Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47238 | −1.74824 | −0.874119 | − | 0.485712i | \(-0.838560\pi\) | ||||
−0.874119 | + | 0.485712i | \(0.838560\pi\) | |||||||
\(3\) | −0.879695 | −0.507892 | −0.253946 | − | 0.967218i | \(-0.581729\pi\) | ||||
−0.253946 | + | 0.967218i | \(0.581729\pi\) | |||||||
\(4\) | 4.11267 | 2.05633 | ||||||||
\(5\) | −2.32585 | −1.04015 | −0.520075 | − | 0.854120i | \(-0.674096\pi\) | ||||
−0.520075 | + | 0.854120i | \(0.674096\pi\) | |||||||
\(6\) | 2.17494 | 0.887916 | ||||||||
\(7\) | 1.92542 | 0.727741 | 0.363871 | − | 0.931450i | \(-0.381455\pi\) | ||||
0.363871 | + | 0.931450i | \(0.381455\pi\) | |||||||
\(8\) | −5.22332 | −1.84672 | ||||||||
\(9\) | −2.22614 | −0.742046 | ||||||||
\(10\) | 5.75038 | 1.81843 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.61789 | −1.04440 | ||||||||
\(13\) | −4.82240 | −1.33749 | −0.668746 | − | 0.743491i | \(-0.733169\pi\) | ||||
−0.668746 | + | 0.743491i | \(0.733169\pi\) | |||||||
\(14\) | −4.76038 | −1.27226 | ||||||||
\(15\) | 2.04604 | 0.528284 | ||||||||
\(16\) | 4.68871 | 1.17218 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 5.50386 | 1.29727 | ||||||||
\(19\) | −4.21529 | −0.967053 | −0.483527 | − | 0.875330i | \(-0.660644\pi\) | ||||
−0.483527 | + | 0.875330i | \(0.660644\pi\) | |||||||
\(20\) | −9.56544 | −2.13890 | ||||||||
\(21\) | −1.69378 | −0.369614 | ||||||||
\(22\) | 2.47238 | 0.527113 | ||||||||
\(23\) | −6.36962 | −1.32816 | −0.664078 | − | 0.747663i | \(-0.731176\pi\) | ||||
−0.664078 | + | 0.747663i | \(0.731176\pi\) | |||||||
\(24\) | 4.59493 | 0.937937 | ||||||||
\(25\) | 0.409567 | 0.0819134 | ||||||||
\(26\) | 11.9228 | 2.33825 | ||||||||
\(27\) | 4.59741 | 0.884771 | ||||||||
\(28\) | 7.91862 | 1.49648 | ||||||||
\(29\) | −3.79631 | −0.704957 | −0.352478 | − | 0.935820i | \(-0.614661\pi\) | ||||
−0.352478 | + | 0.935820i | \(0.614661\pi\) | |||||||
\(30\) | −5.05858 | −0.923567 | ||||||||
\(31\) | 7.93702 | 1.42553 | 0.712765 | − | 0.701402i | \(-0.247442\pi\) | ||||
0.712765 | + | 0.701402i | \(0.247442\pi\) | |||||||
\(32\) | −1.14563 | −0.202521 | ||||||||
\(33\) | 0.879695 | 0.153135 | ||||||||
\(34\) | −2.47238 | −0.424010 | ||||||||
\(35\) | −4.47824 | −0.756960 | ||||||||
\(36\) | −9.15536 | −1.52589 | ||||||||
\(37\) | 2.21625 | 0.364349 | 0.182174 | − | 0.983266i | \(-0.441686\pi\) | ||||
0.182174 | + | 0.983266i | \(0.441686\pi\) | |||||||
\(38\) | 10.4218 | 1.69064 | ||||||||
\(39\) | 4.24224 | 0.679302 | ||||||||
\(40\) | 12.1487 | 1.92087 | ||||||||
\(41\) | 3.28743 | 0.513411 | 0.256705 | − | 0.966490i | \(-0.417363\pi\) | ||||
0.256705 | + | 0.966490i | \(0.417363\pi\) | |||||||
\(42\) | 4.18768 | 0.646173 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −4.11267 | −0.620008 | ||||||||
\(45\) | 5.17765 | 0.771839 | ||||||||
\(46\) | 15.7481 | 2.32193 | ||||||||
\(47\) | 2.42265 | 0.353380 | 0.176690 | − | 0.984267i | \(-0.443461\pi\) | ||||
0.176690 | + | 0.984267i | \(0.443461\pi\) | |||||||
\(48\) | −4.12463 | −0.595340 | ||||||||
\(49\) | −3.29275 | −0.470393 | ||||||||
\(50\) | −1.01261 | −0.143204 | ||||||||
\(51\) | −0.879695 | −0.123182 | ||||||||
\(52\) | −19.8329 | −2.75033 | ||||||||
\(53\) | −2.66086 | −0.365497 | −0.182749 | − | 0.983160i | \(-0.558499\pi\) | ||||
−0.182749 | + | 0.983160i | \(0.558499\pi\) | |||||||
\(54\) | −11.3665 | −1.54679 | ||||||||
\(55\) | 2.32585 | 0.313617 | ||||||||
\(56\) | −10.0571 | −1.34394 | ||||||||
\(57\) | 3.70817 | 0.491159 | ||||||||
\(58\) | 9.38592 | 1.23243 | ||||||||
\(59\) | 15.1369 | 1.97066 | 0.985328 | − | 0.170673i | \(-0.0545942\pi\) | ||||
0.985328 | + | 0.170673i | \(0.0545942\pi\) | |||||||
\(60\) | 8.41467 | 1.08633 | ||||||||
\(61\) | 9.46522 | 1.21190 | 0.605949 | − | 0.795504i | \(-0.292794\pi\) | ||||
0.605949 | + | 0.795504i | \(0.292794\pi\) | |||||||
\(62\) | −19.6233 | −2.49217 | ||||||||
\(63\) | −4.28625 | −0.540017 | ||||||||
\(64\) | −6.54499 | −0.818123 | ||||||||
\(65\) | 11.2162 | 1.39119 | ||||||||
\(66\) | −2.17494 | −0.267717 | ||||||||
\(67\) | 14.5555 | 1.77824 | 0.889121 | − | 0.457672i | \(-0.151317\pi\) | ||||
0.889121 | + | 0.457672i | \(0.151317\pi\) | |||||||
\(68\) | 4.11267 | 0.498734 | ||||||||
\(69\) | 5.60332 | 0.674560 | ||||||||
\(70\) | 11.0719 | 1.32335 | ||||||||
\(71\) | −5.67883 | −0.673954 | −0.336977 | − | 0.941513i | \(-0.609404\pi\) | ||||
−0.336977 | + | 0.941513i | \(0.609404\pi\) | |||||||
\(72\) | 11.6278 | 1.37035 | ||||||||
\(73\) | 7.91191 | 0.926019 | 0.463009 | − | 0.886353i | \(-0.346770\pi\) | ||||
0.463009 | + | 0.886353i | \(0.346770\pi\) | |||||||
\(74\) | −5.47941 | −0.636968 | ||||||||
\(75\) | −0.360294 | −0.0416032 | ||||||||
\(76\) | −17.3361 | −1.98859 | ||||||||
\(77\) | −1.92542 | −0.219422 | ||||||||
\(78\) | −10.4884 | −1.18758 | ||||||||
\(79\) | 3.11018 | 0.349923 | 0.174962 | − | 0.984575i | \(-0.444020\pi\) | ||||
0.174962 | + | 0.984575i | \(0.444020\pi\) | |||||||
\(80\) | −10.9052 | −1.21924 | ||||||||
\(81\) | 2.63409 | 0.292677 | ||||||||
\(82\) | −8.12778 | −0.897564 | ||||||||
\(83\) | −0.124396 | −0.0136543 | −0.00682713 | − | 0.999977i | \(-0.502173\pi\) | ||||
−0.00682713 | + | 0.999977i | \(0.502173\pi\) | |||||||
\(84\) | −6.96597 | −0.760050 | ||||||||
\(85\) | −2.32585 | −0.252274 | ||||||||
\(86\) | −2.47238 | −0.266604 | ||||||||
\(87\) | 3.33959 | 0.358042 | ||||||||
\(88\) | 5.22332 | 0.556808 | ||||||||
\(89\) | −3.66791 | −0.388798 | −0.194399 | − | 0.980923i | \(-0.562276\pi\) | ||||
−0.194399 | + | 0.980923i | \(0.562276\pi\) | |||||||
\(90\) | −12.8011 | −1.34936 | ||||||||
\(91\) | −9.28515 | −0.973348 | ||||||||
\(92\) | −26.1961 | −2.73113 | ||||||||
\(93\) | −6.98216 | −0.724016 | ||||||||
\(94\) | −5.98972 | −0.617792 | ||||||||
\(95\) | 9.80412 | 1.00588 | ||||||||
\(96\) | 1.00780 | 0.102859 | ||||||||
\(97\) | −13.6924 | −1.39026 | −0.695129 | − | 0.718885i | \(-0.744653\pi\) | ||||
−0.695129 | + | 0.718885i | \(0.744653\pi\) | |||||||
\(98\) | 8.14093 | 0.822359 | ||||||||
\(99\) | 2.22614 | 0.223735 | ||||||||
\(100\) | 1.68441 | 0.168441 | ||||||||
\(101\) | −12.0405 | −1.19808 | −0.599039 | − | 0.800720i | \(-0.704450\pi\) | ||||
−0.599039 | + | 0.800720i | \(0.704450\pi\) | |||||||
\(102\) | 2.17494 | 0.215351 | ||||||||
\(103\) | 10.7199 | 1.05627 | 0.528134 | − | 0.849161i | \(-0.322892\pi\) | ||||
0.528134 | + | 0.849161i | \(0.322892\pi\) | |||||||
\(104\) | 25.1889 | 2.46998 | ||||||||
\(105\) | 3.93948 | 0.384454 | ||||||||
\(106\) | 6.57866 | 0.638976 | ||||||||
\(107\) | 10.0113 | 0.967833 | 0.483917 | − | 0.875114i | \(-0.339214\pi\) | ||||
0.483917 | + | 0.875114i | \(0.339214\pi\) | |||||||
\(108\) | 18.9076 | 1.81939 | ||||||||
\(109\) | 16.8931 | 1.61806 | 0.809032 | − | 0.587764i | \(-0.199992\pi\) | ||||
0.809032 | + | 0.587764i | \(0.199992\pi\) | |||||||
\(110\) | −5.75038 | −0.548277 | ||||||||
\(111\) | −1.94962 | −0.185050 | ||||||||
\(112\) | 9.02774 | 0.853042 | ||||||||
\(113\) | −14.5747 | −1.37107 | −0.685536 | − | 0.728039i | \(-0.740432\pi\) | ||||
−0.685536 | + | 0.728039i | \(0.740432\pi\) | |||||||
\(114\) | −9.16801 | −0.858662 | ||||||||
\(115\) | 14.8148 | 1.38148 | ||||||||
\(116\) | −15.6130 | −1.44963 | ||||||||
\(117\) | 10.7353 | 0.992480 | ||||||||
\(118\) | −37.4242 | −3.44517 | ||||||||
\(119\) | 1.92542 | 0.176503 | ||||||||
\(120\) | −10.6871 | −0.975595 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −23.4016 | −2.11868 | ||||||||
\(123\) | −2.89194 | −0.260757 | ||||||||
\(124\) | 32.6423 | 2.93137 | ||||||||
\(125\) | 10.6766 | 0.954948 | ||||||||
\(126\) | 10.5972 | 0.944078 | ||||||||
\(127\) | −2.79346 | −0.247880 | −0.123940 | − | 0.992290i | \(-0.539553\pi\) | ||||
−0.123940 | + | 0.992290i | \(0.539553\pi\) | |||||||
\(128\) | 18.4730 | 1.63279 | ||||||||
\(129\) | −0.879695 | −0.0774528 | ||||||||
\(130\) | −27.7306 | −2.43214 | ||||||||
\(131\) | −14.6459 | −1.27961 | −0.639807 | − | 0.768535i | \(-0.720986\pi\) | ||||
−0.639807 | + | 0.768535i | \(0.720986\pi\) | |||||||
\(132\) | 3.61789 | 0.314897 | ||||||||
\(133\) | −8.11621 | −0.703765 | ||||||||
\(134\) | −35.9868 | −3.10879 | ||||||||
\(135\) | −10.6929 | −0.920295 | ||||||||
\(136\) | −5.22332 | −0.447896 | ||||||||
\(137\) | 7.29802 | 0.623512 | 0.311756 | − | 0.950162i | \(-0.399083\pi\) | ||||
0.311756 | + | 0.950162i | \(0.399083\pi\) | |||||||
\(138\) | −13.8535 | −1.17929 | ||||||||
\(139\) | −8.44780 | −0.716533 | −0.358266 | − | 0.933619i | \(-0.616632\pi\) | ||||
−0.358266 | + | 0.933619i | \(0.616632\pi\) | |||||||
\(140\) | −18.4175 | −1.55656 | ||||||||
\(141\) | −2.13119 | −0.179479 | ||||||||
\(142\) | 14.0402 | 1.17823 | ||||||||
\(143\) | 4.82240 | 0.403269 | ||||||||
\(144\) | −10.4377 | −0.869809 | ||||||||
\(145\) | 8.82964 | 0.733261 | ||||||||
\(146\) | −19.5613 | −1.61890 | ||||||||
\(147\) | 2.89662 | 0.238909 | ||||||||
\(148\) | 9.11469 | 0.749223 | ||||||||
\(149\) | −2.58036 | −0.211391 | −0.105696 | − | 0.994399i | \(-0.533707\pi\) | ||||
−0.105696 | + | 0.994399i | \(0.533707\pi\) | |||||||
\(150\) | 0.890785 | 0.0727323 | ||||||||
\(151\) | 17.5091 | 1.42487 | 0.712436 | − | 0.701737i | \(-0.247592\pi\) | ||||
0.712436 | + | 0.701737i | \(0.247592\pi\) | |||||||
\(152\) | 22.0178 | 1.78588 | ||||||||
\(153\) | −2.22614 | −0.179972 | ||||||||
\(154\) | 4.76038 | 0.383602 | ||||||||
\(155\) | −18.4603 | −1.48277 | ||||||||
\(156\) | 17.4469 | 1.39687 | ||||||||
\(157\) | 0.587939 | 0.0469227 | 0.0234613 | − | 0.999725i | \(-0.492531\pi\) | ||||
0.0234613 | + | 0.999725i | \(0.492531\pi\) | |||||||
\(158\) | −7.68956 | −0.611749 | ||||||||
\(159\) | 2.34075 | 0.185633 | ||||||||
\(160\) | 2.66456 | 0.210652 | ||||||||
\(161\) | −12.2642 | −0.966554 | ||||||||
\(162\) | −6.51248 | −0.511669 | ||||||||
\(163\) | 15.9060 | 1.24585 | 0.622925 | − | 0.782281i | \(-0.285944\pi\) | ||||
0.622925 | + | 0.782281i | \(0.285944\pi\) | |||||||
\(164\) | 13.5201 | 1.05574 | ||||||||
\(165\) | −2.04604 | −0.159284 | ||||||||
\(166\) | 0.307555 | 0.0238709 | ||||||||
\(167\) | −0.386377 | −0.0298988 | −0.0149494 | − | 0.999888i | \(-0.504759\pi\) | ||||
−0.0149494 | + | 0.999888i | \(0.504759\pi\) | |||||||
\(168\) | 8.84718 | 0.682575 | ||||||||
\(169\) | 10.2555 | 0.788885 | ||||||||
\(170\) | 5.75038 | 0.441034 | ||||||||
\(171\) | 9.38381 | 0.717598 | ||||||||
\(172\) | 4.11267 | 0.313588 | ||||||||
\(173\) | −22.5833 | −1.71697 | −0.858486 | − | 0.512836i | \(-0.828595\pi\) | ||||
−0.858486 | + | 0.512836i | \(0.828595\pi\) | |||||||
\(174\) | −8.25675 | −0.625943 | ||||||||
\(175\) | 0.788590 | 0.0596118 | ||||||||
\(176\) | −4.68871 | −0.353425 | ||||||||
\(177\) | −13.3158 | −1.00088 | ||||||||
\(178\) | 9.06847 | 0.679711 | ||||||||
\(179\) | −8.95790 | −0.669545 | −0.334772 | − | 0.942299i | \(-0.608659\pi\) | ||||
−0.334772 | + | 0.942299i | \(0.608659\pi\) | |||||||
\(180\) | 21.2940 | 1.58716 | ||||||||
\(181\) | −4.85208 | −0.360652 | −0.180326 | − | 0.983607i | \(-0.557715\pi\) | ||||
−0.180326 | + | 0.983607i | \(0.557715\pi\) | |||||||
\(182\) | 22.9564 | 1.70164 | ||||||||
\(183\) | −8.32651 | −0.615513 | ||||||||
\(184\) | 33.2706 | 2.45274 | ||||||||
\(185\) | −5.15465 | −0.378978 | ||||||||
\(186\) | 17.2626 | 1.26575 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 9.96356 | 0.726668 | ||||||||
\(189\) | 8.85195 | 0.643884 | ||||||||
\(190\) | −24.2395 | −1.75852 | ||||||||
\(191\) | −21.2646 | −1.53865 | −0.769325 | − | 0.638858i | \(-0.779407\pi\) | ||||
−0.769325 | + | 0.638858i | \(0.779407\pi\) | |||||||
\(192\) | 5.75759 | 0.415518 | ||||||||
\(193\) | 0.104969 | 0.00755585 | 0.00377793 | − | 0.999993i | \(-0.498797\pi\) | ||||
0.00377793 | + | 0.999993i | \(0.498797\pi\) | |||||||
\(194\) | 33.8529 | 2.43050 | ||||||||
\(195\) | −9.86680 | −0.706576 | ||||||||
\(196\) | −13.5420 | −0.967285 | ||||||||
\(197\) | 21.2183 | 1.51174 | 0.755870 | − | 0.654722i | \(-0.227214\pi\) | ||||
0.755870 | + | 0.654722i | \(0.227214\pi\) | |||||||
\(198\) | −5.50386 | −0.391142 | ||||||||
\(199\) | −1.00995 | −0.0715932 | −0.0357966 | − | 0.999359i | \(-0.511397\pi\) | ||||
−0.0357966 | + | 0.999359i | \(0.511397\pi\) | |||||||
\(200\) | −2.13930 | −0.151271 | ||||||||
\(201\) | −12.8044 | −0.903155 | ||||||||
\(202\) | 29.7688 | 2.09452 | ||||||||
\(203\) | −7.30950 | −0.513026 | ||||||||
\(204\) | −3.61789 | −0.253303 | ||||||||
\(205\) | −7.64607 | −0.534024 | ||||||||
\(206\) | −26.5038 | −1.84661 | ||||||||
\(207\) | 14.1796 | 0.985553 | ||||||||
\(208\) | −22.6108 | −1.56778 | ||||||||
\(209\) | 4.21529 | 0.291578 | ||||||||
\(210\) | −9.73991 | −0.672117 | ||||||||
\(211\) | 8.38416 | 0.577189 | 0.288595 | − | 0.957451i | \(-0.406812\pi\) | ||||
0.288595 | + | 0.957451i | \(0.406812\pi\) | |||||||
\(212\) | −10.9432 | −0.751585 | ||||||||
\(213\) | 4.99564 | 0.342296 | ||||||||
\(214\) | −24.7519 | −1.69200 | ||||||||
\(215\) | −2.32585 | −0.158621 | ||||||||
\(216\) | −24.0137 | −1.63393 | ||||||||
\(217\) | 15.2821 | 1.03742 | ||||||||
\(218\) | −41.7662 | −2.82876 | ||||||||
\(219\) | −6.96007 | −0.470318 | ||||||||
\(220\) | 9.56544 | 0.644902 | ||||||||
\(221\) | −4.82240 | −0.324389 | ||||||||
\(222\) | 4.82021 | 0.323511 | ||||||||
\(223\) | 12.0564 | 0.807354 | 0.403677 | − | 0.914902i | \(-0.367732\pi\) | ||||
0.403677 | + | 0.914902i | \(0.367732\pi\) | |||||||
\(224\) | −2.20582 | −0.147382 | ||||||||
\(225\) | −0.911752 | −0.0607835 | ||||||||
\(226\) | 36.0342 | 2.39696 | ||||||||
\(227\) | 2.76081 | 0.183241 | 0.0916206 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916206 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(228\) | 15.2505 | 1.00999 | ||||||||
\(229\) | 3.87880 | 0.256318 | 0.128159 | − | 0.991754i | \(-0.459093\pi\) | ||||
0.128159 | + | 0.991754i | \(0.459093\pi\) | |||||||
\(230\) | −36.6277 | −2.41516 | ||||||||
\(231\) | 1.69378 | 0.111443 | ||||||||
\(232\) | 19.8294 | 1.30186 | ||||||||
\(233\) | −18.3748 | −1.20377 | −0.601886 | − | 0.798582i | \(-0.705584\pi\) | ||||
−0.601886 | + | 0.798582i | \(0.705584\pi\) | |||||||
\(234\) | −26.5418 | −1.73509 | ||||||||
\(235\) | −5.63472 | −0.367568 | ||||||||
\(236\) | 62.2530 | 4.05233 | ||||||||
\(237\) | −2.73601 | −0.177723 | ||||||||
\(238\) | −4.76038 | −0.308569 | ||||||||
\(239\) | −18.5901 | −1.20249 | −0.601245 | − | 0.799064i | \(-0.705329\pi\) | ||||
−0.601245 | + | 0.799064i | \(0.705329\pi\) | |||||||
\(240\) | 9.59327 | 0.619243 | ||||||||
\(241\) | −26.5930 | −1.71300 | −0.856501 | − | 0.516145i | \(-0.827367\pi\) | ||||
−0.856501 | + | 0.516145i | \(0.827367\pi\) | |||||||
\(242\) | −2.47238 | −0.158931 | ||||||||
\(243\) | −16.1094 | −1.03342 | ||||||||
\(244\) | 38.9273 | 2.49207 | ||||||||
\(245\) | 7.65844 | 0.489279 | ||||||||
\(246\) | 7.14997 | 0.455866 | ||||||||
\(247\) | 20.3278 | 1.29343 | ||||||||
\(248\) | −41.4576 | −2.63256 | ||||||||
\(249\) | 0.109431 | 0.00693489 | ||||||||
\(250\) | −26.3967 | −1.66948 | ||||||||
\(251\) | −1.52484 | −0.0962469 | −0.0481234 | − | 0.998841i | \(-0.515324\pi\) | ||||
−0.0481234 | + | 0.998841i | \(0.515324\pi\) | |||||||
\(252\) | −17.6279 | −1.11046 | ||||||||
\(253\) | 6.36962 | 0.400454 | ||||||||
\(254\) | 6.90650 | 0.433352 | ||||||||
\(255\) | 2.04604 | 0.128128 | ||||||||
\(256\) | −32.5822 | −2.03639 | ||||||||
\(257\) | −4.63335 | −0.289020 | −0.144510 | − | 0.989503i | \(-0.546161\pi\) | ||||
−0.144510 | + | 0.989503i | \(0.546161\pi\) | |||||||
\(258\) | 2.17494 | 0.135406 | ||||||||
\(259\) | 4.26721 | 0.265152 | ||||||||
\(260\) | 46.1283 | 2.86076 | ||||||||
\(261\) | 8.45110 | 0.523110 | ||||||||
\(262\) | 36.2101 | 2.23707 | ||||||||
\(263\) | 15.6670 | 0.966066 | 0.483033 | − | 0.875602i | \(-0.339535\pi\) | ||||
0.483033 | + | 0.875602i | \(0.339535\pi\) | |||||||
\(264\) | −4.59493 | −0.282799 | ||||||||
\(265\) | 6.18876 | 0.380172 | ||||||||
\(266\) | 20.0664 | 1.23035 | ||||||||
\(267\) | 3.22664 | 0.197467 | ||||||||
\(268\) | 59.8621 | 3.65666 | ||||||||
\(269\) | −2.11295 | −0.128829 | −0.0644145 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644145 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(270\) | 26.4368 | 1.60890 | ||||||||
\(271\) | 20.2685 | 1.23122 | 0.615611 | − | 0.788050i | \(-0.288909\pi\) | ||||
0.615611 | + | 0.788050i | \(0.288909\pi\) | |||||||
\(272\) | 4.68871 | 0.284295 | ||||||||
\(273\) | 8.16810 | 0.494356 | ||||||||
\(274\) | −18.0435 | −1.09005 | ||||||||
\(275\) | −0.409567 | −0.0246978 | ||||||||
\(276\) | 23.0446 | 1.38712 | ||||||||
\(277\) | 19.6328 | 1.17962 | 0.589810 | − | 0.807542i | \(-0.299203\pi\) | ||||
0.589810 | + | 0.807542i | \(0.299203\pi\) | |||||||
\(278\) | 20.8862 | 1.25267 | ||||||||
\(279\) | −17.6689 | −1.05781 | ||||||||
\(280\) | 23.3913 | 1.39790 | ||||||||
\(281\) | 30.9921 | 1.84884 | 0.924418 | − | 0.381380i | \(-0.124551\pi\) | ||||
0.924418 | + | 0.381380i | \(0.124551\pi\) | |||||||
\(282\) | 5.26913 | 0.313772 | ||||||||
\(283\) | −10.2422 | −0.608834 | −0.304417 | − | 0.952539i | \(-0.598462\pi\) | ||||
−0.304417 | + | 0.952539i | \(0.598462\pi\) | |||||||
\(284\) | −23.3552 | −1.38587 | ||||||||
\(285\) | −8.62463 | −0.510879 | ||||||||
\(286\) | −11.9228 | −0.705010 | ||||||||
\(287\) | 6.32969 | 0.373630 | ||||||||
\(288\) | 2.55033 | 0.150279 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −21.8302 | −1.28192 | ||||||||
\(291\) | 12.0452 | 0.706101 | ||||||||
\(292\) | 32.5391 | 1.90420 | ||||||||
\(293\) | −8.75262 | −0.511333 | −0.255667 | − | 0.966765i | \(-0.582295\pi\) | ||||
−0.255667 | + | 0.966765i | \(0.582295\pi\) | |||||||
\(294\) | −7.16154 | −0.417669 | ||||||||
\(295\) | −35.2061 | −2.04978 | ||||||||
\(296\) | −11.5762 | −0.672852 | ||||||||
\(297\) | −4.59741 | −0.266769 | ||||||||
\(298\) | 6.37963 | 0.369562 | ||||||||
\(299\) | 30.7168 | 1.77640 | ||||||||
\(300\) | −1.48177 | −0.0855501 | ||||||||
\(301\) | 1.92542 | 0.110979 | ||||||||
\(302\) | −43.2892 | −2.49101 | ||||||||
\(303\) | 10.5920 | 0.608494 | ||||||||
\(304\) | −19.7643 | −1.13356 | ||||||||
\(305\) | −22.0147 | −1.26056 | ||||||||
\(306\) | 5.50386 | 0.314635 | ||||||||
\(307\) | 11.7814 | 0.672399 | 0.336200 | − | 0.941791i | \(-0.390858\pi\) | ||||
0.336200 | + | 0.941791i | \(0.390858\pi\) | |||||||
\(308\) | −7.91862 | −0.451205 | ||||||||
\(309\) | −9.43028 | −0.536470 | ||||||||
\(310\) | 45.6409 | 2.59223 | ||||||||
\(311\) | 21.0055 | 1.19111 | 0.595556 | − | 0.803314i | \(-0.296932\pi\) | ||||
0.595556 | + | 0.803314i | \(0.296932\pi\) | |||||||
\(312\) | −22.1586 | −1.25448 | ||||||||
\(313\) | −15.0488 | −0.850611 | −0.425305 | − | 0.905050i | \(-0.639833\pi\) | ||||
−0.425305 | + | 0.905050i | \(0.639833\pi\) | |||||||
\(314\) | −1.45361 | −0.0820319 | ||||||||
\(315\) | 9.96917 | 0.561699 | ||||||||
\(316\) | 12.7912 | 0.719559 | ||||||||
\(317\) | 12.5377 | 0.704189 | 0.352095 | − | 0.935964i | \(-0.385470\pi\) | ||||
0.352095 | + | 0.935964i | \(0.385470\pi\) | |||||||
\(318\) | −5.78722 | −0.324531 | ||||||||
\(319\) | 3.79631 | 0.212553 | ||||||||
\(320\) | 15.2226 | 0.850971 | ||||||||
\(321\) | −8.80693 | −0.491555 | ||||||||
\(322\) | 30.3218 | 1.68977 | ||||||||
\(323\) | −4.21529 | −0.234545 | ||||||||
\(324\) | 10.8332 | 0.601842 | ||||||||
\(325\) | −1.97509 | −0.109559 | ||||||||
\(326\) | −39.3256 | −2.17804 | ||||||||
\(327\) | −14.8608 | −0.821802 | ||||||||
\(328\) | −17.1713 | −0.948127 | ||||||||
\(329\) | 4.66463 | 0.257169 | ||||||||
\(330\) | 5.05858 | 0.278466 | ||||||||
\(331\) | 6.38221 | 0.350798 | 0.175399 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175399 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(332\) | −0.511601 | −0.0280777 | ||||||||
\(333\) | −4.93367 | −0.270363 | ||||||||
\(334\) | 0.955271 | 0.0522701 | ||||||||
\(335\) | −33.8540 | −1.84964 | ||||||||
\(336\) | −7.94166 | −0.433253 | ||||||||
\(337\) | −18.6515 | −1.01601 | −0.508006 | − | 0.861353i | \(-0.669617\pi\) | ||||
−0.508006 | + | 0.861353i | \(0.669617\pi\) | |||||||
\(338\) | −25.3555 | −1.37916 | ||||||||
\(339\) | 12.8213 | 0.696357 | ||||||||
\(340\) | −9.56544 | −0.518759 | ||||||||
\(341\) | −7.93702 | −0.429814 | ||||||||
\(342\) | −23.2003 | −1.25453 | ||||||||
\(343\) | −19.8179 | −1.07007 | ||||||||
\(344\) | −5.22332 | −0.281623 | ||||||||
\(345\) | −13.0325 | −0.701645 | ||||||||
\(346\) | 55.8344 | 3.00168 | ||||||||
\(347\) | 23.4081 | 1.25661 | 0.628306 | − | 0.777966i | \(-0.283748\pi\) | ||||
0.628306 | + | 0.777966i | \(0.283748\pi\) | |||||||
\(348\) | 13.7346 | 0.736254 | ||||||||
\(349\) | −13.5389 | −0.724722 | −0.362361 | − | 0.932038i | \(-0.618029\pi\) | ||||
−0.362361 | + | 0.932038i | \(0.618029\pi\) | |||||||
\(350\) | −1.94969 | −0.104216 | ||||||||
\(351\) | −22.1705 | −1.18337 | ||||||||
\(352\) | 1.14563 | 0.0610622 | ||||||||
\(353\) | −15.2733 | −0.812916 | −0.406458 | − | 0.913669i | \(-0.633236\pi\) | ||||
−0.406458 | + | 0.913669i | \(0.633236\pi\) | |||||||
\(354\) | 32.9219 | 1.74978 | ||||||||
\(355\) | 13.2081 | 0.701013 | ||||||||
\(356\) | −15.0849 | −0.799498 | ||||||||
\(357\) | −1.69378 | −0.0896446 | ||||||||
\(358\) | 22.1473 | 1.17052 | ||||||||
\(359\) | −22.7515 | −1.20078 | −0.600390 | − | 0.799708i | \(-0.704988\pi\) | ||||
−0.600390 | + | 0.799708i | \(0.704988\pi\) | |||||||
\(360\) | −27.0446 | −1.42537 | ||||||||
\(361\) | −1.23135 | −0.0648077 | ||||||||
\(362\) | 11.9962 | 0.630505 | ||||||||
\(363\) | −0.879695 | −0.0461720 | ||||||||
\(364\) | −38.1867 | −2.00153 | ||||||||
\(365\) | −18.4019 | −0.963199 | ||||||||
\(366\) | 20.5863 | 1.07606 | ||||||||
\(367\) | −0.881547 | −0.0460164 | −0.0230082 | − | 0.999735i | \(-0.507324\pi\) | ||||
−0.0230082 | + | 0.999735i | \(0.507324\pi\) | |||||||
\(368\) | −29.8653 | −1.55684 | ||||||||
\(369\) | −7.31827 | −0.380974 | ||||||||
\(370\) | 12.7443 | 0.662543 | ||||||||
\(371\) | −5.12328 | −0.265987 | ||||||||
\(372\) | −28.7153 | −1.48882 | ||||||||
\(373\) | −1.33566 | −0.0691579 | −0.0345789 | − | 0.999402i | \(-0.511009\pi\) | ||||
−0.0345789 | + | 0.999402i | \(0.511009\pi\) | |||||||
\(374\) | 2.47238 | 0.127844 | ||||||||
\(375\) | −9.39219 | −0.485011 | ||||||||
\(376\) | −12.6543 | −0.652595 | ||||||||
\(377\) | 18.3073 | 0.942874 | ||||||||
\(378\) | −21.8854 | −1.12566 | ||||||||
\(379\) | −7.51912 | −0.386231 | −0.193116 | − | 0.981176i | \(-0.561859\pi\) | ||||
−0.193116 | + | 0.981176i | \(0.561859\pi\) | |||||||
\(380\) | 40.3211 | 2.06843 | ||||||||
\(381\) | 2.45739 | 0.125896 | ||||||||
\(382\) | 52.5741 | 2.68993 | ||||||||
\(383\) | 26.2712 | 1.34240 | 0.671198 | − | 0.741278i | \(-0.265780\pi\) | ||||
0.671198 | + | 0.741278i | \(0.265780\pi\) | |||||||
\(384\) | −16.2506 | −0.829284 | ||||||||
\(385\) | 4.47824 | 0.228232 | ||||||||
\(386\) | −0.259524 | −0.0132094 | ||||||||
\(387\) | −2.22614 | −0.113161 | ||||||||
\(388\) | −56.3125 | −2.85883 | ||||||||
\(389\) | −9.85098 | −0.499465 | −0.249732 | − | 0.968315i | \(-0.580343\pi\) | ||||
−0.249732 | + | 0.968315i | \(0.580343\pi\) | |||||||
\(390\) | 24.3945 | 1.23526 | ||||||||
\(391\) | −6.36962 | −0.322125 | ||||||||
\(392\) | 17.1991 | 0.868686 | ||||||||
\(393\) | 12.8839 | 0.649906 | ||||||||
\(394\) | −52.4597 | −2.64288 | ||||||||
\(395\) | −7.23381 | −0.363973 | ||||||||
\(396\) | 9.15536 | 0.460074 | ||||||||
\(397\) | −27.3557 | −1.37294 | −0.686471 | − | 0.727157i | \(-0.740841\pi\) | ||||
−0.686471 | + | 0.727157i | \(0.740841\pi\) | |||||||
\(398\) | 2.49697 | 0.125162 | ||||||||
\(399\) | 7.13979 | 0.357437 | ||||||||
\(400\) | 1.92034 | 0.0960171 | ||||||||
\(401\) | −24.1483 | −1.20591 | −0.602954 | − | 0.797776i | \(-0.706010\pi\) | ||||
−0.602954 | + | 0.797776i | \(0.706010\pi\) | |||||||
\(402\) | 31.6574 | 1.57893 | ||||||||
\(403\) | −38.2754 | −1.90664 | ||||||||
\(404\) | −49.5187 | −2.46365 | ||||||||
\(405\) | −6.12650 | −0.304428 | ||||||||
\(406\) | 18.0719 | 0.896892 | ||||||||
\(407\) | −2.21625 | −0.109855 | ||||||||
\(408\) | 4.59493 | 0.227483 | ||||||||
\(409\) | 33.6102 | 1.66192 | 0.830959 | − | 0.556334i | \(-0.187793\pi\) | ||||
0.830959 | + | 0.556334i | \(0.187793\pi\) | |||||||
\(410\) | 18.9040 | 0.933601 | ||||||||
\(411\) | −6.42003 | −0.316677 | ||||||||
\(412\) | 44.0876 | 2.17204 | ||||||||
\(413\) | 29.1449 | 1.43413 | ||||||||
\(414\) | −35.0575 | −1.72298 | ||||||||
\(415\) | 0.289327 | 0.0142025 | ||||||||
\(416\) | 5.52468 | 0.270870 | ||||||||
\(417\) | 7.43149 | 0.363921 | ||||||||
\(418\) | −10.4218 | −0.509747 | ||||||||
\(419\) | 33.5302 | 1.63806 | 0.819028 | − | 0.573754i | \(-0.194514\pi\) | ||||
0.819028 | + | 0.573754i | \(0.194514\pi\) | |||||||
\(420\) | 16.2018 | 0.790567 | ||||||||
\(421\) | 38.5745 | 1.88001 | 0.940003 | − | 0.341166i | \(-0.110822\pi\) | ||||
0.940003 | + | 0.341166i | \(0.110822\pi\) | |||||||
\(422\) | −20.7288 | −1.00906 | ||||||||
\(423\) | −5.39315 | −0.262224 | ||||||||
\(424\) | 13.8985 | 0.674972 | ||||||||
\(425\) | 0.409567 | 0.0198669 | ||||||||
\(426\) | −12.3511 | −0.598414 | ||||||||
\(427\) | 18.2245 | 0.881948 | ||||||||
\(428\) | 41.1734 | 1.99019 | ||||||||
\(429\) | −4.24224 | −0.204817 | ||||||||
\(430\) | 5.75038 | 0.277308 | ||||||||
\(431\) | −3.38003 | −0.162811 | −0.0814053 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814053 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(432\) | 21.5559 | 1.03711 | ||||||||
\(433\) | 8.55798 | 0.411270 | 0.205635 | − | 0.978629i | \(-0.434074\pi\) | ||||
0.205635 | + | 0.978629i | \(0.434074\pi\) | |||||||
\(434\) | −37.7832 | −1.81365 | ||||||||
\(435\) | −7.76739 | −0.372418 | ||||||||
\(436\) | 69.4757 | 3.32728 | ||||||||
\(437\) | 26.8498 | 1.28440 | ||||||||
\(438\) | 17.2079 | 0.822227 | ||||||||
\(439\) | −26.9160 | −1.28463 | −0.642316 | − | 0.766440i | \(-0.722026\pi\) | ||||
−0.642316 | + | 0.766440i | \(0.722026\pi\) | |||||||
\(440\) | −12.1487 | −0.579164 | ||||||||
\(441\) | 7.33011 | 0.349053 | ||||||||
\(442\) | 11.9228 | 0.567110 | ||||||||
\(443\) | 2.84538 | 0.135188 | 0.0675941 | − | 0.997713i | \(-0.478468\pi\) | ||||
0.0675941 | + | 0.997713i | \(0.478468\pi\) | |||||||
\(444\) | −8.01815 | −0.380525 | ||||||||
\(445\) | 8.53100 | 0.404408 | ||||||||
\(446\) | −29.8079 | −1.41145 | ||||||||
\(447\) | 2.26993 | 0.107364 | ||||||||
\(448\) | −12.6019 | −0.595382 | ||||||||
\(449\) | 4.83131 | 0.228004 | 0.114002 | − | 0.993481i | \(-0.463633\pi\) | ||||
0.114002 | + | 0.993481i | \(0.463633\pi\) | |||||||
\(450\) | 2.25420 | 0.106264 | ||||||||
\(451\) | −3.28743 | −0.154799 | ||||||||
\(452\) | −59.9409 | −2.81938 | ||||||||
\(453\) | −15.4027 | −0.723681 | ||||||||
\(454\) | −6.82577 | −0.320349 | ||||||||
\(455\) | 21.5958 | 1.01243 | ||||||||
\(456\) | −19.3690 | −0.907035 | ||||||||
\(457\) | 7.41184 | 0.346711 | 0.173356 | − | 0.984859i | \(-0.444539\pi\) | ||||
0.173356 | + | 0.984859i | \(0.444539\pi\) | |||||||
\(458\) | −9.58987 | −0.448105 | ||||||||
\(459\) | 4.59741 | 0.214589 | ||||||||
\(460\) | 60.9282 | 2.84079 | ||||||||
\(461\) | −34.8948 | −1.62521 | −0.812607 | − | 0.582812i | \(-0.801952\pi\) | ||||
−0.812607 | + | 0.582812i | \(0.801952\pi\) | |||||||
\(462\) | −4.18768 | −0.194829 | ||||||||
\(463\) | 1.63086 | 0.0757924 | 0.0378962 | − | 0.999282i | \(-0.487934\pi\) | ||||
0.0378962 | + | 0.999282i | \(0.487934\pi\) | |||||||
\(464\) | −17.7998 | −0.826334 | ||||||||
\(465\) | 16.2394 | 0.753086 | ||||||||
\(466\) | 45.4295 | 2.10448 | ||||||||
\(467\) | 40.5057 | 1.87438 | 0.937191 | − | 0.348818i | \(-0.113417\pi\) | ||||
0.937191 | + | 0.348818i | \(0.113417\pi\) | |||||||
\(468\) | 44.1508 | 2.04087 | ||||||||
\(469\) | 28.0256 | 1.29410 | ||||||||
\(470\) | 13.9312 | 0.642597 | ||||||||
\(471\) | −0.517207 | −0.0238317 | ||||||||
\(472\) | −79.0649 | −3.63926 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 6.76447 | 0.310702 | ||||||||
\(475\) | −1.72644 | −0.0792147 | ||||||||
\(476\) | 7.91862 | 0.362950 | ||||||||
\(477\) | 5.92344 | 0.271216 | ||||||||
\(478\) | 45.9617 | 2.10224 | ||||||||
\(479\) | −23.1740 | −1.05885 | −0.529424 | − | 0.848358i | \(-0.677592\pi\) | ||||
−0.529424 | + | 0.848358i | \(0.677592\pi\) | |||||||
\(480\) | −2.34400 | −0.106988 | ||||||||
\(481\) | −10.6876 | −0.487314 | ||||||||
\(482\) | 65.7479 | 2.99474 | ||||||||
\(483\) | 10.7888 | 0.490905 | ||||||||
\(484\) | 4.11267 | 0.186940 | ||||||||
\(485\) | 31.8465 | 1.44608 | ||||||||
\(486\) | 39.8286 | 1.80666 | ||||||||
\(487\) | −13.4942 | −0.611483 | −0.305741 | − | 0.952115i | \(-0.598904\pi\) | ||||
−0.305741 | + | 0.952115i | \(0.598904\pi\) | |||||||
\(488\) | −49.4399 | −2.23804 | ||||||||
\(489\) | −13.9924 | −0.632758 | ||||||||
\(490\) | −18.9346 | −0.855377 | ||||||||
\(491\) | 28.9031 | 1.30438 | 0.652190 | − | 0.758056i | \(-0.273851\pi\) | ||||
0.652190 | + | 0.758056i | \(0.273851\pi\) | |||||||
\(492\) | −11.8936 | −0.536204 | ||||||||
\(493\) | −3.79631 | −0.170977 | ||||||||
\(494\) | −50.2580 | −2.26122 | ||||||||
\(495\) | −5.17765 | −0.232718 | ||||||||
\(496\) | 37.2144 | 1.67097 | ||||||||
\(497\) | −10.9342 | −0.490464 | ||||||||
\(498\) | −0.270555 | −0.0121238 | ||||||||
\(499\) | 25.5567 | 1.14407 | 0.572037 | − | 0.820228i | \(-0.306153\pi\) | ||||
0.572037 | + | 0.820228i | \(0.306153\pi\) | |||||||
\(500\) | 43.9095 | 1.96369 | ||||||||
\(501\) | 0.339894 | 0.0151853 | ||||||||
\(502\) | 3.76998 | 0.168262 | ||||||||
\(503\) | 19.6078 | 0.874268 | 0.437134 | − | 0.899396i | \(-0.355994\pi\) | ||||
0.437134 | + | 0.899396i | \(0.355994\pi\) | |||||||
\(504\) | 22.3885 | 0.997262 | ||||||||
\(505\) | 28.0044 | 1.24618 | ||||||||
\(506\) | −15.7481 | −0.700089 | ||||||||
\(507\) | −9.02171 | −0.400668 | ||||||||
\(508\) | −11.4886 | −0.509723 | ||||||||
\(509\) | −16.5529 | −0.733694 | −0.366847 | − | 0.930281i | \(-0.619563\pi\) | ||||
−0.366847 | + | 0.930281i | \(0.619563\pi\) | |||||||
\(510\) | −5.05858 | −0.223998 | ||||||||
\(511\) | 15.2338 | 0.673902 | ||||||||
\(512\) | 43.6098 | 1.92730 | ||||||||
\(513\) | −19.3794 | −0.855621 | ||||||||
\(514\) | 11.4554 | 0.505276 | ||||||||
\(515\) | −24.9330 | −1.09868 | ||||||||
\(516\) | −3.61789 | −0.159269 | ||||||||
\(517\) | −2.42265 | −0.106548 | ||||||||
\(518\) | −10.5502 | −0.463548 | ||||||||
\(519\) | 19.8664 | 0.872037 | ||||||||
\(520\) | −58.5856 | −2.56915 | ||||||||
\(521\) | −18.9400 | −0.829775 | −0.414888 | − | 0.909873i | \(-0.636179\pi\) | ||||
−0.414888 | + | 0.909873i | \(0.636179\pi\) | |||||||
\(522\) | −20.8943 | −0.914521 | ||||||||
\(523\) | −19.6565 | −0.859517 | −0.429759 | − | 0.902944i | \(-0.641401\pi\) | ||||
−0.429759 | + | 0.902944i | \(0.641401\pi\) | |||||||
\(524\) | −60.2336 | −2.63132 | ||||||||
\(525\) | −0.693718 | −0.0302764 | ||||||||
\(526\) | −38.7347 | −1.68891 | ||||||||
\(527\) | 7.93702 | 0.345742 | ||||||||
\(528\) | 4.12463 | 0.179502 | ||||||||
\(529\) | 17.5720 | 0.764000 | ||||||||
\(530\) | −15.3010 | −0.664631 | ||||||||
\(531\) | −33.6968 | −1.46232 | ||||||||
\(532\) | −33.3793 | −1.44718 | ||||||||
\(533\) | −15.8533 | −0.686682 | ||||||||
\(534\) | −7.97749 | −0.345220 | ||||||||
\(535\) | −23.2849 | −1.00669 | ||||||||
\(536\) | −76.0283 | −3.28392 | ||||||||
\(537\) | 7.88022 | 0.340057 | ||||||||
\(538\) | 5.22402 | 0.225224 | ||||||||
\(539\) | 3.29275 | 0.141829 | ||||||||
\(540\) | −43.9762 | −1.89244 | ||||||||
\(541\) | 16.4944 | 0.709149 | 0.354575 | − | 0.935028i | \(-0.384626\pi\) | ||||
0.354575 | + | 0.935028i | \(0.384626\pi\) | |||||||
\(542\) | −50.1114 | −2.15247 | ||||||||
\(543\) | 4.26835 | 0.183172 | ||||||||
\(544\) | −1.14563 | −0.0491184 | ||||||||
\(545\) | −39.2908 | −1.68303 | ||||||||
\(546\) | −20.1947 | −0.864251 | ||||||||
\(547\) | −5.64959 | −0.241559 | −0.120780 | − | 0.992679i | \(-0.538539\pi\) | ||||
−0.120780 | + | 0.992679i | \(0.538539\pi\) | |||||||
\(548\) | 30.0143 | 1.28215 | ||||||||
\(549\) | −21.0709 | −0.899283 | ||||||||
\(550\) | 1.01261 | 0.0431777 | ||||||||
\(551\) | 16.0025 | 0.681731 | ||||||||
\(552\) | −29.2680 | −1.24573 | ||||||||
\(553\) | 5.98842 | 0.254653 | ||||||||
\(554\) | −48.5397 | −2.06225 | ||||||||
\(555\) | 4.53452 | 0.192480 | ||||||||
\(556\) | −34.7430 | −1.47343 | ||||||||
\(557\) | −14.8480 | −0.629129 | −0.314564 | − | 0.949236i | \(-0.601858\pi\) | ||||
−0.314564 | + | 0.949236i | \(0.601858\pi\) | |||||||
\(558\) | 43.6842 | 1.84930 | ||||||||
\(559\) | −4.82240 | −0.203966 | ||||||||
\(560\) | −20.9972 | −0.887292 | ||||||||
\(561\) | 0.879695 | 0.0371408 | ||||||||
\(562\) | −76.6244 | −3.23221 | ||||||||
\(563\) | 45.5967 | 1.92167 | 0.960836 | − | 0.277118i | \(-0.0893795\pi\) | ||||
0.960836 | + | 0.277118i | \(0.0893795\pi\) | |||||||
\(564\) | −8.76490 | −0.369069 | ||||||||
\(565\) | 33.8985 | 1.42612 | ||||||||
\(566\) | 25.3226 | 1.06439 | ||||||||
\(567\) | 5.07174 | 0.212993 | ||||||||
\(568\) | 29.6624 | 1.24461 | ||||||||
\(569\) | −2.81528 | −0.118023 | −0.0590113 | − | 0.998257i | \(-0.518795\pi\) | ||||
−0.0590113 | + | 0.998257i | \(0.518795\pi\) | |||||||
\(570\) | 21.3234 | 0.893138 | ||||||||
\(571\) | −27.2558 | −1.14062 | −0.570310 | − | 0.821430i | \(-0.693177\pi\) | ||||
−0.570310 | + | 0.821430i | \(0.693177\pi\) | |||||||
\(572\) | 19.8329 | 0.829256 | ||||||||
\(573\) | 18.7063 | 0.781468 | ||||||||
\(574\) | −15.6494 | −0.653194 | ||||||||
\(575\) | −2.60879 | −0.108794 | ||||||||
\(576\) | 14.5700 | 0.607085 | ||||||||
\(577\) | −9.83680 | −0.409511 | −0.204756 | − | 0.978813i | \(-0.565640\pi\) | ||||
−0.204756 | + | 0.978813i | \(0.565640\pi\) | |||||||
\(578\) | −2.47238 | −0.102838 | ||||||||
\(579\) | −0.0923410 | −0.00383756 | ||||||||
\(580\) | 36.3134 | 1.50783 | ||||||||
\(581\) | −0.239515 | −0.00993677 | ||||||||
\(582\) | −29.7803 | −1.23443 | ||||||||
\(583\) | 2.66086 | 0.110202 | ||||||||
\(584\) | −41.3264 | −1.71010 | ||||||||
\(585\) | −24.9687 | −1.03233 | ||||||||
\(586\) | 21.6398 | 0.893932 | ||||||||
\(587\) | 14.7163 | 0.607406 | 0.303703 | − | 0.952767i | \(-0.401777\pi\) | ||||
0.303703 | + | 0.952767i | \(0.401777\pi\) | |||||||
\(588\) | 11.9128 | 0.491277 | ||||||||
\(589\) | −33.4568 | −1.37856 | ||||||||
\(590\) | 87.0429 | 3.58350 | ||||||||
\(591\) | −18.6656 | −0.767801 | ||||||||
\(592\) | 10.3913 | 0.427081 | ||||||||
\(593\) | −37.3870 | −1.53530 | −0.767650 | − | 0.640870i | \(-0.778574\pi\) | ||||
−0.767650 | + | 0.640870i | \(0.778574\pi\) | |||||||
\(594\) | 11.3665 | 0.466375 | ||||||||
\(595\) | −4.47824 | −0.183590 | ||||||||
\(596\) | −10.6122 | −0.434691 | ||||||||
\(597\) | 0.888445 | 0.0363616 | ||||||||
\(598\) | −75.9437 | −3.10557 | ||||||||
\(599\) | −1.18108 | −0.0482575 | −0.0241287 | − | 0.999709i | \(-0.507681\pi\) | ||||
−0.0241287 | + | 0.999709i | \(0.507681\pi\) | |||||||
\(600\) | 1.88193 | 0.0768296 | ||||||||
\(601\) | 15.5749 | 0.635311 | 0.317656 | − | 0.948206i | \(-0.397104\pi\) | ||||
0.317656 | + | 0.948206i | \(0.397104\pi\) | |||||||
\(602\) | −4.76038 | −0.194018 | ||||||||
\(603\) | −32.4026 | −1.31954 | ||||||||
\(604\) | 72.0092 | 2.93001 | ||||||||
\(605\) | −2.32585 | −0.0945592 | ||||||||
\(606\) | −26.1874 | −1.06379 | ||||||||
\(607\) | 24.6929 | 1.00225 | 0.501127 | − | 0.865374i | \(-0.332919\pi\) | ||||
0.501127 | + | 0.865374i | \(0.332919\pi\) | |||||||
\(608\) | 4.82916 | 0.195848 | ||||||||
\(609\) | 6.43013 | 0.260562 | ||||||||
\(610\) | 54.4287 | 2.20375 | ||||||||
\(611\) | −11.6830 | −0.472643 | ||||||||
\(612\) | −9.15536 | −0.370084 | ||||||||
\(613\) | −47.9599 | −1.93708 | −0.968541 | − | 0.248855i | \(-0.919946\pi\) | ||||
−0.968541 | + | 0.248855i | \(0.919946\pi\) | |||||||
\(614\) | −29.1281 | −1.17551 | ||||||||
\(615\) | 6.72621 | 0.271227 | ||||||||
\(616\) | 10.0571 | 0.405212 | ||||||||
\(617\) | −13.2916 | −0.535099 | −0.267549 | − | 0.963544i | \(-0.586214\pi\) | ||||
−0.267549 | + | 0.963544i | \(0.586214\pi\) | |||||||
\(618\) | 23.3153 | 0.937877 | ||||||||
\(619\) | 17.3840 | 0.698722 | 0.349361 | − | 0.936988i | \(-0.386399\pi\) | ||||
0.349361 | + | 0.936988i | \(0.386399\pi\) | |||||||
\(620\) | −75.9211 | −3.04906 | ||||||||
\(621\) | −29.2837 | −1.17511 | ||||||||
\(622\) | −51.9336 | −2.08235 | ||||||||
\(623\) | −7.06228 | −0.282944 | ||||||||
\(624\) | 19.8906 | 0.796262 | ||||||||
\(625\) | −26.8801 | −1.07520 | ||||||||
\(626\) | 37.2065 | 1.48707 | ||||||||
\(627\) | −3.70817 | −0.148090 | ||||||||
\(628\) | 2.41800 | 0.0964887 | ||||||||
\(629\) | 2.21625 | 0.0883676 | ||||||||
\(630\) | −24.6476 | −0.981983 | ||||||||
\(631\) | −17.1739 | −0.683683 | −0.341841 | − | 0.939758i | \(-0.611051\pi\) | ||||
−0.341841 | + | 0.939758i | \(0.611051\pi\) | |||||||
\(632\) | −16.2455 | −0.646211 | ||||||||
\(633\) | −7.37550 | −0.293150 | ||||||||
\(634\) | −30.9981 | −1.23109 | ||||||||
\(635\) | 6.49716 | 0.257832 | ||||||||
\(636\) | 9.62671 | 0.381724 | ||||||||
\(637\) | 15.8789 | 0.629147 | ||||||||
\(638\) | −9.38592 | −0.371592 | ||||||||
\(639\) | 12.6419 | 0.500104 | ||||||||
\(640\) | −42.9653 | −1.69835 | ||||||||
\(641\) | 20.4290 | 0.806898 | 0.403449 | − | 0.915002i | \(-0.367811\pi\) | ||||
0.403449 | + | 0.915002i | \(0.367811\pi\) | |||||||
\(642\) | 21.7741 | 0.859355 | ||||||||
\(643\) | 41.3083 | 1.62904 | 0.814520 | − | 0.580135i | \(-0.197000\pi\) | ||||
0.814520 | + | 0.580135i | \(0.197000\pi\) | |||||||
\(644\) | −50.4386 | −1.98756 | ||||||||
\(645\) | 2.04604 | 0.0805626 | ||||||||
\(646\) | 10.4218 | 0.410040 | ||||||||
\(647\) | 30.7706 | 1.20972 | 0.604859 | − | 0.796333i | \(-0.293230\pi\) | ||||
0.604859 | + | 0.796333i | \(0.293230\pi\) | |||||||
\(648\) | −13.7587 | −0.540494 | ||||||||
\(649\) | −15.1369 | −0.594175 | ||||||||
\(650\) | 4.88319 | 0.191534 | ||||||||
\(651\) | −13.4436 | −0.526896 | ||||||||
\(652\) | 65.4159 | 2.56189 | ||||||||
\(653\) | −29.6311 | −1.15955 | −0.579777 | − | 0.814775i | \(-0.696860\pi\) | ||||
−0.579777 | + | 0.814775i | \(0.696860\pi\) | |||||||
\(654\) | 36.7415 | 1.43671 | ||||||||
\(655\) | 34.0640 | 1.33099 | ||||||||
\(656\) | 15.4138 | 0.601808 | ||||||||
\(657\) | −17.6130 | −0.687148 | ||||||||
\(658\) | −11.5327 | −0.449593 | ||||||||
\(659\) | −9.52150 | −0.370905 | −0.185452 | − | 0.982653i | \(-0.559375\pi\) | ||||
−0.185452 | + | 0.982653i | \(0.559375\pi\) | |||||||
\(660\) | −8.41467 | −0.327541 | ||||||||
\(661\) | −32.8213 | −1.27660 | −0.638300 | − | 0.769787i | \(-0.720362\pi\) | ||||
−0.638300 | + | 0.769787i | \(0.720362\pi\) | |||||||
\(662\) | −15.7793 | −0.613278 | ||||||||
\(663\) | 4.24224 | 0.164755 | ||||||||
\(664\) | 0.649762 | 0.0252156 | ||||||||
\(665\) | 18.8771 | 0.732021 | ||||||||
\(666\) | 12.1979 | 0.472659 | ||||||||
\(667\) | 24.1810 | 0.936293 | ||||||||
\(668\) | −1.58904 | −0.0614818 | ||||||||
\(669\) | −10.6059 | −0.410049 | ||||||||
\(670\) | 83.6999 | 3.23361 | ||||||||
\(671\) | −9.46522 | −0.365401 | ||||||||
\(672\) | 1.94045 | 0.0748544 | ||||||||
\(673\) | 34.9681 | 1.34792 | 0.673960 | − | 0.738768i | \(-0.264592\pi\) | ||||
0.673960 | + | 0.738768i | \(0.264592\pi\) | |||||||
\(674\) | 46.1137 | 1.77623 | ||||||||
\(675\) | 1.88295 | 0.0724747 | ||||||||
\(676\) | 42.1775 | 1.62221 | ||||||||
\(677\) | 16.3441 | 0.628153 | 0.314077 | − | 0.949398i | \(-0.398305\pi\) | ||||
0.314077 | + | 0.949398i | \(0.398305\pi\) | |||||||
\(678\) | −31.6991 | −1.21740 | ||||||||
\(679\) | −26.3637 | −1.01175 | ||||||||
\(680\) | 12.1487 | 0.465880 | ||||||||
\(681\) | −2.42867 | −0.0930668 | ||||||||
\(682\) | 19.6233 | 0.751416 | ||||||||
\(683\) | −5.48141 | −0.209740 | −0.104870 | − | 0.994486i | \(-0.533443\pi\) | ||||
−0.104870 | + | 0.994486i | \(0.533443\pi\) | |||||||
\(684\) | 38.5925 | 1.47562 | ||||||||
\(685\) | −16.9741 | −0.648546 | ||||||||
\(686\) | 48.9974 | 1.87073 | ||||||||
\(687\) | −3.41216 | −0.130182 | ||||||||
\(688\) | 4.68871 | 0.178755 | ||||||||
\(689\) | 12.8317 | 0.488850 | ||||||||
\(690\) | 32.2212 | 1.22664 | ||||||||
\(691\) | 18.5963 | 0.707436 | 0.353718 | − | 0.935352i | \(-0.384917\pi\) | ||||
0.353718 | + | 0.935352i | \(0.384917\pi\) | |||||||
\(692\) | −92.8774 | −3.53067 | ||||||||
\(693\) | 4.28625 | 0.162821 | ||||||||
\(694\) | −57.8738 | −2.19686 | ||||||||
\(695\) | 19.6483 | 0.745302 | ||||||||
\(696\) | −17.4438 | −0.661205 | ||||||||
\(697\) | 3.28743 | 0.124520 | ||||||||
\(698\) | 33.4734 | 1.26699 | ||||||||
\(699\) | 16.1642 | 0.611386 | ||||||||
\(700\) | 3.24321 | 0.122582 | ||||||||
\(701\) | −20.1014 | −0.759218 | −0.379609 | − | 0.925147i | \(-0.623941\pi\) | ||||
−0.379609 | + | 0.925147i | \(0.623941\pi\) | |||||||
\(702\) | 54.8140 | 2.06882 | ||||||||
\(703\) | −9.34212 | −0.352345 | ||||||||
\(704\) | 6.54499 | 0.246673 | ||||||||
\(705\) | 4.95683 | 0.186685 | ||||||||
\(706\) | 37.7614 | 1.42117 | ||||||||
\(707\) | −23.1831 | −0.871890 | ||||||||
\(708\) | −54.7637 | −2.05815 | ||||||||
\(709\) | −45.3423 | −1.70287 | −0.851433 | − | 0.524464i | \(-0.824266\pi\) | ||||
−0.851433 | + | 0.524464i | \(0.824266\pi\) | |||||||
\(710\) | −32.6555 | −1.22554 | ||||||||
\(711\) | −6.92369 | −0.259659 | ||||||||
\(712\) | 19.1587 | 0.718002 | ||||||||
\(713\) | −50.5558 | −1.89333 | ||||||||
\(714\) | 4.18768 | 0.156720 | ||||||||
\(715\) | −11.2162 | −0.419461 | ||||||||
\(716\) | −36.8409 | −1.37681 | ||||||||
\(717\) | 16.3536 | 0.610736 | ||||||||
\(718\) | 56.2504 | 2.09925 | ||||||||
\(719\) | −51.1045 | −1.90588 | −0.952938 | − | 0.303165i | \(-0.901957\pi\) | ||||
−0.952938 | + | 0.303165i | \(0.901957\pi\) | |||||||
\(720\) | 24.2765 | 0.904732 | ||||||||
\(721\) | 20.6404 | 0.768689 | ||||||||
\(722\) | 3.04436 | 0.113299 | ||||||||
\(723\) | 23.3937 | 0.870021 | ||||||||
\(724\) | −19.9550 | −0.741621 | ||||||||
\(725\) | −1.55484 | −0.0577454 | ||||||||
\(726\) | 2.17494 | 0.0807197 | ||||||||
\(727\) | 35.7737 | 1.32677 | 0.663386 | − | 0.748277i | \(-0.269119\pi\) | ||||
0.663386 | + | 0.748277i | \(0.269119\pi\) | |||||||
\(728\) | 48.4993 | 1.79750 | ||||||||
\(729\) | 6.26910 | 0.232189 | ||||||||
\(730\) | 45.4965 | 1.68390 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | −34.2442 | −1.26570 | ||||||||
\(733\) | −22.4995 | −0.831040 | −0.415520 | − | 0.909584i | \(-0.636400\pi\) | ||||
−0.415520 | + | 0.909584i | \(0.636400\pi\) | |||||||
\(734\) | 2.17952 | 0.0804476 | ||||||||
\(735\) | −6.73709 | −0.248501 | ||||||||
\(736\) | 7.29722 | 0.268979 | ||||||||
\(737\) | −14.5555 | −0.536160 | ||||||||
\(738\) | 18.0936 | 0.666033 | ||||||||
\(739\) | −3.80382 | −0.139926 | −0.0699628 | − | 0.997550i | \(-0.522288\pi\) | ||||
−0.0699628 | + | 0.997550i | \(0.522288\pi\) | |||||||
\(740\) | −21.1994 | −0.779305 | ||||||||
\(741\) | −17.8823 | −0.656921 | ||||||||
\(742\) | 12.6667 | 0.465009 | ||||||||
\(743\) | −19.4553 | −0.713746 | −0.356873 | − | 0.934153i | \(-0.616157\pi\) | ||||
−0.356873 | + | 0.934153i | \(0.616157\pi\) | |||||||
\(744\) | 36.4701 | 1.33706 | ||||||||
\(745\) | 6.00152 | 0.219879 | ||||||||
\(746\) | 3.30226 | 0.120904 | ||||||||
\(747\) | 0.276923 | 0.0101321 | ||||||||
\(748\) | −4.11267 | −0.150374 | ||||||||
\(749\) | 19.2761 | 0.704332 | ||||||||
\(750\) | 23.2211 | 0.847914 | ||||||||
\(751\) | 14.6071 | 0.533021 | 0.266511 | − | 0.963832i | \(-0.414129\pi\) | ||||
0.266511 | + | 0.963832i | \(0.414129\pi\) | |||||||
\(752\) | 11.3591 | 0.414224 | ||||||||
\(753\) | 1.34139 | 0.0488830 | ||||||||
\(754\) | −45.2626 | −1.64837 | ||||||||
\(755\) | −40.7235 | −1.48208 | ||||||||
\(756\) | 36.4051 | 1.32404 | ||||||||
\(757\) | 15.1460 | 0.550492 | 0.275246 | − | 0.961374i | \(-0.411241\pi\) | ||||
0.275246 | + | 0.961374i | \(0.411241\pi\) | |||||||
\(758\) | 18.5901 | 0.675224 | ||||||||
\(759\) | −5.60332 | −0.203388 | ||||||||
\(760\) | −51.2101 | −1.85758 | ||||||||
\(761\) | −46.6292 | −1.69031 | −0.845154 | − | 0.534523i | \(-0.820491\pi\) | ||||
−0.845154 | + | 0.534523i | \(0.820491\pi\) | |||||||
\(762\) | −6.07561 | −0.220096 | ||||||||
\(763\) | 32.5263 | 1.17753 | ||||||||
\(764\) | −87.4541 | −3.16398 | ||||||||
\(765\) | 5.17765 | 0.187198 | ||||||||
\(766\) | −64.9525 | −2.34683 | ||||||||
\(767\) | −72.9961 | −2.63574 | ||||||||
\(768\) | 28.6624 | 1.03427 | ||||||||
\(769\) | 29.0299 | 1.04685 | 0.523423 | − | 0.852073i | \(-0.324655\pi\) | ||||
0.523423 | + | 0.852073i | \(0.324655\pi\) | |||||||
\(770\) | −11.0719 | −0.399004 | ||||||||
\(771\) | 4.07593 | 0.146791 | ||||||||
\(772\) | 0.431704 | 0.0155374 | ||||||||
\(773\) | −16.8310 | −0.605369 | −0.302685 | − | 0.953091i | \(-0.597883\pi\) | ||||
−0.302685 | + | 0.953091i | \(0.597883\pi\) | |||||||
\(774\) | 5.50386 | 0.197832 | ||||||||
\(775\) | 3.25074 | 0.116770 | ||||||||
\(776\) | 71.5201 | 2.56742 | ||||||||
\(777\) | −3.75385 | −0.134668 | ||||||||
\(778\) | 24.3554 | 0.873183 | ||||||||
\(779\) | −13.8575 | −0.496495 | ||||||||
\(780\) | −40.5789 | −1.45296 | ||||||||
\(781\) | 5.67883 | 0.203205 | ||||||||
\(782\) | 15.7481 | 0.563152 | ||||||||
\(783\) | −17.4532 | −0.623726 | ||||||||
\(784\) | −15.4387 | −0.551384 | ||||||||
\(785\) | −1.36746 | −0.0488066 | ||||||||
\(786\) | −31.8539 | −1.13619 | ||||||||
\(787\) | −19.2321 | −0.685551 | −0.342775 | − | 0.939417i | \(-0.611367\pi\) | ||||
−0.342775 | + | 0.939417i | \(0.611367\pi\) | |||||||
\(788\) | 87.2637 | 3.10864 | ||||||||
\(789\) | −13.7821 | −0.490657 | ||||||||
\(790\) | 17.8847 | 0.636311 | ||||||||
\(791\) | −28.0624 | −0.997786 | ||||||||
\(792\) | −11.6278 | −0.413177 | ||||||||
\(793\) | −45.6451 | −1.62090 | ||||||||
\(794\) | 67.6337 | 2.40023 | ||||||||
\(795\) | −5.44422 | −0.193087 | ||||||||
\(796\) | −4.15357 | −0.147220 | ||||||||
\(797\) | 6.19905 | 0.219582 | 0.109791 | − | 0.993955i | \(-0.464982\pi\) | ||||
0.109791 | + | 0.993955i | \(0.464982\pi\) | |||||||
\(798\) | −17.6523 | −0.624884 | ||||||||
\(799\) | 2.42265 | 0.0857072 | ||||||||
\(800\) | −0.469212 | −0.0165891 | ||||||||
\(801\) | 8.16527 | 0.288506 | ||||||||
\(802\) | 59.7038 | 2.10822 | ||||||||
\(803\) | −7.91191 | −0.279205 | ||||||||
\(804\) | −52.6604 | −1.85719 | ||||||||
\(805\) | 28.5247 | 1.00536 | ||||||||
\(806\) | 94.6315 | 3.33325 | ||||||||
\(807\) | 1.85875 | 0.0654312 | ||||||||
\(808\) | 62.8916 | 2.21252 | ||||||||
\(809\) | −33.9485 | −1.19357 | −0.596783 | − | 0.802403i | \(-0.703555\pi\) | ||||
−0.596783 | + | 0.802403i | \(0.703555\pi\) | |||||||
\(810\) | 15.1470 | 0.532213 | ||||||||
\(811\) | −45.7766 | −1.60743 | −0.803717 | − | 0.595012i | \(-0.797147\pi\) | ||||
−0.803717 | + | 0.595012i | \(0.797147\pi\) | |||||||
\(812\) | −30.0615 | −1.05495 | ||||||||
\(813\) | −17.8301 | −0.625328 | ||||||||
\(814\) | 5.47941 | 0.192053 | ||||||||
\(815\) | −36.9948 | −1.29587 | ||||||||
\(816\) | −4.12463 | −0.144391 | ||||||||
\(817\) | −4.21529 | −0.147474 | ||||||||
\(818\) | −83.0972 | −2.90543 | ||||||||
\(819\) | 20.6700 | 0.722268 | ||||||||
\(820\) | −31.4457 | −1.09813 | ||||||||
\(821\) | 9.55209 | 0.333370 | 0.166685 | − | 0.986010i | \(-0.446694\pi\) | ||||
0.166685 | + | 0.986010i | \(0.446694\pi\) | |||||||
\(822\) | 15.8728 | 0.553626 | ||||||||
\(823\) | −42.3357 | −1.47573 | −0.737865 | − | 0.674949i | \(-0.764166\pi\) | ||||
−0.737865 | + | 0.674949i | \(0.764166\pi\) | |||||||
\(824\) | −55.9937 | −1.95063 | ||||||||
\(825\) | 0.360294 | 0.0125438 | ||||||||
\(826\) | −72.0573 | −2.50719 | ||||||||
\(827\) | −30.6193 | −1.06474 | −0.532369 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532369 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(828\) | 58.3161 | 2.02663 | ||||||||
\(829\) | −22.9937 | −0.798605 | −0.399303 | − | 0.916819i | \(-0.630748\pi\) | ||||
−0.399303 | + | 0.916819i | \(0.630748\pi\) | |||||||
\(830\) | −0.715326 | −0.0248293 | ||||||||
\(831\) | −17.2709 | −0.599119 | ||||||||
\(832\) | 31.5625 | 1.09423 | ||||||||
\(833\) | −3.29275 | −0.114087 | ||||||||
\(834\) | −18.3735 | −0.636221 | ||||||||
\(835\) | 0.898654 | 0.0310992 | ||||||||
\(836\) | 17.3361 | 0.599581 | ||||||||
\(837\) | 36.4897 | 1.26127 | ||||||||
\(838\) | −82.8993 | −2.86371 | ||||||||
\(839\) | 32.3553 | 1.11703 | 0.558515 | − | 0.829495i | \(-0.311371\pi\) | ||||
0.558515 | + | 0.829495i | \(0.311371\pi\) | |||||||
\(840\) | −20.5772 | −0.709981 | ||||||||
\(841\) | −14.5880 | −0.503036 | ||||||||
\(842\) | −95.3709 | −3.28670 | ||||||||
\(843\) | −27.2636 | −0.939010 | ||||||||
\(844\) | 34.4813 | 1.18689 | ||||||||
\(845\) | −23.8527 | −0.820559 | ||||||||
\(846\) | 13.3339 | 0.458430 | ||||||||
\(847\) | 1.92542 | 0.0661583 | ||||||||
\(848\) | −12.4760 | −0.428428 | ||||||||
\(849\) | 9.00999 | 0.309222 | ||||||||
\(850\) | −1.01261 | −0.0347321 | ||||||||
\(851\) | −14.1166 | −0.483912 | ||||||||
\(852\) | 20.5454 | 0.703875 | ||||||||
\(853\) | −19.6699 | −0.673485 | −0.336743 | − | 0.941597i | \(-0.609325\pi\) | ||||
−0.336743 | + | 0.941597i | \(0.609325\pi\) | |||||||
\(854\) | −45.0580 | −1.54185 | ||||||||
\(855\) | −21.8253 | −0.746410 | ||||||||
\(856\) | −52.2925 | −1.78732 | ||||||||
\(857\) | 8.60350 | 0.293890 | 0.146945 | − | 0.989145i | \(-0.453056\pi\) | ||||
0.146945 | + | 0.989145i | \(0.453056\pi\) | |||||||
\(858\) | 10.4884 | 0.358069 | ||||||||
\(859\) | −9.56397 | −0.326318 | −0.163159 | − | 0.986600i | \(-0.552168\pi\) | ||||
−0.163159 | + | 0.986600i | \(0.552168\pi\) | |||||||
\(860\) | −9.56544 | −0.326179 | ||||||||
\(861\) | −5.56820 | −0.189764 | ||||||||
\(862\) | 8.35673 | 0.284632 | ||||||||
\(863\) | 5.33449 | 0.181588 | 0.0907940 | − | 0.995870i | \(-0.471060\pi\) | ||||
0.0907940 | + | 0.995870i | \(0.471060\pi\) | |||||||
\(864\) | −5.26692 | −0.179184 | ||||||||
\(865\) | 52.5252 | 1.78591 | ||||||||
\(866\) | −21.1586 | −0.718998 | ||||||||
\(867\) | −0.879695 | −0.0298760 | ||||||||
\(868\) | 62.8503 | 2.13328 | ||||||||
\(869\) | −3.11018 | −0.105506 | ||||||||
\(870\) | 19.2039 | 0.651075 | ||||||||
\(871\) | −70.1926 | −2.37838 | ||||||||
\(872\) | −88.2381 | −2.98812 | ||||||||
\(873\) | 30.4813 | 1.03163 | ||||||||
\(874\) | −66.3829 | −2.24543 | ||||||||
\(875\) | 20.5571 | 0.694955 | ||||||||
\(876\) | −28.6244 | −0.967130 | ||||||||
\(877\) | 15.4148 | 0.520521 | 0.260260 | − | 0.965538i | \(-0.416192\pi\) | ||||
0.260260 | + | 0.965538i | \(0.416192\pi\) | |||||||
\(878\) | 66.5467 | 2.24584 | ||||||||
\(879\) | 7.69964 | 0.259702 | ||||||||
\(880\) | 10.9052 | 0.367615 | ||||||||
\(881\) | 32.0065 | 1.07833 | 0.539164 | − | 0.842201i | \(-0.318740\pi\) | ||||
0.539164 | + | 0.842201i | \(0.318740\pi\) | |||||||
\(882\) | −18.1228 | −0.610227 | ||||||||
\(883\) | 42.0395 | 1.41474 | 0.707372 | − | 0.706842i | \(-0.249881\pi\) | ||||
0.707372 | + | 0.706842i | \(0.249881\pi\) | |||||||
\(884\) | −19.8329 | −0.667053 | ||||||||
\(885\) | 30.9706 | 1.04107 | ||||||||
\(886\) | −7.03487 | −0.236341 | ||||||||
\(887\) | 13.6350 | 0.457817 | 0.228909 | − | 0.973448i | \(-0.426484\pi\) | ||||
0.228909 | + | 0.973448i | \(0.426484\pi\) | |||||||
\(888\) | 10.1835 | 0.341736 | ||||||||
\(889\) | −5.37859 | −0.180392 | ||||||||
\(890\) | −21.0919 | −0.707002 | ||||||||
\(891\) | −2.63409 | −0.0882455 | ||||||||
\(892\) | 49.5839 | 1.66019 | ||||||||
\(893\) | −10.2122 | −0.341737 | ||||||||
\(894\) | −5.61213 | −0.187698 | ||||||||
\(895\) | 20.8347 | 0.696428 | ||||||||
\(896\) | 35.5682 | 1.18825 | ||||||||
\(897\) | −27.0214 | −0.902219 | ||||||||
\(898\) | −11.9448 | −0.398605 | ||||||||
\(899\) | −30.1314 | −1.00494 | ||||||||
\(900\) | −3.74974 | −0.124991 | ||||||||
\(901\) | −2.66086 | −0.0886461 | ||||||||
\(902\) | 8.12778 | 0.270626 | ||||||||
\(903\) | −1.69378 | −0.0563656 | ||||||||
\(904\) | 76.1284 | 2.53199 | ||||||||
\(905\) | 11.2852 | 0.375132 | ||||||||
\(906\) | 38.0813 | 1.26517 | ||||||||
\(907\) | 11.6591 | 0.387135 | 0.193568 | − | 0.981087i | \(-0.437994\pi\) | ||||
0.193568 | + | 0.981087i | \(0.437994\pi\) | |||||||
\(908\) | 11.3543 | 0.376805 | ||||||||
\(909\) | 26.8039 | 0.889028 | ||||||||
\(910\) | −53.3931 | −1.76997 | ||||||||
\(911\) | 13.4950 | 0.447109 | 0.223555 | − | 0.974691i | \(-0.428234\pi\) | ||||
0.223555 | + | 0.974691i | \(0.428234\pi\) | |||||||
\(912\) | 17.3865 | 0.575725 | ||||||||
\(913\) | 0.124396 | 0.00411691 | ||||||||
\(914\) | −18.3249 | −0.606134 | ||||||||
\(915\) | 19.3662 | 0.640227 | ||||||||
\(916\) | 15.9522 | 0.527076 | ||||||||
\(917\) | −28.1995 | −0.931228 | ||||||||
\(918\) | −11.3665 | −0.375152 | ||||||||
\(919\) | −56.1596 | −1.85253 | −0.926267 | − | 0.376868i | \(-0.877001\pi\) | ||||
−0.926267 | + | 0.376868i | \(0.877001\pi\) | |||||||
\(920\) | −77.3823 | −2.55122 | ||||||||
\(921\) | −10.3640 | −0.341506 | ||||||||
\(922\) | 86.2733 | 2.84126 | ||||||||
\(923\) | 27.3856 | 0.901407 | ||||||||
\(924\) | 6.96597 | 0.229164 | ||||||||
\(925\) | 0.907702 | 0.0298451 | ||||||||
\(926\) | −4.03210 | −0.132503 | ||||||||
\(927\) | −23.8641 | −0.783799 | ||||||||
\(928\) | 4.34916 | 0.142768 | ||||||||
\(929\) | −29.9165 | −0.981529 | −0.490764 | − | 0.871292i | \(-0.663282\pi\) | ||||
−0.490764 | + | 0.871292i | \(0.663282\pi\) | |||||||
\(930\) | −40.1501 | −1.31657 | ||||||||
\(931\) | 13.8799 | 0.454895 | ||||||||
\(932\) | −75.5694 | −2.47536 | ||||||||
\(933\) | −18.4784 | −0.604957 | ||||||||
\(934\) | −100.146 | −3.27686 | ||||||||
\(935\) | 2.32585 | 0.0760634 | ||||||||
\(936\) | −56.0740 | −1.83284 | ||||||||
\(937\) | −57.7875 | −1.88784 | −0.943918 | − | 0.330181i | \(-0.892890\pi\) | ||||
−0.943918 | + | 0.330181i | \(0.892890\pi\) | |||||||
\(938\) | −69.2899 | −2.26239 | ||||||||
\(939\) | 13.2384 | 0.432019 | ||||||||
\(940\) | −23.1737 | −0.755844 | ||||||||
\(941\) | −24.5572 | −0.800542 | −0.400271 | − | 0.916397i | \(-0.631084\pi\) | ||||
−0.400271 | + | 0.916397i | \(0.631084\pi\) | |||||||
\(942\) | 1.27873 | 0.0416634 | ||||||||
\(943\) | −20.9397 | −0.681890 | ||||||||
\(944\) | 70.9725 | 2.30996 | ||||||||
\(945\) | −20.5883 | −0.669737 | ||||||||
\(946\) | 2.47238 | 0.0803840 | ||||||||
\(947\) | 16.2524 | 0.528132 | 0.264066 | − | 0.964505i | \(-0.414936\pi\) | ||||
0.264066 | + | 0.964505i | \(0.414936\pi\) | |||||||
\(948\) | −11.2523 | −0.365458 | ||||||||
\(949\) | −38.1543 | −1.23854 | ||||||||
\(950\) | 4.26843 | 0.138486 | ||||||||
\(951\) | −11.0294 | −0.357652 | ||||||||
\(952\) | −10.0571 | −0.325953 | ||||||||
\(953\) | 54.5931 | 1.76844 | 0.884222 | − | 0.467066i | \(-0.154689\pi\) | ||||
0.884222 | + | 0.467066i | \(0.154689\pi\) | |||||||
\(954\) | −14.6450 | −0.474149 | ||||||||
\(955\) | 49.4581 | 1.60043 | ||||||||
\(956\) | −76.4548 | −2.47272 | ||||||||
\(957\) | −3.33959 | −0.107954 | ||||||||
\(958\) | 57.2950 | 1.85112 | ||||||||
\(959\) | 14.0518 | 0.453755 | ||||||||
\(960\) | −13.3913 | −0.432202 | ||||||||
\(961\) | 31.9963 | 1.03214 | ||||||||
\(962\) | 26.4239 | 0.851940 | ||||||||
\(963\) | −22.2866 | −0.718176 | ||||||||
\(964\) | −109.368 | −3.52251 | ||||||||
\(965\) | −0.244143 | −0.00785923 | ||||||||
\(966\) | −26.6739 | −0.858219 | ||||||||
\(967\) | −49.1662 | −1.58108 | −0.790539 | − | 0.612412i | \(-0.790200\pi\) | ||||
−0.790539 | + | 0.612412i | \(0.790200\pi\) | |||||||
\(968\) | −5.22332 | −0.167884 | ||||||||
\(969\) | 3.70817 | 0.119124 | ||||||||
\(970\) | −78.7368 | −2.52809 | ||||||||
\(971\) | −22.3824 | −0.718286 | −0.359143 | − | 0.933282i | \(-0.616931\pi\) | ||||
−0.359143 | + | 0.933282i | \(0.616931\pi\) | |||||||
\(972\) | −66.2527 | −2.12506 | ||||||||
\(973\) | −16.2656 | −0.521450 | ||||||||
\(974\) | 33.3629 | 1.06902 | ||||||||
\(975\) | 1.73748 | 0.0556439 | ||||||||
\(976\) | 44.3797 | 1.42056 | ||||||||
\(977\) | 17.3735 | 0.555827 | 0.277914 | − | 0.960606i | \(-0.410357\pi\) | ||||
0.277914 | + | 0.960606i | \(0.410357\pi\) | |||||||
\(978\) | 34.5945 | 1.10621 | ||||||||
\(979\) | 3.66791 | 0.117227 | ||||||||
\(980\) | 31.4966 | 1.00612 | ||||||||
\(981\) | −37.6063 | −1.20068 | ||||||||
\(982\) | −71.4595 | −2.28036 | ||||||||
\(983\) | 44.3865 | 1.41571 | 0.707855 | − | 0.706357i | \(-0.249663\pi\) | ||||
0.707855 | + | 0.706357i | \(0.249663\pi\) | |||||||
\(984\) | 15.1055 | 0.481547 | ||||||||
\(985\) | −49.3505 | −1.57244 | ||||||||
\(986\) | 9.38592 | 0.298909 | ||||||||
\(987\) | −4.10345 | −0.130614 | ||||||||
\(988\) | 83.6015 | 2.65972 | ||||||||
\(989\) | −6.36962 | −0.202542 | ||||||||
\(990\) | 12.8011 | 0.406847 | ||||||||
\(991\) | 36.0813 | 1.14616 | 0.573080 | − | 0.819500i | \(-0.305749\pi\) | ||||
0.573080 | + | 0.819500i | \(0.305749\pi\) | |||||||
\(992\) | −9.09288 | −0.288699 | ||||||||
\(993\) | −5.61440 | −0.178168 | ||||||||
\(994\) | 27.0334 | 0.857447 | ||||||||
\(995\) | 2.34898 | 0.0744677 | ||||||||
\(996\) | 0.450053 | 0.0142605 | ||||||||
\(997\) | 5.97118 | 0.189109 | 0.0945546 | − | 0.995520i | \(-0.469857\pi\) | ||||
0.0945546 | + | 0.995520i | \(0.469857\pi\) | |||||||
\(998\) | −63.1858 | −2.00011 | ||||||||
\(999\) | 10.1890 | 0.322365 |
(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 | 8041.2.a.g.1.7 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.7 | ✓ | 69 | 1.1 | even | 1 | trivial |