Properties

Label 1960.2.q.x.961.4
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.21913473024.16
Defining polynomial: \(x^{8} - 2 x^{7} + 11 x^{6} - 2 x^{5} + 51 x^{4} + 162 x^{2} + 112 x + 196\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.4
Root \(-0.939980 - 1.62809i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.x.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.939980 + 1.62809i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.267126 + 0.462676i) q^{9} +O(q^{10})\) \(q+(0.939980 + 1.62809i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.267126 + 0.462676i) q^{9} +(1.64709 + 2.85284i) q^{11} +4.19292 q^{13} -1.87996 q^{15} +(0.718686 + 1.24480i) q^{17} +(-0.622226 + 1.07773i) q^{19} +(0.136414 - 0.236276i) q^{23} +(-0.500000 - 0.866025i) q^{25} +4.63551 q^{27} -2.36268 q^{29} +(1.86359 + 3.22783i) q^{31} +(-3.09646 + 5.36323i) q^{33} +(-0.0848805 + 0.147017i) q^{37} +(3.94126 + 6.82647i) q^{39} +11.6630 q^{41} -10.1458 q^{43} +(-0.267126 - 0.462676i) q^{45} +(-1.56221 + 2.70582i) q^{47} +(-1.35110 + 2.34018i) q^{51} +(-4.62351 - 8.00815i) q^{53} -3.29417 q^{55} -2.33952 q^{57} +(-4.53553 - 7.85578i) q^{59} +(-3.63551 + 6.29689i) q^{61} +(-2.09646 + 3.63117i) q^{65} +(6.57197 + 11.3830i) q^{67} +0.512907 q^{69} +6.87474 q^{71} +(7.62479 + 13.2065i) q^{73} +(0.939980 - 1.62809i) q^{75} +(-7.47551 + 12.9480i) q^{79} +(5.15867 + 8.93507i) q^{81} +0.167199 q^{83} -1.43737 q^{85} +(-2.22087 - 3.84666i) q^{87} +(-1.54935 + 2.68355i) q^{89} +(-3.50347 + 6.06819i) q^{93} +(-0.622226 - 1.07773i) q^{95} +6.60894 q^{97} -1.75992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 2q^{3} - 4q^{5} - 6q^{9} + O(q^{10}) \) \( 8q - 2q^{3} - 4q^{5} - 6q^{9} - 2q^{11} + 20q^{13} + 4q^{15} - 6q^{17} + 4q^{23} - 4q^{25} + 28q^{27} - 4q^{29} + 12q^{31} - 18q^{33} - 14q^{39} + 24q^{41} - 16q^{43} - 6q^{45} + 2q^{47} - 2q^{51} + 4q^{53} + 4q^{55} - 16q^{57} - 8q^{59} - 20q^{61} - 10q^{65} + 8q^{67} + 48q^{69} + 8q^{71} - 16q^{73} - 2q^{75} - 22q^{79} + 20q^{81} + 72q^{83} + 12q^{85} + 18q^{87} - 40q^{89} + 32q^{93} + 52q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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 0
\(3\) 0.939980 + 1.62809i 0.542698 + 0.939980i 0.998748 + 0.0500262i \(0.0159305\pi\)
−0.456050 + 0.889954i \(0.650736\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.267126 + 0.462676i −0.0890421 + 0.154225i
\(10\) 0 0
\(11\) 1.64709 + 2.85284i 0.496615 + 0.860163i 0.999992 0.00390371i \(-0.00124259\pi\)
−0.503377 + 0.864067i \(0.667909\pi\)
\(12\) 0 0
\(13\) 4.19292 1.16291 0.581453 0.813580i \(-0.302484\pi\)
0.581453 + 0.813580i \(0.302484\pi\)
\(14\) 0 0
\(15\) −1.87996 −0.485404
\(16\) 0 0
\(17\) 0.718686 + 1.24480i 0.174307 + 0.301908i 0.939921 0.341392i \(-0.110898\pi\)
−0.765614 + 0.643300i \(0.777565\pi\)
\(18\) 0 0
\(19\) −0.622226 + 1.07773i −0.142748 + 0.247248i −0.928531 0.371256i \(-0.878927\pi\)
0.785782 + 0.618503i \(0.212261\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.136414 0.236276i 0.0284443 0.0492670i −0.851453 0.524431i \(-0.824278\pi\)
0.879897 + 0.475164i \(0.157611\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 4.63551 0.892104
\(28\) 0 0
\(29\) −2.36268 −0.438739 −0.219369 0.975642i \(-0.570400\pi\)
−0.219369 + 0.975642i \(0.570400\pi\)
\(30\) 0 0
\(31\) 1.86359 + 3.22783i 0.334710 + 0.579735i 0.983429 0.181293i \(-0.0580283\pi\)
−0.648719 + 0.761028i \(0.724695\pi\)
\(32\) 0 0
\(33\) −3.09646 + 5.36323i −0.539024 + 0.933618i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.0848805 + 0.147017i −0.0139543 + 0.0241695i −0.872918 0.487867i \(-0.837775\pi\)
0.858964 + 0.512036i \(0.171109\pi\)
\(38\) 0 0
\(39\) 3.94126 + 6.82647i 0.631107 + 1.09311i
\(40\) 0 0
\(41\) 11.6630 1.82146 0.910730 0.413001i \(-0.135520\pi\)
0.910730 + 0.413001i \(0.135520\pi\)
\(42\) 0 0
\(43\) −10.1458 −1.54721 −0.773607 0.633666i \(-0.781549\pi\)
−0.773607 + 0.633666i \(0.781549\pi\)
\(44\) 0 0
\(45\) −0.267126 0.462676i −0.0398208 0.0689717i
\(46\) 0 0
\(47\) −1.56221 + 2.70582i −0.227871 + 0.394685i −0.957177 0.289503i \(-0.906510\pi\)
0.729306 + 0.684188i \(0.239843\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −1.35110 + 2.34018i −0.189192 + 0.327690i
\(52\) 0 0
\(53\) −4.62351 8.00815i −0.635088 1.10000i −0.986497 0.163782i \(-0.947631\pi\)
0.351409 0.936222i \(-0.385703\pi\)
\(54\) 0 0
\(55\) −3.29417 −0.444186
\(56\) 0 0
\(57\) −2.33952 −0.309877
\(58\) 0 0
\(59\) −4.53553 7.85578i −0.590476 1.02273i −0.994168 0.107840i \(-0.965607\pi\)
0.403692 0.914895i \(-0.367727\pi\)
\(60\) 0 0
\(61\) −3.63551 + 6.29689i −0.465479 + 0.806234i −0.999223 0.0394127i \(-0.987451\pi\)
0.533744 + 0.845646i \(0.320785\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.09646 + 3.63117i −0.260034 + 0.450392i
\(66\) 0 0
\(67\) 6.57197 + 11.3830i 0.802894 + 1.39065i 0.917703 + 0.397266i \(0.130041\pi\)
−0.114809 + 0.993388i \(0.536626\pi\)
\(68\) 0 0
\(69\) 0.512907 0.0617467
\(70\) 0 0
\(71\) 6.87474 0.815882 0.407941 0.913008i \(-0.366247\pi\)
0.407941 + 0.913008i \(0.366247\pi\)
\(72\) 0 0
\(73\) 7.62479 + 13.2065i 0.892414 + 1.54571i 0.836973 + 0.547244i \(0.184323\pi\)
0.0554412 + 0.998462i \(0.482343\pi\)
\(74\) 0 0
\(75\) 0.939980 1.62809i 0.108540 0.187996i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −7.47551 + 12.9480i −0.841061 + 1.45676i 0.0479374 + 0.998850i \(0.484735\pi\)
−0.888998 + 0.457910i \(0.848598\pi\)
\(80\) 0 0
\(81\) 5.15867 + 8.93507i 0.573185 + 0.992786i
\(82\) 0 0
\(83\) 0.167199 0.0183524 0.00917622 0.999958i \(-0.497079\pi\)
0.00917622 + 0.999958i \(0.497079\pi\)
\(84\) 0 0
\(85\) −1.43737 −0.155905
\(86\) 0 0
\(87\) −2.22087 3.84666i −0.238103 0.412406i
\(88\) 0 0
\(89\) −1.54935 + 2.68355i −0.164230 + 0.284455i −0.936382 0.350983i \(-0.885847\pi\)
0.772151 + 0.635439i \(0.219181\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.50347 + 6.06819i −0.363293 + 0.629241i
\(94\) 0 0
\(95\) −0.622226 1.07773i −0.0638391 0.110573i
\(96\) 0 0
\(97\) 6.60894 0.671037 0.335518 0.942034i \(-0.391089\pi\)
0.335518 + 0.942034i \(0.391089\pi\)
\(98\) 0 0
\(99\) −1.75992 −0.176879
\(100\) 0 0
\(101\) −9.41859 16.3135i −0.937185 1.62325i −0.770691 0.637209i \(-0.780089\pi\)
−0.166493 0.986043i \(-0.553244\pi\)
\(102\) 0 0
\(103\) 0.733780 1.27094i 0.0723014 0.125230i −0.827608 0.561306i \(-0.810299\pi\)
0.899910 + 0.436077i \(0.143632\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.78127 + 11.7455i −0.655570 + 1.13548i 0.326181 + 0.945307i \(0.394238\pi\)
−0.981751 + 0.190173i \(0.939095\pi\)
\(108\) 0 0
\(109\) −7.40701 12.8293i −0.709463 1.22883i −0.965057 0.262041i \(-0.915604\pi\)
0.255594 0.966784i \(-0.417729\pi\)
\(110\) 0 0
\(111\) −0.319144 −0.0302918
\(112\) 0 0
\(113\) −13.1903 −1.24084 −0.620418 0.784271i \(-0.713037\pi\)
−0.620418 + 0.784271i \(0.713037\pi\)
\(114\) 0 0
\(115\) 0.136414 + 0.236276i 0.0127207 + 0.0220329i
\(116\) 0 0
\(117\) −1.12004 + 1.93996i −0.103548 + 0.179350i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.0742075 0.128531i 0.00674614 0.0116847i
\(122\) 0 0
\(123\) 10.9630 + 18.9885i 0.988503 + 1.71214i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 6.86118 0.608831 0.304416 0.952539i \(-0.401539\pi\)
0.304416 + 0.952539i \(0.401539\pi\)
\(128\) 0 0
\(129\) −9.53682 16.5182i −0.839670 1.45435i
\(130\) 0 0
\(131\) 0.172854 0.299392i 0.0151023 0.0261580i −0.858375 0.513022i \(-0.828526\pi\)
0.873478 + 0.486864i \(0.161859\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.31775 + 4.01447i −0.199481 + 0.345510i
\(136\) 0 0
\(137\) −5.65685 9.79796i −0.483298 0.837096i 0.516518 0.856276i \(-0.327228\pi\)
−0.999816 + 0.0191800i \(0.993894\pi\)
\(138\) 0 0
\(139\) 2.68885 0.228066 0.114033 0.993477i \(-0.463623\pi\)
0.114033 + 0.993477i \(0.463623\pi\)
\(140\) 0 0
\(141\) −5.87377 −0.494661
\(142\) 0 0
\(143\) 6.90610 + 11.9617i 0.577517 + 1.00029i
\(144\) 0 0
\(145\) 1.18134 2.04614i 0.0981049 0.169923i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.56700 + 11.3744i −0.537990 + 0.931826i 0.461022 + 0.887389i \(0.347483\pi\)
−0.999012 + 0.0444372i \(0.985851\pi\)
\(150\) 0 0
\(151\) −1.50570 2.60795i −0.122532 0.212232i 0.798233 0.602348i \(-0.205768\pi\)
−0.920766 + 0.390116i \(0.872435\pi\)
\(152\) 0 0
\(153\) −0.767920 −0.0620826
\(154\) 0 0
\(155\) −3.72717 −0.299374
\(156\) 0 0
\(157\) −9.73155 16.8555i −0.776662 1.34522i −0.933856 0.357650i \(-0.883578\pi\)
0.157194 0.987568i \(-0.449755\pi\)
\(158\) 0 0
\(159\) 8.69201 15.0550i 0.689321 1.19394i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −6.74611 + 11.6846i −0.528396 + 0.915209i 0.471056 + 0.882103i \(0.343873\pi\)
−0.999452 + 0.0331054i \(0.989460\pi\)
\(164\) 0 0
\(165\) −3.09646 5.36323i −0.241059 0.417527i
\(166\) 0 0
\(167\) 12.3011 0.951889 0.475944 0.879475i \(-0.342106\pi\)
0.475944 + 0.879475i \(0.342106\pi\)
\(168\) 0 0
\(169\) 4.58057 0.352351
\(170\) 0 0
\(171\) −0.332426 0.575779i −0.0254213 0.0440309i
\(172\) 0 0
\(173\) −1.24487 + 2.15619i −0.0946461 + 0.163932i −0.909461 0.415790i \(-0.863505\pi\)
0.814815 + 0.579721i \(0.196839\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 8.52663 14.7685i 0.640900 1.11007i
\(178\) 0 0
\(179\) −7.56700 13.1064i −0.565584 0.979621i −0.996995 0.0774652i \(-0.975317\pi\)
0.431411 0.902156i \(-0.358016\pi\)
\(180\) 0 0
\(181\) 11.0637 0.822357 0.411179 0.911555i \(-0.365117\pi\)
0.411179 + 0.911555i \(0.365117\pi\)
\(182\) 0 0
\(183\) −13.6692 −1.01046
\(184\) 0 0
\(185\) −0.0848805 0.147017i −0.00624054 0.0108089i
\(186\) 0 0
\(187\) −2.36748 + 4.10059i −0.173127 + 0.299865i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.2258 19.4437i 0.812274 1.40690i −0.0989957 0.995088i \(-0.531563\pi\)
0.911269 0.411811i \(-0.135104\pi\)
\(192\) 0 0
\(193\) −1.55741 2.69751i −0.112105 0.194171i 0.804514 0.593934i \(-0.202426\pi\)
−0.916619 + 0.399763i \(0.869093\pi\)
\(194\) 0 0
\(195\) −7.88252 −0.564479
\(196\) 0 0
\(197\) 1.38765 0.0988659 0.0494330 0.998777i \(-0.484259\pi\)
0.0494330 + 0.998777i \(0.484259\pi\)
\(198\) 0 0
\(199\) 0.206732 + 0.358070i 0.0146548 + 0.0253829i 0.873260 0.487255i \(-0.162002\pi\)
−0.858605 + 0.512638i \(0.828668\pi\)
\(200\) 0 0
\(201\) −12.3551 + 21.3996i −0.871458 + 1.50941i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −5.83152 + 10.1005i −0.407291 + 0.705449i
\(206\) 0 0
\(207\) 0.0728797 + 0.126231i 0.00506549 + 0.00877368i
\(208\) 0 0
\(209\) −4.09944 −0.283564
\(210\) 0 0
\(211\) 24.6203 1.69493 0.847464 0.530853i \(-0.178128\pi\)
0.847464 + 0.530853i \(0.178128\pi\)
\(212\) 0 0
\(213\) 6.46212 + 11.1927i 0.442777 + 0.766913i
\(214\) 0 0
\(215\) 5.07288 8.78649i 0.345968 0.599233i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −14.3343 + 24.8277i −0.968622 + 1.67770i
\(220\) 0 0
\(221\) 3.01339 + 5.21935i 0.202703 + 0.351091i
\(222\) 0 0
\(223\) −17.9065 −1.19911 −0.599555 0.800334i \(-0.704656\pi\)
−0.599555 + 0.800334i \(0.704656\pi\)
\(224\) 0 0
\(225\) 0.534253 0.0356168
\(226\) 0 0
\(227\) 6.27428 + 10.8674i 0.416439 + 0.721293i 0.995578 0.0939352i \(-0.0299447\pi\)
−0.579139 + 0.815229i \(0.696611\pi\)
\(228\) 0 0
\(229\) 7.91768 13.7138i 0.523215 0.906235i −0.476420 0.879218i \(-0.658066\pi\)
0.999635 0.0270173i \(-0.00860092\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.6896 20.2470i 0.765811 1.32642i −0.174005 0.984745i \(-0.555671\pi\)
0.939817 0.341680i \(-0.110996\pi\)
\(234\) 0 0
\(235\) −1.56221 2.70582i −0.101907 0.176508i
\(236\) 0 0
\(237\) −28.1073 −1.82577
\(238\) 0 0
\(239\) 20.9135 1.35278 0.676390 0.736544i \(-0.263544\pi\)
0.676390 + 0.736544i \(0.263544\pi\)
\(240\) 0 0
\(241\) 1.67873 + 2.90765i 0.108137 + 0.187298i 0.915015 0.403419i \(-0.132178\pi\)
−0.806879 + 0.590717i \(0.798845\pi\)
\(242\) 0 0
\(243\) −2.74483 + 4.75418i −0.176081 + 0.304981i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.60894 + 4.51882i −0.166003 + 0.287526i
\(248\) 0 0
\(249\) 0.157163 + 0.272215i 0.00995983 + 0.0172509i
\(250\) 0 0
\(251\) 16.5717 1.04600 0.522999 0.852333i \(-0.324813\pi\)
0.522999 + 0.852333i \(0.324813\pi\)
\(252\) 0 0
\(253\) 0.898744 0.0565036
\(254\) 0 0
\(255\) −1.35110 2.34018i −0.0846092 0.146547i
\(256\) 0 0
\(257\) −6.57069 + 11.3808i −0.409869 + 0.709913i −0.994875 0.101116i \(-0.967759\pi\)
0.585006 + 0.811029i \(0.301092\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0.631134 1.09316i 0.0390662 0.0676647i
\(262\) 0 0
\(263\) 1.87740 + 3.25175i 0.115765 + 0.200511i 0.918085 0.396383i \(-0.129735\pi\)
−0.802320 + 0.596894i \(0.796401\pi\)
\(264\) 0 0
\(265\) 9.24701 0.568040
\(266\) 0 0
\(267\) −5.82542 −0.356510
\(268\) 0 0
\(269\) −8.24761 14.2853i −0.502866 0.870989i −0.999995 0.00331226i \(-0.998946\pi\)
0.497129 0.867677i \(-0.334388\pi\)
\(270\) 0 0
\(271\) 11.2710 19.5220i 0.684665 1.18588i −0.288876 0.957366i \(-0.593282\pi\)
0.973542 0.228509i \(-0.0733850\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.64709 2.85284i 0.0993231 0.172033i
\(276\) 0 0
\(277\) 7.49909 + 12.9888i 0.450577 + 0.780422i 0.998422 0.0561578i \(-0.0178850\pi\)
−0.547845 + 0.836580i \(0.684552\pi\)
\(278\) 0 0
\(279\) −1.99125 −0.119213
\(280\) 0 0
\(281\) −28.0283 −1.67203 −0.836014 0.548709i \(-0.815120\pi\)
−0.836014 + 0.548709i \(0.815120\pi\)
\(282\) 0 0
\(283\) 13.0857 + 22.6652i 0.777866 + 1.34730i 0.933169 + 0.359437i \(0.117031\pi\)
−0.155303 + 0.987867i \(0.549635\pi\)
\(284\) 0 0
\(285\) 1.16976 2.02609i 0.0692907 0.120015i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.46698 12.9332i 0.439234 0.760776i
\(290\) 0 0
\(291\) 6.21228 + 10.7600i 0.364170 + 0.630761i
\(292\) 0 0
\(293\) 15.6061 0.911716 0.455858 0.890052i \(-0.349332\pi\)
0.455858 + 0.890052i \(0.349332\pi\)
\(294\) 0 0
\(295\) 9.07107 0.528138
\(296\) 0 0
\(297\) 7.63509 + 13.2244i 0.443033 + 0.767355i
\(298\) 0 0
\(299\) 0.571974 0.990688i 0.0330781 0.0572929i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 17.7066 30.6687i 1.01722 1.76187i
\(304\) 0 0
\(305\) −3.63551 6.29689i −0.208169 0.360559i
\(306\) 0 0
\(307\) 21.3055 1.21597 0.607984 0.793949i \(-0.291978\pi\)
0.607984 + 0.793949i \(0.291978\pi\)
\(308\) 0 0
\(309\) 2.75895 0.156951
\(310\) 0 0
\(311\) 7.43993 + 12.8863i 0.421880 + 0.730717i 0.996123 0.0879671i \(-0.0280370\pi\)
−0.574243 + 0.818685i \(0.694704\pi\)
\(312\) 0 0
\(313\) −1.08137 + 1.87298i −0.0611224 + 0.105867i −0.894967 0.446132i \(-0.852801\pi\)
0.833845 + 0.551999i \(0.186135\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.7297 18.5844i 0.602642 1.04381i −0.389777 0.920909i \(-0.627448\pi\)
0.992419 0.122897i \(-0.0392186\pi\)
\(318\) 0 0
\(319\) −3.89154 6.74034i −0.217884 0.377387i
\(320\) 0 0
\(321\) −25.4970 −1.42311
\(322\) 0 0
\(323\) −1.78874 −0.0995282
\(324\) 0 0
\(325\) −2.09646 3.63117i −0.116291 0.201421i
\(326\) 0 0
\(327\) 13.9249 24.1186i 0.770048 1.33376i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 5.83461 10.1058i 0.320699 0.555468i −0.659933 0.751324i \(-0.729415\pi\)
0.980633 + 0.195857i \(0.0627488\pi\)
\(332\) 0 0
\(333\) −0.0453476 0.0785444i −0.00248504 0.00430421i
\(334\) 0 0
\(335\) −13.1439 −0.718131
\(336\) 0 0
\(337\) 17.1403 0.933693 0.466846 0.884338i \(-0.345390\pi\)
0.466846 + 0.884338i \(0.345390\pi\)
\(338\) 0 0
\(339\) −12.3986 21.4750i −0.673399 1.16636i
\(340\) 0 0
\(341\) −6.13898 + 10.6330i −0.332444 + 0.575810i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.256453 + 0.444190i −0.0138070 + 0.0239144i
\(346\) 0 0
\(347\) −2.60035 4.50394i −0.139594 0.241784i 0.787749 0.615996i \(-0.211246\pi\)
−0.927343 + 0.374212i \(0.877913\pi\)
\(348\) 0 0
\(349\) −33.8645 −1.81272 −0.906362 0.422501i \(-0.861152\pi\)
−0.906362 + 0.422501i \(0.861152\pi\)
\(350\) 0 0
\(351\) 19.4363 1.03743
\(352\) 0 0
\(353\) 11.6226 + 20.1309i 0.618606 + 1.07146i 0.989740 + 0.142878i \(0.0456357\pi\)
−0.371134 + 0.928579i \(0.621031\pi\)
\(354\) 0 0
\(355\) −3.43737 + 5.95370i −0.182437 + 0.315990i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.1421 17.5667i 0.535281 0.927135i −0.463868 0.885904i \(-0.653539\pi\)
0.999150 0.0412304i \(-0.0131278\pi\)
\(360\) 0 0
\(361\) 8.72567 + 15.1133i 0.459246 + 0.795437i
\(362\) 0 0
\(363\) 0.279014 0.0146445
\(364\) 0 0
\(365\) −15.2496 −0.798199
\(366\) 0 0
\(367\) 6.63690 + 11.4954i 0.346443 + 0.600057i 0.985615 0.169007i \(-0.0540560\pi\)
−0.639172 + 0.769064i \(0.720723\pi\)
\(368\) 0 0
\(369\) −3.11551 + 5.39621i −0.162187 + 0.280916i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 17.8541 30.9243i 0.924453 1.60120i 0.132014 0.991248i \(-0.457856\pi\)
0.792439 0.609951i \(-0.208811\pi\)
\(374\) 0 0
\(375\) 0.939980 + 1.62809i 0.0485404 + 0.0840744i
\(376\) 0 0
\(377\) −9.90652 −0.510212
\(378\) 0 0
\(379\) −12.6878 −0.651728 −0.325864 0.945417i \(-0.605655\pi\)
−0.325864 + 0.945417i \(0.605655\pi\)
\(380\) 0 0
\(381\) 6.44937 + 11.1706i 0.330411 + 0.572289i
\(382\) 0 0
\(383\) −18.2853 + 31.6711i −0.934337 + 1.61832i −0.158525 + 0.987355i \(0.550674\pi\)
−0.775812 + 0.630964i \(0.782660\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.71020 4.69420i 0.137767 0.238620i
\(388\) 0 0
\(389\) −15.0543 26.0748i −0.763282 1.32204i −0.941150 0.337989i \(-0.890253\pi\)
0.177868 0.984054i \(-0.443080\pi\)
\(390\) 0 0
\(391\) 0.392156 0.0198322
\(392\) 0 0
\(393\) 0.649918 0.0327840
\(394\) 0 0
\(395\) −7.47551 12.9480i −0.376134 0.651483i
\(396\) 0 0
\(397\) 3.73378 6.46710i 0.187393 0.324574i −0.756987 0.653430i \(-0.773330\pi\)
0.944380 + 0.328855i \(0.106663\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.86657 10.1612i 0.292963 0.507426i −0.681546 0.731775i \(-0.738692\pi\)
0.974509 + 0.224349i \(0.0720255\pi\)
\(402\) 0 0
\(403\) 7.81386 + 13.5340i 0.389236 + 0.674177i
\(404\) 0 0
\(405\) −10.3173 −0.512672
\(406\) 0 0
\(407\) −0.559222 −0.0277196
\(408\) 0 0
\(409\) −8.43006 14.6013i −0.416840 0.721987i 0.578780 0.815484i \(-0.303529\pi\)
−0.995620 + 0.0934964i \(0.970196\pi\)
\(410\) 0 0
\(411\) 10.6347 18.4198i 0.524569 0.908581i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −0.0835993 + 0.144798i −0.00410373 + 0.00710787i
\(416\) 0 0
\(417\) 2.52747 + 4.37771i 0.123771 + 0.214377i
\(418\) 0 0
\(419\) −10.3884 −0.507507 −0.253753 0.967269i \(-0.581665\pi\)
−0.253753 + 0.967269i \(0.581665\pi\)
\(420\) 0 0
\(421\) 13.7758 0.671393 0.335696 0.941970i \(-0.391028\pi\)
0.335696 + 0.941970i \(0.391028\pi\)
\(422\) 0 0
\(423\) −0.834613 1.44559i −0.0405803 0.0702871i
\(424\) 0 0
\(425\) 0.718686 1.24480i 0.0348614 0.0603817i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −12.9832 + 22.4876i −0.626835 + 1.08571i
\(430\) 0 0
\(431\) −15.2284 26.3764i −0.733527 1.27051i −0.955367 0.295422i \(-0.904540\pi\)
0.221840 0.975083i \(-0.428794\pi\)
\(432\) 0 0
\(433\) 25.9182 1.24555 0.622774 0.782402i \(-0.286006\pi\)
0.622774 + 0.782402i \(0.286006\pi\)
\(434\) 0 0
\(435\) 4.44175 0.212965
\(436\) 0 0
\(437\) 0.169761 + 0.294035i 0.00812077 + 0.0140656i
\(438\) 0 0
\(439\) 13.4707 23.3320i 0.642922 1.11357i −0.341855 0.939753i \(-0.611055\pi\)
0.984777 0.173821i \(-0.0556115\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.19292 14.1906i 0.389257 0.674213i −0.603093 0.797671i \(-0.706065\pi\)
0.992350 + 0.123458i \(0.0393984\pi\)
\(444\) 0 0
\(445\) −1.54935 2.68355i −0.0734461 0.127212i
\(446\) 0 0
\(447\) −24.6914 −1.16786
\(448\) 0 0
\(449\) 14.2152 0.670858 0.335429 0.942065i \(-0.391119\pi\)
0.335429 + 0.942065i \(0.391119\pi\)
\(450\) 0 0
\(451\) 19.2100 + 33.2728i 0.904566 + 1.56675i
\(452\) 0 0
\(453\) 2.83066 4.90285i 0.132996 0.230356i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.25464 12.5654i 0.339358 0.587785i −0.644954 0.764221i \(-0.723124\pi\)
0.984312 + 0.176436i \(0.0564569\pi\)
\(458\) 0 0
\(459\) 3.33147 + 5.77028i 0.155500 + 0.269334i
\(460\) 0 0
\(461\) −17.8933 −0.833374 −0.416687 0.909050i \(-0.636809\pi\)
−0.416687 + 0.909050i \(0.636809\pi\)
\(462\) 0 0
\(463\) 15.2657 0.709457 0.354729 0.934969i \(-0.384573\pi\)
0.354729 + 0.934969i \(0.384573\pi\)
\(464\) 0 0
\(465\) −3.50347 6.06819i −0.162469 0.281405i
\(466\) 0 0
\(467\) −11.7746 + 20.3942i −0.544863 + 0.943731i 0.453752 + 0.891128i \(0.350085\pi\)
−0.998616 + 0.0526029i \(0.983248\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 18.2949 31.6877i 0.842986 1.46009i
\(472\) 0 0
\(473\) −16.7110 28.9442i −0.768370 1.33086i
\(474\) 0 0
\(475\) 1.24445 0.0570994
\(476\) 0 0
\(477\) 4.94024 0.226198
\(478\) 0 0
\(479\) −2.32933 4.03452i −0.106430 0.184342i 0.807892 0.589331i \(-0.200609\pi\)
−0.914322 + 0.404989i \(0.867275\pi\)
\(480\) 0 0
\(481\) −0.355897 + 0.616432i −0.0162275 + 0.0281069i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.30447 + 5.72351i −0.150048 + 0.259891i
\(486\) 0 0
\(487\) −5.76052 9.97751i −0.261034 0.452124i 0.705483 0.708727i \(-0.250730\pi\)
−0.966517 + 0.256603i \(0.917397\pi\)
\(488\) 0 0
\(489\) −25.3648 −1.14704
\(490\) 0 0
\(491\) −14.2771 −0.644317 −0.322158 0.946686i \(-0.604408\pi\)
−0.322158 + 0.946686i \(0.604408\pi\)
\(492\) 0 0
\(493\) −1.69802 2.94106i −0.0764752 0.132459i
\(494\) 0 0
\(495\) 0.879961 1.52414i 0.0395513 0.0685049i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −18.4895 + 32.0247i −0.827703 + 1.43362i 0.0721332 + 0.997395i \(0.477019\pi\)
−0.899836 + 0.436228i \(0.856314\pi\)
\(500\) 0 0
\(501\) 11.5628 + 20.0274i 0.516588 + 0.894757i
\(502\) 0 0
\(503\) −8.08985 −0.360709 −0.180354 0.983602i \(-0.557724\pi\)
−0.180354 + 0.983602i \(0.557724\pi\)
\(504\) 0 0
\(505\) 18.8372 0.838243
\(506\) 0 0
\(507\) 4.30564 + 7.45760i 0.191220 + 0.331203i
\(508\) 0 0
\(509\) 14.0403 24.3185i 0.622325 1.07790i −0.366727 0.930329i \(-0.619522\pi\)
0.989052 0.147569i \(-0.0471449\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.88434 + 4.99581i −0.127347 + 0.220571i
\(514\) 0 0
\(515\) 0.733780 + 1.27094i 0.0323342 + 0.0560045i
\(516\) 0 0
\(517\) −10.2924 −0.452658
\(518\) 0 0
\(519\) −4.68063 −0.205457
\(520\) 0 0
\(521\) 6.29048 + 10.8954i 0.275591 + 0.477338i 0.970284 0.241969i \(-0.0777931\pi\)
−0.694693 + 0.719306i \(0.744460\pi\)
\(522\) 0 0
\(523\) 0.742265 1.28564i 0.0324570 0.0562172i −0.849341 0.527845i \(-0.823000\pi\)
0.881798 + 0.471628i \(0.156333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.67866 + 4.63958i −0.116684 + 0.202103i
\(528\) 0 0
\(529\) 11.4628 + 19.8541i 0.498382 + 0.863223i
\(530\) 0 0
\(531\) 4.84624 0.210309
\(532\) 0 0
\(533\) 48.9022 2.11819
\(534\) 0 0
\(535\) −6.78127 11.7455i −0.293180 0.507802i
\(536\) 0 0
\(537\) 14.2257 24.6396i 0.613883 1.06328i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −9.45673 + 16.3795i −0.406577 + 0.704211i −0.994504 0.104703i \(-0.966611\pi\)
0.587927 + 0.808914i \(0.299944\pi\)
\(542\) 0 0
\(543\) 10.3997 + 18.0127i 0.446292 + 0.773000i
\(544\) 0 0
\(545\) 14.8140 0.634563
\(546\) 0 0
\(547\) −17.4403 −0.745693 −0.372846 0.927893i \(-0.621618\pi\)
−0.372846 + 0.927893i \(0.621618\pi\)
\(548\) 0 0
\(549\) −1.94228 3.36413i −0.0828945 0.143577i
\(550\) 0 0
\(551\) 1.47012 2.54633i 0.0626293 0.108477i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.159572 0.276387i 0.00677346 0.0117320i
\(556\) 0 0
\(557\) −9.60532 16.6369i −0.406990 0.704928i 0.587560 0.809180i \(-0.300088\pi\)
−0.994551 + 0.104252i \(0.966755\pi\)
\(558\) 0 0
\(559\) −42.5403 −1.79926
\(560\) 0 0
\(561\) −8.90152 −0.375823
\(562\) 0 0
\(563\) −16.8976 29.2675i −0.712150 1.23348i −0.964049 0.265726i \(-0.914388\pi\)
0.251899 0.967754i \(-0.418945\pi\)
\(564\) 0 0
\(565\) 6.59513 11.4231i 0.277459 0.480574i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.31818 + 4.01520i −0.0971830 + 0.168326i −0.910518 0.413470i \(-0.864317\pi\)
0.813335 + 0.581796i \(0.197650\pi\)
\(570\) 0 0
\(571\) −21.9341 37.9909i −0.917912 1.58987i −0.802581 0.596543i \(-0.796541\pi\)
−0.115330 0.993327i \(-0.536793\pi\)
\(572\) 0 0
\(573\) 42.2083 1.76328
\(574\) 0 0
\(575\) −0.272828 −0.0113777
\(576\) 0 0
\(577\) −4.63878 8.03460i −0.193115 0.334485i 0.753166 0.657830i \(-0.228526\pi\)
−0.946281 + 0.323346i \(0.895192\pi\)
\(578\) 0 0
\(579\) 2.92787 5.07122i 0.121678 0.210753i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 15.2306 26.3802i 0.630789 1.09256i
\(584\) 0 0
\(585\) −1.12004 1.93996i −0.0463079 0.0802077i
\(586\) 0 0
\(587\) 28.9971 1.19684 0.598420 0.801183i \(-0.295796\pi\)
0.598420 + 0.801183i \(0.295796\pi\)
\(588\) 0 0
\(589\) −4.63829 −0.191117
\(590\) 0 0
\(591\) 1.30436 + 2.25922i 0.0536543 + 0.0929320i
\(592\) 0 0
\(593\) 12.7614 22.1034i 0.524047 0.907676i −0.475561 0.879683i \(-0.657755\pi\)
0.999608 0.0279933i \(-0.00891171\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.388647 + 0.673157i −0.0159063 + 0.0275505i
\(598\) 0 0
\(599\) −15.5182 26.8783i −0.634057 1.09822i −0.986714 0.162466i \(-0.948055\pi\)
0.352657 0.935752i \(-0.385278\pi\)
\(600\) 0 0
\(601\) 3.56479 0.145411 0.0727054 0.997353i \(-0.476837\pi\)
0.0727054 + 0.997353i \(0.476837\pi\)
\(602\) 0 0
\(603\) −7.02219 −0.285966
\(604\) 0 0
\(605\) 0.0742075 + 0.128531i 0.00301697 + 0.00522554i
\(606\) 0 0
\(607\) 3.36310 5.82506i 0.136504 0.236432i −0.789667 0.613536i \(-0.789747\pi\)
0.926171 + 0.377104i \(0.123080\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −6.55021 + 11.3453i −0.264993 + 0.458981i
\(612\) 0 0
\(613\) 9.87112 + 17.0973i 0.398691 + 0.690553i 0.993565 0.113266i \(-0.0361314\pi\)
−0.594874 + 0.803819i \(0.702798\pi\)
\(614\) 0 0
\(615\) −21.9261 −0.884144
\(616\) 0 0
\(617\) −16.3958 −0.660069 −0.330035 0.943969i \(-0.607060\pi\)
−0.330035 + 0.943969i \(0.607060\pi\)
\(618\) 0 0
\(619\) −17.7755 30.7881i −0.714458 1.23748i −0.963168 0.268900i \(-0.913340\pi\)
0.248710 0.968578i \(-0.419994\pi\)
\(620\) 0 0
\(621\) 0.632349 1.09526i 0.0253753 0.0439513i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −3.85340 6.67428i −0.153890 0.266545i
\(628\) 0 0
\(629\) −0.244010 −0.00972930
\(630\) 0 0
\(631\) −9.58569 −0.381600 −0.190800 0.981629i \(-0.561108\pi\)
−0.190800 + 0.981629i \(0.561108\pi\)
\(632\) 0 0
\(633\) 23.1426 + 40.0841i 0.919834 + 1.59320i
\(634\) 0 0
\(635\) −3.43059 + 5.94195i −0.136139 + 0.235799i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −1.83643 + 3.18078i −0.0726479 + 0.125830i
\(640\) 0 0
\(641\) −9.75727 16.9001i −0.385389 0.667513i 0.606434 0.795134i \(-0.292599\pi\)
−0.991823 + 0.127621i \(0.959266\pi\)
\(642\) 0 0
\(643\) −18.9895 −0.748872 −0.374436 0.927253i \(-0.622164\pi\)
−0.374436 + 0.927253i \(0.622164\pi\)
\(644\) 0 0
\(645\) 19.0736 0.751023
\(646\) 0 0
\(647\) −20.6285 35.7296i −0.810989 1.40467i −0.912172 0.409807i \(-0.865596\pi\)
0.101183 0.994868i \(-0.467737\pi\)
\(648\) 0 0
\(649\) 14.9408 25.8783i 0.586479 1.01581i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.87474 17.1036i 0.386429 0.669314i −0.605538 0.795817i \(-0.707042\pi\)
0.991966 + 0.126503i \(0.0403753\pi\)
\(654\) 0 0
\(655\) 0.172854 + 0.299392i 0.00675397 + 0.0116982i
\(656\) 0 0
\(657\) −8.14713 −0.317850
\(658\) 0 0
\(659\) 10.1830 0.396672 0.198336 0.980134i \(-0.436446\pi\)
0.198336 + 0.980134i \(0.436446\pi\)
\(660\) 0 0
\(661\) 1.39543 + 2.41696i 0.0542759 + 0.0940087i 0.891887 0.452259i \(-0.149382\pi\)
−0.837611 + 0.546267i \(0.816048\pi\)
\(662\) 0 0
\(663\) −5.66506 + 9.81217i −0.220013 + 0.381073i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.322303 + 0.558245i −0.0124796 + 0.0216153i
\(668\) 0 0
\(669\) −16.8318 29.1535i −0.650754 1.12714i
\(670\) 0 0
\(671\) −23.9520 −0.924657
\(672\) 0 0
\(673\) 18.2879 0.704947 0.352473 0.935822i \(-0.385341\pi\)
0.352473 + 0.935822i \(0.385341\pi\)
\(674\) 0 0
\(675\) −2.31775 4.01447i −0.0892104 0.154517i
\(676\) 0 0
\(677\) −12.0261 + 20.8299i −0.462202 + 0.800558i −0.999070 0.0431084i \(-0.986274\pi\)
0.536868 + 0.843666i \(0.319607\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −11.7954 + 20.4302i −0.452001 + 0.782889i
\(682\) 0 0
\(683\) 19.1100 + 33.0995i 0.731224 + 1.26652i 0.956360 + 0.292190i \(0.0943839\pi\)
−0.225136 + 0.974327i \(0.572283\pi\)
\(684\) 0 0
\(685\) 11.3137 0.432275
\(686\) 0 0
\(687\) 29.7699 1.13579
\(688\) 0 0
\(689\) −19.3860 33.5775i −0.738547 1.27920i
\(690\) 0 0
\(691\) −13.2312 + 22.9171i −0.503337 + 0.871806i 0.496655 + 0.867948i \(0.334561\pi\)
−0.999993 + 0.00385805i \(0.998772\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.34443 + 2.32862i −0.0509970 + 0.0883294i
\(696\) 0 0
\(697\) 8.38206 + 14.5182i 0.317493 + 0.549914i
\(698\) 0 0
\(699\) 43.9520 1.66242
\(700\) 0 0
\(701\) −34.5136 −1.30356 −0.651780 0.758408i \(-0.725977\pi\)
−0.651780 + 0.758408i \(0.725977\pi\)
\(702\) 0 0
\(703\) −0.105630 0.182956i −0.00398390 0.00690032i
\(704\) 0 0
\(705\) 2.93689 5.08684i 0.110610 0.191581i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3.20450 + 5.55035i −0.120347 + 0.208448i −0.919905 0.392142i \(-0.871734\pi\)
0.799557 + 0.600590i \(0.205068\pi\)
\(710\) 0 0
\(711\) −3.99381 6.91749i −0.149780 0.259426i
\(712\) 0 0
\(713\) 1.01688 0.0380824
\(714\) 0 0
\(715\) −13.8122 −0.516547
\(716\) 0 0
\(717\) 19.6582 + 34.0491i 0.734151 + 1.27159i
\(718\) 0 0
\(719\) −19.3035 + 33.4347i −0.719900 + 1.24690i 0.241139 + 0.970491i \(0.422479\pi\)
−0.961039 + 0.276413i \(0.910854\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −3.15595 + 5.46626i −0.117371 + 0.203293i
\(724\) 0 0
\(725\) 1.18134 + 2.04614i 0.0438739 + 0.0759918i
\(726\) 0 0
\(727\) −22.5280 −0.835516 −0.417758 0.908558i \(-0.637184\pi\)
−0.417758 + 0.908558i \(0.637184\pi\)
\(728\) 0 0
\(729\) 20.6317 0.764136
\(730\) 0 0
\(731\) −7.29161 12.6294i −0.269690 0.467117i
\(732\) 0 0
\(733\) 3.75075 6.49649i 0.138537 0.239953i −0.788406 0.615155i \(-0.789093\pi\)
0.926943 + 0.375202i \(0.122427\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.6492 + 37.4976i −0.797460 + 1.38124i
\(738\) 0 0
\(739\) −17.5432 30.3857i −0.645336 1.11776i −0.984224 0.176928i \(-0.943384\pi\)
0.338888 0.940827i \(-0.389949\pi\)
\(740\) 0 0
\(741\) −9.80943 −0.360358
\(742\) 0 0
\(743\) −2.42902 −0.0891122 −0.0445561 0.999007i \(-0.514187\pi\)
−0.0445561 + 0.999007i \(0.514187\pi\)
\(744\) 0 0
\(745\) −6.56700 11.3744i −0.240596 0.416725i
\(746\) 0 0
\(747\) −0.0446632 + 0.0773589i −0.00163414 + 0.00283041i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −10.4799 + 18.1517i −0.382417 + 0.662365i −0.991407 0.130813i \(-0.958241\pi\)
0.608991 + 0.793177i \(0.291575\pi\)
\(752\) 0 0
\(753\) 15.5771 + 26.9803i 0.567661 + 0.983218i
\(754\) 0 0
\(755\) 3.01140 0.109596
\(756\) 0 0
\(757\) −35.9748 −1.30753 −0.653763 0.756699i \(-0.726811\pi\)
−0.653763 + 0.756699i \(0.726811\pi\)
\(758\) 0 0
\(759\) 0.844802 + 1.46324i 0.0306644 + 0.0531123i
\(760\) 0 0
\(761\) 1.22876 2.12828i 0.0445426 0.0771500i −0.842895 0.538079i \(-0.819150\pi\)
0.887437 + 0.460929i \(0.152484\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.383960 0.665038i 0.0138821 0.0240445i
\(766\) 0 0
\(767\) −19.0171 32.9386i −0.686669 1.18934i
\(768\) 0 0
\(769\) 21.6994 0.782501 0.391250 0.920284i \(-0.372043\pi\)
0.391250 + 0.920284i \(0.372043\pi\)
\(770\) 0 0
\(771\) −24.7053 −0.889739
\(772\) 0 0
\(773\) −7.84900 13.5949i −0.282309 0.488973i 0.689644 0.724149i \(-0.257767\pi\)
−0.971953 + 0.235175i \(0.924434\pi\)
\(774\) 0 0
\(775\) 1.86359 3.22783i 0.0669420 0.115947i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.25705 + 12.5696i −0.260011 + 0.450352i
\(780\) 0 0
\(781\) 11.3233 + 19.6125i 0.405180 + 0.701792i
\(782\) 0 0
\(783\) −10.9522 −0.391400
\(784\) 0 0
\(785\) 19.4631 0.694668
\(786\) 0 0
\(787\) 12.2537 + 21.2240i 0.436797 + 0.756554i 0.997440 0.0715029i \(-0.0227795\pi\)
−0.560644 + 0.828057i \(0.689446\pi\)
\(788\) 0 0
\(789\) −3.52944 + 6.11316i −0.125651 + 0.217634i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −15.2434 + 26.4023i −0.541309 + 0.937574i
\(794\) 0 0
\(795\) 8.69201 + 15.0550i 0.308274 + 0.533946i
\(796\) 0 0
\(797\) 5.73557 0.203164 0.101582 0.994827i \(-0.467610\pi\)
0.101582 + 0.994827i \(0.467610\pi\)
\(798\) 0 0
\(799\) −4.49094 −0.158878