Properties

Label 72.3.h.a.53.3
Level $72$
Weight $3$
Character 72.53
Analytic conductor $1.962$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 72 = 2^{3} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 72.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.96185790339\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.33808912384.2
Defining polynomial: \(x^{8} - 2 x^{7} + 11 x^{6} - 18 x^{5} + 47 x^{4} - 28 x^{3} - 44 x^{2} + 48 x + 36\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 53.3
Root \(1.15139 + 2.23537i\) of defining polynomial
Character \(\chi\) \(=\) 72.53
Dual form 72.3.h.a.53.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.16130 - 1.62831i) q^{2} +(-1.30278 + 3.78190i) q^{4} -7.67101 q^{5} -7.21110 q^{7} +(7.67101 - 2.27059i) q^{8} +O(q^{10})\) \(q+(-1.16130 - 1.62831i) q^{2} +(-1.30278 + 3.78190i) q^{4} -7.67101 q^{5} -7.21110 q^{7} +(7.67101 - 2.27059i) q^{8} +(8.90833 + 12.4908i) q^{10} -6.05164 q^{11} +2.29014i q^{13} +(8.37424 + 11.7419i) q^{14} +(-12.6056 - 9.85394i) q^{16} +21.8103i q^{17} -34.8355i q^{19} +(9.99361 - 29.0110i) q^{20} +(7.02776 + 9.85394i) q^{22} -21.5117i q^{23} +33.8444 q^{25} +(3.72905 - 2.65953i) q^{26} +(9.39445 - 27.2717i) q^{28} -10.9098 q^{29} -37.6333 q^{31} +(-1.40645 + 31.9691i) q^{32} +(35.5139 - 25.3282i) q^{34} +55.3164 q^{35} +34.8355i q^{37} +(-56.7229 + 40.4544i) q^{38} +(-58.8444 + 17.4177i) q^{40} -13.3250i q^{41} +60.5104i q^{43} +(7.88393 - 22.8867i) q^{44} +(-35.0278 + 24.9815i) q^{46} +3.34701i q^{47} +3.00000 q^{49} +(-39.3034 - 55.1091i) q^{50} +(-8.66106 - 2.98353i) q^{52} +35.1163 q^{53} +46.4222 q^{55} +(-55.3164 + 16.3735i) q^{56} +(12.6695 + 17.7644i) q^{58} -37.1615 q^{59} +25.6749i q^{61} +(43.7035 + 61.2786i) q^{62} +(53.6888 - 34.8355i) q^{64} -17.5677i q^{65} -25.6749i q^{67} +(-82.4844 - 28.4139i) q^{68} +(-64.2389 - 90.0722i) q^{70} -37.2881i q^{71} -77.6888 q^{73} +(56.7229 - 40.4544i) q^{74} +(131.744 + 45.3828i) q^{76} +43.6390 q^{77} +31.3221 q^{79} +(96.6973 + 75.5897i) q^{80} +(-21.6972 + 15.4743i) q^{82} -55.3164 q^{83} -167.307i q^{85} +(98.5296 - 70.2706i) q^{86} +(-46.4222 + 13.7408i) q^{88} +5.43682i q^{89} -16.5144i q^{91} +(81.3553 + 28.0250i) q^{92} +(5.44996 - 3.88687i) q^{94} +267.223i q^{95} -52.8444 q^{97} +(-3.48389 - 4.88492i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} + 28q^{10} - 72q^{16} - 88q^{22} + 40q^{25} + 104q^{28} - 128q^{31} + 212q^{34} - 240q^{40} - 136q^{46} + 24q^{49} + 248q^{52} + 256q^{55} + 260q^{58} - 32q^{64} - 312q^{70} - 160q^{73} + 304q^{76} - 384q^{79} - 188q^{82} - 256q^{88} - 216q^{94} - 192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(55\) \(65\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16130 1.62831i −0.580649 0.814154i
\(3\) 0 0
\(4\) −1.30278 + 3.78190i −0.325694 + 0.945475i
\(5\) −7.67101 −1.53420 −0.767101 0.641526i \(-0.778302\pi\)
−0.767101 + 0.641526i \(0.778302\pi\)
\(6\) 0 0
\(7\) −7.21110 −1.03016 −0.515079 0.857143i \(-0.672237\pi\)
−0.515079 + 0.857143i \(0.672237\pi\)
\(8\) 7.67101 2.27059i 0.958876 0.283824i
\(9\) 0 0
\(10\) 8.90833 + 12.4908i 0.890833 + 1.24908i
\(11\) −6.05164 −0.550149 −0.275075 0.961423i \(-0.588703\pi\)
−0.275075 + 0.961423i \(0.588703\pi\)
\(12\) 0 0
\(13\) 2.29014i 0.176164i 0.996113 + 0.0880821i \(0.0280738\pi\)
−0.996113 + 0.0880821i \(0.971926\pi\)
\(14\) 8.37424 + 11.7419i 0.598160 + 0.838707i
\(15\) 0 0
\(16\) −12.6056 9.85394i −0.787847 0.615871i
\(17\) 21.8103i 1.28296i 0.767140 + 0.641479i \(0.221679\pi\)
−0.767140 + 0.641479i \(0.778321\pi\)
\(18\) 0 0
\(19\) 34.8355i 1.83345i −0.399523 0.916723i \(-0.630824\pi\)
0.399523 0.916723i \(-0.369176\pi\)
\(20\) 9.99361 29.0110i 0.499680 1.45055i
\(21\) 0 0
\(22\) 7.02776 + 9.85394i 0.319443 + 0.447906i
\(23\) 21.5117i 0.935293i −0.883915 0.467647i \(-0.845102\pi\)
0.883915 0.467647i \(-0.154898\pi\)
\(24\) 0 0
\(25\) 33.8444 1.35378
\(26\) 3.72905 2.65953i 0.143425 0.102290i
\(27\) 0 0
\(28\) 9.39445 27.2717i 0.335516 0.973988i
\(29\) −10.9098 −0.376198 −0.188099 0.982150i \(-0.560233\pi\)
−0.188099 + 0.982150i \(0.560233\pi\)
\(30\) 0 0
\(31\) −37.6333 −1.21398 −0.606989 0.794710i \(-0.707623\pi\)
−0.606989 + 0.794710i \(0.707623\pi\)
\(32\) −1.40645 + 31.9691i −0.0439516 + 0.999034i
\(33\) 0 0
\(34\) 35.5139 25.3282i 1.04453 0.744948i
\(35\) 55.3164 1.58047
\(36\) 0 0
\(37\) 34.8355i 0.941499i 0.882267 + 0.470750i \(0.156017\pi\)
−0.882267 + 0.470750i \(0.843983\pi\)
\(38\) −56.7229 + 40.4544i −1.49271 + 1.06459i
\(39\) 0 0
\(40\) −58.8444 + 17.4177i −1.47111 + 0.435443i
\(41\) 13.3250i 0.325000i −0.986709 0.162500i \(-0.948044\pi\)
0.986709 0.162500i \(-0.0519558\pi\)
\(42\) 0 0
\(43\) 60.5104i 1.40722i 0.710587 + 0.703609i \(0.248430\pi\)
−0.710587 + 0.703609i \(0.751570\pi\)
\(44\) 7.88393 22.8867i 0.179180 0.520152i
\(45\) 0 0
\(46\) −35.0278 + 24.9815i −0.761473 + 0.543077i
\(47\) 3.34701i 0.0712129i 0.999366 + 0.0356065i \(0.0113363\pi\)
−0.999366 + 0.0356065i \(0.988664\pi\)
\(48\) 0 0
\(49\) 3.00000 0.0612245
\(50\) −39.3034 55.1091i −0.786069 1.10218i
\(51\) 0 0
\(52\) −8.66106 2.98353i −0.166559 0.0573756i
\(53\) 35.1163 0.662572 0.331286 0.943530i \(-0.392518\pi\)
0.331286 + 0.943530i \(0.392518\pi\)
\(54\) 0 0
\(55\) 46.4222 0.844040
\(56\) −55.3164 + 16.3735i −0.987794 + 0.292383i
\(57\) 0 0
\(58\) 12.6695 + 17.7644i 0.218439 + 0.306283i
\(59\) −37.1615 −0.629856 −0.314928 0.949116i \(-0.601980\pi\)
−0.314928 + 0.949116i \(0.601980\pi\)
\(60\) 0 0
\(61\) 25.6749i 0.420901i 0.977605 + 0.210450i \(0.0674930\pi\)
−0.977605 + 0.210450i \(0.932507\pi\)
\(62\) 43.7035 + 61.2786i 0.704895 + 0.988365i
\(63\) 0 0
\(64\) 53.6888 34.8355i 0.838888 0.544304i
\(65\) 17.5677i 0.270272i
\(66\) 0 0
\(67\) 25.6749i 0.383208i −0.981472 0.191604i \(-0.938631\pi\)
0.981472 0.191604i \(-0.0613689\pi\)
\(68\) −82.4844 28.4139i −1.21301 0.417852i
\(69\) 0 0
\(70\) −64.2389 90.0722i −0.917698 1.28675i
\(71\) 37.2881i 0.525185i −0.964907 0.262592i \(-0.915423\pi\)
0.964907 0.262592i \(-0.0845775\pi\)
\(72\) 0 0
\(73\) −77.6888 −1.06423 −0.532115 0.846672i \(-0.678603\pi\)
−0.532115 + 0.846672i \(0.678603\pi\)
\(74\) 56.7229 40.4544i 0.766526 0.546681i
\(75\) 0 0
\(76\) 131.744 + 45.3828i 1.73348 + 0.597142i
\(77\) 43.6390 0.566740
\(78\) 0 0
\(79\) 31.3221 0.396483 0.198241 0.980153i \(-0.436477\pi\)
0.198241 + 0.980153i \(0.436477\pi\)
\(80\) 96.6973 + 75.5897i 1.20872 + 0.944871i
\(81\) 0 0
\(82\) −21.6972 + 15.4743i −0.264600 + 0.188711i
\(83\) −55.3164 −0.666463 −0.333232 0.942845i \(-0.608139\pi\)
−0.333232 + 0.942845i \(0.608139\pi\)
\(84\) 0 0
\(85\) 167.307i 1.96832i
\(86\) 98.5296 70.2706i 1.14569 0.817100i
\(87\) 0 0
\(88\) −46.4222 + 13.7408i −0.527525 + 0.156146i
\(89\) 5.43682i 0.0610878i 0.999533 + 0.0305439i \(0.00972394\pi\)
−0.999533 + 0.0305439i \(0.990276\pi\)
\(90\) 0 0
\(91\) 16.5144i 0.181477i
\(92\) 81.3553 + 28.0250i 0.884297 + 0.304619i
\(93\) 0 0
\(94\) 5.44996 3.88687i 0.0579783 0.0413497i
\(95\) 267.223i 2.81288i
\(96\) 0 0
\(97\) −52.8444 −0.544788 −0.272394 0.962186i \(-0.587815\pi\)
−0.272394 + 0.962186i \(0.587815\pi\)
\(98\) −3.48389 4.88492i −0.0355499 0.0498462i
\(99\) 0 0
\(100\) −44.0917 + 127.996i −0.440917 + 1.27996i
\(101\) −90.0069 −0.891158 −0.445579 0.895243i \(-0.647002\pi\)
−0.445579 + 0.895243i \(0.647002\pi\)
\(102\) 0 0
\(103\) 119.211 1.15739 0.578695 0.815544i \(-0.303562\pi\)
0.578695 + 0.815544i \(0.303562\pi\)
\(104\) 5.19996 + 17.5677i 0.0499996 + 0.168920i
\(105\) 0 0
\(106\) −40.7805 57.1802i −0.384722 0.539436i
\(107\) −24.2066 −0.226230 −0.113115 0.993582i \(-0.536083\pi\)
−0.113115 + 0.993582i \(0.536083\pi\)
\(108\) 0 0
\(109\) 132.472i 1.21533i −0.794192 0.607667i \(-0.792105\pi\)
0.794192 0.607667i \(-0.207895\pi\)
\(110\) −53.9100 75.5897i −0.490091 0.687179i
\(111\) 0 0
\(112\) 90.8999 + 71.0578i 0.811606 + 0.634444i
\(113\) 160.560i 1.42089i −0.703754 0.710444i \(-0.748494\pi\)
0.703754 0.710444i \(-0.251506\pi\)
\(114\) 0 0
\(115\) 165.017i 1.43493i
\(116\) 14.2130 41.2596i 0.122525 0.355686i
\(117\) 0 0
\(118\) 43.1556 + 60.5104i 0.365725 + 0.512800i
\(119\) 157.276i 1.32165i
\(120\) 0 0
\(121\) −84.3776 −0.697336
\(122\) 41.8067 29.8162i 0.342678 0.244395i
\(123\) 0 0
\(124\) 49.0278 142.325i 0.395385 1.14779i
\(125\) −67.8456 −0.542765
\(126\) 0 0
\(127\) −146.478 −1.15337 −0.576684 0.816967i \(-0.695654\pi\)
−0.576684 + 0.816967i \(0.695654\pi\)
\(128\) −119.072 46.9676i −0.930247 0.366934i
\(129\) 0 0
\(130\) −28.6056 + 20.4013i −0.220043 + 0.156933i
\(131\) −184.956 −1.41188 −0.705939 0.708273i \(-0.749475\pi\)
−0.705939 + 0.708273i \(0.749475\pi\)
\(132\) 0 0
\(133\) 251.202i 1.88874i
\(134\) −41.8067 + 29.8162i −0.311990 + 0.222509i
\(135\) 0 0
\(136\) 49.5223 + 167.307i 0.364134 + 1.23020i
\(137\) 133.313i 0.973089i 0.873656 + 0.486544i \(0.161743\pi\)
−0.873656 + 0.486544i \(0.838257\pi\)
\(138\) 0 0
\(139\) 165.017i 1.18717i −0.804771 0.593586i \(-0.797712\pi\)
0.804771 0.593586i \(-0.202288\pi\)
\(140\) −72.0649 + 209.201i −0.514749 + 1.49430i
\(141\) 0 0
\(142\) −60.7166 + 43.3026i −0.427582 + 0.304948i
\(143\) 13.8591i 0.0969166i
\(144\) 0 0
\(145\) 83.6888 0.577164
\(146\) 90.2198 + 126.501i 0.617944 + 0.866448i
\(147\) 0 0
\(148\) −131.744 45.3828i −0.890164 0.306641i
\(149\) 228.937 1.53649 0.768244 0.640157i \(-0.221131\pi\)
0.768244 + 0.640157i \(0.221131\pi\)
\(150\) 0 0
\(151\) 162.478 1.07601 0.538006 0.842941i \(-0.319178\pi\)
0.538006 + 0.842941i \(0.319178\pi\)
\(152\) −79.0972 267.223i −0.520376 1.75805i
\(153\) 0 0
\(154\) −50.6779 71.0578i −0.329077 0.461414i
\(155\) 288.686 1.86249
\(156\) 0 0
\(157\) 113.667i 0.723993i 0.932179 + 0.361997i \(0.117905\pi\)
−0.932179 + 0.361997i \(0.882095\pi\)
\(158\) −36.3743 51.0021i −0.230217 0.322798i
\(159\) 0 0
\(160\) 10.7889 245.235i 0.0674306 1.53272i
\(161\) 155.123i 0.963499i
\(162\) 0 0
\(163\) 111.860i 0.686259i 0.939288 + 0.343130i \(0.111487\pi\)
−0.939288 + 0.343130i \(0.888513\pi\)
\(164\) 50.3939 + 17.3595i 0.307280 + 0.105851i
\(165\) 0 0
\(166\) 64.2389 + 90.0722i 0.386981 + 0.542604i
\(167\) 151.541i 0.907430i −0.891147 0.453715i \(-0.850098\pi\)
0.891147 0.453715i \(-0.149902\pi\)
\(168\) 0 0
\(169\) 163.755 0.968966
\(170\) −272.427 + 194.293i −1.60251 + 1.14290i
\(171\) 0 0
\(172\) −228.844 78.8315i −1.33049 0.458323i
\(173\) 98.0198 0.566588 0.283294 0.959033i \(-0.408573\pi\)
0.283294 + 0.959033i \(0.408573\pi\)
\(174\) 0 0
\(175\) −244.056 −1.39460
\(176\) 76.2843 + 59.6325i 0.433433 + 0.338821i
\(177\) 0 0
\(178\) 8.85281 6.31376i 0.0497349 0.0354706i
\(179\) 222.117 1.24088 0.620440 0.784254i \(-0.286954\pi\)
0.620440 + 0.784254i \(0.286954\pi\)
\(180\) 0 0
\(181\) 118.731i 0.655971i −0.944683 0.327985i \(-0.893630\pi\)
0.944683 0.327985i \(-0.106370\pi\)
\(182\) −26.8905 + 19.1781i −0.147750 + 0.105374i
\(183\) 0 0
\(184\) −48.8444 165.017i −0.265459 0.896831i
\(185\) 267.223i 1.44445i
\(186\) 0 0
\(187\) 131.988i 0.705818i
\(188\) −12.6581 4.36040i −0.0673301 0.0231936i
\(189\) 0 0
\(190\) 435.122 310.326i 2.29012 1.63329i
\(191\) 151.541i 0.793408i 0.917947 + 0.396704i \(0.129846\pi\)
−0.917947 + 0.396704i \(0.870154\pi\)
\(192\) 0 0
\(193\) 113.378 0.587449 0.293724 0.955890i \(-0.405105\pi\)
0.293724 + 0.955890i \(0.405105\pi\)
\(194\) 61.3681 + 86.0470i 0.316330 + 0.443541i
\(195\) 0 0
\(196\) −3.90833 + 11.3457i −0.0199404 + 0.0578862i
\(197\) −319.454 −1.62159 −0.810796 0.585329i \(-0.800965\pi\)
−0.810796 + 0.585329i \(0.800965\pi\)
\(198\) 0 0
\(199\) −41.0109 −0.206085 −0.103043 0.994677i \(-0.532858\pi\)
−0.103043 + 0.994677i \(0.532858\pi\)
\(200\) 259.621 76.8469i 1.29810 0.384234i
\(201\) 0 0
\(202\) 104.525 + 146.559i 0.517450 + 0.725540i
\(203\) 78.6713 0.387544
\(204\) 0 0
\(205\) 102.216i 0.498616i
\(206\) −138.440 194.112i −0.672037 0.942293i
\(207\) 0 0
\(208\) 22.5668 28.8684i 0.108494 0.138790i
\(209\) 210.812i 1.00867i
\(210\) 0 0
\(211\) 95.3459i 0.451876i −0.974142 0.225938i \(-0.927455\pi\)
0.974142 0.225938i \(-0.0725447\pi\)
\(212\) −45.7487 + 132.806i −0.215796 + 0.626445i
\(213\) 0 0
\(214\) 28.1110 + 39.4157i 0.131360 + 0.184186i
\(215\) 464.176i 2.15896i
\(216\) 0 0
\(217\) 271.378 1.25059
\(218\) −215.704 + 153.839i −0.989470 + 0.705683i
\(219\) 0 0
\(220\) −60.4777 + 175.564i −0.274899 + 0.798019i
\(221\) −49.9485 −0.226011
\(222\) 0 0
\(223\) −268.167 −1.20254 −0.601270 0.799046i \(-0.705338\pi\)
−0.601270 + 0.799046i \(0.705338\pi\)
\(224\) 10.1421 230.532i 0.0452770 1.02916i
\(225\) 0 0
\(226\) −261.442 + 186.458i −1.15682 + 0.825036i
\(227\) −65.7164 −0.289499 −0.144750 0.989468i \(-0.546238\pi\)
−0.144750 + 0.989468i \(0.546238\pi\)
\(228\) 0 0
\(229\) 155.373i 0.678484i 0.940699 + 0.339242i \(0.110171\pi\)
−0.940699 + 0.339242i \(0.889829\pi\)
\(230\) 268.698 191.634i 1.16825 0.833190i
\(231\) 0 0
\(232\) −83.6888 + 24.7716i −0.360728 + 0.106774i
\(233\) 285.451i 1.22511i 0.790427 + 0.612556i \(0.209859\pi\)
−0.790427 + 0.612556i \(0.790141\pi\)
\(234\) 0 0
\(235\) 25.6749i 0.109255i
\(236\) 48.4131 140.541i 0.205140 0.595514i
\(237\) 0 0
\(238\) −256.094 + 182.645i −1.07603 + 0.767414i
\(239\) 421.153i 1.76214i 0.472982 + 0.881072i \(0.343178\pi\)
−0.472982 + 0.881072i \(0.656822\pi\)
\(240\) 0 0
\(241\) −191.600 −0.795019 −0.397510 0.917598i \(-0.630126\pi\)
−0.397510 + 0.917598i \(0.630126\pi\)
\(242\) 97.9876 + 137.393i 0.404907 + 0.567739i
\(243\) 0 0
\(244\) −97.1001 33.4487i −0.397951 0.137085i
\(245\) −23.0130 −0.0939307
\(246\) 0 0
\(247\) 79.7779 0.322988
\(248\) −288.686 + 85.4499i −1.16405 + 0.344556i
\(249\) 0 0
\(250\) 78.7889 + 110.473i 0.315156 + 0.441894i
\(251\) −483.190 −1.92506 −0.962529 0.271178i \(-0.912587\pi\)
−0.962529 + 0.271178i \(0.912587\pi\)
\(252\) 0 0
\(253\) 130.181i 0.514551i
\(254\) 170.104 + 238.511i 0.669702 + 0.939019i
\(255\) 0 0
\(256\) 61.7998 + 248.429i 0.241406 + 0.970424i
\(257\) 21.2132i 0.0825416i 0.999148 + 0.0412708i \(0.0131406\pi\)
−0.999148 + 0.0412708i \(0.986859\pi\)
\(258\) 0 0
\(259\) 251.202i 0.969893i
\(260\) 66.4391 + 22.8867i 0.255535 + 0.0880258i
\(261\) 0 0
\(262\) 214.789 + 301.165i 0.819805 + 1.14949i
\(263\) 246.670i 0.937910i −0.883222 0.468955i \(-0.844631\pi\)
0.883222 0.468955i \(-0.155369\pi\)
\(264\) 0 0
\(265\) −269.378 −1.01652
\(266\) 409.035 291.721i 1.53772 1.09669i
\(267\) 0 0
\(268\) 97.1001 + 33.4487i 0.362314 + 0.124809i
\(269\) −241.040 −0.896060 −0.448030 0.894019i \(-0.647874\pi\)
−0.448030 + 0.894019i \(0.647874\pi\)
\(270\) 0 0
\(271\) 61.7443 0.227839 0.113919 0.993490i \(-0.463659\pi\)
0.113919 + 0.993490i \(0.463659\pi\)
\(272\) 214.917 274.931i 0.790137 1.01077i
\(273\) 0 0
\(274\) 217.075 154.816i 0.792244 0.565023i
\(275\) −204.814 −0.744779
\(276\) 0 0
\(277\) 379.093i 1.36857i −0.729215 0.684284i \(-0.760115\pi\)
0.729215 0.684284i \(-0.239885\pi\)
\(278\) −268.698 + 191.634i −0.966541 + 0.689330i
\(279\) 0 0
\(280\) 424.333 125.601i 1.51548 0.448575i
\(281\) 301.227i 1.07198i −0.844223 0.535992i \(-0.819938\pi\)
0.844223 0.535992i \(-0.180062\pi\)
\(282\) 0 0
\(283\) 399.705i 1.41238i 0.708020 + 0.706192i \(0.249588\pi\)
−0.708020 + 0.706192i \(0.750412\pi\)
\(284\) 141.020 + 48.5781i 0.496549 + 0.171050i
\(285\) 0 0
\(286\) −22.5668 + 16.0945i −0.0789051 + 0.0562745i
\(287\) 96.0880i 0.334801i
\(288\) 0 0
\(289\) −186.689 −0.645982
\(290\) −97.1876 136.271i −0.335130 0.469901i
\(291\) 0 0
\(292\) 101.211 293.811i 0.346613 1.00620i
\(293\) 258.085 0.880838 0.440419 0.897792i \(-0.354830\pi\)
0.440419 + 0.897792i \(0.354830\pi\)
\(294\) 0 0
\(295\) 285.066 0.966327
\(296\) 79.0972 + 267.223i 0.267220 + 0.902782i
\(297\) 0 0
\(298\) −265.864 372.780i −0.892160 1.25094i
\(299\) 49.2648 0.164765
\(300\) 0 0
\(301\) 436.347i 1.44966i
\(302\) −188.685 264.564i −0.624785 0.876039i
\(303\) 0 0
\(304\) −343.267 + 439.120i −1.12917 + 1.44448i
\(305\) 196.953i 0.645747i
\(306\) 0 0
\(307\) 286.038i 0.931719i −0.884859 0.465859i \(-0.845745\pi\)
0.884859 0.465859i \(-0.154255\pi\)
\(308\) −56.8518 + 165.038i −0.184584 + 0.535839i
\(309\) 0 0
\(310\) −335.250 470.069i −1.08145 1.51635i
\(311\) 464.647i 1.49404i 0.664800 + 0.747021i \(0.268517\pi\)
−0.664800 + 0.747021i \(0.731483\pi\)
\(312\) 0 0
\(313\) 158.000 0.504792 0.252396 0.967624i \(-0.418781\pi\)
0.252396 + 0.967624i \(0.418781\pi\)
\(314\) 185.085 132.001i 0.589442 0.420386i
\(315\) 0 0
\(316\) −40.8057 + 118.457i −0.129132 + 0.374865i
\(317\) 28.6388 0.0903433 0.0451717 0.998979i \(-0.485617\pi\)
0.0451717 + 0.998979i \(0.485617\pi\)
\(318\) 0 0
\(319\) 66.0219 0.206965
\(320\) −411.848 + 267.223i −1.28702 + 0.835073i
\(321\) 0 0
\(322\) 252.589 180.144i 0.784437 0.559455i
\(323\) 759.772 2.35224
\(324\) 0 0
\(325\) 77.5083i 0.238487i
\(326\) 182.143 129.903i 0.558721 0.398476i
\(327\) 0 0
\(328\) −30.2557 102.216i −0.0922429 0.311635i
\(329\) 24.1356i 0.0733605i
\(330\) 0 0
\(331\) 428.993i 1.29605i 0.761619 + 0.648026i \(0.224405\pi\)
−0.761619 + 0.648026i \(0.775595\pi\)
\(332\) 72.0649 209.201i 0.217063 0.630124i
\(333\) 0 0
\(334\) −246.755 + 175.984i −0.738788 + 0.526898i
\(335\) 196.953i 0.587919i
\(336\) 0 0
\(337\) 290.755 0.862775 0.431388 0.902167i \(-0.358024\pi\)
0.431388 + 0.902167i \(0.358024\pi\)
\(338\) −190.169 266.644i −0.562629 0.788888i
\(339\) 0 0
\(340\) 632.738 + 217.963i 1.86100 + 0.641069i
\(341\) 227.743 0.667869
\(342\) 0 0
\(343\) 331.711 0.967087
\(344\) 137.394 + 464.176i 0.399403 + 1.34935i
\(345\) 0 0
\(346\) −113.830 159.606i −0.328989 0.461290i
\(347\) −179.756 −0.518029 −0.259014 0.965873i \(-0.583398\pi\)
−0.259014 + 0.965873i \(0.583398\pi\)
\(348\) 0 0
\(349\) 225.527i 0.646210i −0.946363 0.323105i \(-0.895273\pi\)
0.946363 0.323105i \(-0.104727\pi\)
\(350\) 283.421 + 397.398i 0.809775 + 1.13542i
\(351\) 0 0
\(352\) 8.51133 193.465i 0.0241799 0.549618i
\(353\) 133.784i 0.378992i −0.981881 0.189496i \(-0.939315\pi\)
0.981881 0.189496i \(-0.0606854\pi\)
\(354\) 0 0
\(355\) 286.038i 0.805740i
\(356\) −20.5615 7.08295i −0.0577570 0.0198959i
\(357\) 0 0
\(358\) −257.944 361.676i −0.720515 1.01027i
\(359\) 239.018i 0.665787i −0.942964 0.332894i \(-0.891975\pi\)
0.942964 0.332894i \(-0.108025\pi\)
\(360\) 0 0
\(361\) −852.511 −2.36153
\(362\) −193.330 + 137.882i −0.534061 + 0.380889i
\(363\) 0 0
\(364\) 62.4558 + 21.5146i 0.171582 + 0.0591059i
\(365\) 595.952 1.63274
\(366\) 0 0
\(367\) −188.389 −0.513320 −0.256660 0.966502i \(-0.582622\pi\)
−0.256660 + 0.966502i \(0.582622\pi\)
\(368\) −211.975 + 271.167i −0.576020 + 0.736868i
\(369\) 0 0
\(370\) −435.122 + 310.326i −1.17601 + 0.838718i
\(371\) −253.227 −0.682554
\(372\) 0 0
\(373\) 561.108i 1.50431i 0.658985 + 0.752156i \(0.270986\pi\)
−0.658985 + 0.752156i \(0.729014\pi\)
\(374\) −214.917 + 153.277i −0.574645 + 0.409833i
\(375\) 0 0
\(376\) 7.59969 + 25.6749i 0.0202119 + 0.0682844i
\(377\) 24.9848i 0.0662727i
\(378\) 0 0
\(379\) 328.227i 0.866034i 0.901386 + 0.433017i \(0.142551\pi\)
−0.901386 + 0.433017i \(0.857449\pi\)
\(380\) −1010.61 348.132i −2.65951 0.916137i
\(381\) 0 0
\(382\) 246.755 175.984i 0.645956 0.460691i
\(383\) 204.118i 0.532945i −0.963843 0.266472i \(-0.914142\pi\)
0.963843 0.266472i \(-0.0858581\pi\)
\(384\) 0 0
\(385\) −334.755 −0.869494
\(386\) −131.665 184.614i −0.341102 0.478274i
\(387\) 0 0
\(388\) 68.8444 199.852i 0.177434 0.515083i
\(389\) −60.1746 −0.154690 −0.0773452 0.997004i \(-0.524644\pi\)
−0.0773452 + 0.997004i \(0.524644\pi\)
\(390\) 0 0
\(391\) 469.177 1.19994
\(392\) 23.0130 6.81178i 0.0587067 0.0173770i
\(393\) 0 0
\(394\) 370.981 + 520.169i 0.941575 + 1.32023i
\(395\) −240.272 −0.608285
\(396\) 0 0
\(397\) 592.203i 1.49170i 0.666116 + 0.745848i \(0.267955\pi\)
−0.666116 + 0.745848i \(0.732045\pi\)
\(398\) 47.6259 + 66.7785i 0.119663 + 0.167785i
\(399\) 0 0
\(400\) −426.627 333.501i −1.06657 0.833752i
\(401\) 653.178i 1.62887i −0.580254 0.814436i \(-0.697047\pi\)
0.580254 0.814436i \(-0.302953\pi\)
\(402\) 0 0
\(403\) 86.1854i 0.213859i
\(404\) 117.259 340.397i 0.290245 0.842568i
\(405\) 0 0
\(406\) −91.3608 128.101i −0.225027 0.315520i
\(407\) 210.812i 0.517965i
\(408\) 0 0
\(409\) 355.156 0.868351 0.434176 0.900828i \(-0.357040\pi\)
0.434176 + 0.900828i \(0.357040\pi\)
\(410\) 166.440 118.704i 0.405950 0.289521i
\(411\) 0 0
\(412\) −155.305 + 450.845i −0.376955 + 1.09428i
\(413\) 267.976 0.648851
\(414\) 0 0
\(415\) 424.333 1.02249
\(416\) −73.2135 3.22096i −0.175994 0.00774270i
\(417\) 0 0
\(418\) 343.267 244.815i 0.821212 0.585682i
\(419\) −299.085 −0.713808 −0.356904 0.934141i \(-0.616168\pi\)
−0.356904 + 0.934141i \(0.616168\pi\)
\(420\) 0 0
\(421\) 769.638i 1.82812i −0.405582 0.914059i \(-0.632931\pi\)
0.405582 0.914059i \(-0.367069\pi\)
\(422\) −155.253 + 110.725i −0.367897 + 0.262381i
\(423\) 0 0
\(424\) 269.378 79.7348i 0.635325 0.188054i
\(425\) 738.156i 1.73684i
\(426\) 0 0
\(427\) 185.145i 0.433594i
\(428\) 31.5357 91.5468i 0.0736816 0.213894i
\(429\) 0 0
\(430\) −755.822 + 539.047i −1.75772 + 1.25360i
\(431\) 411.583i 0.954948i 0.878646 + 0.477474i \(0.158448\pi\)
−0.878646 + 0.477474i \(0.841552\pi\)
\(432\) 0 0
\(433\) 516.133 1.19199 0.595996 0.802987i \(-0.296757\pi\)
0.595996 + 0.802987i \(0.296757\pi\)
\(434\) −315.150 441.886i −0.726153 1.01817i
\(435\) 0 0
\(436\) 500.994 + 172.581i 1.14907 + 0.395827i
\(437\) −749.372 −1.71481
\(438\) 0 0
\(439\) −865.788 −1.97218 −0.986091 0.166205i \(-0.946849\pi\)
−0.986091 + 0.166205i \(0.946849\pi\)
\(440\) 356.105 105.406i 0.809330 0.239559i
\(441\) 0 0
\(442\) 58.0051 + 81.3316i 0.131233 + 0.184008i
\(443\) 546.261 1.23310 0.616548 0.787318i \(-0.288531\pi\)
0.616548 + 0.787318i \(0.288531\pi\)
\(444\) 0 0
\(445\) 41.7059i 0.0937211i
\(446\) 311.421 + 436.658i 0.698254 + 0.979053i
\(447\) 0 0
\(448\) −387.156 + 251.202i −0.864187 + 0.560719i
\(449\) 428.978i 0.955407i 0.878521 + 0.477704i \(0.158531\pi\)
−0.878521 + 0.477704i \(0.841469\pi\)
\(450\) 0 0
\(451\) 80.6382i 0.178799i
\(452\) 607.223 + 209.174i 1.34341 + 0.462774i
\(453\) 0 0
\(454\) 76.3163 + 107.007i 0.168098 + 0.235697i
\(455\) 126.682i 0.278422i
\(456\) 0 0
\(457\) 75.5997 0.165426 0.0827130 0.996573i \(-0.473642\pi\)
0.0827130 + 0.996573i \(0.473642\pi\)
\(458\) 252.995 180.434i 0.552391 0.393961i
\(459\) 0 0
\(460\) −624.077 214.980i −1.35669 0.467348i
\(461\) −771.365 −1.67324 −0.836622 0.547781i \(-0.815473\pi\)
−0.836622 + 0.547781i \(0.815473\pi\)
\(462\) 0 0
\(463\) −468.278 −1.01140 −0.505699 0.862710i \(-0.668765\pi\)
−0.505699 + 0.862710i \(0.668765\pi\)
\(464\) 137.523 + 107.504i 0.296387 + 0.231690i
\(465\) 0 0
\(466\) 464.802 331.494i 0.997430 0.711360i
\(467\) 452.842 0.969682 0.484841 0.874602i \(-0.338877\pi\)
0.484841 + 0.874602i \(0.338877\pi\)
\(468\) 0 0
\(469\) 185.145i 0.394765i
\(470\) −41.8067 + 29.8162i −0.0889505 + 0.0634388i
\(471\) 0 0
\(472\) −285.066 + 84.3787i −0.603954 + 0.178768i
\(473\) 366.187i 0.774180i
\(474\) 0 0
\(475\) 1178.99i 2.48208i
\(476\) 594.803 + 204.896i 1.24959 + 0.430453i
\(477\) 0 0
\(478\) 685.766 489.083i 1.43466 1.02319i
\(479\) 467.523i 0.976040i −0.872832 0.488020i \(-0.837719\pi\)
0.872832 0.488020i \(-0.162281\pi\)
\(480\) 0 0
\(481\) −79.7779 −0.165859
\(482\) 222.504 + 311.983i 0.461627 + 0.647268i
\(483\) 0 0
\(484\) 109.925 319.108i 0.227118 0.659314i
\(485\) 405.370 0.835815
\(486\) 0 0
\(487\) −863.766 −1.77365 −0.886824 0.462108i \(-0.847093\pi\)
−0.886824 + 0.462108i \(0.847093\pi\)
\(488\) 58.2973 + 196.953i 0.119462 + 0.403592i
\(489\) 0 0
\(490\) 26.7250 + 37.4723i 0.0545408 + 0.0764741i
\(491\) 149.498 0.304476 0.152238 0.988344i \(-0.451352\pi\)
0.152238 + 0.988344i \(0.451352\pi\)
\(492\) 0 0
\(493\) 237.945i 0.482647i
\(494\) −92.6459 129.903i −0.187542 0.262962i
\(495\) 0 0
\(496\) 474.389 + 370.836i 0.956429 + 0.747654i
\(497\) 268.889i 0.541023i
\(498\) 0 0
\(499\) 205.400i 0.411622i 0.978592 + 0.205811i \(0.0659833\pi\)
−0.978592 + 0.205811i \(0.934017\pi\)
\(500\) 88.3876 256.585i 0.176775 0.513170i
\(501\) 0 0
\(502\) 561.127 + 786.782i 1.11778 + 1.56729i
\(503\) 349.923i 0.695673i 0.937555 + 0.347836i \(0.113084\pi\)
−0.937555 + 0.347836i \(0.886916\pi\)
\(504\) 0 0
\(505\) 690.444 1.36722
\(506\) 211.975 151.179i 0.418924 0.298773i
\(507\) 0 0
\(508\) 190.828 553.964i 0.375645 1.09048i
\(509\) −529.468 −1.04021 −0.520106 0.854102i \(-0.674108\pi\)
−0.520106 + 0.854102i \(0.674108\pi\)
\(510\) 0 0
\(511\) 560.222 1.09632
\(512\) 332.750 389.129i 0.649903 0.760017i
\(513\) 0 0
\(514\) 34.5416 24.6348i 0.0672016 0.0479277i
\(515\) −914.470 −1.77567
\(516\) 0 0
\(517\) 20.2549i 0.0391777i
\(518\) −409.035 + 291.721i −0.789642 + 0.563167i
\(519\) 0 0
\(520\) −39.8890 134.762i −0.0767096 0.259157i
\(521\) 367.318i 0.705026i 0.935807 + 0.352513i \(0.114673\pi\)
−0.935807 + 0.352513i \(0.885327\pi\)
\(522\) 0 0
\(523\) 577.495i 1.10420i −0.833779 0.552099i \(-0.813827\pi\)
0.833779 0.552099i \(-0.186173\pi\)
\(524\) 240.956 699.485i 0.459840 1.33490i
\(525\) 0 0
\(526\) −401.655 + 286.458i −0.763603 + 0.544596i
\(527\) 820.793i 1.55748i
\(528\) 0 0
\(529\) 66.2447 0.125226
\(530\) 312.828 + 438.630i 0.590241 + 0.827603i
\(531\) 0 0
\(532\) −950.022 327.260i −1.78576 0.615151i
\(533\) 30.5161 0.0572534
\(534\) 0 0
\(535\) 185.689 0.347082
\(536\) −58.2973 196.953i −0.108764 0.367449i
\(537\) 0 0
\(538\) 279.919 + 392.488i 0.520296 + 0.729531i
\(539\) −18.1549 −0.0336826
\(540\) 0 0
\(541\) 326.777i 0.604023i −0.953304 0.302012i \(-0.902342\pi\)
0.953304 0.302012i \(-0.0976582\pi\)
\(542\) −71.7035 100.539i −0.132294 0.185496i
\(543\) 0 0
\(544\) −697.255 30.6751i −1.28172 0.0563880i
\(545\) 1016.19i 1.86457i
\(546\) 0 0
\(547\) 273.137i 0.499336i −0.968332 0.249668i \(-0.919679\pi\)
0.968332 0.249668i \(-0.0803214\pi\)
\(548\) −504.177 173.677i −0.920031 0.316929i
\(549\) 0 0
\(550\) 237.850 + 333.501i 0.432455 + 0.606365i
\(551\) 380.046i 0.689739i
\(552\) 0 0
\(553\) −225.867 −0.408440
\(554\) −617.281 + 440.240i −1.11423 + 0.794658i
\(555\) 0 0
\(556\) 624.077 + 214.980i 1.12244 + 0.386655i
\(557\) −93.2457 −0.167407 −0.0837035 0.996491i \(-0.526675\pi\)
−0.0837035 + 0.996491i \(0.526675\pi\)
\(558\) 0 0
\(559\) −138.577 −0.247902
\(560\) −697.294 545.085i −1.24517 0.973366i
\(561\) 0 0
\(562\) −490.491 + 349.815i −0.872760 + 0.622446i
\(563\) −42.3615 −0.0752424 −0.0376212 0.999292i \(-0.511978\pi\)
−0.0376212 + 0.999292i \(0.511978\pi\)
\(564\) 0 0
\(565\) 1231.66i 2.17993i
\(566\) 650.842 464.176i 1.14990 0.820099i
\(567\) 0 0
\(568\) −84.6662 286.038i −0.149060 0.503587i
\(569\) 1055.57i 1.85513i −0.373663 0.927564i \(-0.621898\pi\)
0.373663 0.927564i \(-0.378102\pi\)
\(570\) 0 0
\(571\) 21.9344i 0.0384141i 0.999816 + 0.0192070i \(0.00611417\pi\)
−0.999816 + 0.0192070i \(0.993886\pi\)
\(572\) 52.4137 + 18.0553i 0.0916323 + 0.0315651i
\(573\) 0 0
\(574\) 156.461 111.587i 0.272580 0.194402i
\(575\) 728.052i 1.26618i
\(576\) 0 0
\(577\) 161.378 0.279684 0.139842 0.990174i \(-0.455341\pi\)
0.139842 + 0.990174i \(0.455341\pi\)
\(578\) 216.801 + 303.987i 0.375089 + 0.525929i
\(579\) 0 0
\(580\) −109.028 + 316.503i −0.187979 + 0.545695i
\(581\) 398.893 0.686562
\(582\) 0 0
\(583\) −212.511 −0.364513
\(584\) −595.952 + 176.400i −1.02047 + 0.302054i
\(585\) 0 0
\(586\) −299.714 420.243i −0.511457 0.717138i
\(587\) 481.396 0.820096 0.410048 0.912064i \(-0.365512\pi\)
0.410048 + 0.912064i \(0.365512\pi\)
\(588\) 0 0
\(589\) 1310.97i 2.22576i
\(590\) −331.047 464.176i −0.561097 0.786739i
\(591\) 0 0
\(592\) 343.267 439.120i 0.579842 0.741757i
\(593\) 321.781i 0.542632i −0.962490 0.271316i \(-0.912541\pi\)
0.962490 0.271316i \(-0.0874588\pi\)
\(594\) 0 0
\(595\) 1206.47i 2.02768i
\(596\) −298.253 + 865.816i −0.500425 + 1.45271i
\(597\) 0 0
\(598\) −57.2111 80.2183i −0.0956707 0.134144i
\(599\) 35.8419i 0.0598362i −0.999552 0.0299181i \(-0.990475\pi\)
0.999552 0.0299181i \(-0.00952464\pi\)
\(600\) 0 0
\(601\) 147.867 0.246035 0.123018 0.992404i \(-0.460743\pi\)
0.123018 + 0.992404i \(0.460743\pi\)
\(602\) −710.507 + 506.729i −1.18024 + 0.841742i
\(603\) 0 0
\(604\) −211.672 + 614.475i −0.350450 + 1.01734i
\(605\) 647.262 1.06985
\(606\) 0 0
\(607\) −636.611 −1.04878 −0.524391 0.851478i \(-0.675707\pi\)
−0.524391 + 0.851478i \(0.675707\pi\)
\(608\) 1113.66 + 48.9944i 1.83167 + 0.0805829i
\(609\) 0 0
\(610\) −320.700 + 228.721i −0.525737 + 0.374952i
\(611\) −7.66510 −0.0125452
\(612\) 0 0
\(613\) 870.887i 1.42070i −0.703850 0.710348i \(-0.748537\pi\)
0.703850 0.710348i \(-0.251463\pi\)
\(614\) −465.758 + 332.175i −0.758563 + 0.541001i
\(615\) 0 0
\(616\) 334.755 99.0864i 0.543434 0.160855i
\(617\) 1126.69i 1.82607i 0.407876 + 0.913037i \(0.366270\pi\)
−0.407876 + 0.913037i \(0.633730\pi\)
\(618\) 0 0
\(619\) 311.713i 0.503575i 0.967783 + 0.251787i \(0.0810183\pi\)
−0.967783 + 0.251787i \(0.918982\pi\)
\(620\) −376.092 + 1091.78i −0.606601 + 1.76094i
\(621\) 0 0
\(622\) 756.589 539.594i 1.21638 0.867514i
\(623\) 39.2054i 0.0629301i
\(624\) 0 0
\(625\) −325.666 −0.521066
\(626\) −183.485 257.273i −0.293107 0.410979i
\(627\) 0 0
\(628\) −429.877 148.083i −0.684518 0.235800i
\(629\) −759.772 −1.20790
\(630\) 0 0
\(631\) −203.278 −0.322153 −0.161076 0.986942i \(-0.551497\pi\)
−0.161076 + 0.986942i \(0.551497\pi\)
\(632\) 240.272 71.1198i 0.380178 0.112531i
\(633\) 0 0
\(634\) −33.2582 46.6329i −0.0524577 0.0735534i
\(635\) 1123.63 1.76950
\(636\) 0 0
\(637\) 6.87041i 0.0107856i
\(638\) −76.6711 107.504i −0.120174 0.168502i
\(639\) 0 0
\(640\) 913.400 + 360.289i 1.42719 + 0.562951i
\(641\) 586.490i 0.914960i −0.889220 0.457480i \(-0.848752\pi\)
0.889220 0.457480i \(-0.151248\pi\)
\(642\) 0 0
\(643\) 9.16054i 0.0142466i 0.999975 + 0.00712328i \(0.00226743\pi\)
−0.999975 + 0.00712328i \(0.997733\pi\)
\(644\) −586.661 202.091i −0.910965 0.313806i
\(645\) 0 0
\(646\) −882.321 1237.14i −1.36582 1.91508i
\(647\) 859.040i 1.32773i 0.747853 + 0.663864i \(0.231085\pi\)
−0.747853 + 0.663864i \(0.768915\pi\)
\(648\) 0 0
\(649\) 224.888 0.346515
\(650\) 126.207 90.0102i 0.194165 0.138477i
\(651\) 0 0
\(652\) −423.045 145.729i −0.648841 0.223511i
\(653\) 131.775 0.201799 0.100899 0.994897i \(-0.467828\pi\)
0.100899 + 0.994897i \(0.467828\pi\)
\(654\) 0 0
\(655\) 1418.80 2.16611
\(656\) −131.304 + 167.969i −0.200158 + 0.256050i
\(657\) 0 0
\(658\) −39.3002 + 28.0286i −0.0597268 + 0.0425967i
\(659\) 305.137 0.463030 0.231515 0.972831i \(-0.425632\pi\)
0.231515 + 0.972831i \(0.425632\pi\)
\(660\) 0 0
\(661\) 623.298i 0.942962i −0.881876 0.471481i \(-0.843720\pi\)
0.881876 0.471481i \(-0.156280\pi\)
\(662\) 698.533 498.189i 1.05519 0.752551i
\(663\) 0 0
\(664\) −424.333 + 125.601i −0.639056 + 0.189158i
\(665\) 1926.97i 2.89771i
\(666\) 0 0
\(667\) 234.688i 0.351856i
\(668\) 573.113 + 197.424i 0.857953 + 0.295545i
\(669\) 0 0
\(670\) 320.700 228.721i 0.478656 0.341374i
\(671\) 155.376i 0.231558i
\(672\) 0 0
\(673\) −263.867 −0.392076 −0.196038 0.980596i \(-0.562808\pi\)
−0.196038 + 0.980596i \(0.562808\pi\)
\(674\) −337.653 473.439i −0.500969 0.702432i
\(675\) 0 0
\(676\) −213.336 + 619.306i −0.315586 + 0.916134i
\(677\) 788.411 1.16457 0.582283 0.812986i \(-0.302160\pi\)
0.582283 + 0.812986i \(0.302160\pi\)
\(678\) 0 0
\(679\) 381.066 0.561217
\(680\) −379.886 1283.41i −0.558656 1.88737i
\(681\) 0 0
\(682\) −264.478 370.836i −0.387797 0.543748i
\(683\) −905.773 −1.32617 −0.663084 0.748545i \(-0.730753\pi\)
−0.663084 + 0.748545i \(0.730753\pi\)
\(684\) 0 0
\(685\) 1022.65i 1.49291i
\(686\) −385.215 540.127i −0.561538 0.787358i
\(687\) 0 0
\(688\) 596.266 762.767i 0.866665 1.10867i
\(689\) 80.4211i 0.116721i
\(690\) 0 0
\(691\) 45.8027i 0.0662847i 0.999451 + 0.0331423i \(0.0105515\pi\)
−0.999451 + 0.0331423i \(0.989449\pi\)
\(692\) −127.698 + 370.701i −0.184534 + 0.535695i
\(693\) 0 0
\(694\) 208.750 + 292.698i 0.300793 + 0.421755i
\(695\) 1265.85i 1.82136i
\(696\) 0 0
\(697\) 290.622 0.416962
\(698\) −367.228 + 261.904i −0.526114 + 0.375221i
\(699\) 0 0
\(700\) 317.950 922.994i 0.454214 1.31856i
\(701\) 1019.73 1.45468 0.727339 0.686279i \(-0.240757\pi\)
0.727339 + 0.686279i \(0.240757\pi\)
\(702\) 0 0
\(703\) 1213.51 1.72619
\(704\) −324.905 + 210.812i −0.461513 + 0.299449i
\(705\) 0 0
\(706\) −217.842 + 155.363i −0.308558 + 0.220061i
\(707\) 649.049 0.918033
\(708\) 0 0
\(709\) 84.7350i 0.119513i −0.998213 0.0597567i \(-0.980968\pi\)
0.998213 0.0597567i \(-0.0190325\pi\)
\(710\) 465.758 332.175i 0.655997 0.467852i
\(711\) 0 0
\(712\) 12.3448 + 41.7059i 0.0173382 + 0.0585757i
\(713\) 809.558i 1.13543i
\(714\) 0 0
\(715\) 106.313i 0.148690i
\(716\) −289.369 + 840.026i −0.404147 + 1.17322i
\(717\) 0 0
\(718\) −389.194 + 277.571i −0.542053 + 0.386589i
\(719\) 646.311i 0.898903i −0.893305 0.449451i \(-0.851619\pi\)
0.893305 0.449451i \(-0.148381\pi\)
\(720\) 0 0
\(721\) −859.643 −1.19229
\(722\) 990.018 + 1388.15i 1.37122 + 1.92265i
\(723\) 0 0
\(724\) 449.028 + 154.679i 0.620204 + 0.213646i
\(725\) −369.234 −0.509288
\(726\) 0 0
\(727\) −648.789 −0.892419 −0.446210 0.894928i \(-0.647226\pi\)
−0.446210 + 0.894928i \(0.647226\pi\)
\(728\) −37.4975 126.682i −0.0515075 0.174014i
\(729\) 0 0
\(730\) −692.077 970.393i −0.948051 1.32931i
\(731\) −1319.75 −1.80540
\(732\) 0 0
\(733\) 696.353i 0.950004i −0.879985 0.475002i \(-0.842447\pi\)
0.879985 0.475002i \(-0.157553\pi\)
\(734\) 218.775 + 306.755i 0.298059 + 0.417922i
\(735\) 0 0
\(736\) 687.711 + 30.2552i 0.934390 + 0.0411076i
\(737\) 155.376i 0.210822i
\(738\) 0 0
\(739\) 740.833i 1.00248i −0.865308 0.501240i \(-0.832877\pi\)
0.865308 0.501240i \(-0.167123\pi\)
\(740\) 1010.61 + 348.132i 1.36569 + 0.470449i
\(741\) 0 0
\(742\) 294.072 + 412.332i 0.396324 + 0.555704i
\(743\) 111.377i 0.149901i −0.997187 0.0749507i \(-0.976120\pi\)
0.997187 0.0749507i \(-0.0238800\pi\)
\(744\) 0 0
\(745\) −1756.18 −2.35728
\(746\) 913.657 651.614i 1.22474 0.873477i
\(747\) 0 0
\(748\) 499.166 + 171.951i 0.667334 + 0.229881i
\(749\) 174.556 0.233052
\(750\) 0 0
\(751\) 923.699 1.22996 0.614979 0.788543i \(-0.289164\pi\)
0.614979 + 0.788543i \(0.289164\pi\)
\(752\) 32.9812 42.1909i 0.0438580 0.0561049i
\(753\) 0 0
\(754\) −40.6830 + 29.0148i −0.0539562 + 0.0384812i
\(755\) −1246.37 −1.65082
\(756\) 0 0
\(757\) 1233.47i 1.62941i 0.579873 + 0.814707i \(0.303102\pi\)
−0.579873 + 0.814707i \(0.696898\pi\)
\(758\) 534.455 381.169i 0.705085 0.502862i
\(759\) 0 0
\(760\) 606.755 + 2049.87i 0.798362 + 2.69720i
\(761\) 179.070i 0.235309i 0.993055 + 0.117654i \(0.0375375\pi\)
−0.993055 + 0.117654i \(0.962463\pi\)
\(762\) 0 0
\(763\) 955.266i 1.25199i
\(764\) −573.113 197.424i −0.750147 0.258408i
\(765\) 0 0
\(766\) −332.367 + 237.042i −0.433899 + 0.309454i
\(767\) 85.1049i 0.110958i
\(768\) 0 0
\(769\) −251.511 −0.327062 −0.163531 0.986538i \(-0.552288\pi\)
−0.163531 + 0.986538i \(0.552288\pi\)
\(770\) 388.751 + 545.085i 0.504871 + 0.707902i
\(771\) 0 0
\(772\) −147.706 + 428.783i −0.191329 + 0.555418i
\(773\) −184.110 −0.238176 −0.119088 0.992884i \(-0.537997\pi\)
−0.119088 + 0.992884i \(0.537997\pi\)
\(774\) 0 0
\(775\) −1273.68 −1.64345
\(776\) −405.370 + 119.988i −0.522384 + 0.154624i
\(777\) 0 0
\(778\) 69.8806 + 97.9827i 0.0898208 + 0.125942i
\(779\) −464.183 −0.595870
\(780\) 0 0
\(781\) 225.654i 0.288930i
\(782\) −544.855 763.966i −0.696745 0.976938i
\(783\) 0 0
\(784\) −37.8167 29.5618i −0.0482355 0.0377064i
\(785\) 871.941i 1.11075i
\(786\) 0 0
\(787\) 1351.36i 1.71710i −0.512731 0.858550i \(-0.671366\pi\)
0.512731 0.858550i \(-0.328634\pi\)
\(788\) 416.176 1208.14i 0.528143 1.53317i
\(789\) 0 0
\(790\) 279.028 + 391.238i 0.353200 + 0.495237i
\(791\) 1157.82i 1.46374i