Properties

Label 525.2.m.b.118.7
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 118.7
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.307.7

$q$-expansion

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

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
\(7\) −1.46123 2.20563i −0.552293 0.833650i
\(8\) −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 −0.573183 0.819427i \(-0.694292\pi\)
0.819427 + 0.573183i \(0.194292\pi\)
\(14\) −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 0.403961 0.914776i \(-0.367633\pi\)
−0.914776 + 0.403961i \(0.867633\pi\)
\(18\) −1.86147 1.86147i −0.438752 0.438752i
\(19\) 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
\(22\) −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
\(28\) −10.8740 + 7.20405i −2.05500 + 1.36144i
\(29\) 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 \(-0.815349\pi\)
0.836408 0.548107i \(-0.184651\pi\)
\(32\) −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 \(0.0191497\pi\)
−0.998191 + 0.0601244i \(0.980850\pi\)
\(42\) 5.80635 3.84671i 0.895939 0.593560i
\(43\) 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 \(0.0951394\pi\)
0.294459 + 0.955664i \(0.404861\pi\)
\(48\) 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 \(-0.433284\pi\)
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 \(0.971011\pi\)
\(62\) −11.3614 11.3614i −1.44290 1.44290i
\(63\) −2.20563 + 1.46123i −0.277883 + 0.184098i
\(64\) 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 −0.185207 0.982700i \(-0.559296\pi\)
0.982700 + 0.185207i \(0.0592955\pi\)
\(74\) 8.39746i 0.976185i
\(75\) 0 0
\(76\) 19.5226i 2.23940i
\(77\) 2.13747 + 3.22637i 0.243588 + 0.367679i
\(78\) 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 −0.972921 0.231140i \(-0.925754\pi\)
0.231140 + 0.972921i \(0.425754\pi\)
\(84\) 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 \(-0.520257\pi\)
−0.0635950 + 0.997976i \(0.520257\pi\)
\(90\) 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 0.111592 0.993754i \(-0.464405\pi\)
−0.993754 + 0.111592i \(0.964405\pi\)
\(98\) 6.91770 + 17.0799i 0.698794 + 1.72533i
\(99\) 1.46279i 0.147016i
\(100\) 0 0
\(101\) 15.3420i 1.52659i 0.646050 + 0.763295i \(0.276420\pi\)
−0.646050 + 0.763295i \(0.723580\pi\)
\(102\) 5.54445 5.54445i 0.548982 0.548982i
\(103\) 8.30776 8.30776i 0.818588 0.818588i −0.167316 0.985903i \(-0.553510\pi\)
0.985903 + 0.167316i \(0.0535099\pi\)
\(104\) −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
\(112\) 15.2638 + 23.0397i 1.44230 + 2.17705i
\(113\) −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 \(0.0870465\pi\)
−0.962841 + 0.270069i \(0.912953\pi\)
\(132\) −5.09947 5.09947i −0.443851 0.443851i
\(133\) −5.78628 8.73401i −0.501735 0.757334i
\(134\) 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 \(-0.330184\pi\)
0.508544 + 0.861036i \(0.330184\pi\)
\(140\) 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
\(147\) −2.62780 6.48804i −0.216737 0.535125i
\(148\) 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 0.769789 0.638298i \(-0.220361\pi\)
−0.638298 + 0.769789i \(0.720361\pi\)
\(158\) −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 0.718353 0.695679i \(-0.244896\pi\)
−0.695679 + 0.718353i \(0.744896\pi\)
\(168\) −11.2713 17.0133i −0.869602 1.31261i
\(169\) 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 −0.826046 0.563603i \(-0.809415\pi\)
0.563603 + 0.826046i \(0.309415\pi\)
\(174\) 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 \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) −7.29046 + 4.82993i −0.540405 + 0.358019i
\(183\) −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 \(-0.753156\pi\)
−0.714084 + 0.700061i \(0.753156\pi\)
\(200\) 0 0
\(201\) 8.38646i 0.591535i
\(202\) 28.5587 + 28.5587i 2.00938 + 2.00938i
\(203\) −11.4378 + 7.57754i −0.802775 + 0.531839i
\(204\) 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
\(217\) −13.4620 + 8.91857i −0.913858 + 0.605432i
\(218\) −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 −0.728889 0.684632i \(-0.759963\pi\)
0.684632 + 0.728889i \(0.259963\pi\)
\(224\) 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 \(-0.947168\pi\)
−0.165216 0.986257i \(-0.552832\pi\)
\(228\) 13.8046 + 13.8046i 0.914232 + 0.914232i
\(229\) 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
\(232\) −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
\(238\) 11.4576 + 17.2944i 0.742684 + 1.12103i
\(239\) 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 \(-0.00639905\pi\)
\(242\) −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 \(0.172513\pi\)
−0.856696 + 0.515822i \(0.827487\pi\)
\(252\) 7.20405 + 10.8740i 0.453813 + 0.684999i
\(253\) −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 \(0.138935\pi\)
0.422749 + 0.906247i \(0.361065\pi\)
\(258\) −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 \(-0.331211\pi\)
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 \(0.924062\pi\)
\(272\) 22.0005 + 22.0005i 1.33398 + 1.33398i
\(273\) 2.76939 1.83472i 0.167611 0.111043i
\(274\) 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 −0.623788 0.781594i \(-0.714407\pi\)
0.781594 + 0.623788i \(0.214407\pi\)
\(284\) 37.5977i 2.23101i
\(285\) 0 0
\(286\) 4.83508i 0.285905i
\(287\) 1.69826 1.12510i 0.100245 0.0664126i
\(288\) 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 −0.751400 0.659847i \(-0.770621\pi\)
0.659847 + 0.751400i \(0.270621\pi\)
\(294\) −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 0.00944588 0.999955i \(-0.496993\pi\)
−0.999955 + 0.00944588i \(0.996993\pi\)
\(308\) 15.9064 10.5380i 0.906352 0.600459i
\(309\) 11.7489i 0.668374i
\(310\) 0 0
\(311\) 31.0648i 1.76153i 0.473558 + 0.880763i \(0.342970\pi\)
−0.473558 + 0.880763i \(0.657030\pi\)
\(312\) 6.84846 6.84846i 0.387718 0.387718i
\(313\) 5.72426 5.72426i 0.323554 0.323554i −0.526575 0.850129i \(-0.676524\pi\)
0.850129 + 0.526575i \(0.176524\pi\)
\(314\) 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
\(322\) −22.4679 33.9138i −1.25209 1.88994i
\(323\) −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
\(343\) 18.2058 3.39840i 0.983020 0.183497i
\(344\) 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 \(-0.629328\pi\)
−0.395210 + 0.918591i \(0.629328\pi\)
\(350\) 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 −0.956490 0.291766i \(-0.905757\pi\)
0.291766 + 0.956490i \(0.405757\pi\)
\(354\) 8.41438i 0.447219i
\(355\) 0 0
\(356\) 5.91570i 0.313531i
\(357\) −4.35233 6.56955i −0.230350 0.347697i
\(358\) 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 0.936045 0.351881i \(-0.114458\pi\)
−0.351881 + 0.936045i \(0.614458\pi\)
\(368\) −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
\(378\) −3.84671 5.80635i −0.197853 0.298646i
\(379\) 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 −0.162729 0.986671i \(-0.552030\pi\)
0.986671 + 0.162729i \(0.0520295\pi\)
\(384\) −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
\(392\) 50.0461 20.2697i 2.52771 1.02378i
\(393\) −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 0.984927 0.172972i \(-0.0553370\pi\)
−0.172972 + 0.984927i \(0.555337\pi\)
\(398\) −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 \(-0.705312\pi\)
−0.601203 + 0.799097i \(0.705312\pi\)
\(410\) 0 0
\(411\) 12.8066i 0.631704i
\(412\) −40.9583 40.9583i −2.01787 2.01787i
\(413\) −4.67058 7.04992i −0.229824 0.346904i
\(414\) 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 \(-0.627720\pi\)
−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 \(0.383385\pi\)
\(422\) 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
\(427\) 3.13341 2.07588i 0.151636 0.100459i
\(428\) 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 \(0.651039\pi\)
−0.889520 + 0.456896i \(0.848961\pi\)
\(434\) −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 \(-0.482090\pi\)
0.0562363 + 0.998417i \(0.482090\pi\)
\(440\) 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
\(448\) 24.0131 15.9087i 1.13451 0.751616i
\(449\) 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 \(-0.829071\pi\)
0.859252 0.511553i \(-0.170929\pi\)
\(462\) −8.49347 + 5.62693i −0.395152 + 0.261788i
\(463\) 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 0.852263 0.523113i \(-0.175230\pi\)
−0.523113 + 0.852263i \(0.675230\pi\)
\(468\) −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 \(-0.758584\pi\)
−0.725917 + 0.687782i \(0.758584\pi\)
\(480\) 0 0
\(481\) 4.00524i 0.182623i
\(482\) −1.16180 1.16180i −0.0529184 0.0529184i
\(483\) 8.53477 + 12.8827i 0.388345 + 0.586181i
\(484\) 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
\(497\) −11.1435 16.8204i −0.499855 0.754497i
\(498\) −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 −0.867980 0.496599i \(-0.834582\pi\)
0.496599 + 0.867980i \(0.334582\pi\)
\(504\) 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 \(-0.168515\pi\)
0.863108 + 0.505020i \(0.168515\pi\)
\(510\) 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
\(518\) 18.5217 12.2706i 0.813796 0.539140i
\(519\) 4.88171i 0.214283i
\(520\) 0 0
\(521\) 7.06726i 0.309622i −0.987944 0.154811i \(-0.950523\pi\)
0.987944 0.154811i \(-0.0494769\pi\)
\(522\) −9.65306 + 9.65306i −0.422503 + 0.422503i
\(523\) 14.5887 14.5887i 0.637921 0.637921i −0.312121 0.950042i \(-0.601040\pi\)
0.950042 + 0.312121i \(0.101040\pi\)
\(524\) 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
\(532\) −43.0597 + 28.5271i −1.86688 + 1.23681i
\(533\) 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
\(553\) −9.97009 + 6.60519i −0.423971 + 0.280881i
\(554\) 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 −0.692149 0.721755i \(-0.743336\pi\)
0.721755 + 0.692149i \(0.243336\pi\)
\(564\) 59.7550i 2.51614i
\(565\) 0 0
\(566\) 9.88333i 0.415427i
\(567\) 1.46123 + 2.20563i 0.0613659 + 0.0926278i
\(568\) −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 0.458024 0.888940i \(-0.348558\pi\)
−0.888940 + 0.458024i \(0.848558\pi\)
\(578\) −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 0.120160 0.992755i \(-0.461659\pi\)
−0.992755 + 0.120160i \(0.961659\pi\)
\(588\) −31.9868 + 12.9554i −1.31912 + 0.534270i
\(589\) 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 −0.546678 0.837343i \(-0.684108\pi\)
0.837343 + 0.546678i \(0.184108\pi\)
\(594\) −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 \(0.253815\pi\)
−0.698580 + 0.715532i \(0.746185\pi\)
\(602\) −28.2107 42.5822i −1.14978 1.73552i
\(603\) −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 0.589822 0.807533i \(-0.299198\pi\)
−0.807533 + 0.589822i \(0.799198\pi\)
\(608\) −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 \(-0.422027\pi\)
0.242517 + 0.970147i \(0.422027\pi\)
\(620\) 0 0
\(621\) 5.84081i 0.234383i
\(622\) 57.8262 + 57.8262i 2.31862 + 2.31862i
\(623\) 1.75334 + 2.64655i 0.0702462 + 0.106032i
\(624\) 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
\(637\) 3.29946 + 8.14639i 0.130729 + 0.322772i
\(638\) 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 −0.904405 0.426675i \(-0.859685\pi\)
0.426675 + 0.904405i \(0.359685\pi\)
\(644\) −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 0.223817 0.974631i \(-0.428148\pi\)
−0.974631 + 0.223817i \(0.928148\pi\)
\(648\) 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
\(658\) −46.6236 70.3752i −1.81758 2.74351i
\(659\) 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 \(0.613455\pi\)
\(662\) 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
\(672\) −26.6257 + 17.6396i −1.02711 + 0.680461i
\(673\) 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 0.676882 0.736092i \(-0.263331\pi\)
−0.736092 + 0.676882i \(0.763331\pi\)
\(678\) 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 \(-0.937302\pi\)
0.980664 0.195700i \(-0.0626980\pi\)
\(692\) 17.0182 + 17.0182i 0.646937 + 0.646937i
\(693\) 3.22637 2.13747i 0.122560 0.0811959i
\(694\) 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
\(707\) 33.8389 22.4183i 1.27264 0.843126i
\(708\) 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 \(-0.500045\pi\)
−0.000142099 1.00000i \(0.500045\pi\)
\(720\) 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 \(0.0196352\pi\)
0.0616465 + 0.998098i \(0.480365\pi\)
\(728\) 14.1523 + 21.3619i 0.524519 + 0.791726i
\(729\) 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 −0.994719 0.102636i \(-0.967272\pi\)
0.102636 + 0.994719i \(0.467272\pi\)
\(734\) 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
\(742\) −2.96184 4.47070i −0.108733 0.164125i
\(743\) 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 \(0.219581\pi\)
−0.771351 + 0.636410i \(0.780419\pi\)
\(762\) −20.6922 20.6922i −0.749599 0.749599i
\(763\) −16.4228 + 10.8801i −0.594547 + 0.393887i
\(764\) 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 \(-0.547052\pi\)
−0.147279 + 0.989095i \(0.547052\pi\)
\(770\) 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 −0.750832 0.660494i \(-0.770347\pi\)
0.660494 + 0.750832i \(0.270347\pi\)
\(774\) 19.3061i 0.693944i
\(775\) 0 0
\(776\) 94.7776i 3.40232i
\(777\) −7.03574 + 4.66118i −0.252406 + 0.167219i
\(778\) −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