Properties

Label 2646.2.t.a.2285.8
Level $2646$
Weight $2$
Character 2646.2285
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2285.8
Root \(1.69547 - 0.354107i\) of defining polynomial
Character \(\chi\) \(=\) 2646.2285
Dual form 2646.2.t.a.1979.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.79035 q^{5} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.79035 q^{5} +1.00000i q^{8} +(1.55049 + 0.895175i) q^{10} +2.40150i q^{11} +(4.23601 + 2.44566i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.83233 + 3.17369i) q^{17} +(2.61281 - 1.50851i) q^{19} +(0.895175 + 1.55049i) q^{20} +(-1.20075 + 2.07976i) q^{22} +3.76638i q^{23} -1.79465 q^{25} +(2.44566 + 4.23601i) q^{26} +(5.68202 - 3.28052i) q^{29} +(-4.02408 + 2.32330i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-3.17369 + 1.83233i) q^{34} +(-4.68202 - 8.10950i) q^{37} +3.01701 q^{38} +1.79035i q^{40} +(-4.04094 + 6.99911i) q^{41} +(-3.48127 - 6.02973i) q^{43} +(-2.07976 + 1.20075i) q^{44} +(-1.88319 + 3.26178i) q^{46} +(2.56802 - 4.44794i) q^{47} +(-1.55421 - 0.897324i) q^{50} +4.89133i q^{52} +4.29953i q^{55} +6.56103 q^{58} +(7.29501 + 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} -4.64661 q^{62} -1.00000 q^{64} +(7.58394 + 4.37859i) q^{65} +(-0.285115 - 0.493834i) q^{67} -3.66466 q^{68} +5.96254i q^{71} +(10.7226 + 6.19070i) q^{73} -9.36404i q^{74} +(2.61281 + 1.50851i) q^{76} +(-1.51831 + 2.62979i) q^{79} +(-0.895175 + 1.55049i) q^{80} +(-6.99911 + 4.04094i) q^{82} +(-7.00270 - 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} -6.96254i q^{86} -2.40150 q^{88} +(1.87432 + 3.24641i) q^{89} +(-3.26178 + 1.88319i) q^{92} +(4.44794 - 2.56802i) q^{94} +(4.67784 - 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + O(q^{10}) \) \( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.79035 0.800669 0.400334 0.916369i \(-0.368894\pi\)
0.400334 + 0.916369i \(0.368894\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.55049 + 0.895175i 0.490307 + 0.283079i
\(11\) 2.40150i 0.724081i 0.932162 + 0.362040i \(0.117920\pi\)
−0.932162 + 0.362040i \(0.882080\pi\)
\(12\) 0 0
\(13\) 4.23601 + 2.44566i 1.17486 + 0.678305i 0.954820 0.297186i \(-0.0960482\pi\)
0.220039 + 0.975491i \(0.429382\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.83233 + 3.17369i −0.444406 + 0.769734i −0.998011 0.0630460i \(-0.979919\pi\)
0.553605 + 0.832780i \(0.313252\pi\)
\(18\) 0 0
\(19\) 2.61281 1.50851i 0.599419 0.346075i −0.169394 0.985548i \(-0.554181\pi\)
0.768813 + 0.639474i \(0.220848\pi\)
\(20\) 0.895175 + 1.55049i 0.200167 + 0.346700i
\(21\) 0 0
\(22\) −1.20075 + 2.07976i −0.256001 + 0.443407i
\(23\) 3.76638i 0.785345i 0.919678 + 0.392673i \(0.128449\pi\)
−0.919678 + 0.392673i \(0.871551\pi\)
\(24\) 0 0
\(25\) −1.79465 −0.358930
\(26\) 2.44566 + 4.23601i 0.479634 + 0.830750i
\(27\) 0 0
\(28\) 0 0
\(29\) 5.68202 3.28052i 1.05512 0.609176i 0.131045 0.991376i \(-0.458167\pi\)
0.924080 + 0.382200i \(0.124833\pi\)
\(30\) 0 0
\(31\) −4.02408 + 2.32330i −0.722746 + 0.417278i −0.815763 0.578387i \(-0.803682\pi\)
0.0930163 + 0.995665i \(0.470349\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −3.17369 + 1.83233i −0.544284 + 0.314242i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.68202 8.10950i −0.769719 1.33319i −0.937715 0.347405i \(-0.887063\pi\)
0.167996 0.985788i \(-0.446271\pi\)
\(38\) 3.01701 0.489424
\(39\) 0 0
\(40\) 1.79035i 0.283079i
\(41\) −4.04094 + 6.99911i −0.631088 + 1.09308i 0.356241 + 0.934394i \(0.384058\pi\)
−0.987330 + 0.158683i \(0.949275\pi\)
\(42\) 0 0
\(43\) −3.48127 6.02973i −0.530888 0.919526i −0.999350 0.0360419i \(-0.988525\pi\)
0.468462 0.883484i \(-0.344808\pi\)
\(44\) −2.07976 + 1.20075i −0.313536 + 0.181020i
\(45\) 0 0
\(46\) −1.88319 + 3.26178i −0.277661 + 0.480924i
\(47\) 2.56802 4.44794i 0.374584 0.648799i −0.615680 0.787996i \(-0.711119\pi\)
0.990265 + 0.139197i \(0.0444520\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.55421 0.897324i −0.219799 0.126901i
\(51\) 0 0
\(52\) 4.89133i 0.678305i
\(53\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) 4.29953i 0.579749i
\(56\) 0 0
\(57\) 0 0
\(58\) 6.56103 0.861506
\(59\) 7.29501 + 12.6353i 0.949729 + 1.64498i 0.745994 + 0.665953i \(0.231975\pi\)
0.203735 + 0.979026i \(0.434692\pi\)
\(60\) 0 0
\(61\) 9.81058 + 5.66414i 1.25612 + 0.725219i 0.972317 0.233665i \(-0.0750718\pi\)
0.283799 + 0.958884i \(0.408405\pi\)
\(62\) −4.64661 −0.590120
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 7.58394 + 4.37859i 0.940672 + 0.543097i
\(66\) 0 0
\(67\) −0.285115 0.493834i −0.0348324 0.0603315i 0.848084 0.529862i \(-0.177756\pi\)
−0.882916 + 0.469531i \(0.844423\pi\)
\(68\) −3.66466 −0.444406
\(69\) 0 0
\(70\) 0 0
\(71\) 5.96254i 0.707623i 0.935317 + 0.353811i \(0.115115\pi\)
−0.935317 + 0.353811i \(0.884885\pi\)
\(72\) 0 0
\(73\) 10.7226 + 6.19070i 1.25499 + 0.724567i 0.972096 0.234585i \(-0.0753731\pi\)
0.282891 + 0.959152i \(0.408706\pi\)
\(74\) 9.36404i 1.08855i
\(75\) 0 0
\(76\) 2.61281 + 1.50851i 0.299710 + 0.173037i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.51831 + 2.62979i −0.170824 + 0.295875i −0.938708 0.344713i \(-0.887976\pi\)
0.767884 + 0.640588i \(0.221309\pi\)
\(80\) −0.895175 + 1.55049i −0.100084 + 0.173350i
\(81\) 0 0
\(82\) −6.99911 + 4.04094i −0.772922 + 0.446247i
\(83\) −7.00270 12.1290i −0.768646 1.33133i −0.938297 0.345830i \(-0.887597\pi\)
0.169651 0.985504i \(-0.445736\pi\)
\(84\) 0 0
\(85\) −3.28052 + 5.68202i −0.355822 + 0.616302i
\(86\) 6.96254i 0.750790i
\(87\) 0 0
\(88\) −2.40150 −0.256001
\(89\) 1.87432 + 3.24641i 0.198677 + 0.344119i 0.948100 0.317973i \(-0.103002\pi\)
−0.749423 + 0.662092i \(0.769669\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.26178 + 1.88319i −0.340064 + 0.196336i
\(93\) 0 0
\(94\) 4.44794 2.56802i 0.458770 0.264871i
\(95\) 4.67784 2.70075i 0.479936 0.277091i
\(96\) 0 0
\(97\) −4.77256 + 2.75544i −0.484580 + 0.279772i −0.722323 0.691556i \(-0.756926\pi\)
0.237743 + 0.971328i \(0.423592\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.897324 1.55421i −0.0897324 0.155421i
\(101\) 0.250324 0.0249082 0.0124541 0.999922i \(-0.496036\pi\)
0.0124541 + 0.999922i \(0.496036\pi\)
\(102\) 0 0
\(103\) 0.167931i 0.0165468i 0.999966 + 0.00827339i \(0.00263353\pi\)
−0.999966 + 0.00827339i \(0.997366\pi\)
\(104\) −2.44566 + 4.23601i −0.239817 + 0.415375i
\(105\) 0 0
\(106\) 0 0
\(107\) −6.92024 + 3.99540i −0.669004 + 0.386250i −0.795699 0.605692i \(-0.792896\pi\)
0.126695 + 0.991942i \(0.459563\pi\)
\(108\) 0 0
\(109\) 9.47667 16.4141i 0.907700 1.57218i 0.0904491 0.995901i \(-0.471170\pi\)
0.817251 0.576282i \(-0.195497\pi\)
\(110\) −2.14977 + 3.72350i −0.204972 + 0.355022i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.00418 + 0.579764i 0.0944653 + 0.0545396i 0.546488 0.837467i \(-0.315964\pi\)
−0.452023 + 0.892006i \(0.649298\pi\)
\(114\) 0 0
\(115\) 6.74314i 0.628801i
\(116\) 5.68202 + 3.28052i 0.527562 + 0.304588i
\(117\) 0 0
\(118\) 14.5900i 1.34312i
\(119\) 0 0
\(120\) 0 0
\(121\) 5.23278 0.475707
\(122\) 5.66414 + 9.81058i 0.512807 + 0.888208i
\(123\) 0 0
\(124\) −4.02408 2.32330i −0.361373 0.208639i
\(125\) −12.1648 −1.08805
\(126\) 0 0
\(127\) 1.40150 0.124363 0.0621817 0.998065i \(-0.480194\pi\)
0.0621817 + 0.998065i \(0.480194\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) 4.37859 + 7.58394i 0.384028 + 0.665156i
\(131\) 10.4918 0.916671 0.458335 0.888779i \(-0.348446\pi\)
0.458335 + 0.888779i \(0.348446\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.570231i 0.0492604i
\(135\) 0 0
\(136\) −3.17369 1.83233i −0.272142 0.157121i
\(137\) 4.72056i 0.403305i 0.979457 + 0.201652i \(0.0646311\pi\)
−0.979457 + 0.201652i \(0.935369\pi\)
\(138\) 0 0
\(139\) 2.04707 + 1.18187i 0.173630 + 0.100245i 0.584296 0.811540i \(-0.301371\pi\)
−0.410666 + 0.911786i \(0.634704\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.98127 + 5.16371i −0.250182 + 0.433329i
\(143\) −5.87327 + 10.1728i −0.491148 + 0.850692i
\(144\) 0 0
\(145\) 10.1728 5.87327i 0.844805 0.487749i
\(146\) 6.19070 + 10.7226i 0.512346 + 0.887410i
\(147\) 0 0
\(148\) 4.68202 8.10950i 0.384860 0.666597i
\(149\) 17.3640i 1.42252i −0.702930 0.711259i \(-0.748125\pi\)
0.702930 0.711259i \(-0.251875\pi\)
\(150\) 0 0
\(151\) −11.2328 −0.914110 −0.457055 0.889438i \(-0.651096\pi\)
−0.457055 + 0.889438i \(0.651096\pi\)
\(152\) 1.50851 + 2.61281i 0.122356 + 0.211927i
\(153\) 0 0
\(154\) 0 0
\(155\) −7.20451 + 4.15953i −0.578680 + 0.334101i
\(156\) 0 0
\(157\) 11.9885 6.92154i 0.956783 0.552399i 0.0616014 0.998101i \(-0.480379\pi\)
0.895181 + 0.445702i \(0.147046\pi\)
\(158\) −2.62979 + 1.51831i −0.209215 + 0.120790i
\(159\) 0 0
\(160\) −1.55049 + 0.895175i −0.122577 + 0.0707698i
\(161\) 0 0
\(162\) 0 0
\(163\) 2.16789 + 3.75489i 0.169802 + 0.294106i 0.938350 0.345686i \(-0.112354\pi\)
−0.768548 + 0.639792i \(0.779020\pi\)
\(164\) −8.08188 −0.631088
\(165\) 0 0
\(166\) 14.0054i 1.08703i
\(167\) −6.20756 + 10.7518i −0.480355 + 0.832000i −0.999746 0.0225370i \(-0.992826\pi\)
0.519391 + 0.854537i \(0.326159\pi\)
\(168\) 0 0
\(169\) 5.46254 + 9.46139i 0.420195 + 0.727799i
\(170\) −5.68202 + 3.28052i −0.435791 + 0.251604i
\(171\) 0 0
\(172\) 3.48127 6.02973i 0.265444 0.459763i
\(173\) 8.70908 15.0846i 0.662139 1.14686i −0.317913 0.948120i \(-0.602982\pi\)
0.980052 0.198739i \(-0.0636846\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.07976 1.20075i −0.156768 0.0905101i
\(177\) 0 0
\(178\) 3.74863i 0.280972i
\(179\) −11.3640 6.56103i −0.849388 0.490395i 0.0110562 0.999939i \(-0.496481\pi\)
−0.860444 + 0.509544i \(0.829814\pi\)
\(180\) 0 0
\(181\) 13.3577i 0.992873i 0.868073 + 0.496437i \(0.165359\pi\)
−0.868073 + 0.496437i \(0.834641\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.76638 −0.277661
\(185\) −8.38245 14.5188i −0.616290 1.06745i
\(186\) 0 0
\(187\) −7.62164 4.40035i −0.557349 0.321786i
\(188\) 5.13604 0.374584
\(189\) 0 0
\(190\) 5.40150 0.391866
\(191\) −8.01361 4.62666i −0.579845 0.334774i 0.181227 0.983441i \(-0.441993\pi\)
−0.761072 + 0.648668i \(0.775326\pi\)
\(192\) 0 0
\(193\) 12.2801 + 21.2698i 0.883941 + 1.53103i 0.846923 + 0.531716i \(0.178452\pi\)
0.0370176 + 0.999315i \(0.488214\pi\)
\(194\) −5.51087 −0.395658
\(195\) 0 0
\(196\) 0 0
\(197\) 12.4861i 0.889598i −0.895630 0.444799i \(-0.853275\pi\)
0.895630 0.444799i \(-0.146725\pi\)
\(198\) 0 0
\(199\) −0.155144 0.0895727i −0.0109979 0.00634964i 0.494491 0.869183i \(-0.335355\pi\)
−0.505489 + 0.862833i \(0.668688\pi\)
\(200\) 1.79465i 0.126901i
\(201\) 0 0
\(202\) 0.216787 + 0.125162i 0.0152531 + 0.00880637i
\(203\) 0 0
\(204\) 0 0
\(205\) −7.23469 + 12.5309i −0.505293 + 0.875193i
\(206\) −0.0839657 + 0.145433i −0.00585017 + 0.0101328i
\(207\) 0 0
\(208\) −4.23601 + 2.44566i −0.293715 + 0.169576i
\(209\) 3.62268 + 6.27467i 0.250586 + 0.434028i
\(210\) 0 0
\(211\) 7.56103 13.0961i 0.520523 0.901572i −0.479192 0.877710i \(-0.659070\pi\)
0.999715 0.0238622i \(-0.00759629\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −7.99080 −0.546240
\(215\) −6.23269 10.7953i −0.425066 0.736235i
\(216\) 0 0
\(217\) 0 0
\(218\) 16.4141 9.47667i 1.11170 0.641841i
\(219\) 0 0
\(220\) −3.72350 + 2.14977i −0.251039 + 0.144937i
\(221\) −15.5236 + 8.96254i −1.04423 + 0.602885i
\(222\) 0 0
\(223\) 7.27049 4.19762i 0.486868 0.281093i −0.236406 0.971654i \(-0.575970\pi\)
0.723274 + 0.690561i \(0.242636\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.579764 + 1.00418i 0.0385653 + 0.0667971i
\(227\) −2.42522 −0.160967 −0.0804836 0.996756i \(-0.525646\pi\)
−0.0804836 + 0.996756i \(0.525646\pi\)
\(228\) 0 0
\(229\) 2.01975i 0.133469i 0.997771 + 0.0667344i \(0.0212580\pi\)
−0.997771 + 0.0667344i \(0.978742\pi\)
\(230\) −3.37157 + 5.83973i −0.222315 + 0.385061i
\(231\) 0 0
\(232\) 3.28052 + 5.68202i 0.215376 + 0.373043i
\(233\) 11.0236 6.36446i 0.722178 0.416950i −0.0933759 0.995631i \(-0.529766\pi\)
0.815554 + 0.578681i \(0.196432\pi\)
\(234\) 0 0
\(235\) 4.59766 7.96337i 0.299918 0.519473i
\(236\) −7.29501 + 12.6353i −0.474864 + 0.822489i
\(237\) 0 0
\(238\) 0 0
\(239\) −15.1117 8.72474i −0.977494 0.564356i −0.0759814 0.997109i \(-0.524209\pi\)
−0.901513 + 0.432753i \(0.857542\pi\)
\(240\) 0 0
\(241\) 11.4332i 0.736476i −0.929732 0.368238i \(-0.879961\pi\)
0.929732 0.368238i \(-0.120039\pi\)
\(242\) 4.53172 + 2.61639i 0.291310 + 0.168188i
\(243\) 0 0
\(244\) 11.3283i 0.725219i
\(245\) 0 0
\(246\) 0 0
\(247\) 14.7572 0.938977
\(248\) −2.32330 4.02408i −0.147530 0.255529i
\(249\) 0 0
\(250\) −10.5350 6.08240i −0.666293 0.384685i
\(251\) −27.3560 −1.72669 −0.863347 0.504611i \(-0.831636\pi\)
−0.863347 + 0.504611i \(0.831636\pi\)
\(252\) 0 0
\(253\) −9.04499 −0.568653
\(254\) 1.21374 + 0.700752i 0.0761567 + 0.0439691i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.49673 −0.218120 −0.109060 0.994035i \(-0.534784\pi\)
−0.109060 + 0.994035i \(0.534784\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 8.75718i 0.543097i
\(261\) 0 0
\(262\) 9.08614 + 5.24589i 0.561344 + 0.324092i
\(263\) 9.64348i 0.594643i 0.954777 + 0.297321i \(0.0960932\pi\)
−0.954777 + 0.297321i \(0.903907\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.285115 0.493834i 0.0174162 0.0301657i
\(269\) 3.45554 5.98517i 0.210688 0.364922i −0.741242 0.671238i \(-0.765763\pi\)
0.951930 + 0.306316i \(0.0990963\pi\)
\(270\) 0 0
\(271\) 17.8672 10.3156i 1.08535 0.626629i 0.153017 0.988224i \(-0.451101\pi\)
0.932335 + 0.361595i \(0.117768\pi\)
\(272\) −1.83233 3.17369i −0.111101 0.192433i
\(273\) 0 0
\(274\) −2.36028 + 4.08812i −0.142590 + 0.246973i
\(275\) 4.30986i 0.259894i
\(276\) 0 0
\(277\) −15.5144 −0.932168 −0.466084 0.884740i \(-0.654336\pi\)
−0.466084 + 0.884740i \(0.654336\pi\)
\(278\) 1.18187 + 2.04707i 0.0708841 + 0.122775i
\(279\) 0 0
\(280\) 0 0
\(281\) −11.7759 + 6.79883i −0.702492 + 0.405584i −0.808275 0.588805i \(-0.799599\pi\)
0.105783 + 0.994389i \(0.466265\pi\)
\(282\) 0 0
\(283\) −4.71796 + 2.72392i −0.280454 + 0.161920i −0.633629 0.773637i \(-0.718435\pi\)
0.353175 + 0.935557i \(0.385102\pi\)
\(284\) −5.16371 + 2.98127i −0.306410 + 0.176906i
\(285\) 0 0
\(286\) −10.1728 + 5.87327i −0.601530 + 0.347294i
\(287\) 0 0
\(288\) 0 0
\(289\) 1.78512 + 3.09191i 0.105007 + 0.181877i
\(290\) 11.7465 0.689781
\(291\) 0 0
\(292\) 12.3814i 0.724567i
\(293\) 12.2311 21.1849i 0.714550 1.23764i −0.248583 0.968610i \(-0.579965\pi\)
0.963133 0.269026i \(-0.0867017\pi\)
\(294\) 0 0
\(295\) 13.0606 + 22.6216i 0.760418 + 1.31708i
\(296\) 8.10950 4.68202i 0.471355 0.272137i
\(297\) 0 0
\(298\) 8.68202 15.0377i 0.502936 0.871111i
\(299\) −9.21130 + 15.9544i −0.532703 + 0.922670i
\(300\) 0 0
\(301\) 0 0
\(302\) −9.72787 5.61639i −0.559776 0.323187i
\(303\) 0 0
\(304\) 3.01701i 0.173037i
\(305\) 17.5644 + 10.1408i 1.00573 + 0.580660i
\(306\) 0 0
\(307\) 31.2223i 1.78195i −0.454053 0.890975i \(-0.650022\pi\)
0.454053 0.890975i \(-0.349978\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.31905 −0.472491
\(311\) −5.45501 9.44836i −0.309325 0.535767i 0.668889 0.743362i \(-0.266770\pi\)
−0.978215 + 0.207594i \(0.933437\pi\)
\(312\) 0 0
\(313\) 2.96532 + 1.71203i 0.167610 + 0.0967694i 0.581458 0.813576i \(-0.302482\pi\)
−0.413849 + 0.910346i \(0.635816\pi\)
\(314\) 13.8431 0.781210
\(315\) 0 0
\(316\) −3.03663 −0.170824
\(317\) 16.4953 + 9.52357i 0.926468 + 0.534897i 0.885693 0.464272i \(-0.153684\pi\)
0.0407755 + 0.999168i \(0.487017\pi\)
\(318\) 0 0
\(319\) 7.87817 + 13.6454i 0.441093 + 0.763995i
\(320\) −1.79035 −0.100084
\(321\) 0 0
\(322\) 0 0
\(323\) 11.0563i 0.615191i
\(324\) 0 0
\(325\) −7.60215 4.38910i −0.421692 0.243464i
\(326\) 4.33577i 0.240136i
\(327\) 0 0
\(328\) −6.99911 4.04094i −0.386461 0.223123i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.0366251 + 0.0634366i −0.00201310 + 0.00348679i −0.867030 0.498256i \(-0.833974\pi\)
0.865017 + 0.501742i \(0.167307\pi\)
\(332\) 7.00270 12.1290i 0.384323 0.665667i
\(333\) 0 0
\(334\) −10.7518 + 6.20756i −0.588313 + 0.339663i
\(335\) −0.510456 0.884136i −0.0278892 0.0483055i
\(336\) 0 0
\(337\) 1.11639 1.93364i 0.0608136 0.105332i −0.834016 0.551741i \(-0.813964\pi\)
0.894829 + 0.446408i \(0.147297\pi\)
\(338\) 10.9251i 0.594246i
\(339\) 0 0
\(340\) −6.56103 −0.355822
\(341\) −5.57943 9.66385i −0.302143 0.523327i
\(342\) 0 0
\(343\) 0 0
\(344\) 6.02973 3.48127i 0.325101 0.187697i
\(345\) 0 0
\(346\) 15.0846 8.70908i 0.810952 0.468203i
\(347\) 27.5751 15.9205i 1.48031 0.854656i 0.480556 0.876964i \(-0.340435\pi\)
0.999751 + 0.0223084i \(0.00710156\pi\)
\(348\) 0 0
\(349\) 12.7613 7.36772i 0.683095 0.394385i −0.117925 0.993022i \(-0.537624\pi\)
0.801020 + 0.598637i \(0.204291\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.20075 2.07976i −0.0640003 0.110852i
\(353\) 2.15957 0.114943 0.0574713 0.998347i \(-0.481696\pi\)
0.0574713 + 0.998347i \(0.481696\pi\)
\(354\) 0 0
\(355\) 10.6750i 0.566571i
\(356\) −1.87432 + 3.24641i −0.0993385 + 0.172059i
\(357\) 0 0
\(358\) −6.56103 11.3640i −0.346761 0.600608i
\(359\) −28.2712 + 16.3224i −1.49210 + 0.861463i −0.999959 0.00905364i \(-0.997118\pi\)
−0.492139 + 0.870517i \(0.663785\pi\)
\(360\) 0 0
\(361\) −4.94882 + 8.57161i −0.260464 + 0.451138i
\(362\) −6.67887 + 11.5681i −0.351034 + 0.608008i
\(363\) 0 0
\(364\) 0 0
\(365\) 19.1972 + 11.0835i 1.00483 + 0.580138i
\(366\) 0 0
\(367\) 29.7003i 1.55034i −0.631751 0.775171i \(-0.717664\pi\)
0.631751 0.775171i \(-0.282336\pi\)
\(368\) −3.26178 1.88319i −0.170032 0.0981682i
\(369\) 0 0
\(370\) 16.7649i 0.871566i
\(371\) 0 0
\(372\) 0 0
\(373\) −2.01672 −0.104422 −0.0522109 0.998636i \(-0.516627\pi\)
−0.0522109 + 0.998636i \(0.516627\pi\)
\(374\) −4.40035 7.62164i −0.227537 0.394105i
\(375\) 0 0
\(376\) 4.44794 + 2.56802i 0.229385 + 0.132436i
\(377\) 32.0921 1.65283
\(378\) 0 0
\(379\) −18.8709 −0.969332 −0.484666 0.874699i \(-0.661059\pi\)
−0.484666 + 0.874699i \(0.661059\pi\)
\(380\) 4.67784 + 2.70075i 0.239968 + 0.138546i
\(381\) 0 0
\(382\) −4.62666 8.01361i −0.236721 0.410012i
\(383\) 0.836511 0.0427437 0.0213719 0.999772i \(-0.493197\pi\)
0.0213719 + 0.999772i \(0.493197\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 24.5602i 1.25008i
\(387\) 0 0
\(388\) −4.77256 2.75544i −0.242290 0.139886i
\(389\) 24.8219i 1.25852i −0.777195 0.629260i \(-0.783358\pi\)
0.777195 0.629260i \(-0.216642\pi\)
\(390\) 0 0
\(391\) −11.9533 6.90127i −0.604507 0.349012i
\(392\) 0 0
\(393\) 0 0
\(394\) 6.24305 10.8133i 0.314520 0.544765i
\(395\) −2.71831 + 4.70825i −0.136773 + 0.236898i
\(396\) 0 0
\(397\) −2.62744 + 1.51695i −0.131867 + 0.0761336i −0.564482 0.825445i \(-0.690924\pi\)
0.432615 + 0.901579i \(0.357591\pi\)
\(398\) −0.0895727 0.155144i −0.00448987 0.00777669i
\(399\) 0 0
\(400\) 0.897324 1.55421i 0.0448662 0.0777105i
\(401\) 13.0771i 0.653038i 0.945191 + 0.326519i \(0.105876\pi\)
−0.945191 + 0.326519i \(0.894124\pi\)
\(402\) 0 0
\(403\) −22.7281 −1.13217
\(404\) 0.125162 + 0.216787i 0.00622705 + 0.0107856i
\(405\) 0 0
\(406\) 0 0
\(407\) 19.4750 11.2439i 0.965339 0.557339i
\(408\) 0 0
\(409\) 4.82124 2.78354i 0.238395 0.137637i −0.376044 0.926602i \(-0.622716\pi\)
0.614439 + 0.788965i \(0.289382\pi\)
\(410\) −12.5309 + 7.23469i −0.618855 + 0.357296i
\(411\) 0 0
\(412\) −0.145433 + 0.0839657i −0.00716496 + 0.00413669i
\(413\) 0 0
\(414\) 0 0
\(415\) −12.5373 21.7152i −0.615431 1.06596i
\(416\) −4.89133 −0.239817
\(417\) 0 0
\(418\) 7.24536i 0.354382i
\(419\) 8.19938 14.2017i 0.400566 0.693800i −0.593228 0.805034i \(-0.702147\pi\)
0.993794 + 0.111234i \(0.0354802\pi\)
\(420\) 0 0
\(421\) −7.72892 13.3869i −0.376684 0.652437i 0.613893 0.789389i \(-0.289603\pi\)
−0.990578 + 0.136952i \(0.956269\pi\)
\(422\) 13.0961 7.56103i 0.637508 0.368065i
\(423\) 0 0
\(424\) 0 0
\(425\) 3.28839 5.69566i 0.159510 0.276280i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.92024 3.99540i −0.334502 0.193125i
\(429\) 0 0
\(430\) 12.4654i 0.601134i
\(431\) −21.6737 12.5133i −1.04398 0.602744i −0.123024 0.992404i \(-0.539259\pi\)
−0.920959 + 0.389660i \(0.872593\pi\)
\(432\) 0 0
\(433\) 2.25168i 0.108209i −0.998535 0.0541044i \(-0.982770\pi\)
0.998535 0.0541044i \(-0.0172304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 18.9533 0.907700
\(437\) 5.68161 + 9.84084i 0.271788 + 0.470751i
\(438\) 0 0
\(439\) 16.2293 + 9.37000i 0.774583 + 0.447206i 0.834507 0.550997i \(-0.185752\pi\)
−0.0599239 + 0.998203i \(0.519086\pi\)
\(440\) −4.29953 −0.204972
\(441\) 0 0
\(442\) −17.9251 −0.852609
\(443\) −1.04314 0.602256i −0.0495610 0.0286141i 0.475015 0.879978i \(-0.342443\pi\)
−0.524576 + 0.851364i \(0.675776\pi\)
\(444\) 0 0
\(445\) 3.35568 + 5.81221i 0.159074 + 0.275525i
\(446\) 8.39524 0.397526
\(447\) 0 0
\(448\) 0 0
\(449\) 26.8022i 1.26487i −0.774612 0.632436i \(-0.782055\pi\)
0.774612 0.632436i \(-0.217945\pi\)
\(450\) 0 0
\(451\) −16.8084 9.70433i −0.791476 0.456959i
\(452\) 1.15953i 0.0545396i
\(453\) 0 0
\(454\) −2.10030 1.21261i −0.0985719 0.0569105i
\(455\) 0 0
\(456\) 0 0
\(457\) −6.92442 + 11.9934i −0.323911 + 0.561030i −0.981291 0.192529i \(-0.938331\pi\)
0.657381 + 0.753559i \(0.271664\pi\)
\(458\) −1.00987 + 1.74915i −0.0471883 + 0.0817326i
\(459\) 0 0
\(460\) −5.83973 + 3.37157i −0.272279 + 0.157200i
\(461\) 2.40241 + 4.16110i 0.111892 + 0.193802i 0.916533 0.399959i \(-0.130976\pi\)
−0.804641 + 0.593761i \(0.797642\pi\)
\(462\) 0 0
\(463\) 10.5194 18.2201i 0.488877 0.846760i −0.511041 0.859556i \(-0.670740\pi\)
0.999918 + 0.0127960i \(0.00407321\pi\)
\(464\) 6.56103i 0.304588i
\(465\) 0 0
\(466\) 12.7289 0.589656
\(467\) −2.91151 5.04288i −0.134729 0.233357i 0.790765 0.612120i \(-0.209683\pi\)
−0.925494 + 0.378763i \(0.876350\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.96337 4.59766i 0.367323 0.212074i
\(471\) 0 0
\(472\) −12.6353 + 7.29501i −0.581588 + 0.335780i
\(473\) 14.4804 8.36028i 0.665811 0.384406i
\(474\) 0 0
\(475\) −4.68907 + 2.70724i −0.215149 + 0.124217i
\(476\) 0 0
\(477\) 0 0
\(478\) −8.72474 15.1117i −0.399060 0.691193i
\(479\) −26.9561 −1.23166 −0.615828 0.787881i \(-0.711178\pi\)
−0.615828 + 0.787881i \(0.711178\pi\)
\(480\) 0 0
\(481\) 45.8026i 2.08842i
\(482\) 5.71659 9.90142i 0.260383 0.450997i
\(483\) 0 0
\(484\) 2.61639 + 4.53172i 0.118927 + 0.205987i
\(485\) −8.54455 + 4.93320i −0.387988 + 0.224005i
\(486\) 0 0
\(487\) 6.81338 11.8011i 0.308744 0.534760i −0.669344 0.742953i \(-0.733425\pi\)
0.978088 + 0.208193i \(0.0667581\pi\)
\(488\) −5.66414 + 9.81058i −0.256404 + 0.444104i
\(489\) 0 0
\(490\) 0 0
\(491\) 33.7430 + 19.4815i 1.52280 + 0.879188i 0.999637 + 0.0269544i \(0.00858088\pi\)
0.523162 + 0.852234i \(0.324752\pi\)
\(492\) 0 0
\(493\) 24.0440i 1.08289i
\(494\) 12.7801 + 7.37859i 0.575004 + 0.331979i
\(495\) 0 0
\(496\) 4.64661i 0.208639i
\(497\) 0 0
\(498\) 0 0
\(499\) 26.0097 1.16435 0.582176 0.813063i \(-0.302201\pi\)
0.582176 + 0.813063i \(0.302201\pi\)
\(500\) −6.08240 10.5350i −0.272013 0.471141i
\(501\) 0 0
\(502\) −23.6910 13.6780i −1.05738 0.610478i
\(503\) 10.5271 0.469378 0.234689 0.972070i \(-0.424593\pi\)
0.234689 + 0.972070i \(0.424593\pi\)
\(504\) 0 0
\(505\) 0.448168 0.0199432
\(506\) −7.83319 4.52249i −0.348228 0.201049i
\(507\) 0 0
\(508\) 0.700752 + 1.21374i 0.0310908 + 0.0538509i
\(509\) −0.938871 −0.0416147 −0.0208074 0.999784i \(-0.506624\pi\)
−0.0208074 + 0.999784i \(0.506624\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −3.02826 1.74837i −0.133571 0.0771172i
\(515\) 0.300656i 0.0132485i
\(516\) 0 0
\(517\) 10.6818 + 6.16711i 0.469783 + 0.271229i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.37859 + 7.58394i −0.192014 + 0.332578i
\(521\) 19.7527 34.2127i 0.865382 1.49889i −0.00128461 0.999999i \(-0.500409\pi\)
0.866667 0.498887i \(-0.166258\pi\)
\(522\) 0 0
\(523\) −21.0697 + 12.1646i −0.921315 + 0.531922i −0.884054 0.467384i \(-0.845197\pi\)
−0.0372609 + 0.999306i \(0.511863\pi\)
\(524\) 5.24589 + 9.08614i 0.229168 + 0.396930i
\(525\) 0 0
\(526\) −4.82174 + 8.35150i −0.210238 + 0.364143i
\(527\) 17.0283i 0.741763i
\(528\) 0 0
\(529\) 8.81436 0.383233
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −34.2349 + 19.7655i −1.48288 + 0.856141i
\(534\) 0 0
\(535\) −12.3896 + 7.15316i −0.535651 + 0.309258i
\(536\) 0.493834 0.285115i 0.0213304 0.0123151i
\(537\) 0 0
\(538\) 5.98517 3.45554i 0.258039 0.148979i
\(539\) 0 0
\(540\) 0 0
\(541\) −21.3640 37.0036i −0.918512 1.59091i −0.801677 0.597758i \(-0.796058\pi\)
−0.116835 0.993151i \(-0.537275\pi\)
\(542\) 20.6312 0.886187
\(543\) 0 0
\(544\) 3.66466i 0.157121i
\(545\) 16.9665 29.3869i 0.726767 1.25880i
\(546\) 0 0
\(547\) −12.2477 21.2136i −0.523672 0.907026i −0.999620 0.0275530i \(-0.991229\pi\)
0.475949 0.879473i \(-0.342105\pi\)
\(548\) −4.08812 + 2.36028i −0.174636 + 0.100826i
\(549\) 0 0
\(550\) 2.15493 3.73244i 0.0918864 0.159152i
\(551\) 9.89735 17.1427i 0.421641 0.730304i
\(552\) 0 0
\(553\) 0 0
\(554\) −13.4358 7.75718i −0.570834 0.329571i
\(555\) 0 0
\(556\) 2.36375i 0.100245i
\(557\) −2.20344 1.27216i −0.0933627 0.0539030i 0.452592 0.891718i \(-0.350499\pi\)
−0.545954 + 0.837815i \(0.683833\pi\)
\(558\) 0 0
\(559\) 34.0560i 1.44042i
\(560\) 0 0
\(561\) 0 0
\(562\) −13.5977 −0.573583
\(563\) −7.90707 13.6954i −0.333243 0.577194i 0.649902 0.760018i \(-0.274810\pi\)
−0.983146 + 0.182823i \(0.941476\pi\)
\(564\) 0 0
\(565\) 1.79783 + 1.03798i 0.0756354 + 0.0436681i
\(566\) −5.44783 −0.228990
\(567\) 0 0
\(568\) −5.96254 −0.250182
\(569\) −5.52793 3.19155i −0.231743 0.133797i 0.379633 0.925137i \(-0.376050\pi\)
−0.611376 + 0.791340i \(0.709384\pi\)
\(570\) 0 0
\(571\) 3.91188 + 6.77557i 0.163707 + 0.283549i 0.936195 0.351480i \(-0.114322\pi\)
−0.772488 + 0.635029i \(0.780988\pi\)
\(572\) −11.7465 −0.491148
\(573\) 0 0
\(574\) 0 0
\(575\) 6.75933i 0.281884i
\(576\) 0 0
\(577\) −12.4012 7.15986i −0.516270 0.298069i 0.219137 0.975694i \(-0.429676\pi\)
−0.735407 + 0.677625i \(0.763009\pi\)
\(578\) 3.57023i 0.148502i
\(579\) 0 0
\(580\) 10.1728 + 5.87327i 0.422403 + 0.243874i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −6.19070 + 10.7226i −0.256173 + 0.443705i
\(585\) 0 0
\(586\) 21.1849 12.2311i 0.875141 0.505263i
\(587\) −2.37575 4.11492i −0.0980577 0.169841i 0.812823 0.582511i \(-0.197930\pi\)
−0.910881 + 0.412670i \(0.864596\pi\)
\(588\) 0 0
\(589\) −7.00943 + 12.1407i −0.288819 + 0.500249i
\(590\) 26.1212i 1.07539i
\(591\) 0 0
\(592\) 9.36404 0.384860
\(593\) −1.79035 3.10098i −0.0735208 0.127342i 0.826921 0.562318i \(-0.190090\pi\)
−0.900442 + 0.434976i \(0.856757\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.0377 8.68202i 0.615968 0.355629i
\(597\) 0 0
\(598\) −15.9544 + 9.21130i −0.652426 + 0.376678i
\(599\) −13.0471 + 7.53277i −0.533091 + 0.307780i −0.742274 0.670096i \(-0.766253\pi\)
0.209183 + 0.977877i \(0.432920\pi\)
\(600\) 0 0
\(601\) 19.8704 11.4722i 0.810530 0.467960i −0.0366096 0.999330i \(-0.511656\pi\)
0.847140 + 0.531370i \(0.178322\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.61639 9.72787i −0.228528 0.395821i
\(605\) 9.36850 0.380884
\(606\) 0 0
\(607\) 24.4832i 0.993741i 0.867825 + 0.496870i \(0.165518\pi\)
−0.867825 + 0.496870i \(0.834482\pi\)
\(608\) −1.50851 + 2.61281i −0.0611780 + 0.105963i
\(609\) 0 0
\(610\) 10.1408 + 17.5644i 0.410589 + 0.711161i
\(611\) 21.7563 12.5610i 0.880167 0.508165i
\(612\) 0 0
\(613\) 0.440043 0.762177i 0.0177732 0.0307840i −0.857002 0.515313i \(-0.827676\pi\)
0.874775 + 0.484529i \(0.161009\pi\)
\(614\) 15.6111 27.0393i 0.630014 1.09122i
\(615\) 0 0
\(616\) 0 0
\(617\) 11.7607 + 6.79005i 0.473468 + 0.273357i 0.717690 0.696362i \(-0.245199\pi\)
−0.244222 + 0.969719i \(0.578533\pi\)
\(618\) 0 0
\(619\) 35.4869i 1.42634i 0.700992 + 0.713169i \(0.252741\pi\)
−0.700992 + 0.713169i \(0.747259\pi\)
\(620\) −7.20451 4.15953i −0.289340 0.167051i
\(621\) 0 0
\(622\) 10.9100i 0.437452i
\(623\) 0 0
\(624\) 0 0
\(625\) −12.8060 −0.512240
\(626\) 1.71203 + 2.96532i 0.0684263 + 0.118518i
\(627\) 0 0
\(628\) 11.9885 + 6.92154i 0.478391 + 0.276199i
\(629\) 34.3161 1.36827
\(630\) 0 0
\(631\) 26.9822 1.07415 0.537073 0.843536i \(-0.319530\pi\)
0.537073 + 0.843536i \(0.319530\pi\)
\(632\) −2.62979 1.51831i −0.104608 0.0603952i
\(633\) 0 0
\(634\) 9.52357 + 16.4953i 0.378229 + 0.655112i
\(635\) 2.50918 0.0995739
\(636\) 0 0
\(637\) 0 0
\(638\) 15.7563i 0.623800i
\(639\) 0 0
\(640\) −1.55049 0.895175i −0.0612884 0.0353849i
\(641\) 1.07708i 0.0425420i −0.999774 0.0212710i \(-0.993229\pi\)
0.999774 0.0212710i \(-0.00677128\pi\)
\(642\) 0 0
\(643\) −33.3126 19.2330i −1.31372 0.758477i −0.331010 0.943627i \(-0.607389\pi\)
−0.982710 + 0.185150i \(0.940723\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.52817 + 9.57507i −0.217503 + 0.376726i
\(647\) 4.47605 7.75275i 0.175972 0.304792i −0.764525 0.644594i \(-0.777027\pi\)
0.940497 + 0.339802i \(0.110360\pi\)
\(648\) 0 0
\(649\) −30.3438 + 17.5190i −1.19110 + 0.687680i
\(650\) −4.38910 7.60215i −0.172155 0.298181i
\(651\) 0 0
\(652\) −2.16789 + 3.75489i −0.0849010 + 0.147053i
\(653\) 11.3846i 0.445513i −0.974874 0.222757i \(-0.928494\pi\)
0.974874 0.222757i \(-0.0715055\pi\)
\(654\) 0 0
\(655\) 18.7839 0.733949
\(656\) −4.04094 6.99911i −0.157772 0.273269i
\(657\) 0 0
\(658\) 0 0
\(659\) −31.4373 + 18.1503i −1.22462 + 0.707036i −0.965900 0.258915i \(-0.916635\pi\)
−0.258723 + 0.965952i \(0.583302\pi\)
\(660\) 0 0
\(661\) −31.2425 + 18.0379i −1.21519 + 0.701593i −0.963886 0.266315i \(-0.914194\pi\)
−0.251308 + 0.967907i \(0.580861\pi\)
\(662\) −0.0634366 + 0.0366251i −0.00246553 + 0.00142348i
\(663\) 0 0
\(664\) 12.1290 7.00270i 0.470698 0.271757i
\(665\) 0 0
\(666\) 0 0
\(667\) 12.3557 + 21.4007i 0.478414 + 0.828637i
\(668\) −12.4151 −0.480355
\(669\) 0 0
\(670\) 1.02091i 0.0394413i
\(671\) −13.6025 + 23.5602i −0.525117 + 0.909530i
\(672\) 0 0
\(673\) 4.78512 + 8.28806i 0.184453 + 0.319481i 0.943392 0.331680i \(-0.107615\pi\)
−0.758939 + 0.651161i \(0.774282\pi\)
\(674\) 1.93364 1.11639i 0.0744811 0.0430017i
\(675\) 0 0
\(676\) −5.46254 + 9.46139i −0.210098 + 0.363900i
\(677\) 7.81408 13.5344i 0.300320 0.520169i −0.675889 0.737004i \(-0.736240\pi\)
0.976208 + 0.216835i \(0.0695733\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −5.68202 3.28052i −0.217896 0.125802i
\(681\) 0 0
\(682\) 11.1589i 0.427294i
\(683\) 9.63996 + 5.56563i 0.368863 + 0.212963i 0.672961 0.739678i \(-0.265022\pi\)
−0.304099 + 0.952640i \(0.598355\pi\)
\(684\) 0 0
\(685\) 8.45145i 0.322913i
\(686\) 0 0
\(687\) 0 0
\(688\) 6.96254 0.265444
\(689\) 0 0
\(690\) 0 0
\(691\) 2.61903 + 1.51210i 0.0996324 + 0.0575228i 0.548988 0.835830i \(-0.315013\pi\)
−0.449356 + 0.893353i \(0.648346\pi\)
\(692\) 17.4182 0.662139
\(693\) 0 0
\(694\) 31.8409 1.20867
\(695\) 3.66497 + 2.11597i 0.139020 + 0.0802633i
\(696\) 0 0
\(697\) −14.8087 25.6494i −0.560919 0.971540i
\(698\) 14.7354 0.557745
\(699\) 0 0
\(700\) 0 0
\(701\) 50.1486i 1.89409i −0.321103 0.947044i \(-0.604054\pi\)
0.321103 0.947044i \(-0.395946\pi\)
\(702\) 0 0
\(703\) −24.4664 14.1257i −0.922769 0.532761i
\(704\) 2.40150i 0.0905101i
\(705\) 0 0
\(706\) 1.87025 + 1.07979i 0.0703876 + 0.0406383i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.80385 3.12436i 0.0677449 0.117338i −0.830163 0.557520i \(-0.811753\pi\)
0.897908 + 0.440183i \(0.145086\pi\)
\(710\) −5.33751 + 9.24484i −0.200313 + 0.346953i
\(711\) 0 0
\(712\) −3.24641 + 1.87432i −0.121664 + 0.0702429i
\(713\) −8.75046 15.1562i −0.327707 0.567605i
\(714\) 0 0
\(715\) −10.5152 + 18.2129i −0.393246 + 0.681123i
\(716\) 13.1221i 0.490395i
\(717\) 0 0
\(718\) −32.6448 −1.21829
\(719\) 17.1580 + 29.7186i 0.639887 + 1.10832i 0.985457 + 0.169924i \(0.0543521\pi\)
−0.345571 + 0.938393i \(0.612315\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8.57161 + 4.94882i −0.319002 + 0.184176i
\(723\) 0 0
\(724\) −11.5681 + 6.67887i −0.429927 + 0.248218i
\(725\) −10.1972 + 5.88737i −0.378716 + 0.218651i
\(726\) 0 0
\(727\) −19.4757 + 11.2443i −0.722315 + 0.417029i −0.815604 0.578610i \(-0.803595\pi\)
0.0932892 + 0.995639i \(0.470262\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 11.0835 + 19.1972i 0.410220 + 0.710521i
\(731\) 25.5154 0.943720
\(732\) 0 0
\(733\) 31.1845i 1.15182i 0.817512 + 0.575912i \(0.195353\pi\)
−0.817512 + 0.575912i \(0.804647\pi\)
\(734\) 14.8501 25.7212i 0.548129 0.949387i
\(735\) 0 0
\(736\) −1.88319 3.26178i −0.0694154 0.120231i
\(737\) 1.18595 0.684706i 0.0436849 0.0252215i
\(738\) 0 0
\(739\) −2.04314 + 3.53882i −0.0751581 + 0.130178i −0.901155 0.433497i \(-0.857279\pi\)
0.825997 + 0.563675i \(0.190613\pi\)
\(740\) 8.38245 14.5188i 0.308145 0.533723i
\(741\) 0 0
\(742\) 0 0
\(743\) 1.78246 + 1.02910i 0.0653921 + 0.0377542i 0.532340 0.846531i \(-0.321313\pi\)
−0.466947 + 0.884285i \(0.654646\pi\)
\(744\) 0 0
\(745\) 31.0877i 1.13897i
\(746\) −1.74653 1.00836i −0.0639450 0.0369187i
\(747\) 0 0
\(748\) 8.80071i 0.321786i
\(749\) 0 0
\(750\) 0 0
\(751\) 23.8105 0.868859 0.434429 0.900706i \(-0.356950\pi\)
0.434429 + 0.900706i \(0.356950\pi\)
\(752\) 2.56802 + 4.44794i 0.0936461 + 0.162200i
\(753\) 0 0
\(754\) 27.7926 + 16.0461i 1.01215 + 0.584363i
\(755\) −20.1106 −0.731900
\(756\) 0 0
\(757\) 10.0754 0.366197 0.183098 0.983095i \(-0.441387\pi\)
0.183098 + 0.983095i \(0.441387\pi\)
\(758\) −16.3427 9.43544i −0.593592 0.342711i
\(759\) 0 0
\(760\) 2.70075 + 4.67784i 0.0979666 + 0.169683i
\(761\) −27.8735 −1.01041 −0.505207 0.862998i \(-0.668584\pi\)
−0.505207 + 0.862998i \(0.668584\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 9.25333i 0.334774i
\(765\) 0 0
\(766\) 0.724440 + 0.418256i 0.0261751 + 0.0151122i
\(767\) 71.3645i 2.57682i
\(768\) 0 0
\(769\) 6.21166 + 3.58631i 0.223998 + 0.129326i 0.607800 0.794090i \(-0.292052\pi\)
−0.383802 + 0.923415i \(0.625385\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.2801 + 21.2698i −0.441970 + 0.765515i
\(773\) 1.07077 1.85462i 0.0385128 0.0667061i −0.846127 0.532982i \(-0.821071\pi\)
0.884639 + 0.466276i \(0.154405\pi\)
\(774\) 0 0
\(775\) 7.22181 4.16951i 0.259415 0.149773i
\(776\) −2.75544 4.77256i −0.0989144 0.171325i
\(777\) 0 0
\(778\) 12.4109 21.4964i 0.444954 0.770682i
\(779\) 24.3831i 0.873615i
\(780\) 0 0
\(781\) −14.3191 −0.512376
\(782\) −6.90127 11.9533i −0.246789 0.427451i
\(783\) 0 0
\(784\) 0 0
\(785\) 21.4635 12.3920i 0.766066 0.442288i
\(786\) 0 0
\(787\) 15.8961 9.17759i 0.566633 0.327146i −0.189170 0.981944i \(-0.560580\pi\)
0.755804 + 0.654798i \(0.227247\pi\)
\(788\) 10.8133 6.24305i 0.385207 0.222400i
\(789\) 0 0
\(790\) −4.70825 + 2.71831i −0.167512 + 0.0967131i
\(791\) 0 0
\(792\) 0 0
\(793\) 27.7052 + 47.9868i 0.983839 + 1.70406i
\(794\) −3.03390 −0.107669
\(795\) 0