.20839 −0.604196 0.796836i \(-0.706505\pi\)
−0.604196 + 0.796836i \(0.706505\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0.0835921 + 0.144786i 0.00299885 + 0.00519416i
\(778\) 0 0
\(779\) 0.854102 + 1.47935i 0.0306014 + 0.0530031i
\(780\) 0 0
\(781\) 9.53444 16.5141i 0.341169 0.590922i
\(782\) 0 0
\(783\) 3.35410 5.80948i 0.119866 0.207614i
\(784\) 0 0
\(785\) 38.3607 1.36915
\(786\) 0 0
\(787\) −22.7254 + 39.3616i −0.810074 + 1.40309i 0.102738 + 0.994708i \(0.467240\pi\)
−0.912812 + 0.408381i \(0.866094\pi\)
\(788\) 0 0
\(789\) −2.00658 + 3.47549i −0.0714361 + 0.123731i
\(790\) 0 0
\(791\) −1.57953 + 2.73582i −0.0561615 + 0.0972746i
\(792\) 0 0
\(793\) 6.97214 + 12.0761i 0.247588 + 0.428835i
\(794\) 0 0
\(795\) 4.47214 0.158610
\(796\) 0 0
\(797\) 1.88197 + 3.25966i 0.0666627 + 0.115463i 0.897430 0.441156i \(-0.145432\pi\)
−0.830768 + 0.556619i \(0.812098\pi\)
\(798\) 0 0
\(799\) −19.9894 + 34.6226i −0.707173 + 1.22486i
\(800\) 0 0
\(801\) −13.8541 −0.489511
\(802\) 0 0
\(803\) 3.35410 5.80948i 0.118364 0.205012i
\(804\) 0 0
\(805\) 2.52786 + 4.37839i 0.0890955 + 0.154318i
\(806\) 0