Properties

Label 1960.2.q.x.361.4
Level $1960$
Weight $2$
Character 1960.361
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 361.4
Root \(-0.939980 + 1.62809i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.x.961.4

$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 −0.456050 0.889954i \(-0.650736\pi\)
0.998748 0.0500262i \(-0.0159305\pi\)
\(4\) 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 −0.503377 0.864067i \(-0.667909\pi\)
0.999992 + 0.00390371i \(0.00124259\pi\)
\(12\) 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 −0.765614 0.643300i \(-0.777565\pi\)
0.939921 + 0.341392i \(0.110898\pi\)
\(18\) 0 0
\(19\) −0.622226 1.07773i −0.142748 0.247248i 0.785782 0.618503i \(-0.212261\pi\)
−0.928531 + 0.371256i \(0.878927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.136414 + 0.236276i 0.0284443 + 0.0492670i 0.879897 0.475164i \(-0.157611\pi\)
−0.851453 + 0.524431i \(0.824278\pi\)
\(24\) 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 −0.648719 0.761028i \(-0.724695\pi\)
0.983429 + 0.181293i \(0.0580283\pi\)
\(32\) 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 0.858964 0.512036i \(-0.171109\pi\)
−0.872918 + 0.487867i \(0.837775\pi\)
\(38\) 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 0.729306 0.684188i \(-0.239843\pi\)
−0.957177 + 0.289503i \(0.906510\pi\)
\(48\) 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 0.351409 + 0.936222i \(0.385703\pi\)
−0.986497 + 0.163782i \(0.947631\pi\)
\(54\) 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 0.403692 + 0.914895i \(0.367727\pi\)
−0.994168 + 0.107840i \(0.965607\pi\)
\(60\) 0 0
\(61\) −3.63551 6.29689i −0.465479 0.806234i 0.533744 0.845646i \(-0.320785\pi\)
−0.999223 + 0.0394127i \(0.987451\pi\)
\(62\) 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 −0.114809 0.993388i \(-0.536626\pi\)
0.917703 0.397266i \(-0.130041\pi\)
\(68\) 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 0.0554412 0.998462i \(-0.482343\pi\)
0.836973 0.547244i \(-0.184323\pi\)
\(74\) 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 −0.888998 0.457910i \(-0.848598\pi\)
0.0479374 0.998850i \(-0.484735\pi\)
\(80\) 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 0.772151 0.635439i \(-0.219181\pi\)
−0.936382 + 0.350983i \(0.885847\pi\)
\(90\) 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 −0.166493 + 0.986043i \(0.553244\pi\)
−0.770691 + 0.637209i \(0.780089\pi\)
\(102\) 0 0
\(103\) 0.733780 + 1.27094i 0.0723014 + 0.125230i 0.899910 0.436077i \(-0.143632\pi\)
−0.827608 + 0.561306i \(0.810299\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.78127 11.7455i −0.655570 1.13548i −0.981751 0.190173i \(-0.939095\pi\)
0.326181 0.945307i \(-0.394238\pi\)
\(108\) 0 0
\(109\) −7.40701 + 12.8293i −0.709463 + 1.22883i 0.255594 + 0.966784i \(0.417729\pi\)
−0.965057 + 0.262041i \(0.915604\pi\)
\(110\) 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 0.873478 0.486864i \(-0.161859\pi\)
−0.858375 + 0.513022i \(0.828526\pi\)
\(132\) 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 −0.999816 0.0191800i \(-0.993894\pi\)
0.516518 + 0.856276i \(0.327228\pi\)
\(138\) 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 −0.999012 0.0444372i \(-0.985851\pi\)
0.461022 0.887389i \(-0.347483\pi\)
\(150\) 0 0
\(151\) −1.50570 + 2.60795i −0.122532 + 0.212232i −0.920766 0.390116i \(-0.872435\pi\)
0.798233 + 0.602348i \(0.205768\pi\)
\(152\) 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 0.157194 + 0.987568i \(0.449755\pi\)
−0.933856 + 0.357650i \(0.883578\pi\)
\(158\) 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 −0.999452 0.0331054i \(-0.989460\pi\)
0.471056 0.882103i \(-0.343873\pi\)
\(164\) 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 0.814815 0.579721i \(-0.196839\pi\)
−0.909461 + 0.415790i \(0.863505\pi\)
\(174\) 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 0.431411 + 0.902156i \(0.358016\pi\)
−0.996995 + 0.0774652i \(0.975317\pi\)
\(180\) 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 0.911269 + 0.411811i \(0.135104\pi\)
−0.0989957 + 0.995088i \(0.531563\pi\)
\(192\) 0 0
\(193\) −1.55741 + 2.69751i −0.112105 + 0.194171i −0.916619 0.399763i \(-0.869093\pi\)
0.804514 + 0.593934i \(0.202426\pi\)
\(194\) 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 −0.858605 0.512638i \(-0.828668\pi\)
0.873260 + 0.487255i \(0.162002\pi\)
\(200\) 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 −0.579139 0.815229i \(-0.696611\pi\)
0.995578 + 0.0939352i \(0.0299447\pi\)
\(228\) 0 0
\(229\) 7.91768 + 13.7138i 0.523215 + 0.906235i 0.999635 + 0.0270173i \(0.00860092\pi\)
−0.476420 + 0.879218i \(0.658066\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.6896 + 20.2470i 0.765811 + 1.32642i 0.939817 + 0.341680i \(0.110996\pi\)
−0.174005 + 0.984745i \(0.555671\pi\)
\(234\) 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 −0.806879 0.590717i \(-0.798845\pi\)
0.915015 + 0.403419i \(0.132178\pi\)
\(242\) 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 0.585006 0.811029i \(-0.301092\pi\)
−0.994875 + 0.101116i \(0.967759\pi\)
\(258\) 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 −0.802320 0.596894i \(-0.796401\pi\)
0.918085 + 0.396383i \(0.129735\pi\)
\(264\) 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 0.497129 + 0.867677i \(0.334388\pi\)
−0.999995 + 0.00331226i \(0.998946\pi\)
\(270\) 0 0
\(271\) 11.2710 + 19.5220i 0.684665 + 1.18588i 0.973542 + 0.228509i \(0.0733850\pi\)
−0.288876 + 0.957366i \(0.593282\pi\)
\(272\) 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 −0.547845 0.836580i \(-0.684552\pi\)
0.998422 + 0.0561578i \(0.0178850\pi\)
\(278\) 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 −0.155303 0.987867i \(-0.549635\pi\)
0.933169 0.359437i \(-0.117031\pi\)
\(284\) 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 −0.574243 0.818685i \(-0.694704\pi\)
0.996123 + 0.0879671i \(0.0280370\pi\)
\(312\) 0 0
\(313\) −1.08137 1.87298i −0.0611224 0.105867i 0.833845 0.551999i \(-0.186135\pi\)
−0.894967 + 0.446132i \(0.852801\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.7297 + 18.5844i 0.602642 + 1.04381i 0.992419 + 0.122897i \(0.0392186\pi\)
−0.389777 + 0.920909i \(0.627448\pi\)
\(318\) 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 0.980633 0.195857i \(-0.0627488\pi\)
−0.659933 + 0.751324i \(0.729415\pi\)
\(332\) 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 −0.927343 0.374212i \(-0.877913\pi\)
0.787749 + 0.615996i \(0.211246\pi\)
\(348\) 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 −0.371134 0.928579i \(-0.621031\pi\)
0.989740 0.142878i \(-0.0456357\pi\)
\(354\) 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 0.999150 + 0.0412304i \(0.0131278\pi\)
−0.463868 + 0.885904i \(0.653539\pi\)
\(360\) 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 −0.639172 0.769064i \(-0.720723\pi\)
0.985615 + 0.169007i \(0.0540560\pi\)
\(368\) 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 0.792439 + 0.609951i \(0.208811\pi\)
0.132014 + 0.991248i \(0.457856\pi\)
\(374\) 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 −0.775812 0.630964i \(-0.782660\pi\)
−0.158525 0.987355i \(-0.550674\pi\)
\(384\) 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 0.177868 + 0.984054i \(0.443080\pi\)
−0.941150 + 0.337989i \(0.890253\pi\)
\(390\) 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 0.944380 0.328855i \(-0.106663\pi\)
−0.756987 + 0.653430i \(0.773330\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.86657 + 10.1612i 0.292963 + 0.507426i 0.974509 0.224349i \(-0.0720255\pi\)
−0.681546 + 0.731775i \(0.738692\pi\)
\(402\) 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 −0.995620 0.0934964i \(-0.970196\pi\)
0.578780 + 0.815484i \(0.303529\pi\)
\(410\) 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 0.221840 + 0.975083i \(0.428794\pi\)
−0.955367 + 0.295422i \(0.904540\pi\)
\(432\) 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 0.984777 + 0.173821i \(0.0556115\pi\)
−0.341855 + 0.939753i \(0.611055\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.19292 + 14.1906i 0.389257 + 0.674213i 0.992350 0.123458i \(-0.0393984\pi\)
−0.603093 + 0.797671i \(0.706065\pi\)
\(444\) 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 0.984312 0.176436i \(-0.0564569\pi\)
−0.644954 + 0.764221i \(0.723124\pi\)
\(458\) 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 −0.998616 0.0526029i \(-0.983248\pi\)
0.453752 0.891128i \(-0.350085\pi\)
\(468\) 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 −0.914322 0.404989i \(-0.867275\pi\)
0.807892 + 0.589331i \(0.200609\pi\)
\(480\) 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 −0.966517 0.256603i \(-0.917397\pi\)
0.705483 + 0.708727i \(0.250730\pi\)
\(488\) 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 −0.899836 0.436228i \(-0.856314\pi\)
0.0721332 0.997395i \(-0.477019\pi\)
\(500\) 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 0.989052 + 0.147569i \(0.0471449\pi\)
−0.366727 + 0.930329i \(0.619522\pi\)
\(510\) 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 −0.694693 0.719306i \(-0.744460\pi\)
0.970284 + 0.241969i \(0.0777931\pi\)
\(522\) 0 0
\(523\) 0.742265 + 1.28564i 0.0324570 + 0.0562172i 0.881798 0.471628i \(-0.156333\pi\)
−0.849341 + 0.527845i \(0.823000\pi\)
\(524\) 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 0.587927 0.808914i \(-0.299944\pi\)
−0.994504 + 0.104703i \(0.966611\pi\)
\(542\) 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 −0.994551 0.104252i \(-0.966755\pi\)
0.587560 + 0.809180i \(0.300088\pi\)
\(558\) 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 0.251899 + 0.967754i \(0.418945\pi\)
−0.964049 + 0.265726i \(0.914388\pi\)
\(564\) 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 0.813335 0.581796i \(-0.197650\pi\)
−0.910518 + 0.413470i \(0.864317\pi\)
\(570\) 0 0
\(571\) −21.9341 + 37.9909i −0.917912 + 1.58987i −0.115330 + 0.993327i \(0.536793\pi\)
−0.802581 + 0.596543i \(0.796541\pi\)
\(572\) 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 −0.946281 0.323346i \(-0.895192\pi\)
0.753166 + 0.657830i \(0.228526\pi\)
\(578\) 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 0.999608 + 0.0279933i \(0.00891171\pi\)
−0.475561 + 0.879683i \(0.657755\pi\)
\(594\) 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 0.352657 + 0.935752i \(0.385278\pi\)
−0.986714 + 0.162466i \(0.948055\pi\)
\(600\) 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 0.926171 0.377104i \(-0.123080\pi\)
−0.789667 + 0.613536i \(0.789747\pi\)
\(608\) 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 −0.594874 0.803819i \(-0.702798\pi\)
0.993565 + 0.113266i \(0.0361314\pi\)
\(614\) 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 0.248710 + 0.968578i \(0.419994\pi\)
−0.963168 + 0.268900i \(0.913340\pi\)
\(620\) 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 −0.991823 0.127621i \(-0.959266\pi\)
0.606434 + 0.795134i \(0.292599\pi\)
\(642\) 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 0.101183 + 0.994868i \(0.467737\pi\)
−0.912172 + 0.409807i \(0.865596\pi\)
\(648\) 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 0.991966 0.126503i \(-0.0403753\pi\)
−0.605538 + 0.795817i \(0.707042\pi\)
\(654\) 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 −0.837611 0.546267i \(-0.816048\pi\)
0.891887 + 0.452259i \(0.149382\pi\)
\(662\) 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 0.536868 0.843666i \(-0.319607\pi\)
−0.999070 + 0.0431084i \(0.986274\pi\)
\(678\) 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 −0.225136 0.974327i \(-0.572283\pi\)
0.956360 0.292190i \(-0.0943839\pi\)
\(684\) 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 −0.999993 0.00385805i \(-0.998772\pi\)
0.496655 0.867948i \(-0.334561\pi\)
\(692\) 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 0.799557 0.600590i \(-0.205068\pi\)
−0.919905 + 0.392142i \(0.871734\pi\)
\(710\) 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 −0.961039 0.276413i \(-0.910854\pi\)
0.241139 0.970491i \(-0.422479\pi\)
\(720\) 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 0.926943 0.375202i \(-0.122427\pi\)
−0.788406 + 0.615155i \(0.789093\pi\)
\(734\) 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 0.338888 + 0.940827i \(0.389949\pi\)
−0.984224 + 0.176928i \(0.943384\pi\)
\(740\) 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 0.608991 0.793177i \(-0.291575\pi\)
−0.991407 + 0.130813i \(0.958241\pi\)
\(752\) 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 0.887437 0.460929i \(-0.152484\pi\)
−0.842895 + 0.538079i \(0.819150\pi\)
\(762\) 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 −0.971953 0.235175i \(-0.924434\pi\)
0.689644 + 0.724149i \(0.257767\pi\)
\(774\) 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 −0.560644 0.828057i \(-0.689446\pi\)
0.997440 + 0.0715029i \(0.0227795\pi\)
\(788\) 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