Properties

Label 105.2.m.a.97.1
Level 105
Weight 2
Character 105.97
Analytic conductor 0.838
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 105.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
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: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.1
Root \(-0.517174 - 1.31626i\)
Character \(\chi\) = 105.97
Dual form 105.2.m.a.13.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.86147 - 1.86147i) q^{2} +(-0.707107 - 0.707107i) q^{3} +4.93012i q^{4} +(-1.50619 + 1.65269i) q^{5} +2.63251i q^{6} +(-2.20563 + 1.46123i) q^{7} +(5.45433 - 5.45433i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.86147 - 1.86147i) q^{2} +(-0.707107 - 0.707107i) q^{3} +4.93012i q^{4} +(-1.50619 + 1.65269i) q^{5} +2.63251i q^{6} +(-2.20563 + 1.46123i) q^{7} +(5.45433 - 5.45433i) q^{8} +1.00000i q^{9} +(5.88016 - 0.272713i) q^{10} -1.46279 q^{11} +(3.48612 - 3.48612i) q^{12} +(0.887844 + 0.887844i) q^{13} +(6.82574 + 1.38567i) q^{14} +(2.23367 - 0.103594i) q^{15} -10.4459 q^{16} +(-2.10614 + 2.10614i) q^{17} +(1.86147 - 1.86147i) q^{18} -3.95987 q^{19} +(-8.14798 - 7.42570i) q^{20} +(2.59286 + 0.526369i) q^{21} +(2.72294 + 2.72294i) q^{22} +(-4.13007 + 4.13007i) q^{23} -7.71359 q^{24} +(-0.462789 - 4.97854i) q^{25} -3.30539i q^{26} +(0.707107 - 0.707107i) q^{27} +(-7.20405 - 10.8740i) q^{28} +5.18572i q^{29} +(-4.35074 - 3.96506i) q^{30} -6.10346i q^{31} +(8.53599 + 8.53599i) q^{32} +(1.03435 + 1.03435i) q^{33} +7.84104 q^{34} +(0.907129 - 5.84612i) q^{35} -4.93012 q^{36} +(2.25560 + 2.25560i) q^{37} +(7.37117 + 7.37117i) q^{38} -1.25560i q^{39} +(0.799082 + 17.2296i) q^{40} +0.769968i q^{41} +(-3.84671 - 5.80635i) q^{42} +(-5.18572 + 5.18572i) q^{43} -7.21173i q^{44} +(-1.65269 - 1.50619i) q^{45} +15.3760 q^{46} +(8.57041 - 8.57041i) q^{47} +(7.38635 + 7.38635i) q^{48} +(2.72961 - 6.44587i) q^{49} +(-8.40592 + 10.1289i) q^{50} +2.97854 q^{51} +(-4.37718 + 4.37718i) q^{52} +(-0.544449 + 0.544449i) q^{53} -2.63251 q^{54} +(2.20324 - 2.41754i) q^{55} +(-4.06020 + 20.0003i) q^{56} +(2.80005 + 2.80005i) q^{57} +(9.65306 - 9.65306i) q^{58} -3.19633 q^{59} +(0.510732 + 11.0123i) q^{60} +1.42064i q^{61} +(-11.3614 + 11.3614i) q^{62} +(-1.46123 - 2.20563i) q^{63} -10.8872i q^{64} +(-2.80460 + 0.130073i) q^{65} -3.85081i q^{66} +(-5.93012 - 5.93012i) q^{67} +(-10.3835 - 10.3835i) q^{68} +5.84081 q^{69} +(-12.5710 + 9.19377i) q^{70} +7.62611 q^{71} +(5.45433 + 5.45433i) q^{72} +(6.81378 + 6.81378i) q^{73} -8.39746i q^{74} +(-3.19312 + 3.84760i) q^{75} -19.5226i q^{76} +(3.22637 - 2.13747i) q^{77} +(-2.33726 + 2.33726i) q^{78} +4.52029i q^{79} +(15.7335 - 17.2638i) q^{80} -1.00000 q^{81} +(1.43327 - 1.43327i) q^{82} +(-6.75794 - 6.75794i) q^{83} +(-2.59507 + 12.7831i) q^{84} +(-0.308559 - 6.65306i) q^{85} +19.3061 q^{86} +(3.66686 - 3.66686i) q^{87} +(-7.97854 + 7.97854i) q^{88} +1.19991 q^{89} +(0.272713 + 5.88016i) q^{90} +(-3.25560 - 0.660910i) q^{91} +(-20.3618 - 20.3618i) q^{92} +(-4.31580 + 4.31580i) q^{93} -31.9071 q^{94} +(5.96431 - 6.54445i) q^{95} -12.0717i q^{96} +(-8.68829 + 8.68829i) q^{97} +(-17.0799 + 6.91770i) q^{98} -1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} + 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} + 24q^{8} - 16q^{11} + 8q^{15} - 48q^{16} + 8q^{21} - 16q^{22} - 40q^{23} + 24q^{28} - 8q^{30} + 48q^{32} - 8q^{35} - 16q^{36} + 32q^{37} - 16q^{42} - 16q^{43} + 64q^{46} - 72q^{50} - 16q^{51} + 24q^{53} + 24q^{56} + 8q^{57} + 32q^{58} + 40q^{60} + 8q^{63} + 40q^{65} - 32q^{67} - 40q^{70} + 64q^{71} + 24q^{72} - 24q^{77} - 8q^{78} - 16q^{81} + 48q^{85} + 64q^{86} - 64q^{88} - 48q^{91} - 40q^{92} + 24q^{93} - 72q^{95} - 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

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 −0.916715 0.399541i \(-0.869169\pi\)
−0.399541 0.916715i \(-0.630831\pi\)
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 4.93012i 2.46506i
\(5\) −1.50619 + 1.65269i −0.673588 + 0.739107i
\(6\) 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
\(10\) 5.88016 0.272713i 1.85947 0.0862394i
\(11\) −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 \(-0.194292\pi\)
−0.573183 + 0.819427i \(0.694292\pi\)
\(14\) 6.82574 + 1.38567i 1.82426 + 0.370337i
\(15\) 2.23367 0.103594i 0.576730 0.0267479i
\(16\) −10.4459 −2.61147
\(17\) −2.10614 + 2.10614i −0.510815 + 0.510815i −0.914776 0.403961i \(-0.867633\pi\)
0.403961 + 0.914776i \(0.367633\pi\)
\(18\) 1.86147 1.86147i 0.438752 0.438752i
\(19\) −3.95987 −0.908456 −0.454228 0.890885i \(-0.650085\pi\)
−0.454228 + 0.890885i \(0.650085\pi\)
\(20\) −8.14798 7.42570i −1.82194 1.66044i
\(21\) 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 \(-0.958407\pi\)
0.130295 + 0.991475i \(0.458407\pi\)
\(24\) −7.71359 −1.57453
\(25\) −0.462789 4.97854i −0.0925579 0.995707i
\(26\) 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 \(0.159901\pi\)
−0.876456 + 0.481482i \(0.840099\pi\)
\(30\) −4.35074 3.96506i −0.794332 0.723918i
\(31\) 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
\(35\) 0.907129 5.84612i 0.153333 0.988175i
\(36\) −4.93012 −0.821687
\(37\) 2.25560 + 2.25560i 0.370819 + 0.370819i 0.867775 0.496957i \(-0.165549\pi\)
−0.496957 + 0.867775i \(0.665549\pi\)
\(38\) 7.37117 + 7.37117i 1.19576 + 1.19576i
\(39\) 1.25560i 0.201057i
\(40\) 0.799082 + 17.2296i 0.126346 + 2.72424i
\(41\) 0.769968i 0.120249i 0.998191 + 0.0601244i \(0.0191497\pi\)
−0.998191 + 0.0601244i \(0.980850\pi\)
\(42\) −3.84671 5.80635i −0.593560 0.895939i
\(43\) −5.18572 + 5.18572i −0.790816 + 0.790816i −0.981627 0.190811i \(-0.938888\pi\)
0.190811 + 0.981627i \(0.438888\pi\)
\(44\) 7.21173i 1.08721i
\(45\) −1.65269 1.50619i −0.246369 0.224529i
\(46\) 15.3760 2.26707
\(47\) 8.57041 8.57041i 1.25012 1.25012i 0.294459 0.955664i \(-0.404861\pi\)
0.955664 0.294459i \(-0.0951394\pi\)
\(48\) 7.38635 + 7.38635i 1.06613 + 1.06613i
\(49\) 2.72961 6.44587i 0.389944 0.920839i
\(50\) −8.40592 + 10.1289i −1.18878 + 1.43244i
\(51\) 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 \(-0.766841\pi\)
0.668724 + 0.743510i \(0.266841\pi\)
\(54\) −2.63251 −0.358240
\(55\) 2.20324 2.41754i 0.297084 0.325981i
\(56\) −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 \(0.566716\pi\)
\(60\) 0.510732 + 11.0123i 0.0659352 + 1.42168i
\(61\) 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
\(63\) −1.46123 2.20563i −0.184098 0.277883i
\(64\) 10.8872i 1.36090i
\(65\) −2.80460 + 0.130073i −0.347867 + 0.0161336i
\(66\) 3.85081i 0.474002i
\(67\) −5.93012 5.93012i −0.724480 0.724480i 0.245034 0.969514i \(-0.421201\pi\)
−0.969514 + 0.245034i \(0.921201\pi\)
\(68\) −10.3835 10.3835i −1.25919 1.25919i
\(69\) 5.84081 0.703150
\(70\) −12.5710 + 9.19377i −1.50252 + 1.09887i
\(71\) 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 \(-0.0592955\pi\)
−0.185207 + 0.982700i \(0.559296\pi\)
\(74\) 8.39746i 0.976185i
\(75\) −3.19312 + 3.84760i −0.368709 + 0.444282i
\(76\) 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 \(0.0818405\pi\)
−0.967129 + 0.254286i \(0.918159\pi\)
\(80\) 15.7335 17.2638i 1.75905 1.93015i
\(81\) −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 \(-0.425754\pi\)
−0.972921 + 0.231140i \(0.925754\pi\)
\(84\) −2.59507 + 12.7831i −0.283145 + 1.39475i
\(85\) −0.308559 6.65306i −0.0334679 0.721626i
\(86\) 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 \(0.479743\pi\)
\(90\) 0.272713 + 5.88016i 0.0287465 + 0.619823i
\(91\) −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
\(95\) 5.96431 6.54445i 0.611925 0.671446i
\(96\) 12.0717i 1.23206i
\(97\) −8.68829 + 8.68829i −0.882162 + 0.882162i −0.993754 0.111592i \(-0.964405\pi\)
0.111592 + 0.993754i \(0.464405\pi\)
\(98\) −17.0799 + 6.91770i −1.72533 + 0.698794i
\(99\) 1.46279i 0.147016i
\(100\) 24.5448 2.28161i 2.45448 0.228161i
\(101\) 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 0.985903 0.167316i \(-0.0535099\pi\)
−0.167316 + 0.985903i \(0.553510\pi\)
\(104\) 9.68519 0.949711
\(105\) −4.77527 + 3.49239i −0.466018 + 0.340823i
\(106\) 2.02695 0.196875
\(107\) 4.39022 + 4.39022i 0.424418 + 0.424418i 0.886722 0.462303i \(-0.152977\pi\)
−0.462303 + 0.886722i \(0.652977\pi\)
\(108\) 3.48612 + 3.48612i 0.335452 + 0.335452i
\(109\) 7.44587i 0.713185i 0.934260 + 0.356593i \(0.116062\pi\)
−0.934260 + 0.356593i \(0.883938\pi\)
\(110\) −8.60143 + 0.398921i −0.820114 + 0.0380357i
\(111\) 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 \(-0.695864\pi\)
0.816586 + 0.577224i \(0.195864\pi\)
\(114\) 10.4244i 0.976335i
\(115\) −0.605073 13.0464i −0.0564233 1.21658i
\(116\) −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
\(120\) 11.6181 12.7482i 1.06058 1.16375i
\(121\) −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
\(125\) 8.92504 + 6.73377i 0.798280 + 0.602287i
\(126\) −1.38567 + 6.82574i −0.123446 + 0.608086i
\(127\) 7.86025 + 7.86025i 0.697484 + 0.697484i 0.963867 0.266383i \(-0.0858286\pi\)
−0.266383 + 0.963867i \(0.585829\pi\)
\(128\) −3.19418 + 3.19418i −0.282329 + 0.282329i
\(129\) 7.33372 0.645698
\(130\) 5.46279 + 4.97854i 0.479118 + 0.436647i
\(131\) 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
\(133\) 8.73401 5.78628i 0.757334 0.501735i
\(134\) 22.0775i 1.90720i
\(135\) 0.103594 + 2.23367i 0.00891596 + 0.192243i
\(136\) 22.9752i 1.97011i
\(137\) 9.05565 + 9.05565i 0.773677 + 0.773677i 0.978747 0.205071i \(-0.0657424\pi\)
−0.205071 + 0.978747i \(0.565742\pi\)
\(138\) −10.8725 10.8725i −0.925526 0.925526i
\(139\) −11.9913 −1.01709 −0.508544 0.861036i \(-0.669816\pi\)
−0.508544 + 0.861036i \(0.669816\pi\)
\(140\) 28.8221 + 4.47226i 2.43591 + 0.377975i
\(141\) −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
\(145\) −8.57041 7.81068i −0.711734 0.648642i
\(146\) 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 \(-0.998738\pi\)
0.999992 0.00396615i \(-0.00126247\pi\)
\(150\) 13.1061 1.21830i 1.07011 0.0994737i
\(151\) −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
\(155\) 10.0871 + 9.19296i 0.810219 + 0.738397i
\(156\) 6.19027 0.495618
\(157\) 1.64757 1.64757i 0.131491 0.131491i −0.638298 0.769789i \(-0.720361\pi\)
0.769789 + 0.638298i \(0.220361\pi\)
\(158\) 8.41438 8.41438i 0.669412 0.669412i
\(159\) 0.769968 0.0610624
\(160\) −26.9642 + 1.25056i −2.13171 + 0.0988653i
\(161\) 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 \(-0.942692\pi\)
0.179066 + 0.983837i \(0.442692\pi\)
\(164\) −3.79604 −0.296421
\(165\) −3.26738 + 0.151536i −0.254366 + 0.0117971i
\(166\) 25.1594i 1.95275i
\(167\) 0.293008 0.293008i 0.0226737 0.0226737i −0.695679 0.718353i \(-0.744896\pi\)
0.718353 + 0.695679i \(0.244896\pi\)
\(168\) 17.0133 11.2713i 1.31261 0.869602i
\(169\) 11.4235i 0.878728i
\(170\) −11.8101 + 12.9588i −0.905792 + 0.993897i
\(171\) 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 \(-0.309415\pi\)
−0.826046 + 0.563603i \(0.809415\pi\)
\(174\) −13.6515 −1.03492
\(175\) 8.29554 + 10.3046i 0.627084 + 0.778952i
\(176\) 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 \(-0.976215\pi\)
0.997210 0.0746523i \(-0.0237847\pi\)
\(180\) 7.42570 8.14798i 0.553479 0.607315i
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 4.82993 + 7.29046i 0.358019 + 0.540405i
\(183\) 1.00454 1.00454i 0.0742581 0.0742581i
\(184\) 45.0536i 3.32139i
\(185\) −7.12518 + 0.330455i −0.523854 + 0.0242955i
\(186\) 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
\(190\) −23.2847 + 1.07991i −1.68925 + 0.0783447i
\(191\) −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 \(-0.507490\pi\)
0.999723 + 0.0235293i \(0.00749029\pi\)
\(194\) 32.3459 2.32230
\(195\) 2.07512 + 1.89117i 0.148603 + 0.135430i
\(196\) 31.7789 + 13.4573i 2.26992 + 0.961236i
\(197\) −11.4791 11.4791i −0.817853 0.817853i 0.167943 0.985797i \(-0.446287\pi\)
−0.985797 + 0.167943i \(0.946287\pi\)
\(198\) −2.72294 + 2.72294i −0.193511 + 0.193511i
\(199\) 20.1468 1.42817 0.714084 0.700061i \(-0.246844\pi\)
0.714084 + 0.700061i \(0.246844\pi\)
\(200\) −29.6788 24.6304i −2.09861 1.74163i
\(201\) 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
\(205\) −1.27252 1.15972i −0.0888767 0.0809981i
\(206\) 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
\(210\) 15.3900 + 2.38803i 1.06201 + 0.164790i
\(211\) 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
\(215\) −0.759730 16.3811i −0.0518132 1.11718i
\(216\) 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
\(220\) 11.9188 + 10.8622i 0.803564 + 0.732332i
\(221\) −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 \(-0.259963\pi\)
−0.728889 + 0.684632i \(0.759963\pi\)
\(224\) −31.3003 6.35418i −2.09134 0.424557i
\(225\) 4.97854 0.462789i 0.331902 0.0308526i
\(226\) −9.47282 −0.630123
\(227\) −17.3487 + 17.3487i −1.15147 + 1.15147i −0.165216 + 0.986257i \(0.552832\pi\)
−0.986257 + 0.165216i \(0.947168\pi\)
\(228\) −13.8046 + 13.8046i −0.914232 + 0.914232i
\(229\) −25.0782 −1.65721 −0.828607 0.559831i \(-0.810866\pi\)
−0.828607 + 0.559831i \(0.810866\pi\)
\(230\) −23.1592 + 25.4118i −1.52707 + 1.67560i
\(231\) −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 \(-0.716890\pi\)
0.776704 + 0.629866i \(0.216890\pi\)
\(234\) 3.30539 0.216080
\(235\) 1.25560 + 27.0729i 0.0819064 + 1.76604i
\(236\) 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 \(-0.757003\pi\)
0.722492 0.691380i \(-0.242997\pi\)
\(240\) −23.3326 + 1.08213i −1.50611 + 0.0698512i
\(241\) 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
\(245\) 6.54174 + 14.2199i 0.417937 + 0.908476i
\(246\) −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
\(250\) −4.07899 29.1484i −0.257978 1.84350i
\(251\) 16.3443i 1.03164i 0.856696 + 0.515822i \(0.172513\pi\)
−0.856696 + 0.515822i \(0.827487\pi\)
\(252\) 10.8740 7.20405i 0.684999 0.453813i
\(253\) 6.04143 6.04143i 0.379821 0.379821i
\(254\) 29.2632i 1.83614i
\(255\) −4.48624 + 4.92261i −0.280939 + 0.308266i
\(256\) −9.88265 −0.617666
\(257\) 21.3054 21.3054i 1.32900 1.32900i 0.422749 0.906247i \(-0.361065\pi\)
0.906247 0.422749i \(-0.138935\pi\)
\(258\) −13.6515 13.6515i −0.849904 0.849904i
\(259\) −8.27098 1.67907i −0.513933 0.104332i
\(260\) −0.641275 13.8270i −0.0397702 0.857514i
\(261\) −5.18572 −0.320988
\(262\) 11.5079 11.5079i 0.710960 0.710960i
\(263\) −16.3449 + 16.3449i −1.00787 + 1.00787i −0.00789784 + 0.999969i \(0.502514\pi\)
−0.999969 + 0.00789784i \(0.997486\pi\)
\(264\) 11.2834 0.694442
\(265\) −0.0797641 1.71985i −0.00489987 0.105650i
\(266\) −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 \(0.668789\pi\)
\(270\) 3.96506 4.35074i 0.241306 0.264777i
\(271\) 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
\(273\) 1.83472 + 2.76939i 0.111043 + 0.167611i
\(274\) 33.7136i 2.03671i
\(275\) 0.676964 + 7.28255i 0.0408224 + 0.439154i
\(276\) 28.7959i 1.73331i
\(277\) 21.3107 + 21.3107i 1.28043 + 1.28043i 0.940421 + 0.340013i \(0.110431\pi\)
0.340013 + 0.940421i \(0.389569\pi\)
\(278\) 22.3214 + 22.3214i 1.33875 + 1.33875i
\(279\) 6.10346 0.365405
\(280\) −26.9389 36.8344i −1.60991 2.20128i
\(281\) −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 \(-0.214407\pi\)
−0.623788 + 0.781594i \(0.714407\pi\)
\(284\) 37.5977i 2.23101i
\(285\) −8.84503 + 0.410219i −0.523934 + 0.0242993i
\(286\) 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
\(290\) 1.41421 + 30.4929i 0.0830455 + 1.79060i
\(291\) 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 \(-0.270621\pi\)
−0.751400 + 0.659847i \(0.770621\pi\)
\(294\) 16.9688 + 7.18572i 0.989643 + 0.419080i
\(295\) 4.81428 5.28255i 0.280298 0.307562i
\(296\) 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
\(300\) −18.9691 15.7425i −1.09518 0.908891i
\(301\) 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
\(305\) −2.34788 2.13975i −0.134439 0.122522i
\(306\) 7.84104i 0.448242i
\(307\) −17.3551 + 17.3551i −0.990510 + 0.990510i −0.999955 0.00944588i \(-0.996993\pi\)
0.00944588 + 0.999955i \(0.496993\pi\)
\(308\) 10.5380 + 15.9064i 0.600459 + 0.906352i
\(309\) 11.7489i 0.668374i
\(310\) −1.66449 35.8893i −0.0945368 2.03838i
\(311\) 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 0.850129 0.526575i \(-0.176524\pi\)
−0.526575 + 0.850129i \(0.676524\pi\)
\(314\) −6.13381 −0.346151
\(315\) 5.84612 + 0.907129i 0.329392 + 0.0511109i
\(316\) −22.2856 −1.25366
\(317\) 0.752579 + 0.752579i 0.0422691 + 0.0422691i 0.727925 0.685656i \(-0.240485\pi\)
−0.685656 + 0.727925i \(0.740485\pi\)
\(318\) −1.43327 1.43327i −0.0803738 0.0803738i
\(319\) 7.58562i 0.424713i
\(320\) 17.9932 + 16.3982i 1.00585 + 0.916686i
\(321\) 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
\(325\) 4.00928 4.83105i 0.222395 0.267978i
\(326\) 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
\(330\) 6.36421 + 5.80005i 0.350338 + 0.319282i
\(331\) 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
\(335\) 18.7326 0.868788i 1.02347 0.0474670i
\(336\) −27.0847 5.49839i −1.47759 0.299962i
\(337\) −20.0460 20.0460i −1.09197 1.09197i −0.995318 0.0966558i \(-0.969185\pi\)
−0.0966558 0.995318i \(-0.530815\pi\)
\(338\) −21.2644 + 21.2644i −1.15663 + 1.15663i
\(339\) −3.59839 −0.195438
\(340\) 32.8004 1.52123i 1.77885 0.0825005i
\(341\) 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
\(345\) −8.79736 + 9.65306i −0.473634 + 0.519703i
\(346\) 12.8512i 0.690883i
\(347\) −20.0847 20.0847i −1.07820 1.07820i −0.996671 0.0815328i \(-0.974018\pi\)
−0.0815328 0.996671i \(-0.525982\pi\)
\(348\) 18.0781 + 18.0781i 0.969087 + 0.969087i
\(349\) 14.7663 0.790420 0.395210 0.918591i \(-0.370672\pi\)
0.395210 + 0.918591i \(0.370672\pi\)
\(350\) 3.73975 34.6235i 0.199898 1.85070i
\(351\) 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 \(-0.405757\pi\)
−0.956490 + 0.291766i \(0.905757\pi\)
\(354\) 8.41438i 0.447219i
\(355\) −11.4864 + 12.6036i −0.609633 + 0.668931i
\(356\) 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 \(-0.910306\pi\)
0.960562 0.278066i \(-0.0896935\pi\)
\(360\) −17.2296 + 0.799082i −0.908079 + 0.0421153i
\(361\) −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
\(365\) −21.5239 + 0.998247i −1.12661 + 0.0522507i
\(366\) −3.73985 −0.195485
\(367\) 11.1910 11.1910i 0.584163 0.584163i −0.351881 0.936045i \(-0.614458\pi\)
0.936045 + 0.351881i \(0.114458\pi\)
\(368\) 43.1422 43.1422i 2.24894 2.24894i
\(369\) −0.769968 −0.0400829
\(370\) 13.8784 + 12.6482i 0.721505 + 0.657546i
\(371\) 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 \(-0.532042\pi\)
0.994938 + 0.100492i \(0.0320416\pi\)
\(374\) −11.4698 −0.593088
\(375\) −1.54946 11.0725i −0.0800140 0.571779i
\(376\) 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 \(0.149515\pi\)
−0.891697 + 0.452634i \(0.850485\pi\)
\(380\) 32.2649 + 29.4048i 1.65516 + 1.50843i
\(381\) 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 \(-0.0520295\pi\)
−0.162729 + 0.986671i \(0.552030\pi\)
\(384\) 4.51726 0.230520
\(385\) −1.32694 + 8.55164i −0.0676270 + 0.435832i
\(386\) −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 \(0.127674\pi\)
−0.920632 + 0.390432i \(0.872326\pi\)
\(390\) −0.342419 7.38313i −0.0173390 0.373859i
\(391\) 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
\(395\) −7.47066 6.80841i −0.375889 0.342568i
\(396\) 7.21173 0.362403
\(397\) 16.1781 16.1781i 0.811955 0.811955i −0.172972 0.984927i \(-0.555337\pi\)
0.984927 + 0.172972i \(0.0553370\pi\)
\(398\) −37.5026 37.5026i −1.87983 1.87983i
\(399\) −10.2674 2.08435i −0.514013 0.104348i
\(400\) 4.83424 + 52.0051i 0.241712 + 2.60026i
\(401\) −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
\(405\) 1.50619 1.65269i 0.0748431 0.0821230i
\(406\) −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 \(0.294688\pi\)
\(410\) 0.209980 + 4.52753i 0.0103702 + 0.223599i
\(411\) 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
\(415\) 21.3475 0.990067i 1.04791 0.0486005i
\(416\) 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 \(0.372280\pi\)
\(420\) −17.2179 23.5427i −0.840149 1.14876i
\(421\) 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
\(425\) 11.4602 + 9.51081i 0.555902 + 0.461342i
\(426\) 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
\(430\) −29.0787 + 31.9071i −1.40230 + 1.53870i
\(431\) 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 −0.889520 0.456896i \(-0.848961\pi\)
−0.456896 0.889520i \(-0.651039\pi\)
\(434\) 8.45741 41.6606i 0.405968 1.99978i
\(435\) 0.537211 + 11.5832i 0.0257573 + 0.555371i
\(436\) −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 \(0.517910\pi\)
\(440\) −1.16889 25.2033i −0.0557246 1.20152i
\(441\) 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 \(-0.808856\pi\)
0.565051 + 0.825056i \(0.308856\pi\)
\(444\) 15.7266 0.746352
\(445\) −1.80729 + 1.98308i −0.0856737 + 0.0940071i
\(446\) 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 \(-0.990984\pi\)
0.999599 0.0283205i \(-0.00901591\pi\)
\(450\) −10.1289 8.40592i −0.477479 0.396259i
\(451\) 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
\(455\) 5.99583 4.38505i 0.281089 0.205575i
\(456\) 30.5448 1.43039
\(457\) −21.0775 21.0775i −0.985962 0.985962i 0.0139406 0.999903i \(-0.495562\pi\)
−0.999903 + 0.0139406i \(0.995562\pi\)
\(458\) 46.6823 + 46.6823i 2.18132 + 2.18132i
\(459\) 2.97854i 0.139026i
\(460\) 64.3204 2.98308i 2.99896 0.139087i
\(461\) 21.9670i 1.02311i −0.859252 0.511553i \(-0.829071\pi\)
0.859252 0.511553i \(-0.170929\pi\)
\(462\) 5.62693 + 8.49347i 0.261788 + 0.395152i
\(463\) −21.6776 + 21.6776i −1.00744 + 1.00744i −0.00746987 + 0.999972i \(0.502378\pi\)
−0.999972 + 0.00746987i \(0.997622\pi\)
\(464\) 54.1694i 2.51475i
\(465\) −0.632282 13.6331i −0.0293214 0.632220i
\(466\) −8.34450 −0.386551
\(467\) 7.11299 7.11299i 0.329150 0.329150i −0.523113 0.852263i \(-0.675230\pi\)
0.852263 + 0.523113i \(0.175230\pi\)
\(468\) −4.37718 4.37718i −0.202335 0.202335i
\(469\) 21.7449 + 4.41438i 1.00409 + 0.203837i
\(470\) 48.0581 52.7326i 2.21676 2.43237i
\(471\) −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
\(475\) 1.83259 + 19.7144i 0.0840848 + 0.904557i
\(476\) 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 \(0.241416\pi\)
\(480\) 19.9508 + 18.1823i 0.910627 + 0.829904i
\(481\) 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
\(485\) −1.27287 27.4453i −0.0577981 1.24623i
\(486\) 2.63251i 0.119413i
\(487\) −4.81428 4.81428i −0.218156 0.218156i 0.589565 0.807721i \(-0.299299\pi\)
−0.807721 + 0.589565i \(0.799299\pi\)
\(488\) 7.74864 + 7.74864i 0.350765 + 0.350765i
\(489\) 14.5305 0.657092
\(490\) 14.2926 38.6471i 0.645676 1.74590i
\(491\) 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
\(495\) 2.41754 + 2.20324i 0.108660 + 0.0990282i
\(496\) 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 \(0.0241902\pi\)
−0.997114 + 0.0759227i \(0.975810\pi\)
\(500\) −33.1983 + 44.0016i −1.48467 + 1.96781i
\(501\) −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 \(-0.334582\pi\)
−0.867980 + 0.496599i \(0.834582\pi\)
\(504\) −20.0003 4.06020i −0.890883 0.180856i
\(505\) −25.3557 23.1080i −1.12831 1.02829i
\(506\) −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 \(0.831485\pi\)
\(510\) 17.5143 0.812285i 0.775545 0.0359686i
\(511\) −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
\(515\) −26.2432 + 1.21712i −1.15641 + 0.0536328i
\(516\) 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
\(520\) −14.5877 + 16.0066i −0.639714 + 0.701938i
\(521\) 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 0.950042 0.312121i \(-0.101040\pi\)
−0.312121 + 0.950042i \(0.601040\pi\)
\(524\) −30.4788 −1.33147
\(525\) 1.42060 13.1523i 0.0620001 0.574012i
\(526\) 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
\(530\) −3.05297 + 3.34993i −0.132613 + 0.145511i
\(531\) 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
\(535\) −13.8682 + 0.643185i −0.599574 + 0.0278073i
\(536\) −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
\(540\) −11.0123 + 0.510732i −0.473892 + 0.0219784i
\(541\) 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
\(545\) −12.3057 11.2149i −0.527120 0.480393i
\(546\) 1.73985 8.57041i 0.0744589 0.366780i
\(547\) −7.22715 7.22715i −0.309011 0.309011i 0.535515 0.844526i \(-0.320118\pi\)
−0.844526 + 0.535515i \(0.820118\pi\)
\(548\) −44.6455 + 44.6455i −1.90716 + 1.90716i
\(549\) −1.42064 −0.0606315
\(550\) 12.2961 14.8164i 0.524307 0.631772i
\(551\) 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
\(555\) 5.27193 + 4.80460i 0.223781 + 0.203944i
\(556\) 59.1185i 2.50718i
\(557\) −0.558927 0.558927i −0.0236825 0.0236825i 0.695166 0.718849i \(-0.255331\pi\)
−0.718849 + 0.695166i \(0.755331\pi\)
\(558\) −11.3614 11.3614i −0.480966 0.480966i
\(559\) −9.20823 −0.389467
\(560\) −9.47575 + 61.0678i −0.400423 + 2.58059i
\(561\) −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 \(-0.243336\pi\)
−0.692149 + 0.721755i \(0.743336\pi\)
\(564\) 59.7550i 2.51614i
\(565\) 0.372772 + 8.03762i 0.0156827 + 0.338145i
\(566\) 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 \(0.0653137\pi\)
−0.979023 + 0.203752i \(0.934686\pi\)
\(570\) 17.2283 + 15.7011i 0.721616 + 0.657648i
\(571\) −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
\(575\) 22.4731 + 18.6504i 0.937192 + 0.777774i
\(576\) 10.8872 0.453633
\(577\) −10.3510 + 10.3510i −0.430917 + 0.430917i −0.888940 0.458024i \(-0.848558\pi\)
0.458024 + 0.888940i \(0.348558\pi\)
\(578\) 15.1306 15.1306i 0.629350 0.629350i
\(579\) −19.1792 −0.797059
\(580\) 38.5076 42.2532i 1.59894 1.75447i
\(581\) 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
\(585\) −0.130073 2.80460i −0.00537785 0.115956i
\(586\) 5.83438i 0.241016i
\(587\) −21.1413 + 21.1413i −0.872594 + 0.872594i −0.992755 0.120160i \(-0.961659\pi\)
0.120160 + 0.992755i \(0.461659\pi\)
\(588\) −12.9554 31.9868i −0.534270 1.31912i
\(589\) 24.1689i 0.995862i
\(590\) −18.7949 + 0.871680i −0.773774 + 0.0358865i
\(591\) 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 \(-0.184108\pi\)
−0.546678 + 0.837343i \(0.684108\pi\)
\(594\) 3.85081 0.158001
\(595\) 10.4022 + 14.2233i 0.426450 + 0.583099i
\(596\) 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 \(-0.953413\pi\)
0.989309 0.145835i \(-0.0465869\pi\)
\(600\) 3.56977 + 38.4024i 0.145735 + 1.56777i
\(601\) 35.0829i 1.43106i 0.698580 + 0.715532i \(0.253815\pi\)
−0.698580 + 0.715532i \(0.746185\pi\)
\(602\) −42.5822 + 28.2107i −1.73552 + 1.14978i
\(603\) 5.93012 5.93012i 0.241493 0.241493i
\(604\) 66.3346i 2.69912i
\(605\) 13.3452 14.6433i 0.542560 0.595334i
\(606\) −40.3881 −1.64066
\(607\) −5.36385 + 5.36385i −0.217712 + 0.217712i −0.807533 0.589822i \(-0.799198\pi\)
0.589822 + 0.807533i \(0.299198\pi\)
\(608\) −33.8014 33.8014i −1.37083 1.37083i
\(609\) −2.72961 + 13.4459i −0.110609 + 0.544854i
\(610\) 0.387427 + 8.35359i 0.0156865 + 0.338227i
\(611\) 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 \(-0.846839\pi\)
0.462816 + 0.886454i \(0.346839\pi\)
\(614\) 64.6120 2.60753
\(615\) 0.0797641 + 1.71985i 0.00321640 + 0.0693511i
\(616\) 5.93921 29.2562i 0.239298 1.17877i
\(617\) 19.7986 + 19.7986i 0.797060 + 0.797060i 0.982631 0.185571i \(-0.0594135\pi\)
−0.185571 + 0.982631i \(0.559414\pi\)
\(618\) −21.8703 + 21.8703i −0.879752 + 0.879752i
\(619\) −12.0675 −0.485034 −0.242517 0.970147i \(-0.577973\pi\)
−0.242517 + 0.970147i \(0.577973\pi\)
\(620\) −45.3224 + 49.7309i −1.82019 + 1.99724i
\(621\) 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
\(625\) −24.5717 + 4.60803i −0.982866 + 0.184321i
\(626\) 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
\(630\) −9.19377 12.5710i −0.366289 0.500839i
\(631\) 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
\(635\) −24.8296 + 1.15156i −0.985332 + 0.0456982i
\(636\) 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
\(640\) −0.467961 10.0901i −0.0184978 0.398844i
\(641\) 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 \(-0.359685\pi\)
−0.904405 + 0.426675i \(0.859685\pi\)
\(644\) 74.6638 + 15.1573i 2.94217 + 0.597280i
\(645\) −11.0460 + 12.1204i −0.434935 + 0.477240i
\(646\) −31.0495 −1.22163
\(647\) −19.0978 + 19.0978i −0.750814 + 0.750814i −0.974631 0.223817i \(-0.928148\pi\)
0.223817 + 0.974631i \(0.428148\pi\)
\(648\) −5.45433 + 5.45433i −0.214266 + 0.214266i
\(649\) 4.67556 0.183532
\(650\) −16.4560 + 1.52970i −0.645457 + 0.0599997i
\(651\) 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 \(-0.559383\pi\)
0.982649 + 0.185476i \(0.0593826\pi\)
\(654\) −19.6013 −0.766473
\(655\) −10.2172 9.31151i −0.399220 0.363831i
\(656\) 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 \(0.210160\pi\)
−0.789847 + 0.613304i \(0.789840\pi\)
\(660\) −0.747093 16.1086i −0.0290806 0.627027i
\(661\) 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
\(665\) −3.59211 + 23.1499i −0.139296 + 0.897714i
\(666\) 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
\(670\) −36.4873 33.2528i −1.40963 1.28467i
\(671\) 2.07810i 0.0802241i
\(672\) 17.6396 + 26.6257i 0.680461 + 1.02711i
\(673\) −30.6900 + 30.6900i −1.18301 + 1.18301i −0.204055 + 0.978960i \(0.565412\pi\)
−0.978960 + 0.204055i \(0.934588\pi\)
\(674\) 74.6299i 2.87463i
\(675\) −3.84760 3.19312i −0.148094 0.122903i
\(676\) 56.3191 2.16612
\(677\) −1.54060 + 1.54060i −0.0592101 + 0.0592101i −0.736092 0.676882i \(-0.763331\pi\)
0.676882 + 0.736092i \(0.263331\pi\)
\(678\) 6.69830 + 6.69830i 0.257246 + 0.257246i
\(679\) 6.46755 31.8587i 0.248202 1.22263i
\(680\) −37.9710 34.6050i −1.45612 1.32704i
\(681\) 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 \(-0.624332\pi\)
0.924680 + 0.380744i \(0.124332\pi\)
\(684\) 19.5226 0.746467
\(685\) −28.6057 + 1.32669i −1.09297 + 0.0506903i
\(686\) 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
\(690\) 34.3449 1.59286i 1.30749 0.0606392i
\(691\) 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
\(693\) 2.13747 + 3.22637i 0.0811959 + 0.122560i
\(694\) 74.7741i 2.83838i
\(695\) 18.0611 19.8179i 0.685098 0.751736i
\(696\) 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
\(700\) −50.8028 + 40.8980i −1.92016 + 1.54580i
\(701\) −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
\(705\) 18.2556 20.0313i 0.687546 0.754422i
\(706\) 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 \(-0.995111\pi\)
0.999882 0.0153599i \(-0.00488939\pi\)
\(710\) 44.8427 2.07974i 1.68292 0.0780512i
\(711\) −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
\(715\) 4.10253 0.190269i 0.153426 0.00711567i
\(716\) 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 \(0.499955\pi\)
\(720\) 17.2638 + 15.7335i 0.643385 + 0.586351i
\(721\) −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
\(725\) 25.8173 2.39990i 0.958831 0.0891300i
\(726\) 23.3247i 0.865661i
\(727\) 28.5738 28.5738i 1.05974 1.05974i 0.0616465 0.998098i \(-0.480365\pi\)
0.998098 0.0616465i \(-0.0196352\pi\)
\(728\) −21.3619 + 14.1523i −0.791726 + 0.524519i
\(729\) 1.00000i 0.0370370i
\(730\) 41.9243 + 38.2079i 1.55169 + 1.41414i
\(731\) 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 \(-0.467272\pi\)
−0.994719 + 0.102636i \(0.967272\pi\)
\(734\) −41.6632 −1.53782
\(735\) 5.42928 14.6807i 0.200262 0.541506i
\(736\) −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 \(-0.754053\pi\)
0.716052 0.698047i \(-0.245947\pi\)
\(740\) −1.62918 35.1280i −0.0598900 1.29133i
\(741\) 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 \(-0.912183\pi\)
0.272400 + 0.962184i \(0.412183\pi\)
\(744\) 47.0796i 1.72602i
\(745\) 0.160024 + 0.145838i 0.00586282 + 0.00534311i
\(746\) −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
\(750\) −17.7267 + 23.4953i −0.647289 + 0.857927i
\(751\) 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
\(755\) 20.2657 22.2369i 0.737545 0.809284i
\(756\) −12.7831 2.59507i −0.464918 0.0943816i
\(757\) 3.14514 + 3.14514i 0.114312 + 0.114312i 0.761949 0.647637i \(-0.224243\pi\)
−0.647637 + 0.761949i \(0.724243\pi\)
\(758\) 32.8059 32.8059i 1.19156 1.19156i
\(759\) −8.54387 −0.310123
\(760\) −3.16426 68.2269i −0.114780 2.47485i
\(761\) 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
\(763\) −10.8801 16.4228i −0.393887 0.594547i
\(764\) 38.6238i 1.39736i
\(765\) 6.65306 0.308559i 0.240542 0.0111560i
\(766\) 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 \(0.452948\pi\)
\(770\) 18.3887 13.4486i 0.662681 0.484652i
\(771\) −30.1304 −1.08512
\(772\) 66.8609 + 66.8609i 2.40638 + 2.40638i
\(773\) −2.51166 2.51166i −0.0903382