Properties

Label 700.2.i.f.501.2
Level $700$
Weight $2$
Character 700.501
Analytic conductor $5.590$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.2702336256.1
Defining polynomial: \(x^{8} + 9 x^{6} + 56 x^{4} + 225 x^{2} + 625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 501.2
Root \(1.52274 + 1.63746i\) of defining polynomial
Character \(\chi\) \(=\) 700.501
Dual form 700.2.i.f.401.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{3} +(2.38876 + 1.13746i) q^{7} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{3} +(2.38876 + 1.13746i) q^{7} +(2.63746 - 4.56821i) q^{11} +2.62685 q^{13} +(-0.209313 + 0.362541i) q^{17} +(-1.63746 - 2.83616i) q^{19} +(-3.77492 + 2.59808i) q^{21} +(3.91150 + 6.77492i) q^{23} -5.19615 q^{27} +4.27492 q^{29} +(-1.63746 + 2.83616i) q^{31} +(4.56821 + 7.91238i) q^{33} +(4.98684 + 8.63746i) q^{37} +(-2.27492 + 3.94027i) q^{39} -3.72508 q^{41} -2.15068 q^{43} +(-3.25479 - 5.63746i) q^{47} +(4.41238 + 5.43424i) q^{49} +(-0.362541 - 0.627940i) q^{51} +(2.83616 - 4.91238i) q^{53} +5.67232 q^{57} +(1.63746 - 2.83616i) q^{59} +(6.77492 + 11.7345i) q^{61} +(-1.76082 + 3.04983i) q^{67} -13.5498 q^{69} -4.54983 q^{71} +(-3.25479 + 5.63746i) q^{73} +(11.4964 - 7.91238i) q^{77} +(-3.63746 - 6.30026i) q^{79} +(4.50000 - 7.79423i) q^{81} -7.40437 q^{83} +(-3.70219 + 6.41238i) q^{87} +(3.50000 + 6.06218i) q^{89} +(6.27492 + 2.98793i) q^{91} +(-2.83616 - 4.91238i) q^{93} -6.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + O(q^{10}) \) \( 8 q + 6 q^{11} + 2 q^{19} + 4 q^{29} + 2 q^{31} + 12 q^{39} - 60 q^{41} - 10 q^{49} - 18 q^{51} - 2 q^{59} + 24 q^{61} - 48 q^{69} + 24 q^{71} - 14 q^{79} + 36 q^{81} + 28 q^{89} + 20 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.38876 + 1.13746i 0.902867 + 0.429919i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.63746 4.56821i 0.795224 1.37737i −0.127473 0.991842i \(-0.540687\pi\)
0.922697 0.385526i \(-0.125980\pi\)
\(12\) 0 0
\(13\) 2.62685 0.728557 0.364278 0.931290i \(-0.381316\pi\)
0.364278 + 0.931290i \(0.381316\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.209313 + 0.362541i −0.0507659 + 0.0879292i −0.890292 0.455391i \(-0.849500\pi\)
0.839526 + 0.543320i \(0.182833\pi\)
\(18\) 0 0
\(19\) −1.63746 2.83616i −0.375659 0.650660i 0.614767 0.788709i \(-0.289250\pi\)
−0.990425 + 0.138049i \(0.955917\pi\)
\(20\) 0 0
\(21\) −3.77492 + 2.59808i −0.823754 + 0.566947i
\(22\) 0 0
\(23\) 3.91150 + 6.77492i 0.815604 + 1.41267i 0.908893 + 0.417029i \(0.136929\pi\)
−0.0932891 + 0.995639i \(0.529738\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 4.27492 0.793832 0.396916 0.917855i \(-0.370080\pi\)
0.396916 + 0.917855i \(0.370080\pi\)
\(30\) 0 0
\(31\) −1.63746 + 2.83616i −0.294096 + 0.509390i −0.974774 0.223193i \(-0.928352\pi\)
0.680678 + 0.732583i \(0.261685\pi\)
\(32\) 0 0
\(33\) 4.56821 + 7.91238i 0.795224 + 1.37737i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.98684 + 8.63746i 0.819831 + 1.41999i 0.905806 + 0.423692i \(0.139266\pi\)
−0.0859750 + 0.996297i \(0.527401\pi\)
\(38\) 0 0
\(39\) −2.27492 + 3.94027i −0.364278 + 0.630949i
\(40\) 0 0
\(41\) −3.72508 −0.581760 −0.290880 0.956760i \(-0.593948\pi\)
−0.290880 + 0.956760i \(0.593948\pi\)
\(42\) 0 0
\(43\) −2.15068 −0.327975 −0.163988 0.986462i \(-0.552436\pi\)
−0.163988 + 0.986462i \(0.552436\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.25479 5.63746i −0.474760 0.822308i 0.524823 0.851212i \(-0.324132\pi\)
−0.999582 + 0.0289038i \(0.990798\pi\)
\(48\) 0 0
\(49\) 4.41238 + 5.43424i 0.630339 + 0.776320i
\(50\) 0 0
\(51\) −0.362541 0.627940i −0.0507659 0.0879292i
\(52\) 0 0
\(53\) 2.83616 4.91238i 0.389577 0.674767i −0.602816 0.797880i \(-0.705955\pi\)
0.992393 + 0.123114i \(0.0392880\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.67232 0.751318
\(58\) 0 0
\(59\) 1.63746 2.83616i 0.213179 0.369237i −0.739529 0.673125i \(-0.764952\pi\)
0.952708 + 0.303888i \(0.0982849\pi\)
\(60\) 0 0
\(61\) 6.77492 + 11.7345i 0.867439 + 1.50245i 0.864605 + 0.502453i \(0.167569\pi\)
0.00283468 + 0.999996i \(0.499098\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.76082 + 3.04983i −0.215119 + 0.372597i −0.953309 0.301996i \(-0.902347\pi\)
0.738191 + 0.674592i \(0.235681\pi\)
\(68\) 0 0
\(69\) −13.5498 −1.63121
\(70\) 0 0
\(71\) −4.54983 −0.539966 −0.269983 0.962865i \(-0.587018\pi\)
−0.269983 + 0.962865i \(0.587018\pi\)
\(72\) 0 0
\(73\) −3.25479 + 5.63746i −0.380944 + 0.659815i −0.991197 0.132392i \(-0.957734\pi\)
0.610253 + 0.792206i \(0.291068\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 11.4964 7.91238i 1.31014 0.901699i
\(78\) 0 0
\(79\) −3.63746 6.30026i −0.409246 0.708835i 0.585559 0.810630i \(-0.300875\pi\)
−0.994805 + 0.101795i \(0.967542\pi\)
\(80\) 0 0
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 0 0
\(83\) −7.40437 −0.812736 −0.406368 0.913710i \(-0.633205\pi\)
−0.406368 + 0.913710i \(0.633205\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.70219 + 6.41238i −0.396916 + 0.687479i
\(88\) 0 0
\(89\) 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(90\) 0 0
\(91\) 6.27492 + 2.98793i 0.657790 + 0.313220i
\(92\) 0 0
\(93\) −2.83616 4.91238i −0.294096 0.509390i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.92820 −0.703452 −0.351726 0.936103i \(-0.614405\pi\)
−0.351726 + 0.936103i \(0.614405\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.77492 11.7345i 0.674129 1.16763i −0.302593 0.953120i \(-0.597852\pi\)
0.976723 0.214507i \(-0.0688144\pi\)
\(102\) 0 0
\(103\) −5.64355 9.77492i −0.556076 0.963151i −0.997819 0.0660098i \(-0.978973\pi\)
0.441743 0.897141i \(-0.354360\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.76082 3.04983i −0.170225 0.294839i 0.768273 0.640122i \(-0.221116\pi\)
−0.938499 + 0.345283i \(0.887783\pi\)
\(108\) 0 0
\(109\) 5.77492 10.0025i 0.553137 0.958061i −0.444909 0.895576i \(-0.646764\pi\)
0.998046 0.0624852i \(-0.0199026\pi\)
\(110\) 0 0
\(111\) −17.2749 −1.63966
\(112\) 0 0
\(113\) 4.30136 0.404637 0.202319 0.979320i \(-0.435152\pi\)
0.202319 + 0.979320i \(0.435152\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.912376 + 0.627940i −0.0836374 + 0.0575632i
\(120\) 0 0
\(121\) −8.41238 14.5707i −0.764761 1.32461i
\(122\) 0 0
\(123\) 3.22602 5.58762i 0.290880 0.503819i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −15.6460 −1.38836 −0.694179 0.719802i \(-0.744232\pi\)
−0.694179 + 0.719802i \(0.744232\pi\)
\(128\) 0 0
\(129\) 1.86254 3.22602i 0.163988 0.284035i
\(130\) 0 0
\(131\) 5.36254 + 9.28819i 0.468527 + 0.811513i 0.999353 0.0359678i \(-0.0114514\pi\)
−0.530826 + 0.847481i \(0.678118\pi\)
\(132\) 0 0
\(133\) −0.685484 8.63746i −0.0594390 0.748963i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.6592 18.4622i 0.910674 1.57733i 0.0975588 0.995230i \(-0.468897\pi\)
0.813115 0.582103i \(-0.197770\pi\)
\(138\) 0 0
\(139\) 13.0997 1.11110 0.555550 0.831483i \(-0.312508\pi\)
0.555550 + 0.831483i \(0.312508\pi\)
\(140\) 0 0
\(141\) 11.2749 0.949519
\(142\) 0 0
\(143\) 6.92820 12.0000i 0.579365 1.00349i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −11.9726 + 1.91238i −0.987482 + 0.157730i
\(148\) 0 0
\(149\) 3.77492 + 6.53835i 0.309253 + 0.535642i 0.978199 0.207669i \(-0.0665876\pi\)
−0.668946 + 0.743311i \(0.733254\pi\)
\(150\) 0 0
\(151\) 6.36254 11.0202i 0.517776 0.896815i −0.482011 0.876165i \(-0.660093\pi\)
0.999787 0.0206494i \(-0.00657337\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.10411 1.91238i 0.0881176 0.152624i −0.818598 0.574367i \(-0.805248\pi\)
0.906715 + 0.421743i \(0.138582\pi\)
\(158\) 0 0
\(159\) 4.91238 + 8.50848i 0.389577 + 0.674767i
\(160\) 0 0
\(161\) 1.63746 + 20.6328i 0.129050 + 1.62610i
\(162\) 0 0
\(163\) −2.83616 4.91238i −0.222145 0.384767i 0.733314 0.679890i \(-0.237973\pi\)
−0.955459 + 0.295123i \(0.904639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.476171 −0.0368472 −0.0184236 0.999830i \(-0.505865\pi\)
−0.0184236 + 0.999830i \(0.505865\pi\)
\(168\) 0 0
\(169\) −6.09967 −0.469205
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.2405 17.7371i −0.778573 1.34853i −0.932764 0.360488i \(-0.882610\pi\)
0.154190 0.988041i \(-0.450723\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.83616 + 4.91238i 0.213179 + 0.369237i
\(178\) 0 0
\(179\) 3.63746 6.30026i 0.271876 0.470904i −0.697466 0.716618i \(-0.745689\pi\)
0.969342 + 0.245714i \(0.0790225\pi\)
\(180\) 0 0
\(181\) −24.2749 −1.80434 −0.902170 0.431380i \(-0.858027\pi\)
−0.902170 + 0.431380i \(0.858027\pi\)
\(182\) 0 0
\(183\) −23.4690 −1.73488
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.10411 + 1.91238i 0.0807406 + 0.139847i
\(188\) 0 0
\(189\) −12.4124 5.91041i −0.902867 0.429919i
\(190\) 0 0
\(191\) −0.0876242 0.151770i −0.00634026 0.0109817i 0.862838 0.505481i \(-0.168685\pi\)
−0.869178 + 0.494499i \(0.835352\pi\)
\(192\) 0 0
\(193\) −10.6592 + 18.4622i −0.767263 + 1.32894i 0.171778 + 0.985136i \(0.445049\pi\)
−0.939042 + 0.343803i \(0.888285\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.60271 0.612918 0.306459 0.951884i \(-0.400856\pi\)
0.306459 + 0.951884i \(0.400856\pi\)
\(198\) 0 0
\(199\) −8.63746 + 14.9605i −0.612293 + 1.06052i 0.378560 + 0.925577i \(0.376419\pi\)
−0.990853 + 0.134946i \(0.956914\pi\)
\(200\) 0 0
\(201\) −3.04983 5.28247i −0.215119 0.372597i
\(202\) 0 0
\(203\) 10.2118 + 4.86254i 0.716725 + 0.341284i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −17.2749 −1.19493
\(210\) 0 0
\(211\) 25.6495 1.76578 0.882892 0.469576i \(-0.155593\pi\)
0.882892 + 0.469576i \(0.155593\pi\)
\(212\) 0 0
\(213\) 3.94027 6.82475i 0.269983 0.467624i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −7.13752 + 4.91238i −0.484526 + 0.333474i
\(218\) 0 0
\(219\) −5.63746 9.76436i −0.380944 0.659815i
\(220\) 0 0
\(221\) −0.549834 + 0.952341i −0.0369859 + 0.0640614i
\(222\) 0 0
\(223\) −8.71780 −0.583787 −0.291893 0.956451i \(-0.594285\pi\)
−0.291893 + 0.956451i \(0.594285\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.76436 16.9124i 0.648084 1.12251i −0.335496 0.942041i \(-0.608904\pi\)
0.983580 0.180472i \(-0.0577626\pi\)
\(228\) 0 0
\(229\) −1.63746 2.83616i −0.108206 0.187419i 0.806837 0.590774i \(-0.201177\pi\)
−0.915044 + 0.403355i \(0.867844\pi\)
\(230\) 0 0
\(231\) 1.91238 + 24.0969i 0.125825 + 1.58546i
\(232\) 0 0
\(233\) −7.13752 12.3625i −0.467594 0.809897i 0.531720 0.846920i \(-0.321546\pi\)
−0.999314 + 0.0370231i \(0.988212\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 12.6005 0.818492
\(238\) 0 0
\(239\) 0.549834 0.0355658 0.0177829 0.999842i \(-0.494339\pi\)
0.0177829 + 0.999842i \(0.494339\pi\)
\(240\) 0 0
\(241\) −4.91238 + 8.50848i −0.316434 + 0.548080i −0.979741 0.200267i \(-0.935819\pi\)
0.663307 + 0.748347i \(0.269152\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.30136 7.45017i −0.273689 0.474043i
\(248\) 0 0
\(249\) 6.41238 11.1066i 0.406368 0.703850i
\(250\) 0 0
\(251\) −20.5498 −1.29709 −0.648547 0.761175i \(-0.724623\pi\)
−0.648547 + 0.761175i \(0.724623\pi\)
\(252\) 0 0
\(253\) 41.2657 2.59435
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.82409 + 10.0876i 0.363297 + 0.629249i 0.988501 0.151212i \(-0.0483177\pi\)
−0.625204 + 0.780461i \(0.714984\pi\)
\(258\) 0 0
\(259\) 2.08762 + 26.3052i 0.129719 + 1.63452i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −0.389855 + 0.675248i −0.0240395 + 0.0416376i −0.877795 0.479037i \(-0.840986\pi\)
0.853755 + 0.520674i \(0.174319\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.1244 −0.741999
\(268\) 0 0
\(269\) 7.22508 12.5142i 0.440521 0.763005i −0.557207 0.830374i \(-0.688127\pi\)
0.997728 + 0.0673687i \(0.0214604\pi\)
\(270\) 0 0
\(271\) −4.91238 8.50848i −0.298406 0.516854i 0.677366 0.735646i \(-0.263121\pi\)
−0.975771 + 0.218793i \(0.929788\pi\)
\(272\) 0 0
\(273\) −9.91613 + 6.82475i −0.600152 + 0.413053i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7.13752 + 12.3625i −0.428852 + 0.742793i −0.996771 0.0802909i \(-0.974415\pi\)
0.567920 + 0.823084i \(0.307748\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −5.46301 + 9.46221i −0.324742 + 0.562470i −0.981460 0.191666i \(-0.938611\pi\)
0.656718 + 0.754136i \(0.271944\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.89834 4.23713i −0.525252 0.250110i
\(288\) 0 0
\(289\) 8.41238 + 14.5707i 0.494846 + 0.857098i
\(290\) 0 0
\(291\) 6.00000 10.3923i 0.351726 0.609208i
\(292\) 0 0
\(293\) 6.92820 0.404750 0.202375 0.979308i \(-0.435134\pi\)
0.202375 + 0.979308i \(0.435134\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −13.7046 + 23.7371i −0.795224 + 1.37737i
\(298\) 0 0
\(299\) 10.2749 + 17.7967i 0.594214 + 1.02921i
\(300\) 0 0
\(301\) −5.13746 2.44631i −0.296118 0.141003i
\(302\) 0 0
\(303\) 11.7345 + 20.3248i 0.674129 + 1.16763i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 26.5145 1.51326 0.756631 0.653843i \(-0.226844\pi\)
0.756631 + 0.653843i \(0.226844\pi\)
\(308\) 0 0
\(309\) 19.5498 1.11215
\(310\) 0 0
\(311\) 4.91238 8.50848i 0.278555 0.482472i −0.692471 0.721446i \(-0.743478\pi\)
0.971026 + 0.238974i \(0.0768111\pi\)
\(312\) 0 0
\(313\) 16.7501 + 29.0120i 0.946772 + 1.63986i 0.752163 + 0.658977i \(0.229010\pi\)
0.194609 + 0.980881i \(0.437656\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.8098 22.1873i −0.719472 1.24616i −0.961209 0.275821i \(-0.911050\pi\)
0.241737 0.970342i \(-0.422283\pi\)
\(318\) 0 0
\(319\) 11.2749 19.5287i 0.631274 1.09340i
\(320\) 0 0
\(321\) 6.09967 0.340450
\(322\) 0 0
\(323\) 1.37097 0.0762827
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 10.0025 + 17.3248i 0.553137 + 0.958061i
\(328\) 0 0
\(329\) −1.36254 17.1687i −0.0751193 0.946543i
\(330\) 0 0
\(331\) −8.91238 15.4367i −0.489868 0.848477i 0.510064 0.860137i \(-0.329622\pi\)
−0.999932 + 0.0116596i \(0.996289\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −4.30136 −0.234310 −0.117155 0.993114i \(-0.537377\pi\)
−0.117155 + 0.993114i \(0.537377\pi\)
\(338\) 0 0
\(339\) −3.72508 + 6.45203i −0.202319 + 0.350426i
\(340\) 0 0
\(341\) 8.63746 + 14.9605i 0.467745 + 0.810157i
\(342\) 0 0
\(343\) 4.35890 + 18.0000i 0.235358 + 0.971909i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.06218 + 10.5000i −0.325435 + 0.563670i −0.981600 0.190947i \(-0.938844\pi\)
0.656165 + 0.754617i \(0.272177\pi\)
\(348\) 0 0
\(349\) −3.72508 −0.199399 −0.0996996 0.995018i \(-0.531788\pi\)
−0.0996996 + 0.995018i \(0.531788\pi\)
\(350\) 0 0
\(351\) −13.6495 −0.728557
\(352\) 0 0
\(353\) −4.09204 + 7.08762i −0.217797 + 0.377236i −0.954134 0.299379i \(-0.903221\pi\)
0.736337 + 0.676615i \(0.236554\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −0.151770 1.91238i −0.00803249 0.101214i
\(358\) 0 0
\(359\) −18.1873 31.5013i −0.959889 1.66258i −0.722762 0.691097i \(-0.757128\pi\)
−0.237127 0.971479i \(-0.576206\pi\)
\(360\) 0 0
\(361\) 4.13746 7.16629i 0.217761 0.377173i
\(362\) 0 0
\(363\) 29.1413 1.52952
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3.01670 5.22508i 0.157471 0.272747i −0.776485 0.630135i \(-0.782999\pi\)
0.933956 + 0.357388i \(0.116333\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.3625 8.50848i 0.641831 0.441739i
\(372\) 0 0
\(373\) −4.98684 8.63746i −0.258209 0.447231i 0.707553 0.706660i \(-0.249799\pi\)
−0.965762 + 0.259429i \(0.916466\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.2296 0.578352
\(378\) 0 0
\(379\) −21.6495 −1.11206 −0.556030 0.831162i \(-0.687676\pi\)
−0.556030 + 0.831162i \(0.687676\pi\)
\(380\) 0 0
\(381\) 13.5498 23.4690i 0.694179 1.20235i
\(382\) 0 0
\(383\) 3.07425 + 5.32475i 0.157087 + 0.272082i 0.933817 0.357751i \(-0.116456\pi\)
−0.776730 + 0.629833i \(0.783123\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −16.1873 + 28.0372i −0.820728 + 1.42154i 0.0844123 + 0.996431i \(0.473099\pi\)
−0.905141 + 0.425112i \(0.860235\pi\)
\(390\) 0 0
\(391\) −3.27492 −0.165620
\(392\) 0 0
\(393\) −18.5764 −0.937055
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −5.40547 9.36254i −0.271293 0.469892i 0.697901 0.716195i \(-0.254118\pi\)
−0.969193 + 0.246302i \(0.920784\pi\)
\(398\) 0 0
\(399\) 13.5498 + 6.45203i 0.678340 + 0.323006i
\(400\) 0 0
\(401\) −1.50000 2.59808i −0.0749064 0.129742i 0.826139 0.563466i \(-0.190532\pi\)
−0.901046 + 0.433724i \(0.857199\pi\)
\(402\) 0 0
\(403\) −4.30136 + 7.45017i −0.214266 + 0.371119i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 52.6103 2.60780
\(408\) 0 0
\(409\) 10.0498 17.4068i 0.496932 0.860712i −0.503061 0.864251i \(-0.667793\pi\)
0.999994 + 0.00353862i \(0.00112638\pi\)
\(410\) 0 0
\(411\) 18.4622 + 31.9775i 0.910674 + 1.57733i
\(412\) 0 0
\(413\) 7.13752 4.91238i 0.351214 0.241722i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −11.3446 + 19.6495i −0.555550 + 0.962240i
\(418\) 0 0
\(419\) −13.0997 −0.639961 −0.319980 0.947424i \(-0.603676\pi\)
−0.319980 + 0.947424i \(0.603676\pi\)
\(420\) 0 0
\(421\) −4.27492 −0.208347 −0.104173 0.994559i \(-0.533220\pi\)
−0.104173 + 0.994559i \(0.533220\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2.83616 + 35.7371i 0.137251 + 1.72944i
\(428\) 0 0
\(429\) 12.0000 + 20.7846i 0.579365 + 1.00349i
\(430\) 0 0
\(431\) 9.18729 15.9129i 0.442536 0.766495i −0.555341 0.831623i \(-0.687412\pi\)
0.997877 + 0.0651276i \(0.0207454\pi\)
\(432\) 0 0
\(433\) −18.1578 −0.872606 −0.436303 0.899800i \(-0.643712\pi\)
−0.436303 + 0.899800i \(0.643712\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.8098 22.1873i 0.612778 1.06136i
\(438\) 0 0
\(439\) −11.9124 20.6328i −0.568547 0.984752i −0.996710 0.0810504i \(-0.974173\pi\)
0.428163 0.903701i \(-0.359161\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.06218 + 10.5000i 0.288023 + 0.498870i 0.973338 0.229377i \(-0.0736688\pi\)
−0.685315 + 0.728247i \(0.740335\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −13.0767 −0.618507
\(448\) 0 0
\(449\) −3.17525 −0.149849 −0.0749246 0.997189i \(-0.523872\pi\)
−0.0749246 + 0.997189i \(0.523872\pi\)
\(450\) 0 0
\(451\) −9.82475 + 17.0170i −0.462629 + 0.801298i
\(452\) 0 0
\(453\) 11.0202 + 19.0876i 0.517776 + 0.896815i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.685484 + 1.18729i 0.0320656 + 0.0555392i 0.881613 0.471973i \(-0.156458\pi\)
−0.849547 + 0.527512i \(0.823125\pi\)
\(458\) 0 0
\(459\) 1.08762 1.88382i 0.0507659 0.0879292i
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 2.15068 0.0999505 0.0499752 0.998750i \(-0.484086\pi\)
0.0499752 + 0.998750i \(0.484086\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.85177 13.5997i −0.363337 0.629318i 0.625171 0.780488i \(-0.285029\pi\)
−0.988508 + 0.151170i \(0.951696\pi\)
\(468\) 0 0
\(469\) −7.67525 + 5.28247i −0.354410 + 0.243922i
\(470\) 0 0
\(471\) 1.91238 + 3.31233i 0.0881176 + 0.152624i
\(472\) 0 0
\(473\) −5.67232 + 9.82475i −0.260814 + 0.451743i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.91238 + 8.50848i −0.224452 + 0.388763i −0.956155 0.292861i \(-0.905393\pi\)
0.731703 + 0.681624i \(0.238726\pi\)
\(480\) 0 0
\(481\) 13.0997 + 22.6893i 0.597293 + 1.03454i
\(482\) 0 0
\(483\) −32.3673 15.4124i −1.47277 0.701287i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.46519 + 2.53779i −0.0663943 + 0.114998i −0.897312 0.441398i \(-0.854483\pi\)
0.830917 + 0.556396i \(0.187816\pi\)
\(488\) 0 0
\(489\) 9.82475 0.444291
\(490\) 0 0
\(491\) −28.5498 −1.28844 −0.644218 0.764842i \(-0.722817\pi\)
−0.644218 + 0.764842i \(0.722817\pi\)
\(492\) 0 0
\(493\) −0.894797 + 1.54983i −0.0402996 + 0.0698010i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.8685 5.17525i −0.487518 0.232142i
\(498\) 0 0
\(499\) −0.812707 1.40765i −0.0363818 0.0630151i 0.847261 0.531177i \(-0.178250\pi\)
−0.883643 + 0.468161i \(0.844917\pi\)
\(500\) 0 0
\(501\) 0.412376 0.714256i 0.0184236 0.0319106i
\(502\) 0 0
\(503\) 31.7682 1.41647 0.708236 0.705975i \(-0.249491\pi\)
0.708236 + 0.705975i \(0.249491\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 5.28247 9.14950i 0.234603 0.406344i
\(508\) 0 0
\(509\) 7.22508 + 12.5142i 0.320246 + 0.554683i 0.980539 0.196326i \(-0.0629010\pi\)
−0.660293 + 0.751008i \(0.729568\pi\)
\(510\) 0 0
\(511\) −14.1873 + 9.76436i −0.627609 + 0.431950i
\(512\) 0 0
\(513\) 8.50848 + 14.7371i 0.375659 + 0.650660i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −34.3375 −1.51016
\(518\) 0 0
\(519\) 35.4743 1.55715
\(520\) 0 0
\(521\) −4.91238 + 8.50848i −0.215215 + 0.372763i −0.953339 0.301902i \(-0.902379\pi\)
0.738124 + 0.674665i \(0.235712\pi\)
\(522\) 0 0
\(523\) −3.67341 6.36254i −0.160627 0.278215i 0.774467 0.632615i \(-0.218018\pi\)
−0.935094 + 0.354400i \(0.884685\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.685484 1.18729i −0.0298602 0.0517193i
\(528\) 0 0
\(529\) −19.0997 + 33.0816i −0.830420 + 1.43833i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.78523 −0.423845
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 6.30026 + 10.9124i 0.271876 + 0.470904i
\(538\) 0 0
\(539\) 36.4622 5.82409i 1.57054 0.250861i
\(540\) 0 0
\(541\) 8.77492 + 15.1986i 0.377263 + 0.653439i 0.990663 0.136334i \(-0.0435319\pi\)
−0.613400 + 0.789773i \(0.710199\pi\)
\(542\) 0 0
\(543\) 21.0227 36.4124i 0.902170 1.56260i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.5386 −0.878168 −0.439084 0.898446i \(-0.644697\pi\)
−0.439084 + 0.898446i \(0.644697\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.00000 12.1244i −0.298210 0.516515i
\(552\) 0 0
\(553\) −1.52274 19.1873i −0.0647534 0.815927i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −4.98684 + 8.63746i −0.211299 + 0.365981i −0.952121 0.305720i \(-0.901103\pi\)
0.740822 + 0.671701i \(0.234436\pi\)
\(558\) 0 0
\(559\) −5.64950 −0.238949
\(560\) 0 0
\(561\) −3.82475 −0.161481
\(562\) 0 0
\(563\) 11.3159 19.5997i 0.476907 0.826028i −0.522743 0.852491i \(-0.675091\pi\)
0.999650 + 0.0264630i \(0.00842443\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 19.6150 13.5000i 0.823754 0.566947i
\(568\) 0 0
\(569\) −4.18729 7.25260i −0.175540 0.304045i 0.764808 0.644259i \(-0.222834\pi\)
−0.940348 + 0.340214i \(0.889501\pi\)
\(570\) 0 0
\(571\) −3.63746 + 6.30026i −0.152223 + 0.263658i −0.932044 0.362344i \(-0.881976\pi\)
0.779821 + 0.626002i \(0.215310\pi\)
\(572\) 0 0
\(573\) 0.303539 0.0126805
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.94136 3.36254i 0.0808200 0.139984i −0.822782 0.568357i \(-0.807579\pi\)
0.903602 + 0.428372i \(0.140913\pi\)
\(578\) 0 0
\(579\) −18.4622 31.9775i −0.767263 1.32894i
\(580\) 0 0
\(581\) −17.6873 8.42217i −0.733793 0.349410i
\(582\) 0 0
\(583\) −14.9605 25.9124i −0.619601 1.07318i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.8997 0.862623 0.431311 0.902203i \(-0.358051\pi\)
0.431311 + 0.902203i \(0.358051\pi\)
\(588\) 0 0
\(589\) 10.7251 0.441919
\(590\) 0 0
\(591\) −7.45017 + 12.9041i −0.306459 + 0.530802i
\(592\) 0 0
\(593\) −16.6926 28.9124i −0.685482 1.18729i −0.973285 0.229600i \(-0.926258\pi\)
0.287804 0.957689i \(-0.407075\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −14.9605 25.9124i −0.612293 1.06052i
\(598\) 0 0
\(599\) −2.63746 + 4.56821i −0.107764 + 0.186652i −0.914864 0.403762i \(-0.867702\pi\)
0.807100 + 0.590414i \(0.201036\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −5.70109 9.87459i −0.231400 0.400797i 0.726820 0.686828i \(-0.240997\pi\)
−0.958220 + 0.286031i \(0.907664\pi\)
\(608\) 0 0
\(609\) −16.1375 + 11.1066i −0.653923 + 0.450061i
\(610\) 0 0
\(611\) −8.54983 14.8087i −0.345889 0.599098i
\(612\) 0 0
\(613\) 14.1808 24.5619i 0.572757 0.992045i −0.423524 0.905885i \(-0.639207\pi\)
0.996281 0.0861600i \(-0.0274596\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −31.2920 −1.25977 −0.629884 0.776689i \(-0.716898\pi\)
−0.629884 + 0.776689i \(0.716898\pi\)
\(618\) 0 0
\(619\) 4.46221 7.72877i 0.179351 0.310646i −0.762307 0.647215i \(-0.775933\pi\)
0.941659 + 0.336570i \(0.109267\pi\)
\(620\) 0 0
\(621\) −20.3248 35.2035i −0.815604 1.41267i
\(622\) 0 0
\(623\) 1.46519 + 18.4622i 0.0587017 + 0.739673i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 14.9605 25.9124i 0.597466 1.03484i
\(628\) 0 0
\(629\) −4.17525 −0.166478
\(630\) 0 0
\(631\) 33.0997 1.31768 0.658839 0.752284i \(-0.271048\pi\)
0.658839 + 0.752284i \(0.271048\pi\)
\(632\) 0 0
\(633\) −22.2131 + 38.4743i −0.882892 + 1.52921i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 11.5906 + 14.2749i 0.459238 + 0.565593i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.04983 1.81837i 0.0414660 0.0718212i −0.844548 0.535481i \(-0.820131\pi\)
0.886014 + 0.463659i \(0.153464\pi\)
\(642\) 0 0
\(643\) −31.4071 −1.23857 −0.619287 0.785164i \(-0.712578\pi\)
−0.619287 + 0.785164i \(0.712578\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −13.4666 + 23.3248i −0.529425 + 0.916991i 0.469986 + 0.882674i \(0.344259\pi\)
−0.999411 + 0.0343169i \(0.989074\pi\)
\(648\) 0 0
\(649\) −8.63746 14.9605i −0.339050 0.587252i
\(650\) 0 0
\(651\) −1.18729 14.9605i −0.0465337 0.586349i
\(652\) 0 0
\(653\) −14.1808 24.5619i −0.554938 0.961181i −0.997908 0.0646444i \(-0.979409\pi\)
0.442970 0.896536i \(-0.353925\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −40.5498 −1.57960 −0.789799 0.613366i \(-0.789815\pi\)
−0.789799 + 0.613366i \(0.789815\pi\)
\(660\) 0 0
\(661\) 0.225083 0.389855i 0.00875471 0.0151636i −0.861615 0.507563i \(-0.830547\pi\)
0.870370 + 0.492399i \(0.163880\pi\)
\(662\) 0 0
\(663\) −0.952341 1.64950i −0.0369859 0.0640614i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 16.7213 + 28.9622i 0.647453 + 1.12142i
\(668\) 0 0
\(669\) 7.54983 13.0767i 0.291893 0.505574i
\(670\) 0 0
\(671\) 71.4743 2.75923
\(672\) 0 0
\(673\) −31.2920 −1.20622 −0.603109 0.797659i \(-0.706072\pi\)
−0.603109 + 0.797659i \(0.706072\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.2021 40.1873i −0.891731 1.54452i −0.837799 0.545979i \(-0.816158\pi\)
−0.0539317 0.998545i \(-0.517175\pi\)
\(678\) 0 0
\(679\) −16.5498 7.88054i −0.635124 0.302428i
\(680\) 0 0
\(681\) 16.9124 + 29.2931i 0.648084 + 1.12251i
\(682\) 0 0
\(683\) −9.58382 + 16.5997i −0.366715 + 0.635169i −0.989050 0.147582i \(-0.952851\pi\)
0.622335 + 0.782751i \(0.286184\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.67232 0.216413
\(688\) 0 0
\(689\) 7.45017 12.9041i 0.283829 0.491606i
\(690\) 0 0
\(691\) −15.1873 26.3052i −0.577752 1.00070i −0.995737 0.0922416i \(-0.970597\pi\)
0.417985 0.908454i \(-0.362737\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0.779710 1.35050i 0.0295336 0.0511537i
\(698\) 0 0
\(699\) 24.7251 0.935189
\(700\) 0 0
\(701\) 8.82475 0.333306 0.166653 0.986016i \(-0.446704\pi\)
0.166653 + 0.986016i \(0.446704\pi\)
\(702\) 0 0
\(703\) 16.3315 28.2870i 0.615954 1.06686i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 29.5312 20.3248i 1.11063 0.764391i
\(708\) 0 0
\(709\) 5.22508 + 9.05011i 0.196232 + 0.339884i 0.947304 0.320337i \(-0.103796\pi\)
−0.751072 + 0.660221i \(0.770463\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −25.6197 −0.959465
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.476171 + 0.824752i −0.0177829 + 0.0308009i
\(718\) 0 0
\(719\) 15.1873 + 26.3052i 0.566390 + 0.981017i 0.996919 + 0.0784400i \(0.0249939\pi\)
−0.430528 + 0.902577i \(0.641673\pi\)
\(720\) 0 0
\(721\) −2.36254 29.7693i −0.0879856 1.10867i
\(722\) 0 0
\(723\) −8.50848 14.7371i −0.316434 0.548080i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.10302 0.115085 0.0575423 0.998343i \(-0.481674\pi\)
0.0575423 + 0.998343i \(0.481674\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 0.450166 0.779710i 0.0166500 0.0288386i
\(732\) 0 0
\(733\) −18.8432 32.6375i −0.695991 1.20549i −0.969845 0.243721i \(-0.921632\pi\)
0.273854 0.961771i \(-0.411701\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.28819 + 16.0876i 0.342135 + 0.592595i
\(738\) 0 0
\(739\) 10.4622 18.1211i 0.384859 0.666595i −0.606891 0.794785i \(-0.707584\pi\)
0.991750 + 0.128190i \(0.0409169\pi\)
\(740\) 0 0
\(741\) 14.9003 0.547377
\(742\) 0 0
\(743\) −6.45203 −0.236702 −0.118351 0.992972i \(-0.537761\pi\)
−0.118351 + 0.992972i \(0.537761\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.737127 9.28819i −0.0269341 0.339383i
\(750\) 0 0
\(751\) 7.36254 + 12.7523i 0.268663 + 0.465338i 0.968517 0.248948i \(-0.0800849\pi\)
−0.699854 + 0.714286i \(0.746752\pi\)
\(752\) 0 0
\(753\) 17.7967 30.8248i 0.648547 1.12332i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 35.5934 1.29366 0.646831 0.762633i \(-0.276094\pi\)
0.646831 + 0.762633i \(0.276094\pi\)
\(758\) 0 0
\(759\) −35.7371 + 61.8985i −1.29718 + 2.24677i
\(760\) 0 0
\(761\) −11.4622 19.8531i −0.415505 0.719675i 0.579977 0.814633i \(-0.303062\pi\)
−0.995481 + 0.0949578i \(0.969728\pi\)
\(762\) 0 0
\(763\) 25.1723 17.3248i 0.911298 0.627198i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.30136 7.45017i 0.155313 0.269010i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −20.1752 −0.726594
\(772\) 0 0
\(773\) 20.1567 34.9124i 0.724985 1.25571i −0.233995 0.972238i \(-0.575180\pi\)
0.958980 0.283473i \(-0.0914867\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −41.2657 19.6495i −1.48040 0.704922i
\(778\) 0 0
\(779\) 6.09967 + 10.5649i 0.218543 + 0.378528i
\(780\) 0 0
\(781\) −12.0000 + 20.7846i −0.429394 + 0.743732i
\(782\) 0 0
\(783\) −22.2131 −0.793832
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0.866025 1.50000i 0.0308705 0.0534692i −0.850177 0.526496i \(-0.823505\pi\)
0.881048 + 0.473027i \(0.156839\pi\)
\(788\) 0 0
\(789\) −0.675248 1.16956i −0.0240395 0.0416376i
\(790\) 0 0
\(791\) 10.2749 + 4.89261i 0.365334 + 0.173961i
\(792\) 0 0
\(793\) 17.7967 + 30.8248i 0.631979 + 1.09462i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −46.8229 −1.65855 −0.829276 0.558839i \(-0.811247\pi\)
−0.829276 + 0.558839i \(0.811247\pi\)
\(798\) 0 0
\(799\) 2.72508 0.0964065
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\)