Properties

Label 1680.2.cz.d.97.6
Level 1680
Weight 2
Character 1680.97
Analytic conductor 13.415
Analytic rank 0
Dimension 16
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 97.6
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.433.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{3} +(-1.50619 + 1.65269i) q^{5} +(2.20563 - 1.46123i) q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{3} +(-1.50619 + 1.65269i) q^{5} +(2.20563 - 1.46123i) q^{7} +1.00000i q^{9} +1.46279 q^{11} +(0.887844 + 0.887844i) q^{13} +(-2.23367 + 0.103594i) q^{15} +(-2.10614 + 2.10614i) q^{17} +3.95987 q^{19} +(2.59286 + 0.526369i) q^{21} +(4.13007 - 4.13007i) q^{23} +(-0.462789 - 4.97854i) q^{25} +(-0.707107 + 0.707107i) q^{27} +5.18572i q^{29} +6.10346i q^{31} +(1.03435 + 1.03435i) q^{33} +(-0.907129 + 5.84612i) q^{35} +(2.25560 + 2.25560i) q^{37} +1.25560i q^{39} +0.769968i q^{41} +(5.18572 - 5.18572i) q^{43} +(-1.65269 - 1.50619i) q^{45} +(-8.57041 + 8.57041i) q^{47} +(2.72961 - 6.44587i) q^{49} -2.97854 q^{51} +(-0.544449 + 0.544449i) q^{53} +(-2.20324 + 2.41754i) q^{55} +(2.80005 + 2.80005i) q^{57} +3.19633 q^{59} +1.42064i q^{61} +(1.46123 + 2.20563i) q^{63} +(-2.80460 + 0.130073i) q^{65} +(5.93012 + 5.93012i) q^{67} +5.84081 q^{69} -7.62611 q^{71} +(6.81378 + 6.81378i) q^{73} +(3.19312 - 3.84760i) q^{75} +(3.22637 - 2.13747i) q^{77} -4.52029i q^{79} -1.00000 q^{81} +(6.75794 + 6.75794i) q^{83} +(-0.308559 - 6.65306i) q^{85} +(-3.66686 + 3.66686i) q^{87} +1.19991 q^{89} +(3.25560 + 0.660910i) q^{91} +(-4.31580 + 4.31580i) q^{93} +(-5.96431 + 6.54445i) q^{95} +(-8.68829 + 8.68829i) q^{97} +1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} + O(q^{10}) \) \( 16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100}) \)

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
\(7\) 2.20563 1.46123i 0.833650 0.552293i
\(8\) 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 0.819427 0.573183i \(-0.194292\pi\)
−0.573183 + 0.819427i \(0.694292\pi\)
\(14\) 0 0
\(15\) −2.23367 + 0.103594i −0.576730 + 0.0267479i
\(16\) 0 0
\(17\) −2.10614 + 2.10614i −0.510815 + 0.510815i −0.914776 0.403961i \(-0.867633\pi\)
0.403961 + 0.914776i \(0.367633\pi\)
\(18\) 0 0
\(19\) 3.95987 0.908456 0.454228 0.890885i \(-0.349915\pi\)
0.454228 + 0.890885i \(0.349915\pi\)
\(20\) 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 \(0.184651\pi\)
−0.836408 + 0.548107i \(0.815349\pi\)
\(32\) 0 0
\(33\) 1.03435 + 1.03435i 0.180057 + 0.180057i
\(34\) 0 0
\(35\) −0.907129 + 5.84612i −0.153333 + 0.988175i
\(36\) 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 \(0.0191497\pi\)
−0.998191 + 0.0601244i \(0.980850\pi\)
\(42\) 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 \(0.595139\pi\)
−0.955664 + 0.294459i \(0.904861\pi\)
\(48\) 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 \(-0.433284\pi\)
0.208063 + 0.978115i \(0.433284\pi\)
\(60\) 0 0
\(61\) 1.42064i 0.181894i 0.995856 + 0.0909472i \(0.0289894\pi\)
−0.995856 + 0.0909472i \(0.971011\pi\)
\(62\) 0 0
\(63\) 1.46123 + 2.20563i 0.184098 + 0.277883i
\(64\) 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 0.982700 0.185207i \(-0.0592955\pi\)
−0.185207 + 0.982700i \(0.559296\pi\)
\(74\) 0 0
\(75\) 3.19312 3.84760i 0.368709 0.444282i
\(76\) 0 0
\(77\) 3.22637 2.13747i 0.367679 0.243588i
\(78\) 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 0.972921 0.231140i \(-0.0742455\pi\)
−0.231140 + 0.972921i \(0.574246\pi\)
\(84\) 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 \(-0.479743\pi\)
0.0635950 + 0.997976i \(0.479743\pi\)
\(90\) 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 −0.993754 0.111592i \(-0.964405\pi\)
0.111592 + 0.993754i \(0.464405\pi\)
\(98\) 0 0
\(99\) 1.46279i 0.147016i
\(100\) 0 0
\(101\) 15.3420i 1.52659i 0.646050 + 0.763295i \(0.276420\pi\)
−0.646050 + 0.763295i \(0.723580\pi\)
\(102\) 0 0
\(103\) −8.30776 8.30776i −0.818588 0.818588i 0.167316 0.985903i \(-0.446490\pi\)
−0.985903 + 0.167316i \(0.946490\pi\)
\(104\) 0 0
\(105\) −4.77527 + 3.49239i −0.466018 + 0.340823i
\(106\) 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 \(-0.912953\pi\)
0.962841 0.270069i \(-0.0870465\pi\)
\(132\) 0 0
\(133\) 8.73401 5.78628i 0.757334 0.501735i
\(134\) 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 \(-0.330184\pi\)
0.508544 + 0.861036i \(0.330184\pi\)
\(140\) 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
\(147\) 6.48804 2.62780i 0.535125 0.216737i
\(148\) 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 −0.638298 0.769789i \(-0.720361\pi\)
0.769789 + 0.638298i \(0.220361\pi\)
\(158\) 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 −0.718353 0.695679i \(-0.755104\pi\)
0.695679 + 0.718353i \(0.255104\pi\)
\(168\) 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 0.563603 0.826046i \(-0.309415\pi\)
−0.826046 + 0.563603i \(0.809415\pi\)
\(174\) 0 0
\(175\) −8.29554 10.3046i −0.627084 0.778952i
\(176\) 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 \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 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 \(-0.753156\pi\)
−0.714084 + 0.700061i \(0.753156\pi\)
\(200\) 0 0
\(201\) 8.38646i 0.591535i
\(202\) 0 0
\(203\) 7.57754 + 11.4378i 0.531839 + 0.802775i
\(204\) 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
\(217\) 8.91857 + 13.4620i 0.605432 + 0.913858i
\(218\) 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 0.728889 0.684632i \(-0.240037\pi\)
−0.684632 + 0.728889i \(0.740037\pi\)
\(224\) 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 \(-0.447168\pi\)
0.986257 0.165216i \(-0.0528323\pi\)
\(228\) 0 0
\(229\) −25.0782 −1.65721 −0.828607 0.559831i \(-0.810866\pi\)
−0.828607 + 0.559831i \(0.810866\pi\)
\(230\) 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 \(-0.993601\pi\)
0.999798 0.0201018i \(-0.00639905\pi\)
\(242\) 0 0
\(243\) −0.707107 0.707107i −0.0453609 0.0453609i
\(244\) 0 0
\(245\) 6.54174 + 14.2199i 0.417937 + 0.908476i
\(246\) 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 \(-0.827487\pi\)
0.856696 0.515822i \(-0.172513\pi\)
\(252\) 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 \(-0.361065\pi\)
0.906247 0.422749i \(-0.138935\pi\)
\(258\) 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 \(-0.668789\pi\)
−0.505764 + 0.862672i \(0.668789\pi\)
\(270\) 0 0
\(271\) 7.78033i 0.472621i −0.971678 0.236311i \(-0.924062\pi\)
0.971678 0.236311i \(-0.0759383\pi\)
\(272\) 0 0
\(273\) 1.83472 + 2.76939i 0.111043 + 0.167611i
\(274\) 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 0.623788 0.781594i \(-0.285593\pi\)
−0.781594 + 0.623788i \(0.785593\pi\)
\(284\) 0 0
\(285\) −8.84503 + 0.410219i −0.523934 + 0.0242993i
\(286\) 0 0
\(287\) 1.12510 + 1.69826i 0.0664126 + 0.100245i
\(288\) 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 0.659847 0.751400i \(-0.270621\pi\)
−0.751400 + 0.659847i \(0.770621\pi\)
\(294\) 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 −0.00944588 0.999955i \(-0.503007\pi\)
0.999955 + 0.00944588i \(0.00300676\pi\)
\(308\) 0 0
\(309\) 11.7489i 0.668374i
\(310\) 0 0
\(311\) 31.0648i 1.76153i −0.473558 0.880763i \(-0.657030\pi\)
0.473558 0.880763i \(-0.342970\pi\)
\(312\) 0 0
\(313\) 5.72426 + 5.72426i 0.323554 + 0.323554i 0.850129 0.526575i \(-0.176524\pi\)
−0.526575 + 0.850129i \(0.676524\pi\)
\(314\) 0 0
\(315\) −5.84612 0.907129i −0.329392 0.0511109i
\(316\) 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
\(343\) −3.39840 18.2058i −0.183497 0.983020i
\(344\) 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 \(-0.370672\pi\)
0.395210 + 0.918591i \(0.370672\pi\)
\(350\) 0 0
\(351\) −1.25560 −0.0670190
\(352\) 0 0
\(353\) −12.4890 12.4890i −0.664724 0.664724i 0.291766 0.956490i \(-0.405757\pi\)
−0.956490 + 0.291766i \(0.905757\pi\)
\(354\) 0 0
\(355\) 11.4864 12.6036i 0.609633 0.668931i
\(356\) 0 0
\(357\) −6.56955 + 4.35233i −0.347697 + 0.230350i
\(358\) 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 −0.936045 0.351881i \(-0.885542\pi\)
0.351881 + 0.936045i \(0.385542\pi\)
\(368\) 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 0.162729 0.986671i \(-0.447970\pi\)
−0.986671 + 0.162729i \(0.947970\pi\)
\(384\) 0 0
\(385\) −1.32694 + 8.55164i −0.0676270 + 0.435832i
\(386\) 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 −0.172972 0.984927i \(-0.555337\pi\)
0.984927 + 0.172972i \(0.0553370\pi\)
\(398\) 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 \(-0.294688\pi\)
0.601203 + 0.799097i \(0.294688\pi\)
\(410\) 0 0
\(411\) 12.8066i 0.631704i
\(412\) 0 0
\(413\) 7.04992 4.67058i 0.346904 0.229824i
\(414\) 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 \(-0.627720\pi\)
−0.390563 + 0.920576i \(0.627720\pi\)
\(420\) 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
\(427\) 2.07588 + 3.13341i 0.100459 + 0.151636i
\(428\) 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 \(-0.848961\pi\)
−0.456896 0.889520i \(-0.651039\pi\)
\(434\) 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 \(-0.482090\pi\)
0.0562363 + 0.998417i \(0.482090\pi\)
\(440\) 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
\(455\) −5.99583 + 4.38505i −0.281089 + 0.205575i
\(456\) 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 \(-0.829071\pi\)
0.859252 0.511553i \(-0.170929\pi\)
\(462\) 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 −0.852263 0.523113i \(-0.824770\pi\)
0.523113 + 0.852263i \(0.324770\pi\)
\(468\) 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 \(-0.758584\pi\)
−0.725917 + 0.687782i \(0.758584\pi\)
\(480\) 0 0
\(481\) 4.00524i 0.182623i
\(482\) 0 0
\(483\) 12.8827 8.53477i 0.586181 0.388345i
\(484\) 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
\(497\) −16.8204 + 11.1435i −0.754497 + 0.499855i
\(498\) 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 0.867980 0.496599i \(-0.165418\pi\)
−0.496599 + 0.867980i \(0.665418\pi\)
\(504\) 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 \(-0.831485\pi\)
−0.863108 + 0.505020i \(0.831485\pi\)
\(510\) 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 \(-0.950523\pi\)
0.987944 0.154811i \(-0.0494769\pi\)
\(522\) 0 0
\(523\) −14.5887 14.5887i −0.637921 0.637921i 0.312121 0.950042i \(-0.398960\pi\)
−0.950042 + 0.312121i \(0.898960\pi\)
\(524\) 0 0
\(525\) 1.42060 13.1523i 0.0620001 0.574012i
\(526\) 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
\(553\) −6.60519 9.97009i −0.280881 0.423971i
\(554\) 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 0.692149 0.721755i \(-0.256664\pi\)
−0.721755 + 0.692149i \(0.756664\pi\)
\(564\) 0 0
\(565\) 0.372772 + 8.03762i 0.0156827 + 0.338145i
\(566\) 0 0
\(567\) −2.20563 + 1.46123i −0.0926278 + 0.0613659i
\(568\) 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 −0.888940 0.458024i \(-0.848558\pi\)
0.458024 + 0.888940i \(0.348558\pi\)
\(578\) 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 −0.120160 0.992755i \(-0.538341\pi\)
0.992755 + 0.120160i \(0.0383409\pi\)
\(588\) 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 0.837343 0.546678i \(-0.184108\pi\)
−0.546678 + 0.837343i \(0.684108\pi\)
\(594\) 0 0
\(595\) −10.4022 14.2233i −0.426450 0.583099i
\(596\) 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 \(0.253815\pi\)
−0.698580 + 0.715532i \(0.746185\pi\)
\(602\) 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 −0.589822 0.807533i \(-0.700802\pi\)
0.807533 + 0.589822i \(0.200802\pi\)
\(608\) 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 \(-0.422027\pi\)
0.242517 + 0.970147i \(0.422027\pi\)
\(620\) 0 0
\(621\) 5.84081i 0.234383i
\(622\) 0 0
\(623\) 2.64655 1.75334i 0.106032 0.0702462i
\(624\) 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
\(637\) 8.14639 3.29946i 0.322772 0.130729i
\(638\) 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 0.904405 0.426675i \(-0.140315\pi\)
−0.426675 + 0.904405i \(0.640315\pi\)
\(644\) 0 0
\(645\) −11.0460 + 12.1204i −0.434935 + 0.477240i
\(646\) 0 0
\(647\) 19.0978 19.0978i 0.750814 0.750814i −0.223817 0.974631i \(-0.571852\pi\)
0.974631 + 0.223817i \(0.0718519\pi\)
\(648\) 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 \(0.386545\pi\)
−0.348931 + 0.937149i \(0.613455\pi\)
\(662\) 0 0
\(663\) −2.64448 2.64448i −0.102703 0.102703i
\(664\) 0 0
\(665\) −3.59211 + 23.1499i −0.139296 + 0.897714i
\(666\) 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 −0.736092 0.676882i \(-0.763331\pi\)
0.676882 + 0.736092i \(0.263331\pi\)
\(678\) 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 \(0.0626980\pi\)
−0.980664 + 0.195700i \(0.937302\pi\)
\(692\) 0 0
\(693\) 2.13747 + 3.22637i 0.0811959 + 0.122560i
\(694\) 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
\(707\) 22.4183 + 33.8389i 0.843126 + 1.27264i
\(708\) 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 \(-0.500045\pi\)
−0.000142099 1.00000i \(0.500045\pi\)
\(720\) 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 \(0.519635\pi\)
−0.998098 + 0.0616465i \(0.980365\pi\)
\(728\) 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 0.102636 0.994719i \(-0.467272\pi\)
−0.994719 + 0.102636i \(0.967272\pi\)
\(734\) 0 0
\(735\) −5.42928 + 14.6807i −0.200262 + 0.541506i
\(736\) 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 \(0.219581\pi\)
−0.771351 + 0.636410i \(0.780419\pi\)
\(762\) 0 0
\(763\) 10.8801 + 16.4228i 0.393887 + 0.594547i
\(764\) 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 \(-0.452948\pi\)
0.147279 + 0.989095i \(0.452948\pi\)
\(770\) 0 0
\(771\) 30.1304 1.08512
\(772\) 0 0
\(773\) −2.51166 2.51166i −0.0903382 0.0903382i 0.660494 0.750832i \(-0.270347\pi\)
−0.750832 + 0.660494i \(0.770347\pi\)
\(774\) 0 0
\(775\) 30.3863 2.82462i 1.09151 0.101463i
\(776\) 0 0
\(777\) 4.66118 + 7.03574i 0.167219 + 0.252406i
\(778\) 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 −0.896661 0.442718i \(-0.854014\pi\)
0.442718 + 0.896661i \(0.354014\pi\)
\(788\) 0 0
\(789\) 23.1151 0.822920
\(790\) 0 0
\(791\) 1.89408 9.33014i 0.0673459 0.331742i