Properties

Label 280.2.h.b.251.2
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - x^{15} - 2 x^{12} + 6 x^{11} - 12 x^{9} + 8 x^{8} - 24 x^{7} + 48 x^{5} - 32 x^{4} - 128 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.2
Root \(-1.38133 - 0.303194i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.38133 + 0.303194i) q^{2} +1.34113i q^{3} +(1.81615 - 0.837621i) q^{4} +1.00000 q^{5} +(-0.406623 - 1.85255i) q^{6} +(-1.28003 + 2.31550i) q^{7} +(-2.25474 + 1.70768i) q^{8} +1.20136 q^{9} +O(q^{10})\) \(q+(-1.38133 + 0.303194i) q^{2} +1.34113i q^{3} +(1.81615 - 0.837621i) q^{4} +1.00000 q^{5} +(-0.406623 - 1.85255i) q^{6} +(-1.28003 + 2.31550i) q^{7} +(-2.25474 + 1.70768i) q^{8} +1.20136 q^{9} +(-1.38133 + 0.303194i) q^{10} +2.44809 q^{11} +(1.12336 + 2.43569i) q^{12} -1.57090 q^{13} +(1.06610 - 3.58656i) q^{14} +1.34113i q^{15} +(2.59678 - 3.04249i) q^{16} -1.11987i q^{17} +(-1.65948 + 0.364245i) q^{18} +8.44773i q^{19} +(1.81615 - 0.837621i) q^{20} +(-3.10539 - 1.71669i) q^{21} +(-3.38161 + 0.742244i) q^{22} -2.62959i q^{23} +(-2.29022 - 3.02390i) q^{24} +1.00000 q^{25} +(2.16994 - 0.476288i) q^{26} +5.63459i q^{27} +(-0.385215 + 5.27746i) q^{28} +3.43282i q^{29} +(-0.406623 - 1.85255i) q^{30} -9.70304 q^{31} +(-2.66455 + 4.99001i) q^{32} +3.28321i q^{33} +(0.339538 + 1.54691i) q^{34} +(-1.28003 + 2.31550i) q^{35} +(2.18185 - 1.00629i) q^{36} +6.22712i q^{37} +(-2.56130 - 11.6691i) q^{38} -2.10679i q^{39} +(-2.25474 + 1.70768i) q^{40} -3.13128i q^{41} +(4.81006 + 1.42978i) q^{42} +7.45492 q^{43} +(4.44608 - 2.05057i) q^{44} +1.20136 q^{45} +(0.797275 + 3.63233i) q^{46} +9.40956 q^{47} +(4.08038 + 3.48263i) q^{48} +(-3.72304 - 5.92781i) q^{49} +(-1.38133 + 0.303194i) q^{50} +1.50190 q^{51} +(-2.85299 + 1.31582i) q^{52} -11.6067i q^{53} +(-1.70837 - 7.78322i) q^{54} +2.44809 q^{55} +(-1.06798 - 7.40671i) q^{56} -11.3295 q^{57} +(-1.04081 - 4.74186i) q^{58} -6.16041i q^{59} +(1.12336 + 2.43569i) q^{60} +9.44231 q^{61} +(13.4031 - 2.94190i) q^{62} +(-1.53778 + 2.78175i) q^{63} +(2.16769 - 7.70072i) q^{64} -1.57090 q^{65} +(-0.995448 - 4.53519i) q^{66} -2.15461 q^{67} +(-0.938029 - 2.03385i) q^{68} +3.52663 q^{69} +(1.06610 - 3.58656i) q^{70} -7.87185i q^{71} +(-2.70876 + 2.05154i) q^{72} -12.6145i q^{73} +(-1.88802 - 8.60171i) q^{74} +1.34113i q^{75} +(7.07600 + 15.3423i) q^{76} +(-3.13362 + 5.66853i) q^{77} +(0.638766 + 2.91017i) q^{78} +7.70558i q^{79} +(2.59678 - 3.04249i) q^{80} -3.95264 q^{81} +(0.949384 + 4.32533i) q^{82} -0.813234i q^{83} +(-7.07778 - 0.516625i) q^{84} -1.11987i q^{85} +(-10.2977 + 2.26029i) q^{86} -4.60387 q^{87} +(-5.51979 + 4.18054i) q^{88} -5.12287i q^{89} +(-1.65948 + 0.364245i) q^{90} +(2.01081 - 3.63742i) q^{91} +(-2.20260 - 4.77572i) q^{92} -13.0131i q^{93} +(-12.9977 + 2.85292i) q^{94} +8.44773i q^{95} +(-6.69226 - 3.57352i) q^{96} +0.833955i q^{97} +(6.94003 + 7.05946i) q^{98} +2.94104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + O(q^{10}) \) \( 16q + q^{2} + q^{4} + 16q^{5} + q^{8} - 16q^{9} + q^{10} - 4q^{11} + 14q^{12} - q^{14} + 9q^{16} - 15q^{18} + q^{20} - 4q^{21} + 6q^{22} + 22q^{24} + 16q^{25} - 20q^{26} + q^{28} - 16q^{31} - 19q^{32} - 14q^{34} + 15q^{36} - 30q^{38} + q^{40} + 44q^{42} - 4q^{43} - 20q^{44} - 16q^{45} + 6q^{46} - 34q^{48} - 8q^{49} + q^{50} - 40q^{51} - 38q^{52} + 26q^{54} - 4q^{55} + 33q^{56} - 16q^{57} + 18q^{58} + 14q^{60} - 8q^{61} + 28q^{62} + 28q^{63} - 23q^{64} + 46q^{66} + 20q^{67} + 12q^{68} - 40q^{69} - q^{70} - 13q^{72} - 28q^{74} + 34q^{76} - 4q^{77} - 6q^{78} + 9q^{80} + 24q^{81} - 16q^{82} - 42q^{84} - 24q^{86} + 72q^{87} - 44q^{88} - 15q^{90} - 32q^{91} - 30q^{92} - 58q^{94} - 30q^{96} + 5q^{98} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38133 + 0.303194i −0.976748 + 0.214390i
\(3\) 1.34113i 0.774303i 0.922016 + 0.387152i \(0.126541\pi\)
−0.922016 + 0.387152i \(0.873459\pi\)
\(4\) 1.81615 0.837621i 0.908074 0.418811i
\(5\) 1.00000 0.447214
\(6\) −0.406623 1.85255i −0.166003 0.756299i
\(7\) −1.28003 + 2.31550i −0.483806 + 0.875175i
\(8\) −2.25474 + 1.70768i −0.797170 + 0.603755i
\(9\) 1.20136 0.400454
\(10\) −1.38133 + 0.303194i −0.436815 + 0.0958783i
\(11\) 2.44809 0.738125 0.369063 0.929404i \(-0.379679\pi\)
0.369063 + 0.929404i \(0.379679\pi\)
\(12\) 1.12336 + 2.43569i 0.324287 + 0.703125i
\(13\) −1.57090 −0.435690 −0.217845 0.975983i \(-0.569903\pi\)
−0.217845 + 0.975983i \(0.569903\pi\)
\(14\) 1.06610 3.58656i 0.284928 0.958549i
\(15\) 1.34113i 0.346279i
\(16\) 2.59678 3.04249i 0.649195 0.760622i
\(17\) 1.11987i 0.271609i −0.990736 0.135804i \(-0.956638\pi\)
0.990736 0.135804i \(-0.0433619\pi\)
\(18\) −1.65948 + 0.364245i −0.391143 + 0.0858535i
\(19\) 8.44773i 1.93804i 0.246978 + 0.969021i \(0.420563\pi\)
−0.246978 + 0.969021i \(0.579437\pi\)
\(20\) 1.81615 0.837621i 0.406103 0.187298i
\(21\) −3.10539 1.71669i −0.677651 0.374613i
\(22\) −3.38161 + 0.742244i −0.720963 + 0.158247i
\(23\) 2.62959i 0.548307i −0.961686 0.274154i \(-0.911602\pi\)
0.961686 0.274154i \(-0.0883977\pi\)
\(24\) −2.29022 3.02390i −0.467489 0.617252i
\(25\) 1.00000 0.200000
\(26\) 2.16994 0.476288i 0.425560 0.0934078i
\(27\) 5.63459i 1.08438i
\(28\) −0.385215 + 5.27746i −0.0727988 + 0.997347i
\(29\) 3.43282i 0.637458i 0.947846 + 0.318729i \(0.103256\pi\)
−0.947846 + 0.318729i \(0.896744\pi\)
\(30\) −0.406623 1.85255i −0.0742389 0.338227i
\(31\) −9.70304 −1.74272 −0.871359 0.490647i \(-0.836761\pi\)
−0.871359 + 0.490647i \(0.836761\pi\)
\(32\) −2.66455 + 4.99001i −0.471030 + 0.882117i
\(33\) 3.28321i 0.571533i
\(34\) 0.339538 + 1.54691i 0.0582303 + 0.265294i
\(35\) −1.28003 + 2.31550i −0.216365 + 0.391390i
\(36\) 2.18185 1.00629i 0.363642 0.167714i
\(37\) 6.22712i 1.02373i 0.859065 + 0.511866i \(0.171046\pi\)
−0.859065 + 0.511866i \(0.828954\pi\)
\(38\) −2.56130 11.6691i −0.415497 1.89298i
\(39\) 2.10679i 0.337357i
\(40\) −2.25474 + 1.70768i −0.356505 + 0.270007i
\(41\) 3.13128i 0.489024i −0.969646 0.244512i \(-0.921372\pi\)
0.969646 0.244512i \(-0.0786277\pi\)
\(42\) 4.81006 + 1.42978i 0.742208 + 0.220620i
\(43\) 7.45492 1.13687 0.568433 0.822730i \(-0.307550\pi\)
0.568433 + 0.822730i \(0.307550\pi\)
\(44\) 4.44608 2.05057i 0.670272 0.309135i
\(45\) 1.20136 0.179089
\(46\) 0.797275 + 3.63233i 0.117552 + 0.535558i
\(47\) 9.40956 1.37253 0.686263 0.727354i \(-0.259250\pi\)
0.686263 + 0.727354i \(0.259250\pi\)
\(48\) 4.08038 + 3.48263i 0.588952 + 0.502674i
\(49\) −3.72304 5.92781i −0.531863 0.846830i
\(50\) −1.38133 + 0.303194i −0.195350 + 0.0428781i
\(51\) 1.50190 0.210308
\(52\) −2.85299 + 1.31582i −0.395639 + 0.182472i
\(53\) 11.6067i 1.59430i −0.603778 0.797152i \(-0.706339\pi\)
0.603778 0.797152i \(-0.293661\pi\)
\(54\) −1.70837 7.78322i −0.232480 1.05916i
\(55\) 2.44809 0.330100
\(56\) −1.06798 7.40671i −0.142715 0.989764i
\(57\) −11.3295 −1.50063
\(58\) −1.04081 4.74186i −0.136665 0.622636i
\(59\) 6.16041i 0.802017i −0.916074 0.401009i \(-0.868660\pi\)
0.916074 0.401009i \(-0.131340\pi\)
\(60\) 1.12336 + 2.43569i 0.145025 + 0.314447i
\(61\) 9.44231 1.20896 0.604482 0.796619i \(-0.293380\pi\)
0.604482 + 0.796619i \(0.293380\pi\)
\(62\) 13.4031 2.94190i 1.70220 0.373622i
\(63\) −1.53778 + 2.78175i −0.193742 + 0.350468i
\(64\) 2.16769 7.70072i 0.270961 0.962590i
\(65\) −1.57090 −0.194847
\(66\) −0.995448 4.53519i −0.122531 0.558244i
\(67\) −2.15461 −0.263228 −0.131614 0.991301i \(-0.542016\pi\)
−0.131614 + 0.991301i \(0.542016\pi\)
\(68\) −0.938029 2.03385i −0.113753 0.246641i
\(69\) 3.52663 0.424556
\(70\) 1.06610 3.58656i 0.127423 0.428676i
\(71\) 7.87185i 0.934217i −0.884200 0.467108i \(-0.845296\pi\)
0.884200 0.467108i \(-0.154704\pi\)
\(72\) −2.70876 + 2.05154i −0.319230 + 0.241776i
\(73\) 12.6145i 1.47642i −0.674571 0.738210i \(-0.735671\pi\)
0.674571 0.738210i \(-0.264329\pi\)
\(74\) −1.88802 8.60171i −0.219478 0.999929i
\(75\) 1.34113i 0.154861i
\(76\) 7.07600 + 15.3423i 0.811673 + 1.75989i
\(77\) −3.13362 + 5.66853i −0.357110 + 0.645989i
\(78\) 0.638766 + 2.91017i 0.0723260 + 0.329512i
\(79\) 7.70558i 0.866946i 0.901167 + 0.433473i \(0.142712\pi\)
−0.901167 + 0.433473i \(0.857288\pi\)
\(80\) 2.59678 3.04249i 0.290329 0.340160i
\(81\) −3.95264 −0.439182
\(82\) 0.949384 + 4.32533i 0.104842 + 0.477653i
\(83\) 0.813234i 0.0892640i −0.999003 0.0446320i \(-0.985788\pi\)
0.999003 0.0446320i \(-0.0142115\pi\)
\(84\) −7.07778 0.516625i −0.772249 0.0563684i
\(85\) 1.11987i 0.121467i
\(86\) −10.2977 + 2.26029i −1.11043 + 0.243733i
\(87\) −4.60387 −0.493586
\(88\) −5.51979 + 4.18054i −0.588412 + 0.445647i
\(89\) 5.12287i 0.543023i −0.962435 0.271512i \(-0.912476\pi\)
0.962435 0.271512i \(-0.0875235\pi\)
\(90\) −1.65948 + 0.364245i −0.174924 + 0.0383948i
\(91\) 2.01081 3.63742i 0.210790 0.381305i
\(92\) −2.20260 4.77572i −0.229637 0.497903i
\(93\) 13.0131i 1.34939i
\(94\) −12.9977 + 2.85292i −1.34061 + 0.294256i
\(95\) 8.44773i 0.866719i
\(96\) −6.69226 3.57352i −0.683026 0.364720i
\(97\) 0.833955i 0.0846753i 0.999103 + 0.0423377i \(0.0134805\pi\)
−0.999103 + 0.0423377i \(0.986519\pi\)
\(98\) 6.94003 + 7.05946i 0.701049 + 0.713113i
\(99\) 2.94104 0.295585
\(100\) 1.81615 0.837621i 0.181615 0.0837621i
\(101\) 5.52401 0.549660 0.274830 0.961493i \(-0.411378\pi\)
0.274830 + 0.961493i \(0.411378\pi\)
\(102\) −2.07462 + 0.455366i −0.205418 + 0.0450879i
\(103\) 11.7675 1.15949 0.579745 0.814798i \(-0.303152\pi\)
0.579745 + 0.814798i \(0.303152\pi\)
\(104\) 3.54198 2.68260i 0.347319 0.263050i
\(105\) −3.10539 1.71669i −0.303055 0.167532i
\(106\) 3.51908 + 16.0327i 0.341803 + 1.55723i
\(107\) −1.38992 −0.134369 −0.0671844 0.997741i \(-0.521402\pi\)
−0.0671844 + 0.997741i \(0.521402\pi\)
\(108\) 4.71965 + 10.2332i 0.454148 + 0.984694i
\(109\) 1.07524i 0.102990i 0.998673 + 0.0514949i \(0.0163986\pi\)
−0.998673 + 0.0514949i \(0.983601\pi\)
\(110\) −3.38161 + 0.742244i −0.322424 + 0.0707702i
\(111\) −8.35140 −0.792680
\(112\) 3.72091 + 9.90731i 0.351593 + 0.936153i
\(113\) 11.1967 1.05329 0.526647 0.850084i \(-0.323449\pi\)
0.526647 + 0.850084i \(0.323449\pi\)
\(114\) 15.6498 3.43504i 1.46574 0.321721i
\(115\) 2.62959i 0.245210i
\(116\) 2.87540 + 6.23450i 0.266974 + 0.578859i
\(117\) −1.88722 −0.174474
\(118\) 1.86780 + 8.50956i 0.171945 + 0.783369i
\(119\) 2.59306 + 1.43347i 0.237705 + 0.131406i
\(120\) −2.29022 3.02390i −0.209068 0.276043i
\(121\) −5.00688 −0.455171
\(122\) −13.0429 + 2.86285i −1.18085 + 0.259190i
\(123\) 4.19946 0.378653
\(124\) −17.6221 + 8.12747i −1.58252 + 0.729868i
\(125\) 1.00000 0.0894427
\(126\) 1.28077 4.30876i 0.114100 0.383855i
\(127\) 16.4186i 1.45692i −0.685089 0.728459i \(-0.740237\pi\)
0.685089 0.728459i \(-0.259763\pi\)
\(128\) −0.659479 + 11.2945i −0.0582903 + 0.998300i
\(129\) 9.99804i 0.880279i
\(130\) 2.16994 0.476288i 0.190316 0.0417732i
\(131\) 2.00348i 0.175045i −0.996163 0.0875223i \(-0.972105\pi\)
0.996163 0.0875223i \(-0.0278949\pi\)
\(132\) 2.75008 + 5.96279i 0.239364 + 0.518994i
\(133\) −19.5607 10.8134i −1.69613 0.937637i
\(134\) 2.97623 0.653264i 0.257107 0.0564334i
\(135\) 5.63459i 0.484948i
\(136\) 1.91238 + 2.52502i 0.163985 + 0.216519i
\(137\) 4.20941 0.359634 0.179817 0.983700i \(-0.442449\pi\)
0.179817 + 0.983700i \(0.442449\pi\)
\(138\) −4.87144 + 1.06925i −0.414684 + 0.0910207i
\(139\) 4.20658i 0.356798i −0.983958 0.178399i \(-0.942908\pi\)
0.983958 0.178399i \(-0.0570917\pi\)
\(140\) −0.385215 + 5.27746i −0.0325566 + 0.446027i
\(141\) 12.6195i 1.06275i
\(142\) 2.38669 + 10.8736i 0.200287 + 0.912494i
\(143\) −3.84571 −0.321594
\(144\) 3.11968 3.65513i 0.259973 0.304594i
\(145\) 3.43282i 0.285080i
\(146\) 3.82465 + 17.4249i 0.316530 + 1.44209i
\(147\) 7.94998 4.99310i 0.655704 0.411824i
\(148\) 5.21597 + 11.3094i 0.428750 + 0.929625i
\(149\) 19.1438i 1.56832i 0.620560 + 0.784159i \(0.286906\pi\)
−0.620560 + 0.784159i \(0.713094\pi\)
\(150\) −0.406623 1.85255i −0.0332006 0.151260i
\(151\) 2.73232i 0.222353i −0.993801 0.111177i \(-0.964538\pi\)
0.993801 0.111177i \(-0.0354619\pi\)
\(152\) −14.4260 19.0474i −1.17010 1.54495i
\(153\) 1.34537i 0.108767i
\(154\) 2.60991 8.78021i 0.210312 0.707529i
\(155\) −9.70304 −0.779367
\(156\) −1.76469 3.82624i −0.141289 0.306345i
\(157\) 13.5441 1.08094 0.540468 0.841365i \(-0.318247\pi\)
0.540468 + 0.841365i \(0.318247\pi\)
\(158\) −2.33628 10.6440i −0.185865 0.846788i
\(159\) 15.5661 1.23448
\(160\) −2.66455 + 4.99001i −0.210651 + 0.394495i
\(161\) 6.08880 + 3.36595i 0.479865 + 0.265274i
\(162\) 5.45990 1.19842i 0.428971 0.0941565i
\(163\) −18.5317 −1.45151 −0.725756 0.687953i \(-0.758510\pi\)
−0.725756 + 0.687953i \(0.758510\pi\)
\(164\) −2.62283 5.68687i −0.204808 0.444070i
\(165\) 3.28321i 0.255597i
\(166\) 0.246567 + 1.12334i 0.0191373 + 0.0871884i
\(167\) −7.74592 −0.599397 −0.299699 0.954034i \(-0.596886\pi\)
−0.299699 + 0.954034i \(0.596886\pi\)
\(168\) 9.93339 1.43231i 0.766378 0.110505i
\(169\) −10.5323 −0.810174
\(170\) 0.339538 + 1.54691i 0.0260414 + 0.118643i
\(171\) 10.1488i 0.776097i
\(172\) 13.5392 6.24440i 1.03236 0.476131i
\(173\) −13.6112 −1.03484 −0.517421 0.855731i \(-0.673108\pi\)
−0.517421 + 0.855731i \(0.673108\pi\)
\(174\) 6.35946 1.39586i 0.482109 0.105820i
\(175\) −1.28003 + 2.31550i −0.0967612 + 0.175035i
\(176\) 6.35714 7.44827i 0.479188 0.561434i
\(177\) 8.26193 0.621005
\(178\) 1.55322 + 7.07638i 0.116419 + 0.530397i
\(179\) −17.3370 −1.29583 −0.647914 0.761714i \(-0.724358\pi\)
−0.647914 + 0.761714i \(0.724358\pi\)
\(180\) 2.18185 1.00629i 0.162626 0.0750042i
\(181\) 11.8268 0.879076 0.439538 0.898224i \(-0.355142\pi\)
0.439538 + 0.898224i \(0.355142\pi\)
\(182\) −1.67474 + 5.63414i −0.124140 + 0.417631i
\(183\) 12.6634i 0.936105i
\(184\) 4.49049 + 5.92903i 0.331043 + 0.437094i
\(185\) 6.22712i 0.457827i
\(186\) 3.94548 + 17.9753i 0.289297 + 1.31802i
\(187\) 2.74154i 0.200481i
\(188\) 17.0892 7.88165i 1.24635 0.574828i
\(189\) −13.0469 7.21244i −0.949019 0.524628i
\(190\) −2.56130 11.6691i −0.185816 0.846566i
\(191\) 20.5823i 1.48929i −0.667463 0.744643i \(-0.732620\pi\)
0.667463 0.744643i \(-0.267380\pi\)
\(192\) 10.3277 + 2.90715i 0.745337 + 0.209806i
\(193\) 10.0690 0.724781 0.362391 0.932026i \(-0.381961\pi\)
0.362391 + 0.932026i \(0.381961\pi\)
\(194\) −0.252850 1.15197i −0.0181536 0.0827065i
\(195\) 2.10679i 0.150870i
\(196\) −11.7269 7.64728i −0.837633 0.546234i
\(197\) 4.59538i 0.327407i −0.986510 0.163704i \(-0.947656\pi\)
0.986510 0.163704i \(-0.0523441\pi\)
\(198\) −4.06254 + 0.891704i −0.288712 + 0.0633706i
\(199\) −2.15447 −0.152727 −0.0763633 0.997080i \(-0.524331\pi\)
−0.0763633 + 0.997080i \(0.524331\pi\)
\(200\) −2.25474 + 1.70768i −0.159434 + 0.120751i
\(201\) 2.88962i 0.203818i
\(202\) −7.63049 + 1.67485i −0.536879 + 0.117842i
\(203\) −7.94868 4.39411i −0.557888 0.308406i
\(204\) 2.72767 1.25802i 0.190975 0.0880791i
\(205\) 3.13128i 0.218698i
\(206\) −16.2549 + 3.56784i −1.13253 + 0.248583i
\(207\) 3.15909i 0.219572i
\(208\) −4.07929 + 4.77946i −0.282848 + 0.331396i
\(209\) 20.6808i 1.43052i
\(210\) 4.81006 + 1.42978i 0.331925 + 0.0986644i
\(211\) −11.7444 −0.808515 −0.404258 0.914645i \(-0.632470\pi\)
−0.404258 + 0.914645i \(0.632470\pi\)
\(212\) −9.72203 21.0795i −0.667712 1.44775i
\(213\) 10.5572 0.723367
\(214\) 1.91994 0.421416i 0.131245 0.0288074i
\(215\) 7.45492 0.508422
\(216\) −9.62205 12.7045i −0.654697 0.864433i
\(217\) 12.4202 22.4673i 0.843137 1.52518i
\(218\) −0.326007 1.48527i −0.0220800 0.100595i
\(219\) 16.9178 1.14320
\(220\) 4.44608 2.05057i 0.299755 0.138249i
\(221\) 1.75921i 0.118337i
\(222\) 11.5360 2.53209i 0.774249 0.169943i
\(223\) −6.92127 −0.463482 −0.231741 0.972777i \(-0.574442\pi\)
−0.231741 + 0.972777i \(0.574442\pi\)
\(224\) −8.14364 12.5571i −0.544120 0.839008i
\(225\) 1.20136 0.0800908
\(226\) −15.4663 + 3.39476i −1.02880 + 0.225816i
\(227\) 12.2022i 0.809890i −0.914341 0.404945i \(-0.867291\pi\)
0.914341 0.404945i \(-0.132709\pi\)
\(228\) −20.5761 + 9.48986i −1.36269 + 0.628481i
\(229\) 12.2581 0.810041 0.405021 0.914308i \(-0.367264\pi\)
0.405021 + 0.914308i \(0.367264\pi\)
\(230\) 0.797275 + 3.63233i 0.0525707 + 0.239509i
\(231\) −7.60226 4.20261i −0.500192 0.276511i
\(232\) −5.86214 7.74010i −0.384868 0.508163i
\(233\) −10.1521 −0.665083 −0.332542 0.943089i \(-0.607906\pi\)
−0.332542 + 0.943089i \(0.607906\pi\)
\(234\) 2.60688 0.572195i 0.170417 0.0374055i
\(235\) 9.40956 0.613812
\(236\) −5.16009 11.1882i −0.335893 0.728291i
\(237\) −10.3342 −0.671279
\(238\) −4.01649 1.19390i −0.260350 0.0773889i
\(239\) 5.57510i 0.360624i 0.983610 + 0.180312i \(0.0577107\pi\)
−0.983610 + 0.180312i \(0.942289\pi\)
\(240\) 4.08038 + 3.48263i 0.263387 + 0.224803i
\(241\) 20.9813i 1.35152i 0.737120 + 0.675762i \(0.236185\pi\)
−0.737120 + 0.675762i \(0.763815\pi\)
\(242\) 6.91615 1.51805i 0.444587 0.0975842i
\(243\) 11.6027i 0.744316i
\(244\) 17.1486 7.90908i 1.09783 0.506327i
\(245\) −3.72304 5.92781i −0.237857 0.378714i
\(246\) −5.80085 + 1.27325i −0.369848 + 0.0811795i
\(247\) 13.2706i 0.844386i
\(248\) 21.8778 16.5696i 1.38924 1.05217i
\(249\) 1.09065 0.0691174
\(250\) −1.38133 + 0.303194i −0.0873630 + 0.0191757i
\(251\) 22.8742i 1.44381i −0.691995 0.721903i \(-0.743268\pi\)
0.691995 0.721903i \(-0.256732\pi\)
\(252\) −0.462783 + 6.34014i −0.0291526 + 0.399392i
\(253\) 6.43746i 0.404720i
\(254\) 4.97803 + 22.6796i 0.312349 + 1.42304i
\(255\) 1.50190 0.0940525
\(256\) −2.51345 15.8013i −0.157091 0.987584i
\(257\) 28.8767i 1.80128i 0.434566 + 0.900640i \(0.356902\pi\)
−0.434566 + 0.900640i \(0.643098\pi\)
\(258\) −3.03134 13.8106i −0.188723 0.859811i
\(259\) −14.4189 7.97091i −0.895946 0.495288i
\(260\) −2.85299 + 1.31582i −0.176935 + 0.0816039i
\(261\) 4.12406i 0.255273i
\(262\) 0.607442 + 2.76746i 0.0375279 + 0.170974i
\(263\) 19.6017i 1.20869i 0.796722 + 0.604347i \(0.206566\pi\)
−0.796722 + 0.604347i \(0.793434\pi\)
\(264\) −5.60666 7.40277i −0.345066 0.455609i
\(265\) 11.6067i 0.712995i
\(266\) 30.2983 + 9.00614i 1.85771 + 0.552202i
\(267\) 6.87045 0.420465
\(268\) −3.91309 + 1.80475i −0.239030 + 0.110243i
\(269\) 27.2431 1.66104 0.830520 0.556988i \(-0.188043\pi\)
0.830520 + 0.556988i \(0.188043\pi\)
\(270\) −1.70837 7.78322i −0.103968 0.473672i
\(271\) 26.0339 1.58144 0.790722 0.612175i \(-0.209705\pi\)
0.790722 + 0.612175i \(0.209705\pi\)
\(272\) −3.40720 2.90806i −0.206592 0.176327i
\(273\) 4.87827 + 2.69676i 0.295246 + 0.163215i
\(274\) −5.81458 + 1.27627i −0.351272 + 0.0771020i
\(275\) 2.44809 0.147625
\(276\) 6.40488 2.95398i 0.385528 0.177809i
\(277\) 5.64829i 0.339373i 0.985498 + 0.169687i \(0.0542755\pi\)
−0.985498 + 0.169687i \(0.945724\pi\)
\(278\) 1.27541 + 5.81068i 0.0764940 + 0.348501i
\(279\) −11.6569 −0.697878
\(280\) −1.06798 7.40671i −0.0638242 0.442636i
\(281\) 25.9379 1.54733 0.773663 0.633598i \(-0.218422\pi\)
0.773663 + 0.633598i \(0.218422\pi\)
\(282\) −3.82615 17.4317i −0.227844 1.03804i
\(283\) 12.6062i 0.749358i −0.927155 0.374679i \(-0.877753\pi\)
0.927155 0.374679i \(-0.122247\pi\)
\(284\) −6.59363 14.2964i −0.391260 0.848337i
\(285\) −11.3295 −0.671103
\(286\) 5.31219 1.16599i 0.314116 0.0689467i
\(287\) 7.25047 + 4.00813i 0.427982 + 0.236593i
\(288\) −3.20109 + 5.99481i −0.188626 + 0.353247i
\(289\) 15.7459 0.926229
\(290\) −1.04081 4.74186i −0.0611184 0.278451i
\(291\) −1.11844 −0.0655644
\(292\) −10.5662 22.9099i −0.618341 1.34070i
\(293\) −16.7982 −0.981362 −0.490681 0.871339i \(-0.663252\pi\)
−0.490681 + 0.871339i \(0.663252\pi\)
\(294\) −9.46768 + 9.30750i −0.552166 + 0.542824i
\(295\) 6.16041i 0.358673i
\(296\) −10.6339 14.0405i −0.618083 0.816089i
\(297\) 13.7939i 0.800406i
\(298\) −5.80427 26.4439i −0.336232 1.53185i
\(299\) 4.13083i 0.238892i
\(300\) 1.12336 + 2.43569i 0.0648573 + 0.140625i
\(301\) −9.54253 + 17.2618i −0.550022 + 0.994956i
\(302\) 0.828423 + 3.77424i 0.0476704 + 0.217183i
\(303\) 7.40844i 0.425604i
\(304\) 25.7021 + 21.9369i 1.47412 + 1.25817i
\(305\) 9.44231 0.540665
\(306\) 0.407908 + 1.85840i 0.0233186 + 0.106238i
\(307\) 5.08609i 0.290279i 0.989411 + 0.145139i \(0.0463630\pi\)
−0.989411 + 0.145139i \(0.953637\pi\)
\(308\) −0.943039 + 12.9197i −0.0537347 + 0.736167i
\(309\) 15.7818i 0.897797i
\(310\) 13.4031 2.94190i 0.761245 0.167089i
\(311\) −16.9297 −0.959994 −0.479997 0.877270i \(-0.659362\pi\)
−0.479997 + 0.877270i \(0.659362\pi\)
\(312\) 3.59772 + 4.75026i 0.203681 + 0.268931i
\(313\) 8.30791i 0.469591i −0.972045 0.234795i \(-0.924558\pi\)
0.972045 0.234795i \(-0.0754420\pi\)
\(314\) −18.7089 + 4.10648i −1.05580 + 0.231742i
\(315\) −1.53778 + 2.78175i −0.0866441 + 0.156734i
\(316\) 6.45436 + 13.9945i 0.363086 + 0.787251i
\(317\) 10.7428i 0.603376i −0.953407 0.301688i \(-0.902450\pi\)
0.953407 0.301688i \(-0.0975501\pi\)
\(318\) −21.5020 + 4.71956i −1.20577 + 0.264660i
\(319\) 8.40383i 0.470524i
\(320\) 2.16769 7.70072i 0.121177 0.430484i
\(321\) 1.86407i 0.104042i
\(322\) −9.43119 2.80341i −0.525579 0.156228i
\(323\) 9.46038 0.526390
\(324\) −7.17858 + 3.31082i −0.398810 + 0.183934i
\(325\) −1.57090 −0.0871381
\(326\) 25.5983 5.61868i 1.41776 0.311190i
\(327\) −1.44205 −0.0797453
\(328\) 5.34721 + 7.06022i 0.295250 + 0.389835i
\(329\) −12.0445 + 21.7878i −0.664036 + 1.20120i
\(330\) −0.995448 4.53519i −0.0547976 0.249654i
\(331\) 12.1739 0.669140 0.334570 0.942371i \(-0.391409\pi\)
0.334570 + 0.942371i \(0.391409\pi\)
\(332\) −0.681182 1.47695i −0.0373847 0.0810583i
\(333\) 7.48103i 0.409958i
\(334\) 10.6997 2.34851i 0.585460 0.128505i
\(335\) −2.15461 −0.117719
\(336\) −13.2870 + 4.99023i −0.724867 + 0.272239i
\(337\) −11.5686 −0.630179 −0.315090 0.949062i \(-0.602035\pi\)
−0.315090 + 0.949062i \(0.602035\pi\)
\(338\) 14.5485 3.19331i 0.791336 0.173693i
\(339\) 15.0162i 0.815569i
\(340\) −0.938029 2.03385i −0.0508718 0.110301i
\(341\) −23.7539 −1.28634
\(342\) −3.07705 14.0188i −0.166388 0.758051i
\(343\) 18.4914 1.03291i 0.998444 0.0557721i
\(344\) −16.8089 + 12.7306i −0.906275 + 0.686388i
\(345\) 3.52663 0.189867
\(346\) 18.8016 4.12684i 1.01078 0.221860i
\(347\) −10.6711 −0.572854 −0.286427 0.958102i \(-0.592468\pi\)
−0.286427 + 0.958102i \(0.592468\pi\)
\(348\) −8.36130 + 3.85630i −0.448213 + 0.206719i
\(349\) −14.5060 −0.776486 −0.388243 0.921557i \(-0.626918\pi\)
−0.388243 + 0.921557i \(0.626918\pi\)
\(350\) 1.06610 3.58656i 0.0569855 0.191710i
\(351\) 8.85139i 0.472452i
\(352\) −6.52305 + 12.2160i −0.347680 + 0.651113i
\(353\) 33.2031i 1.76722i 0.468221 + 0.883611i \(0.344895\pi\)
−0.468221 + 0.883611i \(0.655105\pi\)
\(354\) −11.4125 + 2.50496i −0.606565 + 0.133137i
\(355\) 7.87185i 0.417794i
\(356\) −4.29103 9.30389i −0.227424 0.493105i
\(357\) −1.92247 + 3.47764i −0.101748 + 0.184056i
\(358\) 23.9481 5.25646i 1.26570 0.277813i
\(359\) 13.3218i 0.703097i 0.936170 + 0.351549i \(0.114345\pi\)
−0.936170 + 0.351549i \(0.885655\pi\)
\(360\) −2.70876 + 2.05154i −0.142764 + 0.108126i
\(361\) −52.3642 −2.75601
\(362\) −16.3367 + 3.58580i −0.858636 + 0.188465i
\(363\) 6.71489i 0.352440i
\(364\) 0.605136 8.29039i 0.0317177 0.434534i
\(365\) 12.6145i 0.660275i
\(366\) −3.83946 17.4923i −0.200692 0.914338i
\(367\) −25.9412 −1.35412 −0.677059 0.735929i \(-0.736746\pi\)
−0.677059 + 0.735929i \(0.736746\pi\)
\(368\) −8.00049 6.82847i −0.417054 0.355958i
\(369\) 3.76180i 0.195832i
\(370\) −1.88802 8.60171i −0.0981537 0.447182i
\(371\) 26.8753 + 14.8569i 1.39530 + 0.771334i
\(372\) −10.9000 23.6336i −0.565140 1.22535i
\(373\) 30.5923i 1.58401i −0.610515 0.792005i \(-0.709037\pi\)
0.610515 0.792005i \(-0.290963\pi\)
\(374\) 0.831218 + 3.78698i 0.0429813 + 0.195820i
\(375\) 1.34113i 0.0692558i
\(376\) −21.2161 + 16.0685i −1.09414 + 0.828669i
\(377\) 5.39263i 0.277734i
\(378\) 20.2088 + 6.00704i 1.03943 + 0.308969i
\(379\) −10.6930 −0.549262 −0.274631 0.961550i \(-0.588556\pi\)
−0.274631 + 0.961550i \(0.588556\pi\)
\(380\) 7.07600 + 15.3423i 0.362991 + 0.787045i
\(381\) 22.0196 1.12810
\(382\) 6.24044 + 28.4310i 0.319288 + 1.45466i
\(383\) 9.36792 0.478679 0.239339 0.970936i \(-0.423069\pi\)
0.239339 + 0.970936i \(0.423069\pi\)
\(384\) −15.1474 0.884449i −0.772987 0.0451343i
\(385\) −3.13362 + 5.66853i −0.159704 + 0.288895i
\(386\) −13.9086 + 3.05285i −0.707929 + 0.155386i
\(387\) 8.95606 0.455262
\(388\) 0.698539 + 1.51459i 0.0354629 + 0.0768914i
\(389\) 2.30373i 0.116804i 0.998293 + 0.0584019i \(0.0186005\pi\)
−0.998293 + 0.0584019i \(0.981399\pi\)
\(390\) 0.638766 + 2.91017i 0.0323452 + 0.147362i
\(391\) −2.94480 −0.148925
\(392\) 18.5173 + 7.00791i 0.935263 + 0.353953i
\(393\) 2.68693 0.135538
\(394\) 1.39329 + 6.34774i 0.0701929 + 0.319794i
\(395\) 7.70558i 0.387710i
\(396\) 5.34136 2.46348i 0.268413 0.123794i
\(397\) 1.77718 0.0891942 0.0445971 0.999005i \(-0.485800\pi\)
0.0445971 + 0.999005i \(0.485800\pi\)
\(398\) 2.97604 0.653222i 0.149175 0.0327431i
\(399\) 14.5021 26.2335i 0.726015 1.31332i
\(400\) 2.59678 3.04249i 0.129839 0.152124i
\(401\) 17.8159 0.889682 0.444841 0.895609i \(-0.353260\pi\)
0.444841 + 0.895609i \(0.353260\pi\)
\(402\) 0.876114 + 3.99152i 0.0436966 + 0.199079i
\(403\) 15.2425 0.759285
\(404\) 10.0324 4.62703i 0.499132 0.230203i
\(405\) −3.95264 −0.196408
\(406\) 12.3120 + 3.65973i 0.611035 + 0.181629i
\(407\) 15.2445i 0.755643i
\(408\) −3.38639 + 2.56475i −0.167651 + 0.126974i
\(409\) 37.8691i 1.87250i −0.351329 0.936252i \(-0.614270\pi\)
0.351329 0.936252i \(-0.385730\pi\)
\(410\) 0.949384 + 4.32533i 0.0468868 + 0.213613i
\(411\) 5.64538i 0.278466i
\(412\) 21.3716 9.85674i 1.05290 0.485606i
\(413\) 14.2644 + 7.88551i 0.701906 + 0.388021i
\(414\) 0.957816 + 4.36375i 0.0470741 + 0.214466i
\(415\) 0.813234i 0.0399201i
\(416\) 4.18575 7.83882i 0.205223 0.384330i
\(417\) 5.64159 0.276270
\(418\) −6.27028 28.5670i −0.306689 1.39726i
\(419\) 3.11076i 0.151971i −0.997109 0.0759854i \(-0.975790\pi\)
0.997109 0.0759854i \(-0.0242102\pi\)
\(420\) −7.07778 0.516625i −0.345360 0.0252087i
\(421\) 18.8952i 0.920893i 0.887687 + 0.460447i \(0.152311\pi\)
−0.887687 + 0.460447i \(0.847689\pi\)
\(422\) 16.2228 3.56082i 0.789716 0.173338i
\(423\) 11.3043 0.549634
\(424\) 19.8205 + 26.1701i 0.962569 + 1.27093i
\(425\) 1.11987i 0.0543218i
\(426\) −14.5830 + 3.20088i −0.706548 + 0.155083i
\(427\) −12.0864 + 21.8636i −0.584904 + 1.05805i
\(428\) −2.52430 + 1.16423i −0.122017 + 0.0562751i
\(429\) 5.15760i 0.249011i
\(430\) −10.2977 + 2.26029i −0.496600 + 0.109001i
\(431\) 38.2730i 1.84355i −0.387730 0.921773i \(-0.626741\pi\)
0.387730 0.921773i \(-0.373259\pi\)
\(432\) 17.1432 + 14.6318i 0.824800 + 0.703972i
\(433\) 1.50589i 0.0723684i 0.999345 + 0.0361842i \(0.0115203\pi\)
−0.999345 + 0.0361842i \(0.988480\pi\)
\(434\) −10.3444 + 34.8005i −0.496548 + 1.67048i
\(435\) −4.60387 −0.220738
\(436\) 0.900648 + 1.95280i 0.0431332 + 0.0935223i
\(437\) 22.2141 1.06264
\(438\) −23.3690 + 5.12936i −1.11662 + 0.245090i
\(439\) −5.00779 −0.239009 −0.119504 0.992834i \(-0.538131\pi\)
−0.119504 + 0.992834i \(0.538131\pi\)
\(440\) −5.51979 + 4.18054i −0.263146 + 0.199299i
\(441\) −4.47272 7.12145i −0.212987 0.339117i
\(442\) −0.533382 2.43005i −0.0253704 0.115586i
\(443\) −24.9714 −1.18643 −0.593213 0.805046i \(-0.702141\pi\)
−0.593213 + 0.805046i \(0.702141\pi\)
\(444\) −15.1674 + 6.99531i −0.719812 + 0.331983i
\(445\) 5.12287i 0.242847i
\(446\) 9.56056 2.09848i 0.452706 0.0993661i
\(447\) −25.6743 −1.21435
\(448\) 15.0563 + 14.8764i 0.711343 + 0.702845i
\(449\) −4.85721 −0.229226 −0.114613 0.993410i \(-0.536563\pi\)
−0.114613 + 0.993410i \(0.536563\pi\)
\(450\) −1.65948 + 0.364245i −0.0782286 + 0.0171707i
\(451\) 7.66564i 0.360961i
\(452\) 20.3348 9.37857i 0.956468 0.441131i
\(453\) 3.66441 0.172169
\(454\) 3.69964 + 16.8553i 0.173633 + 0.791059i
\(455\) 2.01081 3.63742i 0.0942680 0.170525i
\(456\) 25.5451 19.3472i 1.19626 0.906014i
\(457\) −21.1002 −0.987025 −0.493513 0.869739i \(-0.664287\pi\)
−0.493513 + 0.869739i \(0.664287\pi\)
\(458\) −16.9326 + 3.71659i −0.791206 + 0.173665i
\(459\) 6.31002 0.294526
\(460\) −2.20260 4.77572i −0.102697 0.222669i
\(461\) −11.2426 −0.523620 −0.261810 0.965119i \(-0.584319\pi\)
−0.261810 + 0.965119i \(0.584319\pi\)
\(462\) 11.7754 + 3.50023i 0.547843 + 0.162846i
\(463\) 39.4199i 1.83200i 0.401179 + 0.916000i \(0.368601\pi\)
−0.401179 + 0.916000i \(0.631399\pi\)
\(464\) 10.4443 + 8.91428i 0.484865 + 0.413835i
\(465\) 13.0131i 0.603466i
\(466\) 14.0233 3.07804i 0.649619 0.142587i
\(467\) 26.4941i 1.22600i −0.790083 0.613000i \(-0.789963\pi\)
0.790083 0.613000i \(-0.210037\pi\)
\(468\) −3.42748 + 1.58078i −0.158435 + 0.0730716i
\(469\) 2.75797 4.98899i 0.127351 0.230370i
\(470\) −12.9977 + 2.85292i −0.599540 + 0.131595i
\(471\) 18.1644i 0.836973i
\(472\) 10.5200 + 13.8901i 0.484222 + 0.639344i
\(473\) 18.2503 0.839149
\(474\) 14.2750 3.13327i 0.655671 0.143916i
\(475\) 8.44773i 0.387608i
\(476\) 5.91008 + 0.431392i 0.270888 + 0.0197728i
\(477\) 13.9439i 0.638446i
\(478\) −1.69034 7.70106i −0.0773142 0.352238i
\(479\) −35.7827 −1.63495 −0.817477 0.575961i \(-0.804628\pi\)
−0.817477 + 0.575961i \(0.804628\pi\)
\(480\) −6.69226 3.57352i −0.305459 0.163108i
\(481\) 9.78221i 0.446031i
\(482\) −6.36140 28.9821i −0.289754 1.32010i
\(483\) −4.51419 + 8.16590i −0.205403 + 0.371561i
\(484\) −9.09323 + 4.19387i −0.413329 + 0.190630i
\(485\) 0.833955i 0.0378680i
\(486\) −3.51788 16.0272i −0.159574 0.727009i
\(487\) 12.4491i 0.564125i −0.959396 0.282062i \(-0.908982\pi\)
0.959396 0.282062i \(-0.0910185\pi\)
\(488\) −21.2899 + 16.1244i −0.963750 + 0.729917i
\(489\) 24.8534i 1.12391i
\(490\) 6.94003 + 7.05946i 0.313519 + 0.318914i
\(491\) −14.4396 −0.651649 −0.325824 0.945430i \(-0.605642\pi\)
−0.325824 + 0.945430i \(0.605642\pi\)
\(492\) 7.62684 3.51756i 0.343845 0.158584i
\(493\) 3.84432 0.173139
\(494\) 4.02355 + 18.3310i 0.181028 + 0.824753i
\(495\) 2.94104 0.132190
\(496\) −25.1967 + 29.5214i −1.13136 + 1.32555i
\(497\) 18.2272 + 10.0762i 0.817603 + 0.451980i
\(498\) −1.50655 + 0.330680i −0.0675103 + 0.0148181i
\(499\) 22.0969 0.989195 0.494597 0.869122i \(-0.335315\pi\)
0.494597 + 0.869122i \(0.335315\pi\)
\(500\) 1.81615 0.837621i 0.0812206 0.0374596i
\(501\) 10.3883i 0.464116i
\(502\) 6.93531 + 31.5968i 0.309538 + 1.41023i
\(503\) 21.8311 0.973401 0.486701 0.873569i \(-0.338200\pi\)
0.486701 + 0.873569i \(0.338200\pi\)
\(504\) −1.28304 8.89815i −0.0571509 0.396355i
\(505\) 5.52401 0.245815
\(506\) 1.95180 + 8.89226i 0.0867679 + 0.395309i
\(507\) 14.1252i 0.627320i
\(508\) −13.7526 29.8187i −0.610173 1.32299i
\(509\) −30.6514 −1.35860 −0.679300 0.733861i \(-0.737716\pi\)
−0.679300 + 0.733861i \(0.737716\pi\)
\(510\) −2.07462 + 0.455366i −0.0918656 + 0.0201639i
\(511\) 29.2089 + 16.1470i 1.29213 + 0.714301i
\(512\) 8.26278 + 21.0648i 0.365167 + 0.930942i
\(513\) −47.5995 −2.10157
\(514\) −8.75524 39.8883i −0.386177 1.75940i
\(515\) 11.7675 0.518539
\(516\) 8.37457 + 18.1579i 0.368670 + 0.799358i
\(517\) 23.0354 1.01310
\(518\) 22.3340 + 6.63874i 0.981298 + 0.291690i
\(519\) 18.2545i 0.801282i
\(520\) 3.54198 2.68260i 0.155326 0.117640i
\(521\) 7.13741i 0.312696i −0.987702 0.156348i \(-0.950028\pi\)
0.987702 0.156348i \(-0.0499721\pi\)
\(522\) −1.25039 5.69669i −0.0547280 0.249337i
\(523\) 31.6160i 1.38247i 0.722630 + 0.691235i \(0.242933\pi\)
−0.722630 + 0.691235i \(0.757067\pi\)
\(524\) −1.67816 3.63861i −0.0733105 0.158953i
\(525\) −3.10539 1.71669i −0.135530 0.0749225i
\(526\) −5.94311 27.0764i −0.259132 1.18059i
\(527\) 10.8662i 0.473338i
\(528\) 9.98912 + 8.52577i 0.434721 + 0.371037i
\(529\) 16.0853 0.699359
\(530\) 3.51908 + 16.0327i 0.152859 + 0.696416i
\(531\) 7.40088i 0.321171i
\(532\) −44.5826 3.25419i −1.93290 0.141087i
\(533\) 4.91894i 0.213063i
\(534\) −9.49036 + 2.08308i −0.410688 + 0.0901436i
\(535\) −1.38992 −0.0600916
\(536\) 4.85808 3.67938i 0.209837 0.158925i
\(537\) 23.2512i 1.00336i
\(538\) −37.6317 + 8.25993i −1.62242 + 0.356111i
\(539\) −9.11433 14.5118i −0.392582 0.625067i
\(540\) 4.71965 + 10.2332i 0.203101 + 0.440368i
\(541\) 39.5347i 1.69973i 0.526999 + 0.849866i \(0.323317\pi\)
−0.526999 + 0.849866i \(0.676683\pi\)
\(542\) −35.9614 + 7.89330i −1.54467 + 0.339046i
\(543\) 15.8613i 0.680672i
\(544\) 5.58817 + 2.98396i 0.239591 + 0.127936i
\(545\) 1.07524i 0.0460584i
\(546\) −7.55614 2.24605i −0.323373 0.0961222i
\(547\) 27.6549 1.18244 0.591218 0.806512i \(-0.298647\pi\)
0.591218 + 0.806512i \(0.298647\pi\)
\(548\) 7.64491 3.52589i 0.326574 0.150619i
\(549\) 11.3436 0.484134
\(550\) −3.38161 + 0.742244i −0.144193 + 0.0316494i
\(551\) −28.9995 −1.23542
\(552\) −7.95162 + 6.02234i −0.338444 + 0.256328i
\(553\) −17.8422 9.86338i −0.758730 0.419434i
\(554\) −1.71253 7.80216i −0.0727583 0.331482i
\(555\) −8.35140 −0.354497
\(556\) −3.52352 7.63977i −0.149431 0.323999i
\(557\) 29.2830i 1.24076i 0.784301 + 0.620380i \(0.213022\pi\)
−0.784301 + 0.620380i \(0.786978\pi\)
\(558\) 16.1020 3.53429i 0.681651 0.149618i
\(559\) −11.7110 −0.495321
\(560\) 3.72091 + 9.90731i 0.157237 + 0.418660i
\(561\) 3.67677 0.155234
\(562\) −35.8288 + 7.86421i −1.51135 + 0.331732i
\(563\) 5.22412i 0.220170i 0.993922 + 0.110085i \(0.0351124\pi\)
−0.993922 + 0.110085i \(0.964888\pi\)
\(564\) 10.5703 + 22.9188i 0.445092 + 0.965057i
\(565\) 11.1967 0.471047
\(566\) 3.82211 + 17.4133i 0.160655 + 0.731934i
\(567\) 5.05950 9.15233i 0.212479 0.384362i
\(568\) 13.4426 + 17.7490i 0.564038 + 0.744730i
\(569\) 11.8297 0.495925 0.247963 0.968770i \(-0.420239\pi\)
0.247963 + 0.968770i \(0.420239\pi\)
\(570\) 15.6498 3.43504i 0.655499 0.143878i
\(571\) −22.3223 −0.934158 −0.467079 0.884216i \(-0.654694\pi\)
−0.467079 + 0.884216i \(0.654694\pi\)
\(572\) −6.98437 + 3.22125i −0.292031 + 0.134687i
\(573\) 27.6037 1.15316
\(574\) −11.2305 3.33826i −0.468753 0.139336i
\(575\) 2.62959i 0.109661i
\(576\) 2.60418 9.25136i 0.108507 0.385473i
\(577\) 25.4830i 1.06087i −0.847725 0.530436i \(-0.822028\pi\)
0.847725 0.530436i \(-0.177972\pi\)
\(578\) −21.7503 + 4.77405i −0.904692 + 0.198574i
\(579\) 13.5038i 0.561201i
\(580\) 2.87540 + 6.23450i 0.119395 + 0.258874i
\(581\) 1.88304 + 1.04096i 0.0781216 + 0.0431865i
\(582\) 1.54494 0.339105i 0.0640399 0.0140564i
\(583\) 28.4142i 1.17680i
\(584\) 21.5416 + 28.4425i 0.891396 + 1.17696i
\(585\) −1.88722 −0.0780271
\(586\) 23.2039 5.09311i 0.958543 0.210394i
\(587\) 27.1365i 1.12004i 0.828478 + 0.560021i \(0.189207\pi\)
−0.828478 + 0.560021i \(0.810793\pi\)
\(588\) 10.2560 15.7273i 0.422951 0.648582i
\(589\) 81.9687i 3.37746i
\(590\) 1.86780 + 8.50956i 0.0768960 + 0.350333i
\(591\) 6.16301 0.253512
\(592\) 18.9459 + 16.1705i 0.778673 + 0.664602i
\(593\) 33.7929i 1.38771i −0.720116 0.693853i \(-0.755912\pi\)
0.720116 0.693853i \(-0.244088\pi\)
\(594\) −4.18224 19.0540i −0.171599 0.781795i
\(595\) 2.59306 + 1.43347i 0.106305 + 0.0587666i
\(596\) 16.0352 + 34.7679i 0.656829 + 1.42415i
\(597\) 2.88943i 0.118257i
\(598\) −1.25244 5.70604i −0.0512162 0.233337i
\(599\) 26.0094i 1.06271i −0.847148 0.531357i \(-0.821682\pi\)
0.847148 0.531357i \(-0.178318\pi\)
\(600\) −2.29022 3.02390i −0.0934979 0.123450i
\(601\) 25.5296i 1.04137i −0.853747 0.520687i \(-0.825676\pi\)
0.853747 0.520687i \(-0.174324\pi\)
\(602\) 7.94770 26.7375i 0.323924 1.08974i
\(603\) −2.58847 −0.105411
\(604\) −2.28865 4.96230i −0.0931239 0.201913i
\(605\) −5.00688 −0.203559
\(606\) −2.24619 10.2335i −0.0912453 0.415708i
\(607\) 21.2033 0.860615 0.430307 0.902682i \(-0.358405\pi\)
0.430307 + 0.902682i \(0.358405\pi\)
\(608\) −42.1542 22.5094i −1.70958 0.912877i
\(609\) 5.89309 10.6602i 0.238800 0.431974i
\(610\) −13.0429 + 2.86285i −0.528093 + 0.115913i
\(611\) −14.7815 −0.597996
\(612\) −1.12691 2.44339i −0.0455527 0.0987684i
\(613\) 0.381509i 0.0154090i 0.999970 + 0.00770450i \(0.00245244\pi\)
−0.999970 + 0.00770450i \(0.997548\pi\)
\(614\) −1.54207 7.02557i −0.0622329 0.283529i
\(615\) 4.19946 0.169339
\(616\) −2.61452 18.1323i −0.105342 0.730570i
\(617\) −23.7394 −0.955714 −0.477857 0.878438i \(-0.658586\pi\)
−0.477857 + 0.878438i \(0.658586\pi\)
\(618\) −4.78495 21.7999i −0.192479 0.876921i
\(619\) 3.66231i 0.147201i 0.997288 + 0.0736004i \(0.0234489\pi\)
−0.997288 + 0.0736004i \(0.976551\pi\)
\(620\) −17.6221 + 8.12747i −0.707722 + 0.326407i
\(621\) 14.8166 0.594571
\(622\) 23.3855 5.13297i 0.937672 0.205813i
\(623\) 11.8620 + 6.55743i 0.475240 + 0.262718i
\(624\) −6.40988 5.47088i −0.256601 0.219010i
\(625\) 1.00000 0.0400000
\(626\) 2.51890 + 11.4760i 0.100676 + 0.458672i
\(627\) −27.7357 −1.10766
\(628\) 24.5981 11.3448i 0.981569 0.452707i
\(629\) 6.97358 0.278055
\(630\) 1.28077 4.30876i 0.0510273 0.171665i
\(631\) 10.6277i 0.423080i 0.977369 + 0.211540i \(0.0678479\pi\)
−0.977369 + 0.211540i \(0.932152\pi\)
\(632\) −13.1586 17.3741i −0.523423 0.691103i
\(633\) 15.7508i 0.626036i
\(634\) 3.25715 + 14.8394i 0.129358 + 0.589347i
\(635\) 16.4186i 0.651554i
\(636\) 28.2704 13.0385i 1.12099 0.517011i
\(637\) 5.84854 + 9.31202i 0.231728 + 0.368956i
\(638\) −2.54799 11.6085i −0.100876 0.459584i
\(639\) 9.45694i 0.374111i
\(640\) −0.659479 + 11.2945i −0.0260682 + 0.446453i
\(641\) −31.4300 −1.24141 −0.620705 0.784044i \(-0.713154\pi\)
−0.620705 + 0.784044i \(0.713154\pi\)
\(642\) 0.565174 + 2.57490i 0.0223057 + 0.101623i
\(643\) 7.82074i 0.308420i −0.988038 0.154210i \(-0.950717\pi\)
0.988038 0.154210i \(-0.0492832\pi\)
\(644\) 13.8776 + 1.01296i 0.546852 + 0.0399161i
\(645\) 9.99804i 0.393673i
\(646\) −13.0679 + 2.86833i −0.514150 + 0.112853i
\(647\) 27.3346 1.07463 0.537317 0.843381i \(-0.319438\pi\)
0.537317 + 0.843381i \(0.319438\pi\)
\(648\) 8.91217 6.74983i 0.350103 0.265158i
\(649\) 15.0812i 0.591989i
\(650\) 2.16994 0.476288i 0.0851119 0.0186816i
\(651\) 30.1317 + 16.6571i 1.18095 + 0.652844i
\(652\) −33.6562 + 15.5225i −1.31808 + 0.607908i
\(653\) 19.6566i 0.769221i 0.923079 + 0.384611i \(0.125664\pi\)
−0.923079 + 0.384611i \(0.874336\pi\)
\(654\) 1.99194 0.437219i 0.0778911 0.0170966i
\(655\) 2.00348i 0.0782823i
\(656\) −9.52688 8.13125i −0.371962 0.317472i
\(657\) 15.1546i 0.591239i
\(658\) 10.0315 33.7480i 0.391070 1.31563i
\(659\) 14.1522 0.551293 0.275647 0.961259i \(-0.411108\pi\)
0.275647 + 0.961259i \(0.411108\pi\)
\(660\) 2.75008 + 5.96279i 0.107047 + 0.232101i
\(661\) −7.32100 −0.284754 −0.142377 0.989812i \(-0.545475\pi\)
−0.142377 + 0.989812i \(0.545475\pi\)
\(662\) −16.8162 + 3.69106i −0.653581 + 0.143457i
\(663\) −2.35934 −0.0916291
\(664\) 1.38874 + 1.83363i 0.0538935 + 0.0711586i
\(665\) −19.5607 10.8134i −0.758531 0.419324i
\(666\) −2.26820 10.3338i −0.0878910 0.400426i
\(667\) 9.02690 0.349523
\(668\) −14.0677 + 6.48815i −0.544297 + 0.251034i
\(669\) 9.28234i 0.358876i
\(670\) 2.97623 0.653264i 0.114982 0.0252378i
\(671\) 23.1156 0.892367
\(672\) 16.8408 10.9217i 0.649647 0.421314i
\(673\) 21.5006 0.828786 0.414393 0.910098i \(-0.363994\pi\)
0.414393 + 0.910098i \(0.363994\pi\)
\(674\) 15.9800 3.50751i 0.615527 0.135104i
\(675\) 5.63459i 0.216875i
\(676\) −19.1281 + 8.82205i −0.735698 + 0.339309i
\(677\) −41.7438 −1.60434 −0.802172 0.597093i \(-0.796322\pi\)
−0.802172 + 0.597093i \(0.796322\pi\)
\(678\) −4.55282 20.7424i −0.174850 0.796606i
\(679\) −1.93102 1.06749i −0.0741057 0.0409664i
\(680\) 1.91238 + 2.52502i 0.0733364 + 0.0968300i
\(681\) 16.3648 0.627101
\(682\) 32.8119 7.20202i 1.25643 0.275780i
\(683\) 26.9066 1.02955 0.514777 0.857324i \(-0.327875\pi\)
0.514777 + 0.857324i \(0.327875\pi\)
\(684\) 8.50084 + 18.4317i 0.325038 + 0.704753i
\(685\) 4.20941 0.160833
\(686\) −25.2296 + 7.03328i −0.963271 + 0.268532i
\(687\) 16.4398i 0.627218i
\(688\) 19.3588 22.6815i 0.738048 0.864724i
\(689\) 18.2330i 0.694623i
\(690\) −4.87144 + 1.06925i −0.185453 + 0.0407057i
\(691\) 17.3610i 0.660443i 0.943904 + 0.330221i \(0.107123\pi\)
−0.943904 + 0.330221i \(0.892877\pi\)
\(692\) −24.7200 + 11.4010i −0.939713 + 0.433403i
\(693\) −3.76462 + 6.80996i −0.143006 + 0.258689i
\(694\) 14.7403 3.23541i 0.559534 0.122814i
\(695\) 4.20658i 0.159565i
\(696\) 10.3805 7.86191i 0.393472 0.298005i
\(697\) −3.50663 −0.132823
\(698\) 20.0375 4.39811i 0.758431 0.166471i
\(699\) 13.6153i 0.514976i
\(700\) −0.385215 + 5.27746i −0.0145598 + 0.199469i
\(701\) 31.9368i 1.20624i −0.797651 0.603119i \(-0.793924\pi\)
0.797651 0.603119i \(-0.206076\pi\)
\(702\) 2.68369 + 12.2267i 0.101289 + 0.461467i
\(703\) −52.6051 −1.98404
\(704\) 5.30668 18.8520i 0.200003 0.710513i
\(705\) 12.6195i 0.475277i
\(706\) −10.0670 45.8644i −0.378875 1.72613i
\(707\) −7.07091 + 12.7908i −0.265929 + 0.481049i
\(708\) 15.0049 6.92037i 0.563918 0.260083i
\(709\) 1.65295i 0.0620777i −0.999518 0.0310389i \(-0.990118\pi\)
0.999518 0.0310389i \(-0.00988157\pi\)
\(710\) 2.38669 + 10.8736i 0.0895711 + 0.408080i
\(711\) 9.25720i 0.347172i
\(712\) 8.74820 + 11.5507i 0.327853 + 0.432882i
\(713\) 25.5150i 0.955544i
\(714\) 1.60118 5.38665i 0.0599225 0.201590i
\(715\) −3.84571 −0.143821
\(716\) −31.4865 + 14.5218i −1.17671 + 0.542706i
\(717\) −7.47696 −0.279232
\(718\) −4.03908 18.4018i −0.150737 0.686749i
\(719\) −16.0007 −0.596725 −0.298363 0.954453i \(-0.596440\pi\)
−0.298363 + 0.954453i \(0.596440\pi\)
\(720\) 3.11968 3.65513i 0.116263 0.136219i
\(721\) −15.0628 + 27.2477i −0.560968 + 1.01476i
\(722\) 72.3322 15.8765i 2.69193 0.590861i
\(723\) −28.1387 −1.04649
\(724\) 21.4791 9.90634i 0.798266 0.368166i
\(725\) 3.43282i 0.127492i
\(726\) 2.03591 + 9.27548i 0.0755598 + 0.344245i
\(727\) −7.28793 −0.270294 −0.135147 0.990826i \(-0.543151\pi\)
−0.135147 + 0.990826i \(0.543151\pi\)
\(728\) 1.67770 + 11.6352i 0.0621797 + 0.431231i
\(729\) −27.4187 −1.01551
\(730\) 3.82465 + 17.4249i 0.141557 + 0.644923i
\(731\) 8.34856i 0.308783i
\(732\) 10.6071 + 22.9986i 0.392051 + 0.850052i
\(733\) −4.79246 −0.177013 −0.0885067 0.996076i \(-0.528209\pi\)
−0.0885067 + 0.996076i \(0.528209\pi\)
\(734\) 35.8333 7.86519i 1.32263 0.290310i
\(735\) 7.94998 4.99310i 0.293240 0.184173i
\(736\) 13.1217 + 7.00667i 0.483671 + 0.258269i
\(737\) −5.27467 −0.194295
\(738\) 1.14055 + 5.19629i 0.0419844 + 0.191278i
\(739\) 37.3432 1.37369 0.686845 0.726804i \(-0.258995\pi\)
0.686845 + 0.726804i \(0.258995\pi\)
\(740\) 5.21597 + 11.3094i 0.191743 + 0.415741i
\(741\) 17.7976 0.653811
\(742\) −41.6282 12.3739i −1.52822 0.454261i
\(743\) 14.9317i 0.547789i −0.961760 0.273895i \(-0.911688\pi\)
0.961760 0.273895i \(-0.0883119\pi\)
\(744\) 22.2221 + 29.3410i 0.814702 + 1.07570i
\(745\) 19.1438i 0.701373i
\(746\) 9.27539 + 42.2581i 0.339596 + 1.54718i
\(747\) 0.976988i 0.0357461i
\(748\) −2.29637 4.97905i −0.0839638 0.182052i
\(749\) 1.77914 3.21836i 0.0650085 0.117596i
\(750\) −0.406623 1.85255i −0.0148478 0.0676455i
\(751\) 32.2962i 1.17851i 0.807948 + 0.589253i \(0.200578\pi\)
−0.807948 + 0.589253i \(0.799422\pi\)
\(752\) 24.4346 28.6285i 0.891037 1.04397i
\(753\) 30.6773 1.11794
\(754\) 1.63501 + 7.44900i 0.0595436 + 0.271277i
\(755\) 2.73232i 0.0994394i
\(756\) −29.7363 2.17053i −1.08150 0.0789413i
\(757\) 21.1662i 0.769299i 0.923063 + 0.384650i \(0.125678\pi\)
−0.923063 + 0.384650i \(0.874322\pi\)
\(758\) 14.7705 3.24205i 0.536490 0.117756i
\(759\) 8.63349 0.313376
\(760\) −14.4260 19.0474i −0.523286 0.690922i
\(761\) 8.98517i 0.325712i 0.986650 + 0.162856i \(0.0520706\pi\)
−0.986650 + 0.162856i \(0.947929\pi\)
\(762\) −30.4163 + 6.67620i −1.10187 + 0.241853i
\(763\) −2.48972 1.37635i −0.0901341 0.0498271i
\(764\) −17.2402 37.3806i −0.623729 1.35238i
\(765\) 1.34537i 0.0486420i
\(766\) −12.9402 + 2.84030i −0.467548 + 0.102624i
\(767\) 9.67741i 0.349431i
\(768\) 21.1917 3.37088i 0.764690 0.121636i
\(769\) 38.3718i 1.38372i 0.722031 + 0.691861i \(0.243209\pi\)
−0.722031 + 0.691861i \(0.756791\pi\)
\(770\) 2.60991 8.78021i 0.0940545 0.316417i
\(771\) −38.7275 −1.39474
\(772\) 18.2868 8.43399i 0.658155 0.303546i
\(773\) 5.61383 0.201916 0.100958 0.994891i \(-0.467809\pi\)
0.100958 + 0.994891i \(0.467809\pi\)
\(774\) −12.3713 + 2.71542i −0.444677 + 0.0976038i
\(775\) −9.70304 −0.348543
\(776\) −1.42413 1.88035i −0.0511231 0.0675006i
\(777\) 10.6900 19.3376i 0.383503 0.693734i
\(778\) −0.698477 3.18222i −0.0250416 0.114088i
\(779\) 26.4522 0.947749