Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14986 | −1.52018 | −0.760089 | − | 0.649819i | \(-0.774845\pi\) | ||||
−0.760089 | + | 0.649819i | \(0.774845\pi\) | |||||||
\(3\) | 1.70160 | 0.982421 | 0.491210 | − | 0.871041i | \(-0.336555\pi\) | ||||
0.491210 | + | 0.871041i | \(0.336555\pi\) | |||||||
\(4\) | 2.62188 | 1.31094 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.65820 | −1.49345 | ||||||||
\(7\) | 3.86024 | 1.45903 | 0.729517 | − | 0.683963i | \(-0.239745\pi\) | ||||
0.729517 | + | 0.683963i | \(0.239745\pi\) | |||||||
\(8\) | −1.33695 | −0.472684 | ||||||||
\(9\) | −0.104549 | −0.0348496 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.36727 | −1.01527 | −0.507636 | − | 0.861572i | \(-0.669480\pi\) | ||||
−0.507636 | + | 0.861572i | \(0.669480\pi\) | |||||||
\(12\) | 4.46140 | 1.28789 | ||||||||
\(13\) | 3.60241 | 0.999130 | 0.499565 | − | 0.866276i | \(-0.333493\pi\) | ||||
0.499565 | + | 0.866276i | \(0.333493\pi\) | |||||||
\(14\) | −8.29896 | −2.21799 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.36950 | −0.592376 | ||||||||
\(17\) | −4.80509 | −1.16541 | −0.582703 | − | 0.812685i | \(-0.698005\pi\) | ||||
−0.582703 | + | 0.812685i | \(0.698005\pi\) | |||||||
\(18\) | 0.224765 | 0.0529775 | ||||||||
\(19\) | 0.226945 | 0.0520648 | 0.0260324 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260324 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.56859 | 1.43338 | ||||||||
\(22\) | 7.23915 | 1.54339 | ||||||||
\(23\) | −1.91949 | −0.400242 | −0.200121 | − | 0.979771i | \(-0.564133\pi\) | ||||
−0.200121 | + | 0.979771i | \(0.564133\pi\) | |||||||
\(24\) | −2.27496 | −0.464375 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.74467 | −1.51885 | ||||||||
\(27\) | −5.28271 | −1.01666 | ||||||||
\(28\) | 10.1211 | 1.91271 | ||||||||
\(29\) | −4.83459 | −0.897761 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.43781 | 0.617448 | 0.308724 | − | 0.951152i | \(-0.400098\pi\) | ||||
0.308724 | + | 0.951152i | \(0.400098\pi\) | |||||||
\(32\) | 7.76800 | 1.37320 | ||||||||
\(33\) | −5.72976 | −0.997423 | ||||||||
\(34\) | 10.3303 | 1.77162 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.274114 | −0.0456857 | ||||||||
\(37\) | −1.65269 | −0.271701 | −0.135851 | − | 0.990729i | \(-0.543377\pi\) | ||||
−0.135851 | + | 0.990729i | \(0.543377\pi\) | |||||||
\(38\) | −0.487900 | −0.0791478 | ||||||||
\(39\) | 6.12988 | 0.981566 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.01238 | −0.782803 | −0.391401 | − | 0.920220i | \(-0.628010\pi\) | ||||
−0.391401 | + | 0.920220i | \(0.628010\pi\) | |||||||
\(42\) | −14.1215 | −2.17900 | ||||||||
\(43\) | 1.20938 | 0.184428 | 0.0922141 | − | 0.995739i | \(-0.470606\pi\) | ||||
0.0922141 | + | 0.995739i | \(0.470606\pi\) | |||||||
\(44\) | −8.82859 | −1.33096 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.12663 | 0.608438 | ||||||||
\(47\) | −1.14233 | −0.166626 | −0.0833130 | − | 0.996523i | \(-0.526550\pi\) | ||||
−0.0833130 | + | 0.996523i | \(0.526550\pi\) | |||||||
\(48\) | −4.03195 | −0.581963 | ||||||||
\(49\) | 7.90145 | 1.12878 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.17636 | −1.14492 | ||||||||
\(52\) | 9.44510 | 1.30980 | ||||||||
\(53\) | −4.03982 | −0.554912 | −0.277456 | − | 0.960738i | \(-0.589491\pi\) | ||||
−0.277456 | + | 0.960738i | \(0.589491\pi\) | |||||||
\(54\) | 11.3571 | 1.54550 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.16096 | −0.689662 | ||||||||
\(57\) | 0.386171 | 0.0511496 | ||||||||
\(58\) | 10.3937 | 1.36476 | ||||||||
\(59\) | 9.59775 | 1.24952 | 0.624760 | − | 0.780817i | \(-0.285197\pi\) | ||||
0.624760 | + | 0.780817i | \(0.285197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7276 | −1.88567 | −0.942837 | − | 0.333255i | \(-0.891853\pi\) | ||||
−0.942837 | + | 0.333255i | \(0.891853\pi\) | |||||||
\(62\) | −7.39079 | −0.938631 | ||||||||
\(63\) | −0.403583 | −0.0508467 | ||||||||
\(64\) | −11.9611 | −1.49513 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 12.3182 | 1.51626 | ||||||||
\(67\) | 2.12724 | 0.259883 | 0.129942 | − | 0.991522i | \(-0.458521\pi\) | ||||
0.129942 | + | 0.991522i | \(0.458521\pi\) | |||||||
\(68\) | −12.5984 | −1.52778 | ||||||||
\(69\) | −3.26621 | −0.393206 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.50693 | −0.297518 | −0.148759 | − | 0.988873i | \(-0.547528\pi\) | ||||
−0.148759 | + | 0.988873i | \(0.547528\pi\) | |||||||
\(72\) | 0.139777 | 0.0164728 | ||||||||
\(73\) | −5.03915 | −0.589787 | −0.294894 | − | 0.955530i | \(-0.595284\pi\) | ||||
−0.294894 | + | 0.955530i | \(0.595284\pi\) | |||||||
\(74\) | 3.55305 | 0.413034 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.595023 | 0.0682539 | ||||||||
\(77\) | −12.9985 | −1.48131 | ||||||||
\(78\) | −13.1784 | −1.49215 | ||||||||
\(79\) | 13.6737 | 1.53841 | 0.769207 | − | 0.639000i | \(-0.220651\pi\) | ||||
0.769207 | + | 0.639000i | \(0.220651\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.67542 | −0.963936 | ||||||||
\(82\) | 10.7759 | 1.19000 | ||||||||
\(83\) | −5.82936 | −0.639855 | −0.319928 | − | 0.947442i | \(-0.603659\pi\) | ||||
−0.319928 | + | 0.947442i | \(0.603659\pi\) | |||||||
\(84\) | 17.2221 | 1.87908 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.59998 | −0.280364 | ||||||||
\(87\) | −8.22655 | −0.881979 | ||||||||
\(88\) | 4.50189 | 0.479903 | ||||||||
\(89\) | −1.13959 | −0.120797 | −0.0603984 | − | 0.998174i | \(-0.519237\pi\) | ||||
−0.0603984 | + | 0.998174i | \(0.519237\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9062 | 1.45776 | ||||||||
\(92\) | −5.03268 | −0.524693 | ||||||||
\(93\) | 5.84978 | 0.606594 | ||||||||
\(94\) | 2.45584 | 0.253301 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 13.2180 | 1.34906 | ||||||||
\(97\) | −13.2097 | −1.34124 | −0.670620 | − | 0.741801i | \(-0.733972\pi\) | ||||
−0.670620 | + | 0.741801i | \(0.733972\pi\) | |||||||
\(98\) | −16.9870 | −1.71594 | ||||||||
\(99\) | 0.352044 | 0.0353817 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.43809 | −0.740118 | −0.370059 | − | 0.929008i | \(-0.620663\pi\) | ||||
−0.370059 | + | 0.929008i | \(0.620663\pi\) | |||||||
\(102\) | 17.5780 | 1.74048 | ||||||||
\(103\) | −14.5631 | −1.43494 | −0.717472 | − | 0.696587i | \(-0.754701\pi\) | ||||
−0.717472 | + | 0.696587i | \(0.754701\pi\) | |||||||
\(104\) | −4.81626 | −0.472273 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.68503 | 0.843565 | ||||||||
\(107\) | −9.50646 | −0.919024 | −0.459512 | − | 0.888172i | \(-0.651976\pi\) | ||||
−0.459512 | + | 0.888172i | \(0.651976\pi\) | |||||||
\(108\) | −13.8506 | −1.33278 | ||||||||
\(109\) | 16.0398 | 1.53633 | 0.768165 | − | 0.640252i | \(-0.221170\pi\) | ||||
0.768165 | + | 0.640252i | \(0.221170\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81223 | −0.266925 | ||||||||
\(112\) | −9.14685 | −0.864296 | ||||||||
\(113\) | −13.4925 | −1.26927 | −0.634634 | − | 0.772813i | \(-0.718849\pi\) | ||||
−0.634634 | + | 0.772813i | \(0.718849\pi\) | |||||||
\(114\) | −0.830211 | −0.0777564 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.6757 | −1.17691 | ||||||||
\(117\) | −0.376628 | −0.0348192 | ||||||||
\(118\) | −20.6338 | −1.89949 | ||||||||
\(119\) | −18.5488 | −1.70037 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.338528 | 0.0307753 | ||||||||
\(122\) | 31.6622 | 2.86656 | ||||||||
\(123\) | −8.52908 | −0.769042 | ||||||||
\(124\) | 9.01352 | 0.809438 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.867645 | 0.0772960 | ||||||||
\(127\) | 7.52355 | 0.667607 | 0.333803 | − | 0.942643i | \(-0.391668\pi\) | ||||
0.333803 | + | 0.942643i | \(0.391668\pi\) | |||||||
\(128\) | 10.1786 | 0.899668 | ||||||||
\(129\) | 2.05788 | 0.181186 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.02682 | 0.613936 | 0.306968 | − | 0.951720i | \(-0.400686\pi\) | ||||
0.306968 | + | 0.951720i | \(0.400686\pi\) | |||||||
\(132\) | −15.0227 | −1.30756 | ||||||||
\(133\) | 0.876063 | 0.0759643 | ||||||||
\(134\) | −4.57325 | −0.395069 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.42418 | 0.550869 | ||||||||
\(137\) | −5.86157 | −0.500788 | −0.250394 | − | 0.968144i | \(-0.580560\pi\) | ||||
−0.250394 | + | 0.968144i | \(0.580560\pi\) | |||||||
\(138\) | 7.02188 | 0.597743 | ||||||||
\(139\) | −13.2572 | −1.12446 | −0.562231 | − | 0.826980i | \(-0.690057\pi\) | ||||
−0.562231 | + | 0.826980i | \(0.690057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.94379 | −0.163697 | ||||||||
\(142\) | 5.38954 | 0.452280 | ||||||||
\(143\) | −12.1303 | −1.01439 | ||||||||
\(144\) | 0.247729 | 0.0206440 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.8334 | 0.896582 | ||||||||
\(147\) | 13.4451 | 1.10894 | ||||||||
\(148\) | −4.33316 | −0.356184 | ||||||||
\(149\) | −0.0486387 | −0.00398463 | −0.00199232 | − | 0.999998i | \(-0.500634\pi\) | ||||
−0.00199232 | + | 0.999998i | \(0.500634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.43809 | 0.198409 | 0.0992045 | − | 0.995067i | \(-0.468370\pi\) | ||||
0.0992045 | + | 0.995067i | \(0.468370\pi\) | |||||||
\(152\) | −0.303415 | −0.0246102 | ||||||||
\(153\) | 0.502366 | 0.0406139 | ||||||||
\(154\) | 27.9449 | 2.25186 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.0718 | 1.28677 | ||||||||
\(157\) | −7.69109 | −0.613815 | −0.306908 | − | 0.951739i | \(-0.599294\pi\) | ||||
−0.306908 | + | 0.951739i | \(0.599294\pi\) | |||||||
\(158\) | −29.3965 | −2.33866 | ||||||||
\(159\) | −6.87417 | −0.545157 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.40970 | −0.583966 | ||||||||
\(162\) | 18.6509 | 1.46535 | ||||||||
\(163\) | 16.6059 | 1.30067 | 0.650336 | − | 0.759646i | \(-0.274628\pi\) | ||||
0.650336 | + | 0.759646i | \(0.274628\pi\) | |||||||
\(164\) | −13.1419 | −1.02621 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.5323 | 0.972694 | ||||||||
\(167\) | 15.1961 | 1.17591 | 0.587953 | − | 0.808895i | \(-0.299934\pi\) | ||||
0.587953 | + | 0.808895i | \(0.299934\pi\) | |||||||
\(168\) | −8.78190 | −0.677538 | ||||||||
\(169\) | −0.0226134 | −0.00173949 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0237268 | −0.00181444 | ||||||||
\(172\) | 3.17084 | 0.241774 | ||||||||
\(173\) | −9.72441 | −0.739333 | −0.369667 | − | 0.929164i | \(-0.620528\pi\) | ||||
−0.369667 | + | 0.929164i | \(0.620528\pi\) | |||||||
\(174\) | 17.6859 | 1.34076 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.97877 | 0.601422 | ||||||||
\(177\) | 16.3316 | 1.22755 | ||||||||
\(178\) | 2.44996 | 0.183633 | ||||||||
\(179\) | −13.2615 | −0.991208 | −0.495604 | − | 0.868549i | \(-0.665053\pi\) | ||||
−0.495604 | + | 0.868549i | \(0.665053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.09939 | −0.527694 | −0.263847 | − | 0.964565i | \(-0.584991\pi\) | ||||
−0.263847 | + | 0.964565i | \(0.584991\pi\) | |||||||
\(182\) | −29.8963 | −2.21606 | ||||||||
\(183\) | −25.0605 | −1.85252 | ||||||||
\(184\) | 2.56627 | 0.189188 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.5762 | −0.922131 | ||||||||
\(187\) | 16.1801 | 1.18320 | ||||||||
\(188\) | −2.99505 | −0.218437 | ||||||||
\(189\) | −20.3925 | −1.48334 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.2427 | 1.10293 | 0.551463 | − | 0.834200i | \(-0.314070\pi\) | ||||
0.551463 | + | 0.834200i | \(0.314070\pi\) | |||||||
\(192\) | −20.3530 | −1.46885 | ||||||||
\(193\) | −5.71316 | −0.411242 | −0.205621 | − | 0.978632i | \(-0.565921\pi\) | ||||
−0.205621 | + | 0.978632i | \(0.565921\pi\) | |||||||
\(194\) | 28.3989 | 2.03892 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.7166 | 1.47976 | ||||||||
\(197\) | 15.5073 | 1.10485 | 0.552426 | − | 0.833562i | \(-0.313702\pi\) | ||||
0.552426 | + | 0.833562i | \(0.313702\pi\) | |||||||
\(198\) | −0.756844 | −0.0537865 | ||||||||
\(199\) | −2.50728 | −0.177736 | −0.0888681 | − | 0.996043i | \(-0.528325\pi\) | ||||
−0.0888681 | + | 0.996043i | \(0.528325\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.61971 | 0.255315 | ||||||||
\(202\) | 15.9908 | 1.12511 | ||||||||
\(203\) | −18.6627 | −1.30986 | ||||||||
\(204\) | −21.4374 | −1.50092 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 31.3085 | 2.18137 | ||||||||
\(207\) | 0.200680 | 0.0139482 | ||||||||
\(208\) | −8.53594 | −0.591861 | ||||||||
\(209\) | −0.764187 | −0.0528599 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.8809 | −1.57519 | −0.787593 | − | 0.616196i | \(-0.788673\pi\) | ||||
−0.787593 | + | 0.616196i | \(0.788673\pi\) | |||||||
\(212\) | −10.5919 | −0.727456 | ||||||||
\(213\) | −4.26580 | −0.292288 | ||||||||
\(214\) | 20.4375 | 1.39708 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.06273 | 0.480558 | ||||||||
\(217\) | 13.2708 | 0.900878 | ||||||||
\(218\) | −34.4832 | −2.33549 | ||||||||
\(219\) | −8.57462 | −0.579419 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.3099 | −1.16439 | ||||||||
\(222\) | 6.04588 | 0.405773 | ||||||||
\(223\) | −0.134785 | −0.00902590 | −0.00451295 | − | 0.999990i | \(-0.501437\pi\) | ||||
−0.00451295 | + | 0.999990i | \(0.501437\pi\) | |||||||
\(224\) | 29.9863 | 2.00355 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 29.0069 | 1.92951 | ||||||||
\(227\) | −10.8306 | −0.718849 | −0.359425 | − | 0.933174i | \(-0.617027\pi\) | ||||
−0.359425 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(228\) | 1.01249 | 0.0670540 | ||||||||
\(229\) | 7.89246 | 0.521548 | 0.260774 | − | 0.965400i | \(-0.416022\pi\) | ||||
0.260774 | + | 0.965400i | \(0.416022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.1182 | −1.45527 | ||||||||
\(232\) | 6.46362 | 0.424357 | ||||||||
\(233\) | −8.69503 | −0.569631 | −0.284815 | − | 0.958582i | \(-0.591932\pi\) | ||||
−0.284815 | + | 0.958582i | \(0.591932\pi\) | |||||||
\(234\) | 0.809695 | 0.0529314 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 25.1641 | 1.63805 | ||||||||
\(237\) | 23.2672 | 1.51137 | ||||||||
\(238\) | 39.8772 | 2.58486 | ||||||||
\(239\) | −3.13922 | −0.203059 | −0.101529 | − | 0.994833i | \(-0.532374\pi\) | ||||
−0.101529 | + | 0.994833i | \(0.532374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −0.727787 | −0.0467839 | ||||||||
\(243\) | 1.08600 | 0.0696670 | ||||||||
\(244\) | −38.6140 | −2.47201 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 18.3363 | 1.16908 | ||||||||
\(247\) | 0.817551 | 0.0520195 | ||||||||
\(248\) | −4.59619 | −0.291858 | ||||||||
\(249\) | −9.91925 | −0.628607 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.4720 | 1.35530 | 0.677649 | − | 0.735385i | \(-0.262999\pi\) | ||||
0.677649 | + | 0.735385i | \(0.262999\pi\) | |||||||
\(252\) | −1.05815 | −0.0666569 | ||||||||
\(253\) | 6.46345 | 0.406354 | ||||||||
\(254\) | −16.1745 | −1.01488 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.03967 | 0.127479 | ||||||||
\(257\) | 26.5355 | 1.65524 | 0.827619 | − | 0.561291i | \(-0.189695\pi\) | ||||
0.827619 | + | 0.561291i | \(0.189695\pi\) | |||||||
\(258\) | −4.42414 | −0.275435 | ||||||||
\(259\) | −6.37979 | −0.396421 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.505450 | 0.0312866 | ||||||||
\(262\) | −15.1066 | −0.933291 | ||||||||
\(263\) | −10.2585 | −0.632567 | −0.316283 | − | 0.948665i | \(-0.602435\pi\) | ||||
−0.316283 | + | 0.948665i | \(0.602435\pi\) | |||||||
\(264\) | 7.66042 | 0.471466 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.88341 | −0.115479 | ||||||||
\(267\) | −1.93914 | −0.118673 | ||||||||
\(268\) | 5.57736 | 0.340692 | ||||||||
\(269\) | −0.0604403 | −0.00368511 | −0.00184256 | − | 0.999998i | \(-0.500587\pi\) | ||||
−0.00184256 | + | 0.999998i | \(0.500587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5869 | 1.31131 | 0.655654 | − | 0.755062i | \(-0.272393\pi\) | ||||
0.655654 | + | 0.755062i | \(0.272393\pi\) | |||||||
\(272\) | 11.3857 | 0.690359 | ||||||||
\(273\) | 23.6628 | 1.43214 | ||||||||
\(274\) | 12.6015 | 0.761287 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.56362 | −0.515469 | ||||||||
\(277\) | −22.3807 | −1.34473 | −0.672363 | − | 0.740221i | \(-0.734721\pi\) | ||||
−0.672363 | + | 0.740221i | \(0.734721\pi\) | |||||||
\(278\) | 28.5011 | 1.70938 | ||||||||
\(279\) | −0.359418 | −0.0215178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.8057 | −1.83771 | −0.918856 | − | 0.394594i | \(-0.870885\pi\) | ||||
−0.918856 | + | 0.394594i | \(0.870885\pi\) | |||||||
\(282\) | 4.17887 | 0.248848 | ||||||||
\(283\) | −29.8883 | −1.77668 | −0.888338 | − | 0.459189i | \(-0.848140\pi\) | ||||
−0.888338 | + | 0.459189i | \(0.848140\pi\) | |||||||
\(284\) | −6.57287 | −0.390028 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.0784 | 1.54205 | ||||||||
\(287\) | −19.3490 | −1.14214 | ||||||||
\(288\) | −0.812134 | −0.0478555 | ||||||||
\(289\) | 6.08890 | 0.358170 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.4776 | −1.31766 | ||||||||
\(292\) | −13.2120 | −0.773176 | ||||||||
\(293\) | 19.2209 | 1.12289 | 0.561447 | − | 0.827513i | \(-0.310245\pi\) | ||||
0.561447 | + | 0.827513i | \(0.310245\pi\) | |||||||
\(294\) | −28.9051 | −1.68578 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.20957 | 0.128429 | ||||||||
\(297\) | 17.7883 | 1.03218 | ||||||||
\(298\) | 0.104566 | 0.00605735 | ||||||||
\(299\) | −6.91480 | −0.399893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.66848 | 0.269087 | ||||||||
\(302\) | −5.24154 | −0.301617 | ||||||||
\(303\) | −12.6567 | −0.727107 | ||||||||
\(304\) | −0.537748 | −0.0308420 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.08001 | −0.0617403 | ||||||||
\(307\) | 5.35829 | 0.305814 | 0.152907 | − | 0.988241i | \(-0.451137\pi\) | ||||
0.152907 | + | 0.988241i | \(0.451137\pi\) | |||||||
\(308\) | −34.0805 | −1.94191 | ||||||||
\(309\) | −24.7806 | −1.40972 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7195 | 0.834666 | 0.417333 | − | 0.908754i | \(-0.362965\pi\) | ||||
0.417333 | + | 0.908754i | \(0.362965\pi\) | |||||||
\(312\) | −8.19536 | −0.463971 | ||||||||
\(313\) | 10.4175 | 0.588832 | 0.294416 | − | 0.955677i | \(-0.404875\pi\) | ||||
0.294416 | + | 0.955677i | \(0.404875\pi\) | |||||||
\(314\) | 16.5347 | 0.933109 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 35.8509 | 2.01677 | ||||||||
\(317\) | 6.26700 | 0.351990 | 0.175995 | − | 0.984391i | \(-0.443686\pi\) | ||||
0.175995 | + | 0.984391i | \(0.443686\pi\) | |||||||
\(318\) | 14.7785 | 0.828735 | ||||||||
\(319\) | 16.2794 | 0.911471 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.1762 | −0.902868 | ||||||||
\(322\) | 15.9298 | 0.887732 | ||||||||
\(323\) | −1.09049 | −0.0606766 | ||||||||
\(324\) | −22.7459 | −1.26366 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −35.7002 | −1.97725 | ||||||||
\(327\) | 27.2933 | 1.50932 | ||||||||
\(328\) | 6.70132 | 0.370019 | ||||||||
\(329\) | −4.40967 | −0.243113 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6686 | −0.861226 | −0.430613 | − | 0.902537i | \(-0.641703\pi\) | ||||
−0.430613 | + | 0.902537i | \(0.641703\pi\) | |||||||
\(332\) | −15.2839 | −0.838812 | ||||||||
\(333\) | 0.172787 | 0.00946867 | ||||||||
\(334\) | −32.6693 | −1.78759 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.5643 | −0.849103 | ||||||||
\(337\) | −7.22408 | −0.393521 | −0.196760 | − | 0.980452i | \(-0.563042\pi\) | ||||
−0.196760 | + | 0.980452i | \(0.563042\pi\) | |||||||
\(338\) | 0.0486156 | 0.00264434 | ||||||||
\(339\) | −22.9589 | −1.24695 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.5760 | −0.626877 | ||||||||
\(342\) | 0.0510093 | 0.00275826 | ||||||||
\(343\) | 3.47980 | 0.187892 | ||||||||
\(344\) | −1.61688 | −0.0871763 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.9061 | 1.12392 | ||||||||
\(347\) | 1.93577 | 0.103917 | 0.0519587 | − | 0.998649i | \(-0.483454\pi\) | ||||
0.0519587 | + | 0.998649i | \(0.483454\pi\) | |||||||
\(348\) | −21.5690 | −1.15622 | ||||||||
\(349\) | −10.3941 | −0.556385 | −0.278192 | − | 0.960525i | \(-0.589735\pi\) | ||||
−0.278192 | + | 0.960525i | \(0.589735\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.0305 | −1.01577 | ||||||||
\(352\) | −26.1570 | −1.39417 | ||||||||
\(353\) | 14.4634 | 0.769809 | 0.384905 | − | 0.922956i | \(-0.374234\pi\) | ||||
0.384905 | + | 0.922956i | \(0.374234\pi\) | |||||||
\(354\) | −35.1105 | −1.86610 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.98788 | −0.158357 | ||||||||
\(357\) | −31.5627 | −1.67047 | ||||||||
\(358\) | 28.5102 | 1.50681 | ||||||||
\(359\) | 31.9938 | 1.68857 | 0.844284 | − | 0.535896i | \(-0.180026\pi\) | ||||
0.844284 | + | 0.535896i | \(0.180026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9485 | −0.997289 | ||||||||
\(362\) | 15.2627 | 0.802188 | ||||||||
\(363\) | 0.576041 | 0.0302343 | ||||||||
\(364\) | 36.4603 | 1.91104 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 53.8764 | 2.81617 | ||||||||
\(367\) | −17.0688 | −0.890982 | −0.445491 | − | 0.895286i | \(-0.646971\pi\) | ||||
−0.445491 | + | 0.895286i | \(0.646971\pi\) | |||||||
\(368\) | 4.54824 | 0.237094 | ||||||||
\(369\) | 0.524038 | 0.0272803 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.5947 | −0.809635 | ||||||||
\(372\) | 15.3374 | 0.795209 | ||||||||
\(373\) | 23.2843 | 1.20562 | 0.602808 | − | 0.797886i | \(-0.294048\pi\) | ||||
0.602808 | + | 0.797886i | \(0.294048\pi\) | |||||||
\(374\) | −34.7848 | −1.79868 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.52724 | 0.0787615 | ||||||||
\(377\) | −17.4162 | −0.896980 | ||||||||
\(378\) | 43.8410 | 2.25494 | ||||||||
\(379\) | 33.0919 | 1.69982 | 0.849908 | − | 0.526931i | \(-0.176657\pi\) | ||||
0.849908 | + | 0.526931i | \(0.176657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.8021 | 0.655871 | ||||||||
\(382\) | −32.7697 | −1.67664 | ||||||||
\(383\) | −12.2692 | −0.626926 | −0.313463 | − | 0.949600i | \(-0.601489\pi\) | ||||
−0.313463 | + | 0.949600i | \(0.601489\pi\) | |||||||
\(384\) | 17.3199 | 0.883852 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.2825 | 0.625161 | ||||||||
\(387\) | −0.126439 | −0.00642724 | ||||||||
\(388\) | −34.6342 | −1.75828 | ||||||||
\(389\) | 8.65132 | 0.438639 | 0.219320 | − | 0.975653i | \(-0.429616\pi\) | ||||
0.219320 | + | 0.975653i | \(0.429616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.22333 | 0.466444 | ||||||||
\(392\) | −10.5639 | −0.533556 | ||||||||
\(393\) | 11.9568 | 0.603143 | ||||||||
\(394\) | −33.3385 | −1.67957 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.923017 | 0.0463834 | ||||||||
\(397\) | 10.8717 | 0.545637 | 0.272819 | − | 0.962065i | \(-0.412044\pi\) | ||||
0.272819 | + | 0.962065i | \(0.412044\pi\) | |||||||
\(398\) | 5.39028 | 0.270191 | ||||||||
\(399\) | 1.49071 | 0.0746289 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1654 | −0.657447 | −0.328724 | − | 0.944426i | \(-0.606618\pi\) | ||||
−0.328724 | + | 0.944426i | \(0.606618\pi\) | |||||||
\(402\) | −7.78186 | −0.388124 | ||||||||
\(403\) | 12.3844 | 0.616911 | ||||||||
\(404\) | −19.5018 | −0.970250 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 40.1221 | 1.99122 | ||||||||
\(407\) | 5.56507 | 0.275850 | ||||||||
\(408\) | 10.9314 | 0.541185 | ||||||||
\(409\) | 18.4576 | 0.912670 | 0.456335 | − | 0.889808i | \(-0.349162\pi\) | ||||
0.456335 | + | 0.889808i | \(0.349162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.97407 | −0.491984 | ||||||||
\(412\) | −38.1827 | −1.88113 | ||||||||
\(413\) | 37.0496 | 1.82309 | ||||||||
\(414\) | −0.431434 | −0.0212038 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 27.9835 | 1.37201 | ||||||||
\(417\) | −22.5585 | −1.10470 | ||||||||
\(418\) | 1.64289 | 0.0803564 | ||||||||
\(419\) | 7.30445 | 0.356846 | 0.178423 | − | 0.983954i | \(-0.442901\pi\) | ||||
0.178423 | + | 0.983954i | \(0.442901\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0861 | 1.22262 | 0.611310 | − | 0.791391i | \(-0.290643\pi\) | ||||
0.611310 | + | 0.791391i | \(0.290643\pi\) | |||||||
\(422\) | 49.1906 | 2.39456 | ||||||||
\(423\) | 0.119429 | 0.00580684 | ||||||||
\(424\) | 5.40105 | 0.262298 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.17085 | 0.444329 | ||||||||
\(427\) | −56.8520 | −2.75126 | ||||||||
\(428\) | −24.9248 | −1.20479 | ||||||||
\(429\) | −20.6410 | −0.996555 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.5910 | 1.61802 | 0.809011 | − | 0.587794i | \(-0.200003\pi\) | ||||
0.809011 | + | 0.587794i | \(0.200003\pi\) | |||||||
\(432\) | 12.5174 | 0.602244 | ||||||||
\(433\) | −12.6008 | −0.605557 | −0.302778 | − | 0.953061i | \(-0.597914\pi\) | ||||
−0.302778 | + | 0.953061i | \(0.597914\pi\) | |||||||
\(434\) | −28.5302 | −1.36949 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 42.0543 | 2.01404 | ||||||||
\(437\) | −0.435620 | −0.0208385 | ||||||||
\(438\) | 18.4342 | 0.880820 | ||||||||
\(439\) | 16.4897 | 0.787011 | 0.393506 | − | 0.919322i | \(-0.371262\pi\) | ||||
0.393506 | + | 0.919322i | \(0.371262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.826086 | −0.0393374 | ||||||||
\(442\) | 37.2138 | 1.77008 | ||||||||
\(443\) | −4.44054 | −0.210976 | −0.105488 | − | 0.994421i | \(-0.533641\pi\) | ||||
−0.105488 | + | 0.994421i | \(0.533641\pi\) | |||||||
\(444\) | −7.37332 | −0.349922 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.289769 | 0.0137210 | ||||||||
\(447\) | −0.0827637 | −0.00391459 | ||||||||
\(448\) | −46.1726 | −2.18145 | ||||||||
\(449\) | −35.0886 | −1.65593 | −0.827967 | − | 0.560776i | \(-0.810503\pi\) | ||||
−0.827967 | + | 0.560776i | \(0.810503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8781 | 0.794757 | ||||||||
\(452\) | −35.3757 | −1.66393 | ||||||||
\(453\) | 4.14866 | 0.194921 | ||||||||
\(454\) | 23.2841 | 1.09278 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.516292 | −0.0241776 | ||||||||
\(457\) | −24.1907 | −1.13159 | −0.565797 | − | 0.824544i | \(-0.691432\pi\) | ||||
−0.565797 | + | 0.824544i | \(0.691432\pi\) | |||||||
\(458\) | −16.9677 | −0.792846 | ||||||||
\(459\) | 25.3839 | 1.18482 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4172 | −0.531753 | −0.265876 | − | 0.964007i | \(-0.585661\pi\) | ||||
−0.265876 | + | 0.964007i | \(0.585661\pi\) | |||||||
\(462\) | 47.5510 | 2.21227 | ||||||||
\(463\) | −3.69770 | −0.171847 | −0.0859235 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859235 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(464\) | 11.4556 | 0.531812 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.6931 | 0.865940 | ||||||||
\(467\) | 25.9384 | 1.20028 | 0.600142 | − | 0.799893i | \(-0.295111\pi\) | ||||
0.600142 | + | 0.799893i | \(0.295111\pi\) | |||||||
\(468\) | −0.987473 | −0.0456459 | ||||||||
\(469\) | 8.21164 | 0.379178 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.0872 | −0.603025 | ||||||||
\(472\) | −12.8317 | −0.590629 | ||||||||
\(473\) | −4.07230 | −0.187245 | ||||||||
\(474\) | −50.0212 | −2.29755 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −48.6327 | −2.22908 | ||||||||
\(477\) | 0.422358 | 0.0193384 | ||||||||
\(478\) | 6.74886 | 0.308686 | ||||||||
\(479\) | −15.9509 | −0.728817 | −0.364408 | − | 0.931239i | \(-0.618729\pi\) | ||||
−0.364408 | + | 0.931239i | \(0.618729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.95369 | −0.271465 | ||||||||
\(482\) | −2.14986 | −0.0979233 | ||||||||
\(483\) | −12.6084 | −0.573700 | ||||||||
\(484\) | 0.887581 | 0.0403446 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.33475 | −0.105906 | ||||||||
\(487\) | −2.85926 | −0.129565 | −0.0647826 | − | 0.997899i | \(-0.520635\pi\) | ||||
−0.0647826 | + | 0.997899i | \(0.520635\pi\) | |||||||
\(488\) | 19.6901 | 0.891328 | ||||||||
\(489\) | 28.2566 | 1.27781 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.7086 | −1.56638 | −0.783189 | − | 0.621783i | \(-0.786409\pi\) | ||||
−0.783189 | + | 0.621783i | \(0.786409\pi\) | |||||||
\(492\) | −22.3622 | −1.00817 | ||||||||
\(493\) | 23.2306 | 1.04626 | ||||||||
\(494\) | −1.75762 | −0.0790789 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.14590 | −0.365762 | ||||||||
\(497\) | −9.67735 | −0.434089 | ||||||||
\(498\) | 21.3250 | 0.955595 | ||||||||
\(499\) | 32.6502 | 1.46162 | 0.730812 | − | 0.682579i | \(-0.239142\pi\) | ||||
0.730812 | + | 0.682579i | \(0.239142\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.8577 | 1.15523 | ||||||||
\(502\) | −46.1616 | −2.06029 | ||||||||
\(503\) | 1.74843 | 0.0779587 | 0.0389793 | − | 0.999240i | \(-0.487589\pi\) | ||||
0.0389793 | + | 0.999240i | \(0.487589\pi\) | |||||||
\(504\) | 0.539571 | 0.0240344 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13.8955 | −0.617730 | ||||||||
\(507\) | −0.0384790 | −0.00170891 | ||||||||
\(508\) | 19.7258 | 0.875193 | ||||||||
\(509\) | 22.7486 | 1.00832 | 0.504158 | − | 0.863612i | \(-0.331803\pi\) | ||||
0.504158 | + | 0.863612i | \(0.331803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.4523 | −0.860519 | ||||||||
\(512\) | −24.7421 | −1.09346 | ||||||||
\(513\) | −1.19889 | −0.0529321 | ||||||||
\(514\) | −57.0474 | −2.51625 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.39551 | 0.237524 | ||||||||
\(517\) | 3.84654 | 0.169170 | ||||||||
\(518\) | 13.7156 | 0.602630 | ||||||||
\(519\) | −16.5471 | −0.726336 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8373 | −0.518603 | −0.259301 | − | 0.965796i | \(-0.583492\pi\) | ||||
−0.259301 | + | 0.965796i | \(0.583492\pi\) | |||||||
\(522\) | −1.08664 | −0.0475611 | ||||||||
\(523\) | −18.3947 | −0.804344 | −0.402172 | − | 0.915564i | \(-0.631745\pi\) | ||||
−0.402172 | + | 0.915564i | \(0.631745\pi\) | |||||||
\(524\) | 18.4235 | 0.804833 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.0543 | 0.961614 | ||||||||
\(527\) | −16.5190 | −0.719578 | ||||||||
\(528\) | 13.5767 | 0.590850 | ||||||||
\(529\) | −19.3156 | −0.839807 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00343 | −0.0435452 | ||||||||
\(532\) | 2.29693 | 0.0995846 | ||||||||
\(533\) | −18.0567 | −0.782122 | ||||||||
\(534\) | 4.16887 | 0.180404 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.84402 | −0.122843 | ||||||||
\(537\) | −22.5657 | −0.973783 | ||||||||
\(538\) | 0.129938 | 0.00560203 | ||||||||
\(539\) | −26.6063 | −1.14602 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.8842 | −0.467948 | −0.233974 | − | 0.972243i | \(-0.575173\pi\) | ||||
−0.233974 | + | 0.972243i | \(0.575173\pi\) | |||||||
\(542\) | −46.4086 | −1.99342 | ||||||||
\(543\) | −12.0803 | −0.518417 | ||||||||
\(544\) | −37.3259 | −1.60034 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −50.8716 | −2.17710 | ||||||||
\(547\) | −41.3630 | −1.76855 | −0.884277 | − | 0.466962i | \(-0.845348\pi\) | ||||
−0.884277 | + | 0.466962i | \(0.845348\pi\) | |||||||
\(548\) | −15.3683 | −0.656503 | ||||||||
\(549\) | 1.53975 | 0.0657149 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.09719 | −0.0467418 | ||||||||
\(552\) | 4.36677 | 0.185862 | ||||||||
\(553\) | 52.7838 | 2.24460 | ||||||||
\(554\) | 48.1153 | 2.04422 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −34.7588 | −1.47410 | ||||||||
\(557\) | 11.7230 | 0.496720 | 0.248360 | − | 0.968668i | \(-0.420108\pi\) | ||||
0.248360 | + | 0.968668i | \(0.420108\pi\) | |||||||
\(558\) | 0.772697 | 0.0327109 | ||||||||
\(559\) | 4.35667 | 0.184268 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 27.5320 | 1.16240 | ||||||||
\(562\) | 66.2277 | 2.79365 | ||||||||
\(563\) | 19.6865 | 0.829689 | 0.414844 | − | 0.909892i | \(-0.363836\pi\) | ||||
0.414844 | + | 0.909892i | \(0.363836\pi\) | |||||||
\(564\) | −5.09639 | −0.214597 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 64.2556 | 2.70086 | ||||||||
\(567\) | −33.4892 | −1.40641 | ||||||||
\(568\) | 3.35165 | 0.140632 | ||||||||
\(569\) | 44.1961 | 1.85280 | 0.926399 | − | 0.376542i | \(-0.122887\pi\) | ||||
0.926399 | + | 0.376542i | \(0.122887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.2447 | −1.76789 | −0.883943 | − | 0.467595i | \(-0.845121\pi\) | ||||
−0.883943 | + | 0.467595i | \(0.845121\pi\) | |||||||
\(572\) | −31.8042 | −1.32980 | ||||||||
\(573\) | 25.9371 | 1.08354 | ||||||||
\(574\) | 41.5976 | 1.73625 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.25051 | 0.0521047 | ||||||||
\(577\) | −17.0708 | −0.710668 | −0.355334 | − | 0.934739i | \(-0.615633\pi\) | ||||
−0.355334 | + | 0.934739i | \(0.615633\pi\) | |||||||
\(578\) | −13.0903 | −0.544483 | ||||||||
\(579\) | −9.72153 | −0.404013 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.5027 | −0.933570 | ||||||||
\(582\) | 48.3236 | 2.00308 | ||||||||
\(583\) | 13.6032 | 0.563386 | ||||||||
\(584\) | 6.73710 | 0.278783 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41.3221 | −1.70700 | ||||||||
\(587\) | 25.8807 | 1.06821 | 0.534105 | − | 0.845418i | \(-0.320649\pi\) | ||||
0.534105 | + | 0.845418i | \(0.320649\pi\) | |||||||
\(588\) | 35.2515 | 1.45375 | ||||||||
\(589\) | 0.780194 | 0.0321473 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.3873 | 1.08543 | ||||||||
\(592\) | 3.91606 | 0.160949 | ||||||||
\(593\) | −21.0088 | −0.862729 | −0.431364 | − | 0.902178i | \(-0.641968\pi\) | ||||
−0.431364 | + | 0.902178i | \(0.641968\pi\) | |||||||
\(594\) | −38.2423 | −1.56910 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.127525 | −0.00522362 | ||||||||
\(597\) | −4.26639 | −0.174612 | ||||||||
\(598\) | 14.8658 | 0.607909 | ||||||||
\(599\) | 8.72823 | 0.356626 | 0.178313 | − | 0.983974i | \(-0.442936\pi\) | ||||
0.178313 | + | 0.983974i | \(0.442936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4335 | −0.915080 | −0.457540 | − | 0.889189i | \(-0.651269\pi\) | ||||
−0.457540 | + | 0.889189i | \(0.651269\pi\) | |||||||
\(602\) | −10.0366 | −0.409060 | ||||||||
\(603\) | −0.222400 | −0.00905682 | ||||||||
\(604\) | 6.39238 | 0.260102 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 27.2100 | 1.10533 | ||||||||
\(607\) | 27.7266 | 1.12539 | 0.562693 | − | 0.826666i | \(-0.309765\pi\) | ||||
0.562693 | + | 0.826666i | \(0.309765\pi\) | |||||||
\(608\) | 1.76291 | 0.0714955 | ||||||||
\(609\) | −31.7565 | −1.28684 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.11515 | −0.166481 | ||||||||
\(612\) | 1.31714 | 0.0532424 | ||||||||
\(613\) | 6.18419 | 0.249777 | 0.124888 | − | 0.992171i | \(-0.460143\pi\) | ||||
0.124888 | + | 0.992171i | \(0.460143\pi\) | |||||||
\(614\) | −11.5196 | −0.464892 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 17.3784 | 0.700194 | ||||||||
\(617\) | −11.7107 | −0.471456 | −0.235728 | − | 0.971819i | \(-0.575747\pi\) | ||||
−0.235728 | + | 0.971819i | \(0.575747\pi\) | |||||||
\(618\) | 53.2747 | 2.14302 | ||||||||
\(619\) | 24.6950 | 0.992575 | 0.496288 | − | 0.868158i | \(-0.334696\pi\) | ||||
0.496288 | + | 0.868158i | \(0.334696\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.1401 | 0.406909 | ||||||||
\(622\) | −31.6448 | −1.26884 | ||||||||
\(623\) | −4.39911 | −0.176247 | ||||||||
\(624\) | −14.5248 | −0.581456 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.3961 | −0.895129 | ||||||||
\(627\) | −1.30034 | −0.0519307 | ||||||||
\(628\) | −20.1651 | −0.804675 | ||||||||
\(629\) | 7.94134 | 0.316642 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.11033 | 0.322867 | 0.161434 | − | 0.986884i | \(-0.448388\pi\) | ||||
0.161434 | + | 0.986884i | \(0.448388\pi\) | |||||||
\(632\) | −18.2811 | −0.727184 | ||||||||
\(633\) | −38.9342 | −1.54750 | ||||||||
\(634\) | −13.4732 | −0.535087 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.0232 | −0.714668 | ||||||||
\(637\) | 28.4643 | 1.12780 | ||||||||
\(638\) | −34.9983 | −1.38560 | ||||||||
\(639\) | 0.262096 | 0.0103684 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.59199 | 0.220870 | 0.110435 | − | 0.993883i | \(-0.464776\pi\) | ||||
0.110435 | + | 0.993883i | \(0.464776\pi\) | |||||||
\(642\) | 34.7765 | 1.37252 | ||||||||
\(643\) | 27.6688 | 1.09115 | 0.545575 | − | 0.838062i | \(-0.316311\pi\) | ||||
0.545575 | + | 0.838062i | \(0.316311\pi\) | |||||||
\(644\) | −19.4273 | −0.765544 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.34440 | 0.0922393 | ||||||||
\(647\) | 36.5140 | 1.43551 | 0.717757 | − | 0.696294i | \(-0.245169\pi\) | ||||
0.717757 | + | 0.696294i | \(0.245169\pi\) | |||||||
\(648\) | 11.5986 | 0.455637 | ||||||||
\(649\) | −32.3182 | −1.26860 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.5816 | 0.885041 | ||||||||
\(652\) | 43.5386 | 1.70510 | ||||||||
\(653\) | −25.4592 | −0.996296 | −0.498148 | − | 0.867092i | \(-0.665986\pi\) | ||||
−0.498148 | + | 0.867092i | \(0.665986\pi\) | |||||||
\(654\) | −58.6766 | −2.29444 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.8769 | 0.463714 | ||||||||
\(657\) | 0.526836 | 0.0205538 | ||||||||
\(658\) | 9.48015 | 0.369575 | ||||||||
\(659\) | −24.6793 | −0.961369 | −0.480684 | − | 0.876894i | \(-0.659612\pi\) | ||||
−0.480684 | + | 0.876894i | \(0.659612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.3577 | −0.869615 | −0.434808 | − | 0.900523i | \(-0.643184\pi\) | ||||
−0.434808 | + | 0.900523i | \(0.643184\pi\) | |||||||
\(662\) | 33.6853 | 1.30922 | ||||||||
\(663\) | −29.4546 | −1.14392 | ||||||||
\(664\) | 7.79358 | 0.302450 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.371467 | −0.0143941 | ||||||||
\(667\) | 9.27996 | 0.359321 | ||||||||
\(668\) | 39.8423 | 1.54154 | ||||||||
\(669\) | −0.229351 | −0.00886723 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.5918 | 1.91447 | ||||||||
\(672\) | 51.0248 | 1.96833 | ||||||||
\(673\) | −28.8997 | −1.11400 | −0.557001 | − | 0.830512i | \(-0.688048\pi\) | ||||
−0.557001 | + | 0.830512i | \(0.688048\pi\) | |||||||
\(674\) | 15.5307 | 0.598221 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.0592896 | −0.00228037 | ||||||||
\(677\) | −3.14192 | −0.120754 | −0.0603769 | − | 0.998176i | \(-0.519230\pi\) | ||||
−0.0603769 | + | 0.998176i | \(0.519230\pi\) | |||||||
\(678\) | 49.3582 | 1.89559 | ||||||||
\(679\) | −50.9925 | −1.95691 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.4293 | −0.706212 | ||||||||
\(682\) | 24.8868 | 0.952965 | ||||||||
\(683\) | −12.9423 | −0.495224 | −0.247612 | − | 0.968859i | \(-0.579646\pi\) | ||||
−0.247612 | + | 0.968859i | \(0.579646\pi\) | |||||||
\(684\) | −0.0622089 | −0.00237862 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.48107 | −0.285629 | ||||||||
\(687\) | 13.4298 | 0.512380 | ||||||||
\(688\) | −2.86562 | −0.109251 | ||||||||
\(689\) | −14.5531 | −0.554429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.5562 | −1.35262 | −0.676311 | − | 0.736616i | \(-0.736422\pi\) | ||||
−0.676311 | + | 0.736616i | \(0.736422\pi\) | |||||||
\(692\) | −25.4962 | −0.969222 | ||||||||
\(693\) | 1.35897 | 0.0516231 | ||||||||
\(694\) | −4.16162 | −0.157973 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.9985 | 0.416897 | ||||||||
\(697\) | 24.0850 | 0.912283 | ||||||||
\(698\) | 22.3459 | 0.845803 | ||||||||
\(699\) | −14.7955 | −0.559617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.7109 | 0.593393 | 0.296697 | − | 0.954972i | \(-0.404115\pi\) | ||||
0.296697 | + | 0.954972i | \(0.404115\pi\) | |||||||
\(702\) | 40.9128 | 1.54416 | ||||||||
\(703\) | −0.375071 | −0.0141461 | ||||||||
\(704\) | 40.2762 | 1.51797 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.0942 | −1.17025 | ||||||||
\(707\) | −28.7128 | −1.07986 | ||||||||
\(708\) | 42.8194 | 1.60925 | ||||||||
\(709\) | −11.3414 | −0.425936 | −0.212968 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212968 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.42957 | −0.0536131 | ||||||||
\(712\) | 1.52358 | 0.0570987 | ||||||||
\(713\) | −6.59884 | −0.247129 | ||||||||
\(714\) | 67.8552 | 2.53942 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −34.7700 | −1.29941 | ||||||||
\(717\) | −5.34170 | −0.199489 | ||||||||
\(718\) | −68.7821 | −2.56692 | ||||||||
\(719\) | −27.4225 | −1.02269 | −0.511343 | − | 0.859377i | \(-0.670852\pi\) | ||||
−0.511343 | + | 0.859377i | \(0.670852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.2170 | −2.09363 | ||||||||
\(722\) | 40.7365 | 1.51606 | ||||||||
\(723\) | 1.70160 | 0.0632833 | ||||||||
\(724\) | −18.6138 | −0.691775 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.23840 | −0.0459615 | ||||||||
\(727\) | −26.3265 | −0.976396 | −0.488198 | − | 0.872733i | \(-0.662346\pi\) | ||||
−0.488198 | + | 0.872733i | \(0.662346\pi\) | |||||||
\(728\) | −18.5919 | −0.689062 | ||||||||
\(729\) | 27.8742 | 1.03238 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.81116 | −0.214934 | ||||||||
\(732\) | −65.7056 | −2.42855 | ||||||||
\(733\) | 17.1782 | 0.634490 | 0.317245 | − | 0.948344i | \(-0.397242\pi\) | ||||
0.317245 | + | 0.948344i | \(0.397242\pi\) | |||||||
\(734\) | 36.6954 | 1.35445 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.9106 | −0.549612 | ||||||||
\(737\) | −7.16299 | −0.263852 | ||||||||
\(738\) | −1.12661 | −0.0414710 | ||||||||
\(739\) | 45.5581 | 1.67588 | 0.837940 | − | 0.545762i | \(-0.183760\pi\) | ||||
0.837940 | + | 0.545762i | \(0.183760\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.39115 | 0.0511050 | ||||||||
\(742\) | 33.5263 | 1.23079 | ||||||||
\(743\) | −27.3015 | −1.00160 | −0.500798 | − | 0.865564i | \(-0.666960\pi\) | ||||
−0.500798 | + | 0.865564i | \(0.666960\pi\) | |||||||
\(744\) | −7.82088 | −0.286727 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −50.0579 | −1.83275 | ||||||||
\(747\) | 0.609452 | 0.0222987 | ||||||||
\(748\) | 42.4222 | 1.55111 | ||||||||
\(749\) | −36.6972 | −1.34089 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.3189 | 1.32530 | 0.662648 | − | 0.748931i | \(-0.269433\pi\) | ||||
0.662648 | + | 0.748931i | \(0.269433\pi\) | |||||||
\(752\) | 2.70676 | 0.0987052 | ||||||||
\(753\) | 36.5368 | 1.33147 | ||||||||
\(754\) | 37.4423 | 1.36357 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −53.4667 | −1.94457 | ||||||||
\(757\) | −26.8976 | −0.977611 | −0.488806 | − | 0.872393i | \(-0.662567\pi\) | ||||
−0.488806 | + | 0.872393i | \(0.662567\pi\) | |||||||
\(758\) | −71.1428 | −2.58402 | ||||||||
\(759\) | 10.9982 | 0.399210 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.1591 | −1.70951 | −0.854757 | − | 0.519028i | \(-0.826294\pi\) | ||||
−0.854757 | + | 0.519028i | \(0.826294\pi\) | |||||||
\(762\) | −27.5226 | −0.997040 | ||||||||
\(763\) | 61.9173 | 2.24156 | ||||||||
\(764\) | 39.9646 | 1.44587 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.3770 | 0.953038 | ||||||||
\(767\) | 34.5751 | 1.24843 | ||||||||
\(768\) | 3.47070 | 0.125238 | ||||||||
\(769\) | −6.84252 | −0.246747 | −0.123374 | − | 0.992360i | \(-0.539371\pi\) | ||||
−0.123374 | + | 0.992360i | \(0.539371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.1528 | 1.62614 | ||||||||
\(772\) | −14.9792 | −0.539114 | ||||||||
\(773\) | 19.6772 | 0.707740 | 0.353870 | − | 0.935295i | \(-0.384866\pi\) | ||||
0.353870 | + | 0.935295i | \(0.384866\pi\) | |||||||
\(774\) | 0.271825 | 0.00977054 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17.6607 | 0.633983 | ||||||||
\(777\) | −10.8559 | −0.389452 | ||||||||
\(778\) | −18.5991 | −0.666810 | ||||||||
\(779\) | −1.13754 | −0.0407565 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.44152 | 0.302061 | ||||||||
\(782\) | −19.8288 | −0.709078 | ||||||||
\(783\) | 25.5397 | 0.912715 | ||||||||
\(784\) | −18.7225 | −0.668661 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.7055 | −0.916885 | ||||||||
\(787\) | −26.7410 | −0.953213 | −0.476607 | − | 0.879117i | \(-0.658133\pi\) | ||||
−0.476607 | + | 0.879117i | \(0.658133\pi\) | |||||||
\(788\) | 40.6584 | 1.44839 | ||||||||
\(789\) | −17.4559 | −0.621447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −52.0843 | −1.85190 | ||||||||
\(792\) | −0.470666 | −0.0167244 | ||||||||
\(793\) | −53.0549 | −1.88403 | ||||||||
\(794\) | −23.3727 | −0.829466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.57378 | −0.233001 | ||||||||
\(797\) | −54.6670 | −1.93640 | −0.968202 | − | 0.250171i | \(-0.919513\pi\) | ||||
−0.968202 | + | 0.250171i | \(0.919513\pi\) | |||||||
\(798\) | −3.20481 | −0.113449 | ||||||||
\(799\) | 5.48900 | 0.194187 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.119143 | 0.00420972 | ||||||||
\(802\) | 28.3036 | 0.999437 | ||||||||
\(803\) | 16.9682 | 0.598794 | ||||||||
\(804\) | 9.49045 | 0.334702 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.6247 | −0.937815 | ||||||||
\(807\) | −0.102845 | −0.00362033 | ||||||||
\(808\) | 9.94438 | 0.349842 | ||||||||
\(809\) | −20.5992 | −0.724230 | −0.362115 | − | 0.932133i | \(-0.617945\pi\) | ||||
−0.362115 | + | 0.932133i | \(0.617945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.0273 | 1.86204 | 0.931020 | − | 0.364968i | \(-0.118920\pi\) | ||||
0.931020 | + | 0.364968i | \(0.118920\pi\) | |||||||
\(812\) | −48.9313 | −1.71715 | ||||||||
\(813\) | 36.7322 | 1.28826 | ||||||||
\(814\) | −11.9641 | −0.419342 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 19.3739 | 0.678222 | ||||||||
\(817\) | 0.274462 | 0.00960222 | ||||||||
\(818\) | −39.6812 | −1.38742 | ||||||||
\(819\) | −1.45387 | −0.0508024 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.4856 | −0.610250 | −0.305125 | − | 0.952312i | \(-0.598698\pi\) | ||||
−0.305125 | + | 0.952312i | \(0.598698\pi\) | |||||||
\(822\) | 21.4428 | 0.747904 | ||||||||
\(823\) | −3.94292 | −0.137442 | −0.0687208 | − | 0.997636i | \(-0.521892\pi\) | ||||
−0.0687208 | + | 0.997636i | \(0.521892\pi\) | |||||||
\(824\) | 19.4702 | 0.678275 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −79.6513 | −2.77142 | ||||||||
\(827\) | −46.4685 | −1.61587 | −0.807934 | − | 0.589274i | \(-0.799414\pi\) | ||||
−0.807934 | + | 0.589274i | \(0.799414\pi\) | |||||||
\(828\) | 0.526160 | 0.0182853 | ||||||||
\(829\) | −5.50401 | −0.191162 | −0.0955811 | − | 0.995422i | \(-0.530471\pi\) | ||||
−0.0955811 | + | 0.995422i | \(0.530471\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −38.0831 | −1.32109 | ||||||||
\(832\) | −43.0887 | −1.49383 | ||||||||
\(833\) | −37.9672 | −1.31548 | ||||||||
\(834\) | 48.4976 | 1.67933 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.00361 | −0.0692962 | ||||||||
\(837\) | −18.1609 | −0.627734 | ||||||||
\(838\) | −15.7035 | −0.542469 | ||||||||
\(839\) | −41.1331 | −1.42007 | −0.710037 | − | 0.704165i | \(-0.751322\pi\) | ||||
−0.710037 | + | 0.704165i | \(0.751322\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.62674 | −0.194025 | ||||||||
\(842\) | −53.9314 | −1.85860 | ||||||||
\(843\) | −52.4190 | −1.80541 | ||||||||
\(844\) | −59.9910 | −2.06498 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.256755 | −0.00882743 | ||||||||
\(847\) | 1.30680 | 0.0449022 | ||||||||
\(848\) | 9.57237 | 0.328716 | ||||||||
\(849\) | −50.8581 | −1.74544 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.17233 | 0.108746 | ||||||||
\(852\) | −11.1844 | −0.383172 | ||||||||
\(853\) | 12.6606 | 0.433491 | 0.216746 | − | 0.976228i | \(-0.430456\pi\) | ||||
0.216746 | + | 0.976228i | \(0.430456\pi\) | |||||||
\(854\) | 122.224 | 4.18241 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.7097 | 0.434408 | ||||||||
\(857\) | −29.3491 | −1.00255 | −0.501273 | − | 0.865289i | \(-0.667135\pi\) | ||||
−0.501273 | + | 0.865289i | \(0.667135\pi\) | |||||||
\(858\) | 44.3751 | 1.51494 | ||||||||
\(859\) | −16.5376 | −0.564256 | −0.282128 | − | 0.959377i | \(-0.591040\pi\) | ||||
−0.282128 | + | 0.959377i | \(0.591040\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.9243 | −1.12206 | ||||||||
\(862\) | −72.2158 | −2.45968 | ||||||||
\(863\) | −50.4538 | −1.71747 | −0.858734 | − | 0.512421i | \(-0.828749\pi\) | ||||
−0.858734 | + | 0.512421i | \(0.828749\pi\) | |||||||
\(864\) | −41.0361 | −1.39608 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.0899 | 0.920554 | ||||||||
\(867\) | 10.3609 | 0.351874 | ||||||||
\(868\) | 34.7943 | 1.18100 | ||||||||
\(869\) | −46.0432 | −1.56191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.66319 | 0.259657 | ||||||||
\(872\) | −21.4444 | −0.726199 | ||||||||
\(873\) | 1.38105 | 0.0467416 | ||||||||
\(874\) | 0.936519 | 0.0316782 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.4816 | −0.759584 | ||||||||
\(877\) | −23.3907 | −0.789847 | −0.394924 | − | 0.918714i | \(-0.629229\pi\) | ||||
−0.394924 | + | 0.918714i | \(0.629229\pi\) | |||||||
\(878\) | −35.4505 | −1.19640 | ||||||||
\(879\) | 32.7063 | 1.10315 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.95967 | −0.335550 | −0.167775 | − | 0.985825i | \(-0.553658\pi\) | ||||
−0.167775 | + | 0.985825i | \(0.553658\pi\) | |||||||
\(882\) | 1.77597 | 0.0597999 | ||||||||
\(883\) | −26.5158 | −0.892329 | −0.446165 | − | 0.894951i | \(-0.647210\pi\) | ||||
−0.446165 | + | 0.894951i | \(0.647210\pi\) | |||||||
\(884\) | −45.3846 | −1.52645 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.54652 | 0.320722 | ||||||||
\(887\) | −54.2449 | −1.82137 | −0.910683 | − | 0.413105i | \(-0.864444\pi\) | ||||
−0.910683 | + | 0.413105i | \(0.864444\pi\) | |||||||
\(888\) | 3.75982 | 0.126171 | ||||||||
\(889\) | 29.0427 | 0.974061 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.2125 | 0.978656 | ||||||||
\(892\) | −0.353391 | −0.0118324 | ||||||||
\(893\) | −0.259246 | −0.00867535 | ||||||||
\(894\) | 0.177930 | 0.00595087 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 39.2917 | 1.31264 | ||||||||
\(897\) | −11.7662 | −0.392864 | ||||||||
\(898\) | 75.4355 | 2.51731 | ||||||||
\(899\) | −16.6204 | −0.554321 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.4117 | 0.646697 | ||||||||
\(902\) | −36.2854 | −1.20817 | ||||||||
\(903\) | 7.94390 | 0.264356 | ||||||||
\(904\) | 18.0388 | 0.599963 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.91902 | −0.296315 | ||||||||
\(907\) | −33.0947 | −1.09889 | −0.549447 | − | 0.835529i | \(-0.685161\pi\) | ||||
−0.549447 | + | 0.835529i | \(0.685161\pi\) | |||||||
\(908\) | −28.3964 | −0.942368 | ||||||||
\(909\) | 0.777643 | 0.0257928 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.2776 | 0.671828 | 0.335914 | − | 0.941893i | \(-0.390955\pi\) | ||||
0.335914 | + | 0.941893i | \(0.390955\pi\) | |||||||
\(912\) | −0.915033 | −0.0302998 | ||||||||
\(913\) | 19.6290 | 0.649627 | ||||||||
\(914\) | 52.0066 | 1.72023 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.6931 | 0.683719 | ||||||||
\(917\) | 27.1252 | 0.895753 | ||||||||
\(918\) | −54.5717 | −1.80113 | ||||||||
\(919\) | 38.1612 | 1.25882 | 0.629412 | − | 0.777072i | \(-0.283296\pi\) | ||||
0.629412 | + | 0.777072i | \(0.283296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.11769 | 0.300438 | ||||||||
\(922\) | 24.5454 | 0.808359 | ||||||||
\(923\) | −9.03100 | −0.297259 | ||||||||
\(924\) | −57.9914 | −1.90778 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.94953 | 0.261238 | ||||||||
\(927\) | 1.52255 | 0.0500072 | ||||||||
\(928\) | −37.5551 | −1.23281 | ||||||||
\(929\) | 19.1236 | 0.627425 | 0.313712 | − | 0.949518i | \(-0.398427\pi\) | ||||
0.313712 | + | 0.949518i | \(0.398427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.79320 | 0.0587696 | ||||||||
\(932\) | −22.7973 | −0.746752 | ||||||||
\(933\) | 25.0467 | 0.819994 | ||||||||
\(934\) | −55.7637 | −1.82465 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.503533 | 0.0164585 | ||||||||
\(937\) | 40.2441 | 1.31472 | 0.657359 | − | 0.753578i | \(-0.271674\pi\) | ||||
0.657359 | + | 0.753578i | \(0.271674\pi\) | |||||||
\(938\) | −17.6538 | −0.576419 | ||||||||
\(939\) | 17.7265 | 0.578481 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.7799 | 0.840399 | 0.420200 | − | 0.907432i | \(-0.361960\pi\) | ||||
0.420200 | + | 0.907432i | \(0.361960\pi\) | |||||||
\(942\) | 28.1355 | 0.916705 | ||||||||
\(943\) | 9.62123 | 0.313310 | ||||||||
\(944\) | −22.7419 | −0.740186 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.75486 | 0.284645 | ||||||||
\(947\) | 40.7917 | 1.32555 | 0.662776 | − | 0.748818i | \(-0.269378\pi\) | ||||
0.662776 | + | 0.748818i | \(0.269378\pi\) | |||||||
\(948\) | 61.0039 | 1.98132 | ||||||||
\(949\) | −18.1531 | −0.589274 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.6640 | 0.345802 | ||||||||
\(952\) | 24.7989 | 0.803736 | ||||||||
\(953\) | −36.8213 | −1.19276 | −0.596379 | − | 0.802703i | \(-0.703395\pi\) | ||||
−0.596379 | + | 0.802703i | \(0.703395\pi\) | |||||||
\(954\) | −0.908008 | −0.0293979 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.23065 | −0.266198 | ||||||||
\(957\) | 27.7010 | 0.895448 | ||||||||
\(958\) | 34.2922 | 1.10793 | ||||||||
\(959\) | −22.6271 | −0.730666 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1815 | −0.618757 | ||||||||
\(962\) | 12.7996 | 0.412675 | ||||||||
\(963\) | 0.993888 | 0.0320276 | ||||||||
\(964\) | 2.62188 | 0.0844451 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 27.1062 | 0.872126 | ||||||||
\(967\) | −8.04134 | −0.258592 | −0.129296 | − | 0.991606i | \(-0.541272\pi\) | ||||
−0.129296 | + | 0.991606i | \(0.541272\pi\) | |||||||
\(968\) | −0.452596 | −0.0145470 | ||||||||
\(969\) | −1.85559 | −0.0596100 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.7266 | −0.953972 | −0.476986 | − | 0.878911i | \(-0.658271\pi\) | ||||
−0.476986 | + | 0.878911i | \(0.658271\pi\) | |||||||
\(972\) | 2.84736 | 0.0913293 | ||||||||
\(973\) | −51.1760 | −1.64063 | ||||||||
\(974\) | 6.14699 | 0.196962 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 34.8971 | 1.11703 | ||||||||
\(977\) | −37.3788 | −1.19586 | −0.597928 | − | 0.801550i | \(-0.704009\pi\) | ||||
−0.597928 | + | 0.801550i | \(0.704009\pi\) | |||||||
\(978\) | −60.7476 | −1.94249 | ||||||||
\(979\) | 3.83733 | 0.122641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.67693 | −0.0535404 | ||||||||
\(982\) | 74.6186 | 2.38117 | ||||||||
\(983\) | 29.0852 | 0.927672 | 0.463836 | − | 0.885921i | \(-0.346473\pi\) | ||||
0.463836 | + | 0.885921i | \(0.346473\pi\) | |||||||
\(984\) | 11.4030 | 0.363514 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −49.9425 | −1.59049 | ||||||||
\(987\) | −7.50350 | −0.238839 | ||||||||
\(988\) | 2.14352 | 0.0681945 | ||||||||
\(989\) | −2.32139 | −0.0738158 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1607 | −0.354532 | −0.177266 | − | 0.984163i | \(-0.556725\pi\) | ||||
−0.177266 | + | 0.984163i | \(0.556725\pi\) | |||||||
\(992\) | 26.7049 | 0.847881 | ||||||||
\(993\) | −26.6618 | −0.846087 | ||||||||
\(994\) | 20.8049 | 0.659892 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −26.0071 | −0.824066 | ||||||||
\(997\) | −9.75783 | −0.309034 | −0.154517 | − | 0.987990i | \(-0.549382\pi\) | ||||
−0.154517 | + | 0.987990i | \(0.549382\pi\) | |||||||
\(998\) | −70.1933 | −2.22193 | ||||||||
\(999\) | 8.73070 | 0.276227 |
(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 | 6025.2.a.m.1.9 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.n.1.32 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.9 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.n.1.32 | yes | 40 | 5.4 | even | 2 |