Properties

Label 300.2.h.a.299.4
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 299.4
Root \(0.599676 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 300.299
Dual form 300.2.h.a.299.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} -0.936426 q^{7} +(-0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +O(q^{10})\) \(q+(-1.28078 + 0.599676i) q^{2} +(1.66757 - 0.468213i) q^{3} +(1.28078 - 1.53610i) q^{4} +(-1.85500 + 1.59968i) q^{6} -0.936426 q^{7} +(-0.719224 + 2.73546i) q^{8} +(2.56155 - 1.56155i) q^{9} +4.27156 q^{11} +(1.41656 - 3.16123i) q^{12} +3.12311i q^{13} +(1.19935 - 0.561553i) q^{14} +(-0.719224 - 3.93481i) q^{16} +2.00000 q^{17} +(-2.34435 + 3.53610i) q^{18} -4.27156i q^{19} +(-1.56155 + 0.438447i) q^{21} +(-5.47091 + 2.56155i) q^{22} -7.60669i q^{23} +(0.0814236 + 4.89830i) 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} +(0.882071 - 5.93481i) q^{36} +3.12311i q^{37} +(2.56155 + 5.47091i) q^{38} +(1.46228 + 5.20798i) q^{39} +7.12311i q^{41} +(1.73707 - 1.49798i) q^{42} +1.46228 q^{43} +(5.47091 - 6.56155i) q^{44} +(4.56155 + 9.74247i) q^{46} -0.936426i q^{47} +(-3.04168 - 6.22480i) q^{48} -6.12311 q^{49} +(3.33513 - 0.936426i) q^{51} +(4.79741 + 4.00000i) q^{52} -4.24621 q^{53} +(-2.25371 + 6.99434i) 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} +(-7.92375 + 6.83311i) q^{66} -5.20798 q^{67} +(2.56155 - 3.07221i) q^{68} +(-3.56155 - 12.6847i) q^{69} -6.67026 q^{71} +(2.42923 + 8.13012i) q^{72} -8.24621i q^{73} +(-1.87285 - 4.00000i) q^{74} +(-6.56155 - 5.47091i) q^{76} -4.00000 q^{77} +(-4.99596 - 5.79337i) q^{78} +9.06897i q^{79} +(4.12311 - 8.00000i) q^{81} +(-4.27156 - 9.12311i) q^{82} +4.68213i q^{83} +(-1.32650 + 2.96026i) 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} +(7.62858 + 6.14856i) 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
\(6\) −1.85500 + 1.59968i −0.757302 + 0.653065i
\(7\) −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 \(-0.277290\pi\)
0.643962 + 0.765058i \(0.277290\pi\)
\(12\) 1.41656 3.16123i 0.408924 0.912568i
\(13\) 3.12311i 0.866194i 0.901347 + 0.433097i \(0.142579\pi\)
−0.901347 + 0.433097i \(0.857421\pi\)
\(14\) 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 \(0.422021\pi\)
\(18\) −2.34435 + 3.53610i −0.552569 + 0.833467i
\(19\) 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 \(-0.291509\pi\)
\(24\) 0.0814236 + 4.89830i 0.0166205 + 0.999862i
\(25\) 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 \(0.0691088\pi\)
−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
\(36\) 0.882071 5.93481i 0.147012 0.989135i
\(37\) 3.12311i 0.513435i 0.966486 + 0.256718i \(0.0826411\pi\)
−0.966486 + 0.256718i \(0.917359\pi\)
\(38\) 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 \(0.812251\pi\)
\(42\) 1.73707 1.49798i 0.268036 0.231143i
\(43\) 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 \(-0.0217562\pi\)
\(48\) −3.04168 6.22480i −0.439029 0.898473i
\(49\) −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 \(0.594198\pi\)
\(54\) −2.25371 + 6.99434i −0.306691 + 0.951809i
\(55\) 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 \(-0.655179\pi\)
−0.468427 + 0.883502i \(0.655179\pi\)
\(60\) 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
\(66\) −7.92375 + 6.83311i −0.975347 + 0.841098i
\(67\) −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 \(-0.629535\pi\)
−0.395807 + 0.918334i \(0.629535\pi\)
\(72\) 2.42923 + 8.13012i 0.286287 + 0.958144i
\(73\) 8.24621i 0.965146i −0.875856 0.482573i \(-0.839702\pi\)
0.875856 0.482573i \(-0.160298\pi\)
\(74\) −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
\(78\) −4.99596 5.79337i −0.565681 0.655970i
\(79\) 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 \(0.917277\pi\)
\(84\) −1.32650 + 2.96026i −0.144733 + 0.322991i
\(85\) 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
\(96\) 7.62858 + 6.14856i 0.778589 + 0.627534i
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 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 \(-0.149965\pi\)
\(102\) −3.71001 + 3.19935i −0.367345 + 0.316783i
\(103\) −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 \(0.985587\pi\)
\(108\) −1.30784 10.3097i −0.125847 0.992050i
\(109\) 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 \(0.728811\pi\)
\(114\) 6.83311 + 7.92375i 0.639980 + 0.742127i
\(115\) 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
\(126\) 2.19531 3.31130i 0.195574 0.294994i
\(127\) 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 \(-0.779438\pi\)
−0.769388 + 0.638782i \(0.779438\pi\)
\(132\) 6.05090 13.5034i 0.526663 1.17532i
\(133\) 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 \(0.385413\pi\)
\(138\) 12.1682 + 14.1104i 1.03583 + 1.20116i
\(139\) 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
\(144\) −7.98674 8.95611i −0.665562 0.746343i
\(145\) 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 \(-0.919565\pi\)
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
\(156\) 9.87285 + 4.42405i 0.790461 + 0.354208i
\(157\) 21.3693i 1.70546i −0.522354 0.852729i \(-0.674946\pi\)
0.522354 0.852729i \(-0.325054\pi\)
\(158\) −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
\(162\) −0.483365 + 12.7187i −0.0379768 + 0.999279i
\(163\) 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 \(0.965333\pi\)
\(168\) −0.0762472 4.58690i −0.00588260 0.353887i
\(169\) 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 \(0.524224\pi\)
\(174\) −8.19531 9.50338i −0.621285 0.720449i
\(175\) 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 \(-0.315047\pi\)
0.548899 + 0.835889i \(0.315047\pi\)
\(180\) 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
\(186\) −3.83715 4.44961i −0.281354 0.326261i
\(187\) 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 \(-0.409874\pi\)
0.279371 + 0.960183i \(0.409874\pi\)
\(192\) −13.4577 3.30024i −0.971222 0.238175i
\(193\) 16.2462i 1.16943i 0.811240 + 0.584714i \(0.198793\pi\)
−0.811240 + 0.584714i \(0.801207\pi\)
\(194\) −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 \(0.643695\pi\)
\(198\) −10.0140 + 15.1047i −0.711666 + 1.07344i
\(199\) 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
\(204\) 2.83311 6.32246i 0.198357 0.442661i
\(205\) 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
\(216\) 7.85753 + 12.4201i 0.534637 + 0.845082i
\(217\) 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
\(222\) −4.99596 5.79337i −0.335307 0.388826i
\(223\) −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 \(0.907229\pi\)
\(228\) −13.5034 6.05090i −0.894283 0.400731i
\(229\) −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 \(0.393773\pi\)
\(234\) −11.0436 7.32165i −0.721944 0.478631i
\(235\) 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 \(-0.735319\pi\)
−0.673753 + 0.738957i \(0.735319\pi\)
\(240\) 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
\(246\) −11.3947 13.2134i −0.726497 0.842454i
\(247\) 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 \(-0.208905\pi\)
0.792259 + 0.610184i \(0.208905\pi\)
\(252\) −0.825994 + 5.55751i −0.0520328 + 0.350090i
\(253\) 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 \(0.524769\pi\)
\(258\) −2.71253 + 2.33917i −0.168875 + 0.145631i
\(259\) 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 \(-0.154123\pi\)
\(264\) 0.347806 + 20.9234i 0.0214060 + 1.28775i
\(265\) 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 \(0.415608\pi\)
−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
\(276\) −24.0465 10.7753i −1.44743 0.648597i
\(277\) 1.36932i 0.0822743i 0.999154 + 0.0411371i \(0.0130981\pi\)
−0.999154 + 0.0411371i \(0.986902\pi\)
\(278\) 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 \(-0.308095\pi\)
\(282\) 1.49798 + 1.73707i 0.0892034 + 0.103441i
\(283\) 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
\(288\) 15.6000 + 6.68132i 0.919239 + 0.393701i
\(289\) −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 \(0.150220\pi\)
\(294\) 11.3584 9.79499i 0.662434 0.571255i
\(295\) 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
\(306\) −4.68870 + 7.07221i −0.268035 + 0.404291i
\(307\) −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 \(-0.368483\pi\)
0.401517 + 0.915851i \(0.368483\pi\)
\(312\) −15.2979 + 0.254294i −0.866074 + 0.0143966i
\(313\) 10.4924i 0.593067i 0.955022 + 0.296533i \(0.0958306\pi\)
−0.955022 + 0.296533i \(0.904169\pi\)
\(314\) 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 \(0.128681\pi\)
\(318\) 7.87673 6.79256i 0.441705 0.380908i
\(319\) 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
\(324\) −7.00805 16.5797i −0.389336 0.921096i
\(325\) 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
\(336\) 2.84831 + 5.82907i 0.155388 + 0.318002i
\(337\) 34.4924i 1.87892i 0.342656 + 0.939461i \(0.388674\pi\)
−0.342656 + 0.939461i \(0.611326\pi\)
\(338\) −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
\(342\) 15.1047 + 10.0140i 0.816767 + 0.541497i
\(343\) 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 \(-0.221377\pi\)
\(348\) 16.1953 + 7.25716i 0.868160 + 0.389025i
\(349\) 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 \(0.468149\pi\)
\(354\) 13.3488 11.5115i 0.709482 0.611827i
\(355\) 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 \(-0.491165\pi\)
0.0277535 + 0.999615i \(0.491165\pi\)
\(360\) 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
\(366\) 9.50338 8.19531i 0.496749 0.428376i
\(367\) −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
\(372\) 7.58286 + 3.39790i 0.393153 + 0.176173i
\(373\) 0.876894i 0.0454039i −0.999742 0.0227019i \(-0.992773\pi\)
0.999742 0.0227019i \(-0.00722687\pi\)
\(374\) −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
\(378\) 2.11043 6.54968i 0.108549 0.336879i
\(379\) 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 \(-0.0381685\pi\)
\(384\) 19.2153 3.84336i 0.980578 0.196131i
\(385\) 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
\(396\) 3.76782 25.3509i 0.189340 1.27393i
\(397\) 23.1231i 1.16052i −0.814433 0.580258i \(-0.802952\pi\)
0.814433 0.580258i \(-0.197048\pi\)
\(398\) −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 \(0.795465\pi\)
\(402\) 9.66083 8.33109i 0.481838 0.415517i
\(403\) −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
\(408\) 0.162847 + 9.79661i 0.00806214 + 0.485004i
\(409\) −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
\(414\) 26.8980 + 17.8327i 1.32197 + 0.876432i
\(415\) 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 \(-0.547955\pi\)
−0.150087 + 0.988673i \(0.547955\pi\)
\(420\) 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
\(426\) 12.3734 10.6703i 0.599491 0.516976i
\(427\) 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 \(-0.834672\pi\)
−0.868121 + 0.496353i \(0.834672\pi\)
\(432\) −17.5118 11.1954i −0.842536 0.538640i
\(433\) 18.0000i 0.865025i 0.901628 + 0.432512i \(0.142373\pi\)
−0.901628 + 0.432512i \(0.857627\pi\)
\(434\) 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
\(438\) 13.1913 + 15.2967i 0.630303 + 0.730907i
\(439\) 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 \(0.790533\pi\)
\(444\) 9.87285 + 4.42405i 0.468545 + 0.209956i
\(445\) 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
\(456\) 20.9234 0.347806i 0.979827 0.0162875i
\(457\) 10.0000i 0.467780i 0.972263 + 0.233890i \(0.0751456\pi\)
−0.972263 + 0.233890i \(0.924854\pi\)
\(458\) 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 \(-0.120429\pi\)
\(462\) 7.42001 6.39871i 0.345210 0.297695i
\(463\) −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 \(-0.121898\pi\)
\(468\) 18.5350 + 2.75480i 0.856782 + 0.127341i
\(469\) 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
\(474\) −14.5074 16.8230i −0.666348 0.772704i
\(475\) 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 \(-0.324450\pi\)
0.523971 + 0.851736i \(0.324450\pi\)
\(480\) 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
\(486\) 5.14904 + 21.4357i 0.233565 + 0.972341i
\(487\) 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 \(-0.638371\pi\)
−0.421143 + 0.906994i \(0.638371\pi\)
\(492\) 22.5178 + 10.0903i 1.01518 + 0.454905i
\(493\) 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
\(498\) −7.48990 8.68537i −0.335630 0.389201i
\(499\) 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 \(0.853719\pi\)
\(504\) −2.27479 7.61326i −0.101327 0.339121i
\(505\) 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
\(516\) 2.07140 4.62260i 0.0911883 0.203499i
\(517\) 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 \(-0.158104\pi\)
\(522\) −18.1158 12.0104i −0.792908 0.525679i
\(523\) −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
\(528\) −12.9927 26.5896i −0.565436 1.15716i
\(529\) −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
\(534\) −9.99192 11.5867i −0.432393 0.501407i
\(535\) 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
\(546\) 4.67835 + 5.42506i 0.200215 + 0.232171i
\(547\) −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
\(552\) 37.2599 0.619364i 1.58589 0.0263619i
\(553\) 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 \(0.362557\pi\)
\(558\) −8.48207 5.62341i −0.359075 0.238058i
\(559\) 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 \(0.724221\pi\)
\(564\) −2.96026 1.32650i −0.124649 0.0558557i
\(565\) 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 \(-0.885726\pi\)
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
\(576\) −23.9867 + 0.797675i −0.999448 + 0.0332364i
\(577\) 15.7538i 0.655839i 0.944706 + 0.327919i \(0.106347\pi\)
−0.944706 + 0.327919i \(0.893653\pi\)
\(578\) 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
\(582\) −9.59806 11.1300i −0.397852 0.461354i
\(583\) −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 \(0.712712\pi\)
\(588\) −8.67372 + 19.3565i −0.357698 + 0.798250i
\(589\) 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 \(0.445844\pi\)
\(594\) −9.62685 + 29.8767i −0.394994 + 1.22586i
\(595\) 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 \(-0.228528\pi\)
0.753162 + 0.657836i \(0.228528\pi\)
\(600\) 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
\(606\) 14.5940 + 16.9234i 0.592841 + 0.687466i
\(607\) −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
\(612\) 1.76414 11.8696i 0.0713112 0.479801i
\(613\) 0.876894i 0.0354174i 0.999843 + 0.0177087i \(0.00563715\pi\)
−0.999843 + 0.0177087i \(0.994363\pi\)
\(614\) 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 \(0.590935\pi\)
\(618\) 23.0096 19.8425i 0.925584 0.798184i
\(619\) 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
\(624\) 19.4407 9.49949i 0.778252 0.380284i
\(625\) 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
\(636\) −6.01499 + 13.4232i −0.238510 + 0.532266i
\(637\) 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 \(-0.389502\pi\)
\(642\) −1.49798 1.73707i −0.0591205 0.0685568i
\(643\) −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 \(0.977265\pi\)
\(648\) 18.9182 + 17.0324i 0.743177 + 0.669094i
\(649\) −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 \(0.677058\pi\)
\(654\) −16.9234 + 14.5940i −0.661757 + 0.570671i
\(655\) 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 \(-0.676094\pi\)
−0.525425 + 0.850840i \(0.676094\pi\)
\(660\) 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
\(666\) −11.0436 7.32165i −0.427932 0.283708i
\(667\) 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
\(672\) −7.14361 5.75767i −0.275571 0.222107i
\(673\) 10.4924i 0.404453i −0.979339 0.202227i \(-0.935182\pi\)
0.979339 0.202227i \(-0.0648177\pi\)
\(674\) −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 \(0.269357\pi\)
\(678\) 25.9700 22.3955i 0.997373 0.860093i
\(679\) 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 \(-0.243192\pi\)
\(684\) −25.3509 3.76782i −0.969315 0.144066i
\(685\) 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
\(696\) −25.0945 + 0.417142i −0.951205 + 0.0158117i
\(697\) 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 \(0.597413\pi\)
\(702\) −21.8441 7.03857i −0.824451 0.265654i
\(703\) 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
\(708\) −10.1937 + 22.7486i −0.383103 + 0.854944i
\(709\) 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
\(714\) 3.47415 2.99596i 0.130017 0.112121i
\(715\) 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 \(-0.534787\pi\)
−0.109068 + 0.994034i \(0.534787\pi\)
\(720\) 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
\(726\) −13.4417 + 11.5916i −0.498870 + 0.430204i
\(727\) 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
\(732\) −7.25716 + 16.1953i −0.268233 + 0.598596i
\(733\) 35.1231i 1.29730i −0.761086 0.648651i \(-0.775334\pi\)
0.761086 0.648651i \(-0.224666\pi\)
\(734\) 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
\(738\) −25.1880 16.6991i −0.927184 0.614701i
\(739\) 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 \(0.926935\pi\)
\(744\) −11.7496 + 0.195311i −0.430761 + 0.00716046i
\(745\) 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
\(756\) 1.22470 + 9.65426i 0.0445419 + 0.351122i
\(757\) 19.1231i 0.695041i −0.937672 0.347521i \(-0.887024\pi\)
0.937672 0.347521i \(-0.112976\pi\)
\(758\) 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 \(0.621046\pi\)
\(762\) −8.68537 + 7.48990i −0.314638 + 0.271330i
\(763\) −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
\(768\) −22.3058 + 16.4455i −0.804890 + 0.593424i
\(769\) 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 \(0.594377\pi\)
\(774\) −3.42809 + 5.17077i −0.123220 + 0.185859i
\(775\) 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