Properties

Label 525.2.m.b.118.8
Level 525
Weight 2
Character 525.118
Analytic conductor 4.192
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
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 118.8
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 \(\chi\) \(=\) 525.118
Dual form 525.2.m.b.307.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.86147 - 1.86147i) q^{2} +(0.707107 - 0.707107i) q^{3} -4.93012i q^{4} -2.63251i q^{6} +(2.20563 + 1.46123i) q^{7} +(-5.45433 - 5.45433i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(1.86147 - 1.86147i) q^{2} +(0.707107 - 0.707107i) q^{3} -4.93012i q^{4} -2.63251i q^{6} +(2.20563 + 1.46123i) q^{7} +(-5.45433 - 5.45433i) q^{8} -1.00000i q^{9} -1.46279 q^{11} +(-3.48612 - 3.48612i) q^{12} +(-0.887844 + 0.887844i) q^{13} +(6.82574 - 1.38567i) q^{14} -10.4459 q^{16} +(2.10614 + 2.10614i) q^{17} +(-1.86147 - 1.86147i) q^{18} -3.95987 q^{19} +(2.59286 - 0.526369i) q^{21} +(-2.72294 + 2.72294i) q^{22} +(4.13007 + 4.13007i) q^{23} -7.71359 q^{24} +3.30539i q^{26} +(-0.707107 - 0.707107i) q^{27} +(7.20405 - 10.8740i) q^{28} -5.18572i q^{29} +6.10346i q^{31} +(-8.53599 + 8.53599i) q^{32} +(-1.03435 + 1.03435i) q^{33} +7.84104 q^{34} -4.93012 q^{36} +(-2.25560 + 2.25560i) q^{37} +(-7.37117 + 7.37117i) q^{38} +1.25560i q^{39} -0.769968i q^{41} +(3.84671 - 5.80635i) q^{42} +(5.18572 + 5.18572i) q^{43} +7.21173i q^{44} +15.3760 q^{46} +(-8.57041 - 8.57041i) q^{47} +(-7.38635 + 7.38635i) q^{48} +(2.72961 + 6.44587i) q^{49} +2.97854 q^{51} +(4.37718 + 4.37718i) q^{52} +(0.544449 + 0.544449i) q^{53} -2.63251 q^{54} +(-4.06020 - 20.0003i) q^{56} +(-2.80005 + 2.80005i) q^{57} +(-9.65306 - 9.65306i) q^{58} -3.19633 q^{59} -1.42064i q^{61} +(11.3614 + 11.3614i) q^{62} +(1.46123 - 2.20563i) q^{63} +10.8872i q^{64} +3.85081i q^{66} +(5.93012 - 5.93012i) q^{67} +(10.3835 - 10.3835i) q^{68} +5.84081 q^{69} +7.62611 q^{71} +(-5.45433 + 5.45433i) q^{72} +(-6.81378 + 6.81378i) q^{73} +8.39746i q^{74} +19.5226i q^{76} +(-3.22637 - 2.13747i) q^{77} +(2.33726 + 2.33726i) q^{78} -4.52029i q^{79} -1.00000 q^{81} +(-1.43327 - 1.43327i) q^{82} +(6.75794 - 6.75794i) q^{83} +(-2.59507 - 12.7831i) q^{84} +19.3061 q^{86} +(-3.66686 - 3.66686i) q^{87} +(7.97854 + 7.97854i) q^{88} +1.19991 q^{89} +(-3.25560 + 0.660910i) q^{91} +(20.3618 - 20.3618i) q^{92} +(4.31580 + 4.31580i) q^{93} -31.9071 q^{94} +12.0717i q^{96} +(8.68829 + 8.68829i) q^{97} +(17.0799 + 6.91770i) q^{98} +1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q + 8q^{7} - 24q^{8} - 16q^{11} - 48q^{16} + 8q^{21} + 16q^{22} + 40q^{23} - 24q^{28} - 48q^{32} - 16q^{36} - 32q^{37} + 16q^{42} + 16q^{43} + 64q^{46} - 16q^{51} - 24q^{53} + 24q^{56} - 8q^{57} - 32q^{58} - 8q^{63} + 32q^{67} + 64q^{71} - 24q^{72} + 24q^{77} + 8q^{78} - 16q^{81} + 64q^{86} + 64q^{88} - 48q^{91} + 40q^{92} - 24q^{93} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86147 1.86147i 1.31626 1.31626i 0.399541 0.916715i \(-0.369169\pi\)
0.916715 0.399541i \(-0.130831\pi\)
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 4.93012i 2.46506i
\(5\) 0 0
\(6\) 2.63251i 1.07472i
\(7\) 2.20563 + 1.46123i 0.833650 + 0.552293i
\(8\) −5.45433 5.45433i −1.92840 1.92840i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −1.46279 −0.441048 −0.220524 0.975382i \(-0.570777\pi\)
−0.220524 + 0.975382i \(0.570777\pi\)
\(12\) −3.48612 3.48612i −1.00636 1.00636i
\(13\) −0.887844 + 0.887844i −0.246244 + 0.246244i −0.819427 0.573183i \(-0.805708\pi\)
0.573183 + 0.819427i \(0.305708\pi\)
\(14\) 6.82574 1.38567i 1.82426 0.370337i
\(15\) 0 0
\(16\) −10.4459 −2.61147
\(17\) 2.10614 + 2.10614i 0.510815 + 0.510815i 0.914776 0.403961i \(-0.132367\pi\)
−0.403961 + 0.914776i \(0.632367\pi\)
\(18\) −1.86147 1.86147i −0.438752 0.438752i
\(19\) −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
\(22\) −2.72294 + 2.72294i −0.580532 + 0.580532i
\(23\) 4.13007 + 4.13007i 0.861180 + 0.861180i 0.991475 0.130295i \(-0.0415926\pi\)
−0.130295 + 0.991475i \(0.541593\pi\)
\(24\) −7.71359 −1.57453
\(25\) 0 0
\(26\) 3.30539i 0.648240i
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 7.20405 10.8740i 1.36144 2.05500i
\(29\) 5.18572i 0.962965i −0.876456 0.481482i \(-0.840099\pi\)
0.876456 0.481482i \(-0.159901\pi\)
\(30\) 0 0
\(31\) 6.10346i 1.09621i 0.836408 + 0.548107i \(0.184651\pi\)
−0.836408 + 0.548107i \(0.815349\pi\)
\(32\) −8.53599 + 8.53599i −1.50896 + 1.50896i
\(33\) −1.03435 + 1.03435i −0.180057 + 0.180057i
\(34\) 7.84104 1.34473
\(35\) 0 0
\(36\) −4.93012 −0.821687
\(37\) −2.25560 + 2.25560i −0.370819 + 0.370819i −0.867775 0.496957i \(-0.834451\pi\)
0.496957 + 0.867775i \(0.334451\pi\)
\(38\) −7.37117 + 7.37117i −1.19576 + 1.19576i
\(39\) 1.25560i 0.201057i
\(40\) 0 0
\(41\) 0.769968i 0.120249i −0.998191 0.0601244i \(-0.980850\pi\)
0.998191 0.0601244i \(-0.0191497\pi\)
\(42\) 3.84671 5.80635i 0.593560 0.895939i
\(43\) 5.18572 + 5.18572i 0.790816 + 0.790816i 0.981627 0.190811i \(-0.0611118\pi\)
−0.190811 + 0.981627i \(0.561112\pi\)
\(44\) 7.21173i 1.08721i
\(45\) 0 0
\(46\) 15.3760 2.26707
\(47\) −8.57041 8.57041i −1.25012 1.25012i −0.955664 0.294459i \(-0.904861\pi\)
−0.294459 0.955664i \(-0.595139\pi\)
\(48\) −7.38635 + 7.38635i −1.06613 + 1.06613i
\(49\) 2.72961 + 6.44587i 0.389944 + 0.920839i
\(50\) 0 0
\(51\) 2.97854 0.417079
\(52\) 4.37718 + 4.37718i 0.607006 + 0.607006i
\(53\) 0.544449 + 0.544449i 0.0747859 + 0.0747859i 0.743510 0.668724i \(-0.233159\pi\)
−0.668724 + 0.743510i \(0.733159\pi\)
\(54\) −2.63251 −0.358240
\(55\) 0 0
\(56\) −4.06020 20.0003i −0.542567 2.67265i
\(57\) −2.80005 + 2.80005i −0.370876 + 0.370876i
\(58\) −9.65306 9.65306i −1.26751 1.26751i
\(59\) −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 \(-0.0289894\pi\)
\(62\) 11.3614 + 11.3614i 1.44290 + 1.44290i
\(63\) 1.46123 2.20563i 0.184098 0.277883i
\(64\) 10.8872i 1.36090i
\(65\) 0 0
\(66\) 3.85081i 0.474002i
\(67\) 5.93012 5.93012i 0.724480 0.724480i −0.245034 0.969514i \(-0.578799\pi\)
0.969514 + 0.245034i \(0.0787993\pi\)
\(68\) 10.3835 10.3835i 1.25919 1.25919i
\(69\) 5.84081 0.703150
\(70\) 0 0
\(71\) 7.62611 0.905053 0.452526 0.891751i \(-0.350523\pi\)
0.452526 + 0.891751i \(0.350523\pi\)
\(72\) −5.45433 + 5.45433i −0.642799 + 0.642799i
\(73\) −6.81378 + 6.81378i −0.797493 + 0.797493i −0.982700 0.185207i \(-0.940704\pi\)
0.185207 + 0.982700i \(0.440704\pi\)
\(74\) 8.39746i 0.976185i
\(75\) 0 0
\(76\) 19.5226i 2.23940i
\(77\) −3.22637 2.13747i −0.367679 0.243588i
\(78\) 2.33726 + 2.33726i 0.264643 + 0.264643i
\(79\) 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
\(82\) −1.43327 1.43327i −0.158278 0.158278i
\(83\) 6.75794 6.75794i 0.741781 0.741781i −0.231140 0.972921i \(-0.574246\pi\)
0.972921 + 0.231140i \(0.0742455\pi\)
\(84\) −2.59507 12.7831i −0.283145 1.39475i
\(85\) 0 0
\(86\) 19.3061 2.08183
\(87\) −3.66686 3.66686i −0.393129 0.393129i
\(88\) 7.97854 + 7.97854i 0.850515 + 0.850515i
\(89\) 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
\(92\) 20.3618 20.3618i 2.12286 2.12286i
\(93\) 4.31580 + 4.31580i 0.447527 + 0.447527i
\(94\) −31.9071 −3.29096
\(95\) 0 0
\(96\) 12.0717i 1.23206i
\(97\) 8.68829 + 8.68829i 0.882162 + 0.882162i 0.993754 0.111592i \(-0.0355950\pi\)
−0.111592 + 0.993754i \(0.535595\pi\)
\(98\) 17.0799 + 6.91770i 1.72533 + 0.698794i
\(99\) 1.46279i 0.147016i
\(100\) 0 0
\(101\) 15.3420i 1.52659i −0.646050 0.763295i \(-0.723580\pi\)
0.646050 0.763295i \(-0.276420\pi\)
\(102\) 5.54445 5.54445i 0.548982 0.548982i
\(103\) −8.30776 + 8.30776i −0.818588 + 0.818588i −0.985903 0.167316i \(-0.946490\pi\)
0.167316 + 0.985903i \(0.446490\pi\)
\(104\) 9.68519 0.949711
\(105\) 0 0
\(106\) 2.02695 0.196875
\(107\) −4.39022 + 4.39022i −0.424418 + 0.424418i −0.886722 0.462303i \(-0.847023\pi\)
0.462303 + 0.886722i \(0.347023\pi\)
\(108\) −3.48612 + 3.48612i −0.335452 + 0.335452i
\(109\) 7.44587i 0.713185i −0.934260 0.356593i \(-0.883938\pi\)
0.934260 0.356593i \(-0.116062\pi\)
\(110\) 0 0
\(111\) 3.18990i 0.302772i
\(112\) −23.0397 15.2638i −2.17705 1.44230i
\(113\) −2.54445 2.54445i −0.239362 0.239362i 0.577224 0.816586i \(-0.304136\pi\)
−0.816586 + 0.577224i \(0.804136\pi\)
\(114\) 10.4244i 0.976335i
\(115\) 0 0
\(116\) −25.5663 −2.37377
\(117\) 0.887844 + 0.887844i 0.0820812 + 0.0820812i
\(118\) −5.94986 + 5.94986i −0.547729 + 0.547729i
\(119\) 1.56781 + 7.72294i 0.143721 + 0.707960i
\(120\) 0 0
\(121\) −8.86025 −0.805477
\(122\) −2.64448 2.64448i −0.239420 0.239420i
\(123\) −0.544449 0.544449i −0.0490913 0.0490913i
\(124\) 30.0908 2.70223
\(125\) 0 0
\(126\) −1.38567 6.82574i −0.123446 0.608086i
\(127\) −7.86025 + 7.86025i −0.697484 + 0.697484i −0.963867 0.266383i \(-0.914171\pi\)
0.266383 + 0.963867i \(0.414171\pi\)
\(128\) 3.19418 + 3.19418i 0.282329 + 0.282329i
\(129\) 7.33372 0.645698
\(130\) 0 0
\(131\) 6.18216i 0.540138i −0.962841 0.270069i \(-0.912953\pi\)
0.962841 0.270069i \(-0.0870465\pi\)
\(132\) 5.09947 + 5.09947i 0.443851 + 0.443851i
\(133\) −8.73401 5.78628i −0.757334 0.501735i
\(134\) 22.0775i 1.90720i
\(135\) 0 0
\(136\) 22.9752i 1.97011i
\(137\) −9.05565 + 9.05565i −0.773677 + 0.773677i −0.978747 0.205071i \(-0.934258\pi\)
0.205071 + 0.978747i \(0.434258\pi\)
\(138\) 10.8725 10.8725i 0.925526 0.925526i
\(139\) −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
\(142\) 14.1958 14.1958i 1.19128 1.19128i
\(143\) 1.29873 1.29873i 0.108605 0.108605i
\(144\) 10.4459i 0.870489i
\(145\) 0 0
\(146\) 25.3673i 2.09941i
\(147\) 6.48804 + 2.62780i 0.535125 + 0.216737i
\(148\) 11.1204 + 11.1204i 0.914091 + 0.914091i
\(149\) 0.0968261i 0.00793230i 0.999992 + 0.00396615i \(0.00126247\pi\)
−0.999992 + 0.00396615i \(0.998738\pi\)
\(150\) 0 0
\(151\) −13.4550 −1.09495 −0.547475 0.836822i \(-0.684411\pi\)
−0.547475 + 0.836822i \(0.684411\pi\)
\(152\) 21.5984 + 21.5984i 1.75186 + 1.75186i
\(153\) 2.10614 2.10614i 0.170272 0.170272i
\(154\) −9.98463 + 2.02695i −0.804584 + 0.163336i
\(155\) 0 0
\(156\) 6.19027 0.495618
\(157\) −1.64757 1.64757i −0.131491 0.131491i 0.638298 0.769789i \(-0.279639\pi\)
−0.769789 + 0.638298i \(0.779639\pi\)
\(158\) −8.41438 8.41438i −0.669412 0.669412i
\(159\) 0.769968 0.0610624
\(160\) 0 0
\(161\) 3.07442 + 15.1444i 0.242298 + 1.19355i
\(162\) −1.86147 + 1.86147i −0.146251 + 0.146251i
\(163\) 10.2746 + 10.2746i 0.804771 + 0.804771i 0.983837 0.179066i \(-0.0573077\pi\)
−0.179066 + 0.983837i \(0.557308\pi\)
\(164\) −3.79604 −0.296421
\(165\) 0 0
\(166\) 25.1594i 1.95275i
\(167\) −0.293008 0.293008i −0.0226737 0.0226737i 0.695679 0.718353i \(-0.255104\pi\)
−0.718353 + 0.695679i \(0.755104\pi\)
\(168\) −17.0133 11.2713i −1.31261 0.869602i
\(169\) 11.4235i 0.878728i
\(170\) 0 0
\(171\) 3.95987i 0.302819i
\(172\) 25.5663 25.5663i 1.94941 1.94941i
\(173\) 3.45189 3.45189i 0.262442 0.262442i −0.563603 0.826046i \(-0.690585\pi\)
0.826046 + 0.563603i \(0.190585\pi\)
\(174\) −13.6515 −1.03492
\(175\) 0 0
\(176\) 15.2801 1.15178
\(177\) −2.26015 + 2.26015i −0.169883 + 0.169883i
\(178\) 2.23359 2.23359i 0.167415 0.167415i
\(179\) 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 \(0.897877\pi\)
\(182\) −4.82993 + 7.29046i −0.358019 + 0.540405i
\(183\) −1.00454 1.00454i −0.0742581 0.0742581i
\(184\) 45.0536i 3.32139i
\(185\) 0 0
\(186\) 16.0674 1.17812
\(187\) −3.08084 3.08084i −0.225294 0.225294i
\(188\) −42.2532 + 42.2532i −3.08163 + 3.08163i
\(189\) −0.526369 2.59286i −0.0382877 0.188603i
\(190\) 0 0
\(191\) −7.83424 −0.566866 −0.283433 0.958992i \(-0.591473\pi\)
−0.283433 + 0.958992i \(0.591473\pi\)
\(192\) 7.69841 + 7.69841i 0.555585 + 0.555585i
\(193\) −13.5617 13.5617i −0.976194 0.976194i 0.0235293 0.999723i \(-0.492510\pi\)
−0.999723 + 0.0235293i \(0.992510\pi\)
\(194\) 32.3459 2.32230
\(195\) 0 0
\(196\) 31.7789 13.4573i 2.26992 0.961236i
\(197\) 11.4791 11.4791i 0.817853 0.817853i −0.167943 0.985797i \(-0.553713\pi\)
0.985797 + 0.167943i \(0.0537126\pi\)
\(198\) 2.72294 + 2.72294i 0.193511 + 0.193511i
\(199\) 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
\(202\) −28.5587 28.5587i −2.00938 2.00938i
\(203\) 7.57754 11.4378i 0.531839 0.802775i
\(204\) 14.6846i 1.02812i
\(205\) 0 0
\(206\) 30.9292i 2.15494i
\(207\) 4.13007 4.13007i 0.287060 0.287060i
\(208\) 9.27431 9.27431i 0.643057 0.643057i
\(209\) 5.79246 0.400673
\(210\) 0 0
\(211\) 11.9662 0.823785 0.411892 0.911233i \(-0.364868\pi\)
0.411892 + 0.911233i \(0.364868\pi\)
\(212\) 2.68420 2.68420i 0.184352 0.184352i
\(213\) 5.39247 5.39247i 0.369486 0.369486i
\(214\) 16.3445i 1.11729i
\(215\) 0 0
\(216\) 7.71359i 0.524843i
\(217\) −8.91857 + 13.4620i −0.605432 + 0.913858i
\(218\) −13.8602 13.8602i −0.938734 0.938734i
\(219\) 9.63614i 0.651150i
\(220\) 0 0
\(221\) −3.73985 −0.251570
\(222\) 5.93790 + 5.93790i 0.398526 + 0.398526i
\(223\) 0.660910 0.660910i 0.0442578 0.0442578i −0.684632 0.728889i \(-0.740037\pi\)
0.728889 + 0.684632i \(0.240037\pi\)
\(224\) −31.3003 + 6.35418i −2.09134 + 0.424557i
\(225\) 0 0
\(226\) −9.47282 −0.630123
\(227\) 17.3487 + 17.3487i 1.15147 + 1.15147i 0.986257 + 0.165216i \(0.0528323\pi\)
0.165216 + 0.986257i \(0.447168\pi\)
\(228\) 13.8046 + 13.8046i 0.914232 + 0.914232i
\(229\) −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
\(232\) −28.2847 + 28.2847i −1.85698 + 1.85698i
\(233\) −2.24138 2.24138i −0.146837 0.146837i 0.629866 0.776704i \(-0.283110\pi\)
−0.776704 + 0.629866i \(0.783110\pi\)
\(234\) 3.30539 0.216080
\(235\) 0 0
\(236\) 15.7583i 1.02578i
\(237\) −3.19633 3.19633i −0.207624 0.207624i
\(238\) 17.2944 + 11.4576i 1.12103 + 0.742684i
\(239\) 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 \(0.993601\pi\)
\(242\) −16.4931 + 16.4931i −1.06021 + 1.06021i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −7.00393 −0.448381
\(245\) 0 0
\(246\) −2.02695 −0.129234
\(247\) 3.51575 3.51575i 0.223702 0.223702i
\(248\) 33.2903 33.2903i 2.11394 2.11394i
\(249\) 9.55717i 0.605661i
\(250\) 0 0
\(251\) 16.3443i 1.03164i −0.856696 0.515822i \(-0.827487\pi\)
0.856696 0.515822i \(-0.172513\pi\)
\(252\) −10.8740 7.20405i −0.684999 0.453813i
\(253\) −6.04143 6.04143i −0.379821 0.379821i
\(254\) 29.2632i 1.83614i
\(255\) 0 0
\(256\) −9.88265 −0.617666
\(257\) −21.3054 21.3054i −1.32900 1.32900i −0.906247 0.422749i \(-0.861065\pi\)
−0.422749 0.906247i \(-0.638935\pi\)
\(258\) 13.6515 13.6515i 0.849904 0.849904i
\(259\) −8.27098 + 1.67907i −0.513933 + 0.104332i
\(260\) 0 0
\(261\) −5.18572 −0.320988
\(262\) −11.5079 11.5079i −0.710960 0.710960i
\(263\) 16.3449 + 16.3449i 1.00787 + 1.00787i 0.999969 + 0.00789784i \(0.00251399\pi\)
0.00789784 + 0.999969i \(0.497486\pi\)
\(264\) 11.2834 0.694442
\(265\) 0 0
\(266\) −27.0291 + 5.48709i −1.65726 + 0.336435i
\(267\) 0.848464 0.848464i 0.0519251 0.0519251i
\(268\) −29.2362 29.2362i −1.78589 1.78589i
\(269\) −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 \(-0.0759383\pi\)
\(272\) −22.0005 22.0005i −1.33398 1.33398i
\(273\) −1.83472 + 2.76939i −0.111043 + 0.167611i
\(274\) 33.7136i 2.03671i
\(275\) 0 0
\(276\) 28.7959i 1.73331i
\(277\) −21.3107 + 21.3107i −1.28043 + 1.28043i −0.340013 + 0.940421i \(0.610431\pi\)
−0.940421 + 0.340013i \(0.889569\pi\)
\(278\) −22.3214 + 22.3214i −1.33875 + 1.33875i
\(279\) 6.10346 0.365405
\(280\) 0 0
\(281\) −21.1519 −1.26182 −0.630908 0.775858i \(-0.717317\pi\)
−0.630908 + 0.775858i \(0.717317\pi\)
\(282\) −22.5617 + 22.5617i −1.34353 + 1.34353i
\(283\) −2.65471 + 2.65471i −0.157806 + 0.157806i −0.781594 0.623788i \(-0.785593\pi\)
0.623788 + 0.781594i \(0.285593\pi\)
\(284\) 37.5977i 2.23101i
\(285\) 0 0
\(286\) 4.83508i 0.285905i
\(287\) 1.12510 1.69826i 0.0664126 0.100245i
\(288\) 8.53599 + 8.53599i 0.502988 + 0.502988i
\(289\) 8.12832i 0.478136i
\(290\) 0 0
\(291\) 12.2871 0.720282
\(292\) 33.5928 + 33.5928i 1.96587 + 1.96587i
\(293\) 1.56714 1.56714i 0.0915536 0.0915536i −0.659847 0.751400i \(-0.729379\pi\)
0.751400 + 0.659847i \(0.229379\pi\)
\(294\) 16.9688 7.18572i 0.989643 0.419080i
\(295\) 0 0
\(296\) 24.6056 1.43017
\(297\) 1.03435 + 1.03435i 0.0600190 + 0.0600190i
\(298\) 0.180239 + 0.180239i 0.0104409 + 0.0104409i
\(299\) −7.33372 −0.424120
\(300\) 0 0
\(301\) 3.86025 + 19.0153i 0.222501 + 1.09603i
\(302\) −25.0460 + 25.0460i −1.44123 + 1.44123i
\(303\) −10.8485 10.8485i −0.623228 0.623228i
\(304\) 41.3643 2.37240
\(305\) 0 0
\(306\) 7.84104i 0.448242i
\(307\) 17.3551 + 17.3551i 0.990510 + 0.990510i 0.999955 0.00944588i \(-0.00300676\pi\)
−0.00944588 + 0.999955i \(0.503007\pi\)
\(308\) −10.5380 + 15.9064i −0.600459 + 0.906352i
\(309\) 11.7489i 0.668374i
\(310\) 0 0
\(311\) 31.0648i 1.76153i −0.473558 0.880763i \(-0.657030\pi\)
0.473558 0.880763i \(-0.342970\pi\)
\(312\) 6.84846 6.84846i 0.387718 0.387718i
\(313\) −5.72426 + 5.72426i −0.323554 + 0.323554i −0.850129 0.526575i \(-0.823476\pi\)
0.526575 + 0.850129i \(0.323476\pi\)
\(314\) −6.13381 −0.346151
\(315\) 0 0
\(316\) −22.2856 −1.25366
\(317\) −0.752579 + 0.752579i −0.0422691 + 0.0422691i −0.727925 0.685656i \(-0.759515\pi\)
0.685656 + 0.727925i \(0.259515\pi\)
\(318\) 1.43327 1.43327i 0.0803738 0.0803738i
\(319\) 7.58562i 0.424713i
\(320\) 0 0
\(321\) 6.20871i 0.346536i
\(322\) 33.9138 + 22.4679i 1.88994 + 1.25209i
\(323\) −8.34005 8.34005i −0.464053 0.464053i
\(324\) 4.93012i 0.273896i
\(325\) 0 0
\(326\) 38.2518 2.11857
\(327\) −5.26503 5.26503i −0.291157 0.291157i
\(328\) −4.19966 + 4.19966i −0.231887 + 0.231887i
\(329\) −6.37980 31.4265i −0.351730 1.73260i
\(330\) 0 0
\(331\) 15.8082 0.868899 0.434449 0.900696i \(-0.356943\pi\)
0.434449 + 0.900696i \(0.356943\pi\)
\(332\) −33.3175 33.3175i −1.82853 1.82853i
\(333\) 2.25560 + 2.25560i 0.123606 + 0.123606i
\(334\) −1.09085 −0.0596887
\(335\) 0 0
\(336\) −27.0847 + 5.49839i −1.47759 + 0.299962i
\(337\) 20.0460 20.0460i 1.09197 1.09197i 0.0966558 0.995318i \(-0.469185\pi\)
0.995318 0.0966558i \(-0.0308146\pi\)
\(338\) 21.2644 + 21.2644i 1.15663 + 1.15663i
\(339\) −3.59839 −0.195438
\(340\) 0 0
\(341\) 8.92808i 0.483482i
\(342\) 7.37117 + 7.37117i 0.398587 + 0.398587i
\(343\) −3.39840 + 18.2058i −0.183497 + 0.983020i
\(344\) 56.5693i 3.05001i
\(345\) 0 0
\(346\) 12.8512i 0.690883i
\(347\) 20.0847 20.0847i 1.07820 1.07820i 0.0815328 0.996671i \(-0.474018\pi\)
0.996671 0.0815328i \(-0.0259815\pi\)
\(348\) −18.0781 + 18.0781i −0.969087 + 0.969087i
\(349\) 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
\(352\) 12.4864 12.4864i 0.665525 0.665525i
\(353\) 12.4890 12.4890i 0.664724 0.664724i −0.291766 0.956490i \(-0.594243\pi\)
0.956490 + 0.291766i \(0.0942429\pi\)
\(354\) 8.41438i 0.447219i
\(355\) 0 0
\(356\) 5.91570i 0.313531i
\(357\) 6.56955 + 4.35233i 0.347697 + 0.230350i
\(358\) 3.71839 + 3.71839i 0.196523 + 0.196523i
\(359\) 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
\(362\) 15.7951 + 15.7951i 0.830171 + 0.830171i
\(363\) −6.26514 + 6.26514i −0.328835 + 0.328835i
\(364\) 3.25837 + 16.0505i 0.170785 + 0.841276i
\(365\) 0 0
\(366\) −3.73985 −0.195485
\(367\) −11.1910 11.1910i −0.584163 0.584163i 0.351881 0.936045i \(-0.385542\pi\)
−0.936045 + 0.351881i \(0.885542\pi\)
\(368\) −43.1422 43.1422i −2.24894 2.24894i
\(369\) −0.769968 −0.0400829
\(370\) 0 0
\(371\) 0.405287 + 1.99642i 0.0210415 + 0.103649i
\(372\) 21.2774 21.2774i 1.10318 1.10318i
\(373\) −17.2746 17.2746i −0.894446 0.894446i 0.100492 0.994938i \(-0.467958\pi\)
−0.994938 + 0.100492i \(0.967958\pi\)
\(374\) −11.4698 −0.593088
\(375\) 0 0
\(376\) 93.4917i 4.82147i
\(377\) 4.60412 + 4.60412i 0.237124 + 0.237124i
\(378\) −5.80635 3.84671i −0.298646 0.197853i
\(379\) 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
\(382\) −14.5832 + 14.5832i −0.746141 + 0.746141i
\(383\) −16.1249 + 16.1249i −0.823942 + 0.823942i −0.986671 0.162729i \(-0.947970\pi\)
0.162729 + 0.986671i \(0.447970\pi\)
\(384\) 4.51726 0.230520
\(385\) 0 0
\(386\) −50.4894 −2.56984
\(387\) 5.18572 5.18572i 0.263605 0.263605i
\(388\) 42.8343 42.8343i 2.17458 2.17458i
\(389\) 15.4011i 0.780865i −0.920632 0.390432i \(-0.872326\pi\)
0.920632 0.390432i \(-0.127674\pi\)
\(390\) 0 0
\(391\) 17.3971i 0.879807i
\(392\) 20.2697 50.0461i 1.02378 2.52771i
\(393\) −4.37145 4.37145i −0.220510 0.220510i
\(394\) 42.7360i 2.15301i
\(395\) 0 0
\(396\) 7.21173 0.362403
\(397\) −16.1781 16.1781i −0.811955 0.811955i 0.172972 0.984927i \(-0.444663\pi\)
−0.984927 + 0.172972i \(0.944663\pi\)
\(398\) 37.5026 37.5026i 1.87983 1.87983i
\(399\) −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 \(0.507771\pi\)
\(402\) −15.6111 15.6111i −0.778612 0.778612i
\(403\) −5.41892 5.41892i −0.269936 0.269936i
\(404\) −75.6382 −3.76314
\(405\) 0 0
\(406\) −7.18572 35.3964i −0.356622 1.75670i
\(407\) 3.29947 3.29947i 0.163549 0.163549i
\(408\) −16.2459 16.2459i −0.804293 0.804293i
\(409\) 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
\(412\) 40.9583 + 40.9583i 2.01787 + 2.01787i
\(413\) −7.04992 4.67058i −0.346904 0.229824i
\(414\) 15.3760i 0.755689i
\(415\) 0 0
\(416\) 15.1573i 0.743146i
\(417\) −8.47912 + 8.47912i −0.415224 + 0.415224i
\(418\) 10.7825 10.7825i 0.527388 0.527388i
\(419\) 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 \(0.383385\pi\)
\(422\) 22.2746 22.2746i 1.08431 1.08431i
\(423\) −8.57041 + 8.57041i −0.416708 + 0.416708i
\(424\) 5.93921i 0.288434i
\(425\) 0 0
\(426\) 20.0758i 0.972677i
\(427\) 2.07588 3.13341i 0.100459 0.151636i
\(428\) 21.6443 + 21.6443i 1.04622 + 1.04622i
\(429\) 1.83668i 0.0886758i
\(430\) 0 0
\(431\) 22.2722 1.07281 0.536407 0.843960i \(-0.319781\pi\)
0.536407 + 0.843960i \(0.319781\pi\)
\(432\) 7.38635 + 7.38635i 0.355376 + 0.355376i
\(433\) 28.0171 28.0171i 1.34642 1.34642i 0.456896 0.889520i \(-0.348961\pi\)
0.889520 0.456896i \(-0.151039\pi\)
\(434\) 8.45741 + 41.6606i 0.405968 + 1.99978i
\(435\) 0 0
\(436\) −36.7091 −1.75805
\(437\) −16.3545 16.3545i −0.782344 0.782344i
\(438\) 17.9374 + 17.9374i 0.857080 + 0.857080i
\(439\) −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
\(442\) −6.96162 + 6.96162i −0.331130 + 0.331130i
\(443\) 5.47247 + 5.47247i 0.260005 + 0.260005i 0.825056 0.565051i \(-0.191144\pi\)
−0.565051 + 0.825056i \(0.691144\pi\)
\(444\) 15.7266 0.746352
\(445\) 0 0
\(446\) 2.46053i 0.116509i
\(447\) 0.0684664 + 0.0684664i 0.00323835 + 0.00323835i
\(448\) −15.9087 + 24.0131i −0.751616 + 1.13451i
\(449\) 1.20020i 0.0566410i 0.999599 + 0.0283205i \(0.00901591\pi\)
−0.999599 + 0.0283205i \(0.990984\pi\)
\(450\) 0 0
\(451\) 1.12630i 0.0530354i
\(452\) −12.5444 + 12.5444i −0.590041 + 0.590041i
\(453\) −9.51409 + 9.51409i −0.447011 + 0.447011i
\(454\) 64.5881 3.03127
\(455\) 0 0
\(456\) 30.5448 1.43039
\(457\) 21.0775 21.0775i 0.985962 0.985962i −0.0139406 0.999903i \(-0.504438\pi\)
0.999903 + 0.0139406i \(0.00443756\pi\)
\(458\) −46.6823 + 46.6823i −2.18132 + 2.18132i
\(459\) 2.97854i 0.139026i
\(460\) 0 0
\(461\) 21.9670i 1.02311i 0.859252 + 0.511553i \(0.170929\pi\)
−0.859252 + 0.511553i \(0.829071\pi\)
\(462\) −5.62693 + 8.49347i −0.261788 + 0.395152i
\(463\) 21.6776 + 21.6776i 1.00744 + 1.00744i 0.999972 + 0.00746987i \(0.00237776\pi\)
0.00746987 + 0.999972i \(0.497622\pi\)
\(464\) 54.1694i 2.51475i
\(465\) 0 0
\(466\) −8.34450 −0.386551
\(467\) −7.11299 7.11299i −0.329150 0.329150i 0.523113 0.852263i \(-0.324770\pi\)
−0.852263 + 0.523113i \(0.824770\pi\)
\(468\) 4.37718 4.37718i 0.202335 0.202335i
\(469\) 21.7449 4.41438i 1.00409 0.203837i
\(470\) 0 0
\(471\) −2.33002 −0.107362
\(472\) 17.4338 + 17.4338i 0.802457 + 0.802457i
\(473\) −7.58562 7.58562i −0.348787 0.348787i
\(474\) −11.8997 −0.546572
\(475\) 0 0
\(476\) 38.0750 7.72950i 1.74517 0.354281i
\(477\) 0.544449 0.544449i 0.0249286 0.0249286i
\(478\) 39.7925 + 39.7925i 1.82007 + 1.82007i
\(479\) 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
\(482\) 1.16180 + 1.16180i 0.0529184 + 0.0529184i
\(483\) 12.8827 + 8.53477i 0.586181 + 0.388345i
\(484\) 43.6821i 1.98555i
\(485\) 0 0
\(486\) 2.63251i 0.119413i
\(487\) 4.81428 4.81428i 0.218156 0.218156i −0.589565 0.807721i \(-0.700701\pi\)
0.807721 + 0.589565i \(0.200701\pi\)
\(488\) −7.74864 + 7.74864i −0.350765 + 0.350765i
\(489\) 14.5305 0.657092
\(490\) 0 0
\(491\) 28.3401 1.27897 0.639484 0.768804i \(-0.279148\pi\)
0.639484 + 0.768804i \(0.279148\pi\)
\(492\) −2.68420 + 2.68420i −0.121013 + 0.121013i
\(493\) 10.9219 10.9219i 0.491897 0.491897i
\(494\) 13.0889i 0.588897i
\(495\) 0 0
\(496\) 63.7559i 2.86273i
\(497\) 16.8204 + 11.1435i 0.754497 + 0.499855i
\(498\) −17.7904 17.7904i −0.797206 0.797206i
\(499\) 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
\(502\) −30.4244 30.4244i −1.35791 1.35791i
\(503\) 8.32921 8.32921i 0.371381 0.371381i −0.496599 0.867980i \(-0.665418\pi\)
0.867980 + 0.496599i \(0.165418\pi\)
\(504\) −20.0003 + 4.06020i −0.890883 + 0.180856i
\(505\) 0 0
\(506\) −22.4918 −0.999884
\(507\) 8.07761 + 8.07761i 0.358739 + 0.358739i
\(508\) 38.7520 + 38.7520i 1.71934 + 1.71934i
\(509\) −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
\(512\) −24.7846 + 24.7846i −1.09534 + 1.09534i
\(513\) 2.80005 + 2.80005i 0.123625 + 0.123625i
\(514\) −79.3187 −3.49860
\(515\) 0 0
\(516\) 36.1562i 1.59169i
\(517\) 12.5367 + 12.5367i 0.551364 + 0.551364i
\(518\) −12.2706 + 18.5217i −0.539140 + 0.813796i
\(519\) 4.88171i 0.214283i
\(520\) 0 0
\(521\) 7.06726i 0.309622i 0.987944 + 0.154811i \(0.0494769\pi\)
−0.987944 + 0.154811i \(0.950523\pi\)
\(522\) −9.65306 + 9.65306i −0.422503 + 0.422503i
\(523\) −14.5887 + 14.5887i −0.637921 + 0.637921i −0.950042 0.312121i \(-0.898960\pi\)
0.312121 + 0.950042i \(0.398960\pi\)
\(524\) −30.4788 −1.33147
\(525\) 0 0
\(526\) 60.8508 2.65322
\(527\) −12.8548 + 12.8548i −0.559962 + 0.559962i
\(528\) 10.8047 10.8047i 0.470213 0.470213i
\(529\) 11.1150i 0.483261i
\(530\) 0 0
\(531\) 3.19633i 0.138709i
\(532\) −28.5271 + 43.0597i −1.23681 + 1.86688i
\(533\) 0.683611 + 0.683611i 0.0296105 + 0.0296105i
\(534\) 3.15878i 0.136694i
\(535\) 0 0
\(536\) −64.6897 −2.79417
\(537\) 1.41249 + 1.41249i 0.0609533 + 0.0609533i
\(538\) −30.8823 + 30.8823i −1.33143 + 1.33143i
\(539\) −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 \(0.369057\pi\)
\(542\) −14.4828 14.4828i −0.622091 0.622091i
\(543\) 6.00000 + 6.00000i 0.257485 + 0.257485i
\(544\) −35.9560 −1.54160
\(545\) 0 0
\(546\) 1.73985 + 8.57041i 0.0744589 + 0.366780i
\(547\) 7.22715 7.22715i 0.309011 0.309011i −0.535515 0.844526i \(-0.679882\pi\)
0.844526 + 0.535515i \(0.179882\pi\)
\(548\) 44.6455 + 44.6455i 1.90716 + 1.90716i
\(549\) −1.42064 −0.0606315
\(550\) 0 0
\(551\) 20.5348i 0.874812i
\(552\) −31.8577 31.8577i −1.35595 1.35595i
\(553\) 6.60519 9.97009i 0.280881 0.423971i
\(554\) 79.3382i 3.37076i
\(555\) 0 0
\(556\) 59.1185i 2.50718i
\(557\) 0.558927 0.558927i 0.0236825 0.0236825i −0.695166 0.718849i \(-0.744669\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(558\) 11.3614 11.3614i 0.480966 0.480966i
\(559\) −9.20823 −0.389467
\(560\) 0 0
\(561\) −4.35697 −0.183951
\(562\) −39.3736 + 39.3736i −1.66087 + 1.66087i
\(563\) −0.702475 + 0.702475i −0.0296058 + 0.0296058i −0.721755 0.692149i \(-0.756664\pi\)
0.692149 + 0.721755i \(0.256664\pi\)
\(564\) 59.7550i 2.51614i
\(565\) 0 0
\(566\) 9.88333i 0.415427i
\(567\) −2.20563 1.46123i −0.0926278 0.0613659i
\(568\) −41.5953 41.5953i −1.74530 1.74530i
\(569\) 9.72049i 0.407504i −0.979023 0.203752i \(-0.934686\pi\)
0.979023 0.203752i \(-0.0653137\pi\)
\(570\) 0 0
\(571\) −0.986684 −0.0412914 −0.0206457 0.999787i \(-0.506572\pi\)
−0.0206457 + 0.999787i \(0.506572\pi\)
\(572\) −6.40289 6.40289i −0.267718 0.267718i
\(573\) −5.53964 + 5.53964i −0.231422 + 0.231422i
\(574\) −1.06692 5.25560i −0.0445326 0.219365i
\(575\) 0 0
\(576\) 10.8872 0.453633
\(577\) 10.3510 + 10.3510i 0.430917 + 0.430917i 0.888940 0.458024i \(-0.151442\pi\)
−0.458024 + 0.888940i \(0.651442\pi\)
\(578\) −15.1306 15.1306i −0.629350 0.629350i
\(579\) −19.1792 −0.797059
\(580\) 0 0
\(581\) 24.7804 5.03060i 1.02807 0.208705i
\(582\) 22.8720 22.8720i 0.948076 0.948076i
\(583\) −0.796415 0.796415i −0.0329841 0.0329841i
\(584\) 74.3292 3.07576
\(585\) 0 0
\(586\) 5.83438i 0.241016i
\(587\) 21.1413 + 21.1413i 0.872594 + 0.872594i 0.992755 0.120160i \(-0.0383409\pi\)
−0.120160 + 0.992755i \(0.538341\pi\)
\(588\) 12.9554 31.9868i 0.534270 1.31912i
\(589\) 24.1689i 0.995862i
\(590\) 0 0
\(591\) 16.2339i 0.667774i
\(592\) 23.5617 23.5617i 0.968381 0.968381i
\(593\) −7.07816 + 7.07816i −0.290665 + 0.290665i −0.837343 0.546678i \(-0.815892\pi\)
0.546678 + 0.837343i \(0.315892\pi\)
\(594\) 3.85081 0.158001
\(595\) 0 0
\(596\) 0.477365 0.0195536
\(597\) 14.2459 14.2459i 0.583047 0.583047i
\(598\) −13.6515 + 13.6515i −0.558251 + 0.558251i
\(599\) 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 \(-0.253815\pi\)
\(602\) 42.5822 + 28.2107i 1.73552 + 1.14978i
\(603\) −5.93012 5.93012i −0.241493 0.241493i
\(604\) 66.3346i 2.69912i
\(605\) 0 0
\(606\) −40.3881 −1.64066
\(607\) 5.36385 + 5.36385i 0.217712 + 0.217712i 0.807533 0.589822i \(-0.200802\pi\)
−0.589822 + 0.807533i \(0.700802\pi\)
\(608\) 33.8014 33.8014i 1.37083 1.37083i
\(609\) −2.72961 13.4459i −0.110609 0.544854i
\(610\) 0 0
\(611\) 15.2184 0.615670
\(612\) −10.3835 10.3835i −0.419730 0.419730i
\(613\) 10.4888 + 10.4888i 0.423639 + 0.423639i 0.886454 0.462816i \(-0.153161\pi\)
−0.462816 + 0.886454i \(0.653161\pi\)
\(614\) 64.6120 2.60753
\(615\) 0 0
\(616\) 5.93921 + 29.2562i 0.239298 + 1.17877i
\(617\) −19.7986 + 19.7986i −0.797060 + 0.797060i −0.982631 0.185571i \(-0.940586\pi\)
0.185571 + 0.982631i \(0.440586\pi\)
\(618\) 21.8703 + 21.8703i 0.879752 + 0.879752i
\(619\) −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
\(622\) −57.8262 57.8262i −2.31862 2.31862i
\(623\) 2.64655 + 1.75334i 0.106032 + 0.0702462i
\(624\) 13.1158i 0.525054i
\(625\) 0 0
\(626\) 21.3110i 0.851761i
\(627\) 4.09588 4.09588i 0.163574 0.163574i
\(628\) −8.12275 + 8.12275i −0.324133 + 0.324133i
\(629\) −9.50124 −0.378839
\(630\) 0 0
\(631\) 30.4435 1.21194 0.605969 0.795488i \(-0.292786\pi\)
0.605969 + 0.795488i \(0.292786\pi\)
\(632\) −24.6552 + 24.6552i −0.980730 + 0.980730i
\(633\) 8.46135 8.46135i 0.336309 0.336309i
\(634\) 2.80180i 0.111274i
\(635\) 0 0
\(636\) 3.79604i 0.150523i
\(637\) −8.14639 3.29946i −0.322772 0.130729i
\(638\) 14.1204 + 14.1204i 0.559032 + 0.559032i
\(639\) 7.62611i 0.301684i
\(640\) 0 0
\(641\) 36.5929 1.44533 0.722666 0.691198i \(-0.242917\pi\)
0.722666 + 0.691198i \(0.242917\pi\)
\(642\) 11.5573 + 11.5573i 0.456131 + 0.456131i
\(643\) 12.1140 12.1140i 0.477731 0.477731i −0.426675 0.904405i \(-0.640315\pi\)
0.904405 + 0.426675i \(0.140315\pi\)
\(644\) 74.6638 15.1573i 2.94217 0.597280i
\(645\) 0 0
\(646\) −31.0495 −1.22163
\(647\) 19.0978 + 19.0978i 0.750814 + 0.750814i 0.974631 0.223817i \(-0.0718519\pi\)
−0.223817 + 0.974631i \(0.571852\pi\)
\(648\) 5.45433 + 5.45433i 0.214266 + 0.214266i
\(649\) 4.67556 0.183532
\(650\) 0 0
\(651\) 3.21267 + 15.8254i 0.125915 + 0.620248i
\(652\) 50.6552 50.6552i 1.98381 1.98381i
\(653\) −20.3709 20.3709i −0.797173 0.797173i 0.185476 0.982649i \(-0.440617\pi\)
−0.982649 + 0.185476i \(0.940617\pi\)
\(654\) −19.6013 −0.766473
\(655\) 0 0
\(656\) 8.04298i 0.314026i
\(657\) 6.81378 + 6.81378i 0.265831 + 0.265831i
\(658\) −70.3752 46.6236i −2.74351 1.81758i
\(659\) 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 \(-0.386545\pi\)
\(662\) 29.4265 29.4265i 1.14369 1.14369i
\(663\) −2.64448 + 2.64448i −0.102703 + 0.102703i
\(664\) −73.7201 −2.86089
\(665\) 0 0
\(666\) 8.39746 0.325395
\(667\) 21.4174 21.4174i 0.829286 0.829286i
\(668\) −1.44457 + 1.44457i −0.0558920 + 0.0558920i
\(669\) 0.934668i 0.0361364i
\(670\) 0 0
\(671\) 2.07810i 0.0802241i
\(672\) −17.6396 + 26.6257i −0.680461 + 1.02711i
\(673\) 30.6900 + 30.6900i 1.18301 + 1.18301i 0.978960 + 0.204055i \(0.0654120\pi\)
0.204055 + 0.978960i \(0.434588\pi\)
\(674\) 74.6299i 2.87463i
\(675\) 0 0
\(676\) 56.3191 2.16612
\(677\) 1.54060 + 1.54060i 0.0592101 + 0.0592101i 0.736092 0.676882i \(-0.236669\pi\)
−0.676882 + 0.736092i \(0.736669\pi\)
\(678\) −6.69830 + 6.69830i −0.257246 + 0.257246i
\(679\) 6.46755 + 31.8587i 0.248202 + 1.22263i
\(680\) 0 0
\(681\) 24.5348 0.940174
\(682\) −16.6193 16.6193i −0.636387 0.636387i
\(683\) −14.2154 14.2154i −0.543936 0.543936i 0.380744 0.924680i \(-0.375668\pi\)
−0.924680 + 0.380744i \(0.875668\pi\)
\(684\) 19.5226 0.746467
\(685\) 0 0
\(686\) 27.5635 + 40.2155i 1.05238 + 1.53544i
\(687\) −17.7330 + 17.7330i −0.676555 + 0.676555i
\(688\) −54.1694 54.1694i −2.06519 2.06519i
\(689\) −0.966772 −0.0368311
\(690\) 0 0
\(691\) 10.2887i 0.391401i 0.980664 + 0.195700i \(0.0626980\pi\)
−0.980664 + 0.195700i \(0.937302\pi\)
\(692\) −17.0182 17.0182i −0.646937 0.646937i
\(693\) −2.13747 + 3.22637i −0.0811959 + 0.122560i
\(694\) 74.7741i 2.83838i
\(695\) 0 0
\(696\) 40.0005i 1.51622i
\(697\) 1.62166 1.62166i 0.0614248 0.0614248i
\(698\) 27.4869 27.4869i 1.04040 1.04040i
\(699\) −3.16979 −0.119892
\(700\) 0 0
\(701\) −44.3183 −1.67388 −0.836939 0.547297i \(-0.815657\pi\)
−0.836939 + 0.547297i \(0.815657\pi\)
\(702\) 2.33726 2.33726i 0.0882142 0.0882142i
\(703\) 8.93189 8.93189i 0.336872 0.336872i
\(704\) 15.9257i 0.600222i
\(705\) 0 0
\(706\) 46.4958i 1.74989i
\(707\) 22.4183 33.8389i 0.843126 1.27264i
\(708\) 11.1428 + 11.1428i 0.418772 + 0.418772i
\(709\) 0.817976i 0.0307197i 0.999882 + 0.0153599i \(0.00488939\pi\)
−0.999882 + 0.0153599i \(0.995111\pi\)
\(710\) 0 0
\(711\) −4.52029 −0.169524
\(712\) −6.54470 6.54470i −0.245273 0.245273i
\(713\) −25.2077 + 25.2077i −0.944037 + 0.944037i
\(714\) 20.3307 4.12728i 0.760858 0.154460i
\(715\) 0 0
\(716\) 9.84821 0.368045
\(717\) 15.1158 + 15.1158i 0.564509 + 0.564509i
\(718\) 19.6147 + 19.6147i 0.732013 + 0.732013i
\(719\) 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
\(722\) −6.17902 + 6.17902i −0.229959 + 0.229959i
\(723\) 0.441326 + 0.441326i 0.0164131 + 0.0164131i
\(724\) 41.8335 1.55473
\(725\) 0 0
\(726\) 23.3247i 0.865661i
\(727\) −28.5738 28.5738i −1.05974 1.05974i −0.998098 0.0616465i \(-0.980365\pi\)
−0.0616465 0.998098i \(-0.519635\pi\)
\(728\) 21.3619 + 14.1523i 0.791726 + 0.524519i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 21.8438i 0.807921i
\(732\) −4.95253 + 4.95253i −0.183051 + 0.183051i
\(733\) 24.1522 24.1522i 0.892083 0.892083i −0.102636 0.994719i \(-0.532728\pi\)
0.994719 + 0.102636i \(0.0327275\pi\)
\(734\) −41.6632 −1.53782
\(735\) 0 0
\(736\) −70.5085 −2.59898
\(737\) −8.67452 + 8.67452i −0.319530 + 0.319530i
\(738\) −1.43327 + 1.43327i −0.0527594 + 0.0527594i
\(739\) 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
\(742\) 4.47070 + 2.96184i 0.164125 + 0.108733i
\(743\) 18.8022 + 18.8022i 0.689784 + 0.689784i 0.962184 0.272400i \(-0.0878174\pi\)
−0.272400 + 0.962184i \(0.587817\pi\)
\(744\) 47.0796i 1.72602i
\(745\) 0 0
\(746\) −64.3123 −2.35464
\(747\) −6.75794 6.75794i −0.247260 0.247260i
\(748\) −15.1889 + 15.1889i −0.555363 + 0.555363i
\(749\) −16.0983 + 3.26807i −0.588220 + 0.119413i
\(750\) 0 0
\(751\) 0.105915 0.00386490 0.00193245 0.999998i \(-0.499385\pi\)
0.00193245 + 0.999998i \(0.499385\pi\)
\(752\) 89.5254 + 89.5254i 3.26466 + 3.26466i
\(753\) −11.5572 11.5572i −0.421167 0.421167i
\(754\) 17.1408 0.624232
\(755\) 0 0
\(756\) −12.7831 + 2.59507i −0.464918 + 0.0943816i
\(757\) −3.14514 + 3.14514i −0.114312 + 0.114312i −0.761949 0.647637i \(-0.775757\pi\)
0.647637 + 0.761949i \(0.275757\pi\)
\(758\) −32.8059 32.8059i −1.19156 1.19156i
\(759\) −8.54387 −0.310123
\(760\) 0 0
\(761\) 35.1123i 1.27282i −0.771351 0.636410i \(-0.780419\pi\)
0.771351 0.636410i \(-0.219581\pi\)
\(762\) 20.6922 + 20.6922i 0.749599 + 0.749599i
\(763\) 10.8801 16.4228i 0.393887 0.594547i
\(764\) 38.6238i 1.39736i
\(765\) 0 0
\(766\) 60.0318i 2.16904i
\(767\) 2.83784 2.83784i 0.102469 0.102469i
\(768\) −6.98809 + 6.98809i −0.252161 + 0.252161i
\(769\) 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
\(772\) −66.8609 + 66.8609i −2.40638 + 2.40638i
\(773\) 2.51166 2.51166i 0.0903382 0.0903382i −0.660494 0.750832i \(-0.729653\pi\)
0.750832 + 0.660494i \(0.229653\pi\)
\(774\) 19.3061i 0.693944i
\(775\) 0 0
\(776\) 94.7776i 3.40232i
\(777\) −4.66118 + 7.03574i −0.167219 + 0.252406i
\(778\) −28.6686 28.6686i −1.02782 1.02782i
\(779\) 3.04897i 0.109241i
\(780\) 0 0
\(781\) −11.1554 −0.399171
\(782\) 32.3840 + 32.3840i 1.15805