Properties

Label 300.2.h.a.299.3
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 299.3
Root \(-0.599676 - 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 300.299
Dual form 300.2.h.a.299.1

$q$-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 \(-0.443371\pi\)
0.176968 + 0.984217i \(0.443371\pi\)
\(8\) −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 \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −4.21720 0.463897i −0.994004 0.109342i
\(19\) 4.27156i 0.979963i −0.871733 0.489981i \(-0.837004\pi\)
0.871733 0.489981i \(-0.162996\pi\)
\(20\) 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 \(-0.842206\pi\)
0.879625 0.475668i \(-0.157794\pi\)
\(30\) 0 0
\(31\) 2.39871i 0.430820i 0.976524 + 0.215410i \(0.0691088\pi\)
−0.976524 + 0.215410i \(0.930891\pi\)
\(32\) 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 \(-0.812251\pi\)
0.831034 0.556221i \(-0.187749\pi\)
\(42\) 2.26293 0.374874i 0.349177 0.0578442i
\(43\) −1.46228 −0.222995 −0.111498 0.993765i \(-0.535565\pi\)
−0.111498 + 0.993765i \(0.535565\pi\)
\(44\) −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 \(-0.594198\pi\)
−0.291631 + 0.956531i \(0.594198\pi\)
\(54\) 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 \(-0.396946\pi\)
0.318128 + 0.948048i \(0.396946\pi\)
\(68\) 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 \(0.170417\pi\)
−0.860074 + 0.510169i \(0.829583\pi\)
\(80\) 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 \(-0.892598\pi\)
0.943614 0.331049i \(-0.107402\pi\)
\(90\) 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 \(0.149965\pi\)
−0.891057 + 0.453891i \(0.850035\pi\)
\(102\) 4.83311 0.800647i 0.478549 0.0792759i
\(103\) 12.4041 1.22221 0.611106 0.791549i \(-0.290725\pi\)
0.611106 + 0.791549i \(0.290725\pi\)
\(104\) 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 \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −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 \(-0.566609\pi\)
−0.207736 + 0.978185i \(0.566609\pi\)
\(128\) 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 \(-0.385413\pi\)
0.352261 + 0.935902i \(0.385413\pi\)
\(138\) −3.04514 18.3820i −0.259219 1.56478i
\(139\) 13.8664i 1.17613i −0.808813 0.588066i \(-0.799890\pi\)
0.808813 0.588066i \(-0.200110\pi\)
\(140\) 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 \(-0.805600\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) 0 0
\(151\) 6.14441i 0.500025i −0.968243 0.250013i \(-0.919565\pi\)
0.968243 0.250013i \(-0.0804347\pi\)
\(152\) 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 \(-0.895364\pi\)
−0.946456 + 0.322834i \(0.895364\pi\)
\(164\) −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 \(-0.524224\pi\)
−0.0760286 + 0.997106i \(0.524224\pi\)
\(174\) −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 \(-0.643695\pi\)
−0.436253 + 0.899824i \(0.643695\pi\)
\(198\) 18.0140 + 1.98156i 1.28020 + 0.140824i
\(199\) 17.6121i 1.24849i 0.781230 + 0.624244i \(0.214593\pi\)
−0.781230 + 0.624244i \(0.785407\pi\)
\(200\) 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 \(-0.985236\pi\)
0.998925 0.0463656i \(-0.0147639\pi\)
\(212\) −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 \(-0.293795\pi\)
0.603443 + 0.797406i \(0.293795\pi\)
\(224\) 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 \(-0.393773\pi\)
0.327561 + 0.944830i \(0.393773\pi\)
\(234\) −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 \(-0.524769\pi\)
−0.0777365 + 0.996974i \(0.524769\pi\)
\(258\) −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 \(0.140358\pi\)
−0.904347 + 0.426798i \(0.859642\pi\)
\(270\) 0 0
\(271\) 31.7738i 1.93012i 0.262032 + 0.965059i \(0.415608\pi\)
−0.262032 + 0.965059i \(0.584392\pi\)
\(272\) −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 \(0.308095\pi\)
−0.567023 + 0.823702i \(0.691905\pi\)
\(282\) −0.374874 2.26293i −0.0223234 0.134755i
\(283\) −4.38684 −0.260770 −0.130385 0.991463i \(-0.541621\pi\)
−0.130385 + 0.991463i \(0.541621\pi\)
\(284\) 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 \(-0.150220\pi\)
0.890693 + 0.454605i \(0.150220\pi\)
\(294\) −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 \(-0.425449\pi\)
0.232074 + 0.972698i \(0.425449\pi\)
\(308\) −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 \(-0.128681\pi\)
0.919392 + 0.393342i \(0.128681\pi\)
\(318\) −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 \(-0.720116\pi\)
0.637705 0.770281i \(-0.279884\pi\)
\(332\) 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 \(-0.468149\pi\)
0.0998970 + 0.994998i \(0.468149\pi\)
\(354\) 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 \(-0.256129\pi\)
0.693361 + 0.720590i \(0.256129\pi\)
\(368\) −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 \(-0.776966\pi\)
0.764402 0.644740i \(-0.223034\pi\)
\(380\) 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 \(0.259807\pi\)
−0.684989 + 0.728553i \(0.740193\pi\)
\(390\) 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 \(-0.795465\pi\)
0.800561 0.599251i \(-0.204535\pi\)
\(402\) 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 \(-0.747088\pi\)
0.700608 0.713546i \(-0.252912\pi\)
\(440\) 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 \(-0.980228\pi\)
0.998071 0.0620748i \(-0.0197717\pi\)
\(450\) 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 \(0.120429\pi\)
−0.929279 + 0.369377i \(0.879571\pi\)
\(462\) −9.66622 + 1.60129i −0.449713 + 0.0744990i
\(463\) 0.936426 0.0435194 0.0217597 0.999763i \(-0.493073\pi\)
0.0217597 + 0.999763i \(0.493073\pi\)
\(464\) −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 \(-0.612903\pi\)
−0.347304 + 0.937753i \(0.612903\pi\)
\(488\) 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 \(0.0112421\pi\)
−0.999376 + 0.0353106i \(0.988758\pi\)
\(500\) 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 \(0.0203086\pi\)
−0.997965 + 0.0637581i \(0.979691\pi\)
\(510\) 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 \(0.158104\pi\)
−0.879161 + 0.476525i \(0.841896\pi\)
\(522\) −2.37659 + 21.6052i −0.104021 + 0.945633i
\(523\) 0.641132 0.0280348 0.0140174 0.999902i \(-0.495538\pi\)
0.0140174 + 0.999902i \(0.495538\pi\)
\(524\) 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 \(-0.318750\pi\)
0.539139 + 0.842217i \(0.318750\pi\)
\(548\) 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 \(-0.362557\pi\)
0.418497 + 0.908218i \(0.362557\pi\)
\(558\) 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 \(-0.967404\pi\)
0.994761 0.102225i \(-0.0325962\pi\)
\(570\) 0 0
\(571\) 16.7909i 0.702679i −0.936248 0.351339i \(-0.885726\pi\)
0.936248 0.351339i \(-0.114274\pi\)
\(572\) 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 \(-0.445844\pi\)
0.169316 + 0.985562i \(0.445844\pi\)
\(594\) −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 \(-0.295768\pi\)
0.598488 + 0.801132i \(0.295768\pi\)
\(608\) 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 \(-0.590935\pi\)
−0.281809 + 0.959470i \(0.590935\pi\)
\(618\) 29.9752 4.96565i 1.20578 0.199748i
\(619\) 20.3061i 0.816171i 0.912944 + 0.408085i \(0.133803\pi\)
−0.912944 + 0.408085i \(0.866197\pi\)
\(620\) 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 \(-0.795264\pi\)
0.800182 0.599757i \(-0.204736\pi\)
\(632\) −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 \(0.389502\pi\)
−0.340208 + 0.940350i \(0.610498\pi\)
\(642\) 0.374874 + 2.26293i 0.0147951 + 0.0893106i
\(643\) 20.4214 0.805340 0.402670 0.915345i \(-0.368082\pi\)
0.402670 + 0.915345i \(0.368082\pi\)
\(644\) −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 \(-0.677058\pi\)
−0.527999 + 0.849245i \(0.677058\pi\)
\(654\) 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 \(-0.269357\pi\)
0.662826 + 0.748774i \(0.269357\pi\)
\(678\) −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 \(0.186564\pi\)
−0.833100 + 0.553123i \(0.813436\pi\)
\(692\) −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 \(-0.597413\pi\)
0.301278 0.953536i \(-0.402587\pi\)
\(702\) 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 \(-0.663966\pi\)
−0.492635 + 0.870236i \(0.663966\pi\)
\(728\) 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 \(0.111538\pi\)
−0.939233 + 0.343279i \(0.888462\pi\)
\(740\) 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 \(0.0927133\pi\)
−0.957881 + 0.287166i \(0.907287\pi\)
\(752\) −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 \(-0.621046\pi\)
0.371177 0.928562i \(-0.378954\pi\)
\(762\) −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 \(-0.594377\pi\)
−0.292168 + 0.956367i \(0.594377\pi\)
\(774\) 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