Properties

Label 252.2.b.d.55.4
Level $252$
Weight $2$
Character 252.55
Analytic conductor $2.012$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.2312.1
Defining polynomial: \(x^{4} - x^{3} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.4
Root \(1.28078 + 0.599676i\) of defining polynomial
Character \(\chi\) \(=\) 252.55
Dual form 252.2.b.d.55.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28078 + 0.599676i) q^{2} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.56155 - 2.13578i) q^{7} +(0.719224 + 2.73546i) q^{8} +O(q^{10})\) \(q+(1.28078 + 0.599676i) q^{2} +(1.28078 + 1.53610i) q^{4} -3.33513i q^{5} +(1.56155 - 2.13578i) q^{7} +(0.719224 + 2.73546i) q^{8} +(2.00000 - 4.27156i) q^{10} +0.936426i q^{11} +1.87285i q^{13} +(3.28078 - 1.79903i) q^{14} +(-0.719224 + 3.93481i) q^{16} +5.20798i q^{17} -7.12311 q^{19} +(5.12311 - 4.27156i) q^{20} +(-0.561553 + 1.19935i) q^{22} -0.936426i q^{23} -6.12311 q^{25} +(-1.12311 + 2.39871i) q^{26} +(5.28078 - 0.336750i) q^{28} +2.00000 q^{29} +(-3.28078 + 4.60831i) q^{32} +(-3.12311 + 6.67026i) q^{34} +(-7.12311 - 5.20798i) q^{35} +1.12311 q^{37} +(-9.12311 - 4.27156i) q^{38} +(9.12311 - 2.39871i) q^{40} +1.46228i q^{41} -9.06897i q^{43} +(-1.43845 + 1.19935i) q^{44} +(0.561553 - 1.19935i) q^{46} +6.24621 q^{47} +(-2.12311 - 6.67026i) q^{49} +(-7.84233 - 3.67188i) q^{50} +(-2.87689 + 2.39871i) q^{52} -12.2462 q^{53} +3.12311 q^{55} +(6.96543 + 2.73546i) q^{56} +(2.56155 + 1.19935i) q^{58} +4.00000 q^{59} +4.79741i q^{61} +(-6.96543 + 3.93481i) q^{64} +6.24621 q^{65} +10.9418i q^{67} +(-8.00000 + 6.67026i) q^{68} +(-6.00000 - 10.9418i) q^{70} -3.86098i q^{71} +6.67026i q^{73} +(1.43845 + 0.673500i) q^{74} +(-9.12311 - 10.9418i) q^{76} +(2.00000 + 1.46228i) q^{77} +2.39871i q^{79} +(13.1231 + 2.39871i) q^{80} +(-0.876894 + 1.87285i) q^{82} -10.2462 q^{83} +17.3693 q^{85} +(5.43845 - 11.6153i) q^{86} +(-2.56155 + 0.673500i) q^{88} -1.46228i q^{89} +(4.00000 + 2.92456i) q^{91} +(1.43845 - 1.19935i) q^{92} +(8.00000 + 3.74571i) q^{94} +23.7565i q^{95} -10.4160i q^{97} +(1.28078 - 9.81629i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + q^{2} + q^{4} - 2 q^{7} + 7 q^{8} + O(q^{10}) \) \( 4 q + q^{2} + q^{4} - 2 q^{7} + 7 q^{8} + 8 q^{10} + 9 q^{14} - 7 q^{16} - 12 q^{19} + 4 q^{20} + 6 q^{22} - 8 q^{25} + 12 q^{26} + 17 q^{28} + 8 q^{29} - 9 q^{32} + 4 q^{34} - 12 q^{35} - 12 q^{37} - 20 q^{38} + 20 q^{40} - 14 q^{44} - 6 q^{46} - 8 q^{47} + 8 q^{49} - 19 q^{50} - 28 q^{52} - 16 q^{53} - 4 q^{55} - q^{56} + 2 q^{58} + 16 q^{59} + q^{64} - 8 q^{65} - 32 q^{68} - 24 q^{70} + 14 q^{74} - 20 q^{76} + 8 q^{77} + 36 q^{80} - 20 q^{82} - 8 q^{83} + 20 q^{85} + 30 q^{86} - 2 q^{88} + 16 q^{91} + 14 q^{92} + 32 q^{94} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(3\) 0 0
\(4\) 1.28078 + 1.53610i 0.640388 + 0.768051i
\(5\) 3.33513i 1.49152i −0.666217 0.745758i \(-0.732087\pi\)
0.666217 0.745758i \(-0.267913\pi\)
\(6\) 0 0
\(7\) 1.56155 2.13578i 0.590211 0.807249i
\(8\) 0.719224 + 2.73546i 0.254284 + 0.967130i
\(9\) 0 0
\(10\) 2.00000 4.27156i 0.632456 1.35079i
\(11\) 0.936426i 0.282343i 0.989985 + 0.141172i \(0.0450869\pi\)
−0.989985 + 0.141172i \(0.954913\pi\)
\(12\) 0 0
\(13\) 1.87285i 0.519436i 0.965685 + 0.259718i \(0.0836296\pi\)
−0.965685 + 0.259718i \(0.916370\pi\)
\(14\) 3.28078 1.79903i 0.876824 0.480811i
\(15\) 0 0
\(16\) −0.719224 + 3.93481i −0.179806 + 0.983702i
\(17\) 5.20798i 1.26312i 0.775326 + 0.631561i \(0.217585\pi\)
−0.775326 + 0.631561i \(0.782415\pi\)
\(18\) 0 0
\(19\) −7.12311 −1.63415 −0.817076 0.576530i \(-0.804407\pi\)
−0.817076 + 0.576530i \(0.804407\pi\)
\(20\) 5.12311 4.27156i 1.14556 0.955149i
\(21\) 0 0
\(22\) −0.561553 + 1.19935i −0.119723 + 0.255703i
\(23\) 0.936426i 0.195258i −0.995223 0.0976292i \(-0.968874\pi\)
0.995223 0.0976292i \(-0.0311259\pi\)
\(24\) 0 0
\(25\) −6.12311 −1.22462
\(26\) −1.12311 + 2.39871i −0.220259 + 0.470425i
\(27\) 0 0
\(28\) 5.28078 0.336750i 0.997973 0.0636398i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −3.28078 + 4.60831i −0.579965 + 0.814642i
\(33\) 0 0
\(34\) −3.12311 + 6.67026i −0.535608 + 1.14394i
\(35\) −7.12311 5.20798i −1.20402 0.880310i
\(36\) 0 0
\(37\) 1.12311 0.184637 0.0923187 0.995730i \(-0.470572\pi\)
0.0923187 + 0.995730i \(0.470572\pi\)
\(38\) −9.12311 4.27156i −1.47996 0.692938i
\(39\) 0 0
\(40\) 9.12311 2.39871i 1.44249 0.379269i
\(41\) 1.46228i 0.228370i 0.993460 + 0.114185i \(0.0364256\pi\)
−0.993460 + 0.114185i \(0.963574\pi\)
\(42\) 0 0
\(43\) 9.06897i 1.38300i −0.722374 0.691502i \(-0.756949\pi\)
0.722374 0.691502i \(-0.243051\pi\)
\(44\) −1.43845 + 1.19935i −0.216854 + 0.180809i
\(45\) 0 0
\(46\) 0.561553 1.19935i 0.0827964 0.176835i
\(47\) 6.24621 0.911104 0.455552 0.890209i \(-0.349442\pi\)
0.455552 + 0.890209i \(0.349442\pi\)
\(48\) 0 0
\(49\) −2.12311 6.67026i −0.303301 0.952895i
\(50\) −7.84233 3.67188i −1.10907 0.519283i
\(51\) 0 0
\(52\) −2.87689 + 2.39871i −0.398953 + 0.332641i
\(53\) −12.2462 −1.68215 −0.841073 0.540921i \(-0.818076\pi\)
−0.841073 + 0.540921i \(0.818076\pi\)
\(54\) 0 0
\(55\) 3.12311 0.421119
\(56\) 6.96543 + 2.73546i 0.930795 + 0.365541i
\(57\) 0 0
\(58\) 2.56155 + 1.19935i 0.336348 + 0.157483i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 4.79741i 0.614246i 0.951670 + 0.307123i \(0.0993662\pi\)
−0.951670 + 0.307123i \(0.900634\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −6.96543 + 3.93481i −0.870679 + 0.491851i
\(65\) 6.24621 0.774747
\(66\) 0 0
\(67\) 10.9418i 1.33676i 0.743822 + 0.668378i \(0.233011\pi\)
−0.743822 + 0.668378i \(0.766989\pi\)
\(68\) −8.00000 + 6.67026i −0.970143 + 0.808888i
\(69\) 0 0
\(70\) −6.00000 10.9418i −0.717137 1.30780i
\(71\) 3.86098i 0.458215i −0.973401 0.229107i \(-0.926419\pi\)
0.973401 0.229107i \(-0.0735807\pi\)
\(72\) 0 0
\(73\) 6.67026i 0.780695i 0.920668 + 0.390348i \(0.127645\pi\)
−0.920668 + 0.390348i \(0.872355\pi\)
\(74\) 1.43845 + 0.673500i 0.167216 + 0.0782928i
\(75\) 0 0
\(76\) −9.12311 10.9418i −1.04649 1.25511i
\(77\) 2.00000 + 1.46228i 0.227921 + 0.166642i
\(78\) 0 0
\(79\) 2.39871i 0.269875i 0.990854 + 0.134938i \(0.0430834\pi\)
−0.990854 + 0.134938i \(0.956917\pi\)
\(80\) 13.1231 + 2.39871i 1.46721 + 0.268183i
\(81\) 0 0
\(82\) −0.876894 + 1.87285i −0.0968368 + 0.206822i
\(83\) −10.2462 −1.12467 −0.562334 0.826910i \(-0.690096\pi\)
−0.562334 + 0.826910i \(0.690096\pi\)
\(84\) 0 0
\(85\) 17.3693 1.88397
\(86\) 5.43845 11.6153i 0.586443 1.25251i
\(87\) 0 0
\(88\) −2.56155 + 0.673500i −0.273062 + 0.0717953i
\(89\) 1.46228i 0.155001i −0.996992 0.0775006i \(-0.975306\pi\)
0.996992 0.0775006i \(-0.0246940\pi\)
\(90\) 0 0
\(91\) 4.00000 + 2.92456i 0.419314 + 0.306577i
\(92\) 1.43845 1.19935i 0.149968 0.125041i
\(93\) 0 0
\(94\) 8.00000 + 3.74571i 0.825137 + 0.386340i
\(95\) 23.7565i 2.43737i
\(96\) 0 0
\(97\) 10.4160i 1.05758i −0.848752 0.528791i \(-0.822646\pi\)
0.848752 0.528791i \(-0.177354\pi\)
\(98\) 1.28078 9.81629i 0.129378 0.991595i
\(99\) 0 0
\(100\) −7.84233 9.40572i −0.784233 0.940572i
\(101\) 13.7511i 1.36829i −0.729348 0.684143i \(-0.760176\pi\)
0.729348 0.684143i \(-0.239824\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −5.12311 + 1.34700i −0.502362 + 0.132084i
\(105\) 0 0
\(106\) −15.6847 7.34376i −1.52343 0.713289i
\(107\) 9.47954i 0.916422i −0.888843 0.458211i \(-0.848490\pi\)
0.888843 0.458211i \(-0.151510\pi\)
\(108\) 0 0
\(109\) −8.24621 −0.789844 −0.394922 0.918715i \(-0.629228\pi\)
−0.394922 + 0.918715i \(0.629228\pi\)
\(110\) 4.00000 + 1.87285i 0.381385 + 0.178570i
\(111\) 0 0
\(112\) 7.28078 + 7.68051i 0.687969 + 0.725740i
\(113\) 4.24621 0.399450 0.199725 0.979852i \(-0.435995\pi\)
0.199725 + 0.979852i \(0.435995\pi\)
\(114\) 0 0
\(115\) −3.12311 −0.291231
\(116\) 2.56155 + 3.07221i 0.237834 + 0.285247i
\(117\) 0 0
\(118\) 5.12311 + 2.39871i 0.471620 + 0.220819i
\(119\) 11.1231 + 8.13254i 1.01965 + 0.745509i
\(120\) 0 0
\(121\) 10.1231 0.920282
\(122\) −2.87689 + 6.14441i −0.260462 + 0.556289i
\(123\) 0 0
\(124\) 0 0
\(125\) 3.74571i 0.335026i
\(126\) 0 0
\(127\) 9.89012i 0.877606i 0.898583 + 0.438803i \(0.144597\pi\)
−0.898583 + 0.438803i \(0.855403\pi\)
\(128\) −11.2808 + 0.862603i −0.997089 + 0.0762440i
\(129\) 0 0
\(130\) 8.00000 + 3.74571i 0.701646 + 0.328520i
\(131\) 5.75379 0.502711 0.251355 0.967895i \(-0.419124\pi\)
0.251355 + 0.967895i \(0.419124\pi\)
\(132\) 0 0
\(133\) −11.1231 + 15.2134i −0.964496 + 1.31917i
\(134\) −6.56155 + 14.0140i −0.566832 + 1.21063i
\(135\) 0 0
\(136\) −14.2462 + 3.74571i −1.22160 + 0.321192i
\(137\) −0.246211 −0.0210352 −0.0105176 0.999945i \(-0.503348\pi\)
−0.0105176 + 0.999945i \(0.503348\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) −1.12311 17.6121i −0.0949197 1.48849i
\(141\) 0 0
\(142\) 2.31534 4.94506i 0.194299 0.414980i
\(143\) −1.75379 −0.146659
\(144\) 0 0
\(145\) 6.67026i 0.553935i
\(146\) −4.00000 + 8.54312i −0.331042 + 0.707033i
\(147\) 0 0
\(148\) 1.43845 + 1.72521i 0.118240 + 0.141811i
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 9.06897i 0.738022i 0.929425 + 0.369011i \(0.120304\pi\)
−0.929425 + 0.369011i \(0.879696\pi\)
\(152\) −5.12311 19.4849i −0.415539 1.58044i
\(153\) 0 0
\(154\) 1.68466 + 3.07221i 0.135754 + 0.247565i
\(155\) 0 0
\(156\) 0 0
\(157\) 21.8836i 1.74650i −0.487268 0.873252i \(-0.662007\pi\)
0.487268 0.873252i \(-0.337993\pi\)
\(158\) −1.43845 + 3.07221i −0.114437 + 0.244412i
\(159\) 0 0
\(160\) 15.3693 + 10.9418i 1.21505 + 0.865027i
\(161\) −2.00000 1.46228i −0.157622 0.115244i
\(162\) 0 0
\(163\) 15.7392i 1.23279i −0.787436 0.616396i \(-0.788592\pi\)
0.787436 0.616396i \(-0.211408\pi\)
\(164\) −2.24621 + 1.87285i −0.175400 + 0.146245i
\(165\) 0 0
\(166\) −13.1231 6.14441i −1.01855 0.476899i
\(167\) 14.2462 1.10240 0.551202 0.834372i \(-0.314169\pi\)
0.551202 + 0.834372i \(0.314169\pi\)
\(168\) 0 0
\(169\) 9.49242 0.730186
\(170\) 22.2462 + 10.4160i 1.70621 + 0.798868i
\(171\) 0 0
\(172\) 13.9309 11.6153i 1.06222 0.885660i
\(173\) 16.6757i 1.26783i 0.773404 + 0.633913i \(0.218552\pi\)
−0.773404 + 0.633913i \(0.781448\pi\)
\(174\) 0 0
\(175\) −9.56155 + 13.0776i −0.722785 + 0.988574i
\(176\) −3.68466 0.673500i −0.277742 0.0507670i
\(177\) 0 0
\(178\) 0.876894 1.87285i 0.0657260 0.140376i
\(179\) 16.1498i 1.20709i −0.797328 0.603547i \(-0.793754\pi\)
0.797328 0.603547i \(-0.206246\pi\)
\(180\) 0 0
\(181\) 1.87285i 0.139208i −0.997575 0.0696040i \(-0.977826\pi\)
0.997575 0.0696040i \(-0.0221736\pi\)
\(182\) 3.36932 + 6.14441i 0.249750 + 0.455454i
\(183\) 0 0
\(184\) 2.56155 0.673500i 0.188840 0.0496511i
\(185\) 3.74571i 0.275390i
\(186\) 0 0
\(187\) −4.87689 −0.356634
\(188\) 8.00000 + 9.59482i 0.583460 + 0.699774i
\(189\) 0 0
\(190\) −14.2462 + 30.4268i −1.03353 + 2.20739i
\(191\) 2.80928i 0.203272i 0.994822 + 0.101636i \(0.0324078\pi\)
−0.994822 + 0.101636i \(0.967592\pi\)
\(192\) 0 0
\(193\) −15.3693 −1.10631 −0.553154 0.833079i \(-0.686576\pi\)
−0.553154 + 0.833079i \(0.686576\pi\)
\(194\) 6.24621 13.3405i 0.448452 0.957794i
\(195\) 0 0
\(196\) 7.52699 11.8044i 0.537642 0.843173i
\(197\) 16.2462 1.15749 0.578747 0.815507i \(-0.303542\pi\)
0.578747 + 0.815507i \(0.303542\pi\)
\(198\) 0 0
\(199\) 3.12311 0.221391 0.110696 0.993854i \(-0.464692\pi\)
0.110696 + 0.993854i \(0.464692\pi\)
\(200\) −4.40388 16.7495i −0.311401 1.18437i
\(201\) 0 0
\(202\) 8.24621 17.6121i 0.580201 1.23918i
\(203\) 3.12311 4.27156i 0.219199 0.299805i
\(204\) 0 0
\(205\) 4.87689 0.340617
\(206\) 10.2462 + 4.79741i 0.713887 + 0.334251i
\(207\) 0 0
\(208\) −7.36932 1.34700i −0.510970 0.0933976i
\(209\) 6.67026i 0.461392i
\(210\) 0 0
\(211\) 12.8147i 0.882199i −0.897458 0.441099i \(-0.854589\pi\)
0.897458 0.441099i \(-0.145411\pi\)
\(212\) −15.6847 18.8114i −1.07723 1.29197i
\(213\) 0 0
\(214\) 5.68466 12.1412i 0.388595 0.829954i
\(215\) −30.2462 −2.06277
\(216\) 0 0
\(217\) 0 0
\(218\) −10.5616 4.94506i −0.715319 0.334922i
\(219\) 0 0
\(220\) 4.00000 + 4.79741i 0.269680 + 0.323441i
\(221\) −9.75379 −0.656111
\(222\) 0 0
\(223\) −27.1231 −1.81630 −0.908149 0.418648i \(-0.862504\pi\)
−0.908149 + 0.418648i \(0.862504\pi\)
\(224\) 4.71922 + 14.2031i 0.315316 + 0.948987i
\(225\) 0 0
\(226\) 5.43845 + 2.54635i 0.361760 + 0.169381i
\(227\) −16.4924 −1.09464 −0.547320 0.836923i \(-0.684352\pi\)
−0.547320 + 0.836923i \(0.684352\pi\)
\(228\) 0 0
\(229\) 5.61856i 0.371285i 0.982617 + 0.185642i \(0.0594366\pi\)
−0.982617 + 0.185642i \(0.940563\pi\)
\(230\) −4.00000 1.87285i −0.263752 0.123492i
\(231\) 0 0
\(232\) 1.43845 + 5.47091i 0.0944387 + 0.359183i
\(233\) −22.4924 −1.47353 −0.736764 0.676150i \(-0.763647\pi\)
−0.736764 + 0.676150i \(0.763647\pi\)
\(234\) 0 0
\(235\) 20.8319i 1.35893i
\(236\) 5.12311 + 6.14441i 0.333486 + 0.399967i
\(237\) 0 0
\(238\) 9.36932 + 17.0862i 0.607323 + 1.10754i
\(239\) 16.1498i 1.04464i 0.852748 + 0.522322i \(0.174934\pi\)
−0.852748 + 0.522322i \(0.825066\pi\)
\(240\) 0 0
\(241\) 23.7565i 1.53029i 0.643858 + 0.765145i \(0.277333\pi\)
−0.643858 + 0.765145i \(0.722667\pi\)
\(242\) 12.9654 + 6.07059i 0.833450 + 0.390232i
\(243\) 0 0
\(244\) −7.36932 + 6.14441i −0.471772 + 0.393356i
\(245\) −22.2462 + 7.08084i −1.42126 + 0.452378i
\(246\) 0 0
\(247\) 13.3405i 0.848837i
\(248\) 0 0
\(249\) 0 0
\(250\) −2.24621 + 4.79741i −0.142063 + 0.303415i
\(251\) −5.75379 −0.363176 −0.181588 0.983375i \(-0.558124\pi\)
−0.181588 + 0.983375i \(0.558124\pi\)
\(252\) 0 0
\(253\) 0.876894 0.0551299
\(254\) −5.93087 + 12.6670i −0.372136 + 0.794800i
\(255\) 0 0
\(256\) −14.9654 5.66001i −0.935340 0.353751i
\(257\) 2.28343i 0.142436i −0.997461 0.0712181i \(-0.977311\pi\)
0.997461 0.0712181i \(-0.0226886\pi\)
\(258\) 0 0
\(259\) 1.75379 2.39871i 0.108975 0.149048i
\(260\) 8.00000 + 9.59482i 0.496139 + 0.595046i
\(261\) 0 0
\(262\) 7.36932 + 3.45041i 0.455278 + 0.213167i
\(263\) 24.6929i 1.52263i −0.648382 0.761315i \(-0.724554\pi\)
0.648382 0.761315i \(-0.275446\pi\)
\(264\) 0 0
\(265\) 40.8427i 2.50895i
\(266\) −23.3693 + 12.8147i −1.43286 + 0.785718i
\(267\) 0 0
\(268\) −16.8078 + 14.0140i −1.02670 + 0.856043i
\(269\) 10.8265i 0.660106i 0.943962 + 0.330053i \(0.107067\pi\)
−0.943962 + 0.330053i \(0.892933\pi\)
\(270\) 0 0
\(271\) 28.4924 1.73079 0.865396 0.501089i \(-0.167067\pi\)
0.865396 + 0.501089i \(0.167067\pi\)
\(272\) −20.4924 3.74571i −1.24254 0.227117i
\(273\) 0 0
\(274\) −0.315342 0.147647i −0.0190505 0.00891969i
\(275\) 5.73384i 0.345763i
\(276\) 0 0
\(277\) −5.12311 −0.307818 −0.153909 0.988085i \(-0.549186\pi\)
−0.153909 + 0.988085i \(0.549186\pi\)
\(278\) 15.3693 + 7.19612i 0.921790 + 0.431594i
\(279\) 0 0
\(280\) 9.12311 23.2306i 0.545210 1.38830i
\(281\) −16.2462 −0.969168 −0.484584 0.874745i \(-0.661029\pi\)
−0.484584 + 0.874745i \(0.661029\pi\)
\(282\) 0 0
\(283\) −8.87689 −0.527677 −0.263838 0.964567i \(-0.584989\pi\)
−0.263838 + 0.964567i \(0.584989\pi\)
\(284\) 5.93087 4.94506i 0.351932 0.293435i
\(285\) 0 0
\(286\) −2.24621 1.05171i −0.132821 0.0621887i
\(287\) 3.12311 + 2.28343i 0.184351 + 0.134786i
\(288\) 0 0
\(289\) −10.1231 −0.595477
\(290\) 4.00000 8.54312i 0.234888 0.501669i
\(291\) 0 0
\(292\) −10.2462 + 8.54312i −0.599614 + 0.499948i
\(293\) 13.7511i 0.803348i −0.915783 0.401674i \(-0.868429\pi\)
0.915783 0.401674i \(-0.131571\pi\)
\(294\) 0 0
\(295\) 13.3405i 0.776716i
\(296\) 0.807764 + 3.07221i 0.0469503 + 0.178568i
\(297\) 0 0
\(298\) 12.8078 + 5.99676i 0.741934 + 0.347383i
\(299\) 1.75379 0.101424
\(300\) 0 0
\(301\) −19.3693 14.1617i −1.11643 0.816265i
\(302\) −5.43845 + 11.6153i −0.312947 + 0.668387i
\(303\) 0 0
\(304\) 5.12311 28.0281i 0.293830 1.60752i
\(305\) 16.0000 0.916157
\(306\) 0 0
\(307\) −19.6155 −1.11952 −0.559759 0.828656i \(-0.689106\pi\)
−0.559759 + 0.828656i \(0.689106\pi\)
\(308\) 0.315342 + 4.94506i 0.0179683 + 0.281771i
\(309\) 0 0
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) 22.9354i 1.29638i −0.761478 0.648191i \(-0.775526\pi\)
0.761478 0.648191i \(-0.224474\pi\)
\(314\) 13.1231 28.0281i 0.740580 1.58171i
\(315\) 0 0
\(316\) −3.68466 + 3.07221i −0.207278 + 0.172825i
\(317\) 14.4924 0.813976 0.406988 0.913434i \(-0.366579\pi\)
0.406988 + 0.913434i \(0.366579\pi\)
\(318\) 0 0
\(319\) 1.87285i 0.104860i
\(320\) 13.1231 + 23.2306i 0.733604 + 1.29863i
\(321\) 0 0
\(322\) −1.68466 3.07221i −0.0938823 0.171207i
\(323\) 37.0970i 2.06413i
\(324\) 0 0
\(325\) 11.4677i 0.636112i
\(326\) 9.43845 20.1584i 0.522747 1.11647i
\(327\) 0 0
\(328\) −4.00000 + 1.05171i −0.220863 + 0.0580707i
\(329\) 9.75379 13.3405i 0.537744 0.735487i
\(330\) 0 0
\(331\) 17.6121i 0.968048i 0.875055 + 0.484024i \(0.160825\pi\)
−0.875055 + 0.484024i \(0.839175\pi\)
\(332\) −13.1231 15.7392i −0.720224 0.863803i
\(333\) 0 0
\(334\) 18.2462 + 8.54312i 0.998388 + 0.467459i
\(335\) 36.4924 1.99379
\(336\) 0 0
\(337\) 8.24621 0.449200 0.224600 0.974451i \(-0.427892\pi\)
0.224600 + 0.974451i \(0.427892\pi\)
\(338\) 12.1577 + 5.69238i 0.661290 + 0.309625i
\(339\) 0 0
\(340\) 22.2462 + 26.6811i 1.20647 + 1.44698i
\(341\) 0 0
\(342\) 0 0
\(343\) −17.5616 5.88148i −0.948235 0.317570i
\(344\) 24.8078 6.52262i 1.33754 0.351676i
\(345\) 0 0
\(346\) −10.0000 + 21.3578i −0.537603 + 1.14820i
\(347\) 20.1261i 1.08042i 0.841529 + 0.540212i \(0.181656\pi\)
−0.841529 + 0.540212i \(0.818344\pi\)
\(348\) 0 0
\(349\) 21.8836i 1.17140i −0.810526 0.585702i \(-0.800819\pi\)
0.810526 0.585702i \(-0.199181\pi\)
\(350\) −20.0885 + 11.0156i −1.07378 + 0.588811i
\(351\) 0 0
\(352\) −4.31534 3.07221i −0.230008 0.163749i
\(353\) 28.9645i 1.54162i 0.637063 + 0.770812i \(0.280149\pi\)
−0.637063 + 0.770812i \(0.719851\pi\)
\(354\) 0 0
\(355\) −12.8769 −0.683435
\(356\) 2.24621 1.87285i 0.119049 0.0992610i
\(357\) 0 0
\(358\) 9.68466 20.6843i 0.511850 1.09320i
\(359\) 22.8201i 1.20440i 0.798346 + 0.602199i \(0.205708\pi\)
−0.798346 + 0.602199i \(0.794292\pi\)
\(360\) 0 0
\(361\) 31.7386 1.67045
\(362\) 1.12311 2.39871i 0.0590291 0.126073i
\(363\) 0 0
\(364\) 0.630683 + 9.89012i 0.0330568 + 0.518383i
\(365\) 22.2462 1.16442
\(366\) 0 0
\(367\) 33.3693 1.74186 0.870932 0.491403i \(-0.163516\pi\)
0.870932 + 0.491403i \(0.163516\pi\)
\(368\) 3.68466 + 0.673500i 0.192076 + 0.0351086i
\(369\) 0 0
\(370\) 2.24621 4.79741i 0.116775 0.249406i
\(371\) −19.1231 + 26.1552i −0.992822 + 1.35791i
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) −6.24621 2.92456i −0.322984 0.151225i
\(375\) 0 0
\(376\) 4.49242 + 17.0862i 0.231679 + 0.881155i
\(377\) 3.74571i 0.192914i
\(378\) 0 0
\(379\) 25.1035i 1.28948i 0.764402 + 0.644740i \(0.223034\pi\)
−0.764402 + 0.644740i \(0.776966\pi\)
\(380\) −36.4924 + 30.4268i −1.87202 + 1.56086i
\(381\) 0 0
\(382\) −1.68466 + 3.59806i −0.0861946 + 0.184093i
\(383\) −9.75379 −0.498395 −0.249198 0.968453i \(-0.580167\pi\)
−0.249198 + 0.968453i \(0.580167\pi\)
\(384\) 0 0
\(385\) 4.87689 6.67026i 0.248550 0.339948i
\(386\) −19.6847 9.21662i −1.00192 0.469113i
\(387\) 0 0
\(388\) 16.0000 13.3405i 0.812277 0.677263i
\(389\) 16.2462 0.823716 0.411858 0.911248i \(-0.364880\pi\)
0.411858 + 0.911248i \(0.364880\pi\)
\(390\) 0 0
\(391\) 4.87689 0.246635
\(392\) 16.7192 10.6051i 0.844448 0.535637i
\(393\) 0 0
\(394\) 20.8078 + 9.74247i 1.04828 + 0.490819i
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 18.1379i 0.910317i 0.890410 + 0.455159i \(0.150417\pi\)
−0.890410 + 0.455159i \(0.849583\pi\)
\(398\) 4.00000 + 1.87285i 0.200502 + 0.0938776i
\(399\) 0 0
\(400\) 4.40388 24.0932i 0.220194 1.20466i
\(401\) −8.24621 −0.411796 −0.205898 0.978573i \(-0.566012\pi\)
−0.205898 + 0.978573i \(0.566012\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 21.1231 17.6121i 1.05091 0.876234i
\(405\) 0 0
\(406\) 6.56155 3.59806i 0.325644 0.178569i
\(407\) 1.05171i 0.0521311i
\(408\) 0 0
\(409\) 0.821147i 0.0406031i −0.999794 0.0203016i \(-0.993537\pi\)
0.999794 0.0203016i \(-0.00646263\pi\)
\(410\) 6.24621 + 2.92456i 0.308478 + 0.144434i
\(411\) 0 0
\(412\) 10.2462 + 12.2888i 0.504795 + 0.605427i
\(413\) 6.24621 8.54312i 0.307356 0.420379i
\(414\) 0 0
\(415\) 34.1725i 1.67746i
\(416\) −8.63068 6.14441i −0.423154 0.301255i
\(417\) 0 0
\(418\) 4.00000 8.54312i 0.195646 0.417858i
\(419\) −16.4924 −0.805708 −0.402854 0.915264i \(-0.631982\pi\)
−0.402854 + 0.915264i \(0.631982\pi\)
\(420\) 0 0
\(421\) 10.8769 0.530107 0.265054 0.964234i \(-0.414610\pi\)
0.265054 + 0.964234i \(0.414610\pi\)
\(422\) 7.68466 16.4127i 0.374083 0.798959i
\(423\) 0 0
\(424\) −8.80776 33.4990i −0.427743 1.62685i
\(425\) 31.8890i 1.54685i
\(426\) 0 0
\(427\) 10.2462 + 7.49141i 0.495849 + 0.362535i
\(428\) 14.5616 12.1412i 0.703859 0.586866i
\(429\) 0 0
\(430\) −38.7386 18.1379i −1.86814 0.874689i
\(431\) 4.68213i 0.225530i −0.993622 0.112765i \(-0.964029\pi\)
0.993622 0.112765i \(-0.0359708\pi\)
\(432\) 0 0
\(433\) 13.3405i 0.641105i −0.947231 0.320552i \(-0.896131\pi\)
0.947231 0.320552i \(-0.103869\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.5616 12.6670i −0.505807 0.606641i
\(437\) 6.67026i 0.319082i
\(438\) 0 0
\(439\) 6.63068 0.316465 0.158233 0.987402i \(-0.449420\pi\)
0.158233 + 0.987402i \(0.449420\pi\)
\(440\) 2.24621 + 8.54312i 0.107084 + 0.407277i
\(441\) 0 0
\(442\) −12.4924 5.84912i −0.594204 0.278214i
\(443\) 18.8438i 0.895296i 0.894210 + 0.447648i \(0.147738\pi\)
−0.894210 + 0.447648i \(0.852262\pi\)
\(444\) 0 0
\(445\) −4.87689 −0.231187
\(446\) −34.7386 16.2651i −1.64492 0.770174i
\(447\) 0 0
\(448\) −2.47301 + 21.0210i −0.116839 + 0.993151i
\(449\) −11.7538 −0.554696 −0.277348 0.960770i \(-0.589455\pi\)
−0.277348 + 0.960770i \(0.589455\pi\)
\(450\) 0 0
\(451\) −1.36932 −0.0644786
\(452\) 5.43845 + 6.52262i 0.255803 + 0.306798i
\(453\) 0 0
\(454\) −21.1231 9.89012i −0.991356 0.464166i
\(455\) 9.75379 13.3405i 0.457265 0.625414i
\(456\) 0 0
\(457\) 0.246211 0.0115173 0.00575864 0.999983i \(-0.498167\pi\)
0.00575864 + 0.999983i \(0.498167\pi\)
\(458\) −3.36932 + 7.19612i −0.157438 + 0.336252i
\(459\) 0 0
\(460\) −4.00000 4.79741i −0.186501 0.223680i
\(461\) 6.25969i 0.291543i 0.989318 + 0.145771i \(0.0465664\pi\)
−0.989318 + 0.145771i \(0.953434\pi\)
\(462\) 0 0
\(463\) 39.2652i 1.82481i −0.409292 0.912404i \(-0.634224\pi\)
0.409292 0.912404i \(-0.365776\pi\)
\(464\) −1.43845 + 7.86962i −0.0667782 + 0.365338i
\(465\) 0 0
\(466\) −28.8078 13.4882i −1.33449 0.624828i
\(467\) 34.2462 1.58473 0.792363 0.610050i \(-0.208851\pi\)
0.792363 + 0.610050i \(0.208851\pi\)
\(468\) 0 0
\(469\) 23.3693 + 17.0862i 1.07909 + 0.788969i
\(470\) 12.4924 26.6811i 0.576232 1.23071i
\(471\) 0 0
\(472\) 2.87689 + 10.9418i 0.132420 + 0.503638i
\(473\) 8.49242 0.390482
\(474\) 0 0
\(475\) 43.6155 2.00122
\(476\) 1.75379 + 27.5022i 0.0803848 + 1.26056i
\(477\) 0 0
\(478\) −9.68466 + 20.6843i −0.442966 + 0.946077i
\(479\) 12.4924 0.570793 0.285397 0.958409i \(-0.407875\pi\)
0.285397 + 0.958409i \(0.407875\pi\)
\(480\) 0 0
\(481\) 2.10341i 0.0959073i
\(482\) −14.2462 + 30.4268i −0.648897 + 1.38590i
\(483\) 0 0
\(484\) 12.9654 + 15.5501i 0.589338 + 0.706824i
\(485\) −34.7386 −1.57740
\(486\) 0 0
\(487\) 1.57756i 0.0714860i 0.999361 + 0.0357430i \(0.0113798\pi\)
−0.999361 + 0.0357430i \(0.988620\pi\)
\(488\) −13.1231 + 3.45041i −0.594055 + 0.156193i
\(489\) 0 0
\(490\) −32.7386 4.27156i −1.47898 0.192969i
\(491\) 11.3524i 0.512326i 0.966634 + 0.256163i \(0.0824585\pi\)
−0.966634 + 0.256163i \(0.917542\pi\)
\(492\) 0 0
\(493\) 10.4160i 0.469112i
\(494\) 8.00000 17.0862i 0.359937 0.768746i
\(495\) 0 0
\(496\) 0 0
\(497\) −8.24621 6.02913i −0.369893 0.270444i
\(498\) 0 0
\(499\) 13.8664i 0.620744i 0.950615 + 0.310372i \(0.100454\pi\)
−0.950615 + 0.310372i \(0.899546\pi\)
\(500\) −5.75379 + 4.79741i −0.257317 + 0.214547i
\(501\) 0 0
\(502\) −7.36932 3.45041i −0.328909 0.153999i
\(503\) −26.7386 −1.19222 −0.596108 0.802904i \(-0.703287\pi\)
−0.596108 + 0.802904i \(0.703287\pi\)
\(504\) 0 0
\(505\) −45.8617 −2.04082
\(506\) 1.12311 + 0.525853i 0.0499281 + 0.0233770i
\(507\) 0 0
\(508\) −15.1922 + 12.6670i −0.674046 + 0.562008i
\(509\) 3.33513i 0.147827i 0.997265 + 0.0739136i \(0.0235489\pi\)
−0.997265 + 0.0739136i \(0.976451\pi\)
\(510\) 0 0
\(511\) 14.2462 + 10.4160i 0.630215 + 0.460775i
\(512\) −15.7732 16.2236i −0.697083 0.716990i
\(513\) 0 0
\(514\) 1.36932 2.92456i 0.0603980 0.128997i
\(515\) 26.6811i 1.17571i
\(516\) 0 0
\(517\) 5.84912i 0.257244i
\(518\) 3.68466 2.02050i 0.161895 0.0887757i
\(519\) 0 0
\(520\) 4.49242 + 17.0862i 0.197006 + 0.749281i
\(521\) 29.7856i 1.30493i −0.757818 0.652466i \(-0.773734\pi\)
0.757818 0.652466i \(-0.226266\pi\)
\(522\) 0 0
\(523\) −32.4924 −1.42079 −0.710397 0.703801i \(-0.751485\pi\)
−0.710397 + 0.703801i \(0.751485\pi\)
\(524\) 7.36932 + 8.83841i 0.321930 + 0.386108i
\(525\) 0 0
\(526\) 14.8078 31.6261i 0.645649 1.37896i
\(527\) 0 0
\(528\) 0 0
\(529\) 22.1231 0.961874
\(530\) −24.4924 + 52.3104i −1.06388 + 2.27222i
\(531\) 0 0
\(532\) −37.6155 + 2.39871i −1.63084 + 0.103997i
\(533\) −2.73863 −0.118623
\(534\) 0 0
\(535\) −31.6155 −1.36686
\(536\) −29.9309 + 7.86962i −1.29282 + 0.339916i
\(537\) 0 0
\(538\) −6.49242 + 13.8664i −0.279908 + 0.597822i
\(539\) 6.24621 1.98813i 0.269043 0.0856349i
\(540\) 0 0
\(541\) 2.87689 0.123687 0.0618437 0.998086i \(-0.480302\pi\)
0.0618437 + 0.998086i \(0.480302\pi\)
\(542\) 36.4924 + 17.0862i 1.56748 + 0.733917i
\(543\) 0 0
\(544\) −24.0000 17.0862i −1.02899 0.732566i
\(545\) 27.5022i 1.17806i
\(546\) 0 0
\(547\) 16.7909i 0.717929i 0.933351 + 0.358964i \(0.116870\pi\)
−0.933351 + 0.358964i \(0.883130\pi\)
\(548\) −0.315342 0.378206i −0.0134707 0.0161562i
\(549\) 0 0
\(550\) 3.43845 7.34376i 0.146616 0.313139i
\(551\) −14.2462 −0.606909
\(552\) 0 0
\(553\) 5.12311 + 3.74571i 0.217857 + 0.159284i
\(554\) −6.56155 3.07221i −0.278774 0.130526i
\(555\) 0 0
\(556\) 15.3693 + 18.4332i 0.651804 + 0.781743i
\(557\) −14.0000 −0.593199 −0.296600 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) 16.9848 0.718382
\(560\) 25.6155 24.2824i 1.08245 1.02612i
\(561\) 0 0
\(562\) −20.8078 9.74247i −0.877723 0.410961i
\(563\) 2.24621 0.0946665 0.0473333 0.998879i \(-0.484928\pi\)
0.0473333 + 0.998879i \(0.484928\pi\)
\(564\) 0 0
\(565\) 14.1617i 0.595786i
\(566\) −11.3693 5.32326i −0.477888 0.223753i
\(567\) 0 0
\(568\) 10.5616 2.77691i 0.443153 0.116517i
\(569\) 30.9848 1.29895 0.649476 0.760382i \(-0.274988\pi\)
0.649476 + 0.760382i \(0.274988\pi\)
\(570\) 0 0
\(571\) 8.83841i 0.369876i 0.982750 + 0.184938i \(0.0592084\pi\)
−0.982750 + 0.184938i \(0.940792\pi\)
\(572\) −2.24621 2.69400i −0.0939188 0.112642i
\(573\) 0 0
\(574\) 2.63068 + 4.79741i 0.109803 + 0.200240i
\(575\) 5.73384i 0.239118i
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −12.9654 6.07059i −0.539291 0.252503i
\(579\) 0 0
\(580\) 10.2462 8.54312i 0.425451 0.354734i
\(581\) −16.0000 + 21.8836i −0.663792 + 0.907887i
\(582\) 0 0
\(583\) 11.4677i 0.474943i
\(584\) −18.2462 + 4.79741i −0.755034 + 0.198518i
\(585\) 0 0
\(586\) 8.24621 17.6121i 0.340648 0.727549i
\(587\) −21.7538 −0.897875 −0.448937 0.893563i \(-0.648197\pi\)
−0.448937 + 0.893563i \(0.648197\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 8.00000 17.0862i 0.329355 0.703429i
\(591\) 0 0
\(592\) −0.807764 + 4.41921i −0.0331989 + 0.181628i
\(593\) 26.0399i 1.06933i 0.845064 + 0.534666i \(0.179562\pi\)
−0.845064 + 0.534666i \(0.820438\pi\)
\(594\) 0 0
\(595\) 27.1231 37.0970i 1.11194 1.52083i
\(596\) 12.8078 + 15.3610i 0.524626 + 0.629212i
\(597\) 0 0
\(598\) 2.24621 + 1.05171i 0.0918544 + 0.0430074i
\(599\) 17.2015i 0.702835i −0.936219 0.351417i \(-0.885700\pi\)
0.936219 0.351417i \(-0.114300\pi\)
\(600\) 0 0
\(601\) 17.0862i 0.696962i −0.937316 0.348481i \(-0.886698\pi\)
0.937316 0.348481i \(-0.113302\pi\)
\(602\) −16.3153 29.7533i −0.664964 1.21265i
\(603\) 0 0
\(604\) −13.9309 + 11.6153i −0.566839 + 0.472621i
\(605\) 33.7619i 1.37262i
\(606\) 0 0
\(607\) −7.61553 −0.309105 −0.154552 0.987985i \(-0.549394\pi\)
−0.154552 + 0.987985i \(0.549394\pi\)
\(608\) 23.3693 32.8255i 0.947751 1.33125i
\(609\) 0 0
\(610\) 20.4924 + 9.59482i 0.829714 + 0.388483i
\(611\) 11.6982i 0.473260i
\(612\) 0 0
\(613\) 8.73863 0.352950 0.176475 0.984305i \(-0.443531\pi\)
0.176475 + 0.984305i \(0.443531\pi\)
\(614\) −25.1231 11.7630i −1.01389 0.474715i
\(615\) 0 0
\(616\) −2.56155 + 6.52262i −0.103208 + 0.262804i
\(617\) −32.2462 −1.29818 −0.649092 0.760710i \(-0.724851\pi\)
−0.649092 + 0.760710i \(0.724851\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 10.2462 + 4.79741i 0.410836 + 0.192359i
\(623\) −3.12311 2.28343i −0.125125 0.0914835i
\(624\) 0 0
\(625\) −18.1231 −0.724924
\(626\) 13.7538 29.3751i 0.549712 1.17406i
\(627\) 0 0
\(628\) 33.6155 28.0281i 1.34141 1.11844i
\(629\) 5.84912i 0.233220i
\(630\) 0 0
\(631\) 40.3169i 1.60499i 0.596659 + 0.802495i \(0.296494\pi\)
−0.596659 + 0.802495i \(0.703506\pi\)
\(632\) −6.56155 + 1.72521i −0.261005 + 0.0686250i
\(633\) 0 0
\(634\) 18.5616 + 8.69076i 0.737173 + 0.345154i
\(635\) 32.9848 1.30896
\(636\) 0 0
\(637\) 12.4924 3.97626i 0.494968 0.157545i
\(638\) −1.12311 + 2.39871i −0.0444642 + 0.0949657i
\(639\) 0 0
\(640\) 2.87689 + 37.6229i 0.113719 + 1.48717i
\(641\) 42.4924 1.67835 0.839175 0.543862i \(-0.183038\pi\)
0.839175 + 0.543862i \(0.183038\pi\)
\(642\) 0 0
\(643\) 11.6155 0.458072 0.229036 0.973418i \(-0.426443\pi\)
0.229036 + 0.973418i \(0.426443\pi\)
\(644\) −0.315342 4.94506i −0.0124262 0.194863i
\(645\) 0 0
\(646\) 22.2462 47.5130i 0.875265 1.86937i
\(647\) −32.9848 −1.29677 −0.648384 0.761313i \(-0.724555\pi\)
−0.648384 + 0.761313i \(0.724555\pi\)
\(648\) 0 0
\(649\) 3.74571i 0.147032i
\(650\) 6.87689 14.6875i 0.269734 0.576092i
\(651\) 0 0
\(652\) 24.1771 20.1584i 0.946848 0.789465i
\(653\) −16.7386 −0.655033 −0.327517 0.944845i \(-0.606212\pi\)
−0.327517 + 0.944845i \(0.606212\pi\)
\(654\) 0 0
\(655\) 19.1896i 0.749801i
\(656\) −5.75379 1.05171i −0.224648 0.0410622i
\(657\) 0 0
\(658\) 20.4924 11.2371i 0.798878 0.438068i
\(659\) 26.7963i 1.04384i 0.852995 + 0.521919i \(0.174783\pi\)
−0.852995 + 0.521919i \(0.825217\pi\)
\(660\) 0 0
\(661\) 8.54312i 0.332289i 0.986101 + 0.166144i \(0.0531318\pi\)
−0.986101 + 0.166144i \(0.946868\pi\)
\(662\) −10.5616 + 22.5571i −0.410486 + 0.876708i
\(663\) 0 0
\(664\) −7.36932 28.0281i −0.285985 1.08770i
\(665\) 50.7386 + 37.0970i 1.96756 + 1.43856i
\(666\) 0 0
\(667\) 1.87285i 0.0725171i
\(668\) 18.2462 + 21.8836i 0.705967 + 0.846704i
\(669\) 0 0
\(670\) 46.7386 + 21.8836i 1.80567 + 0.845439i
\(671\) −4.49242 −0.173428
\(672\) 0 0
\(673\) −27.8617 −1.07399 −0.536996 0.843585i \(-0.680441\pi\)
−0.536996 + 0.843585i \(0.680441\pi\)
\(674\) 10.5616 + 4.94506i 0.406816 + 0.190477i
\(675\) 0 0
\(676\) 12.1577 + 14.5813i 0.467603 + 0.560821i
\(677\) 9.18425i 0.352979i −0.984302 0.176490i \(-0.943526\pi\)
0.984302 0.176490i \(-0.0564742\pi\)
\(678\) 0 0
\(679\) −22.2462 16.2651i −0.853731 0.624197i
\(680\) 12.4924 + 47.5130i 0.479063 + 1.82204i
\(681\) 0 0
\(682\) 0 0
\(683\) 32.1843i 1.23150i 0.787942 + 0.615750i \(0.211147\pi\)
−0.787942 + 0.615750i \(0.788853\pi\)
\(684\) 0 0
\(685\) 0.821147i 0.0313744i
\(686\) −18.9654 18.0641i −0.724104 0.689691i
\(687\) 0 0
\(688\) 35.6847 + 6.52262i 1.36046 + 0.248672i
\(689\) 22.9354i 0.873767i
\(690\) 0 0
\(691\) −12.0000 −0.456502 −0.228251 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(692\) −25.6155 + 21.3578i −0.973756 + 0.811901i
\(693\) 0 0
\(694\) −12.0691 + 25.7770i −0.458138 + 0.978481i
\(695\) 40.0216i 1.51811i
\(696\) 0 0
\(697\) −7.61553 −0.288459
\(698\) 13.1231 28.0281i 0.496717 1.06088i
\(699\) 0 0
\(700\) −32.3348 + 2.06196i −1.22214 + 0.0779346i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) −3.68466 6.52262i −0.138871 0.245830i
\(705\) 0 0
\(706\) −17.3693 + 37.0970i −0.653703 + 1.39616i
\(707\) −29.3693 21.4731i −1.10455 0.807578i
\(708\) 0 0
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) −16.4924 7.72197i −0.618950 0.289800i
\(711\) 0 0
\(712\) 4.00000 1.05171i 0.149906 0.0394143i
\(713\) 0 0
\(714\) 0 0
\(715\) 5.84912i 0.218745i
\(716\) 24.8078 20.6843i 0.927110 0.773008i
\(717\) 0 0
\(718\) −13.6847 + 29.2274i −0.510707 + 1.09076i
\(719\) 28.4924 1.06259 0.531294 0.847187i \(-0.321706\pi\)
0.531294 + 0.847187i \(0.321706\pi\)
\(720\) 0 0
\(721\) 12.4924 17.0862i 0.465242 0.636325i
\(722\) 40.6501 + 19.0329i 1.51284 + 0.708332i
\(723\) 0 0
\(724\) 2.87689 2.39871i 0.106919 0.0891472i
\(725\) −12.2462 −0.454813
\(726\) 0 0
\(727\) −32.9848 −1.22334 −0.611670 0.791113i \(-0.709502\pi\)
−0.611670 + 0.791113i \(0.709502\pi\)
\(728\) −5.12311 + 13.0452i −0.189875 + 0.483489i
\(729\) 0 0
\(730\) 28.4924 + 13.3405i 1.05455 + 0.493755i
\(731\) 47.2311 1.74690
\(732\) 0 0
\(733\) 36.0453i 1.33136i 0.746235 + 0.665682i \(0.231859\pi\)
−0.746235 + 0.665682i \(0.768141\pi\)
\(734\) 42.7386 + 20.0108i 1.57751 + 0.738612i
\(735\) 0 0
\(736\) 4.31534 + 3.07221i 0.159066 + 0.113243i
\(737\) −10.2462 −0.377424
\(738\) 0 0
\(739\) 36.5712i 1.34529i −0.739964 0.672646i \(-0.765158\pi\)
0.739964 0.672646i \(-0.234842\pi\)
\(740\) 5.75379 4.79741i 0.211513 0.176356i
\(741\) 0 0
\(742\) −40.1771 + 22.0313i −1.47495 + 0.808794i
\(743\) 35.1089i 1.28802i −0.765017 0.644010i \(-0.777269\pi\)
0.765017 0.644010i \(-0.222731\pi\)
\(744\) 0 0
\(745\) 33.3513i 1.22190i
\(746\) −12.8078 5.99676i −0.468926 0.219557i
\(747\) 0 0
\(748\) −6.24621 7.49141i −0.228384 0.273913i
\(749\) −20.2462 14.8028i −0.739780 0.540883i
\(750\) 0 0
\(751\) 28.8492i 1.05272i −0.850261 0.526361i \(-0.823556\pi\)
0.850261 0.526361i \(-0.176444\pi\)
\(752\) −4.49242 + 24.5776i −0.163822 + 0.896254i
\(753\) 0 0
\(754\) −2.24621 + 4.79741i −0.0818022 + 0.174711i
\(755\) 30.2462 1.10077
\(756\) 0 0
\(757\) −34.9848 −1.27155 −0.635773 0.771876i \(-0.719319\pi\)
−0.635773 + 0.771876i \(0.719319\pi\)
\(758\) −15.0540 + 32.1520i −0.546785 + 1.16781i
\(759\) 0 0
\(760\) −64.9848 + 17.0862i −2.35725 + 0.619783i
\(761\) 29.7856i 1.07973i 0.841752 + 0.539864i \(0.181524\pi\)
−0.841752 + 0.539864i \(0.818476\pi\)
\(762\) 0 0
\(763\) −12.8769 + 17.6121i −0.466175 + 0.637600i
\(764\) −4.31534 + 3.59806i −0.156124 + 0.130173i
\(765\) 0 0
\(766\) −12.4924 5.84912i −0.451370 0.211337i
\(767\) 7.49141i 0.270499i
\(768\) 0 0
\(769\) 32.5302i 1.17307i −0.809925 0.586534i \(-0.800492\pi\)
0.809925 0.586534i \(-0.199508\pi\)
\(770\) 10.2462 5.61856i 0.369248 0.202479i
\(771\) 0 0
\(772\) −19.6847 23.6089i −0.708466 0.849701i
\(773\) 3.33513i 0.119956i −0.998200 0.0599782i \(-0.980897\pi\)
0.998200 0.0599782i \(-0.0191031\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 28.4924 7.49141i 1.02282 0.268926i
\(777\) 0 0
\(778\) 20.8078 + 9.74247i 0.745994 + 0.349284i
\(779\) 10.4160i 0.373191i
\(780\) 0 0
\(781\) 3.61553 0.129374
\(782\) 6.24621 + 2.92456i 0.223364 + 0.104582i
\(783\) 0 0
\(784\) 27.7732 3.55660i 0.991900 0.127022i
\(785\) −72.9848 −2.60494
\(786\) 0 0
\(787\) 44.9848 1.60354 0.801768 0.597635i \(-0.203893\pi\)
0.801768 + 0.597635i \(0.203893\pi\)
\(788\) 20.8078 + 24.9559i 0.741246 + 0.889015i
\(789\) 0 0
\(790\) 10.2462 + 4.79741i 0.364544 + 0.170684i
\(791\) 6.63068 9.06897i 0.235760 0.322455i
\(792\)