Properties

Label 1680.2.f.e.881.3
Level $1680$
Weight $2$
Character 1680.881
Analytic conductor $13.415$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{5})\)
Defining polynomial: \(x^{4} + 3 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 881.3
Root \(-0.618034i\) of defining polynomial
Character \(\chi\) \(=\) 1680.881
Dual form 1680.2.f.e.881.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.618034 - 1.61803i) q^{3} -1.00000 q^{5} +(-0.381966 - 2.61803i) q^{7} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\) \(q+(0.618034 - 1.61803i) q^{3} -1.00000 q^{5} +(-0.381966 - 2.61803i) q^{7} +(-2.23607 - 2.00000i) q^{9} -4.47214i q^{11} +3.23607i q^{13} +(-0.618034 + 1.61803i) q^{15} -0.763932 q^{17} +0.472136i q^{19} +(-4.47214 - 1.00000i) q^{21} -4.00000i q^{23} +1.00000 q^{25} +(-4.61803 + 2.38197i) q^{27} -5.70820i q^{29} +7.23607i q^{31} +(-7.23607 - 2.76393i) q^{33} +(0.381966 + 2.61803i) q^{35} +5.23607 q^{37} +(5.23607 + 2.00000i) q^{39} -6.47214 q^{41} -12.9443 q^{43} +(2.23607 + 2.00000i) q^{45} +2.47214 q^{47} +(-6.70820 + 2.00000i) q^{49} +(-0.472136 + 1.23607i) q^{51} +8.47214i q^{53} +4.47214i q^{55} +(0.763932 + 0.291796i) q^{57} -4.47214 q^{59} +2.76393i q^{61} +(-4.38197 + 6.61803i) q^{63} -3.23607i q^{65} +12.0000 q^{67} +(-6.47214 - 2.47214i) q^{69} -2.76393i q^{71} -6.76393i q^{73} +(0.618034 - 1.61803i) q^{75} +(-11.7082 + 1.70820i) q^{77} -8.94427 q^{79} +(1.00000 + 8.94427i) q^{81} -16.6525 q^{83} +0.763932 q^{85} +(-9.23607 - 3.52786i) q^{87} +14.4721 q^{89} +(8.47214 - 1.23607i) q^{91} +(11.7082 + 4.47214i) q^{93} -0.472136i q^{95} +5.23607i q^{97} +(-8.94427 + 10.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 4q^{5} - 6q^{7} + O(q^{10}) \) \( 4q - 2q^{3} - 4q^{5} - 6q^{7} + 2q^{15} - 12q^{17} + 4q^{25} - 14q^{27} - 20q^{33} + 6q^{35} + 12q^{37} + 12q^{39} - 8q^{41} - 16q^{43} - 8q^{47} + 16q^{51} + 12q^{57} - 22q^{63} + 48q^{67} - 8q^{69} - 2q^{75} - 20q^{77} + 4q^{81} - 4q^{83} + 12q^{85} - 28q^{87} + 40q^{89} + 16q^{91} + 20q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.618034 1.61803i 0.356822 0.934172i
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −0.381966 2.61803i −0.144370 0.989524i
\(8\) 0 0
\(9\) −2.23607 2.00000i −0.745356 0.666667i
\(10\) 0 0
\(11\) 4.47214i 1.34840i −0.738549 0.674200i \(-0.764489\pi\)
0.738549 0.674200i \(-0.235511\pi\)
\(12\) 0 0
\(13\) 3.23607i 0.897524i 0.893651 + 0.448762i \(0.148135\pi\)
−0.893651 + 0.448762i \(0.851865\pi\)
\(14\) 0 0
\(15\) −0.618034 + 1.61803i −0.159576 + 0.417775i
\(16\) 0 0
\(17\) −0.763932 −0.185281 −0.0926404 0.995700i \(-0.529531\pi\)
−0.0926404 + 0.995700i \(0.529531\pi\)
\(18\) 0 0
\(19\) 0.472136i 0.108315i 0.998532 + 0.0541577i \(0.0172474\pi\)
−0.998532 + 0.0541577i \(0.982753\pi\)
\(20\) 0 0
\(21\) −4.47214 1.00000i −0.975900 0.218218i
\(22\) 0 0
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.61803 + 2.38197i −0.888741 + 0.458410i
\(28\) 0 0
\(29\) 5.70820i 1.05999i −0.848002 0.529993i \(-0.822194\pi\)
0.848002 0.529993i \(-0.177806\pi\)
\(30\) 0 0
\(31\) 7.23607i 1.29964i 0.760090 + 0.649818i \(0.225155\pi\)
−0.760090 + 0.649818i \(0.774845\pi\)
\(32\) 0 0
\(33\) −7.23607 2.76393i −1.25964 0.481139i
\(34\) 0 0
\(35\) 0.381966 + 2.61803i 0.0645640 + 0.442529i
\(36\) 0 0
\(37\) 5.23607 0.860804 0.430402 0.902637i \(-0.358372\pi\)
0.430402 + 0.902637i \(0.358372\pi\)
\(38\) 0 0
\(39\) 5.23607 + 2.00000i 0.838442 + 0.320256i
\(40\) 0 0
\(41\) −6.47214 −1.01078 −0.505389 0.862892i \(-0.668651\pi\)
−0.505389 + 0.862892i \(0.668651\pi\)
\(42\) 0 0
\(43\) −12.9443 −1.97398 −0.986991 0.160773i \(-0.948601\pi\)
−0.986991 + 0.160773i \(0.948601\pi\)
\(44\) 0 0
\(45\) 2.23607 + 2.00000i 0.333333 + 0.298142i
\(46\) 0 0
\(47\) 2.47214 0.360598 0.180299 0.983612i \(-0.442293\pi\)
0.180299 + 0.983612i \(0.442293\pi\)
\(48\) 0 0
\(49\) −6.70820 + 2.00000i −0.958315 + 0.285714i
\(50\) 0 0
\(51\) −0.472136 + 1.23607i −0.0661123 + 0.173084i
\(52\) 0 0
\(53\) 8.47214i 1.16374i 0.813283 + 0.581869i \(0.197678\pi\)
−0.813283 + 0.581869i \(0.802322\pi\)
\(54\) 0 0
\(55\) 4.47214i 0.603023i
\(56\) 0 0
\(57\) 0.763932 + 0.291796i 0.101185 + 0.0386493i
\(58\) 0 0
\(59\) −4.47214 −0.582223 −0.291111 0.956689i \(-0.594025\pi\)
−0.291111 + 0.956689i \(0.594025\pi\)
\(60\) 0 0
\(61\) 2.76393i 0.353885i 0.984221 + 0.176943i \(0.0566207\pi\)
−0.984221 + 0.176943i \(0.943379\pi\)
\(62\) 0 0
\(63\) −4.38197 + 6.61803i −0.552076 + 0.833794i
\(64\) 0 0
\(65\) 3.23607i 0.401385i
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0 0
\(69\) −6.47214 2.47214i −0.779154 0.297610i
\(70\) 0 0
\(71\) 2.76393i 0.328018i −0.986459 0.164009i \(-0.947557\pi\)
0.986459 0.164009i \(-0.0524427\pi\)
\(72\) 0 0
\(73\) 6.76393i 0.791658i −0.918324 0.395829i \(-0.870457\pi\)
0.918324 0.395829i \(-0.129543\pi\)
\(74\) 0 0
\(75\) 0.618034 1.61803i 0.0713644 0.186834i
\(76\) 0 0
\(77\) −11.7082 + 1.70820i −1.33427 + 0.194668i
\(78\) 0 0
\(79\) −8.94427 −1.00631 −0.503155 0.864196i \(-0.667827\pi\)
−0.503155 + 0.864196i \(0.667827\pi\)
\(80\) 0 0
\(81\) 1.00000 + 8.94427i 0.111111 + 0.993808i
\(82\) 0 0
\(83\) −16.6525 −1.82785 −0.913923 0.405887i \(-0.866963\pi\)
−0.913923 + 0.405887i \(0.866963\pi\)
\(84\) 0 0
\(85\) 0.763932 0.0828601
\(86\) 0 0
\(87\) −9.23607 3.52786i −0.990210 0.378227i
\(88\) 0 0
\(89\) 14.4721 1.53404 0.767022 0.641621i \(-0.221738\pi\)
0.767022 + 0.641621i \(0.221738\pi\)
\(90\) 0 0
\(91\) 8.47214 1.23607i 0.888121 0.129575i
\(92\) 0 0
\(93\) 11.7082 + 4.47214i 1.21408 + 0.463739i
\(94\) 0 0
\(95\) 0.472136i 0.0484401i
\(96\) 0 0
\(97\) 5.23607i 0.531642i 0.964022 + 0.265821i \(0.0856430\pi\)
−0.964022 + 0.265821i \(0.914357\pi\)
\(98\) 0 0
\(99\) −8.94427 + 10.0000i −0.898933 + 1.00504i
\(100\) 0 0
\(101\) 3.52786 0.351036 0.175518 0.984476i \(-0.443840\pi\)
0.175518 + 0.984476i \(0.443840\pi\)
\(102\) 0 0
\(103\) 16.6525i 1.64082i −0.571778 0.820409i \(-0.693746\pi\)
0.571778 0.820409i \(-0.306254\pi\)
\(104\) 0 0
\(105\) 4.47214 + 1.00000i 0.436436 + 0.0975900i
\(106\) 0 0
\(107\) 15.4164i 1.49036i −0.666863 0.745180i \(-0.732363\pi\)
0.666863 0.745180i \(-0.267637\pi\)
\(108\) 0 0
\(109\) −4.47214 −0.428353 −0.214176 0.976795i \(-0.568707\pi\)
−0.214176 + 0.976795i \(0.568707\pi\)
\(110\) 0 0
\(111\) 3.23607 8.47214i 0.307154 0.804140i
\(112\) 0 0
\(113\) 14.9443i 1.40584i −0.711269 0.702919i \(-0.751879\pi\)
0.711269 0.702919i \(-0.248121\pi\)
\(114\) 0 0
\(115\) 4.00000i 0.373002i
\(116\) 0 0
\(117\) 6.47214 7.23607i 0.598349 0.668975i
\(118\) 0 0
\(119\) 0.291796 + 2.00000i 0.0267489 + 0.183340i
\(120\) 0 0
\(121\) −9.00000 −0.818182
\(122\) 0 0
\(123\) −4.00000 + 10.4721i −0.360668 + 0.944241i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 13.7082 1.21641 0.608203 0.793781i \(-0.291891\pi\)
0.608203 + 0.793781i \(0.291891\pi\)
\(128\) 0 0
\(129\) −8.00000 + 20.9443i −0.704361 + 1.84404i
\(130\) 0 0
\(131\) −21.4164 −1.87116 −0.935580 0.353114i \(-0.885123\pi\)
−0.935580 + 0.353114i \(0.885123\pi\)
\(132\) 0 0
\(133\) 1.23607 0.180340i 0.107181 0.0156375i
\(134\) 0 0
\(135\) 4.61803 2.38197i 0.397457 0.205007i
\(136\) 0 0
\(137\) 12.4721i 1.06557i −0.846252 0.532783i \(-0.821146\pi\)
0.846252 0.532783i \(-0.178854\pi\)
\(138\) 0 0
\(139\) 20.4721i 1.73642i 0.496194 + 0.868212i \(0.334731\pi\)
−0.496194 + 0.868212i \(0.665269\pi\)
\(140\) 0 0
\(141\) 1.52786 4.00000i 0.128669 0.336861i
\(142\) 0 0
\(143\) 14.4721 1.21022
\(144\) 0 0
\(145\) 5.70820i 0.474041i
\(146\) 0 0
\(147\) −0.909830 + 12.0902i −0.0750415 + 0.997180i
\(148\) 0 0
\(149\) 17.7082i 1.45071i 0.688374 + 0.725356i \(0.258325\pi\)
−0.688374 + 0.725356i \(0.741675\pi\)
\(150\) 0 0
\(151\) −3.05573 −0.248672 −0.124336 0.992240i \(-0.539680\pi\)
−0.124336 + 0.992240i \(0.539680\pi\)
\(152\) 0 0
\(153\) 1.70820 + 1.52786i 0.138100 + 0.123520i
\(154\) 0 0
\(155\) 7.23607i 0.581215i
\(156\) 0 0
\(157\) 4.76393i 0.380203i −0.981764 0.190102i \(-0.939118\pi\)
0.981764 0.190102i \(-0.0608817\pi\)
\(158\) 0 0
\(159\) 13.7082 + 5.23607i 1.08713 + 0.415247i
\(160\) 0 0
\(161\) −10.4721 + 1.52786i −0.825320 + 0.120413i
\(162\) 0 0
\(163\) 1.52786 0.119672 0.0598358 0.998208i \(-0.480942\pi\)
0.0598358 + 0.998208i \(0.480942\pi\)
\(164\) 0 0
\(165\) 7.23607 + 2.76393i 0.563327 + 0.215172i
\(166\) 0 0
\(167\) 16.9443 1.31119 0.655594 0.755114i \(-0.272418\pi\)
0.655594 + 0.755114i \(0.272418\pi\)
\(168\) 0 0
\(169\) 2.52786 0.194451
\(170\) 0 0
\(171\) 0.944272 1.05573i 0.0722103 0.0807335i
\(172\) 0 0
\(173\) −17.4164 −1.32414 −0.662072 0.749440i \(-0.730323\pi\)
−0.662072 + 0.749440i \(0.730323\pi\)
\(174\) 0 0
\(175\) −0.381966 2.61803i −0.0288739 0.197905i
\(176\) 0 0
\(177\) −2.76393 + 7.23607i −0.207750 + 0.543896i
\(178\) 0 0
\(179\) 2.94427i 0.220065i 0.993928 + 0.110033i \(0.0350955\pi\)
−0.993928 + 0.110033i \(0.964904\pi\)
\(180\) 0 0
\(181\) 6.18034i 0.459381i 0.973264 + 0.229691i \(0.0737714\pi\)
−0.973264 + 0.229691i \(0.926229\pi\)
\(182\) 0 0
\(183\) 4.47214 + 1.70820i 0.330590 + 0.126274i
\(184\) 0 0
\(185\) −5.23607 −0.384963
\(186\) 0 0
\(187\) 3.41641i 0.249832i
\(188\) 0 0
\(189\) 8.00000 + 11.1803i 0.581914 + 0.813250i
\(190\) 0 0
\(191\) 2.76393i 0.199991i 0.994988 + 0.0999956i \(0.0318829\pi\)
−0.994988 + 0.0999956i \(0.968117\pi\)
\(192\) 0 0
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 0 0
\(195\) −5.23607 2.00000i −0.374963 0.143223i
\(196\) 0 0
\(197\) 12.4721i 0.888603i −0.895877 0.444301i \(-0.853452\pi\)
0.895877 0.444301i \(-0.146548\pi\)
\(198\) 0 0
\(199\) 0.180340i 0.0127840i −0.999980 0.00639198i \(-0.997965\pi\)
0.999980 0.00639198i \(-0.00203464\pi\)
\(200\) 0 0
\(201\) 7.41641 19.4164i 0.523113 1.36953i
\(202\) 0 0
\(203\) −14.9443 + 2.18034i −1.04888 + 0.153030i
\(204\) 0 0
\(205\) 6.47214 0.452034
\(206\) 0 0
\(207\) −8.00000 + 8.94427i −0.556038 + 0.621670i
\(208\) 0 0
\(209\) 2.11146 0.146052
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) 0 0
\(213\) −4.47214 1.70820i −0.306426 0.117044i
\(214\) 0 0
\(215\) 12.9443 0.882792
\(216\) 0 0
\(217\) 18.9443 2.76393i 1.28602 0.187628i
\(218\) 0 0
\(219\) −10.9443 4.18034i −0.739545 0.282481i
\(220\) 0 0
\(221\) 2.47214i 0.166294i
\(222\) 0 0
\(223\) 4.29180i 0.287400i −0.989621 0.143700i \(-0.954100\pi\)
0.989621 0.143700i \(-0.0459000\pi\)
\(224\) 0 0
\(225\) −2.23607 2.00000i −0.149071 0.133333i
\(226\) 0 0
\(227\) 5.23607 0.347530 0.173765 0.984787i \(-0.444407\pi\)
0.173765 + 0.984787i \(0.444407\pi\)
\(228\) 0 0
\(229\) 13.2361i 0.874664i −0.899300 0.437332i \(-0.855923\pi\)
0.899300 0.437332i \(-0.144077\pi\)
\(230\) 0 0
\(231\) −4.47214 + 20.0000i −0.294245 + 1.31590i
\(232\) 0 0
\(233\) 20.4721i 1.34117i −0.741831 0.670587i \(-0.766042\pi\)
0.741831 0.670587i \(-0.233958\pi\)
\(234\) 0 0
\(235\) −2.47214 −0.161264
\(236\) 0 0
\(237\) −5.52786 + 14.4721i −0.359073 + 0.940066i
\(238\) 0 0
\(239\) 22.1803i 1.43473i −0.696699 0.717363i \(-0.745349\pi\)
0.696699 0.717363i \(-0.254651\pi\)
\(240\) 0 0
\(241\) 17.8885i 1.15230i −0.817343 0.576151i \(-0.804554\pi\)
0.817343 0.576151i \(-0.195446\pi\)
\(242\) 0 0
\(243\) 15.0902 + 3.90983i 0.968035 + 0.250816i
\(244\) 0 0
\(245\) 6.70820 2.00000i 0.428571 0.127775i
\(246\) 0 0
\(247\) −1.52786 −0.0972157
\(248\) 0 0
\(249\) −10.2918 + 26.9443i −0.652216 + 1.70752i
\(250\) 0 0
\(251\) −3.52786 −0.222677 −0.111338 0.993783i \(-0.535514\pi\)
−0.111338 + 0.993783i \(0.535514\pi\)
\(252\) 0 0
\(253\) −17.8885 −1.12464
\(254\) 0 0
\(255\) 0.472136 1.23607i 0.0295663 0.0774056i
\(256\) 0 0
\(257\) 8.18034 0.510276 0.255138 0.966905i \(-0.417879\pi\)
0.255138 + 0.966905i \(0.417879\pi\)
\(258\) 0 0
\(259\) −2.00000 13.7082i −0.124274 0.851786i
\(260\) 0 0
\(261\) −11.4164 + 12.7639i −0.706658 + 0.790068i
\(262\) 0 0
\(263\) 4.94427i 0.304877i 0.988313 + 0.152438i \(0.0487126\pi\)
−0.988313 + 0.152438i \(0.951287\pi\)
\(264\) 0 0
\(265\) 8.47214i 0.520439i
\(266\) 0 0
\(267\) 8.94427 23.4164i 0.547381 1.43306i
\(268\) 0 0
\(269\) 4.47214 0.272671 0.136335 0.990663i \(-0.456467\pi\)
0.136335 + 0.990663i \(0.456467\pi\)
\(270\) 0 0
\(271\) 18.2918i 1.11115i −0.831467 0.555574i \(-0.812499\pi\)
0.831467 0.555574i \(-0.187501\pi\)
\(272\) 0 0
\(273\) 3.23607 14.4721i 0.195856 0.875894i
\(274\) 0 0
\(275\) 4.47214i 0.269680i
\(276\) 0 0
\(277\) 23.1246 1.38942 0.694712 0.719288i \(-0.255532\pi\)
0.694712 + 0.719288i \(0.255532\pi\)
\(278\) 0 0
\(279\) 14.4721 16.1803i 0.866424 0.968692i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 0 0
\(283\) 8.76393i 0.520962i −0.965479 0.260481i \(-0.916119\pi\)
0.965479 0.260481i \(-0.0838811\pi\)
\(284\) 0 0
\(285\) −0.763932 0.291796i −0.0452514 0.0172845i
\(286\) 0 0
\(287\) 2.47214 + 16.9443i 0.145926 + 1.00019i
\(288\) 0 0
\(289\) −16.4164 −0.965671
\(290\) 0 0
\(291\) 8.47214 + 3.23607i 0.496645 + 0.189702i
\(292\) 0 0
\(293\) 29.4164 1.71852 0.859262 0.511535i \(-0.170923\pi\)
0.859262 + 0.511535i \(0.170923\pi\)
\(294\) 0 0
\(295\) 4.47214 0.260378
\(296\) 0 0
\(297\) 10.6525 + 20.6525i 0.618119 + 1.19838i
\(298\) 0 0
\(299\) 12.9443 0.748587
\(300\) 0 0
\(301\) 4.94427 + 33.8885i 0.284983 + 1.95330i
\(302\) 0 0
\(303\) 2.18034 5.70820i 0.125257 0.327928i
\(304\) 0 0
\(305\) 2.76393i 0.158262i
\(306\) 0 0
\(307\) 4.18034i 0.238585i −0.992859 0.119292i \(-0.961937\pi\)
0.992859 0.119292i \(-0.0380626\pi\)
\(308\) 0 0
\(309\) −26.9443 10.2918i −1.53281 0.585480i
\(310\) 0 0
\(311\) 26.4721 1.50110 0.750549 0.660815i \(-0.229789\pi\)
0.750549 + 0.660815i \(0.229789\pi\)
\(312\) 0 0
\(313\) 7.70820i 0.435693i 0.975983 + 0.217847i \(0.0699033\pi\)
−0.975983 + 0.217847i \(0.930097\pi\)
\(314\) 0 0
\(315\) 4.38197 6.61803i 0.246896 0.372884i
\(316\) 0 0
\(317\) 6.94427i 0.390029i −0.980800 0.195015i \(-0.937525\pi\)
0.980800 0.195015i \(-0.0624754\pi\)
\(318\) 0 0
\(319\) −25.5279 −1.42929
\(320\) 0 0
\(321\) −24.9443 9.52786i −1.39225 0.531794i
\(322\) 0 0
\(323\) 0.360680i 0.0200688i
\(324\) 0 0
\(325\) 3.23607i 0.179505i
\(326\) 0 0
\(327\) −2.76393 + 7.23607i −0.152846 + 0.400155i
\(328\) 0 0
\(329\) −0.944272 6.47214i −0.0520594 0.356820i
\(330\) 0 0
\(331\) −20.9443 −1.15120 −0.575601 0.817731i \(-0.695232\pi\)
−0.575601 + 0.817731i \(0.695232\pi\)
\(332\) 0 0
\(333\) −11.7082 10.4721i −0.641606 0.573870i
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) −5.41641 −0.295051 −0.147525 0.989058i \(-0.547131\pi\)
−0.147525 + 0.989058i \(0.547131\pi\)
\(338\) 0 0
\(339\) −24.1803 9.23607i −1.31330 0.501634i
\(340\) 0 0
\(341\) 32.3607 1.75243
\(342\) 0 0
\(343\) 7.79837 + 16.7984i 0.421073 + 0.907027i
\(344\) 0 0
\(345\) 6.47214 + 2.47214i 0.348448 + 0.133095i
\(346\) 0 0
\(347\) 6.47214i 0.347442i −0.984795 0.173721i \(-0.944421\pi\)
0.984795 0.173721i \(-0.0555792\pi\)
\(348\) 0 0
\(349\) 2.18034i 0.116711i −0.998296 0.0583555i \(-0.981414\pi\)
0.998296 0.0583555i \(-0.0185857\pi\)
\(350\) 0 0
\(351\) −7.70820 14.9443i −0.411433 0.797666i
\(352\) 0 0
\(353\) 14.2918 0.760676 0.380338 0.924848i \(-0.375808\pi\)
0.380338 + 0.924848i \(0.375808\pi\)
\(354\) 0 0
\(355\) 2.76393i 0.146694i
\(356\) 0 0
\(357\) 3.41641 + 0.763932i 0.180815 + 0.0404316i
\(358\) 0 0
\(359\) 10.1803i 0.537298i 0.963238 + 0.268649i \(0.0865771\pi\)
−0.963238 + 0.268649i \(0.913423\pi\)
\(360\) 0 0
\(361\) 18.7771 0.988268
\(362\) 0 0
\(363\) −5.56231 + 14.5623i −0.291945 + 0.764323i
\(364\) 0 0
\(365\) 6.76393i 0.354040i
\(366\) 0 0
\(367\) 14.1803i 0.740208i −0.928990 0.370104i \(-0.879322\pi\)
0.928990 0.370104i \(-0.120678\pi\)
\(368\) 0 0
\(369\) 14.4721 + 12.9443i 0.753389 + 0.673852i
\(370\) 0 0
\(371\) 22.1803 3.23607i 1.15155 0.168008i
\(372\) 0 0
\(373\) −9.81966 −0.508443 −0.254221 0.967146i \(-0.581819\pi\)
−0.254221 + 0.967146i \(0.581819\pi\)
\(374\) 0 0
\(375\) −0.618034 + 1.61803i −0.0319151 + 0.0835549i
\(376\) 0 0
\(377\) 18.4721 0.951363
\(378\) 0 0
\(379\) −17.8885 −0.918873 −0.459436 0.888211i \(-0.651949\pi\)
−0.459436 + 0.888211i \(0.651949\pi\)
\(380\) 0 0
\(381\) 8.47214 22.1803i 0.434041 1.13633i
\(382\) 0 0
\(383\) 21.8885 1.11845 0.559226 0.829015i \(-0.311098\pi\)
0.559226 + 0.829015i \(0.311098\pi\)
\(384\) 0 0
\(385\) 11.7082 1.70820i 0.596705 0.0870581i
\(386\) 0 0
\(387\) 28.9443 + 25.8885i 1.47132 + 1.31599i
\(388\) 0 0
\(389\) 7.81966i 0.396473i −0.980154 0.198236i \(-0.936479\pi\)
0.980154 0.198236i \(-0.0635213\pi\)
\(390\) 0 0
\(391\) 3.05573i 0.154535i
\(392\) 0 0
\(393\) −13.2361 + 34.6525i −0.667671 + 1.74799i
\(394\) 0 0
\(395\) 8.94427 0.450035
\(396\) 0 0
\(397\) 17.1246i 0.859460i −0.902958 0.429730i \(-0.858609\pi\)
0.902958 0.429730i \(-0.141391\pi\)
\(398\) 0 0
\(399\) 0.472136 2.11146i 0.0236364 0.105705i
\(400\) 0 0
\(401\) 5.52786i 0.276048i −0.990429 0.138024i \(-0.955925\pi\)
0.990429 0.138024i \(-0.0440752\pi\)
\(402\) 0 0
\(403\) −23.4164 −1.16645
\(404\) 0 0
\(405\) −1.00000 8.94427i −0.0496904 0.444444i
\(406\) 0 0
\(407\) 23.4164i 1.16071i
\(408\) 0 0
\(409\) 19.4164i 0.960080i −0.877247 0.480040i \(-0.840622\pi\)
0.877247 0.480040i \(-0.159378\pi\)
\(410\) 0 0
\(411\) −20.1803 7.70820i −0.995423 0.380218i
\(412\) 0 0
\(413\) 1.70820 + 11.7082i 0.0840552 + 0.576123i
\(414\) 0 0
\(415\) 16.6525 0.817438
\(416\) 0 0
\(417\) 33.1246 + 12.6525i 1.62212 + 0.619594i
\(418\) 0 0
\(419\) −16.8328 −0.822337 −0.411168 0.911559i \(-0.634879\pi\)
−0.411168 + 0.911559i \(0.634879\pi\)
\(420\) 0 0
\(421\) −12.4721 −0.607855 −0.303927 0.952695i \(-0.598298\pi\)
−0.303927 + 0.952695i \(0.598298\pi\)
\(422\) 0 0
\(423\) −5.52786 4.94427i −0.268774 0.240399i
\(424\) 0 0
\(425\) −0.763932 −0.0370561
\(426\) 0 0
\(427\) 7.23607 1.05573i 0.350178 0.0510903i
\(428\) 0 0
\(429\) 8.94427 23.4164i 0.431834 1.13055i
\(430\) 0 0
\(431\) 9.59675i 0.462259i 0.972923 + 0.231130i \(0.0742421\pi\)
−0.972923 + 0.231130i \(0.925758\pi\)
\(432\) 0 0
\(433\) 4.65248i 0.223584i −0.993732 0.111792i \(-0.964341\pi\)
0.993732 0.111792i \(-0.0356590\pi\)
\(434\) 0 0
\(435\) 9.23607 + 3.52786i 0.442836 + 0.169148i
\(436\) 0 0
\(437\) 1.88854 0.0903413
\(438\) 0 0
\(439\) 12.1803i 0.581336i 0.956824 + 0.290668i \(0.0938775\pi\)
−0.956824 + 0.290668i \(0.906123\pi\)
\(440\) 0 0
\(441\) 19.0000 + 8.94427i 0.904762 + 0.425918i
\(442\) 0 0
\(443\) 9.52786i 0.452682i −0.974048 0.226341i \(-0.927324\pi\)
0.974048 0.226341i \(-0.0726764\pi\)
\(444\) 0 0
\(445\) −14.4721 −0.686045
\(446\) 0 0
\(447\) 28.6525 + 10.9443i 1.35522 + 0.517646i
\(448\) 0 0
\(449\) 1.52786i 0.0721044i 0.999350 + 0.0360522i \(0.0114783\pi\)
−0.999350 + 0.0360522i \(0.988522\pi\)
\(450\) 0 0
\(451\) 28.9443i 1.36293i
\(452\) 0 0
\(453\) −1.88854 + 4.94427i −0.0887315 + 0.232302i
\(454\) 0 0
\(455\) −8.47214 + 1.23607i −0.397180 + 0.0579478i
\(456\) 0 0
\(457\) 9.05573 0.423609 0.211805 0.977312i \(-0.432066\pi\)
0.211805 + 0.977312i \(0.432066\pi\)
\(458\) 0 0
\(459\) 3.52786 1.81966i 0.164667 0.0849345i
\(460\) 0 0
\(461\) −10.9443 −0.509726 −0.254863 0.966977i \(-0.582030\pi\)
−0.254863 + 0.966977i \(0.582030\pi\)
\(462\) 0 0
\(463\) −0.180340 −0.00838111 −0.00419055 0.999991i \(-0.501334\pi\)
−0.00419055 + 0.999991i \(0.501334\pi\)
\(464\) 0 0
\(465\) −11.7082 4.47214i −0.542955 0.207390i
\(466\) 0 0
\(467\) −20.2918 −0.938992 −0.469496 0.882935i \(-0.655564\pi\)
−0.469496 + 0.882935i \(0.655564\pi\)
\(468\) 0 0
\(469\) −4.58359 31.4164i −0.211651 1.45067i
\(470\) 0 0
\(471\) −7.70820 2.94427i −0.355175 0.135665i
\(472\) 0 0
\(473\) 57.8885i 2.66172i
\(474\) 0 0
\(475\) 0.472136i 0.0216631i
\(476\) 0 0
\(477\) 16.9443 18.9443i 0.775825 0.867399i
\(478\) 0 0
\(479\) 2.11146 0.0964749 0.0482374 0.998836i \(-0.484640\pi\)
0.0482374 + 0.998836i \(0.484640\pi\)
\(480\) 0 0
\(481\) 16.9443i 0.772592i
\(482\) 0 0
\(483\) −4.00000 + 17.8885i −0.182006 + 0.813957i
\(484\) 0 0
\(485\) 5.23607i 0.237758i
\(486\) 0 0
\(487\) 31.5967 1.43179 0.715893 0.698210i \(-0.246020\pi\)
0.715893 + 0.698210i \(0.246020\pi\)
\(488\) 0 0
\(489\) 0.944272 2.47214i 0.0427015 0.111794i
\(490\) 0 0
\(491\) 13.4164i 0.605474i −0.953074 0.302737i \(-0.902100\pi\)
0.953074 0.302737i \(-0.0979004\pi\)
\(492\) 0 0
\(493\) 4.36068i 0.196395i
\(494\) 0 0
\(495\) 8.94427 10.0000i 0.402015 0.449467i
\(496\) 0 0
\(497\) −7.23607 + 1.05573i −0.324582 + 0.0473559i
\(498\) 0 0
\(499\) 17.8885 0.800801 0.400401 0.916340i \(-0.368871\pi\)
0.400401 + 0.916340i \(0.368871\pi\)
\(500\) 0 0
\(501\) 10.4721 27.4164i 0.467861 1.22487i
\(502\) 0 0
\(503\) 16.3607 0.729487 0.364743 0.931108i \(-0.381157\pi\)
0.364743 + 0.931108i \(0.381157\pi\)
\(504\) 0 0
\(505\) −3.52786 −0.156988
\(506\) 0 0
\(507\) 1.56231 4.09017i 0.0693844 0.181651i
\(508\) 0 0
\(509\) −24.4721 −1.08471 −0.542354 0.840150i \(-0.682467\pi\)
−0.542354 + 0.840150i \(0.682467\pi\)
\(510\) 0 0
\(511\) −17.7082 + 2.58359i −0.783365 + 0.114291i
\(512\) 0 0
\(513\) −1.12461 2.18034i −0.0496528 0.0962644i
\(514\) 0 0
\(515\) 16.6525i 0.733796i
\(516\) 0 0
\(517\) 11.0557i 0.486230i
\(518\) 0 0
\(519\) −10.7639 + 28.1803i −0.472484 + 1.23698i
\(520\) 0 0
\(521\) 19.0557 0.834847 0.417423 0.908712i \(-0.362933\pi\)
0.417423 + 0.908712i \(0.362933\pi\)
\(522\) 0 0
\(523\) 24.5410i 1.07310i −0.843867 0.536552i \(-0.819727\pi\)
0.843867 0.536552i \(-0.180273\pi\)
\(524\) 0 0
\(525\) −4.47214 1.00000i −0.195180 0.0436436i
\(526\) 0 0
\(527\) 5.52786i 0.240798i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 10.0000 + 8.94427i 0.433963 + 0.388148i
\(532\) 0 0
\(533\) 20.9443i 0.907197i
\(534\) 0 0
\(535\) 15.4164i 0.666509i
\(536\) 0 0
\(537\) 4.76393 + 1.81966i 0.205579 + 0.0785241i
\(538\) 0 0
\(539\) 8.94427 + 30.0000i 0.385257 + 1.29219i
\(540\) 0 0
\(541\) 13.0557 0.561310 0.280655 0.959809i \(-0.409448\pi\)
0.280655 + 0.959809i \(0.409448\pi\)
\(542\) 0 0
\(543\) 10.0000 + 3.81966i 0.429141 + 0.163917i
\(544\) 0 0
\(545\) 4.47214 0.191565
\(546\) 0 0
\(547\) 8.58359 0.367008 0.183504 0.983019i \(-0.441256\pi\)
0.183504 + 0.983019i \(0.441256\pi\)
\(548\) 0 0
\(549\) 5.52786 6.18034i 0.235923 0.263770i
\(550\) 0 0
\(551\) 2.69505 0.114813
\(552\) 0 0
\(553\) 3.41641 + 23.4164i 0.145280 + 0.995767i
\(554\) 0 0
\(555\) −3.23607 + 8.47214i −0.137363 + 0.359622i
\(556\) 0 0
\(557\) 16.4721i 0.697947i 0.937133 + 0.348973i \(0.113470\pi\)
−0.937133 + 0.348973i \(0.886530\pi\)
\(558\) 0 0
\(559\) 41.8885i 1.77170i
\(560\) 0 0
\(561\) 5.52786 + 2.11146i 0.233387 + 0.0891457i
\(562\) 0 0
\(563\) 17.8197 0.751009 0.375505 0.926821i \(-0.377469\pi\)
0.375505 + 0.926821i \(0.377469\pi\)
\(564\) 0 0
\(565\) 14.9443i 0.628710i
\(566\) 0 0
\(567\) 23.0344 6.03444i 0.967356 0.253423i
\(568\) 0 0
\(569\) 18.4721i 0.774392i −0.921997 0.387196i \(-0.873444\pi\)
0.921997 0.387196i \(-0.126556\pi\)
\(570\) 0 0
\(571\) 34.8328 1.45771 0.728854 0.684669i \(-0.240053\pi\)
0.728854 + 0.684669i \(0.240053\pi\)
\(572\) 0 0
\(573\) 4.47214 + 1.70820i 0.186826 + 0.0713612i
\(574\) 0 0
\(575\) 4.00000i 0.166812i
\(576\) 0 0
\(577\) 14.1803i 0.590335i 0.955445 + 0.295168i \(0.0953755\pi\)
−0.955445 + 0.295168i \(0.904625\pi\)
\(578\) 0 0
\(579\) −3.70820 + 9.70820i −0.154108 + 0.403459i
\(580\) 0 0
\(581\) 6.36068 + 43.5967i 0.263885 + 1.80870i
\(582\) 0 0
\(583\) 37.8885 1.56918
\(584\) 0 0
\(585\) −6.47214 + 7.23607i −0.267590 + 0.299175i
\(586\) 0 0
\(587\) −23.7082 −0.978542 −0.489271 0.872132i \(-0.662737\pi\)
−0.489271 + 0.872132i \(0.662737\pi\)
\(588\) 0 0
\(589\) −3.41641 −0.140771
\(590\) 0 0
\(591\) −20.1803 7.70820i −0.830108 0.317073i
\(592\) 0 0
\(593\) −47.0132 −1.93060 −0.965299 0.261145i \(-0.915900\pi\)
−0.965299 + 0.261145i \(0.915900\pi\)
\(594\) 0 0
\(595\) −0.291796 2.00000i −0.0119625 0.0819920i
\(596\) 0 0
\(597\) −0.291796 0.111456i −0.0119424 0.00456160i
\(598\) 0 0
\(599\) 41.2361i 1.68486i 0.538806 + 0.842430i \(0.318876\pi\)
−0.538806 + 0.842430i \(0.681124\pi\)
\(600\) 0 0
\(601\) 14.4721i 0.590331i 0.955446 + 0.295165i \(0.0953747\pi\)
−0.955446 + 0.295165i \(0.904625\pi\)
\(602\) 0 0
\(603\) −26.8328 24.0000i −1.09272 0.977356i
\(604\) 0 0
\(605\) 9.00000 0.365902
\(606\) 0 0
\(607\) 14.7639i 0.599250i 0.954057 + 0.299625i \(0.0968615\pi\)
−0.954057 + 0.299625i \(0.903139\pi\)
\(608\) 0 0
\(609\) −5.70820 + 25.5279i −0.231308 + 1.03444i
\(610\) 0 0
\(611\) 8.00000i 0.323645i
\(612\) 0 0
\(613\) −20.0689 −0.810575 −0.405287 0.914189i \(-0.632829\pi\)
−0.405287 + 0.914189i \(0.632829\pi\)
\(614\) 0 0
\(615\) 4.00000 10.4721i 0.161296 0.422277i
\(616\) 0 0
\(617\) 2.00000i 0.0805170i 0.999189 + 0.0402585i \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) 0 0
\(619\) 14.0000i 0.562708i −0.959604 0.281354i \(-0.909217\pi\)
0.959604 0.281354i \(-0.0907834\pi\)
\(620\) 0 0
\(621\) 9.52786 + 18.4721i 0.382340 + 0.741261i
\(622\) 0 0
\(623\) −5.52786 37.8885i −0.221469 1.51797i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 1.30495 3.41641i 0.0521148 0.136438i
\(628\) 0 0
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) −29.8885 −1.18984 −0.594922 0.803783i \(-0.702817\pi\)
−0.594922 + 0.803783i \(0.702817\pi\)
\(632\) 0 0
\(633\) 4.94427 12.9443i 0.196517 0.514489i
\(634\) 0 0
\(635\) −13.7082 −0.543993
\(636\) 0 0
\(637\) −6.47214 21.7082i −0.256435 0.860110i
\(638\) 0 0
\(639\) −5.52786 + 6.18034i −0.218679 + 0.244490i
\(640\) 0 0
\(641\) 3.41641i 0.134940i 0.997721 + 0.0674700i \(0.0214927\pi\)
−0.997721 + 0.0674700i \(0.978507\pi\)
\(642\) 0 0
\(643\) 25.7082i 1.01383i 0.861995 + 0.506916i \(0.169215\pi\)
−0.861995 + 0.506916i \(0.830785\pi\)
\(644\) 0 0
\(645\) 8.00000 20.9443i 0.315000 0.824680i
\(646\) 0 0
\(647\) −18.8328 −0.740394 −0.370197 0.928953i \(-0.620710\pi\)
−0.370197 + 0.928953i \(0.620710\pi\)
\(648\) 0 0
\(649\) 20.0000i 0.785069i
\(650\) 0 0
\(651\) 7.23607 32.3607i 0.283604 1.26832i
\(652\) 0 0
\(653\) 11.8885i 0.465235i 0.972568 + 0.232617i \(0.0747290\pi\)
−0.972568 + 0.232617i \(0.925271\pi\)
\(654\) 0 0
\(655\) 21.4164 0.836808
\(656\) 0 0
\(657\) −13.5279 + 15.1246i −0.527772 + 0.590067i
\(658\) 0 0
\(659\) 40.4721i 1.57657i −0.615310 0.788285i \(-0.710969\pi\)
0.615310 0.788285i \(-0.289031\pi\)
\(660\) 0 0
\(661\) 31.7082i 1.23331i 0.787235 + 0.616653i \(0.211512\pi\)
−0.787235 + 0.616653i \(0.788488\pi\)
\(662\) 0 0
\(663\) −4.00000 1.52786i −0.155347 0.0593373i
\(664\) 0 0
\(665\) −1.23607 + 0.180340i −0.0479327 + 0.00699328i
\(666\) 0 0
\(667\) −22.8328 −0.884090
\(668\) 0 0
\(669\) −6.94427 2.65248i −0.268481 0.102551i
\(670\) 0 0
\(671\) 12.3607 0.477179
\(672\) 0 0
\(673\) 28.4721 1.09752 0.548760 0.835980i \(-0.315100\pi\)
0.548760 + 0.835980i \(0.315100\pi\)
\(674\) 0 0
\(675\) −4.61803 + 2.38197i −0.177748 + 0.0916819i
\(676\) 0 0
\(677\) −18.0000 −0.691796 −0.345898 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) 13.7082 2.00000i 0.526073 0.0767530i
\(680\) 0 0
\(681\) 3.23607 8.47214i 0.124006 0.324653i
\(682\) 0 0
\(683\) 36.0000i 1.37750i 0.724998 + 0.688751i \(0.241841\pi\)
−0.724998 + 0.688751i \(0.758159\pi\)
\(684\) 0 0
\(685\) 12.4721i 0.476536i
\(686\) 0 0
\(687\) −21.4164 8.18034i −0.817087 0.312099i
\(688\) 0 0
\(689\) −27.4164 −1.04448
\(690\) 0 0
\(691\) 38.9443i 1.48151i 0.671775 + 0.740755i \(0.265532\pi\)
−0.671775 + 0.740755i \(0.734468\pi\)
\(692\) 0 0
\(693\) 29.5967 + 19.5967i 1.12429 + 0.744419i
\(694\) 0 0
\(695\) 20.4721i 0.776552i
\(696\) 0 0
\(697\) 4.94427 0.187278
\(698\) 0 0
\(699\) −33.1246 12.6525i −1.25289 0.478561i
\(700\) 0 0
\(701\) 14.0689i 0.531374i −0.964059 0.265687i \(-0.914401\pi\)
0.964059 0.265687i \(-0.0855988\pi\)
\(702\) 0 0
\(703\) 2.47214i 0.0932384i
\(704\) 0 0
\(705\) −1.52786 + 4.00000i −0.0575427 + 0.150649i
\(706\) 0 0
\(707\) −1.34752 9.23607i −0.0506789 0.347358i
\(708\) 0 0
\(709\) −24.4721 −0.919070 −0.459535 0.888160i \(-0.651984\pi\)
−0.459535 + 0.888160i \(0.651984\pi\)
\(710\) 0 0
\(711\) 20.0000 + 17.8885i 0.750059 + 0.670873i
\(712\) 0 0
\(713\) 28.9443 1.08397
\(714\) 0 0
\(715\) −14.4721 −0.541227
\(716\) 0 0
\(717\) −35.8885 13.7082i −1.34028 0.511942i
\(718\) 0 0
\(719\) −25.5279 −0.952029 −0.476014 0.879438i \(-0.657919\pi\)
−0.476014 + 0.879438i \(0.657919\pi\)
\(720\) 0 0
\(721\) −43.5967 + 6.36068i −1.62363 + 0.236884i
\(722\) 0 0
\(723\) −28.9443 11.0557i −1.07645 0.411167i
\(724\) 0 0
\(725\) 5.70820i 0.211997i
\(726\) 0 0
\(727\) 39.7082i 1.47270i −0.676603 0.736348i \(-0.736549\pi\)
0.676603 0.736348i \(-0.263451\pi\)
\(728\) 0 0
\(729\) 15.6525 22.0000i 0.579721 0.814815i
\(730\) 0 0
\(731\) 9.88854 0.365741
\(732\) 0 0
\(733\) 38.0689i 1.40611i −0.711137 0.703053i \(-0.751820\pi\)
0.711137 0.703053i \(-0.248180\pi\)
\(734\) 0 0
\(735\) 0.909830 12.0902i 0.0335596 0.445953i
\(736\) 0 0
\(737\) 53.6656i 1.97680i
\(738\) 0 0
\(739\) 8.94427 0.329020 0.164510 0.986375i \(-0.447396\pi\)
0.164510 + 0.986375i \(0.447396\pi\)
\(740\) 0 0
\(741\) −0.944272 + 2.47214i −0.0346887 + 0.0908162i
\(742\) 0 0
\(743\) 1.52786i 0.0560519i 0.999607 + 0.0280259i \(0.00892210\pi\)
−0.999607 + 0.0280259i \(0.991078\pi\)
\(744\) 0 0
\(745\) 17.7082i 0.648778i
\(746\) 0 0
\(747\) 37.2361 + 33.3050i 1.36240 + 1.21856i
\(748\) 0 0
\(749\) −40.3607 + 5.88854i −1.47475 + 0.215163i
\(750\) 0 0
\(751\) −35.4164 −1.29236 −0.646182 0.763184i \(-0.723635\pi\)
−0.646182 + 0.763184i \(0.723635\pi\)
\(752\) 0 0
\(753\) −2.18034 + 5.70820i −0.0794560 + 0.208019i
\(754\) 0 0
\(755\) 3.05573 0.111209
\(756\) 0 0
\(757\) 28.6525 1.04139 0.520696 0.853742i \(-0.325673\pi\)
0.520696 + 0.853742i \(0.325673\pi\)
\(758\) 0 0
\(759\) −11.0557 + 28.9443i −0.401298 + 1.05061i
\(760\) 0 0
\(761\) −29.8885 −1.08346 −0.541729 0.840553i \(-0.682230\pi\)
−0.541729 + 0.840553i \(0.682230\pi\)
\(762\) 0 0
\(763\) 1.70820 + 11.7082i 0.0618411 + 0.423865i
\(764\) 0 0
\(765\) −1.70820 1.52786i −0.0617602 0.0552400i
\(766\) 0 0
\(767\) 14.4721i 0.522559i
\(768\) 0 0
\(769\) 36.0000i 1.29819i −0.760706 0.649097i \(-0.775147\pi\)
0.760706 0.649097i \(-0.224853\pi\)
\(770\) 0 0
\(771\) 5.05573 13.2361i 0.182078 0.476685i
\(772\) 0 0
\(773\) −37.4164 −1.34577 −0.672887 0.739745i \(-0.734946\pi\)
−0.672887 + 0.739745i \(0.734946\pi\)
\(774\) 0 0
\(775\) 7.23607i 0.259927i
\(776\) 0 0
\(777\) −23.4164 5.23607i −0.840059 0.187843i
\(778\) 0 0
\(779\) 3.05573i 0.109483i
\(780\) 0 0
\(781\) −12.3607 −0.442300
\(782\) 0 0
\(783\) 13.5967 + 26.3607i 0.485908 + 0.942054i
\(784\) 0 0
\(785\) 4.76393i 0.170032i
\(786\) 0 0
\(787\) 49.7082i 1.77191i −0.463775 0.885953i \(-0.653505\pi\)
0.463775 0.885953i \(-0.346495\pi\)
\(788\) 0 0
\(789\) 8.00000 + 3.05573i 0.284808 + 0.108787i
\(790\) 0 0
\(791\) −39.1246 + 5.70820i −1.39111 + 0.202960i
\(792\) 0 0
\(793\) −8.94427 −0.317620
\(794\) 0 0
\(795\) −13.7082 5.23607i −0.486180 0.185704i
\(796\) 0 0
\(797\) 5.41641 0.191859 0.0959295 0.995388i \(-0.469418\pi\)
0.0959295 + 0.995388i \(0.469418\pi\)
\(798\) 0 0