Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(445,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.445");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.s (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 445.5 | ||
Character | \(\chi\) | \(=\) | 684.445 |
Dual form | 684.3.s.a.601.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.72361 | + | 1.25776i | −0.907870 | + | 0.419253i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.340706 | + | 0.590120i | 0.0681412 | + | 0.118024i | 0.898083 | − | 0.439826i | \(-0.144960\pi\) |
−0.829942 | + | 0.557850i | \(0.811626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.79581 | − | 4.84248i | −0.399401 | − | 0.691783i | 0.594251 | − | 0.804280i | \(-0.297449\pi\) |
−0.993652 | + | 0.112496i | \(0.964115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.83609 | − | 6.85128i | 0.648454 | − | 0.761254i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.44896 | + | 12.9020i | 0.677179 | + | 1.17291i | 0.975827 | + | 0.218545i | \(0.0701309\pi\) |
−0.298648 | + | 0.954363i | \(0.596536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.36780i | − | 0.182139i | −0.995845 | − | 0.0910694i | \(-0.970971\pi\) | ||
0.995845 | − | 0.0910694i | \(-0.0290285\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67018 | − | 1.17873i | −0.111345 | − | 0.0785821i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.72908 | + | 15.1192i | −0.513475 | + | 0.889365i | 0.486403 | + | 0.873735i | \(0.338309\pi\) |
−0.999878 | + | 0.0156303i | \(0.995025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.2199 | − | 8.02967i | −0.906310 | − | 0.422614i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.7054 | + | 9.67258i | 0.652636 | + | 0.460599i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.4486 | −0.454289 | −0.227144 | − | 0.973861i | \(-0.572939\pi\) | ||||
−0.227144 | + | 0.973861i | \(0.572939\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.2678 | − | 21.2485i | 0.490714 | − | 0.849941i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.27796 | + | 26.0006i | −0.269554 | + | 0.962985i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −37.6328 | − | 21.7273i | −1.29768 | − | 0.749217i | −0.317679 | − | 0.948198i | \(-0.602903\pi\) |
−0.980003 | + | 0.198981i | \(0.936237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 28.9832 | + | 16.7334i | 0.934940 | + | 0.539788i | 0.888371 | − | 0.459127i | \(-0.151838\pi\) |
0.0465698 | + | 0.998915i | \(0.485171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −36.5156 | − | 25.7710i | −1.10653 | − | 0.780938i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.90510 | − | 3.29973i | 0.0544314 | − | 0.0942780i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 30.3219i | − | 0.819510i | −0.912196 | − | 0.409755i | \(-0.865614\pi\) | ||
0.912196 | − | 0.409755i | \(-0.134386\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.97813 | + | 6.44897i | 0.0763622 | + | 0.165358i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.7811 | − | 28.1638i | 1.18978 | − | 0.686921i | 0.231525 | − | 0.972829i | \(-0.425628\pi\) |
0.958257 | + | 0.285908i | \(0.0922951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −62.4810 | −1.45305 | −0.726523 | − | 0.687142i | \(-0.758865\pi\) | ||||
−0.726523 | + | 0.687142i | \(0.758865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.03147 | + | 1.10972i | 0.134033 | + | 0.0246604i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 43.3232 | − | 75.0381i | 0.921771 | − | 1.59655i | 0.125098 | − | 0.992144i | \(-0.460075\pi\) |
0.796673 | − | 0.604410i | \(-0.206591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.86690 | − | 15.3579i | 0.180957 | − | 0.313427i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.75828 | − | 52.1579i | 0.0932996 | − | 1.02270i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 43.7359 | − | 25.2509i | 0.825206 | − | 0.476433i | −0.0270024 | − | 0.999635i | \(-0.508596\pi\) |
0.852208 | + | 0.523202i | \(0.175263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.07582 | + | 8.79157i | −0.0922876 | + | 0.159847i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 56.9996 | + | 0.211226i | 0.999993 | + | 0.00370572i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.9077 | − | 8.02962i | 0.235724 | − | 0.136095i | −0.377486 | − | 0.926015i | \(-0.623211\pi\) |
0.613210 | + | 0.789920i | \(0.289878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.219952 | − | 0.380967i | 0.00360576 | − | 0.00624536i | −0.864217 | − | 0.503119i | \(-0.832186\pi\) |
0.867823 | + | 0.496874i | \(0.165519\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −49.4938 | − | 9.10628i | −0.785616 | − | 0.144544i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.39729 | − | 0.806726i | 0.0214968 | − | 0.0124112i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 41.0728i | − | 0.613027i | −0.951866 | − | 0.306513i | \(-0.900838\pi\) | ||
0.951866 | − | 0.306513i | \(-0.0991624\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 28.4580 | − | 13.1419i | 0.412435 | − | 0.190462i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62.9245 | + | 36.3295i | 0.886260 | + | 0.511683i | 0.872717 | − | 0.488226i | \(-0.162356\pi\) |
0.0135429 | + | 0.999908i | \(0.495689\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38.3367 | − | 66.4012i | 0.525161 | − | 0.909605i | −0.474410 | − | 0.880304i | \(-0.657339\pi\) |
0.999571 | − | 0.0293009i | \(-0.00932811\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.68729 | + | 73.3026i | −0.0891638 | + | 0.977368i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 41.6518 | − | 72.1430i | 0.540932 | − | 0.936922i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 120.760i | 1.52861i | 0.644856 | + | 0.764304i | \(0.276918\pi\) | ||||
−0.644856 | + | 0.764304i | \(0.723082\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.8802 | − | 79.9694i | −0.159014 | − | 0.987276i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −53.7042 | − | 93.0184i | −0.647038 | − | 1.12070i | −0.983827 | − | 0.179123i | \(-0.942674\pi\) |
0.336788 | − | 0.941580i | \(-0.390659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.8962 | −0.139955 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 129.825 | + | 11.8437i | 1.49224 | + | 0.136135i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −122.606 | + | 70.7865i | −1.37759 | + | 0.795354i | −0.991869 | − | 0.127259i | \(-0.959382\pi\) |
−0.385725 | + | 0.922614i | \(0.626049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.4661 | + | 6.61993i | −0.126001 | + | 0.0727465i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −99.9854 | − | 9.12151i | −1.07511 | − | 0.0980808i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.12845 | − | 12.8976i | −0.0118784 | − | 0.135764i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 171.665i | − | 1.76974i | −0.465836 | − | 0.884871i | \(-0.654246\pi\) | ||
0.465836 | − | 0.884871i | \(-0.345754\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 131.868 | + | 24.2621i | 1.33200 | + | 0.245072i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 95.2105 | − | 164.910i | 0.942679 | − | 1.63277i | 0.182345 | − | 0.983235i | \(-0.441631\pi\) |
0.760334 | − | 0.649533i | \(-0.225035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −82.2476 | − | 47.4857i | −0.798520 | − | 0.461026i | 0.0444333 | − | 0.999012i | \(-0.485852\pi\) |
−0.842953 | + | 0.537987i | \(0.819185\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.03848 | + | 11.3833i | −0.00989031 | + | 0.108413i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 21.9122i | 0.204787i | 0.994744 | + | 0.102393i | \(0.0326500\pi\) | ||||
−0.994744 | + | 0.102393i | \(0.967350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −170.338 | − | 98.3447i | −1.56273 | − | 0.902245i | −0.996979 | − | 0.0776724i | \(-0.975251\pi\) |
−0.565756 | − | 0.824573i | \(-0.691415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 38.1376 | + | 82.5850i | 0.343582 | + | 0.744009i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.06724 | + | 2.34822i | 0.0359933 | + | 0.0207807i | 0.517889 | − | 0.855448i | \(-0.326718\pi\) |
−0.481895 | + | 0.876229i | \(0.660051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.55992 | − | 6.16596i | −0.0309558 | − | 0.0536170i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.2225 | − | 13.8187i | −0.138654 | − | 0.118109i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 97.6193 | 0.820331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50.4742 | + | 87.4238i | −0.417142 | + | 0.722511i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −97.4373 | + | 138.062i | −0.792173 | + | 1.12245i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.7542 | 0.270034 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −180.051 | + | 103.952i | −1.41772 | + | 0.818523i | −0.996099 | − | 0.0882482i | \(-0.971873\pi\) |
−0.421624 | + | 0.906771i | \(0.638540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 170.174 | − | 78.5860i | 1.31918 | − | 0.609194i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −101.507 | − | 175.815i | −0.774861 | − | 1.34210i | −0.934873 | − | 0.354983i | \(-0.884487\pi\) |
0.160012 | − | 0.987115i | \(-0.448847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.25996 | + | 105.836i | 0.0696238 | + | 0.795763i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.8231 | + | 4.56369i | −0.132023 | + | 0.0338051i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 44.5917 | − | 77.2351i | 0.325487 | − | 0.563760i | −0.656124 | − | 0.754653i | \(-0.727805\pi\) |
0.981611 | + | 0.190894i | \(0.0611385\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −165.847 | −1.19315 | −0.596573 | − | 0.802559i | \(-0.703471\pi\) | ||||
−0.596573 | + | 0.802559i | \(0.703471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.6158 | + | 258.865i | −0.167488 | + | 1.83592i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 30.5494 | − | 17.6377i | 0.213632 | − | 0.123340i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 29.6105i | − | 0.204210i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.83341 | + | 52.9814i | −0.0328804 | + | 0.360418i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 77.9783 | + | 135.062i | 0.523344 | + | 0.906459i | 0.999631 | + | 0.0271686i | \(0.00864909\pi\) |
−0.476287 | + | 0.879290i | \(0.658018\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 255.830 | − | 147.703i | 1.69424 | − | 0.978168i | 0.743212 | − | 0.669056i | \(-0.233302\pi\) |
0.951026 | − | 0.309112i | \(-0.100032\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 52.6423 | + | 148.042i | 0.344067 | + | 0.967597i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.8047i | 0.147127i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 34.2907 | + | 59.3933i | 0.218412 | + | 0.378301i | 0.954323 | − | 0.298778i | \(-0.0965789\pi\) |
−0.735910 | + | 0.677079i | \(0.763246\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −87.3599 | + | 123.783i | −0.549434 | + | 0.778509i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.2124 | + | 50.5974i | 0.181444 | + | 0.314269i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 54.7677 | 0.335998 | 0.167999 | − | 0.985787i | \(-0.446269\pi\) | ||||
0.167999 | + | 0.985787i | \(0.446269\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.76686 | − | 30.3290i | 0.0167689 | − | 0.183812i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 104.833i | 0.627745i | 0.949465 | + | 0.313873i | \(0.101627\pi\) | ||||
−0.949465 | + | 0.313873i | \(0.898373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.394 | 0.966825 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −155.510 | + | 71.1164i | −0.909417 | + | 0.415886i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 115.208i | 0.665940i | 0.942937 | + | 0.332970i | \(0.108051\pi\) | ||||
−0.942937 | + | 0.332970i | \(0.891949\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −137.194 | −0.783966 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.7798 | + | 39.3621i | −0.156948 | + | 0.222385i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 136.922i | 0.764928i | 0.923970 | + | 0.382464i | \(0.124924\pi\) | ||||
−0.923970 | + | 0.382464i | \(0.875076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −80.6052 | + | 46.5374i | −0.445332 | + | 0.257113i | −0.705857 | − | 0.708354i | \(-0.749438\pi\) |
0.260524 | + | 0.965467i | \(0.416105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.119897 | + | 1.31425i | −0.000655176 | + | 0.00718170i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.8936 | − | 10.3309i | 0.0967220 | − | 0.0558425i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −260.090 | −1.39086 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 146.255 | − | 37.4493i | 0.773837 | − | 0.198145i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8353 | − | 30.8917i | −0.0933786 | − | 0.161737i | 0.815552 | − | 0.578684i | \(-0.196433\pi\) |
−0.908931 | + | 0.416947i | \(0.863100\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −127.581 | + | 73.6587i | −0.661039 | + | 0.381651i | −0.792673 | − | 0.609647i | \(-0.791311\pi\) |
0.131634 | + | 0.991298i | \(0.457978\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.79100 | + | 3.95466i | −0.0143128 | + | 0.0202803i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 91.9844 | 0.466926 | 0.233463 | − | 0.972366i | \(-0.424994\pi\) | ||||
0.233463 | + | 0.972366i | \(0.424994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 79.6590 | + | 137.973i | 0.400296 | + | 0.693334i | 0.993762 | − | 0.111526i | \(-0.0355738\pi\) |
−0.593465 | + | 0.804860i | \(0.702241\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 51.6596 | + | 111.866i | 0.257013 | + | 0.556548i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 242.982i | 1.19695i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.2400 | + | 19.1911i | 0.162146 | + | 0.0936153i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −60.9792 | + | 71.5866i | −0.294586 | + | 0.345829i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.6716 | − | 281.983i | −0.118046 | − | 1.34920i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −237.914 | + | 137.360i | −1.12755 | + | 0.650993i | −0.943318 | − | 0.331889i | \(-0.892314\pi\) |
−0.184235 | + | 0.982882i | \(0.558981\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −217.075 | − | 19.8034i | −1.01913 | − | 0.0929739i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.2877 | − | 36.8713i | −0.0990124 | − | 0.171494i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 187.134i | − | 0.862368i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.8976 | + | 229.069i | −0.0954229 | + | 1.04598i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.7993 | + | 20.6687i | 0.161988 | + | 0.0935237i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 128.065i | 0.574281i | 0.957888 | + | 0.287141i | \(0.0927047\pi\) | ||||
−0.957888 | + | 0.287141i | \(0.907295\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −73.9835 | − | 208.059i | −0.328815 | − | 0.924705i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 79.1787 | − | 45.7138i | 0.348805 | − | 0.201383i | −0.315354 | − | 0.948974i | \(-0.602123\pi\) |
0.664159 | + | 0.747592i | \(0.268790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.3912 | + | 30.1225i | −0.0759442 | + | 0.131539i | −0.901496 | − | 0.432786i | \(-0.857530\pi\) |
0.825552 | + | 0.564326i | \(0.190864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.7047 | + | 248.877i | −0.0982886 | + | 1.07739i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 46.6581 | − | 80.8142i | 0.200249 | − | 0.346842i | −0.748359 | − | 0.663293i | \(-0.769158\pi\) |
0.948609 | + | 0.316452i | \(0.102491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 59.0420 | 0.251243 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −151.887 | − | 328.903i | −0.640874 | − | 1.38778i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 206.209 | − | 357.165i | 0.862801 | − | 1.49441i | −0.00641358 | − | 0.999979i | \(-0.502042\pi\) |
0.869214 | − | 0.494435i | \(-0.164625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −148.987 | − | 86.0178i | −0.618204 | − | 0.356920i | 0.157966 | − | 0.987445i | \(-0.449507\pi\) |
−0.776169 | + | 0.630524i | \(0.782840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 135.663 | + | 201.605i | 0.558283 | + | 0.829651i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.0840 | 0.0493226 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.0127 | + | 40.7733i | −0.0769744 | + | 0.165074i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 263.264 | + | 185.799i | 1.05728 | + | 0.746180i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 186.771 | + | 323.497i | 0.744108 | + | 1.28883i | 0.950610 | + | 0.310387i | \(0.100459\pi\) |
−0.206502 | + | 0.978446i | \(0.566208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −77.8316 | − | 134.808i | −0.307635 | − | 0.532839i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.4006 | − | 14.9626i | 0.127061 | − | 0.0586767i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 130.571i | − | 0.508058i | −0.967197 | − | 0.254029i | \(-0.918244\pi\) | ||
0.967197 | − | 0.254029i | \(-0.0817559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −146.833 | + | 84.7742i | −0.566924 | + | 0.327314i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −368.488 | + | 131.030i | −1.41183 | + | 0.502032i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.3716 | −0.0964699 | −0.0482349 | − | 0.998836i | \(-0.515360\pi\) | ||||
−0.0482349 | + | 0.998836i | \(0.515360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.8022 | + | 17.2063i | 0.112461 | + | 0.0649295i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 244.898 | − | 347.003i | 0.917221 | − | 1.29964i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −128.863 | − | 74.3993i | −0.479046 | − | 0.276577i | 0.240973 | − | 0.970532i | \(-0.422534\pi\) |
−0.720019 | + | 0.693954i | \(0.755867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 198.014 | − | 342.970i | 0.730678 | − | 1.26557i | −0.225916 | − | 0.974147i | \(-0.572537\pi\) |
0.956594 | − | 0.291425i | \(-0.0941292\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.9028 | − | 32.4516i | 0.0838929 | − | 0.118870i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 365.531 | 1.32920 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 137.542 | + | 238.230i | 0.496541 | + | 0.860035i | 0.999992 | − | 0.00398925i | \(-0.00126982\pi\) |
−0.503451 | + | 0.864024i | \(0.667936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 283.794 | − | 100.914i | 1.01718 | − | 0.361699i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 321.322 | + | 185.515i | 1.14349 | + | 0.660197i | 0.947294 | − | 0.320367i | \(-0.103806\pi\) |
0.196201 | + | 0.980564i | \(0.437140\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 49.0115 | + | 84.8904i | 0.173185 | + | 0.299966i | 0.939532 | − | 0.342462i | \(-0.111261\pi\) |
−0.766346 | + | 0.642428i | \(0.777927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.2955 | + | 33.7086i | 0.0677034 | + | 0.118276i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −272.765 | − | 157.481i | −0.950401 | − | 0.548714i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.89361 | − | 13.6721i | −0.0273135 | − | 0.0473084i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 215.913 | + | 467.548i | 0.741969 | + | 1.60669i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −341.458 | − | 197.141i | −1.16538 | − | 0.672835i | −0.212796 | − | 0.977097i | \(-0.568257\pi\) |
−0.952588 | + | 0.304262i | \(0.901590\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.47689 | + | 5.47148i | 0.0321250 | + | 0.0185474i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −389.673 | + | 99.7775i | −1.31203 | + | 0.335951i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.7403i | 0.0827436i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 174.685 | + | 302.563i | 0.580349 | + | 1.00519i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −51.8999 | + | 568.901i | −0.171287 | + | 1.87756i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.299755 | 0.000982805 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −450.819 | − | 260.280i | −1.46847 | − | 0.847819i | −0.469090 | − | 0.883150i | \(-0.655418\pi\) |
−0.999376 | + | 0.0353313i | \(0.988751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 283.736 | + | 25.8848i | 0.918238 | + | 0.0837695i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −89.2653 | + | 154.612i | −0.287027 | + | 0.497145i | −0.973099 | − | 0.230389i | \(-0.926000\pi\) |
0.686072 | + | 0.727534i | \(0.259334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 95.6595 | − | 165.687i | 0.305621 | − | 0.529352i | −0.671778 | − | 0.740752i | \(-0.734469\pi\) |
0.977399 | + | 0.211401i | \(0.0678025\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.4890 | − | 32.3099i | −0.0364732 | − | 0.102571i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 142.358 | + | 82.1907i | 0.449080 | + | 0.259277i | 0.707442 | − | 0.706772i | \(-0.249849\pi\) |
−0.258361 | + | 0.966048i | \(0.583183\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 647.384i | − | 2.02942i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.5602 | − | 59.6802i | −0.0858574 | − | 0.185920i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 271.716 | − | 190.259i | 0.841226 | − | 0.589038i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −50.3123 | − | 29.0478i | −0.154807 | − | 0.0893780i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 587.628 | + | 53.6084i | 1.79703 | + | 0.163940i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −484.494 | −1.47263 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 86.5524 | − | 49.9711i | 0.261488 | − | 0.150970i | −0.363525 | − | 0.931584i | \(-0.618427\pi\) |
0.625013 | + | 0.780614i | \(0.285094\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −207.744 | − | 176.961i | −0.623855 | − | 0.531415i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.2379 | − | 13.9938i | 0.0723519 | − | 0.0417724i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −385.329 | + | 222.470i | −1.14341 | + | 0.660148i | −0.947273 | − | 0.320429i | \(-0.896173\pi\) |
−0.196137 | + | 0.980576i | \(0.562840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0311 | − | 1.28003i | −0.0413896 | − | 0.00377591i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 498.587i | 1.46213i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −373.150 | −1.08790 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.4511 | + | 12.3161i | 0.0505829 | + | 0.0356990i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.7406 | + | 44.5839i | 0.0741803 | + | 0.128484i | 0.900730 | − | 0.434380i | \(-0.143033\pi\) |
−0.826549 | + | 0.562864i | \(0.809699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −46.4841 | − | 80.5128i | −0.133192 | − | 0.230696i | 0.791713 | − | 0.610893i | \(-0.209189\pi\) |
−0.924905 | + | 0.380197i | \(0.875856\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 61.5643 | + | 17.2328i | 0.175397 | + | 0.0490962i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −332.939 | − | 576.668i | −0.943171 | − | 1.63362i | −0.759373 | − | 0.650655i | \(-0.774494\pi\) |
−0.183797 | − | 0.982964i | \(-0.558839\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.5107i | 0.139467i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −265.877 | + | 122.782i | −0.744753 | + | 0.343926i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3255 | + | 30.0087i | −0.0482605 | + | 0.0835897i | −0.889147 | − | 0.457623i | \(-0.848701\pi\) |
0.840886 | + | 0.541212i | \(0.182034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 232.049 | + | 276.540i | 0.642794 | + | 0.766039i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.5138 | − | 301.592i | 0.0757956 | − | 0.830833i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52.2462 | 0.143140 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −223.471 | + | 387.063i | −0.608912 | + | 1.05467i | 0.382508 | + | 0.923952i | \(0.375060\pi\) |
−0.991420 | + | 0.130715i | \(0.958273\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 91.7327 | − | 498.579i | 0.248598 | − | 1.35116i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −244.555 | − | 141.194i | −0.659177 | − | 0.380576i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 359.861 | + | 207.766i | 0.964775 | + | 0.557013i | 0.897639 | − | 0.440731i | \(-0.145281\pi\) |
0.0671357 | + | 0.997744i | \(0.478614\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −91.9333 | + | 42.4547i | −0.245155 | + | 0.113212i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −51.4460 | + | 89.1071i | −0.136462 | + | 0.236358i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 485.460i | 1.28090i | 0.768001 | + | 0.640449i | \(0.221252\pi\) | ||||
−0.768001 | + | 0.640449i | \(0.778748\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 359.641 | − | 509.586i | 0.943939 | − | 1.33750i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −148.710 | + | 85.8577i | −0.388276 | + | 0.224172i | −0.681413 | − | 0.731899i | \(-0.738634\pi\) |
0.293137 | + | 0.956071i | \(0.405301\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 56.7641 | 0.147439 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −364.645 | + | 428.075i | −0.942234 | + | 1.10614i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 141.077 | − | 244.352i | 0.362665 | − | 0.628154i | −0.625734 | − | 0.780037i | \(-0.715200\pi\) |
0.988398 | + | 0.151883i | \(0.0485337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 91.2070 | − | 157.975i | 0.233266 | − | 0.404029i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 497.597 | + | 351.180i | 1.26615 | + | 0.893588i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −71.2630 | + | 41.1437i | −0.180413 | + | 0.104161i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 252.435 | − | 437.231i | 0.635857 | − | 1.10134i | −0.350476 | − | 0.936572i | \(-0.613980\pi\) |
0.986333 | − | 0.164765i | \(-0.0526866\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −158.337 | − | 276.610i | −0.396835 | − | 0.693259i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.8889 | − | 21.2978i | 0.0919923 | − | 0.0531118i | −0.453298 | − | 0.891359i | \(-0.649753\pi\) |
0.545290 | + | 0.838247i | \(0.316419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.6215 | − | 68.6264i | 0.0983163 | − | 0.170289i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 42.8032 | − | 34.8469i | 0.105687 | − | 0.0860418i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 391.213 | − | 225.867i | 0.961210 | − | 0.554955i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 404.458i | − | 0.988896i | −0.869207 | − | 0.494448i | \(-0.835370\pi\) | ||
0.869207 | − | 0.494448i | \(-0.164630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.3072 | + | 266.444i | −0.0591417 | + | 0.648281i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −77.7666 | − | 44.8986i | −0.188297 | − | 0.108713i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.5947 | − | 63.3839i | 0.0881800 | − | 0.152732i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 451.703 | − | 208.596i | 1.08322 | − | 0.500230i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −216.308 | + | 374.657i | −0.516249 | + | 0.894169i | 0.483573 | + | 0.875304i | \(0.339339\pi\) |
−0.999822 | + | 0.0188652i | \(0.993995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 23.5995i | − | 0.0560557i | −0.999607 | − | 0.0280279i | \(-0.991077\pi\) | ||
0.999607 | − | 0.0280279i | \(-0.00892272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −261.269 | − | 734.749i | −0.617657 | − | 1.73699i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 214.174 | + | 370.960i | 0.503938 | + | 0.872847i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.45977 | −0.00576059 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −61.0206 | + | 86.4619i | −0.142239 | + | 0.201543i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 89.7445 | − | 51.8140i | 0.208224 | − | 0.120218i | −0.392262 | − | 0.919854i | \(-0.628307\pi\) |
0.600486 | + | 0.799636i | \(0.294974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −464.495 | + | 268.176i | −1.07274 | + | 0.619344i | −0.928928 | − | 0.370261i | \(-0.879268\pi\) |
−0.143808 | + | 0.989606i | \(0.545935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 37.2429 | + | 80.6474i | 0.0856158 | + | 0.185396i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 179.924 | + | 83.8992i | 0.411726 | + | 0.191989i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 260.499i | − | 0.593392i | −0.954972 | − | 0.296696i | \(-0.904115\pi\) | ||
0.954972 | − | 0.296696i | \(-0.0958848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −53.4735 | − | 150.380i | −0.121255 | − | 0.340997i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 244.994 | − | 424.342i | 0.553034 | − | 0.957882i | −0.445020 | − | 0.895521i | \(-0.646803\pi\) |
0.998054 | − | 0.0623617i | \(-0.0198632\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −83.5452 | − | 48.2348i | −0.187742 | − | 0.108393i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −382.258 | − | 269.779i | −0.855164 | − | 0.603533i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 783.722i | 1.74548i | 0.488182 | + | 0.872742i | \(0.337660\pi\) | ||||
−0.488182 | + | 0.872742i | \(0.662340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 726.737 | + | 419.582i | 1.61139 | + | 0.930336i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −511.005 | + | 724.058i | −1.12805 | + | 1.59836i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.81311 | − | 4.51090i | −0.0171717 | − | 0.00991407i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −166.574 | − | 288.514i | −0.364493 | − | 0.631321i | 0.624201 | − | 0.781264i | \(-0.285425\pi\) |
−0.988695 | + | 0.149942i | \(0.952091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −329.579 | − | 336.998i | −0.718036 | − | 0.734201i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −473.007 | −1.02605 | −0.513023 | − | 0.858375i | \(-0.671474\pi\) | ||||
−0.513023 | + | 0.858375i | \(0.671474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 151.128 | − | 261.762i | 0.326411 | − | 0.565360i | −0.655386 | − | 0.755294i | \(-0.727494\pi\) |
0.981797 | + | 0.189934i | \(0.0608274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −28.6828 | − | 62.1112i | −0.0616835 | − | 0.133572i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 420.810 | 0.901093 | 0.450546 | − | 0.892753i | \(-0.351229\pi\) | ||||
0.450546 | + | 0.892753i | \(0.351229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −198.894 | + | 114.832i | −0.424082 | + | 0.244844i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −168.097 | − | 118.635i | −0.356894 | − | 0.251878i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −465.419 | − | 806.129i | −0.983972 | − | 1.70429i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −381.869 | + | 267.390i | −0.803936 | + | 0.562927i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 82.2453 | − | 447.014i | 0.172422 | − | 0.937136i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 186.508 | − | 323.041i | 0.389369 | − | 0.674407i | −0.602996 | − | 0.797745i | \(-0.706026\pi\) |
0.992365 | + | 0.123337i | \(0.0393597\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −71.7963 | −0.149265 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −143.202 | − | 101.065i | −0.296485 | − | 0.209245i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 101.303 | − | 58.4873i | 0.208872 | − | 0.120592i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 666.331i | − | 1.36824i | −0.729371 | − | 0.684118i | \(-0.760187\pi\) | ||
0.729371 | − | 0.684118i | \(-0.239813\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −149.166 | + | 68.8845i | −0.305042 | + | 0.140868i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −278.509 | − | 482.392i | −0.567228 | − | 0.982468i | −0.996839 | − | 0.0794534i | \(-0.974683\pi\) |
0.429611 | − | 0.903014i | \(-0.358651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 656.999 | − | 379.319i | 1.33266 | − | 0.769409i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 30.6106 | + | 86.0843i | 0.0618397 | + | 0.173908i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 406.281i | − | 0.817467i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 312.553 | + | 541.357i | 0.626358 | + | 1.08488i | 0.988277 | + | 0.152675i | \(0.0487886\pi\) |
−0.361918 | + | 0.932210i | \(0.617878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −131.855 | − | 285.525i | −0.263184 | − | 0.569911i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 99.7875 | + | 172.837i | 0.198385 | + | 0.343613i | 0.948005 | − | 0.318256i | \(-0.103097\pi\) |
−0.749620 | + | 0.661868i | \(0.769764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 129.755 | 0.256941 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −445.020 | + | 205.510i | −0.877751 | + | 0.405344i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 176.640i | 0.347034i | 0.984831 | + | 0.173517i | \(0.0555131\pi\) | ||||
−0.984831 | + | 0.173517i | \(0.944487\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −428.729 | −0.838999 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 334.102 | − | 389.288i | 0.651271 | − | 0.758845i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 64.7146i | − | 0.125659i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1290.85 | 2.49682 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −144.903 | − | 313.780i | −0.279197 | − | 0.604587i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 143.921i | 0.276240i | 0.990415 | + | 0.138120i | \(0.0441060\pi\) | ||||
−0.990415 | + | 0.138120i | \(0.955894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.5109 | − | 12.9967i | 0.0430419 | − | 0.0248503i | −0.478325 | − | 0.878183i | \(-0.658756\pi\) |
0.521367 | + | 0.853333i | \(0.325422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 373.663 | − | 172.557i | 0.711739 | − | 0.328680i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −505.992 | + | 292.135i | −0.960137 | + | 0.554336i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −419.826 | −0.793622 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.1534 | − | 142.147i | 0.0492531 | − | 0.267697i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −66.6863 | − | 115.504i | −0.125115 | − | 0.216705i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.9308 | + | 7.46561i | −0.0241698 | + | 0.0139544i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −172.215 | − | 372.922i | −0.320698 | − | 0.694455i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 264.197 | 0.490161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 387.168 | + | 670.595i | 0.715653 | + | 1.23955i | 0.962707 | + | 0.270546i | \(0.0872041\pi\) |
−0.247054 | + | 0.969002i | \(0.579463\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 161.004 | − | 228.132i | 0.296509 | − | 0.420132i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 134.027i | − | 0.245920i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.4722 | + | 8.35552i | 0.0264574 | + | 0.0152752i | 0.513170 | − | 0.858287i | \(-0.328471\pi\) |
−0.486713 | + | 0.873562i | \(0.661804\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.32646 | − | 3.73031i | −0.00241614 | − | 0.00679473i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 473.569 | + | 676.321i | 0.859472 | + | 1.22744i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 584.779 | − | 337.622i | 1.05747 | − | 0.610528i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −35.7414 | + | 50.6430i | −0.0643988 | + | 0.0912486i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 269.959 | + | 467.583i | 0.484666 | + | 0.839467i | 0.999845 | − | 0.0176161i | \(-0.00560766\pi\) |
−0.515178 | + | 0.857083i | \(0.672274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 147.943i | 0.264656i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 708.384 | − | 327.131i | 1.26272 | − | 0.583121i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −504.214 | − | 291.108i | −0.895585 | − | 0.517066i | −0.0198195 | − | 0.999804i | \(-0.506309\pi\) |
−0.875765 | + | 0.482738i | \(0.839642\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.20022i | 0.00566410i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −351.240 | + | 285.951i | −0.619471 | + | 0.504323i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −520.303 | + | 300.397i | −0.914417 | + | 0.527939i | −0.881850 | − | 0.471531i | \(-0.843702\pi\) |
−0.0325670 | + | 0.999470i | \(0.510368\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 263.244 | − | 455.953i | 0.461023 | − | 0.798516i | −0.537989 | − | 0.842952i | \(-0.680816\pi\) |
0.999012 | + | 0.0444360i | \(0.0141491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 87.4307 | + | 61.7043i | 0.152584 | + | 0.107686i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −128.182 | + | 222.018i | −0.222926 | + | 0.386119i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 679.846 | 1.17824 | 0.589121 | − | 0.808045i | \(-0.299474\pi\) | ||||
0.589121 | + | 0.808045i | \(0.299474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 254.835 | − | 361.083i | 0.440129 | − | 0.623632i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −300.293 | + | 520.123i | −0.516856 | + | 0.895221i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 651.575 | + | 376.187i | 1.11762 | + | 0.645260i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.62760 | − | 14.2813i | 0.00449162 | − | 0.0244126i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 431.522 | 0.735130 | 0.367565 | − | 0.929998i | \(-0.380191\pi\) | ||||
0.367565 | + | 0.929998i | \(0.380191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −364.723 | − | 520.873i | −0.619223 | − | 0.884334i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −250.529 | + | 115.694i | −0.423908 | + | 0.195760i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −184.931 | − | 320.310i | −0.311856 | − | 0.540151i | 0.666908 | − | 0.745140i | \(-0.267617\pi\) |
−0.978764 | + | 0.204989i | \(0.934284\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 33.2595 | + | 57.6072i | 0.0558983 | + | 0.0968188i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −390.497 | − | 275.594i | −0.654099 | − | 0.461631i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 740.472i | − | 1.23618i | −0.786107 | − | 0.618090i | \(-0.787907\pi\) | ||
0.786107 | − | 0.618090i | \(-0.212093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.1465 | − | 8.74483i | 0.0252021 | − | 0.0145505i | −0.487346 | − | 0.873209i | \(-0.662035\pi\) |
0.512548 | + | 0.858658i | \(0.328702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −281.401 | − | 239.704i | −0.466669 | − | 0.397520i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −68.7874 | −0.113698 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 601.906 | + | 347.510i | 0.991607 | + | 0.572505i | 0.905754 | − | 0.423803i | \(-0.139305\pi\) |
0.0858530 | + | 0.996308i | \(0.472638\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −305.612 | − | 661.787i | −0.501826 | − | 1.08668i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −177.675 | − | 102.581i | −0.290795 | − | 0.167890i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 140.459 | − | 243.281i | 0.229133 | − | 0.396870i | −0.728418 | − | 0.685133i | \(-0.759744\pi\) |
0.957551 | + | 0.288263i | \(0.0930776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −114.671 | − | 10.4612i | −0.186456 | − | 0.0170101i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −425.784 | −0.690087 | −0.345044 | − | 0.938587i | \(-0.612136\pi\) | ||||
−0.345044 | + | 0.938587i | \(0.612136\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −268.153 | − | 464.455i | −0.433204 | − | 0.750332i | 0.563943 | − | 0.825814i | \(-0.309284\pi\) |
−0.997147 | + | 0.0754821i | \(0.975950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 76.0448 | − | 271.671i | 0.122455 | − | 0.437474i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 685.565 | + | 395.811i | 1.10043 | + | 0.635331i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −295.196 | − | 511.294i | −0.472313 | − | 0.818070i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 421.863 | + | 736.982i | 0.672827 | + | 1.17541i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 458.443 | + | 264.682i | 0.728844 | + | 0.420798i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.3648 | + | 73.3780i | 0.0671391 | + | 0.116288i | 0.897641 | − | 0.440728i | \(-0.145280\pi\) |
−0.830502 | + | 0.557016i | \(0.811946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 475.219 | − | 673.351i | 0.750740 | − | 1.06375i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −122.689 | − | 70.8344i | −0.193211 | − | 0.111550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −36.3646 | − | 20.9951i | −0.0570872 | − | 0.0329593i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 616.136 | − | 219.092i | 0.964219 | − | 0.342866i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1011.89i | 1.57862i | 0.613996 | + | 0.789309i | \(0.289561\pi\) | ||||
−0.613996 | + | 0.789309i | \(0.710439\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −620.422 | − | 1074.60i | −0.964887 | − | 1.67123i | −0.709919 | − | 0.704283i | \(-0.751269\pi\) |
−0.254967 | − | 0.966950i | \(-0.582065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 104.354 | + | 73.6483i | 0.161790 | + | 0.114183i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −491.485 | −0.759637 | −0.379819 | − | 0.925061i | \(-0.624014\pi\) | ||||
−0.379819 | + | 0.925061i | \(0.624014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 207.196 | + | 119.625i | 0.319254 | + | 0.184322i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 235.369 | + | 509.680i | 0.361550 | + | 0.782918i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −544.371 | + | 942.878i | −0.833646 | + | 1.44392i | 0.0614817 | + | 0.998108i | \(0.480417\pi\) |
−0.895128 | + | 0.445809i | \(0.852916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 69.1680 | − | 119.802i | 0.105600 | − | 0.182905i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −231.197 | − | 650.179i | −0.351898 | − | 0.989618i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.8040 | + | 22.4035i | 0.0588831 | + | 0.0339962i | 0.529153 | − | 0.848527i | \(-0.322510\pi\) |
−0.470269 | + | 0.882523i | \(0.655843\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 626.834i | 0.948312i | 0.880441 | + | 0.474156i | \(0.157247\pi\) | ||||
−0.880441 | + | 0.474156i | \(0.842753\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −123.500 | − | 11.2667i | −0.186274 | − | 0.0169935i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −59.3013 | + | 41.5236i | −0.0891749 | + | 0.0624415i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 393.212 | + | 227.021i | 0.589523 | + | 0.340361i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −161.074 | − | 348.798i | −0.240769 | − | 0.521372i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.55365 | 0.00976698 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 978.836 | − | 565.131i | 1.45444 | − | 0.839719i | 0.455708 | − | 0.890129i | \(-0.349386\pi\) |
0.998729 | + | 0.0504103i | \(0.0160529\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 463.189 | + | 473.617i | 0.686207 | + | 0.701655i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −269.720 | + | 155.723i | −0.398405 | + | 0.230019i | −0.685796 | − | 0.727794i | \(-0.740546\pi\) |
0.287390 | + | 0.957814i | \(0.407212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −831.285 | + | 479.942i | −1.22428 | + | 0.706837i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −158.155 | + | 224.094i | −0.232239 | + | 0.329066i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 30.4855i | − | 0.0446348i | −0.999751 | − | 0.0223174i | \(-0.992896\pi\) | ||
0.999751 | − | 0.0223174i | \(-0.00710443\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 60.7706 | 0.0887163 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.48008 | − | 103.916i | 0.0137992 | − | 0.151260i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −59.7893 | − | 103.558i | −0.0867769 | − | 0.150302i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −231.091 | − | 400.262i | −0.334431 | − | 0.579251i | 0.648945 | − | 0.760836i | \(-0.275211\pi\) |
−0.983375 | + | 0.181585i | \(0.941877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −251.189 | − | 706.401i | −0.362466 | − | 1.01934i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −56.5052 | − | 97.8699i | −0.0813024 | − | 0.140820i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 983.375i | 1.41087i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.4337 | + | 278.791i | −0.0363858 | + | 0.398842i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −640.659 | + | 1109.65i | −0.913922 | + | 1.58296i | −0.105449 | + | 0.994425i | \(0.533628\pi\) |
−0.808473 | + | 0.588534i | \(0.799705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −243.475 | + | 522.139i | −0.346337 | + | 0.742730i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −160.807 | + | 74.2606i | −0.228095 | + | 0.105334i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1064.76 | −1.50603 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 59.5253 | − | 103.101i | 0.0839567 | − | 0.145417i | −0.820989 | − | 0.570943i | \(-0.806578\pi\) |
0.904946 | + | 0.425526i | \(0.139911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 827.362 | + | 704.767i | 1.16366 | + | 0.991233i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −302.835 | − | 174.842i | −0.424733 | − | 0.245220i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.8167 | + | 12.0185i | 0.0291143 | + | 0.0168091i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −112.406 | + | 1232.14i | −0.156773 | + | 1.71847i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4411 | − | 40.6012i | 0.0326024 | − | 0.0564690i | −0.849264 | − | 0.527969i | \(-0.822954\pi\) |
0.881866 | + | 0.471500i | \(0.156287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 531.043i | 0.736537i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 513.972 | + | 46.8889i | 0.710888 | + | 0.0648532i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −923.346 | + | 533.094i | −1.27358 | + | 0.735302i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −922.694 | −1.26918 | −0.634590 | − | 0.772849i | \(-0.718831\pi\) | ||||
−0.634590 | + | 0.772849i | \(0.718831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −623.063 | − | 378.463i | −0.854681 | − | 0.519153i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 545.401 | − | 944.663i | 0.746103 | − | 1.29229i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −379.867 | + | 657.948i | −0.518236 | + | 0.897610i | 0.481540 | + | 0.876424i | \(0.340078\pi\) |
−0.999776 | + | 0.0211862i | \(0.993256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −32.9122 | + | 15.1988i | −0.0447785 | + | 0.0206786i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 529.920 | − | 305.950i | 0.719024 | − | 0.415128i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −455.753 | + | 789.387i | −0.616716 | + | 1.06818i | 0.373365 | + | 0.927684i | \(0.378204\pi\) |
−0.990081 | + | 0.140498i | \(0.955130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.500142 | − | 134.964i | 0.000674956 | − | 0.182138i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −624.251 | + | 360.411i | −0.840176 | + | 0.485076i | −0.857324 | − | 0.514777i | \(-0.827875\pi\) |
0.0171482 | + | 0.999853i | \(0.494541\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −53.1354 | + | 92.0332i | −0.0713226 | + | 0.123534i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −950.718 | − | 174.921i | −1.27271 | − | 0.234164i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 106.109 | − | 61.2623i | 0.141668 | − | 0.0817921i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 204.996i | − | 0.272964i | −0.990643 | − | 0.136482i | \(-0.956420\pi\) | ||
0.990643 | − | 0.136482i | \(-0.0435796\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −915.573 | − | 646.166i | −1.21590 | − | 0.858123i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 174.326 | + | 100.647i | 0.230895 | + | 0.133307i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −144.571 | + | 250.405i | −0.190979 | + | 0.330785i | −0.945575 | − | 0.325404i | \(-0.894500\pi\) |
0.754596 | + | 0.656190i | \(0.227833\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 381.539 | + | 269.272i | 0.502686 | + | 0.354772i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 312.556 | − | 541.362i | 0.410717 | − | 0.711383i | −0.584251 | − | 0.811573i | \(-0.698612\pi\) |
0.994968 | + | 0.100190i | \(0.0319450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1099.81i | 1.44143i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −69.4273 | + | 81.5043i | −0.0907546 | + | 0.106542i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.0126 | − | 32.9307i | −0.0247882 | − | 0.0429345i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 891.808 | 1.15970 | 0.579849 | − | 0.814724i | \(-0.303112\pi\) | ||||
0.579849 | + | 0.814724i | \(0.303112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 164.227 | + | 355.624i | 0.213005 | + | 0.461250i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −508.443 | + | 293.550i | −0.657753 | + | 0.379754i | −0.791420 | − | 0.611272i | \(-0.790658\pi\) |
0.133667 | + | 0.991026i | \(0.457325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 711.121 | − | 410.566i | 0.917576 | − | 0.529763i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 293.291 | − | 415.573i | 0.377466 | − | 0.534842i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1066.15 | + | 93.2808i | −1.36861 | + | 0.119744i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1082.47i | 1.38600i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 838.813 | − | 820.345i | 1.07128 | − | 1.04769i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.3661 | + | 40.4713i | −0.0297658 | + | 0.0515558i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −735.073 | − | 424.395i | −0.934020 | − | 0.539257i | −0.0459391 | − | 0.998944i | \(-0.514628\pi\) |
−0.888081 | + | 0.459688i | \(0.847961\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 69.1022 | − | 31.9113i | 0.0875820 | − | 0.0404453i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 26.2607i | − | 0.0331994i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.902056 | − | 0.520802i | −0.00113752 | − | 0.000656749i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −102.811 | − | 9.37928i | −0.129322 | − | 0.0117978i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 976.928 | + | 564.030i | 1.22576 | + | 0.707691i | 0.966139 | − | 0.258021i | \(-0.0830703\pi\) |
0.259617 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 756.344 | + | 1310.03i | 0.946613 | + | 1.63958i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −230.560 | + | 1253.12i | −0.287840 | + | 1.56445i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1142.28 | 1.42251 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.9057 | + | 34.4777i | −0.0247276 | + | 0.0428294i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 444.550 | + | 40.5556i | 0.550867 | + | 0.0502548i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 909.119 | 1.12376 | 0.561878 | − | 0.827220i | \(-0.310079\pi\) | ||||
0.561878 | + | 0.827220i | \(0.310079\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 645.717 | − | 372.805i | 0.796199 | − | 0.459686i | −0.0459414 | − | 0.998944i | \(-0.514629\pi\) |
0.842140 | + | 0.539258i | \(0.181295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −107.939 | + | 1183.17i | −0.132766 | + | 1.45531i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.6597 | + | 32.3195i | 0.0228953 | + | 0.0396559i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1075.92 | + | 501.702i | 1.31691 | + | 0.614078i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −21.5619 | + | 117.192i | −0.0263271 | + | 0.143091i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 58.9196 | − | 102.052i | 0.0717656 | − | 0.124302i | −0.827910 | − | 0.560862i | \(-0.810470\pi\) |
0.899675 | + | 0.436560i | \(0.143803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −446.415 | −0.542424 | −0.271212 | − | 0.962520i | \(-0.587424\pi\) | ||||
−0.271212 | + | 0.962520i | \(0.587424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −995.563 | + | 459.749i | −1.20674 | + | 0.557272i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −198.286 | + | 114.480i | −0.239765 | + | 0.138428i | −0.615069 | − | 0.788474i | \(-0.710872\pi\) |
0.375304 | + | 0.926902i | \(0.377538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 705.074i | 0.850511i | 0.905073 | + | 0.425256i | \(0.139816\pi\) | ||||
−0.905073 | + | 0.425256i | \(0.860184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −674.246 | − | 475.850i | −0.811367 | − | 0.572623i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 154.800 | + | 268.121i | 0.185834 | + | 0.321874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −61.8644 | + | 35.7174i | −0.0740891 | + | 0.0427754i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −646.017 | + | 631.794i | −0.771825 | + | 0.754832i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 762.069i | 0.908306i | 0.890924 | + | 0.454153i | \(0.150058\pi\) | ||||
−0.890924 | + | 0.454153i | \(0.849942\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 523.651 | + | 906.991i | 0.622653 | + | 1.07847i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1108.49 | − | 101.126i | −1.31493 | − | 0.119959i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 55.6692 | + | 96.4219i | 0.0658807 | + | 0.114109i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 564.464 | 0.666428 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −240.260 | − | 169.564i | −0.282991 | − | 0.199721i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 316.823i | 0.372295i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −545.586 | −0.639608 | −0.319804 | − | 0.947484i | \(-0.603617\pi\) | ||||
−0.319804 | + | 0.947484i | \(0.603617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −94.9506 | − | 67.5400i | −0.111053 | − | 0.0789941i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 107.063i | 0.124927i | 0.998047 | + | 0.0624636i | \(0.0198957\pi\) | ||||
−0.998047 | + | 0.0624636i | \(0.980104\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 844.828 | 0.983502 | 0.491751 | − | 0.870736i | \(-0.336357\pi\) | ||||
0.491751 | + | 0.870736i | \(0.336357\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 940.978 | + | 85.8440i | 1.09289 | + | 0.0997027i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 140.169i | 0.162421i | 0.996697 | + | 0.0812104i | \(0.0258786\pi\) | ||||
−0.996697 | + | 0.0812104i | \(0.974121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −67.9864 | + | 39.2520i | −0.0785970 | + | 0.0453780i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.6953 | + | 27.3093i | 0.0446313 | + | 0.0314986i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1558.05 | + | 899.538i | −1.79292 | + | 1.03514i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −97.2523 | −0.111656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1176.13 | − | 1001.85i | −1.34722 | − | 1.14760i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −94.3704 | − | 163.454i | −0.107852 | − | 0.186805i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 621.612 | − | 358.888i | 0.708794 | − | 0.409222i | −0.101820 | − | 0.994803i | \(-0.532467\pi\) |
0.810614 | + | 0.585581i | \(0.199133\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1177.95 | + | 107.463i | 1.34010 | + | 0.122256i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 973.635 | 1.10515 | 0.552574 | − | 0.833464i | \(-0.313646\pi\) | ||||
0.552574 | + | 0.833464i | \(0.313646\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −810.466 | − | 1403.77i | −0.917855 | − | 1.58977i | −0.802667 | − | 0.596427i | \(-0.796586\pi\) |
−0.115188 | − | 0.993344i | \(-0.536747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32.6931 | − | 2.98254i | −0.0369414 | − | 0.00337011i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 93.3587i | − | 0.105252i | −0.998614 | − | 0.0526261i | \(-0.983241\pi\) | ||
0.998614 | − | 0.0526261i | \(-0.0167591\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1006.78 | + | 581.262i | 1.13248 | + | 0.653838i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 935.820 | − | 761.869i | 1.05030 | − | 0.855072i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1348.55 | + | 944.275i | −1.51014 | + | 1.05742i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −80.8006 | + | 46.6502i | −0.0902800 | + | 0.0521232i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.1174 | − | 67.3830i | −0.0346905 | − | 0.0751204i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −727.145 | − | 1259.45i | −0.808837 | − | 1.40095i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 881.670i | 0.978546i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −856.325 | − | 604.352i | −0.948311 | − | 0.669272i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.9254 | − | 31.7112i | −0.0606910 | − | 0.0350400i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1442.46i | − | 1.59036i | −0.606372 | − | 0.795181i | \(-0.707376\pi\) | ||
0.606372 | − | 0.795181i | \(-0.292624\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −574.185 | − | 1614.74i | −0.631666 | − | 1.77639i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 967.610 | − | 558.650i | 1.06214 | − | 0.613227i | 0.136117 | − | 0.990693i | \(-0.456538\pi\) |
0.926024 | + | 0.377466i | \(0.123204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 800.081 | − | 1385.78i | 0.876321 | − | 1.51783i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.816416 | + | 0.377020i | −0.000892258 | + | 0.000412044i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −567.587 | + | 983.090i | −0.618961 | + | 1.07207i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −150.532 | −0.163800 | −0.0819002 | − | 0.996641i | \(-0.526099\pi\) | ||||
−0.0819002 | + | 0.996641i | \(0.526099\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1555.22 | + | 141.881i | 1.68863 | + | 0.154051i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 86.0211 | − | 148.993i | 0.0931972 | − | 0.161422i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −644.295 | − | 371.984i | −0.696535 | − | 0.402145i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −805.342 | + | 286.371i | −0.868761 | + | 0.308922i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1219.21 | −1.31239 | −0.656193 | − | 0.754593i | \(-0.727834\pi\) | ||||
−0.656193 | + | 0.754593i | \(0.727834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −276.006 | + | 193.263i | −0.296462 | + | 0.207587i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 48.6592 | − | 533.377i | 0.0521535 | − | 0.571680i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −88.6144 | − | 153.485i | −0.0947748 | − | 0.164155i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −584.150 | − | 1011.78i | −0.623426 | − | 1.07981i | −0.988843 | − | 0.148962i | \(-0.952407\pi\) |
0.365417 | − | 0.930844i | \(-0.380926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −52.1447 | + | 571.583i | −0.0555321 | + | 0.608715i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 757.255i | − | 0.804735i | −0.915478 | − | 0.402367i | \(-0.868187\pi\) | ||
0.915478 | − | 0.402367i | \(-0.131813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −509.696 | + | 294.273i | −0.540505 | + | 0.312061i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 71.9297 | + | 73.5490i | 0.0761161 | + | 0.0778296i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 717.348 | 0.757495 | 0.378748 | − | 0.925500i | \(-0.376355\pi\) | ||||
0.378748 | + | 0.925500i | \(0.376355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −157.225 | − | 90.7739i | −0.165674 | − | 0.0956521i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −491.105 | − | 44.8027i | −0.516409 | − | 0.0471112i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 143.573 | + | 82.8922i | 0.150654 | + | 0.0869802i | 0.573432 | − | 0.819253i | \(-0.305612\pi\) |
−0.422778 | + | 0.906233i | \(0.638945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.1532 | − | 21.0500i | 0.0127259 | − | 0.0220419i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 814.252 | + | 1763.22i | 0.850838 | + | 1.84244i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −498.679 | −0.519999 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79.5155 | + | 137.725i | 0.0827424 | + | 0.143314i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 150.127 | + | 127.881i | 0.155895 | + | 0.132795i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −86.9350 | − | 50.1919i | −0.0900881 | − | 0.0520124i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −111.196 | − | 192.596i | −0.114990 | − | 0.199169i | 0.802786 | − | 0.596268i | \(-0.203350\pi\) |
−0.917776 | + | 0.397099i | \(0.870017\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −500.748 | + | 859.945i | −0.516767 | + | 0.887456i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1374.21 | + | 793.401i | 1.41525 | + | 0.817097i | 0.995877 | − | 0.0907152i | \(-0.0289153\pi\) |
0.419377 | + | 0.907812i | \(0.362249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 463.677 | + | 803.113i | 0.476544 | + | 0.825398i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 173.566 | + | 15.8342i | 0.178017 | + | 0.0162402i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 484.548 | + | 279.754i | 0.495955 | + | 0.286340i | 0.727042 | − | 0.686593i | \(-0.240895\pi\) |
−0.231086 | + | 0.972933i | \(0.574228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1826.57 | − | 1054.57i | −1.86575 | − | 1.07719i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1667.90 | + | 593.086i | −1.70020 | + | 0.604573i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 879.650i | 0.894863i | 0.894318 | + | 0.447431i | \(0.147661\pi\) | ||||
−0.894318 | + | 0.447431i | \(0.852339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.3396 | + | 54.2819i | 0.0318169 | + | 0.0551085i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1319.57 | − | 609.377i | 1.33695 | − | 0.617403i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 652.842 | 0.660103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −470.061 | − | 271.390i | −0.474329 | − | 0.273854i | 0.243721 | − | 0.969845i | \(-0.421632\pi\) |
−0.718050 | + | 0.695991i | \(0.754965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −172.883 | + | 244.964i | −0.174102 | + | 0.246691i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.2806 | + | 94.0168i | −0.0545534 | + | 0.0944892i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 381.603 | − | 660.955i | 0.382751 | − | 0.662944i | −0.608703 | − | 0.793398i | \(-0.708310\pi\) |
0.991454 | + | 0.130454i | \(0.0416434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 788.387 | + | 220.681i | 0.789177 | + | 0.220902i |
(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 | 684.3.s.a.445.5 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.s.a.901.18 | 80 | |||
9.2 | odd | 6 | 2052.3.bl.a.1585.23 | 80 | |||
9.7 | even | 3 | 684.3.bl.a.673.21 | yes | 80 | ||
19.12 | odd | 6 | 684.3.bl.a.373.21 | yes | 80 | ||
57.50 | even | 6 | 2052.3.bl.a.145.23 | 80 | |||
171.88 | odd | 6 | inner | 684.3.s.a.601.5 | yes | 80 | |
171.164 | even | 6 | 2052.3.s.a.829.18 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.s.a.445.5 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.s.a.601.5 | yes | 80 | 171.88 | odd | 6 | inner | |
684.3.bl.a.373.21 | yes | 80 | 19.12 | odd | 6 | ||
684.3.bl.a.673.21 | yes | 80 | 9.7 | even | 3 | ||
2052.3.s.a.829.18 | 80 | 171.164 | even | 6 | |||
2052.3.s.a.901.18 | 80 | 3.2 | odd | 2 | |||
2052.3.bl.a.145.23 | 80 | 57.50 | even | 6 | |||
2052.3.bl.a.1585.23 | 80 | 9.2 | odd | 6 |