Properties

Label 1680.2.cz.d.97.3
Level 1680
Weight 2
Character 1680.97
Analytic conductor 13.415
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.cz (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.3
Root \(0.517174 + 1.31626i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 1680.97
Dual form 1680.2.cz.d.433.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{3} +(1.50619 - 1.65269i) q^{5} +(-1.46123 + 2.20563i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{3} +(1.50619 - 1.65269i) q^{5} +(-1.46123 + 2.20563i) q^{7} +1.00000i q^{9} +1.46279 q^{11} +(-0.887844 - 0.887844i) q^{13} +(-2.23367 + 0.103594i) q^{15} +(2.10614 - 2.10614i) q^{17} -3.95987 q^{19} +(2.59286 - 0.526369i) q^{21} +(4.13007 - 4.13007i) q^{23} +(-0.462789 - 4.97854i) q^{25} +(0.707107 - 0.707107i) q^{27} +5.18572i q^{29} -6.10346i q^{31} +(-1.03435 - 1.03435i) q^{33} +(1.44434 + 5.73706i) q^{35} +(2.25560 + 2.25560i) q^{37} +1.25560i q^{39} -0.769968i q^{41} +(5.18572 - 5.18572i) q^{43} +(1.65269 + 1.50619i) q^{45} +(8.57041 - 8.57041i) q^{47} +(-2.72961 - 6.44587i) q^{49} -2.97854 q^{51} +(-0.544449 + 0.544449i) q^{53} +(2.20324 - 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} -3.19633 q^{59} -1.42064i q^{61} +(-2.20563 - 1.46123i) q^{63} +(-2.80460 + 0.130073i) q^{65} +(5.93012 + 5.93012i) q^{67} -5.84081 q^{69} -7.62611 q^{71} +(-6.81378 - 6.81378i) q^{73} +(-3.19312 + 3.84760i) q^{75} +(-2.13747 + 3.22637i) q^{77} -4.52029i q^{79} -1.00000 q^{81} +(-6.75794 - 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(3.66686 - 3.66686i) q^{87} -1.19991 q^{89} +(3.25560 - 0.660910i) q^{91} +(-4.31580 + 4.31580i) q^{93} +(-5.96431 + 6.54445i) q^{95} +(8.68829 - 8.68829i) q^{97} +1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 0 0
\(5\) 1.50619 1.65269i 0.673588 0.739107i
\(6\) 0 0
\(7\) −1.46123 + 2.20563i −0.552293 + 0.833650i
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 1.46279 0.441048 0.220524 0.975382i \(-0.429223\pi\)
0.220524 + 0.975382i \(0.429223\pi\)
\(12\) 0 0
\(13\) −0.887844 0.887844i −0.246244 0.246244i 0.573183 0.819427i \(-0.305708\pi\)
−0.819427 + 0.573183i \(0.805708\pi\)
\(14\) 0 0
\(15\) −2.23367 + 0.103594i −0.576730 + 0.0267479i
\(16\) 0 0
\(17\) 2.10614 2.10614i 0.510815 0.510815i −0.403961 0.914776i \(-0.632367\pi\)
0.914776 + 0.403961i \(0.132367\pi\)
\(18\) 0 0
\(19\) −3.95987 −0.908456 −0.454228 0.890885i \(-0.650085\pi\)
−0.454228 + 0.890885i \(0.650085\pi\)
\(20\) 0 0
\(21\) 2.59286 0.526369i 0.565809 0.114863i
\(22\) 0 0
\(23\) 4.13007 4.13007i 0.861180 0.861180i −0.130295 0.991475i \(-0.541593\pi\)
0.991475 + 0.130295i \(0.0415926\pi\)
\(24\) 0 0
\(25\) −0.462789 4.97854i −0.0925579 0.995707i
\(26\) 0 0
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 0 0
\(29\) 5.18572i 0.962965i 0.876456 + 0.481482i \(0.159901\pi\)
−0.876456 + 0.481482i \(0.840099\pi\)
\(30\) 0 0
\(31\) 6.10346i 1.09621i −0.836408 0.548107i \(-0.815349\pi\)
0.836408 0.548107i \(-0.184651\pi\)
\(32\) 0 0
\(33\) −1.03435 1.03435i −0.180057 0.180057i
\(34\) 0 0
\(35\) 1.44434 + 5.73706i 0.244138 + 0.969741i
\(36\) 0 0
\(37\) 2.25560 + 2.25560i 0.370819 + 0.370819i 0.867775 0.496957i \(-0.165549\pi\)
−0.496957 + 0.867775i \(0.665549\pi\)
\(38\) 0 0
\(39\) 1.25560i 0.201057i
\(40\) 0 0
\(41\) 0.769968i 0.120249i −0.998191 0.0601244i \(-0.980850\pi\)
0.998191 0.0601244i \(-0.0191497\pi\)
\(42\) 0 0
\(43\) 5.18572 5.18572i 0.790816 0.790816i −0.190811 0.981627i \(-0.561112\pi\)
0.981627 + 0.190811i \(0.0611118\pi\)
\(44\) 0 0
\(45\) 1.65269 + 1.50619i 0.246369 + 0.224529i
\(46\) 0 0
\(47\) 8.57041 8.57041i 1.25012 1.25012i 0.294459 0.955664i \(-0.404861\pi\)
0.955664 0.294459i \(-0.0951394\pi\)
\(48\) 0 0
\(49\) −2.72961 6.44587i −0.389944 0.920839i
\(50\) 0 0
\(51\) −2.97854 −0.417079
\(52\) 0 0
\(53\) −0.544449 + 0.544449i −0.0747859 + 0.0747859i −0.743510 0.668724i \(-0.766841\pi\)
0.668724 + 0.743510i \(0.266841\pi\)
\(54\) 0 0
\(55\) 2.20324 2.41754i 0.297084 0.325981i
\(56\) 0 0
\(57\) 2.80005 + 2.80005i 0.370876 + 0.370876i
\(58\) 0 0
\(59\) −3.19633 −0.416127 −0.208063 0.978115i \(-0.566716\pi\)
−0.208063 + 0.978115i \(0.566716\pi\)
\(60\) 0 0
\(61\) 1.42064i 0.181894i −0.995856 0.0909472i \(-0.971011\pi\)
0.995856 0.0909472i \(-0.0289894\pi\)
\(62\) 0 0
\(63\) −2.20563 1.46123i −0.277883 0.184098i
\(64\) 0 0
\(65\) −2.80460 + 0.130073i −0.347867 + 0.0161336i
\(66\) 0 0
\(67\) 5.93012 + 5.93012i 0.724480 + 0.724480i 0.969514 0.245034i \(-0.0787993\pi\)
−0.245034 + 0.969514i \(0.578799\pi\)
\(68\) 0 0
\(69\) −5.84081 −0.703150
\(70\) 0 0
\(71\) −7.62611 −0.905053 −0.452526 0.891751i \(-0.649477\pi\)
−0.452526 + 0.891751i \(0.649477\pi\)
\(72\) 0 0
\(73\) −6.81378 6.81378i −0.797493 0.797493i 0.185207 0.982700i \(-0.440704\pi\)
−0.982700 + 0.185207i \(0.940704\pi\)
\(74\) 0 0
\(75\) −3.19312 + 3.84760i −0.368709 + 0.444282i
\(76\) 0 0
\(77\) −2.13747 + 3.22637i −0.243588 + 0.367679i
\(78\) 0 0
\(79\) 4.52029i 0.508573i −0.967129 0.254286i \(-0.918159\pi\)
0.967129 0.254286i \(-0.0818405\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −6.75794 6.75794i −0.741781 0.741781i 0.231140 0.972921i \(-0.425754\pi\)
−0.972921 + 0.231140i \(0.925754\pi\)
\(84\) 0 0
\(85\) −0.308559 6.65306i −0.0334679 0.721626i
\(86\) 0 0
\(87\) 3.66686 3.66686i 0.393129 0.393129i
\(88\) 0 0
\(89\) −1.19991 −0.127190 −0.0635950 0.997976i \(-0.520257\pi\)
−0.0635950 + 0.997976i \(0.520257\pi\)
\(90\) 0 0
\(91\) 3.25560 0.660910i 0.341280 0.0692822i
\(92\) 0 0
\(93\) −4.31580 + 4.31580i −0.447527 + 0.447527i
\(94\) 0 0
\(95\) −5.96431 + 6.54445i −0.611925 + 0.671446i
\(96\) 0 0
\(97\) 8.68829 8.68829i 0.882162 0.882162i −0.111592 0.993754i \(-0.535595\pi\)
0.993754 + 0.111592i \(0.0355950\pi\)
\(98\) 0 0
\(99\) 1.46279i 0.147016i
\(100\) 0 0
\(101\) 15.3420i 1.52659i −0.646050 0.763295i \(-0.723580\pi\)
0.646050 0.763295i \(-0.276420\pi\)
\(102\) 0 0
\(103\) 8.30776 + 8.30776i 0.818588 + 0.818588i 0.985903 0.167316i \(-0.0535099\pi\)
−0.167316 + 0.985903i \(0.553510\pi\)
\(104\) 0 0
\(105\) 3.03541 5.07802i 0.296226 0.495564i
\(106\) 0 0
\(107\) −4.39022 4.39022i −0.424418 0.424418i 0.462303 0.886722i \(-0.347023\pi\)
−0.886722 + 0.462303i \(0.847023\pi\)
\(108\) 0 0
\(109\) 7.44587i 0.713185i 0.934260 + 0.356593i \(0.116062\pi\)
−0.934260 + 0.356593i \(0.883938\pi\)
\(110\) 0 0
\(111\) 3.18990i 0.302772i
\(112\) 0 0
\(113\) 2.54445 2.54445i 0.239362 0.239362i −0.577224 0.816586i \(-0.695864\pi\)
0.816586 + 0.577224i \(0.195864\pi\)
\(114\) 0 0
\(115\) −0.605073 13.0464i −0.0564233 1.21658i
\(116\) 0 0
\(117\) 0.887844 0.887844i 0.0820812 0.0820812i
\(118\) 0 0
\(119\) 1.56781 + 7.72294i 0.143721 + 0.707960i
\(120\) 0 0
\(121\) −8.86025 −0.805477
\(122\) 0 0
\(123\) −0.544449 + 0.544449i −0.0490913 + 0.0490913i
\(124\) 0 0
\(125\) −8.92504 6.73377i −0.798280 0.602287i
\(126\) 0 0
\(127\) −7.86025 7.86025i −0.697484 0.697484i 0.266383 0.963867i \(-0.414171\pi\)
−0.963867 + 0.266383i \(0.914171\pi\)
\(128\) 0 0
\(129\) −7.33372 −0.645698
\(130\) 0 0
\(131\) 6.18216i 0.540138i 0.962841 + 0.270069i \(0.0870465\pi\)
−0.962841 + 0.270069i \(0.912953\pi\)
\(132\) 0 0
\(133\) 5.78628 8.73401i 0.501735 0.757334i
\(134\) 0 0
\(135\) −0.103594 2.23367i −0.00891596 0.192243i
\(136\) 0 0
\(137\) 9.05565 + 9.05565i 0.773677 + 0.773677i 0.978747 0.205071i \(-0.0657424\pi\)
−0.205071 + 0.978747i \(0.565742\pi\)
\(138\) 0 0
\(139\) −11.9913 −1.01709 −0.508544 0.861036i \(-0.669816\pi\)
−0.508544 + 0.861036i \(0.669816\pi\)
\(140\) 0 0
\(141\) −12.1204 −1.02072
\(142\) 0 0
\(143\) −1.29873 1.29873i −0.108605 0.108605i
\(144\) 0 0
\(145\) 8.57041 + 7.81068i 0.711734 + 0.648642i
\(146\) 0 0
\(147\) −2.62780 + 6.48804i −0.216737 + 0.535125i
\(148\) 0 0
\(149\) 0.0968261i 0.00793230i −0.999992 0.00396615i \(-0.998738\pi\)
0.999992 0.00396615i \(-0.00126247\pi\)
\(150\) 0 0
\(151\) 13.4550 1.09495 0.547475 0.836822i \(-0.315589\pi\)
0.547475 + 0.836822i \(0.315589\pi\)
\(152\) 0 0
\(153\) 2.10614 + 2.10614i 0.170272 + 0.170272i
\(154\) 0 0
\(155\) −10.0871 9.19296i −0.810219 0.738397i
\(156\) 0 0
\(157\) −1.64757 + 1.64757i −0.131491 + 0.131491i −0.769789 0.638298i \(-0.779639\pi\)
0.638298 + 0.769789i \(0.279639\pi\)
\(158\) 0 0
\(159\) 0.769968 0.0610624
\(160\) 0 0
\(161\) 3.07442 + 15.1444i 0.242298 + 1.19355i
\(162\) 0 0
\(163\) 10.2746 10.2746i 0.804771 0.804771i −0.179066 0.983837i \(-0.557308\pi\)
0.983837 + 0.179066i \(0.0573077\pi\)
\(164\) 0 0
\(165\) −3.26738 + 0.151536i −0.254366 + 0.0117971i
\(166\) 0 0
\(167\) 0.293008 0.293008i 0.0226737 0.0226737i −0.695679 0.718353i \(-0.744896\pi\)
0.718353 + 0.695679i \(0.244896\pi\)
\(168\) 0 0
\(169\) 11.4235i 0.878728i
\(170\) 0 0
\(171\) 3.95987i 0.302819i
\(172\) 0 0
\(173\) 3.45189 + 3.45189i 0.262442 + 0.262442i 0.826046 0.563603i \(-0.190585\pi\)
−0.563603 + 0.826046i \(0.690585\pi\)
\(174\) 0 0
\(175\) 11.6571 + 6.25405i 0.881190 + 0.472762i
\(176\) 0 0
\(177\) 2.26015 + 2.26015i 0.169883 + 0.169883i
\(178\) 0 0
\(179\) 1.99756i 0.149305i 0.997210 + 0.0746523i \(0.0237847\pi\)
−0.997210 + 0.0746523i \(0.976215\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 0 0
\(183\) −1.00454 + 1.00454i −0.0742581 + 0.0742581i
\(184\) 0 0
\(185\) 7.12518 0.330455i 0.523854 0.0242955i
\(186\) 0 0
\(187\) 3.08084 3.08084i 0.225294 0.225294i
\(188\) 0 0
\(189\) 0.526369 + 2.59286i 0.0382877 + 0.188603i
\(190\) 0 0
\(191\) 7.83424 0.566866 0.283433 0.958992i \(-0.408527\pi\)
0.283433 + 0.958992i \(0.408527\pi\)
\(192\) 0 0
\(193\) 13.5617 13.5617i 0.976194 0.976194i −0.0235293 0.999723i \(-0.507490\pi\)
0.999723 + 0.0235293i \(0.00749029\pi\)
\(194\) 0 0
\(195\) 2.07512 + 1.89117i 0.148603 + 0.135430i
\(196\) 0 0
\(197\) −11.4791 11.4791i −0.817853 0.817853i 0.167943 0.985797i \(-0.446287\pi\)
−0.985797 + 0.167943i \(0.946287\pi\)
\(198\) 0 0
\(199\) 20.1468 1.42817 0.714084 0.700061i \(-0.246844\pi\)
0.714084 + 0.700061i \(0.246844\pi\)
\(200\) 0 0
\(201\) 8.38646i 0.591535i
\(202\) 0 0
\(203\) −11.4378 7.57754i −0.802775 0.531839i
\(204\) 0 0
\(205\) −1.27252 1.15972i −0.0888767 0.0809981i
\(206\) 0 0
\(207\) 4.13007 + 4.13007i 0.287060 + 0.287060i
\(208\) 0 0
\(209\) −5.79246 −0.400673
\(210\) 0 0
\(211\) −11.9662 −0.823785 −0.411892 0.911233i \(-0.635132\pi\)
−0.411892 + 0.911233i \(0.635132\pi\)
\(212\) 0 0
\(213\) 5.39247 + 5.39247i 0.369486 + 0.369486i
\(214\) 0 0
\(215\) −0.759730 16.3811i −0.0518132 1.11718i
\(216\) 0 0
\(217\) 13.4620 + 8.91857i 0.913858 + 0.605432i
\(218\) 0 0
\(219\) 9.63614i 0.651150i
\(220\) 0 0
\(221\) −3.73985 −0.251570
\(222\) 0 0
\(223\) −0.660910 0.660910i −0.0442578 0.0442578i 0.684632 0.728889i \(-0.259963\pi\)
−0.728889 + 0.684632i \(0.759963\pi\)
\(224\) 0 0
\(225\) 4.97854 0.462789i 0.331902 0.0308526i
\(226\) 0 0
\(227\) −17.3487 + 17.3487i −1.15147 + 1.15147i −0.165216 + 0.986257i \(0.552832\pi\)
−0.986257 + 0.165216i \(0.947168\pi\)
\(228\) 0 0
\(229\) 25.0782 1.65721 0.828607 0.559831i \(-0.189134\pi\)
0.828607 + 0.559831i \(0.189134\pi\)
\(230\) 0 0
\(231\) 3.79281 0.769968i 0.249549 0.0506601i
\(232\) 0 0
\(233\) 2.24138 2.24138i 0.146837 0.146837i −0.629866 0.776704i \(-0.716890\pi\)
0.776704 + 0.629866i \(0.216890\pi\)
\(234\) 0 0
\(235\) −1.25560 27.0729i −0.0819064 1.76604i
\(236\) 0 0
\(237\) −3.19633 + 3.19633i −0.207624 + 0.207624i
\(238\) 0 0
\(239\) 21.3769i 1.38276i 0.722492 + 0.691380i \(0.242997\pi\)
−0.722492 + 0.691380i \(0.757003\pi\)
\(240\) 0 0
\(241\) 0.624129i 0.0402037i 0.999798 + 0.0201018i \(0.00639905\pi\)
−0.999798 + 0.0201018i \(0.993601\pi\)
\(242\) 0 0
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) −14.7643 5.19750i −0.943260 0.332056i
\(246\) 0 0
\(247\) 3.51575 + 3.51575i 0.223702 + 0.223702i
\(248\) 0 0
\(249\) 9.55717i 0.605661i
\(250\) 0 0
\(251\) 16.3443i 1.03164i 0.856696 + 0.515822i \(0.172513\pi\)
−0.856696 + 0.515822i \(0.827487\pi\)
\(252\) 0 0
\(253\) 6.04143 6.04143i 0.379821 0.379821i
\(254\) 0 0
\(255\) −4.48624 + 4.92261i −0.280939 + 0.308266i
\(256\) 0 0
\(257\) −21.3054 + 21.3054i −1.32900 + 1.32900i −0.422749 + 0.906247i \(0.638935\pi\)
−0.906247 + 0.422749i \(0.861065\pi\)
\(258\) 0 0
\(259\) −8.27098 + 1.67907i −0.513933 + 0.104332i
\(260\) 0 0
\(261\) −5.18572 −0.320988
\(262\) 0 0
\(263\) 16.3449 16.3449i 1.00787 1.00787i 0.00789784 0.999969i \(-0.497486\pi\)
0.999969 0.00789784i \(-0.00251399\pi\)
\(264\) 0 0
\(265\) 0.0797641 + 1.71985i 0.00489987 + 0.105650i
\(266\) 0 0
\(267\) 0.848464 + 0.848464i 0.0519251 + 0.0519251i
\(268\) 0 0
\(269\) 16.5903 1.01153 0.505764 0.862672i \(-0.331211\pi\)
0.505764 + 0.862672i \(0.331211\pi\)
\(270\) 0 0
\(271\) 7.78033i 0.472621i 0.971678 + 0.236311i \(0.0759383\pi\)
−0.971678 + 0.236311i \(0.924062\pi\)
\(272\) 0 0
\(273\) −2.76939 1.83472i −0.167611 0.111043i
\(274\) 0 0
\(275\) −0.676964 7.28255i −0.0408224 0.439154i
\(276\) 0 0
\(277\) 21.3107 + 21.3107i 1.28043 + 1.28043i 0.940421 + 0.340013i \(0.110431\pi\)
0.340013 + 0.940421i \(0.389569\pi\)
\(278\) 0 0
\(279\) 6.10346 0.365405
\(280\) 0 0
\(281\) −21.1519 −1.26182 −0.630908 0.775858i \(-0.717317\pi\)
−0.630908 + 0.775858i \(0.717317\pi\)
\(282\) 0 0
\(283\) 2.65471 + 2.65471i 0.157806 + 0.157806i 0.781594 0.623788i \(-0.214407\pi\)
−0.623788 + 0.781594i \(0.714407\pi\)
\(284\) 0 0
\(285\) 8.84503 0.410219i 0.523934 0.0242993i
\(286\) 0 0
\(287\) 1.69826 + 1.12510i 0.100245 + 0.0664126i
\(288\) 0 0
\(289\) 8.12832i 0.478136i
\(290\) 0 0
\(291\) −12.2871 −0.720282
\(292\) 0 0
\(293\) 1.56714 + 1.56714i 0.0915536 + 0.0915536i 0.751400 0.659847i \(-0.229379\pi\)
−0.659847 + 0.751400i \(0.729379\pi\)
\(294\) 0 0
\(295\) −4.81428 + 5.28255i −0.280298 + 0.307562i
\(296\) 0 0
\(297\) 1.03435 1.03435i 0.0600190 0.0600190i
\(298\) 0 0
\(299\) −7.33372 −0.424120
\(300\) 0 0
\(301\) 3.86025 + 19.0153i 0.222501 + 1.09603i
\(302\) 0 0
\(303\) −10.8485 + 10.8485i −0.623228 + 0.623228i
\(304\) 0 0
\(305\) −2.34788 2.13975i −0.134439 0.122522i
\(306\) 0 0
\(307\) −17.3551 + 17.3551i −0.990510 + 0.990510i −0.999955 0.00944588i \(-0.996993\pi\)
0.00944588 + 0.999955i \(0.496993\pi\)
\(308\) 0 0
\(309\) 11.7489i 0.668374i
\(310\) 0 0
\(311\) 31.0648i 1.76153i 0.473558 + 0.880763i \(0.342970\pi\)
−0.473558 + 0.880763i \(0.657030\pi\)
\(312\) 0 0
\(313\) −5.72426 5.72426i −0.323554 0.323554i 0.526575 0.850129i \(-0.323476\pi\)
−0.850129 + 0.526575i \(0.823476\pi\)
\(314\) 0 0
\(315\) −5.73706 + 1.44434i −0.323247 + 0.0813793i
\(316\) 0 0
\(317\) 0.752579 + 0.752579i 0.0422691 + 0.0422691i 0.727925 0.685656i \(-0.240485\pi\)
−0.685656 + 0.727925i \(0.740485\pi\)
\(318\) 0 0
\(319\) 7.58562i 0.424713i
\(320\) 0 0
\(321\) 6.20871i 0.346536i
\(322\) 0 0
\(323\) −8.34005 + 8.34005i −0.464053 + 0.464053i
\(324\) 0 0
\(325\) −4.00928 + 4.83105i −0.222395 + 0.267978i
\(326\) 0 0
\(327\) 5.26503 5.26503i 0.291157 0.291157i
\(328\) 0 0
\(329\) 6.37980 + 31.4265i 0.351730 + 1.73260i
\(330\) 0 0
\(331\) −15.8082 −0.868899 −0.434449 0.900696i \(-0.643057\pi\)
−0.434449 + 0.900696i \(0.643057\pi\)
\(332\) 0 0
\(333\) −2.25560 + 2.25560i −0.123606 + 0.123606i
\(334\) 0 0
\(335\) 18.7326 0.868788i 1.02347 0.0474670i
\(336\) 0 0
\(337\) −20.0460 20.0460i −1.09197 1.09197i −0.995318 0.0966558i \(-0.969185\pi\)
−0.0966558 0.995318i \(-0.530815\pi\)
\(338\) 0 0
\(339\) −3.59839 −0.195438
\(340\) 0 0
\(341\) 8.92808i 0.483482i
\(342\) 0 0
\(343\) 18.2058 + 3.39840i 0.983020 + 0.183497i
\(344\) 0 0
\(345\) −8.79736 + 9.65306i −0.473634 + 0.519703i
\(346\) 0 0
\(347\) 20.0847 + 20.0847i 1.07820 + 1.07820i 0.996671 + 0.0815328i \(0.0259815\pi\)
0.0815328 + 0.996671i \(0.474018\pi\)
\(348\) 0 0
\(349\) −14.7663 −0.790420 −0.395210 0.918591i \(-0.629328\pi\)
−0.395210 + 0.918591i \(0.629328\pi\)
\(350\) 0 0
\(351\) −1.25560 −0.0670190
\(352\) 0 0
\(353\) 12.4890 + 12.4890i 0.664724 + 0.664724i 0.956490 0.291766i \(-0.0942429\pi\)
−0.291766 + 0.956490i \(0.594243\pi\)
\(354\) 0 0
\(355\) −11.4864 + 12.6036i −0.609633 + 0.668931i
\(356\) 0 0
\(357\) 4.35233 6.56955i 0.230350 0.347697i
\(358\) 0 0
\(359\) 10.5372i 0.556133i 0.960562 + 0.278066i \(0.0896935\pi\)
−0.960562 + 0.278066i \(0.910306\pi\)
\(360\) 0 0
\(361\) −3.31943 −0.174707
\(362\) 0 0
\(363\) 6.26514 + 6.26514i 0.328835 + 0.328835i
\(364\) 0 0
\(365\) −21.5239 + 0.998247i −1.12661 + 0.0522507i
\(366\) 0 0
\(367\) 11.1910 11.1910i 0.584163 0.584163i −0.351881 0.936045i \(-0.614458\pi\)
0.936045 + 0.351881i \(0.114458\pi\)
\(368\) 0 0
\(369\) 0.769968 0.0400829
\(370\) 0 0
\(371\) −0.405287 1.99642i −0.0210415 0.103649i
\(372\) 0 0
\(373\) 17.2746 17.2746i 0.894446 0.894446i −0.100492 0.994938i \(-0.532042\pi\)
0.994938 + 0.100492i \(0.0320416\pi\)
\(374\) 0 0
\(375\) 1.54946 + 11.0725i 0.0800140 + 0.571779i
\(376\) 0 0
\(377\) 4.60412 4.60412i 0.237124 0.237124i
\(378\) 0 0
\(379\) 17.6237i 0.905267i −0.891697 0.452634i \(-0.850485\pi\)
0.891697 0.452634i \(-0.149515\pi\)
\(380\) 0 0
\(381\) 11.1161i 0.569493i
\(382\) 0 0
\(383\) 16.1249 + 16.1249i 0.823942 + 0.823942i 0.986671 0.162729i \(-0.0520295\pi\)
−0.162729 + 0.986671i \(0.552030\pi\)
\(384\) 0 0
\(385\) 2.11276 + 8.39211i 0.107676 + 0.427702i
\(386\) 0 0
\(387\) 5.18572 + 5.18572i 0.263605 + 0.263605i
\(388\) 0 0
\(389\) 15.4011i 0.780865i 0.920632 + 0.390432i \(0.127674\pi\)
−0.920632 + 0.390432i \(0.872326\pi\)
\(390\) 0 0
\(391\) 17.3971i 0.879807i
\(392\) 0 0
\(393\) 4.37145 4.37145i 0.220510 0.220510i
\(394\) 0 0
\(395\) −7.47066 6.80841i −0.375889 0.342568i
\(396\) 0 0
\(397\) −16.1781 + 16.1781i −0.811955 + 0.811955i −0.984927 0.172972i \(-0.944663\pi\)
0.172972 + 0.984927i \(0.444663\pi\)
\(398\) 0 0
\(399\) −10.2674 + 2.08435i −0.514013 + 0.104348i
\(400\) 0 0
\(401\) −0.977595 −0.0488188 −0.0244094 0.999702i \(-0.507771\pi\)
−0.0244094 + 0.999702i \(0.507771\pi\)
\(402\) 0 0
\(403\) −5.41892 + 5.41892i −0.269936 + 0.269936i
\(404\) 0 0
\(405\) −1.50619 + 1.65269i −0.0748431 + 0.0821230i
\(406\) 0 0
\(407\) 3.29947 + 3.29947i 0.163549 + 0.163549i
\(408\) 0 0
\(409\) −24.3171 −1.20241 −0.601203 0.799097i \(-0.705312\pi\)
−0.601203 + 0.799097i \(0.705312\pi\)
\(410\) 0 0
\(411\) 12.8066i 0.631704i
\(412\) 0 0
\(413\) 4.67058 7.04992i 0.229824 0.346904i
\(414\) 0 0
\(415\) −21.3475 + 0.990067i −1.04791 + 0.0486005i
\(416\) 0 0
\(417\) 8.47912 + 8.47912i 0.415224 + 0.415224i
\(418\) 0 0
\(419\) 15.9893 0.781127 0.390563 0.920576i \(-0.372280\pi\)
0.390563 + 0.920576i \(0.372280\pi\)
\(420\) 0 0
\(421\) 14.7000 0.716433 0.358216 0.933639i \(-0.383385\pi\)
0.358216 + 0.933639i \(0.383385\pi\)
\(422\) 0 0
\(423\) 8.57041 + 8.57041i 0.416708 + 0.416708i
\(424\) 0 0
\(425\) −11.4602 9.51081i −0.555902 0.461342i
\(426\) 0 0
\(427\) 3.13341 + 2.07588i 0.151636 + 0.100459i
\(428\) 0 0
\(429\) 1.83668i 0.0886758i
\(430\) 0 0
\(431\) −22.2722 −1.07281 −0.536407 0.843960i \(-0.680219\pi\)
−0.536407 + 0.843960i \(0.680219\pi\)
\(432\) 0 0
\(433\) 28.0171 + 28.0171i 1.34642 + 1.34642i 0.889520 + 0.456896i \(0.151039\pi\)
0.456896 + 0.889520i \(0.348961\pi\)
\(434\) 0 0
\(435\) −0.537211 11.5832i −0.0257573 0.555371i
\(436\) 0 0
\(437\) −16.3545 + 16.3545i −0.782344 + 0.782344i
\(438\) 0 0
\(439\) −2.35656 −0.112473 −0.0562363 0.998417i \(-0.517910\pi\)
−0.0562363 + 0.998417i \(0.517910\pi\)
\(440\) 0 0
\(441\) 6.44587 2.72961i 0.306946 0.129981i
\(442\) 0 0
\(443\) 5.47247 5.47247i 0.260005 0.260005i −0.565051 0.825056i \(-0.691144\pi\)
0.825056 + 0.565051i \(0.191144\pi\)
\(444\) 0 0
\(445\) −1.80729 + 1.98308i −0.0856737 + 0.0940071i
\(446\) 0 0
\(447\) −0.0684664 + 0.0684664i −0.00323835 + 0.00323835i
\(448\) 0 0
\(449\) 1.20020i 0.0566410i −0.999599 0.0283205i \(-0.990984\pi\)
0.999599 0.0283205i \(-0.00901591\pi\)
\(450\) 0 0
\(451\) 1.12630i 0.0530354i
\(452\) 0 0
\(453\) −9.51409 9.51409i −0.447011 0.447011i
\(454\) 0 0
\(455\) 3.81127 6.37597i 0.178675 0.298910i
\(456\) 0 0
\(457\) −21.0775 21.0775i −0.985962 0.985962i 0.0139406 0.999903i \(-0.495562\pi\)
−0.999903 + 0.0139406i \(0.995562\pi\)
\(458\) 0 0
\(459\) 2.97854i 0.139026i
\(460\) 0 0
\(461\) 21.9670i 1.02311i 0.859252 + 0.511553i \(0.170929\pi\)
−0.859252 + 0.511553i \(0.829071\pi\)
\(462\) 0 0
\(463\) 21.6776 21.6776i 1.00744 1.00744i 0.00746987 0.999972i \(-0.497622\pi\)
0.999972 0.00746987i \(-0.00237776\pi\)
\(464\) 0 0
\(465\) 0.632282 + 13.6331i 0.0293214 + 0.632220i
\(466\) 0 0
\(467\) 7.11299 7.11299i 0.329150 0.329150i −0.523113 0.852263i \(-0.675230\pi\)
0.852263 + 0.523113i \(0.175230\pi\)
\(468\) 0 0
\(469\) −21.7449 + 4.41438i −1.00409 + 0.203837i
\(470\) 0 0
\(471\) 2.33002 0.107362
\(472\) 0 0
\(473\) 7.58562 7.58562i 0.348787 0.348787i
\(474\) 0 0
\(475\) 1.83259 + 19.7144i 0.0840848 + 0.904557i
\(476\) 0 0
\(477\) −0.544449 0.544449i −0.0249286 0.0249286i
\(478\) 0 0
\(479\) 31.7749 1.45183 0.725917 0.687782i \(-0.241416\pi\)
0.725917 + 0.687782i \(0.241416\pi\)
\(480\) 0 0
\(481\) 4.00524i 0.182623i
\(482\) 0 0
\(483\) 8.53477 12.8827i 0.388345 0.586181i
\(484\) 0 0
\(485\) −1.27287 27.4453i −0.0577981 1.24623i
\(486\) 0 0
\(487\) 4.81428 + 4.81428i 0.218156 + 0.218156i 0.807721 0.589565i \(-0.200701\pi\)
−0.589565 + 0.807721i \(0.700701\pi\)
\(488\) 0 0
\(489\) −14.5305 −0.657092
\(490\) 0 0
\(491\) −28.3401 −1.27897 −0.639484 0.768804i \(-0.720852\pi\)
−0.639484 + 0.768804i \(0.720852\pi\)
\(492\) 0 0
\(493\) 10.9219 + 10.9219i 0.491897 + 0.491897i
\(494\) 0 0
\(495\) 2.41754 + 2.20324i 0.108660 + 0.0990282i
\(496\) 0 0
\(497\) 11.1435 16.8204i 0.499855 0.754497i
\(498\) 0 0
\(499\) 3.39197i 0.151845i −0.997114 0.0759227i \(-0.975810\pi\)
0.997114 0.0759227i \(-0.0241902\pi\)
\(500\) 0 0
\(501\) −0.414376 −0.0185130
\(502\) 0 0
\(503\) −8.32921 8.32921i −0.371381 0.371381i 0.496599 0.867980i \(-0.334582\pi\)
−0.867980 + 0.496599i \(0.834582\pi\)
\(504\) 0 0
\(505\) −25.3557 23.1080i −1.12831 1.02829i
\(506\) 0 0
\(507\) −8.07761 + 8.07761i −0.358739 + 0.358739i
\(508\) 0 0
\(509\) 38.9452 1.72622 0.863108 0.505020i \(-0.168515\pi\)
0.863108 + 0.505020i \(0.168515\pi\)
\(510\) 0 0
\(511\) 24.9852 5.07217i 1.10528 0.224380i
\(512\) 0 0
\(513\) −2.80005 + 2.80005i −0.123625 + 0.123625i
\(514\) 0 0
\(515\) 26.2432 1.21712i 1.15641 0.0536328i
\(516\) 0 0
\(517\) 12.5367 12.5367i 0.551364 0.551364i
\(518\) 0 0
\(519\) 4.88171i 0.214283i
\(520\) 0 0
\(521\) 7.06726i 0.309622i 0.987944 + 0.154811i \(0.0494769\pi\)
−0.987944 + 0.154811i \(0.950523\pi\)
\(522\) 0 0
\(523\) 14.5887 + 14.5887i 0.637921 + 0.637921i 0.950042 0.312121i \(-0.101040\pi\)
−0.312121 + 0.950042i \(0.601040\pi\)
\(524\) 0 0
\(525\) −3.82050 12.6651i −0.166740 0.552749i
\(526\) 0 0
\(527\) −12.8548 12.8548i −0.559962 0.559962i
\(528\) 0 0
\(529\) 11.1150i 0.483261i
\(530\) 0 0
\(531\) 3.19633i 0.138709i
\(532\) 0 0
\(533\) −0.683611 + 0.683611i −0.0296105 + 0.0296105i
\(534\) 0 0
\(535\) −13.8682 + 0.643185i −0.599574 + 0.0278073i
\(536\) 0 0
\(537\) 1.41249 1.41249i 0.0609533 0.0609533i
\(538\) 0 0
\(539\) −3.99284 9.42895i −0.171984 0.406134i
\(540\) 0 0
\(541\) 18.6013 0.799731 0.399865 0.916574i \(-0.369057\pi\)
0.399865 + 0.916574i \(0.369057\pi\)
\(542\) 0 0
\(543\) 6.00000 6.00000i 0.257485 0.257485i
\(544\) 0 0
\(545\) 12.3057 + 11.2149i 0.527120 + 0.480393i
\(546\) 0 0
\(547\) 7.22715 + 7.22715i 0.309011 + 0.309011i 0.844526 0.535515i \(-0.179882\pi\)
−0.535515 + 0.844526i \(0.679882\pi\)
\(548\) 0 0
\(549\) 1.42064 0.0606315
\(550\) 0 0
\(551\) 20.5348i 0.874812i
\(552\) 0 0
\(553\) 9.97009 + 6.60519i 0.423971 + 0.280881i
\(554\) 0 0
\(555\) −5.27193 4.80460i −0.223781 0.203944i
\(556\) 0 0
\(557\) −0.558927 0.558927i −0.0236825 0.0236825i 0.695166 0.718849i \(-0.255331\pi\)
−0.718849 + 0.695166i \(0.755331\pi\)
\(558\) 0 0
\(559\) −9.20823 −0.389467
\(560\) 0 0
\(561\) −4.35697 −0.183951
\(562\) 0 0
\(563\) 0.702475 + 0.702475i 0.0296058 + 0.0296058i 0.721755 0.692149i \(-0.243336\pi\)
−0.692149 + 0.721755i \(0.743336\pi\)
\(564\) 0 0
\(565\) −0.372772 8.03762i −0.0156827 0.338145i
\(566\) 0 0
\(567\) 1.46123 2.20563i 0.0613659 0.0926278i
\(568\) 0 0
\(569\) 9.72049i 0.407504i 0.979023 + 0.203752i \(0.0653137\pi\)
−0.979023 + 0.203752i \(0.934686\pi\)
\(570\) 0 0
\(571\) 0.986684 0.0412914 0.0206457 0.999787i \(-0.493428\pi\)
0.0206457 + 0.999787i \(0.493428\pi\)
\(572\) 0 0
\(573\) −5.53964 5.53964i −0.231422 0.231422i
\(574\) 0 0
\(575\) −22.4731 18.6504i −0.937192 0.777774i
\(576\) 0 0
\(577\) 10.3510 10.3510i 0.430917 0.430917i −0.458024 0.888940i \(-0.651442\pi\)
0.888940 + 0.458024i \(0.151442\pi\)
\(578\) 0 0
\(579\) −19.1792 −0.797059
\(580\) 0 0
\(581\) 24.7804 5.03060i 1.02807 0.208705i
\(582\) 0 0
\(583\) −0.796415 + 0.796415i −0.0329841 + 0.0329841i
\(584\) 0 0
\(585\) −0.130073 2.80460i −0.00537785 0.115956i
\(586\) 0 0
\(587\) −21.1413 + 21.1413i −0.872594 + 0.872594i −0.992755 0.120160i \(-0.961659\pi\)
0.120160 + 0.992755i \(0.461659\pi\)
\(588\) 0 0
\(589\) 24.1689i 0.995862i
\(590\) 0 0
\(591\) 16.2339i 0.667774i
\(592\) 0 0
\(593\) −7.07816 7.07816i −0.290665 0.290665i 0.546678 0.837343i \(-0.315892\pi\)
−0.837343 + 0.546678i \(0.815892\pi\)
\(594\) 0 0
\(595\) 15.1251 + 9.04109i 0.620067 + 0.370649i
\(596\) 0 0
\(597\) −14.2459 14.2459i −0.583047 0.583047i
\(598\) 0 0
\(599\) 7.13847i 0.291670i 0.989309 + 0.145835i \(0.0465869\pi\)
−0.989309 + 0.145835i \(0.953413\pi\)
\(600\) 0 0
\(601\) 35.0829i 1.43106i −0.698580 0.715532i \(-0.746185\pi\)
0.698580 0.715532i \(-0.253815\pi\)
\(602\) 0 0
\(603\) −5.93012 + 5.93012i −0.241493 + 0.241493i
\(604\) 0 0
\(605\) −13.3452 + 14.6433i −0.542560 + 0.595334i
\(606\) 0 0
\(607\) −5.36385 + 5.36385i −0.217712 + 0.217712i −0.807533 0.589822i \(-0.799198\pi\)
0.589822 + 0.807533i \(0.299198\pi\)
\(608\) 0 0
\(609\) 2.72961 + 13.4459i 0.110609 + 0.544854i
\(610\) 0 0
\(611\) −15.2184 −0.615670
\(612\) 0 0
\(613\) −10.4888 + 10.4888i −0.423639 + 0.423639i −0.886454 0.462816i \(-0.846839\pi\)
0.462816 + 0.886454i \(0.346839\pi\)
\(614\) 0 0
\(615\) 0.0797641 + 1.71985i 0.00321640 + 0.0693511i
\(616\) 0 0
\(617\) 19.7986 + 19.7986i 0.797060 + 0.797060i 0.982631 0.185571i \(-0.0594135\pi\)
−0.185571 + 0.982631i \(0.559414\pi\)
\(618\) 0 0
\(619\) −12.0675 −0.485034 −0.242517 0.970147i \(-0.577973\pi\)
−0.242517 + 0.970147i \(0.577973\pi\)
\(620\) 0 0
\(621\) 5.84081i 0.234383i
\(622\) 0 0
\(623\) 1.75334 2.64655i 0.0702462 0.106032i
\(624\) 0 0
\(625\) −24.5717 + 4.60803i −0.982866 + 0.184321i
\(626\) 0 0
\(627\) 4.09588 + 4.09588i 0.163574 + 0.163574i
\(628\) 0 0
\(629\) 9.50124 0.378839
\(630\) 0 0
\(631\) −30.4435 −1.21194 −0.605969 0.795488i \(-0.707214\pi\)
−0.605969 + 0.795488i \(0.707214\pi\)
\(632\) 0 0
\(633\) 8.46135 + 8.46135i 0.336309 + 0.336309i
\(634\) 0 0
\(635\) −24.8296 + 1.15156i −0.985332 + 0.0456982i
\(636\) 0 0
\(637\) −3.29946 + 8.14639i −0.130729 + 0.322772i
\(638\) 0 0
\(639\) 7.62611i 0.301684i
\(640\) 0 0
\(641\) 36.5929 1.44533 0.722666 0.691198i \(-0.242917\pi\)
0.722666 + 0.691198i \(0.242917\pi\)
\(642\) 0 0
\(643\) −12.1140 12.1140i −0.477731 0.477731i 0.426675 0.904405i \(-0.359685\pi\)
−0.904405 + 0.426675i \(0.859685\pi\)
\(644\) 0 0
\(645\) −11.0460 + 12.1204i −0.434935 + 0.477240i
\(646\) 0 0
\(647\) −19.0978 + 19.0978i −0.750814 + 0.750814i −0.974631 0.223817i \(-0.928148\pi\)
0.223817 + 0.974631i \(0.428148\pi\)
\(648\) 0 0
\(649\) −4.67556 −0.183532
\(650\) 0 0
\(651\) −3.21267 15.8254i −0.125915 0.620248i
\(652\) 0 0
\(653\) 20.3709 20.3709i 0.797173 0.797173i −0.185476 0.982649i \(-0.559383\pi\)
0.982649 + 0.185476i \(0.0593826\pi\)
\(654\) 0 0
\(655\) 10.2172 + 9.31151i 0.399220 + 0.363831i
\(656\) 0 0
\(657\) 6.81378 6.81378i 0.265831 0.265831i
\(658\) 0 0
\(659\) 31.4882i 1.22661i −0.789847 0.613304i \(-0.789840\pi\)
0.789847 0.613304i \(-0.210160\pi\)
\(660\) 0 0
\(661\) 48.1880i 1.87430i −0.348931 0.937149i \(-0.613455\pi\)
0.348931 0.937149i \(-0.386545\pi\)
\(662\) 0 0
\(663\) 2.64448 + 2.64448i 0.102703 + 0.102703i
\(664\) 0 0
\(665\) −5.71939 22.7180i −0.221789 0.880967i
\(666\) 0 0
\(667\) 21.4174 + 21.4174i 0.829286 + 0.829286i
\(668\) 0 0
\(669\) 0.934668i 0.0361364i
\(670\) 0 0
\(671\) 2.07810i 0.0802241i
\(672\) 0 0
\(673\) −30.6900 + 30.6900i −1.18301 + 1.18301i −0.204055 + 0.978960i \(0.565412\pi\)
−0.978960 + 0.204055i \(0.934588\pi\)
\(674\) 0 0
\(675\) −3.84760 3.19312i −0.148094 0.122903i
\(676\) 0 0
\(677\) 1.54060 1.54060i 0.0592101 0.0592101i −0.676882 0.736092i \(-0.736669\pi\)
0.736092 + 0.676882i \(0.236669\pi\)
\(678\) 0 0
\(679\) 6.46755 + 31.8587i 0.248202 + 1.22263i
\(680\) 0 0
\(681\) 24.5348 0.940174
\(682\) 0 0
\(683\) −14.2154 + 14.2154i −0.543936 + 0.543936i −0.924680 0.380744i \(-0.875668\pi\)
0.380744 + 0.924680i \(0.375668\pi\)
\(684\) 0 0
\(685\) 28.6057 1.32669i 1.09297 0.0506903i
\(686\) 0 0
\(687\) −17.7330 17.7330i −0.676555 0.676555i
\(688\) 0 0
\(689\) 0.966772 0.0368311
\(690\) 0 0
\(691\) 10.2887i 0.391401i −0.980664 0.195700i \(-0.937302\pi\)
0.980664 0.195700i \(-0.0626980\pi\)
\(692\) 0 0
\(693\) −3.22637 2.13747i −0.122560 0.0811959i
\(694\) 0 0
\(695\) −18.0611 + 19.8179i −0.685098 + 0.751736i
\(696\) 0 0
\(697\) −1.62166 1.62166i −0.0614248 0.0614248i
\(698\) 0 0
\(699\) −3.16979 −0.119892
\(700\) 0 0
\(701\) −44.3183 −1.67388 −0.836939 0.547297i \(-0.815657\pi\)
−0.836939 + 0.547297i \(0.815657\pi\)
\(702\) 0 0
\(703\) −8.93189 8.93189i −0.336872 0.336872i
\(704\) 0 0
\(705\) −18.2556 + 20.0313i −0.687546 + 0.754422i
\(706\) 0 0
\(707\) 33.8389 + 22.4183i 1.27264 + 0.843126i
\(708\) 0 0
\(709\) 0.817976i 0.0307197i −0.999882 0.0153599i \(-0.995111\pi\)
0.999882 0.0153599i \(-0.00488939\pi\)
\(710\) 0 0
\(711\) 4.52029 0.169524
\(712\) 0 0
\(713\) −25.2077 25.2077i −0.944037 0.944037i
\(714\) 0 0
\(715\) −4.10253 + 0.190269i −0.153426 + 0.00711567i
\(716\) 0 0
\(717\) 15.1158 15.1158i 0.564509 0.564509i
\(718\) 0 0
\(719\) 0.00762056 0.000284199 0.000142099 1.00000i \(-0.499955\pi\)
0.000142099 1.00000i \(0.499955\pi\)
\(720\) 0 0
\(721\) −30.4634 + 6.18428i −1.13452 + 0.230315i
\(722\) 0 0
\(723\) 0.441326 0.441326i 0.0164131 0.0164131i
\(724\) 0 0
\(725\) 25.8173 2.39990i 0.958831 0.0891300i
\(726\) 0 0
\(727\) 28.5738 28.5738i 1.05974 1.05974i 0.0616465 0.998098i \(-0.480365\pi\)
0.998098 0.0616465i \(-0.0196352\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 21.8438i 0.807921i
\(732\) 0 0
\(733\) 24.1522 + 24.1522i 0.892083 + 0.892083i 0.994719 0.102636i \(-0.0327275\pi\)
−0.102636 + 0.994719i \(0.532728\pi\)
\(734\) 0 0
\(735\) 6.76479 + 14.1152i 0.249523 + 0.520645i
\(736\) 0 0
\(737\) 8.67452 + 8.67452i 0.319530 + 0.319530i
\(738\) 0 0
\(739\) 37.9522i 1.39609i 0.716052 + 0.698047i \(0.245947\pi\)
−0.716052 + 0.698047i \(0.754053\pi\)
\(740\) 0 0
\(741\) 4.97202i 0.182652i
\(742\) 0 0
\(743\) 18.8022 18.8022i 0.689784 0.689784i −0.272400 0.962184i \(-0.587817\pi\)
0.962184 + 0.272400i \(0.0878174\pi\)
\(744\) 0 0
\(745\) −0.160024 0.145838i −0.00586282 0.00534311i
\(746\) 0 0
\(747\) 6.75794 6.75794i 0.247260 0.247260i
\(748\) 0 0
\(749\) 16.0983 3.26807i 0.588220 0.119413i
\(750\) 0 0
\(751\) −0.105915 −0.00386490 −0.00193245 0.999998i \(-0.500615\pi\)
−0.00193245 + 0.999998i \(0.500615\pi\)
\(752\) 0 0
\(753\) 11.5572 11.5572i 0.421167 0.421167i
\(754\) 0 0
\(755\) 20.2657 22.2369i 0.737545 0.809284i
\(756\) 0 0
\(757\) 3.14514 + 3.14514i 0.114312 + 0.114312i 0.761949 0.647637i \(-0.224243\pi\)
−0.647637 + 0.761949i \(0.724243\pi\)
\(758\) 0 0
\(759\) −8.54387 −0.310123
\(760\) 0 0
\(761\) 35.1123i 1.27282i −0.771351 0.636410i \(-0.780419\pi\)
0.771351 0.636410i \(-0.219581\pi\)
\(762\) 0 0
\(763\) −16.4228 10.8801i −0.594547 0.393887i
\(764\) 0 0
\(765\) 6.65306 0.308559i 0.240542 0.0111560i
\(766\) 0 0
\(767\) 2.83784 + 2.83784i 0.102469 + 0.102469i
\(768\) 0 0
\(769\) −8.16835 −0.294558 −0.147279 0.989095i \(-0.547052\pi\)
−0.147279 + 0.989095i \(0.547052\pi\)
\(770\) 0 0
\(771\) 30.1304 1.08512
\(772\) 0 0
\(773\) 2.51166 + 2.51166i 0.0903382 + 0.0903382i 0.750832 0.660494i \(-0.229653\pi\)
−0.660494 + 0.750832i \(0.729653\pi\)
\(774\) 0 0
\(775\) −30.3863 + 2.82462i −1.09151 + 0.101463i
\(776\) 0 0
\(777\) 7.03574 + 4.66118i 0.252406 + 0.167219i
\(778\) 0 0
\(779\) 3.04897i 0.109241i
\(780\) 0 0
\(781\) −11.1554 −0.399171
\(782\) 0 0
\(783\) 3.66686 + 3.66686i 0.131043 + 0.131043i
\(784\) 0 0
\(785\) 0.241377 + 5.20449i 0.00861510 + 0.185756i
\(786\) 0 0
\(787\) 12.7347 12.7347i 0.453943 0.453943i −0.442718 0.896661i \(-0.645986\pi\)
0.896661 + 0.442718i \(0.145986\pi\)
\(788\) 0 0
\(789\) −23.1151 −0.822920
\(790\) 0 0
\(791\) 1.89408 + 9.33014i 0.0673459 + 0.331742i