Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98064 | −1.40053 | −0.700263 | − | 0.713885i | \(-0.746934\pi\) | ||||
−0.700263 | + | 0.713885i | \(0.746934\pi\) | |||||||
\(3\) | −1.34264 | −0.775174 | −0.387587 | − | 0.921833i | \(-0.626691\pi\) | ||||
−0.387587 | + | 0.921833i | \(0.626691\pi\) | |||||||
\(4\) | 1.92294 | 0.961472 | ||||||||
\(5\) | −0.618382 | −0.276549 | −0.138274 | − | 0.990394i | \(-0.544156\pi\) | ||||
−0.138274 | + | 0.990394i | \(0.544156\pi\) | |||||||
\(6\) | 2.65929 | 1.08565 | ||||||||
\(7\) | −3.38656 | −1.28000 | −0.639999 | − | 0.768375i | \(-0.721065\pi\) | ||||
−0.639999 | + | 0.768375i | \(0.721065\pi\) | |||||||
\(8\) | 0.152622 | 0.0539599 | ||||||||
\(9\) | −1.19732 | −0.399105 | ||||||||
\(10\) | 1.22479 | 0.387314 | ||||||||
\(11\) | 5.41950 | 1.63404 | 0.817020 | − | 0.576609i | \(-0.195624\pi\) | ||||
0.817020 | + | 0.576609i | \(0.195624\pi\) | |||||||
\(12\) | −2.58182 | −0.745308 | ||||||||
\(13\) | −5.35721 | −1.48582 | −0.742911 | − | 0.669390i | \(-0.766556\pi\) | ||||
−0.742911 | + | 0.669390i | \(0.766556\pi\) | |||||||
\(14\) | 6.70756 | 1.79267 | ||||||||
\(15\) | 0.830265 | 0.214373 | ||||||||
\(16\) | −4.14818 | −1.03704 | ||||||||
\(17\) | −2.80946 | −0.681394 | −0.340697 | − | 0.940173i | \(-0.610663\pi\) | ||||
−0.340697 | + | 0.940173i | \(0.610663\pi\) | |||||||
\(18\) | 2.37145 | 0.558957 | ||||||||
\(19\) | −0.931205 | −0.213633 | −0.106817 | − | 0.994279i | \(-0.534066\pi\) | ||||
−0.106817 | + | 0.994279i | \(0.534066\pi\) | |||||||
\(20\) | −1.18911 | −0.265894 | ||||||||
\(21\) | 4.54693 | 0.992222 | ||||||||
\(22\) | −10.7341 | −2.28852 | ||||||||
\(23\) | 5.12484 | 1.06860 | 0.534302 | − | 0.845294i | \(-0.320575\pi\) | ||||
0.534302 | + | 0.845294i | \(0.320575\pi\) | |||||||
\(24\) | −0.204916 | −0.0418283 | ||||||||
\(25\) | −4.61760 | −0.923521 | ||||||||
\(26\) | 10.6107 | 2.08093 | ||||||||
\(27\) | 5.63549 | 1.08455 | ||||||||
\(28\) | −6.51216 | −1.23068 | ||||||||
\(29\) | 8.79269 | 1.63276 | 0.816381 | − | 0.577514i | \(-0.195977\pi\) | ||||
0.816381 | + | 0.577514i | \(0.195977\pi\) | |||||||
\(30\) | −1.64446 | −0.300236 | ||||||||
\(31\) | −0.504047 | −0.0905295 | −0.0452648 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452648 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(32\) | 7.91081 | 1.39845 | ||||||||
\(33\) | −7.27644 | −1.26667 | ||||||||
\(34\) | 5.56454 | 0.954310 | ||||||||
\(35\) | 2.09419 | 0.353982 | ||||||||
\(36\) | −2.30237 | −0.383728 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 1.84438 | 0.299199 | ||||||||
\(39\) | 7.19281 | 1.15177 | ||||||||
\(40\) | −0.0943784 | −0.0149225 | ||||||||
\(41\) | −9.25133 | −1.44481 | −0.722407 | − | 0.691468i | \(-0.756964\pi\) | ||||
−0.722407 | + | 0.691468i | \(0.756964\pi\) | |||||||
\(42\) | −9.00584 | −1.38963 | ||||||||
\(43\) | −8.43110 | −1.28573 | −0.642865 | − | 0.765979i | \(-0.722254\pi\) | ||||
−0.642865 | + | 0.765979i | \(0.722254\pi\) | |||||||
\(44\) | 10.4214 | 1.57108 | ||||||||
\(45\) | 0.740399 | 0.110372 | ||||||||
\(46\) | −10.1505 | −1.49661 | ||||||||
\(47\) | 8.00506 | 1.16766 | 0.583829 | − | 0.811877i | \(-0.301554\pi\) | ||||
0.583829 | + | 0.811877i | \(0.301554\pi\) | |||||||
\(48\) | 5.56951 | 0.803889 | ||||||||
\(49\) | 4.46878 | 0.638397 | ||||||||
\(50\) | 9.14582 | 1.29341 | ||||||||
\(51\) | 3.77210 | 0.528199 | ||||||||
\(52\) | −10.3016 | −1.42858 | ||||||||
\(53\) | 4.86095 | 0.667703 | 0.333852 | − | 0.942626i | \(-0.391652\pi\) | ||||
0.333852 | + | 0.942626i | \(0.391652\pi\) | |||||||
\(54\) | −11.1619 | −1.51894 | ||||||||
\(55\) | −3.35132 | −0.451892 | ||||||||
\(56\) | −0.516862 | −0.0690686 | ||||||||
\(57\) | 1.25027 | 0.165603 | ||||||||
\(58\) | −17.4152 | −2.28672 | ||||||||
\(59\) | 0.278142 | 0.0362110 | 0.0181055 | − | 0.999836i | \(-0.494237\pi\) | ||||
0.0181055 | + | 0.999836i | \(0.494237\pi\) | |||||||
\(60\) | 1.59655 | 0.206114 | ||||||||
\(61\) | −0.247985 | −0.0317512 | −0.0158756 | − | 0.999874i | \(-0.505054\pi\) | ||||
−0.0158756 | + | 0.999874i | \(0.505054\pi\) | |||||||
\(62\) | 0.998337 | 0.126789 | ||||||||
\(63\) | 4.05478 | 0.510854 | ||||||||
\(64\) | −7.37213 | −0.921516 | ||||||||
\(65\) | 3.31280 | 0.410903 | ||||||||
\(66\) | 14.4120 | 1.77400 | ||||||||
\(67\) | 3.46510 | 0.423329 | 0.211665 | − | 0.977342i | \(-0.432112\pi\) | ||||
0.211665 | + | 0.977342i | \(0.432112\pi\) | |||||||
\(68\) | −5.40243 | −0.655141 | ||||||||
\(69\) | −6.88082 | −0.828354 | ||||||||
\(70\) | −4.14783 | −0.495761 | ||||||||
\(71\) | 11.6172 | 1.37870 | 0.689352 | − | 0.724426i | \(-0.257895\pi\) | ||||
0.689352 | + | 0.724426i | \(0.257895\pi\) | |||||||
\(72\) | −0.182736 | −0.0215357 | ||||||||
\(73\) | −2.16574 | −0.253481 | −0.126740 | − | 0.991936i | \(-0.540452\pi\) | ||||
−0.126740 | + | 0.991936i | \(0.540452\pi\) | |||||||
\(74\) | −1.98064 | −0.230245 | ||||||||
\(75\) | 6.19978 | 0.715889 | ||||||||
\(76\) | −1.79066 | −0.205402 | ||||||||
\(77\) | −18.3535 | −2.09157 | ||||||||
\(78\) | −14.2464 | −1.61308 | ||||||||
\(79\) | 12.5551 | 1.41256 | 0.706280 | − | 0.707933i | \(-0.250372\pi\) | ||||
0.706280 | + | 0.707933i | \(0.250372\pi\) | |||||||
\(80\) | 2.56516 | 0.286793 | ||||||||
\(81\) | −3.97449 | −0.441610 | ||||||||
\(82\) | 18.3236 | 2.02350 | ||||||||
\(83\) | −4.43096 | −0.486361 | −0.243180 | − | 0.969981i | \(-0.578191\pi\) | ||||
−0.243180 | + | 0.969981i | \(0.578191\pi\) | |||||||
\(84\) | 8.74349 | 0.953993 | ||||||||
\(85\) | 1.73732 | 0.188439 | ||||||||
\(86\) | 16.6990 | 1.80070 | ||||||||
\(87\) | −11.8054 | −1.26567 | ||||||||
\(88\) | 0.827133 | 0.0881726 | ||||||||
\(89\) | 0.673703 | 0.0714124 | 0.0357062 | − | 0.999362i | \(-0.488632\pi\) | ||||
0.0357062 | + | 0.999362i | \(0.488632\pi\) | |||||||
\(90\) | −1.46646 | −0.154579 | ||||||||
\(91\) | 18.1425 | 1.90185 | ||||||||
\(92\) | 9.85478 | 1.02743 | ||||||||
\(93\) | 0.676754 | 0.0701761 | ||||||||
\(94\) | −15.8552 | −1.63534 | ||||||||
\(95\) | 0.575841 | 0.0590800 | ||||||||
\(96\) | −10.6214 | −1.08404 | ||||||||
\(97\) | −8.48462 | −0.861482 | −0.430741 | − | 0.902475i | \(-0.641748\pi\) | ||||
−0.430741 | + | 0.902475i | \(0.641748\pi\) | |||||||
\(98\) | −8.85105 | −0.894091 | ||||||||
\(99\) | −6.48885 | −0.652154 | ||||||||
\(100\) | −8.87939 | −0.887939 | ||||||||
\(101\) | −2.73137 | −0.271782 | −0.135891 | − | 0.990724i | \(-0.543390\pi\) | ||||
−0.135891 | + | 0.990724i | \(0.543390\pi\) | |||||||
\(102\) | −7.47117 | −0.739757 | ||||||||
\(103\) | −3.58391 | −0.353133 | −0.176566 | − | 0.984289i | \(-0.556499\pi\) | ||||
−0.176566 | + | 0.984289i | \(0.556499\pi\) | |||||||
\(104\) | −0.817626 | −0.0801748 | ||||||||
\(105\) | −2.81174 | −0.274398 | ||||||||
\(106\) | −9.62781 | −0.935136 | ||||||||
\(107\) | 3.24554 | 0.313758 | 0.156879 | − | 0.987618i | \(-0.449857\pi\) | ||||
0.156879 | + | 0.987618i | \(0.449857\pi\) | |||||||
\(108\) | 10.8367 | 1.04276 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 6.63777 | 0.632886 | ||||||||
\(111\) | −1.34264 | −0.127438 | ||||||||
\(112\) | 14.0480 | 1.32741 | ||||||||
\(113\) | 18.0249 | 1.69564 | 0.847820 | − | 0.530284i | \(-0.177915\pi\) | ||||
0.847820 | + | 0.530284i | \(0.177915\pi\) | |||||||
\(114\) | −2.47635 | −0.231931 | ||||||||
\(115\) | −3.16911 | −0.295521 | ||||||||
\(116\) | 16.9078 | 1.56985 | ||||||||
\(117\) | 6.41427 | 0.593000 | ||||||||
\(118\) | −0.550900 | −0.0507145 | ||||||||
\(119\) | 9.51440 | 0.872184 | ||||||||
\(120\) | 0.126716 | 0.0115676 | ||||||||
\(121\) | 18.3710 | 1.67009 | ||||||||
\(122\) | 0.491170 | 0.0444684 | ||||||||
\(123\) | 12.4212 | 1.11998 | ||||||||
\(124\) | −0.969254 | −0.0870416 | ||||||||
\(125\) | 5.94735 | 0.531947 | ||||||||
\(126\) | −8.03107 | −0.715464 | ||||||||
\(127\) | 8.21022 | 0.728539 | 0.364270 | − | 0.931294i | \(-0.381319\pi\) | ||||
0.364270 | + | 0.931294i | \(0.381319\pi\) | |||||||
\(128\) | −1.22007 | −0.107840 | ||||||||
\(129\) | 11.3199 | 0.996664 | ||||||||
\(130\) | −6.56148 | −0.575479 | ||||||||
\(131\) | 0.781469 | 0.0682773 | 0.0341387 | − | 0.999417i | \(-0.489131\pi\) | ||||
0.0341387 | + | 0.999417i | \(0.489131\pi\) | |||||||
\(132\) | −13.9922 | −1.21786 | ||||||||
\(133\) | 3.15358 | 0.273450 | ||||||||
\(134\) | −6.86312 | −0.592884 | ||||||||
\(135\) | −3.48488 | −0.299931 | ||||||||
\(136\) | −0.428784 | −0.0367680 | ||||||||
\(137\) | −13.8217 | −1.18087 | −0.590433 | − | 0.807086i | \(-0.701043\pi\) | ||||
−0.590433 | + | 0.807086i | \(0.701043\pi\) | |||||||
\(138\) | 13.6284 | 1.16013 | ||||||||
\(139\) | 17.2952 | 1.46696 | 0.733479 | − | 0.679712i | \(-0.237895\pi\) | ||||
0.733479 | + | 0.679712i | \(0.237895\pi\) | |||||||
\(140\) | 4.02700 | 0.340344 | ||||||||
\(141\) | −10.7479 | −0.905138 | ||||||||
\(142\) | −23.0095 | −1.93091 | ||||||||
\(143\) | −29.0334 | −2.42789 | ||||||||
\(144\) | 4.96668 | 0.413890 | ||||||||
\(145\) | −5.43724 | −0.451538 | ||||||||
\(146\) | 4.28956 | 0.355007 | ||||||||
\(147\) | −5.99996 | −0.494868 | ||||||||
\(148\) | 1.92294 | 0.158065 | ||||||||
\(149\) | 15.9216 | 1.30435 | 0.652174 | − | 0.758069i | \(-0.273857\pi\) | ||||
0.652174 | + | 0.758069i | \(0.273857\pi\) | |||||||
\(150\) | −12.2796 | −1.00262 | ||||||||
\(151\) | 10.0783 | 0.820163 | 0.410081 | − | 0.912049i | \(-0.365500\pi\) | ||||
0.410081 | + | 0.912049i | \(0.365500\pi\) | |||||||
\(152\) | −0.142122 | −0.0115276 | ||||||||
\(153\) | 3.36381 | 0.271948 | ||||||||
\(154\) | 36.3516 | 2.92930 | ||||||||
\(155\) | 0.311694 | 0.0250358 | ||||||||
\(156\) | 13.8314 | 1.10740 | ||||||||
\(157\) | −17.5447 | −1.40022 | −0.700110 | − | 0.714035i | \(-0.746866\pi\) | ||||
−0.700110 | + | 0.714035i | \(0.746866\pi\) | |||||||
\(158\) | −24.8672 | −1.97833 | ||||||||
\(159\) | −6.52651 | −0.517586 | ||||||||
\(160\) | −4.89190 | −0.386739 | ||||||||
\(161\) | −17.3556 | −1.36781 | ||||||||
\(162\) | 7.87204 | 0.618486 | ||||||||
\(163\) | −13.5562 | −1.06180 | −0.530901 | − | 0.847434i | \(-0.678147\pi\) | ||||
−0.530901 | + | 0.847434i | \(0.678147\pi\) | |||||||
\(164\) | −17.7898 | −1.38915 | ||||||||
\(165\) | 4.49962 | 0.350295 | ||||||||
\(166\) | 8.77614 | 0.681161 | ||||||||
\(167\) | −0.267605 | −0.0207079 | −0.0103539 | − | 0.999946i | \(-0.503296\pi\) | ||||
−0.0103539 | + | 0.999946i | \(0.503296\pi\) | |||||||
\(168\) | 0.693960 | 0.0535402 | ||||||||
\(169\) | 15.6997 | 1.20767 | ||||||||
\(170\) | −3.44101 | −0.263913 | ||||||||
\(171\) | 1.11495 | 0.0852621 | ||||||||
\(172\) | −16.2125 | −1.23619 | ||||||||
\(173\) | −0.882301 | −0.0670801 | −0.0335400 | − | 0.999437i | \(-0.510678\pi\) | ||||
−0.0335400 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(174\) | 23.3823 | 1.77261 | ||||||||
\(175\) | 15.6378 | 1.18211 | ||||||||
\(176\) | −22.4810 | −1.69457 | ||||||||
\(177\) | −0.373445 | −0.0280698 | ||||||||
\(178\) | −1.33436 | −0.100015 | ||||||||
\(179\) | 9.22784 | 0.689721 | 0.344860 | − | 0.938654i | \(-0.387926\pi\) | ||||
0.344860 | + | 0.938654i | \(0.387926\pi\) | |||||||
\(180\) | 1.42374 | 0.106120 | ||||||||
\(181\) | −12.0295 | −0.894148 | −0.447074 | − | 0.894497i | \(-0.647534\pi\) | ||||
−0.447074 | + | 0.894497i | \(0.647534\pi\) | |||||||
\(182\) | −35.9338 | −2.66359 | ||||||||
\(183\) | 0.332955 | 0.0246127 | ||||||||
\(184\) | 0.782162 | 0.0576617 | ||||||||
\(185\) | −0.618382 | −0.0454644 | ||||||||
\(186\) | −1.34041 | −0.0982835 | ||||||||
\(187\) | −15.2259 | −1.11343 | ||||||||
\(188\) | 15.3933 | 1.12267 | ||||||||
\(189\) | −19.0849 | −1.38822 | ||||||||
\(190\) | −1.14053 | −0.0827431 | ||||||||
\(191\) | −11.7806 | −0.852417 | −0.426208 | − | 0.904625i | \(-0.640151\pi\) | ||||
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(192\) | 9.89812 | 0.714335 | ||||||||
\(193\) | 9.60828 | 0.691619 | 0.345810 | − | 0.938305i | \(-0.387604\pi\) | ||||
0.345810 | + | 0.938305i | \(0.387604\pi\) | |||||||
\(194\) | 16.8050 | 1.20653 | ||||||||
\(195\) | −4.44790 | −0.318521 | ||||||||
\(196\) | 8.59320 | 0.613800 | ||||||||
\(197\) | 11.7998 | 0.840702 | 0.420351 | − | 0.907362i | \(-0.361907\pi\) | ||||
0.420351 | + | 0.907362i | \(0.361907\pi\) | |||||||
\(198\) | 12.8521 | 0.913359 | ||||||||
\(199\) | −16.0583 | −1.13835 | −0.569173 | − | 0.822218i | \(-0.692737\pi\) | ||||
−0.569173 | + | 0.822218i | \(0.692737\pi\) | |||||||
\(200\) | −0.704746 | −0.0498331 | ||||||||
\(201\) | −4.65238 | −0.328154 | ||||||||
\(202\) | 5.40987 | 0.380637 | ||||||||
\(203\) | −29.7770 | −2.08993 | ||||||||
\(204\) | 7.25353 | 0.507849 | ||||||||
\(205\) | 5.72085 | 0.399562 | ||||||||
\(206\) | 7.09844 | 0.494572 | ||||||||
\(207\) | −6.13606 | −0.426485 | ||||||||
\(208\) | 22.2226 | 1.54086 | ||||||||
\(209\) | −5.04667 | −0.349085 | ||||||||
\(210\) | 5.56905 | 0.384301 | ||||||||
\(211\) | 8.27089 | 0.569392 | 0.284696 | − | 0.958618i | \(-0.408107\pi\) | ||||
0.284696 | + | 0.958618i | \(0.408107\pi\) | |||||||
\(212\) | 9.34734 | 0.641978 | ||||||||
\(213\) | −15.5977 | −1.06874 | ||||||||
\(214\) | −6.42824 | −0.439426 | ||||||||
\(215\) | 5.21364 | 0.355567 | ||||||||
\(216\) | 0.860097 | 0.0585222 | ||||||||
\(217\) | 1.70699 | 0.115878 | ||||||||
\(218\) | −1.98064 | −0.134146 | ||||||||
\(219\) | 2.90781 | 0.196492 | ||||||||
\(220\) | −6.44440 | −0.434481 | ||||||||
\(221\) | 15.0509 | 1.01243 | ||||||||
\(222\) | 2.65929 | 0.178480 | ||||||||
\(223\) | −4.66570 | −0.312438 | −0.156219 | − | 0.987722i | \(-0.549931\pi\) | ||||
−0.156219 | + | 0.987722i | \(0.549931\pi\) | |||||||
\(224\) | −26.7904 | −1.79001 | ||||||||
\(225\) | 5.52873 | 0.368582 | ||||||||
\(226\) | −35.7009 | −2.37479 | ||||||||
\(227\) | 5.48397 | 0.363984 | 0.181992 | − | 0.983300i | \(-0.441746\pi\) | ||||
0.181992 | + | 0.983300i | \(0.441746\pi\) | |||||||
\(228\) | 2.40421 | 0.159222 | ||||||||
\(229\) | −2.48999 | −0.164543 | −0.0822716 | − | 0.996610i | \(-0.526217\pi\) | ||||
−0.0822716 | + | 0.996610i | \(0.526217\pi\) | |||||||
\(230\) | 6.27687 | 0.413885 | ||||||||
\(231\) | 24.6421 | 1.62133 | ||||||||
\(232\) | 1.34195 | 0.0881036 | ||||||||
\(233\) | −8.34522 | −0.546713 | −0.273357 | − | 0.961913i | \(-0.588134\pi\) | ||||
−0.273357 | + | 0.961913i | \(0.588134\pi\) | |||||||
\(234\) | −12.7044 | −0.830511 | ||||||||
\(235\) | −4.95019 | −0.322915 | ||||||||
\(236\) | 0.534852 | 0.0348159 | ||||||||
\(237\) | −16.8570 | −1.09498 | ||||||||
\(238\) | −18.8446 | −1.22152 | ||||||||
\(239\) | 15.8759 | 1.02692 | 0.513462 | − | 0.858112i | \(-0.328363\pi\) | ||||
0.513462 | + | 0.858112i | \(0.328363\pi\) | |||||||
\(240\) | −3.44408 | −0.222315 | ||||||||
\(241\) | 20.0036 | 1.28855 | 0.644274 | − | 0.764795i | \(-0.277160\pi\) | ||||
0.644274 | + | 0.764795i | \(0.277160\pi\) | |||||||
\(242\) | −36.3863 | −2.33900 | ||||||||
\(243\) | −11.5702 | −0.742226 | ||||||||
\(244\) | −0.476861 | −0.0305279 | ||||||||
\(245\) | −2.76341 | −0.176548 | ||||||||
\(246\) | −24.6020 | −1.56856 | ||||||||
\(247\) | 4.98866 | 0.317421 | ||||||||
\(248\) | −0.0769285 | −0.00488496 | ||||||||
\(249\) | 5.94918 | 0.377014 | ||||||||
\(250\) | −11.7796 | −0.745006 | ||||||||
\(251\) | −11.4032 | −0.719766 | −0.359883 | − | 0.932997i | \(-0.617183\pi\) | ||||
−0.359883 | + | 0.932997i | \(0.617183\pi\) | |||||||
\(252\) | 7.79711 | 0.491172 | ||||||||
\(253\) | 27.7741 | 1.74614 | ||||||||
\(254\) | −16.2615 | −1.02034 | ||||||||
\(255\) | −2.33260 | −0.146073 | ||||||||
\(256\) | 17.1608 | 1.07255 | ||||||||
\(257\) | 6.27447 | 0.391391 | 0.195695 | − | 0.980665i | \(-0.437304\pi\) | ||||
0.195695 | + | 0.980665i | \(0.437304\pi\) | |||||||
\(258\) | −22.4207 | −1.39585 | ||||||||
\(259\) | −3.38656 | −0.210430 | ||||||||
\(260\) | 6.37033 | 0.395071 | ||||||||
\(261\) | −10.5276 | −0.651644 | ||||||||
\(262\) | −1.54781 | −0.0956241 | ||||||||
\(263\) | −20.1199 | −1.24065 | −0.620325 | − | 0.784345i | \(-0.712999\pi\) | ||||
−0.620325 | + | 0.784345i | \(0.712999\pi\) | |||||||
\(264\) | −1.11054 | −0.0683491 | ||||||||
\(265\) | −3.00593 | −0.184653 | ||||||||
\(266\) | −6.24612 | −0.382974 | ||||||||
\(267\) | −0.904541 | −0.0553570 | ||||||||
\(268\) | 6.66319 | 0.407019 | ||||||||
\(269\) | −13.0264 | −0.794234 | −0.397117 | − | 0.917768i | \(-0.629989\pi\) | ||||
−0.397117 | + | 0.917768i | \(0.629989\pi\) | |||||||
\(270\) | 6.90231 | 0.420061 | ||||||||
\(271\) | 9.26068 | 0.562546 | 0.281273 | − | 0.959628i | \(-0.409243\pi\) | ||||
0.281273 | + | 0.959628i | \(0.409243\pi\) | |||||||
\(272\) | 11.6541 | 0.706636 | ||||||||
\(273\) | −24.3589 | −1.47427 | ||||||||
\(274\) | 27.3758 | 1.65383 | ||||||||
\(275\) | −25.0251 | −1.50907 | ||||||||
\(276\) | −13.2314 | −0.796439 | ||||||||
\(277\) | −6.69465 | −0.402242 | −0.201121 | − | 0.979566i | \(-0.564459\pi\) | ||||
−0.201121 | + | 0.979566i | \(0.564459\pi\) | |||||||
\(278\) | −34.2556 | −2.05451 | ||||||||
\(279\) | 0.603504 | 0.0361308 | ||||||||
\(280\) | 0.319618 | 0.0191008 | ||||||||
\(281\) | 26.4566 | 1.57827 | 0.789135 | − | 0.614220i | \(-0.210529\pi\) | ||||
0.789135 | + | 0.614220i | \(0.210529\pi\) | |||||||
\(282\) | 21.2878 | 1.26767 | ||||||||
\(283\) | −13.4905 | −0.801926 | −0.400963 | − | 0.916094i | \(-0.631324\pi\) | ||||
−0.400963 | + | 0.916094i | \(0.631324\pi\) | |||||||
\(284\) | 22.3392 | 1.32559 | ||||||||
\(285\) | −0.773147 | −0.0457973 | ||||||||
\(286\) | 57.5048 | 3.40033 | ||||||||
\(287\) | 31.3302 | 1.84936 | ||||||||
\(288\) | −9.47174 | −0.558127 | ||||||||
\(289\) | −9.10693 | −0.535702 | ||||||||
\(290\) | 10.7692 | 0.632391 | ||||||||
\(291\) | 11.3918 | 0.667799 | ||||||||
\(292\) | −4.16460 | −0.243715 | ||||||||
\(293\) | −2.63011 | −0.153652 | −0.0768262 | − | 0.997044i | \(-0.524479\pi\) | ||||
−0.0768262 | + | 0.997044i | \(0.524479\pi\) | |||||||
\(294\) | 11.8838 | 0.693076 | ||||||||
\(295\) | −0.171998 | −0.0100141 | ||||||||
\(296\) | 0.152622 | 0.00887095 | ||||||||
\(297\) | 30.5415 | 1.77220 | ||||||||
\(298\) | −31.5350 | −1.82677 | ||||||||
\(299\) | −27.4549 | −1.58776 | ||||||||
\(300\) | 11.9218 | 0.688307 | ||||||||
\(301\) | 28.5524 | 1.64573 | ||||||||
\(302\) | −19.9616 | −1.14866 | ||||||||
\(303\) | 3.66725 | 0.210678 | ||||||||
\(304\) | 3.86280 | 0.221547 | ||||||||
\(305\) | 0.153350 | 0.00878077 | ||||||||
\(306\) | −6.66251 | −0.380870 | ||||||||
\(307\) | 10.2071 | 0.582552 | 0.291276 | − | 0.956639i | \(-0.405920\pi\) | ||||
0.291276 | + | 0.956639i | \(0.405920\pi\) | |||||||
\(308\) | −35.2927 | −2.01099 | ||||||||
\(309\) | 4.81190 | 0.273739 | ||||||||
\(310\) | −0.617354 | −0.0350633 | ||||||||
\(311\) | 24.6510 | 1.39783 | 0.698915 | − | 0.715205i | \(-0.253667\pi\) | ||||
0.698915 | + | 0.715205i | \(0.253667\pi\) | |||||||
\(312\) | 1.09778 | 0.0621494 | ||||||||
\(313\) | −34.2154 | −1.93397 | −0.966983 | − | 0.254839i | \(-0.917977\pi\) | ||||
−0.966983 | + | 0.254839i | \(0.917977\pi\) | |||||||
\(314\) | 34.7498 | 1.96104 | ||||||||
\(315\) | −2.50740 | −0.141276 | ||||||||
\(316\) | 24.1428 | 1.35814 | ||||||||
\(317\) | −31.0060 | −1.74147 | −0.870735 | − | 0.491753i | \(-0.836356\pi\) | ||||
−0.870735 | + | 0.491753i | \(0.836356\pi\) | |||||||
\(318\) | 12.9267 | 0.724893 | ||||||||
\(319\) | 47.6520 | 2.66800 | ||||||||
\(320\) | 4.55879 | 0.254844 | ||||||||
\(321\) | −4.35759 | −0.243217 | ||||||||
\(322\) | 34.3752 | 1.91565 | ||||||||
\(323\) | 2.61619 | 0.145568 | ||||||||
\(324\) | −7.64271 | −0.424595 | ||||||||
\(325\) | 24.7375 | 1.37219 | ||||||||
\(326\) | 26.8500 | 1.48708 | ||||||||
\(327\) | −1.34264 | −0.0742482 | ||||||||
\(328\) | −1.41195 | −0.0779620 | ||||||||
\(329\) | −27.1096 | −1.49460 | ||||||||
\(330\) | −8.91214 | −0.490597 | ||||||||
\(331\) | −26.3847 | −1.45024 | −0.725118 | − | 0.688624i | \(-0.758215\pi\) | ||||
−0.725118 | + | 0.688624i | \(0.758215\pi\) | |||||||
\(332\) | −8.52048 | −0.467622 | ||||||||
\(333\) | −1.19732 | −0.0656125 | ||||||||
\(334\) | 0.530029 | 0.0290019 | ||||||||
\(335\) | −2.14276 | −0.117071 | ||||||||
\(336\) | −18.8615 | −1.02898 | ||||||||
\(337\) | −16.2883 | −0.887278 | −0.443639 | − | 0.896206i | \(-0.646313\pi\) | ||||
−0.443639 | + | 0.896206i | \(0.646313\pi\) | |||||||
\(338\) | −31.0955 | −1.69137 | ||||||||
\(339\) | −24.2010 | −1.31442 | ||||||||
\(340\) | 3.34077 | 0.181179 | ||||||||
\(341\) | −2.73168 | −0.147929 | ||||||||
\(342\) | −2.20831 | −0.119412 | ||||||||
\(343\) | 8.57214 | 0.462852 | ||||||||
\(344\) | −1.28677 | −0.0693778 | ||||||||
\(345\) | 4.25498 | 0.229080 | ||||||||
\(346\) | 1.74752 | 0.0939474 | ||||||||
\(347\) | −15.6952 | −0.842565 | −0.421283 | − | 0.906929i | \(-0.638420\pi\) | ||||
−0.421283 | + | 0.906929i | \(0.638420\pi\) | |||||||
\(348\) | −22.7012 | −1.21691 | ||||||||
\(349\) | −15.8380 | −0.847790 | −0.423895 | − | 0.905711i | \(-0.639338\pi\) | ||||
−0.423895 | + | 0.905711i | \(0.639338\pi\) | |||||||
\(350\) | −30.9729 | −1.65557 | ||||||||
\(351\) | −30.1905 | −1.61145 | ||||||||
\(352\) | 42.8726 | 2.28512 | ||||||||
\(353\) | 16.1608 | 0.860155 | 0.430077 | − | 0.902792i | \(-0.358486\pi\) | ||||
0.430077 | + | 0.902792i | \(0.358486\pi\) | |||||||
\(354\) | 0.739661 | 0.0393125 | ||||||||
\(355\) | −7.18385 | −0.381279 | ||||||||
\(356\) | 1.29549 | 0.0686610 | ||||||||
\(357\) | −12.7744 | −0.676094 | ||||||||
\(358\) | −18.2770 | −0.965972 | ||||||||
\(359\) | −33.8353 | −1.78576 | −0.892880 | − | 0.450294i | \(-0.851319\pi\) | ||||
−0.892880 | + | 0.450294i | \(0.851319\pi\) | |||||||
\(360\) | 0.113001 | 0.00595567 | ||||||||
\(361\) | −18.1329 | −0.954361 | ||||||||
\(362\) | 23.8262 | 1.25228 | ||||||||
\(363\) | −24.6656 | −1.29461 | ||||||||
\(364\) | 34.8870 | 1.82858 | ||||||||
\(365\) | 1.33926 | 0.0700999 | ||||||||
\(366\) | −0.659465 | −0.0344708 | ||||||||
\(367\) | 14.1881 | 0.740613 | 0.370306 | − | 0.928910i | \(-0.379253\pi\) | ||||
0.370306 | + | 0.928910i | \(0.379253\pi\) | |||||||
\(368\) | −21.2587 | −1.10819 | ||||||||
\(369\) | 11.0768 | 0.576633 | ||||||||
\(370\) | 1.22479 | 0.0636740 | ||||||||
\(371\) | −16.4619 | −0.854659 | ||||||||
\(372\) | 1.30136 | 0.0674724 | ||||||||
\(373\) | −5.19861 | −0.269174 | −0.134587 | − | 0.990902i | \(-0.542971\pi\) | ||||
−0.134587 | + | 0.990902i | \(0.542971\pi\) | |||||||
\(374\) | 30.1570 | 1.55938 | ||||||||
\(375\) | −7.98516 | −0.412352 | ||||||||
\(376\) | 1.22175 | 0.0630067 | ||||||||
\(377\) | −47.1043 | −2.42599 | ||||||||
\(378\) | 37.8004 | 1.94424 | ||||||||
\(379\) | −7.54158 | −0.387385 | −0.193692 | − | 0.981062i | \(-0.562046\pi\) | ||||
−0.193692 | + | 0.981062i | \(0.562046\pi\) | |||||||
\(380\) | 1.10731 | 0.0568038 | ||||||||
\(381\) | −11.0234 | −0.564745 | ||||||||
\(382\) | 23.3332 | 1.19383 | ||||||||
\(383\) | −34.1790 | −1.74646 | −0.873232 | − | 0.487304i | \(-0.837980\pi\) | ||||
−0.873232 | + | 0.487304i | \(0.837980\pi\) | |||||||
\(384\) | 1.63811 | 0.0835945 | ||||||||
\(385\) | 11.3494 | 0.578421 | ||||||||
\(386\) | −19.0306 | −0.968630 | ||||||||
\(387\) | 10.0947 | 0.513142 | ||||||||
\(388\) | −16.3154 | −0.828291 | ||||||||
\(389\) | 0.377920 | 0.0191613 | 0.00958065 | − | 0.999954i | \(-0.496950\pi\) | ||||
0.00958065 | + | 0.999954i | \(0.496950\pi\) | |||||||
\(390\) | 8.80970 | 0.446097 | ||||||||
\(391\) | −14.3980 | −0.728141 | ||||||||
\(392\) | 0.682032 | 0.0344478 | ||||||||
\(393\) | −1.04923 | −0.0529268 | ||||||||
\(394\) | −23.3712 | −1.17742 | ||||||||
\(395\) | −7.76385 | −0.390642 | ||||||||
\(396\) | −12.4777 | −0.627028 | ||||||||
\(397\) | −11.2555 | −0.564897 | −0.282449 | − | 0.959282i | \(-0.591147\pi\) | ||||
−0.282449 | + | 0.959282i | \(0.591147\pi\) | |||||||
\(398\) | 31.8058 | 1.59428 | ||||||||
\(399\) | −4.23413 | −0.211971 | ||||||||
\(400\) | 19.1546 | 0.957732 | ||||||||
\(401\) | 14.9145 | 0.744796 | 0.372398 | − | 0.928073i | \(-0.378536\pi\) | ||||
0.372398 | + | 0.928073i | \(0.378536\pi\) | |||||||
\(402\) | 9.21471 | 0.459588 | ||||||||
\(403\) | 2.70029 | 0.134511 | ||||||||
\(404\) | −5.25227 | −0.261310 | ||||||||
\(405\) | 2.45775 | 0.122127 | ||||||||
\(406\) | 58.9775 | 2.92700 | ||||||||
\(407\) | 5.41950 | 0.268635 | ||||||||
\(408\) | 0.575703 | 0.0285016 | ||||||||
\(409\) | −29.3022 | −1.44890 | −0.724450 | − | 0.689327i | \(-0.757906\pi\) | ||||
−0.724450 | + | 0.689327i | \(0.757906\pi\) | |||||||
\(410\) | −11.3310 | −0.559596 | ||||||||
\(411\) | 18.5576 | 0.915377 | ||||||||
\(412\) | −6.89165 | −0.339527 | ||||||||
\(413\) | −0.941945 | −0.0463501 | ||||||||
\(414\) | 12.1533 | 0.597304 | ||||||||
\(415\) | 2.74002 | 0.134503 | ||||||||
\(416\) | −42.3799 | −2.07784 | ||||||||
\(417\) | −23.2212 | −1.13715 | ||||||||
\(418\) | 9.99564 | 0.488903 | ||||||||
\(419\) | 18.5845 | 0.907915 | 0.453957 | − | 0.891023i | \(-0.350012\pi\) | ||||
0.453957 | + | 0.891023i | \(0.350012\pi\) | |||||||
\(420\) | −5.40682 | −0.263826 | ||||||||
\(421\) | −18.9421 | −0.923179 | −0.461590 | − | 0.887094i | \(-0.652721\pi\) | ||||
−0.461590 | + | 0.887094i | \(0.652721\pi\) | |||||||
\(422\) | −16.3817 | −0.797448 | ||||||||
\(423\) | −9.58459 | −0.466019 | ||||||||
\(424\) | 0.741886 | 0.0360292 | ||||||||
\(425\) | 12.9730 | 0.629282 | ||||||||
\(426\) | 30.8934 | 1.49679 | ||||||||
\(427\) | 0.839816 | 0.0406415 | ||||||||
\(428\) | 6.24098 | 0.301669 | ||||||||
\(429\) | 38.9814 | 1.88204 | ||||||||
\(430\) | −10.3264 | −0.497981 | ||||||||
\(431\) | 21.5017 | 1.03570 | 0.517851 | − | 0.855471i | \(-0.326732\pi\) | ||||
0.517851 | + | 0.855471i | \(0.326732\pi\) | |||||||
\(432\) | −23.3770 | −1.12473 | ||||||||
\(433\) | −32.5442 | −1.56398 | −0.781988 | − | 0.623293i | \(-0.785794\pi\) | ||||
−0.781988 | + | 0.623293i | \(0.785794\pi\) | |||||||
\(434\) | −3.38093 | −0.162290 | ||||||||
\(435\) | 7.30026 | 0.350021 | ||||||||
\(436\) | 1.92294 | 0.0920923 | ||||||||
\(437\) | −4.77228 | −0.228289 | ||||||||
\(438\) | −5.75934 | −0.275192 | ||||||||
\(439\) | −20.3993 | −0.973607 | −0.486804 | − | 0.873511i | \(-0.661837\pi\) | ||||
−0.486804 | + | 0.873511i | \(0.661837\pi\) | |||||||
\(440\) | −0.511484 | −0.0243840 | ||||||||
\(441\) | −5.35054 | −0.254787 | ||||||||
\(442\) | −29.8104 | −1.41794 | ||||||||
\(443\) | −2.83110 | −0.134510 | −0.0672548 | − | 0.997736i | \(-0.521424\pi\) | ||||
−0.0672548 | + | 0.997736i | \(0.521424\pi\) | |||||||
\(444\) | −2.58182 | −0.122528 | ||||||||
\(445\) | −0.416606 | −0.0197490 | ||||||||
\(446\) | 9.24108 | 0.437578 | ||||||||
\(447\) | −21.3770 | −1.01110 | ||||||||
\(448\) | 24.9661 | 1.17954 | ||||||||
\(449\) | −7.53564 | −0.355629 | −0.177814 | − | 0.984064i | \(-0.556903\pi\) | ||||
−0.177814 | + | 0.984064i | \(0.556903\pi\) | |||||||
\(450\) | −10.9504 | −0.516208 | ||||||||
\(451\) | −50.1376 | −2.36089 | ||||||||
\(452\) | 34.6609 | 1.63031 | ||||||||
\(453\) | −13.5316 | −0.635769 | ||||||||
\(454\) | −10.8618 | −0.509768 | ||||||||
\(455\) | −11.2190 | −0.525955 | ||||||||
\(456\) | 0.190819 | 0.00893591 | ||||||||
\(457\) | 6.71365 | 0.314051 | 0.157026 | − | 0.987595i | \(-0.449809\pi\) | ||||
0.157026 | + | 0.987595i | \(0.449809\pi\) | |||||||
\(458\) | 4.93178 | 0.230447 | ||||||||
\(459\) | −15.8327 | −0.739006 | ||||||||
\(460\) | −6.09402 | −0.284135 | ||||||||
\(461\) | 22.8486 | 1.06417 | 0.532083 | − | 0.846692i | \(-0.321409\pi\) | ||||
0.532083 | + | 0.846692i | \(0.321409\pi\) | |||||||
\(462\) | −48.8072 | −2.27072 | ||||||||
\(463\) | −19.7218 | −0.916552 | −0.458276 | − | 0.888810i | \(-0.651533\pi\) | ||||
−0.458276 | + | 0.888810i | \(0.651533\pi\) | |||||||
\(464\) | −36.4736 | −1.69325 | ||||||||
\(465\) | −0.418493 | −0.0194071 | ||||||||
\(466\) | 16.5289 | 0.765686 | ||||||||
\(467\) | −11.3800 | −0.526605 | −0.263302 | − | 0.964713i | \(-0.584812\pi\) | ||||
−0.263302 | + | 0.964713i | \(0.584812\pi\) | |||||||
\(468\) | 12.3343 | 0.570152 | ||||||||
\(469\) | −11.7348 | −0.541861 | ||||||||
\(470\) | 9.80455 | 0.452250 | ||||||||
\(471\) | 23.5562 | 1.08541 | ||||||||
\(472\) | 0.0424505 | 0.00195394 | ||||||||
\(473\) | −45.6923 | −2.10094 | ||||||||
\(474\) | 33.3877 | 1.53355 | ||||||||
\(475\) | 4.29994 | 0.197295 | ||||||||
\(476\) | 18.2957 | 0.838580 | ||||||||
\(477\) | −5.82010 | −0.266484 | ||||||||
\(478\) | −31.4444 | −1.43823 | ||||||||
\(479\) | −38.7162 | −1.76899 | −0.884495 | − | 0.466550i | \(-0.845497\pi\) | ||||
−0.884495 | + | 0.466550i | \(0.845497\pi\) | |||||||
\(480\) | 6.56807 | 0.299790 | ||||||||
\(481\) | −5.35721 | −0.244268 | ||||||||
\(482\) | −39.6200 | −1.80464 | ||||||||
\(483\) | 23.3023 | 1.06029 | ||||||||
\(484\) | 35.3264 | 1.60574 | ||||||||
\(485\) | 5.24674 | 0.238242 | ||||||||
\(486\) | 22.9163 | 1.03951 | ||||||||
\(487\) | 4.30432 | 0.195048 | 0.0975238 | − | 0.995233i | \(-0.468908\pi\) | ||||
0.0975238 | + | 0.995233i | \(0.468908\pi\) | |||||||
\(488\) | −0.0378479 | −0.00171329 | ||||||||
\(489\) | 18.2011 | 0.823082 | ||||||||
\(490\) | 5.47333 | 0.247260 | ||||||||
\(491\) | 4.44326 | 0.200522 | 0.100261 | − | 0.994961i | \(-0.468032\pi\) | ||||
0.100261 | + | 0.994961i | \(0.468032\pi\) | |||||||
\(492\) | 23.8853 | 1.07683 | ||||||||
\(493\) | −24.7027 | −1.11255 | ||||||||
\(494\) | −9.88075 | −0.444556 | ||||||||
\(495\) | 4.01259 | 0.180353 | ||||||||
\(496\) | 2.09088 | 0.0938831 | ||||||||
\(497\) | −39.3422 | −1.76474 | ||||||||
\(498\) | −11.7832 | −0.528018 | ||||||||
\(499\) | −40.1351 | −1.79669 | −0.898347 | − | 0.439287i | \(-0.855231\pi\) | ||||
−0.898347 | + | 0.439287i | \(0.855231\pi\) | |||||||
\(500\) | 11.4364 | 0.511452 | ||||||||
\(501\) | 0.359297 | 0.0160522 | ||||||||
\(502\) | 22.5857 | 1.00805 | ||||||||
\(503\) | −18.2884 | −0.815440 | −0.407720 | − | 0.913107i | \(-0.633676\pi\) | ||||
−0.407720 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(504\) | 0.618847 | 0.0275656 | ||||||||
\(505\) | 1.68903 | 0.0751609 | ||||||||
\(506\) | −55.0105 | −2.44552 | ||||||||
\(507\) | −21.0790 | −0.936153 | ||||||||
\(508\) | 15.7878 | 0.700470 | ||||||||
\(509\) | −22.5704 | −1.00041 | −0.500207 | − | 0.865906i | \(-0.666743\pi\) | ||||
−0.500207 | + | 0.865906i | \(0.666743\pi\) | |||||||
\(510\) | 4.62004 | 0.204579 | ||||||||
\(511\) | 7.33441 | 0.324455 | ||||||||
\(512\) | −31.5492 | −1.39429 | ||||||||
\(513\) | −5.24780 | −0.231696 | ||||||||
\(514\) | −12.4275 | −0.548153 | ||||||||
\(515\) | 2.21622 | 0.0976585 | ||||||||
\(516\) | 21.7676 | 0.958265 | ||||||||
\(517\) | 43.3834 | 1.90800 | ||||||||
\(518\) | 6.70756 | 0.294713 | ||||||||
\(519\) | 1.18461 | 0.0519987 | ||||||||
\(520\) | 0.505605 | 0.0221722 | ||||||||
\(521\) | 35.6566 | 1.56214 | 0.781072 | − | 0.624441i | \(-0.214673\pi\) | ||||
0.781072 | + | 0.624441i | \(0.214673\pi\) | |||||||
\(522\) | 20.8515 | 0.912644 | ||||||||
\(523\) | 18.7053 | 0.817924 | 0.408962 | − | 0.912552i | \(-0.365891\pi\) | ||||
0.408962 | + | 0.912552i | \(0.365891\pi\) | |||||||
\(524\) | 1.50272 | 0.0656467 | ||||||||
\(525\) | −20.9959 | −0.916337 | ||||||||
\(526\) | 39.8504 | 1.73756 | ||||||||
\(527\) | 1.41610 | 0.0616863 | ||||||||
\(528\) | 30.1840 | 1.31359 | ||||||||
\(529\) | 3.26402 | 0.141914 | ||||||||
\(530\) | 5.95366 | 0.258611 | ||||||||
\(531\) | −0.333024 | −0.0144520 | ||||||||
\(532\) | 6.06416 | 0.262915 | ||||||||
\(533\) | 49.5613 | 2.14674 | ||||||||
\(534\) | 1.79157 | 0.0775289 | ||||||||
\(535\) | −2.00698 | −0.0867693 | ||||||||
\(536\) | 0.528849 | 0.0228428 | ||||||||
\(537\) | −12.3897 | −0.534654 | ||||||||
\(538\) | 25.8006 | 1.11234 | ||||||||
\(539\) | 24.2185 | 1.04317 | ||||||||
\(540\) | −6.70124 | −0.288375 | ||||||||
\(541\) | −16.8553 | −0.724666 | −0.362333 | − | 0.932049i | \(-0.618020\pi\) | ||||
−0.362333 | + | 0.932049i | \(0.618020\pi\) | |||||||
\(542\) | −18.3421 | −0.787860 | ||||||||
\(543\) | 16.1513 | 0.693120 | ||||||||
\(544\) | −22.2251 | −0.952894 | ||||||||
\(545\) | −0.618382 | −0.0264886 | ||||||||
\(546\) | 48.2462 | 2.06475 | ||||||||
\(547\) | −15.5802 | −0.666162 | −0.333081 | − | 0.942898i | \(-0.608088\pi\) | ||||
−0.333081 | + | 0.942898i | \(0.608088\pi\) | |||||||
\(548\) | −26.5783 | −1.13537 | ||||||||
\(549\) | 0.296917 | 0.0126721 | ||||||||
\(550\) | 49.5658 | 2.11349 | ||||||||
\(551\) | −8.18780 | −0.348812 | ||||||||
\(552\) | −1.05016 | −0.0446979 | ||||||||
\(553\) | −42.5186 | −1.80808 | ||||||||
\(554\) | 13.2597 | 0.563351 | ||||||||
\(555\) | 0.830265 | 0.0352428 | ||||||||
\(556\) | 33.2576 | 1.41044 | ||||||||
\(557\) | 30.3804 | 1.28726 | 0.643630 | − | 0.765337i | \(-0.277428\pi\) | ||||
0.643630 | + | 0.765337i | \(0.277428\pi\) | |||||||
\(558\) | −1.19532 | −0.0506021 | ||||||||
\(559\) | 45.1671 | 1.91037 | ||||||||
\(560\) | −8.68705 | −0.367095 | ||||||||
\(561\) | 20.4429 | 0.863099 | ||||||||
\(562\) | −52.4011 | −2.21041 | ||||||||
\(563\) | −16.9390 | −0.713893 | −0.356947 | − | 0.934125i | \(-0.616182\pi\) | ||||
−0.356947 | + | 0.934125i | \(0.616182\pi\) | |||||||
\(564\) | −20.6676 | −0.870265 | ||||||||
\(565\) | −11.1463 | −0.468927 | ||||||||
\(566\) | 26.7198 | 1.12312 | ||||||||
\(567\) | 13.4598 | 0.565260 | ||||||||
\(568\) | 1.77303 | 0.0743947 | ||||||||
\(569\) | 1.18080 | 0.0495017 | 0.0247508 | − | 0.999694i | \(-0.492121\pi\) | ||||
0.0247508 | + | 0.999694i | \(0.492121\pi\) | |||||||
\(570\) | 1.53133 | 0.0641403 | ||||||||
\(571\) | 27.1901 | 1.13787 | 0.568935 | − | 0.822382i | \(-0.307355\pi\) | ||||
0.568935 | + | 0.822382i | \(0.307355\pi\) | |||||||
\(572\) | −55.8296 | −2.33435 | ||||||||
\(573\) | 15.8172 | 0.660771 | ||||||||
\(574\) | −62.0538 | −2.59008 | ||||||||
\(575\) | −23.6645 | −0.986878 | ||||||||
\(576\) | 8.82677 | 0.367782 | ||||||||
\(577\) | 6.24617 | 0.260032 | 0.130016 | − | 0.991512i | \(-0.458497\pi\) | ||||
0.130016 | + | 0.991512i | \(0.458497\pi\) | |||||||
\(578\) | 18.0376 | 0.750264 | ||||||||
\(579\) | −12.9005 | −0.536125 | ||||||||
\(580\) | −10.4555 | −0.434141 | ||||||||
\(581\) | 15.0057 | 0.622541 | ||||||||
\(582\) | −22.5631 | −0.935269 | ||||||||
\(583\) | 26.3439 | 1.09105 | ||||||||
\(584\) | −0.330539 | −0.0136778 | ||||||||
\(585\) | −3.96647 | −0.163993 | ||||||||
\(586\) | 5.20930 | 0.215194 | ||||||||
\(587\) | 5.95229 | 0.245677 | 0.122839 | − | 0.992427i | \(-0.460800\pi\) | ||||
0.122839 | + | 0.992427i | \(0.460800\pi\) | |||||||
\(588\) | −11.5376 | −0.475802 | ||||||||
\(589\) | 0.469371 | 0.0193401 | ||||||||
\(590\) | 0.340667 | 0.0140250 | ||||||||
\(591\) | −15.8429 | −0.651690 | ||||||||
\(592\) | −4.14818 | −0.170489 | ||||||||
\(593\) | 36.1326 | 1.48379 | 0.741893 | − | 0.670518i | \(-0.233928\pi\) | ||||
0.741893 | + | 0.670518i | \(0.233928\pi\) | |||||||
\(594\) | −60.4918 | −2.48201 | ||||||||
\(595\) | −5.88354 | −0.241201 | ||||||||
\(596\) | 30.6163 | 1.25409 | ||||||||
\(597\) | 21.5606 | 0.882416 | ||||||||
\(598\) | 54.3782 | 2.22369 | ||||||||
\(599\) | −8.09365 | −0.330698 | −0.165349 | − | 0.986235i | \(-0.552875\pi\) | ||||
−0.165349 | + | 0.986235i | \(0.552875\pi\) | |||||||
\(600\) | 0.946221 | 0.0386293 | ||||||||
\(601\) | 43.2733 | 1.76515 | 0.882577 | − | 0.470168i | \(-0.155807\pi\) | ||||
0.882577 | + | 0.470168i | \(0.155807\pi\) | |||||||
\(602\) | −56.5521 | −2.30489 | ||||||||
\(603\) | −4.14882 | −0.168953 | ||||||||
\(604\) | 19.3801 | 0.788563 | ||||||||
\(605\) | −11.3603 | −0.461861 | ||||||||
\(606\) | −7.26351 | −0.295060 | ||||||||
\(607\) | 13.3527 | 0.541970 | 0.270985 | − | 0.962584i | \(-0.412651\pi\) | ||||
0.270985 | + | 0.962584i | \(0.412651\pi\) | |||||||
\(608\) | −7.36659 | −0.298755 | ||||||||
\(609\) | 39.9798 | 1.62006 | ||||||||
\(610\) | −0.303731 | −0.0122977 | ||||||||
\(611\) | −42.8848 | −1.73493 | ||||||||
\(612\) | 6.46842 | 0.261470 | ||||||||
\(613\) | 2.16839 | 0.0875804 | 0.0437902 | − | 0.999041i | \(-0.486057\pi\) | ||||
0.0437902 | + | 0.999041i | \(0.486057\pi\) | |||||||
\(614\) | −20.2167 | −0.815879 | ||||||||
\(615\) | −7.68105 | −0.309730 | ||||||||
\(616\) | −2.80113 | −0.112861 | ||||||||
\(617\) | −37.9751 | −1.52882 | −0.764410 | − | 0.644731i | \(-0.776970\pi\) | ||||
−0.764410 | + | 0.644731i | \(0.776970\pi\) | |||||||
\(618\) | −9.53065 | −0.383379 | ||||||||
\(619\) | −27.9924 | −1.12511 | −0.562555 | − | 0.826760i | \(-0.690181\pi\) | ||||
−0.562555 | + | 0.826760i | \(0.690181\pi\) | |||||||
\(620\) | 0.599369 | 0.0240713 | ||||||||
\(621\) | 28.8810 | 1.15895 | ||||||||
\(622\) | −48.8248 | −1.95770 | ||||||||
\(623\) | −2.28153 | −0.0914077 | ||||||||
\(624\) | −29.8370 | −1.19444 | ||||||||
\(625\) | 19.4103 | 0.776411 | ||||||||
\(626\) | 67.7684 | 2.70857 | ||||||||
\(627\) | 6.77586 | 0.270602 | ||||||||
\(628\) | −33.7375 | −1.34627 | ||||||||
\(629\) | −2.80946 | −0.112021 | ||||||||
\(630\) | 4.96627 | 0.197861 | ||||||||
\(631\) | −9.66675 | −0.384827 | −0.192414 | − | 0.981314i | \(-0.561632\pi\) | ||||
−0.192414 | + | 0.981314i | \(0.561632\pi\) | |||||||
\(632\) | 1.91618 | 0.0762216 | ||||||||
\(633\) | −11.1048 | −0.441378 | ||||||||
\(634\) | 61.4118 | 2.43897 | ||||||||
\(635\) | −5.07705 | −0.201477 | ||||||||
\(636\) | −12.5501 | −0.497645 | ||||||||
\(637\) | −23.9402 | −0.948544 | ||||||||
\(638\) | −94.3815 | −3.73660 | ||||||||
\(639\) | −13.9094 | −0.550248 | ||||||||
\(640\) | 0.754467 | 0.0298229 | ||||||||
\(641\) | −5.72871 | −0.226271 | −0.113135 | − | 0.993580i | \(-0.536089\pi\) | ||||
−0.113135 | + | 0.993580i | \(0.536089\pi\) | |||||||
\(642\) | 8.63082 | 0.340631 | ||||||||
\(643\) | 11.4965 | 0.453377 | 0.226689 | − | 0.973967i | \(-0.427210\pi\) | ||||
0.226689 | + | 0.973967i | \(0.427210\pi\) | |||||||
\(644\) | −33.3738 | −1.31511 | ||||||||
\(645\) | −7.00004 | −0.275626 | ||||||||
\(646\) | −5.18173 | −0.203872 | ||||||||
\(647\) | −1.59477 | −0.0626968 | −0.0313484 | − | 0.999509i | \(-0.509980\pi\) | ||||
−0.0313484 | + | 0.999509i | \(0.509980\pi\) | |||||||
\(648\) | −0.606592 | −0.0238292 | ||||||||
\(649\) | 1.50739 | 0.0591703 | ||||||||
\(650\) | −48.9961 | −1.92178 | ||||||||
\(651\) | −2.29187 | −0.0898254 | ||||||||
\(652\) | −26.0678 | −1.02089 | ||||||||
\(653\) | −49.5836 | −1.94036 | −0.970179 | − | 0.242389i | \(-0.922069\pi\) | ||||
−0.970179 | + | 0.242389i | \(0.922069\pi\) | |||||||
\(654\) | 2.65929 | 0.103987 | ||||||||
\(655\) | −0.483247 | −0.0188820 | ||||||||
\(656\) | 38.3761 | 1.49834 | ||||||||
\(657\) | 2.59308 | 0.101166 | ||||||||
\(658\) | 53.6944 | 2.09323 | ||||||||
\(659\) | −42.8682 | −1.66991 | −0.834954 | − | 0.550319i | \(-0.814506\pi\) | ||||
−0.834954 | + | 0.550319i | \(0.814506\pi\) | |||||||
\(660\) | 8.65252 | 0.336799 | ||||||||
\(661\) | −13.2723 | −0.516234 | −0.258117 | − | 0.966114i | \(-0.583102\pi\) | ||||
−0.258117 | + | 0.966114i | \(0.583102\pi\) | |||||||
\(662\) | 52.2587 | 2.03109 | ||||||||
\(663\) | −20.2079 | −0.784810 | ||||||||
\(664\) | −0.676260 | −0.0262440 | ||||||||
\(665\) | −1.95012 | −0.0756223 | ||||||||
\(666\) | 2.37145 | 0.0918920 | ||||||||
\(667\) | 45.0612 | 1.74478 | ||||||||
\(668\) | −0.514588 | −0.0199100 | ||||||||
\(669\) | 6.26436 | 0.242194 | ||||||||
\(670\) | 4.24403 | 0.163961 | ||||||||
\(671\) | −1.34396 | −0.0518828 | ||||||||
\(672\) | 35.9699 | 1.38757 | ||||||||
\(673\) | 26.9109 | 1.03734 | 0.518670 | − | 0.854974i | \(-0.326427\pi\) | ||||
0.518670 | + | 0.854974i | \(0.326427\pi\) | |||||||
\(674\) | 32.2612 | 1.24266 | ||||||||
\(675\) | −26.0224 | −1.00160 | ||||||||
\(676\) | 30.1896 | 1.16114 | ||||||||
\(677\) | −0.906737 | −0.0348487 | −0.0174244 | − | 0.999848i | \(-0.505547\pi\) | ||||
−0.0174244 | + | 0.999848i | \(0.505547\pi\) | |||||||
\(678\) | 47.9335 | 1.84087 | ||||||||
\(679\) | 28.7337 | 1.10270 | ||||||||
\(680\) | 0.265153 | 0.0101681 | ||||||||
\(681\) | −7.36300 | −0.282151 | ||||||||
\(682\) | 5.41049 | 0.207178 | ||||||||
\(683\) | 24.5925 | 0.941007 | 0.470503 | − | 0.882398i | \(-0.344072\pi\) | ||||
0.470503 | + | 0.882398i | \(0.344072\pi\) | |||||||
\(684\) | 2.14398 | 0.0819771 | ||||||||
\(685\) | 8.54709 | 0.326567 | ||||||||
\(686\) | −16.9783 | −0.648236 | ||||||||
\(687\) | 3.34316 | 0.127550 | ||||||||
\(688\) | 34.9737 | 1.33336 | ||||||||
\(689\) | −26.0411 | −0.992089 | ||||||||
\(690\) | −8.42759 | −0.320833 | ||||||||
\(691\) | −36.5197 | −1.38928 | −0.694638 | − | 0.719360i | \(-0.744435\pi\) | ||||
−0.694638 | + | 0.719360i | \(0.744435\pi\) | |||||||
\(692\) | −1.69661 | −0.0644956 | ||||||||
\(693\) | 21.9749 | 0.834757 | ||||||||
\(694\) | 31.0867 | 1.18003 | ||||||||
\(695\) | −10.6950 | −0.405685 | ||||||||
\(696\) | −1.80176 | −0.0682956 | ||||||||
\(697\) | 25.9912 | 0.984488 | ||||||||
\(698\) | 31.3695 | 1.18735 | ||||||||
\(699\) | 11.2046 | 0.423798 | ||||||||
\(700\) | 30.0706 | 1.13656 | ||||||||
\(701\) | 19.8679 | 0.750400 | 0.375200 | − | 0.926944i | \(-0.377574\pi\) | ||||
0.375200 | + | 0.926944i | \(0.377574\pi\) | |||||||
\(702\) | 59.7965 | 2.25688 | ||||||||
\(703\) | −0.931205 | −0.0351211 | ||||||||
\(704\) | −39.9533 | −1.50579 | ||||||||
\(705\) | 6.64632 | 0.250315 | ||||||||
\(706\) | −32.0088 | −1.20467 | ||||||||
\(707\) | 9.24995 | 0.347880 | ||||||||
\(708\) | −0.718114 | −0.0269884 | ||||||||
\(709\) | −2.15409 | −0.0808985 | −0.0404493 | − | 0.999182i | \(-0.512879\pi\) | ||||
−0.0404493 | + | 0.999182i | \(0.512879\pi\) | |||||||
\(710\) | 14.2286 | 0.533991 | ||||||||
\(711\) | −15.0324 | −0.563760 | ||||||||
\(712\) | 0.102822 | 0.00385340 | ||||||||
\(713\) | −2.58316 | −0.0967402 | ||||||||
\(714\) | 25.3016 | 0.946887 | ||||||||
\(715\) | 17.9537 | 0.671431 | ||||||||
\(716\) | 17.7446 | 0.663147 | ||||||||
\(717\) | −21.3156 | −0.796045 | ||||||||
\(718\) | 67.0157 | 2.50100 | ||||||||
\(719\) | 42.5468 | 1.58673 | 0.793363 | − | 0.608749i | \(-0.208328\pi\) | ||||
0.793363 | + | 0.608749i | \(0.208328\pi\) | |||||||
\(720\) | −3.07130 | −0.114461 | ||||||||
\(721\) | 12.1371 | 0.452010 | ||||||||
\(722\) | 35.9147 | 1.33661 | ||||||||
\(723\) | −26.8577 | −0.998848 | ||||||||
\(724\) | −23.1321 | −0.859698 | ||||||||
\(725\) | −40.6012 | −1.50789 | ||||||||
\(726\) | 48.8538 | 1.81313 | ||||||||
\(727\) | 12.2622 | 0.454779 | 0.227390 | − | 0.973804i | \(-0.426981\pi\) | ||||
0.227390 | + | 0.973804i | \(0.426981\pi\) | |||||||
\(728\) | 2.76894 | 0.102624 | ||||||||
\(729\) | 27.4580 | 1.01696 | ||||||||
\(730\) | −2.65259 | −0.0981767 | ||||||||
\(731\) | 23.6868 | 0.876089 | ||||||||
\(732\) | 0.640253 | 0.0236644 | ||||||||
\(733\) | 24.0175 | 0.887106 | 0.443553 | − | 0.896248i | \(-0.353718\pi\) | ||||
0.443553 | + | 0.896248i | \(0.353718\pi\) | |||||||
\(734\) | −28.1016 | −1.03725 | ||||||||
\(735\) | 3.71027 | 0.136855 | ||||||||
\(736\) | 40.5416 | 1.49439 | ||||||||
\(737\) | 18.7791 | 0.691738 | ||||||||
\(738\) | −21.9391 | −0.807589 | ||||||||
\(739\) | −25.9424 | −0.954305 | −0.477152 | − | 0.878821i | \(-0.658331\pi\) | ||||
−0.477152 | + | 0.878821i | \(0.658331\pi\) | |||||||
\(740\) | −1.18911 | −0.0437127 | ||||||||
\(741\) | −6.69798 | −0.246056 | ||||||||
\(742\) | 32.6051 | 1.19697 | ||||||||
\(743\) | −44.7577 | −1.64200 | −0.821000 | − | 0.570928i | \(-0.806584\pi\) | ||||
−0.821000 | + | 0.570928i | \(0.806584\pi\) | |||||||
\(744\) | 0.103287 | 0.00378670 | ||||||||
\(745\) | −9.84563 | −0.360716 | ||||||||
\(746\) | 10.2966 | 0.376985 | ||||||||
\(747\) | 5.30526 | 0.194109 | ||||||||
\(748\) | −29.2785 | −1.07053 | ||||||||
\(749\) | −10.9912 | −0.401609 | ||||||||
\(750\) | 15.8157 | 0.577509 | ||||||||
\(751\) | 20.9474 | 0.764382 | 0.382191 | − | 0.924083i | \(-0.375170\pi\) | ||||
0.382191 | + | 0.924083i | \(0.375170\pi\) | |||||||
\(752\) | −33.2064 | −1.21091 | ||||||||
\(753\) | 15.3104 | 0.557944 | ||||||||
\(754\) | 93.2967 | 3.39767 | ||||||||
\(755\) | −6.23226 | −0.226815 | ||||||||
\(756\) | −36.6992 | −1.33474 | ||||||||
\(757\) | −9.25237 | −0.336283 | −0.168142 | − | 0.985763i | \(-0.553777\pi\) | ||||
−0.168142 | + | 0.985763i | \(0.553777\pi\) | |||||||
\(758\) | 14.9372 | 0.542542 | ||||||||
\(759\) | −37.2906 | −1.35356 | ||||||||
\(760\) | 0.0878857 | 0.00318795 | ||||||||
\(761\) | 32.8736 | 1.19167 | 0.595834 | − | 0.803108i | \(-0.296822\pi\) | ||||
0.595834 | + | 0.803108i | \(0.296822\pi\) | |||||||
\(762\) | 21.8334 | 0.790939 | ||||||||
\(763\) | −3.38656 | −0.122602 | ||||||||
\(764\) | −22.6535 | −0.819574 | ||||||||
\(765\) | −2.08012 | −0.0752069 | ||||||||
\(766\) | 67.6963 | 2.44597 | ||||||||
\(767\) | −1.49007 | −0.0538032 | ||||||||
\(768\) | −23.0408 | −0.831412 | ||||||||
\(769\) | −8.03230 | −0.289652 | −0.144826 | − | 0.989457i | \(-0.546262\pi\) | ||||
−0.144826 | + | 0.989457i | \(0.546262\pi\) | |||||||
\(770\) | −22.4792 | −0.810094 | ||||||||
\(771\) | −8.42436 | −0.303396 | ||||||||
\(772\) | 18.4762 | 0.664972 | ||||||||
\(773\) | 33.0334 | 1.18813 | 0.594064 | − | 0.804418i | \(-0.297523\pi\) | ||||
0.594064 | + | 0.804418i | \(0.297523\pi\) | |||||||
\(774\) | −19.9940 | −0.718668 | ||||||||
\(775\) | 2.32749 | 0.0836059 | ||||||||
\(776\) | −1.29494 | −0.0464855 | ||||||||
\(777\) | 4.54693 | 0.163120 | ||||||||
\(778\) | −0.748524 | −0.0268359 | ||||||||
\(779\) | 8.61488 | 0.308660 | ||||||||
\(780\) | −8.55307 | −0.306249 | ||||||||
\(781\) | 62.9593 | 2.25286 | ||||||||
\(782\) | 28.5174 | 1.01978 | ||||||||
\(783\) | 49.5511 | 1.77081 | ||||||||
\(784\) | −18.5373 | −0.662045 | ||||||||
\(785\) | 10.8493 | 0.387229 | ||||||||
\(786\) | 2.07815 | 0.0741253 | ||||||||
\(787\) | −1.62205 | −0.0578198 | −0.0289099 | − | 0.999582i | \(-0.509204\pi\) | ||||
−0.0289099 | + | 0.999582i | \(0.509204\pi\) | |||||||
\(788\) | 22.6904 | 0.808311 | ||||||||
\(789\) | 27.0139 | 0.961719 | ||||||||
\(790\) | 15.3774 | 0.547104 | ||||||||
\(791\) | −61.0424 | −2.17042 | ||||||||
\(792\) | −0.990339 | −0.0351902 | ||||||||
\(793\) | 1.32851 | 0.0471767 | ||||||||
\(794\) | 22.2931 | 0.791153 | ||||||||
\(795\) | 4.03588 | 0.143138 | ||||||||
\(796\) | −30.8793 | −1.09449 | ||||||||
\(797\) | 22.4418 | 0.794930 | 0.397465 | − | 0.917617i | \(-0.369890\pi\) | ||||
0.397465 | + | 0.917617i | \(0.369890\pi\) | |||||||
\(798\) | 8.38629 | 0.296871 | ||||||||
\(799\) | −22.4899 | −0.795636 | ||||||||
\(800\) | −36.5290 | −1.29149 | ||||||||
\(801\) | −0.806635 | −0.0285011 | ||||||||
\(802\) | −29.5404 | −1.04311 | ||||||||
\(803\) | −11.7372 | −0.414198 | ||||||||
\(804\) | −8.94627 | −0.315511 | ||||||||
\(805\) | 10.7324 | 0.378267 | ||||||||
\(806\) | −5.34830 | −0.188386 | ||||||||
\(807\) | 17.4898 | 0.615670 | ||||||||
\(808\) | −0.416866 | −0.0146653 | ||||||||
\(809\) | 55.8477 | 1.96350 | 0.981750 | − | 0.190177i | \(-0.0609060\pi\) | ||||
0.981750 | + | 0.190177i | \(0.0609060\pi\) | |||||||
\(810\) | −4.86793 | −0.171041 | ||||||||
\(811\) | −1.34389 | −0.0471904 | −0.0235952 | − | 0.999722i | \(-0.507511\pi\) | ||||
−0.0235952 | + | 0.999722i | \(0.507511\pi\) | |||||||
\(812\) | −57.2594 | −2.00941 | ||||||||
\(813\) | −12.4338 | −0.436071 | ||||||||
\(814\) | −10.7341 | −0.376230 | ||||||||
\(815\) | 8.38291 | 0.293640 | ||||||||
\(816\) | −15.6473 | −0.547766 | ||||||||
\(817\) | 7.85108 | 0.274675 | ||||||||
\(818\) | 58.0372 | 2.02922 | ||||||||
\(819\) | −21.7223 | −0.759039 | ||||||||
\(820\) | 11.0009 | 0.384167 | ||||||||
\(821\) | −22.2906 | −0.777947 | −0.388974 | − | 0.921249i | \(-0.627170\pi\) | ||||
−0.388974 | + | 0.921249i | \(0.627170\pi\) | |||||||
\(822\) | −36.7559 | −1.28201 | ||||||||
\(823\) | −19.0993 | −0.665761 | −0.332881 | − | 0.942969i | \(-0.608021\pi\) | ||||
−0.332881 | + | 0.942969i | \(0.608021\pi\) | |||||||
\(824\) | −0.546981 | −0.0190550 | ||||||||
\(825\) | 33.5997 | 1.16979 | ||||||||
\(826\) | 1.86566 | 0.0649144 | ||||||||
\(827\) | 34.2701 | 1.19169 | 0.595844 | − | 0.803100i | \(-0.296818\pi\) | ||||
0.595844 | + | 0.803100i | \(0.296818\pi\) | |||||||
\(828\) | −11.7993 | −0.410054 | ||||||||
\(829\) | 43.4107 | 1.50772 | 0.753858 | − | 0.657038i | \(-0.228191\pi\) | ||||
0.753858 | + | 0.657038i | \(0.228191\pi\) | |||||||
\(830\) | −5.42701 | −0.188374 | ||||||||
\(831\) | 8.98851 | 0.311808 | ||||||||
\(832\) | 39.4940 | 1.36921 | ||||||||
\(833\) | −12.5549 | −0.435000 | ||||||||
\(834\) | 45.9929 | 1.59260 | ||||||||
\(835\) | 0.165482 | 0.00572674 | ||||||||
\(836\) | −9.70446 | −0.335636 | ||||||||
\(837\) | −2.84055 | −0.0981838 | ||||||||
\(838\) | −36.8093 | −1.27156 | ||||||||
\(839\) | −48.7389 | −1.68265 | −0.841327 | − | 0.540527i | \(-0.818225\pi\) | ||||
−0.841327 | + | 0.540527i | \(0.818225\pi\) | |||||||
\(840\) | −0.429132 | −0.0148065 | ||||||||
\(841\) | 48.3114 | 1.66591 | ||||||||
\(842\) | 37.5174 | 1.29294 | ||||||||
\(843\) | −35.5218 | −1.22343 | ||||||||
\(844\) | 15.9045 | 0.547454 | ||||||||
\(845\) | −9.70841 | −0.333979 | ||||||||
\(846\) | 18.9836 | 0.652671 | ||||||||
\(847\) | −62.2144 | −2.13771 | ||||||||
\(848\) | −20.1641 | −0.692438 | ||||||||
\(849\) | 18.1129 | 0.621632 | ||||||||
\(850\) | −25.6948 | −0.881325 | ||||||||
\(851\) | 5.12484 | 0.175677 | ||||||||
\(852\) | −29.9935 | −1.02756 | ||||||||
\(853\) | −32.3940 | −1.10915 | −0.554575 | − | 0.832134i | \(-0.687119\pi\) | ||||
−0.554575 | + | 0.832134i | \(0.687119\pi\) | |||||||
\(854\) | −1.66338 | −0.0569195 | ||||||||
\(855\) | −0.689463 | −0.0235791 | ||||||||
\(856\) | 0.495339 | 0.0169303 | ||||||||
\(857\) | −10.4501 | −0.356969 | −0.178485 | − | 0.983943i | \(-0.557119\pi\) | ||||
−0.178485 | + | 0.983943i | \(0.557119\pi\) | |||||||
\(858\) | −77.2082 | −2.63585 | ||||||||
\(859\) | −23.4961 | −0.801677 | −0.400838 | − | 0.916149i | \(-0.631281\pi\) | ||||
−0.400838 | + | 0.916149i | \(0.631281\pi\) | |||||||
\(860\) | 10.0255 | 0.341868 | ||||||||
\(861\) | −42.0651 | −1.43358 | ||||||||
\(862\) | −42.5872 | −1.45053 | ||||||||
\(863\) | −0.346409 | −0.0117919 | −0.00589595 | − | 0.999983i | \(-0.501877\pi\) | ||||
−0.00589595 | + | 0.999983i | \(0.501877\pi\) | |||||||
\(864\) | 44.5813 | 1.51669 | ||||||||
\(865\) | 0.545599 | 0.0185509 | ||||||||
\(866\) | 64.4585 | 2.19039 | ||||||||
\(867\) | 12.2273 | 0.415262 | ||||||||
\(868\) | 3.28244 | 0.111413 | ||||||||
\(869\) | 68.0424 | 2.30818 | ||||||||
\(870\) | −14.4592 | −0.490213 | ||||||||
\(871\) | −18.5633 | −0.628992 | ||||||||
\(872\) | 0.152622 | 0.00516842 | ||||||||
\(873\) | 10.1588 | 0.343822 | ||||||||
\(874\) | 9.45218 | 0.319725 | ||||||||
\(875\) | −20.1411 | −0.680892 | ||||||||
\(876\) | 5.59156 | 0.188921 | ||||||||
\(877\) | −25.9020 | −0.874647 | −0.437323 | − | 0.899304i | \(-0.644073\pi\) | ||||
−0.437323 | + | 0.899304i | \(0.644073\pi\) | |||||||
\(878\) | 40.4038 | 1.36356 | ||||||||
\(879\) | 3.53129 | 0.119107 | ||||||||
\(880\) | 13.9019 | 0.468632 | ||||||||
\(881\) | 42.8707 | 1.44435 | 0.722175 | − | 0.691711i | \(-0.243143\pi\) | ||||
0.722175 | + | 0.691711i | \(0.243143\pi\) | |||||||
\(882\) | 10.5975 | 0.356836 | ||||||||
\(883\) | 34.5821 | 1.16378 | 0.581891 | − | 0.813267i | \(-0.302313\pi\) | ||||
0.581891 | + | 0.813267i | \(0.302313\pi\) | |||||||
\(884\) | 28.9420 | 0.973424 | ||||||||
\(885\) | 0.230932 | 0.00776268 | ||||||||
\(886\) | 5.60740 | 0.188384 | ||||||||
\(887\) | 23.3777 | 0.784945 | 0.392473 | − | 0.919764i | \(-0.371620\pi\) | ||||
0.392473 | + | 0.919764i | \(0.371620\pi\) | |||||||
\(888\) | −0.204916 | −0.00687653 | ||||||||
\(889\) | −27.8044 | −0.932529 | ||||||||
\(890\) | 0.825147 | 0.0276590 | ||||||||
\(891\) | −21.5397 | −0.721608 | ||||||||
\(892\) | −8.97188 | −0.300401 | ||||||||
\(893\) | −7.45436 | −0.249451 | ||||||||
\(894\) | 42.3401 | 1.41607 | ||||||||
\(895\) | −5.70633 | −0.190742 | ||||||||
\(896\) | 4.13183 | 0.138035 | ||||||||
\(897\) | 36.8620 | 1.23079 | ||||||||
\(898\) | 14.9254 | 0.498067 | ||||||||
\(899\) | −4.43193 | −0.147813 | ||||||||
\(900\) | 10.6314 | 0.354381 | ||||||||
\(901\) | −13.6567 | −0.454969 | ||||||||
\(902\) | 99.3046 | 3.30648 | ||||||||
\(903\) | −38.3356 | −1.27573 | ||||||||
\(904\) | 2.75099 | 0.0914965 | ||||||||
\(905\) | 7.43885 | 0.247276 | ||||||||
\(906\) | 26.8012 | 0.890410 | ||||||||
\(907\) | 10.5157 | 0.349167 | 0.174584 | − | 0.984642i | \(-0.444142\pi\) | ||||
0.174584 | + | 0.984642i | \(0.444142\pi\) | |||||||
\(908\) | 10.5454 | 0.349960 | ||||||||
\(909\) | 3.27032 | 0.108470 | ||||||||
\(910\) | 22.2208 | 0.736613 | ||||||||
\(911\) | 15.8768 | 0.526022 | 0.263011 | − | 0.964793i | \(-0.415284\pi\) | ||||
0.263011 | + | 0.964793i | \(0.415284\pi\) | |||||||
\(912\) | −5.18636 | −0.171737 | ||||||||
\(913\) | −24.0136 | −0.794733 | ||||||||
\(914\) | −13.2973 | −0.439837 | ||||||||
\(915\) | −0.205893 | −0.00680662 | ||||||||
\(916\) | −4.78811 | −0.158204 | ||||||||
\(917\) | −2.64649 | −0.0873949 | ||||||||
\(918\) | 31.3589 | 1.03500 | ||||||||
\(919\) | −3.98228 | −0.131363 | −0.0656816 | − | 0.997841i | \(-0.520922\pi\) | ||||
−0.0656816 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(920\) | −0.483675 | −0.0159463 | ||||||||
\(921\) | −13.7045 | −0.451579 | ||||||||
\(922\) | −45.2549 | −1.49039 | ||||||||
\(923\) | −62.2356 | −2.04851 | ||||||||
\(924\) | 47.3854 | 1.55886 | ||||||||
\(925\) | −4.61760 | −0.151826 | ||||||||
\(926\) | 39.0619 | 1.28365 | ||||||||
\(927\) | 4.29107 | 0.140937 | ||||||||
\(928\) | 69.5573 | 2.28333 | ||||||||
\(929\) | 7.27481 | 0.238679 | 0.119339 | − | 0.992854i | \(-0.461922\pi\) | ||||
0.119339 | + | 0.992854i | \(0.461922\pi\) | |||||||
\(930\) | 0.828884 | 0.0271802 | ||||||||
\(931\) | −4.16135 | −0.136383 | ||||||||
\(932\) | −16.0474 | −0.525649 | ||||||||
\(933\) | −33.0974 | −1.08356 | ||||||||
\(934\) | 22.5398 | 0.737523 | ||||||||
\(935\) | 9.41541 | 0.307917 | ||||||||
\(936\) | 0.978956 | 0.0319982 | ||||||||
\(937\) | 20.1417 | 0.658001 | 0.329001 | − | 0.944330i | \(-0.393288\pi\) | ||||
0.329001 | + | 0.944330i | \(0.393288\pi\) | |||||||
\(938\) | 23.2424 | 0.758890 | ||||||||
\(939\) | 45.9389 | 1.49916 | ||||||||
\(940\) | −9.51893 | −0.310473 | ||||||||
\(941\) | −22.4087 | −0.730503 | −0.365251 | − | 0.930909i | \(-0.619017\pi\) | ||||
−0.365251 | + | 0.930909i | \(0.619017\pi\) | |||||||
\(942\) | −46.6565 | −1.52015 | ||||||||
\(943\) | −47.4116 | −1.54393 | ||||||||
\(944\) | −1.15378 | −0.0375524 | ||||||||
\(945\) | 11.8018 | 0.383911 | ||||||||
\(946\) | 90.5001 | 2.94241 | ||||||||
\(947\) | 53.4987 | 1.73847 | 0.869237 | − | 0.494396i | \(-0.164611\pi\) | ||||
0.869237 | + | 0.494396i | \(0.164611\pi\) | |||||||
\(948\) | −32.4151 | −1.05279 | ||||||||
\(949\) | 11.6023 | 0.376628 | ||||||||
\(950\) | −8.51664 | −0.276316 | ||||||||
\(951\) | 41.6299 | 1.34994 | ||||||||
\(952\) | 1.45210 | 0.0470629 | ||||||||
\(953\) | 58.1206 | 1.88271 | 0.941355 | − | 0.337418i | \(-0.109554\pi\) | ||||
0.941355 | + | 0.337418i | \(0.109554\pi\) | |||||||
\(954\) | 11.5275 | 0.373218 | ||||||||
\(955\) | 7.28493 | 0.235735 | ||||||||
\(956\) | 30.5284 | 0.987359 | ||||||||
\(957\) | −63.9795 | −2.06816 | ||||||||
\(958\) | 76.6830 | 2.47752 | ||||||||
\(959\) | 46.8080 | 1.51151 | ||||||||
\(960\) | −6.12082 | −0.197549 | ||||||||
\(961\) | −30.7459 | −0.991804 | ||||||||
\(962\) | 10.6107 | 0.342103 | ||||||||
\(963\) | −3.88593 | −0.125222 | ||||||||
\(964\) | 38.4658 | 1.23890 | ||||||||
\(965\) | −5.94159 | −0.191267 | ||||||||
\(966\) | −46.1535 | −1.48497 | ||||||||
\(967\) | 28.9234 | 0.930113 | 0.465056 | − | 0.885281i | \(-0.346034\pi\) | ||||
0.465056 | + | 0.885281i | \(0.346034\pi\) | |||||||
\(968\) | 2.80381 | 0.0901178 | ||||||||
\(969\) | −3.51260 | −0.112841 | ||||||||
\(970\) | −10.3919 | −0.333664 | ||||||||
\(971\) | −33.5902 | −1.07796 | −0.538980 | − | 0.842319i | \(-0.681190\pi\) | ||||
−0.538980 | + | 0.842319i | \(0.681190\pi\) | |||||||
\(972\) | −22.2487 | −0.713629 | ||||||||
\(973\) | −58.5711 | −1.87770 | ||||||||
\(974\) | −8.52533 | −0.273169 | ||||||||
\(975\) | −33.2135 | −1.06368 | ||||||||
\(976\) | 1.02869 | 0.0329274 | ||||||||
\(977\) | 25.7667 | 0.824348 | 0.412174 | − | 0.911105i | \(-0.364770\pi\) | ||||
0.412174 | + | 0.911105i | \(0.364770\pi\) | |||||||
\(978\) | −36.0499 | −1.15275 | ||||||||
\(979\) | 3.65113 | 0.116691 | ||||||||
\(980\) | −5.31388 | −0.169746 | ||||||||
\(981\) | −1.19732 | −0.0382274 | ||||||||
\(982\) | −8.80052 | −0.280836 | ||||||||
\(983\) | −31.6310 | −1.00887 | −0.504436 | − | 0.863449i | \(-0.668299\pi\) | ||||
−0.504436 | + | 0.863449i | \(0.668299\pi\) | |||||||
\(984\) | 1.89574 | 0.0604341 | ||||||||
\(985\) | −7.29679 | −0.232495 | ||||||||
\(986\) | 48.9273 | 1.55816 | ||||||||
\(987\) | 36.3985 | 1.15858 | ||||||||
\(988\) | 9.59291 | 0.305191 | ||||||||
\(989\) | −43.2080 | −1.37394 | ||||||||
\(990\) | −7.94751 | −0.252588 | ||||||||
\(991\) | 1.60296 | 0.0509196 | 0.0254598 | − | 0.999676i | \(-0.491895\pi\) | ||||
0.0254598 | + | 0.999676i | \(0.491895\pi\) | |||||||
\(992\) | −3.98742 | −0.126601 | ||||||||
\(993\) | 35.4252 | 1.12419 | ||||||||
\(994\) | 77.9229 | 2.47156 | ||||||||
\(995\) | 9.93019 | 0.314808 | ||||||||
\(996\) | 11.4399 | 0.362488 | ||||||||
\(997\) | 31.0893 | 0.984609 | 0.492304 | − | 0.870423i | \(-0.336155\pi\) | ||||
0.492304 | + | 0.870423i | \(0.336155\pi\) | |||||||
\(998\) | 79.4933 | 2.51632 | ||||||||
\(999\) | 5.63549 | 0.178299 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4033.2.a.c.1.15 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.c.1.15 | ✓ | 77 | 1.1 | even | 1 | trivial |