Properties

Label 300.2.h.b.299.8
Level $300$
Weight $2$
Character 300.299
Analytic conductor $2.396$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 300.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.39551206064\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
Defining polynomial: \(x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 299.8
Root \(-0.599676 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 300.299
Dual form 300.2.h.b.299.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 + 1.53610i) q^{4} +(2.41656 + 0.400324i) q^{6} -0.936426 q^{7} +(0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +O(q^{10})\) \(q+(1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 + 1.53610i) q^{4} +(2.41656 + 0.400324i) q^{6} -0.936426 q^{7} +(0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} -4.27156 q^{11} +(2.85500 + 1.96188i) q^{12} -3.12311i q^{13} +(-1.19935 - 0.561553i) q^{14} +(-0.719224 + 3.93481i) q^{16} -2.00000 q^{17} +(4.21720 - 0.463897i) q^{18} +4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(-5.47091 - 2.56155i) q^{22} -7.60669i q^{23} +(2.48013 + 4.22480i) q^{24} +(1.87285 - 4.00000i) q^{26} +(3.54042 - 3.80335i) q^{27} +(-1.19935 - 1.43845i) q^{28} +5.12311i q^{29} -2.39871i q^{31} +(-3.28078 + 4.60831i) q^{32} +(-7.12311 + 2.00000i) q^{33} +(-2.56155 - 1.19935i) q^{34} +(5.67948 + 1.93481i) q^{36} -3.12311i q^{37} +(-2.56155 + 5.47091i) q^{38} +(-1.46228 - 5.20798i) q^{39} +7.12311i q^{41} +(-2.26293 - 0.374874i) q^{42} +1.46228 q^{43} +(-5.47091 - 6.56155i) q^{44} +(4.56155 - 9.74247i) q^{46} -0.936426i q^{47} +(0.642976 + 6.89830i) q^{48} -6.12311 q^{49} +(-3.33513 + 0.936426i) q^{51} +(4.79741 - 4.00000i) q^{52} +4.24621 q^{53} +(6.81526 - 2.74813i) q^{54} +(-0.673500 - 2.56155i) q^{56} +(2.00000 + 7.12311i) q^{57} +(-3.07221 + 6.56155i) q^{58} +7.19612 q^{59} -5.12311 q^{61} +(1.43845 - 3.07221i) q^{62} +(-2.39871 + 1.46228i) q^{63} +(-6.96543 + 3.93481i) q^{64} +(-10.3225 - 1.71001i) q^{66} -5.20798 q^{67} +(-2.56155 - 3.07221i) q^{68} +(-3.56155 - 12.6847i) q^{69} +6.67026 q^{71} +(6.11389 + 5.88391i) q^{72} +8.24621i q^{73} +(1.87285 - 4.00000i) q^{74} +(-6.56155 + 5.47091i) q^{76} +4.00000 q^{77} +(1.25025 - 7.54716i) q^{78} -9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(-4.27156 + 9.12311i) q^{82} +4.68213i q^{83} +(-2.67350 - 1.83715i) q^{84} +(1.87285 + 0.876894i) q^{86} +(2.39871 + 8.54312i) q^{87} +(-3.07221 - 11.6847i) q^{88} +6.24621i q^{89} +2.92456i q^{91} +(11.6847 - 9.74247i) q^{92} +(-1.12311 - 4.00000i) q^{93} +(0.561553 - 1.19935i) q^{94} +(-3.31324 + 9.22076i) q^{96} -6.00000i q^{97} +(-7.84233 - 3.67188i) q^{98} +(-10.9418 + 6.67026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} + 2q^{4} - 6q^{6} + 14q^{8} + 4q^{9} + O(q^{10}) \) \( 8q + 2q^{2} + 2q^{4} - 6q^{6} + 14q^{8} + 4q^{9} + 14q^{12} - 14q^{16} - 16q^{17} + 18q^{18} + 4q^{21} + 2q^{24} - 18q^{32} - 24q^{33} - 4q^{34} + 18q^{36} - 4q^{38} - 16q^{42} + 20q^{46} - 10q^{48} - 16q^{49} - 32q^{53} + 10q^{54} + 16q^{57} - 8q^{61} + 28q^{62} + 2q^{64} - 40q^{66} - 4q^{68} - 12q^{69} - 10q^{72} - 36q^{76} + 32q^{77} - 8q^{78} - 16q^{84} + 44q^{92} + 24q^{93} - 12q^{94} + 42q^{96} - 38q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(151\) \(277\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28078 + 0.599676i 0.905646 + 0.424035i
\(3\) 1.66757 0.468213i 0.962770 0.270323i
\(4\) 1.28078 + 1.53610i 0.640388 + 0.768051i
\(5\) 0 0
\(6\) 2.41656 + 0.400324i 0.986555 + 0.163431i
\(7\) −0.936426 −0.353936 −0.176968 0.984217i \(-0.556629\pi\)
−0.176968 + 0.984217i \(0.556629\pi\)
\(8\) 0.719224 + 2.73546i 0.254284 + 0.967130i
\(9\) 2.56155 1.56155i 0.853851 0.520518i
\(10\) 0 0
\(11\) −4.27156 −1.28792 −0.643962 0.765058i \(-0.722710\pi\)
−0.643962 + 0.765058i \(0.722710\pi\)
\(12\) 2.85500 + 1.96188i 0.824168 + 0.566345i
\(13\) 3.12311i 0.866194i −0.901347 0.433097i \(-0.857421\pi\)
0.901347 0.433097i \(-0.142579\pi\)
\(14\) −1.19935 0.561553i −0.320541 0.150081i
\(15\) 0 0
\(16\) −0.719224 + 3.93481i −0.179806 + 0.983702i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 4.21720 0.463897i 0.994004 0.109342i
\(19\) 4.27156i 0.979963i 0.871733 + 0.489981i \(0.162996\pi\)
−0.871733 + 0.489981i \(0.837004\pi\)
\(20\) 0 0
\(21\) −1.56155 + 0.438447i −0.340759 + 0.0956770i
\(22\) −5.47091 2.56155i −1.16640 0.546125i
\(23\) 7.60669i 1.58610i −0.609154 0.793052i \(-0.708491\pi\)
0.609154 0.793052i \(-0.291509\pi\)
\(24\) 2.48013 + 4.22480i 0.506254 + 0.862384i
\(25\) 0 0
\(26\) 1.87285 4.00000i 0.367297 0.784465i
\(27\) 3.54042 3.80335i 0.681354 0.731954i
\(28\) −1.19935 1.43845i −0.226656 0.271841i
\(29\) 5.12311i 0.951337i 0.879625 + 0.475668i \(0.157794\pi\)
−0.879625 + 0.475668i \(0.842206\pi\)
\(30\) 0 0
\(31\) 2.39871i 0.430820i −0.976524 0.215410i \(-0.930891\pi\)
0.976524 0.215410i \(-0.0691088\pi\)
\(32\) −3.28078 + 4.60831i −0.579965 + 0.814642i
\(33\) −7.12311 + 2.00000i −1.23997 + 0.348155i
\(34\) −2.56155 1.19935i −0.439303 0.205687i
\(35\) 0 0
\(36\) 5.67948 + 1.93481i 0.946580 + 0.322468i
\(37\) 3.12311i 0.513435i −0.966486 0.256718i \(-0.917359\pi\)
0.966486 0.256718i \(-0.0826411\pi\)
\(38\) −2.56155 + 5.47091i −0.415539 + 0.887499i
\(39\) −1.46228 5.20798i −0.234152 0.833945i
\(40\) 0 0
\(41\) 7.12311i 1.11244i 0.831034 + 0.556221i \(0.187749\pi\)
−0.831034 + 0.556221i \(0.812251\pi\)
\(42\) −2.26293 0.374874i −0.349177 0.0578442i
\(43\) 1.46228 0.222995 0.111498 0.993765i \(-0.464435\pi\)
0.111498 + 0.993765i \(0.464435\pi\)
\(44\) −5.47091 6.56155i −0.824771 0.989191i
\(45\) 0 0
\(46\) 4.56155 9.74247i 0.672564 1.43645i
\(47\) 0.936426i 0.136592i −0.997665 0.0682959i \(-0.978244\pi\)
0.997665 0.0682959i \(-0.0217562\pi\)
\(48\) 0.642976 + 6.89830i 0.0928056 + 0.995684i
\(49\) −6.12311 −0.874729
\(50\) 0 0
\(51\) −3.33513 + 0.936426i −0.467012 + 0.131126i
\(52\) 4.79741 4.00000i 0.665281 0.554700i
\(53\) 4.24621 0.583262 0.291631 0.956531i \(-0.405802\pi\)
0.291631 + 0.956531i \(0.405802\pi\)
\(54\) 6.81526 2.74813i 0.927440 0.373973i
\(55\) 0 0
\(56\) −0.673500 2.56155i −0.0900002 0.342302i
\(57\) 2.00000 + 7.12311i 0.264906 + 0.943478i
\(58\) −3.07221 + 6.56155i −0.403400 + 0.861574i
\(59\) 7.19612 0.936855 0.468427 0.883502i \(-0.344821\pi\)
0.468427 + 0.883502i \(0.344821\pi\)
\(60\) 0 0
\(61\) −5.12311 −0.655946 −0.327973 0.944687i \(-0.606366\pi\)
−0.327973 + 0.944687i \(0.606366\pi\)
\(62\) 1.43845 3.07221i 0.182683 0.390171i
\(63\) −2.39871 + 1.46228i −0.302209 + 0.184230i
\(64\) −6.96543 + 3.93481i −0.870679 + 0.491851i
\(65\) 0 0
\(66\) −10.3225 1.71001i −1.27061 0.210487i
\(67\) −5.20798 −0.636257 −0.318128 0.948048i \(-0.603054\pi\)
−0.318128 + 0.948048i \(0.603054\pi\)
\(68\) −2.56155 3.07221i −0.310634 0.372560i
\(69\) −3.56155 12.6847i −0.428761 1.52705i
\(70\) 0 0
\(71\) 6.67026 0.791615 0.395807 0.918334i \(-0.370465\pi\)
0.395807 + 0.918334i \(0.370465\pi\)
\(72\) 6.11389 + 5.88391i 0.720529 + 0.693425i
\(73\) 8.24621i 0.965146i 0.875856 + 0.482573i \(0.160298\pi\)
−0.875856 + 0.482573i \(0.839702\pi\)
\(74\) 1.87285 4.00000i 0.217715 0.464991i
\(75\) 0 0
\(76\) −6.56155 + 5.47091i −0.752662 + 0.627557i
\(77\) 4.00000 0.455842
\(78\) 1.25025 7.54716i 0.141563 0.854547i
\(79\) 9.06897i 1.02034i −0.860074 0.510169i \(-0.829583\pi\)
0.860074 0.510169i \(-0.170417\pi\)
\(80\) 0 0
\(81\) 4.12311 8.00000i 0.458123 0.888889i
\(82\) −4.27156 + 9.12311i −0.471715 + 1.00748i
\(83\) 4.68213i 0.513931i 0.966421 + 0.256965i \(0.0827226\pi\)
−0.966421 + 0.256965i \(0.917277\pi\)
\(84\) −2.67350 1.83715i −0.291703 0.200450i
\(85\) 0 0
\(86\) 1.87285 + 0.876894i 0.201955 + 0.0945580i
\(87\) 2.39871 + 8.54312i 0.257168 + 0.915918i
\(88\) −3.07221 11.6847i −0.327498 1.24559i
\(89\) 6.24621i 0.662097i 0.943614 + 0.331049i \(0.107402\pi\)
−0.943614 + 0.331049i \(0.892598\pi\)
\(90\) 0 0
\(91\) 2.92456i 0.306577i
\(92\) 11.6847 9.74247i 1.21821 1.01572i
\(93\) −1.12311 4.00000i −0.116461 0.414781i
\(94\) 0.561553 1.19935i 0.0579198 0.123704i
\(95\) 0 0
\(96\) −3.31324 + 9.22076i −0.338156 + 0.941090i
\(97\) 6.00000i 0.609208i −0.952479 0.304604i \(-0.901476\pi\)
0.952479 0.304604i \(-0.0985241\pi\)
\(98\) −7.84233 3.67188i −0.792195 0.370916i
\(99\) −10.9418 + 6.67026i −1.09969 + 0.670387i
\(100\) 0 0
\(101\) 9.12311i 0.907783i −0.891057 0.453891i \(-0.850035\pi\)
0.891057 0.453891i \(-0.149965\pi\)
\(102\) −4.83311 0.800647i −0.478549 0.0792759i
\(103\) −12.4041 −1.22221 −0.611106 0.791549i \(-0.709275\pi\)
−0.611106 + 0.791549i \(0.709275\pi\)
\(104\) 8.54312 2.24621i 0.837722 0.220259i
\(105\) 0 0
\(106\) 5.43845 + 2.54635i 0.528229 + 0.247324i
\(107\) 0.936426i 0.0905278i 0.998975 + 0.0452639i \(0.0144129\pi\)
−0.998975 + 0.0452639i \(0.985587\pi\)
\(108\) 10.3768 + 0.567212i 0.998509 + 0.0545800i
\(109\) 9.12311 0.873835 0.436918 0.899502i \(-0.356070\pi\)
0.436918 + 0.899502i \(0.356070\pi\)
\(110\) 0 0
\(111\) −1.46228 5.20798i −0.138793 0.494320i
\(112\) 0.673500 3.68466i 0.0636398 0.348167i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) −1.71001 + 10.3225i −0.160157 + 0.966787i
\(115\) 0 0
\(116\) −7.86962 + 6.56155i −0.730676 + 0.609225i
\(117\) −4.87689 8.00000i −0.450869 0.739600i
\(118\) 9.21662 + 4.31534i 0.848458 + 0.397259i
\(119\) 1.87285 0.171684
\(120\) 0 0
\(121\) 7.24621 0.658746
\(122\) −6.56155 3.07221i −0.594055 0.278144i
\(123\) 3.33513 + 11.8782i 0.300719 + 1.07103i
\(124\) 3.68466 3.07221i 0.330892 0.275892i
\(125\) 0 0
\(126\) −3.94910 + 0.434406i −0.351814 + 0.0386999i
\(127\) 4.68213 0.415472 0.207736 0.978185i \(-0.433391\pi\)
0.207736 + 0.978185i \(0.433391\pi\)
\(128\) −11.2808 + 0.862603i −0.997089 + 0.0762440i
\(129\) 2.43845 0.684658i 0.214693 0.0602808i
\(130\) 0 0
\(131\) 17.6121 1.53878 0.769388 0.638782i \(-0.220562\pi\)
0.769388 + 0.638782i \(0.220562\pi\)
\(132\) −12.1953 8.38027i −1.06147 0.729409i
\(133\) 4.00000i 0.346844i
\(134\) −6.67026 3.12311i −0.576223 0.269795i
\(135\) 0 0
\(136\) −1.43845 5.47091i −0.123346 0.469127i
\(137\) −8.24621 −0.704521 −0.352261 0.935902i \(-0.614587\pi\)
−0.352261 + 0.935902i \(0.614587\pi\)
\(138\) 3.04514 18.3820i 0.259219 1.56478i
\(139\) 13.8664i 1.17613i 0.808813 + 0.588066i \(0.200110\pi\)
−0.808813 + 0.588066i \(0.799890\pi\)
\(140\) 0 0
\(141\) −0.438447 1.56155i −0.0369239 0.131506i
\(142\) 8.54312 + 4.00000i 0.716922 + 0.335673i
\(143\) 13.3405i 1.11559i
\(144\) 4.30208 + 11.2023i 0.358507 + 0.933527i
\(145\) 0 0
\(146\) −4.94506 + 10.5616i −0.409256 + 0.874080i
\(147\) −10.2107 + 2.86692i −0.842163 + 0.236459i
\(148\) 4.79741 4.00000i 0.394345 0.328798i
\(149\) 14.0000i 1.14692i 0.819232 + 0.573462i \(0.194400\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 6.14441i 0.500025i 0.968243 + 0.250013i \(0.0804347\pi\)
−0.968243 + 0.250013i \(0.919565\pi\)
\(152\) −11.6847 + 3.07221i −0.947751 + 0.249189i
\(153\) −5.12311 + 3.12311i −0.414179 + 0.252488i
\(154\) 5.12311 + 2.39871i 0.412832 + 0.193293i
\(155\) 0 0
\(156\) 6.12715 8.91648i 0.490564 0.713889i
\(157\) 21.3693i 1.70546i 0.522354 + 0.852729i \(0.325054\pi\)
−0.522354 + 0.852729i \(0.674946\pi\)
\(158\) 5.43845 11.6153i 0.432660 0.924065i
\(159\) 7.08084 1.98813i 0.561547 0.157669i
\(160\) 0 0
\(161\) 7.12311i 0.561379i
\(162\) 10.0782 7.77368i 0.791817 0.610758i
\(163\) 24.1671 1.89291 0.946456 0.322834i \(-0.104636\pi\)
0.946456 + 0.322834i \(0.104636\pi\)
\(164\) −10.9418 + 9.12311i −0.854413 + 0.712395i
\(165\) 0 0
\(166\) −2.80776 + 5.99676i −0.217925 + 0.465439i
\(167\) 2.80928i 0.217389i 0.994075 + 0.108694i \(0.0346670\pi\)
−0.994075 + 0.108694i \(0.965333\pi\)
\(168\) −2.32246 3.95622i −0.179182 0.305229i
\(169\) 3.24621 0.249709
\(170\) 0 0
\(171\) 6.67026 + 10.9418i 0.510088 + 0.836742i
\(172\) 1.87285 + 2.24621i 0.142804 + 0.171272i
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) −2.05090 + 12.3803i −0.155478 + 0.938546i
\(175\) 0 0
\(176\) 3.07221 16.8078i 0.231576 1.26693i
\(177\) 12.0000 3.36932i 0.901975 0.253253i
\(178\) −3.74571 + 8.00000i −0.280752 + 0.599625i
\(179\) −14.6875 −1.09780 −0.548899 0.835889i \(-0.684953\pi\)
−0.548899 + 0.835889i \(0.684953\pi\)
\(180\) 0 0
\(181\) 4.24621 0.315618 0.157809 0.987470i \(-0.449557\pi\)
0.157809 + 0.987470i \(0.449557\pi\)
\(182\) −1.75379 + 3.74571i −0.129999 + 0.277650i
\(183\) −8.54312 + 2.39871i −0.631525 + 0.177317i
\(184\) 20.8078 5.47091i 1.53397 0.403321i
\(185\) 0 0
\(186\) 0.960258 5.79661i 0.0704096 0.425028i
\(187\) 8.54312 0.624735
\(188\) 1.43845 1.19935i 0.104910 0.0874718i
\(189\) −3.31534 + 3.56155i −0.241156 + 0.259065i
\(190\) 0 0
\(191\) −7.72197 −0.558742 −0.279371 0.960183i \(-0.590126\pi\)
−0.279371 + 0.960183i \(0.590126\pi\)
\(192\) −9.77299 + 9.82286i −0.705305 + 0.708904i
\(193\) 16.2462i 1.16943i −0.811240 0.584714i \(-0.801207\pi\)
0.811240 0.584714i \(-0.198793\pi\)
\(194\) 3.59806 7.68466i 0.258326 0.551726i
\(195\) 0 0
\(196\) −7.84233 9.40572i −0.560166 0.671837i
\(197\) 12.2462 0.872506 0.436253 0.899824i \(-0.356305\pi\)
0.436253 + 0.899824i \(0.356305\pi\)
\(198\) −18.0140 + 1.98156i −1.28020 + 0.140824i
\(199\) 17.6121i 1.24849i −0.781230 0.624244i \(-0.785407\pi\)
0.781230 0.624244i \(-0.214593\pi\)
\(200\) 0 0
\(201\) −8.68466 + 2.43845i −0.612569 + 0.171995i
\(202\) 5.47091 11.6847i 0.384932 0.822130i
\(203\) 4.79741i 0.336712i
\(204\) −5.71001 3.92375i −0.399780 0.274718i
\(205\) 0 0
\(206\) −15.8869 7.43845i −1.10689 0.518261i
\(207\) −11.8782 19.4849i −0.825595 1.35430i
\(208\) 12.2888 + 2.24621i 0.852077 + 0.155747i
\(209\) 18.2462i 1.26212i
\(210\) 0 0
\(211\) 1.34700i 0.0927313i 0.998925 + 0.0463656i \(0.0147639\pi\)
−0.998925 + 0.0463656i \(0.985236\pi\)
\(212\) 5.43845 + 6.52262i 0.373514 + 0.447975i
\(213\) 11.1231 3.12311i 0.762143 0.213992i
\(214\) −0.561553 + 1.19935i −0.0383870 + 0.0819861i
\(215\) 0 0
\(216\) 12.9502 + 6.94920i 0.881152 + 0.472833i
\(217\) 2.24621i 0.152483i
\(218\) 11.6847 + 5.47091i 0.791385 + 0.370537i
\(219\) 3.86098 + 13.7511i 0.260901 + 0.929213i
\(220\) 0 0
\(221\) 6.24621i 0.420166i
\(222\) 1.25025 7.54716i 0.0839115 0.506532i
\(223\) −18.0227 −1.20689 −0.603443 0.797406i \(-0.706205\pi\)
−0.603443 + 0.797406i \(0.706205\pi\)
\(224\) 3.07221 4.31534i 0.205270 0.288331i
\(225\) 0 0
\(226\) 17.9309 + 8.39547i 1.19274 + 0.558458i
\(227\) 8.65840i 0.574678i 0.957829 + 0.287339i \(0.0927706\pi\)
−0.957829 + 0.287339i \(0.907229\pi\)
\(228\) −8.38027 + 12.1953i −0.554997 + 0.807654i
\(229\) −0.246211 −0.0162701 −0.00813505 0.999967i \(-0.502589\pi\)
−0.00813505 + 0.999967i \(0.502589\pi\)
\(230\) 0 0
\(231\) 6.67026 1.87285i 0.438871 0.123225i
\(232\) −14.0140 + 3.68466i −0.920066 + 0.241910i
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) −1.44880 13.1708i −0.0947110 0.861000i
\(235\) 0 0
\(236\) 9.21662 + 11.0540i 0.599951 + 0.719553i
\(237\) −4.24621 15.1231i −0.275821 0.982351i
\(238\) 2.39871 + 1.12311i 0.155485 + 0.0728001i
\(239\) 20.8319 1.34751 0.673753 0.738957i \(-0.264681\pi\)
0.673753 + 0.738957i \(0.264681\pi\)
\(240\) 0 0
\(241\) −11.3693 −0.732362 −0.366181 0.930544i \(-0.619335\pi\)
−0.366181 + 0.930544i \(0.619335\pi\)
\(242\) 9.28078 + 4.34538i 0.596591 + 0.279332i
\(243\) 3.12985 15.2710i 0.200780 0.979636i
\(244\) −6.56155 7.86962i −0.420060 0.503801i
\(245\) 0 0
\(246\) −2.85155 + 17.2134i −0.181808 + 1.09749i
\(247\) 13.3405 0.848837
\(248\) 6.56155 1.72521i 0.416659 0.109551i
\(249\) 2.19224 + 7.80776i 0.138927 + 0.494797i
\(250\) 0 0
\(251\) −25.1035 −1.58452 −0.792259 0.610184i \(-0.791095\pi\)
−0.792259 + 0.610184i \(0.791095\pi\)
\(252\) −5.31842 1.81181i −0.335029 0.114133i
\(253\) 32.4924i 2.04278i
\(254\) 5.99676 + 2.80776i 0.376270 + 0.176175i
\(255\) 0 0
\(256\) −14.9654 5.66001i −0.935340 0.353751i
\(257\) 2.49242 0.155473 0.0777365 0.996974i \(-0.475231\pi\)
0.0777365 + 0.996974i \(0.475231\pi\)
\(258\) 3.53368 + 0.585385i 0.219997 + 0.0364445i
\(259\) 2.92456i 0.181723i
\(260\) 0 0
\(261\) 8.00000 + 13.1231i 0.495188 + 0.812300i
\(262\) 22.5571 + 10.5616i 1.39359 + 0.652495i
\(263\) 15.0981i 0.930989i −0.885051 0.465494i \(-0.845877\pi\)
0.885051 0.465494i \(-0.154123\pi\)
\(264\) −10.5940 18.0465i −0.652017 1.11068i
\(265\) 0 0
\(266\) 2.39871 5.12311i 0.147074 0.314118i
\(267\) 2.92456 + 10.4160i 0.178980 + 0.637447i
\(268\) −6.67026 8.00000i −0.407451 0.488678i
\(269\) 14.0000i 0.853595i −0.904347 0.426798i \(-0.859642\pi\)
0.904347 0.426798i \(-0.140358\pi\)
\(270\) 0 0
\(271\) 31.7738i 1.93012i −0.262032 0.965059i \(-0.584392\pi\)
0.262032 0.965059i \(-0.415608\pi\)
\(272\) 1.43845 7.86962i 0.0872187 0.477166i
\(273\) 1.36932 + 4.87689i 0.0828748 + 0.295163i
\(274\) −10.5616 4.94506i −0.638047 0.298742i
\(275\) 0 0
\(276\) 14.9234 21.7171i 0.898282 1.30722i
\(277\) 1.36932i 0.0822743i −0.999154 0.0411371i \(-0.986902\pi\)
0.999154 0.0411371i \(-0.0130981\pi\)
\(278\) −8.31534 + 17.7597i −0.498721 + 1.06516i
\(279\) −3.74571 6.14441i −0.224250 0.367856i
\(280\) 0 0
\(281\) 27.6155i 1.64740i −0.567023 0.823702i \(-0.691905\pi\)
0.567023 0.823702i \(-0.308095\pi\)
\(282\) 0.374874 2.26293i 0.0223234 0.134755i
\(283\) 4.38684 0.260770 0.130385 0.991463i \(-0.458379\pi\)
0.130385 + 0.991463i \(0.458379\pi\)
\(284\) 8.54312 + 10.2462i 0.506941 + 0.608001i
\(285\) 0 0
\(286\) −8.00000 + 17.0862i −0.473050 + 1.01033i
\(287\) 6.67026i 0.393733i
\(288\) −1.20777 + 16.9275i −0.0711682 + 0.997464i
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −2.80928 10.0054i −0.164683 0.586527i
\(292\) −12.6670 + 10.5616i −0.741282 + 0.618068i
\(293\) −30.4924 −1.78139 −0.890693 0.454605i \(-0.849780\pi\)
−0.890693 + 0.454605i \(0.849780\pi\)
\(294\) −14.7968 2.45122i −0.862968 0.142958i
\(295\) 0 0
\(296\) 8.54312 2.24621i 0.496559 0.130558i
\(297\) −15.1231 + 16.2462i −0.877532 + 0.942701i
\(298\) −8.39547 + 17.9309i −0.486337 + 1.03871i
\(299\) −23.7565 −1.37387
\(300\) 0 0
\(301\) −1.36932 −0.0789261
\(302\) −3.68466 + 7.86962i −0.212028 + 0.452846i
\(303\) −4.27156 15.2134i −0.245395 0.873986i
\(304\) −16.8078 3.07221i −0.963991 0.176203i
\(305\) 0 0
\(306\) −8.43441 + 0.927794i −0.482163 + 0.0530385i
\(307\) −8.13254 −0.464149 −0.232074 0.972698i \(-0.574551\pi\)
−0.232074 + 0.972698i \(0.574551\pi\)
\(308\) 5.12311 + 6.14441i 0.291916 + 0.350110i
\(309\) −20.6847 + 5.80776i −1.17671 + 0.330392i
\(310\) 0 0
\(311\) −14.1617 −0.803035 −0.401517 0.915851i \(-0.631517\pi\)
−0.401517 + 0.915851i \(0.631517\pi\)
\(312\) 13.1945 7.74571i 0.746992 0.438514i
\(313\) 10.4924i 0.593067i −0.955022 0.296533i \(-0.904169\pi\)
0.955022 0.296533i \(-0.0958306\pi\)
\(314\) −12.8147 + 27.3693i −0.723174 + 1.54454i
\(315\) 0 0
\(316\) 13.9309 11.6153i 0.783673 0.653413i
\(317\) −32.7386 −1.83878 −0.919392 0.393342i \(-0.871319\pi\)
−0.919392 + 0.393342i \(0.871319\pi\)
\(318\) 10.2612 + 1.69986i 0.575420 + 0.0953233i
\(319\) 21.8836i 1.22525i
\(320\) 0 0
\(321\) 0.438447 + 1.56155i 0.0244717 + 0.0871574i
\(322\) −4.27156 + 9.12311i −0.238045 + 0.508411i
\(323\) 8.54312i 0.475352i
\(324\) 17.5696 3.91270i 0.976089 0.217372i
\(325\) 0 0
\(326\) 30.9526 + 14.4924i 1.71431 + 0.802661i
\(327\) 15.2134 4.27156i 0.841302 0.236218i
\(328\) −19.4849 + 5.12311i −1.07588 + 0.282876i
\(329\) 0.876894i 0.0483448i
\(330\) 0 0
\(331\) 28.0281i 1.54056i 0.637705 + 0.770281i \(0.279884\pi\)
−0.637705 + 0.770281i \(0.720116\pi\)
\(332\) −7.19224 + 5.99676i −0.394725 + 0.329115i
\(333\) −4.87689 8.00000i −0.267252 0.438397i
\(334\) −1.68466 + 3.59806i −0.0921804 + 0.196877i
\(335\) 0 0
\(336\) −0.602100 6.45975i −0.0328473 0.352408i
\(337\) 34.4924i 1.87892i −0.342656 0.939461i \(-0.611326\pi\)
0.342656 0.939461i \(-0.388674\pi\)
\(338\) 4.15767 + 1.94668i 0.226147 + 0.105885i
\(339\) 23.3459 6.55498i 1.26798 0.356018i
\(340\) 0 0
\(341\) 10.2462i 0.554863i
\(342\) 1.98156 + 18.0140i 0.107151 + 0.974087i
\(343\) 12.2888 0.663534
\(344\) 1.05171 + 4.00000i 0.0567042 + 0.215666i
\(345\) 0 0
\(346\) 2.56155 + 1.19935i 0.137710 + 0.0644776i
\(347\) 23.8718i 1.28150i −0.767748 0.640752i \(-0.778623\pi\)
0.767748 0.640752i \(-0.221377\pi\)
\(348\) −10.0509 + 14.6265i −0.538785 + 0.784062i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −11.8782 11.0571i −0.634014 0.590184i
\(352\) 14.0140 19.6847i 0.746950 1.04920i
\(353\) −3.75379 −0.199794 −0.0998970 0.994998i \(-0.531851\pi\)
−0.0998970 + 0.994998i \(0.531851\pi\)
\(354\) 17.3898 + 2.88078i 0.924258 + 0.153111i
\(355\) 0 0
\(356\) −9.59482 + 8.00000i −0.508525 + 0.423999i
\(357\) 3.12311 0.876894i 0.165292 0.0464102i
\(358\) −18.8114 8.80776i −0.994215 0.465505i
\(359\) −1.05171 −0.0555069 −0.0277535 0.999615i \(-0.508835\pi\)
−0.0277535 + 0.999615i \(0.508835\pi\)
\(360\) 0 0
\(361\) 0.753789 0.0396731
\(362\) 5.43845 + 2.54635i 0.285838 + 0.133833i
\(363\) 12.0835 3.39277i 0.634221 0.178074i
\(364\) −4.49242 + 3.74571i −0.235467 + 0.196328i
\(365\) 0 0
\(366\) −12.3803 2.05090i −0.647127 0.107202i
\(367\) −26.5658 −1.38672 −0.693361 0.720590i \(-0.743871\pi\)
−0.693361 + 0.720590i \(0.743871\pi\)
\(368\) 29.9309 + 5.47091i 1.56025 + 0.285191i
\(369\) 11.1231 + 18.2462i 0.579046 + 0.949860i
\(370\) 0 0
\(371\) −3.97626 −0.206437
\(372\) 4.70596 6.84831i 0.243993 0.355068i
\(373\) 0.876894i 0.0454039i 0.999742 + 0.0227019i \(0.00722687\pi\)
−0.999742 + 0.0227019i \(0.992773\pi\)
\(374\) 10.9418 + 5.12311i 0.565788 + 0.264909i
\(375\) 0 0
\(376\) 2.56155 0.673500i 0.132102 0.0347331i
\(377\) 16.0000 0.824042
\(378\) −6.38199 + 2.57342i −0.328254 + 0.132362i
\(379\) 25.1035i 1.28948i 0.764402 + 0.644740i \(0.223034\pi\)
−0.764402 + 0.644740i \(0.776966\pi\)
\(380\) 0 0
\(381\) 7.80776 2.19224i 0.400004 0.112312i
\(382\) −9.89012 4.63068i −0.506022 0.236926i
\(383\) 4.68213i 0.239246i −0.992819 0.119623i \(-0.961831\pi\)
0.992819 0.119623i \(-0.0381685\pi\)
\(384\) −18.4076 + 6.72026i −0.939357 + 0.342942i
\(385\) 0 0
\(386\) 9.74247 20.8078i 0.495879 1.05909i
\(387\) 3.74571 2.28343i 0.190405 0.116073i
\(388\) 9.21662 7.68466i 0.467903 0.390129i
\(389\) 28.7386i 1.45711i −0.684989 0.728553i \(-0.740193\pi\)
0.684989 0.728553i \(-0.259807\pi\)
\(390\) 0 0
\(391\) 15.2134i 0.769374i
\(392\) −4.40388 16.7495i −0.222430 0.845977i
\(393\) 29.3693 8.24621i 1.48149 0.415966i
\(394\) 15.6847 + 7.34376i 0.790182 + 0.369973i
\(395\) 0 0
\(396\) −24.2602 8.26465i −1.21912 0.415314i
\(397\) 23.1231i 1.16052i 0.814433 + 0.580258i \(0.197048\pi\)
−0.814433 + 0.580258i \(0.802952\pi\)
\(398\) 10.5616 22.5571i 0.529403 1.13069i
\(399\) −1.87285 6.67026i −0.0937599 0.333931i
\(400\) 0 0
\(401\) 24.0000i 1.19850i 0.800561 + 0.599251i \(0.204535\pi\)
−0.800561 + 0.599251i \(0.795465\pi\)
\(402\) −12.5854 2.08488i −0.627702 0.103984i
\(403\) −7.49141 −0.373174
\(404\) 14.0140 11.6847i 0.697224 0.581333i
\(405\) 0 0
\(406\) 2.87689 6.14441i 0.142778 0.304942i
\(407\) 13.3405i 0.661265i
\(408\) −4.96026 8.44961i −0.245569 0.418318i
\(409\) −0.630683 −0.0311853 −0.0155926 0.999878i \(-0.504963\pi\)
−0.0155926 + 0.999878i \(0.504963\pi\)
\(410\) 0 0
\(411\) −13.7511 + 3.86098i −0.678292 + 0.190448i
\(412\) −15.8869 19.0540i −0.782690 0.938722i
\(413\) −6.73863 −0.331586
\(414\) −3.52872 32.0790i −0.173427 1.57659i
\(415\) 0 0
\(416\) 14.3922 + 10.2462i 0.705637 + 0.502362i
\(417\) 6.49242 + 23.1231i 0.317935 + 1.13234i
\(418\) 10.9418 23.3693i 0.535182 1.14303i
\(419\) 6.14441 0.300174 0.150087 0.988673i \(-0.452045\pi\)
0.150087 + 0.988673i \(0.452045\pi\)
\(420\) 0 0
\(421\) −0.630683 −0.0307376 −0.0153688 0.999882i \(-0.504892\pi\)
−0.0153688 + 0.999882i \(0.504892\pi\)
\(422\) −0.807764 + 1.72521i −0.0393213 + 0.0839817i
\(423\) −1.46228 2.39871i −0.0710985 0.116629i
\(424\) 3.05398 + 11.6153i 0.148314 + 0.564090i
\(425\) 0 0
\(426\) 16.1191 + 2.67026i 0.780971 + 0.129375i
\(427\) 4.79741 0.232163
\(428\) −1.43845 + 1.19935i −0.0695300 + 0.0579729i
\(429\) 6.24621 + 22.2462i 0.301570 + 1.07406i
\(430\) 0 0
\(431\) 36.0453 1.73624 0.868121 0.496353i \(-0.165328\pi\)
0.868121 + 0.496353i \(0.165328\pi\)
\(432\) 12.4191 + 16.6663i 0.597513 + 0.801859i
\(433\) 18.0000i 0.865025i −0.901628 0.432512i \(-0.857627\pi\)
0.901628 0.432512i \(-0.142373\pi\)
\(434\) −1.34700 + 2.87689i −0.0646581 + 0.138095i
\(435\) 0 0
\(436\) 11.6847 + 14.0140i 0.559594 + 0.671150i
\(437\) 32.4924 1.55432
\(438\) −3.30115 + 19.9274i −0.157735 + 0.952169i
\(439\) 29.9009i 1.42709i 0.700608 + 0.713546i \(0.252912\pi\)
−0.700608 + 0.713546i \(0.747088\pi\)
\(440\) 0 0
\(441\) −15.6847 + 9.56155i −0.746888 + 0.455312i
\(442\) −3.74571 + 8.00000i −0.178165 + 0.380521i
\(443\) 25.7446i 1.22316i 0.791181 + 0.611582i \(0.209467\pi\)
−0.791181 + 0.611582i \(0.790533\pi\)
\(444\) 6.12715 8.91648i 0.290782 0.423157i
\(445\) 0 0
\(446\) −23.0830 10.8078i −1.09301 0.511762i
\(447\) 6.55498 + 23.3459i 0.310040 + 1.10422i
\(448\) 6.52262 3.68466i 0.308165 0.174084i
\(449\) 2.63068i 0.124150i 0.998071 + 0.0620748i \(0.0197717\pi\)
−0.998071 + 0.0620748i \(0.980228\pi\)
\(450\) 0 0
\(451\) 30.4268i 1.43274i
\(452\) 17.9309 + 21.5054i 0.843397 + 1.01153i
\(453\) 2.87689 + 10.2462i 0.135168 + 0.481409i
\(454\) −5.19224 + 11.0895i −0.243684 + 0.520455i
\(455\) 0 0
\(456\) −18.0465 + 10.5940i −0.845104 + 0.496110i
\(457\) 10.0000i 0.467780i −0.972263 0.233890i \(-0.924854\pi\)
0.972263 0.233890i \(-0.0751456\pi\)
\(458\) −0.315342 0.147647i −0.0147349 0.00689909i
\(459\) −7.08084 + 7.60669i −0.330505 + 0.355050i
\(460\) 0 0
\(461\) 15.8617i 0.738755i −0.929279 0.369377i \(-0.879571\pi\)
0.929279 0.369377i \(-0.120429\pi\)
\(462\) 9.66622 + 1.60129i 0.449713 + 0.0744990i
\(463\) −0.936426 −0.0435194 −0.0217597 0.999763i \(-0.506927\pi\)
−0.0217597 + 0.999763i \(0.506927\pi\)
\(464\) −20.1584 3.68466i −0.935832 0.171056i
\(465\) 0 0
\(466\) −12.8078 5.99676i −0.593308 0.277795i
\(467\) 16.1498i 0.747324i −0.927565 0.373662i \(-0.878102\pi\)
0.927565 0.373662i \(-0.121898\pi\)
\(468\) 6.04261 17.7376i 0.279320 0.819922i
\(469\) 4.87689 0.225194
\(470\) 0 0
\(471\) 10.0054 + 35.6347i 0.461024 + 1.64196i
\(472\) 5.17562 + 19.6847i 0.238227 + 0.906060i
\(473\) −6.24621 −0.287201
\(474\) 3.63052 21.9157i 0.166755 1.00662i
\(475\) 0 0
\(476\) 2.39871 + 2.87689i 0.109944 + 0.131862i
\(477\) 10.8769 6.63068i 0.498019 0.303598i
\(478\) 26.6811 + 12.4924i 1.22036 + 0.571390i
\(479\) −22.9354 −1.04794 −0.523971 0.851736i \(-0.675550\pi\)
−0.523971 + 0.851736i \(0.675550\pi\)
\(480\) 0 0
\(481\) −9.75379 −0.444734
\(482\) −14.5616 6.81791i −0.663261 0.310547i
\(483\) 3.33513 + 11.8782i 0.151754 + 0.540479i
\(484\) 9.28078 + 11.1309i 0.421853 + 0.505951i
\(485\) 0 0
\(486\) 13.1663 17.6819i 0.597236 0.802066i
\(487\) 15.3287 0.694608 0.347304 0.937753i \(-0.387097\pi\)
0.347304 + 0.937753i \(0.387097\pi\)
\(488\) −3.68466 14.0140i −0.166797 0.634385i
\(489\) 40.3002 11.3153i 1.82244 0.511697i
\(490\) 0 0
\(491\) 18.6638 0.842285 0.421143 0.906994i \(-0.361629\pi\)
0.421143 + 0.906994i \(0.361629\pi\)
\(492\) −13.9747 + 20.3365i −0.630026 + 0.916840i
\(493\) 10.2462i 0.461466i
\(494\) 17.0862 + 8.00000i 0.768746 + 0.359937i
\(495\) 0 0
\(496\) 9.43845 + 1.72521i 0.423799 + 0.0774640i
\(497\) −6.24621 −0.280181
\(498\) −1.87437 + 11.3146i −0.0839924 + 0.507021i
\(499\) 1.57756i 0.0706212i −0.999376 0.0353106i \(-0.988758\pi\)
0.999376 0.0353106i \(-0.0112421\pi\)
\(500\) 0 0
\(501\) 1.31534 + 4.68466i 0.0587651 + 0.209295i
\(502\) −32.1520 15.0540i −1.43501 0.671892i
\(503\) 19.8955i 0.887097i 0.896250 + 0.443549i \(0.146281\pi\)
−0.896250 + 0.443549i \(0.853719\pi\)
\(504\) −5.72521 5.50985i −0.255021 0.245428i
\(505\) 0 0
\(506\) −19.4849 + 41.6155i −0.866211 + 1.85004i
\(507\) 5.41327 1.51992i 0.240412 0.0675020i
\(508\) 5.99676 + 7.19224i 0.266063 + 0.319104i
\(509\) 2.87689i 0.127516i −0.997965 0.0637581i \(-0.979691\pi\)
0.997965 0.0637581i \(-0.0203086\pi\)
\(510\) 0 0
\(511\) 7.72197i 0.341600i
\(512\) −15.7732 16.2236i −0.697083 0.716990i
\(513\) 16.2462 + 15.1231i 0.717288 + 0.667701i
\(514\) 3.19224 + 1.49465i 0.140803 + 0.0659261i
\(515\) 0 0
\(516\) 4.17481 + 2.86881i 0.183786 + 0.126292i
\(517\) 4.00000i 0.175920i
\(518\) −1.75379 + 3.74571i −0.0770571 + 0.164577i
\(519\) 3.33513 0.936426i 0.146396 0.0411046i
\(520\) 0 0
\(521\) 21.7538i 0.953051i −0.879161 0.476525i \(-0.841896\pi\)
0.879161 0.476525i \(-0.158104\pi\)
\(522\) 2.37659 + 21.6052i 0.104021 + 0.945633i
\(523\) −0.641132 −0.0280348 −0.0140174 0.999902i \(-0.504462\pi\)
−0.0140174 + 0.999902i \(0.504462\pi\)
\(524\) 22.5571 + 27.0540i 0.985413 + 1.18186i
\(525\) 0 0
\(526\) 9.05398 19.3373i 0.394772 0.843146i
\(527\) 4.79741i 0.208979i
\(528\) −2.74651 29.4665i −0.119527 1.28236i
\(529\) −34.8617 −1.51573
\(530\) 0 0
\(531\) 18.4332 11.2371i 0.799934 0.487649i
\(532\) 6.14441 5.12311i 0.266394 0.222115i
\(533\) 22.2462 0.963590
\(534\) −2.50051 + 15.0943i −0.108207 + 0.653195i
\(535\) 0 0
\(536\) −3.74571 14.2462i −0.161790 0.615343i
\(537\) −24.4924 + 6.87689i −1.05693 + 0.296760i
\(538\) 8.39547 17.9309i 0.361954 0.773055i
\(539\) 26.1552 1.12658
\(540\) 0 0
\(541\) 38.9848 1.67609 0.838045 0.545602i \(-0.183699\pi\)
0.838045 + 0.545602i \(0.183699\pi\)
\(542\) 19.0540 40.6951i 0.818438 1.74800i
\(543\) 7.08084 1.98813i 0.303868 0.0853189i
\(544\) 6.56155 9.21662i 0.281324 0.395159i
\(545\) 0 0
\(546\) −1.17077 + 7.06736i −0.0501043 + 0.302455i
\(547\) −25.2188 −1.07828 −0.539139 0.842217i \(-0.681250\pi\)
−0.539139 + 0.842217i \(0.681250\pi\)
\(548\) −10.5616 12.6670i −0.451167 0.541109i
\(549\) −13.1231 + 8.00000i −0.560080 + 0.341432i
\(550\) 0 0
\(551\) −21.8836 −0.932275
\(552\) 32.1368 18.8656i 1.36783 0.802972i
\(553\) 8.49242i 0.361135i
\(554\) 0.821147 1.75379i 0.0348872 0.0745113i
\(555\) 0 0
\(556\) −21.3002 + 17.7597i −0.903329 + 0.753180i
\(557\) −19.7538 −0.836995 −0.418497 0.908218i \(-0.637443\pi\)
−0.418497 + 0.908218i \(0.637443\pi\)
\(558\) −1.11275 10.1158i −0.0471066 0.428237i
\(559\) 4.56685i 0.193157i
\(560\) 0 0
\(561\) 14.2462 4.00000i 0.601476 0.168880i
\(562\) 16.5604 35.3693i 0.698558 1.49196i
\(563\) 36.1606i 1.52399i 0.647584 + 0.761994i \(0.275779\pi\)
−0.647584 + 0.761994i \(0.724221\pi\)
\(564\) 1.83715 2.67350i 0.0773581 0.112575i
\(565\) 0 0
\(566\) 5.61856 + 2.63068i 0.236166 + 0.110576i
\(567\) −3.86098 + 7.49141i −0.162146 + 0.314610i
\(568\) 4.79741 + 18.2462i 0.201295 + 0.765594i
\(569\) 4.87689i 0.204450i 0.994761 + 0.102225i \(0.0325962\pi\)
−0.994761 + 0.102225i \(0.967404\pi\)
\(570\) 0 0
\(571\) 16.7909i 0.702679i 0.936248 + 0.351339i \(0.114274\pi\)
−0.936248 + 0.351339i \(0.885726\pi\)
\(572\) −20.4924 + 17.0862i −0.856831 + 0.714411i
\(573\) −12.8769 + 3.61553i −0.537940 + 0.151041i
\(574\) 4.00000 8.54312i 0.166957 0.356583i
\(575\) 0 0
\(576\) −11.6979 + 20.9561i −0.487413 + 0.873171i
\(577\) 15.7538i 0.655839i −0.944706 0.327919i \(-0.893653\pi\)
0.944706 0.327919i \(-0.106347\pi\)
\(578\) −16.6501 7.79579i −0.692553 0.324262i
\(579\) −7.60669 27.0916i −0.316123 1.12589i
\(580\) 0 0
\(581\) 4.38447i 0.181899i
\(582\) 2.40194 14.4993i 0.0995637 0.601017i
\(583\) −18.1379 −0.751197
\(584\) −22.5571 + 5.93087i −0.933421 + 0.245421i
\(585\) 0 0
\(586\) −39.0540 18.2856i −1.61330 0.755371i
\(587\) 38.0335i 1.56981i 0.619617 + 0.784904i \(0.287288\pi\)
−0.619617 + 0.784904i \(0.712712\pi\)
\(588\) −17.4815 12.0128i −0.720924 0.495399i
\(589\) 10.2462 0.422188
\(590\) 0 0
\(591\) 20.4214 5.73384i 0.840023 0.235859i
\(592\) 12.2888 + 2.24621i 0.505067 + 0.0923187i
\(593\) −8.24621 −0.338631 −0.169316 0.985562i \(-0.554156\pi\)
−0.169316 + 0.985562i \(0.554156\pi\)
\(594\) −29.1118 + 11.7388i −1.19447 + 0.481649i
\(595\) 0 0
\(596\) −21.5054 + 17.9309i −0.880897 + 0.734477i
\(597\) −8.24621 29.3693i −0.337495 1.20201i
\(598\) −30.4268 14.2462i −1.24424 0.582571i
\(599\) −36.8665 −1.50632 −0.753162 0.657836i \(-0.771472\pi\)
−0.753162 + 0.657836i \(0.771472\pi\)
\(600\) 0 0
\(601\) 14.8769 0.606841 0.303421 0.952857i \(-0.401871\pi\)
0.303421 + 0.952857i \(0.401871\pi\)
\(602\) −1.75379 0.821147i −0.0714791 0.0334675i
\(603\) −13.3405 + 8.13254i −0.543268 + 0.331183i
\(604\) −9.43845 + 7.86962i −0.384045 + 0.320210i
\(605\) 0 0
\(606\) 3.65219 22.0465i 0.148360 0.895578i
\(607\) −29.4903 −1.19698 −0.598488 0.801132i \(-0.704232\pi\)
−0.598488 + 0.801132i \(0.704232\pi\)
\(608\) −19.6847 14.0140i −0.798318 0.568344i
\(609\) −2.24621 8.00000i −0.0910211 0.324176i
\(610\) 0 0
\(611\) −2.92456 −0.118315
\(612\) −11.3590 3.86962i −0.459159 0.156420i
\(613\) 0.876894i 0.0354174i −0.999843 0.0177087i \(-0.994363\pi\)
0.999843 0.0177087i \(-0.00563715\pi\)
\(614\) −10.4160 4.87689i −0.420354 0.196815i
\(615\) 0 0
\(616\) 2.87689 + 10.9418i 0.115913 + 0.440859i
\(617\) 14.0000 0.563619 0.281809 0.959470i \(-0.409065\pi\)
0.281809 + 0.959470i \(0.409065\pi\)
\(618\) −29.9752 4.96565i −1.20578 0.199748i
\(619\) 20.3061i 0.816171i −0.912944 0.408085i \(-0.866197\pi\)
0.912944 0.408085i \(-0.133803\pi\)
\(620\) 0 0
\(621\) −28.9309 26.9309i −1.16096 1.08070i
\(622\) −18.1379 8.49242i −0.727265 0.340515i
\(623\) 5.84912i 0.234340i
\(624\) 21.5441 2.00808i 0.862455 0.0803877i
\(625\) 0 0
\(626\) 6.29206 13.4384i 0.251481 0.537108i
\(627\) −8.54312 30.4268i −0.341179 1.21513i
\(628\) −32.8255 + 27.3693i −1.30988 + 1.09215i
\(629\) 6.24621i 0.249053i
\(630\) 0 0
\(631\) 30.1315i 1.19951i 0.800182 + 0.599757i \(0.204736\pi\)
−0.800182 + 0.599757i \(0.795264\pi\)
\(632\) 24.8078 6.52262i 0.986800 0.259456i
\(633\) 0.630683 + 2.24621i 0.0250674 + 0.0892789i
\(634\) −41.9309 19.6326i −1.66529 0.779710i
\(635\) 0 0
\(636\) 12.1229 + 8.33054i 0.480706 + 0.330327i
\(637\) 19.1231i 0.757685i
\(638\) 13.1231 28.0281i 0.519549 1.10964i
\(639\) 17.0862 10.4160i 0.675921 0.412049i
\(640\) 0 0
\(641\) 47.6155i 1.88070i −0.340208 0.940350i \(-0.610498\pi\)
0.340208 0.940350i \(-0.389502\pi\)
\(642\) −0.374874 + 2.26293i −0.0147951 + 0.0893106i
\(643\) −20.4214 −0.805340 −0.402670 0.915345i \(-0.631918\pi\)
−0.402670 + 0.915345i \(0.631918\pi\)
\(644\) −10.9418 + 9.12311i −0.431168 + 0.359501i
\(645\) 0 0
\(646\) 5.12311 10.9418i 0.201566 0.430500i
\(647\) 3.63043i 0.142727i 0.997450 + 0.0713634i \(0.0227350\pi\)
−0.997450 + 0.0713634i \(0.977265\pi\)
\(648\) 24.8491 + 5.52478i 0.976164 + 0.217034i
\(649\) −30.7386 −1.20660
\(650\) 0 0
\(651\) 1.05171 + 3.74571i 0.0412196 + 0.146806i
\(652\) 30.9526 + 37.1231i 1.21220 + 1.45385i
\(653\) 26.9848 1.05600 0.527999 0.849245i \(-0.322942\pi\)
0.527999 + 0.849245i \(0.322942\pi\)
\(654\) 22.0465 + 3.65219i 0.862086 + 0.142812i
\(655\) 0 0
\(656\) −28.0281 5.12311i −1.09431 0.200024i
\(657\) 12.8769 + 21.1231i 0.502375 + 0.824091i
\(658\) −0.525853 + 1.12311i −0.0204999 + 0.0437832i
\(659\) 26.9764 1.05085 0.525425 0.850840i \(-0.323906\pi\)
0.525425 + 0.850840i \(0.323906\pi\)
\(660\) 0 0
\(661\) −46.1080 −1.79339 −0.896696 0.442647i \(-0.854039\pi\)
−0.896696 + 0.442647i \(0.854039\pi\)
\(662\) −16.8078 + 35.8977i −0.653252 + 1.39520i
\(663\) 2.92456 + 10.4160i 0.113580 + 0.404523i
\(664\) −12.8078 + 3.36750i −0.497038 + 0.130684i
\(665\) 0 0
\(666\) −1.44880 13.1708i −0.0561399 0.510357i
\(667\) 38.9699 1.50892
\(668\) −4.31534 + 3.59806i −0.166966 + 0.139213i
\(669\) −30.0540 + 8.43845i −1.16195 + 0.326249i
\(670\) 0 0
\(671\) 21.8836 0.844809
\(672\) 3.10261 8.63456i 0.119686 0.333086i
\(673\) 10.4924i 0.404453i 0.979339 + 0.202227i \(0.0648177\pi\)
−0.979339 + 0.202227i \(0.935182\pi\)
\(674\) 20.6843 44.1771i 0.796729 1.70164i
\(675\) 0 0
\(676\) 4.15767 + 4.98651i 0.159910 + 0.191789i
\(677\) −34.4924 −1.32565 −0.662826 0.748774i \(-0.730643\pi\)
−0.662826 + 0.748774i \(0.730643\pi\)
\(678\) 33.8318 + 5.60453i 1.29930 + 0.215241i
\(679\) 5.61856i 0.215620i
\(680\) 0 0
\(681\) 4.05398 + 14.4384i 0.155349 + 0.553282i
\(682\) −6.14441 + 13.1231i −0.235282 + 0.502510i
\(683\) 36.1606i 1.38365i −0.722067 0.691823i \(-0.756808\pi\)
0.722067 0.691823i \(-0.243192\pi\)
\(684\) −8.26465 + 24.2602i −0.316007 + 0.927613i
\(685\) 0 0
\(686\) 15.7392 + 7.36932i 0.600927 + 0.281362i
\(687\) −0.410574 + 0.115279i −0.0156644 + 0.00439818i
\(688\) −1.05171 + 5.75379i −0.0400959 + 0.219361i
\(689\) 13.2614i 0.505218i
\(690\) 0 0
\(691\) 29.0798i 1.10625i −0.833100 0.553123i \(-0.813436\pi\)
0.833100 0.553123i \(-0.186564\pi\)
\(692\) 2.56155 + 3.07221i 0.0973756 + 0.116788i
\(693\) 10.2462 6.24621i 0.389221 0.237274i
\(694\) 14.3153 30.5744i 0.543403 1.16059i
\(695\) 0 0
\(696\) −21.6441 + 12.7060i −0.820418 + 0.481618i
\(697\) 14.2462i 0.539614i
\(698\) 17.9309 + 8.39547i 0.678693 + 0.317773i
\(699\) −16.6757 + 4.68213i −0.630731 + 0.177094i
\(700\) 0 0
\(701\) 50.4924i 1.90707i 0.301278 + 0.953536i \(0.402587\pi\)
−0.301278 + 0.953536i \(0.597413\pi\)
\(702\) −8.58270 21.2848i −0.323933 0.803342i
\(703\) 13.3405 0.503148
\(704\) 29.7533 16.8078i 1.12137 0.633466i
\(705\) 0 0
\(706\) −4.80776 2.25106i −0.180943 0.0847197i
\(707\) 8.54312i 0.321297i
\(708\) 20.5449 + 14.1179i 0.772126 + 0.530583i
\(709\) 26.4924 0.994944 0.497472 0.867480i \(-0.334262\pi\)
0.497472 + 0.867480i \(0.334262\pi\)
\(710\) 0 0
\(711\) −14.1617 23.2306i −0.531104 0.871217i
\(712\) −17.0862 + 4.49242i −0.640334 + 0.168361i
\(713\) −18.2462 −0.683326
\(714\) 4.52585 + 0.749747i 0.169376 + 0.0280586i
\(715\) 0 0
\(716\) −18.8114 22.5616i −0.703016 0.843165i
\(717\) 34.7386 9.75379i 1.29734 0.364262i
\(718\) −1.34700 0.630683i −0.0502696 0.0235369i
\(719\) 5.84912 0.218135 0.109068 0.994034i \(-0.465213\pi\)
0.109068 + 0.994034i \(0.465213\pi\)
\(720\) 0 0
\(721\) 11.6155 0.432585
\(722\) 0.965435 + 0.452029i 0.0359298 + 0.0168228i
\(723\) −18.9591 + 5.32326i −0.705096 + 0.197974i
\(724\) 5.43845 + 6.52262i 0.202118 + 0.242411i
\(725\) 0 0
\(726\) 17.5109 + 2.90083i 0.649889 + 0.107660i
\(727\) 26.5658 0.985270 0.492635 0.870236i \(-0.336034\pi\)
0.492635 + 0.870236i \(0.336034\pi\)
\(728\) −8.00000 + 2.10341i −0.296500 + 0.0779576i
\(729\) −1.93087 26.9309i −0.0715137 0.997440i
\(730\) 0 0
\(731\) −2.92456 −0.108169
\(732\) −14.6265 10.0509i −0.540610 0.371492i
\(733\) 35.1231i 1.29730i 0.761086 + 0.648651i \(0.224666\pi\)
−0.761086 + 0.648651i \(0.775334\pi\)
\(734\) −34.0248 15.9309i −1.25588 0.588019i
\(735\) 0 0
\(736\) 35.0540 + 24.9559i 1.29211 + 0.919885i
\(737\) 22.2462 0.819450
\(738\) 3.30439 + 30.0396i 0.121636 + 1.10577i
\(739\) 18.6638i 0.686559i −0.939233 0.343279i \(-0.888462\pi\)
0.939233 0.343279i \(-0.111538\pi\)
\(740\) 0 0
\(741\) 22.2462 6.24621i 0.817235 0.229460i
\(742\) −5.09271 2.38447i −0.186959 0.0875367i
\(743\) 12.4041i 0.455062i 0.973771 + 0.227531i \(0.0730654\pi\)
−0.973771 + 0.227531i \(0.926935\pi\)
\(744\) 10.1341 5.94910i 0.371533 0.218105i
\(745\) 0 0
\(746\) −0.525853 + 1.12311i −0.0192528 + 0.0411198i
\(747\) 7.31140 + 11.9935i 0.267510 + 0.438820i
\(748\) 10.9418 + 13.1231i 0.400073 + 0.479828i
\(749\) 0.876894i 0.0320410i
\(750\) 0 0
\(751\) 15.7392i 0.574333i −0.957881 0.287166i \(-0.907287\pi\)
0.957881 0.287166i \(-0.0927133\pi\)
\(752\) 3.68466 + 0.673500i 0.134366 + 0.0245600i
\(753\) −41.8617 + 11.7538i −1.52553 + 0.428332i
\(754\) 20.4924 + 9.59482i 0.746290 + 0.349423i
\(755\) 0 0
\(756\) −9.71712 0.531153i −0.353408 0.0193178i
\(757\) 19.1231i 0.695041i 0.937672 + 0.347521i \(0.112976\pi\)
−0.937672 + 0.347521i \(0.887024\pi\)
\(758\) −15.0540 + 32.1520i −0.546785 + 1.16781i
\(759\) 15.2134 + 54.1833i 0.552211 + 1.96673i
\(760\) 0 0
\(761\) 51.2311i 1.85712i 0.371177 + 0.928562i \(0.378954\pi\)
−0.371177 + 0.928562i \(0.621046\pi\)
\(762\) 11.3146 + 1.87437i 0.409886 + 0.0679012i
\(763\) −8.54312 −0.309282
\(764\) −9.89012 11.8617i −0.357812 0.429143i
\(765\) 0 0
\(766\) 2.80776 5.99676i 0.101449 0.216672i
\(767\) 22.4742i 0.811498i
\(768\) −27.6059 2.43143i −0.996144 0.0877368i
\(769\) 26.9848 0.973098 0.486549 0.873653i \(-0.338255\pi\)
0.486549 + 0.873653i \(0.338255\pi\)
\(770\) 0 0
\(771\) 4.15628 1.16699i 0.149685 0.0420279i
\(772\) 24.9559 20.8078i 0.898181 0.748888i
\(773\) 16.2462 0.584336 0.292168 0.956367i \(-0.405623\pi\)
0.292168 + 0.956367i \(0.405623\pi\)
\(774\) 6.16673 0.678347i 0.221658 0.0243827i
\(775\) 0 0
\(776\) 16.4127 4.31534i 0.589183 0.154912i
\(777\) 1.36932 + 4.87689i 0.0491240 + 0.174958i
\(778\) 17.2339 36.8078i 0.617865 1.31962i
\(779\) −30.4268 −1.09015
\(780\) 0 0
\(781\) −28.4924 −1.01954
\(782\) −9.12311 + 19.4849i −0.326242 + 0.696780i
\(783\) 19.4849 + 18.1379i 0.696335 + 0.648197i
\(784\) 4.40388 24.0932i 0.157282 0.860473i
\(785\) 0 0