Properties

Label 980.2.i.l.961.1
Level $980$
Weight $2$
Character 980.961
Analytic conductor $7.825$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
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 961.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 980.961
Dual form 980.2.i.l.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.41421 - 2.44949i) q^{9} +O(q^{10})\) \(q+(-0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(1.41421 - 2.44949i) q^{9} +(1.91421 + 3.31552i) q^{11} -3.58579 q^{13} +0.414214 q^{15} +(3.20711 + 5.55487i) q^{17} +(1.82843 - 3.16693i) q^{19} +(-0.292893 + 0.507306i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.41421 q^{27} +6.65685 q^{29} +(2.29289 + 3.97141i) q^{31} +(0.792893 - 1.37333i) q^{33} +(1.70711 - 2.95680i) q^{37} +(0.742641 + 1.28629i) q^{39} -0.585786 q^{41} +11.6569 q^{43} +(1.41421 + 2.44949i) q^{45} +(-4.44975 + 7.70719i) q^{47} +(1.32843 - 2.30090i) q^{51} +(1.87868 + 3.25397i) q^{53} -3.82843 q^{55} -1.51472 q^{57} +(1.70711 + 2.95680i) q^{59} +(2.58579 - 4.47871i) q^{61} +(1.79289 - 3.10538i) q^{65} +(5.53553 + 9.58783i) q^{67} +0.242641 q^{69} +6.48528 q^{71} +(2.58579 + 4.47871i) q^{73} +(-0.207107 + 0.358719i) q^{75} +(-6.57107 + 11.3814i) q^{79} +(-3.74264 - 6.48244i) q^{81} +8.00000 q^{83} -6.41421 q^{85} +(-1.37868 - 2.38794i) q^{87} +(8.48528 - 14.6969i) q^{89} +(0.949747 - 1.64501i) q^{93} +(1.82843 + 3.16693i) q^{95} -15.7279 q^{97} +10.8284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{3} - 2 q^{5} + 2 q^{11} - 20 q^{13} - 4 q^{15} + 10 q^{17} - 4 q^{19} - 4 q^{23} - 2 q^{25} - 4 q^{27} + 4 q^{29} + 12 q^{31} + 6 q^{33} + 4 q^{37} - 14 q^{39} - 8 q^{41} + 24 q^{43} + 2 q^{47} - 6 q^{51} + 16 q^{53} - 4 q^{55} - 40 q^{57} + 4 q^{59} + 16 q^{61} + 10 q^{65} + 8 q^{67} - 16 q^{69} - 8 q^{71} + 16 q^{73} + 2 q^{75} + 2 q^{79} + 2 q^{81} + 32 q^{83} - 20 q^{85} - 14 q^{87} - 16 q^{93} - 4 q^{95} - 12 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) −0.207107 0.358719i −0.119573 0.207107i 0.800025 0.599966i \(-0.204819\pi\)
−0.919599 + 0.392859i \(0.871486\pi\)
\(4\) 0 0
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.41421 2.44949i 0.471405 0.816497i
\(10\) 0 0
\(11\) 1.91421 + 3.31552i 0.577157 + 0.999665i 0.995804 + 0.0915161i \(0.0291713\pi\)
−0.418646 + 0.908149i \(0.637495\pi\)
\(12\) 0 0
\(13\) −3.58579 −0.994518 −0.497259 0.867602i \(-0.665660\pi\)
−0.497259 + 0.867602i \(0.665660\pi\)
\(14\) 0 0
\(15\) 0.414214 0.106949
\(16\) 0 0
\(17\) 3.20711 + 5.55487i 0.777838 + 1.34725i 0.933186 + 0.359395i \(0.117017\pi\)
−0.155348 + 0.987860i \(0.549650\pi\)
\(18\) 0 0
\(19\) 1.82843 3.16693i 0.419470 0.726543i −0.576416 0.817156i \(-0.695549\pi\)
0.995886 + 0.0906130i \(0.0288826\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.292893 + 0.507306i −0.0610725 + 0.105781i −0.894945 0.446176i \(-0.852785\pi\)
0.833873 + 0.551957i \(0.186119\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −2.41421 −0.464616
\(28\) 0 0
\(29\) 6.65685 1.23615 0.618073 0.786120i \(-0.287913\pi\)
0.618073 + 0.786120i \(0.287913\pi\)
\(30\) 0 0
\(31\) 2.29289 + 3.97141i 0.411816 + 0.713286i 0.995088 0.0989906i \(-0.0315614\pi\)
−0.583273 + 0.812276i \(0.698228\pi\)
\(32\) 0 0
\(33\) 0.792893 1.37333i 0.138025 0.239066i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.70711 2.95680i 0.280647 0.486094i −0.690898 0.722953i \(-0.742784\pi\)
0.971544 + 0.236858i \(0.0761178\pi\)
\(38\) 0 0
\(39\) 0.742641 + 1.28629i 0.118918 + 0.205971i
\(40\) 0 0
\(41\) −0.585786 −0.0914845 −0.0457422 0.998953i \(-0.514565\pi\)
−0.0457422 + 0.998953i \(0.514565\pi\)
\(42\) 0 0
\(43\) 11.6569 1.77765 0.888827 0.458243i \(-0.151521\pi\)
0.888827 + 0.458243i \(0.151521\pi\)
\(44\) 0 0
\(45\) 1.41421 + 2.44949i 0.210819 + 0.365148i
\(46\) 0 0
\(47\) −4.44975 + 7.70719i −0.649062 + 1.12421i 0.334285 + 0.942472i \(0.391505\pi\)
−0.983347 + 0.181737i \(0.941828\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.32843 2.30090i 0.186017 0.322191i
\(52\) 0 0
\(53\) 1.87868 + 3.25397i 0.258056 + 0.446967i 0.965721 0.259581i \(-0.0835846\pi\)
−0.707665 + 0.706548i \(0.750251\pi\)
\(54\) 0 0
\(55\) −3.82843 −0.516225
\(56\) 0 0
\(57\) −1.51472 −0.200629
\(58\) 0 0
\(59\) 1.70711 + 2.95680i 0.222246 + 0.384942i 0.955490 0.295024i \(-0.0953277\pi\)
−0.733243 + 0.679966i \(0.761994\pi\)
\(60\) 0 0
\(61\) 2.58579 4.47871i 0.331076 0.573441i −0.651647 0.758522i \(-0.725922\pi\)
0.982723 + 0.185082i \(0.0592550\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.79289 3.10538i 0.222381 0.385175i
\(66\) 0 0
\(67\) 5.53553 + 9.58783i 0.676273 + 1.17134i 0.976095 + 0.217344i \(0.0697394\pi\)
−0.299822 + 0.953995i \(0.596927\pi\)
\(68\) 0 0
\(69\) 0.242641 0.0292105
\(70\) 0 0
\(71\) 6.48528 0.769661 0.384831 0.922987i \(-0.374260\pi\)
0.384831 + 0.922987i \(0.374260\pi\)
\(72\) 0 0
\(73\) 2.58579 + 4.47871i 0.302643 + 0.524194i 0.976734 0.214455i \(-0.0687975\pi\)
−0.674090 + 0.738649i \(0.735464\pi\)
\(74\) 0 0
\(75\) −0.207107 + 0.358719i −0.0239146 + 0.0414214i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.57107 + 11.3814i −0.739303 + 1.28051i 0.213507 + 0.976942i \(0.431511\pi\)
−0.952810 + 0.303569i \(0.901822\pi\)
\(80\) 0 0
\(81\) −3.74264 6.48244i −0.415849 0.720272i
\(82\) 0 0
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) −6.41421 −0.695719
\(86\) 0 0
\(87\) −1.37868 2.38794i −0.147810 0.256014i
\(88\) 0 0
\(89\) 8.48528 14.6969i 0.899438 1.55787i 0.0712241 0.997460i \(-0.477309\pi\)
0.828214 0.560412i \(-0.189357\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.949747 1.64501i 0.0984842 0.170580i
\(94\) 0 0
\(95\) 1.82843 + 3.16693i 0.187593 + 0.324920i
\(96\) 0 0
\(97\) −15.7279 −1.59693 −0.798464 0.602042i \(-0.794354\pi\)
−0.798464 + 0.602042i \(0.794354\pi\)
\(98\) 0 0
\(99\) 10.8284 1.08830
\(100\) 0 0
\(101\) −2.41421 4.18154i −0.240223 0.416079i 0.720555 0.693398i \(-0.243887\pi\)
−0.960778 + 0.277319i \(0.910554\pi\)
\(102\) 0 0
\(103\) 0.792893 1.37333i 0.0781261 0.135318i −0.824315 0.566131i \(-0.808440\pi\)
0.902441 + 0.430813i \(0.141773\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.41421 14.5738i 0.813433 1.40891i −0.0970151 0.995283i \(-0.530930\pi\)
0.910448 0.413624i \(-0.135737\pi\)
\(108\) 0 0
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) 0 0
\(111\) −1.41421 −0.134231
\(112\) 0 0
\(113\) −5.07107 −0.477046 −0.238523 0.971137i \(-0.576663\pi\)
−0.238523 + 0.971137i \(0.576663\pi\)
\(114\) 0 0
\(115\) −0.292893 0.507306i −0.0273124 0.0473065i
\(116\) 0 0
\(117\) −5.07107 + 8.78335i −0.468820 + 0.812021i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.82843 + 3.16693i −0.166221 + 0.287903i
\(122\) 0 0
\(123\) 0.121320 + 0.210133i 0.0109391 + 0.0189471i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −21.8995 −1.94327 −0.971633 0.236494i \(-0.924002\pi\)
−0.971633 + 0.236494i \(0.924002\pi\)
\(128\) 0 0
\(129\) −2.41421 4.18154i −0.212560 0.368164i
\(130\) 0 0
\(131\) −5.87868 + 10.1822i −0.513623 + 0.889620i 0.486253 + 0.873818i \(0.338364\pi\)
−0.999875 + 0.0158021i \(0.994970\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.20711 2.09077i 0.103891 0.179945i
\(136\) 0 0
\(137\) −6.48528 11.2328i −0.554075 0.959686i −0.997975 0.0636096i \(-0.979739\pi\)
0.443900 0.896076i \(-0.353595\pi\)
\(138\) 0 0
\(139\) 13.8995 1.17894 0.589470 0.807790i \(-0.299337\pi\)
0.589470 + 0.807790i \(0.299337\pi\)
\(140\) 0 0
\(141\) 3.68629 0.310442
\(142\) 0 0
\(143\) −6.86396 11.8887i −0.573993 0.994185i
\(144\) 0 0
\(145\) −3.32843 + 5.76500i −0.276411 + 0.478758i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.75736 + 3.04384i −0.143968 + 0.249361i −0.928988 0.370111i \(-0.879320\pi\)
0.785019 + 0.619472i \(0.212653\pi\)
\(150\) 0 0
\(151\) 5.91421 + 10.2437i 0.481292 + 0.833622i 0.999770 0.0214692i \(-0.00683439\pi\)
−0.518478 + 0.855091i \(0.673501\pi\)
\(152\) 0 0
\(153\) 18.1421 1.46670
\(154\) 0 0
\(155\) −4.58579 −0.368339
\(156\) 0 0
\(157\) 5.24264 + 9.08052i 0.418408 + 0.724704i 0.995780 0.0917773i \(-0.0292548\pi\)
−0.577371 + 0.816482i \(0.695921\pi\)
\(158\) 0 0
\(159\) 0.778175 1.34784i 0.0617133 0.106891i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.7782 + 18.6683i −0.844212 + 1.46222i 0.0420922 + 0.999114i \(0.486598\pi\)
−0.886304 + 0.463104i \(0.846736\pi\)
\(164\) 0 0
\(165\) 0.792893 + 1.37333i 0.0617267 + 0.106914i
\(166\) 0 0
\(167\) −2.41421 −0.186817 −0.0934087 0.995628i \(-0.529776\pi\)
−0.0934087 + 0.995628i \(0.529776\pi\)
\(168\) 0 0
\(169\) −0.142136 −0.0109335
\(170\) 0 0
\(171\) −5.17157 8.95743i −0.395480 0.684992i
\(172\) 0 0
\(173\) 9.27817 16.0703i 0.705407 1.22180i −0.261138 0.965301i \(-0.584098\pi\)
0.966545 0.256499i \(-0.0825689\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.707107 1.22474i 0.0531494 0.0920575i
\(178\) 0 0
\(179\) −3.24264 5.61642i −0.242366 0.419791i 0.719022 0.694988i \(-0.244590\pi\)
−0.961388 + 0.275197i \(0.911257\pi\)
\(180\) 0 0
\(181\) −1.75736 −0.130623 −0.0653117 0.997865i \(-0.520804\pi\)
−0.0653117 + 0.997865i \(0.520804\pi\)
\(182\) 0 0
\(183\) −2.14214 −0.158351
\(184\) 0 0
\(185\) 1.70711 + 2.95680i 0.125509 + 0.217388i
\(186\) 0 0
\(187\) −12.2782 + 21.2664i −0.897869 + 1.55515i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.32843 + 14.4253i −0.602624 + 1.04378i 0.389798 + 0.920900i \(0.372545\pi\)
−0.992422 + 0.122875i \(0.960789\pi\)
\(192\) 0 0
\(193\) −2.82843 4.89898i −0.203595 0.352636i 0.746089 0.665846i \(-0.231929\pi\)
−0.949684 + 0.313210i \(0.898596\pi\)
\(194\) 0 0
\(195\) −1.48528 −0.106363
\(196\) 0 0
\(197\) −27.5563 −1.96331 −0.981654 0.190669i \(-0.938934\pi\)
−0.981654 + 0.190669i \(0.938934\pi\)
\(198\) 0 0
\(199\) −13.3640 23.1471i −0.947346 1.64085i −0.750984 0.660320i \(-0.770421\pi\)
−0.196362 0.980532i \(-0.562913\pi\)
\(200\) 0 0
\(201\) 2.29289 3.97141i 0.161728 0.280121i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.292893 0.507306i 0.0204565 0.0354318i
\(206\) 0 0
\(207\) 0.828427 + 1.43488i 0.0575797 + 0.0997309i
\(208\) 0 0
\(209\) 14.0000 0.968400
\(210\) 0 0
\(211\) −24.3137 −1.67382 −0.836912 0.547337i \(-0.815642\pi\)
−0.836912 + 0.547337i \(0.815642\pi\)
\(212\) 0 0
\(213\) −1.34315 2.32640i −0.0920308 0.159402i
\(214\) 0 0
\(215\) −5.82843 + 10.0951i −0.397495 + 0.688482i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 1.07107 1.85514i 0.0723761 0.125359i
\(220\) 0 0
\(221\) −11.5000 19.9186i −0.773574 1.33987i
\(222\) 0 0
\(223\) −24.0711 −1.61192 −0.805959 0.591971i \(-0.798350\pi\)
−0.805959 + 0.591971i \(0.798350\pi\)
\(224\) 0 0
\(225\) −2.82843 −0.188562
\(226\) 0 0
\(227\) 3.86396 + 6.69258i 0.256460 + 0.444202i 0.965291 0.261176i \(-0.0841104\pi\)
−0.708831 + 0.705378i \(0.750777\pi\)
\(228\) 0 0
\(229\) 11.9497 20.6976i 0.789662 1.36773i −0.136513 0.990638i \(-0.543589\pi\)
0.926174 0.377096i \(-0.123077\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.58579 7.94282i 0.300425 0.520351i −0.675807 0.737078i \(-0.736205\pi\)
0.976232 + 0.216727i \(0.0695382\pi\)
\(234\) 0 0
\(235\) −4.44975 7.70719i −0.290270 0.502762i
\(236\) 0 0
\(237\) 5.44365 0.353603
\(238\) 0 0
\(239\) 14.1716 0.916683 0.458341 0.888776i \(-0.348444\pi\)
0.458341 + 0.888776i \(0.348444\pi\)
\(240\) 0 0
\(241\) −1.77817 3.07989i −0.114542 0.198393i 0.803054 0.595906i \(-0.203207\pi\)
−0.917597 + 0.397513i \(0.869873\pi\)
\(242\) 0 0
\(243\) −5.17157 + 8.95743i −0.331757 + 0.574619i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.55635 + 11.3559i −0.417171 + 0.722561i
\(248\) 0 0
\(249\) −1.65685 2.86976i −0.104999 0.181863i
\(250\) 0 0
\(251\) 27.0711 1.70871 0.854355 0.519689i \(-0.173952\pi\)
0.854355 + 0.519689i \(0.173952\pi\)
\(252\) 0 0
\(253\) −2.24264 −0.140994
\(254\) 0 0
\(255\) 1.32843 + 2.30090i 0.0831893 + 0.144088i
\(256\) 0 0
\(257\) −12.8995 + 22.3426i −0.804648 + 1.39369i 0.111880 + 0.993722i \(0.464313\pi\)
−0.916528 + 0.399970i \(0.869020\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 9.41421 16.3059i 0.582725 1.00931i
\(262\) 0 0
\(263\) −5.00000 8.66025i −0.308313 0.534014i 0.669680 0.742650i \(-0.266431\pi\)
−0.977993 + 0.208635i \(0.933098\pi\)
\(264\) 0 0
\(265\) −3.75736 −0.230813
\(266\) 0 0
\(267\) −7.02944 −0.430195
\(268\) 0 0
\(269\) −8.36396 14.4868i −0.509960 0.883276i −0.999933 0.0115389i \(-0.996327\pi\)
0.489974 0.871737i \(-0.337006\pi\)
\(270\) 0 0
\(271\) 14.4853 25.0892i 0.879918 1.52406i 0.0284886 0.999594i \(-0.490931\pi\)
0.851430 0.524469i \(-0.175736\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.91421 3.31552i 0.115431 0.199933i
\(276\) 0 0
\(277\) 3.70711 + 6.42090i 0.222738 + 0.385794i 0.955639 0.294542i \(-0.0951671\pi\)
−0.732900 + 0.680336i \(0.761834\pi\)
\(278\) 0 0
\(279\) 12.9706 0.776527
\(280\) 0 0
\(281\) −1.00000 −0.0596550 −0.0298275 0.999555i \(-0.509496\pi\)
−0.0298275 + 0.999555i \(0.509496\pi\)
\(282\) 0 0
\(283\) −9.37868 16.2443i −0.557505 0.965626i −0.997704 0.0677263i \(-0.978426\pi\)
0.440199 0.897900i \(-0.354908\pi\)
\(284\) 0 0
\(285\) 0.757359 1.31178i 0.0448621 0.0777034i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −12.0711 + 20.9077i −0.710063 + 1.22986i
\(290\) 0 0
\(291\) 3.25736 + 5.64191i 0.190950 + 0.330735i
\(292\) 0 0
\(293\) 14.4142 0.842087 0.421044 0.907040i \(-0.361664\pi\)
0.421044 + 0.907040i \(0.361664\pi\)
\(294\) 0 0
\(295\) −3.41421 −0.198783
\(296\) 0 0
\(297\) −4.62132 8.00436i −0.268156 0.464460i
\(298\) 0 0
\(299\) 1.05025 1.81909i 0.0607377 0.105201i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1.00000 + 1.73205i −0.0574485 + 0.0995037i
\(304\) 0 0
\(305\) 2.58579 + 4.47871i 0.148062 + 0.256450i
\(306\) 0 0
\(307\) −3.58579 −0.204652 −0.102326 0.994751i \(-0.532628\pi\)
−0.102326 + 0.994751i \(0.532628\pi\)
\(308\) 0 0
\(309\) −0.656854 −0.0373671
\(310\) 0 0
\(311\) 3.48528 + 6.03668i 0.197632 + 0.342309i 0.947760 0.318984i \(-0.103342\pi\)
−0.750128 + 0.661293i \(0.770008\pi\)
\(312\) 0 0
\(313\) 8.27817 14.3382i 0.467910 0.810444i −0.531417 0.847110i \(-0.678340\pi\)
0.999328 + 0.0366660i \(0.0116738\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.48528 12.9649i 0.420415 0.728181i −0.575565 0.817756i \(-0.695218\pi\)
0.995980 + 0.0895756i \(0.0285511\pi\)
\(318\) 0 0
\(319\) 12.7426 + 22.0709i 0.713451 + 1.23573i
\(320\) 0 0
\(321\) −6.97056 −0.389059
\(322\) 0 0
\(323\) 23.4558 1.30512
\(324\) 0 0
\(325\) 1.79289 + 3.10538i 0.0994518 + 0.172256i
\(326\) 0 0
\(327\) −1.86396 + 3.22848i −0.103077 + 0.178535i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.41421 + 4.18154i −0.132697 + 0.229838i −0.924715 0.380659i \(-0.875697\pi\)
0.792018 + 0.610497i \(0.209030\pi\)
\(332\) 0 0
\(333\) −4.82843 8.36308i −0.264596 0.458294i
\(334\) 0 0
\(335\) −11.0711 −0.604877
\(336\) 0 0
\(337\) −18.7279 −1.02017 −0.510087 0.860123i \(-0.670387\pi\)
−0.510087 + 0.860123i \(0.670387\pi\)
\(338\) 0 0
\(339\) 1.05025 + 1.81909i 0.0570419 + 0.0987994i
\(340\) 0 0
\(341\) −8.77817 + 15.2042i −0.475365 + 0.823356i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −0.121320 + 0.210133i −0.00653167 + 0.0113132i
\(346\) 0 0
\(347\) 3.70711 + 6.42090i 0.199008 + 0.344692i 0.948207 0.317653i \(-0.102895\pi\)
−0.749199 + 0.662345i \(0.769561\pi\)
\(348\) 0 0
\(349\) −18.0000 −0.963518 −0.481759 0.876304i \(-0.660002\pi\)
−0.481759 + 0.876304i \(0.660002\pi\)
\(350\) 0 0
\(351\) 8.65685 0.462069
\(352\) 0 0
\(353\) −1.03553 1.79360i −0.0551159 0.0954636i 0.837151 0.546972i \(-0.184219\pi\)
−0.892267 + 0.451508i \(0.850886\pi\)
\(354\) 0 0
\(355\) −3.24264 + 5.61642i −0.172101 + 0.298089i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.65685 + 9.79796i −0.298557 + 0.517116i −0.975806 0.218638i \(-0.929839\pi\)
0.677249 + 0.735754i \(0.263172\pi\)
\(360\) 0 0
\(361\) 2.81371 + 4.87349i 0.148090 + 0.256499i
\(362\) 0 0
\(363\) 1.51472 0.0795021
\(364\) 0 0
\(365\) −5.17157 −0.270692
\(366\) 0 0
\(367\) 9.86396 + 17.0849i 0.514895 + 0.891824i 0.999851 + 0.0172850i \(0.00550227\pi\)
−0.484956 + 0.874539i \(0.661164\pi\)
\(368\) 0 0
\(369\) −0.828427 + 1.43488i −0.0431262 + 0.0746968i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −8.24264 + 14.2767i −0.426788 + 0.739218i −0.996586 0.0825669i \(-0.973688\pi\)
0.569798 + 0.821785i \(0.307022\pi\)
\(374\) 0 0
\(375\) −0.207107 0.358719i −0.0106949 0.0185242i
\(376\) 0 0
\(377\) −23.8701 −1.22937
\(378\) 0 0
\(379\) 14.0000 0.719132 0.359566 0.933120i \(-0.382925\pi\)
0.359566 + 0.933120i \(0.382925\pi\)
\(380\) 0 0
\(381\) 4.53553 + 7.85578i 0.232362 + 0.402464i
\(382\) 0 0
\(383\) −1.75736 + 3.04384i −0.0897969 + 0.155533i −0.907425 0.420214i \(-0.861955\pi\)
0.817628 + 0.575746i \(0.195288\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.4853 28.5533i 0.837994 1.45145i
\(388\) 0 0
\(389\) −6.57107 11.3814i −0.333166 0.577061i 0.649965 0.759965i \(-0.274784\pi\)
−0.983131 + 0.182903i \(0.941450\pi\)
\(390\) 0 0
\(391\) −3.75736 −0.190018
\(392\) 0 0
\(393\) 4.87006 0.245662
\(394\) 0 0
\(395\) −6.57107 11.3814i −0.330626 0.572662i
\(396\) 0 0
\(397\) 7.20711 12.4831i 0.361714 0.626508i −0.626529 0.779398i \(-0.715525\pi\)
0.988243 + 0.152891i \(0.0488582\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.257359 + 0.445759i −0.0128519 + 0.0222602i −0.872380 0.488829i \(-0.837424\pi\)
0.859528 + 0.511089i \(0.170758\pi\)
\(402\) 0 0
\(403\) −8.22183 14.2406i −0.409558 0.709376i
\(404\) 0 0
\(405\) 7.48528 0.371947
\(406\) 0 0
\(407\) 13.0711 0.647909
\(408\) 0 0
\(409\) 16.4142 + 28.4303i 0.811631 + 1.40579i 0.911722 + 0.410807i \(0.134753\pi\)
−0.100092 + 0.994978i \(0.531914\pi\)
\(410\) 0 0
\(411\) −2.68629 + 4.65279i −0.132505 + 0.229505i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −4.00000 + 6.92820i −0.196352 + 0.340092i
\(416\) 0 0
\(417\) −2.87868 4.98602i −0.140970 0.244166i
\(418\) 0 0
\(419\) 9.55635 0.466858 0.233429 0.972374i \(-0.425005\pi\)
0.233429 + 0.972374i \(0.425005\pi\)
\(420\) 0 0
\(421\) 20.3137 0.990030 0.495015 0.868885i \(-0.335163\pi\)
0.495015 + 0.868885i \(0.335163\pi\)
\(422\) 0 0
\(423\) 12.5858 + 21.7992i 0.611942 + 1.05991i
\(424\) 0 0
\(425\) 3.20711 5.55487i 0.155568 0.269451i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.84315 + 4.92447i −0.137268 + 0.237756i
\(430\) 0 0
\(431\) 4.91421 + 8.51167i 0.236709 + 0.409993i 0.959768 0.280794i \(-0.0905978\pi\)
−0.723059 + 0.690787i \(0.757264\pi\)
\(432\) 0 0
\(433\) 22.2843 1.07091 0.535457 0.844563i \(-0.320139\pi\)
0.535457 + 0.844563i \(0.320139\pi\)
\(434\) 0 0
\(435\) 2.75736 0.132205
\(436\) 0 0
\(437\) 1.07107 + 1.85514i 0.0512361 + 0.0887436i
\(438\) 0 0
\(439\) 12.1213 20.9947i 0.578519 1.00202i −0.417130 0.908847i \(-0.636964\pi\)
0.995649 0.0931778i \(-0.0297025\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.7279 30.7057i 0.842279 1.45887i −0.0456844 0.998956i \(-0.514547\pi\)
0.887963 0.459914i \(-0.152120\pi\)
\(444\) 0 0
\(445\) 8.48528 + 14.6969i 0.402241 + 0.696702i
\(446\) 0 0
\(447\) 1.45584 0.0688591
\(448\) 0 0
\(449\) 23.8284 1.12453 0.562267 0.826956i \(-0.309930\pi\)
0.562267 + 0.826956i \(0.309930\pi\)
\(450\) 0 0
\(451\) −1.12132 1.94218i −0.0528009 0.0914539i
\(452\) 0 0
\(453\) 2.44975 4.24309i 0.115099 0.199358i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.53553 13.0519i 0.352497 0.610543i −0.634189 0.773178i \(-0.718666\pi\)
0.986686 + 0.162635i \(0.0519992\pi\)
\(458\) 0 0
\(459\) −7.74264 13.4106i −0.361396 0.625955i
\(460\) 0 0
\(461\) −22.3431 −1.04062 −0.520312 0.853976i \(-0.674184\pi\)
−0.520312 + 0.853976i \(0.674184\pi\)
\(462\) 0 0
\(463\) −13.4558 −0.625346 −0.312673 0.949861i \(-0.601224\pi\)
−0.312673 + 0.949861i \(0.601224\pi\)
\(464\) 0 0
\(465\) 0.949747 + 1.64501i 0.0440435 + 0.0762856i
\(466\) 0 0
\(467\) 0.449747 0.778985i 0.0208118 0.0360471i −0.855432 0.517915i \(-0.826708\pi\)
0.876244 + 0.481868i \(0.160042\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 2.17157 3.76127i 0.100061 0.173310i
\(472\) 0 0
\(473\) 22.3137 + 38.6485i 1.02599 + 1.77706i
\(474\) 0 0
\(475\) −3.65685 −0.167788
\(476\) 0 0
\(477\) 10.6274 0.486596
\(478\) 0 0
\(479\) 4.70711 + 8.15295i 0.215073 + 0.372518i 0.953295 0.302040i \(-0.0976677\pi\)
−0.738222 + 0.674558i \(0.764334\pi\)
\(480\) 0 0
\(481\) −6.12132 + 10.6024i −0.279108 + 0.483430i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.86396 13.6208i 0.357084 0.618488i
\(486\) 0 0
\(487\) 3.70711 + 6.42090i 0.167985 + 0.290959i 0.937711 0.347415i \(-0.112941\pi\)
−0.769726 + 0.638374i \(0.779607\pi\)
\(488\) 0 0
\(489\) 8.92893 0.403780
\(490\) 0 0
\(491\) 17.2843 0.780028 0.390014 0.920809i \(-0.372470\pi\)
0.390014 + 0.920809i \(0.372470\pi\)
\(492\) 0 0
\(493\) 21.3492 + 36.9780i 0.961522 + 1.66540i
\(494\) 0 0
\(495\) −5.41421 + 9.37769i −0.243351 + 0.421496i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6.81371 11.8017i 0.305023 0.528316i −0.672243 0.740331i \(-0.734669\pi\)
0.977267 + 0.212014i \(0.0680024\pi\)
\(500\) 0 0
\(501\) 0.500000 + 0.866025i 0.0223384 + 0.0386912i
\(502\) 0 0
\(503\) −39.0416 −1.74078 −0.870390 0.492363i \(-0.836133\pi\)
−0.870390 + 0.492363i \(0.836133\pi\)
\(504\) 0 0
\(505\) 4.82843 0.214862
\(506\) 0 0
\(507\) 0.0294373 + 0.0509868i 0.00130735 + 0.00226440i
\(508\) 0 0
\(509\) −17.5355 + 30.3724i −0.777249 + 1.34623i 0.156273 + 0.987714i \(0.450052\pi\)
−0.933522 + 0.358521i \(0.883281\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −4.41421 + 7.64564i −0.194892 + 0.337563i
\(514\) 0 0
\(515\) 0.792893 + 1.37333i 0.0349390 + 0.0605162i
\(516\) 0 0
\(517\) −34.0711 −1.49844
\(518\) 0 0
\(519\) −7.68629 −0.337391
\(520\) 0 0
\(521\) 3.34315 + 5.79050i 0.146466 + 0.253686i 0.929919 0.367765i \(-0.119877\pi\)
−0.783453 + 0.621451i \(0.786543\pi\)
\(522\) 0 0
\(523\) 0.928932 1.60896i 0.0406194 0.0703548i −0.845001 0.534765i \(-0.820400\pi\)
0.885620 + 0.464410i \(0.153734\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.7071 + 25.4735i −0.640652 + 1.10964i
\(528\) 0 0
\(529\) 11.3284 + 19.6214i 0.492540 + 0.853105i
\(530\) 0 0
\(531\) 9.65685 0.419072
\(532\) 0 0
\(533\) 2.10051 0.0909830
\(534\) 0 0
\(535\) 8.41421 + 14.5738i 0.363778 + 0.630082i
\(536\) 0 0
\(537\) −1.34315 + 2.32640i −0.0579610 + 0.100391i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −7.98528 + 13.8309i −0.343314 + 0.594637i −0.985046 0.172292i \(-0.944883\pi\)
0.641732 + 0.766929i \(0.278216\pi\)
\(542\) 0 0
\(543\) 0.363961 + 0.630399i 0.0156191 + 0.0270530i
\(544\) 0 0
\(545\) 9.00000 0.385518
\(546\) 0 0
\(547\) 7.51472 0.321306 0.160653 0.987011i \(-0.448640\pi\)
0.160653 + 0.987011i \(0.448640\pi\)
\(548\) 0 0
\(549\) −7.31371 12.6677i −0.312141 0.540645i
\(550\) 0 0
\(551\) 12.1716 21.0818i 0.518526 0.898114i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0.707107 1.22474i 0.0300150 0.0519875i
\(556\) 0 0
\(557\) 3.89949 + 6.75412i 0.165227 + 0.286181i 0.936736 0.350037i \(-0.113831\pi\)
−0.771509 + 0.636218i \(0.780498\pi\)
\(558\) 0 0
\(559\) −41.7990 −1.76791
\(560\) 0 0
\(561\) 10.1716 0.429444
\(562\) 0 0
\(563\) −10.3137 17.8639i −0.434671 0.752872i 0.562598 0.826731i \(-0.309802\pi\)
−0.997269 + 0.0738585i \(0.976469\pi\)
\(564\) 0 0
\(565\) 2.53553 4.39167i 0.106671 0.184759i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 15.8995 27.5387i 0.666542 1.15448i −0.312323 0.949976i \(-0.601107\pi\)
0.978865 0.204508i \(-0.0655594\pi\)
\(570\) 0 0
\(571\) −2.41421 4.18154i −0.101032 0.174992i 0.811078 0.584938i \(-0.198881\pi\)
−0.912110 + 0.409946i \(0.865548\pi\)
\(572\) 0 0
\(573\) 6.89949 0.288231
\(574\) 0 0
\(575\) 0.585786 0.0244290
\(576\) 0 0
\(577\) −7.03553 12.1859i −0.292893 0.507306i 0.681599 0.731725i \(-0.261285\pi\)
−0.974493 + 0.224420i \(0.927951\pi\)
\(578\) 0 0
\(579\) −1.17157 + 2.02922i −0.0486889 + 0.0843317i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −7.19239 + 12.4576i −0.297878 + 0.515940i
\(584\) 0 0
\(585\) −5.07107 8.78335i −0.209663 0.363147i
\(586\) 0 0
\(587\) 30.8284 1.27243 0.636213 0.771514i \(-0.280500\pi\)
0.636213 + 0.771514i \(0.280500\pi\)
\(588\) 0 0
\(589\) 16.7696 0.690977
\(590\) 0 0
\(591\) 5.70711 + 9.88500i 0.234759 + 0.406615i
\(592\) 0 0
\(593\) 8.86396 15.3528i 0.363999 0.630465i −0.624616 0.780932i \(-0.714744\pi\)
0.988615 + 0.150467i \(0.0480777\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5.53553 + 9.58783i −0.226554 + 0.392404i
\(598\) 0 0
\(599\) 6.39949 + 11.0843i 0.261476 + 0.452890i 0.966634 0.256160i \(-0.0824573\pi\)
−0.705158 + 0.709050i \(0.749124\pi\)
\(600\) 0 0
\(601\) −39.6569 −1.61764 −0.808818 0.588058i \(-0.799892\pi\)
−0.808818 + 0.588058i \(0.799892\pi\)
\(602\) 0 0
\(603\) 31.3137 1.27519
\(604\) 0 0
\(605\) −1.82843 3.16693i −0.0743361 0.128754i
\(606\) 0 0
\(607\) 6.96447 12.0628i 0.282679 0.489614i −0.689365 0.724414i \(-0.742110\pi\)
0.972044 + 0.234800i \(0.0754436\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.9558 27.6363i 0.645504 1.11805i
\(612\) 0 0
\(613\) 20.6569 + 35.7787i 0.834322 + 1.44509i 0.894581 + 0.446906i \(0.147474\pi\)
−0.0602584 + 0.998183i \(0.519192\pi\)
\(614\) 0 0
\(615\) −0.242641 −0.00978422
\(616\) 0 0
\(617\) 40.8701 1.64537 0.822683 0.568500i \(-0.192476\pi\)
0.822683 + 0.568500i \(0.192476\pi\)
\(618\) 0 0
\(619\) 5.43503 + 9.41375i 0.218452 + 0.378370i 0.954335 0.298739i \(-0.0965659\pi\)
−0.735883 + 0.677109i \(0.763233\pi\)
\(620\) 0 0
\(621\) 0.707107 1.22474i 0.0283752 0.0491473i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −2.89949 5.02207i −0.115795 0.200562i
\(628\) 0 0
\(629\) 21.8995 0.873190
\(630\) 0 0
\(631\) −39.4853 −1.57188 −0.785942 0.618300i \(-0.787822\pi\)
−0.785942 + 0.618300i \(0.787822\pi\)
\(632\) 0 0
\(633\) 5.03553 + 8.72180i 0.200145 + 0.346660i
\(634\) 0 0
\(635\) 10.9497 18.9655i 0.434527 0.752624i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 9.17157 15.8856i 0.362822 0.628426i
\(640\) 0 0
\(641\) −19.6569 34.0467i −0.776399 1.34476i −0.934005 0.357261i \(-0.883711\pi\)
0.157606 0.987502i \(-0.449622\pi\)
\(642\) 0 0
\(643\) −4.21320 −0.166153 −0.0830763 0.996543i \(-0.526475\pi\)
−0.0830763 + 0.996543i \(0.526475\pi\)
\(644\) 0 0
\(645\) 4.82843 0.190119
\(646\) 0 0
\(647\) 17.5563 + 30.4085i 0.690211 + 1.19548i 0.971768 + 0.235937i \(0.0758158\pi\)
−0.281557 + 0.959544i \(0.590851\pi\)
\(648\) 0 0
\(649\) −6.53553 + 11.3199i −0.256542 + 0.444344i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 13.3431 23.1110i 0.522158 0.904404i −0.477510 0.878626i \(-0.658461\pi\)
0.999668 0.0257773i \(-0.00820608\pi\)
\(654\) 0 0
\(655\) −5.87868 10.1822i −0.229699 0.397850i
\(656\) 0 0
\(657\) 14.6274 0.570670
\(658\) 0 0
\(659\) −20.6569 −0.804677 −0.402338 0.915491i \(-0.631802\pi\)
−0.402338 + 0.915491i \(0.631802\pi\)
\(660\) 0 0
\(661\) −17.0711 29.5680i −0.663988 1.15006i −0.979559 0.201158i \(-0.935529\pi\)
0.315571 0.948902i \(-0.397804\pi\)
\(662\) 0 0
\(663\) −4.76346 + 8.25055i −0.184997 + 0.320425i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.94975 + 3.37706i −0.0754945 + 0.130760i
\(668\) 0 0
\(669\) 4.98528 + 8.63476i 0.192742 + 0.333839i
\(670\) 0 0
\(671\) 19.7990 0.764332
\(672\) 0 0
\(673\) −27.5147 −1.06061 −0.530307 0.847806i \(-0.677923\pi\)
−0.530307 + 0.847806i \(0.677923\pi\)
\(674\) 0 0
\(675\) 1.20711 + 2.09077i 0.0464616 + 0.0804738i
\(676\) 0 0
\(677\) −5.13604 + 8.89588i −0.197394 + 0.341896i −0.947683 0.319214i \(-0.896581\pi\)
0.750289 + 0.661110i \(0.229914\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.60051 2.77216i 0.0613315 0.106229i
\(682\) 0 0
\(683\) −17.5563 30.4085i −0.671775 1.16355i −0.977400 0.211397i \(-0.932199\pi\)
0.305625 0.952152i \(-0.401135\pi\)
\(684\) 0 0
\(685\) 12.9706 0.495580
\(686\) 0 0
\(687\) −9.89949 −0.377689
\(688\) 0 0
\(689\) −6.73654 11.6680i −0.256642 0.444517i
\(690\) 0 0
\(691\) 1.75736 3.04384i 0.0668531 0.115793i −0.830661 0.556778i \(-0.812037\pi\)
0.897515 + 0.440985i \(0.145371\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −6.94975 + 12.0373i −0.263619 + 0.456601i
\(696\) 0 0
\(697\) −1.87868 3.25397i −0.0711601 0.123253i
\(698\) 0 0
\(699\) −3.79899 −0.143691
\(700\) 0 0
\(701\) 0.514719 0.0194407 0.00972033 0.999953i \(-0.496906\pi\)
0.00972033 + 0.999953i \(0.496906\pi\)
\(702\) 0 0
\(703\) −6.24264 10.8126i −0.235446 0.407804i
\(704\) 0 0
\(705\) −1.84315 + 3.19242i −0.0694169 + 0.120234i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −1.81371 + 3.14144i −0.0681153 + 0.117979i −0.898072 0.439849i \(-0.855032\pi\)
0.829956 + 0.557828i \(0.188365\pi\)
\(710\) 0 0
\(711\) 18.5858 + 32.1915i 0.697021 + 1.20728i
\(712\) 0 0
\(713\) −2.68629 −0.100602
\(714\) 0 0
\(715\) 13.7279 0.513395
\(716\) 0 0
\(717\) −2.93503 5.08362i −0.109611 0.189851i
\(718\) 0 0
\(719\) 7.87868 13.6463i 0.293825 0.508920i −0.680886 0.732390i \(-0.738405\pi\)
0.974711 + 0.223470i \(0.0717383\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.736544 + 1.27573i −0.0273924 + 0.0474450i
\(724\) 0 0
\(725\) −3.32843 5.76500i −0.123615 0.214107i
\(726\) 0 0
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) 37.3848 + 64.7523i 1.38273 + 2.39495i
\(732\) 0 0
\(733\) −15.3492 + 26.5857i −0.566937 + 0.981964i 0.429929 + 0.902863i \(0.358538\pi\)
−0.996867 + 0.0791015i \(0.974795\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.1924 + 36.7063i −0.780632 + 1.35209i
\(738\) 0 0
\(739\) −10.3284 17.8894i −0.379937 0.658071i 0.611115 0.791541i \(-0.290721\pi\)
−0.991053 + 0.133471i \(0.957388\pi\)
\(740\) 0 0
\(741\) 5.43146 0.199530
\(742\) 0 0
\(743\) −8.92893 −0.327571 −0.163785 0.986496i \(-0.552370\pi\)
−0.163785 + 0.986496i \(0.552370\pi\)
\(744\) 0 0
\(745\) −1.75736 3.04384i −0.0643847 0.111518i
\(746\) 0 0
\(747\) 11.3137 19.5959i 0.413947 0.716977i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.571068 + 0.989118i −0.0208386 + 0.0360934i −0.876257 0.481845i \(-0.839967\pi\)
0.855418 + 0.517938i \(0.173300\pi\)
\(752\) 0 0
\(753\) −5.60660 9.71092i −0.204316 0.353886i
\(754\) 0 0
\(755\) −11.8284 −0.430481
\(756\) 0 0
\(757\) 37.1716 1.35102 0.675512 0.737349i \(-0.263923\pi\)
0.675512 + 0.737349i \(0.263923\pi\)
\(758\) 0 0
\(759\) 0.464466 + 0.804479i 0.0168591 + 0.0292007i
\(760\) 0 0
\(761\) −9.43503 + 16.3419i −0.342020 + 0.592395i −0.984808 0.173649i \(-0.944444\pi\)
0.642788 + 0.766044i \(0.277778\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −9.07107 + 15.7116i −0.327965 + 0.568052i
\(766\) 0 0
\(767\) −6.12132 10.6024i −0.221028 0.382832i
\(768\) 0 0
\(769\) −28.1421 −1.01483 −0.507416 0.861701i \(-0.669399\pi\)
−0.507416 + 0.861701i \(0.669399\pi\)
\(770\) 0 0
\(771\) 10.6863 0.384857
\(772\) 0 0
\(773\) −21.8640 37.8695i −0.786392 1.36207i −0.928164 0.372172i \(-0.878613\pi\)
0.141772 0.989899i \(-0.454720\pi\)
\(774\) 0 0
\(775\) 2.29289 3.97141i 0.0823632 0.142657i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.07107 + 1.85514i −0.0383750 + 0.0664674i
\(780\) 0 0
\(781\) 12.4142 + 21.5020i 0.444215 + 0.769404i
\(782\) 0 0
\(783\) −16.0711 −0.574333
\(784\) 0 0
\(785\) −10.4853 −0.374236
\(786\) 0 0
\(787\) −21.8640 37.8695i −0.779366 1.34990i −0.932308 0.361666i \(-0.882208\pi\)
0.152942 0.988235i \(-0.451125\pi\)
\(788\) 0 0
\(789\) −2.07107 + 3.58719i −0.0737320 + 0.127708i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −9.27208 + 16.0597i −0.329261 + 0.570297i
\(794\) 0 0
\(795\) 0.778175 + 1.34784i 0.0275990 + 0.0478029i
\(796\) 0 0
\(797\) 35.3848 1.25339 0.626697 0.779263i \(-0.284407\pi\)
0.626697 + 0.779263i \(0.284407\pi\)