Properties

Label 980.2.i.k.361.2
Level $980$
Weight $2$
Character 980.361
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 361.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 980.361
Dual form 980.2.i.k.961.2

$q$-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 \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.207107 0.358719i 0.119573 0.207107i −0.800025 0.599966i \(-0.795181\pi\)
0.919599 + 0.392859i \(0.128514\pi\)
\(4\) 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 −0.418646 0.908149i \(-0.637495\pi\)
0.995804 0.0915161i \(-0.0291713\pi\)
\(12\) 0 0
\(13\) 3.58579 0.994518 0.497259 0.867602i \(-0.334340\pi\)
0.497259 + 0.867602i \(0.334340\pi\)
\(14\) 0 0
\(15\) 0.414214 0.106949
\(16\) 0 0
\(17\) −3.20711 + 5.55487i −0.777838 + 1.34725i 0.155348 + 0.987860i \(0.450350\pi\)
−0.933186 + 0.359395i \(0.882983\pi\)
\(18\) 0 0
\(19\) −1.82843 3.16693i −0.419470 0.726543i 0.576416 0.817156i \(-0.304451\pi\)
−0.995886 + 0.0906130i \(0.971117\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.292893 0.507306i −0.0610725 0.105781i 0.833873 0.551957i \(-0.186119\pi\)
−0.894945 + 0.446176i \(0.852785\pi\)
\(24\) 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 \(-0.968439\pi\)
0.583273 + 0.812276i \(0.301772\pi\)
\(32\) 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 0.971544 0.236858i \(-0.0761178\pi\)
−0.690898 + 0.722953i \(0.742784\pi\)
\(38\) 0 0
\(39\) 0.742641 1.28629i 0.118918 0.205971i
\(40\) 0 0
\(41\) 0.585786 0.0914845 0.0457422 0.998953i \(-0.485435\pi\)
0.0457422 + 0.998953i \(0.485435\pi\)
\(42\) 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 0.983347 + 0.181737i \(0.0581719\pi\)
−0.334285 + 0.942472i \(0.608495\pi\)
\(48\) 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 −0.707665 0.706548i \(-0.750251\pi\)
0.965721 + 0.259581i \(0.0835846\pi\)
\(54\) 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 \(-0.904672\pi\)
0.733243 + 0.679966i \(0.238006\pi\)
\(60\) 0 0
\(61\) −2.58579 4.47871i −0.331076 0.573441i 0.651647 0.758522i \(-0.274078\pi\)
−0.982723 + 0.185082i \(0.940745\pi\)
\(62\) 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 −0.299822 0.953995i \(-0.596927\pi\)
0.976095 0.217344i \(-0.0697394\pi\)
\(68\) 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 \(-0.931202\pi\)
0.674090 + 0.738649i \(0.264536\pi\)
\(74\) 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 −0.952810 0.303569i \(-0.901822\pi\)
0.213507 0.976942i \(-0.431511\pi\)
\(80\) 0 0
\(81\) −3.74264 + 6.48244i −0.415849 + 0.720272i
\(82\) 0 0
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 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 −0.828214 0.560412i \(-0.810643\pi\)
−0.0712241 0.997460i \(-0.522691\pi\)
\(90\) 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 \(-0.205646\pi\)
0.798464 + 0.602042i \(0.205646\pi\)
\(98\) 0 0
\(99\) 10.8284 1.08830
\(100\) 0 0
\(101\) 2.41421 4.18154i 0.240223 0.416079i −0.720555 0.693398i \(-0.756113\pi\)
0.960778 + 0.277319i \(0.0894460\pi\)
\(102\) 0 0
\(103\) −0.792893 1.37333i −0.0781261 0.135318i 0.824315 0.566131i \(-0.191560\pi\)
−0.902441 + 0.430813i \(0.858227\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.41421 + 14.5738i 0.813433 + 1.40891i 0.910448 + 0.413624i \(0.135737\pi\)
−0.0970151 + 0.995283i \(0.530930\pi\)
\(108\) 0 0
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) 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 0.999875 + 0.0158021i \(0.00503019\pi\)
−0.486253 + 0.873818i \(0.661636\pi\)
\(132\) 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 0.443900 + 0.896076i \(0.353595\pi\)
−0.997975 + 0.0636096i \(0.979739\pi\)
\(138\) 0 0
\(139\) −13.8995 −1.17894 −0.589470 0.807790i \(-0.700663\pi\)
−0.589470 + 0.807790i \(0.700663\pi\)
\(140\) 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 0.785019 0.619472i \(-0.212653\pi\)
−0.928988 + 0.370111i \(0.879320\pi\)
\(150\) 0 0
\(151\) 5.91421 10.2437i 0.481292 0.833622i −0.518478 0.855091i \(-0.673501\pi\)
0.999770 + 0.0214692i \(0.00683439\pi\)
\(152\) 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 \(-0.970745\pi\)
0.577371 + 0.816482i \(0.304079\pi\)
\(158\) 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 −0.886304 0.463104i \(-0.846736\pi\)
0.0420922 0.999114i \(-0.486598\pi\)
\(164\) 0 0
\(165\) 0.792893 1.37333i 0.0617267 0.106914i
\(166\) 0 0
\(167\) 2.41421 0.186817 0.0934087 0.995628i \(-0.470224\pi\)
0.0934087 + 0.995628i \(0.470224\pi\)
\(168\) 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 −0.966545 0.256499i \(-0.917431\pi\)
0.261138 0.965301i \(-0.415902\pi\)
\(174\) 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 −0.961388 0.275197i \(-0.911257\pi\)
0.719022 + 0.694988i \(0.244590\pi\)
\(180\) 0 0
\(181\) 1.75736 0.130623 0.0653117 0.997865i \(-0.479196\pi\)
0.0653117 + 0.997865i \(0.479196\pi\)
\(182\) 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 −0.992422 0.122875i \(-0.960789\pi\)
0.389798 0.920900i \(-0.372545\pi\)
\(192\) 0 0
\(193\) −2.82843 + 4.89898i −0.203595 + 0.352636i −0.949684 0.313210i \(-0.898596\pi\)
0.746089 + 0.665846i \(0.231929\pi\)
\(194\) 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 0.196362 0.980532i \(-0.437087\pi\)
0.750984 0.660320i \(-0.229579\pi\)
\(200\) 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 \(-0.201650\pi\)
0.805959 + 0.591971i \(0.201650\pi\)
\(224\) 0 0
\(225\) −2.82843 −0.188562
\(226\) 0 0
\(227\) −3.86396 + 6.69258i −0.256460 + 0.444202i −0.965291 0.261176i \(-0.915890\pi\)
0.708831 + 0.705378i \(0.249223\pi\)
\(228\) 0 0
\(229\) −11.9497 20.6976i −0.789662 1.36773i −0.926174 0.377096i \(-0.876923\pi\)
0.136513 0.990638i \(-0.456411\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.58579 + 7.94282i 0.300425 + 0.520351i 0.976232 0.216727i \(-0.0695382\pi\)
−0.675807 + 0.737078i \(0.736205\pi\)
\(234\) 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 \(-0.796793\pi\)
0.917597 + 0.397513i \(0.130127\pi\)
\(242\) 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 \(-0.826048\pi\)
−0.854355 + 0.519689i \(0.826048\pi\)
\(252\) 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 0.916528 + 0.399970i \(0.130980\pi\)
−0.111880 + 0.993722i \(0.535687\pi\)
\(258\) 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 −0.977993 0.208635i \(-0.933098\pi\)
0.669680 + 0.742650i \(0.266431\pi\)
\(264\) 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 −0.489974 0.871737i \(-0.662994\pi\)
0.999933 0.0115389i \(-0.00367303\pi\)
\(270\) 0 0
\(271\) −14.4853 25.0892i −0.879918 1.52406i −0.851430 0.524469i \(-0.824264\pi\)
−0.0284886 0.999594i \(-0.509069\pi\)
\(272\) 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 −0.732900 0.680336i \(-0.761834\pi\)
0.955639 + 0.294542i \(0.0951671\pi\)
\(278\) 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 −0.440199 0.897900i \(-0.645092\pi\)
0.997704 0.0677263i \(-0.0215745\pi\)
\(284\) 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 \(-0.638336\pi\)
−0.421044 + 0.907040i \(0.638336\pi\)
\(294\) 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 \(-0.467372\pi\)
0.102326 + 0.994751i \(0.467372\pi\)
\(308\) 0 0
\(309\) −0.656854 −0.0373671
\(310\) 0 0
\(311\) −3.48528 + 6.03668i −0.197632 + 0.342309i −0.947760 0.318984i \(-0.896658\pi\)
0.750128 + 0.661293i \(0.229992\pi\)
\(312\) 0 0
\(313\) −8.27817 14.3382i −0.467910 0.810444i 0.531417 0.847110i \(-0.321660\pi\)
−0.999328 + 0.0366660i \(0.988326\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.48528 + 12.9649i 0.420415 + 0.728181i 0.995980 0.0895756i \(-0.0285511\pi\)
−0.575565 + 0.817756i \(0.695218\pi\)
\(318\) 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 0.792018 0.610497i \(-0.209030\pi\)
−0.924715 + 0.380659i \(0.875697\pi\)
\(332\) 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 −0.749199 0.662345i \(-0.769561\pi\)
0.948207 + 0.317653i \(0.102895\pi\)
\(348\) 0 0
\(349\) 18.0000 0.963518 0.481759 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) 0 0
\(351\) 8.65685 0.462069
\(352\) 0 0
\(353\) 1.03553 1.79360i 0.0551159 0.0954636i −0.837151 0.546972i \(-0.815781\pi\)
0.892267 + 0.451508i \(0.149114\pi\)
\(354\) 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 0.677249 0.735754i \(-0.263172\pi\)
−0.975806 + 0.218638i \(0.929839\pi\)
\(360\) 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 0.484956 + 0.874539i \(0.338836\pi\)
−0.999851 + 0.0172850i \(0.994498\pi\)
\(368\) 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 0.569798 0.821785i \(-0.307022\pi\)
−0.996586 + 0.0825669i \(0.973688\pi\)
\(374\) 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 \(-0.138045\pi\)
−0.817628 + 0.575746i \(0.804712\pi\)
\(384\) 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 −0.983131 0.182903i \(-0.941450\pi\)
0.649965 + 0.759965i \(0.274784\pi\)
\(390\) 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 \(-0.284475\pi\)
−0.988243 + 0.152891i \(0.951142\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −0.257359 0.445759i −0.0128519 0.0222602i 0.859528 0.511089i \(-0.170758\pi\)
−0.872380 + 0.488829i \(0.837424\pi\)
\(402\) 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 0.100092 + 0.994978i \(0.468086\pi\)
−0.911722 + 0.410807i \(0.865247\pi\)
\(410\) 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 \(-0.574995\pi\)
−0.233429 + 0.972374i \(0.574995\pi\)
\(420\) 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 −0.723059 0.690787i \(-0.757264\pi\)
0.959768 + 0.280794i \(0.0905978\pi\)
\(432\) 0 0
\(433\) −22.2843 −1.07091 −0.535457 0.844563i \(-0.679861\pi\)
−0.535457 + 0.844563i \(0.679861\pi\)
\(434\) 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 −0.995649 0.0931778i \(-0.970298\pi\)
0.417130 0.908847i \(-0.363036\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.7279 + 30.7057i 0.842279 + 1.45887i 0.887963 + 0.459914i \(0.152120\pi\)
−0.0456844 + 0.998956i \(0.514547\pi\)
\(444\) 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 0.986686 0.162635i \(-0.0519992\pi\)
−0.634189 + 0.773178i \(0.718666\pi\)
\(458\) 0 0
\(459\) −7.74264 + 13.4106i −0.361396 + 0.625955i
\(460\) 0 0
\(461\) 22.3431 1.04062 0.520312 0.853976i \(-0.325816\pi\)
0.520312 + 0.853976i \(0.325816\pi\)
\(462\) 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 \(-0.173292\pi\)
−0.876244 + 0.481868i \(0.839958\pi\)
\(468\) 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 \(-0.902332\pi\)
0.738222 + 0.674558i \(0.235666\pi\)
\(480\) 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 −0.769726 0.638374i \(-0.779607\pi\)
0.937711 + 0.347415i \(0.112941\pi\)
\(488\) 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 0.977267 0.212014i \(-0.0680024\pi\)
−0.672243 + 0.740331i \(0.734669\pi\)
\(500\) 0 0
\(501\) 0.500000 0.866025i 0.0223384 0.0386912i
\(502\) 0 0
\(503\) 39.0416 1.74078 0.870390 0.492363i \(-0.163867\pi\)
0.870390 + 0.492363i \(0.163867\pi\)
\(504\) 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 0.933522 + 0.358521i \(0.116719\pi\)
−0.156273 + 0.987714i \(0.549948\pi\)
\(510\) 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 \(-0.880123\pi\)
0.783453 + 0.621451i \(0.213457\pi\)
\(522\) 0 0
\(523\) −0.928932 1.60896i −0.0406194 0.0703548i 0.845001 0.534765i \(-0.179600\pi\)
−0.885620 + 0.464410i \(0.846266\pi\)
\(524\) 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 0.641732 0.766929i \(-0.278216\pi\)
−0.985046 + 0.172292i \(0.944883\pi\)
\(542\) 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 −0.771509 0.636218i \(-0.780498\pi\)
0.936736 + 0.350037i \(0.113831\pi\)
\(558\) 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 \(-0.690198\pi\)
0.997269 + 0.0738585i \(0.0235313\pi\)
\(564\) 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 0.978865 + 0.204508i \(0.0655594\pi\)
−0.312323 + 0.949976i \(0.601107\pi\)
\(570\) 0 0
\(571\) −2.41421 + 4.18154i −0.101032 + 0.174992i −0.912110 0.409946i \(-0.865548\pi\)
0.811078 + 0.584938i \(0.198881\pi\)
\(572\) 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 \(-0.738715\pi\)
0.974493 + 0.224420i \(0.0720487\pi\)
\(578\) 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 \(-0.719500\pi\)
−0.636213 + 0.771514i \(0.719500\pi\)
\(588\) 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 \(-0.285256\pi\)
−0.988615 + 0.150467i \(0.951922\pi\)
\(594\) 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 −0.705158 0.709050i \(-0.749124\pi\)
0.966634 + 0.256160i \(0.0824573\pi\)
\(600\) 0 0
\(601\) 39.6569 1.61764 0.808818 0.588058i \(-0.200108\pi\)
0.808818 + 0.588058i \(0.200108\pi\)
\(602\) 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 \(-0.257890\pi\)
−0.972044 + 0.234800i \(0.924556\pi\)
\(608\) 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 −0.0602584 0.998183i \(-0.519192\pi\)
0.894581 0.446906i \(-0.147474\pi\)
\(614\) 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 \(-0.903434\pi\)
0.735883 + 0.677109i \(0.236767\pi\)
\(620\) 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 0.157606 + 0.987502i \(0.449622\pi\)
−0.934005 + 0.357261i \(0.883711\pi\)
\(642\) 0 0
\(643\) 4.21320 0.166153 0.0830763 0.996543i \(-0.473525\pi\)
0.0830763 + 0.996543i \(0.473525\pi\)
\(644\) 0 0
\(645\) 4.82843 0.190119
\(646\) 0 0
\(647\) −17.5563 + 30.4085i −0.690211 + 1.19548i 0.281557 + 0.959544i \(0.409149\pi\)
−0.971768 + 0.235937i \(0.924184\pi\)
\(648\) 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 0.999668 + 0.0257773i \(0.00820608\pi\)
−0.477510 + 0.878626i \(0.658461\pi\)
\(654\) 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 −0.315571 0.948902i \(-0.602196\pi\)
0.979559 0.201158i \(-0.0644706\pi\)
\(662\) 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 \(-0.103419\pi\)
−0.750289 + 0.661110i \(0.770086\pi\)
\(678\) 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 0.305625 + 0.952152i \(0.401135\pi\)
−0.977400 + 0.211397i \(0.932199\pi\)
\(684\) 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 \(-0.187963\pi\)
−0.897515 + 0.440985i \(0.854629\pi\)
\(692\) 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 0.829956 0.557828i \(-0.188365\pi\)
−0.898072 + 0.439849i \(0.855032\pi\)
\(710\) 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 \(-0.261595\pi\)
−0.974711 + 0.223470i \(0.928262\pi\)
\(720\) 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 \(-0.608328\pi\)
−0.333792 + 0.942647i \(0.608328\pi\)
\(728\) 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 0.996867 + 0.0791015i \(0.0252051\pi\)
−0.429929 + 0.902863i \(0.641462\pi\)
\(734\) 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 −0.991053 0.133471i \(-0.957388\pi\)
0.611115 + 0.791541i \(0.290721\pi\)
\(740\) 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 0.855418 0.517938i \(-0.173300\pi\)
−0.876257 + 0.481845i \(0.839967\pi\)
\(752\) 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 \(-0.0555558\pi\)
−0.642788 + 0.766044i \(0.722222\pi\)
\(762\) 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 \(-0.330601\pi\)
0.507416 + 0.861701i \(0.330601\pi\)
\(770\) 0 0
\(771\) 10.6863 0.384857
\(772\) 0 0
\(773\) 21.8640 37.8695i 0.786392 1.36207i −0.141772 0.989899i \(-0.545280\pi\)
0.928164 0.372172i \(-0.121387\pi\)
\(774\) 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 −0.152942 0.988235i \(-0.548875\pi\)
0.932308 0.361666i \(-0.117792\pi\)
\(788\) 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 \(-0.715593\pi\)
−0.626697