Properties

Label 1323.2.g.f.361.3
Level $1323$
Weight $2$
Character 1323.361
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.3
Root \(0.247934 - 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.f.667.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} -3.69258 q^{5} -1.86155 q^{8} +O(q^{10})\) \(q+(-0.247934 + 0.429435i) q^{2} +(0.877057 + 1.51911i) q^{4} -3.69258 q^{5} -1.86155 q^{8} +(0.915516 - 1.58572i) q^{10} +0.892568 q^{11} +(-0.598355 + 1.03638i) q^{13} +(-1.29257 + 2.23880i) q^{16} +(-0.124991 + 0.216492i) q^{17} +(-1.40414 - 2.43204i) q^{19} +(-3.23860 - 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} -2.47772 q^{23} +8.63514 q^{25} +(-0.296705 - 0.513909i) q^{26} +(-2.07128 - 3.58755i) q^{29} +(1.79257 + 3.10483i) q^{31} +(-2.50249 - 4.33444i) q^{32} +(-0.0619793 - 0.107351i) q^{34} +(-2.36568 - 4.09747i) q^{37} +1.39253 q^{38} +6.87391 q^{40} +(-2.39093 + 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(0.782834 + 1.35591i) q^{44} +(0.614310 - 1.06402i) q^{46} +(5.08653 - 8.81013i) q^{47} +(-2.14095 + 3.70823i) q^{50} -2.09917 q^{52} +(4.94465 - 8.56438i) q^{53} -3.29588 q^{55} +2.05416 q^{58} +(-0.906186 - 1.56956i) q^{59} +(5.40205 - 9.35663i) q^{61} -1.77776 q^{62} -2.68848 q^{64} +(2.20948 - 3.82692i) q^{65} +(-0.514685 - 0.891460i) q^{67} -0.438499 q^{68} +4.94533 q^{71} +(0.915262 - 1.58528i) q^{73} +2.34613 q^{74} +(2.46302 - 4.26607i) q^{76} +(0.899562 - 1.55809i) q^{79} +(4.77293 - 8.26696i) q^{80} +(-1.18559 - 2.05350i) q^{82} +(6.16156 + 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +4.94806 q^{86} -1.66156 q^{88} +(-1.20370 - 2.08488i) q^{89} +(-2.17310 - 3.76392i) q^{92} +(2.52225 + 4.36867i) q^{94} +(5.18489 + 8.98049i) q^{95} +(-5.52210 - 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 4q^{4} - 8q^{5} + 6q^{8} + 7q^{10} + 8q^{11} + 8q^{13} + 2q^{16} + 12q^{17} - q^{19} + 5q^{20} - q^{22} + 6q^{23} + 2q^{25} + 11q^{26} - 7q^{29} + 3q^{31} + 2q^{32} - 3q^{34} - 40q^{38} - 6q^{40} + 5q^{41} - 7q^{43} + 10q^{44} + 3q^{46} + 27q^{47} - 19q^{50} - 20q^{52} + 21q^{53} - 4q^{55} + 20q^{58} + 30q^{59} + 14q^{61} - 12q^{62} - 50q^{64} + 11q^{65} - 2q^{67} - 54q^{68} + 6q^{71} - 15q^{73} - 72q^{74} - 5q^{76} - 4q^{79} + 20q^{80} + 5q^{82} + 9q^{83} - 6q^{85} - 16q^{86} + 36q^{88} + 28q^{89} - 27q^{92} + 3q^{94} + 14q^{95} + 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.247934 + 0.429435i −0.175316 + 0.303656i −0.940271 0.340428i \(-0.889428\pi\)
0.764955 + 0.644084i \(0.222761\pi\)
\(3\) 0 0
\(4\) 0.877057 + 1.51911i 0.438529 + 0.759554i
\(5\) −3.69258 −1.65137 −0.825686 0.564130i \(-0.809212\pi\)
−0.825686 + 0.564130i \(0.809212\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.86155 −0.658156
\(9\) 0 0
\(10\) 0.915516 1.58572i 0.289512 0.501449i
\(11\) 0.892568 0.269119 0.134560 0.990905i \(-0.457038\pi\)
0.134560 + 0.990905i \(0.457038\pi\)
\(12\) 0 0
\(13\) −0.598355 + 1.03638i −0.165954 + 0.287441i −0.936994 0.349346i \(-0.886404\pi\)
0.771040 + 0.636787i \(0.219737\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.29257 + 2.23880i −0.323143 + 0.559701i
\(17\) −0.124991 + 0.216492i −0.0303149 + 0.0525069i −0.880785 0.473517i \(-0.842984\pi\)
0.850470 + 0.526024i \(0.176318\pi\)
\(18\) 0 0
\(19\) −1.40414 2.43204i −0.322131 0.557948i 0.658796 0.752321i \(-0.271066\pi\)
−0.980928 + 0.194374i \(0.937733\pi\)
\(20\) −3.23860 5.60943i −0.724174 1.25431i
\(21\) 0 0
\(22\) −0.221298 + 0.383300i −0.0471809 + 0.0817198i
\(23\) −2.47772 −0.516639 −0.258320 0.966059i \(-0.583169\pi\)
−0.258320 + 0.966059i \(0.583169\pi\)
\(24\) 0 0
\(25\) 8.63514 1.72703
\(26\) −0.296705 0.513909i −0.0581887 0.100786i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.07128 3.58755i −0.384626 0.666192i 0.607091 0.794632i \(-0.292336\pi\)
−0.991717 + 0.128440i \(0.959003\pi\)
\(30\) 0 0
\(31\) 1.79257 + 3.10483i 0.321956 + 0.557644i 0.980892 0.194555i \(-0.0623264\pi\)
−0.658936 + 0.752199i \(0.728993\pi\)
\(32\) −2.50249 4.33444i −0.442382 0.766229i
\(33\) 0 0
\(34\) −0.0619793 0.107351i −0.0106294 0.0184106i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.36568 4.09747i −0.388915 0.673621i 0.603389 0.797447i \(-0.293817\pi\)
−0.992304 + 0.123826i \(0.960483\pi\)
\(38\) 1.39253 0.225899
\(39\) 0 0
\(40\) 6.87391 1.08686
\(41\) −2.39093 + 4.14121i −0.373400 + 0.646748i −0.990086 0.140461i \(-0.955142\pi\)
0.616686 + 0.787209i \(0.288475\pi\)
\(42\) 0 0
\(43\) −4.98928 8.64169i −0.760859 1.31785i −0.942408 0.334464i \(-0.891445\pi\)
0.181550 0.983382i \(-0.441889\pi\)
\(44\) 0.782834 + 1.35591i 0.118017 + 0.204411i
\(45\) 0 0
\(46\) 0.614310 1.06402i 0.0905751 0.156881i
\(47\) 5.08653 8.81013i 0.741947 1.28509i −0.209661 0.977774i \(-0.567236\pi\)
0.951608 0.307316i \(-0.0994308\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.14095 + 3.70823i −0.302776 + 0.524423i
\(51\) 0 0
\(52\) −2.09917 −0.291102
\(53\) 4.94465 8.56438i 0.679199 1.17641i −0.296023 0.955181i \(-0.595661\pi\)
0.975222 0.221227i \(-0.0710061\pi\)
\(54\) 0 0
\(55\) −3.29588 −0.444416
\(56\) 0 0
\(57\) 0 0
\(58\) 2.05416 0.269724
\(59\) −0.906186 1.56956i −0.117975 0.204339i 0.800990 0.598678i \(-0.204307\pi\)
−0.918965 + 0.394339i \(0.870974\pi\)
\(60\) 0 0
\(61\) 5.40205 9.35663i 0.691662 1.19799i −0.279631 0.960108i \(-0.590212\pi\)
0.971293 0.237886i \(-0.0764546\pi\)
\(62\) −1.77776 −0.225776
\(63\) 0 0
\(64\) −2.68848 −0.336060
\(65\) 2.20948 3.82692i 0.274052 0.474671i
\(66\) 0 0
\(67\) −0.514685 0.891460i −0.0628787 0.108909i 0.832872 0.553465i \(-0.186695\pi\)
−0.895751 + 0.444556i \(0.853361\pi\)
\(68\) −0.438499 −0.0531758
\(69\) 0 0
\(70\) 0 0
\(71\) 4.94533 0.586903 0.293451 0.955974i \(-0.405196\pi\)
0.293451 + 0.955974i \(0.405196\pi\)
\(72\) 0 0
\(73\) 0.915262 1.58528i 0.107123 0.185543i −0.807480 0.589894i \(-0.799169\pi\)
0.914604 + 0.404351i \(0.132503\pi\)
\(74\) 2.34613 0.272732
\(75\) 0 0
\(76\) 2.46302 4.26607i 0.282527 0.489352i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.899562 1.55809i 0.101209 0.175298i −0.810974 0.585082i \(-0.801062\pi\)
0.912183 + 0.409783i \(0.134396\pi\)
\(80\) 4.77293 8.26696i 0.533630 0.924274i
\(81\) 0 0
\(82\) −1.18559 2.05350i −0.130926 0.226771i
\(83\) 6.16156 + 10.6721i 0.676319 + 1.17142i 0.976082 + 0.217405i \(0.0697591\pi\)
−0.299763 + 0.954014i \(0.596908\pi\)
\(84\) 0 0
\(85\) 0.461541 0.799412i 0.0500611 0.0867084i
\(86\) 4.94806 0.533563
\(87\) 0 0
\(88\) −1.66156 −0.177123
\(89\) −1.20370 2.08488i −0.127592 0.220997i 0.795151 0.606412i \(-0.207392\pi\)
−0.922743 + 0.385415i \(0.874058\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.17310 3.76392i −0.226561 0.392416i
\(93\) 0 0
\(94\) 2.52225 + 4.36867i 0.260150 + 0.450593i
\(95\) 5.18489 + 8.98049i 0.531958 + 0.921379i
\(96\) 0 0
\(97\) −5.52210 9.56456i −0.560684 0.971134i −0.997437 0.0715522i \(-0.977205\pi\)
0.436752 0.899582i \(-0.356129\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 7.57351 + 13.1177i 0.757351 + 1.31177i
\(101\) −2.59964 −0.258674 −0.129337 0.991601i \(-0.541285\pi\)
−0.129337 + 0.991601i \(0.541285\pi\)
\(102\) 0 0
\(103\) −9.71155 −0.956908 −0.478454 0.878113i \(-0.658803\pi\)
−0.478454 + 0.878113i \(0.658803\pi\)
\(104\) 1.11387 1.92927i 0.109224 0.189181i
\(105\) 0 0
\(106\) 2.45189 + 4.24680i 0.238149 + 0.412486i
\(107\) 5.45025 + 9.44012i 0.526896 + 0.912610i 0.999509 + 0.0313403i \(0.00997757\pi\)
−0.472613 + 0.881270i \(0.656689\pi\)
\(108\) 0 0
\(109\) −1.06096 + 1.83764i −0.101622 + 0.176014i −0.912353 0.409404i \(-0.865737\pi\)
0.810731 + 0.585419i \(0.199070\pi\)
\(110\) 0.817161 1.41536i 0.0779132 0.134950i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.91318 + 13.7060i −0.744409 + 1.28935i 0.206061 + 0.978539i \(0.433935\pi\)
−0.950470 + 0.310816i \(0.899398\pi\)
\(114\) 0 0
\(115\) 9.14916 0.853164
\(116\) 3.63325 6.29298i 0.337339 0.584289i
\(117\) 0 0
\(118\) 0.898698 0.0827318
\(119\) 0 0
\(120\) 0 0
\(121\) −10.2033 −0.927575
\(122\) 2.67871 + 4.63966i 0.242519 + 0.420055i
\(123\) 0 0
\(124\) −3.14438 + 5.44623i −0.282374 + 0.489086i
\(125\) −13.4230 −1.20059
\(126\) 0 0
\(127\) −1.26946 −0.112647 −0.0563233 0.998413i \(-0.517938\pi\)
−0.0563233 + 0.998413i \(0.517938\pi\)
\(128\) 5.67155 9.82342i 0.501299 0.868275i
\(129\) 0 0
\(130\) 1.09561 + 1.89765i 0.0960912 + 0.166435i
\(131\) −15.0289 −1.31308 −0.656540 0.754291i \(-0.727981\pi\)
−0.656540 + 0.754291i \(0.727981\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.510432 0.0440946
\(135\) 0 0
\(136\) 0.232677 0.403009i 0.0199519 0.0345577i
\(137\) 0.488493 0.0417347 0.0208674 0.999782i \(-0.493357\pi\)
0.0208674 + 0.999782i \(0.493357\pi\)
\(138\) 0 0
\(139\) 4.93487 8.54745i 0.418570 0.724985i −0.577226 0.816585i \(-0.695865\pi\)
0.995796 + 0.0915997i \(0.0291980\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.22612 + 2.12370i −0.102893 + 0.178217i
\(143\) −0.534073 + 0.925042i −0.0446614 + 0.0773559i
\(144\) 0 0
\(145\) 7.64835 + 13.2473i 0.635161 + 1.10013i
\(146\) 0.453849 + 0.786090i 0.0375609 + 0.0650573i
\(147\) 0 0
\(148\) 4.14967 7.18744i 0.341101 0.590804i
\(149\) −21.0240 −1.72235 −0.861175 0.508309i \(-0.830271\pi\)
−0.861175 + 0.508309i \(0.830271\pi\)
\(150\) 0 0
\(151\) 1.49838 0.121937 0.0609683 0.998140i \(-0.480581\pi\)
0.0609683 + 0.998140i \(0.480581\pi\)
\(152\) 2.61387 + 4.52735i 0.212013 + 0.367217i
\(153\) 0 0
\(154\) 0 0
\(155\) −6.61922 11.4648i −0.531669 0.920877i
\(156\) 0 0
\(157\) −8.33982 14.4450i −0.665590 1.15284i −0.979125 0.203259i \(-0.934847\pi\)
0.313535 0.949577i \(-0.398487\pi\)
\(158\) 0.446064 + 0.772606i 0.0354870 + 0.0614652i
\(159\) 0 0
\(160\) 9.24065 + 16.0053i 0.730538 + 1.26533i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.34135 5.78738i −0.261714 0.453303i 0.704983 0.709224i \(-0.250954\pi\)
−0.966698 + 0.255921i \(0.917621\pi\)
\(164\) −8.38793 −0.654987
\(165\) 0 0
\(166\) −6.11064 −0.474278
\(167\) 8.81549 15.2689i 0.682163 1.18154i −0.292156 0.956371i \(-0.594373\pi\)
0.974319 0.225170i \(-0.0722939\pi\)
\(168\) 0 0
\(169\) 5.78394 + 10.0181i 0.444919 + 0.770622i
\(170\) 0.228863 + 0.396403i 0.0175530 + 0.0304027i
\(171\) 0 0
\(172\) 8.75178 15.1585i 0.667317 1.15583i
\(173\) 1.94342 3.36611i 0.147756 0.255920i −0.782642 0.622472i \(-0.786128\pi\)
0.930398 + 0.366552i \(0.119462\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.15371 + 1.99829i −0.0869642 + 0.150626i
\(177\) 0 0
\(178\) 1.19376 0.0894759
\(179\) −3.66758 + 6.35244i −0.274128 + 0.474804i −0.969915 0.243445i \(-0.921723\pi\)
0.695787 + 0.718248i \(0.255056\pi\)
\(180\) 0 0
\(181\) −11.2566 −0.836693 −0.418346 0.908288i \(-0.637390\pi\)
−0.418346 + 0.908288i \(0.637390\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.61238 0.340029
\(185\) 8.73545 + 15.1302i 0.642243 + 1.11240i
\(186\) 0 0
\(187\) −0.111563 + 0.193234i −0.00815833 + 0.0141306i
\(188\) 17.8447 1.30146
\(189\) 0 0
\(190\) −5.14204 −0.373043
\(191\) −11.9230 + 20.6512i −0.862715 + 1.49427i 0.00658302 + 0.999978i \(0.497905\pi\)
−0.869298 + 0.494288i \(0.835429\pi\)
\(192\) 0 0
\(193\) −2.96728 5.13948i −0.213589 0.369948i 0.739246 0.673436i \(-0.235182\pi\)
−0.952835 + 0.303488i \(0.901849\pi\)
\(194\) 5.47647 0.393188
\(195\) 0 0
\(196\) 0 0
\(197\) 15.4682 1.10206 0.551032 0.834484i \(-0.314234\pi\)
0.551032 + 0.834484i \(0.314234\pi\)
\(198\) 0 0
\(199\) −7.74818 + 13.4202i −0.549254 + 0.951336i 0.449072 + 0.893496i \(0.351755\pi\)
−0.998326 + 0.0578402i \(0.981579\pi\)
\(200\) −16.0747 −1.13665
\(201\) 0 0
\(202\) 0.644540 1.11638i 0.0453497 0.0785480i
\(203\) 0 0
\(204\) 0 0
\(205\) 8.82870 15.2917i 0.616623 1.06802i
\(206\) 2.40783 4.17048i 0.167761 0.290571i
\(207\) 0 0
\(208\) −1.54684 2.67920i −0.107254 0.185769i
\(209\) −1.25329 2.17076i −0.0866918 0.150155i
\(210\) 0 0
\(211\) 0.771898 1.33697i 0.0531397 0.0920406i −0.838232 0.545314i \(-0.816410\pi\)
0.891372 + 0.453273i \(0.149744\pi\)
\(212\) 17.3469 1.19139
\(213\) 0 0
\(214\) −5.40522 −0.369493
\(215\) 18.4233 + 31.9101i 1.25646 + 2.17625i
\(216\) 0 0
\(217\) 0 0
\(218\) −0.526098 0.911229i −0.0356319 0.0617162i
\(219\) 0 0
\(220\) −2.89068 5.00680i −0.194889 0.337558i
\(221\) −0.149579 0.259078i −0.0100617 0.0174275i
\(222\) 0 0
\(223\) 2.72171 + 4.71414i 0.182259 + 0.315682i 0.942649 0.333784i \(-0.108326\pi\)
−0.760390 + 0.649466i \(0.774992\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.92389 6.79638i −0.261014 0.452089i
\(227\) −16.0764 −1.06703 −0.533513 0.845792i \(-0.679128\pi\)
−0.533513 + 0.845792i \(0.679128\pi\)
\(228\) 0 0
\(229\) 9.96840 0.658730 0.329365 0.944203i \(-0.393165\pi\)
0.329365 + 0.944203i \(0.393165\pi\)
\(230\) −2.26839 + 3.92897i −0.149573 + 0.259068i
\(231\) 0 0
\(232\) 3.85578 + 6.67840i 0.253144 + 0.438458i
\(233\) −8.27045 14.3248i −0.541815 0.938451i −0.998800 0.0489765i \(-0.984404\pi\)
0.456985 0.889474i \(-0.348929\pi\)
\(234\) 0 0
\(235\) −18.7824 + 32.5321i −1.22523 + 2.12216i
\(236\) 1.58955 2.75319i 0.103471 0.179217i
\(237\) 0 0
\(238\) 0 0
\(239\) 11.0119 19.0732i 0.712303 1.23375i −0.251687 0.967809i \(-0.580985\pi\)
0.963990 0.265937i \(-0.0856813\pi\)
\(240\) 0 0
\(241\) −16.7201 −1.07703 −0.538517 0.842615i \(-0.681015\pi\)
−0.538517 + 0.842615i \(0.681015\pi\)
\(242\) 2.52975 4.38166i 0.162619 0.281664i
\(243\) 0 0
\(244\) 18.9516 1.21325
\(245\) 0 0
\(246\) 0 0
\(247\) 3.36069 0.213836
\(248\) −3.33696 5.77978i −0.211897 0.367017i
\(249\) 0 0
\(250\) 3.32803 5.76432i 0.210483 0.364568i
\(251\) −8.53099 −0.538471 −0.269236 0.963074i \(-0.586771\pi\)
−0.269236 + 0.963074i \(0.586771\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) 0.314743 0.545151i 0.0197488 0.0342058i
\(255\) 0 0
\(256\) 0.123861 + 0.214533i 0.00774131 + 0.0134083i
\(257\) −17.1197 −1.06790 −0.533950 0.845516i \(-0.679293\pi\)
−0.533950 + 0.845516i \(0.679293\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.75135 0.480718
\(261\) 0 0
\(262\) 3.72617 6.45392i 0.230204 0.398725i
\(263\) −20.5527 −1.26733 −0.633666 0.773607i \(-0.718451\pi\)
−0.633666 + 0.773607i \(0.718451\pi\)
\(264\) 0 0
\(265\) −18.2585 + 31.6246i −1.12161 + 1.94269i
\(266\) 0 0
\(267\) 0 0
\(268\) 0.902816 1.56372i 0.0551483 0.0955196i
\(269\) 9.92267 17.1866i 0.604996 1.04788i −0.387057 0.922056i \(-0.626508\pi\)
0.992052 0.125827i \(-0.0401585\pi\)
\(270\) 0 0
\(271\) −5.32056 9.21548i −0.323201 0.559801i 0.657946 0.753065i \(-0.271426\pi\)
−0.981147 + 0.193265i \(0.938092\pi\)
\(272\) −0.323121 0.559663i −0.0195921 0.0339345i
\(273\) 0 0
\(274\) −0.121114 + 0.209776i −0.00731676 + 0.0126730i
\(275\) 7.70745 0.464777
\(276\) 0 0
\(277\) −24.8813 −1.49497 −0.747487 0.664276i \(-0.768740\pi\)
−0.747487 + 0.664276i \(0.768740\pi\)
\(278\) 2.44705 + 4.23841i 0.146764 + 0.254203i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.83733 + 11.8426i 0.407881 + 0.706470i 0.994652 0.103282i \(-0.0329346\pi\)
−0.586771 + 0.809753i \(0.699601\pi\)
\(282\) 0 0
\(283\) 3.16089 + 5.47483i 0.187896 + 0.325445i 0.944548 0.328372i \(-0.106500\pi\)
−0.756653 + 0.653817i \(0.773167\pi\)
\(284\) 4.33734 + 7.51249i 0.257374 + 0.445784i
\(285\) 0 0
\(286\) −0.264830 0.458699i −0.0156597 0.0271234i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.46875 + 14.6683i 0.498162 + 0.862842i
\(290\) −7.58515 −0.445415
\(291\) 0 0
\(292\) 3.21095 0.187907
\(293\) −1.31508 + 2.27778i −0.0768277 + 0.133069i −0.901880 0.431987i \(-0.857812\pi\)
0.825052 + 0.565057i \(0.191146\pi\)
\(294\) 0 0
\(295\) 3.34616 + 5.79573i 0.194821 + 0.337440i
\(296\) 4.40382 + 7.62764i 0.255967 + 0.443348i
\(297\) 0 0
\(298\) 5.21256 9.02841i 0.301955 0.523002i
\(299\) 1.48255 2.56786i 0.0857384 0.148503i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.371500 + 0.643457i −0.0213774 + 0.0370268i
\(303\) 0 0
\(304\) 7.25980 0.416378
\(305\) −19.9475 + 34.5501i −1.14219 + 1.97833i
\(306\) 0 0
\(307\) 2.79496 0.159517 0.0797583 0.996814i \(-0.474585\pi\)
0.0797583 + 0.996814i \(0.474585\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.56452 0.372840
\(311\) 7.55013 + 13.0772i 0.428129 + 0.741541i 0.996707 0.0810885i \(-0.0258396\pi\)
−0.568578 + 0.822629i \(0.692506\pi\)
\(312\) 0 0
\(313\) −12.7392 + 22.0650i −0.720064 + 1.24719i 0.240910 + 0.970548i \(0.422554\pi\)
−0.960974 + 0.276640i \(0.910779\pi\)
\(314\) 8.27090 0.466754
\(315\) 0 0
\(316\) 3.15587 0.177531
\(317\) 16.2605 28.1639i 0.913278 1.58184i 0.103875 0.994590i \(-0.466876\pi\)
0.809403 0.587253i \(-0.199791\pi\)
\(318\) 0 0
\(319\) −1.84875 3.20214i −0.103510 0.179285i
\(320\) 9.92743 0.554960
\(321\) 0 0
\(322\) 0 0
\(323\) 0.702021 0.0390615
\(324\) 0 0
\(325\) −5.16688 + 8.94931i −0.286607 + 0.496418i
\(326\) 3.31373 0.183531
\(327\) 0 0
\(328\) 4.45083 7.70906i 0.245756 0.425661i
\(329\) 0 0
\(330\) 0 0
\(331\) −9.04741 + 15.6706i −0.497291 + 0.861333i −0.999995 0.00312545i \(-0.999005\pi\)
0.502704 + 0.864458i \(0.332338\pi\)
\(332\) −10.8081 + 18.7201i −0.593170 + 1.02740i
\(333\) 0 0
\(334\) 4.37132 + 7.57135i 0.239188 + 0.414286i
\(335\) 1.90051 + 3.29179i 0.103836 + 0.179850i
\(336\) 0 0
\(337\) −12.5086 + 21.6656i −0.681389 + 1.18020i 0.293168 + 0.956061i \(0.405290\pi\)
−0.974557 + 0.224139i \(0.928043\pi\)
\(338\) −5.73615 −0.312005
\(339\) 0 0
\(340\) 1.61919 0.0878130
\(341\) 1.59999 + 2.77127i 0.0866446 + 0.150073i
\(342\) 0 0
\(343\) 0 0
\(344\) 9.28778 + 16.0869i 0.500764 + 0.867348i
\(345\) 0 0
\(346\) 0.963682 + 1.66915i 0.0518078 + 0.0897338i
\(347\) 5.37444 + 9.30881i 0.288515 + 0.499723i 0.973456 0.228876i \(-0.0735051\pi\)
−0.684940 + 0.728599i \(0.740172\pi\)
\(348\) 0 0
\(349\) 1.64301 + 2.84577i 0.0879482 + 0.152331i 0.906644 0.421897i \(-0.138636\pi\)
−0.818695 + 0.574228i \(0.805302\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.23365 3.86879i −0.119054 0.206207i
\(353\) 16.8192 0.895195 0.447598 0.894235i \(-0.352280\pi\)
0.447598 + 0.894235i \(0.352280\pi\)
\(354\) 0 0
\(355\) −18.2610 −0.969195
\(356\) 2.11144 3.65711i 0.111906 0.193827i
\(357\) 0 0
\(358\) −1.81864 3.14997i −0.0961180 0.166481i
\(359\) −11.8921 20.5978i −0.627642 1.08711i −0.988024 0.154303i \(-0.950687\pi\)
0.360382 0.932805i \(-0.382646\pi\)
\(360\) 0 0
\(361\) 5.55680 9.62466i 0.292463 0.506561i
\(362\) 2.79088 4.83395i 0.146686 0.254067i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.37968 + 5.85377i −0.176900 + 0.306401i
\(366\) 0 0
\(367\) 0.689984 0.0360169 0.0180084 0.999838i \(-0.494267\pi\)
0.0180084 + 0.999838i \(0.494267\pi\)
\(368\) 3.20263 5.54712i 0.166949 0.289164i
\(369\) 0 0
\(370\) −8.66327 −0.450382
\(371\) 0 0
\(372\) 0 0
\(373\) −3.76012 −0.194691 −0.0973457 0.995251i \(-0.531035\pi\)
−0.0973457 + 0.995251i \(0.531035\pi\)
\(374\) −0.0553208 0.0958184i −0.00286057 0.00495465i
\(375\) 0 0
\(376\) −9.46882 + 16.4005i −0.488317 + 0.845790i
\(377\) 4.95744 0.255321
\(378\) 0 0
\(379\) 32.8735 1.68860 0.844300 0.535872i \(-0.180017\pi\)
0.844300 + 0.535872i \(0.180017\pi\)
\(380\) −9.09489 + 15.7528i −0.466558 + 0.808102i
\(381\) 0 0
\(382\) −5.91222 10.2403i −0.302495 0.523937i
\(383\) −1.07267 −0.0548109 −0.0274055 0.999624i \(-0.508725\pi\)
−0.0274055 + 0.999624i \(0.508725\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.94276 0.149782
\(387\) 0 0
\(388\) 9.68640 16.7773i 0.491752 0.851740i
\(389\) 23.7436 1.20385 0.601925 0.798553i \(-0.294401\pi\)
0.601925 + 0.798553i \(0.294401\pi\)
\(390\) 0 0
\(391\) 0.309693 0.536405i 0.0156619 0.0271271i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.83510 + 6.64258i −0.193209 + 0.334648i
\(395\) −3.32170 + 5.75336i −0.167133 + 0.289483i
\(396\) 0 0
\(397\) 0.0160489 + 0.0277975i 0.000805471 + 0.00139512i 0.866428 0.499302i \(-0.166410\pi\)
−0.865622 + 0.500697i \(0.833077\pi\)
\(398\) −3.84208 6.65467i −0.192586 0.333569i
\(399\) 0 0
\(400\) −11.1616 + 19.3324i −0.558078 + 0.966619i
\(401\) −24.5256 −1.22475 −0.612374 0.790568i \(-0.709785\pi\)
−0.612374 + 0.790568i \(0.709785\pi\)
\(402\) 0 0
\(403\) −4.29039 −0.213719
\(404\) −2.28004 3.94914i −0.113436 0.196477i
\(405\) 0 0
\(406\) 0 0
\(407\) −2.11153 3.65728i −0.104665 0.181284i
\(408\) 0 0
\(409\) 13.3948 + 23.2006i 0.662333 + 1.14719i 0.980001 + 0.198992i \(0.0637667\pi\)
−0.317669 + 0.948202i \(0.602900\pi\)
\(410\) 4.37787 + 7.58269i 0.216208 + 0.374483i
\(411\) 0 0
\(412\) −8.51759 14.7529i −0.419631 0.726823i
\(413\) 0 0
\(414\) 0 0
\(415\) −22.7520 39.4077i −1.11685 1.93445i
\(416\) 5.98952 0.293660
\(417\) 0 0
\(418\) 1.24293 0.0607938
\(419\) −10.5262 + 18.2320i −0.514240 + 0.890689i 0.485624 + 0.874168i \(0.338593\pi\)
−0.999864 + 0.0165215i \(0.994741\pi\)
\(420\) 0 0
\(421\) −7.44533 12.8957i −0.362863 0.628498i 0.625568 0.780170i \(-0.284867\pi\)
−0.988431 + 0.151672i \(0.951534\pi\)
\(422\) 0.382760 + 0.662959i 0.0186325 + 0.0322724i
\(423\) 0 0
\(424\) −9.20469 + 15.9430i −0.447019 + 0.774260i
\(425\) −1.07932 + 1.86944i −0.0523547 + 0.0906809i
\(426\) 0 0
\(427\) 0 0
\(428\) −9.56037 + 16.5590i −0.462118 + 0.800412i
\(429\) 0 0
\(430\) −18.2711 −0.881110
\(431\) 7.95192 13.7731i 0.383031 0.663428i −0.608463 0.793582i \(-0.708214\pi\)
0.991494 + 0.130154i \(0.0415471\pi\)
\(432\) 0 0
\(433\) 16.3658 0.786490 0.393245 0.919434i \(-0.371352\pi\)
0.393245 + 0.919434i \(0.371352\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3.72210 −0.178256
\(437\) 3.47905 + 6.02590i 0.166426 + 0.288258i
\(438\) 0 0
\(439\) −7.77236 + 13.4621i −0.370954 + 0.642512i −0.989713 0.143070i \(-0.954303\pi\)
0.618758 + 0.785582i \(0.287636\pi\)
\(440\) 6.13543 0.292495
\(441\) 0 0
\(442\) 0.148343 0.00705594
\(443\) 0.895027 1.55023i 0.0425240 0.0736537i −0.843980 0.536375i \(-0.819793\pi\)
0.886504 + 0.462721i \(0.153127\pi\)
\(444\) 0 0
\(445\) 4.44477 + 7.69857i 0.210702 + 0.364947i
\(446\) −2.69922 −0.127812
\(447\) 0 0
\(448\) 0 0
\(449\) −13.5666 −0.640250 −0.320125 0.947375i \(-0.603725\pi\)
−0.320125 + 0.947375i \(0.603725\pi\)
\(450\) 0 0
\(451\) −2.13407 + 3.69631i −0.100489 + 0.174053i
\(452\) −27.7612 −1.30578
\(453\) 0 0
\(454\) 3.98588 6.90375i 0.187067 0.324009i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.28459 + 2.22497i −0.0600905 + 0.104080i −0.894506 0.447057i \(-0.852472\pi\)
0.834415 + 0.551136i \(0.185806\pi\)
\(458\) −2.47151 + 4.28078i −0.115486 + 0.200028i
\(459\) 0 0
\(460\) 8.02434 + 13.8986i 0.374137 + 0.648024i
\(461\) 18.0934 + 31.3388i 0.842695 + 1.45959i 0.887608 + 0.460600i \(0.152366\pi\)
−0.0449122 + 0.998991i \(0.514301\pi\)
\(462\) 0 0
\(463\) 8.19224 14.1894i 0.380726 0.659436i −0.610440 0.792062i \(-0.709008\pi\)
0.991166 + 0.132626i \(0.0423409\pi\)
\(464\) 10.7091 0.497158
\(465\) 0 0
\(466\) 8.20210 0.379955
\(467\) −4.35022 7.53480i −0.201304 0.348669i 0.747645 0.664099i \(-0.231185\pi\)
−0.948949 + 0.315430i \(0.897851\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.31361 16.1316i −0.429605 0.744097i
\(471\) 0 0
\(472\) 1.68691 + 2.92181i 0.0776462 + 0.134487i
\(473\) −4.45328 7.71330i −0.204762 0.354658i
\(474\) 0 0
\(475\) −12.1249 21.0010i −0.556330 0.963591i
\(476\) 0 0
\(477\) 0 0
\(478\) 5.46047 + 9.45782i 0.249756 + 0.432591i
\(479\) −17.7674 −0.811813 −0.405907 0.913915i \(-0.633044\pi\)
−0.405907 + 0.913915i \(0.633044\pi\)
\(480\) 0 0
\(481\) 5.66207 0.258168
\(482\) 4.14548 7.18018i 0.188821 0.327048i
\(483\) 0 0
\(484\) −8.94890 15.4999i −0.406768 0.704543i
\(485\) 20.3908 + 35.3179i 0.925898 + 1.60370i
\(486\) 0 0
\(487\) 8.32763 14.4239i 0.377361 0.653608i −0.613316 0.789837i \(-0.710165\pi\)
0.990677 + 0.136229i \(0.0434983\pi\)
\(488\) −10.0562 + 17.4178i −0.455222 + 0.788467i
\(489\) 0 0
\(490\) 0 0
\(491\) 3.21021 5.56025i 0.144875 0.250930i −0.784451 0.620190i \(-0.787055\pi\)
0.929326 + 0.369260i \(0.120389\pi\)
\(492\) 0 0
\(493\) 1.03557 0.0466396
\(494\) −0.833230 + 1.44320i −0.0374888 + 0.0649325i
\(495\) 0 0
\(496\) −9.26814 −0.416152
\(497\) 0 0
\(498\) 0 0
\(499\) 11.1459 0.498960 0.249480 0.968380i \(-0.419740\pi\)
0.249480 + 0.968380i \(0.419740\pi\)
\(500\) −11.7728 20.3911i −0.526495 0.911916i
\(501\) 0 0
\(502\) 2.11512 3.66350i 0.0944026 0.163510i
\(503\) −17.7223 −0.790200 −0.395100 0.918638i \(-0.629290\pi\)
−0.395100 + 0.918638i \(0.629290\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) 0.548314 0.949708i 0.0243755 0.0422197i
\(507\) 0 0
\(508\) −1.11339 1.92845i −0.0493988 0.0855612i
\(509\) 31.0823 1.37770 0.688848 0.724906i \(-0.258117\pi\)
0.688848 + 0.724906i \(0.258117\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.5634 0.997169
\(513\) 0 0
\(514\) 4.24456 7.35180i 0.187220 0.324274i
\(515\) 35.8607 1.58021
\(516\) 0 0
\(517\) 4.54008 7.86365i 0.199672 0.345843i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.11304 + 7.12399i −0.180369 + 0.312408i
\(521\) −2.37986 + 4.12203i −0.104263 + 0.180590i −0.913437 0.406980i \(-0.866582\pi\)
0.809174 + 0.587570i \(0.199915\pi\)
\(522\) 0 0
\(523\) −20.1258 34.8588i −0.880038 1.52427i −0.851298 0.524683i \(-0.824184\pi\)
−0.0287402 0.999587i \(-0.509150\pi\)
\(524\) −13.1812 22.8305i −0.575823 0.997355i
\(525\) 0 0
\(526\) 5.09571 8.82602i 0.222183 0.384833i
\(527\) −0.896226 −0.0390402
\(528\) 0 0
\(529\) −16.8609 −0.733084
\(530\) −9.05381 15.6817i −0.393272 0.681168i
\(531\) 0 0
\(532\) 0 0
\(533\) −2.86125 4.95583i −0.123935 0.214661i
\(534\) 0 0
\(535\) −20.1255 34.8584i −0.870101 1.50706i
\(536\) 0.958109 + 1.65949i 0.0413840 + 0.0716792i
\(537\) 0 0
\(538\) 4.92033 + 8.52227i 0.212131 + 0.367421i
\(539\) 0 0
\(540\) 0 0
\(541\) 12.0547 + 20.8794i 0.518273 + 0.897675i 0.999775 + 0.0212301i \(0.00675826\pi\)
−0.481502 + 0.876445i \(0.659908\pi\)
\(542\) 5.27659 0.226649
\(543\) 0 0
\(544\) 1.25116 0.0536431
\(545\) 3.91769 6.78564i 0.167815 0.290665i
\(546\) 0 0
\(547\) −6.17751 10.6998i −0.264131 0.457489i 0.703204 0.710988i \(-0.251752\pi\)
−0.967336 + 0.253499i \(0.918419\pi\)
\(548\) 0.428436 + 0.742073i 0.0183019 + 0.0316998i
\(549\) 0 0
\(550\) −1.91094 + 3.30985i −0.0814828 + 0.141132i
\(551\) −5.81671 + 10.0748i −0.247800 + 0.429203i
\(552\) 0 0
\(553\) 0 0
\(554\) 6.16893 10.6849i 0.262093 0.453958i
\(555\) 0 0
\(556\) 17.3127 0.734220
\(557\) −4.03845 + 6.99479i −0.171114 + 0.296379i −0.938810 0.344436i \(-0.888070\pi\)
0.767695 + 0.640815i \(0.221403\pi\)
\(558\) 0 0
\(559\) 11.9415 0.505070
\(560\) 0 0
\(561\) 0 0
\(562\) −6.78083 −0.286032
\(563\) −22.6064 39.1554i −0.952744 1.65020i −0.739448 0.673214i \(-0.764913\pi\)
−0.213296 0.976988i \(-0.568420\pi\)
\(564\) 0 0
\(565\) 29.2200 50.6106i 1.22930 2.12920i
\(566\) −3.13477 −0.131764
\(567\) 0 0
\(568\) −9.20596 −0.386274
\(569\) 11.2149 19.4248i 0.470155 0.814332i −0.529263 0.848458i \(-0.677532\pi\)
0.999418 + 0.0341263i \(0.0108648\pi\)
\(570\) 0 0
\(571\) 10.9134 + 18.9026i 0.456713 + 0.791050i 0.998785 0.0492820i \(-0.0156933\pi\)
−0.542072 + 0.840332i \(0.682360\pi\)
\(572\) −1.87365 −0.0783413
\(573\) 0 0
\(574\) 0 0
\(575\) −21.3954 −0.892251
\(576\) 0 0
\(577\) 16.1022 27.8898i 0.670342 1.16107i −0.307465 0.951559i \(-0.599481\pi\)
0.977807 0.209508i \(-0.0671861\pi\)
\(578\) −8.39877 −0.349343
\(579\) 0 0
\(580\) −13.4161 + 23.2373i −0.557072 + 0.964878i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.41343 7.64429i 0.182786 0.316594i
\(584\) −1.70380 + 2.95107i −0.0705039 + 0.122116i
\(585\) 0 0
\(586\) −0.652105 1.12948i −0.0269382 0.0466584i
\(587\) −9.72304 16.8408i −0.401313 0.695094i 0.592572 0.805518i \(-0.298113\pi\)
−0.993885 + 0.110424i \(0.964779\pi\)
\(588\) 0 0
\(589\) 5.03404 8.71921i 0.207424 0.359269i
\(590\) −3.31851 −0.136621
\(591\) 0 0
\(592\) 12.2313 0.502701
\(593\) −14.4202 24.9766i −0.592168 1.02566i −0.993940 0.109925i \(-0.964939\pi\)
0.401772 0.915740i \(-0.368394\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.4392 31.9377i −0.755300 1.30822i
\(597\) 0 0
\(598\) 0.735152 + 1.27332i 0.0300626 + 0.0520699i
\(599\) −23.4994 40.7022i −0.960161 1.66305i −0.722089 0.691800i \(-0.756818\pi\)
−0.238072 0.971247i \(-0.576516\pi\)
\(600\) 0 0
\(601\) 7.80843 + 13.5246i 0.318512 + 0.551680i 0.980178 0.198119i \(-0.0634834\pi\)
−0.661665 + 0.749799i \(0.730150\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1.31417 + 2.27620i 0.0534727 + 0.0926174i
\(605\) 37.6766 1.53177
\(606\) 0 0
\(607\) 28.6532 1.16300 0.581500 0.813547i \(-0.302466\pi\)
0.581500 + 0.813547i \(0.302466\pi\)
\(608\) −7.02769 + 12.1723i −0.285010 + 0.493652i
\(609\) 0 0
\(610\) −9.89134 17.1323i −0.400489 0.693667i
\(611\) 6.08711 + 10.5432i 0.246258 + 0.426531i
\(612\) 0 0
\(613\) 14.6734 25.4151i 0.592653 1.02651i −0.401220 0.915982i \(-0.631414\pi\)
0.993873 0.110524i \(-0.0352529\pi\)
\(614\) −0.692965 + 1.20025i −0.0279658 + 0.0484382i
\(615\) 0 0
\(616\) 0 0
\(617\) −2.06401 + 3.57497i −0.0830938 + 0.143923i −0.904577 0.426310i \(-0.859813\pi\)
0.821484 + 0.570232i \(0.193147\pi\)
\(618\) 0 0
\(619\) −22.7130 −0.912912 −0.456456 0.889746i \(-0.650881\pi\)
−0.456456 + 0.889746i \(0.650881\pi\)
\(620\) 11.6109 20.1106i 0.466304 0.807662i
\(621\) 0 0
\(622\) −7.48774 −0.300231
\(623\) 0 0
\(624\) 0 0
\(625\) 6.38996 0.255598
\(626\) −6.31698 10.9413i −0.252477 0.437304i
\(627\) 0 0
\(628\) 14.6290 25.3382i 0.583761 1.01110i
\(629\) 1.18276 0.0471597
\(630\) 0 0
\(631\) −38.6411 −1.53828 −0.769138 0.639082i \(-0.779314\pi\)
−0.769138 + 0.639082i \(0.779314\pi\)
\(632\) −1.67458 + 2.90045i −0.0666110 + 0.115374i
\(633\) 0 0
\(634\) 8.06304 + 13.9656i 0.320224 + 0.554645i
\(635\) 4.68759 0.186021
\(636\) 0 0
\(637\) 0 0
\(638\) 1.83348 0.0725881
\(639\) 0 0
\(640\) −20.9427 + 36.2737i −0.827831 + 1.43385i
\(641\) 28.4726 1.12460 0.562301 0.826933i \(-0.309916\pi\)
0.562301 + 0.826933i \(0.309916\pi\)
\(642\) 0 0
\(643\) 8.52125 14.7592i 0.336045 0.582048i −0.647640 0.761947i \(-0.724244\pi\)
0.983685 + 0.179899i \(0.0575771\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.174055 + 0.301472i −0.00684810 + 0.0118613i
\(647\) 1.68809 2.92386i 0.0663657 0.114949i −0.830933 0.556372i \(-0.812193\pi\)
0.897299 + 0.441423i \(0.145526\pi\)
\(648\) 0 0
\(649\) −0.808833 1.40094i −0.0317495 0.0549917i
\(650\) −2.56209 4.43768i −0.100494 0.174060i
\(651\) 0 0
\(652\) 5.86110 10.1517i 0.229538 0.397572i
\(653\) 18.3451 0.717899 0.358950 0.933357i \(-0.383135\pi\)
0.358950 + 0.933357i \(0.383135\pi\)
\(654\) 0 0
\(655\) 55.4954 2.16838
\(656\) −6.18090 10.7056i −0.241324 0.417985i
\(657\) 0 0
\(658\) 0 0
\(659\) 13.9248 + 24.1184i 0.542432 + 0.939519i 0.998764 + 0.0497098i \(0.0158297\pi\)
−0.456332 + 0.889810i \(0.650837\pi\)
\(660\) 0 0
\(661\) 19.5071 + 33.7872i 0.758737 + 1.31417i 0.943495 + 0.331387i \(0.107516\pi\)
−0.184758 + 0.982784i \(0.559150\pi\)
\(662\) −4.48633 7.77054i −0.174366 0.302011i
\(663\) 0 0
\(664\) −11.4700 19.8667i −0.445123 0.770976i
\(665\) 0 0
\(666\) 0 0
\(667\) 5.13203 + 8.88894i 0.198713 + 0.344181i
\(668\) 30.9268 1.19659
\(669\) 0 0
\(670\) −1.88481 −0.0728165
\(671\) 4.82170 8.35143i 0.186140 0.322404i
\(672\) 0 0
\(673\) 24.6154 + 42.6352i 0.948856 + 1.64347i 0.747841 + 0.663878i \(0.231090\pi\)
0.201014 + 0.979588i \(0.435576\pi\)
\(674\) −6.20264 10.7433i −0.238917 0.413816i
\(675\) 0 0
\(676\) −10.1457 + 17.5729i −0.390219 + 0.675879i
\(677\) 11.6958 20.2577i 0.449505 0.778565i −0.548849 0.835922i \(-0.684934\pi\)
0.998354 + 0.0573564i \(0.0182671\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.859180 + 1.48814i −0.0329480 + 0.0570677i
\(681\) 0 0
\(682\) −1.58677 −0.0607607
\(683\) 15.1632 26.2634i 0.580204 1.00494i −0.415251 0.909707i \(-0.636306\pi\)
0.995455 0.0952356i \(-0.0303604\pi\)
\(684\) 0 0
\(685\) −1.80380 −0.0689196
\(686\) 0 0
\(687\) 0 0
\(688\) 25.7961 0.983466
\(689\) 5.91731 + 10.2491i 0.225432 + 0.390459i
\(690\) 0 0
\(691\) −2.05665 + 3.56223i −0.0782387 + 0.135513i −0.902490 0.430711i \(-0.858263\pi\)
0.824251 + 0.566224i \(0.191596\pi\)
\(692\) 6.81797 0.259180
\(693\) 0 0
\(694\) −5.33003 −0.202325
\(695\) −18.2224 + 31.5621i −0.691215 + 1.19722i
\(696\) 0 0
\(697\) −0.597691 1.03523i −0.0226392 0.0392122i
\(698\) −1.62943 −0.0616749
\(699\) 0 0
\(700\) 0 0
\(701\) −29.1835 −1.10225 −0.551123 0.834424i \(-0.685800\pi\)
−0.551123 + 0.834424i \(0.685800\pi\)
\(702\) 0 0
\(703\) −6.64347 + 11.5068i −0.250563 + 0.433988i
\(704\) −2.39965 −0.0904403
\(705\) 0 0
\(706\) −4.17005 + 7.22274i −0.156942 + 0.271831i
\(707\) 0 0
\(708\) 0 0
\(709\) 21.2309 36.7729i 0.797342 1.38104i −0.123999 0.992282i \(-0.539572\pi\)
0.921341 0.388755i \(-0.127095\pi\)
\(710\) 4.52753 7.84192i 0.169915 0.294302i
\(711\) 0 0
\(712\) 2.24075 + 3.88109i 0.0839757 + 0.145450i
\(713\) −4.44149 7.69288i −0.166335 0.288101i
\(714\) 0 0
\(715\) 1.97211 3.41579i 0.0737526 0.127743i
\(716\) −12.8667 −0.480852
\(717\) 0 0
\(718\) 11.7938 0.440142
\(719\) −5.57126 9.64970i −0.207773 0.359873i 0.743240 0.669025i \(-0.233288\pi\)
−0.951013 + 0.309152i \(0.899955\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.75544 + 4.77256i 0.102547 + 0.177616i
\(723\) 0 0
\(724\) −9.87264 17.0999i −0.366914 0.635513i
\(725\) −17.8858 30.9790i −0.664260 1.15053i
\(726\) 0 0
\(727\) 14.3410 + 24.8393i 0.531878 + 0.921239i 0.999308 + 0.0372089i \(0.0118467\pi\)
−0.467430 + 0.884030i \(0.654820\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −1.67588 2.90270i −0.0620269 0.107434i
\(731\) 2.49447 0.0922614
\(732\) 0 0
\(733\) 25.0528 0.925348 0.462674 0.886529i \(-0.346890\pi\)
0.462674 + 0.886529i \(0.346890\pi\)
\(734\) −0.171071 + 0.296303i −0.00631433 + 0.0109367i
\(735\) 0 0
\(736\) 6.20047 + 10.7395i 0.228552 + 0.395864i
\(737\) −0.459391 0.795689i −0.0169219 0.0293096i
\(738\) 0 0
\(739\) 13.7608 23.8344i 0.506198 0.876761i −0.493776 0.869589i \(-0.664384\pi\)
0.999974 0.00717223i \(-0.00228301\pi\)
\(740\) −15.3230 + 26.5402i −0.563284 + 0.975637i
\(741\) 0 0
\(742\) 0 0
\(743\) 7.00608 12.1349i 0.257028 0.445186i −0.708416 0.705795i \(-0.750590\pi\)
0.965444 + 0.260609i \(0.0839233\pi\)
\(744\) 0 0
\(745\) 77.6326 2.84424
\(746\) 0.932261 1.61472i 0.0341325 0.0591192i
\(747\) 0 0
\(748\) −0.391390 −0.0143106
\(749\) 0 0
\(750\) 0 0
\(751\) −52.2594 −1.90697 −0.953486 0.301436i \(-0.902534\pi\)
−0.953486 + 0.301436i \(0.902534\pi\)
\(752\) 13.1494 + 22.7755i 0.479511 + 0.830537i
\(753\) 0 0
\(754\) −1.22912 + 2.12889i −0.0447618 + 0.0775298i
\(755\) −5.53289 −0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) −8.15047 + 14.1170i −0.296038 + 0.512753i
\(759\) 0 0
\(760\) −9.65191 16.7176i −0.350112 0.606411i
\(761\) −17.2510 −0.625348 −0.312674 0.949860i \(-0.601225\pi\)
−0.312674 + 0.949860i \(0.601225\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −41.8285 −1.51330
\(765\) 0 0
\(766\) 0.265952 0.460642i 0.00960922 0.0166437i
\(767\) 2.16889 0.0783139
\(768\) 0 0
\(769\) 10.6727 18.4856i 0.384867 0.666609i −0.606884 0.794790i \(-0.707581\pi\)
0.991751 + 0.128182i \(0.0409141\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.20495 9.01523i 0.187330 0.324465i
\(773\) −6.57357 + 11.3858i −0.236435 + 0.409517i −0.959689 0.281065i \(-0.909312\pi\)
0.723254 + 0.690582i \(0.242646\pi\)
\(774\) 0 0
\(775\) 15.4791 + 26.8106i 0.556027 + 0.963066i
\(776\) 10.2796 + 17.8049i 0.369018 + 0.639158i
\(777\) 0 0
\(778\) −5.88685 + 10.1963i −0.211054 + 0.365556i
\(779\) 13.4288 0.481136
\(780\) 0 0
\(781\) 4.41405 0.157947
\(782\) 0.153567 + 0.265986i 0.00549155 + 0.00951164i
\(783\) 0 0
\(784\) 0 0
\(785\) 30.7954 + 53.3393i 1.09914 + 1.90376i
\(786\) 0 0
\(787\) −14.0650 24.3614i −0.501364 0.868389i −0.999999 0.00157623i \(-0.999498\pi\)
0.498634 0.866812i \(-0.333835\pi\)
\(788\) 13.5665 + 23.4979i 0.483287 + 0.837077i
\(789\) 0 0
\(790\) −1.64713 2.85291i −0.0586021 0.101502i
\(791\) 0 0
\(792\) 0 0
\(793\) 6.46470 + 11.1972i 0.229568 + 0.397624i
\(794\) −0.0159163 −0.000564847
\(795\) 0