Properties

Label 731.2.e.a.307.17
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.17
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.17

$q$-expansion

\(f(q)\) \(=\) \(q+0.469159 q^{2} +(1.22299 - 2.11828i) q^{3} -1.77989 q^{4} +(-1.20485 + 2.08687i) q^{5} +(0.573775 - 0.993808i) q^{6} +(1.21565 + 2.10557i) q^{7} -1.77337 q^{8} +(-1.49139 - 2.58317i) q^{9} +O(q^{10})\) \(q+0.469159 q^{2} +(1.22299 - 2.11828i) q^{3} -1.77989 q^{4} +(-1.20485 + 2.08687i) q^{5} +(0.573775 - 0.993808i) q^{6} +(1.21565 + 2.10557i) q^{7} -1.77337 q^{8} +(-1.49139 - 2.58317i) q^{9} +(-0.565268 + 0.979072i) q^{10} +5.54536 q^{11} +(-2.17678 + 3.77030i) q^{12} +(0.602228 + 1.04309i) q^{13} +(0.570332 + 0.987844i) q^{14} +(2.94704 + 5.10443i) q^{15} +2.72779 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.699701 - 1.21192i) q^{18} +(-0.840542 + 1.45586i) q^{19} +(2.14451 - 3.71440i) q^{20} +5.94689 q^{21} +2.60165 q^{22} +(4.22810 - 7.32328i) q^{23} +(-2.16881 + 3.75648i) q^{24} +(-0.403346 - 0.698616i) q^{25} +(0.282540 + 0.489374i) q^{26} +0.0420982 q^{27} +(-2.16372 - 3.74767i) q^{28} +(1.18338 + 2.04967i) q^{29} +(1.38263 + 2.39479i) q^{30} +(1.47298 - 2.55127i) q^{31} +4.82650 q^{32} +(6.78191 - 11.7466i) q^{33} +(0.234579 + 0.406303i) q^{34} -5.85872 q^{35} +(2.65452 + 4.59776i) q^{36} +(-5.14856 + 8.91757i) q^{37} +(-0.394348 + 0.683030i) q^{38} +2.94607 q^{39} +(2.13665 - 3.70079i) q^{40} -8.54362 q^{41} +2.79004 q^{42} +(6.14525 + 2.28821i) q^{43} -9.87013 q^{44} +7.18765 q^{45} +(1.98365 - 3.43578i) q^{46} +0.538653 q^{47} +(3.33605 - 5.77821i) q^{48} +(0.544396 - 0.942922i) q^{49} +(-0.189233 - 0.327762i) q^{50} +2.44597 q^{51} +(-1.07190 - 1.85658i) q^{52} +(-6.43981 + 11.1541i) q^{53} +0.0197508 q^{54} +(-6.68135 + 11.5724i) q^{55} +(-2.15579 - 3.73394i) q^{56} +(2.05594 + 3.56100i) q^{57} +(0.555193 + 0.961622i) q^{58} +8.86543 q^{59} +(-5.24541 - 9.08532i) q^{60} +(-3.02182 - 5.23394i) q^{61} +(0.691059 - 1.19695i) q^{62} +(3.62602 - 6.28046i) q^{63} -3.19118 q^{64} -2.90239 q^{65} +(3.18179 - 5.51102i) q^{66} +(3.11456 - 5.39458i) q^{67} +(-0.889945 - 1.54143i) q^{68} +(-10.3418 - 17.9125i) q^{69} -2.74867 q^{70} +(3.37073 + 5.83827i) q^{71} +(2.64479 + 4.58091i) q^{72} +(-3.31308 - 5.73843i) q^{73} +(-2.41549 + 4.18376i) q^{74} -1.97315 q^{75} +(1.49607 - 2.59127i) q^{76} +(6.74121 + 11.6761i) q^{77} +1.38217 q^{78} +(-3.85283 - 6.67329i) q^{79} +(-3.28659 + 5.69254i) q^{80} +(4.52567 - 7.83869i) q^{81} -4.00832 q^{82} +(0.342282 - 0.592849i) q^{83} -10.5848 q^{84} -2.40971 q^{85} +(2.88310 + 1.07354i) q^{86} +5.78903 q^{87} -9.83397 q^{88} +(1.77324 - 3.07133i) q^{89} +3.37215 q^{90} +(-1.46419 + 2.53606i) q^{91} +(-7.52555 + 13.0346i) q^{92} +(-3.60286 - 6.24034i) q^{93} +0.252714 q^{94} +(-2.02546 - 3.50820i) q^{95} +(5.90275 - 10.2239i) q^{96} -1.52535 q^{97} +(0.255408 - 0.442380i) q^{98} +(-8.27032 - 14.3246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.469159 0.331745 0.165873 0.986147i \(-0.446956\pi\)
0.165873 + 0.986147i \(0.446956\pi\)
\(3\) 1.22299 2.11828i 0.706092 1.22299i −0.260204 0.965554i \(-0.583790\pi\)
0.966296 0.257433i \(-0.0828768\pi\)
\(4\) −1.77989 −0.889945
\(5\) −1.20485 + 2.08687i −0.538827 + 0.933276i 0.460140 + 0.887846i \(0.347799\pi\)
−0.998968 + 0.0454297i \(0.985534\pi\)
\(6\) 0.573775 0.993808i 0.234243 0.405720i
\(7\) 1.21565 + 2.10557i 0.459472 + 0.795829i 0.998933 0.0461817i \(-0.0147053\pi\)
−0.539461 + 0.842011i \(0.681372\pi\)
\(8\) −1.77337 −0.626980
\(9\) −1.49139 2.58317i −0.497131 0.861057i
\(10\) −0.565268 + 0.979072i −0.178753 + 0.309610i
\(11\) 5.54536 1.67199 0.835995 0.548737i \(-0.184891\pi\)
0.835995 + 0.548737i \(0.184891\pi\)
\(12\) −2.17678 + 3.77030i −0.628383 + 1.08839i
\(13\) 0.602228 + 1.04309i 0.167028 + 0.289301i 0.937374 0.348326i \(-0.113250\pi\)
−0.770346 + 0.637627i \(0.779916\pi\)
\(14\) 0.570332 + 0.987844i 0.152428 + 0.264013i
\(15\) 2.94704 + 5.10443i 0.760923 + 1.31796i
\(16\) 2.72779 0.681947
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −0.699701 1.21192i −0.164921 0.285652i
\(19\) −0.840542 + 1.45586i −0.192834 + 0.333998i −0.946188 0.323617i \(-0.895101\pi\)
0.753355 + 0.657615i \(0.228434\pi\)
\(20\) 2.14451 3.71440i 0.479526 0.830564i
\(21\) 5.94689 1.29772
\(22\) 2.60165 0.554675
\(23\) 4.22810 7.32328i 0.881619 1.52701i 0.0320787 0.999485i \(-0.489787\pi\)
0.849540 0.527524i \(-0.176879\pi\)
\(24\) −2.16881 + 3.75648i −0.442706 + 0.766789i
\(25\) −0.403346 0.698616i −0.0806692 0.139723i
\(26\) 0.282540 + 0.489374i 0.0554107 + 0.0959742i
\(27\) 0.0420982 0.00810181
\(28\) −2.16372 3.74767i −0.408905 0.708244i
\(29\) 1.18338 + 2.04967i 0.219748 + 0.380615i 0.954731 0.297471i \(-0.0961431\pi\)
−0.734983 + 0.678086i \(0.762810\pi\)
\(30\) 1.38263 + 2.39479i 0.252433 + 0.437226i
\(31\) 1.47298 2.55127i 0.264554 0.458221i −0.702892 0.711296i \(-0.748109\pi\)
0.967447 + 0.253075i \(0.0814418\pi\)
\(32\) 4.82650 0.853213
\(33\) 6.78191 11.7466i 1.18058 2.04482i
\(34\) 0.234579 + 0.406303i 0.0402300 + 0.0696805i
\(35\) −5.85872 −0.990304
\(36\) 2.65452 + 4.59776i 0.442420 + 0.766293i
\(37\) −5.14856 + 8.91757i −0.846418 + 1.46604i 0.0379657 + 0.999279i \(0.487912\pi\)
−0.884384 + 0.466760i \(0.845421\pi\)
\(38\) −0.394348 + 0.683030i −0.0639717 + 0.110802i
\(39\) 2.94607 0.471748
\(40\) 2.13665 3.70079i 0.337834 0.585146i
\(41\) −8.54362 −1.33429 −0.667145 0.744928i \(-0.732484\pi\)
−0.667145 + 0.744928i \(0.732484\pi\)
\(42\) 2.79004 0.430512
\(43\) 6.14525 + 2.28821i 0.937142 + 0.348949i
\(44\) −9.87013 −1.48798
\(45\) 7.18765 1.07147
\(46\) 1.98365 3.43578i 0.292473 0.506578i
\(47\) 0.538653 0.0785707 0.0392853 0.999228i \(-0.487492\pi\)
0.0392853 + 0.999228i \(0.487492\pi\)
\(48\) 3.33605 5.77821i 0.481517 0.834013i
\(49\) 0.544396 0.942922i 0.0777709 0.134703i
\(50\) −0.189233 0.327762i −0.0267616 0.0463525i
\(51\) 2.44597 0.342505
\(52\) −1.07190 1.85658i −0.148646 0.257462i
\(53\) −6.43981 + 11.1541i −0.884577 + 1.53213i −0.0383783 + 0.999263i \(0.512219\pi\)
−0.846198 + 0.532868i \(0.821114\pi\)
\(54\) 0.0197508 0.00268774
\(55\) −6.68135 + 11.5724i −0.900913 + 1.56043i
\(56\) −2.15579 3.73394i −0.288080 0.498969i
\(57\) 2.05594 + 3.56100i 0.272317 + 0.471666i
\(58\) 0.555193 + 0.961622i 0.0729004 + 0.126267i
\(59\) 8.86543 1.15418 0.577090 0.816680i \(-0.304188\pi\)
0.577090 + 0.816680i \(0.304188\pi\)
\(60\) −5.24541 9.08532i −0.677180 1.17291i
\(61\) −3.02182 5.23394i −0.386904 0.670138i 0.605127 0.796129i \(-0.293122\pi\)
−0.992031 + 0.125991i \(0.959789\pi\)
\(62\) 0.691059 1.19695i 0.0877646 0.152013i
\(63\) 3.62602 6.28046i 0.456836 0.791263i
\(64\) −3.19118 −0.398898
\(65\) −2.90239 −0.359997
\(66\) 3.18179 5.51102i 0.391651 0.678360i
\(67\) 3.11456 5.39458i 0.380504 0.659053i −0.610630 0.791916i \(-0.709084\pi\)
0.991134 + 0.132863i \(0.0424171\pi\)
\(68\) −0.889945 1.54143i −0.107922 0.186926i
\(69\) −10.3418 17.9125i −1.24501 2.15642i
\(70\) −2.74867 −0.328529
\(71\) 3.37073 + 5.83827i 0.400032 + 0.692875i 0.993729 0.111813i \(-0.0356657\pi\)
−0.593697 + 0.804688i \(0.702332\pi\)
\(72\) 2.64479 + 4.58091i 0.311692 + 0.539866i
\(73\) −3.31308 5.73843i −0.387767 0.671632i 0.604382 0.796695i \(-0.293420\pi\)
−0.992149 + 0.125063i \(0.960087\pi\)
\(74\) −2.41549 + 4.18376i −0.280795 + 0.486352i
\(75\) −1.97315 −0.227840
\(76\) 1.49607 2.59127i 0.171611 0.297240i
\(77\) 6.74121 + 11.6761i 0.768232 + 1.33062i
\(78\) 1.38217 0.156500
\(79\) −3.85283 6.67329i −0.433477 0.750804i 0.563693 0.825984i \(-0.309380\pi\)
−0.997170 + 0.0751801i \(0.976047\pi\)
\(80\) −3.28659 + 5.69254i −0.367452 + 0.636445i
\(81\) 4.52567 7.83869i 0.502852 0.870965i
\(82\) −4.00832 −0.442644
\(83\) 0.342282 0.592849i 0.0375703 0.0650736i −0.846629 0.532184i \(-0.821372\pi\)
0.884199 + 0.467110i \(0.154705\pi\)
\(84\) −10.5848 −1.15490
\(85\) −2.40971 −0.261370
\(86\) 2.88310 + 1.07354i 0.310892 + 0.115762i
\(87\) 5.78903 0.620649
\(88\) −9.83397 −1.04830
\(89\) 1.77324 3.07133i 0.187963 0.325561i −0.756608 0.653869i \(-0.773145\pi\)
0.944571 + 0.328308i \(0.106478\pi\)
\(90\) 3.37215 0.355456
\(91\) −1.46419 + 2.53606i −0.153489 + 0.265851i
\(92\) −7.52555 + 13.0346i −0.784593 + 1.35895i
\(93\) −3.60286 6.24034i −0.373599 0.647093i
\(94\) 0.252714 0.0260654
\(95\) −2.02546 3.50820i −0.207808 0.359934i
\(96\) 5.90275 10.2239i 0.602447 1.04347i
\(97\) −1.52535 −0.154876 −0.0774380 0.996997i \(-0.524674\pi\)
−0.0774380 + 0.996997i \(0.524674\pi\)
\(98\) 0.255408 0.442380i 0.0258001 0.0446872i
\(99\) −8.27032 14.3246i −0.831199 1.43968i
\(100\) 0.717912 + 1.24346i 0.0717912 + 0.124346i
\(101\) 6.88312 + 11.9219i 0.684896 + 1.18627i 0.973470 + 0.228817i \(0.0734856\pi\)
−0.288574 + 0.957458i \(0.593181\pi\)
\(102\) 1.14755 0.113624
\(103\) −1.50457 2.60599i −0.148249 0.256775i 0.782331 0.622863i \(-0.214031\pi\)
−0.930581 + 0.366087i \(0.880697\pi\)
\(104\) −1.06797 1.84978i −0.104723 0.181386i
\(105\) −7.16513 + 12.4104i −0.699246 + 1.21113i
\(106\) −3.02130 + 5.23304i −0.293454 + 0.508277i
\(107\) 9.76720 0.944231 0.472115 0.881537i \(-0.343491\pi\)
0.472115 + 0.881537i \(0.343491\pi\)
\(108\) −0.0749302 −0.00721017
\(109\) −7.15752 + 12.3972i −0.685566 + 1.18743i 0.287693 + 0.957723i \(0.407112\pi\)
−0.973259 + 0.229712i \(0.926222\pi\)
\(110\) −3.13461 + 5.42931i −0.298874 + 0.517665i
\(111\) 12.5932 + 21.8121i 1.19530 + 2.07032i
\(112\) 3.31603 + 5.74354i 0.313336 + 0.542713i
\(113\) −15.0764 −1.41827 −0.709136 0.705072i \(-0.750915\pi\)
−0.709136 + 0.705072i \(0.750915\pi\)
\(114\) 0.964564 + 1.67067i 0.0903397 + 0.156473i
\(115\) 10.1885 + 17.6470i 0.950080 + 1.64559i
\(116\) −2.10629 3.64819i −0.195564 0.338726i
\(117\) 1.79632 3.11131i 0.166070 0.287641i
\(118\) 4.15929 0.382894
\(119\) −1.21565 + 2.10557i −0.111438 + 0.193017i
\(120\) −5.22619 9.05203i −0.477084 0.826333i
\(121\) 19.7510 1.79555
\(122\) −1.41771 2.45555i −0.128354 0.222315i
\(123\) −10.4487 + 18.0977i −0.942131 + 1.63182i
\(124\) −2.62173 + 4.54098i −0.235439 + 0.407792i
\(125\) −10.1046 −0.903787
\(126\) 1.70118 2.94653i 0.151553 0.262498i
\(127\) 2.61546 0.232084 0.116042 0.993244i \(-0.462979\pi\)
0.116042 + 0.993244i \(0.462979\pi\)
\(128\) −11.1502 −0.985546
\(129\) 12.3626 10.2189i 1.08847 0.899722i
\(130\) −1.36168 −0.119427
\(131\) −8.75682 −0.765087 −0.382544 0.923937i \(-0.624952\pi\)
−0.382544 + 0.923937i \(0.624952\pi\)
\(132\) −12.0710 + 20.9077i −1.05065 + 1.81978i
\(133\) −4.08722 −0.354407
\(134\) 1.46122 2.53091i 0.126231 0.218638i
\(135\) −0.0507222 + 0.0878535i −0.00436547 + 0.00756122i
\(136\) −0.886684 1.53578i −0.0760325 0.131692i
\(137\) −16.2222 −1.38596 −0.692978 0.720958i \(-0.743702\pi\)
−0.692978 + 0.720958i \(0.743702\pi\)
\(138\) −4.85195 8.40383i −0.413026 0.715381i
\(139\) 9.02148 15.6257i 0.765192 1.32535i −0.174953 0.984577i \(-0.555977\pi\)
0.940145 0.340775i \(-0.110689\pi\)
\(140\) 10.4279 0.881316
\(141\) 0.658766 1.14102i 0.0554781 0.0960909i
\(142\) 1.58141 + 2.73908i 0.132709 + 0.229858i
\(143\) 3.33957 + 5.78431i 0.279269 + 0.483708i
\(144\) −4.06821 7.04634i −0.339017 0.587195i
\(145\) −5.70320 −0.473625
\(146\) −1.55436 2.69223i −0.128640 0.222811i
\(147\) −1.33158 2.30636i −0.109827 0.190226i
\(148\) 9.16387 15.8723i 0.753266 1.30469i
\(149\) −0.214832 + 0.372100i −0.0175997 + 0.0304837i −0.874691 0.484681i \(-0.838936\pi\)
0.857091 + 0.515164i \(0.172269\pi\)
\(150\) −0.925720 −0.0755847
\(151\) −19.7277 −1.60542 −0.802710 0.596369i \(-0.796610\pi\)
−0.802710 + 0.596369i \(0.796610\pi\)
\(152\) 1.49059 2.58178i 0.120903 0.209410i
\(153\) 1.49139 2.58317i 0.120572 0.208837i
\(154\) 3.16270 + 5.47795i 0.254858 + 0.441426i
\(155\) 3.54944 + 6.14781i 0.285098 + 0.493804i
\(156\) −5.24368 −0.419830
\(157\) −4.18820 7.25417i −0.334255 0.578946i 0.649087 0.760714i \(-0.275151\pi\)
−0.983341 + 0.181768i \(0.941818\pi\)
\(158\) −1.80759 3.13083i −0.143804 0.249076i
\(159\) 15.7516 + 27.2826i 1.24918 + 2.16365i
\(160\) −5.81523 + 10.0723i −0.459734 + 0.796283i
\(161\) 20.5595 1.62032
\(162\) 2.12326 3.67759i 0.166819 0.288939i
\(163\) 3.83561 + 6.64346i 0.300428 + 0.520356i 0.976233 0.216724i \(-0.0695372\pi\)
−0.675805 + 0.737080i \(0.736204\pi\)
\(164\) 15.2067 1.18744
\(165\) 16.3424 + 28.3059i 1.27225 + 2.20361i
\(166\) 0.160584 0.278140i 0.0124638 0.0215879i
\(167\) 2.08907 3.61838i 0.161657 0.279998i −0.773806 0.633423i \(-0.781649\pi\)
0.935463 + 0.353424i \(0.114983\pi\)
\(168\) −10.5460 −0.813644
\(169\) 5.77464 10.0020i 0.444203 0.769383i
\(170\) −1.13054 −0.0867081
\(171\) 5.01432 0.383455
\(172\) −10.9379 4.07277i −0.834005 0.310546i
\(173\) 20.8642 1.58628 0.793139 0.609040i \(-0.208445\pi\)
0.793139 + 0.609040i \(0.208445\pi\)
\(174\) 2.71598 0.205898
\(175\) 0.980655 1.69854i 0.0741305 0.128398i
\(176\) 15.1266 1.14021
\(177\) 10.8423 18.7794i 0.814957 1.41155i
\(178\) 0.831929 1.44094i 0.0623557 0.108003i
\(179\) −9.91290 17.1696i −0.740925 1.28332i −0.952075 0.305865i \(-0.901054\pi\)
0.211150 0.977454i \(-0.432279\pi\)
\(180\) −12.7932 −0.953551
\(181\) −6.84309 11.8526i −0.508643 0.880995i −0.999950 0.0100089i \(-0.996814\pi\)
0.491307 0.870986i \(-0.336519\pi\)
\(182\) −0.686940 + 1.18981i −0.0509194 + 0.0881949i
\(183\) −14.7826 −1.09276
\(184\) −7.49797 + 12.9869i −0.552758 + 0.957405i
\(185\) −12.4065 21.4887i −0.912146 1.57988i
\(186\) −1.69031 2.92771i −0.123940 0.214670i
\(187\) 2.77268 + 4.80242i 0.202759 + 0.351188i
\(188\) −0.958744 −0.0699236
\(189\) 0.0511767 + 0.0886406i 0.00372256 + 0.00644765i
\(190\) −0.950263 1.64590i −0.0689393 0.119406i
\(191\) −0.298921 + 0.517747i −0.0216292 + 0.0374628i −0.876637 0.481152i \(-0.840219\pi\)
0.855008 + 0.518614i \(0.173552\pi\)
\(192\) −3.90277 + 6.75980i −0.281658 + 0.487847i
\(193\) −1.24993 −0.0899717 −0.0449859 0.998988i \(-0.514324\pi\)
−0.0449859 + 0.998988i \(0.514324\pi\)
\(194\) −0.715632 −0.0513794
\(195\) −3.54958 + 6.14805i −0.254191 + 0.440271i
\(196\) −0.968966 + 1.67830i −0.0692118 + 0.119878i
\(197\) −2.05471 3.55887i −0.146392 0.253559i 0.783499 0.621393i \(-0.213433\pi\)
−0.929892 + 0.367834i \(0.880100\pi\)
\(198\) −3.88009 6.72052i −0.275746 0.477607i
\(199\) 12.1525 0.861464 0.430732 0.902480i \(-0.358255\pi\)
0.430732 + 0.902480i \(0.358255\pi\)
\(200\) 0.715281 + 1.23890i 0.0505780 + 0.0876037i
\(201\) −7.61814 13.1950i −0.537342 0.930704i
\(202\) 3.22927 + 5.59327i 0.227211 + 0.393541i
\(203\) −2.87715 + 4.98337i −0.201936 + 0.349764i
\(204\) −4.35356 −0.304811
\(205\) 10.2938 17.8294i 0.718951 1.24526i
\(206\) −0.705881 1.22262i −0.0491810 0.0851841i
\(207\) −25.2230 −1.75312
\(208\) 1.64275 + 2.84533i 0.113904 + 0.197288i
\(209\) −4.66111 + 8.07328i −0.322416 + 0.558441i
\(210\) −3.36159 + 5.82244i −0.231971 + 0.401786i
\(211\) −20.2554 −1.39444 −0.697218 0.716859i \(-0.745579\pi\)
−0.697218 + 0.716859i \(0.745579\pi\)
\(212\) 11.4622 19.8530i 0.787224 1.36351i
\(213\) 16.4894 1.12984
\(214\) 4.58237 0.313244
\(215\) −12.1793 + 10.0674i −0.830623 + 0.686588i
\(216\) −0.0746557 −0.00507968
\(217\) 7.16248 0.486221
\(218\) −3.35801 + 5.81625i −0.227433 + 0.393926i
\(219\) −16.2074 −1.09520
\(220\) 11.8921 20.5977i 0.801763 1.38869i
\(221\) −0.602228 + 1.04309i −0.0405102 + 0.0701658i
\(222\) 5.90823 + 10.2334i 0.396535 + 0.686818i
\(223\) −19.7621 −1.32337 −0.661684 0.749783i \(-0.730158\pi\)
−0.661684 + 0.749783i \(0.730158\pi\)
\(224\) 5.86733 + 10.1625i 0.392028 + 0.679012i
\(225\) −1.20310 + 2.08382i −0.0802064 + 0.138922i
\(226\) −7.07324 −0.470505
\(227\) 10.7636 18.6431i 0.714404 1.23738i −0.248785 0.968559i \(-0.580031\pi\)
0.963189 0.268825i \(-0.0866353\pi\)
\(228\) −3.65936 6.33819i −0.242347 0.419757i
\(229\) −12.2775 21.2653i −0.811321 1.40525i −0.911940 0.410324i \(-0.865416\pi\)
0.100619 0.994925i \(-0.467918\pi\)
\(230\) 4.78001 + 8.27923i 0.315185 + 0.545916i
\(231\) 32.9777 2.16977
\(232\) −2.09857 3.63483i −0.137778 0.238638i
\(233\) 1.93026 + 3.34331i 0.126455 + 0.219027i 0.922301 0.386472i \(-0.126307\pi\)
−0.795845 + 0.605500i \(0.792973\pi\)
\(234\) 0.842758 1.45970i 0.0550928 0.0954236i
\(235\) −0.648999 + 1.12410i −0.0423360 + 0.0733281i
\(236\) −15.7795 −1.02716
\(237\) −18.8478 −1.22430
\(238\) −0.570332 + 0.987844i −0.0369691 + 0.0640324i
\(239\) −12.6429 + 21.8982i −0.817802 + 1.41647i 0.0894966 + 0.995987i \(0.471474\pi\)
−0.907298 + 0.420487i \(0.861859\pi\)
\(240\) 8.03891 + 13.9238i 0.518909 + 0.898777i
\(241\) 5.40172 + 9.35605i 0.347955 + 0.602676i 0.985886 0.167418i \(-0.0535428\pi\)
−0.637931 + 0.770094i \(0.720209\pi\)
\(242\) 9.26637 0.595665
\(243\) −11.0065 19.0639i −0.706069 1.22295i
\(244\) 5.37850 + 9.31584i 0.344323 + 0.596386i
\(245\) 1.31184 + 2.27217i 0.0838102 + 0.145163i
\(246\) −4.90212 + 8.49072i −0.312548 + 0.541348i
\(247\) −2.02479 −0.128834
\(248\) −2.61213 + 4.52434i −0.165870 + 0.287296i
\(249\) −0.837212 1.45009i −0.0530561 0.0918959i
\(250\) −4.74068 −0.299827
\(251\) −3.07673 5.32906i −0.194202 0.336367i 0.752437 0.658664i \(-0.228878\pi\)
−0.946638 + 0.322297i \(0.895545\pi\)
\(252\) −6.45392 + 11.1785i −0.406559 + 0.704181i
\(253\) 23.4463 40.6102i 1.47406 2.55314i
\(254\) 1.22706 0.0769929
\(255\) −2.94704 + 5.10443i −0.184551 + 0.319652i
\(256\) 1.15116 0.0719475
\(257\) −3.37336 −0.210425 −0.105212 0.994450i \(-0.533552\pi\)
−0.105212 + 0.994450i \(0.533552\pi\)
\(258\) 5.80003 4.79427i 0.361094 0.298478i
\(259\) −25.0354 −1.55562
\(260\) 5.16593 0.320377
\(261\) 3.52977 6.11374i 0.218487 0.378431i
\(262\) −4.10834 −0.253814
\(263\) 5.74822 9.95622i 0.354451 0.613927i −0.632573 0.774501i \(-0.718001\pi\)
0.987024 + 0.160574i \(0.0513346\pi\)
\(264\) −12.0268 + 20.8311i −0.740199 + 1.28206i
\(265\) −15.5181 26.8781i −0.953268 1.65111i
\(266\) −1.91755 −0.117573
\(267\) −4.33729 7.51240i −0.265438 0.459752i
\(268\) −5.54358 + 9.60176i −0.338628 + 0.586521i
\(269\) 18.5934 1.13366 0.566829 0.823835i \(-0.308170\pi\)
0.566829 + 0.823835i \(0.308170\pi\)
\(270\) −0.0237968 + 0.0412172i −0.00144823 + 0.00250840i
\(271\) −9.35483 16.2030i −0.568265 0.984265i −0.996738 0.0807097i \(-0.974281\pi\)
0.428472 0.903555i \(-0.359052\pi\)
\(272\) 1.36389 + 2.36233i 0.0826982 + 0.143238i
\(273\) 3.58138 + 6.20314i 0.216755 + 0.375431i
\(274\) −7.61079 −0.459785
\(275\) −2.23670 3.87408i −0.134878 0.233616i
\(276\) 18.4073 + 31.8824i 1.10799 + 1.91909i
\(277\) 2.34852 4.06775i 0.141109 0.244408i −0.786806 0.617201i \(-0.788267\pi\)
0.927914 + 0.372793i \(0.121600\pi\)
\(278\) 4.23251 7.33092i 0.253849 0.439679i
\(279\) −8.78715 −0.526073
\(280\) 10.3897 0.620901
\(281\) −12.3267 + 21.3505i −0.735352 + 1.27367i 0.219217 + 0.975676i \(0.429650\pi\)
−0.954569 + 0.297990i \(0.903684\pi\)
\(282\) 0.309066 0.535318i 0.0184046 0.0318777i
\(283\) −2.63158 4.55803i −0.156431 0.270947i 0.777148 0.629318i \(-0.216666\pi\)
−0.933579 + 0.358371i \(0.883332\pi\)
\(284\) −5.99952 10.3915i −0.356006 0.616621i
\(285\) −9.90845 −0.586926
\(286\) 1.56679 + 2.71376i 0.0926462 + 0.160468i
\(287\) −10.3860 17.9892i −0.613069 1.06187i
\(288\) −7.19822 12.4677i −0.424159 0.734665i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −2.67571 −0.157123
\(291\) −1.86549 + 3.23112i −0.109357 + 0.189411i
\(292\) 5.89692 + 10.2138i 0.345091 + 0.597716i
\(293\) −29.6786 −1.73384 −0.866921 0.498445i \(-0.833905\pi\)
−0.866921 + 0.498445i \(0.833905\pi\)
\(294\) −0.624722 1.08205i −0.0364345 0.0631065i
\(295\) −10.6815 + 18.5010i −0.621904 + 1.07717i
\(296\) 9.13030 15.8141i 0.530688 0.919178i
\(297\) 0.233450 0.0135461
\(298\) −0.100790 + 0.174574i −0.00583863 + 0.0101128i
\(299\) 10.1851 0.589020
\(300\) 3.51199 0.202765
\(301\) 2.65248 + 15.7209i 0.152886 + 0.906137i
\(302\) −9.25544 −0.532591
\(303\) 33.6718 1.93440
\(304\) −2.29282 + 3.97128i −0.131502 + 0.227769i
\(305\) 14.5634 0.833898
\(306\) 0.699701 1.21192i 0.0399992 0.0692807i
\(307\) 7.62297 13.2034i 0.435066 0.753556i −0.562235 0.826977i \(-0.690058\pi\)
0.997301 + 0.0734215i \(0.0233918\pi\)
\(308\) −11.9986 20.7822i −0.683685 1.18418i
\(309\) −7.36026 −0.418711
\(310\) 1.66525 + 2.88430i 0.0945799 + 0.163817i
\(311\) −0.131831 + 0.228338i −0.00747546 + 0.0129479i −0.869739 0.493512i \(-0.835713\pi\)
0.862263 + 0.506460i \(0.169046\pi\)
\(312\) −5.22446 −0.295777
\(313\) 2.53402 4.38905i 0.143231 0.248084i −0.785480 0.618887i \(-0.787584\pi\)
0.928712 + 0.370803i \(0.120917\pi\)
\(314\) −1.96493 3.40336i −0.110887 0.192063i
\(315\) 8.73766 + 15.1341i 0.492311 + 0.852708i
\(316\) 6.85761 + 11.8777i 0.385771 + 0.668175i
\(317\) 27.9509 1.56988 0.784938 0.619574i \(-0.212695\pi\)
0.784938 + 0.619574i \(0.212695\pi\)
\(318\) 7.39001 + 12.7999i 0.414411 + 0.717781i
\(319\) 6.56227 + 11.3662i 0.367417 + 0.636384i
\(320\) 3.84491 6.65958i 0.214937 0.372282i
\(321\) 11.9452 20.6896i 0.666714 1.15478i
\(322\) 9.64568 0.537533
\(323\) −1.68108 −0.0935381
\(324\) −8.05519 + 13.9520i −0.447511 + 0.775111i
\(325\) 0.485813 0.841452i 0.0269480 0.0466754i
\(326\) 1.79951 + 3.11684i 0.0996655 + 0.172626i
\(327\) 17.5071 + 30.3232i 0.968145 + 1.67688i
\(328\) 15.1510 0.836574
\(329\) 0.654813 + 1.13417i 0.0361010 + 0.0625288i
\(330\) 7.66719 + 13.2800i 0.422065 + 0.731037i
\(331\) −9.04798 15.6716i −0.497322 0.861387i 0.502673 0.864477i \(-0.332350\pi\)
−0.999995 + 0.00308935i \(0.999017\pi\)
\(332\) −0.609223 + 1.05521i −0.0334355 + 0.0579120i
\(333\) 30.7141 1.68312
\(334\) 0.980106 1.69759i 0.0536290 0.0928882i
\(335\) 7.50518 + 12.9994i 0.410052 + 0.710231i
\(336\) 16.2219 0.884975
\(337\) −5.30362 9.18613i −0.288906 0.500400i 0.684643 0.728879i \(-0.259958\pi\)
−0.973549 + 0.228478i \(0.926625\pi\)
\(338\) 2.70922 4.69251i 0.147362 0.255239i
\(339\) −18.4383 + 31.9361i −1.00143 + 1.73453i
\(340\) 4.28902 0.232605
\(341\) 8.16818 14.1477i 0.442332 0.766141i
\(342\) 2.35251 0.127209
\(343\) 19.6663 1.06188
\(344\) −10.8978 4.05785i −0.587569 0.218784i
\(345\) 49.8415 2.68338
\(346\) 9.78864 0.526241
\(347\) 0.847047 1.46713i 0.0454719 0.0787596i −0.842394 0.538863i \(-0.818854\pi\)
0.887866 + 0.460103i \(0.152188\pi\)
\(348\) −10.3038 −0.552344
\(349\) −2.05372 + 3.55715i −0.109933 + 0.190410i −0.915743 0.401765i \(-0.868397\pi\)
0.805810 + 0.592174i \(0.201730\pi\)
\(350\) 0.460083 0.796887i 0.0245925 0.0425954i
\(351\) 0.0253527 + 0.0439122i 0.00135323 + 0.00234386i
\(352\) 26.7647 1.42656
\(353\) −0.239974 0.415647i −0.0127725 0.0221227i 0.859568 0.511021i \(-0.170732\pi\)
−0.872341 + 0.488898i \(0.837399\pi\)
\(354\) 5.08676 8.81053i 0.270358 0.468274i
\(355\) −16.2449 −0.862192
\(356\) −3.15617 + 5.46664i −0.167276 + 0.289731i
\(357\) 2.97345 + 5.15016i 0.157371 + 0.272575i
\(358\) −4.65072 8.05529i −0.245798 0.425735i
\(359\) 13.6448 + 23.6335i 0.720146 + 1.24733i 0.960941 + 0.276753i \(0.0892584\pi\)
−0.240795 + 0.970576i \(0.577408\pi\)
\(360\) −12.7464 −0.671792
\(361\) 8.08698 + 14.0071i 0.425630 + 0.737213i
\(362\) −3.21050 5.56074i −0.168740 0.292266i
\(363\) 24.1553 41.8381i 1.26782 2.19593i
\(364\) 2.60611 4.51391i 0.136597 0.236593i
\(365\) 15.9671 0.835758
\(366\) −6.93538 −0.362518
\(367\) 2.33913 4.05150i 0.122102 0.211487i −0.798495 0.602002i \(-0.794370\pi\)
0.920596 + 0.390515i \(0.127703\pi\)
\(368\) 11.5334 19.9764i 0.601218 1.04134i
\(369\) 12.7419 + 22.0696i 0.663317 + 1.14890i
\(370\) −5.82063 10.0816i −0.302600 0.524119i
\(371\) −31.3142 −1.62575
\(372\) 6.41270 + 11.1071i 0.332483 + 0.575877i
\(373\) −0.198338 0.343532i −0.0102696 0.0177874i 0.860845 0.508867i \(-0.169936\pi\)
−0.871115 + 0.491080i \(0.836602\pi\)
\(374\) 1.30083 + 2.25310i 0.0672642 + 0.116505i
\(375\) −12.3579 + 21.4044i −0.638157 + 1.10532i
\(376\) −0.955231 −0.0492623
\(377\) −1.42533 + 2.46874i −0.0734081 + 0.127147i
\(378\) 0.0240100 + 0.0415865i 0.00123494 + 0.00213898i
\(379\) −9.16932 −0.470996 −0.235498 0.971875i \(-0.575672\pi\)
−0.235498 + 0.971875i \(0.575672\pi\)
\(380\) 3.60510 + 6.24421i 0.184938 + 0.320321i
\(381\) 3.19867 5.54026i 0.163873 0.283836i
\(382\) −0.140242 + 0.242905i −0.00717538 + 0.0124281i
\(383\) 32.4990 1.66062 0.830312 0.557299i \(-0.188162\pi\)
0.830312 + 0.557299i \(0.188162\pi\)
\(384\) −13.6365 + 23.6191i −0.695886 + 1.20531i
\(385\) −32.4887 −1.65578
\(386\) −0.586414 −0.0298477
\(387\) −3.25414 19.2869i −0.165417 0.980406i
\(388\) 2.71496 0.137831
\(389\) 25.6446 1.30023 0.650116 0.759835i \(-0.274720\pi\)
0.650116 + 0.759835i \(0.274720\pi\)
\(390\) −1.66532 + 2.88441i −0.0843266 + 0.146058i
\(391\) 8.45619 0.427648
\(392\) −0.965416 + 1.67215i −0.0487608 + 0.0844563i
\(393\) −10.7095 + 18.5494i −0.540222 + 0.935692i
\(394\) −0.963987 1.66967i −0.0485650 0.0841170i
\(395\) 18.5684 0.934277
\(396\) 14.7203 + 25.4962i 0.739721 + 1.28123i
\(397\) −4.52898 + 7.84443i −0.227303 + 0.393701i −0.957008 0.290062i \(-0.906324\pi\)
0.729705 + 0.683762i \(0.239657\pi\)
\(398\) 5.70143 0.285787
\(399\) −4.99861 + 8.65785i −0.250244 + 0.433435i
\(400\) −1.10024 1.90568i −0.0550122 0.0952839i
\(401\) 4.68840 + 8.12055i 0.234128 + 0.405521i 0.959019 0.283343i \(-0.0914433\pi\)
−0.724891 + 0.688863i \(0.758110\pi\)
\(402\) −3.57412 6.19055i −0.178261 0.308757i
\(403\) 3.54827 0.176752
\(404\) −12.2512 21.2197i −0.609520 1.05572i
\(405\) 10.9055 + 18.8889i 0.541901 + 0.938599i
\(406\) −1.34984 + 2.33799i −0.0669914 + 0.116032i
\(407\) −28.5506 + 49.4511i −1.41520 + 2.45120i
\(408\) −4.33761 −0.214744
\(409\) −12.2302 −0.604745 −0.302373 0.953190i \(-0.597779\pi\)
−0.302373 + 0.953190i \(0.597779\pi\)
\(410\) 4.82943 8.36483i 0.238509 0.413109i
\(411\) −19.8395 + 34.3631i −0.978613 + 1.69501i
\(412\) 2.67796 + 4.63837i 0.131934 + 0.228516i
\(413\) 10.7772 + 18.6667i 0.530314 + 0.918530i
\(414\) −11.8336 −0.581590
\(415\) 0.824799 + 1.42859i 0.0404878 + 0.0701269i
\(416\) 2.90665 + 5.03447i 0.142510 + 0.246835i
\(417\) −22.0663 38.2200i −1.08059 1.87164i
\(418\) −2.18680 + 3.78765i −0.106960 + 0.185260i
\(419\) 6.27652 0.306628 0.153314 0.988178i \(-0.451005\pi\)
0.153314 + 0.988178i \(0.451005\pi\)
\(420\) 12.7532 22.0891i 0.622290 1.07784i
\(421\) −7.91138 13.7029i −0.385577 0.667839i 0.606272 0.795257i \(-0.292664\pi\)
−0.991849 + 0.127418i \(0.959331\pi\)
\(422\) −9.50298 −0.462598
\(423\) −0.803345 1.39143i −0.0390599 0.0676538i
\(424\) 11.4202 19.7803i 0.554612 0.960616i
\(425\) 0.403346 0.698616i 0.0195652 0.0338879i
\(426\) 7.73616 0.374818
\(427\) 7.34694 12.7253i 0.355543 0.615819i
\(428\) −17.3845 −0.840313
\(429\) 16.3370 0.788758
\(430\) −5.71404 + 4.72319i −0.275555 + 0.227772i
\(431\) 23.7291 1.14299 0.571496 0.820605i \(-0.306363\pi\)
0.571496 + 0.820605i \(0.306363\pi\)
\(432\) 0.114835 0.00552501
\(433\) −8.27790 + 14.3377i −0.397811 + 0.689028i −0.993456 0.114220i \(-0.963563\pi\)
0.595645 + 0.803248i \(0.296897\pi\)
\(434\) 3.36034 0.161302
\(435\) −6.97494 + 12.0809i −0.334423 + 0.579237i
\(436\) 12.7396 22.0656i 0.610116 1.05675i
\(437\) 7.10779 + 12.3111i 0.340012 + 0.588917i
\(438\) −7.60386 −0.363326
\(439\) −14.8563 25.7318i −0.709052 1.22811i −0.965209 0.261479i \(-0.915790\pi\)
0.256158 0.966635i \(-0.417543\pi\)
\(440\) 11.8485 20.5222i 0.564855 0.978357i
\(441\) −3.24764 −0.154649
\(442\) −0.282540 + 0.489374i −0.0134391 + 0.0232772i
\(443\) −17.5183 30.3426i −0.832320 1.44162i −0.896194 0.443663i \(-0.853679\pi\)
0.0638732 0.997958i \(-0.479655\pi\)
\(444\) −22.4146 38.8232i −1.06375 1.84247i
\(445\) 4.27298 + 7.40102i 0.202559 + 0.350842i
\(446\) −9.27156 −0.439021
\(447\) 0.525474 + 0.910148i 0.0248541 + 0.0430485i
\(448\) −3.87936 6.71924i −0.183282 0.317454i
\(449\) 5.41794 9.38414i 0.255688 0.442865i −0.709394 0.704812i \(-0.751031\pi\)
0.965082 + 0.261947i \(0.0843646\pi\)
\(450\) −0.564443 + 0.977644i −0.0266081 + 0.0460866i
\(451\) −47.3775 −2.23092
\(452\) 26.8344 1.26218
\(453\) −24.1268 + 41.7888i −1.13357 + 1.96341i
\(454\) 5.04983 8.74656i 0.237000 0.410496i
\(455\) −3.52828 6.11116i −0.165408 0.286496i
\(456\) −3.64595 6.31497i −0.170737 0.295725i
\(457\) 9.02952 0.422383 0.211192 0.977445i \(-0.432266\pi\)
0.211192 + 0.977445i \(0.432266\pi\)
\(458\) −5.76010 9.97679i −0.269152 0.466185i
\(459\) 0.0210491 + 0.0364581i 0.000982489 + 0.00170172i
\(460\) −18.1344 31.4097i −0.845519 1.46448i
\(461\) −15.0723 + 26.1060i −0.701988 + 1.21588i 0.265779 + 0.964034i \(0.414371\pi\)
−0.967768 + 0.251845i \(0.918963\pi\)
\(462\) 15.4718 0.719811
\(463\) 18.7387 32.4564i 0.870863 1.50838i 0.00975673 0.999952i \(-0.496894\pi\)
0.861106 0.508426i \(-0.169772\pi\)
\(464\) 3.22801 + 5.59108i 0.149857 + 0.259559i
\(465\) 17.3637 0.805222
\(466\) 0.905598 + 1.56854i 0.0419510 + 0.0726613i
\(467\) 3.17399 5.49751i 0.146875 0.254394i −0.783196 0.621775i \(-0.786412\pi\)
0.930071 + 0.367380i \(0.119745\pi\)
\(468\) −3.19725 + 5.53780i −0.147793 + 0.255985i
\(469\) 15.1449 0.699324
\(470\) −0.304483 + 0.527381i −0.0140448 + 0.0243263i
\(471\) −20.4884 −0.944058
\(472\) −15.7217 −0.723649
\(473\) 34.0776 + 12.6890i 1.56689 + 0.583440i
\(474\) −8.84263 −0.406155
\(475\) 1.35612 0.0622230
\(476\) 2.16372 3.74767i 0.0991740 0.171774i
\(477\) 38.4172 1.75900
\(478\) −5.93153 + 10.2737i −0.271302 + 0.469909i
\(479\) −0.819851 + 1.42002i −0.0374599 + 0.0648825i −0.884148 0.467208i \(-0.845260\pi\)
0.846688 + 0.532090i \(0.178593\pi\)
\(480\) 14.2239 + 24.6365i 0.649229 + 1.12450i
\(481\) −12.4024 −0.565502
\(482\) 2.53426 + 4.38947i 0.115432 + 0.199935i
\(483\) 25.1440 43.5507i 1.14409 1.98163i
\(484\) −35.1547 −1.59794
\(485\) 1.83783 3.18321i 0.0834514 0.144542i
\(486\) −5.16381 8.94397i −0.234235 0.405707i
\(487\) 12.5725 + 21.7762i 0.569714 + 0.986774i 0.996594 + 0.0824653i \(0.0262794\pi\)
−0.426880 + 0.904308i \(0.640387\pi\)
\(488\) 5.35880 + 9.28171i 0.242581 + 0.420163i
\(489\) 18.7636 0.848518
\(490\) 0.615460 + 1.06601i 0.0278036 + 0.0481573i
\(491\) 4.75429 + 8.23468i 0.214558 + 0.371626i 0.953136 0.302543i \(-0.0978355\pi\)
−0.738578 + 0.674169i \(0.764502\pi\)
\(492\) 18.5976 32.2120i 0.838445 1.45223i
\(493\) −1.18338 + 2.04967i −0.0532967 + 0.0923127i
\(494\) −0.949949 −0.0427402
\(495\) 39.8581 1.79149
\(496\) 4.01797 6.95932i 0.180412 0.312483i
\(497\) −8.19524 + 14.1946i −0.367607 + 0.636714i
\(498\) −0.392785 0.680324i −0.0176011 0.0304860i
\(499\) −1.89983 3.29060i −0.0850480 0.147308i 0.820364 0.571842i \(-0.193771\pi\)
−0.905412 + 0.424535i \(0.860438\pi\)
\(500\) 17.9852 0.804321
\(501\) −5.10981 8.85046i −0.228290 0.395409i
\(502\) −1.44348 2.50017i −0.0644255 0.111588i
\(503\) −6.39530 11.0770i −0.285152 0.493898i 0.687494 0.726190i \(-0.258711\pi\)
−0.972646 + 0.232292i \(0.925378\pi\)
\(504\) −6.43028 + 11.1376i −0.286427 + 0.496107i
\(505\) −33.1726 −1.47616
\(506\) 11.0000 19.0526i 0.489012 0.846993i
\(507\) −14.1246 24.4646i −0.627297 1.08651i
\(508\) −4.65523 −0.206542
\(509\) 12.0725 + 20.9103i 0.535106 + 0.926831i 0.999158 + 0.0410228i \(0.0130616\pi\)
−0.464052 + 0.885808i \(0.653605\pi\)
\(510\) −1.38263 + 2.39479i −0.0612239 + 0.106043i
\(511\) 8.05509 13.9518i 0.356336 0.617192i
\(512\) 22.8404 1.00941
\(513\) −0.0353854 + 0.0612892i −0.00156230 + 0.00270599i
\(514\) −1.58264 −0.0698074
\(515\) 7.25113 0.319523
\(516\) −22.0041 + 18.1885i −0.968677 + 0.800703i
\(517\) 2.98703 0.131369
\(518\) −11.7456 −0.516070
\(519\) 25.5167 44.1962i 1.12006 1.94000i
\(520\) 5.14700 0.225711
\(521\) −21.6857 + 37.5607i −0.950066 + 1.64556i −0.204790 + 0.978806i \(0.565651\pi\)
−0.745276 + 0.666757i \(0.767682\pi\)
\(522\) 1.65602 2.86832i 0.0724822 0.125543i
\(523\) 1.49321 + 2.58631i 0.0652933 + 0.113091i 0.896824 0.442387i \(-0.145868\pi\)
−0.831531 + 0.555479i \(0.812535\pi\)
\(524\) 15.5862 0.680886
\(525\) −2.39866 4.15459i −0.104686 0.181321i
\(526\) 2.69683 4.67105i 0.117587 0.203667i
\(527\) 2.94595 0.128328
\(528\) 18.4996 32.0423i 0.805092 1.39446i
\(529\) −24.2536 42.0085i −1.05450 1.82646i
\(530\) −7.28044 12.6101i −0.316242 0.547747i
\(531\) −13.2219 22.9009i −0.573779 0.993815i
\(532\) 7.27480 0.315402
\(533\) −5.14521 8.91176i −0.222864 0.386011i
\(534\) −2.03488 3.52451i −0.0880577 0.152520i
\(535\) −11.7680 + 20.3829i −0.508777 + 0.881228i
\(536\) −5.52327 + 9.56658i −0.238569 + 0.413213i
\(537\) −48.4934 −2.09264
\(538\) 8.72325 0.376086
\(539\) 3.01888 5.22885i 0.130032 0.225222i
\(540\) 0.0902800 0.156370i 0.00388503 0.00672907i
\(541\) 1.69442 + 2.93483i 0.0728489 + 0.126178i 0.900149 0.435582i \(-0.143458\pi\)
−0.827300 + 0.561761i \(0.810124\pi\)
\(542\) −4.38890 7.60180i −0.188519 0.326525i
\(543\) −33.4760 −1.43659
\(544\) 2.41325 + 4.17987i 0.103467 + 0.179211i
\(545\) −17.2475 29.8736i −0.738803 1.27964i
\(546\) 1.68024 + 2.91026i 0.0719075 + 0.124547i
\(547\) −6.71750 + 11.6350i −0.287219 + 0.497479i −0.973145 0.230193i \(-0.926064\pi\)
0.685926 + 0.727672i \(0.259398\pi\)
\(548\) 28.8737 1.23343
\(549\) −9.01345 + 15.6117i −0.384685 + 0.666293i
\(550\) −1.04937 1.81756i −0.0447452 0.0775009i
\(551\) −3.97872 −0.169499
\(552\) 18.3398 + 31.7655i 0.780596 + 1.35203i
\(553\) 9.36737 16.2248i 0.398341 0.689947i
\(554\) 1.10183 1.90842i 0.0468122 0.0810811i
\(555\) −60.6921 −2.57624
\(556\) −16.0572 + 27.8120i −0.680979 + 1.17949i
\(557\) 2.04567 0.0866776 0.0433388 0.999060i \(-0.486201\pi\)
0.0433388 + 0.999060i \(0.486201\pi\)
\(558\) −4.12257 −0.174522
\(559\) 1.31403 + 7.78807i 0.0555775 + 0.329400i
\(560\) −15.9813 −0.675335
\(561\) 13.5638 0.572665
\(562\) −5.78320 + 10.0168i −0.243949 + 0.422533i
\(563\) 9.26283 0.390382 0.195191 0.980765i \(-0.437467\pi\)
0.195191 + 0.980765i \(0.437467\pi\)
\(564\) −1.17253 + 2.03088i −0.0493725 + 0.0855156i
\(565\) 18.1649 31.4625i 0.764203 1.32364i
\(566\) −1.23463 2.13844i −0.0518953 0.0898853i
\(567\) 22.0065 0.924186
\(568\) −5.97754 10.3534i −0.250812 0.434419i
\(569\) −21.1653 + 36.6595i −0.887297 + 1.53684i −0.0442397 + 0.999021i \(0.514087\pi\)
−0.843058 + 0.537823i \(0.819247\pi\)
\(570\) −4.64864 −0.194710
\(571\) 2.78784 4.82869i 0.116668 0.202074i −0.801778 0.597623i \(-0.796112\pi\)
0.918445 + 0.395548i \(0.129445\pi\)
\(572\) −5.94407 10.2954i −0.248534 0.430474i
\(573\) 0.731154 + 1.26640i 0.0305444 + 0.0529044i
\(574\) −4.87270 8.43977i −0.203383 0.352269i
\(575\) −6.82155 −0.284478
\(576\) 4.75931 + 8.24337i 0.198305 + 0.343474i
\(577\) 0.504170 + 0.873248i 0.0209889 + 0.0363538i 0.876329 0.481713i \(-0.159985\pi\)
−0.855340 + 0.518067i \(0.826652\pi\)
\(578\) −0.234579 + 0.406303i −0.00975722 + 0.0169000i
\(579\) −1.52864 + 2.64769i −0.0635283 + 0.110034i
\(580\) 10.1511 0.421500
\(581\) 1.66438 0.0690500
\(582\) −0.875209 + 1.51591i −0.0362786 + 0.0628363i
\(583\) −35.7111 + 61.8534i −1.47900 + 2.56171i
\(584\) 5.87532 + 10.1763i 0.243122 + 0.421100i
\(585\) 4.32860 + 7.49736i 0.178966 + 0.309978i
\(586\) −13.9240 −0.575194
\(587\) 14.3255 + 24.8125i 0.591276 + 1.02412i 0.994061 + 0.108826i \(0.0347091\pi\)
−0.402784 + 0.915295i \(0.631958\pi\)
\(588\) 2.37007 + 4.10507i 0.0977398 + 0.169290i
\(589\) 2.47620 + 4.28890i 0.102030 + 0.176721i
\(590\) −5.01134 + 8.67990i −0.206314 + 0.357346i
\(591\) −10.0516 −0.413466
\(592\) −14.0442 + 24.3252i −0.577213 + 0.999761i
\(593\) −0.412859 0.715093i −0.0169541 0.0293653i 0.857424 0.514611i \(-0.172064\pi\)
−0.874378 + 0.485245i \(0.838730\pi\)
\(594\) 0.109525 0.00449387
\(595\) −2.92936 5.07380i −0.120092 0.208005i
\(596\) 0.382378 0.662298i 0.0156628 0.0271288i
\(597\) 14.8623 25.7422i 0.608273 1.05356i
\(598\) 4.77843 0.195405
\(599\) −6.81784 + 11.8088i −0.278569 + 0.482496i −0.971029 0.238960i \(-0.923194\pi\)
0.692460 + 0.721456i \(0.256527\pi\)
\(600\) 3.49912 0.142851
\(601\) −20.8449 −0.850281 −0.425141 0.905127i \(-0.639775\pi\)
−0.425141 + 0.905127i \(0.639775\pi\)
\(602\) 1.24443 + 7.37559i 0.0507193 + 0.300607i
\(603\) −18.5802 −0.756643
\(604\) 35.1132 1.42874
\(605\) −23.7971 + 41.2178i −0.967490 + 1.67574i
\(606\) 15.7974 0.641727
\(607\) −9.51473 + 16.4800i −0.386191 + 0.668902i −0.991934 0.126758i \(-0.959543\pi\)
0.605743 + 0.795661i \(0.292876\pi\)
\(608\) −4.05688 + 7.02672i −0.164528 + 0.284971i
\(609\) 7.03743 + 12.1892i 0.285171 + 0.493931i
\(610\) 6.83255 0.276642
\(611\) 0.324392 + 0.561863i 0.0131235 + 0.0227306i
\(612\) −2.65452 + 4.59776i −0.107303 + 0.185853i
\(613\) −11.8513 −0.478668 −0.239334 0.970937i \(-0.576929\pi\)
−0.239334 + 0.970937i \(0.576929\pi\)
\(614\) 3.57638 6.19447i 0.144331 0.249989i
\(615\) −25.1784 43.6103i −1.01529 1.75854i
\(616\) −11.9547 20.7061i −0.481667 0.834271i
\(617\) 17.9486 + 31.0879i 0.722584 + 1.25155i 0.959961 + 0.280134i \(0.0903790\pi\)
−0.237377 + 0.971418i \(0.576288\pi\)
\(618\) −3.45313 −0.138905
\(619\) −8.58500 14.8697i −0.345060 0.597662i 0.640304 0.768121i \(-0.278808\pi\)
−0.985365 + 0.170459i \(0.945475\pi\)
\(620\) −6.31762 10.9424i −0.253722 0.439459i
\(621\) 0.177995 0.308297i 0.00714271 0.0123715i
\(622\) −0.0618497 + 0.107127i −0.00247995 + 0.00429540i
\(623\) 8.62253 0.345454
\(624\) 8.03625 0.321707
\(625\) 14.1914 24.5801i 0.567654 0.983206i
\(626\) 1.18886 2.05916i 0.0475163 0.0823007i
\(627\) 11.4010 + 19.7470i 0.455310 + 0.788621i
\(628\) 7.45453 + 12.9116i 0.297468 + 0.515230i
\(629\) −10.2971 −0.410573
\(630\) 4.09935 + 7.10028i 0.163322 + 0.282882i
\(631\) 12.8843 + 22.3163i 0.512916 + 0.888397i 0.999888 + 0.0149789i \(0.00476810\pi\)
−0.486972 + 0.873418i \(0.661899\pi\)
\(632\) 6.83248 + 11.8342i 0.271782 + 0.470740i
\(633\) −24.7720 + 42.9064i −0.984600 + 1.70538i
\(634\) 13.1134 0.520799
\(635\) −3.15124 + 5.45811i −0.125053 + 0.216599i
\(636\) −28.0361 48.5600i −1.11171 1.92553i
\(637\) 1.31140 0.0519597
\(638\) 3.07875 + 5.33254i 0.121889 + 0.211117i
\(639\) 10.0542 17.4143i 0.397737 0.688900i
\(640\) 13.4343 23.2689i 0.531039 0.919786i
\(641\) 41.5637 1.64167 0.820833 0.571168i \(-0.193510\pi\)
0.820833 + 0.571168i \(0.193510\pi\)
\(642\) 5.60417 9.70671i 0.221179 0.383093i
\(643\) 11.9280 0.470396 0.235198 0.971947i \(-0.424426\pi\)
0.235198 + 0.971947i \(0.424426\pi\)
\(644\) −36.5937 −1.44199
\(645\) 6.43029 + 38.1114i 0.253192 + 1.50064i
\(646\) −0.788696 −0.0310308
\(647\) −46.0062 −1.80869 −0.904345 0.426802i \(-0.859640\pi\)
−0.904345 + 0.426802i \(0.859640\pi\)
\(648\) −8.02568 + 13.9009i −0.315278 + 0.546078i
\(649\) 49.1620 1.92978
\(650\) 0.227923 0.394775i 0.00893988 0.0154843i
\(651\) 8.75963 15.1721i 0.343317 0.594642i
\(652\) −6.82696 11.8246i −0.267364 0.463088i
\(653\) −39.3376 −1.53940 −0.769701 0.638405i \(-0.779594\pi\)
−0.769701 + 0.638405i \(0.779594\pi\)
\(654\) 8.21361 + 14.2264i 0.321177 + 0.556296i
\(655\) 10.5507 18.2743i 0.412250 0.714038i
\(656\) −23.3052 −0.909915
\(657\) −9.88223 + 17.1165i −0.385542 + 0.667779i
\(658\) 0.307211 + 0.532106i 0.0119763 + 0.0207436i
\(659\) −14.6725 25.4136i −0.571560 0.989971i −0.996406 0.0847057i \(-0.973005\pi\)
0.424846 0.905266i \(-0.360328\pi\)
\(660\) −29.0877 50.3814i −1.13224 1.96109i
\(661\) 30.9953 1.20558 0.602789 0.797901i \(-0.294056\pi\)
0.602789 + 0.797901i \(0.294056\pi\)
\(662\) −4.24494 7.35245i −0.164984 0.285761i
\(663\) 1.47303 + 2.55137i 0.0572079 + 0.0990870i
\(664\) −0.606991 + 1.05134i −0.0235558 + 0.0407999i
\(665\) 4.92450 8.52948i 0.190964 0.330759i
\(666\) 14.4098 0.558369
\(667\) 20.0138 0.774936
\(668\) −3.71832 + 6.44031i −0.143866 + 0.249183i
\(669\) −24.1688 + 41.8616i −0.934419 + 1.61846i
\(670\) 3.52112 + 6.09876i 0.136033 + 0.235616i
\(671\) −16.7571 29.0241i −0.646900 1.12046i
\(672\) 28.7027 1.10723
\(673\) −10.8069 18.7181i −0.416575 0.721530i 0.579017 0.815315i \(-0.303436\pi\)
−0.995592 + 0.0937858i \(0.970103\pi\)
\(674\) −2.48824 4.30975i −0.0958433 0.166006i
\(675\) −0.0169802 0.0294105i −0.000653567 0.00113201i
\(676\) −10.2782 + 17.8024i −0.395317 + 0.684708i
\(677\) 19.8967 0.764690 0.382345 0.924020i \(-0.375117\pi\)
0.382345 + 0.924020i \(0.375117\pi\)
\(678\) −8.65048 + 14.9831i −0.332220 + 0.575422i
\(679\) −1.85429 3.21173i −0.0711612 0.123255i
\(680\) 4.27330 0.163874
\(681\) −26.3274 45.6004i −1.00887 1.74741i
\(682\) 3.83217 6.63752i 0.146742 0.254164i
\(683\) −1.69346 + 2.93316i −0.0647986 + 0.112234i −0.896605 0.442832i \(-0.853974\pi\)
0.831806 + 0.555066i \(0.187307\pi\)
\(684\) −8.92494 −0.341254
\(685\) 19.5454 33.8536i 0.746791 1.29348i
\(686\) 9.22660 0.352273
\(687\) −60.0610 −2.29147
\(688\) 16.7629 + 6.24176i 0.639081 + 0.237965i
\(689\) −15.5129 −0.590996
\(690\) 23.3836 0.890198
\(691\) 3.12067 5.40517i 0.118716 0.205622i −0.800543 0.599275i \(-0.795456\pi\)
0.919259 + 0.393653i \(0.128789\pi\)
\(692\) −37.1361 −1.41170
\(693\) 20.1076 34.8274i 0.763825 1.32298i
\(694\) 0.397400 0.688316i 0.0150851 0.0261281i
\(695\) 21.7391 + 37.6533i 0.824613 + 1.42827i
\(696\) −10.2661 −0.389135
\(697\) −4.27181 7.39899i −0.161806 0.280257i
\(698\) −0.963521 + 1.66887i −0.0364698 + 0.0631676i
\(699\) 9.44273 0.357157
\(700\) −1.74546 + 3.02322i −0.0659721 + 0.114267i
\(701\) 19.0390 + 32.9765i 0.719092 + 1.24550i 0.961360 + 0.275295i \(0.0887756\pi\)
−0.242267 + 0.970210i \(0.577891\pi\)
\(702\) 0.0118945 + 0.0206018i 0.000448927 + 0.000777565i
\(703\) −8.65517 14.9912i −0.326436 0.565403i
\(704\) −17.6963 −0.666953
\(705\) 1.58743 + 2.74952i 0.0597862 + 0.103553i
\(706\) −0.112586 0.195004i −0.00423723 0.00733909i
\(707\) −16.7349 + 28.9857i −0.629381 + 1.09012i
\(708\) −19.2981 + 33.4253i −0.725267 + 1.25620i
\(709\) 17.9802 0.675260 0.337630 0.941279i \(-0.390375\pi\)
0.337630 + 0.941279i \(0.390375\pi\)
\(710\) −7.62145 −0.286028
\(711\) −11.4922 + 19.9050i −0.430990 + 0.746497i
\(712\) −3.14460 + 5.44661i −0.117849 + 0.204120i
\(713\) −12.4558 21.5740i −0.466472 0.807953i
\(714\) 1.39502 + 2.41624i 0.0522072 + 0.0904256i
\(715\) −16.0948 −0.601911
\(716\) 17.6439 + 30.5601i 0.659382 + 1.14208i
\(717\) 30.9242 + 53.5623i 1.15489 + 2.00032i
\(718\) 6.40158 + 11.0879i 0.238905 + 0.413796i
\(719\) 5.14116 8.90475i 0.191733 0.332091i −0.754092 0.656769i \(-0.771923\pi\)
0.945825 + 0.324678i \(0.105256\pi\)
\(720\) 19.6064 0.730687
\(721\) 3.65805 6.33593i 0.136233 0.235962i
\(722\) 3.79408 + 6.57153i 0.141201 + 0.244567i
\(723\) 26.4249 0.982753
\(724\) 12.1799 + 21.0963i 0.452664 + 0.784037i
\(725\) 0.954623 1.65346i 0.0354538 0.0614078i
\(726\) 11.3327 19.6287i 0.420594 0.728490i
\(727\) 5.44852 0.202074 0.101037 0.994883i \(-0.467784\pi\)
0.101037 + 0.994883i \(0.467784\pi\)
\(728\) 2.59656 4.49737i 0.0962348 0.166684i
\(729\) −26.6893 −0.988493
\(730\) 7.49112 0.277259
\(731\) 1.09097 + 6.46605i 0.0403511 + 0.239155i
\(732\) 26.3114 0.972496
\(733\) −40.6409 −1.50111 −0.750553 0.660811i \(-0.770213\pi\)
−0.750553 + 0.660811i \(0.770213\pi\)
\(734\) 1.09743 1.90080i 0.0405067 0.0701597i
\(735\) 6.41744 0.236711
\(736\) 20.4069 35.3458i 0.752209 1.30286i
\(737\) 17.2714 29.9149i 0.636199 1.10193i
\(738\) 5.97798 + 10.3542i 0.220052 + 0.381142i
\(739\) −22.4700 −0.826571 −0.413286 0.910601i \(-0.635619\pi\)
−0.413286 + 0.910601i \(0.635619\pi\)
\(740\) 22.0823 + 38.2476i 0.811760 + 1.40601i
\(741\) −2.47629 + 4.28907i −0.0909689 + 0.157563i
\(742\) −14.6913 −0.539336
\(743\) −9.62588 + 16.6725i −0.353139 + 0.611655i −0.986798 0.161958i \(-0.948219\pi\)
0.633658 + 0.773613i \(0.281553\pi\)
\(744\) 6.38920 + 11.0664i 0.234239 + 0.405715i
\(745\) −0.517683 0.896653i −0.0189664 0.0328508i
\(746\) −0.0930521 0.161171i −0.00340688 0.00590089i
\(747\) −2.04191 −0.0747095
\(748\) −4.93507 8.54779i −0.180444 0.312538i
\(749\) 11.8735 + 20.5655i 0.433848 + 0.751446i
\(750\) −5.79779 + 10.0421i −0.211706 + 0.366685i
\(751\) 13.1719 22.8144i 0.480649 0.832508i −0.519104 0.854711i \(-0.673734\pi\)
0.999753 + 0.0222023i \(0.00706779\pi\)
\(752\) 1.46933 0.0535810
\(753\) −15.0512 −0.548497
\(754\) −0.668705 + 1.15823i −0.0243528 + 0.0421803i
\(755\) 23.7690 41.1692i 0.865044 1.49830i
\(756\) −0.0910889 0.157771i −0.00331287 0.00573806i
\(757\) 6.61142 + 11.4513i 0.240296 + 0.416205i 0.960799 0.277247i \(-0.0894222\pi\)
−0.720503 + 0.693452i \(0.756089\pi\)
\(758\) −4.30187 −0.156251
\(759\) −57.3491 99.3316i −2.08164 3.60551i
\(760\) 3.59189 + 6.22134i 0.130292 + 0.225672i
\(761\) −19.0528 33.0004i −0.690663 1.19626i −0.971621 0.236544i \(-0.923985\pi\)
0.280958 0.959720i \(-0.409348\pi\)
\(762\) 1.50068 2.59926i 0.0543640 0.0941613i
\(763\) −34.8041 −1.25999
\(764\) 0.532047 0.921532i 0.0192488 0.0333399i
\(765\) 3.59382 + 6.22469i 0.129935 + 0.225054i
\(766\) 15.2472 0.550904
\(767\) 5.33901 + 9.24743i 0.192780 + 0.333905i
\(768\) 1.40785